LMFDB - Embedded newform 177.14.a.c.1.15

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			1.15
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)

$f(q)$	$=$	$q-1.12446 q^{2} +729.000 q^{3} -8190.74 q^{4} -53521.6 q^{5} -819.732 q^{6} +445275. q^{7} +18421.7 q^{8} +531441. q^{9} +O(q^{10})$	\(q-1.12446 q^{2} +729.000 q^{3} -8190.74 q^{4} -53521.6 q^{5} -819.732 q^{6} +445275. q^{7} +18421.7 q^{8} +531441. q^{9} +60183.0 q^{10} +4.07152e6 q^{11} -5.97105e6 q^{12} +2.06685e7 q^{13} -500694. q^{14} -3.90173e7 q^{15} +6.70778e7 q^{16} +1.55027e7 q^{17} -597585. q^{18} -3.30972e8 q^{19} +4.38382e8 q^{20} +3.24605e8 q^{21} -4.57826e6 q^{22} -3.80918e8 q^{23} +1.34294e7 q^{24} +1.64386e9 q^{25} -2.32409e7 q^{26} +3.87420e8 q^{27} -3.64713e9 q^{28} +3.38409e9 q^{29} +4.38734e7 q^{30} +6.98563e9 q^{31} -2.26337e8 q^{32} +2.96814e9 q^{33} -1.74321e7 q^{34} -2.38318e10 q^{35} -4.35289e9 q^{36} +8.29474e9 q^{37} +3.72165e8 q^{38} +1.50673e10 q^{39} -9.85962e8 q^{40} +4.02532e10 q^{41} -3.65006e8 q^{42} -5.64046e10 q^{43} -3.33487e10 q^{44} -2.84436e10 q^{45} +4.28327e8 q^{46} -1.39143e11 q^{47} +4.88997e10 q^{48} +1.01381e11 q^{49} -1.84846e9 q^{50} +1.13014e10 q^{51} -1.69290e11 q^{52} +3.09377e10 q^{53} -4.35639e8 q^{54} -2.17914e11 q^{55} +8.20274e9 q^{56} -2.41279e11 q^{57} -3.80528e9 q^{58} -4.21805e10 q^{59} +3.19580e11 q^{60} -6.44956e11 q^{61} -7.85507e9 q^{62} +2.36637e11 q^{63} -5.49247e11 q^{64} -1.10621e12 q^{65} -3.33755e9 q^{66} -1.03241e12 q^{67} -1.26978e11 q^{68} -2.77689e11 q^{69} +2.67980e10 q^{70} +1.62556e12 q^{71} +9.79007e9 q^{72} -8.01233e11 q^{73} -9.32711e9 q^{74} +1.19838e12 q^{75} +2.71091e12 q^{76} +1.81295e12 q^{77} -1.69426e10 q^{78} -1.43639e12 q^{79} -3.59011e12 q^{80} +2.82430e11 q^{81} -4.52632e10 q^{82} +1.93924e12 q^{83} -2.65876e12 q^{84} -8.29728e11 q^{85} +6.34247e10 q^{86} +2.46700e12 q^{87} +7.50045e10 q^{88} +1.58905e12 q^{89} +3.19837e10 q^{90} +9.20317e12 q^{91} +3.12000e12 q^{92} +5.09252e12 q^{93} +1.56461e11 q^{94} +1.77142e13 q^{95} -1.65000e11 q^{96} +9.46461e12 q^{97} -1.13999e11 q^{98} +2.16377e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.12446	−0.0124237	−0.00621183	−	0.999981i	$-0.501977\pi$
$2$	−1.12446	−0.0124237	−0.00621183	+	0.999981i	$0.501977\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−8190.74	−0.999846
$5$	−53521.6	−1.53188	−0.765939	−	0.642913i	$-0.777726\pi$
$5$	−53521.6	−1.53188	−0.765939	+	0.642913i	$0.777726\pi$
$6$	−819.732	−0.00717280
$7$	445275.	1.43051	0.715255	−	0.698863i	$-0.246310\pi$
$7$	445275.	1.43051	0.715255	+	0.698863i	$0.246310\pi$
$8$	18421.7	0.0248454
$9$	531441.	0.333333
$10$	60183.0	0.0190315
$11$	4.07152e6	0.692954	0.346477	−	0.938059i	$-0.387378\pi$
$11$	4.07152e6	0.692954	0.346477	+	0.938059i	$0.387378\pi$
$12$	−5.97105e6	−0.577261
$13$	2.06685e7	1.18762	0.593810	−	0.804605i	$-0.297623\pi$
$13$	2.06685e7	1.18762	0.593810	+	0.804605i	$0.297623\pi$
$14$	−500694.	−0.0177722
$15$	−3.90173e7	−0.884431
$16$	6.70778e7	0.999537
$17$	1.55027e7	0.155772	0.0778858	−	0.996962i	$-0.475183\pi$
$17$	1.55027e7	0.155772	0.0778858	+	0.996962i	$0.475183\pi$
$18$	−597585.	−0.00414122
$19$	−3.30972e8	−1.61396	−0.806981	−	0.590578i	$-0.798900\pi$
$19$	−3.30972e8	−1.61396	−0.806981	+	0.590578i	$0.798900\pi$
$20$	4.38382e8	1.53164
$21$	3.24605e8	0.825906
$22$	−4.57826e6	−0.00860901
$23$	−3.80918e8	−0.536538	−0.268269	−	0.963344i	$-0.586452\pi$
$23$	−3.80918e8	−0.536538	−0.268269	+	0.963344i	$0.586452\pi$
$24$	1.34294e7	0.0143445
$25$	1.64386e9	1.34665
$26$	−2.32409e7	−0.0147546
$27$	3.87420e8	0.192450
$28$	−3.64713e9	−1.43029
$29$	3.38409e9	1.05646	0.528232	−	0.849100i	$-0.322855\pi$
$29$	3.38409e9	1.05646	0.528232	+	0.849100i	$0.322855\pi$
$30$	4.38734e7	0.0109879
$31$	6.98563e9	1.41369	0.706846	−	0.707368i	$-0.250118\pi$
$31$	6.98563e9	1.41369	0.706846	+	0.707368i	$0.250118\pi$
$32$	−2.26337e8	−0.0372633
$33$	2.96814e9	0.400077
$34$	−1.74321e7	−0.00193525
$35$	−2.38318e10	−2.19137
$36$	−4.35289e9	−0.333282
$37$	8.29474e9	0.531486	0.265743	−	0.964044i	$-0.414383\pi$
$37$	8.29474e9	0.531486	0.265743	+	0.964044i	$0.414383\pi$
$38$	3.72165e8	0.0200513
$39$	1.50673e10	0.685673
$40$	−9.85962e8	−0.0380601
$41$	4.02532e10	1.32344	0.661722	−	0.749749i	$-0.269826\pi$
$41$	4.02532e10	1.32344	0.661722	+	0.749749i	$0.269826\pi$
$42$	−3.65006e8	−0.0102608
$43$	−5.64046e10	−1.36072	−0.680361	−	0.732877i	$-0.738177\pi$
$43$	−5.64046e10	−1.36072	−0.680361	+	0.732877i	$0.738177\pi$
$44$	−3.33487e10	−0.692847
$45$	−2.84436e10	−0.510626
$46$	4.28327e8	0.00666576
$47$	−1.39143e11	−1.88290	−0.941448	−	0.337158i	$-0.890534\pi$
$47$	−1.39143e11	−1.88290	−0.941448	+	0.337158i	$0.890534\pi$
$48$	4.88997e10	0.577083
$49$	1.01381e11	1.04636
$50$	−1.84846e9	−0.0167303
$51$	1.13014e10	0.0899347
$52$	−1.69290e11	−1.18744
$53$	3.09377e10	0.191732	0.0958662	−	0.995394i	$-0.469438\pi$
$53$	3.09377e10	0.191732	0.0958662	+	0.995394i	$0.469438\pi$
$54$	−4.35639e8	−0.00239093
$55$	−2.17914e11	−1.06152
$56$	8.20274e9	0.0355416
$57$	−2.41279e11	−0.931821
$58$	−3.80528e9	−0.0131251
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	3.19580e11	0.884294
$61$	−6.44956e11	−1.60283	−0.801413	−	0.598111i	$-0.795918\pi$
$61$	−6.44956e11	−1.60283	−0.801413	+	0.598111i	$0.795918\pi$
$62$	−7.85507e9	−0.0175632
$63$	2.36637e11	0.476837
$64$	−5.49247e11	−0.999074
$65$	−1.10621e12	−1.81929
$66$	−3.33755e9	−0.00497042
$67$	−1.03241e12	−1.39434	−0.697168	−	0.716908i	$-0.745557\pi$
$67$	−1.03241e12	−1.39434	−0.697168	+	0.716908i	$0.745557\pi$
$68$	−1.26978e11	−0.155748
$69$	−2.77689e11	−0.309771
$70$	2.67980e10	0.0272248
$71$	1.62556e12	1.50599	0.752997	−	0.658024i	$-0.228608\pi$
$71$	1.62556e12	1.50599	0.752997	+	0.658024i	$0.228608\pi$
$72$	9.79007e9	0.00828180
$73$	−8.01233e11	−0.619669	−0.309835	−	0.950790i	$-0.600274\pi$
$73$	−8.01233e11	−0.619669	−0.309835	+	0.950790i	$0.600274\pi$
$74$	−9.32711e9	−0.00660299
$75$	1.19838e12	0.777490
$76$	2.71091e12	1.61371
$77$	1.81295e12	0.991277
$78$	−1.69426e10	−0.00851856
$79$	−1.43639e12	−0.664809	−0.332405	−	0.943137i	$-0.607860\pi$
$79$	−1.43639e12	−0.664809	−0.332405	+	0.943137i	$0.607860\pi$
$80$	−3.59011e12	−1.53117
$81$	2.82430e11	0.111111
$82$	−4.52632e10	−0.0164420
$83$	1.93924e12	0.651065	0.325532	−	0.945531i	$-0.394457\pi$
$83$	1.93924e12	0.651065	0.325532	+	0.945531i	$0.394457\pi$
$84$	−2.65876e12	−0.825778
$85$	−8.29728e11	−0.238623
$86$	6.34247e10	0.0169051
$87$	2.46700e12	0.609950
$88$	7.50045e10	0.0172167
$89$	1.58905e12	0.338924	0.169462	−	0.985537i	$-0.445797\pi$
$89$	1.58905e12	0.338924	0.169462	+	0.985537i	$0.445797\pi$
$90$	3.19837e10	0.00634384
$91$	9.20317e12	1.69890
$92$	3.12000e12	0.536455
$93$	5.09252e12	0.816195
$94$	1.56461e11	0.0233924
$95$	1.77142e13	2.47239
$96$	−1.65000e11	−0.0215140
$97$	9.46461e12	1.15368	0.576841	−	0.816856i	$-0.304285\pi$
$97$	9.46461e12	1.15368	0.576841	+	0.816856i	$0.304285\pi$
$98$	−1.13999e11	−0.0129996
$99$	2.16377e12	0.230985
$100$	−1.34644e13	−1.34644
$101$	−4.54631e12	−0.426158	−0.213079	−	0.977035i	$-0.568349\pi$
$101$	−4.54631e12	−0.426158	−0.213079	+	0.977035i	$0.568349\pi$
$102$	−1.27080e10	−0.00111732
$103$	1.34900e13	1.11319	0.556595	−	0.830784i	$-0.312108\pi$
$103$	1.34900e13	1.11319	0.556595	+	0.830784i	$0.312108\pi$
$104$	3.80750e11	0.0295069
$105$	−1.73734e13	−1.26519
$106$	−3.47883e10	−0.00238202
$107$	2.11168e13	1.36029	0.680147	−	0.733075i	$-0.261916\pi$
$107$	2.11168e13	1.36029	0.680147	+	0.733075i	$0.261916\pi$
$108$	−3.17326e12	−0.192420
$109$	−1.62894e13	−0.930324	−0.465162	−	0.885226i	$-0.654004\pi$
$109$	−1.62894e13	−0.930324	−0.465162	+	0.885226i	$0.654004\pi$
$110$	2.45036e11	0.0131880
$111$	6.04686e12	0.306853
$112$	2.98681e13	1.42985
$113$	2.30674e12	0.104229	0.0521144	−	0.998641i	$-0.483404\pi$
$113$	2.30674e12	0.104229	0.0521144	+	0.998641i	$0.483404\pi$
$114$	2.71308e11	0.0115766
$115$	2.03874e13	0.821912
$116$	−2.77182e13	−1.05630
$117$	1.09841e13	0.395873
$118$	4.74304e10	0.00161742
$119$	6.90294e12	0.222833
$120$	−7.18766e11	−0.0219740
$121$	−1.79454e13	−0.519815
$122$	7.25228e11	0.0199130
$123$	2.93446e13	0.764091
$124$	−5.72174e13	−1.41347
$125$	−2.26482e13	−0.531029
$126$	−2.66089e11	−0.00592405
$127$	−4.24645e13	−0.898053	−0.449026	−	0.893519i	$-0.648229\pi$
$127$	−4.24645e13	−0.898053	−0.449026	+	0.893519i	$0.648229\pi$
$128$	2.47176e12	0.0496754
$129$	−4.11189e13	−0.785613
$130$	1.24389e12	0.0226022
$131$	5.15262e13	0.890768	0.445384	−	0.895340i	$-0.353067\pi$
$131$	5.15262e13	0.890768	0.445384	+	0.895340i	$0.353067\pi$
$132$	−2.43112e13	−0.400015
$133$	−1.47374e14	−2.30879
$134$	1.16091e12	0.0173227
$135$	−2.07354e13	−0.294810
$136$	2.85586e11	0.00387020
$137$	1.11549e14	1.44139	0.720695	−	0.693253i	$-0.243823\pi$
$137$	1.11549e14	1.44139	0.720695	+	0.693253i	$0.243823\pi$
$138$	3.12251e11	0.00384848
$139$	−7.68261e13	−0.903467	−0.451734	−	0.892153i	$-0.649194\pi$
$139$	−7.68261e13	−0.903467	−0.451734	+	0.892153i	$0.649194\pi$
$140$	1.95200e14	2.19103
$141$	−1.01435e14	−1.08709
$142$	−1.82788e12	−0.0187099
$143$	8.41523e13	0.822965
$144$	3.56479e13	0.333179
$145$	−1.81122e14	−1.61838
$146$	9.00955e11	0.00769856
$147$	7.39066e13	0.604116
$148$	−6.79400e13	−0.531404
$149$	2.24493e14	1.68071	0.840354	−	0.542038i	$-0.182347\pi$
$149$	2.24493e14	1.68071	0.840354	+	0.542038i	$0.182347\pi$
$150$	−1.34753e12	−0.00965927
$151$	4.25744e13	0.292279	0.146140	−	0.989264i	$-0.453315\pi$
$151$	4.25744e13	0.292279	0.146140	+	0.989264i	$0.453315\pi$
$152$	−6.09709e12	−0.0400995
$153$	8.23875e12	0.0519238
$154$	−2.03859e12	−0.0123153
$155$	−3.73882e14	−2.16560
$156$	−1.23413e14	−0.685567
$157$	1.87965e14	1.00168	0.500840	−	0.865540i	$-0.333024\pi$
$157$	1.87965e14	1.00168	0.500840	+	0.865540i	$0.333024\pi$
$158$	1.61517e12	0.00825936
$159$	2.25536e13	0.110697
$160$	1.21139e13	0.0570828
$161$	−1.69613e14	−0.767524
$162$	−3.17581e11	−0.00138041
$163$	4.26662e14	1.78182	0.890911	−	0.454178i	$-0.150067\pi$
$163$	4.26662e14	1.78182	0.890911	+	0.454178i	$0.150067\pi$
$164$	−3.29703e14	−1.32324
$165$	−1.58860e14	−0.612869
$166$	−2.18060e12	−0.00808860
$167$	−1.93549e14	−0.690452	−0.345226	−	0.938520i	$-0.612198\pi$
$167$	−1.93549e14	−0.690452	−0.345226	+	0.938520i	$0.612198\pi$
$168$	5.97980e12	0.0205199
$169$	1.24312e14	0.410441
$170$	9.32996e11	0.00296457
$171$	−1.75892e14	−0.537987
$172$	4.61995e14	1.36051
$173$	3.70120e14	1.04965	0.524823	−	0.851212i	$-0.324132\pi$
$173$	3.70120e14	1.04965	0.524823	+	0.851212i	$0.324132\pi$
$174$	−2.77405e12	−0.00757781
$175$	7.31971e14	1.92640
$176$	2.73109e14	0.692633
$177$	−3.07496e13	−0.0751646
$178$	−1.78682e12	−0.00421068
$179$	1.44118e14	0.327471	0.163735	−	0.986504i	$-0.447646\pi$
$179$	1.44118e14	0.327471	0.163735	+	0.986504i	$0.447646\pi$
$180$	2.32974e14	0.510547
$181$	4.26043e14	0.900623	0.450311	−	0.892872i	$-0.351313\pi$
$181$	4.26043e14	0.900623	0.450311	+	0.892872i	$0.351313\pi$
$182$	−1.03486e13	−0.0211066
$183$	−4.70173e14	−0.925392
$184$	−7.01718e12	−0.0133305
$185$	−4.43948e14	−0.814171
$186$	−5.72634e12	−0.0101401
$187$	6.31194e13	0.107942
$188$	1.13969e15	1.88261
$189$	1.72509e14	0.275302
$190$	−1.99189e13	−0.0307162
$191$	5.86860e14	0.874617	0.437308	−	0.899312i	$-0.355932\pi$
$191$	5.86860e14	0.874617	0.437308	+	0.899312i	$0.355932\pi$
$192$	−4.00401e14	−0.576816
$193$	3.83722e14	0.534435	0.267217	−	0.963636i	$-0.413896\pi$
$193$	3.83722e14	0.534435	0.267217	+	0.963636i	$0.413896\pi$
$194$	−1.06426e13	−0.0143329
$195$	−8.06429e14	−1.05037
$196$	−8.30383e14	−1.04620
$197$	−1.46844e15	−1.78989	−0.894943	−	0.446181i	$-0.852784\pi$
$197$	−1.46844e15	−1.78989	−0.894943	+	0.446181i	$0.852784\pi$
$198$	−2.43308e12	−0.00286967
$199$	1.36051e14	0.155295	0.0776475	−	0.996981i	$-0.475259\pi$
$199$	1.36051e14	0.155295	0.0776475	+	0.996981i	$0.475259\pi$
$200$	3.02828e13	0.0334581
$201$	−7.52629e14	−0.805020
$202$	5.11215e12	0.00529444
$203$	1.50685e15	1.51128
$204$	−9.25671e13	−0.0899209
$205$	−2.15442e15	−2.02736
$206$	−1.51690e13	−0.0138299
$207$	−2.02436e14	−0.178846
$208$	1.38640e15	1.18707
$209$	−1.34756e15	−1.11840
$210$	1.95357e13	0.0157182
$211$	1.48597e15	1.15925	0.579623	−	0.814885i	$-0.303200\pi$
$211$	1.48597e15	1.15925	0.579623	+	0.814885i	$0.303200\pi$
$212$	−2.53403e14	−0.191703
$213$	1.18503e15	0.869486
$214$	−2.37450e13	−0.0168998
$215$	3.01887e15	2.08446
$216$	7.13696e12	0.00478150
$217$	3.11053e15	2.02230
$218$	1.83168e13	0.0115580
$219$	−5.84099e14	−0.357766
$220$	1.78488e15	1.06136
$221$	3.20417e14	0.184997
$222$	−6.79946e12	−0.00381224
$223$	2.09683e15	1.14178	0.570888	−	0.821028i	$-0.306599\pi$
$223$	2.09683e15	1.14178	0.570888	+	0.821028i	$0.306599\pi$
$224$	−1.00782e14	−0.0533055
$225$	8.73616e14	0.448884
$226$	−2.59383e12	−0.00129490
$227$	1.30180e15	0.631505	0.315752	−	0.948842i	$-0.397743\pi$
$227$	1.30180e15	0.631505	0.315752	+	0.948842i	$0.397743\pi$
$228$	1.97625e15	0.931677
$229$	−3.18073e15	−1.45746	−0.728729	−	0.684802i	$-0.759889\pi$
$229$	−3.18073e15	−1.45746	−0.728729	+	0.684802i	$0.759889\pi$
$230$	−2.29248e13	−0.0102111
$231$	1.32164e15	0.572314
$232$	6.23408e13	0.0262483
$233$	6.38047e14	0.261240	0.130620	−	0.991433i	$-0.458303\pi$
$233$	6.38047e14	0.261240	0.130620	+	0.991433i	$0.458303\pi$
$234$	−1.23512e13	−0.00491819
$235$	7.44718e15	2.88437
$236$	3.45490e14	0.130169
$237$	−1.04713e15	−0.383828
$238$	−7.76209e12	−0.00276840
$239$	6.97606e14	0.242116	0.121058	−	0.992645i	$-0.461371\pi$
$239$	6.97606e14	0.242116	0.121058	+	0.992645i	$0.461371\pi$
$240$	−2.61719e15	−0.884021
$241$	2.84997e14	0.0936979	0.0468489	−	0.998902i	$-0.485082\pi$
$241$	2.84997e14	0.0936979	0.0468489	+	0.998902i	$0.485082\pi$
$242$	2.01789e13	0.00645801
$243$	2.05891e14	0.0641500
$244$	5.28267e15	1.60258
$245$	−5.42607e15	−1.60290
$246$	−3.29968e13	−0.00949280
$247$	−6.84070e15	−1.91677
$248$	1.28687e14	0.0351237
$249$	1.41371e15	0.375892
$250$	2.54670e13	0.00659732
$251$	3.10520e14	0.0783809	0.0391905	−	0.999232i	$-0.487522\pi$
$251$	3.10520e14	0.0783809	0.0391905	+	0.999232i	$0.487522\pi$
$252$	−1.93823e15	−0.476763
$253$	−1.55092e15	−0.371796
$254$	4.77497e13	0.0111571
$255$	−6.04871e14	−0.137769
$256$	4.49665e15	0.998457
$257$	−3.87421e15	−0.838721	−0.419361	−	0.907820i	$-0.637746\pi$
$257$	−3.87421e15	−0.838721	−0.419361	+	0.907820i	$0.637746\pi$
$258$	4.62366e13	0.00976019
$259$	3.69344e15	0.760296
$260$	9.06070e15	1.81901
$261$	1.79844e15	0.352155
$262$	−5.79392e13	−0.0110666
$263$	−7.16286e15	−1.33467	−0.667335	−	0.744758i	$-0.732565\pi$
$263$	−7.16286e15	−1.33467	−0.667335	+	0.744758i	$0.732565\pi$
$264$	5.46783e13	0.00994007
$265$	−1.65584e15	−0.293711
$266$	1.65716e14	0.0286836
$267$	1.15842e15	0.195678
$268$	8.45622e15	1.39412
$269$	8.10069e15	1.30356	0.651782	−	0.758407i	$-0.274022\pi$
$269$	8.10069e15	1.30356	0.651782	+	0.758407i	$0.274022\pi$
$270$	2.33161e13	0.00366262
$271$	−1.42961e15	−0.219239	−0.109620	−	0.993974i	$-0.534963\pi$
$271$	−1.42961e15	−0.219239	−0.109620	+	0.993974i	$0.534963\pi$
$272$	1.03988e15	0.155699
$273$	6.70911e15	0.980862
$274$	−1.25432e14	−0.0179073
$275$	6.69302e15	0.933168
$276$	2.27448e15	0.309723
$277$	3.07872e15	0.409499	0.204749	−	0.978814i	$-0.434362\pi$
$277$	3.07872e15	0.409499	0.204749	+	0.978814i	$0.434362\pi$
$278$	8.63879e13	0.0112244
$279$	3.71245e15	0.471230
$280$	−4.39024e14	−0.0544454
$281$	−1.00829e16	−1.22178	−0.610891	−	0.791714i	$-0.709189\pi$
$281$	−1.00829e16	−1.22178	−0.610891	+	0.791714i	$0.709189\pi$
$282$	1.14060e14	0.0135056
$283$	−1.32688e16	−1.53539	−0.767696	−	0.640814i	$-0.778597\pi$
$283$	−1.32688e16	−1.53539	−0.767696	+	0.640814i	$0.778597\pi$
$284$	−1.33145e16	−1.50576
$285$	1.29136e16	1.42744
$286$	−9.46259e13	−0.0102242
$287$	1.79238e16	1.89320
$288$	−1.20285e14	−0.0124211
$289$	−9.66425e15	−0.975735
$290$	2.03665e14	0.0201061
$291$	6.89970e15	0.666079
$292$	6.56268e15	0.619574
$293$	−2.25725e15	−0.208421	−0.104210	−	0.994555i	$-0.533231\pi$
$293$	−2.25725e15	−0.208421	−0.104210	+	0.994555i	$0.533231\pi$
$294$	−8.31051e13	−0.00750533
$295$	2.25757e15	0.199434
$296$	1.52804e14	0.0132050
$297$	1.57739e15	0.133359
$298$	−2.52434e14	−0.0208805
$299$	−7.87301e15	−0.637203
$300$	−9.81558e15	−0.777370
$301$	−2.51156e16	−1.94653
$302$	−4.78732e13	−0.00363118
$303$	−3.31426e15	−0.246042
$304$	−2.22009e16	−1.61321
$305$	3.45191e16	2.45534
$306$	−9.26415e12	−0.000645084 0
$307$	−1.24992e15	−0.0852085	−0.0426043	−	0.999092i	$-0.513565\pi$
$307$	−1.24992e15	−0.0852085	−0.0426043	+	0.999092i	$0.513565\pi$
$308$	−1.48494e16	−0.991124
$309$	9.83420e15	0.642701
$310$	4.20416e14	0.0269047
$311$	8.96059e15	0.561557	0.280779	−	0.959773i	$-0.409407\pi$
$311$	8.96059e15	0.561557	0.280779	+	0.959773i	$0.409407\pi$
$312$	2.77567e14	0.0170358
$313$	3.29749e16	1.98219	0.991094	−	0.133165i	$-0.0425140\pi$
$313$	3.29749e16	1.98219	0.991094	+	0.133165i	$0.0425140\pi$
$314$	−2.11359e14	−0.0124445
$315$	−1.26652e16	−0.730456
$316$	1.17651e16	0.664707
$317$	−3.26982e16	−1.80983	−0.904916	−	0.425590i	$-0.860067\pi$
$317$	−3.26982e16	−1.80983	−0.904916	+	0.425590i	$0.860067\pi$
$318$	−2.53606e13	−0.00137526
$319$	1.37784e16	0.732081
$320$	2.93966e16	1.53046
$321$	1.53941e16	0.785366
$322$	1.90723e14	0.00953545
$323$	−5.13095e15	−0.251409
$324$	−2.31331e15	−0.111094
$325$	3.39762e16	1.59931
$326$	−4.79764e14	−0.0221367
$327$	−1.18750e16	−0.537123
$328$	7.41534e14	0.0328815
$329$	−6.19570e16	−2.69350
$330$	1.78631e14	0.00761408
$331$	7.92757e15	0.331328	0.165664	−	0.986182i	$-0.447023\pi$
$331$	7.92757e15	0.331328	0.165664	+	0.986182i	$0.447023\pi$
$332$	−1.58838e16	−0.650964
$333$	4.40816e15	0.177162
$334$	2.17638e14	0.00857793
$335$	5.52564e16	2.13595
$336$	2.17738e16	0.825523
$337$	−9.13829e15	−0.339837	−0.169918	−	0.985458i	$-0.554350\pi$
$337$	−9.13829e15	−0.339837	−0.169918	+	0.985458i	$0.554350\pi$
$338$	−1.39784e14	−0.00509917
$339$	1.68161e15	0.0601766
$340$	6.79608e15	0.238586
$341$	2.84421e16	0.979622
$342$	1.97784e14	0.00668377
$343$	2.00008e15	0.0663186
$344$	−1.03907e15	−0.0338077
$345$	1.48624e16	0.474531
$346$	−4.16185e14	−0.0130404
$347$	5.15300e16	1.58460	0.792299	−	0.610133i	$-0.208884\pi$
$347$	5.15300e16	1.58460	0.792299	+	0.610133i	$0.208884\pi$
$348$	−2.02066e16	−0.609856
$349$	−2.85815e15	−0.0846680	−0.0423340	−	0.999104i	$-0.513479\pi$
$349$	−2.85815e15	−0.0846680	−0.0423340	+	0.999104i	$0.513479\pi$
$350$	−8.23072e14	−0.0239329
$351$	8.00741e15	0.228558
$352$	−9.21537e14	−0.0258217
$353$	2.47280e16	0.680227	0.340114	−	0.940384i	$-0.389534\pi$
$353$	2.47280e16	0.680227	0.340114	+	0.940384i	$0.389534\pi$
$354$	3.45767e13	0.000933819 0
$355$	−8.70025e16	−2.30700
$356$	−1.30155e16	−0.338872
$357$	5.03225e15	0.128653
$358$	−1.62055e14	−0.00406838
$359$	3.14105e16	0.774392	0.387196	−	0.921997i	$-0.373444\pi$
$359$	3.14105e16	0.774392	0.387196	+	0.921997i	$0.373444\pi$
$360$	−5.23981e14	−0.0126867
$361$	6.74897e16	1.60487
$362$	−4.79069e14	−0.0111890
$363$	−1.30822e16	−0.300116
$364$	−7.53807e16	−1.69864
$365$	4.28833e16	0.949258
$366$	5.28691e14	0.0114967
$367$	2.15939e16	0.461320	0.230660	−	0.973034i	$-0.425911\pi$
$367$	2.15939e16	0.461320	0.230660	+	0.973034i	$0.425911\pi$
$368$	−2.55511e16	−0.536290
$369$	2.13922e16	0.441148
$370$	4.99202e14	0.0101150
$371$	1.37758e16	0.274275
$372$	−4.17115e16	−0.816069
$373$	6.94694e16	1.33563	0.667815	−	0.744328i	$-0.267230\pi$
$373$	6.94694e16	1.33563	0.667815	+	0.744328i	$0.267230\pi$
$374$	−7.09753e13	−0.00134104
$375$	−1.65105e16	−0.306590
$376$	−2.56326e15	−0.0467813
$377$	6.99441e16	1.25468
$378$	−1.93979e14	−0.00342025
$379$	−3.13899e16	−0.544045	−0.272022	−	0.962291i	$-0.587692\pi$
$379$	−3.13899e16	−0.544045	−0.272022	+	0.962291i	$0.587692\pi$
$380$	−1.45092e17	−2.47201
$381$	−3.09566e16	−0.518491
$382$	−6.59901e14	−0.0108659
$383$	4.88712e16	0.791154	0.395577	−	0.918433i	$-0.370545\pi$
$383$	4.88712e16	0.791154	0.395577	+	0.918433i	$0.370545\pi$
$384$	1.80191e15	0.0286801
$385$	−9.70318e16	−1.51852
$386$	−4.31481e14	−0.00663963
$387$	−2.99757e16	−0.453574
$388$	−7.75221e16	−1.15350
$389$	−1.97403e16	−0.288856	−0.144428	−	0.989515i	$-0.546134\pi$
$389$	−1.97403e16	−0.288856	−0.144428	+	0.989515i	$0.546134\pi$
$390$	9.06798e14	0.0130494
$391$	−5.90524e15	−0.0835774
$392$	1.86761e15	0.0259972
$393$	3.75626e16	0.514285
$394$	1.65120e15	0.0222369
$395$	7.68781e16	1.01841
$396$	−1.77229e16	−0.230949
$397$	−9.34519e16	−1.19798	−0.598990	−	0.800756i	$-0.704431\pi$
$397$	−9.34519e16	−1.19798	−0.598990	+	0.800756i	$0.704431\pi$
$398$	−1.52984e14	−0.00192933
$399$	−1.07435e17	−1.33298
$400$	1.10267e17	1.34603
$401$	9.36404e16	1.12467	0.562335	−	0.826910i	$-0.309903\pi$
$401$	9.36404e16	1.12467	0.562335	+	0.826910i	$0.309903\pi$
$402$	8.46302e14	0.0100013
$403$	1.44383e17	1.67893
$404$	3.72377e16	0.426092
$405$	−1.51161e16	−0.170209
$406$	−1.69439e15	−0.0187757
$407$	3.37722e16	0.368295
$408$	2.08192e14	0.00223446
$409$	2.67006e16	0.282045	0.141023	−	0.990006i	$-0.454961\pi$
$409$	2.67006e16	0.282045	0.141023	+	0.990006i	$0.454961\pi$
$410$	2.42256e15	0.0251872
$411$	8.13191e16	0.832186
$412$	−1.10493e17	−1.11302
$413$	−1.87819e16	−0.186237
$414$	2.27631e14	0.00222192
$415$	−1.03791e17	−0.997352
$416$	−4.67805e15	−0.0442546
$417$	−5.60062e16	−0.521617
$418$	1.51528e15	0.0138946
$419$	−1.60374e17	−1.44792	−0.723959	−	0.689843i	$-0.757680\pi$
$419$	−1.60374e17	−1.44792	−0.723959	+	0.689843i	$0.757680\pi$
$420$	1.42301e17	1.26499
$421$	8.30141e15	0.0726638	0.0363319	−	0.999340i	$-0.488433\pi$
$421$	8.30141e15	0.0726638	0.0363319	+	0.999340i	$0.488433\pi$
$422$	−1.67092e15	−0.0144021
$423$	−7.39465e16	−0.627632
$424$	5.69927e14	0.00476366
$425$	2.54842e16	0.209770
$426$	−1.33252e15	−0.0108022
$427$	−2.87183e17	−2.29286
$428$	−1.72962e17	−1.36008
$429$	6.13470e16	0.475139
$430$	−3.39460e15	−0.0258966
$431$	1.19959e17	0.901428	0.450714	−	0.892668i	$-0.351169\pi$
$431$	1.19959e17	0.901428	0.450714	+	0.892668i	$0.351169\pi$
$432$	2.59873e16	0.192361
$433$	2.48061e16	0.180879	0.0904393	−	0.995902i	$-0.471173\pi$
$433$	2.48061e16	0.180879	0.0904393	+	0.995902i	$0.471173\pi$
$434$	−3.49766e15	−0.0251244
$435$	−1.32038e17	−0.934369
$436$	1.33423e17	0.930180
$437$	1.26073e17	0.865952
$438$	6.56796e14	0.00444476
$439$	−1.05987e17	−0.706696	−0.353348	−	0.935492i	$-0.614957\pi$
$439$	−1.05987e17	−0.706696	−0.353348	+	0.935492i	$0.614957\pi$
$440$	−4.01436e15	−0.0263739
$441$	5.38779e16	0.348787
$442$	−3.60296e14	−0.00229834
$443$	−9.53388e16	−0.599301	−0.299651	−	0.954049i	$-0.596870\pi$
$443$	−9.53388e16	−0.599301	−0.299651	+	0.954049i	$0.596870\pi$
$444$	−4.95283e16	−0.306806
$445$	−8.50486e16	−0.519191
$446$	−2.35780e15	−0.0141850
$447$	1.63655e17	0.970357
$448$	−2.44566e17	−1.42919
$449$	−9.16969e16	−0.528146	−0.264073	−	0.964503i	$-0.585066\pi$
$449$	−9.16969e16	−0.528146	−0.264073	+	0.964503i	$0.585066\pi$
$450$	−9.82347e14	−0.00557678
$451$	1.63892e17	0.917085
$452$	−1.88939e16	−0.104213
$453$	3.10367e16	0.168748
$454$	−1.46382e15	−0.00784559
$455$	−4.92569e17	−2.60251
$456$	−4.44478e15	−0.0231515
$457$	2.27967e17	1.17062	0.585312	−	0.810808i	$-0.300972\pi$
$457$	2.27967e17	1.17062	0.585312	+	0.810808i	$0.300972\pi$
$458$	3.57660e15	0.0181070
$459$	6.00605e15	0.0299782
$460$	−1.66987e17	−0.821785
$461$	−3.71823e17	−1.80418	−0.902091	−	0.431546i	$-0.857968\pi$
$461$	−3.71823e17	−1.80418	−0.902091	+	0.431546i	$0.857968\pi$
$462$	−1.48613e15	−0.00711023
$463$	−1.92774e17	−0.909437	−0.454719	−	0.890635i	$-0.650260\pi$
$463$	−1.92774e17	−0.909437	−0.454719	+	0.890635i	$0.650260\pi$
$464$	2.26997e17	1.05598
$465$	−2.72560e17	−1.25031
$466$	−7.17458e14	−0.00324555
$467$	−3.41906e17	−1.52527	−0.762635	−	0.646829i	$-0.776095\pi$
$467$	−3.41906e17	−1.52527	−0.762635	+	0.646829i	$0.776095\pi$
$468$	−8.99678e16	−0.395812
$469$	−4.59708e17	−1.99461
$470$	−8.37406e15	−0.0358344
$471$	1.37027e17	0.578321
$472$	−7.77039e14	−0.00323459
$473$	−2.29652e17	−0.942917
$474$	1.17746e15	0.00476854
$475$	−5.44073e17	−2.17345
$476$	−5.65402e16	−0.222798
$477$	1.64416e16	0.0639108
$478$	−7.84431e14	−0.00300797
$479$	3.99856e17	1.51259	0.756297	−	0.654228i	$-0.227006\pi$
$479$	3.99856e17	1.51259	0.756297	+	0.654228i	$0.227006\pi$
$480$	8.83106e15	0.0329568
$481$	1.71440e17	0.631203
$482$	−3.20468e14	−0.00116407
$483$	−1.23648e17	−0.443130
$484$	1.46986e17	0.519735
$485$	−5.06561e17	−1.76730
$486$	−2.31516e14	−0.000796978 0
$487$	3.49349e17	1.18665	0.593324	−	0.804964i	$-0.297815\pi$
$487$	3.49349e17	1.18665	0.593324	+	0.804964i	$0.297815\pi$
$488$	−1.18812e16	−0.0398228
$489$	3.11036e17	1.02874
$490$	6.10140e15	0.0199138
$491$	1.16774e17	0.376112	0.188056	−	0.982158i	$-0.439781\pi$
$491$	1.16774e17	0.376112	0.188056	+	0.982158i	$0.439781\pi$
$492$	−2.40354e17	−0.763973
$493$	5.24624e16	0.164567
$494$	7.69210e15	0.0238133
$495$	−1.15809e17	−0.353840
$496$	4.68581e17	1.41304
$497$	7.23820e17	2.15434
$498$	−1.58966e15	−0.00466996
$499$	3.16782e17	0.918558	0.459279	−	0.888292i	$-0.348108\pi$
$499$	3.16782e17	0.918558	0.459279	+	0.888292i	$0.348108\pi$
$500$	1.85505e17	0.530947
$501$	−1.41097e17	−0.398632
$502$	−3.49168e14	−0.000973778 0
$503$	6.06056e16	0.166848	0.0834239	−	0.996514i	$-0.473414\pi$
$503$	6.06056e16	0.166848	0.0834239	+	0.996514i	$0.473414\pi$
$504$	4.35927e15	0.0118472
$505$	2.43326e17	0.652822
$506$	1.74394e15	0.00461907
$507$	9.06237e16	0.236968
$508$	3.47815e17	0.897914
$509$	3.53468e16	0.0900917	0.0450458	−	0.998985i	$-0.485657\pi$
$509$	3.53468e16	0.0900917	0.0450458	+	0.998985i	$0.485657\pi$
$510$	6.80154e14	0.00171160
$511$	−3.56769e17	−0.886443
$512$	−2.53050e16	−0.0620799
$513$	−1.28225e17	−0.310607
$514$	4.35639e15	0.0104200
$515$	−7.22006e17	−1.70527
$516$	3.36794e17	0.785492
$517$	−5.66525e17	−1.30476
$518$	−4.15313e15	−0.00944565
$519$	2.69817e17	0.606013
$520$	−2.03784e16	−0.0452010
$521$	6.04157e17	1.32344	0.661720	−	0.749751i	$-0.269827\pi$
$521$	6.04157e17	1.32344	0.661720	+	0.749751i	$0.269827\pi$
$522$	−2.02228e15	−0.00437505
$523$	3.36130e17	0.718202	0.359101	−	0.933299i	$-0.383083\pi$
$523$	3.36130e17	0.718202	0.359101	+	0.933299i	$0.383083\pi$
$524$	−4.22038e17	−0.890631
$525$	5.33607e17	1.11221
$526$	8.05435e15	0.0165815
$527$	1.08296e17	0.220213
$528$	1.99096e17	0.399892
$529$	−3.58938e17	−0.712127
$530$	1.86192e15	0.00364896
$531$	−2.24165e16	−0.0433963
$532$	1.20710e18	2.30843
$533$	8.31974e17	1.57175
$534$	−1.30259e15	−0.00243103
$535$	−1.13020e18	−2.08381
$536$	−1.90189e16	−0.0346428
$537$	1.05062e17	0.189065
$538$	−9.10891e15	−0.0161950
$539$	4.12774e17	0.725079
$540$	1.69838e17	0.294765
$541$	−6.98559e17	−1.19790	−0.598950	−	0.800786i	$-0.704415\pi$
$541$	−6.98559e17	−1.19790	−0.598950	+	0.800786i	$0.704415\pi$
$542$	1.60754e15	0.00272375
$543$	3.10586e17	0.519975
$544$	−3.50883e15	−0.00580456
$545$	8.71838e17	1.42514
$546$	−7.54413e15	−0.0121859
$547$	−3.12942e17	−0.499512	−0.249756	−	0.968309i	$-0.580350\pi$
$547$	−3.12942e17	−0.499512	−0.249756	+	0.968309i	$0.580350\pi$
$548$	−9.13667e17	−1.44117
$549$	−3.42756e17	−0.534275
$550$	−7.52604e15	−0.0115933
$551$	−1.12004e18	−1.70509
$552$	−5.11552e15	−0.00769637
$553$	−6.39590e17	−0.951017
$554$	−3.46190e15	−0.00508747
$555$	−3.23638e17	−0.470062
$556$	6.29262e17	0.903328
$557$	1.01552e18	1.44089	0.720443	−	0.693514i	$-0.243938\pi$
$557$	1.01552e18	1.44089	0.720443	+	0.693514i	$0.243938\pi$
$558$	−4.17450e15	−0.00585440
$559$	−1.16580e18	−1.61602
$560$	−1.59859e18	−2.19035
$561$	4.60140e16	0.0623206
$562$	1.13378e16	0.0151790
$563$	4.95596e17	0.655878	0.327939	−	0.944699i	$-0.393646\pi$
$563$	4.95596e17	0.655878	0.327939	+	0.944699i	$0.393646\pi$
$564$	8.30831e17	1.08692
$565$	−1.23460e17	−0.159666
$566$	1.49202e16	0.0190752
$567$	1.25759e17	0.158946
$568$	2.99456e16	0.0374170
$569$	−9.92143e17	−1.22559	−0.612794	−	0.790243i	$-0.709955\pi$
$569$	−9.92143e17	−1.22559	−0.612794	+	0.790243i	$0.709955\pi$
$570$	−1.45209e16	−0.0177340
$571$	3.28537e17	0.396689	0.198345	−	0.980132i	$-0.436444\pi$
$571$	3.28537e17	0.396689	0.198345	+	0.980132i	$0.436444\pi$
$572$	−6.89269e17	−0.822838
$573$	4.27821e17	0.504960
$574$	−2.01546e16	−0.0235205
$575$	−6.26177e17	−0.722530
$576$	−2.91892e17	−0.333025
$577$	1.36727e18	1.54245	0.771223	−	0.636565i	$-0.219645\pi$
$577$	1.36727e18	1.54245	0.771223	+	0.636565i	$0.219645\pi$
$578$	1.08671e16	0.0121222
$579$	2.79734e17	0.308556
$580$	1.48352e18	1.61813
$581$	8.63495e17	0.931355
$582$	−7.75844e15	−0.00827513
$583$	1.25964e17	0.132862
$584$	−1.47601e16	−0.0153959
$585$	−5.87887e17	−0.606430
$586$	2.53819e15	0.00258934
$587$	−6.01986e16	−0.0607349	−0.0303675	−	0.999539i	$-0.509668\pi$
$587$	−6.01986e16	−0.0607349	−0.0303675	+	0.999539i	$0.509668\pi$
$588$	−6.05349e17	−0.604023
$589$	−2.31205e18	−2.28164
$590$	−2.53855e15	−0.00247769
$591$	−1.07049e18	−1.03339
$592$	5.56393e17	0.531239
$593$	4.65893e17	0.439977	0.219989	−	0.975502i	$-0.429398\pi$
$593$	4.65893e17	0.439977	0.219989	+	0.975502i	$0.429398\pi$
$594$	−1.77371e15	−0.00165681
$595$	−3.69457e17	−0.341353
$596$	−1.83876e18	−1.68045
$597$	9.91813e16	0.0896596
$598$	8.85289e15	0.00791639
$599$	1.36134e18	1.20419	0.602093	−	0.798426i	$-0.294333\pi$
$599$	1.36134e18	1.20419	0.602093	+	0.798426i	$0.294333\pi$
$600$	2.20762e16	0.0193170
$601$	2.18572e18	1.89195	0.945976	−	0.324238i	$-0.105108\pi$
$601$	2.18572e18	1.89195	0.945976	+	0.324238i	$0.105108\pi$
$602$	2.82415e16	0.0241830
$603$	−5.48667e17	−0.464779
$604$	−3.48716e17	−0.292234
$605$	9.60469e17	0.796294
$606$	3.72676e15	0.00305675
$607$	2.26851e18	1.84084	0.920418	−	0.390936i	$-0.127849\pi$
$607$	2.26851e18	1.84084	0.920418	+	0.390936i	$0.127849\pi$
$608$	7.49114e16	0.0601415
$609$	1.09849e18	0.872540
$610$	−3.88154e16	−0.0305042
$611$	−2.87589e18	−2.23616
$612$	−6.74814e16	−0.0519158
$613$	−7.43957e17	−0.566311	−0.283155	−	0.959074i	$-0.591381\pi$
$613$	−7.43957e17	−0.566311	−0.283155	+	0.959074i	$0.591381\pi$
$614$	1.40549e15	0.00105860
$615$	−1.57057e18	−1.17049
$616$	3.33976e16	0.0246287
$617$	−1.56850e16	−0.0114454	−0.00572271	−	0.999984i	$-0.501822\pi$
$617$	−1.56850e16	−0.0114454	−0.00572271	+	0.999984i	$0.501822\pi$
$618$	−1.10582e16	−0.00798469
$619$	−1.65308e18	−1.18115	−0.590576	−	0.806982i	$-0.701099\pi$
$619$	−1.65308e18	−1.18115	−0.590576	+	0.806982i	$0.701099\pi$
$620$	3.06237e18	2.16527
$621$	−1.47575e17	−0.103257
$622$	−1.00758e16	−0.00697659
$623$	7.07564e17	0.484834
$624$	1.01068e18	0.685355
$625$	−7.94500e17	−0.533180
$626$	−3.70789e16	−0.0246260
$627$	−9.82371e17	−0.645709
$628$	−1.53957e18	−1.00153
$629$	1.28590e17	0.0827903
$630$	1.42415e16	0.00907493
$631$	−2.83524e18	−1.78813	−0.894066	−	0.447936i	$-0.852159\pi$
$631$	−2.83524e18	−1.78813	−0.894066	+	0.447936i	$0.852159\pi$
$632$	−2.64609e16	−0.0165174
$633$	1.08328e18	0.669290
$634$	3.67678e16	0.0224847
$635$	2.27277e18	1.37571
$636$	−1.84731e17	−0.110680
$637$	2.09539e18	1.24268
$638$	−1.54933e16	−0.00909512
$639$	8.63888e17	0.501998
$640$	−1.32293e17	−0.0760967
$641$	3.20277e18	1.82368	0.911841	−	0.410543i	$-0.134661\pi$
$641$	3.20277e18	1.82368	0.911841	+	0.410543i	$0.134661\pi$
$642$	−1.73101e16	−0.00975712
$643$	3.43410e18	1.91620	0.958102	−	0.286428i	$-0.0924679\pi$
$643$	3.43410e18	1.91620	0.958102	+	0.286428i	$0.0924679\pi$
$644$	1.38926e18	0.767405
$645$	2.20075e18	1.20346
$646$	5.76955e15	0.00312342
$647$	−5.45681e17	−0.292456	−0.146228	−	0.989251i	$-0.546713\pi$
$647$	−5.45681e17	−0.292456	−0.146228	+	0.989251i	$0.546713\pi$
$648$	5.20284e15	0.00276060
$649$	−1.71739e17	−0.0902149
$650$	−3.82049e16	−0.0198693
$651$	2.26757e18	1.16758
$652$	−3.49467e18	−1.78155
$653$	−1.11656e17	−0.0563570	−0.0281785	−	0.999603i	$-0.508971\pi$
$653$	−1.11656e17	−0.0563570	−0.0281785	+	0.999603i	$0.508971\pi$
$654$	1.33530e16	0.00667303
$655$	−2.75777e18	−1.36455
$656$	2.70010e18	1.32283
$657$	−4.25808e17	−0.206556
$658$	6.96683e16	0.0334631
$659$	3.58335e18	1.70425	0.852127	−	0.523336i	$-0.175313\pi$
$659$	3.58335e18	1.70425	0.852127	+	0.523336i	$0.175313\pi$
$660$	1.30118e18	0.612775
$661$	−3.38067e18	−1.57650	−0.788248	−	0.615358i	$-0.789011\pi$
$661$	−3.38067e18	−1.57650	−0.788248	+	0.615358i	$0.789011\pi$
$662$	−8.91424e15	−0.00411630
$663$	2.33584e17	0.106808
$664$	3.57242e16	0.0161760
$665$	7.88768e18	3.53678
$666$	−4.95681e15	−0.00220100
$667$	−1.28906e18	−0.566833
$668$	1.58531e18	0.690345
$669$	1.52859e18	0.659205
$670$	−6.21337e16	−0.0265363
$671$	−2.62595e18	−1.11068
$672$	−7.34703e16	−0.0307760
$673$	1.07005e18	0.443920	0.221960	−	0.975056i	$-0.428755\pi$
$673$	1.07005e18	0.443920	0.221960	+	0.975056i	$0.428755\pi$
$674$	1.02756e16	0.00422202
$675$	6.36866e17	0.259163
$676$	−1.01821e18	−0.410377
$677$	3.14098e18	1.25383	0.626915	−	0.779088i	$-0.284318\pi$
$677$	3.14098e18	1.25383	0.626915	+	0.779088i	$0.284318\pi$
$678$	−1.89091e15	−0.000747613 0
$679$	4.21435e18	1.65035
$680$	−1.52850e16	−0.00592868
$681$	9.49013e17	0.364599
$682$	−3.19821e16	−0.0121705
$683$	3.36551e18	1.26858	0.634288	−	0.773097i	$-0.281293\pi$
$683$	3.36551e18	1.26858	0.634288	+	0.773097i	$0.281293\pi$
$684$	1.44069e18	0.537904
$685$	−5.97028e18	−2.20803
$686$	−2.24901e15	−0.000823919 0
$687$	−2.31875e18	−0.841464
$688$	−3.78350e18	−1.36009
$689$	6.39437e17	0.227705
$690$	−1.67122e16	−0.00589541
$691$	3.37273e18	1.17862	0.589311	−	0.807907i	$-0.299399\pi$
$691$	3.37273e18	1.17862	0.589311	+	0.807907i	$0.299399\pi$
$692$	−3.03155e18	−1.04948
$693$	9.63474e17	0.330426
$694$	−5.79435e16	−0.0196865
$695$	4.11186e18	1.38400
$696$	4.54465e16	0.0151544
$697$	6.24032e17	0.206155
$698$	3.21387e15	0.00105189
$699$	4.65136e17	0.150827
$700$	−5.99538e18	−1.92610
$701$	1.98301e18	0.631187	0.315594	−	0.948894i	$-0.397796\pi$
$701$	1.98301e18	0.631187	0.315594	+	0.948894i	$0.397796\pi$
$702$	−9.00401e15	−0.00283952
$703$	−2.74533e18	−0.857797
$704$	−2.23627e18	−0.692312
$705$	5.42899e18	1.66529
$706$	−2.78057e16	−0.00845091
$707$	−2.02436e18	−0.609623
$708$	2.51862e17	0.0751530
$709$	2.34828e18	0.694303	0.347151	−	0.937809i	$-0.387149\pi$
$709$	2.34828e18	0.694303	0.347151	+	0.937809i	$0.387149\pi$
$710$	9.78309e16	0.0286614
$711$	−7.63358e17	−0.221603
$712$	2.92731e16	0.00842070
$713$	−2.66095e18	−0.758499
$714$	−5.65856e15	−0.00159834
$715$	−4.50397e18	−1.26068
$716$	−1.18043e18	−0.327420
$717$	5.08555e17	0.139786
$718$	−3.53199e16	−0.00962077
$719$	−3.00538e18	−0.811264	−0.405632	−	0.914036i	$-0.632949\pi$
$719$	−3.00538e18	−0.811264	−0.405632	+	0.914036i	$0.632949\pi$
$720$	−1.90793e18	−0.510390
$721$	6.00675e18	1.59243
$722$	−7.58895e16	−0.0199384
$723$	2.07763e17	0.0540965
$724$	−3.48961e18	−0.900484
$725$	5.56298e18	1.42269
$726$	1.47104e16	0.00372853
$727$	2.58278e18	0.648805	0.324403	−	0.945919i	$-0.394837\pi$
$727$	2.58278e18	0.648805	0.324403	+	0.945919i	$0.394837\pi$
$728$	1.69538e17	0.0422099
$729$	1.50095e17	0.0370370
$730$	−4.82206e16	−0.0117933
$731$	−8.74421e17	−0.211962
$732$	3.85106e18	0.925249
$733$	−1.76946e18	−0.421371	−0.210686	−	0.977554i	$-0.567570\pi$
$733$	−1.76946e18	−0.421371	−0.210686	+	0.977554i	$0.567570\pi$
$734$	−2.42815e16	−0.00573128
$735$	−3.95560e18	−0.925433
$736$	8.62160e16	0.0199932
$737$	−4.20349e18	−0.966210
$738$	−2.40547e16	−0.00548067
$739$	5.41661e18	1.22332	0.611658	−	0.791122i	$-0.290503\pi$
$739$	5.41661e18	1.22332	0.611658	+	0.791122i	$0.290503\pi$
$740$	3.63626e18	0.814046
$741$	−4.98687e18	−1.10665
$742$	−1.54903e16	−0.00340750
$743$	6.37375e18	1.38985	0.694924	−	0.719083i	$-0.255438\pi$
$743$	6.37375e18	1.38985	0.694924	+	0.719083i	$0.255438\pi$
$744$	9.38132e16	0.0202787
$745$	−1.20152e19	−2.57464
$746$	−7.81156e16	−0.0165934
$747$	1.03059e18	0.217022
$748$	−5.16994e17	−0.107926
$749$	9.40277e18	1.94592
$750$	1.85654e16	0.00380897
$751$	−1.12823e18	−0.229476	−0.114738	−	0.993396i	$-0.536603\pi$
$751$	−1.12823e18	−0.229476	−0.114738	+	0.993396i	$0.536603\pi$
$752$	−9.33343e18	−1.88202
$753$	2.26369e17	0.0452533
$754$	−7.86494e16	−0.0155877
$755$	−2.27865e18	−0.447737
$756$	−1.41297e18	−0.275259
$757$	−4.88523e18	−0.943544	−0.471772	−	0.881721i	$-0.656385\pi$
$757$	−4.88523e18	−0.943544	−0.471772	+	0.881721i	$0.656385\pi$
$758$	3.52967e16	0.00675902
$759$	−1.13062e18	−0.214657
$760$	3.26326e17	0.0614276
$761$	−3.48808e18	−0.651008	−0.325504	−	0.945541i	$-0.605534\pi$
$761$	−3.48808e18	−0.651008	−0.325504	+	0.945541i	$0.605534\pi$
$762$	3.48095e16	0.00644155
$763$	−7.25328e18	−1.33084
$764$	−4.80682e18	−0.874482
$765$	−4.40951e17	−0.0795410
$766$	−5.49537e16	−0.00982902
$767$	−8.71809e17	−0.154615
$768$	3.27806e18	0.576459
$769$	−6.70756e18	−1.16962	−0.584808	−	0.811172i	$-0.698830\pi$
$769$	−6.70756e18	−1.16962	−0.584808	+	0.811172i	$0.698830\pi$
$770$	1.09108e17	0.0188655
$771$	−2.82430e18	−0.484236
$772$	−3.14297e18	−0.534352
$773$	4.75122e18	0.801011	0.400505	−	0.916294i	$-0.368835\pi$
$773$	4.75122e18	0.801011	0.400505	+	0.916294i	$0.368835\pi$
$774$	3.37065e16	0.00563505
$775$	1.14834e19	1.90375
$776$	1.74355e17	0.0286637
$777$	2.69252e18	0.438957
$778$	2.21972e16	0.00358865
$779$	−1.33227e19	−2.13599
$780$	6.60525e18	1.05021
$781$	6.61849e18	1.04358
$782$	6.64021e15	0.00103834
$783$	1.31107e18	0.203317
$784$	6.80040e18	1.04588
$785$	−1.00602e19	−1.53445
$786$	−4.22377e16	−0.00638930
$787$	−1.78667e18	−0.268046	−0.134023	−	0.990978i	$-0.542790\pi$
$787$	−1.78667e18	−0.268046	−0.134023	+	0.990978i	$0.542790\pi$
$788$	1.20276e19	1.78961
$789$	−5.22172e18	−0.770572
$790$	−8.64464e16	−0.0126523
$791$	1.02713e18	0.149101
$792$	3.98605e16	0.00573890
$793$	−1.33303e19	−1.90355
$794$	1.05083e17	0.0148833
$795$	−1.20711e18	−0.169574
$796$	−1.11436e18	−0.155271
$797$	6.89988e18	0.953591	0.476796	−	0.879014i	$-0.341798\pi$
$797$	6.89988e18	0.953591	0.476796	+	0.879014i	$0.341798\pi$
$798$	1.20807e17	0.0165605
$799$	−2.15709e18	−0.293302
$800$	−3.72067e17	−0.0501807
$801$	8.44486e17	0.112975
$802$	−1.05295e17	−0.0139725
$803$	−3.26223e18	−0.429402
$804$	6.16459e18	0.804896
$805$	9.07798e18	1.17575
$806$	−1.62353e17	−0.0208584
$807$	5.90540e18	0.752613
$808$	−8.37510e16	−0.0105881
$809$	8.48455e18	1.06405	0.532026	−	0.846728i	$-0.321431\pi$
$809$	8.48455e18	1.06405	0.532026	+	0.846728i	$0.321431\pi$
$810$	1.69975e16	0.00211461
$811$	−2.81505e18	−0.347416	−0.173708	−	0.984797i	$-0.555575\pi$
$811$	−2.81505e18	−0.347416	−0.173708	+	0.984797i	$0.555575\pi$
$812$	−1.23422e19	−1.51105
$813$	−1.04219e18	−0.126578
$814$	−3.79755e16	−0.00457557
$815$	−2.28356e19	−2.72954
$816$	7.58075e17	0.0898931
$817$	1.86684e19	2.19615
$818$	−3.00237e16	−0.00350404
$819$	4.89094e18	0.566301
$820$	1.76463e19	2.02704
$821$	6.28035e18	0.715737	0.357869	−	0.933772i	$-0.383504\pi$
$821$	6.28035e18	0.715737	0.357869	+	0.933772i	$0.383504\pi$
$822$	−9.14401e16	−0.0103388
$823$	3.52404e18	0.395314	0.197657	−	0.980271i	$-0.436667\pi$
$823$	3.52404e18	0.395314	0.197657	+	0.980271i	$0.436667\pi$
$824$	2.48509e17	0.0276576
$825$	4.87921e18	0.538765
$826$	2.11195e16	0.00231374
$827$	−6.15138e17	−0.0668631	−0.0334315	−	0.999441i	$-0.510644\pi$
$827$	−6.15138e17	−0.0668631	−0.0334315	+	0.999441i	$0.510644\pi$
$828$	1.65810e18	0.178818
$829$	1.60126e19	1.71339	0.856695	−	0.515823i	$-0.172514\pi$
$829$	1.60126e19	1.71339	0.856695	+	0.515823i	$0.172514\pi$
$830$	1.16709e17	0.0123908
$831$	2.24439e18	0.236424
$832$	−1.13521e19	−1.18652
$833$	1.57167e18	0.162993
$834$	6.29768e16	0.00648039
$835$	1.03590e19	1.05769
$836$	1.10375e19	1.11823
$837$	2.70638e18	0.272065
$838$	1.80335e17	0.0179884
$839$	7.18767e18	0.711435	0.355717	−	0.934594i	$-0.384237\pi$
$839$	7.18767e18	0.711435	0.355717	+	0.934594i	$0.384237\pi$
$840$	−3.20049e17	−0.0314341
$841$	1.19143e18	0.116117
$842$	−9.33460e15	−0.000902750 0
$843$	−7.35043e18	−0.705397
$844$	−1.21712e19	−1.15907
$845$	−6.65340e18	−0.628746
$846$	8.31499e16	0.00779748
$847$	−7.99065e18	−0.743601
$848$	2.07523e18	0.191644
$849$	−9.67294e18	−0.886459
$850$	−2.86560e16	−0.00260611
$851$	−3.15962e18	−0.285162
$852$	−9.70628e18	−0.869351
$853$	8.10442e18	0.720366	0.360183	−	0.932882i	$-0.382714\pi$
$853$	8.10442e18	0.720366	0.360183	+	0.932882i	$0.382714\pi$
$854$	3.22926e17	0.0284857
$855$	9.41404e18	0.824131
$856$	3.89008e17	0.0337970
$857$	−9.13174e18	−0.787369	−0.393684	−	0.919246i	$-0.628800\pi$
$857$	−9.13174e18	−0.787369	−0.393684	+	0.919246i	$0.628800\pi$
$858$	−6.89823e16	−0.00590297
$859$	−3.12025e18	−0.264993	−0.132496	−	0.991184i	$-0.542299\pi$
$859$	−3.12025e18	−0.264993	−0.132496	+	0.991184i	$0.542299\pi$
$860$	−2.47267e19	−2.08414
$861$	1.30664e19	1.09304
$862$	−1.34889e17	−0.0111990
$863$	−1.32191e19	−1.08926	−0.544629	−	0.838677i	$-0.683330\pi$
$863$	−1.32191e19	−1.08926	−0.544629	+	0.838677i	$0.683330\pi$
$864$	−8.76877e16	−0.00717132
$865$	−1.98094e19	−1.60793
$866$	−2.78935e16	−0.00224717
$867$	−7.04524e18	−0.563341
$868$	−2.54775e19	−2.02199
$869$	−5.84830e18	−0.460682
$870$	1.48471e17	0.0116083
$871$	−2.13384e19	−1.65594
$872$	−3.00080e17	−0.0231143
$873$	5.02988e18	0.384561
$874$	−1.41765e17	−0.0107583
$875$	−1.00847e19	−0.759643
$876$	4.78420e18	0.357711
$877$	−7.08727e18	−0.525995	−0.262998	−	0.964796i	$-0.584711\pi$
$877$	−7.08727e18	−0.525995	−0.262998	+	0.964796i	$0.584711\pi$
$878$	1.19178e17	0.00877975
$879$	−1.64554e18	−0.120332
$880$	−1.46172e19	−1.06103
$881$	3.85374e18	0.277676	0.138838	−	0.990315i	$-0.455663\pi$
$881$	3.85374e18	0.277676	0.138838	+	0.990315i	$0.455663\pi$
$882$	−6.05836e16	−0.00433320
$883$	1.09510e18	0.0777519	0.0388760	−	0.999244i	$-0.487622\pi$
$883$	1.09510e18	0.0777519	0.0388760	+	0.999244i	$0.487622\pi$
$884$	−2.62445e18	−0.184969
$885$	1.64577e18	0.115143
$886$	1.07205e17	0.00744551
$887$	−9.84951e18	−0.679065	−0.339532	−	0.940594i	$-0.610269\pi$
$887$	−9.84951e18	−0.679065	−0.339532	+	0.940594i	$0.610269\pi$
$888$	1.11394e17	0.00762389
$889$	−1.89084e19	−1.28467
$890$	9.56338e16	0.00645024
$891$	1.14992e18	0.0769948
$892$	−1.71746e19	−1.14160
$893$	4.60526e19	3.03892
$894$	−1.84024e17	−0.0120554
$895$	−7.71341e18	−0.501645
$896$	1.10061e18	0.0710612
$897$	−5.73942e18	−0.367890
$898$	1.03110e17	0.00656150
$899$	2.36400e19	1.49351
$900$	−7.15556e18	−0.448815
$901$	4.79617e17	0.0298664
$902$	−1.84290e17	−0.0113935
$903$	−1.83092e19	−1.12383
$904$	4.24941e16	0.00258961
$905$	−2.28025e19	−1.37964
$906$	−3.48996e16	−0.00209646
$907$	−1.44051e19	−0.859149	−0.429575	−	0.903031i	$-0.641336\pi$
$907$	−1.44051e19	−0.859149	−0.429575	+	0.903031i	$0.641336\pi$
$908$	−1.06627e19	−0.631407
$909$	−2.41610e18	−0.142053
$910$	5.53874e17	0.0323327
$911$	5.81274e18	0.336908	0.168454	−	0.985710i	$-0.446123\pi$
$911$	5.81274e18	0.336908	0.168454	+	0.985710i	$0.446123\pi$
$912$	−1.61844e19	−0.931390
$913$	7.89566e18	0.451158
$914$	−2.56340e17	−0.0145434
$915$	2.51644e19	1.41759
$916$	2.60525e19	1.45723
$917$	2.29433e19	1.27425
$918$	−6.75356e15	−0.000372439 0
$919$	4.63641e18	0.253881	0.126941	−	0.991910i	$-0.459484\pi$
$919$	4.63641e18	0.253881	0.126941	+	0.991910i	$0.459484\pi$
$920$	3.75571e17	0.0204207
$921$	−9.11192e17	−0.0491952
$922$	4.18101e17	0.0224145
$923$	3.35978e19	1.78855
$924$	−1.08252e19	−0.572226
$925$	1.36354e19	0.715726
$926$	2.16767e17	0.0112985
$927$	7.16913e18	0.371063
$928$	−7.65945e17	−0.0393673
$929$	4.69170e18	0.239457	0.119729	−	0.992807i	$-0.461798\pi$
$929$	4.69170e18	0.239457	0.119729	+	0.992807i	$0.461798\pi$
$930$	3.06483e17	0.0155334
$931$	−3.35542e19	−1.68878
$932$	−5.22607e18	−0.261199
$933$	6.53227e18	0.324215
$934$	3.84459e17	0.0189494
$935$	−3.37825e18	−0.165355
$936$	2.02346e17	0.00983562
$937$	−6.16165e18	−0.297433	−0.148717	−	0.988880i	$-0.547514\pi$
$937$	−6.16165e18	−0.297433	−0.148717	+	0.988880i	$0.547514\pi$
$938$	5.16923e17	0.0247804
$939$	2.40387e19	1.14442
$940$	−6.09979e19	−2.88392
$941$	−1.52437e19	−0.715742	−0.357871	−	0.933771i	$-0.616497\pi$
$941$	−1.52437e19	−0.715742	−0.357871	+	0.933771i	$0.616497\pi$
$942$	−1.54081e17	−0.00718485
$943$	−1.53332e19	−0.710078
$944$	−2.82938e18	−0.130129
$945$	−9.23295e18	−0.421729
$946$	2.58235e17	0.0117145
$947$	−4.08281e19	−1.83943	−0.919717	−	0.392583i	$-0.871582\pi$
$947$	−4.08281e19	−1.83943	−0.919717	+	0.392583i	$0.871582\pi$
$948$	8.57677e18	0.383769
$949$	−1.65603e19	−0.735932
$950$	6.11789e17	0.0270021
$951$	−2.38370e19	−1.04491
$952$	1.27164e17	0.00553637
$953$	1.20791e18	0.0522312	0.0261156	−	0.999659i	$-0.491686\pi$
$953$	1.20791e18	0.0522312	0.0261156	+	0.999659i	$0.491686\pi$
$954$	−1.84879e16	−0.000794005 0
$955$	−3.14097e19	−1.33981
$956$	−5.71391e18	−0.242079
$957$	1.00444e19	0.422667
$958$	−4.49622e17	−0.0187920
$959$	4.96699e19	2.06192
$960$	2.14301e19	0.883612
$961$	2.43815e19	0.998522
$962$	−1.92777e17	−0.00784184
$963$	1.12223e19	0.453432
$964$	−2.33434e18	−0.0936834
$965$	−2.05374e19	−0.818689
$966$	1.39037e17	0.00550529
$967$	6.72408e18	0.264460	0.132230	−	0.991219i	$-0.457786\pi$
$967$	6.72408e18	0.264460	0.132230	+	0.991219i	$0.457786\pi$
$968$	−3.30586e17	−0.0129150
$969$	−3.74046e18	−0.145151
$970$	5.69608e17	0.0219563
$971$	2.78301e19	1.06559	0.532795	−	0.846244i	$-0.321141\pi$
$971$	2.78301e19	1.06559	0.532795	+	0.846244i	$0.321141\pi$
$972$	−1.68640e18	−0.0641401
$973$	−3.42087e19	−1.29242
$974$	−3.92829e17	−0.0147425
$975$	2.47686e19	0.923363
$976$	−4.32622e19	−1.60208
$977$	−1.34400e19	−0.494408	−0.247204	−	0.968963i	$-0.579512\pi$
$977$	−1.34400e19	−0.494408	−0.247204	+	0.968963i	$0.579512\pi$
$978$	−3.49748e17	−0.0127807
$979$	6.46985e18	0.234859
$980$	4.44435e19	1.60265
$981$	−8.65688e18	−0.310108
$982$	−1.31308e17	−0.00467268
$983$	−3.07556e18	−0.108724	−0.0543620	−	0.998521i	$-0.517313\pi$
$983$	−3.07556e18	−0.108724	−0.0543620	+	0.998521i	$0.517313\pi$
$984$	5.40579e17	0.0189841
$985$	7.85932e19	2.74189
$986$	−5.89919e16	−0.00204452
$987$	−4.51667e19	−1.55509
$988$	5.60304e19	1.91648
$989$	2.14855e19	0.730080
$990$	1.30222e17	0.00439599
$991$	4.46469e18	0.149731	0.0748657	−	0.997194i	$-0.476147\pi$
$991$	4.46469e18	0.149731	0.0748657	+	0.997194i	$0.476147\pi$
$992$	−1.58111e18	−0.0526788
$993$	5.77920e18	0.191292
$994$	−8.13907e17	−0.0267648
$995$	−7.28168e18	−0.237893
$996$	−1.15793e19	−0.375834
$997$	−4.98823e19	−1.60853	−0.804263	−	0.594274i	$-0.797439\pi$
$997$	−4.98823e19	−1.60853	−0.804263	+	0.594274i	$0.797439\pi$
$998$	−3.56209e17	−0.0114119
$999$	3.21355e18	0.102284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.15	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-1.12446 q^{2} +729.000 q^{3} -8190.74 q^{4} -53521.6 q^{5} -819.732 q^{6} +445275. q^{7} +18421.7 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-1.12446 q^{2} +729.000 q^{3} -8190.74 q^{4} -53521.6 q^{5} -819.732 q^{6} +445275. q^{7} +18421.7 q^{8} +531441. q^{9} +60183.0 q^{10} +4.07152e6 q^{11} -5.97105e6 q^{12} +2.06685e7 q^{13} -500694. q^{14} -3.90173e7 q^{15} +6.70778e7 q^{16} +1.55027e7 q^{17} -597585. q^{18} -3.30972e8 q^{19} +4.38382e8 q^{20} +3.24605e8 q^{21} -4.57826e6 q^{22} -3.80918e8 q^{23} +1.34294e7 q^{24} +1.64386e9 q^{25} -2.32409e7 q^{26} +3.87420e8 q^{27} -3.64713e9 q^{28} +3.38409e9 q^{29} +4.38734e7 q^{30} +6.98563e9 q^{31} -2.26337e8 q^{32} +2.96814e9 q^{33} -1.74321e7 q^{34} -2.38318e10 q^{35} -4.35289e9 q^{36} +8.29474e9 q^{37} +3.72165e8 q^{38} +1.50673e10 q^{39} -9.85962e8 q^{40} +4.02532e10 q^{41} -3.65006e8 q^{42} -5.64046e10 q^{43} -3.33487e10 q^{44} -2.84436e10 q^{45} +4.28327e8 q^{46} -1.39143e11 q^{47} +4.88997e10 q^{48} +1.01381e11 q^{49} -1.84846e9 q^{50} +1.13014e10 q^{51} -1.69290e11 q^{52} +3.09377e10 q^{53} -4.35639e8 q^{54} -2.17914e11 q^{55} +8.20274e9 q^{56} -2.41279e11 q^{57} -3.80528e9 q^{58} -4.21805e10 q^{59} +3.19580e11 q^{60} -6.44956e11 q^{61} -7.85507e9 q^{62} +2.36637e11 q^{63} -5.49247e11 q^{64} -1.10621e12 q^{65} -3.33755e9 q^{66} -1.03241e12 q^{67} -1.26978e11 q^{68} -2.77689e11 q^{69} +2.67980e10 q^{70} +1.62556e12 q^{71} +9.79007e9 q^{72} -8.01233e11 q^{73} -9.32711e9 q^{74} +1.19838e12 q^{75} +2.71091e12 q^{76} +1.81295e12 q^{77} -1.69426e10 q^{78} -1.43639e12 q^{79} -3.59011e12 q^{80} +2.82430e11 q^{81} -4.52632e10 q^{82} +1.93924e12 q^{83} -2.65876e12 q^{84} -8.29728e11 q^{85} +6.34247e10 q^{86} +2.46700e12 q^{87} +7.50045e10 q^{88} +1.58905e12 q^{89} +3.19837e10 q^{90} +9.20317e12 q^{91} +3.12000e12 q^{92} +5.09252e12 q^{93} +1.56461e11 q^{94} +1.77142e13 q^{95} -1.65000e11 q^{96} +9.46461e12 q^{97} -1.13999e11 q^{98} +2.16377e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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