LMFDB - Embedded newform 177.11.c.a.58.97

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,11,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, 11, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 11 $
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:	$112.458233723$
Analytic rank:	$0$
Dimension:	$100$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.97
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+59.5712i q^{2} +140.296 q^{3} -2524.73 q^{4} -4763.75 q^{5} +8357.61i q^{6} +8815.37 q^{7} -89400.5i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q+59.5712i q^{2} +140.296 q^{3} -2524.73 q^{4} -4763.75 q^{5} +8357.61i q^{6} +8815.37 q^{7} -89400.5i q^{8} +19683.0 q^{9} -283782. i q^{10} +307379. i q^{11} -354210. q^{12} +68920.8i q^{13} +525142. i q^{14} -668335. q^{15} +2.74037e6 q^{16} +1.05697e6 q^{17} +1.17254e6i q^{18} +4.26559e6 q^{19} +1.20272e7 q^{20} +1.23676e6 q^{21} -1.83109e7 q^{22} +3.74201e6i q^{23} -1.25425e7i q^{24} +1.29277e7 q^{25} -4.10570e6 q^{26} +2.76145e6 q^{27} -2.22564e7 q^{28} +1.29563e7 q^{29} -3.98136e7i q^{30} +5.38973e7i q^{31} +7.17012e7i q^{32} +4.31241e7i q^{33} +6.29652e7i q^{34} -4.19942e7 q^{35} -4.96943e7 q^{36} +2.46831e7i q^{37} +2.54107e8i q^{38} +9.66932e6i q^{39} +4.25881e8i q^{40} +1.00932e8 q^{41} +7.36754e7i q^{42} +1.57771e8i q^{43} -7.76050e8i q^{44} -9.37648e7 q^{45} -2.22916e8 q^{46} -1.16768e8i q^{47} +3.84463e8 q^{48} -2.04765e8 q^{49} +7.70117e8i q^{50} +1.48289e8 q^{51} -1.74007e8i q^{52} +6.16971e8 q^{53} +1.64503e8i q^{54} -1.46428e9i q^{55} -7.88098e8i q^{56} +5.98446e8 q^{57} +7.71821e8i q^{58} +(-2.89308e8 + 6.53772e8i) q^{59} +1.68737e9 q^{60} -9.65398e7i q^{61} -3.21073e9 q^{62} +1.73513e8 q^{63} -1.46519e9 q^{64} -3.28321e8i q^{65} -2.56896e9 q^{66} -1.44219e9i q^{67} -2.66857e9 q^{68} +5.24990e8i q^{69} -2.50165e9i q^{70} +1.91425e9 q^{71} -1.75967e9i q^{72} -1.00218e9i q^{73} -1.47040e9 q^{74} +1.81370e9 q^{75} -1.07695e10 q^{76} +2.70966e9i q^{77} -5.76013e8 q^{78} +4.68097e8 q^{79} -1.30544e10 q^{80} +3.87420e8 q^{81} +6.01266e9i q^{82} -3.18460e9i q^{83} -3.12249e9 q^{84} -5.03515e9 q^{85} -9.39859e9 q^{86} +1.81771e9 q^{87} +2.74798e10 q^{88} +7.27168e9i q^{89} -5.58569e9i q^{90} +6.07562e8i q^{91} -9.44757e9i q^{92} +7.56159e9i q^{93} +6.95600e9 q^{94} -2.03202e10 q^{95} +1.00594e10i q^{96} -1.55181e10i q^{97} -1.21981e10i q^{98} +6.05014e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) $ 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	$ 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) $ 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * 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 $

$2$			59.5712i			1.86160i	0.365527	+	0.930801i	$0.380889\pi$
$2$			59.5712i			1.86160i	−0.365527	+	0.930801i	$0.619111\pi$
$3$	140.296			0.577350
$3$	140.296			0.577350
$4$	−2524.73			−2.46556
$5$	−4763.75			−1.52440			−0.762200	−	0.647342i	$-0.775881\pi$
$5$	−4763.75			−1.52440			−0.762200	+	0.647342i	$0.775881\pi$
$6$			8357.61i			1.07480i
$7$	8815.37			0.524506			0.262253	−	0.964999i	$-0.415535\pi$
$7$	8815.37			0.524506			0.262253	+	0.964999i	$0.415535\pi$
$8$		−	89400.5i		−	2.72829i
$9$	19683.0			0.333333
$10$		−	283782.i		−	2.83782i
$11$			307379.i			1.90858i	0.298879	+	0.954291i	$0.403387\pi$
$11$			307379.i			1.90858i	−0.298879	+	0.954291i	$0.596613\pi$
$12$	−354210.			−1.42349
$13$			68920.8i			0.185624i	0.995684	+	0.0928119i	$0.0295855\pi$
$13$			68920.8i			0.185624i	−0.995684	+	0.0928119i	$0.970414\pi$
$14$			525142.i			0.976420i
$15$	−668335.			−0.880112
$16$	2.74037e6			2.61342
$17$	1.05697e6			0.744422			0.372211	−	0.928148i	$-0.378600\pi$
$17$	1.05697e6			0.744422			0.372211	+	0.928148i	$0.378600\pi$
$18$			1.17254e6i			0.620534i
$19$	4.26559e6			1.72271			0.861354	−	0.508006i	$-0.169617\pi$
$19$	4.26559e6			1.72271			0.861354	+	0.508006i	$0.169617\pi$
$20$	1.20272e7			3.75850
$21$	1.23676e6			0.302823
$22$	−1.83109e7			−3.55302
$23$			3.74201e6i			0.581388i	0.956816	+	0.290694i	$0.0938861\pi$
$23$			3.74201e6i			0.581388i	−0.956816	+	0.290694i	$0.906114\pi$
$24$		−	1.25425e7i		−	1.57518i
$25$	1.29277e7			1.32379
$26$	−4.10570e6			−0.345557
$27$	2.76145e6			0.192450
$28$	−2.22564e7			−1.29320
$29$	1.29563e7			0.631670			0.315835	−	0.948814i	$-0.397715\pi$
$29$	1.29563e7			0.631670			0.315835	+	0.948814i	$0.397715\pi$
$30$		−	3.98136e7i		−	1.63842i
$31$			5.38973e7i			1.88260i	0.337567	+	0.941302i	$0.390396\pi$
$31$			5.38973e7i			1.88260i	−0.337567	+	0.941302i	$0.609604\pi$
$32$			7.17012e7i			2.13686i
$33$			4.31241e7i			1.10192i
$34$			6.29652e7i			1.38582i
$35$	−4.19942e7			−0.799556
$36$	−4.96943e7			−0.821853
$37$			2.46831e7i			0.355952i	0.984035	+	0.177976i	$0.0569549\pi$
$37$			2.46831e7i			0.355952i	−0.984035	+	0.177976i	$0.943045\pi$
$38$			2.54107e8i			3.20699i
$39$			9.66932e6i			0.107170i
$40$			4.25881e8i			4.15900i
$41$	1.00932e8			0.871186			0.435593	−	0.900144i	$-0.356539\pi$
$41$	1.00932e8			0.871186			0.435593	+	0.900144i	$0.356539\pi$
$42$			7.36754e7i			0.563736i
$43$			1.57771e8i			1.07321i	0.843834	+	0.536604i	$0.180293\pi$
$43$			1.57771e8i			1.07321i	−0.843834	+	0.536604i	$0.819707\pi$
$44$		−	7.76050e8i		−	4.70572i
$45$	−9.37648e7			−0.508133
$46$	−2.22916e8			−1.08231
$47$		−	1.16768e8i		−	0.509136i	−0.967055	−	0.254568i	$-0.918067\pi$
$47$		−	1.16768e8i		−	0.509136i	0.967055	−	0.254568i	$-0.0819333\pi$
$48$	3.84463e8			1.50886
$49$	−2.04765e8			−0.724894
$50$			7.70117e8i			2.46437i
$51$	1.48289e8			0.429792
$52$		−	1.74007e8i		−	0.457666i
$53$	6.16971e8			1.47532			0.737659	−	0.675174i	$-0.235931\pi$
$53$	6.16971e8			1.47532			0.737659	+	0.675174i	$0.235931\pi$
$54$			1.64503e8i			0.358265i
$55$		−	1.46428e9i		−	2.90944i
$56$		−	7.88098e8i		−	1.43100i
$57$	5.98446e8			0.994606
$58$			7.71821e8i			1.17592i
$59$	−2.89308e8	+	6.53772e8i	−0.404670	+	0.914463i
$59$	−2.89308e8	+	6.53772e8i	−0.404670	+	0.914463i
$60$	1.68737e9			2.16997
$61$		−	9.65398e7i		−	0.114303i	−0.998366	−	0.0571515i	$-0.981798\pi$
$61$		−	9.65398e7i		−	0.114303i	0.998366	−	0.0571515i	$-0.0182018\pi$
$62$	−3.21073e9			−3.50466
$63$	1.73513e8			0.174835
$64$	−1.46519e9			−1.36456
$65$		−	3.28321e8i		−	0.282965i
$66$	−2.56896e9			−2.05134
$67$		−	1.44219e9i		−	1.06819i	−0.845423	−	0.534097i	$-0.820652\pi$
$67$		−	1.44219e9i		−	1.06819i	0.845423	−	0.534097i	$-0.179348\pi$
$68$	−2.66857e9			−1.83542
$69$			5.24990e8i			0.335664i
$70$		−	2.50165e9i		−	1.48845i
$71$	1.91425e9			1.06098			0.530491	−	0.847691i	$-0.322008\pi$
$71$	1.91425e9			1.06098			0.530491	+	0.847691i	$0.322008\pi$
$72$		−	1.75967e9i		−	0.909429i
$73$		−	1.00218e9i		−	0.483429i	−0.970347	−	0.241714i	$-0.922290\pi$
$73$		−	1.00218e9i		−	0.483429i	0.970347	−	0.241714i	$-0.0777097\pi$
$74$	−1.47040e9			−0.662640
$75$	1.81370e9			0.764292
$76$	−1.07695e10			−4.24744
$77$			2.70966e9i			1.00106i
$78$	−5.76013e8			−0.199508
$79$	4.68097e8			0.152125			0.0760625	−	0.997103i	$-0.475765\pi$
$79$	4.68097e8			0.152125			0.0760625	+	0.997103i	$0.475765\pi$
$80$	−1.30544e10			−3.98390
$81$	3.87420e8			0.111111
$82$			6.01266e9i			1.62180i
$83$		−	3.18460e9i		−	0.808472i	−0.914655	−	0.404236i	$-0.867537\pi$
$83$		−	3.18460e9i		−	0.808472i	0.914655	−	0.404236i	$-0.132463\pi$
$84$	−3.12249e9			−0.746629
$85$	−5.03515e9			−1.13480
$86$	−9.39859e9			−1.99788
$87$	1.81771e9			0.364695
$88$	2.74798e10			5.20716
$89$			7.27168e9i			1.30222i	0.758983	+	0.651110i	$0.225696\pi$
$89$			7.27168e9i			1.30222i	−0.758983	+	0.651110i	$0.774304\pi$
$90$		−	5.58569e9i		−	0.945941i
$91$			6.07562e8i			0.0973607i
$92$		−	9.44757e9i		−	1.43345i
$93$			7.56159e9i			1.08692i
$94$	6.95600e9			0.947808
$95$	−2.03202e10			−2.62609
$96$			1.00594e10i			1.23372i
$97$		−	1.55181e10i		−	1.80709i	−0.428495	−	0.903544i	$-0.640956\pi$
$97$		−	1.55181e10i		−	1.80709i	0.428495	−	0.903544i	$-0.359044\pi$
$98$		−	1.21981e10i		−	1.34946i
$99$			6.05014e9i			0.636194i
$100$	−3.26389e10			−3.26389
$101$			6.63900e9i			0.631678i	0.948813	+	0.315839i	$0.102286\pi$
$101$			6.63900e9i			0.631678i	−0.948813	+	0.315839i	$0.897714\pi$
$102$			8.83377e9i			0.800102i
$103$		−	1.17829e9i		−	0.101640i	−0.998708	−	0.0508202i	$-0.983816\pi$
$103$		−	1.17829e9i		−	0.101640i	0.998708	−	0.0508202i	$-0.0161836\pi$
$104$	6.16155e9			0.506435
$105$	−5.89162e9			−0.461624
$106$			3.67537e10i			2.74645i
$107$	1.76272e10			1.25679			0.628397	−	0.777893i	$-0.283711\pi$
$107$	1.76272e10			1.25679			0.628397	+	0.777893i	$0.283711\pi$
$108$	−6.97192e9			−0.474497
$109$		−	5.60648e8i		−	0.0364383i	−0.999834	−	0.0182191i	$-0.994200\pi$
$109$		−	5.60648e8i		−	0.0364383i	0.999834	−	0.0182191i	$-0.00579966\pi$
$110$	8.72287e10			5.41622
$111$			3.46294e9i			0.205509i
$112$	2.41574e10			1.37075
$113$			8.03621e9i			0.436174i	0.975929	+	0.218087i	$0.0699816\pi$
$113$			8.03621e9i			0.436174i	−0.975929	+	0.218087i	$0.930018\pi$
$114$			3.56502e10i			1.85156i
$115$		−	1.78260e10i		−	0.886267i
$116$	−3.27111e10			−1.55742
$117$			1.35657e9i			0.0618746i
$118$	−3.89460e10	−	1.72344e10i	−1.70237	−	0.753334i
$119$	9.31760e9			0.390454
$120$			5.97495e10i			2.40120i
$121$	−6.85445e10			−2.64269
$122$	5.75100e9			0.212786
$123$	1.41604e10			0.502979
$124$		−	1.36076e11i		−	4.64167i
$125$	−1.50632e10			−0.493590
$126$			1.03364e10i			0.325473i
$127$	−6.34339e10			−1.92001			−0.960003	−	0.279990i	$-0.909669\pi$
$127$	−6.34339e10			−1.92001			−0.960003	+	0.279990i	$0.909669\pi$
$128$		−	1.38611e10i		−	0.403411i
$129$			2.21346e10i			0.619617i
$130$	1.95585e10			0.526767
$131$			1.65942e10i			0.430130i	0.976600	+	0.215065i	$0.0689963\pi$
$131$			1.65942e10i			0.430130i	−0.976600	+	0.215065i	$0.931004\pi$
$132$		−	1.08877e11i		−	2.71685i
$133$	3.76028e10			0.903570
$134$	8.59133e10			1.98855
$135$	−1.31548e10			−0.293371
$136$		−	9.44939e10i		−	2.03100i
$137$	5.76929e9			0.119542			0.0597709	−	0.998212i	$-0.480963\pi$
$137$	5.76929e9			0.119542			0.0597709	+	0.998212i	$0.480963\pi$
$138$	−3.12743e10			−0.624873
$139$	−7.84083e10			−1.51108			−0.755541	−	0.655102i	$-0.772626\pi$
$139$	−7.84083e10			−1.51108			−0.755541	+	0.655102i	$0.772626\pi$
$140$	1.06024e11			1.97135
$141$		−	1.63821e10i		−	0.293950i
$142$			1.14034e11i			1.97512i
$143$	−2.11848e10			−0.354278
$144$	5.39387e10			0.871140
$145$	−6.17204e10			−0.962917
$146$	5.97013e10			0.899952
$147$	−2.87277e10			−0.418518
$148$		−	6.23182e10i		−	0.877620i
$149$			1.01063e11i			1.37613i	0.725648	+	0.688066i	$0.241540\pi$
$149$			1.01063e11i			1.37613i	−0.725648	+	0.688066i	$0.758460\pi$
$150$			1.08044e11i			1.42281i
$151$			7.82666e10i			0.996993i	0.866892	+	0.498496i	$0.166114\pi$
$151$			7.82666e10i			0.996993i	−0.866892	+	0.498496i	$0.833886\pi$
$152$		−	3.81346e11i		−	4.70004i
$153$	2.08044e10			0.248141
$154$	−1.61418e11			−1.86358
$155$		−	2.56753e11i		−	2.86984i
$156$		−	2.44124e10i		−	0.264234i
$157$		−	6.29703e9i		−	0.0660143i	−0.999455	−	0.0330071i	$-0.989492\pi$
$157$		−	6.29703e9i		−	0.0660143i	0.999455	−	0.0330071i	$-0.0105084\pi$
$158$			2.78851e10i			0.283196i
$159$	8.65586e10			0.851775
$160$		−	3.41566e11i		−	3.25743i
$161$			3.29872e10i			0.304941i
$162$			2.30791e10i			0.206845i
$163$	1.18731e11			1.03187			0.515936	−	0.856627i	$-0.327444\pi$
$163$	1.18731e11			1.03187			0.515936	+	0.856627i	$0.327444\pi$
$164$	−2.54827e11			−2.14796
$165$		−	2.05432e11i		−	1.67977i
$166$	1.89711e11			1.50505
$167$	1.46766e11			1.12991			0.564953	−	0.825123i	$-0.308894\pi$
$167$	1.46766e11			1.12991			0.564953	+	0.825123i	$0.308894\pi$
$168$		−	1.10567e11i		−	0.826189i
$169$	1.33108e11			0.965544
$170$		−	2.99950e11i		−	2.11254i
$171$	8.39597e10			0.574236
$172$		−	3.98328e11i		−	2.64606i
$173$		−	2.48584e11i		−	1.60414i	−0.597228	−	0.802071i	$-0.703731\pi$
$173$		−	2.48584e11i		−	1.60414i	0.597228	−	0.802071i	$-0.296269\pi$
$174$			1.08283e11i			0.678916i
$175$	1.13962e11			0.694337
$176$			8.42333e11i			4.98793i
$177$	−4.05888e10	+	9.17216e10i	−0.233636	+	0.527965i
$178$	−4.33183e11			−2.42422
$179$			1.83522e11i			0.998672i	0.866408	+	0.499336i	$0.166423\pi$
$179$			1.83522e11i			0.998672i	−0.866408	+	0.499336i	$0.833577\pi$
$180$	2.36731e11			1.25283
$181$	2.33072e11			1.19977			0.599885	−	0.800086i	$-0.295213\pi$
$181$	2.33072e11			1.19977			0.599885	+	0.800086i	$0.295213\pi$
$182$	−3.61932e10			−0.181247
$183$		−	1.35442e10i		−	0.0659928i
$184$	3.34537e11			1.58619
$185$		−	1.17584e11i		−	0.542613i
$186$	−4.50453e11			−2.02341
$187$			3.24891e11i			1.42079i
$188$			2.94807e11i			1.25531i
$189$	2.43432e10			0.100941
$190$		−	1.21050e12i		−	4.88874i
$191$			6.46864e10i			0.254476i	0.991872	+	0.127238i	$0.0406111\pi$
$191$			6.46864e10i			0.254476i	−0.991872	+	0.127238i	$0.959389\pi$
$192$	−2.05560e11			−0.787831
$193$	−3.39025e11			−1.26604			−0.633018	−	0.774137i	$-0.718184\pi$
$193$	−3.39025e11			−1.26604			−0.633018	+	0.774137i	$0.718184\pi$
$194$	9.24431e11			3.36408
$195$		−	4.60622e10i		−	0.163370i
$196$	5.16976e11			1.78727
$197$	−1.17018e11			−0.394385			−0.197192	−	0.980365i	$-0.563182\pi$
$197$	−1.17018e11			−0.394385			−0.197192	+	0.980365i	$0.563182\pi$
$198$	−3.60414e11			−1.18434
$199$	−9.16201e9			−0.0293579			−0.0146790	−	0.999892i	$-0.504673\pi$
$199$	−9.16201e9			−0.0293579			−0.0146790	+	0.999892i	$0.504673\pi$
$200$		−	1.15574e12i		−	3.61169i
$201$		−	2.02334e11i		−	0.616722i
$202$	−3.95493e11			−1.17593
$203$	1.14214e11			0.331314
$204$	−3.74391e11			−1.05968
$205$	−4.80816e11			−1.32804
$206$	7.01923e10			0.189214
$207$			7.36540e10i			0.193796i
$208$			1.88869e11i			0.485113i
$209$			1.31115e12i			3.28793i
$210$		−	3.50971e11i		−	0.859359i
$211$		−	3.54835e11i		−	0.848425i	−0.905563	−	0.424213i	$-0.860551\pi$
$211$		−	3.54835e11i		−	0.848425i	0.905563	−	0.424213i	$-0.139449\pi$
$212$	−1.55769e12			−3.63748
$213$	2.68562e11			0.612558
$214$			1.05007e12i			2.33965i
$215$		−	7.51579e11i		−	1.63600i
$216$		−	2.46875e11i		−	0.525059i
$217$			4.75125e11i			0.987436i
$218$	3.33985e10			0.0678336
$219$		−	1.40602e11i		−	0.279108i
$220$			3.69691e12i			7.17340i
$221$			7.28474e10i			0.138182i
$222$	−2.06292e11			−0.382576
$223$	1.19156e11			0.216068			0.108034	−	0.994147i	$-0.465544\pi$
$223$	1.19156e11			0.216068			0.108034	+	0.994147i	$0.465544\pi$
$224$			6.32072e11i			1.12080i
$225$	2.54455e11			0.441264
$226$	−4.78727e11			−0.811981
$227$			6.14134e10i			0.101891i	0.998701	+	0.0509453i	$0.0162234\pi$
$227$			6.14134e10i			0.101891i	−0.998701	+	0.0509453i	$0.983777\pi$
$228$	−1.51092e12			−2.45226
$229$			8.61736e11i			1.36835i	0.729318	+	0.684175i	$0.239837\pi$
$229$			8.61736e11i			1.36835i	−0.729318	+	0.684175i	$0.760163\pi$
$230$	1.06192e12			1.64988
$231$			3.80155e11i			0.577963i
$232$		−	1.15830e12i		−	1.72338i
$233$			6.75198e10i			0.0983222i	0.998791	+	0.0491611i	$0.0156548\pi$
$233$			6.75198e10i			0.0983222i	−0.998791	+	0.0491611i	$0.984345\pi$
$234$	−8.08124e10			−0.115186
$235$			5.56252e11i			0.776127i
$236$	7.30426e11	−	1.65060e12i	0.997737	−	2.25466i
$237$	6.56722e10			0.0878294
$238$			5.55061e11i			0.726869i
$239$	2.58785e11			0.331857			0.165928	−	0.986138i	$-0.446938\pi$
$239$	2.58785e11			0.331857			0.165928	+	0.986138i	$0.446938\pi$
$240$	−1.83149e12			−2.30010
$241$	−1.33896e12			−1.64696			−0.823478	−	0.567348i	$-0.807969\pi$
$241$	−1.33896e12			−1.64696			−0.823478	+	0.567348i	$0.807969\pi$
$242$		−	4.08328e12i		−	4.91963i
$243$	5.43536e10			0.0641500
$244$			2.43737e11i			0.281821i
$245$	9.75447e11			1.10503
$246$			8.43553e11i			0.936347i
$247$			2.93988e11i			0.319775i
$248$	4.81845e12			5.13628
$249$		−	4.46787e11i		−	0.466771i
$250$		−	8.97332e11i		−	0.918868i
$251$	−1.54586e12			−1.55168			−0.775838	−	0.630932i	$-0.782673\pi$
$251$	−1.54586e12			−1.55168			−0.775838	+	0.630932i	$0.782673\pi$
$252$	−4.38073e11			−0.431066
$253$	−1.15022e12			−1.10963
$254$		−	3.77883e12i		−	3.57428i
$255$	−7.06412e11			−0.655175
$256$	−6.74631e11			−0.613573
$257$	1.34163e12			1.19665			0.598324	−	0.801254i	$-0.295834\pi$
$257$	1.34163e12			1.19665			0.598324	+	0.801254i	$0.295834\pi$
$258$	−1.31859e12			−1.15348
$259$			2.17591e11i			0.186699i
$260$			8.28923e11i			0.697666i
$261$	2.55018e11			0.210557
$262$	−9.88536e11			−0.800730
$263$	−1.31680e12			−1.04650			−0.523252	−	0.852178i	$-0.675281\pi$
$263$	−1.31680e12			−1.04650			−0.523252	+	0.852178i	$0.675281\pi$
$264$	3.85531e12			3.00635
$265$	−2.93909e12			−2.24897
$266$			2.24004e12i			1.68209i
$267$			1.02019e12i			0.751837i
$268$			3.64116e12i			2.63369i
$269$			1.94110e12i			1.37812i	0.724703	+	0.689061i	$0.241977\pi$
$269$			1.94110e12i			1.37812i	−0.724703	+	0.689061i	$0.758023\pi$
$270$		−	7.83650e11i		−	0.546139i
$271$	9.78319e11			0.669321			0.334660	−	0.942339i	$-0.391378\pi$
$271$	9.78319e11			0.669321			0.334660	+	0.942339i	$0.391378\pi$
$272$	2.89650e12			1.94549
$273$			8.52386e10i			0.0562112i
$274$			3.43684e11i			0.222539i
$275$			3.97369e12i			2.52657i
$276$		−	1.32546e12i		−	0.827600i
$277$	−1.22302e11			−0.0749957			−0.0374978	−	0.999297i	$-0.511939\pi$
$277$	−1.22302e11			−0.0749957			−0.0374978	+	0.999297i	$0.511939\pi$
$278$		−	4.67088e12i		−	2.81303i
$279$			1.06086e12i			0.627534i
$280$			3.75430e12i			2.18142i
$281$	−2.67988e12			−1.52962			−0.764811	−	0.644254i	$-0.777168\pi$
$281$	−2.67988e12			−1.52962			−0.764811	+	0.644254i	$0.777168\pi$
$282$	9.75900e11			0.547217
$283$		−	2.07320e12i		−	1.14211i	−0.820910	−	0.571057i	$-0.806534\pi$
$283$		−	2.07320e12i		−	1.14211i	0.820910	−	0.571057i	$-0.193466\pi$
$284$	−4.83298e12			−2.61591
$285$	−2.85085e12			−1.51618
$286$		−	1.26201e12i		−	0.659525i
$287$	8.89755e11			0.456942
$288$			1.41129e12i			0.712287i
$289$	−8.98802e11			−0.445836
$290$		−	3.67676e12i		−	1.79257i
$291$		−	2.17713e12i		−	1.04332i
$292$			2.53024e12i			1.19192i
$293$	−1.16615e11			−0.0540027			−0.0270014	−	0.999635i	$-0.508596\pi$
$293$	−1.16615e11			−0.0540027			−0.0270014	+	0.999635i	$0.508596\pi$
$294$		−	1.71134e12i		−	0.779113i
$295$	1.37819e12	−	3.11440e12i	0.616878	−	1.39401i
$296$	2.20668e12			0.971138
$297$			8.48811e11i			0.367307i
$298$	−6.02044e12			−2.56181
$299$	−2.57902e11			−0.107919
$300$	−4.57911e12			−1.88441
$301$			1.39081e12i			0.562903i
$302$	−4.66244e12			−1.85600
$303$			9.31426e11i			0.364699i
$304$	1.16893e13			4.50216
$305$			4.59891e11i			0.174243i
$306$			1.23934e12i			0.461939i
$307$	−1.00943e12			−0.370155			−0.185077	−	0.982724i	$-0.559254\pi$
$307$	−1.00943e12			−0.370155			−0.185077	+	0.982724i	$0.559254\pi$
$308$		−	6.84116e12i		−	2.46818i
$309$		−	1.65310e11i		−	0.0586822i
$310$	1.52951e13			5.34250
$311$	4.42123e12			1.51964			0.759821	−	0.650133i	$-0.225287\pi$
$311$	4.42123e12			1.51964			0.759821	+	0.650133i	$0.225287\pi$
$312$	8.64442e11			0.292390
$313$		−	1.33939e12i		−	0.445847i	−0.974836	−	0.222924i	$-0.928440\pi$
$313$		−	1.33939e12i		−	0.445847i	0.974836	−	0.222924i	$-0.0715600\pi$
$314$	3.75122e11			0.122892
$315$	−8.26571e11			−0.266519
$316$	−1.18182e12			−0.375073
$317$	2.96670e12			0.926782			0.463391	−	0.886154i	$-0.346632\pi$
$317$	2.96670e12			0.926782			0.463391	+	0.886154i	$0.346632\pi$
$318$			5.15641e12i			1.58567i
$319$			3.98249e12i			1.20559i
$320$	6.97979e12			2.08014
$321$	2.47303e12			0.725611
$322$	−1.96509e12			−0.567679
$323$	4.50862e12			1.28242
$324$	−9.78133e11			−0.273951
$325$			8.90985e11i			0.245727i
$326$			7.07294e12i			1.92093i
$327$		−	7.86568e10i		−	0.0210377i
$328$		−	9.02339e12i		−	2.37684i
$329$		−	1.02935e12i		−	0.267045i
$330$	1.22379e13			3.12706
$331$	4.58261e12			1.15338			0.576691	−	0.816962i	$-0.304344\pi$
$331$	4.58261e12			1.15338			0.576691	+	0.816962i	$0.304344\pi$
$332$			8.04027e12i			1.99333i
$333$			4.85838e11i			0.118651i
$334$			8.74301e12i			2.10343i
$335$			6.87025e12i			1.62835i
$336$	3.38919e12			0.791405
$337$		−	4.93314e12i		−	1.13494i	−0.823393	−	0.567471i	$-0.807922\pi$
$337$		−	4.93314e12i		−	1.13494i	0.823393	−	0.567471i	$-0.192078\pi$
$338$			7.92943e12i			1.79746i
$339$			1.12745e12i			0.251825i
$340$	1.27124e13			2.79791
$341$	−1.65669e13			−3.59310
$342$			5.00158e12i			1.06900i
$343$	−4.29520e12			−0.904716
$344$	1.41048e13			2.92802
$345$		−	2.50092e12i		−	0.511686i
$346$	1.48085e13			2.98627
$347$		−	6.30374e12i		−	1.25300i	−0.779421	−	0.626500i	$-0.784487\pi$
$347$		−	6.30374e12i		−	1.25300i	0.779421	−	0.626500i	$-0.215513\pi$
$348$	−4.58924e12			−0.899176
$349$		−	1.03542e12i		−	0.199981i	−0.994988	−	0.0999905i	$-0.968119\pi$
$349$		−	1.03542e12i		−	0.199981i	0.994988	−	0.0999905i	$-0.0318812\pi$
$350$			6.78886e12i			1.29258i
$351$			1.90321e11i			0.0357233i
$352$	−2.20394e13			−4.07838
$353$		−	3.93173e12i		−	0.717315i	−0.933469	−	0.358657i	$-0.883235\pi$
$353$		−	3.93173e12i		−	0.717315i	0.933469	−	0.358657i	$-0.116765\pi$
$354$	−5.46397e12	−	2.41793e12i	−0.982861	−	0.434937i
$355$	−9.11902e12			−1.61736
$356$		−	1.83590e13i		−	3.21070i
$357$	1.30722e12			0.225428
$358$	−1.09326e13			−1.85913
$359$	−8.10572e11			−0.135931			−0.0679656	−	0.997688i	$-0.521651\pi$
$359$	−8.10572e11			−0.135931			−0.0679656	+	0.997688i	$0.521651\pi$
$360$			8.38262e12i			1.38633i
$361$	1.20642e13			1.96772
$362$			1.38844e13i			2.23349i
$363$	−9.61652e12			−1.52576
$364$		−	1.53393e12i		−	0.240049i
$365$			4.77414e12i			0.736939i
$366$	8.06842e11			0.122852
$367$			5.56208e12i			0.835424i	0.908579	+	0.417712i	$0.137168\pi$
$367$			5.56208e12i			0.835424i	−0.908579	+	0.417712i	$0.862832\pi$
$368$			1.02545e13i			1.51941i
$369$	1.98665e12			0.290395
$370$	7.00463e12			1.01013
$371$	5.43883e12			0.773812
$372$		−	1.90910e13i		−	2.67987i
$373$	−1.16740e13			−1.61687			−0.808433	−	0.588589i	$-0.799684\pi$
$373$	−1.16740e13			−1.61687			−0.808433	+	0.588589i	$0.799684\pi$
$374$	−1.93542e13			−2.64495
$375$	−2.11330e12			−0.284974
$376$	−1.04391e13			−1.38907
$377$			8.92956e11i			0.117253i
$378$			1.45015e12i			0.187912i
$379$	−8.15197e12			−1.04248			−0.521239	−	0.853411i	$-0.674530\pi$
$379$	−8.15197e12			−1.04248			−0.521239	+	0.853411i	$0.674530\pi$
$380$	5.13031e13			6.47479
$381$	−8.89952e12			−1.10852
$382$	−3.85345e12			−0.473732
$383$	−3.46373e11			−0.0420291			−0.0210146	−	0.999779i	$-0.506690\pi$
$383$	−3.46373e11			−0.0420291			−0.0210146	+	0.999779i	$0.506690\pi$
$384$		−	1.94466e12i		−	0.232909i
$385$		−	1.29081e13i		−	1.52602i
$386$		−	2.01962e13i		−	2.35685i
$387$			3.10540e12i			0.357736i
$388$			3.91790e13i			4.45548i
$389$	−4.90715e12			−0.550911			−0.275455	−	0.961314i	$-0.588829\pi$
$389$	−4.90715e12			−0.550911			−0.275455	+	0.961314i	$0.588829\pi$
$390$	2.74398e12			0.304129
$391$			3.95520e12i			0.432798i
$392$			1.83060e13i			1.97772i
$393$			2.32810e12i			0.248335i
$394$		−	6.97089e12i		−	0.734187i
$395$	−2.22990e12			−0.231899
$396$		−	1.52750e13i		−	1.56857i
$397$		−	1.52710e13i		−	1.54852i	−0.632870	−	0.774258i	$-0.718123\pi$
$397$		−	1.52710e13i		−	1.54852i	0.632870	−	0.774258i	$-0.281877\pi$
$398$		−	5.45792e11i		−	0.0546528i
$399$	5.27552e12			0.521676
$400$	3.54266e13			3.45963
$401$		−	1.28285e13i		−	1.23724i	−0.785691	−	0.618619i	$-0.787692\pi$
$401$		−	1.28285e13i		−	1.23724i	0.785691	−	0.618619i	$-0.212308\pi$
$402$	1.20533e13			1.14809
$403$	−3.71465e12			−0.349456
$404$		−	1.67617e13i		−	1.55744i
$405$	−1.84557e12			−0.169378
$406$			6.80388e12i			0.616775i
$407$	−7.58707e12			−0.679363
$408$		−	1.32571e13i		−	1.17260i
$409$		−	3.71099e12i		−	0.324245i	−0.986771	−	0.162122i	$-0.948166\pi$
$409$		−	3.71099e12i		−	0.324245i	0.986771	−	0.162122i	$-0.0518339\pi$
$410$		−	2.86428e13i		−	2.47227i
$411$	8.09409e11			0.0690175
$412$			2.97487e12i			0.250601i
$413$	−2.55036e12	+	5.76324e12i	−0.212252	+	0.479641i
$414$	−4.38766e12			−0.360771
$415$			1.51706e13i			1.23243i
$416$	−4.94170e12			−0.396652
$417$	−1.10004e13			−0.872423
$418$	−7.81071e13			−6.12081
$419$			1.91177e13i			1.48035i	0.672412	+	0.740177i	$0.265258\pi$
$419$			1.91177e13i			1.48035i	−0.672412	+	0.740177i	$0.734742\pi$
$420$	1.48748e13			1.13816
$421$			3.47260e12i			0.262570i	0.991345	+	0.131285i	$0.0419102\pi$
$421$			3.47260e12i			0.262570i	−0.991345	+	0.131285i	$0.958090\pi$
$422$	2.11379e13			1.57943
$423$		−	2.29834e12i		−	0.169712i
$424$		−	5.51575e13i		−	4.02509i
$425$	1.36642e13			0.985461
$426$			1.59986e13i			1.14034i
$427$		−	8.51034e11i		−	0.0599525i
$428$	−4.45039e13			−3.09870
$429$	−2.97215e12			−0.204543
$430$	4.47725e13			3.04557
$431$			8.12194e12i			0.546102i	0.962000	+	0.273051i	$0.0880327\pi$
$431$			8.12194e12i			0.546102i	−0.962000	+	0.273051i	$0.911967\pi$
$432$	7.56739e12			0.502953
$433$	−3.57079e12			−0.234598			−0.117299	−	0.993097i	$-0.537424\pi$
$433$	−3.57079e12			−0.234598			−0.117299	+	0.993097i	$0.537424\pi$
$434$	−2.83038e13			−1.83821
$435$	−8.65913e12			−0.555940
$436$			1.41549e12i			0.0898407i
$437$			1.59619e13i			1.00156i
$438$	8.37585e12			0.519587
$439$	−6.08525e12			−0.373212			−0.186606	−	0.982435i	$-0.559749\pi$
$439$	−6.08525e12			−0.373212			−0.186606	+	0.982435i	$0.559749\pi$
$440$	−1.30907e14			−7.93779
$441$	−4.03038e12			−0.241631
$442$	−4.33961e12			−0.257241
$443$			8.84077e12i			0.518169i	0.965855	+	0.259084i	$0.0834208\pi$
$443$			8.84077e12i			0.518169i	−0.965855	+	0.259084i	$0.916579\pi$
$444$		−	8.74301e12i		−	0.506694i
$445$		−	3.46404e13i		−	1.98510i
$446$			7.09825e12i			0.402232i
$447$			1.41787e13i			0.794511i
$448$	−1.29162e13			−0.715721
$449$	2.04538e13			1.12084			0.560419	−	0.828209i	$-0.310640\pi$
$449$	2.04538e13			1.12084			0.560419	+	0.828209i	$0.310640\pi$
$450$			1.51582e13i			0.821458i
$451$			3.10245e13i			1.66273i
$452$		−	2.02893e13i		−	1.07541i
$453$			1.09805e13i			0.575614i
$454$	−3.65847e12			−0.189680
$455$		−	2.89427e12i		−	0.148417i
$456$		−	5.35014e13i		−	2.71357i
$457$			2.70573e12i			0.135739i	0.997694	+	0.0678693i	$0.0216201\pi$
$457$			2.70573e12i			0.135739i	−0.997694	+	0.0678693i	$0.978380\pi$
$458$	−5.13347e13			−2.54732
$459$	2.91878e12			0.143264
$460$			4.50059e13i			2.18514i
$461$	−6.63428e11			−0.0318632			−0.0159316	−	0.999873i	$-0.505071\pi$
$461$	−6.63428e11			−0.0318632			−0.0159316	+	0.999873i	$0.505071\pi$
$462$	−2.26463e13			−1.07594
$463$			2.63519e13i			1.23853i	0.785182	+	0.619266i	$0.212570\pi$
$463$			2.63519e13i			1.23853i	−0.785182	+	0.619266i	$0.787430\pi$
$464$	3.55050e13			1.65082
$465$		−	3.60215e13i		−	1.65690i
$466$	−4.02224e12			−0.183037
$467$		−	4.60839e12i		−	0.207475i	−0.994605	−	0.103737i	$-0.966920\pi$
$467$		−	4.60839e12i		−	0.207475i	0.994605	−	0.103737i	$-0.0330801\pi$
$468$		−	3.42497e12i		−	0.152555i
$469$		−	1.27135e13i		−	0.560273i
$470$	−3.31366e13			−1.44484
$471$		−	8.83449e11i		−	0.0381134i
$472$	5.84475e13	+	2.58643e13i	2.49492	+	1.10405i
$473$	−4.84954e13			−2.04830
$474$			3.91218e12i			0.163503i
$475$	5.51442e13			2.28051
$476$	−2.35245e13			−0.962686
$477$	1.21438e13			0.491772
$478$			1.54162e13i			0.617785i
$479$	4.03658e13			1.60080			0.800399	−	0.599468i	$-0.204621\pi$
$479$	4.03658e13			1.60080			0.800399	+	0.599468i	$0.204621\pi$
$480$		−	4.79204e13i		−	1.88068i
$481$	−1.70118e12			−0.0660731
$482$		−	7.97634e13i		−	3.06598i
$483$			4.62797e12i			0.176058i
$484$	1.73056e14			6.51570
$485$			7.39242e13i			2.75472i
$486$			3.23791e12i			0.119422i
$487$	1.09680e13			0.400391			0.200196	−	0.979756i	$-0.435842\pi$
$487$	1.09680e13			0.400391			0.200196	+	0.979756i	$0.435842\pi$
$488$	−8.63071e12			−0.311851
$489$	1.66575e13			0.595751
$490$			5.81086e13i			2.05712i
$491$	−2.14337e13			−0.751085			−0.375542	−	0.926805i	$-0.622544\pi$
$491$	−2.14337e13			−0.751085			−0.375542	+	0.926805i	$0.622544\pi$
$492$	−3.57512e13			−1.24013
$493$	1.36944e13			0.470229
$494$	−1.75132e13			−0.595294
$495$		−	2.88213e13i		−	0.969814i
$496$			1.47699e14i			4.92004i
$497$	1.68749e13			0.556491
$498$	2.66157e13			0.868942
$499$	−3.10709e13			−1.00427			−0.502136	−	0.864789i	$-0.667452\pi$
$499$	−3.10709e13			−1.00427			−0.502136	+	0.864789i	$0.667452\pi$
$500$	3.80305e13			1.21697
$501$	2.05907e13			0.652351
$502$		−	9.20887e13i		−	2.88860i
$503$			2.00583e13i			0.622952i	0.950254	+	0.311476i	$0.100823\pi$
$503$			2.00583e13i			0.622952i	−0.950254	+	0.311476i	$0.899177\pi$
$504$		−	1.55121e13i		−	0.477000i
$505$		−	3.16265e13i		−	0.962930i
$506$		−	6.85198e13i		−	2.06568i
$507$	1.86746e13			0.557457
$508$	1.60153e14			4.73389
$509$		−	2.00516e13i		−	0.586894i	−0.955975	−	0.293447i	$-0.905198\pi$
$509$		−	2.00516e13i		−	0.586894i	0.955975	−	0.293447i	$-0.0948024\pi$
$510$		−	4.20819e13i		−	1.21967i
$511$		−	8.83461e12i		−	0.253561i
$512$		−	5.43824e13i		−	1.54564i
$513$	1.17792e13			0.331535
$514$			7.99224e13i			2.22768i
$515$			5.61308e12i			0.154941i
$516$		−	5.58839e13i		−	1.52770i
$517$	3.58920e13			0.971728
$518$	−1.29621e13			−0.347559
$519$		−	3.48754e13i		−	0.926152i
$520$	−2.93521e13			−0.772009
$521$	−2.12115e13			−0.552564			−0.276282	−	0.961077i	$-0.589102\pi$
$521$	−2.12115e13			−0.552564			−0.276282	+	0.961077i	$0.589102\pi$
$522$			1.51918e13i			0.391972i
$523$	3.90091e13			0.996913			0.498457	−	0.866915i	$-0.333900\pi$
$523$	3.90091e13			0.996913			0.498457	+	0.866915i	$0.333900\pi$
$524$		−	4.18959e13i		−	1.06051i
$525$	1.59884e13			0.400876
$526$		−	7.84434e13i		−	1.94817i
$527$			5.69680e13i			1.40145i
$528$			1.18176e14i			2.87978i
$529$	2.74239e13			0.661988
$530$		−	1.75086e14i		−	4.18669i
$531$	−5.69445e12	+	1.28682e13i	−0.134890	+	0.304821i
$532$	−9.49369e13			−2.22780
$533$			6.95633e12i			0.161713i
$534$	−6.07739e13			−1.39962
$535$	−8.39715e13			−1.91586
$536$	−1.28933e14			−2.91434
$537$			2.57474e13i			0.576583i
$538$	−1.15634e14			−2.56551
$539$		−	6.29403e13i		−	1.38352i
$540$	3.32125e13			0.723323
$541$			2.97252e13i			0.641415i	0.947178	+	0.320707i	$0.103921\pi$
$541$			2.97252e13i			0.641415i	−0.947178	+	0.320707i	$0.896079\pi$
$542$			5.82797e13i			1.24601i
$543$	3.26992e13			0.692688
$544$			7.57862e13i			1.59073i
$545$			2.67079e12i			0.0555465i
$546$	−5.07777e12			−0.104643
$547$	1.57133e12			0.0320871			0.0160436	−	0.999871i	$-0.494893\pi$
$547$	1.57133e12			0.0320871			0.0160436	+	0.999871i	$0.494893\pi$
$548$	−1.45659e13			−0.294737
$549$		−	1.90019e12i		−	0.0381010i
$550$	−2.36718e14			−4.70346
$551$	5.52662e13			1.08818
$552$	4.69343e13			0.915788
$553$	4.12645e12			0.0797904
$554$		−	7.28571e12i		−	0.139612i
$555$		−	1.64966e13i		−	0.313278i
$556$	1.97960e14			3.72566
$557$	1.01564e14			1.89436			0.947181	−	0.320699i	$-0.103918\pi$
$557$	1.01564e14			1.89436			0.947181	+	0.320699i	$0.103918\pi$
$558$	−6.31968e13			−1.16822
$559$	−1.08737e13			−0.199213
$560$	−1.15080e14			−2.08958
$561$			4.55810e13i			0.820294i
$562$		−	1.59644e14i		−	2.84755i
$563$			2.62954e13i			0.464877i	0.972611	+	0.232438i	$0.0746704\pi$
$563$			2.62954e13i			0.464877i	−0.972611	+	0.232438i	$0.925330\pi$
$564$			4.13603e13i			0.724751i
$565$		−	3.82825e13i		−	0.664903i
$566$	1.23503e14			2.12616
$567$	3.41525e12			0.0582784
$568$		−	1.71135e14i		−	2.89466i
$569$		−	9.01712e13i		−	1.51184i	−0.654662	−	0.755921i	$-0.727189\pi$
$569$		−	9.01712e13i		−	1.51184i	0.654662	−	0.755921i	$-0.272811\pi$
$570$		−	1.69828e14i		−	2.82252i
$571$			9.16721e13i			1.51028i	0.655565	+	0.755138i	$0.272430\pi$
$571$			9.16721e13i			1.51028i	−0.655565	+	0.755138i	$0.727570\pi$
$572$	5.34860e13			0.873494
$573$			9.07525e12i			0.146922i
$574$			5.30038e13i			0.850644i
$575$			4.83755e13i			0.769637i
$576$	−2.88393e13			−0.454855
$577$	−9.46419e13			−1.47980			−0.739902	−	0.672714i	$-0.765128\pi$
$577$	−9.46419e13			−1.47980			−0.739902	+	0.672714i	$0.765128\pi$
$578$		−	5.35427e13i		−	0.829968i
$579$	−4.75640e13			−0.730946
$580$	1.55827e14			2.37413
$581$		−	2.80734e13i		−	0.424048i
$582$	1.29694e14			1.94225
$583$			1.89644e14i			2.81576i
$584$	−8.95956e13			−1.31893
$585$		−	6.46235e12i		−	0.0943216i
$586$		−	6.94689e12i		−	0.100532i
$587$		−	3.82820e13i		−	0.549292i	−0.961545	−	0.274646i	$-0.911439\pi$
$587$		−	3.82820e13i		−	0.549292i	0.961545	−	0.274646i	$-0.0885607\pi$
$588$	7.25297e13			1.03188
$589$			2.29904e14i			3.24317i
$590$	1.85529e14	+	8.21006e13i	2.59508	+	1.14838i
$591$	−1.64171e13			−0.227698
$592$			6.76409e13i			0.930252i
$593$	−1.13813e14			−1.55209			−0.776044	−	0.630678i	$-0.782777\pi$
$593$	−1.13813e14			−1.55209			−0.776044	+	0.630678i	$0.782777\pi$
$594$	−5.05647e13			−0.683779
$595$	−4.43867e13			−0.595207
$596$		−	2.55157e14i		−	3.39294i
$597$	−1.28539e12			−0.0169498
$598$		−	1.53636e13i		−	0.200903i
$599$	−2.06483e13			−0.267763			−0.133881	−	0.990997i	$-0.542744\pi$
$599$	−2.06483e13			−0.267763			−0.133881	+	0.990997i	$0.542744\pi$
$600$		−	1.62146e14i		−	2.08521i
$601$		−	1.03016e14i		−	1.31380i	−0.753976	−	0.656902i	$-0.771867\pi$
$601$		−	1.03016e14i		−	1.31380i	0.753976	−	0.656902i	$-0.228133\pi$
$602$	−8.28520e13			−1.04790
$603$		−	2.83867e13i		−	0.356065i
$604$		−	1.97602e14i		−	2.45814i
$605$	3.26528e14			4.02851
$606$	−5.54862e13			−0.678925
$607$	9.74616e13			1.18274			0.591371	−	0.806400i	$-0.298587\pi$
$607$	9.74616e13			1.18274			0.591371	+	0.806400i	$0.298587\pi$
$608$			3.05848e14i			3.68119i
$609$	1.60238e13			0.191284
$610$	−2.73963e13			−0.324371
$611$	8.04773e12			0.0945078
$612$	−5.25255e13			−0.611805
$613$		−	1.46820e14i		−	1.69622i	−0.529820	−	0.848110i	$-0.677740\pi$
$613$		−	1.46820e14i		−	1.69622i	0.529820	−	0.848110i	$-0.322260\pi$
$614$		−	6.01329e13i		−	0.689081i
$615$	−6.74566e13			−0.766741
$616$	2.42245e14			2.73118
$617$	−5.74060e13			−0.641995			−0.320997	−	0.947080i	$-0.604018\pi$
$617$	−5.74060e13			−0.641995			−0.320997	+	0.947080i	$0.604018\pi$
$618$	9.84771e12			0.109243
$619$	1.74878e14			1.92434			0.962170	−	0.272448i	$-0.0878334\pi$
$619$	1.74878e14			1.92434			0.962170	+	0.272448i	$0.0878334\pi$
$620$			6.48233e14i			7.07576i
$621$			1.03334e13i			0.111888i
$622$			2.63378e14i			2.82897i
$623$			6.41025e13i			0.683022i
$624$			2.64975e13i			0.280080i
$625$	−5.44896e13			−0.571365
$626$	7.97892e13			0.829990
$627$			1.83950e14i			1.89829i
$628$			1.58983e13i			0.162762i
$629$			2.60894e13i			0.264978i
$630$		−	4.92399e13i		−	0.496151i
$631$	−4.23221e13			−0.423078			−0.211539	−	0.977370i	$-0.567848\pi$
$631$	−4.23221e13			−0.423078			−0.211539	+	0.977370i	$0.567848\pi$
$632$		−	4.18481e13i		−	0.415040i
$633$		−	4.97819e13i		−	0.489839i
$634$			1.76730e14i			1.72530i
$635$	3.02183e14			2.92686
$636$	−2.18537e14			−2.10010
$637$		−	1.41125e13i		−	0.134558i
$638$	−2.37242e14			−2.24433
$639$	3.76783e13			0.353661
$640$			6.60308e13i			0.614959i
$641$	−1.07607e14			−0.994379			−0.497190	−	0.867642i	$-0.665635\pi$
$641$	−1.07607e14			−0.994379			−0.497190	+	0.867642i	$0.665635\pi$
$642$			1.47321e14i			1.35080i
$643$	−4.82800e13			−0.439251			−0.219625	−	0.975584i	$-0.570483\pi$
$643$	−4.82800e13			−0.439251			−0.219625	+	0.975584i	$0.570483\pi$
$644$		−	8.32838e13i		−	0.751850i
$645$		−	1.05444e14i		−	0.944543i
$646$			2.68584e14i			2.38736i
$647$	1.99080e14			1.75593			0.877963	−	0.478728i	$-0.158902\pi$
$647$	1.99080e14			1.75593			0.877963	+	0.478728i	$0.158902\pi$
$648$		−	3.46356e13i		−	0.303143i
$649$	−2.00956e14	−	8.89273e13i	−1.74533	−	0.772345i
$650$	−5.30771e13			−0.457446
$651$			6.66582e13i			0.570096i
$652$	−2.99764e14			−2.54414
$653$	−1.58076e14			−1.33138			−0.665689	−	0.746229i	$-0.731862\pi$
$653$	−1.58076e14			−1.33138			−0.665689	+	0.746229i	$0.731862\pi$
$654$	4.68568e12			0.0391637
$655$		−	7.90505e13i		−	0.655689i
$656$	2.76592e14			2.27678
$657$		−	1.97260e13i		−	0.161143i
$658$	6.13197e13			0.497131
$659$		−	4.18691e13i		−	0.336874i	−0.985712	−	0.168437i	$-0.946128\pi$
$659$		−	4.18691e13i		−	0.336874i	0.985712	−	0.168437i	$-0.0538719\pi$
$660$			5.18661e14i			4.14156i
$661$	1.58756e14			1.25812			0.629062	−	0.777355i	$-0.283439\pi$
$661$	1.58756e14			1.25812			0.629062	+	0.777355i	$0.283439\pi$
$662$			2.72992e14i			2.14714i
$663$			1.02202e13i			0.0797797i
$664$	−2.84705e14			−2.20574
$665$	−1.79130e14			−1.37740
$666$	−2.89420e13			−0.220880
$667$			4.84825e13i			0.367245i
$668$	−3.70544e14			−2.78585
$669$	1.67171e13			0.124747
$670$	−4.09269e14			−3.03134
$671$	2.96743e13			0.218156
$672$			8.86773e13i			0.647092i
$673$		−	1.29737e13i		−	0.0939697i	−0.998896	−	0.0469849i	$-0.985039\pi$
$673$		−	1.29737e13i		−	0.0939697i	0.998896	−	0.0469849i	$-0.0149613\pi$
$674$	2.93873e14			2.11281
$675$	3.56991e13			0.254764
$676$	−3.36063e14			−2.38061
$677$	−1.52016e14			−1.06892			−0.534462	−	0.845192i	$-0.679486\pi$
$677$	−1.52016e14			−1.06892			−0.534462	+	0.845192i	$0.679486\pi$
$678$	−6.71636e13			−0.468798
$679$		−	1.36798e14i		−	0.947828i
$680$			4.50145e14i			3.09605i
$681$			8.61606e12i			0.0588265i
$682$		−	9.86911e14i		−	6.68892i
$683$		−	2.93309e14i		−	1.97343i	−0.162451	−	0.986717i	$-0.551940\pi$
$683$		−	2.93309e14i		−	1.97343i	0.162451	−	0.986717i	$-0.448060\pi$
$684$	−2.11976e14			−1.41581
$685$	−2.74834e13			−0.182229
$686$		−	2.55870e14i		−	1.68422i
$687$			1.20898e14i			0.790017i
$688$			4.32350e14i			2.80474i
$689$			4.25221e13i			0.273854i
$690$	1.48983e14			0.952556
$691$		−	2.21613e13i		−	0.140671i	−0.997523	−	0.0703356i	$-0.977593\pi$
$691$		−	2.21613e13i		−	0.140671i	0.997523	−	0.0703356i	$-0.0224070\pi$
$692$			6.27608e14i			3.95511i
$693$			5.33342e13i			0.333687i
$694$	3.75522e14			2.33259
$695$	3.73517e14			2.30349
$696$		−	1.62505e14i		−	0.994991i
$697$	1.06683e14			0.648530
$698$	6.16812e13			0.372285
$699$			9.47277e12i			0.0567664i
$700$	−2.87724e14			−1.71193
$701$		−	1.12954e14i		−	0.667285i	−0.942700	−	0.333643i	$-0.891722\pi$
$701$		−	1.12954e14i		−	0.667285i	0.942700	−	0.333643i	$-0.108278\pi$
$702$	−1.13377e13			−0.0665026
$703$			1.05288e14i			0.613201i
$704$		−	4.50368e14i		−	2.60438i
$705$			7.80401e13i			0.448097i
$706$	2.34218e14			1.33535
$707$			5.85252e13i			0.331319i
$708$	1.02476e14	−	2.31573e14i	0.576044	−	1.30173i
$709$	2.71154e14			1.51351			0.756755	−	0.653698i	$-0.226783\pi$
$709$	2.71154e14			1.51351			0.756755	+	0.653698i	$0.226783\pi$
$710$		−	5.43232e14i		−	3.01088i
$711$	9.21356e12			0.0507083
$712$	6.50091e14			3.55283
$713$	−2.01684e14			−1.09452
$714$			7.78729e13i			0.419658i
$715$	1.00919e14			0.540061
$716$		−	4.63344e14i		−	2.46228i
$717$	3.63066e13			0.191597
$718$		−	4.82868e13i		−	0.253050i
$719$			3.12625e13i			0.162697i	0.996686	+	0.0813485i	$0.0259227\pi$
$719$			3.12625e13i			0.162697i	−0.996686	+	0.0813485i	$0.974077\pi$
$720$	−2.56950e14			−1.32797
$721$		−	1.03871e13i		−	0.0533110i
$722$			7.18681e14i			3.66311i
$723$	−1.87851e14			−0.950870
$724$	−5.88445e14			−2.95810
$725$	1.67494e14			0.836200
$726$		−	5.72868e14i		−	2.84035i
$727$	1.46683e13			0.0722284			0.0361142	−	0.999348i	$-0.488502\pi$
$727$	1.46683e13			0.0722284			0.0361142	+	0.999348i	$0.488502\pi$
$728$	5.43163e13			0.265628
$729$	7.62560e12			0.0370370
$730$	−2.84402e14			−1.37189
$731$			1.66759e14i			0.798919i
$732$			3.41954e13i			0.162709i
$733$	−1.72116e14			−0.813393			−0.406696	−	0.913563i	$-0.633319\pi$
$733$	−1.72116e14			−0.813393			−0.406696	+	0.913563i	$0.633319\pi$
$734$	−3.31340e14			−1.55523
$735$	1.36851e14			0.637988
$736$	−2.68307e14			−1.24235
$737$	4.43300e14			2.03873
$738$			1.18347e14i			0.540600i
$739$			1.77557e14i			0.805595i	0.915289	+	0.402797i	$0.131962\pi$
$739$			1.77557e14i			0.805595i	−0.915289	+	0.402797i	$0.868038\pi$
$740$			2.96868e14i			1.33784i
$741$			4.12454e13i			0.184622i
$742$			3.23998e14i			1.44053i
$743$	2.33449e14			1.03097			0.515487	−	0.856897i	$-0.327611\pi$
$743$	2.33449e14			1.03097			0.515487	+	0.856897i	$0.327611\pi$
$744$	6.76009e14			2.96543
$745$		−	4.81438e14i		−	2.09778i
$746$		−	6.95432e14i		−	3.00996i
$747$		−	6.26825e13i		−	0.269491i
$748$		−	8.20264e14i		−	3.50304i
$749$	1.55390e14			0.659196
$750$		−	1.25892e14i		−	0.530508i
$751$			8.63557e13i			0.361486i	0.983530	+	0.180743i	$0.0578502\pi$
$751$			8.63557e13i			0.361486i	−0.983530	+	0.180743i	$0.942150\pi$
$752$		−	3.19987e14i		−	1.33059i
$753$	−2.16878e14			−0.895861
$754$	−5.31945e13			−0.218278
$755$		−	3.72843e14i		−	1.51981i
$756$	−6.14600e13			−0.248876
$757$	−1.30911e14			−0.526621			−0.263311	−	0.964711i	$-0.584814\pi$
$757$	−1.30911e14			−0.526621			−0.263311	+	0.964711i	$0.584814\pi$
$758$		−	4.85623e14i		−	1.94068i
$759$	−1.61371e14			−0.640643
$760$			1.81664e15i			7.16474i
$761$	3.64240e14			1.42713			0.713566	−	0.700588i	$-0.247079\pi$
$761$	3.64240e14			1.42713			0.713566	+	0.700588i	$0.247079\pi$
$762$		−	5.30156e14i		−	2.06361i
$763$		−	4.94232e12i		−	0.0191121i
$764$		−	1.63316e14i		−	0.627425i
$765$	−9.91069e13			−0.378266
$766$		−	2.06339e13i		−	0.0782415i
$767$	−4.50585e13	−	1.99394e13i	−0.169746	−	0.0751163i
$768$	−9.46481e13			−0.354247
$769$			1.91581e14i			0.712393i	0.934411	+	0.356197i	$0.115927\pi$
$769$			1.91581e14i			0.712393i	−0.934411	+	0.356197i	$0.884073\pi$
$770$	7.68953e14			2.84084
$771$	1.88225e14			0.690885
$772$	8.55948e14			3.12148
$773$		−	2.83544e14i		−	1.02736i	−0.857982	−	0.513680i	$-0.828282\pi$
$773$		−	2.83544e14i		−	1.02736i	0.857982	−	0.513680i	$-0.171718\pi$
$774$	−1.84992e14			−0.665961
$775$			6.96767e14i			2.49218i
$776$	−1.38732e15			−4.93025
$777$			3.05271e13i			0.107791i
$778$		−	2.92325e14i		−	1.02558i
$779$	4.30536e14			1.50080
$780$			1.16295e14i			0.402798i
$781$			5.88402e14i			2.02497i
$782$	−2.35616e14			−0.805697
$783$	3.57781e13			0.121565
$784$	−5.61131e14			−1.89445
$785$			2.99975e13i			0.100632i
$786$	−1.38688e14			−0.462302
$787$	1.87057e14			0.619583			0.309791	−	0.950805i	$-0.399741\pi$
$787$	1.87057e14			0.619583			0.309791	+	0.950805i	$0.399741\pi$
$788$	2.95438e14			0.972379
$789$	−1.84742e14			−0.604199
$790$		−	1.32838e14i		−	0.431704i
$791$			7.08422e13i			0.228775i
$792$	5.40886e14			1.73572
$793$	6.65360e12			0.0212173
$794$	9.09714e14			2.88272
$795$	−4.12344e14			−1.29845
$796$	2.31316e13			0.0723837
$797$		−	4.47696e13i		−	0.139217i	−0.997574	−	0.0696084i	$-0.977825\pi$
$797$		−	4.47696e13i		−	0.139217i	0.997574	−	0.0696084i	$-0.0221750\pi$
$798$			3.14269e14i			0.971153i
$799$		−	1.23420e14i		−	0.379012i
$800$			9.26929e14i			2.82876i
$801$			1.43128e14i			0.434074i
$802$	7.64209e14			2.30324
$803$	3.08050e14			0.922664
$804$			5.10840e14i			1.52056i
$805$		−	1.57143e14i		−	0.464852i
$806$		−	2.21286e14i		−	0.650547i
$807$			2.72329e14i			0.795659i
$808$	5.93530e14			1.72340
$809$		−	4.60280e14i		−	1.32825i	−0.747622	−	0.664124i	$-0.768805\pi$
$809$		−	4.60280e14i		−	1.32825i	0.747622	−	0.664124i	$-0.231195\pi$
$810$		−	1.09943e14i		−	0.315314i
$811$			6.80137e13i			0.193862i	0.995291	+	0.0969308i	$0.0309026\pi$
$811$			6.80137e13i			0.193862i	−0.995291	+	0.0969308i	$0.969097\pi$
$812$	−2.88360e14			−0.816875
$813$	1.37254e14			0.386432
$814$		−	4.51971e14i		−	1.26470i
$815$	−5.65604e14			−1.57298
$816$	4.06367e14			1.12323
$817$			6.72985e14i			1.84882i
$818$	2.21068e14			0.603614
$819$			1.19586e13i			0.0324536i
$820$	1.21393e15			3.27435
$821$			4.03696e14i			1.08228i	0.840933	+	0.541139i	$0.182007\pi$
$821$			4.03696e14i			1.08228i	−0.840933	+	0.541139i	$0.817993\pi$
$822$			4.82175e13i			0.128483i
$823$		−	6.40411e14i		−	1.69613i	−0.529890	−	0.848067i	$-0.677767\pi$
$823$		−	6.40411e14i		−	1.69613i	0.529890	−	0.848067i	$-0.322233\pi$
$824$	−1.05340e14			−0.277304
$825$			5.57494e14i			1.45871i
$826$	−3.43323e14	−	1.51928e14i	−0.892900	−	0.395128i
$827$	3.24789e14			0.839603			0.419802	−	0.907616i	$-0.362100\pi$
$827$	3.24789e14			0.839603			0.419802	+	0.907616i	$0.362100\pi$
$828$		−	1.85957e14i		−	0.477815i
$829$	7.46958e14			1.90776			0.953879	−	0.300191i	$-0.0970503\pi$
$829$	7.46958e14			1.90776			0.953879	+	0.300191i	$0.0970503\pi$
$830$	−9.03734e14			−2.29430
$831$	−1.71586e13			−0.0432988
$832$		−	1.00982e14i		−	0.253295i
$833$	−2.16431e14			−0.539627
$834$		−	6.55306e14i		−	1.62410i
$835$	−6.99155e14			−1.72243
$836$		−	3.31031e15i		−	8.10658i
$837$			1.48835e14i			0.362307i
$838$	−1.13887e15			−2.75583
$839$			3.85926e14i			0.928312i	0.885753	+	0.464156i	$0.153642\pi$
$839$			3.85926e14i			0.928312i	−0.885753	+	0.464156i	$0.846358\pi$
$840$			5.26714e14i			1.25944i
$841$	−2.52842e14			−0.600993
$842$	−2.06867e14			−0.488800
$843$	−3.75977e14			−0.883128
$844$			8.95862e14i			2.09184i
$845$	−6.34095e14			−1.47187
$846$	1.36915e14			0.315936
$847$	−6.04244e14			−1.38610
$848$	1.69073e15			3.85563
$849$		−	2.90862e14i		−	0.659400i
$850$			8.13993e14i			1.83454i
$851$	−9.23645e13			−0.206946
$852$	−6.78048e14			−1.51030
$853$	3.95715e14			0.876270			0.438135	−	0.898909i	$-0.355639\pi$
$853$	3.95715e14			0.876270			0.438135	+	0.898909i	$0.355639\pi$
$854$	5.06971e13			0.111608
$855$	−3.99963e14			−0.875365
$856$		−	1.57588e15i		−	3.42889i
$857$		−	1.65201e12i		−	0.00357362i	−0.999998	−	0.00178681i	$-0.999431\pi$
$857$		−	1.65201e12i		−	0.00357362i	0.999998	−	0.00178681i	$-0.000568760\pi$
$858$		−	1.77054e14i		−	0.380777i
$859$		−	6.35113e14i		−	1.35796i	−0.734159	−	0.678978i	$-0.762423\pi$
$859$		−	6.35113e14i		−	1.35796i	0.734159	−	0.678978i	$-0.237577\pi$
$860$			1.89754e15i			4.03365i
$861$	1.24829e14			0.263816
$862$	−4.83834e14			−1.01662
$863$		−	3.15327e14i		−	0.658730i	−0.944203	−	0.329365i	$-0.893165\pi$
$863$		−	3.15327e14i		−	0.658730i	0.944203	−	0.329365i	$-0.106835\pi$
$864$			1.97999e14i			0.411239i
$865$			1.18419e15i			2.44535i
$866$		−	2.12716e14i		−	0.436728i
$867$	−1.26098e14			−0.257403
$868$		−	1.19956e15i		−	2.43458i
$869$			1.43883e14i			0.290343i
$870$		−	5.15835e14i		−	1.03494i
$871$	9.93972e13			0.198282
$872$	−5.01222e13			−0.0994141
$873$		−	3.05442e14i		−	0.602363i
$874$	−9.50870e14			−1.86451
$875$	−1.32787e14			−0.258891
$876$			3.54983e14i			0.688157i
$877$	−3.02735e14			−0.583532			−0.291766	−	0.956490i	$-0.594243\pi$
$877$	−3.02735e14			−0.583532			−0.291766	+	0.956490i	$0.594243\pi$
$878$		−	3.62506e14i		−	0.694773i
$879$	−1.63606e13			−0.0311785
$880$		−	4.01266e15i		−	7.60359i
$881$			8.18199e14i			1.54163i	0.637061	+	0.770813i	$0.280150\pi$
$881$			8.18199e14i			1.54163i	−0.637061	+	0.770813i	$0.719850\pi$
$882$		−	2.40095e14i		−	0.449821i
$883$	4.85539e14			0.904525			0.452263	−	0.891885i	$-0.350617\pi$
$883$	4.85539e14			0.904525			0.452263	+	0.891885i	$0.350617\pi$
$884$		−	1.83920e14i		−	0.340697i
$885$	1.93355e14	−	4.36939e14i	0.356155	−	0.804830i
$886$	−5.26656e14			−0.964624
$887$			9.73850e14i			1.77367i	0.462082	+	0.886837i	$0.347103\pi$
$887$			9.73850e14i			1.77367i	−0.462082	+	0.886837i	$0.652897\pi$
$888$	3.09589e14			0.560687
$889$	−5.59193e14			−1.00705
$890$	2.06357e15			3.69547
$891$			1.19085e14i			0.212065i
$892$	−3.00836e14			−0.532728
$893$		−	4.98084e14i		−	0.877093i
$894$	−8.44644e14			−1.47906
$895$		−	8.74252e14i		−	1.52237i
$896$		−	1.22191e14i		−	0.211591i
$897$	−3.61827e13			−0.0623073
$898$			1.21846e15i			2.08655i
$899$			6.98308e14i			1.18918i
$900$	−6.42431e14			−1.08796
$901$	6.52122e14			1.09826
$902$	−1.84817e15			−3.09534
$903$			1.95125e14i			0.324992i
$904$	7.18441e14			1.19001
$905$	−1.11030e15			−1.82893
$906$	−6.54122e14			−1.07156
$907$	−2.76535e14			−0.450520			−0.225260	−	0.974299i	$-0.572323\pi$
$907$	−2.76535e14			−0.450520			−0.225260	+	0.974299i	$0.572323\pi$
$908$		−	1.55052e14i		−	0.251217i
$909$			1.30675e14i			0.210559i
$910$	1.72415e14			0.276292
$911$	−3.19444e14			−0.509100			−0.254550	−	0.967060i	$-0.581927\pi$
$911$	−3.19444e14			−0.509100			−0.254550	+	0.967060i	$0.581927\pi$
$912$	1.63996e15			2.59932
$913$	9.78880e14			1.54303
$914$	−1.61184e14			−0.252691
$915$			6.45210e13i			0.100599i
$916$		−	2.17565e15i		−	3.37375i
$917$			1.46284e14i			0.225605i
$918$			1.73875e14i			0.266701i
$919$			9.84536e14i			1.50194i	0.660334	+	0.750972i	$0.270415\pi$
$919$			9.84536e14i			1.50194i	−0.660334	+	0.750972i	$0.729585\pi$
$920$	−1.59365e15			−2.41799
$921$	−1.41619e14			−0.213709
$922$		−	3.95212e13i		−	0.0593165i
$923$			1.31932e14i			0.196943i
$924$		−	9.59789e14i		−	1.42500i
$925$			3.19095e14i			0.471207i
$926$	−1.56981e15			−2.30565
$927$		−	2.31923e13i		−	0.0338802i
$928$			9.28980e14i			1.34979i
$929$			4.38868e13i			0.0634243i	0.999497	+	0.0317121i	$0.0100960\pi$
$929$			4.38868e13i			0.0634243i	−0.999497	+	0.0317121i	$0.989904\pi$
$930$	2.14584e15			3.08449
$931$	−8.73443e14			−1.24878
$932$		−	1.70469e14i		−	0.242419i
$933$	6.20281e14			0.877366
$934$	2.74528e14			0.386235
$935$		−	1.54770e15i		−	2.16585i
$936$	1.21278e14			0.168812
$937$			6.65236e14i			0.921038i	0.887650	+	0.460519i	$0.152337\pi$
$937$			6.65236e14i			0.921038i	−0.887650	+	0.460519i	$0.847663\pi$
$938$	7.57357e14			1.04301
$939$		−	1.87911e14i		−	0.257410i
$940$		−	1.40439e15i		−	1.91359i
$941$		−	8.49635e14i		−	1.15155i	−0.817607	−	0.575777i	$-0.804700\pi$
$941$		−	8.49635e14i		−	1.15155i	0.817607	−	0.575777i	$-0.195300\pi$
$942$	5.26282e13			0.0709519
$943$			3.77690e14i			0.506497i
$944$	−7.92812e14	+	1.79158e15i	−1.05757	+	2.38988i
$945$	−1.15965e14			−0.153875
$946$		−	2.88893e15i		−	3.81313i
$947$	−1.36518e15			−1.79243			−0.896214	−	0.443623i	$-0.853693\pi$
$947$	−1.36518e15			−1.79243			−0.896214	+	0.443623i	$0.853693\pi$
$948$	−1.65805e14			−0.216549
$949$	6.90712e13			0.0897359
$950$			3.28501e15i			4.24540i
$951$	4.16217e14			0.535078
$952$		−	8.32998e14i		−	1.06527i
$953$	−3.57381e14			−0.454640			−0.227320	−	0.973820i	$-0.572996\pi$
$953$	−3.57381e14			−0.454640			−0.227320	+	0.973820i	$0.572996\pi$
$954$			7.23424e14i			0.915484i
$955$		−	3.08150e14i		−	0.387922i
$956$	−6.53364e14			−0.818212
$957$			5.58727e14i			0.696050i
$958$			2.40464e15i			2.98005i
$959$	5.08584e13			0.0627003
$960$	9.79237e14			1.20097
$961$	−2.08529e15			−2.54420
$962$		−	1.01341e14i		−	0.123002i
$963$	3.46956e14			0.418932
$964$	3.38051e15			4.06067
$965$	1.61503e15			1.92994
$966$	−2.75694e14			−0.327749
$967$		−	1.10344e15i		−	1.30502i	−0.757779	−	0.652512i	$-0.773715\pi$
$967$		−	1.10344e15i		−	1.30502i	0.757779	−	0.652512i	$-0.226285\pi$
$968$			6.12791e15i			7.21000i
$969$	6.32542e14			0.740406
$970$	−4.40376e15			−5.12820
$971$	−9.09113e13			−0.105323			−0.0526613	−	0.998612i	$-0.516770\pi$
$971$	−9.09113e13			−0.105323			−0.0526613	+	0.998612i	$0.516770\pi$
$972$	−1.37228e14			−0.158166
$973$	−6.91198e14			−0.792571
$974$			6.53380e14i			0.745369i
$975$			1.25002e14i			0.141871i
$976$		−	2.64555e14i		−	0.298722i
$977$		−	7.71645e14i		−	0.866851i	−0.901189	−	0.433426i	$-0.857305\pi$
$977$		−	7.71645e14i		−	0.866851i	0.901189	−	0.433426i	$-0.142695\pi$
$978$			9.92306e14i			1.10905i
$979$	−2.23516e15			−2.48539
$980$	−2.46274e15			−2.72451
$981$		−	1.10352e13i		−	0.0121461i
$982$		−	1.27683e15i		−	1.39822i
$983$		−	8.22306e14i		−	0.895913i	−0.894055	−	0.447956i	$-0.852152\pi$
$983$		−	8.22306e14i		−	0.895913i	0.894055	−	0.447956i	$-0.147848\pi$
$984$		−	1.26595e15i		−	1.37227i
$985$	5.57443e14			0.601200
$986$			8.15794e14i			0.875379i
$987$		−	1.44414e14i		−	0.154178i
$988$		−	7.42241e14i		−	0.788425i
$989$	−5.90379e14			−0.623950
$990$	1.71692e15			1.80541
$991$		−	1.31757e14i		−	0.137849i	−0.997622	−	0.0689247i	$-0.978043\pi$
$991$		−	1.31757e14i		−	0.137849i	0.997622	−	0.0689247i	$-0.0219568\pi$
$992$	−3.86450e15			−4.02286
$993$	6.42923e14			0.665905
$994$			1.00526e15i			1.03596i
$995$	4.36455e13			0.0447532
$996$			1.12802e15i			1.15085i
$997$	−3.60374e14			−0.365829			−0.182915	−	0.983129i	$-0.558553\pi$
$997$	−3.60374e14			−0.365829			−0.182915	+	0.983129i	$0.558553\pi$
$998$		−	1.85093e15i		−	1.86955i
$999$			6.81611e13i			0.0685030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.97	yes	100
59.58	odd	2	inner	177.11.c.a.58.4	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.4	✓	100	59.58	odd	2	inner
177.11.c.a.58.97	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+59.5712i q^{2} +140.296 q^{3} -2524.73 q^{4} -4763.75 q^{5} +8357.61i q^{6} +8815.37 q^{7} -89400.5i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q+59.5712i q^{2} +140.296 q^{3} -2524.73 q^{4} -4763.75 q^{5} +8357.61i q^{6} +8815.37 q^{7} -89400.5i q^{8} +19683.0 q^{9} -283782. i q^{10} +307379. i q^{11} -354210. q^{12} +68920.8i q^{13} +525142. i q^{14} -668335. q^{15} +2.74037e6 q^{16} +1.05697e6 q^{17} +1.17254e6i q^{18} +4.26559e6 q^{19} +1.20272e7 q^{20} +1.23676e6 q^{21} -1.83109e7 q^{22} +3.74201e6i q^{23} -1.25425e7i q^{24} +1.29277e7 q^{25} -4.10570e6 q^{26} +2.76145e6 q^{27} -2.22564e7 q^{28} +1.29563e7 q^{29} -3.98136e7i q^{30} +5.38973e7i q^{31} +7.17012e7i q^{32} +4.31241e7i q^{33} +6.29652e7i q^{34} -4.19942e7 q^{35} -4.96943e7 q^{36} +2.46831e7i q^{37} +2.54107e8i q^{38} +9.66932e6i q^{39} +4.25881e8i q^{40} +1.00932e8 q^{41} +7.36754e7i q^{42} +1.57771e8i q^{43} -7.76050e8i q^{44} -9.37648e7 q^{45} -2.22916e8 q^{46} -1.16768e8i q^{47} +3.84463e8 q^{48} -2.04765e8 q^{49} +7.70117e8i q^{50} +1.48289e8 q^{51} -1.74007e8i q^{52} +6.16971e8 q^{53} +1.64503e8i q^{54} -1.46428e9i q^{55} -7.88098e8i q^{56} +5.98446e8 q^{57} +7.71821e8i q^{58} +(-2.89308e8 + 6.53772e8i) q^{59} +1.68737e9 q^{60} -9.65398e7i q^{61} -3.21073e9 q^{62} +1.73513e8 q^{63} -1.46519e9 q^{64} -3.28321e8i q^{65} -2.56896e9 q^{66} -1.44219e9i q^{67} -2.66857e9 q^{68} +5.24990e8i q^{69} -2.50165e9i q^{70} +1.91425e9 q^{71} -1.75967e9i q^{72} -1.00218e9i q^{73} -1.47040e9 q^{74} +1.81370e9 q^{75} -1.07695e10 q^{76} +2.70966e9i q^{77} -5.76013e8 q^{78} +4.68097e8 q^{79} -1.30544e10 q^{80} +3.87420e8 q^{81} +6.01266e9i q^{82} -3.18460e9i q^{83} -3.12249e9 q^{84} -5.03515e9 q^{85} -9.39859e9 q^{86} +1.81771e9 q^{87} +2.74798e10 q^{88} +7.27168e9i q^{89} -5.58569e9i q^{90} +6.07562e8i q^{91} -9.44757e9i q^{92} +7.56159e9i q^{93} +6.95600e9 q^{94} -2.03202e10 q^{95} +1.00594e10i q^{96} -1.55181e10i q^{97} -1.21981e10i q^{98} +6.05014e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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