LMFDB - Embedded newform 21.18.a.d.1.1

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			1.1
Root			$-658.650$ 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)

$f(q)$	$=$	$q-709.650 q^{2} +6561.00 q^{3} +372531. q^{4} -1.31505e6 q^{5} -4.65601e6 q^{6} -5.76480e6 q^{7} -1.71351e8 q^{8} +4.30467e7 q^{9} +O(q^{10})$	\(q-709.650 q^{2} +6561.00 q^{3} +372531. q^{4} -1.31505e6 q^{5} -4.65601e6 q^{6} -5.76480e6 q^{7} -1.71351e8 q^{8} +4.30467e7 q^{9} +9.33224e8 q^{10} +7.09802e8 q^{11} +2.44417e9 q^{12} -3.34343e9 q^{13} +4.09099e9 q^{14} -8.62804e9 q^{15} +7.27708e10 q^{16} -3.89845e10 q^{17} -3.05481e10 q^{18} +5.37884e10 q^{19} -4.89896e11 q^{20} -3.78229e10 q^{21} -5.03711e11 q^{22} -4.45041e11 q^{23} -1.12423e12 q^{24} +9.66414e11 q^{25} +2.37266e12 q^{26} +2.82430e11 q^{27} -2.14756e12 q^{28} -3.25985e12 q^{29} +6.12288e12 q^{30} -9.89984e10 q^{31} -2.91825e13 q^{32} +4.65701e12 q^{33} +2.76653e13 q^{34} +7.58100e12 q^{35} +1.60362e13 q^{36} -1.33773e13 q^{37} -3.81709e13 q^{38} -2.19362e13 q^{39} +2.25335e14 q^{40} +2.18414e13 q^{41} +2.68410e13 q^{42} -4.29370e13 q^{43} +2.64423e14 q^{44} -5.66085e13 q^{45} +3.15823e14 q^{46} -9.94703e13 q^{47} +4.77449e14 q^{48} +3.32329e13 q^{49} -6.85815e14 q^{50} -2.55777e14 q^{51} -1.24553e15 q^{52} +4.58643e14 q^{53} -2.00426e14 q^{54} -9.33425e14 q^{55} +9.87804e14 q^{56} +3.52906e14 q^{57} +2.31335e15 q^{58} +1.36981e15 q^{59} -3.21421e15 q^{60} +2.32347e14 q^{61} +7.02542e13 q^{62} -2.48156e14 q^{63} +1.11711e16 q^{64} +4.39677e15 q^{65} -3.30485e15 q^{66} +4.61272e14 q^{67} -1.45229e16 q^{68} -2.91991e15 q^{69} -5.37985e15 q^{70} +3.27411e15 q^{71} -7.37610e15 q^{72} +3.54172e15 q^{73} +9.49317e15 q^{74} +6.34064e15 q^{75} +2.00378e16 q^{76} -4.09187e15 q^{77} +1.55670e16 q^{78} +1.17172e16 q^{79} -9.56972e16 q^{80} +1.85302e15 q^{81} -1.54997e16 q^{82} +1.42944e16 q^{83} -1.40902e16 q^{84} +5.12665e16 q^{85} +3.04702e16 q^{86} -2.13879e16 q^{87} -1.21625e17 q^{88} +1.04458e16 q^{89} +4.01722e16 q^{90} +1.92742e16 q^{91} -1.65791e17 q^{92} -6.49529e14 q^{93} +7.05891e16 q^{94} -7.07344e16 q^{95} -1.91466e17 q^{96} +3.23350e16 q^{97} -2.35837e16 q^{98} +3.05547e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−709.650	−1.96015	−0.980074	−	0.198631i	$-0.936350\pi$
$2$	−709.650	−1.96015	−0.980074	+	0.198631i	$0.936350\pi$
$3$	6561.00	0.577350
$3$	6561.00	0.577350
$4$	372531.	2.84218
$5$	−1.31505e6	−1.50556	−0.752778	−	0.658275i	$-0.771287\pi$
$5$	−1.31505e6	−1.50556	−0.752778	+	0.658275i	$0.771287\pi$
$6$	−4.65601e6	−1.13169
$7$	−5.76480e6	−0.377964
$7$	−5.76480e6	−0.377964
$8$	−1.71351e8	−3.61095
$9$	4.30467e7	0.333333
$10$	9.33224e8	2.95111
$11$	7.09802e8	0.998389	0.499194	−	0.866490i	$-0.333629\pi$
$11$	7.09802e8	0.998389	0.499194	+	0.866490i	$0.333629\pi$
$12$	2.44417e9	1.64093
$13$	−3.34343e9	−1.13677	−0.568386	−	0.822762i	$-0.692432\pi$
$13$	−3.34343e9	−1.13677	−0.568386	+	0.822762i	$0.692432\pi$
$14$	4.09099e9	0.740867
$15$	−8.62804e9	−0.869233
$16$	7.27708e10	4.23582
$17$	−3.89845e10	−1.35543	−0.677714	−	0.735326i	$-0.737029\pi$
$17$	−3.89845e10	−1.35543	−0.677714	+	0.735326i	$0.737029\pi$
$18$	−3.05481e10	−0.653383
$19$	5.37884e10	0.726579	0.363290	−	0.931676i	$-0.381654\pi$
$19$	5.37884e10	0.726579	0.363290	+	0.931676i	$0.381654\pi$
$20$	−4.89896e11	−4.27906
$21$	−3.78229e10	−0.218218
$22$	−5.03711e11	−1.95699
$23$	−4.45041e11	−1.18499	−0.592493	−	0.805576i	$-0.701856\pi$
$23$	−4.45041e11	−1.18499	−0.592493	+	0.805576i	$0.701856\pi$
$24$	−1.12423e12	−2.08478
$25$	9.66414e11	1.26670
$26$	2.37266e12	2.22824
$27$	2.82430e11	0.192450
$28$	−2.14756e12	−1.07424
$29$	−3.25985e12	−1.21008	−0.605041	−	0.796194i	$-0.706843\pi$
$29$	−3.25985e12	−1.21008	−0.605041	+	0.796194i	$0.706843\pi$
$30$	6.12288e12	1.70383
$31$	−9.89984e10	−0.0208475	−0.0104238	−	0.999946i	$-0.503318\pi$
$31$	−9.89984e10	−0.0208475	−0.0104238	+	0.999946i	$0.503318\pi$
$32$	−2.91825e13	−4.69188
$33$	4.65701e12	0.576420
$34$	2.76653e13	2.65684
$35$	7.58100e12	0.569047
$36$	1.60362e13	0.947394
$37$	−1.33773e13	−0.626113	−0.313056	−	0.949735i	$-0.601353\pi$
$37$	−1.33773e13	−0.626113	−0.313056	+	0.949735i	$0.601353\pi$
$38$	−3.81709e13	−1.42420
$39$	−2.19362e13	−0.656316
$40$	2.25335e14	5.43649
$41$	2.18414e13	0.427187	0.213593	−	0.976923i	$-0.431483\pi$
$41$	2.18414e13	0.427187	0.213593	+	0.976923i	$0.431483\pi$
$42$	2.68410e13	0.427739
$43$	−4.29370e13	−0.560208	−0.280104	−	0.959970i	$-0.590369\pi$
$43$	−4.29370e13	−0.560208	−0.280104	+	0.959970i	$0.590369\pi$
$44$	2.64423e14	2.83760
$45$	−5.66085e13	−0.501852
$46$	3.15823e14	2.32275
$47$	−9.94703e13	−0.609343	−0.304671	−	0.952458i	$-0.598547\pi$
$47$	−9.94703e13	−0.609343	−0.304671	+	0.952458i	$0.598547\pi$
$48$	4.77449e14	2.44555
$49$	3.32329e13	0.142857
$50$	−6.85815e14	−2.48292
$51$	−2.55777e14	−0.782556
$52$	−1.24553e15	−3.23092
$53$	4.58643e14	1.01188	0.505941	−	0.862568i	$-0.331145\pi$
$53$	4.58643e14	1.01188	0.505941	+	0.862568i	$0.331145\pi$
$54$	−2.00426e14	−0.377231
$55$	−9.33425e14	−1.50313
$56$	9.87804e14	1.36481
$57$	3.52906e14	0.419491
$58$	2.31335e15	2.37194
$59$	1.36981e15	1.21456	0.607281	−	0.794487i	$-0.292260\pi$
$59$	1.36981e15	1.21456	0.607281	+	0.794487i	$0.292260\pi$
$60$	−3.21421e15	−2.47052
$61$	2.32347e14	0.155179	0.0775896	−	0.996985i	$-0.475278\pi$
$61$	2.32347e14	0.155179	0.0775896	+	0.996985i	$0.475278\pi$
$62$	7.02542e13	0.0408642
$63$	−2.48156e14	−0.125988
$64$	1.11711e16	4.96097
$65$	4.39677e15	1.71147
$66$	−3.30485e15	−1.12987
$67$	4.61272e14	0.138778	0.0693891	−	0.997590i	$-0.477895\pi$
$67$	4.61272e14	0.138778	0.0693891	+	0.997590i	$0.477895\pi$
$68$	−1.45229e16	−3.85237
$69$	−2.91991e15	−0.684152
$70$	−5.37985e15	−1.11542
$71$	3.27411e15	0.601724	0.300862	−	0.953668i	$-0.402726\pi$
$71$	3.27411e15	0.601724	0.300862	+	0.953668i	$0.402726\pi$
$72$	−7.37610e15	−1.20365
$73$	3.54172e15	0.514008	0.257004	−	0.966410i	$-0.417265\pi$
$73$	3.54172e15	0.514008	0.257004	+	0.966410i	$0.417265\pi$
$74$	9.49317e15	1.22727
$75$	6.34064e15	0.731329
$76$	2.00378e16	2.06507
$77$	−4.09187e15	−0.377355
$78$	1.55670e16	1.28648
$79$	1.17172e16	0.868947	0.434473	−	0.900685i	$-0.356934\pi$
$79$	1.17172e16	0.868947	0.434473	+	0.900685i	$0.356934\pi$
$80$	−9.56972e16	−6.37726
$81$	1.85302e15	0.111111
$82$	−1.54997e16	−0.837350
$83$	1.42944e16	0.696629	0.348315	−	0.937378i	$-0.386754\pi$
$83$	1.42944e16	0.696629	0.348315	+	0.937378i	$0.386754\pi$
$84$	−1.40902e16	−0.620215
$85$	5.12665e16	2.04067
$86$	3.04702e16	1.09809
$87$	−2.13879e16	−0.698641
$88$	−1.21625e17	−3.60513
$89$	1.04458e16	0.281271	0.140635	−	0.990061i	$-0.455085\pi$
$89$	1.04458e16	0.281271	0.140635	+	0.990061i	$0.455085\pi$
$90$	4.01722e16	0.983704
$91$	1.92742e16	0.429660
$92$	−1.65791e17	−3.36795
$93$	−6.49529e14	−0.0120363
$94$	7.05891e16	1.19440
$95$	−7.07344e16	−1.09391
$96$	−1.91466e17	−2.70886
$97$	3.23350e16	0.418903	0.209452	−	0.977819i	$-0.432832\pi$
$97$	3.23350e16	0.418903	0.209452	+	0.977819i	$0.432832\pi$
$98$	−2.35837e16	−0.280021
$99$	3.05547e16	0.332796
$100$	3.60019e17	3.60019
$101$	−1.04483e17	−0.960097	−0.480048	−	0.877242i	$-0.659381\pi$
$101$	−1.04483e17	−0.960097	−0.480048	+	0.877242i	$0.659381\pi$
$102$	1.81512e17	1.53393
$103$	−4.70064e16	−0.365629	−0.182815	−	0.983147i	$-0.558521\pi$
$103$	−4.70064e16	−0.365629	−0.182815	+	0.983147i	$0.558521\pi$
$104$	5.72900e17	4.10483
$105$	4.97389e16	0.328539
$106$	−3.25476e17	−1.98344
$107$	3.11125e17	1.75054	0.875271	−	0.483633i	$-0.160683\pi$
$107$	3.11125e17	1.75054	0.875271	+	0.483633i	$0.160683\pi$
$108$	1.05214e17	0.546978
$109$	4.34709e16	0.208965	0.104483	−	0.994527i	$-0.466681\pi$
$109$	4.34709e16	0.208965	0.104483	+	0.994527i	$0.466681\pi$
$110$	6.62405e17	2.94636
$111$	−8.77682e16	−0.361486
$112$	−4.19509e17	−1.60099
$113$	4.21097e17	1.49010	0.745051	−	0.667008i	$-0.232425\pi$
$113$	4.21097e17	1.49010	0.745051	+	0.667008i	$0.232425\pi$
$114$	−2.50439e17	−0.822264
$115$	5.85250e17	1.78406
$116$	−1.21439e18	−3.43927
$117$	−1.43924e17	−0.378924
$118$	−9.72088e17	−2.38072
$119$	2.24738e17	0.512303
$120$	1.47842e18	3.13876
$121$	−1.62753e15	−0.00321998
$122$	−1.64885e17	−0.304174
$123$	1.43301e17	0.246636
$124$	−3.68799e16	−0.0592524
$125$	−2.67579e17	−0.401529
$126$	1.76104e17	0.246956
$127$	7.57737e17	0.993544	0.496772	−	0.867881i	$-0.334519\pi$
$127$	7.57737e17	0.993544	0.496772	+	0.867881i	$0.334519\pi$
$128$	−4.10257e18	−5.03235
$129$	−2.81709e17	−0.323436
$130$	−3.12017e18	−3.35474
$131$	−8.90186e17	−0.896757	−0.448378	−	0.893844i	$-0.647998\pi$
$131$	−8.90186e17	−0.896757	−0.448378	+	0.893844i	$0.647998\pi$
$132$	1.73488e18	1.63829
$133$	−3.10079e17	−0.274621
$134$	−3.27341e17	−0.272026
$135$	−3.71409e17	−0.289744
$136$	6.68003e18	4.89438
$137$	2.11172e18	1.45382	0.726912	−	0.686730i	$-0.240955\pi$
$137$	2.11172e18	1.45382	0.726912	+	0.686730i	$0.240955\pi$
$138$	2.07211e18	1.34104
$139$	−3.04391e18	−1.85270	−0.926352	−	0.376660i	$-0.877073\pi$
$139$	−3.04391e18	−1.85270	−0.926352	+	0.376660i	$0.877073\pi$
$140$	2.82415e18	1.61733
$141$	−6.52625e17	−0.351804
$142$	−2.32347e18	−1.17947
$143$	−2.37317e18	−1.13494
$144$	3.13254e18	1.41194
$145$	4.28687e18	1.82185
$146$	−2.51338e18	−1.00753
$147$	2.18041e17	0.0824786
$148$	−4.98344e18	−1.77953
$149$	3.84925e18	1.29805	0.649027	−	0.760766i	$-0.275176\pi$
$149$	3.84925e18	1.29805	0.649027	+	0.760766i	$0.275176\pi$
$150$	−4.49963e18	−1.43351
$151$	−4.46007e18	−1.34288	−0.671441	−	0.741058i	$-0.734324\pi$
$151$	−4.46007e18	−1.34288	−0.671441	+	0.741058i	$0.734324\pi$
$152$	−9.21669e18	−2.62364
$153$	−1.67816e18	−0.451809
$154$	2.90379e18	0.739673
$155$	1.30188e17	0.0313871
$156$	−8.17192e18	−1.86537
$157$	4.88978e18	1.05716	0.528582	−	0.848882i	$-0.322724\pi$
$157$	4.88978e18	1.05716	0.528582	+	0.848882i	$0.322724\pi$
$158$	−8.31510e18	−1.70327
$159$	3.00916e18	0.584210
$160$	3.83764e19	7.06389
$161$	2.56557e18	0.447882
$162$	−1.31499e18	−0.217794
$163$	−1.44995e18	−0.227908	−0.113954	−	0.993486i	$-0.536352\pi$
$163$	−1.44995e18	−0.227908	−0.113954	+	0.993486i	$0.536352\pi$
$164$	8.13659e18	1.21414
$165$	−6.12420e18	−0.867832
$166$	−1.01440e19	−1.36550
$167$	−3.94593e18	−0.504731	−0.252365	−	0.967632i	$-0.581208\pi$
$167$	−3.94593e18	−0.504731	−0.252365	+	0.967632i	$0.581208\pi$
$168$	6.48098e18	0.787974
$169$	2.52810e18	0.292252
$170$	−3.63813e19	−4.00002
$171$	2.31541e18	0.242193
$172$	−1.59953e19	−1.59221
$173$	−2.66187e18	−0.252229	−0.126115	−	0.992016i	$-0.540251\pi$
$173$	−2.66187e18	−0.252229	−0.126115	+	0.992016i	$0.540251\pi$
$174$	1.51779e19	1.36944
$175$	−5.57119e18	−0.478767
$176$	5.16529e19	4.22899
$177$	8.98735e18	0.701228
$178$	−7.41283e18	−0.551333
$179$	−1.91064e19	−1.35496	−0.677481	−	0.735540i	$-0.736929\pi$
$179$	−1.91064e19	−1.35496	−0.677481	+	0.735540i	$0.736929\pi$
$180$	−2.10884e19	−1.42635
$181$	−9.51107e18	−0.613707	−0.306854	−	0.951757i	$-0.599276\pi$
$181$	−9.51107e18	−0.613707	−0.306854	+	0.951757i	$0.599276\pi$
$182$	−1.36779e19	−0.842197
$183$	1.52443e18	0.0895927
$184$	7.62581e19	4.27893
$185$	1.75918e19	0.942648
$186$	4.60938e17	0.0235930
$187$	−2.76713e19	−1.35324
$188$	−3.70557e19	−1.73186
$189$	−1.62815e18	−0.0727393
$190$	5.01966e19	2.14422
$191$	4.26691e19	1.74313	0.871566	−	0.490278i	$-0.163105\pi$
$191$	4.26691e19	1.74313	0.871566	+	0.490278i	$0.163105\pi$
$192$	7.32936e19	2.86422
$193$	3.25397e19	1.21668	0.608339	−	0.793677i	$-0.291836\pi$
$193$	3.25397e19	1.21668	0.608339	+	0.793677i	$0.291836\pi$
$194$	−2.29466e19	−0.821113
$195$	2.88472e19	0.988120
$196$	1.23803e19	0.406026
$197$	−6.46054e17	−0.0202911	−0.0101456	−	0.999949i	$-0.503229\pi$
$197$	−6.46054e17	−0.0202911	−0.0101456	+	0.999949i	$0.503229\pi$
$198$	−2.16831e19	−0.652330
$199$	−8.34990e18	−0.240674	−0.120337	−	0.992733i	$-0.538398\pi$
$199$	−8.34990e18	−0.240674	−0.120337	+	0.992733i	$0.538398\pi$
$200$	−1.65596e20	−4.57399
$201$	3.02640e18	0.0801236
$202$	7.41465e19	1.88193
$203$	1.87924e19	0.457368
$204$	−9.52849e19	−2.22417
$205$	−2.87225e19	−0.643154
$206$	3.33581e19	0.716688
$207$	−1.91575e19	−0.394995
$208$	−2.43304e20	−4.81516
$209$	3.81791e19	0.725408
$210$	−3.52972e19	−0.643986
$211$	−6.36935e19	−1.11608	−0.558039	−	0.829815i	$-0.688446\pi$
$211$	−6.36935e19	−1.11608	−0.558039	+	0.829815i	$0.688446\pi$
$212$	1.70858e20	2.87595
$213$	2.14814e19	0.347405
$214$	−2.20790e20	−3.43132
$215$	5.64642e19	0.843425
$216$	−4.83946e19	−0.694928
$217$	5.70706e17	0.00787961
$218$	−3.08491e19	−0.409603
$219$	2.32372e19	0.296763
$220$	−3.47729e20	−4.27217
$221$	1.30342e20	1.54081
$222$	6.22847e19	0.708567
$223$	1.77854e20	1.94748	0.973741	−	0.227660i	$-0.0731073\pi$
$223$	1.77854e20	1.94748	0.973741	+	0.227660i	$0.0731073\pi$
$224$	1.68231e20	1.77336
$225$	4.16010e19	0.422233
$226$	−2.98832e20	−2.92082
$227$	1.53025e20	1.44059	0.720296	−	0.693666i	$-0.244006\pi$
$227$	1.53025e20	1.44059	0.720296	+	0.693666i	$0.244006\pi$
$228$	1.31468e20	1.19227
$229$	8.17318e19	0.714150	0.357075	−	0.934076i	$-0.383774\pi$
$229$	8.17318e19	0.714150	0.357075	+	0.934076i	$0.383774\pi$
$230$	−4.15323e20	−3.49703
$231$	−2.68468e19	−0.217866
$232$	5.58579e20	4.36955
$233$	1.15470e20	0.870851	0.435425	−	0.900225i	$-0.356598\pi$
$233$	1.15470e20	0.870851	0.435425	+	0.900225i	$0.356598\pi$
$234$	1.02135e20	0.742748
$235$	1.30808e20	0.917399
$236$	5.10298e20	3.45201
$237$	7.68765e19	0.501687
$238$	−1.59485e20	−1.00419
$239$	−2.82617e20	−1.71718	−0.858591	−	0.512661i	$-0.828660\pi$
$239$	−2.82617e20	−1.71718	−0.858591	+	0.512661i	$0.828660\pi$
$240$	−6.27869e20	−3.68191
$241$	1.75484e20	0.993326	0.496663	−	0.867943i	$-0.334558\pi$
$241$	1.75484e20	0.993326	0.496663	+	0.867943i	$0.334558\pi$
$242$	1.15497e18	0.00631163
$243$	1.21577e19	0.0641500
$244$	8.65563e19	0.441047
$245$	−4.37029e19	−0.215079
$246$	−1.01694e20	−0.483444
$247$	−1.79838e20	−0.825955
$248$	1.69635e19	0.0752793
$249$	9.37855e19	0.402199
$250$	1.89887e20	0.787057
$251$	2.12498e19	0.0851391	0.0425695	−	0.999094i	$-0.486446\pi$
$251$	2.12498e19	0.0851391	0.0425695	+	0.999094i	$0.486446\pi$
$252$	−9.24456e19	−0.358081
$253$	−3.15891e20	−1.18308
$254$	−5.37728e20	−1.94749
$255$	3.36360e20	1.17818
$256$	1.44717e21	4.90319
$257$	−5.46763e20	−1.79212	−0.896062	−	0.443929i	$-0.853584\pi$
$257$	−5.46763e20	−1.79212	−0.896062	+	0.443929i	$0.853584\pi$
$258$	1.99915e20	0.633983
$259$	7.71173e19	0.236648
$260$	1.63793e21	4.86432
$261$	−1.40326e20	−0.403361
$262$	6.31720e20	1.75778
$263$	−2.38442e20	−0.642330	−0.321165	−	0.947023i	$-0.604074\pi$
$263$	−2.38442e20	−0.642330	−0.321165	+	0.947023i	$0.604074\pi$
$264$	−7.97984e20	−2.08142
$265$	−6.03138e20	−1.52344
$266$	2.20048e20	0.538298
$267$	6.85346e19	0.162392
$268$	1.71838e20	0.394433
$269$	−4.55785e20	−1.01360	−0.506798	−	0.862065i	$-0.669171\pi$
$269$	−4.55785e20	−1.01360	−0.506798	+	0.862065i	$0.669171\pi$
$270$	2.63570e20	0.567942
$271$	−4.90898e20	−1.02507	−0.512534	−	0.858667i	$-0.671293\pi$
$271$	−4.90898e20	−1.02507	−0.512534	+	0.858667i	$0.671293\pi$
$272$	−2.83693e21	−5.74134
$273$	1.26458e20	0.248064
$274$	−1.49858e21	−2.84971
$275$	6.85963e20	1.26466
$276$	−1.08776e21	−1.94448
$277$	7.90505e19	0.137033	0.0685167	−	0.997650i	$-0.478173\pi$
$277$	7.90505e19	0.137033	0.0685167	+	0.997650i	$0.478173\pi$
$278$	2.16011e21	3.63157
$279$	−4.26156e18	−0.00694917
$280$	−1.29901e21	−2.05480
$281$	7.88426e20	1.20992	0.604960	−	0.796255i	$-0.293189\pi$
$281$	7.88426e20	1.20992	0.604960	+	0.796255i	$0.293189\pi$
$282$	4.63135e20	0.689588
$283$	−3.18868e20	−0.460709	−0.230354	−	0.973107i	$-0.573989\pi$
$283$	−3.18868e20	−0.460709	−0.230354	+	0.973107i	$0.573989\pi$
$284$	1.21971e21	1.71021
$285$	−4.64088e20	−0.631567
$286$	1.68412e21	2.22465
$287$	−1.25911e20	−0.161461
$288$	−1.25621e21	−1.56396
$289$	6.92551e20	0.837183
$290$	−3.04217e21	−3.57109
$291$	2.12150e20	0.241854
$292$	1.31940e21	1.46091
$293$	−1.22458e21	−1.31709	−0.658543	−	0.752543i	$-0.728827\pi$
$293$	−1.22458e21	−1.31709	−0.658543	+	0.752543i	$0.728827\pi$
$294$	−1.54733e20	−0.161670
$295$	−1.80137e21	−1.82859
$296$	2.29221e21	2.26086
$297$	2.00469e20	0.192140
$298$	−2.73162e21	−2.54438
$299$	1.48796e21	1.34706
$300$	2.36208e21	2.07857
$301$	2.47523e20	0.211739
$302$	3.16509e21	2.63225
$303$	−6.85514e20	−0.554312
$304$	3.91422e21	3.07766
$305$	−3.05548e20	−0.233631
$306$	1.19090e21	0.885613
$307$	−2.03078e21	−1.46888	−0.734440	−	0.678674i	$-0.762555\pi$
$307$	−2.03078e21	−1.46888	−0.734440	+	0.678674i	$0.762555\pi$
$308$	−1.52435e21	−1.07251
$309$	−3.08409e20	−0.211096
$310$	−9.23877e19	−0.0615233
$311$	6.75731e20	0.437835	0.218917	−	0.975743i	$-0.429747\pi$
$311$	6.75731e20	0.437835	0.218917	+	0.975743i	$0.429747\pi$
$312$	3.75879e21	2.36992
$313$	−1.46148e21	−0.896739	−0.448369	−	0.893848i	$-0.647995\pi$
$313$	−1.46148e21	−0.896739	−0.448369	+	0.893848i	$0.647995\pi$
$314$	−3.47003e21	−2.07220
$315$	3.26337e20	0.189682
$316$	4.36501e21	2.46971
$317$	2.86207e21	1.57644	0.788219	−	0.615395i	$-0.211003\pi$
$317$	2.86207e21	1.57644	0.788219	+	0.615395i	$0.211003\pi$
$318$	−2.13545e21	−1.14514
$319$	−2.31385e21	−1.20813
$320$	−1.46905e22	−7.46901
$321$	2.04129e21	1.01068
$322$	−1.82066e21	−0.877916
$323$	−2.09691e21	−0.984825
$324$	6.90307e20	0.315798
$325$	−3.23114e21	−1.43995
$326$	1.02896e21	0.446733
$327$	2.85213e20	0.120646
$328$	−3.74255e21	−1.54255
$329$	5.73426e20	0.230310
$330$	4.34604e21	1.70108
$331$	−1.60404e21	−0.611895	−0.305948	−	0.952048i	$-0.598973\pi$
$331$	−1.60404e21	−0.611895	−0.305948	+	0.952048i	$0.598973\pi$
$332$	5.32510e21	1.97995
$333$	−5.75847e20	−0.208704
$334$	2.80023e21	0.989347
$335$	−6.06595e20	−0.208938
$336$	−2.75240e21	−0.924331
$337$	1.94260e21	0.636106	0.318053	−	0.948073i	$-0.396971\pi$
$337$	1.94260e21	0.636106	0.318053	+	0.948073i	$0.396971\pi$
$338$	−1.79407e21	−0.572858
$339$	2.76282e21	0.860310
$340$	1.90983e22	5.79996
$341$	−7.02693e19	−0.0208139
$342$	−1.64313e21	−0.474734
$343$	−1.91581e20	−0.0539949
$344$	7.35729e21	2.02288
$345$	3.83983e21	1.03003
$346$	1.88900e21	0.494406
$347$	6.00428e21	1.53342	0.766708	−	0.641996i	$-0.221893\pi$
$347$	6.00428e21	1.53342	0.766708	+	0.641996i	$0.221893\pi$
$348$	−7.96764e21	−1.98567
$349$	6.16401e21	1.49916	0.749578	−	0.661916i	$-0.230256\pi$
$349$	6.16401e21	1.49916	0.749578	+	0.661916i	$0.230256\pi$
$350$	3.95359e21	0.938454
$351$	−9.44283e20	−0.218772
$352$	−2.07138e22	−4.68432
$353$	−4.57956e21	−1.01097	−0.505486	−	0.862835i	$-0.668687\pi$
$353$	−4.57956e21	−1.01097	−0.505486	+	0.862835i	$0.668687\pi$
$354$	−6.37787e21	−1.37451
$355$	−4.30561e21	−0.905929
$356$	3.89136e21	0.799423
$357$	1.47451e21	0.295778
$358$	1.35588e22	2.65593
$359$	−7.07727e20	−0.135383	−0.0676913	−	0.997706i	$-0.521563\pi$
$359$	−7.07727e20	−0.135383	−0.0676913	+	0.997706i	$0.521563\pi$
$360$	9.69993e21	1.81216
$361$	−2.58720e21	−0.472083
$362$	6.74952e21	1.20296
$363$	−1.06782e19	−0.00185905
$364$	7.18023e21	1.22117
$365$	−4.65754e21	−0.773868
$366$	−1.08181e21	−0.175615
$367$	−2.02746e21	−0.321581	−0.160790	−	0.986989i	$-0.551404\pi$
$367$	−2.02746e21	−0.321581	−0.160790	+	0.986989i	$0.551404\pi$
$368$	−3.23860e22	−5.01938
$369$	9.40201e20	0.142396
$370$	−1.24840e22	−1.84773
$371$	−2.64399e21	−0.382455
$372$	−2.41969e20	−0.0342094
$373$	−6.44473e21	−0.890594	−0.445297	−	0.895383i	$-0.646902\pi$
$373$	−6.44473e21	−0.890594	−0.445297	+	0.895383i	$0.646902\pi$
$374$	1.96369e22	2.65256
$375$	−1.75559e21	−0.231823
$376$	1.70443e22	2.20031
$377$	1.08991e22	1.37559
$378$	1.15542e21	0.142580
$379$	7.50017e20	0.0904978	0.0452489	−	0.998976i	$-0.485592\pi$
$379$	7.50017e20	0.0904978	0.0452489	+	0.998976i	$0.485592\pi$
$380$	−2.63507e22	−3.10908
$381$	4.97151e21	0.573623
$382$	−3.02801e22	−3.41680
$383$	9.71613e21	1.07227	0.536134	−	0.844133i	$-0.319884\pi$
$383$	9.71613e21	1.07227	0.536134	+	0.844133i	$0.319884\pi$
$384$	−2.69169e22	−2.90543
$385$	5.38101e21	0.568130
$386$	−2.30918e22	−2.38487
$387$	−1.84830e21	−0.186736
$388$	1.20458e22	1.19060
$389$	1.53024e22	1.47975	0.739875	−	0.672744i	$-0.234885\pi$
$389$	1.53024e22	1.47975	0.739875	+	0.672744i	$0.234885\pi$
$390$	−2.04714e22	−1.93686
$391$	1.73497e22	1.60616
$392$	−5.69449e21	−0.515850
$393$	−5.84051e21	−0.517743
$394$	4.58472e20	0.0397736
$395$	−1.54087e22	−1.30825
$396$	1.13825e22	0.945868
$397$	−9.93985e21	−0.808464	−0.404232	−	0.914657i	$-0.632461\pi$
$397$	−9.93985e21	−0.808464	−0.404232	+	0.914657i	$0.632461\pi$
$398$	5.92550e21	0.471758
$399$	−2.03443e21	−0.158553
$400$	7.03267e22	5.36550
$401$	−6.58497e21	−0.491843	−0.245922	−	0.969290i	$-0.579091\pi$
$401$	−6.58497e21	−0.491843	−0.245922	+	0.969290i	$0.579091\pi$
$402$	−2.14769e21	−0.157054
$403$	3.30994e20	0.0236989
$404$	−3.89232e22	−2.72877
$405$	−2.43681e21	−0.167284
$406$	−1.33360e22	−0.896510
$407$	−9.49521e21	−0.625104
$408$	4.38277e22	2.82577
$409$	−5.74377e19	−0.00362701	−0.00181350	−	0.999998i	$-0.500577\pi$
$409$	−5.74377e19	−0.00362701	−0.00181350	+	0.999998i	$0.500577\pi$
$410$	2.03829e22	1.26068
$411$	1.38550e22	0.839366
$412$	−1.75113e22	−1.03919
$413$	−7.89671e21	−0.459061
$414$	1.35951e22	0.774249
$415$	−1.87978e22	−1.04881
$416$	9.75695e22	5.33360
$417$	−1.99711e22	−1.06966
$418$	−2.70938e22	−1.42191
$419$	−1.71702e22	−0.882990	−0.441495	−	0.897264i	$-0.645552\pi$
$419$	−1.71702e22	−0.882990	−0.441495	+	0.897264i	$0.645552\pi$
$420$	1.85293e22	0.933768
$421$	1.52694e22	0.754091	0.377045	−	0.926195i	$-0.376940\pi$
$421$	1.52694e22	0.754091	0.377045	+	0.926195i	$0.376940\pi$
$422$	4.52001e22	2.18768
$423$	−4.28187e21	−0.203114
$424$	−7.85889e22	−3.65386
$425$	−3.76752e22	−1.71692
$426$	−1.52443e22	−0.680966
$427$	−1.33943e21	−0.0586522
$428$	1.15903e23	4.97536
$429$	−1.55704e22	−0.655259
$430$	−4.00698e22	−1.65324
$431$	2.06204e22	0.834143	0.417072	−	0.908874i	$-0.363056\pi$
$431$	2.06204e22	0.834143	0.417072	+	0.908874i	$0.363056\pi$
$432$	2.05526e22	0.815184
$433$	2.90774e22	1.13086	0.565430	−	0.824797i	$-0.308710\pi$
$433$	2.90774e22	1.13086	0.565430	+	0.824797i	$0.308710\pi$
$434$	−4.05002e20	−0.0154452
$435$	2.81261e22	1.05184
$436$	1.61942e22	0.593917
$437$	−2.39380e22	−0.860986
$438$	−1.64903e22	−0.581699
$439$	4.31313e22	1.49226	0.746129	−	0.665802i	$-0.231910\pi$
$439$	4.31313e22	1.49226	0.746129	+	0.665802i	$0.231910\pi$
$440$	1.59943e23	5.42773
$441$	1.43057e21	0.0476190
$442$	−9.24971e22	−3.02022
$443$	4.15467e22	1.33078	0.665388	−	0.746497i	$-0.268266\pi$
$443$	4.15467e22	1.33078	0.665388	+	0.746497i	$0.268266\pi$
$444$	−3.26963e22	−1.02741
$445$	−1.37367e22	−0.423469
$446$	−1.26214e23	−3.81735
$447$	2.52549e22	0.749432
$448$	−6.43992e22	−1.87507
$449$	−5.51324e22	−1.57512	−0.787559	−	0.616239i	$-0.788655\pi$
$449$	−5.51324e22	−1.57512	−0.787559	+	0.616239i	$0.788655\pi$
$450$	−2.95221e22	−0.827639
$451$	1.55031e22	0.426499
$452$	1.56872e23	4.23514
$453$	−2.92625e22	−0.775313
$454$	−1.08594e23	−2.82378
$455$	−2.53465e22	−0.646877
$456$	−6.04707e22	−1.51476
$457$	6.93022e22	1.70396	0.851980	−	0.523574i	$-0.175402\pi$
$457$	6.93022e22	1.70396	0.851980	+	0.523574i	$0.175402\pi$
$458$	−5.80009e22	−1.39984
$459$	−1.10104e22	−0.260852
$460$	2.18024e23	5.07063
$461$	−7.17076e21	−0.163722	−0.0818610	−	0.996644i	$-0.526086\pi$
$461$	−7.17076e21	−0.163722	−0.0818610	+	0.996644i	$0.526086\pi$
$462$	1.90518e22	0.427050
$463$	2.59981e22	0.572141	0.286071	−	0.958209i	$-0.407651\pi$
$463$	2.59981e22	0.572141	0.286071	+	0.958209i	$0.407651\pi$
$464$	−2.37222e23	−5.12569
$465$	8.54162e20	0.0181213
$466$	−8.19432e22	−1.70700
$467$	5.59192e22	1.14385	0.571923	−	0.820308i	$-0.306198\pi$
$467$	5.59192e22	1.14385	0.571923	+	0.820308i	$0.306198\pi$
$468$	−5.36160e22	−1.07697
$469$	−2.65914e21	−0.0524532
$470$	−9.28281e22	−1.79824
$471$	3.20818e22	0.610354
$472$	−2.34719e23	−4.38572
$473$	−3.04768e22	−0.559305
$474$	−5.45554e22	−0.983381
$475$	5.19819e22	0.920357
$476$	8.37217e22	1.45606
$477$	1.97431e22	0.337294
$478$	2.00559e23	3.36593
$479$	2.79993e22	0.461631	0.230816	−	0.972998i	$-0.425861\pi$
$479$	2.79993e22	0.461631	0.230816	+	0.972998i	$0.425861\pi$
$480$	2.51787e23	4.07834
$481$	4.47259e22	0.711748
$482$	−1.24532e23	−1.94707
$483$	1.68327e22	0.258585
$484$	−6.06304e20	−0.00915176
$485$	−4.25222e22	−0.630682
$486$	−8.62768e21	−0.125744
$487$	−6.23980e22	−0.893664	−0.446832	−	0.894618i	$-0.647448\pi$
$487$	−6.23980e22	−0.893664	−0.446832	+	0.894618i	$0.647448\pi$
$488$	−3.98129e22	−0.560344
$489$	−9.51314e21	−0.131583
$490$	3.10138e22	0.421588
$491$	4.41349e22	0.589644	0.294822	−	0.955552i	$-0.404740\pi$
$491$	4.41349e22	0.589644	0.294822	+	0.955552i	$0.404740\pi$
$492$	5.33842e22	0.700986
$493$	1.27084e23	1.64018
$494$	1.27622e23	1.61900
$495$	−4.01809e22	−0.501043
$496$	−7.20420e21	−0.0883062
$497$	−1.88746e22	−0.227430
$498$	−6.65548e22	−0.788370
$499$	−6.21080e22	−0.723257	−0.361629	−	0.932322i	$-0.617779\pi$
$499$	−6.21080e22	−0.723257	−0.361629	+	0.932322i	$0.617779\pi$
$500$	−9.96814e22	−1.14122
$501$	−2.58893e22	−0.291406
$502$	−1.50799e22	−0.166885
$503$	−5.47475e22	−0.595713	−0.297856	−	0.954611i	$-0.596272\pi$
$503$	−5.47475e22	−0.595713	−0.297856	+	0.954611i	$0.596272\pi$
$504$	4.25217e22	0.454937
$505$	1.37401e23	1.44548
$506$	2.24172e23	2.31901
$507$	1.65869e22	0.168732
$508$	2.82280e23	2.82383
$509$	9.52145e22	0.936703	0.468352	−	0.883542i	$-0.344848\pi$
$509$	9.52145e22	0.936703	0.468352	+	0.883542i	$0.344848\pi$
$510$	−2.38698e23	−2.30941
$511$	−2.04173e22	−0.194277
$512$	−4.89249e23	−4.57862
$513$	1.51914e22	0.139830
$514$	3.88010e23	3.51283
$515$	6.18158e22	0.550475
$516$	−1.04945e23	−0.919265
$517$	−7.06043e22	−0.608361
$518$	−5.47262e22	−0.463866
$519$	−1.74645e22	−0.145625
$520$	−7.53391e23	−6.18005
$521$	−1.00893e23	−0.814221	−0.407110	−	0.913379i	$-0.633464\pi$
$521$	−1.00893e23	−0.814221	−0.407110	+	0.913379i	$0.633464\pi$
$522$	9.95823e22	0.790647
$523$	4.21022e22	0.328883	0.164441	−	0.986387i	$-0.447418\pi$
$523$	4.21022e22	0.328883	0.164441	+	0.986387i	$0.447418\pi$
$524$	−3.31621e23	−2.54875
$525$	−3.65525e22	−0.276416
$526$	1.69210e23	1.25906
$527$	3.85941e21	0.0282573
$528$	3.38895e23	2.44161
$529$	5.70112e22	0.404191
$530$	4.28017e23	2.98618
$531$	5.89660e22	0.404854
$532$	−1.15514e23	−0.780523
$533$	−7.30252e22	−0.485614
$534$	−4.86356e22	−0.318312
$535$	−4.09144e23	−2.63554
$536$	−7.90394e22	−0.501121
$537$	−1.25357e23	−0.782288
$538$	3.23447e23	1.98680
$539$	2.35888e22	0.142627
$540$	−1.38361e23	−0.823506
$541$	2.78620e23	1.63243	0.816217	−	0.577745i	$-0.196067\pi$
$541$	2.78620e23	1.63243	0.816217	+	0.577745i	$0.196067\pi$
$542$	3.48366e23	2.00929
$543$	−6.24021e22	−0.354324
$544$	1.13766e24	6.35950
$545$	−5.71664e22	−0.314609
$546$	−8.97409e22	−0.486243
$547$	4.35097e22	0.232110	0.116055	−	0.993243i	$-0.462975\pi$
$547$	4.35097e22	0.232110	0.116055	+	0.993243i	$0.462975\pi$
$548$	7.86681e23	4.13203
$549$	1.00018e22	0.0517264
$550$	−4.86793e23	−2.47892
$551$	−1.75342e23	−0.879221
$552$	5.00330e23	2.47044
$553$	−6.75473e22	−0.328431
$554$	−5.60982e22	−0.268606
$555$	1.15420e23	0.544238
$556$	−1.13395e24	−5.26572
$557$	−2.26465e23	−1.03570	−0.517848	−	0.855473i	$-0.673267\pi$
$557$	−2.26465e23	−1.03570	−0.517848	+	0.855473i	$0.673267\pi$
$558$	3.02421e21	0.0136214
$559$	1.43557e23	0.636829
$560$	5.51675e23	2.41038
$561$	−1.81551e23	−0.781295
$562$	−5.59506e23	−2.37162
$563$	−2.13808e23	−0.892693	−0.446347	−	0.894860i	$-0.647275\pi$
$563$	−2.13808e23	−0.892693	−0.446347	+	0.894860i	$0.647275\pi$
$564$	−2.43123e23	−0.999892
$565$	−5.53764e23	−2.24343
$566$	2.26285e23	0.903057
$567$	−1.06823e22	−0.0419961
$568$	−5.61022e23	−2.17279
$569$	−6.03782e22	−0.230370	−0.115185	−	0.993344i	$-0.536746\pi$
$569$	−6.03782e22	−0.230370	−0.115185	+	0.993344i	$0.536746\pi$
$570$	3.29340e23	1.23796
$571$	3.26516e23	1.20920	0.604600	−	0.796529i	$-0.293333\pi$
$571$	3.26516e23	1.20920	0.604600	+	0.796529i	$0.293333\pi$
$572$	−8.84080e23	−3.22571
$573$	2.79952e23	1.00640
$574$	8.93530e22	0.316488
$575$	−4.30094e23	−1.50102
$576$	4.80879e23	1.65366
$577$	4.82707e23	1.63565	0.817823	−	0.575469i	$-0.195181\pi$
$577$	4.82707e23	1.63565	0.817823	+	0.575469i	$0.195181\pi$
$578$	−4.91469e23	−1.64100
$579$	2.13493e23	0.702450
$580$	1.59699e24	5.17802
$581$	−8.24043e22	−0.263301
$582$	−1.50552e23	−0.474070
$583$	3.25546e23	1.01025
$584$	−6.06877e23	−1.85606
$585$	1.89267e23	0.570492
$586$	8.69026e23	2.58168
$587$	1.01172e23	0.296235	0.148118	−	0.988970i	$-0.452679\pi$
$587$	1.01172e23	0.296235	0.148118	+	0.988970i	$0.452679\pi$
$588$	8.12270e22	0.234419
$589$	−5.32497e21	−0.0151474
$590$	1.27834e24	3.58431
$591$	−4.23876e21	−0.0117151
$592$	−9.73474e23	−2.65210
$593$	−7.06394e23	−1.89707	−0.948533	−	0.316679i	$-0.897432\pi$
$593$	−7.06394e23	−1.89707	−0.948533	+	0.316679i	$0.897432\pi$
$594$	−1.42263e23	−0.376623
$595$	−2.95541e23	−0.771301
$596$	1.43396e24	3.68930
$597$	−5.47837e22	−0.138953
$598$	−1.05593e24	−2.64044
$599$	−2.23905e23	−0.551997	−0.275998	−	0.961158i	$-0.589008\pi$
$599$	−2.23905e23	−0.551997	−0.275998	+	0.961158i	$0.589008\pi$
$600$	−1.08648e24	−2.64079
$601$	−2.44409e22	−0.0585711	−0.0292856	−	0.999571i	$-0.509323\pi$
$601$	−2.44409e22	−0.0585711	−0.0292856	+	0.999571i	$0.509323\pi$
$602$	−1.75655e23	−0.415039
$603$	1.98562e22	0.0462594
$604$	−1.66151e24	−3.81671
$605$	2.14028e21	0.00484785
$606$	4.86475e23	1.08653
$607$	−8.77084e23	−1.93169	−0.965845	−	0.259122i	$-0.916567\pi$
$607$	−8.77084e23	−1.93169	−0.965845	+	0.259122i	$0.916567\pi$
$608$	−1.56968e24	−3.40902
$609$	1.23297e23	0.264062
$610$	2.16832e23	0.457951
$611$	3.32572e23	0.692684
$612$	−6.25164e23	−1.28412
$613$	−5.80620e23	−1.17619	−0.588096	−	0.808791i	$-0.700122\pi$
$613$	−5.80620e23	−1.17619	−0.588096	+	0.808791i	$0.700122\pi$
$614$	1.44114e24	2.87922
$615$	−1.88448e23	−0.371325
$616$	7.01146e23	1.36261
$617$	8.08554e23	1.54983	0.774917	−	0.632063i	$-0.217792\pi$
$617$	8.08554e23	1.54983	0.774917	+	0.632063i	$0.217792\pi$
$618$	2.18863e23	0.413780
$619$	9.05655e22	0.168885	0.0844427	−	0.996428i	$-0.473089\pi$
$619$	9.05655e22	0.168885	0.0844427	+	0.996428i	$0.473089\pi$
$620$	4.84989e22	0.0892078
$621$	−1.25693e23	−0.228051
$622$	−4.79532e23	−0.858221
$623$	−6.02177e22	−0.106310
$624$	−1.59632e24	−2.78004
$625$	−3.85436e23	−0.662174
$626$	1.03714e24	1.75774
$627$	2.50493e23	0.418815
$628$	1.82159e24	3.00465
$629$	5.21506e23	0.848650
$630$	−2.31585e23	−0.371805
$631$	1.00909e23	0.159838	0.0799188	−	0.996801i	$-0.474534\pi$
$631$	1.00909e23	0.159838	0.0799188	+	0.996801i	$0.474534\pi$
$632$	−2.00775e24	−3.13772
$633$	−4.17893e23	−0.644368
$634$	−2.03107e24	−3.09005
$635$	−9.96462e23	−1.49584
$636$	1.12100e24	1.66043
$637$	−1.11112e23	−0.162396
$638$	1.64202e24	2.36812
$639$	1.40940e23	0.200575
$640$	5.39507e24	7.57648
$641$	−1.07424e24	−1.48870	−0.744351	−	0.667789i	$-0.767241\pi$
$641$	−1.07424e24	−1.48870	−0.744351	+	0.667789i	$0.767241\pi$
$642$	−1.44860e24	−1.98107
$643$	8.84469e23	1.19368	0.596842	−	0.802359i	$-0.296422\pi$
$643$	8.84469e23	1.19368	0.596842	+	0.802359i	$0.296422\pi$
$644$	9.55753e23	1.27296
$645$	3.70462e23	0.486951
$646$	1.48807e24	1.93040
$647$	−8.12876e22	−0.104073	−0.0520365	−	0.998645i	$-0.516571\pi$
$647$	−8.12876e22	−0.104073	−0.0520365	+	0.998645i	$0.516571\pi$
$648$	−3.17517e23	−0.401217
$649$	9.72298e23	1.21260
$650$	2.29298e24	2.82251
$651$	3.74440e21	0.00454930
$652$	−5.40151e23	−0.647755
$653$	2.70011e23	0.319610	0.159805	−	0.987149i	$-0.448913\pi$
$653$	2.70011e23	0.319610	0.159805	+	0.987149i	$0.448913\pi$
$654$	−2.02401e23	−0.236484
$655$	1.17064e24	1.35012
$656$	1.58942e24	1.80949
$657$	1.52460e23	0.171336
$658$	−4.06932e23	−0.451442
$659$	4.89100e23	0.535638	0.267819	−	0.963469i	$-0.413697\pi$
$659$	4.89100e23	0.535638	0.267819	+	0.963469i	$0.413697\pi$
$660$	−2.28145e24	−2.46654
$661$	−9.68394e23	−1.03357	−0.516785	−	0.856115i	$-0.672871\pi$
$661$	−9.68394e23	−1.03357	−0.516785	+	0.856115i	$0.672871\pi$
$662$	1.13831e24	1.19941
$663$	8.55173e23	0.889589
$664$	−2.44936e24	−2.51549
$665$	4.07770e23	0.413457
$666$	4.08650e23	0.409091
$667$	1.45077e24	1.43393
$668$	−1.46998e24	−1.43454
$669$	1.16690e24	1.12438
$670$	4.30470e23	0.409550
$671$	1.64920e23	0.154929
$672$	1.10376e24	1.02385
$673$	−3.89550e23	−0.356808	−0.178404	−	0.983957i	$-0.557093\pi$
$673$	−3.89550e23	−0.356808	−0.178404	+	0.983957i	$0.557093\pi$
$674$	−1.37857e24	−1.24686
$675$	2.72944e23	0.243776
$676$	9.41795e23	0.830634
$677$	−3.92236e23	−0.341621	−0.170810	−	0.985304i	$-0.554639\pi$
$677$	−3.92236e23	−0.341621	−0.170810	+	0.985304i	$0.554639\pi$
$678$	−1.96063e24	−1.68634
$679$	−1.86405e23	−0.158331
$680$	−8.78457e24	−7.36876
$681$	1.00399e24	0.831727
$682$	4.98666e22	0.0407984
$683$	9.51983e23	0.769225	0.384612	−	0.923078i	$-0.374335\pi$
$683$	9.51983e23	0.769225	0.384612	+	0.923078i	$0.374335\pi$
$684$	8.62562e23	0.688357
$685$	−2.77702e24	−2.18881
$686$	1.35956e23	0.105838
$687$	5.36242e23	0.412315
$688$	−3.12456e24	−2.37294
$689$	−1.53344e24	−1.15028
$690$	−2.72493e24	−2.01901
$691$	−1.40863e23	−0.103094	−0.0515470	−	0.998671i	$-0.516415\pi$
$691$	−1.40863e23	−0.103094	−0.0515470	+	0.998671i	$0.516415\pi$
$692$	−9.91628e23	−0.716881
$693$	−1.76142e23	−0.125785
$694$	−4.26093e24	−3.00572
$695$	4.00289e24	2.78935
$696$	3.66484e24	2.52276
$697$	−8.51477e23	−0.579021
$698$	−4.37428e24	−2.93857
$699$	7.57599e23	0.502786
$700$	−2.07544e24	−1.36074
$701$	1.06778e24	0.691637	0.345818	−	0.938301i	$-0.387601\pi$
$701$	1.06778e24	0.691637	0.345818	+	0.938301i	$0.387601\pi$
$702$	6.70110e23	0.428826
$703$	−7.19541e23	−0.454921
$704$	7.92928e24	4.95297
$705$	8.58233e23	0.529661
$706$	3.24989e24	1.98166
$707$	6.02325e23	0.362882
$708$	3.34806e24	1.99302
$709$	1.61640e24	0.950729	0.475364	−	0.879789i	$-0.342316\pi$
$709$	1.61640e24	0.950729	0.475364	+	0.879789i	$0.342316\pi$
$710$	3.05548e24	1.77575
$711$	5.04387e23	0.289649
$712$	−1.78989e24	−1.01566
$713$	4.40583e22	0.0247040
$714$	−1.04638e24	−0.579770
$715$	3.12084e24	1.70872
$716$	−7.11771e24	−3.85105
$717$	−1.85425e24	−0.991415
$718$	5.02238e23	0.265370
$719$	−1.04728e24	−0.546847	−0.273423	−	0.961894i	$-0.588156\pi$
$719$	−1.04728e24	−0.546847	−0.273423	+	0.961894i	$0.588156\pi$
$720$	−4.11945e24	−2.12575
$721$	2.70983e23	0.138195
$722$	1.83600e24	0.925352
$723$	1.15135e24	0.573497
$724$	−3.54316e24	−1.74427
$725$	−3.15037e24	−1.53281
$726$	7.57779e21	0.00364402
$727$	9.16926e23	0.435805	0.217902	−	0.975971i	$-0.430079\pi$
$727$	9.16926e23	0.435805	0.217902	+	0.975971i	$0.430079\pi$
$728$	−3.30265e24	−1.55148
$729$	7.97664e22	0.0370370
$730$	3.30522e24	1.51690
$731$	1.67388e24	0.759321
$732$	5.67896e23	0.254639
$733$	−1.94460e24	−0.861879	−0.430940	−	0.902381i	$-0.641818\pi$
$733$	−1.94460e24	−0.861879	−0.430940	+	0.902381i	$0.641818\pi$
$734$	1.43878e24	0.630346
$735$	−2.86735e23	−0.124176
$736$	1.29874e25	5.55981
$737$	3.27412e23	0.138555
$738$	−6.67213e23	−0.279117
$739$	−3.20437e24	−1.32515	−0.662574	−	0.748996i	$-0.730536\pi$
$739$	−3.20437e24	−1.32515	−0.662574	+	0.748996i	$0.730536\pi$
$740$	6.55347e24	2.67918
$741$	−1.17992e24	−0.476866
$742$	1.87630e24	0.749669
$743$	−2.70961e24	−1.07029	−0.535146	−	0.844759i	$-0.679744\pi$
$743$	−2.70961e24	−1.07029	−0.535146	+	0.844759i	$0.679744\pi$
$744$	1.11297e23	0.0434625
$745$	−5.06195e24	−1.95429
$746$	4.57350e24	1.74570
$747$	6.15327e23	0.232210
$748$	−1.03084e25	−3.84616
$749$	−1.79357e24	−0.661643
$750$	1.24585e24	0.454408
$751$	7.73264e23	0.278861	0.139431	−	0.990232i	$-0.455473\pi$
$751$	7.73264e23	0.278861	0.139431	+	0.990232i	$0.455473\pi$
$752$	−7.23853e24	−2.58106
$753$	1.39420e23	0.0491551
$754$	−7.73453e24	−2.69636
$755$	5.86521e24	2.02178
$756$	−6.06536e23	−0.206738
$757$	2.29385e24	0.773125	0.386563	−	0.922263i	$-0.373662\pi$
$757$	2.29385e24	0.773125	0.386563	+	0.922263i	$0.373662\pi$
$758$	−5.32250e23	−0.177389
$759$	−2.07256e24	−0.683049
$760$	1.21204e25	3.95004
$761$	2.50959e24	0.808786	0.404393	−	0.914585i	$-0.367483\pi$
$761$	2.50959e24	0.808786	0.404393	+	0.914585i	$0.367483\pi$
$762$	−3.52803e24	−1.12439
$763$	−2.50601e23	−0.0789814
$764$	1.58956e25	4.95430
$765$	2.20686e24	0.680224
$766$	−6.89505e24	−2.10181
$767$	−4.57988e24	−1.38068
$768$	9.49485e24	2.83086
$769$	−7.81121e23	−0.230327	−0.115163	−	0.993347i	$-0.536739\pi$
$769$	−7.81121e23	−0.230327	−0.115163	+	0.993347i	$0.536739\pi$
$770$	−3.81863e24	−1.11362
$771$	−3.58732e24	−1.03468
$772$	1.21220e25	3.45802
$773$	−5.75821e24	−1.62466	−0.812329	−	0.583199i	$-0.801801\pi$
$773$	−5.75821e24	−1.62466	−0.812329	+	0.583199i	$0.801801\pi$
$774$	1.31164e24	0.366030
$775$	−9.56735e22	−0.0264075
$776$	−5.54064e24	−1.51264
$777$	5.05966e23	0.136629
$778$	−1.08594e25	−2.90053
$779$	1.17481e24	0.310385
$780$	1.07465e25	2.80842
$781$	2.32397e24	0.600754
$782$	−1.23122e25	−3.14832
$783$	−9.20679e23	−0.232880
$784$	2.41839e24	0.605117
$785$	−6.43030e24	−1.59162
$786$	4.14472e24	1.01485
$787$	3.31374e24	0.802664	0.401332	−	0.915933i	$-0.368547\pi$
$787$	3.31374e24	0.802664	0.401332	+	0.915933i	$0.368547\pi$
$788$	−2.40675e23	−0.0576711
$789$	−1.56442e24	−0.370849
$790$	1.09348e25	2.56436
$791$	−2.42754e24	−0.563205
$792$	−5.23557e24	−1.20171
$793$	−7.76836e23	−0.176403
$794$	7.05381e24	1.58471
$795$	−3.95719e24	−0.879561
$796$	−3.11059e24	−0.684041
$797$	5.01788e24	1.09175	0.545877	−	0.837866i	$-0.316197\pi$
$797$	5.01788e24	1.09175	0.545877	+	0.837866i	$0.316197\pi$
$798$	1.44373e24	0.310787
$799$	3.87780e24	0.825920
$800$	−2.82023e25	−5.94320
$801$	4.49656e23	0.0937570
$802$	4.67302e24	0.964086
$803$	2.51392e24	0.513180
$804$	1.12743e24	0.227726
$805$	−3.37385e24	−0.674312
$806$	−2.34890e23	−0.0464533
$807$	−2.99040e24	−0.585200
$808$	1.79033e25	3.46686
$809$	−6.53004e24	−1.25128	−0.625638	−	0.780114i	$-0.715161\pi$
$809$	−6.53004e24	−1.25128	−0.625638	+	0.780114i	$0.715161\pi$
$810$	1.72928e24	0.327901
$811$	4.78535e24	0.897917	0.448959	−	0.893553i	$-0.351795\pi$
$811$	4.78535e24	0.897917	0.448959	+	0.893553i	$0.351795\pi$
$812$	7.00074e24	1.29992
$813$	−3.22078e24	−0.591823
$814$	6.73827e24	1.22530
$815$	1.90676e24	0.343128
$816$	−1.86131e25	−3.31477
$817$	−2.30951e24	−0.407036
$818$	4.07606e22	0.00710948
$819$	8.29691e23	0.143220
$820$	−1.07000e25	−1.82796
$821$	7.93062e24	1.34088	0.670441	−	0.741963i	$-0.266105\pi$
$821$	7.93062e24	1.34088	0.670441	+	0.741963i	$0.266105\pi$
$822$	−9.83220e24	−1.64528
$823$	8.24812e24	1.36602	0.683009	−	0.730410i	$-0.260671\pi$
$823$	8.24812e24	1.36602	0.683009	+	0.730410i	$0.260671\pi$
$824$	8.05460e24	1.32027
$825$	4.50060e24	0.730150
$826$	5.60390e24	0.899828
$827$	−2.36975e24	−0.376623	−0.188311	−	0.982109i	$-0.560301\pi$
$827$	−2.36975e24	−0.376623	−0.188311	+	0.982109i	$0.560301\pi$
$828$	−7.13677e24	−1.12265
$829$	2.92107e24	0.454808	0.227404	−	0.973800i	$-0.426976\pi$
$829$	2.92107e24	0.454808	0.227404	+	0.973800i	$0.426976\pi$
$830$	1.33399e25	2.05583
$831$	5.18650e23	0.0791163
$832$	−3.73498e25	−5.63949
$833$	−1.29557e24	−0.193632
$834$	1.41725e25	2.09669
$835$	5.18910e24	0.759900
$836$	1.42229e25	2.06174
$837$	−2.79601e22	−0.00401210
$838$	1.21848e25	1.73079
$839$	−5.56183e24	−0.782062	−0.391031	−	0.920378i	$-0.627881\pi$
$839$	−5.56183e24	−0.782062	−0.391031	+	0.920378i	$0.627881\pi$
$840$	−8.52281e24	−1.18634
$841$	3.36949e24	0.464300
$842$	−1.08359e25	−1.47813
$843$	5.17286e24	0.698548
$844$	−2.37278e25	−3.17210
$845$	−3.32458e24	−0.440002
$846$	3.03863e24	0.398134
$847$	9.38237e21	0.00121704
$848$	3.33758e25	4.28615
$849$	−2.09209e24	−0.265990
$850$	2.67362e25	3.36541
$851$	5.95343e24	0.741935
$852$	8.00249e24	0.987389
$853$	−1.36694e25	−1.66986	−0.834932	−	0.550353i	$-0.814493\pi$
$853$	−1.36694e25	−1.66986	−0.834932	+	0.550353i	$0.814493\pi$
$854$	9.50529e23	0.114967
$855$	−3.04488e24	−0.364635
$856$	−5.33115e25	−6.32112
$857$	−8.64762e24	−1.01522	−0.507609	−	0.861587i	$-0.669471\pi$
$857$	−8.64762e24	−1.01522	−0.507609	+	0.861587i	$0.669471\pi$
$858$	1.10495e25	1.28440
$859$	−2.98424e23	−0.0343472	−0.0171736	−	0.999853i	$-0.505467\pi$
$859$	−2.98424e23	−0.0343472	−0.0171736	+	0.999853i	$0.505467\pi$
$860$	2.10346e25	2.39717
$861$	−8.26105e23	−0.0932198
$862$	−1.46333e25	−1.63504
$863$	−7.54136e24	−0.834368	−0.417184	−	0.908822i	$-0.636983\pi$
$863$	−7.54136e24	−0.834368	−0.417184	+	0.908822i	$0.636983\pi$
$864$	−8.24199e24	−0.902953
$865$	3.50049e24	0.379745
$866$	−2.06348e25	−2.21665
$867$	4.54383e24	0.483348
$868$	2.12606e23	0.0223953
$869$	8.31689e24	0.867547
$870$	−1.99597e25	−2.06177
$871$	−1.54223e24	−0.157759
$872$	−7.44878e24	−0.754562
$873$	1.39192e24	0.139634
$874$	1.69876e25	1.68766
$875$	1.54254e24	0.151764
$876$	8.65658e24	0.843454
$877$	4.83896e24	0.466934	0.233467	−	0.972365i	$-0.424993\pi$
$877$	4.83896e24	0.466934	0.233467	+	0.972365i	$0.424993\pi$
$878$	−3.06081e25	−2.92505
$879$	−8.03450e24	−0.760420
$880$	−6.79261e25	−6.36698
$881$	−1.14844e25	−1.06614	−0.533068	−	0.846072i	$-0.678961\pi$
$881$	−1.14844e25	−1.06614	−0.533068	+	0.846072i	$0.678961\pi$
$882$	−1.01520e24	−0.0933404
$883$	1.40332e25	1.27788	0.638942	−	0.769255i	$-0.279372\pi$
$883$	1.40332e25	1.27788	0.638942	+	0.769255i	$0.279372\pi$
$884$	4.85563e25	4.37927
$885$	−1.18188e25	−1.05574
$886$	−2.94836e25	−2.60852
$887$	1.16146e25	1.01778	0.508888	−	0.860833i	$-0.330057\pi$
$887$	1.16146e25	1.01778	0.508888	+	0.860833i	$0.330057\pi$
$888$	1.50392e25	1.30531
$889$	−4.36820e24	−0.375524
$890$	9.74823e24	0.830062
$891$	1.31528e24	0.110932
$892$	6.62562e25	5.53510
$893$	−5.35035e24	−0.442736
$894$	−1.79221e25	−1.46900
$895$	2.51258e25	2.03997
$896$	2.36505e25	1.90205
$897$	9.76252e24	0.777725
$898$	3.91247e25	3.08746
$899$	3.22720e23	0.0252272
$900$	1.54976e25	1.20006
$901$	−1.78800e25	−1.37153
$902$	−1.10018e25	−0.836001
$903$	1.62400e24	0.122247
$904$	−7.21554e25	−5.38068
$905$	1.25075e25	0.923971
$906$	2.07661e25	1.51973
$907$	−1.29818e25	−0.941182	−0.470591	−	0.882351i	$-0.655959\pi$
$907$	−1.29818e25	−0.941182	−0.470591	+	0.882351i	$0.655959\pi$
$908$	5.70063e25	4.09443
$909$	−4.49766e24	−0.320032
$910$	1.79871e25	1.26797
$911$	−3.94564e24	−0.275557	−0.137778	−	0.990463i	$-0.543996\pi$
$911$	−3.94564e24	−0.275557	−0.137778	+	0.990463i	$0.543996\pi$
$912$	2.56812e25	1.77689
$913$	1.01462e25	0.695507
$914$	−4.91803e25	−3.34002
$915$	−2.00470e24	−0.134887
$916$	3.04476e25	2.02974
$917$	5.13175e24	0.338942
$918$	7.81351e24	0.511309
$919$	7.63928e24	0.495302	0.247651	−	0.968849i	$-0.420341\pi$
$919$	7.63928e24	0.495302	0.247651	+	0.968849i	$0.420341\pi$
$920$	−1.00283e26	−6.44216
$921$	−1.33239e25	−0.848058
$922$	5.08872e24	0.320919
$923$	−1.09468e25	−0.684023
$924$	−1.00012e25	−0.619216
$925$	−1.29280e25	−0.793096
$926$	−1.84495e25	−1.12148
$927$	−2.02347e24	−0.121876
$928$	9.51305e25	5.67756
$929$	2.66866e25	1.57819	0.789096	−	0.614270i	$-0.210549\pi$
$929$	2.66866e25	1.57819	0.789096	+	0.614270i	$0.210549\pi$
$930$	−6.06156e23	−0.0355205
$931$	1.78755e24	0.103797
$932$	4.30161e25	2.47512
$933$	4.43347e24	0.252784
$934$	−3.96830e25	−2.24211
$935$	3.63891e25	2.03738
$936$	2.46615e25	1.36828
$937$	−2.54191e25	−1.39757	−0.698784	−	0.715333i	$-0.746275\pi$
$937$	−2.54191e25	−1.39757	−0.698784	+	0.715333i	$0.746275\pi$
$938$	1.88706e24	0.102816
$939$	−9.58877e24	−0.517732
$940$	4.87301e25	2.60742
$941$	9.03633e24	0.479160	0.239580	−	0.970877i	$-0.422990\pi$
$941$	9.03633e24	0.479160	0.239580	+	0.970877i	$0.422990\pi$
$942$	−2.27669e25	−1.19638
$943$	−9.72032e24	−0.506210
$944$	9.96825e25	5.14466
$945$	2.14110e24	0.109513
$946$	2.16278e25	1.09632
$947$	8.97578e24	0.450918	0.225459	−	0.974253i	$-0.427612\pi$
$947$	8.97578e24	0.450918	0.225459	+	0.974253i	$0.427612\pi$
$948$	2.86388e25	1.42589
$949$	−1.18415e25	−0.584311
$950$	−3.68889e25	−1.80404
$951$	1.87781e25	0.910157
$952$	−3.85091e25	−1.84990
$953$	−3.56154e25	−1.69569	−0.847847	−	0.530240i	$-0.822102\pi$
$953$	−3.56154e25	−1.69569	−0.847847	+	0.530240i	$0.822102\pi$
$954$	−1.40107e25	−0.661146
$955$	−5.61120e25	−2.62438
$956$	−1.05283e26	−4.88054
$957$	−1.51812e25	−0.697516
$958$	−1.98697e25	−0.904866
$959$	−1.21737e25	−0.549494
$960$	−9.63847e25	−4.31224
$961$	−2.25403e25	−0.999565
$962$	−3.17397e25	−1.39513
$963$	1.33929e25	0.583514
$964$	6.53730e25	2.82321
$965$	−4.27913e25	−1.83178
$966$	−1.19453e25	−0.506865
$967$	2.47463e25	1.04084	0.520422	−	0.853909i	$-0.325774\pi$
$967$	2.47463e25	1.04084	0.520422	+	0.853909i	$0.325774\pi$
$968$	2.78878e23	0.0116272
$969$	−1.37579e25	−0.568589
$970$	3.01758e25	1.23623
$971$	−1.14088e25	−0.463315	−0.231657	−	0.972797i	$-0.574415\pi$
$971$	−1.14088e25	−0.463315	−0.231657	+	0.972797i	$0.574415\pi$
$972$	4.52910e24	0.182326
$973$	1.75475e25	0.700256
$974$	4.42807e25	1.75172
$975$	−2.11995e25	−0.831354
$976$	1.69081e25	0.657311
$977$	4.13224e25	1.59251	0.796255	−	0.604962i	$-0.206812\pi$
$977$	4.13224e25	1.59251	0.796255	+	0.604962i	$0.206812\pi$
$978$	6.75099e24	0.257921
$979$	7.41442e24	0.280818
$980$	−1.62807e25	−0.611295
$981$	1.87128e24	0.0696550
$982$	−3.13203e25	−1.15579
$983$	3.64968e25	1.33521	0.667606	−	0.744515i	$-0.267319\pi$
$983$	3.64968e25	1.33521	0.667606	+	0.744515i	$0.267319\pi$
$984$	−2.45548e25	−0.890592
$985$	8.49593e23	0.0305494
$986$	−9.01849e25	−3.21499
$987$	3.76225e24	0.132969
$988$	−6.69950e25	−2.34752
$989$	1.91087e25	0.663839
$990$	2.85143e25	0.982119
$991$	3.75564e25	1.28250	0.641250	−	0.767332i	$-0.278416\pi$
$991$	3.75564e25	1.28250	0.641250	+	0.767332i	$0.278416\pi$
$992$	2.88902e24	0.0978140
$993$	−1.05241e25	−0.353278
$994$	1.33943e25	0.445797
$995$	1.09805e25	0.362349
$996$	3.49380e25	1.14312
$997$	1.11835e25	0.362801	0.181400	−	0.983409i	$-0.441937\pi$
$997$	1.11835e25	0.362801	0.181400	+	0.983409i	$0.441937\pi$
$998$	4.40749e25	1.41769
$999$	−3.77813e24	−0.120495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.18.a.d.1.1	✓	5
3.2	odd	2		63.18.a.f.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.18.a.d.1.1	✓	5	1.1	even	1	trivial
63.18.a.f.1.5		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)

\(f(q)\)	\(=\)	\(q-709.650 q^{2} +6561.00 q^{3} +372531. q^{4} -1.31505e6 q^{5} -4.65601e6 q^{6} -5.76480e6 q^{7} -1.71351e8 q^{8} +4.30467e7 q^{9} +O(q^{10})\)	\(q-709.650 q^{2} +6561.00 q^{3} +372531. q^{4} -1.31505e6 q^{5} -4.65601e6 q^{6} -5.76480e6 q^{7} -1.71351e8 q^{8} +4.30467e7 q^{9} +9.33224e8 q^{10} +7.09802e8 q^{11} +2.44417e9 q^{12} -3.34343e9 q^{13} +4.09099e9 q^{14} -8.62804e9 q^{15} +7.27708e10 q^{16} -3.89845e10 q^{17} -3.05481e10 q^{18} +5.37884e10 q^{19} -4.89896e11 q^{20} -3.78229e10 q^{21} -5.03711e11 q^{22} -4.45041e11 q^{23} -1.12423e12 q^{24} +9.66414e11 q^{25} +2.37266e12 q^{26} +2.82430e11 q^{27} -2.14756e12 q^{28} -3.25985e12 q^{29} +6.12288e12 q^{30} -9.89984e10 q^{31} -2.91825e13 q^{32} +4.65701e12 q^{33} +2.76653e13 q^{34} +7.58100e12 q^{35} +1.60362e13 q^{36} -1.33773e13 q^{37} -3.81709e13 q^{38} -2.19362e13 q^{39} +2.25335e14 q^{40} +2.18414e13 q^{41} +2.68410e13 q^{42} -4.29370e13 q^{43} +2.64423e14 q^{44} -5.66085e13 q^{45} +3.15823e14 q^{46} -9.94703e13 q^{47} +4.77449e14 q^{48} +3.32329e13 q^{49} -6.85815e14 q^{50} -2.55777e14 q^{51} -1.24553e15 q^{52} +4.58643e14 q^{53} -2.00426e14 q^{54} -9.33425e14 q^{55} +9.87804e14 q^{56} +3.52906e14 q^{57} +2.31335e15 q^{58} +1.36981e15 q^{59} -3.21421e15 q^{60} +2.32347e14 q^{61} +7.02542e13 q^{62} -2.48156e14 q^{63} +1.11711e16 q^{64} +4.39677e15 q^{65} -3.30485e15 q^{66} +4.61272e14 q^{67} -1.45229e16 q^{68} -2.91991e15 q^{69} -5.37985e15 q^{70} +3.27411e15 q^{71} -7.37610e15 q^{72} +3.54172e15 q^{73} +9.49317e15 q^{74} +6.34064e15 q^{75} +2.00378e16 q^{76} -4.09187e15 q^{77} +1.55670e16 q^{78} +1.17172e16 q^{79} -9.56972e16 q^{80} +1.85302e15 q^{81} -1.54997e16 q^{82} +1.42944e16 q^{83} -1.40902e16 q^{84} +5.12665e16 q^{85} +3.04702e16 q^{86} -2.13879e16 q^{87} -1.21625e17 q^{88} +1.04458e16 q^{89} +4.01722e16 q^{90} +1.92742e16 q^{91} -1.65791e17 q^{92} -6.49529e14 q^{93} +7.05891e16 q^{94} -7.07344e16 q^{95} -1.91466e17 q^{96} +3.23350e16 q^{97} -2.35837e16 q^{98} +3.05547e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 253 q^{2} + 32805 q^{3} + 441613 q^{4} - 906662 q^{5} - 1659933 q^{6} - 28824005 q^{7} - 182238651 q^{8} + 215233605 q^{9}+O(q^{10}) \) 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

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