LMFDB - Embedded newform 177.14.a.c.1.30

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			1.30
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)

$f(q)$	$=$	$q+174.739 q^{2} +729.000 q^{3} +22341.8 q^{4} -38561.4 q^{5} +127385. q^{6} -236058. q^{7} +2.47253e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q+174.739 q^{2} +729.000 q^{3} +22341.8 q^{4} -38561.4 q^{5} +127385. q^{6} -236058. q^{7} +2.47253e6 q^{8} +531441. q^{9} -6.73820e6 q^{10} +7.91074e6 q^{11} +1.62872e7 q^{12} +3.86463e6 q^{13} -4.12485e7 q^{14} -2.81113e7 q^{15} +2.49024e8 q^{16} -8.38759e7 q^{17} +9.28636e7 q^{18} +1.09809e8 q^{19} -8.61532e8 q^{20} -1.72086e8 q^{21} +1.38232e9 q^{22} +5.43275e8 q^{23} +1.80247e9 q^{24} +2.66280e8 q^{25} +6.75302e8 q^{26} +3.87420e8 q^{27} -5.27395e9 q^{28} -6.42640e8 q^{29} -4.91214e9 q^{30} +6.97293e9 q^{31} +2.32593e10 q^{32} +5.76693e9 q^{33} -1.46564e10 q^{34} +9.10271e9 q^{35} +1.18734e10 q^{36} -2.07338e9 q^{37} +1.91880e10 q^{38} +2.81731e9 q^{39} -9.53442e10 q^{40} +2.58258e10 q^{41} -3.00702e10 q^{42} -5.08755e9 q^{43} +1.76740e11 q^{44} -2.04931e10 q^{45} +9.49315e10 q^{46} +5.45094e10 q^{47} +1.81538e11 q^{48} -4.11659e10 q^{49} +4.65296e10 q^{50} -6.11455e10 q^{51} +8.63428e10 q^{52} -8.09687e10 q^{53} +6.76976e10 q^{54} -3.05049e11 q^{55} -5.83659e11 q^{56} +8.00508e10 q^{57} -1.12295e11 q^{58} -4.21805e10 q^{59} -6.28057e11 q^{60} +8.52456e10 q^{61} +1.21844e12 q^{62} -1.25451e11 q^{63} +2.02431e12 q^{64} -1.49026e11 q^{65} +1.00771e12 q^{66} +6.87562e11 q^{67} -1.87394e12 q^{68} +3.96048e11 q^{69} +1.59060e12 q^{70} +1.01676e12 q^{71} +1.31400e12 q^{72} +1.75257e12 q^{73} -3.62302e11 q^{74} +1.94118e11 q^{75} +2.45333e12 q^{76} -1.86739e12 q^{77} +4.92295e11 q^{78} +1.74363e12 q^{79} -9.60271e12 q^{80} +2.82430e11 q^{81} +4.51278e12 q^{82} +2.86302e12 q^{83} -3.84471e12 q^{84} +3.23437e12 q^{85} -8.88995e11 q^{86} -4.68485e11 q^{87} +1.95595e13 q^{88} +7.08189e12 q^{89} -3.58095e12 q^{90} -9.12274e11 q^{91} +1.21378e13 q^{92} +5.08326e12 q^{93} +9.52494e12 q^{94} -4.23439e12 q^{95} +1.69560e13 q^{96} +1.48484e12 q^{97} -7.19329e12 q^{98} +4.20409e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	174.739	1.93061	0.965307	−	0.261117i	$-0.0840907\pi$
$2$	174.739	1.93061	0.965307	+	0.261117i	$0.0840907\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	22341.8	2.72727
$5$	−38561.4	−1.10369	−0.551846	−	0.833946i	$-0.686076\pi$
$5$	−38561.4	−1.10369	−0.551846	+	0.833946i	$0.686076\pi$
$6$	127385.	1.11464
$7$	−236058.	−0.758369	−0.379185	−	0.925321i	$-0.623795\pi$
$7$	−236058.	−0.758369	−0.379185	+	0.925321i	$0.623795\pi$
$8$	2.47253e6	3.33470
$9$	531441.	0.333333
$10$	−6.73820e6	−2.13080
$11$	7.91074e6	1.34637	0.673185	−	0.739474i	$-0.264926\pi$
$11$	7.91074e6	1.34637	0.673185	+	0.739474i	$0.264926\pi$
$12$	1.62872e7	1.57459
$13$	3.86463e6	0.222063	0.111031	−	0.993817i	$-0.464585\pi$
$13$	3.86463e6	0.222063	0.111031	+	0.993817i	$0.464585\pi$
$14$	−4.12485e7	−1.46412
$15$	−2.81113e7	−0.637217
$16$	2.49024e8	3.71074
$17$	−8.38759e7	−0.842790	−0.421395	−	0.906877i	$-0.638459\pi$
$17$	−8.38759e7	−0.842790	−0.421395	+	0.906877i	$0.638459\pi$
$18$	9.28636e7	0.643538
$19$	1.09809e8	0.535476	0.267738	−	0.963492i	$-0.413724\pi$
$19$	1.09809e8	0.535476	0.267738	+	0.963492i	$0.413724\pi$
$20$	−8.61532e8	−3.01007
$21$	−1.72086e8	−0.437845
$22$	1.38232e9	2.59932
$23$	5.43275e8	0.765225	0.382612	−	0.923909i	$-0.375024\pi$
$23$	5.43275e8	0.765225	0.382612	+	0.923909i	$0.375024\pi$
$24$	1.80247e9	1.92529
$25$	2.66280e8	0.218137
$26$	6.75302e8	0.428718
$27$	3.87420e8	0.192450
$28$	−5.27395e9	−2.06828
$29$	−6.42640e8	−0.200623	−0.100312	−	0.994956i	$-0.531984\pi$
$29$	−6.42640e8	−0.200623	−0.100312	+	0.994956i	$0.531984\pi$
$30$	−4.91214e9	−1.23022
$31$	6.97293e9	1.41112	0.705560	−	0.708650i	$-0.250695\pi$
$31$	6.97293e9	1.41112	0.705560	+	0.708650i	$0.250695\pi$
$32$	2.32593e10	3.82932
$33$	5.76693e9	0.777327
$34$	−1.46564e10	−1.62710
$35$	9.10271e9	0.837006
$36$	1.18734e10	0.909091
$37$	−2.07338e9	−0.132852	−0.0664261	−	0.997791i	$-0.521160\pi$
$37$	−2.07338e9	−0.132852	−0.0664261	+	0.997791i	$0.521160\pi$
$38$	1.91880e10	1.03380
$39$	2.81731e9	0.128208
$40$	−9.53442e10	−3.68048
$41$	2.58258e10	0.849099	0.424549	−	0.905405i	$-0.360433\pi$
$41$	2.58258e10	0.849099	0.424549	+	0.905405i	$0.360433\pi$
$42$	−3.00702e10	−0.845309
$43$	−5.08755e9	−0.122734	−0.0613668	−	0.998115i	$-0.519546\pi$
$43$	−5.08755e9	−0.122734	−0.0613668	+	0.998115i	$0.519546\pi$
$44$	1.76740e11	3.67192
$45$	−2.04931e10	−0.367897
$46$	9.49315e10	1.47735
$47$	5.45094e10	0.737625	0.368812	−	0.929504i	$-0.379764\pi$
$47$	5.45094e10	0.737625	0.368812	+	0.929504i	$0.379764\pi$
$48$	1.81538e11	2.14240
$49$	−4.11659e10	−0.424876
$50$	4.65296e10	0.421138
$51$	−6.11455e10	−0.486585
$52$	8.63428e10	0.605626
$53$	−8.09687e10	−0.501792	−0.250896	−	0.968014i	$-0.580725\pi$
$53$	−8.09687e10	−0.501792	−0.250896	+	0.968014i	$0.580725\pi$
$54$	6.76976e10	0.371547
$55$	−3.05049e11	−1.48598
$56$	−5.83659e11	−2.52893
$57$	8.00508e10	0.309157
$58$	−1.12295e11	−0.387326
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−6.28057e11	−1.73786
$61$	8.52456e10	0.211850	0.105925	−	0.994374i	$-0.466220\pi$
$61$	8.52456e10	0.211850	0.105925	+	0.994374i	$0.466220\pi$
$62$	1.21844e12	2.72433
$63$	−1.25451e11	−0.252790
$64$	2.02431e12	3.68219
$65$	−1.49026e11	−0.245089
$66$	1.00771e12	1.50072
$67$	6.87562e11	0.928593	0.464297	−	0.885680i	$-0.346307\pi$
$67$	6.87562e11	0.928593	0.464297	+	0.885680i	$0.346307\pi$
$68$	−1.87394e12	−2.29852
$69$	3.96048e11	0.441803
$70$	1.59060e12	1.61594
$71$	1.01676e12	0.941976	0.470988	−	0.882140i	$-0.343897\pi$
$71$	1.01676e12	0.941976	0.470988	+	0.882140i	$0.343897\pi$
$72$	1.31400e12	1.11157
$73$	1.75257e12	1.35543	0.677714	−	0.735326i	$-0.262971\pi$
$73$	1.75257e12	1.35543	0.677714	+	0.735326i	$0.262971\pi$
$74$	−3.62302e11	−0.256486
$75$	1.94118e11	0.125941
$76$	2.45333e12	1.46039
$77$	−1.86739e12	−1.02105
$78$	4.92295e11	0.247520
$79$	1.74363e12	0.807007	0.403503	−	0.914978i	$-0.367792\pi$
$79$	1.74363e12	0.807007	0.403503	+	0.914978i	$0.367792\pi$
$80$	−9.60271e12	−4.09552
$81$	2.82430e11	0.111111
$82$	4.51278e12	1.63928
$83$	2.86302e12	0.961205	0.480603	−	0.876938i	$-0.340418\pi$
$83$	2.86302e12	0.961205	0.480603	+	0.876938i	$0.340418\pi$
$84$	−3.84471e12	−1.19412
$85$	3.23437e12	0.930180
$86$	−8.88995e11	−0.236951
$87$	−4.68485e11	−0.115830
$88$	1.95595e13	4.48974
$89$	7.08189e12	1.51048	0.755239	−	0.655449i	$-0.227521\pi$
$89$	7.08189e12	1.51048	0.755239	+	0.655449i	$0.227521\pi$
$90$	−3.58095e12	−0.710268
$91$	−9.12274e11	−0.168406
$92$	1.21378e13	2.08698
$93$	5.08326e12	0.814711
$94$	9.52494e12	1.42407
$95$	−4.23439e12	−0.591000
$96$	1.69560e13	2.21086
$97$	1.48484e12	0.180993	0.0904967	−	0.995897i	$-0.471155\pi$
$97$	1.48484e12	0.180993	0.0904967	+	0.995897i	$0.471155\pi$
$98$	−7.19329e12	−0.820273
$99$	4.20409e12	0.448790
$100$	5.94918e12	0.594918
$101$	−7.14651e11	−0.0669892	−0.0334946	−	0.999439i	$-0.510664\pi$
$101$	−7.14651e11	−0.0669892	−0.0334946	+	0.999439i	$0.510664\pi$
$102$	−1.06845e13	−0.939408
$103$	1.33156e13	1.09880	0.549400	−	0.835560i	$-0.314856\pi$
$103$	1.33156e13	1.09880	0.549400	+	0.835560i	$0.314856\pi$
$104$	9.55540e12	0.740512
$105$	6.63588e12	0.483246
$106$	−1.41484e13	−0.968768
$107$	−1.65624e13	−1.06691	−0.533456	−	0.845828i	$-0.679107\pi$
$107$	−1.65624e13	−1.06691	−0.533456	+	0.845828i	$0.679107\pi$
$108$	8.65568e12	0.524864
$109$	−2.36965e13	−1.35336	−0.676678	−	0.736279i	$-0.736581\pi$
$109$	−2.36965e13	−1.35336	−0.676678	+	0.736279i	$0.736581\pi$
$110$	−5.33041e13	−2.86885
$111$	−1.51150e12	−0.0767022
$112$	−5.87839e13	−2.81411
$113$	−2.15450e13	−0.973501	−0.486751	−	0.873541i	$-0.661818\pi$
$113$	−2.15450e13	−0.973501	−0.486751	+	0.873541i	$0.661818\pi$
$114$	1.39880e13	0.596863
$115$	−2.09495e13	−0.844573
$116$	−1.43578e13	−0.547154
$117$	2.05382e12	0.0740209
$118$	−7.37060e12	−0.251345
$119$	1.97995e13	0.639146
$120$	−6.95059e13	−2.12493
$121$	2.80571e13	0.812714
$122$	1.48957e13	0.409000
$123$	1.88270e13	0.490227
$124$	1.55788e14	3.84851
$125$	3.68039e13	0.862936
$126$	−2.19212e13	−0.488039
$127$	−5.90520e13	−1.24885	−0.624425	−	0.781085i	$-0.714667\pi$
$127$	−5.90520e13	−1.24885	−0.624425	+	0.781085i	$0.714667\pi$
$128$	1.63186e14	3.27958
$129$	−3.70882e12	−0.0708603
$130$	−2.60406e13	−0.473172
$131$	−6.10551e13	−1.05550	−0.527750	−	0.849400i	$-0.676964\pi$
$131$	−6.10551e13	−1.05550	−0.527750	+	0.849400i	$0.676964\pi$
$132$	1.28844e14	2.11998
$133$	−2.59213e13	−0.406088
$134$	1.20144e14	1.79276
$135$	−1.49395e13	−0.212406
$136$	−2.07386e14	−2.81045
$137$	1.37159e14	1.77232	0.886159	−	0.463381i	$-0.153364\pi$
$137$	1.37159e14	1.77232	0.886159	+	0.463381i	$0.153364\pi$
$138$	6.92051e13	0.852951
$139$	1.27686e13	0.150158	0.0750789	−	0.997178i	$-0.476079\pi$
$139$	1.27686e13	0.150158	0.0750789	+	0.997178i	$0.476079\pi$
$140$	2.03371e14	2.28274
$141$	3.97374e13	0.425868
$142$	1.77668e14	1.81859
$143$	3.05721e13	0.298979
$144$	1.32341e14	1.23691
$145$	2.47811e13	0.221426
$146$	3.06242e14	2.61681
$147$	−3.00099e13	−0.245302
$148$	−4.63232e13	−0.362324
$149$	−2.14033e14	−1.60239	−0.801197	−	0.598401i	$-0.795803\pi$
$149$	−2.14033e14	−1.60239	−0.801197	+	0.598401i	$0.795803\pi$
$150$	3.39201e13	0.243144
$151$	6.75489e13	0.463733	0.231867	−	0.972748i	$-0.425517\pi$
$151$	6.75489e13	0.463733	0.231867	+	0.972748i	$0.425517\pi$
$152$	2.71506e14	1.78565
$153$	−4.45751e13	−0.280930
$154$	−3.26306e14	−1.97125
$155$	−2.68886e14	−1.55744
$156$	6.29439e13	0.349658
$157$	2.79610e14	1.49007	0.745033	−	0.667027i	$-0.232434\pi$
$157$	2.79610e14	1.49007	0.745033	+	0.667027i	$0.232434\pi$
$158$	3.04680e14	1.55802
$159$	−5.90262e13	−0.289710
$160$	−8.96911e14	−4.22639
$161$	−1.28244e14	−0.580323
$162$	4.93515e13	0.214513
$163$	−2.60686e14	−1.08867	−0.544337	−	0.838866i	$-0.683219\pi$
$163$	−2.60686e14	−1.08867	−0.544337	+	0.838866i	$0.683219\pi$
$164$	5.76995e14	2.31572
$165$	−2.22381e14	−0.857930
$166$	5.00281e14	1.85572
$167$	−3.83118e14	−1.36671	−0.683354	−	0.730087i	$-0.739479\pi$
$167$	−3.83118e14	−1.36671	−0.683354	+	0.730087i	$0.739479\pi$
$168$	−4.25487e14	−1.46008
$169$	−2.87940e14	−0.950688
$170$	5.65172e14	1.79582
$171$	5.83570e13	0.178492
$172$	−1.13665e14	−0.334728
$173$	4.01527e14	1.13871	0.569357	−	0.822090i	$-0.307192\pi$
$173$	4.01527e14	1.13871	0.569357	+	0.822090i	$0.307192\pi$
$174$	−8.18627e13	−0.223623
$175$	−6.28574e13	−0.165428
$176$	1.96996e15	4.99604
$177$	−3.07496e13	−0.0751646
$178$	1.23749e15	2.91615
$179$	−2.61995e14	−0.595316	−0.297658	−	0.954673i	$-0.596205\pi$
$179$	−2.61995e14	−0.595316	−0.297658	+	0.954673i	$0.596205\pi$
$180$	−4.57854e14	−1.00336
$181$	−1.41340e14	−0.298781	−0.149391	−	0.988778i	$-0.547731\pi$
$181$	−1.41340e14	−0.298781	−0.149391	+	0.988778i	$0.547731\pi$
$182$	−1.59410e14	−0.325126
$183$	6.21440e13	0.122311
$184$	1.34326e15	2.55179
$185$	7.99526e13	0.146628
$186$	8.88246e14	1.57289
$187$	−6.63520e14	−1.13471
$188$	1.21784e15	2.01170
$189$	−9.14535e13	−0.145948
$190$	−7.39915e14	−1.14099
$191$	−6.30374e14	−0.939467	−0.469734	−	0.882808i	$-0.655650\pi$
$191$	−6.30374e14	−0.939467	−0.469734	+	0.882808i	$0.655650\pi$
$192$	1.47572e15	2.12591
$193$	−8.94829e14	−1.24629	−0.623143	−	0.782108i	$-0.714144\pi$
$193$	−8.94829e14	−1.24629	−0.623143	+	0.782108i	$0.714144\pi$
$194$	2.59460e14	0.349429
$195$	−1.08640e14	−0.141502
$196$	−9.19720e14	−1.15875
$197$	−1.13344e15	−1.38156	−0.690778	−	0.723067i	$-0.742732\pi$
$197$	−1.13344e15	−1.38156	−0.690778	+	0.723067i	$0.742732\pi$
$198$	7.34620e14	0.866441
$199$	1.46651e15	1.67394	0.836971	−	0.547247i	$-0.184324\pi$
$199$	1.46651e15	1.67394	0.836971	+	0.547247i	$0.184324\pi$
$200$	6.58386e14	0.727420
$201$	5.01233e14	0.536124
$202$	−1.24878e14	−0.129330
$203$	1.51700e14	0.152146
$204$	−1.36610e15	−1.32705
$205$	−9.95878e14	−0.937144
$206$	2.32676e15	2.12136
$207$	2.88719e14	0.255075
$208$	9.62384e14	0.824018
$209$	8.68671e14	0.720949
$210$	1.15955e15	0.932961
$211$	−4.19842e14	−0.327529	−0.163765	−	0.986499i	$-0.552364\pi$
$211$	−4.19842e14	−0.327529	−0.163765	+	0.986499i	$0.552364\pi$
$212$	−1.80899e15	−1.36852
$213$	7.41219e14	0.543850
$214$	−2.89410e15	−2.05980
$215$	1.96183e14	0.135460
$216$	9.57908e14	0.641763
$217$	−1.64601e15	−1.07015
$218$	−4.14071e15	−2.61281
$219$	1.27762e15	0.782556
$220$	−6.81536e15	−4.05267
$221$	−3.24149e14	−0.187152
$222$	−2.64118e14	−0.148082
$223$	−3.28042e15	−1.78627	−0.893137	−	0.449786i	$-0.851500\pi$
$223$	−3.28042e15	−1.78627	−0.893137	+	0.449786i	$0.851500\pi$
$224$	−5.49053e15	−2.90404
$225$	1.41512e14	0.0727122
$226$	−3.76476e15	−1.87946
$227$	−3.31739e15	−1.60927	−0.804633	−	0.593772i	$-0.797638\pi$
$227$	−3.31739e15	−1.60927	−0.804633	+	0.593772i	$0.797638\pi$
$228$	1.78848e15	0.843156
$229$	2.07877e15	0.952526	0.476263	−	0.879303i	$-0.341991\pi$
$229$	2.07877e15	0.952526	0.476263	+	0.879303i	$0.341991\pi$
$230$	−3.66070e15	−1.63054
$231$	−1.36133e15	−0.589501
$232$	−1.58895e15	−0.669017
$233$	3.34096e15	1.36791	0.683955	−	0.729524i	$-0.260258\pi$
$233$	3.34096e15	1.36791	0.683955	+	0.729524i	$0.260258\pi$
$234$	3.58883e14	0.142906
$235$	−2.10196e15	−0.814111
$236$	−9.42390e14	−0.355061
$237$	1.27110e15	0.465926
$238$	3.45976e15	1.23394
$239$	−1.42043e15	−0.492985	−0.246493	−	0.969145i	$-0.579278\pi$
$239$	−1.42043e15	−0.492985	−0.246493	+	0.969145i	$0.579278\pi$
$240$	−7.00038e15	−2.36455
$241$	−5.31994e15	−1.74902	−0.874512	−	0.485003i	$-0.838819\pi$
$241$	−5.31994e15	−1.74902	−0.874512	+	0.485003i	$0.838819\pi$
$242$	4.90268e15	1.56904
$243$	2.05891e14	0.0641500
$244$	1.90454e15	0.577772
$245$	1.58741e15	0.468933
$246$	3.28981e15	0.946440
$247$	4.24371e14	0.118909
$248$	1.72408e16	4.70566
$249$	2.08714e15	0.554952
$250$	6.43109e15	1.66600
$251$	−3.39356e15	−0.856596	−0.428298	−	0.903638i	$-0.640887\pi$
$251$	−3.39356e15	−0.856596	−0.428298	+	0.903638i	$0.640887\pi$
$252$	−2.80280e15	−0.689426
$253$	4.29771e15	1.03028
$254$	−1.03187e16	−2.41105
$255$	2.35786e15	0.537040
$256$	1.19319e16	2.64941
$257$	−2.06240e15	−0.446487	−0.223243	−	0.974763i	$-0.571664\pi$
$257$	−2.06240e15	−0.446487	−0.223243	+	0.974763i	$0.571664\pi$
$258$	−6.48077e14	−0.136804
$259$	4.89438e14	0.100751
$260$	−3.32950e15	−0.668425
$261$	−3.41525e14	−0.0668744
$262$	−1.06687e16	−2.03776
$263$	7.11288e15	1.32536	0.662679	−	0.748904i	$-0.269419\pi$
$263$	7.11288e15	1.32536	0.662679	+	0.748904i	$0.269419\pi$
$264$	1.42589e16	2.59215
$265$	3.12227e15	0.553824
$266$	−4.52946e15	−0.784000
$267$	5.16270e15	0.872075
$268$	1.53614e16	2.53253
$269$	−6.50640e15	−1.04701	−0.523506	−	0.852022i	$-0.675376\pi$
$269$	−6.50640e15	−1.04701	−0.523506	+	0.852022i	$0.675376\pi$
$270$	−2.61051e15	−0.410074
$271$	−1.18092e15	−0.181100	−0.0905501	−	0.995892i	$-0.528863\pi$
$271$	−1.18092e15	−0.181100	−0.0905501	+	0.995892i	$0.528863\pi$
$272$	−2.08871e16	−3.12738
$273$	−6.65048e14	−0.0972290
$274$	2.39671e16	3.42166
$275$	2.10647e15	0.293693
$276$	8.84843e15	1.20492
$277$	−8.66226e14	−0.115216	−0.0576080	−	0.998339i	$-0.518347\pi$
$277$	−8.66226e14	−0.115216	−0.0576080	+	0.998339i	$0.518347\pi$
$278$	2.23118e15	0.289897
$279$	3.70570e15	0.470373
$280$	2.25067e16	2.79116
$281$	1.64189e15	0.198954	0.0994770	−	0.995040i	$-0.468283\pi$
$281$	1.64189e15	0.198954	0.0994770	+	0.995040i	$0.468283\pi$
$282$	6.94368e15	0.822187
$283$	5.47926e15	0.634031	0.317015	−	0.948420i	$-0.397319\pi$
$283$	5.47926e15	0.634031	0.317015	+	0.948420i	$0.397319\pi$
$284$	2.27163e16	2.56903
$285$	−3.08687e15	−0.341214
$286$	5.34214e15	0.577213
$287$	−6.09637e15	−0.643930
$288$	1.23609e16	1.27644
$289$	−2.86941e15	−0.289706
$290$	4.33024e15	0.427489
$291$	1.08245e15	0.104497
$292$	3.91555e16	3.69662
$293$	1.10393e16	1.01930	0.509651	−	0.860381i	$-0.329774\pi$
$293$	1.10393e16	1.01930	0.509651	+	0.860381i	$0.329774\pi$
$294$	−5.24391e15	−0.473585
$295$	1.62654e15	0.143689
$296$	−5.12650e15	−0.443022
$297$	3.06478e15	0.259109
$298$	−3.73999e16	−3.09361
$299$	2.09956e15	0.169928
$300$	4.33695e15	0.343476
$301$	1.20095e15	0.0930774
$302$	1.18034e16	0.895290
$303$	−5.20980e14	−0.0386762
$304$	2.73451e16	1.98701
$305$	−3.28719e15	−0.233817
$306$	−7.78902e15	−0.542367
$307$	−8.78933e15	−0.599179	−0.299589	−	0.954068i	$-0.596850\pi$
$307$	−8.78933e15	−0.599179	−0.299589	+	0.954068i	$0.596850\pi$
$308$	−4.17209e16	−2.78467
$309$	9.70707e15	0.634392
$310$	−4.69849e16	−3.00682
$311$	2.64124e16	1.65526	0.827629	−	0.561276i	$-0.189689\pi$
$311$	2.64124e16	1.65526	0.827629	+	0.561276i	$0.189689\pi$
$312$	6.96589e15	0.427535
$313$	5.92606e15	0.356228	0.178114	−	0.984010i	$-0.443000\pi$
$313$	5.92606e15	0.356228	0.178114	+	0.984010i	$0.443000\pi$
$314$	4.88589e16	2.87674
$315$	4.83756e15	0.279002
$316$	3.89558e16	2.20093
$317$	−3.46823e16	−1.91965	−0.959826	−	0.280597i	$-0.909468\pi$
$317$	−3.46823e16	−1.91965	−0.959826	+	0.280597i	$0.909468\pi$
$318$	−1.03142e16	−0.559318
$319$	−5.08376e15	−0.270113
$320$	−7.80602e16	−4.06401
$321$	−1.20740e16	−0.615982
$322$	−2.24093e16	−1.12038
$323$	−9.21033e15	−0.451293
$324$	6.30999e15	0.303030
$325$	1.02907e15	0.0484401
$326$	−4.55521e16	−2.10181
$327$	−1.72747e16	−0.781360
$328$	6.38550e16	2.83149
$329$	−1.28674e16	−0.559392
$330$	−3.88587e16	−1.65633
$331$	−2.28041e16	−0.953082	−0.476541	−	0.879152i	$-0.658110\pi$
$331$	−2.28041e16	−0.953082	−0.476541	+	0.879152i	$0.658110\pi$
$332$	6.39650e16	2.62147
$333$	−1.10188e15	−0.0442840
$334$	−6.69458e16	−2.63859
$335$	−2.65134e16	−1.02488
$336$	−4.28535e16	−1.62473
$337$	3.56176e16	1.32456	0.662278	−	0.749258i	$-0.269590\pi$
$337$	3.56176e16	1.32456	0.662278	+	0.749258i	$0.269590\pi$
$338$	−5.03144e16	−1.83541
$339$	−1.57063e16	−0.562051
$340$	7.22618e16	2.53686
$341$	5.51610e16	1.89989
$342$	1.01973e16	0.344599
$343$	3.25889e16	1.08058
$344$	−1.25791e16	−0.409280
$345$	−1.52722e16	−0.487614
$346$	7.01625e16	2.19842
$347$	1.09146e15	0.0335633	0.0167816	−	0.999859i	$-0.494658\pi$
$347$	1.09146e15	0.0335633	0.0167816	+	0.999859i	$0.494658\pi$
$348$	−1.04668e16	−0.315899
$349$	−1.08396e16	−0.321106	−0.160553	−	0.987027i	$-0.551328\pi$
$349$	−1.08396e16	−0.321106	−0.160553	+	0.987027i	$0.551328\pi$
$350$	−1.09837e16	−0.319378
$351$	1.49724e15	0.0427360
$352$	1.83998e17	5.15568
$353$	1.70476e16	0.468952	0.234476	−	0.972122i	$-0.424663\pi$
$353$	1.70476e16	0.468952	0.234476	+	0.972122i	$0.424663\pi$
$354$	−5.37316e15	−0.145114
$355$	−3.92078e16	−1.03965
$356$	1.58222e17	4.11949
$357$	1.44339e16	0.369011
$358$	−4.57807e16	−1.14933
$359$	−1.49078e16	−0.367535	−0.183767	−	0.982970i	$-0.558829\pi$
$359$	−1.49078e16	−0.367535	−0.183767	+	0.982970i	$0.558829\pi$
$360$	−5.06698e16	−1.22683
$361$	−2.99950e16	−0.713266
$362$	−2.46976e16	−0.576832
$363$	2.04536e16	0.469221
$364$	−2.03819e16	−0.459288
$365$	−6.75815e16	−1.49597
$366$	1.08590e16	0.236136
$367$	8.10614e16	1.73175	0.865874	−	0.500262i	$-0.166763\pi$
$367$	8.10614e16	1.73175	0.865874	+	0.500262i	$0.166763\pi$
$368$	1.35288e17	2.83955
$369$	1.37249e16	0.283033
$370$	1.39709e16	0.283082
$371$	1.91133e16	0.380544
$372$	1.13569e17	2.22194
$373$	6.54562e16	1.25847	0.629236	−	0.777215i	$-0.283368\pi$
$373$	6.54562e16	1.25847	0.629236	+	0.777215i	$0.283368\pi$
$374$	−1.15943e17	−2.19068
$375$	2.68300e16	0.498217
$376$	1.34776e17	2.45976
$377$	−2.48357e15	−0.0445509
$378$	−1.59805e16	−0.281770
$379$	−2.41657e16	−0.418836	−0.209418	−	0.977826i	$-0.567157\pi$
$379$	−2.41657e16	−0.418836	−0.209418	+	0.977826i	$0.567157\pi$
$380$	−9.46040e16	−1.61182
$381$	−4.30489e16	−0.721024
$382$	−1.10151e17	−1.81375
$383$	−4.17370e16	−0.675661	−0.337831	−	0.941207i	$-0.609693\pi$
$383$	−4.17370e16	−0.675661	−0.337831	+	0.941207i	$0.609693\pi$
$384$	1.18963e17	1.89346
$385$	7.20092e16	1.12692
$386$	−1.56362e17	−2.40610
$387$	−2.70373e15	−0.0409112
$388$	3.31740e16	0.493619
$389$	−4.20527e16	−0.615349	−0.307674	−	0.951492i	$-0.599551\pi$
$389$	−4.20527e16	−0.615349	−0.307674	+	0.951492i	$0.599551\pi$
$390$	−1.89836e16	−0.273186
$391$	−4.55677e16	−0.644924
$392$	−1.01784e17	−1.41683
$393$	−4.45092e16	−0.609393
$394$	−1.98057e17	−2.66725
$395$	−6.72367e16	−0.890687
$396$	9.39270e16	1.22397
$397$	−8.97559e16	−1.15060	−0.575300	−	0.817942i	$-0.695115\pi$
$397$	−8.97559e16	−1.15060	−0.575300	+	0.817942i	$0.695115\pi$
$398$	2.56257e17	3.23174
$399$	−1.88966e16	−0.234455
$400$	6.63101e16	0.809449
$401$	5.95901e15	0.0715708	0.0357854	−	0.999359i	$-0.488607\pi$
$401$	5.95901e15	0.0715708	0.0357854	+	0.999359i	$0.488607\pi$
$402$	8.75850e16	1.03505
$403$	2.69478e16	0.313357
$404$	−1.59666e16	−0.182698
$405$	−1.08909e16	−0.122632
$406$	2.65080e16	0.293736
$407$	−1.64020e16	−0.178868
$408$	−1.51184e17	−1.62261
$409$	−1.73092e16	−0.182842	−0.0914211	−	0.995812i	$-0.529141\pi$
$409$	−1.73092e16	−0.182842	−0.0914211	+	0.995812i	$0.529141\pi$
$410$	−1.74019e17	−1.80926
$411$	9.99891e16	1.02325
$412$	2.97495e17	2.99673
$413$	9.95703e15	0.0987312
$414$	5.04505e16	0.492451
$415$	−1.10402e17	−1.06088
$416$	8.98884e16	0.850349
$417$	9.30833e15	0.0866936
$418$	1.51791e17	1.39187
$419$	−5.37594e16	−0.485360	−0.242680	−	0.970106i	$-0.578026\pi$
$419$	−5.37594e16	−0.485360	−0.242680	+	0.970106i	$0.578026\pi$
$420$	1.48258e17	1.31794
$421$	−3.77153e16	−0.330129	−0.165064	−	0.986283i	$-0.552783\pi$
$421$	−3.77153e16	−0.330129	−0.165064	+	0.986283i	$0.552783\pi$
$422$	−7.33629e16	−0.632332
$423$	2.89685e16	0.245875
$424$	−2.00197e17	−1.67333
$425$	−2.23345e16	−0.183843
$426$	1.29520e17	1.04997
$427$	−2.01229e16	−0.160660
$428$	−3.70034e17	−2.90976
$429$	2.22870e16	0.172616
$430$	3.42809e16	0.261521
$431$	2.01887e17	1.51707	0.758534	−	0.651633i	$-0.225916\pi$
$431$	2.01887e17	1.51707	0.758534	+	0.651633i	$0.225916\pi$
$432$	9.64769e16	0.714133
$433$	−7.35397e15	−0.0536229	−0.0268115	−	0.999641i	$-0.508535\pi$
$433$	−7.35397e15	−0.0536229	−0.0268115	+	0.999641i	$0.508535\pi$
$434$	−2.87623e17	−2.06605
$435$	1.80654e16	0.127840
$436$	−5.29423e17	−3.69097
$437$	5.96566e16	0.409759
$438$	2.23251e17	1.51081
$439$	−1.17638e17	−0.784381	−0.392191	−	0.919884i	$-0.628283\pi$
$439$	−1.17638e17	−0.784381	−0.392191	+	0.919884i	$0.628283\pi$
$440$	−7.54243e17	−4.95529
$441$	−2.18772e16	−0.141625
$442$	−5.66416e16	−0.361319
$443$	−3.53726e16	−0.222353	−0.111176	−	0.993801i	$-0.535462\pi$
$443$	−3.53726e16	−0.222353	−0.111176	+	0.993801i	$0.535462\pi$
$444$	−3.37696e16	−0.209188
$445$	−2.73088e17	−1.66710
$446$	−5.73218e17	−3.44860
$447$	−1.56030e17	−0.925143
$448$	−4.77853e17	−2.79246
$449$	1.77135e17	1.02024	0.510122	−	0.860102i	$-0.329600\pi$
$449$	1.77135e17	1.02024	0.510122	+	0.860102i	$0.329600\pi$
$450$	2.47277e16	0.140379
$451$	2.04301e17	1.14320
$452$	−4.81354e17	−2.65500
$453$	4.92431e16	0.267736
$454$	−5.79678e17	−3.10687
$455$	3.51786e16	0.185868
$456$	1.97928e17	1.03095
$457$	2.13848e17	1.09812	0.549061	−	0.835782i	$-0.314985\pi$
$457$	2.13848e17	1.09812	0.549061	+	0.835782i	$0.314985\pi$
$458$	3.63244e17	1.83896
$459$	−3.24952e16	−0.162195
$460$	−4.68049e17	−2.30338
$461$	3.43140e17	1.66500	0.832502	−	0.554023i	$-0.186908\pi$
$461$	3.43140e17	1.66500	0.832502	+	0.554023i	$0.186908\pi$
$462$	−2.37877e17	−1.13810
$463$	5.49015e16	0.259005	0.129502	−	0.991579i	$-0.458662\pi$
$463$	5.49015e16	0.259005	0.129502	+	0.991579i	$0.458662\pi$
$464$	−1.60033e17	−0.744461
$465$	−1.96018e17	−0.899190
$466$	5.83797e17	2.64091
$467$	−1.79803e17	−0.802116	−0.401058	−	0.916053i	$-0.631357\pi$
$467$	−1.79803e17	−0.802116	−0.401058	+	0.916053i	$0.631357\pi$
$468$	4.58861e16	0.201875
$469$	−1.62304e17	−0.704216
$470$	−3.67295e17	−1.57173
$471$	2.03836e17	0.860290
$472$	−1.04293e17	−0.434141
$473$	−4.02463e16	−0.165245
$474$	2.22112e17	0.899523
$475$	2.92400e16	0.116807
$476$	4.42358e17	1.74312
$477$	−4.30301e16	−0.167264
$478$	−2.48205e17	−0.951764
$479$	4.78018e17	1.80827	0.904136	−	0.427246i	$-0.140516\pi$
$479$	4.78018e17	1.80827	0.904136	+	0.427246i	$0.140516\pi$
$480$	−6.53848e17	−2.44011
$481$	−8.01285e15	−0.0295015
$482$	−9.29603e17	−3.37669
$483$	−9.34901e16	−0.335050
$484$	6.26846e17	2.21649
$485$	−5.72575e16	−0.199761
$486$	3.59773e16	0.123849
$487$	−6.97382e16	−0.236882	−0.118441	−	0.992961i	$-0.537790\pi$
$487$	−6.97382e16	−0.236882	−0.118441	+	0.992961i	$0.537790\pi$
$488$	2.10772e17	0.706455
$489$	−1.90040e17	−0.628547
$490$	2.77384e17	0.905329
$491$	−2.15005e17	−0.692499	−0.346250	−	0.938142i	$-0.612545\pi$
$491$	−2.15005e17	−0.692499	−0.346250	+	0.938142i	$0.612545\pi$
$492$	4.20629e17	1.33698
$493$	5.39020e16	0.169083
$494$	7.41543e16	0.229568
$495$	−1.62116e17	−0.495326
$496$	1.73642e18	5.23631
$497$	−2.40014e17	−0.714366
$498$	3.64705e17	1.07140
$499$	−3.20439e17	−0.929163	−0.464581	−	0.885530i	$-0.653795\pi$
$499$	−3.20439e17	−0.929163	−0.464581	+	0.885530i	$0.653795\pi$
$500$	8.22266e17	2.35346
$501$	−2.79293e17	−0.789069
$502$	−5.92988e17	−1.65376
$503$	−5.72762e16	−0.157682	−0.0788410	−	0.996887i	$-0.525122\pi$
$503$	−5.72762e16	−0.157682	−0.0788410	+	0.996887i	$0.525122\pi$
$504$	−3.10180e17	−0.842977
$505$	2.75580e16	0.0739355
$506$	7.50979e17	1.98907
$507$	−2.09908e17	−0.548880
$508$	−1.31933e18	−3.40595
$509$	−4.67193e17	−1.19078	−0.595390	−	0.803437i	$-0.703002\pi$
$509$	−4.67193e17	−1.19078	−0.595390	+	0.803437i	$0.703002\pi$
$510$	4.12011e17	1.03682
$511$	−4.13707e17	−1.02791
$512$	7.48147e17	1.83541
$513$	4.25423e16	0.103052
$514$	−3.60383e17	−0.861994
$515$	−5.13468e17	−1.21274
$516$	−8.28619e16	−0.193255
$517$	4.31210e17	0.993116
$518$	8.55240e16	0.194511
$519$	2.92713e17	0.657437
$520$	−3.68470e17	−0.817298
$521$	1.26406e17	0.276900	0.138450	−	0.990369i	$-0.455788\pi$
$521$	1.26406e17	0.276900	0.138450	+	0.990369i	$0.455788\pi$
$522$	−5.96779e16	−0.129109
$523$	−4.95698e17	−1.05915	−0.529574	−	0.848264i	$-0.677648\pi$
$523$	−4.95698e17	−1.05915	−0.529574	+	0.848264i	$0.677648\pi$
$524$	−1.36408e18	−2.87864
$525$	−4.58231e16	−0.0955100
$526$	1.24290e18	2.55875
$527$	−5.84860e17	−1.18928
$528$	1.43610e18	2.88446
$529$	−2.08888e17	−0.414431
$530$	5.45583e17	1.06922
$531$	−2.24165e16	−0.0433963
$532$	−5.79128e17	−1.10751
$533$	9.98070e16	0.188553
$534$	9.02127e17	1.68364
$535$	6.38670e17	1.17754
$536$	1.70002e18	3.09658
$537$	−1.90994e17	−0.343706
$538$	−1.13692e18	−2.02137
$539$	−3.25652e17	−0.572041
$540$	−3.33775e17	−0.579288
$541$	−8.55126e17	−1.46638	−0.733192	−	0.680021i	$-0.761970\pi$
$541$	−8.55126e17	−1.46638	−0.733192	+	0.680021i	$0.761970\pi$
$542$	−2.06353e17	−0.349635
$543$	−1.03037e17	−0.172502
$544$	−1.95089e18	−3.22731
$545$	9.13771e17	1.49369
$546$	−1.16210e17	−0.187712
$547$	−7.48475e17	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$547$	−7.48475e17	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$548$	3.06439e18	4.83359
$549$	4.53030e16	0.0706166
$550$	3.68084e17	0.567008
$551$	−7.05677e16	−0.107429
$552$	9.79239e17	1.47328
$553$	−4.11596e17	−0.612009
$554$	−1.51364e17	−0.222438
$555$	5.82855e16	0.0846556
$556$	2.85274e17	0.409521
$557$	−3.90201e17	−0.553643	−0.276822	−	0.960921i	$-0.589281\pi$
$557$	−3.90201e17	−0.553643	−0.276822	+	0.960921i	$0.589281\pi$
$558$	6.47531e17	0.908110
$559$	−1.96615e16	−0.0272546
$560$	2.26679e18	3.10591
$561$	−4.83706e17	−0.655124
$562$	2.86903e17	0.384104
$563$	1.70160e17	0.225191	0.112596	−	0.993641i	$-0.464084\pi$
$563$	1.70160e17	0.225191	0.112596	+	0.993641i	$0.464084\pi$
$564$	8.87805e17	1.16146
$565$	8.30806e17	1.07445
$566$	9.57442e17	1.22407
$567$	−6.66696e16	−0.0842632
$568$	2.51397e18	3.14121
$569$	4.48182e17	0.553637	0.276818	−	0.960922i	$-0.410720\pi$
$569$	4.48182e17	0.553637	0.276818	+	0.960922i	$0.410720\pi$
$570$	−5.39398e17	−0.658753
$571$	8.92926e17	1.07815	0.539077	−	0.842257i	$-0.318773\pi$
$571$	8.92926e17	1.07815	0.539077	+	0.842257i	$0.318773\pi$
$572$	6.83035e17	0.815397
$573$	−4.59543e17	−0.542402
$574$	−1.06527e18	−1.24318
$575$	1.44663e17	0.166924
$576$	1.07580e18	1.22740
$577$	−3.24314e16	−0.0365867	−0.0182933	−	0.999833i	$-0.505823\pi$
$577$	−3.24314e16	−0.0365867	−0.0182933	+	0.999833i	$0.505823\pi$
$578$	−5.01399e17	−0.559310
$579$	−6.52330e17	−0.719543
$580$	5.53655e17	0.603890
$581$	−6.75837e17	−0.728948
$582$	1.89146e17	0.201743
$583$	−6.40522e17	−0.675599
$584$	4.33327e18	4.51994
$585$	−7.91983e16	−0.0816963
$586$	1.92900e18	1.96788
$587$	−5.64607e17	−0.569638	−0.284819	−	0.958581i	$-0.591933\pi$
$587$	−5.64607e17	−0.569638	−0.284819	+	0.958581i	$0.591933\pi$
$588$	−6.70476e17	−0.669007
$589$	7.65690e17	0.755621
$590$	2.84221e17	0.277407
$591$	−8.26278e17	−0.797641
$592$	−5.16322e17	−0.492980
$593$	−1.76162e18	−1.66363	−0.831814	−	0.555055i	$-0.812697\pi$
$593$	−1.76162e18	−1.66363	−0.831814	+	0.555055i	$0.812697\pi$
$594$	5.35538e17	0.500240
$595$	−7.63498e17	−0.705420
$596$	−4.78188e18	−4.37016
$597$	1.06909e18	0.966451
$598$	3.66875e17	0.328065
$599$	−7.77624e17	−0.687852	−0.343926	−	0.938997i	$-0.611757\pi$
$599$	−7.77624e17	−0.687852	−0.343926	+	0.938997i	$0.611757\pi$
$600$	4.79963e17	0.419976
$601$	1.78602e18	1.54598	0.772989	−	0.634420i	$-0.218761\pi$
$601$	1.78602e18	1.54598	0.772989	+	0.634420i	$0.218761\pi$
$602$	2.09854e17	0.179697
$603$	3.65399e17	0.309531
$604$	1.50916e18	1.26473
$605$	−1.08192e18	−0.896986
$606$	−9.10358e16	−0.0746689
$607$	1.02483e18	0.831619	0.415810	−	0.909452i	$-0.363498\pi$
$607$	1.02483e18	0.831619	0.415810	+	0.909452i	$0.363498\pi$
$608$	2.55408e18	2.05051
$609$	1.10589e17	0.0878417
$610$	−5.74401e17	−0.451410
$611$	2.10659e17	0.163799
$612$	−9.95889e17	−0.766172
$613$	−7.89850e17	−0.601245	−0.300623	−	0.953743i	$-0.597194\pi$
$613$	−7.89850e17	−0.601245	−0.300623	+	0.953743i	$0.597194\pi$
$614$	−1.53584e18	−1.15678
$615$	−7.25995e17	−0.541060
$616$	−4.61718e18	−3.40488
$617$	2.43798e18	1.77900	0.889501	−	0.456933i	$-0.151052\pi$
$617$	2.43798e18	1.77900	0.889501	+	0.456933i	$0.151052\pi$
$618$	1.69621e18	1.22477
$619$	1.40832e18	1.00626	0.503131	−	0.864210i	$-0.332181\pi$
$619$	1.40832e18	1.00626	0.503131	+	0.864210i	$0.332181\pi$
$620$	−6.00740e18	−4.24757
$621$	2.10476e17	0.147268
$622$	4.61529e18	3.19567
$623$	−1.67173e18	−1.14550
$624$	7.01578e17	0.475747
$625$	−1.74426e18	−1.17055
$626$	1.03552e18	0.687739
$627$	6.33261e17	0.416240
$628$	6.24701e18	4.06382
$629$	1.73907e17	0.111966
$630$	8.45311e17	0.538645
$631$	3.08473e18	1.94548	0.972738	−	0.231907i	$-0.0744966\pi$
$631$	3.08473e18	1.94548	0.972738	+	0.231907i	$0.0744966\pi$
$632$	4.31117e18	2.69112
$633$	−3.06065e17	−0.189099
$634$	−6.06036e18	−3.70611
$635$	2.27713e18	1.37835
$636$	−1.31875e18	−0.790118
$637$	−1.59091e17	−0.0943492
$638$	−8.88333e17	−0.521484
$639$	5.40349e17	0.313992
$640$	−6.29268e18	−3.61964
$641$	−2.98725e18	−1.70096	−0.850480	−	0.526007i	$-0.823689\pi$
$641$	−2.98725e18	−1.70096	−0.850480	+	0.526007i	$0.823689\pi$
$642$	−2.10980e18	−1.18922
$643$	1.23955e18	0.691657	0.345829	−	0.938298i	$-0.387598\pi$
$643$	1.23955e18	0.691657	0.345829	+	0.938298i	$0.387598\pi$
$644$	−2.86521e18	−1.58270
$645$	1.43018e17	0.0782080
$646$	−1.60941e18	−0.871274
$647$	−2.26814e18	−1.21560	−0.607802	−	0.794089i	$-0.707949\pi$
$647$	−2.26814e18	−1.21560	−0.607802	+	0.794089i	$0.707949\pi$
$648$	6.98315e17	0.370522
$649$	−3.33679e17	−0.175283
$650$	1.79820e17	0.0935191
$651$	−1.19994e18	−0.617851
$652$	−5.82420e18	−2.96911
$653$	−1.74983e18	−0.883204	−0.441602	−	0.897211i	$-0.645590\pi$
$653$	−1.74983e18	−0.883204	−0.441602	+	0.897211i	$0.645590\pi$
$654$	−3.01858e18	−1.50851
$655$	2.35437e18	1.16495
$656$	6.43123e18	3.15079
$657$	9.31386e17	0.451809
$658$	−2.24843e18	−1.07997
$659$	5.33013e17	0.253503	0.126751	−	0.991935i	$-0.459545\pi$
$659$	5.33013e17	0.253503	0.126751	+	0.991935i	$0.459545\pi$
$660$	−4.96840e18	−2.33981
$661$	−1.19976e18	−0.559480	−0.279740	−	0.960076i	$-0.590248\pi$
$661$	−1.19976e18	−0.559480	−0.279740	+	0.960076i	$0.590248\pi$
$662$	−3.98476e18	−1.84003
$663$	−2.36305e17	−0.108052
$664$	7.07889e18	3.20533
$665$	9.99560e17	0.448196
$666$	−1.92542e17	−0.0854954
$667$	−3.49131e17	−0.153522
$668$	−8.55955e18	−3.72738
$669$	−2.39143e18	−1.03131
$670$	−4.63293e18	−1.97865
$671$	6.74355e17	0.285228
$672$	−4.00259e18	−1.67665
$673$	−1.73483e18	−0.719714	−0.359857	−	0.933008i	$-0.617174\pi$
$673$	−1.73483e18	−0.719714	−0.359857	+	0.933008i	$0.617174\pi$
$674$	6.22379e18	2.55721
$675$	1.03162e17	0.0419804
$676$	−6.43310e18	−2.59279
$677$	2.90271e18	1.15872	0.579358	−	0.815073i	$-0.303303\pi$
$677$	2.90271e18	1.15872	0.579358	+	0.815073i	$0.303303\pi$
$678$	−2.74451e18	−1.08510
$679$	−3.50507e17	−0.137260
$680$	7.99708e18	3.10187
$681$	−2.41837e18	−0.929111
$682$	9.63879e18	3.66796
$683$	−2.10203e18	−0.792327	−0.396164	−	0.918180i	$-0.629659\pi$
$683$	−2.10203e18	−0.792327	−0.396164	+	0.918180i	$0.629659\pi$
$684$	1.30380e18	0.486796
$685$	−5.28906e18	−1.95609
$686$	5.69456e18	2.08619
$687$	1.51543e18	0.549941
$688$	−1.26692e18	−0.455433
$689$	−3.12914e17	−0.111429
$690$	−2.66865e18	−0.941395
$691$	−8.37340e17	−0.292614	−0.146307	−	0.989239i	$-0.546739\pi$
$691$	−8.37340e17	−0.292614	−0.146307	+	0.989239i	$0.546739\pi$
$692$	8.97084e18	3.10559
$693$	−9.92407e17	−0.340349
$694$	1.90720e17	0.0647978
$695$	−4.92376e17	−0.165728
$696$	−1.15834e18	−0.386257
$697$	−2.16616e18	−0.715612
$698$	−1.89411e18	−0.619932
$699$	2.43556e18	0.789763
$700$	−1.40435e18	−0.451168
$701$	4.60814e18	1.46676	0.733379	−	0.679820i	$-0.237942\pi$
$701$	4.60814e18	1.46676	0.733379	+	0.679820i	$0.237942\pi$
$702$	2.61626e17	0.0825068
$703$	−2.27676e17	−0.0711391
$704$	1.60138e19	4.95760
$705$	−1.53233e18	−0.470027
$706$	2.97889e18	0.905366
$707$	1.68699e17	0.0508026
$708$	−6.87002e17	−0.204994
$709$	−2.41621e17	−0.0714389	−0.0357195	−	0.999362i	$-0.511372\pi$
$709$	−2.41621e17	−0.0714389	−0.0357195	+	0.999362i	$0.511372\pi$
$710$	−6.85114e18	−2.00717
$711$	9.26634e17	0.269002
$712$	1.75102e19	5.03699
$713$	3.78822e18	1.07982
$714$	2.52216e18	0.712418
$715$	−1.17890e18	−0.329981
$716$	−5.85343e18	−1.62359
$717$	−1.03549e18	−0.284625
$718$	−2.60497e18	−0.709568
$719$	−1.79374e17	−0.0484197	−0.0242099	−	0.999707i	$-0.507707\pi$
$719$	−1.79374e17	−0.0484197	−0.0242099	+	0.999707i	$0.507707\pi$
$720$	−5.10327e18	−1.36517
$721$	−3.14325e18	−0.833296
$722$	−5.24130e18	−1.37704
$723$	−3.87824e18	−1.00980
$724$	−3.15779e18	−0.814858
$725$	−1.71122e17	−0.0437633
$726$	3.57405e18	0.905884
$727$	−5.66051e18	−1.42194	−0.710971	−	0.703221i	$-0.751744\pi$
$727$	−5.66051e18	−1.42194	−0.710971	+	0.703221i	$0.751744\pi$
$728$	−2.25562e18	−0.561582
$729$	1.50095e17	0.0370370
$730$	−1.18091e19	−2.88815
$731$	4.26723e17	0.103439
$732$	1.38841e18	0.333577
$733$	3.26326e18	0.777099	0.388549	−	0.921428i	$-0.372976\pi$
$733$	3.26326e18	0.777099	0.388549	+	0.921428i	$0.372976\pi$
$734$	1.41646e19	3.34334
$735$	1.15722e18	0.270738
$736$	1.26362e19	2.93029
$737$	5.43912e18	1.25023
$738$	2.39827e18	0.546427
$739$	1.66320e17	0.0375626	0.0187813	−	0.999824i	$-0.494021\pi$
$739$	1.66320e17	0.0375626	0.0187813	+	0.999824i	$0.494021\pi$
$740$	1.78629e18	0.399894
$741$	3.09367e17	0.0686523
$742$	3.33984e18	0.734683
$743$	5.34811e18	1.16620	0.583100	−	0.812400i	$-0.301839\pi$
$743$	5.34811e18	1.16620	0.583100	+	0.812400i	$0.301839\pi$
$744$	1.25685e19	2.71681
$745$	8.25340e18	1.76855
$746$	1.14378e19	2.42962
$747$	1.52152e18	0.320402
$748$	−1.48243e19	−3.09466
$749$	3.90968e18	0.809113
$750$	4.68826e18	0.961864
$751$	−7.66087e18	−1.55818	−0.779091	−	0.626910i	$-0.784319\pi$
$751$	−7.66087e18	−1.55818	−0.779091	+	0.626910i	$0.784319\pi$
$752$	1.35741e19	2.73714
$753$	−2.47390e18	−0.494556
$754$	−4.33976e17	−0.0860107
$755$	−2.60478e18	−0.511819
$756$	−2.04324e18	−0.398041
$757$	1.61527e18	0.311977	0.155988	−	0.987759i	$-0.450144\pi$
$757$	1.61527e18	0.311977	0.155988	+	0.987759i	$0.450144\pi$
$758$	−4.22269e18	−0.808610
$759$	3.13303e18	0.594830
$760$	−1.04697e19	−1.97081
$761$	1.05049e19	1.96061	0.980305	−	0.197488i	$-0.0632784\pi$
$761$	1.05049e19	1.96061	0.980305	+	0.197488i	$0.0632784\pi$
$762$	−7.52233e18	−1.39202
$763$	5.59374e18	1.02634
$764$	−1.40837e19	−2.56218
$765$	1.71888e18	0.310060
$766$	−7.29309e18	−1.30444
$767$	−1.63012e17	−0.0289101
$768$	8.69833e18	1.52964
$769$	−8.44291e18	−1.47221	−0.736107	−	0.676865i	$-0.763338\pi$
$769$	−8.44291e18	−1.47221	−0.736107	+	0.676865i	$0.763338\pi$
$770$	1.25828e19	2.17565
$771$	−1.50349e18	−0.257779
$772$	−1.99921e19	−3.39896
$773$	−9.32986e18	−1.57293	−0.786463	−	0.617637i	$-0.788090\pi$
$773$	−9.32986e18	−1.57293	−0.786463	+	0.617637i	$0.788090\pi$
$774$	−4.72448e17	−0.0789838
$775$	1.85675e18	0.307817
$776$	3.67131e18	0.603559
$777$	3.56800e17	0.0581686
$778$	−7.34825e18	−1.18800
$779$	2.83590e18	0.454672
$780$	−2.42721e18	−0.385915
$781$	8.04334e18	1.26825
$782$	−7.96247e18	−1.24510
$783$	−2.48972e17	−0.0386099
$784$	−1.02513e19	−1.57661
$785$	−1.07822e19	−1.64458
$786$	−7.77750e18	−1.17650
$787$	−1.07820e19	−1.61757	−0.808783	−	0.588107i	$-0.799874\pi$
$787$	−1.07820e19	−1.61757	−0.808783	+	0.588107i	$0.799874\pi$
$788$	−2.53231e19	−3.76788
$789$	5.18529e18	0.765196
$790$	−1.17489e19	−1.71957
$791$	5.08586e18	0.738273
$792$	1.03947e19	1.49658
$793$	3.29442e17	0.0470439
$794$	−1.56839e19	−2.22137
$795$	2.27613e18	0.319751
$796$	3.27645e19	4.56530
$797$	1.00051e19	1.38274	0.691372	−	0.722499i	$-0.257007\pi$
$797$	1.00051e19	1.38274	0.691372	+	0.722499i	$0.257007\pi$
$798$	−3.30198e18	−0.452642
$799$	−4.57203e18	−0.621663
$800$	6.19349e18	0.835315
$801$	3.76361e18	0.503493
$802$	1.04127e18	0.138176
$803$	1.38641e19	1.82491
$804$	1.11984e19	1.46216
$805$	4.94528e18	0.640498
$806$	4.70883e18	0.604972
$807$	−4.74317e18	−0.604492
$808$	−1.76699e18	−0.223389
$809$	−2.56239e18	−0.321351	−0.160676	−	0.987007i	$-0.551367\pi$
$809$	−2.56239e18	−0.321351	−0.160676	+	0.987007i	$0.551367\pi$
$810$	−1.90307e18	−0.236756
$811$	7.41054e18	0.914565	0.457282	−	0.889322i	$-0.348823\pi$
$811$	7.41054e18	0.914565	0.457282	+	0.889322i	$0.348823\pi$
$812$	3.38926e18	0.414945
$813$	−8.60888e17	−0.104558
$814$	−2.86607e18	−0.345326
$815$	1.00524e19	1.20156
$816$	−1.52267e19	−1.80559
$817$	−5.58659e17	−0.0657209
$818$	−3.02460e18	−0.352998
$819$	−4.84820e17	−0.0561352
$820$	−2.22497e19	−2.55585
$821$	−6.83660e18	−0.779130	−0.389565	−	0.920999i	$-0.627375\pi$
$821$	−6.83660e18	−0.779130	−0.389565	+	0.920999i	$0.627375\pi$
$822$	1.74720e19	1.97550
$823$	−4.81090e17	−0.0539669	−0.0269835	−	0.999636i	$-0.508590\pi$
$823$	−4.81090e17	−0.0539669	−0.0269835	+	0.999636i	$0.508590\pi$
$824$	3.29232e19	3.66417
$825$	1.53562e18	0.169564
$826$	1.73988e18	0.190612
$827$	−2.62381e18	−0.285198	−0.142599	−	0.989781i	$-0.545546\pi$
$827$	−2.62381e18	−0.285198	−0.142599	+	0.989781i	$0.545546\pi$
$828$	6.45050e18	0.695659
$829$	1.20188e19	1.28604	0.643022	−	0.765847i	$-0.277680\pi$
$829$	1.20188e19	1.28604	0.643022	+	0.765847i	$0.277680\pi$
$830$	−1.92916e19	−2.04814
$831$	−6.31479e17	−0.0665200
$832$	7.82319e18	0.817678
$833$	3.45282e18	0.358081
$834$	1.62653e18	0.167372
$835$	1.47736e19	1.50842
$836$	1.94077e19	1.96622
$837$	2.70145e18	0.271570
$838$	−9.39389e18	−0.937042
$839$	−1.63890e19	−1.62219	−0.811093	−	0.584917i	$-0.801127\pi$
$839$	−1.63890e19	−1.62219	−0.811093	+	0.584917i	$0.801127\pi$
$840$	1.64074e19	1.61148
$841$	−9.84764e18	−0.959750
$842$	−6.59034e18	−0.637352
$843$	1.19694e18	0.114866
$844$	−9.38003e18	−0.893261
$845$	1.11034e19	1.04927
$846$	5.06194e18	0.474690
$847$	−6.62309e18	−0.616337
$848$	−2.01631e19	−1.86202
$849$	3.99438e18	0.366058
$850$	−3.90271e18	−0.354931
$851$	−1.12642e18	−0.101662
$852$	1.65602e19	1.48323
$853$	−1.88350e18	−0.167416	−0.0837082	−	0.996490i	$-0.526676\pi$
$853$	−1.88350e18	−0.167416	−0.0837082	+	0.996490i	$0.526676\pi$
$854$	−3.51625e18	−0.310173
$855$	−2.25033e18	−0.197000
$856$	−4.09510e19	−3.55783
$857$	1.63854e19	1.41281	0.706404	−	0.707809i	$-0.250316\pi$
$857$	1.63854e19	1.41281	0.706404	+	0.707809i	$0.250316\pi$
$858$	3.89442e18	0.333254
$859$	8.34996e18	0.709135	0.354568	−	0.935030i	$-0.384628\pi$
$859$	8.34996e18	0.709135	0.354568	+	0.935030i	$0.384628\pi$
$860$	4.38309e18	0.369437
$861$	−4.44425e18	−0.371773
$862$	3.52775e19	2.92888
$863$	7.12624e17	0.0587206	0.0293603	−	0.999569i	$-0.490653\pi$
$863$	7.12624e17	0.0587206	0.0293603	+	0.999569i	$0.490653\pi$
$864$	9.01112e18	0.736952
$865$	−1.54834e19	−1.25679
$866$	−1.28503e18	−0.103525
$867$	−2.09180e18	−0.167262
$868$	−3.67749e19	−2.91859
$869$	1.37934e19	1.08653
$870$	3.15674e18	0.246811
$871$	2.65717e18	0.206206
$872$	−5.85903e19	−4.51303
$873$	7.89104e17	0.0603312
$874$	1.04243e19	0.791087
$875$	−8.68784e18	−0.654424
$876$	2.85444e19	2.13424
$877$	2.11611e19	1.57051	0.785255	−	0.619172i	$-0.212532\pi$
$877$	2.11611e19	1.57051	0.785255	+	0.619172i	$0.212532\pi$
$878$	−2.05559e19	−1.51434
$879$	8.04767e18	0.588495
$880$	−7.59645e19	−5.51409
$881$	2.15336e19	1.55157	0.775787	−	0.630995i	$-0.217353\pi$
$881$	2.15336e19	1.55157	0.775787	+	0.630995i	$0.217353\pi$
$882$	−3.82281e18	−0.273424
$883$	3.91490e18	0.277956	0.138978	−	0.990295i	$-0.455618\pi$
$883$	3.91490e18	0.277956	0.138978	+	0.990295i	$0.455618\pi$
$884$	−7.24208e18	−0.510415
$885$	1.18575e18	0.0829586
$886$	−6.18097e18	−0.429277
$887$	−5.95492e18	−0.410556	−0.205278	−	0.978704i	$-0.565810\pi$
$887$	−5.95492e18	−0.410556	−0.205278	+	0.978704i	$0.565810\pi$
$888$	−3.73722e18	−0.255779
$889$	1.39397e19	0.947089
$890$	−4.77192e19	−3.21853
$891$	2.23423e18	0.149597
$892$	−7.32905e19	−4.87165
$893$	5.98563e18	0.394980
$894$	−2.72645e19	−1.78609
$895$	1.01029e19	0.657046
$896$	−3.85213e19	−2.48713
$897$	1.53058e18	0.0981080
$898$	3.09525e19	1.96970
$899$	−4.48108e18	−0.283103
$900$	3.16164e18	0.198306
$901$	6.79132e18	0.422905
$902$	3.56994e19	2.20708
$903$	8.75496e17	0.0537383
$904$	−5.32706e19	−3.24633
$905$	5.45026e18	0.329763
$906$	8.60471e18	0.516896
$907$	9.42548e17	0.0562155	0.0281078	−	0.999605i	$-0.491052\pi$
$907$	9.42548e17	0.0562155	0.0281078	+	0.999605i	$0.491052\pi$
$908$	−7.41164e19	−4.38891
$909$	−3.79795e17	−0.0223297
$910$	6.14708e18	0.358839
$911$	2.03338e19	1.17855	0.589275	−	0.807932i	$-0.299413\pi$
$911$	2.03338e19	1.17855	0.589275	+	0.807932i	$0.299413\pi$
$912$	1.99346e19	1.14720
$913$	2.26486e19	1.29414
$914$	3.73677e19	2.12005
$915$	−2.39636e18	−0.134994
$916$	4.64436e19	2.59780
$917$	1.44125e19	0.800459
$918$	−5.67820e18	−0.313136
$919$	−2.93286e19	−1.60598	−0.802992	−	0.595990i	$-0.796760\pi$
$919$	−2.93286e19	−1.60598	−0.802992	+	0.595990i	$0.796760\pi$
$920$	−5.17982e19	−2.81639
$921$	−6.40742e18	−0.345936
$922$	5.99600e19	3.21448
$923$	3.92940e18	0.209178
$924$	−3.04145e19	−1.60773
$925$	−5.52101e17	−0.0289799
$926$	9.59346e18	0.500039
$927$	7.07645e18	0.366267
$928$	−1.49473e19	−0.768250
$929$	1.55314e18	0.0792699	0.0396350	−	0.999214i	$-0.487380\pi$
$929$	1.55314e18	0.0792699	0.0396350	+	0.999214i	$0.487380\pi$
$930$	−3.42520e19	−1.73599
$931$	−4.52038e18	−0.227511
$932$	7.46431e19	3.73066
$933$	1.92547e19	0.955664
$934$	−3.14186e19	−1.54858
$935$	2.55863e19	1.25237
$936$	5.07813e18	0.246837
$937$	3.41526e19	1.64860	0.824302	−	0.566151i	$-0.191568\pi$
$937$	3.41526e19	1.64860	0.824302	+	0.566151i	$0.191568\pi$
$938$	−2.83609e19	−1.35957
$939$	4.32010e18	0.205668
$940$	−4.69616e19	−2.22030
$941$	−2.13667e19	−1.00324	−0.501620	−	0.865088i	$-0.667262\pi$
$941$	−2.13667e19	−1.00324	−0.501620	+	0.865088i	$0.667262\pi$
$942$	3.56182e19	1.66089
$943$	1.40305e19	0.649751
$944$	−1.05040e19	−0.483098
$945$	3.52658e18	0.161082
$946$	−7.03261e18	−0.319024
$947$	−3.86064e19	−1.73934	−0.869670	−	0.493633i	$-0.835669\pi$
$947$	−3.86064e19	−1.73934	−0.869670	+	0.493633i	$0.835669\pi$
$948$	2.83988e19	1.27071
$949$	6.77302e18	0.300990
$950$	5.10937e18	0.225509
$951$	−2.52834e19	−1.10831
$952$	4.89549e19	2.13136
$953$	3.41329e19	1.47594	0.737970	−	0.674833i	$-0.235784\pi$
$953$	3.41329e19	1.47594	0.737970	+	0.674833i	$0.235784\pi$
$954$	−7.51905e18	−0.322923
$955$	2.43081e19	1.03688
$956$	−3.17350e19	−1.34450
$957$	−3.70606e18	−0.155950
$958$	8.35286e19	3.49107
$959$	−3.23775e19	−1.34407
$960$	−5.69059e19	−2.34636
$961$	2.42041e19	0.991260
$962$	−1.40016e18	−0.0569561
$963$	−8.80194e18	−0.355638
$964$	−1.18857e20	−4.77007
$965$	3.45059e19	1.37552
$966$	−1.63364e19	−0.646852
$967$	−2.38107e18	−0.0936482	−0.0468241	−	0.998903i	$-0.514910\pi$
$967$	−2.38107e18	−0.0936482	−0.0468241	+	0.998903i	$0.514910\pi$
$968$	6.93720e19	2.71016
$969$	−6.71433e18	−0.260554
$970$	−1.00051e19	−0.385662
$971$	−4.95746e19	−1.89817	−0.949083	−	0.315027i	$-0.897987\pi$
$971$	−4.95746e19	−1.89817	−0.949083	+	0.315027i	$0.897987\pi$
$972$	4.59998e18	0.174955
$973$	−3.01413e18	−0.113875
$974$	−1.21860e19	−0.457328
$975$	7.50195e17	0.0279669
$976$	2.12282e19	0.786120
$977$	3.69404e19	1.35890	0.679450	−	0.733722i	$-0.262219\pi$
$977$	3.69404e19	1.35890	0.679450	+	0.733722i	$0.262219\pi$
$978$	−3.32075e19	−1.21348
$979$	5.60230e19	2.03366
$980$	3.54657e19	1.27891
$981$	−1.25933e19	−0.451119
$982$	−3.75699e19	−1.33695
$983$	1.35273e19	0.478205	0.239103	−	0.970994i	$-0.423147\pi$
$983$	1.35273e19	0.478205	0.239103	+	0.970994i	$0.423147\pi$
$984$	4.65503e19	1.63476
$985$	4.37071e19	1.52481
$986$	9.41880e18	0.326434
$987$	−9.38031e18	−0.322965
$988$	9.48122e18	0.324298
$989$	−2.76394e18	−0.0939189
$990$	−2.83280e19	−0.956284
$991$	5.57620e18	0.187008	0.0935038	−	0.995619i	$-0.470193\pi$
$991$	5.57620e18	0.187008	0.0935038	+	0.995619i	$0.470193\pi$
$992$	1.62185e20	5.40363
$993$	−1.66242e19	−0.550262
$994$	−4.19399e19	−1.37916
$995$	−5.65508e19	−1.84752
$996$	4.66305e19	1.51351
$997$	−2.46042e18	−0.0793398	−0.0396699	−	0.999213i	$-0.512631\pi$
$997$	−2.46042e18	−0.0793398	−0.0396699	+	0.999213i	$0.512631\pi$
$998$	−5.59933e19	−1.79386
$999$	−8.03271e17	−0.0255674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.30	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.30	✓	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)

\(f(q)\)	\(=\)	\(q+174.739 q^{2} +729.000 q^{3} +22341.8 q^{4} -38561.4 q^{5} +127385. q^{6} -236058. q^{7} +2.47253e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q+174.739 q^{2} +729.000 q^{3} +22341.8 q^{4} -38561.4 q^{5} +127385. q^{6} -236058. q^{7} +2.47253e6 q^{8} +531441. q^{9} -6.73820e6 q^{10} +7.91074e6 q^{11} +1.62872e7 q^{12} +3.86463e6 q^{13} -4.12485e7 q^{14} -2.81113e7 q^{15} +2.49024e8 q^{16} -8.38759e7 q^{17} +9.28636e7 q^{18} +1.09809e8 q^{19} -8.61532e8 q^{20} -1.72086e8 q^{21} +1.38232e9 q^{22} +5.43275e8 q^{23} +1.80247e9 q^{24} +2.66280e8 q^{25} +6.75302e8 q^{26} +3.87420e8 q^{27} -5.27395e9 q^{28} -6.42640e8 q^{29} -4.91214e9 q^{30} +6.97293e9 q^{31} +2.32593e10 q^{32} +5.76693e9 q^{33} -1.46564e10 q^{34} +9.10271e9 q^{35} +1.18734e10 q^{36} -2.07338e9 q^{37} +1.91880e10 q^{38} +2.81731e9 q^{39} -9.53442e10 q^{40} +2.58258e10 q^{41} -3.00702e10 q^{42} -5.08755e9 q^{43} +1.76740e11 q^{44} -2.04931e10 q^{45} +9.49315e10 q^{46} +5.45094e10 q^{47} +1.81538e11 q^{48} -4.11659e10 q^{49} +4.65296e10 q^{50} -6.11455e10 q^{51} +8.63428e10 q^{52} -8.09687e10 q^{53} +6.76976e10 q^{54} -3.05049e11 q^{55} -5.83659e11 q^{56} +8.00508e10 q^{57} -1.12295e11 q^{58} -4.21805e10 q^{59} -6.28057e11 q^{60} +8.52456e10 q^{61} +1.21844e12 q^{62} -1.25451e11 q^{63} +2.02431e12 q^{64} -1.49026e11 q^{65} +1.00771e12 q^{66} +6.87562e11 q^{67} -1.87394e12 q^{68} +3.96048e11 q^{69} +1.59060e12 q^{70} +1.01676e12 q^{71} +1.31400e12 q^{72} +1.75257e12 q^{73} -3.62302e11 q^{74} +1.94118e11 q^{75} +2.45333e12 q^{76} -1.86739e12 q^{77} +4.92295e11 q^{78} +1.74363e12 q^{79} -9.60271e12 q^{80} +2.82430e11 q^{81} +4.51278e12 q^{82} +2.86302e12 q^{83} -3.84471e12 q^{84} +3.23437e12 q^{85} -8.88995e11 q^{86} -4.68485e11 q^{87} +1.95595e13 q^{88} +7.08189e12 q^{89} -3.58095e12 q^{90} -9.12274e11 q^{91} +1.21378e13 q^{92} +5.08326e12 q^{93} +9.52494e12 q^{94} -4.23439e12 q^{95} +1.69560e13 q^{96} +1.48484e12 q^{97} -7.19329e12 q^{98} +4.20409e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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

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