LMFDB - Embedded newform 950.2.w.a.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	950.37
Dual form			950.2.w.a.873.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(-0.581458 + 1.14117i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.37992 + 1.75950i) q^{5} +(0.395780 - 1.21809i) q^{6} +(1.14962 + 1.14962i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.799169 + 1.09996i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.581458 + 1.14117i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.37992 + 1.75950i) q^{5} +(0.395780 - 1.21809i) q^{6} +(1.14962 + 1.14962i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.799169 + 1.09996i) q^{9} +(-1.63817 - 1.52197i) q^{10} +(-3.19712 - 2.32284i) q^{11} +(-0.200357 + 1.26500i) q^{12} +(-5.75812 - 0.911997i) q^{13} +(-1.31531 - 0.955626i) q^{14} +(-2.81026 + 0.551654i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-4.49759 + 2.29164i) q^{17} +(-0.961402 - 0.961402i) q^{18} +(-4.34386 - 0.361800i) q^{19} +(1.85609 + 1.24696i) q^{20} +(-1.98037 + 0.643462i) q^{21} +(3.52113 + 1.79411i) q^{22} +(5.94611 - 0.941771i) q^{23} -1.28077i q^{24} +(-1.19166 + 4.85592i) q^{25} +5.82990 q^{26} +(-5.51494 + 0.873480i) q^{27} +(1.44861 + 0.738101i) q^{28} +(-1.81756 - 5.59388i) q^{29} +(2.68936 - 0.984483i) q^{30} +(6.21715 + 2.02008i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.50976 - 2.29784i) q^{33} +(4.08373 - 2.96700i) q^{34} +(-0.436372 + 3.60913i) q^{35} +(1.09996 + 0.799169i) q^{36} +(-0.687877 + 4.34308i) q^{37} +(4.34698 - 0.322184i) q^{38} +(4.38885 - 6.04073i) q^{39} +(-2.02831 - 0.941254i) q^{40} +(-0.382258 - 0.526132i) q^{41} +(1.85533 - 0.945338i) q^{42} +(-3.87822 + 3.87822i) q^{43} +(-3.75844 - 1.22119i) q^{44} +(-0.832592 + 2.92399i) q^{45} +(-5.72558 + 1.86035i) q^{46} +(2.56737 - 5.03875i) q^{47} +(0.200357 + 1.26500i) q^{48} -4.35675i q^{49} +(0.417352 - 4.98255i) q^{50} -6.46503i q^{51} +(-5.75812 + 0.911997i) q^{52} +(-2.35675 + 4.62538i) q^{53} +(5.31040 - 1.72545i) q^{54} +(-0.324726 - 8.83065i) q^{55} +(-1.54623 - 0.502402i) q^{56} +(2.93865 - 4.74673i) q^{57} +(2.67026 + 5.24068i) q^{58} +(-6.66502 + 4.84242i) q^{59} +(-2.50224 + 1.39307i) q^{60} +(-3.44048 - 2.49965i) q^{61} +(-6.45662 - 1.02263i) q^{62} +(-0.345797 + 2.18328i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-6.34108 - 11.3899i) q^{65} +(-4.09478 + 2.97503i) q^{66} +(4.82711 + 9.47374i) q^{67} +(-3.56931 + 3.56931i) q^{68} +(-2.38269 + 7.33315i) q^{69} +(-0.133593 - 3.63296i) q^{70} +(8.10333 - 2.63293i) q^{71} +(-1.21144 - 0.617258i) q^{72} +(-14.8227 + 2.34768i) q^{73} -4.39722i q^{74} +(-4.84856 - 4.18340i) q^{75} +(-4.24306 + 0.998234i) q^{76} +(-1.00509 - 6.34586i) q^{77} +(-3.38984 + 6.65293i) q^{78} +(1.07073 + 3.29537i) q^{79} +(2.15058 + 0.612368i) q^{80} +(0.949465 - 2.92215i) q^{81} +(0.459857 + 0.459857i) q^{82} +(-0.620262 - 1.21733i) q^{83} +(-1.68460 + 1.22394i) q^{84} +(-10.2384 - 4.75122i) q^{85} +(3.22379 - 4.43716i) q^{86} +(7.44043 + 1.17845i) q^{87} +(3.90320 + 0.618207i) q^{88} +(-8.05799 - 5.85447i) q^{89} +(0.364928 - 3.01824i) q^{90} +(-5.57120 - 7.66810i) q^{91} +(5.36406 - 2.73313i) q^{92} +(-5.92027 + 5.92027i) q^{93} +(-1.74753 + 5.37834i) q^{94} +(-5.35758 - 8.14226i) q^{95} +(-0.395780 - 1.21809i) q^{96} +(11.4836 + 5.85118i) q^{97} +(0.681546 + 4.30311i) q^{98} -5.37305i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

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 $

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	−0.581458	+	1.14117i	−0.335705	+	0.658858i	−0.995723	−	0.0923922i	$-0.970549\pi$
$3$	−0.581458	+	1.14117i	−0.335705	+	0.658858i	0.660018	+	0.751250i	$0.270549\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	1.37992	+	1.75950i	0.617118	+	0.786871i
$5$	1.37992	+	1.75950i	0.617118	+	0.786871i
$6$	0.395780	−	1.21809i	0.161576	−	0.497281i
$7$	1.14962	+	1.14962i	0.434515	+	0.434515i	0.890161	−	0.455646i	$-0.150592\pi$
$7$	1.14962	+	1.14962i	0.434515	+	0.434515i	−0.455646	+	0.890161i	$0.650592\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	0.799169	+	1.09996i	0.266390	+	0.366654i
$10$	−1.63817	−	1.52197i	−0.518036	−	0.481288i
$11$	−3.19712	−	2.32284i	−0.963968	−	0.700364i	−0.00989893	−	0.999951i	$-0.503151\pi$
$11$	−3.19712	−	2.32284i	−0.963968	−	0.700364i	−0.954069	+	0.299587i	$0.903151\pi$
$12$	−0.200357	+	1.26500i	−0.0578380	+	0.365175i
$13$	−5.75812	−	0.911997i	−1.59702	−	0.252942i	−0.706438	−	0.707775i	$-0.749699\pi$
$13$	−5.75812	−	0.911997i	−1.59702	−	0.252942i	−0.890577	+	0.454832i	$0.849699\pi$
$14$	−1.31531	−	0.955626i	−0.351530	−	0.255402i
$15$	−2.81026	+	0.551654i	−0.725605	+	0.142437i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−4.49759	+	2.29164i	−1.09083	+	0.555803i	−0.904409	−	0.426667i	$-0.859688\pi$
$17$	−4.49759	+	2.29164i	−1.09083	+	0.555803i	−0.186417	+	0.982471i	$0.559688\pi$
$18$	−0.961402	−	0.961402i	−0.226605	−	0.226605i
$19$	−4.34386	−	0.361800i	−0.996549	−	0.0830025i
$19$	−4.34386	−	0.361800i	−0.996549	−	0.0830025i
$20$	1.85609	+	1.24696i	0.415035	+	0.278829i
$21$	−1.98037	+	0.643462i	−0.432153	+	0.140415i
$22$	3.52113	+	1.79411i	0.750708	+	0.382505i
$23$	5.94611	−	0.941771i	1.23985	−	0.196373i	0.498142	−	0.867096i	$-0.334016\pi$
$23$	5.94611	−	0.941771i	1.23985	−	0.196373i	0.741708	+	0.670723i	$0.234016\pi$
$24$		−	1.28077i		−	0.261436i
$25$	−1.19166	+	4.85592i	−0.238331	+	0.971184i
$26$	5.82990			1.14334
$27$	−5.51494	+	0.873480i	−1.06135	+	0.168101i
$28$	1.44861	+	0.738101i	0.273761	+	0.139488i
$29$	−1.81756	−	5.59388i	−0.337513	−	1.03876i	−0.965471	−	0.260511i	$-0.916109\pi$
$29$	−1.81756	−	5.59388i	−0.337513	−	1.03876i	0.627958	−	0.778247i	$-0.283891\pi$
$30$	2.68936	−	0.984483i	0.491008	−	0.179741i
$31$	6.21715	+	2.02008i	1.11663	+	0.362816i	0.808482	−	0.588521i	$-0.200290\pi$
$31$	6.21715	+	2.02008i	1.11663	+	0.362816i	0.308152	+	0.951337i	$0.400290\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	4.50976	−	2.29784i	0.785048	−	0.400002i
$34$	4.08373	−	2.96700i	0.700353	−	0.508836i
$35$	−0.436372	+	3.60913i	−0.0737603	+	0.610055i
$36$	1.09996	+	0.799169i	0.183327	+	0.133195i
$37$	−0.687877	+	4.34308i	−0.113086	+	0.713999i	0.864369	+	0.502857i	$0.167718\pi$
$37$	−0.687877	+	4.34308i	−0.113086	+	0.713999i	−0.977456	+	0.211141i	$0.932282\pi$
$38$	4.34698	−	0.322184i	0.705173	−	0.0522651i
$39$	4.38885	−	6.04073i	0.702779	−	0.967292i
$40$	−2.02831	−	0.941254i	−0.320704	−	0.148825i
$41$	−0.382258	−	0.526132i	−0.0596986	−	0.0821681i	0.778124	−	0.628111i	$-0.216172\pi$
$41$	−0.382258	−	0.526132i	−0.0596986	−	0.0821681i	−0.837822	+	0.545943i	$0.816172\pi$
$42$	1.85533	−	0.945338i	0.286284	−	0.145869i
$43$	−3.87822	+	3.87822i	−0.591424	+	0.591424i	−0.938016	−	0.346592i	$-0.887339\pi$
$43$	−3.87822	+	3.87822i	−0.591424	+	0.591424i	0.346592	+	0.938016i	$0.387339\pi$
$44$	−3.75844	−	1.22119i	−0.566606	−	0.184101i
$45$	−0.832592	+	2.92399i	−0.124115	+	0.435883i
$46$	−5.72558	+	1.86035i	−0.844191	+	0.274294i
$47$	2.56737	−	5.03875i	0.374490	−	0.734977i	−0.624448	−	0.781067i	$-0.714676\pi$
$47$	2.56737	−	5.03875i	0.374490	−	0.734977i	0.998937	+	0.0460894i	$0.0146759\pi$
$48$	0.200357	+	1.26500i	0.0289190	+	0.182587i
$49$		−	4.35675i		−	0.622393i
$50$	0.417352	−	4.98255i	0.0590224	−	0.704639i
$51$		−	6.46503i		−	0.905285i
$52$	−5.75812	+	0.911997i	−0.798508	+	0.126471i
$53$	−2.35675	+	4.62538i	−0.323725	+	0.635345i	−0.994315	−	0.106483i	$-0.966041\pi$
$53$	−2.35675	+	4.62538i	−0.323725	+	0.635345i	0.670590	+	0.741828i	$0.266041\pi$
$54$	5.31040	−	1.72545i	0.722653	−	0.234804i
$55$	−0.324726	−	8.83065i	−0.0437860	−	1.19072i
$56$	−1.54623	−	0.502402i	−0.206624	−	0.0671363i
$57$	2.93865	−	4.74673i	0.389233	−	0.628720i
$58$	2.67026	+	5.24068i	0.350622	+	0.688135i
$59$	−6.66502	+	4.84242i	−0.867712	+	0.630430i	−0.929972	−	0.367630i	$-0.880169\pi$
$59$	−6.66502	+	4.84242i	−0.867712	+	0.630430i	0.0622599	+	0.998060i	$0.480169\pi$
$60$	−2.50224	+	1.39307i	−0.323038	+	0.179845i
$61$	−3.44048	−	2.49965i	−0.440508	−	0.320048i	0.345329	−	0.938482i	$-0.387767\pi$
$61$	−3.44048	−	2.49965i	−0.440508	−	0.320048i	−0.785837	+	0.618434i	$0.787767\pi$
$62$	−6.45662	−	1.02263i	−0.819991	−	0.129874i
$63$	−0.345797	+	2.18328i	−0.0435664	+	0.275067i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−6.34108	−	11.3899i	−0.786514	−	1.41274i
$66$	−4.09478	+	2.97503i	−0.504032	+	0.366201i
$67$	4.82711	+	9.47374i	0.589725	+	1.15740i	0.972357	+	0.233500i	$0.0750180\pi$
$67$	4.82711	+	9.47374i	0.589725	+	1.15740i	−0.382631	+	0.923901i	$0.624982\pi$
$68$	−3.56931	+	3.56931i	−0.432842	+	0.432842i
$69$	−2.38269	+	7.33315i	−0.286842	+	0.882808i
$70$	−0.133593	−	3.63296i	−0.0159675	−	0.434222i
$71$	8.10333	−	2.63293i	0.961689	−	0.312472i	0.214232	−	0.976783i	$-0.431275\pi$
$71$	8.10333	−	2.63293i	0.961689	−	0.312472i	0.747456	+	0.664311i	$0.231275\pi$
$72$	−1.21144	−	0.617258i	−0.142769	−	0.0727445i
$73$	−14.8227	+	2.34768i	−1.73487	+	0.274776i	−0.942241	−	0.334935i	$-0.891286\pi$
$73$	−14.8227	+	2.34768i	−1.73487	+	0.274776i	−0.792624	+	0.609710i	$0.791286\pi$
$74$		−	4.39722i		−	0.511167i
$75$	−4.84856	−	4.18340i	−0.559863	−	0.483057i
$76$	−4.24306	+	0.998234i	−0.486712	+	0.114505i
$77$	−1.00509	−	6.34586i	−0.114540	−	0.723178i
$78$	−3.38984	+	6.65293i	−0.383824	+	0.753296i
$79$	1.07073	+	3.29537i	0.120467	+	0.370758i	0.993048	−	0.117711i	$-0.0375555\pi$
$79$	1.07073	+	3.29537i	0.120467	+	0.370758i	−0.872581	+	0.488469i	$0.837556\pi$
$80$	2.15058	+	0.612368i	0.240442	+	0.0684648i
$81$	0.949465	−	2.92215i	0.105496	−	0.324684i
$82$	0.459857	+	0.459857i	0.0507827	+	0.0507827i
$83$	−0.620262	−	1.21733i	−0.0680826	−	0.133620i	0.854457	−	0.519522i	$-0.173890\pi$
$83$	−0.620262	−	1.21733i	−0.0680826	−	0.133620i	−0.922540	+	0.385903i	$0.873890\pi$
$84$	−1.68460	+	1.22394i	−0.183805	+	0.133542i
$85$	−10.2384	−	4.75122i	−1.11051	−	0.515343i
$86$	3.22379	−	4.43716i	0.347630	−	0.478472i
$87$	7.44043	+	1.17845i	0.797698	+	0.126343i
$88$	3.90320	+	0.618207i	0.416083	+	0.0659010i
$89$	−8.05799	−	5.85447i	−0.854145	−	0.620573i	0.0721407	−	0.997394i	$-0.477017\pi$
$89$	−8.05799	−	5.85447i	−0.854145	−	0.620573i	−0.926286	+	0.376822i	$0.877017\pi$
$90$	0.364928	−	3.01824i	0.0384668	−	0.318150i
$91$	−5.57120	−	7.66810i	−0.584020	−	0.803835i
$92$	5.36406	−	2.73313i	0.559242	−	0.284948i
$93$	−5.92027	+	5.92027i	−0.613903	+	0.613903i
$94$	−1.74753	+	5.37834i	−0.180244	+	0.554733i
$95$	−5.35758	−	8.14226i	−0.549676	−	0.835378i
$96$	−0.395780	−	1.21809i	−0.0403941	−	0.124320i
$97$	11.4836	+	5.85118i	1.16598	+	0.594097i	0.926312	−	0.376757i	$-0.122961\pi$
$97$	11.4836	+	5.85118i	1.16598	+	0.594097i	0.239670	+	0.970855i	$0.422961\pi$
$98$	0.681546	+	4.30311i	0.0688465	+	0.434680i
$99$		−	5.37305i		−	0.540012i
$100$	0.367229	+	4.98650i	0.0367229	+	0.498650i
$101$	8.86919			0.882518			0.441259	−	0.897380i	$-0.354532\pi$
$101$	8.86919			0.882518			0.441259	+	0.897380i	$0.354532\pi$
$102$	1.01135	+	6.38543i	0.100139	+	0.632252i
$103$	−4.73536	+	9.29367i	−0.466589	+	0.915733i	0.531068	+	0.847329i	$0.321791\pi$
$103$	−4.73536	+	9.29367i	−0.466589	+	0.915733i	−0.997658	+	0.0684040i	$0.978209\pi$
$104$	5.54456	−	1.80154i	0.543689	−	0.176655i
$105$	−3.86492	−	2.59653i	−0.377177	−	0.253396i
$106$	1.60417	−	4.93712i	0.155810	−	0.479535i
$107$	13.5389	−	13.5389i	1.30886	−	1.30886i	0.386614	−	0.922242i	$-0.373645\pi$
$107$	13.5389	−	13.5389i	1.30886	−	1.30886i	0.922242	−	0.386614i	$-0.126355\pi$
$108$	−4.97510	+	2.53494i	−0.478729	+	0.243925i
$109$	−4.65830	+	3.38445i	−0.446184	+	0.324172i	−0.788087	−	0.615563i	$-0.788929\pi$
$109$	−4.65830	+	3.38445i	−0.446184	+	0.324172i	0.341903	+	0.939735i	$0.388929\pi$
$110$	1.70215	+	8.67113i	0.162293	+	0.826760i
$111$	−4.55625	−	3.31031i	−0.432460	−	0.314200i
$112$	1.60579	+	0.254332i	0.151733	+	0.0240321i
$113$	−9.63001	−	1.52524i	−0.905915	−	0.143483i	−0.313944	−	0.949442i	$-0.601650\pi$
$113$	−9.63001	−	1.52524i	−0.905915	−	0.143483i	−0.591972	+	0.805959i	$0.701650\pi$
$114$	−2.15991	+	5.14800i	−0.202294	+	0.482154i
$115$	9.86218	+	9.16259i	0.919653	+	0.854416i
$116$	−3.45721	−	4.75844i	−0.320994	−	0.441810i
$117$	−3.59855	−	7.06255i	−0.332686	−	0.652933i
$118$	5.82544	−	5.82544i	0.536276	−	0.536276i
$119$	−7.80503	−	2.53601i	−0.715486	−	0.232475i
$120$	2.25351	−	1.76736i	0.205716	−	0.161337i
$121$	1.42679	+	4.39119i	0.129708	+	0.399199i
$122$	3.78915	+	1.93067i	0.343054	+	0.174795i
$123$	0.822676	−	0.130299i	0.0741782	−	0.0117487i
$124$	6.53710			0.587049
$125$	−10.1884	+	4.60405i	−0.911275	+	0.411799i
$126$		−	2.21049i		−	0.196926i
$127$	4.11863	−	0.652326i	0.365469	−	0.0578846i	0.0290007	−	0.999579i	$-0.490767\pi$
$127$	4.11863	−	0.652326i	0.365469	−	0.0578846i	0.336468	+	0.941695i	$0.390767\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	−2.17071	−	6.68075i	−0.191120	−	0.588208i
$130$	8.04478	+	10.2577i	0.705573	+	0.899658i
$131$	−4.85376	+	14.9383i	−0.424075	+	1.30517i	0.479802	+	0.877377i	$0.340708\pi$
$131$	−4.85376	+	14.9383i	−0.424075	+	1.30517i	−0.903877	+	0.427792i	$0.859292\pi$
$132$	3.57897	−	3.57897i	0.311509	−	0.311509i
$133$	−4.57785	−	5.40972i	−0.396950	−	0.469082i
$134$	−6.24970	−	8.60197i	−0.539892	−	0.743097i
$135$	−9.14704	−	8.49818i	−0.787252	−	0.731407i
$136$	2.96700	−	4.08373i	0.254418	−	0.350177i
$137$	−14.6553	−	2.32118i	−1.25209	−	0.198312i	−0.505050	−	0.863090i	$-0.668526\pi$
$137$	−14.6553	−	2.32118i	−1.25209	−	0.198312i	−0.747041	+	0.664778i	$0.768526\pi$
$138$	1.20619	−	7.61560i	0.102678	−	0.648283i
$139$	−2.97907	+	4.10034i	−0.252682	+	0.347786i	−0.916448	−	0.400153i	$-0.868957\pi$
$139$	−2.97907	+	4.10034i	−0.252682	+	0.347786i	0.663767	+	0.747940i	$0.268957\pi$
$140$	0.700269	+	3.56733i	0.0591835	+	0.301495i
$141$	4.25728	+	5.85964i	0.358527	+	0.493471i
$142$	−7.59169	+	3.86816i	−0.637080	+	0.324609i
$143$	16.2910	+	16.2910i	1.36232	+	1.36232i
$144$	1.29308	+	0.420148i	0.107757	+	0.0350123i
$145$	7.33433	−	10.9171i	0.609083	−	0.906615i
$146$	14.2729	−	4.63756i	1.18124	−	0.383807i
$147$	4.97181	+	2.53327i	0.410068	+	0.208940i
$148$	0.687877	+	4.34308i	0.0565431	+	0.356999i
$149$		−	3.44194i		−	0.281975i	−0.990011	−	0.140987i	$-0.954972\pi$
$149$		−	3.44194i		−	0.281975i	0.990011	−	0.140987i	$-0.0450277\pi$
$150$	5.44329	+	3.37341i	0.444443	+	0.275438i
$151$		−	10.2744i		−	0.836115i	−0.908420	−	0.418058i	$-0.862711\pi$
$151$		−	10.2744i		−	0.836115i	0.908420	−	0.418058i	$-0.137289\pi$
$152$	4.03466	−	1.64970i	0.327254	−	0.133809i
$153$	−6.11505	−	3.11577i	−0.494372	−	0.251895i
$154$	1.98542	+	6.11050i	0.159990	+	0.492398i
$155$	5.02484	+	13.7266i	0.403605	+	1.10255i
$156$	2.30736	−	7.10131i	0.184736	−	0.568560i
$157$	9.47251	+	9.47251i	0.755989	+	0.755989i	0.975590	−	0.219601i	$-0.0704756\pi$
$157$	9.47251	+	9.47251i	0.755989	+	0.755989i	−0.219601	+	0.975590i	$0.570476\pi$
$158$	−1.57306	−	3.08730i	−0.125146	−	0.245613i
$159$	−3.90802	−	5.37893i	−0.309926	−	0.426577i
$160$	−2.21990	−	0.268403i	−0.175499	−	0.0212191i
$161$	7.91844	+	5.75309i	0.624061	+	0.453407i
$162$	−0.480650	+	3.03470i	−0.0377634	+	0.238429i
$163$	−3.42430	+	21.6202i	−0.268212	+	1.69342i	0.374430	+	0.927255i	$0.377838\pi$
$163$	−3.42430	+	21.6202i	−0.268212	+	1.69342i	−0.642642	+	0.766167i	$0.722162\pi$
$164$	−0.526132	−	0.382258i	−0.0410840	−	0.0298493i
$165$	10.2661	+	4.76408i	0.799217	+	0.370883i
$166$	0.803058	+	1.10531i	0.0623294	+	0.0857891i
$167$	0.268470	+	0.526902i	0.0207748	+	0.0407729i	0.901161	−	0.433485i	$-0.142716\pi$
$167$	0.268470	+	0.526902i	0.0207748	+	0.0407729i	−0.880386	+	0.474258i	$0.842716\pi$
$168$	1.47240	−	1.47240i	0.113598	−	0.113598i
$169$	19.9605	+	6.48555i	1.53542	+	0.498889i
$170$	10.8556	+	3.09109i	0.832589	+	0.237075i
$171$	−3.07351	−	5.06722i	−0.235037	−	0.387500i
$172$	−2.48997	+	4.88685i	−0.189859	+	0.372619i
$173$	−2.03128	−	12.8250i	−0.154435	−	0.975065i	−0.936194	−	0.351484i	$-0.885677\pi$
$173$	−2.03128	−	12.8250i	−0.154435	−	0.975065i	0.781759	−	0.623581i	$-0.214323\pi$
$174$	−7.53318			−0.571089
$175$	−6.95241	+	4.21251i	−0.525553	+	0.318436i
$176$	−3.95186			−0.297882
$177$	−1.65062	−	10.4216i	−0.124068	−	0.783337i
$178$	8.87462	+	4.52185i	0.665181	+	0.338927i
$179$	2.79262	+	8.59481i	0.208730	+	0.642406i	0.999540	+	0.0303432i	$0.00966002\pi$
$179$	2.79262	+	8.59481i	0.208730	+	0.642406i	−0.790809	+	0.612063i	$0.790340\pi$
$180$	0.111721	+	3.03817i	0.00832721	+	0.226451i
$181$	−4.67655	−	1.51950i	−0.347605	−	0.112944i	0.130011	−	0.991513i	$-0.458499\pi$
$181$	−4.67655	−	1.51950i	−0.347605	−	0.112944i	−0.477616	+	0.878569i	$0.658499\pi$
$182$	6.70216	+	6.70216i	0.496797	+	0.496797i
$183$	4.85304	−	2.47275i	0.358747	−	0.182791i
$184$	−4.87047	+	3.53860i	−0.359056	+	0.260869i
$185$	−8.59085	+	4.78278i	−0.631612	+	0.351637i
$186$	4.92125	−	6.77352i	0.360843	−	0.496658i
$187$	19.7024	+	3.12056i	1.44079	+	0.228198i
$188$	0.884656	−	5.58550i	0.0645202	−	0.407364i
$189$	−7.34425	−	5.33591i	−0.534216	−	0.388130i
$190$	6.56535	+	7.20390i	0.476300	+	0.522626i
$191$	−0.845955	+	0.614623i	−0.0612112	+	0.0444725i	−0.617970	−	0.786202i	$-0.712045\pi$
$191$	−0.845955	+	0.614623i	−0.0612112	+	0.0444725i	0.556759	+	0.830674i	$0.312045\pi$
$192$	0.581458	+	1.14117i	0.0419631	+	0.0823572i
$193$	10.0513	+	10.0513i	0.723510	+	0.723510i	0.969318	−	0.245809i	$-0.0790535\pi$
$193$	10.0513	+	10.0513i	0.723510	+	0.723510i	−0.245809	+	0.969318i	$0.579054\pi$
$194$	−12.2575	−	3.98271i	−0.880039	−	0.285942i
$195$	16.6849	−	0.613547i	1.19483	−	0.0439370i
$196$	−1.34631	−	4.14351i	−0.0961650	−	0.295965i
$197$	−5.61004	+	11.0103i	−0.399699	+	0.784453i	−0.999881	−	0.0154103i	$-0.995095\pi$
$197$	−5.61004	+	11.0103i	−0.399699	+	0.784453i	0.600183	+	0.799863i	$0.295095\pi$
$198$	0.840531	+	5.30690i	0.0597339	+	0.377145i
$199$		−	4.14782i		−	0.294031i	−0.989134	−	0.147016i	$-0.953033\pi$
$199$		−	4.14782i		−	0.294031i	0.989134	−	0.147016i	$-0.0469668\pi$
$200$	−1.14277	−	4.86766i	−0.0808059	−	0.344195i
$201$	−13.6180			−0.960536
$202$	−8.76000	+	1.38745i	−0.616351	+	0.0976205i
$203$	4.34133	−	8.52034i	0.304702	−	0.598011i
$204$	−1.99780	−	6.14860i	−0.139874	−	0.430488i
$205$	0.398244	−	1.39860i	0.0278146	−	0.0976825i
$206$	3.22321	−	9.92003i	0.224572	−	0.691161i
$207$	5.78786	+	5.78786i	0.402284	+	0.402284i
$208$	−5.19448	+	2.64672i	−0.360172	+	0.183517i
$209$	13.0474	+	11.2468i	0.902510	+	0.777959i
$210$	4.22352	+	1.95996i	0.291451	+	0.135250i
$211$	−5.96913	+	8.21580i	−0.410932	+	0.565599i	−0.963445	−	0.267905i	$-0.913669\pi$
$211$	−5.96913	+	8.21580i	−0.410932	+	0.565599i	0.552514	+	0.833504i	$0.313669\pi$
$212$	−0.812081	+	5.12728i	−0.0557740	+	0.352143i
$213$	−1.70711	+	10.7783i	−0.116969	+	0.738514i
$214$	−11.2543	+	15.4902i	−0.769326	+	1.05889i
$215$	−12.1753	−	1.47209i	−0.830352	−	0.100396i
$216$	4.51729	−	3.28201i	0.307363	−	0.223312i
$217$	4.82504	+	9.46968i	0.327545	+	0.642844i
$218$	4.07150	−	4.07150i	0.275757	−	0.275757i
$219$	5.93965	−	18.2804i	0.401364	−	1.23527i
$220$	−3.03765	−	8.29810i	−0.204799	−	0.559458i
$221$	27.9876	−	9.09373i	1.88265	−	0.611711i
$222$	5.01800	+	2.55680i	0.336786	+	0.171601i
$223$	1.14372	+	7.22117i	0.0765893	+	0.483566i	0.995932	+	0.0901080i	$0.0287212\pi$
$223$	1.14372	+	7.22117i	0.0765893	+	0.483566i	−0.919343	+	0.393458i	$0.871279\pi$
$224$	−1.62581			−0.108629
$225$	−6.29366	+	2.56992i	−0.419577	+	0.171328i
$226$	9.75005			0.648564
$227$	14.5896	−	2.31076i	0.968344	−	0.153371i	0.347823	−	0.937560i	$-0.386921\pi$
$227$	14.5896	−	2.31076i	0.968344	−	0.153371i	0.620521	+	0.784190i	$0.286921\pi$
$228$	1.32800	−	5.42250i	0.0879488	−	0.359114i
$229$	−0.348257	+	0.113156i	−0.0230135	+	0.00747754i	−0.320501	−	0.947248i	$-0.603851\pi$
$229$	−0.348257	+	0.113156i	−0.0230135	+	0.00747754i	0.297488	+	0.954726i	$0.403851\pi$
$230$	−11.1741	−	7.50700i	−0.736799	−	0.494997i
$231$	7.82615	+	2.54287i	0.514923	+	0.167309i
$232$	4.15903	+	4.15903i	0.273054	+	0.273054i
$233$	6.26989	+	12.3054i	0.410754	+	0.806151i	0.999998	−	0.00180440i	$-0.000574360\pi$
$233$	6.26989	+	12.3054i	0.410754	+	0.806151i	−0.589244	+	0.807955i	$0.700574\pi$
$234$	4.65907	+	6.41266i	0.304573	+	0.419209i
$235$	12.4084	−	2.43578i	0.809436	−	0.158893i
$236$	−4.84242	+	6.66502i	−0.315215	+	0.433856i
$237$	−4.38318	−	0.694228i	−0.284718	−	0.0450949i
$238$	8.10565	+	1.28381i	0.525411	+	0.0832170i
$239$	14.4063	−	19.8286i	0.931865	−	1.28260i	−0.0272623	−	0.999628i	$-0.508679\pi$
$239$	14.4063	−	19.8286i	0.931865	−	1.28260i	0.959128	−	0.282974i	$-0.0913211\pi$
$240$	−1.94929	+	2.09812i	−0.125826	+	0.135433i
$241$	4.03278	+	5.55065i	0.259775	+	0.357549i	0.918904	−	0.394480i	$-0.129075\pi$
$241$	4.03278	+	5.55065i	0.259775	+	0.357549i	−0.659130	+	0.752029i	$0.729075\pi$
$242$	−2.09615	−	4.11393i	−0.134746	−	0.264454i
$243$	−9.06216	−	9.06216i	−0.581338	−	0.581338i
$244$	−4.04453	−	1.31415i	−0.258924	−	0.0841296i
$245$	7.66569	−	6.01195i	0.489743	−	0.384090i
$246$	−0.792164	+	0.257390i	−0.0505065	+	0.0164106i
$247$	24.6825	+	6.04487i	1.57051	+	0.384626i
$248$	−6.45662	+	1.02263i	−0.409996	+	0.0649369i
$249$	1.74985			0.110892
$250$	9.34269	−	6.14118i	0.590884	−	0.388402i
$251$	−3.11876			−0.196854			−0.0984271	−	0.995144i	$-0.531381\pi$
$251$	−3.11876			−0.196854			−0.0984271	+	0.995144i	$0.531381\pi$
$252$	0.345797	+	2.18328i	0.0217832	+	0.137534i
$253$	−21.1980	−	10.8009i	−1.33271	−	0.679048i
$254$	−3.96587	+	1.28859i	−0.248841	+	0.0808534i
$255$	11.3752	−	8.92120i	0.712342	−	0.558667i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.29633	+	2.29633i	−0.143241	+	0.143241i	−0.775091	−	0.631850i	$-0.782296\pi$
$257$	−2.29633	+	2.29633i	−0.143241	+	0.143241i	0.631850	+	0.775091i	$0.282296\pi$
$258$	3.18908	+	6.25893i	0.198544	+	0.389664i
$259$	−5.78369	+	4.20210i	−0.359381	+	0.261106i
$260$	−9.55039	−	8.87291i	−0.592290	−	0.550275i
$261$	4.70052	−	6.46971i	0.290955	−	0.400465i
$262$	2.45713	−	15.5137i	0.151802	−	0.958440i
$263$	−1.65501	+	10.4493i	−0.102052	+	0.644331i	0.882643	+	0.470044i	$0.155762\pi$
$263$	−1.65501	+	10.4493i	−0.102052	+	0.644331i	−0.984695	+	0.174287i	$0.944238\pi$
$264$	−2.97503	+	4.09478i	−0.183100	+	0.252016i
$265$	−11.3905	+	2.23595i	−0.699711	+	0.137354i
$266$	5.36776	+	4.62698i	0.329118	+	0.283698i
$267$	11.3664	−	5.79145i	0.695610	−	0.354431i
$268$	7.51840	+	7.51840i	0.459259	+	0.459259i
$269$	−8.72615	+	26.8563i	−0.532043	+	1.63746i	0.217911	+	0.975969i	$0.430076\pi$
$269$	−8.72615	+	26.8563i	−0.532043	+	1.63746i	−0.749954	+	0.661490i	$0.769924\pi$
$270$	10.3638	+	6.96264i	0.630723	+	0.423733i
$271$	5.78323	+	17.7990i	0.351306	+	1.08121i	0.958120	+	0.286366i	$0.0924472\pi$
$271$	5.78323	+	17.7990i	0.351306	+	1.08121i	−0.606814	+	0.794844i	$0.707553\pi$
$272$	−2.29164	+	4.49759i	−0.138951	+	0.272706i
$273$	11.9901	−	1.89904i	0.725671	−	0.114935i
$274$	14.8380			0.896398
$275$	15.0894	−	12.7569i	0.909926	−	0.769272i
$276$			7.71053i			0.464119i
$277$	−2.18543	−	13.7982i	−0.131310	−	0.829056i	−0.962145	−	0.272538i	$-0.912137\pi$
$277$	−2.18543	−	13.7982i	−0.131310	−	0.829056i	0.830836	−	0.556518i	$-0.187863\pi$
$278$	2.30096	−	4.51589i	0.138002	−	0.270845i
$279$	2.74655	+	8.45301i	0.164432	+	0.506068i
$280$	−1.24970	−	3.41387i	−0.0746840	−	0.204018i
$281$	11.9606	+	3.88624i	0.713511	+	0.231834i	0.643207	−	0.765692i	$-0.277603\pi$
$281$	11.9606	+	3.88624i	0.713511	+	0.231834i	0.0703032	+	0.997526i	$0.477603\pi$
$282$	−5.12151	−	5.12151i	−0.304982	−	0.304982i
$283$	−9.23009	−	18.1151i	−0.548672	−	1.07683i	−0.984267	−	0.176687i	$-0.943462\pi$
$283$	−9.23009	−	18.1151i	−0.548672	−	1.07683i	0.435595	−	0.900143i	$-0.356538\pi$
$284$	6.89311	−	5.00814i	0.409031	−	0.297178i
$285$	12.4069	−	1.37956i	0.734924	−	0.0817180i
$286$	−18.6389	−	13.5419i	−1.10214	−	0.800751i
$287$	0.165401	−	1.04430i	0.00976333	−	0.0616432i
$288$	−1.34289	−	0.212693i	−0.0791304	−	0.0125330i
$289$	4.98437	−	6.86039i	0.293198	−	0.403552i
$290$	−5.53622	+	11.9300i	−0.325098	+	0.700555i
$291$	−13.3544	+	9.70257i	−0.782851	+	0.568775i
$292$	−13.3717	+	6.81325i	−0.782522	+	0.398715i
$293$	−0.612349	−	0.612349i	−0.0357738	−	0.0357738i	0.688994	−	0.724767i	$-0.258053\pi$
$293$	−0.612349	−	0.612349i	−0.0357738	−	0.0357738i	−0.724767	+	0.688994i	$0.758053\pi$
$294$	−5.30689	−	1.72431i	−0.309504	−	0.100564i
$295$	−17.7174	−	5.04494i	−1.03155	−	0.293728i
$296$	−1.35882	−	4.18201i	−0.0789796	−	0.243074i
$297$	19.6609	+	10.0177i	1.14084	+	0.581287i
$298$	0.538438	+	3.39956i	0.0311909	+	0.196931i
$299$	−35.0973			−2.02973
$300$	−5.90399	−	2.48036i	−0.340867	−	0.143204i
$301$	−8.91696			−0.513965
$302$	1.60726	+	10.1479i	0.0924876	+	0.583944i
$303$	−5.15706	+	10.1213i	−0.296265	+	0.581453i
$304$	−3.72692	+	2.26055i	−0.213753	+	0.129652i
$305$	−0.349444	−	9.50283i	−0.0200091	−	0.544130i
$306$	6.52717	+	2.12081i	0.373134	+	0.121238i
$307$	−10.1169	+	10.1169i	−0.577401	+	0.577401i	−0.934186	−	0.356785i	$-0.883873\pi$
$307$	−10.1169	+	10.1169i	−0.577401	+	0.577401i	0.356785	+	0.934186i	$0.383873\pi$
$308$	−2.91687	−	5.72468i	−0.166204	−	0.326194i
$309$	−7.85229	−	10.8078i	−0.446701	−	0.614832i
$310$	−7.11029	−	12.7715i	−0.403837	−	0.725375i
$311$	10.8555	+	7.88695i	0.615557	+	0.447228i	0.851367	−	0.524571i	$-0.175774\pi$
$311$	10.8555	+	7.88695i	0.615557	+	0.447228i	−0.235810	+	0.971799i	$0.575774\pi$
$312$	−1.16806	+	7.37483i	−0.0661283	+	0.417518i
$313$	1.56289	−	9.86771i	0.0883398	−	0.557756i	−0.903330	−	0.428947i	$-0.858885\pi$
$313$	1.56289	−	9.86771i	0.0883398	−	0.557756i	0.991669	−	0.128809i	$-0.0411153\pi$
$314$	−10.8377	−	7.87406i	−0.611608	−	0.444359i
$315$	−4.31864	+	2.40431i	−0.243328	+	0.135468i
$316$	2.03665	+	2.80321i	0.114571	+	0.157693i
$317$	−13.5415	−	26.5768i	−0.760568	−	1.49270i	−0.866961	−	0.498375i	$-0.833930\pi$
$317$	−13.5415	−	26.5768i	−0.760568	−	1.49270i	0.106393	−	0.994324i	$-0.466070\pi$
$318$	4.70136	+	4.70136i	0.263639	+	0.263639i
$319$	−7.18275	+	22.1062i	−0.402157	+	1.23771i
$320$	2.23456	−	0.0821705i	0.124916	−	0.00459347i
$321$	7.57796	+	23.3226i	0.422960	+	1.30174i
$322$	−8.72094	−	4.44354i	−0.485999	−	0.247629i
$323$	20.3660	−	8.32732i	1.13319	−	0.463344i
$324$		−	3.07253i		−	0.170696i
$325$	11.2903	−	26.8742i	0.626272	−	1.49071i
$326$		−	21.8897i		−	1.21236i
$327$	−1.15365	−	7.28385i	−0.0637969	−	0.402798i
$328$	0.579453	+	0.295246i	0.0319949	+	0.0163022i
$329$	8.74415	−	2.84115i	0.482080	−	0.156637i
$330$	−10.8850	−	3.09945i	−0.599200	−	0.170619i
$331$	8.00304	+	2.60034i	0.439887	+	0.142928i	0.520583	−	0.853811i	$-0.325714\pi$
$331$	8.00304	+	2.60034i	0.439887	+	0.142928i	−0.0806966	+	0.996739i	$0.525714\pi$
$332$	−0.966081	−	0.966081i	−0.0530206	−	0.0530206i
$333$	−5.32695	+	2.71422i	−0.291915	+	0.148738i
$334$	−0.347590	−	0.478417i	−0.0190193	−	0.0261778i
$335$	−10.0080	+	21.5663i	−0.546795	+	1.17829i
$336$	−1.22394	+	1.68460i	−0.0667712	+	0.0919027i
$337$	−3.69643	+	23.3383i	−0.201357	+	1.27132i	0.655274	+	0.755391i	$0.272553\pi$
$337$	−3.69643	+	23.3383i	−0.201357	+	1.27132i	−0.856632	+	0.515929i	$0.827447\pi$
$338$	−20.7293	−	3.28320i	−1.12753	−	0.178582i
$339$	7.34001	−	10.1027i	0.398655	−	0.548701i
$340$	−11.2055	−	1.35483i	−0.607705	−	0.0734762i
$341$	−15.1847	−	20.8999i	−0.822295	−	1.13179i
$342$	3.82836	+	4.52403i	0.207014	+	0.244631i
$343$	13.0559	−	13.0559i	0.704955	−	0.704955i
$344$	1.69485	−	5.21620i	0.0913800	−	0.281239i
$345$	−16.1906	+	5.92682i	−0.871671	+	0.319089i
$346$	4.01254	+	12.3493i	0.215715	+	0.663903i
$347$	12.5003	−	24.5333i	0.671053	−	1.31702i	−0.264690	−	0.964334i	$-0.585270\pi$
$347$	12.5003	−	24.5333i	0.671053	−	1.31702i	0.935743	−	0.352682i	$-0.114730\pi$
$348$	7.44043	−	1.17845i	0.398849	−	0.0631715i
$349$			31.7503i			1.69955i	0.527144	+	0.849776i	$0.323263\pi$
$349$			31.7503i			1.69955i	−0.527144	+	0.849776i	$0.676737\pi$
$350$	6.20783	−	5.24824i	0.331823	−	0.280530i
$351$	32.5523			1.73751
$352$	3.90320	−	0.618207i	0.208041	−	0.0329505i
$353$	−32.7613	−	16.6927i	−1.74371	−	0.888463i	−0.965479	−	0.260482i	$-0.916119\pi$
$353$	−32.7613	−	16.6927i	−1.74371	−	0.888463i	−0.778228	−	0.627981i	$-0.783881\pi$
$354$	3.26060	+	10.0351i	0.173299	+	0.533359i
$355$	15.8146	+	10.6246i	0.839350	+	0.563893i
$356$	−9.47273	−	3.07788i	−0.502054	−	0.163127i
$357$	7.43232	−	7.43232i	0.393360	−	0.393360i
$358$	−4.10276	−	8.05213i	−0.216838	−	0.425568i
$359$	19.5172	+	26.8631i	1.03008	+	1.41778i	0.904888	+	0.425649i	$0.139954\pi$
$359$	19.5172	+	26.8631i	1.03008	+	1.41778i	0.125191	+	0.992133i	$0.460046\pi$
$360$	−0.585620	−	2.98328i	−0.0308649	−	0.157233i
$361$	18.7382	+	3.14321i	0.986221	+	0.165432i
$362$	4.85667	+	0.769221i	0.255261	+	0.0404294i
$363$	−5.84073	−	0.925081i	−0.306559	−	0.0485542i
$364$	−7.66810	−	5.57120i	−0.401918	−	0.292010i
$365$	−24.5848	−	22.8409i	−1.28683	−	1.19555i
$366$	−4.40646	+	3.20148i	−0.230330	+	0.167344i
$367$	−9.11543	+	4.64455i	−0.475822	+	0.242443i	−0.675418	−	0.737435i	$-0.736037\pi$
$367$	−9.11543	+	4.64455i	−0.475822	+	0.242443i	0.199596	+	0.979878i	$0.436037\pi$
$368$	4.25695	−	4.25695i	0.221909	−	0.221909i
$369$	0.273237	−	0.840937i	0.0142242	−	0.0437774i
$370$	7.73689	−	6.06780i	0.402222	−	0.315450i
$371$	−8.02680	+	2.60807i	−0.416731	+	0.135404i
$372$	−3.80105	+	7.45997i	−0.197075	+	0.386782i
$373$	5.19259	+	32.7847i	0.268862	+	1.69753i	0.639532	+	0.768765i	$0.279128\pi$
$373$	5.19259	+	32.7847i	0.268862	+	1.69753i	−0.370669	+	0.928765i	$0.620872\pi$
$374$	−19.9480			−1.03149
$375$	0.670071	−	14.3038i	0.0346023	−	0.738643i
$376$			5.65512i			0.291641i
$377$	5.36414	+	33.8679i	0.276267	+	1.74428i
$378$	8.08855	+	4.12132i	0.416030	+	0.211978i
$379$	4.92074	+	15.1445i	0.252761	+	0.777919i	0.994263	+	0.106968i	$0.0341141\pi$
$379$	4.92074	+	15.1445i	0.252761	+	0.777919i	−0.741501	+	0.670951i	$0.765886\pi$
$380$	−7.61146	−	6.08816i	−0.390459	−	0.312316i
$381$	−1.65039	+	5.07937i	−0.0845520	+	0.260224i
$382$	0.739392	−	0.739392i	0.0378306	−	0.0378306i
$383$	11.5278	−	5.87372i	0.589045	−	0.300133i	−0.133949	−	0.990988i	$-0.542766\pi$
$383$	11.5278	−	5.87372i	0.589045	−	0.300133i	0.722993	+	0.690855i	$0.242766\pi$
$384$	−0.752818	−	1.03617i	−0.0384171	−	0.0528766i
$385$	9.77858	−	10.5252i	0.498363	−	0.536414i
$386$	−11.4999	−	8.35519i	−0.585331	−	0.425268i
$387$	−7.36525	−	1.16654i	−0.374397	−	0.0592986i
$388$	12.7297	+	2.01618i	0.646250	+	0.102356i
$389$	−15.5086	+	21.3457i	−0.786316	+	1.08227i	0.208241	+	0.978077i	$0.433226\pi$
$389$	−15.5086	+	21.3457i	−0.786316	+	1.08227i	−0.994557	+	0.104193i	$0.966774\pi$
$390$	−16.3835	+	3.21609i	−0.829611	+	0.162853i
$391$	−24.5850	+	17.8620i	−1.24332	+	0.903321i
$392$	1.97792	+	3.88189i	0.0999002	+	0.196065i
$393$	−14.2250	−	14.2250i	−0.717556	−	0.717556i
$394$	3.81858	−	11.7524i	0.192377	−	0.592076i
$395$	−4.32068	+	6.43129i	−0.217397	+	0.323593i
$396$	−1.66036	−	5.11008i	−0.0834365	−	0.256791i
$397$	8.01699	−	15.7342i	0.402361	−	0.789679i	−0.597565	−	0.801821i	$-0.703865\pi$
$397$	8.01699	−	15.7342i	0.402361	−	0.789679i	0.999926	+	0.0121419i	$0.00386497\pi$
$398$	0.648862	+	4.09676i	0.0325245	+	0.205352i
$399$	8.83526	−	2.07861i	0.442316	−	0.104061i
$400$	1.89017	+	4.62896i	0.0945084	+	0.231448i
$401$			0.995104i			0.0496931i	0.999691	+	0.0248466i	$0.00790972\pi$
$401$			0.995104i			0.0496931i	−0.999691	+	0.0248466i	$0.992090\pi$
$402$	13.4503	−	2.13032i	0.670840	−	0.106251i
$403$	−33.9568	−	17.3019i	−1.69151	−	0.861867i
$404$	8.43510	−	2.74073i	0.419662	−	0.136356i
$405$	6.45170	−	2.36175i	0.320587	−	0.117356i
$406$	−2.95501	+	9.09458i	−0.146655	+	0.451356i
$407$	12.2875	−	12.2875i	0.609070	−	0.609070i
$408$	2.93506	+	5.76038i	0.145307	+	0.285181i
$409$	10.2137	−	7.42072i	0.505037	−	0.366931i	−0.305900	−	0.952064i	$-0.598957\pi$
$409$	10.2137	−	7.42072i	0.505037	−	0.366931i	0.810938	+	0.585132i	$0.198957\pi$
$410$	−0.174552	+	1.44368i	−0.00862051	+	0.0712983i
$411$	11.1703	−	15.3746i	0.550992	−	0.758375i
$412$	−1.63170	+	10.3021i	−0.0803878	+	0.507549i
$413$	−13.2292	−	2.09530i	−0.650966	−	0.103103i
$414$	−6.62202	−	4.81118i	−0.325455	−	0.236457i
$415$	1.28598	−	2.77117i	0.0631264	−	0.136031i
$416$	4.71649	−	3.42673i	0.231245	−	0.168009i
$417$	−2.94700	−	5.78382i	−0.144315	−	0.283235i
$418$	−14.6462	−	9.06728i	−0.716368	−	0.443495i
$419$	5.91233	+	1.92103i	0.288836	+	0.0938486i	0.449852	−	0.893103i	$-0.351477\pi$
$419$	5.91233	+	1.92103i	0.288836	+	0.0938486i	−0.161015	+	0.986952i	$0.551477\pi$
$420$	−4.47813	−	1.27512i	−0.218510	−	0.0622197i
$421$	32.4538	−	10.5449i	1.58170	−	0.513926i	0.619206	−	0.785228i	$-0.287454\pi$
$421$	32.4538	−	10.5449i	1.58170	−	0.513926i	0.962494	+	0.271303i	$0.0874545\pi$
$422$	4.61040	−	9.04843i	0.224431	−	0.440471i
$423$	7.59419	−	1.20280i	0.369242	−	0.0584822i
$424$		−	5.19119i		−	0.252107i
$425$	−5.76842	−	24.5708i	−0.279810	−	1.19186i
$426$		−	10.9126i		−	0.528718i
$427$	−1.08159	−	6.82890i	−0.0523418	−	0.330473i
$428$	8.69251	−	17.0600i	0.420168	−	0.824627i
$429$	−28.0634	+	9.11834i	−1.35491	+	0.440238i
$430$	12.2557	−	0.450675i	0.591024	−	0.0217335i
$431$	−35.2618	−	11.4573i	−1.69850	−	0.551877i	−0.710148	−	0.704052i	$-0.751372\pi$
$431$	−35.2618	−	11.4573i	−1.69850	−	0.551877i	−0.988353	+	0.152176i	$0.951372\pi$
$432$	−3.94826	+	3.94826i	−0.189961	+	0.189961i
$433$	−17.6896	+	9.01333i	−0.850110	+	0.433153i	−0.824056	−	0.566508i	$-0.808294\pi$
$433$	−17.6896	+	9.01333i	−0.850110	+	0.433153i	−0.0260538	+	0.999661i	$0.508294\pi$
$434$	−6.24702	−	8.59829i	−0.299867	−	0.412731i
$435$	8.19371	+	14.7176i	0.392858	+	0.705654i
$436$	−3.38445	+	4.65830i	−0.162086	+	0.223092i
$437$	−26.1698	+	1.93962i	−1.25187	+	0.0927847i
$438$	−3.00685	+	18.9845i	−0.143673	+	0.907113i
$439$	−21.5563	−	15.6616i	−1.02883	−	0.747486i	−0.0607532	−	0.998153i	$-0.519350\pi$
$439$	−21.5563	−	15.6616i	−1.02883	−	0.747486i	−0.968074	+	0.250667i	$0.919350\pi$
$440$	4.29837	+	7.72075i	0.204917	+	0.368072i
$441$	4.79226	−	3.48178i	0.228203	−	0.165799i
$442$	−26.2205	+	13.3600i	−1.24718	+	0.635471i
$443$	−4.27525	+	4.27525i	−0.203123	+	0.203123i	−0.801337	−	0.598213i	$-0.795877\pi$
$443$	−4.27525	+	4.27525i	−0.203123	+	0.203123i	0.598213	+	0.801337i	$0.295877\pi$
$444$	−5.35619	−	1.74033i	−0.254193	−	0.0825925i
$445$	−0.818436	−	22.2567i	−0.0387976	−	1.05507i
$446$	−2.25928	−	6.95335i	−0.106980	−	0.329251i
$447$	3.92785	+	2.00134i	0.185781	+	0.0946602i
$448$	1.60579	−	0.254332i	0.0758665	−	0.0120161i
$449$	−22.0348			−1.03989			−0.519943	−	0.854201i	$-0.674047\pi$
$449$	−22.0348			−1.03989			−0.519943	+	0.854201i	$0.674047\pi$
$450$	5.81415	−	3.52283i	0.274082	−	0.166068i
$451$			2.57003i			0.121018i
$452$	−9.63001	+	1.52524i	−0.452958	+	0.0717414i
$453$	11.7248	+	5.97410i	0.550881	+	0.280688i
$454$	−14.0485	+	4.56462i	−0.659327	+	0.214228i
$455$	5.80420	−	20.3838i	0.272105	−	0.955609i
$456$	−0.463382	+	5.56348i	−0.0216999	+	0.260534i
$457$	24.0728	+	24.0728i	1.12608	+	1.12608i	0.990809	+	0.135271i	$0.0431906\pi$
$457$	24.0728	+	24.0728i	1.12608	+	1.12608i	0.135271	+	0.990809i	$0.456809\pi$
$458$	0.326268	−	0.166242i	0.0152455	−	0.00776798i
$459$	22.8022	−	16.5668i	1.06432	−	0.773271i
$460$	12.2109	+	5.66656i	0.569336	+	0.264205i
$461$	−2.17094	−	1.57728i	−0.101111	−	0.0734614i	0.536081	−	0.844167i	$-0.319904\pi$
$461$	−2.17094	−	1.57728i	−0.101111	−	0.0734614i	−0.637192	+	0.770705i	$0.719904\pi$
$462$	−8.12759	−	1.28728i	−0.378130	−	0.0598898i
$463$	−3.49936	+	22.0941i	−0.162629	+	1.02680i	0.762456	+	0.647040i	$0.223993\pi$
$463$	−3.49936	+	22.0941i	−0.162629	+	1.02680i	−0.925085	+	0.379759i	$0.876007\pi$
$464$	−4.75844	−	3.45721i	−0.220905	−	0.160497i
$465$	−18.5862	−	2.24721i	−0.861913	−	0.104212i
$466$	−8.11768	−	11.1730i	−0.376044	−	0.517581i
$467$	18.9124	−	9.63633i	0.875160	−	0.445916i	0.0421092	−	0.999113i	$-0.486592\pi$
$467$	18.9124	−	9.63633i	0.875160	−	0.445916i	0.833051	+	0.553197i	$0.186592\pi$
$468$	−5.60487	−	5.60487i	−0.259085	−	0.259085i
$469$	−5.34185	+	16.4405i	−0.246664	+	0.759153i
$470$	−11.8746	+	4.34689i	−0.547735	+	0.200507i
$471$	−16.3177	+	5.30193i	−0.751878	+	0.244300i
$472$	3.74017	−	7.34049i	0.172155	−	0.337873i
$473$	21.4076	−	3.39064i	0.984325	−	0.155902i
$474$	4.43782			0.203836
$475$	6.93325	−	20.6623i	0.318120	−	0.948051i
$476$	−8.20669			−0.376153
$477$	−6.97119	+	1.10413i	−0.319189	+	0.0505545i
$478$	−11.1271	+	21.8381i	−0.508940	+	0.998850i
$479$	17.2804	−	5.61476i	0.789564	−	0.256545i	0.113645	−	0.993521i	$-0.463747\pi$
$479$	17.2804	−	5.61476i	0.789564	−	0.256545i	0.675918	+	0.736977i	$0.263747\pi$
$480$	1.59707	−	2.37723i	0.0728961	−	0.108505i
$481$	7.92176	−	24.3807i	0.361201	−	1.11166i
$482$	−4.85145	−	4.85145i	−0.220977	−	0.220977i
$483$	−11.1695	+	5.69115i	−0.508231	+	0.258956i
$484$	2.71391	+	3.73537i	0.123359	+	0.169790i
$485$	5.55127	+	28.2795i	0.252070	+	1.28410i
$486$	10.3682	+	7.53296i	0.470312	+	0.341702i
$487$	1.78944	−	11.2981i	0.0810874	−	0.511966i	−0.913396	−	0.407072i	$-0.866550\pi$
$487$	1.78944	−	11.2981i	0.0810874	−	0.511966i	0.994483	−	0.104894i	$-0.0334502\pi$
$488$	4.20031	+	0.665264i	0.190139	+	0.0301151i
$489$	−22.6813	−	16.4789i	−1.02568	−	0.745203i
$490$	−6.63083	+	7.13711i	−0.299550	+	0.322422i
$491$	25.7131	−	18.6816i	1.16042	−	0.843091i	0.170585	−	0.985343i	$-0.445434\pi$
$491$	25.7131	−	18.6816i	1.16042	−	0.843091i	0.989830	+	0.142252i	$0.0454344\pi$
$492$	0.742146	−	0.378142i	0.0334585	−	0.0170480i
$493$	20.9938	+	20.9938i	0.945513	+	0.945513i
$494$	−25.3242	−	2.10925i	−1.13939	−	0.0948998i
$495$	9.45387	−	7.41437i	0.424920	−	0.333251i
$496$	6.21715	−	2.02008i	0.279158	−	0.0907041i
$497$	12.3426	+	6.28888i	0.553642	+	0.282095i
$498$	−1.72830	+	0.273736i	−0.0774471	+	0.0122664i
$499$			4.80232i			0.214981i	0.994206	+	0.107491i	$0.0342816\pi$
$499$			4.80232i			0.214981i	−0.994206	+	0.107491i	$0.965718\pi$
$500$	−8.26698	+	7.52709i	−0.369710	+	0.336622i
$501$	−0.757391			−0.0338377
$502$	3.08036	−	0.487881i	0.137483	−	0.0217752i
$503$	−11.9472	−	6.08738i	−0.532698	−	0.271423i	0.166883	−	0.985977i	$-0.446630\pi$
$503$	−11.9472	−	6.08738i	−0.532698	−	0.271423i	−0.699581	+	0.714554i	$0.746630\pi$
$504$	−0.683080	−	2.10230i	−0.0304268	−	0.0936440i
$505$	12.2388	+	15.6053i	0.544617	+	0.694427i
$506$	22.6267	+	7.35185i	1.00588	+	0.326830i
$507$	−19.0073	+	19.0073i	−0.844145	+	0.844145i
$508$	3.71547	−	1.89312i	0.164847	−	0.0839938i
$509$	−9.24371	+	6.71595i	−0.409720	+	0.297679i	−0.773488	−	0.633810i	$-0.781490\pi$
$509$	−9.24371	+	6.71595i	−0.409720	+	0.297679i	0.363768	+	0.931489i	$0.381490\pi$
$510$	−9.83956	+	10.5908i	−0.435703	+	0.468970i
$511$	−19.7394	−	14.3415i	−0.873220	−	0.634431i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	24.2721	−	1.79897i	1.07164	−	0.0794266i
$514$	1.90883	−	2.62728i	0.0841950	−	0.115884i
$515$	−22.8866	+	4.49265i	−1.00850	+	0.197970i
$516$	−4.12893	−	5.68299i	−0.181766	−	0.250180i
$517$	−19.9124	+	10.1459i	−0.875747	+	0.446215i
$518$	5.05513	−	5.05513i	0.222110	−	0.222110i
$519$	15.8166	+	5.13914i	0.694273	+	0.225583i
$520$	10.8208	+	7.26966i	0.474525	+	0.318796i
$521$	−0.244756	+	0.0795259i	−0.0107229	+	0.00348409i	−0.314374	−	0.949299i	$-0.601794\pi$
$521$	−0.244756	+	0.0795259i	−0.0107229	+	0.00348409i	0.303651	+	0.952783i	$0.401794\pi$
$522$	−3.63056	+	7.12538i	−0.158905	+	0.311869i
$523$	−1.05585	−	6.66640i	−0.0461693	−	0.291501i	0.953790	−	0.300472i	$-0.0971444\pi$
$523$	−1.05585	−	6.66640i	−0.0461693	−	0.291501i	−0.999960	+	0.00897117i	$0.997144\pi$
$524$			15.7071i			0.686168i
$525$	−0.764677	−	10.3833i	−0.0333732	−	0.453165i
$526$		−	10.5795i		−	0.461290i
$527$	−32.5915	+	5.16198i	−1.41971	+	0.224860i
$528$	2.29784	−	4.50976i	0.100001	−	0.196262i
$529$	12.5950	−	4.09236i	0.547609	−	0.177929i
$530$	10.9005	−	3.99029i	0.473485	−	0.173327i
$531$	−10.6530	−	3.46136i	−0.462299	−	0.150210i
$532$	−6.02549	−	3.73031i	−0.261238	−	0.161730i
$533$	1.72125	+	3.37815i	0.0745558	+	0.146324i
$534$	−10.3204	+	7.49823i	−0.446609	+	0.324480i
$535$	42.5042	+	5.13909i	1.83762	+	0.222182i
$536$	−8.60197	−	6.24970i	−0.371549	−	0.269946i
$537$	−11.4320	−	1.81065i	−0.493326	−	0.0781351i
$538$	4.41746	−	27.8907i	0.190450	−	1.20246i
$539$	−10.1200	+	13.9290i	−0.435901	+	0.599967i
$540$	−11.3254	−	5.25566i	−0.487369	−	0.226168i
$541$	4.22189	−	3.06738i	0.181513	−	0.131877i	−0.493318	−	0.869849i	$-0.664216\pi$
$541$	4.22189	−	3.06738i	0.181513	−	0.131877i	0.674832	+	0.737972i	$0.264216\pi$
$542$	−8.49640	−	16.6751i	−0.364952	−	0.716258i
$543$	4.45323	−	4.45323i	0.191106	−	0.191106i
$544$	1.55984	−	4.80071i	0.0668778	−	0.205829i
$545$	−12.3830	−	3.52600i	−0.530430	−	0.151037i
$546$	−11.5454	+	3.75132i	−0.494096	+	0.160541i
$547$	−38.4178	−	19.5748i	−1.64263	−	0.836960i	−0.997330	−	0.0730265i	$-0.976734\pi$
$547$	−38.4178	−	19.5748i	−1.64263	−	0.836960i	−0.645296	−	0.763933i	$-0.723266\pi$
$548$	−14.6553	+	2.32118i	−0.626045	+	0.0991558i
$549$		−	5.78204i		−	0.246772i
$550$	−12.9080	+	14.9604i	−0.550399	+	0.637912i
$551$	5.87137	+	24.9566i	0.250129	+	1.06319i
$552$	−1.20619	−	7.61560i	−0.0513390	−	0.324142i
$553$	−2.55749	+	5.01936i	−0.108756	+	0.213445i
$554$	4.31704	+	13.2865i	0.183413	+	0.564489i
$555$	−0.462770	−	12.5846i	−0.0196435	−	0.534189i
$556$	−1.56619	+	4.82024i	−0.0664213	+	0.204424i
$557$	30.4945	+	30.4945i	1.29209	+	1.29209i	0.933490	+	0.358603i	$0.116747\pi$
$557$	30.4945	+	30.4945i	1.29209	+	1.29209i	0.358603	+	0.933490i	$0.383253\pi$
$558$	−4.03508	−	7.91928i	−0.170818	−	0.335250i
$559$	25.8682	−	18.7944i	1.09411	−	0.794916i
$560$	1.76836	+	3.17634i	0.0747269	+	0.134225i
$561$	−15.0172	+	20.6695i	−0.634028	+	0.872665i
$562$	−12.4213	−	1.96734i	−0.523961	−	0.0829873i
$563$	−35.4473	−	5.61430i	−1.49393	−	0.236615i	−0.644615	−	0.764507i	$-0.722982\pi$
$563$	−35.4473	−	5.61430i	−1.49393	−	0.236615i	−0.849311	+	0.527892i	$0.822982\pi$
$564$	5.85964	+	4.25728i	0.246735	+	0.179264i
$565$	−10.6050	−	19.0487i	−0.446154	−	0.801384i
$566$	11.9503	+	16.4481i	0.502308	+	0.691367i
$567$	4.45089	−	2.26784i	0.186920	−	0.0952403i
$568$	−6.02480	+	6.02480i	−0.252795	+	0.252795i
$569$	−9.81893	+	30.2196i	−0.411631	+	1.26687i	0.503599	+	0.863938i	$0.332009\pi$
$569$	−9.81893	+	30.2196i	−0.411631	+	1.26687i	−0.915230	+	0.402932i	$0.867991\pi$
$570$	−12.0384	+	3.30345i	−0.504232	+	0.138366i
$571$	11.0959	+	34.1495i	0.464347	+	1.42911i	0.859802	+	0.510627i	$0.170587\pi$
$571$	11.0959	+	34.1495i	0.464347	+	1.42911i	−0.395455	+	0.918485i	$0.629413\pi$
$572$	20.5278	+	10.4594i	0.858311	+	0.437332i
$573$	−0.209505	−	1.32276i	−0.00875218	−	0.0552591i
$574$			1.05732i			0.0441317i
$575$	−2.51255	+	29.9961i	−0.104781	+	1.25092i
$576$	1.35963			0.0566511
$577$	−4.81135	−	30.3777i	−0.200299	−	1.26464i	−0.858898	−	0.512146i	$-0.828851\pi$
$577$	−4.81135	−	30.3777i	−0.200299	−	1.26464i	0.658599	−	0.752494i	$-0.271149\pi$
$578$	−3.84980	+	7.55566i	−0.160131	+	0.314274i
$579$	−17.3147	+	5.62589i	−0.719575	+	0.233804i
$580$	3.60180	−	12.6492i	0.149556	−	0.525230i
$581$	0.686404	−	2.11253i	0.0284768	−	0.0876427i
$582$	11.6722	−	11.6722i	0.483829	−	0.483829i
$583$	18.2789	−	9.31354i	0.757033	−	0.385728i
$584$	12.1413	−	8.82117i	0.502410	−	0.365022i
$585$	7.46083	−	16.0774i	0.308467	−	0.664717i
$586$	0.700603	+	0.509018i	0.0289416	+	0.0210273i
$587$	−9.93070	−	1.57287i	−0.409884	−	0.0649192i	−0.0519122	−	0.998652i	$-0.516532\pi$
$587$	−9.93070	−	1.57287i	−0.409884	−	0.0649192i	−0.357972	+	0.933732i	$0.616532\pi$
$588$	5.51130	+	0.872904i	0.227282	+	0.0359979i
$589$	−26.2756	−	11.0243i	−1.08267	−	0.454248i
$590$	18.2885	+	2.21122i	0.752925	+	0.0910344i
$591$	−9.30270	−	12.8041i	−0.382662	−	0.526689i
$592$	1.99630	+	3.91795i	0.0820473	+	0.161027i
$593$	2.02125	−	2.02125i	0.0830029	−	0.0830029i	−0.664386	−	0.747389i	$-0.731307\pi$
$593$	2.02125	−	2.02125i	0.0830029	−	0.0830029i	0.747389	+	0.664386i	$0.231307\pi$
$594$	−20.9859	−	6.81874i	−0.861063	−	0.279776i
$595$	−6.30820	−	17.2324i	−0.258611	−	0.706459i
$596$	−1.06362	−	3.27348i	−0.0435675	−	0.134087i
$597$	4.73339	+	2.41178i	0.193725	+	0.0987077i
$598$	34.6652	−	5.49043i	1.41757	−	0.224520i
$599$	39.5741			1.61695			0.808476	−	0.588529i	$-0.200293\pi$
$599$	39.5741			1.61695			0.808476	+	0.588529i	$0.200293\pi$
$600$	6.21932	+	1.52624i	0.253903	+	0.0623084i
$601$			45.9510i			1.87438i	0.348820	+	0.937190i	$0.386582\pi$
$601$			45.9510i			1.87438i	−0.348820	+	0.937190i	$0.613418\pi$
$602$	8.80718	−	1.39492i	0.358954	−	0.0568527i
$603$	−6.56307	+	12.8808i	−0.267269	+	0.524545i
$604$	−3.17495	−	9.77149i	−0.129187	−	0.397596i
$605$	−5.75744	+	8.56991i	−0.234073	+	0.348416i
$606$	3.51025	−	10.8034i	0.142594	−	0.438859i
$607$	−6.19165	+	6.19165i	−0.251311	+	0.251311i	−0.821508	−	0.570197i	$-0.806867\pi$
$607$	−6.19165	+	6.19165i	−0.251311	+	0.251311i	0.570197	+	0.821508i	$0.306867\pi$
$608$	3.32740	−	2.81574i	0.134944	−	0.114193i
$609$	7.19890	+	9.90844i	0.291714	+	0.401510i
$610$	1.83171	+	9.33117i	0.0741638	+	0.377808i
$611$	−19.3786	+	26.6723i	−0.783972	+	1.07905i
$612$	−6.77858	−	1.07362i	−0.274008	−	0.0433986i
$613$	−0.369526	+	2.33310i	−0.0149250	+	0.0942329i	−0.994026	−	0.109140i	$-0.965190\pi$
$613$	−0.369526	+	2.33310i	−0.0149250	+	0.0942329i	0.979101	+	0.203373i	$0.0651904\pi$
$614$	8.40970	−	11.5750i	0.339388	−	0.467128i
$615$	1.36448	+	1.26769i	0.0550213	+	0.0511183i
$616$	3.77650	+	5.19790i	0.152159	+	0.209429i
$617$	−38.9380	+	19.8399i	−1.56758	+	0.798724i	−0.999703	−	0.0243859i	$-0.992237\pi$
$617$	−38.9380	+	19.8399i	−1.56758	+	0.798724i	−0.567882	+	0.823110i	$0.692237\pi$
$618$	9.44632	+	9.44632i	0.379987	+	0.379987i
$619$	7.85721	+	2.55296i	0.315808	+	0.102612i	0.462632	−	0.886550i	$-0.346905\pi$
$619$	7.85721	+	2.55296i	0.315808	+	0.102612i	−0.146824	+	0.989163i	$0.546905\pi$
$620$	9.02066	+	11.5020i	0.362278	+	0.461932i
$621$	−31.9698	+	10.3876i	−1.28290	+	0.416841i
$622$	−11.9556	−	6.09168i	−0.479376	−	0.244254i
$623$	−2.53321	−	15.9940i	−0.101491	−	0.640788i
$624$		−	7.46676i		−	0.298910i
$625$	−22.1599	−	11.5732i	−0.886396	−	0.462927i
$626$			9.99071i			0.399309i
$627$	−20.4211	+	8.34985i	−0.815541	+	0.333461i
$628$	11.9361	+	6.08173i	0.476301	+	0.242687i
$629$	−6.85898	−	21.1098i	−0.273485	−	0.841702i
$630$	3.88935	−	3.05030i	0.154956	−	0.121527i
$631$	5.71815	−	17.5987i	0.227636	−	0.700592i	−0.770377	−	0.637588i	$-0.779932\pi$
$631$	5.71815	−	17.5987i	0.227636	−	0.700592i	0.998013	−	0.0630035i	$-0.0200679\pi$
$632$	−2.45010	−	2.45010i	−0.0974596	−	0.0974596i
$633$	−5.90487	−	11.5890i	−0.234697	−	0.460620i
$634$	17.5323	+	24.1312i	0.696298	+	0.958372i
$635$	6.83113	+	6.34655i	0.271085	+	0.251855i
$636$	−5.37893	−	3.90802i	−0.213288	−	0.154963i
$637$	−3.97334	+	25.0867i	−0.157430	+	0.993971i
$638$	3.63614	−	22.9577i	0.143956	−	0.908904i
$639$	9.37206	+	6.80920i	0.370753	+	0.269368i
$640$	−2.19419	+	0.430721i	−0.0867331	+	0.0170257i
$641$	−27.6101	−	38.0020i	−1.09053	−	1.50099i	−0.847371	−	0.531002i	$-0.821816\pi$
$641$	−27.6101	−	38.0020i	−1.09053	−	1.50099i	−0.243161	−	0.969986i	$-0.578184\pi$
$642$	−11.1331	−	21.8500i	−0.439389	−	0.862349i
$643$	15.9706	−	15.9706i	0.629818	−	0.629818i	−0.318204	−	0.948022i	$-0.603080\pi$
$643$	15.9706	−	15.9706i	0.629818	−	0.629818i	0.948022	+	0.318204i	$0.103080\pi$
$644$	9.30869	+	3.02458i	0.366814	+	0.119185i
$645$	8.75936	−	13.0382i	0.344900	−	0.513380i
$646$	−18.8126	+	11.4107i	−0.740171	+	0.448950i
$647$	16.4714	−	32.3270i	0.647558	−	1.27090i	−0.300795	−	0.953689i	$-0.597252\pi$
$647$	16.4714	−	32.3270i	0.647558	−	1.27090i	0.948353	−	0.317216i	$-0.102748\pi$
$648$	0.480650	+	3.03470i	0.0188817	+	0.119214i
$649$	32.5571			1.27798
$650$	−6.94723	+	28.3095i	−0.272493	+	1.11039i
$651$	−13.6121			−0.533501
$652$	3.42430	+	21.6202i	0.134106	+	0.846711i
$653$	17.6559	+	8.99614i	0.690929	+	0.352046i	0.763942	−	0.645285i	$-0.223261\pi$
$653$	17.6559	+	8.99614i	0.690929	+	0.352046i	−0.0730126	+	0.997331i	$0.523261\pi$
$654$	2.27889	+	7.01370i	0.0891117	+	0.274257i
$655$	−32.9817	+	12.0735i	−1.28870	+	0.471750i
$656$	−0.618506	−	0.200965i	−0.0241486	−	0.00784635i
$657$	−14.4282	−	14.4282i	−0.562898	−	0.562898i
$658$	−8.19204	+	4.17405i	−0.319359	+	0.162721i
$659$	28.3111	−	20.5692i	1.10284	−	0.801264i	0.121323	−	0.992613i	$-0.461286\pi$
$659$	28.3111	−	20.5692i	1.10284	−	0.801264i	0.981522	+	0.191349i	$0.0612864\pi$
$660$	11.2359	+	1.35850i	0.437355	+	0.0528796i
$661$	17.4887	−	24.0712i	0.680232	−	0.936260i	−0.319704	−	0.947517i	$-0.603584\pi$
$661$	17.4887	−	24.0712i	0.680232	−	0.936260i	0.999937	+	0.0112579i	$0.00358356\pi$
$662$	−8.31129	−	1.31638i	−0.323028	−	0.0511625i
$663$	−5.89608	+	37.2264i	−0.228985	+	1.44575i
$664$	1.10531	+	0.803058i	0.0428945	+	0.0311647i
$665$	3.20132	−	15.5197i	0.124142	−	0.601827i
$666$	4.83677	−	3.51412i	0.187421	−	0.136169i
$667$	−16.0756	−	31.5501i	−0.622449	−	1.22163i
$668$	0.418152	+	0.418152i	0.0161788	+	0.0161788i
$669$	−8.90565	−	2.89362i	−0.344312	−	0.111874i
$670$	6.51107	−	22.8663i	0.251545	−	0.883404i
$671$	5.19332	+	15.9834i	0.200486	+	0.617032i
$672$	0.945338	−	1.85533i	0.0364672	−	0.0715709i
$673$	−0.688108	−	4.34454i	−0.0265246	−	0.167470i	0.970870	−	0.239606i	$-0.0770183\pi$
$673$	−0.688108	−	4.34454i	−0.0265246	−	0.167470i	−0.997395	+	0.0721364i	$0.977018\pi$
$674$		−	23.6292i		−	0.910164i
$675$	2.33036	−	27.8210i	0.0896956	−	1.07083i
$676$	20.9877			0.807219
$677$	8.02552	−	1.27112i	0.308446	−	0.0488530i	−0.000292712	−	1.00000i	$-0.500093\pi$
$677$	8.02552	−	1.27112i	0.308446	−	0.0488530i	0.308739	+	0.951147i	$0.400093\pi$
$678$	−5.66924	+	11.1265i	−0.217726	+	0.427311i
$679$	6.47513	+	19.9284i	0.248493	+	0.764781i
$680$	11.2795	−	0.414777i	0.432550	−	0.0159060i
$681$	−5.84623	+	17.9929i	−0.224028	+	0.689488i
$682$	18.2672	+	18.2672i	0.699486	+	0.699486i
$683$	44.5697	−	22.7094i	1.70541	−	0.868950i	0.721028	−	0.692906i	$-0.243670\pi$
$683$	44.5697	−	22.7094i	1.70541	−	0.868950i	0.984382	−	0.176044i	$-0.0563302\pi$
$684$	−4.48894	−	3.86944i	−0.171639	−	0.147952i
$685$	−16.1391	−	28.9891i	−0.616642	−	1.10762i
$686$	−10.8528	+	14.9376i	−0.414362	+	0.570320i
$687$	0.0733665	−	0.463218i	0.00279911	−	0.0176729i
$688$	−0.857986	+	5.41711i	−0.0327104	+	0.206525i
$689$	17.7888	−	24.4842i	0.677699	−	0.932773i
$690$	15.0641	−	8.38661i	0.573479	−	0.319273i
$691$	5.69017	−	4.13415i	0.216464	−	0.157270i	−0.474269	−	0.880380i	$-0.657288\pi$
$691$	5.69017	−	4.13415i	0.216464	−	0.157270i	0.690734	+	0.723109i	$0.257288\pi$
$692$	−5.89499	−	11.5696i	−0.224094	−	0.439809i
$693$	6.17697	−	6.17697i	0.234644	−	0.234644i
$694$	−8.50858	+	26.1867i	−0.322981	+	0.994034i
$695$	−11.3254	+	0.416465i	−0.429597	+	0.0157974i
$696$	−7.16448	+	2.32788i	−0.271569	+	0.0882381i
$697$	2.92494	+	1.49033i	0.110790	+	0.0564504i
$698$	−4.96683	−	31.3594i	−0.187997	−	1.18697i
$699$	−17.6882			−0.669031
$700$	−5.31040	+	6.15475i	−0.200714	+	0.232628i
$701$	30.0497			1.13496			0.567480	−	0.823387i	$-0.307918\pi$
$701$	30.0497			1.13496			0.567480	+	0.823387i	$0.307918\pi$
$702$	−32.1515	+	5.09230i	−1.21348	+	0.192196i
$703$	4.55937	−	18.6169i	0.171960	−	0.702148i
$704$	−3.75844	+	1.22119i	−0.141652	+	0.0460254i
$705$	−4.43532	+	15.5765i	−0.167044	+	0.586644i
$706$	34.9693	+	11.3622i	1.31609	+	0.427622i
$707$	10.1962	+	10.1962i	0.383467	+	0.383467i
$708$	−4.79029	−	9.40148i	−0.180030	−	0.353329i
$709$	17.4998	+	24.0864i	0.657219	+	0.904584i	0.999385	−	0.0350553i	$-0.0111608\pi$
$709$	17.4998	+	24.0864i	0.657219	+	0.904584i	−0.342167	+	0.939639i	$0.611161\pi$
$710$	−17.2819	−	8.01981i	−0.648578	−	0.300978i
$711$	−2.76909	+	3.81132i	−0.103849	+	0.142936i
$712$	9.83759	+	1.55812i	0.368679	+	0.0583931i
$713$	38.8703	+	6.15645i	1.45571	+	0.230561i
$714$	−6.17814	+	8.50349i	−0.231211	+	0.318235i
$715$	−6.18371	+	51.1441i	−0.231258	+	1.91268i
$716$	5.31188	+	7.31118i	0.198514	+	0.273232i
$717$	14.2512	+	27.9696i	0.532221	+	1.04454i
$718$	−23.4792	−	23.4792i	−0.876237	−	0.876237i
$719$	4.72934	+	1.53665i	0.176374	+	0.0573075i	0.395873	−	0.918305i	$-0.370442\pi$
$719$	4.72934	+	1.53665i	0.176374	+	0.0573075i	−0.219498	+	0.975613i	$0.570442\pi$
$720$	1.04510	+	2.85494i	0.0389485	+	0.106397i
$721$	−16.1281	+	5.24032i	−0.600640	+	0.195160i
$722$	−18.9992	−	0.173213i	−0.707077	−	0.00644631i
$723$	−8.67916	+	1.37464i	−0.322781	+	0.0511235i
$724$	−4.91721			−0.182747
$725$	29.3294	−	2.15995i	1.08926	−	0.0802186i
$726$	5.91354			0.219472
$727$	−2.48960	−	15.7187i	−0.0923340	−	0.582974i	−0.989864	−	0.142020i	$-0.954640\pi$
$727$	−2.48960	−	15.7187i	−0.0923340	−	0.582974i	0.897530	−	0.440954i	$-0.145360\pi$
$728$	8.44522	+	4.30305i	0.313001	+	0.159482i
$729$	24.3772	−	7.92064i	0.902860	−	0.293357i
$730$	27.8553	+	18.7137i	1.03097	+	0.692627i
$731$	8.55518	−	26.3301i	0.316425	−	0.973855i
$732$	3.85139	−	3.85139i	0.142352	−	0.142352i
$733$	−1.23290	−	2.41970i	−0.0455382	−	0.0893737i	0.867116	−	0.498106i	$-0.165971\pi$
$733$	−1.23290	−	2.41970i	−0.0455382	−	0.0893737i	−0.912654	+	0.408732i	$0.865971\pi$
$734$	8.27664	−	6.01333i	0.305496	−	0.221956i
$735$	2.40342	+	12.2436i	0.0886515	+	0.451611i
$736$	−3.53860	+	4.87047i	−0.130435	+	0.179528i
$737$	6.57316	−	41.5013i	0.242125	−	1.52872i
$738$	−0.138321	+	0.873328i	−0.00509168	+	0.0321476i
$739$	7.25842	−	9.99036i	0.267005	−	0.367501i	−0.654371	−	0.756174i	$-0.727066\pi$
$739$	7.25842	−	9.99036i	0.267005	−	0.367501i	0.921376	+	0.388673i	$0.127066\pi$
$740$	−6.69243	+	7.20341i	−0.246019	+	0.264803i
$741$	−21.2501	+	24.6522i	−0.780641	+	0.905621i
$742$	7.51999	−	3.83162i	0.276067	−	0.140663i
$743$	−18.5724	−	18.5724i	−0.681355	−	0.681355i	0.278951	−	0.960305i	$-0.410013\pi$
$743$	−18.5724	−	18.5724i	−0.681355	−	0.681355i	−0.960305	+	0.278951i	$0.910013\pi$
$744$	2.58725	−	7.96274i	0.0948533	−	0.291928i
$745$	6.05608	−	4.74959i	0.221878	−	0.174012i
$746$	−10.2573	−	31.5688i	−0.375547	−	1.15582i
$747$	0.843325	−	1.65512i	0.0308557	−	0.0605576i
$748$	19.7024	−	3.12056i	0.720393	−	0.114099i
$749$	31.1292			1.13744
$750$	1.57578	+	14.2325i	0.0575394	+	0.519697i
$751$			27.1680i			0.991373i	0.868502	+	0.495686i	$0.165083\pi$
$751$			27.1680i			0.991373i	−0.868502	+	0.495686i	$0.834917\pi$
$752$	−0.884656	−	5.58550i	−0.0322601	−	0.203682i
$753$	1.81342	−	3.55905i	0.0660848	−	0.129699i
$754$	−10.5962	−	32.6118i	−0.385891	−	1.18765i
$755$	18.0777	−	14.1778i	0.657915	−	0.515982i
$756$	−8.63368	−	2.80525i	−0.314004	−	0.102026i
$757$	−10.9784	−	10.9784i	−0.399015	−	0.399015i	0.478870	−	0.877886i	$-0.341046\pi$
$757$	−10.9784	−	10.9784i	−0.399015	−	0.399015i	−0.877886	+	0.478870i	$0.841046\pi$
$758$	−7.22927	−	14.1882i	−0.262579	−	0.515340i
$759$	24.6515	−	17.9104i	0.894792	−	0.650105i
$760$	8.47015	+	4.82251i	0.307244	+	0.174931i
$761$	4.78271	+	3.47484i	0.173373	+	0.125963i	0.671088	−	0.741378i	$-0.265827\pi$
$761$	4.78271	+	3.47484i	0.173373	+	0.125963i	−0.497715	+	0.867341i	$0.665827\pi$
$762$	0.835480	−	5.27502i	0.0302663	−	0.191094i
$763$	−9.24611	−	1.46444i	−0.334732	−	0.0530163i
$764$	−0.614623	+	0.845955i	−0.0222363	+	0.0306056i
$765$	−2.95607	−	15.0589i	−0.106877	−	0.544456i
$766$	−10.4671	+	7.60476i	−0.378190	+	0.274771i
$767$	42.7943	−	21.8048i	1.54521	−	0.787325i
$768$	0.905641	+	0.905641i	0.0326795	+	0.0326795i
$769$	−8.64333	−	2.80839i	−0.311686	−	0.101273i	0.148997	−	0.988838i	$-0.452396\pi$
$769$	−8.64333	−	2.80839i	−0.311686	−	0.101273i	−0.460683	+	0.887565i	$0.652396\pi$
$770$	−8.01168	+	11.9253i	−0.288721	+	0.429759i
$771$	−1.28530	−	3.95573i	−0.0462888	−	0.142462i
$772$	12.6654	+	6.45334i	0.455838	+	0.232261i
$773$	0.782536	+	4.94074i	0.0281458	+	0.177706i	0.997757	−	0.0669472i	$-0.0213259\pi$
$773$	0.782536	+	4.94074i	0.0281458	+	0.177706i	−0.969611	+	0.244653i	$0.921326\pi$
$774$	7.45706			0.268039
$775$	−17.2180	+	27.7828i	−0.618490	+	0.997986i
$776$	−12.8883			−0.462664
$777$	−1.43236	−	9.04354i	−0.0513855	−	0.324435i
$778$	11.9784	−	23.5090i	0.429447	−	0.842838i
$779$	1.47012	+	2.42374i	0.0526724	+	0.0868397i
$780$	15.6787	−	5.73944i	0.561387	−	0.205505i
$781$	−32.0232	−	10.4050i	−1.14588	−	0.372319i
$782$	21.4880	−	21.4880i	0.768411	−	0.768411i
$783$	14.9099	+	29.2623i	0.532836	+	1.04575i
$784$	−2.56083	−	3.52468i	−0.0914583	−	0.125882i
$785$	−3.59557	+	29.7381i	−0.128331	+	1.06140i
$786$	16.2751	+	11.8246i	0.580515	+	0.421769i
$787$	−1.81002	+	11.4280i	−0.0645201	+	0.407364i	0.934198	+	0.356754i	$0.116117\pi$
$787$	−1.81002	+	11.4280i	−0.0645201	+	0.407364i	−0.998718	+	0.0506101i	$0.983883\pi$
$788$	−1.93309	+	12.2050i	−0.0688634	+	0.434786i
$789$	−10.9622	−	7.96447i	−0.390263	−	0.283543i
$790$	3.26141	−	7.02801i	0.116036	−	0.250045i
$791$	−9.31740	−	12.8243i	−0.331289	−	0.455980i
$792$	2.43931	+	4.78742i	0.0866773	+	0.170114i
$793$	17.5310	+	17.5310i	0.622545	+	0.622545i
$794$	−5.45691	+	16.7947i	−0.193659	+	0.596020i
$795$	4.07146	−	14.2986i	0.144400	−	0.507120i
$796$	−1.28175	−	3.94481i	−0.0454303	−	0.139820i
$797$	−10.1228	−	5.15781i	−0.358567	−	0.182699i	0.265422	−	0.964132i	$-0.414489\pi$
$797$	−10.1228	−	5.15781i	−0.358567	−	0.182699i	−0.623989	+	0.781434i	$0.714489\pi$
$798$	−8.40132	+	3.43516i	−0.297403	+	0.121603i
$799$			28.5457i			1.00987i
$800$	−2.59103	−	4.27628i	−0.0916066	−	0.151189i
$801$		−	13.5422i		−	0.478490i
$802$	−0.155669	−	0.982853i	−0.00549685	−	0.0347057i
$803$	52.8432	+	26.9250i	1.86480	+	0.950162i
$804$	−12.9514	+	4.20818i	−0.456762	+	0.148411i
$805$	0.804263	+	21.8713i	0.0283465	+	0.770861i
$806$	36.2454	+	11.7768i	1.27669	+	0.414821i
$807$	−25.5739	−	25.5739i	−0.900243	−	0.900243i
$808$	−7.90251	+	4.02653i	−0.278009	+	0.141653i
$809$	0.369603	+	0.508715i	0.0129946	+	0.0178855i	0.815465	−	0.578807i	$-0.196481\pi$
$809$	0.369603	+	0.508715i	0.0129946	+	0.0178855i	−0.802470	+	0.596692i	$0.796481\pi$
$810$	−6.00281	+	3.34194i	−0.210917	+	0.117424i
$811$	15.9385	−	21.9375i	0.559678	−	0.770330i	−0.431608	−	0.902061i	$-0.642054\pi$
$811$	15.9385	−	21.9375i	0.559678	−	0.770330i	0.991285	+	0.131731i	$0.0420536\pi$
$812$	1.49592	−	9.44487i	0.0524965	−	0.331450i
$813$	−23.6744	−	3.74966i	−0.830298	−	0.131506i
$814$	−10.2141	+	14.0584i	−0.358002	+	0.492748i
$815$	−42.7658	+	23.8090i	−1.49802	+	0.833993i
$816$	−3.80005	−	5.23032i	−0.133028	−	0.183098i
$817$	18.2496	−	15.4433i	0.638472	−	0.540293i
$818$	−8.92714	+	8.92714i	−0.312130	+	0.312130i
$819$	3.98228	−	12.2562i	0.139152	−	0.428267i
$820$	−0.0534384	−	1.45321i	−0.00186615	−	0.0507484i
$821$	8.55061	+	26.3161i	0.298418	+	0.918437i	0.982052	+	0.188611i	$0.0603987\pi$
$821$	8.55061	+	26.3161i	0.298418	+	0.918437i	−0.683634	+	0.729825i	$0.739601\pi$
$822$	−8.62768	+	16.9328i	−0.300925	+	0.590599i
$823$	−28.2405	+	4.47285i	−0.984401	+	0.155914i	−0.627827	−	0.778353i	$-0.716055\pi$
$823$	−28.2405	+	4.47285i	−0.984401	+	0.155914i	−0.356574	+	0.934267i	$0.616055\pi$
$824$		−	10.4305i		−	0.363365i
$825$	5.78403	+	24.6373i	0.201374	+	0.857759i
$826$	13.3941			0.466040
$827$	20.9372	−	3.31613i	0.728058	−	0.115313i	0.218607	−	0.975813i	$-0.429849\pi$
$827$	20.9372	−	3.31613i	0.728058	−	0.115313i	0.509451	+	0.860500i	$0.329849\pi$
$828$	7.29313	+	3.71603i	0.253454	+	0.129141i
$829$	−0.908705	−	2.79671i	−0.0315606	−	0.0971336i	0.934035	−	0.357181i	$-0.116262\pi$
$829$	−0.908705	−	2.79671i	−0.0315606	−	0.0971336i	−0.965596	+	0.260047i	$0.916262\pi$
$830$	−0.836644	+	2.93822i	−0.0290403	+	0.101987i
$831$	17.0169	+	5.52914i	0.590311	+	0.191804i
$832$	−4.12236	+	4.12236i	−0.142917	+	0.142917i
$833$	9.98409	+	19.5949i	0.345928	+	0.678922i
$834$	3.81551	+	5.25159i	0.132120	+	0.181848i
$835$	−0.556616	+	1.19945i	−0.0192625	+	0.0415088i
$836$	15.8843	+	6.66448i	0.549370	+	0.230496i
$837$	−36.0517	−	5.71003i	−1.24613	−	0.197367i
$838$	−6.14006	−	0.972489i	−0.212105	−	0.0335941i
$839$	5.48852	+	3.98765i	0.189485	+	0.137669i	0.678483	−	0.734616i	$-0.262638\pi$
$839$	5.48852	+	3.98765i	0.189485	+	0.137669i	−0.488998	+	0.872285i	$0.662638\pi$
$840$	4.62247	+	0.558892i	0.159490	+	0.0192836i
$841$	−4.52649	+	3.28869i	−0.156086	+	0.113403i
$842$	−30.4046	+	15.4919i	−1.04781	+	0.533887i
$843$	−11.3895	+	11.3895i	−0.392274	+	0.392274i
$844$	−3.13816	+	9.65825i	−0.108020	+	0.332451i
$845$	16.1325	+	44.0699i	0.554975	+	1.51605i
$846$	−7.31254	+	2.37599i	−0.251410	+	0.0816881i
$847$	−3.40794	+	6.68846i	−0.117098	+	0.229818i
$848$	0.812081	+	5.12728i	0.0278870	+	0.176071i
$849$	26.0394			0.893669
$850$	9.54112	+	23.3659i	0.327258	+	0.801443i
$851$			26.4723i			0.907458i
$852$	1.70711	+	10.7783i	0.0584846	+	0.369257i
$853$	−21.4795	−	10.9443i	−0.735444	−	0.374727i	0.0458024	−	0.998951i	$-0.485416\pi$
$853$	−21.4795	−	10.9443i	−0.735444	−	0.374727i	−0.781246	+	0.624223i	$0.785416\pi$
$854$	2.13655	+	6.57562i	0.0731112	+	0.225013i
$855$	4.67456	−	12.4002i	0.159867	−	0.424077i
$856$	−5.91672	+	18.2098i	−0.202229	+	0.622398i
$857$	−3.70118	+	3.70118i	−0.126430	+	0.126430i	−0.767490	−	0.641061i	$-0.778495\pi$
$857$	−3.70118	+	3.70118i	−0.126430	+	0.126430i	0.641061	+	0.767490i	$0.278495\pi$
$858$	26.2914	−	13.3962i	0.897575	−	0.457337i
$859$	−17.3447	−	23.8730i	−0.591794	−	0.814535i	0.403132	−	0.915142i	$-0.367922\pi$
$859$	−17.3447	−	23.8730i	−0.591794	−	0.814535i	−0.994926	+	0.100607i	$0.967922\pi$
$860$	−12.0343	+	2.36235i	−0.410368	+	0.0805553i
$861$	1.09556	+	0.795970i	0.0373365	+	0.0271266i
$862$	36.6200	+	5.80004i	1.24728	+	0.197550i
$863$	10.8240	+	1.71435i	0.368453	+	0.0583571i	0.337915	−	0.941176i	$-0.390278\pi$
$863$	10.8240	+	1.71435i	0.368453	+	0.0583571i	0.0305371	+	0.999534i	$0.490278\pi$
$864$	3.28201	−	4.51729i	0.111656	−	0.153681i
$865$	19.7625	−	21.2714i	0.671945	−	0.723250i
$866$	16.0619	−	11.6696i	0.545804	−	0.396550i
$867$	4.93071	+	9.67706i	0.167456	+	0.328650i
$868$	7.51518	+	7.51518i	0.255082	+	0.255082i
$869$	4.23138	−	13.0228i	0.143540	−	0.441770i
$870$	−10.3952	−	13.2546i	−0.352429	−	0.449373i
$871$	−19.1551	−	58.9532i	−0.649045	−	1.99755i
$872$	2.61407	−	5.13039i	0.0885234	−	0.173737i
$873$	2.74125	+	17.3076i	0.0927773	+	0.585773i
$874$	25.5442	−	6.00960i	0.864045	−	0.203278i
$875$	−17.0056	−	6.41983i	−0.574896	−	0.217030i
$876$		−	19.2211i		−	0.649421i
$877$	20.3560	−	3.22407i	0.687374	−	0.108869i	0.197029	−	0.980398i	$-0.436871\pi$
$877$	20.3560	−	3.22407i	0.687374	−	0.108869i	0.490345	+	0.871528i	$0.336871\pi$
$878$	23.7409	+	12.0966i	0.801218	+	0.408241i
$879$	1.05485	−	0.342742i	0.0355793	−	0.0115604i
$880$	−5.45324	−	6.95328i	−0.183829	−	0.234395i
$881$	−8.72894	+	26.8649i	−0.294085	+	0.905102i	0.689442	+	0.724341i	$0.257856\pi$
$881$	−8.72894	+	26.8649i	−0.294085	+	0.905102i	−0.983527	+	0.180761i	$0.942144\pi$
$882$	−4.18859	+	4.18859i	−0.141037	+	0.141037i
$883$	0.812172	+	1.59398i	0.0273318	+	0.0536416i	0.904269	−	0.426964i	$-0.140417\pi$
$883$	0.812172	+	1.59398i	0.0273318	+	0.0536416i	−0.876937	+	0.480606i	$0.840417\pi$
$884$	23.8077	−	17.2973i	0.800740	−	0.581771i
$885$	16.0591	−	17.2852i	0.539820	−	0.581037i
$886$	3.55382	−	4.89141i	0.119393	−	0.164330i
$887$	−7.12019	+	44.9551i	−0.239073	+	1.50945i	0.517584	+	0.855633i	$0.326832\pi$
$887$	−7.12019	+	44.9551i	−0.239073	+	1.50945i	−0.756656	+	0.653813i	$0.773168\pi$
$888$	5.56249	+	0.881012i	0.186665	+	0.0295648i
$889$	5.48478	+	3.98493i	0.183954	+	0.133650i
$890$	4.29007	+	21.8546i	0.143804	+	0.732569i
$891$	−9.82325	+	7.13701i	−0.329091	+	0.239099i
$892$	3.31921	+	6.51432i	0.111135	+	0.218115i
$893$	−12.9753	+	20.9587i	−0.434202	+	0.701357i
$894$	−4.19257	−	1.36225i	−0.140221	−	0.0455604i
$895$	−11.2689	+	16.7737i	−0.376679	+	0.560684i
$896$	−1.54623	+	0.502402i	−0.0516561	+	0.0167841i
$897$	20.4076	−	40.0522i	0.681390	−	1.33730i
$898$	21.7635	−	3.44700i	0.726258	−	0.115028i
$899$		−	38.4496i		−	1.28237i
$900$	−5.19148	+	4.38899i	−0.173049	+	0.146300i
$901$		−	26.2039i		−	0.872978i
$902$	−0.402042	−	2.53839i	−0.0133865	−	0.0845192i
$903$	5.18484	−	10.1758i	0.172541	−	0.338630i
$904$	9.27285	−	3.01293i	0.308410	−	0.100209i
$905$	−3.77969	−	10.3252i	−0.125641	−	0.343220i
$906$	−12.5150	−	4.06638i	−0.415784	−	0.135097i
$907$	34.9869	−	34.9869i	1.16172	−	1.16172i	0.177623	−	0.984099i	$-0.443159\pi$
$907$	34.9869	−	34.9869i	1.16172	−	1.16172i	0.984099	−	0.177623i	$-0.0568407\pi$
$908$	13.1614	−	6.70609i	0.436778	−	0.222549i
$909$	7.08798	+	9.75577i	0.235094	+	0.323578i
$910$	−2.54400	+	21.0409i	−0.0843328	+	0.697498i
$911$	−11.8005	+	16.2420i	−0.390967	+	0.538120i	−0.958448	−	0.285266i	$-0.907918\pi$
$911$	−11.8005	+	16.2420i	−0.390967	+	0.538120i	0.567481	+	0.823386i	$0.307918\pi$
$912$	−0.412644	−	5.56748i	−0.0136640	−	0.184358i
$913$	−0.844621	+	5.33273i	−0.0279529	+	0.176488i
$914$	−27.5423	−	20.0106i	−0.911018	−	0.661893i
$915$	11.0476	+	5.12672i	0.365222	+	0.169484i
$916$	−0.296245	+	0.215235i	−0.00978822	+	0.00711156i
$917$	−22.7534	+	11.5934i	−0.751383	+	0.382849i
$918$	−19.9299	+	19.9299i	−0.657784	+	0.657784i
$919$	−14.9492	−	4.85729i	−0.493129	−	0.160227i	0.0518872	−	0.998653i	$-0.483476\pi$
$919$	−14.9492	−	4.85729i	−0.493129	−	0.160227i	−0.545016	+	0.838426i	$0.683476\pi$
$920$	−12.9470	−	3.68659i	−0.426850	−	0.121543i
$921$	−5.66260	−	17.4277i	−0.186589	−	0.574262i
$922$	2.39096	+	1.21825i	0.0787419	+	0.0401210i
$923$	−49.0612	+	7.77053i	−1.61487	+	0.255770i
$924$	8.22890			0.270711
$925$	−20.2700	−	8.51574i	−0.666472	−	0.279996i
$926$		−	22.3695i		−	0.735107i
$927$	−14.0070	+	2.21850i	−0.460052	+	0.0728650i
$928$	5.24068	+	2.67026i	0.172034	+	0.0876556i
$929$	6.05352	−	1.96691i	0.198610	−	0.0645322i	−0.208023	−	0.978124i	$-0.566703\pi$
$929$	6.05352	−	1.96691i	0.198610	−	0.0645322i	0.406633	+	0.913592i	$0.366703\pi$
$930$	18.7089	−	0.687974i	0.613489	−	0.0225596i
$931$	−1.57627	+	18.9251i	−0.0516602	+	0.620245i
$932$	9.76559	+	9.76559i	0.319882	+	0.319882i
$933$	−15.3124	+	7.80205i	−0.501305	+	0.255428i
$934$	−17.1721	+	12.4762i	−0.561887	+	0.408235i
$935$	21.6971	+	38.9725i	0.709572	+	1.27454i
$936$	6.41266	+	4.65907i	0.209604	+	0.152287i
$937$	30.7112	+	4.86417i	1.00329	+	0.158906i	0.636401	−	0.771359i	$-0.280423\pi$
$937$	30.7112	+	4.86417i	1.00329	+	0.158906i	0.366890	+	0.930264i	$0.380423\pi$
$938$	2.70422	−	17.0738i	0.0882959	−	0.557479i
$939$	10.3520	+	7.52118i	0.337825	+	0.245445i
$940$	11.0484	−	6.15098i	0.360360	−	0.200623i
$941$	30.2414	+	41.6238i	0.985843	+	1.35690i	0.933622	+	0.358261i	$0.116630\pi$
$941$	30.2414	+	41.6238i	0.985843	+	1.35690i	0.0522212	+	0.998636i	$0.483370\pi$
$942$	15.2873	−	7.78929i	0.498089	−	0.253789i
$943$	−2.76844	−	2.76844i	−0.0901529	−	0.0901529i
$944$	−2.54581	+	7.83521i	−0.0828591	+	0.255014i
$945$	−0.745943	−	20.2853i	−0.0242655	−	0.659881i
$946$	−20.6137	+	6.69779i	−0.670208	+	0.217764i
$947$	−23.1962	+	45.5251i	−0.753774	+	1.47937i	0.119864	+	0.992790i	$0.461754\pi$
$947$	−23.1962	+	45.5251i	−0.753774	+	1.47937i	−0.873639	+	0.486575i	$0.838246\pi$
$948$	−4.38318	+	0.694228i	−0.142359	+	0.0225475i
$949$	87.4920			2.84011
$950$	−3.61560	+	21.4925i	−0.117306	+	0.697309i
$951$	38.2025			1.23880
$952$	8.10565	−	1.28381i	0.262706	−	0.0416085i
$953$	22.4426	−	44.0461i	0.726987	−	1.42679i	−0.170322	−	0.985388i	$-0.554481\pi$
$953$	22.4426	−	44.0461i	0.726987	−	1.42679i	0.897309	−	0.441403i	$-0.145519\pi$
$954$	6.71264	−	2.18107i	0.217330	−	0.0706147i
$955$	−2.24877	−	0.640327i	−0.0727686	−	0.0207205i
$956$	7.57383	−	23.3099i	0.244955	−	0.753895i
$957$	−21.0506	−	21.0506i	−0.680469	−	0.680469i
$958$	−16.1894	+	8.24889i	−0.523054	+	0.266509i
$959$	−14.1796	−	19.5165i	−0.457883	−	0.630222i
$960$	−1.20553	+	2.59780i	−0.0389083	+	0.0838436i
$961$	9.49275	+	6.89689i	0.306218	+	0.222480i
$962$	−4.01025	+	25.3197i	−0.129296	+	0.816341i
$963$	25.7121	+	4.07240i	0.828562	+	0.131231i
$964$	5.55065	+	4.03278i	0.178774	+	0.129887i
$965$	−3.81527	+	31.5552i	−0.122818	+	1.01580i
$966$	10.1417	−	7.36838i	0.326304	−	0.237074i
$967$	−3.70134	+	1.88593i	−0.119027	+	0.0606474i	−0.512490	−	0.858693i	$-0.671277\pi$
$967$	−3.70134	+	1.88593i	−0.119027	+	0.0606474i	0.393463	+	0.919340i	$0.371277\pi$
$968$	−3.26483	−	3.26483i	−0.104936	−	0.104936i
$969$	−2.33904	+	28.0832i	−0.0751409	+	0.902161i
$970$	−9.90681	−	27.0629i	−0.318089	−	0.868937i
$971$	29.1552	−	9.47310i	0.935635	−	0.304006i	0.198770	−	0.980046i	$-0.436305\pi$
$971$	29.1552	−	9.47310i	0.935635	−	0.304006i	0.736865	+	0.676040i	$0.236305\pi$
$972$	−11.4190	−	5.81827i	−0.366264	−	0.186621i
$973$	−8.13863	+	1.28903i	−0.260913	+	0.0413245i
$974$			11.4389i			0.366527i
$975$	24.1033	+	28.5104i	0.771924	+	0.913063i
$976$	−4.25267			−0.136125
$977$	−11.3014	+	1.78997i	−0.361564	+	0.0572661i	−0.334574	−	0.942370i	$-0.608592\pi$
$977$	−11.3014	+	1.78997i	−0.361564	+	0.0572661i	−0.0269902	+	0.999636i	$0.508592\pi$
$978$	24.9799	+	12.7279i	0.798770	+	0.406994i
$979$	12.1633	+	37.4349i	0.388742	+	1.19642i
$980$	5.43270	−	8.08654i	0.173541	−	0.258315i
$981$	−7.44554	−	2.41920i	−0.237718	−	0.0772392i
$982$	−22.4741	+	22.4741i	−0.717176	+	0.717176i
$983$	−40.4341	+	20.6022i	−1.28965	+	0.657109i	−0.958128	−	0.286339i	$-0.907562\pi$
$983$	−40.4341	+	20.6022i	−1.28965	+	0.657109i	−0.331521	+	0.943448i	$0.607562\pi$
$984$	−0.673855	+	0.489584i	−0.0214817	+	0.0156074i
$985$	−27.1140	+	5.32249i	−0.863924	+	0.169589i
$986$	−24.0195	−	17.4512i	−0.764936	−	0.555759i
$987$	−1.84211	+	11.6306i	−0.0586349	+	0.370206i
$988$	25.3424	−	1.87830i	0.806250	−	0.0597566i
$989$	−19.4079	+	26.7127i	−0.617137	+	0.849416i
$990$	−8.17761	+	8.80200i	−0.259902	+	0.279746i
$991$	−0.0163796	−	0.0225446i	−0.000520316	−	0.000716154i	0.808757	−	0.588143i	$-0.200141\pi$
$991$	−0.0163796	−	0.0225446i	−0.000520316	−	0.000716154i	−0.809277	+	0.587427i	$0.800141\pi$
$992$	−5.82460	+	2.96778i	−0.184931	+	0.0942272i
$993$	−7.62088	+	7.62088i	−0.241841	+	0.241841i
$994$	−13.1745	−	4.28064i	−0.417869	−	0.135774i
$995$	7.29808	−	5.72365i	0.231365	−	0.181452i
$996$	1.66420	−	0.540732i	0.0527323	−	0.0171337i
$997$	−24.0253	+	47.1523i	−0.760888	+	1.49333i	0.105751	+	0.994393i	$0.466275\pi$
$997$	−24.0253	+	47.1523i	−0.760888	+	1.49333i	−0.866640	+	0.498935i	$0.833725\pi$
$998$	−0.751249	−	4.74320i	−0.0237804	−	0.150143i
$999$		−	24.5527i		−	0.776812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.37.8	✓	400
19.18	odd	2	inner	950.2.w.a.37.43	yes	400
25.23	odd	20	inner	950.2.w.a.873.43	yes	400
475.398	even	20	inner	950.2.w.a.873.8	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.37.8	✓	400	1.1	even	1	trivial
950.2.w.a.37.43	yes	400	19.18	odd	2	inner
950.2.w.a.873.8	yes	400	475.398	even	20	inner
950.2.w.a.873.43	yes	400	25.23	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.581458 + 1.14117i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.37992 + 1.75950i) q^{5} +(0.395780 - 1.21809i) q^{6} +(1.14962 + 1.14962i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.799169 + 1.09996i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-0.581458 + 1.14117i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.37992 + 1.75950i) q^{5} +(0.395780 - 1.21809i) q^{6} +(1.14962 + 1.14962i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.799169 + 1.09996i) q^{9} +(-1.63817 - 1.52197i) q^{10} +(-3.19712 - 2.32284i) q^{11} +(-0.200357 + 1.26500i) q^{12} +(-5.75812 - 0.911997i) q^{13} +(-1.31531 - 0.955626i) q^{14} +(-2.81026 + 0.551654i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-4.49759 + 2.29164i) q^{17} +(-0.961402 - 0.961402i) q^{18} +(-4.34386 - 0.361800i) q^{19} +(1.85609 + 1.24696i) q^{20} +(-1.98037 + 0.643462i) q^{21} +(3.52113 + 1.79411i) q^{22} +(5.94611 - 0.941771i) q^{23} -1.28077i q^{24} +(-1.19166 + 4.85592i) q^{25} +5.82990 q^{26} +(-5.51494 + 0.873480i) q^{27} +(1.44861 + 0.738101i) q^{28} +(-1.81756 - 5.59388i) q^{29} +(2.68936 - 0.984483i) q^{30} +(6.21715 + 2.02008i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.50976 - 2.29784i) q^{33} +(4.08373 - 2.96700i) q^{34} +(-0.436372 + 3.60913i) q^{35} +(1.09996 + 0.799169i) q^{36} +(-0.687877 + 4.34308i) q^{37} +(4.34698 - 0.322184i) q^{38} +(4.38885 - 6.04073i) q^{39} +(-2.02831 - 0.941254i) q^{40} +(-0.382258 - 0.526132i) q^{41} +(1.85533 - 0.945338i) q^{42} +(-3.87822 + 3.87822i) q^{43} +(-3.75844 - 1.22119i) q^{44} +(-0.832592 + 2.92399i) q^{45} +(-5.72558 + 1.86035i) q^{46} +(2.56737 - 5.03875i) q^{47} +(0.200357 + 1.26500i) q^{48} -4.35675i q^{49} +(0.417352 - 4.98255i) q^{50} -6.46503i q^{51} +(-5.75812 + 0.911997i) q^{52} +(-2.35675 + 4.62538i) q^{53} +(5.31040 - 1.72545i) q^{54} +(-0.324726 - 8.83065i) q^{55} +(-1.54623 - 0.502402i) q^{56} +(2.93865 - 4.74673i) q^{57} +(2.67026 + 5.24068i) q^{58} +(-6.66502 + 4.84242i) q^{59} +(-2.50224 + 1.39307i) q^{60} +(-3.44048 - 2.49965i) q^{61} +(-6.45662 - 1.02263i) q^{62} +(-0.345797 + 2.18328i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-6.34108 - 11.3899i) q^{65} +(-4.09478 + 2.97503i) q^{66} +(4.82711 + 9.47374i) q^{67} +(-3.56931 + 3.56931i) q^{68} +(-2.38269 + 7.33315i) q^{69} +(-0.133593 - 3.63296i) q^{70} +(8.10333 - 2.63293i) q^{71} +(-1.21144 - 0.617258i) q^{72} +(-14.8227 + 2.34768i) q^{73} -4.39722i q^{74} +(-4.84856 - 4.18340i) q^{75} +(-4.24306 + 0.998234i) q^{76} +(-1.00509 - 6.34586i) q^{77} +(-3.38984 + 6.65293i) q^{78} +(1.07073 + 3.29537i) q^{79} +(2.15058 + 0.612368i) q^{80} +(0.949465 - 2.92215i) q^{81} +(0.459857 + 0.459857i) q^{82} +(-0.620262 - 1.21733i) q^{83} +(-1.68460 + 1.22394i) q^{84} +(-10.2384 - 4.75122i) q^{85} +(3.22379 - 4.43716i) q^{86} +(7.44043 + 1.17845i) q^{87} +(3.90320 + 0.618207i) q^{88} +(-8.05799 - 5.85447i) q^{89} +(0.364928 - 3.01824i) q^{90} +(-5.57120 - 7.66810i) q^{91} +(5.36406 - 2.73313i) q^{92} +(-5.92027 + 5.92027i) q^{93} +(-1.74753 + 5.37834i) q^{94} +(-5.35758 - 8.14226i) q^{95} +(-0.395780 - 1.21809i) q^{96} +(11.4836 + 5.85118i) q^{97} +(0.681546 + 4.30311i) q^{98} -5.37305i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

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