LMFDB - Embedded newform 21.18.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,18,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

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

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	21.a (trivial)

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:	yes
Analytic conductor:	$38.4766383424$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 542084x^{3} + 28429210x^{2} + 53238758035x - 7826067153800 $ x^5 - 2x^4 - 542084x^3 + 28429210x^2 + 53238758035x - 7826067153800
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{5}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$220.674$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+169.674 q^{2} +6561.00 q^{3} -102283. q^{4} +291836. q^{5} +1.11323e6 q^{6} -5.76480e6 q^{7} -3.95942e7 q^{8} +4.30467e7 q^{9} +O(q^{10})$	\(q+169.674 q^{2} +6561.00 q^{3} -102283. q^{4} +291836. q^{5} +1.11323e6 q^{6} -5.76480e6 q^{7} -3.95942e7 q^{8} +4.30467e7 q^{9} +4.95168e7 q^{10} +9.20155e8 q^{11} -6.71078e8 q^{12} -3.54811e9 q^{13} -9.78135e8 q^{14} +1.91473e9 q^{15} +6.68833e9 q^{16} +1.33551e10 q^{17} +7.30390e9 q^{18} +1.01556e11 q^{19} -2.98498e10 q^{20} -3.78229e10 q^{21} +1.56126e11 q^{22} +5.71257e11 q^{23} -2.59777e11 q^{24} -6.77771e11 q^{25} -6.02022e11 q^{26} +2.82430e11 q^{27} +5.89640e11 q^{28} +2.09059e12 q^{29} +3.24880e11 q^{30} -7.36060e12 q^{31} +6.32452e12 q^{32} +6.03714e12 q^{33} +2.26601e12 q^{34} -1.68237e12 q^{35} -4.40294e12 q^{36} +4.05978e13 q^{37} +1.72313e13 q^{38} -2.32792e13 q^{39} -1.15550e13 q^{40} +6.41353e13 q^{41} -6.41754e12 q^{42} -6.38323e13 q^{43} -9.41161e13 q^{44} +1.25626e13 q^{45} +9.69273e13 q^{46} +2.90148e14 q^{47} +4.38821e13 q^{48} +3.32329e13 q^{49} -1.15000e14 q^{50} +8.76228e13 q^{51} +3.62911e14 q^{52} +5.20904e14 q^{53} +4.79209e13 q^{54} +2.68534e14 q^{55} +2.28253e14 q^{56} +6.66308e14 q^{57} +3.54718e14 q^{58} +8.11878e14 q^{59} -1.95844e14 q^{60} +7.20690e14 q^{61} -1.24890e15 q^{62} -2.48156e14 q^{63} +1.96452e14 q^{64} -1.03547e15 q^{65} +1.02434e15 q^{66} -4.00961e15 q^{67} -1.36600e15 q^{68} +3.74802e15 q^{69} -2.85455e14 q^{70} -1.62921e15 q^{71} -1.70440e15 q^{72} -1.98765e15 q^{73} +6.88838e15 q^{74} -4.44686e15 q^{75} -1.03874e16 q^{76} -5.30451e15 q^{77} -3.94986e15 q^{78} -1.79646e16 q^{79} +1.95189e15 q^{80} +1.85302e15 q^{81} +1.08821e16 q^{82} -1.19809e16 q^{83} +3.86863e15 q^{84} +3.89749e15 q^{85} -1.08307e16 q^{86} +1.37164e16 q^{87} -3.64328e16 q^{88} +3.90684e16 q^{89} +2.13154e15 q^{90} +2.04542e16 q^{91} -5.84298e16 q^{92} -4.82929e16 q^{93} +4.92304e16 q^{94} +2.96376e16 q^{95} +4.14952e16 q^{96} -1.12062e17 q^{97} +5.63875e15 q^{98} +3.96097e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 253 q^{2} + 32805 q^{3} + 441613 q^{4} - 906662 q^{5} - 1659933 q^{6} - 28824005 q^{7} - 182238651 q^{8} + 215233605 q^{9}+O(q^{10}) $ 5 * q - 253 * q^2 + 32805 * q^3 + 441613 * q^4 - 906662 * q^5 - 1659933 * q^6 - 28824005 * q^7 - 182238651 * q^8 + 215233605 * q^9	\( 5 q - 253 q^{2} + 32805 q^{3} + 441613 q^{4} - 906662 q^{5} - 1659933 q^{6} - 28824005 q^{7} - 182238651 q^{8} + 215233605 q^{9} + 1194057802 q^{10} + 1111338736 q^{11} + 2897422893 q^{12} + 5215478294 q^{13} + 1458494653 q^{14} - 5948609382 q^{15} + 62775861505 q^{16} + 25747891566 q^{17} - 10890820413 q^{18} + 142208068556 q^{19} - 129890562778 q^{20} - 189114296805 q^{21} - 448421189252 q^{22} - 700488736068 q^{23} - 1195667789211 q^{24} + 1178351016379 q^{25} + 2889360071546 q^{26} + 1412147682405 q^{27} - 2545811064013 q^{28} - 3529421241410 q^{29} + 7834213238922 q^{30} + 1688850702072 q^{31} - 17321396050955 q^{32} + 7291493446896 q^{33} + 40556147819358 q^{34} + 5226726004262 q^{35} + 19009991600973 q^{36} + 16886745594894 q^{37} - 20515887907732 q^{38} + 34218753086934 q^{39} + 320653834434294 q^{40} + 58103631330302 q^{41} + 9569183418333 q^{42} + 49458422903068 q^{43} + 401313211061300 q^{44} - 39028826155302 q^{45} + 325662527133360 q^{46} + 321151801515192 q^{47} + 411872427334305 q^{48} + 166164652848005 q^{49} - 130885367368259 q^{50} + 168931916564526 q^{51} - 447415499102234 q^{52} + 16\!\cdots\!54 q^{53}+ \cdots + 47\!\cdots\!56 q^{99}+O(q^{100}) \) 5 * q - 253 * q^2 + 32805 * q^3 + 441613 * q^4 - 906662 * q^5 - 1659933 * q^6 - 28824005 * q^7 - 182238651 * q^8 + 215233605 * q^9 + 1194057802 * q^10 + 1111338736 * q^11 + 2897422893 * q^12 + 5215478294 * q^13 + 1458494653 * q^14 - 5948609382 * q^15 + 62775861505 * q^16 + 25747891566 * q^17 - 10890820413 * q^18 + 142208068556 * q^19 - 129890562778 * q^20 - 189114296805 * q^21 - 448421189252 * q^22 - 700488736068 * q^23 - 1195667789211 * q^24 + 1178351016379 * q^25 + 2889360071546 * q^26 + 1412147682405 * q^27 - 2545811064013 * q^28 - 3529421241410 * q^29 + 7834213238922 * q^30 + 1688850702072 * q^31 - 17321396050955 * q^32 + 7291493446896 * q^33 + 40556147819358 * q^34 + 5226726004262 * q^35 + 19009991600973 * q^36 + 16886745594894 * q^37 - 20515887907732 * q^38 + 34218753086934 * q^39 + 320653834434294 * q^40 + 58103631330302 * q^41 + 9569183418333 * q^42 + 49458422903068 * q^43 + 401313211061300 * q^44 - 39028826155302 * q^45 + 325662527133360 * q^46 + 321151801515192 * q^47 + 411872427334305 * q^48 + 166164652848005 * q^49 - 130885367368259 * q^50 + 168931916564526 * q^51 - 447415499102234 * q^52 + 1624886228519454 * q^53 - 71454672729693 * q^54 + 1551981825532832 * q^55 + 1050569557523451 * q^56 + 933027137795916 * q^57 + 3599479065043546 * q^58 + 4642231410191796 * q^59 - 852211982386458 * q^60 + 383521828948430 * q^61 + 3303800808324960 * q^62 - 1240778901337605 * q^63 + 7678662933303305 * q^64 + 1668701347292044 * q^65 - 2942091422682372 * q^66 - 4060475251851460 * q^67 - 16890755118576270 * q^68 - 4595906597342148 * q^69 - 6883505611027402 * q^70 + 6398015136563460 * q^71 - 7844776365013371 * q^72 - 15734132975098902 * q^73 - 25189581013328238 * q^74 + 7731161018462619 * q^75 - 14323380376996940 * q^76 - 6406646656631536 * q^77 + 18957091429413306 * q^78 + 2199683795891080 * q^79 - 115762642448214658 * q^80 + 9265100944259205 * q^81 - 6015570522729706 * q^82 + 23947511376405780 * q^83 - 16703066390989293 * q^84 + 21310596918487932 * q^85 - 3933835697843468 * q^86 - 23156532764891010 * q^87 - 87148613365646124 * q^88 - 12131366869070066 * q^89 + 51400273060567242 * q^90 - 30066194484729494 * q^91 - 198814114679296704 * q^92 + 11080549456294392 * q^93 + 14990206001176800 * q^94 - 239731994312770088 * q^95 - 113645679490315755 * q^96 + 4112564616338706 * q^97 - 8407931434109053 * q^98 + 47839488505084656 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	169.674	0.468662	0.234331	−	0.972157i	$-0.424710\pi$
$2$	169.674	0.468662	0.234331	+	0.972157i	$0.424710\pi$
$3$	6561.00	0.577350
$3$	6561.00	0.577350
$4$	−102283.	−0.780356
$5$	291836.	0.334113	0.167056	−	0.985947i	$-0.446574\pi$
$5$	291836.	0.334113	0.167056	+	0.985947i	$0.446574\pi$
$6$	1.11323e6	0.270582
$7$	−5.76480e6	−0.377964
$7$	−5.76480e6	−0.377964
$8$	−3.95942e7	−0.834385
$9$	4.30467e7	0.333333
$10$	4.95168e7	0.156586
$11$	9.20155e8	1.29427	0.647133	−	0.762378i	$-0.275968\pi$
$11$	9.20155e8	1.29427	0.647133	+	0.762378i	$0.275968\pi$
$12$	−6.71078e8	−0.450539
$13$	−3.54811e9	−1.20637	−0.603183	−	0.797603i	$-0.706101\pi$
$13$	−3.54811e9	−1.20637	−0.603183	+	0.797603i	$0.706101\pi$
$14$	−9.78135e8	−0.177137
$15$	1.91473e9	0.192900
$16$	6.68833e9	0.389312
$17$	1.33551e10	0.464335	0.232167	−	0.972676i	$-0.425418\pi$
$17$	1.33551e10	0.464335	0.232167	+	0.972676i	$0.425418\pi$
$18$	7.30390e9	0.156221
$19$	1.01556e11	1.37183	0.685913	−	0.727683i	$-0.259403\pi$
$19$	1.01556e11	1.37183	0.685913	+	0.727683i	$0.259403\pi$
$20$	−2.98498e10	−0.260727
$21$	−3.78229e10	−0.218218
$22$	1.56126e11	0.606572
$23$	5.71257e11	1.52106	0.760528	−	0.649305i	$-0.224940\pi$
$23$	5.71257e11	1.52106	0.760528	+	0.649305i	$0.224940\pi$
$24$	−2.59777e11	−0.481732
$25$	−6.77771e11	−0.888369
$26$	−6.02022e11	−0.565378
$27$	2.82430e11	0.192450
$28$	5.89640e11	0.294947
$29$	2.09059e12	0.776044	0.388022	−	0.921650i	$-0.373158\pi$
$29$	2.09059e12	0.776044	0.388022	+	0.921650i	$0.373158\pi$
$30$	3.24880e11	0.0904049
$31$	−7.36060e12	−1.55002	−0.775012	−	0.631946i	$-0.782256\pi$
$31$	−7.36060e12	−1.55002	−0.775012	+	0.631946i	$0.782256\pi$
$32$	6.32452e12	1.01684
$33$	6.03714e12	0.747244
$34$	2.26601e12	0.217616
$35$	−1.68237e12	−0.126283
$36$	−4.40294e12	−0.260119
$37$	4.05978e13	1.90015	0.950075	−	0.312021i	$-0.101006\pi$
$37$	4.05978e13	1.90015	0.950075	+	0.312021i	$0.101006\pi$
$38$	1.72313e13	0.642922
$39$	−2.32792e13	−0.696496
$40$	−1.15550e13	−0.278779
$41$	6.41353e13	1.25440	0.627198	−	0.778860i	$-0.284202\pi$
$41$	6.41353e13	1.25440	0.627198	+	0.778860i	$0.284202\pi$
$42$	−6.41754e12	−0.102270
$43$	−6.38323e13	−0.832835	−0.416417	−	0.909174i	$-0.636714\pi$
$43$	−6.38323e13	−0.832835	−0.416417	+	0.909174i	$0.636714\pi$
$44$	−9.41161e13	−1.00999
$45$	1.25626e13	0.111371
$46$	9.69273e13	0.712861
$47$	2.90148e14	1.77741	0.888705	−	0.458480i	$-0.151606\pi$
$47$	2.90148e14	1.77741	0.888705	+	0.458480i	$0.151606\pi$
$48$	4.38821e13	0.224769
$49$	3.32329e13	0.142857
$50$	−1.15000e14	−0.416344
$51$	8.76228e13	0.268084
$52$	3.62911e14	0.941395
$53$	5.20904e14	1.14925	0.574623	−	0.818418i	$-0.305149\pi$
$53$	5.20904e14	1.14925	0.574623	+	0.818418i	$0.305149\pi$
$54$	4.79209e13	0.0901940
$55$	2.68534e14	0.432431
$56$	2.28253e14	0.315368
$57$	6.66308e14	0.792024
$58$	3.54718e14	0.363702
$59$	8.11878e14	0.719861	0.359931	−	0.932979i	$-0.382800\pi$
$59$	8.11878e14	0.719861	0.359931	+	0.932979i	$0.382800\pi$
$60$	−1.95844e14	−0.150531
$61$	7.20690e14	0.481332	0.240666	−	0.970608i	$-0.422634\pi$
$61$	7.20690e14	0.481332	0.240666	+	0.970608i	$0.422634\pi$
$62$	−1.24890e15	−0.726437
$63$	−2.48156e14	−0.125988
$64$	1.96452e14	0.0872422
$65$	−1.03547e15	−0.403063
$66$	1.02434e15	0.350205
$67$	−4.00961e15	−1.20633	−0.603166	−	0.797616i	$-0.706094\pi$
$67$	−4.00961e15	−1.20633	−0.603166	+	0.797616i	$0.706094\pi$
$68$	−1.36600e15	−0.362346
$69$	3.74802e15	0.878182
$70$	−2.85455e14	−0.0591839
$71$	−1.62921e15	−0.299420	−0.149710	−	0.988730i	$-0.547834\pi$
$71$	−1.62921e15	−0.299420	−0.149710	+	0.988730i	$0.547834\pi$
$72$	−1.70440e15	−0.278128
$73$	−1.98765e15	−0.288467	−0.144234	−	0.989544i	$-0.546072\pi$
$73$	−1.98765e15	−0.288467	−0.144234	+	0.989544i	$0.546072\pi$
$74$	6.88838e15	0.890528
$75$	−4.44686e15	−0.512900
$76$	−1.03874e16	−1.07051
$77$	−5.30451e15	−0.489186
$78$	−3.94986e15	−0.326421
$79$	−1.79646e16	−1.33225	−0.666126	−	0.745840i	$-0.732049\pi$
$79$	−1.79646e16	−1.33225	−0.666126	+	0.745840i	$0.732049\pi$
$80$	1.95189e15	0.130074
$81$	1.85302e15	0.111111
$82$	1.08821e16	0.587887
$83$	−1.19809e16	−0.583881	−0.291941	−	0.956436i	$-0.594301\pi$
$83$	−1.19809e16	−0.583881	−0.291941	+	0.956436i	$0.594301\pi$
$84$	3.86863e15	0.170288
$85$	3.89749e15	0.155140
$86$	−1.08307e16	−0.390318
$87$	1.37164e16	0.448049
$88$	−3.64328e16	−1.07992
$89$	3.90684e16	1.05199	0.525994	−	0.850488i	$-0.323693\pi$
$89$	3.90684e16	1.05199	0.525994	+	0.850488i	$0.323693\pi$
$90$	2.13154e15	0.0521953
$91$	2.04542e16	0.455964
$92$	−5.84298e16	−1.18697
$93$	−4.82929e16	−0.894907
$94$	4.92304e16	0.833004
$95$	2.96376e16	0.458345
$96$	4.14952e16	0.587073
$97$	−1.12062e17	−1.45177	−0.725887	−	0.687814i	$-0.758570\pi$
$97$	−1.12062e17	−1.45177	−0.725887	+	0.687814i	$0.758570\pi$
$98$	5.63875e15	0.0669517
$99$	3.96097e16	0.431422
$100$	6.93244e16	0.693244
$101$	−1.58365e17	−1.45521	−0.727607	−	0.685994i	$-0.759368\pi$
$101$	−1.58365e17	−1.45521	−0.727607	+	0.685994i	$0.759368\pi$
$102$	1.48673e16	0.125641
$103$	1.10715e17	0.861170	0.430585	−	0.902550i	$-0.358307\pi$
$103$	1.10715e17	0.861170	0.430585	+	0.902550i	$0.358307\pi$
$104$	1.40485e17	1.00657
$105$	−1.10381e16	−0.0729094
$106$	8.83837e16	0.538607
$107$	−2.03902e17	−1.14725	−0.573626	−	0.819117i	$-0.694464\pi$
$107$	−2.03902e17	−1.14725	−0.573626	+	0.819117i	$0.694464\pi$
$108$	−2.88877e16	−0.150180
$109$	8.56307e16	0.411628	0.205814	−	0.978591i	$-0.434016\pi$
$109$	8.56307e16	0.411628	0.205814	+	0.978591i	$0.434016\pi$
$110$	4.55632e16	0.202664
$111$	2.66362e17	1.09705
$112$	−3.85569e16	−0.147146
$113$	2.39017e17	0.845790	0.422895	−	0.906179i	$-0.361014\pi$
$113$	2.39017e17	0.845790	0.422895	+	0.906179i	$0.361014\pi$
$114$	1.13055e17	0.371191
$115$	1.66713e17	0.508205
$116$	−2.13832e17	−0.605591
$117$	−1.52735e17	−0.402122
$118$	1.37754e17	0.337371
$119$	−7.69894e16	−0.175502
$120$	−7.58123e16	−0.160953
$121$	3.41238e17	0.675122
$122$	1.22282e17	0.225582
$123$	4.20792e17	0.724226
$124$	7.52863e17	1.20957
$125$	−4.20451e17	−0.630928
$126$	−4.21055e16	−0.0590458
$127$	4.42726e17	0.580501	0.290251	−	0.956951i	$-0.406261\pi$
$127$	4.42726e17	0.580501	0.290251	+	0.956951i	$0.406261\pi$
$128$	−7.95635e17	−0.975953
$129$	−4.18804e17	−0.480837
$130$	−1.75691e17	−0.188900
$131$	−5.09779e17	−0.513542	−0.256771	−	0.966472i	$-0.582659\pi$
$131$	−5.09779e17	−0.513542	−0.256771	+	0.966472i	$0.582659\pi$
$132$	−6.17496e17	−0.583117
$133$	−5.85449e17	−0.518502
$134$	−6.80326e17	−0.565361
$135$	8.24230e16	0.0643001
$136$	−5.28784e17	−0.387434
$137$	−8.48788e17	−0.584352	−0.292176	−	0.956365i	$-0.594379\pi$
$137$	−8.48788e17	−0.584352	−0.292176	+	0.956365i	$0.594379\pi$
$138$	6.35940e17	0.411570
$139$	1.56163e17	0.0950502	0.0475251	−	0.998870i	$-0.484867\pi$
$139$	1.56163e17	0.0950502	0.0475251	+	0.998870i	$0.484867\pi$
$140$	1.72078e17	0.0985456
$141$	1.90366e18	1.02619
$142$	−2.76434e17	−0.140327
$143$	−3.26482e18	−1.56136
$144$	2.87911e17	0.129771
$145$	6.10109e17	0.259286
$146$	−3.37253e17	−0.135194
$147$	2.18041e17	0.0824786
$148$	−4.15246e18	−1.48279
$149$	1.55747e18	0.525214	0.262607	−	0.964903i	$-0.415418\pi$
$149$	1.55747e18	0.525214	0.262607	+	0.964903i	$0.415418\pi$
$150$	−7.54515e17	−0.240377
$151$	1.47356e18	0.443673	0.221837	−	0.975084i	$-0.428795\pi$
$151$	1.47356e18	0.443673	0.221837	+	0.975084i	$0.428795\pi$
$152$	−4.02102e18	−1.14463
$153$	5.74893e17	0.154778
$154$	−9.00036e17	−0.229263
$155$	−2.14808e18	−0.517883
$156$	2.38106e18	0.543515
$157$	5.10804e18	1.10435	0.552176	−	0.833728i	$-0.313798\pi$
$157$	5.10804e18	1.10435	0.552176	+	0.833728i	$0.313798\pi$
$158$	−3.04811e18	−0.624375
$159$	3.41765e18	0.663517
$160$	1.84572e18	0.339740
$161$	−3.29319e18	−0.574905
$162$	3.14409e17	0.0520735
$163$	6.07675e18	0.955161	0.477580	−	0.878588i	$-0.341514\pi$
$163$	6.07675e18	0.955161	0.477580	+	0.878588i	$0.341514\pi$
$164$	−6.55994e18	−0.978875
$165$	1.76185e18	0.249664
$166$	−2.03284e18	−0.273643
$167$	−4.14077e18	−0.529653	−0.264827	−	0.964296i	$-0.585315\pi$
$167$	−4.14077e18	−0.529653	−0.264827	+	0.964296i	$0.585315\pi$
$168$	1.49756e18	0.182078
$169$	3.93870e18	0.455319
$170$	6.61302e17	0.0727083
$171$	4.37164e18	0.457275
$172$	6.52895e18	0.649908
$173$	7.62197e18	0.722229	0.361115	−	0.932521i	$-0.382396\pi$
$173$	7.62197e18	0.722229	0.361115	+	0.932521i	$0.382396\pi$
$174$	2.32731e18	0.209983
$175$	3.90722e18	0.335772
$176$	6.15430e18	0.503873
$177$	5.32673e18	0.415612
$178$	6.62889e18	0.493027
$179$	2.43355e19	1.72580	0.862898	−	0.505377i	$-0.168647\pi$
$179$	2.43355e19	1.72580	0.862898	+	0.505377i	$0.168647\pi$
$180$	−1.28494e18	−0.0869090
$181$	−1.00605e19	−0.649158	−0.324579	−	0.945859i	$-0.605223\pi$
$181$	−1.00605e19	−0.649158	−0.324579	+	0.945859i	$0.605223\pi$
$182$	3.47053e18	0.213693
$183$	4.72845e18	0.277897
$184$	−2.26185e19	−1.26915
$185$	1.18479e19	0.634865
$186$	−8.19403e18	−0.419409
$187$	1.22888e19	0.600972
$188$	−2.96771e19	−1.38701
$189$	−1.62815e18	−0.0727393
$190$	5.02872e18	0.214809
$191$	−1.39085e19	−0.568196	−0.284098	−	0.958795i	$-0.591694\pi$
$191$	−1.39085e19	−0.568196	−0.284098	+	0.958795i	$0.591694\pi$
$192$	1.28892e18	0.0503693
$193$	2.93143e19	1.09608	0.548040	−	0.836452i	$-0.315374\pi$
$193$	2.93143e19	1.09608	0.548040	+	0.836452i	$0.315374\pi$
$194$	−1.90140e19	−0.680391
$195$	−6.79369e18	−0.232708
$196$	−3.39916e18	−0.111479
$197$	−5.50386e19	−1.72864	−0.864320	−	0.502943i	$-0.832251\pi$
$197$	−5.50386e19	−1.72864	−0.864320	+	0.502943i	$0.832251\pi$
$198$	6.72072e18	0.202191
$199$	−3.27987e19	−0.945377	−0.472688	−	0.881230i	$-0.656716\pi$
$199$	−3.27987e19	−0.945377	−0.472688	+	0.881230i	$0.656716\pi$
$200$	2.68358e19	0.741241
$201$	−2.63071e19	−0.696476
$202$	−2.68703e19	−0.682003
$203$	−1.20518e19	−0.293317
$204$	−8.96230e18	−0.209201
$205$	1.87170e19	0.419110
$206$	1.87854e19	0.403597
$207$	2.45908e19	0.507019
$208$	−2.37310e19	−0.469653
$209$	9.34471e19	1.77551
$210$	−1.87287e18	−0.0341699
$211$	4.61906e19	0.809380	0.404690	−	0.914454i	$-0.367379\pi$
$211$	4.61906e19	0.809380	0.404690	+	0.914454i	$0.367379\pi$
$212$	−5.32795e19	−0.896821
$213$	−1.06892e19	−0.172870
$214$	−3.45968e19	−0.537674
$215$	−1.86285e19	−0.278261
$216$	−1.11826e19	−0.160577
$217$	4.24324e19	0.585854
$218$	1.45293e19	0.192914
$219$	−1.30410e19	−0.166547
$220$	−2.74664e19	−0.337450
$221$	−4.73854e19	−0.560157
$222$	4.51947e19	0.514146
$223$	−1.09000e20	−1.19354	−0.596768	−	0.802414i	$-0.703549\pi$
$223$	−1.09000e20	−1.19354	−0.596768	+	0.802414i	$0.703549\pi$
$224$	−3.64596e19	−0.384330
$225$	−2.91758e19	−0.296123
$226$	4.05549e19	0.396389
$227$	7.95341e18	0.0748745	0.0374372	−	0.999299i	$-0.488081\pi$
$227$	7.95341e18	0.0748745	0.0374372	+	0.999299i	$0.488081\pi$
$228$	−6.81518e19	−0.618061
$229$	5.82844e19	0.509273	0.254636	−	0.967037i	$-0.418044\pi$
$229$	5.82844e19	0.509273	0.254636	+	0.967037i	$0.418044\pi$
$230$	2.82869e19	0.238176
$231$	−3.48029e19	−0.282432
$232$	−8.27752e19	−0.647519
$233$	1.50170e20	1.13255	0.566276	−	0.824216i	$-0.308384\pi$
$233$	1.50170e20	1.13255	0.566276	+	0.824216i	$0.308384\pi$
$234$	−2.59151e19	−0.188459
$235$	8.46755e19	0.593856
$236$	−8.30412e19	−0.561748
$237$	−1.17865e20	−0.769176
$238$	−1.30631e19	−0.0822511
$239$	2.45916e20	1.49419	0.747093	−	0.664720i	$-0.231449\pi$
$239$	2.45916e20	1.49419	0.747093	+	0.664720i	$0.231449\pi$
$240$	1.28064e19	0.0750984
$241$	6.21102e19	0.351575	0.175787	−	0.984428i	$-0.443753\pi$
$241$	6.21102e19	0.351575	0.175787	+	0.984428i	$0.443753\pi$
$242$	5.78992e19	0.316404
$243$	1.21577e19	0.0641500
$244$	−7.37142e19	−0.375611
$245$	9.69855e18	0.0477304
$246$	7.13973e19	0.339417
$247$	−3.60332e20	−1.65492
$248$	2.91437e20	1.29332
$249$	−7.86065e19	−0.337104
$250$	−7.13394e19	−0.295692
$251$	3.51341e20	1.40768	0.703838	−	0.710361i	$-0.251468\pi$
$251$	3.51341e20	1.40768	0.703838	+	0.710361i	$0.251468\pi$
$252$	2.53821e19	0.0983156
$253$	5.25645e20	1.96865
$254$	7.51189e19	0.272059
$255$	2.55714e19	0.0895702
$256$	−1.60748e20	−0.544634
$257$	1.70495e20	0.558829	0.279415	−	0.960171i	$-0.409860\pi$
$257$	1.70495e20	0.558829	0.279415	+	0.960171i	$0.409860\pi$
$258$	−7.10600e19	−0.225350
$259$	−2.34038e20	−0.718189
$260$	1.05910e20	0.314532
$261$	8.99931e19	0.258681
$262$	−8.64961e19	−0.240678
$263$	2.05201e20	0.552784	0.276392	−	0.961045i	$-0.410861\pi$
$263$	2.05201e20	0.552784	0.276392	+	0.961045i	$0.410861\pi$
$264$	−2.39035e20	−0.623489
$265$	1.52018e20	0.383978
$266$	−9.93353e19	−0.243002
$267$	2.56328e20	0.607366
$268$	4.10115e20	0.941368
$269$	−4.30812e19	−0.0958062	−0.0479031	−	0.998852i	$-0.515254\pi$
$269$	−4.30812e19	−0.0958062	−0.0479031	+	0.998852i	$0.515254\pi$
$270$	1.39850e19	0.0301350
$271$	−5.41493e20	−1.13072	−0.565358	−	0.824845i	$-0.691262\pi$
$271$	−5.41493e20	−1.13072	−0.565358	+	0.824845i	$0.691262\pi$
$272$	8.93232e19	0.180771
$273$	1.34200e20	0.263251
$274$	−1.44017e20	−0.273863
$275$	−6.23655e20	−1.14978
$276$	−3.83358e20	−0.685295
$277$	−7.21087e20	−1.25000	−0.625000	−	0.780625i	$-0.714901\pi$
$277$	−7.21087e20	−1.25000	−0.625000	+	0.780625i	$0.714901\pi$
$278$	2.64968e19	0.0445464
$279$	−3.16850e20	−0.516675
$280$	6.66122e19	0.105368
$281$	3.40535e20	0.522586	0.261293	−	0.965260i	$-0.415851\pi$
$281$	3.40535e20	0.522586	0.261293	+	0.965260i	$0.415851\pi$
$282$	3.23001e20	0.480935
$283$	7.89527e20	1.14073	0.570364	−	0.821392i	$-0.306802\pi$
$283$	7.89527e20	1.14073	0.570364	+	0.821392i	$0.306802\pi$
$284$	1.66640e20	0.233654
$285$	1.94452e20	0.264626
$286$	−5.53953e20	−0.731748
$287$	−3.69727e20	−0.474117
$288$	2.72250e20	0.338947
$289$	−6.48882e20	−0.784393
$290$	1.03519e20	0.121518
$291$	−7.35239e20	−0.838182
$292$	2.03303e20	0.225107
$293$	−9.20811e20	−0.990366	−0.495183	−	0.868789i	$-0.664899\pi$
$293$	−9.20811e20	−0.990366	−0.495183	+	0.868789i	$0.664899\pi$
$294$	3.69959e19	0.0386546
$295$	2.36935e20	0.240515
$296$	−1.60744e21	−1.58546
$297$	2.59879e20	0.249081
$298$	2.64262e20	0.246148
$299$	−2.02689e21	−1.83495
$300$	4.54837e20	0.400245
$301$	3.67981e20	0.314782
$302$	2.50024e20	0.207933
$303$	−1.03903e21	−0.840168
$304$	6.79238e20	0.534068
$305$	2.10323e20	0.160819
$306$	9.75442e19	0.0725386
$307$	−1.04338e20	−0.0754684	−0.0377342	−	0.999288i	$-0.512014\pi$
$307$	−1.04338e20	−0.0754684	−0.0377342	+	0.999288i	$0.512014\pi$
$308$	5.42560e20	0.381739
$309$	7.26399e20	0.497197
$310$	−3.64473e20	−0.242712
$311$	5.25503e20	0.340496	0.170248	−	0.985401i	$-0.445543\pi$
$311$	5.25503e20	0.340496	0.170248	+	0.985401i	$0.445543\pi$
$312$	9.21720e20	0.581146
$313$	−1.35655e21	−0.832354	−0.416177	−	0.909284i	$-0.636630\pi$
$313$	−1.35655e21	−0.832354	−0.416177	+	0.909284i	$0.636630\pi$
$314$	8.66700e20	0.517567
$315$	−7.24207e19	−0.0420943
$316$	1.83747e21	1.03963
$317$	−8.62613e20	−0.475130	−0.237565	−	0.971372i	$-0.576349\pi$
$317$	−8.62613e20	−0.475130	−0.237565	+	0.971372i	$0.576349\pi$
$318$	5.79885e20	0.310965
$319$	1.92367e21	1.00441
$320$	5.73317e19	0.0291488
$321$	−1.33780e21	−0.662367
$322$	−5.58767e20	−0.269436
$323$	1.35629e21	0.636986
$324$	−1.89532e20	−0.0867062
$325$	2.40481e21	1.07170
$326$	1.03106e21	0.447647
$327$	5.61823e20	0.237653
$328$	−2.53939e21	−1.04665
$329$	−1.67264e21	−0.671798
$330$	2.98940e20	0.117008
$331$	2.23356e21	0.852038	0.426019	−	0.904714i	$-0.359916\pi$
$331$	2.23356e21	0.852038	0.426019	+	0.904714i	$0.359916\pi$
$332$	1.22544e21	0.455635
$333$	1.74760e21	0.633383
$334$	−7.02580e20	−0.248228
$335$	−1.17015e21	−0.403051
$336$	−2.52972e20	−0.0849548
$337$	5.42566e21	1.77664	0.888318	−	0.459229i	$-0.151874\pi$
$337$	5.42566e21	1.77664	0.888318	+	0.459229i	$0.151874\pi$
$338$	6.68294e20	0.213391
$339$	1.56819e21	0.488317
$340$	−3.98647e20	−0.121065
$341$	−6.77289e21	−2.00614
$342$	7.41753e20	0.214307
$343$	−1.91581e20	−0.0539949
$344$	2.52739e21	0.694905
$345$	1.09381e21	0.293412
$346$	1.29325e21	0.338481
$347$	−3.37032e21	−0.860737	−0.430368	−	0.902653i	$-0.641616\pi$
$347$	−3.37032e21	−0.860737	−0.430368	+	0.902653i	$0.641616\pi$
$348$	−1.40295e21	−0.349638
$349$	−4.53090e21	−1.10197	−0.550983	−	0.834517i	$-0.685747\pi$
$349$	−4.53090e21	−1.10197	−0.550983	+	0.834517i	$0.685747\pi$
$350$	6.62952e20	0.157363
$351$	−1.00209e21	−0.232165
$352$	5.81954e21	1.31606
$353$	3.02965e21	0.668818	0.334409	−	0.942428i	$-0.391463\pi$
$353$	3.02965e21	0.668818	0.334409	+	0.942428i	$0.391463\pi$
$354$	9.03806e20	0.194781
$355$	−4.75461e20	−0.100040
$356$	−3.99603e21	−0.820926
$357$	−5.05128e20	−0.101326
$358$	4.12909e21	0.808815
$359$	−5.05829e21	−0.967612	−0.483806	−	0.875175i	$-0.660746\pi$
$359$	−5.05829e21	−0.967612	−0.483806	+	0.875175i	$0.660746\pi$
$360$	−4.97404e20	−0.0929263
$361$	4.83319e21	0.881907
$362$	−1.70700e21	−0.304235
$363$	2.23887e21	0.389782
$364$	−2.09211e21	−0.355814
$365$	−5.80068e20	−0.0963806
$366$	8.02293e20	0.130240
$367$	−1.19647e22	−1.89775	−0.948876	−	0.315648i	$-0.897778\pi$
$367$	−1.19647e22	−1.89775	−0.948876	+	0.315648i	$0.897778\pi$
$368$	3.82076e21	0.592165
$369$	2.76082e21	0.418132
$370$	2.01027e21	0.297537
$371$	−3.00291e21	−0.434374
$372$	4.93953e21	0.698346
$373$	−1.01919e22	−1.40842	−0.704209	−	0.709992i	$-0.748698\pi$
$373$	−1.01919e22	−1.40842	−0.704209	+	0.709992i	$0.748698\pi$
$374$	2.08508e21	0.281653
$375$	−2.75858e21	−0.364267
$376$	−1.14882e22	−1.48304
$377$	−7.41766e21	−0.936193
$378$	−2.76254e20	−0.0340901
$379$	1.18402e21	0.142865	0.0714324	−	0.997445i	$-0.477243\pi$
$379$	1.18402e21	0.142865	0.0714324	+	0.997445i	$0.477243\pi$
$380$	−3.03142e21	−0.357672
$381$	2.90472e21	0.335153
$382$	−2.35991e21	−0.266292
$383$	9.05732e21	0.999563	0.499781	−	0.866152i	$-0.333414\pi$
$383$	9.05732e21	0.999563	0.499781	+	0.866152i	$0.333414\pi$
$384$	−5.22016e21	−0.563467
$385$	−1.54805e21	−0.163443
$386$	4.97387e21	0.513691
$387$	−2.74777e21	−0.277612
$388$	1.14620e22	1.13290
$389$	−2.27494e20	−0.0219988	−0.0109994	−	0.999940i	$-0.503501\pi$
$389$	−2.27494e20	−0.0219988	−0.0109994	+	0.999940i	$0.503501\pi$
$390$	−1.15271e21	−0.109061
$391$	7.62920e21	0.706279
$392$	−1.31583e21	−0.119198
$393$	−3.34466e21	−0.296494
$394$	−9.33860e21	−0.810147
$395$	−5.24270e21	−0.445122
$396$	−4.05139e21	−0.336663
$397$	−2.31568e22	−1.88347	−0.941736	−	0.336354i	$-0.890806\pi$
$397$	−2.31568e22	−1.88347	−0.941736	+	0.336354i	$0.890806\pi$
$398$	−5.56507e21	−0.443062
$399$	−3.84113e21	−0.299357
$400$	−4.53316e21	−0.345852
$401$	1.82783e22	1.36524	0.682619	−	0.730774i	$-0.260841\pi$
$401$	1.82783e22	1.36524	0.682619	+	0.730774i	$0.260841\pi$
$402$	−4.46362e21	−0.326412
$403$	2.61162e22	1.86990
$404$	1.61980e22	1.13559
$405$	5.40777e20	0.0371237
$406$	−2.04488e21	−0.137466
$407$	3.73563e22	2.45930
$408$	−3.46935e21	−0.223685
$409$	7.68503e21	0.485286	0.242643	−	0.970116i	$-0.421986\pi$
$409$	7.68503e21	0.485286	0.242643	+	0.970116i	$0.421986\pi$
$410$	3.17578e21	0.196421
$411$	−5.56890e21	−0.337376
$412$	−1.13242e22	−0.672019
$413$	−4.68032e21	−0.272082
$414$	4.17240e21	0.237620
$415$	−3.49644e21	−0.195082
$416$	−2.24401e22	−1.22668
$417$	1.02459e21	0.0548772
$418$	1.58555e22	0.832112
$419$	−1.60766e22	−0.826753	−0.413377	−	0.910560i	$-0.635651\pi$
$419$	−1.60766e22	−0.826753	−0.413377	+	0.910560i	$0.635651\pi$
$420$	1.12900e21	0.0568953
$421$	1.66192e22	0.820751	0.410375	−	0.911917i	$-0.365398\pi$
$421$	1.66192e22	0.820751	0.410375	+	0.911917i	$0.365398\pi$
$422$	7.83732e21	0.379325
$423$	1.24899e22	0.592470
$424$	−2.06248e22	−0.958913
$425$	−9.05170e21	−0.412500
$426$	−1.81368e21	−0.0810176
$427$	−4.15463e21	−0.181926
$428$	2.08557e22	0.895266
$429$	−2.14205e22	−0.901450
$430$	−3.16077e21	−0.130410
$431$	2.73146e22	1.10494	0.552468	−	0.833534i	$-0.313686\pi$
$431$	2.73146e22	1.10494	0.552468	+	0.833534i	$0.313686\pi$
$432$	1.88898e21	0.0749231
$433$	−1.90830e21	−0.0742164	−0.0371082	−	0.999311i	$-0.511815\pi$
$433$	−1.90830e21	−0.0742164	−0.0371082	+	0.999311i	$0.511815\pi$
$434$	7.19966e21	0.274567
$435$	4.00293e21	0.149699
$436$	−8.75856e21	−0.321216
$437$	5.80145e22	2.08662
$438$	−2.21271e21	−0.0780540
$439$	2.45247e22	0.848506	0.424253	−	0.905544i	$-0.360537\pi$
$439$	2.45247e22	0.848506	0.424253	+	0.905544i	$0.360537\pi$
$440$	−1.06324e22	−0.360814
$441$	1.43057e21	0.0476190
$442$	−8.04005e21	−0.262524
$443$	−3.10174e22	−0.993514	−0.496757	−	0.867890i	$-0.665476\pi$
$443$	−3.10174e22	−0.993514	−0.496757	+	0.867890i	$0.665476\pi$
$444$	−2.72443e22	−0.856092
$445$	1.14016e22	0.351483
$446$	−1.84945e22	−0.559365
$447$	1.02186e22	0.303232
$448$	−1.13251e21	−0.0329745
$449$	−1.10133e22	−0.314646	−0.157323	−	0.987547i	$-0.550286\pi$
$449$	−1.10133e22	−0.314646	−0.157323	+	0.987547i	$0.550286\pi$
$450$	−4.95037e21	−0.138781
$451$	5.90145e22	1.62352
$452$	−2.44474e22	−0.660017
$453$	9.66801e21	0.256155
$454$	1.34949e21	0.0350908
$455$	5.96926e21	0.152343
$456$	−2.63819e22	−0.660853
$457$	−9.29048e21	−0.228429	−0.114214	−	0.993456i	$-0.536435\pi$
$457$	−9.29048e21	−0.228429	−0.114214	+	0.993456i	$0.536435\pi$
$458$	9.88932e21	0.238677
$459$	3.77187e21	0.0893612
$460$	−1.70519e22	−0.396581
$461$	3.76152e22	0.858826	0.429413	−	0.903108i	$-0.358721\pi$
$461$	3.76152e22	0.858826	0.429413	+	0.903108i	$0.358721\pi$
$462$	−5.90514e21	−0.132365
$463$	−3.54538e22	−0.780232	−0.390116	−	0.920766i	$-0.627565\pi$
$463$	−3.54538e22	−0.780232	−0.390116	+	0.920766i	$0.627565\pi$
$464$	1.39826e22	0.302123
$465$	−1.40936e22	−0.299000
$466$	2.54799e22	0.530784
$467$	6.19686e22	1.26759	0.633794	−	0.773502i	$-0.281497\pi$
$467$	6.19686e22	1.26759	0.633794	+	0.773502i	$0.281497\pi$
$468$	1.56221e22	0.313798
$469$	2.31146e22	0.455950
$470$	1.43672e22	0.278317
$471$	3.35139e22	0.637598
$472$	−3.21456e22	−0.600641
$473$	−5.87356e22	−1.07791
$474$	−1.99987e22	−0.360483
$475$	−6.88316e22	−1.21869
$476$	7.87470e21	0.136954
$477$	2.24232e22	0.383082
$478$	4.17255e22	0.700267
$479$	−9.73266e22	−1.60465	−0.802324	−	0.596889i	$-0.796403\pi$
$479$	−9.73266e22	−1.60465	−0.802324	+	0.596889i	$0.796403\pi$
$480$	1.21098e22	0.196149
$481$	−1.44046e23	−2.29228
$482$	1.05385e22	0.164770
$483$	−2.16066e22	−0.331922
$484$	−3.49028e22	−0.526836
$485$	−3.27037e22	−0.485056
$486$	2.06284e21	0.0300647
$487$	−4.54443e22	−0.650854	−0.325427	−	0.945567i	$-0.605508\pi$
$487$	−4.54443e22	−0.650854	−0.325427	+	0.945567i	$0.605508\pi$
$488$	−2.85351e22	−0.401616
$489$	3.98695e22	0.551462
$490$	1.64559e21	0.0223694
$491$	−6.81622e22	−0.910649	−0.455324	−	0.890326i	$-0.650477\pi$
$491$	−6.81622e22	−0.910649	−0.455324	+	0.890326i	$0.650477\pi$
$492$	−4.30398e22	−0.565154
$493$	2.79200e22	0.360344
$494$	−6.11388e22	−0.775600
$495$	1.15595e22	0.144144
$496$	−4.92301e22	−0.603443
$497$	9.39206e21	0.113170
$498$	−1.33374e22	−0.157988
$499$	1.17826e23	1.37211	0.686054	−	0.727551i	$-0.259342\pi$
$499$	1.17826e23	1.37211	0.686054	+	0.727551i	$0.259342\pi$
$500$	4.30049e22	0.492349
$501$	−2.71676e22	−0.305795
$502$	5.96134e22	0.659724
$503$	2.37499e22	0.258425	0.129212	−	0.991617i	$-0.458755\pi$
$503$	2.37499e22	0.258425	0.129212	+	0.991617i	$0.458755\pi$
$504$	9.82552e21	0.105123
$505$	−4.62165e22	−0.486206
$506$	8.91882e22	0.922631
$507$	2.58418e22	0.262879
$508$	−4.52832e22	−0.452998
$509$	−9.62819e22	−0.947204	−0.473602	−	0.880739i	$-0.657046\pi$
$509$	−9.62819e22	−0.947204	−0.473602	+	0.880739i	$0.657046\pi$
$510$	4.33880e21	0.0419781
$511$	1.14584e22	0.109030
$512$	7.70108e22	0.720704
$513$	2.86824e22	0.264008
$514$	2.89284e22	0.261902
$515$	3.23105e22	0.287728
$516$	4.28365e22	0.375224
$517$	2.66981e23	2.30044
$518$	−3.97101e22	−0.336588
$519$	5.00077e22	0.416979
$520$	4.09984e22	0.336309
$521$	−1.28582e23	−1.03767	−0.518834	−	0.854875i	$-0.673634\pi$
$521$	−1.28582e23	−1.03767	−0.518834	+	0.854875i	$0.673634\pi$
$522$	1.52695e22	0.121234
$523$	4.24893e21	0.0331906	0.0165953	−	0.999862i	$-0.494717\pi$
$523$	4.24893e21	0.0331906	0.0165953	+	0.999862i	$0.494717\pi$
$524$	5.21417e22	0.400746
$525$	2.56353e22	0.193858
$526$	3.48172e22	0.259069
$527$	−9.83014e22	−0.719730
$528$	4.03784e22	0.290911
$529$	1.85285e23	1.31361
$530$	2.57935e22	0.179956
$531$	3.49487e22	0.239954
$532$	5.98814e22	0.404616
$533$	−2.27559e23	−1.51326
$534$	4.34921e22	0.284649
$535$	−5.95058e22	−0.383312
$536$	1.58757e23	1.00654
$537$	1.59665e23	0.996389
$538$	−7.30975e21	−0.0449007
$539$	3.05795e22	0.184895
$540$	−8.43046e21	−0.0501770
$541$	−1.38337e23	−0.810516	−0.405258	−	0.914202i	$-0.632818\pi$
$541$	−1.38337e23	−0.810516	−0.405258	+	0.914202i	$0.632818\pi$
$542$	−9.18771e22	−0.529924
$543$	−6.60067e22	−0.374791
$544$	8.44645e22	0.472154
$545$	2.49901e22	0.137530
$546$	2.27702e22	0.123376
$547$	−1.61112e23	−0.859480	−0.429740	−	0.902953i	$-0.641395\pi$
$547$	−1.61112e23	−0.859480	−0.429740	+	0.902953i	$0.641395\pi$
$548$	8.68165e22	0.456003
$549$	3.10233e22	0.160444
$550$	−1.05818e23	−0.538860
$551$	2.12312e23	1.06460
$552$	−1.48400e23	−0.732742
$553$	1.03562e23	0.503544
$554$	−1.22349e23	−0.585827
$555$	7.77340e22	0.366539
$556$	−1.59728e22	−0.0741730
$557$	−3.83446e23	−1.75362	−0.876808	−	0.480840i	$-0.840332\pi$
$557$	−3.83446e23	−1.75362	−0.876808	+	0.480840i	$0.840332\pi$
$558$	−5.37610e22	−0.242146
$559$	2.26484e23	1.00470
$560$	−1.12523e22	−0.0491634
$561$	8.06265e22	0.346971
$562$	5.77798e22	0.244916
$563$	−1.12860e23	−0.471217	−0.235608	−	0.971848i	$-0.575708\pi$
$563$	−1.12860e23	−0.471217	−0.235608	+	0.971848i	$0.575708\pi$
$564$	−1.94712e23	−0.800792
$565$	6.97537e22	0.282589
$566$	1.33962e23	0.534615
$567$	−1.06823e22	−0.0419961
$568$	6.45072e22	0.249831
$569$	−1.50174e23	−0.572981	−0.286490	−	0.958083i	$-0.592489\pi$
$569$	−1.50174e23	−0.572981	−0.286490	+	0.958083i	$0.592489\pi$
$570$	3.29934e22	0.124020
$571$	−1.01524e21	−0.00375976	−0.00187988	−	0.999998i	$-0.500598\pi$
$571$	−1.01524e21	−0.00375976	−0.00187988	+	0.999998i	$0.500598\pi$
$572$	3.33935e23	1.21841
$573$	−9.12540e22	−0.328048
$574$	−6.27330e22	−0.222201
$575$	−3.87182e23	−1.35126
$576$	8.45662e21	0.0290807
$577$	−2.29872e23	−0.778917	−0.389458	−	0.921044i	$-0.627338\pi$
$577$	−2.29872e23	−0.778917	−0.389458	+	0.921044i	$0.627338\pi$
$578$	−1.10098e23	−0.367615
$579$	1.92331e23	0.632823
$580$	−6.24037e22	−0.202336
$581$	6.90673e22	0.220686
$582$	−1.24751e23	−0.392824
$583$	4.79312e23	1.48743
$584$	7.86995e22	0.240693
$585$	−4.45734e22	−0.134354
$586$	−1.56237e23	−0.464147
$587$	−8.88716e22	−0.260219	−0.130110	−	0.991500i	$-0.541533\pi$
$587$	−8.88716e22	−0.260219	−0.130110	+	0.991500i	$0.541533\pi$
$588$	−2.23019e22	−0.0643627
$589$	−7.47511e23	−2.12636
$590$	4.02016e22	0.112720
$591$	−3.61108e23	−0.998030
$592$	2.71532e23	0.739751
$593$	1.75217e23	0.470557	0.235278	−	0.971928i	$-0.424400\pi$
$593$	1.75217e23	0.470557	0.235278	+	0.971928i	$0.424400\pi$
$594$	4.40946e22	0.116735
$595$	−2.24683e22	−0.0586375
$596$	−1.59302e23	−0.409854
$597$	−2.15192e23	−0.545813
$598$	−3.43909e23	−0.859971
$599$	5.34079e23	1.31667	0.658336	−	0.752724i	$-0.271261\pi$
$599$	5.34079e23	1.31667	0.658336	+	0.752724i	$0.271261\pi$
$600$	1.76070e23	0.427956
$601$	−5.23655e23	−1.25491	−0.627454	−	0.778653i	$-0.715903\pi$
$601$	−5.23655e23	−1.25491	−0.627454	+	0.778653i	$0.715903\pi$
$602$	6.24366e22	0.147526
$603$	−1.72601e23	−0.402110
$604$	−1.50720e23	−0.346223
$605$	9.95855e22	0.225567
$606$	−1.76296e23	−0.393755
$607$	4.32161e23	0.951791	0.475895	−	0.879502i	$-0.342124\pi$
$607$	4.32161e23	0.951791	0.475895	+	0.879502i	$0.342124\pi$
$608$	6.42292e23	1.39493
$609$	−7.90722e22	−0.169347
$610$	3.56863e22	0.0753699
$611$	−1.02948e24	−2.14421
$612$	−5.88017e22	−0.120782
$613$	−3.42612e23	−0.694046	−0.347023	−	0.937857i	$-0.612807\pi$
$613$	−3.42612e23	−0.694046	−0.347023	+	0.937857i	$0.612807\pi$
$614$	−1.77034e22	−0.0353691
$615$	1.22802e23	0.241973
$616$	2.10028e23	0.408170
$617$	4.02144e23	0.770828	0.385414	−	0.922744i	$-0.374059\pi$
$617$	4.02144e23	0.770828	0.385414	+	0.922744i	$0.374059\pi$
$618$	1.23251e23	0.233017
$619$	5.86756e23	1.09418	0.547088	−	0.837075i	$-0.315736\pi$
$619$	5.86756e23	1.09418	0.547088	+	0.837075i	$0.315736\pi$
$620$	2.19712e23	0.404133
$621$	1.61340e23	0.292727
$622$	8.91640e22	0.159577
$623$	−2.25222e23	−0.397614
$624$	−1.55699e23	−0.271154
$625$	3.94396e23	0.677567
$626$	−2.30170e23	−0.390093
$627$	6.13106e23	1.02509
$628$	−5.22465e23	−0.861787
$629$	5.42188e23	0.882306
$630$	−1.22879e22	−0.0197280
$631$	−1.71101e23	−0.271021	−0.135511	−	0.990776i	$-0.543267\pi$
$631$	−1.71101e23	−0.271021	−0.135511	+	0.990776i	$0.543267\pi$
$632$	7.11292e23	1.11161
$633$	3.03056e23	0.467296
$634$	−1.46363e23	−0.222675
$635$	1.29203e23	0.193953
$636$	−3.49567e23	−0.517780
$637$	−1.17914e23	−0.172338
$638$	3.26396e23	0.470727
$639$	−7.01321e22	−0.0998066
$640$	−2.32195e23	−0.326079
$641$	−1.93358e21	−0.00267959	−0.00133980	−	0.999999i	$-0.500426\pi$
$641$	−1.93358e21	−0.00267959	−0.00133980	+	0.999999i	$0.500426\pi$
$642$	−2.26990e23	−0.310426
$643$	−7.75825e23	−1.04706	−0.523529	−	0.852008i	$-0.675385\pi$
$643$	−7.75825e23	−1.04706	−0.523529	+	0.852008i	$0.675385\pi$
$644$	3.36836e23	0.448631
$645$	−1.22222e23	−0.160654
$646$	2.30126e23	0.298531
$647$	−4.87052e23	−0.623576	−0.311788	−	0.950152i	$-0.600928\pi$
$647$	−4.87052e23	−0.623576	−0.311788	+	0.950152i	$0.600928\pi$
$648$	−7.33688e22	−0.0927094
$649$	7.47054e23	0.931691
$650$	4.08033e23	0.502264
$651$	2.78399e23	0.338243
$652$	−6.21547e23	−0.745366
$653$	7.39792e23	0.875684	0.437842	−	0.899052i	$-0.355743\pi$
$653$	7.39792e23	0.875684	0.437842	+	0.899052i	$0.355743\pi$
$654$	9.53266e22	0.111379
$655$	−1.48772e23	−0.171581
$656$	4.28958e23	0.488351
$657$	−8.55620e22	−0.0961557
$658$	−2.83804e23	−0.314846
$659$	−4.70939e22	−0.0515749	−0.0257875	−	0.999667i	$-0.508209\pi$
$659$	−4.70939e22	−0.0515749	−0.0257875	+	0.999667i	$0.508209\pi$
$660$	−1.80207e23	−0.194827
$661$	−6.85000e21	−0.00731103	−0.00365551	−	0.999993i	$-0.501164\pi$
$661$	−6.85000e21	−0.00731103	−0.00365551	+	0.999993i	$0.501164\pi$
$662$	3.78976e23	0.399318
$663$	−3.10896e23	−0.323407
$664$	4.74372e23	0.487181
$665$	−1.70855e23	−0.173238
$666$	2.96522e23	0.296843
$667$	1.19427e24	1.18041
$668$	4.23530e23	0.413318
$669$	−7.15150e23	−0.689089
$670$	−1.98543e23	−0.188895
$671$	6.63147e23	0.622971
$672$	−2.39211e23	−0.221893
$673$	7.05203e23	0.645931	0.322966	−	0.946411i	$-0.395320\pi$
$673$	7.05203e23	0.645931	0.322966	+	0.946411i	$0.395320\pi$
$674$	9.20592e23	0.832641
$675$	−1.91423e23	−0.170967
$676$	−4.02861e23	−0.355311
$677$	−1.31444e24	−1.14482	−0.572409	−	0.819968i	$-0.693991\pi$
$677$	−1.31444e24	−1.14482	−0.572409	+	0.819968i	$0.693991\pi$
$678$	2.66081e23	0.228855
$679$	6.46016e23	0.548719
$680$	−1.54318e23	−0.129447
$681$	5.21824e22	0.0432288
$682$	−1.14918e24	−0.940202
$683$	8.44133e23	0.682080	0.341040	−	0.940049i	$-0.389221\pi$
$683$	8.44133e23	0.682080	0.341040	+	0.940049i	$0.389221\pi$
$684$	−4.47144e23	−0.356838
$685$	−2.47707e23	−0.195240
$686$	−3.25063e22	−0.0253054
$687$	3.82404e23	0.294029
$688$	−4.26932e23	−0.324232
$689$	−1.84823e24	−1.38641
$690$	1.85590e23	0.137511
$691$	−1.54835e24	−1.13320	−0.566600	−	0.823993i	$-0.691741\pi$
$691$	−1.54835e24	−1.13320	−0.566600	+	0.823993i	$0.691741\pi$
$692$	−7.79597e23	−0.563596
$693$	−2.28342e23	−0.163062
$694$	−5.71854e23	−0.403394
$695$	4.55740e22	0.0317575
$696$	−5.43088e23	−0.373845
$697$	8.56533e23	0.582459
$698$	−7.68774e23	−0.516449
$699$	9.85266e23	0.653879
$700$	−3.99641e23	−0.262022
$701$	1.05664e24	0.684419	0.342209	−	0.939624i	$-0.388825\pi$
$701$	1.05664e24	0.684419	0.342209	+	0.939624i	$0.388825\pi$
$702$	−1.70029e23	−0.108807
$703$	4.12294e24	2.60668
$704$	1.80766e23	0.112915
$705$	5.55556e23	0.342863
$706$	5.14053e23	0.313449
$707$	9.12942e23	0.550019
$708$	−5.44833e23	−0.324325
$709$	−2.37391e24	−1.39628	−0.698138	−	0.715964i	$-0.745988\pi$
$709$	−2.37391e24	−1.39628	−0.698138	+	0.715964i	$0.745988\pi$
$710$	−8.06732e22	−0.0468849
$711$	−7.73315e23	−0.444084
$712$	−1.54688e24	−0.877763
$713$	−4.20480e24	−2.35767
$714$	−8.57069e22	−0.0474877
$715$	−9.52790e23	−0.521670
$716$	−2.48910e24	−1.34674
$717$	1.61345e24	0.862668
$718$	−8.58259e23	−0.453483
$719$	1.29765e24	0.677581	0.338790	−	0.940862i	$-0.389982\pi$
$719$	1.29765e24	0.677581	0.338790	+	0.940862i	$0.389982\pi$
$720$	8.40226e22	0.0433581
$721$	−6.38248e23	−0.325492
$722$	8.20066e23	0.413316
$723$	4.07505e23	0.202982
$724$	1.02901e24	0.506574
$725$	−1.41694e24	−0.689413
$726$	3.79876e23	0.182676
$727$	1.48171e24	0.704240	0.352120	−	0.935955i	$-0.385461\pi$
$727$	1.48171e24	0.704240	0.352120	+	0.935955i	$0.385461\pi$
$728$	−8.09866e23	−0.380449
$729$	7.97664e22	0.0370370
$730$	−9.84223e22	−0.0451699
$731$	−8.52486e23	−0.386714
$732$	−4.83639e23	−0.216859
$733$	1.47050e24	0.651750	0.325875	−	0.945413i	$-0.394341\pi$
$733$	1.47050e24	0.651750	0.325875	+	0.945413i	$0.394341\pi$
$734$	−2.03009e24	−0.889404
$735$	6.36322e22	0.0275572
$736$	3.61293e24	1.54667
$737$	−3.68947e24	−1.56131
$738$	4.68438e23	0.195962
$739$	2.95680e24	1.22277	0.611384	−	0.791334i	$-0.290613\pi$
$739$	2.95680e24	1.22277	0.611384	+	0.791334i	$0.290613\pi$
$740$	−1.21184e24	−0.495421
$741$	−2.36414e24	−0.955471
$742$	−5.09514e23	−0.203574
$743$	3.52761e24	1.39340	0.696699	−	0.717364i	$-0.254651\pi$
$743$	3.52761e24	1.39340	0.696699	+	0.717364i	$0.254651\pi$
$744$	1.91212e24	0.746697
$745$	4.54525e23	0.175481
$746$	−1.72930e24	−0.660072
$747$	−5.15737e23	−0.194627
$748$	−1.25693e24	−0.468972
$749$	1.17545e24	0.433621
$750$	−4.68058e23	−0.170718
$751$	−1.71735e24	−0.619328	−0.309664	−	0.950846i	$-0.600217\pi$
$751$	−1.71735e24	−0.619328	−0.309664	+	0.950846i	$0.600217\pi$
$752$	1.94060e24	0.691967
$753$	2.30515e24	0.812722
$754$	−1.25858e24	−0.438758
$755$	4.30037e23	0.148237
$756$	1.66532e23	0.0567626
$757$	3.29628e24	1.11099	0.555494	−	0.831521i	$-0.312529\pi$
$757$	3.29628e24	1.11099	0.555494	+	0.831521i	$0.312529\pi$
$758$	2.00897e23	0.0669552
$759$	3.44876e24	1.13660
$760$	−1.17348e24	−0.382436
$761$	−5.06982e24	−1.63389	−0.816945	−	0.576715i	$-0.804334\pi$
$761$	−5.06982e24	−1.63389	−0.816945	+	0.576715i	$0.804334\pi$
$762$	4.92855e23	0.157073
$763$	−4.93644e23	−0.155581
$764$	1.42261e24	0.443395
$765$	1.67774e23	0.0517134
$766$	1.53679e24	0.468457
$767$	−2.88064e24	−0.868416
$768$	−1.05467e24	−0.314445
$769$	1.74162e24	0.513548	0.256774	−	0.966472i	$-0.417340\pi$
$769$	1.74162e24	0.513548	0.256774	+	0.966472i	$0.417340\pi$
$770$	−2.62663e23	−0.0765997
$771$	1.11861e24	0.322640
$772$	−2.99835e24	−0.855333
$773$	2.01656e23	0.0568965	0.0284482	−	0.999595i	$-0.490943\pi$
$773$	2.01656e23	0.0568965	0.0284482	+	0.999595i	$0.490943\pi$
$774$	−4.66225e23	−0.130106
$775$	4.98880e24	1.37699
$776$	4.43701e24	1.21134
$777$	−1.53553e24	−0.414647
$778$	−3.85998e22	−0.0103100
$779$	6.51331e24	1.72081
$780$	6.94878e23	0.181595
$781$	−1.49912e24	−0.387529
$782$	1.29447e24	0.331006
$783$	5.90445e23	0.149350
$784$	2.22273e23	0.0556160
$785$	1.49071e24	0.368978
$786$	−5.67501e23	−0.138955
$787$	−2.23637e24	−0.541699	−0.270850	−	0.962622i	$-0.587305\pi$
$787$	−2.23637e24	−0.541699	−0.270850	+	0.962622i	$0.587305\pi$
$788$	5.62950e24	1.34895
$789$	1.34632e24	0.319150
$790$	−8.89548e23	−0.208612
$791$	−1.37789e24	−0.319678
$792$	−1.56831e24	−0.359972
$793$	−2.55709e24	−0.580663
$794$	−3.92910e24	−0.882711
$795$	9.97392e23	0.221690
$796$	3.35474e24	0.737731
$797$	−1.69195e24	−0.368122	−0.184061	−	0.982915i	$-0.558924\pi$
$797$	−1.69195e24	−0.368122	−0.184061	+	0.982915i	$0.558924\pi$
$798$	−6.51739e23	−0.140297
$799$	3.87495e24	0.825313
$800$	−4.28658e24	−0.903329
$801$	1.68177e24	0.350663
$802$	3.10134e24	0.639835
$803$	−1.82895e24	−0.373353
$804$	2.69076e24	0.543499
$805$	−9.61069e23	−0.192083
$806$	4.43124e24	0.876349
$807$	−2.82656e23	−0.0553137
$808$	6.27032e24	1.21421
$809$	4.88049e23	0.0935192	0.0467596	−	0.998906i	$-0.485111\pi$
$809$	4.88049e23	0.0935192	0.0467596	+	0.998906i	$0.485111\pi$
$810$	9.17557e22	0.0173984
$811$	−7.28775e24	−1.36747	−0.683733	−	0.729733i	$-0.739644\pi$
$811$	−7.28775e24	−1.36747	−0.683733	+	0.729733i	$0.739644\pi$
$812$	1.23270e24	0.228892
$813$	−3.55273e24	−0.652819
$814$	6.33838e24	1.15258
$815$	1.77341e24	0.319132
$816$	5.86050e23	0.104368
$817$	−6.48254e24	−1.14250
$818$	1.30395e24	0.227435
$819$	8.80485e23	0.151988
$820$	−1.91443e24	−0.327055
$821$	−8.68268e24	−1.46804	−0.734018	−	0.679130i	$-0.762357\pi$
$821$	−8.68268e24	−1.46804	−0.734018	+	0.679130i	$0.762357\pi$
$822$	−9.44895e23	−0.158115
$823$	−8.01837e24	−1.32797	−0.663984	−	0.747747i	$-0.731136\pi$
$823$	−8.01837e24	−1.32797	−0.663984	+	0.747747i	$0.731136\pi$
$824$	−4.38366e24	−0.718547
$825$	−4.09180e24	−0.663828
$826$	−7.94126e23	−0.127514
$827$	1.04025e25	1.65325	0.826627	−	0.562751i	$-0.190257\pi$
$827$	1.04025e25	1.65325	0.826627	+	0.562751i	$0.190257\pi$
$828$	−2.51521e24	−0.395655
$829$	−8.40608e24	−1.30882	−0.654410	−	0.756140i	$-0.727083\pi$
$829$	−8.40608e24	−1.30882	−0.654410	+	0.756140i	$0.727083\pi$
$830$	−5.93254e23	−0.0914276
$831$	−4.73105e24	−0.721687
$832$	−6.97034e23	−0.105246
$833$	4.43829e23	0.0663335
$834$	1.73845e23	0.0257189
$835$	−1.20843e24	−0.176964
$836$	−9.55803e24	−1.38553
$837$	−2.07885e24	−0.298302
$838$	−2.72778e24	−0.387468
$839$	−8.68249e24	−1.22086	−0.610432	−	0.792068i	$-0.709004\pi$
$839$	−8.68249e24	−1.22086	−0.610432	+	0.792068i	$0.709004\pi$
$840$	4.37043e23	0.0608345
$841$	−2.88657e24	−0.397756
$842$	2.81983e24	0.384654
$843$	2.23425e24	0.301715
$844$	−4.72450e24	−0.631605
$845$	1.14945e24	0.152128
$846$	2.11921e24	0.277668
$847$	−1.96717e24	−0.255172
$848$	3.48398e24	0.447415
$849$	5.18008e24	0.658600
$850$	−1.53583e24	−0.193323
$851$	2.31918e25	2.89024
$852$	1.09333e24	0.134900
$853$	−1.10718e25	−1.35255	−0.676274	−	0.736650i	$-0.736406\pi$
$853$	−1.10718e25	−1.35255	−0.676274	+	0.736650i	$0.736406\pi$
$854$	−7.04932e23	−0.0852620
$855$	1.27580e24	0.152782
$856$	8.07333e24	0.957250
$857$	−4.56561e24	−0.535997	−0.267998	−	0.963419i	$-0.586362\pi$
$857$	−4.56561e24	−0.535997	−0.267998	+	0.963419i	$0.586362\pi$
$858$	−3.63449e24	−0.422475
$859$	2.37515e24	0.273369	0.136685	−	0.990615i	$-0.456355\pi$
$859$	2.37515e24	0.273369	0.136685	+	0.990615i	$0.456355\pi$
$860$	1.90538e24	0.217143
$861$	−2.42578e24	−0.273732
$862$	4.63456e24	0.517842
$863$	−1.17701e24	−0.130224	−0.0651119	−	0.997878i	$-0.520740\pi$
$863$	−1.17701e24	−0.130224	−0.0651119	+	0.997878i	$0.520740\pi$
$864$	1.78623e24	0.195691
$865$	2.22436e24	0.241306
$866$	−3.23788e23	−0.0347824
$867$	−4.25731e24	−0.452870
$868$	−4.34010e24	−0.457175
$869$	−1.65302e25	−1.72429
$870$	6.79191e23	0.0701582
$871$	1.42266e25	1.45528
$872$	−3.39048e24	−0.343456
$873$	−4.82390e24	−0.483925
$874$	9.84353e24	0.977921
$875$	2.42382e24	0.238469
$876$	1.33387e24	0.129966
$877$	2.33893e24	0.225695	0.112847	−	0.993612i	$-0.464003\pi$
$877$	2.33893e24	0.225695	0.112847	+	0.993612i	$0.464003\pi$
$878$	4.16119e24	0.397662
$879$	−6.04144e24	−0.571788
$880$	1.79604e24	0.168350
$881$	1.77952e25	1.65199	0.825994	−	0.563679i	$-0.190614\pi$
$881$	1.77952e25	1.65199	0.825994	+	0.563679i	$0.190614\pi$
$882$	2.42730e23	0.0223172
$883$	3.71235e24	0.338051	0.169026	−	0.985612i	$-0.445938\pi$
$883$	3.71235e24	0.338051	0.169026	+	0.985612i	$0.445938\pi$
$884$	4.84671e24	0.437122
$885$	1.55453e24	0.138861
$886$	−5.26284e24	−0.465622
$887$	−9.79998e24	−0.858765	−0.429383	−	0.903123i	$-0.641269\pi$
$887$	−9.79998e24	−0.858765	−0.429383	+	0.903123i	$0.641269\pi$
$888$	−1.05464e25	−0.915364
$889$	−2.55223e24	−0.219409
$890$	1.93455e24	0.164727
$891$	1.70507e24	0.143807
$892$	1.11488e25	0.931384
$893$	2.94662e25	2.43830
$894$	1.73382e24	0.142113
$895$	7.10197e24	0.576611
$896$	4.58668e24	0.368876
$897$	−1.32984e25	−1.05941
$898$	−1.86866e24	−0.147463
$899$	−1.53880e25	−1.20289
$900$	2.98419e24	0.231081
$901$	6.95672e24	0.533634
$902$	1.00132e25	0.760882
$903$	2.41432e24	0.181739
$904$	−9.46369e24	−0.705714
$905$	−2.93600e24	−0.216892
$906$	1.64041e24	0.120050
$907$	−1.35840e25	−0.984842	−0.492421	−	0.870357i	$-0.663888\pi$
$907$	−1.35840e25	−0.984842	−0.492421	+	0.870357i	$0.663888\pi$
$908$	−8.13498e23	−0.0584288
$909$	−6.81709e24	−0.485071
$910$	1.01283e24	0.0713975
$911$	1.80678e25	1.26183	0.630913	−	0.775853i	$-0.282680\pi$
$911$	1.80678e25	1.26183	0.630913	+	0.775853i	$0.282680\pi$
$912$	4.45648e24	0.308344
$913$	−1.10243e25	−0.755697
$914$	−1.57635e24	−0.107056
$915$	1.37993e24	0.0928491
$916$	−5.96149e24	−0.397414
$917$	2.93878e24	0.194101
$918$	6.39987e23	0.0418802
$919$	−1.39175e24	−0.0902362	−0.0451181	−	0.998982i	$-0.514366\pi$
$919$	−1.39175e24	−0.0902362	−0.0451181	+	0.998982i	$0.514366\pi$
$920$	−6.60087e24	−0.424038
$921$	−6.84560e23	−0.0435717
$922$	6.38230e24	0.402499
$923$	5.78062e24	0.361210
$924$	3.55974e24	0.220397
$925$	−2.75160e25	−1.68803
$926$	−6.01557e24	−0.365665
$927$	4.76590e24	0.287057
$928$	1.32220e25	0.789113
$929$	1.74710e25	1.03320	0.516601	−	0.856226i	$-0.327197\pi$
$929$	1.74710e25	1.03320	0.516601	+	0.856226i	$0.327197\pi$
$930$	−2.39131e24	−0.140130
$931$	3.37500e24	0.195975
$932$	−1.53598e25	−0.883794
$933$	3.44782e24	0.196585
$934$	1.05144e25	0.594070
$935$	3.58630e24	0.200793
$936$	6.04740e24	0.335525
$937$	−4.17552e24	−0.229575	−0.114787	−	0.993390i	$-0.536619\pi$
$937$	−4.17552e24	−0.229575	−0.114787	+	0.993390i	$0.536619\pi$
$938$	3.92194e24	0.213687
$939$	−8.90031e24	−0.480560
$940$	−8.66085e24	−0.463419
$941$	9.89797e23	0.0524849	0.0262425	−	0.999656i	$-0.491646\pi$
$941$	9.89797e23	0.0524849	0.0262425	+	0.999656i	$0.491646\pi$
$942$	5.68642e24	0.298818
$943$	3.66378e25	1.90801
$944$	5.43011e24	0.280251
$945$	−4.75152e23	−0.0243031
$946$	−9.96589e24	−0.505175
$947$	−9.70314e24	−0.487459	−0.243729	−	0.969843i	$-0.578371\pi$
$947$	−9.70314e24	−0.487459	−0.243729	+	0.969843i	$0.578371\pi$
$948$	1.20556e25	0.600231
$949$	7.05242e24	0.347997
$950$	−1.16789e25	−0.571152
$951$	−5.65961e24	−0.274316
$952$	3.04833e24	0.146436
$953$	7.79627e24	0.371191	0.185595	−	0.982626i	$-0.440579\pi$
$953$	7.79627e24	0.371191	0.185595	+	0.982626i	$0.440579\pi$
$954$	3.80463e24	0.179536
$955$	−4.05901e24	−0.189842
$956$	−2.51530e25	−1.16600
$957$	1.26212e25	0.579894
$958$	−1.65138e25	−0.752037
$959$	4.89309e24	0.220864
$960$	3.76153e23	0.0168290
$961$	3.16283e25	1.40258
$962$	−2.44408e25	−1.07430
$963$	−8.77731e24	−0.382418
$964$	−6.35280e24	−0.274354
$965$	8.55496e24	0.366215
$966$	−3.66607e24	−0.155559
$967$	−3.46373e25	−1.45686	−0.728432	−	0.685118i	$-0.759751\pi$
$967$	−3.46373e25	−1.45686	−0.728432	+	0.685118i	$0.759751\pi$
$968$	−1.35111e25	−0.563312
$969$	8.89860e24	0.367764
$970$	−5.54896e24	−0.227327
$971$	1.73405e25	0.704203	0.352102	−	0.935962i	$-0.385467\pi$
$971$	1.73405e25	0.704203	0.352102	+	0.935962i	$0.385467\pi$
$972$	−1.24352e24	−0.0500599
$973$	−9.00250e23	−0.0359256
$974$	−7.71070e24	−0.305030
$975$	1.57780e25	0.618745
$976$	4.82021e24	0.187388
$977$	−2.75581e25	−1.06205	−0.531025	−	0.847356i	$-0.678193\pi$
$977$	−2.75581e25	−1.06205	−0.531025	+	0.847356i	$0.678193\pi$
$978$	6.76481e24	0.258449
$979$	3.59490e25	1.36155
$980$	−9.91996e23	−0.0372467
$981$	3.68612e24	0.137209
$982$	−1.15653e25	−0.426786
$983$	−4.00417e25	−1.46490	−0.732450	−	0.680821i	$-0.761623\pi$
$983$	−4.00417e25	−1.46490	−0.732450	+	0.680821i	$0.761623\pi$
$984$	−1.66609e25	−0.604283
$985$	−1.60622e25	−0.577561
$986$	4.73730e24	0.168879
$987$	−1.09742e25	−0.387863
$988$	3.68557e25	1.29143
$989$	−3.64647e25	−1.26679
$990$	1.96134e24	0.0675546
$991$	−3.64139e25	−1.24349	−0.621744	−	0.783221i	$-0.713576\pi$
$991$	−3.64139e25	−1.24349	−0.621744	+	0.783221i	$0.713576\pi$
$992$	−4.65522e25	−1.57613
$993$	1.46544e25	0.491924
$994$	1.59359e24	0.0530385
$995$	−9.57182e24	−0.315863
$996$	8.04009e24	0.263061
$997$	−3.05694e25	−0.991695	−0.495847	−	0.868410i	$-0.665142\pi$
$997$	−3.05694e25	−0.991695	−0.495847	+	0.868410i	$0.665142\pi$
$998$	1.99920e25	0.643054
$999$	1.14660e25	0.365684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.18.a.d.1.4	✓	5
3.2	odd	2		63.18.a.f.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.18.a.d.1.4	✓	5	1.1	even	1	trivial
63.18.a.f.1.2		5	3.2	odd	2

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.a (trivial)

\(f(q)\)	\(=\)	\(q+169.674 q^{2} +6561.00 q^{3} -102283. q^{4} +291836. q^{5} +1.11323e6 q^{6} -5.76480e6 q^{7} -3.95942e7 q^{8} +4.30467e7 q^{9} +O(q^{10})\)	\(q+169.674 q^{2} +6561.00 q^{3} -102283. q^{4} +291836. q^{5} +1.11323e6 q^{6} -5.76480e6 q^{7} -3.95942e7 q^{8} +4.30467e7 q^{9} +4.95168e7 q^{10} +9.20155e8 q^{11} -6.71078e8 q^{12} -3.54811e9 q^{13} -9.78135e8 q^{14} +1.91473e9 q^{15} +6.68833e9 q^{16} +1.33551e10 q^{17} +7.30390e9 q^{18} +1.01556e11 q^{19} -2.98498e10 q^{20} -3.78229e10 q^{21} +1.56126e11 q^{22} +5.71257e11 q^{23} -2.59777e11 q^{24} -6.77771e11 q^{25} -6.02022e11 q^{26} +2.82430e11 q^{27} +5.89640e11 q^{28} +2.09059e12 q^{29} +3.24880e11 q^{30} -7.36060e12 q^{31} +6.32452e12 q^{32} +6.03714e12 q^{33} +2.26601e12 q^{34} -1.68237e12 q^{35} -4.40294e12 q^{36} +4.05978e13 q^{37} +1.72313e13 q^{38} -2.32792e13 q^{39} -1.15550e13 q^{40} +6.41353e13 q^{41} -6.41754e12 q^{42} -6.38323e13 q^{43} -9.41161e13 q^{44} +1.25626e13 q^{45} +9.69273e13 q^{46} +2.90148e14 q^{47} +4.38821e13 q^{48} +3.32329e13 q^{49} -1.15000e14 q^{50} +8.76228e13 q^{51} +3.62911e14 q^{52} +5.20904e14 q^{53} +4.79209e13 q^{54} +2.68534e14 q^{55} +2.28253e14 q^{56} +6.66308e14 q^{57} +3.54718e14 q^{58} +8.11878e14 q^{59} -1.95844e14 q^{60} +7.20690e14 q^{61} -1.24890e15 q^{62} -2.48156e14 q^{63} +1.96452e14 q^{64} -1.03547e15 q^{65} +1.02434e15 q^{66} -4.00961e15 q^{67} -1.36600e15 q^{68} +3.74802e15 q^{69} -2.85455e14 q^{70} -1.62921e15 q^{71} -1.70440e15 q^{72} -1.98765e15 q^{73} +6.88838e15 q^{74} -4.44686e15 q^{75} -1.03874e16 q^{76} -5.30451e15 q^{77} -3.94986e15 q^{78} -1.79646e16 q^{79} +1.95189e15 q^{80} +1.85302e15 q^{81} +1.08821e16 q^{82} -1.19809e16 q^{83} +3.86863e15 q^{84} +3.89749e15 q^{85} -1.08307e16 q^{86} +1.37164e16 q^{87} -3.64328e16 q^{88} +3.90684e16 q^{89} +2.13154e15 q^{90} +2.04542e16 q^{91} -5.84298e16 q^{92} -4.82929e16 q^{93} +4.92304e16 q^{94} +2.96376e16 q^{95} +4.14952e16 q^{96} -1.12062e17 q^{97} +5.63875e15 q^{98} +3.96097e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 253 q^{2} + 32805 q^{3} + 441613 q^{4} - 906662 q^{5} - 1659933 q^{6} - 28824005 q^{7} - 182238651 q^{8} + 215233605 q^{9}+O(q^{10}) \) 5 * q - 253 * q^2 + 32805 * q^3 + 441613 * q^4 - 906662 * q^5 - 1659933 * q^6 - 28824005 * q^7 - 182238651 * q^8 + 215233605 * q^9	\( 5 q - 253 q^{2} + 32805 q^{3} + 441613 q^{4} - 906662 q^{5} - 1659933 q^{6} - 28824005 q^{7} - 182238651 q^{8} + 215233605 q^{9} + 1194057802 q^{10} + 1111338736 q^{11} + 2897422893 q^{12} + 5215478294 q^{13} + 1458494653 q^{14} - 5948609382 q^{15} + 62775861505 q^{16} + 25747891566 q^{17} - 10890820413 q^{18} + 142208068556 q^{19} - 129890562778 q^{20} - 189114296805 q^{21} - 448421189252 q^{22} - 700488736068 q^{23} - 1195667789211 q^{24} + 1178351016379 q^{25} + 2889360071546 q^{26} + 1412147682405 q^{27} - 2545811064013 q^{28} - 3529421241410 q^{29} + 7834213238922 q^{30} + 1688850702072 q^{31} - 17321396050955 q^{32} + 7291493446896 q^{33} + 40556147819358 q^{34} + 5226726004262 q^{35} + 19009991600973 q^{36} + 16886745594894 q^{37} - 20515887907732 q^{38} + 34218753086934 q^{39} + 320653834434294 q^{40} + 58103631330302 q^{41} + 9569183418333 q^{42} + 49458422903068 q^{43} + 401313211061300 q^{44} - 39028826155302 q^{45} + 325662527133360 q^{46} + 321151801515192 q^{47} + 411872427334305 q^{48} + 166164652848005 q^{49} - 130885367368259 q^{50} + 168931916564526 q^{51} - 447415499102234 q^{52} + 16\!\cdots\!54 q^{53}+ \cdots + 47\!\cdots\!56 q^{99}+O(q^{100}) \) 5 * q - 253 * q^2 + 32805 * q^3 + 441613 * q^4 - 906662 * q^5 - 1659933 * q^6 - 28824005 * q^7 - 182238651 * q^8 + 215233605 * q^9 + 1194057802 * q^10 + 1111338736 * q^11 + 2897422893 * q^12 + 5215478294 * q^13 + 1458494653 * q^14 - 5948609382 * q^15 + 62775861505 * q^16 + 25747891566 * q^17 - 10890820413 * q^18 + 142208068556 * q^19 - 129890562778 * q^20 - 189114296805 * q^21 - 448421189252 * q^22 - 700488736068 * q^23 - 1195667789211 * q^24 + 1178351016379 * q^25 + 2889360071546 * q^26 + 1412147682405 * q^27 - 2545811064013 * q^28 - 3529421241410 * q^29 + 7834213238922 * q^30 + 1688850702072 * q^31 - 17321396050955 * q^32 + 7291493446896 * q^33 + 40556147819358 * q^34 + 5226726004262 * q^35 + 19009991600973 * q^36 + 16886745594894 * q^37 - 20515887907732 * q^38 + 34218753086934 * q^39 + 320653834434294 * q^40 + 58103631330302 * q^41 + 9569183418333 * q^42 + 49458422903068 * q^43 + 401313211061300 * q^44 - 39028826155302 * q^45 + 325662527133360 * q^46 + 321151801515192 * q^47 + 411872427334305 * q^48 + 166164652848005 * q^49 - 130885367368259 * q^50 + 168931916564526 * q^51 - 447415499102234 * q^52 + 1624886228519454 * q^53 - 71454672729693 * q^54 + 1551981825532832 * q^55 + 1050569557523451 * q^56 + 933027137795916 * q^57 + 3599479065043546 * q^58 + 4642231410191796 * q^59 - 852211982386458 * q^60 + 383521828948430 * q^61 + 3303800808324960 * q^62 - 1240778901337605 * q^63 + 7678662933303305 * q^64 + 1668701347292044 * q^65 - 2942091422682372 * q^66 - 4060475251851460 * q^67 - 16890755118576270 * q^68 - 4595906597342148 * q^69 - 6883505611027402 * q^70 + 6398015136563460 * q^71 - 7844776365013371 * q^72 - 15734132975098902 * q^73 - 25189581013328238 * q^74 + 7731161018462619 * q^75 - 14323380376996940 * q^76 - 6406646656631536 * q^77 + 18957091429413306 * q^78 + 2199683795891080 * q^79 - 115762642448214658 * q^80 + 9265100944259205 * q^81 - 6015570522729706 * q^82 + 23947511376405780 * q^83 - 16703066390989293 * q^84 + 21310596918487932 * q^85 - 3933835697843468 * q^86 - 23156532764891010 * q^87 - 87148613365646124 * q^88 - 12131366869070066 * q^89 + 51400273060567242 * q^90 - 30066194484729494 * q^91 - 198814114679296704 * q^92 + 11080549456294392 * q^93 + 14990206001176800 * q^94 - 239731994312770088 * q^95 - 113645679490315755 * q^96 + 4112564616338706 * q^97 - 8407931434109053 * q^98 + 47839488505084656 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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