LMFDB - Embedded newform 177.14.a.c.1.14

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			1.14
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)

$f(q)$	$=$	$q-7.03559 q^{2} +729.000 q^{3} -8142.50 q^{4} +12466.0 q^{5} -5128.95 q^{6} -179621. q^{7} +114923. q^{8} +531441. q^{9} +O(q^{10})$	\(q-7.03559 q^{2} +729.000 q^{3} -8142.50 q^{4} +12466.0 q^{5} -5128.95 q^{6} -179621. q^{7} +114923. q^{8} +531441. q^{9} -87705.8 q^{10} -8.91138e6 q^{11} -5.93588e6 q^{12} +2.94142e7 q^{13} +1.26374e6 q^{14} +9.08773e6 q^{15} +6.58948e7 q^{16} -1.63264e7 q^{17} -3.73900e6 q^{18} -1.07100e8 q^{19} -1.01505e8 q^{20} -1.30944e8 q^{21} +6.26968e7 q^{22} +5.82137e8 q^{23} +8.37788e7 q^{24} -1.06530e9 q^{25} -2.06946e8 q^{26} +3.87420e8 q^{27} +1.46257e9 q^{28} -1.37246e9 q^{29} -6.39375e7 q^{30} -5.70742e9 q^{31} -1.40506e9 q^{32} -6.49640e9 q^{33} +1.14866e8 q^{34} -2.23916e9 q^{35} -4.32726e9 q^{36} +6.03624e9 q^{37} +7.53511e8 q^{38} +2.14429e10 q^{39} +1.43263e9 q^{40} -1.15612e10 q^{41} +9.21268e8 q^{42} -1.85518e9 q^{43} +7.25609e10 q^{44} +6.62495e9 q^{45} -4.09568e9 q^{46} +4.15668e9 q^{47} +4.80373e10 q^{48} -6.46252e10 q^{49} +7.49503e9 q^{50} -1.19020e10 q^{51} -2.39505e11 q^{52} +1.45626e11 q^{53} -2.72573e9 q^{54} -1.11089e11 q^{55} -2.06426e10 q^{56} -7.80758e10 q^{57} +9.65605e9 q^{58} -4.21805e10 q^{59} -7.39968e10 q^{60} -4.25126e11 q^{61} +4.01551e10 q^{62} -9.54581e10 q^{63} -5.29925e11 q^{64} +3.66678e11 q^{65} +4.57060e10 q^{66} +2.63627e11 q^{67} +1.32938e11 q^{68} +4.24378e11 q^{69} +1.57538e10 q^{70} +3.12180e11 q^{71} +6.10747e10 q^{72} -7.30451e11 q^{73} -4.24686e10 q^{74} -7.76605e11 q^{75} +8.72060e11 q^{76} +1.60067e12 q^{77} -1.50864e11 q^{78} +2.67532e12 q^{79} +8.21446e11 q^{80} +2.82430e11 q^{81} +8.13402e10 q^{82} -1.18393e12 q^{83} +1.06621e12 q^{84} -2.03526e11 q^{85} +1.30523e10 q^{86} -1.00052e12 q^{87} -1.02412e12 q^{88} +3.66061e11 q^{89} -4.66105e10 q^{90} -5.28341e12 q^{91} -4.74005e12 q^{92} -4.16071e12 q^{93} -2.92447e10 q^{94} -1.33511e12 q^{95} -1.02429e12 q^{96} +1.46548e13 q^{97} +4.54676e11 q^{98} -4.73587e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.03559	−0.0777330	−0.0388665	−	0.999244i	$-0.512375\pi$
$2$	−7.03559	−0.0777330	−0.0388665	+	0.999244i	$0.512375\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−8142.50	−0.993958
$5$	12466.0	0.356798	0.178399	−	0.983958i	$-0.442908\pi$
$5$	12466.0	0.356798	0.178399	+	0.983958i	$0.442908\pi$
$6$	−5128.95	−0.0448792
$7$	−179621.	−0.577060	−0.288530	−	0.957471i	$-0.593166\pi$
$7$	−179621.	−0.577060	−0.288530	+	0.957471i	$0.593166\pi$
$8$	114923.	0.154996
$9$	531441.	0.333333
$10$	−87705.8	−0.0277350
$11$	−8.91138e6	−1.51668	−0.758338	−	0.651862i	$-0.773988\pi$
$11$	−8.91138e6	−1.51668	−0.758338	+	0.651862i	$0.773988\pi$
$12$	−5.93588e6	−0.573862
$13$	2.94142e7	1.69015	0.845074	−	0.534649i	$-0.179556\pi$
$13$	2.94142e7	1.69015	0.845074	+	0.534649i	$0.179556\pi$
$14$	1.26374e6	0.0448566
$15$	9.08773e6	0.205998
$16$	6.58948e7	0.981909
$17$	−1.63264e7	−0.164049	−0.0820245	−	0.996630i	$-0.526139\pi$
$17$	−1.63264e7	−0.164049	−0.0820245	+	0.996630i	$0.526139\pi$
$18$	−3.73900e6	−0.0259110
$19$	−1.07100e8	−0.522264	−0.261132	−	0.965303i	$-0.584096\pi$
$19$	−1.07100e8	−0.522264	−0.261132	+	0.965303i	$0.584096\pi$
$20$	−1.01505e8	−0.354642
$21$	−1.30944e8	−0.333166
$22$	6.26968e7	0.117896
$23$	5.82137e8	0.819964	0.409982	−	0.912094i	$-0.365535\pi$
$23$	5.82137e8	0.819964	0.409982	+	0.912094i	$0.365535\pi$
$24$	8.37788e7	0.0894872
$25$	−1.06530e9	−0.872695
$26$	−2.06946e8	−0.131380
$27$	3.87420e8	0.192450
$28$	1.46257e9	0.573573
$29$	−1.37246e9	−0.428462	−0.214231	−	0.976783i	$-0.568724\pi$
$29$	−1.37246e9	−0.428462	−0.214231	+	0.976783i	$0.568724\pi$
$30$	−6.39375e7	−0.0160128
$31$	−5.70742e9	−1.15502	−0.577509	−	0.816384i	$-0.695975\pi$
$31$	−5.70742e9	−1.15502	−0.577509	+	0.816384i	$0.695975\pi$
$32$	−1.40506e9	−0.231323
$33$	−6.49640e9	−0.875653
$34$	1.14866e8	0.0127520
$35$	−2.23916e9	−0.205894
$36$	−4.32726e9	−0.331319
$37$	6.03624e9	0.386773	0.193386	−	0.981123i	$-0.438053\pi$
$37$	6.03624e9	0.386773	0.193386	+	0.981123i	$0.438053\pi$
$38$	7.53511e8	0.0405972
$39$	2.14429e10	0.975808
$40$	1.43263e9	0.0553024
$41$	−1.15612e10	−0.380110	−0.190055	−	0.981773i	$-0.560867\pi$
$41$	−1.15612e10	−0.380110	−0.190055	+	0.981773i	$0.560867\pi$
$42$	9.21268e8	0.0258980
$43$	−1.85518e9	−0.0447549	−0.0223775	−	0.999750i	$-0.507124\pi$
$43$	−1.85518e9	−0.0447549	−0.0223775	+	0.999750i	$0.507124\pi$
$44$	7.25609e10	1.50751
$45$	6.62495e9	0.118933
$46$	−4.09568e9	−0.0637383
$47$	4.15668e9	0.0562484	0.0281242	−	0.999604i	$-0.491047\pi$
$47$	4.15668e9	0.0562484	0.0281242	+	0.999604i	$0.491047\pi$
$48$	4.80373e10	0.566906
$49$	−6.46252e10	−0.667002
$50$	7.49503e9	0.0678372
$51$	−1.19020e10	−0.0947137
$52$	−2.39505e11	−1.67994
$53$	1.45626e11	0.902499	0.451249	−	0.892398i	$-0.350978\pi$
$53$	1.45626e11	0.902499	0.451249	+	0.892398i	$0.350978\pi$
$54$	−2.72573e9	−0.0149597
$55$	−1.11089e11	−0.541147
$56$	−2.06426e10	−0.0894421
$57$	−7.80758e10	−0.301529
$58$	9.65605e9	0.0333056
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−7.39968e10	−0.204753
$61$	−4.25126e11	−1.05651	−0.528255	−	0.849086i	$-0.677154\pi$
$61$	−4.25126e11	−1.05651	−0.528255	+	0.849086i	$0.677154\pi$
$62$	4.01551e10	0.0897831
$63$	−9.54581e10	−0.192353
$64$	−5.29925e11	−0.963928
$65$	3.66678e11	0.603042
$66$	4.57060e10	0.0680672
$67$	2.63627e11	0.356044	0.178022	−	0.984026i	$-0.443030\pi$
$67$	2.63627e11	0.356044	0.178022	+	0.984026i	$0.443030\pi$
$68$	1.32938e11	0.163058
$69$	4.24378e11	0.473406
$70$	1.57538e10	0.0160048
$71$	3.12180e11	0.289218	0.144609	−	0.989489i	$-0.453808\pi$
$71$	3.12180e11	0.289218	0.144609	+	0.989489i	$0.453808\pi$
$72$	6.10747e10	0.0516655
$73$	−7.30451e11	−0.564927	−0.282464	−	0.959278i	$-0.591152\pi$
$73$	−7.30451e11	−0.564927	−0.282464	+	0.959278i	$0.591152\pi$
$74$	−4.24686e10	−0.0300650
$75$	−7.76605e11	−0.503851
$76$	8.72060e11	0.519109
$77$	1.60067e12	0.875212
$78$	−1.50864e11	−0.0758525
$79$	2.67532e12	1.23823	0.619113	−	0.785302i	$-0.287492\pi$
$79$	2.67532e12	1.23823	0.619113	+	0.785302i	$0.287492\pi$
$80$	8.21446e11	0.350344
$81$	2.82430e11	0.111111
$82$	8.13402e10	0.0295471
$83$	−1.18393e12	−0.397484	−0.198742	−	0.980052i	$-0.563686\pi$
$83$	−1.18393e12	−0.397484	−0.198742	+	0.980052i	$0.563686\pi$
$84$	1.06621e12	0.331152
$85$	−2.03526e11	−0.0585324
$86$	1.30523e10	0.00347894
$87$	−1.00052e12	−0.247372
$88$	−1.02412e12	−0.235079
$89$	3.66061e11	0.0780762	0.0390381	−	0.999238i	$-0.487571\pi$
$89$	3.66061e11	0.0780762	0.0390381	+	0.999238i	$0.487571\pi$
$90$	−4.66105e10	−0.00924501
$91$	−5.28341e12	−0.975317
$92$	−4.74005e12	−0.815009
$93$	−4.16071e12	−0.666850
$94$	−2.92447e10	−0.00437236
$95$	−1.33511e12	−0.186343
$96$	−1.02429e12	−0.133554
$97$	1.46548e13	1.78634	0.893169	−	0.449722i	$-0.148477\pi$
$97$	1.46548e13	1.78634	0.893169	+	0.449722i	$0.148477\pi$
$98$	4.54676e11	0.0518481
$99$	−4.73587e12	−0.505558
$100$	8.67422e12	0.867422
$101$	−1.06442e13	−0.997754	−0.498877	−	0.866673i	$-0.666254\pi$
$101$	−1.06442e13	−0.997754	−0.498877	+	0.866673i	$0.666254\pi$
$102$	8.37374e10	0.00736239
$103$	1.23712e13	1.02087	0.510433	−	0.859918i	$-0.329485\pi$
$103$	1.23712e13	1.02087	0.510433	+	0.859918i	$0.329485\pi$
$104$	3.38036e12	0.261967
$105$	−1.63235e12	−0.118873
$106$	−1.02457e12	−0.0701540
$107$	−6.47425e12	−0.417057	−0.208528	−	0.978016i	$-0.566867\pi$
$107$	−6.47425e12	−0.417057	−0.208528	+	0.978016i	$0.566867\pi$
$108$	−3.15457e12	−0.191287
$109$	4.60180e12	0.262818	0.131409	−	0.991328i	$-0.458050\pi$
$109$	4.60180e12	0.262818	0.131409	+	0.991328i	$0.458050\pi$
$110$	7.81580e11	0.0420650
$111$	4.40042e12	0.223303
$112$	−1.18361e13	−0.566620
$113$	4.25972e12	0.192474	0.0962368	−	0.995358i	$-0.469319\pi$
$113$	4.25972e12	0.192474	0.0962368	+	0.995358i	$0.469319\pi$
$114$	5.49309e11	0.0234388
$115$	7.25694e12	0.292562
$116$	1.11752e13	0.425873
$117$	1.56319e13	0.563383
$118$	2.96765e11	0.0101200
$119$	2.93258e12	0.0946660
$120$	1.04439e12	0.0319289
$121$	4.48900e13	1.30030
$122$	2.99101e12	0.0821258
$123$	−8.42815e12	−0.219457
$124$	4.64727e13	1.14804
$125$	−2.84974e13	−0.668174
$126$	6.71604e11	0.0149522
$127$	5.28410e13	1.11750	0.558749	−	0.829337i	$-0.311282\pi$
$127$	5.28410e13	1.11750	0.558749	+	0.829337i	$0.311282\pi$
$128$	1.52386e13	0.306252
$129$	−1.35243e12	−0.0258393
$130$	−2.57980e12	−0.0468763
$131$	2.73432e13	0.472700	0.236350	−	0.971668i	$-0.424049\pi$
$131$	2.73432e13	0.472700	0.236350	+	0.971668i	$0.424049\pi$
$132$	5.28969e13	0.870362
$133$	1.92374e13	0.301378
$134$	−1.85477e12	−0.0276764
$135$	4.82959e12	0.0686659
$136$	−1.87628e12	−0.0254270
$137$	1.79816e13	0.232351	0.116176	−	0.993229i	$-0.462936\pi$
$137$	1.79816e13	0.232351	0.116176	+	0.993229i	$0.462936\pi$
$138$	−2.98575e12	−0.0367993
$139$	−7.96675e13	−0.936883	−0.468441	−	0.883495i	$-0.655184\pi$
$139$	−7.96675e13	−0.936883	−0.468441	+	0.883495i	$0.655184\pi$
$140$	1.82324e13	0.204650
$141$	3.03022e12	0.0324750
$142$	−2.19637e12	−0.0224818
$143$	−2.62121e14	−2.56341
$144$	3.50192e13	0.327303
$145$	−1.71091e13	−0.152874
$146$	5.13915e12	0.0439135
$147$	−4.71118e13	−0.385094
$148$	−4.91501e13	−0.384436
$149$	−1.42990e14	−1.07052	−0.535260	−	0.844687i	$-0.679786\pi$
$149$	−1.42990e14	−1.07052	−0.535260	+	0.844687i	$0.679786\pi$
$150$	5.46387e12	0.0391658
$151$	−6.78139e12	−0.0465552	−0.0232776	−	0.999729i	$-0.507410\pi$
$151$	−6.78139e12	−0.0465552	−0.0232776	+	0.999729i	$0.507410\pi$
$152$	−1.23082e13	−0.0809491
$153$	−8.67654e12	−0.0546830
$154$	−1.12617e13	−0.0680329
$155$	−7.11488e13	−0.412109
$156$	−1.74599e14	−0.969912
$157$	−2.37938e13	−0.126799	−0.0633995	−	0.997988i	$-0.520194\pi$
$157$	−2.37938e13	−0.126799	−0.0633995	+	0.997988i	$0.520194\pi$
$158$	−1.88225e13	−0.0962511
$159$	1.06162e14	0.521058
$160$	−1.75155e13	−0.0825357
$161$	−1.04564e14	−0.473168
$162$	−1.98706e12	−0.00863700
$163$	−3.02948e14	−1.26517	−0.632586	−	0.774491i	$-0.718006\pi$
$163$	−3.02948e14	−1.26517	−0.632586	+	0.774491i	$0.718006\pi$
$164$	9.41374e13	0.377813
$165$	−8.09842e13	−0.312431
$166$	8.32967e12	0.0308976
$167$	3.90932e14	1.39458	0.697291	−	0.716788i	$-0.254388\pi$
$167$	3.90932e14	1.39458	0.697291	+	0.716788i	$0.254388\pi$
$168$	−1.50485e13	−0.0516394
$169$	5.62319e14	1.85660
$170$	1.43192e12	0.00454990
$171$	−5.69172e13	−0.174088
$172$	1.51058e13	0.0444845
$173$	3.21297e14	0.911185	0.455592	−	0.890188i	$-0.349427\pi$
$173$	3.21297e14	0.911185	0.455592	+	0.890188i	$0.349427\pi$
$174$	7.03926e12	0.0192290
$175$	1.91351e14	0.503597
$176$	−5.87214e14	−1.48924
$177$	−3.07496e13	−0.0751646
$178$	−2.57546e12	−0.00606910
$179$	5.49082e14	1.24765	0.623825	−	0.781564i	$-0.285578\pi$
$179$	5.49082e14	1.24765	0.623825	+	0.781564i	$0.285578\pi$
$180$	−5.39437e13	−0.118214
$181$	−1.94033e14	−0.410172	−0.205086	−	0.978744i	$-0.565747\pi$
$181$	−1.94033e14	−0.410172	−0.205086	+	0.978744i	$0.565747\pi$
$182$	3.71719e13	0.0758143
$183$	−3.09917e14	−0.609977
$184$	6.69009e13	0.127091
$185$	7.52480e13	0.138000
$186$	2.92731e13	0.0518363
$187$	1.45491e14	0.248809
$188$	−3.38458e13	−0.0559085
$189$	−6.95890e13	−0.111055
$190$	9.39328e12	0.0144850
$191$	4.48927e14	0.669051	0.334525	−	0.942387i	$-0.391424\pi$
$191$	4.48927e14	0.669051	0.334525	+	0.942387i	$0.391424\pi$
$192$	−3.86315e14	−0.556524
$193$	5.66130e14	0.788485	0.394243	−	0.919006i	$-0.371007\pi$
$193$	5.66130e14	0.788485	0.394243	+	0.919006i	$0.371007\pi$
$194$	−1.03105e14	−0.138857
$195$	2.67308e14	0.348167
$196$	5.26211e14	0.662972
$197$	−1.04131e14	−0.126925	−0.0634626	−	0.997984i	$-0.520214\pi$
$197$	−1.04131e14	−0.126925	−0.0634626	+	0.997984i	$0.520214\pi$
$198$	3.33197e13	0.0392986
$199$	6.44197e13	0.0735315	0.0367658	−	0.999324i	$-0.488294\pi$
$199$	6.44197e13	0.0735315	0.0367658	+	0.999324i	$0.488294\pi$
$200$	−1.22428e14	−0.135265
$201$	1.92184e14	0.205562
$202$	7.48882e13	0.0775585
$203$	2.46523e14	0.247248
$204$	9.69118e13	0.0941414
$205$	−1.44123e14	−0.135623
$206$	−8.70384e13	−0.0793549
$207$	3.09372e14	0.273321
$208$	1.93824e15	1.65957
$209$	9.54408e14	0.792105
$210$	1.14845e13	0.00924035
$211$	9.34027e14	0.728657	0.364329	−	0.931270i	$-0.381298\pi$
$211$	9.34027e14	0.728657	0.364329	+	0.931270i	$0.381298\pi$
$212$	−1.18576e15	−0.897046
$213$	2.27579e14	0.166980
$214$	4.55502e13	0.0324191
$215$	−2.31267e13	−0.0159685
$216$	4.45235e13	0.0298291
$217$	1.02517e15	0.666514
$218$	−3.23764e13	−0.0204297
$219$	−5.32499e14	−0.326161
$220$	9.04546e14	0.537877
$221$	−4.80229e14	−0.277267
$222$	−3.09596e13	−0.0173580
$223$	1.24475e15	0.677799	0.338900	−	0.940823i	$-0.389945\pi$
$223$	1.24475e15	0.677799	0.338900	+	0.940823i	$0.389945\pi$
$224$	2.52378e14	0.133487
$225$	−5.66145e14	−0.290898
$226$	−2.99696e13	−0.0149616
$227$	3.20457e15	1.55454	0.777270	−	0.629167i	$-0.216604\pi$
$227$	3.20457e15	1.55454	0.777270	+	0.629167i	$0.216604\pi$
$228$	6.35732e14	0.299707
$229$	3.77559e15	1.73003	0.865016	−	0.501744i	$-0.167308\pi$
$229$	3.77559e15	1.73003	0.865016	+	0.501744i	$0.167308\pi$
$230$	−5.10568e13	−0.0227417
$231$	1.16689e15	0.505304
$232$	−1.57727e14	−0.0664100
$233$	2.48828e15	1.01879	0.509397	−	0.860532i	$-0.329869\pi$
$233$	2.48828e15	1.01879	0.509397	+	0.860532i	$0.329869\pi$
$234$	−1.09980e14	−0.0437935
$235$	5.18172e13	0.0200693
$236$	3.43455e14	0.129402
$237$	1.95031e15	0.714890
$238$	−2.06324e13	−0.00735868
$239$	3.56407e15	1.23697	0.618486	−	0.785796i	$-0.287746\pi$
$239$	3.56407e15	1.23697	0.618486	+	0.785796i	$0.287746\pi$
$240$	5.98834e14	0.202271
$241$	1.24378e14	0.0408914	0.0204457	−	0.999791i	$-0.493491\pi$
$241$	1.24378e14	0.0408914	0.0204457	+	0.999791i	$0.493491\pi$
$242$	−3.15828e14	−0.101077
$243$	2.05891e14	0.0641500
$244$	3.46159e15	1.05013
$245$	−8.05619e14	−0.237985
$246$	5.92970e13	0.0170590
$247$	−3.15025e15	−0.882705
$248$	−6.55913e14	−0.179024
$249$	−8.63087e14	−0.229487
$250$	2.00496e14	0.0519392
$251$	3.21526e15	0.811590	0.405795	−	0.913964i	$-0.366995\pi$
$251$	3.21526e15	0.811590	0.405795	+	0.913964i	$0.366995\pi$
$252$	7.77268e14	0.191191
$253$	−5.18765e15	−1.24362
$254$	−3.71767e14	−0.0868665
$255$	−1.48370e14	−0.0337937
$256$	4.23393e15	0.940122
$257$	−2.73468e15	−0.592026	−0.296013	−	0.955184i	$-0.595657\pi$
$257$	−2.73468e15	−0.592026	−0.296013	+	0.955184i	$0.595657\pi$
$258$	9.51511e12	0.00200856
$259$	−1.08424e15	−0.223191
$260$	−2.98567e15	−0.599398
$261$	−7.29380e14	−0.142821
$262$	−1.92376e14	−0.0367444
$263$	−7.63743e15	−1.42310	−0.711549	−	0.702636i	$-0.752006\pi$
$263$	−7.63743e15	−1.42310	−0.711549	+	0.702636i	$0.752006\pi$
$264$	−7.46585e14	−0.135723
$265$	1.81538e15	0.322010
$266$	−1.35347e14	−0.0234270
$267$	2.66859e14	0.0450773
$268$	−2.14658e15	−0.353893
$269$	−1.61454e15	−0.259811	−0.129906	−	0.991526i	$-0.541467\pi$
$269$	−1.61454e15	−0.259811	−0.129906	+	0.991526i	$0.541467\pi$
$270$	−3.39790e13	−0.00533761
$271$	1.26053e16	1.93310	0.966549	−	0.256483i	$-0.0825637\pi$
$271$	1.26053e16	1.93310	0.966549	+	0.256483i	$0.0825637\pi$
$272$	−1.07583e15	−0.161081
$273$	−3.85161e15	−0.563099
$274$	−1.26511e14	−0.0180614
$275$	9.49331e15	1.32359
$276$	−3.45550e15	−0.470546
$277$	−3.71246e15	−0.493791	−0.246895	−	0.969042i	$-0.579410\pi$
$277$	−3.71246e15	−0.493791	−0.246895	+	0.969042i	$0.579410\pi$
$278$	5.60508e14	0.0728267
$279$	−3.03316e15	−0.385006
$280$	−2.57331e14	−0.0319128
$281$	1.22310e16	1.48208	0.741039	−	0.671462i	$-0.234333\pi$
$281$	1.22310e16	1.48208	0.741039	+	0.671462i	$0.234333\pi$
$282$	−2.13194e13	−0.00252438
$283$	2.91187e15	0.336946	0.168473	−	0.985706i	$-0.446116\pi$
$283$	2.91187e15	0.336946	0.168473	+	0.985706i	$0.446116\pi$
$284$	−2.54192e15	−0.287470
$285$	−9.73294e14	−0.107585
$286$	1.84418e15	0.199261
$287$	2.07665e15	0.219346
$288$	−7.46705e14	−0.0771077
$289$	−9.63803e15	−0.973088
$290$	1.20373e14	0.0118834
$291$	1.06833e16	1.03134
$292$	5.94770e15	0.561514
$293$	1.09631e16	1.01227	0.506133	−	0.862455i	$-0.331074\pi$
$293$	1.09631e16	1.01227	0.506133	+	0.862455i	$0.331074\pi$
$294$	3.31459e14	0.0299345
$295$	−5.25823e14	−0.0464512
$296$	6.93703e14	0.0599483
$297$	−3.45245e15	−0.291884
$298$	1.00602e15	0.0832148
$299$	1.71231e16	1.38586
$300$	6.32350e15	0.500806
$301$	3.33230e14	0.0258263
$302$	4.77111e13	0.00361888
$303$	−7.75961e15	−0.576054
$304$	−7.05732e15	−0.512816
$305$	−5.29963e15	−0.376961
$306$	6.10446e13	0.00425068
$307$	1.75297e16	1.19502	0.597510	−	0.801861i	$-0.296157\pi$
$307$	1.75297e16	1.19502	0.597510	+	0.801861i	$0.296157\pi$
$308$	−1.30335e16	−0.869924
$309$	9.01857e15	0.589397
$310$	5.00574e14	0.0320344
$311$	2.05232e16	1.28618	0.643092	−	0.765789i	$-0.277651\pi$
$311$	2.05232e16	1.28618	0.643092	+	0.765789i	$0.277651\pi$
$312$	2.46428e15	0.151247
$313$	−1.67629e16	−1.00765	−0.503826	−	0.863805i	$-0.668075\pi$
$313$	−1.67629e16	−1.00765	−0.503826	+	0.863805i	$0.668075\pi$
$314$	1.67403e14	0.00985647
$315$	−1.18998e15	−0.0686313
$316$	−2.17838e16	−1.23074
$317$	1.94562e15	0.107689	0.0538447	−	0.998549i	$-0.482852\pi$
$317$	1.94562e15	0.107689	0.0538447	+	0.998549i	$0.482852\pi$
$318$	−7.46909e14	−0.0405034
$319$	1.22305e16	0.649837
$320$	−6.60605e15	−0.343928
$321$	−4.71973e15	−0.240788
$322$	7.35672e14	0.0367808
$323$	1.74856e15	0.0856769
$324$	−2.29968e15	−0.110440
$325$	−3.13350e16	−1.47498
$326$	2.13142e15	0.0983456
$327$	3.35471e15	0.151738
$328$	−1.32865e15	−0.0589157
$329$	−7.46628e14	−0.0324587
$330$	5.69772e14	0.0242863
$331$	3.46353e16	1.44756	0.723781	−	0.690030i	$-0.242403\pi$
$331$	3.46353e16	1.44756	0.723781	+	0.690030i	$0.242403\pi$
$332$	9.64018e15	0.395082
$333$	3.20791e15	0.128924
$334$	−2.75044e15	−0.108405
$335$	3.28638e15	0.127036
$336$	−8.62853e15	−0.327138
$337$	8.51087e15	0.316504	0.158252	−	0.987399i	$-0.449414\pi$
$337$	8.51087e15	0.316504	0.158252	+	0.987399i	$0.449414\pi$
$338$	−3.95625e15	−0.144319
$339$	3.10533e15	0.111125
$340$	1.65721e15	0.0581787
$341$	5.08610e16	1.75179
$342$	4.00446e14	0.0135324
$343$	2.90114e16	0.961960
$344$	−2.13202e14	−0.00693685
$345$	5.29031e15	0.168911
$346$	−2.26051e15	−0.0708292
$347$	5.87073e16	1.80530	0.902652	−	0.430370i	$-0.141617\pi$
$347$	5.87073e16	1.80530	0.902652	+	0.430370i	$0.141617\pi$
$348$	8.14675e15	0.245878
$349$	−3.61511e16	−1.07092	−0.535459	−	0.844561i	$-0.679861\pi$
$349$	−3.61511e16	−1.07092	−0.535459	+	0.844561i	$0.679861\pi$
$350$	−1.34627e15	−0.0391461
$351$	1.13957e16	0.325269
$352$	1.25210e16	0.350842
$353$	−1.87312e16	−0.515264	−0.257632	−	0.966243i	$-0.582942\pi$
$353$	−1.87312e16	−0.515264	−0.257632	+	0.966243i	$0.582942\pi$
$354$	2.16342e14	0.00584277
$355$	3.89164e15	0.103192
$356$	−2.98066e15	−0.0776045
$357$	2.13785e15	0.0546555
$358$	−3.86312e15	−0.0969836
$359$	−4.30600e16	−1.06160	−0.530799	−	0.847497i	$-0.678108\pi$
$359$	−4.30600e16	−1.06160	−0.530799	+	0.847497i	$0.678108\pi$
$360$	7.61359e14	0.0184341
$361$	−3.05826e16	−0.727240
$362$	1.36514e15	0.0318839
$363$	3.27248e16	0.750731
$364$	4.30202e16	0.969423
$365$	−9.10582e15	−0.201565
$366$	2.18045e15	0.0474153
$367$	4.70659e16	1.00549	0.502744	−	0.864436i	$-0.332324\pi$
$367$	4.70659e16	1.00549	0.502744	+	0.864436i	$0.332324\pi$
$368$	3.83598e16	0.805130
$369$	−6.14412e15	−0.126703
$370$	−5.29414e14	−0.0107271
$371$	−2.61576e16	−0.520796
$372$	3.38786e16	0.662821
$373$	−2.01671e15	−0.0387736	−0.0193868	−	0.999812i	$-0.506171\pi$
$373$	−2.01671e15	−0.0387736	−0.0193868	+	0.999812i	$0.506171\pi$
$374$	−1.02362e15	−0.0193407
$375$	−2.07746e16	−0.385771
$376$	4.77697e14	0.00871830
$377$	−4.03697e16	−0.724164
$378$	4.89600e14	0.00863266
$379$	−1.27882e16	−0.221643	−0.110822	−	0.993840i	$-0.535348\pi$
$379$	−1.27882e16	−0.221643	−0.110822	+	0.993840i	$0.535348\pi$
$380$	1.08711e16	0.185217
$381$	3.85211e16	0.645188
$382$	−3.15847e15	−0.0520073
$383$	2.55954e16	0.414352	0.207176	−	0.978304i	$-0.433573\pi$
$383$	2.55954e16	0.414352	0.207176	+	0.978304i	$0.433573\pi$
$384$	1.11089e16	0.176815
$385$	1.99540e16	0.312274
$386$	−3.98306e15	−0.0612914
$387$	−9.85918e14	−0.0149183
$388$	−1.19327e17	−1.77554
$389$	−1.14620e17	−1.67722	−0.838608	−	0.544735i	$-0.816630\pi$
$389$	−1.14620e17	−1.67722	−0.838608	+	0.544735i	$0.816630\pi$
$390$	−1.88067e15	−0.0270641
$391$	−9.50423e15	−0.134514
$392$	−7.42691e15	−0.103383
$393$	1.99332e16	0.272914
$394$	7.32620e14	0.00986628
$395$	3.33506e16	0.441797
$396$	3.85619e16	0.502504
$397$	−7.43340e16	−0.952904	−0.476452	−	0.879200i	$-0.658077\pi$
$397$	−7.43340e16	−0.952904	−0.476452	+	0.879200i	$0.658077\pi$
$398$	−4.53230e14	−0.00571583
$399$	1.40241e16	0.174000
$400$	−7.01978e16	−0.856907
$401$	−7.00311e16	−0.841109	−0.420555	−	0.907267i	$-0.638164\pi$
$401$	−7.00311e16	−0.841109	−0.420555	+	0.907267i	$0.638164\pi$
$402$	−1.35213e15	−0.0159790
$403$	−1.67879e17	−1.95215
$404$	8.66703e16	0.991725
$405$	3.52077e15	0.0396443
$406$	−1.73443e15	−0.0192193
$407$	−5.37913e16	−0.586608
$408$	−1.36781e15	−0.0146803
$409$	−4.06796e16	−0.429710	−0.214855	−	0.976646i	$-0.568928\pi$
$409$	−4.06796e16	−0.429710	−0.214855	+	0.976646i	$0.568928\pi$
$410$	1.01399e15	0.0105424
$411$	1.31086e16	0.134148
$412$	−1.00732e17	−1.01470
$413$	7.57652e15	0.0751268
$414$	−2.17661e15	−0.0212461
$415$	−1.47589e16	−0.141822
$416$	−4.13286e16	−0.390971
$417$	−5.80776e16	−0.540909
$418$	−6.71482e15	−0.0615728
$419$	9.40621e16	0.849227	0.424613	−	0.905375i	$-0.360410\pi$
$419$	9.40621e16	0.849227	0.424613	+	0.905375i	$0.360410\pi$
$420$	1.32914e16	0.118155
$421$	−1.72503e16	−0.150996	−0.0754978	−	0.997146i	$-0.524055\pi$
$421$	−1.72503e16	−0.150996	−0.0754978	+	0.997146i	$0.524055\pi$
$422$	−6.57143e15	−0.0566408
$423$	2.20903e15	0.0187495
$424$	1.67358e16	0.139884
$425$	1.73926e16	0.143165
$426$	−1.60115e15	−0.0129799
$427$	7.63617e16	0.609669
$428$	5.27166e16	0.414537
$429$	−1.91086e17	−1.47998
$430$	1.62710e14	0.00124128
$431$	−1.23734e17	−0.929795	−0.464898	−	0.885364i	$-0.653909\pi$
$431$	−1.23734e17	−0.929795	−0.464898	+	0.885364i	$0.653909\pi$
$432$	2.55290e16	0.188969
$433$	−3.00092e16	−0.218818	−0.109409	−	0.993997i	$-0.534896\pi$
$433$	−3.00092e16	−0.218818	−0.109409	+	0.993997i	$0.534896\pi$
$434$	−7.21271e15	−0.0518102
$435$	−1.24725e16	−0.0882621
$436$	−3.74702e16	−0.261230
$437$	−6.23468e16	−0.428238
$438$	3.74644e15	0.0253535
$439$	1.25024e17	0.833630	0.416815	−	0.908991i	$-0.363146\pi$
$439$	1.25024e17	0.833630	0.416815	+	0.908991i	$0.363146\pi$
$440$	−1.27667e16	−0.0838759
$441$	−3.43445e16	−0.222334
$442$	3.37869e15	0.0215528
$443$	−2.66955e17	−1.67808	−0.839041	−	0.544068i	$-0.816883\pi$
$443$	−2.66955e17	−1.67808	−0.839041	+	0.544068i	$0.816883\pi$
$444$	−3.58304e16	−0.221954
$445$	4.56333e15	0.0278575
$446$	−8.75757e15	−0.0526874
$447$	−1.04240e17	−0.618065
$448$	9.51858e16	0.556244
$449$	2.78758e17	1.60556	0.802778	−	0.596278i	$-0.203354\pi$
$449$	2.78758e17	1.60556	0.802778	+	0.596278i	$0.203354\pi$
$450$	3.98316e15	0.0226124
$451$	1.03027e17	0.576504
$452$	−3.46848e16	−0.191311
$453$	−4.94363e15	−0.0268787
$454$	−2.25461e16	−0.120839
$455$	−6.58632e16	−0.347991
$456$	−8.97269e15	−0.0467360
$457$	8.18878e16	0.420498	0.210249	−	0.977648i	$-0.432573\pi$
$457$	8.18878e16	0.420498	0.210249	+	0.977648i	$0.432573\pi$
$458$	−2.65635e16	−0.134481
$459$	−6.32520e15	−0.0315712
$460$	−5.90896e16	−0.290794
$461$	−2.00345e17	−0.972128	−0.486064	−	0.873923i	$-0.661568\pi$
$461$	−2.00345e17	−0.972128	−0.486064	+	0.873923i	$0.661568\pi$
$462$	−8.20977e15	−0.0392788
$463$	−8.54155e16	−0.402958	−0.201479	−	0.979493i	$-0.564575\pi$
$463$	−8.54155e16	−0.402958	−0.201479	+	0.979493i	$0.564575\pi$
$464$	−9.04378e16	−0.420710
$465$	−5.18675e16	−0.237931
$466$	−1.75065e16	−0.0791939
$467$	9.72001e16	0.433618	0.216809	−	0.976214i	$-0.430435\pi$
$467$	9.72001e16	0.433618	0.216809	+	0.976214i	$0.430435\pi$
$468$	−1.27283e17	−0.559979
$469$	−4.73530e16	−0.205459
$470$	−3.64565e14	−0.00156005
$471$	−1.73457e16	−0.0732074
$472$	−4.84751e15	−0.0201788
$473$	1.65322e16	0.0678787
$474$	−1.37216e16	−0.0555706
$475$	1.14094e17	0.455777
$476$	−2.38785e16	−0.0940940
$477$	7.73918e16	0.300833
$478$	−2.50753e16	−0.0961536
$479$	−2.68070e17	−1.01407	−0.507035	−	0.861925i	$-0.669258\pi$
$479$	−2.68070e17	−1.01407	−0.507035	+	0.861925i	$0.669258\pi$
$480$	−1.27688e16	−0.0476520
$481$	1.77551e17	0.653703
$482$	−8.75071e14	−0.00317861
$483$	−7.62274e16	−0.273184
$484$	−3.65517e17	−1.29245
$485$	1.82687e17	0.637362
$486$	−1.44857e15	−0.00498658
$487$	2.93239e17	0.996054	0.498027	−	0.867161i	$-0.334058\pi$
$487$	2.93239e17	0.996054	0.498027	+	0.867161i	$0.334058\pi$
$488$	−4.88567e16	−0.163755
$489$	−2.20849e17	−0.730447
$490$	5.66801e15	0.0184993
$491$	2.35700e17	0.759154	0.379577	−	0.925160i	$-0.376070\pi$
$491$	2.35700e17	0.759154	0.379577	+	0.925160i	$0.376070\pi$
$492$	6.86262e16	0.218131
$493$	2.24073e16	0.0702887
$494$	2.21639e16	0.0686153
$495$	−5.90375e16	−0.180382
$496$	−3.76089e17	−1.13412
$497$	−5.60741e16	−0.166896
$498$	6.07233e15	0.0178388
$499$	2.95486e17	0.856807	0.428404	−	0.903587i	$-0.359076\pi$
$499$	2.95486e17	0.856807	0.428404	+	0.903587i	$0.359076\pi$
$500$	2.32040e17	0.664137
$501$	2.84990e17	0.805163
$502$	−2.26213e16	−0.0630874
$503$	6.45285e15	0.0177648	0.00888238	−	0.999961i	$-0.497173\pi$
$503$	6.45285e15	0.0177648	0.00888238	+	0.999961i	$0.497173\pi$
$504$	−1.09703e16	−0.0298140
$505$	−1.32691e17	−0.355997
$506$	3.64982e16	0.0966703
$507$	4.09931e17	1.07191
$508$	−4.30258e17	−1.11075
$509$	−2.90108e17	−0.739425	−0.369713	−	0.929146i	$-0.620544\pi$
$509$	−2.90108e17	−0.739425	−0.369713	+	0.929146i	$0.620544\pi$
$510$	1.04387e15	0.00262689
$511$	1.31205e17	0.325997
$512$	−1.54623e17	−0.379331
$513$	−4.14927e16	−0.100510
$514$	1.92401e16	0.0460200
$515$	1.54219e17	0.364243
$516$	1.10121e16	0.0256831
$517$	−3.70418e16	−0.0853106
$518$	7.62826e15	0.0173493
$519$	2.34225e17	0.526073
$520$	4.21397e16	0.0934694
$521$	−4.12174e17	−0.902891	−0.451445	−	0.892299i	$-0.649091\pi$
$521$	−4.12174e17	−0.902891	−0.451445	+	0.892299i	$0.649091\pi$
$522$	5.13162e15	0.0111019
$523$	−2.59656e17	−0.554802	−0.277401	−	0.960754i	$-0.589473\pi$
$523$	−2.59656e17	−0.554802	−0.277401	+	0.960754i	$0.589473\pi$
$524$	−2.22642e17	−0.469844
$525$	1.39495e17	0.290752
$526$	5.37338e16	0.110622
$527$	9.31819e16	0.189480
$528$	−4.28079e17	−0.859812
$529$	−1.65152e17	−0.327660
$530$	−1.27723e16	−0.0250308
$531$	−2.24165e16	−0.0433963
$532$	−1.56641e17	−0.299557
$533$	−3.40065e17	−0.642443
$534$	−1.87751e15	−0.00350400
$535$	−8.07082e16	−0.148805
$536$	3.02968e16	0.0551855
$537$	4.00281e17	0.720331
$538$	1.13592e16	0.0201959
$539$	5.75900e17	1.01163
$540$	−3.93250e16	−0.0682510
$541$	−3.59080e17	−0.615757	−0.307878	−	0.951426i	$-0.599619\pi$
$541$	−3.59080e17	−0.615757	−0.307878	+	0.951426i	$0.599619\pi$
$542$	−8.86859e16	−0.150266
$543$	−1.41450e17	−0.236813
$544$	2.29396e16	0.0379483
$545$	5.73661e16	0.0937731
$546$	2.70983e16	0.0437714
$547$	−6.59660e17	−1.05294	−0.526469	−	0.850194i	$-0.676484\pi$
$547$	−6.59660e17	−1.05294	−0.526469	+	0.850194i	$0.676484\pi$
$548$	−1.46415e17	−0.230947
$549$	−2.25929e17	−0.352170
$550$	−6.67910e16	−0.102887
$551$	1.46990e17	0.223770
$552$	4.87708e16	0.0733763
$553$	−4.80545e17	−0.714530
$554$	2.61193e16	0.0383839
$555$	5.48558e16	0.0796742
$556$	6.48693e17	0.931222
$557$	2.33181e17	0.330853	0.165426	−	0.986222i	$-0.447100\pi$
$557$	2.33181e17	0.330853	0.165426	+	0.986222i	$0.447100\pi$
$558$	2.13401e16	0.0299277
$559$	−5.45686e16	−0.0756425
$560$	−1.47549e17	−0.202169
$561$	1.06063e17	0.143650
$562$	−8.60523e16	−0.115206
$563$	−9.44765e17	−1.25031	−0.625157	−	0.780499i	$-0.714965\pi$
$563$	−9.44765e17	−1.25031	−0.625157	+	0.780499i	$0.714965\pi$
$564$	−2.46736e16	−0.0322788
$565$	5.31017e16	0.0686742
$566$	−2.04867e16	−0.0261918
$567$	−5.07304e16	−0.0641177
$568$	3.58766e16	0.0448277
$569$	9.68935e17	1.19692	0.598460	−	0.801153i	$-0.295780\pi$
$569$	9.68935e17	1.19692	0.598460	+	0.801153i	$0.295780\pi$
$570$	6.84770e15	0.00836292
$571$	5.42831e17	0.655436	0.327718	−	0.944776i	$-0.393720\pi$
$571$	5.42831e17	0.655436	0.327718	+	0.944776i	$0.393720\pi$
$572$	2.13432e18	2.54792
$573$	3.27268e17	0.386276
$574$	−1.46104e16	−0.0170504
$575$	−6.20152e17	−0.715578
$576$	−2.81624e17	−0.321309
$577$	−7.74916e17	−0.874203	−0.437101	−	0.899412i	$-0.643995\pi$
$577$	−7.74916e17	−0.874203	−0.437101	+	0.899412i	$0.643995\pi$
$578$	6.78092e16	0.0756411
$579$	4.12709e17	0.455232
$580$	1.39311e17	0.151951
$581$	2.12660e17	0.229372
$582$	−7.51637e16	−0.0801694
$583$	−1.29773e18	−1.36880
$584$	−8.39455e16	−0.0875617
$585$	1.94868e17	0.201014
$586$	−7.71321e16	−0.0786866
$587$	−1.28751e17	−0.129898	−0.0649491	−	0.997889i	$-0.520688\pi$
$587$	−1.28751e17	−0.129898	−0.0649491	+	0.997889i	$0.520688\pi$
$588$	3.83608e17	0.382767
$589$	6.11264e17	0.603225
$590$	3.69948e15	0.00361079
$591$	−7.59112e16	−0.0732803
$592$	3.97757e17	0.379776
$593$	2.83120e17	0.267372	0.133686	−	0.991024i	$-0.457319\pi$
$593$	2.83120e17	0.267372	0.133686	+	0.991024i	$0.457319\pi$
$594$	2.42900e16	0.0226891
$595$	3.65576e16	0.0337767
$596$	1.16430e18	1.06405
$597$	4.69619e16	0.0424534
$598$	−1.20471e17	−0.107727
$599$	−3.18328e17	−0.281579	−0.140789	−	0.990040i	$-0.544964\pi$
$599$	−3.18328e17	−0.281579	−0.140789	+	0.990040i	$0.544964\pi$
$600$	−8.92497e16	−0.0780950
$601$	3.31331e17	0.286799	0.143399	−	0.989665i	$-0.454197\pi$
$601$	3.31331e17	0.286799	0.143399	+	0.989665i	$0.454197\pi$
$602$	−2.34447e15	−0.00200755
$603$	1.40102e17	0.118681
$604$	5.52174e16	0.0462739
$605$	5.59600e17	0.463946
$606$	5.45935e16	0.0447784
$607$	5.29921e17	0.430016	0.215008	−	0.976612i	$-0.431022\pi$
$607$	5.29921e17	0.430016	0.215008	+	0.976612i	$0.431022\pi$
$608$	1.50481e17	0.120812
$609$	1.79715e17	0.142749
$610$	3.72860e16	0.0293023
$611$	1.22265e17	0.0950682
$612$	7.06487e16	0.0543526
$613$	−2.12461e18	−1.61728	−0.808640	−	0.588303i	$-0.799796\pi$
$613$	−2.12461e18	−1.61728	−0.808640	+	0.588303i	$0.799796\pi$
$614$	−1.23332e17	−0.0928925
$615$	−1.05065e17	−0.0783018
$616$	1.83954e17	0.135655
$617$	−1.71451e17	−0.125108	−0.0625542	−	0.998042i	$-0.519925\pi$
$617$	−1.71451e17	−0.125108	−0.0625542	+	0.998042i	$0.519925\pi$
$618$	−6.34510e16	−0.0458156
$619$	1.45191e18	1.03741	0.518704	−	0.854954i	$-0.326415\pi$
$619$	1.45191e18	1.03741	0.518704	+	0.854954i	$0.326415\pi$
$620$	5.79329e17	0.409618
$621$	2.25532e17	0.157802
$622$	−1.44393e17	−0.0999791
$623$	−6.57524e16	−0.0450546
$624$	1.41298e18	0.958155
$625$	9.45168e17	0.634291
$626$	1.17937e17	0.0783278
$627$	6.95763e17	0.457322
$628$	1.93741e17	0.126033
$629$	−9.85504e16	−0.0634496
$630$	8.37224e15	0.00533492
$631$	−1.56293e18	−0.985708	−0.492854	−	0.870112i	$-0.664046\pi$
$631$	−1.56293e18	−0.985708	−0.492854	+	0.870112i	$0.664046\pi$
$632$	3.07456e17	0.191921
$633$	6.80905e17	0.420691
$634$	−1.36886e16	−0.00837102
$635$	6.58717e17	0.398721
$636$	−8.64421e17	−0.517909
$637$	−1.90090e18	−1.12733
$638$	−8.60487e16	−0.0505138
$639$	1.65905e17	0.0964060
$640$	1.89964e17	0.109270
$641$	−1.11430e18	−0.634488	−0.317244	−	0.948344i	$-0.602757\pi$
$641$	−1.11430e18	−0.634488	−0.317244	+	0.948344i	$0.602757\pi$
$642$	3.32061e16	0.0187172
$643$	−1.82846e18	−1.02027	−0.510133	−	0.860096i	$-0.670404\pi$
$643$	−1.82846e18	−1.02027	−0.510133	+	0.860096i	$0.670404\pi$
$644$	8.51415e17	0.470309
$645$	−1.68594e16	−0.00921941
$646$	−1.23021e16	−0.00665993
$647$	2.98220e18	1.59830	0.799152	−	0.601129i	$-0.205282\pi$
$647$	2.98220e18	1.59830	0.799152	+	0.601129i	$0.205282\pi$
$648$	3.24576e16	0.0172218
$649$	3.75887e17	0.197454
$650$	2.20460e17	0.114655
$651$	7.47352e17	0.384812
$652$	2.46676e18	1.25753
$653$	2.52221e18	1.27305	0.636525	−	0.771256i	$-0.280371\pi$
$653$	2.52221e18	1.27305	0.636525	+	0.771256i	$0.280371\pi$
$654$	−2.36024e16	−0.0117951
$655$	3.40861e17	0.168659
$656$	−7.61826e17	−0.373234
$657$	−3.88192e17	−0.188309
$658$	5.25297e15	0.00252311
$659$	1.01758e18	0.483963	0.241982	−	0.970281i	$-0.422203\pi$
$659$	1.01758e18	0.483963	0.241982	+	0.970281i	$0.422203\pi$
$660$	6.59414e17	0.310544
$661$	−6.78275e17	−0.316298	−0.158149	−	0.987415i	$-0.550553\pi$
$661$	−6.78275e17	−0.316298	−0.158149	+	0.987415i	$0.550553\pi$
$662$	−2.43680e17	−0.112523
$663$	−3.50087e17	−0.160080
$664$	−1.36061e17	−0.0616086
$665$	2.39814e17	0.107531
$666$	−2.25695e16	−0.0100217
$667$	−7.98959e17	−0.351323
$668$	−3.18317e18	−1.38616
$669$	9.07424e17	0.391328
$670$	−2.31216e16	−0.00987489
$671$	3.78846e18	1.60238
$672$	1.83984e17	0.0770689
$673$	1.41680e18	0.587776	0.293888	−	0.955840i	$-0.405051\pi$
$673$	1.41680e18	0.587776	0.293888	+	0.955840i	$0.405051\pi$
$674$	−5.98790e16	−0.0246028
$675$	−4.12720e17	−0.167950
$676$	−4.57868e18	−1.84539
$677$	4.12787e18	1.64778	0.823890	−	0.566749i	$-0.191799\pi$
$677$	4.12787e18	1.64778	0.823890	+	0.566749i	$0.191799\pi$
$678$	−2.18479e16	−0.00863806
$679$	−2.63231e18	−1.03082
$680$	−2.33898e16	−0.00907231
$681$	2.33613e18	0.897514
$682$	−3.57837e17	−0.136172
$683$	−4.54626e18	−1.71364	−0.856820	−	0.515615i	$-0.827563\pi$
$683$	−4.54626e18	−1.71364	−0.856820	+	0.515615i	$0.827563\pi$
$684$	4.63449e17	0.173036
$685$	2.24159e17	0.0829025
$686$	−2.04112e17	−0.0747760
$687$	2.75241e18	0.998835
$688$	−1.22247e17	−0.0439453
$689$	4.28348e18	1.52536
$690$	−3.72204e16	−0.0131299
$691$	1.09870e18	0.383946	0.191973	−	0.981400i	$-0.438511\pi$
$691$	1.09870e18	0.383946	0.191973	+	0.981400i	$0.438511\pi$
$692$	−2.61616e18	−0.905679
$693$	8.50664e17	0.291737
$694$	−4.13041e17	−0.140332
$695$	−9.93137e17	−0.334278
$696$	−1.14983e17	−0.0383418
$697$	1.88754e17	0.0623567
$698$	2.54344e17	0.0832457
$699$	1.81396e18	0.588201
$700$	−1.55807e18	−0.500554
$701$	7.97555e17	0.253859	0.126930	−	0.991912i	$-0.459488\pi$
$701$	7.97555e17	0.253859	0.126930	+	0.991912i	$0.459488\pi$
$702$	−8.01752e16	−0.0252842
$703$	−6.46481e17	−0.201998
$704$	4.72236e18	1.46197
$705$	3.77748e16	0.0115870
$706$	1.31785e17	0.0400531
$707$	1.91192e18	0.575764
$708$	2.50379e17	0.0747104
$709$	1.42619e18	0.421675	0.210838	−	0.977521i	$-0.432381\pi$
$709$	1.42619e18	0.421675	0.210838	+	0.977521i	$0.432381\pi$
$710$	−2.73800e16	−0.00802146
$711$	1.42178e18	0.412742
$712$	4.20688e16	0.0121015
$713$	−3.32250e18	−0.947073
$714$	−1.50410e16	−0.00424853
$715$	−3.26761e18	−0.914619
$716$	−4.47090e18	−1.24011
$717$	2.59821e18	0.714166
$718$	3.02953e17	0.0825213
$719$	2.76714e18	0.746954	0.373477	−	0.927639i	$-0.378165\pi$
$719$	2.76714e18	0.746954	0.373477	+	0.927639i	$0.378165\pi$
$720$	4.36550e17	0.116781
$721$	−2.22212e18	−0.589100
$722$	2.15167e17	0.0565306
$723$	9.06714e16	0.0236087
$724$	1.57992e18	0.407693
$725$	1.46208e18	0.373916
$726$	−2.30239e17	−0.0583566
$727$	−1.88892e18	−0.474505	−0.237252	−	0.971448i	$-0.576247\pi$
$727$	−1.88892e18	−0.474505	−0.237252	+	0.971448i	$0.576247\pi$
$728$	−6.07185e17	−0.151171
$729$	1.50095e17	0.0370370
$730$	6.40648e16	0.0156683
$731$	3.02885e16	0.00734200
$732$	2.52350e18	0.606291
$733$	2.87686e18	0.685082	0.342541	−	0.939503i	$-0.388712\pi$
$733$	2.87686e18	0.685082	0.342541	+	0.939503i	$0.388712\pi$
$734$	−3.31136e17	−0.0781596
$735$	−5.87296e17	−0.137401
$736$	−8.17936e17	−0.189677
$737$	−2.34928e18	−0.540003
$738$	4.32275e16	0.00984904
$739$	−4.90104e16	−0.0110688	−0.00553438	−	0.999985i	$-0.501762\pi$
$739$	−4.90104e16	−0.0110688	−0.00553438	+	0.999985i	$0.501762\pi$
$740$	−6.12706e17	−0.137166
$741$	−2.29654e18	−0.509630
$742$	1.84034e17	0.0404830
$743$	2.87146e18	0.626146	0.313073	−	0.949729i	$-0.398641\pi$
$743$	2.87146e18	0.626146	0.313073	+	0.949729i	$0.398641\pi$
$744$	−4.78161e17	−0.103359
$745$	−1.78252e18	−0.381960
$746$	1.41887e16	0.00301399
$747$	−6.29191e17	−0.132495
$748$	−1.18466e18	−0.247306
$749$	1.16291e18	0.240667
$750$	1.46162e17	0.0299871
$751$	4.30483e18	0.875581	0.437791	−	0.899077i	$-0.355761\pi$
$751$	4.30483e18	0.875581	0.437791	+	0.899077i	$0.355761\pi$
$752$	2.73904e17	0.0552308
$753$	2.34392e18	0.468572
$754$	2.84025e17	0.0562915
$755$	−8.45369e16	−0.0166108
$756$	5.66628e17	0.110384
$757$	−1.57319e18	−0.303849	−0.151925	−	0.988392i	$-0.548547\pi$
$757$	−1.57319e18	−0.303849	−0.151925	+	0.988392i	$0.548547\pi$
$758$	8.99725e16	0.0172290
$759$	−3.78180e18	−0.718004
$760$	−1.53435e17	−0.0288825
$761$	4.55145e18	0.849472	0.424736	−	0.905317i	$-0.360367\pi$
$761$	4.55145e18	0.849472	0.424736	+	0.905317i	$0.360367\pi$
$762$	−2.71018e17	−0.0501524
$763$	−8.26582e17	−0.151662
$764$	−3.65539e18	−0.665008
$765$	−1.08162e17	−0.0195108
$766$	−1.80079e17	−0.0322089
$767$	−1.24071e18	−0.220039
$768$	3.08654e18	0.542780
$769$	5.31422e18	0.926655	0.463327	−	0.886187i	$-0.346655\pi$
$769$	5.31422e18	0.926655	0.463327	+	0.886187i	$0.346655\pi$
$770$	−1.40388e17	−0.0242740
$771$	−1.99358e18	−0.341806
$772$	−4.60971e18	−0.783721
$773$	−5.62082e18	−0.947617	−0.473809	−	0.880628i	$-0.657121\pi$
$773$	−5.62082e18	−0.947617	−0.473809	+	0.880628i	$0.657121\pi$
$774$	6.93652e15	0.00115965
$775$	6.08012e18	1.00798
$776$	1.68417e18	0.276876
$777$	−7.90410e17	−0.128859
$778$	8.06422e17	0.130375
$779$	1.23821e18	0.198518
$780$	−2.17656e18	−0.346063
$781$	−2.78195e18	−0.438650
$782$	6.68679e16	0.0104562
$783$	−5.31718e17	−0.0824575
$784$	−4.25846e18	−0.654936
$785$	−2.96614e17	−0.0452417
$786$	−1.40242e17	−0.0212144
$787$	4.85685e18	0.728651	0.364325	−	0.931272i	$-0.381300\pi$
$787$	4.85685e18	0.728651	0.364325	+	0.931272i	$0.381300\pi$
$788$	8.47883e17	0.126158
$789$	−5.56769e18	−0.821626
$790$	−2.34641e17	−0.0343422
$791$	−7.65136e17	−0.111069
$792$	−5.44260e17	−0.0783597
$793$	−1.25047e19	−1.78566
$794$	5.22984e17	0.0740722
$795$	1.32341e18	0.185913
$796$	−5.24537e17	−0.0730872
$797$	9.06607e18	1.25297	0.626484	−	0.779434i	$-0.284493\pi$
$797$	9.06607e18	1.25297	0.626484	+	0.779434i	$0.284493\pi$
$798$	−9.86677e16	−0.0135256
$799$	−6.78638e16	−0.00922750
$800$	1.49681e18	0.201875
$801$	1.94540e17	0.0260254
$802$	4.92710e17	0.0653820
$803$	6.50933e18	0.856811
$804$	−1.56486e18	−0.204320
$805$	−1.30350e18	−0.168826
$806$	1.18113e18	0.151747
$807$	−1.17700e18	−0.150002
$808$	−1.22326e18	−0.154648
$809$	1.42718e18	0.178984	0.0894918	−	0.995988i	$-0.471476\pi$
$809$	1.42718e18	0.178984	0.0894918	+	0.995988i	$0.471476\pi$
$810$	−2.47707e16	−0.00308167
$811$	−6.88423e18	−0.849610	−0.424805	−	0.905285i	$-0.639657\pi$
$811$	−6.88423e18	−0.849610	−0.424805	+	0.905285i	$0.639657\pi$
$812$	−2.00731e18	−0.245754
$813$	9.18928e18	1.11607
$814$	3.78454e17	0.0455989
$815$	−3.77656e18	−0.451411
$816$	−7.84278e17	−0.0930003
$817$	1.98689e17	0.0233739
$818$	2.86205e17	0.0334027
$819$	−2.80782e18	−0.325106
$820$	1.17352e18	0.134803
$821$	−3.82786e18	−0.436240	−0.218120	−	0.975922i	$-0.569992\pi$
$821$	−3.82786e18	−0.436240	−0.218120	+	0.975922i	$0.569992\pi$
$822$	−9.22267e16	−0.0104277
$823$	−4.05729e18	−0.455132	−0.227566	−	0.973763i	$-0.573077\pi$
$823$	−4.05729e18	−0.455132	−0.227566	+	0.973763i	$0.573077\pi$
$824$	1.42173e18	0.158230
$825$	6.92062e18	0.764178
$826$	−5.33053e16	−0.00583983
$827$	3.43912e18	0.373819	0.186909	−	0.982377i	$-0.440153\pi$
$827$	3.43912e18	0.373819	0.186909	+	0.982377i	$0.440153\pi$
$828$	−2.51906e18	−0.271670
$829$	−1.20942e19	−1.29411	−0.647055	−	0.762443i	$-0.724000\pi$
$829$	−1.20942e19	−1.29411	−0.647055	+	0.762443i	$0.724000\pi$
$830$	1.03838e17	0.0110242
$831$	−2.70638e18	−0.285090
$832$	−1.55873e19	−1.62918
$833$	1.05510e18	0.109421
$834$	4.08611e17	0.0420465
$835$	4.87337e18	0.497585
$836$	−7.77126e18	−0.787319
$837$	−2.21117e18	−0.222283
$838$	−6.61783e17	−0.0660130
$839$	−7.44376e18	−0.736783	−0.368391	−	0.929671i	$-0.620091\pi$
$839$	−7.44376e18	−0.736783	−0.368391	+	0.929671i	$0.620091\pi$
$840$	−1.87594e17	−0.0184249
$841$	−8.37699e18	−0.816421
$842$	1.21366e17	0.0117373
$843$	8.91640e18	0.855678
$844$	−7.60531e18	−0.724254
$845$	7.00988e18	0.662433
$846$	−1.55418e16	−0.00145745
$847$	−8.06321e18	−0.750353
$848$	9.59602e18	0.886172
$849$	2.12275e18	0.194536
$850$	−1.22367e17	−0.0111286
$851$	3.51392e18	0.317139
$852$	−1.85306e18	−0.165971
$853$	−2.12204e19	−1.88619	−0.943093	−	0.332529i	$-0.892098\pi$
$853$	−2.12204e19	−1.88619	−0.943093	+	0.332529i	$0.892098\pi$
$854$	−5.37250e17	−0.0473915
$855$	−7.09531e17	−0.0621143
$856$	−7.44040e17	−0.0646423
$857$	1.88453e18	0.162490	0.0812452	−	0.996694i	$-0.474110\pi$
$857$	1.88453e18	0.162490	0.0812452	+	0.996694i	$0.474110\pi$
$858$	1.34440e18	0.115044
$859$	7.91055e18	0.671817	0.335909	−	0.941895i	$-0.390957\pi$
$859$	7.91055e18	0.671817	0.335909	+	0.941895i	$0.390957\pi$
$860$	1.88309e17	0.0158720
$861$	1.51388e18	0.126640
$862$	8.70543e17	0.0722758
$863$	3.54292e18	0.291938	0.145969	−	0.989289i	$-0.453370\pi$
$863$	3.54292e18	0.291938	0.145969	+	0.989289i	$0.453370\pi$
$864$	−5.44348e17	−0.0445182
$865$	4.00529e18	0.325109
$866$	2.11133e17	0.0170094
$867$	−7.02612e18	−0.561813
$868$	−8.34748e18	−0.662487
$869$	−2.38408e19	−1.87799
$870$	8.77516e16	0.00686088
$871$	7.75437e18	0.601768
$872$	5.28852e17	0.0407359
$873$	7.78816e18	0.595446
$874$	4.38647e17	0.0332882
$875$	5.11874e18	0.385576
$876$	4.33587e18	0.324190
$877$	−1.44911e19	−1.07548	−0.537741	−	0.843110i	$-0.680722\pi$
$877$	−1.44911e19	−1.07548	−0.537741	+	0.843110i	$0.680722\pi$
$878$	−8.79616e17	−0.0648006
$879$	7.99212e18	0.584432
$880$	−7.32022e18	−0.531357
$881$	−4.15928e18	−0.299692	−0.149846	−	0.988709i	$-0.547878\pi$
$881$	−4.15928e18	−0.299692	−0.149846	+	0.988709i	$0.547878\pi$
$882$	2.41634e17	0.0172827
$883$	7.17085e18	0.509127	0.254564	−	0.967056i	$-0.418068\pi$
$883$	7.17085e18	0.509127	0.254564	+	0.967056i	$0.418068\pi$
$884$	3.91026e18	0.275592
$885$	−3.83325e17	−0.0268186
$886$	1.87818e18	0.130442
$887$	−6.89321e18	−0.475246	−0.237623	−	0.971357i	$-0.576368\pi$
$887$	−6.89321e18	−0.475246	−0.237623	+	0.971357i	$0.576368\pi$
$888$	5.05709e17	0.0346112
$889$	−9.49137e18	−0.644863
$890$	−3.21057e16	−0.00216545
$891$	−2.51684e18	−0.168519
$892$	−1.01354e19	−0.673704
$893$	−4.45180e17	−0.0293765
$894$	7.33388e17	0.0480441
$895$	6.84487e18	0.445159
$896$	−2.73717e18	−0.176726
$897$	1.24827e19	0.800127
$898$	−1.96122e18	−0.124805
$899$	7.83319e18	0.494881
$900$	4.60983e18	0.289141
$901$	−2.37756e18	−0.148054
$902$	−7.24854e17	−0.0448134
$903$	2.42924e17	0.0149108
$904$	4.89539e17	0.0298327
$905$	−2.41882e18	−0.146349
$906$	3.47814e16	0.00208936
$907$	2.30526e19	1.37490	0.687452	−	0.726230i	$-0.258729\pi$
$907$	2.30526e19	1.37490	0.687452	+	0.726230i	$0.258729\pi$
$908$	−2.60932e19	−1.54515
$909$	−5.65676e18	−0.332585
$910$	4.63386e17	0.0270504
$911$	1.67243e18	0.0969344	0.0484672	−	0.998825i	$-0.484566\pi$
$911$	1.67243e18	0.0969344	0.0484672	+	0.998825i	$0.484566\pi$
$912$	−5.14479e18	−0.296075
$913$	1.05505e19	0.602854
$914$	−5.76129e17	−0.0326866
$915$	−3.86343e18	−0.217639
$916$	−3.07427e19	−1.71958
$917$	−4.91142e18	−0.272776
$918$	4.45015e16	0.00245413
$919$	−1.51946e18	−0.0832027	−0.0416013	−	0.999134i	$-0.513246\pi$
$919$	−1.51946e18	−0.0832027	−0.0416013	+	0.999134i	$0.513246\pi$
$920$	8.33988e17	0.0453460
$921$	1.27792e19	0.689945
$922$	1.40955e18	0.0755664
$923$	9.18251e18	0.488821
$924$	−9.50142e18	−0.502251
$925$	−6.43042e18	−0.337534
$926$	6.00948e17	0.0313232
$927$	6.57454e18	0.340288
$928$	1.92838e18	0.0991131
$929$	2.11638e19	1.08017	0.540084	−	0.841611i	$-0.318392\pi$
$929$	2.11638e19	1.08017	0.540084	+	0.841611i	$0.318392\pi$
$930$	3.64918e17	0.0184951
$931$	6.92135e18	0.348351
$932$	−2.02608e19	−1.01264
$933$	1.49614e19	0.742579
$934$	−6.83860e17	−0.0337064
$935$	1.81370e18	0.0887746
$936$	1.79646e18	0.0873223
$937$	−1.20261e19	−0.580519	−0.290259	−	0.956948i	$-0.593742\pi$
$937$	−1.20261e19	−0.580519	−0.290259	+	0.956948i	$0.593742\pi$
$938$	3.33157e17	0.0159709
$939$	−1.22201e19	−0.581768
$940$	−4.21922e17	−0.0199481
$941$	−3.92961e19	−1.84509	−0.922544	−	0.385893i	$-0.873894\pi$
$941$	−3.92961e19	−1.84509	−0.922544	+	0.385893i	$0.873894\pi$
$942$	1.22037e17	0.00569064
$943$	−6.73023e18	−0.311677
$944$	−2.77948e18	−0.127834
$945$	−8.67498e17	−0.0396243
$946$	−1.16314e17	−0.00527642
$947$	−1.46194e19	−0.658648	−0.329324	−	0.944217i	$-0.606821\pi$
$947$	−1.46194e19	−0.658648	−0.329324	+	0.944217i	$0.606821\pi$
$948$	−1.58804e19	−0.710570
$949$	−2.14856e19	−0.954811
$950$	−8.02716e17	−0.0354290
$951$	1.41836e18	0.0621745
$952$	3.37020e17	0.0146729
$953$	1.43682e19	0.621298	0.310649	−	0.950525i	$-0.399454\pi$
$953$	1.43682e19	0.621298	0.310649	+	0.950525i	$0.399454\pi$
$954$	−5.44497e17	−0.0233847
$955$	5.59633e18	0.238716
$956$	−2.90204e19	−1.22950
$957$	8.91603e18	0.375184
$958$	1.88603e18	0.0788267
$959$	−3.22988e18	−0.134080
$960$	−4.81581e18	−0.198567
$961$	8.15710e18	0.334067
$962$	−1.24918e18	−0.0508143
$963$	−3.44068e18	−0.139019
$964$	−1.01275e18	−0.0406443
$965$	7.05739e18	0.281330
$966$	5.36305e17	0.0212354
$967$	−4.32204e19	−1.69987	−0.849936	−	0.526886i	$-0.823360\pi$
$967$	−4.32204e19	−1.69987	−0.849936	+	0.526886i	$0.823360\pi$
$968$	5.15889e18	0.201542
$969$	1.27470e18	0.0494656
$970$	−1.28531e18	−0.0495441
$971$	3.91080e19	1.49741	0.748705	−	0.662903i	$-0.230676\pi$
$971$	3.91080e19	1.49741	0.748705	+	0.662903i	$0.230676\pi$
$972$	−1.67647e18	−0.0637624
$973$	1.43100e19	0.540637
$974$	−2.06311e18	−0.0774263
$975$	−2.28432e19	−0.851583
$976$	−2.80136e19	−1.03740
$977$	−5.18308e18	−0.190666	−0.0953329	−	0.995445i	$-0.530392\pi$
$977$	−5.18308e18	−0.190666	−0.0953329	+	0.995445i	$0.530392\pi$
$978$	1.55381e18	0.0567799
$979$	−3.26211e18	−0.118416
$980$	6.55975e18	0.236547
$981$	2.44559e18	0.0876061
$982$	−1.65829e18	−0.0590113
$983$	4.57127e19	1.61599	0.807996	−	0.589188i	$-0.200552\pi$
$983$	4.57127e19	1.61599	0.807996	+	0.589188i	$0.200552\pi$
$984$	−9.68587e17	−0.0340150
$985$	−1.29809e18	−0.0452867
$986$	−1.57649e17	−0.00546375
$987$	−5.44292e17	−0.0187400
$988$	2.56509e19	0.877371
$989$	−1.07997e18	−0.0366974
$990$	4.15364e17	0.0140217
$991$	−2.18298e19	−0.732100	−0.366050	−	0.930595i	$-0.619290\pi$
$991$	−2.18298e19	−0.732100	−0.366050	+	0.930595i	$0.619290\pi$
$992$	8.01925e18	0.267182
$993$	2.52491e19	0.835750
$994$	3.94514e17	0.0129733
$995$	8.03057e17	0.0262359
$996$	7.02769e18	0.228101
$997$	5.24614e19	1.69169	0.845846	−	0.533427i	$-0.179096\pi$
$997$	5.24614e19	1.69169	0.845846	+	0.533427i	$0.179096\pi$
$998$	−2.07892e18	−0.0666022
$999$	2.33856e18	0.0744344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.14	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-7.03559 q^{2} +729.000 q^{3} -8142.50 q^{4} +12466.0 q^{5} -5128.95 q^{6} -179621. q^{7} +114923. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-7.03559 q^{2} +729.000 q^{3} -8142.50 q^{4} +12466.0 q^{5} -5128.95 q^{6} -179621. q^{7} +114923. q^{8} +531441. q^{9} -87705.8 q^{10} -8.91138e6 q^{11} -5.93588e6 q^{12} +2.94142e7 q^{13} +1.26374e6 q^{14} +9.08773e6 q^{15} +6.58948e7 q^{16} -1.63264e7 q^{17} -3.73900e6 q^{18} -1.07100e8 q^{19} -1.01505e8 q^{20} -1.30944e8 q^{21} +6.26968e7 q^{22} +5.82137e8 q^{23} +8.37788e7 q^{24} -1.06530e9 q^{25} -2.06946e8 q^{26} +3.87420e8 q^{27} +1.46257e9 q^{28} -1.37246e9 q^{29} -6.39375e7 q^{30} -5.70742e9 q^{31} -1.40506e9 q^{32} -6.49640e9 q^{33} +1.14866e8 q^{34} -2.23916e9 q^{35} -4.32726e9 q^{36} +6.03624e9 q^{37} +7.53511e8 q^{38} +2.14429e10 q^{39} +1.43263e9 q^{40} -1.15612e10 q^{41} +9.21268e8 q^{42} -1.85518e9 q^{43} +7.25609e10 q^{44} +6.62495e9 q^{45} -4.09568e9 q^{46} +4.15668e9 q^{47} +4.80373e10 q^{48} -6.46252e10 q^{49} +7.49503e9 q^{50} -1.19020e10 q^{51} -2.39505e11 q^{52} +1.45626e11 q^{53} -2.72573e9 q^{54} -1.11089e11 q^{55} -2.06426e10 q^{56} -7.80758e10 q^{57} +9.65605e9 q^{58} -4.21805e10 q^{59} -7.39968e10 q^{60} -4.25126e11 q^{61} +4.01551e10 q^{62} -9.54581e10 q^{63} -5.29925e11 q^{64} +3.66678e11 q^{65} +4.57060e10 q^{66} +2.63627e11 q^{67} +1.32938e11 q^{68} +4.24378e11 q^{69} +1.57538e10 q^{70} +3.12180e11 q^{71} +6.10747e10 q^{72} -7.30451e11 q^{73} -4.24686e10 q^{74} -7.76605e11 q^{75} +8.72060e11 q^{76} +1.60067e12 q^{77} -1.50864e11 q^{78} +2.67532e12 q^{79} +8.21446e11 q^{80} +2.82430e11 q^{81} +8.13402e10 q^{82} -1.18393e12 q^{83} +1.06621e12 q^{84} -2.03526e11 q^{85} +1.30523e10 q^{86} -1.00052e12 q^{87} -1.02412e12 q^{88} +3.66061e11 q^{89} -4.66105e10 q^{90} -5.28341e12 q^{91} -4.74005e12 q^{92} -4.16071e12 q^{93} -2.92447e10 q^{94} -1.33511e12 q^{95} -1.02429e12 q^{96} +1.46548e13 q^{97} +4.54676e11 q^{98} -4.73587e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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