LMFDB - Embedded newform 177.14.a.c.1.23

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			1.23
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)

$f(q)$	$=$	$q+116.798 q^{2} +729.000 q^{3} +5449.77 q^{4} -23284.9 q^{5} +85145.7 q^{6} -557119. q^{7} -320287. q^{8} +531441. q^{9} +O(q^{10})$	\(q+116.798 q^{2} +729.000 q^{3} +5449.77 q^{4} -23284.9 q^{5} +85145.7 q^{6} -557119. q^{7} -320287. q^{8} +531441. q^{9} -2.71963e6 q^{10} +2.68829e6 q^{11} +3.97288e6 q^{12} -2.49854e7 q^{13} -6.50704e7 q^{14} -1.69747e7 q^{15} -8.20534e7 q^{16} +1.26429e8 q^{17} +6.20712e7 q^{18} -2.65229e8 q^{19} -1.26898e8 q^{20} -4.06140e8 q^{21} +3.13987e8 q^{22} +2.77293e8 q^{23} -2.33489e8 q^{24} -6.78515e8 q^{25} -2.91824e9 q^{26} +3.87420e8 q^{27} -3.03617e9 q^{28} +4.45180e9 q^{29} -1.98261e9 q^{30} +5.87821e9 q^{31} -6.95988e9 q^{32} +1.95976e9 q^{33} +1.47666e10 q^{34} +1.29725e10 q^{35} +2.89623e9 q^{36} -7.00004e9 q^{37} -3.09782e10 q^{38} -1.82143e10 q^{39} +7.45785e9 q^{40} -8.11827e9 q^{41} -4.74363e10 q^{42} -3.05475e10 q^{43} +1.46506e10 q^{44} -1.23746e10 q^{45} +3.23873e10 q^{46} -3.22065e10 q^{47} -5.98169e10 q^{48} +2.13492e11 q^{49} -7.92492e10 q^{50} +9.21665e10 q^{51} -1.36165e11 q^{52} -4.59207e10 q^{53} +4.52499e10 q^{54} -6.25967e10 q^{55} +1.78438e11 q^{56} -1.93352e11 q^{57} +5.19961e11 q^{58} -4.21805e10 q^{59} -9.25083e10 q^{60} +5.48411e11 q^{61} +6.86563e11 q^{62} -2.96076e11 q^{63} -1.40719e11 q^{64} +5.81783e11 q^{65} +2.28897e11 q^{66} +7.48892e11 q^{67} +6.89008e11 q^{68} +2.02147e11 q^{69} +1.51516e12 q^{70} -1.36505e11 q^{71} -1.70213e11 q^{72} -4.36896e11 q^{73} -8.17590e11 q^{74} -4.94638e11 q^{75} -1.44544e12 q^{76} -1.49770e12 q^{77} -2.12740e12 q^{78} +3.74160e12 q^{79} +1.91061e12 q^{80} +2.82430e11 q^{81} -9.48198e11 q^{82} +2.29306e12 q^{83} -2.21337e12 q^{84} -2.94388e12 q^{85} -3.56789e12 q^{86} +3.24536e12 q^{87} -8.61024e11 q^{88} -3.64309e12 q^{89} -1.44532e12 q^{90} +1.39198e13 q^{91} +1.51118e12 q^{92} +4.28522e12 q^{93} -3.76165e12 q^{94} +6.17583e12 q^{95} -5.07375e12 q^{96} +1.41054e13 q^{97} +2.49355e13 q^{98} +1.42867e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	116.798	1.29045	0.645224	−	0.763994i	$-0.276764\pi$
$2$	116.798	1.29045	0.645224	+	0.763994i	$0.276764\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	5449.77	0.665256
$5$	−23284.9	−0.666453	−0.333227	−	0.942847i	$-0.608137\pi$
$5$	−23284.9	−0.666453	−0.333227	+	0.942847i	$0.608137\pi$
$6$	85145.7	0.745040
$7$	−557119.	−1.78982	−0.894912	−	0.446242i	$-0.852762\pi$
$7$	−557119.	−1.78982	−0.894912	+	0.446242i	$0.852762\pi$
$8$	−320287.	−0.431970
$9$	531441.	0.333333
$10$	−2.71963e6	−0.860023
$11$	2.68829e6	0.457534	0.228767	−	0.973481i	$-0.426531\pi$
$11$	2.68829e6	0.457534	0.228767	+	0.973481i	$0.426531\pi$
$12$	3.97288e6	0.384085
$13$	−2.49854e7	−1.43567	−0.717834	−	0.696214i	$-0.754866\pi$
$13$	−2.49854e7	−1.43567	−0.717834	+	0.696214i	$0.754866\pi$
$14$	−6.50704e7	−2.30968
$15$	−1.69747e7	−0.384777
$16$	−8.20534e7	−1.22269
$17$	1.26429e8	1.27036	0.635181	−	0.772363i	$-0.280925\pi$
$17$	1.26429e8	1.27036	0.635181	+	0.772363i	$0.280925\pi$
$18$	6.20712e7	0.430149
$19$	−2.65229e8	−1.29337	−0.646684	−	0.762758i	$-0.723845\pi$
$19$	−2.65229e8	−1.29337	−0.646684	+	0.762758i	$0.723845\pi$
$20$	−1.26898e8	−0.443362
$21$	−4.06140e8	−1.03336
$22$	3.13987e8	0.590424
$23$	2.77293e8	0.390578	0.195289	−	0.980746i	$-0.437435\pi$
$23$	2.77293e8	0.390578	0.195289	+	0.980746i	$0.437435\pi$
$24$	−2.33489e8	−0.249398
$25$	−6.78515e8	−0.555840
$26$	−2.91824e9	−1.85266
$27$	3.87420e8	0.192450
$28$	−3.03617e9	−1.19069
$29$	4.45180e9	1.38979	0.694894	−	0.719112i	$-0.255451\pi$
$29$	4.45180e9	1.38979	0.694894	+	0.719112i	$0.255451\pi$
$30$	−1.98261e9	−0.496535
$31$	5.87821e9	1.18958	0.594791	−	0.803881i	$-0.297235\pi$
$31$	5.87821e9	1.18958	0.594791	+	0.803881i	$0.297235\pi$
$32$	−6.95988e9	−1.14585
$33$	1.95976e9	0.264158
$34$	1.47666e10	1.63934
$35$	1.29725e10	1.19283
$36$	2.89623e9	0.221752
$37$	−7.00004e9	−0.448527	−0.224264	−	0.974528i	$-0.571998\pi$
$37$	−7.00004e9	−0.448527	−0.224264	+	0.974528i	$0.571998\pi$
$38$	−3.09782e10	−1.66902
$39$	−1.82143e10	−0.828884
$40$	7.45785e9	0.287888
$41$	−8.11827e9	−0.266912	−0.133456	−	0.991055i	$-0.542608\pi$
$41$	−8.11827e9	−0.266912	−0.133456	+	0.991055i	$0.542608\pi$
$42$	−4.74363e10	−1.33349
$43$	−3.05475e10	−0.736938	−0.368469	−	0.929640i	$-0.620118\pi$
$43$	−3.05475e10	−0.736938	−0.368469	+	0.929640i	$0.620118\pi$
$44$	1.46506e10	0.304377
$45$	−1.23746e10	−0.222151
$46$	3.23873e10	0.504021
$47$	−3.22065e10	−0.435820	−0.217910	−	0.975969i	$-0.569924\pi$
$47$	−3.22065e10	−0.435820	−0.217910	+	0.975969i	$0.569924\pi$
$48$	−5.98169e10	−0.705921
$49$	2.13492e11	2.20347
$50$	−7.92492e10	−0.717282
$51$	9.21665e10	0.733444
$52$	−1.36165e11	−0.955087
$53$	−4.59207e10	−0.284587	−0.142294	−	0.989824i	$-0.545448\pi$
$53$	−4.59207e10	−0.284587	−0.142294	+	0.989824i	$0.545448\pi$
$54$	4.52499e10	0.248347
$55$	−6.25967e10	−0.304925
$56$	1.78438e11	0.773151
$57$	−1.93352e11	−0.746726
$58$	5.19961e11	1.79345
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−9.25083e10	−0.255975
$61$	5.48411e11	1.36289	0.681447	−	0.731867i	$-0.261351\pi$
$61$	5.48411e11	1.36289	0.681447	+	0.731867i	$0.261351\pi$
$62$	6.86563e11	1.53509
$63$	−2.96076e11	−0.596608
$64$	−1.40719e11	−0.255967
$65$	5.81783e11	0.956806
$66$	2.28897e11	0.340882
$67$	7.48892e11	1.01142	0.505712	−	0.862703i	$-0.331230\pi$
$67$	7.48892e11	1.01142	0.505712	+	0.862703i	$0.331230\pi$
$68$	6.89008e11	0.845115
$69$	2.02147e11	0.225500
$70$	1.51516e12	1.53929
$71$	−1.36505e11	−0.126465	−0.0632323	−	0.997999i	$-0.520141\pi$
$71$	−1.36505e11	−0.126465	−0.0632323	+	0.997999i	$0.520141\pi$
$72$	−1.70213e11	−0.143990
$73$	−4.36896e11	−0.337893	−0.168947	−	0.985625i	$-0.554037\pi$
$73$	−4.36896e11	−0.337893	−0.168947	+	0.985625i	$0.554037\pi$
$74$	−8.17590e11	−0.578801
$75$	−4.94638e11	−0.320914
$76$	−1.44544e12	−0.860420
$77$	−1.49770e12	−0.818907
$78$	−2.12740e12	−1.06963
$79$	3.74160e12	1.73174	0.865868	−	0.500272i	$-0.166767\pi$
$79$	3.74160e12	1.73174	0.865868	+	0.500272i	$0.166767\pi$
$80$	1.91061e12	0.814866
$81$	2.82430e11	0.111111
$82$	−9.48198e11	−0.344436
$83$	2.29306e12	0.769854	0.384927	−	0.922947i	$-0.374227\pi$
$83$	2.29306e12	0.769854	0.384927	+	0.922947i	$0.374227\pi$
$84$	−2.21337e12	−0.687446
$85$	−2.94388e12	−0.846637
$86$	−3.56789e12	−0.950980
$87$	3.24536e12	0.802394
$88$	−8.61024e11	−0.197641
$89$	−3.64309e12	−0.777024	−0.388512	−	0.921444i	$-0.627011\pi$
$89$	−3.64309e12	−0.777024	−0.388512	+	0.921444i	$0.627011\pi$
$90$	−1.44532e12	−0.286674
$91$	1.39198e13	2.56960
$92$	1.51118e12	0.259834
$93$	4.28522e12	0.686805
$94$	−3.76165e12	−0.562403
$95$	6.17583e12	0.861970
$96$	−5.07375e12	−0.661556
$97$	1.41054e13	1.71936	0.859682	−	0.510830i	$-0.170662\pi$
$97$	1.41054e13	1.71936	0.859682	+	0.510830i	$0.170662\pi$
$98$	2.49355e13	2.84347
$99$	1.42867e12	0.152511
$100$	−3.69775e12	−0.369775
$101$	−9.73579e12	−0.912604	−0.456302	−	0.889825i	$-0.650826\pi$
$101$	−9.73579e12	−0.912604	−0.456302	+	0.889825i	$0.650826\pi$
$102$	1.07649e13	0.946471
$103$	−8.41658e11	−0.0694535	−0.0347267	−	0.999397i	$-0.511056\pi$
$103$	−8.41658e11	−0.0694535	−0.0347267	+	0.999397i	$0.511056\pi$
$104$	8.00248e12	0.620166
$105$	9.45693e12	0.688684
$106$	−5.36345e12	−0.367245
$107$	−2.77510e13	−1.78766	−0.893828	−	0.448410i	$-0.851991\pi$
$107$	−2.77510e13	−1.78766	−0.893828	+	0.448410i	$0.851991\pi$
$108$	2.11135e12	0.128028
$109$	2.20540e13	1.25955	0.629776	−	0.776777i	$-0.283147\pi$
$109$	2.20540e13	1.25955	0.629776	+	0.776777i	$0.283147\pi$
$110$	−7.31116e12	−0.393490
$111$	−5.10303e12	−0.258957
$112$	4.57135e13	2.18840
$113$	−1.48027e13	−0.668852	−0.334426	−	0.942422i	$-0.608542\pi$
$113$	−1.48027e13	−0.668852	−0.334426	+	0.942422i	$0.608542\pi$
$114$	−2.25831e13	−0.963611
$115$	−6.45675e12	−0.260302
$116$	2.42613e13	0.924564
$117$	−1.32783e13	−0.478556
$118$	−4.92660e12	−0.168002
$119$	−7.04358e13	−2.27373
$120$	5.43677e12	0.166212
$121$	−2.72958e13	−0.790662
$122$	6.40533e13	1.75874
$123$	−5.91822e12	−0.154102
$124$	3.20349e13	0.791376
$125$	4.42232e13	1.03689
$126$	−3.45811e13	−0.769892
$127$	3.36474e13	0.711585	0.355793	−	0.934565i	$-0.384211\pi$
$127$	3.36474e13	0.711585	0.355793	+	0.934565i	$0.384211\pi$
$128$	4.05796e13	0.815537
$129$	−2.22691e13	−0.425471
$130$	6.79511e13	1.23471
$131$	9.04470e13	1.56362	0.781809	−	0.623518i	$-0.214297\pi$
$131$	9.04470e13	1.56362	0.781809	+	0.623518i	$0.214297\pi$
$132$	1.06803e13	0.175732
$133$	1.47764e14	2.31490
$134$	8.74691e13	1.30519
$135$	−9.02106e12	−0.128259
$136$	−4.04934e13	−0.548759
$137$	4.61467e12	0.0596289	0.0298145	−	0.999555i	$-0.490508\pi$
$137$	4.61467e12	0.0596289	0.0298145	+	0.999555i	$0.490508\pi$
$138$	2.36103e13	0.290997
$139$	−1.41217e14	−1.66069	−0.830347	−	0.557247i	$-0.811858\pi$
$139$	−1.41217e14	−1.66069	−0.830347	+	0.557247i	$0.811858\pi$
$140$	7.06970e13	0.793540
$141$	−2.34785e13	−0.251621
$142$	−1.59435e13	−0.163196
$143$	−6.71680e13	−0.656868
$144$	−4.36065e13	−0.407564
$145$	−1.03660e14	−0.926229
$146$	−5.10285e13	−0.436033
$147$	1.55636e14	1.27218
$148$	−3.81486e13	−0.298385
$149$	1.10685e14	0.828662	0.414331	−	0.910126i	$-0.364016\pi$
$149$	1.10685e14	0.828662	0.414331	+	0.910126i	$0.364016\pi$
$150$	−5.77727e13	−0.414123
$151$	−2.28736e14	−1.57031	−0.785155	−	0.619300i	$-0.787417\pi$
$151$	−2.28736e14	−1.57031	−0.785155	+	0.619300i	$0.787417\pi$
$152$	8.49492e13	0.558697
$153$	6.71894e13	0.423454
$154$	−1.74928e14	−1.05676
$155$	−1.36874e14	−0.792801
$156$	−9.92640e13	−0.551419
$157$	−7.72622e13	−0.411737	−0.205868	−	0.978580i	$-0.566002\pi$
$157$	−7.72622e13	−0.411737	−0.205868	+	0.978580i	$0.566002\pi$
$158$	4.37012e14	2.23472
$159$	−3.34762e13	−0.164306
$160$	1.62060e14	0.763654
$161$	−1.54485e14	−0.699067
$162$	3.29872e13	0.143383
$163$	2.95282e14	1.23316	0.616578	−	0.787294i	$-0.288518\pi$
$163$	2.95282e14	1.23316	0.616578	+	0.787294i	$0.288518\pi$
$164$	−4.42428e13	−0.177565
$165$	−4.56330e13	−0.176049
$166$	2.67825e14	0.993456
$167$	4.02665e14	1.43644	0.718219	−	0.695817i	$-0.244958\pi$
$167$	4.02665e14	1.43644	0.718219	+	0.695817i	$0.244958\pi$
$168$	1.30081e14	0.446379
$169$	3.21394e14	1.06114
$170$	−3.43840e14	−1.09254
$171$	−1.40953e14	−0.431123
$172$	−1.66477e14	−0.490252
$173$	−5.27411e14	−1.49572	−0.747858	−	0.663859i	$-0.768918\pi$
$173$	−5.27411e14	−1.49572	−0.747858	+	0.663859i	$0.768918\pi$
$174$	3.79052e14	1.03545
$175$	3.78014e14	0.994856
$176$	−2.20583e14	−0.559423
$177$	−3.07496e13	−0.0751646
$178$	−4.25505e14	−1.00271
$179$	1.83479e14	0.416909	0.208454	−	0.978032i	$-0.433157\pi$
$179$	1.83479e14	0.416909	0.208454	+	0.978032i	$0.433157\pi$
$180$	−6.74386e13	−0.147787
$181$	−2.46320e14	−0.520702	−0.260351	−	0.965514i	$-0.583838\pi$
$181$	−2.46320e14	−0.520702	−0.260351	+	0.965514i	$0.583838\pi$
$182$	1.62581e15	3.31593
$183$	3.99792e14	0.786868
$184$	−8.88132e13	−0.168718
$185$	1.62995e14	0.298923
$186$	5.00505e14	0.886286
$187$	3.39877e14	0.581234
$188$	−1.75518e14	−0.289932
$189$	−2.15839e14	−0.344452
$190$	7.21325e14	1.11233
$191$	−8.76182e14	−1.30580	−0.652901	−	0.757443i	$-0.726448\pi$
$191$	−8.76182e14	−1.30580	−0.652901	+	0.757443i	$0.726448\pi$
$192$	−1.02584e14	−0.147782
$193$	1.41135e14	0.196568	0.0982839	−	0.995158i	$-0.468665\pi$
$193$	1.41135e14	0.196568	0.0982839	+	0.995158i	$0.468665\pi$
$194$	1.64748e15	2.21875
$195$	4.24120e14	0.552412
$196$	1.16348e15	1.46587
$197$	7.30007e14	0.889809	0.444904	−	0.895578i	$-0.353238\pi$
$197$	7.30007e14	0.889809	0.444904	+	0.895578i	$0.353238\pi$
$198$	1.66866e14	0.196808
$199$	−1.07054e15	−1.22196	−0.610980	−	0.791646i	$-0.709225\pi$
$199$	−1.07054e15	−1.22196	−0.610980	+	0.791646i	$0.709225\pi$
$200$	2.17319e14	0.240106
$201$	5.45942e14	0.583946
$202$	−1.13712e15	−1.17767
$203$	−2.48018e15	−2.48748
$204$	5.02286e14	0.487928
$205$	1.89033e14	0.177885
$206$	−9.83040e13	−0.0896261
$207$	1.47365e14	0.130193
$208$	2.05014e15	1.75538
$209$	−7.13012e14	−0.591760
$210$	1.10455e15	0.888710
$211$	−1.85381e15	−1.44620	−0.723101	−	0.690742i	$-0.757284\pi$
$211$	−1.85381e15	−1.44620	−0.723101	+	0.690742i	$0.757284\pi$
$212$	−2.50257e14	−0.189323
$213$	−9.95121e13	−0.0730144
$214$	−3.24126e15	−2.30688
$215$	7.11296e14	0.491135
$216$	−1.24086e14	−0.0831327
$217$	−3.27486e15	−2.12914
$218$	2.57587e15	1.62539
$219$	−3.18497e14	−0.195083
$220$	−3.41138e14	−0.202853
$221$	−3.15887e15	−1.82382
$222$	−5.96023e14	−0.334171
$223$	2.18893e15	1.19193	0.595963	−	0.803012i	$-0.296770\pi$
$223$	2.18893e15	1.19193	0.595963	+	0.803012i	$0.296770\pi$
$224$	3.87748e15	2.05087
$225$	−3.60591e14	−0.185280
$226$	−1.72892e15	−0.863119
$227$	−3.12748e15	−1.51715	−0.758573	−	0.651589i	$-0.774103\pi$
$227$	−3.12748e15	−1.51715	−0.758573	+	0.651589i	$0.774103\pi$
$228$	−1.05372e15	−0.496764
$229$	1.17823e15	0.539881	0.269940	−	0.962877i	$-0.412996\pi$
$229$	1.17823e15	0.539881	0.269940	+	0.962877i	$0.412996\pi$
$230$	−7.54135e14	−0.335906
$231$	−1.09182e15	−0.472796
$232$	−1.42585e15	−0.600347
$233$	2.33087e15	0.954342	0.477171	−	0.878810i	$-0.341662\pi$
$233$	2.33087e15	0.954342	0.477171	+	0.878810i	$0.341662\pi$
$234$	−1.55087e15	−0.617552
$235$	7.49925e14	0.290454
$236$	−2.29874e14	−0.0866089
$237$	2.72763e15	0.999819
$238$	−8.22676e15	−2.93412
$239$	4.69908e15	1.63090	0.815448	−	0.578831i	$-0.196491\pi$
$239$	4.69908e15	1.63090	0.815448	+	0.578831i	$0.196491\pi$
$240$	1.39283e15	0.470463
$241$	−4.52087e15	−1.48632	−0.743158	−	0.669116i	$-0.766673\pi$
$241$	−4.52087e15	−1.48632	−0.743158	+	0.669116i	$0.766673\pi$
$242$	−3.18810e15	−1.02031
$243$	2.05891e14	0.0641500
$244$	2.98872e15	0.906673
$245$	−4.97115e15	−1.46851
$246$	−6.91237e14	−0.198860
$247$	6.62684e15	1.85685
$248$	−1.88271e15	−0.513864
$249$	1.67164e15	0.444475
$250$	5.16518e15	1.33806
$251$	7.12607e15	1.79875	0.899375	−	0.437177i	$-0.144022\pi$
$251$	7.12607e15	1.79875	0.899375	+	0.437177i	$0.144022\pi$
$252$	−1.61355e15	−0.396897
$253$	7.45444e14	0.178703
$254$	3.92995e15	0.918264
$255$	−2.14609e15	−0.488806
$256$	5.89239e15	1.30837
$257$	−4.23271e15	−0.916333	−0.458166	−	0.888866i	$-0.651494\pi$
$257$	−4.23271e15	−0.916333	−0.458166	+	0.888866i	$0.651494\pi$
$258$	−2.60099e15	−0.549048
$259$	3.89985e15	0.802786
$260$	3.17058e15	0.636521
$261$	2.36587e15	0.463263
$262$	1.05640e16	2.01777
$263$	−4.29323e15	−0.799966	−0.399983	−	0.916523i	$-0.630984\pi$
$263$	−4.29323e15	−0.799966	−0.399983	+	0.916523i	$0.630984\pi$
$264$	−6.27686e14	−0.114108
$265$	1.06926e15	0.189664
$266$	1.72585e16	2.98726
$267$	−2.65581e15	−0.448615
$268$	4.08129e15	0.672855
$269$	7.28496e15	1.17230	0.586148	−	0.810204i	$-0.300644\pi$
$269$	7.28496e15	1.17230	0.586148	+	0.810204i	$0.300644\pi$
$270$	−1.05364e15	−0.165512
$271$	6.59887e15	1.01197	0.505987	−	0.862541i	$-0.331128\pi$
$271$	6.59887e15	1.01197	0.505987	+	0.862541i	$0.331128\pi$
$272$	−1.03739e16	−1.55326
$273$	1.01476e16	1.48356
$274$	5.38984e14	0.0769480
$275$	−1.82405e15	−0.254316
$276$	1.10165e15	0.150015
$277$	1.24577e15	0.165699	0.0828493	−	0.996562i	$-0.473598\pi$
$277$	1.24577e15	0.165699	0.0828493	+	0.996562i	$0.473598\pi$
$278$	−1.64938e16	−2.14304
$279$	3.12392e15	0.396527
$280$	−4.15491e15	−0.515269
$281$	−1.58530e15	−0.192097	−0.0960486	−	0.995377i	$-0.530620\pi$
$281$	−1.58530e15	−0.192097	−0.0960486	+	0.995377i	$0.530620\pi$
$282$	−2.74224e15	−0.324703
$283$	6.54530e15	0.757387	0.378693	−	0.925522i	$-0.376373\pi$
$283$	6.54530e15	0.757387	0.378693	+	0.925522i	$0.376373\pi$
$284$	−7.43921e14	−0.0841313
$285$	4.50218e15	0.497658
$286$	−7.84509e15	−0.847654
$287$	4.52284e15	0.477726
$288$	−3.69877e15	−0.381949
$289$	6.07963e15	0.613820
$290$	−1.21073e16	−1.19525
$291$	1.02828e16	0.992675
$292$	−2.38098e15	−0.224785
$293$	1.54014e16	1.42207	0.711033	−	0.703159i	$-0.248228\pi$
$293$	1.54014e16	1.42207	0.711033	+	0.703159i	$0.248228\pi$
$294$	1.81780e16	1.64168
$295$	9.82171e14	0.0867649
$296$	2.24202e15	0.193751
$297$	1.04150e15	0.0880525
$298$	1.29278e16	1.06934
$299$	−6.92827e15	−0.560741
$300$	−2.69566e15	−0.213490
$301$	1.70186e16	1.31899
$302$	−2.67160e16	−2.02640
$303$	−7.09739e15	−0.526892
$304$	2.17629e16	1.58139
$305$	−1.27697e16	−0.908306
$306$	7.84758e15	0.546445
$307$	1.72741e16	1.17760	0.588798	−	0.808280i	$-0.299601\pi$
$307$	1.72741e16	1.17760	0.588798	+	0.808280i	$0.299601\pi$
$308$	−8.16211e15	−0.544782
$309$	−6.13569e14	−0.0400990
$310$	−1.59866e16	−1.02307
$311$	−1.41768e16	−0.888454	−0.444227	−	0.895914i	$-0.646522\pi$
$311$	−1.41768e16	−0.888454	−0.444227	+	0.895914i	$0.646522\pi$
$312$	5.83381e15	0.358053
$313$	1.35840e16	0.816561	0.408280	−	0.912857i	$-0.366129\pi$
$313$	1.35840e16	0.816561	0.408280	+	0.912857i	$0.366129\pi$
$314$	−9.02407e15	−0.531324
$315$	6.89410e15	0.397612
$316$	2.03909e16	1.15205
$317$	−1.32953e16	−0.735891	−0.367946	−	0.929847i	$-0.619939\pi$
$317$	−1.32953e16	−0.735891	−0.367946	+	0.929847i	$0.619939\pi$
$318$	−3.90995e15	−0.212029
$319$	1.19677e16	0.635876
$320$	3.27663e15	0.170590
$321$	−2.02305e16	−1.03210
$322$	−1.80436e16	−0.902109
$323$	−3.35325e16	−1.64305
$324$	1.53918e15	0.0739173
$325$	1.69530e16	0.798002
$326$	3.44884e16	1.59132
$327$	1.60774e16	0.727203
$328$	2.60017e15	0.115298
$329$	1.79428e16	0.780041
$330$	−5.32984e15	−0.227182
$331$	1.40494e16	0.587188	0.293594	−	0.955930i	$-0.405149\pi$
$331$	1.40494e16	0.587188	0.293594	+	0.955930i	$0.405149\pi$
$332$	1.24967e16	0.512150
$333$	−3.72011e15	−0.149509
$334$	4.70305e16	1.85365
$335$	−1.74379e16	−0.674067
$336$	3.33251e16	1.26347
$337$	−2.87828e16	−1.07038	−0.535192	−	0.844731i	$-0.679761\pi$
$337$	−2.87828e16	−1.07038	−0.535192	+	0.844731i	$0.679761\pi$
$338$	3.75382e16	1.36935
$339$	−1.07911e16	−0.386162
$340$	−1.60435e16	−0.563230
$341$	1.58023e16	0.544275
$342$	−1.64631e16	−0.556341
$343$	−6.49619e16	−2.15401
$344$	9.78396e15	0.318335
$345$	−4.70697e15	−0.150286
$346$	−6.16005e16	−1.93014
$347$	5.69163e16	1.75023	0.875115	−	0.483915i	$-0.160786\pi$
$347$	5.69163e16	1.75023	0.875115	+	0.483915i	$0.160786\pi$
$348$	1.76865e16	0.533797
$349$	−1.56127e16	−0.462501	−0.231250	−	0.972894i	$-0.574282\pi$
$349$	−1.56127e16	−0.462501	−0.231250	+	0.972894i	$0.574282\pi$
$350$	4.41512e16	1.28381
$351$	−9.67985e15	−0.276295
$352$	−1.87102e16	−0.524265
$353$	3.26691e16	0.898673	0.449337	−	0.893363i	$-0.351660\pi$
$353$	3.26691e16	0.898673	0.449337	+	0.893363i	$0.351660\pi$
$354$	−3.59149e15	−0.0969960
$355$	3.17851e15	0.0842828
$356$	−1.98540e16	−0.516920
$357$	−5.13477e16	−1.31274
$358$	2.14299e16	0.537999
$359$	−3.91866e16	−0.966103	−0.483052	−	0.875592i	$-0.660472\pi$
$359$	−3.91866e16	−0.966103	−0.483052	+	0.875592i	$0.660472\pi$
$360$	3.96341e15	0.0959627
$361$	2.82933e16	0.672801
$362$	−2.87697e16	−0.671938
$363$	−1.98986e16	−0.456489
$364$	7.58599e16	1.70944
$365$	1.01731e16	0.225190
$366$	4.66949e16	1.01541
$367$	5.57492e16	1.19099	0.595496	−	0.803358i	$-0.296955\pi$
$367$	5.57492e16	1.19099	0.595496	+	0.803358i	$0.296955\pi$
$368$	−2.27528e16	−0.477556
$369$	−4.31438e15	−0.0889708
$370$	1.90375e16	0.385744
$371$	2.55833e16	0.509361
$372$	2.33535e16	0.456901
$373$	6.98303e16	1.34257	0.671285	−	0.741200i	$-0.265743\pi$
$373$	6.98303e16	1.34257	0.671285	+	0.741200i	$0.265743\pi$
$374$	3.96970e16	0.750053
$375$	3.22387e16	0.598652
$376$	1.03153e16	0.188261
$377$	−1.11230e17	−1.99528
$378$	−2.52096e16	−0.444497
$379$	−6.99664e15	−0.121265	−0.0606324	−	0.998160i	$-0.519312\pi$
$379$	−6.99664e15	−0.121265	−0.0606324	+	0.998160i	$0.519312\pi$
$380$	3.36569e16	0.573430
$381$	2.45289e16	0.410834
$382$	−1.02336e17	−1.68507
$383$	4.75718e16	0.770119	0.385059	−	0.922892i	$-0.374181\pi$
$383$	4.75718e16	0.770119	0.385059	+	0.922892i	$0.374181\pi$
$384$	2.95826e16	0.470850
$385$	3.48738e16	0.545763
$386$	1.64843e16	0.253660
$387$	−1.62342e16	−0.245646
$388$	7.68710e16	1.14382
$389$	−2.73808e16	−0.400658	−0.200329	−	0.979729i	$-0.564201\pi$
$389$	−2.73808e16	−0.400658	−0.200329	+	0.979729i	$0.564201\pi$
$390$	4.95363e16	0.712859
$391$	3.50578e16	0.496176
$392$	−6.83787e16	−0.951835
$393$	6.59358e16	0.902755
$394$	8.52634e16	1.14825
$395$	−8.71230e16	−1.15412
$396$	7.78592e15	0.101459
$397$	−4.69609e16	−0.602002	−0.301001	−	0.953624i	$-0.597321\pi$
$397$	−4.69609e16	−0.602002	−0.301001	+	0.953624i	$0.597321\pi$
$398$	−1.25037e17	−1.57688
$399$	1.07720e17	1.33651
$400$	5.56745e16	0.679620
$401$	−8.12683e16	−0.976074	−0.488037	−	0.872823i	$-0.662287\pi$
$401$	−8.12683e16	−0.976074	−0.488037	+	0.872823i	$0.662287\pi$
$402$	6.37650e16	0.753551
$403$	−1.46869e17	−1.70784
$404$	−5.30578e16	−0.607115
$405$	−6.57635e15	−0.0740504
$406$	−2.89680e17	−3.20996
$407$	−1.88181e16	−0.205217
$408$	−2.95197e16	−0.316826
$409$	4.05510e16	0.428351	0.214176	−	0.976795i	$-0.431293\pi$
$409$	4.05510e16	0.428351	0.214176	+	0.976795i	$0.431293\pi$
$410$	2.20787e16	0.229551
$411$	3.36409e15	0.0344268
$412$	−4.58685e15	−0.0462043
$413$	2.34996e16	0.233015
$414$	1.72119e16	0.168007
$415$	−5.33938e16	−0.513072
$416$	1.73895e17	1.64506
$417$	−1.02947e17	−0.958802
$418$	−8.32784e16	−0.763636
$419$	−1.22380e17	−1.10489	−0.552447	−	0.833548i	$-0.686306\pi$
$419$	−1.22380e17	−1.10489	−0.552447	+	0.833548i	$0.686306\pi$
$420$	5.15381e16	0.458151
$421$	1.26689e17	1.10894	0.554468	−	0.832205i	$-0.312922\pi$
$421$	1.26689e17	1.10894	0.554468	+	0.832205i	$0.312922\pi$
$422$	−2.16521e17	−1.86625
$423$	−1.71158e16	−0.145273
$424$	1.47078e16	0.122933
$425$	−8.57838e16	−0.706118
$426$	−1.16228e16	−0.0942212
$427$	−3.05530e17	−2.43934
$428$	−1.51237e17	−1.18925
$429$	−4.89655e16	−0.379243
$430$	8.30780e16	0.633784
$431$	1.49436e17	1.12293	0.561464	−	0.827501i	$-0.310238\pi$
$431$	1.49436e17	1.12293	0.561464	+	0.827501i	$0.310238\pi$
$432$	−3.17892e16	−0.235307
$433$	−1.41572e17	−1.03230	−0.516151	−	0.856498i	$-0.672636\pi$
$433$	−1.41572e17	−1.03230	−0.516151	+	0.856498i	$0.672636\pi$
$434$	−3.82497e17	−2.74755
$435$	−7.55680e16	−0.534759
$436$	1.20190e17	0.837924
$437$	−7.35461e16	−0.505161
$438$	−3.71998e16	−0.251744
$439$	−1.33714e17	−0.891574	−0.445787	−	0.895139i	$-0.647076\pi$
$439$	−1.33714e17	−0.891574	−0.445787	+	0.895139i	$0.647076\pi$
$440$	2.00489e16	0.131719
$441$	1.13459e17	0.734491
$442$	−3.68949e17	−2.35354
$443$	2.72714e17	1.71429	0.857143	−	0.515078i	$-0.172237\pi$
$443$	2.72714e17	1.71429	0.857143	+	0.515078i	$0.172237\pi$
$444$	−2.78103e16	−0.172273
$445$	8.48290e16	0.517851
$446$	2.55662e17	1.53812
$447$	8.06892e16	0.478428
$448$	7.83973e16	0.458135
$449$	4.18563e16	0.241079	0.120539	−	0.992709i	$-0.461538\pi$
$449$	4.18563e16	0.241079	0.120539	+	0.992709i	$0.461538\pi$
$450$	−4.21163e16	−0.239094
$451$	−2.18243e16	−0.122122
$452$	−8.06712e16	−0.444958
$453$	−1.66749e17	−0.906619
$454$	−3.65284e17	−1.95780
$455$	−3.24122e17	−1.71252
$456$	6.19280e16	0.322564
$457$	1.97303e17	1.01316	0.506580	−	0.862193i	$-0.330909\pi$
$457$	1.97303e17	1.01316	0.506580	+	0.862193i	$0.330909\pi$
$458$	1.37614e17	0.696688
$459$	4.89811e16	0.244481
$460$	−3.51878e16	−0.173167
$461$	−1.72093e17	−0.835041	−0.417520	−	0.908668i	$-0.637101\pi$
$461$	−1.72093e17	−0.835041	−0.417520	+	0.908668i	$0.637101\pi$
$462$	−1.27523e17	−0.610118
$463$	−4.12360e16	−0.194536	−0.0972680	−	0.995258i	$-0.531010\pi$
$463$	−4.12360e16	−0.194536	−0.0972680	+	0.995258i	$0.531010\pi$
$464$	−3.65285e17	−1.69928
$465$	−9.97809e16	−0.457724
$466$	2.72241e17	1.23153
$467$	−2.32601e17	−1.03765	−0.518827	−	0.854880i	$-0.673631\pi$
$467$	−2.32601e17	−1.03765	−0.518827	+	0.854880i	$0.673631\pi$
$468$	−7.23635e16	−0.318362
$469$	−4.17222e17	−1.81027
$470$	8.75898e16	0.374815
$471$	−5.63241e16	−0.237716
$472$	1.35099e16	0.0562377
$473$	−8.21206e16	−0.337174
$474$	3.18582e17	1.29021
$475$	1.79962e17	0.718905
$476$	−3.83859e17	−1.51261
$477$	−2.44041e16	−0.0948624
$478$	5.48843e17	2.10459
$479$	7.71358e16	0.291793	0.145897	−	0.989300i	$-0.453393\pi$
$479$	7.71358e16	0.291793	0.145897	+	0.989300i	$0.453393\pi$
$480$	1.18142e17	0.440896
$481$	1.74899e17	0.643937
$482$	−5.28029e17	−1.91801
$483$	−1.12620e17	−0.403606
$484$	−1.48756e17	−0.525992
$485$	−3.28442e17	−1.14588
$486$	2.40477e16	0.0827823
$487$	−2.87251e17	−0.975715	−0.487858	−	0.872923i	$-0.662222\pi$
$487$	−2.87251e17	−0.975715	−0.487858	+	0.872923i	$0.662222\pi$
$488$	−1.75649e17	−0.588730
$489$	2.15261e17	0.711963
$490$	−5.80621e17	−1.89504
$491$	−2.01850e17	−0.650130	−0.325065	−	0.945692i	$-0.605386\pi$
$491$	−2.01850e17	−0.650130	−0.325065	+	0.945692i	$0.605386\pi$
$492$	−3.22530e16	−0.102517
$493$	5.62835e17	1.76553
$494$	7.74002e17	2.39617
$495$	−3.32664e16	−0.101642
$496$	−4.82327e17	−1.45449
$497$	7.60494e16	0.226349
$498$	1.95245e17	0.573572
$499$	−3.61832e17	−1.04919	−0.524595	−	0.851352i	$-0.675783\pi$
$499$	−3.61832e17	−1.04919	−0.524595	+	0.851352i	$0.675783\pi$
$500$	2.41006e17	0.689800
$501$	2.93543e17	0.829328
$502$	8.32311e17	2.32119
$503$	−1.60255e17	−0.441183	−0.220591	−	0.975366i	$-0.570799\pi$
$503$	−1.60255e17	−0.441183	−0.220591	+	0.975366i	$0.570799\pi$
$504$	9.48291e16	0.257717
$505$	2.26697e17	0.608208
$506$	8.70664e16	0.230607
$507$	2.34296e17	0.612652
$508$	1.83371e17	0.473386
$509$	−3.64486e17	−0.929000	−0.464500	−	0.885573i	$-0.653766\pi$
$509$	−3.64486e17	−0.929000	−0.464500	+	0.885573i	$0.653766\pi$
$510$	−2.50659e17	−0.630779
$511$	2.43403e17	0.604769
$512$	3.55791e17	0.872852
$513$	−1.02755e17	−0.248909
$514$	−4.94372e17	−1.18248
$515$	1.95980e16	0.0462875
$516$	−1.21362e17	−0.283047
$517$	−8.65804e16	−0.199403
$518$	4.55495e17	1.03595
$519$	−3.84482e17	−0.863552
$520$	−1.86337e17	−0.413312
$521$	−5.85800e17	−1.28323	−0.641614	−	0.767028i	$-0.721735\pi$
$521$	−5.85800e17	−1.28323	−0.641614	+	0.767028i	$0.721735\pi$
$522$	2.76329e17	0.597816
$523$	6.74948e17	1.44215	0.721073	−	0.692859i	$-0.243649\pi$
$523$	6.74948e17	1.44215	0.721073	+	0.692859i	$0.243649\pi$
$524$	4.92916e17	1.04021
$525$	2.75572e17	0.574380
$526$	−5.01440e17	−1.03231
$527$	7.43174e17	1.51120
$528$	−1.60805e17	−0.322983
$529$	−4.27145e17	−0.847449
$530$	1.24887e17	0.244752
$531$	−2.24165e16	−0.0433963
$532$	8.05280e17	1.54000
$533$	2.02838e17	0.383198
$534$	−3.10193e17	−0.578915
$535$	6.46180e17	1.19139
$536$	−2.39860e17	−0.436905
$537$	1.33756e17	0.240702
$538$	8.50869e17	1.51279
$539$	5.73929e17	1.00816
$540$	−4.91627e16	−0.0853250
$541$	−4.91656e17	−0.843099	−0.421550	−	0.906805i	$-0.638514\pi$
$541$	−4.91656e17	−0.843099	−0.421550	+	0.906805i	$0.638514\pi$
$542$	7.70735e17	1.30590
$543$	−1.79567e17	−0.300627
$544$	−8.79929e17	−1.45564
$545$	−5.13527e17	−0.839433
$546$	1.18521e18	1.91445
$547$	5.89745e17	0.941340	0.470670	−	0.882309i	$-0.344012\pi$
$547$	5.89745e17	0.941340	0.470670	+	0.882309i	$0.344012\pi$
$548$	2.51489e16	0.0396685
$549$	2.91448e17	0.454298
$550$	−2.13045e17	−0.328181
$551$	−1.18074e18	−1.79751
$552$	−6.47449e16	−0.0974095
$553$	−2.08452e18	−3.09950
$554$	1.45503e17	0.213825
$555$	1.18824e17	0.172583
$556$	−7.69598e17	−1.10479
$557$	−9.43161e17	−1.33822	−0.669109	−	0.743164i	$-0.733324\pi$
$557$	−9.43161e17	−1.33822	−0.669109	+	0.743164i	$0.733324\pi$
$558$	3.64868e17	0.511698
$559$	7.63241e17	1.05800
$560$	−1.06443e18	−1.45847
$561$	2.47770e17	0.335576
$562$	−1.85160e17	−0.247891
$563$	1.41018e18	1.86624	0.933122	−	0.359559i	$-0.117073\pi$
$563$	1.41018e18	1.86624	0.933122	+	0.359559i	$0.117073\pi$
$564$	−1.27953e17	−0.167392
$565$	3.44679e17	0.445759
$566$	7.64478e17	0.977368
$567$	−1.57347e17	−0.198869
$568$	4.37207e16	0.0546289
$569$	8.02927e16	0.0991851	0.0495925	−	0.998770i	$-0.484208\pi$
$569$	8.02927e16	0.0991851	0.0495925	+	0.998770i	$0.484208\pi$
$570$	5.25846e17	0.642202
$571$	−9.39151e17	−1.13397	−0.566984	−	0.823729i	$-0.691890\pi$
$571$	−9.39151e17	−1.13397	−0.566984	+	0.823729i	$0.691890\pi$
$572$	−3.66050e17	−0.436985
$573$	−6.38736e17	−0.753905
$574$	5.28259e17	0.616481
$575$	−1.88148e17	−0.217099
$576$	−7.47839e16	−0.0853222
$577$	7.47681e17	0.843478	0.421739	−	0.906717i	$-0.361420\pi$
$577$	7.47681e17	0.843478	0.421739	+	0.906717i	$0.361420\pi$
$578$	7.10088e17	0.792102
$579$	1.02887e17	0.113488
$580$	−5.64922e17	−0.616179
$581$	−1.27751e18	−1.37790
$582$	1.20101e18	1.28099
$583$	−1.23448e17	−0.130208
$584$	1.39932e17	0.145960
$585$	3.09183e17	0.318935
$586$	1.79885e18	1.83510
$587$	1.19147e17	0.120209	0.0601045	−	0.998192i	$-0.480857\pi$
$587$	1.19147e17	0.120209	0.0601045	+	0.998192i	$0.480857\pi$
$588$	8.48180e17	0.846322
$589$	−1.55907e18	−1.53857
$590$	1.14716e17	0.111966
$591$	5.32175e17	0.513731
$592$	5.74377e17	0.548410
$593$	1.81407e18	1.71316	0.856580	−	0.516015i	$-0.172585\pi$
$593$	1.81407e18	1.71316	0.856580	+	0.516015i	$0.172585\pi$
$594$	1.21645e17	0.113627
$595$	1.64009e18	1.51533
$596$	6.03207e17	0.551272
$597$	−7.80423e17	−0.705499
$598$	−8.09208e17	−0.723607
$599$	1.97352e18	1.74569	0.872843	−	0.488001i	$-0.162274\pi$
$599$	1.97352e18	1.74569	0.872843	+	0.488001i	$0.162274\pi$
$600$	1.58426e17	0.138625
$601$	−4.78539e17	−0.414222	−0.207111	−	0.978317i	$-0.566406\pi$
$601$	−4.78539e17	−0.414222	−0.207111	+	0.978317i	$0.566406\pi$
$602$	1.98774e18	1.70209
$603$	3.97992e17	0.337141
$604$	−1.24656e18	−1.04466
$605$	6.35581e17	0.526940
$606$	−8.28961e17	−0.679926
$607$	−2.35692e16	−0.0191258	−0.00956289	−	0.999954i	$-0.503044\pi$
$607$	−2.35692e16	−0.0191258	−0.00956289	+	0.999954i	$0.503044\pi$
$608$	1.84596e18	1.48200
$609$	−1.80805e18	−1.43615
$610$	−1.49148e18	−1.17212
$611$	8.04691e17	0.625693
$612$	3.66167e17	0.281705
$613$	−1.37835e17	−0.104922	−0.0524608	−	0.998623i	$-0.516706\pi$
$613$	−1.37835e17	−0.104922	−0.0524608	+	0.998623i	$0.516706\pi$
$614$	2.01758e18	1.51963
$615$	1.37805e17	0.102702
$616$	4.79692e17	0.353743
$617$	−5.19483e17	−0.379069	−0.189534	−	0.981874i	$-0.560698\pi$
$617$	−5.19483e17	−0.379069	−0.189534	+	0.981874i	$0.560698\pi$
$618$	−7.16636e16	−0.0517456
$619$	1.45972e18	1.04299	0.521494	−	0.853255i	$-0.325375\pi$
$619$	1.45972e18	1.04299	0.521494	+	0.853255i	$0.325375\pi$
$620$	−7.45931e17	−0.527415
$621$	1.07429e17	0.0751668
$622$	−1.65582e18	−1.14650
$623$	2.02963e18	1.39074
$624$	1.49455e18	1.01347
$625$	−2.01467e17	−0.135202
$626$	1.58658e18	1.05373
$627$	−5.19786e17	−0.341653
$628$	−4.21062e17	−0.273910
$629$	−8.85005e17	−0.569792
$630$	8.05217e17	0.513097
$631$	−7.47133e15	−0.00471202	−0.00235601	−	0.999997i	$-0.500750\pi$
$631$	−7.47133e15	−0.00471202	−0.00235601	+	0.999997i	$0.500750\pi$
$632$	−1.19839e18	−0.748059
$633$	−1.35143e18	−0.834966
$634$	−1.55287e18	−0.949629
$635$	−7.83477e17	−0.474238
$636$	−1.82438e17	−0.109306
$637$	−5.33419e18	−3.16346
$638$	1.39781e18	0.820565
$639$	−7.25443e16	−0.0421549
$640$	−9.44894e17	−0.543517
$641$	2.68716e18	1.53009	0.765045	−	0.643977i	$-0.222717\pi$
$641$	2.68716e18	1.53009	0.765045	+	0.643977i	$0.222717\pi$
$642$	−2.36288e18	−1.33188
$643$	1.86712e18	1.04184	0.520919	−	0.853606i	$-0.325589\pi$
$643$	1.86712e18	1.04184	0.520919	+	0.853606i	$0.325589\pi$
$644$	−8.41909e17	−0.465058
$645$	5.18535e17	0.283557
$646$	−3.91653e18	−2.12026
$647$	9.03956e17	0.484473	0.242237	−	0.970217i	$-0.422119\pi$
$647$	9.03956e17	0.484473	0.242237	+	0.970217i	$0.422119\pi$
$648$	−9.04584e16	−0.0479967
$649$	−1.13394e17	−0.0595659
$650$	1.98007e18	1.02978
$651$	−2.38737e18	−1.22926
$652$	1.60922e18	0.820364
$653$	−1.80119e18	−0.909124	−0.454562	−	0.890715i	$-0.650204\pi$
$653$	−1.80119e18	−0.909124	−0.454562	+	0.890715i	$0.650204\pi$
$654$	1.87781e18	0.938417
$655$	−2.10605e18	−1.04208
$656$	6.66132e17	0.326351
$657$	−2.32184e17	−0.112631
$658$	2.09569e18	1.00660
$659$	−1.63795e18	−0.779014	−0.389507	−	0.921024i	$-0.627355\pi$
$659$	−1.63795e18	−0.779014	−0.389507	+	0.921024i	$0.627355\pi$
$660$	−2.48689e17	−0.117117
$661$	1.01223e18	0.472029	0.236015	−	0.971750i	$-0.424159\pi$
$661$	1.01223e18	0.472029	0.236015	+	0.971750i	$0.424159\pi$
$662$	1.64095e18	0.757736
$663$	−2.30281e18	−1.05298
$664$	−7.34437e17	−0.332554
$665$	−3.44067e18	−1.54277
$666$	−4.34501e17	−0.192934
$667$	1.23445e18	0.542821
$668$	2.19443e18	0.955598
$669$	1.59573e18	0.688159
$670$	−2.03671e18	−0.869848
$671$	1.47429e18	0.623571
$672$	2.82668e18	1.18407
$673$	2.92923e18	1.21522	0.607611	−	0.794235i	$-0.292128\pi$
$673$	2.92923e18	1.21522	0.607611	+	0.794235i	$0.292128\pi$
$674$	−3.36178e18	−1.38127
$675$	−2.62871e17	−0.106971
$676$	1.75153e18	0.705932
$677$	7.33913e17	0.292967	0.146483	−	0.989213i	$-0.453205\pi$
$677$	7.33913e17	0.292967	0.146483	+	0.989213i	$0.453205\pi$
$678$	−1.26038e18	−0.498322
$679$	−7.85836e18	−3.07736
$680$	9.42886e17	0.365722
$681$	−2.27994e18	−0.875924
$682$	1.84568e18	0.702358
$683$	−1.06515e18	−0.401492	−0.200746	−	0.979643i	$-0.564337\pi$
$683$	−1.06515e18	−0.401492	−0.200746	+	0.979643i	$0.564337\pi$
$684$	−7.68164e17	−0.286807
$685$	−1.07452e17	−0.0397399
$686$	−7.58742e18	−2.77963
$687$	8.58927e17	0.311700
$688$	2.50653e18	0.901047
$689$	1.14735e18	0.408573
$690$	−5.49765e17	−0.193936
$691$	−8.19153e17	−0.286258	−0.143129	−	0.989704i	$-0.545716\pi$
$691$	−8.19153e17	−0.286258	−0.143129	+	0.989704i	$0.545716\pi$
$692$	−2.87427e18	−0.995034
$693$	−7.95938e17	−0.272969
$694$	6.64771e18	2.25858
$695$	3.28822e18	1.10678
$696$	−1.03945e18	−0.346611
$697$	−1.02638e18	−0.339075
$698$	−1.82353e18	−0.596833
$699$	1.69920e18	0.550990
$700$	2.06009e18	0.661833
$701$	7.78719e17	0.247864	0.123932	−	0.992291i	$-0.460449\pi$
$701$	7.78719e17	0.247864	0.123932	+	0.992291i	$0.460449\pi$
$702$	−1.13059e18	−0.356544
$703$	1.85661e18	0.580111
$704$	−3.78294e17	−0.117114
$705$	5.46696e17	0.167694
$706$	3.81569e18	1.15969
$707$	5.42399e18	1.63340
$708$	−1.67578e17	−0.0500037
$709$	−3.85071e18	−1.13852	−0.569259	−	0.822158i	$-0.692770\pi$
$709$	−3.85071e18	−1.13852	−0.569259	+	0.822158i	$0.692770\pi$
$710$	3.71243e17	0.108763
$711$	1.98844e18	0.577245
$712$	1.16683e18	0.335651
$713$	1.62999e18	0.464625
$714$	−5.99731e18	−1.69402
$715$	1.56400e18	0.437772
$716$	9.99917e17	0.277351
$717$	3.42563e18	0.941598
$718$	−4.57692e18	−1.24671
$719$	1.62957e18	0.439880	0.219940	−	0.975513i	$-0.429414\pi$
$719$	1.62957e18	0.439880	0.219940	+	0.975513i	$0.429414\pi$
$720$	1.01537e18	0.271622
$721$	4.68904e17	0.124310
$722$	3.30460e18	0.868214
$723$	−3.29571e18	−0.858125
$724$	−1.34239e18	−0.346400
$725$	−3.02061e18	−0.772499
$726$	−2.32412e18	−0.589075
$727$	5.68195e18	1.42733	0.713664	−	0.700488i	$-0.247034\pi$
$727$	5.68195e18	1.42733	0.713664	+	0.700488i	$0.247034\pi$
$728$	−4.45833e18	−1.10999
$729$	1.50095e17	0.0370370
$730$	1.18820e18	0.290596
$731$	−3.86208e18	−0.936178
$732$	2.17877e18	0.523468
$733$	−1.64336e18	−0.391342	−0.195671	−	0.980670i	$-0.562689\pi$
$733$	−1.64336e18	−0.391342	−0.195671	+	0.980670i	$0.562689\pi$
$734$	6.51139e18	1.53691
$735$	−3.62397e18	−0.847846
$736$	−1.92993e18	−0.447543
$737$	2.01324e18	0.462761
$738$	−5.03911e17	−0.114812
$739$	7.64086e17	0.172565	0.0862827	−	0.996271i	$-0.472501\pi$
$739$	7.64086e17	0.172565	0.0862827	+	0.996271i	$0.472501\pi$
$740$	8.88288e17	0.198860
$741$	4.83097e18	1.07205
$742$	2.98808e18	0.657304
$743$	−4.01583e18	−0.875686	−0.437843	−	0.899051i	$-0.644257\pi$
$743$	−4.01583e18	−0.875686	−0.437843	+	0.899051i	$0.644257\pi$
$744$	−1.37250e18	−0.296679
$745$	−2.57729e18	−0.552264
$746$	8.15604e18	1.73252
$747$	1.21863e18	0.256618
$748$	1.85225e18	0.386669
$749$	1.54606e19	3.19959
$750$	3.76541e18	0.772529
$751$	3.18806e16	0.00648436	0.00324218	−	0.999995i	$-0.498968\pi$
$751$	3.18806e16	0.00648436	0.00324218	+	0.999995i	$0.498968\pi$
$752$	2.64265e18	0.532873
$753$	5.19491e18	1.03851
$754$	−1.29914e19	−2.57480
$755$	5.32611e18	1.04654
$756$	−1.17627e18	−0.229149
$757$	−4.23598e18	−0.818145	−0.409072	−	0.912502i	$-0.634148\pi$
$757$	−4.23598e18	−0.818145	−0.409072	+	0.912502i	$0.634148\pi$
$758$	−8.17194e17	−0.156486
$759$	5.43429e17	0.103174
$760$	−1.97804e18	−0.372345
$761$	1.44750e18	0.270158	0.135079	−	0.990835i	$-0.456871\pi$
$761$	1.44750e18	0.270158	0.135079	+	0.990835i	$0.456871\pi$
$762$	2.86493e18	0.530160
$763$	−1.22867e19	−2.25438
$764$	−4.77499e18	−0.868692
$765$	−1.56450e18	−0.282212
$766$	5.55629e18	0.993798
$767$	1.05390e18	0.186908
$768$	4.29555e18	0.755390
$769$	1.04357e19	1.81969	0.909847	−	0.414943i	$-0.136198\pi$
$769$	1.04357e19	1.81969	0.909847	+	0.414943i	$0.136198\pi$
$770$	4.07319e18	0.704279
$771$	−3.08565e18	−0.529045
$772$	7.69154e17	0.130768
$773$	7.70471e18	1.29894	0.649471	−	0.760387i	$-0.274991\pi$
$773$	7.70471e18	1.29894	0.649471	+	0.760387i	$0.274991\pi$
$774$	−1.89612e18	−0.316993
$775$	−3.98846e18	−0.661217
$776$	−4.51775e18	−0.742714
$777$	2.84299e18	0.463488
$778$	−3.19802e18	−0.517028
$779$	2.15320e18	0.345216
$780$	2.31136e18	0.367495
$781$	−3.66965e17	−0.0578619
$782$	4.09468e18	0.640289
$783$	1.72472e18	0.267465
$784$	−1.75178e19	−2.69417
$785$	1.79904e18	0.274403
$786$	7.70118e18	1.16496
$787$	1.05605e17	0.0158434	0.00792171	−	0.999969i	$-0.497478\pi$
$787$	1.05605e17	0.0158434	0.00792171	+	0.999969i	$0.497478\pi$
$788$	3.97837e18	0.591950
$789$	−3.12976e18	−0.461860
$790$	−1.01758e19	−1.48933
$791$	8.24684e18	1.19713
$792$	−4.57583e17	−0.0658804
$793$	−1.37023e19	−1.95666
$794$	−5.48494e18	−0.776852
$795$	7.79491e17	0.109503
$796$	−5.83419e18	−0.812916
$797$	4.84201e17	0.0669186	0.0334593	−	0.999440i	$-0.489348\pi$
$797$	4.84201e17	0.0669186	0.0334593	+	0.999440i	$0.489348\pi$
$798$	1.25815e19	1.72470
$799$	−4.07182e18	−0.553649
$800$	4.72239e18	0.636908
$801$	−1.93609e18	−0.259008
$802$	−9.49198e18	−1.25957
$803$	−1.17450e18	−0.154598
$804$	2.97526e18	0.388473
$805$	3.59718e18	0.465895
$806$	−1.71540e19	−2.20388
$807$	5.31073e18	0.676825
$808$	3.11824e18	0.394218
$809$	3.43245e18	0.430466	0.215233	−	0.976563i	$-0.430949\pi$
$809$	3.43245e18	0.430466	0.215233	+	0.976563i	$0.430949\pi$
$810$	−7.68105e17	−0.0955582
$811$	−1.33415e19	−1.64653	−0.823264	−	0.567659i	$-0.807849\pi$
$811$	−1.33415e19	−1.64653	−0.823264	+	0.567659i	$0.807849\pi$
$812$	−1.35164e19	−1.65481
$813$	4.81058e18	0.584263
$814$	−2.19792e18	−0.264822
$815$	−6.87563e18	−0.821841
$816$	−7.56257e18	−0.896775
$817$	8.10208e18	0.953132
$818$	4.73628e18	0.552765
$819$	7.39757e18	0.856532
$820$	1.03019e18	0.118339
$821$	8.34696e18	0.951257	0.475628	−	0.879646i	$-0.342221\pi$
$821$	8.34696e18	0.951257	0.475628	+	0.879646i	$0.342221\pi$
$822$	3.92919e17	0.0444259
$823$	4.02317e18	0.451305	0.225652	−	0.974208i	$-0.427549\pi$
$823$	4.02317e18	0.451305	0.225652	+	0.974208i	$0.427549\pi$
$824$	2.69572e17	0.0300018
$825$	−1.32973e18	−0.146829
$826$	2.74470e18	0.300694
$827$	−1.20554e17	−0.0131038	−0.00655188	−	0.999979i	$-0.502086\pi$
$827$	−1.20554e17	−0.0131038	−0.00655188	+	0.999979i	$0.502086\pi$
$828$	8.03105e17	0.0866114
$829$	−4.76047e18	−0.509384	−0.254692	−	0.967022i	$-0.581974\pi$
$829$	−4.76047e18	−0.509384	−0.254692	+	0.967022i	$0.581974\pi$
$830$	−6.23629e18	−0.662092
$831$	9.08165e17	0.0956661
$832$	3.51592e18	0.367483
$833$	2.69915e19	2.79921
$834$	−1.20240e19	−1.23728
$835$	−9.37603e18	−0.957319
$836$	−3.88575e18	−0.393672
$837$	2.27734e18	0.228935
$838$	−1.42938e19	−1.42581
$839$	2.72815e18	0.270032	0.135016	−	0.990843i	$-0.456891\pi$
$839$	2.72815e18	0.270032	0.135016	+	0.990843i	$0.456891\pi$
$840$	−3.02893e18	−0.297491
$841$	9.55789e18	0.931511
$842$	1.47971e19	1.43102
$843$	−1.15569e18	−0.110907
$844$	−1.01028e19	−0.962094
$845$	−7.48364e18	−0.707203
$846$	−1.99910e18	−0.187468
$847$	1.52070e19	1.41515
$848$	3.76795e18	0.347962
$849$	4.77152e18	0.437277
$850$	−1.00194e19	−0.911208
$851$	−1.94106e18	−0.175185
$852$	−5.42318e17	−0.0485732
$853$	−2.58903e18	−0.230127	−0.115064	−	0.993358i	$-0.536707\pi$
$853$	−2.58903e18	−0.230127	−0.115064	+	0.993358i	$0.536707\pi$
$854$	−3.56853e19	−3.14784
$855$	3.28209e18	0.287323
$856$	8.88827e18	0.772214
$857$	1.53476e19	1.32332	0.661659	−	0.749805i	$-0.269853\pi$
$857$	1.53476e19	1.32332	0.661659	+	0.749805i	$0.269853\pi$
$858$	−5.71907e18	−0.489393
$859$	−7.44079e18	−0.631922	−0.315961	−	0.948772i	$-0.602327\pi$
$859$	−7.44079e18	−0.631922	−0.315961	+	0.948772i	$0.602327\pi$
$860$	3.87640e18	0.326730
$861$	3.29715e18	0.275815
$862$	1.74538e19	1.44908
$863$	−5.27978e18	−0.435057	−0.217528	−	0.976054i	$-0.569799\pi$
$863$	−5.27978e18	−0.435057	−0.217528	+	0.976054i	$0.569799\pi$
$864$	−2.69640e18	−0.220519
$865$	1.22807e19	0.996825
$866$	−1.65353e19	−1.33213
$867$	4.43205e18	0.354389
$868$	−1.78473e19	−1.41642
$869$	1.00585e19	0.792329
$870$	−8.82619e18	−0.690078
$871$	−1.87114e19	−1.45207
$872$	−7.06361e18	−0.544089
$873$	7.49616e18	0.573121
$874$	−8.59003e18	−0.651884
$875$	−2.46376e19	−1.85586
$876$	−1.73574e18	−0.129780
$877$	2.12655e19	1.57826	0.789130	−	0.614226i	$-0.210532\pi$
$877$	2.12655e19	1.57826	0.789130	+	0.614226i	$0.210532\pi$
$878$	−1.56175e19	−1.15053
$879$	1.12276e19	0.821030
$880$	5.13627e18	0.372829
$881$	9.80315e18	0.706354	0.353177	−	0.935557i	$-0.385101\pi$
$881$	9.80315e18	0.706354	0.353177	+	0.935557i	$0.385101\pi$
$882$	1.32517e19	0.947822
$883$	−2.05255e19	−1.45730	−0.728649	−	0.684887i	$-0.759852\pi$
$883$	−2.05255e19	−1.45730	−0.728649	+	0.684887i	$0.759852\pi$
$884$	−1.72151e19	−1.21331
$885$	7.16002e17	0.0500937
$886$	3.18525e19	2.21220
$887$	1.93855e19	1.33651	0.668257	−	0.743930i	$-0.267040\pi$
$887$	1.93855e19	1.33651	0.668257	+	0.743930i	$0.267040\pi$
$888$	1.63443e18	0.111862
$889$	−1.87456e19	−1.27361
$890$	9.90786e18	0.668259
$891$	7.59253e17	0.0508372
$892$	1.19292e19	0.792936
$893$	8.54208e18	0.563675
$894$	9.42434e18	0.617386
$895$	−4.27229e18	−0.277850
$896$	−2.26077e19	−1.45967
$897$	−5.05071e18	−0.323744
$898$	4.88873e18	0.311100
$899$	2.61686e19	1.65327
$900$	−1.96514e18	−0.123258
$901$	−5.80569e18	−0.361529
$902$	−2.54903e18	−0.157592
$903$	1.24066e19	0.761519
$904$	4.74110e18	0.288924
$905$	5.73554e18	0.347024
$906$	−1.94759e19	−1.16994
$907$	−7.76895e18	−0.463356	−0.231678	−	0.972793i	$-0.574422\pi$
$907$	−7.76895e18	−0.463356	−0.231678	+	0.972793i	$0.574422\pi$
$908$	−1.70441e19	−1.00929
$909$	−5.17400e18	−0.304201
$910$	−3.78568e19	−2.20991
$911$	1.08603e19	0.629465	0.314733	−	0.949180i	$-0.398085\pi$
$911$	1.08603e19	0.629465	0.314733	+	0.949180i	$0.398085\pi$
$912$	1.58652e19	0.913015
$913$	6.16442e18	0.352235
$914$	2.30446e19	1.30743
$915$	−9.30912e18	−0.524411
$916$	6.42107e18	0.359159
$917$	−5.03897e19	−2.79860
$918$	5.72089e18	0.315490
$919$	3.43717e19	1.88213	0.941066	−	0.338224i	$-0.109826\pi$
$919$	3.43717e19	1.88213	0.941066	+	0.338224i	$0.109826\pi$
$920$	2.06801e18	0.112443
$921$	1.25928e19	0.679885
$922$	−2.01001e19	−1.07758
$923$	3.41063e18	0.181561
$924$	−5.95018e18	−0.314530
$925$	4.74963e18	0.249309
$926$	−4.81628e18	−0.251038
$927$	−4.47292e17	−0.0231512
$928$	−3.09840e19	−1.59249
$929$	−2.02384e19	−1.03294	−0.516469	−	0.856306i	$-0.672754\pi$
$929$	−2.02384e19	−1.03294	−0.516469	+	0.856306i	$0.672754\pi$
$930$	−1.16542e19	−0.590669
$931$	−5.66243e19	−2.84990
$932$	1.27027e19	0.634881
$933$	−1.03349e19	−0.512949
$934$	−2.71674e19	−1.33904
$935$	−7.91401e18	−0.387366
$936$	4.25285e18	0.206722
$937$	9.73620e18	0.469983	0.234991	−	0.971997i	$-0.424494\pi$
$937$	9.73620e18	0.469983	0.234991	+	0.971997i	$0.424494\pi$
$938$	−4.87307e19	−2.33606
$939$	9.90271e18	0.471441
$940$	4.08692e18	0.193226
$941$	−3.03039e19	−1.42287	−0.711437	−	0.702750i	$-0.751955\pi$
$941$	−3.03039e19	−1.42287	−0.711437	+	0.702750i	$0.751955\pi$
$942$	−6.57855e18	−0.306760
$943$	−2.25114e18	−0.104250
$944$	3.46106e18	0.159181
$945$	5.02580e18	0.229561
$946$	−9.59152e18	−0.435106
$947$	−2.42543e19	−1.09273	−0.546366	−	0.837547i	$-0.683989\pi$
$947$	−2.42543e19	−1.09273	−0.546366	+	0.837547i	$0.683989\pi$
$948$	1.48650e19	0.665135
$949$	1.09160e19	0.485102
$950$	2.10192e19	0.927710
$951$	−9.69229e18	−0.424867
$952$	2.25596e19	0.982182
$953$	−1.92326e19	−0.831637	−0.415819	−	0.909448i	$-0.636505\pi$
$953$	−1.92326e19	−0.831637	−0.415819	+	0.909448i	$0.636505\pi$
$954$	−2.85035e18	−0.122415
$955$	2.04018e19	0.870256
$956$	2.56089e19	1.08496
$957$	8.72448e18	0.367123
$958$	9.00930e18	0.376544
$959$	−2.57092e18	−0.106725
$960$	2.38867e18	0.0984901
$961$	1.01358e19	0.415104
$962$	2.04278e19	0.830967
$963$	−1.47480e19	−0.595885
$964$	−2.46377e19	−0.988780
$965$	−3.28632e18	−0.131003
$966$	−1.31538e19	−0.520833
$967$	9.52273e18	0.374532	0.187266	−	0.982309i	$-0.440037\pi$
$967$	9.52273e18	0.374532	0.187266	+	0.982309i	$0.440037\pi$
$968$	8.74248e18	0.341543
$969$	−2.44452e19	−0.948613
$970$	−3.83614e19	−1.47869
$971$	1.52030e19	0.582110	0.291055	−	0.956706i	$-0.405994\pi$
$971$	1.52030e19	0.582110	0.291055	+	0.956706i	$0.405994\pi$
$972$	1.12206e18	0.0426762
$973$	7.86744e19	2.97235
$974$	−3.35503e19	−1.25911
$975$	1.23587e19	0.460726
$976$	−4.49990e19	−1.66640
$977$	5.19368e18	0.191056	0.0955280	−	0.995427i	$-0.469546\pi$
$977$	5.19368e18	0.191056	0.0955280	+	0.995427i	$0.469546\pi$
$978$	2.51420e19	0.918751
$979$	−9.79368e18	−0.355515
$980$	−2.70917e19	−0.976936
$981$	1.17204e19	0.419851
$982$	−2.35757e19	−0.838958
$983$	−1.50654e19	−0.532578	−0.266289	−	0.963893i	$-0.585798\pi$
$983$	−1.50654e19	−0.532578	−0.266289	+	0.963893i	$0.585798\pi$
$984$	1.89553e18	0.0665674
$985$	−1.69982e19	−0.593016
$986$	6.57380e19	2.27833
$987$	1.30803e19	0.450357
$988$	3.61148e19	1.23528
$989$	−8.47061e18	−0.287832
$990$	−3.88545e18	−0.131163
$991$	5.42042e19	1.81783	0.908916	−	0.416979i	$-0.136911\pi$
$991$	5.42042e19	1.81783	0.908916	+	0.416979i	$0.136911\pi$
$992$	−4.09117e19	−1.36308
$993$	1.02420e19	0.339013
$994$	8.88242e18	0.292092
$995$	2.49274e19	0.814380
$996$	9.11007e18	0.295690
$997$	5.12467e19	1.65252	0.826261	−	0.563288i	$-0.190464\pi$
$997$	5.12467e19	1.65252	0.826261	+	0.563288i	$0.190464\pi$
$998$	−4.22613e19	−1.35392
$999$	−2.71196e18	−0.0863192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.23	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.23	✓	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)

\(f(q)\)	\(=\)	\(q+116.798 q^{2} +729.000 q^{3} +5449.77 q^{4} -23284.9 q^{5} +85145.7 q^{6} -557119. q^{7} -320287. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+116.798 q^{2} +729.000 q^{3} +5449.77 q^{4} -23284.9 q^{5} +85145.7 q^{6} -557119. q^{7} -320287. q^{8} +531441. q^{9} -2.71963e6 q^{10} +2.68829e6 q^{11} +3.97288e6 q^{12} -2.49854e7 q^{13} -6.50704e7 q^{14} -1.69747e7 q^{15} -8.20534e7 q^{16} +1.26429e8 q^{17} +6.20712e7 q^{18} -2.65229e8 q^{19} -1.26898e8 q^{20} -4.06140e8 q^{21} +3.13987e8 q^{22} +2.77293e8 q^{23} -2.33489e8 q^{24} -6.78515e8 q^{25} -2.91824e9 q^{26} +3.87420e8 q^{27} -3.03617e9 q^{28} +4.45180e9 q^{29} -1.98261e9 q^{30} +5.87821e9 q^{31} -6.95988e9 q^{32} +1.95976e9 q^{33} +1.47666e10 q^{34} +1.29725e10 q^{35} +2.89623e9 q^{36} -7.00004e9 q^{37} -3.09782e10 q^{38} -1.82143e10 q^{39} +7.45785e9 q^{40} -8.11827e9 q^{41} -4.74363e10 q^{42} -3.05475e10 q^{43} +1.46506e10 q^{44} -1.23746e10 q^{45} +3.23873e10 q^{46} -3.22065e10 q^{47} -5.98169e10 q^{48} +2.13492e11 q^{49} -7.92492e10 q^{50} +9.21665e10 q^{51} -1.36165e11 q^{52} -4.59207e10 q^{53} +4.52499e10 q^{54} -6.25967e10 q^{55} +1.78438e11 q^{56} -1.93352e11 q^{57} +5.19961e11 q^{58} -4.21805e10 q^{59} -9.25083e10 q^{60} +5.48411e11 q^{61} +6.86563e11 q^{62} -2.96076e11 q^{63} -1.40719e11 q^{64} +5.81783e11 q^{65} +2.28897e11 q^{66} +7.48892e11 q^{67} +6.89008e11 q^{68} +2.02147e11 q^{69} +1.51516e12 q^{70} -1.36505e11 q^{71} -1.70213e11 q^{72} -4.36896e11 q^{73} -8.17590e11 q^{74} -4.94638e11 q^{75} -1.44544e12 q^{76} -1.49770e12 q^{77} -2.12740e12 q^{78} +3.74160e12 q^{79} +1.91061e12 q^{80} +2.82430e11 q^{81} -9.48198e11 q^{82} +2.29306e12 q^{83} -2.21337e12 q^{84} -2.94388e12 q^{85} -3.56789e12 q^{86} +3.24536e12 q^{87} -8.61024e11 q^{88} -3.64309e12 q^{89} -1.44532e12 q^{90} +1.39198e13 q^{91} +1.51118e12 q^{92} +4.28522e12 q^{93} -3.76165e12 q^{94} +6.17583e12 q^{95} -5.07375e12 q^{96} +1.41054e13 q^{97} +2.49355e13 q^{98} +1.42867e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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