LMFDB - Embedded newform 177.14.a.c.1.18

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			1.18
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)

$f(q)$	$=$	$q+28.6646 q^{2} +729.000 q^{3} -7370.34 q^{4} -9309.96 q^{5} +20896.5 q^{6} +216532. q^{7} -446089. q^{8} +531441. q^{9} +O(q^{10})$	\(q+28.6646 q^{2} +729.000 q^{3} -7370.34 q^{4} -9309.96 q^{5} +20896.5 q^{6} +216532. q^{7} -446089. q^{8} +531441. q^{9} -266867. q^{10} +5.39906e6 q^{11} -5.37298e6 q^{12} +2.36936e7 q^{13} +6.20682e6 q^{14} -6.78696e6 q^{15} +4.75908e7 q^{16} +9.98122e7 q^{17} +1.52336e7 q^{18} +2.92098e8 q^{19} +6.86175e7 q^{20} +1.57852e8 q^{21} +1.54762e8 q^{22} -6.28110e8 q^{23} -3.25199e8 q^{24} -1.13403e9 q^{25} +6.79169e8 q^{26} +3.87420e8 q^{27} -1.59592e9 q^{28} -1.36461e9 q^{29} -1.94546e8 q^{30} +3.47253e8 q^{31} +5.01853e9 q^{32} +3.93592e9 q^{33} +2.86108e9 q^{34} -2.01591e9 q^{35} -3.91690e9 q^{36} -2.74111e9 q^{37} +8.37289e9 q^{38} +1.72726e10 q^{39} +4.15307e9 q^{40} -3.57931e10 q^{41} +4.52477e9 q^{42} -4.48542e10 q^{43} -3.97929e10 q^{44} -4.94769e9 q^{45} -1.80045e10 q^{46} +1.39902e11 q^{47} +3.46937e10 q^{48} -5.00028e10 q^{49} -3.25065e10 q^{50} +7.27631e10 q^{51} -1.74630e11 q^{52} -5.29436e9 q^{53} +1.11053e10 q^{54} -5.02650e10 q^{55} -9.65926e10 q^{56} +2.12940e11 q^{57} -3.91161e10 q^{58} -4.21805e10 q^{59} +5.00222e10 q^{60} +3.45027e11 q^{61} +9.95389e9 q^{62} +1.15074e11 q^{63} -2.46010e11 q^{64} -2.20587e11 q^{65} +1.12822e11 q^{66} -5.99003e11 q^{67} -7.35649e11 q^{68} -4.57892e11 q^{69} -5.77852e10 q^{70} -6.16912e11 q^{71} -2.37070e11 q^{72} +1.52900e12 q^{73} -7.85728e10 q^{74} -8.26706e11 q^{75} -2.15286e12 q^{76} +1.16907e12 q^{77} +4.95114e11 q^{78} +2.64250e12 q^{79} -4.43069e11 q^{80} +2.82430e11 q^{81} -1.02600e12 q^{82} +3.15524e12 q^{83} -1.16342e12 q^{84} -9.29247e11 q^{85} -1.28573e12 q^{86} -9.94803e11 q^{87} -2.40846e12 q^{88} +5.43970e12 q^{89} -1.41824e11 q^{90} +5.13043e12 q^{91} +4.62938e12 q^{92} +2.53147e11 q^{93} +4.01023e12 q^{94} -2.71942e12 q^{95} +3.65851e12 q^{96} -2.80648e12 q^{97} -1.43331e12 q^{98} +2.86928e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	28.6646	0.316703	0.158351	−	0.987383i	$-0.449382\pi$
$2$	28.6646	0.316703	0.158351	+	0.987383i	$0.449382\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−7370.34	−0.899700
$5$	−9309.96	−0.266467	−0.133233	−	0.991085i	$-0.542536\pi$
$5$	−9309.96	−0.266467	−0.133233	+	0.991085i	$0.542536\pi$
$6$	20896.5	0.182848
$7$	216532.	0.695641	0.347821	−	0.937561i	$-0.386922\pi$
$7$	216532.	0.695641	0.347821	+	0.937561i	$0.386922\pi$
$8$	−446089.	−0.601640
$9$	531441.	0.333333
$10$	−266867.	−0.0843906
$11$	5.39906e6	0.918895	0.459448	−	0.888205i	$-0.348047\pi$
$11$	5.39906e6	0.918895	0.459448	+	0.888205i	$0.348047\pi$
$12$	−5.37298e6	−0.519442
$13$	2.36936e7	1.36144	0.680722	−	0.732542i	$-0.261666\pi$
$13$	2.36936e7	1.36144	0.680722	+	0.732542i	$0.261666\pi$
$14$	6.20682e6	0.220311
$15$	−6.78696e6	−0.153845
$16$	4.75908e7	0.709159
$17$	9.98122e7	1.00292	0.501459	−	0.865181i	$-0.332797\pi$
$17$	9.98122e7	1.00292	0.501459	+	0.865181i	$0.332797\pi$
$18$	1.52336e7	0.105568
$19$	2.92098e8	1.42440	0.712198	−	0.701979i	$-0.247700\pi$
$19$	2.92098e8	1.42440	0.712198	+	0.701979i	$0.247700\pi$
$20$	6.86175e7	0.239740
$21$	1.57852e8	0.401629
$22$	1.54762e8	0.291016
$23$	−6.28110e8	−0.884717	−0.442359	−	0.896838i	$-0.645858\pi$
$23$	−6.28110e8	−0.884717	−0.442359	+	0.896838i	$0.645858\pi$
$24$	−3.25199e8	−0.347357
$25$	−1.13403e9	−0.928996
$26$	6.79169e8	0.431173
$27$	3.87420e8	0.192450
$28$	−1.59592e9	−0.625868
$29$	−1.36461e9	−0.426013	−0.213006	−	0.977051i	$-0.568325\pi$
$29$	−1.36461e9	−0.426013	−0.213006	+	0.977051i	$0.568325\pi$
$30$	−1.94546e8	−0.0487229
$31$	3.47253e8	0.0702741	0.0351370	−	0.999383i	$-0.488813\pi$
$31$	3.47253e8	0.0702741	0.0351370	+	0.999383i	$0.488813\pi$
$32$	5.01853e9	0.826232
$33$	3.93592e9	0.530524
$34$	2.86108e9	0.317627
$35$	−2.01591e9	−0.185365
$36$	−3.91690e9	−0.299900
$37$	−2.74111e9	−0.175636	−0.0878182	−	0.996137i	$-0.527989\pi$
$37$	−2.74111e9	−0.175636	−0.0878182	+	0.996137i	$0.527989\pi$
$38$	8.37289e9	0.451110
$39$	1.72726e10	0.786030
$40$	4.15307e9	0.160317
$41$	−3.57931e10	−1.17680	−0.588402	−	0.808568i	$-0.700243\pi$
$41$	−3.57931e10	−1.17680	−0.588402	+	0.808568i	$0.700243\pi$
$42$	4.52477e9	0.127197
$43$	−4.48542e10	−1.08208	−0.541038	−	0.840998i	$-0.681968\pi$
$43$	−4.48542e10	−1.08208	−0.541038	+	0.840998i	$0.681968\pi$
$44$	−3.97929e10	−0.826730
$45$	−4.94769e9	−0.0888222
$46$	−1.80045e10	−0.280192
$47$	1.39902e11	1.89316	0.946578	−	0.322474i	$-0.104514\pi$
$47$	1.39902e11	1.89316	0.946578	+	0.322474i	$0.104514\pi$
$48$	3.46937e10	0.409433
$49$	−5.00028e10	−0.516084
$50$	−3.25065e10	−0.294215
$51$	7.27631e10	0.579035
$52$	−1.74630e11	−1.22489
$53$	−5.29436e9	−0.0328111	−0.0164055	−	0.999865i	$-0.505222\pi$
$53$	−5.29436e9	−0.0328111	−0.0164055	+	0.999865i	$0.505222\pi$
$54$	1.11053e10	0.0609494
$55$	−5.02650e10	−0.244855
$56$	−9.65926e10	−0.418525
$57$	2.12940e11	0.822375
$58$	−3.91161e10	−0.134919
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	5.00222e10	0.138414
$61$	3.45027e11	0.857452	0.428726	−	0.903435i	$-0.358963\pi$
$61$	3.45027e11	0.857452	0.428726	+	0.903435i	$0.358963\pi$
$62$	9.95389e9	0.0222560
$63$	1.15074e11	0.231880
$64$	−2.46010e11	−0.447489
$65$	−2.20587e11	−0.362779
$66$	1.12822e11	0.168018
$67$	−5.99003e11	−0.808989	−0.404495	−	0.914540i	$-0.632553\pi$
$67$	−5.99003e11	−0.808989	−0.404495	+	0.914540i	$0.632553\pi$
$68$	−7.35649e11	−0.902325
$69$	−4.57892e11	−0.510792
$70$	−5.77852e10	−0.0587056
$71$	−6.16912e11	−0.571536	−0.285768	−	0.958299i	$-0.592249\pi$
$71$	−6.16912e11	−0.571536	−0.285768	+	0.958299i	$0.592249\pi$
$72$	−2.37070e11	−0.200547
$73$	1.52900e12	1.18252	0.591259	−	0.806482i	$-0.298631\pi$
$73$	1.52900e12	1.18252	0.591259	+	0.806482i	$0.298631\pi$
$74$	−7.85728e10	−0.0556245
$75$	−8.26706e11	−0.536356
$76$	−2.15286e12	−1.28153
$77$	1.16907e12	0.639221
$78$	4.95114e11	0.248938
$79$	2.64250e12	1.22304	0.611518	−	0.791230i	$-0.290559\pi$
$79$	2.64250e12	1.22304	0.611518	+	0.791230i	$0.290559\pi$
$80$	−4.43069e11	−0.188967
$81$	2.82430e11	0.111111
$82$	−1.02600e12	−0.372697
$83$	3.15524e12	1.05932	0.529658	−	0.848211i	$-0.322320\pi$
$83$	3.15524e12	1.05932	0.529658	+	0.848211i	$0.322320\pi$
$84$	−1.16342e12	−0.361345
$85$	−9.29247e11	−0.267244
$86$	−1.28573e12	−0.342696
$87$	−9.94803e11	−0.245959
$88$	−2.40846e12	−0.552844
$89$	5.43970e12	1.16022	0.580109	−	0.814539i	$-0.303010\pi$
$89$	5.43970e12	1.16022	0.580109	+	0.814539i	$0.303010\pi$
$90$	−1.41824e11	−0.0281302
$91$	5.13043e12	0.947076
$92$	4.62938e12	0.795980
$93$	2.53147e11	0.0405728
$94$	4.01023e12	0.599568
$95$	−2.71942e12	−0.379554
$96$	3.65851e12	0.477025
$97$	−2.80648e12	−0.342094	−0.171047	−	0.985263i	$-0.554715\pi$
$97$	−2.80648e12	−0.342094	−0.171047	+	0.985263i	$0.554715\pi$
$98$	−1.43331e12	−0.163445
$99$	2.86928e12	0.306298
$100$	8.35817e12	0.835817
$101$	1.79795e13	1.68534	0.842671	−	0.538429i	$-0.180982\pi$
$101$	1.79795e13	1.68534	0.842671	+	0.538429i	$0.180982\pi$
$102$	2.08573e12	0.183382
$103$	−1.22631e13	−1.01195	−0.505973	−	0.862549i	$-0.668867\pi$
$103$	−1.22631e13	−1.01195	−0.505973	+	0.862549i	$0.668867\pi$
$104$	−1.05695e13	−0.819098
$105$	−1.46959e12	−0.107021
$106$	−1.51761e11	−0.0103913
$107$	2.81693e12	0.181460	0.0907301	−	0.995876i	$-0.471080\pi$
$107$	2.81693e12	0.181460	0.0907301	+	0.995876i	$0.471080\pi$
$108$	−2.85542e12	−0.173147
$109$	1.61963e13	0.925006	0.462503	−	0.886618i	$-0.346951\pi$
$109$	1.61963e13	0.925006	0.462503	+	0.886618i	$0.346951\pi$
$110$	−1.44083e12	−0.0775461
$111$	−1.99827e12	−0.101404
$112$	1.03049e13	0.493320
$113$	2.60181e13	1.17562	0.587808	−	0.809001i	$-0.299991\pi$
$113$	2.60181e13	1.17562	0.587808	+	0.809001i	$0.299991\pi$
$114$	6.10384e12	0.260448
$115$	5.84767e12	0.235748
$116$	1.00577e13	0.383283
$117$	1.25918e13	0.453814
$118$	−1.20909e12	−0.0412312
$119$	2.16125e13	0.697671
$120$	3.02759e12	0.0925590
$121$	−5.37283e12	−0.155632
$122$	9.89009e12	0.271557
$123$	−2.60932e13	−0.679429
$124$	−2.55937e12	−0.0632255
$125$	2.19224e13	0.514013
$126$	3.29856e12	0.0734371
$127$	−2.54106e13	−0.537391	−0.268695	−	0.963225i	$-0.586592\pi$
$127$	−2.54106e13	−0.537391	−0.268695	+	0.963225i	$0.586592\pi$
$128$	−4.81636e13	−0.967953
$129$	−3.26987e13	−0.624737
$130$	−6.32303e12	−0.114893
$131$	2.68732e13	0.464575	0.232287	−	0.972647i	$-0.425379\pi$
$131$	2.68732e13	0.464575	0.232287	+	0.972647i	$0.425379\pi$
$132$	−2.90090e13	−0.477312
$133$	6.32487e13	0.990868
$134$	−1.71702e13	−0.256209
$135$	−3.60687e12	−0.0512815
$136$	−4.45251e13	−0.603395
$137$	−8.59536e13	−1.11066	−0.555329	−	0.831631i	$-0.687408\pi$
$137$	−8.59536e13	−1.11066	−0.555329	+	0.831631i	$0.687408\pi$
$138$	−1.31253e13	−0.161769
$139$	4.62143e13	0.543476	0.271738	−	0.962371i	$-0.412402\pi$
$139$	4.62143e13	0.543476	0.271738	+	0.962371i	$0.412402\pi$
$140$	1.48579e13	0.166773
$141$	1.01988e14	1.09301
$142$	−1.76835e13	−0.181007
$143$	1.27923e14	1.25102
$144$	2.52917e13	0.236386
$145$	1.27045e13	0.113518
$146$	4.38281e13	0.374506
$147$	−3.64521e13	−0.297961
$148$	2.02029e13	0.158020
$149$	−1.36864e13	−0.102466	−0.0512328	−	0.998687i	$-0.516315\pi$
$149$	−1.36864e13	−0.102466	−0.0512328	+	0.998687i	$0.516315\pi$
$150$	−2.36972e13	−0.169865
$151$	−1.86371e14	−1.27946	−0.639732	−	0.768598i	$-0.720955\pi$
$151$	−1.86371e14	−1.27946	−0.639732	+	0.768598i	$0.720955\pi$
$152$	−1.30302e14	−0.856973
$153$	5.30443e13	0.334306
$154$	3.35110e13	0.202443
$155$	−3.23291e12	−0.0187257
$156$	−1.27305e14	−0.707191
$157$	−3.36680e14	−1.79420	−0.897098	−	0.441832i	$-0.854329\pi$
$157$	−3.36680e14	−1.79420	−0.897098	+	0.441832i	$0.854329\pi$
$158$	7.57464e13	0.387339
$159$	−3.85959e12	−0.0189435
$160$	−4.67223e13	−0.220163
$161$	−1.36006e14	−0.615446
$162$	8.09574e12	0.0351892
$163$	4.64591e14	1.94022	0.970110	−	0.242665i	$-0.0780215\pi$
$163$	4.64591e14	1.94022	0.970110	+	0.242665i	$0.0780215\pi$
$164$	2.63807e14	1.05877
$165$	−3.66432e13	−0.141367
$166$	9.04440e13	0.335488
$167$	1.82192e14	0.649937	0.324968	−	0.945725i	$-0.394646\pi$
$167$	1.82192e14	0.649937	0.324968	+	0.945725i	$0.394646\pi$
$168$	−7.04160e13	−0.241636
$169$	2.58512e14	0.853528
$170$	−2.66365e13	−0.0846369
$171$	1.55233e14	0.474799
$172$	3.30590e14	0.973543
$173$	−4.23492e14	−1.20101	−0.600504	−	0.799622i	$-0.705033\pi$
$173$	−4.23492e14	−1.20101	−0.600504	+	0.799622i	$0.705033\pi$
$174$	−2.85157e13	−0.0778957
$175$	−2.45554e14	−0.646247
$176$	2.56946e14	0.651642
$177$	−3.07496e13	−0.0751646
$178$	1.55927e14	0.367444
$179$	−3.39561e14	−0.771567	−0.385783	−	0.922589i	$-0.626069\pi$
$179$	−3.39561e14	−0.771567	−0.385783	+	0.922589i	$0.626069\pi$
$180$	3.64662e13	0.0799133
$181$	2.38283e14	0.503711	0.251856	−	0.967765i	$-0.418959\pi$
$181$	2.38283e14	0.503711	0.251856	+	0.967765i	$0.418959\pi$
$182$	1.47062e14	0.299941
$183$	2.51525e14	0.495050
$184$	2.80193e14	0.532281
$185$	2.55196e13	0.0468012
$186$	7.25638e12	0.0128495
$187$	5.38892e14	0.921577
$188$	−1.03112e15	−1.70327
$189$	8.38890e13	0.133876
$190$	−7.79513e13	−0.120206
$191$	−9.38453e14	−1.39861	−0.699303	−	0.714825i	$-0.746506\pi$
$191$	−9.38453e14	−1.39861	−0.699303	+	0.714825i	$0.746506\pi$
$192$	−1.79341e14	−0.258358
$193$	4.43345e13	0.0617474	0.0308737	−	0.999523i	$-0.490171\pi$
$193$	4.43345e13	0.0617474	0.0308737	+	0.999523i	$0.490171\pi$
$194$	−8.04468e13	−0.108342
$195$	−1.60808e14	−0.209451
$196$	3.68538e14	0.464320
$197$	3.95536e14	0.482121	0.241060	−	0.970510i	$-0.422505\pi$
$197$	3.95536e14	0.482121	0.241060	+	0.970510i	$0.422505\pi$
$198$	8.22470e13	0.0970055
$199$	9.44102e14	1.07764	0.538821	−	0.842421i	$-0.318870\pi$
$199$	9.44102e14	1.07764	0.538821	+	0.842421i	$0.318870\pi$
$200$	5.05877e14	0.558921
$201$	−4.36673e14	−0.467070
$202$	5.15375e14	0.533752
$203$	−2.95483e14	−0.296352
$204$	−5.36288e14	−0.520958
$205$	3.33232e14	0.313579
$206$	−3.51517e14	−0.320486
$207$	−3.33803e14	−0.294906
$208$	1.12760e15	0.965479
$209$	1.57706e15	1.30887
$210$	−4.21254e13	−0.0338937
$211$	1.72253e14	0.134379	0.0671893	−	0.997740i	$-0.478597\pi$
$211$	1.72253e14	0.134379	0.0671893	+	0.997740i	$0.478597\pi$
$212$	3.90212e13	0.0295201
$213$	−4.49729e14	−0.329977
$214$	8.07463e13	0.0574689
$215$	4.17590e14	0.288337
$216$	−1.72824e14	−0.115786
$217$	7.51915e13	0.0488855
$218$	4.64262e14	0.292952
$219$	1.11464e15	0.682727
$220$	3.70470e14	0.220296
$221$	2.36491e15	1.36542
$222$	−5.72796e13	−0.0321148
$223$	2.68101e15	1.45988	0.729938	−	0.683513i	$-0.239549\pi$
$223$	2.68101e15	1.45988	0.729938	+	0.683513i	$0.239549\pi$
$224$	1.08667e15	0.574761
$225$	−6.02669e14	−0.309665
$226$	7.45799e14	0.372320
$227$	−2.87857e15	−1.39640	−0.698199	−	0.715903i	$-0.746015\pi$
$227$	−2.87857e15	−1.39640	−0.698199	+	0.715903i	$0.746015\pi$
$228$	−1.56944e15	−0.739891
$229$	8.60452e14	0.394272	0.197136	−	0.980376i	$-0.436836\pi$
$229$	8.60452e14	0.394272	0.197136	+	0.980376i	$0.436836\pi$
$230$	1.67621e14	0.0746618
$231$	8.52253e14	0.369055
$232$	6.08739e14	0.256306
$233$	4.56845e15	1.87049	0.935246	−	0.353999i	$-0.115178\pi$
$233$	4.56845e15	1.87049	0.935246	+	0.353999i	$0.115178\pi$
$234$	3.60938e14	0.143724
$235$	−1.30248e15	−0.504463
$236$	3.10885e14	0.117131
$237$	1.92639e15	0.706121
$238$	6.19516e14	0.220954
$239$	1.00186e15	0.347712	0.173856	−	0.984771i	$-0.444377\pi$
$239$	1.00186e15	0.347712	0.173856	+	0.984771i	$0.444377\pi$
$240$	−3.22997e14	−0.109100
$241$	−2.70267e15	−0.888551	−0.444276	−	0.895890i	$-0.646539\pi$
$241$	−2.70267e15	−0.888551	−0.444276	+	0.895890i	$0.646539\pi$
$242$	−1.54010e14	−0.0492890
$243$	2.05891e14	0.0641500
$244$	−2.54297e15	−0.771449
$245$	4.65524e14	0.137519
$246$	−7.47952e14	−0.215177
$247$	6.92087e15	1.93923
$248$	−1.54906e14	−0.0422797
$249$	2.30017e15	0.611596
$250$	6.28399e14	0.162789
$251$	4.19231e15	1.05822	0.529108	−	0.848554i	$-0.322527\pi$
$251$	4.19231e15	1.05822	0.529108	+	0.848554i	$0.322527\pi$
$252$	−8.48135e14	−0.208623
$253$	−3.39120e15	−0.812962
$254$	−7.28385e14	−0.170193
$255$	−6.77421e14	−0.154293
$256$	6.34718e14	0.140936
$257$	−4.55534e15	−0.986179	−0.493089	−	0.869979i	$-0.664132\pi$
$257$	−4.55534e15	−0.986179	−0.493089	+	0.869979i	$0.664132\pi$
$258$	−9.37296e14	−0.197856
$259$	−5.93538e14	−0.122180
$260$	1.62580e15	0.326392
$261$	−7.25211e14	−0.142004
$262$	7.70310e14	0.147132
$263$	6.22519e15	1.15995	0.579976	−	0.814634i	$-0.303062\pi$
$263$	6.22519e15	1.15995	0.579976	+	0.814634i	$0.303062\pi$
$264$	−1.75577e15	−0.319184
$265$	4.92903e13	0.00874305
$266$	1.81300e15	0.313810
$267$	3.96554e15	0.669853
$268$	4.41485e15	0.727847
$269$	−1.00784e16	−1.62181	−0.810906	−	0.585176i	$-0.801025\pi$
$269$	−1.00784e16	−1.62181	−0.810906	+	0.585176i	$0.801025\pi$
$270$	−1.03390e14	−0.0162410
$271$	−7.10285e15	−1.08926	−0.544631	−	0.838676i	$-0.683330\pi$
$271$	−7.10285e15	−1.08926	−0.544631	+	0.838676i	$0.683330\pi$
$272$	4.75014e15	0.711228
$273$	3.74008e15	0.546795
$274$	−2.46383e15	−0.351748
$275$	−6.12269e15	−0.853650
$276$	3.37482e15	0.459559
$277$	−1.31312e15	−0.174657	−0.0873285	−	0.996180i	$-0.527833\pi$
$277$	−1.31312e15	−0.174657	−0.0873285	+	0.996180i	$0.527833\pi$
$278$	1.32472e15	0.172120
$279$	1.84545e14	0.0234247
$280$	8.99273e14	0.111523
$281$	7.47650e15	0.905957	0.452978	−	0.891522i	$-0.350362\pi$
$281$	7.47650e15	0.905957	0.452978	+	0.891522i	$0.350362\pi$
$282$	2.92346e15	0.346160
$283$	8.94157e15	1.03467	0.517335	−	0.855783i	$-0.326924\pi$
$283$	8.94157e15	1.03467	0.517335	+	0.855783i	$0.326924\pi$
$284$	4.54685e15	0.514211
$285$	−1.98246e15	−0.219135
$286$	3.66688e15	0.396202
$287$	−7.75036e15	−0.818634
$288$	2.66705e15	0.275411
$289$	5.78903e13	0.00584480
$290$	3.64170e14	0.0359515
$291$	−2.04593e15	−0.197508
$292$	−1.12692e16	−1.06391
$293$	8.88122e15	0.820036	0.410018	−	0.912077i	$-0.365522\pi$
$293$	8.88122e15	0.820036	0.410018	+	0.912077i	$0.365522\pi$
$294$	−1.04489e15	−0.0943650
$295$	3.92699e14	0.0346910
$296$	1.22278e15	0.105670
$297$	2.09171e15	0.176841
$298$	−3.92316e14	−0.0324511
$299$	−1.48822e16	−1.20449
$300$	6.09311e15	0.482559
$301$	−9.71237e15	−0.752736
$302$	−5.34226e15	−0.405210
$303$	1.31070e16	0.973033
$304$	1.39012e16	1.01012
$305$	−3.21219e15	−0.228482
$306$	1.52050e15	0.105876
$307$	2.88891e16	1.96940	0.984700	−	0.174257i	$-0.0557524\pi$
$307$	2.88891e16	1.96940	0.984700	+	0.174257i	$0.0557524\pi$
$308$	−8.61645e15	−0.575107
$309$	−8.93979e15	−0.584248
$310$	−9.26702e13	−0.00593047
$311$	1.20012e16	0.752111	0.376055	−	0.926597i	$-0.377280\pi$
$311$	1.20012e16	0.752111	0.376055	+	0.926597i	$0.377280\pi$
$312$	−7.70514e15	−0.472907
$313$	1.97347e16	1.18630	0.593148	−	0.805093i	$-0.297885\pi$
$313$	1.97347e16	1.18630	0.593148	+	0.805093i	$0.297885\pi$
$314$	−9.65082e15	−0.568226
$315$	−1.07133e15	−0.0617883
$316$	−1.94761e16	−1.10037
$317$	−8.35961e15	−0.462701	−0.231351	−	0.972870i	$-0.574314\pi$
$317$	−8.35961e15	−0.462701	−0.231351	+	0.972870i	$0.574314\pi$
$318$	−1.10634e14	−0.00599945
$319$	−7.36763e15	−0.391461
$320$	2.29034e15	0.119241
$321$	2.05354e15	0.104766
$322$	−3.89856e15	−0.194913
$323$	2.91550e16	1.42855
$324$	−2.08160e15	−0.0999666
$325$	−2.68692e16	−1.26477
$326$	1.33173e16	0.614473
$327$	1.18071e16	0.534053
$328$	1.59669e16	0.708013
$329$	3.02932e16	1.31696
$330$	−1.05036e15	−0.0447713
$331$	2.10739e16	0.880771	0.440385	−	0.897809i	$-0.354842\pi$
$331$	2.10739e16	0.880771	0.440385	+	0.897809i	$0.354842\pi$
$332$	−2.32552e16	−0.953066
$333$	−1.45674e15	−0.0585455
$334$	5.22245e15	0.205837
$335$	5.57669e15	0.215569
$336$	7.51231e15	0.284818
$337$	3.71003e16	1.37969	0.689847	−	0.723955i	$-0.257678\pi$
$337$	3.71003e16	1.37969	0.689847	+	0.723955i	$0.257678\pi$
$338$	7.41017e15	0.270315
$339$	1.89672e16	0.678742
$340$	6.84886e15	0.240439
$341$	1.87484e15	0.0645745
$342$	4.44970e15	0.150370
$343$	−3.18068e16	−1.05465
$344$	2.00089e16	0.651020
$345$	4.26295e15	0.136109
$346$	−1.21393e16	−0.380362
$347$	3.09426e16	0.951514	0.475757	−	0.879577i	$-0.342174\pi$
$347$	3.09426e16	0.951514	0.475757	+	0.879577i	$0.342174\pi$
$348$	7.33203e15	0.221289
$349$	5.69288e16	1.68642	0.843212	−	0.537581i	$-0.180662\pi$
$349$	5.69288e16	1.68642	0.843212	+	0.537581i	$0.180662\pi$
$350$	−7.03870e15	−0.204668
$351$	9.17939e15	0.262010
$352$	2.70954e16	0.759221
$353$	8.38615e14	0.0230689	0.0115344	−	0.999933i	$-0.496328\pi$
$353$	8.38615e14	0.0230689	0.0115344	+	0.999933i	$0.496328\pi$
$354$	−8.81427e14	−0.0238048
$355$	5.74342e15	0.152295
$356$	−4.00924e16	−1.04385
$357$	1.57555e16	0.402801
$358$	−9.73340e15	−0.244357
$359$	3.37122e16	0.831138	0.415569	−	0.909562i	$-0.363582\pi$
$359$	3.37122e16	0.831138	0.415569	+	0.909562i	$0.363582\pi$
$360$	2.20711e15	0.0534389
$361$	4.32685e16	1.02890
$362$	6.83029e15	0.159527
$363$	−3.91679e15	−0.0898540
$364$	−3.78130e16	−0.852084
$365$	−1.42349e16	−0.315101
$366$	7.20987e15	0.156784
$367$	−6.86074e16	−1.46569	−0.732844	−	0.680397i	$-0.761808\pi$
$367$	−6.86074e16	−1.46569	−0.732844	+	0.680397i	$0.761808\pi$
$368$	−2.98923e16	−0.627405
$369$	−1.90219e16	−0.392268
$370$	7.31510e14	0.0148221
$371$	−1.14640e15	−0.0228247
$372$	−1.86578e15	−0.0365033
$373$	−7.44207e16	−1.43083	−0.715413	−	0.698702i	$-0.753761\pi$
$373$	−7.44207e16	−1.43083	−0.715413	+	0.698702i	$0.753761\pi$
$374$	1.54472e16	0.291866
$375$	1.59815e16	0.296765
$376$	−6.24085e16	−1.13900
$377$	−3.23326e16	−0.579992
$378$	2.40465e15	0.0423989
$379$	1.37559e16	0.238416	0.119208	−	0.992869i	$-0.461965\pi$
$379$	1.37559e16	0.238416	0.119208	+	0.992869i	$0.461965\pi$
$380$	2.00431e16	0.341484
$381$	−1.85243e16	−0.310263
$382$	−2.69004e16	−0.442942
$383$	−2.47689e16	−0.400973	−0.200487	−	0.979696i	$-0.564252\pi$
$383$	−2.47689e16	−0.400973	−0.200487	+	0.979696i	$0.564252\pi$
$384$	−3.51113e16	−0.558848
$385$	−1.08840e16	−0.170331
$386$	1.27083e15	0.0195556
$387$	−2.38373e16	−0.360692
$388$	2.06847e16	0.307782
$389$	6.14774e16	0.899587	0.449793	−	0.893133i	$-0.351498\pi$
$389$	6.14774e16	0.899587	0.449793	+	0.893133i	$0.351498\pi$
$390$	−4.60949e15	−0.0663335
$391$	−6.26930e16	−0.887299
$392$	2.23057e16	0.310496
$393$	1.95906e16	0.268222
$394$	1.13379e16	0.152689
$395$	−2.46016e16	−0.325898
$396$	−2.11476e16	−0.275577
$397$	2.26904e16	0.290873	0.145437	−	0.989368i	$-0.453541\pi$
$397$	2.26904e16	0.290873	0.145437	+	0.989368i	$0.453541\pi$
$398$	2.70624e16	0.341292
$399$	4.61083e16	0.572078
$400$	−5.39693e16	−0.658805
$401$	6.61849e16	0.794915	0.397458	−	0.917621i	$-0.369893\pi$
$401$	6.61849e16	0.794915	0.397458	+	0.917621i	$0.369893\pi$
$402$	−1.25171e16	−0.147922
$403$	8.22768e15	0.0956742
$404$	−1.32515e17	−1.51630
$405$	−2.62941e15	−0.0296074
$406$	−8.46990e15	−0.0938554
$407$	−1.47994e16	−0.161392
$408$	−3.24588e16	−0.348370
$409$	−1.11947e17	−1.18253	−0.591265	−	0.806477i	$-0.701371\pi$
$409$	−1.11947e17	−1.18253	−0.591265	+	0.806477i	$0.701371\pi$
$410$	9.55199e15	0.0993113
$411$	−6.26602e16	−0.641239
$412$	9.03831e16	0.910448
$413$	−9.13344e15	−0.0905648
$414$	−9.56835e15	−0.0933974
$415$	−2.93752e16	−0.282272
$416$	1.18907e17	1.12487
$417$	3.36902e16	0.313776
$418$	4.52058e16	0.414523
$419$	−1.11992e17	−1.01110	−0.505551	−	0.862797i	$-0.668711\pi$
$419$	−1.11992e17	−1.01110	−0.505551	+	0.862797i	$0.668711\pi$
$420$	1.08314e16	0.0962863
$421$	4.59146e16	0.401899	0.200950	−	0.979602i	$-0.435597\pi$
$421$	4.59146e16	0.401899	0.200950	+	0.979602i	$0.435597\pi$
$422$	4.93756e15	0.0425581
$423$	7.43494e16	0.631052
$424$	2.36176e15	0.0197404
$425$	−1.13190e17	−0.931707
$426$	−1.28913e16	−0.104504
$427$	7.47096e16	0.596479
$428$	−2.07617e16	−0.163260
$429$	9.32561e16	0.722279
$430$	1.19701e16	0.0913170
$431$	−4.95234e16	−0.372141	−0.186071	−	0.982536i	$-0.559575\pi$
$431$	−4.95234e16	−0.372141	−0.186071	+	0.982536i	$0.559575\pi$
$432$	1.84377e16	0.136478
$433$	5.90197e16	0.430354	0.215177	−	0.976575i	$-0.430967\pi$
$433$	5.90197e16	0.430354	0.215177	+	0.976575i	$0.430967\pi$
$434$	2.15534e15	0.0154822
$435$	9.26157e15	0.0655397
$436$	−1.19373e17	−0.832228
$437$	−1.83470e17	−1.26019
$438$	3.19507e16	0.216221
$439$	−1.95409e17	−1.30294	−0.651470	−	0.758675i	$-0.725847\pi$
$439$	−1.95409e17	−1.30294	−0.651470	+	0.758675i	$0.725847\pi$
$440$	2.24227e16	0.147314
$441$	−2.65735e16	−0.172028
$442$	6.77893e16	0.432431
$443$	−2.63628e17	−1.65717	−0.828584	−	0.559864i	$-0.810853\pi$
$443$	−2.63628e17	−1.65717	−0.828584	+	0.559864i	$0.810853\pi$
$444$	1.47279e16	0.0912329
$445$	−5.06434e16	−0.309159
$446$	7.68501e16	0.462347
$447$	−9.97738e15	−0.0591586
$448$	−5.32690e16	−0.311292
$449$	−1.37870e17	−0.794090	−0.397045	−	0.917799i	$-0.629964\pi$
$449$	−1.37870e17	−0.794090	−0.397045	+	0.917799i	$0.629964\pi$
$450$	−1.72753e16	−0.0980718
$451$	−1.93249e17	−1.08136
$452$	−1.91762e17	−1.05770
$453$	−1.35864e17	−0.738699
$454$	−8.25133e16	−0.442243
$455$	−4.77641e16	−0.252364
$456$	−9.49900e16	−0.494774
$457$	1.14822e17	0.589617	0.294808	−	0.955556i	$-0.404744\pi$
$457$	1.14822e17	0.589617	0.294808	+	0.955556i	$0.404744\pi$
$458$	2.46645e16	0.124867
$459$	3.86693e16	0.193012
$460$	−4.30993e16	−0.212102
$461$	−6.94164e16	−0.336826	−0.168413	−	0.985717i	$-0.553864\pi$
$461$	−6.94164e16	−0.336826	−0.168413	+	0.985717i	$0.553864\pi$
$462$	2.44295e16	0.116881
$463$	−4.95155e16	−0.233596	−0.116798	−	0.993156i	$-0.537263\pi$
$463$	−4.95155e16	−0.233596	−0.116798	+	0.993156i	$0.537263\pi$
$464$	−6.49431e16	−0.302111
$465$	−2.35679e15	−0.0108113
$466$	1.30953e17	0.592389
$467$	2.23463e17	0.996886	0.498443	−	0.866923i	$-0.333905\pi$
$467$	2.23463e17	0.996886	0.498443	+	0.866923i	$0.333905\pi$
$468$	−9.28055e16	−0.408297
$469$	−1.29703e17	−0.562766
$470$	−3.73351e16	−0.159765
$471$	−2.45440e17	−1.03588
$472$	1.88163e16	0.0783268
$473$	−2.42170e17	−0.994314
$474$	5.52191e16	0.223630
$475$	−3.31248e17	−1.32326
$476$	−1.59292e17	−0.627694
$477$	−2.81364e15	−0.0109370
$478$	2.87179e16	0.110121
$479$	3.02476e17	1.14422	0.572111	−	0.820176i	$-0.306125\pi$
$479$	3.02476e17	1.14422	0.572111	+	0.820176i	$0.306125\pi$
$480$	−3.40606e16	−0.127111
$481$	−6.49467e16	−0.239119
$482$	−7.74711e16	−0.281406
$483$	−9.91483e16	−0.355328
$484$	3.95996e16	0.140022
$485$	2.61282e16	0.0911567
$486$	5.90180e15	0.0203165
$487$	−3.10898e15	−0.0105604	−0.00528018	−	0.999986i	$-0.501681\pi$
$487$	−3.10898e15	−0.0105604	−0.00528018	+	0.999986i	$0.501681\pi$
$488$	−1.53913e17	−0.515877
$489$	3.38687e17	1.12019
$490$	1.33441e16	0.0435526
$491$	4.82801e17	1.55503	0.777515	−	0.628865i	$-0.216480\pi$
$491$	4.82801e17	1.55503	0.777515	+	0.628865i	$0.216480\pi$
$492$	1.92316e17	0.611282
$493$	−1.36205e17	−0.427256
$494$	1.98384e17	0.614160
$495$	−2.67129e16	−0.0816183
$496$	1.65261e16	0.0498355
$497$	−1.33581e17	−0.397584
$498$	6.59336e16	0.193694
$499$	−3.83978e17	−1.11341	−0.556703	−	0.830712i	$-0.687934\pi$
$499$	−3.83978e17	−1.11341	−0.556703	+	0.830712i	$0.687934\pi$
$500$	−1.61576e17	−0.462457
$501$	1.32818e17	0.375241
$502$	1.20171e17	0.335140
$503$	−4.43802e17	−1.22179	−0.610896	−	0.791711i	$-0.709191\pi$
$503$	−4.43802e17	−1.22179	−0.610896	+	0.791711i	$0.709191\pi$
$504$	−5.13333e16	−0.139508
$505$	−1.67388e17	−0.449087
$506$	−9.72076e16	−0.257467
$507$	1.88456e17	0.492785
$508$	1.87284e17	0.483490
$509$	9.92092e16	0.252864	0.126432	−	0.991975i	$-0.459647\pi$
$509$	9.92092e16	0.252864	0.126432	+	0.991975i	$0.459647\pi$
$510$	−1.94180e16	−0.0488651
$511$	3.31077e17	0.822608
$512$	4.12750e17	1.01259
$513$	1.13165e17	0.274125
$514$	−1.30577e17	−0.312325
$515$	1.14169e17	0.269650
$516$	2.41000e17	0.562075
$517$	7.55338e17	1.73961
$518$	−1.70135e16	−0.0386947
$519$	−3.08726e17	−0.693402
$520$	9.84012e16	0.218262
$521$	5.01190e17	1.09789	0.548943	−	0.835860i	$-0.315030\pi$
$521$	5.01190e17	1.09789	0.548943	+	0.835860i	$0.315030\pi$
$522$	−2.07879e16	−0.0449731
$523$	2.59670e17	0.554831	0.277415	−	0.960750i	$-0.410522\pi$
$523$	2.59670e17	0.554831	0.277415	+	0.960750i	$0.410522\pi$
$524$	−1.98064e17	−0.417978
$525$	−1.79009e17	−0.373111
$526$	1.78443e17	0.367360
$527$	3.46601e16	0.0704791
$528$	1.87314e17	0.376226
$529$	−1.09515e17	−0.217275
$530$	1.41289e15	0.00276895
$531$	−2.24165e16	−0.0433963
$532$	−4.66164e17	−0.891484
$533$	−8.48068e17	−1.60215
$534$	1.13671e17	0.212144
$535$	−2.62255e16	−0.0483531
$536$	2.67209e17	0.486720
$537$	−2.47540e17	−0.445464
$538$	−2.88893e17	−0.513632
$539$	−2.69968e17	−0.474227
$540$	2.65838e16	0.0461379
$541$	8.63101e17	1.48006	0.740030	−	0.672574i	$-0.234811\pi$
$541$	8.63101e17	1.48006	0.740030	+	0.672574i	$0.234811\pi$
$542$	−2.03601e17	−0.344972
$543$	1.73708e17	0.290818
$544$	5.00911e17	0.828643
$545$	−1.50787e17	−0.246483
$546$	1.07208e17	0.173171
$547$	−9.16310e17	−1.46260	−0.731299	−	0.682057i	$-0.761085\pi$
$547$	−9.16310e17	−1.46260	−0.731299	+	0.682057i	$0.761085\pi$
$548$	6.33507e17	0.999259
$549$	1.83362e17	0.285817
$550$	−1.75505e17	−0.270353
$551$	−3.98601e17	−0.606811
$552$	2.04260e17	0.307313
$553$	5.72187e17	0.850795
$554$	−3.76401e16	−0.0553143
$555$	1.86038e16	0.0270207
$556$	−3.40615e17	−0.488965
$557$	4.86125e17	0.689746	0.344873	−	0.938649i	$-0.387922\pi$
$557$	4.86125e17	0.689746	0.344873	+	0.938649i	$0.387922\pi$
$558$	5.28990e15	0.00741866
$559$	−1.06276e18	−1.47318
$560$	−9.59386e16	−0.131453
$561$	3.92852e17	0.532073
$562$	2.14311e17	0.286919
$563$	2.64634e17	0.350220	0.175110	−	0.984549i	$-0.443972\pi$
$563$	2.64634e17	0.350220	0.175110	+	0.984549i	$0.443972\pi$
$564$	−7.51688e17	−0.983385
$565$	−2.42227e17	−0.313262
$566$	2.56307e17	0.327683
$567$	6.11551e16	0.0772935
$568$	2.75197e17	0.343859
$569$	6.30017e17	0.778256	0.389128	−	0.921184i	$-0.372776\pi$
$569$	6.30017e17	0.778256	0.389128	+	0.921184i	$0.372776\pi$
$570$	−5.68265e16	−0.0694008
$571$	−1.02890e18	−1.24234	−0.621168	−	0.783677i	$-0.713342\pi$
$571$	−1.02890e18	−1.24234	−0.621168	+	0.783677i	$0.713342\pi$
$572$	−9.42838e17	−1.12555
$573$	−6.84132e17	−0.807486
$574$	−2.22161e17	−0.259263
$575$	7.12294e17	0.821898
$576$	−1.30740e17	−0.149163
$577$	−5.82838e17	−0.657514	−0.328757	−	0.944415i	$-0.606630\pi$
$577$	−5.82838e17	−0.657514	−0.328757	+	0.944415i	$0.606630\pi$
$578$	1.65941e15	0.00185106
$579$	3.23198e16	0.0356499
$580$	−9.36364e16	−0.102132
$581$	6.83212e17	0.736904
$582$	−5.86457e16	−0.0625514
$583$	−2.85846e16	−0.0301499
$584$	−6.82068e17	−0.711450
$585$	−1.17229e17	−0.120926
$586$	2.54577e17	0.259708
$587$	1.71056e17	0.172581	0.0862903	−	0.996270i	$-0.472499\pi$
$587$	1.71056e17	0.172581	0.0862903	+	0.996270i	$0.472499\pi$
$588$	2.68664e17	0.268075
$589$	1.01432e17	0.100098
$590$	1.12566e16	0.0109867
$591$	2.88346e17	0.278352
$592$	−1.30452e17	−0.124554
$593$	−5.23667e17	−0.494538	−0.247269	−	0.968947i	$-0.579533\pi$
$593$	−5.23667e17	−0.494538	−0.247269	+	0.968947i	$0.579533\pi$
$594$	5.99581e16	0.0560061
$595$	−2.01212e17	−0.185906
$596$	1.00873e17	0.0921883
$597$	6.88251e17	0.622176
$598$	−4.26593e17	−0.381466
$599$	−4.23616e17	−0.374712	−0.187356	−	0.982292i	$-0.559992\pi$
$599$	−4.23616e17	−0.374712	−0.187356	+	0.982292i	$0.559992\pi$
$600$	3.68784e17	0.322693
$601$	−6.43390e17	−0.556917	−0.278458	−	0.960448i	$-0.589823\pi$
$601$	−6.43390e17	−0.556917	−0.278458	+	0.960448i	$0.589823\pi$
$602$	−2.78402e17	−0.238394
$603$	−3.18335e17	−0.269663
$604$	1.37362e18	1.15113
$605$	5.00208e16	0.0414706
$606$	3.75708e17	0.308162
$607$	6.08498e17	0.493779	0.246890	−	0.969044i	$-0.420591\pi$
$607$	6.08498e17	0.493779	0.246890	+	0.969044i	$0.420591\pi$
$608$	1.46591e18	1.17688
$609$	−2.15407e17	−0.171099
$610$	−9.20763e16	−0.0723609
$611$	3.31477e18	2.57743
$612$	−3.90954e17	−0.300775
$613$	1.06005e18	0.806923	0.403462	−	0.914997i	$-0.367807\pi$
$613$	1.06005e18	0.806923	0.403462	+	0.914997i	$0.367807\pi$
$614$	8.28095e17	0.623714
$615$	2.42926e17	0.181045
$616$	−5.21510e17	−0.384581
$617$	9.42378e17	0.687656	0.343828	−	0.939033i	$-0.388276\pi$
$617$	9.42378e17	0.687656	0.343828	+	0.939033i	$0.388276\pi$
$618$	−2.56256e17	−0.185033
$619$	−2.65447e18	−1.89666	−0.948329	−	0.317290i	$-0.897227\pi$
$619$	−2.65447e18	−1.89666	−0.948329	+	0.317290i	$0.897227\pi$
$620$	2.38276e16	0.0168475
$621$	−2.43343e17	−0.170264
$622$	3.44010e17	0.238195
$623$	1.17787e18	0.807096
$624$	8.22020e17	0.557420
$625$	1.18021e18	0.792028
$626$	5.65689e17	0.375703
$627$	1.14967e18	0.755677
$628$	2.48145e18	1.61424
$629$	−2.73596e17	−0.176149
$630$	−3.07094e16	−0.0195685
$631$	4.03638e17	0.254566	0.127283	−	0.991866i	$-0.459374\pi$
$631$	4.03638e17	0.254566	0.127283	+	0.991866i	$0.459374\pi$
$632$	−1.17879e18	−0.735827
$633$	1.25572e17	0.0775836
$634$	−2.39625e17	−0.146539
$635$	2.36571e17	0.143197
$636$	2.84465e16	0.0170434
$637$	−1.18475e18	−0.702618
$638$	−2.11191e17	−0.123977
$639$	−3.27852e17	−0.190512
$640$	4.48401e17	0.257927
$641$	−5.77734e17	−0.328966	−0.164483	−	0.986380i	$-0.552596\pi$
$641$	−5.77734e17	−0.328966	−0.164483	+	0.986380i	$0.552596\pi$
$642$	5.88640e16	0.0331797
$643$	−1.99793e18	−1.11483	−0.557415	−	0.830234i	$-0.688207\pi$
$643$	−1.99793e18	−1.11483	−0.557415	+	0.830234i	$0.688207\pi$
$644$	1.00241e18	0.553716
$645$	3.04423e17	0.166471
$646$	8.35717e17	0.452426
$647$	−7.05000e17	−0.377843	−0.188922	−	0.981992i	$-0.560499\pi$
$647$	−7.05000e17	−0.377843	−0.188922	+	0.981992i	$0.560499\pi$
$648$	−1.25989e17	−0.0668489
$649$	−2.27735e17	−0.119630
$650$	−7.70197e17	−0.400557
$651$	5.48146e16	0.0282241
$652$	−3.42419e18	−1.74562
$653$	2.73122e18	1.37854	0.689272	−	0.724503i	$-0.257931\pi$
$653$	2.73122e18	1.37854	0.689272	+	0.724503i	$0.257931\pi$
$654$	3.38447e17	0.169136
$655$	−2.50188e17	−0.123794
$656$	−1.70342e18	−0.834541
$657$	8.12571e17	0.394173
$658$	8.68344e17	0.417084
$659$	−9.55271e17	−0.454330	−0.227165	−	0.973856i	$-0.572946\pi$
$659$	−9.55271e17	−0.454330	−0.227165	+	0.973856i	$0.572946\pi$
$660$	2.70073e17	0.127188
$661$	4.95508e17	0.231069	0.115534	−	0.993303i	$-0.463142\pi$
$661$	4.95508e17	0.231069	0.115534	+	0.993303i	$0.463142\pi$
$662$	6.04076e17	0.278942
$663$	1.72402e18	0.788323
$664$	−1.40752e18	−0.637326
$665$	−5.88843e17	−0.264033
$666$	−4.17568e16	−0.0185415
$667$	8.57127e17	0.376901
$668$	−1.34281e18	−0.584748
$669$	1.95445e18	0.842860
$670$	1.59854e17	0.0682711
$671$	1.86283e18	0.787908
$672$	7.92185e17	0.331838
$673$	−1.15745e18	−0.480180	−0.240090	−	0.970751i	$-0.577177\pi$
$673$	−1.15745e18	−0.480180	−0.240090	+	0.970751i	$0.577177\pi$
$674$	1.06347e18	0.436953
$675$	−4.39346e17	−0.178785
$676$	−1.90532e18	−0.767919
$677$	4.40348e18	1.75780	0.878899	−	0.477007i	$-0.158278\pi$
$677$	4.40348e18	1.75780	0.878899	+	0.477007i	$0.158278\pi$
$678$	5.43687e17	0.214959
$679$	−6.07694e17	−0.237975
$680$	4.14527e17	0.160785
$681$	−2.09848e18	−0.806211
$682$	5.37417e16	0.0204509
$683$	3.59605e18	1.35547	0.677737	−	0.735304i	$-0.262961\pi$
$683$	3.59605e18	1.35547	0.677737	+	0.735304i	$0.262961\pi$
$684$	−1.14412e18	−0.427176
$685$	8.00224e17	0.295953
$686$	−9.11731e17	−0.334010
$687$	6.27269e17	0.227633
$688$	−2.13465e18	−0.767363
$689$	−1.25443e17	−0.0446704
$690$	1.22196e17	0.0431060
$691$	−2.36146e18	−0.825226	−0.412613	−	0.910906i	$-0.635384\pi$
$691$	−2.36146e18	−0.825226	−0.412613	+	0.910906i	$0.635384\pi$
$692$	3.12128e18	1.08055
$693$	6.21292e17	0.213074
$694$	8.86959e17	0.301347
$695$	−4.30253e17	−0.144818
$696$	4.43770e17	0.147978
$697$	−3.57259e18	−1.18024
$698$	1.63184e18	0.534095
$699$	3.33040e18	1.07993
$700$	1.80981e18	0.581429
$701$	4.90181e18	1.56023	0.780116	−	0.625635i	$-0.215160\pi$
$701$	4.90181e18	1.56023	0.780116	+	0.625635i	$0.215160\pi$
$702$	2.63124e17	0.0829792
$703$	−8.00673e17	−0.250176
$704$	−1.32822e18	−0.411195
$705$	−9.49506e17	−0.291252
$706$	2.40386e16	0.00730598
$707$	3.89313e18	1.17239
$708$	2.26635e17	0.0676256
$709$	−5.28943e17	−0.156390	−0.0781949	−	0.996938i	$-0.524916\pi$
$709$	−5.28943e17	−0.156390	−0.0781949	+	0.996938i	$0.524916\pi$
$710$	1.64633e17	0.0482323
$711$	1.40433e18	0.407679
$712$	−2.42659e18	−0.698034
$713$	−2.18113e17	−0.0621727
$714$	4.51627e17	0.127568
$715$	−1.19096e18	−0.333356
$716$	2.50268e18	0.694178
$717$	7.30355e17	0.200752
$718$	9.66348e17	0.263224
$719$	−3.32936e17	−0.0898718	−0.0449359	−	0.998990i	$-0.514308\pi$
$719$	−3.32936e17	−0.0898718	−0.0449359	+	0.998990i	$0.514308\pi$
$720$	−2.35465e17	−0.0629890
$721$	−2.65535e18	−0.703952
$722$	1.24028e18	0.325856
$723$	−1.97025e18	−0.513005
$724$	−1.75622e18	−0.453189
$725$	1.54751e18	0.395764
$726$	−1.12273e17	−0.0284570
$727$	−4.92404e18	−1.23694	−0.618469	−	0.785810i	$-0.712247\pi$
$727$	−4.92404e18	−1.23694	−0.618469	+	0.785810i	$0.712247\pi$
$728$	−2.28863e18	−0.569798
$729$	1.50095e17	0.0370370
$730$	−4.08038e17	−0.0997934
$731$	−4.47699e18	−1.08523
$732$	−1.85382e18	−0.445396
$733$	−3.40343e18	−0.810478	−0.405239	−	0.914211i	$-0.632812\pi$
$733$	−3.40343e18	−0.810478	−0.405239	+	0.914211i	$0.632812\pi$
$734$	−1.96661e18	−0.464187
$735$	3.39367e17	0.0793966
$736$	−3.15219e18	−0.730982
$737$	−3.23406e18	−0.743376
$738$	−5.45257e17	−0.124232
$739$	4.10703e18	0.927553	0.463777	−	0.885952i	$-0.346494\pi$
$739$	4.10703e18	0.927553	0.463777	+	0.885952i	$0.346494\pi$
$740$	−1.88088e17	−0.0421071
$741$	5.04531e18	1.11962
$742$	−3.28611e16	−0.00722865
$743$	2.15656e18	0.470256	0.235128	−	0.971964i	$-0.424449\pi$
$743$	2.15656e18	0.470256	0.235128	+	0.971964i	$0.424449\pi$
$744$	−1.12926e17	−0.0244102
$745$	1.27420e17	0.0273037
$746$	−2.13324e18	−0.453146
$747$	1.67683e18	0.353105
$748$	−3.97182e18	−0.829142
$749$	6.09956e17	0.126231
$750$	4.58103e17	0.0939863
$751$	−5.70403e18	−1.16017	−0.580086	−	0.814555i	$-0.696981\pi$
$751$	−5.70403e18	−1.16017	−0.580086	+	0.814555i	$0.696981\pi$
$752$	6.65803e18	1.34255
$753$	3.05619e18	0.610961
$754$	−9.26803e17	−0.183685
$755$	1.73511e18	0.340934
$756$	−6.18290e17	−0.120448
$757$	6.80967e18	1.31523	0.657617	−	0.753353i	$-0.271565\pi$
$757$	6.80967e18	1.31523	0.657617	+	0.753353i	$0.271565\pi$
$758$	3.94308e17	0.0755068
$759$	−2.47219e18	−0.469364
$760$	1.21310e18	0.228355
$761$	−7.27192e18	−1.35722	−0.678608	−	0.734501i	$-0.737417\pi$
$761$	−7.27192e18	−1.35722	−0.678608	+	0.734501i	$0.737417\pi$
$762$	−5.30993e17	−0.0982610
$763$	3.50703e18	0.643472
$764$	6.91671e18	1.25833
$765$	−4.93840e17	−0.0890814
$766$	−7.09993e17	−0.126989
$767$	−9.99409e17	−0.177245
$768$	4.62710e17	0.0813693
$769$	−5.26207e18	−0.917562	−0.458781	−	0.888549i	$-0.651714\pi$
$769$	−5.26207e18	−0.917562	−0.458781	+	0.888549i	$0.651714\pi$
$770$	−3.11986e17	−0.0539443
$771$	−3.32084e18	−0.569371
$772$	−3.26760e17	−0.0555541
$773$	5.20743e18	0.877924	0.438962	−	0.898506i	$-0.355346\pi$
$773$	5.20743e18	0.877924	0.438962	+	0.898506i	$0.355346\pi$
$774$	−6.83289e17	−0.114232
$775$	−3.93795e17	−0.0652843
$776$	1.25194e18	0.205818
$777$	−4.32689e17	−0.0705406
$778$	1.76223e18	0.284901
$779$	−1.04551e19	−1.67624
$780$	1.18521e18	0.188443
$781$	−3.33074e18	−0.525182
$782$	−1.79707e18	−0.281010
$783$	−5.28679e17	−0.0819862
$784$	−2.37968e18	−0.365985
$785$	3.13448e18	0.478093
$786$	5.61556e17	0.0849467
$787$	1.23580e19	1.85401	0.927006	−	0.375047i	$-0.122373\pi$
$787$	1.23580e19	1.85401	0.927006	+	0.375047i	$0.122373\pi$
$788$	−2.91523e18	−0.433764
$789$	4.53816e18	0.669699
$790$	−7.05196e17	−0.103213
$791$	5.63375e18	0.817806
$792$	−1.27996e18	−0.184281
$793$	8.17495e18	1.16737
$794$	6.50412e17	0.0921202
$795$	3.59326e16	0.00504780
$796$	−6.95835e18	−0.969553
$797$	−4.92356e18	−0.680456	−0.340228	−	0.940343i	$-0.610504\pi$
$797$	−4.92356e18	−0.680456	−0.340228	+	0.940343i	$0.610504\pi$
$798$	1.32168e18	0.181179
$799$	1.39639e19	1.89868
$800$	−5.69116e18	−0.767566
$801$	2.89088e18	0.386740
$802$	1.89717e18	0.251752
$803$	8.25514e18	1.08661
$804$	3.21843e18	0.420223
$805$	1.26621e18	0.163996
$806$	2.35844e17	0.0303003
$807$	−7.34714e18	−0.936354
$808$	−8.02044e18	−1.01397
$809$	−7.88987e18	−0.989474	−0.494737	−	0.869043i	$-0.664736\pi$
$809$	−7.88987e18	−0.989474	−0.494737	+	0.869043i	$0.664736\pi$
$810$	−7.53710e16	−0.00937674
$811$	1.10628e19	1.36531	0.682653	−	0.730743i	$-0.260826\pi$
$811$	1.10628e19	1.36531	0.682653	+	0.730743i	$0.260826\pi$
$812$	2.17781e18	0.266628
$813$	−5.17798e18	−0.628885
$814$	−4.24220e17	−0.0511131
$815$	−4.32532e18	−0.517004
$816$	3.46286e18	0.410628
$817$	−1.31018e19	−1.54130
$818$	−3.20893e18	−0.374510
$819$	2.72652e18	0.315692
$820$	−2.45604e18	−0.282127
$821$	4.81763e17	0.0549039	0.0274520	−	0.999623i	$-0.491261\pi$
$821$	4.81763e17	0.0549039	0.0274520	+	0.999623i	$0.491261\pi$
$822$	−1.79613e18	−0.203082
$823$	1.32130e19	1.48218	0.741092	−	0.671404i	$-0.234308\pi$
$823$	1.32130e19	1.48218	0.741092	+	0.671404i	$0.234308\pi$
$824$	5.47042e18	0.608827
$825$	−4.46344e18	−0.492855
$826$	−2.61807e17	−0.0286821
$827$	1.31017e18	0.142411	0.0712055	−	0.997462i	$-0.477315\pi$
$827$	1.31017e18	0.142411	0.0712055	+	0.997462i	$0.477315\pi$
$828$	2.46024e18	0.265327
$829$	3.40684e18	0.364542	0.182271	−	0.983248i	$-0.441655\pi$
$829$	3.40684e18	0.364542	0.182271	+	0.983248i	$0.441655\pi$
$830$	−8.42029e17	−0.0893963
$831$	−9.57264e17	−0.100838
$832$	−5.82886e18	−0.609231
$833$	−4.99089e18	−0.517590
$834$	9.65718e17	0.0993736
$835$	−1.69620e18	−0.173186
$836$	−1.16234e19	−1.17759
$837$	1.34533e17	0.0135243
$838$	−3.21020e18	−0.320219
$839$	−2.82067e18	−0.279190	−0.139595	−	0.990209i	$-0.544580\pi$
$839$	−2.82067e18	−0.279190	−0.139595	+	0.990209i	$0.544580\pi$
$840$	6.55570e17	0.0643878
$841$	−8.39846e18	−0.818513
$842$	1.31613e18	0.127283
$843$	5.45037e18	0.523054
$844$	−1.26956e18	−0.120900
$845$	−2.40674e18	−0.227437
$846$	2.13120e18	0.199856
$847$	−1.16339e18	−0.108264
$848$	−2.51963e17	−0.0232683
$849$	6.51840e18	0.597367
$850$	−3.24454e18	−0.295074
$851$	1.72172e18	0.155389
$852$	3.31465e18	0.296880
$853$	−3.84425e17	−0.0341698	−0.0170849	−	0.999854i	$-0.505439\pi$
$853$	−3.84425e17	−0.0341698	−0.0170849	+	0.999854i	$0.505439\pi$
$854$	2.14152e18	0.188906
$855$	−1.44521e18	−0.126518
$856$	−1.25660e18	−0.109174
$857$	3.39679e18	0.292882	0.146441	−	0.989219i	$-0.453218\pi$
$857$	3.39679e18	0.292882	0.146441	+	0.989219i	$0.453218\pi$
$858$	2.67315e18	0.228748
$859$	−2.05123e19	−1.74204	−0.871022	−	0.491245i	$-0.836542\pi$
$859$	−2.05123e19	−1.74204	−0.871022	+	0.491245i	$0.836542\pi$
$860$	−3.07778e18	−0.259417
$861$	−5.65001e18	−0.472638
$862$	−1.41957e18	−0.117858
$863$	−4.66645e18	−0.384518	−0.192259	−	0.981344i	$-0.561581\pi$
$863$	−4.66645e18	−0.384518	−0.192259	+	0.981344i	$0.561581\pi$
$864$	1.94428e18	0.159008
$865$	3.94270e18	0.320028
$866$	1.69178e18	0.136294
$867$	4.22020e16	0.00337450
$868$	−5.54187e17	−0.0439823
$869$	1.42670e19	1.12384
$870$	2.65480e17	0.0207566
$871$	−1.41925e19	−1.10139
$872$	−7.22501e18	−0.556520
$873$	−1.49148e18	−0.114031
$874$	−5.25910e18	−0.399105
$875$	4.74691e18	0.357568
$876$	−8.21526e18	−0.614249
$877$	−1.53247e19	−1.13735	−0.568676	−	0.822562i	$-0.692544\pi$
$877$	−1.53247e19	−1.13735	−0.568676	+	0.822562i	$0.692544\pi$
$878$	−5.60132e18	−0.412644
$879$	6.47441e18	0.473448
$880$	−2.39216e18	−0.173641
$881$	7.53364e18	0.542827	0.271414	−	0.962463i	$-0.412509\pi$
$881$	7.53364e18	0.542827	0.271414	+	0.962463i	$0.412509\pi$
$882$	−7.61721e17	−0.0544817
$883$	−1.72537e19	−1.22500	−0.612502	−	0.790469i	$-0.709837\pi$
$883$	−1.72537e19	−1.22500	−0.612502	+	0.790469i	$0.709837\pi$
$884$	−1.74302e19	−1.22846
$885$	2.86278e17	0.0200288
$886$	−7.55679e18	−0.524830
$887$	−2.58215e17	−0.0178024	−0.00890120	−	0.999960i	$-0.502833\pi$
$887$	−2.58215e17	−0.0178024	−0.00890120	+	0.999960i	$0.502833\pi$
$888$	8.91405e17	0.0610085
$889$	−5.50221e18	−0.373831
$890$	−1.45167e18	−0.0979116
$891$	1.52485e18	0.102099
$892$	−1.97599e19	−1.31345
$893$	4.08650e19	2.69660
$894$	−2.85998e17	−0.0187357
$895$	3.16130e18	0.205597
$896$	−1.04290e19	−0.673348
$897$	−1.08491e19	−0.695414
$898$	−3.95201e18	−0.251490
$899$	−4.73866e17	−0.0299376
$900$	4.44187e18	0.278606
$901$	−5.28442e17	−0.0329068
$902$	−5.53942e18	−0.342470
$903$	−7.08032e18	−0.434593
$904$	−1.16064e19	−0.707297
$905$	−2.21840e18	−0.134222
$906$	−3.89451e18	−0.233948
$907$	−2.92969e19	−1.74733	−0.873664	−	0.486530i	$-0.838262\pi$
$907$	−2.92969e19	−1.74733	−0.873664	+	0.486530i	$0.838262\pi$
$908$	2.12161e19	1.25634
$909$	9.55503e18	0.561781
$910$	−1.36914e18	−0.0799243
$911$	2.84837e19	1.65092	0.825462	−	0.564458i	$-0.190915\pi$
$911$	2.84837e19	1.65092	0.825462	+	0.564458i	$0.190915\pi$
$912$	1.01340e19	0.583195
$913$	1.70354e19	0.973400
$914$	3.29133e18	0.186733
$915$	−2.34169e18	−0.131914
$916$	−6.34182e18	−0.354726
$917$	5.81891e18	0.323177
$918$	1.10844e18	0.0611273
$919$	−1.04671e19	−0.573161	−0.286580	−	0.958056i	$-0.592519\pi$
$919$	−1.04671e19	−0.573161	−0.286580	+	0.958056i	$0.592519\pi$
$920$	−2.60858e18	−0.141835
$921$	2.10601e19	1.13703
$922$	−1.98980e18	−0.106674
$923$	−1.46169e19	−0.778114
$924$	−6.28139e18	−0.332038
$925$	3.10849e18	0.163166
$926$	−1.41934e18	−0.0739804
$927$	−6.51710e18	−0.337316
$928$	−6.84836e18	−0.351985
$929$	1.24768e19	0.636799	0.318399	−	0.947957i	$-0.396855\pi$
$929$	1.24768e19	0.636799	0.318399	+	0.947957i	$0.396855\pi$
$930$	−6.75566e16	−0.00342396
$931$	−1.46057e19	−0.735107
$932$	−3.36711e19	−1.68288
$933$	8.74887e18	0.434231
$934$	6.40548e18	0.315716
$935$	−5.01706e18	−0.245569
$936$	−5.61704e18	−0.273033
$937$	2.05527e19	0.992112	0.496056	−	0.868291i	$-0.334781\pi$
$937$	2.05527e19	0.992112	0.496056	+	0.868291i	$0.334781\pi$
$938$	−3.71790e18	−0.178229
$939$	1.43866e19	0.684908
$940$	9.59970e18	0.453865
$941$	−3.02681e19	−1.42119	−0.710595	−	0.703601i	$-0.751574\pi$
$941$	−3.02681e19	−1.42119	−0.710595	+	0.703601i	$0.751574\pi$
$942$	−7.03545e18	−0.328066
$943$	2.24820e19	1.04114
$944$	−2.00741e18	−0.0923246
$945$	−7.81003e17	−0.0356735
$946$	−6.94173e18	−0.314902
$947$	−3.41885e19	−1.54030	−0.770150	−	0.637862i	$-0.779819\pi$
$947$	−3.41885e19	−1.54030	−0.770150	+	0.637862i	$0.779819\pi$
$948$	−1.41981e19	−0.635296
$949$	3.62274e19	1.60993
$950$	−9.49510e18	−0.419079
$951$	−6.09415e18	−0.267141
$952$	−9.64112e18	−0.419747
$953$	1.70835e19	0.738710	0.369355	−	0.929288i	$-0.379579\pi$
$953$	1.70835e19	0.738710	0.369355	+	0.929288i	$0.379579\pi$
$954$	−8.06520e16	−0.00346378
$955$	8.73695e18	0.372682
$956$	−7.38404e18	−0.312837
$957$	−5.37100e18	−0.226010
$958$	8.67036e18	0.362378
$959$	−1.86117e19	−0.772620
$960$	1.66966e18	0.0688437
$961$	−2.42970e19	−0.995062
$962$	−1.86167e18	−0.0757296
$963$	1.49703e18	0.0604867
$964$	1.99196e19	0.799429
$965$	−4.12752e17	−0.0164536
$966$	−2.84205e18	−0.112533
$967$	−4.48509e19	−1.76400	−0.882002	−	0.471246i	$-0.843804\pi$
$967$	−4.48509e19	−1.76400	−0.882002	+	0.471246i	$0.843804\pi$
$968$	2.39676e18	0.0936342
$969$	2.12540e19	0.824775
$970$	7.48956e17	0.0288696
$971$	3.21613e19	1.23143	0.615713	−	0.787971i	$-0.288868\pi$
$971$	3.21613e19	1.23143	0.615713	+	0.787971i	$0.288868\pi$
$972$	−1.51749e18	−0.0577157
$973$	1.00069e19	0.378064
$974$	−8.91177e16	−0.00334450
$975$	−1.95877e19	−0.730218
$976$	1.64201e19	0.608069
$977$	−1.01925e19	−0.374942	−0.187471	−	0.982270i	$-0.560029\pi$
$977$	−1.01925e19	−0.374942	−0.187471	+	0.982270i	$0.560029\pi$
$978$	9.70833e18	0.354766
$979$	2.93693e19	1.06612
$980$	−3.43107e18	−0.123726
$981$	8.60740e18	0.308335
$982$	1.38393e19	0.492482
$983$	6.79418e18	0.240181	0.120091	−	0.992763i	$-0.461681\pi$
$983$	6.79418e18	0.240181	0.120091	+	0.992763i	$0.461681\pi$
$984$	1.16399e19	0.408771
$985$	−3.68242e18	−0.128469
$986$	−3.90427e18	−0.135313
$987$	2.20837e19	0.760346
$988$	−5.10091e19	−1.74473
$989$	2.81733e19	0.957331
$990$	−7.65716e17	−0.0258487
$991$	−2.27185e19	−0.761905	−0.380952	−	0.924595i	$-0.624404\pi$
$991$	−2.27185e19	−0.761905	−0.380952	+	0.924595i	$0.624404\pi$
$992$	1.74270e18	0.0580627
$993$	1.53629e19	0.508513
$994$	−3.82906e18	−0.125916
$995$	−8.78955e18	−0.287155
$996$	−1.69531e19	−0.550253
$997$	−3.14471e19	−1.01406	−0.507028	−	0.861929i	$-0.669256\pi$
$997$	−3.14471e19	−1.01406	−0.507028	+	0.861929i	$0.669256\pi$
$998$	−1.10066e19	−0.352618
$999$	−1.06196e18	−0.0338013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.18	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+28.6646 q^{2} +729.000 q^{3} -7370.34 q^{4} -9309.96 q^{5} +20896.5 q^{6} +216532. q^{7} -446089. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+28.6646 q^{2} +729.000 q^{3} -7370.34 q^{4} -9309.96 q^{5} +20896.5 q^{6} +216532. q^{7} -446089. q^{8} +531441. q^{9} -266867. q^{10} +5.39906e6 q^{11} -5.37298e6 q^{12} +2.36936e7 q^{13} +6.20682e6 q^{14} -6.78696e6 q^{15} +4.75908e7 q^{16} +9.98122e7 q^{17} +1.52336e7 q^{18} +2.92098e8 q^{19} +6.86175e7 q^{20} +1.57852e8 q^{21} +1.54762e8 q^{22} -6.28110e8 q^{23} -3.25199e8 q^{24} -1.13403e9 q^{25} +6.79169e8 q^{26} +3.87420e8 q^{27} -1.59592e9 q^{28} -1.36461e9 q^{29} -1.94546e8 q^{30} +3.47253e8 q^{31} +5.01853e9 q^{32} +3.93592e9 q^{33} +2.86108e9 q^{34} -2.01591e9 q^{35} -3.91690e9 q^{36} -2.74111e9 q^{37} +8.37289e9 q^{38} +1.72726e10 q^{39} +4.15307e9 q^{40} -3.57931e10 q^{41} +4.52477e9 q^{42} -4.48542e10 q^{43} -3.97929e10 q^{44} -4.94769e9 q^{45} -1.80045e10 q^{46} +1.39902e11 q^{47} +3.46937e10 q^{48} -5.00028e10 q^{49} -3.25065e10 q^{50} +7.27631e10 q^{51} -1.74630e11 q^{52} -5.29436e9 q^{53} +1.11053e10 q^{54} -5.02650e10 q^{55} -9.65926e10 q^{56} +2.12940e11 q^{57} -3.91161e10 q^{58} -4.21805e10 q^{59} +5.00222e10 q^{60} +3.45027e11 q^{61} +9.95389e9 q^{62} +1.15074e11 q^{63} -2.46010e11 q^{64} -2.20587e11 q^{65} +1.12822e11 q^{66} -5.99003e11 q^{67} -7.35649e11 q^{68} -4.57892e11 q^{69} -5.77852e10 q^{70} -6.16912e11 q^{71} -2.37070e11 q^{72} +1.52900e12 q^{73} -7.85728e10 q^{74} -8.26706e11 q^{75} -2.15286e12 q^{76} +1.16907e12 q^{77} +4.95114e11 q^{78} +2.64250e12 q^{79} -4.43069e11 q^{80} +2.82430e11 q^{81} -1.02600e12 q^{82} +3.15524e12 q^{83} -1.16342e12 q^{84} -9.29247e11 q^{85} -1.28573e12 q^{86} -9.94803e11 q^{87} -2.40846e12 q^{88} +5.43970e12 q^{89} -1.41824e11 q^{90} +5.13043e12 q^{91} +4.62938e12 q^{92} +2.53147e11 q^{93} +4.01023e12 q^{94} -2.71942e12 q^{95} +3.65851e12 q^{96} -2.80648e12 q^{97} -1.43331e12 q^{98} +2.86928e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9} + 4647481 q^{10} + 17937316 q^{11} + 92499894 q^{12} + 40664720 q^{13} + 139193613 q^{14} + 59054832 q^{15} + 370110498 q^{16} + 213442823 q^{17} + 164746710 q^{18} - 62592329 q^{19} + 1637085153 q^{20} + 731143989 q^{21} + 4142028314 q^{22} + 1873486387 q^{23} + 3377255067 q^{24} + 8307272395 q^{25} - 534777728 q^{26} + 12010035159 q^{27} + 766416778 q^{28} + 13765513563 q^{29} + 3388013649 q^{30} + 14274077235 q^{31} + 30574460156 q^{32} + 13076303364 q^{33} - 677551028 q^{34} + 36023610185 q^{35} + 67432422726 q^{36} - 18278838391 q^{37} - 23650502933 q^{38} + 29644580880 q^{39} + 10045447572 q^{40} + 34748006725 q^{41} + 101472143877 q^{42} + 40350158146 q^{43} + 163101196592 q^{44} + 43050972528 q^{45} + 296118466353 q^{46} + 233954631099 q^{47} + 269810553042 q^{48} + 324065402790 q^{49} - 102960745787 q^{50} + 155599817967 q^{51} + 668297695096 q^{52} + 500927963876 q^{53} + 120100351590 q^{54} + 884972340924 q^{55} + 1392234478810 q^{56} - 45629807841 q^{57} + 689262776200 q^{58} - 1307596542871 q^{59} + 1193435076537 q^{60} + 1716832157925 q^{61} + 1816094290366 q^{62} + 533003967981 q^{63} + 4381780009133 q^{64} + 1457007885906 q^{65} + 3019538640906 q^{66} + 1212131702006 q^{67} + 6552992665503 q^{68} + 1365771576123 q^{69} + 8806714081634 q^{70} + 6074000239936 q^{71} + 2462018943843 q^{72} + 3756145185973 q^{73} + 8066450143602 q^{74} + 6056001575955 q^{75} + 7913230001992 q^{76} + 6031241575915 q^{77} - 389852963712 q^{78} + 11377744190862 q^{79} + 16473302366969 q^{80} + 8755315630911 q^{81} + 10413363680159 q^{82} + 19915461517429 q^{83} + 558717831162 q^{84} + 15280981141573 q^{85} + 7573325358452 q^{86} + 10035059387427 q^{87} + 19271409121081 q^{88} + 14115863121241 q^{89} + 2469861950121 q^{90} + 18296287784699 q^{91} + 15158951168774 q^{92} + 10405802304315 q^{93} - 18637923572412 q^{94} - 2294034679397 q^{95} + 22288781453724 q^{96} + 38558536599054 q^{97} - 1998410212380 q^{98} + 9532625152356 q^{99}+O(q^{100}) \) 31 * q + 310 * q^2 + 22599 * q^3 + 126886 * q^4 + 81008 * q^5 + 225990 * q^6 + 1002941 * q^7 + 4632723 * q^8 + 16474671 * q^9 + 4647481 * q^10 + 17937316 * q^11 + 92499894 * q^12 + 40664720 * q^13 + 139193613 * q^14 + 59054832 * q^15 + 370110498 * q^16 + 213442823 * q^17 + 164746710 * q^18 - 62592329 * q^19 + 1637085153 * q^20 + 731143989 * q^21 + 4142028314 * q^22 + 1873486387 * q^23 + 3377255067 * q^24 + 8307272395 * q^25 - 534777728 * q^26 + 12010035159 * q^27 + 766416778 * q^28 + 13765513563 * q^29 + 3388013649 * q^30 + 14274077235 * q^31 + 30574460156 * q^32 + 13076303364 * q^33 - 677551028 * q^34 + 36023610185 * q^35 + 67432422726 * q^36 - 18278838391 * q^37 - 23650502933 * q^38 + 29644580880 * q^39 + 10045447572 * q^40 + 34748006725 * q^41 + 101472143877 * q^42 + 40350158146 * q^43 + 163101196592 * q^44 + 43050972528 * q^45 + 296118466353 * q^46 + 233954631099 * q^47 + 269810553042 * q^48 + 324065402790 * q^49 - 102960745787 * q^50 + 155599817967 * q^51 + 668297695096 * q^52 + 500927963876 * q^53 + 120100351590 * q^54 + 884972340924 * q^55 + 1392234478810 * q^56 - 45629807841 * q^57 + 689262776200 * q^58 - 1307596542871 * q^59 + 1193435076537 * q^60 + 1716832157925 * q^61 + 1816094290366 * q^62 + 533003967981 * q^63 + 4381780009133 * q^64 + 1457007885906 * q^65 + 3019538640906 * q^66 + 1212131702006 * q^67 + 6552992665503 * q^68 + 1365771576123 * q^69 + 8806714081634 * q^70 + 6074000239936 * q^71 + 2462018943843 * q^72 + 3756145185973 * q^73 + 8066450143602 * q^74 + 6056001575955 * q^75 + 7913230001992 * q^76 + 6031241575915 * q^77 - 389852963712 * q^78 + 11377744190862 * q^79 + 16473302366969 * q^80 + 8755315630911 * q^81 + 10413363680159 * q^82 + 19915461517429 * q^83 + 558717831162 * q^84 + 15280981141573 * q^85 + 7573325358452 * q^86 + 10035059387427 * q^87 + 19271409121081 * q^88 + 14115863121241 * q^89 + 2469861950121 * q^90 + 18296287784699 * q^91 + 15158951168774 * q^92 + 10405802304315 * q^93 - 18637923572412 * q^94 - 2294034679397 * q^95 + 22288781453724 * q^96 + 38558536599054 * q^97 - 1998410212380 * q^98 + 9532625152356 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more