LMFDB - Embedded newform 177.9.c.a.58.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,9,Mod(58,177)]

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, 1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	177.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$72.1060139808$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.18
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.63

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20.4085i q^{2} -46.7654 q^{3} -160.507 q^{4} -745.364 q^{5} +954.411i q^{6} -9.58116 q^{7} -1948.88i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q-20.4085i q^{2} -46.7654 q^{3} -160.507 q^{4} -745.364 q^{5} +954.411i q^{6} -9.58116 q^{7} -1948.88i q^{8} +2187.00 q^{9} +15211.8i q^{10} -18868.6i q^{11} +7506.15 q^{12} -7491.72i q^{13} +195.537i q^{14} +34857.2 q^{15} -80863.3 q^{16} -51296.7 q^{17} -44633.4i q^{18} -247403. q^{19} +119636. q^{20} +448.067 q^{21} -385080. q^{22} +518429. i q^{23} +91139.9i q^{24} +164942. q^{25} -152895. q^{26} -102276. q^{27} +1537.84 q^{28} -610858. q^{29} -711383. i q^{30} -514584. i q^{31} +1.15139e6i q^{32} +882397. i q^{33} +1.04689e6i q^{34} +7141.45 q^{35} -351028. q^{36} -3.23289e6i q^{37} +5.04913e6i q^{38} +350353. i q^{39} +1.45262e6i q^{40} -208023. q^{41} -9144.36i q^{42} -1.29880e6i q^{43} +3.02854e6i q^{44} -1.63011e6 q^{45} +1.05804e7 q^{46} -676594. i q^{47} +3.78160e6 q^{48} -5.76471e6 q^{49} -3.36622e6i q^{50} +2.39891e6 q^{51} +1.20247e6i q^{52} +9.26736e6 q^{53} +2.08730e6i q^{54} +1.40640e7i q^{55} +18672.5i q^{56} +1.15699e7 q^{57} +1.24667e7i q^{58} +(1.13610e7 + 4.21401e6i) q^{59} -5.59482e6 q^{60} -2.59096e6i q^{61} -1.05019e7 q^{62} -20954.0 q^{63} +2.79706e6 q^{64} +5.58406e6i q^{65} +1.80084e7 q^{66} -1.85490e7i q^{67} +8.23346e6 q^{68} -2.42445e7i q^{69} -145746. i q^{70} -1.90851e6 q^{71} -4.26219e6i q^{72} +3.02899e7i q^{73} -6.59784e7 q^{74} -7.71359e6 q^{75} +3.97099e7 q^{76} +180783. i q^{77} +7.15018e6 q^{78} +4.69983e7 q^{79} +6.02726e7 q^{80} +4.78297e6 q^{81} +4.24543e6i q^{82} +1.76048e7i q^{83} -71917.7 q^{84} +3.82347e7 q^{85} -2.65065e7 q^{86} +2.85670e7 q^{87} -3.67726e7 q^{88} +4.02754e7i q^{89} +3.32681e7i q^{90} +71779.4i q^{91} -8.32113e7i q^{92} +2.40647e7i q^{93} -1.38083e7 q^{94} +1.84405e8 q^{95} -5.38450e7i q^{96} -1.49120e7i q^{97} +1.17649e8i q^{98} -4.12656e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	20.4085i		−	1.27553i	−0.770231	−	0.637765i	$-0.779859\pi$
$2$		−	20.4085i		−	1.27553i	0.770231	−	0.637765i	$-0.220141\pi$
$3$	−46.7654			−0.577350
$3$	−46.7654			−0.577350
$4$	−160.507			−0.626979
$5$	−745.364			−1.19258			−0.596291	−	0.802768i	$-0.703360\pi$
$5$	−745.364			−1.19258			−0.596291	+	0.802768i	$0.703360\pi$
$6$			954.411i			0.736428i
$7$	−9.58116			−0.00399049			−0.00199524	−	0.999998i	$-0.500635\pi$
$7$	−9.58116			−0.00399049			−0.00199524	+	0.999998i	$0.500635\pi$
$8$		−	1948.88i		−	0.475800i
$9$	2187.00			0.333333
$10$			15211.8i			1.52118i
$11$		−	18868.6i		−	1.28875i	−0.764709	−	0.644375i	$-0.777117\pi$
$11$		−	18868.6i		−	1.28875i	0.764709	−	0.644375i	$-0.222883\pi$
$12$	7506.15			0.361987
$13$		−	7491.72i		−	0.262306i	−0.991362	−	0.131153i	$-0.958132\pi$
$13$		−	7491.72i		−	0.262306i	0.991362	−	0.131153i	$-0.0418679\pi$
$14$			195.537i			0.00508999i
$15$	34857.2			0.688538
$16$	−80863.3			−1.23388
$17$	−51296.7			−0.614177			−0.307089	−	0.951681i	$-0.599355\pi$
$17$	−51296.7			−0.614177			−0.307089	+	0.951681i	$0.599355\pi$
$18$		−	44633.4i		−	0.425177i
$19$	−247403.			−1.89841			−0.949207	−	0.314652i	$-0.898112\pi$
$19$	−247403.			−1.89841			−0.949207	+	0.314652i	$0.898112\pi$
$20$	119636.			0.747724
$21$	448.067			0.00230391
$22$	−385080.			−1.64384
$23$			518429.i			1.85258i	0.376807	+	0.926292i	$0.377022\pi$
$23$			518429.i			1.85258i	−0.376807	+	0.926292i	$0.622978\pi$
$24$			91139.9i			0.274703i
$25$	164942.			0.422252
$26$	−152895.			−0.334579
$27$	−102276.			−0.192450
$28$	1537.84			0.00250195
$29$	−610858.			−0.863670			−0.431835	−	0.901953i	$-0.642134\pi$
$29$	−610858.			−0.863670			−0.431835	+	0.901953i	$0.642134\pi$
$30$		−	711383.i		−	0.878251i
$31$		−	514584.i		−	0.557198i	−0.960408	−	0.278599i	$-0.910130\pi$
$31$		−	514584.i		−	0.557198i	0.960408	−	0.278599i	$-0.0898700\pi$
$32$			1.15139e6i			1.09805i
$33$			882397.i			0.744061i
$34$			1.04689e6i			0.783402i
$35$	7141.45			0.00475898
$36$	−351028.			−0.208993
$37$		−	3.23289e6i		−	1.72498i	−0.506075	−	0.862489i	$-0.668904\pi$
$37$		−	3.23289e6i		−	1.72498i	0.506075	−	0.862489i	$-0.331096\pi$
$38$			5.04913e6i			2.42149i
$39$			350353.i			0.151442i
$40$			1.45262e6i			0.567430i
$41$	−208023.			−0.0736165			−0.0368083	−	0.999322i	$-0.511719\pi$
$41$	−208023.			−0.0736165			−0.0368083	+	0.999322i	$0.511719\pi$
$42$		−	9144.36i		−	0.00293871i
$43$		−	1.29880e6i		−	0.379898i	−0.981794	−	0.189949i	$-0.939168\pi$
$43$		−	1.29880e6i		−	0.379898i	0.981794	−	0.189949i	$-0.0608323\pi$
$44$			3.02854e6i			0.808020i
$45$	−1.63011e6			−0.397527
$46$	1.05804e7			2.36303
$47$		−	676594.i		−	0.138655i	−0.997594	−	0.0693276i	$-0.977915\pi$
$47$		−	676594.i		−	0.138655i	0.997594	−	0.0693276i	$-0.0220854\pi$
$48$	3.78160e6			0.712379
$49$	−5.76471e6			−0.999984
$50$		−	3.36622e6i		−	0.538596i
$51$	2.39891e6			0.354595
$52$			1.20247e6i			0.164460i
$53$	9.26736e6			1.17450			0.587249	−	0.809406i	$-0.300211\pi$
$53$	9.26736e6			1.17450			0.587249	+	0.809406i	$0.300211\pi$
$54$			2.08730e6i			0.245476i
$55$			1.40640e7i			1.53694i
$56$			18672.5i			0.00189867i
$57$	1.15699e7			1.09605
$58$			1.24667e7i			1.10164i
$59$	1.13610e7	+	4.21401e6i	0.937581	+	0.347766i
$59$	1.13610e7	+	4.21401e6i	0.937581	+	0.347766i
$60$	−5.59482e6			−0.431699
$61$		−	2.59096e6i		−	0.187129i	−0.995613	−	0.0935647i	$-0.970174\pi$
$61$		−	2.59096e6i		−	0.187129i	0.995613	−	0.0935647i	$-0.0298262\pi$
$62$	−1.05019e7			−0.710723
$63$	−20954.0			−0.00133016
$64$	2.79706e6			0.166718
$65$			5.58406e6i			0.312821i
$66$	1.80084e7			0.949072
$67$		−	1.85490e7i		−	0.920493i	−0.887791	−	0.460247i	$-0.847761\pi$
$67$		−	1.85490e7i		−	0.920493i	0.887791	−	0.460247i	$-0.152239\pi$
$68$	8.23346e6			0.385076
$69$		−	2.42445e7i		−	1.06959i
$70$		−	145746.i		−	0.00607023i
$71$	−1.90851e6			−0.0751038			−0.0375519	−	0.999295i	$-0.511956\pi$
$71$	−1.90851e6			−0.0751038			−0.0375519	+	0.999295i	$0.511956\pi$
$72$		−	4.26219e6i		−	0.158600i
$73$			3.02899e7i			1.06661i	0.845922	+	0.533306i	$0.179051\pi$
$73$			3.02899e7i			1.06661i	−0.845922	+	0.533306i	$0.820949\pi$
$74$	−6.59784e7			−2.20026
$75$	−7.71359e6			−0.243787
$76$	3.97099e7			1.19027
$77$			180783.i			0.00514274i
$78$	7.15018e6			0.193169
$79$	4.69983e7			1.20663			0.603315	−	0.797503i	$-0.293846\pi$
$79$	4.69983e7			1.20663			0.603315	+	0.797503i	$0.293846\pi$
$80$	6.02726e7			1.47150
$81$	4.78297e6			0.111111
$82$			4.24543e6i			0.0939001i
$83$			1.76048e7i			0.370953i	0.982649	+	0.185477i	$0.0593829\pi$
$83$			1.76048e7i			0.370953i	−0.982649	+	0.185477i	$0.940617\pi$
$84$	−71917.7			−0.00144450
$85$	3.82347e7			0.732457
$86$	−2.65065e7			−0.484572
$87$	2.85670e7			0.498640
$88$	−3.67726e7			−0.613187
$89$			4.02754e7i			0.641919i	0.947093	+	0.320959i	$0.104005\pi$
$89$			4.02754e7i			0.641919i	−0.947093	+	0.320959i	$0.895995\pi$
$90$			3.32681e7i			0.507058i
$91$			71779.4i			0.00104673i
$92$		−	8.32113e7i		−	1.16153i
$93$			2.40647e7i			0.321698i
$94$	−1.38083e7			−0.176859
$95$	1.84405e8			2.26402
$96$		−	5.38450e7i		−	0.633958i
$97$		−	1.49120e7i		−	0.168441i	−0.996447	−	0.0842205i	$-0.973160\pi$
$97$		−	1.49120e7i		−	0.168441i	0.996447	−	0.0842205i	$-0.0268400\pi$
$98$			1.17649e8i			1.27551i
$99$		−	4.12656e7i		−	0.429584i
$100$	−2.64743e7			−0.264743
$101$		−	6.64302e7i		−	0.638381i	−0.947691	−	0.319190i	$-0.896589\pi$
$101$		−	6.64302e7i		−	0.638381i	0.947691	−	0.319190i	$-0.103411\pi$
$102$		−	4.89581e7i		−	0.452297i
$103$			4.90921e7i			0.436177i	0.975929	+	0.218089i	$0.0699821\pi$
$103$			4.90921e7i			0.436177i	−0.975929	+	0.218089i	$0.930018\pi$
$104$	−1.46004e7			−0.124805
$105$	−333973.			−0.00274760
$106$		−	1.89133e8i		−	1.49811i
$107$	−6.05131e7			−0.461652			−0.230826	−	0.972995i	$-0.574143\pi$
$107$	−6.05131e7			−0.461652			−0.230826	+	0.972995i	$0.574143\pi$
$108$	1.64160e7			0.120662
$109$		−	1.84365e8i		−	1.30609i	−0.757319	−	0.653045i	$-0.773491\pi$
$109$		−	1.84365e8i		−	1.30609i	0.757319	−	0.653045i	$-0.226509\pi$
$110$	2.87025e8			1.96042
$111$			1.51187e8i			0.995917i
$112$	774764.			0.00492377
$113$		−	6.09578e7i		−	0.373866i	−0.982373	−	0.186933i	$-0.940145\pi$
$113$		−	6.09578e7i		−	0.373866i	0.982373	−	0.186933i	$-0.0598547\pi$
$114$		−	2.36124e8i		−	1.39805i
$115$		−	3.86418e8i		−	2.20936i
$116$	9.80467e7			0.541503
$117$		−	1.63844e7i		−	0.0874353i
$118$	8.60015e7	−	2.31861e8i	0.443586	−	1.19591i
$119$	491482.			0.00245087
$120$		−	6.79324e7i		−	0.327606i
$121$	−1.41665e8			−0.660879
$122$	−5.28777e7			−0.238689
$123$	9.72826e6			0.0425025
$124$			8.25942e7i			0.349351i
$125$	1.68216e8			0.689012
$126$			427640.i			0.00169666i
$127$	−2.19348e8			−0.843178			−0.421589	−	0.906787i	$-0.638528\pi$
$127$	−2.19348e8			−0.843178			−0.421589	+	0.906787i	$0.638528\pi$
$128$			2.37671e8i			0.885394i
$129$			6.07387e7i			0.219334i
$130$	1.13962e8			0.399013
$131$		−	2.41637e8i		−	0.820498i	−0.911973	−	0.410249i	$-0.865442\pi$
$131$		−	2.41637e8i		−	0.820498i	0.911973	−	0.410249i	$-0.134558\pi$
$132$		−	1.41631e8i		−	0.466511i
$133$	2.37041e6			0.00757560
$134$	−3.78557e8			−1.17412
$135$	7.62327e7			0.229513
$136$			9.99709e7i			0.292225i
$137$	5.38039e8			1.52733			0.763663	−	0.645615i	$-0.223399\pi$
$137$	5.38039e8			1.52733			0.763663	+	0.645615i	$0.223399\pi$
$138$	−4.94794e8			−1.36429
$139$	4.35719e8			1.16720			0.583602	−	0.812040i	$-0.301643\pi$
$139$	4.35719e8			1.16720			0.583602	+	0.812040i	$0.301643\pi$
$140$	−1.14625e6			−0.00298378
$141$			3.16411e7i			0.0800527i
$142$			3.89499e7i			0.0957973i
$143$	−1.41358e8			−0.338047
$144$	−1.76848e8			−0.411292
$145$	4.55311e8			1.03000
$146$	6.18172e8			1.36050
$147$	2.69589e8			0.577341
$148$			5.18900e8i			1.08153i
$149$			3.83709e8i			0.778496i	0.921133	+	0.389248i	$0.127265\pi$
$149$			3.83709e8i			0.778496i	−0.921133	+	0.389248i	$0.872735\pi$
$150$			1.57423e8i			0.310958i
$151$		−	4.20489e8i		−	0.808811i	−0.914580	−	0.404405i	$-0.867479\pi$
$151$		−	4.20489e8i		−	0.808811i	0.914580	−	0.404405i	$-0.132521\pi$
$152$			4.82158e8i			0.903265i
$153$	−1.12186e8			−0.204726
$154$	3.68951e6			0.00655973
$155$			3.83552e8i			0.664504i
$156$		−	5.62340e7i		−	0.0949512i
$157$			6.63546e8i			1.09213i	0.837744	+	0.546063i	$0.183874\pi$
$157$			6.63546e8i			1.09213i	−0.837744	+	0.546063i	$0.816126\pi$
$158$		−	9.59165e8i		−	1.53909i
$159$	−4.33391e8			−0.678097
$160$		−	8.58202e8i		−	1.30951i
$161$		−	4.96715e6i		−	0.00739271i
$162$		−	9.76132e7i		−	0.141726i
$163$	−1.11230e9			−1.57569			−0.787844	−	0.615875i	$-0.788803\pi$
$163$	−1.11230e9			−1.57569			−0.787844	+	0.615875i	$0.788803\pi$
$164$	3.33890e7			0.0461560
$165$		−	6.57707e8i		−	0.887354i
$166$	3.59288e8			0.473162
$167$	1.07732e9			1.38509			0.692545	−	0.721375i	$-0.256490\pi$
$167$	1.07732e9			1.38509			0.692545	+	0.721375i	$0.256490\pi$
$168$		−	873226.i		−	0.00109620i
$169$	7.59605e8			0.931196
$170$		−	7.80313e8i		−	0.934271i
$171$	−5.41071e8			−0.632805
$172$			2.08466e8i			0.238188i
$173$			1.16285e9i			1.29819i	0.760708	+	0.649094i	$0.224852\pi$
$173$			1.16285e9i			1.29819i	−0.760708	+	0.649094i	$0.775148\pi$
$174$		−	5.83009e8i		−	0.636031i
$175$	−1.58034e6			−0.00168499
$176$			1.52578e9i			1.59016i
$177$	−5.31302e8	−	1.97070e8i	−0.541313	−	0.200783i
$178$	8.21961e8			0.818787
$179$		−	2.40794e8i		−	0.234549i	−0.993100	−	0.117275i	$-0.962584\pi$
$179$		−	2.40794e8i		−	0.234549i	0.993100	−	0.117275i	$-0.0374158\pi$
$180$	2.61644e8			0.249241
$181$	2.27371e8			0.211846			0.105923	−	0.994374i	$-0.466220\pi$
$181$	2.27371e8			0.211846			0.105923	+	0.994374i	$0.466220\pi$
$182$	1.46491e6			0.00133513
$183$			1.21167e8i			0.108039i
$184$	1.01035e9			0.881458
$185$			2.40968e9i			2.05718i
$186$	4.91125e8			0.410336
$187$			9.67897e8i			0.791521i
$188$			1.08598e8i			0.0869340i
$189$	979921.			0.000767970
$190$		−	3.76344e9i		−	2.88782i
$191$			2.24021e9i			1.68328i	0.540041	+	0.841639i	$0.318409\pi$
$191$			2.24021e9i			1.68328i	−0.540041	+	0.841639i	$0.681591\pi$
$192$	−1.30805e8			−0.0962545
$193$	1.85555e9			1.33735			0.668673	−	0.743557i	$-0.266863\pi$
$193$	1.85555e9			1.33735			0.668673	+	0.743557i	$0.266863\pi$
$194$	−3.04331e8			−0.214852
$195$		−	2.61141e8i		−	0.180608i
$196$	9.25274e8			0.626969
$197$	−1.47257e9			−0.977711			−0.488856	−	0.872365i	$-0.662586\pi$
$197$	−1.47257e9			−0.977711			−0.488856	+	0.872365i	$0.662586\pi$
$198$	−8.42169e8			−0.547947
$199$	−2.12427e9			−1.35456			−0.677280	−	0.735725i	$-0.736841\pi$
$199$	−2.12427e9			−1.35456			−0.677280	+	0.735725i	$0.736841\pi$
$200$		−	3.21452e8i		−	0.200907i
$201$			8.67450e8i			0.531447i
$202$	−1.35574e9			−0.814275
$203$	5.85272e6			0.00344647
$204$	−3.85041e8			−0.222324
$205$	1.55053e8			0.0877937
$206$	1.00190e9			0.556357
$207$			1.13380e9i			0.617528i
$208$			6.05805e8i			0.323653i
$209$			4.66815e9i			2.44658i
$210$			6.81588e6i			0.00350465i
$211$			9.65517e8i			0.487113i	0.969887	+	0.243557i	$0.0783142\pi$
$211$			9.65517e8i			0.487113i	−0.969887	+	0.243557i	$0.921686\pi$
$212$	−1.48747e9			−0.736386
$213$	8.92524e7			0.0433612
$214$			1.23498e9i			0.588851i
$215$			9.68076e8i			0.453060i
$216$			1.99323e8i			0.0915677i
$217$			4.93031e6i			0.00222349i
$218$	−3.76262e9			−1.66596
$219$		−	1.41652e9i		−	0.615809i
$220$		−	2.25736e9i		−	0.963630i
$221$			3.84301e8i			0.161102i
$222$	3.08550e9			1.27032
$223$	−7.11385e8			−0.287664			−0.143832	−	0.989602i	$-0.545942\pi$
$223$	−7.11385e8			−0.287664			−0.143832	+	0.989602i	$0.545942\pi$
$224$		−	1.10316e7i		−	0.00438175i
$225$	3.60729e8			0.140751
$226$	−1.24406e9			−0.476877
$227$		−	3.41826e9i		−	1.28736i	−0.765293	−	0.643682i	$-0.777406\pi$
$227$		−	3.41826e9i		−	1.28736i	0.765293	−	0.643682i	$-0.222594\pi$
$228$	−1.85705e9			−0.687201
$229$		−	3.98469e9i		−	1.44895i	−0.689302	−	0.724474i	$-0.742083\pi$
$229$		−	3.98469e9i		−	1.44895i	0.689302	−	0.724474i	$-0.257917\pi$
$230$	−7.88621e9			−2.81810
$231$		−	8.45439e6i		−	0.00296916i
$232$			1.19049e9i			0.410934i
$233$		−	1.78068e9i		−	0.604173i	−0.953281	−	0.302086i	$-0.902317\pi$
$233$		−	1.78068e9i		−	0.604173i	0.953281	−	0.302086i	$-0.0976831\pi$
$234$	−3.34381e8			−0.111526
$235$			5.04308e8i			0.165358i
$236$	−1.82352e9	−	6.76376e8i	−0.587844	−	0.218042i
$237$	−2.19789e9			−0.696648
$238$		−	1.00304e7i		−	0.00312616i
$239$	2.78608e9			0.853889			0.426944	−	0.904278i	$-0.359590\pi$
$239$	2.78608e9			0.853889			0.426944	+	0.904278i	$0.359590\pi$
$240$	−2.81867e9			−0.849570
$241$	−5.34206e9			−1.58358			−0.791791	−	0.610792i	$-0.790851\pi$
$241$	−5.34206e9			−1.58358			−0.791791	+	0.610792i	$0.790851\pi$
$242$			2.89118e9i			0.842972i
$243$	−2.23677e8			−0.0641500
$244$			4.15867e8i			0.117326i
$245$	4.29681e9			1.19256
$246$		−	1.98539e8i		−	0.0542133i
$247$			1.85348e9i			0.497965i
$248$	−1.00286e9			−0.265115
$249$		−	8.23296e8i		−	0.214170i
$250$		−	3.43303e9i		−	0.878856i
$251$	−1.54496e9			−0.389245			−0.194623	−	0.980878i	$-0.562348\pi$
$251$	−1.54496e9			−0.389245			−0.194623	+	0.980878i	$0.562348\pi$
$252$	3.36326e6			0.000833984
$253$	9.78203e9			2.38752
$254$			4.47657e9i			1.07550i
$255$	−1.78806e9			−0.422884
$256$	5.56656e9			1.29607
$257$	−4.83589e9			−1.10852			−0.554260	−	0.832343i	$-0.686999\pi$
$257$	−4.83589e9			−1.10852			−0.554260	+	0.832343i	$0.686999\pi$
$258$	1.23959e9			0.279768
$259$			3.09748e7i			0.00688351i
$260$		−	8.96279e8i		−	0.196133i
$261$	−1.33595e9			−0.287890
$262$	−4.93144e9			−1.04657
$263$	−2.71747e9			−0.567991			−0.283996	−	0.958826i	$-0.591660\pi$
$263$	−2.71747e9			−0.567991			−0.283996	+	0.958826i	$0.591660\pi$
$264$	1.71968e9			0.354024
$265$	−6.90755e9			−1.40069
$266$		−	4.83765e7i		−	0.00966291i
$267$		−	1.88349e9i		−	0.370612i
$268$			2.97723e9i			0.577130i
$269$		−	2.89769e9i		−	0.553405i	−0.960956	−	0.276703i	$-0.910758\pi$
$269$		−	2.89769e9i		−	0.553405i	0.960956	−	0.276703i	$-0.0892417\pi$
$270$		−	1.55580e9i		−	0.292750i
$271$	9.35608e8			0.173467			0.0867335	−	0.996232i	$-0.472357\pi$
$271$	9.35608e8			0.173467			0.0867335	+	0.996232i	$0.472357\pi$
$272$	4.14802e9			0.757819
$273$		−	3.35679e6i		−	0.000604329i
$274$		−	1.09806e10i		−	1.94815i
$275$		−	3.11223e9i		−	0.544178i
$276$			3.89141e9i			0.670610i
$277$	7.02822e9			1.19379			0.596893	−	0.802321i	$-0.296402\pi$
$277$	7.02822e9			1.19379			0.596893	+	0.802321i	$0.296402\pi$
$278$		−	8.89236e9i		−	1.48881i
$279$		−	1.12540e9i		−	0.185733i
$280$		−	1.39178e7i		−	0.00226432i
$281$	−6.80104e9			−1.09081			−0.545406	−	0.838172i	$-0.683625\pi$
$281$	−6.80104e9			−1.09081			−0.545406	+	0.838172i	$0.683625\pi$
$282$	6.45748e8			0.102110
$283$			1.19844e10i			1.86840i	0.356748	+	0.934201i	$0.383886\pi$
$283$			1.19844e10i			1.86840i	−0.356748	+	0.934201i	$0.616114\pi$
$284$	3.06329e8			0.0470885
$285$	−8.62379e9			−1.30713
$286$			2.88491e9i			0.431189i
$287$	1.99310e6			0.000293766
$288$			2.51808e9i			0.366016i
$289$	−4.34441e9			−0.622786
$290$		−	9.29221e9i		−	1.31379i
$291$			6.97364e8i			0.0972495i
$292$		−	4.86173e9i		−	0.668744i
$293$	−4.51579e9			−0.612722			−0.306361	−	0.951915i	$-0.599111\pi$
$293$	−4.51579e9			−0.612722			−0.306361	+	0.951915i	$0.599111\pi$
$294$		−	5.50190e9i		−	0.736416i
$295$	−8.46809e9	−	3.14097e9i	−1.11814	−	0.414740i
$296$	−6.30050e9			−0.820744
$297$			1.92980e9i			0.248020i
$298$	7.83091e9			0.992996
$299$	3.88392e9			0.485944
$300$	1.23808e9			0.152850
$301$			1.24440e7i			0.00151598i
$302$	−8.58155e9			−1.03166
$303$			3.10663e9i			0.368569i
$304$	2.00058e10			2.34241
$305$			1.93121e9i			0.223167i
$306$			2.28954e9i			0.261134i
$307$	−1.32798e9			−0.149499			−0.0747493	−	0.997202i	$-0.523816\pi$
$307$	−1.32798e9			−0.149499			−0.0747493	+	0.997202i	$0.523816\pi$
$308$		−	2.90169e7i		−	0.00322439i
$309$		−	2.29581e9i		−	0.251827i
$310$	7.82773e9			0.847596
$311$	8.76178e9			0.936592			0.468296	−	0.883572i	$-0.344868\pi$
$311$	8.76178e9			0.936592			0.468296	+	0.883572i	$0.344868\pi$
$312$	6.82794e8			0.0720562
$313$		−	9.86985e9i		−	1.02833i	−0.857691	−	0.514166i	$-0.828102\pi$
$313$		−	9.86985e9i		−	1.02833i	0.857691	−	0.514166i	$-0.171898\pi$
$314$	1.35420e10			1.39304
$315$	1.56184e7			0.00158633
$316$	−7.54354e9			−0.756532
$317$	1.42367e10			1.40985			0.704923	−	0.709283i	$-0.250981\pi$
$317$	1.42367e10			1.40985			0.704923	+	0.709283i	$0.250981\pi$
$318$			8.84486e9i			0.864934i
$319$			1.15260e10i			1.11306i
$320$	−2.08483e9			−0.198824
$321$	2.82992e9			0.266535
$322$	−1.01372e8			−0.00942963
$323$	1.26910e10			1.16596
$324$	−7.67698e8			−0.0696644
$325$		−	1.23570e9i		−	0.110759i
$326$			2.27003e10i			2.00984i
$327$			8.62191e9i			0.754071i
$328$			4.05410e8i			0.0350267i
$329$			6.48255e6i			0.000553302i
$330$	−1.34228e10			−1.13185
$331$	4.64201e8			0.0386718			0.0193359	−	0.999813i	$-0.493845\pi$
$331$	4.64201e8			0.0386718			0.0193359	+	0.999813i	$0.493845\pi$
$332$		−	2.82569e9i		−	0.232580i
$333$		−	7.07033e9i		−	0.574993i
$334$		−	2.19864e10i		−	1.76672i
$335$			1.38257e10i			1.09776i
$336$	−3.62321e7			−0.00284274
$337$			2.28503e10i			1.77162i	0.464044	+	0.885812i	$0.346398\pi$
$337$			2.28503e10i			1.77162i	−0.464044	+	0.885812i	$0.653602\pi$
$338$		−	1.55024e10i		−	1.18777i
$339$			2.85071e9i			0.215851i
$340$	−6.13692e9			−0.459235
$341$	−9.70948e9			−0.718089
$342$			1.10424e10i			0.807162i
$343$	1.10466e8			0.00798091
$344$	−2.53119e9			−0.180755
$345$			1.80710e10i			1.27557i
$346$	2.37319e10			1.65588
$347$		−	3.93570e9i		−	0.271459i	−0.990746	−	0.135729i	$-0.956662\pi$
$347$		−	3.93570e9i		−	0.271459i	0.990746	−	0.135729i	$-0.0433377\pi$
$348$	−4.58519e9			−0.312637
$349$			1.21596e10i			0.819627i	0.912169	+	0.409814i	$0.134406\pi$
$349$			1.21596e10i			0.819627i	−0.912169	+	0.409814i	$0.865594\pi$
$350$			3.22523e7i			0.00214926i
$351$			7.66222e8i			0.0504808i
$352$	2.17251e10			1.41511
$353$		−	2.82640e8i		−	0.0182027i	−0.999959	−	0.00910133i	$-0.997103\pi$
$353$		−	2.82640e8i		−	0.0182027i	0.999959	−	0.00910133i	$-0.00289708\pi$
$354$	−4.02189e9	+	1.08431e10i	−0.256105	+	0.690461i
$355$	1.42254e9			0.0895675
$356$		−	6.46447e9i		−	0.402470i
$357$	−2.29843e7			−0.00141501
$358$	−4.91425e9			−0.299175
$359$	−2.95778e10			−1.78069			−0.890345	−	0.455286i	$-0.849537\pi$
$359$	−2.95778e10			−1.78069			−0.890345	+	0.455286i	$0.849537\pi$
$360$			3.17688e9i			0.189143i
$361$	4.42248e10			2.60398
$362$		−	4.64029e9i		−	0.270216i
$363$	6.62503e9			0.381559
$364$		−	1.15211e7i		−	0.000656277i
$365$		−	2.25770e10i		−	1.27202i
$366$	2.47284e9			0.137807
$367$		−	2.17893e9i		−	0.120110i	−0.998195	−	0.0600549i	$-0.980872\pi$
$367$		−	2.17893e9i		−	0.120110i	0.998195	−	0.0600549i	$-0.0191276\pi$
$368$		−	4.19219e10i		−	2.28586i
$369$	−4.54946e8			−0.0245388
$370$	4.91779e10			2.62400
$371$	−8.87920e7			−0.00468682
$372$		−	3.86255e9i		−	0.201698i
$373$	1.38820e10			0.717162			0.358581	−	0.933499i	$-0.383261\pi$
$373$	1.38820e10			0.717162			0.358581	+	0.933499i	$0.383261\pi$
$374$	1.97533e10			1.00961
$375$	−7.86667e9			−0.397801
$376$	−1.31860e9			−0.0659721
$377$			4.57637e9i			0.226546i
$378$		−	1.99987e7i		−	0.000979569i
$379$	−3.68929e10			−1.78808			−0.894038	−	0.447992i	$-0.852139\pi$
$379$	−3.68929e10			−1.78808			−0.894038	+	0.447992i	$0.852139\pi$
$380$	−2.95983e10			−1.41949
$381$	1.02579e10			0.486809
$382$	4.57194e10			2.14707
$383$	2.01201e10			0.935051			0.467525	−	0.883980i	$-0.345146\pi$
$383$	2.01201e10			0.935051			0.467525	+	0.883980i	$0.345146\pi$
$384$		−	1.11148e10i		−	0.511183i
$385$		−	1.34749e8i		−	0.00613314i
$386$		−	3.78690e10i		−	1.70583i
$387$		−	2.84047e9i		−	0.126633i
$388$			2.39347e9i			0.105609i
$389$	3.43685e9			0.150094			0.0750468	−	0.997180i	$-0.476089\pi$
$389$	3.43685e9			0.150094			0.0750468	+	0.997180i	$0.476089\pi$
$390$	−5.32949e9			−0.230370
$391$		−	2.65937e10i		−	1.13781i
$392$			1.12347e10i			0.475792i
$393$			1.13002e10i			0.473715i
$394$			3.00529e10i			1.24710i
$395$	−3.50308e10			−1.43900
$396$			6.62341e9i			0.269340i
$397$		−	1.45748e10i		−	0.586735i	−0.956000	−	0.293367i	$-0.905224\pi$
$397$		−	1.45748e10i		−	0.586735i	0.956000	−	0.293367i	$-0.0947759\pi$
$398$			4.33532e10i			1.72778i
$399$	−1.10853e8			−0.00437377
$400$	−1.33378e10			−0.521007
$401$			1.18427e10i			0.458007i	0.973426	+	0.229004i	$0.0735468\pi$
$401$			1.18427e10i			0.458007i	−0.973426	+	0.229004i	$0.926453\pi$
$402$	1.77033e10			0.677877
$403$	−3.85512e9			−0.146156
$404$			1.06625e10i			0.400252i
$405$	−3.56505e9			−0.132509
$406$		−	1.19445e8i		−	0.00439607i
$407$	−6.10001e10			−2.22307
$408$		−	4.67517e9i		−	0.168716i
$409$			4.23668e10i			1.51402i	0.653402	+	0.757011i	$0.273341\pi$
$409$			4.23668e10i			1.51402i	−0.653402	+	0.757011i	$0.726659\pi$
$410$		−	3.16439e9i		−	0.111984i
$411$	−2.51616e10			−0.881802
$412$		−	7.87961e9i		−	0.273474i
$413$	−1.08852e8	−	4.03751e7i	−0.00374141	−	0.00138776i
$414$	2.31392e10			0.787676
$415$		−	1.31220e10i		−	0.442392i
$416$	8.62587e9			0.288024
$417$	−2.03765e10			−0.673886
$418$	9.52700e10			3.12069
$419$			4.74282e10i			1.53880i	0.638770	+	0.769398i	$0.279444\pi$
$419$			4.74282e10i			1.53880i	−0.638770	+	0.769398i	$0.720556\pi$
$420$	5.36048e7			0.00172269
$421$		−	3.98015e10i		−	1.26698i	−0.773750	−	0.633492i	$-0.781621\pi$
$421$		−	3.98015e10i		−	1.26698i	0.773750	−	0.633492i	$-0.218379\pi$
$422$	1.97047e10			0.621328
$423$		−	1.47971e9i		−	0.0462184i
$424$		−	1.80609e10i		−	0.558826i
$425$	−8.46099e9			−0.259338
$426$		−	1.82151e9i		−	0.0553086i
$427$			2.48244e7i			0.000746737i
$428$	9.71276e9			0.289446
$429$	6.61067e9			0.195172
$430$	1.97570e10			0.577892
$431$			8.98991e9i			0.260523i	0.991480	+	0.130262i	$0.0415817\pi$
$431$			8.98991e9i			0.260523i	−0.991480	+	0.130262i	$0.958418\pi$
$432$	8.27037e9			0.237460
$433$	−3.14066e10			−0.893447			−0.446724	−	0.894672i	$-0.647409\pi$
$433$	−3.14066e10			−0.893447			−0.446724	+	0.894672i	$0.647409\pi$
$434$	1.00620e8			0.00283613
$435$	−2.12928e10			−0.594669
$436$			2.95918e10i			0.818891i
$437$		−	1.28261e11i		−	3.51697i
$438$	−2.89090e10			−0.785483
$439$	2.85002e10			0.767342			0.383671	−	0.923470i	$-0.374660\pi$
$439$	2.85002e10			0.767342			0.383671	+	0.923470i	$0.374660\pi$
$440$	2.74089e10			0.731276
$441$	−1.26074e10			−0.333328
$442$	7.84300e9			0.205491
$443$		−	9.12836e9i		−	0.237016i	−0.992953	−	0.118508i	$-0.962189\pi$
$443$		−	9.12836e9i		−	0.237016i	0.992953	−	0.118508i	$-0.0378112\pi$
$444$		−	2.42666e10i		−	0.624419i
$445$		−	3.00198e10i		−	0.765541i
$446$			1.45183e10i			0.366924i
$447$		−	1.79443e10i		−	0.449465i
$448$	−2.67991e7			−0.000665284
$449$	−5.59798e10			−1.37736			−0.688678	−	0.725068i	$-0.741808\pi$
$449$	−5.59798e10			−1.37736			−0.688678	+	0.725068i	$0.741808\pi$
$450$		−	7.36193e9i		−	0.179532i
$451$			3.92510e9i			0.0948733i
$452$			9.78413e9i			0.234406i
$453$			1.96643e10i			0.466967i
$454$	−6.97615e10			−1.64207
$455$		−	5.35018e7i		−	0.00124831i
$456$		−	2.25483e10i		−	0.521500i
$457$		−	8.40061e10i		−	1.92596i	−0.269581	−	0.962978i	$-0.586885\pi$
$457$		−	8.40061e10i		−	1.92596i	0.269581	−	0.962978i	$-0.413115\pi$
$458$	−8.13216e10			−1.84818
$459$	5.24641e9			0.118198
$460$			6.20227e10i			1.38522i
$461$	−1.23474e10			−0.273383			−0.136691	−	0.990614i	$-0.543647\pi$
$461$	−1.23474e10			−0.273383			−0.136691	+	0.990614i	$0.543647\pi$
$462$	−1.72541e8			−0.00378726
$463$		−	7.27727e10i		−	1.58360i	−0.610782	−	0.791799i	$-0.709145\pi$
$463$		−	7.27727e10i		−	1.58360i	0.610782	−	0.791799i	$-0.290855\pi$
$464$	4.93960e10			1.06566
$465$		−	1.79370e10i		−	0.383652i
$466$	−3.63409e10			−0.770641
$467$			4.37284e10i			0.919382i	0.888079	+	0.459691i	$0.152040\pi$
$467$			4.37284e10i			0.919382i	−0.888079	+	0.459691i	$0.847960\pi$
$468$			2.62980e9i			0.0548201i
$469$			1.77721e8i			0.00367322i
$470$	1.02922e10			0.210919
$471$		−	3.10310e10i		−	0.630539i
$472$	8.21257e9	−	2.21412e10i	0.165467	−	0.446101i
$473$	−2.45065e10			−0.489594
$474$			4.48557e10i			0.888596i
$475$	−4.08073e10			−0.801610
$476$	−7.88861e7			−0.00153664
$477$	2.02677e10			0.391499
$478$		−	5.68596e10i		−	1.08916i
$479$	1.70958e9			0.0324748			0.0162374	−	0.999868i	$-0.494831\pi$
$479$	1.70958e9			0.0324748			0.0162374	+	0.999868i	$0.494831\pi$
$480$			4.01341e10i			0.756047i
$481$	−2.42199e10			−0.452472
$482$			1.09023e11i			2.01991i
$483$			2.32291e8i			0.00426818i
$484$	2.27382e10			0.414357
$485$			1.11148e10i			0.200880i
$486$			4.56492e9i			0.0818253i
$487$	−5.61408e10			−0.998074			−0.499037	−	0.866581i	$-0.666313\pi$
$487$	−5.61408e10			−0.998074			−0.499037	+	0.866581i	$0.666313\pi$
$488$	−5.04946e9			−0.0890361
$489$	5.20169e10			0.909724
$490$		−	8.76913e10i		−	1.52115i
$491$	7.10838e10			1.22305			0.611526	−	0.791224i	$-0.290556\pi$
$491$	7.10838e10			1.22305			0.611526	+	0.791224i	$0.290556\pi$
$492$	−1.56145e9			−0.0266482
$493$	3.13350e10			0.530447
$494$	3.78267e10			0.635170
$495$			3.07579e10i			0.512314i
$496$			4.16110e10i			0.687513i
$497$	1.82858e7			0.000299701
$498$	−1.68022e10			−0.273180
$499$	1.00041e11			1.61353			0.806764	−	0.590873i	$-0.201217\pi$
$499$	1.00041e11			1.61353			0.806764	+	0.590873i	$0.201217\pi$
$500$	−2.69998e10			−0.431996
$501$	−5.03811e10			−0.799682
$502$			3.15304e10i			0.496495i
$503$			4.91625e10i			0.768001i	0.923333	+	0.384000i	$0.125454\pi$
$503$			4.91625e10i			0.768001i	−0.923333	+	0.384000i	$0.874546\pi$
$504$			4.08367e7i			0.000632891i
$505$			4.95147e10i			0.761322i
$506$		−	1.99636e11i		−	3.04535i
$507$	−3.55232e10			−0.537626
$508$	3.52069e10			0.528655
$509$			3.67029e10i			0.546801i	0.961900	+	0.273401i	$0.0881485\pi$
$509$			3.67029e10i			0.546801i	−0.961900	+	0.273401i	$0.911851\pi$
$510$			3.64916e10i			0.539402i
$511$		−	2.90212e8i		−	0.00425630i
$512$		−	5.27613e10i		−	0.767777i
$513$	2.53034e10			0.365350
$514$			9.86932e10i			1.41395i
$515$		−	3.65915e10i		−	0.520177i
$516$		−	9.74897e9i		−	0.137518i
$517$	−1.27664e10			−0.178692
$518$	6.32149e8			0.00878013
$519$		−	5.43809e10i		−	0.749509i
$520$	1.08826e10			0.148840
$521$	1.06289e10			0.144257			0.0721284	−	0.997395i	$-0.477021\pi$
$521$	1.06289e10			0.144257			0.0721284	+	0.997395i	$0.477021\pi$
$522$			2.72646e10i			0.367213i
$523$	−8.08156e10			−1.08016			−0.540081	−	0.841613i	$-0.681606\pi$
$523$	−8.08156e10			−1.08016			−0.540081	+	0.841613i	$0.681606\pi$
$524$			3.87843e10i			0.514435i
$525$	7.39051e7			0.000972830
$526$			5.54595e10i			0.724491i
$527$			2.63965e10i			0.342218i
$528$		−	7.13536e10i		−	0.918079i
$529$	−1.90457e11			−2.43206
$530$			1.40973e11i			1.78662i
$531$	2.48465e10	+	9.21603e9i	0.312527	+	0.115922i
$532$	−3.80467e8			−0.00474974
$533$			1.55845e9i			0.0193100i
$534$	−3.84393e10			−0.472727
$535$	4.51043e10			0.550558
$536$	−3.61496e10			−0.437970
$537$			1.12608e10i			0.135417i
$538$	−5.91375e10			−0.705885
$539$			1.08772e11i			1.28873i
$540$	−1.22359e10			−0.143900
$541$			1.39091e11i			1.62372i	0.583852	+	0.811860i	$0.301545\pi$
$541$			1.39091e11i			1.62372i	−0.583852	+	0.811860i	$0.698455\pi$
$542$		−	1.90943e10i		−	0.221262i
$543$	−1.06331e10			−0.122309
$544$		−	5.90623e10i		−	0.674396i
$545$			1.37419e11i			1.55762i
$546$	−6.85070e7			−0.000770840
$547$	−1.46170e11			−1.63271			−0.816356	−	0.577549i	$-0.804009\pi$
$547$	−1.46170e11			−1.63271			−0.816356	+	0.577549i	$0.804009\pi$
$548$	−8.63589e10			−0.957601
$549$		−	5.66644e9i		−	0.0623765i
$550$	−6.35159e10			−0.694116
$551$	1.51128e11			1.63960
$552$	−4.72495e10			−0.508910
$553$	−4.50298e8			−0.00481504
$554$		−	1.43435e11i		−	1.52271i
$555$		−	1.12689e11i		−	1.18771i
$556$	−6.99357e10			−0.731813
$557$	−1.35038e11			−1.40292			−0.701461	−	0.712707i	$-0.747469\pi$
$557$	−1.35038e11			−1.40292			−0.701461	+	0.712707i	$0.747469\pi$
$558$	−2.29676e10			−0.236908
$559$	−9.73022e9			−0.0996496
$560$	−5.77481e8			−0.00587200
$561$		−	4.52641e10i		−	0.456985i
$562$			1.38799e11i			1.39137i
$563$			6.90974e10i			0.687746i	0.939016	+	0.343873i	$0.111739\pi$
$563$			6.90974e10i			0.687746i	−0.939016	+	0.343873i	$0.888261\pi$
$564$		−	5.07862e9i		−	0.0501914i
$565$			4.54357e10i			0.445865i
$566$	2.44583e11			2.38320
$567$	−4.58264e7			−0.000443387
$568$			3.71946e9i			0.0357344i
$569$			1.44373e11i			1.37733i	0.725082	+	0.688663i	$0.241802\pi$
$569$			1.44373e11i			1.37733i	−0.725082	+	0.688663i	$0.758198\pi$
$570$			1.75999e11i			1.66728i
$571$		−	1.99214e11i		−	1.87402i	−0.349301	−	0.937010i	$-0.613581\pi$
$571$		−	1.99214e11i		−	1.87402i	0.349301	−	0.937010i	$-0.386419\pi$
$572$	2.26890e10			0.211948
$573$		−	1.04764e11i		−	0.971841i
$574$		−	4.06761e7i		−	0.000374707i
$575$			8.55108e10i			0.782257i
$576$	6.11716e9			0.0555725
$577$	3.59503e9			0.0324339			0.0162170	−	0.999868i	$-0.494838\pi$
$577$	3.59503e9			0.0324339			0.0162170	+	0.999868i	$0.494838\pi$
$578$			8.86628e10i			0.794383i
$579$	−8.67755e10			−0.772117
$580$	−7.30805e10			−0.645787
$581$		−	1.68675e8i		−	0.00148028i
$582$	1.42321e10			0.124045
$583$		−	1.74862e11i		−	1.51364i
$584$	5.90313e10			0.507494
$585$			1.22123e10i			0.104274i
$586$			9.21605e10i			0.781546i
$587$			2.44880e10i			0.206253i	0.994668	+	0.103127i	$0.0328847\pi$
$587$			2.44880e10i			0.206253i	−0.994668	+	0.103127i	$0.967115\pi$
$588$	−4.32708e10			−0.361981
$589$			1.27310e11i			1.05779i
$590$	−6.41024e10	+	1.72821e11i	−0.529013	+	1.42623i
$591$	6.88652e10			0.564482
$592$			2.61422e11i			2.12841i
$593$	−2.20863e10			−0.178609			−0.0893047	−	0.996004i	$-0.528464\pi$
$593$	−2.20863e10			−0.178609			−0.0893047	+	0.996004i	$0.528464\pi$
$594$	3.93844e10			0.316357
$595$	−3.66333e8			−0.00292286
$596$		−	6.15878e10i		−	0.488101i
$597$	9.93425e10			0.782056
$598$		−	7.92650e10i		−	0.619836i
$599$	9.41366e9			0.0731225			0.0365612	−	0.999331i	$-0.488360\pi$
$599$	9.41366e9			0.0731225			0.0365612	+	0.999331i	$0.488360\pi$
$600$			1.50328e10i			0.115994i
$601$			2.30456e11i			1.76640i	0.468996	+	0.883200i	$0.344616\pi$
$601$			2.30456e11i			1.76640i	−0.468996	+	0.883200i	$0.655384\pi$
$602$	2.53963e8			0.00193368
$603$		−	4.05666e10i		−	0.306831i
$604$			6.74913e10i			0.507107i
$605$	1.05592e11			0.788153
$606$	6.34017e10			0.470122
$607$	−1.33548e11			−0.983747			−0.491873	−	0.870667i	$-0.663688\pi$
$607$	−1.33548e11			−0.983747			−0.491873	+	0.870667i	$0.663688\pi$
$608$		−	2.84857e11i		−	2.08455i
$609$	−2.73705e8			−0.00198982
$610$	3.94131e10			0.284657
$611$	−5.06885e9			−0.0363701
$612$	1.80066e10			0.128359
$613$		−	1.23977e11i		−	0.878011i	−0.898484	−	0.439005i	$-0.855331\pi$
$613$		−	1.23977e11i		−	0.878011i	0.898484	−	0.439005i	$-0.144669\pi$
$614$			2.71020e10i			0.190690i
$615$	−7.25109e9			−0.0506877
$616$	3.52324e8			0.00244692
$617$	3.54912e10			0.244895			0.122448	−	0.992475i	$-0.460926\pi$
$617$	3.54912e10			0.244895			0.122448	+	0.992475i	$0.460926\pi$
$618$	−4.68540e10			−0.321213
$619$	5.21829e10			0.355439			0.177720	−	0.984081i	$-0.443128\pi$
$619$	5.21829e10			0.355439			0.177720	+	0.984081i	$0.443128\pi$
$620$		−	6.15627e10i		−	0.416630i
$621$		−	5.30228e10i		−	0.356530i
$622$		−	1.78815e11i		−	1.19465i
$623$		−	3.85885e8i		−	0.00256157i
$624$		−	2.83307e10i		−	0.186861i
$625$	−1.89813e11			−1.24396
$626$	−2.01429e11			−1.31167
$627$		−	2.18308e11i		−	1.41254i
$628$		−	1.06504e11i		−	0.684740i
$629$			1.65836e11i			1.05944i
$630$		−	3.18747e8i		−	0.00202341i
$631$	2.09062e11			1.31873			0.659367	−	0.751821i	$-0.270824\pi$
$631$	2.09062e11			1.31873			0.659367	+	0.751821i	$0.270824\pi$
$632$		−	9.15939e10i		−	0.574114i
$633$		−	4.51527e10i		−	0.281235i
$634$		−	2.90549e11i		−	1.79830i
$635$	1.63494e11			1.00556
$636$	6.95622e10			0.425153
$637$			4.31876e10i			0.262302i
$638$	2.35229e11			1.41974
$639$	−4.17392e9			−0.0250346
$640$		−	1.77152e11i		−	1.05591i
$641$	−1.35735e11			−0.804009			−0.402004	−	0.915638i	$-0.631686\pi$
$641$	−1.35735e11			−0.804009			−0.402004	+	0.915638i	$0.631686\pi$
$642$		−	5.77544e10i		−	0.339973i
$643$	2.93118e11			1.71474			0.857372	−	0.514697i	$-0.172096\pi$
$643$	2.93118e11			1.71474			0.857372	+	0.514697i	$0.172096\pi$
$644$			7.97261e8i			0.00463508i
$645$		−	4.52724e10i		−	0.261574i
$646$		−	2.59004e11i		−	1.48722i
$647$	1.79140e11			1.02229			0.511147	−	0.859493i	$-0.329221\pi$
$647$	1.79140e11			1.02229			0.511147	+	0.859493i	$0.329221\pi$
$648$		−	9.32141e9i		−	0.0528666i
$649$	7.95124e10	−	2.14366e11i	0.448184	−	1.20831i
$650$	−2.52188e10			−0.141277
$651$		−	2.30568e8i		−	0.00128373i
$652$	1.78531e11			0.987923
$653$	4.74277e10			0.260843			0.130422	−	0.991459i	$-0.458367\pi$
$653$	4.74277e10			0.260843			0.130422	+	0.991459i	$0.458367\pi$
$654$	1.75960e11			0.961841
$655$			1.80107e11i			0.978512i
$656$	1.68214e10			0.0908337
$657$			6.62440e10i			0.355537i
$658$	1.32299e8			0.000705754
$659$			1.18263e11i			0.627057i	0.949579	+	0.313529i	$0.101511\pi$
$659$			1.18263e11i			0.627057i	−0.949579	+	0.313529i	$0.898489\pi$
$660$			1.05566e11i			0.556352i
$661$	−1.08992e11			−0.570935			−0.285468	−	0.958388i	$-0.592149\pi$
$661$	−1.08992e11			−0.570935			−0.285468	+	0.958388i	$0.592149\pi$
$662$		−	9.47364e9i		−	0.0493270i
$663$		−	1.79720e10i		−	0.0930125i
$664$	3.43096e10			0.176499
$665$	−1.76682e9			−0.00903452
$666$	−1.44295e11			−0.733421
$667$		−	3.16686e11i		−	1.60002i
$668$	−1.72917e11			−0.868422
$669$	3.32682e10			0.166083
$670$	2.82162e11			1.40023
$671$	−4.88879e10			−0.241163
$672$			5.15898e8i			0.00252980i
$673$		−	1.57368e11i		−	0.767110i	−0.923518	−	0.383555i	$-0.874700\pi$
$673$		−	1.57368e11i		−	0.767110i	0.923518	−	0.383555i	$-0.125300\pi$
$674$	4.66339e11			2.25976
$675$	−1.68696e10			−0.0812625
$676$	−1.21922e11			−0.583840
$677$	−3.19743e11			−1.52211			−0.761056	−	0.648686i	$-0.775319\pi$
$677$	−3.19743e11			−1.52211			−0.761056	+	0.648686i	$0.775319\pi$
$678$	5.81788e10			0.275325
$679$			1.42874e8i			0.000672162i
$680$		−	7.45147e10i		−	0.348503i
$681$			1.59856e11i			0.743260i
$682$			1.98156e11i			0.915945i
$683$		−	2.81760e11i		−	1.29478i	−0.762157	−	0.647392i	$-0.775860\pi$
$683$		−	2.81760e11i		−	1.29478i	0.762157	−	0.647392i	$-0.224140\pi$
$684$	8.68455e10			0.396755
$685$	−4.01035e11			−1.82146
$686$		−	2.25445e9i		−	0.0101799i
$687$			1.86346e11i			0.836551i
$688$			1.05025e11i			0.468748i
$689$		−	6.94284e10i		−	0.308078i
$690$	3.68802e11			1.62703
$691$		−	1.05880e11i		−	0.464409i	−0.972667	−	0.232204i	$-0.925406\pi$
$691$		−	1.05880e11i		−	0.464409i	0.972667	−	0.232204i	$-0.0745938\pi$
$692$		−	1.86644e11i		−	0.813937i
$693$			3.95373e8i			0.00171425i
$694$	−8.03216e10			−0.346254
$695$	−3.24769e11			−1.39199
$696$		−	5.56735e10i		−	0.237253i
$697$	1.06709e10			0.0452136
$698$	2.48159e11			1.04546
$699$			8.32740e10i			0.348819i
$700$	2.53655e8			0.00105645
$701$		−	2.03854e10i		−	0.0844203i	−0.999109	−	0.0422102i	$-0.986560\pi$
$701$		−	2.03854e10i		−	0.0844203i	0.999109	−	0.0422102i	$-0.0134399\pi$
$702$	1.56374e10			0.0643898
$703$			7.99827e11i			3.27473i
$704$		−	5.27766e10i		−	0.214857i
$705$		−	2.35842e10i		−	0.0954694i
$706$	−5.76826e9			−0.0232181
$707$			6.36478e8i			0.00254745i
$708$	8.52775e10	+	3.16310e10i	0.339392	+	0.125887i
$709$	−7.84044e10			−0.310281			−0.155141	−	0.987892i	$-0.549583\pi$
$709$	−7.84044e10			−0.310281			−0.155141	+	0.987892i	$0.549583\pi$
$710$		−	2.90319e10i		−	0.114246i
$711$	1.02785e11			0.402210
$712$	7.84918e10			0.305425
$713$	2.66775e11			1.03226
$714$			4.69076e8i			0.00180489i
$715$	1.05363e11			0.403149
$716$			3.86491e10i			0.147057i
$717$	−1.30292e11			−0.492993
$718$			6.03639e11i			2.27133i
$719$		−	2.56436e11i		−	0.959542i	−0.877394	−	0.479771i	$-0.840720\pi$
$719$		−	2.56436e11i		−	0.959542i	0.877394	−	0.479771i	$-0.159280\pi$
$720$	1.31816e11			0.490500
$721$		−	4.70359e8i		−	0.00174056i
$722$		−	9.02562e11i		−	3.32145i
$723$	2.49823e11			0.914281
$724$	−3.64945e10			−0.132823
$725$	−1.00756e11			−0.364687
$726$		−	1.35207e11i		−	0.486690i
$727$	1.68647e11			0.603729			0.301864	−	0.953351i	$-0.402391\pi$
$727$	1.68647e11			0.603729			0.301864	+	0.953351i	$0.402391\pi$
$728$	1.39889e8			0.000498033
$729$	1.04604e10			0.0370370
$730$	−4.60763e11			−1.62250
$731$			6.66240e10i			0.233325i
$732$		−	1.94482e10i		−	0.0677383i
$733$	−1.48717e11			−0.515162			−0.257581	−	0.966257i	$-0.582925\pi$
$733$	−1.48717e11			−0.515162			−0.257581	+	0.966257i	$0.582925\pi$
$734$	−4.44686e10			−0.153204
$735$	−2.00942e11			−0.688527
$736$	−5.96912e11			−2.03422
$737$	−3.49993e11			−1.18629
$738$			9.28475e9i			0.0313000i
$739$			2.57928e11i			0.864809i	0.901680	+	0.432405i	$0.142335\pi$
$739$			2.57928e11i			0.864809i	−0.901680	+	0.432405i	$0.857665\pi$
$740$		−	3.86769e11i		−	1.28981i
$741$		−	8.66785e10i		−	0.287500i
$742$			1.81211e9i			0.00597818i
$743$	−3.83734e10			−0.125914			−0.0629571	−	0.998016i	$-0.520053\pi$
$743$	−3.83734e10			−0.125914			−0.0629571	+	0.998016i	$0.520053\pi$
$744$	4.68991e10			0.153064
$745$		−	2.86002e11i		−	0.928420i
$746$		−	2.83311e11i		−	0.914762i
$747$			3.85017e10i			0.123651i
$748$		−	1.55354e11i		−	0.496267i
$749$	5.79786e8			0.00184222
$750$			1.60547e11i			0.507408i
$751$			5.65819e10i			0.177876i	0.996037	+	0.0889380i	$0.0283473\pi$
$751$			5.65819e10i			0.177876i	−0.996037	+	0.0889380i	$0.971653\pi$
$752$			5.47116e10i			0.171083i
$753$	7.22508e10			0.224731
$754$	9.33969e10			0.288966
$755$			3.13417e11i			0.964573i
$756$	−1.57284e8			−0.000481501
$757$	2.69700e11			0.821292			0.410646	−	0.911795i	$-0.365303\pi$
$757$	2.69700e11			0.821292			0.410646	+	0.911795i	$0.365303\pi$
$758$			7.52928e11i			2.28075i
$759$	−4.57460e11			−1.37843
$760$		−	3.59383e11i		−	1.07722i
$761$	5.23769e11			1.56171			0.780856	−	0.624711i	$-0.214783\pi$
$761$	5.23769e11			1.56171			0.780856	+	0.624711i	$0.214783\pi$
$762$		−	2.09348e11i		−	0.620940i
$763$			1.76643e9i			0.00521193i
$764$		−	3.59569e11i		−	1.05538i
$765$	8.36193e10			0.244152
$766$		−	4.10621e11i		−	1.19269i
$767$	3.15702e10	−	8.51135e10i	0.0912211	−	0.245933i
$768$	−2.60322e11			−0.748284
$769$			3.65241e11i			1.04442i	0.852818	+	0.522208i	$0.174892\pi$
$769$			3.65241e11i			1.04442i	−0.852818	+	0.522208i	$0.825108\pi$
$770$	−2.75003e9			−0.00782302
$771$	2.26152e11			0.640005
$772$	−2.97828e11			−0.838488
$773$			5.96411e11i			1.67043i	0.549924	+	0.835214i	$0.314657\pi$
$773$			5.96411e11i			1.67043i	−0.549924	+	0.835214i	$0.685343\pi$
$774$	−5.79697e10			−0.161524
$775$		−	8.48766e10i		−	0.235278i
$776$	−2.90616e10			−0.0801442
$777$		−	1.44855e9i		−	0.00397419i
$778$		−	7.01409e10i		−	0.191449i
$779$	5.14655e10			0.139755
$780$			4.19148e10i			0.113237i
$781$			3.60110e10i			0.0967901i
$782$	−5.42737e11			−1.45132
$783$	6.24760e10			0.166213
$784$	4.66154e11			1.23386
$785$		−	4.94583e11i		−	1.30245i
$786$	2.30621e11			0.604238
$787$	−7.02048e10			−0.183007			−0.0915036	−	0.995805i	$-0.529167\pi$
$787$	−7.02048e10			−0.183007			−0.0915036	+	0.995805i	$0.529167\pi$
$788$	2.36357e11			0.613005
$789$	1.27084e11			0.327930
$790$			7.14927e11i			1.83550i
$791$			5.84046e8i			0.00149191i
$792$	−8.04216e10			−0.204396
$793$	−1.94108e10			−0.0490852
$794$	−2.97451e11			−0.748399
$795$	3.23034e11			0.808686
$796$	3.40960e11			0.849281
$797$		−	3.91006e11i		−	0.969059i	−0.874775	−	0.484529i	$-0.838991\pi$
$797$		−	3.91006e11i		−	0.969059i	0.874775	−	0.484529i	$-0.161009\pi$
$798$			2.26235e9i			0.00557888i
$799$			3.47070e10i			0.0851589i
$800$			1.89912e11i			0.463653i
$801$			8.80823e10i			0.213973i
$802$	2.41691e11			0.584202
$803$	5.71528e11			1.37460
$804$		−	1.39231e11i		−	0.333206i
$805$			3.70233e9i			0.00881641i
$806$			7.86772e10i			0.186427i
$807$			1.35512e11i			0.319509i
$808$	−1.29464e11			−0.303741
$809$			4.06765e11i			0.949618i	0.880089	+	0.474809i	$0.157483\pi$
$809$			4.06765e11i			0.949618i	−0.880089	+	0.474809i	$0.842517\pi$
$810$			7.27573e10i			0.169019i
$811$			8.67660e10i			0.200570i	0.994959	+	0.100285i	$0.0319755\pi$
$811$			8.67660e10i			0.200570i	−0.994959	+	0.100285i	$0.968025\pi$
$812$	−9.39401e8			−0.00216086
$813$	−4.37541e10			−0.100151
$814$			1.24492e12i			2.83559i
$815$	8.29065e11			1.87914
$816$	−1.93984e11			−0.437527
$817$			3.21327e11i			0.721204i
$818$	8.64642e11			1.93118
$819$			1.56981e8i			0.000348910i
$820$	−2.48870e10			−0.0550448
$821$			4.58552e11i			1.00929i	0.863327	+	0.504645i	$0.168377\pi$
$821$			4.58552e11i			1.00929i	−0.863327	+	0.504645i	$0.831623\pi$
$822$			5.13510e11i			1.12477i
$823$			5.39103e11i			1.17509i	0.809190	+	0.587547i	$0.199906\pi$
$823$			5.39103e11i			1.17509i	−0.809190	+	0.587547i	$0.800094\pi$
$824$	9.56744e10			0.207533
$825$			1.45545e11i			0.314181i
$826$	−8.23994e8	+	2.22150e9i	−0.00177013	+	0.00477228i
$827$	5.49079e11			1.17385			0.586925	−	0.809641i	$-0.300338\pi$
$827$	5.49079e11			1.17385			0.586925	+	0.809641i	$0.300338\pi$
$828$		−	1.81983e11i		−	0.387177i
$829$	−5.54877e11			−1.17484			−0.587420	−	0.809282i	$-0.699856\pi$
$829$	−5.54877e11			−1.17484			−0.587420	+	0.809282i	$0.699856\pi$
$830$	−2.67800e11			−0.564285
$831$	−3.28677e11			−0.689232
$832$		−	2.09548e10i		−	0.0437310i
$833$	2.95711e11			0.614167
$834$			4.15855e11i			0.859562i
$835$	−8.02993e11			−1.65183
$836$		−	7.49270e11i		−	1.53396i
$837$			5.26295e10i			0.107233i
$838$	9.67939e11			1.96278
$839$		−	3.30239e11i		−	0.666470i	−0.942844	−	0.333235i	$-0.891860\pi$
$839$		−	3.30239e11i		−	0.666470i	0.942844	−	0.333235i	$-0.108140\pi$
$840$			6.50871e8i			0.00130731i
$841$	−1.27099e11			−0.254074
$842$	−8.12288e11			−1.61608
$843$	3.18053e11			0.629781
$844$		−	1.54972e11i		−	0.305410i
$845$	−5.66182e11			−1.11053
$846$	−3.01987e10			−0.0589530
$847$	1.35732e9			0.00263723
$848$	−7.49389e11			−1.44919
$849$		−	5.60455e11i		−	1.07872i
$850$			1.72676e11i			0.330793i
$851$	1.67602e12			3.19567
$852$	−1.43256e10			−0.0271866
$853$	−2.67618e11			−0.505498			−0.252749	−	0.967532i	$-0.581335\pi$
$853$	−2.67618e11			−0.505498			−0.252749	+	0.967532i	$0.581335\pi$
$854$	5.06629e8			0.000952487
$855$	4.03295e11			0.754672
$856$			1.17933e11i			0.219654i
$857$			4.95368e11i			0.918343i	0.888348	+	0.459172i	$0.151854\pi$
$857$			4.95368e11i			0.918343i	−0.888348	+	0.459172i	$0.848146\pi$
$858$		−	1.34914e11i		−	0.248947i
$859$		−	3.63181e10i		−	0.0667038i	−0.999444	−	0.0333519i	$-0.989382\pi$
$859$		−	3.63181e10i		−	0.0667038i	0.999444	−	0.0333519i	$-0.0106182\pi$
$860$		−	1.55383e11i		−	0.284059i
$861$	−9.32080e7			−0.000169606
$862$	1.83470e11			0.332305
$863$		−	6.01541e11i		−	1.08448i	−0.840223	−	0.542241i	$-0.817576\pi$
$863$		−	6.01541e11i		−	1.08448i	0.840223	−	0.542241i	$-0.182424\pi$
$864$		−	1.17759e11i		−	0.211319i
$865$		−	8.66743e11i		−	1.54820i
$866$			6.40961e11i			1.13962i
$867$	2.03168e11			0.359566
$868$		−	7.91348e8i		−	0.00139408i
$869$		−	8.86793e11i		−	1.55504i
$870$			4.34554e11i			0.758519i
$871$	−1.38964e11			−0.241451
$872$	−3.59305e11			−0.621437
$873$		−	3.26125e10i		−	0.0561470i
$874$	−2.61761e12			−4.48601
$875$	−1.61170e9			−0.00274949
$876$			2.27361e11i			0.386099i
$877$	5.69956e11			0.963480			0.481740	−	0.876314i	$-0.340005\pi$
$877$	5.69956e11			0.963480			0.481740	+	0.876314i	$0.340005\pi$
$878$		−	5.81645e11i		−	0.978769i
$879$	2.11183e11			0.353755
$880$		−	1.13726e12i		−	1.89640i
$881$			9.16157e11i			1.52078i	0.649467	+	0.760390i	$0.274992\pi$
$881$			9.16157e11i			1.52078i	−0.649467	+	0.760390i	$0.725008\pi$
$882$			2.57298e11i			0.425170i
$883$	−8.88897e11			−1.46221			−0.731103	−	0.682267i	$-0.760994\pi$
$883$	−8.88897e11			−1.46221			−0.731103	+	0.682267i	$0.760994\pi$
$884$		−	6.16828e10i		−	0.101008i
$885$	3.96013e11	+	1.46889e11i	0.645560	+	0.239450i
$886$	−1.86296e11			−0.302321
$887$		−	8.01932e11i		−	1.29552i	−0.761846	−	0.647758i	$-0.775707\pi$
$887$		−	8.01932e11i		−	1.29552i	0.761846	−	0.647758i	$-0.224293\pi$
$888$	2.94645e11			0.473857
$889$	2.10161e9			0.00336469
$890$	−6.12660e11			−0.976471
$891$		−	9.02479e10i		−	0.143195i
$892$	1.14182e11			0.180359
$893$			1.67391e11i			0.263225i
$894$	−3.66216e11			−0.573306
$895$			1.79479e11i			0.279719i
$896$		−	2.27717e9i		−	0.00353315i
$897$	−1.81633e11			−0.280560
$898$			1.14246e12i			1.75686i
$899$			3.14338e11i			0.481235i
$900$	−5.78994e10			−0.0882478
$901$	−4.75385e11			−0.721350
$902$	8.01053e10			0.121014
$903$		−	5.81947e8i		−	0.000875251i
$904$	−1.18799e11			−0.177885
$905$	−1.69474e11			−0.252644
$906$	4.01319e11			0.595631
$907$	−8.27007e11			−1.22203			−0.611013	−	0.791621i	$-0.709238\pi$
$907$	−8.27007e11			−1.22203			−0.611013	+	0.791621i	$0.709238\pi$
$908$			5.48653e11i			0.807151i
$909$		−	1.45283e11i		−	0.212794i
$910$	−1.09189e9			−0.00159226
$911$	−1.14601e11			−0.166386			−0.0831930	−	0.996533i	$-0.526512\pi$
$911$	−1.14601e11			−0.166386			−0.0831930	+	0.996533i	$0.526512\pi$
$912$	−9.35581e11			−1.35239
$913$	3.32178e11			0.478066
$914$	−1.71444e12			−2.45662
$915$		−	9.03138e10i		−	0.128846i
$916$			6.39570e11i			0.908460i
$917$			2.31516e9i			0.00327419i
$918$		−	1.07071e11i		−	0.150766i
$919$		−	8.78468e11i		−	1.23158i	−0.787909	−	0.615792i	$-0.788836\pi$
$919$		−	8.78468e11i		−	1.23158i	0.787909	−	0.615792i	$-0.211164\pi$
$920$	−7.53081e11			−1.05121
$921$	6.21033e10			0.0863130
$922$			2.51991e11i			0.348708i
$923$			1.42981e10i			0.0197002i
$924$			1.35699e9i			0.00186160i
$925$		−	5.33240e11i		−	0.728376i
$926$	−1.48518e12			−2.01993
$927$			1.07364e11i			0.145392i
$928$		−	7.03333e11i		−	0.948351i
$929$			1.85008e11i			0.248386i	0.992258	+	0.124193i	$0.0396342\pi$
$929$			1.85008e11i			0.248386i	−0.992258	+	0.124193i	$0.960366\pi$
$930$	−3.66066e11			−0.489360
$931$	1.42621e12			1.89838
$932$			2.85810e11i			0.378804i
$933$	−4.09748e11			−0.540742
$934$	8.92431e11			1.17270
$935$		−	7.21435e11i		−	0.943954i
$936$	−3.19311e10			−0.0416017
$937$			4.94364e11i			0.641341i	0.947191	+	0.320670i	$0.103908\pi$
$937$			4.94364e11i			0.641341i	−0.947191	+	0.320670i	$0.896092\pi$
$938$	3.62701e9			0.00468530
$939$			4.61567e11i			0.593708i
$940$		−	8.09449e10i		−	0.103676i
$941$			3.48069e11i			0.443922i	0.975056	+	0.221961i	$0.0712458\pi$
$941$			3.48069e11i			0.443922i	−0.975056	+	0.221961i	$0.928754\pi$
$942$	−6.33295e11			−0.804272
$943$		−	1.07845e11i		−	0.136381i
$944$	−9.18689e11	−	3.40759e11i	−1.15686	−	0.429100i
$945$	−7.30398e8			−0.000915867
$946$			5.00140e11i			0.624493i
$947$	−1.86256e11			−0.231585			−0.115792	−	0.993273i	$-0.536941\pi$
$947$	−1.86256e11			−0.231585			−0.115792	+	0.993273i	$0.536941\pi$
$948$	3.52777e11			0.436784
$949$	2.26924e11			0.279779
$950$			8.32815e11i			1.02248i
$951$	−6.65784e11			−0.813975
$952$		−	9.57837e8i		−	0.00116612i
$953$	6.71862e11			0.814533			0.407266	−	0.913309i	$-0.366482\pi$
$953$	6.71862e11			0.814533			0.407266	+	0.913309i	$0.366482\pi$
$954$		−	4.13633e11i		−	0.499370i
$955$		−	1.66977e12i		−	2.00745i
$956$	−4.47184e11			−0.535370
$957$		−	5.39019e11i		−	0.642623i
$958$		−	3.48899e10i		−	0.0414227i
$959$	−5.15504e9			−0.00609477
$960$	9.74976e10			0.114791
$961$	5.88094e11			0.689530
$962$			4.94292e11i			0.577142i
$963$	−1.32342e11			−0.153884
$964$	8.57436e11			0.992873
$965$	−1.38306e12			−1.59489
$966$	4.74070e9			0.00544420
$967$			7.96501e11i			0.910920i	0.890256	+	0.455460i	$0.150525\pi$
$967$			7.96501e11i			0.910920i	−0.890256	+	0.455460i	$0.849475\pi$
$968$			2.76088e11i			0.314446i
$969$	−5.93498e11			−0.673169
$970$	2.26837e11			0.256228
$971$	5.07923e11			0.571374			0.285687	−	0.958323i	$-0.407778\pi$
$971$	5.07923e11			0.571374			0.285687	+	0.958323i	$0.407778\pi$
$972$	3.59017e10			0.0402207
$973$	−4.17469e9			−0.00465771
$974$			1.14575e12i			1.27307i
$975$			5.77880e10i			0.0639469i
$976$			2.09514e11i			0.230894i
$977$		−	5.48778e11i		−	0.602308i	−0.953576	−	0.301154i	$-0.902628\pi$
$977$		−	5.48778e11i		−	0.602308i	0.953576	−	0.301154i	$-0.0973718\pi$
$978$		−	1.06159e12i		−	1.16038i
$979$	7.59941e11			0.827273
$980$	−6.89666e11			−0.747712
$981$		−	4.03207e11i		−	0.435363i
$982$		−	1.45071e12i		−	1.56004i
$983$			1.03981e12i			1.11363i	0.830637	+	0.556814i	$0.187976\pi$
$983$			1.03981e12i			1.11363i	−0.830637	+	0.556814i	$0.812024\pi$
$984$		−	1.89592e10i		−	0.0202227i
$985$	1.09760e12			1.16600
$986$		−	6.39500e11i		−	0.676601i
$987$		−	3.03159e8i		−	0.000319449i
$988$		−	2.97495e11i		−	0.312214i
$989$	6.73334e11			0.703793
$990$	6.27723e11			0.653472
$991$		−	1.11218e12i		−	1.15313i	−0.817051	−	0.576566i	$-0.804392\pi$
$991$		−	1.11218e12i		−	1.15313i	0.817051	−	0.576566i	$-0.195608\pi$
$992$	5.92485e11			0.611830
$993$	−2.17085e10			−0.0223272
$994$		−	3.73185e8i		−	0.000382278i
$995$	1.58336e12			1.61542
$996$			1.32145e11i			0.134280i
$997$	−9.52275e11			−0.963789			−0.481894	−	0.876229i	$-0.660051\pi$
$997$	−9.52275e11			−0.963789			−0.481894	+	0.876229i	$0.660051\pi$
$998$		−	2.04169e12i		−	2.05811i
$999$			3.30646e11i			0.331972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.18	✓	80
59.58	odd	2	inner	177.9.c.a.58.63	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.18	✓	80	1.1	even	1	trivial
177.9.c.a.58.63	yes	80	59.58	odd	2	inner

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-20.4085i q^{2} -46.7654 q^{3} -160.507 q^{4} -745.364 q^{5} +954.411i q^{6} -9.58116 q^{7} -1948.88i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q-20.4085i q^{2} -46.7654 q^{3} -160.507 q^{4} -745.364 q^{5} +954.411i q^{6} -9.58116 q^{7} -1948.88i q^{8} +2187.00 q^{9} +15211.8i q^{10} -18868.6i q^{11} +7506.15 q^{12} -7491.72i q^{13} +195.537i q^{14} +34857.2 q^{15} -80863.3 q^{16} -51296.7 q^{17} -44633.4i q^{18} -247403. q^{19} +119636. q^{20} +448.067 q^{21} -385080. q^{22} +518429. i q^{23} +91139.9i q^{24} +164942. q^{25} -152895. q^{26} -102276. q^{27} +1537.84 q^{28} -610858. q^{29} -711383. i q^{30} -514584. i q^{31} +1.15139e6i q^{32} +882397. i q^{33} +1.04689e6i q^{34} +7141.45 q^{35} -351028. q^{36} -3.23289e6i q^{37} +5.04913e6i q^{38} +350353. i q^{39} +1.45262e6i q^{40} -208023. q^{41} -9144.36i q^{42} -1.29880e6i q^{43} +3.02854e6i q^{44} -1.63011e6 q^{45} +1.05804e7 q^{46} -676594. i q^{47} +3.78160e6 q^{48} -5.76471e6 q^{49} -3.36622e6i q^{50} +2.39891e6 q^{51} +1.20247e6i q^{52} +9.26736e6 q^{53} +2.08730e6i q^{54} +1.40640e7i q^{55} +18672.5i q^{56} +1.15699e7 q^{57} +1.24667e7i q^{58} +(1.13610e7 + 4.21401e6i) q^{59} -5.59482e6 q^{60} -2.59096e6i q^{61} -1.05019e7 q^{62} -20954.0 q^{63} +2.79706e6 q^{64} +5.58406e6i q^{65} +1.80084e7 q^{66} -1.85490e7i q^{67} +8.23346e6 q^{68} -2.42445e7i q^{69} -145746. i q^{70} -1.90851e6 q^{71} -4.26219e6i q^{72} +3.02899e7i q^{73} -6.59784e7 q^{74} -7.71359e6 q^{75} +3.97099e7 q^{76} +180783. i q^{77} +7.15018e6 q^{78} +4.69983e7 q^{79} +6.02726e7 q^{80} +4.78297e6 q^{81} +4.24543e6i q^{82} +1.76048e7i q^{83} -71917.7 q^{84} +3.82347e7 q^{85} -2.65065e7 q^{86} +2.85670e7 q^{87} -3.67726e7 q^{88} +4.02754e7i q^{89} +3.32681e7i q^{90} +71779.4i q^{91} -8.32113e7i q^{92} +2.40647e7i q^{93} -1.38083e7 q^{94} +1.84405e8 q^{95} -5.38450e7i q^{96} -1.49120e7i q^{97} +1.17649e8i q^{98} -4.12656e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Introduction

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