LMFDB - Embedded newform 177.14.a.c.1.11

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			1.11
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)

$f(q)$	$=$	$q-59.5570 q^{2} +729.000 q^{3} -4644.96 q^{4} -45189.8 q^{5} -43417.1 q^{6} -134821. q^{7} +764531. q^{8} +531441. q^{9} +O(q^{10})$	\(q-59.5570 q^{2} +729.000 q^{3} -4644.96 q^{4} -45189.8 q^{5} -43417.1 q^{6} -134821. q^{7} +764531. q^{8} +531441. q^{9} +2.69137e6 q^{10} +9.07000e6 q^{11} -3.38617e6 q^{12} -1.72380e6 q^{13} +8.02957e6 q^{14} -3.29434e7 q^{15} -7.48174e6 q^{16} +5.25990e7 q^{17} -3.16511e7 q^{18} +1.91390e8 q^{19} +2.09905e8 q^{20} -9.82849e7 q^{21} -5.40183e8 q^{22} +6.96259e8 q^{23} +5.57343e8 q^{24} +8.21418e8 q^{25} +1.02665e8 q^{26} +3.87420e8 q^{27} +6.26240e8 q^{28} -5.96170e8 q^{29} +1.96201e9 q^{30} +4.04822e9 q^{31} -5.81745e9 q^{32} +6.61203e9 q^{33} -3.13264e9 q^{34} +6.09256e9 q^{35} -2.46852e9 q^{36} +5.23136e9 q^{37} -1.13986e10 q^{38} -1.25665e9 q^{39} -3.45490e10 q^{40} -5.61271e10 q^{41} +5.85356e9 q^{42} +3.71000e10 q^{43} -4.21298e10 q^{44} -2.40157e10 q^{45} -4.14671e10 q^{46} -7.30879e10 q^{47} -5.45419e9 q^{48} -7.87122e10 q^{49} -4.89213e10 q^{50} +3.83447e10 q^{51} +8.00699e9 q^{52} -6.59362e10 q^{53} -2.30736e10 q^{54} -4.09872e11 q^{55} -1.03075e11 q^{56} +1.39523e11 q^{57} +3.55061e10 q^{58} -4.21805e10 q^{59} +1.53021e11 q^{60} +5.17079e11 q^{61} -2.41100e11 q^{62} -7.16497e10 q^{63} +4.07761e11 q^{64} +7.78983e10 q^{65} -3.93793e11 q^{66} +1.40765e11 q^{67} -2.44320e11 q^{68} +5.07573e11 q^{69} -3.62855e11 q^{70} +7.79097e11 q^{71} +4.06303e11 q^{72} -1.35323e12 q^{73} -3.11564e11 q^{74} +5.98814e11 q^{75} -8.88999e11 q^{76} -1.22283e12 q^{77} +7.48425e10 q^{78} +1.33603e12 q^{79} +3.38098e11 q^{80} +2.82430e11 q^{81} +3.34277e12 q^{82} -9.97241e11 q^{83} +4.56529e11 q^{84} -2.37694e12 q^{85} -2.20957e12 q^{86} -4.34608e11 q^{87} +6.93430e12 q^{88} +6.23630e12 q^{89} +1.43031e12 q^{90} +2.32406e11 q^{91} -3.23409e12 q^{92} +2.95115e12 q^{93} +4.35290e12 q^{94} -8.64889e12 q^{95} -4.24092e12 q^{96} +8.66937e12 q^{97} +4.68786e12 q^{98} +4.82017e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−59.5570	−0.658019	−0.329009	−	0.944327i	$-0.606715\pi$
$2$	−59.5570	−0.658019	−0.329009	+	0.944327i	$0.606715\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−4644.96	−0.567011
$5$	−45189.8	−1.29341	−0.646704	−	0.762741i	$-0.723853\pi$
$5$	−45189.8	−1.29341	−0.646704	+	0.762741i	$0.723853\pi$
$6$	−43417.1	−0.379907
$7$	−134821.	−0.433134	−0.216567	−	0.976268i	$-0.569486\pi$
$7$	−134821.	−0.433134	−0.216567	+	0.976268i	$0.569486\pi$
$8$	764531.	1.03112
$9$	531441.	0.333333
$10$	2.69137e6	0.851087
$11$	9.07000e6	1.54367	0.771836	−	0.635822i	$-0.219339\pi$
$11$	9.07000e6	1.54367	0.771836	+	0.635822i	$0.219339\pi$
$12$	−3.38617e6	−0.327364
$13$	−1.72380e6	−0.0990503	−0.0495251	−	0.998773i	$-0.515771\pi$
$13$	−1.72380e6	−0.0990503	−0.0495251	+	0.998773i	$0.515771\pi$
$14$	8.02957e6	0.285010
$15$	−3.29434e7	−0.746750
$16$	−7.48174e6	−0.111487
$17$	5.25990e7	0.528518	0.264259	−	0.964452i	$-0.414873\pi$
$17$	5.25990e7	0.528518	0.264259	+	0.964452i	$0.414873\pi$
$18$	−3.16511e7	−0.219340
$19$	1.91390e8	0.933299	0.466650	−	0.884442i	$-0.345461\pi$
$19$	1.91390e8	0.933299	0.466650	+	0.884442i	$0.345461\pi$
$20$	2.09905e8	0.733378
$21$	−9.82849e7	−0.250070
$22$	−5.40183e8	−1.01576
$23$	6.96259e8	0.980708	0.490354	−	0.871523i	$-0.336867\pi$
$23$	6.96259e8	0.980708	0.490354	+	0.871523i	$0.336867\pi$
$24$	5.57343e8	0.595319
$25$	8.21418e8	0.672906
$26$	1.02665e8	0.0651769
$27$	3.87420e8	0.192450
$28$	6.26240e8	0.245592
$29$	−5.96170e8	−0.186116	−0.0930579	−	0.995661i	$-0.529664\pi$
$29$	−5.96170e8	−0.186116	−0.0930579	+	0.995661i	$0.529664\pi$
$30$	1.96201e9	0.491375
$31$	4.04822e9	0.819243	0.409622	−	0.912255i	$-0.365661\pi$
$31$	4.04822e9	0.819243	0.409622	+	0.912255i	$0.365661\pi$
$32$	−5.81745e9	−0.957763
$33$	6.61203e9	0.891239
$34$	−3.13264e9	−0.347775
$35$	6.09256e9	0.560219
$36$	−2.46852e9	−0.189004
$37$	5.23136e9	0.335199	0.167600	−	0.985855i	$-0.446398\pi$
$37$	5.23136e9	0.335199	0.167600	+	0.985855i	$0.446398\pi$
$38$	−1.13986e10	−0.614128
$39$	−1.25665e9	−0.0571867
$40$	−3.45490e10	−1.33366
$41$	−5.61271e10	−1.84535	−0.922673	−	0.385584i	$-0.874000\pi$
$41$	−5.61271e10	−1.84535	−0.922673	+	0.385584i	$0.874000\pi$
$42$	5.85356e9	0.164551
$43$	3.71000e10	0.895012	0.447506	−	0.894281i	$-0.352312\pi$
$43$	3.71000e10	0.895012	0.447506	+	0.894281i	$0.352312\pi$
$44$	−4.21298e10	−0.875279
$45$	−2.40157e10	−0.431136
$46$	−4.14671e10	−0.645324
$47$	−7.30879e10	−0.989030	−0.494515	−	0.869169i	$-0.664654\pi$
$47$	−7.30879e10	−0.989030	−0.494515	+	0.869169i	$0.664654\pi$
$48$	−5.45419e9	−0.0643668
$49$	−7.87122e10	−0.812395
$50$	−4.89213e10	−0.442785
$51$	3.83447e10	0.305140
$52$	8.00699e9	0.0561626
$53$	−6.59362e10	−0.408630	−0.204315	−	0.978905i	$-0.565497\pi$
$53$	−6.59362e10	−0.408630	−0.204315	+	0.978905i	$0.565497\pi$
$54$	−2.30736e10	−0.126636
$55$	−4.09872e11	−1.99660
$56$	−1.03075e11	−0.446614
$57$	1.39523e11	0.538841
$58$	3.55061e10	0.122468
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.53021e11	0.423416
$61$	5.17079e11	1.28503	0.642515	−	0.766273i	$-0.277891\pi$
$61$	5.17079e11	1.28503	0.642515	+	0.766273i	$0.277891\pi$
$62$	−2.41100e11	−0.539077
$63$	−7.16497e10	−0.144378
$64$	4.07761e11	0.741712
$65$	7.78983e10	0.128112
$66$	−3.93793e11	−0.586452
$67$	1.40765e11	0.190112	0.0950558	−	0.995472i	$-0.469697\pi$
$67$	1.40765e11	0.190112	0.0950558	+	0.995472i	$0.469697\pi$
$68$	−2.44320e11	−0.299676
$69$	5.07573e11	0.566212
$70$	−3.62855e11	−0.368634
$71$	7.79097e11	0.721792	0.360896	−	0.932606i	$-0.382471\pi$
$71$	7.79097e11	0.721792	0.360896	+	0.932606i	$0.382471\pi$
$72$	4.06303e11	0.343708
$73$	−1.35323e12	−1.04658	−0.523289	−	0.852155i	$-0.675295\pi$
$73$	−1.35323e12	−1.04658	−0.523289	+	0.852155i	$0.675295\pi$
$74$	−3.11564e11	−0.220567
$75$	5.98814e11	0.388502
$76$	−8.88999e11	−0.529191
$77$	−1.22283e12	−0.668616
$78$	7.48425e10	0.0376299
$79$	1.33603e12	0.618356	0.309178	−	0.951004i	$-0.399946\pi$
$79$	1.33603e12	0.618356	0.309178	+	0.951004i	$0.399946\pi$
$80$	3.38098e11	0.144198
$81$	2.82430e11	0.111111
$82$	3.34277e12	1.21427
$83$	−9.97241e11	−0.334805	−0.167403	−	0.985889i	$-0.553538\pi$
$83$	−9.97241e11	−0.334805	−0.167403	+	0.985889i	$0.553538\pi$
$84$	4.56529e11	0.141792
$85$	−2.37694e12	−0.683590
$86$	−2.20957e12	−0.588935
$87$	−4.34608e11	−0.107454
$88$	6.93430e12	1.59171
$89$	6.23630e12	1.33012	0.665062	−	0.746788i	$-0.268405\pi$
$89$	6.23630e12	1.33012	0.665062	+	0.746788i	$0.268405\pi$
$90$	1.43031e12	0.283696
$91$	2.32406e11	0.0429020
$92$	−3.23409e12	−0.556073
$93$	2.95115e12	0.472990
$94$	4.35290e12	0.650800
$95$	−8.64889e12	−1.20714
$96$	−4.24092e12	−0.552964
$97$	8.66937e12	1.05675	0.528374	−	0.849012i	$-0.322802\pi$
$97$	8.66937e12	1.05675	0.528374	+	0.849012i	$0.322802\pi$
$98$	4.68786e12	0.534571
$99$	4.82017e12	0.514557
$100$	−3.81545e12	−0.381545
$101$	−7.77831e12	−0.729115	−0.364558	−	0.931181i	$-0.618780\pi$
$101$	−7.77831e12	−0.729115	−0.364558	+	0.931181i	$0.618780\pi$
$102$	−2.28370e12	−0.200788
$103$	−7.94006e12	−0.655212	−0.327606	−	0.944814i	$-0.606242\pi$
$103$	−7.94006e12	−0.655212	−0.327606	+	0.944814i	$0.606242\pi$
$104$	−1.31790e12	−0.102133
$105$	4.44148e12	0.323442
$106$	3.92696e12	0.268886
$107$	1.15110e13	0.741515	0.370757	−	0.928730i	$-0.379098\pi$
$107$	1.15110e13	0.741515	0.370757	+	0.928730i	$0.379098\pi$
$108$	−1.79955e12	−0.109121
$109$	−2.40502e13	−1.37355	−0.686777	−	0.726868i	$-0.740975\pi$
$109$	−2.40502e13	−1.37355	−0.686777	+	0.726868i	$0.740975\pi$
$110$	2.44108e13	1.31380
$111$	3.81366e12	0.193527
$112$	1.00870e12	0.0482886
$113$	1.17525e13	0.531033	0.265516	−	0.964106i	$-0.414458\pi$
$113$	1.17525e13	0.531033	0.265516	+	0.964106i	$0.414458\pi$
$114$	−8.30960e12	−0.354567
$115$	−3.14638e13	−1.26846
$116$	2.76919e12	0.105530
$117$	−9.16099e11	−0.0330168
$118$	2.51215e12	0.0856667
$119$	−7.09148e12	−0.228919
$120$	−2.51863e13	−0.769991
$121$	4.77422e13	1.38292
$122$	−3.07957e13	−0.845574
$123$	−4.09167e13	−1.06541
$124$	−1.88038e13	−0.464520
$125$	1.80436e13	0.423066
$126$	4.26724e12	0.0950033
$127$	3.63379e13	0.768486	0.384243	−	0.923232i	$-0.374463\pi$
$127$	3.63379e13	0.768486	0.384243	+	0.923232i	$0.374463\pi$
$128$	2.33715e13	0.469702
$129$	2.70459e13	0.516736
$130$	−4.63940e12	−0.0843004
$131$	−2.87549e13	−0.497106	−0.248553	−	0.968618i	$-0.579955\pi$
$131$	−2.87549e13	−0.497106	−0.248553	+	0.968618i	$0.579955\pi$
$132$	−3.07126e13	−0.505343
$133$	−2.58035e13	−0.404243
$134$	−8.38355e12	−0.125097
$135$	−1.75075e13	−0.248917
$136$	4.02136e13	0.544967
$137$	−8.80067e13	−1.13719	−0.568594	−	0.822618i	$-0.692512\pi$
$137$	−8.80067e13	−1.13719	−0.568594	+	0.822618i	$0.692512\pi$
$138$	−3.02295e13	−0.372578
$139$	−1.49388e14	−1.75679	−0.878395	−	0.477935i	$-0.841385\pi$
$139$	−1.49388e14	−1.75679	−0.878395	+	0.477935i	$0.841385\pi$
$140$	−2.82997e13	−0.317650
$141$	−5.32811e13	−0.571017
$142$	−4.64007e13	−0.474953
$143$	−1.56349e13	−0.152901
$144$	−3.97610e12	−0.0371622
$145$	2.69408e13	0.240724
$146$	8.05941e13	0.688668
$147$	−5.73812e13	−0.469037
$148$	−2.42994e13	−0.190062
$149$	1.77691e14	1.33032	0.665158	−	0.746703i	$-0.268364\pi$
$149$	1.77691e14	1.33032	0.665158	+	0.746703i	$0.268364\pi$
$150$	−3.56636e13	−0.255642
$151$	1.90855e14	1.31025	0.655124	−	0.755521i	$-0.272616\pi$
$151$	1.90855e14	1.31025	0.655124	+	0.755521i	$0.272616\pi$
$152$	1.46324e14	0.962346
$153$	2.79533e13	0.176173
$154$	7.28282e13	0.439962
$155$	−1.82938e14	−1.05962
$156$	5.83710e12	0.0324255
$157$	−1.22982e13	−0.0655378	−0.0327689	−	0.999463i	$-0.510433\pi$
$157$	−1.22982e13	−0.0655378	−0.0327689	+	0.999463i	$0.510433\pi$
$158$	−7.95698e13	−0.406890
$159$	−4.80675e13	−0.235923
$160$	2.62890e14	1.23878
$161$	−9.38707e13	−0.424778
$162$	−1.68207e13	−0.0731132
$163$	−4.25701e14	−1.77781	−0.888906	−	0.458090i	$-0.848534\pi$
$163$	−4.25701e14	−1.77781	−0.888906	+	0.458090i	$0.848534\pi$
$164$	2.60708e14	1.04633
$165$	−2.98797e14	−1.15274
$166$	5.93927e13	0.220308
$167$	1.67407e14	0.597197	0.298598	−	0.954379i	$-0.403481\pi$
$167$	1.67407e14	0.597197	0.298598	+	0.954379i	$0.403481\pi$
$168$	−7.51419e13	−0.257853
$169$	−2.99904e14	−0.990189
$170$	1.41564e14	0.449815
$171$	1.01713e14	0.311100
$172$	−1.72328e14	−0.507482
$173$	−7.92408e13	−0.224724	−0.112362	−	0.993667i	$-0.535842\pi$
$173$	−7.92408e13	−0.224724	−0.112362	+	0.993667i	$0.535842\pi$
$174$	2.58840e13	0.0707067
$175$	−1.10745e14	−0.291458
$176$	−6.78594e13	−0.172099
$177$	−3.07496e13	−0.0751646
$178$	−3.71416e14	−0.875247
$179$	4.77119e14	1.08413	0.542065	−	0.840336i	$-0.317643\pi$
$179$	4.77119e14	1.08413	0.542065	+	0.840336i	$0.317643\pi$
$180$	1.11552e14	0.244459
$181$	−8.76045e12	−0.0185189	−0.00925946	−	0.999957i	$-0.502947\pi$
$181$	−8.76045e12	−0.0185189	−0.00925946	+	0.999957i	$0.502947\pi$
$182$	−1.38414e13	−0.0282303
$183$	3.76951e14	0.741912
$184$	5.32312e14	1.01123
$185$	−2.36404e14	−0.433550
$186$	−1.75762e14	−0.311237
$187$	4.77073e14	0.815858
$188$	3.39490e14	0.560791
$189$	−5.22326e13	−0.0833566
$190$	5.15102e14	0.794319
$191$	4.85886e14	0.724132	0.362066	−	0.932153i	$-0.382072\pi$
$191$	4.85886e14	0.724132	0.362066	+	0.932153i	$0.382072\pi$
$192$	2.97257e14	0.428228
$193$	−1.31300e15	−1.82870	−0.914349	−	0.404926i	$-0.867297\pi$
$193$	−1.31300e15	−1.82870	−0.914349	+	0.404926i	$0.867297\pi$
$194$	−5.16322e14	−0.695360
$195$	5.67879e13	0.0739658
$196$	3.65615e14	0.460637
$197$	1.08128e15	1.31798	0.658991	−	0.752151i	$-0.270983\pi$
$197$	1.08128e15	1.31798	0.658991	+	0.752151i	$0.270983\pi$
$198$	−2.87075e14	−0.338588
$199$	1.77636e14	0.202762	0.101381	−	0.994848i	$-0.467674\pi$
$199$	1.77636e14	0.202762	0.101381	+	0.994848i	$0.467674\pi$
$200$	6.28000e14	0.693849
$201$	1.02618e14	0.109761
$202$	4.63253e14	0.479771
$203$	8.03766e13	0.0806130
$204$	−1.78110e14	−0.173018
$205$	2.53638e15	2.38679
$206$	4.72887e14	0.431142
$207$	3.70021e14	0.326903
$208$	1.28970e13	0.0110428
$209$	1.73591e15	1.44071
$210$	−2.64521e14	−0.212831
$211$	−4.09611e14	−0.319548	−0.159774	−	0.987154i	$-0.551077\pi$
$211$	−4.09611e14	−0.319548	−0.159774	+	0.987154i	$0.551077\pi$
$212$	3.06271e14	0.231698
$213$	5.67961e14	0.416727
$214$	−6.85563e14	−0.487931
$215$	−1.67654e15	−1.15762
$216$	2.96195e14	0.198440
$217$	−5.45787e14	−0.354842
$218$	1.43236e15	0.903824
$219$	−9.86501e14	−0.604242
$220$	1.90384e15	1.13209
$221$	−9.06703e13	−0.0523499
$222$	−2.27130e14	−0.127345
$223$	2.39484e15	1.30405	0.652025	−	0.758197i	$-0.273920\pi$
$223$	2.39484e15	1.30405	0.652025	+	0.758197i	$0.273920\pi$
$224$	7.84317e14	0.414839
$225$	4.36535e14	0.224302
$226$	−6.99946e14	−0.349429
$227$	2.73801e15	1.32821	0.664105	−	0.747639i	$-0.268813\pi$
$227$	2.73801e15	1.32821	0.664105	+	0.747639i	$0.268813\pi$
$228$	−6.48080e14	−0.305529
$229$	1.06226e15	0.486742	0.243371	−	0.969933i	$-0.421747\pi$
$229$	1.06226e15	0.486742	0.243371	+	0.969933i	$0.421747\pi$
$230$	1.87389e15	0.834668
$231$	−8.91444e14	−0.386026
$232$	−4.55791e14	−0.191908
$233$	−2.15492e15	−0.882303	−0.441151	−	0.897433i	$-0.645430\pi$
$233$	−2.15492e15	−0.882303	−0.441151	+	0.897433i	$0.645430\pi$
$234$	5.45602e13	0.0217256
$235$	3.30283e15	1.27922
$236$	1.95927e14	0.0738186
$237$	9.73963e14	0.357008
$238$	4.22348e14	0.150633
$239$	−4.00486e15	−1.38995	−0.694977	−	0.719031i	$-0.744586\pi$
$239$	−4.00486e15	−1.38995	−0.694977	+	0.719031i	$0.744586\pi$
$240$	2.46474e14	0.0832526
$241$	4.38531e15	1.44175	0.720874	−	0.693066i	$-0.243741\pi$
$241$	4.38531e15	1.44175	0.720874	+	0.693066i	$0.243741\pi$
$242$	−2.84339e15	−0.909988
$243$	2.05891e14	0.0641500
$244$	−2.40181e15	−0.728627
$245$	3.55699e15	1.05076
$246$	2.43688e15	0.701060
$247$	−3.29919e14	−0.0924436
$248$	3.09499e15	0.844741
$249$	−7.26988e14	−0.193300
$250$	−1.07462e15	−0.278386
$251$	−4.46785e15	−1.12777	−0.563884	−	0.825854i	$-0.690693\pi$
$251$	−4.46785e15	−1.12777	−0.563884	+	0.825854i	$0.690693\pi$
$252$	3.32810e14	0.0818639
$253$	6.31507e15	1.51389
$254$	−2.16418e15	−0.505678
$255$	−1.73279e15	−0.394671
$256$	−4.73231e15	−1.05078
$257$	8.62081e15	1.86631	0.933153	−	0.359479i	$-0.117046\pi$
$257$	8.62081e15	1.86631	0.933153	+	0.359479i	$0.117046\pi$
$258$	−1.61077e15	−0.340022
$259$	−7.05300e14	−0.145186
$260$	−3.61835e14	−0.0726412
$261$	−3.16829e14	−0.0620386
$262$	1.71256e15	0.327105
$263$	−4.99556e15	−0.930832	−0.465416	−	0.885092i	$-0.654095\pi$
$263$	−4.99556e15	−0.930832	−0.465416	+	0.885092i	$0.654095\pi$
$264$	5.05510e15	0.918977
$265$	2.97964e15	0.528526
$266$	1.53678e15	0.266000
$267$	4.54627e15	0.767948
$268$	−6.53848e14	−0.107795
$269$	3.62083e15	0.582664	0.291332	−	0.956622i	$-0.405902\pi$
$269$	3.62083e15	0.582664	0.291332	+	0.956622i	$0.405902\pi$
$270$	1.04269e15	0.163792
$271$	8.66129e15	1.32826	0.664129	−	0.747618i	$-0.268803\pi$
$271$	8.66129e15	1.32826	0.664129	+	0.747618i	$0.268803\pi$
$272$	−3.93532e14	−0.0589227
$273$	1.69424e14	0.0247695
$274$	5.24142e15	0.748291
$275$	7.45027e15	1.03875
$276$	−2.35765e15	−0.321049
$277$	−1.49263e15	−0.198533	−0.0992665	−	0.995061i	$-0.531650\pi$
$277$	−1.49263e15	−0.198533	−0.0992665	+	0.995061i	$0.531650\pi$
$278$	8.89712e15	1.15600
$279$	2.15139e15	0.273081
$280$	4.65795e15	0.577654
$281$	−4.11381e15	−0.498487	−0.249243	−	0.968441i	$-0.580182\pi$
$281$	−4.11381e15	−0.498487	−0.249243	+	0.968441i	$0.580182\pi$
$282$	3.17326e15	0.375740
$283$	1.32900e16	1.53784	0.768921	−	0.639343i	$-0.220794\pi$
$283$	1.32900e16	1.53784	0.768921	+	0.639343i	$0.220794\pi$
$284$	−3.61887e15	−0.409264
$285$	−6.30504e15	−0.696941
$286$	9.31168e14	0.100612
$287$	7.56714e15	0.799281
$288$	−3.09163e15	−0.319254
$289$	−7.13792e15	−0.720669
$290$	−1.60452e15	−0.158401
$291$	6.31997e15	0.610114
$292$	6.28567e15	0.593421
$293$	−8.91714e15	−0.823353	−0.411676	−	0.911330i	$-0.635057\pi$
$293$	−8.91714e15	−0.823353	−0.411676	+	0.911330i	$0.635057\pi$
$294$	3.41745e15	0.308635
$295$	1.90613e15	0.168387
$296$	3.99954e15	0.345632
$297$	3.51390e15	0.297080
$298$	−1.05827e16	−0.875372
$299$	−1.20021e15	−0.0971394
$300$	−2.78147e15	−0.220285
$301$	−5.00188e15	−0.387660
$302$	−1.13668e16	−0.862168
$303$	−5.67039e15	−0.420955
$304$	−1.43193e15	−0.104050
$305$	−2.33667e16	−1.66207
$306$	−1.66482e15	−0.115925
$307$	9.61918e15	0.655750	0.327875	−	0.944721i	$-0.393667\pi$
$307$	9.61918e15	0.655750	0.327875	+	0.944721i	$0.393667\pi$
$308$	5.68000e15	0.379113
$309$	−5.78831e15	−0.378287
$310$	1.08953e16	0.697247
$311$	−1.90887e16	−1.19628	−0.598141	−	0.801391i	$-0.704094\pi$
$311$	−1.90887e16	−1.19628	−0.598141	+	0.801391i	$0.704094\pi$
$312$	−9.60750e14	−0.0589665
$313$	−1.53859e16	−0.924881	−0.462440	−	0.886650i	$-0.653026\pi$
$313$	−1.53859e16	−0.924881	−0.462440	+	0.886650i	$0.653026\pi$
$314$	7.32442e14	0.0431251
$315$	3.23784e15	0.186740
$316$	−6.20579e15	−0.350615
$317$	1.66660e16	0.922456	0.461228	−	0.887282i	$-0.347409\pi$
$317$	1.66660e16	0.922456	0.461228	+	0.887282i	$0.347409\pi$
$318$	2.86276e15	0.155242
$319$	−5.40726e15	−0.287302
$320$	−1.84266e16	−0.959337
$321$	8.39154e15	0.428114
$322$	5.59066e15	0.279512
$323$	1.00669e16	0.493266
$324$	−1.31187e15	−0.0630013
$325$	−1.41596e15	−0.0666515
$326$	2.53535e16	1.16983
$327$	−1.75326e16	−0.793022
$328$	−4.29109e16	−1.90278
$329$	9.85382e15	0.428382
$330$	1.77954e16	0.758522
$331$	−4.11778e16	−1.72100	−0.860500	−	0.509450i	$-0.829849\pi$
$331$	−4.11778e16	−1.72100	−0.860500	+	0.509450i	$0.829849\pi$
$332$	4.63214e15	0.189838
$333$	2.78016e15	0.111733
$334$	−9.97029e15	−0.392967
$335$	−6.36115e15	−0.245892
$336$	7.35341e14	0.0278794
$337$	2.75920e16	1.02610	0.513049	−	0.858359i	$-0.328516\pi$
$337$	2.75920e16	1.02610	0.513049	+	0.858359i	$0.328516\pi$
$338$	1.78614e16	0.651563
$339$	8.56759e15	0.306592
$340$	1.10408e16	0.387603
$341$	3.67174e16	1.26464
$342$	−6.05770e15	−0.204709
$343$	2.36748e16	0.785009
$344$	2.83641e16	0.922868
$345$	−2.29371e16	−0.732344
$346$	4.71935e15	0.147872
$347$	6.36051e16	1.95592	0.977959	−	0.208799i	$-0.0669554\pi$
$347$	6.36051e16	1.95592	0.977959	+	0.208799i	$0.0669554\pi$
$348$	2.01874e15	0.0609277
$349$	1.43799e16	0.425982	0.212991	−	0.977054i	$-0.431679\pi$
$349$	1.43799e16	0.425982	0.212991	+	0.977054i	$0.431679\pi$
$350$	6.59564e15	0.191785
$351$	−6.67836e14	−0.0190622
$352$	−5.27643e16	−1.47847
$353$	1.93706e16	0.532853	0.266426	−	0.963855i	$-0.414157\pi$
$353$	1.93706e16	0.532853	0.266426	+	0.963855i	$0.414157\pi$
$354$	1.83136e15	0.0494597
$355$	−3.52073e16	−0.933572
$356$	−2.89674e16	−0.754196
$357$	−5.16969e15	−0.132166
$358$	−2.84158e16	−0.713378
$359$	2.49972e16	0.616280	0.308140	−	0.951341i	$-0.400293\pi$
$359$	2.49972e16	0.616280	0.308140	+	0.951341i	$0.400293\pi$
$360$	−1.83608e16	−0.444554
$361$	−5.42282e15	−0.128952
$362$	5.21746e14	0.0121858
$363$	3.48041e16	0.798430
$364$	−1.07951e15	−0.0243259
$365$	6.11520e16	1.35365
$366$	−2.24501e16	−0.488192
$367$	−4.85759e16	−1.03775	−0.518874	−	0.854851i	$-0.673648\pi$
$367$	−4.85759e16	−1.03775	−0.518874	+	0.854851i	$0.673648\pi$
$368$	−5.20923e15	−0.109336
$369$	−2.98283e16	−0.615115
$370$	1.40795e16	0.285284
$371$	8.88961e15	0.176991
$372$	−1.37080e16	−0.268191
$373$	−1.31338e15	−0.0252513	−0.0126256	−	0.999920i	$-0.504019\pi$
$373$	−1.31338e15	−0.0252513	−0.0126256	+	0.999920i	$0.504019\pi$
$374$	−2.84131e16	−0.536850
$375$	1.31538e16	0.244257
$376$	−5.58780e16	−1.01981
$377$	1.02768e15	0.0184348
$378$	3.11082e15	0.0548502
$379$	1.05317e16	0.182534	0.0912669	−	0.995826i	$-0.470908\pi$
$379$	1.05317e16	0.182534	0.0912669	+	0.995826i	$0.470908\pi$
$380$	4.01737e16	0.684461
$381$	2.64903e16	0.443686
$382$	−2.89379e16	−0.476492
$383$	6.55176e16	1.06063	0.530317	−	0.847799i	$-0.322073\pi$
$383$	6.55176e16	1.06063	0.530317	+	0.847799i	$0.322073\pi$
$384$	1.70379e16	0.271183
$385$	5.52595e16	0.864794
$386$	7.81984e16	1.20332
$387$	1.97165e16	0.298337
$388$	−4.02689e16	−0.599188
$389$	1.20482e17	1.76299	0.881496	−	0.472191i	$-0.156537\pi$
$389$	1.20482e17	1.76299	0.881496	+	0.472191i	$0.156537\pi$
$390$	−3.38212e15	−0.0486709
$391$	3.66226e16	0.518322
$392$	−6.01779e16	−0.837679
$393$	−2.09623e16	−0.287004
$394$	−6.43981e16	−0.867257
$395$	−6.03748e16	−0.799788
$396$	−2.23895e16	−0.291760
$397$	1.15995e17	1.48697	0.743483	−	0.668754i	$-0.233172\pi$
$397$	1.15995e17	1.48697	0.743483	+	0.668754i	$0.233172\pi$
$398$	−1.05795e16	−0.133421
$399$	−1.88107e16	−0.233390
$400$	−6.14564e15	−0.0750200
$401$	−1.24610e17	−1.49663	−0.748315	−	0.663344i	$-0.769137\pi$
$401$	−1.24610e17	−1.49663	−0.748315	+	0.663344i	$0.769137\pi$
$402$	−6.11161e15	−0.0722248
$403$	−6.97833e15	−0.0811463
$404$	3.61299e16	0.413417
$405$	−1.27629e16	−0.143712
$406$	−4.78699e15	−0.0530449
$407$	4.74484e16	0.517438
$408$	2.93157e16	0.314637
$409$	2.38763e16	0.252212	0.126106	−	0.992017i	$-0.459752\pi$
$409$	2.38763e16	0.252212	0.126106	+	0.992017i	$0.459752\pi$
$410$	−1.51059e17	−1.57055
$411$	−6.41569e16	−0.656556
$412$	3.68813e16	0.371513
$413$	5.68684e15	0.0563892
$414$	−2.20373e16	−0.215108
$415$	4.50651e16	0.433040
$416$	1.00281e16	0.0948666
$417$	−1.08904e17	−1.01428
$418$	−1.03386e17	−0.948013
$419$	3.35191e16	0.302623	0.151311	−	0.988486i	$-0.451650\pi$
$419$	3.35191e16	0.302623	0.151311	+	0.988486i	$0.451650\pi$
$420$	−2.06305e16	−0.183396
$421$	−2.88845e16	−0.252831	−0.126416	−	0.991977i	$-0.540347\pi$
$421$	−2.88845e16	−0.252831	−0.126416	+	0.991977i	$0.540347\pi$
$422$	2.43952e16	0.210268
$423$	−3.88419e16	−0.329677
$424$	−5.04103e16	−0.421348
$425$	4.32058e16	0.355643
$426$	−3.38261e16	−0.274214
$427$	−6.97134e16	−0.556590
$428$	−5.34683e16	−0.420447
$429$	−1.13978e16	−0.0882775
$430$	9.98500e16	0.761733
$431$	−1.21328e17	−0.911716	−0.455858	−	0.890053i	$-0.650667\pi$
$431$	−1.21328e17	−0.911716	−0.455858	+	0.890053i	$0.650667\pi$
$432$	−2.89858e15	−0.0214556
$433$	1.90552e16	0.138945	0.0694723	−	0.997584i	$-0.477868\pi$
$433$	1.90552e16	0.138945	0.0694723	+	0.997584i	$0.477868\pi$
$434$	3.25055e16	0.233493
$435$	1.96399e16	0.138982
$436$	1.11712e17	0.778821
$437$	1.33257e17	0.915295
$438$	5.87531e16	0.397602
$439$	−8.69195e15	−0.0579559	−0.0289780	−	0.999580i	$-0.509225\pi$
$439$	−8.69195e15	−0.0579559	−0.0289780	+	0.999580i	$0.509225\pi$
$440$	−3.13360e17	−2.05874
$441$	−4.18309e16	−0.270798
$442$	5.40006e15	0.0344472
$443$	−1.09768e16	−0.0690002	−0.0345001	−	0.999405i	$-0.510984\pi$
$443$	−1.09768e16	−0.0690002	−0.0345001	+	0.999405i	$0.510984\pi$
$444$	−1.77143e16	−0.109732
$445$	−2.81818e17	−1.72039
$446$	−1.42629e17	−0.858089
$447$	1.29537e17	0.768058
$448$	−5.49749e16	−0.321260
$449$	1.62989e17	0.938764	0.469382	−	0.882995i	$-0.344477\pi$
$449$	1.62989e17	0.938764	0.469382	+	0.882995i	$0.344477\pi$
$450$	−2.59988e16	−0.147595
$451$	−5.09073e17	−2.84861
$452$	−5.45900e16	−0.301102
$453$	1.39133e17	0.756472
$454$	−1.63068e17	−0.873987
$455$	−1.05024e16	−0.0554898
$456$	1.06670e17	0.555611
$457$	−1.14683e17	−0.588904	−0.294452	−	0.955666i	$-0.595137\pi$
$457$	−1.14683e17	−0.588904	−0.294452	+	0.955666i	$0.595137\pi$
$458$	−6.32648e16	−0.320285
$459$	2.03779e16	0.101713
$460$	1.46148e17	0.719230
$461$	4.02933e17	1.95514	0.977568	−	0.210620i	$-0.0675482\pi$
$461$	4.02933e17	1.95514	0.977568	+	0.210620i	$0.0675482\pi$
$462$	5.30918e16	0.254012
$463$	−1.40505e17	−0.662851	−0.331425	−	0.943481i	$-0.607530\pi$
$463$	−1.40505e17	−0.662851	−0.331425	+	0.943481i	$0.607530\pi$
$464$	4.46039e15	0.0207494
$465$	−1.33362e17	−0.611770
$466$	1.28341e17	0.580572
$467$	−1.70827e17	−0.762075	−0.381038	−	0.924560i	$-0.624433\pi$
$467$	−1.70827e17	−0.762075	−0.381038	+	0.924560i	$0.624433\pi$
$468$	4.25524e15	0.0187209
$469$	−1.89782e16	−0.0823437
$470$	−1.96707e17	−0.841751
$471$	−8.96535e15	−0.0378383
$472$	−3.22483e16	−0.134241
$473$	3.36497e17	1.38161
$474$	−5.80064e16	−0.234918
$475$	1.57211e17	0.628023
$476$	3.29396e16	0.129800
$477$	−3.50412e16	−0.136210
$478$	2.38518e17	0.914616
$479$	−3.06124e17	−1.15802	−0.579011	−	0.815320i	$-0.696561\pi$
$479$	−3.06124e17	−1.15802	−0.579011	+	0.815320i	$0.696561\pi$
$480$	1.91647e17	0.715209
$481$	−9.01783e15	−0.0332016
$482$	−2.61176e17	−0.948697
$483$	−6.84317e16	−0.245246
$484$	−2.21761e17	−0.784133
$485$	−3.91768e17	−1.36681
$486$	−1.22623e16	−0.0422119
$487$	1.69965e17	0.577325	0.288662	−	0.957431i	$-0.406789\pi$
$487$	1.69965e17	0.577325	0.288662	+	0.957431i	$0.406789\pi$
$488$	3.95323e17	1.32502
$489$	−3.10336e17	−1.02642
$490$	−2.11844e17	−0.691419
$491$	2.78093e17	0.895696	0.447848	−	0.894110i	$-0.352191\pi$
$491$	2.78093e17	0.895696	0.447848	+	0.894110i	$0.352191\pi$
$492$	1.90056e17	0.604100
$493$	−3.13580e16	−0.0983656
$494$	1.96490e16	0.0608296
$495$	−2.17823e17	−0.665533
$496$	−3.02877e16	−0.0913346
$497$	−1.05039e17	−0.312632
$498$	4.32973e16	0.127195
$499$	3.02691e17	0.877699	0.438849	−	0.898561i	$-0.355386\pi$
$499$	3.02691e17	0.877699	0.438849	+	0.898561i	$0.355386\pi$
$500$	−8.38118e16	−0.239883
$501$	1.22040e17	0.344792
$502$	2.66092e17	0.742092
$503$	1.29667e17	0.356975	0.178488	−	0.983942i	$-0.442880\pi$
$503$	1.29667e17	0.356975	0.178488	+	0.983942i	$0.442880\pi$
$504$	−5.47784e16	−0.148871
$505$	3.51500e17	0.943044
$506$	−3.76107e17	−0.996169
$507$	−2.18630e17	−0.571686
$508$	−1.68788e17	−0.435740
$509$	−2.39374e17	−0.610114	−0.305057	−	0.952334i	$-0.598675\pi$
$509$	−2.39374e17	−0.610114	−0.305057	+	0.952334i	$0.598675\pi$
$510$	1.03200e17	0.259701
$511$	1.82444e17	0.453308
$512$	9.03830e16	0.221734
$513$	7.41484e16	0.179614
$514$	−5.13430e17	−1.22806
$515$	3.58810e17	0.847457
$516$	−1.25627e17	−0.292995
$517$	−6.62908e17	−1.52674
$518$	4.20056e16	0.0955352
$519$	−5.77665e16	−0.129744
$520$	5.95557e16	0.132100
$521$	3.97041e17	0.869742	0.434871	−	0.900493i	$-0.356794\pi$
$521$	3.97041e17	0.869742	0.434871	+	0.900493i	$0.356794\pi$
$522$	1.88694e16	0.0408226
$523$	−6.11723e16	−0.130706	−0.0653528	−	0.997862i	$-0.520817\pi$
$523$	−6.11723e16	−0.130706	−0.0653528	+	0.997862i	$0.520817\pi$
$524$	1.33565e17	0.281865
$525$	−8.07330e16	−0.168273
$526$	2.97521e17	0.612505
$527$	2.12932e17	0.432985
$528$	−4.94695e16	−0.0993612
$529$	−1.92597e16	−0.0382109
$530$	−1.77459e17	−0.347780
$531$	−2.24165e16	−0.0433963
$532$	1.19856e17	0.229211
$533$	9.67521e16	0.182782
$534$	−2.70762e17	−0.505324
$535$	−5.20182e17	−0.959082
$536$	1.07619e17	0.196028
$537$	3.47819e17	0.625923
$538$	−2.15646e17	−0.383404
$539$	−7.13920e17	−1.25407
$540$	8.13215e16	0.141139
$541$	−2.03828e17	−0.349527	−0.174764	−	0.984610i	$-0.555916\pi$
$541$	−2.03828e17	−0.349527	−0.174764	+	0.984610i	$0.555916\pi$
$542$	−5.15841e17	−0.874018
$543$	−6.38637e15	−0.0106919
$544$	−3.05992e17	−0.506195
$545$	1.08682e18	1.77657
$546$	−1.00904e16	−0.0162988
$547$	−1.15064e17	−0.183663	−0.0918317	−	0.995775i	$-0.529272\pi$
$547$	−1.15064e17	−0.183663	−0.0918317	+	0.995775i	$0.529272\pi$
$548$	4.08788e17	0.644799
$549$	2.74797e17	0.428343
$550$	−4.43716e17	−0.683514
$551$	−1.14101e17	−0.173702
$552$	3.88055e17	0.583834
$553$	−1.80125e17	−0.267831
$554$	8.88964e16	0.130638
$555$	−1.72339e17	−0.250310
$556$	6.93902e17	0.996120
$557$	−7.47413e17	−1.06048	−0.530239	−	0.847848i	$-0.677898\pi$
$557$	−7.47413e17	−1.06048	−0.530239	+	0.847848i	$0.677898\pi$
$558$	−1.28130e17	−0.179692
$559$	−6.39531e16	−0.0886512
$560$	−4.55829e16	−0.0624569
$561$	3.47786e17	0.471036
$562$	2.45007e17	0.328013
$563$	−2.82012e16	−0.0373218	−0.0186609	−	0.999826i	$-0.505940\pi$
$563$	−2.82012e16	−0.0373218	−0.0186609	+	0.999826i	$0.505940\pi$
$564$	2.47488e17	0.323773
$565$	−5.31095e17	−0.686842
$566$	−7.91511e17	−1.01193
$567$	−3.80776e16	−0.0481260
$568$	5.95644e17	0.744256
$569$	−5.71155e17	−0.705544	−0.352772	−	0.935709i	$-0.614761\pi$
$569$	−5.71155e17	−0.705544	−0.352772	+	0.935709i	$0.614761\pi$
$570$	3.75509e17	0.458600
$571$	−2.15094e17	−0.259712	−0.129856	−	0.991533i	$-0.541452\pi$
$571$	−2.15094e17	−0.259712	−0.129856	+	0.991533i	$0.541452\pi$
$572$	7.26234e16	0.0866967
$573$	3.54211e17	0.418078
$574$	−4.50677e17	−0.525942
$575$	5.71920e17	0.659925
$576$	2.16701e17	0.247237
$577$	−2.62228e17	−0.295826	−0.147913	−	0.989000i	$-0.547256\pi$
$577$	−2.62228e17	−0.295826	−0.147913	+	0.989000i	$0.547256\pi$
$578$	4.25113e17	0.474213
$579$	−9.57177e17	−1.05580
$580$	−1.25139e17	−0.136493
$581$	1.34449e17	0.145015
$582$	−3.76399e17	−0.401466
$583$	−5.98041e17	−0.630791
$584$	−1.03458e18	−1.07915
$585$	4.13984e16	0.0427042
$586$	5.31079e17	0.541782
$587$	1.05272e18	1.06210	0.531052	−	0.847339i	$-0.321797\pi$
$587$	1.05272e18	1.06210	0.531052	+	0.847339i	$0.321797\pi$
$588$	2.66533e17	0.265949
$589$	7.74789e17	0.764599
$590$	−1.13524e17	−0.110802
$591$	7.88256e17	0.760937
$592$	−3.91396e16	−0.0373702
$593$	4.55448e17	0.430114	0.215057	−	0.976602i	$-0.431006\pi$
$593$	4.55448e17	0.430114	0.215057	+	0.976602i	$0.431006\pi$
$594$	−2.09278e17	−0.195484
$595$	3.20463e17	0.296086
$596$	−8.25367e17	−0.754304
$597$	1.29497e17	0.117065
$598$	7.14811e16	0.0639196
$599$	8.24583e17	0.729391	0.364695	−	0.931127i	$-0.381173\pi$
$599$	8.24583e17	0.729391	0.364695	+	0.931127i	$0.381173\pi$
$600$	4.57812e17	0.400594
$601$	−1.28978e17	−0.111643	−0.0558215	−	0.998441i	$-0.517778\pi$
$601$	−1.28978e17	−0.111643	−0.0558215	+	0.998441i	$0.517778\pi$
$602$	2.97897e17	0.255087
$603$	7.48083e16	0.0633705
$604$	−8.86514e17	−0.742926
$605$	−2.15746e18	−1.78868
$606$	3.37711e17	0.276996
$607$	−3.83628e17	−0.311303	−0.155652	−	0.987812i	$-0.549748\pi$
$607$	−3.83628e17	−0.311303	−0.155652	+	0.987812i	$0.549748\pi$
$608$	−1.11340e18	−0.893879
$609$	5.85945e16	0.0465419
$610$	1.39165e18	1.09367
$611$	1.25989e17	0.0979637
$612$	−1.29842e17	−0.0998919
$613$	1.02087e16	0.00777104	0.00388552	−	0.999992i	$-0.498763\pi$
$613$	1.02087e16	0.00777104	0.00388552	+	0.999992i	$0.498763\pi$
$614$	−5.72890e17	−0.431496
$615$	1.84902e18	1.37801
$616$	−9.34893e17	−0.689425
$617$	1.89669e18	1.38402	0.692010	−	0.721888i	$-0.256726\pi$
$617$	1.89669e18	1.38402	0.692010	+	0.721888i	$0.256726\pi$
$618$	3.44734e17	0.248920
$619$	3.10704e17	0.222003	0.111001	−	0.993820i	$-0.464594\pi$
$619$	3.10704e17	0.222003	0.111001	+	0.993820i	$0.464594\pi$
$620$	8.49741e17	0.600815
$621$	2.69745e17	0.188737
$622$	1.13687e18	0.787175
$623$	−8.40788e17	−0.576122
$624$	9.40194e15	0.00637555
$625$	−1.81810e18	−1.22010
$626$	9.16341e17	0.608589
$627$	1.26548e18	0.831793
$628$	5.71244e16	0.0371607
$629$	2.75164e17	0.177159
$630$	−1.92836e17	−0.122878
$631$	5.18274e17	0.326865	0.163433	−	0.986555i	$-0.447743\pi$
$631$	5.18274e17	0.326865	0.163433	+	0.986555i	$0.447743\pi$
$632$	1.02143e18	0.637601
$633$	−2.98607e17	−0.184491
$634$	−9.92576e17	−0.606993
$635$	−1.64210e18	−0.993966
$636$	2.23271e17	0.133771
$637$	1.35684e17	0.0804680
$638$	3.22041e17	0.189050
$639$	4.14044e17	0.240597
$640$	−1.05616e18	−0.607517
$641$	1.84752e18	1.05199	0.525995	−	0.850488i	$-0.323693\pi$
$641$	1.84752e18	1.05199	0.525995	+	0.850488i	$0.323693\pi$
$642$	−4.99776e17	−0.281707
$643$	−1.43063e18	−0.798279	−0.399140	−	0.916890i	$-0.630691\pi$
$643$	−1.43063e18	−0.798279	−0.399140	+	0.916890i	$0.630691\pi$
$644$	4.36025e17	0.240854
$645$	−1.22220e18	−0.668350
$646$	−5.99557e17	−0.324578
$647$	3.09734e17	0.166001	0.0830004	−	0.996550i	$-0.473550\pi$
$647$	3.09734e17	0.166001	0.0830004	+	0.996550i	$0.473550\pi$
$648$	2.15926e17	0.114569
$649$	−3.82578e17	−0.200969
$650$	8.43306e16	0.0438579
$651$	−3.97879e17	−0.204868
$652$	1.97736e18	1.00804
$653$	−1.28762e18	−0.649907	−0.324953	−	0.945730i	$-0.605349\pi$
$653$	−1.28762e18	−0.649907	−0.324953	+	0.945730i	$0.605349\pi$
$654$	1.04419e18	0.521823
$655$	1.29943e18	0.642961
$656$	4.19928e17	0.205731
$657$	−7.19159e17	−0.348859
$658$	−5.86865e17	−0.281883
$659$	3.11431e18	1.48118	0.740589	−	0.671959i	$-0.234547\pi$
$659$	3.11431e18	1.48118	0.740589	+	0.671959i	$0.234547\pi$
$660$	1.38790e18	0.653615
$661$	1.19424e18	0.556908	0.278454	−	0.960450i	$-0.410178\pi$
$661$	1.19424e18	0.556908	0.278454	+	0.960450i	$0.410178\pi$
$662$	2.45243e18	1.13245
$663$	−6.60987e16	−0.0302242
$664$	−7.62422e17	−0.345225
$665$	1.16606e18	0.522852
$666$	−1.65578e17	−0.0735225
$667$	−4.15089e17	−0.182525
$668$	−7.77600e17	−0.338617
$669$	1.74584e18	0.752894
$670$	3.78851e17	0.161802
$671$	4.68991e18	1.98366
$672$	5.71767e17	0.239507
$673$	1.38397e18	0.574156	0.287078	−	0.957907i	$-0.407316\pi$
$673$	1.38397e18	0.574156	0.287078	+	0.957907i	$0.407316\pi$
$674$	−1.64330e18	−0.675192
$675$	3.18234e17	0.129501
$676$	1.39304e18	0.561449
$677$	1.01189e18	0.403929	0.201965	−	0.979393i	$-0.435267\pi$
$677$	1.01189e18	0.403929	0.201965	+	0.979393i	$0.435267\pi$
$678$	−5.10260e17	−0.201743
$679$	−1.16882e18	−0.457713
$680$	−1.81725e18	−0.704865
$681$	1.99601e18	0.766843
$682$	−2.18678e18	−0.832159
$683$	9.89456e17	0.372960	0.186480	−	0.982459i	$-0.440292\pi$
$683$	9.89456e17	0.372960	0.186480	+	0.982459i	$0.440292\pi$
$684$	−4.72450e17	−0.176397
$685$	3.97701e18	1.47085
$686$	−1.41000e18	−0.516551
$687$	7.74385e17	0.281020
$688$	−2.77572e17	−0.0997818
$689$	1.13661e17	0.0404749
$690$	1.36607e18	0.481896
$691$	−5.17046e17	−0.180685	−0.0903425	−	0.995911i	$-0.528796\pi$
$691$	−5.17046e17	−0.180685	−0.0903425	+	0.995911i	$0.528796\pi$
$692$	3.68070e17	0.127421
$693$	−6.49863e17	−0.222872
$694$	−3.78813e18	−1.28703
$695$	6.75083e18	2.27225
$696$	−3.32271e17	−0.110798
$697$	−2.95223e18	−0.975298
$698$	−8.56426e17	−0.280304
$699$	−1.57094e18	−0.509398
$700$	5.14405e17	0.165260
$701$	1.68136e18	0.535174	0.267587	−	0.963534i	$-0.413774\pi$
$701$	1.68136e18	0.535174	0.267587	+	0.963534i	$0.413774\pi$
$702$	3.97744e16	0.0125433
$703$	1.00123e18	0.312841
$704$	3.69839e18	1.14496
$705$	2.40776e18	0.738558
$706$	−1.15366e18	−0.350627
$707$	1.04868e18	0.315804
$708$	1.42831e17	0.0426192
$709$	−6.90252e17	−0.204083	−0.102042	−	0.994780i	$-0.532537\pi$
$709$	−6.90252e17	−0.204083	−0.102042	+	0.994780i	$0.532537\pi$
$710$	2.09684e18	0.614308
$711$	7.10019e17	0.206119
$712$	4.76785e18	1.37152
$713$	2.81861e18	0.803439
$714$	3.07891e17	0.0869680
$715$	7.06538e17	0.197764
$716$	−2.21620e18	−0.614714
$717$	−2.91954e18	−0.802491
$718$	−1.48876e18	−0.405524
$719$	5.40242e18	1.45831	0.729156	−	0.684347i	$-0.239913\pi$
$719$	5.40242e18	1.45831	0.729156	+	0.684347i	$0.239913\pi$
$720$	1.79679e17	0.0480659
$721$	1.07049e18	0.283794
$722$	3.22967e17	0.0848529
$723$	3.19689e18	0.832394
$724$	4.06919e16	0.0105004
$725$	−4.89705e17	−0.125238
$726$	−2.07283e18	−0.525382
$727$	−1.24875e18	−0.313690	−0.156845	−	0.987623i	$-0.550132\pi$
$727$	−1.24875e18	−0.313690	−0.156845	+	0.987623i	$0.550132\pi$
$728$	1.77681e17	0.0442372
$729$	1.50095e17	0.0370370
$730$	−3.64203e18	−0.890729
$731$	1.95142e18	0.473030
$732$	−1.75092e18	−0.420673
$733$	4.46147e18	1.06243	0.531217	−	0.847236i	$-0.321735\pi$
$733$	4.46147e18	1.06243	0.531217	+	0.847236i	$0.321735\pi$
$734$	2.89304e18	0.682857
$735$	2.59305e18	0.606656
$736$	−4.05045e18	−0.939286
$737$	1.27674e18	0.293470
$738$	1.77648e18	0.404757
$739$	−5.61390e17	−0.126787	−0.0633936	−	0.997989i	$-0.520192\pi$
$739$	−5.61390e17	−0.126787	−0.0633936	+	0.997989i	$0.520192\pi$
$740$	1.09809e18	0.245828
$741$	−2.40511e17	−0.0533723
$742$	−5.29439e17	−0.116464
$743$	−8.20357e18	−1.78886	−0.894429	−	0.447210i	$-0.852418\pi$
$743$	−8.20357e18	−1.78886	−0.894429	+	0.447210i	$0.852418\pi$
$744$	2.25625e18	0.487711
$745$	−8.02982e18	−1.72064
$746$	7.82211e16	0.0166158
$747$	−5.29974e17	−0.111602
$748$	−2.21599e18	−0.462601
$749$	−1.55194e18	−0.321175
$750$	−7.83401e17	−0.160726
$751$	−8.99630e18	−1.82980	−0.914901	−	0.403677i	$-0.867732\pi$
$751$	−8.99630e18	−1.82980	−0.914901	+	0.403677i	$0.867732\pi$
$752$	5.46825e17	0.110264
$753$	−3.25706e18	−0.651117
$754$	−6.12056e16	−0.0121305
$755$	−8.62471e18	−1.69469
$756$	2.42618e17	0.0472641
$757$	2.59715e18	0.501619	0.250809	−	0.968037i	$-0.419303\pi$
$757$	2.59715e18	0.501619	0.250809	+	0.968037i	$0.419303\pi$
$758$	−6.27237e17	−0.120111
$759$	4.60369e18	0.874046
$760$	−6.61234e18	−1.24471
$761$	−5.82680e18	−1.08750	−0.543751	−	0.839247i	$-0.682996\pi$
$761$	−5.82680e18	−1.08750	−0.543751	+	0.839247i	$0.682996\pi$
$762$	−1.57769e18	−0.291953
$763$	3.24248e18	0.594932
$764$	−2.25692e18	−0.410591
$765$	−1.26320e18	−0.227863
$766$	−3.90203e18	−0.697917
$767$	7.27109e16	0.0128952
$768$	−3.44986e18	−0.606671
$769$	−2.94972e18	−0.514352	−0.257176	−	0.966365i	$-0.582792\pi$
$769$	−2.94972e18	−0.514352	−0.257176	+	0.966365i	$0.582792\pi$
$770$	−3.29110e18	−0.569050
$771$	6.28457e18	1.07751
$772$	6.09883e18	1.03689
$773$	5.71839e18	0.964066	0.482033	−	0.876153i	$-0.339899\pi$
$773$	5.71839e18	0.964066	0.482033	+	0.876153i	$0.339899\pi$
$774$	−1.17425e18	−0.196312
$775$	3.32528e18	0.551274
$776$	6.62801e18	1.08964
$777$	−5.14163e17	−0.0838233
$778$	−7.17557e18	−1.16008
$779$	−1.07422e19	−1.72226
$780$	−2.63777e17	−0.0419394
$781$	7.06641e18	1.11421
$782$	−2.18113e18	−0.341066
$783$	−2.30969e17	−0.0358180
$784$	5.88904e17	0.0905712
$785$	5.55751e17	0.0847672
$786$	1.24846e18	0.188854
$787$	6.57880e18	0.986985	0.493493	−	0.869750i	$-0.335720\pi$
$787$	6.57880e18	0.986985	0.493493	+	0.869750i	$0.335720\pi$
$788$	−5.02252e18	−0.747311
$789$	−3.64176e18	−0.537416
$790$	3.59575e18	0.526275
$791$	−1.58449e18	−0.230008
$792$	3.68517e18	0.530572
$793$	−8.91342e17	−0.127283
$794$	−6.90832e18	−0.978452
$795$	2.17216e18	0.305145
$796$	−8.25112e17	−0.114968
$797$	−1.87746e18	−0.259473	−0.129736	−	0.991549i	$-0.541413\pi$
$797$	−1.87746e18	−0.259473	−0.129736	+	0.991549i	$0.541413\pi$
$798$	1.12031e18	0.153575
$799$	−3.84435e18	−0.522720
$800$	−4.77856e18	−0.644484
$801$	3.31423e18	0.443375
$802$	7.42140e18	0.984810
$803$	−1.22738e19	−1.61557
$804$	−4.76655e17	−0.0622357
$805$	4.24200e18	0.549411
$806$	4.15609e17	0.0533958
$807$	2.63959e18	0.336401
$808$	−5.94676e18	−0.751807
$809$	−3.09582e17	−0.0388249	−0.0194124	−	0.999812i	$-0.506180\pi$
$809$	−3.09582e17	−0.0388249	−0.0194124	+	0.999812i	$0.506180\pi$
$810$	7.60123e17	0.0945652
$811$	−6.98595e18	−0.862164	−0.431082	−	0.902313i	$-0.641868\pi$
$811$	−6.98595e18	−0.862164	−0.431082	+	0.902313i	$0.641868\pi$
$812$	−3.73346e17	−0.0457085
$813$	6.31408e18	0.766870
$814$	−2.82589e18	−0.340484
$815$	1.92374e19	2.29944
$816$	−2.86885e17	−0.0340190
$817$	7.10057e18	0.835315
$818$	−1.42200e18	−0.165960
$819$	1.23510e17	0.0143007
$820$	−1.17814e19	−1.35333
$821$	9.33305e18	1.06364	0.531818	−	0.846859i	$-0.321509\pi$
$821$	9.33305e18	1.06364	0.531818	+	0.846859i	$0.321509\pi$
$822$	3.82100e18	0.432026
$823$	5.87090e18	0.658576	0.329288	−	0.944230i	$-0.393191\pi$
$823$	5.87090e18	0.658576	0.329288	+	0.944230i	$0.393191\pi$
$824$	−6.07043e18	−0.675604
$825$	5.43124e18	0.599720
$826$	−3.38692e17	−0.0371051
$827$	−1.37779e19	−1.49761	−0.748803	−	0.662793i	$-0.769371\pi$
$827$	−1.37779e19	−1.49761	−0.748803	+	0.662793i	$0.769371\pi$
$828$	−1.71873e18	−0.185358
$829$	−2.95388e18	−0.316074	−0.158037	−	0.987433i	$-0.550516\pi$
$829$	−2.95388e18	−0.316074	−0.158037	+	0.987433i	$0.550516\pi$
$830$	−2.68395e18	−0.284948
$831$	−1.08812e18	−0.114623
$832$	−7.02899e17	−0.0734668
$833$	−4.14018e18	−0.429366
$834$	6.48600e18	0.667417
$835$	−7.56511e18	−0.772420
$836$	−8.06322e18	−0.816898
$837$	1.56836e18	0.157663
$838$	−1.99630e18	−0.199132
$839$	−9.73635e18	−0.963704	−0.481852	−	0.876253i	$-0.660036\pi$
$839$	−9.73635e18	−0.963704	−0.481852	+	0.876253i	$0.660036\pi$
$840$	3.39565e18	0.333509
$841$	−9.90521e18	−0.965361
$842$	1.72027e18	0.166368
$843$	−2.99897e18	−0.287801
$844$	1.90263e18	0.181187
$845$	1.35526e19	1.28072
$846$	2.31331e18	0.216933
$847$	−6.43668e18	−0.598990
$848$	4.93317e17	0.0455568
$849$	9.68838e18	0.887874
$850$	−2.57321e18	−0.234020
$851$	3.64238e18	0.328733
$852$	−2.63816e18	−0.236289
$853$	7.50937e18	0.667475	0.333737	−	0.942666i	$-0.391690\pi$
$853$	7.50937e18	0.667475	0.333737	+	0.942666i	$0.391690\pi$
$854$	4.15192e18	0.366246
$855$	−4.59637e18	−0.402379
$856$	8.80055e18	0.764593
$857$	1.31637e19	1.13502	0.567511	−	0.823366i	$-0.307907\pi$
$857$	1.31637e19	1.13502	0.567511	+	0.823366i	$0.307907\pi$
$858$	6.78821e17	0.0580882
$859$	−1.51845e19	−1.28957	−0.644783	−	0.764365i	$-0.723052\pi$
$859$	−1.51845e19	−1.28957	−0.644783	+	0.764365i	$0.723052\pi$
$860$	7.78747e18	0.656382
$861$	5.51645e18	0.461465
$862$	7.22595e18	0.599926
$863$	−1.82119e19	−1.50067	−0.750333	−	0.661060i	$-0.770107\pi$
$863$	−1.82119e19	−1.50067	−0.750333	+	0.661060i	$0.770107\pi$
$864$	−2.25380e18	−0.184321
$865$	3.58088e18	0.290660
$866$	−1.13487e18	−0.0914281
$867$	−5.20354e18	−0.416078
$868$	2.53516e18	0.201199
$869$	1.21178e19	0.954539
$870$	−1.16969e18	−0.0914527
$871$	−2.42651e17	−0.0188306
$872$	−1.83871e19	−1.41630
$873$	4.60726e18	0.352249
$874$	−7.93640e18	−0.602281
$875$	−2.43267e18	−0.183244
$876$	4.58226e18	0.342612
$877$	−1.82543e19	−1.35478	−0.677388	−	0.735626i	$-0.736888\pi$
$877$	−1.82543e19	−1.35478	−0.677388	+	0.735626i	$0.736888\pi$
$878$	5.17667e17	0.0381361
$879$	−6.50059e18	−0.475363
$880$	3.06655e18	0.222594
$881$	−1.73508e19	−1.25019	−0.625096	−	0.780548i	$-0.714940\pi$
$881$	−1.73508e19	−1.25019	−0.625096	+	0.780548i	$0.714940\pi$
$882$	2.49132e18	0.178190
$883$	−2.73186e19	−1.93960	−0.969802	−	0.243892i	$-0.921576\pi$
$883$	−2.73186e19	−1.93960	−0.969802	+	0.243892i	$0.921576\pi$
$884$	4.21160e17	0.0296830
$885$	1.38957e18	0.0972185
$886$	6.53744e17	0.0454034
$887$	−2.81597e17	−0.0194144	−0.00970721	−	0.999953i	$-0.503090\pi$
$887$	−2.81597e17	−0.0194144	−0.00970721	+	0.999953i	$0.503090\pi$
$888$	2.91566e18	0.199551
$889$	−4.89913e18	−0.332857
$890$	1.67842e19	1.13205
$891$	2.56164e18	0.171519
$892$	−1.11239e19	−0.739411
$893$	−1.39883e19	−0.923061
$894$	−7.71482e18	−0.505396
$895$	−2.15609e19	−1.40222
$896$	−3.15099e18	−0.203444
$897$	−8.74955e17	−0.0560835
$898$	−9.70713e18	−0.617724
$899$	−2.41343e18	−0.152474
$900$	−2.02769e18	−0.127182
$901$	−3.46818e18	−0.215968
$902$	3.03189e19	1.87444
$903$	−3.64637e18	−0.223816
$904$	8.98517e18	0.547560
$905$	3.95883e17	0.0239525
$906$	−8.28637e18	−0.497773
$907$	8.76691e17	0.0522877	0.0261438	−	0.999658i	$-0.491677\pi$
$907$	8.76691e17	0.0522877	0.0261438	+	0.999658i	$0.491677\pi$
$908$	−1.27179e19	−0.753110
$909$	−4.13371e18	−0.243038
$910$	6.25490e17	0.0365133
$911$	7.44433e18	0.431475	0.215738	−	0.976451i	$-0.430784\pi$
$911$	7.44433e18	0.431475	0.215738	+	0.976451i	$0.430784\pi$
$912$	−1.04388e18	−0.0600735
$913$	−9.04497e18	−0.516829
$914$	6.83019e18	0.387510
$915$	−1.70343e19	−0.959596
$916$	−4.93413e18	−0.275988
$917$	3.87678e18	0.215313
$918$	−1.21365e18	−0.0669293
$919$	−2.98040e18	−0.163202	−0.0816008	−	0.996665i	$-0.526003\pi$
$919$	−2.98040e18	−0.163202	−0.0816008	+	0.996665i	$0.526003\pi$
$920$	−2.40551e19	−1.30793
$921$	7.01238e18	0.378598
$922$	−2.39975e19	−1.28652
$923$	−1.34301e18	−0.0714937
$924$	4.14072e18	0.218881
$925$	4.29713e18	0.225558
$926$	8.36807e18	0.436168
$927$	−4.21968e18	−0.218404
$928$	3.46819e18	0.178255
$929$	3.31642e19	1.69265	0.846324	−	0.532668i	$-0.178810\pi$
$929$	3.31642e19	1.69265	0.846324	+	0.532668i	$0.178810\pi$
$930$	7.94265e18	0.402556
$931$	−1.50647e19	−0.758208
$932$	1.00095e19	0.500276
$933$	−1.39156e19	−0.690673
$934$	1.01740e19	0.501460
$935$	−2.15589e19	−1.05524
$936$	−7.00387e17	−0.0340443
$937$	5.45377e18	0.263263	0.131631	−	0.991299i	$-0.457978\pi$
$937$	5.45377e18	0.263263	0.131631	+	0.991299i	$0.457978\pi$
$938$	1.13028e18	0.0541837
$939$	−1.12163e19	−0.533980
$940$	−1.53415e19	−0.725332
$941$	1.56407e19	0.734383	0.367192	−	0.930145i	$-0.380319\pi$
$941$	1.56407e19	0.734383	0.367192	+	0.930145i	$0.380319\pi$
$942$	5.33950e17	0.0248983
$943$	−3.90790e19	−1.80975
$944$	3.15584e17	0.0145143
$945$	2.36038e18	0.107814
$946$	−2.00408e19	−0.909122
$947$	2.79136e19	1.25760	0.628798	−	0.777569i	$-0.283547\pi$
$947$	2.79136e19	1.25760	0.628798	+	0.777569i	$0.283547\pi$
$948$	−4.52402e18	−0.202428
$949$	2.33269e18	0.103664
$950$	−9.36304e18	−0.413251
$951$	1.21495e19	0.532580
$952$	−5.42166e18	−0.236044
$953$	4.06069e19	1.75588	0.877942	−	0.478767i	$-0.158916\pi$
$953$	4.06069e19	1.75588	0.877942	+	0.478767i	$0.158916\pi$
$954$	2.08695e18	0.0896288
$955$	−2.19571e19	−0.936598
$956$	1.86024e19	0.788120
$957$	−3.94190e18	−0.165874
$958$	1.82318e19	0.762000
$959$	1.18652e19	0.492554
$960$	−1.34330e19	−0.553873
$961$	−8.02947e18	−0.328840
$962$	5.37075e17	0.0218473
$963$	6.11744e18	0.247172
$964$	−2.03696e19	−0.817488
$965$	5.93343e19	2.36525
$966$	4.07559e18	0.161376
$967$	5.39868e18	0.212332	0.106166	−	0.994348i	$-0.466143\pi$
$967$	5.39868e18	0.212332	0.106166	+	0.994348i	$0.466143\pi$
$968$	3.65004e19	1.42596
$969$	7.33880e18	0.284787
$970$	2.33325e19	0.899385
$971$	1.69667e19	0.649639	0.324819	−	0.945776i	$-0.394696\pi$
$971$	1.69667e19	0.649639	0.324819	+	0.945776i	$0.394696\pi$
$972$	−9.56356e17	−0.0363738
$973$	2.01407e19	0.760925
$974$	−1.01226e19	−0.379891
$975$	−1.03224e18	−0.0384813
$976$	−3.86865e18	−0.143264
$977$	−2.06032e19	−0.757914	−0.378957	−	0.925414i	$-0.623717\pi$
$977$	−2.06032e19	−0.757914	−0.378957	+	0.925414i	$0.623717\pi$
$978$	1.84827e19	0.675403
$979$	5.65633e19	2.05328
$980$	−1.65221e19	−0.595792
$981$	−1.27812e19	−0.457851
$982$	−1.65624e19	−0.589385
$983$	−2.09589e19	−0.740918	−0.370459	−	0.928849i	$-0.620800\pi$
$983$	−2.09589e19	−0.740918	−0.370459	+	0.928849i	$0.620800\pi$
$984$	−3.12821e19	−1.09857
$985$	−4.88631e19	−1.70469
$986$	1.86759e18	0.0647264
$987$	7.18344e18	0.247327
$988$	1.53246e18	0.0524166
$989$	2.58312e19	0.877746
$990$	1.29729e19	0.437933
$991$	−1.89520e19	−0.635588	−0.317794	−	0.948160i	$-0.602942\pi$
$991$	−1.89520e19	−0.635588	−0.317794	+	0.948160i	$0.602942\pi$
$992$	−2.35503e19	−0.784641
$993$	−3.00186e19	−0.993620
$994$	6.25581e18	0.205718
$995$	−8.02734e18	−0.262254
$996$	3.37683e18	0.109603
$997$	4.77772e19	1.54064	0.770322	−	0.637655i	$-0.220095\pi$
$997$	4.77772e19	1.54064	0.770322	+	0.637655i	$0.220095\pi$
$998$	−1.80274e19	−0.577542
$999$	2.02674e18	0.0645092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.11	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-59.5570 q^{2} +729.000 q^{3} -4644.96 q^{4} -45189.8 q^{5} -43417.1 q^{6} -134821. q^{7} +764531. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-59.5570 q^{2} +729.000 q^{3} -4644.96 q^{4} -45189.8 q^{5} -43417.1 q^{6} -134821. q^{7} +764531. q^{8} +531441. q^{9} +2.69137e6 q^{10} +9.07000e6 q^{11} -3.38617e6 q^{12} -1.72380e6 q^{13} +8.02957e6 q^{14} -3.29434e7 q^{15} -7.48174e6 q^{16} +5.25990e7 q^{17} -3.16511e7 q^{18} +1.91390e8 q^{19} +2.09905e8 q^{20} -9.82849e7 q^{21} -5.40183e8 q^{22} +6.96259e8 q^{23} +5.57343e8 q^{24} +8.21418e8 q^{25} +1.02665e8 q^{26} +3.87420e8 q^{27} +6.26240e8 q^{28} -5.96170e8 q^{29} +1.96201e9 q^{30} +4.04822e9 q^{31} -5.81745e9 q^{32} +6.61203e9 q^{33} -3.13264e9 q^{34} +6.09256e9 q^{35} -2.46852e9 q^{36} +5.23136e9 q^{37} -1.13986e10 q^{38} -1.25665e9 q^{39} -3.45490e10 q^{40} -5.61271e10 q^{41} +5.85356e9 q^{42} +3.71000e10 q^{43} -4.21298e10 q^{44} -2.40157e10 q^{45} -4.14671e10 q^{46} -7.30879e10 q^{47} -5.45419e9 q^{48} -7.87122e10 q^{49} -4.89213e10 q^{50} +3.83447e10 q^{51} +8.00699e9 q^{52} -6.59362e10 q^{53} -2.30736e10 q^{54} -4.09872e11 q^{55} -1.03075e11 q^{56} +1.39523e11 q^{57} +3.55061e10 q^{58} -4.21805e10 q^{59} +1.53021e11 q^{60} +5.17079e11 q^{61} -2.41100e11 q^{62} -7.16497e10 q^{63} +4.07761e11 q^{64} +7.78983e10 q^{65} -3.93793e11 q^{66} +1.40765e11 q^{67} -2.44320e11 q^{68} +5.07573e11 q^{69} -3.62855e11 q^{70} +7.79097e11 q^{71} +4.06303e11 q^{72} -1.35323e12 q^{73} -3.11564e11 q^{74} +5.98814e11 q^{75} -8.88999e11 q^{76} -1.22283e12 q^{77} +7.48425e10 q^{78} +1.33603e12 q^{79} +3.38098e11 q^{80} +2.82430e11 q^{81} +3.34277e12 q^{82} -9.97241e11 q^{83} +4.56529e11 q^{84} -2.37694e12 q^{85} -2.20957e12 q^{86} -4.34608e11 q^{87} +6.93430e12 q^{88} +6.23630e12 q^{89} +1.43031e12 q^{90} +2.32406e11 q^{91} -3.23409e12 q^{92} +2.95115e12 q^{93} +4.35290e12 q^{94} -8.64889e12 q^{95} -4.24092e12 q^{96} +8.66937e12 q^{97} +4.68786e12 q^{98} +4.82017e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 310 q^{2} + 22599 q^{3} + 126886 q^{4} + 81008 q^{5} + 225990 q^{6} + 1002941 q^{7} + 4632723 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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