LMFDB - Embedded newform 177.14.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q+66.7973 q^{2} +729.000 q^{3} -3730.11 q^{4} +36075.7 q^{5} +48695.3 q^{6} -269744. q^{7} -796366. q^{8} +531441. q^{9} +O(q^{10})$	\(q+66.7973 q^{2} +729.000 q^{3} -3730.11 q^{4} +36075.7 q^{5} +48695.3 q^{6} -269744. q^{7} -796366. q^{8} +531441. q^{9} +2.40976e6 q^{10} +1.04015e7 q^{11} -2.71925e6 q^{12} -7.55745e6 q^{13} -1.80182e7 q^{14} +2.62992e7 q^{15} -2.26380e7 q^{16} -1.33275e8 q^{17} +3.54989e7 q^{18} +2.81117e8 q^{19} -1.34567e8 q^{20} -1.96643e8 q^{21} +6.94792e8 q^{22} +2.81992e8 q^{23} -5.80551e8 q^{24} +8.07543e7 q^{25} -5.04818e8 q^{26} +3.87420e8 q^{27} +1.00618e9 q^{28} +3.19316e9 q^{29} +1.75672e9 q^{30} -5.46963e9 q^{31} +5.01167e9 q^{32} +7.58269e9 q^{33} -8.90243e9 q^{34} -9.73121e9 q^{35} -1.98234e9 q^{36} -7.12239e9 q^{37} +1.87779e10 q^{38} -5.50938e9 q^{39} -2.87295e10 q^{40} +2.84811e10 q^{41} -1.31353e10 q^{42} -4.95408e10 q^{43} -3.87988e10 q^{44} +1.91721e10 q^{45} +1.88363e10 q^{46} -1.09577e10 q^{47} -1.65031e10 q^{48} -2.41272e10 q^{49} +5.39418e9 q^{50} -9.71577e10 q^{51} +2.81902e10 q^{52} +2.87608e11 q^{53} +2.58787e10 q^{54} +3.75241e11 q^{55} +2.14815e11 q^{56} +2.04934e11 q^{57} +2.13295e11 q^{58} -4.21805e10 q^{59} -9.80990e10 q^{60} +1.11011e11 q^{61} -3.65357e11 q^{62} -1.43353e11 q^{63} +5.20217e11 q^{64} -2.72641e11 q^{65} +5.06504e11 q^{66} +9.50274e11 q^{67} +4.97132e11 q^{68} +2.05572e11 q^{69} -6.50019e11 q^{70} +2.78596e11 q^{71} -4.23221e11 q^{72} +5.64617e11 q^{73} -4.75757e11 q^{74} +5.88699e10 q^{75} -1.04860e12 q^{76} -2.80574e12 q^{77} -3.68012e11 q^{78} +1.36889e12 q^{79} -8.16683e11 q^{80} +2.82430e11 q^{81} +1.90246e12 q^{82} +2.62840e12 q^{83} +7.33502e11 q^{84} -4.80800e12 q^{85} -3.30920e12 q^{86} +2.32781e12 q^{87} -8.28339e12 q^{88} -7.86312e12 q^{89} +1.28065e12 q^{90} +2.03858e12 q^{91} -1.05186e12 q^{92} -3.98736e12 q^{93} -7.31947e11 q^{94} +1.01415e13 q^{95} +3.65351e12 q^{96} +8.83232e12 q^{97} -1.61163e12 q^{98} +5.52778e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	66.7973	0.738013	0.369007	−	0.929427i	$-0.379698\pi$
$2$	66.7973	0.738013	0.369007	+	0.929427i	$0.379698\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−3730.11	−0.455336
$5$	36075.7	1.03255	0.516274	−	0.856424i	$-0.327319\pi$
$5$	36075.7	1.03255	0.516274	+	0.856424i	$0.327319\pi$
$6$	48695.3	0.426092
$7$	−269744.	−0.866592	−0.433296	−	0.901252i	$-0.642649\pi$
$7$	−269744.	−0.866592	−0.433296	+	0.901252i	$0.642649\pi$
$8$	−796366.	−1.07406
$9$	531441.	0.333333
$10$	2.40976e6	0.762034
$11$	1.04015e7	1.77029	0.885143	−	0.465320i	$-0.154061\pi$
$11$	1.04015e7	1.77029	0.885143	+	0.465320i	$0.154061\pi$
$12$	−2.71925e6	−0.262888
$13$	−7.55745e6	−0.434254	−0.217127	−	0.976143i	$-0.569669\pi$
$13$	−7.55745e6	−0.434254	−0.217127	+	0.976143i	$0.569669\pi$
$14$	−1.80182e7	−0.639556
$15$	2.62992e7	0.596141
$16$	−2.26380e7	−0.337333
$17$	−1.33275e8	−1.33916	−0.669579	−	0.742741i	$-0.733525\pi$
$17$	−1.33275e8	−1.33916	−0.669579	+	0.742741i	$0.733525\pi$
$18$	3.54989e7	0.246004
$19$	2.81117e8	1.37085	0.685423	−	0.728145i	$-0.259617\pi$
$19$	2.81117e8	1.37085	0.685423	+	0.728145i	$0.259617\pi$
$20$	−1.34567e8	−0.470156
$21$	−1.96643e8	−0.500327
$22$	6.94792e8	1.30649
$23$	2.81992e8	0.397197	0.198599	−	0.980081i	$-0.436361\pi$
$23$	2.81992e8	0.397197	0.198599	+	0.980081i	$0.436361\pi$
$24$	−5.80551e8	−0.620107
$25$	8.07543e7	0.0661540
$26$	−5.04818e8	−0.320485
$27$	3.87420e8	0.192450
$28$	1.00618e9	0.394590
$29$	3.19316e9	0.996858	0.498429	−	0.866930i	$-0.333910\pi$
$29$	3.19316e9	0.996858	0.498429	+	0.866930i	$0.333910\pi$
$30$	1.75672e9	0.439960
$31$	−5.46963e9	−1.10690	−0.553449	−	0.832883i	$-0.686688\pi$
$31$	−5.46963e9	−1.10690	−0.553449	+	0.832883i	$0.686688\pi$
$32$	5.01167e9	0.825102
$33$	7.58269e9	1.02207
$34$	−8.90243e9	−0.988316
$35$	−9.73121e9	−0.894797
$36$	−1.98234e9	−0.151779
$37$	−7.12239e9	−0.456367	−0.228184	−	0.973618i	$-0.573279\pi$
$37$	−7.12239e9	−0.456367	−0.228184	+	0.973618i	$0.573279\pi$
$38$	1.87779e10	1.01170
$39$	−5.50938e9	−0.250717
$40$	−2.87295e10	−1.10902
$41$	2.84811e10	0.936400	0.468200	−	0.883622i	$-0.344903\pi$
$41$	2.84811e10	0.936400	0.468200	+	0.883622i	$0.344903\pi$
$42$	−1.31353e10	−0.369248
$43$	−4.95408e10	−1.19514	−0.597569	−	0.801817i	$-0.703867\pi$
$43$	−4.95408e10	−1.19514	−0.597569	+	0.801817i	$0.703867\pi$
$44$	−3.87988e10	−0.806075
$45$	1.91721e10	0.344182
$46$	1.88363e10	0.293137
$47$	−1.09577e10	−0.148281	−0.0741403	−	0.997248i	$-0.523621\pi$
$47$	−1.09577e10	−0.148281	−0.0741403	+	0.997248i	$0.523621\pi$
$48$	−1.65031e10	−0.194759
$49$	−2.41272e10	−0.249019
$50$	5.39418e9	0.0488225
$51$	−9.71577e10	−0.773163
$52$	2.81902e10	0.197731
$53$	2.87608e11	1.78241	0.891205	−	0.453601i	$-0.149861\pi$
$53$	2.87608e11	1.78241	0.891205	+	0.453601i	$0.149861\pi$
$54$	2.58787e10	0.142031
$55$	3.75241e11	1.82790
$56$	2.14815e11	0.930769
$57$	2.04934e11	0.791458
$58$	2.13295e11	0.735695
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−9.80990e10	−0.271445
$61$	1.11011e11	0.275882	0.137941	−	0.990440i	$-0.455952\pi$
$61$	1.11011e11	0.275882	0.137941	+	0.990440i	$0.455952\pi$
$62$	−3.65357e11	−0.816905
$63$	−1.43353e11	−0.288864
$64$	5.20217e11	0.946269
$65$	−2.72641e11	−0.448388
$66$	5.06504e11	0.754305
$67$	9.50274e11	1.28340	0.641701	−	0.766955i	$-0.278229\pi$
$67$	9.50274e11	1.28340	0.641701	+	0.766955i	$0.278229\pi$
$68$	4.97132e11	0.609767
$69$	2.05572e11	0.229322
$70$	−6.50019e11	−0.660372
$71$	2.78596e11	0.258104	0.129052	−	0.991638i	$-0.458807\pi$
$71$	2.78596e11	0.258104	0.129052	+	0.991638i	$0.458807\pi$
$72$	−4.23221e11	−0.358019
$73$	5.64617e11	0.436672	0.218336	−	0.975874i	$-0.429937\pi$
$73$	5.64617e11	0.436672	0.218336	+	0.975874i	$0.429937\pi$
$74$	−4.75757e11	−0.336805
$75$	5.88699e10	0.0381940
$76$	−1.04860e12	−0.624196
$77$	−2.80574e12	−1.53411
$78$	−3.68012e11	−0.185032
$79$	1.36889e12	0.633565	0.316783	−	0.948498i	$-0.397397\pi$
$79$	1.36889e12	0.633565	0.316783	+	0.948498i	$0.397397\pi$
$80$	−8.16683e11	−0.348312
$81$	2.82430e11	0.111111
$82$	1.90246e12	0.691076
$83$	2.62840e12	0.882437	0.441218	−	0.897400i	$-0.354546\pi$
$83$	2.62840e12	0.882437	0.441218	+	0.897400i	$0.354546\pi$
$84$	7.33502e11	0.227817
$85$	−4.80800e12	−1.38274
$86$	−3.30920e12	−0.882028
$87$	2.32781e12	0.575536
$88$	−8.28339e12	−1.90139
$89$	−7.86312e12	−1.67710	−0.838552	−	0.544822i	$-0.816597\pi$
$89$	−7.86312e12	−1.67710	−0.838552	+	0.544822i	$0.816597\pi$
$90$	1.28065e12	0.254011
$91$	2.03858e12	0.376321
$92$	−1.05186e12	−0.180858
$93$	−3.98736e12	−0.639067
$94$	−7.31947e11	−0.109433
$95$	1.01415e13	1.41546
$96$	3.65351e12	0.476373
$97$	8.83232e12	1.07661	0.538305	−	0.842750i	$-0.319065\pi$
$97$	8.83232e12	1.07661	0.538305	+	0.842750i	$0.319065\pi$
$98$	−1.61163e12	−0.183779
$99$	5.52778e12	0.590095
$100$	−3.01223e11	−0.0301223
$101$	1.31591e13	1.23349	0.616746	−	0.787163i	$-0.288451\pi$
$101$	1.31591e13	1.23349	0.616746	+	0.787163i	$0.288451\pi$
$102$	−6.48987e12	−0.570604
$103$	7.79654e12	0.643368	0.321684	−	0.946847i	$-0.395751\pi$
$103$	7.79654e12	0.643368	0.321684	+	0.946847i	$0.395751\pi$
$104$	6.01850e12	0.466414
$105$	−7.09405e12	−0.516611
$106$	1.92114e13	1.31544
$107$	9.30476e12	0.599391	0.299696	−	0.954035i	$-0.403115\pi$
$107$	9.30476e12	0.599391	0.299696	+	0.954035i	$0.403115\pi$
$108$	−1.44512e12	−0.0876295
$109$	−1.22871e13	−0.701740	−0.350870	−	0.936424i	$-0.614114\pi$
$109$	−1.22871e13	−0.701740	−0.350870	+	0.936424i	$0.614114\pi$
$110$	2.50651e13	1.34902
$111$	−5.19222e12	−0.263484
$112$	6.10647e12	0.292330
$113$	2.41725e13	1.09222	0.546112	−	0.837712i	$-0.316107\pi$
$113$	2.41725e13	1.09222	0.546112	+	0.837712i	$0.316107\pi$
$114$	1.36891e13	0.584107
$115$	1.01731e13	0.410125
$116$	−1.19108e13	−0.453906
$117$	−4.01634e12	−0.144751
$118$	−2.81755e12	−0.0960812
$119$	3.59502e13	1.16050
$120$	−2.09438e13	−0.640290
$121$	7.36684e13	2.13391
$122$	7.41527e12	0.203605
$123$	2.07627e13	0.540631
$124$	2.04024e13	0.504010
$125$	−4.11245e13	−0.964240
$126$	−9.57560e12	−0.213185
$127$	5.48079e13	1.15909	0.579547	−	0.814939i	$-0.303230\pi$
$127$	5.48079e13	1.15909	0.579547	+	0.814939i	$0.303230\pi$
$128$	−6.30648e12	−0.126742
$129$	−3.61153e13	−0.690014
$130$	−1.82117e13	−0.330916
$131$	−7.41441e13	−1.28178	−0.640889	−	0.767633i	$-0.721434\pi$
$131$	−7.41441e13	−1.28178	−0.640889	+	0.767633i	$0.721434\pi$
$132$	−2.82843e13	−0.465388
$133$	−7.58296e13	−1.18796
$134$	6.34758e13	0.947168
$135$	1.39765e13	0.198714
$136$	1.06136e14	1.43833
$137$	4.34145e13	0.560985	0.280493	−	0.959856i	$-0.409502\pi$
$137$	4.34145e13	0.560985	0.280493	+	0.959856i	$0.409502\pi$
$138$	1.37317e13	0.169243
$139$	−6.68955e13	−0.786684	−0.393342	−	0.919392i	$-0.628681\pi$
$139$	−6.68955e13	−0.786684	−0.393342	+	0.919392i	$0.628681\pi$
$140$	3.62985e13	0.407433
$141$	−7.98818e12	−0.0856098
$142$	1.86095e13	0.190484
$143$	−7.86088e13	−0.768753
$144$	−1.20308e13	−0.112444
$145$	1.15195e14	1.02930
$146$	3.77149e13	0.322270
$147$	−1.75887e13	−0.143771
$148$	2.65673e13	0.207801
$149$	6.45815e13	0.483501	0.241751	−	0.970338i	$-0.422278\pi$
$149$	6.45815e13	0.483501	0.241751	+	0.970338i	$0.422278\pi$
$150$	3.93235e12	0.0281877
$151$	1.68635e14	1.15770	0.578852	−	0.815433i	$-0.303501\pi$
$151$	1.68635e14	1.15770	0.578852	+	0.815433i	$0.303501\pi$
$152$	−2.23872e14	−1.47237
$153$	−7.08279e13	−0.446386
$154$	−1.87416e14	−1.13220
$155$	−1.97321e14	−1.14292
$156$	2.05506e13	0.114160
$157$	2.08951e14	1.11352	0.556758	−	0.830674i	$-0.312045\pi$
$157$	2.08951e14	1.11352	0.556758	+	0.830674i	$0.312045\pi$
$158$	9.14380e13	0.467580
$159$	2.09666e14	1.02907
$160$	1.80800e14	0.851956
$161$	−7.60657e13	−0.344208
$162$	1.88655e13	0.0820015
$163$	9.07004e13	0.378782	0.189391	−	0.981902i	$-0.439349\pi$
$163$	9.07004e13	0.378782	0.189391	+	0.981902i	$0.439349\pi$
$164$	−1.06238e14	−0.426377
$165$	2.73551e14	1.05534
$166$	1.75570e14	0.651250
$167$	−4.26672e14	−1.52208	−0.761040	−	0.648705i	$-0.775311\pi$
$167$	−4.26672e14	−1.52208	−0.761040	+	0.648705i	$0.775311\pi$
$168$	1.56600e14	0.537380
$169$	−2.45760e14	−0.811424
$170$	−3.21162e14	−1.02048
$171$	1.49397e14	0.456949
$172$	1.84793e14	0.544190
$173$	−3.01561e14	−0.855214	−0.427607	−	0.903965i	$-0.640643\pi$
$173$	−3.01561e14	−0.855214	−0.427607	+	0.903965i	$0.640643\pi$
$174$	1.55492e14	0.424754
$175$	−2.17830e13	−0.0573285
$176$	−2.35469e14	−0.597175
$177$	−3.07496e13	−0.0751646
$178$	−5.25236e14	−1.23773
$179$	2.66888e14	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$179$	2.66888e14	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$180$	−7.15142e13	−0.156719
$181$	3.88509e14	0.821279	0.410640	−	0.911798i	$-0.365305\pi$
$181$	3.88509e14	0.821279	0.410640	+	0.911798i	$0.365305\pi$
$182$	1.36172e14	0.277730
$183$	8.09274e13	0.159281
$184$	−2.24569e14	−0.426613
$185$	−2.56945e14	−0.471221
$186$	−2.66345e14	−0.471640
$187$	−1.38626e15	−2.37069
$188$	4.08736e13	0.0675175
$189$	−1.04504e14	−0.166776
$190$	6.77425e14	1.04463
$191$	3.48286e14	0.519062	0.259531	−	0.965735i	$-0.416432\pi$
$191$	3.48286e14	0.519062	0.259531	+	0.965735i	$0.416432\pi$
$192$	3.79238e14	0.546329
$193$	1.27197e15	1.77155	0.885777	−	0.464111i	$-0.153626\pi$
$193$	1.27197e15	1.77155	0.885777	+	0.464111i	$0.153626\pi$
$194$	5.89976e14	0.794553
$195$	−1.98755e14	−0.258877
$196$	8.99973e13	0.113387
$197$	7.47060e14	0.910595	0.455297	−	0.890339i	$-0.349533\pi$
$197$	7.47060e14	0.910595	0.455297	+	0.890339i	$0.349533\pi$
$198$	3.69241e14	0.435498
$199$	6.97898e14	0.796612	0.398306	−	0.917253i	$-0.369598\pi$
$199$	6.97898e14	0.796612	0.398306	+	0.917253i	$0.369598\pi$
$200$	−6.43100e13	−0.0710532
$201$	6.92750e14	0.740972
$202$	8.78991e14	0.910333
$203$	−8.61335e14	−0.863869
$204$	3.62409e14	0.352049
$205$	1.02748e15	0.966877
$206$	5.20788e14	0.474815
$207$	1.49862e14	0.132399
$208$	1.71086e14	0.146488
$209$	2.92404e15	2.42679
$210$	−4.73864e14	−0.381266
$211$	−1.54920e15	−1.20857	−0.604286	−	0.796768i	$-0.706541\pi$
$211$	−1.54920e15	−1.20857	−0.604286	+	0.796768i	$0.706541\pi$
$212$	−1.07281e15	−0.811596
$213$	2.03096e14	0.149017
$214$	6.21533e14	0.442359
$215$	−1.78722e15	−1.23404
$216$	−3.08528e14	−0.206702
$217$	1.47540e15	0.959228
$218$	−8.20744e14	−0.517893
$219$	4.11606e14	0.252113
$220$	−1.39969e15	−0.832311
$221$	1.00722e15	0.581534
$222$	−3.46827e14	−0.194455
$223$	−1.50741e15	−0.820823	−0.410412	−	0.911900i	$-0.634615\pi$
$223$	−1.50741e15	−0.820823	−0.410412	+	0.911900i	$0.634615\pi$
$224$	−1.35187e15	−0.715026
$225$	4.29162e13	0.0220513
$226$	1.61466e15	0.806075
$227$	3.92080e15	1.90198	0.950990	−	0.309221i	$-0.100068\pi$
$227$	3.92080e15	1.90198	0.950990	+	0.309221i	$0.100068\pi$
$228$	−7.64428e14	−0.360380
$229$	1.37291e15	0.629090	0.314545	−	0.949243i	$-0.398148\pi$
$229$	1.37291e15	0.629090	0.314545	+	0.949243i	$0.398148\pi$
$230$	6.79534e14	0.302678
$231$	−2.04538e15	−0.885721
$232$	−2.54292e15	−1.07068
$233$	−3.53572e15	−1.44765	−0.723827	−	0.689982i	$-0.757618\pi$
$233$	−3.53572e15	−1.44765	−0.723827	+	0.689982i	$0.757618\pi$
$234$	−2.68281e14	−0.106828
$235$	−3.95308e14	−0.153107
$236$	1.57338e14	0.0592797
$237$	9.97918e14	0.365789
$238$	2.40138e15	0.856466
$239$	3.42983e15	1.19038	0.595191	−	0.803584i	$-0.297076\pi$
$239$	3.42983e15	1.19038	0.595191	+	0.803584i	$0.297076\pi$
$240$	−5.95362e14	−0.201098
$241$	3.54669e15	1.16604	0.583019	−	0.812458i	$-0.301871\pi$
$241$	3.54669e15	1.16604	0.583019	+	0.812458i	$0.301871\pi$
$242$	4.92085e15	1.57485
$243$	2.05891e14	0.0641500
$244$	−4.14085e14	−0.125619
$245$	−8.70407e14	−0.257124
$246$	1.38689e15	0.398993
$247$	−2.12453e15	−0.595295
$248$	4.35583e15	1.18887
$249$	1.91610e15	0.509475
$250$	−2.74701e15	−0.711622
$251$	2.73465e15	0.690275	0.345137	−	0.938552i	$-0.387832\pi$
$251$	2.73465e15	0.690275	0.345137	+	0.938552i	$0.387832\pi$
$252$	5.34723e14	0.131530
$253$	2.93314e15	0.703153
$254$	3.66102e15	0.855427
$255$	−3.50503e15	−0.798327
$256$	−4.68287e15	−1.03981
$257$	6.15631e15	1.33277	0.666385	−	0.745608i	$-0.267841\pi$
$257$	6.15631e15	1.33277	0.666385	+	0.745608i	$0.267841\pi$
$258$	−2.41240e15	−0.509239
$259$	1.92122e15	0.395484
$260$	1.01698e15	0.204167
$261$	1.69698e15	0.332286
$262$	−4.95263e15	−0.945970
$263$	−7.90796e15	−1.47351	−0.736753	−	0.676162i	$-0.763642\pi$
$263$	−7.90796e15	−1.47351	−0.736753	+	0.676162i	$0.763642\pi$
$264$	−6.03859e15	−1.09777
$265$	1.03757e16	1.84042
$266$	−5.06522e15	−0.876733
$267$	−5.73222e15	−0.968276
$268$	−3.54463e15	−0.584379
$269$	5.00304e15	0.805089	0.402544	−	0.915400i	$-0.368126\pi$
$269$	5.00304e15	0.805089	0.402544	+	0.915400i	$0.368126\pi$
$270$	9.33591e14	0.146653
$271$	6.11108e15	0.937168	0.468584	−	0.883419i	$-0.344764\pi$
$271$	6.11108e15	0.937168	0.468584	+	0.883419i	$0.344764\pi$
$272$	3.01709e15	0.451742
$273$	1.48612e15	0.217269
$274$	2.89998e15	0.414015
$275$	8.39966e14	0.117111
$276$	−7.66808e14	−0.104419
$277$	1.15576e15	0.153727	0.0768634	−	0.997042i	$-0.475509\pi$
$277$	1.15576e15	0.153727	0.0768634	+	0.997042i	$0.475509\pi$
$278$	−4.46844e15	−0.580584
$279$	−2.90679e15	−0.368966
$280$	7.74960e15	0.961063
$281$	−1.61496e16	−1.95691	−0.978453	−	0.206470i	$-0.933802\pi$
$281$	−1.61496e16	−1.95691	−0.978453	+	0.206470i	$0.933802\pi$
$282$	−5.33589e14	−0.0631812
$283$	3.53645e15	0.409219	0.204609	−	0.978844i	$-0.434408\pi$
$283$	3.53645e15	0.409219	0.204609	+	0.978844i	$0.434408\pi$
$284$	−1.03919e15	−0.117524
$285$	7.39315e15	0.817218
$286$	−5.25086e15	−0.567350
$287$	−7.68260e15	−0.811476
$288$	2.66341e15	0.275034
$289$	7.85772e15	0.793342
$290$	7.69475e15	0.759640
$291$	6.43876e15	0.621582
$292$	−2.10609e15	−0.198833
$293$	−9.99081e15	−0.922489	−0.461245	−	0.887273i	$-0.652597\pi$
$293$	−9.99081e15	−0.922489	−0.461245	+	0.887273i	$0.652597\pi$
$294$	−1.17488e15	−0.106105
$295$	−1.52169e15	−0.134426
$296$	5.67203e15	0.490165
$297$	4.02975e15	0.340692
$298$	4.31387e15	0.356830
$299$	−2.13114e15	−0.172484
$300$	−2.19592e14	−0.0173911
$301$	1.33633e16	1.03570
$302$	1.12644e16	0.854401
$303$	9.59296e15	0.712156
$304$	−6.36393e15	−0.462431
$305$	4.00482e15	0.284862
$306$	−4.73112e15	−0.329439
$307$	−6.51657e15	−0.444242	−0.222121	−	0.975019i	$-0.571298\pi$
$307$	−6.51657e15	−0.444242	−0.222121	+	0.975019i	$0.571298\pi$
$308$	1.04657e16	0.698538
$309$	5.68368e15	0.371449
$310$	−1.31805e16	−0.843493
$311$	−8.66465e15	−0.543011	−0.271506	−	0.962437i	$-0.587522\pi$
$311$	−8.66465e15	−0.543011	−0.271506	+	0.962437i	$0.587522\pi$
$312$	4.38748e15	0.269284
$313$	3.17591e16	1.90911	0.954553	−	0.298040i	$-0.0963328\pi$
$313$	3.17591e16	1.90911	0.954553	+	0.298040i	$0.0963328\pi$
$314$	1.39574e16	0.821790
$315$	−5.17156e15	−0.298266
$316$	−5.10610e15	−0.288485
$317$	−2.76487e15	−0.153035	−0.0765173	−	0.997068i	$-0.524380\pi$
$317$	−2.76487e15	−0.153035	−0.0765173	+	0.997068i	$0.524380\pi$
$318$	1.40051e16	0.759471
$319$	3.32136e16	1.76472
$320$	1.87672e16	0.977067
$321$	6.78317e15	0.346059
$322$	−5.08099e15	−0.254030
$323$	−3.74659e16	−1.83578
$324$	−1.05349e15	−0.0505929
$325$	−6.10297e14	−0.0287276
$326$	6.05855e15	0.279547
$327$	−8.95727e15	−0.405150
$328$	−2.26814e16	−1.00575
$329$	2.95578e15	0.128499
$330$	1.82725e16	0.778855
$331$	1.88942e16	0.789672	0.394836	−	0.918752i	$-0.370801\pi$
$331$	1.88942e16	0.789672	0.394836	+	0.918752i	$0.370801\pi$
$332$	−9.80423e15	−0.401805
$333$	−3.78513e15	−0.152122
$334$	−2.85006e16	−1.12332
$335$	3.42818e16	1.32517
$336$	4.45162e15	0.168777
$337$	2.73402e15	0.101673	0.0508367	−	0.998707i	$-0.483811\pi$
$337$	2.73402e15	0.101673	0.0508367	+	0.998707i	$0.483811\pi$
$338$	−1.64161e16	−0.598842
$339$	1.76217e16	0.630595
$340$	1.79344e16	0.629613
$341$	−5.68924e16	−1.95952
$342$	9.97933e15	0.337234
$343$	3.26434e16	1.08239
$344$	3.94526e16	1.28365
$345$	7.41617e15	0.236786
$346$	−2.01435e16	−0.631160
$347$	4.42948e16	1.36211	0.681053	−	0.732234i	$-0.261522\pi$
$347$	4.42948e16	1.36211	0.681053	+	0.732234i	$0.261522\pi$
$348$	−8.68301e15	−0.262063
$349$	−1.74421e16	−0.516695	−0.258348	−	0.966052i	$-0.583178\pi$
$349$	−1.74421e16	−0.516695	−0.258348	+	0.966052i	$0.583178\pi$
$350$	−1.45505e15	−0.0423092
$351$	−2.92791e15	−0.0835722
$352$	5.21288e16	1.46067
$353$	4.68774e16	1.28952	0.644760	−	0.764385i	$-0.276957\pi$
$353$	4.68774e16	1.28952	0.644760	+	0.764385i	$0.276957\pi$
$354$	−2.05399e15	−0.0554725
$355$	1.00505e16	0.266505
$356$	2.93303e16	0.763646
$357$	2.62077e16	0.670016
$358$	1.78274e16	0.447557
$359$	4.02884e15	0.0993268	0.0496634	−	0.998766i	$-0.484185\pi$
$359$	4.02884e15	0.0993268	0.0496634	+	0.998766i	$0.484185\pi$
$360$	−1.52680e16	−0.369672
$361$	3.69738e16	0.879219
$362$	2.59514e16	0.606115
$363$	5.37042e16	1.23201
$364$	−7.60413e15	−0.171352
$365$	2.03690e16	0.450885
$366$	5.40573e15	0.117551
$367$	−1.29453e16	−0.276555	−0.138277	−	0.990394i	$-0.544157\pi$
$367$	−1.29453e16	−0.276555	−0.138277	+	0.990394i	$0.544157\pi$
$368$	−6.38375e15	−0.133988
$369$	1.51360e16	0.312133
$370$	−1.71633e16	−0.347767
$371$	−7.75805e16	−1.54462
$372$	1.48733e16	0.290991
$373$	−7.16111e16	−1.37681	−0.688403	−	0.725328i	$-0.741688\pi$
$373$	−7.16111e16	−1.37681	−0.688403	+	0.725328i	$0.741688\pi$
$374$	−9.25986e16	−1.74960
$375$	−2.99797e16	−0.556704
$376$	8.72635e15	0.159262
$377$	−2.41321e16	−0.432890
$378$	−6.98061e15	−0.123083
$379$	−7.79312e16	−1.35069	−0.675347	−	0.737501i	$-0.736006\pi$
$379$	−7.79312e16	−1.35069	−0.675347	+	0.737501i	$0.736006\pi$
$380$	−3.78289e16	−0.644512
$381$	3.99549e16	0.669203
$382$	2.32646e16	0.383075
$383$	−2.34127e16	−0.379017	−0.189509	−	0.981879i	$-0.560690\pi$
$383$	−2.34127e16	−0.379017	−0.189509	+	0.981879i	$0.560690\pi$
$384$	−4.59742e15	−0.0731748
$385$	−1.01219e17	−1.58405
$386$	8.49642e16	1.30743
$387$	−2.63280e16	−0.398380
$388$	−3.29456e16	−0.490220
$389$	−1.24503e17	−1.82182	−0.910911	−	0.412602i	$-0.864620\pi$
$389$	−1.24503e17	−1.82182	−0.910911	+	0.412602i	$0.864620\pi$
$390$	−1.32763e16	−0.191054
$391$	−3.75826e16	−0.531910
$392$	1.92141e16	0.267461
$393$	−5.40510e16	−0.740035
$394$	4.99016e16	0.672031
$395$	4.93836e16	0.654186
$396$	−2.06193e16	−0.268692
$397$	5.19525e16	0.665991	0.332996	−	0.942928i	$-0.391941\pi$
$397$	5.19525e16	0.665991	0.332996	+	0.942928i	$0.391941\pi$
$398$	4.66177e16	0.587910
$399$	−5.52798e16	−0.685871
$400$	−1.82812e15	−0.0223159
$401$	−4.99087e16	−0.599429	−0.299715	−	0.954029i	$-0.596891\pi$
$401$	−4.99087e16	−0.599429	−0.299715	+	0.954029i	$0.596891\pi$
$402$	4.62738e16	0.546847
$403$	4.13365e16	0.480674
$404$	−4.90848e16	−0.561653
$405$	1.01888e16	0.114727
$406$	−5.75349e16	−0.637547
$407$	−7.40835e16	−0.807900
$408$	7.73730e16	0.830421
$409$	−1.76276e16	−0.186205	−0.0931027	−	0.995657i	$-0.529678\pi$
$409$	−1.76276e16	−0.186205	−0.0931027	+	0.995657i	$0.529678\pi$
$410$	6.86327e16	0.713569
$411$	3.16492e16	0.323885
$412$	−2.90820e16	−0.292949
$413$	1.13779e16	0.112821
$414$	1.00104e16	0.0977123
$415$	9.48214e16	0.911158
$416$	−3.78754e16	−0.358303
$417$	−4.87668e16	−0.454192
$418$	1.95318e17	1.79100
$419$	−1.36737e17	−1.23451	−0.617254	−	0.786764i	$-0.711755\pi$
$419$	−1.36737e17	−1.23451	−0.617254	+	0.786764i	$0.711755\pi$
$420$	2.64616e16	0.235232
$421$	−1.16180e17	−1.01695	−0.508474	−	0.861077i	$-0.669790\pi$
$421$	−1.16180e17	−1.01695	−0.508474	+	0.861077i	$0.669790\pi$
$422$	−1.03483e17	−0.891942
$423$	−5.82338e15	−0.0494269
$424$	−2.29041e17	−1.91441
$425$	−1.07626e16	−0.0885905
$426$	1.35663e16	0.109976
$427$	−2.99447e16	−0.239077
$428$	−3.47078e16	−0.272925
$429$	−5.73058e16	−0.443840
$430$	−1.19382e17	−0.910736
$431$	−2.00159e17	−1.50408	−0.752042	−	0.659116i	$-0.770931\pi$
$431$	−2.00159e17	−1.50408	−0.752042	+	0.659116i	$0.770931\pi$
$432$	−8.77043e15	−0.0649197
$433$	1.95873e17	1.42825	0.714123	−	0.700020i	$-0.246826\pi$
$433$	1.95873e17	1.42825	0.714123	+	0.700020i	$0.246826\pi$
$434$	9.85529e16	0.707923
$435$	8.39775e16	0.594269
$436$	4.58322e16	0.319527
$437$	7.92728e16	0.544496
$438$	2.74942e16	0.186063
$439$	−7.85789e16	−0.523946	−0.261973	−	0.965075i	$-0.584373\pi$
$439$	−7.85789e16	−0.523946	−0.261973	+	0.965075i	$0.584373\pi$
$440$	−2.98829e17	−1.96327
$441$	−1.28222e16	−0.0830064
$442$	6.72797e16	0.429180
$443$	−1.51027e17	−0.949358	−0.474679	−	0.880159i	$-0.657436\pi$
$443$	−1.51027e17	−0.949358	−0.474679	+	0.880159i	$0.657436\pi$
$444$	1.93676e16	0.119974
$445$	−2.83668e17	−1.73169
$446$	−1.00691e17	−0.605779
$447$	4.70799e16	0.279150
$448$	−1.40325e17	−0.820029
$449$	−2.18212e17	−1.25683	−0.628416	−	0.777878i	$-0.716296\pi$
$449$	−2.18212e17	−1.25683	−0.628416	+	0.777878i	$0.716296\pi$
$450$	2.86669e15	0.0162742
$451$	2.96246e17	1.65770
$452$	−9.01661e16	−0.497329
$453$	1.22935e17	0.668401
$454$	2.61899e17	1.40369
$455$	7.35431e16	0.388569
$456$	−1.63203e17	−0.850072
$457$	1.89865e17	0.974969	0.487484	−	0.873132i	$-0.337915\pi$
$457$	1.89865e17	0.974969	0.487484	+	0.873132i	$0.337915\pi$
$458$	9.17071e16	0.464277
$459$	−5.16336e16	−0.257721
$460$	−3.79467e16	−0.186745
$461$	2.49093e17	1.20866	0.604331	−	0.796733i	$-0.293441\pi$
$461$	2.49093e17	1.20866	0.604331	+	0.796733i	$0.293441\pi$
$462$	−1.36626e17	−0.653674
$463$	−3.15470e17	−1.48827	−0.744135	−	0.668029i	$-0.767138\pi$
$463$	−3.15470e17	−1.48827	−0.744135	+	0.668029i	$0.767138\pi$
$464$	−7.22868e16	−0.336273
$465$	−1.43847e17	−0.659867
$466$	−2.36177e17	−1.06839
$467$	−2.61403e17	−1.16614	−0.583071	−	0.812421i	$-0.698149\pi$
$467$	−2.61403e17	−1.16614	−0.583071	+	0.812421i	$0.698149\pi$
$468$	1.49814e16	0.0659105
$469$	−2.56331e17	−1.11219
$470$	−2.64055e16	−0.112995
$471$	1.52325e17	0.642889
$472$	3.35911e16	0.139830
$473$	−5.15299e17	−2.11574
$474$	6.66583e16	0.269957
$475$	2.27014e16	0.0906869
$476$	−1.34098e17	−0.528419
$477$	1.52847e17	0.594137
$478$	2.29104e17	0.878518
$479$	1.91515e16	0.0724472	0.0362236	−	0.999344i	$-0.488467\pi$
$479$	1.91515e16	0.0724472	0.0362236	+	0.999344i	$0.488467\pi$
$480$	1.31803e17	0.491877
$481$	5.38271e16	0.198179
$482$	2.36910e17	0.860552
$483$	−5.54519e16	−0.198728
$484$	−2.74791e17	−0.971647
$485$	3.18632e17	1.11165
$486$	1.37530e16	0.0473436
$487$	8.83888e15	0.0300233	0.0150117	−	0.999887i	$-0.495221\pi$
$487$	8.83888e15	0.0300233	0.0150117	+	0.999887i	$0.495221\pi$
$488$	−8.84057e16	−0.296314
$489$	6.61206e16	0.218690
$490$	−5.81409e16	−0.189761
$491$	2.01895e17	0.650272	0.325136	−	0.945667i	$-0.394590\pi$
$491$	2.01895e17	0.650272	0.325136	+	0.945667i	$0.394590\pi$
$492$	−7.74473e16	−0.246169
$493$	−4.25569e17	−1.33495
$494$	−1.41913e17	−0.439336
$495$	1.99419e17	0.609301
$496$	1.23822e17	0.373393
$497$	−7.51495e16	−0.223671
$498$	1.27991e17	0.376000
$499$	−2.92605e17	−0.848452	−0.424226	−	0.905556i	$-0.639454\pi$
$499$	−2.92605e17	−0.848452	−0.424226	+	0.905556i	$0.639454\pi$
$500$	1.53399e17	0.439053
$501$	−3.11044e17	−0.878773
$502$	1.82667e17	0.509432
$503$	2.49375e17	0.686532	0.343266	−	0.939238i	$-0.388467\pi$
$503$	2.49375e17	0.686532	0.343266	+	0.939238i	$0.388467\pi$
$504$	1.14161e17	0.310256
$505$	4.74723e17	1.27364
$506$	1.95926e17	0.518936
$507$	−1.79159e17	−0.468476
$508$	−2.04440e17	−0.527777
$509$	−3.19866e17	−0.815271	−0.407635	−	0.913145i	$-0.633647\pi$
$509$	−3.19866e17	−0.815271	−0.407635	+	0.913145i	$0.633647\pi$
$510$	−2.34127e17	−0.589176
$511$	−1.52302e17	−0.378417
$512$	−2.61141e17	−0.640649
$513$	1.08910e17	0.263819
$514$	4.11225e17	0.983602
$515$	2.81266e17	0.664308
$516$	1.34714e17	0.314188
$517$	−1.13977e17	−0.262499
$518$	1.28332e17	0.291873
$519$	−2.19838e17	−0.493758
$520$	2.17122e17	0.481594
$521$	5.68272e15	0.0124483	0.00622416	−	0.999981i	$-0.498019\pi$
$521$	5.68272e15	0.0124483	0.00622416	+	0.999981i	$0.498019\pi$
$522$	1.13353e17	0.245232
$523$	−2.23120e17	−0.476735	−0.238367	−	0.971175i	$-0.576612\pi$
$523$	−2.23120e17	−0.476735	−0.238367	+	0.971175i	$0.576612\pi$
$524$	2.76566e17	0.583640
$525$	−1.58798e16	−0.0330986
$526$	−5.28231e17	−1.08747
$527$	7.28967e17	1.48231
$528$	−1.71657e17	−0.344779
$529$	−4.24517e17	−0.842234
$530$	6.93067e17	1.35826
$531$	−2.24165e16	−0.0433963
$532$	2.82853e17	0.540923
$533$	−2.15244e17	−0.406635
$534$	−3.82897e17	−0.714601
$535$	3.35676e17	0.618900
$536$	−7.56765e17	−1.37845
$537$	1.94561e17	0.350125
$538$	3.34190e17	0.594166
$539$	−2.50959e17	−0.440835
$540$	−5.21338e16	−0.0904816
$541$	6.72211e17	1.15272	0.576360	−	0.817196i	$-0.304473\pi$
$541$	6.72211e17	1.15272	0.576360	+	0.817196i	$0.304473\pi$
$542$	4.08204e17	0.691643
$543$	2.83223e17	0.474166
$544$	−6.67931e17	−1.10494
$545$	−4.43265e17	−0.724579
$546$	9.92691e16	0.160347
$547$	−1.12671e18	−1.79844	−0.899218	−	0.437500i	$-0.855864\pi$
$547$	−1.12671e18	−1.79844	−0.899218	+	0.437500i	$0.855864\pi$
$548$	−1.61941e17	−0.255437
$549$	5.89961e16	0.0919608
$550$	5.61075e16	0.0864298
$551$	8.97651e17	1.36654
$552$	−1.63711e17	−0.246305
$553$	−3.69249e17	−0.549042
$554$	7.72018e16	0.113452
$555$	−1.87313e17	−0.272059
$556$	2.49528e17	0.358206
$557$	1.42157e17	0.201702	0.100851	−	0.994902i	$-0.467844\pi$
$557$	1.42157e17	0.201702	0.100851	+	0.994902i	$0.467844\pi$
$558$	−1.94166e17	−0.272302
$559$	3.74402e17	0.518994
$560$	2.20295e17	0.301844
$561$	−1.01058e18	−1.36872
$562$	−1.07875e18	−1.44422
$563$	−4.66727e17	−0.617673	−0.308836	−	0.951115i	$-0.599940\pi$
$563$	−4.66727e17	−0.617673	−0.308836	+	0.951115i	$0.599940\pi$
$564$	2.97968e16	0.0389813
$565$	8.72040e17	1.12777
$566$	2.36225e17	0.302009
$567$	−7.61837e16	−0.0962879
$568$	−2.21864e17	−0.277219
$569$	7.21466e17	0.891222	0.445611	−	0.895227i	$-0.352986\pi$
$569$	7.21466e17	0.891222	0.445611	+	0.895227i	$0.352986\pi$
$570$	4.93843e17	0.603118
$571$	−2.19647e17	−0.265211	−0.132605	−	0.991169i	$-0.542334\pi$
$571$	−2.19647e17	−0.265211	−0.132605	+	0.991169i	$0.542334\pi$
$572$	2.93220e17	0.350041
$573$	2.53901e17	0.299681
$574$	−5.13177e17	−0.598881
$575$	2.27721e16	0.0262762
$576$	2.76465e17	0.315423
$577$	6.19858e16	0.0699277	0.0349638	−	0.999389i	$-0.488868\pi$
$577$	6.19858e16	0.0699277	0.0349638	+	0.999389i	$0.488868\pi$
$578$	5.24875e17	0.585497
$579$	9.27266e17	1.02281
$580$	−4.29692e17	−0.468679
$581$	−7.08995e17	−0.764712
$582$	4.30092e17	0.458736
$583$	2.99155e18	3.15537
$584$	−4.49642e17	−0.469011
$585$	−1.44892e17	−0.149463
$586$	−6.67360e17	−0.680810
$587$	2.62939e17	0.265281	0.132641	−	0.991164i	$-0.457654\pi$
$587$	2.62939e17	0.265281	0.132641	+	0.991164i	$0.457654\pi$
$588$	6.56080e16	0.0654642
$589$	−1.53761e18	−1.51739
$590$	−1.01645e17	−0.0992083
$591$	5.44607e17	0.525732
$592$	1.61237e17	0.153948
$593$	1.03795e18	0.980213	0.490107	−	0.871663i	$-0.336958\pi$
$593$	1.03795e18	0.980213	0.490107	+	0.871663i	$0.336958\pi$
$594$	2.69177e17	0.251435
$595$	1.29693e18	1.19827
$596$	−2.40896e17	−0.220156
$597$	5.08767e17	0.459924
$598$	−1.42355e17	−0.127296
$599$	−1.10082e18	−0.973740	−0.486870	−	0.873475i	$-0.661861\pi$
$599$	−1.10082e18	−0.973740	−0.486870	+	0.873475i	$0.661861\pi$
$600$	−4.68820e16	−0.0410226
$601$	−7.27854e17	−0.630028	−0.315014	−	0.949087i	$-0.602009\pi$
$601$	−7.27854e17	−0.630028	−0.315014	+	0.949087i	$0.602009\pi$
$602$	8.92636e17	0.764358
$603$	5.05015e17	0.427801
$604$	−6.29028e17	−0.527145
$605$	2.65764e18	2.20336
$606$	6.40784e17	0.525581
$607$	−1.40498e18	−1.14011	−0.570053	−	0.821608i	$-0.693077\pi$
$607$	−1.40498e18	−1.14011	−0.570053	+	0.821608i	$0.693077\pi$
$608$	1.40887e18	1.13109
$609$	−6.27913e17	−0.498755
$610$	2.67511e17	0.210232
$611$	8.28125e16	0.0643914
$612$	2.64196e17	0.203256
$613$	8.32972e17	0.634070	0.317035	−	0.948414i	$-0.397313\pi$
$613$	8.32972e17	0.634070	0.317035	+	0.948414i	$0.397313\pi$
$614$	−4.35290e17	−0.327857
$615$	7.49030e17	0.558227
$616$	2.23439e18	1.64773
$617$	−2.11893e18	−1.54619	−0.773095	−	0.634290i	$-0.781292\pi$
$617$	−2.11893e18	−1.54619	−0.773095	+	0.634290i	$0.781292\pi$
$618$	3.79654e17	0.274134
$619$	−1.45912e17	−0.104256	−0.0521280	−	0.998640i	$-0.516600\pi$
$619$	−1.45912e17	−0.104256	−0.0521280	+	0.998640i	$0.516600\pi$
$620$	7.36030e17	0.520415
$621$	1.09250e17	0.0764407
$622$	−5.78776e17	−0.400749
$623$	2.12103e18	1.45336
$624$	1.24722e17	0.0845749
$625$	−1.58217e18	−1.06178
$626$	2.12143e18	1.40895
$627$	2.13162e18	1.40111
$628$	−7.79411e17	−0.507024
$629$	9.49238e17	0.611148
$630$	−3.45447e17	−0.220124
$631$	−4.40838e17	−0.278028	−0.139014	−	0.990290i	$-0.544393\pi$
$631$	−4.40838e17	−0.278028	−0.139014	+	0.990290i	$0.544393\pi$
$632$	−1.09013e18	−0.680486
$633$	−1.12937e18	−0.697769
$634$	−1.84686e17	−0.112942
$635$	1.97723e18	1.19682
$636$	−7.82079e17	−0.468575
$637$	1.82340e17	0.108137
$638$	2.21858e18	1.30239
$639$	1.48057e17	0.0860348
$640$	−2.27511e17	−0.130868
$641$	−2.84230e18	−1.61842	−0.809212	−	0.587517i	$-0.800106\pi$
$641$	−2.84230e18	−1.61842	−0.809212	+	0.587517i	$0.800106\pi$
$642$	4.53098e17	0.255396
$643$	1.88114e18	1.04966	0.524832	−	0.851206i	$-0.324128\pi$
$643$	1.88114e18	1.04966	0.524832	+	0.851206i	$0.324128\pi$
$644$	2.83734e17	0.156730
$645$	−1.30288e18	−0.712472
$646$	−2.50263e18	−1.35483
$647$	−3.13644e18	−1.68096	−0.840482	−	0.541839i	$-0.817728\pi$
$647$	−3.13644e18	−1.68096	−0.840482	+	0.541839i	$0.817728\pi$
$648$	−2.24917e17	−0.119340
$649$	−4.38741e17	−0.230472
$650$	−4.07662e16	−0.0212014
$651$	1.07557e18	0.553810
$652$	−3.38323e17	−0.172473
$653$	1.64408e18	0.829829	0.414914	−	0.909860i	$-0.363812\pi$
$653$	1.64408e18	0.829829	0.414914	+	0.909860i	$0.363812\pi$
$654$	−5.98322e17	−0.299006
$655$	−2.67480e18	−1.32350
$656$	−6.44755e17	−0.315878
$657$	3.00061e17	0.145557
$658$	1.97438e17	0.0948338
$659$	−2.42234e18	−1.15207	−0.576036	−	0.817425i	$-0.695401\pi$
$659$	−2.42234e18	−1.15207	−0.576036	+	0.817425i	$0.695401\pi$
$660$	−1.02038e18	−0.480535
$661$	−1.73436e18	−0.808778	−0.404389	−	0.914587i	$-0.632516\pi$
$661$	−1.73436e18	−0.808778	−0.404389	+	0.914587i	$0.632516\pi$
$662$	1.26208e18	0.582789
$663$	7.34264e17	0.335749
$664$	−2.09317e18	−0.947788
$665$	−2.73561e18	−1.22663
$666$	−2.52837e17	−0.112268
$667$	9.00446e17	0.395949
$668$	1.59154e18	0.693058
$669$	−1.09890e18	−0.473903
$670$	2.28993e18	0.977995
$671$	1.15469e18	0.488391
$672$	−9.85511e17	−0.412820
$673$	−1.75908e16	−0.00729772	−0.00364886	−	0.999993i	$-0.501161\pi$
$673$	−1.75908e16	−0.00729772	−0.00364886	+	0.999993i	$0.501161\pi$
$674$	1.82625e17	0.0750363
$675$	3.12859e16	0.0127313
$676$	9.16713e17	0.369471
$677$	5.81829e17	0.232257	0.116129	−	0.993234i	$-0.462952\pi$
$677$	5.81829e17	0.232257	0.116129	+	0.993234i	$0.462952\pi$
$678$	1.17709e18	0.465388
$679$	−2.38247e18	−0.932982
$680$	3.82893e18	1.48515
$681$	2.85826e18	1.09811
$682$	−3.80026e18	−1.44616
$683$	3.50818e18	1.32235	0.661176	−	0.750230i	$-0.270057\pi$
$683$	3.50818e18	1.32235	0.661176	+	0.750230i	$0.270057\pi$
$684$	−5.57268e17	−0.208065
$685$	1.56621e18	0.579244
$686$	2.18049e18	0.798818
$687$	1.00085e18	0.363205
$688$	1.12151e18	0.403159
$689$	−2.17358e18	−0.774018
$690$	4.95381e17	0.174751
$691$	−2.68406e18	−0.937961	−0.468981	−	0.883208i	$-0.655379\pi$
$691$	−2.68406e18	−0.937961	−0.468981	+	0.883208i	$0.655379\pi$
$692$	1.12486e18	0.389410
$693$	−1.49109e18	−0.511371
$694$	2.95877e18	1.00525
$695$	−2.41330e18	−0.812289
$696$	−1.85379e18	−0.618159
$697$	−3.79582e18	−1.25399
$698$	−1.16509e18	−0.381328
$699$	−2.57754e18	−0.835803
$700$	8.12531e16	0.0261037
$701$	−1.57761e18	−0.502148	−0.251074	−	0.967968i	$-0.580784\pi$
$701$	−1.57761e18	−0.502148	−0.251074	+	0.967968i	$0.580784\pi$
$702$	−1.95577e17	−0.0616774
$703$	−2.00222e18	−0.625609
$704$	5.41103e18	1.67517
$705$	−2.88179e17	−0.0883962
$706$	3.13129e18	0.951683
$707$	−3.54958e18	−1.06893
$708$	1.14700e17	0.0342252
$709$	−1.16804e18	−0.345348	−0.172674	−	0.984979i	$-0.555241\pi$
$709$	−1.16804e18	−0.345348	−0.172674	+	0.984979i	$0.555241\pi$
$710$	6.71350e17	0.196684
$711$	7.27482e17	0.211188
$712$	6.26192e18	1.80131
$713$	−1.54239e18	−0.439657
$714$	1.75060e18	0.494481
$715$	−2.83587e18	−0.793774
$716$	−9.95523e17	−0.276132
$717$	2.50035e18	0.687268
$718$	2.69116e17	0.0733045
$719$	−5.83232e18	−1.57436	−0.787180	−	0.616724i	$-0.788460\pi$
$719$	−5.83232e18	−1.57436	−0.787180	+	0.616724i	$0.788460\pi$
$720$	−4.34019e17	−0.116104
$721$	−2.10307e18	−0.557538
$722$	2.46975e18	0.648876
$723$	2.58554e18	0.673213
$724$	−1.44918e18	−0.373958
$725$	2.57861e17	0.0659461
$726$	3.58730e18	0.909243
$727$	3.99779e17	0.100426	0.0502131	−	0.998739i	$-0.484010\pi$
$727$	3.99779e17	0.100426	0.0502131	+	0.998739i	$0.484010\pi$
$728$	−1.62345e18	−0.404190
$729$	1.50095e17	0.0370370
$730$	1.36059e18	0.332759
$731$	6.60257e18	1.60048
$732$	−3.01868e17	−0.0725263
$733$	−5.86421e18	−1.39648	−0.698238	−	0.715866i	$-0.746032\pi$
$733$	−5.86421e18	−1.39648	−0.698238	+	0.715866i	$0.746032\pi$
$734$	−8.64709e17	−0.204101
$735$	−6.34526e17	−0.148451
$736$	1.41325e18	0.327728
$737$	9.88427e18	2.27199
$738$	1.01105e18	0.230359
$739$	2.01623e18	0.455357	0.227679	−	0.973736i	$-0.426886\pi$
$739$	2.01623e18	0.455357	0.227679	+	0.973736i	$0.426886\pi$
$740$	9.58435e17	0.214564
$741$	−1.54878e18	−0.343694
$742$	−5.18217e18	−1.13995
$743$	7.56368e18	1.64932	0.824661	−	0.565627i	$-0.191366\pi$
$743$	7.56368e18	1.64932	0.824661	+	0.565627i	$0.191366\pi$
$744$	3.17540e18	0.686395
$745$	2.32982e18	0.499238
$746$	−4.78343e18	−1.01610
$747$	1.39684e18	0.294146
$748$	5.17091e18	1.07946
$749$	−2.50990e18	−0.519427
$750$	−2.00257e18	−0.410855
$751$	7.77646e18	1.58169	0.790847	−	0.612014i	$-0.209641\pi$
$751$	7.77646e18	1.58169	0.790847	+	0.612014i	$0.209641\pi$
$752$	2.48061e17	0.0500199
$753$	1.99356e18	0.398530
$754$	−1.61196e18	−0.319478
$755$	6.08363e18	1.19538
$756$	3.89813e17	0.0759390
$757$	−6.02493e18	−1.16367	−0.581834	−	0.813308i	$-0.697665\pi$
$757$	−6.02493e18	−1.16367	−0.581834	+	0.813308i	$0.697665\pi$
$758$	−5.20560e18	−0.996830
$759$	2.13826e18	0.405965
$760$	−8.07634e18	−1.52029
$761$	5.12637e18	0.956775	0.478388	−	0.878149i	$-0.341221\pi$
$761$	5.12637e18	0.956775	0.478388	+	0.878149i	$0.341221\pi$
$762$	2.66888e18	0.493881
$763$	3.31436e18	0.608122
$764$	−1.29915e18	−0.236348
$765$	−2.55517e18	−0.460914
$766$	−1.56391e18	−0.279720
$767$	3.18777e17	0.0565350
$768$	−3.41381e18	−0.600333
$769$	−1.48785e18	−0.259440	−0.129720	−	0.991551i	$-0.541408\pi$
$769$	−1.48785e18	−0.259440	−0.129720	+	0.991551i	$0.541408\pi$
$770$	−6.76117e18	−1.16905
$771$	4.48795e18	0.769475
$772$	−4.74459e18	−0.806653
$773$	1.00543e19	1.69506	0.847529	−	0.530749i	$-0.178089\pi$
$773$	1.00543e19	1.69506	0.847529	+	0.530749i	$0.178089\pi$
$774$	−1.75864e18	−0.294009
$775$	−4.41697e17	−0.0732256
$776$	−7.03376e18	−1.15634
$777$	1.40057e18	0.228333
$778$	−8.31644e18	−1.34453
$779$	8.00652e18	1.28366
$780$	7.41379e17	0.117876
$781$	2.89781e18	0.456918
$782$	−2.51042e18	−0.392556
$783$	1.23710e18	0.191845
$784$	5.46192e17	0.0840023
$785$	7.53806e18	1.14976
$786$	−3.61046e18	−0.546156
$787$	1.08288e19	1.62459	0.812296	−	0.583245i	$-0.198217\pi$
$787$	1.08288e19	1.62459	0.812296	+	0.583245i	$0.198217\pi$
$788$	−2.78662e18	−0.414627
$789$	−5.76490e18	−0.850729
$790$	3.29869e18	0.482798
$791$	−6.52038e18	−0.946511
$792$	−4.40213e18	−0.633796
$793$	−8.38964e17	−0.119803
$794$	3.47029e18	0.491511
$795$	7.56386e18	1.06257
$796$	−2.60324e18	−0.362726
$797$	1.20554e19	1.66610	0.833051	−	0.553197i	$-0.186592\pi$
$797$	1.20554e19	1.66610	0.833051	+	0.553197i	$0.186592\pi$
$798$	−3.69254e18	−0.506182
$799$	1.46039e18	0.198571
$800$	4.04714e17	0.0545837
$801$	−4.17879e18	−0.559035
$802$	−3.33377e18	−0.442387
$803$	5.87286e18	0.773035
$804$	−2.58404e18	−0.337392
$805$	−2.74413e18	−0.355411
$806$	2.76117e18	0.354744
$807$	3.64721e18	0.464818
$808$	−1.04794e19	−1.32484
$809$	2.12593e18	0.266614	0.133307	−	0.991075i	$-0.457440\pi$
$809$	2.12593e18	0.266614	0.133307	+	0.991075i	$0.457440\pi$
$810$	6.80588e17	0.0846704
$811$	−4.63622e18	−0.572174	−0.286087	−	0.958204i	$-0.592355\pi$
$811$	−4.63622e18	−0.572174	−0.286087	+	0.958204i	$0.592355\pi$
$812$	3.21288e18	0.393351
$813$	4.45498e18	0.541074
$814$	−4.94858e18	−0.596241
$815$	3.27208e18	0.391111
$816$	2.19946e18	0.260813
$817$	−1.39268e19	−1.63835
$818$	−1.17748e18	−0.137422
$819$	1.08338e18	0.125440
$820$	−3.83260e18	−0.440254
$821$	−8.98267e18	−1.02371	−0.511853	−	0.859073i	$-0.671041\pi$
$821$	−8.98267e18	−1.02371	−0.511853	+	0.859073i	$0.671041\pi$
$822$	2.11408e18	0.239032
$823$	7.07899e18	0.794094	0.397047	−	0.917798i	$-0.370035\pi$
$823$	7.07899e18	0.794094	0.397047	+	0.917798i	$0.370035\pi$
$824$	−6.20889e18	−0.691015
$825$	6.12335e17	0.0676143
$826$	7.60016e17	0.0832631
$827$	9.08590e17	0.0987603	0.0493801	−	0.998780i	$-0.484275\pi$
$827$	9.08590e17	0.0987603	0.0493801	+	0.998780i	$0.484275\pi$
$828$	−5.59003e17	−0.0602861
$829$	1.79622e19	1.92201	0.961005	−	0.276532i	$-0.0891850\pi$
$829$	1.79622e19	1.92201	0.961005	+	0.276532i	$0.0891850\pi$
$830$	6.33382e18	0.672447
$831$	8.42550e17	0.0887542
$832$	−3.93151e18	−0.410921
$833$	3.21556e18	0.333476
$834$	−3.25749e18	−0.335200
$835$	−1.53925e19	−1.57162
$836$	−1.09070e19	−1.10500
$837$	−2.11905e18	−0.213022
$838$	−9.13366e18	−0.911084
$839$	−8.03402e18	−0.795207	−0.397603	−	0.917557i	$-0.630158\pi$
$839$	−8.03402e18	−0.795207	−0.397603	+	0.917557i	$0.630158\pi$
$840$	5.64946e18	0.554870
$841$	−6.43673e16	−0.00627323
$842$	−7.76053e18	−0.750521
$843$	−1.17730e19	−1.12982
$844$	5.77870e18	0.550306
$845$	−8.86597e18	−0.837833
$846$	−3.88987e17	−0.0364777
$847$	−1.98716e19	−1.84923
$848$	−6.51087e18	−0.601265
$849$	2.57807e18	0.236262
$850$	−7.18910e17	−0.0653810
$851$	−2.00846e18	−0.181268
$852$	−7.57573e17	−0.0678527
$853$	−1.05725e18	−0.0939740	−0.0469870	−	0.998896i	$-0.514962\pi$
$853$	−1.05725e18	−0.0939740	−0.0469870	+	0.998896i	$0.514962\pi$
$854$	−2.00022e18	−0.176442
$855$	5.38961e18	0.471821
$856$	−7.40999e18	−0.643781
$857$	−6.94534e18	−0.598850	−0.299425	−	0.954120i	$-0.596795\pi$
$857$	−6.94534e18	−0.598850	−0.299425	+	0.954120i	$0.596795\pi$
$858$	−3.82788e18	−0.327560
$859$	2.23388e18	0.189716	0.0948580	−	0.995491i	$-0.469760\pi$
$859$	2.23388e18	0.189716	0.0948580	+	0.995491i	$0.469760\pi$
$860$	6.66654e18	0.561902
$861$	−5.60062e18	−0.468506
$862$	−1.33701e19	−1.11003
$863$	1.73634e19	1.43076	0.715378	−	0.698737i	$-0.246254\pi$
$863$	1.73634e19	1.43076	0.715378	+	0.698737i	$0.246254\pi$
$864$	1.94162e18	0.158791
$865$	−1.08790e19	−0.883049
$866$	1.30838e19	1.05407
$867$	5.72827e18	0.458036
$868$	−5.50341e18	−0.436771
$869$	1.42385e19	1.12159
$870$	5.60948e18	0.438578
$871$	−7.18165e18	−0.557322
$872$	9.78500e18	0.753709
$873$	4.69386e18	0.358870
$874$	5.29521e18	0.401846
$875$	1.10931e19	0.835602
$876$	−1.53534e18	−0.114796
$877$	1.75887e19	1.30538	0.652690	−	0.757625i	$-0.273641\pi$
$877$	1.75887e19	1.30538	0.652690	+	0.757625i	$0.273641\pi$
$878$	−5.24886e18	−0.386679
$879$	−7.28330e18	−0.532599
$880$	−8.49472e18	−0.616612
$881$	−1.52042e19	−1.09552	−0.547761	−	0.836635i	$-0.684520\pi$
$881$	−1.52042e19	−1.09552	−0.547761	+	0.836635i	$0.684520\pi$
$882$	−8.56488e17	−0.0612598
$883$	8.94666e18	0.635209	0.317604	−	0.948223i	$-0.397122\pi$
$883$	8.94666e18	0.635209	0.317604	+	0.948223i	$0.397122\pi$
$884$	−3.75705e18	−0.264794
$885$	−1.10931e18	−0.0776110
$886$	−1.00882e19	−0.700639
$887$	6.60815e18	0.455592	0.227796	−	0.973709i	$-0.426848\pi$
$887$	6.60815e18	0.455592	0.227796	+	0.973709i	$0.426848\pi$
$888$	4.13491e18	0.282997
$889$	−1.47841e19	−1.00446
$890$	−1.89483e19	−1.27801
$891$	2.93769e18	0.196698
$892$	5.62281e18	0.373751
$893$	−3.08040e18	−0.203270
$894$	3.14481e18	0.206016
$895$	9.62818e18	0.626173
$896$	1.70113e18	0.109834
$897$	−1.55360e18	−0.0995839
$898$	−1.45760e19	−0.927559
$899$	−1.74654e19	−1.10342
$900$	−1.60082e17	−0.0100408
$901$	−3.83310e19	−2.38693
$902$	1.97884e19	1.22340
$903$	9.74187e18	0.597960
$904$	−1.92501e19	−1.17311
$905$	1.40158e19	0.848009
$906$	8.21173e18	0.493289
$907$	6.83270e18	0.407517	0.203758	−	0.979021i	$-0.434684\pi$
$907$	6.83270e18	0.407517	0.203758	+	0.979021i	$0.434684\pi$
$908$	−1.46250e19	−0.866041
$909$	6.99327e18	0.411164
$910$	4.91249e18	0.286769
$911$	4.40333e18	0.255218	0.127609	−	0.991825i	$-0.459270\pi$
$911$	4.40333e18	0.255218	0.127609	+	0.991825i	$0.459270\pi$
$912$	−4.63931e18	−0.266985
$913$	2.73393e19	1.56217
$914$	1.26825e19	0.719540
$915$	2.91951e18	0.164465
$916$	−5.12113e18	−0.286448
$917$	1.99999e19	1.11078
$918$	−3.44899e18	−0.190201
$919$	−1.14720e19	−0.628188	−0.314094	−	0.949392i	$-0.601701\pi$
$919$	−1.14720e19	−0.628188	−0.314094	+	0.949392i	$0.601701\pi$
$920$	−8.10149e18	−0.440498
$921$	−4.75058e18	−0.256483
$922$	1.66387e19	0.892009
$923$	−2.10547e18	−0.112083
$924$	7.62952e18	0.403301
$925$	−5.75164e17	−0.0301905
$926$	−2.10726e19	−1.09836
$927$	4.14340e18	0.214456
$928$	1.60030e19	0.822509
$929$	1.33511e19	0.681418	0.340709	−	0.940169i	$-0.389333\pi$
$929$	1.33511e19	0.681418	0.340709	+	0.940169i	$0.389333\pi$
$930$	−9.60860e18	−0.486991
$931$	−6.78257e18	−0.341367
$932$	1.31886e19	0.659169
$933$	−6.31653e18	−0.313508
$934$	−1.74610e19	−0.860628
$935$	−5.00104e19	−2.44785
$936$	3.19848e18	0.155471
$937$	3.33608e19	1.61039	0.805193	−	0.593013i	$-0.202062\pi$
$937$	3.33608e19	1.61039	0.805193	+	0.593013i	$0.202062\pi$
$938$	−1.71222e19	−0.820807
$939$	2.31524e19	1.10222
$940$	1.47454e18	0.0697150
$941$	−1.45632e18	−0.0683792	−0.0341896	−	0.999415i	$-0.510885\pi$
$941$	−1.45632e18	−0.0683792	−0.0341896	+	0.999415i	$0.510885\pi$
$942$	1.01749e19	0.474461
$943$	8.03145e18	0.371936
$944$	9.54884e17	0.0439170
$945$	−3.77007e18	−0.172204
$946$	−3.44206e19	−1.56144
$947$	−2.86414e19	−1.29038	−0.645192	−	0.764021i	$-0.723222\pi$
$947$	−2.86414e19	−1.29038	−0.645192	+	0.764021i	$0.723222\pi$
$948$	−3.72235e18	−0.166557
$949$	−4.26707e18	−0.189627
$950$	1.51639e18	0.0669282
$951$	−2.01559e18	−0.0883546
$952$	−2.86295e19	−1.24645
$953$	1.06857e19	0.462063	0.231031	−	0.972946i	$-0.425790\pi$
$953$	1.06857e19	0.462063	0.231031	+	0.972946i	$0.425790\pi$
$954$	1.02097e19	0.438481
$955$	1.25647e19	0.535956
$956$	−1.27937e19	−0.542024
$957$	2.42127e19	1.01886
$958$	1.27927e18	0.0534670
$959$	−1.17108e19	−0.486145
$960$	1.36813e19	0.564110
$961$	5.49936e18	0.225222
$962$	3.59551e18	0.146259
$963$	4.94493e18	0.199797
$964$	−1.32296e19	−0.530940
$965$	4.58872e19	1.82921
$966$	−3.70404e18	−0.146664
$967$	1.65593e19	0.651284	0.325642	−	0.945493i	$-0.394420\pi$
$967$	1.65593e19	0.651284	0.325642	+	0.945493i	$0.394420\pi$
$968$	−5.86670e19	−2.29194
$969$	−2.73127e19	−1.05989
$970$	2.12838e19	0.820414
$971$	−4.50154e19	−1.72360	−0.861799	−	0.507250i	$-0.830662\pi$
$971$	−4.50154e19	−1.72360	−0.861799	+	0.507250i	$0.830662\pi$
$972$	−7.67997e17	−0.0292098
$973$	1.80447e19	0.681734
$974$	5.90413e17	0.0221576
$975$	−4.44907e17	−0.0165859
$976$	−2.51308e18	−0.0930642
$977$	−1.62274e19	−0.596944	−0.298472	−	0.954418i	$-0.596477\pi$
$977$	−1.62274e19	−0.596944	−0.298472	+	0.954418i	$0.596477\pi$
$978$	4.41668e18	0.161396
$979$	−8.17882e19	−2.96895
$980$	3.24672e18	0.117078
$981$	−6.52985e18	−0.233913
$982$	1.34860e19	0.479910
$983$	5.11823e18	0.180935	0.0904674	−	0.995899i	$-0.471164\pi$
$983$	5.11823e18	0.180935	0.0904674	+	0.995899i	$0.471164\pi$
$984$	−1.65347e19	−0.580669
$985$	2.69507e19	0.940232
$986$	−2.84269e19	−0.985211
$987$	2.15476e18	0.0741888
$988$	7.92473e18	0.271059
$989$	−1.39701e19	−0.474706
$990$	1.33206e19	0.449672
$991$	2.02170e19	0.678012	0.339006	−	0.940784i	$-0.389909\pi$
$991$	2.02170e19	0.678012	0.339006	+	0.940784i	$0.389909\pi$
$992$	−2.74120e19	−0.913303
$993$	1.37739e19	0.455918
$994$	−5.01979e18	−0.165072
$995$	2.51772e19	0.822539
$996$	−7.14728e18	−0.231982
$997$	−2.06510e19	−0.665921	−0.332960	−	0.942941i	$-0.608048\pi$
$997$	−2.06510e19	−0.665921	−0.332960	+	0.942941i	$0.608048\pi$
$998$	−1.95452e19	−0.626169
$999$	−2.75936e18	−0.0878279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.19	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+66.7973 q^{2} +729.000 q^{3} -3730.11 q^{4} +36075.7 q^{5} +48695.3 q^{6} -269744. q^{7} -796366. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+66.7973 q^{2} +729.000 q^{3} -3730.11 q^{4} +36075.7 q^{5} +48695.3 q^{6} -269744. q^{7} -796366. q^{8} +531441. q^{9} +2.40976e6 q^{10} +1.04015e7 q^{11} -2.71925e6 q^{12} -7.55745e6 q^{13} -1.80182e7 q^{14} +2.62992e7 q^{15} -2.26380e7 q^{16} -1.33275e8 q^{17} +3.54989e7 q^{18} +2.81117e8 q^{19} -1.34567e8 q^{20} -1.96643e8 q^{21} +6.94792e8 q^{22} +2.81992e8 q^{23} -5.80551e8 q^{24} +8.07543e7 q^{25} -5.04818e8 q^{26} +3.87420e8 q^{27} +1.00618e9 q^{28} +3.19316e9 q^{29} +1.75672e9 q^{30} -5.46963e9 q^{31} +5.01167e9 q^{32} +7.58269e9 q^{33} -8.90243e9 q^{34} -9.73121e9 q^{35} -1.98234e9 q^{36} -7.12239e9 q^{37} +1.87779e10 q^{38} -5.50938e9 q^{39} -2.87295e10 q^{40} +2.84811e10 q^{41} -1.31353e10 q^{42} -4.95408e10 q^{43} -3.87988e10 q^{44} +1.91721e10 q^{45} +1.88363e10 q^{46} -1.09577e10 q^{47} -1.65031e10 q^{48} -2.41272e10 q^{49} +5.39418e9 q^{50} -9.71577e10 q^{51} +2.81902e10 q^{52} +2.87608e11 q^{53} +2.58787e10 q^{54} +3.75241e11 q^{55} +2.14815e11 q^{56} +2.04934e11 q^{57} +2.13295e11 q^{58} -4.21805e10 q^{59} -9.80990e10 q^{60} +1.11011e11 q^{61} -3.65357e11 q^{62} -1.43353e11 q^{63} +5.20217e11 q^{64} -2.72641e11 q^{65} +5.06504e11 q^{66} +9.50274e11 q^{67} +4.97132e11 q^{68} +2.05572e11 q^{69} -6.50019e11 q^{70} +2.78596e11 q^{71} -4.23221e11 q^{72} +5.64617e11 q^{73} -4.75757e11 q^{74} +5.88699e10 q^{75} -1.04860e12 q^{76} -2.80574e12 q^{77} -3.68012e11 q^{78} +1.36889e12 q^{79} -8.16683e11 q^{80} +2.82430e11 q^{81} +1.90246e12 q^{82} +2.62840e12 q^{83} +7.33502e11 q^{84} -4.80800e12 q^{85} -3.30920e12 q^{86} +2.32781e12 q^{87} -8.28339e12 q^{88} -7.86312e12 q^{89} +1.28065e12 q^{90} +2.03858e12 q^{91} -1.05186e12 q^{92} -3.98736e12 q^{93} -7.31947e11 q^{94} +1.01415e13 q^{95} +3.65351e12 q^{96} +8.83232e12 q^{97} -1.61163e12 q^{98} +5.52778e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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