LMFDB - Embedded newform 177.9.c.a.58.13

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			58.13
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.68

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-23.8187i q^{2} +46.7654 q^{3} -311.333 q^{4} +925.940 q^{5} -1113.89i q^{6} -3176.58 q^{7} +1317.95i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q-23.8187i q^{2} +46.7654 q^{3} -311.333 q^{4} +925.940 q^{5} -1113.89i q^{6} -3176.58 q^{7} +1317.95i q^{8} +2187.00 q^{9} -22054.7i q^{10} +8879.23i q^{11} -14559.6 q^{12} +30696.0i q^{13} +75662.2i q^{14} +43301.9 q^{15} -48309.2 q^{16} -7149.59 q^{17} -52091.6i q^{18} -83033.0 q^{19} -288275. q^{20} -148554. q^{21} +211492. q^{22} +117469. i q^{23} +61634.5i q^{24} +466740. q^{25} +731139. q^{26} +102276. q^{27} +988973. q^{28} -1.19671e6 q^{29} -1.03140e6i q^{30} +138856. i q^{31} +1.48806e6i q^{32} +415240. i q^{33} +170294. i q^{34} -2.94133e6 q^{35} -680884. q^{36} -1.23654e6i q^{37} +1.97774e6i q^{38} +1.43551e6i q^{39} +1.22034e6i q^{40} -1.16558e6 q^{41} +3.53837e6i q^{42} +3.96763e6i q^{43} -2.76439e6i q^{44} +2.02503e6 q^{45} +2.79798e6 q^{46} +3.87623e6i q^{47} -2.25920e6 q^{48} +4.32588e6 q^{49} -1.11172e7i q^{50} -334353. q^{51} -9.55665e6i q^{52} -9.23542e6 q^{53} -2.43608e6i q^{54} +8.22163e6i q^{55} -4.18658e6i q^{56} -3.88307e6 q^{57} +2.85042e7i q^{58} +(-1.00090e7 + 6.83014e6i) q^{59} -1.34813e7 q^{60} +1.02656e7i q^{61} +3.30737e6 q^{62} -6.94719e6 q^{63} +2.30766e7 q^{64} +2.84226e7i q^{65} +9.89050e6 q^{66} +1.75285e7i q^{67} +2.22590e6 q^{68} +5.49350e6i q^{69} +7.00587e7i q^{70} +8.47639e6 q^{71} +2.88236e6i q^{72} +2.09288e7i q^{73} -2.94529e7 q^{74} +2.18273e7 q^{75} +2.58509e7 q^{76} -2.82056e7i q^{77} +3.41920e7 q^{78} +2.15211e7 q^{79} -4.47314e7 q^{80} +4.78297e6 q^{81} +2.77625e7i q^{82} -6.11488e7i q^{83} +4.62497e7 q^{84} -6.62010e6 q^{85} +9.45039e7 q^{86} -5.59647e7 q^{87} -1.17024e7 q^{88} -2.64859e7i q^{89} -4.82337e7i q^{90} -9.75082e7i q^{91} -3.65721e7i q^{92} +6.49365e6i q^{93} +9.23270e7 q^{94} -7.68836e7 q^{95} +6.95897e7i q^{96} -6.83477e7i q^{97} -1.03037e8i q^{98} +1.94189e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	23.8187i		−	1.48867i	−0.667806	−	0.744336i	$-0.732766\pi$
$2$		−	23.8187i		−	1.48867i	0.667806	−	0.744336i	$-0.267234\pi$
$3$	46.7654			0.577350
$3$	46.7654			0.577350
$4$	−311.333			−1.21614
$5$	925.940			1.48150			0.740752	−	0.671779i	$-0.234469\pi$
$5$	925.940			1.48150			0.740752	+	0.671779i	$0.234469\pi$
$6$		−	1113.89i		−	0.859485i
$7$	−3176.58			−1.32302			−0.661512	−	0.749934i	$-0.730085\pi$
$7$	−3176.58			−1.32302			−0.661512	+	0.749934i	$0.730085\pi$
$8$			1317.95i			0.321765i
$9$	2187.00			0.333333
$10$		−	22054.7i		−	2.20547i
$11$			8879.23i			0.606463i	0.952917	+	0.303232i	$0.0980656\pi$
$11$			8879.23i			0.606463i	−0.952917	+	0.303232i	$0.901934\pi$
$12$	−14559.6			−0.702140
$13$			30696.0i			1.07475i	0.843343	+	0.537375i	$0.180584\pi$
$13$			30696.0i			1.07475i	−0.843343	+	0.537375i	$0.819416\pi$
$14$			75662.2i			1.96955i
$15$	43301.9			0.855347
$16$	−48309.2			−0.737140
$17$	−7149.59			−0.0856024			−0.0428012	−	0.999084i	$-0.513628\pi$
$17$	−7149.59			−0.0856024			−0.0428012	+	0.999084i	$0.513628\pi$
$18$		−	52091.6i		−	0.496224i
$19$	−83033.0			−0.637142			−0.318571	−	0.947899i	$-0.603203\pi$
$19$	−83033.0			−0.637142			−0.318571	+	0.947899i	$0.603203\pi$
$20$	−288275.			−1.80172
$21$	−148554.			−0.763849
$22$	211492.			0.902824
$23$			117469.i			0.419772i	0.977726	+	0.209886i	$0.0673093\pi$
$23$			117469.i			0.419772i	−0.977726	+	0.209886i	$0.932691\pi$
$24$			61634.5i			0.185771i
$25$	466740.			1.19485
$26$	731139.			1.59995
$27$	102276.			0.192450
$28$	988973.			1.60899
$29$	−1.19671e6			−1.69199			−0.845996	−	0.533190i	$-0.820993\pi$
$29$	−1.19671e6			−1.69199			−0.845996	+	0.533190i	$0.820993\pi$
$30$		−	1.03140e6i		−	1.27333i
$31$			138856.i			0.150355i	0.997170	+	0.0751774i	$0.0239523\pi$
$31$			138856.i			0.150355i	−0.997170	+	0.0751774i	$0.976048\pi$
$32$			1.48806e6i			1.41912i
$33$			415240.i			0.350142i
$34$			170294.i			0.127434i
$35$	−2.94133e6			−1.96007
$36$	−680884.			−0.405381
$37$		−	1.23654e6i		−	0.659784i	−0.944019	−	0.329892i	$-0.892988\pi$
$37$		−	1.23654e6i		−	0.659784i	0.944019	−	0.329892i	$-0.107012\pi$
$38$			1.97774e6i			0.948496i
$39$			1.43551e6i			0.620508i
$40$			1.22034e6i			0.476697i
$41$	−1.16558e6			−0.412482			−0.206241	−	0.978501i	$-0.566123\pi$
$41$	−1.16558e6			−0.412482			−0.206241	+	0.978501i	$0.566123\pi$
$42$			3.53837e6i			1.13712i
$43$			3.96763e6i			1.16053i	0.814427	+	0.580266i	$0.197051\pi$
$43$			3.96763e6i			1.16053i	−0.814427	+	0.580266i	$0.802949\pi$
$44$		−	2.76439e6i		−	0.737546i
$45$	2.02503e6			0.493835
$46$	2.79798e6			0.624903
$47$			3.87623e6i			0.794362i	0.917740	+	0.397181i	$0.130012\pi$
$47$			3.87623e6i			0.794362i	−0.917740	+	0.397181i	$0.869988\pi$
$48$	−2.25920e6			−0.425588
$49$	4.32588e6			0.750395
$50$		−	1.11172e7i		−	1.77875i
$51$	−334353.			−0.0494225
$52$		−	9.55665e6i		−	1.30705i
$53$	−9.23542e6			−1.17045			−0.585225	−	0.810871i	$-0.698994\pi$
$53$	−9.23542e6			−1.17045			−0.585225	+	0.810871i	$0.698994\pi$
$54$		−	2.43608e6i		−	0.286495i
$55$			8.22163e6i			0.898478i
$56$		−	4.18658e6i		−	0.425704i
$57$	−3.88307e6			−0.367854
$58$			2.85042e7i			2.51882i
$59$	−1.00090e7	+	6.83014e6i	−0.826003	+	0.563666i
$59$	−1.00090e7	+	6.83014e6i	−0.826003	+	0.563666i
$60$	−1.34813e7			−1.04022
$61$			1.02656e7i			0.741419i	0.928749	+	0.370710i	$0.120886\pi$
$61$			1.02656e7i			0.741419i	−0.928749	+	0.370710i	$0.879114\pi$
$62$	3.30737e6			0.223829
$63$	−6.94719e6			−0.441008
$64$	2.30766e7			1.37547
$65$			2.84226e7i			1.59225i
$66$	9.89050e6			0.521246
$67$			1.75285e7i			0.869851i	0.900466	+	0.434926i	$0.143225\pi$
$67$			1.75285e7i			0.869851i	−0.900466	+	0.434926i	$0.856775\pi$
$68$	2.22590e6			0.104105
$69$			5.49350e6i			0.242356i
$70$			7.00587e7i			2.91790i
$71$	8.47639e6			0.333563			0.166781	−	0.985994i	$-0.446663\pi$
$71$	8.47639e6			0.333563			0.166781	+	0.985994i	$0.446663\pi$
$72$			2.88236e6i			0.107255i
$73$			2.09288e7i			0.736976i	0.929633	+	0.368488i	$0.120124\pi$
$73$			2.09288e7i			0.736976i	−0.929633	+	0.368488i	$0.879876\pi$
$74$	−2.94529e7			−0.982201
$75$	2.18273e7			0.689849
$76$	2.58509e7			0.774856
$77$		−	2.82056e7i		−	0.802366i
$78$	3.41920e7			0.923732
$79$	2.15211e7			0.552531			0.276265	−	0.961081i	$-0.410903\pi$
$79$	2.15211e7			0.552531			0.276265	+	0.961081i	$0.410903\pi$
$80$	−4.47314e7			−1.09208
$81$	4.78297e6			0.111111
$82$			2.77625e7i			0.614050i
$83$		−	6.11488e7i		−	1.28847i	−0.764826	−	0.644237i	$-0.777175\pi$
$83$		−	6.11488e7i		−	1.28847i	0.764826	−	0.644237i	$-0.222825\pi$
$84$	4.62497e7			0.928949
$85$	−6.62010e6			−0.126820
$86$	9.45039e7			1.72765
$87$	−5.59647e7			−0.976872
$88$	−1.17024e7			−0.195139
$89$		−	2.64859e7i		−	0.422138i	−0.977471	−	0.211069i	$-0.932306\pi$
$89$		−	2.64859e7i		−	0.422138i	0.977471	−	0.211069i	$-0.0676944\pi$
$90$		−	4.82337e7i		−	0.735158i
$91$		−	9.75082e7i		−	1.42192i
$92$		−	3.65721e7i		−	0.510503i
$93$			6.49365e6i			0.0868074i
$94$	9.23270e7			1.18254
$95$	−7.68836e7			−0.943929
$96$			6.95897e7i			0.819332i
$97$		−	6.83477e7i		−	0.772035i	−0.922491	−	0.386017i	$-0.873850\pi$
$97$		−	6.83477e7i		−	0.772035i	0.922491	−	0.386017i	$-0.126150\pi$
$98$		−	1.03037e8i		−	1.11709i
$99$			1.94189e7i			0.202154i
$100$	−1.45311e8			−1.45311
$101$			1.43956e8i			1.38339i	0.722189	+	0.691696i	$0.243136\pi$
$101$			1.43956e8i			1.38339i	−0.722189	+	0.691696i	$0.756864\pi$
$102$			7.96388e6i			0.0735739i
$103$		−	9.23448e7i		−	0.820471i	−0.911980	−	0.410236i	$-0.865446\pi$
$103$		−	9.23448e7i		−	0.820471i	0.911980	−	0.410236i	$-0.134554\pi$
$104$	−4.04558e7			−0.345818
$105$	−1.37552e8			−1.13165
$106$			2.19976e8i			1.74242i
$107$	8.88588e7			0.677899			0.338950	−	0.940805i	$-0.389928\pi$
$107$	8.88588e7			0.677899			0.338950	+	0.940805i	$0.389928\pi$
$108$	−3.18418e7			−0.234047
$109$		−	2.61781e8i		−	1.85452i	−0.374414	−	0.927262i	$-0.622156\pi$
$109$		−	2.61781e8i		−	1.85452i	0.374414	−	0.927262i	$-0.377844\pi$
$110$	1.95829e8			1.33754
$111$		−	5.78273e7i		−	0.380926i
$112$	1.53458e8			0.975254
$113$		−	6.11567e7i		−	0.375086i	−0.982256	−	0.187543i	$-0.939948\pi$
$113$		−	6.11567e7i		−	0.375086i	0.982256	−	0.187543i	$-0.0600523\pi$
$114$			9.24899e7i			0.547614i
$115$			1.08770e8i			0.621894i
$116$	3.72576e8			2.05770
$117$			6.71321e7i			0.358250i
$118$	1.62685e8	+	2.38401e8i	0.839113	+	1.22965i
$119$	2.27113e7			0.113254
$120$			5.70698e7i			0.275221i
$121$	1.35518e8			0.632203
$122$	2.44513e8			1.10373
$123$	−5.45086e7			−0.238147
$124$		−	4.32304e7i		−	0.182853i
$125$	7.04779e7			0.288677
$126$			1.65473e8i			0.656516i
$127$	−1.68592e8			−0.648070			−0.324035	−	0.946045i	$-0.605040\pi$
$127$	−1.68592e8			−0.648070			−0.324035	+	0.946045i	$0.605040\pi$
$128$		−	1.68711e8i		−	0.628499i
$129$			1.85548e8i			0.670034i
$130$	6.76991e8			2.37033
$131$			1.64969e8i			0.560165i	0.959976	+	0.280083i	$0.0903619\pi$
$131$			1.64969e8i			0.560165i	−0.959976	+	0.280083i	$0.909638\pi$
$132$		−	1.29278e8i		−	0.425822i
$133$	2.63761e8			0.842955
$134$	4.17506e8			1.29492
$135$	9.47013e7			0.285116
$136$		−	9.42282e6i		−	0.0275439i
$137$	6.18803e6			0.0175659			0.00878295	−	0.999961i	$-0.497204\pi$
$137$	6.18803e6			0.0175659			0.00878295	+	0.999961i	$0.497204\pi$
$138$	1.30848e8			0.360788
$139$	5.51090e8			1.47626			0.738131	−	0.674658i	$-0.235709\pi$
$139$	5.51090e8			1.47626			0.738131	+	0.674658i	$0.235709\pi$
$140$	9.15730e8			2.38372
$141$			1.81274e8i			0.458625i
$142$		−	2.01897e8i		−	0.496565i
$143$	−2.72556e8			−0.651797
$144$	−1.05652e8			−0.245713
$145$	−1.10808e9			−2.50669
$146$	4.98498e8			1.09711
$147$	2.02301e8			0.433241
$148$			3.84975e8i			0.802391i
$149$		−	2.41337e7i		−	0.0489642i	−0.999700	−	0.0244821i	$-0.992206\pi$
$149$		−	2.41337e7i		−	0.0489642i	0.999700	−	0.0244821i	$-0.00779367\pi$
$150$		−	5.19898e8i		−	1.02696i
$151$			7.10939e8i			1.36749i	0.729721	+	0.683745i	$0.239650\pi$
$151$			7.10939e8i			1.36749i	−0.729721	+	0.683745i	$0.760350\pi$
$152$		−	1.09433e8i		−	0.205010i
$153$	−1.56362e7			−0.0285341
$154$	−6.71822e8			−1.19446
$155$			1.28572e8i			0.222751i
$156$		−	4.46920e8i		−	0.754626i
$157$		−	3.99591e8i		−	0.657684i	−0.944385	−	0.328842i	$-0.893342\pi$
$157$		−	3.99591e8i		−	0.657684i	0.944385	−	0.328842i	$-0.106658\pi$
$158$		−	5.12606e8i		−	0.822537i
$159$	−4.31898e8			−0.675760
$160$			1.37785e9i			2.10244i
$161$		−	3.73152e8i		−	0.555369i
$162$		−	1.13924e8i		−	0.165408i
$163$	−3.44412e8			−0.487896			−0.243948	−	0.969788i	$-0.578443\pi$
$163$	−3.44412e8			−0.487896			−0.243948	+	0.969788i	$0.578443\pi$
$164$	3.62882e8			0.501637
$165$			3.84488e8i			0.518736i
$166$	−1.45649e9			−1.91811
$167$	7.07060e8			0.909055			0.454528	−	0.890733i	$-0.349808\pi$
$167$	7.07060e8			0.909055			0.454528	+	0.890733i	$0.349808\pi$
$168$		−	1.95787e8i		−	0.245780i
$169$	−1.26511e8			−0.155089
$170$			1.57682e8i			0.188794i
$171$	−1.81593e8			−0.212381
$172$		−	1.23525e9i		−	1.41137i
$173$			1.20190e9i			1.34179i	0.741552	+	0.670896i	$0.234090\pi$
$173$			1.20190e9i			1.34179i	−0.741552	+	0.670896i	$0.765910\pi$
$174$			1.33301e9i			1.45424i
$175$	−1.48264e9			−1.58082
$176$		−	4.28948e8i		−	0.447048i
$177$	−4.68074e8	+	3.19414e8i	−0.476893	+	0.325432i
$178$	−6.30860e8			−0.628424
$179$		−	2.78198e8i		−	0.270983i	−0.990778	−	0.135492i	$-0.956739\pi$
$179$		−	2.78198e8i		−	0.270983i	0.990778	−	0.135492i	$-0.0432614\pi$
$180$	−6.30458e8			−0.600573
$181$	−1.66642e9			−1.55264			−0.776318	−	0.630341i	$-0.782915\pi$
$181$	−1.66642e9			−1.55264			−0.776318	+	0.630341i	$0.782915\pi$
$182$	−2.32252e9			−2.11677
$183$			4.80073e8i			0.428059i
$184$	−1.54819e8			−0.135068
$185$		−	1.14496e9i		−	0.977472i
$186$	1.54671e8			0.129228
$187$		−	6.34829e7i		−	0.0519147i
$188$		−	1.20680e9i		−	0.966058i
$189$	−3.24888e8			−0.254616
$190$			1.83127e9i			1.40520i
$191$		−	1.72448e9i		−	1.29576i	−0.761741	−	0.647882i	$-0.775655\pi$
$191$		−	1.72448e9i		−	1.29576i	0.761741	−	0.647882i	$-0.224345\pi$
$192$	1.07918e9			0.794128
$193$	−1.65533e9			−1.19304			−0.596522	−	0.802597i	$-0.703451\pi$
$193$	−1.65533e9			−1.19304			−0.596522	+	0.802597i	$0.703451\pi$
$194$	−1.62796e9			−1.14931
$195$			1.32919e9i			0.919285i
$196$	−1.34679e9			−0.912587
$197$	1.44601e9			0.960077			0.480039	−	0.877247i	$-0.340623\pi$
$197$	1.44601e9			0.960077			0.480039	+	0.877247i	$0.340623\pi$
$198$	4.62533e8			0.300941
$199$	2.48184e9			1.58256			0.791281	−	0.611453i	$-0.209415\pi$
$199$	2.48184e9			1.58256			0.791281	+	0.611453i	$0.209415\pi$
$200$			6.15140e8i			0.384463i
$201$			8.19726e8i			0.502209i
$202$	3.42886e9			2.05942
$203$	3.80146e9			2.23855
$204$	1.04095e8			0.0601049
$205$	−1.07925e9			−0.611094
$206$	−2.19954e9			−1.22141
$207$			2.56906e8i			0.139924i
$208$		−	1.48290e9i		−	0.792241i
$209$		−	7.37269e8i		−	0.386403i
$210$			3.27632e9i			1.68465i
$211$			1.23047e8i			0.0620786i	0.999518	+	0.0310393i	$0.00988171\pi$
$211$			1.23047e8i			0.0620786i	−0.999518	+	0.0310393i	$0.990118\pi$
$212$	2.87529e9			1.42343
$213$	3.96401e8			0.192583
$214$		−	2.11650e9i		−	1.00917i
$215$			3.67379e9i			1.71933i
$216$			1.34795e8i			0.0619238i
$217$		−	4.41087e8i		−	0.198923i
$218$	−6.23530e9			−2.76078
$219$			9.78744e8i			0.425493i
$220$		−	2.55966e9i		−	1.09268i
$221$		−	2.19464e8i		−	0.0920012i
$222$	−1.37737e9			−0.567074
$223$	−2.92225e9			−1.18167			−0.590837	−	0.806791i	$-0.701202\pi$
$223$	−2.92225e9			−1.18167			−0.590837	+	0.806791i	$0.701202\pi$
$224$		−	4.72694e9i		−	1.87754i
$225$	1.02076e9			0.398285
$226$	−1.45668e9			−0.558379
$227$			3.19057e9i			1.20161i	0.799395	+	0.600806i	$0.205154\pi$
$227$			3.19057e9i			1.20161i	−0.799395	+	0.600806i	$0.794846\pi$
$228$	1.20893e9			0.447363
$229$			1.08652e9i			0.395089i	0.980294	+	0.197544i	$0.0632966\pi$
$229$			1.08652e9i			0.395089i	−0.980294	+	0.197544i	$0.936703\pi$
$230$	2.59076e9			0.925796
$231$		−	1.31905e9i		−	0.463246i
$232$		−	1.57721e9i		−	0.544424i
$233$			1.44416e9i			0.489995i	0.969524	+	0.244998i	$0.0787872\pi$
$233$			1.44416e9i			0.489995i	−0.969524	+	0.244998i	$0.921213\pi$
$234$	1.59900e9			0.533317
$235$			3.58916e9i			1.17685i
$236$	3.11612e9	−	2.12644e9i	1.00454	−	0.685498i
$237$	1.00644e9			0.319004
$238$		−	5.40954e8i		−	0.168598i
$239$	−1.66479e9			−0.510232			−0.255116	−	0.966910i	$-0.582114\pi$
$239$	−1.66479e9			−0.510232			−0.255116	+	0.966910i	$0.582114\pi$
$240$	−2.09188e9			−0.630510
$241$	−3.43370e9			−1.01787			−0.508937	−	0.860804i	$-0.669961\pi$
$241$	−3.43370e9			−1.01787			−0.508937	+	0.860804i	$0.669961\pi$
$242$		−	3.22787e9i		−	0.941142i
$243$	2.23677e8			0.0641500
$244$		−	3.19601e9i		−	0.901672i
$245$	4.00550e9			1.11171
$246$			1.29833e9i			0.354522i
$247$		−	2.54878e9i		−	0.684769i
$248$	−1.83005e8			−0.0483790
$249$		−	2.85965e9i		−	0.743901i
$250$		−	1.67869e9i		−	0.429746i
$251$	2.77076e9			0.698077			0.349039	−	0.937108i	$-0.386508\pi$
$251$	2.77076e9			0.698077			0.349039	+	0.937108i	$0.386508\pi$
$252$	2.16289e9			0.536329
$253$	−1.04304e9			−0.254576
$254$			4.01565e9i			0.964764i
$255$	−3.09591e8			−0.0732197
$256$	1.88911e9			0.439842
$257$	−2.75354e9			−0.631188			−0.315594	−	0.948894i	$-0.602204\pi$
$257$	−2.75354e9			−0.631188			−0.315594	+	0.948894i	$0.602204\pi$
$258$	4.41951e9			0.997460
$259$			3.92797e9i			0.872910i
$260$		−	8.84888e9i		−	1.93640i
$261$	−2.61721e9			−0.563997
$262$	3.92935e9			0.833902
$263$	−5.38741e9			−1.12605			−0.563024	−	0.826441i	$-0.690362\pi$
$263$	−5.38741e9			−1.12605			−0.563024	+	0.826441i	$0.690362\pi$
$264$	−5.47266e8			−0.112663
$265$	−8.55144e9			−1.73403
$266$		−	6.28246e9i		−	1.25488i
$267$		−	1.23862e9i		−	0.243721i
$268$		−	5.45718e9i		−	1.05786i
$269$		−	9.59021e9i		−	1.83155i	−0.401690	−	0.915776i	$-0.631577\pi$
$269$		−	9.59021e9i		−	1.83155i	0.401690	−	0.915776i	$-0.368423\pi$
$270$		−	2.25567e9i		−	0.424443i
$271$	6.67311e9			1.23723			0.618616	−	0.785694i	$-0.287694\pi$
$271$	6.67311e9			1.23723			0.618616	+	0.785694i	$0.287694\pi$
$272$	3.45391e8			0.0631009
$273$		−	4.56001e9i		−	0.820947i
$274$		−	1.47391e8i		−	0.0261499i
$275$			4.14429e9i			0.724635i
$276$		−	1.71031e9i		−	0.294739i
$277$	−8.90902e9			−1.51325			−0.756625	−	0.653849i	$-0.773153\pi$
$277$	−8.90902e9			−1.51325			−0.756625	+	0.653849i	$0.773153\pi$
$278$		−	1.31263e10i		−	2.19767i
$279$			3.03678e8i			0.0501183i
$280$		−	3.87652e9i		−	0.630682i
$281$	−7.50541e9			−1.20379			−0.601893	−	0.798577i	$-0.705586\pi$
$281$	−7.50541e9			−1.20379			−0.601893	+	0.798577i	$0.705586\pi$
$282$	4.31771e9			0.682742
$283$			5.74822e9i			0.896164i	0.893993	+	0.448082i	$0.147893\pi$
$283$			5.74822e9i			0.896164i	−0.893993	+	0.448082i	$0.852107\pi$
$284$	−2.63898e9			−0.405660
$285$	−3.59549e9			−0.544978
$286$			6.49195e9i			0.970311i
$287$	3.70255e9			0.545724
$288$			3.25439e9i			0.473041i
$289$	−6.92464e9			−0.992672
$290$			2.63932e10i			3.73164i
$291$		−	3.19631e9i		−	0.445735i
$292$		−	6.51582e9i		−	0.896268i
$293$	−9.53755e9			−1.29410			−0.647048	−	0.762449i	$-0.723997\pi$
$293$	−9.53755e9			−1.29410			−0.647048	+	0.762449i	$0.723997\pi$
$294$		−	4.81856e9i		−	0.644953i
$295$	−9.26771e9	+	6.32430e9i	−1.22373	+	0.835073i
$296$	1.62970e9			0.212296
$297$			9.08131e8i			0.116714i
$298$	−5.74834e8			−0.0728916
$299$	−3.60584e9			−0.451151
$300$	−6.79554e9			−0.838955
$301$		−	1.26035e10i		−	1.53541i
$302$	1.69337e10			2.03574
$303$			6.73217e9i			0.798702i
$304$	4.01126e9			0.469663
$305$			9.50531e9i			1.09842i
$306$			3.72434e8i			0.0424779i
$307$	1.74059e10			1.95949			0.979744	−	0.200255i	$-0.0641770\pi$
$307$	1.74059e10			1.95949			0.979744	+	0.200255i	$0.0641770\pi$
$308$			8.78132e9i			0.975791i
$309$		−	4.31854e9i		−	0.473699i
$310$	3.06243e9			0.331604
$311$	−1.67200e9			−0.178729			−0.0893643	−	0.995999i	$-0.528484\pi$
$311$	−1.67200e9			−0.178729			−0.0893643	+	0.995999i	$0.528484\pi$
$312$	−1.89193e9			−0.199658
$313$		−	1.74970e10i		−	1.82300i	−0.411304	−	0.911498i	$-0.634926\pi$
$313$		−	1.74970e10i		−	1.82300i	0.411304	−	0.911498i	$-0.365074\pi$
$314$	−9.51777e9			−0.979076
$315$	−6.43268e9			−0.653356
$316$	−6.70022e9			−0.671956
$317$	1.12301e10			1.11211			0.556053	−	0.831147i	$-0.312315\pi$
$317$	1.12301e10			1.11211			0.556053	+	0.831147i	$0.312315\pi$
$318$			1.02873e10i			1.00598i
$319$		−	1.06259e10i		−	1.02613i
$320$	2.13675e10			2.03776
$321$	4.15551e9			0.391385
$322$	−8.88800e9			−0.826762
$323$	5.93653e8			0.0545409
$324$	−1.48909e9			−0.135127
$325$			1.43270e10i			1.28417i
$326$			8.20346e9i			0.726317i
$327$		−	1.22423e10i		−	1.07071i
$328$		−	1.53617e9i		−	0.132722i
$329$		−	1.23132e10i		−	1.05096i
$330$	9.15801e9			0.772228
$331$	1.13799e10			0.948043			0.474022	−	0.880513i	$-0.342802\pi$
$331$	1.13799e10			0.948043			0.474022	+	0.880513i	$0.342802\pi$
$332$			1.90376e10i			1.56697i
$333$		−	2.70432e9i		−	0.219928i
$334$		−	1.68413e10i		−	1.35328i
$335$			1.62303e10i			1.28869i
$336$	7.17653e9			0.563063
$337$			2.74377e9i			0.212730i	0.994327	+	0.106365i	$0.0339212\pi$
$337$			2.74377e9i			0.212730i	−0.994327	+	0.106365i	$0.966079\pi$
$338$			3.01333e9i			0.230877i
$339$		−	2.86002e9i		−	0.216556i
$340$	2.06105e9			0.154232
$341$	−1.23293e9			−0.0911847
$342$			4.32532e9i			0.316165i
$343$	4.57086e9			0.330234
$344$	−5.22914e9			−0.373419
$345$			5.08666e9i			0.359051i
$346$	2.86278e10			1.99749
$347$			7.58960e9i			0.523481i	0.965138	+	0.261741i	$0.0842965\pi$
$347$			7.58960e9i			0.523481i	−0.965138	+	0.261741i	$0.915704\pi$
$348$	1.74236e10			1.18802
$349$			1.19166e8i			0.00803249i	0.999992	+	0.00401624i	$0.00127841\pi$
$349$			1.19166e8i			0.00803249i	−0.999992	+	0.00401624i	$0.998722\pi$
$350$			3.53146e10i			2.35332i
$351$			3.13946e9i			0.206836i
$352$	−1.32128e10			−0.860646
$353$			2.67034e10i			1.71976i	0.510497	+	0.859880i	$0.329462\pi$
$353$			2.67034e10i			1.71976i	−0.510497	+	0.859880i	$0.670538\pi$
$354$	7.60804e9	+	1.11489e10i	0.484462	+	0.709937i
$355$	7.84863e9			0.494174
$356$			8.24591e9i			0.513380i
$357$	1.06210e9			0.0653873
$358$	−6.62634e9			−0.403405
$359$	−1.92840e10			−1.16096			−0.580482	−	0.814273i	$-0.697136\pi$
$359$	−1.92840e10			−1.16096			−0.580482	+	0.814273i	$0.697136\pi$
$360$			2.66889e9i			0.158899i
$361$	−1.00891e10			−0.594050
$362$			3.96920e10i			2.31137i
$363$	6.33756e9			0.365002
$364$			3.03575e10i			1.72926i
$365$			1.93788e10i			1.09183i
$366$	1.14347e10			0.637239
$367$		−	1.69746e10i		−	0.935697i	−0.883809	−	0.467848i	$-0.845029\pi$
$367$		−	1.69746e10i		−	0.935697i	0.883809	−	0.467848i	$-0.154971\pi$
$368$		−	5.67486e9i		−	0.309431i
$369$	−2.54911e9			−0.137494
$370$	−2.72716e10			−1.45514
$371$	2.93371e10			1.54853
$372$		−	2.02168e9i		−	0.105570i
$373$	−1.24757e10			−0.644511			−0.322256	−	0.946653i	$-0.604441\pi$
$373$	−1.24757e10			−0.644511			−0.322256	+	0.946653i	$0.604441\pi$
$374$	−1.51208e9			−0.0772839
$375$	3.29592e9			0.166668
$376$	−5.10869e9			−0.255598
$377$		−	3.67343e10i		−	1.81847i
$378$			7.73842e9i			0.379040i
$379$	−2.77496e10			−1.34493			−0.672466	−	0.740128i	$-0.734765\pi$
$379$	−2.77496e10			−1.34493			−0.672466	+	0.740128i	$0.734765\pi$
$380$	2.39364e10			1.14795
$381$	−7.88427e9			−0.374164
$382$	−4.10751e10			−1.92897
$383$	−9.19768e9			−0.427448			−0.213724	−	0.976894i	$-0.568559\pi$
$383$	−9.19768e9			−0.427448			−0.213724	+	0.976894i	$0.568559\pi$
$384$		−	7.88985e9i		−	0.362864i
$385$		−	2.61167e10i		−	1.18871i
$386$			3.94280e10i			1.77605i
$387$			8.67720e9i			0.386844i
$388$			2.12789e10i			0.938905i
$389$	−5.01240e9			−0.218901			−0.109450	−	0.993992i	$-0.534909\pi$
$389$	−5.01240e9			−0.218901			−0.109450	+	0.993992i	$0.534909\pi$
$390$	3.16597e10			1.36851
$391$		−	8.39859e8i		−	0.0359335i
$392$			5.70129e9i			0.241451i
$393$			7.71482e9i			0.323412i
$394$		−	3.44421e10i		−	1.42924i
$395$	1.99273e10			0.818577
$396$		−	6.04572e9i		−	0.245849i
$397$			4.62675e10i			1.86258i	0.364282	+	0.931289i	$0.381315\pi$
$397$			4.62675e10i			1.86258i	−0.364282	+	0.931289i	$0.618685\pi$
$398$		−	5.91142e10i		−	2.35591i
$399$	1.23349e10			0.486680
$400$	−2.25478e10			−0.880774
$401$		−	1.80362e10i		−	0.697539i	−0.937209	−	0.348770i	$-0.886600\pi$
$401$		−	1.80362e10i		−	0.697539i	0.937209	−	0.348770i	$-0.113400\pi$
$402$	1.95248e10			0.747624
$403$	−4.26231e9			−0.161594
$404$		−	4.48183e10i		−	1.68240i
$405$	4.42874e9			0.164612
$406$		−	9.05460e10i		−	3.33246i
$407$	1.09795e10			0.400135
$408$		−	4.40661e8i		−	0.0159025i
$409$			2.93023e10i			1.04715i	0.851979	+	0.523575i	$0.175402\pi$
$409$			2.93023e10i			1.04715i	−0.851979	+	0.523575i	$0.824598\pi$
$410$			2.57064e10i			0.909718i
$411$	2.89386e8			0.0101417
$412$			2.87499e10i			0.997810i
$413$	3.17943e10	−	2.16965e10i	1.09282	−	0.745744i
$414$	6.11917e9			0.208301
$415$		−	5.66201e10i		−	1.90888i
$416$	−4.56774e10			−1.52520
$417$	2.57719e10			0.852320
$418$	−1.75608e10			−0.575228
$419$			3.66218e10i			1.18818i	0.804398	+	0.594091i	$0.202488\pi$
$419$			3.66218e10i			1.18818i	−0.804398	+	0.594091i	$0.797512\pi$
$420$	4.28245e10			1.37624
$421$		−	5.62614e9i		−	0.179094i	−0.995983	−	0.0895472i	$-0.971458\pi$
$421$		−	5.62614e9i		−	0.179094i	0.995983	−	0.0895472i	$-0.0285420\pi$
$422$	2.93083e9			0.0924147
$423$			8.47732e9i			0.264787i
$424$		−	1.21718e10i		−	0.376610i
$425$	−3.33700e9			−0.102282
$426$		−	9.44179e9i		−	0.286692i
$427$		−	3.26095e10i		−	0.980916i
$428$	−2.76646e10			−0.824422
$429$	−1.27462e10			−0.376315
$430$	8.75050e10			2.55952
$431$		−	4.51983e10i		−	1.30983i	−0.755704	−	0.654913i	$-0.772705\pi$
$431$		−	4.51983e10i		−	1.30983i	0.755704	−	0.654913i	$-0.227295\pi$
$432$	−4.94086e9			−0.141863
$433$	−6.64155e8			−0.0188937			−0.00944687	−	0.999955i	$-0.503007\pi$
$433$	−6.64155e8			−0.0188937			−0.00944687	+	0.999955i	$0.503007\pi$
$434$	−1.05061e10			−0.296131
$435$	−5.18200e10			−1.44724
$436$			8.15010e10i			2.25536i
$437$		−	9.75385e9i		−	0.267455i
$438$	2.33124e10			0.633419
$439$	3.66246e10			0.986087			0.493044	−	0.870005i	$-0.335884\pi$
$439$	3.66246e10			0.986087			0.493044	+	0.870005i	$0.335884\pi$
$440$	−1.08357e10			−0.289099
$441$	9.46069e9			0.250132
$442$	−5.22735e9			−0.136960
$443$			1.40820e10i			0.365636i	0.983147	+	0.182818i	$0.0585219\pi$
$443$			1.40820e10i			0.365636i	−0.983147	+	0.182818i	$0.941478\pi$
$444$			1.80035e10i			0.463261i
$445$		−	2.45243e10i		−	0.625399i
$446$			6.96043e10i			1.75913i
$447$		−	1.12862e9i		−	0.0282695i
$448$	−7.33046e10			−1.81978
$449$	5.89422e9			0.145024			0.0725122	−	0.997368i	$-0.476898\pi$
$449$	5.89422e9			0.145024			0.0725122	+	0.997368i	$0.476898\pi$
$450$		−	2.43132e10i		−	0.592915i
$451$		−	1.03494e10i		−	0.250155i
$452$			1.90401e10i			0.456158i
$453$			3.32473e10i			0.789521i
$454$	7.59953e10			1.78881
$455$		−	9.02868e10i		−	2.10658i
$456$		−	5.11770e9i		−	0.118363i
$457$		−	5.48090e10i		−	1.25657i	−0.777983	−	0.628286i	$-0.783757\pi$
$457$		−	5.48090e10i		−	1.25657i	0.777983	−	0.628286i	$-0.216243\pi$
$458$	2.58795e10			0.588157
$459$	−7.31231e8			−0.0164742
$460$		−	3.38635e10i		−	0.756312i
$461$	−8.10683e8			−0.0179493			−0.00897465	−	0.999960i	$-0.502857\pi$
$461$	−8.10683e8			−0.0179493			−0.00897465	+	0.999960i	$0.502857\pi$
$462$	−3.14180e10			−0.689621
$463$			8.44778e10i			1.83831i	0.393897	+	0.919155i	$0.371127\pi$
$463$			8.44778e10i			1.83831i	−0.393897	+	0.919155i	$0.628873\pi$
$464$	5.78122e10			1.24723
$465$			6.01273e9i			0.128606i
$466$	3.43981e10			0.729442
$467$			3.28861e10i			0.691424i	0.938341	+	0.345712i	$0.112363\pi$
$467$			3.28861e10i			0.691424i	−0.938341	+	0.345712i	$0.887637\pi$
$468$		−	2.09004e10i		−	0.435683i
$469$		−	5.56807e10i		−	1.15083i
$470$	8.54893e10			1.75194
$471$		−	1.86870e10i		−	0.379714i
$472$	−9.00179e9	−	1.31913e10i	−0.181368	−	0.265779i
$473$	−3.52295e10			−0.703820
$474$		−	2.39722e10i		−	0.474892i
$475$	−3.87548e10			−0.761292
$476$	−7.07076e9			−0.137733
$477$	−2.01979e10			−0.390150
$478$			3.96532e10i			0.759567i
$479$	−2.74359e10			−0.521168			−0.260584	−	0.965451i	$-0.583915\pi$
$479$	−2.74359e10			−0.521168			−0.260584	+	0.965451i	$0.583915\pi$
$480$			6.44359e10i			1.21384i
$481$	3.79568e10			0.709103
$482$			8.17864e10i			1.51528i
$483$		−	1.74506e10i		−	0.320643i
$484$	−4.21912e10			−0.768848
$485$		−	6.32859e10i		−	1.14377i
$486$		−	5.32771e9i		−	0.0954983i
$487$	4.77225e10			0.848413			0.424206	−	0.905566i	$-0.360553\pi$
$487$	4.77225e10			0.848413			0.424206	+	0.905566i	$0.360553\pi$
$488$	−1.35295e10			−0.238563
$489$	−1.61065e10			−0.281687
$490$		−	9.54060e10i		−	1.65498i
$491$	−2.30522e10			−0.396631			−0.198316	−	0.980138i	$-0.563547\pi$
$491$	−2.30522e10			−0.396631			−0.198316	+	0.980138i	$0.563547\pi$
$492$	1.69703e10			0.289620
$493$	8.55601e9			0.144838
$494$	−6.07087e10			−1.01940
$495$			1.79807e10i			0.299493i
$496$		−	6.70802e9i		−	0.110833i
$497$	−2.69260e10			−0.441312
$498$	−6.81132e10			−1.10742
$499$	−2.51107e10			−0.405002			−0.202501	−	0.979282i	$-0.564907\pi$
$499$	−2.51107e10			−0.405002			−0.202501	+	0.979282i	$0.564907\pi$
$500$	−2.19420e10			−0.351073
$501$	3.30659e10			0.524843
$502$		−	6.59959e10i		−	1.03921i
$503$		−	7.61944e10i		−	1.19029i	−0.803620	−	0.595143i	$-0.797096\pi$
$503$		−	7.61944e10i		−	1.19029i	0.803620	−	0.595143i	$-0.202904\pi$
$504$		−	9.15605e9i		−	0.141901i
$505$			1.33295e11i			2.04950i
$506$			2.48439e10i			0.378981i
$507$	−5.91633e9			−0.0895407
$508$	5.24882e10			0.788146
$509$		−	1.02580e11i		−	1.52824i	−0.645073	−	0.764121i	$-0.723173\pi$
$509$		−	1.02580e11i		−	1.52824i	0.645073	−	0.764121i	$-0.276827\pi$
$510$			7.37407e9i			0.109000i
$511$		−	6.64821e10i		−	0.975037i
$512$		−	8.81863e10i		−	1.28328i
$513$	−8.49228e9			−0.122618
$514$			6.55858e10i			0.939631i
$515$		−	8.55057e10i		−	1.21553i
$516$		−	5.77670e10i		−	0.814856i
$517$	−3.44180e10			−0.481751
$518$	9.35594e10			1.29948
$519$			5.62075e10i			0.774684i
$520$	−3.74596e10			−0.512330
$521$	−9.90363e10			−1.34414			−0.672068	−	0.740489i	$-0.734594\pi$
$521$	−9.90363e10			−1.34414			−0.672068	+	0.740489i	$0.734594\pi$
$522$			6.23387e10i			0.839606i
$523$	−7.70542e10			−1.02989			−0.514944	−	0.857224i	$-0.672187\pi$
$523$	−7.70542e10			−1.02989			−0.514944	+	0.857224i	$0.672187\pi$
$524$		−	5.13601e10i		−	0.681241i
$525$	−6.93361e10			−0.912688
$526$			1.28321e11i			1.67631i
$527$		−	9.92763e8i		−	0.0128707i
$528$		−	2.00599e10i		−	0.258103i
$529$	6.45119e10			0.823791
$530$			2.03685e11i			2.58140i
$531$	−2.18896e10	+	1.49375e10i	−0.275334	+	0.187889i
$532$	−8.21175e10			−1.02515
$533$		−	3.57785e10i		−	0.443315i
$534$	−2.95024e10			−0.362821
$535$	8.22779e10			1.00431
$536$	−2.31017e10			−0.279888
$537$		−	1.30101e10i		−	0.156452i
$538$	−2.28427e11			−2.72658
$539$			3.84104e10i			0.455087i
$540$	−2.94836e10			−0.346741
$541$			1.47107e11i			1.71729i	0.512567	+	0.858647i	$0.328695\pi$
$541$			1.47107e11i			1.71729i	−0.512567	+	0.858647i	$0.671305\pi$
$542$		−	1.58945e11i		−	1.84183i
$543$	−7.79307e10			−0.896415
$544$		−	1.06390e10i		−	0.121480i
$545$		−	2.42394e11i		−	2.74748i
$546$	−1.08614e11			−1.22212
$547$	−1.13267e11			−1.26518			−0.632592	−	0.774485i	$-0.718009\pi$
$547$	−1.13267e11			−1.26518			−0.632592	+	0.774485i	$0.718009\pi$
$548$	−1.92654e9			−0.0213626
$549$			2.24508e10i			0.247140i
$550$	9.87118e10			1.07874
$551$	9.93667e10			1.07804
$552$	−7.24017e9			−0.0779817
$553$	−6.83636e10			−0.731012
$554$			2.12202e11i			2.25273i
$555$		−	5.35446e10i		−	0.564344i
$556$	−1.71572e11			−1.79534
$557$	−6.78423e10			−0.704823			−0.352411	−	0.935845i	$-0.614638\pi$
$557$	−6.78423e10			−0.704823			−0.352411	+	0.935845i	$0.614638\pi$
$558$	7.23322e9			0.0746097
$559$	−1.21790e11			−1.24728
$560$	1.42093e11			1.44484
$561$		−	2.96880e9i		−	0.0299730i
$562$			1.78769e11i			1.79204i
$563$		−	1.92579e11i		−	1.91679i	−0.285445	−	0.958395i	$-0.592141\pi$
$563$		−	1.92579e11i		−	1.91679i	0.285445	−	0.958395i	$-0.407859\pi$
$564$		−	5.64363e10i		−	0.557754i
$565$		−	5.66275e10i		−	0.555691i
$566$	1.36915e11			1.33409
$567$	−1.51935e10			−0.147003
$568$			1.11715e10i			0.107329i
$569$		−	4.04335e10i		−	0.385738i	−0.981225	−	0.192869i	$-0.938221\pi$
$569$		−	4.04335e10i		−	0.385738i	0.981225	−	0.192869i	$-0.0617792\pi$
$570$			8.56401e10i			0.811293i
$571$			5.37255e10i			0.505401i	0.967545	+	0.252701i	$0.0813187\pi$
$571$			5.37255e10i			0.505401i	−0.967545	+	0.252701i	$0.918681\pi$
$572$	8.48556e10			0.792678
$573$		−	8.06462e10i		−	0.748110i
$574$		−	8.81900e10i		−	0.812404i
$575$			5.48277e10i			0.501567i
$576$	5.04684e10			0.458490
$577$	−4.05383e10			−0.365731			−0.182865	−	0.983138i	$-0.558537\pi$
$577$	−4.05383e10			−0.365731			−0.182865	+	0.983138i	$0.558537\pi$
$578$			1.64936e11i			1.47776i
$579$	−7.74123e10			−0.688804
$580$	3.44983e11			3.04849
$581$			1.94244e11i			1.70468i
$582$	−7.61320e10			−0.663552
$583$		−	8.20033e10i		−	0.709835i
$584$	−2.75831e10			−0.237133
$585$			6.21603e10i			0.530749i
$586$			2.27173e11i			1.92648i
$587$		−	9.05099e10i		−	0.762331i	−0.924507	−	0.381166i	$-0.875523\pi$
$587$		−	9.05099e10i		−	0.762331i	0.924507	−	0.381166i	$-0.124477\pi$
$588$	−6.29830e10			−0.526882
$589$		−	1.15296e10i		−	0.0957975i
$590$	1.50637e11	+	2.20745e11i	1.24315	+	1.82173i
$591$	6.76232e10			0.554301
$592$			5.97363e10i			0.486353i
$593$	1.25627e11			1.01593			0.507966	−	0.861377i	$-0.330397\pi$
$593$	1.25627e11			1.01593			0.507966	+	0.861377i	$0.330397\pi$
$594$	2.16305e10			0.173749
$595$	2.10293e10			0.167786
$596$			7.51360e9i			0.0595475i
$597$	1.16064e11			0.913693
$598$			8.58865e10i			0.671615i
$599$	−1.49470e11			−1.16104			−0.580519	−	0.814247i	$-0.697150\pi$
$599$	−1.49470e11			−1.16104			−0.580519	+	0.814247i	$0.697150\pi$
$600$			2.87673e10i			0.221970i
$601$		−	2.03842e10i		−	0.156241i	−0.996944	−	0.0781205i	$-0.975108\pi$
$601$		−	2.03842e10i		−	0.156241i	0.996944	−	0.0781205i	$-0.0248919\pi$
$602$	−3.00200e11			−2.28573
$603$			3.83348e10i			0.289950i
$604$		−	2.21338e11i		−	1.66306i
$605$	1.25482e11			0.936611
$606$	1.60352e11			1.18900
$607$	3.36149e10			0.247615			0.123808	−	0.992306i	$-0.460489\pi$
$607$	3.36149e10			0.247615			0.123808	+	0.992306i	$0.460489\pi$
$608$		−	1.23558e11i		−	0.904184i
$609$	1.77777e11			1.29243
$610$	2.26404e11			1.63518
$611$	−1.18985e11			−0.853741
$612$	4.86805e9			0.0347016
$613$			9.02842e10i			0.639396i	0.947520	+	0.319698i	$0.103581\pi$
$613$			9.02842e10i			0.639396i	−0.947520	+	0.319698i	$0.896419\pi$
$614$		−	4.14586e11i		−	2.91703i
$615$	−5.04717e10			−0.352815
$616$	3.71736e10			0.258174
$617$	6.24555e10			0.430953			0.215477	−	0.976509i	$-0.430870\pi$
$617$	6.24555e10			0.430953			0.215477	+	0.976509i	$0.430870\pi$
$618$	−1.02862e11			−0.705183
$619$	−1.95074e11			−1.32873			−0.664366	−	0.747408i	$-0.731298\pi$
$619$	−1.95074e11			−1.32873			−0.664366	+	0.747408i	$0.731298\pi$
$620$		−	4.00287e10i		−	0.270897i
$621$			1.20143e10i			0.0807852i
$622$			3.98249e10i			0.266068i
$623$			8.41345e10i			0.558499i
$624$		−	6.93482e10i		−	0.457401i
$625$	−1.17062e11			−0.767178
$626$	−4.16756e11			−2.71384
$627$		−	3.44787e10i		−	0.223090i
$628$			1.24406e11i			0.799838i
$629$			8.84077e9i			0.0564791i
$630$			1.53218e11i			0.972632i
$631$	1.44763e11			0.913146			0.456573	−	0.889686i	$-0.349077\pi$
$631$	1.44763e11			0.913146			0.456573	+	0.889686i	$0.349077\pi$
$632$			2.83638e10i			0.177785i
$633$			5.75435e9i			0.0358411i
$634$		−	2.67487e11i		−	1.65556i
$635$	−1.56106e11			−0.960119
$636$	1.34464e11			0.821820
$637$			1.32787e11i			0.806487i
$638$	−2.53095e11			−1.52757
$639$	1.85379e10			0.111188
$640$		−	1.56217e11i		−	0.931123i
$641$	2.45615e11			1.45486			0.727432	−	0.686180i	$-0.240714\pi$
$641$	2.45615e11			1.45486			0.727432	+	0.686180i	$0.240714\pi$
$642$		−	9.89791e10i		−	0.582644i
$643$	1.83446e11			1.07316			0.536580	−	0.843849i	$-0.319716\pi$
$643$	1.83446e11			1.07316			0.536580	+	0.843849i	$0.319716\pi$
$644$			1.16174e11i			0.675408i
$645$			1.71806e11i			0.992657i
$646$		−	1.41401e10i		−	0.0811935i
$647$	−2.70631e11			−1.54440			−0.772201	−	0.635378i	$-0.780844\pi$
$647$	−2.70631e11			−1.54440			−0.772201	+	0.635378i	$0.780844\pi$
$648$			6.30372e9i			0.0357517i
$649$	−6.06464e10	−	8.88720e10i	−0.341842	−	0.500940i
$650$	3.41252e11			1.91171
$651$		−	2.06276e10i		−	0.114848i
$652$	1.07227e11			0.593352
$653$	1.17779e11			0.647760			0.323880	−	0.946098i	$-0.395013\pi$
$653$	1.17779e11			0.647760			0.323880	+	0.946098i	$0.395013\pi$
$654$	−2.91596e11			−1.59393
$655$			1.52751e11i			0.829887i
$656$	5.63080e10			0.304057
$657$			4.57713e10i			0.245659i
$658$	−2.93284e11			−1.56454
$659$			2.67635e11i			1.41906i	0.704675	+	0.709530i	$0.251093\pi$
$659$			2.67635e11i			1.41906i	−0.704675	+	0.709530i	$0.748907\pi$
$660$		−	1.19703e11i		−	0.630857i
$661$	1.10057e11			0.576516			0.288258	−	0.957553i	$-0.406924\pi$
$661$	1.10057e11			0.576516			0.288258	+	0.957553i	$0.406924\pi$
$662$		−	2.71056e11i		−	1.41133i
$663$		−	1.02633e10i		−	0.0531169i
$664$	8.05912e10			0.414586
$665$	2.44227e11			1.24884
$666$	−6.44134e10			−0.327400
$667$		−	1.40577e11i		−	0.710251i
$668$	−2.20131e11			−1.10554
$669$	−1.36660e11			−0.682240
$670$	3.86586e11			1.91843
$671$	−9.11504e10			−0.449644
$672$		−	2.21057e11i		−	1.08400i
$673$		−	1.24589e11i		−	0.607323i	−0.952780	−	0.303662i	$-0.901791\pi$
$673$		−	1.24589e11i		−	0.607323i	0.952780	−	0.303662i	$-0.0982092\pi$
$674$	6.53532e10			0.316685
$675$	4.77362e10			0.229950
$676$	3.93870e10			0.188610
$677$	2.46766e11			1.17471			0.587356	−	0.809329i	$-0.300169\pi$
$677$	2.46766e11			1.17471			0.587356	+	0.809329i	$0.300169\pi$
$678$	−6.81220e10			−0.322380
$679$			2.17112e11i			1.02142i
$680$		−	8.72496e9i		−	0.0408064i
$681$			1.49208e11i			0.693751i
$682$			2.93669e10i			0.135744i
$683$		−	2.14225e11i		−	0.984437i	−0.870472	−	0.492218i	$-0.836186\pi$
$683$		−	2.14225e11i		−	0.984437i	0.870472	−	0.492218i	$-0.163814\pi$
$684$	5.65359e10			0.258285
$685$	5.72975e9			0.0260240
$686$		−	1.08872e11i		−	0.491610i
$687$			5.08114e10i			0.228105i
$688$		−	1.91673e11i		−	0.855474i
$689$		−	2.83490e11i		−	1.25794i
$690$	1.21158e11			0.534509
$691$		−	3.64118e10i		−	0.159709i	−0.996807	−	0.0798545i	$-0.974554\pi$
$691$		−	3.64118e10i		−	0.159709i	0.996807	−	0.0798545i	$-0.0254456\pi$
$692$		−	3.74192e11i		−	1.63181i
$693$		−	6.16856e10i		−	0.267455i
$694$	1.80775e11			0.779291
$695$	5.10276e11			2.18709
$696$		−	7.37588e10i		−	0.314323i
$697$	8.33339e9			0.0353094
$698$	2.83838e9			0.0119577
$699$			6.75367e10i			0.282899i
$700$	4.61593e11			1.92250
$701$			4.29534e11i			1.77879i	0.457138	+	0.889396i	$0.348875\pi$
$701$			4.29534e11i			1.77879i	−0.457138	+	0.889396i	$0.651125\pi$
$702$	7.47779e10			0.307911
$703$			1.02674e11i			0.420376i
$704$			2.04902e11i			0.834172i
$705$			1.67848e11i			0.679455i
$706$	6.36041e11			2.56016
$707$		−	4.57289e11i		−	1.83026i
$708$	1.45727e11	−	9.94440e10i	0.579970	−	0.395772i
$709$	5.68750e10			0.225080			0.112540	−	0.993647i	$-0.464101\pi$
$709$	5.68750e10			0.225080			0.112540	+	0.993647i	$0.464101\pi$
$710$		−	1.86944e11i		−	0.735663i
$711$	4.70667e10			0.184177
$712$	3.49071e10			0.135829
$713$	−1.63113e10			−0.0631148
$714$		−	2.52979e10i		−	0.0973401i
$715$	−2.52371e11			−0.965639
$716$			8.66122e10i			0.329554i
$717$	−7.78544e10			−0.294582
$718$			4.59320e11i			1.72829i
$719$		−	1.39660e11i		−	0.522586i	−0.965259	−	0.261293i	$-0.915851\pi$
$719$		−	1.39660e11i		−	0.522586i	0.965259	−	0.261293i	$-0.0841489\pi$
$720$	−9.78276e10			−0.364025
$721$			2.93341e11i			1.08550i
$722$			2.40309e11i			0.884345i
$723$	−1.60578e11			−0.587670
$724$	5.18810e11			1.88823
$725$	−5.58554e11			−2.02168
$726$		−	1.50953e11i		−	0.543368i
$727$	2.91728e11			1.04434			0.522168	−	0.852842i	$-0.325123\pi$
$727$	2.91728e11			1.04434			0.522168	+	0.852842i	$0.325123\pi$
$728$	1.28511e11			0.457525
$729$	1.04604e10			0.0370370
$730$	4.61579e11			1.62538
$731$		−	2.83669e10i		−	0.0993443i
$732$		−	1.49462e11i		−	0.520580i
$733$	−1.99431e11			−0.690838			−0.345419	−	0.938448i	$-0.612263\pi$
$733$	−1.99431e11			−0.690838			−0.345419	+	0.938448i	$0.612263\pi$
$734$	−4.04313e11			−1.39295
$735$	1.87319e11			0.641848
$736$	−1.74802e11			−0.595709
$737$	−1.55639e11			−0.527533
$738$			6.07167e10i			0.204683i
$739$			3.66763e11i			1.22972i	0.788635	+	0.614862i	$0.210788\pi$
$739$			3.66763e11i			1.22972i	−0.788635	+	0.614862i	$0.789212\pi$
$740$			3.56464e11i			1.18875i
$741$		−	1.19195e11i		−	0.395352i
$742$		−	6.98772e11i		−	2.30526i
$743$	1.14130e11			0.374493			0.187246	−	0.982313i	$-0.440044\pi$
$743$	1.14130e11			0.374493			0.187246	+	0.982313i	$0.440044\pi$
$744$	−8.55831e9			−0.0279316
$745$		−	2.23464e10i		−	0.0725407i
$746$			2.97156e11i			0.959465i
$747$		−	1.33732e11i		−	0.429491i
$748$			1.97643e10i			0.0631356i
$749$	−2.82267e11			−0.896878
$750$		−	7.85047e10i		−	0.248114i
$751$			2.45993e9i			0.00773326i	0.999993	+	0.00386663i	$0.00123079\pi$
$751$			2.45993e9i			0.00773326i	−0.999993	+	0.00386663i	$0.998769\pi$
$752$		−	1.87258e11i		−	0.585556i
$753$	1.29575e11			0.403035
$754$	−8.74964e11			−2.70710
$755$			6.58287e11i			2.02594i
$756$	1.01148e11			0.309650
$757$	3.77625e10			0.114995			0.0574973	−	0.998346i	$-0.481688\pi$
$757$	3.77625e10			0.114995			0.0574973	+	0.998346i	$0.481688\pi$
$758$			6.60962e11i			2.00216i
$759$	−4.87781e10			−0.146980
$760$		−	1.01329e11i		−	0.303724i
$761$	4.66930e11			1.39224			0.696118	−	0.717928i	$-0.254909\pi$
$761$	4.66930e11			1.39224			0.696118	+	0.717928i	$0.254909\pi$
$762$			1.87793e11i			0.557007i
$763$			8.31569e11i			2.45358i
$764$			5.36888e11i			1.57583i
$765$	−1.44781e10			−0.0422734
$766$			2.19077e11i			0.636330i
$767$	−2.09658e11	−	3.07235e11i	−0.605800	−	0.887747i
$768$	8.83448e10			0.253943
$769$			4.41563e11i			1.26266i	0.775513	+	0.631331i	$0.217491\pi$
$769$			4.41563e11i			1.26266i	−0.775513	+	0.631331i	$0.782509\pi$
$770$	−6.22067e11			−1.76960
$771$	−1.28770e11			−0.364416
$772$	5.15359e11			1.45091
$773$		−	1.37042e11i		−	0.383826i	−0.981412	−	0.191913i	$-0.938531\pi$
$773$		−	1.37042e11i		−	0.383826i	0.981412	−	0.191913i	$-0.0614692\pi$
$774$	2.06680e11			0.575884
$775$			6.48096e10i			0.179652i
$776$	9.00789e10			0.248414
$777$			1.83693e11i			0.503975i
$778$			1.19389e11i			0.325872i
$779$	9.67813e10			0.262810
$780$		−	4.13821e11i		−	1.11798i
$781$			7.52638e10i			0.202293i
$782$	−2.00044e10			−0.0534932
$783$	−1.22395e11			−0.325624
$784$	−2.08980e11			−0.553146
$785$		−	3.69998e11i		−	0.974362i
$786$	1.83757e11			0.481454
$787$	4.47724e11			1.16711			0.583554	−	0.812074i	$-0.301662\pi$
$787$	4.47724e11			1.16711			0.583554	+	0.812074i	$0.301662\pi$
$788$	−4.50190e11			−1.16759
$789$	−2.51944e11			−0.650124
$790$		−	4.74642e11i		−	1.21859i
$791$			1.94269e11i			0.496248i
$792$	−2.55931e10			−0.0650463
$793$	−3.15112e11			−0.796841
$794$	1.10203e12			2.77277
$795$	−3.99911e11			−1.00114
$796$	−7.72676e11			−1.92462
$797$			1.80975e10i			0.0448523i	0.999749	+	0.0224261i	$0.00713906\pi$
$797$			1.80975e10i			0.0448523i	−0.999749	+	0.0224261i	$0.992861\pi$
$798$		−	2.93802e11i		−	0.724507i
$799$		−	2.77135e10i		−	0.0679993i
$800$			6.94537e11i			1.69565i
$801$		−	5.79246e10i		−	0.140713i
$802$	−4.29601e11			−1.03841
$803$	−1.85832e11			−0.446949
$804$		−	2.55207e11i		−	0.610758i
$805$		−	3.45516e11i		−	0.822782i
$806$			1.01523e11i			0.240560i
$807$		−	4.48490e11i		−	1.05745i
$808$	−1.89727e11			−0.445128
$809$			7.98881e11i			1.86504i	0.361119	+	0.932520i	$0.382395\pi$
$809$			7.98881e11i			1.86504i	−0.361119	+	0.932520i	$0.617605\pi$
$810$		−	1.05487e11i		−	0.245053i
$811$		−	4.92165e11i		−	1.13770i	−0.822442	−	0.568849i	$-0.807389\pi$
$811$		−	4.92165e11i		−	1.13770i	0.822442	−	0.568849i	$-0.192611\pi$
$812$	−1.18352e12			−2.72239
$813$	3.12070e11			0.714316
$814$		−	2.61519e11i		−	0.595669i
$815$	−3.18905e11			−0.722821
$816$	1.61523e10			0.0364313
$817$		−	3.29444e11i		−	0.739424i
$818$	6.97945e11			1.55886
$819$		−	2.13251e11i		−	0.473974i
$820$	3.36007e11			0.743177
$821$			2.19942e10i			0.0484100i	0.999707	+	0.0242050i	$0.00770545\pi$
$821$			2.19942e10i			0.0484100i	−0.999707	+	0.0242050i	$0.992295\pi$
$822$		−	6.89280e9i		−	0.0150976i
$823$		−	4.93965e11i		−	1.07670i	−0.842720	−	0.538352i	$-0.819047\pi$
$823$		−	4.93965e11i		−	1.07670i	0.842720	−	0.538352i	$-0.180953\pi$
$824$	1.21706e11			0.263999
$825$			1.93809e11i			0.418368i
$826$	−5.16783e11	−	7.57301e11i	−1.11017	−	1.62685i
$827$	7.45255e11			1.59325			0.796624	−	0.604476i	$-0.206617\pi$
$827$	7.45255e11			1.59325			0.796624	+	0.604476i	$0.206617\pi$
$828$		−	7.99831e10i		−	0.170168i
$829$	4.21688e11			0.892838			0.446419	−	0.894824i	$-0.352699\pi$
$829$	4.21688e11			0.892838			0.446419	+	0.894824i	$0.352699\pi$
$830$	−1.34862e12			−2.84170
$831$	−4.16634e11			−0.873676
$832$			7.08357e11i			1.47829i
$833$	−3.09283e10			−0.0642356
$834$		−	6.13855e11i		−	1.26882i
$835$	6.54695e11			1.34677
$836$			2.29536e11i			0.469922i
$837$			1.42016e10i			0.0289358i
$838$	8.72284e11			1.76881
$839$			4.29173e11i			0.866134i	0.901362	+	0.433067i	$0.142569\pi$
$839$			4.29173e11i			0.866134i	−0.901362	+	0.433067i	$0.857431\pi$
$840$		−	1.81287e11i		−	0.364124i
$841$	9.31876e11			1.86283
$842$	−1.34008e11			−0.266613
$843$	−3.50993e11			−0.695006
$844$		−	3.83086e10i		−	0.0754965i
$845$	−1.17142e11			−0.229765
$846$	2.01919e11			0.394181
$847$	−4.30485e11			−0.836420
$848$	4.46155e11			0.862785
$849$			2.68817e11i			0.517400i
$850$			7.94832e10i			0.152265i
$851$	1.45256e11			0.276959
$852$	−1.23413e11			−0.234208
$853$	−1.78032e11			−0.336281			−0.168141	−	0.985763i	$-0.553776\pi$
$853$	−1.78032e11			−0.336281			−0.168141	+	0.985763i	$0.553776\pi$
$854$	−7.76716e11			−1.46026
$855$	−1.68144e11			−0.314643
$856$			1.17111e11i			0.218124i
$857$			7.68555e11i			1.42479i	0.701777	+	0.712396i	$0.252390\pi$
$857$			7.68555e11i			1.42479i	−0.701777	+	0.712396i	$0.747610\pi$
$858$			3.03598e11i			0.560209i
$859$			7.86018e11i			1.44364i	0.692079	+	0.721822i	$0.256695\pi$
$859$			7.86018e11i			1.44364i	−0.692079	+	0.721822i	$0.743305\pi$
$860$		−	1.14377e12i		−	2.09095i
$861$	1.73151e11			0.315074
$862$	−1.07657e12			−1.94990
$863$		−	9.02699e11i		−	1.62742i	−0.581271	−	0.813710i	$-0.697444\pi$
$863$		−	9.02699e11i		−	1.62742i	0.581271	−	0.813710i	$-0.302556\pi$
$864$			1.52193e11i			0.273111i
$865$			1.11289e12i			1.98787i
$866$			1.58193e10i			0.0281266i
$867$	−3.23833e11			−0.573120
$868$			1.37325e11i			0.241919i
$869$			1.91091e11i			0.335090i
$870$			1.23429e12i			2.15446i
$871$	−5.38053e11			−0.934873
$872$	3.45015e11			0.596721
$873$		−	1.49476e11i		−	0.257345i
$874$	−2.32324e11			−0.398152
$875$	−2.23879e11			−0.381927
$876$		−	3.04715e11i		−	0.517460i
$877$	−2.80080e11			−0.473460			−0.236730	−	0.971575i	$-0.576076\pi$
$877$	−2.80080e11			−0.473460			−0.236730	+	0.971575i	$0.576076\pi$
$878$		−	8.72353e11i		−	1.46796i
$879$	−4.46027e11			−0.747147
$880$		−	3.97180e11i		−	0.662303i
$881$		−	2.69104e10i		−	0.0446701i	−0.999751	−	0.0223351i	$-0.992890\pi$
$881$		−	2.69104e10i		−	0.0446701i	0.999751	−	0.0223351i	$-0.00711006\pi$
$882$		−	2.25342e11i		−	0.372364i
$883$	5.68680e11			0.935459			0.467730	−	0.883872i	$-0.345072\pi$
$883$	5.68680e11			0.935459			0.467730	+	0.883872i	$0.345072\pi$
$884$			6.83262e10i			0.111887i
$885$	−4.33408e11	+	2.95758e11i	−0.706519	+	0.482130i
$886$	3.35415e11			0.544312
$887$			2.53570e11i			0.409641i	0.978800	+	0.204821i	$0.0656611\pi$
$887$			2.53570e11i			0.409641i	−0.978800	+	0.204821i	$0.934339\pi$
$888$	7.62135e10			0.122569
$889$	5.35547e11			0.857413
$890$	−5.84138e11			−0.931013
$891$			4.24691e10i			0.0673848i
$892$	9.09791e11			1.43708
$893$		−	3.21855e11i		−	0.506122i
$894$	−2.68823e10			−0.0420840
$895$		−	2.57595e11i		−	0.401463i
$896$			5.35925e11i			0.831519i
$897$	−1.68628e11			−0.260472
$898$		−	1.40393e11i		−	0.215894i
$899$		−	1.66171e11i		−	0.254399i
$900$	−3.17796e11			−0.484371
$901$	6.60295e10			0.100193
$902$	−2.46510e11			−0.372399
$903$		−	5.89407e11i		−	0.886471i
$904$	8.06016e10			0.120690
$905$	−1.54300e12			−2.30024
$906$	7.91909e11			1.17534
$907$	−5.74206e11			−0.848474			−0.424237	−	0.905551i	$-0.639458\pi$
$907$	−5.74206e11			−0.848474			−0.424237	+	0.905551i	$0.639458\pi$
$908$		−	9.93327e11i		−	1.46133i
$909$			3.14832e11i			0.461131i
$910$	−2.15052e12			−3.13601
$911$	1.11272e12			1.61553			0.807763	−	0.589508i	$-0.200678\pi$
$911$	1.11272e12			1.61553			0.807763	+	0.589508i	$0.200678\pi$
$912$	1.87588e11			0.271160
$913$	5.42954e11			0.781412
$914$	−1.30548e12			−1.87062
$915$			4.44519e11i			0.634171i
$916$		−	3.38268e11i		−	0.480484i
$917$		−	5.24036e11i		−	0.741113i
$918$			1.74170e10i			0.0245246i
$919$			6.76636e11i			0.948621i	0.880357	+	0.474311i	$0.157303\pi$
$919$			6.76636e11i			0.948621i	−0.880357	+	0.474311i	$0.842697\pi$
$920$	−1.43353e11			−0.200104
$921$	8.13993e11			1.13131
$922$			1.93095e10i			0.0267206i
$923$			2.60191e11i			0.358497i
$924$			4.10662e11i			0.563373i
$925$		−	5.77143e11i		−	0.788345i
$926$	2.01215e12			2.73664
$927$		−	2.01958e11i		−	0.273490i
$928$		−	1.78078e12i		−	2.40115i
$929$			1.00268e11i			0.134617i	0.997732	+	0.0673083i	$0.0214411\pi$
$929$			1.00268e11i			0.134617i	−0.997732	+	0.0673083i	$0.978559\pi$
$930$	1.43216e11			0.191451
$931$	−3.59191e11			−0.478108
$932$		−	4.49614e11i		−	0.595904i
$933$	−7.81916e10			−0.103189
$934$	7.83305e11			1.02930
$935$		−	5.87813e10i		−	0.0769118i
$936$	−8.84768e10			−0.115273
$937$		−	1.02979e12i		−	1.33595i	−0.744184	−	0.667975i	$-0.767161\pi$
$937$		−	1.02979e12i		−	1.33595i	0.744184	−	0.667975i	$-0.232839\pi$
$938$	−1.32624e12			−1.71321
$939$		−	8.18253e11i		−	1.05251i
$940$		−	1.11742e12i		−	1.43122i
$941$		−	1.48299e12i		−	1.89139i	−0.325056	−	0.945695i	$-0.605383\pi$
$941$		−	1.48299e12i		−	1.89139i	0.325056	−	0.945695i	$-0.394617\pi$
$942$	−4.45102e11			−0.565270
$943$		−	1.36920e11i		−	0.173148i
$944$	4.83526e11	−	3.29958e11i	0.608880	−	0.415500i
$945$	−3.00827e11			−0.377215
$946$			8.39122e11i			1.04776i
$947$	6.96480e11			0.865982			0.432991	−	0.901398i	$-0.357458\pi$
$947$	6.96480e11			0.865982			0.432991	+	0.901398i	$0.357458\pi$
$948$	−3.13338e11			−0.387954
$949$	−6.42430e11			−0.792065
$950$			9.23091e11i			1.13331i
$951$	5.25179e11			0.642075
$952$			2.99324e10i			0.0364412i
$953$	6.41724e11			0.777995			0.388998	−	0.921239i	$-0.372821\pi$
$953$	6.41724e11			0.777995			0.388998	+	0.921239i	$0.372821\pi$
$954$			4.81087e11i			0.580805i
$955$		−	1.59677e12i		−	1.91968i
$956$	5.18303e11			0.620514
$957$		−	4.96924e11i		−	0.592437i
$958$			6.53490e11i			0.775848i
$959$	−1.96568e10			−0.0232401
$960$	9.99259e11			1.17650
$961$	8.33610e11			0.977393
$962$		−	9.04083e11i		−	1.05562i
$963$	1.94334e11			0.225966
$964$	1.06902e12			1.23788
$965$	−1.53274e12			−1.76750
$966$	−4.15651e11			−0.477331
$967$			3.13467e11i			0.358498i	0.983804	+	0.179249i	$0.0573667\pi$
$967$			3.13467e11i			0.358498i	−0.983804	+	0.179249i	$0.942633\pi$
$968$			1.78606e11i			0.203421i
$969$	2.77624e10			0.0314892
$970$	−1.50739e12			−1.70270
$971$	1.42363e12			1.60148			0.800738	−	0.599014i	$-0.204441\pi$
$971$	1.42363e12			1.60148			0.800738	+	0.599014i	$0.204441\pi$
$972$	−6.96380e10			−0.0780156
$973$	−1.75058e12			−1.95313
$974$		−	1.13669e12i		−	1.26301i
$975$			6.70009e11i			0.741416i
$976$		−	4.95922e11i		−	0.546530i
$977$		−	1.04719e12i		−	1.14933i	−0.818388	−	0.574666i	$-0.805132\pi$
$977$		−	1.04719e12i		−	1.14933i	0.818388	−	0.574666i	$-0.194868\pi$
$978$			3.83638e11i			0.419340i
$979$	2.35174e11			0.256011
$980$	−1.24704e12			−1.35200
$981$		−	5.72515e11i		−	0.618174i
$982$			5.49075e11i			0.590454i
$983$			9.27920e11i			0.993795i	0.867809	+	0.496897i	$0.165527\pi$
$983$			9.27920e11i			0.993795i	−0.867809	+	0.496897i	$0.834473\pi$
$984$		−	7.18396e10i		−	0.0766273i
$985$	1.33892e12			1.42236
$986$		−	2.03794e11i		−	0.215617i
$987$		−	5.75830e11i		−	0.606773i
$988$			7.93518e11i			0.832777i
$989$	−4.66075e11			−0.487159
$990$	4.28278e11			0.445846
$991$			1.81765e12i			1.88459i	0.334790	+	0.942293i	$0.391335\pi$
$991$			1.81765e12i			1.88459i	−0.334790	+	0.942293i	$0.608665\pi$
$992$	−2.06626e11			−0.213372
$993$	5.32187e11			0.547353
$994$			6.41342e11i			0.656968i
$995$	2.29803e12			2.34457
$996$			8.90301e11i			0.904690i
$997$	3.14898e11			0.318705			0.159353	−	0.987222i	$-0.449059\pi$
$997$	3.14898e11			0.318705			0.159353	+	0.987222i	$0.449059\pi$
$998$			5.98106e11i			0.602915i
$999$		−	1.26468e11i		−	0.126975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.13	✓	80
59.58	odd	2	inner	177.9.c.a.58.68	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.13	✓	80	1.1	even	1	trivial
177.9.c.a.58.68	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)

\(f(q)\)	\(=\)	\(q-23.8187i q^{2} +46.7654 q^{3} -311.333 q^{4} +925.940 q^{5} -1113.89i q^{6} -3176.58 q^{7} +1317.95i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q-23.8187i q^{2} +46.7654 q^{3} -311.333 q^{4} +925.940 q^{5} -1113.89i q^{6} -3176.58 q^{7} +1317.95i q^{8} +2187.00 q^{9} -22054.7i q^{10} +8879.23i q^{11} -14559.6 q^{12} +30696.0i q^{13} +75662.2i q^{14} +43301.9 q^{15} -48309.2 q^{16} -7149.59 q^{17} -52091.6i q^{18} -83033.0 q^{19} -288275. q^{20} -148554. q^{21} +211492. q^{22} +117469. i q^{23} +61634.5i q^{24} +466740. q^{25} +731139. q^{26} +102276. q^{27} +988973. q^{28} -1.19671e6 q^{29} -1.03140e6i q^{30} +138856. i q^{31} +1.48806e6i q^{32} +415240. i q^{33} +170294. i q^{34} -2.94133e6 q^{35} -680884. q^{36} -1.23654e6i q^{37} +1.97774e6i q^{38} +1.43551e6i q^{39} +1.22034e6i q^{40} -1.16558e6 q^{41} +3.53837e6i q^{42} +3.96763e6i q^{43} -2.76439e6i q^{44} +2.02503e6 q^{45} +2.79798e6 q^{46} +3.87623e6i q^{47} -2.25920e6 q^{48} +4.32588e6 q^{49} -1.11172e7i q^{50} -334353. q^{51} -9.55665e6i q^{52} -9.23542e6 q^{53} -2.43608e6i q^{54} +8.22163e6i q^{55} -4.18658e6i q^{56} -3.88307e6 q^{57} +2.85042e7i q^{58} +(-1.00090e7 + 6.83014e6i) q^{59} -1.34813e7 q^{60} +1.02656e7i q^{61} +3.30737e6 q^{62} -6.94719e6 q^{63} +2.30766e7 q^{64} +2.84226e7i q^{65} +9.89050e6 q^{66} +1.75285e7i q^{67} +2.22590e6 q^{68} +5.49350e6i q^{69} +7.00587e7i q^{70} +8.47639e6 q^{71} +2.88236e6i q^{72} +2.09288e7i q^{73} -2.94529e7 q^{74} +2.18273e7 q^{75} +2.58509e7 q^{76} -2.82056e7i q^{77} +3.41920e7 q^{78} +2.15211e7 q^{79} -4.47314e7 q^{80} +4.78297e6 q^{81} +2.77625e7i q^{82} -6.11488e7i q^{83} +4.62497e7 q^{84} -6.62010e6 q^{85} +9.45039e7 q^{86} -5.59647e7 q^{87} -1.17024e7 q^{88} -2.64859e7i q^{89} -4.82337e7i q^{90} -9.75082e7i q^{91} -3.65721e7i q^{92} +6.49365e6i q^{93} +9.23270e7 q^{94} -7.68836e7 q^{95} +6.95897e7i q^{96} -6.83477e7i q^{97} -1.03037e8i q^{98} +1.94189e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 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

L-functions

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