LMFDB - Embedded newform 756.2.cf.a.239.77

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(155,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 7, 0]))

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

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

chi := DirichletCharacter("756.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.77
Character	$\chi$	$=$	756.239
Dual form			756.2.cf.a.155.77

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.840806 + 1.13712i) q^{2} +(-0.740762 + 1.56565i) q^{3} +(-0.586089 + 1.91220i) q^{4} +(3.54867 + 0.625726i) q^{5} +(-2.40318 + 0.474076i) q^{6} +(-0.642788 - 0.766044i) q^{7} +(-2.66719 + 0.941333i) q^{8} +(-1.90254 - 2.31955i) q^{9} +O(q^{10})$	\(q+(0.840806 + 1.13712i) q^{2} +(-0.740762 + 1.56565i) q^{3} +(-0.586089 + 1.91220i) q^{4} +(3.54867 + 0.625726i) q^{5} +(-2.40318 + 0.474076i) q^{6} +(-0.642788 - 0.766044i) q^{7} +(-2.66719 + 0.941333i) q^{8} +(-1.90254 - 2.31955i) q^{9} +(2.27222 + 4.56138i) q^{10} +(0.571956 + 3.24372i) q^{11} +(-2.55969 - 2.33410i) q^{12} +(-0.926577 + 0.337246i) q^{13} +(0.330626 - 1.37502i) q^{14} +(-3.60839 + 5.09247i) q^{15} +(-3.31300 - 2.24144i) q^{16} +(-0.192637 - 0.111219i) q^{17} +(1.03794 - 4.11372i) q^{18} +(-6.44241 + 3.71952i) q^{19} +(-3.27635 + 6.41902i) q^{20} +(1.67551 - 0.438927i) q^{21} +(-3.20760 + 3.37773i) q^{22} +(4.63223 + 3.88691i) q^{23} +(0.501949 - 4.87320i) q^{24} +(7.50306 + 2.73089i) q^{25} +(-1.16256 - 0.770071i) q^{26} +(5.04095 - 1.26049i) q^{27} +(1.84156 - 0.780166i) q^{28} +(-0.179401 + 0.492900i) q^{29} +(-8.82472 + 0.178609i) q^{30} +(2.50675 - 2.98743i) q^{31} +(-0.236804 - 5.65190i) q^{32} +(-5.50223 - 1.50734i) q^{33} +(-0.0355010 - 0.312566i) q^{34} +(-1.80171 - 3.12065i) q^{35} +(5.55050 - 2.27858i) q^{36} +(2.26147 - 3.91698i) q^{37} +(-9.64637 - 4.19840i) q^{38} +(0.158361 - 1.70052i) q^{39} +(-10.0540 + 1.67155i) q^{40} +(3.26279 + 8.96443i) q^{41} +(1.90789 + 1.53621i) q^{42} +(-7.14795 + 1.26038i) q^{43} +(-6.53786 - 0.807419i) q^{44} +(-5.30010 - 9.42180i) q^{45} +(-0.525071 + 8.53554i) q^{46} +(2.47403 - 2.07596i) q^{47} +(5.96346 - 3.52664i) q^{48} +(-0.173648 + 0.984808i) q^{49} +(3.20327 + 10.8280i) q^{50} +(0.316829 - 0.219217i) q^{51} +(-0.101825 - 1.96945i) q^{52} -5.43299i q^{53} +(5.67179 + 4.67234i) q^{54} +11.8688i q^{55} +(2.43554 + 1.43811i) q^{56} +(-1.05120 - 12.8419i) q^{57} +(-0.711328 + 0.210433i) q^{58} +(2.12933 - 12.0760i) q^{59} +(-7.62298 - 9.88460i) q^{60} +(8.42803 - 7.07195i) q^{61} +(5.50476 + 0.338630i) q^{62} +(-0.553948 + 2.94841i) q^{63} +(6.22778 - 5.02142i) q^{64} +(-3.49914 + 0.616993i) q^{65} +(-2.91228 - 7.52408i) q^{66} +(-1.87280 - 5.14547i) q^{67} +(0.325576 - 0.303176i) q^{68} +(-9.51693 + 4.37320i) q^{69} +(2.03367 - 4.67262i) q^{70} +(0.208934 - 0.361884i) q^{71} +(7.25792 + 4.39576i) q^{72} +(3.78435 + 6.55468i) q^{73} +(6.35554 - 0.721856i) q^{74} +(-9.83360 + 9.72425i) q^{75} +(-3.33664 - 14.4991i) q^{76} +(2.11719 - 2.52317i) q^{77} +(2.06685 - 1.24973i) q^{78} +(-1.87769 + 5.15890i) q^{79} +(-10.3542 - 10.0272i) q^{80} +(-1.76065 + 8.82610i) q^{81} +(-7.45028 + 11.2475i) q^{82} +(14.0348 + 5.10825i) q^{83} +(-0.142686 + 3.46116i) q^{84} +(-0.614014 - 0.515219i) q^{85} +(-7.44324 - 7.06835i) q^{86} +(-0.638817 - 0.646001i) q^{87} +(-4.57894 - 8.11322i) q^{88} +(5.39232 - 3.11326i) q^{89} +(6.25737 - 13.9488i) q^{90} +(0.853938 + 0.493021i) q^{91} +(-10.1474 + 6.57967i) q^{92} +(2.82038 + 6.13768i) q^{93} +(4.44080 + 1.06779i) q^{94} +(-25.1894 + 9.16818i) q^{95} +(9.02433 + 3.81595i) q^{96} +(2.91501 + 16.5318i) q^{97} +(-1.26585 + 0.630574i) q^{98} +(6.43581 - 7.49801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q+O(q^{10}) $ 648 * q	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66} - 78 q^{68} - 42 q^{72} - 24 q^{81} - 30 q^{86} - 36 q^{89} + 198 q^{90} + 114 q^{92} - 144 q^{93} - 54 q^{94} + 156 q^{96} + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$-1$

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 $

$2$	0.840806	+	1.13712i	0.594540	+	0.804066i
$2$	0.840806	+	1.13712i	0.594540	+	0.804066i
$3$	−0.740762	+	1.56565i	−0.427679	+	0.903931i
$3$	−0.740762	+	1.56565i	−0.427679	+	0.903931i
$4$	−0.586089	+	1.91220i	−0.293045	+	0.956099i
$5$	3.54867	+	0.625726i	1.58701	+	0.279833i	0.896351	−	0.443345i	$-0.146208\pi$
$5$	3.54867	+	0.625726i	1.58701	+	0.279833i	0.690662	+	0.723178i	$0.257319\pi$
$6$	−2.40318	+	0.474076i	−0.981092	+	0.193541i
$7$	−0.642788	−	0.766044i	−0.242951	−	0.289538i
$7$	−0.642788	−	0.766044i	−0.242951	−	0.289538i
$8$	−2.66719	+	0.941333i	−0.942993	+	0.332811i
$9$	−1.90254	−	2.31955i	−0.634181	−	0.773184i
$10$	2.27222	+	4.56138i	0.718538	+	1.44244i
$11$	0.571956	+	3.24372i	0.172451	+	0.978019i	0.941045	+	0.338282i	$0.109846\pi$
$11$	0.571956	+	3.24372i	0.172451	+	0.978019i	−0.768594	+	0.639737i	$0.779043\pi$
$12$	−2.55969	−	2.33410i	−0.738918	−	0.673795i
$13$	−0.926577	+	0.337246i	−0.256986	+	0.0935353i	−0.467301	−	0.884098i	$-0.654773\pi$
$13$	−0.926577	+	0.337246i	−0.256986	+	0.0935353i	0.210314	+	0.977634i	$0.432551\pi$
$14$	0.330626	−	1.37502i	0.0883634	−	0.367490i
$15$	−3.60839	+	5.09247i	−0.931682	+	1.31487i
$16$	−3.31300	−	2.24144i	−0.828250	−	0.560359i
$17$	−0.192637	−	0.111219i	−0.0467215	−	0.0269746i	0.476457	−	0.879198i	$-0.341921\pi$
$17$	−0.192637	−	0.111219i	−0.0467215	−	0.0269746i	−0.523179	+	0.852223i	$0.675254\pi$
$18$	1.03794	−	4.11372i	0.244645	−	0.969613i
$19$	−6.44241	+	3.71952i	−1.47799	+	0.853317i	−0.999690	−	0.0248798i	$-0.992080\pi$
$19$	−6.44241	+	3.71952i	−1.47799	+	0.853317i	−0.478299	+	0.878197i	$0.658746\pi$
$20$	−3.27635	+	6.41902i	−0.732614	+	1.43534i
$21$	1.67551	−	0.438927i	0.365627	−	0.0957816i
$22$	−3.20760	+	3.37773i	−0.683863	+	0.720134i
$23$	4.63223	+	3.88691i	0.965887	+	0.810476i	0.981901	−	0.189396i	$-0.0606530\pi$
$23$	4.63223	+	3.88691i	0.965887	+	0.810476i	−0.0160134	+	0.999872i	$0.505097\pi$
$24$	0.501949	−	4.87320i	0.102460	−	0.994737i
$25$	7.50306	+	2.73089i	1.50061	+	0.546178i
$26$	−1.16256	−	0.770071i	−0.227997	−	0.151023i
$27$	5.04095	−	1.26049i	0.970131	−	0.242582i
$28$	1.84156	−	0.780166i	0.348022	−	0.147438i
$29$	−0.179401	+	0.492900i	−0.0333139	+	0.0915292i	−0.955235	−	0.295850i	$-0.904397\pi$
$29$	−0.179401	+	0.492900i	−0.0333139	+	0.0915292i	0.921921	+	0.387379i	$0.126619\pi$
$30$	−8.82472	+	0.178609i	−1.61117	+	0.0326094i
$31$	2.50675	−	2.98743i	0.450226	−	0.536558i	−0.492418	−	0.870359i	$-0.663887\pi$
$31$	2.50675	−	2.98743i	0.450226	−	0.536558i	0.942644	+	0.333801i	$0.108331\pi$
$32$	−0.236804	−	5.65190i	−0.0418614	−	0.999123i
$33$	−5.50223	−	1.50734i	−0.957815	−	0.262394i
$34$	−0.0355010	−	0.312566i	−0.00608837	−	0.0536046i
$35$	−1.80171	−	3.12065i	−0.304544	−	0.527486i
$36$	5.55050	−	2.27858i	0.925084	−	0.379763i
$37$	2.26147	−	3.91698i	0.371783	−	0.643947i	−0.618057	−	0.786133i	$-0.712080\pi$
$37$	2.26147	−	3.91698i	0.371783	−	0.643947i	0.989840	+	0.142186i	$0.0454132\pi$
$38$	−9.64637	−	4.19840i	−1.56485	−	0.681070i
$39$	0.158361	−	1.70052i	0.0253581	−	0.272301i
$40$	−10.0540	+	1.67155i	−1.58967	+	0.264295i
$41$	3.26279	+	8.96443i	0.509562	+	1.40001i	0.881691	+	0.471828i	$0.156406\pi$
$41$	3.26279	+	8.96443i	0.509562	+	1.40001i	−0.372129	+	0.928181i	$0.621372\pi$
$42$	1.90789	+	1.53621i	0.294395	+	0.237042i
$43$	−7.14795	+	1.26038i	−1.09005	+	0.192206i	−0.689656	−	0.724137i	$-0.742238\pi$
$43$	−7.14795	+	1.26038i	−1.09005	+	0.192206i	−0.400396	+	0.916342i	$0.631127\pi$
$44$	−6.53786	−	0.807419i	−0.985619	−	0.121723i
$45$	−5.30010	−	9.42180i	−0.790092	−	1.40452i
$46$	−0.525071	+	8.53554i	−0.0774176	+	1.25850i
$47$	2.47403	−	2.07596i	0.360875	−	0.302810i	−0.444265	−	0.895896i	$-0.646535\pi$
$47$	2.47403	−	2.07596i	0.360875	−	0.302810i	0.805139	+	0.593086i	$0.202091\pi$
$48$	5.96346	−	3.52664i	0.860751	−	0.509026i
$49$	−0.173648	+	0.984808i	−0.0248069	+	0.140687i
$50$	3.20327	+	10.8280i	0.453010	+	1.53132i
$51$	0.316829	−	0.219217i	0.0443650	−	0.0306965i
$52$	−0.101825	−	1.96945i	−0.0141206	−	0.273114i
$53$		−	5.43299i		−	0.746278i	−0.927775	−	0.373139i	$-0.878281\pi$
$53$		−	5.43299i		−	0.746278i	0.927775	−	0.373139i	$-0.121719\pi$
$54$	5.67179	+	4.67234i	0.771833	+	0.635825i
$55$			11.8688i			1.60039i
$56$	2.43554	+	1.43811i	0.325462	+	0.192175i
$57$	−1.05120	−	12.8419i	−0.139235	−	1.70095i
$58$	−0.711328	+	0.210433i	−0.0934020	+	0.0276312i
$59$	2.12933	−	12.0760i	0.277215	−	1.57216i	−0.454622	−	0.890684i	$-0.650226\pi$
$59$	2.12933	−	12.0760i	0.277215	−	1.57216i	0.731837	−	0.681480i	$-0.238663\pi$
$60$	−7.62298	−	9.88460i	−0.984122	−	1.27610i
$61$	8.42803	−	7.07195i	1.07910	−	0.905471i	0.0832527	−	0.996528i	$-0.473469\pi$
$61$	8.42803	−	7.07195i	1.07910	−	0.905471i	0.995846	+	0.0910575i	$0.0290247\pi$
$62$	5.50476	+	0.338630i	0.699105	+	0.0430061i
$63$	−0.553948	+	2.94841i	−0.0697909	+	0.371465i
$64$	6.22778	−	5.02142i	0.778473	−	0.627678i
$65$	−3.49914	+	0.616993i	−0.434015	+	0.0765285i
$66$	−2.91228	−	7.52408i	−0.358477	−	0.926151i
$67$	−1.87280	−	5.14547i	−0.228798	−	0.628619i	0.771169	−	0.636630i	$-0.219672\pi$
$67$	−1.87280	−	5.14547i	−0.228798	−	0.628619i	−0.999968	+	0.00801131i	$0.997450\pi$
$68$	0.325576	−	0.303176i	0.0394819	−	0.0367655i
$69$	−9.51693	+	4.37320i	−1.14570	+	0.526472i
$70$	2.03367	−	4.67262i	0.243070	−	0.558485i
$71$	0.208934	−	0.361884i	0.0247959	−	0.0429478i	−0.853361	−	0.521320i	$-0.825440\pi$
$71$	0.208934	−	0.361884i	0.0247959	−	0.0429478i	0.878157	+	0.478372i	$0.158773\pi$
$72$	7.25792	+	4.39576i	0.855354	+	0.518045i
$73$	3.78435	+	6.55468i	0.442925	+	0.767168i	0.997905	−	0.0646955i	$-0.0206076\pi$
$73$	3.78435	+	6.55468i	0.442925	+	0.767168i	−0.554981	+	0.831863i	$0.687274\pi$
$74$	6.35554	−	0.721856i	0.738816	−	0.0839141i
$75$	−9.83360	+	9.72425i	−1.13549	+	1.12286i
$76$	−3.33664	−	14.4991i	−0.382739	−	1.66316i
$77$	2.11719	−	2.52317i	0.241276	−	0.287542i
$78$	2.06685	−	1.24973i	0.234024	−	0.141504i
$79$	−1.87769	+	5.15890i	−0.211256	+	0.580422i	−0.999384	−	0.0350896i	$-0.988828\pi$
$79$	−1.87769	+	5.15890i	−0.211256	+	0.580422i	0.788128	+	0.615512i	$0.211051\pi$
$80$	−10.3542	−	10.0272i	−1.15764	−	1.12107i
$81$	−1.76065	+	8.82610i	−0.195628	+	0.980678i
$82$	−7.45028	+	11.2475i	−0.822745	+	1.24208i
$83$	14.0348	+	5.10825i	1.54052	+	0.560703i	0.966170	−	0.257908i	$-0.0830331\pi$
$83$	14.0348	+	5.10825i	1.54052	+	0.560703i	0.574349	+	0.818611i	$0.305255\pi$
$84$	−0.142686	+	3.46116i	−0.0155683	+	0.377644i
$85$	−0.614014	−	0.515219i	−0.0665992	−	0.0558833i
$86$	−7.44324	−	7.06835i	−0.802625	−	0.762200i
$87$	−0.638817	−	0.646001i	−0.0684884	−	0.0692586i
$88$	−4.57894	−	8.11322i	−0.488116	−	0.864872i
$89$	5.39232	−	3.11326i	0.571585	−	0.330005i	−0.186197	−	0.982512i	$-0.559616\pi$
$89$	5.39232	−	3.11326i	0.571585	−	0.330005i	0.757782	+	0.652508i	$0.226283\pi$
$90$	6.25737	−	13.9488i	0.659585	−	1.47033i
$91$	0.853938	+	0.493021i	0.0895170	+	0.0516827i
$92$	−10.1474	+	6.57967i	−1.05794	+	0.685978i
$93$	2.82038	+	6.13768i	0.292459	+	0.636447i
$94$	4.44080	+	1.06779i	0.458033	+	0.110135i
$95$	−25.1894	+	9.16818i	−2.58437	+	0.940635i
$96$	9.02433	+	3.81595i	0.921042	+	0.389464i
$97$	2.91501	+	16.5318i	0.295974	+	1.67855i	0.663217	+	0.748427i	$0.269191\pi$
$97$	2.91501	+	16.5318i	0.295974	+	1.67855i	−0.367243	+	0.930125i	$0.619698\pi$
$98$	−1.26585	+	0.630574i	−0.127870	+	0.0636975i
$99$	6.43581	−	7.49801i	0.646824	−	0.753578i
$100$	−9.61946	+	12.7468i	−0.961946	+	1.27468i
$101$	−4.88544	−	5.82224i	−0.486119	−	0.579334i	0.466107	−	0.884728i	$-0.345656\pi$
$101$	−4.88544	−	5.82224i	−0.486119	−	0.579334i	−0.952226	+	0.305394i	$0.901212\pi$
$102$	0.515668	+	0.175955i	0.0510587	+	0.0174221i
$103$	18.0520	+	3.18305i	1.77871	+	0.313635i	0.963936	−	0.266136i	$-0.0857470\pi$
$103$	18.0520	+	3.18305i	1.77871	+	0.313635i	0.814779	+	0.579771i	$0.196858\pi$
$104$	2.15389	−	1.77172i	0.211207	−	0.173731i
$105$	6.22049	−	0.509193i	0.607058	−	0.0496922i
$106$	6.17796	−	4.56809i	0.600057	−	0.443692i
$107$	−13.0804			−1.26453			−0.632264	−	0.774753i	$-0.717874\pi$
$107$	−13.0804			−1.26453			−0.632264	+	0.774753i	$0.717874\pi$
$108$	−0.544140	+	10.3780i	−0.0523599	+	0.998628i
$109$	6.13210			0.587349			0.293674	−	0.955905i	$-0.405122\pi$
$109$	6.13210			0.587349			0.293674	+	0.955905i	$0.405122\pi$
$110$	−13.4963	+	9.97935i	−1.28682	+	0.951494i
$111$	4.45742	+	6.44222i	0.423080	+	0.611469i
$112$	0.412513	+	3.97867i	0.0389789	+	0.375949i
$113$	−13.8784	−	2.44713i	−1.30557	−	0.230207i	−0.522766	−	0.852477i	$-0.675100\pi$
$113$	−13.8784	−	2.44713i	−1.30557	−	0.230207i	−0.782803	+	0.622270i	$0.786211\pi$
$114$	13.7189	−	11.9929i	1.28489	−	1.12323i
$115$	14.0061	+	16.6918i	1.30608	+	1.55652i
$116$	−0.837377	−	0.631933i	−0.0777485	−	0.0586735i
$117$	2.54511	+	1.50762i	0.235296	+	0.139379i
$118$	15.5223	−	7.73229i	1.42894	−	0.711815i
$119$	0.0386261	+	0.219059i	0.00354085	+	0.0200811i
$120$	4.83054	−	16.9793i	0.440966	−	1.54999i
$121$	0.142014	−	0.0516890i	0.0129104	−	0.00469900i
$122$	15.1280	+	3.63754i	1.36963	+	0.329328i
$123$	−16.4521	−	1.53211i	−1.48344	−	0.138146i
$124$	4.24337	+	6.54430i	0.381066	+	0.587696i
$125$	9.31384	+	5.37735i	0.833055	+	0.480965i
$126$	−3.81847	+	1.84914i	−0.340176	+	0.164734i
$127$	9.20125	−	5.31234i	0.816479	−	0.471394i	−0.0327219	−	0.999464i	$-0.510418\pi$
$127$	9.20125	−	5.31234i	0.816479	−	0.471394i	0.849201	+	0.528070i	$0.177084\pi$
$128$	10.9463	+	2.85970i	0.967528	+	0.252764i
$129$	3.32161	−	12.1249i	0.292452	−	1.06753i
$130$	−3.64369	−	3.46017i	−0.319573	−	0.303477i
$131$	−3.82717	−	3.21138i	−0.334382	−	0.280579i	0.460101	−	0.887867i	$-0.347813\pi$
$131$	−3.82717	−	3.21138i	−0.334382	−	0.280579i	−0.794482	+	0.607287i	$0.792258\pi$
$132$	6.10713	−	9.63791i	0.531558	−	0.838873i
$133$	6.99042	+	2.54430i	0.606146	+	0.220619i
$134$	4.27636	−	6.45594i	0.369421	−	0.557708i
$135$	18.6774	−	1.31881i	1.60749	−	0.113505i
$136$	0.618495	+	0.115307i	0.0530355	+	0.00988748i
$137$	−3.51150	+	9.64775i	−0.300007	+	0.824263i	0.694490	+	0.719502i	$0.255630\pi$
$137$	−3.51150	+	9.64775i	−0.300007	+	0.824263i	−0.994497	+	0.104761i	$0.966592\pi$
$138$	−12.9748	−	7.14488i	−1.10448	−	0.608213i
$139$	−3.63065	+	4.32684i	−0.307948	+	0.366998i	−0.897716	−	0.440575i	$-0.854775\pi$
$139$	−3.63065	+	4.32684i	−0.307948	+	0.366998i	0.589768	+	0.807573i	$0.299219\pi$
$140$	7.02326	−	1.61624i	0.593573	−	0.136597i
$141$	1.41757	+	5.41127i	0.119381	+	0.455711i
$142$	0.587179	−	0.0666913i	0.0492750	−	0.00559661i
$143$	−1.62389	−	2.81267i	−0.135797	−	0.235207i
$144$	1.10399	+	11.9491i	0.0919995	+	0.995759i
$145$	−0.945055	+	1.63688i	−0.0784825	+	0.135936i
$146$	−4.27157	+	9.81448i	−0.353517	+	0.812252i
$147$	−1.41324	−	1.00138i	−0.116562	−	0.0825925i
$148$	6.16461	+	6.62007i	0.506728	+	0.544167i
$149$	−2.41925	−	6.64683i	−0.198193	−	0.544530i	0.800289	−	0.599614i	$-0.204679\pi$
$149$	−2.41925	−	6.64683i	−0.198193	−	0.544530i	−0.998482	+	0.0550846i	$0.982457\pi$
$150$	−19.3258	−	3.00579i	−1.57795	−	0.245422i
$151$	16.4616	−	2.90262i	1.33962	−	0.236212i	0.542513	−	0.840047i	$-0.317473\pi$
$151$	16.4616	−	2.90262i	1.33962	−	0.236212i	0.797109	+	0.603836i	$0.206362\pi$
$152$	13.6818	−	15.9851i	1.10974	−	1.29656i
$153$	0.108522	+	0.658432i	0.00877351	+	0.0532311i
$154$	4.64930	+	0.286005i	0.374651	+	0.0230470i
$155$	10.7649	−	9.03286i	0.864661	−	0.725537i
$156$	3.15891	+	1.29947i	0.252915	+	0.104041i
$157$	0.161794	−	0.917578i	0.0129126	−	0.0732307i	−0.977671	−	0.210143i	$-0.932607\pi$
$157$	0.161794	−	0.917578i	0.0129126	−	0.0732307i	0.990583	+	0.136913i	$0.0437180\pi$
$158$	−7.44507	+	2.20248i	−0.592298	+	0.175220i
$159$	8.50618	+	4.02455i	0.674584	+	0.319167i
$160$	2.69620	−	20.2049i	0.213153	−	1.59734i
$161$		−	6.04695i		−	0.476566i
$162$	−11.5167	+	5.41897i	−0.904839	+	0.425755i
$163$		−	5.48026i		−	0.429247i	−0.976697	−	0.214623i	$-0.931148\pi$
$163$		−	5.48026i		−	0.429247i	0.976697	−	0.214623i	$-0.0688524\pi$
$164$	−19.0541	+	0.985133i	−1.48787	+	0.0769260i
$165$	−18.5824	−	8.79194i	−1.44664	−	0.684452i
$166$	5.99185	+	20.2543i	0.465057	+	1.57204i
$167$	−0.102286	+	0.580094i	−0.00791515	+	0.0448891i	−0.988510	−	0.151159i	$-0.951700\pi$
$167$	−0.102286	+	0.580094i	−0.00791515	+	0.0448891i	0.980594	+	0.196048i	$0.0628107\pi$
$168$	−4.05573	+	2.74792i	−0.312907	+	0.212006i
$169$	−9.21377	+	7.73127i	−0.708751	+	0.594713i
$170$	0.0695995	−	1.13141i	0.00533804	−	0.0867750i
$171$	20.8846	+	7.86694i	1.59708	+	0.601600i
$172$	1.77925	−	14.4070i	0.135666	−	1.09852i
$173$	20.7277	−	3.65486i	1.57590	−	0.277874i	0.683786	−	0.729682i	$-0.260332\pi$
$173$	20.7277	−	3.65486i	1.57590	−	0.277874i	0.892115	+	0.451809i	$0.149221\pi$
$174$	0.197460	−	1.26957i	0.0149694	−	0.0962462i
$175$	−2.73089	−	7.50306i	−0.206436	−	0.567178i
$176$	5.37571	−	12.0285i	0.405210	−	0.906679i
$177$	17.3295	+	12.2792i	1.30257	+	0.922964i
$178$	8.07405	+	3.51408i	0.605176	+	0.263391i
$179$	2.64452	−	4.58043i	0.197660	−	0.342358i	−0.750109	−	0.661314i	$-0.769999\pi$
$179$	2.64452	−	4.58043i	0.197660	−	0.342358i	0.947769	+	0.318956i	$0.103332\pi$
$180$	21.1227	−	4.61281i	1.57439	−	0.343819i
$181$	6.75802	+	11.7052i	0.502320	+	0.870043i	0.999996	+	0.00268049i	$0.000853227\pi$
$181$	6.75802	+	11.7052i	0.502320	+	0.870043i	−0.497677	+	0.867363i	$0.665813\pi$
$182$	0.157371	+	1.38557i	0.0116651	+	0.102705i
$183$	4.82907	+	18.4340i	0.356975	+	1.36268i
$184$	−16.0139	−	6.00663i	−1.18056	−	0.442815i
$185$	10.4762	−	12.4850i	0.770223	−	0.917916i
$186$	−4.60789	+	8.36771i	−0.337867	+	0.613550i
$187$	0.250584	−	0.688475i	0.0183246	−	0.0503463i
$188$	2.51964	+	5.94753i	0.183764	+	0.433769i
$189$	−4.20585	−	3.05136i	−0.305931	−	0.221954i
$190$	−31.6047	−	20.9347i	−2.29285	−	1.51876i
$191$	8.92469	+	3.24832i	0.645768	+	0.235040i	0.644080	−	0.764958i	$-0.277240\pi$
$191$	8.92469	+	3.24832i	0.645768	+	0.235040i	0.00168803	+	0.999999i	$0.499463\pi$
$192$	3.24851	+	13.4702i	0.234441	+	0.972130i
$193$	−5.10892	−	4.28689i	−0.367748	−	0.308577i	0.440122	−	0.897938i	$-0.354935\pi$
$193$	−5.10892	−	4.28689i	−0.367748	−	0.308577i	−0.807870	+	0.589361i	$0.799380\pi$
$194$	−16.3477	+	17.2148i	−1.17370	+	1.23595i
$195$	1.62603	−	5.93548i	0.116442	−	0.425049i
$196$	−1.78137	−	0.909235i	−0.127241	−	0.0649454i
$197$	−15.5012	+	8.94965i	−1.10442	+	0.637636i	−0.937378	−	0.348314i	$-0.886754\pi$
$197$	−15.5012	+	8.94965i	−1.10442	+	0.637636i	−0.167040	+	0.985950i	$0.553421\pi$
$198$	13.9374	+	1.01393i	0.990489	+	0.0720568i
$199$	13.9099	+	8.03090i	0.986049	+	0.569295i	0.904091	−	0.427340i	$-0.140549\pi$
$199$	13.9099	+	8.03090i	0.986049	+	0.569295i	0.0819578	+	0.996636i	$0.473883\pi$
$200$	−22.5827	−	0.220921i	−1.59684	−	0.0156215i
$201$	9.44331	+	0.879413i	0.666080	+	0.0620290i
$202$	2.51288	−	10.4507i	0.176806	−	0.735309i
$203$	0.492900	−	0.179401i	0.0345948	−	0.0125915i
$204$	0.233495	+	0.734321i	0.0163479	+	0.0514128i
$205$	5.96927	+	33.8534i	0.416912	+	2.36443i
$206$	11.5587	+	23.2036i	0.805333	+	1.61667i
$207$	0.202852	−	18.1397i	0.0140992	−	1.26080i
$208$	3.82566	+	0.959567i	0.265262	+	0.0665340i
$209$	−15.7499	−	18.7700i	−1.08944	−	1.29835i
$210$	5.80924	+	6.64532i	0.400876	+	0.458570i
$211$	−23.8065	−	4.19773i	−1.63891	−	0.288984i	−0.723143	−	0.690698i	$-0.757303\pi$
$211$	−23.8065	−	4.19773i	−1.63891	−	0.288984i	−0.915765	+	0.401714i	$0.868414\pi$
$212$	10.3889	+	3.18422i	0.713516	+	0.218693i
$213$	0.411815	+	0.595188i	0.0282171	+	0.0407816i
$214$	−10.9981	−	14.8740i	−0.751812	−	1.01676i
$215$	−26.1544			−1.78371
$216$	−12.2586	+	8.10718i	−0.834093	+	0.551623i
$217$	−3.89981			−0.264736
$218$	5.15591	+	6.97294i	0.349202	+	0.472267i
$219$	−13.0657	+	1.06952i	−0.882896	+	0.0722716i
$220$	−22.6955	−	6.95617i	−1.53013	−	0.468985i
$221$	0.216002	+	0.0380869i	0.0145298	+	0.00256200i
$222$	−3.57776	+	10.4853i	−0.240124	+	0.703727i
$223$	−10.7526	−	12.8144i	−0.720046	−	0.858117i	0.274589	−	0.961562i	$-0.411458\pi$
$223$	−10.7526	−	12.8144i	−0.720046	−	0.858117i	−0.994635	+	0.103444i	$0.967014\pi$
$224$	−4.17739	+	3.81437i	−0.279114	+	0.254858i
$225$	−7.94046	−	22.5994i	−0.529364	−	1.50662i
$226$	−8.88635	−	17.8390i	−0.591111	−	1.18663i
$227$	−4.22210	−	23.9447i	−0.280230	−	1.58927i	−0.721841	−	0.692059i	$-0.756704\pi$
$227$	−4.22210	−	23.9447i	−0.280230	−	1.58927i	0.441611	−	0.897207i	$-0.354407\pi$
$228$	25.1723	+	5.51637i	1.66707	+	0.365331i
$229$	−24.7373	+	9.00363i	−1.63468	+	0.594977i	−0.986098	−	0.166164i	$-0.946862\pi$
$229$	−24.7373	+	9.00363i	−1.63468	+	0.594977i	−0.648586	+	0.761141i	$0.724640\pi$
$230$	−7.20422	+	29.9613i	−0.475032	+	1.97559i
$231$	2.38208	+	5.18385i	0.156729	+	0.341072i
$232$	0.0145130	−	1.48353i	0.000952826	−	0.0973987i
$233$	−6.28698	−	3.62979i	−0.411874	−	0.237796i	0.279721	−	0.960081i	$-0.409758\pi$
$233$	−6.28698	−	3.62979i	−0.411874	−	0.237796i	−0.691595	+	0.722286i	$0.743092\pi$
$234$	0.425604	+	4.16172i	0.0278226	+	0.272060i
$235$	10.0785	−	5.81883i	0.657449	−	0.379578i
$236$	21.8438	+	11.1493i	1.42191	+	0.725759i
$237$	−6.68614	−	6.76133i	−0.434311	−	0.439195i
$238$	−0.216620	+	0.228109i	−0.0140414	+	0.0147861i
$239$	−11.7744	−	9.87989i	−0.761622	−	0.639077i	0.176926	−	0.984224i	$-0.443385\pi$
$239$	−11.7744	−	9.87989i	−0.761622	−	0.639077i	−0.938549	+	0.345147i	$0.887829\pi$
$240$	23.3690	−	8.78338i	1.50847	−	0.566965i
$241$	12.1877	+	4.43597i	0.785081	+	0.285746i	0.703290	−	0.710903i	$-0.251714\pi$
$241$	12.1877	+	4.43597i	0.785081	+	0.285746i	0.0817913	+	0.996649i	$0.473936\pi$
$242$	0.178183	+	0.118027i	0.0114540	+	0.00758706i
$243$	−12.5144	−	9.29461i	−0.802799	−	0.596249i
$244$	8.58340	+	20.2609i	0.549496	+	1.29707i
$245$	−1.23244	+	3.38610i	−0.0787377	+	0.216330i
$246$	−12.0909	−	19.9963i	−0.770886	−	1.27492i
$247$	4.71499	−	5.61910i	0.300007	−	0.357535i
$248$	−3.87381	+	10.3277i	−0.245987	+	0.655811i
$249$	−18.3942	+	18.1896i	−1.16568	+	1.15272i
$250$	1.71644	+	15.1123i	0.108557	+	0.955784i
$251$	−0.0408746	−	0.0707970i	−0.00257998	−	0.00446866i	0.864733	−	0.502233i	$-0.167488\pi$
$251$	−0.0408746	−	0.0707970i	−0.00257998	−	0.00446866i	−0.867313	+	0.497764i	$0.834155\pi$
$252$	−5.31329	−	2.78729i	−0.334706	−	0.175583i
$253$	−9.95861	+	17.2488i	−0.626092	+	1.08442i
$254$	13.7772	+	5.99628i	0.864461	+	0.376240i
$255$	1.26149	−	0.579679i	0.0789977	−	0.0363009i
$256$	5.95192	+	14.8518i	0.371995	+	0.928235i
$257$	9.09995	+	25.0019i	0.567639	+	1.55958i	0.808179	+	0.588937i	$0.200453\pi$
$257$	9.09995	+	25.0019i	0.567639	+	1.55958i	−0.240539	+	0.970639i	$0.577324\pi$
$258$	16.5803	−	6.41758i	1.03224	−	0.399541i
$259$	−4.45422	+	0.785400i	−0.276772	+	0.0488024i
$260$	0.870997	−	7.05266i	0.0540169	−	0.437387i
$261$	1.48463	−	0.521634i	0.0918960	−	0.0322883i
$262$	0.433816	−	7.05210i	0.0268013	−	0.435680i
$263$	2.49549	−	2.09396i	0.153878	−	0.129119i	−0.562598	−	0.826731i	$-0.690198\pi$
$263$	2.49549	−	2.09396i	0.153878	−	0.129119i	0.716476	+	0.697611i	$0.245754\pi$
$264$	16.0944	−	1.15907i	0.990541	−	0.0713358i
$265$	3.39956	−	19.2799i	0.208833	−	1.18435i
$266$	2.98441	+	10.0882i	0.182986	+	0.618549i
$267$	0.879861	+	10.7487i	0.0538466	+	0.657810i
$268$	10.9368	−	0.565453i	0.668070	−	0.0345406i
$269$		−	32.7193i		−	1.99493i	−0.0711608	−	0.997465i	$-0.522670\pi$
$269$		−	32.7193i		−	1.99493i	0.0711608	−	0.997465i	$-0.477330\pi$
$270$	17.2037	+	20.1296i	1.04698	+	1.22505i
$271$		−	19.8402i		−	1.20521i	−0.798040	−	0.602605i	$-0.794130\pi$
$271$		−	19.8402i		−	1.20521i	0.798040	−	0.602605i	$-0.205870\pi$
$272$	0.388917	+	0.800254i	0.0235815	+	0.0485225i
$273$	−1.40446	+	0.971760i	−0.0850021	+	0.0588136i
$274$	−13.9232	+	4.11890i	−0.841128	+	0.248832i
$275$	−4.56683	+	25.8998i	−0.275390	+	1.56182i
$276$	−2.78466	−	20.7613i	−0.167617	−	1.24969i
$277$	−6.37849	+	5.35219i	−0.383246	+	0.321582i	−0.813975	−	0.580900i	$-0.802701\pi$
$277$	−6.37849	+	5.35219i	−0.383246	+	0.321582i	0.430729	+	0.902481i	$0.358256\pi$
$278$	−7.97281	−	0.490455i	−0.478178	−	0.0294155i
$279$	−11.6987	−	0.130824i	−0.700383	−	0.00783220i
$280$	7.74306	+	6.62735i	0.462736	+	0.396060i
$281$	23.7723	−	4.19170i	1.41814	−	0.250056i	0.588563	−	0.808451i	$-0.299694\pi$
$281$	23.7723	−	4.19170i	1.41814	−	0.250056i	0.829575	+	0.558395i	$0.188583\pi$
$282$	−4.96137	+	6.16177i	−0.295445	+	0.366928i
$283$	−3.57225	−	9.81467i	−0.212348	−	0.583422i	0.787094	−	0.616834i	$-0.211585\pi$
$283$	−3.57225	−	9.81467i	−0.212348	−	0.583422i	−0.999442	+	0.0334121i	$0.989363\pi$
$284$	0.569540	+	0.611619i	0.0337960	+	0.0362929i
$285$	4.30512	−	46.2293i	0.255013	−	2.73839i
$286$	1.83296	−	4.21147i	0.108385	−	0.249030i
$287$	4.76988	−	8.26167i	0.281557	−	0.487671i
$288$	−12.6593	+	11.3023i	−0.745959	+	0.665992i
$289$	−8.47526	−	14.6796i	−0.498545	−	0.863505i
$290$	−2.65594	+	0.301660i	−0.155962	+	0.0177141i
$291$	−28.0424	−	7.68225i	−1.64388	−	0.450341i
$292$	−14.7518	+	3.39479i	−0.863285	+	0.198665i
$293$	−15.0325	+	17.9150i	−0.878206	+	1.04660i	0.120342	+	0.992732i	$0.461601\pi$
$293$	−15.0325	+	17.9150i	−0.878206	+	1.04660i	−0.998548	+	0.0538722i	$0.982844\pi$
$294$	−0.0495666	−	2.44899i	−0.00289078	−	0.142828i
$295$	15.1126	−	41.5214i	0.879887	−	2.41747i
$296$	−2.34458	+	12.5761i	−0.136276	+	0.730972i
$297$	6.97188	+	15.6305i	0.404550	+	0.906973i
$298$	5.52414	−	8.33968i	0.320005	−	0.483105i
$299$	−5.60296	−	2.03931i	−0.324028	−	0.117936i
$300$	−12.8313	−	24.5031i	−0.740817	−	1.41469i
$301$	5.56012	+	4.66549i	0.320480	+	0.268914i
$302$	17.1416	+	16.2782i	0.986388	+	0.936708i
$303$	12.7346	−	3.33601i	0.731581	−	0.191649i
$304$	29.6808	+	2.11747i	1.70231	+	0.121445i
$305$	34.3334	−	19.8224i	1.96592	−	1.13503i
$306$	−0.657471	+	0.677017i	−0.0375851	+	0.0387025i
$307$	11.7585	+	6.78876i	0.671092	+	0.387455i	0.796490	−	0.604651i	$-0.206688\pi$
$307$	11.7585	+	6.78876i	0.671092	+	0.387455i	−0.125398	+	0.992106i	$0.540021\pi$
$308$	3.58393	+	5.52729i	0.204214	+	0.314946i
$309$	−18.3558	+	25.9053i	−1.04422	+	1.47370i
$310$	19.3227	+	4.64616i	1.09745	+	0.263884i
$311$	−20.9049	+	7.60874i	−1.18541	+	0.431452i	−0.858108	−	0.513469i	$-0.828360\pi$
$311$	−20.9049	+	7.60874i	−1.18541	+	0.431452i	−0.327297	+	0.944921i	$0.606138\pi$
$312$	1.17837	+	4.68467i	0.0667123	+	0.265217i
$313$	−0.158265	−	0.897566i	−0.00894567	−	0.0507334i	0.980008	−	0.198957i	$-0.0637555\pi$
$313$	−0.158265	−	0.897566i	−0.00894567	−	0.0507334i	−0.988954	+	0.148224i	$0.952644\pi$
$314$	1.17944	−	0.587527i	0.0665594	−	0.0331560i
$315$	−3.81068	+	10.1163i	−0.214707	+	0.569990i
$316$	−8.76435	−	6.61409i	−0.493033	−	0.372071i
$317$	−1.21356	−	1.44626i	−0.0681601	−	0.0812300i	0.730887	−	0.682499i	$-0.239107\pi$
$317$	−1.21356	−	1.44626i	−0.0681601	−	0.0812300i	−0.799047	+	0.601269i	$0.794662\pi$
$318$	2.57565	+	13.0564i	0.144435	+	0.732168i
$319$	−1.70144	−	0.300010i	−0.0952624	−	0.0167973i
$320$	25.2424	−	13.9225i	1.41109	−	0.778291i
$321$	9.68944	−	20.4793i	0.540812	−	1.14304i
$322$	6.87612	−	5.08431i	0.383191	−	0.283338i
$323$	1.65473			0.0920717
$324$	−15.8454	−	8.53960i	−0.880298	−	0.474422i
$325$	−7.87314			−0.436723
$326$	6.23172	−	4.60783i	0.345143	−	0.255204i
$327$	−4.54243	+	9.60075i	−0.251197	+	0.530923i
$328$	−17.1410	−	20.8385i	−0.946452	−	1.15061i
$329$	−3.18055	−	0.560817i	−0.175350	−	0.0309189i
$330$	−5.62671	−	28.5228i	−0.309740	−	1.57013i
$331$	2.83257	+	3.37573i	0.155692	+	0.185547i	0.838252	−	0.545283i	$-0.183578\pi$
$331$	2.83257	+	3.37573i	0.155692	+	0.185547i	−0.682560	+	0.730830i	$0.739133\pi$
$332$	−17.9936	+	23.8434i	−0.987528	+	1.30858i
$333$	−13.3882	+	2.20663i	−0.733668	+	0.120923i
$334$	−0.745641	+	0.371435i	−0.0407996	+	0.0203240i
$335$	−3.42628	−	19.4314i	−0.187198	−	1.06165i
$336$	−6.53480	−	2.30139i	−0.356502	−	0.125551i
$337$	−18.7685	+	6.83118i	−1.02239	+	0.372118i	−0.798177	−	0.602423i	$-0.794202\pi$
$337$	−18.7685	+	6.83118i	−1.02239	+	0.372118i	−0.224209	+	0.974541i	$0.571980\pi$
$338$	−16.5384	−	3.97667i	−0.899570	−	0.216302i
$339$	14.1119	−	19.9160i	0.766455	−	1.08169i
$340$	1.34507	−	0.872152i	0.0729465	−	0.0472991i
$341$	11.1241	+	6.42253i	0.602406	+	0.347799i
$342$	8.61424	+	30.3629i	0.465805	+	1.64184i
$343$	0.866025	−	0.500000i	0.0467610	−	0.0269975i
$344$	17.8785	−	10.0903i	0.963944	−	0.544030i
$345$	−36.5089	+	9.56406i	−1.96557	+	0.514912i
$346$	21.5840	+	20.4969i	1.16037	+	1.10192i
$347$	9.14902	+	7.67694i	0.491145	+	0.412120i	0.854436	−	0.519556i	$-0.173903\pi$
$347$	9.14902	+	7.67694i	0.491145	+	0.412120i	−0.363291	+	0.931676i	$0.618347\pi$
$348$	1.60969	−	0.842931i	0.0862882	−	0.0451858i
$349$	7.09781	+	2.58339i	0.379937	+	0.138286i	0.524927	−	0.851147i	$-0.324093\pi$
$349$	7.09781	+	2.58339i	0.379937	+	0.138286i	−0.144990	+	0.989433i	$0.546315\pi$
$350$	6.23574	−	9.41397i	0.333314	−	0.503198i
$351$	−4.24573	+	2.86798i	−0.226620	+	0.153082i
$352$	18.1977	−	4.00076i	0.969943	−	0.213241i
$353$	0.957132	−	2.62970i	0.0509430	−	0.139965i	−0.911612	−	0.411053i	$-0.865161\pi$
$353$	0.957132	−	2.62970i	0.0509430	−	0.139965i	0.962555	+	0.271088i	$0.0873834\pi$
$354$	0.607802	+	30.0303i	0.0323043	+	1.59609i
$355$	0.967878	−	1.15347i	0.0513696	−	0.0612199i
$356$	2.79278	+	12.1358i	0.148017	+	0.643198i
$357$	−0.371584	−	0.101796i	−0.0196663	−	0.00538760i
$358$	7.43203	−	0.844124i	0.392795	−	0.0446133i
$359$	−8.43471	−	14.6093i	−0.445167	−	0.771052i	0.552897	−	0.833250i	$-0.313522\pi$
$359$	−8.43471	−	14.6093i	−0.445167	−	0.771052i	−0.998064	+	0.0621980i	$0.980189\pi$
$360$	23.0054	+	20.1405i	1.21249	+	1.06150i
$361$	18.1697	−	31.4709i	0.956301	−	1.65636i
$362$	−7.62808	+	17.5265i	−0.400923	+	0.921173i
$363$	−0.0242717	+	0.260634i	−0.00127393	+	0.0136798i
$364$	−1.44324	+	1.34394i	−0.0756462	+	0.0704418i
$365$	9.32797	+	25.6284i	0.488248	+	1.34145i
$366$	−16.9014	+	20.9907i	−0.883449	+	1.09720i
$367$	−19.3128	+	3.40537i	−1.00812	+	0.177759i	−0.653238	−	0.757152i	$-0.726590\pi$
$367$	−19.3128	+	3.40537i	−1.00812	+	0.177759i	−0.354882	+	0.934911i	$0.615479\pi$
$368$	−6.63433	−	23.2602i	−0.345838	−	1.21252i
$369$	14.5859	−	24.6234i	0.759311	−	1.28185i
$370$	23.0054	+	1.41520i	1.19599	+	0.0735725i
$371$	−4.16191	+	3.49226i	−0.216076	+	0.181309i
$372$	−13.3894	+	1.79589i	−0.694210	+	0.0931124i
$373$	−1.35616	+	7.69116i	−0.0702193	+	0.398233i	0.929359	+	0.369178i	$0.120361\pi$
$373$	−1.35616	+	7.69116i	−0.0702193	+	0.398233i	−0.999578	+	0.0290550i	$0.990750\pi$
$374$	0.993573	−	0.293929i	0.0513764	−	0.0151987i
$375$	−15.3184	+	10.5989i	−0.791039	+	0.547326i
$376$	−4.64454	+	7.86586i	−0.239524	+	0.405651i
$377$		−	0.517212i		−	0.0266378i
$378$	−0.0665365	−	7.34817i	−0.00342227	−	0.377949i
$379$		−	11.6283i		−	0.597304i	−0.954362	−	0.298652i	$-0.903463\pi$
$379$		−	11.6283i		−	0.597304i	0.954362	−	0.298652i	$-0.0965370\pi$
$380$	−2.76815	−	53.5404i	−0.142003	−	2.74657i
$381$	1.50136	+	18.3412i	0.0769170	+	0.939646i
$382$	3.81020	+	12.8797i	0.194947	+	0.658981i
$383$	−0.684161	+	3.88007i	−0.0349590	+	0.198262i	−0.997285	−	0.0736350i	$-0.976540\pi$
$383$	−0.684161	+	3.88007i	−0.0349590	+	0.198262i	0.962326	+	0.271897i	$0.0876511\pi$
$384$	−12.5859	+	15.0198i	−0.642273	+	0.766476i
$385$	9.09202	−	7.62911i	0.463372	−	0.388815i
$386$	0.579105	−	9.41391i	0.0294757	−	0.479155i
$387$	16.5228	+	14.1821i	0.839901	+	0.720918i
$388$	−33.3206	−	4.11506i	−1.69159	−	0.208910i
$389$	−12.2660	+	2.16282i	−0.621910	+	0.109659i	−0.475720	−	0.879597i	$-0.657812\pi$
$389$	−12.2660	+	2.16282i	−0.621910	+	0.109659i	−0.146190	+	0.989256i	$0.546701\pi$
$390$	8.11654	−	3.14160i	0.410997	−	0.159081i
$391$	−0.460043	−	1.26396i	−0.0232654	−	0.0639211i
$392$	−0.463880	−	2.79013i	−0.0234295	−	0.140923i
$393$	7.86293	−	3.61316i	0.396632	−	0.182260i
$394$	−23.2104	−	10.1019i	−1.16932	−	0.508925i
$395$	−9.89135	+	17.1323i	−0.497688	+	0.862021i
$396$	10.5657	+	16.7011i	0.530947	+	0.839259i
$397$	0.494897	+	0.857187i	0.0248382	+	0.0430210i	0.878177	−	0.478335i	$-0.158760\pi$
$397$	0.494897	+	0.857187i	0.0248382	+	0.0430210i	−0.853339	+	0.521356i	$0.825426\pi$
$398$	2.56345	+	22.5697i	0.128494	+	1.13132i
$399$	−9.16173	+	9.05985i	−0.458660	+	0.453560i
$400$	−18.7365	−	25.8651i	−0.936825	−	1.29325i
$401$	10.6479	−	12.6897i	0.531731	−	0.633692i	−0.431582	−	0.902074i	$-0.642044\pi$
$401$	10.6479	−	12.6897i	0.531731	−	0.633692i	0.963313	+	0.268381i	$0.0864888\pi$
$402$	6.94000	+	11.4776i	0.346136	+	0.572451i
$403$	−1.31520	+	3.61347i	−0.0655146	+	0.180000i
$404$	13.9966	−	5.92957i	0.696355	−	0.295007i
$405$	−11.7707	+	30.2192i	−0.584890	+	1.50161i
$406$	0.618434	+	0.409646i	0.0306924	+	0.0203304i
$407$	13.9991	+	5.09524i	0.693907	+	0.252562i
$408$	−0.638688	+	0.882934i	−0.0316198	+	0.0437117i
$409$	−15.8759	−	13.3215i	−0.785012	−	0.658703i	0.159493	−	0.987199i	$-0.449014\pi$
$409$	−15.8759	−	13.3215i	−0.785012	−	0.658703i	−0.944506	+	0.328496i	$0.893458\pi$
$410$	−33.4764	+	35.2520i	−1.65328	+	1.74097i
$411$	−12.5039	−	12.6445i	−0.616770	−	0.623706i
$412$	−16.6667	+	32.6534i	−0.821109	+	1.60872i
$413$	−10.6195	+	6.13116i	−0.522550	+	0.301694i
$414$	20.7976	−	15.0213i	1.02215	−	0.738258i
$415$	46.6085	+	26.9094i	2.28792	+	1.32093i
$416$	2.12550	+	5.15705i	0.104211	+	0.252845i
$417$	−4.08489	−	8.88950i	−0.200038	−	0.435321i
$418$	8.10114	−	33.6914i	0.396240	−	1.64790i
$419$	19.4060	−	7.06321i	0.948046	−	0.345060i	0.178708	−	0.983902i	$-0.442808\pi$
$419$	19.4060	−	7.06321i	0.948046	−	0.345060i	0.769338	+	0.638842i	$0.220586\pi$
$420$	−2.67209	+	12.1932i	−0.130384	+	0.594969i
$421$	−5.82099	−	33.0125i	−0.283698	−	1.60893i	−0.709900	−	0.704303i	$-0.751260\pi$
$421$	−5.82099	−	33.0125i	−0.283698	−	1.60893i	0.426202	−	0.904628i	$-0.359851\pi$
$422$	−15.2433	−	30.6004i	−0.742034	−	1.48960i
$423$	−9.52225	−	1.78904i	−0.462988	−	0.0869862i
$424$	5.11425	+	14.4908i	0.248370	+	0.703735i
$425$	−1.14164	−	1.36056i	−0.0553778	−	0.0659967i
$426$	−0.330544	+	0.968722i	−0.0160149	+	0.0469347i
$427$	−10.8349	−	1.91048i	−0.524336	−	0.0924545i
$428$	7.66627	−	25.0123i	0.370563	−	1.20901i
$429$	5.60658	−	0.458941i	0.270688	−	0.0221579i
$430$	−21.9907	−	29.7407i	−1.06049	−	1.43422i
$431$	−4.52872			−0.218141			−0.109070	−	0.994034i	$-0.534787\pi$
$431$	−4.52872			−0.218141			−0.109070	+	0.994034i	$0.534787\pi$
$432$	−19.5260	−	7.12297i	−0.939443	−	0.342704i
$433$	29.2321			1.40481			0.702403	−	0.711779i	$-0.252110\pi$
$433$	29.2321			1.40481			0.702403	+	0.711779i	$0.252110\pi$
$434$	−3.27899	−	4.43456i	−0.157396	−	0.212866i
$435$	−1.86273	−	2.69217i	−0.0893112	−	0.129080i
$436$	−3.59396	+	11.7258i	−0.172120	+	0.561564i
$437$	−44.3002	−	7.81131i	−2.11916	−	0.373666i
$438$	−12.2019	−	13.9580i	−0.583028	−	0.666938i
$439$	−2.09404	−	2.49558i	−0.0999429	−	0.119107i	0.713755	−	0.700396i	$-0.246993\pi$
$439$	−2.09404	−	2.49558i	−0.0999429	−	0.119107i	−0.813697	+	0.581289i	$0.802549\pi$
$440$	−11.1725	−	31.6563i	−0.532627	−	1.50915i
$441$	2.61469	−	1.47085i	0.124509	−	0.0700407i
$442$	0.138306	+	0.277644i	0.00657855	+	0.0132062i
$443$	−0.0845748	−	0.479648i	−0.00401827	−	0.0227887i	0.982733	−	0.185031i	$-0.0592385\pi$
$443$	−0.0845748	−	0.479648i	−0.00401827	−	0.0227887i	−0.986751	+	0.162242i	$0.948127\pi$
$444$	−14.9313	+	4.74775i	−0.708606	+	0.225318i
$445$	21.0836	−	7.67381i	0.999460	−	0.363774i
$446$	5.53072	−	23.0014i	0.261887	−	1.08915i
$447$	12.1987	+	1.13601i	0.576980	+	0.0537315i
$448$	−7.84978	−	1.54305i	−0.370867	−	0.0729023i
$449$	−5.97285	−	3.44843i	−0.281876	−	0.162741i	0.352396	−	0.935851i	$-0.385367\pi$
$449$	−5.97285	−	3.44843i	−0.281876	−	0.162741i	−0.634272	+	0.773110i	$0.718700\pi$
$450$	19.0218	−	28.0310i	0.896698	−	1.32139i
$451$	−27.2120	+	15.7108i	−1.28136	+	0.739794i
$452$	12.8134	−	25.1040i	0.602691	−	1.18079i
$453$	−7.64959	+	27.9232i	−0.359409	+	1.31195i
$454$	23.6781	−	24.9339i	1.11127	−	1.17021i
$455$	2.72185	+	2.28390i	0.127602	+	0.107071i
$456$	14.8922	+	33.2621i	0.697392	+	1.55764i
$457$	−3.70342	−	1.34793i	−0.173239	−	0.0630537i	0.253945	−	0.967219i	$-0.418272\pi$
$457$	−3.70342	−	1.34793i	−0.173239	−	0.0630537i	−0.427183	+	0.904165i	$0.640494\pi$
$458$	−31.0375	−	20.5590i	−1.45029	−	0.960657i
$459$	−1.11127	−	0.317833i	−0.0518695	−	0.0148352i
$460$	−40.1270	+	16.9996i	−1.87093	+	0.792609i
$461$	9.98831	−	27.4427i	0.465202	−	1.27813i	−0.456323	−	0.889814i	$-0.650834\pi$
$461$	9.98831	−	27.4427i	0.465202	−	1.27813i	0.921525	−	0.388318i	$-0.126944\pi$
$462$	−3.89180	+	7.06733i	−0.181063	+	0.328802i
$463$	−8.40287	+	10.0141i	−0.390514	+	0.465397i	−0.925103	−	0.379715i	$-0.876022\pi$
$463$	−8.40287	+	10.0141i	−0.390514	+	0.465397i	0.534589	+	0.845112i	$0.320466\pi$
$464$	1.69916	−	1.23086i	0.0788815	−	0.0571413i
$465$	6.16807	+	23.5454i	0.286038	+	1.09189i
$466$	−1.15862	−	10.2010i	−0.0536722	−	0.472553i
$467$	1.79902	+	3.11599i	0.0832485	+	0.144191i	0.904644	−	0.426169i	$-0.140137\pi$
$467$	1.79902	+	3.11599i	0.0832485	+	0.144191i	−0.821395	+	0.570360i	$0.806804\pi$
$468$	−4.37453	+	3.98316i	−0.202213	+	0.184122i
$469$	−2.73784	+	4.74209i	−0.126422	+	0.218969i
$470$	15.0908	+	6.56797i	0.696086	+	0.302958i
$471$	1.31676	+	0.933020i	0.0606731	+	0.0429913i
$472$	5.68824	+	34.2134i	0.261822	+	1.57480i
$473$	−8.17662	−	22.4651i	−0.375961	−	1.03295i
$474$	2.06670	−	13.2879i	0.0949267	−	0.610334i
$475$	−58.4953	+	10.3143i	−2.68395	+	0.473253i
$476$	−0.441523	−	0.0545277i	−0.0202372	−	0.00249927i
$477$	−12.6021	+	10.3365i	−0.577010	+	0.473276i
$478$	1.33465	−	21.6960i	0.0610454	−	0.992351i
$479$	−3.71490	+	3.11718i	−0.169738	+	0.142427i	−0.723700	−	0.690115i	$-0.757560\pi$
$479$	−3.71490	+	3.11718i	−0.169738	+	0.142427i	0.553961	+	0.832542i	$0.313116\pi$
$480$	29.6366	+	19.1883i	1.35272	+	0.875823i
$481$	−0.774438	+	4.39205i	−0.0353113	+	0.200260i
$482$	5.20329	+	17.5887i	0.237003	+	0.801144i
$483$	9.46743	+	4.47935i	0.430783	+	0.203817i
$484$	0.0156064	+	0.301854i	0.000709384	+	0.0137206i
$485$			60.4900i			2.74671i
$486$	0.0469056	−	22.0454i	0.00212768	−	0.999998i
$487$			21.3165i			0.965942i	0.875636	+	0.482971i	$0.160442\pi$
$487$			21.3165i			0.965942i	−0.875636	+	0.482971i	$0.839558\pi$
$488$	−15.8221	+	26.7958i	−0.716231	+	1.21299i
$489$	8.58019	+	4.05956i	0.388009	+	0.183580i
$490$	−4.88665	+	1.44562i	−0.220756	+	0.0653065i
$491$	7.37133	−	41.8049i	0.332663	−	1.88663i	−0.116520	−	0.993188i	$-0.537174\pi$
$491$	7.37133	−	41.8049i	0.332663	−	1.88663i	0.449183	−	0.893440i	$-0.351715\pi$
$492$	12.5721	−	30.5618i	0.566796	−	1.37783i
$493$	0.0893793	−	0.0749982i	0.00402544	−	0.00337775i
$494$	10.3540	+	0.636935i	0.465848	+	0.0286571i
$495$	27.5303	−	22.5809i	1.23739	−	1.01494i
$496$	−15.0010	+	4.27862i	−0.673565	+	0.192116i
$497$	−0.411520	+	0.0725620i	−0.0184592	+	0.00325485i
$498$	−36.1498	−	5.62245i	−1.61991	−	0.251948i
$499$	−4.96155	−	13.6317i	−0.222110	−	0.610241i	0.777722	−	0.628609i	$-0.216375\pi$
$499$	−4.96155	−	13.6317i	−0.222110	−	0.610241i	−0.999831	+	0.0183678i	$0.994153\pi$
$500$	−15.7413	+	14.6583i	−0.703972	+	0.655539i
$501$	−0.832457	−	0.589857i	−0.0371915	−	0.0263529i
$502$	0.0461371	−	0.106006i	0.00205920	−	0.00473128i
$503$	−7.44200	+	12.8899i	−0.331822	+	0.574733i	−0.982869	−	0.184304i	$-0.940997\pi$
$503$	−7.44200	+	12.8899i	−0.331822	+	0.574733i	0.651047	+	0.759038i	$0.274330\pi$
$504$	−1.29795	−	8.38542i	−0.0578155	−	0.373516i
$505$	−13.6937	−	23.7181i	−0.609360	−	1.05544i
$506$	−27.9873	+	3.17877i	−1.24419	+	0.141313i
$507$	−5.27929	−	20.1526i	−0.234461	−	0.895008i
$508$	4.76549	+	20.7081i	0.211435	+	0.918774i
$509$	11.5214	−	13.7306i	0.510676	−	0.608600i	−0.447674	−	0.894197i	$-0.647747\pi$
$509$	11.5214	−	13.7306i	0.510676	−	0.608600i	0.958350	+	0.285597i	$0.0921918\pi$
$510$	1.71984	+	0.947072i	0.0761556	+	0.0419371i
$511$	2.58865	−	7.11225i	0.114515	−	0.314627i
$512$	−11.8838	+	19.2555i	−0.525197	+	0.850981i
$513$	−27.7874	+	26.8705i	−1.22684	+	1.18636i
$514$	−20.7789	+	31.3695i	−0.916518	+	1.38365i
$515$	62.0688	+	22.5912i	2.73508	+	0.995487i
$516$	21.2383	+	13.4578i	0.934966	+	0.592448i
$517$	8.14887	+	6.83772i	0.358387	+	0.300722i
$518$	−4.63823	−	4.40462i	−0.203792	−	0.193528i
$519$	−9.63207	+	35.1599i	−0.422801	+	1.54335i
$520$	8.75207	−	4.93949i	0.383803	−	0.216611i
$521$	27.4387	−	15.8418i	1.20211	−	0.694040i	0.241088	−	0.970503i	$-0.422496\pi$
$521$	27.4387	−	15.8418i	1.20211	−	0.694040i	0.961025	+	0.276463i	$0.0891623\pi$
$522$	1.84144	+	1.24961i	0.0805978	+	0.0546938i
$523$	32.4891	+	18.7576i	1.42065	+	0.820212i	0.996354	−	0.0853114i	$-0.0271885\pi$
$523$	32.4891	+	18.7576i	1.42065	+	0.820212i	0.424295	+	0.905524i	$0.360522\pi$
$524$	8.38385	−	5.43615i	0.366250	−	0.237479i
$525$	13.7701	+	1.28235i	0.600978	+	0.0559663i
$526$	4.47931	+	1.07705i	0.195307	+	0.0469618i
$527$	−0.815154	+	0.296692i	−0.0355087	+	0.0129241i
$528$	14.8503	+	17.3267i	0.646275	+	0.754049i
$529$	2.35564	+	13.3595i	0.102419	+	0.580849i
$530$	24.7819	−	12.3449i	1.07646	−	0.536229i
$531$	−32.0621	+	18.0361i	−1.39138	+	0.782699i
$532$	−8.96222	+	11.8759i	−0.388562	+	0.514884i
$533$	−6.04645	−	7.20587i	−0.261901	−	0.312121i
$534$	−11.4828	+	10.0381i	−0.496908	+	0.434390i
$535$	−46.4179	−	8.18473i	−2.00682	−	0.353857i
$536$	9.83870	+	11.9610i	0.424967	+	0.516636i
$537$	5.21242	+	7.53341i	0.224933	+	0.325090i
$538$	37.2058	−	27.5106i	1.60406	−	1.18607i
$539$	−3.29376			−0.141872
$540$	−8.42479	+	36.4878i	−0.362545	+	1.57018i
$541$	−45.3930			−1.95160			−0.975798	−	0.218673i	$-0.929827\pi$
$541$	−45.3930			−1.95160			−0.975798	+	0.218673i	$0.929827\pi$
$542$	22.5608	−	16.6818i	0.969068	−	0.716545i
$543$	−23.3324	+	1.90993i	−1.00129	+	0.0819630i
$544$	−0.582983	+	1.11510i	−0.0249952	+	0.0478097i
$545$	21.7608	+	3.83702i	0.932130	+	0.164360i
$546$	−2.28589	−	0.779985i	−0.0978271	−	0.0333803i
$547$	18.7382	+	22.3313i	0.801186	+	0.954817i	0.999680	−	0.0252855i	$-0.00804948\pi$
$547$	18.7382	+	22.3313i	0.801186	+	0.954817i	−0.198494	+	0.980102i	$0.563605\pi$
$548$	−16.3904	−	12.3691i	−0.700161	−	0.528383i
$549$	−32.4385	−	6.09455i	−1.38444	−	0.260109i
$550$	−33.2910	+	16.5837i	−1.41953	+	0.707130i
$551$	−0.677580	−	3.84275i	−0.0288659	−	0.163707i
$552$	21.2668	−	20.6228i	0.905175	−	0.877763i
$553$	5.15890	−	1.87769i	0.219379	−	0.0798474i
$554$	−11.4492	−	2.75296i	−0.486428	−	0.116962i
$555$	11.7869	+	25.6505i	0.500324	+	1.08880i
$556$	−6.14589	−	9.47843i	−0.260644	−	0.401975i
$557$	35.7468	+	20.6384i	1.51464	+	0.874479i	0.999853	+	0.0171624i	$0.00546322\pi$
$557$	35.7468	+	20.6384i	1.51464	+	0.874479i	0.514789	+	0.857317i	$0.327870\pi$
$558$	−9.68758	−	13.4128i	−0.410108	−	0.567811i
$559$	6.19807	−	3.57846i	0.262150	−	0.151353i
$560$	−1.02569	+	14.3771i	−0.0433431	+	0.607544i
$561$	0.892291	+	0.902325i	0.0376725	+	0.0380962i
$562$	24.7544	+	23.5076i	1.04420	+	0.991608i
$563$	−19.4935	−	16.3570i	−0.821555	−	0.689366i	0.131781	−	0.991279i	$-0.457931\pi$
$563$	−19.4935	−	16.3570i	−0.821555	−	0.689366i	−0.953336	+	0.301912i	$0.902375\pi$
$564$	−11.1782	−	0.460822i	−0.470689	−	0.0194041i
$565$	−47.7186	−	17.3681i	−2.00753	−	0.730683i
$566$	8.15690	−	12.3143i	0.342860	−	0.517609i
$567$	7.89291	−	4.32457i	0.331471	−	0.181615i
$568$	−0.216613	+	1.16189i	−0.00908886	+	0.0487518i
$569$	−6.85262	+	18.8274i	−0.287277	+	0.789286i	0.709168	+	0.705039i	$0.249071\pi$
$569$	−6.85262	+	18.8274i	−0.287277	+	0.789286i	−0.996445	+	0.0842471i	$0.973152\pi$
$570$	56.1881	−	33.9744i	2.35346	−	1.42303i
$571$	14.9789	−	17.8511i	0.626846	−	0.747046i	−0.355385	−	0.934720i	$-0.615650\pi$
$571$	14.9789	−	17.8511i	0.626846	−	0.747046i	0.982231	+	0.187674i	$0.0600948\pi$
$572$	6.33012	−	1.45673i	0.264676	−	0.0609090i
$573$	−11.6968	+	11.5667i	−0.488641	+	0.483208i
$574$	13.4051	−	1.52253i	0.559516	−	0.0635494i
$575$	24.1412	+	41.8138i	1.00676	+	1.74376i
$576$	−23.4961	−	4.89219i	−0.979004	−	0.203841i
$577$	−3.44507	+	5.96704i	−0.143420	+	0.248411i	−0.928782	−	0.370625i	$-0.879143\pi$
$577$	−3.44507	+	5.96704i	−0.143420	+	0.248411i	0.785362	+	0.619037i	$0.212477\pi$
$578$	9.56641	−	21.9801i	0.397910	−	0.914251i
$579$	10.4963	−	4.82324i	0.436211	−	0.200447i
$580$	−2.57616	−	2.76649i	−0.106969	−	0.114872i
$581$	−5.10825	−	14.0348i	−0.211926	−	0.582261i
$582$	−14.8426	−	38.3469i	−0.615246	−	1.58953i
$583$	17.6231	−	3.10743i	0.729874	−	0.128697i
$584$	−16.2637	−	13.9202i	−0.672997	−	0.576024i
$585$	8.08841	+	6.94258i	0.334415	+	0.287040i
$586$	−33.0109	−	2.03069i	−1.36367	−	0.0838872i
$587$	26.6593	−	22.3698i	1.10035	−	0.923299i	0.102897	−	0.994692i	$-0.467189\pi$
$587$	26.6593	−	22.3698i	1.10035	−	0.923299i	0.997448	+	0.0713927i	$0.0227443\pi$
$588$	2.74312	−	2.11549i	0.113124	−	0.0872413i
$589$	−5.03769	+	28.5701i	−0.207574	+	1.17721i
$590$	59.9216	−	17.7267i	2.46693	−	0.729795i
$591$	−2.52932	−	30.8991i	−0.104043	−	1.27102i
$592$	−16.2719	+	7.90800i	−0.668771	+	0.325017i
$593$		−	17.8842i		−	0.734418i	−0.930138	−	0.367209i	$-0.880313\pi$
$593$		−	17.8842i		−	0.734418i	0.930138	−	0.367209i	$-0.119687\pi$
$594$	−11.9118	+	21.0701i	−0.488746	+	0.864516i
$595$			0.801538i			0.0328599i
$596$	14.1280	−	0.730444i	0.578704	−	0.0299201i
$597$	−22.8776	+	15.8292i	−0.936316	+	0.647844i
$598$	−2.39206	−	8.08592i	−0.0978187	−	0.330658i
$599$	2.22226	−	12.6031i	0.0907992	−	0.514948i	−0.905155	−	0.425082i	$-0.860245\pi$
$599$	2.22226	−	12.6031i	0.0907992	−	0.514948i	0.995954	−	0.0898655i	$-0.0286437\pi$
$600$	17.0743	−	35.1931i	0.697056	−	1.43675i
$601$	−22.5453	+	18.9178i	−0.919643	+	0.771672i	−0.973929	−	0.226854i	$-0.927156\pi$
$601$	−22.5453	+	18.9178i	−0.919643	+	0.771672i	0.0542862	+	0.998525i	$0.482712\pi$
$602$	−0.630249	+	10.2453i	−0.0256870	+	0.417567i
$603$	−8.37210	+	14.1335i	−0.340938	+	0.575562i
$604$	−4.09757	+	33.1789i	−0.166728	+	1.35003i
$605$	0.536305	−	0.0945650i	0.0218039	−	0.00384461i
$606$	14.5007	+	11.6758i	0.589052	+	0.474296i
$607$	−2.69143	−	7.39463i	−0.109242	−	0.300139i	0.873011	−	0.487700i	$-0.162164\pi$
$607$	−2.69143	−	7.39463i	−0.109242	−	0.300139i	−0.982253	+	0.187561i	$0.939942\pi$
$608$	22.5479	+	35.5310i	0.914440	+	1.44097i
$609$	−0.0842416	+	0.904604i	−0.00341364	+	0.0366564i
$610$	51.4082	+	22.3744i	2.08146	+	0.905914i
$611$	−1.59227	+	2.75789i	−0.0644164	+	0.111572i
$612$	−1.32266	−	0.178384i	−0.0534652	−	0.00721075i
$613$	−17.0823	−	29.5874i	−0.689947	−	1.19502i	−0.971855	−	0.235582i	$-0.924301\pi$
$613$	−17.0823	−	29.5874i	−0.689947	−	1.19502i	0.281908	−	0.959442i	$-0.409033\pi$
$614$	2.16696	+	19.0789i	0.0874514	+	0.769960i
$615$	−57.4245	−	15.7315i	−2.31558	−	0.634355i
$616$	−3.27180	+	8.72275i	−0.131825	+	0.351449i
$617$	−4.19961	+	5.00491i	−0.169070	+	0.201490i	−0.843926	−	0.536460i	$-0.819761\pi$
$617$	−4.19961	+	5.00491i	−0.169070	+	0.201490i	0.674856	+	0.737950i	$0.264206\pi$
$618$	−44.8911	+	0.908579i	−1.80578	+	0.0365484i
$619$	8.47349	−	23.2807i	0.340579	−	0.935732i	−0.644649	−	0.764479i	$-0.722996\pi$
$619$	8.47349	−	23.2807i	0.340579	−	0.935732i	0.985227	−	0.171253i	$-0.0547815\pi$
$620$	10.9634	+	25.8788i	0.440300	+	1.03932i
$621$	28.2503	+	13.7548i	1.13364	+	0.551961i
$622$	−26.2290	−	17.3739i	−1.05169	−	0.696629i
$623$	−5.85101	−	2.12960i	−0.234416	−	0.0853204i
$624$	−4.33626	+	5.27886i	−0.173589	+	0.211323i
$625$	−0.895746	−	0.751620i	−0.0358299	−	0.0300648i
$626$	0.887571	−	0.934646i	0.0354745	−	0.0373560i
$627$	41.0542	−	10.7548i	1.63955	−	0.429505i
$628$	1.65977	+	0.847165i	0.0662319	+	0.0338056i
$629$	−0.871287	+	0.503038i	−0.0347405	+	0.0200574i
$630$	−14.7075	+	4.17266i	−0.585962	+	0.166243i
$631$	17.7021	+	10.2203i	0.704709	+	0.406864i	0.809099	−	0.587673i	$-0.199956\pi$
$631$	17.7021	+	10.2203i	0.704709	+	0.406864i	−0.104390	+	0.994536i	$0.533289\pi$
$632$	0.151899	−	15.5273i	0.00604224	−	0.617643i
$633$	24.2071	−	34.1632i	0.962148	−	1.35787i
$634$	0.624207	−	2.59598i	0.0247904	−	0.103100i
$635$	35.9763	−	13.0943i	1.42767	−	0.519631i
$636$	−12.6811	+	13.9067i	−0.502839	+	0.551438i
$637$	−0.171224	−	0.971062i	−0.00678416	−	0.0384749i
$638$	−1.08943	−	2.18699i	−0.0431311	−	0.0865839i
$639$	−1.23692	+	0.203867i	−0.0489316	+	0.00806487i
$640$	37.0555	+	16.9975i	1.46475	+	0.671887i
$641$	−7.37581	−	8.79015i	−0.291327	−	0.347190i	0.600452	−	0.799661i	$-0.294987\pi$
$641$	−7.37581	−	8.79015i	−0.291327	−	0.347190i	−0.891779	+	0.452471i	$0.850543\pi$
$642$	31.4344	−	6.20109i	1.24062	−	0.244737i
$643$	10.2998	+	1.81613i	0.406185	+	0.0716213i	0.373008	−	0.927828i	$-0.378326\pi$
$643$	10.2998	+	1.81613i	0.406185	+	0.0716213i	0.0331768	+	0.999449i	$0.489438\pi$
$644$	11.5630	+	3.54405i	0.455645	+	0.139655i
$645$	19.3741	−	40.9487i	0.762856	−	1.61235i
$646$	1.39131	+	1.88163i	0.0547403	+	0.0740318i
$647$	−2.13700			−0.0840143			−0.0420071	−	0.999117i	$-0.513375\pi$
$647$	−2.13700			−0.0840143			−0.0420071	+	0.999117i	$0.513375\pi$
$648$	−3.61232	−	25.1982i	−0.141905	−	0.989880i
$649$	40.3891			1.58541
$650$	−6.61979	−	8.95272i	−0.259649	−	0.351154i
$651$	2.88883	−	6.10576i	0.113222	−	0.239303i
$652$	10.4793	+	3.21192i	0.410402	+	0.125789i
$653$	−27.8098	−	4.90362i	−1.08828	−	0.191894i	−0.399408	−	0.916773i	$-0.630784\pi$
$653$	−27.8098	−	4.90362i	−1.08828	−	0.191894i	−0.688875	+	0.724880i	$0.741895\pi$
$654$	−14.7365	+	2.90708i	−0.576243	+	0.113676i
$655$	−11.5719	−	13.7909i	−0.452152	−	0.538854i
$656$	9.28361	−	37.0125i	0.362464	−	1.44509i
$657$	8.00404	−	21.2486i	0.312268	−	0.828986i
$658$	−2.03651	−	4.08821i	−0.0793915	−	0.159375i
$659$	0.337289	+	1.91286i	0.0131389	+	0.0745144i	0.990672	−	0.136267i	$-0.0435104\pi$
$659$	0.337289	+	1.91286i	0.0131389	+	0.0745144i	−0.977533	+	0.210781i	$0.932399\pi$
$660$	27.7029	−	30.3804i	1.07833	−	1.18255i
$661$	33.1620	−	12.0700i	1.28985	−	0.469468i	0.396174	−	0.918175i	$-0.370338\pi$
$661$	33.1620	−	12.0700i	1.28985	−	0.469468i	0.893679	+	0.448707i	$0.148115\pi$
$662$	−1.45697	+	6.05931i	−0.0566266	+	0.235502i
$663$	−0.219637	+	0.309971i	−0.00852999	+	0.0120383i
$664$	−42.2420	−	0.413242i	−1.63931	−	0.0160369i
$665$	23.2146	+	13.4030i	0.900225	+	0.519745i
$666$	−13.7661	−	13.3686i	−0.533425	−	0.518024i
$667$	−2.74688	+	1.58591i	−0.106360	+	0.0614068i
$668$	−1.04931	−	0.535579i	−0.0405989	−	0.0207222i
$669$	28.0281	−	7.34238i	1.08363	−	0.283873i
$670$	19.2150	−	20.2342i	0.742341	−	0.781714i
$671$	27.7599	+	23.2933i	1.07166	+	0.899229i
$672$	−2.87753	−	9.36588i	−0.111003	−	0.361297i
$673$	19.0711	+	6.94133i	0.735139	+	0.267569i	0.682338	−	0.731037i	$-0.260963\pi$
$673$	19.0711	+	6.94133i	0.735139	+	0.267569i	0.0528003	+	0.998605i	$0.483185\pi$
$674$	−23.5486	−	15.5984i	−0.907056	−	0.600827i
$675$	41.2648	+	4.30874i	1.58828	+	0.165844i
$676$	−9.38362	−	22.1498i	−0.360909	−	0.851914i
$677$	−8.98154	+	24.6766i	−0.345189	+	0.948398i	0.638675	+	0.769477i	$0.279483\pi$
$677$	−8.98154	+	24.6766i	−0.345189	+	0.948398i	−0.983863	+	0.178921i	$0.942739\pi$
$678$	34.5123	−	0.698517i	1.32544	−	0.0268264i
$679$	10.7904	−	12.8595i	0.414097	−	0.493501i
$680$	2.12268	+	0.796194i	0.0814012	+	0.0305326i
$681$	40.6167	+	11.1270i	1.55643	+	0.426387i
$682$	2.05006	+	18.0496i	0.0785008	+	0.691155i
$683$	9.68191	+	16.7696i	0.370468	+	0.641670i	0.989638	−	0.143588i	$-0.0458639\pi$
$683$	9.68191	+	16.7696i	0.370468	+	0.641670i	−0.619169	+	0.785257i	$0.712531\pi$
$684$	−27.2834	+	35.3247i	−1.04321	+	1.35068i
$685$	−18.4980	+	32.0395i	−0.706772	+	1.22416i
$686$	1.29672	+	0.564373i	0.0495090	+	0.0215479i
$687$	4.22785	−	45.3995i	0.161303	−	1.73210i
$688$	26.5062	+	11.8461i	1.01054	+	0.451627i
$689$	1.83226	+	5.03408i	0.0698034	+	0.191783i
$690$	−41.5724	−	33.4735i	−1.58263	−	1.27431i
$691$	−39.6595	+	6.99303i	−1.50872	+	0.266028i	−0.865988	−	0.500066i	$-0.833309\pi$
$691$	−39.6595	+	6.99303i	−1.50872	+	0.266028i	−0.642730	+	0.766093i	$0.722198\pi$
$692$	−5.15950	+	41.7776i	−0.196135	+	1.58815i
$693$	−9.88067	−	0.110493i	−0.375336	−	0.00419728i
$694$	−1.03706	+	16.8584i	−0.0393661	+	0.639935i
$695$	−15.5914	+	13.0827i	−0.591415	+	0.496256i
$696$	2.31195	+	1.12167i	0.0876342	+	0.0425167i
$697$	0.368483	−	2.08977i	0.0139573	−	0.0791557i
$698$	3.03025	+	10.2432i	0.114697	+	0.387711i
$699$	10.3402	−	7.15443i	0.391101	−	0.270605i
$700$	15.9479	−	0.824537i	0.602773	−	0.0311646i
$701$			23.2350i			0.877574i	0.898591	+	0.438787i	$0.144592\pi$
$701$			23.2350i			0.877574i	−0.898591	+	0.438787i	$0.855408\pi$
$702$	−6.83108	−	2.41649i	−0.257823	−	0.0912046i
$703$			33.6464i			1.26900i
$704$	19.8501	+	17.3292i	0.748130	+	0.653118i
$705$	1.64450	+	20.0898i	0.0619355	+	0.756626i
$706$	3.79505	−	1.12269i	0.142829	−	0.0422531i
$707$	−1.31979	+	7.48492i	−0.0496360	+	0.281499i
$708$	−33.6370	+	25.9408i	−1.26416	+	0.974914i
$709$	−16.6131	+	13.9400i	−0.623918	+	0.523529i	−0.899032	−	0.437882i	$-0.855729\pi$
$709$	−16.6131	+	13.9400i	−0.623918	+	0.523529i	0.275115	+	0.961411i	$0.411284\pi$
$710$	2.12544	+	0.130748i	0.0797662	+	0.00490688i
$711$	15.5387	−	5.45965i	0.582748	−	0.204753i
$712$	−11.4517	+	13.3796i	−0.429172	+	0.501423i
$713$	23.2237	−	4.09497i	0.869735	−	0.153358i
$714$	−0.196676	−	0.508126i	−0.00736041	−	0.0190161i
$715$	−4.00271	−	10.9973i	−0.149693	−	0.411277i
$716$	7.20877	+	7.74138i	0.269404	+	0.289309i
$717$	24.1905	−	11.1160i	0.903411	−	0.415134i
$718$	9.52064	−	21.8749i	0.355307	−	0.816365i
$719$	−21.4012	+	37.0680i	−0.798130	+	1.38240i	0.122702	+	0.992444i	$0.460844\pi$
$719$	−21.4012	+	37.0680i	−0.798130	+	1.38240i	−0.920832	+	0.389958i	$0.872489\pi$
$720$	−3.55916	+	43.0942i	−0.132642	+	1.60603i
$721$	−9.16523	−	15.8746i	−0.341331	−	0.591203i
$722$	51.0634	−	5.79974i	1.90038	−	0.215844i
$723$	−15.9734	+	15.7958i	−0.594057	+	0.587451i
$724$	−26.3435	+	6.06235i	−0.979049	+	0.225306i
$725$	−2.69211	+	3.20833i	−0.0999825	+	0.119154i
$726$	−0.316781	+	0.191543i	−0.0117568	+	0.00710883i
$727$	−4.75776	+	13.0718i	−0.176456	+	0.484808i	−0.996117	−	0.0880408i	$-0.971939\pi$
$727$	−4.75776	+	13.0718i	−0.176456	+	0.484808i	0.819661	+	0.572848i	$0.194162\pi$
$728$	−2.74171	−	0.511141i	−0.101615	−	0.0189441i
$729$	23.8223	−	12.7081i	0.882308	−	0.470672i
$730$	−21.2996	+	32.1555i	−0.788332	+	1.19013i
$731$	1.51714	+	0.552194i	0.0561135	+	0.0204236i
$732$	−38.0797	−	1.56983i	−1.40747	−	0.0580227i
$733$	−21.3852	−	17.9443i	−0.789880	−	0.662788i	0.155836	−	0.987783i	$-0.450193\pi$
$733$	−21.3852	−	17.9443i	−0.789880	−	0.662788i	−0.945716	+	0.324995i	$0.894637\pi$
$734$	−20.1107	−	19.0978i	−0.742298	−	0.704911i
$735$	−4.38852	−	4.43787i	−0.161873	−	0.163693i
$736$	20.8715	−	27.1013i	0.769332	−	0.998968i
$737$	15.6193	−	9.01781i	0.575345	−	0.332175i
$738$	40.2637	−	4.11763i	1.48213	−	0.151572i
$739$	−35.9008	−	20.7274i	−1.32063	−	0.762468i	−0.336804	−	0.941575i	$-0.609346\pi$
$739$	−35.9008	−	20.7274i	−1.32063	−	0.762468i	−0.983830	+	0.179106i	$0.942679\pi$
$740$	17.7338	+	27.3498i	0.651908	+	1.00540i
$741$	5.30489	+	11.5445i	0.194880	+	0.424096i
$742$	−7.47048	−	1.79628i	−0.274250	−	0.0659437i
$743$	−42.9947	+	15.6488i	−1.57732	+	0.574098i	−0.974619	−	0.223868i	$-0.928131\pi$
$743$	−42.9947	+	15.6488i	−1.57732	+	0.574098i	−0.602702	+	0.797966i	$0.705909\pi$
$744$	−13.3001	−	13.7154i	−0.487604	−	0.502832i
$745$	−4.42602	−	25.1012i	−0.162157	−	0.919637i
$746$	−9.88605	+	4.92466i	−0.361954	+	0.180305i
$747$	−14.8530	−	42.2731i	−0.543442	−	1.54669i
$748$	1.16964	+	0.882675i	0.0427661	+	0.0322738i
$749$	8.40790	+	10.0201i	0.307218	+	0.366128i
$750$	−24.9321	−	8.50724i	−0.910390	−	0.310641i
$751$	36.3279	+	6.40559i	1.32562	+	0.233743i	0.791244	−	0.611501i	$-0.209434\pi$
$751$	36.3279	+	6.40559i	1.32562	+	0.233743i	0.534380	+	0.845244i	$0.320545\pi$
$752$	−12.8496	+	1.33226i	−0.468577	+	0.0485826i
$753$	0.141122	−	0.0115519i	0.00514277	−	0.000420974i
$754$	0.588133	−	0.434875i	0.0214185	−	0.0158372i
$755$	60.2328			2.19210
$756$	8.29981	−	6.25405i	0.301861	−	0.227457i
$757$	15.3248			0.556990			0.278495	−	0.960438i	$-0.410164\pi$
$757$	15.3248			0.556990			0.278495	+	0.960438i	$0.410164\pi$
$758$	13.2227	−	9.77712i	0.480272	−	0.355121i
$759$	−19.6287	−	28.3690i	−0.712478	−	1.02973i
$760$	58.5545	−	48.1648i	2.12399	−	1.74712i
$761$	−12.0471	−	2.12422i	−0.436706	−	0.0770030i	−0.0490267	−	0.998797i	$-0.515612\pi$
$761$	−12.0471	−	2.12422i	−0.436706	−	0.0770030i	−0.387679	+	0.921795i	$0.626723\pi$
$762$	−19.5938	+	17.1286i	−0.709807	+	0.620503i
$763$	−3.94164	−	4.69746i	−0.142697	−	0.170060i
$764$	−11.4421	+	15.1620i	−0.413961	+	0.548540i
$765$	−0.0268885	+	2.40446i	−0.000972156	+	0.0869336i
$766$	−4.98736	+	2.48441i	−0.180201	+	0.0897655i
$767$	2.09961	+	11.9075i	0.0758125	+	0.429954i
$768$	−27.6617	−	1.68297i	−0.998154	−	0.0607290i
$769$	−19.5016	+	7.09800i	−0.703245	+	0.255960i	−0.668796	−	0.743446i	$-0.733190\pi$
$769$	−19.5016	+	7.09800i	−0.703245	+	0.255960i	−0.0344494	+	0.999406i	$0.510968\pi$
$770$	16.3198	+	3.92412i	0.588127	+	0.141416i
$771$	−45.8852	−	4.27308i	−1.65252	−	0.153891i
$772$	11.1917	−	7.25676i	0.402797	−	0.261177i
$773$	26.7274	+	15.4311i	0.961319	+	0.555018i	0.896579	−	0.442885i	$-0.146045\pi$
$773$	26.7274	+	15.4311i	0.961319	+	0.555018i	0.0647401	+	0.997902i	$0.479378\pi$
$774$	−2.23432	+	30.7128i	−0.0803109	+	1.10395i
$775$	26.9666	−	15.5692i	0.968670	−	0.559262i
$776$	−23.3368	−	41.3495i	−0.837743	−	1.48436i
$777$	2.06985	−	7.55557i	0.0742556	−	0.271054i
$778$	−12.7727	−	12.1294i	−0.457924	−	0.434860i
$779$	−54.3636	−	45.6165i	−1.94778	−	1.63438i
$780$	10.3968	+	6.58802i	0.372266	+	0.235889i
$781$	1.29335	+	0.470742i	0.0462798	+	0.0168445i
$782$	1.05047	−	1.58587i	0.0375646	−	0.0567105i
$783$	−0.283055	+	2.71082i	−0.0101156	+	0.0968767i
$784$	2.78268	−	2.87344i	0.0993815	−	0.102623i
$785$	1.14831	−	3.15494i	0.0409848	−	0.112605i
$786$	10.7198	+	5.90313i	0.382363	+	0.210558i
$787$	−26.0770	+	31.0773i	−0.929543	+	1.10779i	0.0644036	+	0.997924i	$0.479485\pi$
$787$	−26.0770	+	31.0773i	−0.929543	+	1.10779i	−0.993947	+	0.109862i	$0.964959\pi$
$788$	−8.02838	−	34.8867i	−0.285999	−	1.24279i
$789$	1.42986	+	5.45820i	0.0509043	+	0.194317i
$790$	−27.7982	+	3.15730i	−0.989017	+	0.112332i
$791$	7.04624	+	12.2044i	0.250535	+	0.433940i
$792$	−10.1074	+	26.0568i	−0.359151	+	0.925890i
$793$	−5.42422	+	9.39503i	−0.192620	+	0.333627i
$794$	−0.558613	+	1.28349i	−0.0198244	+	0.0455492i
$795$	27.6673	+	19.6043i	0.981260	+	0.695294i
$796$	−23.5091	+	21.8917i	−0.833259	+	0.775931i
$797$	−12.4509	−	34.2087i	−0.441035	−	1.21173i	−0.938813	−	0.344428i	$-0.888073\pi$
$797$	−12.4509	−	34.2087i	−0.441035	−	1.21173i	0.497778	−	0.867305i	$-0.334150\pi$
$798$	−18.0054	−	2.80042i	−0.637384	−	0.0991338i
$799$	−0.707478	+	0.124747i	−0.0250288	+	0.00441325i
$800$	13.6580	−	43.0532i	0.482881	−	1.52216i
$801$	−17.4805	−	6.58466i	−0.617643	−	0.232658i
$802$	23.3825	+	1.43840i	0.825666	+	0.0507916i
$803$	−19.0971	+	16.0244i	−0.673922	+	0.565488i
$804$	−7.21624	+	17.5421i	−0.254497	+	0.618661i
$805$	3.78374	−	21.4586i	0.133359	−	0.756317i
$806$	−5.21479	+	1.54269i	−0.183683	+	0.0543391i
$807$	51.2271	+	24.2372i	1.80328	+	0.853189i
$808$	18.5110	+	10.9302i	0.651216	+	0.384522i
$809$		−	50.8071i		−	1.78628i	−0.449775	−	0.893142i	$-0.648496\pi$
$809$		−	50.8071i		−	1.78628i	0.449775	−	0.893142i	$-0.351504\pi$
$810$	−44.2598	+	12.0238i	−1.55513	+	0.422474i
$811$			54.4961i			1.91362i	0.290717	+	0.956809i	$0.406106\pi$
$811$			54.4961i			1.91362i	−0.290717	+	0.956809i	$0.593894\pi$
$812$	0.0541665	+	1.04767i	0.00190087	+	0.0367659i
$813$	31.0630	+	14.6969i	1.08943	+	0.515443i
$814$	5.97659	+	20.2027i	0.209479	+	0.708105i
$815$	3.42914	−	19.4476i	0.120118	−	0.681220i
$816$	−1.54102	+	0.0161111i	−0.0539463	+	0.000564000i
$817$	41.3620	−	34.7068i	1.44707	−	1.21424i
$818$	1.79956	−	29.2536i	0.0629201	−	1.02283i
$819$	−0.481066	−	2.91875i	−0.0168098	−	0.101989i
$820$	−68.2330	−	8.42671i	−2.38280	−	0.294273i
$821$	2.85109	−	0.502724i	0.0995037	−	0.0175452i	−0.123675	−	0.992323i	$-0.539468\pi$
$821$	2.85109	−	0.502724i	0.0995037	−	0.0175452i	0.223178	+	0.974778i	$0.428357\pi$
$822$	3.86497	−	24.8500i	0.134806	−	0.866742i
$823$	−7.01813	−	19.2822i	−0.244637	−	0.672134i	−0.999861	−	0.0166674i	$-0.994694\pi$
$823$	−7.01813	−	19.2822i	−0.244637	−	0.672134i	0.755224	−	0.655466i	$-0.227528\pi$
$824$	−51.1443	+	8.50313i	−1.78170	+	0.296221i
$825$	−37.1672	−	26.3356i	−1.29399	−	0.916889i
$826$	−15.9008	−	6.92051i	−0.553259	−	0.240796i
$827$	−17.0603	+	29.5493i	−0.593244	+	1.02753i	0.400548	+	0.916276i	$0.368820\pi$
$827$	−17.0603	+	29.5493i	−0.593244	+	1.02753i	−0.993792	+	0.111253i	$0.964514\pi$
$828$	34.5678	+	11.0194i	1.20132	+	0.382950i
$829$	−3.62521	−	6.27905i	−0.125909	−	0.218080i	0.796179	−	0.605061i	$-0.206851\pi$
$829$	−3.62521	−	6.27905i	−0.125909	−	0.218080i	−0.922088	+	0.386981i	$0.873518\pi$
$830$	8.58943	+	75.6251i	0.298143	+	2.62498i
$831$	−3.65473	−	13.9512i	−0.126781	−	0.483962i
$832$	−4.07706	+	6.75303i	−0.141347	+	0.234119i
$833$	0.142981	−	0.170398i	0.00495399	−	0.00590394i
$834$	6.67384	−	12.1194i	0.231096	−	0.419659i
$835$	−0.725961	+	1.99456i	−0.0251229	+	0.0690246i
$836$	45.1227	−	19.1160i	1.56060	−	0.661140i
$837$	8.87077	−	18.2192i	0.306619	−	0.629748i
$838$	24.3484	+	16.1282i	0.841102	+	0.557139i
$839$	1.56446	+	0.569417i	0.0540112	+	0.0196585i	0.368884	−	0.929475i	$-0.379740\pi$
$839$	1.56446	+	0.569417i	0.0540112	+	0.0196585i	−0.314873	+	0.949134i	$0.601962\pi$
$840$	−16.1119	+	7.21366i	−0.555913	+	0.248895i
$841$	22.0045	+	18.4640i	0.758777	+	0.636689i
$842$	32.6449	−	34.3763i	1.12502	−	1.18469i
$843$	−11.0469	+	40.3243i	−0.380474	+	1.38884i
$844$	21.9796	−	43.0625i	0.756570	−	1.48227i
$845$	−37.5343	+	21.6704i	−1.29122	+	0.745485i
$846$	−5.97201	−	12.3322i	−0.205322	−	0.423990i
$847$	−0.130881	−	0.0755642i	−0.00449713	−	0.00259642i
$848$	−12.1777	+	17.9995i	−0.418184	+	0.618105i
$849$	18.0126	+	1.67743i	0.618189	+	0.0575691i
$850$	0.587217	−	2.44215i	0.0201414	−	0.0837651i
$851$	25.7006	−	9.35424i	0.881004	−	0.320659i
$852$	−1.37948	+	0.438638i	−0.0472601	+	0.0150275i
$853$	0.736640	+	4.17769i	0.0252221	+	0.143041i	0.994818	−	0.101669i	$-0.0324182\pi$
$853$	0.736640	+	4.17769i	0.0252221	+	0.143041i	−0.969596	+	0.244710i	$0.921307\pi$
$854$	−6.93758	−	13.9269i	−0.237399	−	0.476569i
$855$	69.1900	+	40.9852i	2.36625	+	1.40166i
$856$	34.8878	−	12.3130i	1.19244	−	0.420849i
$857$	3.93085	+	4.68460i	0.134275	+	0.160023i	0.828992	−	0.559260i	$-0.188915\pi$
$857$	3.93085	+	4.68460i	0.134275	+	0.160023i	−0.694717	+	0.719283i	$0.744470\pi$
$858$	5.23592	+	5.98949i	0.178751	+	0.204478i
$859$	−5.86289	−	1.03378i	−0.200039	−	0.0352723i	0.0727307	−	0.997352i	$-0.476829\pi$
$859$	−5.86289	−	1.03378i	−0.200039	−	0.0352723i	−0.272770	+	0.962079i	$0.587940\pi$
$860$	15.3288	−	50.0123i	0.522707	−	1.70540i
$861$	9.40157	+	13.5879i	0.320405	+	0.463074i
$862$	−3.80778	−	5.14971i	−0.129693	−	0.175400i
$863$	−14.8459			−0.505360			−0.252680	−	0.967550i	$-0.581312\pi$
$863$	−14.8459			−0.505360			−0.252680	+	0.967550i	$0.581312\pi$
$864$	−8.31788	−	28.1924i	−0.282980	−	0.959126i
$865$	75.8428			2.57873
$866$	24.5786	+	33.2405i	0.835214	+	1.12956i
$867$	29.2613	−	2.39525i	0.993766	−	0.0813471i
$868$	2.28564	−	7.45721i	0.0775796	−	0.253114i
$869$	−17.8080	−	3.14003i	−0.604095	−	0.106518i
$870$	1.49513	−	4.38174i	0.0506895	−	0.148555i
$871$	3.47058	+	4.13608i	0.117596	+	0.140146i
$872$	−16.3555	+	5.77235i	−0.553866	+	0.195476i
$873$	32.8005	−	38.2140i	1.11013	−	1.29335i
$874$	−28.3654	−	56.9425i	−0.959475	−	1.92611i
$875$	−1.86753	−	10.5913i	−0.0631342	−	0.358052i
$876$	5.61251	−	25.6110i	0.189629	−	0.865315i
$877$	47.7258	−	17.3708i	1.61159	−	0.586570i	0.629834	−	0.776730i	$-0.283123\pi$
$877$	47.7258	−	17.3708i	1.61159	−	0.586570i	0.981753	+	0.190160i	$0.0609007\pi$
$878$	1.07709	−	4.47947i	0.0363501	−	0.151175i
$879$	−16.9132	−	36.8064i	−0.570468	−	1.24145i
$880$	26.6031	−	39.3213i	0.896792	−	1.32552i
$881$	−39.0913	−	22.5694i	−1.31702	−	0.760382i	−0.333773	−	0.942654i	$-0.608322\pi$
$881$	−39.0913	−	22.5694i	−1.31702	−	0.760382i	−0.983248	+	0.182271i	$0.941655\pi$
$882$	3.87099	+	1.73651i	0.130343	+	0.0584714i
$883$	3.86475	−	2.23132i	0.130059	−	0.0750898i	−0.433559	−	0.901125i	$-0.642742\pi$
$883$	3.86475	−	2.23132i	0.130059	−	0.0750898i	0.563618	+	0.826036i	$0.309409\pi$
$884$	−0.199426	+	0.390716i	−0.00670743	+	0.0131412i
$885$	53.8134	+	54.4185i	1.80892	+	1.82926i
$886$	0.474306	−	0.499463i	0.0159346	−	0.0167798i
$887$	2.23816	+	1.87804i	0.0751501	+	0.0630584i	0.679589	−	0.733593i	$-0.262158\pi$
$887$	2.23816	+	1.87804i	0.0751501	+	0.0630584i	−0.604439	+	0.796652i	$0.706603\pi$
$888$	−17.9531	−	12.9867i	−0.602465	−	0.435805i
$889$	−9.98394	−	3.63386i	−0.334851	−	0.121876i
$890$	26.4533	+	17.5224i	0.886717	+	0.587354i
$891$	−29.6364	−	0.662917i	−0.992858	−	0.0222085i
$892$	30.8057	−	13.0507i	1.03145	−	0.436968i
$893$	−8.21713	+	22.5764i	−0.274976	+	0.755490i
$894$	8.96499	+	14.8266i	0.299834	+	0.495876i
$895$	12.2506	−	14.5997i	0.409493	−	0.488014i
$896$	−4.84551	−	10.2236i	−0.161877	−	0.341545i
$897$	7.34332	−	7.26166i	0.245186	−	0.242460i
$898$	−1.10073	−	9.69131i	−0.0367319	−	0.323403i
$899$	1.02279	+	1.77152i	0.0341120	+	0.0590837i
$900$	47.8683	−	1.93847i	1.59561	−	0.0646156i
$901$	−0.604253	+	1.04660i	−0.0201306	+	0.0348672i
$902$	−40.7451	−	17.7335i	−1.35666	−	0.590462i
$903$	−11.4233	+	5.24920i	−0.380143	+	0.174682i
$904$	39.3198	−	6.53721i	1.30776	−	0.217425i
$905$	16.6577	+	45.7667i	0.553721	+	1.52134i
$906$	−38.1839	+	14.7795i	−1.26858	+	0.491017i
$907$	22.1356	−	3.90311i	0.735002	−	0.129601i	0.206396	−	0.978468i	$-0.433826\pi$
$907$	22.1356	−	3.90311i	0.735002	−	0.129601i	0.528605	+	0.848868i	$0.322715\pi$
$908$	48.2615	+	5.96025i	1.60161	+	0.197798i
$909$	−4.21022	+	22.4091i	−0.139644	+	0.743263i
$910$	−0.308526	+	5.01539i	−0.0102275	+	0.166258i
$911$	9.89141	−	8.29988i	0.327717	−	0.274987i	−0.464052	−	0.885808i	$-0.653605\pi$
$911$	9.89141	−	8.29988i	0.327717	−	0.274987i	0.791769	+	0.610821i	$0.209160\pi$
$912$	−25.3016	+	44.9013i	−0.837820	+	1.48683i
$913$	−8.54245	+	48.4467i	−0.282714	+	1.60335i
$914$	−1.58109	−	5.34459i	−0.0522979	−	0.176783i
$915$	5.60215	+	68.4379i	0.185201	+	2.26249i
$916$	−2.71846	−	52.5795i	−0.0898206	−	1.73727i
$917$			4.99602i			0.164983i
$918$	−0.572945	−	1.53088i	−0.0189100	−	0.0505266i
$919$		−	10.7337i		−	0.354072i	−0.984204	−	0.177036i	$-0.943349\pi$
$919$		−	10.7337i		−	0.354072i	0.984204	−	0.177036i	$-0.0566508\pi$
$920$	−53.0696	−	31.3359i	−1.74965	−	1.03311i
$921$	−19.3391	+	13.3809i	−0.637245	+	0.440914i
$922$	39.6039	−	11.7160i	1.30428	−	0.385847i
$923$	−0.0715492	+	0.405776i	−0.00235507	+	0.0133563i
$924$	−11.3087	+	1.51680i	−0.372028	+	0.0498990i
$925$	27.6648	−	23.2135i	0.909612	−	0.763255i
$926$	−18.4525	−	1.13512i	−0.606386	−	0.0373024i
$927$	−26.9614	−	47.9284i	−0.885530	−	1.57418i
$928$	2.82830	+	0.897235i	0.0928436	+	0.0294532i
$929$	29.4431	−	5.19162i	0.965998	−	0.170332i	0.331670	−	0.943395i	$-0.392388\pi$
$929$	29.4431	−	5.19162i	0.965998	−	0.170332i	0.634328	+	0.773064i	$0.281277\pi$
$930$	−21.5878	+	26.8109i	−0.707891	+	0.879165i
$931$	−2.54430	−	6.99042i	−0.0833862	−	0.229102i
$932$	10.6256	−	9.89457i	0.348054	−	0.324108i
$933$	3.57285	−	38.3660i	0.116970	−	1.25605i
$934$	−2.03063	+	4.66564i	−0.0664443	+	0.152664i
$935$	1.32004	−	2.28637i	0.0431699	−	0.0747724i
$936$	−8.20747	−	1.62530i	−0.268270	−	0.0531246i
$937$	−8.42949	−	14.6003i	−0.275379	−	0.476971i	0.694851	−	0.719153i	$-0.255470\pi$
$937$	−8.42949	−	14.6003i	−0.275379	−	0.476971i	−0.970231	+	0.242182i	$0.922137\pi$
$938$	−7.69432	+	0.873915i	−0.251229	+	0.0285343i
$939$	1.52251	+	0.417094i	0.0496854	+	0.0136114i
$940$	5.21984	+	22.6824i	0.170252	+	0.739820i
$941$	7.96979	−	9.49803i	0.259808	−	0.309627i	−0.620334	−	0.784338i	$-0.713003\pi$
$941$	7.96979	−	9.49803i	0.259808	−	0.309627i	0.880142	+	0.474711i	$0.157447\pi$
$942$	0.0461829	+	2.28180i	0.00150472	+	0.0743452i
$943$	−19.7299	+	54.2075i	−0.642494	+	1.76524i
$944$	−34.1221	+	35.2351i	−1.11058	+	1.14680i
$945$	−13.0159	−	13.4600i	−0.423406	−	0.437853i
$946$	18.6706	−	28.1866i	0.607033	−	0.916425i
$947$	20.4224	+	7.43314i	0.663638	+	0.241545i	0.651806	−	0.758385i	$-0.274011\pi$
$947$	20.4224	+	7.43314i	0.663638	+	0.241545i	0.0118320	+	0.999930i	$0.496234\pi$
$948$	16.8477	−	8.82248i	0.547187	−	0.286541i
$949$	−5.71703	−	4.79716i	−0.185583	−	0.155722i
$950$	−60.9119	−	57.8440i	−1.97624	−	1.87671i
$951$	3.16330	−	0.828675i	0.102577	−	0.0268716i
$952$	−0.309231	−	0.547912i	−0.0100222	−	0.0177579i
$953$	−17.3933	+	10.0420i	−0.563424	+	0.325293i	−0.754519	−	0.656279i	$-0.772130\pi$
$953$	−17.3933	+	10.0420i	−0.563424	+	0.325293i	0.191095	+	0.981572i	$0.438796\pi$
$954$	−22.3498	−	5.63912i	−0.723601	−	0.182573i
$955$	29.6382	+	17.1116i	0.959070	+	0.553719i
$956$	25.7931	−	16.7245i	0.834210	−	0.540908i
$957$	1.73007	−	2.44163i	0.0559253	−	0.0789267i
$958$	−6.66812	−	1.60336i	−0.215437	−	0.0518021i
$959$	9.64775	−	3.51150i	0.311542	−	0.113392i
$960$	3.09920	+	49.8341i	0.100026	+	1.60839i
$961$	2.74216	+	15.5516i	0.0884568	+	0.501663i
$962$	−5.64545	+	2.81224i	−0.182017	+	0.0906702i
$963$	24.8860	+	30.3406i	0.801940	+	0.977712i
$964$	−15.6256	+	20.7055i	−0.503265	+	0.666879i
$965$	−15.4474	−	18.4096i	−0.497271	−	0.592624i
$966$	2.86671	+	14.5319i	0.0922350	+	0.467556i
$967$	23.2600	+	4.10137i	0.747992	+	0.131891i	0.534635	−	0.845083i	$-0.320449\pi$
$967$	23.2600	+	4.10137i	0.747992	+	0.131891i	0.213357	+	0.976974i	$0.431560\pi$
$968$	−0.330122	+	0.271547i	−0.0106105	+	0.00872785i
$969$	−1.22576	+	2.59074i	−0.0393771	+	0.0832265i
$970$	−68.7844	+	50.8603i	−2.20853	+	1.63303i
$971$	0.778985			0.0249988			0.0124994	−	0.999922i	$-0.496021\pi$
$971$	0.778985			0.0249988			0.0124994	+	0.999922i	$0.496021\pi$
$972$	25.1077	−	18.4825i	0.805329	−	0.592828i
$973$	5.64829			0.181076
$974$	−24.2394	+	17.9230i	−0.776681	+	0.574291i
$975$	5.83212	−	12.3266i	0.186777	−	0.394768i
$976$	−43.7734	+	4.53848i	−1.40115	+	0.145273i
$977$	−58.9790	−	10.3996i	−1.88691	−	0.332713i	−0.893661	−	0.448743i	$-0.851872\pi$
$977$	−58.9790	−	10.3996i	−1.88691	−	0.332713i	−0.993246	+	0.116030i	$0.962983\pi$
$978$	2.59806	+	13.1700i	0.0830767	+	0.421131i
$979$	13.1827	+	15.7106i	0.421322	+	0.502112i
$980$	−5.75257	−	4.34123i	−0.183759	−	0.138675i
$981$	−11.6666	−	14.2237i	−0.372486	−	0.454129i
$982$	53.7351	−	26.7677i	1.71476	−	0.854192i
$983$	4.04888	+	22.9623i	0.129139	+	0.732384i	0.978763	+	0.204995i	$0.0657178\pi$
$983$	4.04888	+	22.9623i	0.129139	+	0.732384i	−0.849624	+	0.527389i	$0.823171\pi$
$984$	45.3232	−	11.4005i	1.44485	−	0.363435i
$985$	−60.6088	+	22.0598i	−1.93116	+	0.702884i
$986$	0.160433	+	0.0385762i	0.00510922	+	0.00122852i
$987$	3.23408	−	4.56421i	0.102942	−	0.145281i
$988$	7.98143	+	12.3093i	0.253923	+	0.391610i
$989$	−38.0099	−	21.9450i	−1.20865	−	0.697812i
$990$	48.8248	+	12.3191i	1.55176	+	0.391527i
$991$	−49.9992	+	28.8670i	−1.58828	+	0.916991i	−0.594684	+	0.803959i	$0.702723\pi$
$991$	−49.9992	+	28.8670i	−1.58828	+	0.916991i	−0.993591	+	0.113032i	$0.963944\pi$
$992$	−17.4782	−	13.4605i	−0.554935	−	0.427370i
$993$	−7.38348	+	1.93422i	−0.234308	+	0.0613805i
$994$	−0.428520	−	0.406937i	−0.0135918	−	0.0129073i
$995$	44.3366	+	37.2028i	1.40556	+	1.17941i
$996$	−24.0015	−	45.8341i	−0.760518	−	1.45231i
$997$	12.6276	+	4.59608i	0.399921	+	0.145559i	0.534147	−	0.845391i	$-0.320633\pi$
$997$	12.6276	+	4.59608i	0.399921	+	0.145559i	−0.134226	+	0.990951i	$0.542855\pi$
$998$	11.3292	−	17.1035i	0.358621	−	0.541403i
$999$	6.46263	−	22.5958i	0.204469	−	0.714901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.239.77	yes	648
4.3	odd	2	inner	756.2.cf.a.239.5	yes	648
27.20	odd	18	inner	756.2.cf.a.155.5	✓	648
108.47	even	18	inner	756.2.cf.a.155.77	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.155.5	✓	648	27.20	odd	18	inner
756.2.cf.a.155.77	yes	648	108.47	even	18	inner
756.2.cf.a.239.5	yes	648	4.3	odd	2	inner
756.2.cf.a.239.77	yes	648	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.840806 + 1.13712i) q^{2} +(-0.740762 + 1.56565i) q^{3} +(-0.586089 + 1.91220i) q^{4} +(3.54867 + 0.625726i) q^{5} +(-2.40318 + 0.474076i) q^{6} +(-0.642788 - 0.766044i) q^{7} +(-2.66719 + 0.941333i) q^{8} +(-1.90254 - 2.31955i) q^{9} +O(q^{10})\)	\(q+(0.840806 + 1.13712i) q^{2} +(-0.740762 + 1.56565i) q^{3} +(-0.586089 + 1.91220i) q^{4} +(3.54867 + 0.625726i) q^{5} +(-2.40318 + 0.474076i) q^{6} +(-0.642788 - 0.766044i) q^{7} +(-2.66719 + 0.941333i) q^{8} +(-1.90254 - 2.31955i) q^{9} +(2.27222 + 4.56138i) q^{10} +(0.571956 + 3.24372i) q^{11} +(-2.55969 - 2.33410i) q^{12} +(-0.926577 + 0.337246i) q^{13} +(0.330626 - 1.37502i) q^{14} +(-3.60839 + 5.09247i) q^{15} +(-3.31300 - 2.24144i) q^{16} +(-0.192637 - 0.111219i) q^{17} +(1.03794 - 4.11372i) q^{18} +(-6.44241 + 3.71952i) q^{19} +(-3.27635 + 6.41902i) q^{20} +(1.67551 - 0.438927i) q^{21} +(-3.20760 + 3.37773i) q^{22} +(4.63223 + 3.88691i) q^{23} +(0.501949 - 4.87320i) q^{24} +(7.50306 + 2.73089i) q^{25} +(-1.16256 - 0.770071i) q^{26} +(5.04095 - 1.26049i) q^{27} +(1.84156 - 0.780166i) q^{28} +(-0.179401 + 0.492900i) q^{29} +(-8.82472 + 0.178609i) q^{30} +(2.50675 - 2.98743i) q^{31} +(-0.236804 - 5.65190i) q^{32} +(-5.50223 - 1.50734i) q^{33} +(-0.0355010 - 0.312566i) q^{34} +(-1.80171 - 3.12065i) q^{35} +(5.55050 - 2.27858i) q^{36} +(2.26147 - 3.91698i) q^{37} +(-9.64637 - 4.19840i) q^{38} +(0.158361 - 1.70052i) q^{39} +(-10.0540 + 1.67155i) q^{40} +(3.26279 + 8.96443i) q^{41} +(1.90789 + 1.53621i) q^{42} +(-7.14795 + 1.26038i) q^{43} +(-6.53786 - 0.807419i) q^{44} +(-5.30010 - 9.42180i) q^{45} +(-0.525071 + 8.53554i) q^{46} +(2.47403 - 2.07596i) q^{47} +(5.96346 - 3.52664i) q^{48} +(-0.173648 + 0.984808i) q^{49} +(3.20327 + 10.8280i) q^{50} +(0.316829 - 0.219217i) q^{51} +(-0.101825 - 1.96945i) q^{52} -5.43299i q^{53} +(5.67179 + 4.67234i) q^{54} +11.8688i q^{55} +(2.43554 + 1.43811i) q^{56} +(-1.05120 - 12.8419i) q^{57} +(-0.711328 + 0.210433i) q^{58} +(2.12933 - 12.0760i) q^{59} +(-7.62298 - 9.88460i) q^{60} +(8.42803 - 7.07195i) q^{61} +(5.50476 + 0.338630i) q^{62} +(-0.553948 + 2.94841i) q^{63} +(6.22778 - 5.02142i) q^{64} +(-3.49914 + 0.616993i) q^{65} +(-2.91228 - 7.52408i) q^{66} +(-1.87280 - 5.14547i) q^{67} +(0.325576 - 0.303176i) q^{68} +(-9.51693 + 4.37320i) q^{69} +(2.03367 - 4.67262i) q^{70} +(0.208934 - 0.361884i) q^{71} +(7.25792 + 4.39576i) q^{72} +(3.78435 + 6.55468i) q^{73} +(6.35554 - 0.721856i) q^{74} +(-9.83360 + 9.72425i) q^{75} +(-3.33664 - 14.4991i) q^{76} +(2.11719 - 2.52317i) q^{77} +(2.06685 - 1.24973i) q^{78} +(-1.87769 + 5.15890i) q^{79} +(-10.3542 - 10.0272i) q^{80} +(-1.76065 + 8.82610i) q^{81} +(-7.45028 + 11.2475i) q^{82} +(14.0348 + 5.10825i) q^{83} +(-0.142686 + 3.46116i) q^{84} +(-0.614014 - 0.515219i) q^{85} +(-7.44324 - 7.06835i) q^{86} +(-0.638817 - 0.646001i) q^{87} +(-4.57894 - 8.11322i) q^{88} +(5.39232 - 3.11326i) q^{89} +(6.25737 - 13.9488i) q^{90} +(0.853938 + 0.493021i) q^{91} +(-10.1474 + 6.57967i) q^{92} +(2.82038 + 6.13768i) q^{93} +(4.44080 + 1.06779i) q^{94} +(-25.1894 + 9.16818i) q^{95} +(9.02433 + 3.81595i) q^{96} +(2.91501 + 16.5318i) q^{97} +(-1.26585 + 0.630574i) q^{98} +(6.43581 - 7.49801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q+O(q^{10}) \) 648 * q	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66} - 78 q^{68} - 42 q^{72} - 24 q^{81} - 30 q^{86} - 36 q^{89} + 198 q^{90} + 114 q^{92} - 144 q^{93} - 54 q^{94} + 156 q^{96} + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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