LMFDB - Embedded newform 570.2.x.b.103.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, degree $4$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.8
Character	$\chi$	$=$	570.103
Dual form			570.2.x.b.487.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.649262 + 2.13973i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.55332 + 2.55332i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.649262 + 2.13973i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.55332 + 2.55332i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.18094 + 1.89878i) q^{10} -2.10070 q^{11} +(0.707107 + 0.707107i) q^{12} +(-0.336465 - 0.0901556i) q^{13} +(-1.80547 + 3.12716i) q^{14} +(-1.89878 + 1.18094i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.11690 + 4.16833i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(4.05014 + 1.61133i) q^{19} +(1.63214 + 1.52843i) q^{20} +(-3.12716 - 1.80547i) q^{21} +(-2.02912 + 0.543700i) q^{22} +(0.916939 - 3.42206i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.15692 + 2.77850i) q^{25} -0.348335 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.934578 + 3.48789i) q^{28} +(-0.205030 - 0.355122i) q^{29} +(-1.52843 + 1.63214i) q^{30} -9.24205i q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.543700 - 2.02912i) q^{33} +(2.15768 + 3.73722i) q^{34} +(-7.12119 - 3.80564i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.61173 + 3.61173i) q^{37} +(4.32918 + 0.508171i) q^{38} -0.348335i q^{39} +(1.97212 + 1.05392i) q^{40} +(6.95086 + 4.01308i) q^{41} +(-3.48789 - 0.934578i) q^{42} +(-2.24564 + 0.601718i) q^{43} +(-1.81926 + 1.05035i) q^{44} +(-1.63214 - 1.52843i) q^{45} -3.54278i q^{46} +(6.52433 + 1.74819i) q^{47} +(0.965926 + 0.258819i) q^{48} -6.03884i q^{49} +(-3.29615 + 3.75971i) q^{50} +(-3.73722 + 2.15768i) q^{51} +(-0.336465 + 0.0901556i) q^{52} +(12.4622 + 3.33923i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.36390 - 4.49493i) q^{55} +3.61093i q^{56} +(-0.508171 + 4.32918i) q^{57} +(-0.289956 - 0.289956i) q^{58} +(6.55422 - 11.3522i) q^{59} +(-1.05392 + 1.97212i) q^{60} +(0.171384 + 0.296845i) q^{61} +(-2.39202 - 8.92714i) q^{62} +(0.934578 - 3.48789i) q^{63} -1.00000i q^{64} +(-0.0255453 - 0.778481i) q^{65} +(-1.05035 - 1.81926i) q^{66} +(-1.54479 + 5.76524i) q^{67} +(3.05143 + 3.05143i) q^{68} +3.54278 q^{69} +(-7.86351 - 1.83287i) q^{70} +(0.442835 + 0.255671i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-5.52581 + 1.48064i) q^{73} +(4.42345 + 2.55388i) q^{74} +(-3.75971 - 3.29615i) q^{75} +(4.31319 - 0.629617i) q^{76} +(5.36374 - 5.36374i) q^{77} +(-0.0901556 - 0.336465i) q^{78} +(-4.99199 + 8.64638i) q^{79} +(2.17769 + 0.507589i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.75267 + 2.07732i) q^{82} +(-4.69214 - 4.69214i) q^{83} -3.61093 q^{84} +(-8.19394 + 5.09620i) q^{85} +(-2.01339 + 1.16243i) q^{86} +(0.289956 - 0.289956i) q^{87} +(-1.48542 + 1.48542i) q^{88} +(-8.24426 - 14.2795i) q^{89} +(-1.97212 - 1.05392i) q^{90} +(1.08930 - 0.628907i) q^{91} +(-0.916939 - 3.42206i) q^{92} +(8.92714 - 2.39202i) q^{93} +6.75448 q^{94} +(-0.818212 + 9.71239i) q^{95} +1.00000 q^{96} +(-12.5271 + 3.35662i) q^{97} +(-1.56297 - 5.83307i) q^{98} +(1.81926 - 1.05035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q + 20 * q^6 - 8 * q^7	$ 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	0.649262	+	2.13973i	0.290359	+	0.956918i
$5$	0.649262	+	2.13973i	0.290359	+	0.956918i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−2.55332	+	2.55332i	−0.965063	+	0.965063i	−0.999410	−	0.0343474i	$-0.989065\pi$
$7$	−2.55332	+	2.55332i	−0.965063	+	0.965063i	0.0343474	+	0.999410i	$0.489065\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	1.18094	+	1.89878i	0.373447	+	0.600448i
$11$	−2.10070			−0.633384			−0.316692	−	0.948528i	$-0.602572\pi$
$11$	−2.10070			−0.633384			−0.316692	+	0.948528i	$0.602572\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−0.336465	−	0.0901556i	−0.0933187	−	0.0250047i	0.211858	−	0.977301i	$-0.432049\pi$
$13$	−0.336465	−	0.0901556i	−0.0933187	−	0.0250047i	−0.305176	+	0.952296i	$0.598715\pi$
$14$	−1.80547	+	3.12716i	−0.482531	+	0.835769i
$15$	−1.89878	+	1.18094i	−0.490263	+	0.304918i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.11690	+	4.16833i	0.270888	+	1.01097i	0.958547	+	0.284934i	$0.0919716\pi$
$17$	1.11690	+	4.16833i	0.270888	+	1.01097i	−0.687659	+	0.726034i	$0.741362\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	4.05014	+	1.61133i	0.929165	+	0.369664i
$19$	4.05014	+	1.61133i	0.929165	+	0.369664i
$20$	1.63214	+	1.52843i	0.364959	+	0.341768i
$21$	−3.12716	−	1.80547i	−0.682402	−	0.393985i
$22$	−2.02912	+	0.543700i	−0.432609	+	0.115917i
$23$	0.916939	−	3.42206i	0.191195	−	0.713549i	−0.802024	−	0.597292i	$-0.796244\pi$
$23$	0.916939	−	3.42206i	0.191195	−	0.713549i	0.993219	−	0.116258i	$-0.0370898\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−4.15692	+	2.77850i	−0.831383	+	0.555699i
$26$	−0.348335			−0.0683140
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−0.934578	+	3.48789i	−0.176619	+	0.659150i
$29$	−0.205030	−	0.355122i	−0.0380731	−	0.0659445i	0.846361	−	0.532610i	$-0.178789\pi$
$29$	−0.205030	−	0.355122i	−0.0380731	−	0.0659445i	−0.884434	+	0.466665i	$0.845455\pi$
$30$	−1.52843	+	1.63214i	−0.279052	+	0.297987i
$31$		−	9.24205i		−	1.65992i	−0.557822	−	0.829961i	$-0.688363\pi$
$31$		−	9.24205i		−	1.65992i	0.557822	−	0.829961i	$-0.311637\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.543700	−	2.02912i	−0.0946461	−	0.353224i
$34$	2.15768	+	3.73722i	0.370040	+	0.640928i
$35$	−7.12119	−	3.80564i	−1.20370	−	0.643271i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	3.61173	+	3.61173i	0.593765	+	0.593765i	0.938646	−	0.344881i	$-0.112081\pi$
$37$	3.61173	+	3.61173i	0.593765	+	0.593765i	−0.344881	+	0.938646i	$0.612081\pi$
$38$	4.32918	+	0.508171i	0.702285	+	0.0824363i
$39$		−	0.348335i		−	0.0557782i
$40$	1.97212	+	1.05392i	0.311819	+	0.166640i
$41$	6.95086	+	4.01308i	1.08554	+	0.626738i	0.932386	−	0.361464i	$-0.117723\pi$
$41$	6.95086	+	4.01308i	1.08554	+	0.626738i	0.153156	+	0.988202i	$0.451056\pi$
$42$	−3.48789	−	0.934578i	−0.538194	−	0.144209i
$43$	−2.24564	+	0.601718i	−0.342457	+	0.0917612i	−0.425949	−	0.904747i	$-0.640060\pi$
$43$	−2.24564	+	0.601718i	−0.342457	+	0.0917612i	0.0834913	+	0.996509i	$0.473393\pi$
$44$	−1.81926	+	1.05035i	−0.274263	+	0.158346i
$45$	−1.63214	−	1.52843i	−0.243306	−	0.227845i
$46$		−	3.54278i		−	0.522354i
$47$	6.52433	+	1.74819i	0.951671	+	0.255000i	0.701071	−	0.713091i	$-0.252705\pi$
$47$	6.52433	+	1.74819i	0.951671	+	0.255000i	0.250600	+	0.968091i	$0.419372\pi$
$48$	0.965926	+	0.258819i	0.139419	+	0.0373573i
$49$		−	6.03884i		−	0.862691i
$50$	−3.29615	+	3.75971i	−0.466145	+	0.531703i
$51$	−3.73722	+	2.15768i	−0.523315	+	0.302136i
$52$	−0.336465	+	0.0901556i	−0.0466594	+	0.0125023i
$53$	12.4622	+	3.33923i	1.71181	+	0.458678i	0.975867	−	0.218364i	$-0.0700720\pi$
$53$	12.4622	+	3.33923i	1.71181	+	0.458678i	0.735944	+	0.677042i	$0.236739\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−1.36390	−	4.49493i	−0.183909	−	0.606096i
$56$			3.61093i			0.482531i
$57$	−0.508171	+	4.32918i	−0.0673090	+	0.573413i
$58$	−0.289956	−	0.289956i	−0.0380731	−	0.0380731i
$59$	6.55422	−	11.3522i	0.853287	−	1.47794i	−0.0249375	−	0.999689i	$-0.507939\pi$
$59$	6.55422	−	11.3522i	0.853287	−	1.47794i	0.878225	−	0.478248i	$-0.158728\pi$
$60$	−1.05392	+	1.97212i	−0.136061	+	0.254599i
$61$	0.171384	+	0.296845i	0.0219434	+	0.0380071i	0.876789	−	0.480876i	$-0.159681\pi$
$61$	0.171384	+	0.296845i	0.0219434	+	0.0380071i	−0.854845	+	0.518883i	$0.826348\pi$
$62$	−2.39202	−	8.92714i	−0.303787	−	1.13375i
$63$	0.934578	−	3.48789i	0.117746	−	0.439433i
$64$		−	1.00000i		−	0.125000i
$65$	−0.0255453	−	0.778481i	−0.00316851	−	0.0965587i
$66$	−1.05035	−	1.81926i	−0.129289	−	0.223935i
$67$	−1.54479	+	5.76524i	−0.188726	+	0.704336i	0.805076	+	0.593172i	$0.202125\pi$
$67$	−1.54479	+	5.76524i	−0.188726	+	0.704336i	−0.993802	+	0.111164i	$0.964542\pi$
$68$	3.05143	+	3.05143i	0.370040	+	0.370040i
$69$	3.54278			0.426501
$70$	−7.86351	−	1.83287i	−0.939869	−	0.219070i
$71$	0.442835	+	0.255671i	0.0525548	+	0.0303425i	0.526047	−	0.850455i	$-0.323674\pi$
$71$	0.442835	+	0.255671i	0.0525548	+	0.0303425i	−0.473492	+	0.880798i	$0.657007\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−5.52581	+	1.48064i	−0.646748	+	0.173295i	−0.567258	−	0.823540i	$-0.691996\pi$
$73$	−5.52581	+	1.48064i	−0.646748	+	0.173295i	−0.0794897	+	0.996836i	$0.525329\pi$
$74$	4.42345	+	2.55388i	0.514216	+	0.296883i
$75$	−3.75971	−	3.29615i	−0.434134	−	0.380606i
$76$	4.31319	−	0.629617i	0.494756	−	0.0722220i
$77$	5.36374	−	5.36374i	0.611255	−	0.611255i
$78$	−0.0901556	−	0.336465i	−0.0102081	−	0.0380972i
$79$	−4.99199	+	8.64638i	−0.561643	+	0.972794i	0.435711	+	0.900087i	$0.356497\pi$
$79$	−4.99199	+	8.64638i	−0.561643	+	0.972794i	−0.997353	+	0.0727070i	$0.976836\pi$
$80$	2.17769	+	0.507589i	0.243474	+	0.0567502i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	7.75267	+	2.07732i	0.856139	+	0.229402i
$83$	−4.69214	−	4.69214i	−0.515029	−	0.515029i	0.401034	−	0.916063i	$-0.368651\pi$
$83$	−4.69214	−	4.69214i	−0.515029	−	0.515029i	−0.916063	+	0.401034i	$0.868651\pi$
$84$	−3.61093			−0.393985
$85$	−8.19394	+	5.09620i	−0.888758	+	0.552761i
$86$	−2.01339	+	1.16243i	−0.217109	+	0.125348i
$87$	0.289956	−	0.289956i	0.0310865	−	0.0310865i
$88$	−1.48542	+	1.48542i	−0.158346	+	0.158346i
$89$	−8.24426	−	14.2795i	−0.873890	−	1.51362i	−0.857941	−	0.513749i	$-0.828256\pi$
$89$	−8.24426	−	14.2795i	−0.873890	−	1.51362i	−0.0159489	−	0.999873i	$-0.505077\pi$
$90$	−1.97212	−	1.05392i	−0.207879	−	0.111093i
$91$	1.08930	−	0.628907i	0.114189	−	0.0659273i
$92$	−0.916939	−	3.42206i	−0.0955975	−	0.356775i
$93$	8.92714	−	2.39202i	0.925701	−	0.248041i
$94$	6.75448			0.696672
$95$	−0.818212	+	9.71239i	−0.0839468	+	0.996470i
$96$	1.00000			0.102062
$97$	−12.5271	+	3.35662i	−1.27193	+	0.340813i	−0.830770	−	0.556615i	$-0.812100\pi$
$97$	−12.5271	+	3.35662i	−1.27193	+	0.340813i	−0.441161	+	0.897428i	$0.645433\pi$
$98$	−1.56297	−	5.83307i	−0.157883	−	0.589229i
$99$	1.81926	−	1.05035i	0.182842	−	0.105564i
$100$	−2.21075	+	4.48471i	−0.221075	+	0.448471i
$101$	2.04489	+	3.54184i	0.203474	+	0.352427i	0.949645	−	0.313327i	$-0.101444\pi$
$101$	2.04489	+	3.54184i	0.203474	+	0.352427i	−0.746172	+	0.665754i	$0.768110\pi$
$102$	−3.05143	+	3.05143i	−0.302136	+	0.302136i
$103$	9.80360	−	9.80360i	0.965977	−	0.965977i	−0.0334625	−	0.999440i	$-0.510653\pi$
$103$	9.80360	−	9.80360i	0.965977	−	0.965977i	0.999440	+	0.0334625i	$0.0106534\pi$
$104$	−0.301667	+	0.174167i	−0.0295808	+	0.0170785i
$105$	1.83287	−	7.86351i	0.178870	−	0.767400i
$106$	12.9018			1.25313
$107$	−2.94121	−	2.94121i	−0.284338	−	0.284338i	0.550498	−	0.834836i	$-0.314438\pi$
$107$	−2.94121	−	2.94121i	−0.284338	−	0.284338i	−0.834836	+	0.550498i	$0.814438\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	1.56833	−	2.71643i	0.150219	−	0.260187i	−0.781089	−	0.624420i	$-0.785335\pi$
$109$	1.56833	−	2.71643i	0.150219	−	0.260187i	0.931308	+	0.364233i	$0.118669\pi$
$110$	−2.48080	−	3.98876i	−0.236535	−	0.380314i
$111$	−2.55388	+	4.42345i	−0.242404	+	0.419855i
$112$	0.934578	+	3.48789i	0.0883094	+	0.329575i
$113$	12.7427	−	12.7427i	1.19874	−	1.19874i	0.224190	−	0.974545i	$-0.428026\pi$
$113$	12.7427	−	12.7427i	1.19874	−	1.19874i	0.974545	−	0.224190i	$-0.0719737\pi$
$114$	0.629617	+	4.31319i	0.0589691	+	0.403967i
$115$	7.91763	−	0.259812i	0.738323	−	0.0242276i
$116$	−0.355122	−	0.205030i	−0.0329722	−	0.0190365i
$117$	0.336465	−	0.0901556i	0.0311062	−	0.00833489i
$118$	3.39272	−	12.6618i	0.312325	−	1.16561i
$119$	−13.4948	−	7.79125i	−1.23707	−	0.714223i
$120$	−0.507589	+	2.17769i	−0.0463363	+	0.198795i
$121$	−6.58707			−0.598825
$122$	0.242373	+	0.242373i	0.0219434	+	0.0219434i
$123$	−2.07732	+	7.75267i	−0.187306	+	0.699035i
$124$	−4.62103	−	8.00385i	−0.414980	−	0.718767i
$125$	−8.64417	−	7.09072i	−0.773158	−	0.634213i
$126$		−	3.61093i		−	0.321688i
$127$	0.957135	−	3.57208i	0.0849320	−	0.316971i	−0.910369	−	0.413797i	$-0.864202\pi$
$127$	0.957135	−	3.57208i	0.0849320	−	0.316971i	0.995301	+	0.0968262i	$0.0308691\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−1.16243	−	2.01339i	−0.102346	−	0.177269i
$130$	−0.226161	−	0.745343i	−0.0198356	−	0.0653709i
$131$	6.97423	−	12.0797i	0.609341	−	1.05541i	−0.382008	−	0.924159i	$-0.624767\pi$
$131$	6.97423	−	12.0797i	0.609341	−	1.05541i	0.991349	−	0.131251i	$-0.0418995\pi$
$132$	−1.48542	−	1.48542i	−0.129289	−	0.129289i
$133$	−14.4555	+	6.22705i	−1.25345	+	0.539954i
$134$			5.96862i			0.515610i
$135$	1.05392	−	1.97212i	0.0907072	−	0.169733i
$136$	3.73722	+	2.15768i	0.320464	+	0.185020i
$137$	10.2446	+	2.74503i	0.875256	+	0.234524i	0.668359	−	0.743839i	$-0.266997\pi$
$137$	10.2446	+	2.74503i	0.875256	+	0.234524i	0.206897	+	0.978363i	$0.433664\pi$
$138$	3.42206	−	0.916939i	0.291305	−	0.0780550i
$139$	−3.66655	+	2.11689i	−0.310993	+	0.179552i	−0.647371	−	0.762175i	$-0.724131\pi$
$139$	−3.66655	+	2.11689i	−0.310993	+	0.179552i	0.336378	+	0.941727i	$0.390798\pi$
$140$	−8.06995	+	0.264810i	−0.682035	+	0.0223805i
$141$			6.75448i			0.568830i
$142$	0.493918	+	0.132345i	0.0414487	+	0.0111061i
$143$	0.706812	+	0.189390i	0.0591066	+	0.0158376i
$144$			1.00000i			0.0833333i
$145$	0.626748	−	0.669276i	0.0520486	−	0.0555804i
$146$	−4.95431	+	2.86037i	−0.410022	+	0.236726i
$147$	5.83307	−	1.56297i	0.481104	−	0.128911i
$148$	4.93372	+	1.32199i	0.405549	+	0.108667i
$149$	11.0405	+	6.37423i	0.904473	+	0.522197i	0.878649	−	0.477469i	$-0.158446\pi$
$149$	11.0405	+	6.37423i	0.904473	+	0.522197i	0.0258240	+	0.999667i	$0.491779\pi$
$150$	−4.48471	−	2.21075i	−0.366175	−	0.180507i
$151$		−	3.11702i		−	0.253660i	−0.991924	−	0.126830i	$-0.959520\pi$
$151$		−	3.11702i		−	0.253660i	0.991924	−	0.126830i	$-0.0404802\pi$
$152$	4.00326	−	1.72450i	0.324707	−	0.139875i
$153$	−3.05143	−	3.05143i	−0.246693	−	0.246693i
$154$	3.79274	−	6.56921i	0.305627	−	0.529362i
$155$	19.7755	−	6.00052i	1.58841	−	0.481973i
$156$	−0.174167	−	0.301667i	−0.0139445	−	0.0241527i
$157$	3.48618	+	13.0106i	0.278228	+	1.03836i	0.953647	+	0.300926i	$0.0972957\pi$
$157$	3.48618	+	13.0106i	0.278228	+	1.03836i	−0.675420	+	0.737433i	$0.736038\pi$
$158$	−2.58404	+	9.64378i	−0.205576	+	0.767218i
$159$			12.9018i			1.02318i
$160$	2.23487	−	0.0733356i	0.176682	−	0.00579769i
$161$	6.39637	+	11.0788i	0.504105	+	0.873135i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−11.9295	−	11.9295i	−0.934394	−	0.934394i	0.0635829	−	0.997977i	$-0.479747\pi$
$163$	−11.9295	−	11.9295i	−0.934394	−	0.934394i	−0.997977	+	0.0635829i	$0.979747\pi$
$164$	8.02616			0.626738
$165$	3.98876	−	2.48080i	0.310525	−	0.193130i
$166$	−5.74667	−	3.31784i	−0.446028	−	0.257515i
$167$	−3.78603	+	14.1297i	−0.292972	+	1.09339i	0.649843	+	0.760069i	$0.274835\pi$
$167$	−3.78603	+	14.1297i	−0.292972	+	1.09339i	−0.942815	+	0.333318i	$0.891832\pi$
$168$	−3.48789	+	0.934578i	−0.269097	+	0.0721043i
$169$	−11.1532	−	6.43933i	−0.857942	−	0.495333i
$170$	−6.59575	+	7.04330i	−0.505871	+	0.540197i
$171$	−4.31319	+	0.629617i	−0.329838	+	0.0481480i
$172$	−1.64392	+	1.64392i	−0.125348	+	0.125348i
$173$	0.996399	+	3.71861i	0.0757548	+	0.282721i	0.993403	−	0.114672i	$-0.0365817\pi$
$173$	0.996399	+	3.71861i	0.0757548	+	0.282721i	−0.917649	+	0.397393i	$0.869915\pi$
$174$	0.205030	−	0.355122i	0.0155433	−	0.0269217i
$175$	3.51954	−	17.7083i	0.266052	−	1.33862i
$176$	−1.05035	+	1.81926i	−0.0791730	+	0.137132i
$177$	12.6618	+	3.39272i	0.951718	+	0.255012i
$178$	−11.6591	−	11.6591i	−0.873890	−	0.873890i
$179$	−16.9895			−1.26985			−0.634926	−	0.772573i	$-0.718969\pi$
$179$	−16.9895			−1.26985			−0.634926	+	0.772573i	$0.718969\pi$
$180$	−2.17769	−	0.507589i	−0.162316	−	0.0378334i
$181$	3.80982	−	2.19960i	0.283182	−	0.163495i	−0.351681	−	0.936120i	$-0.614390\pi$
$181$	3.80982	−	2.19960i	0.283182	−	0.163495i	0.634863	+	0.772625i	$0.281057\pi$
$182$	0.889408	−	0.889408i	0.0659273	−	0.0659273i
$183$	−0.242373	+	0.242373i	−0.0179167	+	0.0179167i
$184$	−1.77139	−	3.06814i	−0.130589	−	0.226186i
$185$	−5.38318	+	10.0731i	−0.395779	+	0.740589i
$186$	8.00385	−	4.62103i	0.586871	−	0.338830i
$187$	−2.34627	−	8.75639i	−0.171576	−	0.640330i
$188$	6.52433	−	1.74819i	0.475836	−	0.127500i
$189$	3.61093			0.262657
$190$	1.72342	+	9.59322i	0.125030	+	0.695965i
$191$	−0.439783			−0.0318216			−0.0159108	−	0.999873i	$-0.505065\pi$
$191$	−0.439783			−0.0318216			−0.0159108	+	0.999873i	$0.505065\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	2.85237	+	10.6452i	0.205318	+	0.766258i	0.989352	+	0.145540i	$0.0464921\pi$
$193$	2.85237	+	10.6452i	0.205318	+	0.766258i	−0.784034	+	0.620718i	$0.786841\pi$
$194$	−11.2315	+	6.48449i	−0.806372	+	0.465559i
$195$	0.745343	−	0.226161i	0.0533751	−	0.0161957i
$196$	−3.01942	−	5.22979i	−0.215673	−	0.373556i
$197$	1.81311	−	1.81311i	0.129179	−	0.129179i	−0.639561	−	0.768740i	$-0.720884\pi$
$197$	1.81311	−	1.81311i	0.129179	−	0.129179i	0.768740	+	0.639561i	$0.220884\pi$
$198$	1.48542	−	1.48542i	0.105564	−	0.105564i
$199$	−16.7198	+	9.65315i	−1.18523	+	0.684294i	−0.957219	−	0.289364i	$-0.906556\pi$
$199$	−16.7198	+	9.65315i	−1.18523	+	0.684294i	−0.228013	+	0.973658i	$0.573223\pi$
$200$	−0.974690	+	4.90408i	−0.0689210	+	0.346771i
$201$	−5.96862			−0.420994
$202$	2.89190	+	2.89190i	0.203474	+	0.203474i
$203$	1.43024	+	0.383233i	0.100383	+	0.0268977i
$204$	−2.15768	+	3.73722i	−0.151068	+	0.261658i
$205$	−4.07399	+	17.4785i	−0.284540	+	1.22075i
$206$	6.93219	−	12.0069i	0.482989	−	0.836561i
$207$	0.916939	+	3.42206i	0.0637317	+	0.237850i
$208$	−0.246310	+	0.246310i	−0.0170785	+	0.0170785i
$209$	−8.50811	−	3.38491i	−0.588518	−	0.234139i
$210$	−0.264810	−	8.06995i	−0.0182736	−	0.556879i
$211$	−22.0409	−	12.7253i	−1.51736	−	0.876047i	−0.999792	−	0.0204046i	$-0.993505\pi$
$211$	−22.0409	−	12.7253i	−1.51736	−	0.876047i	−0.517567	−	0.855643i	$-0.673162\pi$
$212$	12.4622	−	3.33923i	0.855906	−	0.229339i
$213$	−0.132345	+	0.493918i	−0.00906813	+	0.0338427i
$214$	−3.60223	−	2.07975i	−0.246244	−	0.142169i
$215$	−2.74553	−	4.41440i	−0.187243	−	0.301060i
$216$	−1.00000			−0.0680414
$217$	23.5979	+	23.5979i	1.60193	+	1.60193i
$218$	0.811829	−	3.02979i	0.0549840	−	0.205203i
$219$	−2.86037	−	4.95431i	−0.193286	−	0.334781i
$220$	−3.42864	−	3.21077i	−0.231159	−	0.216470i
$221$		−	1.50319i		−	0.101116i
$222$	−1.32199	+	4.93372i	−0.0887259	+	0.331129i
$223$	5.09189	+	19.0032i	0.340978	+	1.27255i	0.897241	+	0.441541i	$0.145568\pi$
$223$	5.09189	+	19.0032i	0.340978	+	1.27255i	−0.556263	+	0.831006i	$0.687765\pi$
$224$	1.80547	+	3.12716i	0.120633	+	0.208942i
$225$	2.21075	−	4.48471i	0.147383	−	0.298980i
$226$	9.01047	−	15.6066i	0.599368	−	1.03814i
$227$	−1.15211	−	1.15211i	−0.0764685	−	0.0764685i	0.667838	−	0.744307i	$-0.267220\pi$
$227$	−1.15211	−	1.15211i	−0.0764685	−	0.0764685i	−0.744307	+	0.667838i	$0.767220\pi$
$228$	1.72450	+	4.00326i	0.114208	+	0.265122i
$229$		−	16.4589i		−	1.08763i	−0.839204	−	0.543816i	$-0.816979\pi$
$229$		−	16.4589i		−	1.08763i	0.839204	−	0.543816i	$-0.183021\pi$
$230$	7.58060	−	2.30019i	0.499850	−	0.151670i
$231$	6.56921	+	3.79274i	0.432223	+	0.249544i
$232$	−0.396087	−	0.106131i	−0.0260044	−	0.00696785i
$233$	−0.758821	+	0.203326i	−0.0497120	+	0.0133203i	−0.283589	−	0.958946i	$-0.591525\pi$
$233$	−0.758821	+	0.203326i	−0.0497120	+	0.0133203i	0.233877	+	0.972266i	$0.424859\pi$
$234$	0.301667	−	0.174167i	0.0197206	−	0.0113857i
$235$	0.495344	+	15.0954i	0.0323127	+	0.984712i
$236$		−	13.1084i		−	0.853287i
$237$	−9.64378	−	2.58404i	−0.626431	−	0.167852i
$238$	−15.0515	−	4.03305i	−0.975647	−	0.261424i
$239$			29.1615i			1.88630i	0.332363	+	0.943152i	$0.392154\pi$
$239$			29.1615i			1.88630i	−0.332363	+	0.943152i	$0.607846\pi$
$240$	0.0733356	+	2.23487i	0.00473379	+	0.144260i
$241$	9.82040	−	5.66981i	0.632588	−	0.365225i	−0.149166	−	0.988812i	$-0.547659\pi$
$241$	9.82040	−	5.66981i	0.632588	−	0.365225i	0.781753	+	0.623588i	$0.214326\pi$
$242$	−6.36263	+	1.70486i	−0.409005	+	0.109593i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	0.296845	+	0.171384i	0.0190036	+	0.0109717i
$245$	12.9215	−	3.92079i	0.825525	−	0.250490i
$246$			8.02616i			0.511729i
$247$	−1.21746	−	0.907299i	−0.0774652	−	0.0577301i
$248$	−6.53512	−	6.53512i	−0.414980	−	0.414980i
$249$	3.31784	−	5.74667i	0.210260	−	0.364181i
$250$	−10.1848	−	4.61183i	−0.644146	−	0.291678i
$251$	1.79991	+	3.11753i	0.113609	+	0.196777i	0.917223	−	0.398374i	$-0.130425\pi$
$251$	1.79991	+	3.11753i	0.113609	+	0.196777i	−0.803614	+	0.595151i	$0.797092\pi$
$252$	−0.934578	−	3.48789i	−0.0588729	−	0.219717i
$253$	−1.92621	+	7.18871i	−0.121100	+	0.451951i
$254$		−	3.69809i		−	0.232039i
$255$	−7.04330	−	6.59575i	−0.441069	−	0.413042i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.44719	+	16.5971i	−0.277408	+	1.03530i	0.676803	+	0.736164i	$0.263365\pi$
$257$	−4.44719	+	16.5971i	−0.277408	+	1.03530i	−0.954211	+	0.299136i	$0.903302\pi$
$258$	−1.64392	−	1.64392i	−0.102346	−	0.102346i
$259$	−18.4438			−1.14604
$260$	−0.411363	−	0.661412i	−0.0255117	−	0.0410190i
$261$	0.355122	+	0.205030i	0.0219815	+	0.0126910i
$262$	3.61013	−	13.4732i	0.223034	−	0.832376i
$263$	28.9353	−	7.75319i	1.78423	−	0.478082i	0.792882	−	0.609375i	$-0.208579\pi$
$263$	28.9353	−	7.75319i	1.78423	−	0.478082i	0.991344	+	0.131293i	$0.0419128\pi$
$264$	−1.81926	−	1.05035i	−0.111967	−	0.0646445i
$265$	0.946161	+	28.8338i	0.0581222	+	1.77124i
$266$	−12.3513	+	9.75623i	−0.757305	+	0.598193i
$267$	11.6591	−	11.6591i	0.713528	−	0.713528i
$268$	1.54479	+	5.76524i	0.0943632	+	0.352168i
$269$	0.746279	−	1.29259i	0.0455015	−	0.0788108i	−0.842378	−	0.538888i	$-0.818845\pi$
$269$	0.746279	−	1.29259i	0.0455015	−	0.0788108i	0.887879	+	0.460077i	$0.152178\pi$
$270$	0.507589	−	2.17769i	0.0308909	−	0.132530i
$271$	9.57368	−	16.5821i	0.581560	−	1.00729i	−0.413735	−	0.910397i	$-0.635776\pi$
$271$	9.57368	−	16.5821i	0.581560	−	1.00729i	0.995295	−	0.0968935i	$-0.0308906\pi$
$272$	4.16833	+	1.11690i	0.252742	+	0.0677220i
$273$	0.889408	+	0.889408i	0.0538294	+	0.0538294i
$274$	10.6060			0.640732
$275$	8.73242	−	5.83678i	0.526585	−	0.351971i
$276$	3.06814	−	1.77139i	0.184680	−	0.106625i
$277$	−8.61938	+	8.61938i	−0.517888	+	0.517888i	−0.916932	−	0.399044i	$-0.869342\pi$
$277$	−8.61938	+	8.61938i	−0.517888	+	0.517888i	0.399044	+	0.916932i	$0.369342\pi$
$278$	−2.99373	+	2.99373i	−0.179552	+	0.179552i
$279$	4.62103	+	8.00385i	0.276654	+	0.479178i
$280$	−7.72643	+	2.34444i	−0.461743	+	0.140107i
$281$	10.3774	−	5.99142i	0.619066	−	0.357418i	−0.157439	−	0.987529i	$-0.550324\pi$
$281$	10.3774	−	5.99142i	0.619066	−	0.357418i	0.776505	+	0.630111i	$0.216990\pi$
$282$	1.74819	+	6.52433i	0.104103	+	0.388518i
$283$	21.4520	−	5.74805i	1.27519	−	0.341686i	0.443173	−	0.896436i	$-0.353853\pi$
$283$	21.4520	−	5.74805i	1.27519	−	0.341686i	0.832017	+	0.554750i	$0.187186\pi$
$284$	0.511342			0.0303425
$285$	−9.59322	+	1.72342i	−0.568253	+	0.102087i
$286$	0.731745			0.0432690
$287$	−27.9944	+	7.50107i	−1.65246	+	0.442774i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−1.40504	+	0.811201i	−0.0826495	+	0.0477177i
$290$	0.432171	−	0.808685i	0.0253779	−	0.0474876i
$291$	−6.48449	−	11.2315i	−0.380127	−	0.658400i
$292$	−4.04518	+	4.04518i	−0.236726	+	0.236726i
$293$	8.79369	−	8.79369i	0.513733	−	0.513733i	−0.401935	−	0.915668i	$-0.631662\pi$
$293$	8.79369	−	8.79369i	0.513733	−	0.513733i	0.915668	+	0.401935i	$0.131662\pi$
$294$	5.22979	−	3.01942i	0.305007	−	0.176096i
$295$	28.5462	+	6.65370i	1.66202	+	0.387394i
$296$	5.10776			0.296883
$297$	1.48542	+	1.48542i	0.0861926	+	0.0861926i
$298$	12.3141	+	3.29955i	0.713335	+	0.191138i
$299$	−0.617036	+	1.06874i	−0.0356841	+	0.0618067i
$300$	−4.90408	−	0.974690i	−0.283137	−	0.0562738i
$301$	4.19746	−	7.27021i	0.241938	−	0.419048i
$302$	−0.806745	−	3.01081i	−0.0464230	−	0.173253i
$303$	−2.89190	+	2.89190i	−0.166136	+	0.166136i
$304$	3.42052	−	2.70186i	0.196180	−	0.154962i
$305$	−0.523896	+	0.559445i	−0.0299982	+	0.0320338i
$306$	−3.73722	−	2.15768i	−0.213643	−	0.123347i
$307$	−2.42695	+	0.650298i	−0.138513	+	0.0371145i	−0.327409	−	0.944883i	$-0.606176\pi$
$307$	−2.42695	+	0.650298i	−0.138513	+	0.0371145i	0.188896	+	0.981997i	$0.439509\pi$
$308$	1.96327	−	7.32701i	0.111867	−	0.417495i
$309$	12.0069	+	6.93219i	0.683049	+	0.394359i
$310$	17.5486	−	10.9143i	0.996696	−	0.619893i
$311$	−25.2295			−1.43064			−0.715318	−	0.698799i	$-0.753718\pi$
$311$	−25.2295			−1.43064			−0.715318	+	0.698799i	$0.753718\pi$
$312$	−0.246310	−	0.246310i	−0.0139445	−	0.0139445i
$313$	−3.76378	+	14.0466i	−0.212742	+	0.793962i	0.774208	+	0.632931i	$0.218149\pi$
$313$	−3.76378	+	14.0466i	−0.212742	+	0.793962i	−0.986949	+	0.161031i	$0.948518\pi$
$314$	6.73479	+	11.6650i	0.380066	+	0.658293i
$315$	8.06995	−	0.264810i	0.454690	−	0.0149204i
$316$			9.98398i			0.561643i
$317$	−7.12134	+	26.5772i	−0.399974	+	1.49272i	0.413165	+	0.910656i	$0.364423\pi$
$317$	−7.12134	+	26.5772i	−0.399974	+	1.49272i	−0.813140	+	0.582069i	$0.802244\pi$
$318$	3.33923	+	12.4622i	0.187255	+	0.698844i
$319$	0.430705	+	0.746003i	0.0241149	+	0.0417682i
$320$	2.13973	−	0.649262i	0.119615	−	0.0362949i
$321$	2.07975	−	3.60223i	0.116080	−	0.201057i
$322$	9.04583	+	9.04583i	0.504105	+	0.504105i
$323$	−2.19295	+	18.6820i	−0.122019	+	1.03949i
$324$		−	1.00000i		−	0.0555556i
$325$	1.64916	−	0.560099i	0.0914787	−	0.0310687i
$326$	−14.6106	−	8.43546i	−0.809209	−	0.467197i
$327$	3.02979	+	0.811829i	0.167548	+	0.0448943i
$328$	7.75267	−	2.07732i	0.428070	−	0.114701i
$329$	−21.1223	+	12.1950i	−1.16451	+	0.672332i
$330$	3.21077	−	3.42864i	0.176747	−	0.188740i
$331$			11.2451i			0.618089i	0.951048	+	0.309044i	$0.100009\pi$
$331$			11.2451i			0.618089i	−0.951048	+	0.309044i	$0.899991\pi$
$332$	−6.40958	−	1.71744i	−0.351771	−	0.0942569i
$333$	−4.93372	−	1.32199i	−0.270366	−	0.0724444i
$334$			14.6281i			0.800415i
$335$	−13.3391	+	0.437712i	−0.728790	+	0.0239148i
$336$	−3.12716	+	1.80547i	−0.170601	+	0.0984963i
$337$	20.3573	−	5.45473i	1.10893	−	0.297138i	0.342537	−	0.939504i	$-0.388714\pi$
$337$	20.3573	−	5.45473i	1.10893	−	0.297138i	0.766398	+	0.642366i	$0.222047\pi$
$338$	−12.4398	−	3.33324i	−0.676638	−	0.181305i
$339$	15.6066	+	9.01047i	0.847634	+	0.489382i
$340$	−4.54806	+	8.51041i	−0.246653	+	0.461542i
$341$			19.4147i			1.05137i
$342$	−4.00326	+	1.72450i	−0.216472	+	0.0932502i
$343$	−2.45415	−	2.45415i	−0.132511	−	0.132511i
$344$	−1.16243	+	2.01339i	−0.0626741	+	0.108555i
$345$	2.30019	+	7.58060i	0.123838	+	0.408126i
$346$	1.92490	+	3.33402i	0.103483	+	0.179238i
$347$	−5.01349	−	18.7106i	−0.269138	−	1.00444i	−0.959669	−	0.281134i	$-0.909290\pi$
$347$	−5.01349	−	18.7106i	−0.269138	−	1.00444i	0.690531	−	0.723303i	$-0.257377\pi$
$348$	0.106131	−	0.396087i	0.00568923	−	0.0212325i
$349$		−	14.9066i		−	0.797930i	−0.916966	−	0.398965i	$-0.869369\pi$
$349$		−	14.9066i		−	0.797930i	0.916966	−	0.398965i	$-0.130631\pi$
$350$	−1.18363	−	18.0158i	−0.0632677	−	0.962986i
$351$	0.174167	+	0.301667i	0.00929636	+	0.0161018i
$352$	−0.543700	+	2.02912i	−0.0289793	+	0.108152i
$353$	−7.95535	−	7.95535i	−0.423421	−	0.423421i	0.462959	−	0.886380i	$-0.346788\pi$
$353$	−7.95535	−	7.95535i	−0.423421	−	0.423421i	−0.886380	+	0.462959i	$0.846788\pi$
$354$	13.1084			0.696706
$355$	−0.259551	+	1.11355i	−0.0137756	+	0.0591009i
$356$	−14.2795	−	8.24426i	−0.756811	−	0.436945i
$357$	4.03305	−	15.0515i	0.213452	−	0.796612i
$358$	−16.4106	+	4.39719i	−0.867325	+	0.232399i
$359$	17.9192	+	10.3457i	0.945740	+	0.546023i	0.891755	−	0.452518i	$-0.149474\pi$
$359$	17.9192	+	10.3457i	0.945740	+	0.546023i	0.0539852	+	0.998542i	$0.482808\pi$
$360$	−2.23487	+	0.0733356i	−0.117788	+	0.00386513i
$361$	13.8072	+	13.0522i	0.726697	+	0.686958i
$362$	3.11071	−	3.11071i	0.163495	−	0.163495i
$363$	−1.70486	−	6.36263i	−0.0894820	−	0.333951i
$364$	0.628907	−	1.08930i	0.0329637	−	0.0570947i
$365$	−6.75587	−	10.8624i	−0.353618	−	0.568566i
$366$	−0.171384	+	0.296845i	−0.00895836	+	0.0155163i
$367$	10.6485	+	2.85326i	0.555847	+	0.148939i	0.525798	−	0.850610i	$-0.323767\pi$
$367$	10.6485	+	2.85326i	0.555847	+	0.148939i	0.0300493	+	0.999548i	$0.490434\pi$
$368$	−2.50512	−	2.50512i	−0.130589	−	0.130589i
$369$	−8.02616			−0.417825
$370$	−2.59264	+	11.1231i	−0.134785	+	0.578265i
$371$	−40.3460	+	23.2938i	−2.09466	+	1.20935i
$372$	6.53512	−	6.53512i	0.338830	−	0.338830i
$373$	7.47821	−	7.47821i	0.387207	−	0.387207i	−0.486483	−	0.873690i	$-0.661721\pi$
$373$	7.47821	−	7.47821i	0.387207	−	0.387207i	0.873690	+	0.486483i	$0.161721\pi$
$374$	−4.53264	−	7.85076i	−0.234377	−	0.405953i
$375$	4.61183	−	10.1848i	0.238154	−	0.525943i
$376$	5.84955	−	3.37724i	0.301668	−	0.174168i
$377$	0.0369692	+	0.137971i	0.00190401	+	0.00710586i
$378$	3.48789	−	0.934578i	0.179398	−	0.0480695i
$379$	−30.7818			−1.58116			−0.790578	−	0.612362i	$-0.790220\pi$
$379$	−30.7818			−1.58116			−0.790578	+	0.612362i	$0.790220\pi$
$380$	4.14760	+	8.82028i	0.212768	+	0.452471i
$381$	3.69809			0.189459
$382$	−0.424798	+	0.113824i	−0.0217346	+	0.00582376i
$383$	0.627763	+	2.34284i	0.0320772	+	0.119714i	0.980108	−	0.198465i	$-0.0635955\pi$
$383$	0.627763	+	2.34284i	0.0320772	+	0.119714i	−0.948031	+	0.318178i	$0.896929\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	14.9594	+	7.99450i	0.762404	+	0.407437i
$386$	5.51036	+	9.54423i	0.280470	+	0.485788i
$387$	1.64392	−	1.64392i	0.0835654	−	0.0835654i
$388$	−9.17045	+	9.17045i	−0.465559	+	0.465559i
$389$	22.5537	−	13.0214i	1.14352	−	0.660211i	0.196220	−	0.980560i	$-0.437133\pi$
$389$	22.5537	−	13.0214i	1.14352	−	0.660211i	0.947300	+	0.320349i	$0.103800\pi$
$390$	0.661412	−	0.411363i	0.0334919	−	0.0208302i
$391$	15.2884			0.773167
$392$	−4.27010	−	4.27010i	−0.215673	−	0.215673i
$393$	13.4732	+	3.61013i	0.679632	+	0.182107i
$394$	1.28206	−	2.22059i	0.0645893	−	0.111872i
$395$	−21.7421	−	5.06776i	−1.09396	−	0.254987i
$396$	1.05035	−	1.81926i	0.0527820	−	0.0914211i
$397$	−7.54265	−	28.1496i	−0.378555	−	1.41279i	−0.848081	−	0.529867i	$-0.822242\pi$
$397$	−7.54265	−	28.1496i	−0.378555	−	1.41279i	0.469526	−	0.882919i	$-0.344425\pi$
$398$	−13.6516	+	13.6516i	−0.684294	+	0.684294i
$399$	−9.75623	−	12.3513i	−0.488422	−	0.618337i
$400$	0.327790	+	4.98924i	0.0163895	+	0.249462i
$401$	−25.6507	−	14.8094i	−1.28094	−	0.739548i	−0.303916	−	0.952699i	$-0.598294\pi$
$401$	−25.6507	−	14.8094i	−1.28094	−	0.739548i	−0.977019	+	0.213151i	$0.931627\pi$
$402$	−5.76524	+	1.54479i	−0.287544	+	0.0770472i
$403$	−0.833223	+	3.10963i	−0.0415058	+	0.154902i
$404$	3.54184	+	2.04489i	0.176213	+	0.101737i
$405$	2.17769	+	0.507589i	0.108211	+	0.0252223i
$406$	1.48070			0.0734858
$407$	−7.58715	−	7.58715i	−0.376081	−	0.376081i
$408$	−1.11690	+	4.16833i	−0.0552948	+	0.206363i
$409$	13.1467	+	22.7708i	0.650062	+	1.12594i	0.983107	+	0.183030i	$0.0585906\pi$
$409$	13.1467	+	22.7708i	0.650062	+	1.12594i	−0.333045	+	0.942911i	$0.608076\pi$
$410$	0.588603	+	17.9374i	0.0290690	+	0.885864i
$411$			10.6060i			0.523155i
$412$	3.58837	−	13.3920i	0.176786	−	0.659775i
$413$	12.2509	+	45.7209i	0.602826	+	2.24978i
$414$	1.77139	+	3.06814i	0.0870591	+	0.150791i
$415$	6.99350	−	13.0864i	0.343297	−	0.642384i
$416$	−0.174167	+	0.301667i	−0.00853926	+	0.0147904i
$417$	−2.99373	−	2.99373i	−0.146604	−	0.146604i
$418$	−9.09428	−	1.06751i	−0.444816	−	0.0522138i
$419$		−	17.8031i		−	0.869740i	−0.900493	−	0.434870i	$-0.856794\pi$
$419$		−	17.8031i		−	0.869740i	0.900493	−	0.434870i	$-0.143206\pi$
$420$	−2.34444	−	7.72643i	−0.114397	−	0.377011i
$421$	30.6780	+	17.7119i	1.49515	+	0.863226i	0.999984	−	0.00557118i	$-0.00177337\pi$
$421$	30.6780	+	17.7119i	1.49515	+	0.863226i	0.495167	+	0.868798i	$0.335107\pi$
$422$	−24.5834	−	6.58711i	−1.19670	−	0.320656i
$423$	−6.52433	+	1.74819i	−0.317224	+	0.0849998i
$424$	11.1733	−	6.45090i	0.542622	−	0.313283i
$425$	−16.2245	−	14.2241i	−0.787006	−	0.689969i
$426$			0.511342i			0.0247746i
$427$	−1.19554	−	0.320343i	−0.0578560	−	0.0155025i
$428$	−4.01777	−	1.07656i	−0.194206	−	0.0520374i
$429$			0.731745i			0.0353290i
$430$	−3.79451	−	3.55339i	−0.182987	−	0.171360i
$431$	−13.0045	+	7.50814i	−0.626404	+	0.361655i	−0.779358	−	0.626579i	$-0.784455\pi$
$431$	−13.0045	+	7.50814i	−0.626404	+	0.361655i	0.152954	+	0.988233i	$0.451121\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	−27.3438	−	7.32676i	−1.31406	−	0.352101i	−0.467311	−	0.884093i	$-0.654777\pi$
$433$	−27.3438	−	7.32676i	−1.31406	−	0.352101i	−0.846750	+	0.531992i	$0.821444\pi$
$434$	28.9014	+	16.6862i	1.38731	+	0.800964i
$435$	0.808685	+	0.432171i	0.0387735	+	0.0207210i
$436$		−	3.13667i		−	0.150219i
$437$	9.22780	−	12.3823i	0.441425	−	0.592327i
$438$	−4.04518	−	4.04518i	−0.193286	−	0.193286i
$439$	15.4901	−	26.8296i	0.739301	−	1.28051i	−0.213510	−	0.976941i	$-0.568489\pi$
$439$	15.4901	−	26.8296i	0.739301	−	1.28051i	0.952811	−	0.303566i	$-0.0981772\pi$
$440$	−4.14282	−	2.21397i	−0.197501	−	0.105547i
$441$	3.01942	+	5.22979i	0.143782	+	0.249038i
$442$	−0.389055	−	1.45197i	−0.0185054	−	0.0690633i
$443$	1.08544	−	4.05091i	0.0515707	−	0.192464i	−0.935335	−	0.353764i	$-0.884902\pi$
$443$	1.08544	−	4.05091i	0.0515707	−	0.192464i	0.986906	+	0.161299i	$0.0515684\pi$
$444$			5.10776i			0.242404i
$445$	25.2016	−	26.9116i	1.19467	−	1.27573i
$446$	9.83677	+	17.0378i	0.465785	+	0.806763i
$447$	−3.29955	+	12.3141i	−0.156063	+	0.582436i
$448$	2.55332	+	2.55332i	0.120633	+	0.120633i
$449$	−1.06168			−0.0501037			−0.0250519	−	0.999686i	$-0.507975\pi$
$449$	−1.06168			−0.0501037			−0.0250519	+	0.999686i	$0.507975\pi$
$450$	0.974690	−	4.90408i	0.0459473	−	0.231180i
$451$	−14.6016	−	8.43026i	−0.687564	−	0.396965i
$452$	4.66416	−	17.4069i	0.219384	−	0.818752i
$453$	3.01081	−	0.806745i	0.141460	−	0.0379042i
$454$	−1.41105	−	0.814668i	−0.0662237	−	0.0382343i
$455$	2.05293	+	1.92248i	0.0962430	+	0.0901274i
$456$	2.70186	+	3.42052i	0.126526	+	0.160181i
$457$	−27.1293	+	27.1293i	−1.26905	+	1.26905i	−0.322477	+	0.946577i	$0.604515\pi$
$457$	−27.1293	+	27.1293i	−1.26905	+	1.26905i	−0.946577	+	0.322477i	$0.895485\pi$
$458$	−4.25987	−	15.8980i	−0.199051	−	0.742867i
$459$	2.15768	−	3.73722i	0.100712	−	0.174438i
$460$	6.72697	−	4.18382i	0.313646	−	0.195072i
$461$	−2.05885	+	3.56603i	−0.0958900	+	0.166086i	−0.909980	−	0.414653i	$-0.863903\pi$
$461$	−2.05885	+	3.56603i	−0.0958900	+	0.166086i	0.814090	+	0.580739i	$0.197236\pi$
$462$	7.32701	+	1.96327i	0.340883	+	0.0913394i
$463$	1.64021	+	1.64021i	0.0762270	+	0.0762270i	0.744192	−	0.667965i	$-0.232835\pi$
$463$	1.64021	+	1.64021i	0.0762270	+	0.0762270i	−0.667965	+	0.744192i	$0.732835\pi$
$464$	−0.410059			−0.0190365
$465$	10.9143	+	17.5486i	0.506140	+	0.813799i
$466$	−0.680341	+	0.392795i	−0.0315162	+	0.0181959i
$467$	−26.3268	+	26.3268i	−1.21826	+	1.21826i	−0.250020	+	0.968241i	$0.580437\pi$
$467$	−26.3268	+	26.3268i	−1.21826	+	1.21826i	−0.968241	+	0.250020i	$0.919563\pi$
$468$	0.246310	−	0.246310i	0.0113857	−	0.0113857i
$469$	−10.7761	−	18.6648i	−0.497596	−	0.861861i
$470$	4.38543	+	14.4528i	0.202285	+	0.666657i
$471$	−11.6650	+	6.73479i	−0.537494	+	0.310323i
$472$	−3.39272	−	12.6618i	−0.156162	−	0.582806i
$473$	4.71741	−	1.26403i	0.216907	−	0.0581200i
$474$	−9.98398			−0.458579
$475$	−21.3132	+	4.55514i	−0.977915	+	0.209004i
$476$	−15.5825			−0.714223
$477$	−12.4622	+	3.33923i	−0.570604	+	0.152893i
$478$	7.54756	+	28.1679i	0.345217	+	1.28837i
$479$	12.1166	−	6.99550i	0.553620	−	0.319633i	−0.196961	−	0.980411i	$-0.563107\pi$
$479$	12.1166	−	6.99550i	0.553620	−	0.319633i	0.750581	+	0.660779i	$0.229774\pi$
$480$	0.649262	+	2.13973i	0.0296346	+	0.0976650i
$481$	−0.889605	−	1.54084i	−0.0405625	−	0.0702563i
$482$	8.01832	−	8.01832i	0.365225	−	0.365225i
$483$	−9.04583	+	9.04583i	−0.411600	+	0.411600i
$484$	−5.70457	+	3.29354i	−0.259299	+	0.149706i
$485$	−15.3156	−	24.6253i	−0.695447	−	1.11818i
$486$	1.00000			0.0453609
$487$	4.19344	+	4.19344i	0.190023	+	0.190023i	0.795706	−	0.605683i	$-0.207100\pi$
$487$	4.19344	+	4.19344i	0.190023	+	0.190023i	−0.605683	+	0.795706i	$0.707100\pi$
$488$	0.331088	+	0.0887147i	0.0149876	+	0.00401592i
$489$	8.43546	−	14.6106i	0.381465	−	0.660716i
$490$	11.4664	−	7.13153i	0.518001	−	0.322169i
$491$	7.03900	−	12.1919i	0.317666	−	0.550213i	−0.662335	−	0.749208i	$-0.730434\pi$
$491$	7.03900	−	12.1919i	0.317666	−	0.550213i	0.980001	+	0.198995i	$0.0637677\pi$
$492$	2.07732	+	7.75267i	0.0936529	+	0.349517i
$493$	1.25127	−	1.25127i	0.0563542	−	0.0563542i
$494$	−1.41080	−	0.561282i	−0.0634750	−	0.0252533i
$495$	3.42864	+	3.21077i	0.154106	+	0.144313i
$496$	−8.00385	−	4.62103i	−0.359384	−	0.207490i
$497$	−1.78351	+	0.477889i	−0.0800012	+	0.0214362i
$498$	1.71744	−	6.40958i	0.0769604	−	0.287220i
$499$	4.70862	+	2.71852i	0.210787	+	0.121698i	0.601677	−	0.798739i	$-0.294499\pi$
$499$	4.70862	+	2.71852i	0.210787	+	0.121698i	−0.390890	+	0.920437i	$0.627833\pi$
$500$	−11.0314	−	1.81866i	−0.493341	−	0.0813328i
$501$	−14.6281			−0.653536
$502$	2.54545	+	2.54545i	0.113609	+	0.113609i
$503$	3.85177	−	14.3750i	0.171742	−	0.640950i	−0.825342	−	0.564634i	$-0.809017\pi$
$503$	3.85177	−	14.3750i	0.171742	−	0.640950i	0.997084	−	0.0763163i	$-0.0243159\pi$
$504$	−1.80547	−	3.12716i	−0.0804219	−	0.139295i
$505$	−6.25094	+	6.67510i	−0.278163	+	0.297038i
$506$			7.44230i			0.330851i
$507$	3.33324	−	12.4398i	0.148035	−	0.552472i
$508$	−0.957135	−	3.57208i	−0.0424660	−	0.158485i
$509$	−8.43101	−	14.6029i	−0.373698	−	0.647264i	0.616433	−	0.787407i	$-0.288577\pi$
$509$	−8.43101	−	14.6029i	−0.373698	−	0.647264i	−0.990131	+	0.140143i	$0.955244\pi$
$510$	−8.51041	−	4.54806i	−0.376847	−	0.201392i
$511$	10.3286	−	17.8897i	0.456911	−	0.791393i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.72450	−	4.00326i	−0.0761385	−	0.176748i
$514$			17.1826i			0.757892i
$515$	27.3422	+	14.6120i	1.20484	+	0.643881i
$516$	−2.01339	−	1.16243i	−0.0886345	−	0.0511731i
$517$	−13.7056	−	3.67241i	−0.602773	−	0.161513i
$518$	−17.8153	+	4.77360i	−0.782761	+	0.209740i
$519$	−3.33402	+	1.92490i	−0.146347	+	0.0844935i
$520$	−0.568532	−	0.532406i	−0.0249318	−	0.0233475i
$521$		−	4.21584i		−	0.184699i	−0.995727	−	0.0923497i	$-0.970562\pi$
$521$		−	4.21584i		−	0.184699i	0.995727	−	0.0923497i	$-0.0294378\pi$
$522$	0.396087	+	0.106131i	0.0173363	+	0.00464524i
$523$	−24.1023	−	6.45819i	−1.05392	−	0.282397i	−0.310049	−	0.950721i	$-0.600346\pi$
$523$	−24.1023	−	6.45819i	−1.05392	−	0.282397i	−0.743871	+	0.668324i	$0.767012\pi$
$524$		−	13.9485i		−	0.609341i
$525$	18.0158	−	1.18363i	0.786275	−	0.0516578i
$526$	25.9427	−	14.9780i	1.13115	−	0.653072i
$527$	38.5239	−	10.3224i	1.67813	−	0.449653i
$528$	−2.02912	−	0.543700i	−0.0883060	−	0.0236615i
$529$	9.04885	+	5.22436i	0.393428	+	0.227146i
$530$	8.37665	+	27.6064i	0.363858	+	1.19915i
$531$			13.1084i			0.568858i
$532$	−9.40532	+	12.6205i	−0.407772	+	0.547170i
$533$	−1.97692	−	1.97692i	−0.0856300	−	0.0856300i
$534$	8.24426	−	14.2795i	0.356764	−	0.617933i
$535$	4.38379	−	8.20303i	0.189528	−	0.354648i
$536$	2.98431	+	5.16897i	0.128902	+	0.223266i
$537$	−4.39719	−	16.4106i	−0.189753	−	0.708168i
$538$	0.386303	−	1.44170i	0.0166547	−	0.0621561i
$539$			12.6858i			0.546415i
$540$	−0.0733356	−	2.23487i	−0.00315586	−	0.0961733i
$541$	−9.74261	−	16.8747i	−0.418868	−	0.725500i	0.576958	−	0.816774i	$-0.304240\pi$
$541$	−9.74261	−	16.8747i	−0.418868	−	0.725500i	−0.995826	+	0.0912737i	$0.970906\pi$
$542$	4.95570	−	18.4949i	0.212866	−	0.794425i
$543$	3.11071	+	3.11071i	0.133493	+	0.133493i
$544$	4.31537			0.185020
$545$	6.83070	+	1.59214i	0.292595	+	0.0681997i
$546$	1.08930	+	0.628907i	0.0466177	+	0.0269147i
$547$	8.55327	−	31.9212i	0.365711	−	1.36485i	−0.500742	−	0.865596i	$-0.666940\pi$
$547$	8.55327	−	31.9212i	0.365711	−	1.36485i	0.866454	−	0.499257i	$-0.166394\pi$
$548$	10.2446	−	2.74503i	0.437628	−	0.117262i
$549$	−0.296845	−	0.171384i	−0.0126690	−	0.00731447i
$550$	6.92420	−	7.89801i	0.295249	−	0.336772i
$551$	−0.258180	−	1.76866i	−0.0109989	−	0.0753476i
$552$	2.50512	−	2.50512i	0.106625	−	0.106625i
$553$	−9.33081	−	34.8231i	−0.396786	−	1.48083i
$554$	−6.09482	+	10.5565i	−0.258944	+	0.448505i
$555$	−11.1231	−	2.59264i	−0.472151	−	0.110052i
$556$	−2.11689	+	3.66655i	−0.0897759	+	0.155496i
$557$	−4.92592	−	1.31990i	−0.208718	−	0.0559258i	0.152945	−	0.988235i	$-0.451124\pi$
$557$	−4.92592	−	1.31990i	−0.208718	−	0.0559258i	−0.361663	+	0.932309i	$0.617791\pi$
$558$	6.53512	+	6.53512i	0.276654	+	0.276654i
$559$	0.809830			0.0342521
$560$	−6.85638	+	4.26431i	−0.289735	+	0.180200i
$561$	7.85076	−	4.53264i	0.331459	−	0.191368i
$562$	8.47315	−	8.47315i	0.357418	−	0.357418i
$563$	−26.6625	+	26.6625i	−1.12369	+	1.12369i	−0.132508	+	0.991182i	$0.542303\pi$
$563$	−26.6625	+	26.6625i	−1.12369	+	1.12369i	−0.991182	+	0.132508i	$0.957697\pi$
$564$	3.37724	+	5.84955i	0.142207	+	0.246311i
$565$	35.5394	+	18.9927i	1.49515	+	0.799028i
$566$	19.2334	−	11.1044i	0.808438	−	0.466752i
$567$	0.934578	+	3.48789i	0.0392486	+	0.146478i
$568$	0.493918	−	0.132345i	0.0207243	−	0.00555307i
$569$	15.1158			0.633686			0.316843	−	0.948478i	$-0.397377\pi$
$569$	15.1158			0.633686			0.316843	+	0.948478i	$0.397377\pi$
$570$	−8.82028	+	4.14760i	−0.369441	+	0.173724i
$571$	33.9088			1.41904			0.709519	−	0.704686i	$-0.248912\pi$
$571$	33.9088			1.41904			0.709519	+	0.704686i	$0.248912\pi$
$572$	0.706812	−	0.189390i	0.0295533	−	0.00791878i
$573$	−0.113824	−	0.424798i	−0.00475508	−	0.0177462i
$574$	−25.0991	+	14.4910i	−1.04762	+	0.604841i
$575$	5.69655	+	16.7729i	0.237563	+	0.699480i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	27.6664	−	27.6664i	1.15177	−	1.15177i	0.165569	−	0.986198i	$-0.447054\pi$
$577$	27.6664	−	27.6664i	1.15177	−	1.15177i	0.986198	−	0.165569i	$-0.0529460\pi$
$578$	−1.14721	+	1.14721i	−0.0477177	+	0.0477177i
$579$	−9.54423	+	5.51036i	−0.396644	+	0.229003i
$580$	0.208142	−	0.892984i	0.00864261	−	0.0370791i
$581$	23.9610			0.994071
$582$	−9.17045	−	9.17045i	−0.380127	−	0.380127i
$583$	−26.1792	−	7.01471i	−1.08423	−	0.290520i
$584$	−2.86037	+	4.95431i	−0.118363	+	0.205011i
$585$	0.411363	+	0.661412i	0.0170078	+	0.0273460i
$586$	6.21808	−	10.7700i	0.256866	−	0.444906i
$587$	−6.40696	−	23.9111i	−0.264443	−	0.986916i	−0.962590	−	0.270962i	$-0.912658\pi$
$587$	−6.40696	−	23.9111i	−0.264443	−	0.986916i	0.698147	−	0.715955i	$-0.254008\pi$
$588$	4.27010	−	4.27010i	0.176096	−	0.176096i
$589$	14.8920	−	37.4316i	0.613614	−	1.54234i
$590$	29.2956	−	0.961316i	1.20608	−	0.0395768i
$591$	2.22059	+	1.28206i	0.0913430	+	0.0527369i
$592$	4.93372	−	1.32199i	0.202775	−	0.0543333i
$593$	8.41381	−	31.4008i	0.345514	−	1.28947i	−0.546497	−	0.837461i	$-0.684039\pi$
$593$	8.41381	−	31.4008i	0.345514	−	1.28947i	0.892011	−	0.452014i	$-0.149294\pi$
$594$	1.81926	+	1.05035i	0.0746450	+	0.0430963i
$595$	7.90951	−	33.9339i	0.324258	−	1.39116i
$596$	12.7485			0.522197
$597$	−13.6516	−	13.6516i	−0.558724	−	0.558724i
$598$	−0.319402	+	1.19202i	−0.0130613	+	0.0487454i
$599$	−12.8343	−	22.2297i	−0.524396	−	0.908281i	−0.999597	−	0.0284033i	$-0.990958\pi$
$599$	−12.8343	−	22.2297i	−0.524396	−	0.908281i	0.475200	−	0.879878i	$-0.342376\pi$
$600$	−4.98924	+	0.327790i	−0.203685	+	0.0133820i
$601$			19.9085i			0.812087i	0.913854	+	0.406043i	$0.133092\pi$
$601$			19.9085i			0.812087i	−0.913854	+	0.406043i	$0.866908\pi$
$602$	2.17276	−	8.10887i	0.0885553	−	0.330493i
$603$	−1.54479	−	5.76524i	−0.0629088	−	0.234779i
$604$	−1.55851	−	2.69942i	−0.0634149	−	0.109838i
$605$	−4.27674	−	14.0946i	−0.173874	−	0.573026i
$606$	−2.04489	+	3.54184i	−0.0830678	+	0.143878i
$607$	9.82532	+	9.82532i	0.398797	+	0.398797i	0.877809	−	0.479011i	$-0.159005\pi$
$607$	9.82532	+	9.82532i	0.398797	+	0.398797i	−0.479011	+	0.877809i	$0.659005\pi$
$608$	2.60468	−	3.49509i	0.105634	−	0.141745i
$609$			1.48070i			0.0600009i
$610$	−0.361250	+	0.675977i	−0.0146266	+	0.0273695i
$611$	−2.03760	−	1.17641i	−0.0824325	−	0.0475925i
$612$	−4.16833	−	1.11690i	−0.168495	−	0.0451480i
$613$	−20.6147	+	5.52370i	−0.832621	+	0.223100i	−0.649857	−	0.760057i	$-0.725171\pi$
$613$	−20.6147	+	5.52370i	−0.832621	+	0.223100i	−0.182764	+	0.983157i	$0.558504\pi$
$614$	−2.17594	+	1.25628i	−0.0878138	+	0.0506993i
$615$	−17.9374	+	0.588603i	−0.723305	+	0.0237348i
$616$		−	7.58547i		−	0.305627i
$617$	−23.4472	−	6.28265i	−0.943947	−	0.252930i	−0.246155	−	0.969230i	$-0.579167\pi$
$617$	−23.4472	−	6.28265i	−0.943947	−	0.252930i	−0.697792	+	0.716301i	$0.745834\pi$
$618$	13.3920	+	3.58837i	0.538704	+	0.144345i
$619$		−	16.3404i		−	0.656777i	−0.944543	−	0.328389i	$-0.893494\pi$
$619$		−	16.3404i		−	0.656777i	0.944543	−	0.328389i	$-0.106506\pi$
$620$	14.1258	−	15.0844i	0.567308	−	0.605803i
$621$	−3.06814	+	1.77139i	−0.123120	+	0.0710834i
$622$	−24.3699	+	6.52988i	−0.977142	+	0.261824i
$623$	57.5102	+	15.4098i	2.30410	+	0.617381i
$624$	−0.301667	−	0.174167i	−0.0120763	−	0.00697227i
$625$	9.55991	−	23.1000i	0.382396	−	0.923998i
$626$			14.5421i			0.581221i
$627$	1.06751	−	9.09428i	0.0426324	−	0.363191i
$628$	9.52442	+	9.52442i	0.380066	+	0.380066i
$629$	−11.0209	+	19.0888i	−0.439433	+	0.761121i
$630$	7.72643	−	2.34444i	0.307829	−	0.0934049i
$631$	2.68120	+	4.64397i	0.106737	+	0.184874i	0.914446	−	0.404707i	$-0.132626\pi$
$631$	2.68120	+	4.64397i	0.106737	+	0.184874i	−0.807710	+	0.589580i	$0.799293\pi$
$632$	2.58404	+	9.64378i	0.102788	+	0.383609i
$633$	6.58711	−	24.5834i	0.261814	−	0.977104i
$634$			27.5147i			1.09275i
$635$	8.26472	−	0.271201i	0.327976	−	0.0107623i
$636$	6.45090	+	11.1733i	0.255795	+	0.443049i
$637$	−0.544435	+	2.03186i	−0.0215713	+	0.0805053i
$638$	0.609109	+	0.609109i	0.0241149	+	0.0241149i
$639$	−0.511342			−0.0202284
$640$	1.89878	−	1.18094i	0.0750560	−	0.0466809i
$641$	0.239266	+	0.138140i	0.00945043	+	0.00545621i	0.504718	−	0.863284i	$-0.331597\pi$
$641$	0.239266	+	0.138140i	0.00945043	+	0.00545621i	−0.495267	+	0.868741i	$0.664930\pi$
$642$	1.07656	−	4.01777i	0.0424884	−	0.158569i
$643$	−26.8427	+	7.19249i	−1.05857	+	0.283644i	−0.745791	−	0.666180i	$-0.767928\pi$
$643$	−26.8427	+	7.19249i	−1.05857	+	0.283644i	−0.312784	+	0.949824i	$0.601261\pi$
$644$	11.0788	+	6.39637i	0.436567	+	0.252052i
$645$	3.55339	−	3.79451i	0.139915	−	0.149409i
$646$	2.71703	+	18.6130i	0.106900	+	0.732318i
$647$	11.9653	−	11.9653i	0.470405	−	0.470405i	−0.431641	−	0.902046i	$-0.642065\pi$
$647$	11.9653	−	11.9653i	0.470405	−	0.470405i	0.902046	+	0.431641i	$0.142065\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−13.7684	+	23.8476i	−0.540458	+	0.936101i
$650$	1.44800	−	0.967847i	0.0567952	−	0.0379621i
$651$	−16.6862	+	28.9014i	−0.653984	+	1.13273i
$652$	−16.2961	−	4.36651i	−0.638203	−	0.171006i
$653$	−25.9411	−	25.9411i	−1.01515	−	1.01515i	−0.999883	−	0.0152712i	$-0.995139\pi$
$653$	−25.9411	−	25.9411i	−1.01515	−	1.01515i	−0.0152712	−	0.999883i	$-0.504861\pi$
$654$	3.13667			0.122653
$655$	30.3755	+	7.08008i	1.18687	+	0.276642i
$656$	6.95086	−	4.01308i	0.271385	−	0.156684i
$657$	4.04518	−	4.04518i	0.157817	−	0.157817i
$658$	−17.2463	+	17.2463i	−0.672332	+	0.672332i
$659$	−7.67096	−	13.2865i	−0.298818	−	0.517568i	0.677048	−	0.735939i	$-0.263259\pi$
$659$	−7.67096	−	13.2865i	−0.298818	−	0.517568i	−0.975866	+	0.218371i	$0.929926\pi$
$660$	2.21397	−	4.14282i	0.0861787	−	0.161259i
$661$	−9.50421	+	5.48726i	−0.369671	+	0.213430i	−0.673315	−	0.739356i	$-0.735130\pi$
$661$	−9.50421	+	5.48726i	−0.369671	+	0.213430i	0.303644	+	0.952786i	$0.401797\pi$
$662$	2.91046	+	10.8620i	0.113118	+	0.422162i
$663$	1.45197	−	0.389055i	0.0563899	−	0.0151096i
$664$	−6.63569			−0.257515
$665$	−22.7096	−	26.8879i	−0.880642	−	1.04267i
$666$	−5.10776			−0.197922
$667$	−1.40325	+	0.375999i	−0.0543340	+	0.0145588i
$668$	3.78603	+	14.1297i	0.146486	+	0.546693i
$669$	−17.0378	+	9.83677i	−0.658719	+	0.380312i
$670$	−12.7712	+	3.87520i	−0.493396	+	0.149712i
$671$	−0.360025	−	0.623581i	−0.0138986	−	0.0240731i
$672$	−2.55332	+	2.55332i	−0.0984963	+	0.0984963i
$673$	21.9694	−	21.9694i	0.846858	−	0.846858i	−0.142881	−	0.989740i	$-0.545637\pi$
$673$	21.9694	−	21.9694i	0.846858	−	0.846858i	0.989740	+	0.142881i	$0.0456368\pi$
$674$	18.2519	−	10.5377i	0.703036	−	0.405898i
$675$	4.90408	+	0.974690i	0.188758	+	0.0375158i
$676$	−12.8787			−0.495333
$677$	−23.8620	−	23.8620i	−0.917091	−	0.917091i	0.0797259	−	0.996817i	$-0.474595\pi$
$677$	−23.8620	−	23.8620i	−0.917091	−	0.917091i	−0.996817	+	0.0797259i	$0.974595\pi$
$678$	17.4069	+	4.66416i	0.668508	+	0.179126i
$679$	23.4151	−	40.5561i	0.898587	−	1.55640i
$680$	−2.19043	+	9.39755i	−0.0839993	+	0.360380i
$681$	0.814668	−	1.41105i	0.0312181	−	0.0540714i
$682$	5.02491	+	18.7532i	0.192414	+	0.718097i
$683$	−23.3602	+	23.3602i	−0.893855	+	0.893855i	−0.994884	−	0.101028i	$-0.967787\pi$
$683$	−23.3602	+	23.3602i	−0.893855	+	0.893855i	0.101028	+	0.994884i	$0.467787\pi$
$684$	−3.42052	+	2.70186i	−0.130787	+	0.103308i
$685$	0.777797	+	23.7030i	0.0297181	+	0.905644i
$686$	−3.00570	−	1.73534i	−0.114758	−	0.0662557i
$687$	15.8980	−	4.25987i	0.606548	−	0.162524i
$688$	−0.601718	+	2.24564i	−0.0229403	+	0.0856143i
$689$	−3.89204	−	2.24707i	−0.148275	−	0.0856066i
$690$	4.18382	+	6.72697i	0.159275	+	0.256091i
$691$	−48.2999			−1.83742			−0.918708	−	0.394938i	$-0.870766\pi$
$691$	−48.2999			−1.83742			−0.918708	+	0.394938i	$0.870766\pi$
$692$	2.72221	+	2.72221i	0.103483	+	0.103483i
$693$	−1.96327	+	7.32701i	−0.0745783	+	0.278330i
$694$	−9.68531	−	16.7754i	−0.367649	−	0.636787i
$695$	−6.91013	−	6.47103i	−0.262116	−	0.245460i
$696$		−	0.410059i		−	0.0155433i
$697$	−8.96441	+	33.4556i	−0.339551	+	1.26722i
$698$	−3.85810	−	14.3986i	−0.146031	−	0.544997i
$699$	−0.392795	−	0.680341i	−0.0148569	−	0.0257328i
$700$	−5.80614	−	17.0956i	−0.219451	−	0.646153i
$701$	7.03494	−	12.1849i	0.265706	−	0.460216i	−0.702042	−	0.712135i	$-0.747728\pi$
$701$	7.03494	−	12.1849i	0.265706	−	0.460216i	0.967748	+	0.251919i	$0.0810616\pi$
$702$	0.246310	+	0.246310i	0.00929636	+	0.00929636i
$703$	8.80833	+	20.4477i	0.332212	+	0.771200i
$704$			2.10070i			0.0791730i
$705$	−14.4528	+	4.38543i	−0.544324	+	0.165165i
$706$	−9.74327	−	5.62528i	−0.366693	−	0.211710i
$707$	−14.2647	−	3.82221i	−0.536479	−	0.143749i
$708$	12.6618	−	3.39272i	0.475859	−	0.127506i
$709$	−34.5593	+	19.9528i	−1.29790	+	0.749343i	−0.980041	−	0.198794i	$-0.936297\pi$
$709$	−34.5593	+	19.9528i	−1.29790	+	0.749343i	−0.317860	+	0.948138i	$0.602964\pi$
$710$	0.0374996	+	1.14278i	0.00140733	+	0.0428878i
$711$		−	9.98398i		−	0.374429i
$712$	−15.9267	−	4.26754i	−0.596878	−	0.159933i
$713$	−31.6269	−	8.47440i	−1.18444	−	0.317369i
$714$		−	15.5825i		−	0.583161i
$715$	0.0536630	+	1.63535i	0.00200688	+	0.0611587i
$716$	−14.7133	+	8.49473i	−0.549862	+	0.317463i
$717$	−28.1679	+	7.54756i	−1.05195	+	0.281869i
$718$	19.9863	+	5.35531i	0.745882	+	0.199858i
$719$	36.1835	+	20.8905i	1.34942	+	0.779085i	0.988167	−	0.153384i	$-0.0490172\pi$
$719$	36.1835	+	20.8905i	1.34942	+	0.779085i	0.361249	+	0.932470i	$0.382351\pi$
$720$	−2.13973	+	0.649262i	−0.0797431	+	0.0241966i
$721$			50.0634i			1.86446i
$722$	16.7149	+	9.03389i	0.622065	+	0.336207i
$723$	8.01832	+	8.01832i	0.298205	+	0.298205i
$724$	2.19960	−	3.80982i	0.0817475	−	0.141591i
$725$	1.83900	+	0.906538i	0.0682986	+	0.0336680i
$726$	−3.29354	−	5.70457i	−0.122235	−	0.211717i
$727$	−8.83275	−	32.9643i	−0.327589	−	1.22258i	−0.911684	−	0.410893i	$-0.865217\pi$
$727$	−8.83275	−	32.9643i	−0.327589	−	1.22258i	0.584095	−	0.811685i	$-0.301450\pi$
$728$	0.325546	−	1.21495i	0.0120655	−	0.0450292i
$729$			1.00000i			0.0370370i
$730$	−9.33708	−	8.74377i	−0.345581	−	0.323621i
$731$	−5.01632	−	8.68851i	−0.185535	−	0.321356i
$732$	−0.0887147	+	0.331088i	−0.00327899	+	0.0122374i
$733$	−30.1762	−	30.1762i	−1.11458	−	1.11458i	−0.992523	−	0.122060i	$-0.961050\pi$
$733$	−30.1762	−	30.1762i	−1.11458	−	1.11458i	−0.122060	−	0.992523i	$-0.538950\pi$
$734$	11.0241			0.406908
$735$	7.13153	+	11.4664i	0.263050	+	0.422946i
$736$	−3.06814	−	1.77139i	−0.113093	−	0.0652943i
$737$	3.24514	−	12.1110i	0.119536	−	0.446115i
$738$	−7.75267	+	2.07732i	−0.285380	+	0.0764673i
$739$	40.6851	+	23.4896i	1.49663	+	0.864077i	0.999992	−	0.00388331i	$-0.00123610\pi$
$739$	40.6851	+	23.4896i	1.49663	+	0.864077i	0.496633	+	0.867961i	$0.334569\pi$
$740$	0.374581	+	11.4152i	0.0137699	+	0.419630i
$741$	0.561282	−	1.41080i	0.0206192	−	0.0518272i
$742$	−32.9423	+	32.9423i	−1.20935	+	1.20935i
$743$	5.82804	+	21.7505i	0.213810	+	0.797950i	0.986582	+	0.163266i	$0.0522029\pi$
$743$	5.82804	+	21.7505i	0.213810	+	0.797950i	−0.772772	+	0.634684i	$0.781130\pi$
$744$	4.62103	−	8.00385i	0.169415	−	0.293435i
$745$	−6.47098	+	27.7623i	−0.237078	+	1.01713i
$746$	5.28789	−	9.15889i	0.193603	−	0.335331i
$747$	6.40958	+	1.71744i	0.234514	+	0.0628379i
$748$	−6.41012	−	6.41012i	−0.234377	−	0.234377i
$749$	15.0197			0.548807
$750$	1.81866	−	11.0314i	0.0664080	−	0.402811i
$751$	8.67517	−	5.00861i	0.316561	−	0.182767i	−0.333297	−	0.942822i	$-0.608161\pi$
$751$	8.67517	−	5.00861i	0.316561	−	0.182767i	0.649859	+	0.760055i	$0.274828\pi$
$752$	4.77614	−	4.77614i	0.174168	−	0.174168i
$753$	−2.54545	+	2.54545i	−0.0927615	+	0.0927615i
$754$	0.0714189	+	0.123701i	0.00260092	+	0.00450493i
$755$	6.66960	−	2.02377i	0.242731	−	0.0736524i
$756$	3.12716	−	1.80547i	0.113734	−	0.0656642i
$757$	−3.74198	−	13.9652i	−0.136004	−	0.507575i	−0.999992	−	0.00406187i	$-0.998707\pi$
$757$	−3.74198	−	13.9652i	−0.136004	−	0.507575i	0.863987	−	0.503514i	$-0.167960\pi$
$758$	−29.7329	+	7.96692i	−1.07995	+	0.289371i
$759$	−7.44230			−0.270139
$760$	6.28913	+	7.44626i	0.228131	+	0.270104i
$761$	6.10595			0.221340			0.110670	−	0.993857i	$-0.464700\pi$
$761$	6.10595			0.221340			0.110670	+	0.993857i	$0.464700\pi$
$762$	3.57208	−	0.957135i	0.129403	−	0.0346733i
$763$	2.93146	+	10.9404i	0.106126	+	0.396068i
$764$	−0.380863	+	0.219892i	−0.0137792	+	0.00795540i
$765$	4.54806	−	8.51041i	0.164436	−	0.307695i
$766$	1.21275	+	2.10054i	0.0438183	+	0.0758955i
$767$	−3.22874	+	3.22874i	−0.116583	+	0.116583i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	5.75768	−	3.32420i	0.207627	−	0.119874i	−0.392581	−	0.919717i	$-0.628418\pi$
$769$	5.75768	−	3.32420i	0.207627	−	0.119874i	0.600208	+	0.799844i	$0.295084\pi$
$770$	16.5188	+	3.85030i	0.595298	+	0.138755i
$771$	−17.1826			−0.618817
$772$	7.79283	+	7.79283i	0.280470	+	0.280470i
$773$	−19.8392	−	5.31590i	−0.713567	−	0.191200i	−0.116267	−	0.993218i	$-0.537093\pi$
$773$	−19.8392	−	5.31590i	−0.713567	−	0.191200i	−0.597300	+	0.802018i	$0.703760\pi$
$774$	1.16243	−	2.01339i	0.0417827	−	0.0723698i
$775$	25.6790	+	38.4184i	0.922417	+	1.38003i
$776$	−6.48449	+	11.2315i	−0.232780	+	0.403186i
$777$	−4.77360	−	17.8153i	−0.171252	−	0.639121i
$778$	18.4150	−	18.4150i	0.660211	−	0.660211i
$779$	21.6855	+	27.4536i	0.776965	+	0.983629i
$780$	0.532406	−	0.568532i	0.0190632	−	0.0203567i
$781$	−0.930262	−	0.537087i	−0.0332874	−	0.0192185i
$782$	14.7675	−	3.95693i	0.528083	−	0.141499i
$783$	−0.106131	+	0.396087i	−0.00379282	+	0.0141550i
$784$	−5.22979	−	3.01942i	−0.186778	−	0.107836i
$785$	−25.5758	+	15.9068i	−0.912839	+	0.567738i
$786$	13.9485			0.497525
$787$	19.0545	+	19.0545i	0.679221	+	0.679221i	0.959824	−	0.280603i	$-0.0905345\pi$
$787$	19.0545	+	19.0545i	0.679221	+	0.679221i	−0.280603	+	0.959824i	$0.590535\pi$
$788$	0.663643	−	2.47675i	0.0236413	−	0.0882306i
$789$	14.9780	+	25.9427i	0.533231	+	0.923583i
$790$	−22.3128	+	0.732181i	−0.793856	+	0.0260498i
$791$			65.0724i			2.31371i
$792$	0.543700	−	2.02912i	0.0193195	−	0.0721015i
$793$	−0.0309024	−	0.115329i	−0.00109738	−	0.00409546i
$794$	−14.5713	−	25.2382i	−0.517115	−	0.895670i
$795$	−27.6064	+	8.37665i	−0.979098	+	0.297089i
$796$	−9.65315	+	16.7198i	−0.342147	+	0.592616i
$797$	−1.79325	−	1.79325i	−0.0635202	−	0.0635202i	0.674633	−	0.738153i	$-0.264302\pi$
$797$	−1.79325	−	1.79325i	−0.0635202	−	0.0635202i	−0.738153	+	0.674633i	$0.764302\pi$
$798$	−12.6205	−	9.40532i	−0.446762	−	0.332945i
$799$			29.1481i			1.03118i
$800$	1.60793	+	4.73440i	0.0568490	+	0.167386i
$801$	14.2795	+	8.24426i	0.504540	+	0.291297i
$802$	−28.6096	−	7.66593i	−1.01024	−	0.270693i
$803$	11.6081	−	3.11037i	0.409639	−	0.109763i
$804$	−5.16897	+	2.98431i	−0.182296	+	0.105248i
$805$	−19.5528	+	20.8796i	−0.689147	+	0.735909i
$806$			3.21933i			0.113396i
$807$	1.44170	+	0.386303i	0.0507503	+	0.0135985i
$808$	3.95041	+	1.05851i	0.138975	+	0.0372383i
$809$			16.8282i			0.591649i	0.955242	+	0.295825i	$0.0955944\pi$
$809$			16.8282i			0.591649i	−0.955242	+	0.295825i	$0.904406\pi$
$810$	2.23487	−	0.0733356i	0.0785252	−	0.00257675i
$811$	−28.2330	+	16.3003i	−0.991394	+	0.572381i	−0.905691	−	0.423939i	$-0.860647\pi$
$811$	−28.2330	+	16.3003i	−0.991394	+	0.572381i	−0.0857031	+	0.996321i	$0.527314\pi$
$812$	1.43024	−	0.383233i	0.0501917	−	0.0134488i
$813$	18.4949	+	4.95570i	0.648645	+	0.173804i
$814$	−9.29233	−	5.36493i	−0.325696	−	0.188041i
$815$	17.7806	−	33.2714i	0.622828	−	1.16545i
$816$			4.31537i			0.151068i
$817$	−10.0647	−	1.18143i	−0.352120	−	0.0413329i
$818$	18.5922	+	18.5922i	0.650062	+	0.650062i
$819$	−0.628907	+	1.08930i	−0.0219758	+	0.0380632i
$820$	5.21108	+	17.1738i	0.181979	+	0.599736i
$821$	17.9017	+	31.0067i	0.624774	+	1.08214i	0.988585	+	0.150667i	$0.0481422\pi$
$821$	17.9017	+	31.0067i	0.624774	+	1.08214i	−0.363811	+	0.931473i	$0.618524\pi$
$822$	2.74503	+	10.2446i	0.0957440	+	0.357322i
$823$	−2.37997	+	8.88216i	−0.0829605	+	0.309613i	−0.994920	−	0.100667i	$-0.967902\pi$
$823$	−2.37997	+	8.88216i	−0.0829605	+	0.309613i	0.911960	+	0.410280i	$0.134569\pi$
$824$		−	13.8644i		−	0.482989i
$825$	7.89801	+	6.92420i	0.274973	+	0.241070i
$826$	23.6669	+	40.9922i	0.823476	+	1.42630i
$827$	−4.29416	+	16.0260i	−0.149323	+	0.557280i	0.850202	+	0.526456i	$0.176480\pi$
$827$	−4.29416	+	16.0260i	−0.149323	+	0.557280i	−0.999525	+	0.0308234i	$0.990187\pi$
$828$	2.50512	+	2.50512i	0.0870591	+	0.0870591i
$829$	31.8941			1.10773			0.553864	−	0.832607i	$-0.313153\pi$
$829$	31.8941			1.10773			0.553864	+	0.832607i	$0.313153\pi$
$830$	3.36820	−	14.4505i	0.116912	−	0.501584i
$831$	−10.5565	−	6.09482i	−0.366202	−	0.211427i
$832$	−0.0901556	+	0.336465i	−0.00312558	+	0.0116648i
$833$	25.1718	−	6.74478i	0.872153	−	0.233693i
$834$	−3.66655	−	2.11689i	−0.126962	−	0.0733018i
$835$	−32.6919	+	1.07276i	−1.13135	+	0.0371244i
$836$	−9.06070	+	1.32263i	−0.313371	+	0.0457443i
$837$	−6.53512	+	6.53512i	−0.225887	+	0.225887i
$838$	−4.60779	−	17.1965i	−0.159174	−	0.594044i
$839$	3.92529	−	6.79881i	0.135516	−	0.234721i	−0.790278	−	0.612748i	$-0.790064\pi$
$839$	3.92529	−	6.79881i	0.135516	−	0.234721i	0.925795	+	0.378027i	$0.123397\pi$
$840$	−4.26431	−	6.85638i	−0.147133	−	0.236567i
$841$	14.4159	−	24.9691i	0.497101	−	0.861004i
$842$	34.2168	+	9.16837i	1.17919	+	0.315963i
$843$	8.47315	+	8.47315i	0.291831	+	0.291831i
$844$	−25.4506			−0.876047
$845$	6.53707	−	28.0458i	0.224882	−	0.964805i
$846$	−5.84955	+	3.37724i	−0.201112	+	0.116112i
$847$	16.8189	−	16.8189i	0.577904	−	0.577904i
$848$	9.12295	−	9.12295i	0.313283	−	0.313283i
$849$	11.1044	+	19.2334i	0.381101	+	0.660087i
$850$	−19.3532	−	9.54019i	−0.663808	−	0.327226i
$851$	15.6713	−	9.04784i	0.537206	−	0.310156i
$852$	0.132345	+	0.493918i	0.00453406	+	0.0169214i
$853$	−47.0145	+	12.5975i	−1.60974	+	0.431330i	−0.947967	−	0.318370i	$-0.896865\pi$
$853$	−47.0145	+	12.5975i	−1.60974	+	0.431330i	−0.661778	+	0.749700i	$0.730198\pi$
$854$	−1.23771			−0.0423535
$855$	−4.14760	−	8.82028i	−0.141845	−	0.301647i
$856$	−4.15950			−0.142169
$857$	−10.0170	+	2.68404i	−0.342173	+	0.0916849i	−0.425813	−	0.904811i	$-0.640012\pi$
$857$	−10.0170	+	2.68404i	−0.342173	+	0.0916849i	0.0836405	+	0.996496i	$0.473345\pi$
$858$	0.189390	+	0.706812i	0.00646566	+	0.0241302i
$859$	33.6433	−	19.4240i	1.14789	−	0.662737i	0.199521	−	0.979894i	$-0.436061\pi$
$859$	33.6433	−	19.4240i	1.14789	−	0.662737i	0.948373	+	0.317157i	$0.102728\pi$
$860$	−4.58490	−	2.45022i	−0.156344	−	0.0835519i
$861$	−14.4910	−	25.0991i	−0.493851	−	0.855374i
$862$	−10.6181	+	10.6181i	−0.361655	+	0.361655i
$863$	7.55551	−	7.55551i	0.257193	−	0.257193i	−0.566719	−	0.823911i	$-0.691787\pi$
$863$	7.55551	−	7.55551i	0.257193	−	0.257193i	0.823911	+	0.566719i	$0.191787\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−7.30992	+	4.54638i	−0.248545	+	0.154582i
$866$	−28.3084			−0.961959
$867$	−1.14721	−	1.14721i	−0.0389613	−	0.0389613i
$868$	32.2353	+	8.63742i	1.09414	+	0.293173i
$869$	10.4867	−	18.1634i	0.355735	−	0.616152i
$870$	0.892984	+	0.208142i	0.0302750	+	0.00705666i
$871$	1.03954	−	1.80053i	0.0352234	−	0.0610087i
$872$	−0.811829	−	3.02979i	−0.0274920	−	0.102602i
$873$	9.17045	−	9.17045i	0.310373	−	0.310373i
$874$	5.70858	−	14.3487i	0.193096	−	0.485354i
$875$	40.1761	−	3.96645i	1.35820	−	0.134091i
$876$	−4.95431	−	2.86037i	−0.167391	−	0.0966430i
$877$	−19.3997	+	5.19814i	−0.655083	+	0.175529i	−0.571026	−	0.820932i	$-0.693454\pi$
$877$	−19.3997	+	5.19814i	−0.655083	+	0.175529i	−0.0840569	+	0.996461i	$0.526788\pi$
$878$	8.01825	−	29.9245i	0.270603	−	1.00990i
$879$	10.7700	+	6.21808i	0.363264	+	0.209731i
$880$	−4.57468	−	1.06629i	−0.154212	−	0.0359446i
$881$	49.8255			1.67866			0.839332	−	0.543619i	$-0.182946\pi$
$881$	49.8255			1.67866			0.839332	+	0.543619i	$0.182946\pi$
$882$	4.27010	+	4.27010i	0.143782	+	0.143782i
$883$	6.95865	−	25.9700i	0.234177	−	0.873962i	−0.744341	−	0.667800i	$-0.767236\pi$
$883$	6.95865	−	25.9700i	0.234177	−	0.873962i	0.978518	−	0.206161i	$-0.0660972\pi$
$884$	−0.751596	−	1.30180i	−0.0252789	−	0.0437844i
$885$	0.961316	+	29.2956i	0.0323143	+	0.984761i
$886$		−	4.19381i		−	0.140894i
$887$	4.28209	−	15.9810i	0.143779	−	0.536589i	−0.856028	−	0.516929i	$-0.827075\pi$
$887$	4.28209	−	15.9810i	0.143779	−	0.536589i	0.999807	−	0.0196598i	$-0.00625832\pi$
$888$	1.32199	+	4.93372i	0.0443629	+	0.165565i
$889$	6.67677	+	11.5645i	0.223932	+	0.387861i
$890$	17.3776	−	32.5173i	0.582499	−	1.08998i
$891$	−1.05035	+	1.81926i	−0.0351880	+	0.0609474i
$892$	13.9113	+	13.9113i	0.465785	+	0.465785i
$893$	23.6075	+	17.5932i	0.789996	+	0.588735i
$894$			12.7485i			0.426372i
$895$	−11.0306	−	36.3529i	−0.368713	−	1.21514i
$896$	3.12716	+	1.80547i	0.104471	+	0.0603164i
$897$	−1.19202	−	0.319402i	−0.0398005	−	0.0106645i
$898$	−1.02550	+	0.274783i	−0.0342215	+	0.00916962i
$899$	−3.28205	+	1.89490i	−0.109463	+	0.0631983i
$900$	−0.327790	−	4.98924i	−0.0109263	−	0.166308i
$901$			55.6760i			1.85484i
$902$	−16.2860	−	4.36382i	−0.542265	−	0.145299i
$903$	8.10887	+	2.17276i	0.269846	+	0.0723051i
$904$		−	18.0209i		−	0.599368i
$905$	7.18013	+	6.72388i	0.238676	+	0.223509i
$906$	2.69942	−	1.55851i	0.0896823	−	0.0517781i
$907$	30.6709	−	8.21824i	1.01841	−	0.272882i	0.289270	−	0.957247i	$-0.406587\pi$
$907$	30.6709	−	8.21824i	1.01841	−	0.272882i	0.729139	+	0.684365i	$0.239921\pi$
$908$	−1.57382	−	0.421703i	−0.0522290	−	0.0139947i
$909$	−3.54184	−	2.04489i	−0.117476	−	0.0678246i
$910$	2.48056	+	1.32564i	0.0822296	+	0.0439444i
$911$			17.5316i			0.580847i	0.956898	+	0.290424i	$0.0937962\pi$
$911$			17.5316i			0.580847i	−0.956898	+	0.290424i	$0.906204\pi$
$912$	3.49509	+	2.60468i	0.115734	+	0.0862495i
$913$	9.85676	+	9.85676i	0.326211	+	0.326211i
$914$	−19.1833	+	33.2264i	−0.634527	+	1.09903i
$915$	−0.675977	−	0.361250i	−0.0223471	−	0.0119426i
$916$	−8.22943	−	14.2538i	−0.271908	−	0.470959i
$917$	13.0359	+	48.6508i	0.430484	+	1.60659i
$918$	1.11690	−	4.16833i	0.0368632	−	0.137575i
$919$			53.5050i			1.76497i	0.470344	+	0.882483i	$0.344130\pi$
$919$			53.5050i			1.76497i	−0.470344	+	0.882483i	$0.655870\pi$
$920$	5.41490	−	5.78233i	0.178524	−	0.190638i
$921$	−1.25628	−	2.17594i	−0.0413958	−	0.0716997i
$922$	−1.06574	+	3.97739i	−0.0350982	+	0.130988i
$923$	−0.125948	−	0.125948i	−0.00414564	−	0.00414564i
$924$	7.58547			0.249544
$925$	−25.0489	−	4.97848i	−0.823601	−	0.163692i
$926$	2.00884	+	1.15980i	0.0660145	+	0.0381135i
$927$	−3.58837	+	13.3920i	−0.117857	+	0.439850i
$928$	−0.396087	+	0.106131i	−0.0130022	+	0.00348393i
$929$	0.839101	+	0.484455i	0.0275300	+	0.0158945i	0.513702	−	0.857969i	$-0.328274\pi$
$929$	0.839101	+	0.484455i	0.0275300	+	0.0158945i	−0.486172	+	0.873863i	$0.661607\pi$
$930$	15.0844	+	14.1258i	0.494636	+	0.463205i
$931$	9.73056	−	24.4581i	0.318906	−	0.801583i
$932$	−0.555496	+	0.555496i	−0.0181959	+	0.0181959i
$933$	−6.52988	−	24.3699i	−0.213779	−	0.797833i
$934$	−18.6159	+	32.2437i	−0.609130	+	1.05504i
$935$	17.2130	−	10.7056i	0.562925	−	0.350110i
$936$	0.174167	−	0.301667i	0.00569284	−	0.00986028i
$937$	−38.3002	−	10.2625i	−1.25121	−	0.335261i	−0.428407	−	0.903586i	$-0.640925\pi$
$937$	−38.3002	−	10.2625i	−1.25121	−	0.335261i	−0.822804	+	0.568325i	$0.807592\pi$
$938$	−15.2398	−	15.2398i	−0.497596	−	0.497596i
$939$	−14.5421			−0.474565
$940$	7.97666	+	12.8253i	0.260170	+	0.418315i
$941$	26.9536	−	15.5617i	0.878664	−	0.507297i	0.00844603	−	0.999964i	$-0.497312\pi$
$941$	26.9536	−	15.5617i	0.878664	−	0.507297i	0.870218	+	0.492668i	$0.163978\pi$
$942$	−9.52442	+	9.52442i	−0.310323	+	0.310323i
$943$	20.1065	−	20.1065i	0.654758	−	0.654758i
$944$	−6.55422	−	11.3522i	−0.213322	−	0.369484i
$945$	2.34444	+	7.72643i	0.0762647	+	0.251341i
$946$	4.22952	−	2.44191i	0.137514	−	0.0793935i
$947$	9.63120	+	35.9441i	0.312972	+	1.16803i	0.925863	+	0.377859i	$0.123340\pi$
$947$	9.63120	+	35.9441i	0.312972	+	1.16803i	−0.612891	+	0.790167i	$0.709994\pi$
$948$	−9.64378	+	2.58404i	−0.313216	+	0.0839259i
$949$	1.99273			0.0646869
$950$	−19.4080	+	9.91617i	−0.629678	+	0.321723i
$951$	−27.5147			−0.892227
$952$	−15.0515	+	4.03305i	−0.487823	+	0.130712i
$953$	8.26705	+	30.8531i	0.267796	+	0.999428i	0.960517	+	0.278222i	$0.0897452\pi$
$953$	8.26705	+	30.8531i	0.267796	+	0.999428i	−0.692721	+	0.721206i	$0.743588\pi$
$954$	−11.1733	+	6.45090i	−0.361748	+	0.208855i
$955$	−0.285535	−	0.941019i	−0.00923969	−	0.0304507i
$956$	14.5808	+	25.2546i	0.471576	+	0.816793i
$957$	−0.609109	+	0.609109i	−0.0196897	+	0.0196897i
$958$	9.89314	−	9.89314i	0.319633	−	0.319633i
$959$	−33.1666	+	19.1488i	−1.07101	+	0.618346i
$960$	1.18094	+	1.89878i	0.0381148	+	0.0612829i
$961$	−54.4155			−1.75534
$962$	−1.25809	−	1.25809i	−0.0405625	−	0.0405625i
$963$	4.01777	+	1.07656i	0.129471	+	0.0346916i
$964$	5.66981	−	9.82040i	0.182612	−	0.316294i
$965$	−20.9260	+	13.0148i	−0.673630	+	0.418963i
$966$	−6.39637	+	11.0788i	−0.205800	+	0.356456i
$967$	−4.10727	−	15.3285i	−0.132081	−	0.492933i	0.867912	−	0.496718i	$-0.165462\pi$
$967$	−4.10727	−	15.3285i	−0.132081	−	0.492933i	−0.999993	+	0.00378551i	$0.998795\pi$
$968$	−4.65777	+	4.65777i	−0.149706	+	0.149706i
$969$	−18.6130	+	2.71703i	−0.597935	+	0.0872836i
$970$	−21.1672	−	19.8222i	−0.679639	−	0.636453i
$971$	16.5768	+	9.57063i	0.531975	+	0.307136i	0.741820	−	0.670599i	$-0.233963\pi$
$971$	16.5768	+	9.57063i	0.531975	+	0.307136i	−0.209845	+	0.977735i	$0.567296\pi$
$972$	0.965926	−	0.258819i	0.0309821	−	0.00830162i
$973$	3.95679	−	14.7669i	0.126849	−	0.473406i
$974$	5.13589	+	2.96521i	0.164565	+	0.0950114i
$975$	0.967847	+	1.44800i	0.0309959	+	0.0463731i
$976$	0.342767			0.0109717
$977$	−4.62126	−	4.62126i	−0.147847	−	0.147847i	0.629309	−	0.777156i	$-0.283338\pi$
$977$	−4.62126	−	4.62126i	−0.147847	−	0.147847i	−0.777156	+	0.629309i	$0.783338\pi$
$978$	4.36651	−	16.2961i	0.139626	−	0.521090i
$979$	17.3187	+	29.9968i	0.553508	+	0.958703i
$980$	9.22996	−	9.85626i	0.294840	−	0.314847i
$981$			3.13667i			0.100146i
$982$	3.64366	−	13.5983i	0.116274	−	0.433940i
$983$	6.64976	+	24.8172i	0.212094	+	0.791547i	0.987169	+	0.159678i	$0.0510455\pi$
$983$	6.64976	+	24.8172i	0.212094	+	0.791547i	−0.775075	+	0.631869i	$0.782288\pi$
$984$	4.01308	+	6.95086i	0.127932	+	0.221585i
$985$	5.05675	+	2.70238i	0.161121	+	0.0861051i
$986$	0.884779	−	1.53248i	0.0281771	−	0.0488042i
$987$	−17.2463	−	17.2463i	−0.548956	−	0.548956i
$988$	−1.50800	−	0.177014i	−0.0479759	−	0.00563156i
$989$			8.23647i			0.261904i
$990$	4.14282	+	2.21397i	0.131667	+	0.0703646i
$991$	−13.5501	−	7.82313i	−0.430432	−	0.248510i	0.269099	−	0.963113i	$-0.413274\pi$
$991$	−13.5501	−	7.82313i	−0.430432	−	0.248510i	−0.699531	+	0.714603i	$0.746608\pi$
$992$	−8.92714	−	2.39202i	−0.283437	−	0.0759467i
$993$	−10.8620	+	2.91046i	−0.344694	+	0.0923605i
$994$	−1.59905	+	0.923210i	−0.0507187	+	0.0292825i
$995$	−31.5107	−	29.5084i	−0.998956	−	0.935479i
$996$		−	6.63569i		−	0.210260i
$997$	−26.1670	−	7.01143i	−0.828718	−	0.222054i	−0.180563	−	0.983563i	$-0.557792\pi$
$997$	−26.1670	−	7.01143i	−0.828718	−	0.222054i	−0.648154	+	0.761509i	$0.724459\pi$
$998$	5.25178	+	1.40721i	0.166242	+	0.0445445i
$999$		−	5.10776i		−	0.161602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.103.8	✓	40
5.2	odd	4	inner	570.2.x.b.217.6	yes	40
19.12	odd	6	inner	570.2.x.b.373.6	yes	40
95.12	even	12	inner	570.2.x.b.487.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.8	✓	40	1.1	even	1	trivial
570.2.x.b.217.6	yes	40	5.2	odd	4	inner
570.2.x.b.373.6	yes	40	19.12	odd	6	inner
570.2.x.b.487.8	yes	40	95.12	even	12	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.649262 + 2.13973i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.55332 + 2.55332i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.649262 + 2.13973i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.55332 + 2.55332i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.18094 + 1.89878i) q^{10} -2.10070 q^{11} +(0.707107 + 0.707107i) q^{12} +(-0.336465 - 0.0901556i) q^{13} +(-1.80547 + 3.12716i) q^{14} +(-1.89878 + 1.18094i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.11690 + 4.16833i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(4.05014 + 1.61133i) q^{19} +(1.63214 + 1.52843i) q^{20} +(-3.12716 - 1.80547i) q^{21} +(-2.02912 + 0.543700i) q^{22} +(0.916939 - 3.42206i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.15692 + 2.77850i) q^{25} -0.348335 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.934578 + 3.48789i) q^{28} +(-0.205030 - 0.355122i) q^{29} +(-1.52843 + 1.63214i) q^{30} -9.24205i q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.543700 - 2.02912i) q^{33} +(2.15768 + 3.73722i) q^{34} +(-7.12119 - 3.80564i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.61173 + 3.61173i) q^{37} +(4.32918 + 0.508171i) q^{38} -0.348335i q^{39} +(1.97212 + 1.05392i) q^{40} +(6.95086 + 4.01308i) q^{41} +(-3.48789 - 0.934578i) q^{42} +(-2.24564 + 0.601718i) q^{43} +(-1.81926 + 1.05035i) q^{44} +(-1.63214 - 1.52843i) q^{45} -3.54278i q^{46} +(6.52433 + 1.74819i) q^{47} +(0.965926 + 0.258819i) q^{48} -6.03884i q^{49} +(-3.29615 + 3.75971i) q^{50} +(-3.73722 + 2.15768i) q^{51} +(-0.336465 + 0.0901556i) q^{52} +(12.4622 + 3.33923i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.36390 - 4.49493i) q^{55} +3.61093i q^{56} +(-0.508171 + 4.32918i) q^{57} +(-0.289956 - 0.289956i) q^{58} +(6.55422 - 11.3522i) q^{59} +(-1.05392 + 1.97212i) q^{60} +(0.171384 + 0.296845i) q^{61} +(-2.39202 - 8.92714i) q^{62} +(0.934578 - 3.48789i) q^{63} -1.00000i q^{64} +(-0.0255453 - 0.778481i) q^{65} +(-1.05035 - 1.81926i) q^{66} +(-1.54479 + 5.76524i) q^{67} +(3.05143 + 3.05143i) q^{68} +3.54278 q^{69} +(-7.86351 - 1.83287i) q^{70} +(0.442835 + 0.255671i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-5.52581 + 1.48064i) q^{73} +(4.42345 + 2.55388i) q^{74} +(-3.75971 - 3.29615i) q^{75} +(4.31319 - 0.629617i) q^{76} +(5.36374 - 5.36374i) q^{77} +(-0.0901556 - 0.336465i) q^{78} +(-4.99199 + 8.64638i) q^{79} +(2.17769 + 0.507589i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.75267 + 2.07732i) q^{82} +(-4.69214 - 4.69214i) q^{83} -3.61093 q^{84} +(-8.19394 + 5.09620i) q^{85} +(-2.01339 + 1.16243i) q^{86} +(0.289956 - 0.289956i) q^{87} +(-1.48542 + 1.48542i) q^{88} +(-8.24426 - 14.2795i) q^{89} +(-1.97212 - 1.05392i) q^{90} +(1.08930 - 0.628907i) q^{91} +(-0.916939 - 3.42206i) q^{92} +(8.92714 - 2.39202i) q^{93} +6.75448 q^{94} +(-0.818212 + 9.71239i) q^{95} +1.00000 q^{96} +(-12.5271 + 3.35662i) q^{97} +(-1.56297 - 5.83307i) q^{98} +(1.81926 - 1.05035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q + 20 * q^6 - 8 * q^7	\( 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more