LMFDB - Embedded newform 177.14.a.c.1.7

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			1.7
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)

$f(q)$	$=$	$q-107.990 q^{2} +729.000 q^{3} +3469.94 q^{4} +5614.85 q^{5} -78725.0 q^{6} -441395. q^{7} +509938. q^{8} +531441. q^{9} +O(q^{10})$	\(q-107.990 q^{2} +729.000 q^{3} +3469.94 q^{4} +5614.85 q^{5} -78725.0 q^{6} -441395. q^{7} +509938. q^{8} +531441. q^{9} -606350. q^{10} -9.58760e6 q^{11} +2.52958e6 q^{12} -1.04119e6 q^{13} +4.76664e7 q^{14} +4.09323e6 q^{15} -8.34941e7 q^{16} +8.94693e7 q^{17} -5.73906e7 q^{18} -1.31769e8 q^{19} +1.94832e7 q^{20} -3.21777e8 q^{21} +1.03537e9 q^{22} -6.51675e8 q^{23} +3.71745e8 q^{24} -1.18918e9 q^{25} +1.12438e8 q^{26} +3.87420e8 q^{27} -1.53161e9 q^{28} -4.82241e9 q^{29} -4.42029e8 q^{30} +6.29557e9 q^{31} +4.83916e9 q^{32} -6.98936e9 q^{33} -9.66183e9 q^{34} -2.47837e9 q^{35} +1.84407e9 q^{36} -1.75409e10 q^{37} +1.42298e10 q^{38} -7.59024e8 q^{39} +2.86322e9 q^{40} -3.34544e10 q^{41} +3.47488e10 q^{42} +1.01527e10 q^{43} -3.32684e10 q^{44} +2.98396e9 q^{45} +7.03747e10 q^{46} -7.21820e10 q^{47} -6.08672e10 q^{48} +9.79404e10 q^{49} +1.28420e11 q^{50} +6.52231e10 q^{51} -3.61285e9 q^{52} -1.09457e11 q^{53} -4.18377e10 q^{54} -5.38329e10 q^{55} -2.25084e11 q^{56} -9.60597e10 q^{57} +5.20774e11 q^{58} -4.21805e10 q^{59} +1.42032e10 q^{60} -2.31061e11 q^{61} -6.79861e11 q^{62} -2.34575e11 q^{63} +1.61401e11 q^{64} -5.84610e9 q^{65} +7.54784e11 q^{66} +1.73456e11 q^{67} +3.10453e11 q^{68} -4.75071e11 q^{69} +2.67640e11 q^{70} +1.31392e12 q^{71} +2.71002e11 q^{72} +1.72064e12 q^{73} +1.89425e12 q^{74} -8.66910e11 q^{75} -4.57231e11 q^{76} +4.23191e12 q^{77} +8.19674e10 q^{78} -2.25052e12 q^{79} -4.68807e11 q^{80} +2.82430e11 q^{81} +3.61276e12 q^{82} +2.25693e12 q^{83} -1.11655e12 q^{84} +5.02357e11 q^{85} -1.09639e12 q^{86} -3.51554e12 q^{87} -4.88908e12 q^{88} -3.90720e12 q^{89} -3.22239e11 q^{90} +4.59574e11 q^{91} -2.26127e12 q^{92} +4.58947e12 q^{93} +7.79497e12 q^{94} -7.39864e11 q^{95} +3.52775e12 q^{96} -9.75846e12 q^{97} -1.05766e13 q^{98} -5.09524e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−107.990	−1.19314	−0.596569	−	0.802562i	$-0.703470\pi$
$2$	−107.990	−1.19314	−0.596569	+	0.802562i	$0.703470\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	3469.94	0.423576
$5$	5614.85	0.160706	0.0803532	−	0.996766i	$-0.474395\pi$
$5$	5614.85	0.160706	0.0803532	+	0.996766i	$0.474395\pi$
$6$	−78725.0	−0.688858
$7$	−441395.	−1.41804	−0.709022	−	0.705186i	$-0.750863\pi$
$7$	−441395.	−1.41804	−0.709022	+	0.705186i	$0.750863\pi$
$8$	509938.	0.687752
$9$	531441.	0.333333
$10$	−606350.	−0.191745
$11$	−9.58760e6	−1.63176	−0.815882	−	0.578219i	$-0.803748\pi$
$11$	−9.58760e6	−1.63176	−0.815882	+	0.578219i	$0.803748\pi$
$12$	2.52958e6	0.244552
$13$	−1.04119e6	−0.0598269	−0.0299134	−	0.999552i	$-0.509523\pi$
$13$	−1.04119e6	−0.0598269	−0.0299134	+	0.999552i	$0.509523\pi$
$14$	4.76664e7	1.69192
$15$	4.09323e6	0.0927839
$16$	−8.34941e7	−1.24416
$17$	8.94693e7	0.898993	0.449496	−	0.893282i	$-0.351604\pi$
$17$	8.94693e7	0.898993	0.449496	+	0.893282i	$0.351604\pi$
$18$	−5.73906e7	−0.397712
$19$	−1.31769e8	−0.642562	−0.321281	−	0.946984i	$-0.604113\pi$
$19$	−1.31769e8	−0.642562	−0.321281	+	0.946984i	$0.604113\pi$
$20$	1.94832e7	0.0680714
$21$	−3.21777e8	−0.818709
$22$	1.03537e9	1.94692
$23$	−6.51675e8	−0.917910	−0.458955	−	0.888460i	$-0.651776\pi$
$23$	−6.51675e8	−0.917910	−0.458955	+	0.888460i	$0.651776\pi$
$24$	3.71745e8	0.397074
$25$	−1.18918e9	−0.974173
$26$	1.12438e8	0.0713817
$27$	3.87420e8	0.192450
$28$	−1.53161e9	−0.600650
$29$	−4.82241e9	−1.50549	−0.752744	−	0.658313i	$-0.771270\pi$
$29$	−4.82241e9	−1.50549	−0.752744	+	0.658313i	$0.771270\pi$
$30$	−4.42029e8	−0.110704
$31$	6.29557e9	1.27404	0.637021	−	0.770846i	$-0.280166\pi$
$31$	6.29557e9	1.27404	0.637021	+	0.770846i	$0.280166\pi$
$32$	4.83916e9	0.796700
$33$	−6.98936e9	−0.942099
$34$	−9.66183e9	−1.07262
$35$	−2.47837e9	−0.227889
$36$	1.84407e9	0.141192
$37$	−1.75409e10	−1.12393	−0.561966	−	0.827160i	$-0.689955\pi$
$37$	−1.75409e10	−1.12393	−0.561966	+	0.827160i	$0.689955\pi$
$38$	1.42298e10	0.766665
$39$	−7.59024e8	−0.0345411
$40$	2.86322e9	0.110526
$41$	−3.34544e10	−1.09991	−0.549956	−	0.835193i	$-0.685356\pi$
$41$	−3.34544e10	−1.09991	−0.549956	+	0.835193i	$0.685356\pi$
$42$	3.47488e10	0.976832
$43$	1.01527e10	0.244926	0.122463	−	0.992473i	$-0.460921\pi$
$43$	1.01527e10	0.244926	0.122463	+	0.992473i	$0.460921\pi$
$44$	−3.32684e10	−0.691177
$45$	2.98396e9	0.0535688
$46$	7.03747e10	1.09519
$47$	−7.21820e10	−0.976771	−0.488386	−	0.872628i	$-0.662414\pi$
$47$	−7.21820e10	−0.976771	−0.488386	+	0.872628i	$0.662414\pi$
$48$	−6.08672e10	−0.718316
$49$	9.79404e10	1.01085
$50$	1.28420e11	1.16232
$51$	6.52231e10	0.519034
$52$	−3.61285e9	−0.0253413
$53$	−1.09457e11	−0.678347	−0.339173	−	0.940724i	$-0.610147\pi$
$53$	−1.09457e11	−0.678347	−0.339173	+	0.940724i	$0.610147\pi$
$54$	−4.18377e10	−0.229619
$55$	−5.38329e10	−0.262235
$56$	−2.25084e11	−0.975264
$57$	−9.60597e10	−0.370984
$58$	5.20774e11	1.79625
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.42032e10	0.0393011
$61$	−2.31061e11	−0.574226	−0.287113	−	0.957897i	$-0.592695\pi$
$61$	−2.31061e11	−0.574226	−0.287113	+	0.957897i	$0.592695\pi$
$62$	−6.79861e11	−1.52011
$63$	−2.34575e11	−0.472682
$64$	1.61401e11	0.293586
$65$	−5.84610e9	−0.00961456
$66$	7.54784e11	1.12405
$67$	1.73456e11	0.234263	0.117131	−	0.993116i	$-0.462630\pi$
$67$	1.73456e11	0.234263	0.117131	+	0.993116i	$0.462630\pi$
$68$	3.10453e11	0.380792
$69$	−4.75071e11	−0.529955
$70$	2.67640e11	0.271903
$71$	1.31392e12	1.21728	0.608639	−	0.793447i	$-0.291716\pi$
$71$	1.31392e12	1.21728	0.608639	+	0.793447i	$0.291716\pi$
$72$	2.71002e11	0.229251
$73$	1.72064e12	1.33073	0.665365	−	0.746518i	$-0.268276\pi$
$73$	1.72064e12	1.33073	0.665365	+	0.746518i	$0.268276\pi$
$74$	1.89425e12	1.34101
$75$	−8.66910e11	−0.562439
$76$	−4.57231e11	−0.272174
$77$	4.23191e12	2.31391
$78$	8.19674e10	0.0412122
$79$	−2.25052e12	−1.04162	−0.520808	−	0.853674i	$-0.674369\pi$
$79$	−2.25052e12	−1.04162	−0.520808	+	0.853674i	$0.674369\pi$
$80$	−4.68807e11	−0.199944
$81$	2.82430e11	0.111111
$82$	3.61276e12	1.31235
$83$	2.25693e12	0.757725	0.378862	−	0.925453i	$-0.376315\pi$
$83$	2.25693e12	0.757725	0.378862	+	0.925453i	$0.376315\pi$
$84$	−1.11655e12	−0.346786
$85$	5.02357e11	0.144474
$86$	−1.09639e12	−0.292230
$87$	−3.51554e12	−0.869194
$88$	−4.88908e12	−1.12225
$89$	−3.90720e12	−0.833356	−0.416678	−	0.909054i	$-0.636806\pi$
$89$	−3.90720e12	−0.833356	−0.416678	+	0.909054i	$0.636806\pi$
$90$	−3.22239e11	−0.0639149
$91$	4.59574e11	0.0848372
$92$	−2.26127e12	−0.388805
$93$	4.58947e12	0.735569
$94$	7.79497e12	1.16542
$95$	−7.39864e11	−0.103264
$96$	3.52775e12	0.459975
$97$	−9.75846e12	−1.18950	−0.594751	−	0.803910i	$-0.702749\pi$
$97$	−9.75846e12	−1.18950	−0.594751	+	0.803910i	$0.702749\pi$
$98$	−1.05766e13	−1.20608
$99$	−5.09524e12	−0.543921
$100$	−4.12637e12	−0.412637
$101$	−4.75087e12	−0.445332	−0.222666	−	0.974895i	$-0.571476\pi$
$101$	−4.75087e12	−0.445332	−0.222666	+	0.974895i	$0.571476\pi$
$102$	−7.04347e12	−0.619278
$103$	−2.35557e13	−1.94381	−0.971904	−	0.235378i	$-0.924367\pi$
$103$	−2.35557e13	−1.94381	−0.971904	+	0.235378i	$0.924367\pi$
$104$	−5.30940e11	−0.0411461
$105$	−1.80673e12	−0.131572
$106$	1.18204e13	0.809361
$107$	−2.68262e13	−1.72808	−0.864041	−	0.503422i	$-0.832074\pi$
$107$	−2.68262e13	−1.72808	−0.864041	+	0.503422i	$0.832074\pi$
$108$	1.34432e12	0.0815173
$109$	−1.67914e13	−0.958989	−0.479494	−	0.877545i	$-0.659180\pi$
$109$	−1.67914e13	−0.958989	−0.479494	+	0.877545i	$0.659180\pi$
$110$	5.81344e12	0.312882
$111$	−1.27873e13	−0.648903
$112$	3.68539e13	1.76427
$113$	1.40641e12	0.0635482	0.0317741	−	0.999495i	$-0.489884\pi$
$113$	1.40641e12	0.0635482	0.0317741	+	0.999495i	$0.489884\pi$
$114$	1.03735e13	0.442634
$115$	−3.65906e12	−0.147514
$116$	−1.67335e13	−0.637689
$117$	−5.53329e11	−0.0199423
$118$	4.55509e12	0.155333
$119$	−3.94913e13	−1.27481
$120$	2.08729e12	0.0638123
$121$	5.73993e13	1.66265
$122$	2.49524e13	0.685130
$123$	−2.43883e13	−0.635035
$124$	2.18452e13	0.539654
$125$	−1.35311e13	−0.317262
$126$	2.53319e13	0.563974
$127$	5.02216e13	1.06210	0.531051	−	0.847340i	$-0.321797\pi$
$127$	5.02216e13	1.06210	0.531051	+	0.847340i	$0.321797\pi$
$128$	−5.70721e13	−1.14699
$129$	7.40129e12	0.141408
$130$	6.31323e11	0.0114715
$131$	−7.45761e13	−1.28925	−0.644624	−	0.764500i	$-0.722986\pi$
$131$	−7.45761e13	−1.28925	−0.644624	+	0.764500i	$0.722986\pi$
$132$	−2.42526e13	−0.399051
$133$	5.81622e13	0.911182
$134$	−1.87316e13	−0.279508
$135$	2.17531e12	0.0309280
$136$	4.56238e13	0.618284
$137$	−5.10006e13	−0.659010	−0.329505	−	0.944154i	$-0.606882\pi$
$137$	−5.10006e13	−0.659010	−0.329505	+	0.944154i	$0.606882\pi$
$138$	5.13031e13	0.632310
$139$	−2.16189e12	−0.0254236	−0.0127118	−	0.999919i	$-0.504046\pi$
$139$	−2.16189e12	−0.0254236	−0.0127118	+	0.999919i	$0.504046\pi$
$140$	−8.59977e12	−0.0965283
$141$	−5.26207e13	−0.563939
$142$	−1.41891e14	−1.45238
$143$	9.98247e12	0.0976233
$144$	−4.43722e13	−0.414720
$145$	−2.70771e13	−0.241942
$146$	−1.85812e14	−1.58774
$147$	7.13985e13	0.583615
$148$	−6.08658e13	−0.476071
$149$	1.34291e14	1.00539	0.502696	−	0.864463i	$-0.332342\pi$
$149$	1.34291e14	1.00539	0.502696	+	0.864463i	$0.332342\pi$
$150$	9.36180e13	0.671067
$151$	−1.49735e14	−1.02795	−0.513977	−	0.857804i	$-0.671829\pi$
$151$	−1.49735e14	−1.02795	−0.513977	+	0.857804i	$0.671829\pi$
$152$	−6.71941e13	−0.441924
$153$	4.75477e13	0.299664
$154$	−4.57006e14	−2.76082
$155$	3.53487e13	0.204747
$156$	−2.63377e12	−0.0146308
$157$	−8.62203e12	−0.0459475	−0.0229737	−	0.999736i	$-0.507313\pi$
$157$	−8.62203e12	−0.0459475	−0.0229737	+	0.999736i	$0.507313\pi$
$158$	2.43035e14	1.24279
$159$	−7.97944e13	−0.391644
$160$	2.71712e13	0.128035
$161$	2.87646e14	1.30164
$162$	−3.04997e13	−0.132571
$163$	−1.36347e14	−0.569411	−0.284706	−	0.958615i	$-0.591896\pi$
$163$	−1.36347e14	−0.569411	−0.284706	+	0.958615i	$0.591896\pi$
$164$	−1.16085e14	−0.465897
$165$	−3.92442e13	−0.151401
$166$	−2.43727e14	−0.904069
$167$	−1.40374e14	−0.500759	−0.250379	−	0.968148i	$-0.580555\pi$
$167$	−1.40374e14	−0.500759	−0.250379	+	0.968148i	$0.580555\pi$
$168$	−1.64086e14	−0.563069
$169$	−3.01791e14	−0.996421
$170$	−5.42497e13	−0.172377
$171$	−7.00275e13	−0.214187
$172$	3.52291e13	0.103745
$173$	2.88987e14	0.819557	0.409778	−	0.912185i	$-0.365606\pi$
$173$	2.88987e14	0.819557	0.409778	+	0.912185i	$0.365606\pi$
$174$	3.79644e14	1.03707
$175$	5.24896e14	1.38142
$176$	8.00508e14	2.03017
$177$	−3.07496e13	−0.0751646
$178$	4.21940e14	0.994307
$179$	3.70795e14	0.842537	0.421268	−	0.906936i	$-0.361585\pi$
$179$	3.70795e14	0.842537	0.421268	+	0.906936i	$0.361585\pi$
$180$	1.03542e13	0.0226905
$181$	5.97550e14	1.26317	0.631587	−	0.775305i	$-0.282404\pi$
$181$	5.97550e14	1.26317	0.631587	+	0.775305i	$0.282404\pi$
$182$	−4.96296e13	−0.101222
$183$	−1.68443e14	−0.331529
$184$	−3.32314e14	−0.631295
$185$	−9.84895e13	−0.180623
$186$	−4.95619e14	−0.877634
$187$	−8.57796e14	−1.46694
$188$	−2.50467e14	−0.413737
$189$	−1.71005e14	−0.272903
$190$	7.98983e13	0.123208
$191$	−5.89234e14	−0.878155	−0.439077	−	0.898449i	$-0.644695\pi$
$191$	−5.89234e14	−0.878155	−0.439077	+	0.898449i	$0.644695\pi$
$192$	1.17661e14	0.169502
$193$	−5.66671e14	−0.789239	−0.394619	−	0.918845i	$-0.629124\pi$
$193$	−5.66671e14	−0.789239	−0.394619	+	0.918845i	$0.629124\pi$
$194$	1.05382e15	1.41924
$195$	−4.26181e12	−0.00555097
$196$	3.39847e14	0.428173
$197$	−3.03408e14	−0.369825	−0.184912	−	0.982755i	$-0.559200\pi$
$197$	−3.03408e14	−0.369825	−0.184912	+	0.982755i	$0.559200\pi$
$198$	5.50237e14	0.648973
$199$	7.49175e14	0.855142	0.427571	−	0.903982i	$-0.359369\pi$
$199$	7.49175e14	0.855142	0.427571	+	0.903982i	$0.359369\pi$
$200$	−6.06406e14	−0.669990
$201$	1.26449e14	0.135252
$202$	5.13048e14	0.531342
$203$	2.12859e15	2.13485
$204$	2.26320e14	0.219850
$205$	−1.87842e14	−0.176763
$206$	2.54379e15	2.31923
$207$	−3.46327e14	−0.305970
$208$	8.69329e13	0.0744342
$209$	1.26335e15	1.04851
$210$	1.95109e14	0.156983
$211$	6.38277e14	0.497936	0.248968	−	0.968512i	$-0.419909\pi$
$211$	6.38277e14	0.497936	0.248968	+	0.968512i	$0.419909\pi$
$212$	−3.79810e14	−0.287332
$213$	9.57849e14	0.702796
$214$	2.89697e15	2.06184
$215$	5.70056e13	0.0393612
$216$	1.97560e14	0.132358
$217$	−2.77883e15	−1.80665
$218$	1.81331e15	1.14421
$219$	1.25434e15	0.768298
$220$	−1.86797e14	−0.111076
$221$	−9.31542e13	−0.0537839
$222$	1.38091e15	0.774230
$223$	2.42026e15	1.31789	0.658946	−	0.752190i	$-0.271002\pi$
$223$	2.42026e15	1.31789	0.658946	+	0.752190i	$0.271002\pi$
$224$	−2.13598e15	−1.12976
$225$	−6.31977e14	−0.324724
$226$	−1.51879e14	−0.0758218
$227$	2.13210e15	1.03428	0.517141	−	0.855900i	$-0.326996\pi$
$227$	2.13210e15	1.03428	0.517141	+	0.855900i	$0.326996\pi$
$228$	−3.33321e14	−0.157140
$229$	−1.66361e15	−0.762292	−0.381146	−	0.924515i	$-0.624470\pi$
$229$	−1.66361e15	−0.762292	−0.381146	+	0.924515i	$0.624470\pi$
$230$	3.95143e14	0.176004
$231$	3.08507e15	1.33594
$232$	−2.45913e15	−1.03540
$233$	−1.58920e15	−0.650677	−0.325338	−	0.945598i	$-0.605478\pi$
$233$	−1.58920e15	−0.650677	−0.325338	+	0.945598i	$0.605478\pi$
$234$	5.97542e13	0.0237939
$235$	−4.05291e14	−0.156973
$236$	−1.46364e14	−0.0551449
$237$	−1.64063e15	−0.601377
$238$	4.26468e15	1.52103
$239$	5.29417e15	1.83743	0.918716	−	0.394918i	$-0.129227\pi$
$239$	5.29417e15	1.83743	0.918716	+	0.394918i	$0.129227\pi$
$240$	−3.41760e14	−0.115438
$241$	3.21625e14	0.105740	0.0528700	−	0.998601i	$-0.483163\pi$
$241$	3.21625e14	0.105740	0.0528700	+	0.998601i	$0.483163\pi$
$242$	−6.19857e15	−1.98377
$243$	2.05891e14	0.0641500
$244$	−8.01767e14	−0.243228
$245$	5.49920e14	0.162450
$246$	2.63370e15	0.757684
$247$	1.37196e14	0.0384425
$248$	3.21035e15	0.876226
$249$	1.64531e15	0.437472
$250$	1.46123e15	0.378537
$251$	6.74063e15	1.70146	0.850729	−	0.525605i	$-0.176161\pi$
$251$	6.74063e15	1.70146	0.850729	+	0.525605i	$0.176161\pi$
$252$	−8.13962e14	−0.200217
$253$	6.24799e15	1.49781
$254$	−5.42346e15	−1.26723
$255$	3.66218e14	0.0834120
$256$	4.84105e15	1.07493
$257$	5.56284e15	1.20429	0.602145	−	0.798386i	$-0.294313\pi$
$257$	5.56284e15	1.20429	0.602145	+	0.798386i	$0.294313\pi$
$258$	−7.99268e14	−0.168719
$259$	7.74246e15	1.59379
$260$	−2.02856e13	−0.00407250
$261$	−2.56283e15	−0.501829
$262$	8.05351e15	1.53825
$263$	−3.16501e15	−0.589743	−0.294871	−	0.955537i	$-0.595277\pi$
$263$	−3.16501e15	−0.589743	−0.294871	+	0.955537i	$0.595277\pi$
$264$	−3.56414e15	−0.647931
$265$	−6.14587e14	−0.109015
$266$	−6.28096e15	−1.08717
$267$	−2.84835e15	−0.481138
$268$	6.01882e14	0.0992282
$269$	1.06354e16	1.71145	0.855725	−	0.517432i	$-0.173112\pi$
$269$	1.06354e16	1.71145	0.855725	+	0.517432i	$0.173112\pi$
$270$	−2.34913e14	−0.0369013
$271$	−4.20543e15	−0.644927	−0.322463	−	0.946582i	$-0.604511\pi$
$271$	−4.20543e15	−0.644927	−0.322463	+	0.946582i	$0.604511\pi$
$272$	−7.47016e15	−1.11849
$273$	3.35029e14	0.0489808
$274$	5.50758e15	0.786289
$275$	1.14013e16	1.58962
$276$	−1.64847e15	−0.224477
$277$	−2.75757e15	−0.366782	−0.183391	−	0.983040i	$-0.558707\pi$
$277$	−2.75757e15	−0.366782	−0.183391	+	0.983040i	$0.558707\pi$
$278$	2.33463e14	0.0303338
$279$	3.34572e15	0.424681
$280$	−1.26381e15	−0.156731
$281$	−6.56319e15	−0.795286	−0.397643	−	0.917540i	$-0.630172\pi$
$281$	−6.56319e15	−0.795286	−0.397643	+	0.917540i	$0.630172\pi$
$282$	5.68253e15	0.672857
$283$	−7.25297e15	−0.839275	−0.419637	−	0.907692i	$-0.637843\pi$
$283$	−7.25297e15	−0.839275	−0.419637	+	0.907692i	$0.637843\pi$
$284$	4.55923e15	0.515611
$285$	−5.39361e14	−0.0596194
$286$	−1.07801e15	−0.116478
$287$	1.47666e16	1.55973
$288$	2.57173e15	0.265567
$289$	−1.89982e15	−0.191812
$290$	2.92407e15	0.288669
$291$	−7.11392e15	−0.686759
$292$	5.97050e15	0.563666
$293$	1.91677e16	1.76983	0.884914	−	0.465754i	$-0.154217\pi$
$293$	1.91677e16	1.76983	0.884914	+	0.465754i	$0.154217\pi$
$294$	−7.71036e15	−0.696333
$295$	−2.36837e14	−0.0209222
$296$	−8.94476e15	−0.772988
$297$	−3.71443e15	−0.314033
$298$	−1.45021e16	−1.19957
$299$	6.78515e14	0.0549157
$300$	−3.00812e15	−0.238236
$301$	−4.48133e15	−0.347316
$302$	1.61700e16	1.22649
$303$	−3.46338e15	−0.257112
$304$	1.10020e16	0.799450
$305$	−1.29737e15	−0.0922818
$306$	−5.13469e15	−0.357540
$307$	−2.39237e16	−1.63090	−0.815451	−	0.578825i	$-0.803511\pi$
$307$	−2.39237e16	−1.63090	−0.815451	+	0.578825i	$0.803511\pi$
$308$	1.46845e16	0.980119
$309$	−1.71721e16	−1.12226
$310$	−3.81732e15	−0.244291
$311$	1.29630e16	0.812388	0.406194	−	0.913787i	$-0.366856\pi$
$311$	1.29630e16	0.812388	0.406194	+	0.913787i	$0.366856\pi$
$312$	−3.87055e14	−0.0237557
$313$	5.96928e15	0.358826	0.179413	−	0.983774i	$-0.442580\pi$
$313$	5.96928e15	0.358826	0.179413	+	0.983774i	$0.442580\pi$
$314$	9.31097e14	0.0548217
$315$	−1.31711e15	−0.0759630
$316$	−7.80917e15	−0.441204
$317$	−2.23734e16	−1.23836	−0.619180	−	0.785249i	$-0.712535\pi$
$317$	−2.23734e16	−1.23836	−0.619180	+	0.785249i	$0.712535\pi$
$318$	8.61704e15	0.467285
$319$	4.62353e16	2.45660
$320$	9.06242e14	0.0471812
$321$	−1.95563e16	−0.997709
$322$	−3.10630e16	−1.55303
$323$	−1.17893e16	−0.577659
$324$	9.80013e14	0.0470640
$325$	1.23815e15	0.0582818
$326$	1.47242e16	0.679386
$327$	−1.22409e16	−0.553672
$328$	−1.70597e16	−0.756468
$329$	3.18608e16	1.38511
$330$	4.23800e15	0.180643
$331$	−8.39910e15	−0.351035	−0.175518	−	0.984476i	$-0.556160\pi$
$331$	−8.39910e15	−0.351035	−0.175518	+	0.984476i	$0.556160\pi$
$332$	7.83142e15	0.320954
$333$	−9.32195e15	−0.374644
$334$	1.51590e16	0.597474
$335$	9.73930e14	0.0376475
$336$	2.68665e16	1.01860
$337$	6.82874e15	0.253949	0.126974	−	0.991906i	$-0.459473\pi$
$337$	6.82874e15	0.253949	0.126974	+	0.991906i	$0.459473\pi$
$338$	3.25906e16	1.18887
$339$	1.02528e15	0.0366896
$340$	1.74315e15	0.0611957
$341$	−6.03593e16	−2.07894
$342$	7.56230e15	0.255555
$343$	−4.64057e14	−0.0153872
$344$	5.17722e15	0.168448
$345$	−2.66745e15	−0.0851672
$346$	−3.12079e16	−0.977844
$347$	−2.67733e16	−0.823305	−0.411653	−	0.911341i	$-0.635048\pi$
$347$	−2.67733e16	−0.823305	−0.411653	+	0.911341i	$0.635048\pi$
$348$	−1.21987e16	−0.368170
$349$	5.66261e16	1.67746	0.838729	−	0.544549i	$-0.183299\pi$
$349$	5.66261e16	1.67746	0.838729	+	0.544549i	$0.183299\pi$
$350$	−5.66838e16	−1.64823
$351$	−4.03377e14	−0.0115137
$352$	−4.63959e16	−1.30003
$353$	−1.05506e16	−0.290229	−0.145114	−	0.989415i	$-0.546355\pi$
$353$	−1.05506e16	−0.290229	−0.145114	+	0.989415i	$0.546355\pi$
$354$	3.32066e15	0.0896817
$355$	7.37747e15	0.195624
$356$	−1.35577e16	−0.352990
$357$	−2.87891e16	−0.736013
$358$	−4.00423e16	−1.00526
$359$	4.74699e16	1.17032	0.585159	−	0.810918i	$-0.301032\pi$
$359$	4.74699e16	1.17032	0.585159	+	0.810918i	$0.301032\pi$
$360$	1.52163e15	0.0368421
$361$	−2.46899e16	−0.587113
$362$	−6.45297e16	−1.50714
$363$	4.18441e16	0.959933
$364$	1.59469e15	0.0359350
$365$	9.66111e15	0.213857
$366$	1.81903e16	0.395560
$367$	1.91625e16	0.409375	0.204688	−	0.978827i	$-0.434382\pi$
$367$	1.91625e16	0.409375	0.204688	+	0.978827i	$0.434382\pi$
$368$	5.44110e16	1.14203
$369$	−1.77790e16	−0.366638
$370$	1.06359e16	0.215508
$371$	4.83139e16	0.961926
$372$	1.59252e16	0.311569
$373$	−4.60121e16	−0.884635	−0.442318	−	0.896858i	$-0.645844\pi$
$373$	−4.60121e16	−0.884635	−0.442318	+	0.896858i	$0.645844\pi$
$374$	9.26337e16	1.75026
$375$	−9.86418e15	−0.183171
$376$	−3.68083e16	−0.671777
$377$	5.02103e15	0.0900687
$378$	1.84669e16	0.325611
$379$	4.29578e15	0.0744539	0.0372269	−	0.999307i	$-0.488148\pi$
$379$	4.29578e15	0.0744539	0.0372269	+	0.999307i	$0.488148\pi$
$380$	−2.56728e15	−0.0437401
$381$	3.66116e16	0.613205
$382$	6.36317e16	1.04776
$383$	−3.00763e16	−0.486892	−0.243446	−	0.969914i	$-0.578278\pi$
$383$	−3.00763e16	−0.486892	−0.243446	+	0.969914i	$0.578278\pi$
$384$	−4.16056e16	−0.662215
$385$	2.37616e16	0.371861
$386$	6.11950e16	0.941670
$387$	5.39554e15	0.0816420
$388$	−3.38613e16	−0.503845
$389$	1.20445e17	1.76244	0.881221	−	0.472705i	$-0.156722\pi$
$389$	1.20445e17	1.76244	0.881221	+	0.472705i	$0.156722\pi$
$390$	4.60235e14	0.00662307
$391$	−5.83049e16	−0.825194
$392$	4.99435e16	0.695215
$393$	−5.43660e16	−0.744348
$394$	3.27651e16	0.441252
$395$	−1.26363e16	−0.167394
$396$	−1.76802e16	−0.230392
$397$	4.39605e16	0.563539	0.281770	−	0.959482i	$-0.409079\pi$
$397$	4.39605e16	0.563539	0.281770	+	0.959482i	$0.409079\pi$
$398$	−8.09038e16	−1.02030
$399$	4.24003e16	0.526071
$400$	9.92893e16	1.21203
$401$	−1.97572e16	−0.237294	−0.118647	−	0.992937i	$-0.537856\pi$
$401$	−1.97572e16	−0.237294	−0.118647	+	0.992937i	$0.537856\pi$
$402$	−1.36553e16	−0.161374
$403$	−6.55485e15	−0.0762220
$404$	−1.64852e16	−0.188632
$405$	1.58580e15	0.0178563
$406$	−2.29867e17	−2.54717
$407$	1.68175e17	1.83399
$408$	3.32597e16	0.356967
$409$	−4.32602e16	−0.456969	−0.228485	−	0.973548i	$-0.573377\pi$
$409$	−4.32602e16	−0.456969	−0.228485	+	0.973548i	$0.573377\pi$
$410$	2.02851e16	0.210903
$411$	−3.71795e16	−0.380479
$412$	−8.17367e16	−0.823351
$413$	1.86183e16	0.184614
$414$	3.74000e16	0.365064
$415$	1.26723e16	0.121771
$416$	−5.03846e15	−0.0476641
$417$	−1.57602e15	−0.0146783
$418$	−1.36430e17	−1.25102
$419$	−2.75196e16	−0.248456	−0.124228	−	0.992254i	$-0.539645\pi$
$419$	−2.75196e16	−0.248456	−0.124228	+	0.992254i	$0.539645\pi$
$420$	−6.26924e15	−0.0557307
$421$	−1.15862e17	−1.01416	−0.507081	−	0.861899i	$-0.669275\pi$
$421$	−1.15862e17	−1.01416	−0.507081	+	0.861899i	$0.669275\pi$
$422$	−6.89278e16	−0.594106
$423$	−3.83605e16	−0.325590
$424$	−5.58164e16	−0.466535
$425$	−1.06395e17	−0.875775
$426$	−1.03439e17	−0.838532
$427$	1.01989e17	0.814278
$428$	−9.30852e16	−0.731975
$429$	7.27722e15	0.0563629
$430$	−6.15607e15	−0.0469633
$431$	1.39883e17	1.05114	0.525572	−	0.850749i	$-0.323851\pi$
$431$	1.39883e17	1.05114	0.525572	+	0.850749i	$0.323851\pi$
$432$	−3.23473e16	−0.239439
$433$	1.04847e17	0.764512	0.382256	−	0.924057i	$-0.375147\pi$
$433$	1.04847e17	0.764512	0.382256	+	0.924057i	$0.375147\pi$
$434$	3.00087e17	2.15558
$435$	−1.97392e16	−0.139685
$436$	−5.82650e16	−0.406205
$437$	8.58706e16	0.589814
$438$	−1.35457e17	−0.916685
$439$	−1.13279e17	−0.755321	−0.377661	−	0.925944i	$-0.623271\pi$
$439$	−1.13279e17	−0.755321	−0.377661	+	0.925944i	$0.623271\pi$
$440$	−2.74514e16	−0.180353
$441$	5.20495e16	0.336950
$442$	1.00598e16	0.0641716
$443$	−1.06437e17	−0.669065	−0.334533	−	0.942384i	$-0.608578\pi$
$443$	−1.06437e17	−0.669065	−0.334533	+	0.942384i	$0.608578\pi$
$444$	−4.43712e16	−0.274860
$445$	−2.19383e16	−0.133926
$446$	−2.61365e17	−1.57243
$447$	9.78980e16	0.580463
$448$	−7.12415e16	−0.416319
$449$	−1.73315e17	−0.998242	−0.499121	−	0.866532i	$-0.666344\pi$
$449$	−1.73315e17	−0.998242	−0.499121	+	0.866532i	$0.666344\pi$
$450$	6.82475e16	0.387441
$451$	3.20747e17	1.79480
$452$	4.88017e15	0.0269175
$453$	−1.09157e17	−0.593490
$454$	−2.30246e17	−1.23404
$455$	2.58044e15	0.0136339
$456$	−4.89845e16	−0.255145
$457$	3.33307e17	1.71155	0.855775	−	0.517349i	$-0.173081\pi$
$457$	3.33307e17	1.71155	0.855775	+	0.517349i	$0.173081\pi$
$458$	1.79654e17	0.909519
$459$	3.46622e16	0.173011
$460$	−1.26967e16	−0.0624834
$461$	1.90878e16	0.0926191	0.0463096	−	0.998927i	$-0.485254\pi$
$461$	1.90878e16	0.0926191	0.0463096	+	0.998927i	$0.485254\pi$
$462$	−3.33158e17	−1.59396
$463$	−8.20003e15	−0.0386847	−0.0193423	−	0.999813i	$-0.506157\pi$
$463$	−8.20003e15	−0.0386847	−0.0193423	+	0.999813i	$0.506157\pi$
$464$	4.02643e17	1.87307
$465$	2.57692e16	0.118211
$466$	1.71619e17	0.776347
$467$	2.90621e17	1.29648	0.648242	−	0.761435i	$-0.275505\pi$
$467$	2.90621e17	1.29648	0.648242	+	0.761435i	$0.275505\pi$
$468$	−1.92002e15	−0.00844709
$469$	−7.65626e16	−0.332195
$470$	4.37676e16	0.187291
$471$	−6.28546e15	−0.0265278
$472$	−2.15094e16	−0.0895377
$473$	−9.73396e16	−0.399661
$474$	1.77172e17	0.717525
$475$	1.56697e17	0.625967
$476$	−1.37032e17	−0.539980
$477$	−5.81701e16	−0.226116
$478$	−5.71720e17	−2.19231
$479$	4.11421e17	1.55634	0.778172	−	0.628051i	$-0.216147\pi$
$479$	4.11421e17	1.55634	0.778172	+	0.628051i	$0.216147\pi$
$480$	1.98078e16	0.0739210
$481$	1.82633e16	0.0672414
$482$	−3.47325e16	−0.126162
$483$	2.09694e17	0.751501
$484$	1.99172e17	0.704260
$485$	−5.47923e16	−0.191161
$486$	−2.22343e16	−0.0765398
$487$	−8.50507e16	−0.288895	−0.144447	−	0.989512i	$-0.546140\pi$
$487$	−8.50507e16	−0.288895	−0.144447	+	0.989512i	$0.546140\pi$
$488$	−1.17827e17	−0.394925
$489$	−9.93970e16	−0.328750
$490$	−5.93862e16	−0.193825
$491$	5.33038e17	1.71683	0.858417	−	0.512953i	$-0.171448\pi$
$491$	5.33038e17	1.71683	0.858417	+	0.512953i	$0.171448\pi$
$492$	−8.46258e16	−0.268986
$493$	−4.31458e17	−1.35342
$494$	−1.48159e16	−0.0458672
$495$	−2.86090e16	−0.0874116
$496$	−5.25643e17	−1.58511
$497$	−5.79958e17	−1.72616
$498$	−1.77677e17	−0.521965
$499$	1.21583e16	0.0352549	0.0176274	−	0.999845i	$-0.494389\pi$
$499$	1.21583e16	0.0352549	0.0176274	+	0.999845i	$0.494389\pi$
$500$	−4.69521e16	−0.134385
$501$	−1.02332e17	−0.289113
$502$	−7.27923e17	−2.03007
$503$	−3.19223e17	−0.878826	−0.439413	−	0.898285i	$-0.644814\pi$
$503$	−3.19223e17	−0.878826	−0.439413	+	0.898285i	$0.644814\pi$
$504$	−1.19619e17	−0.325088
$505$	−2.66754e16	−0.0715677
$506$	−6.74724e17	−1.78710
$507$	−2.20006e17	−0.575284
$508$	1.74266e17	0.449882
$509$	3.64045e17	0.927875	0.463938	−	0.885868i	$-0.346436\pi$
$509$	3.64045e17	0.927875	0.463938	+	0.885868i	$0.346436\pi$
$510$	−3.95481e16	−0.0995220
$511$	−7.59479e17	−1.88704
$512$	−5.52523e16	−0.135549
$513$	−5.10501e16	−0.123661
$514$	−6.00734e17	−1.43688
$515$	−1.32261e17	−0.312382
$516$	2.56820e16	0.0598971
$517$	6.92052e17	1.59386
$518$	−8.36111e17	−1.90161
$519$	2.10672e17	0.473171
$520$	−2.98115e15	−0.00661244
$521$	9.58656e16	0.209999	0.105000	−	0.994472i	$-0.466516\pi$
$521$	9.58656e16	0.209999	0.105000	+	0.994472i	$0.466516\pi$
$522$	2.76761e17	0.598751
$523$	5.04150e17	1.07721	0.538603	−	0.842560i	$-0.318952\pi$
$523$	5.04150e17	1.07721	0.538603	+	0.842560i	$0.318952\pi$
$524$	−2.58775e17	−0.546095
$525$	3.82649e17	0.797564
$526$	3.41791e17	0.703644
$527$	5.63260e17	1.14535
$528$	5.83570e17	1.17212
$529$	−7.93563e16	−0.157442
$530$	6.63695e16	0.130069
$531$	−2.24165e16	−0.0433963
$532$	2.01819e17	0.385955
$533$	3.48323e16	0.0658044
$534$	3.07594e17	0.574064
$535$	−1.50625e17	−0.277714
$536$	8.84518e16	0.161115
$537$	2.70309e17	0.486439
$538$	−1.14852e18	−2.04199
$539$	−9.39013e17	−1.64947
$540$	7.54818e15	0.0131004
$541$	−1.00143e18	−1.71727	−0.858634	−	0.512590i	$-0.828686\pi$
$541$	−1.00143e18	−1.71727	−0.858634	+	0.512590i	$0.828686\pi$
$542$	4.54147e17	0.769486
$543$	4.35614e17	0.729294
$544$	4.32956e17	0.716228
$545$	−9.42810e16	−0.154116
$546$	−3.61800e16	−0.0584408
$547$	2.37772e17	0.379528	0.189764	−	0.981830i	$-0.439228\pi$
$547$	2.37772e17	0.379528	0.189764	+	0.981830i	$0.439228\pi$
$548$	−1.76969e17	−0.279141
$549$	−1.22795e17	−0.191409
$550$	−1.23124e18	−1.89664
$551$	6.35445e17	0.967370
$552$	−2.42257e17	−0.364478
$553$	9.93369e17	1.47706
$554$	2.97791e17	0.437621
$555$	−7.17988e16	−0.104283
$556$	−7.50161e15	−0.0107688
$557$	−8.07829e17	−1.14620	−0.573101	−	0.819485i	$-0.694260\pi$
$557$	−8.07829e17	−1.14620	−0.573101	+	0.819485i	$0.694260\pi$
$558$	−3.61306e17	−0.506702
$559$	−1.05708e16	−0.0146532
$560$	2.06929e17	0.283530
$561$	−6.25333e17	−0.846940
$562$	7.08761e17	0.948886
$563$	8.75664e17	1.15886	0.579432	−	0.815020i	$-0.303274\pi$
$563$	8.75664e17	1.15886	0.579432	+	0.815020i	$0.303274\pi$
$564$	−1.82590e17	−0.238871
$565$	7.89681e15	0.0102126
$566$	7.83252e17	1.00137
$567$	−1.24663e17	−0.157561
$568$	6.70018e17	0.837187
$569$	8.68202e17	1.07248	0.536242	−	0.844064i	$-0.319843\pi$
$569$	8.68202e17	1.07248	0.536242	+	0.844064i	$0.319843\pi$
$570$	5.82458e16	0.0711342
$571$	8.14188e17	0.983082	0.491541	−	0.870854i	$-0.336434\pi$
$571$	8.14188e17	0.983082	0.491541	+	0.870854i	$0.336434\pi$
$572$	3.46385e16	0.0413509
$573$	−4.29552e17	−0.507003
$574$	−1.59465e18	−1.86097
$575$	7.74956e17	0.894203
$576$	8.57750e16	0.0978622
$577$	−1.09707e17	−0.123763	−0.0618816	−	0.998083i	$-0.519710\pi$
$577$	−1.09707e17	−0.123763	−0.0618816	+	0.998083i	$0.519710\pi$
$578$	2.05163e17	0.228859
$579$	−4.13103e17	−0.455667
$580$	−9.39559e16	−0.102481
$581$	−9.96199e17	−1.07449
$582$	7.68235e17	0.819398
$583$	1.04943e18	1.10690
$584$	8.77417e17	0.915213
$585$	−3.10686e15	−0.00320485
$586$	−2.06993e18	−2.11165
$587$	−6.34760e17	−0.640416	−0.320208	−	0.947347i	$-0.603753\pi$
$587$	−6.34760e17	−0.640416	−0.320208	+	0.947347i	$0.603753\pi$
$588$	2.47748e17	0.247206
$589$	−8.29562e17	−0.818652
$590$	2.55762e16	0.0249630
$591$	−2.21184e17	−0.213518
$592$	1.46456e18	1.39835
$593$	4.62954e17	0.437202	0.218601	−	0.975814i	$-0.429851\pi$
$593$	4.62954e17	0.437202	0.218601	+	0.975814i	$0.429851\pi$
$594$	4.01123e17	0.374685
$595$	−2.21738e17	−0.204870
$596$	4.65981e17	0.425860
$597$	5.46149e17	0.493717
$598$	−7.32731e16	−0.0655220
$599$	−1.37740e18	−1.21838	−0.609192	−	0.793023i	$-0.708506\pi$
$599$	−1.37740e18	−1.21838	−0.609192	+	0.793023i	$0.708506\pi$
$600$	−4.42070e17	−0.386819
$601$	−8.29177e17	−0.717734	−0.358867	−	0.933389i	$-0.616837\pi$
$601$	−8.29177e17	−0.717734	−0.358867	+	0.933389i	$0.616837\pi$
$602$	4.83941e17	0.414395
$603$	9.21817e16	0.0780876
$604$	−5.19572e17	−0.435417
$605$	3.22288e17	0.267199
$606$	3.74012e17	0.306770
$607$	1.98534e18	1.61105	0.805525	−	0.592562i	$-0.201883\pi$
$607$	1.98534e18	1.61105	0.805525	+	0.592562i	$0.201883\pi$
$608$	−6.37652e17	−0.511930
$609$	1.55174e18	1.23256
$610$	1.40104e17	0.110105
$611$	7.51549e16	0.0584372
$612$	1.64987e17	0.126931
$613$	−1.90822e18	−1.45256	−0.726282	−	0.687397i	$-0.758753\pi$
$613$	−1.90822e18	−1.45256	−0.726282	+	0.687397i	$0.758753\pi$
$614$	2.58353e18	1.94589
$615$	−1.36936e17	−0.102054
$616$	2.15801e18	1.59140
$617$	−3.31213e16	−0.0241687	−0.0120843	−	0.999927i	$-0.503847\pi$
$617$	−3.31213e16	−0.0241687	−0.0120843	+	0.999927i	$0.503847\pi$
$618$	1.85442e18	1.33901
$619$	−2.33375e18	−1.66749	−0.833747	−	0.552146i	$-0.813809\pi$
$619$	−2.33375e18	−1.66749	−0.833747	+	0.552146i	$0.813809\pi$
$620$	1.22658e17	0.0867259
$621$	−2.52472e17	−0.176652
$622$	−1.39988e18	−0.969290
$623$	1.72462e18	1.18174
$624$	6.33741e16	0.0429746
$625$	1.37566e18	0.923187
$626$	−6.44625e17	−0.428128
$627$	9.20982e17	0.605358
$628$	−2.99179e16	−0.0194623
$629$	−1.56937e18	−1.01041
$630$	1.42235e17	0.0906342
$631$	−1.41731e18	−0.893870	−0.446935	−	0.894566i	$-0.647484\pi$
$631$	−1.41731e18	−0.893870	−0.446935	+	0.894566i	$0.647484\pi$
$632$	−1.14763e18	−0.716373
$633$	4.65304e17	0.287483
$634$	2.41611e18	1.47753
$635$	2.81987e17	0.170687
$636$	−2.76882e17	−0.165891
$637$	−1.01974e17	−0.0604761
$638$	−4.99297e18	−2.93106
$639$	6.98272e17	0.405760
$640$	−3.20452e17	−0.184329
$641$	−1.06228e18	−0.604872	−0.302436	−	0.953170i	$-0.597800\pi$
$641$	−1.06228e18	−0.604872	−0.302436	+	0.953170i	$0.597800\pi$
$642$	2.11189e18	1.19040
$643$	−2.13065e18	−1.18889	−0.594443	−	0.804138i	$-0.702627\pi$
$643$	−2.13065e18	−1.18889	−0.594443	+	0.804138i	$0.702627\pi$
$644$	9.98113e17	0.551343
$645$	4.15571e16	0.0227252
$646$	1.27313e18	0.689226
$647$	−8.87594e17	−0.475704	−0.237852	−	0.971301i	$-0.576443\pi$
$647$	−8.87594e17	−0.475704	−0.237852	+	0.971301i	$0.576443\pi$
$648$	1.44021e17	0.0764169
$649$	4.04410e17	0.212438
$650$	−1.33709e17	−0.0695381
$651$	−2.02577e18	−1.04307
$652$	−4.73116e17	−0.241189
$653$	−1.93108e17	−0.0974686	−0.0487343	−	0.998812i	$-0.515519\pi$
$653$	−1.93108e17	−0.0974686	−0.0487343	+	0.998812i	$0.515519\pi$
$654$	1.32190e18	0.660607
$655$	−4.18734e17	−0.207190
$656$	2.79325e18	1.36847
$657$	9.14416e17	0.443577
$658$	−3.44066e18	−1.65262
$659$	−1.37220e18	−0.652622	−0.326311	−	0.945262i	$-0.605806\pi$
$659$	−1.37220e18	−0.652622	−0.326311	+	0.945262i	$0.605806\pi$
$660$	−1.36175e17	−0.0641300
$661$	2.68051e18	1.24999	0.624997	−	0.780627i	$-0.285100\pi$
$661$	2.68051e18	1.24999	0.624997	+	0.780627i	$0.285100\pi$
$662$	9.07022e17	0.418833
$663$	−6.79094e16	−0.0310522
$664$	1.15090e18	0.521127
$665$	3.26572e17	0.146433
$666$	1.00668e18	0.447002
$667$	3.14264e18	1.38190
$668$	−4.87088e17	−0.212110
$669$	1.76437e18	0.760886
$670$	−1.05175e17	−0.0449187
$671$	2.21532e18	0.937001
$672$	−1.55713e18	−0.652265
$673$	−1.49388e16	−0.00619750	−0.00309875	−	0.999995i	$-0.500986\pi$
$673$	−1.49388e16	−0.00619750	−0.00309875	+	0.999995i	$0.500986\pi$
$674$	−7.37439e17	−0.302996
$675$	−4.60711e17	−0.187480
$676$	−1.04720e18	−0.422060
$677$	1.94890e18	0.777970	0.388985	−	0.921244i	$-0.372826\pi$
$677$	1.94890e18	0.777970	0.388985	+	0.921244i	$0.372826\pi$
$678$	−1.10720e17	−0.0437757
$679$	4.30733e18	1.68677
$680$	2.56171e17	0.0993622
$681$	1.55430e18	0.597143
$682$	6.51823e18	2.48046
$683$	3.07859e18	1.16042	0.580212	−	0.814465i	$-0.302970\pi$
$683$	3.07859e18	1.16042	0.580212	+	0.814465i	$0.302970\pi$
$684$	−2.42991e17	−0.0907248
$685$	−2.86361e17	−0.105907
$686$	5.01137e16	0.0183590
$687$	−1.21277e18	−0.440109
$688$	−8.47687e17	−0.304727
$689$	1.13965e17	0.0405834
$690$	2.88059e17	0.101616
$691$	−2.21151e17	−0.0772825	−0.0386413	−	0.999253i	$-0.512303\pi$
$691$	−2.21151e17	−0.0772825	−0.0386413	+	0.999253i	$0.512303\pi$
$692$	1.00277e18	0.347145
$693$	2.24901e18	0.771305
$694$	2.89127e18	0.982316
$695$	−1.21387e16	−0.00408573
$696$	−1.79270e18	−0.597790
$697$	−2.99314e18	−0.988813
$698$	−6.11508e18	−2.00144
$699$	−1.15853e18	−0.375668
$700$	1.82136e18	0.585138
$701$	−3.85220e18	−1.22614	−0.613072	−	0.790027i	$-0.710067\pi$
$701$	−3.85220e18	−1.22614	−0.613072	+	0.790027i	$0.710067\pi$
$702$	4.35608e16	0.0137374
$703$	2.31135e18	0.722197
$704$	−1.54745e18	−0.479064
$705$	−2.95457e17	−0.0906286
$706$	1.13936e18	0.346283
$707$	2.09701e18	0.631501
$708$	−1.06699e17	−0.0318380
$709$	6.13648e18	1.81434	0.907171	−	0.420763i	$-0.138238\pi$
$709$	6.13648e18	1.81434	0.907171	+	0.420763i	$0.138238\pi$
$710$	−7.96696e17	−0.233407
$711$	−1.19602e18	−0.347205
$712$	−1.99243e18	−0.573142
$713$	−4.10266e18	−1.16946
$714$	3.10895e18	0.878164
$715$	5.60501e16	0.0156887
$716$	1.28663e18	0.356879
$717$	3.85945e18	1.06084
$718$	−5.12629e18	−1.39635
$719$	9.80939e17	0.264791	0.132396	−	0.991197i	$-0.457733\pi$
$719$	9.80939e17	0.264791	0.132396	+	0.991197i	$0.457733\pi$
$720$	−2.49143e17	−0.0666481
$721$	1.03973e19	2.75641
$722$	2.66627e18	0.700507
$723$	2.34465e17	0.0610491
$724$	2.07346e18	0.535051
$725$	5.73470e18	1.46661
$726$	−4.51876e18	−1.14533
$727$	2.54365e18	0.638975	0.319488	−	0.947590i	$-0.396489\pi$
$727$	2.54365e18	0.638975	0.319488	+	0.947590i	$0.396489\pi$
$728$	2.34354e17	0.0583470
$729$	1.50095e17	0.0370370
$730$	−1.04331e18	−0.255161
$731$	9.08351e17	0.220187
$732$	−5.84488e17	−0.140428
$733$	−5.65641e18	−1.34699	−0.673496	−	0.739191i	$-0.735208\pi$
$733$	−5.65641e18	−1.34699	−0.673496	+	0.739191i	$0.735208\pi$
$734$	−2.06936e18	−0.488441
$735$	4.00892e17	0.0937907
$736$	−3.15356e18	−0.731299
$737$	−1.66303e18	−0.382262
$738$	1.91997e18	0.437449
$739$	4.68683e17	0.105850	0.0529249	−	0.998598i	$-0.483146\pi$
$739$	4.68683e17	0.105850	0.0529249	+	0.998598i	$0.483146\pi$
$740$	−3.41752e17	−0.0765077
$741$	1.00016e17	0.0221948
$742$	−5.21744e18	−1.14771
$743$	5.69331e18	1.24147	0.620737	−	0.784019i	$-0.286833\pi$
$743$	5.69331e18	1.24147	0.620737	+	0.784019i	$0.286833\pi$
$744$	2.34034e18	0.505889
$745$	7.54023e17	0.161573
$746$	4.96886e18	1.05549
$747$	1.19943e18	0.252575
$748$	−2.97650e18	−0.621363
$749$	1.18409e19	2.45050
$750$	1.06524e18	0.218549
$751$	3.66106e18	0.744642	0.372321	−	0.928104i	$-0.378562\pi$
$751$	3.66106e18	0.744642	0.372321	+	0.928104i	$0.378562\pi$
$752$	6.02677e18	1.21526
$753$	4.91392e18	0.982337
$754$	−5.42223e17	−0.107464
$755$	−8.40741e17	−0.165199
$756$	−5.93378e17	−0.115595
$757$	−6.93767e18	−1.33996	−0.669978	−	0.742381i	$-0.733697\pi$
$757$	−6.93767e18	−1.33996	−0.669978	+	0.742381i	$0.733697\pi$
$758$	−4.63903e17	−0.0888337
$759$	4.55479e18	0.864762
$760$	−3.77285e17	−0.0710200
$761$	−6.12248e18	−1.14269	−0.571344	−	0.820711i	$-0.693578\pi$
$761$	−6.12248e18	−1.14269	−0.571344	+	0.820711i	$0.693578\pi$
$762$	−3.95370e18	−0.731638
$763$	7.41162e18	1.35989
$764$	−2.04461e18	−0.371966
$765$	2.66973e17	0.0481579
$766$	3.24796e18	0.580929
$767$	4.39178e16	0.00778880
$768$	3.52913e18	0.620611
$769$	−9.93053e18	−1.73162	−0.865808	−	0.500377i	$-0.833195\pi$
$769$	−9.93053e18	−1.73162	−0.865808	+	0.500377i	$0.833195\pi$
$770$	−2.56602e18	−0.443681
$771$	4.05531e18	0.695298
$772$	−1.96631e18	−0.334303
$773$	3.16993e18	0.534420	0.267210	−	0.963638i	$-0.413898\pi$
$773$	3.16993e18	0.534420	0.267210	+	0.963638i	$0.413898\pi$
$774$	−5.82667e17	−0.0974101
$775$	−7.48654e18	−1.24114
$776$	−4.97621e18	−0.818083
$777$	5.64425e18	0.920174
$778$	−1.30069e19	−2.10283
$779$	4.40826e18	0.706763
$780$	−1.47882e16	−0.00235126
$781$	−1.25973e19	−1.98631
$782$	6.29637e18	0.984570
$783$	−1.86830e18	−0.289731
$784$	−8.17744e18	−1.25766
$785$	−4.84114e16	−0.00738406
$786$	5.87101e18	0.888109
$787$	−6.37388e18	−0.956243	−0.478121	−	0.878294i	$-0.658682\pi$
$787$	−6.37388e18	−0.956243	−0.478121	+	0.878294i	$0.658682\pi$
$788$	−1.05281e18	−0.156649
$789$	−2.30729e18	−0.340488
$790$	1.36461e18	0.199724
$791$	−6.20784e17	−0.0901142
$792$	−2.59826e18	−0.374083
$793$	2.40577e17	0.0343541
$794$	−4.74731e18	−0.672380
$795$	−4.48034e17	−0.0629397
$796$	2.59959e18	0.362218
$797$	−1.04831e19	−1.44880	−0.724402	−	0.689378i	$-0.757884\pi$
$797$	−1.04831e19	−1.44880	−0.724402	+	0.689378i	$0.757884\pi$
$798$	−4.57882e18	−0.627675
$799$	−6.45807e18	−0.878110
$800$	−5.75461e18	−0.776124
$801$	−2.07644e18	−0.277785
$802$	2.13358e18	0.283124
$803$	−1.64968e19	−2.17144
$804$	4.38772e17	0.0572894
$805$	1.61509e18	0.209181
$806$	7.07862e17	0.0909433
$807$	7.75321e18	0.988106
$808$	−2.42265e18	−0.306278
$809$	−1.22376e19	−1.53472	−0.767360	−	0.641216i	$-0.778430\pi$
$809$	−1.22376e19	−1.53472	−0.767360	+	0.641216i	$0.778430\pi$
$810$	−1.71251e17	−0.0213050
$811$	−6.68310e18	−0.824789	−0.412394	−	0.911005i	$-0.635307\pi$
$811$	−6.68310e18	−0.824789	−0.412394	+	0.911005i	$0.635307\pi$
$812$	7.38606e18	0.904272
$813$	−3.06576e18	−0.372349
$814$	−1.81613e19	−2.18821
$815$	−7.65568e17	−0.0915081
$816$	−5.44575e18	−0.645761
$817$	−1.33781e18	−0.157380
$818$	4.67169e18	0.545227
$819$	2.44236e17	0.0282791
$820$	−6.51798e17	−0.0748726
$821$	−1.11425e19	−1.26984	−0.634922	−	0.772576i	$-0.718968\pi$
$821$	−1.11425e19	−1.26984	−0.634922	+	0.772576i	$0.718968\pi$
$822$	4.01503e18	0.453964
$823$	−1.21999e19	−1.36854	−0.684270	−	0.729228i	$-0.739879\pi$
$823$	−1.21999e19	−1.36854	−0.684270	+	0.729228i	$0.739879\pi$
$824$	−1.20119e19	−1.33686
$825$	8.31158e18	0.917768
$826$	−2.01060e18	−0.220269
$827$	4.78529e18	0.520143	0.260072	−	0.965589i	$-0.416254\pi$
$827$	4.78529e18	0.520143	0.260072	+	0.965589i	$0.416254\pi$
$828$	−1.20173e18	−0.129602
$829$	4.69672e18	0.502562	0.251281	−	0.967914i	$-0.419148\pi$
$829$	4.69672e18	0.502562	0.251281	+	0.967914i	$0.419148\pi$
$830$	−1.36849e18	−0.145290
$831$	−2.01027e18	−0.211762
$832$	−1.68048e17	−0.0175644
$833$	8.76266e18	0.908747
$834$	1.70195e17	0.0175132
$835$	−7.88177e17	−0.0804751
$836$	4.38374e18	0.444124
$837$	2.43903e18	0.245190
$838$	2.97185e18	0.296443
$839$	−2.91089e18	−0.288120	−0.144060	−	0.989569i	$-0.546016\pi$
$839$	−2.91089e18	−0.288120	−0.144060	+	0.989569i	$0.546016\pi$
$840$	−9.21319e17	−0.0904888
$841$	1.29950e19	1.26649
$842$	1.25120e19	1.21003
$843$	−4.78456e18	−0.459159
$844$	2.21478e18	0.210914
$845$	−1.69451e18	−0.160131
$846$	4.14256e18	0.388474
$847$	−2.53357e19	−2.35772
$848$	9.13905e18	0.843972
$849$	−5.28742e18	−0.484555
$850$	1.14896e19	1.04492
$851$	1.14310e19	1.03167
$852$	3.32368e18	0.297688
$853$	1.64993e19	1.46655	0.733275	−	0.679932i	$-0.237991\pi$
$853$	1.64993e19	1.46655	0.733275	+	0.679932i	$0.237991\pi$
$854$	−1.10139e19	−0.971545
$855$	−3.93194e17	−0.0344213
$856$	−1.36797e19	−1.18849
$857$	−8.81932e18	−0.760431	−0.380215	−	0.924898i	$-0.624150\pi$
$857$	−8.81932e18	−0.760431	−0.380215	+	0.924898i	$0.624150\pi$
$858$	−7.85870e17	−0.0672486
$859$	−1.23566e19	−1.04940	−0.524702	−	0.851286i	$-0.675823\pi$
$859$	−1.23566e19	−1.04940	−0.524702	+	0.851286i	$0.675823\pi$
$860$	1.97806e17	0.0166725
$861$	1.07649e19	0.900508
$862$	−1.51060e19	−1.25416
$863$	−7.53367e18	−0.620778	−0.310389	−	0.950610i	$-0.600459\pi$
$863$	−7.53367e18	−0.620778	−0.310389	+	0.950610i	$0.600459\pi$
$864$	1.87479e18	0.153325
$865$	1.62262e18	0.131708
$866$	−1.13225e19	−0.912167
$867$	−1.38497e18	−0.110743
$868$	−9.64237e18	−0.765254
$869$	2.15771e19	1.69967
$870$	2.13165e18	0.166663
$871$	−1.80600e17	−0.0140152
$872$	−8.56254e18	−0.659547
$873$	−5.18605e18	−0.396501
$874$	−9.27321e18	−0.703730
$875$	5.97256e18	0.449892
$876$	4.35249e18	0.325433
$877$	−2.06459e19	−1.53228	−0.766139	−	0.642675i	$-0.777825\pi$
$877$	−2.06459e19	−1.53228	−0.766139	+	0.642675i	$0.777825\pi$
$878$	1.22331e19	0.901202
$879$	1.39733e19	1.02181
$880$	4.49473e18	0.326262
$881$	4.71322e18	0.339605	0.169802	−	0.985478i	$-0.445687\pi$
$881$	4.71322e18	0.339605	0.169802	+	0.985478i	$0.445687\pi$
$882$	−5.62085e18	−0.402028
$883$	−1.89929e19	−1.34848	−0.674242	−	0.738511i	$-0.735529\pi$
$883$	−1.89929e19	−1.34848	−0.674242	+	0.738511i	$0.735529\pi$
$884$	−3.23239e17	−0.0227816
$885$	−1.72654e17	−0.0120794
$886$	1.14942e19	0.798287
$887$	2.12032e19	1.46183	0.730917	−	0.682466i	$-0.239092\pi$
$887$	2.12032e19	1.46183	0.730917	+	0.682466i	$0.239092\pi$
$888$	−6.52073e18	−0.446285
$889$	−2.21676e19	−1.50611
$890$	2.36913e18	0.159792
$891$	−2.70782e18	−0.181307
$892$	8.39814e18	0.558228
$893$	9.51136e18	0.627636
$894$	−1.05720e19	−0.692572
$895$	2.08196e18	0.135401
$896$	2.51913e19	1.62648
$897$	4.94637e17	0.0317056
$898$	1.87164e19	1.19104
$899$	−3.03598e19	−1.91805
$900$	−2.19292e18	−0.137546
$901$	−9.79307e18	−0.609829
$902$	−3.46377e19	−2.14144
$903$	−3.26689e18	−0.200523
$904$	7.17184e17	0.0437055
$905$	3.35515e18	0.203000
$906$	1.17879e19	0.708115
$907$	−4.05898e18	−0.242086	−0.121043	−	0.992647i	$-0.538624\pi$
$907$	−4.05898e18	−0.242086	−0.121043	+	0.992647i	$0.538624\pi$
$908$	7.39825e18	0.438098
$909$	−2.52480e18	−0.148444
$910$	−2.78663e17	−0.0162671
$911$	2.16568e19	1.25524	0.627618	−	0.778521i	$-0.284030\pi$
$911$	2.16568e19	1.25524	0.627618	+	0.778521i	$0.284030\pi$
$912$	8.02042e18	0.461563
$913$	−2.16386e19	−1.23643
$914$	−3.59940e19	−2.04211
$915$	−9.45785e17	−0.0532789
$916$	−5.77263e18	−0.322889
$917$	3.29175e19	1.82821
$918$	−3.74319e18	−0.206426
$919$	1.14013e19	0.624312	0.312156	−	0.950031i	$-0.398949\pi$
$919$	1.14013e19	0.624312	0.312156	+	0.950031i	$0.398949\pi$
$920$	−1.86589e18	−0.101453
$921$	−1.74403e19	−0.941602
$922$	−2.06130e18	−0.110507
$923$	−1.36804e18	−0.0728260
$924$	1.07050e19	0.565872
$925$	2.08592e19	1.09491
$926$	8.85525e17	0.0461561
$927$	−1.25184e19	−0.647936
$928$	−2.33364e19	−1.19942
$929$	2.09772e19	1.07064	0.535322	−	0.844648i	$-0.320190\pi$
$929$	2.09772e19	1.07064	0.535322	+	0.844648i	$0.320190\pi$
$930$	−2.78282e18	−0.141041
$931$	−1.29055e19	−0.649535
$932$	−5.51443e18	−0.275611
$933$	9.45004e18	0.469032
$934$	−3.13843e19	−1.54688
$935$	−4.81639e18	−0.235747
$936$	−2.82163e17	−0.0137154
$937$	2.77478e19	1.33943	0.669717	−	0.742616i	$-0.266415\pi$
$937$	2.77478e19	1.33943	0.669717	+	0.742616i	$0.266415\pi$
$938$	8.26803e18	0.396354
$939$	4.35160e18	0.207168
$940$	−1.40633e18	−0.0664902
$941$	−2.64142e19	−1.24024	−0.620120	−	0.784507i	$-0.712916\pi$
$941$	−2.64142e19	−1.24024	−0.620120	+	0.784507i	$0.712916\pi$
$942$	6.78770e17	0.0316513
$943$	2.18014e19	1.00962
$944$	3.52183e18	0.161976
$945$	−9.60170e17	−0.0438572
$946$	1.05117e19	0.476851
$947$	1.13680e19	0.512163	0.256082	−	0.966655i	$-0.417568\pi$
$947$	1.13680e19	0.512163	0.256082	+	0.966655i	$0.417568\pi$
$948$	−5.69289e18	−0.254729
$949$	−1.79150e18	−0.0796135
$950$	−1.69218e19	−0.746865
$951$	−1.63102e19	−0.714967
$952$	−2.01381e19	−0.876755
$953$	−2.57112e19	−1.11178	−0.555889	−	0.831256i	$-0.687622\pi$
$953$	−2.57112e19	−1.11178	−0.555889	+	0.831256i	$0.687622\pi$
$954$	6.28182e18	0.269787
$955$	−3.30846e18	−0.141125
$956$	1.83704e19	0.778293
$957$	3.37056e19	1.41832
$958$	−4.44296e19	−1.85693
$959$	2.25114e19	0.934505
$960$	6.60650e17	0.0272401
$961$	1.52166e19	0.623184
$962$	−1.97226e18	−0.0802282
$963$	−1.42565e19	−0.576027
$964$	1.11602e18	0.0447890
$965$	−3.18177e18	−0.126836
$966$	−2.26449e19	−0.896643
$967$	4.06994e19	1.60072	0.800361	−	0.599519i	$-0.204641\pi$
$967$	4.06994e19	1.60072	0.800361	+	0.599519i	$0.204641\pi$
$968$	2.92701e19	1.14349
$969$	−8.59440e18	−0.333511
$970$	5.91705e18	0.228081
$971$	2.06387e19	0.790239	0.395119	−	0.918630i	$-0.370703\pi$
$971$	2.06387e19	0.790239	0.395119	+	0.918630i	$0.370703\pi$
$972$	7.14429e17	0.0271724
$973$	9.54245e17	0.0360518
$974$	9.18467e18	0.344691
$975$	9.02614e17	0.0336490
$976$	1.92922e19	0.714428
$977$	−6.87975e18	−0.253080	−0.126540	−	0.991961i	$-0.540387\pi$
$977$	−6.87975e18	−0.253080	−0.126540	+	0.991961i	$0.540387\pi$
$978$	1.07339e19	0.392244
$979$	3.74606e19	1.35984
$980$	1.90819e18	0.0688101
$981$	−8.92362e18	−0.319663
$982$	−5.75630e19	−2.04842
$983$	−9.57656e17	−0.0338541	−0.0169271	−	0.999857i	$-0.505388\pi$
$983$	−9.57656e17	−0.0338541	−0.0169271	+	0.999857i	$0.505388\pi$
$984$	−1.24365e19	−0.436747
$985$	−1.70359e18	−0.0594332
$986$	4.65933e19	1.61482
$987$	2.32265e19	0.799691
$988$	4.76062e17	0.0162833
$989$	−6.61623e18	−0.224820
$990$	3.08950e18	0.104294
$991$	3.70859e19	1.24374	0.621870	−	0.783120i	$-0.286373\pi$
$991$	3.70859e19	1.24374	0.621870	+	0.783120i	$0.286373\pi$
$992$	3.04652e19	1.01503
$993$	−6.12294e18	−0.202670
$994$	6.26299e19	2.05954
$995$	4.20651e18	0.137427
$996$	5.70911e18	0.185303
$997$	−2.10142e19	−0.677633	−0.338816	−	0.940853i	$-0.610027\pi$
$997$	−2.10142e19	−0.677633	−0.338816	+	0.940853i	$0.610027\pi$
$998$	−1.31298e18	−0.0420639
$999$	−6.79570e18	−0.216301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.7	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-107.990 q^{2} +729.000 q^{3} +3469.94 q^{4} +5614.85 q^{5} -78725.0 q^{6} -441395. q^{7} +509938. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-107.990 q^{2} +729.000 q^{3} +3469.94 q^{4} +5614.85 q^{5} -78725.0 q^{6} -441395. q^{7} +509938. q^{8} +531441. q^{9} -606350. q^{10} -9.58760e6 q^{11} +2.52958e6 q^{12} -1.04119e6 q^{13} +4.76664e7 q^{14} +4.09323e6 q^{15} -8.34941e7 q^{16} +8.94693e7 q^{17} -5.73906e7 q^{18} -1.31769e8 q^{19} +1.94832e7 q^{20} -3.21777e8 q^{21} +1.03537e9 q^{22} -6.51675e8 q^{23} +3.71745e8 q^{24} -1.18918e9 q^{25} +1.12438e8 q^{26} +3.87420e8 q^{27} -1.53161e9 q^{28} -4.82241e9 q^{29} -4.42029e8 q^{30} +6.29557e9 q^{31} +4.83916e9 q^{32} -6.98936e9 q^{33} -9.66183e9 q^{34} -2.47837e9 q^{35} +1.84407e9 q^{36} -1.75409e10 q^{37} +1.42298e10 q^{38} -7.59024e8 q^{39} +2.86322e9 q^{40} -3.34544e10 q^{41} +3.47488e10 q^{42} +1.01527e10 q^{43} -3.32684e10 q^{44} +2.98396e9 q^{45} +7.03747e10 q^{46} -7.21820e10 q^{47} -6.08672e10 q^{48} +9.79404e10 q^{49} +1.28420e11 q^{50} +6.52231e10 q^{51} -3.61285e9 q^{52} -1.09457e11 q^{53} -4.18377e10 q^{54} -5.38329e10 q^{55} -2.25084e11 q^{56} -9.60597e10 q^{57} +5.20774e11 q^{58} -4.21805e10 q^{59} +1.42032e10 q^{60} -2.31061e11 q^{61} -6.79861e11 q^{62} -2.34575e11 q^{63} +1.61401e11 q^{64} -5.84610e9 q^{65} +7.54784e11 q^{66} +1.73456e11 q^{67} +3.10453e11 q^{68} -4.75071e11 q^{69} +2.67640e11 q^{70} +1.31392e12 q^{71} +2.71002e11 q^{72} +1.72064e12 q^{73} +1.89425e12 q^{74} -8.66910e11 q^{75} -4.57231e11 q^{76} +4.23191e12 q^{77} +8.19674e10 q^{78} -2.25052e12 q^{79} -4.68807e11 q^{80} +2.82430e11 q^{81} +3.61276e12 q^{82} +2.25693e12 q^{83} -1.11655e12 q^{84} +5.02357e11 q^{85} -1.09639e12 q^{86} -3.51554e12 q^{87} -4.88908e12 q^{88} -3.90720e12 q^{89} -3.22239e11 q^{90} +4.59574e11 q^{91} -2.26127e12 q^{92} +4.58947e12 q^{93} +7.79497e12 q^{94} -7.39864e11 q^{95} +3.52775e12 q^{96} -9.75846e12 q^{97} -1.05766e13 q^{98} -5.09524e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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