LMFDB - Embedded newform 21.18.g.b.17.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,18,Mod(5,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 18, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$38.4766383424$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.38
Character	$\chi$	$=$	21.17
Dual form			21.18.g.b.5.38

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(525.807 - 303.575i) q^{2} +(4083.40 + 10605.0i) q^{3} +(118779. - 205731. i) q^{4} +(-215905. - 373958. i) q^{5} +(5.36649e6 + 4.33656e6i) q^{6} +(-1.19269e7 - 9.50679e6i) q^{7} -6.46530e7i q^{8} +(-9.57918e7 + 8.66089e7i) q^{9} +O(q^{10})$	\(q+(525.807 - 303.575i) q^{2} +(4083.40 + 10605.0i) q^{3} +(118779. - 205731. i) q^{4} +(-215905. - 373958. i) q^{5} +(5.36649e6 + 4.33656e6i) q^{6} +(-1.19269e7 - 9.50679e6i) q^{7} -6.46530e7i q^{8} +(-9.57918e7 + 8.66089e7i) q^{9} +(-2.27048e8 - 1.31086e8i) q^{10} +(-6.59660e8 - 3.80855e8i) q^{11} +(2.66680e9 + 4.19568e8i) q^{12} -4.71045e9i q^{13} +(-9.15727e9 - 1.37802e9i) q^{14} +(3.08420e9 - 3.81669e9i) q^{15} +(-4.05839e9 - 7.02933e9i) q^{16} +(-6.97171e9 + 1.20754e10i) q^{17} +(-2.40757e10 + 7.46195e10i) q^{18} +(-8.26780e10 + 4.77342e10i) q^{19} -1.02580e11 q^{20} +(5.21171e10 - 1.65305e11i) q^{21} -4.62471e11 q^{22} +(4.82272e11 - 2.78440e11i) q^{23} +(6.85645e11 - 2.64004e11i) q^{24} +(2.88240e11 - 4.99246e11i) q^{25} +(-1.42997e12 - 2.47678e12i) q^{26} +(-1.30964e12 - 6.62213e11i) q^{27} +(-3.37251e12 + 1.32453e12i) q^{28} -1.71297e12i q^{29} +(4.63042e11 - 2.94312e12i) q^{30} +(-3.57451e12 - 2.06374e12i) q^{31} +(3.07101e12 + 1.77305e12i) q^{32} +(1.34531e12 - 8.55087e12i) q^{33} +8.46574e12i q^{34} +(-9.80060e11 + 6.51273e12i) q^{35} +(6.44011e12 + 2.99947e13i) q^{36} +(-9.07107e11 - 1.57116e12i) q^{37} +(-2.89818e13 + 5.01979e13i) q^{38} +(4.99543e13 - 1.92346e13i) q^{39} +(-2.41775e13 + 1.39589e13i) q^{40} +2.39525e12 q^{41} +(-2.27789e13 - 1.02740e14i) q^{42} -1.02439e14 q^{43} +(-1.56708e14 + 9.04751e13i) q^{44} +(5.30700e13 + 1.71228e13i) q^{45} +(1.69054e14 - 2.92811e14i) q^{46} +(6.55762e13 + 1.13581e14i) q^{47} +(5.79740e13 - 7.17428e13i) q^{48} +(5.18725e13 + 2.26773e14i) q^{49} -3.50009e14i q^{50} +(-1.56527e14 - 2.46265e13i) q^{51} +(-9.69086e14 - 5.59502e14i) q^{52} +(1.38993e14 + 8.02475e13i) q^{53} +(-8.89651e14 + 4.93784e13i) q^{54} +3.28913e14i q^{55} +(-6.14642e14 + 7.71111e14i) q^{56} +(-8.43828e14 - 6.81882e14i) q^{57} +(-5.20015e14 - 9.00693e14i) q^{58} +(-3.96614e14 + 6.86955e14i) q^{59} +(-4.18874e14 - 1.08786e15i) q^{60} +(1.34274e15 - 7.75230e14i) q^{61} -2.50600e15 q^{62} +(1.96587e15 - 1.22305e14i) q^{63} +3.21689e15 q^{64} +(-1.76151e15 + 1.01701e15i) q^{65} +(-1.88846e15 - 4.90451e15i) q^{66} +(1.18812e15 - 2.05789e15i) q^{67} +(1.65619e15 + 2.86860e15i) q^{68} +(4.92216e15 + 3.97751e15i) q^{69} +(1.46178e15 + 3.72196e15i) q^{70} +5.99999e15i q^{71} +(5.59952e15 + 6.19323e15i) q^{72} +(-2.33668e15 - 1.34908e15i) q^{73} +(-9.53926e14 - 5.50749e14i) q^{74} +(6.47151e15 + 1.01816e15i) q^{75} +2.26793e16i q^{76} +(4.24700e15 + 1.08137e16i) q^{77} +(2.04271e16 - 2.52785e16i) q^{78} +(-7.25575e15 - 1.25673e16i) q^{79} +(-1.75245e15 + 3.03533e15i) q^{80} +(1.67497e15 - 1.65929e16i) q^{81} +(1.25944e15 - 7.27138e14i) q^{82} +3.03966e16 q^{83} +(-2.78180e16 - 3.03569e16i) q^{84} +6.02090e15 q^{85} +(-5.38631e16 + 3.10979e16i) q^{86} +(1.81661e16 - 6.99476e15i) q^{87} +(-2.46234e16 + 4.26489e16i) q^{88} +(-7.16207e15 - 1.24051e16i) q^{89} +(3.31026e16 - 7.10740e15i) q^{90} +(-4.47812e16 + 5.61811e16i) q^{91} -1.32291e17i q^{92} +(7.28984e15 - 4.63347e16i) q^{93} +(6.89608e16 + 3.98145e16i) q^{94} +(3.57011e16 + 2.06121e16i) q^{95} +(-6.26302e15 + 3.98082e16i) q^{96} -3.14938e16i q^{97} +(9.61175e16 + 1.03492e17i) q^{98} +(9.61754e16 - 2.06496e16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 19686 q^{3} + 2752510 q^{4} - 4340518 q^{7} - 98670996 q^{9}+O(q^{10}) $ 84 * q - 19686 * q^3 + 2752510 * q^4 - 4340518 * q^7 - 98670996 * q^9	$ 84 q - 19686 q^{3} + 2752510 q^{4} - 4340518 q^{7} - 98670996 q^{9} + 465470970 q^{10} - 2491764528 q^{12} - 7104382296 q^{15} - 110459605130 q^{16} - 14553542550 q^{18} + 404032278750 q^{19} + 228767508522 q^{21} - 832496305460 q^{22} - 1354439880378 q^{24} - 7199868598470 q^{25} - 7749926510914 q^{28} + 284772818082 q^{30} + 20192079903726 q^{31} - 18426553023870 q^{33} - 6006594191052 q^{36} + 46546034438938 q^{37} + 156966454169838 q^{39} + 52009146351690 q^{40} + 273411312457290 q^{42} + 262809922393900 q^{43} - 463828715581158 q^{45} - 691873824309656 q^{46} + 158652002613594 q^{49} + 123926983295328 q^{51} + 180256725379488 q^{52} + 528953393499678 q^{54} - 13\!\cdots\!84 q^{57}+ \cdots + 30\!\cdots\!80 q^{99}+O(q^{100}) $ 84 * q - 19686 * q^3 + 2752510 * q^4 - 4340518 * q^7 - 98670996 * q^9 + 465470970 * q^10 - 2491764528 * q^12 - 7104382296 * q^15 - 110459605130 * q^16 - 14553542550 * q^18 + 404032278750 * q^19 + 228767508522 * q^21 - 832496305460 * q^22 - 1354439880378 * q^24 - 7199868598470 * q^25 - 7749926510914 * q^28 + 284772818082 * q^30 + 20192079903726 * q^31 - 18426553023870 * q^33 - 6006594191052 * q^36 + 46546034438938 * q^37 + 156966454169838 * q^39 + 52009146351690 * q^40 + 273411312457290 * q^42 + 262809922393900 * q^43 - 463828715581158 * q^45 - 691873824309656 * q^46 + 158652002613594 * q^49 + 123926983295328 * q^51 + 180256725379488 * q^52 + 528953393499678 * q^54 - 1311284732111784 * q^57 + 521920547533210 * q^58 - 416477060451846 * q^60 - 6052836877037172 * q^61 - 13769533594398750 * q^63 + 1053936792659996 * q^64 + 21705058495057878 * q^66 + 3639355527884298 * q^67 + 44463964567209810 * q^70 + 7798479140884800 * q^72 - 31719690947775954 * q^73 + 17256341731591290 * q^75 - 67997864561346840 * q^78 - 31267401781398294 * q^79 + 44133415784265492 * q^81 + 4877409168868320 * q^82 + 25637268676337472 * q^84 + 2464288230356616 * q^85 - 61426317616508880 * q^87 - 112618869011616970 * q^88 - 223816788036276750 * q^91 + 104033604109825260 * q^93 + 248077621213302516 * q^94 - 363875964512101146 * q^96 + 303894121197814080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	525.807	−	303.575i	1.45235	−	0.838514i	0.453735	−	0.891137i	$-0.350091\pi$
$2$	525.807	−	303.575i	1.45235	−	0.838514i	0.998614	+	0.0526225i	$0.0167580\pi$
$3$	4083.40	+	10605.0i	0.359328	+	0.933211i
$3$	4083.40	+	10605.0i	0.359328	+	0.933211i
$4$	118779.	−	205731.i	0.906212	−	1.56961i
$5$	−215905.	−	373958.i	−0.247182	−	0.428132i	0.715561	−	0.698550i	$-0.246171\pi$
$5$	−215905.	−	373958.i	−0.247182	−	0.428132i	−0.962743	+	0.270419i	$0.912838\pi$
$6$	5.36649e6	+	4.33656e6i	1.30438	+	1.05405i
$7$	−1.19269e7	−	9.50679e6i	−0.781979	−	0.623305i
$7$	−1.19269e7	−	9.50679e6i	−0.781979	−	0.623305i
$8$		−	6.46530e7i		−	1.36246i
$9$	−9.57918e7	+	8.66089e7i	−0.741766	+	0.670658i
$10$	−2.27048e8	−	1.31086e8i	−0.717989	−	0.414531i
$11$	−6.59660e8	−	3.80855e8i	−0.927859	−	0.535700i	−0.0417253	−	0.999129i	$-0.513285\pi$
$11$	−6.59660e8	−	3.80855e8i	−0.927859	−	0.535700i	−0.886134	+	0.463429i	$0.846619\pi$
$12$	2.66680e9	+	4.19568e8i	1.79040	+	0.281684i
$13$		−	4.71045e9i		−	1.60156i	−0.598958	−	0.800780i	$-0.704418\pi$
$13$		−	4.71045e9i		−	1.60156i	0.598958	−	0.800780i	$-0.295582\pi$
$14$	−9.15727e9	−	1.37802e9i	−1.65836	−	0.249556i
$15$	3.08420e9	−	3.81669e9i	0.310718	−	0.384513i
$16$	−4.05839e9	−	7.02933e9i	−0.236229	−	0.409161i
$17$	−6.97171e9	+	1.20754e10i	−0.242395	+	0.419840i	−0.961396	−	0.275169i	$-0.911266\pi$
$17$	−6.97171e9	+	1.20754e10i	−0.242395	+	0.419840i	0.719001	+	0.695009i	$0.244600\pi$
$18$	−2.40757e10	+	7.46195e10i	−0.514947	+	1.59601i
$19$	−8.26780e10	+	4.77342e10i	−1.11682	+	0.644798i	−0.940588	−	0.339550i	$-0.889725\pi$
$19$	−8.26780e10	+	4.77342e10i	−1.11682	+	0.644798i	−0.176235	+	0.984348i	$0.556392\pi$
$20$	−1.02580e11			−0.895998
$21$	5.21171e10	−	1.65305e11i	0.300688	−	0.953723i
$22$	−4.62471e11			−1.79677
$23$	4.82272e11	−	2.78440e11i	1.28412	−	0.741386i	0.306520	−	0.951864i	$-0.400835\pi$
$23$	4.82272e11	−	2.78440e11i	1.28412	−	0.741386i	0.977599	+	0.210478i	$0.0675020\pi$
$24$	6.85645e11	−	2.64004e11i	1.27146	−	0.489570i
$25$	2.88240e11	−	4.99246e11i	0.377802	−	0.654372i
$26$	−1.42997e12	−	2.47678e12i	−1.34293	−	2.32603i
$27$	−1.30964e12	−	6.62213e11i	−0.892403	−	0.451238i
$28$	−3.37251e12	+	1.32453e12i	−1.68698	+	0.662552i
$29$		−	1.71297e12i		−	0.635869i	−0.948113	−	0.317935i	$-0.897011\pi$
$29$		−	1.71297e12i		−	0.635869i	0.948113	−	0.317935i	$-0.102989\pi$
$30$	4.63042e11	−	2.94312e12i	0.128851	−	0.818989i
$31$	−3.57451e12	−	2.06374e12i	−0.752734	−	0.434591i	0.0739468	−	0.997262i	$-0.476441\pi$
$31$	−3.57451e12	−	2.06374e12i	−0.752734	−	0.434591i	−0.826681	+	0.562671i	$0.809774\pi$
$32$	3.07101e12	+	1.77305e12i	0.493750	+	0.285067i
$33$	1.34531e12	−	8.55087e12i	0.166515	−	1.05838i
$34$			8.46574e12i			0.813006i
$35$	−9.80060e11	+	6.51273e12i	−0.0735655	+	0.488860i
$36$	6.44011e12	+	2.99947e13i	0.380471	+	1.77204i
$37$	−9.07107e11	−	1.57116e12i	−0.0424565	−	0.0735367i	0.844016	−	0.536318i	$-0.180185\pi$
$37$	−9.07107e11	−	1.57116e12i	−0.0424565	−	0.0735367i	−0.886473	+	0.462781i	$0.846852\pi$
$38$	−2.89818e13	+	5.01979e13i	−1.08134	+	1.87294i
$39$	4.99543e13	−	1.92346e13i	1.49459	−	0.575486i
$40$	−2.41775e13	+	1.39589e13i	−0.583312	+	0.336776i
$41$	2.39525e12			0.0468478			0.0234239	−	0.999726i	$-0.492543\pi$
$41$	2.39525e12			0.0468478			0.0234239	+	0.999726i	$0.492543\pi$
$42$	−2.27789e13	−	1.02740e14i	−0.363006	−	1.63727i
$43$	−1.02439e14			−1.33654			−0.668272	−	0.743917i	$-0.732966\pi$
$43$	−1.02439e14			−1.33654			−0.668272	+	0.743917i	$0.732966\pi$
$44$	−1.56708e14	+	9.04751e13i	−1.68167	+	0.970915i
$45$	5.30700e13	+	1.71228e13i	0.470482	+	0.151799i
$46$	1.69054e14	−	2.92811e14i	1.24333	−	2.15350i
$47$	6.55762e13	+	1.13581e14i	0.401712	+	0.695785i	0.993933	−	0.109991i	$-0.0350821\pi$
$47$	6.55762e13	+	1.13581e14i	0.401712	+	0.695785i	−0.592221	+	0.805776i	$0.701749\pi$
$48$	5.79740e13	−	7.17428e13i	0.296950	−	0.367475i
$49$	5.18725e13	+	2.26773e14i	0.222982	+	0.974823i
$50$		−	3.50009e14i		−	1.26717i
$51$	−1.56527e14	−	2.46265e13i	−0.478899	−	0.0753452i
$52$	−9.69086e14	−	5.59502e14i	−2.51382	−	1.45135i
$53$	1.38993e14	+	8.02475e13i	0.306653	+	0.177046i	0.645428	−	0.763821i	$-0.276679\pi$
$53$	1.38993e14	+	8.02475e13i	0.306653	+	0.177046i	−0.338775	+	0.940867i	$0.610012\pi$
$54$	−8.89651e14	+	4.93784e13i	−1.67445	+	0.0929373i
$55$			3.28913e14i			0.529662i
$56$	−6.14642e14	+	7.71111e14i	−0.849227	+	1.06541i
$57$	−8.43828e14	−	6.81882e14i	−1.00304	−	0.810538i
$58$	−5.20015e14	−	9.00693e14i	−0.533185	−	0.923504i
$59$	−3.96614e14	+	6.86955e14i	−0.351662	+	0.609097i	−0.986541	−	0.163515i	$-0.947717\pi$
$59$	−3.96614e14	+	6.86955e14i	−0.351662	+	0.609097i	0.634879	+	0.772612i	$0.281050\pi$
$60$	−4.18874e14	−	1.08786e15i	−0.321957	−	0.836155i
$61$	1.34274e15	−	7.75230e14i	0.896784	−	0.517758i	0.0206283	−	0.999787i	$-0.493433\pi$
$61$	1.34274e15	−	7.75230e14i	0.896784	−	0.517758i	0.876155	+	0.482029i	$0.160100\pi$
$62$	−2.50600e15			−1.45764
$63$	1.96587e15	−	1.22305e14i	0.998070	−	0.0620940i
$64$	3.21689e15			1.42859
$65$	−1.76151e15	+	1.01701e15i	−0.685679	+	0.395877i
$66$	−1.88846e15	−	4.90451e15i	−0.645629	−	1.67676i
$67$	1.18812e15	−	2.05789e15i	0.357459	−	0.619137i	−0.630077	−	0.776533i	$-0.716977\pi$
$67$	1.18812e15	−	2.05789e15i	0.357459	−	0.619137i	0.987536	+	0.157396i	$0.0503099\pi$
$68$	1.65619e15	+	2.86860e15i	0.439322	+	0.760929i
$69$	4.92216e15	+	3.97751e15i	1.15329	+	0.931953i
$70$	1.46178e15	+	3.72196e15i	0.303073	+	0.771681i
$71$			5.99999e15i			1.10269i	0.834277	+	0.551346i	$0.185886\pi$
$71$			5.99999e15i			1.10269i	−0.834277	+	0.551346i	$0.814114\pi$
$72$	5.59952e15	+	6.19323e15i	0.913745	+	1.01063i
$73$	−2.33668e15	−	1.34908e15i	−0.339121	−	0.195791i	0.320762	−	0.947160i	$-0.396061\pi$
$73$	−2.33668e15	−	1.34908e15i	−0.339121	−	0.195791i	−0.659883	+	0.751368i	$0.729394\pi$
$74$	−9.53926e14	−	5.50749e14i	−0.123323	−	0.0712007i
$75$	6.47151e15	+	1.01816e15i	0.746423	+	0.117435i
$76$			2.26793e16i			2.33730i
$77$	4.24700e15	+	1.08137e16i	0.391662	+	0.997245i
$78$	2.04271e16	−	2.52785e16i	1.68812	−	2.08905i
$79$	−7.25575e15	−	1.25673e16i	−0.538086	−	0.931993i	−0.999007	−	0.0445516i	$-0.985814\pi$
$79$	−7.25575e15	−	1.25673e16i	−0.538086	−	0.931993i	0.460921	−	0.887441i	$-0.347519\pi$
$80$	−1.75245e15	+	3.03533e15i	−0.116783	+	0.202275i
$81$	1.67497e15	−	1.65929e16i	0.100435	−	0.994944i
$82$	1.25944e15	−	7.27138e14i	0.0680393	−	0.0392825i
$83$	3.03966e16			1.48136			0.740681	−	0.671857i	$-0.234503\pi$
$83$	3.03966e16			1.48136			0.740681	+	0.671857i	$0.234503\pi$
$84$	−2.78180e16	−	3.03569e16i	−1.22448	−	1.33624i
$85$	6.02090e15			0.239663
$86$	−5.38631e16	+	3.10979e16i	−1.94113	+	1.12071i
$87$	1.81661e16	−	6.99476e15i	0.593400	−	0.228486i
$88$	−2.46234e16	+	4.26489e16i	−0.729869	+	1.26417i
$89$	−7.16207e15	−	1.24051e16i	−0.192852	−	0.334029i	0.753342	−	0.657628i	$-0.228440\pi$
$89$	−7.16207e15	−	1.24051e16i	−0.192852	−	0.334029i	−0.946194	+	0.323599i	$0.895107\pi$
$90$	3.31026e16	−	7.10740e15i	0.810589	−	0.174040i
$91$	−4.47812e16	+	5.61811e16i	−0.998261	+	1.25239i
$92$		−	1.32291e17i		−	2.68741i
$93$	7.28984e15	−	4.63347e16i	0.135087	−	0.858621i
$94$	6.89608e16	+	3.98145e16i	1.16685	+	0.673682i
$95$	3.57011e16	+	2.06121e16i	0.552117	+	0.318765i
$96$	−6.26302e15	+	3.98082e16i	−0.0886091	+	0.563205i
$97$		−	3.14938e16i		−	0.408005i	−0.978970	−	0.204002i	$-0.934605\pi$
$97$		−	3.14938e16i		−	0.408005i	0.978970	−	0.204002i	$-0.0653951\pi$
$98$	9.61175e16	+	1.03492e17i	1.14125	+	1.22881i
$99$	9.61754e16	−	2.06496e16i	1.04753	−	0.224912i
$100$	−6.84738e16	−	1.18600e17i	−0.684738	−	1.18600i
$101$	−9.56210e16	+	1.65620e17i	−0.878662	+	1.52189i	−0.0258518	+	0.999666i	$0.508230\pi$
$101$	−9.56210e16	+	1.65620e17i	−0.878662	+	1.52189i	−0.852810	+	0.522221i	$0.825104\pi$
$102$	−8.97791e16	+	3.45690e16i	−0.758707	+	0.292136i
$103$	1.40216e17	−	8.09536e16i	1.09064	−	0.629680i	0.156891	−	0.987616i	$-0.449853\pi$
$103$	1.40216e17	−	8.09536e16i	1.09064	−	0.629680i	0.933746	+	0.357936i	$0.116519\pi$
$104$	−3.04544e17			−2.18206
$105$	−7.30694e16	+	1.62005e16i	−0.482644	+	0.107009i
$106$	9.74444e16			0.593823
$107$	2.26476e17	−	1.30756e17i	1.27426	−	0.735696i	0.298476	−	0.954417i	$-0.403522\pi$
$107$	2.26476e17	−	1.30756e17i	1.27426	−	0.735696i	0.975787	+	0.218721i	$0.0701885\pi$
$108$	−2.91796e17	+	1.90778e17i	−1.51697	+	0.991804i
$109$	1.21424e17	−	2.10312e17i	0.583686	−	1.01097i	−0.411352	−	0.911476i	$-0.634943\pi$
$109$	1.21424e17	−	2.10312e17i	0.583686	−	1.01097i	0.995038	−	0.0994968i	$-0.0317233\pi$
$110$	9.98497e16	+	1.72945e17i	0.444129	+	0.769254i
$111$	1.29580e16	−	1.60355e16i	0.0533695	−	0.0660447i
$112$	−1.84223e16	+	1.22421e17i	−0.0703057	+	0.467198i
$113$		−	1.12666e17i		−	0.398680i	−0.979930	−	0.199340i	$-0.936120\pi$
$113$		−	1.12666e17i		−	0.398680i	0.979930	−	0.199340i	$-0.0638799\pi$
$114$	−6.50693e17	−	1.02373e17i	−2.13641	−	0.336121i
$115$	−2.08249e17	−	1.20233e17i	−0.634822	−	0.366515i
$116$	−3.52412e17	−	2.03465e17i	−0.998064	−	0.576232i
$117$	4.07967e17	+	4.51222e17i	1.07410	+	1.18798i
$118$			4.81608e17i			1.17950i
$119$	1.97949e17	−	7.77433e16i	0.451236	−	0.177220i
$120$	−2.46760e17	−	1.99402e17i	−0.523883	−	0.423341i
$121$	3.73770e16	+	6.47389e16i	0.0739485	+	0.128083i
$122$	4.70680e17	−	8.15242e17i	0.868295	−	1.50393i
$123$	9.78078e15	+	2.54017e16i	0.0168337	+	0.0437189i
$124$	−8.49153e17	+	4.90259e17i	−1.36427	+	0.787664i
$125$	−5.78374e17			−0.867908
$126$	9.96541e17	−	6.61098e17i	1.39748	−	0.927078i
$127$	−7.64991e17			−1.00305			−0.501527	−	0.865142i	$-0.667228\pi$
$127$	−7.64991e17			−1.00305			−0.501527	+	0.865142i	$0.667228\pi$
$128$	1.28894e18	−	7.44170e17i	1.58106	−	0.912825i
$129$	−4.18299e17	−	1.08637e18i	−0.480258	−	1.24728i
$130$	−6.17475e17	+	1.06950e18i	−0.663897	+	1.14990i
$131$	−2.16814e17	−	3.75533e17i	−0.218414	−	0.378305i	0.735909	−	0.677080i	$-0.236755\pi$
$131$	−2.16814e17	−	3.75533e17i	−0.218414	−	0.378305i	−0.954323	+	0.298776i	$0.903422\pi$
$132$	−1.59939e18	−	1.29244e18i	−1.51034	−	1.22048i
$133$	1.43989e18	+	2.16681e17i	1.27524	+	0.191903i
$134$		−	1.44274e18i		−	1.19894i
$135$	3.51183e16	+	6.32727e17i	0.0273966	+	0.493604i
$136$	7.80707e17	+	4.50742e17i	0.572015	+	0.330253i
$137$	7.80938e17	+	4.50875e17i	0.537640	+	0.310407i	0.744122	−	0.668044i	$-0.232868\pi$
$137$	7.80938e17	+	4.50875e17i	0.537640	+	0.310407i	−0.206482	+	0.978450i	$0.566201\pi$
$138$	3.79558e18	+	5.97158e17i	2.45644	+	0.386471i
$139$			5.62899e17i			0.342614i	0.985218	+	0.171307i	$0.0547990\pi$
$139$			5.62899e17i			0.342614i	−0.985218	+	0.171307i	$0.945201\pi$
$140$	1.22346e18	+	9.75205e17i	0.700651	+	0.558480i
$141$	−9.36756e17	+	1.15923e18i	−0.504968	+	0.624897i
$142$	1.82144e18	+	3.15483e18i	0.924623	+	1.60149i
$143$	−1.79400e18	+	3.10729e18i	−0.857956	+	1.48602i
$144$	9.97563e17	+	3.21860e17i	0.449634	+	0.145073i
$145$	−6.40580e17	+	3.69839e17i	−0.272236	+	0.157175i
$146$	−1.63819e18			−0.656696
$147$	−2.19312e18	+	1.47611e18i	−0.829592	+	0.558371i
$148$	−4.30981e17			−0.153898
$149$	4.21297e18	−	2.43236e18i	1.42071	−	0.820246i	0.424348	−	0.905499i	$-0.360503\pi$
$149$	4.21297e18	−	2.43236e18i	1.42071	−	0.820246i	0.996359	+	0.0852534i	$0.0271700\pi$
$150$	3.71185e18	−	1.42923e18i	1.18254	−	0.455330i
$151$	−1.32450e18	+	2.29409e18i	−0.398792	+	0.690728i	−0.993577	−	0.113157i	$-0.963904\pi$
$151$	−1.32450e18	+	2.29409e18i	−0.398792	+	0.690728i	0.594785	+	0.803885i	$0.297237\pi$
$152$	3.08615e18	+	5.34538e18i	0.878511	+	1.52163i
$153$	−3.78001e17	−	1.76053e18i	−0.101769	−	0.473988i
$154$	5.51586e18	+	4.39662e18i	1.40503	+	1.11993i
$155$			1.78229e18i			0.429693i
$156$	1.97635e18	−	1.25618e19i	0.451134	−	2.86744i
$157$	9.49040e17	+	5.47928e17i	0.205181	+	0.118461i	0.599070	−	0.800697i	$-0.295537\pi$
$157$	9.49040e17	+	5.47928e17i	0.205181	+	0.118461i	−0.393889	+	0.919158i	$0.628870\pi$
$158$	−7.63024e18	−	4.40532e18i	−1.56298	−	0.902386i
$159$	−2.83461e17	+	1.80170e18i	−0.0550324	+	0.349790i
$160$		−	1.53124e18i		−	0.281853i
$161$	−8.39908e18	−	1.26393e18i	−1.46626	−	0.220649i
$162$	−4.15646e18	−	9.23311e18i	−0.688408	−	1.52922i
$163$	−2.50164e18	−	4.33296e18i	−0.393214	−	0.681067i	0.599657	−	0.800257i	$-0.295304\pi$
$163$	−2.50164e18	−	4.33296e18i	−0.393214	−	0.681067i	−0.992872	+	0.119190i	$0.961970\pi$
$164$	2.84506e17	−	4.92779e17i	0.0424540	−	0.0735325i
$165$	−3.48812e18	+	1.34308e18i	−0.494286	+	0.190322i
$166$	1.59827e19	−	9.22763e18i	2.15145	−	1.24214i
$167$	−5.22745e18			−0.668651			−0.334326	−	0.942458i	$-0.608509\pi$
$167$	−5.22745e18			−0.668651			−0.334326	+	0.942458i	$0.608509\pi$
$168$	−1.06875e19	−	3.36952e18i	−1.29941	−	0.409675i
$169$	−1.35379e19			−1.56500
$170$	3.16583e18	−	1.82779e18i	0.348074	−	0.200961i
$171$	3.78567e18	−	1.17332e19i	0.395983	−	1.22730i
$172$	−1.21676e19	+	2.10749e19i	−1.21119	+	2.09785i
$173$	8.93518e18	+	1.54762e19i	0.846665	+	1.46647i	0.884168	+	0.467170i	$0.154726\pi$
$173$	8.93518e18	+	1.54762e19i	0.846665	+	1.46647i	−0.0375032	+	0.999297i	$0.511940\pi$
$174$	7.42842e18	−	9.19265e18i	0.670236	−	0.829416i
$175$	−8.18405e18	+	3.21424e18i	−0.703307	+	0.276220i
$176$			6.18262e18i			0.506192i
$177$	−8.90469e18	−	1.40098e18i	−0.694778	−	0.109309i
$178$	−7.53173e18	−	4.34844e18i	−0.560176	−	0.323418i
$179$	−2.03368e19	−	1.17414e19i	−1.44222	−	0.832666i	−0.444222	−	0.895917i	$-0.646520\pi$
$179$	−2.03368e19	−	1.17414e19i	−1.44222	−	0.832666i	−0.997998	+	0.0632507i	$0.979853\pi$
$180$	9.82631e18	−	8.88433e18i	0.664621	−	0.600908i
$181$			2.92620e19i			1.88815i	0.329734	+	0.944074i	$0.393041\pi$
$181$			2.92620e19i			1.88815i	−0.329734	+	0.944074i	$0.606959\pi$
$182$	−6.49110e18	+	4.31348e19i	−0.399679	+	2.65596i
$183$	1.37043e19	+	1.10742e19i	0.805417	+	0.650843i
$184$	−1.80019e19	−	3.11803e19i	−1.01011	−	1.74956i
$185$	−3.91697e17	+	6.78439e17i	−0.0209890	+	0.0363539i
$186$	−1.02330e19	−	2.65761e19i	−0.523773	−	1.36029i
$187$	9.19791e18	−	5.31042e18i	0.449817	−	0.259702i
$188$	3.11563e19			1.45614
$189$	9.32450e18	+	2.03487e19i	0.416582	+	0.909098i
$190$	2.50292e19			1.06916
$191$	−5.19645e16	+	3.00017e16i	−0.00212287	+	0.00122564i	−0.501061	−	0.865412i	$-0.667057\pi$
$191$	−5.19645e16	+	3.00017e16i	−0.00212287	+	0.00122564i	0.498938	+	0.866638i	$0.333723\pi$
$192$	1.31359e19	+	3.41152e19i	0.513332	+	1.33317i
$193$	9.62656e18	−	1.66737e19i	0.359943	−	0.623440i	−0.628008	−	0.778207i	$-0.716129\pi$
$193$	9.62656e18	−	1.66737e19i	0.359943	−	0.623440i	0.987951	+	0.154767i	$0.0494627\pi$
$194$	−9.56072e18	−	1.65596e19i	−0.342118	−	0.592566i
$195$	−1.79783e19	−	1.45279e19i	−0.615821	−	0.497634i
$196$	5.28158e19	+	1.62641e19i	1.73216	+	0.533402i
$197$		−	3.46256e19i		−	1.08751i	−0.839244	−	0.543756i	$-0.817002\pi$
$197$		−	3.46256e19i		−	1.08751i	0.839244	−	0.543756i	$-0.182998\pi$
$198$	4.43010e19	−	4.00541e19i	1.33278	−	1.20502i
$199$	−5.19261e19	−	2.99796e19i	−1.49670	−	0.864120i	−0.496707	−	0.867918i	$-0.665458\pi$
$199$	−5.19261e19	−	2.99796e19i	−1.49670	−	0.864120i	−0.999993	+	0.00379827i	$0.998791\pi$
$200$	−3.22778e19	−	1.86356e19i	−0.891556	−	0.514740i
$201$	2.66755e19	+	4.19686e18i	0.706231	+	0.111111i
$202$			1.16112e20i			2.94708i
$203$	−1.62849e19	+	2.04305e19i	−0.396340	+	0.497236i
$204$	−2.36586e19	+	2.92775e19i	−0.552246	+	0.683404i
$205$	−5.17147e17	−	8.95724e17i	−0.0115799	−	0.0200570i
$206$	4.91509e19	−	8.51319e19i	1.05599	−	1.82903i
$207$	−2.20823e19	+	6.84413e19i	−0.455299	+	1.41114i
$208$	−3.31113e19	+	1.91168e19i	−0.655296	+	0.378335i
$209$	7.27191e19			1.38167
$210$	−3.35023e19	+	3.07004e19i	−0.611239	+	0.560118i
$211$	−3.14924e19			−0.551829			−0.275915	−	0.961182i	$-0.588981\pi$
$211$	−3.14924e19			−0.551829			−0.275915	+	0.961182i	$0.588981\pi$
$212$	3.30188e19	−	1.90634e19i	0.555785	−	0.320883i
$213$	−6.36299e19	+	2.45004e19i	−1.02905	+	0.396229i
$214$	7.93882e19	−	1.37504e20i	1.23378	−	2.13698i
$215$	2.21170e19	+	3.83079e19i	0.330370	+	0.572217i
$216$	−4.28141e19	+	8.46724e19i	−0.614794	+	1.21586i
$217$	2.30133e19	+	5.85962e19i	0.317739	+	0.809024i
$218$		−	1.47445e20i		−	1.95772i
$219$	4.76541e18	−	3.02893e19i	0.0608591	−	0.386825i
$220$	6.76678e19	+	3.90680e19i	0.831360	+	0.479986i
$221$	5.68803e19	+	3.28399e19i	0.672400	+	0.388210i
$222$	1.94543e18	−	1.23653e19i	0.0221318	−	0.140671i
$223$		−	1.25758e20i		−	1.37703i	−0.725221	−	0.688517i	$-0.758262\pi$
$223$		−	1.25758e20i		−	1.37703i	0.725221	−	0.688517i	$-0.241738\pi$
$224$	−1.97717e19	−	5.03425e19i	−0.208419	−	0.530673i
$225$	1.56281e19	+	7.27879e19i	0.158619	+	0.738767i
$226$	−3.42024e19	−	5.92404e19i	−0.334299	−	0.579023i
$227$	3.30020e19	−	5.71612e19i	0.310685	−	0.538123i	−0.667826	−	0.744318i	$-0.732775\pi$
$227$	3.30020e19	−	5.71612e19i	0.310685	−	0.538123i	0.978511	+	0.206195i	$0.0661081\pi$
$228$	−2.40514e20	+	9.26086e19i	−2.18119	+	0.839856i
$229$	5.48593e19	−	3.16730e19i	0.479346	−	0.276750i	−0.240798	−	0.970575i	$-0.577409\pi$
$229$	5.48593e19	−	3.16730e19i	0.479346	−	0.276750i	0.720144	+	0.693825i	$0.244076\pi$
$230$	−1.45999e20			−1.22931
$231$	−9.73367e19	+	8.91960e19i	−0.789905	+	0.723842i
$232$	−1.10749e20			−0.866346
$233$	−2.76819e19	+	1.59821e19i	−0.208771	+	0.120534i	−0.600740	−	0.799444i	$-0.705127\pi$
$233$	−2.76819e19	+	1.59821e19i	−0.208771	+	0.120534i	0.391969	+	0.919978i	$0.371794\pi$
$234$	3.51491e20	+	1.13407e20i	2.55611	+	0.824720i
$235$	2.83164e19	−	4.90455e19i	0.198592	−	0.343971i
$236$	9.42188e19	+	1.63192e20i	0.637361	+	1.10394i
$237$	1.03648e20	−	1.28265e20i	0.676397	−	0.837040i
$238$	8.04820e19	−	1.00970e20i	0.506751	−	0.635754i
$239$			2.24975e20i			1.36695i	0.729974	+	0.683474i	$0.239532\pi$
$239$			2.24975e20i			1.36695i	−0.729974	+	0.683474i	$0.760468\pi$
$240$	−3.93456e19	−	6.19025e18i	−0.230728	−	0.0363005i
$241$	−1.27641e20	−	7.36938e19i	−0.722515	−	0.417144i	0.0931628	−	0.995651i	$-0.470302\pi$
$241$	−1.27641e20	−	7.36938e19i	−0.722515	−	0.417144i	−0.815678	+	0.578507i	$0.803636\pi$
$242$	3.93062e19	+	2.26934e19i	0.214798	+	0.124014i
$243$	1.82807e20	−	4.99922e19i	0.964582	−	0.263784i
$244$		−	3.68324e20i		−	1.87680i
$245$	7.36042e19	−	6.83596e19i	0.362235	−	0.336424i
$246$	1.28541e19	+	1.03872e19i	0.0611073	+	0.0493797i
$247$	2.24849e20	+	3.89450e20i	1.03268	+	1.78866i
$248$	−1.33427e20	+	2.31102e20i	−0.592113	+	1.02557i
$249$	1.24121e20	+	3.22356e20i	0.532295	+	1.38242i
$250$	−3.04113e20	+	1.75580e20i	−1.26051	+	0.727753i
$251$	−2.61051e20			−1.04592			−0.522961	−	0.852357i	$-0.675173\pi$
$251$	−2.61051e20			−1.04592			−0.522961	+	0.852357i	$0.675173\pi$
$252$	2.08343e20	−	4.18969e20i	0.807000	−	1.62285i
$253$	−4.24180e20			−1.58864
$254$	−4.02237e20	+	2.32232e20i	−1.45679	+	0.841076i
$255$	2.45857e19	+	6.38516e19i	0.0861176	+	0.223656i
$256$	2.41000e20	−	4.17424e20i	0.816539	−	1.41429i
$257$	−1.33680e20	−	2.31541e20i	−0.438163	−	0.758921i	0.559385	−	0.828908i	$-0.311037\pi$
$257$	−1.33680e20	−	2.31541e20i	−0.438163	−	0.758921i	−0.997548	+	0.0699875i	$0.977704\pi$
$258$	−5.49737e20	−	4.44233e20i	−1.74336	−	1.40878i
$259$	−4.11765e18	+	2.73627e19i	−0.0126358	+	0.0839675i
$260$			4.83197e20i			1.43500i
$261$	1.48359e20	+	1.64089e20i	0.426451	+	0.471666i
$262$	−2.28004e20	−	1.31638e20i	−0.634428	−	0.366287i
$263$	−4.97791e20	−	2.87400e20i	−1.34098	−	0.774216i	−0.354030	−	0.935234i	$-0.615189\pi$
$263$	−4.97791e20	−	2.87400e20i	−1.34098	−	0.774216i	−0.986952	+	0.161018i	$0.948522\pi$
$264$	−5.52839e20	−	8.69782e19i	−1.44200	−	0.226870i
$265$		−	6.93032e19i		−	0.175051i
$266$	8.22884e20	−	3.23183e20i	2.01300	−	0.790595i
$267$	1.02310e20	−	1.26609e20i	0.242423	−	0.299997i
$268$	−2.82249e20	−	4.88869e20i	−0.647867	−	1.12214i
$269$	1.07506e19	−	1.86207e19i	0.0239078	−	0.0414096i	−0.853824	−	0.520562i	$-0.825723\pi$
$269$	1.07506e19	−	1.86207e19i	0.0239078	−	0.0414096i	0.877732	+	0.479152i	$0.159056\pi$
$270$	2.10545e20	+	3.22031e20i	0.453684	+	0.693914i
$271$	−4.05114e20	+	2.33893e20i	−0.845939	+	0.488403i	−0.859278	−	0.511508i	$-0.829087\pi$
$271$	−4.05114e20	+	2.33893e20i	−0.845939	+	0.488403i	0.0133399	+	0.999911i	$0.495754\pi$
$272$	1.13176e20			0.229043
$273$	−7.78660e20	−	2.45495e20i	−1.52744	−	0.481570i
$274$	5.47496e20			1.04112
$275$	−3.80281e20	+	2.19555e20i	−0.701094	+	0.404777i
$276$	1.40295e21	−	5.40198e20i	2.50792	−	0.965663i
$277$	5.61119e20	−	9.71887e20i	0.972696	−	1.68476i	0.285356	−	0.958421i	$-0.407888\pi$
$277$	5.61119e20	−	9.71887e20i	0.972696	−	1.68476i	0.687339	−	0.726337i	$-0.258779\pi$
$278$	1.70882e20	+	2.95976e20i	0.287287	+	0.497595i
$279$	5.21147e20	−	1.11894e20i	0.849815	−	0.182462i
$280$	4.21067e20	+	6.33638e19i	0.666052	+	0.100230i
$281$		−	7.13886e20i		−	1.09553i	−0.836631	−	0.547766i	$-0.815478\pi$
$281$		−	7.13886e20i		−	1.09553i	0.836631	−	0.547766i	$-0.184522\pi$
$282$	−1.40639e20	+	8.93908e20i	−0.209405	+	1.33099i
$283$	3.82552e19	+	2.20867e19i	0.0552721	+	0.0319114i	0.527381	−	0.849629i	$-0.323174\pi$
$283$	3.82552e19	+	2.20867e19i	0.0552721	+	0.0319114i	−0.472109	+	0.881540i	$0.656507\pi$
$284$	1.23439e21	+	7.12673e20i	1.73079	+	0.999273i
$285$	−7.28088e19	+	4.62778e20i	−0.0990838	+	0.629783i
$286$			2.17845e21i			2.87763i
$287$	−2.85680e19	−	2.27712e19i	−0.0366340	−	0.0292004i
$288$	−4.47740e20	+	9.61334e19i	−0.557429	+	0.119685i
$289$	3.16411e20	+	5.48039e20i	0.382489	+	0.662491i
$290$	−2.24547e20	+	3.88928e20i	−0.263588	+	0.456547i
$291$	3.33992e20	−	1.28602e20i	0.380755	−	0.146608i
$292$	−5.55096e20	+	3.20485e20i	−0.614631	+	0.354857i
$293$	1.81787e20			0.195519			0.0977593	−	0.995210i	$-0.468832\pi$
$293$	1.81787e20			0.195519			0.0977593	+	0.995210i	$0.468832\pi$
$294$	−7.05044e20	+	1.44193e21i	−0.736655	+	1.50657i
$295$	3.42523e20			0.347698
$296$	−1.01580e20	+	5.86471e19i	−0.100191	+	0.0578452i
$297$	6.11712e20	+	9.35619e20i	0.586297	+	0.896746i
$298$	1.47680e21	−	2.55790e21i	1.37558	−	2.38257i
$299$	−1.31157e21	−	2.27171e21i	−1.18738	−	2.05659i
$300$	9.78148e20	−	1.21046e21i	0.860743	−	1.06517i
$301$	1.22178e21	+	9.73866e20i	1.04515	+	0.833074i
$302$			1.60833e21i			1.33757i
$303$	−2.14686e21	−	3.37766e20i	−1.73597	−	0.273120i
$304$	6.71078e20	+	3.87447e20i	0.527652	+	0.304640i
$305$	−5.79807e20	−	3.34752e20i	−0.443338	−	0.255961i
$306$	−7.33208e20	−	8.10948e20i	−0.545249	−	0.603061i
$307$			4.27176e20i			0.308980i	0.987994	+	0.154490i	$0.0493735\pi$
$307$			4.27176e20i			0.308980i	−0.987994	+	0.154490i	$0.950627\pi$
$308$	2.72917e21	+	4.10695e20i	1.92021	+	0.288961i
$309$	1.43107e21	+	1.15642e21i	0.979521	+	0.791533i
$310$	5.41057e20	+	9.37138e20i	0.360304	+	0.624064i
$311$	2.31659e20	−	4.01245e20i	0.150102	−	0.259984i	−0.781163	−	0.624327i	$-0.785373\pi$
$311$	2.31659e20	−	4.01245e20i	0.150102	−	0.259984i	0.931265	+	0.364343i	$0.118707\pi$
$312$	−1.24358e21	−	3.22969e21i	−0.784076	−	2.03632i
$313$	−9.96170e20	+	5.75139e20i	−0.611233	+	0.352895i	−0.773448	−	0.633860i	$-0.781469\pi$
$313$	−9.96170e20	+	5.75139e20i	−0.611233	+	0.352895i	0.162215	+	0.986755i	$0.448136\pi$
$314$	6.65349e20			0.397326
$315$	−4.70178e20	−	7.08748e20i	−0.273290	−	0.411957i
$316$	−3.44732e21			−1.95048
$317$	1.29202e21	−	7.45950e20i	0.711650	−	0.410871i	−0.100022	−	0.994985i	$-0.531891\pi$
$317$	1.29202e21	−	7.45950e20i	0.711650	−	0.410871i	0.811672	+	0.584114i	$0.198558\pi$
$318$	3.97904e20	+	1.03340e21i	0.213377	+	0.554162i
$319$	−6.52394e20	+	1.12998e21i	−0.340635	+	0.589997i
$320$	−6.94542e20	−	1.20298e21i	−0.353121	−	0.611624i
$321$	2.31145e21	+	1.86784e21i	1.14444	+	0.924800i
$322$	−4.79999e21	+	1.88517e21i	−2.31454	+	0.909023i
$323$		−	1.33115e21i		−	0.625183i
$324$	−3.21472e21	−	2.31548e21i	−1.47065	−	1.05927i
$325$	−2.35167e21	−	1.35774e21i	−1.04802	−	0.605073i
$326$	−2.63075e21	−	1.51887e21i	−1.14217	−	0.659432i
$327$	2.72619e21	+	4.28911e20i	1.15319	+	0.181431i
$328$		−	1.54860e20i		−	0.0638282i
$329$	2.97671e20	−	1.97809e21i	0.119556	−	0.794478i
$330$	−1.42635e21	+	1.76511e21i	−0.558288	+	0.690880i
$331$	1.02838e20	+	1.78121e20i	0.0392299	+	0.0679483i	0.884974	−	0.465641i	$-0.154176\pi$
$331$	1.02838e20	+	1.78121e20i	0.0392299	+	0.0679483i	−0.845744	+	0.533589i	$0.820843\pi$
$332$	3.61048e21	−	6.25353e21i	1.34243	−	2.32515i
$333$	2.22969e20	+	7.19403e19i	0.0808108	+	0.0260733i
$334$	−2.74863e21	+	1.58692e21i	−0.971115	+	0.560674i
$335$	−1.02609e21			−0.353430
$336$	−1.37350e21	+	3.04523e20i	−0.461257	+	0.102267i
$337$	5.38405e21			1.76301			0.881506	−	0.472173i	$-0.156530\pi$
$337$	5.38405e21			1.76301			0.881506	+	0.472173i	$0.156530\pi$
$338$	−7.11831e21	+	4.10976e21i	−2.27292	+	1.31227i
$339$	1.19482e21	−	4.60059e20i	0.372053	−	0.143257i
$340$	7.15157e20	−	1.23869e21i	0.217185	−	0.376176i
$341$	1.57197e21	+	2.72273e21i	0.465621	+	0.806479i
$342$	−1.57137e21	−	7.31863e21i	−0.454000	−	2.11450i
$343$	1.53721e21	−	3.19785e21i	0.433244	−	0.901277i
$344$			6.62298e21i			1.82099i
$345$	4.24703e20	−	2.69944e21i	0.113926	−	0.724122i
$346$	9.39635e21	+	5.42499e21i	2.45931	+	1.41988i
$347$	8.23058e19	+	4.75193e19i	0.0210199	+	0.0121358i	0.510473	−	0.859894i	$-0.329470\pi$
$347$	8.23058e19	+	4.75193e19i	0.0210199	+	0.0121358i	−0.489453	+	0.872030i	$0.662804\pi$
$348$	7.18709e20	−	4.56816e21i	0.179114	−	1.13846i
$349$		−	3.63464e21i		−	0.883985i	−0.897019	−	0.441992i	$-0.854272\pi$
$349$		−	3.63464e21i		−	0.883985i	0.897019	−	0.441992i	$-0.145728\pi$
$350$	−3.32747e21	+	4.17454e21i	−0.789833	+	0.990900i
$351$	−3.11932e21	+	6.16901e21i	−0.722686	+	1.42924i
$352$	−1.35055e21	−	2.33922e21i	−0.305420	−	0.529003i
$353$	−5.88336e20	+	1.01903e21i	−0.129879	+	0.224958i	−0.923630	−	0.383286i	$-0.874792\pi$
$353$	−5.88336e20	+	1.01903e21i	−0.129879	+	0.224958i	0.793750	+	0.608244i	$0.208126\pi$
$354$	−5.10745e21	+	1.96660e21i	−1.10072	+	0.423826i
$355$	2.24374e21	−	1.29543e21i	0.472098	−	0.272566i
$356$	−3.40282e21			−0.699058
$357$	1.63277e21	+	1.78179e21i	0.327526	+	0.357418i
$358$	−1.42576e22			−2.79281
$359$	6.46720e21	−	3.73384e21i	1.23713	−	0.714255i	0.268620	−	0.963246i	$-0.413433\pi$
$359$	6.46720e21	−	3.73384e21i	1.23713	−	0.714255i	0.968506	+	0.248992i	$0.0800992\pi$
$360$	1.10704e21	−	3.43113e21i	0.206820	−	0.641012i
$361$	1.81691e21	−	3.14697e21i	0.331529	−	0.574225i
$362$	8.88320e21	+	1.53862e22i	1.58324	+	2.74225i
$363$	−5.33931e20	+	6.60738e20i	−0.0929563	+	0.115033i
$364$	6.23915e21	+	1.58860e22i	1.06112	+	2.70180i
$365$			1.16509e21i			0.193585i
$366$	1.05676e22	+	1.66260e21i	1.71549	+	0.269898i
$367$	1.08141e22	+	6.24353e21i	1.71526	+	0.990304i	0.927087	+	0.374847i	$0.122305\pi$
$367$	1.08141e22	+	6.24353e21i	1.71526	+	0.990304i	0.788170	+	0.615457i	$0.211029\pi$
$368$	−3.91449e21	−	2.26003e21i	−0.606693	−	0.350274i
$369$	−2.29446e20	+	2.07450e20i	−0.0347501	+	0.0314188i
$370$			4.75637e20i			0.0703981i
$371$	−8.94859e20	−	2.27848e21i	−0.129442	−	0.329585i
$372$	−8.66663e21	−	7.00334e21i	−1.22528	−	0.990126i
$373$	−2.05037e20	−	3.55134e20i	−0.0283339	−	0.0490758i	0.851511	−	0.524337i	$-0.175687\pi$
$373$	−2.05037e20	−	3.55134e20i	−0.0283339	−	0.0490758i	−0.879845	+	0.475261i	$0.842354\pi$
$374$	3.22421e21	−	5.58450e21i	0.435527	−	0.754355i
$375$	−2.36173e21	−	6.13365e21i	−0.311864	−	0.809941i
$376$	7.34337e21	−	4.23970e21i	0.947979	−	0.547316i
$377$	−8.06887e21			−1.01838
$378$	1.10802e22	+	7.86879e21i	1.36731	+	0.971019i
$379$	−9.99540e21			−1.20605			−0.603027	−	0.797721i	$-0.706039\pi$
$379$	−9.99540e21			−1.20605			−0.603027	+	0.797721i	$0.706039\pi$
$380$	8.48109e21	−	4.89656e21i	1.00067	−	0.577738i
$381$	−3.12376e21	−	8.11273e21i	−0.360426	−	0.936062i
$382$	−1.82155e19	+	3.15502e19i	−0.00205543	+	0.00356011i
$383$	−9.70481e20	−	1.68092e21i	−0.107102	−	0.185506i	0.807493	−	0.589877i	$-0.200824\pi$
$383$	−9.70481e20	−	1.68092e21i	−0.107102	−	0.185506i	−0.914595	+	0.404371i	$0.867490\pi$
$384$	1.31552e22	+	1.06305e22i	1.41998	+	1.14746i
$385$	3.12691e21	−	3.92292e21i	0.330141	−	0.414184i
$386$		−	1.16895e22i		−	1.20727i
$387$	9.81282e21	−	8.87213e21i	0.991404	−	0.896364i
$388$	−6.47926e21	−	3.74080e21i	−0.640407	−	0.369739i
$389$	−7.63916e21	−	4.41047e21i	−0.738710	−	0.426494i	0.0828901	−	0.996559i	$-0.473585\pi$
$389$	−7.63916e21	−	4.41047e21i	−0.738710	−	0.426494i	−0.821600	+	0.570064i	$0.806918\pi$
$390$	−1.38634e22	−	2.18113e21i	−1.31166	−	0.206364i
$391$			7.76480e21i			0.718833i
$392$	1.46616e22	−	3.35371e21i	1.32816	−	0.303804i
$393$	3.09719e21	−	3.83276e21i	0.274556	−	0.339762i
$394$	−1.05114e22	−	1.82063e22i	−0.911894	−	1.57945i
$395$	−3.13310e21	+	5.42669e21i	−0.266011	+	0.460744i
$396$	7.17535e21	−	2.22390e22i	0.596258	−	1.84802i
$397$	−1.00437e22	+	5.79876e21i	−0.816914	+	0.471645i	−0.849351	−	0.527828i	$-0.823006\pi$
$397$	−1.00437e22	+	5.79876e21i	−0.816914	+	0.471645i	0.0324373	+	0.999474i	$0.489673\pi$
$398$	−3.64041e22			−2.89831
$399$	3.58176e21	+	1.61549e22i	0.279143	+	1.25902i
$400$	−4.67916e21			−0.356991
$401$	−7.60048e21	+	4.38814e21i	−0.567693	+	0.327758i	−0.756228	−	0.654309i	$-0.772960\pi$
$401$	−7.60048e21	+	4.38814e21i	−0.567693	+	0.327758i	0.188534	+	0.982067i	$0.439626\pi$
$402$	1.53002e22	−	5.89128e21i	1.11886	−	0.430812i
$403$	−9.72114e21	+	1.68375e22i	−0.696024	+	1.20555i
$404$	2.27156e22	+	3.93445e22i	1.59251	+	2.75831i
$405$	−6.56666e21	+	2.95611e21i	−0.450793	+	0.202933i
$406$	−2.36051e21	+	1.56862e22i	−0.158685	+	1.05450i
$407$			1.38190e21i			0.0909757i
$408$	−1.59217e21	+	1.01200e22i	−0.102655	+	0.652480i
$409$	6.93984e21	+	4.00672e21i	0.438229	+	0.253012i	0.702846	−	0.711342i	$-0.251912\pi$
$409$	6.93984e21	+	4.00672e21i	0.438229	+	0.253012i	−0.264617	+	0.964354i	$0.585246\pi$
$410$	−5.43838e20	−	3.13985e20i	−0.0336362	−	0.0194199i
$411$	−1.59264e21	+	1.01229e22i	−0.0964857	+	0.613269i
$412$		−	3.84624e22i		−	2.28249i
$413$	1.12611e22	−	4.42274e21i	0.654646	−	0.257108i
$414$	9.16600e21	+	4.26905e22i	0.522008	+	2.43124i
$415$	−6.56276e21	−	1.13670e22i	−0.366166	−	0.634218i
$416$	8.35186e21	−	1.44658e22i	0.456551	−	0.790770i
$417$	−5.96955e21	+	2.29854e21i	−0.319731	+	0.123111i
$418$	3.82362e22	−	2.20757e22i	2.00667	−	1.15855i
$419$	1.83842e22			0.945419			0.472710	−	0.881218i	$-0.343276\pi$
$419$	1.83842e22			0.945419			0.472710	+	0.881218i	$0.343276\pi$
$420$	−5.34616e21	+	1.69570e22i	−0.269416	+	0.854533i
$421$	9.39038e21			0.463751			0.231876	−	0.972745i	$-0.425514\pi$
$421$	9.39038e21			0.463751			0.231876	+	0.972745i	$0.425514\pi$
$422$	−1.65589e22	+	9.56029e21i	−0.801449	+	0.462717i
$423$	−1.61188e22	−	5.20068e21i	−0.764610	−	0.246699i
$424$	5.18824e21	−	8.98629e21i	0.241218	−	0.417802i
$425$	4.01905e21	+	6.96120e21i	0.183155	+	0.317233i
$426$	−2.60193e22	+	3.21989e22i	−1.16229	+	1.43833i
$427$	−2.33847e22	−	3.51902e21i	−1.02399	−	0.154093i
$428$		−	6.21242e22i		−	2.66679i
$429$	−4.02784e22	−	6.33700e21i	−1.69506	−	0.266684i
$430$	2.32586e22	+	1.34283e22i	0.959625	+	0.554039i
$431$	−1.85826e22	−	1.07287e22i	−0.751710	−	0.434000i	0.0746016	−	0.997213i	$-0.476232\pi$
$431$	−1.85826e22	−	1.07287e22i	−0.751710	−	0.434000i	−0.826311	+	0.563214i	$0.809565\pi$
$432$	6.60123e20	+	1.18934e22i	0.0261826	+	0.471732i
$433$		−	5.24792e21i		−	0.204099i	−0.994779	−	0.102049i	$-0.967460\pi$
$433$		−	5.24792e21i		−	0.204099i	0.994779	−	0.102049i	$-0.0325400\pi$
$434$	2.98889e22	+	2.38240e22i	1.13985	+	0.908557i
$435$	−6.53789e21	−	5.28315e21i	−0.244500	−	0.197576i
$436$	−2.88452e22	−	4.99614e22i	−1.05789	−	1.83231i
$437$	−2.65822e22	+	4.60417e22i	−0.956089	+	1.65599i
$438$	−6.68937e21	−	1.73730e22i	−0.235969	−	0.612836i
$439$	1.24764e22	−	7.20327e21i	0.431660	−	0.249219i	−0.268394	−	0.963309i	$-0.586493\pi$
$439$	1.24764e22	−	7.20327e21i	0.431660	−	0.249219i	0.700054	+	0.714090i	$0.253159\pi$
$440$	2.12652e22			0.721642
$441$	−2.46096e22	−	1.72304e22i	−0.819173	−	0.573546i
$442$	3.98774e22			1.30208
$443$	1.97680e22	−	1.14131e22i	0.633186	−	0.365570i	−0.148799	−	0.988867i	$-0.547541\pi$
$443$	1.97680e22	−	1.14131e22i	0.633186	−	0.365570i	0.781985	+	0.623297i	$0.214207\pi$
$444$	−1.75987e21	−	4.57056e21i	−0.0553000	−	0.143620i
$445$	−3.09265e21	+	5.35662e21i	−0.0953390	+	0.165132i
$446$	−3.81769e22	−	6.61244e22i	−1.15466	−	1.99993i
$447$	4.29984e22	+	3.47462e22i	1.27596	+	1.03108i
$448$	−3.83676e22	−	3.05823e22i	−1.11713	−	0.890446i
$449$		−	1.83318e22i		−	0.523733i	−0.965104	−	0.261867i	$-0.915662\pi$
$449$		−	1.83318e22i		−	0.523733i	0.965104	−	0.261867i	$-0.0843381\pi$
$450$	3.03139e22	+	3.35280e22i	0.849838	+	0.939944i
$451$	−1.58005e21	−	9.12244e20i	−0.0434681	−	0.0250963i
$452$	−2.31789e22	−	1.33823e22i	−0.625771	−	0.361289i
$453$	−2.97373e22	−	4.67857e21i	−0.787892	−	0.123959i
$454$		−	4.00743e22i		−	1.04206i
$455$	3.06778e22	+	4.61652e21i	0.782939	+	0.117820i
$456$	−4.40857e22	+	5.45560e22i	−1.10432	+	1.36660i
$457$	5.38689e21	+	9.33037e21i	0.132450	+	0.229409i	0.924620	−	0.380890i	$-0.124382\pi$
$457$	5.38689e21	+	9.33037e21i	0.132450	+	0.229409i	−0.792171	+	0.610300i	$0.791049\pi$
$458$	1.92303e22	−	3.33078e22i	0.464118	−	0.803876i
$459$	1.71269e22	−	1.11977e22i	0.405762	−	0.265289i
$460$	−4.94713e22	+	2.85623e22i	−1.15057	+	0.664280i
$461$	−4.68490e22			−1.06965			−0.534826	−	0.844962i	$-0.679623\pi$
$461$	−4.68490e22			−1.06965			−0.534826	+	0.844962i	$0.679623\pi$
$462$	−2.41026e22	+	7.64488e22i	−0.540266	+	1.71362i
$463$	−1.30242e22			−0.286624			−0.143312	−	0.989678i	$-0.545775\pi$
$463$	−1.30242e22			−0.286624			−0.143312	+	0.989678i	$0.545775\pi$
$464$	−1.20411e22	+	6.95191e21i	−0.260173	+	0.150211i
$465$	−1.89011e22	+	7.27779e21i	−0.400994	+	0.154401i
$466$	−9.70354e21	+	1.68070e22i	−0.202139	+	0.350115i
$467$	4.33851e22	+	7.51452e22i	0.887457	+	1.53712i	0.842872	+	0.538114i	$0.180863\pi$
$467$	4.33851e22	+	7.51452e22i	0.887457	+	1.53712i	0.0445848	+	0.999006i	$0.485804\pi$
$468$	1.41288e23	−	3.03358e22i	2.83803	−	0.609348i
$469$	−3.37346e22	+	1.32491e22i	−0.665436	+	0.261346i
$470$		−	3.43846e22i		−	0.666088i
$471$	−1.93547e21	+	1.23020e22i	−0.0368221	+	0.234044i
$472$	4.44137e22	+	2.56423e22i	0.829870	+	0.479126i
$473$	6.75748e22	+	3.90144e22i	1.24012	+	0.715986i
$474$	1.55611e22	−	9.89074e22i	0.280495	−	1.78284i
$475$			5.50356e22i			0.974424i
$476$	7.51796e21	−	4.99586e22i	0.130750	−	0.868862i
$477$	−2.02645e22	+	4.35095e21i	−0.346202	+	0.0743324i
$478$	6.82967e22	+	1.18293e23i	1.14621	+	1.98529i
$479$	−9.30109e21	+	1.61100e22i	−0.153349	+	0.265609i	−0.932457	−	0.361282i	$-0.882339\pi$
$479$	−9.30109e21	+	1.61100e22i	−0.153349	+	0.265609i	0.779107	+	0.626890i	$0.215673\pi$
$480$	1.62388e22	−	6.25266e21i	0.263029	−	0.101278i
$481$	−7.40084e21	+	4.27288e21i	−0.117774	+	0.0679966i
$482$	−8.94863e22			−1.39913
$483$	−2.08929e22	−	9.42334e22i	−0.320958	−	1.44762i
$484$	1.77584e22			0.268052
$485$	−1.17774e22	+	6.79966e21i	−0.174680	+	0.100851i
$486$	8.09447e22	−	8.17817e22i	1.17972	−	1.19192i
$487$	5.23442e22	−	9.06627e22i	0.749673	−	1.29847i	−0.198306	−	0.980140i	$-0.563544\pi$
$487$	5.23442e22	−	9.06627e22i	0.749673	−	1.29847i	0.947979	−	0.318332i	$-0.103123\pi$
$488$	−5.01209e22	−	8.68120e22i	−0.705424	−	1.22183i
$489$	3.57359e22	−	4.42231e22i	0.494287	−	0.611679i
$490$	1.79494e22	−	5.82883e22i	0.243996	−	0.792345i
$491$			1.21343e23i			1.62115i	0.585634	+	0.810576i	$0.300846\pi$
$491$			1.21343e23i			1.62115i	−0.585634	+	0.810576i	$0.699154\pi$
$492$	6.38767e21	+	1.00497e21i	0.0838763	+	0.0131963i
$493$	2.06848e22	+	1.19424e22i	0.266963	+	0.154131i
$494$	2.36454e23	+	1.36517e23i	2.99963	+	1.73184i
$495$	−2.84868e22	−	3.15072e22i	−0.355222	−	0.392885i
$496$			3.35019e22i			0.410653i
$497$	5.70406e22	−	7.15614e22i	0.687314	−	0.862282i
$498$	1.63123e23	+	1.31817e23i	1.93226	+	1.56142i
$499$	4.32992e22	+	7.49965e22i	0.504226	+	0.873345i	0.999988	+	0.00488696i	$0.00155557\pi$
$499$	4.32992e22	+	7.49965e22i	0.504226	+	0.873345i	−0.495762	+	0.868459i	$0.665111\pi$
$500$	−6.86987e22	+	1.18990e23i	−0.786509	+	1.36227i
$501$	−2.13458e22	−	5.54371e22i	−0.240265	−	0.623993i
$502$	−1.37262e23	+	7.92485e22i	−1.51904	+	0.877020i
$503$	1.72397e22			0.187586			0.0937930	−	0.995592i	$-0.470101\pi$
$503$	1.72397e22			0.187586			0.0937930	+	0.995592i	$0.470101\pi$
$504$	−7.90739e21	−	1.27100e23i	−0.0846006	−	1.35983i
$505$	8.25801e22			0.868758
$506$	−2.23037e23	+	1.28770e23i	−2.30726	+	1.33210i
$507$	−5.52806e22	−	1.43569e23i	−0.562348	−	1.46047i
$508$	−9.08649e22	+	1.57383e23i	−0.908981	+	1.57440i
$509$	1.67415e22	+	2.89972e22i	0.164700	+	0.285269i	0.936549	−	0.350537i	$-0.114001\pi$
$509$	1.67415e22	+	2.89972e22i	0.164700	+	0.285269i	−0.771849	+	0.635806i	$0.780668\pi$
$510$	3.23111e22	+	2.61100e22i	0.312611	+	0.252616i
$511$	1.50439e22	+	3.83047e22i	0.143147	+	0.364480i
$512$		−	9.75660e22i		−	0.913069i
$513$	1.39889e23	−	7.76428e21i	1.28761	−	0.0714667i
$514$	−1.40580e23	−	8.11638e22i	−1.27273	−	0.734812i
$515$	−6.05465e22	−	3.49565e22i	−0.539172	−	0.311291i
$516$	−2.73185e23	−	4.29801e22i	−2.39295	−	0.376483i
$517$		−	9.99000e22i		−	0.860787i
$518$	6.14154e21	+	1.56375e22i	0.0520564	+	0.132545i
$519$	−1.27639e23	+	1.57953e23i	−1.06429	+	1.31706i
$520$	6.57525e22	+	1.13887e23i	0.539367	+	0.934210i
$521$	−8.79423e21	+	1.52321e22i	−0.0709704	+	0.122924i	−0.899327	−	0.437277i	$-0.855943\pi$
$521$	−8.79423e21	+	1.52321e22i	−0.0709704	+	0.122924i	0.828356	+	0.560201i	$0.189276\pi$
$522$	1.27821e23	+	4.12411e22i	1.01485	+	0.327439i
$523$	9.72371e22	−	5.61399e22i	0.759570	−	0.438538i	−0.0695714	−	0.997577i	$-0.522163\pi$
$523$	9.72371e22	−	5.61399e22i	0.759570	−	0.438538i	0.829141	+	0.559039i	$0.188830\pi$
$524$	−1.03012e23			−0.791719
$525$	−6.75057e22	−	7.36668e22i	−0.510489	−	0.557080i
$526$	−3.48989e23			−2.59677
$527$	4.98408e22	−	2.87756e22i	0.364918	−	0.210685i
$528$	−6.55667e22	+	2.52461e22i	−0.472384	+	0.181889i
$529$	8.45323e22	−	1.46414e23i	0.599307	−	1.03803i
$530$	−2.10387e22	−	3.64401e22i	−0.146782	−	0.254235i
$531$	−2.15041e22	−	1.00155e23i	−0.147645	−	0.687653i
$532$	2.15607e23	−	2.70494e23i	1.45685	−	1.82772i
$533$		−	1.12827e22i		−	0.0750296i
$534$	1.53602e22	−	9.76304e22i	0.100530	−	0.638976i
$535$	−9.77942e22	−	5.64615e22i	−0.629950	−	0.363702i
$536$	−1.33049e23	−	7.68158e22i	−0.843549	−	0.487023i
$537$	4.14748e22	−	2.63617e23i	0.258823	−	1.64510i
$538$		−	1.30545e22i		−	0.0801882i
$539$	5.21496e22	−	1.69349e23i	0.315316	−	1.02395i
$540$	1.34343e23	+	6.79297e22i	0.799592	+	0.404309i
$541$	2.52946e22	+	4.38115e22i	0.148201	+	0.256691i	0.930563	−	0.366133i	$-0.119318\pi$
$541$	2.52946e22	+	4.38115e22i	0.148201	+	0.256691i	−0.782362	+	0.622824i	$0.785985\pi$
$542$	−1.42008e23	+	2.45965e23i	−0.819065	+	1.41866i
$543$	−3.10323e23	+	1.19488e23i	−1.76204	+	0.678465i
$544$	−4.28204e22	+	2.47224e22i	−0.239365	+	0.138197i
$545$	−1.04864e23			−0.577107
$546$	−4.83951e23	+	1.07299e23i	−2.62219	+	0.581376i
$547$	2.98927e23			1.59468			0.797340	−	0.603531i	$-0.206240\pi$
$547$	2.98927e23			1.59468			0.797340	+	0.603531i	$0.206240\pi$
$548$	1.85518e23	−	1.07109e23i	0.974432	−	0.562588i
$549$	−6.14815e22	+	1.90554e23i	−0.317965	+	0.985491i
$550$	−1.33303e23	+	2.30887e23i	−0.678822	+	1.17575i
$551$	8.17674e22	+	1.41625e23i	0.410007	+	0.710153i
$552$	2.57158e23	−	3.18232e23i	1.26975	−	1.57131i
$553$	−3.29362e22	+	2.18868e23i	−0.160143	+	1.06419i
$554$		−	6.81366e23i		−	3.26248i
$555$	−8.79431e21	−	1.38361e21i	−0.0414678	−	0.00652413i
$556$	1.15806e23	+	6.68606e22i	0.537769	+	0.310481i
$557$	3.32168e23	+	1.91777e23i	1.51911	+	0.877057i	0.999747	+	0.0225016i	$0.00716310\pi$
$557$	3.32168e23	+	1.91777e23i	1.51911	+	0.877057i	0.519360	+	0.854555i	$0.326170\pi$
$558$	2.40054e23	−	2.17042e23i	1.08123	−	0.977581i
$559$			4.82533e23i			2.14056i
$560$	4.97576e22	−	1.95420e22i	0.217401	−	0.0853828i
$561$	9.38757e22	+	7.58593e22i	0.403988	+	0.326456i
$562$	−2.16718e23	−	3.75366e23i	−0.918620	−	1.59110i
$563$	2.46470e22	−	4.26898e22i	0.102906	−	0.178239i	−0.809975	−	0.586465i	$-0.800519\pi$
$563$	2.46470e22	−	4.26898e22i	0.102906	−	0.178239i	0.912881	+	0.408226i	$0.133852\pi$
$564$	1.27224e23	+	3.30413e23i	0.523234	+	1.35889i
$565$	−4.21322e22	+	2.43250e22i	−0.170688	+	0.0985467i
$566$	2.68198e22			0.107033
$567$	−1.77722e23	+	1.81978e23i	−0.698691	+	0.715423i
$568$	3.87917e23			1.50237
$569$	−8.16749e22	+	4.71550e22i	−0.311627	+	0.179918i	−0.647654	−	0.761934i	$-0.724250\pi$
$569$	−8.16749e22	+	4.71550e22i	−0.311627	+	0.179918i	0.336028	+	0.941852i	$0.390916\pi$
$570$	1.02204e23	+	2.65434e23i	0.384178	+	0.997748i
$571$	−6.94524e22	+	1.20295e23i	−0.257206	+	0.445493i	−0.965492	−	0.260432i	$-0.916135\pi$
$571$	−6.94524e22	+	1.20295e23i	−0.257206	+	0.445493i	0.708287	+	0.705925i	$0.249468\pi$
$572$	4.26178e23	+	7.38162e23i	1.55498	+	2.69330i
$573$	−5.30360e20	−	4.28574e20i	−0.00190659	−	0.00154068i
$574$	−2.19340e22	−	3.30071e21i	−0.0776903	−	0.0116911i
$575$		−	3.21030e23i		−	1.12039i
$576$	−3.08152e23	+	2.78612e23i	−1.05968	+	0.958094i
$577$	−7.27727e22	−	4.20153e22i	−0.246589	−	0.142368i	0.371612	−	0.928388i	$-0.378805\pi$
$577$	−7.27727e22	−	4.20153e22i	−0.246589	−	0.142368i	−0.618201	+	0.786020i	$0.712138\pi$
$578$	3.32742e23	+	1.92108e23i	1.11102	+	0.641446i
$579$	2.16134e23	+	3.40043e22i	0.711139	+	0.111884i
$580$			1.75717e23i			0.569737i
$581$	−3.62538e23	−	2.88974e23i	−1.15839	−	0.923340i
$582$	1.36575e23	−	1.69011e23i	0.430056	−	0.532194i
$583$	−6.11252e22	−	1.05872e23i	−0.189687	−	0.328548i
$584$	−8.72221e22	+	1.51073e23i	−0.266758	+	0.462038i
$585$	8.06562e22	−	2.49983e23i	0.243116	−	0.753505i
$586$	9.55849e22	−	5.51859e22i	0.283961	−	0.163945i
$587$	−5.05471e23			−1.48004			−0.740018	−	0.672587i	$-0.765183\pi$
$587$	−5.05471e23			−1.48004			−0.740018	+	0.672587i	$0.765183\pi$
$588$	4.31867e22	+	6.26524e23i	0.124636	+	1.80813i
$589$	3.94044e23			1.12089
$590$	1.80101e23	−	1.03981e23i	0.504980	−	0.291550i
$591$	3.67204e23	−	1.41390e23i	1.01488	−	0.390774i
$592$	−7.36278e21	+	1.27527e22i	−0.0200589	+	0.0347431i
$593$	1.59897e22	+	2.76949e22i	0.0429413	+	0.0743765i	0.886697	−	0.462351i	$-0.152994\pi$
$593$	1.59897e22	+	2.76949e22i	0.0429413	+	0.0743765i	−0.843756	+	0.536727i	$0.819660\pi$
$594$	6.05673e23	+	3.06255e23i	1.60344	+	0.810770i
$595$	−7.18108e22	−	5.72394e22i	−0.187411	−	0.149383i
$596$		−	1.15565e24i		−	2.97327i
$597$	1.05898e23	−	6.73095e23i	0.268600	−	1.70724i
$598$	−1.37927e24	−	7.96322e23i	−3.44897	−	1.99126i
$599$	−4.95163e23	−	2.85883e23i	−1.22073	−	0.704790i	−0.255658	−	0.966767i	$-0.582292\pi$
$599$	−4.95163e23	−	2.85883e23i	−1.22073	−	0.704790i	−0.965074	+	0.261978i	$0.915625\pi$
$600$	6.58272e22	−	4.18402e23i	0.160000	−	1.01697i
$601$			5.09504e23i			1.22100i	0.792018	+	0.610498i	$0.209031\pi$
$601$			5.09504e23i			1.22100i	−0.792018	+	0.610498i	$0.790969\pi$
$602$	9.38062e23	+	1.41163e23i	2.21647	+	0.333542i
$603$	6.44192e22	+	3.00031e23i	0.150078	+	0.698988i
$604$	3.14645e23	+	5.44981e23i	0.722780	+	1.25189i
$605$	1.61398e22	−	2.79549e22i	0.0365575	−	0.0633194i
$606$	−1.23137e24	+	4.74134e23i	−2.75025	+	1.05897i
$607$	1.81278e23	−	1.04661e23i	0.399246	−	0.230505i	−0.286913	−	0.957957i	$-0.592629\pi$
$607$	1.81278e23	−	1.04661e23i	0.399246	−	0.230505i	0.686158	+	0.727452i	$0.259296\pi$
$608$	−3.38540e23			−0.735241
$609$	−2.83163e23	−	8.92752e22i	−0.606443	−	0.191198i
$610$	−4.06488e23			−0.858508
$611$	5.35019e23	−	3.08893e23i	1.11434	−	0.643366i
$612$	−4.07095e23	−	1.31348e23i	−0.836198	−	0.269796i
$613$	8.37345e22	−	1.45032e23i	0.169625	−	0.293799i	−0.768663	−	0.639654i	$-0.779078\pi$
$613$	8.37345e22	−	1.45032e23i	0.169625	−	0.293799i	0.938288	+	0.345855i	$0.112411\pi$
$614$	1.29680e23	+	2.24612e23i	0.259084	+	0.448747i
$615$	7.38744e21	−	9.14194e21i	0.0145564	−	0.0180136i
$616$	6.99136e23	−	2.74581e23i	1.35871	−	0.533624i
$617$		−	1.06793e23i		−	0.204701i	−0.994748	−	0.102350i	$-0.967364\pi$
$617$		−	1.06793e23i		−	0.204701i	0.994748	−	0.102350i	$-0.0326363\pi$
$618$	1.10353e24	+	1.73618e23i	2.08632	+	0.328241i
$619$	−1.12407e23	−	6.48981e22i	−0.209615	−	0.121021i	0.391518	−	0.920171i	$-0.371950\pi$
$619$	−1.12407e23	−	6.48981e22i	−0.209615	−	0.121021i	−0.601132	+	0.799149i	$0.705284\pi$
$620$	3.66672e23	+	2.11698e23i	0.674448	+	0.389393i
$621$	−8.15991e23	+	4.52901e22i	−1.48049	+	0.0821721i
$622$		−	2.81303e23i		−	0.503449i
$623$	−3.25109e22	+	2.16043e23i	−0.0573959	+	0.381409i
$624$	−3.37940e23	−	2.73084e23i	−0.588533	−	0.475583i
$625$	−9.50361e22	−	1.64607e23i	−0.163271	−	0.282793i
$626$	−3.49195e23	+	6.04824e23i	−0.591815	+	1.02505i
$627$	2.96941e23	+	7.71186e23i	0.496474	+	1.28939i
$628$	2.25452e23	−	1.30165e23i	0.371875	−	0.214702i
$629$	2.52963e22			0.0411649
$630$	−4.62381e23	−	2.29930e23i	−0.742344	−	0.369149i
$631$	3.91770e23			0.620557			0.310278	−	0.950646i	$-0.399578\pi$
$631$	3.91770e23			0.620557			0.310278	+	0.950646i	$0.399578\pi$
$632$	−8.12515e23	+	4.69106e23i	−1.26980	+	0.733121i
$633$	−1.28596e23	−	3.33977e23i	−0.198288	−	0.514973i
$634$	4.52903e23	−	7.84450e23i	0.689043	−	1.19346i
$635$	1.65165e23	+	2.86074e23i	0.247937	+	0.429440i
$636$	3.36997e23	+	2.72321e23i	0.499161	+	0.403363i
$637$	1.06820e24	−	2.44342e23i	1.56124	−	0.357120i
$638$			7.92201e23i			1.14251i
$639$	−5.19652e23	−	5.74750e23i	−0.739530	−	0.817940i
$640$	−5.56576e23	−	3.21340e23i	−0.781619	−	0.451268i
$641$	−3.47206e23	−	2.00459e23i	−0.481165	−	0.277801i	0.239737	−	0.970838i	$-0.422939\pi$
$641$	−3.47206e23	−	2.00459e23i	−0.481165	−	0.277801i	−0.720902	+	0.693037i	$0.756272\pi$
$642$	1.78241e24	+	2.80426e23i	2.43758	+	0.383505i
$643$			1.88461e23i			0.254349i	0.991880	+	0.127174i	$0.0405908\pi$
$643$			1.88461e23i			0.254349i	−0.991880	+	0.127174i	$0.959409\pi$
$644$	−1.25766e24	+	1.57783e24i	−1.67508	+	2.10150i
$645$	−3.15942e23	+	3.90978e23i	−0.415288	+	0.513919i
$646$	−4.04105e23	−	6.99930e23i	−0.524225	−	0.907984i
$647$	1.56425e23	−	2.70936e23i	0.200272	−	0.346881i	−0.748344	−	0.663311i	$-0.769151\pi$
$647$	1.56425e23	−	2.70936e23i	0.200272	−	0.346881i	0.948616	+	0.316430i	$0.102484\pi$
$648$	−1.07278e24	−	1.08292e23i	−1.35557	−	0.136839i
$649$	5.23260e23	−	3.02104e23i	0.652586	−	0.376771i
$650$	−1.64870e24			−2.02945
$651$	−5.27440e23	+	4.83328e23i	−0.640818	+	0.587223i
$652$	−1.18857e24			−1.42534
$653$	2.30834e23	−	1.33272e23i	0.273235	−	0.157753i	−0.357122	−	0.934058i	$-0.616242\pi$
$653$	2.30834e23	−	1.33272e23i	0.273235	−	0.157753i	0.630357	+	0.776305i	$0.282908\pi$
$654$	1.56365e24	−	6.02077e23i	1.82696	−	0.703462i
$655$	−9.36223e22	+	1.62159e23i	−0.107976	+	0.187020i
$656$	−9.72087e21	−	1.68370e22i	−0.0110668	−	0.0191683i
$657$	3.40677e23	−	7.31461e22i	0.382857	−	0.0822026i
$658$	−4.43982e23	−	1.13046e24i	−0.492544	−	1.25411i
$659$			1.30518e24i			1.42937i	0.699448	+	0.714683i	$0.253429\pi$
$659$			1.30518e24i			1.42937i	−0.699448	+	0.714683i	$0.746571\pi$
$660$	−1.38002e23	+	8.77147e23i	−0.149197	+	0.948307i
$661$	1.23865e24	+	7.15134e23i	1.32201	+	0.763264i	0.984049	−	0.177895i	$-0.0569287\pi$
$661$	1.23865e24	+	7.15134e23i	1.32201	+	0.763264i	0.337963	+	0.941159i	$0.390262\pi$
$662$	1.08146e23	+	6.24383e22i	0.113951	+	0.0657897i
$663$	−1.16002e23	+	7.37314e23i	−0.120670	+	0.766986i
$664$		−	1.96523e24i		−	2.01829i
$665$	−2.29850e23	−	5.85241e23i	−0.233056	−	0.593405i
$666$	1.39078e23	−	2.98612e22i	0.139228	−	0.0298935i
$667$	−4.76960e23	−	8.26119e23i	−0.471425	−	0.816531i
$668$	−6.20911e23	+	1.07545e24i	−0.605940	+	1.04952i
$669$	1.33366e24	−	5.13520e23i	1.28506	−	0.494807i
$670$	−5.39523e23	+	3.11494e23i	−0.513303	+	0.296356i
$671$	−1.18100e24			−1.10945
$672$	4.53146e23	−	4.15248e23i	0.420339	−	0.385184i
$673$	−8.16768e23			−0.748119			−0.374060	−	0.927405i	$-0.622034\pi$
$673$	−8.16768e23			−0.748119			−0.374060	+	0.927405i	$0.622034\pi$
$674$	2.83097e24	−	1.63446e24i	2.56051	−	1.47831i
$675$	−7.08100e23	+	4.62959e23i	−0.632430	+	0.413485i
$676$	−1.60802e24	+	2.78517e24i	−1.41822	+	2.45643i
$677$	−1.06417e23	−	1.84320e23i	−0.0926846	−	0.160534i	0.815955	−	0.578115i	$-0.196211\pi$
$677$	−1.06417e23	−	1.84320e23i	−0.0926846	−	0.160534i	−0.908640	+	0.417581i	$0.862878\pi$
$678$	4.88582e23	−	6.04619e23i	0.420228	−	0.520031i
$679$	−2.99405e23	+	3.75624e23i	−0.254311	+	0.319051i
$680$		−	3.89269e23i		−	0.326531i
$681$	7.40955e23	+	1.16574e23i	0.613820	+	0.0965723i
$682$	1.65311e24	+	9.54421e23i	1.35249	+	0.780860i
$683$	1.52432e24	+	8.80068e23i	1.23169	+	0.711116i	0.967382	−	0.253323i	$-0.0815234\pi$
$683$	1.52432e24	+	8.80068e23i	1.23169	+	0.711116i	0.264307	+	0.964439i	$0.414857\pi$
$684$	−1.96423e24	−	2.17249e24i	−1.56753	−	1.73373i
$685$		−	3.89384e23i		−	0.306908i
$686$	−1.62512e23	−	2.14811e24i	−0.126511	−	1.67225i
$687$	5.59905e23	+	4.52449e23i	0.430509	+	0.347886i
$688$	4.15737e23	+	7.20077e23i	0.315731	+	0.546862i
$689$	3.78001e23	−	6.54717e23i	0.283550	−	0.491123i
$690$	−5.96171e23	−	1.54831e24i	−0.441726	−	1.14721i
$691$	−1.38352e24	+	7.98776e23i	−1.01256	+	0.584604i	−0.911941	−	0.410321i	$-0.865417\pi$
$691$	−1.38352e24	+	7.98776e23i	−1.01256	+	0.584604i	−0.100622	+	0.994925i	$0.532083\pi$
$692$	4.24525e24			3.06903
$693$	−1.34339e24	−	6.68033e23i	−0.959332	−	0.477052i
$694$	5.77026e22			0.0407042
$695$	2.10501e23	−	1.21533e23i	0.146684	−	0.0846880i
$696$	−4.52232e23	−	1.17449e24i	−0.311302	−	0.808484i
$697$	−1.66990e22	+	2.89235e22i	−0.0113557	+	0.0196686i
$698$	−1.10338e24	−	1.91112e24i	−0.741234	−	1.28385i
$699$	−2.82527e23	−	2.28305e23i	−0.187501	−	0.151516i
$700$	−3.10824e23	+	2.06550e24i	−0.203789	+	1.35423i
$701$			6.48030e23i			0.419751i	0.977728	+	0.209876i	$0.0673059\pi$
$701$			6.48030e23i			0.419751i	−0.977728	+	0.209876i	$0.932694\pi$
$702$	2.32594e23	+	4.19065e24i	0.148845	+	2.68174i
$703$	1.49996e23	+	8.66000e22i	0.0948327	+	0.0547517i
$704$	−2.12205e24	−	1.22517e24i	−1.32553	−	0.765294i
$705$	6.35754e23	+	1.00023e23i	0.392357	+	0.0617296i
$706$			7.14415e23i			0.435623i
$707$	2.71498e24	−	1.06629e24i	1.63569	−	0.642409i
$708$	−1.34592e24	+	1.66557e24i	−0.801189	+	0.991470i
$709$	−8.20842e23	−	1.42174e24i	−0.482799	−	0.836233i	0.517006	−	0.855982i	$-0.327047\pi$
$709$	−8.20842e23	−	1.42174e24i	−0.482799	−	0.836233i	−0.999805	+	0.0197493i	$0.993713\pi$
$710$	7.86516e23	−	1.36229e24i	0.457101	−	0.791722i
$711$	1.78348e24	+	5.75435e23i	1.02418	+	0.330449i
$712$	−8.02024e23	+	4.63049e23i	−0.455101	+	0.262753i
$713$	−2.29851e24			−1.28880
$714$	1.39943e24	+	4.41209e23i	0.775382	+	0.244461i
$715$	1.54933e24			0.848285
$716$	−4.83117e24	+	2.78928e24i	−2.61391	+	1.50914i
$717$	−2.38586e24	+	9.18663e23i	−1.27565	+	0.491183i
$718$	2.26700e24	−	3.92656e24i	1.19783	−	2.07469i
$719$	−3.67703e23	−	6.36880e23i	−0.192000	−	0.332554i	0.753913	−	0.656974i	$-0.228164\pi$
$719$	−3.67703e23	−	6.36880e23i	−0.192000	−	0.332554i	−0.945913	+	0.324421i	$0.894831\pi$
$720$	−9.50164e22	−	4.42538e23i	−0.0490312	−	0.228362i
$721$	−2.44195e24	−	3.67474e23i	−1.24534	−	0.187403i
$722$		−	2.20627e24i		−	1.11197i
$723$	2.60312e23	−	1.65456e24i	0.129664	−	0.824151i
$724$	6.02011e24	+	3.47571e24i	2.96365	+	1.71106i
$725$	−8.55196e23	−	4.93748e23i	−0.416095	−	0.240233i
$726$	−8.01610e22	+	5.09509e23i	−0.0385480	+	0.245014i
$727$			2.81751e24i			1.33913i	0.742753	+	0.669566i	$0.233520\pi$
$727$			2.81751e24i			1.33913i	−0.742753	+	0.669566i	$0.766480\pi$
$728$	3.63228e24	+	2.89524e24i	1.70633	+	1.36009i
$729$	1.27664e24	+	1.73453e24i	0.592768	+	0.805373i
$730$	3.53692e23	+	6.12613e23i	0.162323	+	0.281152i
$731$	7.14175e23	−	1.23699e24i	0.323971	−	0.561135i
$732$	3.90608e24	−	1.50402e24i	1.75145	−	0.674386i
$733$	2.53152e24	−	1.46158e24i	1.12201	−	0.647795i	0.180099	−	0.983648i	$-0.442358\pi$
$733$	2.53152e24	−	1.46158e24i	1.12201	−	0.647795i	0.941914	+	0.335854i	$0.109025\pi$
$734$	7.58151e24			3.32154
$735$	1.02551e24	+	5.01433e23i	0.444116	+	0.217155i
$736$	1.97475e24			0.845378
$737$	−1.56752e24	+	9.05005e23i	−0.663343	+	0.382981i
$738$	−5.76675e22	+	1.78733e23i	−0.0241241	+	0.0747696i
$739$	−1.32157e24	+	2.28902e24i	−0.546526	+	0.946611i	0.451983	+	0.892027i	$0.350717\pi$
$739$	−1.32157e24	+	2.28902e24i	−0.546526	+	0.946611i	−0.998509	+	0.0545846i	$0.982617\pi$
$740$	9.30508e22	+	1.61169e23i	0.0380409	+	0.0658888i
$741$	−3.21197e24	+	3.97481e24i	−1.29813	+	1.60643i
$742$	−1.16221e24	−	9.26383e23i	−0.464357	−	0.370133i
$743$			3.41182e24i			1.34766i	0.738885	+	0.673831i	$0.235353\pi$
$743$			3.41182e24i			1.34766i	−0.738885	+	0.673831i	$0.764647\pi$
$744$	−2.99568e24	−	4.71310e23i	−1.16984	−	0.184050i
$745$	−1.81920e24	−	1.05031e24i	−0.702347	−	0.405500i
$746$	−2.15619e23	−	1.24488e23i	−0.0823015	−	0.0475168i
$747$	−2.91174e24	+	2.63262e24i	−1.09882	+	0.993487i
$748$		−	2.52306e24i		−	0.941380i
$749$	−3.94422e24	−	5.93542e23i	−1.45501	−	0.218955i
$750$	−3.10384e24	−	2.50815e24i	−1.13208	−	0.914815i
$751$	2.47113e24	+	4.28012e24i	0.891161	+	1.54354i	0.838485	+	0.544925i	$0.183442\pi$
$751$	2.47113e24	+	4.28012e24i	0.891161	+	1.54354i	0.0526765	+	0.998612i	$0.483225\pi$
$752$	5.32267e23	−	9.21914e23i	0.189792	−	0.328729i
$753$	−1.06598e24	−	2.76845e24i	−0.375829	−	0.976065i
$754$	−4.24266e24	+	2.44950e24i	−1.47905	+	0.853929i
$755$	1.14386e24			0.394297
$756$	5.29392e24	+	4.98655e23i	1.80444	+	0.169967i
$757$	2.48253e24			0.836719			0.418359	−	0.908282i	$-0.362605\pi$
$757$	2.48253e24			0.836719			0.418359	+	0.908282i	$0.362605\pi$
$758$	−5.25565e24	+	3.03435e24i	−1.75161	+	1.01129i
$759$	−1.73210e24	−	4.49843e24i	−0.570844	−	1.48254i
$760$	1.33263e24	−	2.30818e24i	0.434304	−	0.752237i
$761$	−1.63276e24	−	2.82803e24i	−0.526203	−	0.911410i	−0.999534	−	0.0305256i	$-0.990282\pi$
$761$	−1.63276e24	−	2.82803e24i	−0.526203	−	0.911410i	0.473331	−	0.880885i	$-0.343051\pi$
$762$	−4.10531e24	−	3.31743e24i	−1.30837	−	1.05727i
$763$	−3.44761e24	+	1.35403e24i	−1.08657	+	0.426746i
$764$			1.42543e22i			0.00444276i
$765$	−5.76753e23	+	5.21464e23i	−0.177774	+	0.160732i
$766$	−1.02057e24	−	5.89227e23i	−0.311099	−	0.179613i
$767$	3.23587e24	+	1.86823e24i	0.975506	+	0.563209i
$768$	5.41088e24	+	8.51294e23i	1.61323	+	0.253810i
$769$		−	8.78837e23i		−	0.259140i	−0.991570	−	0.129570i	$-0.958640\pi$
$769$		−	8.78837e23i		−	0.259140i	0.991570	−	0.129570i	$-0.0413597\pi$
$770$	4.53250e23	−	3.01195e24i	0.132180	−	0.878368i
$771$	1.90962e24	−	2.36315e24i	0.550789	−	0.681600i
$772$	−2.28687e24	−	3.96097e24i	−0.652370	−	1.12994i
$773$	2.15905e24	−	3.73958e24i	0.609167	−	1.05511i	−0.382211	−	0.924075i	$-0.624837\pi$
$773$	2.15905e24	−	3.73958e24i	0.609167	−	1.05511i	0.991378	−	0.131033i	$-0.0418294\pi$
$774$	2.46629e24	−	7.64395e24i	0.688250	−	2.13314i
$775$	−2.06063e24	+	1.18971e24i	−0.568769	+	0.328379i
$776$	−2.03617e24			−0.555890
$777$	−3.06996e23	+	6.80653e22i	−0.0828998	+	0.0183801i
$778$	−5.35563e24			−1.43049
$779$	−1.98035e23	+	1.14335e23i	−0.0523207	+	0.0302073i
$780$	−5.12430e24	+	1.97309e24i	−1.33915	+	0.515634i
$781$	2.28512e24	−	3.95795e24i	0.590712	−	1.02314i
$782$	2.35720e24	+	4.08278e24i	0.602752	+	1.04400i
$783$	−1.13435e24	+	2.24339e24i	−0.286929	+	0.567452i
$784$	1.38355e24	−	1.28496e24i	0.346184	−	0.321517i
$785$		−	4.73201e23i		−	0.117126i
$786$	4.64992e23	−	2.95552e24i	0.113855	−	0.723672i
$787$	3.67670e24	+	2.12274e24i	0.890579	+	0.514176i	0.874132	−	0.485688i	$-0.161431\pi$
$787$	3.67670e24	+	2.12274e24i	0.890579	+	0.514176i	0.0164475	+	0.999865i	$0.494764\pi$
$788$	−7.12356e24	−	4.11279e24i	−1.70696	−	0.985516i
$789$	1.01519e24	−	6.45264e24i	0.240655	−	1.52962i
$790$			3.80452e24i			0.892215i
$791$	−1.07109e24	+	1.34375e24i	−0.248499	+	0.311760i
$792$	−1.33506e24	−	6.21803e24i	−0.306434	−	1.42721i
$793$	−3.65168e24	−	6.32489e24i	−0.829221	−	1.43625i
$794$	−3.52071e24	+	6.09805e24i	−0.790963	+	1.36999i
$795$	7.34960e23	−	2.82993e23i	0.163359	−	0.0629006i
$796$	−1.23355e25	+	7.12189e24i	−2.71266	+	1.56615i
$797$	−7.90812e24			−1.72059			−0.860296	−	0.509796i	$-0.829721\pi$
$797$	−7.90812e24			−1.72059			−0.860296	+	0.509796i	$0.829721\pi$
$798$	6.78752e24	+	7.40700e24i	1.46112	+	1.59447i
$799$	−1.82871e24			−0.389491
$800$	1.77038e24	−	1.02213e24i	0.373079	−	0.215397i
$801$	1.76046e24	+	5.68005e23i	0.367070	+	0.118434i
$802$	−2.66426e24	+	4.61463e24i	−0.549659	+	0.952038i
$803$	1.02761e24	+	1.77987e24i	0.209771	+	0.363334i
$804$	4.03192e24	−	4.98949e24i	0.814396	−	1.00781i
$805$	1.34075e24	+	3.41379e24i	0.267967	+	0.682295i
$806$			1.18044e25i			2.33451i
$807$	2.41371e23	+	3.79749e22i	0.0472346	+	0.00743142i
$808$	1.07079e25	+	6.18218e24i	2.07351	+	1.19714i
$809$	6.10015e24	+	3.52192e24i	1.16890	+	0.674865i	0.953421	−	0.301643i	$-0.0975350\pi$
$809$	6.10015e24	+	3.52192e24i	1.16890	+	0.674865i	0.215480	+	0.976508i	$0.430868\pi$
$810$	−2.55540e24	+	3.54781e24i	−0.484547	+	0.672726i
$811$		−	2.08463e24i		−	0.391157i	−0.980688	−	0.195578i	$-0.937342\pi$
$811$		−	2.08463e24i		−	0.391157i	0.980688	−	0.195578i	$-0.0626584\pi$
$812$	2.26889e24	+	5.77703e24i	0.421296	+	1.07270i
$813$	−4.13468e24	−	3.34116e24i	−0.759753	−	0.613942i
$814$	4.19511e23	+	7.26614e23i	0.0762844	+	0.132128i
$815$	−1.08023e24	+	1.87101e24i	−0.194391	+	0.336695i
$816$	4.62141e23	+	1.20023e24i	0.0823016	+	0.213745i
$817$	8.46945e24	−	4.88984e24i	1.49268	−	0.861801i
$818$	4.86535e24			0.848616
$819$	−5.76112e23	−	9.26014e24i	−0.0994474	−	1.59847i
$820$	−2.45705e23			−0.0419755
$821$	2.74499e24	−	1.58482e24i	0.464113	−	0.267956i	−0.249659	−	0.968334i	$-0.580319\pi$
$821$	2.74499e24	−	1.58482e24i	0.464113	−	0.267956i	0.713772	+	0.700378i	$0.246985\pi$
$822$	2.23565e24	+	5.80620e24i	0.374104	+	0.971586i
$823$	−2.50783e24	+	4.34369e24i	−0.415336	+	0.719383i	−0.995464	−	0.0951426i	$-0.969669\pi$
$823$	−2.50783e24	+	4.34369e24i	−0.415336	+	0.719383i	0.580128	+	0.814526i	$0.303003\pi$
$824$	−5.23389e24	−	9.06536e24i	−0.857913	−	1.48595i
$825$	−3.88122e24	−	3.13634e24i	−0.629665	−	0.508821i
$826$	4.57854e24	−	5.74410e24i	0.735185	−	0.922341i
$827$			5.88096e24i			0.934655i	0.884084	+	0.467327i	$0.154783\pi$
$827$			5.88096e24i			0.934655i	−0.884084	+	0.467327i	$0.845217\pi$
$828$	1.14576e25	+	1.26724e25i	1.80234	+	1.99343i
$829$	3.81791e24	+	2.20427e24i	0.594445	+	0.343203i	0.766853	−	0.641823i	$-0.221821\pi$
$829$	3.81791e24	+	2.20427e24i	0.594445	+	0.343203i	−0.172408	+	0.985026i	$0.555155\pi$
$830$	−6.90149e24	−	3.98458e24i	−1.06360	−	0.614071i
$831$	1.25981e25	+	1.98206e24i	1.92175	+	0.302349i
$832$		−	1.51530e25i		−	2.28797i
$833$	−3.10001e24	−	9.54620e23i	−0.463319	−	0.142675i
$834$	−2.44105e24	+	3.02079e24i	−0.361131	+	0.446899i
$835$	1.12863e24	+	1.95484e24i	0.165279	+	0.286271i
$836$	8.63751e24	−	1.49606e25i	1.25209	−	2.16868i
$837$	3.31469e24	+	5.06985e24i	0.475638	+	0.727493i
$838$	9.66651e24	−	5.58096e24i	1.37308	−	0.792748i
$839$	1.99053e24			0.279893			0.139947	−	0.990159i	$-0.455307\pi$
$839$	1.99053e24			0.279893			0.139947	+	0.990159i	$0.455307\pi$
$840$	1.04741e24	+	4.72416e24i	0.145795	+	0.657582i
$841$	4.32287e24			0.595670
$842$	4.93752e24	−	2.85068e24i	0.673529	−	0.388862i
$843$	7.57077e24	−	2.91508e24i	1.02236	−	0.393656i
$844$	−3.74064e24	+	6.47897e24i	−0.500075	+	0.866155i
$845$	2.92289e24	+	5.06260e24i	0.386839	+	0.670025i
$846$	−1.00542e25	+	2.15871e24i	−1.31734	+	0.282844i
$847$	1.69666e23	−	1.12747e24i	0.0220083	−	0.146250i
$848$		−	1.30270e24i		−	0.167294i
$849$	−7.80176e22	+	4.95885e23i	−0.00991922	+	0.0630472i
$850$	4.22649e24	+	2.44016e24i	0.532009	+	0.307155i
$851$	−8.74944e23	−	5.05149e23i	−0.109038	−	0.0629533i
$852$	−2.51740e24	+	1.60008e25i	−0.310611	+	1.97426i
$853$		−	2.21372e24i		−	0.270431i	−0.990816	−	0.135215i	$-0.956827\pi$
$853$		−	2.21372e24i		−	0.270431i	0.990816	−	0.135215i	$-0.0431726\pi$
$854$	−1.33641e25	+	5.24867e24i	−1.61640	+	0.634830i
$855$	−5.20506e24	+	1.11757e24i	−0.623324	+	0.133833i
$856$	−8.45374e24	−	1.46423e25i	−1.00236	−	1.73613i
$857$	4.31904e24	−	7.48079e24i	0.507049	−	0.878235i	−0.492918	−	0.870076i	$-0.664070\pi$
$857$	4.31904e24	−	7.48079e24i	0.507049	−	0.878235i	0.999967	−	0.00815888i	$-0.00259708\pi$
$858$	−2.31024e25	+	8.89546e24i	−2.68544	+	1.03401i
$859$	−2.98368e24	+	1.72263e24i	−0.343408	+	0.198267i	−0.661778	−	0.749700i	$-0.730198\pi$
$859$	−2.98368e24	+	1.72263e24i	−0.343408	+	0.198267i	0.318370	+	0.947966i	$0.396864\pi$
$860$	1.05082e25			1.19754
$861$	1.24834e23	−	3.95948e23i	0.0140866	−	0.0446798i
$862$	−1.30278e25			−1.45566
$863$	1.35731e25	−	7.83641e24i	1.50171	−	0.867012i	0.501711	−	0.865035i	$-0.332704\pi$
$863$	1.35731e25	−	7.83641e24i	1.50171	−	0.867012i	0.999998	−	0.00197702i	$-0.000629305\pi$
$864$	−2.84780e24	−	4.35573e24i	−0.311991	−	0.477193i
$865$	3.85829e24	−	6.68276e24i	0.418561	−	0.724968i
$866$	−1.59314e24	−	2.75939e24i	−0.171140	−	0.296423i
$867$	−4.51993e24	+	5.59340e24i	−0.480805	+	0.594995i
$868$	1.47886e25	+	2.22544e24i	1.55779	+	0.234422i
$869$			1.10535e25i			1.15301i
$870$	−5.04149e24	−	7.93178e23i	−0.520770	−	0.0819327i
$871$	−9.69359e24	−	5.59659e24i	−0.991586	−	0.572492i
$872$	−1.35973e25	−	7.85042e24i	−1.37741	−	0.795248i
$873$	2.72764e24	+	3.01685e24i	0.273632	+	0.302644i
$874$			3.22787e25i			3.20678i
$875$	6.89822e24	+	5.49848e24i	0.678686	+	0.540971i
$876$	−5.66543e24	−	4.57813e24i	−0.552011	−	0.446070i
$877$	−5.71985e24	−	9.90707e24i	−0.551935	−	0.955979i	−0.998135	−	0.0610462i	$-0.980556\pi$
$877$	−5.71985e24	−	9.90707e24i	−0.551935	−	0.955979i	0.446200	−	0.894933i	$-0.352777\pi$
$878$	4.37346e24	−	7.57505e24i	0.417947	−	0.723906i
$879$	7.42310e23	+	1.92785e24i	0.0702554	+	0.182460i
$880$	2.31204e24	−	1.33486e24i	0.216717	−	0.125122i
$881$	2.58777e24			0.240232			0.120116	−	0.992760i	$-0.461673\pi$
$881$	2.58777e24			0.240232			0.120116	+	0.992760i	$0.461673\pi$
$882$	−1.81706e25	−	1.58904e24i	−1.67065	−	0.146100i
$883$	1.69329e24			0.154193			0.0770967	−	0.997024i	$-0.475435\pi$
$883$	1.69329e24			0.154193			0.0770967	+	0.997024i	$0.475435\pi$
$884$	1.35124e25	−	7.80137e24i	1.21867	−	0.703602i
$885$	1.39866e24	+	3.63246e24i	0.124938	+	0.324476i
$886$	6.92943e24	−	1.20021e25i	0.613072	−	1.06187i
$887$	−3.10235e24	−	5.37342e24i	−0.271856	−	0.470869i	0.697481	−	0.716603i	$-0.254304\pi$
$887$	−3.10235e24	−	5.37342e24i	−0.271856	−	0.470869i	−0.969337	+	0.245734i	$0.920971\pi$
$888$	−1.03674e24	−	8.37774e23i	−0.0899832	−	0.0727138i
$889$	9.12399e24	+	7.27261e24i	0.784368	+	0.625209i
$890$			3.75540e24i			0.319772i
$891$	−7.42438e24	+	1.03077e25i	−0.626181	+	0.869365i
$892$	−2.58724e25	−	1.49374e25i	−2.16140	−	1.24788i
$893$	−1.08434e25	−	6.26045e24i	−0.897282	−	0.518046i
$894$	3.31569e25	+	5.21657e24i	2.71772	+	0.427579i
$895$			1.01401e25i			0.823280i
$896$	−2.24478e25	−	3.37802e24i	−1.80532	−	0.271672i
$897$	1.87358e25	−	2.31856e25i	1.49258	−	1.84706i
$898$	−5.56505e24	−	9.63896e24i	−0.439158	−	0.760644i
$899$	−3.53514e24	+	6.12304e24i	−0.276343	+	0.478640i
$900$	1.68311e25	+	5.43048e24i	1.30332	+	0.420510i
$901$	−1.93803e24	+	1.11892e24i	−0.148662	+	0.0858302i
$902$	−1.10774e24			−0.0841745
$903$	−5.33882e24	+	1.69337e25i	−0.401883	+	1.27469i
$904$	−7.28417e24			−0.543186
$905$	1.09428e25	−	6.31780e24i	0.808376	−	0.466716i
$906$	−1.70564e25	+	6.56747e24i	−1.24824	+	0.480627i
$907$	5.59763e24	−	9.69539e24i	0.405828	−	0.702916i	−0.588589	−	0.808432i	$-0.700316\pi$
$907$	5.59763e24	−	9.69539e24i	0.405828	−	0.702916i	0.994418	+	0.105517i	$0.0336497\pi$
$908$	−7.83990e24	−	1.35791e25i	−0.563094	−	0.975307i
$909$	−5.18450e24	−	2.41467e25i	−0.368904	−	1.71817i
$910$	1.75321e25	−	6.88562e24i	1.23589	−	0.485390i
$911$			7.53663e24i			0.526346i	0.964749	+	0.263173i	$0.0847690\pi$
$911$			7.53663e24i			0.526346i	−0.964749	+	0.263173i	$0.915231\pi$
$912$	−1.36860e24	+	8.69889e24i	−0.0946933	+	0.601877i
$913$	−2.00514e25	−	1.15767e25i	−1.37449	−	0.793565i
$914$	5.66493e24	+	3.27065e24i	0.384726	+	0.222122i
$915$	1.18246e24	−	7.51577e24i	0.0795621	−	0.505702i
$916$		−	1.50484e25i		−	1.00318i
$917$	−9.84187e23	+	6.54015e24i	−0.0650037	+	0.431965i
$918$	5.60612e24	−	1.10871e25i	0.366860	−	0.725530i
$919$	9.80232e23	+	1.69781e24i	0.0635546	+	0.110080i	0.896052	−	0.443949i	$-0.146423\pi$
$919$	9.80232e23	+	1.69781e24i	0.0635546	+	0.110080i	−0.832497	+	0.554029i	$0.813090\pi$
$920$	−7.77341e24	+	1.34639e25i	−0.499361	+	0.864919i
$921$	−4.53020e24	+	1.74433e24i	−0.288344	+	0.111025i
$922$	−2.46335e25	+	1.42222e25i	−1.55351	+	0.896918i
$923$	2.82626e25			1.76603
$924$	6.78885e24	+	3.06198e25i	0.420325	+	1.89579i
$925$	−1.04586e24			−0.0641605
$926$	−6.84820e24	+	3.95381e24i	−0.416278	+	0.240338i
$927$	−6.42022e24	+	1.98986e25i	−0.386698	+	1.19852i
$928$	3.03719e24	−	5.26057e24i	0.181265	−	0.313960i
$929$	−4.65362e24	−	8.06030e24i	−0.275205	−	0.476670i	0.694982	−	0.719028i	$-0.255413\pi$
$929$	−4.65362e24	−	8.06030e24i	−0.275205	−	0.476670i	−0.970187	+	0.242358i	$0.922079\pi$
$930$	−7.72899e24	+	9.56462e24i	−0.452916	+	0.560483i
$931$	−1.51136e25	−	1.62731e25i	−0.877595	−	0.944926i
$932$			7.59337e24i			0.436917i
$933$	5.20116e24	+	8.18298e23i	0.296555	+	0.0466571i
$934$	4.56243e25	+	2.63412e25i	2.57779	+	1.48829i
$935$	−3.97174e24	−	2.29309e24i	−0.222373	−	0.128387i
$936$	2.91729e25	−	2.63762e25i	1.61858	−	1.46342i
$937$			2.93849e25i			1.61561i	0.589447	+	0.807807i	$0.299346\pi$
$937$			2.93849e25i			1.61561i	−0.589447	+	0.807807i	$0.700654\pi$
$938$	−1.37158e25	+	1.72074e25i	−0.747303	+	0.937544i
$939$	−1.01671e25	−	8.21586e24i	−0.548959	−	0.443604i
$940$	−6.72679e24	−	1.16512e25i	−0.359933	−	0.623422i
$941$	−6.00297e24	+	1.03974e25i	−0.318313	+	0.551334i	−0.980136	−	0.198326i	$-0.936450\pi$
$941$	−6.00297e24	+	1.03974e25i	−0.318313	+	0.551334i	0.661823	+	0.749660i	$0.269783\pi$
$942$	2.71689e24	+	7.05602e24i	0.142771	+	0.370789i
$943$	1.15516e24	−	6.66934e23i	0.0601581	−	0.0347323i
$944$	6.43845e24			0.332292
$945$	5.59634e24	−	7.88034e24i	0.286242	−	0.403065i
$946$	4.73751e25			2.40146
$947$	−3.07188e25	+	1.77355e25i	−1.54323	+	0.890982i	−0.544594	+	0.838700i	$0.683316\pi$
$947$	−3.07188e25	+	1.77355e25i	−1.54323	+	0.890982i	−0.998632	+	0.0522822i	$0.983350\pi$
$948$	−1.40768e25	−	3.65589e25i	−0.700863	−	1.82021i
$949$	−6.35477e24	+	1.10068e25i	−0.313572	+	0.543122i
$950$	1.67074e25	+	2.89381e25i	0.817068	+	1.41520i
$951$	1.31866e25	+	1.06559e25i	0.639146	+	0.516482i
$952$	−5.02633e24	−	1.27980e25i	−0.241455	−	0.614791i
$953$		−	1.40460e25i		−	0.668749i	−0.942440	−	0.334375i	$-0.891475\pi$
$953$		−	1.40460e25i		−	0.668749i	0.942440	−	0.334375i	$-0.108525\pi$
$954$	−9.33437e24	+	8.43955e24i	−0.440478	+	0.398252i
$955$	2.24388e22	+	1.29550e22i	0.00104947	+	0.000605912i
$956$	4.62844e25	+	2.67223e25i	2.14557	+	1.23875i
$957$	−1.46474e25	−	2.30448e24i	−0.672992	−	0.105882i
$958$			1.12943e25i			0.514343i
$959$	−5.02781e24	−	1.28018e25i	−0.226945	−	0.577845i
$960$	9.92154e24	−	1.22779e25i	0.443888	−	0.549311i
$961$	−2.75699e24	−	4.77525e24i	−0.122261	−	0.211762i
$962$	−2.59427e24	+	4.49341e24i	−0.114032	+	0.197510i
$963$	−1.03699e25	+	3.21401e25i	−0.451805	+	1.40031i
$964$	−3.03223e25	+	1.75066e25i	−1.30950	+	0.756042i
$965$	−8.31368e24			−0.355886
$966$	−3.95925e25	−	4.32060e25i	−1.67999	−	1.83332i
$967$	−2.10226e25			−0.884224			−0.442112	−	0.896960i	$-0.645771\pi$
$967$	−2.10226e25			−0.884224			−0.442112	+	0.896960i	$0.645771\pi$
$968$	4.18556e24	−	2.41654e24i	0.174507	−	0.100752i
$969$	1.41169e25	−	5.43564e24i	0.583428	−	0.224646i
$970$	−4.12841e24	+	7.15061e24i	−0.169131	+	0.292943i
$971$	−9.17685e24	−	1.58948e25i	−0.372675	−	0.645492i	0.617301	−	0.786727i	$-0.288226\pi$
$971$	−9.17685e24	−	1.58948e25i	−0.372675	−	0.645492i	−0.989976	+	0.141235i	$0.954893\pi$
$972$	1.14287e25	−	4.35471e25i	0.460078	−	1.75306i
$973$	5.35136e24	−	6.71366e24i	0.213553	−	0.267917i
$974$		−	6.35614e25i		−	2.51445i
$975$	4.79600e24	−	3.04837e25i	0.188079	−	1.19544i
$976$	−1.08987e25	−	6.29237e24i	−0.423693	−	0.244619i
$977$	−3.19936e25	−	1.84715e25i	−1.23299	−	0.711867i	−0.265338	−	0.964156i	$-0.585483\pi$
$977$	−3.19936e25	−	1.84715e25i	−1.23299	−	0.711867i	−0.967652	+	0.252289i	$0.918817\pi$
$978$	5.36515e24	−	3.41013e25i	0.204975	−	1.30284i
$979$			1.09108e25i			0.413242i
$980$	−5.32107e24	−	2.32624e25i	−0.199792	−	0.873439i
$981$	6.58351e24	+	3.06626e25i	0.245059	+	1.14136i
$982$	3.68368e25	+	6.38032e25i	1.35936	+	2.35448i
$983$	6.74319e24	−	1.16796e25i	0.246695	−	0.427289i	−0.715912	−	0.698191i	$-0.753989\pi$
$983$	6.74319e24	−	1.16796e25i	0.246695	−	0.427289i	0.962607	+	0.270902i	$0.0873220\pi$
$984$	1.64229e24	−	6.32357e23i	0.0595652	−	0.0229353i
$985$	−1.29485e25	+	7.47582e24i	−0.465598	+	0.268813i
$986$	1.45016e25			0.516966
$987$	2.21932e25	−	4.92055e24i	0.784376	−	0.173907i
$988$	1.06829e26			3.74332
$989$	−4.94034e25	+	2.85231e25i	−1.71628	+	0.990895i
$990$	−2.45433e25	−	7.91882e24i	−0.845346	−	0.272748i
$991$	−6.25785e24	+	1.08389e25i	−0.213697	+	0.370134i	−0.952869	−	0.303383i	$-0.901884\pi$
$991$	−6.25785e24	+	1.08389e25i	−0.213697	+	0.370134i	0.739172	+	0.673517i	$0.235217\pi$
$992$	−7.31824e24	−	1.26756e25i	−0.247775	−	0.429159i
$993$	−1.46905e24	+	1.81794e24i	−0.0493137	+	0.0610256i
$994$	8.26811e24	−	5.49435e25i	0.275183	−	1.82866i
$995$			2.58909e25i			0.854380i
$996$	8.10617e25	+	1.27534e25i	2.65223	+	0.417276i
$997$	−1.49431e25	−	8.62742e24i	−0.484767	−	0.279880i	0.237634	−	0.971355i	$-0.423628\pi$
$997$	−1.49431e25	−	8.62742e24i	−0.484767	−	0.279880i	−0.722401	+	0.691474i	$0.756961\pi$
$998$	4.55340e25	+	2.62891e25i	1.46463	+	0.845602i
$999$	1.47547e23	+	2.65835e24i	0.00470569	+	0.0847824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.18.g.b.17.38	yes	84
3.2	odd	2	inner	21.18.g.b.17.5	yes	84
7.5	odd	6	inner	21.18.g.b.5.5	✓	84
21.5	even	6	inner	21.18.g.b.5.38	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.18.g.b.5.5	✓	84	7.5	odd	6	inner
21.18.g.b.5.38	yes	84	21.5	even	6	inner
21.18.g.b.17.5	yes	84	3.2	odd	2	inner
21.18.g.b.17.38	yes	84	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(525.807 - 303.575i) q^{2} +(4083.40 + 10605.0i) q^{3} +(118779. - 205731. i) q^{4} +(-215905. - 373958. i) q^{5} +(5.36649e6 + 4.33656e6i) q^{6} +(-1.19269e7 - 9.50679e6i) q^{7} -6.46530e7i q^{8} +(-9.57918e7 + 8.66089e7i) q^{9} +O(q^{10})\)	\(q+(525.807 - 303.575i) q^{2} +(4083.40 + 10605.0i) q^{3} +(118779. - 205731. i) q^{4} +(-215905. - 373958. i) q^{5} +(5.36649e6 + 4.33656e6i) q^{6} +(-1.19269e7 - 9.50679e6i) q^{7} -6.46530e7i q^{8} +(-9.57918e7 + 8.66089e7i) q^{9} +(-2.27048e8 - 1.31086e8i) q^{10} +(-6.59660e8 - 3.80855e8i) q^{11} +(2.66680e9 + 4.19568e8i) q^{12} -4.71045e9i q^{13} +(-9.15727e9 - 1.37802e9i) q^{14} +(3.08420e9 - 3.81669e9i) q^{15} +(-4.05839e9 - 7.02933e9i) q^{16} +(-6.97171e9 + 1.20754e10i) q^{17} +(-2.40757e10 + 7.46195e10i) q^{18} +(-8.26780e10 + 4.77342e10i) q^{19} -1.02580e11 q^{20} +(5.21171e10 - 1.65305e11i) q^{21} -4.62471e11 q^{22} +(4.82272e11 - 2.78440e11i) q^{23} +(6.85645e11 - 2.64004e11i) q^{24} +(2.88240e11 - 4.99246e11i) q^{25} +(-1.42997e12 - 2.47678e12i) q^{26} +(-1.30964e12 - 6.62213e11i) q^{27} +(-3.37251e12 + 1.32453e12i) q^{28} -1.71297e12i q^{29} +(4.63042e11 - 2.94312e12i) q^{30} +(-3.57451e12 - 2.06374e12i) q^{31} +(3.07101e12 + 1.77305e12i) q^{32} +(1.34531e12 - 8.55087e12i) q^{33} +8.46574e12i q^{34} +(-9.80060e11 + 6.51273e12i) q^{35} +(6.44011e12 + 2.99947e13i) q^{36} +(-9.07107e11 - 1.57116e12i) q^{37} +(-2.89818e13 + 5.01979e13i) q^{38} +(4.99543e13 - 1.92346e13i) q^{39} +(-2.41775e13 + 1.39589e13i) q^{40} +2.39525e12 q^{41} +(-2.27789e13 - 1.02740e14i) q^{42} -1.02439e14 q^{43} +(-1.56708e14 + 9.04751e13i) q^{44} +(5.30700e13 + 1.71228e13i) q^{45} +(1.69054e14 - 2.92811e14i) q^{46} +(6.55762e13 + 1.13581e14i) q^{47} +(5.79740e13 - 7.17428e13i) q^{48} +(5.18725e13 + 2.26773e14i) q^{49} -3.50009e14i q^{50} +(-1.56527e14 - 2.46265e13i) q^{51} +(-9.69086e14 - 5.59502e14i) q^{52} +(1.38993e14 + 8.02475e13i) q^{53} +(-8.89651e14 + 4.93784e13i) q^{54} +3.28913e14i q^{55} +(-6.14642e14 + 7.71111e14i) q^{56} +(-8.43828e14 - 6.81882e14i) q^{57} +(-5.20015e14 - 9.00693e14i) q^{58} +(-3.96614e14 + 6.86955e14i) q^{59} +(-4.18874e14 - 1.08786e15i) q^{60} +(1.34274e15 - 7.75230e14i) q^{61} -2.50600e15 q^{62} +(1.96587e15 - 1.22305e14i) q^{63} +3.21689e15 q^{64} +(-1.76151e15 + 1.01701e15i) q^{65} +(-1.88846e15 - 4.90451e15i) q^{66} +(1.18812e15 - 2.05789e15i) q^{67} +(1.65619e15 + 2.86860e15i) q^{68} +(4.92216e15 + 3.97751e15i) q^{69} +(1.46178e15 + 3.72196e15i) q^{70} +5.99999e15i q^{71} +(5.59952e15 + 6.19323e15i) q^{72} +(-2.33668e15 - 1.34908e15i) q^{73} +(-9.53926e14 - 5.50749e14i) q^{74} +(6.47151e15 + 1.01816e15i) q^{75} +2.26793e16i q^{76} +(4.24700e15 + 1.08137e16i) q^{77} +(2.04271e16 - 2.52785e16i) q^{78} +(-7.25575e15 - 1.25673e16i) q^{79} +(-1.75245e15 + 3.03533e15i) q^{80} +(1.67497e15 - 1.65929e16i) q^{81} +(1.25944e15 - 7.27138e14i) q^{82} +3.03966e16 q^{83} +(-2.78180e16 - 3.03569e16i) q^{84} +6.02090e15 q^{85} +(-5.38631e16 + 3.10979e16i) q^{86} +(1.81661e16 - 6.99476e15i) q^{87} +(-2.46234e16 + 4.26489e16i) q^{88} +(-7.16207e15 - 1.24051e16i) q^{89} +(3.31026e16 - 7.10740e15i) q^{90} +(-4.47812e16 + 5.61811e16i) q^{91} -1.32291e17i q^{92} +(7.28984e15 - 4.63347e16i) q^{93} +(6.89608e16 + 3.98145e16i) q^{94} +(3.57011e16 + 2.06121e16i) q^{95} +(-6.26302e15 + 3.98082e16i) q^{96} -3.14938e16i q^{97} +(9.61175e16 + 1.03492e17i) q^{98} +(9.61754e16 - 2.06496e16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 19686 q^{3} + 2752510 q^{4} - 4340518 q^{7} - 98670996 q^{9}+O(q^{10}) \) 84 * q - 19686 * q^3 + 2752510 * q^4 - 4340518 * q^7 - 98670996 * q^9	\( 84 q - 19686 q^{3} + 2752510 q^{4} - 4340518 q^{7} - 98670996 q^{9} + 465470970 q^{10} - 2491764528 q^{12} - 7104382296 q^{15} - 110459605130 q^{16} - 14553542550 q^{18} + 404032278750 q^{19} + 228767508522 q^{21} - 832496305460 q^{22} - 1354439880378 q^{24} - 7199868598470 q^{25} - 7749926510914 q^{28} + 284772818082 q^{30} + 20192079903726 q^{31} - 18426553023870 q^{33} - 6006594191052 q^{36} + 46546034438938 q^{37} + 156966454169838 q^{39} + 52009146351690 q^{40} + 273411312457290 q^{42} + 262809922393900 q^{43} - 463828715581158 q^{45} - 691873824309656 q^{46} + 158652002613594 q^{49} + 123926983295328 q^{51} + 180256725379488 q^{52} + 528953393499678 q^{54} - 13\!\cdots\!84 q^{57}+ \cdots + 30\!\cdots\!80 q^{99}+O(q^{100}) \) 84 * q - 19686 * q^3 + 2752510 * q^4 - 4340518 * q^7 - 98670996 * q^9 + 465470970 * q^10 - 2491764528 * q^12 - 7104382296 * q^15 - 110459605130 * q^16 - 14553542550 * q^18 + 404032278750 * q^19 + 228767508522 * q^21 - 832496305460 * q^22 - 1354439880378 * q^24 - 7199868598470 * q^25 - 7749926510914 * q^28 + 284772818082 * q^30 + 20192079903726 * q^31 - 18426553023870 * q^33 - 6006594191052 * q^36 + 46546034438938 * q^37 + 156966454169838 * q^39 + 52009146351690 * q^40 + 273411312457290 * q^42 + 262809922393900 * q^43 - 463828715581158 * q^45 - 691873824309656 * q^46 + 158652002613594 * q^49 + 123926983295328 * q^51 + 180256725379488 * q^52 + 528953393499678 * q^54 - 1311284732111784 * q^57 + 521920547533210 * q^58 - 416477060451846 * q^60 - 6052836877037172 * q^61 - 13769533594398750 * q^63 + 1053936792659996 * q^64 + 21705058495057878 * q^66 + 3639355527884298 * q^67 + 44463964567209810 * q^70 + 7798479140884800 * q^72 - 31719690947775954 * q^73 + 17256341731591290 * q^75 - 67997864561346840 * q^78 - 31267401781398294 * q^79 + 44133415784265492 * q^81 + 4877409168868320 * q^82 + 25637268676337472 * q^84 + 2464288230356616 * q^85 - 61426317616508880 * q^87 - 112618869011616970 * q^88 - 223816788036276750 * q^91 + 104033604109825260 * q^93 + 248077621213302516 * q^94 - 363875964512101146 * q^96 + 303894121197814080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more