LMFDB - Embedded newform 252.2.ba.a.239.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			239.17
Character	$\chi$	$=$	252.239
Dual form			252.2.ba.a.155.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0405943 + 1.41363i) q^{2} +(0.586217 - 1.62983i) q^{3} +(-1.99670 - 0.114771i) q^{4} +(-2.16781 - 1.25159i) q^{5} +(2.28018 + 0.894856i) q^{6} +(0.866025 - 0.500000i) q^{7} +(0.243298 - 2.81794i) q^{8} +(-2.31270 - 1.91087i) q^{9} +O(q^{10})$	\(q+(-0.0405943 + 1.41363i) q^{2} +(0.586217 - 1.62983i) q^{3} +(-1.99670 - 0.114771i) q^{4} +(-2.16781 - 1.25159i) q^{5} +(2.28018 + 0.894856i) q^{6} +(0.866025 - 0.500000i) q^{7} +(0.243298 - 2.81794i) q^{8} +(-2.31270 - 1.91087i) q^{9} +(1.85728 - 3.01367i) q^{10} +(-0.351433 - 0.608700i) q^{11} +(-1.35756 + 3.18701i) q^{12} +(1.55324 - 2.69030i) q^{13} +(0.671660 + 1.24454i) q^{14} +(-3.31068 + 2.79946i) q^{15} +(3.97366 + 0.458326i) q^{16} -7.91554i q^{17} +(2.79515 - 3.19173i) q^{18} +2.37413i q^{19} +(4.18483 + 2.74785i) q^{20} +(-0.307237 - 1.70458i) q^{21} +(0.874743 - 0.472087i) q^{22} +(-0.346619 + 0.600362i) q^{23} +(-4.45015 - 2.04846i) q^{24} +(0.632931 + 1.09627i) q^{25} +(3.74003 + 2.30492i) q^{26} +(-4.47014 + 2.64912i) q^{27} +(-1.78658 + 0.898958i) q^{28} +(-8.70126 + 5.02368i) q^{29} +(-3.82301 - 4.79372i) q^{30} +(7.34846 + 4.24264i) q^{31} +(-0.809212 + 5.59868i) q^{32} +(-1.19809 + 0.215946i) q^{33} +(11.1896 + 0.321326i) q^{34} -2.50317 q^{35} +(4.39846 + 4.08087i) q^{36} +2.85107 q^{37} +(-3.35614 - 0.0963760i) q^{38} +(-3.47419 - 4.10862i) q^{39} +(-4.05432 + 5.80426i) q^{40} +(5.82034 + 3.36037i) q^{41} +(2.42212 - 0.365123i) q^{42} +(3.17043 - 1.83045i) q^{43} +(0.631847 + 1.25573i) q^{44} +(2.62187 + 7.03694i) q^{45} +(-0.834620 - 0.514363i) q^{46} +(3.67787 + 6.37026i) q^{47} +(3.07642 - 6.20771i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-1.57541 + 0.850229i) q^{50} +(-12.9010 - 4.64022i) q^{51} +(-3.41013 + 5.19346i) q^{52} -0.889576i q^{53} +(-3.56342 - 6.42666i) q^{54} +1.75939i q^{55} +(-1.19827 - 2.56206i) q^{56} +(3.86942 + 1.39175i) q^{57} +(-6.74840 - 12.5043i) q^{58} +(3.63052 - 6.28824i) q^{59} +(6.93174 - 5.20973i) q^{60} +(-2.39732 - 4.15228i) q^{61} +(-6.29583 + 10.2158i) q^{62} +(-2.95829 - 0.498512i) q^{63} +(-7.88161 - 1.37120i) q^{64} +(-6.73427 + 3.88803i) q^{65} +(-0.256633 - 1.70243i) q^{66} +(-7.40811 - 4.27707i) q^{67} +(-0.908472 + 15.8050i) q^{68} +(0.775295 + 0.916874i) q^{69} +(0.101614 - 3.53856i) q^{70} +6.34514 q^{71} +(-5.94740 + 6.05214i) q^{72} +8.20222 q^{73} +(-0.115737 + 4.03035i) q^{74} +(2.15777 - 0.388920i) q^{75} +(0.272480 - 4.74043i) q^{76} +(-0.608700 - 0.351433i) q^{77} +(5.94911 - 4.74444i) q^{78} +(2.27268 - 1.31214i) q^{79} +(-8.04049 - 5.96693i) q^{80} +(1.69715 + 8.83853i) q^{81} +(-4.98660 + 8.09139i) q^{82} +(-6.50432 - 11.2658i) q^{83} +(0.417825 + 3.43881i) q^{84} +(-9.90697 + 17.1594i) q^{85} +(2.45887 + 4.55612i) q^{86} +(3.08692 + 17.1266i) q^{87} +(-1.80079 + 0.842223i) q^{88} -1.71842i q^{89} +(-10.0541 + 3.42070i) q^{90} -3.10649i q^{91} +(0.761000 - 1.15896i) q^{92} +(11.2226 - 9.48965i) q^{93} +(-9.15449 + 4.94056i) q^{94} +(2.97142 - 5.14665i) q^{95} +(8.65052 + 4.60092i) q^{96} +(-6.81083 - 11.7967i) q^{97} +(1.20394 + 0.741971i) q^{98} +(-0.350387 + 2.07928i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0405943	+	1.41363i	−0.0287045	+	0.999588i
$2$	−0.0405943	+	1.41363i	−0.0287045	+	0.999588i
$3$	0.586217	−	1.62983i	0.338453	−	0.940983i
$3$	0.586217	−	1.62983i	0.338453	−	0.940983i
$4$	−1.99670	−	0.114771i	−0.998352	−	0.0573853i
$5$	−2.16781	−	1.25159i	−0.969474	−	0.559726i	−0.0703980	−	0.997519i	$-0.522427\pi$
$5$	−2.16781	−	1.25159i	−0.969474	−	0.559726i	−0.899076	+	0.437793i	$0.855760\pi$
$6$	2.28018	+	0.894856i	0.930881	+	0.365324i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$	0.243298	−	2.81794i	0.0860189	−	0.996294i
$9$	−2.31270	−	1.91087i	−0.770900	−	0.636957i
$10$	1.85728	−	3.01367i	0.587324	−	0.953008i
$11$	−0.351433	−	0.608700i	−0.105961	−	0.183530i	0.808169	−	0.588950i	$-0.200459\pi$
$11$	−0.351433	−	0.608700i	−0.105961	−	0.183530i	−0.914130	+	0.405420i	$0.867125\pi$
$12$	−1.35756	+	3.18701i	−0.391893	+	0.920011i
$13$	1.55324	−	2.69030i	0.430792	−	0.746154i	−0.566150	−	0.824302i	$-0.691568\pi$
$13$	1.55324	−	2.69030i	0.430792	−	0.746154i	0.996942	+	0.0781487i	$0.0249009\pi$
$14$	0.671660	+	1.24454i	0.179509	+	0.332617i
$15$	−3.31068	+	2.79946i	−0.854814	+	0.722818i
$16$	3.97366	+	0.458326i	0.993414	+	0.114582i
$17$		−	7.91554i		−	1.91980i	−0.280343	−	0.959900i	$-0.590448\pi$
$17$		−	7.91554i		−	1.91980i	0.280343	−	0.959900i	$-0.409552\pi$
$18$	2.79515	−	3.19173i	0.658822	−	0.752299i
$19$			2.37413i			0.544662i	0.962204	+	0.272331i	$0.0877945\pi$
$19$			2.37413i			0.544662i	−0.962204	+	0.272331i	$0.912205\pi$
$20$	4.18483	+	2.74785i	0.935756	+	0.614437i
$21$	−0.307237	−	1.70458i	−0.0670445	−	0.371971i
$22$	0.874743	−	0.472087i	0.186496	−	0.100649i
$23$	−0.346619	+	0.600362i	−0.0722751	+	0.125184i	−0.899898	−	0.436100i	$-0.856359\pi$
$23$	−0.346619	+	0.600362i	−0.0722751	+	0.125184i	0.827623	+	0.561284i	$0.189693\pi$
$24$	−4.45015	−	2.04846i	−0.908382	−	0.418140i
$25$	0.632931	+	1.09627i	0.126586	+	0.219254i
$26$	3.74003	+	2.30492i	0.733481	+	0.452033i
$27$	−4.47014	+	2.64912i	−0.860279	+	0.509824i
$28$	−1.78658	+	0.898958i	−0.337632	+	0.169887i
$29$	−8.70126	+	5.02368i	−1.61578	+	0.932873i	−0.627789	+	0.778383i	$0.716040\pi$
$29$	−8.70126	+	5.02368i	−1.61578	+	0.932873i	−0.987994	+	0.154490i	$0.950627\pi$
$30$	−3.82301	−	4.79372i	−0.697983	−	0.875210i
$31$	7.34846	+	4.24264i	1.31982	+	0.762000i	0.983700	−	0.179818i	$-0.0575509\pi$
$31$	7.34846	+	4.24264i	1.31982	+	0.762000i	0.336123	+	0.941818i	$0.390884\pi$
$32$	−0.809212	+	5.59868i	−0.143050	+	0.989715i
$33$	−1.19809	+	0.215946i	−0.208561	+	0.0375914i
$34$	11.1896	+	0.321326i	1.91901	+	0.0551069i
$35$	−2.50317			−0.423113
$36$	4.39846	+	4.08087i	0.733077	+	0.680145i
$37$	2.85107			0.468712			0.234356	−	0.972151i	$-0.424702\pi$
$37$	2.85107			0.468712			0.234356	+	0.972151i	$0.424702\pi$
$38$	−3.35614	−	0.0963760i	−0.544437	−	0.0156342i
$39$	−3.47419	−	4.10862i	−0.556316	−	0.657906i
$40$	−4.05432	+	5.80426i	−0.641044	+	0.917733i
$41$	5.82034	+	3.36037i	0.908984	+	0.524802i	0.880104	−	0.474781i	$-0.157473\pi$
$41$	5.82034	+	3.36037i	0.908984	+	0.524802i	0.0288798	+	0.999583i	$0.490806\pi$
$42$	2.42212	−	0.365123i	0.373742	−	0.0563397i
$43$	3.17043	−	1.83045i	0.483485	−	0.279140i	−0.238383	−	0.971171i	$-0.576617\pi$
$43$	3.17043	−	1.83045i	0.483485	−	0.279140i	0.721868	+	0.692031i	$0.243284\pi$
$44$	0.631847	+	1.25573i	0.0952545	+	0.189308i
$45$	2.62187	+	7.03694i	0.390846	+	1.04901i
$46$	−0.834620	−	0.514363i	−0.123058	−	0.0758387i
$47$	3.67787	+	6.37026i	0.536473	+	0.929198i	0.999091	+	0.0426400i	$0.0135768\pi$
$47$	3.67787	+	6.37026i	0.536473	+	0.929198i	−0.462618	+	0.886558i	$0.653090\pi$
$48$	3.07642	−	6.20771i	0.444043	−	0.896006i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−1.57541	+	0.850229i	−0.222797	+	0.120241i
$51$	−12.9010	−	4.64022i	−1.80650	−	0.649761i
$52$	−3.41013	+	5.19346i	−0.472900	+	0.720203i
$53$		−	0.889576i		−	0.122193i	−0.998132	−	0.0610964i	$-0.980540\pi$
$53$		−	0.889576i		−	0.122193i	0.998132	−	0.0610964i	$-0.0194597\pi$
$54$	−3.56342	−	6.42666i	−0.484920	−	0.874558i
$55$			1.75939i			0.237237i
$56$	−1.19827	−	2.56206i	−0.160125	−	0.342370i
$57$	3.86942	+	1.39175i	0.512518	+	0.184342i
$58$	−6.74840	−	12.5043i	−0.886109	−	1.64190i
$59$	3.63052	−	6.28824i	0.472653	−	0.818660i	−0.526857	−	0.849954i	$-0.676630\pi$
$59$	3.63052	−	6.28824i	0.472653	−	0.818660i	0.999510	+	0.0312945i	$0.00996296\pi$
$60$	6.93174	−	5.20973i	0.894884	−	0.672573i
$61$	−2.39732	−	4.15228i	−0.306946	−	0.531645i	0.670747	−	0.741686i	$-0.265974\pi$
$61$	−2.39732	−	4.15228i	−0.306946	−	0.531645i	−0.977693	+	0.210041i	$0.932640\pi$
$62$	−6.29583	+	10.2158i	−0.799571	+	1.29741i
$63$	−2.95829	−	0.498512i	−0.372710	−	0.0628066i
$64$	−7.88161	−	1.37120i	−0.985201	−	0.171400i
$65$	−6.73427	+	3.88803i	−0.835283	+	0.482251i
$66$	−0.256633	−	1.70243i	−0.0315893	−	0.209555i
$67$	−7.40811	−	4.27707i	−0.905044	−	0.522528i	−0.0262109	−	0.999656i	$-0.508344\pi$
$67$	−7.40811	−	4.27707i	−0.905044	−	0.522528i	−0.878833	+	0.477129i	$0.841677\pi$
$68$	−0.908472	+	15.8050i	−0.110168	+	1.91664i
$69$	0.775295	+	0.916874i	0.0933345	+	0.110379i
$70$	0.101614	−	3.53856i	0.0121452	−	0.422939i
$71$	6.34514			0.753030			0.376515	−	0.926411i	$-0.377122\pi$
$71$	6.34514			0.753030			0.376515	+	0.926411i	$0.377122\pi$
$72$	−5.94740	+	6.05214i	−0.700908	+	0.713252i
$73$	8.20222			0.959998			0.479999	−	0.877269i	$-0.340637\pi$
$73$	8.20222			0.959998			0.479999	+	0.877269i	$0.340637\pi$
$74$	−0.115737	+	4.03035i	−0.0134542	+	0.468519i
$75$	2.15777	−	0.388920i	0.249158	−	0.0449086i
$76$	0.272480	−	4.74043i	0.0312556	−	0.543764i
$77$	−0.608700	−	0.351433i	−0.0693678	−	0.0400495i
$78$	5.94911	−	4.74444i	0.673604	−	0.537202i
$79$	2.27268	−	1.31214i	0.255697	−	0.147627i	−0.366673	−	0.930350i	$-0.619503\pi$
$79$	2.27268	−	1.31214i	0.255697	−	0.147627i	0.622370	+	0.782723i	$0.286170\pi$
$80$	−8.04049	−	5.96693i	−0.898954	−	0.667123i
$81$	1.69715	+	8.83853i	0.188573	+	0.982059i
$82$	−4.98660	+	8.09139i	−0.550678	+	0.893545i
$83$	−6.50432	−	11.2658i	−0.713942	−	1.23658i	−0.963366	−	0.268189i	$-0.913575\pi$
$83$	−6.50432	−	11.2658i	−0.713942	−	1.23658i	0.249425	−	0.968394i	$-0.419759\pi$
$84$	0.417825	+	3.43881i	0.0455884	+	0.375205i
$85$	−9.90697	+	17.1594i	−1.07456	+	1.86120i
$86$	2.45887	+	4.55612i	0.265147	+	0.491299i
$87$	3.08692	+	17.1266i	0.330952	+	1.83616i
$88$	−1.80079	+	0.842223i	−0.191964	+	0.0897813i
$89$		−	1.71842i		−	0.182152i	−0.995844	−	0.0910760i	$-0.970969\pi$
$89$		−	1.71842i		−	0.182152i	0.995844	−	0.0910760i	$-0.0290306\pi$
$90$	−10.0541	+	3.42070i	−1.05979	+	0.360574i
$91$		−	3.10649i		−	0.325648i
$92$	0.761000	−	1.15896i	0.0793398	−	0.120830i
$93$	11.2226	−	9.48965i	1.16373	−	0.984031i
$94$	−9.15449	+	4.94056i	−0.944214	+	0.509579i
$95$	2.97142	−	5.14665i	0.304861	−	0.528035i
$96$	8.65052	+	4.60092i	0.882890	+	0.469579i
$97$	−6.81083	−	11.7967i	−0.691535	−	1.19777i	−0.971335	−	0.237716i	$-0.923601\pi$
$97$	−6.81083	−	11.7967i	−0.691535	−	1.19777i	0.279800	−	0.960058i	$-0.409732\pi$
$98$	1.20394	+	0.741971i	0.121617	+	0.0749504i
$99$	−0.350387	+	2.07928i	−0.0352153	+	0.208976i
$100$	−1.13796	−	2.26157i	−0.113796	−	0.226157i
$101$	2.23784	−	1.29202i	0.222673	−	0.128560i	−0.384514	−	0.923119i	$-0.625631\pi$
$101$	2.23784	−	1.29202i	0.222673	−	0.128560i	0.607187	+	0.794559i	$0.292298\pi$
$102$	7.08327	−	18.0489i	0.701348	−	1.78710i
$103$	11.6579	+	6.73069i	1.14869	+	0.663195i	0.948567	−	0.316576i	$-0.102533\pi$
$103$	11.6579	+	6.73069i	1.14869	+	0.663195i	0.200120	+	0.979771i	$0.435867\pi$
$104$	−7.20320	−	5.03149i	−0.706332	−	0.493379i
$105$	−1.46740	+	4.07975i	−0.143204	+	0.398142i
$106$	1.25753	+	0.0361117i	0.122142	+	0.00350748i
$107$	17.0371			1.64703			0.823517	−	0.567291i	$-0.192009\pi$
$107$	17.0371			1.64703			0.823517	+	0.567291i	$0.192009\pi$
$108$	9.22959	−	4.77648i	0.888117	−	0.459617i
$109$	−2.43459			−0.233191			−0.116596	−	0.993179i	$-0.537198\pi$
$109$	−2.43459			−0.233191			−0.116596	+	0.993179i	$0.537198\pi$
$110$	−2.48713	−	0.0714214i	−0.237139	−	0.00680976i
$111$	1.67134	−	4.64675i	0.158637	−	0.441050i
$112$	3.67045	−	1.58991i	0.346825	−	0.150232i
$113$	−4.13789	−	2.38901i	−0.389260	−	0.224739i	0.292580	−	0.956241i	$-0.405486\pi$
$113$	−4.13789	−	2.38901i	−0.389260	−	0.224739i	−0.681839	+	0.731502i	$0.738820\pi$
$114$	−2.12450	+	5.41344i	−0.198978	+	0.507015i
$115$	1.50281	−	0.867647i	0.140138	−	0.0809085i
$116$	17.9504	−	9.03215i	1.66665	−	0.838614i
$117$	−8.73299	+	3.25380i	−0.807365	+	0.300814i
$118$	8.74188	+	5.38748i	0.804755	+	0.495958i
$119$	−3.95777	−	6.85506i	−0.362808	−	0.628402i
$120$	7.08325	+	10.0104i	0.646609	+	0.913821i
$121$	5.25299	−	9.09844i	0.477544	−	0.827131i
$122$	5.96711	−	3.22037i	0.540237	−	0.291559i
$123$	8.88882	−	7.51626i	0.801478	−	0.677718i
$124$	−14.1858	−	9.31468i	−1.27392	−	0.836483i
$125$			9.34718i			0.836037i
$126$	0.824802	−	4.16169i	0.0734792	−	0.370753i
$127$			4.91393i			0.436041i	0.975944	+	0.218020i	$0.0699599\pi$
$127$			4.91393i			0.436041i	−0.975944	+	0.218020i	$0.930040\pi$
$128$	2.25832	−	11.0860i	0.199609	−	0.979876i
$129$	−1.12476	−	6.24030i	−0.0990296	−	0.549427i
$130$	−5.22287	−	9.67760i	−0.458076	−	0.848782i
$131$	−2.61968	+	4.53741i	−0.228882	+	0.396435i	−0.957477	−	0.288509i	$-0.906840\pi$
$131$	−2.61968	+	4.53741i	−0.228882	+	0.396435i	0.728595	+	0.684945i	$0.240174\pi$
$132$	2.41702	−	0.293675i	0.210375	−	0.0255611i
$133$	1.18706	+	2.05605i	0.102931	+	0.178282i
$134$	6.34693	−	10.2987i	0.548291	−	0.889672i
$135$	13.0060	−	0.148038i	1.11938	−	0.0127411i
$136$	−22.3055	−	1.92584i	−1.91268	−	0.165139i
$137$	9.03659	−	5.21728i	0.772048	−	0.445742i	−0.0615566	−	0.998104i	$-0.519606\pi$
$137$	9.03659	−	5.21728i	0.772048	−	0.445742i	0.833605	+	0.552361i	$0.186273\pi$
$138$	−1.32759	+	1.05876i	−0.113012	+	0.0901277i
$139$	10.2848	+	5.93796i	0.872349	+	0.503651i	0.868128	−	0.496340i	$-0.165323\pi$
$139$	10.2848	+	5.93796i	0.872349	+	0.503651i	0.00422072	+	0.999991i	$0.498656\pi$
$140$	4.99809	+	0.287291i	0.422416	+	0.0242805i
$141$	12.5385	−	2.25995i	1.05593	−	0.190322i
$142$	−0.257577	+	8.96969i	−0.0216153	+	0.752719i
$143$	−2.18344			−0.182589
$144$	−8.31407	−	8.65311i	−0.692839	−	0.721092i
$145$	25.1502			2.08861
$146$	−0.332963	+	11.5949i	−0.0275563	+	0.959602i
$147$	−1.11837	−	1.32259i	−0.0922413	−	0.109086i
$148$	−5.69273	−	0.327219i	−0.467940	−	0.0268972i
$149$	15.3300	+	8.85079i	1.25588	+	0.725085i	0.972272	−	0.233854i	$-0.0751337\pi$
$149$	15.3300	+	8.85079i	1.25588	+	0.725085i	0.283612	+	0.958939i	$0.408467\pi$
$150$	0.462196	+	3.06608i	0.0377381	+	0.250344i
$151$	−18.1796	+	10.4960i	−1.47944	+	0.854152i	−0.999729	−	0.0232767i	$-0.992590\pi$
$151$	−18.1796	+	10.4960i	−1.47944	+	0.854152i	−0.479706	+	0.877429i	$0.659257\pi$
$152$	6.69015	+	0.577621i	0.542643	+	0.0468512i
$153$	−15.1256	+	18.3063i	−1.22283	+	1.47997i
$154$	0.521507	−	0.846211i	0.0420242	−	0.0681896i
$155$	−10.6200	−	18.3945i	−0.853022	−	1.47748i
$156$	6.46538	+	8.60244i	0.517645	+	0.688746i
$157$	−0.841990	+	1.45837i	−0.0671981	+	0.116391i	−0.897667	−	0.440675i	$-0.854739\pi$
$157$	−0.841990	+	1.45837i	−0.0671981	+	0.116391i	0.830469	+	0.557065i	$0.188073\pi$
$158$	1.76262	+	3.26600i	0.140226	+	0.259829i
$159$	−1.44986	−	0.521485i	−0.114981	−	0.0413564i
$160$	8.76144	−	11.1241i	0.692652	−	0.879435i
$161$			0.693239i			0.0546349i
$162$	−12.5633	+	2.04036i	−0.987067	+	0.160306i
$163$			14.9299i			1.16940i	0.811249	+	0.584700i	$0.198788\pi$
$163$			14.9299i			1.16940i	−0.811249	+	0.584700i	$0.801212\pi$
$164$	−11.2358	−	7.37767i	−0.877370	−	0.576100i
$165$	2.86752	+	1.03139i	0.223236	+	0.0802934i
$166$	16.1897	−	8.73738i	1.25657	−	0.678152i
$167$	1.17066	−	2.02764i	0.0905885	−	0.156904i	−0.817170	−	0.576396i	$-0.804459\pi$
$167$	1.17066	−	2.02764i	0.0905885	−	0.156904i	0.907759	+	0.419492i	$0.137792\pi$
$168$	−4.87817	+	0.451054i	−0.376359	+	0.0347995i
$169$	1.67487	+	2.90097i	0.128836	+	0.223151i
$170$	−23.8549	−	14.7014i	−1.82958	−	1.12754i
$171$	4.53665	−	5.49064i	0.346926	−	0.419880i
$172$	−6.54048	+	3.29099i	−0.498707	+	0.250935i
$173$	0.875908	−	0.505706i	0.0665940	−	0.0384481i	−0.466333	−	0.884609i	$-0.654425\pi$
$173$	0.875908	−	0.505706i	0.0665940	−	0.0384481i	0.532927	+	0.846161i	$0.321092\pi$
$174$	−24.3359	+	3.66852i	−1.84490	+	0.278110i
$175$	1.09627	+	0.632931i	0.0828702	+	0.0478451i
$176$	−1.11749	−	2.57984i	−0.0842341	−	0.194462i
$177$	−8.12050	−	9.60341i	−0.610374	−	0.721836i
$178$	2.42921	+	0.0697580i	0.182077	+	0.00522858i
$179$	−11.8651			−0.886837			−0.443419	−	0.896315i	$-0.646235\pi$
$179$	−11.8651			−0.886837			−0.443419	+	0.896315i	$0.646235\pi$
$180$	−4.42747	−	14.3516i	−0.330004	−	1.06971i
$181$	−11.7216			−0.871262			−0.435631	−	0.900125i	$-0.643475\pi$
$181$	−11.7216			−0.871262			−0.435631	+	0.900125i	$0.643475\pi$
$182$	4.39142	+	0.126106i	0.325514	+	0.00934757i
$183$	−8.17287	+	1.47309i	−0.604156	+	0.108894i
$184$	1.60746	+	1.12282i	0.118503	+	0.0827754i
$185$	−6.18057	−	3.56835i	−0.454404	−	0.262350i
$186$	12.9593	+	16.2498i	0.950221	+	1.19149i
$187$	−4.81819	+	2.78178i	−0.352341	+	0.203424i
$188$	−6.61250	−	13.1416i	−0.482266	−	0.958452i
$189$	−2.54669	+	4.52928i	−0.185245	+	0.329457i
$190$	7.15484	+	4.40942i	0.519067	+	0.319893i
$191$	3.38132	+	5.85662i	0.244664	+	0.423770i	0.962037	−	0.272919i	$-0.0879891\pi$
$191$	3.38132	+	5.85662i	0.244664	+	0.423770i	−0.717373	+	0.696689i	$0.754656\pi$
$192$	−6.85516	+	12.0419i	−0.494729	+	0.869047i
$193$	−1.38307	+	2.39554i	−0.0995553	+	0.172435i	−0.911501	−	0.411299i	$-0.865075\pi$
$193$	−1.38307	+	2.39554i	−0.0995553	+	0.172435i	0.811945	+	0.583733i	$0.198409\pi$
$194$	16.9527	−	9.14912i	1.21713	−	0.656869i
$195$	2.38909	+	13.2550i	0.171086	+	0.949207i
$196$	−1.09775	+	1.67181i	−0.0784105	+	0.119415i
$197$		−	17.2636i		−	1.22998i	−0.788536	−	0.614989i	$-0.789161\pi$
$197$		−	17.2636i		−	1.22998i	0.788536	−	0.614989i	$-0.210839\pi$
$198$	−2.92512	−	0.579725i	−0.207879	−	0.0411993i
$199$		−	14.4922i		−	1.02732i	−0.857993	−	0.513662i	$-0.828289\pi$
$199$		−	14.4922i		−	1.02732i	0.857993	−	0.513662i	$-0.171711\pi$
$200$	3.24322	−	1.51684i	0.229330	−	0.107257i
$201$	−11.3137	+	9.56667i	−0.798004	+	0.674781i
$202$	1.73559	+	3.21592i	0.122116	+	0.226272i
$203$	−5.02368	+	8.70126i	−0.352593	+	0.610709i
$204$	25.2269	+	10.7458i	1.76624	+	0.752357i
$205$	−8.41159	−	14.5693i	−0.587491	−	1.01756i
$206$	−9.98796	+	16.2067i	−0.695894	+	1.12918i
$207$	1.94884	−	0.726113i	0.135454	−	0.0504683i
$208$	7.40509	−	9.97842i	0.513450	−	0.691879i
$209$	1.44513	−	0.834347i	0.0999618	−	0.0577130i
$210$	−5.70769	−	2.23998i	−0.393868	−	0.154573i
$211$	−22.1795	−	12.8053i	−1.52690	−	0.881555i	−0.999490	−	0.0319420i	$-0.989831\pi$
$211$	−22.1795	−	12.8053i	−1.52690	−	0.881555i	−0.527407	−	0.849612i	$-0.676836\pi$
$212$	−0.102097	+	1.77622i	−0.00701207	+	0.121991i
$213$	3.71963	−	10.3415i	0.254865	−	0.708589i
$214$	−0.691607	+	24.0841i	−0.0472773	+	1.64636i
$215$	−9.16384			−0.624968
$216$	6.37751	+	13.2411i	0.433934	+	0.900944i
$217$	8.48527			0.576018
$218$	0.0988305	−	3.44161i	0.00669364	−	0.233095i
$219$	4.80828	−	13.3682i	0.324914	−	0.903342i
$220$	0.201927	−	3.51299i	0.0136139	−	0.236846i
$221$	−21.2951	−	12.2948i	−1.43247	−	0.827035i
$222$	6.50095	+	2.55129i	0.436315	+	0.171232i
$223$	−13.2137	+	7.62891i	−0.884853	+	0.510870i	−0.872255	−	0.489051i	$-0.837343\pi$
$223$	−13.2137	+	7.62891i	−0.884853	+	0.510870i	−0.0125973	+	0.999921i	$0.504010\pi$
$224$	2.09854	+	5.25320i	0.140215	+	0.350994i
$225$	0.631048	−	3.74479i	0.0420699	−	0.249653i
$226$	3.54515	−	5.75247i	0.235820	−	0.382648i
$227$	3.88279	+	6.72519i	0.257710	+	0.446367i	0.965628	−	0.259928i	$-0.0836988\pi$
$227$	3.88279	+	6.72519i	0.257710	+	0.446367i	−0.707918	+	0.706295i	$0.750365\pi$
$228$	−7.56636	−	3.22302i	−0.501095	−	0.213449i
$229$	−5.70048	+	9.87351i	−0.376698	+	0.652460i	−0.990580	−	0.136938i	$-0.956274\pi$
$229$	−5.70048	+	9.87351i	−0.376698	+	0.652460i	0.613882	+	0.789398i	$0.289607\pi$
$230$	1.16553	+	2.15964i	0.0768526	+	0.142402i
$231$	−0.929607	+	0.786062i	−0.0611637	+	0.0517191i
$232$	12.0394	+	25.7419i	0.790428	+	1.69004i
$233$			19.4113i			1.27167i	0.771824	+	0.635837i	$0.219345\pi$
$233$			19.4113i			1.27167i	−0.771824	+	0.635837i	$0.780655\pi$
$234$	−4.24516	−	12.4773i	−0.277515	−	0.815667i
$235$		−	18.4127i		−	1.20111i
$236$	−7.97078	+	12.1391i	−0.518853	+	0.790187i
$237$	−0.806272	−	4.47329i	−0.0523730	−	0.290571i
$238$	9.85118	−	5.31655i	0.638557	−	0.344621i
$239$	−3.57434	+	6.19093i	−0.231205	+	0.400458i	−0.958163	−	0.286224i	$-0.907600\pi$
$239$	−3.57434	+	6.19093i	−0.231205	+	0.400458i	0.726958	+	0.686682i	$0.240933\pi$
$240$	−14.4386	+	9.60673i	−0.932005	+	0.620112i
$241$	−1.19735	−	2.07386i	−0.0771279	−	0.133589i	0.824882	−	0.565305i	$-0.191242\pi$
$241$	−1.19735	−	2.07386i	−0.0771279	−	0.133589i	−0.902010	+	0.431716i	$0.857908\pi$
$242$	12.6486	+	7.79513i	0.813083	+	0.501090i
$243$	15.4002	+	2.41522i	0.987924	+	0.154937i
$244$	4.31018	+	8.56602i	0.275931	+	0.548383i
$245$	−2.16781	+	1.25159i	−0.138496	+	0.0799609i
$246$	10.2644	+	12.8706i	0.654433	+	0.820601i
$247$	6.38710	+	3.68759i	0.406401	+	0.234636i
$248$	13.7434	−	19.6753i	0.872705	−	1.24938i
$249$	−22.1743	+	3.99673i	−1.40524	+	0.253283i
$250$	−13.2135	−	0.379442i	−0.835693	−	0.0239980i
$251$	−3.05973			−0.193129			−0.0965644	−	0.995327i	$-0.530785\pi$
$251$	−3.05973			−0.193129			−0.0965644	+	0.995327i	$0.530785\pi$
$252$	5.84962	+	1.33491i	0.368491	+	0.0840912i
$253$	0.487254			0.0306334
$254$	−6.94648	−	0.199478i	−0.435861	−	0.0125163i
$255$	22.1593	+	26.2058i	1.38767	+	1.64107i
$256$	15.5799	+	3.64246i	0.973742	+	0.227654i
$257$	17.1928	+	9.92624i	1.07245	+	0.619182i	0.928851	−	0.370453i	$-0.120798\pi$
$257$	17.1928	+	9.92624i	1.07245	+	0.619182i	0.143603	+	0.989635i	$0.454131\pi$
$258$	8.86713	−	1.33668i	0.552044	−	0.0832178i
$259$	2.46909	−	1.42553i	0.153422	−	0.0885783i
$260$	13.8926	−	6.99035i	0.861581	−	0.433523i
$261$	29.7230	+	5.00873i	1.83981	+	0.310032i
$262$	−6.30788	−	3.88745i	−0.389702	−	0.240167i
$263$	9.51239	+	16.4759i	0.586559	+	1.01595i	0.994679	+	0.103022i	$0.0328511\pi$
$263$	9.51239	+	16.4759i	0.586559	+	1.01595i	−0.408120	+	0.912928i	$0.633816\pi$
$264$	0.317030	+	3.42870i	0.0195119	+	0.211022i
$265$	−1.11338	+	1.92843i	−0.0683944	+	0.118463i
$266$	−2.95469	+	1.59460i	−0.181164	+	0.0977715i
$267$	−2.80073	−	1.00737i	−0.171402	−	0.0616498i
$268$	14.3009	+	9.39028i	0.873567	+	0.573603i
$269$		−	27.0790i		−	1.65103i	−0.564378	−	0.825517i	$-0.690884\pi$
$269$		−	27.0790i		−	1.65103i	0.564378	−	0.825517i	$-0.309116\pi$
$270$	−0.318699	+	18.3917i	−0.0193954	+	1.11928i
$271$		−	29.1249i		−	1.76921i	−0.466337	−	0.884607i	$-0.654427\pi$
$271$		−	29.1249i		−	1.76921i	0.466337	−	0.884607i	$-0.345573\pi$
$272$	3.62790	−	31.4536i	0.219974	−	1.90716i
$273$	−5.06305	−	1.82107i	−0.306430	−	0.110216i
$274$	7.00847	+	12.9862i	0.423397	+	0.784525i
$275$	0.444866	−	0.770531i	0.0268264	−	0.0464648i
$276$	−1.44280	−	1.91971i	−0.0868466	−	0.115553i
$277$	8.22279	+	14.2423i	0.494060	+	0.855737i	0.999977	−	0.00684565i	$-0.00217905\pi$
$277$	8.22279	+	14.2423i	0.494060	+	0.855737i	−0.505917	+	0.862582i	$0.668846\pi$
$278$	−8.81158	+	14.2979i	−0.528484	+	0.857532i
$279$	−8.88766	−	23.8539i	−0.532090	−	1.42810i
$280$	−0.609017	+	7.05379i	−0.0363957	+	0.421545i
$281$	5.47490	−	3.16093i	0.326605	−	0.188566i	−0.327728	−	0.944772i	$-0.606283\pi$
$281$	5.47490	−	3.16093i	0.326605	−	0.188566i	0.654333	+	0.756207i	$0.272950\pi$
$282$	2.68575	+	17.8165i	0.159934	+	1.06096i
$283$	7.14839	+	4.12712i	0.424927	+	0.245332i	0.697183	−	0.716893i	$-0.254436\pi$
$283$	7.14839	+	4.12712i	0.424927	+	0.245332i	−0.272256	+	0.962225i	$0.587770\pi$
$284$	−12.6694	−	0.728236i	−0.751789	−	0.0432129i
$285$	−6.64628	−	7.85997i	−0.393691	−	0.465584i
$286$	0.0886354	−	3.08658i	0.00524112	−	0.182514i
$287$	6.72075			0.396713
$288$	12.5698	−	11.4018i	0.740683	−	0.671855i
$289$	−45.6557			−2.68563
$290$	−1.02096	+	35.5531i	−0.0599526	+	2.08775i
$291$	−23.2193	+	4.18508i	−1.36114	+	0.245333i
$292$	−16.3774	−	0.941375i	−0.958416	−	0.0550898i
$293$	6.70404	+	3.87058i	0.391654	+	0.226122i	0.682877	−	0.730534i	$-0.260729\pi$
$293$	6.70404	+	3.87058i	0.391654	+	0.226122i	−0.291222	+	0.956655i	$0.594062\pi$
$294$	1.91506	−	1.52727i	0.111689	−	0.0890721i
$295$	−15.7405	+	9.08781i	−0.916450	+	0.529113i
$296$	0.693659	−	8.03414i	0.0403181	−	0.466975i
$297$	3.18348	+	1.78998i	0.184724	+	0.103865i
$298$	−13.1341	+	21.3117i	−0.760836	+	1.23455i
$299$	1.07677	+	1.86502i	0.0622711	+	0.107857i
$300$	−4.35306	+	0.528909i	−0.251324	+	0.0305366i
$301$	1.83045	−	3.17043i	0.105505	−	0.182740i
$302$	−14.0995	−	26.1253i	−0.811334	−	1.50334i
$303$	−0.793909	−	4.40470i	−0.0456089	−	0.253043i
$304$	−1.08812	+	9.43396i	−0.0624082	+	0.541075i
$305$			12.0018i			0.687222i
$306$	−25.2643	−	22.1251i	−1.44426	−	1.26481i
$307$		−	14.7032i		−	0.839154i	−0.907720	−	0.419577i	$-0.862178\pi$
$307$		−	14.7032i		−	0.839154i	0.907720	−	0.419577i	$-0.137822\pi$
$308$	1.17506	+	0.771569i	0.0669553	+	0.0439642i
$309$	17.8040	−	15.0548i	1.01283	−	0.856436i
$310$	26.4341	−	14.2661i	1.50135	−	0.810261i
$311$	−6.26710	+	10.8549i	−0.355375	+	0.615527i	−0.987182	−	0.159599i	$-0.948980\pi$
$311$	−6.26710	+	10.8549i	−0.355375	+	0.615527i	0.631807	+	0.775125i	$0.282313\pi$
$312$	−12.4231	+	8.79045i	−0.703321	+	0.497661i
$313$	−11.6110	−	20.1108i	−0.656292	−	1.13673i	−0.981568	−	0.191112i	$-0.938790\pi$
$313$	−11.6110	−	20.1108i	−0.656292	−	1.13673i	0.325276	−	0.945619i	$-0.394543\pi$
$314$	−2.02742	−	1.24946i	−0.114414	−	0.0705113i
$315$	5.78908	+	4.78323i	0.326178	+	0.269505i
$316$	−4.68847	+	2.35911i	−0.263747	+	0.132710i
$317$	5.93134	−	3.42446i	0.333137	−	0.192337i	−0.324096	−	0.946024i	$-0.605060\pi$
$317$	5.93134	−	3.42446i	0.333137	−	0.192337i	0.657233	+	0.753687i	$0.271727\pi$
$318$	0.796043	−	2.02840i	0.0446399	−	0.113747i
$319$	6.11582	+	3.53097i	0.342420	+	0.197697i
$320$	15.3697	+	12.8370i	0.859190	+	0.717611i
$321$	9.98741	−	27.7675i	0.557443	−	1.54983i
$322$	−0.979983	−	0.0281415i	−0.0546123	−	0.00156827i
$323$	18.7925			1.04564
$324$	−2.37431	−	17.8427i	−0.131906	−	0.991262i
$325$	3.93239			0.218129
$326$	−21.1054	−	0.606069i	−1.16892	−	0.0335671i
$327$	−1.42720	+	3.96797i	−0.0789242	+	0.219429i
$328$	10.8854	−	15.5838i	0.601047	−	0.860472i
$329$	6.37026	+	3.67787i	0.351204	+	0.202768i
$330$	−1.57441	+	4.01174i	−0.0866682	+	0.220839i
$331$	−6.98234	+	4.03126i	−0.383784	+	0.221578i	−0.679463	−	0.733709i	$-0.737787\pi$
$331$	−6.98234	+	4.03126i	−0.383784	+	0.221578i	0.295679	+	0.955287i	$0.404454\pi$
$332$	11.6942	+	23.2410i	0.641803	+	1.27552i
$333$	−6.59366	−	5.44801i	−0.361330	−	0.298549i
$334$	2.81882	+	1.73719i	0.154239	+	0.0950550i
$335$	10.7062	+	18.5438i	0.584944	+	1.01315i
$336$	−0.439597	−	6.91424i	−0.0239820	−	0.377203i
$337$	−8.08375	+	14.0015i	−0.440350	+	0.762708i	−0.997715	−	0.0675590i	$-0.978479\pi$
$337$	−8.08375	+	14.0015i	−0.440350	+	0.762708i	0.557365	+	0.830267i	$0.311812\pi$
$338$	−4.16888	+	2.24989i	−0.226757	+	0.122378i
$339$	−6.31939	+	5.34358i	−0.343222	+	0.290223i
$340$	21.7507	−	33.1252i	1.17960	−	1.79646i
$341$		−	5.96401i		−	0.322969i
$342$	7.57757	+	6.63603i	0.409748	+	0.358835i
$343$		−	1.00000i		−	0.0539949i
$344$	−4.38673	−	9.37942i	−0.236517	−	0.505705i
$345$	−0.533146	−	2.95795i	−0.0287036	−	0.159251i
$346$	0.679324	+	1.25874i	0.0365207	+	0.0676702i
$347$	−3.82900	+	6.63203i	−0.205552	+	0.356026i	−0.950308	−	0.311310i	$-0.899232\pi$
$347$	−3.82900	+	6.63203i	−0.205552	+	0.356026i	0.744757	+	0.667336i	$0.232566\pi$
$348$	−4.19803	−	34.5509i	−0.225038	−	1.85213i
$349$	4.40927	+	7.63708i	0.236023	+	0.408803i	0.959569	−	0.281472i	$-0.0908227\pi$
$349$	4.40927	+	7.63708i	0.236023	+	0.408803i	−0.723547	+	0.690275i	$0.757489\pi$
$350$	−0.939234	+	1.52403i	−0.0502042	+	0.0814627i
$351$	0.183718	+	16.1407i	0.00980613	+	0.861528i
$352$	3.69230	−	1.47499i	0.196800	−	0.0786174i
$353$	−2.81435	+	1.62487i	−0.149793	+	0.0864830i	−0.573023	−	0.819539i	$-0.694229\pi$
$353$	−2.81435	+	1.62487i	−0.149793	+	0.0864830i	0.423230	+	0.906022i	$0.360896\pi$
$354$	13.9053	−	11.0895i	0.739059	−	0.589403i
$355$	−13.7551	−	7.94149i	−0.730043	−	0.421490i
$356$	−0.197224	+	3.43117i	−0.0104529	+	0.181852i
$357$	−13.4927	+	2.43194i	−0.714109	+	0.128712i
$358$	0.481654	−	16.7728i	0.0254562	−	0.886472i
$359$	−28.4033			−1.49907			−0.749533	−	0.661967i	$-0.769722\pi$
$359$	−28.4033			−1.49907			−0.749533	+	0.661967i	$0.769722\pi$
$360$	20.4676	−	5.67622i	1.07874	−	0.299163i
$361$	13.3635			0.703343
$362$	0.475831	−	16.5701i	0.0250091	−	0.870903i
$363$	−11.7495	−	13.8951i	−0.616691	−	0.729306i
$364$	−0.356534	+	6.20273i	−0.0186874	+	0.325112i
$365$	−17.7809	−	10.2658i	−0.930692	−	0.537336i
$366$	−1.75063	−	11.6132i	−0.0915071	−	0.607033i
$367$	4.00164	−	2.31035i	0.208884	−	0.120599i	−0.391909	−	0.920004i	$-0.628185\pi$
$367$	4.00164	−	2.31035i	0.208884	−	0.120599i	0.600793	+	0.799405i	$0.294852\pi$
$368$	−1.65251	+	2.22677i	−0.0861429	+	0.116078i
$369$	−7.03945	−	18.8934i	−0.366459	−	0.983553i
$370$	5.29523	−	8.59218i	0.275286	−	0.446686i
$371$	−0.444788	−	0.770396i	−0.0230923	−	0.0399970i
$372$	−23.4973	+	17.6600i	−1.21828	+	0.915628i
$373$	−13.7859	+	23.8779i	−0.713808	+	1.23635i	0.249609	+	0.968347i	$0.419698\pi$
$373$	−13.7859	+	23.8779i	−0.713808	+	1.23635i	−0.963417	+	0.268005i	$0.913636\pi$
$374$	−3.73682	−	6.92406i	−0.193226	−	0.358035i
$375$	15.2343	+	5.47948i	0.786697	+	0.282959i
$376$	18.8458	−	8.81416i	0.971900	−	0.454556i
$377$			31.2120i			1.60750i
$378$	−6.29935	−	3.78394i	−0.324003	−	0.194625i
$379$		−	20.5766i		−	1.05695i	−0.848949	−	0.528475i	$-0.822764\pi$
$379$		−	20.5766i		−	1.05695i	0.848949	−	0.528475i	$-0.177236\pi$
$380$	−6.52373	+	9.93531i	−0.334660	+	0.509671i
$381$	8.00888	+	2.88063i	0.410307	+	0.147579i
$382$	−8.41636	+	4.54219i	−0.430618	+	0.232399i
$383$	−0.0457558	+	0.0792514i	−0.00233801	+	0.00404955i	−0.867192	−	0.497974i	$-0.834078\pi$
$383$	−0.0457558	+	0.0792514i	−0.00233801	+	0.00404955i	0.864854	+	0.502023i	$0.167411\pi$
$384$	−16.7445	−	10.1795i	−0.854488	−	0.519470i
$385$	0.879697	+	1.52368i	0.0448335	+	0.0776539i
$386$	−3.33027	−	2.05239i	−0.169506	−	0.104464i
$387$	−10.8300	−	1.82500i	−0.550519	−	0.0927699i
$388$	12.2453	+	24.3362i	0.621661	+	1.23548i
$389$	−1.65481	+	0.955404i	−0.0839021	+	0.0484409i	−0.541364	−	0.840788i	$-0.682092\pi$
$389$	−1.65481	+	0.955404i	−0.0839021	+	0.0484409i	0.457462	+	0.889229i	$0.348759\pi$
$390$	−18.8346	+	2.83922i	−0.953727	+	0.143769i
$391$	4.75219	+	2.74368i	0.240329	+	0.138754i
$392$	−2.31876	−	1.61967i	−0.117115	−	0.0818059i
$393$	5.85951	+	6.92954i	0.295573	+	0.349549i
$394$	24.4043	+	0.700802i	1.22947	+	0.0353059i
$395$	−6.56900			−0.330522
$396$	0.938261	−	4.11150i	0.0471494	−	0.206611i
$397$	30.4353			1.52750			0.763751	−	0.645511i	$-0.223355\pi$
$397$	30.4353			1.52750			0.763751	+	0.645511i	$0.223355\pi$
$398$	20.4866	+	0.588300i	1.02690	+	0.0294888i
$399$	4.04690	−	0.729419i	0.202598	−	0.0365166i
$400$	2.01260	+	4.64629i	0.100630	+	0.232314i
$401$	18.9221	+	10.9247i	0.944922	+	0.545551i	0.891500	−	0.453021i	$-0.149654\pi$
$401$	18.9221	+	10.9247i	0.944922	+	0.545551i	0.0534223	+	0.998572i	$0.482987\pi$
$402$	−13.0645	−	16.3817i	−0.651596	−	0.817045i
$403$	22.8279	−	13.1797i	1.13714	−	0.656527i
$404$	−4.61658	+	2.32294i	−0.229684	+	0.115570i
$405$	7.38307	−	21.2844i	0.366868	−	1.05763i
$406$	−12.0964	−	7.45484i	−0.600336	−	0.369978i
$407$	−1.00196	−	1.73544i	−0.0496653	−	0.0860228i
$408$	−16.2147	+	35.2253i	−0.802746	+	1.74391i
$409$	2.23786	−	3.87609i	0.110655	−	0.191660i	−0.805379	−	0.592760i	$-0.798038\pi$
$409$	2.23786	−	3.87609i	0.110655	−	0.191660i	0.916035	+	0.401099i	$0.131372\pi$
$410$	20.9371	−	11.2994i	1.03401	−	0.558040i
$411$	−3.20588	−	17.7866i	−0.158134	−	0.877347i
$412$	−22.5049	−	14.7772i	−1.10874	−	0.728020i
$413$		−	7.26104i		−	0.357292i
$414$	0.947344	+	2.78442i	0.0465594	+	0.136847i
$415$			32.5628i			1.59845i
$416$	13.8052	+	10.8731i	0.676855	+	0.533099i
$417$	15.7070	−	13.2816i	0.769176	−	0.650404i
$418$	1.12079	+	2.07675i	0.0548198	+	0.101577i
$419$	−11.4022	+	19.7492i	−0.557033	+	0.964809i	0.440709	+	0.897650i	$0.354727\pi$
$419$	−11.4022	+	19.7492i	−0.557033	+	0.964809i	−0.997742	+	0.0671595i	$0.978606\pi$
$420$	3.39820	−	7.97763i	0.165815	−	0.389268i
$421$	−14.0510	−	24.3370i	−0.684803	−	1.18611i	−0.973499	−	0.228693i	$-0.926555\pi$
$421$	−14.0510	−	24.3370i	−0.684803	−	1.18611i	0.288696	−	0.957421i	$-0.406778\pi$
$422$	19.0024	−	30.8337i	0.925020	−	1.50096i
$423$	3.66693	−	21.7604i	0.178292	−	1.05803i
$424$	−2.50678	−	0.216432i	−0.121740	−	0.0105109i
$425$	8.67756	−	5.00999i	0.420924	−	0.243020i
$426$	14.4681	+	5.67799i	0.700981	+	0.275100i
$427$	−4.15228	−	2.39732i	−0.200943	−	0.116015i
$428$	−34.0180	−	1.95535i	−1.64432	−	0.0945156i
$429$	−1.27997	+	3.55865i	−0.0617976	+	0.171813i
$430$	0.371999	−	12.9543i	0.0179394	−	0.624711i
$431$	−0.610755			−0.0294190			−0.0147095	−	0.999892i	$-0.504682\pi$
$431$	−0.610755			−0.0294190			−0.0147095	+	0.999892i	$0.504682\pi$
$432$	−18.9770	+	8.47793i	−0.913029	+	0.407894i
$433$	10.5169			0.505410			0.252705	−	0.967543i	$-0.418680\pi$
$433$	10.5169			0.505410			0.252705	+	0.967543i	$0.418680\pi$
$434$	−0.344454	+	11.9950i	−0.0165343	+	0.575781i
$435$	14.7435	−	40.9906i	0.706897	−	1.96535i
$436$	4.86116	+	0.279420i	0.232807	+	0.0133818i
$437$	−1.42534	−	0.822918i	−0.0681830	−	0.0393655i
$438$	18.7026	+	7.33981i	0.893643	+	0.350710i
$439$	32.6334	−	18.8409i	1.55751	−	0.899227i	0.560012	−	0.828485i	$-0.310797\pi$
$439$	32.6334	−	18.8409i	1.55751	−	0.899227i	0.997495	−	0.0707423i	$-0.0225368\pi$
$440$	4.95787	+	0.428057i	0.236357	+	0.0204068i
$441$	−2.81121	+	1.04742i	−0.133867	+	0.0498772i
$442$	18.2447	−	29.6044i	0.867812	−	1.40814i
$443$	20.7455	+	35.9322i	0.985647	+	1.70719i	0.639025	+	0.769186i	$0.279338\pi$
$443$	20.7455	+	35.9322i	0.985647	+	1.70719i	0.346622	+	0.938005i	$0.387329\pi$
$444$	−3.87049	+	9.08637i	−0.183685	+	0.431220i
$445$	−2.15075	+	3.72520i	−0.101955	+	0.176592i
$446$	−10.2481	−	18.9889i	−0.485260	−	0.899152i
$447$	23.4120	−	19.7969i	1.10735	−	0.936359i
$448$	−7.51128	+	2.75331i	−0.354874	+	0.130082i
$449$			31.9656i			1.50855i	0.656559	+	0.754275i	$0.272011\pi$
$449$			31.9656i			1.50855i	−0.656559	+	0.754275i	$0.727989\pi$
$450$	5.26813	+	1.04409i	0.248342	+	0.0492187i
$451$		−	4.72379i		−	0.222434i
$452$	7.98795	+	5.24506i	0.375722	+	0.246707i
$453$	6.44951	+	35.7826i	0.303025	+	1.68121i
$454$	−9.66456	+	5.21583i	−0.453580	+	0.244791i
$455$	−3.88803	+	6.73427i	−0.182274	+	0.315707i
$456$	4.86331	−	10.5652i	0.227745	−	0.494761i
$457$	−14.8515	−	25.7236i	−0.694724	−	1.20330i	−0.970274	−	0.242011i	$-0.922193\pi$
$457$	−14.8515	−	25.7236i	−0.694724	−	1.20330i	0.275549	−	0.961287i	$-0.411140\pi$
$458$	−13.7261	−	8.45918i	−0.641378	−	0.395271i
$459$	20.9692	+	35.3835i	0.978761	+	1.65156i
$460$	−3.10025	+	1.55996i	−0.144550	+	0.0727333i
$461$	−8.96753	+	5.17741i	−0.417659	+	0.241136i	−0.694075	−	0.719902i	$-0.744187\pi$
$461$	−8.96753	+	5.17741i	−0.417659	+	0.241136i	0.276416	+	0.961038i	$0.410853\pi$
$462$	−1.07347	−	1.34603i	−0.0499421	−	0.0626230i
$463$	13.7219	+	7.92236i	0.637712	+	0.368183i	0.783733	−	0.621098i	$-0.213313\pi$
$463$	13.7219	+	7.92236i	0.637712	+	0.368183i	−0.146021	+	0.989282i	$0.546647\pi$
$464$	−36.8783	+	15.9743i	−1.71203	+	0.741590i
$465$	−36.2055	+	6.52573i	−1.67899	+	0.302624i
$466$	−27.4403	−	0.787986i	−1.27115	−	0.0365028i
$467$	−27.9844			−1.29496			−0.647481	−	0.762081i	$-0.724178\pi$
$467$	−27.9844			−1.29496			−0.647481	+	0.762081i	$0.724178\pi$
$468$	17.8106	−	5.49458i	0.823297	−	0.253987i
$469$	−8.55414			−0.394994
$470$	26.0287	+	0.747450i	1.20062	+	0.0344773i
$471$	1.88331	+	2.22722i	0.0867782	+	0.102625i
$472$	−16.8366	−	11.7605i	−0.774968	−	0.541322i
$473$	−2.22839	−	1.28656i	−0.102461	−	0.0591560i
$474$	6.35631	−	0.958181i	0.291955	−	0.0440107i
$475$	−2.60268	+	1.50266i	−0.119419	+	0.0689467i
$476$	7.11573	+	14.1418i	0.326149	+	0.648186i
$477$	−1.69986	+	2.05732i	−0.0778314	+	0.0941983i
$478$	−8.60659	−	5.30411i	−0.393656	−	0.242604i
$479$	11.5844	+	20.0648i	0.529306	+	0.916785i	0.999416	+	0.0341768i	$0.0108809\pi$
$479$	11.5844	+	20.0648i	0.529306	+	0.916785i	−0.470110	+	0.882608i	$0.655786\pi$
$480$	−12.9942	−	20.8008i	−0.593103	−	0.949421i
$481$	4.42840	−	7.67021i	0.201918	−	0.349731i
$482$	2.98028	−	1.60842i	0.135748	−	0.0732615i
$483$	1.12986	+	0.406388i	0.0514105	+	0.0184913i
$484$	−11.5329	+	17.5640i	−0.524223	+	0.798364i
$485$			34.0973i			1.54828i
$486$	−4.03940	+	21.6722i	−0.183231	+	0.983070i
$487$		−	13.8456i		−	0.627406i	−0.949521	−	0.313703i	$-0.898430\pi$
$487$		−	13.8456i		−	0.627406i	0.949521	−	0.313703i	$-0.101570\pi$
$488$	−12.2842	+	5.74527i	−0.556078	+	0.260076i
$489$	24.3332	+	8.75216i	1.10039	+	0.395787i
$490$	−1.68128	−	3.11529i	−0.0759524	−	0.140734i
$491$	1.97999	−	3.42944i	0.0893557	−	0.154769i	−0.817883	−	0.575384i	$-0.804853\pi$
$491$	1.97999	−	3.42944i	0.0893557	−	0.154769i	0.907239	+	0.420616i	$0.138186\pi$
$492$	−18.6110	+	13.9876i	−0.839048	+	0.630608i
$493$	39.7651	+	68.8752i	1.79093	+	3.10198i
$494$	−5.47218	+	8.87931i	−0.246205	+	0.399499i
$495$	3.36197	−	4.06895i	0.151109	−	0.182886i
$496$	27.2557	+	20.2268i	1.22382	+	0.908209i
$497$	5.49505	−	3.17257i	0.246487	−	0.142309i
$498$	−4.74975	−	31.5085i	−0.212841	−	1.41193i
$499$	−18.6834	−	10.7868i	−0.836382	−	0.482886i	0.0196506	−	0.999807i	$-0.493745\pi$
$499$	−18.6834	−	10.7868i	−0.836382	−	0.482886i	−0.856033	+	0.516921i	$0.827078\pi$
$500$	1.07278	−	18.6636i	0.0479763	−	0.834660i
$501$	−2.61846	−	3.09662i	−0.116984	−	0.138347i
$502$	0.124208	−	4.32534i	0.00554366	−	0.193049i
$503$	24.7621			1.10409			0.552044	−	0.833815i	$-0.313848\pi$
$503$	24.7621			1.10409			0.552044	+	0.833815i	$0.313848\pi$
$504$	−2.12453	+	8.21501i	−0.0946339	+	0.365926i
$505$	−6.46827			−0.287834
$506$	−0.0197797	+	0.688797i	−0.000879317	+	0.0306208i
$507$	5.70992	−	1.02916i	0.253587	−	0.0457068i
$508$	0.563975	−	9.81166i	0.0250224	−	0.435322i
$509$	−22.5133	−	12.9980i	−0.997882	−	0.576128i	−0.0902614	−	0.995918i	$-0.528770\pi$
$509$	−22.5133	−	12.9980i	−0.997882	−	0.576128i	−0.907621	+	0.419790i	$0.862104\pi$
$510$	−37.9449	+	30.2612i	−1.68023	+	1.33999i
$511$	7.10333	−	4.10111i	0.314233	−	0.181422i
$512$	−5.78155	+	21.8763i	−0.255511	+	0.966806i
$513$	−6.28936	−	10.6127i	−0.277682	−	0.468561i
$514$	−14.7300	+	23.9013i	−0.649711	+	1.05424i
$515$	−16.8481	−	29.1817i	−0.742415	−	1.28590i
$516$	1.52961	+	12.5891i	0.0673373	+	0.554205i
$517$	2.58505	−	4.47744i	0.113690	−	0.196918i
$518$	1.91495	+	3.54826i	0.0841379	+	0.155901i
$519$	−0.310743	−	1.72404i	−0.0136401	−	0.0756767i
$520$	9.31782	+	19.9227i	0.408613	+	0.873670i
$521$		−	16.4772i		−	0.721880i	−0.932589	−	0.360940i	$-0.882456\pi$
$521$		−	16.4772i		−	0.721880i	0.932589	−	0.360940i	$-0.117544\pi$
$522$	−8.28707	+	41.8140i	−0.362715	+	1.83015i
$523$			35.6352i			1.55822i	0.626888	+	0.779110i	$0.284329\pi$
$523$			35.6352i			1.55822i	−0.626888	+	0.779110i	$0.715671\pi$
$524$	5.75148	−	8.75921i	0.251255	−	0.382648i
$525$	1.67422	−	1.41570i	0.0730691	−	0.0617862i
$526$	−23.6770	+	12.7782i	−1.03237	+	0.557155i
$527$	33.5827	−	58.1670i	1.46289	−	2.53380i
$528$	−4.85979	+	0.308978i	−0.211495	+	0.0134466i
$529$	11.2597	+	19.5024i	0.489553	+	0.847930i
$530$	−2.68089	−	1.65219i	−0.116451	−	0.0717667i
$531$	−20.4123	+	7.60537i	−0.885819	+	0.330045i
$532$	−2.13424	−	4.24157i	−0.0925310	−	0.183895i
$533$	18.0808	−	10.4390i	0.783166	−	0.452161i
$534$	1.53774	−	3.91831i	0.0665444	−	0.169562i
$535$	−36.9331	−	21.3233i	−1.59676	−	0.921888i
$536$	−13.8549	+	19.8350i	−0.598442	+	0.856742i
$537$	−6.95551	+	19.3381i	−0.300152	+	0.834499i
$538$	38.2796	+	1.09925i	1.65035	+	0.0473921i
$539$	−0.702866			−0.0302746
$540$	−25.9862	−	1.19712i	−1.11827	−	0.0515159i
$541$	16.0235			0.688903			0.344452	−	0.938804i	$-0.388065\pi$
$541$	16.0235			0.688903			0.344452	+	0.938804i	$0.388065\pi$
$542$	41.1719	+	1.18231i	1.76849	+	0.0507844i
$543$	−6.87142	+	19.1043i	−0.294881	+	0.819843i
$544$	44.3165	+	6.40535i	1.90006	+	0.274627i
$545$	5.27773	+	3.04710i	0.226073	+	0.130523i
$546$	2.77986	−	7.08335i	0.118967	−	0.303140i
$547$	−9.75181	+	5.63021i	−0.416957	+	0.240730i	−0.693775	−	0.720192i	$-0.744054\pi$
$547$	−9.75181	+	5.63021i	−0.416957	+	0.240730i	0.276817	+	0.960923i	$0.410720\pi$
$548$	−18.6422	+	9.38023i	−0.796355	+	0.400703i
$549$	−2.39019	+	14.1840i	−0.102011	+	0.605356i
$550$	1.07119	+	0.660156i	0.0456756	+	0.0281491i
$551$	−11.9268	−	20.6579i	−0.508100	−	0.880056i
$552$	2.77233	−	1.96166i	0.117998	−	0.0834940i
$553$	1.31214	−	2.27268i	0.0557977	−	0.0966444i
$554$	−20.4671	+	11.0458i	−0.869566	+	0.469293i
$555$	−9.43896	+	7.98145i	−0.400662	+	0.338794i
$556$	−19.8543	−	13.0367i	−0.842009	−	0.552881i
$557$		−	25.2666i		−	1.07058i	−0.844669	−	0.535289i	$-0.820203\pi$
$557$		−	25.2666i		−	1.07058i	0.844669	−	0.535289i	$-0.179797\pi$
$558$	34.0814	−	11.5955i	1.44278	−	0.490878i
$559$		−	11.3725i		−	0.481006i
$560$	−9.94674	−	1.14727i	−0.420326	−	0.0484810i
$561$	1.70933	+	9.48356i	0.0721680	+	0.400396i
$562$	4.24614	+	7.86780i	0.179113	+	0.331883i
$563$	6.29010	−	10.8948i	0.265096	−	0.459160i	−0.702493	−	0.711691i	$-0.747930\pi$
$563$	6.29010	−	10.8948i	0.265096	−	0.459160i	0.967589	+	0.252531i	$0.0812630\pi$
$564$	−25.2950	+	3.07341i	−1.06511	+	0.129414i
$565$	5.98010	+	10.3578i	0.251585	+	0.435758i
$566$	−6.12441	+	9.93764i	−0.257428	+	0.417710i
$567$	5.88905	+	6.80582i	0.247317	+	0.285817i
$568$	1.54376	−	17.8803i	0.0647748	−	0.750239i
$569$	−9.64118	+	5.56634i	−0.404179	+	0.233353i	−0.688286	−	0.725440i	$-0.741636\pi$
$569$	−9.64118	+	5.56634i	−0.404179	+	0.233353i	0.284107	+	0.958793i	$0.408303\pi$
$570$	11.3809	−	9.07631i	0.476693	−	0.380165i
$571$	38.6886	+	22.3369i	1.61907	+	0.934769i	0.987162	+	0.159724i	$0.0510605\pi$
$571$	38.6886	+	22.3369i	1.61907	+	0.934769i	0.631906	+	0.775045i	$0.282273\pi$
$572$	4.35969	+	0.250595i	0.182288	+	0.0104779i
$573$	11.5275	−	2.07773i	0.481568	−	0.0867985i
$574$	−0.272824	+	9.50065i	−0.0113875	+	0.396550i
$575$	−0.877545			−0.0365962
$576$	15.6076	+	18.2319i	0.650317	+	0.759663i
$577$	0.773772			0.0322125			0.0161063	−	0.999870i	$-0.494873\pi$
$577$	0.773772			0.0322125			0.0161063	+	0.999870i	$0.494873\pi$
$578$	1.85336	−	64.5404i	0.0770897	−	2.68452i
$579$	3.09355	+	3.65847i	0.128564	+	0.152041i
$580$	−50.2176	−	2.88651i	−2.08517	−	0.119856i
$581$	−11.2658	−	6.50432i	−0.467385	−	0.269845i
$582$	−4.97358	−	32.9934i	−0.206162	−	1.36762i
$583$	−0.541485	+	0.312627i	−0.0224260	+	0.0129477i
$584$	1.99559	−	23.1134i	0.0825779	−	0.956439i
$585$	23.0039	+	3.87646i	0.951093	+	0.160272i
$586$	−5.74372	+	9.31992i	−0.237271	+	0.385002i
$587$	−3.95356	−	6.84776i	−0.163181	−	0.282637i	0.772827	−	0.634617i	$-0.218842\pi$
$587$	−3.95356	−	6.84776i	−0.163181	−	0.282637i	−0.936008	+	0.351979i	$0.885509\pi$
$588$	2.08125	+	2.76919i	0.0858294	+	0.114199i
$589$	−10.0726	+	17.4462i	−0.415032	+	0.718857i
$590$	−12.2078	−	22.6202i	−0.502588	−	0.931260i
$591$	−28.1367	−	10.1202i	−1.15739	−	0.416289i
$592$	11.3292	+	1.30672i	0.465625	+	0.0537058i
$593$		−	13.0459i		−	0.535732i	−0.963456	−	0.267866i	$-0.913682\pi$
$593$		−	13.0459i		−	0.535732i	0.963456	−	0.267866i	$-0.0863184\pi$
$594$	−2.65961	+	4.42760i	−0.109125	+	0.181667i
$595$			19.8139i			0.812292i
$596$	−29.5937	−	19.4319i	−1.21221	−	0.795960i
$597$	−23.6198	−	8.49557i	−0.966695	−	0.347700i
$598$	−2.68016	+	1.44644i	−0.109600	+	0.0591495i
$599$	−5.35898	+	9.28202i	−0.218962	+	0.379253i	−0.954491	−	0.298240i	$-0.903600\pi$
$599$	−5.35898	+	9.28202i	−0.218962	+	0.379253i	0.735529	+	0.677493i	$0.236934\pi$
$600$	−0.570972	−	6.17510i	−0.0233098	−	0.252097i
$601$	−2.22698	−	3.85725i	−0.0908406	−	0.157341i	0.817024	−	0.576603i	$-0.195622\pi$
$601$	−2.22698	−	3.85725i	−0.0908406	−	0.157341i	−0.907865	+	0.419262i	$0.862289\pi$
$602$	4.40750	+	2.71628i	0.179636	+	0.110707i
$603$	8.95979	+	24.0475i	0.364871	+	0.979290i
$604$	37.5039	−	18.8709i	1.52601	−	0.767847i
$605$	−22.7750	+	13.1491i	−0.925934	+	0.534588i
$606$	6.25885	−	0.943489i	0.254248	−	0.0383266i
$607$	−29.7000	−	17.1473i	−1.20549	−	0.695988i	−0.243717	−	0.969846i	$-0.578367\pi$
$607$	−29.7000	−	17.1473i	−1.20549	−	0.695988i	−0.961770	+	0.273858i	$0.911700\pi$
$608$	−13.2920	−	1.92117i	−0.539060	−	0.0779138i
$609$	11.2366	+	13.2886i	0.455331	+	0.538480i
$610$	−16.9661	−	0.487205i	−0.686938	−	0.0197264i
$611$	22.8505			0.924433
$612$	32.3023	−	34.8162i	1.30574	−	1.40736i
$613$	−27.5606			−1.11316			−0.556581	−	0.830794i	$-0.687887\pi$
$613$	−27.5606			−1.11316			−0.556581	+	0.830794i	$0.687887\pi$
$614$	20.7849	+	0.596865i	0.838808	+	0.0240875i
$615$	−28.6765	+	5.16870i	−1.15635	+	0.208422i
$616$	−1.13841	+	1.62978i	−0.0458680	+	0.0656657i
$617$	21.8157	+	12.5953i	0.878268	+	0.507068i	0.870087	−	0.492899i	$-0.164063\pi$
$617$	21.8157	+	12.5953i	0.878268	+	0.507068i	0.00818075	+	0.999967i	$0.497396\pi$
$618$	20.5591	+	25.7794i	0.827010	+	1.03700i
$619$	−2.44808	+	1.41340i	−0.0983968	+	0.0568094i	−0.548391	−	0.836222i	$-0.684759\pi$
$619$	−2.44808	+	1.41340i	−0.0983968	+	0.0568094i	0.449994	+	0.893032i	$0.351426\pi$
$620$	19.0939	+	37.9472i	0.766831	+	1.52399i
$621$	−0.0409982	−	3.60194i	−0.00164520	−	0.144541i
$622$	−15.0905	−	9.30001i	−0.605072	−	0.372897i
$623$	−0.859209	−	1.48819i	−0.0344235	−	0.0596232i
$624$	−11.9221	−	17.9186i	−0.477268	−	0.717316i
$625$	14.8635	−	25.7443i	0.594538	−	1.02977i
$626$	28.9006	−	15.5973i	1.15510	−	0.623393i
$627$	−0.512684	−	2.84443i	−0.0204746	−	0.113595i
$628$	1.84858	−	2.81530i	0.0737665	−	0.112343i
$629$		−	22.5677i		−	0.899834i
$630$	−6.99673	+	7.98945i	−0.278756	+	0.318307i
$631$			35.3279i			1.40638i	0.711002	+	0.703190i	$0.248242\pi$
$631$			35.3279i			1.40638i	−0.711002	+	0.703190i	$0.751758\pi$
$632$	−3.14458	−	6.72354i	−0.125085	−	0.267448i
$633$	−33.8725	+	28.6421i	−1.34631	+	1.13842i
$634$	4.60015	+	8.52374i	0.182695	+	0.338521i
$635$	6.15020	−	10.6525i	0.244063	−	0.422730i
$636$	2.83509	+	1.20765i	0.112419	+	0.0478865i
$637$	−1.55324	−	2.69030i	−0.0615417	−	0.106593i
$638$	−5.23976	+	8.50218i	−0.207444	+	0.336605i
$639$	−14.6744	−	12.1247i	−0.580510	−	0.479647i
$640$	−18.7707	+	21.2059i	−0.741978	+	0.838237i
$641$	17.8094	−	10.2823i	0.703431	−	0.406126i	−0.105193	−	0.994452i	$-0.533546\pi$
$641$	17.8094	−	10.2823i	0.703431	−	0.406126i	0.808624	+	0.588326i	$0.200213\pi$
$642$	38.8476	+	15.2457i	1.53319	+	0.601700i
$643$	16.6218	+	9.59659i	0.655499	+	0.378453i	0.790560	−	0.612385i	$-0.209790\pi$
$643$	16.6218	+	9.59659i	0.655499	+	0.378453i	−0.135061	+	0.990837i	$0.543123\pi$
$644$	0.0795635	−	1.38419i	0.00313524	−	0.0545448i
$645$	−5.37200	+	14.9355i	−0.211522	+	0.588085i
$646$	−0.762868	+	26.5656i	−0.0300146	+	1.04521i
$647$	−30.9160			−1.21544			−0.607718	−	0.794153i	$-0.707915\pi$
$647$	−30.9160			−1.21544			−0.607718	+	0.794153i	$0.707915\pi$
$648$	25.3194	−	2.63209i	0.994640	−	0.103398i
$649$	−5.10354			−0.200331
$650$	−0.159632	+	5.55894i	−0.00626130	+	0.218040i
$651$	4.97421	−	13.8296i	0.194955	−	0.542023i
$652$	1.71352	−	29.8106i	0.0671064	−	1.16747i
$653$	−14.2740	−	8.24109i	−0.558584	−	0.322499i	0.193993	−	0.981003i	$-0.437856\pi$
$653$	−14.2740	−	8.24109i	−0.558584	−	0.322499i	−0.752577	+	0.658504i	$0.771190\pi$
$654$	−5.55131	−	2.17861i	−0.217073	−	0.0851903i
$655$	11.3579	−	6.55749i	0.443790	−	0.256222i
$656$	21.5879	+	16.0206i	0.842864	+	0.625498i
$657$	−18.9693	−	15.6734i	−0.740062	−	0.611477i
$658$	−5.45775	+	8.85589i	−0.212765	+	0.345239i
$659$	13.7838	+	23.8743i	0.536942	+	0.930010i	0.999067	+	0.0431955i	$0.0137538\pi$
$659$	13.7838	+	23.8743i	0.536942	+	0.930010i	−0.462125	+	0.886815i	$0.652913\pi$
$660$	−5.60721	−	2.38848i	−0.218260	−	0.0929715i
$661$	5.86138	−	10.1522i	0.227981	−	0.394875i	−0.729229	−	0.684270i	$-0.760121\pi$
$661$	5.86138	−	10.1522i	0.227981	−	0.394875i	0.957210	+	0.289395i	$0.0934542\pi$
$662$	−5.41527	−	10.0341i	−0.210470	−	0.389986i
$663$	−32.5219	+	27.5001i	−1.26305	+	1.06801i
$664$	−33.3289	+	15.5879i	−1.29341	+	0.604926i
$665$		−	5.94284i		−	0.230454i
$666$	7.96914	−	9.09984i	0.308798	−	0.352612i
$667$		−	6.96521i		−	0.269694i
$668$	−2.57018	+	3.91425i	−0.0994432	+	0.151447i
$669$	4.68777	+	26.0082i	0.181239	+	1.00554i
$670$	−26.6486	+	14.3819i	−1.02953	+	0.555621i
$671$	−1.68500	+	2.91850i	−0.0650486	+	0.112667i
$672$	9.79203	−	0.340750i	0.377736	−	0.0131447i
$673$	−3.04565	−	5.27522i	−0.117401	−	0.203345i	0.801336	−	0.598215i	$-0.204123\pi$
$673$	−3.04565	−	5.27522i	−0.117401	−	0.203345i	−0.918737	+	0.394870i	$0.870790\pi$
$674$	−19.4647	−	11.9958i	−0.749754	−	0.462062i
$675$	−5.73345	−	3.22376i	−0.220680	−	0.124083i
$676$	−3.01128	−	5.98460i	−0.115818	−	0.230177i
$677$	25.8756	−	14.9393i	0.994481	−	0.574164i	0.0878702	−	0.996132i	$-0.471994\pi$
$677$	25.8756	−	14.9393i	0.994481	−	0.574164i	0.906611	+	0.421968i	$0.138661\pi$
$678$	−7.29732	−	9.15020i	−0.280252	−	0.351411i
$679$	−11.7967	−	6.81083i	−0.452716	−	0.261376i
$680$	45.9438	+	32.0921i	1.76186	+	1.23068i
$681$	13.2371	−	2.38587i	0.507246	−	0.0914268i
$682$	8.43091	+	0.242105i	0.322836	+	0.00927068i
$683$	5.57818			0.213443			0.106722	−	0.994289i	$-0.465965\pi$
$683$	5.57818			0.213443			0.106722	+	0.994289i	$0.465965\pi$
$684$	−9.68850	+	10.4425i	−0.370449	+	0.399279i
$685$	−26.1195			−0.997974
$686$	1.41363	+	0.0405943i	0.0539727	+	0.00154990i
$687$	12.7504	+	15.0788i	0.486460	+	0.575294i
$688$	13.4371	−	5.82047i	0.512285	−	0.221903i
$689$	−2.39322	−	1.38173i	−0.0911745	−	0.0526396i
$690$	4.20310	−	0.633596i	0.160009	−	0.0241206i
$691$	6.59535	−	3.80783i	0.250899	−	0.144857i	−0.369277	−	0.929319i	$-0.620395\pi$
$691$	6.59535	−	3.80783i	0.250899	−	0.144857i	0.620176	+	0.784463i	$0.287061\pi$
$692$	−1.80697	+	0.909216i	−0.0686907	+	0.0345632i
$693$	0.736197	+	1.97591i	0.0279658	+	0.0750585i
$694$	−9.21981	−	5.68202i	−0.349979	−	0.215687i
$695$	−14.8637	−	25.7447i	−0.563813	−	0.976553i
$696$	49.0127	−	4.53189i	1.85782	−	0.171781i
$697$	26.5992	−	46.0711i	1.00751	−	1.74507i
$698$	−10.9750	+	5.92306i	−0.415410	+	0.224191i
$699$	31.6371	+	11.3792i	1.19662	+	0.430401i
$700$	−2.11628	−	1.38960i	−0.0799880	−	0.0525218i
$701$			13.6591i			0.515896i	0.966159	+	0.257948i	$0.0830463\pi$
$701$			13.6591i			0.515896i	−0.966159	+	0.257948i	$0.916954\pi$
$702$	−22.8245	−	0.395512i	−0.861455	−	0.0149277i
$703$			6.76879i			0.255290i
$704$	1.93521	+	5.27942i	0.0729360	+	0.198976i
$705$	−30.0096	−	10.7938i	−1.13023	−	0.406519i
$706$	−2.18272	−	4.04442i	−0.0821476	−	0.152214i
$707$	1.29202	−	2.23784i	0.0485913	−	0.0841625i
$708$	15.1121	+	20.1072i	0.567946	+	0.755673i
$709$	−11.1244	−	19.2680i	−0.417784	−	0.723624i	0.577932	−	0.816085i	$-0.303860\pi$
$709$	−11.1244	−	19.2680i	−0.417784	−	0.723624i	−0.995716	+	0.0924613i	$0.970527\pi$
$710$	11.7847	−	19.1222i	0.442272	−	0.717643i
$711$	−7.76336	−	1.30823i	−0.291149	−	0.0490625i
$712$	−4.84241	−	0.418088i	−0.181477	−	0.0156685i
$713$	−5.09424	+	2.94116i	−0.190781	+	0.110147i
$714$	−2.89014	−	19.1724i	−0.108161	−	0.717510i
$715$	4.73329	+	2.73277i	0.177015	+	0.102200i
$716$	23.6910	+	1.36176i	0.885376	+	0.0508915i
$717$	7.99484	+	9.45479i	0.298573	+	0.353096i
$718$	1.15301	−	40.1517i	0.0430299	−	1.49845i
$719$	−17.7827			−0.663184			−0.331592	−	0.943423i	$-0.607586\pi$
$719$	−17.7827			−0.663184			−0.331592	+	0.943423i	$0.607586\pi$
$720$	7.19321	+	29.1641i	0.268075	+	1.08688i
$721$	13.4614			0.501328
$722$	−0.542483	+	18.8911i	−0.0201891	+	0.703054i
$723$	−4.08195	+	0.735737i	−0.151810	+	0.0273624i
$724$	23.4046	+	1.34530i	0.869826	+	0.0499977i
$725$	−11.0146	−	6.35929i	−0.409072	−	0.236178i
$726$	20.1196	−	16.0454i	0.746707	−	0.595502i
$727$	−45.2123	+	26.1034i	−1.67683	+	0.968120i	−0.713173	+	0.700988i	$0.752742\pi$
$727$	−45.2123	+	26.1034i	−1.67683	+	0.968120i	−0.963660	+	0.267131i	$0.913924\pi$
$728$	−8.75390	−	0.755802i	−0.324441	−	0.0280119i
$729$	12.9643	−	23.6839i	0.480158	−	0.877182i
$730$	15.2338	−	24.7188i	0.563829	−	0.914885i
$731$	−14.4890	−	25.0956i	−0.535894	−	0.928195i
$732$	16.4879	−	2.00332i	0.609409	−	0.0740448i
$733$	−5.30936	+	9.19609i	−0.196106	+	0.339665i	−0.947262	−	0.320459i	$-0.896163\pi$
$733$	−5.30936	+	9.19609i	−0.196106	+	0.339665i	0.751157	+	0.660124i	$0.229496\pi$
$734$	3.10354	+	5.75063i	0.114554	+	0.212260i
$735$	0.769066	+	4.26686i	0.0283674	+	0.157386i
$736$	−3.08075	−	2.42643i	−0.113558	−	0.0894394i
$737$			6.01242i			0.221470i
$738$	26.9941	−	9.18422i	0.993667	−	0.338076i
$739$			25.7536i			0.947362i	0.880696	+	0.473681i	$0.157075\pi$
$739$			25.7536i			0.947362i	−0.880696	+	0.473681i	$0.842925\pi$
$740$	11.9312	+	7.83429i	0.438600	+	0.287994i
$741$	9.75438	−	8.24816i	0.358336	−	0.303004i
$742$	1.10711	−	0.597493i	0.0406433	−	0.0219346i
$743$	1.97016	−	3.41241i	0.0722780	−	0.125189i	−0.827621	−	0.561287i	$-0.810306\pi$
$743$	1.97016	−	3.41241i	0.0722780	−	0.125189i	0.899899	+	0.436098i	$0.143640\pi$
$744$	−24.0109	−	33.9334i	−0.880281	−	1.24406i
$745$	−22.1550	−	38.3737i	−0.811698	−	1.40590i
$746$	−33.1949	−	20.4575i	−1.21535	−	0.749003i
$747$	−6.48496	+	38.4833i	−0.237272	+	1.40803i
$748$	9.93976	−	5.00141i	0.363434	−	0.182870i
$749$	14.7545	−	8.51853i	0.539119	−	0.311260i
$750$	−8.36439	+	21.3133i	−0.305424	+	0.778251i
$751$	10.3540	+	5.97786i	0.377821	+	0.218135i	0.676870	−	0.736103i	$-0.263336\pi$
$751$	10.3540	+	5.97786i	0.377821	+	0.218135i	−0.299049	+	0.954238i	$0.596669\pi$
$752$	11.6949	+	26.9989i	0.426470	+	0.984548i
$753$	−1.79367	+	4.98685i	−0.0653649	+	0.181731i
$754$	−44.1222	−	1.26703i	−1.60684	−	0.0461424i
$755$	52.5466			1.91237
$756$	5.60482	−	8.75134i	0.203845	−	0.318283i
$757$	1.73758			0.0631534			0.0315767	−	0.999501i	$-0.489947\pi$
$757$	1.73758			0.0631534			0.0315767	+	0.999501i	$0.489947\pi$
$758$	29.0877	+	0.835293i	1.05651	+	0.0303392i
$759$	0.285637	−	0.794142i	0.0103680	−	0.0288255i
$760$	−13.7800	−	9.62547i	−0.499854	−	0.349152i
$761$	−25.7786	−	14.8833i	−0.934473	−	0.539518i	−0.0462496	−	0.998930i	$-0.514727\pi$
$761$	−25.7786	−	14.8833i	−0.934473	−	0.539518i	−0.888223	+	0.459412i	$0.848060\pi$
$762$	−4.39726	+	11.2047i	−0.159296	+	0.405902i
$763$	−2.10842	+	1.21729i	−0.0763298	+	0.0440690i
$764$	−6.07933	−	12.0820i	−0.219942	−	0.437112i
$765$	55.7012	−	20.7535i	2.01388	−	0.750346i
$766$	−0.110175	−	0.0678989i	−0.00398077	−	0.00245329i
$767$	−11.2782	−	19.5343i	−0.407231	−	0.705344i
$768$	15.0698	−	23.2573i	0.543784	−	0.839225i
$769$	11.5167	−	19.9475i	0.415303	−	0.719327i	−0.580157	−	0.814505i	$-0.697009\pi$
$769$	11.5167	−	19.9475i	0.415303	−	0.719327i	0.995460	+	0.0951782i	$0.0303421\pi$
$770$	−2.18963	+	1.18171i	−0.0789089	+	0.0425860i
$771$	26.2568	−	22.2024i	0.945615	−	0.799598i
$772$	3.03651	−	4.62445i	0.109287	−	0.166438i
$773$		−	1.33102i		−	0.0478734i	−0.999713	−	0.0239367i	$-0.992380\pi$
$773$		−	1.33102i		−	0.0478734i	0.999713	−	0.0239367i	$-0.00762002\pi$
$774$	3.01951	−	15.2355i	0.108534	−	0.547629i
$775$			10.7412i			0.385835i
$776$	−34.8995	+	16.3224i	−1.25282	+	0.585941i
$777$	−0.875952	−	4.85988i	−0.0314246	−	0.174347i
$778$	−1.28341	−	2.37807i	−0.0460126	−	0.0852580i
$779$	−7.97795	+	13.8182i	−0.285840	+	0.495089i
$780$	−3.24903	−	26.7404i	−0.116334	−	0.957460i
$781$	−2.22989	−	3.86229i	−0.0797919	−	0.138204i
$782$	−4.07146	+	6.60646i	−0.145595	+	0.236247i
$783$	25.5875	−	45.5073i	0.914423	−	1.62630i
$784$	2.38375	−	3.21212i	0.0851339	−	0.114719i
$785$	3.65055	−	2.10764i	0.130294	−	0.0752250i
$786$	−10.0337	+	8.00189i	−0.357889	+	0.285418i
$787$	1.23901	+	0.715343i	0.0441659	+	0.0254992i	0.521920	−	0.852994i	$-0.325216\pi$
$787$	1.23901	+	0.715343i	0.0441659	+	0.0254992i	−0.477754	+	0.878493i	$0.658549\pi$
$788$	−1.98135	+	34.4702i	−0.0705827	+	1.22795i
$789$	32.4293	−	5.84511i	1.15451	−	0.208091i
$790$	0.266664	−	9.28614i	0.00948747	−	0.330386i
$791$	−4.77802			−0.169887
$792$	5.77405	+	1.49326i	0.205172	+	0.0530606i
$793$	−14.8945			−0.528919
$794$	−1.23550	+	43.0242i	−0.0438462	+	1.52687i
$795$	2.49034	+	2.94510i	0.0883231	+	0.104452i
$796$	−1.66328	+	28.9366i	−0.0589533	+	1.02563i
$797$	−29.9747	−	17.3059i	−1.06176	−	0.613007i	−0.135841	−	0.990731i	$-0.543373\pi$
$797$	−29.9747	−	17.3059i	−1.06176	−	0.613007i	−0.925918	+	0.377724i	$0.876707\pi$
$798$	0.866848	+	5.75043i	0.0306861	+	0.203563i
$799$	50.4240	−	29.1123i	1.78387	−	1.02992i
$800$	−6.64983	+	2.65646i	−0.235107	+	0.0939202i
$801$	−3.28367	+	3.97418i	−0.116023	+	0.140421i
$802$	−16.2116	+	26.3053i	−0.572450	+	0.928873i
$803$	−2.88253	−	4.99269i	−0.101722	−	0.176188i
$804$	23.6880	−	17.8033i	0.835412	−	0.627875i
$805$	0.867647	−	1.50281i	0.0305805	−	0.0529671i
$806$	17.7045	+	32.8052i	0.623616	+	1.15552i
$807$	−44.1341	−	15.8741i	−1.55359	−	0.558796i
$808$	−3.09637	−	6.62044i	−0.108930	−	0.232906i
$809$			21.7895i			0.766078i	0.923732	+	0.383039i	$0.125122\pi$
$809$			21.7895i			0.766078i	−0.923732	+	0.383039i	$0.874878\pi$
$810$	29.7886	+	11.3010i	1.04666	+	0.397075i
$811$			14.6383i			0.514020i	0.966409	+	0.257010i	$0.0827374\pi$
$811$			14.6383i			0.514020i	−0.966409	+	0.257010i	$0.917263\pi$
$812$	11.0294	−	16.7973i	0.387058	−	0.589469i
$813$	−47.4687	−	17.0735i	−1.66480	−	0.598795i
$814$	2.49395	−	1.34595i	0.0874129	−	0.0471756i
$815$	18.6860	−	32.3652i	0.654544	−	1.13370i
$816$	−49.1374	−	24.3515i	−1.72015	−	0.852473i
$817$	4.34571	+	7.52699i	0.152037	+	0.263336i
$818$	5.38851	+	3.32086i	0.188405	+	0.116111i
$819$	−5.93609	+	7.18437i	−0.207424	+	0.251042i
$820$	15.1233	+	30.0560i	0.528129	+	1.04960i
$821$	−15.6555	+	9.03872i	−0.546382	+	0.315454i	−0.747661	−	0.664080i	$-0.768823\pi$
$821$	−15.6555	+	9.03872i	−0.546382	+	0.315454i	0.201280	+	0.979534i	$0.435490\pi$
$822$	25.2738	−	3.80990i	0.881525	−	0.132885i
$823$	−10.4800	−	6.05062i	−0.365309	−	0.210911i	0.306098	−	0.952000i	$-0.400976\pi$
$823$	−10.4800	−	6.05062i	−0.365309	−	0.210911i	−0.671407	+	0.741089i	$0.734310\pi$
$824$	21.8031	−	31.2138i	0.759546	−	1.08738i
$825$	−0.995047	−	1.17676i	−0.0346431	−	0.0409694i
$826$	10.2644	+	0.294757i	0.357145	+	0.0102559i
$827$	50.7180			1.76364			0.881819	−	0.471588i	$-0.156319\pi$
$827$	50.7180			1.76364			0.881819	+	0.471588i	$0.156319\pi$
$828$	−3.97459	+	1.22616i	−0.138127	+	0.0426121i
$829$	−14.5505			−0.505359			−0.252679	−	0.967550i	$-0.581312\pi$
$829$	−14.5505			−0.505359			−0.252679	+	0.967550i	$0.581312\pi$
$830$	−46.0318	−	1.32187i	−1.59779	−	0.0458826i
$831$	28.0329	−	5.05269i	0.972450	−	0.175276i
$832$	−15.9310	+	19.0741i	−0.552308	+	0.661274i
$833$	−6.85506	−	3.95777i	−0.237514	−	0.137129i
$834$	18.1377	+	22.7431i	0.628057	+	0.787528i
$835$	−5.07554	+	2.93036i	−0.175646	+	0.101409i
$836$	−2.98126	+	1.50008i	−0.103109	+	0.0518815i
$837$	−44.0879	+	0.501820i	−1.52390	+	0.0173454i
$838$	−27.4552	−	16.9202i	−0.948423	−	0.584498i
$839$	−7.34607	−	12.7238i	−0.253615	−	0.439273i	0.710904	−	0.703289i	$-0.248286\pi$
$839$	−7.34607	−	12.7238i	−0.253615	−	0.439273i	−0.964518	+	0.264016i	$0.914953\pi$
$840$	11.1395	+	5.12765i	0.384348	+	0.176921i
$841$	35.9746	−	62.3099i	1.24050	−	2.14862i
$842$	34.9739	−	18.8750i	1.20528	−	0.650474i
$843$	−1.94231	−	10.7762i	−0.0668967	−	0.371150i
$844$	42.8162	+	28.1140i	1.47379	+	0.967723i
$845$		−	8.38499i		−	0.288452i
$846$	30.6123	+	6.06703i	1.05247	+	0.208589i
$847$		−	10.5060i		−	0.360990i
$848$	0.407716	−	3.53487i	0.0140010	−	0.121388i
$849$	10.9170	−	9.23127i	0.374671	−	0.316816i
$850$	6.73002	+	12.4702i	0.230838	+	0.427726i
$851$	−0.988234	+	1.71167i	−0.0338762	+	0.0586754i
$852$	−8.61390	+	20.2220i	−0.295107	+	0.692795i
$853$	0.885883	+	1.53439i	0.0303321	+	0.0525367i	0.880793	−	0.473502i	$-0.157010\pi$
$853$	0.885883	+	1.53439i	0.0303321	+	0.0525367i	−0.850461	+	0.526038i	$0.823677\pi$
$854$	3.55749	−	5.77248i	0.121735	−	0.197530i
$855$	−16.7066	+	6.22466i	−0.571353	+	0.212879i
$856$	4.14508	−	48.0095i	0.141676	−	1.64093i
$857$	0.277829	−	0.160404i	0.00949045	−	0.00547931i	−0.495247	−	0.868752i	$-0.664923\pi$
$857$	0.277829	−	0.160404i	0.00949045	−	0.00547931i	0.504738	+	0.863273i	$0.331589\pi$
$858$	−4.97865	−	1.95387i	−0.169968	−	0.0667040i
$859$	27.9931	+	16.1618i	0.955112	+	0.551434i	0.894665	−	0.446737i	$-0.147414\pi$
$859$	27.9931	+	16.1618i	0.955112	+	0.551434i	0.0604467	+	0.998171i	$0.480747\pi$
$860$	18.2975	+	1.05174i	0.623939	+	0.0358640i
$861$	3.93982	−	10.9537i	0.134269	−	0.373300i
$862$	0.0247931	−	0.863381i	0.000844458	−	0.0294069i
$863$	−18.8459			−0.641522			−0.320761	−	0.947160i	$-0.603939\pi$
$863$	−18.8459			−0.641522			−0.320761	+	0.947160i	$0.603939\pi$
$864$	−11.2143	−	27.1706i	−0.381518	−	0.924361i
$865$	−2.53174			−0.0860816
$866$	−0.426926	+	14.8670i	−0.0145075	+	0.505202i
$867$	−26.7642	+	74.4111i	−0.908959	+	2.52713i
$868$	−16.9426	−	0.973861i	−0.575069	−	0.0330550i
$869$	−1.59739	−	0.922256i	−0.0541879	−	0.0312854i
$870$	57.3471	+	22.5058i	1.94425	+	0.763020i
$871$	−23.0132	+	13.2867i	−0.779772	+	0.450201i
$872$	−0.592331	+	6.86054i	−0.0200589	+	0.232327i
$873$	−6.79056	+	40.2968i	−0.229826	+	1.36384i
$874$	1.22116	−	1.98149i	0.0413064	−	0.0670250i
$875$	4.67359	+	8.09490i	0.157996	+	0.273657i
$876$	−11.1350	+	26.1406i	−0.376217	+	0.883208i
$877$	−20.0001	+	34.6412i	−0.675355	+	1.16975i	0.301010	+	0.953621i	$0.402676\pi$
$877$	−20.0001	+	34.6412i	−0.675355	+	1.16975i	−0.976365	+	0.216129i	$0.930657\pi$
$878$	25.3093	+	46.8964i	0.854149	+	1.58268i
$879$	10.2384	−	8.65746i	0.345333	−	0.292009i
$880$	−0.806377	+	6.99123i	−0.0271830	+	0.235674i
$881$			4.11680i			0.138699i	0.997592	+	0.0693493i	$0.0220923\pi$
$881$			4.11680i			0.138699i	−0.997592	+	0.0693493i	$0.977908\pi$
$882$	−1.36655	−	4.01653i	−0.0460141	−	0.135244i
$883$			58.6257i			1.97291i	0.164027	+	0.986456i	$0.447551\pi$
$883$			58.6257i			1.97291i	−0.164027	+	0.986456i	$0.552449\pi$
$884$	41.1090	+	26.9930i	1.38265	+	0.907874i
$885$	5.58422	+	30.9819i	0.187711	+	1.04144i
$886$	−51.6370	+	27.8678i	−1.73478	+	0.936237i
$887$	14.3027	−	24.7730i	0.480238	−	0.831797i	−0.519505	−	0.854468i	$-0.673883\pi$
$887$	14.3027	−	24.7730i	0.480238	−	0.831797i	0.999743	+	0.0226703i	$0.00721678\pi$
$888$	−12.6877	−	5.84030i	−0.425770	−	0.195988i
$889$	2.45696	+	4.25559i	0.0824040	+	0.142728i
$890$	−5.17875	−	3.19158i	−0.173592	−	0.106982i
$891$	4.78358	−	4.13921i	0.160256	−	0.138669i
$892$	27.2594	−	13.7161i	0.912711	−	0.459250i
$893$	−15.1238	+	8.73173i	−0.506099	+	0.292196i
$894$	27.0351	+	33.8996i	0.904188	+	1.13377i
$895$	25.7212	+	14.8502i	0.859766	+	0.496386i
$896$	−3.58725	−	10.7299i	−0.119842	−	0.358462i
$897$	3.67088	−	0.661645i	0.122567	−	0.0220917i
$898$	−45.1876	−	1.29762i	−1.50793	−	0.0433022i
$899$	−85.2545			−2.84340
$900$	−1.68981	+	7.40481i	−0.0563269	+	0.246827i
$901$	−7.04147			−0.234586
$902$	6.67769	+	0.191759i	0.222343	+	0.00638487i
$903$	−4.09422	−	4.84187i	−0.136247	−	0.161128i
$904$	−7.73884	+	11.0791i	−0.257390	+	0.368485i
$905$	25.4103	+	14.6706i	0.844666	+	0.487668i
$906$	−50.8452	+	7.66466i	−1.68922	+	0.254641i
$907$	−9.05264	+	5.22654i	−0.300588	+	0.173545i	−0.642707	−	0.766112i	$-0.722189\pi$
$907$	−9.05264	+	5.22654i	−0.300588	+	0.173545i	0.342119	+	0.939657i	$0.388855\pi$
$908$	−6.98093	−	13.8739i	−0.231670	−	0.460420i
$909$	−7.64432	−	1.28817i	−0.253546	−	0.0427259i
$910$	−9.36194	−	5.76961i	−0.310345	−	0.191261i
$911$	−7.21831	−	12.5025i	−0.239153	−	0.414226i	0.721318	−	0.692604i	$-0.243537\pi$
$911$	−7.21831	−	12.5025i	−0.239153	−	0.414226i	−0.960472	+	0.278378i	$0.910203\pi$
$912$	14.7379	+	7.30381i	0.488020	+	0.241853i
$913$	−4.57167	+	7.91836i	−0.151300	+	0.262059i
$914$	36.9665	−	19.9503i	1.22274	−	0.659898i
$915$	19.5609	+	7.03567i	0.646664	+	0.232592i
$916$	12.5154	−	19.0602i	0.413519	−	0.629768i
$917$			5.23935i			0.173019i
$918$	−50.8705	+	28.2064i	−1.67898	+	0.930950i
$919$			12.1505i			0.400810i	0.979713	+	0.200405i	$0.0642257\pi$
$919$			12.1505i			0.400810i	−0.979713	+	0.200405i	$0.935774\pi$
$920$	−2.07935	−	4.44593i	−0.0685541	−	0.146578i
$921$	−23.9637	−	8.61925i	−0.789630	−	0.284014i
$922$	−6.95491	−	12.8869i	−0.229048	−	0.424409i
$923$	9.85555	−	17.0703i	0.324399	−	0.561876i
$924$	1.94637	−	1.46284i	0.0640308	−	0.0481240i
$925$	1.80453	+	3.12554i	0.0593325	+	0.102767i
$926$	−11.7563	+	19.0761i	−0.386337	+	0.626881i
$927$	−14.0997	−	37.8428i	−0.463096	−	1.24292i
$928$	−21.0848	−	52.7808i	−0.692142	−	1.73261i
$929$	−38.7325	+	22.3622i	−1.27077	+	0.733680i	−0.975133	−	0.221620i	$-0.928866\pi$
$929$	−38.7325	+	22.3622i	−1.27077	+	0.733680i	−0.295638	+	0.955300i	$0.595532\pi$
$930$	−7.75524	−	51.4461i	−0.254304	−	1.68698i
$931$	2.05605	+	1.18706i	0.0673844	+	0.0389044i
$932$	2.22784	−	38.7585i	0.0729754	−	1.26958i
$933$	14.0178	+	16.5777i	0.458923	+	0.542728i
$934$	1.13601	−	39.5596i	0.0371713	−	1.29443i
$935$	13.9266			0.455447
$936$	7.04430	+	25.4007i	0.230250	+	0.830248i
$937$	−28.8712			−0.943180			−0.471590	−	0.881818i	$-0.656320\pi$
$937$	−28.8712			−0.943180			−0.471590	+	0.881818i	$0.656320\pi$
$938$	0.347249	−	12.0924i	0.0113381	−	0.394831i
$939$	−39.5838	+	7.13465i	−1.29177	+	0.232830i
$940$	−2.11324	+	36.7647i	−0.0689261	+	1.19913i
$941$	31.0674	+	17.9368i	1.01277	+	0.584723i	0.912001	−	0.410187i	$-0.134537\pi$
$941$	31.0674	+	17.9368i	1.01277	+	0.584723i	0.100768	+	0.994910i	$0.467870\pi$
$942$	−3.22492	+	2.57189i	−0.105074	+	0.0837966i
$943$	−4.03488	+	2.32954i	−0.131394	+	0.0758603i
$944$	17.3085	−	23.3233i	0.563344	−	0.759110i
$945$	11.1895	−	6.63121i	0.363995	−	0.215713i
$946$	1.90918	−	3.09789i	0.0620728	−	0.100721i
$947$	−8.81974	−	15.2762i	−0.286603	−	0.496411i	0.686394	−	0.727230i	$-0.259193\pi$
$947$	−8.81974	−	15.2762i	−0.286603	−	0.496411i	−0.972997	+	0.230819i	$0.925859\pi$
$948$	1.09648	+	9.02437i	0.0356122	+	0.293098i
$949$	12.7400	−	22.0664i	0.413559	−	0.716306i
$950$	−2.01855	−	3.74023i	−0.0654904	−	0.121349i
$951$	−2.10424	−	11.6746i	−0.0682347	−	0.378574i
$952$	−20.2801	+	9.48495i	−0.657281	+	0.307409i
$953$		−	9.66882i		−	0.313204i	−0.987662	−	0.156602i	$-0.949946\pi$
$953$		−	9.66882i		−	0.313204i	0.987662	−	0.156602i	$-0.0500540\pi$
$954$	−2.83929	−	2.48650i	−0.0919254	−	0.0805033i
$955$		−	16.9280i		−	0.547779i
$956$	7.84743	−	11.9512i	0.253804	−	0.386530i
$957$	9.34009	−	7.89784i	0.301922	−	0.255301i
$958$	−28.8345	+	15.5616i	−0.931600	+	0.502772i
$959$	5.21728	−	9.03659i	0.168475	−	0.291807i
$960$	29.9321	−	17.5247i	0.966055	−	0.565606i
$961$	20.4999	+	35.5069i	0.661288	+	1.14538i
$962$	10.6631	+	6.57148i	0.343791	+	0.211873i
$963$	−39.4016	−	32.5556i	−1.26970	−	1.04909i
$964$	2.15273	+	4.27831i	0.0693347	+	0.137795i
$965$	5.99645	−	3.46205i	0.193033	−	0.111447i
$966$	−0.620349	+	1.58071i	−0.0199594	+	0.0508585i
$967$	−2.67131	−	1.54228i	−0.0859036	−	0.0495964i	0.456433	−	0.889758i	$-0.349127\pi$
$967$	−2.67131	−	1.54228i	−0.0859036	−	0.0495964i	−0.542336	+	0.840161i	$0.682460\pi$
$968$	−24.3609	−	17.0163i	−0.782988	−	0.546923i
$969$	11.0165	−	30.6286i	0.353900	−	0.983932i
$970$	−48.2011	−	1.38416i	−1.54764	−	0.0444426i
$971$	24.5223			0.786958			0.393479	−	0.919334i	$-0.371271\pi$
$971$	24.5223			0.786958			0.393479	+	0.919334i	$0.371271\pi$
$972$	−30.4725	−	6.58998i	−0.977405	−	0.211374i
$973$	11.8759			0.380724
$974$	19.5726	+	0.562054i	0.627147	+	0.0180094i
$975$	2.30523	−	6.40912i	0.0738265	−	0.205256i
$976$	−7.62303	−	17.5985i	−0.244007	−	0.563314i
$977$	9.43845	+	5.44929i	0.301963	+	0.174338i	0.643324	−	0.765594i	$-0.277555\pi$
$977$	9.43845	+	5.44929i	0.301963	+	0.174338i	−0.341362	+	0.939932i	$0.610888\pi$
$978$	−13.3601	+	34.0429i	−0.427210	+	1.08857i
$979$	−1.04600	+	0.603909i	−0.0334304	+	0.0193010i
$980$	4.47212	−	2.25024i	0.142857	−	0.0718814i
$981$	5.63047	+	4.65218i	0.179767	+	0.148533i
$982$	4.76759	+	2.93819i	0.152140	+	0.0937615i
$983$	14.8209	+	25.6706i	0.472715	+	0.818766i	0.999512	−	0.0312247i	$-0.00994074\pi$
$983$	14.8209	+	25.6706i	0.472715	+	0.818766i	−0.526798	+	0.849991i	$0.676607\pi$
$984$	−19.0178	−	26.8769i	−0.606264	−	0.856804i
$985$	−21.6068	+	37.4241i	−0.688450	+	1.19243i
$986$	−98.9783	+	53.4172i	−3.15211	+	1.70115i
$987$	9.72866	−	8.22642i	0.309667	−	0.261850i
$988$	−12.3299	−	8.09609i	−0.392267	−	0.257571i
$989$			2.53787i			0.0806996i
$990$	5.61552	+	4.91777i	0.178473	+	0.156297i
$991$		−	20.5496i		−	0.652779i	−0.945235	−	0.326390i	$-0.894168\pi$
$991$		−	20.5496i		−	0.652779i	0.945235	−	0.326390i	$-0.105832\pi$
$992$	−29.6996	+	37.7085i	−0.942964	+	1.19725i
$993$	2.47710	+	13.7432i	0.0786084	+	0.436128i
$994$	4.26178	+	7.89677i	0.135175	+	0.250470i
$995$	−18.1382	+	31.4163i	−0.575020	+	0.995963i
$996$	44.7342	−	5.43533i	1.41746	−	0.172225i
$997$	6.42074	+	11.1210i	0.203347	+	0.352207i	0.949605	−	0.313450i	$-0.101485\pi$
$997$	6.42074	+	11.1210i	0.203347	+	0.352207i	−0.746258	+	0.665657i	$0.768151\pi$
$998$	16.0071	−	25.9735i	0.506695	−	0.822177i
$999$	−12.7447	+	7.55283i	−0.403223	+	0.238961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.239.17	yes	72
3.2	odd	2		756.2.ba.a.71.20		72
4.3	odd	2	inner	252.2.ba.a.239.6	yes	72
9.2	odd	6	inner	252.2.ba.a.155.6	✓	72
9.7	even	3		756.2.ba.a.575.31		72
12.11	even	2		756.2.ba.a.71.31		72
36.7	odd	6		756.2.ba.a.575.20		72
36.11	even	6	inner	252.2.ba.a.155.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.6	✓	72	9.2	odd	6	inner
252.2.ba.a.155.17	yes	72	36.11	even	6	inner
252.2.ba.a.239.6	yes	72	4.3	odd	2	inner
252.2.ba.a.239.17	yes	72	1.1	even	1	trivial
756.2.ba.a.71.20		72	3.2	odd	2
756.2.ba.a.71.31		72	12.11	even	2
756.2.ba.a.575.20		72	36.7	odd	6
756.2.ba.a.575.31		72	9.7	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0405943 + 1.41363i) q^{2} +(0.586217 - 1.62983i) q^{3} +(-1.99670 - 0.114771i) q^{4} +(-2.16781 - 1.25159i) q^{5} +(2.28018 + 0.894856i) q^{6} +(0.866025 - 0.500000i) q^{7} +(0.243298 - 2.81794i) q^{8} +(-2.31270 - 1.91087i) q^{9} +O(q^{10})\)	\(q+(-0.0405943 + 1.41363i) q^{2} +(0.586217 - 1.62983i) q^{3} +(-1.99670 - 0.114771i) q^{4} +(-2.16781 - 1.25159i) q^{5} +(2.28018 + 0.894856i) q^{6} +(0.866025 - 0.500000i) q^{7} +(0.243298 - 2.81794i) q^{8} +(-2.31270 - 1.91087i) q^{9} +(1.85728 - 3.01367i) q^{10} +(-0.351433 - 0.608700i) q^{11} +(-1.35756 + 3.18701i) q^{12} +(1.55324 - 2.69030i) q^{13} +(0.671660 + 1.24454i) q^{14} +(-3.31068 + 2.79946i) q^{15} +(3.97366 + 0.458326i) q^{16} -7.91554i q^{17} +(2.79515 - 3.19173i) q^{18} +2.37413i q^{19} +(4.18483 + 2.74785i) q^{20} +(-0.307237 - 1.70458i) q^{21} +(0.874743 - 0.472087i) q^{22} +(-0.346619 + 0.600362i) q^{23} +(-4.45015 - 2.04846i) q^{24} +(0.632931 + 1.09627i) q^{25} +(3.74003 + 2.30492i) q^{26} +(-4.47014 + 2.64912i) q^{27} +(-1.78658 + 0.898958i) q^{28} +(-8.70126 + 5.02368i) q^{29} +(-3.82301 - 4.79372i) q^{30} +(7.34846 + 4.24264i) q^{31} +(-0.809212 + 5.59868i) q^{32} +(-1.19809 + 0.215946i) q^{33} +(11.1896 + 0.321326i) q^{34} -2.50317 q^{35} +(4.39846 + 4.08087i) q^{36} +2.85107 q^{37} +(-3.35614 - 0.0963760i) q^{38} +(-3.47419 - 4.10862i) q^{39} +(-4.05432 + 5.80426i) q^{40} +(5.82034 + 3.36037i) q^{41} +(2.42212 - 0.365123i) q^{42} +(3.17043 - 1.83045i) q^{43} +(0.631847 + 1.25573i) q^{44} +(2.62187 + 7.03694i) q^{45} +(-0.834620 - 0.514363i) q^{46} +(3.67787 + 6.37026i) q^{47} +(3.07642 - 6.20771i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-1.57541 + 0.850229i) q^{50} +(-12.9010 - 4.64022i) q^{51} +(-3.41013 + 5.19346i) q^{52} -0.889576i q^{53} +(-3.56342 - 6.42666i) q^{54} +1.75939i q^{55} +(-1.19827 - 2.56206i) q^{56} +(3.86942 + 1.39175i) q^{57} +(-6.74840 - 12.5043i) q^{58} +(3.63052 - 6.28824i) q^{59} +(6.93174 - 5.20973i) q^{60} +(-2.39732 - 4.15228i) q^{61} +(-6.29583 + 10.2158i) q^{62} +(-2.95829 - 0.498512i) q^{63} +(-7.88161 - 1.37120i) q^{64} +(-6.73427 + 3.88803i) q^{65} +(-0.256633 - 1.70243i) q^{66} +(-7.40811 - 4.27707i) q^{67} +(-0.908472 + 15.8050i) q^{68} +(0.775295 + 0.916874i) q^{69} +(0.101614 - 3.53856i) q^{70} +6.34514 q^{71} +(-5.94740 + 6.05214i) q^{72} +8.20222 q^{73} +(-0.115737 + 4.03035i) q^{74} +(2.15777 - 0.388920i) q^{75} +(0.272480 - 4.74043i) q^{76} +(-0.608700 - 0.351433i) q^{77} +(5.94911 - 4.74444i) q^{78} +(2.27268 - 1.31214i) q^{79} +(-8.04049 - 5.96693i) q^{80} +(1.69715 + 8.83853i) q^{81} +(-4.98660 + 8.09139i) q^{82} +(-6.50432 - 11.2658i) q^{83} +(0.417825 + 3.43881i) q^{84} +(-9.90697 + 17.1594i) q^{85} +(2.45887 + 4.55612i) q^{86} +(3.08692 + 17.1266i) q^{87} +(-1.80079 + 0.842223i) q^{88} -1.71842i q^{89} +(-10.0541 + 3.42070i) q^{90} -3.10649i q^{91} +(0.761000 - 1.15896i) q^{92} +(11.2226 - 9.48965i) q^{93} +(-9.15449 + 4.94056i) q^{94} +(2.97142 - 5.14665i) q^{95} +(8.65052 + 4.60092i) q^{96} +(-6.81083 - 11.7967i) q^{97} +(1.20394 + 0.741971i) q^{98} +(-0.350387 + 2.07928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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