LMFDB - Embedded newform 177.14.a.c.1.9

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			1.9
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)

$f(q)$	$=$	$q-83.5640 q^{2} +729.000 q^{3} -1209.07 q^{4} +55860.4 q^{5} -60918.1 q^{6} -515369. q^{7} +785590. q^{8} +531441. q^{9} +O(q^{10})$	\(q-83.5640 q^{2} +729.000 q^{3} -1209.07 q^{4} +55860.4 q^{5} -60918.1 q^{6} -515369. q^{7} +785590. q^{8} +531441. q^{9} -4.66791e6 q^{10} +3.72299e6 q^{11} -881409. q^{12} -9.32855e6 q^{13} +4.30663e7 q^{14} +4.07222e7 q^{15} -5.57424e7 q^{16} -7.95874e6 q^{17} -4.44093e7 q^{18} -6.13400e7 q^{19} -6.75389e7 q^{20} -3.75704e8 q^{21} -3.11108e8 q^{22} +5.74053e8 q^{23} +5.72695e8 q^{24} +1.89968e9 q^{25} +7.79530e8 q^{26} +3.87420e8 q^{27} +6.23115e8 q^{28} -1.68012e9 q^{29} -3.40291e9 q^{30} -7.08624e9 q^{31} -1.77750e9 q^{32} +2.71406e9 q^{33} +6.65064e8 q^{34} -2.87887e10 q^{35} -6.42547e8 q^{36} -2.19046e9 q^{37} +5.12581e9 q^{38} -6.80051e9 q^{39} +4.38834e10 q^{40} +7.06872e9 q^{41} +3.13953e10 q^{42} +4.21711e10 q^{43} -4.50134e9 q^{44} +2.96865e10 q^{45} -4.79702e10 q^{46} +3.35142e10 q^{47} -4.06362e10 q^{48} +1.68716e11 q^{49} -1.58745e11 q^{50} -5.80192e9 q^{51} +1.12788e10 q^{52} +1.04251e11 q^{53} -3.23744e10 q^{54} +2.07967e11 q^{55} -4.04869e11 q^{56} -4.47168e10 q^{57} +1.40398e11 q^{58} -4.21805e10 q^{59} -4.92358e10 q^{60} +1.12562e11 q^{61} +5.92155e11 q^{62} -2.73888e11 q^{63} +6.05177e11 q^{64} -5.21096e11 q^{65} -2.26797e11 q^{66} +5.18952e11 q^{67} +9.62264e9 q^{68} +4.18485e11 q^{69} +2.40570e12 q^{70} -7.67141e11 q^{71} +4.17495e11 q^{72} -6.21825e11 q^{73} +1.83043e11 q^{74} +1.38486e12 q^{75} +7.41641e10 q^{76} -1.91871e12 q^{77} +5.68278e11 q^{78} +2.09547e12 q^{79} -3.11379e12 q^{80} +2.82430e11 q^{81} -5.90690e11 q^{82} +8.75347e11 q^{83} +4.54251e11 q^{84} -4.44578e11 q^{85} -3.52398e12 q^{86} -1.22481e12 q^{87} +2.92474e12 q^{88} +4.59522e12 q^{89} -2.48072e12 q^{90} +4.80765e12 q^{91} -6.94068e11 q^{92} -5.16587e12 q^{93} -2.80058e12 q^{94} -3.42647e12 q^{95} -1.29580e12 q^{96} -4.07043e12 q^{97} -1.40986e13 q^{98} +1.97855e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−83.5640	−0.923260	−0.461630	−	0.887073i	$-0.652735\pi$
$2$	−83.5640	−0.923260	−0.461630	+	0.887073i	$0.652735\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−1209.07	−0.147591
$5$	55860.4	1.59882	0.799409	−	0.600788i	$-0.205146\pi$
$5$	55860.4	1.59882	0.799409	+	0.600788i	$0.205146\pi$
$6$	−60918.1	−0.533044
$7$	−515369.	−1.65570	−0.827849	−	0.560951i	$-0.810436\pi$
$7$	−515369.	−1.65570	−0.827849	+	0.560951i	$0.810436\pi$
$8$	785590.	1.05952
$9$	531441.	0.333333
$10$	−4.66791e6	−1.47612
$11$	3.72299e6	0.633635	0.316817	−	0.948487i	$-0.397386\pi$
$11$	3.72299e6	0.633635	0.316817	+	0.948487i	$0.397386\pi$
$12$	−881409.	−0.0852117
$13$	−9.32855e6	−0.536022	−0.268011	−	0.963416i	$-0.586366\pi$
$13$	−9.32855e6	−0.536022	−0.268011	+	0.963416i	$0.586366\pi$
$14$	4.30663e7	1.52864
$15$	4.07222e7	0.923077
$16$	−5.57424e7	−0.830626
$17$	−7.95874e6	−0.0799699	−0.0399849	−	0.999200i	$-0.512731\pi$
$17$	−7.95874e6	−0.0799699	−0.0399849	+	0.999200i	$0.512731\pi$
$18$	−4.44093e7	−0.307753
$19$	−6.13400e7	−0.299120	−0.149560	−	0.988753i	$-0.547786\pi$
$19$	−6.13400e7	−0.299120	−0.149560	+	0.988753i	$0.547786\pi$
$20$	−6.75389e7	−0.235971
$21$	−3.75704e8	−0.955918
$22$	−3.11108e8	−0.585010
$23$	5.74053e8	0.808577	0.404288	−	0.914632i	$-0.367519\pi$
$23$	5.74053e8	0.808577	0.404288	+	0.914632i	$0.367519\pi$
$24$	5.72695e8	0.611717
$25$	1.89968e9	1.55622
$26$	7.79530e8	0.494887
$27$	3.87420e8	0.192450
$28$	6.23115e8	0.244366
$29$	−1.68012e9	−0.524511	−0.262255	−	0.964998i	$-0.584466\pi$
$29$	−1.68012e9	−0.524511	−0.262255	+	0.964998i	$0.584466\pi$
$30$	−3.40291e9	−0.852240
$31$	−7.08624e9	−1.43405	−0.717026	−	0.697046i	$-0.754497\pi$
$31$	−7.08624e9	−1.43405	−0.717026	+	0.697046i	$0.754497\pi$
$32$	−1.77750e9	−0.292641
$33$	2.71406e9	0.365829
$34$	6.65064e8	0.0738330
$35$	−2.87887e10	−2.64716
$36$	−6.42547e8	−0.0491970
$37$	−2.19046e9	−0.140354	−0.0701768	−	0.997535i	$-0.522356\pi$
$37$	−2.19046e9	−0.140354	−0.0701768	+	0.997535i	$0.522356\pi$
$38$	5.12581e9	0.276165
$39$	−6.80051e9	−0.309472
$40$	4.38834e10	1.69399
$41$	7.06872e9	0.232405	0.116203	−	0.993226i	$-0.462928\pi$
$41$	7.06872e9	0.232405	0.116203	+	0.993226i	$0.462928\pi$
$42$	3.13953e10	0.882561
$43$	4.21711e10	1.01735	0.508674	−	0.860959i	$-0.330136\pi$
$43$	4.21711e10	1.01735	0.508674	+	0.860959i	$0.330136\pi$
$44$	−4.50134e9	−0.0935188
$45$	2.96865e10	0.532939
$46$	−4.79702e10	−0.746527
$47$	3.35142e10	0.453517	0.226758	−	0.973951i	$-0.427187\pi$
$47$	3.35142e10	0.453517	0.226758	+	0.973951i	$0.427187\pi$
$48$	−4.06362e10	−0.479562
$49$	1.68716e11	1.74134
$50$	−1.58745e11	−1.43679
$51$	−5.80192e9	−0.0461706
$52$	1.12788e10	0.0791120
$53$	1.04251e11	0.646084	0.323042	−	0.946385i	$-0.395295\pi$
$53$	1.04251e11	0.646084	0.323042	+	0.946385i	$0.395295\pi$
$54$	−3.23744e10	−0.177681
$55$	2.07967e11	1.01307
$56$	−4.04869e11	−1.75425
$57$	−4.47168e10	−0.172697
$58$	1.40398e11	0.484260
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−4.92358e10	−0.136238
$61$	1.12562e11	0.279736	0.139868	−	0.990170i	$-0.455332\pi$
$61$	1.12562e11	0.279736	0.139868	+	0.990170i	$0.455332\pi$
$62$	5.92155e11	1.32400
$63$	−2.73888e11	−0.551899
$64$	6.05177e11	1.10081
$65$	−5.21096e11	−0.857000
$66$	−2.26797e11	−0.337756
$67$	5.18952e11	0.700876	0.350438	−	0.936586i	$-0.386033\pi$
$67$	5.18952e11	0.700876	0.350438	+	0.936586i	$0.386033\pi$
$68$	9.62264e9	0.0118028
$69$	4.18485e11	0.466832
$70$	2.40570e12	2.44402
$71$	−7.67141e11	−0.710715	−0.355358	−	0.934730i	$-0.615641\pi$
$71$	−7.67141e11	−0.710715	−0.355358	+	0.934730i	$0.615641\pi$
$72$	4.17495e11	0.353175
$73$	−6.21825e11	−0.480916	−0.240458	−	0.970660i	$-0.577298\pi$
$73$	−6.21825e11	−0.480916	−0.240458	+	0.970660i	$0.577298\pi$
$74$	1.83043e11	0.129583
$75$	1.38486e12	0.898482
$76$	7.41641e10	0.0441474
$77$	−1.91871e12	−1.04911
$78$	5.68278e11	0.285723
$79$	2.09547e12	0.969854	0.484927	−	0.874555i	$-0.338846\pi$
$79$	2.09547e12	0.969854	0.484927	+	0.874555i	$0.338846\pi$
$80$	−3.11379e12	−1.32802
$81$	2.82430e11	0.111111
$82$	−5.90690e11	−0.214570
$83$	8.75347e11	0.293882	0.146941	−	0.989145i	$-0.453057\pi$
$83$	8.75347e11	0.293882	0.146941	+	0.989145i	$0.453057\pi$
$84$	4.54251e11	0.141085
$85$	−4.44578e11	−0.127857
$86$	−3.52398e12	−0.939277
$87$	−1.22481e12	−0.302826
$88$	2.92474e12	0.671352
$89$	4.59522e12	0.980102	0.490051	−	0.871694i	$-0.336978\pi$
$89$	4.59522e12	0.980102	0.490051	+	0.871694i	$0.336978\pi$
$90$	−2.48072e12	−0.492041
$91$	4.80765e12	0.887490
$92$	−6.94068e11	−0.119339
$93$	−5.16587e12	−0.827951
$94$	−2.80058e12	−0.418714
$95$	−3.42647e12	−0.478238
$96$	−1.29580e12	−0.168957
$97$	−4.07043e12	−0.496162	−0.248081	−	0.968739i	$-0.579800\pi$
$97$	−4.07043e12	−0.496162	−0.248081	+	0.968739i	$0.579800\pi$
$98$	−1.40986e13	−1.60771
$99$	1.97855e12	0.211212
$100$	−2.29683e12	−0.229683
$101$	−1.75220e13	−1.64246	−0.821230	−	0.570597i	$-0.806712\pi$
$101$	−1.75220e13	−1.64246	−0.821230	+	0.570597i	$0.806712\pi$
$102$	4.84832e11	0.0426275
$103$	−5.35352e12	−0.441771	−0.220886	−	0.975300i	$-0.570895\pi$
$103$	−5.35352e12	−0.441771	−0.220886	+	0.975300i	$0.570895\pi$
$104$	−7.32842e12	−0.567928
$105$	−2.09870e13	−1.52834
$106$	−8.71166e12	−0.596503
$107$	9.14307e12	0.588976	0.294488	−	0.955655i	$-0.404851\pi$
$107$	9.14307e12	0.588976	0.294488	+	0.955655i	$0.404851\pi$
$108$	−4.68417e11	−0.0284039
$109$	2.30859e13	1.31848	0.659242	−	0.751931i	$-0.270877\pi$
$109$	2.30859e13	1.31848	0.659242	+	0.751931i	$0.270877\pi$
$110$	−1.73786e13	−0.935324
$111$	−1.59684e12	−0.0810332
$112$	2.87279e13	1.37527
$113$	−1.78769e13	−0.807759	−0.403880	−	0.914812i	$-0.632339\pi$
$113$	−1.78769e13	−0.807759	−0.403880	+	0.914812i	$0.632339\pi$
$114$	3.73672e12	0.159444
$115$	3.20668e13	1.29277
$116$	2.03138e12	0.0774131
$117$	−4.95757e12	−0.178674
$118$	3.52477e12	0.120198
$119$	4.10169e12	0.132406
$120$	3.19910e13	0.978023
$121$	−2.06621e13	−0.598507
$122$	−9.40614e12	−0.258269
$123$	5.15309e12	0.134179
$124$	8.56773e12	0.211653
$125$	3.79278e13	0.889287
$126$	2.28872e13	0.509547
$127$	−6.19688e13	−1.31053	−0.655267	−	0.755397i	$-0.727444\pi$
$127$	−6.19688e13	−1.31053	−0.655267	+	0.755397i	$0.727444\pi$
$128$	−3.60096e13	−0.723692
$129$	3.07427e13	0.587366
$130$	4.35449e13	0.791234
$131$	3.70185e13	0.639963	0.319982	−	0.947424i	$-0.396323\pi$
$131$	3.70185e13	0.639963	0.319982	+	0.947424i	$0.396323\pi$
$132$	−3.28147e12	−0.0539931
$133$	3.16127e13	0.495252
$134$	−4.33657e13	−0.647090
$135$	2.16415e13	0.307692
$136$	−6.25231e12	−0.0847301
$137$	−1.30239e14	−1.68290	−0.841451	−	0.540334i	$-0.818298\pi$
$137$	−1.30239e14	−1.68290	−0.841451	+	0.540334i	$0.818298\pi$
$138$	−3.49702e13	−0.431007
$139$	1.01862e14	1.19789	0.598946	−	0.800790i	$-0.295587\pi$
$139$	1.01862e14	1.19789	0.598946	+	0.800790i	$0.295587\pi$
$140$	3.48074e13	0.390697
$141$	2.44319e13	0.261838
$142$	6.41053e13	0.656175
$143$	−3.47301e13	−0.339642
$144$	−2.96238e13	−0.276875
$145$	−9.38524e13	−0.838597
$146$	5.19621e13	0.444011
$147$	1.22994e14	1.00536
$148$	2.64841e12	0.0207149
$149$	5.81338e13	0.435229	0.217614	−	0.976035i	$-0.430172\pi$
$149$	5.81338e13	0.435229	0.217614	+	0.976035i	$0.430172\pi$
$150$	−1.15725e14	−0.829532
$151$	9.07930e12	0.0623307	0.0311654	−	0.999514i	$-0.490078\pi$
$151$	9.07930e12	0.0623307	0.0311654	+	0.999514i	$0.490078\pi$
$152$	−4.81881e13	−0.316925
$153$	−4.22960e12	−0.0266566
$154$	1.60335e14	0.968600
$155$	−3.95840e14	−2.29279
$156$	8.22227e12	0.0456753
$157$	−9.06368e13	−0.483011	−0.241505	−	0.970400i	$-0.577641\pi$
$157$	−9.06368e13	−0.483011	−0.241505	+	0.970400i	$0.577641\pi$
$158$	−1.75106e14	−0.895427
$159$	7.59993e13	0.373017
$160$	−9.92920e13	−0.467880
$161$	−2.95849e14	−1.33876
$162$	−2.36009e13	−0.102584
$163$	−4.00116e13	−0.167096	−0.0835481	−	0.996504i	$-0.526625\pi$
$163$	−4.00116e13	−0.167096	−0.0835481	+	0.996504i	$0.526625\pi$
$164$	−8.54654e12	−0.0343009
$165$	1.51608e14	0.584894
$166$	−7.31474e13	−0.271329
$167$	1.02841e14	0.366867	0.183433	−	0.983032i	$-0.441279\pi$
$167$	1.02841e14	0.366867	0.183433	+	0.983032i	$0.441279\pi$
$168$	−2.95149e14	−1.01282
$169$	−2.15853e14	−0.712681
$170$	3.71507e13	0.118045
$171$	−3.25986e13	−0.0997066
$172$	−5.09876e13	−0.150152
$173$	1.62858e14	0.461859	0.230929	−	0.972971i	$-0.425823\pi$
$173$	1.62858e14	0.461859	0.230929	+	0.972971i	$0.425823\pi$
$174$	1.02350e14	0.279588
$175$	−9.79035e14	−2.57662
$176$	−2.07528e14	−0.526314
$177$	−3.07496e13	−0.0751646
$178$	−3.83995e14	−0.904889
$179$	−2.78658e14	−0.633180	−0.316590	−	0.948563i	$-0.602538\pi$
$179$	−2.78658e14	−0.633180	−0.316590	+	0.948563i	$0.602538\pi$
$180$	−3.58929e13	−0.0786570
$181$	3.64782e14	0.771121	0.385561	−	0.922682i	$-0.374008\pi$
$181$	3.64782e14	0.771121	0.385561	+	0.922682i	$0.374008\pi$
$182$	−4.01746e14	−0.819384
$183$	8.20579e13	0.161506
$184$	4.50971e14	0.856707
$185$	−1.22360e14	−0.224400
$186$	4.31681e14	0.764414
$187$	−2.96303e13	−0.0506717
$188$	−4.05209e13	−0.0669350
$189$	−1.99665e14	−0.318639
$190$	2.86330e14	0.441538
$191$	1.32894e15	1.98056	0.990282	−	0.139076i	$-0.0444133\pi$
$191$	1.32894e15	1.98056	0.990282	+	0.139076i	$0.0444133\pi$
$192$	4.41174e14	0.635553
$193$	7.90275e14	1.10067	0.550333	−	0.834945i	$-0.314501\pi$
$193$	7.90275e14	1.10067	0.550333	+	0.834945i	$0.314501\pi$
$194$	3.40141e14	0.458086
$195$	−3.79879e14	−0.494789
$196$	−2.03989e14	−0.257006
$197$	1.54814e15	1.88703	0.943517	−	0.331324i	$-0.107495\pi$
$197$	1.54814e15	1.88703	0.943517	+	0.331324i	$0.107495\pi$
$198$	−1.65335e14	−0.195003
$199$	6.10207e14	0.696518	0.348259	−	0.937398i	$-0.386773\pi$
$199$	6.10207e14	0.696518	0.348259	+	0.937398i	$0.386773\pi$
$200$	1.49237e15	1.64885
$201$	3.78316e14	0.404651
$202$	1.46421e15	1.51642
$203$	8.65884e14	0.868432
$204$	7.01491e12	0.00681437
$205$	3.94861e14	0.371573
$206$	4.47361e14	0.407870
$207$	3.05075e14	0.269526
$208$	5.19995e14	0.445233
$209$	−2.28368e14	−0.189533
$210$	1.75375e15	1.41105
$211$	8.00376e14	0.624393	0.312197	−	0.950018i	$-0.398935\pi$
$211$	8.00376e14	0.624393	0.312197	+	0.950018i	$0.398935\pi$
$212$	−1.26047e14	−0.0953562
$213$	−5.59246e14	−0.410332
$214$	−7.64031e14	−0.543778
$215$	2.35569e15	1.62655
$216$	3.04354e14	0.203906
$217$	3.65203e15	2.37436
$218$	−1.92915e15	−1.21730
$219$	−4.53310e14	−0.277657
$220$	−2.51446e14	−0.149519
$221$	7.42435e13	0.0428656
$222$	1.33439e14	0.0748147
$223$	−1.00189e15	−0.545553	−0.272777	−	0.962077i	$-0.587942\pi$
$223$	−1.00189e15	−0.545553	−0.272777	+	0.962077i	$0.587942\pi$
$224$	9.16070e14	0.484526
$225$	1.00957e15	0.518739
$226$	1.49386e15	0.745772
$227$	−3.52434e15	−1.70966	−0.854829	−	0.518909i	$-0.826338\pi$
$227$	−3.52434e15	−1.70966	−0.854829	+	0.518909i	$0.826338\pi$
$228$	5.40656e13	0.0254885
$229$	6.59620e14	0.302248	0.151124	−	0.988515i	$-0.451711\pi$
$229$	6.59620e14	0.302248	0.151124	+	0.988515i	$0.451711\pi$
$230$	−2.67963e15	−1.19356
$231$	−1.39874e15	−0.605703
$232$	−1.31989e15	−0.555732
$233$	4.30079e15	1.76090	0.880450	−	0.474140i	$-0.157241\pi$
$233$	4.30079e15	1.76090	0.880450	+	0.474140i	$0.157241\pi$
$234$	4.14274e14	0.164962
$235$	1.87212e15	0.725090
$236$	5.09990e13	0.0192147
$237$	1.52760e15	0.559945
$238$	−3.42754e14	−0.122245
$239$	1.93932e15	0.673075	0.336537	−	0.941670i	$-0.390744\pi$
$239$	1.93932e15	0.673075	0.336537	+	0.941670i	$0.390744\pi$
$240$	−2.26995e15	−0.766732
$241$	1.38139e15	0.454157	0.227079	−	0.973876i	$-0.427083\pi$
$241$	1.38139e15	0.454157	0.227079	+	0.973876i	$0.427083\pi$
$242$	1.72660e15	0.552577
$243$	2.05891e14	0.0641500
$244$	−1.36095e14	−0.0412866
$245$	9.42456e15	2.78408
$246$	−4.30613e14	−0.123882
$247$	5.72213e14	0.160335
$248$	−5.56688e15	−1.51941
$249$	6.38128e14	0.169673
$250$	−3.16939e15	−0.821043
$251$	1.56790e15	0.395767	0.197883	−	0.980226i	$-0.436593\pi$
$251$	1.56790e15	0.395767	0.197883	+	0.980226i	$0.436593\pi$
$252$	3.31149e14	0.0814554
$253$	2.13719e15	0.512342
$254$	5.17835e15	1.20996
$255$	−3.24098e14	−0.0738184
$256$	−1.94850e15	−0.432654
$257$	−1.82226e15	−0.394498	−0.197249	−	0.980353i	$-0.563201\pi$
$257$	−1.82226e15	−0.394498	−0.197249	+	0.980353i	$0.563201\pi$
$258$	−2.56898e15	−0.542292
$259$	1.12889e15	0.232383
$260$	6.30039e14	0.126486
$261$	−8.92887e14	−0.174837
$262$	−3.09341e15	−0.590852
$263$	9.80099e15	1.82624	0.913119	−	0.407693i	$-0.133667\pi$
$263$	9.80099e15	1.82624	0.913119	+	0.407693i	$0.133667\pi$
$264$	2.13214e15	0.387605
$265$	5.82352e15	1.03297
$266$	−2.64168e15	−0.457246
$267$	3.34992e15	0.565862
$268$	−6.27447e14	−0.103443
$269$	1.08167e16	1.74062	0.870311	−	0.492502i	$-0.163918\pi$
$269$	1.08167e16	1.74062	0.870311	+	0.492502i	$0.163918\pi$
$270$	−1.80845e15	−0.284080
$271$	−6.40238e14	−0.0981841	−0.0490921	−	0.998794i	$-0.515633\pi$
$271$	−6.40238e14	−0.0981841	−0.0490921	+	0.998794i	$0.515633\pi$
$272$	4.43639e14	0.0664251
$273$	3.50477e15	0.512393
$274$	1.08833e16	1.55376
$275$	7.07248e15	0.986073
$276$	−5.05976e14	−0.0689002
$277$	4.12047e15	0.548060	0.274030	−	0.961721i	$-0.411643\pi$
$277$	4.12047e15	0.548060	0.274030	+	0.961721i	$0.411643\pi$
$278$	−8.51202e15	−1.10596
$279$	−3.76592e15	−0.478017
$280$	−2.26161e16	−2.80473
$281$	7.69016e15	0.931846	0.465923	−	0.884825i	$-0.345722\pi$
$281$	7.69016e15	0.931846	0.465923	+	0.884825i	$0.345722\pi$
$282$	−2.04162e15	−0.241744
$283$	1.20369e16	1.39285	0.696423	−	0.717632i	$-0.254774\pi$
$283$	1.20369e16	1.39285	0.696423	+	0.717632i	$0.254774\pi$
$284$	9.27524e14	0.104895
$285$	−2.49790e15	−0.276111
$286$	2.90218e15	0.313578
$287$	−3.64300e15	−0.384793
$288$	−9.44638e14	−0.0975471
$289$	−9.84124e15	−0.993605
$290$	7.84268e15	0.774243
$291$	−2.96734e15	−0.286459
$292$	7.51827e14	0.0709789
$293$	−1.22346e16	−1.12967	−0.564835	−	0.825204i	$-0.691060\pi$
$293$	−1.22346e16	−1.12967	−0.564835	+	0.825204i	$0.691060\pi$
$294$	−1.02779e16	−0.928210
$295$	−2.35622e15	−0.208148
$296$	−1.72080e15	−0.148708
$297$	1.44236e15	0.121943
$298$	−4.85789e15	−0.401829
$299$	−5.35508e15	−0.433415
$300$	−1.67439e15	−0.132608
$301$	−2.17337e16	−1.68442
$302$	−7.58702e14	−0.0575474
$303$	−1.27735e16	−0.948275
$304$	3.41923e15	0.248457
$305$	6.28777e15	0.447247
$306$	3.53442e14	0.0246110
$307$	1.71522e16	1.16928	0.584642	−	0.811291i	$-0.301235\pi$
$307$	1.71522e16	1.16928	0.584642	+	0.811291i	$0.301235\pi$
$308$	2.31985e15	0.154839
$309$	−3.90272e15	−0.255057
$310$	3.30780e16	2.11684
$311$	3.52488e15	0.220903	0.110451	−	0.993882i	$-0.464770\pi$
$311$	3.52488e15	0.220903	0.110451	+	0.993882i	$0.464770\pi$
$312$	−5.34242e15	−0.327893
$313$	−3.32294e15	−0.199749	−0.0998744	−	0.995000i	$-0.531844\pi$
$313$	−3.32294e15	−0.199749	−0.0998744	+	0.995000i	$0.531844\pi$
$314$	7.57397e15	0.445944
$315$	−1.52995e16	−0.882386
$316$	−2.53357e15	−0.143142
$317$	1.65296e16	0.914905	0.457453	−	0.889234i	$-0.348762\pi$
$317$	1.65296e16	0.914905	0.457453	+	0.889234i	$0.348762\pi$
$318$	−6.35080e15	−0.344391
$319$	−6.25508e15	−0.332348
$320$	3.38054e16	1.75999
$321$	6.66530e15	0.340045
$322$	2.47223e16	1.23602
$323$	4.88189e14	0.0239206
$324$	−3.41476e14	−0.0163990
$325$	−1.77212e16	−0.834165
$326$	3.34353e15	0.154273
$327$	1.68296e16	0.761227
$328$	5.55311e15	0.246239
$329$	−1.72722e16	−0.750886
$330$	−1.26690e16	−0.540009
$331$	−1.38641e16	−0.579441	−0.289721	−	0.957111i	$-0.593562\pi$
$331$	−1.38641e16	−0.579441	−0.289721	+	0.957111i	$0.593562\pi$
$332$	−1.05835e15	−0.0433743
$333$	−1.16410e15	−0.0467846
$334$	−8.59378e15	−0.338713
$335$	2.89888e16	1.12057
$336$	2.09426e16	0.794010
$337$	5.52508e15	0.205468	0.102734	−	0.994709i	$-0.467241\pi$
$337$	5.52508e15	0.205468	0.102734	+	0.994709i	$0.467241\pi$
$338$	1.80376e16	0.657990
$339$	−1.30323e16	−0.466360
$340$	5.37524e14	0.0188706
$341$	−2.63820e16	−0.908666
$342$	2.72407e15	0.0920551
$343$	−3.70176e16	−1.22743
$344$	3.31292e16	1.07791
$345$	2.33767e16	0.746379
$346$	−1.36090e16	−0.426416
$347$	4.31784e15	0.132778	0.0663889	−	0.997794i	$-0.478852\pi$
$347$	4.31784e15	0.132778	0.0663889	+	0.997794i	$0.478852\pi$
$348$	1.48088e15	0.0446945
$349$	3.12984e16	0.927165	0.463583	−	0.886054i	$-0.346564\pi$
$349$	3.12984e16	0.927165	0.463583	+	0.886054i	$0.346564\pi$
$350$	8.18121e16	2.37889
$351$	−3.61407e15	−0.103157
$352$	−6.61762e15	−0.185428
$353$	−4.26852e16	−1.17420	−0.587100	−	0.809514i	$-0.699730\pi$
$353$	−4.26852e16	−1.17420	−0.587100	+	0.809514i	$0.699730\pi$
$354$	2.56956e15	0.0693965
$355$	−4.28528e16	−1.13630
$356$	−5.55593e15	−0.144654
$357$	2.99013e15	0.0764446
$358$	2.32858e16	0.584589
$359$	2.40663e16	0.593328	0.296664	−	0.954982i	$-0.404126\pi$
$359$	2.40663e16	0.593328	0.296664	+	0.954982i	$0.404126\pi$
$360$	2.33214e16	0.564662
$361$	−3.82904e16	−0.910527
$362$	−3.04826e16	−0.711946
$363$	−1.50627e16	−0.345548
$364$	−5.81276e15	−0.130986
$365$	−3.47354e16	−0.768897
$366$	−6.85708e15	−0.149112
$367$	−2.70999e16	−0.578945	−0.289473	−	0.957186i	$-0.593480\pi$
$367$	−2.70999e16	−0.578945	−0.289473	+	0.957186i	$0.593480\pi$
$368$	−3.19991e16	−0.671625
$369$	3.75661e15	0.0774683
$370$	1.02249e16	0.207179
$371$	−5.37280e16	−1.06972
$372$	6.24588e15	0.122198
$373$	8.49106e16	1.63251	0.816253	−	0.577695i	$-0.196048\pi$
$373$	8.49106e16	1.63251	0.816253	+	0.577695i	$0.196048\pi$
$374$	2.47603e15	0.0467832
$375$	2.76493e16	0.513430
$376$	2.63284e16	0.480512
$377$	1.56731e16	0.281149
$378$	1.66848e16	0.294187
$379$	8.76162e16	1.51855	0.759276	−	0.650769i	$-0.225553\pi$
$379$	8.76162e16	1.51855	0.759276	+	0.650769i	$0.225553\pi$
$380$	4.14283e15	0.0705836
$381$	−4.51752e16	−0.756638
$382$	−1.11052e17	−1.82857
$383$	−3.34691e16	−0.541817	−0.270908	−	0.962605i	$-0.587324\pi$
$383$	−3.34691e16	−0.541817	−0.270908	+	0.962605i	$0.587324\pi$
$384$	−2.62510e16	−0.417824
$385$	−1.07180e17	−1.67733
$386$	−6.60385e16	−1.01620
$387$	2.24114e16	0.339116
$388$	4.92141e15	0.0732291
$389$	−2.30023e16	−0.336588	−0.168294	−	0.985737i	$-0.553826\pi$
$389$	−2.30023e16	−0.336588	−0.168294	+	0.985737i	$0.553826\pi$
$390$	3.17442e16	0.456819
$391$	−4.56874e15	−0.0646618
$392$	1.32542e17	1.84499
$393$	2.69865e16	0.369483
$394$	−1.29369e17	−1.74222
$395$	1.17054e17	1.55062
$396$	−2.39219e15	−0.0311729
$397$	−5.74109e16	−0.735963	−0.367982	−	0.929833i	$-0.619951\pi$
$397$	−5.74109e16	−0.735963	−0.367982	+	0.929833i	$0.619951\pi$
$398$	−5.09913e16	−0.643067
$399$	2.30457e16	0.285934
$400$	−1.05893e17	−1.29263
$401$	1.62668e17	1.95372	0.976860	−	0.213878i	$-0.0686096\pi$
$401$	1.62668e17	1.95372	0.976860	+	0.213878i	$0.0686096\pi$
$402$	−3.16136e16	−0.373598
$403$	6.61044e16	0.768683
$404$	2.11853e16	0.242412
$405$	1.57766e16	0.177646
$406$	−7.23567e16	−0.801788
$407$	−8.15505e15	−0.0889330
$408$	−4.55793e15	−0.0489189
$409$	5.15674e16	0.544720	0.272360	−	0.962195i	$-0.412196\pi$
$409$	5.15674e16	0.544720	0.272360	+	0.962195i	$0.412196\pi$
$410$	−3.29962e16	−0.343059
$411$	−9.49445e16	−0.971624
$412$	6.47276e15	0.0652015
$413$	2.17385e16	0.215554
$414$	−2.54933e16	−0.248842
$415$	4.88972e16	0.469863
$416$	1.65815e16	0.156862
$417$	7.42576e16	0.691603
$418$	1.90833e16	0.174988
$419$	−1.02469e17	−0.925130	−0.462565	−	0.886585i	$-0.653071\pi$
$419$	−1.02469e17	−0.925130	−0.462565	+	0.886585i	$0.653071\pi$
$420$	2.53746e16	0.225569
$421$	−1.46859e17	−1.28549	−0.642744	−	0.766081i	$-0.722204\pi$
$421$	−1.46859e17	−1.28549	−0.642744	+	0.766081i	$0.722204\pi$
$422$	−6.68826e16	−0.576477
$423$	1.78108e16	0.151172
$424$	8.18989e16	0.684542
$425$	−1.51190e16	−0.124450
$426$	4.67328e16	0.378843
$427$	−5.80111e16	−0.463159
$428$	−1.10546e16	−0.0869275
$429$	−2.53182e16	−0.196092
$430$	−1.96851e17	−1.50173
$431$	−1.02127e17	−0.767430	−0.383715	−	0.923452i	$-0.625355\pi$
$431$	−1.02127e17	−0.767430	−0.383715	+	0.923452i	$0.625355\pi$
$432$	−2.15957e16	−0.159854
$433$	5.61120e16	0.409152	0.204576	−	0.978851i	$-0.434418\pi$
$433$	5.61120e16	0.409152	0.204576	+	0.978851i	$0.434418\pi$
$434$	−3.05178e17	−2.19215
$435$	−6.84184e16	−0.484164
$436$	−2.79124e16	−0.194596
$437$	−3.52124e16	−0.241861
$438$	3.78804e16	0.256350
$439$	1.76400e17	1.17620	0.588098	−	0.808790i	$-0.299877\pi$
$439$	1.76400e17	1.17620	0.588098	+	0.808790i	$0.299877\pi$
$440$	1.63377e17	1.07337
$441$	8.96628e16	0.580445
$442$	−6.20408e15	−0.0395761
$443$	−6.99154e15	−0.0439489	−0.0219745	−	0.999759i	$-0.506995\pi$
$443$	−6.99154e15	−0.0439489	−0.0219745	+	0.999759i	$0.506995\pi$
$444$	1.93069e15	0.0119598
$445$	2.56691e17	1.56700
$446$	8.37217e16	0.503688
$447$	4.23795e16	0.251279
$448$	−3.11889e17	−1.82261
$449$	−2.01295e16	−0.115939	−0.0579697	−	0.998318i	$-0.518463\pi$
$449$	−2.01295e16	−0.115939	−0.0579697	+	0.998318i	$0.518463\pi$
$450$	−8.43634e16	−0.478931
$451$	2.63167e16	0.147260
$452$	2.16143e16	0.119218
$453$	6.61881e15	0.0359867
$454$	2.94508e17	1.57846
$455$	2.68557e17	1.41893
$456$	−3.51291e16	−0.182977
$457$	1.52901e17	0.785156	0.392578	−	0.919719i	$-0.371583\pi$
$457$	1.52901e17	0.785156	0.392578	+	0.919719i	$0.371583\pi$
$458$	−5.51205e16	−0.279053
$459$	−3.08338e15	−0.0153902
$460$	−3.87709e16	−0.190801
$461$	9.80386e16	0.475709	0.237854	−	0.971301i	$-0.423556\pi$
$461$	9.80386e16	0.475709	0.237854	+	0.971301i	$0.423556\pi$
$462$	1.16884e17	0.559221
$463$	3.94572e17	1.86144	0.930722	−	0.365726i	$-0.119179\pi$
$463$	3.94572e17	1.86144	0.930722	+	0.365726i	$0.119179\pi$
$464$	9.36541e16	0.435672
$465$	−2.88567e17	−1.32374
$466$	−3.59391e17	−1.62577
$467$	−1.44630e17	−0.645205	−0.322602	−	0.946535i	$-0.604558\pi$
$467$	−1.44630e17	−0.645205	−0.322602	+	0.946535i	$0.604558\pi$
$468$	5.99403e15	0.0263707
$469$	−2.67452e17	−1.16044
$470$	−1.56441e17	−0.669446
$471$	−6.60742e16	−0.278866
$472$	−3.31366e16	−0.137938
$473$	1.57002e17	0.644628
$474$	−1.27652e17	−0.516975
$475$	−1.16526e17	−0.465495
$476$	−4.95921e15	−0.0195419
$477$	5.54035e16	0.215361
$478$	−1.62057e17	−0.621423
$479$	5.08752e17	1.92453	0.962267	−	0.272108i	$-0.0877208\pi$
$479$	5.08752e17	1.92453	0.962267	+	0.272108i	$0.0877208\pi$
$480$	−7.23839e16	−0.270131
$481$	2.04338e16	0.0752326
$482$	−1.15435e17	−0.419305
$483$	−2.15674e17	−0.772933
$484$	2.49818e16	0.0883342
$485$	−2.27375e17	−0.793272
$486$	−1.72051e16	−0.0592272
$487$	4.72252e17	1.60412	0.802058	−	0.597246i	$-0.203739\pi$
$487$	4.72252e17	1.60412	0.802058	+	0.597246i	$0.203739\pi$
$488$	8.84278e16	0.296387
$489$	−2.91685e16	−0.0964730
$490$	−7.87553e17	−2.57043
$491$	5.42778e16	0.174821	0.0874103	−	0.996172i	$-0.472141\pi$
$491$	5.42778e16	0.174821	0.0874103	+	0.996172i	$0.472141\pi$
$492$	−6.23043e15	−0.0198036
$493$	1.33717e16	0.0419451
$494$	−4.78164e16	−0.148031
$495$	1.10522e17	0.337689
$496$	3.95004e17	1.19116
$497$	3.95361e17	1.17673
$498$	−5.33245e16	−0.156652
$499$	6.89495e16	0.199930	0.0999649	−	0.994991i	$-0.468127\pi$
$499$	6.89495e16	0.199930	0.0999649	+	0.994991i	$0.468127\pi$
$500$	−4.58572e16	−0.131251
$501$	7.49709e16	0.211811
$502$	−1.31020e17	−0.365396
$503$	−2.89523e17	−0.797059	−0.398530	−	0.917155i	$-0.630479\pi$
$503$	−2.89523e17	−0.797059	−0.398530	+	0.917155i	$0.630479\pi$
$504$	−2.15164e17	−0.584751
$505$	−9.78785e17	−2.62599
$506$	−1.78592e17	−0.473025
$507$	−1.57357e17	−0.411466
$508$	7.49243e16	0.193423
$509$	−2.58627e17	−0.659188	−0.329594	−	0.944123i	$-0.606912\pi$
$509$	−2.58627e17	−0.659188	−0.329594	+	0.944123i	$0.606912\pi$
$510$	2.70829e16	0.0681536
$511$	3.20469e17	0.796252
$512$	4.57815e17	1.12314
$513$	−2.37644e16	−0.0575656
$514$	1.52275e17	0.364224
$515$	−2.99050e17	−0.706311
$516$	−3.71700e16	−0.0866900
$517$	1.24773e17	0.287364
$518$	−9.43349e16	−0.214550
$519$	1.18723e17	0.266654
$520$	−4.09368e17	−0.908013
$521$	−6.53363e17	−1.43123	−0.715615	−	0.698495i	$-0.753854\pi$
$521$	−6.53363e17	−1.43123	−0.715615	+	0.698495i	$0.753854\pi$
$522$	7.46132e16	0.161420
$523$	7.08667e17	1.51419	0.757097	−	0.653303i	$-0.226617\pi$
$523$	7.08667e17	1.51419	0.757097	+	0.653303i	$0.226617\pi$
$524$	−4.47578e16	−0.0944528
$525$	−7.13717e17	−1.48761
$526$	−8.19009e17	−1.68609
$527$	5.63976e16	0.114681
$528$	−1.51288e17	−0.303867
$529$	−1.74499e17	−0.346204
$530$	−4.86637e17	−0.953700
$531$	−2.24165e16	−0.0433963
$532$	−3.82219e16	−0.0730948
$533$	−6.59409e16	−0.124574
$534$	−2.79932e17	−0.522438
$535$	5.10735e17	0.941664
$536$	4.07684e17	0.742595
$537$	−2.03142e17	−0.365566
$538$	−9.03885e17	−1.60705
$539$	6.28129e17	1.10337
$540$	−2.61659e16	−0.0454126
$541$	−8.19026e17	−1.40448	−0.702240	−	0.711940i	$-0.747817\pi$
$541$	−8.19026e17	−1.40448	−0.702240	+	0.711940i	$0.747817\pi$
$542$	5.35008e16	0.0906495
$543$	2.65926e17	0.445207
$544$	1.41467e16	0.0234025
$545$	1.28959e18	2.10802
$546$	−2.92873e17	−0.473072
$547$	−2.29479e17	−0.366290	−0.183145	−	0.983086i	$-0.558628\pi$
$547$	−2.29479e17	−0.366290	−0.183145	+	0.983086i	$0.558628\pi$
$548$	1.57468e17	0.248381
$549$	5.98202e16	0.0932454
$550$	−5.91004e17	−0.910401
$551$	1.03059e17	0.156892
$552$	3.28758e17	0.494620
$553$	−1.07994e18	−1.60578
$554$	−3.44322e17	−0.506001
$555$	−8.92003e16	−0.129557
$556$	−1.23158e17	−0.176798
$557$	4.44343e17	0.630463	0.315231	−	0.949015i	$-0.397918\pi$
$557$	4.44343e17	0.630463	0.315231	+	0.949015i	$0.397918\pi$
$558$	3.14695e17	0.441334
$559$	−3.93395e17	−0.545321
$560$	1.60475e18	2.19880
$561$	−2.16005e16	−0.0292553
$562$	−6.42620e17	−0.860336
$563$	5.88678e17	0.779064	0.389532	−	0.921013i	$-0.372637\pi$
$563$	5.88678e17	0.779064	0.389532	+	0.921013i	$0.372637\pi$
$564$	−2.95397e16	−0.0386449
$565$	−9.98610e17	−1.29146
$566$	−1.00585e18	−1.28596
$567$	−1.45555e17	−0.183966
$568$	−6.02658e17	−0.753021
$569$	−3.38634e17	−0.418312	−0.209156	−	0.977882i	$-0.567072\pi$
$569$	−3.38634e17	−0.418312	−0.209156	+	0.977882i	$0.567072\pi$
$570$	2.08734e17	0.254922
$571$	−1.82851e16	−0.0220781	−0.0110391	−	0.999939i	$-0.503514\pi$
$571$	−1.82851e16	−0.0220781	−0.0110391	+	0.999939i	$0.503514\pi$
$572$	4.19909e16	0.0501281
$573$	9.68798e17	1.14348
$574$	3.04423e17	0.355264
$575$	1.09052e18	1.25832
$576$	3.21616e17	0.366937
$577$	−3.76678e17	−0.424940	−0.212470	−	0.977168i	$-0.568151\pi$
$577$	−3.76678e17	−0.424940	−0.212470	+	0.977168i	$0.568151\pi$
$578$	8.22373e17	0.917356
$579$	5.76111e17	0.635470
$580$	1.13474e17	0.123769
$581$	−4.51127e17	−0.486579
$582$	2.47963e17	0.264476
$583$	3.88127e17	0.409381
$584$	−4.88499e17	−0.509543
$585$	−2.76932e17	−0.285667
$586$	1.02237e18	1.04298
$587$	7.60927e17	0.767707	0.383853	−	0.923394i	$-0.374597\pi$
$587$	7.60927e17	0.767707	0.383853	+	0.923394i	$0.374597\pi$
$588$	−1.48708e17	−0.148382
$589$	4.34670e17	0.428954
$590$	1.96895e17	0.192175
$591$	1.12859e18	1.08948
$592$	1.22101e17	0.116581
$593$	3.34908e17	0.316279	0.158139	−	0.987417i	$-0.449451\pi$
$593$	3.34908e17	0.316279	0.158139	+	0.987417i	$0.449451\pi$
$594$	−1.20529e17	−0.112585
$595$	2.29122e17	0.211693
$596$	−7.02875e16	−0.0642359
$597$	4.44841e17	0.402135
$598$	4.47492e17	0.400154
$599$	−3.26843e17	−0.289111	−0.144555	−	0.989497i	$-0.546175\pi$
$599$	−3.26843e17	−0.289111	−0.144555	+	0.989497i	$0.546175\pi$
$600$	1.08794e18	0.951964
$601$	1.60372e17	0.138818	0.0694089	−	0.997588i	$-0.477889\pi$
$601$	1.60372e17	0.138818	0.0694089	+	0.997588i	$0.477889\pi$
$602$	1.81615e18	1.55516
$603$	2.75792e17	0.233625
$604$	−1.09775e16	−0.00919945
$605$	−1.15419e18	−0.956903
$606$	1.06741e18	0.875504
$607$	1.52099e18	1.23424	0.617120	−	0.786869i	$-0.288299\pi$
$607$	1.52099e18	1.23424	0.617120	+	0.786869i	$0.288299\pi$
$608$	1.09032e17	0.0875348
$609$	6.31230e17	0.501389
$610$	−5.25431e17	−0.412925
$611$	−3.12639e17	−0.243095
$612$	5.11387e15	0.00393428
$613$	1.84862e18	1.40720	0.703598	−	0.710598i	$-0.251576\pi$
$613$	1.84862e18	1.40720	0.703598	+	0.710598i	$0.251576\pi$
$614$	−1.43331e18	−1.07955
$615$	2.87854e17	0.214528
$616$	−1.50732e18	−1.11156
$617$	7.09719e17	0.517885	0.258942	−	0.965893i	$-0.416626\pi$
$617$	7.09719e17	0.517885	0.258942	+	0.965893i	$0.416626\pi$
$618$	3.26126e17	0.235484
$619$	1.82133e18	1.30137	0.650683	−	0.759350i	$-0.274483\pi$
$619$	1.82133e18	1.30137	0.650683	+	0.759350i	$0.274483\pi$
$620$	4.78597e17	0.338395
$621$	2.22400e17	0.155611
$622$	−2.94553e17	−0.203951
$623$	−2.36824e18	−1.62275
$624$	3.79077e17	0.257056
$625$	−2.00284e17	−0.134408
$626$	2.77678e17	0.184420
$627$	−1.66480e17	−0.109427
$628$	1.09586e17	0.0712880
$629$	1.74333e16	0.0112241
$630$	1.27849e18	0.814672
$631$	1.05239e18	0.663718	0.331859	−	0.943329i	$-0.392324\pi$
$631$	1.05239e18	0.663718	0.331859	+	0.943329i	$0.392324\pi$
$632$	1.64618e18	1.02758
$633$	5.83474e17	0.360493
$634$	−1.38128e18	−0.844695
$635$	−3.46160e18	−2.09531
$636$	−9.18881e16	−0.0550539
$637$	−1.57388e18	−0.933394
$638$	5.22699e17	0.306844
$639$	−4.07690e17	−0.236905
$640$	−2.01151e18	−1.15705
$641$	−3.43637e18	−1.95669	−0.978346	−	0.206977i	$-0.933637\pi$
$641$	−3.43637e18	−1.95669	−0.978346	+	0.206977i	$0.933637\pi$
$642$	−5.56979e17	−0.313950
$643$	8.38738e17	0.468010	0.234005	−	0.972235i	$-0.424817\pi$
$643$	8.38738e17	0.468010	0.234005	+	0.972235i	$0.424817\pi$
$644$	3.57701e17	0.197589
$645$	1.71730e18	0.939092
$646$	−4.07950e16	−0.0220849
$647$	−1.25796e18	−0.674202	−0.337101	−	0.941469i	$-0.609446\pi$
$647$	−1.25796e18	−0.674202	−0.337101	+	0.941469i	$0.609446\pi$
$648$	2.21874e17	0.117725
$649$	−1.57038e17	−0.0824922
$650$	1.48086e18	0.770151
$651$	2.66233e18	1.37084
$652$	4.83767e16	0.0246619
$653$	−2.84285e18	−1.43489	−0.717444	−	0.696616i	$-0.754688\pi$
$653$	−2.84285e18	−1.43489	−0.717444	+	0.696616i	$0.754688\pi$
$654$	−1.40635e18	−0.702811
$655$	2.06787e18	1.02318
$656$	−3.94027e17	−0.193042
$657$	−3.30463e17	−0.160305
$658$	1.44333e18	0.693263
$659$	−3.56178e18	−1.69399	−0.846997	−	0.531598i	$-0.821592\pi$
$659$	−3.56178e18	−1.69399	−0.846997	+	0.531598i	$0.821592\pi$
$660$	−1.83304e17	−0.0863251
$661$	2.84891e18	1.32852	0.664262	−	0.747500i	$-0.268746\pi$
$661$	2.84891e18	1.32852	0.664262	+	0.747500i	$0.268746\pi$
$662$	1.15854e18	0.534975
$663$	5.41235e16	0.0247485
$664$	6.87664e17	0.311375
$665$	1.76590e18	0.791818
$666$	9.72768e16	0.0431943
$667$	−9.64481e17	−0.424107
$668$	−1.24341e17	−0.0541462
$669$	−7.30376e17	−0.314975
$670$	−2.42242e18	−1.03458
$671$	4.19068e17	0.177251
$672$	6.67815e17	0.279741
$673$	2.02250e18	0.839056	0.419528	−	0.907742i	$-0.362196\pi$
$673$	2.02250e18	0.839056	0.419528	+	0.907742i	$0.362196\pi$
$674$	−4.61698e17	−0.189700
$675$	7.35974e17	0.299494
$676$	2.60981e17	0.105185
$677$	−3.87383e18	−1.54637	−0.773185	−	0.634180i	$-0.781338\pi$
$677$	−3.87383e18	−1.54637	−0.773185	+	0.634180i	$0.781338\pi$
$678$	1.08903e18	0.430572
$679$	2.09777e18	0.821494
$680$	−3.49256e17	−0.135468
$681$	−2.56924e18	−0.987072
$682$	2.20458e18	0.838935
$683$	−1.03330e18	−0.389485	−0.194742	−	0.980854i	$-0.562387\pi$
$683$	−1.03330e18	−0.389485	−0.194742	+	0.980854i	$0.562387\pi$
$684$	3.94138e16	0.0147158
$685$	−7.27522e18	−2.69065
$686$	3.09334e18	1.13324
$687$	4.80863e17	0.174503
$688$	−2.35072e18	−0.845036
$689$	−9.72515e17	−0.346315
$690$	−1.95345e18	−0.689102
$691$	3.95212e18	1.38109	0.690546	−	0.723288i	$-0.257370\pi$
$691$	3.95212e18	1.38109	0.690546	+	0.723288i	$0.257370\pi$
$692$	−1.96906e17	−0.0681662
$693$	−1.01968e18	−0.349703
$694$	−3.60816e17	−0.122588
$695$	5.69007e18	1.91521
$696$	−9.62199e17	−0.320852
$697$	−5.62581e16	−0.0185854
$698$	−2.61542e18	−0.856014
$699$	3.13527e18	1.01666
$700$	1.18372e18	0.380287
$701$	5.62189e18	1.78943	0.894716	−	0.446635i	$-0.147378\pi$
$701$	5.62189e18	1.78943	0.894716	+	0.446635i	$0.147378\pi$
$702$	3.02006e17	0.0952411
$703$	1.34363e17	0.0419826
$704$	2.25306e18	0.697512
$705$	1.36477e18	0.418631
$706$	3.56695e18	1.08409
$707$	9.03030e18	2.71942
$708$	3.71783e16	0.0110936
$709$	−1.41248e18	−0.417619	−0.208810	−	0.977956i	$-0.566959\pi$
$709$	−1.41248e18	−0.417619	−0.208810	+	0.977956i	$0.566959\pi$
$710$	3.58095e18	1.04910
$711$	1.11362e18	0.323285
$712$	3.60996e18	1.03844
$713$	−4.06788e18	−1.15954
$714$	−2.49867e17	−0.0705783
$715$	−1.94003e18	−0.543025
$716$	3.36916e17	0.0934516
$717$	1.41377e18	0.388600
$718$	−2.01107e18	−0.547796
$719$	2.38512e16	0.00643833	0.00321917	−	0.999995i	$-0.498975\pi$
$719$	2.38512e16	0.00643833	0.00321917	+	0.999995i	$0.498975\pi$
$720$	−1.65479e18	−0.442673
$721$	2.75904e18	0.731440
$722$	3.19970e18	0.840653
$723$	1.00703e18	0.262208
$724$	−4.41046e17	−0.113811
$725$	−3.19169e18	−0.816252
$726$	1.25869e18	0.319031
$727$	7.36669e18	1.85054	0.925271	−	0.379307i	$-0.123838\pi$
$727$	7.36669e18	1.85054	0.925271	+	0.379307i	$0.123838\pi$
$728$	3.77684e18	0.940318
$729$	1.50095e17	0.0370370
$730$	2.90262e18	0.709892
$731$	−3.35629e17	−0.0813573
$732$	−9.92133e16	−0.0238368
$733$	4.19615e18	0.999252	0.499626	−	0.866241i	$-0.333471\pi$
$733$	4.19615e18	0.999252	0.499626	+	0.866241i	$0.333471\pi$
$734$	2.26457e18	0.534517
$735$	6.87050e18	1.60739
$736$	−1.02038e18	−0.236623
$737$	1.93205e18	0.444099
$738$	−3.13917e17	−0.0715234
$739$	2.45421e17	0.0554271	0.0277135	−	0.999616i	$-0.491177\pi$
$739$	2.45421e17	0.0554271	0.0277135	+	0.999616i	$0.491177\pi$
$740$	1.47941e17	0.0331194
$741$	4.17143e17	0.0925693
$742$	4.48972e18	0.987630
$743$	2.08967e18	0.455671	0.227835	−	0.973700i	$-0.426835\pi$
$743$	2.08967e18	0.455671	0.227835	+	0.973700i	$0.426835\pi$
$744$	−4.05826e18	−0.877234
$745$	3.24737e18	0.695851
$746$	−7.09547e18	−1.50723
$747$	4.65195e17	0.0979606
$748$	3.58250e16	0.00747869
$749$	−4.71206e18	−0.975166
$750$	−2.31049e18	−0.474030
$751$	8.21538e17	0.167097	0.0835484	−	0.996504i	$-0.473375\pi$
$751$	8.21538e17	0.167097	0.0835484	+	0.996504i	$0.473375\pi$
$752$	−1.86816e18	−0.376703
$753$	1.14300e18	0.228496
$754$	−1.30971e18	−0.259574
$755$	5.07173e17	0.0996554
$756$	2.41408e17	0.0470283
$757$	−4.94446e18	−0.954983	−0.477492	−	0.878636i	$-0.658454\pi$
$757$	−4.94446e18	−0.954983	−0.477492	+	0.878636i	$0.658454\pi$
$758$	−7.32156e18	−1.40202
$759$	1.55801e18	0.295801
$760$	−2.69180e18	−0.506705
$761$	9.65676e18	1.80232	0.901158	−	0.433490i	$-0.142718\pi$
$761$	9.65676e18	1.80232	0.901158	+	0.433490i	$0.142718\pi$
$762$	3.77502e18	0.698573
$763$	−1.18978e19	−2.18301
$764$	−1.60678e18	−0.292313
$765$	−2.36267e17	−0.0426191
$766$	2.79681e18	0.500238
$767$	3.93483e17	0.0697841
$768$	−1.42046e18	−0.249793
$769$	−1.12349e19	−1.95907	−0.979535	−	0.201275i	$-0.935492\pi$
$769$	−1.12349e19	−1.95907	−0.979535	+	0.201275i	$0.935492\pi$
$770$	8.95639e18	1.54861
$771$	−1.32843e18	−0.227764
$772$	−9.55495e17	−0.162449
$773$	5.07788e18	0.856083	0.428041	−	0.903759i	$-0.359204\pi$
$773$	5.07788e18	0.856083	0.428041	+	0.903759i	$0.359204\pi$
$774$	−1.87279e18	−0.313092
$775$	−1.34616e19	−2.23170
$776$	−3.19769e18	−0.525696
$777$	8.22964e17	0.134167
$778$	1.92216e18	0.310758
$779$	−4.33595e17	−0.0695170
$780$	4.59299e17	0.0730265
$781$	−2.85606e18	−0.450334
$782$	3.81782e17	0.0596996
$783$	−6.50915e17	−0.100942
$784$	−9.40465e18	−1.44640
$785$	−5.06300e18	−0.772245
$786$	−2.25510e18	−0.341129
$787$	−3.40847e17	−0.0511356	−0.0255678	−	0.999673i	$-0.508139\pi$
$787$	−3.40847e17	−0.0511356	−0.0255678	+	0.999673i	$0.508139\pi$
$788$	−1.87180e18	−0.278509
$789$	7.14492e18	1.05438
$790$	−9.78149e18	−1.43162
$791$	9.21320e18	1.33741
$792$	1.55433e18	0.223784
$793$	−1.05004e18	−0.149945
$794$	4.79748e18	0.679486
$795$	4.24535e18	0.596385
$796$	−7.37780e17	−0.102800
$797$	1.25420e18	0.173336	0.0866678	−	0.996237i	$-0.472378\pi$
$797$	1.25420e18	0.173336	0.0866678	+	0.996237i	$0.472378\pi$
$798$	−1.92579e18	−0.263991
$799$	−2.66731e17	−0.0362677
$800$	−3.37668e18	−0.455413
$801$	2.44209e18	0.326701
$802$	−1.35931e19	−1.80379
$803$	−2.31505e18	−0.304725
$804$	−4.57409e17	−0.0597228
$805$	−1.65263e19	−2.14043
$806$	−5.52394e18	−0.709694
$807$	7.88537e18	1.00495
$808$	−1.37651e19	−1.74023
$809$	−8.23011e18	−1.03214	−0.516072	−	0.856545i	$-0.672606\pi$
$809$	−8.23011e18	−1.03214	−0.516072	+	0.856545i	$0.672606\pi$
$810$	−1.31836e18	−0.164014
$811$	−1.24128e19	−1.53191	−0.765957	−	0.642892i	$-0.777734\pi$
$811$	−1.24128e19	−1.53191	−0.765957	+	0.642892i	$0.777734\pi$
$812$	−1.04691e18	−0.128173
$813$	−4.66734e17	−0.0566866
$814$	6.81468e17	0.0821083
$815$	−2.23506e18	−0.267156
$816$	3.23413e17	0.0383505
$817$	−2.58677e18	−0.304309
$818$	−4.30917e18	−0.502918
$819$	2.55498e18	0.295830
$820$	−4.77413e17	−0.0548409
$821$	8.33949e18	0.950406	0.475203	−	0.879876i	$-0.342375\pi$
$821$	8.33949e18	0.950406	0.475203	+	0.879876i	$0.342375\pi$
$822$	7.93394e18	0.897061
$823$	−4.95643e18	−0.555994	−0.277997	−	0.960582i	$-0.589671\pi$
$823$	−4.95643e18	−0.555994	−0.277997	+	0.960582i	$0.589671\pi$
$824$	−4.20567e18	−0.468068
$825$	5.15583e18	0.569309
$826$	−1.81656e18	−0.199012
$827$	−5.45088e18	−0.592489	−0.296245	−	0.955112i	$-0.595734\pi$
$827$	−5.45088e18	−0.592489	−0.296245	+	0.955112i	$0.595734\pi$
$828$	−3.68856e17	−0.0397796
$829$	9.31288e18	0.996506	0.498253	−	0.867032i	$-0.333975\pi$
$829$	9.31288e18	0.996506	0.498253	+	0.867032i	$0.333975\pi$
$830$	−4.08604e18	−0.433806
$831$	3.00382e18	0.316422
$832$	−5.64542e18	−0.590058
$833$	−1.34277e18	−0.139254
$834$	−6.20526e18	−0.638529
$835$	5.74472e18	0.586553
$836$	2.76112e17	0.0279733
$837$	−2.74536e18	−0.275984
$838$	8.56274e18	0.854136
$839$	1.64140e19	1.62466	0.812331	−	0.583197i	$-0.198198\pi$
$839$	1.64140e19	1.62466	0.812331	+	0.583197i	$0.198198\pi$
$840$	−1.64872e19	−1.61931
$841$	−7.43781e18	−0.724888
$842$	1.22722e19	1.18684
$843$	5.60613e18	0.538002
$844$	−9.67707e17	−0.0921548
$845$	−1.20576e19	−1.13945
$846$	−1.48834e18	−0.139571
$847$	1.06486e19	0.990947
$848$	−5.81122e18	−0.536654
$849$	8.77490e18	0.804160
$850$	1.26341e18	0.114900
$851$	−1.25744e18	−0.113487
$852$	6.76165e17	0.0605613
$853$	−1.68479e19	−1.49753	−0.748767	−	0.662833i	$-0.769354\pi$
$853$	−1.68479e19	−1.49753	−0.748767	+	0.662833i	$0.769354\pi$
$854$	4.84764e18	0.427616
$855$	−1.82097e18	−0.159413
$856$	7.18270e18	0.624034
$857$	−1.30913e19	−1.12877	−0.564385	−	0.825511i	$-0.690887\pi$
$857$	−1.30913e19	−1.12877	−0.564385	+	0.825511i	$0.690887\pi$
$858$	2.11569e18	0.181044
$859$	−1.79226e19	−1.52211	−0.761053	−	0.648689i	$-0.775317\pi$
$859$	−1.79226e19	−1.52211	−0.761053	+	0.648689i	$0.775317\pi$
$860$	−2.84819e18	−0.240065
$861$	−2.65575e18	−0.222160
$862$	8.53414e18	0.708537
$863$	7.68168e18	0.632974	0.316487	−	0.948597i	$-0.397497\pi$
$863$	7.68168e18	0.632974	0.316487	+	0.948597i	$0.397497\pi$
$864$	−6.88641e17	−0.0563188
$865$	9.09730e18	0.738427
$866$	−4.68894e18	−0.377754
$867$	−7.17426e18	−0.573658
$868$	−4.41555e18	−0.350434
$869$	7.80142e18	0.614533
$870$	5.71731e18	0.447009
$871$	−4.84107e18	−0.375684
$872$	1.81361e19	1.39697
$873$	−2.16319e18	−0.165387
$874$	2.94249e18	0.223301
$875$	−1.95468e19	−1.47239
$876$	5.48082e17	0.0409797
$877$	1.62154e19	1.20346	0.601730	−	0.798700i	$-0.294478\pi$
$877$	1.62154e19	1.20346	0.601730	+	0.798700i	$0.294478\pi$
$878$	−1.47407e19	−1.08593
$879$	−8.91905e18	−0.652215
$880$	−1.15926e19	−0.841479
$881$	5.88155e18	0.423788	0.211894	−	0.977293i	$-0.432037\pi$
$881$	5.88155e18	0.423788	0.211894	+	0.977293i	$0.432037\pi$
$882$	−7.49258e18	−0.535902
$883$	−2.33752e19	−1.65963	−0.829815	−	0.558038i	$-0.811554\pi$
$883$	−2.33752e19	−1.65963	−0.829815	+	0.558038i	$0.811554\pi$
$884$	−8.97653e16	−0.00632658
$885$	−1.71768e18	−0.120174
$886$	5.84240e17	0.0405763
$887$	1.34784e19	0.929255	0.464628	−	0.885506i	$-0.346188\pi$
$887$	1.34784e19	0.929255	0.464628	+	0.885506i	$0.346188\pi$
$888$	−1.25447e18	−0.0858567
$889$	3.19368e19	2.16985
$890$	−2.14501e19	−1.44675
$891$	1.05148e18	0.0704039
$892$	1.21135e18	0.0805188
$893$	−2.05576e18	−0.135656
$894$	−3.54140e18	−0.231996
$895$	−1.55659e19	−1.01234
$896$	1.85583e19	1.19822
$897$	−3.90386e18	−0.250232
$898$	1.68210e18	0.107042
$899$	1.19058e19	0.752176
$900$	−1.22063e18	−0.0765612
$901$	−8.29710e17	−0.0516673
$902$	−2.19913e18	−0.135959
$903$	−1.58438e19	−0.972502
$904$	−1.40439e19	−0.855841
$905$	2.03769e19	1.23288
$906$	−5.53094e17	−0.0332250
$907$	−1.01366e19	−0.604569	−0.302285	−	0.953218i	$-0.597749\pi$
$907$	−1.01366e19	−0.604569	−0.302285	+	0.953218i	$0.597749\pi$
$908$	4.26116e18	0.252330
$909$	−9.31191e18	−0.547487
$910$	−2.24417e19	−1.31004
$911$	1.21184e19	0.702385	0.351193	−	0.936303i	$-0.385776\pi$
$911$	1.21184e19	0.702385	0.351193	+	0.936303i	$0.385776\pi$
$912$	2.49262e18	0.143447
$913$	3.25890e18	0.186214
$914$	−1.27770e19	−0.724903
$915$	4.58378e18	0.258218
$916$	−7.97524e17	−0.0446091
$917$	−1.90782e19	−1.05959
$918$	2.57659e17	0.0142092
$919$	−3.21337e19	−1.75958	−0.879792	−	0.475360i	$-0.842318\pi$
$919$	−3.21337e19	−1.75958	−0.879792	+	0.475360i	$0.842318\pi$
$920$	2.51914e19	1.36972
$921$	1.25039e19	0.675087
$922$	−8.19249e18	−0.439203
$923$	7.15631e18	0.380959
$924$	1.69117e18	0.0893963
$925$	−4.16116e18	−0.218421
$926$	−3.29720e19	−1.71860
$927$	−2.84508e18	−0.147257
$928$	2.98643e18	0.153494
$929$	−2.06077e19	−1.05179	−0.525894	−	0.850550i	$-0.676269\pi$
$929$	−2.06077e19	−1.05179	−0.525894	+	0.850550i	$0.676269\pi$
$930$	2.41138e19	1.22216
$931$	−1.03491e19	−0.520868
$932$	−5.19993e18	−0.259893
$933$	2.56963e18	0.127538
$934$	1.20858e19	0.595692
$935$	−1.65516e18	−0.0810148
$936$	−3.89462e18	−0.189309
$937$	−4.34044e18	−0.209521	−0.104760	−	0.994498i	$-0.533408\pi$
$937$	−4.34044e18	−0.209521	−0.104760	+	0.994498i	$0.533408\pi$
$938$	2.23493e19	1.07139
$939$	−2.42242e18	−0.115325
$940$	−2.26351e18	−0.107017
$941$	1.54600e19	0.725902	0.362951	−	0.931808i	$-0.381769\pi$
$941$	1.54600e19	0.725902	0.362951	+	0.931808i	$0.381769\pi$
$942$	5.52142e18	0.257466
$943$	4.05782e18	0.187917
$944$	2.35124e18	0.108138
$945$	−1.11533e19	−0.509446
$946$	−1.31197e19	−0.595159
$947$	1.58525e19	0.714204	0.357102	−	0.934065i	$-0.383765\pi$
$947$	1.58525e19	0.714204	0.357102	+	0.934065i	$0.383765\pi$
$948$	−1.84697e18	−0.0826429
$949$	5.80072e18	0.257781
$950$	9.73739e18	0.429773
$951$	1.20500e19	0.528221
$952$	3.22225e18	0.140287
$953$	−3.84094e19	−1.66086	−0.830431	−	0.557122i	$-0.811906\pi$
$953$	−3.84094e19	−1.66086	−0.830431	+	0.557122i	$0.811906\pi$
$954$	−4.62973e18	−0.198834
$955$	7.42351e19	3.16656
$956$	−2.34477e18	−0.0993398
$957$	−4.55996e18	−0.191881
$958$	−4.25133e19	−1.77684
$959$	6.71214e19	2.78638
$960$	2.46441e19	1.01613
$961$	2.57973e19	1.05651
$962$	−1.70753e18	−0.0694592
$963$	4.85900e18	0.196325
$964$	−1.67019e18	−0.0670295
$965$	4.41451e19	1.75976
$966$	1.80226e19	0.713618
$967$	3.32794e19	1.30889	0.654446	−	0.756109i	$-0.272902\pi$
$967$	3.32794e19	1.30889	0.654446	+	0.756109i	$0.272902\pi$
$968$	−1.62319e19	−0.634133
$969$	3.55890e17	0.0138106
$970$	1.90004e19	0.732396
$971$	2.86499e19	1.09698	0.548490	−	0.836157i	$-0.315203\pi$
$971$	2.86499e19	1.09698	0.548490	+	0.836157i	$0.315203\pi$
$972$	−2.48936e17	−0.00946797
$973$	−5.24967e19	−1.98335
$974$	−3.94633e19	−1.48102
$975$	−1.29188e19	−0.481606
$976$	−6.27448e18	−0.232356
$977$	7.48660e18	0.275404	0.137702	−	0.990474i	$-0.456028\pi$
$977$	7.48660e18	0.275404	0.137702	+	0.990474i	$0.456028\pi$
$978$	2.43743e18	0.0890697
$979$	1.71080e19	0.621027
$980$	−1.13949e19	−0.410905
$981$	1.22688e19	0.439495
$982$	−4.53567e18	−0.161405
$983$	−2.71555e19	−0.959975	−0.479987	−	0.877275i	$-0.659359\pi$
$983$	−2.71555e19	−0.959975	−0.479987	+	0.877275i	$0.659359\pi$
$984$	4.04822e18	0.142166
$985$	8.64797e19	3.01702
$986$	−1.11739e18	−0.0387262
$987$	−1.25914e19	−0.433524
$988$	−6.91843e17	−0.0236640
$989$	2.42084e19	0.822604
$990$	−9.23569e18	−0.311775
$991$	−4.34033e19	−1.45561	−0.727803	−	0.685786i	$-0.759459\pi$
$991$	−4.34033e19	−1.45561	−0.727803	+	0.685786i	$0.759459\pi$
$992$	1.25958e19	0.419663
$993$	−1.01069e19	−0.334540
$994$	−3.30379e19	−1.08643
$995$	3.40864e19	1.11360
$996$	−7.71538e17	−0.0250422
$997$	−5.70975e19	−1.84119	−0.920595	−	0.390519i	$-0.872296\pi$
$997$	−5.70975e19	−1.84119	−0.920595	+	0.390519i	$0.872296\pi$
$998$	−5.76170e18	−0.184587
$999$	−8.48628e17	−0.0270111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-83.5640 q^{2} +729.000 q^{3} -1209.07 q^{4} +55860.4 q^{5} -60918.1 q^{6} -515369. q^{7} +785590. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-83.5640 q^{2} +729.000 q^{3} -1209.07 q^{4} +55860.4 q^{5} -60918.1 q^{6} -515369. q^{7} +785590. q^{8} +531441. q^{9} -4.66791e6 q^{10} +3.72299e6 q^{11} -881409. q^{12} -9.32855e6 q^{13} +4.30663e7 q^{14} +4.07222e7 q^{15} -5.57424e7 q^{16} -7.95874e6 q^{17} -4.44093e7 q^{18} -6.13400e7 q^{19} -6.75389e7 q^{20} -3.75704e8 q^{21} -3.11108e8 q^{22} +5.74053e8 q^{23} +5.72695e8 q^{24} +1.89968e9 q^{25} +7.79530e8 q^{26} +3.87420e8 q^{27} +6.23115e8 q^{28} -1.68012e9 q^{29} -3.40291e9 q^{30} -7.08624e9 q^{31} -1.77750e9 q^{32} +2.71406e9 q^{33} +6.65064e8 q^{34} -2.87887e10 q^{35} -6.42547e8 q^{36} -2.19046e9 q^{37} +5.12581e9 q^{38} -6.80051e9 q^{39} +4.38834e10 q^{40} +7.06872e9 q^{41} +3.13953e10 q^{42} +4.21711e10 q^{43} -4.50134e9 q^{44} +2.96865e10 q^{45} -4.79702e10 q^{46} +3.35142e10 q^{47} -4.06362e10 q^{48} +1.68716e11 q^{49} -1.58745e11 q^{50} -5.80192e9 q^{51} +1.12788e10 q^{52} +1.04251e11 q^{53} -3.23744e10 q^{54} +2.07967e11 q^{55} -4.04869e11 q^{56} -4.47168e10 q^{57} +1.40398e11 q^{58} -4.21805e10 q^{59} -4.92358e10 q^{60} +1.12562e11 q^{61} +5.92155e11 q^{62} -2.73888e11 q^{63} +6.05177e11 q^{64} -5.21096e11 q^{65} -2.26797e11 q^{66} +5.18952e11 q^{67} +9.62264e9 q^{68} +4.18485e11 q^{69} +2.40570e12 q^{70} -7.67141e11 q^{71} +4.17495e11 q^{72} -6.21825e11 q^{73} +1.83043e11 q^{74} +1.38486e12 q^{75} +7.41641e10 q^{76} -1.91871e12 q^{77} +5.68278e11 q^{78} +2.09547e12 q^{79} -3.11379e12 q^{80} +2.82430e11 q^{81} -5.90690e11 q^{82} +8.75347e11 q^{83} +4.54251e11 q^{84} -4.44578e11 q^{85} -3.52398e12 q^{86} -1.22481e12 q^{87} +2.92474e12 q^{88} +4.59522e12 q^{89} -2.48072e12 q^{90} +4.80765e12 q^{91} -6.94068e11 q^{92} -5.16587e12 q^{93} -2.80058e12 q^{94} -3.42647e12 q^{95} -1.29580e12 q^{96} -4.07043e12 q^{97} -1.40986e13 q^{98} +1.97855e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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