LMFDB - Embedded newform 403.2.l.c.25.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.10
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46972i q^{2} +(0.869265 + 1.50561i) q^{3} -0.160067 q^{4} +(0.337316 + 0.194750i) q^{5} +(2.21282 - 1.27757i) q^{6} +(1.34672 - 0.777530i) q^{7} -2.70418i q^{8} +(-0.0112448 + 0.0194765i) q^{9} +O(q^{10})$	\(q-1.46972i q^{2} +(0.869265 + 1.50561i) q^{3} -0.160067 q^{4} +(0.337316 + 0.194750i) q^{5} +(2.21282 - 1.27757i) q^{6} +(1.34672 - 0.777530i) q^{7} -2.70418i q^{8} +(-0.0112448 + 0.0194765i) q^{9} +(0.286227 - 0.495759i) q^{10} +(0.846696 + 0.488840i) q^{11} +(-0.139141 - 0.240999i) q^{12} +(-2.33127 + 2.75049i) q^{13} +(-1.14275 - 1.97930i) q^{14} +0.677157i q^{15} -4.29451 q^{16} +(1.62295 + 2.81103i) q^{17} +(0.0286250 + 0.0165267i) q^{18} +(2.33691 - 1.34921i) q^{19} +(-0.0539932 - 0.0311730i) q^{20} +(2.34132 + 1.35176i) q^{21} +(0.718456 - 1.24440i) q^{22} +3.56702 q^{23} +(4.07145 - 2.35065i) q^{24} +(-2.42415 - 4.19874i) q^{25} +(4.04244 + 3.42631i) q^{26} +5.17649 q^{27} +(-0.215566 + 0.124457i) q^{28} +2.24686 q^{29} +0.995228 q^{30} +(-5.55918 + 0.308974i) q^{31} +0.903357i q^{32} +1.69973i q^{33} +(4.13142 - 2.38527i) q^{34} +0.605695 q^{35} +(0.00179992 - 0.00311755i) q^{36} +(-5.27552 + 3.04582i) q^{37} +(-1.98296 - 3.43459i) q^{38} +(-6.16766 - 1.11908i) q^{39} +(0.526638 - 0.912164i) q^{40} +(-1.79085 - 1.03395i) q^{41} +(1.98670 - 3.44107i) q^{42} +(-1.47008 - 2.54626i) q^{43} +(-0.135528 - 0.0782472i) q^{44} +(-0.00758610 + 0.00437984i) q^{45} -5.24251i q^{46} +11.5129i q^{47} +(-3.73307 - 6.46587i) q^{48} +(-2.29089 + 3.96794i) q^{49} +(-6.17096 + 3.56281i) q^{50} +(-2.82155 + 4.88706i) q^{51} +(0.373160 - 0.440263i) q^{52} +(4.84072 - 8.38438i) q^{53} -7.60798i q^{54} +(0.190403 + 0.329787i) q^{55} +(-2.10258 - 3.64178i) q^{56} +(4.06278 + 2.34565i) q^{57} -3.30225i q^{58} +(-1.85412 + 1.07048i) q^{59} -0.108390i q^{60} -10.4105 q^{61} +(0.454104 + 8.17043i) q^{62} +0.0349727i q^{63} -7.26135 q^{64} +(-1.32203 + 0.473770i) q^{65} +2.49812 q^{66} +(-10.4078 - 6.00894i) q^{67} +(-0.259781 - 0.449953i) q^{68} +(3.10069 + 5.37055i) q^{69} -0.890200i q^{70} +(-5.78974 - 3.34271i) q^{71} +(0.0526681 + 0.0304079i) q^{72} +(9.56745 + 5.52377i) q^{73} +(4.47650 + 7.75352i) q^{74} +(4.21445 - 7.29964i) q^{75} +(-0.374062 + 0.215965i) q^{76} +1.52035 q^{77} +(-1.64474 + 9.06471i) q^{78} +(2.68445 + 4.64961i) q^{79} +(-1.44861 - 0.836355i) q^{80} +(4.53348 + 7.85222i) q^{81} +(-1.51961 + 2.63205i) q^{82} +(-12.9187 - 7.45862i) q^{83} +(-0.374768 - 0.216372i) q^{84} +1.26427i q^{85} +(-3.74228 + 2.16061i) q^{86} +(1.95312 + 3.38290i) q^{87} +(1.32191 - 2.28962i) q^{88} +5.51995i q^{89} +(0.00643712 + 0.0111494i) q^{90} +(-1.00099 + 5.51677i) q^{91} -0.570963 q^{92} +(-5.29760 - 8.10139i) q^{93} +16.9208 q^{94} +1.05104 q^{95} +(-1.36010 + 0.785257i) q^{96} -5.77397i q^{97} +(5.83175 + 3.36696i) q^{98} +(-0.0190418 + 0.0109938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.46972i		−	1.03925i	−0.854395	−	0.519623i	$-0.826072\pi$
$2$		−	1.46972i		−	1.03925i	0.854395	−	0.519623i	$-0.173928\pi$
$3$	0.869265	+	1.50561i	0.501871	+	0.869265i	0.999998	+	0.00216137i	$0.000687986\pi$
$3$	0.869265	+	1.50561i	0.501871	+	0.869265i	−0.498127	+	0.867104i	$0.665979\pi$
$4$	−0.160067			−0.0800336
$5$	0.337316	+	0.194750i	0.150852	+	0.0870947i	0.573526	−	0.819187i	$-0.305575\pi$
$5$	0.337316	+	0.194750i	0.150852	+	0.0870947i	−0.422674	+	0.906282i	$0.638908\pi$
$6$	2.21282	−	1.27757i	0.903381	−	0.521567i
$7$	1.34672	−	0.777530i	0.509013	−	0.293879i	−0.223415	−	0.974723i	$-0.571720\pi$
$7$	1.34672	−	0.777530i	0.509013	−	0.293879i	0.732428	+	0.680845i	$0.238387\pi$
$8$		−	2.70418i		−	0.956072i
$9$	−0.0112448	+	0.0194765i	−0.00374826	+	0.00649218i
$10$	0.286227	−	0.495759i	0.0905129	−	0.156773i
$11$	0.846696	+	0.488840i	0.255288	+	0.147391i	0.622183	−	0.782872i	$-0.286246\pi$
$11$	0.846696	+	0.488840i	0.255288	+	0.147391i	−0.366895	+	0.930262i	$0.619579\pi$
$12$	−0.139141	−	0.240999i	−0.0401665	−	0.0695704i
$13$	−2.33127	+	2.75049i	−0.646578	+	0.762848i
$13$	−2.33127	+	2.75049i	−0.646578	+	0.762848i
$14$	−1.14275	−	1.97930i	−0.305413	−	0.528990i
$15$			0.677157i			0.174841i
$16$	−4.29451			−1.07363
$17$	1.62295	+	2.81103i	0.393623	+	0.681775i	0.992924	−	0.118749i	$-0.0378883\pi$
$17$	1.62295	+	2.81103i	0.393623	+	0.681775i	−0.599302	+	0.800523i	$0.704555\pi$
$18$	0.0286250	+	0.0165267i	0.00674698	+	0.00389537i
$19$	2.33691	−	1.34921i	0.536123	−	0.309531i	−0.207383	−	0.978260i	$-0.566495\pi$
$19$	2.33691	−	1.34921i	0.536123	−	0.309531i	0.743506	+	0.668729i	$0.233161\pi$
$20$	−0.0539932	−	0.0311730i	−0.0120733	−	0.00697050i
$21$	2.34132	+	1.35176i	0.510917	+	0.294978i
$22$	0.718456	−	1.24440i	0.153175	−	0.265308i
$23$	3.56702			0.743775			0.371888	−	0.928278i	$-0.378711\pi$
$23$	3.56702			0.743775			0.371888	+	0.928278i	$0.378711\pi$
$24$	4.07145	−	2.35065i	0.831080	−	0.479824i
$25$	−2.42415	−	4.19874i	−0.484829	−	0.839749i
$26$	4.04244	+	3.42631i	0.792787	+	0.671954i
$27$	5.17649			0.996217
$28$	−0.215566	+	0.124457i	−0.0407381	+	0.0235202i
$29$	2.24686			0.417232			0.208616	−	0.977998i	$-0.433104\pi$
$29$	2.24686			0.417232			0.208616	+	0.977998i	$0.433104\pi$
$30$	0.995228			0.181703
$31$	−5.55918	+	0.308974i	−0.998459	+	0.0554933i
$31$	−5.55918	+	0.308974i	−0.998459	+	0.0554933i
$32$			0.903357i			0.159692i
$33$			1.69973i			0.295884i
$34$	4.13142	−	2.38527i	0.708532	−	0.409071i
$35$	0.605695			0.102381
$36$	0.00179992	−	0.00311755i	0.000299987	−	0.000519592i
$37$	−5.27552	+	3.04582i	−0.867290	+	0.500730i	−0.866447	−	0.499269i	$-0.833602\pi$
$37$	−5.27552	+	3.04582i	−0.867290	+	0.500730i	−0.000843382		1.00000i	$0.500268\pi$
$38$	−1.98296	−	3.43459i	−0.321679	−	0.557164i
$39$	−6.16766	−	1.11908i	−0.987616	−	0.179197i
$40$	0.526638	−	0.912164i	0.0832688	−	0.144226i
$41$	−1.79085	−	1.03395i	−0.279684	−	0.161476i	0.353596	−	0.935398i	$-0.384959\pi$
$41$	−1.79085	−	1.03395i	−0.279684	−	0.161476i	−0.633280	+	0.773922i	$0.718292\pi$
$42$	1.98670	−	3.44107i	0.306555	−	0.530969i
$43$	−1.47008	−	2.54626i	−0.224186	−	0.388301i	0.731889	−	0.681424i	$-0.238639\pi$
$43$	−1.47008	−	2.54626i	−0.224186	−	0.388301i	−0.956075	+	0.293123i	$0.905306\pi$
$44$	−0.135528	−	0.0782472i	−0.0204316	−	0.0117962i
$45$	−0.00758610	+	0.00437984i	−0.00113087	+	0.000652908i
$46$		−	5.24251i		−	0.772966i
$47$			11.5129i			1.67933i	0.543101	+	0.839667i	$0.317250\pi$
$47$			11.5129i			1.67933i	−0.543101	+	0.839667i	$0.682750\pi$
$48$	−3.73307	−	6.46587i	−0.538822	−	0.933268i
$49$	−2.29089	+	3.96794i	−0.327270	+	0.566849i
$50$	−6.17096	+	3.56281i	−0.872706	+	0.503857i
$51$	−2.82155	+	4.88706i	−0.395095	+	0.684325i
$52$	0.373160	−	0.440263i	0.0517479	−	0.0610534i
$53$	4.84072	−	8.38438i	0.664925	−	1.15168i	−0.314381	−	0.949297i	$-0.601797\pi$
$53$	4.84072	−	8.38438i	0.664925	−	1.15168i	0.979306	−	0.202386i	$-0.0648697\pi$
$54$		−	7.60798i		−	1.03531i
$55$	0.190403	+	0.329787i	0.0256739	+	0.0444685i
$56$	−2.10258	−	3.64178i	−0.280969	−	0.486653i
$57$	4.06278	+	2.34565i	0.538129	+	0.310689i
$58$		−	3.30225i		−	0.433607i
$59$	−1.85412	+	1.07048i	−0.241386	+	0.139364i	−0.615813	−	0.787892i	$-0.711173\pi$
$59$	−1.85412	+	1.07048i	−0.241386	+	0.139364i	0.374428	+	0.927256i	$0.377839\pi$
$60$		−	0.108390i		−	0.0139932i
$61$	−10.4105			−1.33292			−0.666461	−	0.745540i	$-0.732192\pi$
$61$	−10.4105			−1.33292			−0.666461	+	0.745540i	$0.732192\pi$
$62$	0.454104	+	8.17043i	0.0576712	+	1.03765i
$63$			0.0349727i			0.00440614i
$64$	−7.26135			−0.907668
$65$	−1.32203	+	0.473770i	−0.163978	+	0.0587640i
$66$	2.49812			0.307497
$67$	−10.4078	−	6.00894i	−1.27151	−	0.734108i	−0.296240	−	0.955113i	$-0.595733\pi$
$67$	−10.4078	−	6.00894i	−1.27151	−	0.734108i	−0.975273	+	0.221005i	$0.929066\pi$
$68$	−0.259781	−	0.449953i	−0.0315030	−	0.0545649i
$69$	3.10069	+	5.37055i	0.373279	+	0.646538i
$70$		−	0.890200i		−	0.106399i
$71$	−5.78974	−	3.34271i	−0.687116	−	0.396706i	0.115415	−	0.993317i	$-0.463180\pi$
$71$	−5.78974	−	3.34271i	−0.687116	−	0.396706i	−0.802531	+	0.596611i	$0.796514\pi$
$72$	0.0526681	+	0.0304079i	0.00620699	+	0.00358361i
$73$	9.56745	+	5.52377i	1.11979	+	0.646508i	0.941346	−	0.337443i	$-0.109562\pi$
$73$	9.56745	+	5.52377i	1.11979	+	0.646508i	0.178439	+	0.983951i	$0.442895\pi$
$74$	4.47650	+	7.75352i	0.520382	+	0.901328i
$75$	4.21445	−	7.29964i	0.486643	−	0.842890i
$76$	−0.374062	+	0.215965i	−0.0429078	+	0.0247729i
$77$	1.52035			0.173260
$78$	−1.64474	+	9.06471i	−0.186230	+	1.02638i
$79$	2.68445	+	4.64961i	0.302024	+	0.523122i	0.976594	−	0.215089i	$-0.0690042\pi$
$79$	2.68445	+	4.64961i	0.302024	+	0.523122i	−0.674570	+	0.738211i	$0.735671\pi$
$80$	−1.44861	−	0.836355i	−0.161959	−	0.0935073i
$81$	4.53348	+	7.85222i	0.503720	+	0.872469i
$82$	−1.51961	+	2.63205i	−0.167813	+	0.290661i
$83$	−12.9187	−	7.45862i	−1.41801	−	0.818690i	−0.421889	−	0.906648i	$-0.638633\pi$
$83$	−12.9187	−	7.45862i	−1.41801	−	0.818690i	−0.996124	+	0.0879573i	$0.971966\pi$
$84$	−0.374768	−	0.216372i	−0.0408905	−	0.0236082i
$85$			1.26427i			0.137130i
$86$	−3.74228	+	2.16061i	−0.403540	+	0.232984i
$87$	1.95312	+	3.38290i	0.209396	+	0.362685i
$88$	1.32191	−	2.28962i	0.140916	−	0.244074i
$89$			5.51995i			0.585113i	0.956248	+	0.292557i	$0.0945060\pi$
$89$			5.51995i			0.585113i	−0.956248	+	0.292557i	$0.905494\pi$
$90$	0.00643712	+	0.0111494i	0.000678532	+	0.00117525i
$91$	−1.00099	+	5.51677i	−0.104932	+	0.578315i
$92$	−0.570963			−0.0595270
$93$	−5.29760	−	8.10139i	−0.549336	−	0.840075i
$94$	16.9208			1.74524
$95$	1.05104			0.107834
$96$	−1.36010	+	0.785257i	−0.138815	+	0.0801450i
$97$		−	5.77397i		−	0.586258i	−0.956073	−	0.293129i	$-0.905303\pi$
$97$		−	5.77397i		−	0.586258i	0.956073	−	0.293129i	$-0.0946965\pi$
$98$	5.83175	+	3.36696i	0.589096	+	0.340115i
$99$	−0.0190418	+	0.0109938i	−0.00191378	+	0.00110492i
$100$	0.388026	+	0.672081i	0.0388026	+	0.0672081i
$101$	3.83015			0.381114			0.190557	−	0.981676i	$-0.438971\pi$
$101$	3.83015			0.381114			0.190557	+	0.981676i	$0.438971\pi$
$102$	7.18259	+	4.14687i	0.711183	+	0.410602i
$103$	−4.06720	+	7.04459i	−0.400753	+	0.694124i	−0.993817	−	0.111031i	$-0.964585\pi$
$103$	−4.06720	+	7.04459i	−0.400753	+	0.694124i	0.593064	+	0.805155i	$0.297918\pi$
$104$	7.43781	+	6.30417i	0.729338	+	0.618175i
$105$	0.526510	+	0.911942i	0.0513821	+	0.0889964i
$106$	−12.3227	−	7.11449i	−1.19688	−	0.691021i
$107$	1.28973	+	2.23387i	0.124682	+	0.215956i	0.921609	−	0.388120i	$-0.126875\pi$
$107$	1.28973	+	2.23387i	0.124682	+	0.215956i	−0.796926	+	0.604077i	$0.793542\pi$
$108$	−0.828586			−0.0797308
$109$			11.2650i			1.07899i	0.841988	+	0.539497i	$0.181385\pi$
$109$			11.2650i			1.07899i	−0.841988	+	0.539497i	$0.818615\pi$
$110$	0.484694	−	0.279838i	0.0462138	−	0.0266815i
$111$	−9.17165	−	5.29526i	−0.870535	−	0.502604i
$112$	−5.78351	+	3.33911i	−0.546491	+	0.315517i
$113$	2.11620	−	3.66536i	0.199075	−	0.344808i	−0.749154	−	0.662396i	$-0.769540\pi$
$113$	2.11620	−	3.66536i	0.199075	−	0.344808i	0.948229	+	0.317588i	$0.102873\pi$
$114$	3.44744	−	5.97114i	0.322882	−	0.559249i
$115$	1.20321	+	0.694676i	0.112200	+	0.0647789i
$116$	−0.359649			−0.0333925
$117$	−0.0273554	−	0.0763337i	−0.00252900	−	0.00705706i
$118$	1.57330	+	2.72503i	0.144834	+	0.250859i
$119$	4.37132	+	2.52378i	0.400718	+	0.231355i
$120$	1.83115			0.167161
$121$	−5.02207	−	8.69848i	−0.456552	−	0.790771i
$122$			15.3004i			1.38523i
$123$		−	3.59511i		−	0.324160i
$124$	0.889843	−	0.0494565i	0.0799102	−	0.00444133i
$125$		−	3.83590i		−	0.343094i
$126$	0.0513999			0.00457907
$127$	0.626367	+	1.08490i	0.0555811	+	0.0962693i	0.892477	−	0.451092i	$-0.148966\pi$
$127$	0.626367	+	1.08490i	0.0555811	+	0.0962693i	−0.836896	+	0.547362i	$0.815632\pi$
$128$			12.4788i			1.10298i
$129$	2.55579	−	4.42675i	0.225024	−	0.389754i
$130$	0.696308	+	1.94301i	0.0610702	+	0.170413i
$131$	6.92016	+	11.9861i	0.604617	+	1.04723i	0.992112	+	0.125356i	$0.0400072\pi$
$131$	6.92016	+	11.9861i	0.604617	+	1.04723i	−0.387495	+	0.921872i	$0.626659\pi$
$132$		−	0.272070i		−	0.0236807i
$133$	2.09811	−	3.63403i	0.181929	−	0.315110i
$134$	−8.83143	+	15.2965i	−0.762920	+	1.32142i
$135$	1.74612	+	1.00812i	0.150282	+	0.0867652i
$136$	7.60153	−	4.38874i	0.651826	−	0.376332i
$137$	9.42496	+	5.44151i	0.805229	+	0.464899i	0.845296	−	0.534298i	$-0.179424\pi$
$137$	9.42496	+	5.44151i	0.805229	+	0.464899i	−0.0400673	+	0.999197i	$0.512757\pi$
$138$	7.89319	−	4.55713i	0.671913	−	0.387929i
$139$	−21.4981			−1.82344			−0.911722	−	0.410809i	$-0.865246\pi$
$139$	−21.4981			−1.82344			−0.911722	+	0.410809i	$0.865246\pi$
$140$	−0.0969519			−0.00819393
$141$	−17.3340	+	10.0078i	−1.45979	+	0.842809i
$142$	−4.91283	+	8.50928i	−0.412276	+	0.714083i
$143$	−3.31842	+	1.18921i	−0.277501	+	0.0994466i
$144$	0.0482909	−	0.0836423i	0.00402424	−	0.00697019i
$145$	0.757903	+	0.437576i	0.0629404	+	0.0363387i
$146$	8.11838	−	14.0614i	0.671882	−	1.16373i
$147$	−7.96558			−0.656990
$148$	0.844437	−	0.487536i	0.0694123	−	0.0400752i
$149$	1.73954	−	1.00432i	0.142508	−	0.0822773i	−0.427051	−	0.904228i	$-0.640447\pi$
$149$	1.73954	−	1.00432i	0.142508	−	0.0822773i	0.569559	+	0.821950i	$0.307114\pi$
$150$	−10.7284	−	6.19405i	−0.875971	−	0.505742i
$151$			2.19032i			0.178245i	0.996021	+	0.0891227i	$0.0284063\pi$
$151$			2.19032i			0.178245i	−0.996021	+	0.0891227i	$0.971594\pi$
$152$	−3.64852	−	6.31942i	−0.295934	−	0.512572i
$153$	−0.0729989			−0.00590161
$154$		−	2.23449i		−	0.180060i
$155$	−1.93538	−	0.978427i	−0.155453	−	0.0785892i
$156$	0.987239	+	0.179129i	0.0790424	+	0.0143418i
$157$	3.83161			0.305795			0.152898	−	0.988242i	$-0.451139\pi$
$157$	3.83161			0.305795			0.152898	+	0.988242i	$0.451139\pi$
$158$	6.83361	−	3.94538i	0.543652	−	0.313878i
$159$	16.8315			1.33482
$160$	−0.175928	+	0.304717i	−0.0139084	+	0.0240900i
$161$	4.80379	−	2.77347i	0.378591	−	0.218580i
$162$	11.5405	−	6.66293i	0.906710	−	0.523489i
$163$		−	8.36953i		−	0.655552i	−0.944755	−	0.327776i	$-0.893701\pi$
$163$		−	8.36953i		−	0.655552i	0.944755	−	0.327776i	$-0.106299\pi$
$164$	0.286657	+	0.165501i	0.0223841	+	0.0129235i
$165$	−0.331021	+	0.573346i	−0.0257700	+	0.0446349i
$166$	−10.9621	+	18.9869i	−0.850821	+	1.47367i
$167$	0.343241	−	0.198171i	0.0265608	−	0.0153349i	−0.486661	−	0.873591i	$-0.661785\pi$
$167$	0.343241	−	0.198171i	0.0265608	−	0.0153349i	0.513222	+	0.858256i	$0.328452\pi$
$168$	3.65540	−	6.33134i	0.282021	−	0.488474i
$169$	−2.13036	−	12.8243i	−0.163874	−	0.986481i
$170$	1.85813			0.142512
$171$			0.0606865i			0.00464081i
$172$	0.235312	+	0.407572i	0.0179424	+	0.0310771i
$173$	8.40943	−	14.5656i	0.639357	−	1.10740i	−0.346217	−	0.938155i	$-0.612534\pi$
$173$	8.40943	−	14.5656i	0.639357	−	1.10740i	0.985574	−	0.169245i	$-0.0541329\pi$
$174$	4.97191	−	2.87053i	0.376919	−	0.217615i
$175$	−6.52930	−	3.76969i	−0.493569	−	0.284962i
$176$	−3.63615	−	2.09933i	−0.274085	−	0.158243i
$177$	−3.22344	−	1.86106i	−0.242289	−	0.139886i
$178$	8.11276			0.608077
$179$	−8.60517	−	14.9046i	−0.643181	−	1.11402i	−0.984718	−	0.174154i	$-0.944281\pi$
$179$	−8.60517	−	14.9046i	−0.643181	−	1.11402i	0.341538	−	0.939868i	$-0.389052\pi$
$180$	0.00121429		0.000701068i	9.05075e−5		5.22545e-5i
$181$	−6.42149	+	11.1223i	−0.477305	+	0.826717i	−0.999662	−	0.0260101i	$-0.991720\pi$
$181$	−6.42149	+	11.1223i	−0.477305	+	0.826717i	0.522356	+	0.852727i	$0.325053\pi$
$182$	8.10810	+	1.47116i	0.601012	+	0.109050i
$183$	−9.04945	−	15.6741i	−0.668954	−	1.15866i
$184$		−	9.64587i		−	0.711103i
$185$	−2.37269			−0.174444
$186$	−11.9068	+	7.78597i	−0.873046	+	0.570895i
$187$			3.17345i			0.232066i
$188$		−	1.84284i		−	0.134403i
$189$	6.97130	−	4.02488i	0.507087	−	0.292767i
$190$		−	1.54472i		−	0.112066i
$191$	−3.27980	+	5.68079i	−0.237318	+	0.411047i	−0.959944	−	0.280192i	$-0.909602\pi$
$191$	−3.27980	+	5.68079i	−0.237318	+	0.411047i	0.722626	+	0.691240i	$0.242935\pi$
$192$	−6.31204	−	10.9328i	−0.455532	−	0.789005i
$193$	16.0012	−	9.23830i	1.15179	−	0.664987i	0.202468	−	0.979289i	$-0.435104\pi$
$193$	16.0012	−	9.23830i	1.15179	−	0.664987i	0.949323	+	0.314302i	$0.101770\pi$
$194$	−8.48610			−0.609266
$195$	−1.86251	−	1.57863i	−0.133377	−	0.113048i
$196$	0.366697	−	0.635137i	0.0261926	−	0.0453669i
$197$	16.0772	+	9.28215i	1.14545	+	0.661326i	0.947774	−	0.318942i	$-0.103327\pi$
$197$	16.0772	+	9.28215i	1.14545	+	0.661326i	0.197676	+	0.980267i	$0.436661\pi$
$198$	0.0161578	+	0.0279861i	0.00114828	+	0.00198889i
$199$	13.1137	−	22.7136i	0.929607	−	1.61013i	0.145629	−	0.989339i	$-0.453479\pi$
$199$	13.1137	−	22.7136i	0.929607	−	1.61013i	0.783979	−	0.620788i	$-0.213187\pi$
$200$	−11.3542	+	6.55532i	−0.802860	+	0.463531i
$201$		−	20.8934i		−	1.47371i
$202$		−	5.62924i		−	0.396072i
$203$	3.02590	−	1.74700i	0.212376	−	0.122616i
$204$	0.451637	−	0.782258i	0.0316209	−	0.0547690i
$205$	−0.402723	−	0.697536i	−0.0281274	−	0.0487180i
$206$	10.3536	+	5.97763i	0.721366	+	0.416481i
$207$	−0.0401104	+	0.0694733i	−0.00278787	+	0.00482873i
$208$	10.0117	−	11.8120i	0.694184	−	0.819015i
$209$	2.63820			0.182488
$210$	1.34030	−	0.773820i	0.0924892	−	0.0533987i
$211$	−4.80264	−	8.31842i	−0.330628	−	0.572664i	0.652008	−	0.758212i	$-0.273927\pi$
$211$	−4.80264	−	8.31842i	−0.330628	−	0.572664i	−0.982635	+	0.185549i	$0.940594\pi$
$212$	−0.774841	+	1.34206i	−0.0532163	+	0.0921733i
$213$		−	11.6228i		−	0.796381i
$214$	3.28316	−	1.89553i	0.224432	−	0.129576i
$215$		−	1.14519i		−	0.0781015i
$216$		−	13.9982i		−	0.952455i
$217$	−7.24644	+	4.73854i	−0.491920	+	0.321673i
$218$	16.5564			1.12134
$219$			19.2065i			1.29785i
$220$	−0.0304772	−	0.0527881i	−0.00205477	−	0.00355897i
$221$	−11.5152	−	2.08937i	−0.774598	−	0.140546i
$222$	−7.78253	+	13.4797i	−0.522329	+	0.904700i
$223$	−4.28203	+	2.47223i	−0.286746	+	0.165553i	−0.636473	−	0.771299i	$-0.719608\pi$
$223$	−4.28203	+	2.47223i	−0.286746	+	0.165553i	0.349727	+	0.936851i	$0.386274\pi$
$224$	0.702387	+	1.21657i	0.0469302	+	0.0812855i
$225$	0.109036			0.00726907
$226$	−5.38705	−	3.11021i	−0.358341	−	0.206888i
$227$	−8.88540	−	5.12999i	−0.589745	−	0.340489i	0.175252	−	0.984524i	$-0.443926\pi$
$227$	−8.88540	−	5.12999i	−0.589745	−	0.340489i	−0.764997	+	0.644034i	$0.777259\pi$
$228$	−0.650318	−	0.375461i	−0.0430684	−	0.0248655i
$229$	6.79828	−	3.92499i	0.449243	−	0.259371i	−0.258267	−	0.966073i	$-0.583152\pi$
$229$	6.79828	−	3.92499i	0.449243	−	0.259371i	0.707511	+	0.706703i	$0.249818\pi$
$230$	1.02098	−	1.76838i	0.0673212	−	0.116604i
$231$	1.32159	+	2.28906i	0.0869542	+	0.150609i
$232$		−	6.07592i		−	0.398904i
$233$	−8.17268			−0.535410			−0.267705	−	0.963501i	$-0.586265\pi$
$233$	−8.17268			−0.535410			−0.267705	+	0.963501i	$0.586265\pi$
$234$	−0.112189	+	0.0402046i	−0.00733402	+	0.00262826i
$235$	−2.24214	+	3.88350i	−0.146261	+	0.253332i
$236$	0.296783	−	0.171348i	0.0193190	−	0.0111538i
$237$	−4.66700	+	8.08349i	−0.303154	+	0.525079i
$238$	3.70925	−	6.42460i	0.240435	−	0.416445i
$239$	21.1448	+	12.2080i	1.36775	+	0.789669i	0.990640	−	0.136501i	$-0.0435858\pi$
$239$	21.1448	+	12.2080i	1.36775	+	0.789669i	0.377106	+	0.926170i	$0.376919\pi$
$240$		−	2.90806i		−	0.187714i
$241$	17.4267	−	10.0613i	1.12255	−	0.648105i	0.180500	−	0.983575i	$-0.442229\pi$
$241$	17.4267	−	10.0613i	1.12255	−	0.648105i	0.942051	+	0.335470i	$0.108895\pi$
$242$	−12.7843	+	7.38102i	−0.821806	+	0.474470i
$243$	−0.116857	+	0.202402i	−0.00749637	+	0.0129841i
$244$	1.66637			0.106678
$245$	−1.54551	+	0.892301i	−0.0987391	+	0.0570070i
$246$	−5.28379			−0.336882
$247$	−1.73696	+	9.57301i	−0.110520	+	0.609116i
$248$	0.835520	+	15.0330i	0.0530556	+	0.954599i
$249$		−	25.9341i		−	1.64351i
$250$	−5.63769			−0.356559
$251$	7.76312	+	13.4461i	0.490004	+	0.848711i	0.999934	−	0.0115047i	$-0.00366213\pi$
$251$	7.76312	+	13.4461i	0.490004	+	0.848711i	−0.509930	+	0.860216i	$0.670329\pi$
$252$		−	0.00559797i		−	0.000352639i
$253$	3.02018	+	1.74370i	0.189877	+	0.109626i
$254$	1.59450	−	0.920582i	0.100048	−	0.0577625i
$255$	−1.90351	+	1.09899i	−0.119202	+	0.0688214i
$256$	3.81766			0.238604
$257$	3.86016	−	6.68600i	0.240790	−	0.417061i	−0.720149	−	0.693819i	$-0.755927\pi$
$257$	3.86016	−	6.68600i	0.240790	−	0.417061i	0.960940	+	0.276758i	$0.0892600\pi$
$258$	−6.50607	−	3.75628i	−0.405050	−	0.233856i
$259$	−4.73644	+	8.20375i	−0.294308	+	0.509756i
$260$	0.211614	−	0.0758350i	0.0131237	−	0.00470309i
$261$	−0.0252655	+	0.0437611i	−0.00156389	+	0.00270875i
$262$	17.6161	−	10.1707i	1.08833	−	0.628346i
$263$	−1.28168			−0.0790318			−0.0395159	−	0.999219i	$-0.512582\pi$
$263$	−1.28168			−0.0790318			−0.0395159	+	0.999219i	$0.512582\pi$
$264$	4.59637			0.282887
$265$	3.26571	−	1.88546i	0.200611	−	0.115823i
$266$	−5.34100	−	3.08363i	−0.327478	−	0.189069i
$267$	−8.31090	+	4.79830i	−0.508619	+	0.293651i
$268$	1.66594	+	0.961833i	0.101764	+	0.0587533i
$269$	−0.0307505	+	0.0532615i	−0.00187489	+	0.00324741i	−0.866961	−	0.498375i	$-0.833930\pi$
$269$	−0.0307505	+	0.0532615i	−0.00187489	+	0.00324741i	0.865086	+	0.501623i	$0.167263\pi$
$270$	1.48165	−	2.56630i	0.0901704	−	0.156180i
$271$			32.0614i			1.94759i	0.227423	+	0.973796i	$0.426970\pi$
$271$			32.0614i			1.94759i	−0.227423	+	0.973796i	$0.573030\pi$
$272$	−6.96977	−	12.0720i	−0.422605	−	0.731973i
$273$	−9.17624	+	3.28845i	−0.555372	+	0.199026i
$274$	7.99747	−	13.8520i	0.483145	−	0.836832i
$275$		−	4.74008i		−	0.285837i
$276$	−0.496318	−	0.859649i	−0.0298749	−	0.0517448i
$277$	4.73652			0.284590			0.142295	−	0.989824i	$-0.454552\pi$
$277$	4.73652			0.284590			0.142295	+	0.989824i	$0.454552\pi$
$278$			31.5961i			1.89501i
$279$	0.0564941	−	0.111748i	0.00338221	−	0.00669018i
$280$		−	1.63791i		−	0.0978837i
$281$			15.4404i			0.921099i	0.887634	+	0.460550i	$0.152348\pi$
$281$			15.4404i			0.921099i	−0.887634	+	0.460550i	$0.847652\pi$
$282$	14.7086	+	25.4761i	0.875886	+	1.51708i
$283$	10.8876			0.647201			0.323600	−	0.946194i	$-0.395107\pi$
$283$	10.8876			0.647201			0.323600	+	0.946194i	$0.395107\pi$
$284$	0.926747	+	0.535058i	0.0549923	+	0.0317498i
$285$	0.913629	+	1.58245i	0.0541187	+	0.0937363i
$286$	1.74780	+	4.87714i	0.103350	+	0.288392i
$287$	−3.21571			−0.189817
$288$	−0.0175943	−	0.0101581i	−0.00103675	−	0.000598569i
$289$	3.23208	−	5.59812i	0.190122	−	0.329301i
$290$	0.643112	−	1.11390i	0.0377648	−	0.0654106i
$291$	8.69336	−	5.01911i	0.509614	−	0.294226i
$292$	−1.53143	−	0.884174i	−0.0896204	−	0.0517424i
$293$	−3.05940	+	1.76635i	−0.178732	+	0.103191i	−0.586697	−	0.809807i	$-0.699572\pi$
$293$	−3.05940	+	1.76635i	−0.178732	+	0.103191i	0.407965	+	0.912998i	$0.366239\pi$
$294$			11.7071i			0.682774i
$295$	−0.833899			−0.0485515
$296$	8.23645	+	14.2660i	0.478734	+	0.829192i
$297$	4.38292	+	2.53048i	0.254323	+	0.146833i
$298$	−1.47607	−	2.55663i	−0.0855064	−	0.148101i
$299$	−8.31569	+	9.81105i	−0.480909	+	0.567388i
$300$	−0.674595	+	1.16843i	−0.0389478	+	0.0674595i
$301$	−3.95959	−	2.28607i	−0.228227	−	0.131767i
$302$	3.21914			0.185241
$303$	3.32942	+	5.76672i	0.191270	+	0.331290i
$304$	−10.0359	+	5.79422i	−0.575597	+	0.332321i
$305$	−3.51161	−	2.02743i	−0.201074	−	0.116090i
$306$			0.107288i			0.00613323i
$307$	6.66400	−	3.84746i	0.380335	−	0.219586i	−0.297629	−	0.954682i	$-0.596196\pi$
$307$	6.66400	−	3.84746i	0.380335	−	0.219586i	0.677964	+	0.735095i	$0.262863\pi$
$308$	−0.243358			−0.0138666
$309$	−14.1419			−0.804504
$310$	−1.43801	+	2.84445i	−0.0816735	+	0.161554i
$311$	26.1336			1.48190			0.740951	−	0.671559i	$-0.234375\pi$
$311$	26.1336			1.48190			0.740951	+	0.671559i	$0.234375\pi$
$312$	−3.02620	+	16.6785i	−0.171325	+	0.944232i
$313$	2.96918	+	5.14276i	0.167828	+	0.290686i	0.937656	−	0.347565i	$-0.112991\pi$
$313$	2.96918	+	5.14276i	0.167828	+	0.290686i	−0.769828	+	0.638251i	$0.779658\pi$
$314$		−	5.63137i		−	0.317797i
$315$	−0.00681091	+	0.0117968i	−0.000383751	+	0.000664677i
$316$	−0.429693	−	0.744249i	−0.0241721	−	0.0418673i
$317$	12.9082	−	7.45253i	0.724994	−	0.418576i	−0.0915938	−	0.995796i	$-0.529196\pi$
$317$	12.9082	−	7.45253i	0.724994	−	0.418576i	0.816588	+	0.577221i	$0.195863\pi$
$318$		−	24.7375i		−	1.38721i
$319$	1.90241	+	1.09836i	0.106514	+	0.0614961i
$320$	−2.44937	−	1.41414i	−0.136924	−	0.0790531i
$321$	−2.24223	+	3.88365i	−0.125149	+	0.216764i
$322$	−4.07621	−	7.06021i	−0.227158	−	0.393450i
$323$	7.58536	+	4.37941i	0.422061	+	0.243677i
$324$	−0.725661	−	1.25688i	−0.0403145	−	0.0698268i
$325$	17.1999	+	3.12082i	0.954080	+	0.173112i
$326$	−12.3008			−0.681280
$327$	−16.9608	+	9.79230i	−0.937932	+	0.541515i
$328$	−2.79599	+	4.84279i	−0.154382	+	0.267398i
$329$	8.95166	+	15.5047i	0.493521	+	0.854803i
$330$	0.842655	+	0.486507i	0.0463867	+	0.0267813i
$331$	−21.2208	−	12.2518i	−1.16640	−	0.673421i	−0.213570	−	0.976928i	$-0.568509\pi$
$331$	−21.2208	−	12.2518i	−1.16640	−	0.673421i	−0.952829	+	0.303507i	$0.901843\pi$
$332$	2.06786	+	1.19388i	0.113489	+	0.0655227i
$333$		−	0.136999i		−	0.00750747i
$334$	−0.291255	−	0.504468i	−0.0159367	−	0.0276032i
$335$	−2.34048	−	4.05382i	−0.127874	−	0.221484i
$336$	−10.0548	−	5.80515i	−0.548535	−	0.316697i
$337$	22.4952			1.22539			0.612696	−	0.790319i	$-0.290085\pi$
$337$	22.4952			1.22539			0.612696	+	0.790319i	$0.290085\pi$
$338$	−18.8480	+	3.13103i	−1.02520	+	0.170305i
$339$	7.35815			0.399640
$340$		−	0.202369i		−	0.0109750i
$341$	−4.85798	−	2.45595i	−0.263074	−	0.132997i
$342$	0.0891920			0.00482295
$343$			18.0104i			0.972469i
$344$	−6.88554	+	3.97537i	−0.371244	+	0.214338i
$345$			2.41543i			0.130042i
$346$	−21.4073	−	12.3595i	−1.15086	−	0.664450i
$347$	−6.02546	−	10.4364i	−0.323464	−	0.560256i	0.657736	−	0.753248i	$-0.271514\pi$
$347$	−6.02546	−	10.4364i	−0.323464	−	0.560256i	−0.981200	+	0.192992i	$0.938181\pi$
$348$	−0.312630	−	0.541491i	−0.0167587	−	0.0290270i
$349$			7.04409i			0.377062i	0.982067	+	0.188531i	$0.0603725\pi$
$349$			7.04409i			0.377062i	−0.982067	+	0.188531i	$0.939627\pi$
$350$	−5.54038	+	9.59622i	−0.296146	+	0.512940i
$351$	−12.0678	+	14.2379i	−0.644132	+	0.759962i
$352$	−0.441597	+	0.764868i	−0.0235372	+	0.0407676i
$353$	21.3757	−	12.3412i	1.13771	−	0.656858i	0.191849	−	0.981425i	$-0.438552\pi$
$353$	21.3757	−	12.3412i	1.13771	−	0.656858i	0.945863	+	0.324567i	$0.105218\pi$
$354$	−2.73522	+	4.73755i	−0.145376	+	0.251798i
$355$	−1.30198	−	2.25510i	−0.0691020	−	0.119688i
$356$		−	0.883562i		−	0.0468287i
$357$			8.77535i			0.464441i
$358$	−21.9055	+	12.6472i	−1.15774	+	0.668423i
$359$	−3.18993	−	1.84171i	−0.168358	−	0.0972016i	0.413453	−	0.910525i	$-0.364322\pi$
$359$	−3.18993	−	1.84171i	−0.168358	−	0.0972016i	−0.581811	+	0.813324i	$0.697656\pi$
$360$	0.0118439	+	0.0205142i	0.000624227	+	0.00108119i
$361$	−5.85925	+	10.1485i	−0.308381	+	0.534132i
$362$	16.3467	+	9.43777i	0.859163	+	0.496038i
$363$	8.73103	−	15.1226i	0.458260	−	0.793730i
$364$	0.160225	−	0.883054i	0.00839806	−	0.0462846i
$365$	2.15150	+	3.72651i	0.112615	+	0.195055i
$366$	−23.0365	+	13.3001i	−1.20414	+	0.695208i
$367$	−3.96192	+	6.86224i	−0.206810	+	0.358206i	−0.950708	−	0.310088i	$-0.899642\pi$
$367$	−3.96192	+	6.86224i	−0.206810	+	0.358206i	0.743898	+	0.668294i	$0.232975\pi$
$368$	−15.3186			−0.798538
$369$	0.0402755	−	0.0232531i	0.00209666	−	0.00121051i
$370$			3.48718i			0.181290i
$371$		−	15.0552i		−	0.781629i
$372$	0.847972	+	1.29677i	0.0439653	+	0.0672342i
$373$	19.8356			1.02705			0.513525	−	0.858075i	$-0.328340\pi$
$373$	19.8356			1.02705			0.513525	+	0.858075i	$0.328340\pi$
$374$	4.66407			0.241173
$375$	5.77538	−	3.33442i	0.298239	−	0.172189i
$376$	31.1331			1.60556
$377$	−5.23804	+	6.17997i	−0.269773	+	0.318284i
$378$	−5.91543	−	10.2458i	−0.304257	−	0.526989i
$379$	18.5981	−	10.7376i	0.955323	−	0.551556i	0.0605924	−	0.998163i	$-0.480701\pi$
$379$	18.5981	−	10.7376i	0.955323	−	0.551556i	0.894730	+	0.446607i	$0.147368\pi$
$380$	−0.168236			−0.00863034
$381$	−1.08896	+	1.88613i	−0.0557891	+	0.0966295i
$382$	8.34915	+	4.82038i	0.427180	+	0.246632i
$383$	−12.9955	−	7.50293i	−0.664037	−	0.383382i	0.129777	−	0.991543i	$-0.458574\pi$
$383$	−12.9955	−	7.50293i	−0.664037	−	0.383382i	−0.793813	+	0.608162i	$0.791907\pi$
$384$	−18.7883	+	10.8474i	−0.958786	+	0.553555i
$385$	0.512839	+	0.296088i	0.0261367	+	0.0150900i
$386$	−13.5777	−	23.5172i	−0.691086	−	1.19700i
$387$	0.0661231			0.00336123
$388$			0.924223i			0.0469203i
$389$	−10.9004	−	18.8801i	−0.552672	−	0.957257i	−0.998081	−	0.0619291i	$-0.980275\pi$
$389$	−10.9004	−	18.8801i	−0.552672	−	0.957257i	0.445408	−	0.895328i	$-0.353059\pi$
$390$	−2.32015	+	2.73736i	−0.117485	+	0.138612i
$391$	5.78909	+	10.0270i	0.292767	+	0.507087i
$392$	10.7300	+	6.19499i	0.541949	+	0.312894i
$393$	−12.0309	+	20.8381i	−0.606879	+	1.05115i
$394$	13.6421	−	23.6289i	0.687281	−	1.19041i
$395$			2.09118i			0.105219i
$396$	0.00304797	−	0.00175975i	0.000153166	−	8.84306e-5i
$397$	14.9594	−	8.63680i	0.750789	−	0.433468i	−0.0751898	−	0.997169i	$-0.523956\pi$
$397$	14.9594	−	8.63680i	0.750789	−	0.433468i	0.825979	+	0.563701i	$0.190623\pi$
$398$	−33.3826	−	19.2735i	−1.67332	−	0.966091i
$399$	7.29525			0.365220
$400$	10.4105	+	18.0316i	0.520526	+	0.901578i
$401$		−	4.41871i		−	0.220660i	−0.993895	−	0.110330i	$-0.964809\pi$
$401$		−	4.41871i		−	0.220660i	0.993895	−	0.110330i	$-0.0351908\pi$
$402$	−30.7074			−1.53155
$403$	12.1101	−	16.0108i	0.603249	−	0.797553i
$404$	−0.613081			−0.0305019
$405$			3.53158i			0.175485i
$406$	−2.56760	−	4.44721i	−0.127428	−	0.220712i
$407$	−5.95568			−0.295212
$408$	13.2155	+	7.62997i	0.654264	+	0.377740i
$409$	5.80123	−	3.34934i	0.286853	−	0.165614i	−0.349669	−	0.936873i	$-0.613706\pi$
$409$	5.80123	−	3.34934i	0.286853	−	0.165614i	0.636522	+	0.771259i	$0.280373\pi$
$410$	−1.02518	+	0.591888i	−0.0506300	+	0.0292313i
$411$			18.9205i			0.933277i
$412$	0.651025	−	1.12761i	0.0320737	−	0.0555532i
$413$	−1.66466	+	2.88327i	−0.0819123	+	0.141876i
$414$	0.102106	+	0.0589509i	0.00501824	+	0.00289728i
$415$	−2.90513	−	5.03183i	−0.142607	−	0.247003i
$416$	−2.48467	−	2.10597i	−0.121821	−	0.103254i
$417$	−18.6875	−	32.3678i	−0.915133	−	1.58506i
$418$		−	3.87740i		−	0.189650i
$419$	−34.5125			−1.68604			−0.843022	−	0.537879i	$-0.819226\pi$
$419$	−34.5125			−1.68604			−0.843022	+	0.537879i	$0.819226\pi$
$420$	−0.0842769	−	0.145972i	−0.00411229	−	0.00712270i
$421$	−20.6778	−	11.9383i	−1.00777	−	0.581838i	−0.0972342	−	0.995262i	$-0.531000\pi$
$421$	−20.6778	−	11.9383i	−1.00777	−	0.581838i	−0.910539	+	0.413423i	$0.864333\pi$
$422$	−12.2257	+	7.05852i	−0.595139	+	0.343604i
$423$	−0.224232	−	0.129461i	−0.0109025	−	0.00629459i
$424$	−22.6729	−	13.0902i	−1.10109	−	0.635716i
$425$	7.86852	−	13.6287i	0.381680	−	0.661088i
$426$	−17.0822			−0.827636
$427$	−14.0200	+	8.09444i	−0.678475	+	0.391717i
$428$	−0.206443	−	0.357569i	−0.00997878	−	0.0172838i
$429$	−4.67508	−	3.96252i	−0.225715	−	0.191312i
$430$	−1.68311			−0.0811667
$431$	−16.3390	+	9.43330i	−0.787020	+	0.454386i	−0.838912	−	0.544266i	$-0.816808\pi$
$431$	−16.3390	+	9.43330i	−0.787020	+	0.454386i	0.0518924	+	0.998653i	$0.483475\pi$
$432$	−22.2305			−1.06957
$433$	−3.11799			−0.149841			−0.0749206	−	0.997190i	$-0.523870\pi$
$433$	−3.11799			−0.149841			−0.0749206	+	0.997190i	$0.523870\pi$
$434$	6.96431	+	10.6502i	0.334297	+	0.511227i
$435$			1.52148i			0.0729493i
$436$		−	1.80316i		−	0.0863557i
$437$	8.33580	−	4.81267i	0.398755	−	0.230221i
$438$	28.2281			1.34879
$439$	1.35695	−	2.35031i	0.0647638	−	0.112174i	−0.831825	−	0.555037i	$-0.812704\pi$
$439$	1.35695	−	2.35031i	0.0647638	−	0.112174i	0.896589	+	0.442863i	$0.146037\pi$
$440$	0.891804	−	0.514884i	0.0425151	−	0.0245461i
$441$	−0.0515212	−	0.0892374i	−0.00245339	−	0.00424940i
$442$	−3.07078	+	16.9241i	−0.146062	+	0.804999i
$443$	12.4314	−	21.5317i	0.590631	−	1.02300i	−0.403516	−	0.914973i	$-0.632212\pi$
$443$	12.4314	−	21.5317i	0.590631	−	1.02300i	0.994148	−	0.108031i	$-0.0344546\pi$
$444$	1.46808	+	0.847597i	0.0696720	+	0.0402252i
$445$	−1.07501	+	1.86197i	−0.0509602	+	0.0882657i
$446$	3.63348	+	6.29337i	0.172050	+	0.298000i
$447$	3.02424	+	1.74605i	0.143042	+	0.0825851i
$448$	−9.77902	+	5.64592i	−0.462015	+	0.266745i
$449$		−	21.9080i		−	1.03390i	−0.856014	−	0.516952i	$-0.827067\pi$
$449$		−	21.9080i		−	1.03390i	0.856014	−	0.516952i	$-0.172933\pi$
$450$		−	0.160252i		−	0.00755435i
$451$	−1.01087	−	1.75088i	−0.0476001	−	0.0824458i
$452$	−0.338734	+	0.586704i	−0.0159327	+	0.0275962i
$453$	−3.29777	+	1.90397i	−0.154943	+	0.0894561i
$454$	−7.53963	+	13.0590i	−0.353853	+	0.612891i
$455$	−1.41204	+	1.66596i	−0.0661974	+	0.0781012i
$456$	6.34306	−	10.9865i	0.297041	−	0.514490i
$457$			23.8155i			1.11404i	0.830499	+	0.557020i	$0.188055\pi$
$457$			23.8155i			1.11404i	−0.830499	+	0.557020i	$0.811945\pi$
$458$	−5.76862	−	9.99155i	−0.269550	−	0.466874i
$459$	8.40118	+	14.5513i	0.392134	+	0.679195i
$460$	−0.192595	−	0.111195i	−0.00897979	−	0.00518449i
$461$		−	33.1166i		−	1.54240i	−0.636596	−	0.771198i	$-0.719658\pi$
$461$		−	33.1166i		−	1.54240i	0.636596	−	0.771198i	$-0.280342\pi$
$462$	3.36427	−	1.94236i	0.156520	−	0.0903668i
$463$			12.5034i			0.581084i	0.956862	+	0.290542i	$0.0938356\pi$
$463$			12.5034i			0.581084i	−0.956862	+	0.290542i	$0.906164\pi$
$464$	−9.64918			−0.447952
$465$	−0.209223	−	3.76444i	−0.00970251	−	0.174572i
$466$			12.0115i			0.556423i
$467$	39.4658			1.82626			0.913130	−	0.407669i	$-0.133658\pi$
$467$	39.4658			1.82626			0.913130	+	0.407669i	$0.133658\pi$
$468$	0.00437869	+	0.0122185i	0.000202405	+	0.000564801i
$469$	−18.6885			−0.862956
$470$	5.70765	+	3.29531i	0.263274	+	0.152001i
$471$	3.33068	+	5.76891i	0.153470	+	0.265817i
$472$	2.89476	+	5.01387i	0.133242	+	0.230782i
$473$		−	2.87454i		−	0.132172i
$474$	11.8804	+	6.85917i	0.545686	+	0.315052i
$475$	−11.3300	−	6.54138i	−0.519856	−	0.300139i
$476$	−0.699705	−	0.403975i	−0.0320709	−	0.0185161i
$477$	0.108866	+	0.188561i	0.00498462	+	0.00863362i
$478$	17.9423	−	31.0769i	0.820660	−	1.42143i
$479$	−8.90360	+	5.14050i	−0.406816	+	0.234875i	−0.689421	−	0.724361i	$-0.742135\pi$
$479$	−8.90360	+	5.14050i	−0.406816	+	0.234875i	0.282605	+	0.959236i	$0.408802\pi$
$480$	−0.611714			−0.0279208
$481$	3.92116	−	21.6109i	0.178790	−	0.985372i
$482$	−14.7872	−	25.6123i	−0.673541	−	1.16661i
$483$	8.35153	+	4.82176i	0.380008	+	0.219398i
$484$	0.803868	+	1.39234i	0.0365395	+	0.0632882i
$485$	1.12448	−	1.94765i	0.0510599	−	0.0884384i
$486$	0.297474	+	0.171746i	0.0134937	+	0.00779058i
$487$	7.81903	+	4.51432i	0.354314	+	0.204563i	0.666584	−	0.745430i	$-0.267756\pi$
$487$	7.81903	+	4.51432i	0.354314	+	0.204563i	−0.312270	+	0.949993i	$0.601089\pi$
$488$			28.1517i			1.27437i
$489$	12.6013	−	7.27534i	0.569849	−	0.329002i
$490$	1.31143	+	2.27146i	0.0592444	+	0.102614i
$491$	−18.8136	+	32.5860i	−0.849044	+	1.47059i	0.0330181	+	0.999455i	$0.489488\pi$
$491$	−18.8136	+	32.5860i	−0.849044	+	1.47059i	−0.882062	+	0.471133i	$0.843845\pi$
$492$			0.575458i			0.0259437i
$493$	3.64654	+	6.31600i	0.164232	+	0.284458i
$494$	14.0696	+	2.55285i	0.633022	+	0.114858i
$495$	−0.00856416			−0.000384930
$496$	23.8740	−	1.32689i	1.07197	−	0.0595792i
$497$	−10.3962			−0.466334
$498$	−38.1158			−1.70801
$499$	−12.8977	+	7.44649i	−0.577380	+	0.333351i	−0.760092	−	0.649816i	$-0.774846\pi$
$499$	−12.8977	+	7.44649i	−0.577380	+	0.333351i	0.182711	+	0.983167i	$0.441513\pi$
$500$			0.614002i			0.0274590i
$501$	0.596736	+	0.344526i	0.0266602	+	0.0153923i
$502$	19.7620	−	11.4096i	0.882020	−	0.509235i
$503$	0.123939	+	0.214668i	0.00552615	+	0.00957157i	0.868775	−	0.495207i	$-0.164908\pi$
$503$	0.123939	+	0.214668i	0.00552615	+	0.00957157i	−0.863249	+	0.504778i	$0.831574\pi$
$504$	0.0945724			0.00421259
$505$	1.29197	+	0.745921i	0.0574920	+	0.0331930i
$506$	2.56275	−	4.43881i	0.113928	−	0.197329i
$507$	17.4565	−	14.3552i	0.775271	−	0.637536i
$508$	−0.100261	−	0.173657i	−0.00444835	−	0.00770478i
$509$	21.0290	+	12.1411i	0.932096	+	0.538146i	0.887474	−	0.460858i	$-0.152458\pi$
$509$	21.0290	+	12.1411i	0.932096	+	0.538146i	0.0446221	+	0.999004i	$0.485792\pi$
$510$	1.61520	+	2.79762i	0.0715224	+	0.123880i
$511$	17.1796			0.759980
$512$			19.3468i			0.855016i
$513$	12.0970	−	6.98420i	0.534095	−	0.308360i
$514$	−9.82653	−	5.67335i	−0.433430	−	0.250241i
$515$	−2.74386	+	1.58417i	−0.120909	+	0.0698069i
$516$	−0.409097	+	0.708577i	−0.0180095	+	0.0311934i
$517$	−5.62798	+	9.74795i	−0.247518	+	0.428714i
$518$	12.0572	+	6.96122i	0.529763	+	0.305859i
$519$	29.2401			1.28350
$520$	1.28116	+	3.57501i	0.0561826	+	0.156775i
$521$	6.73109	+	11.6586i	0.294894	+	0.510772i	0.974960	−	0.222379i	$-0.0713822\pi$
$521$	6.73109	+	11.6586i	0.294894	+	0.510772i	−0.680066	+	0.733151i	$0.738049\pi$
$522$	0.0643164	+	0.0371331i	0.00281505	+	0.00162527i
$523$	14.3740			0.628531			0.314265	−	0.949335i	$-0.398242\pi$
$523$	14.3740			0.628531			0.314265	+	0.949335i	$0.398242\pi$
$524$	−1.10769	−	1.91858i	−0.0483897	−	0.0838134i
$525$		−	13.1075i		−	0.572056i
$526$			1.88371i			0.0821335i
$527$	−9.89080	−	15.1256i	−0.430850	−	0.658881i
$528$		−	7.29950i		−	0.317670i
$529$	−10.2764			−0.446798
$530$	−2.77109	−	4.79967i	−0.120368	−	0.208484i
$531$		−	0.0481491i		−	0.00208949i
$532$	−0.335838	+	0.581689i	−0.0145604	+	0.0252194i
$533$	7.01883	−	2.51530i	0.304019	−	0.108950i
$534$	7.05214	+	12.2147i	0.305176	+	0.528580i
$535$			1.00469i			0.0434367i
$536$	−16.2492	+	28.1445i	−0.701860	+	1.21566i
$537$	14.9604	−	25.9121i	0.645587	−	1.11819i
$538$	0.0782793	+	0.0451946i	0.00337486	+	0.00194848i
$539$	−3.87938	+	2.23976i	−0.167097	+	0.0964733i
$540$	−0.279496	−	0.161367i	−0.0120276	−	0.00694413i
$541$	−30.0665	+	17.3589i	−1.29266	+	0.746319i	−0.979125	−	0.203257i	$-0.934847\pi$
$541$	−30.0665	+	17.3589i	−1.29266	+	0.746319i	−0.313537	+	0.949576i	$0.601514\pi$
$542$	47.1212			2.02403
$543$	−22.3279			−0.958182
$544$	−2.53936	+	1.46610i	−0.108874	+	0.0628586i
$545$	−2.19386	+	3.79988i	−0.0939746	+	0.162769i
$546$	4.83308	+	13.4865i	0.206837	+	0.577168i
$547$	−5.13705	+	8.89763i	−0.219644	+	0.380435i	−0.954699	−	0.297572i	$-0.903823\pi$
$547$	−5.13705	+	8.89763i	−0.219644	+	0.380435i	0.735055	+	0.678008i	$0.237156\pi$
$548$	−1.50863	−	0.871006i	−0.0644453	−	0.0372075i
$549$	0.117063	−	0.202760i	0.00499614	−	0.00865357i
$550$	−6.96657			−0.297056
$551$	5.25071	−	3.03150i	0.223688	−	0.129146i
$552$	14.5229	−	8.38482i	0.618137	−	0.356882i
$553$	7.23042	+	4.17449i	0.307469	+	0.177517i
$554$		−	6.96134i		−	0.295759i
$555$	−2.06250	−	3.57235i	−0.0875482	−	0.151638i
$556$	3.44114			0.145937
$557$		−	0.457655i		−	0.0193915i	−0.999953	−	0.00969573i	$-0.996914\pi$
$557$		−	0.457655i		−	0.0193915i	0.999953	−	0.00969573i	$-0.00308630\pi$
$558$	−0.164238	−	0.0830304i	−0.00695275	−	0.00351496i
$559$	10.4306	+	1.89257i	0.441168	+	0.0800472i
$560$	−2.60116			−0.109919
$561$	−4.77798	+	2.75857i	−0.201727	+	0.116467i
$562$	22.6931			0.957249
$563$	−21.4948	+	37.2301i	−0.905899	+	1.56906i	−0.0861922	+	0.996279i	$0.527470\pi$
$563$	−21.4948	+	37.2301i	−0.905899	+	1.56906i	−0.819706	+	0.572784i	$0.805863\pi$
$564$	2.77461	−	1.60192i	0.116832	−	0.0674530i
$565$	1.42766	−	0.824258i	0.0600620	−	0.0346768i
$566$		−	16.0017i		−	0.672601i
$567$	12.2107	+	7.04984i	0.512800	+	0.296065i
$568$	−9.03928	+	15.6565i	−0.379280	+	0.656932i
$569$	−8.46773	+	14.6665i	−0.354986	+	0.614853i	−0.987116	−	0.160009i	$-0.948848\pi$
$569$	−8.46773	+	14.6665i	−0.354986	+	0.614853i	0.632130	+	0.774862i	$0.282181\pi$
$570$	2.32576	−	1.34278i	0.0974152	−	0.0562427i
$571$	5.27107	−	9.12977i	0.220588	−	0.382069i	−0.734399	−	0.678718i	$-0.762536\pi$
$571$	5.27107	−	9.12977i	0.220588	−	0.382069i	0.954987	+	0.296649i	$0.0958692\pi$
$572$	0.531171	−	0.190353i	0.0222094	−	0.00795906i
$573$	−11.4041			−0.476412
$574$			4.72618i			0.197267i
$575$	−8.64698	−	14.9770i	−0.360604	−	0.624584i
$576$	0.0816523	−	0.141426i	0.00340218	−	0.00589275i
$577$	38.6921	−	22.3389i	1.61077	−	0.929980i	0.621582	−	0.783349i	$-0.286490\pi$
$577$	38.6921	−	22.3389i	1.61077	−	0.929980i	0.989191	−	0.146631i	$-0.0468430\pi$
$578$	−8.22765	−	4.75024i	−0.342225	−	0.197584i
$579$	27.8186	+	16.0611i	1.15610	+	0.667475i
$580$	−0.121315	−	0.0700415i	−0.00503735	−	0.00290831i
$581$	−23.1972			−0.962383
$582$	−7.37667	−	12.7768i	−0.305773	−	0.529614i
$583$	8.19724	−	4.73268i	0.339495	−	0.196008i
$584$	14.9373	−	25.8721i	0.618109	−	1.07060i
$585$	0.00563856	−	0.0310761i	0.000233126	−	0.00128484i
$586$	2.59603	+	4.49645i	0.107241	+	0.185747i
$587$		−	35.8347i		−	1.47906i	−0.673125	−	0.739529i	$-0.735048\pi$
$587$		−	35.8347i		−	1.47906i	0.673125	−	0.739529i	$-0.264952\pi$
$588$	1.27503			0.0525812
$589$	−12.5744	+	8.22257i	−0.518120	+	0.338805i
$590$			1.22560i			0.0504570i
$591$			32.2746i			1.32760i
$592$	22.6558	−	13.0803i	0.931147	−	0.537598i
$593$		−	20.2472i		−	0.831451i	−0.909490	−	0.415726i	$-0.863528\pi$
$593$		−	20.2472i		−	0.831451i	0.909490	−	0.415726i	$-0.136472\pi$
$594$	3.71908	−	6.44164i	0.152596	−	0.264304i
$595$	0.983012	+	1.70263i	0.0402996	+	0.0698009i
$596$	−0.278443	+	0.160759i	−0.0114055	+	0.00658495i
$597$	45.5972			1.86617
$598$	14.4195	+	12.2217i	0.589656	+	0.499783i
$599$	−12.8811	+	22.3107i	−0.526306	+	0.911589i	0.473224	+	0.880942i	$0.343090\pi$
$599$	−12.8811	+	22.3107i	−0.526306	+	0.911589i	−0.999530	+	0.0306470i	$0.990243\pi$
$600$	−19.7396	−	11.3966i	−0.805864	−	0.465266i
$601$	−18.5408	−	32.1137i	−0.756297	−	1.30994i	−0.944727	−	0.327858i	$-0.893673\pi$
$601$	−18.5408	−	32.1137i	−0.756297	−	1.30994i	0.188430	−	0.982087i	$-0.439660\pi$
$602$	−3.35987	+	5.81947i	−0.136938	+	0.237184i
$603$	0.234067	−	0.135138i	0.00953193	−	0.00550326i
$604$		−	0.350598i		−	0.0142656i
$605$		−	3.91219i		−	0.159053i
$606$	8.47545	−	4.89330i	0.344292	−	0.198777i
$607$	−5.44988	+	9.43946i	−0.221204	+	0.383136i	−0.955174	−	0.296046i	$-0.904332\pi$
$607$	−5.44988	+	9.43946i	−0.221204	+	0.383136i	0.733970	+	0.679182i	$0.237665\pi$
$608$	1.21882	+	2.11106i	0.0494297	+	0.0856148i
$609$	5.26062	+	3.03722i	0.213171	+	0.123074i
$610$	−2.97975	+	5.16108i	−0.120647	+	0.208966i
$611$	−31.6662	−	26.8398i	−1.28108	−	1.08582i
$612$	0.0116847			0.000472327
$613$	3.96470	−	2.28902i	0.160133	−	0.0924527i	−0.417792	−	0.908543i	$-0.637196\pi$
$613$	3.96470	−	2.28902i	0.160133	−	0.0924527i	0.577925	+	0.816090i	$0.303863\pi$
$614$	−5.65468	−	9.79419i	−0.228204	−	0.395261i
$615$	0.700146	−	1.21269i	0.0282326	−	0.0489003i
$616$		−	4.11130i		−	0.165649i
$617$	20.0246	−	11.5612i	0.806161	−	0.465437i	−0.0394602	−	0.999221i	$-0.512564\pi$
$617$	20.0246	−	11.5612i	0.806161	−	0.465437i	0.845621	+	0.533784i	$0.179231\pi$
$618$			20.7846i			0.836079i
$619$			36.3061i			1.45927i	0.683838	+	0.729633i	$0.260309\pi$
$619$			36.3061i			1.45927i	−0.683838	+	0.729633i	$0.739691\pi$
$620$	0.309790	+	0.156614i	0.0124415	+	0.00628977i
$621$	18.4647			0.740962
$622$		−	38.4090i		−	1.54006i
$623$	4.29192	+	7.43383i	0.171952	+	0.297830i
$624$	26.4871	+	4.80592i	1.06033	+	0.192391i
$625$	−11.3737	+	19.6998i	−0.454947	+	0.787992i
$626$	7.55840	−	4.36385i	0.302095	−	0.174414i
$627$	2.29329	+	3.97210i	0.0915854	+	0.158631i
$628$	−0.613314			−0.0244739
$629$	−17.1238	−	9.88643i	−0.682770	−	0.394198i
$630$	0.0173380	+	0.0100101i	0.000690763	+	0.000398812i
$631$	24.1532	+	13.9448i	0.961523	+	0.555136i	0.896641	−	0.442757i	$-0.146000\pi$
$631$	24.1532	+	13.9448i	0.961523	+	0.555136i	0.0648817	+	0.997893i	$0.479333\pi$
$632$	12.5734	−	7.25924i	0.500142	−	0.288757i
$633$	8.34954	−	14.4618i	0.331864	−	0.574806i
$634$	−10.9531	−	18.9713i	−0.435003	−	0.753448i
$635$			0.487939i			0.0193633i
$636$	−2.69417			−0.106831
$637$	−5.57309	−	15.5514i	−0.220814	−	0.616170i
$638$	1.61427	−	2.79600i	0.0639097	−	0.110695i
$639$	0.130209	−	0.0751761i	0.00515098	−	0.00297392i
$640$	−2.43025	+	4.20931i	−0.0960640	+	0.166388i
$641$	2.68739	−	4.65470i	0.106146	−	0.183849i	−0.808060	−	0.589100i	$-0.799482\pi$
$641$	2.68739	−	4.65470i	0.106146	−	0.183849i	0.914206	+	0.405251i	$0.132816\pi$
$642$	5.70787	+	3.29544i	0.225272	+	0.130061i
$643$		−	0.209474i		−	0.00826084i	−0.999991	−	0.00413042i	$-0.998685\pi$
$643$		−	0.209474i		−	0.00826084i	0.999991	−	0.00413042i	$-0.00131476\pi$
$644$	−0.768928	+	0.443941i	−0.0303000	+	0.0174937i
$645$	1.72422	−	0.995477i	0.0678909	−	0.0391968i
$646$	6.43649	−	11.1483i	0.253240	−	0.438625i
$647$	−11.7716			−0.462790			−0.231395	−	0.972860i	$-0.574329\pi$
$647$	−11.7716			−0.462790			−0.231395	+	0.972860i	$0.574329\pi$
$648$	21.2338	−	12.2594i	0.834143	−	0.481593i
$649$	−2.09317			−0.0821640
$650$	4.58672	−	25.2790i	0.179906	−	0.991525i
$651$	−13.4335	−	6.79128i	−0.526499	−	0.266171i
$652$			1.33969i			0.0524661i
$653$	11.6901			0.457468			0.228734	−	0.973489i	$-0.426541\pi$
$653$	11.6901			0.457468			0.228734	+	0.973489i	$0.426541\pi$
$654$	14.3919	+	24.9275i	0.562768	+	0.974742i
$655$			5.39079i			0.210636i
$656$	7.69084	+	4.44031i	0.300277	+	0.173365i
$657$	−0.215168	+	0.124227i	−0.00839450	+	0.00484657i
$658$	22.7876	−	13.1564i	0.888351	−	0.512890i
$659$	12.0310			0.468660			0.234330	−	0.972157i	$-0.424710\pi$
$659$	12.0310			0.468660			0.234330	+	0.972157i	$0.424710\pi$
$660$	0.0529856	−	0.0917738i	0.00206246	−	0.00357229i
$661$	−22.2928	−	12.8708i	−0.867091	−	0.500615i	−0.000710311	−	1.00000i	$-0.500226\pi$
$661$	−22.2928	−	12.8708i	−0.867091	−	0.500615i	−0.866380	+	0.499385i	$0.833559\pi$
$662$	−18.0067	+	31.1885i	−0.699851	+	1.21218i
$663$	−6.86401	−	19.1537i	−0.266576	−	0.743867i
$664$	−20.1695	+	34.9345i	−0.782727	+	1.35572i
$665$	1.41545	−	0.817212i	0.0548889	−	0.0316901i
$666$	−0.201349			−0.00780212
$667$	8.01461			0.310327
$668$	−0.0549417	+	0.0317206i	−0.00212576	+	0.00122731i
$669$	−7.44444	−	4.29805i	−0.287819	−	0.166172i
$670$	−5.95797	+	3.43984i	−0.230177	+	0.132892i
$671$	−8.81448	−	5.08905i	−0.340279	−	0.196460i
$672$	−1.22112	+	2.11505i	−0.0471058	+	0.0815897i
$673$	−11.9764	+	20.7437i	−0.461655	+	0.799610i	−0.999044	−	0.0437251i	$-0.986077\pi$
$673$	−11.9764	+	20.7437i	−0.461655	+	0.799610i	0.537389	+	0.843335i	$0.319411\pi$
$674$		−	33.0616i		−	1.27348i
$675$	−12.5486	−	21.7348i	−0.482995	−	0.836571i
$676$	0.341001	+	2.05274i	0.0131154	+	0.0789516i
$677$	12.2525	−	21.2220i	0.470903	−	0.815627i	−0.528543	−	0.848906i	$-0.677262\pi$
$677$	12.2525	−	21.2220i	0.470903	−	0.815627i	0.999446	+	0.0332790i	$0.0105950\pi$
$678$		−	10.8144i		−	0.415325i
$679$	−4.48944	−	7.77593i	−0.172289	−	0.298413i
$680$	3.41883			0.131106
$681$		−	17.8373i		−	0.683527i
$682$	−3.60954	+	7.13985i	−0.138217	+	0.273399i
$683$		−	30.2422i		−	1.15718i	−0.815617	−	0.578592i	$-0.803602\pi$
$683$		−	30.2422i		−	1.15718i	0.815617	−	0.578592i	$-0.196398\pi$
$684$		−	0.00971391i		−	0.000371421i
$685$	2.11946	+	3.67102i	0.0809805	+	0.140262i
$686$	26.4702			1.01064
$687$	11.8190	+	6.82372i	0.450924	+	0.260341i
$688$	6.31329	+	10.9349i	0.240692	+	0.416891i
$689$	11.7761	+	32.8606i	0.448634	+	1.25189i
$690$	3.55000			0.135146
$691$	−37.8542	−	21.8551i	−1.44004	−	0.831408i	−0.442190	−	0.896922i	$-0.645798\pi$
$691$	−37.8542	−	21.8551i	−1.44004	−	0.831408i	−0.997852	+	0.0655134i	$0.979131\pi$
$692$	−1.34607	+	2.33147i	−0.0511700	+	0.0886291i
$693$	−0.0170960	+	0.0296112i	−0.000649425	+	0.00112484i
$694$	−15.3386	+	8.85572i	−0.582244	+	0.336159i
$695$	−7.25165	−	4.18674i	−0.275071	−	0.158812i
$696$	9.14798	−	5.28159i	0.346753	−	0.200198i
$697$		−	6.71219i		−	0.254242i
$698$	10.3528			0.391860
$699$	−7.10423	−	12.3049i	−0.268707	−	0.465414i
$700$	1.04513	+	0.603404i	0.0395021	+	0.0228065i
$701$	10.3763	+	17.9723i	0.391908	+	0.678804i	0.992701	−	0.120600i	$-0.0384819\pi$
$701$	10.3763	+	17.9723i	0.391908	+	0.678804i	−0.600793	+	0.799404i	$0.705149\pi$
$702$	20.9257	+	17.7363i	0.789788	+	0.669412i
$703$	−8.21893	+	14.2356i	−0.309983	+	0.536906i
$704$	−6.14815	−	3.54964i	−0.231717	−	0.133782i
$705$	−7.79606			−0.293617
$706$	−18.1381	−	31.4162i	−0.682637	−	1.18236i
$707$	5.15815	−	2.97806i	0.193992	−	0.112001i
$708$	0.515967	+	0.297894i	0.0193912	+	0.0111955i
$709$			43.4466i			1.63167i	0.578285	+	0.815835i	$0.303722\pi$
$709$			43.4466i			1.63167i	−0.578285	+	0.815835i	$0.696278\pi$
$710$	−3.31436	+	1.91354i	−0.124386	+	0.0718141i
$711$	−0.120744			−0.00452827
$712$	14.9269			0.559410
$713$	−19.8297	+	1.10212i	−0.742629	+	0.0412745i
$714$	12.8973			0.482669
$715$	−1.35096	−	0.245123i	−0.0505229	−	0.00916707i
$716$	1.37741	+	2.38574i	0.0514760	+	0.0891591i
$717$			42.4479i			1.58525i
$718$	−2.70679	+	4.68829i	−0.101016	+	0.174966i
$719$	−10.5613	−	18.2926i	−0.393869	−	0.682201i	0.599087	−	0.800684i	$-0.295530\pi$
$719$	−10.5613	−	18.2926i	−0.393869	−	0.682201i	−0.992956	+	0.118483i	$0.962197\pi$
$720$	0.0325786	−	0.0188093i	0.00121413	−	0.000700980i
$721$			12.6495i			0.471091i
$722$	14.9154	+	8.61143i	0.555095	+	0.320484i
$723$	30.2968	+	17.4919i	1.12675	+	0.650530i
$724$	1.02787	−	1.78032i	0.0382005	−	0.0661651i
$725$	−5.44672	−	9.43400i	−0.202286	−	0.350370i
$726$	−22.2259	−	12.8321i	−0.824881	−	0.476245i
$727$	−12.4725	−	21.6030i	−0.462579	−	0.801210i	0.536510	−	0.843894i	$-0.319743\pi$
$727$	−12.4725	−	21.6030i	−0.462579	−	0.801210i	−0.999089	+	0.0426838i	$0.986409\pi$
$728$	14.9184	+	2.70684i	0.552911	+	0.100322i
$729$	26.7946			0.992391
$730$	5.47692	−	3.16210i	0.202710	−	0.117035i
$731$	4.77174	−	8.26489i	0.176489	−	0.305688i
$732$	1.44852	+	2.50891i	0.0535388	+	0.0927319i
$733$	−42.2584	−	24.3979i	−1.56085	−	0.901158i	−0.997171	−	0.0751642i	$-0.976052\pi$
$733$	−42.2584	−	24.3979i	−1.56085	−	0.901158i	−0.563680	−	0.825993i	$-0.690615\pi$
$734$	10.0855	+	5.82289i	0.372264	+	0.214927i
$735$	−2.68692	−	1.55129i	−0.0991085	−	0.0572203i
$736$			3.22229i			0.118775i
$737$	−5.87482	−	10.1755i	−0.216402	−	0.374819i
$738$	−0.0341755	−	0.0591936i	−0.00125802	−	0.00217895i
$739$	30.4203	+	17.5632i	1.11903	+	0.646072i	0.941153	−	0.337981i	$-0.109744\pi$
$739$	30.4203	+	17.5632i	1.11903	+	0.646072i	0.177876	+	0.984053i	$0.443077\pi$
$740$	0.379790			0.0139614
$741$	−15.9231	+	5.70629i	−0.584951	+	0.209626i
$742$	−22.1269			−0.812305
$743$			9.54791i			0.350279i	0.984544	+	0.175139i	$0.0560376\pi$
$743$			9.54791i			0.350279i	−0.984544	+	0.175139i	$0.943962\pi$
$744$	−21.9076	+	14.3257i	−0.803173	+	0.525204i
$745$	0.782366			0.0286637
$746$		−	29.1527i		−	1.06736i
$747$	0.290536	−	0.167741i	0.0106302	−	0.00613733i
$748$		−	0.507965i		−	0.0185730i
$749$	3.47380	+	2.00560i	0.126930	+	0.0732831i
$750$	−4.90065	−	8.48817i	−0.178946	−	0.309944i
$751$	−17.6906	−	30.6410i	−0.645538	−	1.11810i	−0.984177	−	0.177188i	$-0.943300\pi$
$751$	−17.6906	−	30.6410i	−0.645538	−	1.11810i	0.338639	−	0.940916i	$-0.390033\pi$
$752$		−	49.4424i		−	1.80298i
$753$	−13.4964	+	23.3765i	−0.491837	+	0.851886i
$754$	9.08280	+	7.69844i	0.330776	+	0.280361i
$755$	−0.426563	+	0.738829i	−0.0155242	+	0.0268888i
$756$	−1.11588	+	0.644251i	−0.0405840	+	0.0234312i
$757$	7.43273	−	12.8739i	0.270147	−	0.467909i	−0.698752	−	0.715364i	$-0.746261\pi$
$757$	7.43273	−	12.8739i	0.270147	−	0.467909i	0.968899	+	0.247455i	$0.0795943\pi$
$758$	−15.7813	−	27.3340i	−0.573203	−	0.992816i
$759$			6.06296i			0.220072i
$760$		−	2.84219i		−	0.103097i
$761$	−25.4217	+	14.6772i	−0.921535	+	0.532049i	−0.884124	−	0.467251i	$-0.845244\pi$
$761$	−25.4217	+	14.6772i	−0.921535	+	0.532049i	−0.0374106	+	0.999300i	$0.511911\pi$
$762$	2.77208	+	1.60046i	0.100422	+	0.0579786i
$763$	8.75890	+	15.1709i	0.317093	+	0.549222i
$764$	0.524989	−	0.909307i	0.0189934	−	0.0328976i
$765$	−0.0246237	−	0.0142165i	−0.000890272	−	0.000513999i
$766$	−11.0272	+	19.0996i	−0.398428	+	0.690098i
$767$	1.37812	−	7.59530i	0.0497611	−	0.274250i
$768$	3.31856	+	5.74791i	0.119748	+	0.207410i
$769$	−12.1362	+	7.00682i	−0.437641	+	0.252672i	−0.702597	−	0.711588i	$-0.747976\pi$
$769$	−12.1362	+	7.00682i	−0.437641	+	0.252672i	0.264955	+	0.964261i	$0.414643\pi$
$770$	0.435165	−	0.753729i	0.0156823	−	0.0271625i
$771$	13.4220			0.483383
$772$	−2.56127	+	1.47875i	−0.0921820	+	0.0532213i
$773$			36.7759i			1.32274i	0.750062	+	0.661368i	$0.230024\pi$
$773$			36.7759i			1.32274i	−0.750062	+	0.661368i	$0.769976\pi$
$774$		−	0.0971822i		−	0.00349314i
$775$	14.7736	+	22.5926i	0.530682	+	0.811550i
$776$	−15.6139			−0.560505
$777$	−16.4689			−0.590818
$778$	−27.7483	+	16.0205i	−0.994826	+	0.574363i
$779$	−5.58007			−0.199927
$780$	0.298127	+	0.252687i	0.0106746	+	0.00904766i
$781$	−3.26810	−	5.66051i	−0.116942	−	0.202549i
$782$	14.7369	−	8.50833i	0.526989	−	0.304257i
$783$	11.6309			0.415653
$784$	9.83827	−	17.0404i	0.351367	−	0.608585i
$785$	1.29246	+	0.746204i	0.0461300	+	0.0266332i
$786$	30.6262	+	17.6820i	1.09240	+	0.630697i
$787$	−28.0414	+	16.1897i	−0.999568	+	0.577101i	−0.908120	−	0.418709i	$-0.862483\pi$
$787$	−28.0414	+	16.1897i	−0.999568	+	0.577101i	−0.0914475	+	0.995810i	$0.529149\pi$
$788$	−2.57342	−	1.48577i	−0.0916744	−	0.0529283i
$789$	−1.11412	−	1.92971i	−0.0396637	−	0.0686996i
$790$	3.07345			0.109348
$791$		−	6.58163i		−	0.234016i
$792$	0.0297292	+	0.0514925i	0.00105638	+	0.00182971i
$793$	24.2696	−	28.6338i	0.861838	−	1.01682i
$794$	−12.6936	−	21.9860i	−0.450481	−	0.780255i
$795$	5.67754	+	3.27793i	0.201362	+	0.116256i
$796$	−2.09908	+	3.63571i	−0.0743998	+	0.128864i
$797$	−1.83693	+	3.18165i	−0.0650673	+	0.112700i	−0.896724	−	0.442590i	$-0.854060\pi$
$797$	−1.83693	+	3.18165i	−0.0650673	+	0.112700i	0.831657	+	0.555290i	$0.187393\pi$
$798$		−	10.7220i		−	0.379553i
$799$	−32.3632	+	18.6849i	−1.14493	+	0.661024i
$800$	3.79296	−	2.18987i	0.134101	−	0.0774235i
$801$	−0.107509	−	0.0620706i	−0.00379866	−	0.00219316i
$802$	−6.49426			−0.229320
$803$	5.40048	+	9.35390i	0.190579	+	0.330092i
$804$			3.34435i			0.117946i
$805$	2.16053			0.0761486
$806$	−23.5313	−	17.7985i	−0.828854	−	0.626924i
$807$	−0.106922			−0.00376382
$808$		−	10.3574i		−	0.364373i
$809$	−4.86399	−	8.42468i	−0.171009	−	0.296196i	0.767764	−	0.640733i	$-0.221369\pi$
$809$	−4.86399	−	8.42468i	−0.171009	−	0.296196i	−0.938773	+	0.344537i	$0.888036\pi$
$810$	5.19042			0.182373
$811$	−3.41735	−	1.97301i	−0.119999	−	0.0692817i	0.438799	−	0.898585i	$-0.355404\pi$
$811$	−3.41735	−	1.97301i	−0.119999	−	0.0692817i	−0.558798	+	0.829304i	$0.688737\pi$
$812$	−0.484347	+	0.279638i	−0.0169972	+	0.00981336i
$813$	−48.2720	+	27.8699i	−1.69297	+	0.977439i
$814$			8.75316i			0.306798i
$815$	1.62996	−	2.82318i	0.0570951	−	0.0988916i
$816$	12.1172	−	20.9875i	0.424186	−	0.734711i
$817$	−6.87089	−	3.96691i	−0.240382	−	0.138785i
$818$	−4.92259	−	8.52617i	−0.172114	−	0.298111i
$819$	−0.0961919	−	0.0815307i	−0.00336122	−	0.00284891i
$820$	0.0644626	+	0.111653i	0.00225113	+	0.00389908i
$821$			53.0254i			1.85060i	0.379235	+	0.925300i	$0.376187\pi$
$821$			53.0254i			1.85060i	−0.379235	+	0.925300i	$0.623813\pi$
$822$	27.8077			0.969905
$823$	−8.77062	−	15.1912i	−0.305725	−	0.529531i	0.671698	−	0.740825i	$-0.265565\pi$
$823$	−8.77062	−	15.1912i	−0.305725	−	0.529531i	−0.977422	+	0.211295i	$0.932232\pi$
$824$	19.0498	+	10.9984i	0.663633	+	0.383149i
$825$	7.13672	−	4.12038i	0.248469	−	0.143453i
$826$	4.23759	+	2.44657i	0.147444	+	0.0851271i
$827$	−17.2377	−	9.95220i	−0.599414	−	0.346072i	0.169397	−	0.985548i	$-0.445818\pi$
$827$	−17.2377	−	9.95220i	−0.599414	−	0.346072i	−0.768811	+	0.639476i	$0.779151\pi$
$828$	0.00642036	−	0.0111204i	0.000223123	−	0.000386460i
$829$	−27.2935			−0.947941			−0.473971	−	0.880541i	$-0.657180\pi$
$829$	−27.2935			−0.947941			−0.473971	+	0.880541i	$0.657180\pi$
$830$	−7.39536	+	4.26972i	−0.256697	+	0.148204i
$831$	4.11729	+	7.13136i	0.142827	+	0.247384i
$832$	16.9282	−	19.9722i	0.586878	−	0.692413i
$833$	−14.8720			−0.515284
$834$	−47.5714	+	27.4654i	−1.64726	+	0.951048i
$835$	0.154375			0.00534235
$836$	−0.422289			−0.0146052
$837$	−28.7771	+	1.59940i	−0.994682	+	0.0552833i
$838$			50.7236i			1.75222i
$839$		−	47.9392i		−	1.65505i	−0.561431	−	0.827523i	$-0.689749\pi$
$839$		−	47.9392i		−	1.65505i	0.561431	−	0.827523i	$-0.310251\pi$
$840$	2.46605	−	1.42378i	0.0850870	−	0.0491250i
$841$	−23.9516			−0.825918
$842$	−17.5459	+	30.3905i	−0.604673	+	1.04732i
$843$	−23.2473	+	13.4218i	−0.800680	+	0.462273i
$844$	0.768745	+	1.33151i	0.0264613	+	0.0458323i
$845$	1.77891	−	4.74072i	0.0611965	−	0.163086i
$846$	−0.190270	+	0.329558i	−0.00654163	+	0.0113304i
$847$	−13.5267	−	7.80962i	−0.464782	−	0.268342i
$848$	−20.7886	+	36.0068i	−0.713882	+	1.23648i
$849$	9.46422	+	16.3925i	0.324811	+	0.562589i
$850$	−20.0303	−	11.5645i	−0.687034	−	0.396659i
$851$	−18.8179	+	10.8645i	−0.645069	+	0.372431i
$852$			1.86043i			0.0637372i
$853$			35.8879i			1.22878i	0.789003	+	0.614389i	$0.210597\pi$
$853$			35.8879i			1.22878i	−0.789003	+	0.614389i	$0.789403\pi$
$854$	11.8965	+	20.6054i	0.407091	+	0.705102i
$855$	−0.0118187	+	0.0204705i	−0.000404190	+	0.000700078i
$856$	6.04079	−	3.48765i	0.206470	−	0.119205i
$857$	21.6216	−	37.4497i	0.738580	−	1.27926i	−0.214555	−	0.976712i	$-0.568830\pi$
$857$	21.6216	−	37.4497i	0.738580	−	1.27926i	0.953135	−	0.302545i	$-0.0978364\pi$
$858$	−5.82378	+	6.87104i	−0.198821	+	0.234573i
$859$	−6.46455	+	11.1969i	−0.220568	+	0.382034i	−0.954980	−	0.296669i	$-0.904124\pi$
$859$	−6.46455	+	11.1969i	−0.220568	+	0.382034i	0.734413	+	0.678703i	$0.237458\pi$
$860$			0.183308i			0.00625074i
$861$	−2.79530	−	4.84161i	−0.0952637	−	0.165002i
$862$	13.8643	+	24.0136i	0.472219	+	0.817908i
$863$	21.2540	+	12.2710i	0.723494	+	0.417709i	0.816037	−	0.577999i	$-0.196166\pi$
$863$	21.2540	+	12.2710i	0.723494	+	0.417709i	−0.0925435	+	0.995709i	$0.529500\pi$
$864$			4.67622i			0.159088i
$865$	5.67328	−	3.27547i	0.192897	−	0.111369i
$866$			4.58257i			0.155722i
$867$	11.2381			0.381667
$868$	1.15992	−	0.758484i	0.0393701	−	0.0257446i
$869$			5.24907i			0.178063i
$870$	2.23614			0.0758123
$871$	40.7909	−	14.6180i	1.38215	−	0.495313i
$872$	30.4627			1.03160
$873$	0.112457	+	0.0649271i	0.00380609	+	0.00219745i
$874$	−7.07327	−	12.2513i	−0.239257	−	0.414405i
$875$	−2.98253	−	5.16589i	−0.100828	−	0.174639i
$876$		−	3.07433i		−	0.103872i
$877$	14.7682	+	8.52644i	0.498688	+	0.287917i	0.728171	−	0.685395i	$-0.240370\pi$
$877$	14.7682	+	8.52644i	0.498688	+	0.287917i	−0.229484	+	0.973312i	$0.573704\pi$
$878$	−3.45429	−	1.99434i	−0.116577	−	0.0673056i
$879$	−5.31886	−	3.07085i	−0.179401	−	0.103577i
$880$	−0.817687	−	1.41628i	−0.0275642	−	0.0477427i
$881$	18.8833	−	32.7069i	0.636195	−	1.10192i	−0.350066	−	0.936725i	$-0.613841\pi$
$881$	18.8833	−	32.7069i	0.636195	−	1.10192i	0.986261	−	0.165197i	$-0.0528259\pi$
$882$	−0.131154	+	0.0757216i	−0.00441617	+	0.00254968i
$883$	−5.66638			−0.190689			−0.0953444	−	0.995444i	$-0.530395\pi$
$883$	−5.66638			−0.190689			−0.0953444	+	0.995444i	$0.530395\pi$
$884$	1.84321	+	0.334439i	0.0619939	+	0.0112484i
$885$	−0.724880	−	1.25553i	−0.0243666	−	0.0422041i
$886$	−31.6456	−	18.2706i	−1.06315	−	0.613812i
$887$	0.878049	+	1.52082i	0.0294820	+	0.0510643i	0.880390	−	0.474251i	$-0.157281\pi$
$887$	0.878049	+	1.52082i	0.0294820	+	0.0510643i	−0.850908	+	0.525315i	$0.823948\pi$
$888$	−14.3193	+	24.8018i	−0.480525	+	0.832294i
$889$	1.68709	+	0.974039i	0.0565830	+	0.0326682i
$890$	2.73656	+	1.57996i	0.0917298	+	0.0529603i
$891$			8.86459i			0.296975i
$892$	0.685412	−	0.395723i	0.0229493	−	0.0132498i
$893$	15.5334	+	26.9047i	0.519806	+	0.900330i
$894$	2.56619	−	4.44478i	0.0858263	−	0.148656i
$895$		−	6.70342i		−	0.224071i
$896$	9.70267	+	16.8055i	0.324144	+	0.561433i
$897$	−22.0002	−	3.99180i	−0.734564	−	0.133282i
$898$	−32.1986			−1.07448
$899$	−12.4907	+	0.694221i	−0.416589	+	0.0231536i
$900$	−0.0174531			−0.000581769
$901$	31.4250			1.04692
$902$	−2.57330	+	1.48569i	−0.0856815	+	0.0494682i
$903$		−	7.94880i		−	0.264520i
$904$	−9.91180	−	5.72258i	−0.329662	−	0.190330i
$905$	−4.33214	+	2.50116i	−0.144005	+	0.0831415i
$906$	2.79829	+	4.84678i	0.0929670	+	0.161024i
$907$	24.5050			0.813674			0.406837	−	0.913501i	$-0.366632\pi$
$907$	24.5050			0.813674			0.406837	+	0.913501i	$0.366632\pi$
$908$	1.42226	+	0.821143i	0.0471994	+	0.0272506i
$909$	−0.0430693	+	0.0745981i	−0.00142852	+	0.00247426i
$910$	2.44848	+	2.07530i	0.0811665	+	0.0687954i
$911$	−9.15423	−	15.8556i	−0.303293	−	0.525319i	0.673587	−	0.739108i	$-0.264753\pi$
$911$	−9.15423	−	15.8556i	−0.303293	−	0.525319i	−0.976880	+	0.213789i	$0.931419\pi$
$912$	−17.4477	−	10.0734i	−0.577750	−	0.333564i
$913$	−7.29215	−	12.6304i	−0.241335	−	0.418004i
$914$	35.0020			1.15776
$915$		−	7.04951i		−	0.233049i
$916$	−1.08818	+	0.628262i	−0.0359545	+	0.0207584i
$917$	18.6391	+	10.7613i	0.615516	+	0.355368i
$918$	21.3863	−	12.3474i	0.705851	−	0.407524i
$919$	−8.81660	+	15.2708i	−0.290833	+	0.503737i	−0.974007	−	0.226518i	$-0.927266\pi$
$919$	−8.81660	+	15.2708i	−0.290833	+	0.503737i	0.683174	+	0.730256i	$0.260599\pi$
$920$	1.87853	−	3.25371i	0.0619333	−	0.107272i
$921$	11.5856	+	6.68893i	0.381757	+	0.220408i
$922$	−48.6721			−1.60293
$923$	22.6915	−	8.13185i	0.746900	−	0.267663i
$924$	−0.211543	−	0.366403i	−0.00695925	−	0.0120538i
$925$	25.5773	+	14.7670i	0.840975	+	0.485537i
$926$	18.3765			0.603890
$927$	−0.0914696	−	0.158430i	−0.00300425	−	0.00520352i
$928$			2.02972i			0.0666288i
$929$			10.2188i			0.335268i	0.985849	+	0.167634i	$0.0536127\pi$
$929$			10.2188i			0.335268i	−0.985849	+	0.167634i	$0.946387\pi$
$930$	−5.53266	+	0.307499i	−0.181423	+	0.0100833i
$931$			12.3636i			0.405201i
$932$	1.30818			0.0428508
$933$	22.7171	+	39.3471i	0.743723	+	1.28817i
$934$		−	58.0036i		−	1.89793i
$935$	−0.618028	+	1.07046i	−0.0202117	+	0.0350076i
$936$	−0.206420	+	0.0739738i	−0.00674705	+	0.00241791i
$937$	25.8373	+	44.7516i	0.844069	+	1.46197i	0.886427	+	0.462868i	$0.153180\pi$
$937$	25.8373	+	44.7516i	0.844069	+	1.46197i	−0.0423580	+	0.999102i	$0.513487\pi$
$938$			27.4668i			0.896824i
$939$	−5.16200	+	8.94085i	−0.168456	+	0.291774i
$940$	0.358893	−	0.621621i	0.0117058	−	0.0202750i
$941$	−40.5694	−	23.4228i	−1.32253	−	0.763560i	−0.338394	−	0.941004i	$-0.609884\pi$
$941$	−40.5694	−	23.4228i	−1.32253	−	0.763560i	−0.984131	+	0.177444i	$0.943217\pi$
$942$	8.47866	−	4.89516i	0.276250	−	0.159493i
$943$	−6.38801	−	3.68812i	−0.208022	−	0.120102i
$944$	7.96254	−	4.59717i	0.259159	−	0.149625i
$945$	3.13538			0.101994
$946$	−4.22476			−0.137359
$947$	23.6097	−	13.6311i	0.767213	−	0.442951i	−0.0646664	−	0.997907i	$-0.520598\pi$
$947$	23.6097	−	13.6311i	0.767213	−	0.442951i	0.831880	+	0.554956i	$0.187265\pi$
$948$	0.747034	−	1.29390i	0.0242625	−	0.0420239i
$949$	−37.4974	+	13.4378i	−1.21722	+	0.436208i
$950$	−9.61397	+	16.6519i	−0.311919	+	0.540259i
$951$	22.4412	+	12.9565i	0.727707	+	0.420142i
$952$	6.82476	−	11.8208i	0.221192	−	0.383116i
$953$	−1.37919			−0.0446764			−0.0223382	−	0.999750i	$-0.507111\pi$
$953$	−1.37919			−0.0446764			−0.0223382	+	0.999750i	$0.507111\pi$
$954$	0.277132	−	0.160002i	0.00897246	−	0.00518025i
$955$	−2.21266	+	1.27748i	−0.0716001	+	0.0413383i
$956$	−3.38459	−	1.95410i	−0.109466	−	0.0632000i
$957$			3.81905i			0.123452i
$958$	7.55508	+	13.0858i	0.244093	+	0.422782i
$959$	16.9237			0.546496
$960$		−	4.91707i		−	0.158698i
$961$	30.8091	−	3.43528i	0.993841	−	0.110816i
$962$	−31.7619	−	5.76300i	−1.02404	−	0.185807i
$963$	−0.0580108			−0.00186937
$964$	−2.78944	+	1.61048i	−0.0898417	+	0.0518701i
$965$	7.19662			0.231667
$966$	7.08662	−	12.2744i	0.228008	−	0.394922i
$967$	−40.7599	+	23.5327i	−1.31075	+	0.756762i	−0.982220	−	0.187731i	$-0.939887\pi$
$967$	−40.7599	+	23.5327i	−1.31075	+	0.756762i	−0.328530	+	0.944494i	$0.606553\pi$
$968$	−23.5223	+	13.5806i	−0.756034	+	0.436497i
$969$			15.2275i			0.489177i
$970$	−2.86250	−	1.65266i	−0.0919093	−	0.0530639i
$971$	17.0471	−	29.5265i	0.547068	−	0.947550i	−0.451405	−	0.892319i	$-0.649077\pi$
$971$	17.0471	−	29.5265i	0.547068	−	0.947550i	0.998474	−	0.0552311i	$-0.0175895\pi$
$972$	0.0187049	−	0.0323979i	0.000599961	−	0.00103916i
$973$	−28.9519	+	16.7154i	−0.928156	+	0.535871i
$974$	6.63477	−	11.4918i	0.212592	−	0.368219i
$975$	10.2526	+	28.6092i	0.328345	+	0.916229i
$976$	44.7078			1.43106
$977$		−	11.8687i		−	0.379713i	−0.981812	−	0.189857i	$-0.939198\pi$
$977$		−	11.8687i		−	0.379713i	0.981812	−	0.189857i	$-0.0608023\pi$
$978$	−10.6927	−	18.5203i	−0.341914	−	0.592213i
$979$	−2.69837	+	4.67371i	−0.0862403	+	0.149373i
$980$	0.247386	−	0.142828i	0.00790244	−	0.00456248i
$981$	−0.219404	−	0.126673i	−0.00700502	−	0.00404435i
$982$	47.8923	+	27.6506i	1.52830	+	0.882366i
$983$	−28.2129	−	16.2887i	−0.899852	−	0.519530i	−0.0227000	−	0.999742i	$-0.507226\pi$
$983$	−28.2129	−	16.2887i	−0.899852	−	0.519530i	−0.877152	+	0.480212i	$0.840560\pi$
$984$	−9.72181			−0.309920
$985$	3.61539	+	6.26204i	0.115196	+	0.199525i
$986$	9.28272	−	5.35938i	0.295622	−	0.170678i
$987$	−15.5627	+	26.9554i	−0.495367	+	0.858001i
$988$	0.278031	−	1.53232i	0.00884534	−	0.0487497i
$989$	−5.24382	−	9.08256i	−0.166744	−	0.288809i
$990$			0.0125869i			0.000400038i
$991$	−23.9787			−0.761709			−0.380855	−	0.924635i	$-0.624370\pi$
$991$	−23.9787			−0.761709			−0.380855	+	0.924635i	$0.624370\pi$
$992$	−0.279113	−	5.02193i	−0.00886186	−	0.159446i
$993$		−	42.6003i		−	1.35188i
$994$			15.2795i			0.484637i
$995$	8.84695	−	5.10779i	0.280467	−	0.161928i
$996$			4.15120i			0.131536i
$997$	−17.8552	+	30.9262i	−0.565481	+	0.979442i	0.431524	+	0.902102i	$0.357976\pi$
$997$	−17.8552	+	30.9262i	−0.565481	+	0.979442i	−0.997005	+	0.0773404i	$0.975357\pi$
$998$	10.9442	+	18.9560i	0.346434	+	0.600040i
$999$	−27.3087	+	15.7667i	−0.864009	+	0.498836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.10	✓	68
13.12	even	2	inner	403.2.l.c.25.25	yes	68
31.5	even	3	inner	403.2.l.c.129.10	yes	68
403.129	even	6	inner	403.2.l.c.129.25	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.10	✓	68	1.1	even	1	trivial
403.2.l.c.25.25	yes	68	13.12	even	2	inner
403.2.l.c.129.10	yes	68	31.5	even	3	inner
403.2.l.c.129.25	yes	68	403.129	even	6	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.46972i q^{2} +(0.869265 + 1.50561i) q^{3} -0.160067 q^{4} +(0.337316 + 0.194750i) q^{5} +(2.21282 - 1.27757i) q^{6} +(1.34672 - 0.777530i) q^{7} -2.70418i q^{8} +(-0.0112448 + 0.0194765i) q^{9} +O(q^{10})\)	\(q-1.46972i q^{2} +(0.869265 + 1.50561i) q^{3} -0.160067 q^{4} +(0.337316 + 0.194750i) q^{5} +(2.21282 - 1.27757i) q^{6} +(1.34672 - 0.777530i) q^{7} -2.70418i q^{8} +(-0.0112448 + 0.0194765i) q^{9} +(0.286227 - 0.495759i) q^{10} +(0.846696 + 0.488840i) q^{11} +(-0.139141 - 0.240999i) q^{12} +(-2.33127 + 2.75049i) q^{13} +(-1.14275 - 1.97930i) q^{14} +0.677157i q^{15} -4.29451 q^{16} +(1.62295 + 2.81103i) q^{17} +(0.0286250 + 0.0165267i) q^{18} +(2.33691 - 1.34921i) q^{19} +(-0.0539932 - 0.0311730i) q^{20} +(2.34132 + 1.35176i) q^{21} +(0.718456 - 1.24440i) q^{22} +3.56702 q^{23} +(4.07145 - 2.35065i) q^{24} +(-2.42415 - 4.19874i) q^{25} +(4.04244 + 3.42631i) q^{26} +5.17649 q^{27} +(-0.215566 + 0.124457i) q^{28} +2.24686 q^{29} +0.995228 q^{30} +(-5.55918 + 0.308974i) q^{31} +0.903357i q^{32} +1.69973i q^{33} +(4.13142 - 2.38527i) q^{34} +0.605695 q^{35} +(0.00179992 - 0.00311755i) q^{36} +(-5.27552 + 3.04582i) q^{37} +(-1.98296 - 3.43459i) q^{38} +(-6.16766 - 1.11908i) q^{39} +(0.526638 - 0.912164i) q^{40} +(-1.79085 - 1.03395i) q^{41} +(1.98670 - 3.44107i) q^{42} +(-1.47008 - 2.54626i) q^{43} +(-0.135528 - 0.0782472i) q^{44} +(-0.00758610 + 0.00437984i) q^{45} -5.24251i q^{46} +11.5129i q^{47} +(-3.73307 - 6.46587i) q^{48} +(-2.29089 + 3.96794i) q^{49} +(-6.17096 + 3.56281i) q^{50} +(-2.82155 + 4.88706i) q^{51} +(0.373160 - 0.440263i) q^{52} +(4.84072 - 8.38438i) q^{53} -7.60798i q^{54} +(0.190403 + 0.329787i) q^{55} +(-2.10258 - 3.64178i) q^{56} +(4.06278 + 2.34565i) q^{57} -3.30225i q^{58} +(-1.85412 + 1.07048i) q^{59} -0.108390i q^{60} -10.4105 q^{61} +(0.454104 + 8.17043i) q^{62} +0.0349727i q^{63} -7.26135 q^{64} +(-1.32203 + 0.473770i) q^{65} +2.49812 q^{66} +(-10.4078 - 6.00894i) q^{67} +(-0.259781 - 0.449953i) q^{68} +(3.10069 + 5.37055i) q^{69} -0.890200i q^{70} +(-5.78974 - 3.34271i) q^{71} +(0.0526681 + 0.0304079i) q^{72} +(9.56745 + 5.52377i) q^{73} +(4.47650 + 7.75352i) q^{74} +(4.21445 - 7.29964i) q^{75} +(-0.374062 + 0.215965i) q^{76} +1.52035 q^{77} +(-1.64474 + 9.06471i) q^{78} +(2.68445 + 4.64961i) q^{79} +(-1.44861 - 0.836355i) q^{80} +(4.53348 + 7.85222i) q^{81} +(-1.51961 + 2.63205i) q^{82} +(-12.9187 - 7.45862i) q^{83} +(-0.374768 - 0.216372i) q^{84} +1.26427i q^{85} +(-3.74228 + 2.16061i) q^{86} +(1.95312 + 3.38290i) q^{87} +(1.32191 - 2.28962i) q^{88} +5.51995i q^{89} +(0.00643712 + 0.0111494i) q^{90} +(-1.00099 + 5.51677i) q^{91} -0.570963 q^{92} +(-5.29760 - 8.10139i) q^{93} +16.9208 q^{94} +1.05104 q^{95} +(-1.36010 + 0.785257i) q^{96} -5.77397i q^{97} +(5.83175 + 3.36696i) q^{98} +(-0.0190418 + 0.0109938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

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