LMFDB - Embedded newform 177.14.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q+28.6118 q^{2} +729.000 q^{3} -7373.36 q^{4} +60045.3 q^{5} +20858.0 q^{6} +428045. q^{7} -445354. q^{8} +531441. q^{9} +O(q^{10})$	\(q+28.6118 q^{2} +729.000 q^{3} -7373.36 q^{4} +60045.3 q^{5} +20858.0 q^{6} +428045. q^{7} -445354. q^{8} +531441. q^{9} +1.71801e6 q^{10} -5.05028e6 q^{11} -5.37518e6 q^{12} +8.30885e6 q^{13} +1.22472e7 q^{14} +4.37730e7 q^{15} +4.76602e7 q^{16} -3.21092e7 q^{17} +1.52055e7 q^{18} +9.20230e7 q^{19} -4.42736e8 q^{20} +3.12045e8 q^{21} -1.44498e8 q^{22} +2.82456e8 q^{23} -3.24663e8 q^{24} +2.38473e9 q^{25} +2.37732e8 q^{26} +3.87420e8 q^{27} -3.15613e9 q^{28} -1.86463e9 q^{29} +1.25243e9 q^{30} -1.29741e9 q^{31} +5.01198e9 q^{32} -3.68166e9 q^{33} -9.18703e8 q^{34} +2.57021e10 q^{35} -3.91851e9 q^{36} -5.91028e9 q^{37} +2.63295e9 q^{38} +6.05716e9 q^{39} -2.67414e10 q^{40} +4.67448e10 q^{41} +8.92817e9 q^{42} +5.00850e10 q^{43} +3.72376e10 q^{44} +3.19105e10 q^{45} +8.08158e9 q^{46} +5.50206e10 q^{47} +3.47443e10 q^{48} +8.63335e10 q^{49} +6.82315e10 q^{50} -2.34076e10 q^{51} -6.12642e10 q^{52} -5.12531e10 q^{53} +1.10848e10 q^{54} -3.03246e11 q^{55} -1.90631e11 q^{56} +6.70848e10 q^{57} -5.33504e10 q^{58} -4.21805e10 q^{59} -3.22754e11 q^{60} +4.21271e11 q^{61} -3.71212e10 q^{62} +2.27481e11 q^{63} -2.47031e11 q^{64} +4.98907e11 q^{65} -1.05339e11 q^{66} -6.77755e9 q^{67} +2.36753e11 q^{68} +2.05910e11 q^{69} +7.35384e11 q^{70} +6.84243e11 q^{71} -2.36679e11 q^{72} -1.74954e12 q^{73} -1.69104e11 q^{74} +1.73847e12 q^{75} -6.78519e11 q^{76} -2.16175e12 q^{77} +1.73306e11 q^{78} -4.15612e12 q^{79} +2.86177e12 q^{80} +2.82430e11 q^{81} +1.33745e12 q^{82} +1.01331e12 q^{83} -2.30082e12 q^{84} -1.92801e12 q^{85} +1.43302e12 q^{86} -1.35931e12 q^{87} +2.24916e12 q^{88} -4.21516e12 q^{89} +9.13018e11 q^{90} +3.55656e12 q^{91} -2.08265e12 q^{92} -9.45810e11 q^{93} +1.57424e12 q^{94} +5.52555e12 q^{95} +3.65373e12 q^{96} -3.08119e12 q^{97} +2.47016e12 q^{98} -2.68393e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	28.6118	0.316119	0.158060	−	0.987430i	$-0.449476\pi$
$2$	28.6118	0.316119	0.158060	+	0.987430i	$0.449476\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−7373.36	−0.900069
$5$	60045.3	1.71860	0.859298	−	0.511475i	$-0.170901\pi$
$5$	60045.3	1.71860	0.859298	+	0.511475i	$0.170901\pi$
$6$	20858.0	0.182511
$7$	428045.	1.37516	0.687578	−	0.726110i	$-0.258674\pi$
$7$	428045.	1.37516	0.687578	+	0.726110i	$0.258674\pi$
$8$	−445354.	−0.600648
$9$	531441.	0.333333
$10$	1.71801e6	0.543281
$11$	−5.05028e6	−0.859535	−0.429767	−	0.902940i	$-0.641404\pi$
$11$	−5.05028e6	−0.859535	−0.429767	+	0.902940i	$0.641404\pi$
$12$	−5.37518e6	−0.519655
$13$	8.30885e6	0.477430	0.238715	−	0.971090i	$-0.423274\pi$
$13$	8.30885e6	0.477430	0.238715	+	0.971090i	$0.423274\pi$
$14$	1.22472e7	0.434713
$15$	4.37730e7	0.992232
$16$	4.76602e7	0.710193
$17$	−3.21092e7	−0.322635	−0.161318	−	0.986903i	$-0.551574\pi$
$17$	−3.21092e7	−0.322635	−0.161318	+	0.986903i	$0.551574\pi$
$18$	1.52055e7	0.105373
$19$	9.20230e7	0.448744	0.224372	−	0.974504i	$-0.427967\pi$
$19$	9.20230e7	0.448744	0.224372	+	0.974504i	$0.427967\pi$
$20$	−4.42736e8	−1.54685
$21$	3.12045e8	0.793947
$22$	−1.44498e8	−0.271715
$23$	2.82456e8	0.397851	0.198925	−	0.980015i	$-0.436255\pi$
$23$	2.82456e8	0.397851	0.198925	+	0.980015i	$0.436255\pi$
$24$	−3.24663e8	−0.346784
$25$	2.38473e9	1.95357
$26$	2.37732e8	0.150925
$27$	3.87420e8	0.192450
$28$	−3.15613e9	−1.23774
$29$	−1.86463e9	−0.582110	−0.291055	−	0.956706i	$-0.594006\pi$
$29$	−1.86463e9	−0.582110	−0.291055	+	0.956706i	$0.594006\pi$
$30$	1.25243e9	0.313663
$31$	−1.29741e9	−0.262558	−0.131279	−	0.991345i	$-0.541908\pi$
$31$	−1.29741e9	−0.262558	−0.131279	+	0.991345i	$0.541908\pi$
$32$	5.01198e9	0.825153
$33$	−3.68166e9	−0.496253
$34$	−9.18703e8	−0.101991
$35$	2.57021e10	2.36334
$36$	−3.91851e9	−0.300023
$37$	−5.91028e9	−0.378701	−0.189351	−	0.981910i	$-0.560638\pi$
$37$	−5.91028e9	−0.378701	−0.189351	+	0.981910i	$0.560638\pi$
$38$	2.63295e9	0.141856
$39$	6.05716e9	0.275644
$40$	−2.67414e10	−1.03227
$41$	4.67448e10	1.53687	0.768437	−	0.639926i	$-0.221035\pi$
$41$	4.67448e10	1.53687	0.768437	+	0.639926i	$0.221035\pi$
$42$	8.92817e9	0.250982
$43$	5.00850e10	1.20827	0.604134	−	0.796883i	$-0.293519\pi$
$43$	5.00850e10	1.20827	0.604134	+	0.796883i	$0.293519\pi$
$44$	3.72376e10	0.773640
$45$	3.19105e10	0.572865
$46$	8.08158e9	0.125768
$47$	5.50206e10	0.744542	0.372271	−	0.928124i	$-0.378579\pi$
$47$	5.50206e10	0.744542	0.372271	+	0.928124i	$0.378579\pi$
$48$	3.47443e10	0.410030
$49$	8.63335e10	0.891056
$50$	6.82315e10	0.617561
$51$	−2.34076e10	−0.186273
$52$	−6.12642e10	−0.429720
$53$	−5.12531e10	−0.317634	−0.158817	−	0.987308i	$-0.550768\pi$
$53$	−5.12531e10	−0.317634	−0.158817	+	0.987308i	$0.550768\pi$
$54$	1.10848e10	0.0608371
$55$	−3.03246e11	−1.47719
$56$	−1.90631e11	−0.825985
$57$	6.70848e10	0.259082
$58$	−5.33504e10	−0.184016
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−3.22754e11	−0.893077
$61$	4.21271e11	1.04693	0.523465	−	0.852047i	$-0.324639\pi$
$61$	4.21271e11	1.04693	0.523465	+	0.852047i	$0.324639\pi$
$62$	−3.71212e10	−0.0829996
$63$	2.27481e11	0.458386
$64$	−2.47031e11	−0.449346
$65$	4.98907e11	0.820509
$66$	−1.05339e11	−0.156875
$67$	−6.77755e9	−0.00915348	−0.00457674	−	0.999990i	$-0.501457\pi$
$67$	−6.77755e9	−0.00915348	−0.00457674	+	0.999990i	$0.501457\pi$
$68$	2.36753e11	0.290394
$69$	2.05910e11	0.229699
$70$	7.35384e11	0.747096
$71$	6.84243e11	0.633915	0.316958	−	0.948440i	$-0.397339\pi$
$71$	6.84243e11	0.633915	0.316958	+	0.948440i	$0.397339\pi$
$72$	−2.36679e11	−0.200216
$73$	−1.74954e12	−1.35308	−0.676542	−	0.736404i	$-0.736522\pi$
$73$	−1.74954e12	−1.35308	−0.676542	+	0.736404i	$0.736522\pi$
$74$	−1.69104e11	−0.119715
$75$	1.73847e12	1.12790
$76$	−6.78519e11	−0.403900
$77$	−2.16175e12	−1.18199
$78$	1.73306e11	0.0871364
$79$	−4.15612e12	−1.92359	−0.961794	−	0.273773i	$-0.911728\pi$
$79$	−4.15612e12	−1.92359	−0.961794	+	0.273773i	$0.911728\pi$
$80$	2.86177e12	1.22053
$81$	2.82430e11	0.111111
$82$	1.33745e12	0.485835
$83$	1.01331e12	0.340201	0.170101	−	0.985427i	$-0.445591\pi$
$83$	1.01331e12	0.340201	0.170101	+	0.985427i	$0.445591\pi$
$84$	−2.30082e12	−0.714607
$85$	−1.92801e12	−0.554479
$86$	1.43302e12	0.381956
$87$	−1.35931e12	−0.336081
$88$	2.24916e12	0.516278
$89$	−4.21516e12	−0.899039	−0.449520	−	0.893270i	$-0.648405\pi$
$89$	−4.21516e12	−0.899039	−0.449520	+	0.893270i	$0.648405\pi$
$90$	9.13018e11	0.181094
$91$	3.55656e12	0.656541
$92$	−2.08265e12	−0.358093
$93$	−9.45810e11	−0.151588
$94$	1.57424e12	0.235364
$95$	5.52555e12	0.771209
$96$	3.65373e12	0.476402
$97$	−3.08119e12	−0.375580	−0.187790	−	0.982209i	$-0.560132\pi$
$97$	−3.08119e12	−0.375580	−0.187790	+	0.982209i	$0.560132\pi$
$98$	2.47016e12	0.281680
$99$	−2.68393e12	−0.286512
$100$	−1.75835e13	−1.75835
$101$	3.98600e12	0.373635	0.186818	−	0.982395i	$-0.440183\pi$
$101$	3.98600e12	0.373635	0.186818	+	0.982395i	$0.440183\pi$
$102$	−6.69734e11	−0.0588846
$103$	−6.75982e12	−0.557818	−0.278909	−	0.960317i	$-0.589973\pi$
$103$	−6.75982e12	−0.557818	−0.278909	+	0.960317i	$0.589973\pi$
$104$	−3.70038e12	−0.286767
$105$	1.87368e13	1.36447
$106$	−1.46644e12	−0.100410
$107$	1.94180e13	1.25086	0.625432	−	0.780279i	$-0.284923\pi$
$107$	1.94180e13	1.25086	0.625432	+	0.780279i	$0.284923\pi$
$108$	−2.85659e12	−0.173218
$109$	3.32706e13	1.90015	0.950076	−	0.312018i	$-0.101005\pi$
$109$	3.32706e13	1.90015	0.950076	+	0.312018i	$0.101005\pi$
$110$	−8.67642e12	−0.466969
$111$	−4.30859e12	−0.218643
$112$	2.04007e13	0.976626
$113$	2.33760e13	1.05623	0.528116	−	0.849172i	$-0.322899\pi$
$113$	2.33760e13	1.05623	0.528116	+	0.849172i	$0.322899\pi$
$114$	1.91942e12	0.0819008
$115$	1.69602e13	0.683744
$116$	1.37486e13	0.523939
$117$	4.41567e12	0.159143
$118$	−1.20686e12	−0.0411552
$119$	−1.37442e13	−0.443674
$120$	−1.94945e13	−0.595982
$121$	−9.01734e12	−0.261200
$122$	1.20533e13	0.330955
$123$	3.40769e13	0.887314
$124$	9.56625e12	0.236320
$125$	6.98944e13	1.63881
$126$	6.50864e12	0.144904
$127$	−2.01180e13	−0.425461	−0.212730	−	0.977111i	$-0.568236\pi$
$127$	−2.01180e13	−0.425461	−0.212730	+	0.977111i	$0.568236\pi$
$128$	−4.81261e13	−0.967200
$129$	3.65120e13	0.697593
$130$	1.42747e13	0.259378
$131$	−1.03263e14	−1.78517	−0.892587	−	0.450876i	$-0.851112\pi$
$131$	−1.03263e14	−1.78517	−0.892587	+	0.450876i	$0.851112\pi$
$132$	2.71462e13	0.446661
$133$	3.93900e13	0.617093
$134$	−1.93918e11	−0.00289359
$135$	2.32628e13	0.330744
$136$	1.42999e13	0.193790
$137$	−3.98625e13	−0.515088	−0.257544	−	0.966267i	$-0.582913\pi$
$137$	−3.98625e13	−0.515088	−0.257544	+	0.966267i	$0.582913\pi$
$138$	5.89148e12	0.0726123
$139$	8.28297e13	0.974069	0.487035	−	0.873383i	$-0.338079\pi$
$139$	8.28297e13	0.974069	0.487035	+	0.873383i	$0.338079\pi$
$140$	−1.89511e14	−2.12717
$141$	4.01100e13	0.429862
$142$	1.95774e13	0.200393
$143$	−4.19621e13	−0.410367
$144$	2.53286e13	0.236731
$145$	−1.11962e14	−1.00041
$146$	−5.00575e13	−0.427735
$147$	6.29371e13	0.514451
$148$	4.35786e13	0.340857
$149$	1.89703e14	1.42024	0.710122	−	0.704079i	$-0.248640\pi$
$149$	1.89703e14	1.42024	0.710122	+	0.704079i	$0.248640\pi$
$150$	4.97408e13	0.356549
$151$	4.48388e12	0.0307825	0.0153913	−	0.999882i	$-0.495101\pi$
$151$	4.48388e12	0.0307825	0.0153913	+	0.999882i	$0.495101\pi$
$152$	−4.09828e13	−0.269537
$153$	−1.70641e13	−0.107545
$154$	−6.18516e13	−0.373651
$155$	−7.79032e13	−0.451231
$156$	−4.46616e13	−0.248099
$157$	1.71354e14	0.913159	0.456579	−	0.889683i	$-0.349074\pi$
$157$	1.71354e14	0.913159	0.456579	+	0.889683i	$0.349074\pi$
$158$	−1.18914e14	−0.608083
$159$	−3.73635e13	−0.183386
$160$	3.00946e14	1.41811
$161$	1.20904e14	0.547107
$162$	8.08083e12	0.0351243
$163$	3.63350e14	1.51742	0.758709	−	0.651429i	$-0.225830\pi$
$163$	3.63350e14	1.51742	0.758709	+	0.651429i	$0.225830\pi$
$164$	−3.44666e14	−1.38329
$165$	−2.21066e14	−0.852858
$166$	2.89927e13	0.107544
$167$	−2.08346e14	−0.743240	−0.371620	−	0.928385i	$-0.621197\pi$
$167$	−2.08346e14	−0.743240	−0.371620	+	0.928385i	$0.621197\pi$
$168$	−1.38970e14	−0.476883
$169$	−2.33838e14	−0.772061
$170$	−5.51638e13	−0.175281
$171$	4.89048e13	0.149581
$172$	−3.69295e14	−1.08752
$173$	1.06883e14	0.303115	0.151558	−	0.988448i	$-0.451571\pi$
$173$	1.06883e14	0.303115	0.151558	+	0.988448i	$0.451571\pi$
$174$	−3.88924e13	−0.106242
$175$	1.02077e15	2.68647
$176$	−2.40698e14	−0.610435
$177$	−3.07496e13	−0.0751646
$178$	−1.20603e14	−0.284203
$179$	7.38037e13	0.167700	0.0838501	−	0.996478i	$-0.473278\pi$
$179$	7.38037e13	0.167700	0.0838501	+	0.996478i	$0.473278\pi$
$180$	−2.35288e14	−0.515618
$181$	4.34002e13	0.0917446	0.0458723	−	0.998947i	$-0.485393\pi$
$181$	4.34002e13	0.0917446	0.0458723	+	0.998947i	$0.485393\pi$
$182$	1.01760e14	0.207545
$183$	3.07107e14	0.604445
$184$	−1.25793e14	−0.238968
$185$	−3.54884e14	−0.650834
$186$	−2.70613e13	−0.0479198
$187$	1.62161e14	0.277316
$188$	−4.05687e14	−0.670139
$189$	1.65833e14	0.264649
$190$	1.58096e14	0.243794
$191$	6.53880e14	0.974498	0.487249	−	0.873263i	$-0.338000\pi$
$191$	6.53880e14	0.974498	0.487249	+	0.873263i	$0.338000\pi$
$192$	−1.80085e14	−0.259430
$193$	2.02162e14	0.281564	0.140782	−	0.990041i	$-0.455038\pi$
$193$	2.02162e14	0.281564	0.140782	+	0.990041i	$0.455038\pi$
$194$	−8.81585e13	−0.118728
$195$	3.63704e14	0.473721
$196$	−6.36568e14	−0.802012
$197$	−5.32924e14	−0.649583	−0.324791	−	0.945786i	$-0.605294\pi$
$197$	−5.32924e14	−0.649583	−0.324791	+	0.945786i	$0.605294\pi$
$198$	−7.67921e13	−0.0905718
$199$	−5.68355e14	−0.648746	−0.324373	−	0.945929i	$-0.605153\pi$
$199$	−5.68355e14	−0.648746	−0.324373	+	0.945929i	$0.605153\pi$
$200$	−1.06205e15	−1.17341
$201$	−4.94083e12	−0.00528477
$202$	1.14047e14	0.118113
$203$	−7.98144e14	−0.800492
$204$	1.72593e14	0.167659
$205$	2.80680e15	2.64126
$206$	−1.93411e14	−0.176337
$207$	1.50109e14	0.132617
$208$	3.96002e14	0.339067
$209$	−4.64743e14	−0.385711
$210$	5.36095e14	0.431336
$211$	1.67860e15	1.30952	0.654758	−	0.755839i	$-0.272771\pi$
$211$	1.67860e15	1.30952	0.654758	+	0.755839i	$0.272771\pi$
$212$	3.77908e14	0.285892
$213$	4.98813e14	0.365991
$214$	5.55584e14	0.395422
$215$	3.00737e15	2.07652
$216$	−1.72539e14	−0.115595
$217$	−5.55349e14	−0.361058
$218$	9.51933e14	0.600674
$219$	−1.27541e15	−0.781203
$220$	2.23594e15	1.32958
$221$	−2.66791e14	−0.154036
$222$	−1.23277e14	−0.0691173
$223$	3.31081e15	1.80282	0.901410	−	0.432966i	$-0.142533\pi$
$223$	3.31081e15	1.80282	0.901410	+	0.432966i	$0.142533\pi$
$224$	2.14535e15	1.13472
$225$	1.26734e15	0.651191
$226$	6.68829e14	0.333895
$227$	1.02924e15	0.499287	0.249643	−	0.968338i	$-0.419687\pi$
$227$	1.02924e15	0.499287	0.249643	+	0.968338i	$0.419687\pi$
$228$	−4.94641e14	−0.233192
$229$	9.90704e14	0.453955	0.226978	−	0.973900i	$-0.427116\pi$
$229$	9.90704e14	0.453955	0.226978	+	0.973900i	$0.427116\pi$
$230$	4.85261e14	0.216145
$231$	−1.57592e15	−0.682425
$232$	8.30418e14	0.349643
$233$	1.52144e15	0.622931	0.311466	−	0.950257i	$-0.399180\pi$
$233$	1.52144e15	0.622931	0.311466	+	0.950257i	$0.399180\pi$
$234$	1.26340e14	0.0503082
$235$	3.30373e15	1.27957
$236$	3.11012e14	0.117179
$237$	−3.02981e15	−1.11058
$238$	−3.93246e14	−0.140254
$239$	−1.07681e15	−0.373726	−0.186863	−	0.982386i	$-0.559832\pi$
$239$	−1.07681e15	−0.373726	−0.186863	+	0.982386i	$0.559832\pi$
$240$	2.08623e15	0.704676
$241$	2.34050e15	0.769481	0.384741	−	0.923025i	$-0.374291\pi$
$241$	2.34050e15	0.769481	0.384741	+	0.923025i	$0.374291\pi$
$242$	−2.58002e14	−0.0825703
$243$	2.05891e14	0.0641500
$244$	−3.10618e15	−0.942309
$245$	5.18392e15	1.53137
$246$	9.75004e14	0.280497
$247$	7.64606e14	0.214243
$248$	5.77805e14	0.157705
$249$	7.38705e14	0.196415
$250$	1.99981e15	0.518058
$251$	3.17723e15	0.801992	0.400996	−	0.916080i	$-0.368664\pi$
$251$	3.17723e15	0.801992	0.400996	+	0.916080i	$0.368664\pi$
$252$	−1.67730e15	−0.412579
$253$	−1.42648e15	−0.341966
$254$	−5.75611e14	−0.134496
$255$	−1.40552e15	−0.320129
$256$	6.46697e14	0.143596
$257$	2.52119e15	0.545809	0.272905	−	0.962041i	$-0.412016\pi$
$257$	2.52119e15	0.545809	0.272905	+	0.962041i	$0.412016\pi$
$258$	1.04467e15	0.220523
$259$	−2.52986e15	−0.520773
$260$	−3.67863e15	−0.738514
$261$	−9.90939e14	−0.194037
$262$	−2.95454e15	−0.564327
$263$	−9.14713e14	−0.170440	−0.0852202	−	0.996362i	$-0.527159\pi$
$263$	−9.14713e14	−0.170440	−0.0852202	+	0.996362i	$0.527159\pi$
$264$	1.63964e15	0.298073
$265$	−3.07750e15	−0.545884
$266$	1.12702e15	0.195075
$267$	−3.07285e15	−0.519061
$268$	4.99733e13	0.00823876
$269$	9.66114e15	1.55467	0.777336	−	0.629086i	$-0.216571\pi$
$269$	9.66114e15	1.55467	0.777336	+	0.629086i	$0.216571\pi$
$270$	6.65590e14	0.104554
$271$	−1.13859e16	−1.74610	−0.873048	−	0.487635i	$-0.837860\pi$
$271$	−1.13859e16	−1.74610	−0.873048	+	0.487635i	$0.837860\pi$
$272$	−1.53033e15	−0.229133
$273$	2.59274e15	0.379054
$274$	−1.14054e15	−0.162829
$275$	−1.20436e16	−1.67916
$276$	−1.51825e15	−0.206745
$277$	−1.05903e16	−1.40861	−0.704304	−	0.709899i	$-0.748741\pi$
$277$	−1.05903e16	−1.40861	−0.704304	+	0.709899i	$0.748741\pi$
$278$	2.36991e15	0.307922
$279$	−6.89495e14	−0.0875193
$280$	−1.14465e16	−1.41953
$281$	−9.53225e15	−1.15506	−0.577529	−	0.816370i	$-0.695983\pi$
$281$	−9.53225e15	−1.15506	−0.577529	+	0.816370i	$0.695983\pi$
$282$	1.14762e15	0.135887
$283$	−4.46032e15	−0.516124	−0.258062	−	0.966128i	$-0.583084\pi$
$283$	−4.46032e15	−0.516124	−0.258062	+	0.966128i	$0.583084\pi$
$284$	−5.04517e15	−0.570567
$285$	4.02813e15	0.445258
$286$	−1.20061e15	−0.129725
$287$	2.00089e16	2.11344
$288$	2.66357e15	0.275051
$289$	−8.87358e15	−0.895907
$290$	−3.20344e15	−0.316249
$291$	−2.24619e15	−0.216841
$292$	1.29000e16	1.21787
$293$	1.77460e16	1.63855	0.819277	−	0.573398i	$-0.194375\pi$
$293$	1.77460e16	1.63855	0.819277	+	0.573398i	$0.194375\pi$
$294$	1.80075e15	0.162628
$295$	−2.53274e15	−0.223742
$296$	2.63216e15	0.227466
$297$	−1.95658e15	−0.165418
$298$	5.42774e15	0.448966
$299$	2.34689e15	0.189946
$300$	−1.28184e16	−1.01518
$301$	2.14386e16	1.66156
$302$	1.28292e14	0.00973094
$303$	2.90579e15	0.215718
$304$	4.38584e15	0.318694
$305$	2.52953e16	1.79925
$306$	−4.88236e14	−0.0339970
$307$	1.42327e16	0.970259	0.485129	−	0.874442i	$-0.338772\pi$
$307$	1.42327e16	0.970259	0.485129	+	0.874442i	$0.338772\pi$
$308$	1.59394e16	1.06388
$309$	−4.92791e15	−0.322057
$310$	−2.22895e15	−0.142643
$311$	6.96725e15	0.436636	0.218318	−	0.975878i	$-0.429943\pi$
$311$	6.96725e15	0.436636	0.218318	+	0.975878i	$0.429943\pi$
$312$	−2.69758e15	−0.165565
$313$	−1.86288e16	−1.11981	−0.559907	−	0.828556i	$-0.689163\pi$
$313$	−1.86288e16	−1.11981	−0.559907	+	0.828556i	$0.689163\pi$
$314$	4.90275e15	0.288667
$315$	1.36591e16	0.787780
$316$	3.06446e16	1.73136
$317$	2.34802e15	0.129962	0.0649810	−	0.997887i	$-0.479301\pi$
$317$	2.34802e15	0.129962	0.0649810	+	0.997887i	$0.479301\pi$
$318$	−1.06904e15	−0.0579718
$319$	9.41690e15	0.500344
$320$	−1.48330e16	−0.772244
$321$	1.41557e16	0.722186
$322$	3.45928e15	0.172951
$323$	−2.95479e15	−0.144780
$324$	−2.08246e15	−0.100008
$325$	1.98144e16	0.932693
$326$	1.03961e16	0.479685
$327$	2.42543e16	1.09705
$328$	−2.08180e16	−0.923120
$329$	2.35513e16	1.02386
$330$	−6.32511e15	−0.269605
$331$	−2.75150e16	−1.14997	−0.574986	−	0.818163i	$-0.694992\pi$
$331$	−2.75150e16	−1.14997	−0.574986	+	0.818163i	$0.694992\pi$
$332$	−7.47152e15	−0.306204
$333$	−3.14096e15	−0.126234
$334$	−5.96117e15	−0.234952
$335$	−4.06960e14	−0.0157311
$336$	1.48721e16	0.563855
$337$	3.01597e16	1.12159	0.560794	−	0.827956i	$-0.310496\pi$
$337$	3.01597e16	1.12159	0.560794	+	0.827956i	$0.310496\pi$
$338$	−6.69053e15	−0.244063
$339$	1.70411e16	0.609816
$340$	1.42159e16	0.499069
$341$	6.55227e15	0.225678
$342$	1.39926e15	0.0472855
$343$	−4.51822e15	−0.149815
$344$	−2.23055e16	−0.725743
$345$	1.23640e16	0.394760
$346$	3.05811e15	0.0958205
$347$	2.92206e16	0.898562	0.449281	−	0.893391i	$-0.351680\pi$
$347$	2.92206e16	0.898562	0.449281	+	0.893391i	$0.351680\pi$
$348$	1.00227e16	0.302496
$349$	2.57396e16	0.762494	0.381247	−	0.924473i	$-0.375495\pi$
$349$	2.57396e16	0.762494	0.381247	+	0.924473i	$0.375495\pi$
$350$	2.92062e16	0.849244
$351$	3.21902e15	0.0918814
$352$	−2.53119e16	−0.709248
$353$	1.98344e16	0.545610	0.272805	−	0.962069i	$-0.412049\pi$
$353$	1.98344e16	0.545610	0.272805	+	0.962069i	$0.412049\pi$
$354$	−8.79803e14	−0.0237610
$355$	4.10856e16	1.08944
$356$	3.10799e16	0.809197
$357$	−1.00195e16	−0.256155
$358$	2.11166e15	0.0530132
$359$	−6.75022e16	−1.66419	−0.832097	−	0.554630i	$-0.812860\pi$
$359$	−6.75022e16	−1.66419	−0.832097	+	0.554630i	$0.812860\pi$
$360$	−1.42115e16	−0.344090
$361$	−3.35847e16	−0.798629
$362$	1.24176e15	0.0290022
$363$	−6.57364e15	−0.150804
$364$	−2.62238e16	−0.590932
$365$	−1.05051e17	−2.32540
$366$	8.78688e15	0.191077
$367$	6.55766e16	1.40094	0.700470	−	0.713682i	$-0.252974\pi$
$367$	6.55766e16	1.40094	0.700470	+	0.713682i	$0.252974\pi$
$368$	1.34619e16	0.282550
$369$	2.48421e16	0.512291
$370$	−1.01539e16	−0.205741
$371$	−2.19386e16	−0.436796
$372$	6.97380e15	0.136440
$373$	3.93729e16	0.756989	0.378495	−	0.925603i	$-0.376442\pi$
$373$	3.93729e16	0.756989	0.378495	+	0.925603i	$0.376442\pi$
$374$	4.63971e15	0.0876649
$375$	5.09530e16	0.946165
$376$	−2.45036e16	−0.447208
$377$	−1.54929e16	−0.277917
$378$	4.74480e15	0.0836606
$379$	−2.09052e16	−0.362326	−0.181163	−	0.983453i	$-0.557986\pi$
$379$	−2.09052e16	−0.362326	−0.181163	+	0.983453i	$0.557986\pi$
$380$	−4.07419e16	−0.694141
$381$	−1.46660e16	−0.245640
$382$	1.87087e16	0.308057
$383$	−4.89324e16	−0.792145	−0.396073	−	0.918219i	$-0.629627\pi$
$383$	−4.89324e16	−0.792145	−0.396073	+	0.918219i	$0.629627\pi$
$384$	−3.50840e16	−0.558413
$385$	−1.29803e17	−2.03137
$386$	5.78423e15	0.0890078
$387$	2.66172e16	0.402756
$388$	2.27187e16	0.338048
$389$	6.05798e15	0.0886452	0.0443226	−	0.999017i	$-0.485887\pi$
$389$	6.05798e15	0.0886452	0.0443226	+	0.999017i	$0.485887\pi$
$390$	1.04062e16	0.149752
$391$	−9.06944e15	−0.128361
$392$	−3.84489e16	−0.535211
$393$	−7.52786e16	−1.03067
$394$	−1.52479e16	−0.205346
$395$	−2.49556e17	−3.30587
$396$	1.97896e16	0.257880
$397$	−1.10851e16	−0.142103	−0.0710513	−	0.997473i	$-0.522635\pi$
$397$	−1.10851e16	−0.142103	−0.0710513	+	0.997473i	$0.522635\pi$
$398$	−1.62617e16	−0.205081
$399$	2.87153e16	0.356279
$400$	1.13657e17	1.38741
$401$	−1.48299e17	−1.78115	−0.890574	−	0.454838i	$-0.849697\pi$
$401$	−1.48299e17	−1.78115	−0.890574	+	0.454838i	$0.849697\pi$
$402$	−1.41366e14	−0.00167062
$403$	−1.07800e16	−0.125353
$404$	−2.93902e16	−0.336298
$405$	1.69586e16	0.190955
$406$	−2.28364e16	−0.253051
$407$	2.98486e16	0.325507
$408$	1.04247e16	0.111885
$409$	−6.53952e16	−0.690787	−0.345393	−	0.938458i	$-0.612255\pi$
$409$	−6.53952e16	−0.690787	−0.345393	+	0.938458i	$0.612255\pi$
$410$	8.03078e16	0.834954
$411$	−2.90598e16	−0.297386
$412$	4.98426e16	0.502075
$413$	−1.80552e16	−0.179030
$414$	4.29489e15	0.0419227
$415$	6.08446e16	0.584668
$416$	4.16438e16	0.393953
$417$	6.03828e16	0.562379
$418$	−1.32971e16	−0.121930
$419$	−2.96994e16	−0.268137	−0.134069	−	0.990972i	$-0.542804\pi$
$419$	−2.96994e16	−0.268137	−0.134069	+	0.990972i	$0.542804\pi$
$420$	−1.38153e17	−1.22812
$421$	−3.74709e16	−0.327990	−0.163995	−	0.986461i	$-0.552438\pi$
$421$	−3.74709e16	−0.327990	−0.163995	+	0.986461i	$0.552438\pi$
$422$	4.80277e16	0.413963
$423$	2.92402e16	0.248181
$424$	2.28257e16	0.190786
$425$	−7.65718e16	−0.630291
$426$	1.42720e16	0.115697
$427$	1.80323e17	1.43969
$428$	−1.43176e17	−1.12586
$429$	−3.05904e16	−0.236926
$430$	8.60463e16	0.656428
$431$	2.25892e17	1.69745	0.848727	−	0.528831i	$-0.177369\pi$
$431$	2.25892e17	1.69745	0.848727	+	0.528831i	$0.177369\pi$
$432$	1.84645e16	0.136677
$433$	−3.17126e16	−0.231238	−0.115619	−	0.993294i	$-0.536885\pi$
$433$	−3.17126e16	−0.231238	−0.115619	+	0.993294i	$0.536885\pi$
$434$	−1.58895e16	−0.114137
$435$	−8.16203e16	−0.577588
$436$	−2.45316e17	−1.71027
$437$	2.59925e16	0.178533
$438$	−3.64919e16	−0.246953
$439$	−5.45505e16	−0.363730	−0.181865	−	0.983324i	$-0.558213\pi$
$439$	−5.45505e16	−0.363730	−0.181865	+	0.983324i	$0.558213\pi$
$440$	1.35052e17	0.887273
$441$	4.58812e16	0.297019
$442$	−7.63337e15	−0.0486936
$443$	5.75290e16	0.361628	0.180814	−	0.983517i	$-0.442127\pi$
$443$	5.75290e16	0.361628	0.180814	+	0.983517i	$0.442127\pi$
$444$	3.17688e16	0.196794
$445$	−2.53100e17	−1.54509
$446$	9.47283e16	0.569906
$447$	1.38293e17	0.819978
$448$	−1.05740e17	−0.617921
$449$	−2.78144e17	−1.60202	−0.801011	−	0.598649i	$-0.795704\pi$
$449$	−2.78144e17	−1.60202	−0.801011	+	0.598649i	$0.795704\pi$
$450$	3.62610e16	0.205854
$451$	−2.36074e17	−1.32100
$452$	−1.72359e17	−0.950682
$453$	3.26875e15	0.0177723
$454$	2.94485e16	0.157834
$455$	2.13555e17	1.12833
$456$	−2.98764e16	−0.155617
$457$	−3.44104e17	−1.76699	−0.883496	−	0.468438i	$-0.844817\pi$
$457$	−3.44104e17	−1.76699	−0.883496	+	0.468438i	$0.844817\pi$
$458$	2.83459e16	0.143504
$459$	−1.24398e16	−0.0620911
$460$	−1.25053e17	−0.615417
$461$	2.94568e17	1.42932	0.714660	−	0.699472i	$-0.246582\pi$
$461$	2.94568e17	1.42932	0.714660	+	0.699472i	$0.246582\pi$
$462$	−4.50898e16	−0.215728
$463$	2.54307e16	0.119972	0.0599862	−	0.998199i	$-0.480894\pi$
$463$	2.54307e16	0.119972	0.0599862	+	0.998199i	$0.480894\pi$
$464$	−8.88685e16	−0.413410
$465$	−5.67914e16	−0.260518
$466$	4.35311e16	0.196920
$467$	−8.60939e16	−0.384072	−0.192036	−	0.981388i	$-0.561509\pi$
$467$	−8.60939e16	−0.384072	−0.192036	+	0.981388i	$0.561509\pi$
$468$	−3.25583e16	−0.143240
$469$	−2.90110e15	−0.0125875
$470$	9.45257e16	0.404496
$471$	1.24917e17	0.527212
$472$	1.87852e16	0.0781977
$473$	−2.52944e17	−1.03855
$474$	−8.66885e16	−0.351077
$475$	2.19450e17	0.876653
$476$	1.01341e17	0.399337
$477$	−2.72380e16	−0.105878
$478$	−3.08096e16	−0.118142
$479$	−1.88707e17	−0.713852	−0.356926	−	0.934133i	$-0.616175\pi$
$479$	−1.88707e17	−0.713852	−0.356926	+	0.934133i	$0.616175\pi$
$480$	2.19390e17	0.818743
$481$	−4.91076e16	−0.180803
$482$	6.69660e16	0.243248
$483$	8.81390e16	0.315872
$484$	6.64881e16	0.235098
$485$	−1.85011e17	−0.645470
$486$	5.89092e15	0.0202790
$487$	−4.58622e17	−1.55782	−0.778908	−	0.627138i	$-0.784226\pi$
$487$	−4.58622e17	−1.55782	−0.778908	+	0.627138i	$0.784226\pi$
$488$	−1.87615e17	−0.628836
$489$	2.64882e17	0.876082
$490$	1.48321e17	0.484094
$491$	−4.21466e17	−1.35748	−0.678739	−	0.734380i	$-0.737473\pi$
$491$	−4.21466e17	−1.35748	−0.678739	+	0.734380i	$0.737473\pi$
$492$	−2.51262e17	−0.798644
$493$	5.98717e16	0.187809
$494$	2.18768e16	0.0677264
$495$	−1.61157e17	−0.492398
$496$	−6.18347e16	−0.186467
$497$	2.92887e17	0.871733
$498$	2.11357e16	0.0620906
$499$	4.93358e17	1.43057	0.715285	−	0.698833i	$-0.246297\pi$
$499$	4.93358e17	1.43057	0.715285	+	0.698833i	$0.246297\pi$
$500$	−5.15357e17	−1.47504
$501$	−1.51884e17	−0.429110
$502$	9.09065e16	0.253525
$503$	−3.34056e17	−0.919661	−0.459831	−	0.888007i	$-0.652090\pi$
$503$	−3.34056e17	−0.919661	−0.459831	+	0.888007i	$0.652090\pi$
$504$	−1.01309e17	−0.275328
$505$	2.39340e17	0.642128
$506$	−4.08143e16	−0.108102
$507$	−1.70468e17	−0.445750
$508$	1.48337e17	0.382944
$509$	6.63987e17	1.69236	0.846182	−	0.532894i	$-0.178896\pi$
$509$	6.63987e17	1.69236	0.846182	+	0.532894i	$0.178896\pi$
$510$	−4.02144e16	−0.101199
$511$	−7.48881e17	−1.86070
$512$	4.12753e17	1.01259
$513$	3.56516e16	0.0863607
$514$	7.21360e16	0.172541
$515$	−4.05895e17	−0.958665
$516$	−2.69216e17	−0.627882
$517$	−2.77870e17	−0.639960
$518$	−7.23840e16	−0.164626
$519$	7.79175e16	0.175004
$520$	−2.22190e17	−0.492837
$521$	−2.59732e17	−0.568958	−0.284479	−	0.958682i	$-0.591821\pi$
$521$	−2.59732e17	−0.568958	−0.284479	+	0.958682i	$0.591821\pi$
$522$	−2.83526e16	−0.0613387
$523$	−2.00639e17	−0.428701	−0.214350	−	0.976757i	$-0.568763\pi$
$523$	−2.00639e17	−0.428701	−0.214350	+	0.976757i	$0.568763\pi$
$524$	7.61394e17	1.60678
$525$	7.44143e17	1.55103
$526$	−2.61716e16	−0.0538795
$527$	4.16587e16	0.0847104
$528$	−1.75469e17	−0.352435
$529$	−4.24255e17	−0.841715
$530$	−8.80530e16	−0.172564
$531$	−2.24165e16	−0.0433963
$532$	−2.90437e17	−0.555426
$533$	3.88396e17	0.733749
$534$	−8.79198e16	−0.164085
$535$	1.16596e18	2.14973
$536$	3.01840e15	0.00549802
$537$	5.38029e16	0.0968217
$538$	2.76423e17	0.491461
$539$	−4.36009e17	−0.765894
$540$	−1.71525e17	−0.297692
$541$	−2.36614e17	−0.405750	−0.202875	−	0.979205i	$-0.565028\pi$
$541$	−2.36614e17	−0.405750	−0.202875	+	0.979205i	$0.565028\pi$
$542$	−3.25772e17	−0.551974
$543$	3.16387e16	0.0529688
$544$	−1.60931e17	−0.266223
$545$	1.99774e18	3.26559
$546$	7.41829e16	0.119826
$547$	2.15614e17	0.344159	0.172079	−	0.985083i	$-0.444951\pi$
$547$	2.15614e17	0.344159	0.172079	+	0.985083i	$0.444951\pi$
$548$	2.93921e17	0.463614
$549$	2.23881e17	0.348977
$550$	−3.44589e17	−0.530815
$551$	−1.71589e17	−0.261218
$552$	−9.17030e16	−0.137968
$553$	−1.77901e18	−2.64524
$554$	−3.03008e17	−0.445288
$555$	−2.58711e17	−0.375759
$556$	−6.10733e17	−0.876729
$557$	−8.75029e17	−1.24155	−0.620774	−	0.783990i	$-0.713182\pi$
$557$	−8.75029e17	−1.24155	−0.620774	+	0.783990i	$0.713182\pi$
$558$	−1.97277e16	−0.0276665
$559$	4.16149e17	0.576863
$560$	1.22497e18	1.67843
$561$	1.18215e17	0.160108
$562$	−2.72735e17	−0.365136
$563$	9.12606e17	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$563$	9.12606e17	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$564$	−2.95746e17	−0.386905
$565$	1.40362e18	1.81524
$566$	−1.27618e17	−0.163157
$567$	1.20893e17	0.152795
$568$	−3.04730e17	−0.380760
$569$	−4.32429e17	−0.534177	−0.267089	−	0.963672i	$-0.586062\pi$
$569$	−4.32429e17	−0.534177	−0.267089	+	0.963672i	$0.586062\pi$
$570$	1.15252e17	0.140754
$571$	−3.05605e17	−0.368999	−0.184500	−	0.982833i	$-0.559066\pi$
$571$	−3.05605e17	−0.368999	−0.184500	+	0.982833i	$0.559066\pi$
$572$	3.09402e17	0.369359
$573$	4.76678e17	0.562627
$574$	5.72490e17	0.668099
$575$	6.73582e17	0.777230
$576$	−1.31282e17	−0.149782
$577$	2.04890e17	0.231141	0.115571	−	0.993299i	$-0.463130\pi$
$577$	2.04890e17	0.231141	0.115571	+	0.993299i	$0.463130\pi$
$578$	−2.53889e17	−0.283213
$579$	1.47376e17	0.162561
$580$	8.25537e17	0.900440
$581$	4.33743e17	0.467830
$582$	−6.42676e16	−0.0685476
$583$	2.58843e17	0.273017
$584$	7.79162e17	0.812727
$585$	2.65140e17	0.273503
$586$	5.07745e17	0.517978
$587$	−8.18615e17	−0.825909	−0.412954	−	0.910752i	$-0.635503\pi$
$587$	−8.18615e17	−0.825909	−0.412954	+	0.910752i	$0.635503\pi$
$588$	−4.64058e17	−0.463042
$589$	−1.19391e17	−0.117821
$590$	−7.24664e16	−0.0707292
$591$	−3.88501e17	−0.375037
$592$	−2.81685e17	−0.268951
$593$	−2.63935e17	−0.249254	−0.124627	−	0.992204i	$-0.539773\pi$
$593$	−2.63935e17	−0.249254	−0.124627	+	0.992204i	$0.539773\pi$
$594$	−5.59814e16	−0.0522916
$595$	−8.25273e17	−0.762496
$596$	−1.39875e18	−1.27832
$597$	−4.14331e17	−0.374554
$598$	6.71487e16	0.0600454
$599$	6.06960e17	0.536890	0.268445	−	0.963295i	$-0.413490\pi$
$599$	6.06960e17	0.536890	0.268445	+	0.963295i	$0.413490\pi$
$600$	−7.74234e17	−0.677468
$601$	−9.28222e17	−0.803467	−0.401733	−	0.915757i	$-0.631592\pi$
$601$	−9.28222e17	−0.803467	−0.401733	+	0.915757i	$0.631592\pi$
$602$	6.13399e17	0.525250
$603$	−3.60187e15	−0.00305116
$604$	−3.30613e16	−0.0277064
$605$	−5.41448e17	−0.448897
$606$	8.31400e16	0.0681927
$607$	−1.02008e18	−0.827766	−0.413883	−	0.910330i	$-0.635828\pi$
$607$	−1.02008e18	−0.827766	−0.413883	+	0.910330i	$0.635828\pi$
$608$	4.61218e17	0.370282
$609$	−5.81847e17	−0.462165
$610$	7.23746e17	0.568777
$611$	4.57158e17	0.355466
$612$	1.25820e17	0.0967979
$613$	1.38898e18	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$613$	1.38898e18	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$614$	4.07223e17	0.306717
$615$	2.04616e18	1.52493
$616$	9.62743e17	0.709963
$617$	1.27962e18	0.933740	0.466870	−	0.884326i	$-0.345382\pi$
$617$	1.27962e18	0.933740	0.466870	+	0.884326i	$0.345382\pi$
$618$	−1.40996e17	−0.101808
$619$	7.14427e17	0.510468	0.255234	−	0.966879i	$-0.417847\pi$
$619$	7.14427e17	0.510468	0.255234	+	0.966879i	$0.417847\pi$
$620$	5.74408e17	0.406139
$621$	1.09429e17	0.0765664
$622$	1.99346e17	0.138029
$623$	−1.80428e18	−1.23632
$624$	2.88685e17	0.195760
$625$	1.28578e18	0.862873
$626$	−5.33003e17	−0.353994
$627$	−3.38797e17	−0.222690
$628$	−1.26345e18	−0.821906
$629$	1.89774e17	0.122182
$630$	3.90813e17	0.249032
$631$	1.73070e18	1.09152	0.545758	−	0.837943i	$-0.316242\pi$
$631$	1.73070e18	1.09152	0.545758	+	0.837943i	$0.316242\pi$
$632$	1.85094e18	1.15540
$633$	1.22370e18	0.756049
$634$	6.71811e16	0.0410835
$635$	−1.20799e18	−0.731195
$636$	2.75495e17	0.165060
$637$	7.17333e17	0.425417
$638$	2.69435e17	0.158168
$639$	3.63635e17	0.211305
$640$	−2.88975e18	−1.66223
$641$	1.48780e18	0.847163	0.423581	−	0.905858i	$-0.360773\pi$
$641$	1.48780e18	0.847163	0.423581	+	0.905858i	$0.360773\pi$
$642$	4.05021e17	0.228297
$643$	1.41403e18	0.789016	0.394508	−	0.918892i	$-0.370915\pi$
$643$	1.41403e18	0.789016	0.394508	+	0.918892i	$0.370915\pi$
$644$	−8.91468e17	−0.492434
$645$	2.19237e18	1.19888
$646$	−8.45418e16	−0.0457678
$647$	2.03762e18	1.09206	0.546029	−	0.837766i	$-0.316139\pi$
$647$	2.03762e18	1.09206	0.546029	+	0.837766i	$0.316139\pi$
$648$	−1.25781e17	−0.0667387
$649$	2.13024e17	0.111902
$650$	5.66926e17	0.294842
$651$	−4.04849e17	−0.208457
$652$	−2.67911e18	−1.36578
$653$	−9.92522e17	−0.500962	−0.250481	−	0.968122i	$-0.580589\pi$
$653$	−9.92522e17	−0.500962	−0.250481	+	0.968122i	$0.580589\pi$
$654$	6.93959e17	0.346800
$655$	−6.20044e18	−3.06799
$656$	2.22787e18	1.09148
$657$	−9.29776e17	−0.451028
$658$	6.73846e17	0.323662
$659$	1.22480e17	0.0582520	0.0291260	−	0.999576i	$-0.490728\pi$
$659$	1.22480e17	0.0582520	0.0291260	+	0.999576i	$0.490728\pi$
$660$	1.63000e18	0.767631
$661$	3.12167e17	0.145572	0.0727860	−	0.997348i	$-0.476811\pi$
$661$	3.12167e17	0.145572	0.0727860	+	0.997348i	$0.476811\pi$
$662$	−7.87254e17	−0.363528
$663$	−1.94490e17	−0.0889325
$664$	−4.51282e17	−0.204341
$665$	2.36518e18	1.06053
$666$	−8.98687e16	−0.0399049
$667$	−5.26675e17	−0.231593
$668$	1.53621e18	0.668967
$669$	2.41358e18	1.04086
$670$	−1.16439e16	−0.00497291
$671$	−2.12754e18	−0.899873
$672$	1.56396e18	0.655128
$673$	−2.67413e18	−1.10939	−0.554696	−	0.832053i	$-0.687166\pi$
$673$	−2.67413e18	−1.10939	−0.554696	+	0.832053i	$0.687166\pi$
$674$	8.62925e17	0.354555
$675$	9.23894e17	0.375965
$676$	1.72417e18	0.694908
$677$	−4.28300e18	−1.70971	−0.854854	−	0.518868i	$-0.826354\pi$
$677$	−4.28300e18	−1.70971	−0.854854	+	0.518868i	$0.826354\pi$
$678$	4.87576e17	0.192774
$679$	−1.31889e18	−0.516481
$680$	8.58644e17	0.333047
$681$	7.50319e17	0.288263
$682$	1.87473e17	0.0713410
$683$	−7.31913e17	−0.275883	−0.137941	−	0.990440i	$-0.544049\pi$
$683$	−7.31913e17	−0.275883	−0.137941	+	0.990440i	$0.544049\pi$
$684$	−3.60593e17	−0.134633
$685$	−2.39356e18	−0.885228
$686$	−1.29275e17	−0.0473594
$687$	7.22223e17	0.262091
$688$	2.38706e18	0.858102
$689$	−4.25854e17	−0.151648
$690$	3.53755e17	0.124791
$691$	7.91680e17	0.276657	0.138329	−	0.990386i	$-0.455827\pi$
$691$	7.91680e17	0.276657	0.138329	+	0.990386i	$0.455827\pi$
$692$	−7.88085e17	−0.272825
$693$	−1.14884e18	−0.393998
$694$	8.36055e17	0.284052
$695$	4.97353e18	1.67403
$696$	6.05375e17	0.201867
$697$	−1.50094e18	−0.495849
$698$	7.36457e17	0.241039
$699$	1.10913e18	0.359650
$700$	−7.52653e18	−2.41801
$701$	1.65035e18	0.525302	0.262651	−	0.964891i	$-0.415403\pi$
$701$	1.65035e18	0.525302	0.262651	+	0.964891i	$0.415403\pi$
$702$	9.21021e16	0.0290455
$703$	−5.43882e17	−0.169940
$704$	1.24757e18	0.386228
$705$	2.40842e18	0.738758
$706$	5.67497e17	0.172478
$707$	1.70619e18	0.513807
$708$	2.26728e17	0.0676533
$709$	−6.24771e18	−1.84723	−0.923614	−	0.383324i	$-0.874779\pi$
$709$	−6.24771e18	−1.84723	−0.923614	+	0.383324i	$0.874779\pi$
$710$	1.17553e18	0.344394
$711$	−2.20873e18	−0.641196
$712$	1.87723e18	0.540006
$713$	−3.66460e17	−0.104459
$714$	−2.86676e17	−0.0809755
$715$	−2.51962e18	−0.705256
$716$	−5.44182e17	−0.150942
$717$	−7.84996e17	−0.215771
$718$	−1.93136e18	−0.526083
$719$	5.85211e18	1.57970	0.789850	−	0.613300i	$-0.210158\pi$
$719$	5.85211e18	1.57970	0.789850	+	0.613300i	$0.210158\pi$
$720$	1.52086e18	0.406845
$721$	−2.89351e18	−0.767088
$722$	−9.60921e17	−0.252462
$723$	1.70623e18	0.444260
$724$	−3.20005e17	−0.0825765
$725$	−4.44664e18	−1.13719
$726$	−1.88084e17	−0.0476720
$727$	1.76655e17	0.0443765	0.0221882	−	0.999754i	$-0.492937\pi$
$727$	1.76655e17	0.0443765	0.0221882	+	0.999754i	$0.492937\pi$
$728$	−1.58393e18	−0.394350
$729$	1.50095e17	0.0370370
$730$	−3.00571e18	−0.735104
$731$	−1.60819e18	−0.389829
$732$	−2.26441e18	−0.544042
$733$	3.03756e18	0.723350	0.361675	−	0.932304i	$-0.382205\pi$
$733$	3.03756e18	0.723350	0.361675	+	0.932304i	$0.382205\pi$
$734$	1.87627e18	0.442864
$735$	3.77908e18	0.884134
$736$	1.41566e18	0.328288
$737$	3.42285e16	0.00786774
$738$	7.10778e17	0.161945
$739$	−4.10920e18	−0.928044	−0.464022	−	0.885824i	$-0.653594\pi$
$739$	−4.10920e18	−0.928044	−0.464022	+	0.885824i	$0.653594\pi$
$740$	2.61669e18	0.585795
$741$	5.57398e17	0.123694
$742$	−6.27704e17	−0.138080
$743$	−7.88870e18	−1.72020	−0.860098	−	0.510128i	$-0.829598\pi$
$743$	−7.88870e18	−1.72020	−0.860098	+	0.510128i	$0.829598\pi$
$744$	4.21220e17	0.0910510
$745$	1.13908e19	2.44083
$746$	1.12653e18	0.239299
$747$	5.38516e17	0.113400
$748$	−1.19567e18	−0.249603
$749$	8.31178e18	1.72013
$750$	1.45786e18	0.299101
$751$	−2.55663e18	−0.520006	−0.260003	−	0.965608i	$-0.583724\pi$
$751$	−2.55663e18	−0.520006	−0.260003	+	0.965608i	$0.583724\pi$
$752$	2.62229e18	0.528768
$753$	2.31620e18	0.463030
$754$	−4.43281e17	−0.0878547
$755$	2.69236e17	0.0529027
$756$	−1.22275e18	−0.238202
$757$	5.09571e18	0.984195	0.492098	−	0.870540i	$-0.336230\pi$
$757$	5.09571e18	0.984195	0.492098	+	0.870540i	$0.336230\pi$
$758$	−5.98136e17	−0.114538
$759$	−1.03991e18	−0.197434
$760$	−2.46082e18	−0.463225
$761$	−3.34517e18	−0.624336	−0.312168	−	0.950027i	$-0.601055\pi$
$761$	−3.34517e18	−0.624336	−0.312168	+	0.950027i	$0.601055\pi$
$762$	−4.19621e17	−0.0776515
$763$	1.42413e19	2.61301
$764$	−4.82129e18	−0.877115
$765$	−1.02462e18	−0.184826
$766$	−1.40005e18	−0.250412
$767$	−3.50472e17	−0.0621560
$768$	4.71442e17	0.0829049
$769$	3.54959e18	0.618952	0.309476	−	0.950907i	$-0.399846\pi$
$769$	3.54959e18	0.618952	0.309476	+	0.950907i	$0.399846\pi$
$770$	−3.71390e18	−0.642155
$771$	1.83795e18	0.315123
$772$	−1.49062e18	−0.253427
$773$	−2.46328e18	−0.415285	−0.207643	−	0.978205i	$-0.566579\pi$
$773$	−2.46328e18	−0.415285	−0.207643	+	0.978205i	$0.566579\pi$
$774$	7.61568e17	0.127319
$775$	−3.09397e18	−0.512926
$776$	1.37222e18	0.225591
$777$	−1.84427e18	−0.300669
$778$	1.73330e17	0.0280224
$779$	4.30160e18	0.689662
$780$	−2.68172e18	−0.426381
$781$	−3.45562e18	−0.544872
$782$	−2.59493e17	−0.0405772
$783$	−7.22395e17	−0.112027
$784$	4.11467e18	0.632821
$785$	1.02890e19	1.56935
$786$	−2.15386e18	−0.325815
$787$	−5.08722e18	−0.763211	−0.381605	−	0.924325i	$-0.624629\pi$
$787$	−5.08722e18	−0.763211	−0.381605	+	0.924325i	$0.624629\pi$
$788$	3.92944e18	0.584669
$789$	−6.66826e17	−0.0984038
$790$	−7.14024e18	−1.04505
$791$	1.00060e19	1.45248
$792$	1.19530e18	0.172093
$793$	3.50028e18	0.499835
$794$	−3.17166e17	−0.0449214
$795$	−2.24350e18	−0.315166
$796$	4.19069e18	0.583916
$797$	−9.51239e18	−1.31465	−0.657325	−	0.753607i	$-0.728312\pi$
$797$	−9.51239e18	−1.31465	−0.657325	+	0.753607i	$0.728312\pi$
$798$	8.21598e17	0.112626
$799$	−1.76667e18	−0.240215
$800$	1.19522e19	1.61200
$801$	−2.24011e18	−0.299680
$802$	−4.24311e18	−0.563055
$803$	8.83566e18	1.16302
$804$	3.64306e16	0.00475665
$805$	7.25971e18	0.940256
$806$	−3.08435e17	−0.0396265
$807$	7.04297e18	0.897590
$808$	−1.77518e18	−0.224423
$809$	4.48219e18	0.562114	0.281057	−	0.959691i	$-0.409315\pi$
$809$	4.48219e18	0.562114	0.281057	+	0.959691i	$0.409315\pi$
$810$	4.85215e17	0.0603645
$811$	−1.01306e19	−1.25025	−0.625127	−	0.780523i	$-0.714953\pi$
$811$	−1.01306e19	−1.25025	−0.625127	+	0.780523i	$0.714953\pi$
$812$	5.88501e18	0.720498
$813$	−8.30034e18	−1.00811
$814$	8.54022e17	0.102899
$815$	2.18174e19	2.60783
$816$	−1.11561e18	−0.132290
$817$	4.60898e18	0.542202
$818$	−1.87108e18	−0.218371
$819$	1.89010e18	0.218847
$820$	−2.06956e19	−2.37732
$821$	−1.44455e19	−1.64627	−0.823136	−	0.567845i	$-0.807777\pi$
$821$	−1.44455e19	−1.64627	−0.823136	+	0.567845i	$0.807777\pi$
$822$	−8.31454e17	−0.0940094
$823$	−1.87229e18	−0.210026	−0.105013	−	0.994471i	$-0.533488\pi$
$823$	−1.87229e18	−0.210026	−0.105013	+	0.994471i	$0.533488\pi$
$824$	3.01051e18	0.335053
$825$	−8.77977e18	−0.969465
$826$	−5.16591e17	−0.0565948
$827$	−8.21859e18	−0.893329	−0.446665	−	0.894701i	$-0.647388\pi$
$827$	−8.21859e18	−0.893329	−0.446665	+	0.894701i	$0.647388\pi$
$828$	−1.10681e18	−0.119364
$829$	−6.85548e18	−0.733557	−0.366778	−	0.930308i	$-0.619539\pi$
$829$	−6.85548e18	−0.733557	−0.366778	+	0.930308i	$0.619539\pi$
$830$	1.74088e18	0.184825
$831$	−7.72033e18	−0.813260
$832$	−2.05254e18	−0.214531
$833$	−2.77210e18	−0.287486
$834$	1.72766e18	0.177779
$835$	−1.25102e19	−1.27733
$836$	3.42672e18	0.347166
$837$	−5.02642e17	−0.0505293
$838$	−8.49755e17	−0.0847633
$839$	−1.29934e19	−1.28608	−0.643041	−	0.765832i	$-0.722327\pi$
$839$	−1.29934e19	−1.28608	−0.643041	+	0.765832i	$0.722327\pi$
$840$	−8.34451e18	−0.819569
$841$	−6.78379e18	−0.661148
$842$	−1.07211e18	−0.103684
$843$	−6.94901e18	−0.666874
$844$	−1.23769e19	−1.17865
$845$	−1.40409e19	−1.32686
$846$	8.36616e17	0.0784546
$847$	−3.85983e18	−0.359191
$848$	−2.44273e18	−0.225581
$849$	−3.25157e18	−0.297984
$850$	−2.19086e18	−0.199247
$851$	−1.66939e18	−0.150666
$852$	−3.67793e18	−0.329417
$853$	−6.44498e18	−0.572866	−0.286433	−	0.958100i	$-0.592470\pi$
$853$	−6.44498e18	−0.572866	−0.286433	+	0.958100i	$0.592470\pi$
$854$	5.15937e18	0.455114
$855$	2.93650e18	0.257070
$856$	−8.64787e18	−0.751329
$857$	−1.91734e19	−1.65319	−0.826596	−	0.562795i	$-0.809726\pi$
$857$	−1.91734e19	−1.65319	−0.826596	+	0.562795i	$0.809726\pi$
$858$	−8.75246e17	−0.0748967
$859$	1.33684e19	1.13533	0.567667	−	0.823259i	$-0.307846\pi$
$859$	1.33684e19	1.13533	0.567667	+	0.823259i	$0.307846\pi$
$860$	−2.21744e19	−1.86901
$861$	1.45865e19	1.22020
$862$	6.46318e18	0.536598
$863$	1.08501e19	0.894056	0.447028	−	0.894520i	$-0.352482\pi$
$863$	1.08501e19	0.894056	0.447028	+	0.894520i	$0.352482\pi$
$864$	1.94174e18	0.158801
$865$	6.41780e18	0.520933
$866$	−9.07354e17	−0.0730989
$867$	−6.46884e18	−0.517252
$868$	4.09479e18	0.324977
$869$	2.09896e19	1.65339
$870$	−2.33531e18	−0.182587
$871$	−5.63137e16	−0.00437014
$872$	−1.48172e19	−1.14132
$873$	−1.63747e18	−0.125193
$874$	7.43692e17	0.0564376
$875$	2.99180e19	2.25361
$876$	9.40408e18	0.703136
$877$	−7.91821e18	−0.587665	−0.293832	−	0.955857i	$-0.594931\pi$
$877$	−7.91821e18	−0.587665	−0.293832	+	0.955857i	$0.594931\pi$
$878$	−1.56079e18	−0.114982
$879$	1.29368e19	0.946020
$880$	−1.44528e19	−1.04909
$881$	2.63411e18	0.189797	0.0948987	−	0.995487i	$-0.469747\pi$
$881$	2.63411e18	0.189797	0.0948987	+	0.995487i	$0.469747\pi$
$882$	1.31274e18	0.0938933
$883$	2.30340e19	1.63540	0.817702	−	0.575641i	$-0.195248\pi$
$883$	2.30340e19	1.63540	0.817702	+	0.575641i	$0.195248\pi$
$884$	1.96714e18	0.138643
$885$	−1.84637e18	−0.129178
$886$	1.64601e18	0.114318
$887$	4.21937e18	0.290901	0.145450	−	0.989366i	$-0.453537\pi$
$887$	4.21937e18	0.290901	0.145450	+	0.989366i	$0.453537\pi$
$888$	1.91885e18	0.131328
$889$	−8.61139e18	−0.585075
$890$	−7.24166e18	−0.488431
$891$	−1.42635e18	−0.0955039
$892$	−2.44118e19	−1.62266
$893$	5.06316e18	0.334108
$894$	3.95683e18	0.259211
$895$	4.43156e18	0.288209
$896$	−2.06002e19	−1.33005
$897$	1.71088e18	0.109665
$898$	−7.95821e18	−0.506430
$899$	2.41918e18	0.152838
$900$	−9.34459e18	−0.586116
$901$	1.64570e18	0.102480
$902$	−6.75452e18	−0.417592
$903$	1.56288e19	0.959300
$904$	−1.04106e19	−0.634424
$905$	2.60598e18	0.157672
$906$	9.35249e16	0.00561816
$907$	−2.00406e18	−0.119526	−0.0597631	−	0.998213i	$-0.519035\pi$
$907$	−2.00406e18	−0.119526	−0.0597631	+	0.998213i	$0.519035\pi$
$908$	−7.58899e18	−0.449392
$909$	2.11832e18	0.124545
$910$	6.11020e18	0.356686
$911$	1.33766e19	0.775311	0.387656	−	0.921804i	$-0.373285\pi$
$911$	1.33766e19	0.775311	0.387656	+	0.921804i	$0.373285\pi$
$912$	3.19728e18	0.183998
$913$	−5.11752e18	−0.292415
$914$	−9.84545e18	−0.558580
$915$	1.84403e19	1.03880
$916$	−7.30482e18	−0.408591
$917$	−4.42011e19	−2.45489
$918$	−3.55924e17	−0.0196282
$919$	−5.46503e18	−0.299255	−0.149628	−	0.988742i	$-0.547808\pi$
$919$	−5.46503e18	−0.299255	−0.149628	+	0.988742i	$0.547808\pi$
$920$	−7.55326e18	−0.410690
$921$	1.03756e19	0.560179
$922$	8.42812e18	0.451835
$923$	5.68528e18	0.302650
$924$	1.16198e19	0.614229
$925$	−1.40944e19	−0.739820
$926$	7.27618e17	0.0379256
$927$	−3.59244e18	−0.185939
$928$	−9.34548e18	−0.480330
$929$	2.03703e19	1.03967	0.519834	−	0.854267i	$-0.325994\pi$
$929$	2.03703e19	1.03967	0.519834	+	0.854267i	$0.325994\pi$
$930$	−1.62491e18	−0.0823548
$931$	7.94467e18	0.399856
$932$	−1.12181e19	−0.560681
$933$	5.07913e18	0.252092
$934$	−2.46331e18	−0.121413
$935$	9.73698e18	0.476594
$936$	−1.96653e18	−0.0955890
$937$	−2.26477e19	−1.09324	−0.546621	−	0.837380i	$-0.684086\pi$
$937$	−2.26477e19	−1.09324	−0.546621	+	0.837380i	$0.684086\pi$
$938$	−8.30057e16	−0.00397914
$939$	−1.35804e19	−0.646525
$940$	−2.43596e19	−1.15170
$941$	−4.52873e17	−0.0212639	−0.0106320	−	0.999943i	$-0.503384\pi$
$941$	−4.52873e17	−0.0212639	−0.0106320	+	0.999943i	$0.503384\pi$
$942$	3.57410e18	0.166662
$943$	1.32033e19	0.611446
$944$	−2.01033e18	−0.0924592
$945$	9.95751e18	0.454825
$946$	−7.23718e18	−0.328305
$947$	2.29988e19	1.03617	0.518083	−	0.855330i	$-0.326646\pi$
$947$	2.29988e19	1.03617	0.518083	+	0.855330i	$0.326646\pi$
$948$	2.23399e19	0.999602
$949$	−1.45366e19	−0.646002
$950$	6.27887e18	0.277127
$951$	1.71171e18	0.0750336
$952$	6.12102e18	0.266492
$953$	3.27952e19	1.41810	0.709050	−	0.705158i	$-0.249124\pi$
$953$	3.27952e19	1.41810	0.709050	+	0.705158i	$0.249124\pi$
$954$	−7.79329e17	−0.0334700
$955$	3.92624e19	1.67477
$956$	7.93973e18	0.336379
$957$	6.86492e18	0.288874
$958$	−5.39927e18	−0.225662
$959$	−1.70630e19	−0.708326
$960$	−1.08133e19	−0.445855
$961$	−2.27343e19	−0.931063
$962$	−1.40506e18	−0.0571553
$963$	1.03195e19	0.416954
$964$	−1.72574e19	−0.692586
$965$	1.21389e19	0.483895
$966$	2.52182e18	0.0998532
$967$	2.96901e19	1.16772	0.583861	−	0.811853i	$-0.301541\pi$
$967$	2.96901e19	1.16772	0.583861	+	0.811853i	$0.301541\pi$
$968$	4.01590e18	0.156889
$969$	−2.15404e18	−0.0835890
$970$	−5.29350e18	−0.204045
$971$	−1.17847e19	−0.451225	−0.225613	−	0.974217i	$-0.572438\pi$
$971$	−1.17847e19	−0.451225	−0.225613	+	0.974217i	$0.572438\pi$
$972$	−1.51811e18	−0.0577394
$973$	3.54548e19	1.33950
$974$	−1.31220e19	−0.492455
$975$	1.44447e19	0.538491
$976$	2.00779e19	0.743522
$977$	−4.47194e19	−1.64506	−0.822529	−	0.568723i	$-0.807438\pi$
$977$	−4.47194e19	−1.64506	−0.822529	+	0.568723i	$0.807438\pi$
$978$	7.57876e18	0.276946
$979$	2.12877e19	0.772755
$980$	−3.82229e19	−1.37833
$981$	1.76814e19	0.633384
$982$	−1.20589e19	−0.429125
$983$	−1.95000e19	−0.689345	−0.344673	−	0.938723i	$-0.612010\pi$
$983$	−1.95000e19	−0.689345	−0.344673	+	0.938723i	$0.612010\pi$
$984$	−1.51763e19	−0.532963
$985$	−3.19996e19	−1.11637
$986$	1.71304e18	0.0593700
$987$	1.71689e19	0.591127
$988$	−5.63772e18	−0.192834
$989$	1.41468e19	0.480710
$990$	−4.61100e18	−0.155656
$991$	3.83680e18	0.128674	0.0643369	−	0.997928i	$-0.479507\pi$
$991$	3.83680e18	0.128674	0.0643369	+	0.997928i	$0.479507\pi$
$992$	−6.50258e18	−0.216651
$993$	−2.00584e19	−0.663936
$994$	8.38003e18	0.275571
$995$	−3.41270e19	−1.11493
$996$	−5.44674e18	−0.176787
$997$	−9.82416e18	−0.316794	−0.158397	−	0.987376i	$-0.550633\pi$
$997$	−9.82416e18	−0.316794	−0.158397	+	0.987376i	$0.550633\pi$
$998$	1.41159e19	0.452230
$999$	−2.28976e18	−0.0728811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.17	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+28.6118 q^{2} +729.000 q^{3} -7373.36 q^{4} +60045.3 q^{5} +20858.0 q^{6} +428045. q^{7} -445354. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+28.6118 q^{2} +729.000 q^{3} -7373.36 q^{4} +60045.3 q^{5} +20858.0 q^{6} +428045. q^{7} -445354. q^{8} +531441. q^{9} +1.71801e6 q^{10} -5.05028e6 q^{11} -5.37518e6 q^{12} +8.30885e6 q^{13} +1.22472e7 q^{14} +4.37730e7 q^{15} +4.76602e7 q^{16} -3.21092e7 q^{17} +1.52055e7 q^{18} +9.20230e7 q^{19} -4.42736e8 q^{20} +3.12045e8 q^{21} -1.44498e8 q^{22} +2.82456e8 q^{23} -3.24663e8 q^{24} +2.38473e9 q^{25} +2.37732e8 q^{26} +3.87420e8 q^{27} -3.15613e9 q^{28} -1.86463e9 q^{29} +1.25243e9 q^{30} -1.29741e9 q^{31} +5.01198e9 q^{32} -3.68166e9 q^{33} -9.18703e8 q^{34} +2.57021e10 q^{35} -3.91851e9 q^{36} -5.91028e9 q^{37} +2.63295e9 q^{38} +6.05716e9 q^{39} -2.67414e10 q^{40} +4.67448e10 q^{41} +8.92817e9 q^{42} +5.00850e10 q^{43} +3.72376e10 q^{44} +3.19105e10 q^{45} +8.08158e9 q^{46} +5.50206e10 q^{47} +3.47443e10 q^{48} +8.63335e10 q^{49} +6.82315e10 q^{50} -2.34076e10 q^{51} -6.12642e10 q^{52} -5.12531e10 q^{53} +1.10848e10 q^{54} -3.03246e11 q^{55} -1.90631e11 q^{56} +6.70848e10 q^{57} -5.33504e10 q^{58} -4.21805e10 q^{59} -3.22754e11 q^{60} +4.21271e11 q^{61} -3.71212e10 q^{62} +2.27481e11 q^{63} -2.47031e11 q^{64} +4.98907e11 q^{65} -1.05339e11 q^{66} -6.77755e9 q^{67} +2.36753e11 q^{68} +2.05910e11 q^{69} +7.35384e11 q^{70} +6.84243e11 q^{71} -2.36679e11 q^{72} -1.74954e12 q^{73} -1.69104e11 q^{74} +1.73847e12 q^{75} -6.78519e11 q^{76} -2.16175e12 q^{77} +1.73306e11 q^{78} -4.15612e12 q^{79} +2.86177e12 q^{80} +2.82430e11 q^{81} +1.33745e12 q^{82} +1.01331e12 q^{83} -2.30082e12 q^{84} -1.92801e12 q^{85} +1.43302e12 q^{86} -1.35931e12 q^{87} +2.24916e12 q^{88} -4.21516e12 q^{89} +9.13018e11 q^{90} +3.55656e12 q^{91} -2.08265e12 q^{92} -9.45810e11 q^{93} +1.57424e12 q^{94} +5.52555e12 q^{95} +3.65373e12 q^{96} -3.08119e12 q^{97} +2.47016e12 q^{98} -2.68393e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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