LMFDB - Embedded newform 430.2.l.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(7,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("430.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.l (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	430.7
Dual form			430.2.l.a.123.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.653568 - 2.43915i) q^{3} -1.00000i q^{4} +(1.81492 + 1.30616i) q^{5} +(1.26260 + 2.18688i) q^{6} +(-0.0630011 - 0.235123i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.92423 - 1.68830i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.653568 - 2.43915i) q^{3} -1.00000i q^{4} +(1.81492 + 1.30616i) q^{5} +(1.26260 + 2.18688i) q^{6} +(-0.0630011 - 0.235123i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.92423 - 1.68830i) q^{9} +(-2.20694 + 0.359750i) q^{10} +5.80063 q^{11} +(-2.43915 - 0.653568i) q^{12} +(1.57803 + 5.88929i) q^{13} +(0.210806 + 0.121709i) q^{14} +(4.37210 - 3.57321i) q^{15} -1.00000 q^{16} +(0.958139 - 0.256733i) q^{17} +(3.26155 - 0.873930i) q^{18} +(-3.53101 - 6.11588i) q^{19} +(1.30616 - 1.81492i) q^{20} -0.614677 q^{21} +(-4.10167 + 4.10167i) q^{22} +(-3.90391 - 1.04605i) q^{23} +(2.18688 - 1.26260i) q^{24} +(1.58789 + 4.74116i) q^{25} +(-5.28020 - 3.04852i) q^{26} +(-0.672464 + 0.672464i) q^{27} +(-0.235123 + 0.0630011i) q^{28} +(1.24979 - 2.16470i) q^{29} +(-0.564900 + 5.61818i) q^{30} +(-3.64235 - 6.30874i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.79111 - 14.1486i) q^{33} +(-0.495969 + 0.859044i) q^{34} +(0.192767 - 0.509021i) q^{35} +(-1.68830 + 2.92423i) q^{36} +(6.38755 + 1.71154i) q^{37} +(6.82138 + 1.82778i) q^{38} +15.3962 q^{39} +(0.359750 + 2.20694i) q^{40} -10.1750 q^{41} +(0.434642 - 0.434642i) q^{42} +(-1.34365 + 6.41830i) q^{43} -5.80063i q^{44} +(-3.10206 - 6.88365i) q^{45} +(3.50015 - 2.02081i) q^{46} +(-3.04626 - 3.04626i) q^{47} +(-0.653568 + 2.43915i) q^{48} +(6.01086 - 3.47037i) q^{49} +(-4.47532 - 2.22970i) q^{50} -2.50484i q^{51} +(5.88929 - 1.57803i) q^{52} +(-4.02329 - 1.07804i) q^{53} -0.951007i q^{54} +(10.5277 + 7.57655i) q^{55} +(0.121709 - 0.210806i) q^{56} +(-17.2253 + 4.61551i) q^{57} +(0.646938 + 2.41441i) q^{58} -0.386098i q^{59} +(-3.57321 - 4.37210i) q^{60} +(6.83165 + 3.94425i) q^{61} +(7.03649 + 1.88542i) q^{62} +(-0.212730 + 0.793920i) q^{63} +1.00000i q^{64} +(-4.82835 + 12.7498i) q^{65} +(7.32386 + 12.6853i) q^{66} +(-3.52632 + 13.1604i) q^{67} +(-0.256733 - 0.958139i) q^{68} +(-5.10294 + 8.83855i) q^{69} +(0.223625 + 0.496239i) q^{70} +(8.61404 + 4.97332i) q^{71} +(-0.873930 - 3.26155i) q^{72} +(-10.1217 + 2.71209i) q^{73} +(-5.72692 + 3.30644i) q^{74} +(12.6022 - 0.774441i) q^{75} +(-6.11588 + 3.53101i) q^{76} +(-0.365447 - 1.36387i) q^{77} +(-10.8868 + 10.8868i) q^{78} +(0.363827 + 0.210056i) q^{79} +(-1.81492 - 1.30616i) q^{80} +(-3.86417 - 6.69294i) q^{81} +(7.19481 - 7.19481i) q^{82} +(-0.00529113 - 0.00141775i) q^{83} +0.614677i q^{84} +(2.07428 + 0.785532i) q^{85} +(-3.58832 - 5.48853i) q^{86} +(-4.46320 - 4.46320i) q^{87} +(4.10167 + 4.10167i) q^{88} +(-3.93115 - 6.80895i) q^{89} +(7.06096 + 2.67399i) q^{90} +(1.28529 - 0.742064i) q^{91} +(-1.04605 + 3.90391i) q^{92} +(-17.7685 + 4.76106i) q^{93} +4.30806 q^{94} +(1.57981 - 15.7119i) q^{95} +(-1.26260 - 2.18688i) q^{96} +(-1.36503 - 1.36503i) q^{97} +(-1.79640 + 6.70425i) q^{98} +(-16.9624 - 9.79323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) $ 88 * q + 4 * q^6 + 12 * q^7	$ 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) $ 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.653568	−	2.43915i	0.377338	−	1.40824i	−0.472561	−	0.881298i	$-0.656670\pi$
$3$	0.653568	−	2.43915i	0.377338	−	1.40824i	0.849899	−	0.526946i	$-0.176663\pi$
$4$		−	1.00000i		−	0.500000i
$5$	1.81492	+	1.30616i	0.811658	+	0.584132i
$5$	1.81492	+	1.30616i	0.811658	+	0.584132i
$6$	1.26260	+	2.18688i	0.515453	+	0.892791i
$7$	−0.0630011	−	0.235123i	−0.0238122	−	0.0888683i	0.952997	−	0.302979i	$-0.0979813\pi$
$7$	−0.0630011	−	0.235123i	−0.0238122	−	0.0888683i	−0.976809	+	0.214111i	$0.931315\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.92423	−	1.68830i	−0.974743	−	0.562768i
$10$	−2.20694	+	0.359750i	−0.697895	+	0.113763i
$11$	5.80063			1.74896			0.874478	−	0.485064i	$-0.161204\pi$
$11$	5.80063			1.74896			0.874478	+	0.485064i	$0.161204\pi$
$12$	−2.43915	−	0.653568i	−0.704122	−	0.188669i
$13$	1.57803	+	5.88929i	0.437667	+	1.63340i	0.734602	+	0.678498i	$0.237369\pi$
$13$	1.57803	+	5.88929i	0.437667	+	1.63340i	−0.296935	+	0.954898i	$0.595964\pi$
$14$	0.210806	+	0.121709i	0.0563403	+	0.0325281i
$15$	4.37210	−	3.57321i	1.12887	−	0.922598i
$16$	−1.00000			−0.250000
$17$	0.958139	−	0.256733i	0.232383	−	0.0622668i	−0.140748	−	0.990045i	$-0.544951\pi$
$17$	0.958139	−	0.256733i	0.232383	−	0.0622668i	0.373131	+	0.927779i	$0.378284\pi$
$18$	3.26155	−	0.873930i	0.768755	−	0.205987i
$19$	−3.53101	−	6.11588i	−0.810069	−	1.40308i	−0.912815	−	0.408372i	$-0.866097\pi$
$19$	−3.53101	−	6.11588i	−0.810069	−	1.40308i	0.102747	−	0.994708i	$-0.467237\pi$
$20$	1.30616	−	1.81492i	0.292066	−	0.405829i
$21$	−0.614677			−0.134134
$22$	−4.10167	+	4.10167i	−0.874478	+	0.874478i
$23$	−3.90391	−	1.04605i	−0.814021	−	0.218116i	−0.172290	−	0.985046i	$-0.555117\pi$
$23$	−3.90391	−	1.04605i	−0.814021	−	0.218116i	−0.641731	+	0.766930i	$0.721783\pi$
$24$	2.18688	−	1.26260i	0.446396	−	0.257727i
$25$	1.58789	+	4.74116i	0.317579	+	0.948232i
$26$	−5.28020	−	3.04852i	−1.03553	−	0.597864i
$27$	−0.672464	+	0.672464i	−0.129416	+	0.129416i
$28$	−0.235123	+	0.0630011i	−0.0444342	+	0.0119061i
$29$	1.24979	−	2.16470i	0.232080	−	0.401974i	−0.726340	−	0.687335i	$-0.758780\pi$
$29$	1.24979	−	2.16470i	0.232080	−	0.401974i	0.958420	+	0.285361i	$0.0921136\pi$
$30$	−0.564900	+	5.61818i	−0.103136	+	1.02573i
$31$	−3.64235	−	6.30874i	−0.654186	−	1.13308i	−0.982097	−	0.188375i	$-0.939678\pi$
$31$	−3.64235	−	6.30874i	−0.654186	−	1.13308i	0.327911	−	0.944709i	$-0.393655\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.79111	−	14.1486i	0.659948	−	2.46296i
$34$	−0.495969	+	0.859044i	−0.0850580	+	0.147325i
$35$	0.192767	−	0.509021i	0.0325835	−	0.0860402i
$36$	−1.68830	+	2.92423i	−0.281384	+	0.487371i
$37$	6.38755	+	1.71154i	1.05011	+	0.281375i	0.742296	−	0.670073i	$-0.233737\pi$
$37$	6.38755	+	1.71154i	1.05011	+	0.281375i	0.307810	+	0.951448i	$0.400404\pi$
$38$	6.82138	+	1.82778i	1.10657	+	0.296506i
$39$	15.3962			2.46537
$40$	0.359750	+	2.20694i	0.0568815	+	0.348948i
$41$	−10.1750			−1.58907			−0.794534	−	0.607220i	$-0.792285\pi$
$41$	−10.1750			−1.58907			−0.794534	+	0.607220i	$0.792285\pi$
$42$	0.434642	−	0.434642i	0.0670668	−	0.0670668i
$43$	−1.34365	+	6.41830i	−0.204905	+	0.978782i
$43$	−1.34365	+	6.41830i	−0.204905	+	0.978782i
$44$		−	5.80063i		−	0.874478i
$45$	−3.10206	−	6.88365i	−0.462427	−	1.02615i
$46$	3.50015	−	2.02081i	0.516069	−	0.297952i
$47$	−3.04626	−	3.04626i	−0.444342	−	0.444342i	0.449126	−	0.893468i	$-0.351735\pi$
$47$	−3.04626	−	3.04626i	−0.444342	−	0.444342i	−0.893468	+	0.449126i	$0.851735\pi$
$48$	−0.653568	+	2.43915i	−0.0943345	+	0.352061i
$49$	6.01086	−	3.47037i	0.858695	−	0.495768i
$50$	−4.47532	−	2.22970i	−0.632905	−	0.315326i
$51$		−	2.50484i		−	0.350747i
$52$	5.88929	−	1.57803i	0.816698	−	0.218834i
$53$	−4.02329	−	1.07804i	−0.552641	−	0.148080i	−0.0283178	−	0.999599i	$-0.509015\pi$
$53$	−4.02329	−	1.07804i	−0.552641	−	0.148080i	−0.524323	+	0.851519i	$0.675682\pi$
$54$		−	0.951007i		−	0.129416i
$55$	10.5277	+	7.57655i	1.41956	+	1.02162i
$56$	0.121709	−	0.210806i	0.0162640	−	0.0281701i
$57$	−17.2253	+	4.61551i	−2.28155	+	0.611339i
$58$	0.646938	+	2.41441i	0.0849471	+	0.317027i
$59$		−	0.386098i		−	0.0502657i	−0.999684	−	0.0251329i	$-0.991999\pi$
$59$		−	0.386098i		−	0.0502657i	0.999684	−	0.0251329i	$-0.00800088\pi$
$60$	−3.57321	−	4.37210i	−0.461299	−	0.564435i
$61$	6.83165	+	3.94425i	0.874703	+	0.505010i	0.868908	−	0.494973i	$-0.164822\pi$
$61$	6.83165	+	3.94425i	0.874703	+	0.505010i	0.00579446	+	0.999983i	$0.498156\pi$
$62$	7.03649	+	1.88542i	0.893635	+	0.239449i
$63$	−0.212730	+	0.793920i	−0.0268015	+	0.100024i
$64$			1.00000i			0.125000i
$65$	−4.82835	+	12.7498i	−0.598883	+	1.58142i
$66$	7.32386	+	12.6853i	0.901505	+	1.56145i
$67$	−3.52632	+	13.1604i	−0.430808	+	1.60780i	0.320095	+	0.947385i	$0.396285\pi$
$67$	−3.52632	+	13.1604i	−0.430808	+	1.60780i	−0.750903	+	0.660412i	$0.770382\pi$
$68$	−0.256733	−	0.958139i	−0.0311334	−	0.116191i
$69$	−5.10294	+	8.83855i	−0.614322	+	1.06404i
$70$	0.223625	+	0.496239i	0.0267284	+	0.0593118i
$71$	8.61404	+	4.97332i	1.02230	+	0.590224i	0.914769	−	0.403978i	$-0.132373\pi$
$71$	8.61404	+	4.97332i	1.02230	+	0.590224i	0.107529	+	0.994202i	$0.465706\pi$
$72$	−0.873930	−	3.26155i	−0.102994	−	0.384378i
$73$	−10.1217	+	2.71209i	−1.18465	+	0.317426i	−0.796770	−	0.604283i	$-0.793460\pi$
$73$	−10.1217	+	2.71209i	−1.18465	+	0.317426i	−0.387882	+	0.921709i	$0.626793\pi$
$74$	−5.72692	+	3.30644i	−0.665741	+	0.384365i
$75$	12.6022	−	0.774441i	1.45518	−	0.0894248i
$76$	−6.11588	+	3.53101i	−0.701540	+	0.405034i
$77$	−0.365447	−	1.36387i	−0.0416465	−	0.155427i
$78$	−10.8868	+	10.8868i	−1.23268	+	1.23268i
$79$	0.363827	+	0.210056i	0.0409338	+	0.0236331i	0.520327	−	0.853967i	$-0.325810\pi$
$79$	0.363827	+	0.210056i	0.0409338	+	0.0236331i	−0.479393	+	0.877600i	$0.659143\pi$
$80$	−1.81492	−	1.30616i	−0.202915	−	0.146033i
$81$	−3.86417	−	6.69294i	−0.429352	−	0.743660i
$82$	7.19481	−	7.19481i	0.794534	−	0.794534i
$83$	−0.00529113	−	0.00141775i	−0.000580777	−	0.000155619i	0.258529	−	0.966004i	$-0.416762\pi$
$83$	−0.00529113	−	0.00141775i	−0.000580777	−	0.000155619i	−0.259109	+	0.965848i	$0.583429\pi$
$84$			0.614677i			0.0670668i
$85$	2.07428	+	0.785532i	0.224988	+	0.0852030i
$86$	−3.58832	−	5.48853i	−0.386939	−	0.591843i
$87$	−4.46320	−	4.46320i	−0.478505	−	0.478505i
$88$	4.10167	+	4.10167i	0.437239	+	0.437239i
$89$	−3.93115	−	6.80895i	−0.416701	−	0.721747i	0.578905	−	0.815395i	$-0.303480\pi$
$89$	−3.93115	−	6.80895i	−0.416701	−	0.721747i	−0.995605	+	0.0936485i	$0.970147\pi$
$90$	7.06096	+	2.67399i	0.744291	+	0.281863i
$91$	1.28529	−	0.742064i	0.134735	−	0.0777895i
$92$	−1.04605	+	3.90391i	−0.109058	+	0.407010i
$93$	−17.7685	+	4.76106i	−1.84251	+	0.493699i
$94$	4.30806			0.444342
$95$	1.57981	−	15.7119i	0.162085	−	1.61201i
$96$	−1.26260	−	2.18688i	−0.128863	−	0.223198i
$97$	−1.36503	−	1.36503i	−0.138598	−	0.138598i	0.634404	−	0.773002i	$-0.281246\pi$
$97$	−1.36503	−	1.36503i	−0.138598	−	0.138598i	−0.773002	+	0.634404i	$0.781246\pi$
$98$	−1.79640	+	6.70425i	−0.181464	+	0.677231i
$99$	−16.9624	−	9.79323i	−1.70478	−	0.984257i
$100$	4.74116	−	1.58789i	0.474116	−	0.158789i
$101$	−8.81756	+	15.2725i	−0.877380	+	1.51967i	−0.0231747	+	0.999731i	$0.507377\pi$
$101$	−8.81756	+	15.2725i	−0.877380	+	1.51967i	−0.854205	+	0.519936i	$0.825956\pi$
$102$	1.77119	+	1.77119i	0.175374	+	0.175374i
$103$	0.675783	+	2.52206i	0.0665869	+	0.248506i	0.991194	−	0.132416i	$-0.0422734\pi$
$103$	0.675783	+	2.52206i	0.0665869	+	0.248506i	−0.924607	+	0.380922i	$0.875607\pi$
$104$	−3.04852	+	5.28020i	−0.298932	+	0.517766i
$105$	−1.11559	−	0.802866i	−0.108871	−	0.0783517i
$106$	3.60718	−	2.08261i	0.350360	−	0.202281i
$107$	−4.89232	−	4.89232i	−0.472958	−	0.472958i	0.429912	−	0.902871i	$-0.358544\pi$
$107$	−4.89232	−	4.89232i	−0.472958	−	0.472958i	−0.902871	+	0.429912i	$0.858544\pi$
$108$	0.672464	+	0.672464i	0.0647079	+	0.0647079i
$109$	1.56231	−	0.902001i	0.149642	−	0.0863960i	−0.423309	−	0.905985i	$-0.639132\pi$
$109$	1.56231	−	0.902001i	0.149642	−	0.0863960i	0.572952	+	0.819589i	$0.305798\pi$
$110$	−12.8016	+	2.08678i	−1.22059	+	0.198967i
$111$	8.34940	−	14.4616i	0.792490	−	1.37263i
$112$	0.0630011	+	0.235123i	0.00595305	+	0.0222171i
$113$	−13.1824	−	13.1824i	−1.24009	−	1.24009i	−0.959961	−	0.280133i	$-0.909622\pi$
$113$	−13.1824	−	13.1824i	−1.24009	−	1.24009i	−0.280133	−	0.959961i	$-0.590378\pi$
$114$	8.91648	−	15.4438i	0.835105	−	1.44644i
$115$	−5.71899	−	6.99762i	−0.533298	−	0.652532i
$116$	−2.16470	−	1.24979i	−0.200987	−	0.116040i
$117$	5.32839	−	19.8858i	0.492610	−	1.83845i
$118$	0.273013	+	0.273013i	0.0251329	+	0.0251329i
$119$	−0.120728	−	0.209107i	−0.0110671	−	0.0191688i
$120$	5.61818	+	0.564900i	0.512867	+	0.0515681i
$121$	22.6474			2.05885
$122$	−7.61971	+	2.04170i	−0.689856	+	0.184846i
$123$	−6.65006	+	24.8183i	−0.599615	+	2.23780i
$124$	−6.30874	+	3.64235i	−0.566542	+	0.327093i
$125$	−3.31080	+	10.6789i	−0.296127	+	0.955148i
$126$	−0.410963	−	0.711809i	−0.0366115	−	0.0634130i
$127$	0.743952	+	0.743952i	0.0660151	+	0.0660151i	0.739344	−	0.673328i	$-0.235136\pi$
$127$	0.743952	+	0.743952i	0.0660151	+	0.0660151i	−0.673328	+	0.739344i	$0.735136\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	14.7770	+	7.47216i	1.30105	+	0.657887i
$130$	−5.60129	−	12.4296i	−0.491266	−	1.09015i
$131$			2.86916i			0.250680i	0.992114	+	0.125340i	$0.0400022\pi$
$131$			2.86916i			0.250680i	−0.992114	+	0.125340i	$0.959998\pi$
$132$	−14.1486	−	3.79111i	−1.23148	−	0.329974i
$133$	−1.21553	+	1.21553i	−0.105400	+	0.105400i
$134$	−6.81232	−	11.7993i	−0.588495	−	1.01930i
$135$	−2.09882	+	0.342125i	−0.180637	+	0.0294455i
$136$	0.859044	+	0.495969i	0.0736624	+	0.0425290i
$137$	1.07249	−	1.07249i	0.0916289	−	0.0916289i	−0.659807	−	0.751435i	$-0.729362\pi$
$137$	1.07249	−	1.07249i	0.0916289	−	0.0916289i	0.751435	+	0.659807i	$0.229362\pi$
$138$	−2.64148	−	9.85812i	−0.224857	−	0.839179i
$139$	−10.1997	+	5.88877i	−0.865123	+	0.499479i	−0.865725	−	0.500521i	$-0.833142\pi$
$139$	−10.1997	+	5.88877i	−0.865123	+	0.499479i	0.000601195		1.00000i	$0.499809\pi$
$140$	−0.509021	−	0.192767i	−0.0430201	−	0.0162917i
$141$	−9.42121	+	5.43934i	−0.793409	+	0.458075i
$142$	−9.60771	+	2.57438i	−0.806261	+	0.216037i
$143$	9.15358	+	34.1616i	0.765461	+	2.85674i
$144$	2.92423	+	1.68830i	0.243686	+	0.140692i
$145$	5.09571	−	2.29634i	0.423176	−	0.190700i
$146$	5.23936	−	9.07484i	0.433613	−	0.751039i
$147$	−4.53625	−	16.9295i	−0.374144	−	1.39632i
$148$	1.71154	−	6.38755i	0.140688	−	0.525053i
$149$	3.81354	+	6.60524i	0.312417	+	0.541123i	0.978885	−	0.204411i	$-0.0655280\pi$
$149$	3.81354	+	6.60524i	0.312417	+	0.541123i	−0.666468	+	0.745534i	$0.732195\pi$
$150$	−8.36349	+	9.45871i	−0.682876	+	0.772301i
$151$		−	1.55809i		−	0.126796i	−0.997988	−	0.0633980i	$-0.979806\pi$
$151$		−	1.55809i		−	0.126796i	0.997988	−	0.0633980i	$-0.0201937\pi$
$152$	1.82778	−	6.82138i	0.148253	−	0.553287i
$153$	−3.23526	−	0.866885i	−0.261555	−	0.0700835i
$154$	1.22281	+	0.705989i	0.0985367	+	0.0568902i
$155$	1.62963	−	16.2074i	0.130895	−	1.30181i
$156$		−	15.3962i		−	1.23268i
$157$	2.31443	+	8.63758i	0.184712	+	0.689354i	0.994692	+	0.102897i	$0.0328112\pi$
$157$	2.31443	+	8.63758i	0.184712	+	0.689354i	−0.809980	+	0.586457i	$0.800522\pi$
$158$	−0.405797	+	0.108733i	−0.0322835	+	0.00865033i
$159$	−5.25899	+	9.10884i	−0.417065	+	0.722378i
$160$	2.20694	−	0.359750i	0.174474	−	0.0284408i
$161$			0.983803i			0.0775345i
$162$	7.46501	+	2.00024i	0.586506	+	0.157154i
$163$	5.85916	−	1.56996i	0.458925	−	0.122968i	−0.0219477	−	0.999759i	$-0.506987\pi$
$163$	5.85916	−	1.56996i	0.458925	−	0.122968i	0.480872	+	0.876791i	$0.340320\pi$
$164$			10.1750i			0.794534i
$165$	25.3609	−	20.7269i	1.97435	−	1.61358i
$166$	0.00474390	−	0.00273889i	0.000368198	−	0.000212579i
$167$	−3.69695	+	13.7972i	−0.286079	+	1.06766i	0.661969	+	0.749531i	$0.269721\pi$
$167$	−3.69695	+	13.7972i	−0.286079	+	1.06766i	−0.948048	+	0.318129i	$0.896946\pi$
$168$	−0.434642	−	0.434642i	−0.0335334	−	0.0335334i
$169$	−20.9353	+	12.0870i	−1.61040	+	0.929768i
$170$	−2.02219	+	0.911284i	−0.155095	+	0.0698923i
$171$			23.8456i			1.82352i
$172$	6.41830	+	1.34365i	0.489391	+	0.102452i
$173$	4.26640	−	4.26640i	0.324368	−	0.324368i	−0.526072	−	0.850440i	$-0.676336\pi$
$173$	4.26640	−	4.26640i	0.324368	−	0.324368i	0.850440	+	0.526072i	$0.176336\pi$
$174$	6.31192			0.478505
$175$	1.01472	−	0.672050i	0.0767055	−	0.0508022i
$176$	−5.80063			−0.437239
$177$	−0.941752	−	0.252342i	−0.0707864	−	0.0189672i
$178$	7.59439	+	2.03491i	0.569224	+	0.152523i
$179$	2.62111	−	4.53989i	0.195911	−	0.339328i	−0.751288	−	0.659975i	$-0.770567\pi$
$179$	2.62111	−	4.53989i	0.195911	−	0.339328i	0.947199	+	0.320647i	$0.103900\pi$
$180$	−6.88365	+	3.10206i	−0.513077	+	0.231214i
$181$	4.66270	−	8.07604i	0.346576	−	0.600287i	−0.639063	−	0.769154i	$-0.720678\pi$
$181$	4.66270	−	8.07604i	0.346576	−	0.600287i	0.985639	+	0.168867i	$0.0540110\pi$
$182$	−0.384121	+	1.43356i	−0.0284729	+	0.106262i
$183$	14.0856	−	14.0856i	1.04124	−	1.04124i
$184$	−2.02081	−	3.50015i	−0.148976	−	0.258034i
$185$	9.35736	+	11.4495i	0.687967	+	0.841781i
$186$	9.19765	−	15.9308i	0.674405	−	1.16810i
$187$	5.55781	−	1.48921i	0.406428	−	0.108902i
$188$	−3.04626	+	3.04626i	−0.222171	+	0.222171i
$189$	0.200478	+	0.115746i	0.0145826	+	0.00841928i
$190$	9.99291	+	12.2271i	0.724962	+	0.887047i
$191$	−9.61841	+	5.55319i	−0.695963	+	0.401815i	−0.805842	−	0.592130i	$-0.798287\pi$
$191$	−9.61841	+	5.55319i	−0.695963	+	0.401815i	0.109879	+	0.993945i	$0.464954\pi$
$192$	2.43915	+	0.653568i	0.176031	+	0.0471672i
$193$	−4.13802	+	4.13802i	−0.297861	+	0.297861i	−0.840176	−	0.542314i	$-0.817548\pi$
$193$	−4.13802	+	4.13802i	−0.297861	+	0.297861i	0.542314	+	0.840176i	$0.317548\pi$
$194$	1.93045			0.138598
$195$	27.9430	+	20.1099i	2.00104	+	1.44010i
$196$	−3.47037	−	6.01086i	−0.247884	−	0.429347i
$197$	9.48692	−	2.54201i	0.675915	−	0.181111i	0.0954973	−	0.995430i	$-0.469556\pi$
$197$	9.48692	−	2.54201i	0.675915	−	0.181111i	0.580418	+	0.814319i	$0.302889\pi$
$198$	18.9191	−	5.06935i	1.34452	−	0.360263i
$199$	2.24807			0.159361			0.0796807	−	0.996820i	$-0.474610\pi$
$199$	2.24807			0.159361			0.0796807	+	0.996820i	$0.474610\pi$
$200$	−2.22970	+	4.47532i	−0.157663	+	0.316453i
$201$	29.7955	+	17.2024i	2.10161	+	1.21337i
$202$	−4.56431	−	17.0342i	−0.321143	−	1.19852i
$203$	−0.587709	−	0.157476i	−0.0412491	−	0.0110527i
$204$	−2.50484			−0.175374
$205$	−18.4668	−	13.2902i	−1.28978	−	0.928226i
$206$	−2.26121	−	1.30551i	−0.157546	−	0.0909594i
$207$	9.64987	+	9.64987i	0.670712	+	0.670712i
$208$	−1.57803	−	5.88929i	−0.109417	−	0.408349i
$209$	−20.4821	−	35.4760i	−1.41677	−	2.45393i
$210$	1.35656	−	0.221130i	0.0936112	−	0.0152594i
$211$			4.15172i			0.285816i	0.989736	+	0.142908i	$0.0456454\pi$
$211$			4.15172i			0.285816i	−0.989736	+	0.142908i	$0.954355\pi$
$212$	−1.07804	+	4.02329i	−0.0740399	+	0.276321i
$213$	17.7605	−	17.7605i	1.21693	−	1.21693i
$214$	6.91878			0.472958
$215$	−10.8219	+	9.89371i	−0.738051	+	0.674745i
$216$	−0.951007			−0.0647079
$217$	−1.25386	+	1.25386i	−0.0851176	+	0.0851176i
$218$	−0.466910	+	1.74253i	−0.0316231	+	0.118019i
$219$			26.4608i			1.78806i
$220$	7.57655	−	10.5277i	0.510811	−	0.709778i
$221$	3.02395	+	5.23763i	0.203413	+	0.352321i
$222$	4.32197	+	16.1298i	0.290071	+	1.08256i
$223$	13.1987	+	13.1987i	0.883850	+	0.883850i	0.993923	−	0.110074i	$-0.0351087\pi$
$223$	13.1987	+	13.1987i	0.883850	+	0.883850i	−0.110074	+	0.993923i	$0.535109\pi$
$224$	−0.210806	−	0.121709i	−0.0140851	−	0.00813202i
$225$	3.36115	−	16.5451i	0.224077	−	1.10301i
$226$	18.6427			1.24009
$227$	−16.2569	−	4.35603i	−1.07901	−	0.289120i	−0.324819	−	0.945776i	$-0.605304\pi$
$227$	−16.2569	−	4.35603i	−1.07901	−	0.289120i	−0.754190	+	0.656656i	$0.771970\pi$
$228$	4.61551	+	17.2253i	0.305670	+	1.14077i
$229$	−9.42234	−	5.43999i	−0.622646	−	0.359485i	0.155253	−	0.987875i	$-0.450381\pi$
$229$	−9.42234	−	5.43999i	−0.622646	−	0.359485i	−0.777898	+	0.628390i	$0.783714\pi$
$230$	8.99200	+	0.904134i	0.592915	+	0.0596168i
$231$	−3.56552			−0.234594
$232$	2.41441	−	0.646938i	0.158513	−	0.0424736i
$233$	−5.80101	+	1.55438i	−0.380037	+	0.101831i	−0.443780	−	0.896136i	$-0.646363\pi$
$233$	−5.80101	+	1.55438i	−0.380037	+	0.101831i	0.0637431	+	0.997966i	$0.479696\pi$
$234$	10.2937	+	17.8291i	0.672918	+	1.16553i
$235$	−1.54983	−	9.50762i	−0.101099	−	0.620209i
$236$	−0.386098			−0.0251329
$237$	0.750144	−	0.750144i	0.0487271	−	0.0487271i
$238$	0.233228	+	0.0624933i	0.0151179	+	0.00405084i
$239$	1.31625	−	0.759940i	0.0851414	−	0.0491564i	−0.456825	−	0.889557i	$-0.651013\pi$
$239$	1.31625	−	0.759940i	0.0851414	−	0.0491564i	0.541966	+	0.840400i	$0.317680\pi$
$240$	−4.37210	+	3.57321i	−0.282218	+	0.230650i
$241$	17.2968	+	9.98629i	1.11418	+	0.643273i	0.939909	−	0.341424i	$-0.110909\pi$
$241$	17.2968	+	9.98629i	1.11418	+	0.643273i	0.174273	+	0.984697i	$0.444242\pi$
$242$	−16.0141	+	16.0141i	−1.02943	+	1.02943i
$243$	−21.6064	+	5.78942i	−1.38605	+	0.371391i
$244$	3.94425	−	6.83165i	0.252505	−	0.437351i
$245$	15.4421	+	1.55268i	0.986561	+	0.0991974i
$246$	−12.8469	−	22.2515i	−0.819090	−	1.41871i
$247$	30.4462	−	30.4462i	1.93724	−	1.93724i
$248$	1.88542	−	7.03649i	0.119724	−	0.446817i
$249$	−0.00691623	+	0.0119793i	−0.000438298	+	0.000759155i
$250$	−5.21002	−	9.89220i	−0.329511	−	0.625638i
$251$	14.8794	−	25.7719i	0.939179	−	1.62671i	0.172172	−	0.985067i	$-0.444921\pi$
$251$	14.8794	−	25.7719i	0.939179	−	1.62671i	0.767007	−	0.641639i	$-0.221745\pi$
$252$	0.793920	+	0.212730i	0.0500122	+	0.0134007i
$253$	−22.6451	−	6.06775i	−1.42369	−	0.381476i
$254$	−1.05211			−0.0660151
$255$	3.27172	−	4.54609i	0.204883	−	0.284687i
$256$	1.00000			0.0625000
$257$	−10.9752	+	10.9752i	−0.684612	+	0.684612i	−0.961036	−	0.276424i	$-0.910851\pi$
$257$	−10.9752	+	10.9752i	−0.684612	+	0.684612i	0.276424	+	0.961036i	$0.410851\pi$
$258$	−15.7326	+	5.16533i	−0.979467	+	0.321579i
$259$		−	1.60969i		−	0.100021i
$260$	12.7498	+	4.82835i	0.790708	+	0.299442i
$261$	−7.30933	+	4.22004i	−0.452436	+	0.261214i
$262$	−2.02880	−	2.02880i	−0.125340	−	0.125340i
$263$	5.56418	−	20.7658i	0.343102	−	1.28048i	−0.551711	−	0.834035i	$-0.686025\pi$
$263$	5.56418	−	20.7658i	0.343102	−	1.28048i	0.894814	−	0.446440i	$-0.147308\pi$
$264$	12.6853	−	7.32386i	0.780727	−	0.450753i
$265$	−5.89387	−	7.21161i	−0.362058	−	0.443006i
$266$		−	1.71902i		−	0.105400i
$267$	−19.1773	+	5.13855i	−1.17363	+	0.314474i
$268$	13.1604	+	3.52632i	0.803899	+	0.215404i
$269$		−	28.9822i		−	1.76708i	−0.468357	−	0.883539i	$-0.655154\pi$
$269$		−	28.9822i		−	1.76708i	0.468357	−	0.883539i	$-0.344846\pi$
$270$	1.24217	−	1.72601i	0.0755959	−	0.105041i
$271$	−7.48507	+	12.9645i	−0.454686	+	0.787539i	−0.998670	−	0.0515566i	$-0.983582\pi$
$271$	−7.48507	+	12.9645i	−0.454686	+	0.787539i	0.543984	+	0.839095i	$0.316915\pi$
$272$	−0.958139	+	0.256733i	−0.0580957	+	0.0155667i
$273$	−0.969980	−	3.62001i	−0.0587059	−	0.219093i
$274$			1.51673i			0.0916289i
$275$	9.21079	+	27.5017i	0.555432	+	1.65842i
$276$	8.83855	+	5.10294i	0.532018	+	0.307161i
$277$	12.7803	+	3.42447i	0.767895	+	0.205757i	0.621441	−	0.783461i	$-0.286547\pi$
$277$	12.7803	+	3.42447i	0.767895	+	0.205757i	0.146453	+	0.989218i	$0.453214\pi$
$278$	3.04825	−	11.3762i	0.182822	−	0.682301i
$279$			24.5976i			1.47262i
$280$	0.496239	−	0.223625i	0.0296559	−	0.0133642i
$281$	1.07509	+	1.86210i	0.0641343	+	0.111084i	0.896310	−	0.443429i	$-0.146238\pi$
$281$	1.07509	+	1.86210i	0.0641343	+	0.111084i	−0.832175	+	0.554513i	$0.812905\pi$
$282$	2.81561	−	10.5080i	0.167667	−	0.625742i
$283$	3.24305	+	12.1032i	0.192779	+	0.719462i	0.992831	+	0.119530i	$0.0381389\pi$
$283$	3.24305	+	12.1032i	0.192779	+	0.719462i	−0.800051	+	0.599932i	$0.795194\pi$
$284$	4.97332	−	8.61404i	0.295112	−	0.511149i
$285$	−37.2912	−	14.1222i	−2.20894	−	0.836528i
$286$	−30.6285	−	17.6834i	−1.81110	−	1.04564i
$287$	0.641036	+	2.39238i	0.0378392	+	0.141218i
$288$	−3.26155	+	0.873930i	−0.192189	+	0.0514968i
$289$	−13.8703	+	8.00803i	−0.815901	+	0.471061i
$290$	−1.97946	+	5.22697i	−0.116238	+	0.306938i
$291$	−4.22167	+	2.43738i	−0.247478	+	0.142882i
$292$	2.71209	+	10.1217i	0.158713	+	0.592326i
$293$	15.2505	−	15.2505i	0.890946	−	0.890946i	−0.103666	−	0.994612i	$-0.533057\pi$
$293$	15.2505	−	15.2505i	0.890946	−	0.890946i	0.994612	+	0.103666i	$0.0330573\pi$
$294$	15.1786	+	8.76337i	0.885234	+	0.511090i
$295$	0.504306	−	0.700739i	0.0293618	−	0.0407986i
$296$	3.30644	+	5.72692i	0.192183	+	0.332870i
$297$	−3.90072	+	3.90072i	−0.226342	+	0.226342i
$298$	−7.36719	−	1.97403i	−0.426770	−	0.114353i
$299$		−	24.6420i		−	1.42508i
$300$	−0.774441	−	12.6022i	−0.0447124	−	0.727588i
$301$	1.59375	−	0.0884367i	0.0918619	−	0.00509741i
$302$	1.10174	+	1.10174i	0.0633980	+	0.0633980i
$303$	31.4890	+	31.4890i	1.80899	+	1.80899i
$304$	3.53101	+	6.11588i	0.202517	+	0.350770i
$305$	7.24709	+	16.0817i	0.414967	+	0.920837i
$306$	2.90065	−	1.67469i	0.165819	−	0.0957359i
$307$	4.94734	−	18.4637i	0.282360	−	1.05378i	−0.668388	−	0.743813i	$-0.733015\pi$
$307$	4.94734	−	18.4637i	0.282360	−	1.05378i	0.950747	−	0.309967i	$-0.100318\pi$
$308$	−1.36387	+	0.365447i	−0.0777134	+	0.0208233i
$309$	6.59335			0.375083
$310$	10.3080	+	12.6127i	0.585457	+	0.716352i
$311$	−2.20599	−	3.82088i	−0.125090	−	0.216662i	0.796678	−	0.604404i	$-0.206589\pi$
$311$	−2.20599	−	3.82088i	−0.125090	−	0.216662i	−0.921768	+	0.387742i	$0.873255\pi$
$312$	10.8868	+	10.8868i	0.616342	+	0.616342i
$313$	−0.435476	+	1.62522i	−0.0246146	+	0.0918629i	−0.977140	−	0.212595i	$-0.931809\pi$
$313$	−0.435476	+	1.62522i	−0.0246146	+	0.0918629i	0.952526	+	0.304458i	$0.0984752\pi$
$314$	−7.74425	−	4.47114i	−0.437033	−	0.252321i
$315$	−1.42307	+	1.16304i	−0.0801812	+	0.0655301i
$316$	0.210056	−	0.363827i	0.0118166	−	0.0204669i
$317$	−20.1622	−	20.1622i	−1.13242	−	1.13242i	−0.989773	−	0.142651i	$-0.954437\pi$
$317$	−20.1622	−	20.1622i	−1.13242	−	1.13242i	−0.142651	−	0.989773i	$-0.545563\pi$
$318$	−2.72225	−	10.1596i	−0.152656	−	0.569721i
$319$	7.24956	−	12.5566i	0.405898	−	0.703035i
$320$	−1.30616	+	1.81492i	−0.0730165	+	0.101457i
$321$	−15.1306	+	8.73563i	−0.844506	+	0.487576i
$322$	−0.695653	−	0.695653i	−0.0387672	−	0.0387672i
$323$	−4.95334	−	4.95334i	−0.275611	−	0.275611i
$324$	−6.69294	+	3.86417i	−0.371830	+	0.214676i
$325$	−25.4163	+	16.8333i	−1.40984	+	0.933742i
$326$	−3.03292	+	5.25318i	−0.167978	+	0.290947i
$327$	−1.17904	−	4.40023i	−0.0652010	−	0.243333i
$328$	−7.19481	−	7.19481i	−0.397267	−	0.397267i
$329$	−0.524329	+	0.908164i	−0.0289072	+	0.0500687i
$330$	−3.27678	+	32.5890i	−0.180381	+	1.79397i
$331$	−22.1459	−	12.7859i	−1.21725	−	0.702779i	−0.252920	−	0.967487i	$-0.581391\pi$
$331$	−22.1459	−	12.7859i	−1.21725	−	0.702779i	−0.964329	+	0.264708i	$0.914724\pi$
$332$	−0.00141775	+	0.00529113i	−7.78094e−5	+	0.000290388i
$333$	−15.7890	−	15.7890i	−0.865234	−	0.865234i
$334$	−7.14196	−	12.3702i	−0.390791	−	0.676869i
$335$	−23.5896	+	19.2792i	−1.28884	+	1.05333i
$336$	0.614677			0.0335334
$337$	0.422672	−	0.113254i	0.0230244	−	0.00616937i	−0.247288	−	0.968942i	$-0.579540\pi$
$337$	0.422672	−	0.113254i	0.0230244	−	0.00616937i	0.270313	+	0.962773i	$0.412873\pi$
$338$	6.25668	−	23.3502i	0.340319	−	1.27009i
$339$	−40.7694	+	23.5382i	−2.21429	+	1.27842i
$340$	0.785532	−	2.07428i	0.0426015	−	0.112494i
$341$	−21.1280	−	36.5947i	−1.14414	−	1.98171i
$342$	−16.8614	−	16.8614i	−0.911761	−	0.911761i
$343$	−2.39951	−	2.39951i	−0.129562	−	0.129562i
$344$	−5.48853	+	3.58832i	−0.295922	+	0.193469i
$345$	−20.8060	+	9.37604i	−1.12016	+	0.504789i
$346$			6.03360i			0.324368i
$347$	25.8282	+	6.92064i	1.38653	+	0.371519i	0.873488	−	0.486845i	$-0.161852\pi$
$347$	25.8282	+	6.92064i	1.38653	+	0.371519i	0.513041	+	0.858364i	$0.328519\pi$
$348$	−4.46320	+	4.46320i	−0.239253	+	0.239253i
$349$	5.98327	+	10.3633i	0.320277	+	0.554736i	0.980545	−	0.196294i	$-0.0628907\pi$
$349$	5.98327	+	10.3633i	0.320277	+	0.554736i	−0.660268	+	0.751030i	$0.729557\pi$
$350$	−0.242304	+	1.19273i	−0.0129517	+	0.0637539i
$351$	−5.02150	−	2.89917i	−0.268028	−	0.154746i
$352$	4.10167	−	4.10167i	0.218620	−	0.218620i
$353$	0.164829	+	0.615149i	0.00877295	+	0.0327411i	0.970174	−	0.242411i	$-0.0779383\pi$
$353$	0.164829	+	0.615149i	0.00877295	+	0.0327411i	−0.961401	+	0.275152i	$0.911272\pi$
$354$	0.844352	−	0.487487i	0.0448768	−	0.0259096i
$355$	9.13787	+	20.2775i	0.484988	+	1.07622i
$356$	−6.80895	+	3.93115i	−0.360873	+	0.208350i
$357$	−0.588946	+	0.157808i	−0.0311703	+	0.00835207i
$358$	1.35679	+	5.06359i	0.0717084	+	0.267619i
$359$	−6.15313	−	3.55251i	−0.324750	−	0.187494i	0.328758	−	0.944414i	$-0.393370\pi$
$359$	−6.15313	−	3.55251i	−0.324750	−	0.187494i	−0.653508	+	0.756920i	$0.726703\pi$
$360$	2.67399	−	7.06096i	0.140932	−	0.372145i
$361$	−15.4360	+	26.7360i	−0.812422	+	1.40716i
$362$	2.41359	+	9.00765i	0.126856	+	0.473431i
$363$	14.8016	−	55.2403i	0.776882	−	2.89936i
$364$	−0.742064	−	1.28529i	−0.0388947	−	0.0673677i
$365$	−21.9125	−	8.29827i	−1.14695	−	0.434351i
$366$			19.9200i			1.04124i
$367$	5.04872	−	18.8421i	0.263541	−	0.983549i	−0.699596	−	0.714538i	$-0.746637\pi$
$367$	5.04872	−	18.8421i	0.263541	−	0.983549i	0.963137	−	0.269010i	$-0.0866966\pi$
$368$	3.90391	+	1.04605i	0.203505	+	0.0545291i
$369$	29.7540	+	17.1785i	1.54893	+	0.894276i
$370$	−14.7126	−	1.47934i	−0.764874	−	0.0769071i
$371$			1.01389i			0.0526384i
$372$	4.76106	+	17.7685i	0.246849	+	0.921254i
$373$	−6.35222	+	1.70207i	−0.328905	+	0.0881299i	−0.419493	−	0.907759i	$-0.637792\pi$
$373$	−6.35222	+	1.70207i	−0.328905	+	0.0881299i	0.0905876	+	0.995888i	$0.471125\pi$
$374$	−2.87694	+	4.98300i	−0.148763	+	0.257665i
$375$	23.8836	+	15.0549i	1.23334	+	0.777433i
$376$		−	4.30806i		−	0.222171i
$377$	14.7207	+	3.94441i	0.758157	+	0.203147i
$378$	−0.223604	+	0.0599146i	−0.0115010	+	0.00308167i
$379$			17.0267i			0.874605i	0.899314	+	0.437303i	$0.144066\pi$
$379$			17.0267i			0.874605i	−0.899314	+	0.437303i	$0.855934\pi$
$380$	−15.7119	−	1.57981i	−0.806004	−	0.0810427i
$381$	2.30084	−	1.32839i	0.117875	−	0.0680554i
$382$	2.87454	−	10.7279i	0.147074	−	0.548889i
$383$	−8.62178	−	8.62178i	−0.440552	−	0.440552i	0.451645	−	0.892198i	$-0.350837\pi$
$383$	−8.62178	−	8.62178i	−0.440552	−	0.440552i	−0.892198	+	0.451645i	$0.850837\pi$
$384$	−2.18688	+	1.26260i	−0.111599	+	0.0644316i
$385$	1.11817	−	2.95264i	0.0569871	−	0.150481i
$386$		−	5.85204i		−	0.297861i
$387$	14.7652	−	16.5001i	0.750556	−	0.838747i
$388$	−1.36503	+	1.36503i	−0.0692991	+	0.0692991i
$389$	15.8335			0.802790			0.401395	−	0.915905i	$-0.368525\pi$
$389$	15.8335			0.802790			0.401395	+	0.915905i	$0.368525\pi$
$390$	−33.9785	+	5.53880i	−1.72057	+	0.280468i
$391$	−4.00904			−0.202746
$392$	6.70425	+	1.79640i	0.338616	+	0.0907318i
$393$	6.99832	+	1.87519i	0.353019	+	0.0945911i
$394$	−4.91079	+	8.50574i	−0.247402	+	0.428513i
$395$	0.385952	+	0.856452i	0.0194194	+	0.0430928i
$396$	−9.79323	+	16.9624i	−0.492128	+	0.852391i
$397$	−4.83770	+	18.0545i	−0.242797	+	0.906131i	0.731681	+	0.681647i	$0.238736\pi$
$397$	−4.83770	+	18.0545i	−0.242797	+	0.906131i	−0.974478	+	0.224484i	$0.927931\pi$
$398$	−1.58962	+	1.58962i	−0.0796807	+	0.0796807i
$399$	2.17043	+	3.75929i	0.108657	+	0.188200i
$400$	−1.58789	−	4.74116i	−0.0793947	−	0.237058i
$401$	2.05447	−	3.55845i	0.102595	−	0.177701i	−0.810158	−	0.586212i	$-0.800619\pi$
$401$	2.05447	−	3.55845i	0.102595	−	0.177701i	0.912753	+	0.408511i	$0.133952\pi$
$402$	−33.2325	+	8.90463i	−1.65749	+	0.444123i
$403$	31.4063	−	31.4063i	1.56446	−	1.56446i
$404$	15.2725	+	8.81756i	0.759834	+	0.438690i
$405$	1.72887	−	17.1944i	0.0859084	−	0.854397i
$406$	0.526926	−	0.304221i	0.0261509	−	0.0150982i
$407$	37.0518	+	9.92800i	1.83659	+	0.492113i
$408$	1.77119	−	1.77119i	0.0876869	−	0.0876869i
$409$	9.85952			0.487522			0.243761	−	0.969835i	$-0.421619\pi$
$409$	9.85952			0.487522			0.243761	+	0.969835i	$0.421619\pi$
$410$	22.4556	−	3.66046i	1.10900	−	0.180777i
$411$	−1.91502	−	3.31691i	−0.0944608	−	0.163611i
$412$	2.52206	−	0.675783i	0.124253	−	0.0332935i
$413$	−0.0907808	+	0.0243246i	−0.00446703	+	0.00119694i
$414$	−13.6470			−0.670712
$415$	−0.00775118	−	0.00948417i	−0.000380491	−	0.000465560i
$416$	5.28020	+	3.04852i	0.258883	+	0.149466i
$417$	7.69743	+	28.7272i	0.376945	+	1.40678i
$418$	39.5683	+	10.6023i	1.93535	+	0.518576i
$419$	−18.7502			−0.916006			−0.458003	−	0.888951i	$-0.651435\pi$
$419$	−18.7502			−0.916006			−0.458003	+	0.888951i	$0.651435\pi$
$420$	−0.802866	+	1.11559i	−0.0391759	+	0.0544353i
$421$	−2.28330	−	1.31826i	−0.111281	−	0.0642482i	0.443326	−	0.896360i	$-0.353798\pi$
$421$	−2.28330	−	1.31826i	−0.111281	−	0.0642482i	−0.554608	+	0.832112i	$0.687132\pi$
$422$	−2.93571	−	2.93571i	−0.142908	−	0.142908i
$423$	3.76494	+	14.0510i	0.183058	+	0.683181i
$424$	−2.08261	−	3.60718i	−0.101140	−	0.175180i
$425$	2.73863	+	4.13503i	0.132843	+	0.200578i
$426$			25.1172i			1.21693i
$427$	0.496985	−	1.85477i	0.0240508	−	0.0897587i
$428$	−4.89232	+	4.89232i	−0.236479	+	0.236479i
$429$	89.3079			4.31182
$430$	0.656367	−	14.6482i	0.0316528	−	0.706398i
$431$	−10.2566			−0.494043			−0.247022	−	0.969010i	$-0.579452\pi$
$431$	−10.2566			−0.494043			−0.247022	+	0.969010i	$0.579452\pi$
$432$	0.672464	−	0.672464i	0.0323539	−	0.0323539i
$433$	−0.460282	+	1.71780i	−0.0221198	+	0.0825521i	−0.976103	−	0.217307i	$-0.930273\pi$
$433$	−0.460282	+	1.71780i	−0.0221198	+	0.0825521i	0.953984	+	0.299859i	$0.0969395\pi$
$434$		−	1.77323i		−	0.0851176i
$435$	−2.27071	−	13.9300i	−0.108872	−	0.667893i
$436$	−0.902001	−	1.56231i	−0.0431980	−	0.0748212i
$437$	7.38721	+	27.5694i	0.353378	+	1.31883i
$438$	−18.7106	−	18.7106i	−0.894028	−	0.894028i
$439$	−20.7194	−	11.9623i	−0.988881	−	0.570931i	−0.0839414	−	0.996471i	$-0.526751\pi$
$439$	−20.7194	−	11.9623i	−0.988881	−	0.570931i	−0.904940	+	0.425540i	$0.860084\pi$
$440$	2.08678	+	12.8016i	0.0994833	+	0.610294i
$441$	−23.4362			−1.11601
$442$	−5.84182	−	1.56531i	−0.277867	−	0.0744542i
$443$	−3.75940	−	14.0303i	−0.178615	−	0.666599i	−0.995908	−	0.0903766i	$-0.971193\pi$
$443$	−3.75940	−	14.0303i	−0.178615	−	0.666599i	0.817293	−	0.576222i	$-0.195474\pi$
$444$	−14.4616	−	8.34940i	−0.686316	−	0.396245i
$445$	1.75884	−	17.4924i	0.0833770	−	0.829220i
$446$	−18.6658			−0.883850
$447$	18.6036	−	4.98482i	0.879920	−	0.235774i
$448$	0.235123	−	0.0630011i	0.0111085	−	0.00297652i
$449$	13.8010	+	23.9040i	0.651308	+	1.12810i	0.982806	+	0.184643i	$0.0591129\pi$
$449$	13.8010	+	23.9040i	0.651308	+	1.12810i	−0.331497	+	0.943456i	$0.607554\pi$
$450$	9.32244	+	14.0758i	0.439464	+	0.663541i
$451$	−59.0214			−2.77921
$452$	−13.1824	+	13.1824i	−0.620047	+	0.620047i
$453$	−3.80043	−	1.01832i	−0.178560	−	0.0478449i
$454$	14.5756	−	8.41520i	0.684065	−	0.394945i
$455$	3.30196	+	0.332008i	0.154798	+	0.0155648i
$456$	−15.4438	−	8.91648i	−0.723222	−	0.417552i
$457$	19.0970	−	19.0970i	0.893322	−	0.893322i	−0.101512	−	0.994834i	$-0.532368\pi$
$457$	19.0970	−	19.0970i	0.893322	−	0.893322i	0.994834	+	0.101512i	$0.0323681\pi$
$458$	10.5093	−	2.81595i	0.491065	−	0.131581i
$459$	−0.471670	+	0.816957i	−0.0220157	+	0.0381323i
$460$	−6.99762	+	5.71899i	−0.326266	+	0.266649i
$461$	−5.87745	−	10.1800i	−0.273740	−	0.474132i	0.696076	−	0.717968i	$-0.254927\pi$
$461$	−5.87745	−	10.1800i	−0.273740	−	0.474132i	−0.969816	+	0.243836i	$0.921594\pi$
$462$	2.52120	−	2.52120i	0.117297	−	0.117297i
$463$	−8.45851	+	31.5676i	−0.393100	+	1.46707i	0.431891	+	0.901926i	$0.357846\pi$
$463$	−8.45851	+	31.5676i	−0.393100	+	1.46707i	−0.824992	+	0.565145i	$0.808820\pi$
$464$	−1.24979	+	2.16470i	−0.0580200	+	0.100494i
$465$	−38.4672	−	14.5675i	−1.78387	−	0.675554i
$466$	3.00282	−	5.20104i	0.139103	−	0.240934i
$467$	−21.9845	−	5.89072i	−1.01732	−	0.272590i	−0.288635	−	0.957439i	$-0.593201\pi$
$467$	−21.9845	−	5.89072i	−1.01732	−	0.272590i	−0.728685	+	0.684849i	$0.759868\pi$
$468$	−19.8858	−	5.32839i	−0.919223	−	0.246305i
$469$	3.31648			0.153141
$470$	7.81879	+	5.62701i	0.360654	+	0.259555i
$471$	22.5810			1.04048
$472$	0.273013	−	0.273013i	0.0125664	−	0.0125664i
$473$	−7.79402	+	37.2302i	−0.358370	+	1.71185i
$474$			1.06086i			0.0487271i
$475$	23.3895	−	26.4524i	1.07318	−	1.21372i
$476$	−0.209107	+	0.120728i	−0.00958438	+	0.00553355i
$477$	9.94496	+	9.94496i	0.455348	+	0.455348i
$478$	−0.393374	+	1.46809i	−0.0179925	+	0.0671489i
$479$	−35.4576	+	20.4714i	−1.62010	+	0.935364i	−0.633206	+	0.773983i	$0.718262\pi$
$479$	−35.4576	+	20.4714i	−1.62010	+	0.935364i	−0.986892	+	0.161381i	$0.948405\pi$
$480$	0.564900	−	5.61818i	0.0257841	−	0.256434i
$481$			40.3190i			1.83839i
$482$	−19.2920	+	5.16928i	−0.878728	+	0.235454i
$483$	2.39964	+	0.642982i	0.109188	+	0.0292567i
$484$		−	22.6474i		−	1.02943i
$485$	−0.694480	−	4.26038i	−0.0315347	−	0.193454i
$486$	11.1843	−	19.3718i	0.507330	−	0.878721i
$487$	1.50720	−	0.403853i	0.0682978	−	0.0183003i	−0.224508	−	0.974472i	$-0.572078\pi$
$487$	1.50720	−	0.403853i	0.0682978	−	0.0183003i	0.292806	+	0.956172i	$0.405411\pi$
$488$	2.04170	+	7.61971i	0.0924232	+	0.344928i
$489$		−	15.3174i		−	0.692679i
$490$	−12.0171	+	9.82131i	−0.542879	+	0.443682i
$491$	16.7429	+	9.66652i	0.755596	+	0.436244i	0.827712	−	0.561152i	$-0.189642\pi$
$491$	16.7429	+	9.66652i	0.755596	+	0.436244i	−0.0721160	+	0.997396i	$0.522975\pi$
$492$	24.8183	+	6.65006i	1.11890	+	0.299808i
$493$	0.641723	−	2.39494i	0.0289017	−	0.107863i
$494$			43.0574i			1.93724i
$495$	−17.9939	−	39.9295i	−0.808765	−	1.79470i
$496$	3.64235	+	6.30874i	0.163547	+	0.283271i
$497$	0.626649	−	2.33869i	0.0281091	−	0.104904i
$498$	−0.00358010	−	0.0133611i	−0.000160428	−	0.000598727i
$499$	0.307938	−	0.533363i	0.0137852	−	0.0238766i	−0.859051	−	0.511891i	$-0.828945\pi$
$499$	0.307938	−	0.533363i	0.0137852	−	0.0238766i	0.872836	+	0.488014i	$0.162279\pi$
$500$	10.6789	+	3.31080i	0.477574	+	0.148064i
$501$	31.2373	+	18.0348i	1.39558	+	0.805737i
$502$	7.70214	+	28.7448i	0.343763	+	1.28294i
$503$	10.1585	−	2.72196i	0.452946	−	0.121366i	−0.0251318	−	0.999684i	$-0.508001\pi$
$503$	10.1585	−	2.72196i	0.452946	−	0.121366i	0.478077	+	0.878318i	$0.341334\pi$
$504$	−0.711809	+	0.410963i	−0.0317065	+	0.0183058i
$505$	−35.9515	+	16.2012i	−1.59982	+	0.720944i
$506$	20.3031	−	11.7220i	0.902582	−	0.521106i
$507$	15.7993	+	58.9639i	0.701673	+	2.61868i
$508$	0.743952	−	0.743952i	0.0330076	−	0.0330076i
$509$	35.4424	+	20.4627i	1.57096	+	0.906993i	0.996052	+	0.0887745i	$0.0282950\pi$
$509$	35.4424	+	20.4627i	1.57096	+	0.906993i	0.574907	+	0.818219i	$0.305038\pi$
$510$	0.901116	+	5.52802i	0.0399021	+	0.244785i
$511$	1.27535	+	2.20898i	0.0564183	+	0.0977194i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	6.48718	+	1.73824i	0.286416	+	0.0767450i
$514$		−	15.5212i		−	0.684612i
$515$	−2.06771	+	5.46002i	−0.0911144	+	0.240597i
$516$	7.47216	−	14.7770i	0.328944	−	0.650523i
$517$	−17.6702	−	17.6702i	−0.777135	−	0.777135i
$518$	1.13822	+	1.13822i	0.0500107	+	0.0500107i
$519$	−7.61800	−	13.1948i	−0.334393	−	0.579186i
$520$	−12.4296	+	5.60129i	−0.545075	+	0.245633i
$521$	12.1943	−	7.04037i	0.534241	−	0.308444i	−0.208501	−	0.978022i	$-0.566858\pi$
$521$	12.1943	−	7.04037i	0.534241	−	0.308444i	0.742742	+	0.669578i	$0.233525\pi$
$522$	2.18446	−	8.15250i	0.0956110	−	0.356825i
$523$	−30.6878	+	8.22278i	−1.34188	+	0.359557i	−0.857133	−	0.515095i	$-0.827757\pi$
$523$	−30.6878	+	8.22278i	−1.34188	+	0.359557i	−0.484751	+	0.874652i	$0.661090\pi$
$524$	2.86916			0.125340
$525$	−0.976042	−	2.91428i	−0.0425980	−	0.127190i
$526$	10.7492	+	18.6181i	0.468686	+	0.811789i
$527$	−5.10954	−	5.10954i	−0.222575	−	0.222575i
$528$	−3.79111	+	14.1486i	−0.164987	+	0.615740i
$529$	−5.77231	−	3.33265i	−0.250970	−	0.144898i
$530$	9.26698	+	0.931782i	0.402532	+	0.0404740i
$531$	−0.651852	+	1.12904i	−0.0282879	+	0.0489962i
$532$	1.21553	+	1.21553i	0.0526999	+	0.0526999i
$533$	−16.0565	−	59.9235i	−0.695483	−	2.59558i
$534$	9.92691	−	17.1939i	0.429579	−	0.744053i
$535$	−2.48903	−	15.2693i	−0.107610	−	0.660151i
$536$	−11.7993	+	6.81232i	−0.509651	+	0.294247i
$537$	−9.36041	−	9.36041i	−0.403932	−	0.403932i
$538$	20.4935	+	20.4935i	0.883539	+	0.883539i
$539$	34.8668	−	20.1304i	1.50182	−	0.867076i
$540$	0.342125	+	2.09882i	0.0147227	+	0.0903186i
$541$	14.3101	−	24.7859i	0.615241	−	1.06563i	−0.375101	−	0.926984i	$-0.622392\pi$
$541$	14.3101	−	24.7859i	0.615241	−	1.06563i	0.990342	−	0.138645i	$-0.0442746\pi$
$542$	−3.87456	−	14.4600i	−0.166427	−	0.621112i
$543$	−16.6513	−	16.6513i	−0.714574	−	0.714574i
$544$	0.495969	−	0.859044i	0.0212645	−	0.0368312i
$545$	4.01363	+	0.403565i	0.171925	+	0.0172868i
$546$	3.24562	+	1.87386i	0.138900	+	0.0801937i
$547$	−3.84560	+	14.3520i	−0.164426	+	0.613645i	0.833687	+	0.552237i	$0.186226\pi$
$547$	−3.84560	+	14.3520i	−0.164426	+	0.613645i	−0.998113	+	0.0614081i	$0.980441\pi$
$548$	−1.07249	−	1.07249i	−0.0458144	−	0.0458144i
$549$	−13.3182	−	23.0678i	−0.568407	−	0.984509i
$550$	−25.9597	−	12.9336i	−1.10692	−	0.551492i
$551$	−17.6520			−0.752002
$552$	−9.85812	+	2.64148i	−0.419590	+	0.112429i
$553$	0.0264675	−	0.0987781i	0.00112551	−	0.00420047i
$554$	−11.4585	+	6.61558i	−0.486826	+	0.281069i
$555$	34.0426	−	15.3410i	1.44503	−	0.651190i
$556$	5.88877	+	10.1997i	0.249740	+	0.432562i
$557$	17.5295	+	17.5295i	0.742748	+	0.742748i	0.973106	−	0.230358i	$-0.0739896\pi$
$557$	17.5295	+	17.5295i	0.742748	+	0.742748i	−0.230358	+	0.973106i	$0.573990\pi$
$558$	−17.3931	−	17.3931i	−0.736310	−	0.736310i
$559$	−39.9196	+	2.21513i	−1.68842	+	0.0936901i
$560$	−0.192767	+	0.509021i	−0.00814587	+	0.0215101i
$561$		−	14.5296i		−	0.613442i
$562$	−2.07691	−	0.556505i	−0.0876090	−	0.0234748i
$563$	1.96514	−	1.96514i	0.0828209	−	0.0828209i	−0.664483	−	0.747304i	$-0.731348\pi$
$563$	1.96514	−	1.96514i	0.0828209	−	0.0828209i	0.747304	+	0.664483i	$0.231348\pi$
$564$	5.43934	+	9.42121i	0.229038	+	0.396705i
$565$	−6.70672	−	41.1433i	−0.282154	−	1.73091i
$566$	−10.8515	−	6.26509i	−0.456121	−	0.263341i
$567$	−1.33022	+	1.33022i	−0.0558640	+	0.0558640i
$568$	2.57438	+	9.60771i	0.108019	+	0.403131i
$569$	11.5387	−	6.66187i	0.483727	−	0.279280i	−0.238241	−	0.971206i	$-0.576571\pi$
$569$	11.5387	−	6.66187i	0.483727	−	0.279280i	0.721968	+	0.691926i	$0.243238\pi$
$570$	36.3548	−	16.3830i	1.52273	−	0.686207i
$571$	18.7603	−	10.8312i	0.785093	−	0.453273i	−0.0531394	−	0.998587i	$-0.516923\pi$
$571$	18.7603	−	10.8312i	0.785093	−	0.453273i	0.838232	+	0.545314i	$0.183589\pi$
$572$	34.1616	−	9.15358i	1.42837	−	0.382730i
$573$	7.25878	+	27.0901i	0.303240	+	1.13171i
$574$	−2.14495	−	1.23839i	−0.0895285	−	0.0516893i
$575$	−1.23951	−	20.1701i	−0.0516911	−	0.841150i
$576$	1.68830	−	2.92423i	0.0703460	−	0.121843i
$577$	−12.0713	−	45.0505i	−0.502533	−	1.87548i	−0.482909	−	0.875671i	$-0.660420\pi$
$577$	−12.0713	−	45.0505i	−0.502533	−	1.87548i	−0.0196241	−	0.999807i	$-0.506247\pi$
$578$	4.14526	−	15.4703i	0.172420	−	0.643481i
$579$	7.38877	+	12.7977i	0.307067	+	0.531856i
$580$	−2.29634	−	5.09571i	−0.0953502	−	0.211588i
$581$			0.00133339i			5.53183e-5i
$582$	1.26168	−	4.70866i	0.0522983	−	0.195180i
$583$	−23.3376	−	6.25330i	−0.966546	−	0.258985i
$584$	−9.07484	−	5.23936i	−0.375520	−	0.216806i
$585$	35.6447	−	29.1315i	1.47373	−	1.20444i
$586$			21.5675i			0.890946i
$587$	−5.36802	−	20.0337i	−0.221562	−	0.826880i	−0.983753	−	0.179528i	$-0.942543\pi$
$587$	−5.36802	−	20.0337i	−0.221562	−	0.826880i	0.762191	−	0.647352i	$-0.224124\pi$
$588$	−16.9295	+	4.53625i	−0.698162	+	0.187072i
$589$	−25.7224	+	44.5524i	−1.05987	+	1.83575i
$590$	0.138899	+	0.852096i	0.00571838	+	0.0350802i
$591$		−	24.8014i		−	1.02019i
$592$	−6.38755	−	1.71154i	−0.262526	−	0.0703438i
$593$	23.8298	−	6.38518i	0.978573	−	0.262208i	0.266129	−	0.963937i	$-0.414255\pi$
$593$	23.8298	−	6.38518i	0.978573	−	0.262208i	0.712443	+	0.701730i	$0.247588\pi$
$594$		−	5.51645i		−	0.226342i
$595$	0.0540149	−	0.537202i	0.00221440	−	0.0220231i
$596$	6.60524	−	3.81354i	0.270561	−	0.156209i
$597$	1.46927	−	5.48338i	0.0601331	−	0.224420i
$598$	17.4245	+	17.4245i	0.712540	+	0.712540i
$599$	18.4654	−	10.6610i	0.754476	−	0.435597i	−0.0728331	−	0.997344i	$-0.523204\pi$
$599$	18.4654	−	10.6610i	0.754476	−	0.435597i	0.827309	+	0.561747i	$0.189871\pi$
$600$	9.45871	+	8.36349i	0.386150	+	0.341438i
$601$			23.6249i			0.963679i	0.876259	+	0.481840i	$0.160031\pi$
$601$			23.6249i			0.963679i	−0.876259	+	0.481840i	$0.839969\pi$
$602$	−1.06441	+	1.18948i	−0.0433823	+	0.0484797i
$603$	32.5305	−	32.5305i	1.32474	−	1.32474i
$604$	−1.55809			−0.0633980
$605$	41.1032	+	29.5811i	1.67108	+	1.20264i
$606$	−44.5321			−1.80899
$607$	−13.3572	−	3.57904i	−0.542151	−	0.145269i	−0.0226574	−	0.999743i	$-0.507213\pi$
$607$	−13.3572	−	3.57904i	−0.542151	−	0.145269i	−0.519494	+	0.854474i	$0.673879\pi$
$608$	−6.82138	−	1.82778i	−0.276644	−	0.0741264i
$609$	−0.768216	+	1.33059i	−0.0311297	+	0.0539182i
$610$	−16.4960	−	6.24704i	−0.667902	−	0.252935i
$611$	13.1332	−	22.7474i	0.531313	−	0.920261i
$612$	−0.866885	+	3.23526i	−0.0350418	+	0.130778i
$613$	−4.37201	+	4.37201i	−0.176584	+	0.176584i	−0.789865	−	0.613281i	$-0.789849\pi$
$613$	−4.37201	+	4.37201i	−0.176584	+	0.176584i	0.613281	+	0.789865i	$0.289849\pi$
$614$	9.55753	+	16.5541i	0.385710	+	0.668070i
$615$	−44.4861	+	36.3574i	−1.79385	+	1.46607i
$616$	0.705989	−	1.22281i	0.0284451	−	0.0492683i
$617$	−27.0597	+	7.25063i	−1.08938	+	0.291900i	−0.758435	−	0.651749i	$-0.774036\pi$
$617$	−27.0597	+	7.25063i	−1.08938	+	0.291900i	−0.330949	+	0.943649i	$0.607369\pi$
$618$	−4.66220	+	4.66220i	−0.187541	+	0.187541i
$619$	−10.3906	−	5.99901i	−0.417633	−	0.241120i	0.276431	−	0.961034i	$-0.410848\pi$
$619$	−10.3906	−	5.99901i	−0.417633	−	0.241120i	−0.694064	+	0.719913i	$0.744182\pi$
$620$	−16.2074	−	1.62963i	−0.650904	−	0.0654475i
$621$	3.32867	−	1.92181i	0.133575	−	0.0771194i
$622$	4.26164	+	1.14190i	0.170876	+	0.0457861i
$623$	−1.35328	+	1.35328i	−0.0542179	+	0.0542179i
$624$	−15.3962			−0.616342
$625$	−19.9572	+	15.0569i	−0.798287	+	0.602277i
$626$	−0.841276	−	1.45713i	−0.0336241	−	0.0582387i
$627$	−99.9177	+	26.7729i	−3.99033	+	1.06921i
$628$	8.63758	−	2.31443i	0.344677	−	0.0923560i
$629$	6.55956			0.261547
$630$	0.183870	−	1.82866i	0.00732554	−	0.0728556i
$631$	−9.54860	−	5.51288i	−0.380124	−	0.219464i	0.297748	−	0.954644i	$-0.403764\pi$
$631$	−9.54860	−	5.51288i	−0.380124	−	0.219464i	−0.677872	+	0.735180i	$0.737098\pi$
$632$	0.108733	+	0.405797i	0.00432516	+	0.0161417i
$633$	10.1267	+	2.71344i	0.402499	+	0.107849i
$634$	28.5137			1.13242
$635$	0.378496	+	2.32194i	0.0150202	+	0.0921433i
$636$	9.10884	+	5.25899i	0.361189	+	0.208532i
$637$	29.9234	+	29.9234i	1.18561	+	1.18561i
$638$	3.75265	+	14.0051i	0.148569	+	0.554467i
$639$	−16.7929	−	29.0862i	−0.664318	−	1.15063i
$640$	−0.359750	−	2.20694i	−0.0142204	−	0.0872369i
$641$			16.9129i			0.668018i	0.942570	+	0.334009i	$0.108402\pi$
$641$			16.9129i			0.668018i	−0.942570	+	0.334009i	$0.891598\pi$
$642$	4.52190	−	16.8759i	0.178465	−	0.666041i
$643$	−34.2925	+	34.2925i	−1.35237	+	1.35237i	−0.469356	+	0.883009i	$0.655514\pi$
$643$	−34.2925	+	34.2925i	−1.35237	+	1.35237i	−0.883009	+	0.469356i	$0.844486\pi$
$644$	0.983803			0.0387672
$645$	17.0594	+	32.8626i	0.671711	+	1.29396i
$646$	7.00508			0.275611
$647$	13.4871	−	13.4871i	0.530234	−	0.530234i	−0.390408	−	0.920642i	$-0.627666\pi$
$647$	13.4871	−	13.4871i	0.530234	−	0.530234i	0.920642	+	0.390408i	$0.127666\pi$
$648$	2.00024	−	7.46501i	0.0785770	−	0.293253i
$649$		−	2.23962i		−	0.0879126i
$650$	6.06914	−	29.8750i	0.238051	−	1.17179i
$651$	2.23887	+	3.87784i	0.0877483	+	0.151985i
$652$	−1.56996	−	5.85916i	−0.0614842	−	0.229462i
$653$	5.16735	+	5.16735i	0.202214	+	0.202214i	0.800948	−	0.598734i	$-0.204329\pi$
$653$	5.16735	+	5.16735i	0.202214	+	0.202214i	−0.598734	+	0.800948i	$0.704329\pi$
$654$	3.94514	+	2.27773i	0.154267	+	0.0890662i
$655$	−3.74758	+	5.20731i	−0.146430	+	0.203466i
$656$	10.1750			0.397267
$657$	34.1769	+	9.15767i	1.33337	+	0.357275i
$658$	−0.271413	−	1.01293i	−0.0105808	−	0.0394879i
$659$	−25.1073	−	14.4957i	−0.978042	−	0.564673i	−0.0763635	−	0.997080i	$-0.524331\pi$
$659$	−25.1073	−	14.4957i	−0.978042	−	0.564673i	−0.901678	+	0.432407i	$0.857664\pi$
$660$	−20.7269	−	25.3609i	−0.806792	−	0.987173i
$661$	16.3030			0.634112			0.317056	−	0.948407i	$-0.397306\pi$
$661$	16.3030			0.634112			0.317056	+	0.948407i	$0.397306\pi$
$662$	24.7005	−	6.61849i	0.960014	−	0.257235i
$663$	14.7517	−	3.95271i	0.572909	−	0.153511i
$664$	−0.00273889	−	0.00474390i	−0.000106290	−	0.000184099i
$665$	−3.79377	+	0.618418i	−0.147116	+	0.0239812i
$666$	22.3291			0.865234
$667$	−7.14344	+	7.14344i	−0.276595	+	0.276595i
$668$	13.7972	+	3.69695i	0.533830	+	0.143039i
$669$	40.8198	−	23.5673i	1.57819	−	0.911166i
$670$	3.04791	−	30.3128i	0.117751	−	1.17108i
$671$	39.6279	+	22.8792i	1.52982	+	0.883240i
$672$	−0.434642	+	0.434642i	−0.0167667	+	0.0167667i
$673$	40.3246	−	10.8049i	1.55440	−	0.416500i	0.623513	−	0.781813i	$-0.285705\pi$
$673$	40.3246	−	10.8049i	1.55440	−	0.416500i	0.930885	+	0.365313i	$0.119038\pi$
$674$	−0.218791	+	0.378957i	−0.00842751	+	0.0145969i
$675$	−4.25606	−	2.12046i	−0.163816	−	0.0816164i
$676$	12.0870	+	20.9353i	0.464884	+	0.805202i
$677$	−4.46206	+	4.46206i	−0.171491	+	0.171491i	−0.787634	−	0.616143i	$-0.788694\pi$
$677$	−4.46206	+	4.46206i	−0.171491	+	0.171491i	0.616143	+	0.787634i	$0.288694\pi$
$678$	12.1843	−	45.4724i	0.467934	−	1.74636i
$679$	−0.234953	+	0.406950i	−0.00901666	+	0.0156173i
$680$	0.911284	+	2.02219i	0.0349461	+	0.0775476i
$681$	−21.2500	+	36.8061i	−0.814302	+	1.41041i
$682$	40.8161	+	10.9366i	1.56293	+	0.418786i
$683$	13.1338	+	3.51919i	0.502551	+	0.134658i	0.501184	−	0.865341i	$-0.332898\pi$
$683$	13.1338	+	3.51919i	0.502551	+	0.134658i	0.00136722	+	0.999999i	$0.499565\pi$
$684$	23.8456			0.911761
$685$	3.34733	−	0.545644i	0.127895	−	0.0208480i
$686$	3.39343			0.129562
$687$	−19.4271	+	19.4271i	−0.741190	+	0.741190i
$688$	1.34365	−	6.41830i	0.0512262	−	0.244695i
$689$		−	25.3955i		−	0.967492i
$690$	8.08221	−	21.3419i	0.307684	−	0.812473i
$691$	40.1724	−	23.1936i	1.52823	−	0.882325i	0.528795	−	0.848750i	$-0.322644\pi$
$691$	40.1724	−	23.1936i	1.52823	−	0.882325i	0.999436	−	0.0335752i	$-0.0106893\pi$
$692$	−4.26640	−	4.26640i	−0.162184	−	0.162184i
$693$	−1.23397	+	4.60524i	−0.0468746	+	0.174939i
$694$	−23.1569	+	13.3696i	−0.879024	+	0.507505i
$695$	−26.2033	−	2.63470i	−0.993947	−	0.0999400i
$696$		−	6.31192i		−	0.239253i
$697$	−9.74906	+	2.61225i	−0.369272	+	0.0989461i
$698$	−11.5588	−	3.09717i	−0.437507	−	0.117230i
$699$			15.1654i			0.573609i
$700$	−0.672050	−	1.01472i	−0.0254011	−	0.0383528i
$701$	−4.75551	+	8.23678i	−0.179613	+	0.311099i	−0.941748	−	0.336319i	$-0.890818\pi$
$701$	−4.75551	+	8.23678i	−0.179613	+	0.311099i	0.762135	+	0.647418i	$0.224151\pi$
$702$	5.60076	−	1.50072i	0.211387	−	0.0566410i
$703$	−12.0869	−	45.1089i	−0.455866	−	1.70132i
$704$			5.80063i			0.218620i
$705$	−24.2034	−	2.43362i	−0.911554	−	0.0916555i
$706$	−0.551528	−	0.318425i	−0.0207570	−	0.0119841i
$707$	4.14643	+	1.11103i	0.155943	+	0.0417847i
$708$	−0.252342	+	0.941752i	−0.00948358	+	0.0353932i
$709$			32.7924i			1.23154i	0.787925	+	0.615772i	$0.211156\pi$
$709$			32.7924i			1.23154i	−0.787925	+	0.615772i	$0.788844\pi$
$710$	−20.7998	−	7.87690i	−0.780603	−	0.295615i
$711$	−0.709276	−	1.22850i	−0.0265999	−	0.0460724i
$712$	2.03491	−	7.59439i	0.0762615	−	0.284612i
$713$	7.62016	+	28.4388i	0.285377	+	1.06504i
$714$	0.304861	−	0.528035i	0.0114091	−	0.0197612i
$715$	−28.0075	+	73.9568i	−1.04742	+	2.76583i
$716$	−4.53989	−	2.62111i	−0.169664	−	0.0979554i
$717$	−0.993345	−	3.70722i	−0.0370972	−	0.138449i
$718$	6.86292	−	1.83891i	0.256122	−	0.0686277i
$719$	23.2605	−	13.4295i	0.867472	−	0.500835i	0.000964640	−	1.00000i	$-0.499693\pi$
$719$	23.2605	−	13.4295i	0.867472	−	0.500835i	0.866507	+	0.499164i	$0.166360\pi$
$720$	3.10206	+	6.88365i	0.115607	+	0.256539i
$721$	0.550420	−	0.317785i	0.0204987	−	0.0118349i
$722$	−7.99027	−	29.8201i	−0.297367	−	1.10979i
$723$	35.6627	−	35.6627i	1.32631	−	1.32631i
$724$	−8.07604	−	4.66270i	−0.300143	−	0.173288i
$725$	12.2477	+	2.48814i	0.454868	+	0.0924070i
$726$	28.5945	+	49.5271i	1.06124	+	1.83812i
$727$	17.4630	−	17.4630i	0.647666	−	0.647666i	−0.304763	−	0.952428i	$-0.598577\pi$
$727$	17.4630	−	17.4630i	0.647666	−	0.647666i	0.952428	+	0.304763i	$0.0985771\pi$
$728$	1.43356	+	0.384121i	0.0531312	+	0.0142365i
$729$			33.3000i			1.23333i
$730$	21.3622	−	9.62670i	0.790651	−	0.356300i
$731$	0.360384	+	6.49458i	0.0133293	+	0.240211i
$732$	−14.0856	−	14.0856i	−0.520618	−	0.520618i
$733$	−6.43667	−	6.43667i	−0.237744	−	0.237744i	0.578172	−	0.815915i	$-0.303766\pi$
$733$	−6.43667	−	6.43667i	−0.237744	−	0.237744i	−0.815915	+	0.578172i	$0.803766\pi$
$734$	9.75338	+	16.8934i	0.360004	+	0.623545i
$735$	13.8797	−	36.6509i	0.511961	−	1.35189i
$736$	−3.50015	+	2.02081i	−0.129017	+	0.0744881i
$737$	−20.4549	+	76.3386i	−0.753465	+	2.81197i
$738$	−33.1863	+	8.89224i	−1.22160	+	0.327328i
$739$	41.5555			1.52864			0.764322	−	0.644835i	$-0.223074\pi$
$739$	41.5555			1.52864			0.764322	+	0.644835i	$0.223074\pi$
$740$	11.4495	−	9.35736i	0.420891	−	0.343984i
$741$	−54.3642	−	94.1615i	−1.99712	−	3.45911i
$742$	−0.716926	−	0.716926i	−0.0263192	−	0.0263192i
$743$	−5.59437	+	20.8785i	−0.205237	+	0.765956i	0.784140	+	0.620584i	$0.213105\pi$
$743$	−5.59437	+	20.8785i	−0.205237	+	0.765956i	−0.989377	+	0.145372i	$0.953562\pi$
$744$	−15.9308	−	9.19765i	−0.584052	−	0.337202i
$745$	−1.70622	+	16.9691i	−0.0625111	+	0.621700i
$746$	3.28815	−	5.69524i	0.120388	−	0.208518i
$747$	0.0130789	+	0.0130789i	0.000478531	+	0.000478531i
$748$	−1.48921	−	5.55781i	−0.0544510	−	0.203214i
$749$	−0.842077	+	1.45852i	−0.0307688	+	0.0532932i
$750$	−27.5337	+	6.24279i	−1.00539	+	0.227954i
$751$	42.0855	−	24.2981i	1.53572	−	0.886649i	0.536640	−	0.843811i	$-0.319693\pi$
$751$	42.0855	−	24.2981i	1.53572	−	0.886649i	0.999082	−	0.0428379i	$-0.0136399\pi$
$752$	3.04626	+	3.04626i	0.111086	+	0.111086i
$753$	−53.1368	−	53.1368i	−1.93641	−	1.93641i
$754$	−13.1983	+	7.62001i	−0.480652	+	0.277505i
$755$	2.03512	−	2.82782i	0.0740656	−	0.102915i
$756$	0.115746	−	0.200478i	0.00420964	−	0.00729131i
$757$	−5.23270	−	19.5287i	−0.190186	−	0.709783i	−0.993461	−	0.114175i	$-0.963578\pi$
$757$	−5.23270	−	19.5287i	−0.190186	−	0.709783i	0.803275	−	0.595609i	$-0.203089\pi$
$758$	−12.0397	−	12.0397i	−0.437303	−	0.437303i
$759$	−29.6003	+	51.2692i	−1.07442	+	1.86095i
$760$	12.2271	−	9.99291i	0.443524	−	0.362481i
$761$	−6.64266	−	3.83514i	−0.240796	−	0.139024i	0.374746	−	0.927127i	$-0.377730\pi$
$761$	−6.64266	−	3.83514i	−0.240796	−	0.139024i	−0.615543	+	0.788104i	$0.711063\pi$
$762$	−0.687624	+	2.56625i	−0.0249100	+	0.0929654i
$763$	−0.310509	−	0.310509i	−0.0112412	−	0.0112412i
$764$	5.55319	+	9.61841i	0.200907	+	0.347982i
$765$	−4.73946	−	5.79910i	−0.171355	−	0.209667i
$766$	12.1930			0.440552
$767$	2.27385	−	0.609276i	0.0821039	−	0.0219997i
$768$	0.653568	−	2.43915i	0.0235836	−	0.0880153i
$769$	30.8383	−	17.8045i	1.11206	−	0.642046i	0.172695	−	0.984975i	$-0.444752\pi$
$769$	30.8383	−	17.8045i	1.11206	−	0.642046i	0.939361	+	0.342929i	$0.111419\pi$
$770$	1.29717	+	2.87850i	0.0467467	+	0.103734i
$771$	19.5971	+	33.9431i	0.705771	+	1.22243i
$772$	4.13802	+	4.13802i	0.148931	+	0.148931i
$773$	5.01978	+	5.01978i	0.180549	+	0.180549i	0.791595	−	0.611046i	$-0.209251\pi$
$773$	5.01978	+	5.01978i	0.180549	+	0.180549i	−0.611046	+	0.791595i	$0.709251\pi$
$774$	1.22676	+	22.1079i	0.0440951	+	0.794652i
$775$	24.1271	−	27.2866i	0.866670	−	0.980164i
$776$		−	1.93045i		−	0.0692991i
$777$	−3.92628	−	1.05204i	−0.140854	−	0.0377418i
$778$	−11.1960	+	11.1960i	−0.401395	+	0.401395i
$779$	35.9280	+	62.2291i	1.28725	+	2.22959i
$780$	20.1099	−	27.9430i	0.720051	−	1.00052i
$781$	49.9669	+	28.8484i	1.78796	+	1.03228i
$782$	2.83482	−	2.83482i	0.101373	−	0.101373i
$783$	0.615243	+	2.29612i	0.0219870	+	0.0820565i
$784$	−6.01086	+	3.47037i	−0.214674	+	0.123942i
$785$	−7.08154	+	18.6996i	−0.252751	+	0.667416i
$786$	−6.27452	+	3.62260i	−0.223805	+	0.129214i
$787$	28.1469	−	7.54194i	1.00333	−	0.268841i	0.280489	−	0.959857i	$-0.409503\pi$
$787$	28.1469	−	7.54194i	1.00333	−	0.268841i	0.722839	+	0.691016i	$0.242837\pi$
$788$	−2.54201	−	9.48692i	−0.0905555	−	0.337958i
$789$	−47.0144	−	27.1438i	−1.67376	−	0.966344i
$790$	−0.878513	−	0.332693i	−0.0312561	−	0.0118367i
$791$	−2.26898	+	3.92999i	−0.0806757	+	0.139734i
$792$	−5.06935	−	18.9191i	−0.180132	−	0.672260i
$793$	−12.4483	+	46.4577i	−0.442052	+	1.64976i
$794$	−9.34571	−	16.1872i	−0.331667	−	0.574464i
$795$	−21.4423	+	9.66276i	−0.760478	+	0.342703i
$796$		−	2.24807i		−	0.0796807i
$797$	8.34108	−	31.1293i	0.295456	−	1.10266i	−0.645398	−	0.763846i	$-0.723309\pi$
$797$	8.34108	−	31.1293i	0.295456	−	1.10266i	0.940854	−	0.338811i	$-0.110025\pi$
$798$	−4.19295	−	1.12350i	−0.148429	−	0.0397714i
$799$	−3.70081	−	2.13666i	−0.130925	−	0.0755897i
$800$	4.47532	+	2.22970i	0.158226	+	0.0788316i
$801$			26.5479i			0.938023i
$802$	1.06347	+	3.96894i	0.0375525	+	0.140148i
$803$	−58.7121	+	15.7319i	−2.07190	+	0.555165i
$804$	17.2024	−	29.7955i	0.606683	−	1.05081i
$805$	−1.28500	+	1.78553i	−0.0452904	+	0.0629315i
$806$			44.4152i			1.56446i
$807$	−70.6920	−	18.9419i	−2.48848	−	0.666786i
$808$	−17.0342	+	4.56431i	−0.599262	+	0.160572i
$809$			37.5138i			1.31892i	0.751741	+	0.659458i	$0.229214\pi$
$809$			37.5138i			1.31892i	−0.751741	+	0.659458i	$0.770786\pi$
$810$	10.9358	+	13.3808i	0.384244	+	0.470153i
$811$	9.48055	−	5.47360i	0.332907	−	0.192204i	−0.324224	−	0.945980i	$-0.605103\pi$
$811$	9.48055	−	5.47360i	0.332907	−	0.192204i	0.657131	+	0.753776i	$0.271770\pi$
$812$	−0.157476	+	0.587709i	−0.00552633	+	0.0206245i
$813$	26.7304	+	26.7304i	0.937477	+	0.937477i
$814$	−33.2197	+	19.1794i	−1.16435	+	0.672239i
$815$	12.6845	+	4.80364i	0.444320	+	0.168264i
$816$			2.50484i			0.0876869i
$817$	43.9980	−	14.4455i	1.53930	−	0.505383i
$818$	−6.97173	+	6.97173i	−0.243761	+	0.243761i
$819$	−5.01132			−0.175110
$820$	−13.2902	+	18.4668i	−0.464113	+	0.644890i
$821$	1.90320			0.0664223			0.0332111	−	0.999448i	$-0.489427\pi$
$821$	1.90320			0.0664223			0.0332111	+	0.999448i	$0.489427\pi$
$822$	3.69953	+	0.991286i	0.129036	+	0.0345751i
$823$	34.6169	+	9.27557i	1.20667	+	0.323326i	0.805454	−	0.592658i	$-0.201921\pi$
$823$	34.6169	+	9.27557i	1.20667	+	0.323326i	0.401215	+	0.915984i	$0.368588\pi$
$824$	−1.30551	+	2.26121i	−0.0454797	+	0.0787732i
$825$	73.1007	−	4.49225i	2.54504	−	0.156400i
$826$	0.0469916	−	0.0813919i	0.00163505	−	0.00283198i
$827$	4.75204	−	17.7349i	0.165245	−	0.616702i	−0.832764	−	0.553628i	$-0.813243\pi$
$827$	4.75204	−	17.7349i	0.165245	−	0.616702i	0.998009	−	0.0630737i	$-0.0200903\pi$
$828$	9.64987	−	9.64987i	0.335356	−	0.335356i
$829$	−8.59879	−	14.8935i	−0.298648	−	0.517274i	0.677179	−	0.735819i	$-0.263202\pi$
$829$	−8.59879	−	14.8935i	−0.298648	−	0.517274i	−0.975827	+	0.218545i	$0.929869\pi$
$830$	0.0121872	+	0.00122541i	0.000423025	+	4.25346e-5i
$831$	16.7056	−	28.9350i	0.579512	−	1.00374i
$832$	−5.88929	+	1.57803i	−0.204175	+	0.0547084i
$833$	4.86829	−	4.86829i	0.168676	−	0.168676i
$834$	−25.7561	−	14.8703i	−0.891861	−	0.514916i
$835$	−24.7310	+	20.2121i	−0.855853	+	0.699467i
$836$	−35.4760	+	20.4821i	−1.22696	+	0.708387i
$837$	6.69175	+	1.79305i	0.231301	+	0.0619769i
$838$	13.2584	−	13.2584i	0.458003	−	0.458003i
$839$	−14.2923			−0.493426			−0.246713	−	0.969089i	$-0.579350\pi$
$839$	−14.2923			−0.493426			−0.246713	+	0.969089i	$0.579350\pi$
$840$	−0.221130	−	1.35656i	−0.00762972	−	0.0468056i
$841$	11.3761	+	19.7039i	0.392278	+	0.679445i
$842$	2.54669	−	0.682383i	0.0877647	−	0.0235165i
$843$	5.24459	−	1.40528i	0.180633	−	0.0484006i
$844$	4.15172			0.142908
$845$	−53.7834	−	5.40785i	−1.85021	−	0.186036i
$846$	−12.5977	−	7.27331i	−0.433119	−	0.250061i
$847$	−1.42681	−	5.32492i	−0.0490257	−	0.182967i
$848$	4.02329	+	1.07804i	0.138160	+	0.0370199i
$849$	31.6411			1.08592
$850$	−4.86041	−	0.987398i	−0.166711	−	0.0338675i
$851$	−23.1460	−	13.3634i	−0.793436	−	0.458090i
$852$	−17.7605	−	17.7605i	−0.608466	−	0.608466i
$853$	3.59739	+	13.4256i	0.123172	+	0.459685i	0.999768	−	0.0215427i	$-0.00685780\pi$
$853$	3.59739	+	13.4256i	0.123172	+	0.459685i	−0.876596	+	0.481227i	$0.840191\pi$
$854$	0.960101	+	1.66294i	0.0328540	+	0.0569048i
$855$	−31.1462	+	43.2780i	−1.06518	+	1.48008i
$856$		−	6.91878i		−	0.236479i
$857$	3.39362	−	12.6652i	0.115924	−	0.432634i	−0.883431	−	0.468562i	$-0.844772\pi$
$857$	3.39362	−	12.6652i	0.115924	−	0.432634i	0.999354	+	0.0359285i	$0.0114389\pi$
$858$	−63.1502	+	63.1502i	−2.15591	+	2.15591i
$859$	44.0460			1.50283			0.751416	−	0.659829i	$-0.229371\pi$
$859$	44.0460			1.50283			0.751416	+	0.659829i	$0.229371\pi$
$860$	9.89371	+	10.8219i	0.337373	+	0.369025i
$861$	6.25434			0.213147
$862$	7.25251	−	7.25251i	0.247022	−	0.247022i
$863$	9.68200	−	36.1337i	0.329579	−	1.23001i	−0.580049	−	0.814582i	$-0.696966\pi$
$863$	9.68200	−	36.1337i	0.329579	−	1.23001i	0.909628	−	0.415424i	$-0.136367\pi$
$864$			0.951007i			0.0323539i
$865$	13.3158	−	2.17059i	0.452750	−	0.0738022i
$866$	−0.889197	−	1.54013i	−0.0302162	−	0.0523359i
$867$	10.4676	+	39.0656i	0.355498	+	1.32674i
$868$	1.25386	+	1.25386i	0.0425588	+	0.0425588i
$869$	2.11043	+	1.21846i	0.0715914	+	0.0413333i
$870$	11.4556	+	8.24437i	0.388383	+	0.279510i
$871$	−83.0700			−2.81472
$872$	1.74253	+	0.466910i	0.0590096	+	0.0158116i
$873$	1.68708	+	6.29626i	0.0570989	+	0.213096i
$874$	−24.7181	−	14.2710i	−0.836102	−	0.482724i
$875$	2.71944	+	0.105666i	0.0919339	+	0.00357215i
$876$	26.4608			0.894028
$877$	−56.4692	+	15.1309i	−1.90683	+	0.510933i	−0.911892	+	0.410429i	$0.865379\pi$
$877$	−56.4692	+	15.1309i	−1.90683	+	0.510933i	−0.994937	+	0.100504i	$0.967954\pi$
$878$	23.1094	−	6.19216i	0.779906	−	0.208975i
$879$	−27.2311	−	47.1656i	−0.918482	−	1.59086i
$880$	−10.5277	−	7.57655i	−0.354889	−	0.255406i
$881$	31.5236			1.06206			0.531029	−	0.847354i	$-0.321805\pi$
$881$	31.5236			1.06206			0.531029	+	0.847354i	$0.321805\pi$
$882$	16.5719	−	16.5719i	0.558004	−	0.558004i
$883$	−26.2382	−	7.03050i	−0.882986	−	0.236595i	−0.211291	−	0.977423i	$-0.567767\pi$
$883$	−26.2382	−	7.03050i	−0.882986	−	0.236595i	−0.671695	+	0.740828i	$0.734433\pi$
$884$	5.23763	−	3.02395i	0.176161	−	0.101706i
$885$	−1.37961	−	1.68806i	−0.0463751	−	0.0567435i
$886$	12.5792	+	7.26261i	0.422607	+	0.243992i
$887$	15.2124	−	15.2124i	0.510781	−	0.510781i	−0.403985	−	0.914766i	$-0.632375\pi$
$887$	15.2124	−	15.2124i	0.510781	−	0.510781i	0.914766	+	0.403985i	$0.132375\pi$
$888$	16.1298	−	4.32197i	0.541280	−	0.145036i
$889$	0.128051	−	0.221791i	0.00429469	−	0.00743862i
$890$	11.1253	+	13.6127i	0.372922	+	0.456299i
$891$	−22.4146	−	38.8233i	−0.750919	−	1.30063i
$892$	13.1987	−	13.1987i	0.441925	−	0.441925i
$893$	−7.87420	+	29.3869i	−0.263500	+	0.983395i
$894$	−9.62993	+	16.6795i	−0.322073	+	0.557847i
$895$	10.6869	−	4.81597i	0.357225	−	0.160980i
$896$	−0.121709	+	0.210806i	−0.00406601	+	0.00704253i
$897$	−60.1054	−	16.1052i	−2.00686	−	0.537737i
$898$	−26.6614	−	7.14391i	−0.889704	−	0.238395i
$899$	−18.2087			−0.607294
$900$	−16.5451	−	3.36115i	−0.551503	−	0.112038i
$901$	−4.13164			−0.137645
$902$	41.7345	−	41.7345i	1.38961	−	1.38961i
$903$	0.825911	−	3.94518i	0.0274846	−	0.131287i
$904$		−	18.6427i		−	0.620047i
$905$	19.0110	−	8.56715i	0.631948	−	0.284782i
$906$	3.40737	−	1.96725i	0.113202	−	0.0653574i
$907$	−12.8041	−	12.8041i	−0.425154	−	0.425154i	0.461820	−	0.886974i	$-0.347197\pi$
$907$	−12.8041	−	12.8041i	−0.425154	−	0.425154i	−0.886974	+	0.461820i	$0.847197\pi$
$908$	−4.35603	+	16.2569i	−0.144560	+	0.539505i
$909$	51.5691	−	29.7734i	1.71044	−	0.987523i
$910$	−2.56961	+	2.10008i	−0.0851816	+	0.0696168i
$911$		−	12.1226i		−	0.401641i	−0.979628	−	0.200821i	$-0.935639\pi$
$911$		−	12.1226i		−	0.401641i	0.979628	−	0.200821i	$-0.0643608\pi$
$912$	17.2253	−	4.61551i	0.570387	−	0.152835i
$913$	−0.0306919	−	0.00822387i	−0.00101575	−	0.000272170i
$914$			27.0073i			0.893322i
$915$	43.9622	−	7.16623i	1.45335	−	0.236908i
$916$	−5.43999	+	9.42234i	−0.179742	+	0.311323i
$917$	0.674608	−	0.180761i	0.0222775	−	0.00596924i
$918$	−0.244155	−	0.911197i	−0.00805830	−	0.0300740i
$919$			14.0861i			0.464658i	0.972637	+	0.232329i	$0.0746345\pi$
$919$			14.0861i			0.464658i	−0.972637	+	0.232329i	$0.925365\pi$
$920$	0.904134	−	8.99200i	0.0298084	−	0.296457i
$921$	−41.8024	−	24.1346i	−1.37744	−	0.795263i
$922$	11.3544	+	3.04239i	0.373936	+	0.100196i
$923$	−15.6961	+	58.5786i	−0.516643	+	1.92814i
$924$			3.56552i			0.117297i
$925$	2.02807	+	33.0021i	0.0666827	+	1.08510i
$926$	−16.3406	−	28.3027i	−0.536985	−	0.930086i
$927$	2.28185	−	8.51600i	0.0749459	−	0.279702i
$928$	−0.646938	−	2.41441i	−0.0212368	−	0.0792567i
$929$	7.77964	−	13.4747i	0.255242	−	0.442092i	−0.709719	−	0.704484i	$-0.751178\pi$
$929$	7.77964	−	13.4747i	0.255242	−	0.442092i	0.964961	+	0.262393i	$0.0845116\pi$
$930$	37.5012	−	16.8996i	1.22971	−	0.554159i
$931$	−42.4488	−	24.5078i	−1.39120	−	0.803212i
$932$	1.55438	+	5.80101i	0.0509153	+	0.190018i
$933$	−10.7615	+	2.88353i	−0.352315	+	0.0944024i
$934$	19.7107	−	11.3800i	0.644955	−	0.372365i
$935$	12.0322	+	4.55659i	0.393494	+	0.149016i
$936$	17.8291	−	10.2937i	0.582764	−	0.336459i
$937$	−2.19571	−	8.19450i	−0.0717307	−	0.267703i	0.920741	−	0.390173i	$-0.127585\pi$
$937$	−2.19571	−	8.19450i	−0.0717307	−	0.267703i	−0.992472	+	0.122471i	$0.960918\pi$
$938$	−2.34510	+	2.34510i	−0.0765704	+	0.0765704i
$939$	3.67954	+	2.12438i	0.120077	+	0.0693267i
$940$	−9.50762	+	1.54983i	−0.310104	+	0.0505497i
$941$	−26.8892	−	46.5735i	−0.876564	−	1.51825i	−0.855087	−	0.518484i	$-0.826497\pi$
$941$	−26.8892	−	46.5735i	−0.876564	−	1.51825i	−0.0214764	−	0.999769i	$-0.506837\pi$
$942$	−15.9672	+	15.9672i	−0.520239	+	0.520239i
$943$	39.7222	+	10.6435i	1.29353	+	0.346601i
$944$			0.386098i			0.0125664i
$945$	0.212669	+	0.471926i	0.00691814	+	0.0153518i
$946$	−20.8145	−	31.8369i	−0.676739	−	1.03511i
$947$	21.2854	+	21.2854i	0.691682	+	0.691682i	0.962602	−	0.270920i	$-0.0873278\pi$
$947$	21.2854	+	21.2854i	0.691682	+	0.691682i	−0.270920	+	0.962602i	$0.587328\pi$
$948$	−0.750144	−	0.750144i	−0.0243635	−	0.0243635i
$949$	−31.9446	−	55.3297i	−1.03697	−	1.79608i
$950$	2.16582	+	35.2436i	0.0702685	+	1.14345i
$951$	−62.3561	+	36.0013i	−2.02204	+	1.16742i
$952$	0.0624933	−	0.233228i	0.00202542	−	0.00755896i
$953$	11.7879	−	3.15856i	0.381848	−	0.102316i	−0.0627887	−	0.998027i	$-0.519999\pi$
$953$	11.7879	−	3.15856i	0.381848	−	0.102316i	0.444637	+	0.895711i	$0.353333\pi$
$954$	−14.0643			−0.455348
$955$	−24.7100	−	2.48456i	−0.799598	−	0.0803985i
$956$	−0.759940	−	1.31625i	−0.0245782	−	0.0425707i
$957$	−25.8894	−	25.8894i	−0.836885	−	0.836885i
$958$	10.5968	−	39.5478i	0.342367	−	1.27773i
$959$	−0.319735	−	0.184599i	−0.0103248	−	0.00596102i
$960$	3.57321	+	4.37210i	0.115325	+	0.141109i
$961$	−11.0335	+	19.1106i	−0.355919	+	0.616470i
$962$	−28.5098	−	28.5098i	−0.919194	−	0.919194i
$963$	6.04653	+	22.5660i	0.194847	+	0.727178i
$964$	9.98629	−	17.2968i	0.321637	−	0.557091i
$965$	−12.9151	+	2.10527i	−0.415752	+	0.0677712i
$966$	−2.15146	+	1.24215i	−0.0692221	+	0.0399654i
$967$	25.2605	+	25.2605i	0.812322	+	0.812322i	0.984981	−	0.172660i	$-0.0552362\pi$
$967$	25.2605	+	25.2605i	0.812322	+	0.812322i	−0.172660	+	0.984981i	$0.555236\pi$
$968$	16.0141	+	16.0141i	0.514713	+	0.514713i
$969$	−15.3193	+	8.84460i	−0.492127	+	0.284129i
$970$	3.50362	+	2.52147i	0.112494	+	0.0809597i
$971$	31.0291	−	53.7439i	0.995770	−	1.72472i	0.418310	−	0.908304i	$-0.362622\pi$
$971$	31.0291	−	53.7439i	0.995770	−	1.72472i	0.577459	−	0.816420i	$-0.304044\pi$
$972$	5.78942	+	21.6064i	0.185696	+	0.693026i
$973$	2.02718	+	2.02718i	0.0649884	+	0.0649884i
$974$	−0.780184	+	1.35132i	−0.0249987	+	0.0432990i
$975$	24.4476	+	72.9960i	0.782949	+	2.33774i
$976$	−6.83165	−	3.94425i	−0.218676	−	0.126252i
$977$	−7.45263	+	27.8136i	−0.238431	+	0.889836i	0.738141	+	0.674646i	$0.235704\pi$
$977$	−7.45263	+	27.8136i	−0.238431	+	0.889836i	−0.976572	+	0.215190i	$0.930963\pi$
$978$	10.8311	+	10.8311i	0.346339	+	0.346339i
$979$	−22.8031	−	39.4962i	−0.728792	−	1.26230i
$980$	1.55268	−	15.4421i	0.0495987	−	0.493280i
$981$	−6.09141			−0.194484
$982$	−18.6743	+	5.00376i	−0.595920	+	0.159676i
$983$	−7.43335	+	27.7416i	−0.237087	+	0.884821i	0.740110	+	0.672486i	$0.234774\pi$
$983$	−7.43335	+	27.7416i	−0.237087	+	0.884821i	−0.977197	+	0.212335i	$0.931893\pi$
$984$	−22.2515	+	12.8469i	−0.709353	+	0.409545i
$985$	20.5383	+	7.77787i	0.654405	+	0.247824i
$986$	1.23971	+	2.14725i	0.0394805	+	0.0683822i
$987$	1.87246	+	1.87246i	0.0596012	+	0.0596012i
$988$	−30.4462	−	30.4462i	−0.968622	−	0.968622i
$989$	11.9593	−	23.6509i	0.380285	−	0.752056i
$990$	40.9580	+	15.5108i	1.30173	+	0.492967i
$991$		−	10.3539i		−	0.328903i	−0.986385	−	0.164451i	$-0.947415\pi$
$991$		−	10.3539i		−	0.328903i	0.986385	−	0.164451i	$-0.0525853\pi$
$992$	−7.03649	−	1.88542i	−0.223409	−	0.0598622i
$993$	−45.6607	+	45.6607i	−1.44900	+	1.44900i
$994$	1.21059	+	2.09681i	0.0383977	+	0.0665068i
$995$	4.08007	+	2.93634i	0.129347	+	0.0930881i
$996$	0.0119793	+	0.00691623i	0.000379577	+	0.000219149i
$997$	−30.9823	+	30.9823i	−0.981219	+	0.981219i	−0.999827	−	0.0186077i	$-0.994077\pi$
$997$	−30.9823	+	30.9823i	−0.981219	+	0.981219i	0.0186077	+	0.999827i	$0.494077\pi$
$998$	0.159400	+	0.594890i	0.00504572	+	0.0188309i
$999$	−5.44634	+	3.14445i	−0.172315	+	0.0994859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.l.a.7.10	✓	88
5.3	odd	4	inner	430.2.l.a.93.21	yes	88
43.37	odd	6	inner	430.2.l.a.37.21	yes	88
215.123	even	12	inner	430.2.l.a.123.10	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.l.a.7.10	✓	88	1.1	even	1	trivial
430.2.l.a.37.21	yes	88	43.37	odd	6	inner
430.2.l.a.93.21	yes	88	5.3	odd	4	inner
430.2.l.a.123.10	yes	88	215.123	even	12	inner

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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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.653568 - 2.43915i) q^{3} -1.00000i q^{4} +(1.81492 + 1.30616i) q^{5} +(1.26260 + 2.18688i) q^{6} +(-0.0630011 - 0.235123i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.92423 - 1.68830i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.653568 - 2.43915i) q^{3} -1.00000i q^{4} +(1.81492 + 1.30616i) q^{5} +(1.26260 + 2.18688i) q^{6} +(-0.0630011 - 0.235123i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.92423 - 1.68830i) q^{9} +(-2.20694 + 0.359750i) q^{10} +5.80063 q^{11} +(-2.43915 - 0.653568i) q^{12} +(1.57803 + 5.88929i) q^{13} +(0.210806 + 0.121709i) q^{14} +(4.37210 - 3.57321i) q^{15} -1.00000 q^{16} +(0.958139 - 0.256733i) q^{17} +(3.26155 - 0.873930i) q^{18} +(-3.53101 - 6.11588i) q^{19} +(1.30616 - 1.81492i) q^{20} -0.614677 q^{21} +(-4.10167 + 4.10167i) q^{22} +(-3.90391 - 1.04605i) q^{23} +(2.18688 - 1.26260i) q^{24} +(1.58789 + 4.74116i) q^{25} +(-5.28020 - 3.04852i) q^{26} +(-0.672464 + 0.672464i) q^{27} +(-0.235123 + 0.0630011i) q^{28} +(1.24979 - 2.16470i) q^{29} +(-0.564900 + 5.61818i) q^{30} +(-3.64235 - 6.30874i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.79111 - 14.1486i) q^{33} +(-0.495969 + 0.859044i) q^{34} +(0.192767 - 0.509021i) q^{35} +(-1.68830 + 2.92423i) q^{36} +(6.38755 + 1.71154i) q^{37} +(6.82138 + 1.82778i) q^{38} +15.3962 q^{39} +(0.359750 + 2.20694i) q^{40} -10.1750 q^{41} +(0.434642 - 0.434642i) q^{42} +(-1.34365 + 6.41830i) q^{43} -5.80063i q^{44} +(-3.10206 - 6.88365i) q^{45} +(3.50015 - 2.02081i) q^{46} +(-3.04626 - 3.04626i) q^{47} +(-0.653568 + 2.43915i) q^{48} +(6.01086 - 3.47037i) q^{49} +(-4.47532 - 2.22970i) q^{50} -2.50484i q^{51} +(5.88929 - 1.57803i) q^{52} +(-4.02329 - 1.07804i) q^{53} -0.951007i q^{54} +(10.5277 + 7.57655i) q^{55} +(0.121709 - 0.210806i) q^{56} +(-17.2253 + 4.61551i) q^{57} +(0.646938 + 2.41441i) q^{58} -0.386098i q^{59} +(-3.57321 - 4.37210i) q^{60} +(6.83165 + 3.94425i) q^{61} +(7.03649 + 1.88542i) q^{62} +(-0.212730 + 0.793920i) q^{63} +1.00000i q^{64} +(-4.82835 + 12.7498i) q^{65} +(7.32386 + 12.6853i) q^{66} +(-3.52632 + 13.1604i) q^{67} +(-0.256733 - 0.958139i) q^{68} +(-5.10294 + 8.83855i) q^{69} +(0.223625 + 0.496239i) q^{70} +(8.61404 + 4.97332i) q^{71} +(-0.873930 - 3.26155i) q^{72} +(-10.1217 + 2.71209i) q^{73} +(-5.72692 + 3.30644i) q^{74} +(12.6022 - 0.774441i) q^{75} +(-6.11588 + 3.53101i) q^{76} +(-0.365447 - 1.36387i) q^{77} +(-10.8868 + 10.8868i) q^{78} +(0.363827 + 0.210056i) q^{79} +(-1.81492 - 1.30616i) q^{80} +(-3.86417 - 6.69294i) q^{81} +(7.19481 - 7.19481i) q^{82} +(-0.00529113 - 0.00141775i) q^{83} +0.614677i q^{84} +(2.07428 + 0.785532i) q^{85} +(-3.58832 - 5.48853i) q^{86} +(-4.46320 - 4.46320i) q^{87} +(4.10167 + 4.10167i) q^{88} +(-3.93115 - 6.80895i) q^{89} +(7.06096 + 2.67399i) q^{90} +(1.28529 - 0.742064i) q^{91} +(-1.04605 + 3.90391i) q^{92} +(-17.7685 + 4.76106i) q^{93} +4.30806 q^{94} +(1.57981 - 15.7119i) q^{95} +(-1.26260 - 2.18688i) q^{96} +(-1.36503 - 1.36503i) q^{97} +(-1.79640 + 6.70425i) q^{98} +(-16.9624 - 9.79323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) 88 * q + 4 * q^6 + 12 * q^7	\( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

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