LMFDB - Embedded newform 177.14.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.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:	$189.798744245$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-60.0941 q^{2} +729.000 q^{3} -4580.70 q^{4} -50851.6 q^{5} -43808.6 q^{6} -259334. q^{7} +767564. q^{8} +531441. q^{9} +O(q^{10})$	\(q-60.0941 q^{2} +729.000 q^{3} -4580.70 q^{4} -50851.6 q^{5} -43808.6 q^{6} -259334. q^{7} +767564. q^{8} +531441. q^{9} +3.05588e6 q^{10} -1.61611e6 q^{11} -3.33933e6 q^{12} +3.32755e6 q^{13} +1.55844e7 q^{14} -3.70708e7 q^{15} -8.60088e6 q^{16} -9.95689e7 q^{17} -3.19364e7 q^{18} +9.24640e7 q^{19} +2.32936e8 q^{20} -1.89055e8 q^{21} +9.71188e7 q^{22} -5.67360e8 q^{23} +5.59554e8 q^{24} +1.36518e9 q^{25} -1.99966e8 q^{26} +3.87420e8 q^{27} +1.18793e9 q^{28} +3.47908e9 q^{29} +2.22773e9 q^{30} -8.56644e9 q^{31} -5.77102e9 q^{32} -1.17815e9 q^{33} +5.98350e9 q^{34} +1.31876e10 q^{35} -2.43437e9 q^{36} -1.81122e10 q^{37} -5.55654e9 q^{38} +2.42579e9 q^{39} -3.90318e10 q^{40} -1.66711e8 q^{41} +1.13611e10 q^{42} -5.81369e10 q^{43} +7.40294e9 q^{44} -2.70246e10 q^{45} +3.40949e10 q^{46} -8.85067e10 q^{47} -6.27004e9 q^{48} -2.96348e10 q^{49} -8.20392e10 q^{50} -7.25857e10 q^{51} -1.52425e10 q^{52} -1.79141e11 q^{53} -2.32817e10 q^{54} +8.21819e10 q^{55} -1.99056e11 q^{56} +6.74063e10 q^{57} -2.09072e11 q^{58} -4.21805e10 q^{59} +1.69810e11 q^{60} -3.70046e11 q^{61} +5.14792e11 q^{62} -1.37821e11 q^{63} +4.17262e11 q^{64} -1.69211e11 q^{65} +7.07996e10 q^{66} -3.15486e11 q^{67} +4.56096e11 q^{68} -4.13605e11 q^{69} -7.92494e11 q^{70} -1.56042e12 q^{71} +4.07915e11 q^{72} +1.08742e12 q^{73} +1.08843e12 q^{74} +9.95216e11 q^{75} -4.23550e11 q^{76} +4.19114e11 q^{77} -1.45775e11 q^{78} +1.56095e12 q^{79} +4.37368e11 q^{80} +2.82430e11 q^{81} +1.00183e10 q^{82} +2.63040e12 q^{83} +8.66004e11 q^{84} +5.06324e12 q^{85} +3.49368e12 q^{86} +2.53625e12 q^{87} -1.24047e12 q^{88} -6.98019e12 q^{89} +1.62402e12 q^{90} -8.62948e11 q^{91} +2.59891e12 q^{92} -6.24493e12 q^{93} +5.31873e12 q^{94} -4.70194e12 q^{95} -4.20707e12 q^{96} -1.52218e13 q^{97} +1.78087e12 q^{98} -8.58869e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * 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 $

$2$	−60.0941	−0.663952	−0.331976	−	0.943288i	$-0.607715\pi$
$2$	−60.0941	−0.663952	−0.331976	+	0.943288i	$0.607715\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−4580.70	−0.559168
$5$	−50851.6	−1.45546	−0.727729	−	0.685865i	$-0.759424\pi$
$5$	−50851.6	−1.45546	−0.727729	+	0.685865i	$0.759424\pi$
$6$	−43808.6	−0.383333
$7$	−259334.	−0.833149	−0.416574	−	0.909102i	$-0.636769\pi$
$7$	−259334.	−0.833149	−0.416574	+	0.909102i	$0.636769\pi$
$8$	767564.	1.03521
$9$	531441.	0.333333
$10$	3.05588e6	0.966353
$11$	−1.61611e6	−0.275055	−0.137527	−	0.990498i	$-0.543916\pi$
$11$	−1.61611e6	−0.275055	−0.137527	+	0.990498i	$0.543916\pi$
$12$	−3.33933e6	−0.322836
$13$	3.32755e6	0.191202	0.0956012	−	0.995420i	$-0.469523\pi$
$13$	3.32755e6	0.191202	0.0956012	+	0.995420i	$0.469523\pi$
$14$	1.55844e7	0.553171
$15$	−3.70708e7	−0.840309
$16$	−8.60088e6	−0.128163
$17$	−9.95689e7	−1.00047	−0.500237	−	0.865889i	$-0.666754\pi$
$17$	−9.95689e7	−1.00047	−0.500237	+	0.865889i	$0.666754\pi$
$18$	−3.19364e7	−0.221317
$19$	9.24640e7	0.450894	0.225447	−	0.974255i	$-0.427616\pi$
$19$	9.24640e7	0.450894	0.225447	+	0.974255i	$0.427616\pi$
$20$	2.32936e8	0.813845
$21$	−1.89055e8	−0.481019
$22$	9.71188e7	0.182623
$23$	−5.67360e8	−0.799149	−0.399574	−	0.916701i	$-0.630842\pi$
$23$	−5.67360e8	−0.799149	−0.399574	+	0.916701i	$0.630842\pi$
$24$	5.59554e8	0.597680
$25$	1.36518e9	1.11836
$26$	−1.99966e8	−0.126949
$27$	3.87420e8	0.192450
$28$	1.18793e9	0.465870
$29$	3.47908e9	1.08612	0.543060	−	0.839694i	$-0.317266\pi$
$29$	3.47908e9	1.08612	0.543060	+	0.839694i	$0.317266\pi$
$30$	2.22773e9	0.557924
$31$	−8.56644e9	−1.73360	−0.866801	−	0.498655i	$-0.833827\pi$
$31$	−8.56644e9	−1.73360	−0.866801	+	0.498655i	$0.833827\pi$
$32$	−5.77102e9	−0.950118
$33$	−1.17815e9	−0.158803
$34$	5.98350e9	0.664266
$35$	1.31876e10	1.21261
$36$	−2.43437e9	−0.186389
$37$	−1.81122e10	−1.16054	−0.580269	−	0.814425i	$-0.697053\pi$
$37$	−1.81122e10	−1.16054	−0.580269	+	0.814425i	$0.697053\pi$
$38$	−5.55654e9	−0.299372
$39$	2.42579e9	0.110391
$40$	−3.90318e10	−1.50671
$41$	−1.66711e8	−0.00548112	−0.00274056	−	0.999996i	$-0.500872\pi$
$41$	−1.66711e8	−0.00548112	−0.00274056	+	0.999996i	$0.500872\pi$
$42$	1.13611e10	0.319373
$43$	−5.81369e10	−1.40251	−0.701256	−	0.712909i	$-0.747377\pi$
$43$	−5.81369e10	−1.40251	−0.701256	+	0.712909i	$0.747377\pi$
$44$	7.40294e9	0.153802
$45$	−2.70246e10	−0.485152
$46$	3.40949e10	0.530596
$47$	−8.85067e10	−1.19768	−0.598839	−	0.800869i	$-0.704371\pi$
$47$	−8.85067e10	−1.19768	−0.598839	+	0.800869i	$0.704371\pi$
$48$	−6.27004e9	−0.0739950
$49$	−2.96348e10	−0.305863
$50$	−8.20392e10	−0.742534
$51$	−7.25857e10	−0.577624
$52$	−1.52425e10	−0.106914
$53$	−1.79141e11	−1.11020	−0.555100	−	0.831783i	$-0.687320\pi$
$53$	−1.79141e11	−1.11020	−0.555100	+	0.831783i	$0.687320\pi$
$54$	−2.32817e10	−0.127778
$55$	8.21819e10	0.400331
$56$	−1.99056e11	−0.862486
$57$	6.74063e10	0.260324
$58$	−2.09072e11	−0.721131
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.69810e11	0.469874
$61$	−3.70046e11	−0.919626	−0.459813	−	0.888016i	$-0.652084\pi$
$61$	−3.70046e11	−0.919626	−0.459813	+	0.888016i	$0.652084\pi$
$62$	5.14792e11	1.15103
$63$	−1.37821e11	−0.277716
$64$	4.17262e11	0.758996
$65$	−1.69211e11	−0.278287
$66$	7.07996e10	0.105438
$67$	−3.15486e11	−0.426083	−0.213042	−	0.977043i	$-0.568337\pi$
$67$	−3.15486e11	−0.426083	−0.213042	+	0.977043i	$0.568337\pi$
$68$	4.56096e11	0.559433
$69$	−4.13605e11	−0.461389
$70$	−7.92494e11	−0.805116
$71$	−1.56042e12	−1.44565	−0.722825	−	0.691032i	$-0.757157\pi$
$71$	−1.56042e12	−1.44565	−0.722825	+	0.691032i	$0.757157\pi$
$72$	4.07915e11	0.345071
$73$	1.08742e12	0.841006	0.420503	−	0.907291i	$-0.361854\pi$
$73$	1.08742e12	0.841006	0.420503	+	0.907291i	$0.361854\pi$
$74$	1.08843e12	0.770542
$75$	9.95216e11	0.645683
$76$	−4.23550e11	−0.252125
$77$	4.19114e11	0.229162
$78$	−1.45775e11	−0.0732941
$79$	1.56095e12	0.722457	0.361229	−	0.932477i	$-0.382357\pi$
$79$	1.56095e12	0.722457	0.361229	+	0.932477i	$0.382357\pi$
$80$	4.37368e11	0.186536
$81$	2.82430e11	0.111111
$82$	1.00183e10	0.00363920
$83$	2.63040e12	0.883108	0.441554	−	0.897235i	$-0.354427\pi$
$83$	2.63040e12	0.883108	0.441554	+	0.897235i	$0.354427\pi$
$84$	8.66004e11	0.268970
$85$	5.06324e12	1.45615
$86$	3.49368e12	0.931201
$87$	2.53625e12	0.627072
$88$	−1.24047e12	−0.284740
$89$	−6.98019e12	−1.48879	−0.744393	−	0.667741i	$-0.767261\pi$
$89$	−6.98019e12	−1.48879	−0.744393	+	0.667741i	$0.767261\pi$
$90$	1.62402e12	0.322118
$91$	−8.62948e11	−0.159300
$92$	2.59891e12	0.446858
$93$	−6.24493e12	−1.00090
$94$	5.31873e12	0.795201
$95$	−4.70194e12	−0.656257
$96$	−4.20707e12	−0.548551
$97$	−1.52218e13	−1.85546	−0.927728	−	0.373257i	$-0.878241\pi$
$97$	−1.52218e13	−1.85546	−0.927728	+	0.373257i	$0.878241\pi$
$98$	1.78087e12	0.203078
$99$	−8.58869e11	−0.0916850
$100$	−6.25348e12	−0.625348
$101$	4.49762e12	0.421594	0.210797	−	0.977530i	$-0.432394\pi$
$101$	4.49762e12	0.421594	0.210797	+	0.977530i	$0.432394\pi$
$102$	4.36197e12	0.383514
$103$	1.22877e12	0.101398	0.0506991	−	0.998714i	$-0.483855\pi$
$103$	1.22877e12	0.101398	0.0506991	+	0.998714i	$0.483855\pi$
$104$	2.55411e12	0.197935
$105$	9.61373e12	0.700102
$106$	1.07653e13	0.737120
$107$	−1.24501e13	−0.802008	−0.401004	−	0.916076i	$-0.631339\pi$
$107$	−1.24501e13	−0.802008	−0.401004	+	0.916076i	$0.631339\pi$
$108$	−1.77466e12	−0.107612
$109$	2.75070e13	1.57098	0.785490	−	0.618875i	$-0.212411\pi$
$109$	2.75070e13	1.57098	0.785490	+	0.618875i	$0.212411\pi$
$110$	−4.93864e12	−0.265800
$111$	−1.32038e13	−0.670037
$112$	2.23050e12	0.106779
$113$	−1.25235e13	−0.565870	−0.282935	−	0.959139i	$-0.591308\pi$
$113$	−1.25235e13	−0.565870	−0.282935	+	0.959139i	$0.591308\pi$
$114$	−4.05072e12	−0.172842
$115$	2.88511e13	1.16313
$116$	−1.59367e13	−0.607324
$117$	1.76840e12	0.0637341
$118$	2.53480e12	0.0864392
$119$	2.58216e13	0.833544
$120$	−2.84542e13	−0.869898
$121$	−3.19109e13	−0.924345
$122$	2.22375e13	0.610588
$123$	−1.21532e11	−0.00316453
$124$	3.92403e13	0.969374
$125$	−7.34686e12	−0.172261
$126$	8.28221e12	0.184390
$127$	−4.01254e13	−0.848584	−0.424292	−	0.905525i	$-0.639477\pi$
$127$	−4.01254e13	−0.848584	−0.424292	+	0.905525i	$0.639477\pi$
$128$	2.22012e13	0.446182
$129$	−4.23818e13	−0.809741
$130$	1.01686e13	0.184769
$131$	−5.35754e13	−0.926193	−0.463097	−	0.886308i	$-0.653262\pi$
$131$	−5.35754e13	−0.926193	−0.463097	+	0.886308i	$0.653262\pi$
$132$	5.39674e12	0.0887976
$133$	−2.39791e13	−0.375662
$134$	1.89589e13	0.282899
$135$	−1.97009e13	−0.280103
$136$	−7.64255e13	−1.03570
$137$	2.14872e13	0.277648	0.138824	−	0.990317i	$-0.455668\pi$
$137$	2.14872e13	0.277648	0.138824	+	0.990317i	$0.455668\pi$
$138$	2.48552e13	0.306340
$139$	−1.11909e13	−0.131604	−0.0658018	−	0.997833i	$-0.520961\pi$
$139$	−1.11909e13	−0.131604	−0.0658018	+	0.997833i	$0.520961\pi$
$140$	−6.04083e13	−0.678054
$141$	−6.45214e13	−0.691480
$142$	9.37721e13	0.959841
$143$	−5.37770e12	−0.0525911
$144$	−4.57086e12	−0.0427210
$145$	−1.76917e14	−1.58080
$146$	−6.53475e13	−0.558387
$147$	−2.16037e13	−0.176590
$148$	8.29665e13	0.648936
$149$	−1.68046e14	−1.25810	−0.629052	−	0.777364i	$-0.716557\pi$
$149$	−1.68046e14	−1.25810	−0.629052	+	0.777364i	$0.716557\pi$
$150$	−5.98066e13	−0.428702
$151$	−1.63072e14	−1.11951	−0.559757	−	0.828657i	$-0.689106\pi$
$151$	−1.63072e14	−1.11951	−0.559757	+	0.828657i	$0.689106\pi$
$152$	7.09720e13	0.466771
$153$	−5.29150e13	−0.333491
$154$	−2.51862e13	−0.152152
$155$	4.35617e14	2.52318
$156$	−1.11118e13	−0.0617270
$157$	8.10870e13	0.432119	0.216060	−	0.976380i	$-0.430679\pi$
$157$	8.10870e13	0.432119	0.216060	+	0.976380i	$0.430679\pi$
$158$	−9.38036e13	−0.479677
$159$	−1.30594e14	−0.640975
$160$	2.93465e14	1.38286
$161$	1.47136e14	0.665810
$162$	−1.69723e13	−0.0737724
$163$	1.62941e14	0.680472	0.340236	−	0.940340i	$-0.389493\pi$
$163$	1.62941e14	0.680472	0.340236	+	0.940340i	$0.389493\pi$
$164$	7.63654e11	0.00306487
$165$	5.99106e13	0.231131
$166$	−1.58071e14	−0.586341
$167$	−2.13090e13	−0.0760161	−0.0380081	−	0.999277i	$-0.512101\pi$
$167$	−2.13090e13	−0.0760161	−0.0380081	+	0.999277i	$0.512101\pi$
$168$	−1.45111e14	−0.497957
$169$	−2.91802e14	−0.963442
$170$	−3.04270e14	−0.966811
$171$	4.91392e13	0.150298
$172$	2.66308e14	0.784240
$173$	1.17673e14	0.333715	0.166857	−	0.985981i	$-0.446638\pi$
$173$	1.17673e14	0.333715	0.166857	+	0.985981i	$0.446638\pi$
$174$	−1.52414e14	−0.416345
$175$	−3.54038e14	−0.931756
$176$	1.39000e13	0.0352519
$177$	−3.07496e13	−0.0751646
$178$	4.19468e14	0.988483
$179$	4.83367e14	1.09833	0.549164	−	0.835714i	$-0.314946\pi$
$179$	4.83367e14	1.09833	0.549164	+	0.835714i	$0.314946\pi$
$180$	1.23792e14	0.271282
$181$	−8.13641e14	−1.71998	−0.859988	−	0.510315i	$-0.829529\pi$
$181$	−8.13641e14	−1.71998	−0.859988	+	0.510315i	$0.829529\pi$
$182$	5.18581e13	0.105768
$183$	−2.69763e14	−0.530947
$184$	−4.35485e14	−0.827289
$185$	9.21033e14	1.68911
$186$	3.75283e14	0.664546
$187$	1.60915e14	0.275185
$188$	4.05423e14	0.669703
$189$	−1.00471e14	−0.160340
$190$	2.82559e14	0.435723
$191$	5.56459e14	0.829309	0.414654	−	0.909979i	$-0.363902\pi$
$191$	5.56459e14	0.829309	0.414654	+	0.909979i	$0.363902\pi$
$192$	3.04184e14	0.438206
$193$	1.36392e14	0.189962	0.0949812	−	0.995479i	$-0.469721\pi$
$193$	1.36392e14	0.189962	0.0949812	+	0.995479i	$0.469721\pi$
$194$	9.14742e14	1.23193
$195$	−1.23355e14	−0.160669
$196$	1.35748e14	0.171029
$197$	1.02604e15	1.25064	0.625320	−	0.780368i	$-0.284968\pi$
$197$	1.02604e15	1.25064	0.625320	+	0.780368i	$0.284968\pi$
$198$	5.16129e13	0.0608744
$199$	2.51769e14	0.287381	0.143690	−	0.989623i	$-0.454103\pi$
$199$	2.51769e14	0.287381	0.143690	+	0.989623i	$0.454103\pi$
$200$	1.04786e15	1.15774
$201$	−2.29990e14	−0.245999
$202$	−2.70281e14	−0.279918
$203$	−9.02246e14	−0.904900
$204$	3.32494e14	0.322989
$205$	8.47752e12	0.00797753
$206$	−7.38420e13	−0.0673235
$207$	−3.01518e14	−0.266383
$208$	−2.86199e13	−0.0245051
$209$	−1.49432e14	−0.124021
$210$	−5.77728e14	−0.464834
$211$	−1.32712e15	−1.03532	−0.517659	−	0.855587i	$-0.673196\pi$
$211$	−1.32712e15	−1.03532	−0.517659	+	0.855587i	$0.673196\pi$
$212$	8.20591e14	0.620789
$213$	−1.13755e15	−0.834646
$214$	7.48178e14	0.532495
$215$	2.95635e15	2.04130
$216$	2.97370e14	0.199227
$217$	2.22157e15	1.44435
$218$	−1.65301e15	−1.04305
$219$	7.92730e14	0.485555
$220$	−3.76451e14	−0.223852
$221$	−3.31321e14	−0.191293
$222$	7.93469e14	0.444872
$223$	2.42173e15	1.31870	0.659348	−	0.751838i	$-0.270832\pi$
$223$	2.42173e15	1.31870	0.659348	+	0.751838i	$0.270832\pi$
$224$	1.49662e15	0.791590
$225$	7.25512e14	0.372785
$226$	7.52589e14	0.375710
$227$	−3.17178e14	−0.153863	−0.0769316	−	0.997036i	$-0.524512\pi$
$227$	−3.17178e14	−0.153863	−0.0769316	+	0.997036i	$0.524512\pi$
$228$	−3.08768e14	−0.145565
$229$	4.14941e15	1.90132	0.950660	−	0.310234i	$-0.100407\pi$
$229$	4.14941e15	1.90132	0.950660	+	0.310234i	$0.100407\pi$
$230$	−1.73378e15	−0.772260
$231$	3.05534e14	0.132307
$232$	2.67042e15	1.12437
$233$	−1.02774e15	−0.420793	−0.210397	−	0.977616i	$-0.567476\pi$
$233$	−1.02774e15	−0.420793	−0.210397	+	0.977616i	$0.567476\pi$
$234$	−1.06270e14	−0.0423164
$235$	4.50071e15	1.74317
$236$	1.93217e14	0.0727975
$237$	1.13793e15	0.417111
$238$	−1.55173e15	−0.553433
$239$	−3.04875e15	−1.05812	−0.529060	−	0.848584i	$-0.677455\pi$
$239$	−3.04875e15	−1.05812	−0.529060	+	0.848584i	$0.677455\pi$
$240$	3.18842e14	0.107697
$241$	−4.17433e15	−1.37239	−0.686193	−	0.727419i	$-0.740720\pi$
$241$	−4.17433e15	−1.37239	−0.686193	+	0.727419i	$0.740720\pi$
$242$	1.91765e15	0.613720
$243$	2.05891e14	0.0641500
$244$	1.69507e15	0.514226
$245$	1.50697e15	0.445170
$246$	7.30337e12	0.00210109
$247$	3.07679e14	0.0862120
$248$	−6.57528e15	−1.79465
$249$	1.91756e15	0.509862
$250$	4.41503e14	0.114373
$251$	−3.46969e15	−0.875812	−0.437906	−	0.899021i	$-0.644280\pi$
$251$	−3.46969e15	−0.875812	−0.437906	+	0.899021i	$0.644280\pi$
$252$	6.31317e14	0.155290
$253$	9.16918e14	0.219810
$254$	2.41130e15	0.563419
$255$	3.69110e15	0.840707
$256$	−4.75237e15	−1.05524
$257$	−5.20108e15	−1.12597	−0.562986	−	0.826466i	$-0.690348\pi$
$257$	−5.20108e15	−1.12597	−0.562986	+	0.826466i	$0.690348\pi$
$258$	2.54689e15	0.537629
$259$	4.69711e15	0.966901
$260$	7.75107e14	0.155609
$261$	1.84893e15	0.362040
$262$	3.21956e15	0.614948
$263$	7.74985e15	1.44405	0.722023	−	0.691869i	$-0.243213\pi$
$263$	7.74985e15	1.44405	0.722023	+	0.691869i	$0.243213\pi$
$264$	−9.04303e14	−0.164395
$265$	9.10959e15	1.61585
$266$	1.44100e15	0.249421
$267$	−5.08856e15	−0.859551
$268$	1.44515e15	0.238252
$269$	6.57041e15	1.05731	0.528655	−	0.848837i	$-0.322696\pi$
$269$	6.57041e15	1.05731	0.528655	+	0.848837i	$0.322696\pi$
$270$	1.18391e15	0.185975
$271$	2.74962e15	0.421670	0.210835	−	0.977522i	$-0.432382\pi$
$271$	2.74962e15	0.421670	0.210835	+	0.977522i	$0.432382\pi$
$272$	8.56381e14	0.128224
$273$	−6.29089e14	−0.0919719
$274$	−1.29125e15	−0.184345
$275$	−2.20629e15	−0.307609
$276$	1.89460e15	0.257994
$277$	8.55484e15	1.13787	0.568936	−	0.822382i	$-0.307355\pi$
$277$	8.55484e15	1.13787	0.568936	+	0.822382i	$0.307355\pi$
$278$	6.72505e14	0.0873785
$279$	−4.55256e15	−0.577867
$280$	1.01223e16	1.25531
$281$	1.74791e15	0.211801	0.105901	−	0.994377i	$-0.466227\pi$
$281$	1.74791e15	0.211801	0.105901	+	0.994377i	$0.466227\pi$
$282$	3.87735e15	0.459109
$283$	−8.40698e15	−0.972811	−0.486405	−	0.873733i	$-0.661692\pi$
$283$	−8.40698e15	−0.972811	−0.486405	+	0.873733i	$0.661692\pi$
$284$	7.14783e15	0.808361
$285$	−3.42772e15	−0.378890
$286$	3.23168e14	0.0349180
$287$	4.32339e13	0.00456659
$288$	−3.06696e15	−0.316706
$289$	9.39118e12	0.000948165 0
$290$	1.06317e16	1.04958
$291$	−1.10967e16	−1.07125
$292$	−4.98115e15	−0.470263
$293$	4.85086e15	0.447898	0.223949	−	0.974601i	$-0.428105\pi$
$293$	4.85086e15	0.447898	0.223949	+	0.974601i	$0.428105\pi$
$294$	1.29826e15	0.117247
$295$	2.14495e15	0.189484
$296$	−1.39023e16	−1.20140
$297$	−6.26115e14	−0.0529343
$298$	1.00985e16	0.835320
$299$	−1.88792e15	−0.152799
$300$	−4.55879e15	−0.361045
$301$	1.50769e16	1.16850
$302$	9.79967e15	0.743304
$303$	3.27877e15	0.243407
$304$	−7.95272e14	−0.0577880
$305$	1.88174e16	1.33848
$306$	3.17988e15	0.221422
$307$	−1.21767e16	−0.830098	−0.415049	−	0.909799i	$-0.636236\pi$
$307$	−1.21767e16	−0.830098	−0.415049	+	0.909799i	$0.636236\pi$
$308$	−1.91984e15	−0.128140
$309$	8.95777e14	0.0585423
$310$	−2.61780e16	−1.67527
$311$	2.99183e15	0.187497	0.0937485	−	0.995596i	$-0.470115\pi$
$311$	2.99183e15	0.187497	0.0937485	+	0.995596i	$0.470115\pi$
$312$	1.86195e15	0.114278
$313$	−7.73766e15	−0.465127	−0.232563	−	0.972581i	$-0.574711\pi$
$313$	−7.73766e15	−0.465127	−0.232563	+	0.972581i	$0.574711\pi$
$314$	−4.87285e15	−0.286906
$315$	7.00841e15	0.404204
$316$	−7.15024e15	−0.403975
$317$	−1.97145e16	−1.09119	−0.545596	−	0.838048i	$-0.683697\pi$
$317$	−1.97145e16	−1.09119	−0.545596	+	0.838048i	$0.683697\pi$
$318$	7.84790e15	0.425576
$319$	−5.62259e15	−0.298743
$320$	−2.12185e16	−1.10469
$321$	−9.07614e15	−0.463040
$322$	−8.84199e15	−0.442066
$323$	−9.20654e15	−0.451108
$324$	−1.29373e15	−0.0621298
$325$	4.54271e15	0.213832
$326$	−9.79177e15	−0.451800
$327$	2.00526e16	0.907005
$328$	−1.27961e14	−0.00567412
$329$	2.29528e16	0.997845
$330$	−3.60027e15	−0.153460
$331$	−9.82251e15	−0.410526	−0.205263	−	0.978707i	$-0.565805\pi$
$331$	−9.82251e15	−0.410526	−0.205263	+	0.978707i	$0.565805\pi$
$332$	−1.20491e16	−0.493805
$333$	−9.62556e15	−0.386846
$334$	1.28054e15	0.0504711
$335$	1.60430e16	0.620146
$336$	1.62604e15	0.0616489
$337$	−4.07241e16	−1.51446	−0.757230	−	0.653149i	$-0.773448\pi$
$337$	−4.07241e16	−1.51446	−0.757230	+	0.653149i	$0.773448\pi$
$338$	1.75356e16	0.639679
$339$	−9.12965e15	−0.326705
$340$	−2.31932e16	−0.814231
$341$	1.38443e16	0.476835
$342$	−2.95297e15	−0.0997906
$343$	3.28119e16	1.08798
$344$	−4.46238e16	−1.45190
$345$	2.10325e16	0.671531
$346$	−7.07142e15	−0.221571
$347$	4.15074e16	1.27639	0.638196	−	0.769874i	$-0.279681\pi$
$347$	4.15074e16	1.27639	0.638196	+	0.769874i	$0.279681\pi$
$348$	−1.16178e16	−0.350638
$349$	−5.66660e16	−1.67864	−0.839320	−	0.543638i	$-0.817046\pi$
$349$	−5.66660e16	−1.67864	−0.839320	+	0.543638i	$0.817046\pi$
$350$	2.12756e16	0.618641
$351$	1.28916e15	0.0367969
$352$	9.32662e15	0.261335
$353$	5.77632e16	1.58897	0.794485	−	0.607284i	$-0.207741\pi$
$353$	5.77632e16	1.58897	0.794485	+	0.607284i	$0.207741\pi$
$354$	1.84787e15	0.0499057
$355$	7.93499e16	2.10408
$356$	3.19742e16	0.832482
$357$	1.88240e16	0.481247
$358$	−2.90475e16	−0.729237
$359$	4.44467e16	1.09579	0.547893	−	0.836548i	$-0.315430\pi$
$359$	4.44467e16	1.09579	0.547893	+	0.836548i	$0.315430\pi$
$360$	−2.07431e16	−0.502236
$361$	−3.35034e16	−0.796695
$362$	4.88950e16	1.14198
$363$	−2.32630e16	−0.533671
$364$	3.95291e15	0.0890755
$365$	−5.52970e16	−1.22405
$366$	1.62112e16	0.352523
$367$	5.59013e16	1.19424	0.597121	−	0.802151i	$-0.296311\pi$
$367$	5.59013e16	1.19424	0.597121	+	0.802151i	$0.296311\pi$
$368$	4.87979e15	0.102421
$369$	−8.85971e13	−0.00182704
$370$	−5.53486e16	−1.12149
$371$	4.64573e16	0.924962
$372$	2.86062e16	0.559669
$373$	−3.17044e16	−0.609554	−0.304777	−	0.952424i	$-0.598582\pi$
$373$	−3.17044e16	−0.609554	−0.304777	+	0.952424i	$0.598582\pi$
$374$	−9.67002e15	−0.182710
$375$	−5.35586e15	−0.0994549
$376$	−6.79346e16	−1.23985
$377$	1.15768e16	0.207669
$378$	6.03773e15	0.106458
$379$	4.78027e16	0.828509	0.414254	−	0.910161i	$-0.364042\pi$
$379$	4.78027e16	0.828509	0.414254	+	0.910161i	$0.364042\pi$
$380$	2.15382e16	0.366958
$381$	−2.92514e16	−0.489930
$382$	−3.34399e16	−0.550621
$383$	9.39040e16	1.52017	0.760085	−	0.649824i	$-0.225157\pi$
$383$	9.39040e16	1.52017	0.760085	+	0.649824i	$0.225157\pi$
$384$	1.61847e16	0.257603
$385$	−2.13126e16	−0.333535
$386$	−8.19638e15	−0.126126
$387$	−3.08963e16	−0.467504
$388$	6.97267e16	1.03751
$389$	5.23650e16	0.766248	0.383124	−	0.923697i	$-0.374848\pi$
$389$	5.23650e16	0.766248	0.383124	+	0.923697i	$0.374848\pi$
$390$	7.41290e15	0.106676
$391$	5.64914e16	0.799527
$392$	−2.27466e16	−0.316633
$393$	−3.90564e16	−0.534738
$394$	−6.16587e16	−0.830365
$395$	−7.93766e16	−1.05151
$396$	3.93422e15	0.0512673
$397$	7.39522e16	0.948010	0.474005	−	0.880522i	$-0.342808\pi$
$397$	7.39522e16	0.948010	0.474005	+	0.880522i	$0.342808\pi$
$398$	−1.51298e16	−0.190807
$399$	−1.74808e16	−0.216888
$400$	−1.17418e16	−0.143332
$401$	4.83656e16	0.580896	0.290448	−	0.956891i	$-0.406196\pi$
$401$	4.83656e16	0.580896	0.290448	+	0.956891i	$0.406196\pi$
$402$	1.38210e16	0.163332
$403$	−2.85053e16	−0.331469
$404$	−2.06023e16	−0.235742
$405$	−1.43620e16	−0.161717
$406$	5.42196e16	0.600810
$407$	2.92713e16	0.319212
$408$	−5.57142e16	−0.597963
$409$	−1.51915e17	−1.60472	−0.802360	−	0.596840i	$-0.796423\pi$
$409$	−1.51915e17	−1.60472	−0.802360	+	0.596840i	$0.796423\pi$
$410$	−5.09449e14	−0.00529670
$411$	1.56641e16	0.160300
$412$	−5.62865e15	−0.0566986
$413$	1.09389e16	0.108467
$414$	1.81195e16	0.176865
$415$	−1.33760e17	−1.28533
$416$	−1.92034e16	−0.181665
$417$	−8.15815e15	−0.0759814
$418$	8.98000e15	0.0823437
$419$	1.61912e17	1.46180	0.730901	−	0.682483i	$-0.239100\pi$
$419$	1.61912e17	1.46180	0.730901	+	0.682483i	$0.239100\pi$
$420$	−4.40376e16	−0.391475
$421$	−1.21796e16	−0.106610	−0.0533052	−	0.998578i	$-0.516976\pi$
$421$	−1.21796e16	−0.106610	−0.0533052	+	0.998578i	$0.516976\pi$
$422$	7.97520e16	0.687402
$423$	−4.70361e16	−0.399226
$424$	−1.37502e17	−1.14929
$425$	−1.35929e17	−1.11889
$426$	6.83599e16	0.554165
$427$	9.59655e16	0.766186
$428$	5.70303e16	0.448457
$429$	−3.92035e15	−0.0303635
$430$	−1.77659e17	−1.35532
$431$	−1.65911e17	−1.24673	−0.623365	−	0.781931i	$-0.714235\pi$
$431$	−1.65911e17	−1.24673	−0.623365	+	0.781931i	$0.714235\pi$
$432$	−3.33216e15	−0.0246650
$433$	−2.02278e17	−1.47495	−0.737476	−	0.675374i	$-0.763982\pi$
$433$	−2.02278e17	−1.47495	−0.737476	+	0.675374i	$0.763982\pi$
$434$	−1.33503e17	−0.958977
$435$	−1.28972e17	−0.912676
$436$	−1.26001e17	−0.878441
$437$	−5.24604e16	−0.360331
$438$	−4.76383e16	−0.322385
$439$	1.02811e17	0.685519	0.342759	−	0.939423i	$-0.388638\pi$
$439$	1.02811e17	0.685519	0.342759	+	0.939423i	$0.388638\pi$
$440$	6.30799e16	0.414427
$441$	−1.57491e16	−0.101954
$442$	1.99104e16	0.127009
$443$	2.13575e17	1.34254	0.671268	−	0.741215i	$-0.265750\pi$
$443$	2.13575e17	1.34254	0.671268	+	0.741215i	$0.265750\pi$
$444$	6.04826e16	0.374663
$445$	3.54954e17	2.16686
$446$	−1.45532e17	−0.875550
$447$	−1.22505e17	−0.726366
$448$	−1.08210e17	−0.632357
$449$	−2.67823e17	−1.54258	−0.771289	−	0.636485i	$-0.780388\pi$
$449$	−2.67823e17	−1.54258	−0.771289	+	0.636485i	$0.780388\pi$
$450$	−4.35990e16	−0.247511
$451$	2.69424e14	0.00150761
$452$	5.73665e16	0.316416
$453$	−1.18880e17	−0.646352
$454$	1.90605e16	0.102158
$455$	4.38823e16	0.231854
$456$	5.17386e16	0.269490
$457$	−3.14940e16	−0.161723	−0.0808617	−	0.996725i	$-0.525767\pi$
$457$	−3.14940e16	−0.161723	−0.0808617	+	0.996725i	$0.525767\pi$
$458$	−2.49355e17	−1.26239
$459$	−3.85750e16	−0.192541
$460$	−1.32159e17	−0.650383
$461$	−5.04154e14	−0.00244629	−0.00122314	−	0.999999i	$-0.500389\pi$
$461$	−5.04154e14	−0.00244629	−0.00122314	+	0.999999i	$0.500389\pi$
$462$	−1.83608e16	−0.0878452
$463$	1.00687e17	0.475002	0.237501	−	0.971387i	$-0.423672\pi$
$463$	1.00687e17	0.475002	0.237501	+	0.971387i	$0.423672\pi$
$464$	−2.99232e16	−0.139201
$465$	3.17565e17	1.45676
$466$	6.17610e16	0.279387
$467$	−6.15520e16	−0.274589	−0.137294	−	0.990530i	$-0.543841\pi$
$467$	−6.15520e16	−0.274589	−0.137294	+	0.990530i	$0.543841\pi$
$468$	−8.10051e15	−0.0356381
$469$	8.18164e16	0.354991
$470$	−2.70466e17	−1.15738
$471$	5.91124e16	0.249484
$472$	−3.23762e16	−0.134773
$473$	9.39558e16	0.385768
$474$	−6.83829e16	−0.276941
$475$	1.26230e17	0.504260
$476$	−1.18281e17	−0.466091
$477$	−9.52028e16	−0.370067
$478$	1.83212e17	0.702541
$479$	9.25663e16	0.350165	0.175082	−	0.984554i	$-0.443981\pi$
$479$	9.25663e16	0.350165	0.175082	+	0.984554i	$0.443981\pi$
$480$	2.13936e17	0.798392
$481$	−6.02692e16	−0.221898
$482$	2.50853e17	0.911198
$483$	1.07262e17	0.384405
$484$	1.46174e17	0.516864
$485$	7.74054e17	2.70054
$486$	−1.23728e16	−0.0425925
$487$	−5.04053e17	−1.71214	−0.856068	−	0.516864i	$-0.827099\pi$
$487$	−5.04053e17	−1.71214	−0.856068	+	0.516864i	$0.827099\pi$
$488$	−2.84034e17	−0.952009
$489$	1.18784e17	0.392871
$490$	−9.05602e16	−0.295572
$491$	−2.25723e17	−0.727019	−0.363510	−	0.931590i	$-0.618422\pi$
$491$	−2.25723e17	−0.727019	−0.363510	+	0.931590i	$0.618422\pi$
$492$	5.56704e14	0.00176950
$493$	−3.46409e17	−1.08663
$494$	−1.84897e16	−0.0572406
$495$	4.36748e16	0.133444
$496$	7.36789e16	0.222184
$497$	4.04671e17	1.20444
$498$	−1.15234e17	−0.338524
$499$	−5.02541e17	−1.45720	−0.728598	−	0.684942i	$-0.759828\pi$
$499$	−5.02541e17	−1.45720	−0.728598	+	0.684942i	$0.759828\pi$
$500$	3.36538e16	0.0963228
$501$	−1.55343e16	−0.0438879
$502$	2.08508e17	0.581497
$503$	−5.56546e17	−1.53218	−0.766089	−	0.642735i	$-0.777800\pi$
$503$	−5.56546e17	−1.53218	−0.766089	+	0.642735i	$0.777800\pi$
$504$	−1.05786e17	−0.287495
$505$	−2.28711e17	−0.613612
$506$	−5.51013e16	−0.145943
$507$	−2.12724e17	−0.556243
$508$	1.83803e17	0.474501
$509$	−9.61699e15	−0.0245117	−0.0122558	−	0.999925i	$-0.503901\pi$
$509$	−9.61699e15	−0.0245117	−0.0122558	+	0.999925i	$0.503901\pi$
$510$	−2.21813e17	−0.558189
$511$	−2.82005e17	−0.700683
$512$	1.03717e17	0.254446
$513$	3.58225e16	0.0867746
$514$	3.12554e17	0.747592
$515$	−6.24851e16	−0.147581
$516$	1.94138e17	0.452781
$517$	1.43037e17	0.329427
$518$	−2.82268e17	−0.641976
$519$	8.57833e16	0.192670
$520$	−1.29880e17	−0.288086
$521$	2.18076e17	0.477708	0.238854	−	0.971055i	$-0.423228\pi$
$521$	2.18076e17	0.477708	0.238854	+	0.971055i	$0.423228\pi$
$522$	−1.11110e17	−0.240377
$523$	−3.66482e17	−0.783054	−0.391527	−	0.920167i	$-0.628053\pi$
$523$	−3.66482e17	−0.783054	−0.391527	+	0.920167i	$0.628053\pi$
$524$	2.45413e17	0.517898
$525$	−2.58094e17	−0.537950
$526$	−4.65720e17	−0.958777
$527$	8.52951e17	1.73442
$528$	1.01331e16	0.0203527
$529$	−1.82139e17	−0.361362
$530$	−5.47432e17	−1.07285
$531$	−2.24165e16	−0.0433963
$532$	1.09841e17	0.210058
$533$	−5.54740e14	−0.00104800
$534$	3.05792e17	0.570701
$535$	6.33108e17	1.16729
$536$	−2.42156e17	−0.441086
$537$	3.52374e17	0.634120
$538$	−3.94843e17	−0.702003
$539$	4.78931e16	0.0841291
$540$	9.02442e16	0.156625
$541$	2.04481e17	0.350648	0.175324	−	0.984511i	$-0.443903\pi$
$541$	2.04481e17	0.350648	0.175324	+	0.984511i	$0.443903\pi$
$542$	−1.65236e17	−0.279968
$543$	−5.93145e17	−0.993028
$544$	5.74614e17	0.950569
$545$	−1.39877e18	−2.28649
$546$	3.78045e16	0.0610649
$547$	2.66578e17	0.425507	0.212753	−	0.977106i	$-0.431757\pi$
$547$	2.66578e17	0.425507	0.212753	+	0.977106i	$0.431757\pi$
$548$	−9.84263e16	−0.155252
$549$	−1.96657e17	−0.306542
$550$	1.32585e17	0.204238
$551$	3.21690e17	0.489725
$552$	−3.17468e17	−0.477635
$553$	−4.04807e17	−0.601914
$554$	−5.14095e17	−0.755492
$555$	6.71433e17	0.975210
$556$	5.12621e16	0.0735885
$557$	1.21966e18	1.73054	0.865268	−	0.501309i	$-0.167148\pi$
$557$	1.21966e18	1.73054	0.865268	+	0.501309i	$0.167148\pi$
$558$	2.73582e17	0.383676
$559$	−1.93454e17	−0.268164
$560$	−1.13425e17	−0.155412
$561$	1.17307e17	0.158878
$562$	−1.05039e17	−0.140626
$563$	3.55279e17	0.470181	0.235090	−	0.971974i	$-0.424461\pi$
$563$	3.55279e17	0.470181	0.235090	+	0.971974i	$0.424461\pi$
$564$	2.95554e17	0.386653
$565$	6.36841e17	0.823599
$566$	5.05210e17	0.645899
$567$	−7.32437e16	−0.0925721
$568$	−1.19772e18	−1.49655
$569$	−9.08963e17	−1.12284	−0.561418	−	0.827532i	$-0.689744\pi$
$569$	−9.08963e17	−1.12284	−0.561418	+	0.827532i	$0.689744\pi$
$570$	2.05985e17	0.251565
$571$	−5.88871e16	−0.0711026	−0.0355513	−	0.999368i	$-0.511319\pi$
$571$	−5.88871e16	−0.0711026	−0.0355513	+	0.999368i	$0.511319\pi$
$572$	2.46337e16	0.0294073
$573$	4.05659e17	0.478802
$574$	−2.59810e15	−0.00303200
$575$	−7.74548e17	−0.893732
$576$	2.21750e17	0.252999
$577$	−4.27206e16	−0.0481941	−0.0240971	−	0.999710i	$-0.507671\pi$
$577$	−4.27206e16	−0.0481941	−0.0240971	+	0.999710i	$0.507671\pi$
$578$	−5.64354e14	−0.000629536 0
$579$	9.94301e16	0.109675
$580$	8.10404e17	0.883933
$581$	−6.82152e17	−0.735760
$582$	6.66847e17	0.711257
$583$	2.89512e17	0.305366
$584$	8.34664e17	0.870619
$585$	−8.99258e16	−0.0927623
$586$	−2.91508e17	−0.297383
$587$	1.77715e17	0.179298	0.0896492	−	0.995973i	$-0.471425\pi$
$587$	1.77715e17	0.179298	0.0896492	+	0.995973i	$0.471425\pi$
$588$	9.89603e16	0.0987435
$589$	−7.92087e17	−0.781670
$590$	−1.28899e17	−0.125808
$591$	7.47981e17	0.722058
$592$	1.55781e17	0.148738
$593$	−1.45819e18	−1.37708	−0.688541	−	0.725197i	$-0.741749\pi$
$593$	−1.45819e18	−1.37708	−0.688541	+	0.725197i	$0.741749\pi$
$594$	3.76258e16	0.0351459
$595$	−1.31307e18	−1.21319
$596$	7.69767e17	0.703491
$597$	1.83540e17	0.165919
$598$	1.13453e17	0.101451
$599$	6.23019e16	0.0551096	0.0275548	−	0.999620i	$-0.491228\pi$
$599$	6.23019e16	0.0551096	0.0275548	+	0.999620i	$0.491228\pi$
$600$	7.63892e17	0.668419
$601$	−7.12658e17	−0.616875	−0.308437	−	0.951245i	$-0.599806\pi$
$601$	−7.12658e17	−0.616875	−0.308437	+	0.951245i	$0.599806\pi$
$602$	−9.06031e17	−0.775829
$603$	−1.67662e17	−0.142028
$604$	7.46985e17	0.625997
$605$	1.62272e18	1.34534
$606$	−1.97034e17	−0.161611
$607$	−1.59346e18	−1.29305	−0.646525	−	0.762893i	$-0.723778\pi$
$607$	−1.59346e18	−1.29305	−0.646525	+	0.762893i	$0.723778\pi$
$608$	−5.33612e17	−0.428403
$609$	−6.57737e17	−0.522444
$610$	−1.13081e18	−0.888684
$611$	−2.94511e17	−0.228999
$612$	2.42388e17	0.186478
$613$	1.53584e18	1.16910	0.584552	−	0.811356i	$-0.301270\pi$
$613$	1.53584e18	1.16910	0.584552	+	0.811356i	$0.301270\pi$
$614$	7.31746e17	0.551145
$615$	6.18011e15	0.00460583
$616$	3.21696e17	0.237231
$617$	1.69013e18	1.23329	0.616647	−	0.787240i	$-0.288491\pi$
$617$	1.69013e18	1.23329	0.616647	+	0.787240i	$0.288491\pi$
$618$	−5.38308e16	−0.0388692
$619$	−1.01975e18	−0.728628	−0.364314	−	0.931276i	$-0.618696\pi$
$619$	−1.01975e18	−0.728628	−0.364314	+	0.931276i	$0.618696\pi$
$620$	−1.99543e18	−1.41088
$621$	−2.19807e17	−0.153796
$622$	−1.79791e17	−0.124489
$623$	1.81020e18	1.24038
$624$	−2.08639e16	−0.0141480
$625$	−1.29288e18	−0.867637
$626$	4.64987e17	0.308822
$627$	−1.08936e17	−0.0716033
$628$	−3.71436e17	−0.241627
$629$	1.80341e18	1.16109
$630$	−4.21164e17	−0.268372
$631$	1.17079e18	0.738392	0.369196	−	0.929352i	$-0.379633\pi$
$631$	1.17079e18	0.738392	0.369196	+	0.929352i	$0.379633\pi$
$632$	1.19813e18	0.747897
$633$	−9.67470e17	−0.597741
$634$	1.18473e18	0.724499
$635$	2.04044e18	1.23508
$636$	5.98211e17	0.358412
$637$	−9.86112e16	−0.0584817
$638$	3.37884e17	0.198351
$639$	−8.29272e17	−0.481883
$640$	−1.12897e18	−0.649398
$641$	1.48643e17	0.0846381	0.0423191	−	0.999104i	$-0.486525\pi$
$641$	1.48643e17	0.0846381	0.0423191	+	0.999104i	$0.486525\pi$
$642$	5.45422e17	0.307436
$643$	5.73901e17	0.320233	0.160116	−	0.987098i	$-0.448813\pi$
$643$	5.73901e17	0.320233	0.160116	+	0.987098i	$0.448813\pi$
$644$	−6.73986e17	−0.372300
$645$	2.15518e18	1.17854
$646$	5.53259e17	0.299514
$647$	−3.48724e18	−1.86898	−0.934489	−	0.355992i	$-0.884143\pi$
$647$	−3.48724e18	−1.86898	−0.934489	+	0.355992i	$0.884143\pi$
$648$	2.16783e17	0.115024
$649$	6.81685e16	0.0358091
$650$	−2.72990e17	−0.141974
$651$	1.61952e18	0.833895
$652$	−7.46383e17	−0.380498
$653$	1.51158e18	0.762950	0.381475	−	0.924379i	$-0.375416\pi$
$653$	1.51158e18	0.762950	0.381475	+	0.924379i	$0.375416\pi$
$654$	−1.20504e18	−0.602208
$655$	2.72439e18	1.34803
$656$	1.43386e15	0.000702478 0
$657$	5.77900e17	0.280335
$658$	−1.37933e18	−0.662521
$659$	8.36218e17	0.397708	0.198854	−	0.980029i	$-0.436278\pi$
$659$	8.36218e17	0.397708	0.198854	+	0.980029i	$0.436278\pi$
$660$	−2.74433e17	−0.129241
$661$	−6.16807e16	−0.0287634	−0.0143817	−	0.999897i	$-0.504578\pi$
$661$	−6.16807e16	−0.0287634	−0.0143817	+	0.999897i	$0.504578\pi$
$662$	5.90274e17	0.272569
$663$	−2.41533e17	−0.110443
$664$	2.01900e18	0.914204
$665$	1.21937e18	0.546760
$666$	5.78439e17	0.256847
$667$	−1.97389e18	−0.867971
$668$	9.76102e16	0.0425058
$669$	1.76544e18	0.761349
$670$	−9.64087e17	−0.411747
$671$	5.98036e17	0.252948
$672$	1.09104e18	0.457025
$673$	−2.26568e17	−0.0939940	−0.0469970	−	0.998895i	$-0.514965\pi$
$673$	−2.26568e17	−0.0939940	−0.0469970	+	0.998895i	$0.514965\pi$
$674$	2.44728e18	1.00553
$675$	5.28899e17	0.215228
$676$	1.33666e18	0.538726
$677$	3.02856e18	1.20895	0.604476	−	0.796623i	$-0.293382\pi$
$677$	3.02856e18	1.20895	0.604476	+	0.796623i	$0.293382\pi$
$678$	5.48638e17	0.216916
$679$	3.94754e18	1.54587
$680$	3.88636e18	1.50742
$681$	−2.31223e17	−0.0888330
$682$	−8.31962e17	−0.316596
$683$	4.54159e18	1.71188	0.855941	−	0.517074i	$-0.172979\pi$
$683$	4.54159e18	1.71188	0.855941	+	0.517074i	$0.172979\pi$
$684$	−2.25092e17	−0.0840418
$685$	−1.09266e18	−0.404105
$686$	−1.97180e18	−0.722365
$687$	3.02492e18	1.09773
$688$	5.00028e17	0.179750
$689$	−5.96101e17	−0.212273
$690$	−1.26393e18	−0.445864
$691$	−1.64481e18	−0.574788	−0.287394	−	0.957812i	$-0.592789\pi$
$691$	−1.64481e18	−0.574788	−0.287394	+	0.957812i	$0.592789\pi$
$692$	−5.39023e17	−0.186603
$693$	2.22734e17	0.0763872
$694$	−2.49435e18	−0.847462
$695$	5.69074e17	0.191543
$696$	1.94673e18	0.649152
$697$	1.65992e16	0.00548372
$698$	3.40529e18	1.11454
$699$	−7.49221e17	−0.242945
$700$	1.62174e18	0.521008
$701$	3.67549e17	0.116990	0.0584949	−	0.998288i	$-0.481370\pi$
$701$	3.67549e17	0.116990	0.0584949	+	0.998288i	$0.481370\pi$
$702$	−7.74710e16	−0.0244314
$703$	−1.67473e18	−0.523280
$704$	−6.74343e17	−0.208766
$705$	3.28102e18	1.00642
$706$	−3.47123e18	−1.05500
$707$	−1.16639e18	−0.351250
$708$	1.40855e17	0.0420296
$709$	−4.11055e15	−0.00121534	−0.000607672	−	1.00000i	$-0.500193\pi$
$709$	−4.11055e15	−0.00121534	−0.000607672		1.00000i	$0.500193\pi$
$710$	−4.76846e18	−1.39701
$711$	8.29551e17	0.240819
$712$	−5.35774e18	−1.54121
$713$	4.86025e18	1.38540
$714$	−1.13121e18	−0.319525
$715$	2.73465e17	0.0765441
$716$	−2.21416e18	−0.614150
$717$	−2.22254e18	−0.610906
$718$	−2.67099e18	−0.727550
$719$	−2.98850e18	−0.806707	−0.403354	−	0.915044i	$-0.632156\pi$
$719$	−2.98850e18	−0.806707	−0.403354	+	0.915044i	$0.632156\pi$
$720$	2.32436e17	0.0621787
$721$	−3.18663e17	−0.0844798
$722$	2.01335e18	0.528967
$723$	−3.04309e18	−0.792348
$724$	3.72705e18	0.961755
$725$	4.74957e18	1.21467
$726$	1.39797e18	0.354332
$727$	4.78687e18	1.20248	0.601241	−	0.799068i	$-0.294673\pi$
$727$	4.78687e18	1.20248	0.601241	+	0.799068i	$0.294673\pi$
$728$	−6.62368e17	−0.164909
$729$	1.50095e17	0.0370370
$730$	3.32302e18	0.812709
$731$	5.78863e18	1.40318
$732$	1.23571e18	0.296888
$733$	1.57343e18	0.374689	0.187344	−	0.982294i	$-0.440012\pi$
$733$	1.57343e18	0.374689	0.187344	+	0.982294i	$0.440012\pi$
$734$	−3.35934e18	−0.792919
$735$	1.09858e18	0.257019
$736$	3.27424e18	0.759286
$737$	5.09862e17	0.117196
$738$	5.32416e15	0.00121307
$739$	−3.70489e18	−0.836731	−0.418366	−	0.908279i	$-0.637397\pi$
$739$	−3.70489e18	−0.836731	−0.418366	+	0.908279i	$0.637397\pi$
$740$	−4.21898e18	−0.944498
$741$	2.24298e17	0.0497745
$742$	−2.79181e18	−0.614130
$743$	−3.08237e18	−0.672136	−0.336068	−	0.941838i	$-0.609097\pi$
$743$	−3.08237e18	−0.672136	−0.336068	+	0.941838i	$0.609097\pi$
$744$	−4.79338e18	−1.03614
$745$	8.54538e18	1.83112
$746$	1.90525e18	0.404715
$747$	1.39790e18	0.294369
$748$	−7.37103e17	−0.153875
$749$	3.22874e18	0.668192
$750$	3.21855e17	0.0660332
$751$	−4.35431e18	−0.885646	−0.442823	−	0.896609i	$-0.646023\pi$
$751$	−4.35431e18	−0.885646	−0.442823	+	0.896609i	$0.646023\pi$
$752$	7.61236e17	0.153498
$753$	−2.52940e18	−0.505650
$754$	−6.95699e17	−0.137882
$755$	8.29248e18	1.62941
$756$	4.60230e17	0.0896568
$757$	2.06249e18	0.398353	0.199177	−	0.979964i	$-0.436173\pi$
$757$	2.06249e18	0.398353	0.199177	+	0.979964i	$0.436173\pi$
$758$	−2.87266e18	−0.550090
$759$	6.68433e17	0.126907
$760$	−3.60904e18	−0.679365
$761$	−9.83309e17	−0.183523	−0.0917613	−	0.995781i	$-0.529250\pi$
$761$	−9.83309e17	−0.183523	−0.0917613	+	0.995781i	$0.529250\pi$
$762$	1.75784e18	0.325290
$763$	−7.13350e18	−1.30886
$764$	−2.54897e18	−0.463723
$765$	2.69081e18	0.485382
$766$	−5.64307e18	−1.00932
$767$	−1.40358e17	−0.0248924
$768$	−3.46448e18	−0.609242
$769$	1.44487e18	0.251946	0.125973	−	0.992034i	$-0.459795\pi$
$769$	1.44487e18	0.251946	0.125973	+	0.992034i	$0.459795\pi$
$770$	1.28076e18	0.221451
$771$	−3.79158e18	−0.650081
$772$	−6.24773e17	−0.106221
$773$	−1.13834e19	−1.91914	−0.959568	−	0.281476i	$-0.909176\pi$
$773$	−1.13834e19	−1.91914	−0.959568	+	0.281476i	$0.909176\pi$
$774$	1.85669e18	0.310400
$775$	−1.16947e19	−1.93878
$776$	−1.16837e19	−1.92079
$777$	3.42419e18	0.558241
$778$	−3.14683e18	−0.508751
$779$	−1.54148e16	−0.00247140
$780$	5.65053e17	0.0898409
$781$	2.52182e18	0.397633
$782$	−3.39480e18	−0.530848
$783$	1.34787e18	0.209024
$784$	2.54885e17	0.0392003
$785$	−4.12340e18	−0.628931
$786$	2.34706e18	0.355040
$787$	−6.01503e18	−0.902406	−0.451203	−	0.892421i	$-0.649005\pi$
$787$	−6.01503e18	−0.902406	−0.451203	+	0.892421i	$0.649005\pi$
$788$	−4.69997e18	−0.699318
$789$	5.64964e18	0.833720
$790$	4.77006e18	0.698149
$791$	3.24778e18	0.471454
$792$	−6.59237e17	−0.0949134
$793$	−1.23135e18	−0.175835
$794$	−4.44409e18	−0.629433
$795$	6.64089e18	0.932911
$796$	−1.15328e18	−0.160694
$797$	1.50872e18	0.208511	0.104256	−	0.994551i	$-0.466754\pi$
$797$	1.50872e18	0.208511	0.104256	+	0.994551i	$0.466754\pi$
$798$	1.05049e18	0.144003
$799$	8.81252e18	1.19825
$800$	−7.87848e18	−1.06257
$801$	−3.70956e18	−0.496262
$802$	−2.90648e18	−0.385687
$803$	−1.75739e18	−0.231323
$804$	1.05351e18	0.137555
$805$	−7.48209e18	−0.969057
$806$	1.71300e18	0.220079
$807$	4.78983e18	0.610439
$808$	3.45221e18	0.436439
$809$	−5.57340e17	−0.0698964	−0.0349482	−	0.999389i	$-0.511127\pi$
$809$	−5.57340e17	−0.0698964	−0.0349482	+	0.999389i	$0.511127\pi$
$810$	8.63070e17	0.107373
$811$	7.21194e18	0.890054	0.445027	−	0.895517i	$-0.353194\pi$
$811$	7.21194e18	0.890054	0.445027	+	0.895517i	$0.353194\pi$
$812$	4.13292e18	0.505991
$813$	2.00447e18	0.243451
$814$	−1.75903e18	−0.211941
$815$	−8.28579e18	−0.990397
$816$	6.24301e17	0.0740301
$817$	−5.37557e18	−0.632384
$818$	9.12919e18	1.06546
$819$	−4.58606e17	−0.0531000
$820$	−3.88330e16	−0.00446078
$821$	−1.02826e18	−0.117185	−0.0585925	−	0.998282i	$-0.518661\pi$
$821$	−1.02826e18	−0.117185	−0.0585925	+	0.998282i	$0.518661\pi$
$822$	−9.41321e17	−0.106432
$823$	−5.25999e18	−0.590046	−0.295023	−	0.955490i	$-0.595327\pi$
$823$	−5.25999e18	−0.590046	−0.295023	+	0.955490i	$0.595327\pi$
$824$	9.43163e17	0.104969
$825$	−1.60838e18	−0.177598
$826$	−6.57360e17	−0.0720167
$827$	−4.84358e18	−0.526479	−0.263239	−	0.964731i	$-0.584791\pi$
$827$	−4.84358e18	−0.526479	−0.263239	+	0.964731i	$0.584791\pi$
$828$	1.38117e18	0.148953
$829$	−5.32238e18	−0.569510	−0.284755	−	0.958600i	$-0.591912\pi$
$829$	−5.32238e18	−0.569510	−0.284755	+	0.958600i	$0.591912\pi$
$830$	8.03817e18	0.853394
$831$	6.23648e18	0.656951
$832$	1.38846e18	0.145122
$833$	2.95070e18	0.306008
$834$	4.90256e17	0.0504480
$835$	1.08360e18	0.110638
$836$	6.84506e17	0.0693484
$837$	−3.31881e18	−0.333632
$838$	−9.72997e18	−0.970566
$839$	−1.15945e19	−1.14763	−0.573813	−	0.818986i	$-0.694536\pi$
$839$	−1.15945e19	−1.14763	−0.573813	+	0.818986i	$0.694536\pi$
$840$	7.37915e18	0.724754
$841$	1.84339e18	0.179657
$842$	7.31922e17	0.0707842
$843$	1.27423e18	0.122284
$844$	6.07914e18	0.578917
$845$	1.48386e19	1.40225
$846$	2.82659e18	0.265067
$847$	8.27559e18	0.770117
$848$	1.54077e18	0.142287
$849$	−6.12869e18	−0.561652
$850$	8.16855e18	0.742886
$851$	1.02761e19	0.927443
$852$	5.21077e18	0.466707
$853$	−1.81956e19	−1.61732	−0.808661	−	0.588275i	$-0.799807\pi$
$853$	−1.81956e19	−1.61732	−0.808661	+	0.588275i	$0.799807\pi$
$854$	−5.76696e18	−0.508710
$855$	−2.49880e18	−0.218752
$856$	−9.55626e18	−0.830249
$857$	−1.55587e17	−0.0134153	−0.00670763	−	0.999978i	$-0.502135\pi$
$857$	−1.55587e17	−0.0134153	−0.00670763	+	0.999978i	$0.502135\pi$
$858$	2.35589e17	0.0201599
$859$	−2.21845e19	−1.88406	−0.942030	−	0.335529i	$-0.891085\pi$
$859$	−2.21845e19	−1.88406	−0.942030	+	0.335529i	$0.891085\pi$
$860$	−1.35422e19	−1.14143
$861$	3.15175e16	0.00263652
$862$	9.97025e18	0.827769
$863$	−1.43516e19	−1.18258	−0.591289	−	0.806460i	$-0.701381\pi$
$863$	−1.43516e19	−1.18258	−0.591289	+	0.806460i	$0.701381\pi$
$864$	−2.23581e18	−0.182850
$865$	−5.98384e18	−0.485708
$866$	1.21557e19	0.979297
$867$	6.84617e15	0.000547423 0
$868$	−1.01764e19	−0.807633
$869$	−2.52267e18	−0.198715
$870$	7.75047e18	0.605973
$871$	−1.04980e18	−0.0814681
$872$	2.11133e19	1.62630
$873$	−8.08950e18	−0.618485
$874$	3.15256e18	0.239243
$875$	1.90529e18	0.143519
$876$	−3.63126e18	−0.271507
$877$	2.37126e18	0.175988	0.0879939	−	0.996121i	$-0.471954\pi$
$877$	2.37126e18	0.175988	0.0879939	+	0.996121i	$0.471954\pi$
$878$	−6.17832e18	−0.455151
$879$	3.53628e18	0.258594
$880$	−7.06837e17	−0.0513076
$881$	−1.27667e19	−0.919888	−0.459944	−	0.887948i	$-0.652130\pi$
$881$	−1.27667e19	−0.919888	−0.459944	+	0.887948i	$0.652130\pi$
$882$	9.46429e17	0.0676927
$883$	2.78599e18	0.197804	0.0989018	−	0.995097i	$-0.468467\pi$
$883$	2.78599e18	0.197804	0.0989018	+	0.995097i	$0.468467\pi$
$884$	1.51768e18	0.106965
$885$	1.56367e18	0.109399
$886$	−1.28346e19	−0.891379
$887$	−5.15165e18	−0.355175	−0.177588	−	0.984105i	$-0.556829\pi$
$887$	−5.15165e18	−0.355175	−0.177588	+	0.984105i	$0.556829\pi$
$888$	−1.01347e19	−0.693631
$889$	1.04059e19	0.706997
$890$	−2.13306e19	−1.43869
$891$	−4.56438e17	−0.0305617
$892$	−1.10932e19	−0.737373
$893$	−8.18369e18	−0.540026
$894$	7.36184e18	0.482272
$895$	−2.45800e19	−1.59857
$896$	−5.75753e18	−0.371736
$897$	−1.37629e18	−0.0882186
$898$	1.60946e19	1.02420
$899$	−2.98033e19	−1.88290
$900$	−3.32336e18	−0.208449
$901$	1.78369e19	1.11073
$902$	−1.61908e16	−0.00100098
$903$	1.09910e19	0.674635
$904$	−9.61260e18	−0.585796
$905$	4.13749e19	2.50335
$906$	7.14396e18	0.429147
$907$	−1.31359e19	−0.783452	−0.391726	−	0.920082i	$-0.628122\pi$
$907$	−1.31359e19	−0.783452	−0.391726	+	0.920082i	$0.628122\pi$
$908$	1.45290e18	0.0860354
$909$	2.39022e18	0.140531
$910$	−2.63706e18	−0.153940
$911$	−1.27123e19	−0.736810	−0.368405	−	0.929665i	$-0.620096\pi$
$911$	−1.27123e19	−0.736810	−0.368405	+	0.929665i	$0.620096\pi$
$912$	−5.79754e17	−0.0333639
$913$	−4.25102e18	−0.242903
$914$	1.89260e18	0.107377
$915$	1.37179e19	0.772770
$916$	−1.90072e19	−1.06316
$917$	1.38939e19	0.771657
$918$	2.31813e18	0.127838
$919$	−2.80232e19	−1.53450	−0.767251	−	0.641347i	$-0.778376\pi$
$919$	−2.80232e19	−1.53450	−0.767251	+	0.641347i	$0.778376\pi$
$920$	2.21451e19	1.20408
$921$	−8.87680e18	−0.479258
$922$	3.02967e16	0.00162422
$923$	−5.19239e18	−0.276411
$924$	−1.39956e18	−0.0739816
$925$	−2.47264e19	−1.29789
$926$	−6.05067e18	−0.315379
$927$	6.53021e17	0.0337994
$928$	−2.00779e19	−1.03194
$929$	3.48107e19	1.77669	0.888343	−	0.459180i	$-0.151857\pi$
$929$	3.48107e19	1.77669	0.888343	+	0.459180i	$0.151857\pi$
$930$	−1.90837e19	−0.967218
$931$	−2.74015e18	−0.137912
$932$	4.70776e18	0.235294
$933$	2.18104e18	0.108251
$934$	3.69891e18	0.182314
$935$	−8.18276e18	−0.400520
$936$	1.35736e18	0.0659783
$937$	−1.42948e19	−0.690033	−0.345016	−	0.938597i	$-0.612127\pi$
$937$	−1.42948e19	−0.690033	−0.345016	+	0.938597i	$0.612127\pi$
$938$	−4.91668e18	−0.235697
$939$	−5.64075e18	−0.268541
$940$	−2.06164e19	−0.974725
$941$	2.64152e19	1.24028	0.620141	−	0.784490i	$-0.287075\pi$
$941$	2.64152e19	1.24028	0.620141	+	0.784490i	$0.287075\pi$
$942$	−3.55231e18	−0.165645
$943$	9.45851e16	0.00438023
$944$	3.62790e17	0.0166854
$945$	5.10913e18	0.233367
$946$	−5.64618e18	−0.256131
$947$	3.19369e18	0.143886	0.0719429	−	0.997409i	$-0.477080\pi$
$947$	3.19369e18	0.143886	0.0719429	+	0.997409i	$0.477080\pi$
$948$	−5.21252e18	−0.233235
$949$	3.61845e18	0.160802
$950$	−7.58567e18	−0.334804
$951$	−1.43719e19	−0.630000
$952$	1.98197e19	0.862895
$953$	1.15302e19	0.498576	0.249288	−	0.968429i	$-0.419803\pi$
$953$	1.15302e19	0.498576	0.249288	+	0.968429i	$0.419803\pi$
$954$	5.72112e18	0.245707
$955$	−2.82968e19	−1.20702
$956$	1.39654e19	0.591667
$957$	−4.09887e18	−0.172479
$958$	−5.56269e18	−0.232492
$959$	−5.57235e18	−0.231322
$960$	−1.54683e19	−0.637791
$961$	4.89663e19	2.00537
$962$	3.62182e18	0.147329
$963$	−6.61650e18	−0.267336
$964$	1.91214e19	0.767395
$965$	−6.93577e18	−0.276482
$966$	−6.44581e18	−0.255227
$967$	4.94665e17	0.0194554	0.00972768	−	0.999953i	$-0.496904\pi$
$967$	4.94665e17	0.0194554	0.00972768	+	0.999953i	$0.496904\pi$
$968$	−2.44936e19	−0.956893
$969$	−6.71157e18	−0.260447
$970$	−4.65160e19	−1.79303
$971$	−1.35153e19	−0.517490	−0.258745	−	0.965946i	$-0.583309\pi$
$971$	−1.35153e19	−0.517490	−0.258745	+	0.965946i	$0.583309\pi$
$972$	−9.43126e17	−0.0358706
$973$	2.90218e18	0.109645
$974$	3.02906e19	1.13678
$975$	3.31163e18	0.123456
$976$	3.18272e18	0.117862
$977$	2.64407e19	0.972655	0.486328	−	0.873777i	$-0.338336\pi$
$977$	2.64407e19	0.972655	0.486328	+	0.873777i	$0.338336\pi$
$978$	−7.13820e18	−0.260847
$979$	1.12808e19	0.409498
$980$	−6.90300e18	−0.248925
$981$	1.46183e19	0.523660
$982$	1.35646e19	0.482706
$983$	1.35645e19	0.479519	0.239759	−	0.970832i	$-0.422931\pi$
$983$	1.35645e19	0.479519	0.239759	+	0.970832i	$0.422931\pi$
$984$	−9.32838e16	−0.00327596
$985$	−5.21756e19	−1.82025
$986$	2.08171e19	0.721473
$987$	1.67326e19	0.576106
$988$	−1.40939e18	−0.0482070
$989$	3.29845e19	1.12082
$990$	−2.62460e18	−0.0886001
$991$	1.07510e19	0.360552	0.180276	−	0.983616i	$-0.442301\pi$
$991$	1.07510e19	0.360552	0.180276	+	0.983616i	$0.442301\pi$
$992$	4.94371e19	1.64713
$993$	−7.16061e18	−0.237017
$994$	−2.43183e19	−0.799691
$995$	−1.28029e19	−0.418271
$996$	−8.78377e18	−0.285099
$997$	4.04824e19	1.30541	0.652706	−	0.757612i	$-0.273634\pi$
$997$	4.04824e19	1.30541	0.652706	+	0.757612i	$0.273634\pi$
$998$	3.01997e19	0.967508
$999$	−7.01703e18	−0.223346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.10	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.10	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-60.0941 q^{2} +729.000 q^{3} -4580.70 q^{4} -50851.6 q^{5} -43808.6 q^{6} -259334. q^{7} +767564. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-60.0941 q^{2} +729.000 q^{3} -4580.70 q^{4} -50851.6 q^{5} -43808.6 q^{6} -259334. q^{7} +767564. q^{8} +531441. q^{9} +3.05588e6 q^{10} -1.61611e6 q^{11} -3.33933e6 q^{12} +3.32755e6 q^{13} +1.55844e7 q^{14} -3.70708e7 q^{15} -8.60088e6 q^{16} -9.95689e7 q^{17} -3.19364e7 q^{18} +9.24640e7 q^{19} +2.32936e8 q^{20} -1.89055e8 q^{21} +9.71188e7 q^{22} -5.67360e8 q^{23} +5.59554e8 q^{24} +1.36518e9 q^{25} -1.99966e8 q^{26} +3.87420e8 q^{27} +1.18793e9 q^{28} +3.47908e9 q^{29} +2.22773e9 q^{30} -8.56644e9 q^{31} -5.77102e9 q^{32} -1.17815e9 q^{33} +5.98350e9 q^{34} +1.31876e10 q^{35} -2.43437e9 q^{36} -1.81122e10 q^{37} -5.55654e9 q^{38} +2.42579e9 q^{39} -3.90318e10 q^{40} -1.66711e8 q^{41} +1.13611e10 q^{42} -5.81369e10 q^{43} +7.40294e9 q^{44} -2.70246e10 q^{45} +3.40949e10 q^{46} -8.85067e10 q^{47} -6.27004e9 q^{48} -2.96348e10 q^{49} -8.20392e10 q^{50} -7.25857e10 q^{51} -1.52425e10 q^{52} -1.79141e11 q^{53} -2.32817e10 q^{54} +8.21819e10 q^{55} -1.99056e11 q^{56} +6.74063e10 q^{57} -2.09072e11 q^{58} -4.21805e10 q^{59} +1.69810e11 q^{60} -3.70046e11 q^{61} +5.14792e11 q^{62} -1.37821e11 q^{63} +4.17262e11 q^{64} -1.69211e11 q^{65} +7.07996e10 q^{66} -3.15486e11 q^{67} +4.56096e11 q^{68} -4.13605e11 q^{69} -7.92494e11 q^{70} -1.56042e12 q^{71} +4.07915e11 q^{72} +1.08742e12 q^{73} +1.08843e12 q^{74} +9.95216e11 q^{75} -4.23550e11 q^{76} +4.19114e11 q^{77} -1.45775e11 q^{78} +1.56095e12 q^{79} +4.37368e11 q^{80} +2.82430e11 q^{81} +1.00183e10 q^{82} +2.63040e12 q^{83} +8.66004e11 q^{84} +5.06324e12 q^{85} +3.49368e12 q^{86} +2.53625e12 q^{87} -1.24047e12 q^{88} -6.98019e12 q^{89} +1.62402e12 q^{90} -8.62948e11 q^{91} +2.59891e12 q^{92} -6.24493e12 q^{93} +5.31873e12 q^{94} -4.70194e12 q^{95} -4.20707e12 q^{96} -1.52218e13 q^{97} +1.78087e12 q^{98} -8.58869e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more