LMFDB - Embedded newform 950.2.w.a.113.10

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			113.10
Character	$\chi$	$=$	950.113
Dual form			950.2.w.a.227.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(-0.833741 - 0.424812i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-2.09765 + 0.774512i) q^{5} +(-0.289156 + 0.889931i) q^{6} +(2.58136 - 2.58136i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-1.24870 - 1.71868i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.833741 - 0.424812i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-2.09765 + 0.774512i) q^{5} +(-0.289156 + 0.889931i) q^{6} +(2.58136 - 2.58136i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-1.24870 - 1.71868i) q^{9} +(1.09312 + 1.95066i) q^{10} +(3.46098 + 2.51455i) q^{11} +(0.924209 + 0.146380i) q^{12} +(0.601065 - 3.79498i) q^{13} +(-2.95339 - 2.14576i) q^{14} +(2.07792 + 0.245364i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.28152 + 4.47773i) q^{17} +(-1.50219 + 1.50219i) q^{18} +(-1.76197 - 3.98691i) q^{19} +(1.75565 - 1.38481i) q^{20} +(-3.24877 + 1.05559i) q^{21} +(1.94217 - 3.81173i) q^{22} +(0.419531 + 2.64881i) q^{23} -0.935729i q^{24} +(3.80026 - 3.24931i) q^{25} -3.84228 q^{26} +(0.750113 + 4.73603i) q^{27} +(-1.65733 + 3.25270i) q^{28} +(-2.92060 - 8.98867i) q^{29} +(-0.0827147 - 2.09072i) q^{30} +(-4.54771 - 1.47764i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.81735 - 3.56675i) q^{33} +(4.06570 - 2.95390i) q^{34} +(-3.41549 + 7.41407i) q^{35} +(1.71868 + 1.24870i) q^{36} +(-6.33105 - 1.00274i) q^{37} +(-3.66219 + 2.36397i) q^{38} +(-2.11328 + 2.90869i) q^{39} +(-1.64241 - 1.51740i) q^{40} +(-0.395595 - 0.544490i) q^{41} +(1.55081 + 3.04365i) q^{42} +(-0.0431995 - 0.0431995i) q^{43} +(-4.06863 - 1.32198i) q^{44} +(3.95047 + 2.63806i) q^{45} +(2.55057 - 0.828732i) q^{46} +(-10.4320 - 5.31537i) q^{47} +(-0.924209 + 0.146380i) q^{48} -6.32680i q^{49} +(-3.80380 - 3.24517i) q^{50} -4.70249i q^{51} +(0.601065 + 3.79498i) q^{52} +(-4.61679 - 2.35237i) q^{53} +(4.56037 - 1.48176i) q^{54} +(-9.20747 - 2.59407i) q^{55} +(3.47192 + 1.12809i) q^{56} +(-0.224658 + 4.07256i) q^{57} +(-8.42113 + 4.29078i) q^{58} +(10.3201 - 7.49798i) q^{59} +(-2.05204 + 0.408757i) q^{60} +(-6.46404 - 4.69640i) q^{61} +(-0.748029 + 4.72287i) q^{62} +(-7.65987 - 1.21320i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(1.67843 + 8.42606i) q^{65} +(-3.23854 + 2.35294i) q^{66} +(-4.99046 + 2.54277i) q^{67} +(-3.55355 - 3.55355i) q^{68} +(0.775468 - 2.38665i) q^{69} +(7.85709 + 2.21362i) q^{70} +(-8.49285 + 2.75949i) q^{71} +(0.964462 - 1.89286i) q^{72} +(0.0348056 + 0.219754i) q^{73} +6.40997i q^{74} +(-4.54878 + 1.09469i) q^{75} +(2.90776 + 3.24730i) q^{76} +(15.4250 - 2.44308i) q^{77} +(3.20347 + 1.63225i) q^{78} +(0.951427 + 2.92819i) q^{79} +(-1.24179 + 1.85956i) q^{80} +(-0.582915 + 1.79403i) q^{81} +(-0.475901 + 0.475901i) q^{82} +(6.33062 - 3.22561i) q^{83} +(2.76357 - 2.00785i) q^{84} +(-8.25388 - 7.62565i) q^{85} +(-0.0359097 + 0.0494255i) q^{86} +(-1.38348 + 8.73493i) q^{87} +(-0.669228 + 4.22534i) q^{88} +(0.123437 + 0.0896820i) q^{89} +(1.98760 - 4.31452i) q^{90} +(-8.24462 - 11.3477i) q^{91} +(-1.21753 - 2.38953i) q^{92} +(3.16389 + 3.16389i) q^{93} +(-3.61800 + 11.1351i) q^{94} +(6.78391 + 6.99847i) q^{95} +(0.289156 + 0.889931i) q^{96} +(6.22905 - 12.2252i) q^{97} +(-6.24891 + 0.989730i) q^{98} -9.08824i 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$-1$

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 $

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	−0.833741	−	0.424812i	−0.481361	−	0.245265i	0.196434	−	0.980517i	$-0.437064\pi$
$3$	−0.833741	−	0.424812i	−0.481361	−	0.245265i	−0.677794	+	0.735252i	$0.737064\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−2.09765	+	0.774512i	−0.938097	+	0.346372i
$5$	−2.09765	+	0.774512i	−0.938097	+	0.346372i
$6$	−0.289156	+	0.889931i	−0.118048	+	0.363313i
$7$	2.58136	−	2.58136i	0.975661	−	0.975661i	−0.0240497	−	0.999711i	$-0.507656\pi$
$7$	2.58136	−	2.58136i	0.975661	−	0.975661i	0.999711	+	0.0240497i	$0.00765600\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	−1.24870	−	1.71868i	−0.416232	−	0.572895i
$10$	1.09312	+	1.95066i	0.345675	+	0.616854i
$11$	3.46098	+	2.51455i	1.04352	+	0.758165i	0.970971	−	0.239199i	$-0.0768849\pi$
$11$	3.46098	+	2.51455i	1.04352	+	0.758165i	0.0725544	+	0.997364i	$0.476885\pi$
$12$	0.924209	+	0.146380i	0.266796	+	0.0422564i
$13$	0.601065	−	3.79498i	0.166705	−	1.05254i	−0.752452	−	0.658647i	$-0.771129\pi$
$13$	0.601065	−	3.79498i	0.166705	−	1.05254i	0.919158	−	0.393890i	$-0.128871\pi$
$14$	−2.95339	−	2.14576i	−0.789326	−	0.573479i
$15$	2.07792	+	0.245364i	0.536516	+	0.0633527i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	2.28152	+	4.47773i	0.553350	+	1.08601i	0.983101	+	0.183063i	$0.0586011\pi$
$17$	2.28152	+	4.47773i	0.553350	+	1.08601i	−0.429752	+	0.902947i	$0.641399\pi$
$18$	−1.50219	+	1.50219i	−0.354068	+	0.354068i
$19$	−1.76197	−	3.98691i	−0.404224	−	0.914660i
$19$	−1.76197	−	3.98691i	−0.404224	−	0.914660i
$20$	1.75565	−	1.38481i	0.392574	−	0.309654i
$21$	−3.24877	+	1.05559i	−0.708941	+	0.230349i
$22$	1.94217	−	3.81173i	0.414073	−	0.812664i
$23$	0.419531	+	2.64881i	0.0874782	+	0.552316i	0.992035	+	0.125963i	$0.0402019\pi$
$23$	0.419531	+	2.64881i	0.0874782	+	0.552316i	−0.904557	+	0.426353i	$0.859798\pi$
$24$		−	0.935729i		−	0.191005i
$25$	3.80026	−	3.24931i	0.760052	−	0.649862i
$26$	−3.84228			−0.753533
$27$	0.750113	+	4.73603i	0.144359	+	0.911449i
$28$	−1.65733	+	3.25270i	−0.313206	+	0.614702i
$29$	−2.92060	−	8.98867i	−0.542341	−	1.66915i	−0.727229	−	0.686395i	$-0.759192\pi$
$29$	−2.92060	−	8.98867i	−0.542341	−	1.66915i	0.184888	−	0.982760i	$-0.440808\pi$
$30$	−0.0827147	−	2.09072i	−0.0151016	−	0.381711i
$31$	−4.54771	−	1.47764i	−0.816792	−	0.265392i	−0.129320	−	0.991603i	$-0.541280\pi$
$31$	−4.54771	−	1.47764i	−0.816792	−	0.265392i	−0.687472	+	0.726211i	$0.741280\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.81735	−	3.56675i	−0.316360	−	0.620891i
$34$	4.06570	−	2.95390i	0.697261	−	0.506590i
$35$	−3.41549	+	7.41407i	−0.577323	+	1.25321i
$36$	1.71868	+	1.24870i	0.286447	+	0.208116i
$37$	−6.33105	−	1.00274i	−1.04082	−	0.164849i	−0.387451	−	0.921890i	$-0.626644\pi$
$37$	−6.33105	−	1.00274i	−1.04082	−	0.164849i	−0.653368	+	0.757041i	$0.726644\pi$
$38$	−3.66219	+	2.36397i	−0.594086	+	0.383487i
$39$	−2.11328	+	2.90869i	−0.338396	+	0.465763i
$40$	−1.64241	−	1.51740i	−0.259688	−	0.239922i
$41$	−0.395595	−	0.544490i	−0.0617815	−	0.0850350i	0.777008	−	0.629490i	$-0.216736\pi$
$41$	−0.395595	−	0.544490i	−0.0617815	−	0.0850350i	−0.838790	+	0.544455i	$0.816736\pi$
$42$	1.55081	+	3.04365i	0.239296	+	0.469645i
$43$	−0.0431995	−	0.0431995i	−0.00658786	−	0.00658786i	0.703805	−	0.710393i	$-0.251483\pi$
$43$	−0.0431995	−	0.0431995i	−0.00658786	−	0.00658786i	−0.710393	+	0.703805i	$0.751483\pi$
$44$	−4.06863	−	1.32198i	−0.613369	−	0.199296i
$45$	3.95047	+	2.63806i	0.588901	+	0.393259i
$46$	2.55057	−	0.828732i	0.376062	−	0.122190i
$47$	−10.4320	−	5.31537i	−1.52166	−	0.775326i	−0.524559	−	0.851374i	$-0.675770\pi$
$47$	−10.4320	−	5.31537i	−1.52166	−	0.775326i	−0.997104	+	0.0760486i	$0.975770\pi$
$48$	−0.924209	+	0.146380i	−0.133398	+	0.0211282i
$49$		−	6.32680i		−	0.903829i
$50$	−3.80380	−	3.24517i	−0.537938	−	0.458936i
$51$		−	4.70249i		−	0.658480i
$52$	0.601065	+	3.79498i	0.0833527	+	0.526268i
$53$	−4.61679	−	2.35237i	−0.634165	−	0.323123i	0.107188	−	0.994239i	$-0.465815\pi$
$53$	−4.61679	−	2.35237i	−0.634165	−	0.323123i	−0.741353	+	0.671115i	$0.765815\pi$
$54$	4.56037	−	1.48176i	0.620588	−	0.201641i
$55$	−9.20747	−	2.59407i	−1.24154	−	0.349784i
$56$	3.47192	+	1.12809i	0.463954	+	0.150748i
$57$	−0.224658	+	4.07256i	−0.0297567	+	0.539423i
$58$	−8.42113	+	4.29078i	−1.10575	+	0.563407i
$59$	10.3201	−	7.49798i	1.34356	−	0.976154i	0.344256	−	0.938876i	$-0.388131\pi$
$59$	10.3201	−	7.49798i	1.34356	−	0.976154i	0.999305	−	0.0372785i	$-0.0118689\pi$
$60$	−2.05204	+	0.408757i	−0.264917	+	0.0527703i
$61$	−6.46404	−	4.69640i	−0.827635	−	0.601312i	0.0912540	−	0.995828i	$-0.470912\pi$
$61$	−6.46404	−	4.69640i	−0.827635	−	0.601312i	−0.918889	+	0.394515i	$0.870912\pi$
$62$	−0.748029	+	4.72287i	−0.0949998	+	0.599805i
$63$	−7.65987	−	1.21320i	−0.965053	−	0.152849i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	1.67843	+	8.42606i	0.208184	+	1.04512i
$66$	−3.23854	+	2.35294i	−0.398637	+	0.289627i
$67$	−4.99046	+	2.54277i	−0.609682	+	0.310648i	−0.731434	−	0.681912i	$-0.761149\pi$
$67$	−4.99046	+	2.54277i	−0.609682	+	0.310648i	0.121752	+	0.992561i	$0.461149\pi$
$68$	−3.55355	−	3.55355i	−0.430931	−	0.430931i
$69$	0.775468	−	2.38665i	0.0933554	−	0.287318i
$70$	7.85709	+	2.21362i	0.939102	+	0.264578i
$71$	−8.49285	+	2.75949i	−1.00792	+	0.327492i	−0.766024	−	0.642812i	$-0.777768\pi$
$71$	−8.49285	+	2.75949i	−1.00792	+	0.327492i	−0.241892	+	0.970303i	$0.577768\pi$
$72$	0.964462	−	1.89286i	0.113663	−	0.223076i
$73$	0.0348056	+	0.219754i	0.00407369	+	0.0257203i	0.989641	−	0.143561i	$-0.0458553\pi$
$73$	0.0348056	+	0.219754i	0.00407369	+	0.0257203i	−0.985568	+	0.169281i	$0.945855\pi$
$74$			6.40997i			0.745144i
$75$	−4.54878	+	1.09469i	−0.525248	+	0.126403i
$76$	2.90776	+	3.24730i	0.333543	+	0.372490i
$77$	15.4250	−	2.44308i	1.75784	−	0.278414i
$78$	3.20347	+	1.63225i	0.362721	+	0.184816i
$79$	0.951427	+	2.92819i	0.107044	+	0.329447i	0.990205	−	0.139623i	$-0.0445891\pi$
$79$	0.951427	+	2.92819i	0.107044	+	0.329447i	−0.883161	+	0.469070i	$0.844589\pi$
$80$	−1.24179	+	1.85956i	−0.138836	+	0.207905i
$81$	−0.582915	+	1.79403i	−0.0647683	+	0.199336i
$82$	−0.475901	+	0.475901i	−0.0525545	+	0.0525545i
$83$	6.33062	−	3.22561i	0.694876	−	0.354057i	−0.0706150	−	0.997504i	$-0.522496\pi$
$83$	6.33062	−	3.22561i	0.694876	−	0.354057i	0.765491	+	0.643447i	$0.222496\pi$
$84$	2.76357	−	2.00785i	0.301530	−	0.219075i
$85$	−8.25388	−	7.62565i	−0.895259	−	0.827117i
$86$	−0.0359097	+	0.0494255i	−0.00387225	+	0.00532969i
$87$	−1.38348	+	8.73493i	−0.148324	+	0.936483i
$88$	−0.669228	+	4.22534i	−0.0713399	+	0.450423i
$89$	0.123437	+	0.0896820i	0.0130843	+	0.00950627i	0.594308	−	0.804237i	$-0.297426\pi$
$89$	0.123437	+	0.0896820i	0.0130843	+	0.00950627i	−0.581224	+	0.813744i	$0.697426\pi$
$90$	1.98760	−	4.31452i	0.209511	−	0.454790i
$91$	−8.24462	−	11.3477i	−0.864271	−	1.18957i
$92$	−1.21753	−	2.38953i	−0.126936	−	0.249126i
$93$	3.16389	+	3.16389i	0.328080	+	0.328080i
$94$	−3.61800	+	11.1351i	−0.373168	+	1.14849i
$95$	6.78391	+	6.99847i	0.696015	+	0.718027i
$96$	0.289156	+	0.889931i	0.0295119	+	0.0908282i
$97$	6.22905	−	12.2252i	0.632464	−	1.24128i	−0.323063	−	0.946378i	$-0.604712\pi$
$97$	6.22905	−	12.2252i	0.632464	−	1.24128i	0.955527	−	0.294904i	$-0.0952876\pi$
$98$	−6.24891	+	0.989730i	−0.631235	+	0.0999778i
$99$		−	9.08824i		−	0.913403i
$100$	−2.61017	+	4.26462i	−0.261017	+	0.426462i
$101$	13.5624			1.34951			0.674757	−	0.738040i	$-0.264249\pi$
$101$	13.5624			1.34951			0.674757	+	0.738040i	$0.264249\pi$
$102$	−4.64459	+	0.735631i	−0.459883	+	0.0728383i
$103$	15.5288	+	7.91234i	1.53010	+	0.779626i	0.997760	−	0.0669025i	$-0.0213116\pi$
$103$	15.5288	+	7.91234i	1.53010	+	0.779626i	0.532343	+	0.846529i	$0.321312\pi$
$104$	3.65423	−	1.18733i	0.358326	−	0.116427i
$105$	5.99722	−	4.73047i	0.585269	−	0.461647i
$106$	−1.60119	+	4.92795i	−0.155521	+	0.478644i
$107$	−4.70203	−	4.70203i	−0.454562	−	0.454562i	0.442303	−	0.896866i	$-0.354162\pi$
$107$	−4.70203	−	4.70203i	−0.454562	−	0.454562i	−0.896866	+	0.442303i	$0.854162\pi$
$108$	−2.17691	−	4.27243i	−0.209473	−	0.411115i
$109$	−7.94547	+	5.77272i	−0.761038	+	0.552926i	−0.899228	−	0.437479i	$-0.855871\pi$
$109$	−7.94547	+	5.77272i	−0.761038	+	0.552926i	0.138191	+	0.990406i	$0.455871\pi$
$110$	−1.12177	+	9.49991i	−0.106956	+	0.905781i
$111$	4.85248	+	3.52553i	0.460577	+	0.334629i
$112$	0.571078	−	3.60564i	0.0539618	−	0.340701i
$113$	−2.34028	+	14.7759i	−0.220155	+	1.39000i	0.591708	+	0.806153i	$0.298454\pi$
$113$	−2.34028	+	14.7759i	−0.220155	+	1.39000i	−0.811862	+	0.583849i	$0.801546\pi$
$114$	4.05756	−	0.415196i	0.380025	−	0.0388867i
$115$	−2.93157	−	5.23135i	−0.273370	−	0.487826i
$116$	5.55531	+	7.64622i	0.515797	+	0.709934i
$117$	−7.27291	+	3.70573i	−0.672381	+	0.342595i
$118$	−9.02009	−	9.02009i	−0.830366	−	0.830366i
$119$	17.4480	+	5.66921i	1.59946	+	0.519696i
$120$	0.724734	+	1.96283i	0.0661589	+	0.179181i
$121$	2.25624	+	6.94399i	0.205113	+	0.631272i
$122$	−3.62738	+	7.11913i	−0.328408	+	0.644536i
$123$	0.0985178	+	0.622017i	0.00888305	+	0.0560854i
$124$	4.78174			0.429413
$125$	−5.45498	+	9.75926i	−0.487908	+	0.872895i
$126$			7.75535i			0.690902i
$127$	−1.89836	−	11.9858i	−0.168452	−	1.06357i	−0.916533	−	0.399958i	$-0.869025\pi$
$127$	−1.89836	−	11.9858i	−0.168452	−	1.06357i	0.748081	−	0.663607i	$-0.230975\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$	0.0176655	+	0.0543689i	0.00155536	+	0.00478691i
$130$	8.05976	−	2.97589i	0.706887	−	0.261003i
$131$	6.48159	−	19.9483i	0.566299	−	1.74289i	−0.0977601	−	0.995210i	$-0.531168\pi$
$131$	6.48159	−	19.9483i	0.566299	−	1.74289i	0.664059	−	0.747680i	$-0.268832\pi$
$132$	2.83059	+	2.83059i	0.246371	+	0.246371i
$133$	−14.8399	−	5.74335i	−1.28678	−	0.498012i
$134$	3.29214	+	4.53124i	0.284398	+	0.391440i
$135$	−5.24158	−	9.35355i	−0.451124	−	0.805025i
$136$	−2.95390	+	4.06570i	−0.253295	+	0.348631i
$137$	−3.04074	+	19.1985i	−0.259788	+	1.64024i	0.420500	+	0.907292i	$0.361855\pi$
$137$	−3.04074	+	19.1985i	−0.259788	+	1.64024i	−0.680288	+	0.732945i	$0.738145\pi$
$138$	−2.47857	−	0.392567i	−0.210990	−	0.0334176i
$139$	2.08223	−	2.86594i	0.176612	−	0.243086i	−0.711529	−	0.702657i	$-0.751997\pi$
$139$	2.08223	−	2.86594i	0.176612	−	0.243086i	0.888141	+	0.459571i	$0.151997\pi$
$140$	0.957247	−	8.10665i	0.0809021	−	0.685137i
$141$	6.43955	+	8.86328i	0.542308	+	0.746423i
$142$	4.05410	+	7.95661i	0.340212	+	0.667704i
$143$	11.6229	−	11.6229i	0.971958	−	0.971958i
$144$	−2.02043	−	0.656479i	−0.168370	−	0.0547066i
$145$	13.0882	+	16.5930i	1.08692	+	1.37798i
$146$	0.211604	−	0.0687542i	0.0175125	−	0.00569014i
$147$	−2.68770	+	5.27491i	−0.221678	+	0.435068i
$148$	6.33105	−	1.00274i	0.520409	−	0.0824247i
$149$		−	15.2902i		−	1.25262i	−0.779575	−	0.626309i	$-0.784565\pi$
$149$		−	15.2902i		−	1.25262i	0.779575	−	0.626309i	$-0.215435\pi$
$150$	1.79279	+	4.32153i	0.146381	+	0.352851i
$151$			14.3824i			1.17043i	0.810880	+	0.585213i	$0.198989\pi$
$151$			14.3824i			1.17043i	−0.810880	+	0.585213i	$0.801011\pi$
$152$	2.75244	−	3.37995i	0.223253	−	0.274150i
$153$	4.84688	−	9.51254i	0.391847	−	0.769043i
$154$	−4.82600	−	14.8529i	−0.388890	−	1.19688i
$155$	10.6839	−	0.422687i	0.858155	−	0.0339510i
$156$	1.11102	−	3.41937i	0.0889527	−	0.273768i
$157$	0.765292	−	0.765292i	0.0610770	−	0.0610770i	−0.675909	−	0.736986i	$-0.736249\pi$
$157$	0.765292	−	0.765292i	0.0610770	−	0.0610770i	0.736986	+	0.675909i	$0.236249\pi$
$158$	2.74330	−	1.39778i	0.218245	−	0.111202i
$159$	2.84989	+	3.92254i	0.226011	+	0.311078i
$160$	2.03092	+	0.935599i	0.160559	+	0.0739656i
$161$	7.92049	+	5.75457i	0.624222	+	0.453524i
$162$	1.86313	+	0.295091i	0.146381	+	0.0231845i
$163$	−19.3474	−	3.06432i	−1.51540	−	0.240016i	−0.657353	−	0.753582i	$-0.728324\pi$
$163$	−19.3474	−	3.06432i	−1.51540	−	0.240016i	−0.858050	+	0.513566i	$0.828324\pi$
$164$	0.544490	+	0.395595i	0.0425175	+	0.0308908i
$165$	6.57465	+	6.07423i	0.511836	+	0.472878i
$166$	−4.17623	−	5.74808i	−0.324138	−	0.446138i
$167$	−12.6967	+	6.46929i	−0.982500	+	0.500609i	−0.870005	−	0.493044i	$-0.835884\pi$
$167$	−12.6967	+	6.46929i	−0.982500	+	0.500609i	−0.112495	+	0.993652i	$0.535884\pi$
$168$	−2.41545	−	2.41545i	−0.186356	−	0.186356i
$169$	−1.67683	−	0.544834i	−0.128987	−	0.0419103i
$170$	−6.24057	+	9.34518i	−0.478630	+	0.716742i
$171$	−4.65207	+	8.00672i	−0.355752	+	0.612289i
$172$	0.0544345	+	0.0277358i	0.00415059	+	0.00211483i
$173$	12.5163	−	1.98239i	0.951600	−	0.150719i	0.338713	−	0.940890i	$-0.390008\pi$
$173$	12.5163	−	1.98239i	0.951600	−	0.150719i	0.612886	+	0.790171i	$0.290008\pi$
$174$	8.84381			0.670448
$175$	1.42220	−	18.1975i	0.107508	−	1.37560i
$176$	4.27801			0.322467
$177$	−11.7895	+	1.86728i	−0.886154	+	0.140353i
$178$	0.0692681	−	0.135946i	0.00519186	−	0.0101896i
$179$	−6.45266	−	19.8592i	−0.482294	−	1.48435i	−0.835862	−	0.548940i	$-0.815032\pi$
$179$	−6.45266	−	19.8592i	−0.482294	−	1.48435i	0.353568	−	0.935409i	$-0.384968\pi$
$180$	−4.57233	−	1.28819i	−0.340801	−	0.0960157i
$181$	0.123888	+	0.0402536i	0.00920851	+	0.00299203i	0.313618	−	0.949549i	$-0.398459\pi$
$181$	0.123888	+	0.0402536i	0.00920851	+	0.00299203i	−0.304409	+	0.952541i	$0.598459\pi$
$182$	−9.91830	+	9.91830i	−0.735193	+	0.735193i
$183$	3.39425	+	6.66158i	0.250910	+	0.492438i
$184$	−2.16965	+	1.57634i	−0.159949	+	0.116209i
$185$	14.0570	−	2.80008i	1.03349	−	0.205866i
$186$	2.63000	−	3.61988i	0.192841	−	0.265422i
$187$	−3.36319	+	21.2343i	−0.245941	+	1.55281i
$188$	11.5640	+	1.83155i	0.843388	+	0.133580i
$189$	14.1617	+	10.2891i	1.03011	+	0.748419i
$190$	5.85107	−	7.79519i	0.424481	−	0.565523i
$191$	10.6455	−	7.73439i	0.770280	−	0.559641i	−0.131766	−	0.991281i	$-0.542065\pi$
$191$	10.6455	−	7.73439i	0.770280	−	0.559641i	0.902046	+	0.431640i	$0.142065\pi$
$192$	0.833741	−	0.424812i	0.0601701	−	0.0306582i
$193$	9.16932	−	9.16932i	0.660022	−	0.660022i	−0.295363	−	0.955385i	$-0.595441\pi$
$193$	9.16932	−	9.16932i	0.660022	−	0.660022i	0.955385	+	0.295363i	$0.0954405\pi$
$194$	−13.0491	−	4.23992i	−0.936873	−	0.304408i
$195$	2.18011	−	7.73817i	0.156121	−	0.554142i
$196$	1.95509	+	6.01715i	0.139649	+	0.429796i
$197$	8.16213	+	4.15881i	0.581527	+	0.296303i	0.719901	−	0.694077i	$-0.244187\pi$
$197$	8.16213	+	4.15881i	0.581527	+	0.296303i	−0.138373	+	0.990380i	$0.544187\pi$
$198$	−8.97635	+	1.42171i	−0.637922	+	0.101037i
$199$		−	21.2164i		−	1.50399i	−0.659169	−	0.751995i	$-0.729092\pi$
$199$		−	21.2164i		−	1.50399i	0.659169	−	0.751995i	$-0.270908\pi$
$200$	4.62044	+	1.91090i	0.326714	+	0.135121i
$201$	5.24095			0.369668
$202$	−2.12163	−	13.3955i	−0.149278	−	0.942502i
$203$	−30.7421	−	15.6639i	−2.15767	−	1.09939i
$204$	1.45315	+	4.47233i	0.101741	+	0.313126i
$205$	1.25153	+	0.835755i	0.0874108	+	0.0583716i
$206$	5.38568	−	16.5754i	0.375238	−	1.15486i
$207$	4.02861	−	4.02861i	0.280008	−	0.280008i
$208$	−1.74436	−	3.42350i	−0.120950	−	0.237377i
$209$	3.92713	−	18.2292i	0.271645	−	1.26094i
$210$	−5.61041	−	5.18337i	−0.387155	−	0.357687i
$211$	3.50526	−	4.82457i	0.241312	−	0.332137i	−0.671133	−	0.741337i	$-0.734192\pi$
$211$	3.50526	−	4.82457i	0.241312	−	0.332137i	0.912445	+	0.409200i	$0.134192\pi$
$212$	5.11776	+	0.810573i	0.351489	+	0.0556704i
$213$	8.25310	+	1.30716i	0.565493	+	0.0895654i
$214$	−3.90858	+	5.37970i	−0.267185	+	0.367749i
$215$	0.124076	+	0.0571588i	0.00846191	+	0.00389820i
$216$	−3.87929	+	2.81847i	−0.263952	+	0.191772i
$217$	−15.5536	+	7.92494i	−1.05584	+	0.537980i
$218$	6.94459	+	6.94459i	0.470347	+	0.470347i
$219$	0.0643354	−	0.198004i	0.00434738	−	0.0133799i
$220$	9.55844	−	0.378159i	0.644430	−	0.0254955i
$221$	18.3642	−	5.96690i	1.23531	−	0.401377i
$222$	2.72303	−	5.34425i	0.182758	−	0.358683i
$223$	−16.2834	+	2.57904i	−1.09042	+	0.172705i	−0.675650	−	0.737223i	$-0.736137\pi$
$223$	−16.2834	+	2.57904i	−1.09042	+	0.172705i	−0.414767	+	0.909928i	$0.636137\pi$
$224$	−3.65059			−0.243915
$225$	−10.3299	−	2.47404i	−0.688661	−	0.164936i
$226$	14.9601			0.995131
$227$	−1.93118	−	12.1930i	−0.128177	−	0.809276i	−0.965086	−	0.261934i	$-0.915640\pi$
$227$	−1.93118	−	12.1930i	−0.128177	−	0.809276i	0.836909	−	0.547342i	$-0.184360\pi$
$228$	−1.04483	−	3.94266i	−0.0691953	−	0.261109i
$229$	2.33428	−	0.758454i	0.154254	−	0.0501201i	−0.230872	−	0.972984i	$-0.574158\pi$
$229$	2.33428	−	0.758454i	0.154254	−	0.0501201i	0.385126	+	0.922864i	$0.374158\pi$
$230$	−4.70834	+	3.71384i	−0.310459	+	0.244883i
$231$	−13.8983	−	4.51582i	−0.914440	−	0.297119i
$232$	6.68304	−	6.68304i	0.438763	−	0.438763i
$233$	−16.8462	+	8.58358i	−1.10363	+	0.562329i	−0.908263	−	0.418401i	$-0.862591\pi$
$233$	−16.8462	+	8.58358i	−1.10363	+	0.562329i	−0.195370	+	0.980730i	$0.562591\pi$
$234$	4.79785	+	6.60367i	0.313645	+	0.431695i
$235$	25.9995	+	3.07006i	1.69602	+	0.200269i
$236$	−7.49798	+	10.3201i	−0.488077	+	0.671781i
$237$	0.450688	−	2.84553i	0.0292753	−	0.184837i
$238$	2.86994	−	18.1201i	0.186031	−	1.17455i
$239$	7.13392	−	9.81900i	0.461455	−	0.635139i	−0.513355	−	0.858177i	$-0.671597\pi$
$239$	7.13392	−	9.81900i	0.461455	−	0.635139i	0.974810	+	0.223038i	$0.0715974\pi$
$240$	1.82529	−	1.02287i	0.117822	−	0.0660257i
$241$	7.73742	+	10.6496i	0.498411	+	0.686004i	0.981912	−	0.189340i	$-0.0606349\pi$
$241$	7.73742	+	10.6496i	0.498411	+	0.686004i	−0.483500	+	0.875344i	$0.660635\pi$
$242$	6.50555	−	3.31474i	0.418192	−	0.213080i
$243$	11.4200	−	11.4200i	0.732592	−	0.732592i
$244$	7.59893	+	2.46904i	0.486472	+	0.158064i
$245$	4.90019	+	13.2714i	0.313062	+	0.847879i
$246$	0.598947	−	0.194610i	0.0381875	−	0.0124079i
$247$	−16.1893	+	4.29026i	−1.03010	+	0.272982i
$248$	−0.748029	−	4.72287i	−0.0474999	−	0.299903i
$249$	−6.64838			−0.421324
$250$	10.4925	+	3.86114i	0.663601	+	0.244200i
$251$	11.5292			0.727716			0.363858	−	0.931454i	$-0.381459\pi$
$251$	11.5292			0.727716			0.363858	+	0.931454i	$0.381459\pi$
$252$	7.65987	−	1.21320i	0.482526	−	0.0764247i
$253$	−5.20859	+	10.2224i	−0.327461	+	0.642678i
$254$	−11.5412	+	3.74998i	−0.724162	+	0.235294i
$255$	3.64213	+	9.86416i	0.228079	+	0.617718i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	15.5388	+	15.5388i	0.969281	+	0.969281i	0.999542	−	0.0302613i	$-0.00963394\pi$
$257$	15.5388	+	15.5388i	0.969281	+	0.969281i	−0.0302613	+	0.999542i	$0.509634\pi$
$258$	0.0509360	−	0.0259532i	0.00317114	−	0.00161577i
$259$	−18.9311	+	13.7543i	−1.17632	+	0.854649i
$260$	−4.20008	−	7.49499i	−0.260478	−	0.464820i
$261$	−11.8018	+	16.2437i	−0.730510	+	1.00546i
$262$	−20.7166	−	3.28119i	−1.27988	−	0.202713i
$263$	−5.74323	−	0.909639i	−0.354143	−	0.0560907i	−0.0231715	−	0.999732i	$-0.507376\pi$
$263$	−5.74323	−	0.909639i	−0.354143	−	0.0560907i	−0.330971	+	0.943641i	$0.607376\pi$
$264$	2.35294	−	3.23854i	0.144813	−	0.199318i
$265$	11.5064	+	1.35869i	0.706830	+	0.0834637i
$266$	−3.35117	+	15.5557i	−0.205473	+	0.953779i
$267$	−0.0648162	−	0.127209i	−0.00396669	−	0.00778506i
$268$	3.96045	−	3.96045i	0.241923	−	0.241923i
$269$	−6.71348	+	20.6620i	−0.409328	+	1.25978i	0.507899	+	0.861417i	$0.330422\pi$
$269$	−6.71348	+	20.6620i	−0.409328	+	1.25978i	−0.917227	+	0.398365i	$0.869578\pi$
$270$	−8.41843	+	6.64027i	−0.512329	+	0.404114i
$271$	−0.874766	−	2.69225i	−0.0531383	−	0.163543i	0.920966	−	0.389644i	$-0.127402\pi$
$271$	−0.874766	−	2.69225i	−0.0531383	−	0.163543i	−0.974104	+	0.226101i	$0.927402\pi$
$272$	4.47773	+	2.28152i	0.271502	+	0.138337i
$273$	2.05322	+	12.9635i	0.124266	+	0.784587i
$274$	19.4378			1.17428
$275$	21.3232	−	1.68985i	1.28584	−	0.101902i
$276$			2.50947i			0.151052i
$277$	1.62516	−	0.257400i	0.0976465	−	0.0154657i	−0.107420	−	0.994214i	$-0.534259\pi$
$277$	1.62516	−	0.257400i	0.0976465	−	0.0154657i	0.205066	+	0.978748i	$0.434259\pi$
$278$	−3.15638	−	1.60826i	−0.189307	−	0.0964569i
$279$	3.13911	+	9.66120i	0.187934	+	0.578401i
$280$	−8.15659	+	0.322697i	−0.487449	+	0.0192849i
$281$	6.79522	+	2.20790i	0.405369	+	0.131712i	0.504603	−	0.863352i	$-0.331639\pi$
$281$	6.79522	+	2.20790i	0.405369	+	0.131712i	−0.0992334	+	0.995064i	$0.531639\pi$
$282$	7.74679	−	7.74679i	0.461314	−	0.461314i
$283$	−4.36434	+	2.22374i	−0.259433	+	0.132188i	−0.578870	−	0.815420i	$-0.696506\pi$
$283$	−4.36434	+	2.22374i	−0.259433	+	0.132188i	0.319437	+	0.947607i	$0.396506\pi$
$284$	7.22445	−	5.24887i	0.428692	−	0.311463i
$285$	−2.68299	−	8.71680i	−0.158927	−	0.516338i
$286$	−13.2981	−	9.66161i	−0.786331	−	0.571303i
$287$	−2.42669	−	0.384350i	−0.143243	−	0.0226875i
$288$	−0.332331	+	2.09826i	−0.0195828	+	0.123641i
$289$	−4.85241	+	6.67877i	−0.285436	+	0.392869i
$290$	14.3413	−	15.5228i	0.842150	−	0.911531i
$291$	−10.3868	+	7.54647i	−0.608887	+	0.442382i
$292$	−0.101010	−	0.198243i	−0.00591116	−	0.0116013i
$293$	−15.9442	+	15.9442i	−0.931470	+	0.931470i	−0.997798	−	0.0663279i	$-0.978872\pi$
$293$	−15.9442	+	15.9442i	−0.931470	+	0.931470i	0.0663279	+	0.997798i	$0.478872\pi$
$294$	5.63042	+	1.82943i	0.328373	+	0.106695i
$295$	−15.8406	+	23.7212i	−0.922278	+	1.38110i
$296$	−1.98079	−	6.09624i	−0.115131	−	0.354337i
$297$	−9.31285	+	18.2775i	−0.540386	+	1.06057i
$298$	−15.1019	+	2.39191i	−0.874830	+	0.138559i
$299$	10.3044			0.595916
$300$	3.98787	−	2.44676i	0.230240	−	0.141264i
$301$	−0.223027			−0.0128550
$302$	14.2054	−	2.24991i	0.817427	−	0.129468i
$303$	−11.3076	−	5.76149i	−0.649603	−	0.330989i
$304$	−3.76891	−	2.18982i	−0.216162	−	0.125595i
$305$	17.1967	+	4.84492i	0.984680	+	0.277419i
$306$	−10.1536	−	3.29912i	−0.580445	−	0.188598i
$307$	22.7428	+	22.7428i	1.29800	+	1.29800i	0.929710	+	0.368292i	$0.120057\pi$
$307$	22.7428	+	22.7428i	1.29800	+	1.29800i	0.368292	+	0.929710i	$0.379943\pi$
$308$	−13.9151	+	7.09008i	−0.792885	+	0.403995i
$309$	−9.58577	−	13.1937i	−0.545316	−	0.750563i
$310$	−2.08882	−	10.4863i	−0.118637	−	0.595581i
$311$	−4.31546	−	3.13537i	−0.244707	−	0.177790i	0.458671	−	0.888606i	$-0.348326\pi$
$311$	−4.31546	−	3.13537i	−0.244707	−	0.177790i	−0.703378	+	0.710816i	$0.748326\pi$
$312$	−3.55107	−	0.562434i	−0.201040	−	0.0318416i
$313$	13.9547	+	2.21021i	0.788767	+	0.124928i	0.537806	−	0.843069i	$-0.319253\pi$
$313$	13.9547	+	2.21021i	0.788767	+	0.124928i	0.250961	+	0.967997i	$0.419253\pi$
$314$	−0.875588	−	0.636152i	−0.0494123	−	0.0359001i
$315$	17.0074	−	3.38779i	0.958256	−	0.190880i
$316$	−1.80972	−	2.49087i	−0.101805	−	0.140122i
$317$	19.5862	−	9.97968i	1.10007	−	0.560515i	0.192876	−	0.981223i	$-0.438218\pi$
$317$	19.5862	−	9.97968i	1.10007	−	0.560515i	0.907196	+	0.420708i	$0.138218\pi$
$318$	3.42843	−	3.42843i	0.192257	−	0.192257i
$319$	12.4943	−	38.4536i	0.699548	−	2.15299i
$320$	0.606373	−	2.15228i	0.0338973	−	0.120316i
$321$	1.92280	+	5.91775i	0.107320	+	0.330297i
$322$	4.44469	−	8.72319i	0.247693	−	0.486124i
$323$	13.8323	−	16.9859i	0.769652	−	0.945118i
$324$		−	1.88635i		−	0.104797i
$325$	−10.0468	−	16.3749i	−0.557299	−	0.908319i
$326$			19.5885i			1.08491i
$327$	9.07678	−	1.43762i	0.501947	−	0.0795006i
$328$	0.305547	−	0.599671i	0.0168710	−	0.0331113i
$329$	−40.6495	+	13.2078i	−2.24108	+	0.728172i
$330$	4.97094	−	7.44393i	0.273641	−	0.409775i
$331$	4.56118	+	1.48202i	0.250705	+	0.0814589i	0.431674	−	0.902030i	$-0.357923\pi$
$331$	4.56118	+	1.48202i	0.250705	+	0.0814589i	−0.180969	+	0.983489i	$0.557923\pi$
$332$	−5.02401	+	5.02401i	−0.275728	+	0.275728i
$333$	6.18217	+	12.1332i	0.338781	+	0.664895i
$334$	8.37584	+	11.5284i	0.458306	+	0.630804i
$335$	8.49883	−	9.19901i	0.464341	−	0.502595i
$336$	−2.00785	+	2.76357i	−0.109537	+	0.150765i
$337$	21.8221	+	3.45628i	1.18873	+	0.188276i	0.719302	−	0.694697i	$-0.244462\pi$
$337$	21.8221	+	3.45628i	1.18873	+	0.188276i	0.469424	+	0.882973i	$0.344462\pi$
$338$	−0.275813	+	1.74141i	−0.0150022	+	0.0947204i
$339$	8.22818	−	11.3251i	0.446893	−	0.615096i
$340$	10.2064	+	4.70183i	0.553518	+	0.254992i
$341$	−12.0239	−	16.5495i	−0.651132	−	0.896206i
$342$	8.63589	+	3.34227i	0.466975	+	0.180729i
$343$	1.73776	+	1.73776i	0.0938303	+	0.0938303i
$344$	0.0188789	−	0.0581032i	0.00101788	−	0.00313271i
$345$	0.221827	+	5.60696i	0.0119428	+	0.301868i
$346$	−3.91597	−	12.0521i	−0.210524	−	0.647926i
$347$	13.0477	+	6.64812i	0.700436	+	0.356890i	0.767668	−	0.640847i	$-0.221417\pi$
$347$	13.0477	+	6.64812i	0.700436	+	0.356890i	−0.0672324	+	0.997737i	$0.521417\pi$
$348$	−1.38348	−	8.73493i	−0.0741621	−	0.468241i
$349$		−	15.1924i		−	0.813229i	−0.913600	−	0.406614i	$-0.866709\pi$
$349$		−	15.1924i		−	0.813229i	0.913600	−	0.406614i	$-0.133291\pi$
$350$	−18.1959	+	1.44202i	−0.972612	+	0.0770791i
$351$	18.4240			0.983399
$352$	−0.669228	−	4.22534i	−0.0356700	−	0.225211i
$353$	8.22337	−	16.1393i	0.437686	−	0.859006i	−0.561811	−	0.827266i	$-0.689895\pi$
$353$	8.22337	−	16.1393i	0.437686	−	0.859006i	0.999496	−	0.0317404i	$-0.0101050\pi$
$354$	3.68857	+	11.3523i	0.196045	+	0.603366i
$355$	15.6778	−	12.3663i	0.832089	−	0.656333i
$356$	−0.145108	−	0.0471486i	−0.00769073	−	0.00249887i
$357$	−12.1388	−	12.1388i	−0.642453	−	0.642453i
$358$	−18.6053	+	9.47988i	−0.983322	+	0.501027i
$359$	8.77213	+	12.0738i	0.462975	+	0.637231i	0.975122	−	0.221667i	$-0.0711498\pi$
$359$	8.77213	+	12.0738i	0.462975	+	0.637231i	−0.512147	+	0.858898i	$0.671150\pi$
$360$	−0.557057	+	4.71755i	−0.0293595	+	0.248637i
$361$	−12.7909	+	14.0497i	−0.673205	+	0.739456i
$362$	0.0203777	−	0.128660i	0.00107103	−	0.00676220i
$363$	1.06877	−	6.74797i	0.0560961	−	0.354177i
$364$	11.3477	+	8.24462i	0.594784	+	0.432136i
$365$	−0.243212	−	0.434010i	−0.0127303	−	0.0227171i
$366$	6.04859	−	4.39456i	0.316165	−	0.229707i
$367$	−10.0268	−	19.6787i	−0.523396	−	1.02722i	−0.989775	−	0.142637i	$-0.954442\pi$
$367$	−10.0268	−	19.6787i	−0.523396	−	1.02722i	0.466380	−	0.884585i	$-0.345558\pi$
$368$	1.89634	+	1.89634i	0.0988536	+	0.0988536i
$369$	−0.441827	+	1.35981i	−0.0230006	+	0.0707886i
$370$	−4.96460	−	13.4459i	−0.258097	−	0.699017i
$371$	−17.9899	+	5.84527i	−0.933989	+	0.303472i
$372$	−3.98673	−	2.03134i	−0.206702	−	0.105320i
$373$	−3.92418	+	0.621528i	−0.203186	+	0.0321815i	−0.257198	−	0.966359i	$-0.582799\pi$
$373$	−3.92418	+	0.621528i	−0.203186	+	0.0321815i	0.0540117	+	0.998540i	$0.482799\pi$
$374$	21.4990			1.11169
$375$	8.69389	−	5.81935i	0.448951	−	0.300510i
$376$		−	11.7081i		−	0.603799i
$377$	−35.8673	+	5.68082i	−1.84726	+	0.292577i
$378$	7.94701	−	15.5969i	0.408750	−	0.802217i
$379$	−3.03322	−	9.33530i	−0.155806	−	0.479522i	0.842435	−	0.538797i	$-0.181121\pi$
$379$	−3.03322	−	9.33530i	−0.155806	−	0.479522i	−0.998242	+	0.0592750i	$0.981121\pi$
$380$	−8.61453	−	4.55959i	−0.441916	−	0.233902i
$381$	−3.50896	+	10.7995i	−0.179770	+	0.553274i
$382$	−9.30449	−	9.30449i	−0.476059	−	0.476059i
$383$	11.0722	+	21.7303i	0.565761	+	1.11037i	0.979776	+	0.200099i	$0.0641263\pi$
$383$	11.0722	+	21.7303i	0.565761	+	1.11037i	−0.414014	+	0.910270i	$0.635874\pi$
$384$	−0.550008	−	0.757021i	−0.0280675	−	0.0386316i
$385$	−30.4640	+	17.0715i	−1.55259	+	0.870047i
$386$	−10.4908	−	7.62204i	−0.533969	−	0.387951i
$387$	−0.0203032	+	0.128189i	−0.00103207	+	0.00651623i
$388$	−2.14638	+	13.5517i	−0.108966	+	0.687985i
$389$	−16.2684	+	22.3916i	−0.824843	+	1.13530i	0.164018	+	0.986457i	$0.447554\pi$
$389$	−16.2684	+	22.3916i	−0.824843	+	1.13530i	−0.988861	+	0.148841i	$0.952446\pi$
$390$	−7.98394	−	0.942758i	−0.404283	−	0.0477384i
$391$	−10.9035	+	7.92187i	−0.551414	+	0.400626i
$392$	5.63722	−	2.87231i	0.284723	−	0.145073i
$393$	−13.8782	+	13.8782i	−0.700065	+	0.700065i
$394$	2.83077	−	8.71222i	0.142612	−	0.438915i
$395$	−4.26368	−	5.40542i	−0.214529	−	0.271976i
$396$	2.80842	+	8.64343i	0.141129	+	0.434349i
$397$	5.35083	+	2.72638i	0.268550	+	0.136833i	0.583081	−	0.812414i	$-0.301847\pi$
$397$	5.35083	+	2.72638i	0.268550	+	0.136833i	−0.314530	+	0.949247i	$0.601847\pi$
$398$	−20.9552	+	3.31898i	−1.05039	+	0.166365i
$399$	9.93280	+	11.0926i	0.497262	+	0.555327i
$400$	1.16458	−	4.86248i	0.0582290	−	0.243124i
$401$		−	17.0596i		−	0.851917i	−0.904743	−	0.425958i	$-0.859937\pi$
$401$		−	17.0596i		−	0.851917i	0.904743	−	0.425958i	$-0.140063\pi$
$402$	−0.819865	−	5.17643i	−0.0408912	−	0.258177i
$403$	−8.34107	+	16.3703i	−0.415498	+	0.815462i
$404$	−12.8987	+	4.19103i	−0.641732	+	0.208511i
$405$	−0.166746	−	4.21472i	−0.00828568	−	0.209431i
$406$	−10.6619	+	32.8140i	−0.529141	+	1.62853i
$407$	−19.3902	−	19.3902i	−0.961137	−	0.961137i
$408$	4.18995	−	2.13488i	0.207433	−	0.105692i
$409$	−9.06077	+	6.58303i	−0.448026	+	0.325510i	−0.788816	−	0.614629i	$-0.789306\pi$
$409$	−9.06077	+	6.58303i	−0.448026	+	0.325510i	0.340790	+	0.940140i	$0.389306\pi$
$410$	0.629682	−	1.36687i	0.0310978	−	0.0675047i
$411$	10.6909	−	14.7148i	0.527345	−	0.725828i
$412$	−17.2139	−	2.72641i	−0.848066	−	0.134320i
$413$	7.28486	−	45.9948i	0.358465	−	2.26326i
$414$	−4.60922	−	3.34880i	−0.226531	−	0.164584i
$415$	−10.7811	+	11.6693i	−0.529225	+	0.572826i
$416$	−3.10847	+	2.25844i	−0.152405	+	0.110729i
$417$	−2.95352	+	1.50489i	−0.144635	+	0.0736950i
$418$	−18.6191	−	1.02710i	−0.910690	−	0.0502372i
$419$	−25.1956	−	8.18656i	−1.23089	−	0.399940i	−0.379852	−	0.925047i	$-0.624025\pi$
$419$	−25.1956	−	8.18656i	−1.23089	−	0.399940i	−0.851036	+	0.525108i	$0.824025\pi$
$420$	−4.24190	+	6.35219i	−0.206983	+	0.309955i
$421$	5.53528	−	1.79852i	0.269773	−	0.0876546i	−0.171007	−	0.985270i	$-0.554702\pi$
$421$	5.53528	−	1.79852i	0.269773	−	0.0876546i	0.440780	+	0.897615i	$0.354702\pi$
$422$	−5.31352	−	2.70737i	−0.258658	−	0.131793i
$423$	3.89097	+	24.5666i	0.189185	+	1.19447i
$424$		−	5.18155i		−	0.251638i
$425$	23.2199	+	9.60319i	1.12633	+	0.465823i
$426$		−	8.35598i		−	0.404849i
$427$	−28.8091	+	4.56291i	−1.39417	+	0.220815i
$428$	5.92490	+	3.01889i	0.286391	+	0.145924i
$429$	−14.6281	+	4.75295i	−0.706250	+	0.229475i
$430$	0.0370454	−	0.131490i	0.00178649	−	0.00634101i
$431$	11.0290	+	3.58355i	0.531250	+	0.172614i	0.562345	−	0.826903i	$-0.309899\pi$
$431$	11.0290	+	3.58355i	0.531250	+	0.172614i	−0.0310948	+	0.999516i	$0.509899\pi$
$432$	3.39062	+	3.39062i	0.163131	+	0.163131i
$433$	−5.42689	−	10.6509i	−0.260800	−	0.511849i	0.723061	−	0.690784i	$-0.242735\pi$
$433$	−5.42689	−	10.6509i	−0.260800	−	0.511849i	−0.983861	+	0.178936i	$0.942735\pi$
$434$	10.2605	+	14.1223i	0.492519	+	0.677894i
$435$	−3.86326	−	19.3943i	−0.185229	−	0.929887i
$436$	5.77272	−	7.94547i	0.276463	−	0.380519i
$437$	9.82138	−	6.33977i	0.469820	−	0.303272i
$438$	−0.205630	−	0.0325687i	−0.00982540	−	0.00155619i
$439$	−7.02002	−	5.10034i	−0.335047	−	0.243426i	0.407522	−	0.913195i	$-0.366393\pi$
$439$	−7.02002	−	5.10034i	−0.335047	−	0.243426i	−0.742569	+	0.669769i	$0.766393\pi$
$440$	−1.86877	−	9.38160i	−0.0890902	−	0.447250i
$441$	−10.8738	+	7.90026i	−0.517799	+	0.376203i
$442$	−8.76623	−	17.2047i	−0.416967	−	0.818344i
$443$	10.5358	+	10.5358i	0.500573	+	0.500573i	0.911616	−	0.411043i	$-0.134835\pi$
$443$	10.5358	+	10.5358i	0.500573	+	0.500573i	−0.411043	+	0.911616i	$0.634835\pi$
$444$	−5.70443	−	1.85348i	−0.270720	−	0.0879624i
$445$	−0.328387	−	0.0925181i	−0.0155670	−	0.00438578i
$446$	5.09457	+	15.6795i	0.241235	+	0.742444i
$447$	−6.49544	+	12.7480i	−0.307224	+	0.602961i
$448$	0.571078	+	3.60564i	0.0269809	+	0.170351i
$449$	−8.63220			−0.407379			−0.203689	−	0.979036i	$-0.565293\pi$
$449$	−8.63220			−0.407379			−0.203689	+	0.979036i	$0.565293\pi$
$450$	−0.827630	+	10.5898i	−0.0390149	+	0.499206i
$451$		−	2.87921i		−	0.135577i
$452$	−2.34028	−	14.7759i	−0.110077	−	0.695001i
$453$	6.10983	−	11.9912i	0.287065	−	0.563397i
$454$	−11.7407	+	3.81480i	−0.551021	+	0.179037i
$455$	26.0833	+	17.4180i	1.22280	+	0.816570i
$456$	−3.73067	+	1.64873i	−0.174705	+	0.0772089i
$457$	−9.98649	+	9.98649i	−0.467148	+	0.467148i	−0.900989	−	0.433841i	$-0.857158\pi$
$457$	−9.98649	+	9.98649i	−0.467148	+	0.467148i	0.433841	+	0.900989i	$0.357158\pi$
$458$	−1.11428	−	2.18690i	−0.0520668	−	0.102187i
$459$	−19.4953	+	14.1641i	−0.909961	+	0.661125i
$460$	4.40466	+	4.06940i	0.205368	+	0.189737i
$461$	−3.36827	−	2.44719i	−0.156876	−	0.113977i	0.506578	−	0.862194i	$-0.330910\pi$
$461$	−3.36827	−	2.44719i	−0.156876	−	0.113977i	−0.663454	+	0.748217i	$0.730910\pi$
$462$	−2.28606	+	14.4336i	−0.106357	+	0.671512i
$463$	7.03392	+	1.11406i	0.326894	+	0.0517749i	0.317725	−	0.948183i	$-0.397081\pi$
$463$	7.03392	+	1.11406i	0.326894	+	0.0517749i	0.00916934	+	0.999958i	$0.497081\pi$
$464$	−7.64622	−	5.55531i	−0.354967	−	0.257899i
$465$	−9.08720	−	4.18626i	−0.421409	−	0.194133i
$466$	11.1132	+	15.2961i	0.514810	+	0.708576i
$467$	10.5176	+	20.6419i	0.486696	+	0.955195i	0.995540	+	0.0943362i	$0.0300729\pi$
$467$	10.5176	+	20.6419i	0.486696	+	0.955195i	−0.508844	+	0.860859i	$0.669927\pi$
$468$	5.77182	−	5.77182i	0.266802	−	0.266802i
$469$	−6.31837	+	19.4459i	−0.291755	+	0.897930i
$470$	−1.03495	−	26.1596i	−0.0477386	−	1.20665i
$471$	−0.963161	+	0.312950i	−0.0443801	+	0.0144200i
$472$	11.3660	+	5.79125i	0.523161	+	0.266564i
$473$	−0.0408853	−	0.258140i	−0.00187991	−	0.0118693i
$474$	−2.88100			−0.132329
$475$	−19.6507	−	9.42610i	−0.901634	−	0.432499i
$476$	−18.3460			−0.840885
$477$	1.72199	+	10.8722i	0.0788445	+	0.497804i
$478$	−10.8141	−	5.51006i	−0.494626	−	0.252024i
$479$	1.04845	−	0.340662i	0.0479049	−	0.0155652i	−0.284967	−	0.958537i	$-0.591982\pi$
$479$	1.04845	−	0.340662i	0.0479049	−	0.0155652i	0.332871	+	0.942972i	$0.391982\pi$
$480$	−1.29581	−	1.64281i	−0.0591454	−	0.0749836i
$481$	−7.61075	+	23.4235i	−0.347020	+	1.06802i
$482$	9.30813	−	9.30813i	0.423974	−	0.423974i
$483$	−4.15902	−	8.16255i	−0.189242	−	0.371409i
$484$	−4.29162	−	5.90691i	−0.195074	−	0.268496i
$485$	−3.59779	+	30.4687i	−0.163367	+	1.38351i
$486$	−13.0659	−	9.49291i	−0.592680	−	0.430607i
$487$	7.09151	+	1.12319i	0.321347	+	0.0508964i	0.315024	−	0.949084i	$-0.397987\pi$
$487$	7.09151	+	1.12319i	0.321347	+	0.0508964i	0.00632292	+	0.999980i	$0.497987\pi$
$488$	1.24991	−	7.89162i	0.0565808	−	0.357237i
$489$	14.8289	+	10.7739i	0.670588	+	0.487210i
$490$	12.3415	−	6.91596i	0.557530	−	0.312431i
$491$	8.41487	−	6.11376i	0.379758	−	0.275910i	−0.381488	−	0.924374i	$-0.624588\pi$
$491$	8.41487	−	6.11376i	0.379758	−	0.275910i	0.761246	+	0.648464i	$0.224588\pi$
$492$	−0.285910	−	0.561129i	−0.0128898	−	0.0252977i
$493$	33.5855	−	33.5855i	1.51261	−	1.51261i
$494$	6.77000	+	15.3188i	0.304597	+	0.689227i
$495$	7.03896	+	19.0639i	0.316378	+	0.856861i
$496$	−4.54771	+	1.47764i	−0.204198	+	0.0663480i
$497$	−14.7998	+	29.0463i	−0.663863	+	1.30291i
$498$	1.04004	+	6.56652i	0.0466051	+	0.294253i
$499$		−	37.4660i		−	1.67721i	−0.544743	−	0.838603i	$-0.683373\pi$
$499$		−	37.4660i		−	1.67721i	0.544743	−	0.838603i	$-0.316627\pi$
$500$	2.17222	−	10.9673i	0.0971446	−	0.490472i
$501$	13.3340			0.595718
$502$	−1.80356	−	11.3873i	−0.0804970	−	0.508238i
$503$	−1.54574	+	3.03369i	−0.0689212	+	0.135266i	−0.922897	−	0.385048i	$-0.874185\pi$
$503$	−1.54574	+	3.03369i	−0.0689212	+	0.135266i	0.853975	+	0.520314i	$0.174185\pi$
$504$	−2.39654	−	7.37578i	−0.106750	−	0.328543i
$505$	−28.4492	+	10.5043i	−1.26597	+	0.467434i
$506$	10.9114	+	3.54532i	0.485070	+	0.157609i
$507$	1.16659	+	1.16659i	0.0518100	+	0.0518100i
$508$	5.50925	+	10.8125i	0.244434	+	0.479728i
$509$	−0.610561	+	0.443599i	−0.0270627	+	0.0196622i	−0.601234	−	0.799073i	$-0.705324\pi$
$509$	−0.610561	+	0.443599i	−0.0270627	+	0.0196622i	0.574172	+	0.818735i	$0.305324\pi$
$510$	9.17296	−	5.14039i	0.406186	−	0.227620i
$511$	0.657110	+	0.477418i	0.0290688	+	0.0211197i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	17.5604	−	11.3354i	0.775312	−	0.500469i
$514$	12.9166	−	17.7782i	0.569729	−	0.784165i
$515$	−38.7023	−	4.57003i	−1.70543	−	0.201380i
$516$	−0.0336018	−	0.0462489i	−0.00147924	−	0.00203599i
$517$	−22.7392	−	44.6281i	−1.00007	−	1.96274i
$518$	16.5464	+	16.5464i	0.727008	+	0.727008i
$519$	−11.2775	−	3.66429i	−0.495029	−	0.160845i
$520$	−6.74568	+	5.32084i	−0.295818	+	0.233334i
$521$	42.6356	−	13.8532i	1.86790	−	0.606918i	0.875606	−	0.483027i	$-0.160463\pi$
$521$	42.6356	−	13.8532i	1.86790	−	0.606918i	0.992296	−	0.123891i	$-0.0395374\pi$
$522$	17.8899	+	9.11537i	0.783021	+	0.398969i
$523$	19.5823	−	3.10154i	0.856276	−	0.135621i	0.287165	−	0.957881i	$-0.407287\pi$
$523$	19.5823	−	3.10154i	0.856276	−	0.135621i	0.569111	+	0.822260i	$0.307287\pi$
$524$			20.9749i			0.916291i
$525$	−8.91625	+	14.5678i	−0.389137	+	0.635791i
$526$			5.81482i			0.253538i
$527$	−3.75920	−	23.7347i	−0.163753	−	1.03390i
$528$	−3.56675	−	1.81735i	−0.155223	−	0.0790900i
$529$	15.0341	−	4.88487i	0.653656	−	0.212386i
$530$	−0.458028	−	11.5772i	−0.0198955	−	0.502883i
$531$	−25.7733	−	8.37426i	−1.11847	−	0.363412i
$532$	15.8884	+	0.876466i	0.688849	+	0.0379996i
$533$	−2.30410	+	1.17400i	−0.0998018	+	0.0508515i
$534$	−0.115503	+	0.0839181i	−0.00499832	+	0.00363149i
$535$	13.5050	+	6.22143i	0.583872	+	0.268976i
$536$	−4.53124	−	3.29214i	−0.195720	−	0.142199i
$537$	−3.05660	+	19.2986i	−0.131902	+	0.832797i
$538$	21.4578	+	3.39858i	0.925111	+	0.146523i
$539$	15.9091	−	21.8969i	0.685252	−	0.943168i
$540$	7.87545	+	7.27601i	0.338905	+	0.313110i
$541$	17.7936	−	12.9278i	0.765005	−	0.555808i	−0.135437	−	0.990786i	$-0.543244\pi$
$541$	17.7936	−	12.9278i	0.765005	−	0.555808i	0.900441	+	0.434978i	$0.143244\pi$
$542$	−2.52226	+	1.28516i	−0.108341	+	0.0552023i
$543$	−0.0861901	−	0.0861901i	−0.00369877	−	0.00369877i
$544$	1.55296	−	4.77951i	0.0665825	−	0.204920i
$545$	12.1958	−	18.2630i	0.522409	−	0.782301i
$546$	12.4827	−	4.05588i	0.534210	−	0.173575i
$547$	−7.62897	+	14.9727i	−0.326191	+	0.640187i	−0.994620	−	0.103590i	$-0.966967\pi$
$547$	−7.62897	+	14.9727i	−0.326191	+	0.640187i	0.668429	+	0.743776i	$0.266967\pi$
$548$	−3.04074	−	19.1985i	−0.129894	−	0.820119i
$549$			16.9740i			0.724434i
$550$	−5.00473	−	20.7963i	−0.213402	−	0.886757i
$551$	−30.6910	+	27.4820i	−1.30748	+	1.17077i
$552$	2.47857	−	0.392567i	0.105495	−	0.0167088i
$553$	10.0147	+	5.10273i	0.425867	+	0.216990i
$554$	−0.508463	−	1.56489i	−0.0216025	−	0.0664857i
$555$	−12.9094	−	3.63702i	−0.547972	−	0.154383i
$556$	−1.09469	+	3.36911i	−0.0464252	+	0.142882i
$557$	−2.59844	+	2.59844i	−0.110099	+	0.110099i	−0.760010	−	0.649911i	$-0.774806\pi$
$557$	−2.59844	+	2.59844i	−0.110099	+	0.110099i	0.649911	+	0.760010i	$0.274806\pi$
$558$	9.05118	−	4.61181i	0.383167	−	0.195233i
$559$	−0.189907	+	0.137975i	−0.00803220	+	0.00583573i
$560$	1.59470	+	8.00568i	0.0673882	+	0.338302i
$561$	11.8246	−	16.2752i	0.499236	−	0.687140i
$562$	1.11771	−	7.05696i	0.0471478	−	0.297680i
$563$	−3.14412	+	19.8512i	−0.132509	+	0.836628i	0.828476	+	0.560025i	$0.189209\pi$
$563$	−3.14412	+	19.8512i	−0.132509	+	0.836628i	−0.960984	+	0.276603i	$0.910791\pi$
$564$	−8.86328	−	6.43955i	−0.373211	−	0.271154i
$565$	−6.53506	−	32.8073i	−0.274932	−	1.38021i
$566$	2.87910	+	3.96274i	0.121018	+	0.166566i
$567$	3.12631	+	6.13574i	0.131293	+	0.257677i
$568$	−6.31440	−	6.31440i	−0.264946	−	0.264946i
$569$	−13.7551	+	42.3339i	−0.576645	+	1.77473i	0.0538644	+	0.998548i	$0.482846\pi$
$569$	−13.7551	+	42.3339i	−0.576645	+	1.77473i	−0.630509	+	0.776182i	$0.717154\pi$
$570$	−8.18977	+	4.01357i	−0.343032	+	0.168110i
$571$	1.19632	+	3.68189i	0.0500644	+	0.154082i	0.972963	−	0.230960i	$-0.0741868\pi$
$571$	1.19632	+	3.68189i	0.0500644	+	0.154082i	−0.922899	+	0.385043i	$0.874187\pi$
$572$	−7.46238	+	14.6457i	−0.312018	+	0.612369i
$573$	−12.1612	+	1.92615i	−0.508043	+	0.0804661i
$574$			2.45694i			0.102551i
$575$	10.2011	+	8.70300i	0.425417	+	0.362940i
$576$	2.12441			0.0885171
$577$	−4.46991	+	0.707965i	−0.186085	+	0.0294730i	−0.248781	−	0.968560i	$-0.580030\pi$
$577$	−4.46991	+	0.707965i	−0.186085	+	0.0294730i	0.0626963	+	0.998033i	$0.480030\pi$
$578$	7.35563	+	3.74788i	0.305954	+	0.155891i
$579$	−11.5401	+	3.74960i	−0.479589	+	0.155828i
$580$	−17.5752	−	11.7364i	−0.729769	−	0.487329i
$581$	8.01513	−	24.6680i	0.332524	−	1.02340i
$582$	9.07842	+	9.07842i	0.376313	+	0.376313i
$583$	−10.0635	−	19.7507i	−0.416786	−	0.817989i
$584$	−0.180001	+	0.130778i	−0.00744849	+	0.00541165i
$585$	12.3859	−	13.4063i	0.512093	−	0.554282i
$586$	18.2421	+	13.2537i	0.753575	+	0.547504i
$587$	−5.57237	+	35.1826i	−0.229996	+	1.45214i	0.554592	+	0.832122i	$0.312874\pi$
$587$	−5.57237	+	35.1826i	−0.229996	+	1.45214i	−0.784588	+	0.620017i	$0.787126\pi$
$588$	0.926119	−	5.84729i	0.0381925	−	0.241138i
$589$	2.12172	+	20.7349i	0.0874241	+	0.854365i
$590$	25.9071	+	11.9348i	1.06658	+	0.491348i
$591$	−5.03838	−	6.93474i	−0.207251	−	0.285257i
$592$	−5.71132	+	2.91007i	−0.234734	+	0.119603i
$593$	21.9971	+	21.9971i	0.903314	+	0.903314i	0.995721	−	0.0924072i	$-0.0294562\pi$
$593$	21.9971	+	21.9971i	0.903314	+	0.903314i	−0.0924072	+	0.995721i	$0.529456\pi$
$594$	19.5093	+	6.33896i	0.800477	+	0.260091i
$595$	−40.9907	+	1.62171i	−1.68046	+	0.0664836i
$596$	4.72492	+	14.5418i	0.193540	+	0.595655i
$597$	−9.01298	+	17.6890i	−0.368877	+	0.723962i
$598$	−1.61196	−	10.1775i	−0.0659178	−	0.416188i
$599$	−34.5128			−1.41015			−0.705077	−	0.709131i	$-0.749088\pi$
$599$	−34.5128			−1.41015			−0.705077	+	0.709131i	$0.749088\pi$
$600$	−3.04047	−	3.55602i	−0.124127	−	0.145174i
$601$		−	23.1363i		−	0.943751i	−0.881665	−	0.471876i	$-0.843577\pi$
$601$		−	23.1363i		−	0.943751i	0.881665	−	0.471876i	$-0.156423\pi$
$602$	0.0348890	+	0.220281i	0.00142197	+	0.00897797i
$603$	10.6018	+	5.40188i	0.431738	+	0.219982i
$604$	−4.44442	−	13.6785i	−0.180841	−	0.556571i
$605$	−10.1110	−	12.8186i	−0.411071	−	0.521149i
$606$	−3.92167	+	12.0696i	−0.159307	+	0.490296i
$607$	−18.9418	−	18.9418i	−0.768822	−	0.768822i	0.209077	−	0.977899i	$-0.432954\pi$
$607$	−18.9418	−	18.9418i	−0.768822	−	0.768822i	−0.977899	+	0.209077i	$0.932954\pi$
$608$	−1.57327	+	4.06507i	−0.0638044	+	0.164861i
$609$	18.9767	+	26.1192i	0.768975	+	1.05840i
$610$	2.09511	−	17.7429i	0.0848286	−	0.718389i
$611$	−26.4420	+	36.3943i	−1.06973	+	1.47236i
$612$	−1.67012	+	10.5447i	−0.0675107	+	0.426246i
$613$	−3.96062	−	0.627301i	−0.159968	−	0.0253365i	0.0759366	−	0.997113i	$-0.475805\pi$
$613$	−3.96062	−	0.627301i	−0.159968	−	0.0253365i	−0.235905	+	0.971776i	$0.575805\pi$
$614$	18.9051	−	26.0206i	0.762946	−	1.05011i
$615$	−0.688415	−	1.22847i	−0.0277596	−	0.0495367i
$616$	9.17959	+	12.6346i	0.369856	+	0.509063i
$617$	−20.3009	−	39.8427i	−0.817282	−	1.60401i	−0.796821	−	0.604216i	$-0.793486\pi$
$617$	−20.3009	−	39.8427i	−0.817282	−	1.60401i	−0.0204616	−	0.999791i	$-0.506514\pi$
$618$	−11.5317	+	11.5317i	−0.463873	+	0.463873i
$619$	−31.6900	−	10.2967i	−1.27373	−	0.413859i	−0.407361	−	0.913267i	$-0.633551\pi$
$619$	−31.6900	−	10.2967i	−1.27373	−	0.413859i	−0.866367	+	0.499408i	$0.833551\pi$
$620$	−10.0304	+	3.70352i	−0.402831	+	0.148737i
$621$	−12.2302	+	3.97382i	−0.490779	+	0.159464i
$622$	−2.42168	+	4.75281i	−0.0971004	+	0.190570i
$623$	0.550135	−	0.0871328i	0.0220407	−	0.00349090i
$624$			3.59533i			0.143929i
$625$	3.88397	−	24.6965i	0.155359	−	0.987858i
$626$		−	14.1287i		−	0.564695i
$627$	−11.0182	+	13.5301i	−0.440024	+	0.540341i
$628$	−0.491348	+	0.964324i	−0.0196069	+	0.0384807i
$629$	−9.95441	−	30.6365i	−0.396908	−	1.22156i
$630$	−6.00662	−	16.2680i	−0.239309	−	0.648133i
$631$	−0.635102	+	1.95464i	−0.0252830	+	0.0778132i	−0.962902	−	0.269852i	$-0.913025\pi$
$631$	−0.635102	+	1.95464i	−0.0252830	+	0.0778132i	0.937619	+	0.347665i	$0.113025\pi$
$632$	−2.17710	+	2.17710i	−0.0866003	+	0.0866003i
$633$	−4.97201	+	2.53337i	−0.197620	+	0.100692i
$634$	−12.9208	−	17.7839i	−0.513150	−	0.706290i
$635$	13.2652	+	23.6716i	0.526414	+	0.939380i
$636$	−3.92254	−	2.84989i	−0.155539	−	0.113006i
$637$	−24.0101	−	3.80282i	−0.951313	−	0.150673i
$638$	−39.9347	−	6.32504i	−1.58103	−	0.250411i
$639$	15.3477	+	11.1508i	0.607146	+	0.441117i
$640$	−2.22064	−	0.262217i	−0.0877785	−	0.0103650i
$641$	−10.0576	−	13.8432i	−0.397253	−	0.546772i	0.562799	−	0.826594i	$-0.309725\pi$
$641$	−10.0576	−	13.8432i	−0.397253	−	0.546772i	−0.960052	+	0.279822i	$0.909725\pi$
$642$	5.54411	−	2.82486i	0.218808	−	0.111488i
$643$	1.68280	+	1.68280i	0.0663631	+	0.0663631i	0.739509	−	0.673146i	$-0.235058\pi$
$643$	1.68280	+	1.68280i	0.0663631	+	0.0663631i	−0.673146	+	0.739509i	$0.735058\pi$
$644$	−9.31110	−	3.02536i	−0.366909	−	0.119216i
$645$	−0.0791654	−	0.100365i	−0.00311713	−	0.00395185i
$646$	−18.9406	−	11.0049i	−0.745207	−	0.432981i
$647$	4.90912	+	2.50132i	0.192998	+	0.0983371i	0.547819	−	0.836597i	$-0.315458\pi$
$647$	4.90912	+	2.50132i	0.192998	+	0.0983371i	−0.354821	+	0.934934i	$0.615458\pi$
$648$	−1.86313	+	0.295091i	−0.0731906	+	0.0115923i
$649$	54.5717			2.14213
$650$	−14.6017	+	12.4848i	−0.572725	+	0.489693i
$651$	16.3343			0.640190
$652$	19.3474	−	3.06432i	0.757702	−	0.120008i
$653$	−18.8267	+	36.9494i	−0.736744	+	1.44594i	0.152402	+	0.988319i	$0.451299\pi$
$653$	−18.8267	+	36.9494i	−0.736744	+	1.44594i	−0.889146	+	0.457623i	$0.848701\pi$
$654$	−2.83984	−	8.74014i	−0.111047	−	0.341767i
$655$	1.85409	+	46.8646i	0.0724455	+	1.83115i
$656$	−0.640086	−	0.207976i	−0.0249912	−	0.00812012i
$657$	0.334226	−	0.334226i	0.0130394	−	0.0130394i
$658$	19.4042	+	38.0829i	0.756455	+	1.48463i
$659$	−29.2877	+	21.2787i	−1.14089	+	0.828902i	−0.987242	−	0.159224i	$-0.949101\pi$
$659$	−29.2877	+	21.2787i	−1.14089	+	0.828902i	−0.153643	+	0.988126i	$0.549101\pi$
$660$	−8.12991	−	3.74525i	−0.316456	−	0.145784i
$661$	13.4238	−	18.4762i	0.522124	−	0.718642i	−0.463781	−	0.885950i	$-0.653507\pi$
$661$	13.4238	−	18.4762i	0.522124	−	0.718642i	0.985905	+	0.167308i	$0.0535074\pi$
$662$	0.750245	−	4.73686i	0.0291591	−	0.184103i
$663$	−17.8458	−	2.82650i	−0.693074	−	0.109772i
$664$	5.74808	+	4.17623i	0.223069	+	0.162069i
$665$	35.5772	+	0.553836i	1.37963	+	0.0214769i
$666$	11.0167	−	8.00411i	0.426889	−	0.310153i
$667$	22.5840	−	11.5071i	0.874458	−	0.445558i
$668$	10.0762	−	10.0762i	0.389858	−	0.389858i
$669$	14.6717	+	4.76714i	0.567242	+	0.184308i
$670$	−10.4153	−	6.95515i	−0.402377	−	0.268701i
$671$	−10.5626	−	32.5083i	−0.407764	−	1.25497i
$672$	3.04365	+	1.55081i	0.117411	+	0.0598240i
$673$	45.9018	−	7.27013i	1.76938	−	0.280243i	0.815138	−	0.579266i	$-0.196661\pi$
$673$	45.9018	−	7.27013i	1.76938	−	0.280243i	0.954246	+	0.299023i	$0.0966608\pi$
$674$		−	22.0941i		−	0.851034i
$675$	18.2394	+	15.5608i	0.702036	+	0.598935i
$676$	1.76312			0.0678123
$677$	1.83311	+	11.5738i	0.0704521	+	0.444817i	0.997548	+	0.0699919i	$0.0222974\pi$
$677$	1.83311	+	11.5738i	0.0704521	+	0.444817i	−0.927095	+	0.374825i	$0.877703\pi$
$678$	−12.4729	−	6.35524i	−0.479017	−	0.244071i
$679$	−15.4782	−	47.6370i	−0.593999	−	1.82814i
$680$	3.04731	−	10.8162i	0.116859	−	0.414784i
$681$	−3.56962	+	10.9862i	−0.136788	+	0.420991i
$682$	−14.4648	+	14.4648i	−0.553886	+	0.553886i
$683$	−8.92109	−	17.5086i	−0.341356	−	0.669949i	0.654964	−	0.755660i	$-0.272684\pi$
$683$	−8.92109	−	17.5086i	−0.341356	−	0.669949i	−0.996320	+	0.0857112i	$0.972684\pi$
$684$	1.95017	−	9.05241i	0.0745665	−	0.346128i
$685$	−8.49106	−	42.6268i	−0.324427	−	1.62869i
$686$	1.44452	−	1.98821i	0.0551521	−	0.0759103i
$687$	−2.26839	−	0.359277i	−0.0865444	−	0.0137073i
$688$	−0.0603412	−	0.00955710i	−0.00230048	−	0.000364361i
$689$	−11.7022	+	16.1067i	−0.445818	+	0.613616i
$690$	5.50322	−	1.09622i	0.209504	−	0.0417323i
$691$	23.7046	−	17.2224i	0.901764	−	0.655170i	−0.0371543	−	0.999310i	$-0.511829\pi$
$691$	23.7046	−	17.2224i	0.901764	−	0.655170i	0.938919	+	0.344140i	$0.111829\pi$
$692$	−11.2912	+	5.75313i	−0.429225	+	0.218701i
$693$	−23.4600	−	23.4600i	−0.891172	−	0.891172i
$694$	4.52517	−	13.9270i	0.171773	−	0.528663i
$695$	−2.14807	+	7.62444i	−0.0814811	+	0.289211i
$696$	−8.41096	+	2.73289i	−0.318817	+	0.103590i
$697$	1.53552	−	3.01363i	0.0581620	−	0.114149i
$698$	−15.0053	+	2.37661i	−0.567960	+	0.0899560i
$699$	17.6918			0.669165
$700$	4.27073	+	17.7463i	0.161418	+	0.670747i
$701$	−14.5670			−0.550189			−0.275094	−	0.961417i	$-0.588709\pi$
$701$	−14.5670			−0.550189			−0.275094	+	0.961417i	$0.588709\pi$
$702$	−2.88214	−	18.1971i	−0.108780	−	0.686807i
$703$	7.15731	+	27.0081i	0.269943	+	1.01863i
$704$	−4.06863	+	1.32198i	−0.153342	+	0.0498239i
$705$	−20.3726	−	13.6045i	−0.767277	−	0.512376i
$706$	−17.2270	−	5.59738i	−0.648346	−	0.210660i
$707$	35.0095	−	35.0095i	1.31667	−	1.31667i
$708$	10.6355	−	5.41905i	0.399706	−	0.203660i
$709$	20.7023	+	28.4943i	0.777492	+	1.07013i	0.995554	+	0.0941911i	$0.0300265\pi$
$709$	20.7023	+	28.4943i	0.777492	+	1.07013i	−0.218062	+	0.975935i	$0.569974\pi$
$710$	−14.6666	−	13.5502i	−0.550426	−	0.508531i
$711$	3.84459	−	5.29162i	0.144183	−	0.198451i
$712$	−0.0238682	+	0.150698i	−0.000894497	+	0.00564763i
$713$	2.00609	−	12.6659i	0.0751286	−	0.474343i
$714$	−10.0904	+	13.8883i	−0.377624	+	0.519755i
$715$	−15.3787	+	33.3829i	−0.575132	+	1.24845i
$716$	12.2737	+	16.8933i	0.458689	+	0.631331i
$717$	−10.1191	+	5.15593i	−0.377904	+	0.192552i
$718$	10.5529	−	10.5529i	0.393830	−	0.393830i
$719$	25.7814	+	8.37690i	0.961486	+	0.312406i	0.747374	−	0.664404i	$-0.231314\pi$
$719$	25.7814	+	8.37690i	0.961486	+	0.312406i	0.214112	+	0.976809i	$0.431314\pi$
$720$	4.74661	−	0.187789i	0.176896	−	0.00699850i
$721$	60.5101	−	19.6609i	2.25351	−	0.732211i
$722$	15.8776	+	10.4356i	0.590904	+	0.388372i
$723$	−1.92690	−	12.1660i	−0.0716624	−	0.452458i
$724$	−0.130263			−0.00484120
$725$	−40.3060	−	24.6694i	−1.49693	−	0.916198i
$726$	−6.83208			−0.253562
$727$	35.4168	−	5.60946i	1.31353	−	0.208043i	0.539929	−	0.841711i	$-0.318451\pi$
$727$	35.4168	−	5.60946i	1.31353	−	0.208043i	0.773606	+	0.633667i	$0.218451\pi$
$728$	6.36794	−	12.4978i	0.236011	−	0.463199i
$729$	−8.99057	+	2.92121i	−0.332984	+	0.108193i
$730$	−0.390619	+	0.308112i	−0.0144575	+	0.0114037i
$731$	0.0948753	−	0.291996i	0.00350909	−	0.0107999i
$732$	−5.28666	−	5.28666i	−0.195401	−	0.195401i
$733$	45.0849	−	22.9719i	1.66525	−	0.848488i	0.670994	−	0.741463i	$-0.265868\pi$
$733$	45.0849	−	22.9719i	1.66525	−	0.848488i	0.994256	−	0.107025i	$-0.0341325\pi$
$734$	−17.8679	+	12.9818i	−0.659517	+	0.479167i
$735$	1.55237	−	13.1466i	0.0572600	−	0.484919i
$736$	1.57634	−	2.16965i	0.0581047	−	0.0799743i
$737$	−23.6658	−	3.74830i	−0.871741	−	0.138070i
$738$	1.41218	+	0.223667i	0.0519831	+	0.00823331i
$739$	−0.580828	+	0.799441i	−0.0213661	+	0.0294079i	−0.819566	−	0.572984i	$-0.805786\pi$
$739$	−0.580828	+	0.799441i	−0.0213661	+	0.0294079i	0.798200	+	0.602392i	$0.205786\pi$
$740$	−12.5037	+	7.00688i	−0.459645	+	0.257578i
$741$	15.3202	+	3.30045i	0.562802	+	0.121245i
$742$	8.58755	+	16.8540i	0.315259	+	0.618730i
$743$	2.57986	−	2.57986i	0.0946458	−	0.0946458i	−0.658199	−	0.752844i	$-0.728681\pi$
$743$	2.57986	−	2.57986i	0.0946458	−	0.0946458i	0.752844	+	0.658199i	$0.228681\pi$
$744$	−1.38267	+	4.25542i	−0.0506912	+	0.156011i
$745$	11.8424	+	32.0734i	0.433873	+	1.17508i
$746$	1.22775	+	3.77863i	0.0449512	+	0.138346i
$747$	−13.4488	−	6.85253i	−0.492067	−	0.250721i
$748$	−3.36319	−	21.2343i	−0.122970	−	0.776404i
$749$	−24.2752			−0.886998
$750$	−7.10773	−	7.67651i	−0.259538	−	0.280307i
$751$			1.56478i			0.0570996i	0.999592	+	0.0285498i	$0.00908892\pi$
$751$			1.56478i			0.0570996i	−0.999592	+	0.0285498i	$0.990911\pi$
$752$	−11.5640	+	1.83155i	−0.421694	+	0.0667898i
$753$	−9.61236	−	4.89774i	−0.350294	−	0.178484i
$754$	11.2218	+	34.5370i	0.408672	+	1.25776i
$755$	−11.1394	−	30.1693i	−0.405403	−	1.09797i
$756$	−16.6481	−	5.40928i	−0.605484	−	0.196734i
$757$	19.0908	−	19.0908i	0.693868	−	0.693868i	−0.269213	−	0.963081i	$-0.586763\pi$
$757$	19.0908	−	19.0908i	0.693868	−	0.693868i	0.963081	+	0.269213i	$0.0867634\pi$
$758$	−8.74587	+	4.45624i	−0.317664	+	0.161858i
$759$	8.68522	−	6.31018i	0.315254	−	0.229045i
$760$	−3.15585	+	9.22175i	−0.114475	+	0.334508i
$761$	17.4203	+	12.6566i	0.631485	+	0.458801i	0.856914	−	0.515459i	$-0.172378\pi$
$761$	17.4203	+	12.6566i	0.631485	+	0.458801i	−0.225429	+	0.974260i	$0.572378\pi$
$762$	11.2154	+	1.77635i	0.406292	+	0.0643504i
$763$	−5.60864	+	35.4115i	−0.203046	+	1.28198i
$764$	−7.73439	+	10.6455i	−0.279821	+	0.385140i
$765$	−2.79947	+	23.7079i	−0.101215	+	0.857163i
$766$	19.7307	−	14.3352i	0.712901	−	0.517953i
$767$	−22.2516	−	43.6713i	−0.803459	−	1.57688i
$768$	−0.661661	+	0.661661i	−0.0238756	+	0.0238756i
$769$	35.6017	+	11.5677i	1.28383	+	0.417142i	0.869928	−	0.493179i	$-0.164165\pi$
$769$	35.6017	+	11.5677i	1.28383	+	0.417142i	0.413903	+	0.910321i	$0.364165\pi$
$770$	21.6270	+	27.4183i	0.779383	+	0.988089i
$771$	−6.35424	−	19.5563i	−0.228842	−	0.704305i
$772$	−5.88707	+	11.5540i	−0.211880	+	0.415838i
$773$	18.1754	−	2.87870i	0.653724	−	0.103540i	0.179242	−	0.983805i	$-0.442635\pi$
$773$	18.1754	−	2.87870i	0.653724	−	0.103540i	0.474482	+	0.880265i	$0.342635\pi$
$774$	0.129787			0.00466511
$775$	−22.0838	+	9.16149i	−0.793273	+	0.329091i
$776$	13.7207			0.492543
$777$	21.6266	−	3.42532i	0.775851	−	0.122883i
$778$	24.6609	+	12.5653i	0.884135	+	0.450489i
$779$	−1.47380	+	2.53658i	−0.0528045	+	0.0908823i
$780$	0.317813	+	8.03313i	0.0113795	+	0.287632i
$781$	−36.3325	−	11.8051i	−1.30008	−	0.422421i
$782$	9.53002	+	9.53002i	0.340793	+	0.340793i
$783$	40.3798	−	20.5745i	1.44306	−	0.735274i
$784$	−3.71880	−	5.11849i	−0.132814	−	0.182803i
$785$	−1.01259	+	2.19804i	−0.0361407	+	0.0784515i
$786$	15.8784	+	11.5363i	0.566364	+	0.411488i
$787$	−1.09689	−	0.173731i	−0.0391000	−	0.00619284i	0.136854	−	0.990591i	$-0.456301\pi$
$787$	−1.09689	−	0.173731i	−0.0391000	−	0.00619284i	−0.175954	+	0.984398i	$0.556301\pi$
$788$	−9.04779	−	1.43303i	−0.322314	−	0.0510495i
$789$	4.40194	+	3.19820i	0.156713	+	0.113859i
$790$	−4.67189	+	5.05678i	−0.166218	+	0.179912i
$791$	32.1008	+	44.1830i	1.14137	+	1.57097i
$792$	8.09769	−	4.12598i	0.287739	−	0.146610i
$793$	−21.7080	+	21.7080i	−0.770875	+	0.770875i
$794$	1.85576	−	5.71145i	0.0658586	−	0.202692i
$795$	−9.01613	−	6.02084i	−0.319769	−	0.213537i
$796$	6.55623	+	20.1780i	0.232379	+	0.715190i
$797$	12.1023	−	23.7520i	0.428684	−	0.841340i	−0.571106	−	0.820876i	$-0.693486\pi$
$797$	12.1023	−	23.7520i	0.428684	−	0.841340i	0.999791	−	0.0204642i	$-0.00651441\pi$
$798$	9.40225	−	11.5458i	0.332836	−	0.408716i
$799$		−	58.8388i		−	2.08157i
$800$	−4.98480	−	0.389581i	−0.176239	−	0.0137738i
$801$		−	0.324134i		−	0.0114527i
$802$	−16.8496	+	2.66871i	−0.594980	+	0.0942355i
$803$	−0.432121	+	0.848085i	−0.0152492	+	0.0299283i
$804$	−4.98444	+	1.61954i	−0.175788	+	0.0571169i
$805$	−21.0714	−	5.93656i	−0.742669	−	0.209236i
$806$	17.4736	+	5.67750i	0.615480	+	0.199982i
$807$	14.3748	−	14.3748i	0.506015	−	0.506015i
$808$	6.15722	+	12.0842i	0.216610	+	0.425122i
$809$	28.5002	+	39.2272i	1.00201	+	1.37916i	0.924081	+	0.382197i	$0.124832\pi$
$809$	28.5002	+	39.2272i	1.00201	+	1.37916i	0.0779338	+	0.996959i	$0.475168\pi$
$810$	−4.13674	+	0.824020i	−0.145350	+	0.0289531i
$811$	−6.81720	+	9.38307i	−0.239384	+	0.329484i	−0.911758	−	0.410727i	$-0.865275\pi$
$811$	−6.81720	+	9.38307i	−0.239384	+	0.329484i	0.672374	+	0.740212i	$0.265275\pi$
$812$	34.0778	+	5.39740i	1.19590	+	0.189412i
$813$	−0.414374	+	2.61625i	−0.0145327	+	0.0917560i
$814$	−16.1182	+	22.1848i	−0.564942	+	0.777576i
$815$	42.9574	−	8.55691i	1.50473	−	0.299735i
$816$	−2.76405	−	3.80439i	−0.0967612	−	0.133180i
$817$	−0.0961161	+	0.248349i	−0.00336268	+	0.00868863i
$818$	7.91940	+	7.91940i	0.276895	+	0.276895i
$819$	−9.20816	+	28.3398i	−0.321759	+	0.990273i
$820$	−1.44854	−	0.408105i	−0.0505852	−	0.0142516i
$821$	10.5382	+	32.4332i	0.367785	+	1.13193i	0.948219	+	0.317619i	$0.102883\pi$
$821$	10.5382	+	32.4332i	0.367785	+	1.13193i	−0.580433	+	0.814308i	$0.697117\pi$
$822$	−16.2061	−	8.25741i	−0.565252	−	0.288010i
$823$	−4.66061	−	29.4260i	−0.162459	−	1.02572i	−0.925327	−	0.379170i	$-0.876209\pi$
$823$	−4.66061	−	29.4260i	−0.162459	−	1.02572i	0.762868	−	0.646554i	$-0.223791\pi$
$824$			17.4284i			0.607148i
$825$	−18.4959	−	7.64945i	−0.643944	−	0.266320i
$826$	−46.5681			−1.62031
$827$	−7.59982	−	47.9834i	−0.264272	−	1.66855i	−0.660830	−	0.750536i	$-0.729796\pi$
$827$	−7.59982	−	47.9834i	−0.264272	−	1.66855i	0.396558	−	0.918010i	$-0.370204\pi$
$828$	−2.58653	+	5.07634i	−0.0898880	+	0.176415i
$829$	−8.48735	−	26.1214i	−0.294778	−	0.907233i	−0.983296	−	0.182014i	$-0.941738\pi$
$829$	−8.48735	−	26.1214i	−0.294778	−	0.907233i	0.688518	−	0.725219i	$-0.258262\pi$
$830$	13.2122	+	8.82292i	0.458603	+	0.306248i
$831$	−1.46431	−	0.475783i	−0.0507964	−	0.0165047i
$832$	2.71690	+	2.71690i	0.0941917	+	0.0941917i
$833$	28.3297	−	14.4347i	0.981567	−	0.500133i
$834$	1.94840	+	2.68174i	0.0674675	+	0.0928611i
$835$	21.6227	−	23.4040i	0.748283	−	0.809930i
$836$	1.89821	+	18.5505i	0.0656510	+	0.641584i
$837$	3.58685	−	22.6464i	0.123980	−	0.782776i
$838$	−4.14430	+	26.1661i	−0.143163	+	0.903893i
$839$	9.98718	+	7.25611i	0.344796	+	0.250509i	0.746683	−	0.665181i	$-0.231645\pi$
$839$	9.98718	+	7.25611i	0.344796	+	0.250509i	−0.401887	+	0.915689i	$0.631645\pi$
$840$	6.93756	+	3.19597i	0.239369	+	0.110271i
$841$	−48.8049	+	35.4588i	−1.68293	+	1.22272i
$842$	−2.64229	−	5.18578i	−0.0910593	−	0.178714i
$843$	−4.72751	−	4.72751i	−0.162824	−	0.162824i
$844$	−1.84282	+	5.67162i	−0.0634326	+	0.195225i
$845$	3.93938	−	0.155853i	0.135519	−	0.00536150i
$846$	23.6555	−	7.68612i	0.813291	−	0.264254i
$847$	23.7491	+	12.1008i	0.816028	+	0.415787i
$848$	−5.11776	+	0.810573i	−0.175744	+	0.0278352i
$849$	4.58340			0.157302
$850$	5.85256	−	24.4363i	0.200741	−	0.838158i
$851$		−	17.1905i		−	0.589281i
$852$	−8.25310	+	1.30716i	−0.282747	+	0.0447827i
$853$	19.6569	−	38.5787i	0.673038	−	1.32091i	−0.261554	−	0.965189i	$-0.584235\pi$
$853$	19.6569	−	38.5787i	0.673038	−	1.32091i	0.934592	−	0.355722i	$-0.115765\pi$
$854$	9.01346	+	27.7406i	0.308434	+	0.949263i
$855$	3.55710	−	20.3984i	0.121650	−	0.697610i
$856$	2.05486	−	6.32422i	0.0702338	−	0.216157i
$857$	21.3881	+	21.3881i	0.730603	+	0.730603i	0.970739	−	0.240136i	$-0.0771922\pi$
$857$	21.3881	+	21.3881i	0.730603	+	0.730603i	−0.240136	+	0.970739i	$0.577192\pi$
$858$	6.98277	+	13.7045i	0.238388	+	0.467862i
$859$	−5.78352	−	7.96033i	−0.197331	−	0.271603i	0.698872	−	0.715247i	$-0.253686\pi$
$859$	−5.78352	−	7.96033i	−0.197331	−	0.271603i	−0.896203	+	0.443644i	$0.853686\pi$
$860$	−0.135666	−	0.0160197i	−0.00462618	−	0.000546267i
$861$	1.85996	+	1.35134i	0.0633871	+	0.0460535i
$862$	1.81411	−	11.4538i	0.0617888	−	0.390119i
$863$	−2.10090	+	13.2646i	−0.0715155	+	0.451531i	0.925782	+	0.378058i	$0.123408\pi$
$863$	−2.10090	+	13.2646i	−0.0715155	+	0.451531i	−0.997297	+	0.0734726i	$0.976592\pi$
$864$	2.81847	−	3.87929i	0.0958862	−	0.131976i
$865$	−24.7195	+	13.8524i	−0.840488	+	0.470997i
$866$	−9.67080	+	7.02625i	−0.328627	+	0.238762i
$867$	6.88288	−	3.50700i	0.233755	−	0.119104i
$868$	12.3434	−	12.3434i	0.418962	−	0.418962i
$869$	−4.07021	+	12.5268i	−0.138072	+	0.424943i
$870$	−18.5512	+	6.84964i	−0.628945	+	0.232225i
$871$	6.65015	+	20.4670i	0.225332	+	0.693499i
$872$	−8.75070	−	4.45870i	−0.296336	−	0.150991i
$873$	−28.7895	+	4.55980i	−0.974376	+	0.154326i
$874$	−7.79812	−	8.70870i	−0.263775	−	0.294576i
$875$	11.1109	+	39.2734i	0.375616	+	1.32768i
$876$			0.208194i			0.00703421i
$877$	0.220242	+	1.39056i	0.00743706	+	0.0469558i	0.991128	−	0.132912i	$-0.0424329\pi$
$877$	0.220242	+	1.39056i	0.00743706	+	0.0469558i	−0.983691	+	0.179868i	$0.942433\pi$
$878$	−3.93938	+	7.73146i	−0.132948	+	0.260924i
$879$	20.0666	−	6.52004i	0.676830	−	0.219915i
$880$	−8.97376	+	3.31337i	−0.302505	+	0.111694i
$881$	9.64817	−	29.6940i	0.325055	−	1.00042i	−0.646361	−	0.763032i	$-0.723710\pi$
$881$	9.64817	−	29.6940i	0.325055	−	1.00042i	0.971416	−	0.237384i	$-0.0762901\pi$
$882$	9.50403	+	9.50403i	0.320017	+	0.320017i
$883$	5.70786	−	2.90830i	0.192085	−	0.0978721i	−0.355303	−	0.934751i	$-0.615622\pi$
$883$	5.70786	−	2.90830i	0.192085	−	0.0978721i	0.547388	+	0.836879i	$0.315622\pi$
$884$	−15.6215	+	11.3497i	−0.525409	+	0.381732i
$885$	23.2840	−	13.0480i	0.782684	−	0.438604i
$886$	8.75796	−	12.0543i	0.294229	−	0.404972i
$887$	25.4069	+	4.02406i	0.853081	+	0.135115i	0.567635	−	0.823280i	$-0.307858\pi$
$887$	25.4069	+	4.02406i	0.853081	+	0.135115i	0.285446	+	0.958395i	$0.407858\pi$
$888$	−0.938293	+	5.92415i	−0.0314871	+	0.198801i
$889$	−35.8399	−	26.0392i	−1.20203	−	0.873327i
$890$	−0.0400080	+	0.338817i	−0.00134107	+	0.0113572i
$891$	−6.52863	+	4.74333i	−0.218717	+	0.158907i
$892$	14.6895	−	7.48466i	0.491840	−	0.250605i
$893$	−2.81099	+	50.9570i	−0.0940661	+	1.70521i
$894$	13.6072	+	4.42124i	0.455093	+	0.147869i
$895$	28.9166	+	36.6600i	0.966576	+	1.22541i
$896$	3.47192	−	1.12809i	0.115989	−	0.0376870i
$897$	−8.59116	−	4.37741i	−0.286850	−	0.146158i
$898$	1.35037	+	8.52592i	0.0450625	+	0.284514i
$899$			45.1934i			1.50729i
$900$	10.5889	−	0.839163i	0.352962	−	0.0279721i
$901$		−	26.0398i		−	0.867510i
$902$	−2.84376	+	0.450408i	−0.0946869	+	0.0149969i
$903$	0.185946	+	0.0947444i	0.00618791	+	0.00315290i
$904$	−14.2279	+	4.62293i	−0.473213	+	0.153756i
$905$	−0.291050	+	0.0115148i	−0.00967483	+	0.000382764i
$906$	−12.7994	−	4.15877i	−0.425231	−	0.138166i
$907$	14.7475	+	14.7475i	0.489682	+	0.489682i	0.908206	−	0.418524i	$-0.137452\pi$
$907$	14.7475	+	14.7475i	0.489682	+	0.489682i	−0.418524	+	0.908206i	$0.637452\pi$
$908$	5.60449	+	10.9994i	0.185992	+	0.365029i
$909$	−16.9354	−	23.3096i	−0.561711	−	0.773129i
$910$	13.1233	−	28.4869i	0.435032	−	0.944333i
$911$	−4.72882	+	6.50866i	−0.156673	+	0.215642i	−0.880136	−	0.474721i	$-0.842549\pi$
$911$	−4.72882	+	6.50866i	−0.156673	+	0.215642i	0.723464	+	0.690363i	$0.242549\pi$
$912$	2.21204	+	3.42682i	0.0732479	+	0.113473i
$913$	30.0211	+	4.75488i	0.993554	+	0.157363i
$914$	11.4258	+	8.30131i	0.377931	+	0.274583i
$915$	−12.2794	−	11.3448i	−0.405945	−	0.375047i
$916$	−1.98566	+	1.44267i	−0.0656080	+	0.0476670i
$917$	−34.7623	−	68.2249i	−1.14795	−	2.25299i
$918$	17.0395	+	17.0395i	0.562387	+	0.562387i
$919$	46.6624	+	15.1615i	1.53925	+	0.500132i	0.951169	−	0.308671i	$-0.0998841\pi$
$919$	46.6624	+	15.1615i	1.53925	+	0.500132i	0.588080	+	0.808803i	$0.299884\pi$
$920$	3.33026	−	4.98703i	0.109796	−	0.164417i
$921$	−9.30020	−	28.6231i	−0.306452	−	0.943162i
$922$	−1.89015	+	3.70963i	−0.0622487	+	0.122170i
$923$	5.36746	+	33.8888i	0.176672	+	1.11546i
$924$	14.6135			0.480749
$925$	−27.3179	+	16.7609i	−0.898206	+	0.551094i
$926$		−	7.12160i		−	0.234030i
$927$	−5.79201	−	36.5693i	−0.190235	−	1.20109i
$928$	−4.29078	+	8.42113i	−0.140852	+	0.276437i
$929$	26.6051	−	8.64453i	0.872886	−	0.283618i	0.161886	−	0.986810i	$-0.448242\pi$
$929$	26.6051	−	8.64453i	0.872886	−	0.283618i	0.711000	+	0.703192i	$0.248242\pi$
$930$	−2.71317	+	9.63020i	−0.0889682	+	0.315787i
$931$	−25.2244	+	11.1477i	−0.826696	+	0.365350i
$932$	13.3692	−	13.3692i	0.437924	−	0.437924i
$933$	2.26603	+	4.44734i	0.0741866	+	0.145599i
$934$	18.7425	−	13.6172i	0.613273	−	0.445569i
$935$	−9.39147	−	47.1470i	−0.307134	−	1.54187i
$936$	−6.60367	−	4.79785i	−0.215848	−	0.156822i
$937$	−0.317437	+	2.00422i	−0.0103702	+	0.0654750i	−0.992331	−	0.123611i	$-0.960552\pi$
$937$	−0.317437	+	2.00422i	−0.0103702	+	0.0654750i	0.981961	+	0.189086i	$0.0605525\pi$
$938$	20.1949	+	3.19857i	0.659388	+	0.104437i
$939$	−10.6957	−	7.77087i	−0.349041	−	0.253593i
$940$	−25.6757	+	5.11448i	−0.837448	+	0.166816i
$941$	26.1246	+	35.9574i	0.851637	+	1.17218i	0.983500	+	0.180910i	$0.0579042\pi$
$941$	26.1246	+	35.9574i	0.851637	+	1.17218i	−0.131863	+	0.991268i	$0.542096\pi$
$942$	0.459768	+	0.902346i	0.0149801	+	0.0294000i
$943$	1.27629	−	1.27629i	0.0415616	−	0.0415616i
$944$	3.94192	−	12.1320i	0.128299	−	0.394863i
$945$	−37.6752	−	10.6144i	−1.22558	−	0.345288i
$946$	−0.248566	+	0.0807639i	−0.00808157	+	0.00262586i
$947$	2.61511	+	1.33247i	0.0849797	+	0.0432993i	0.495964	−	0.868343i	$-0.334815\pi$
$947$	2.61511	+	1.33247i	0.0849797	+	0.0432993i	−0.410984	+	0.911642i	$0.634815\pi$
$948$	0.450688	+	2.84553i	0.0146377	+	0.0924185i
$949$	0.854882			0.0277507
$950$	−6.23601	+	20.8833i	−0.202323	+	0.677544i
$951$	−20.5693			−0.667006
$952$	2.86994	+	18.1201i	0.0930153	+	0.587275i
$953$	40.7044	+	20.7399i	1.31855	+	0.671832i	0.964670	−	0.263460i	$-0.0848639\pi$
$953$	40.7044	+	20.7399i	1.31855	+	0.671832i	0.353875	+	0.935293i	$0.384864\pi$
$954$	10.4690	−	3.40158i	0.338946	−	0.110130i
$955$	−16.3401	+	24.4691i	−0.528753	+	0.791801i
$956$	−3.75053	+	11.5429i	−0.121301	+	0.373325i
$957$	−26.7526	+	26.7526i	−0.864789	+	0.864789i
$958$	−0.500481	−	0.982250i	−0.0161698	−	0.0317351i
$959$	41.7089	+	57.4074i	1.34685	+	1.85378i
$960$	−1.41987	+	1.53685i	−0.0458262	+	0.0496016i
$961$	−6.58132	−	4.78161i	−0.212300	−	0.154245i
$962$	24.3257	+	3.85281i	0.784291	+	0.124220i
$963$	−2.20989	+	13.9527i	−0.0712128	+	0.449620i
$964$	−10.6496	−	7.73742i	−0.343002	−	0.249206i
$965$	−12.1323	+	26.3358i	−0.390551	+	0.847779i
$966$	−7.41144	+	5.38472i	−0.238459	+	0.173251i
$967$	9.08253	+	17.8255i	0.292074	+	0.573228i	0.989687	−	0.143247i	$-0.0457543\pi$
$967$	9.08253	+	17.8255i	0.292074	+	0.573228i	−0.697613	+	0.716475i	$0.745754\pi$
$968$	−5.16283	+	5.16283i	−0.165940	+	0.165940i
$969$	−18.7484	+	8.28566i	−0.602285	+	0.266174i
$970$	30.6564	−	1.21285i	0.984316	−	0.0389423i
$971$	18.1832	−	5.90809i	0.583527	−	0.189599i	−0.00235289	−	0.999997i	$-0.500749\pi$
$971$	18.1832	−	5.90809i	0.583527	−	0.189599i	0.585880	+	0.810398i	$0.300749\pi$
$972$	−7.33208	+	14.3900i	−0.235177	+	0.461560i
$973$	−2.02304	−	12.7730i	−0.0648557	−	0.409483i
$974$		−	7.17991i		−	0.230059i
$975$	1.42019	+	17.9205i	0.0454826	+	0.573915i
$976$	−7.98999			−0.255753
$977$	5.45242	+	34.4252i	0.174438	+	1.10136i	0.907146	+	0.420816i	$0.138256\pi$
$977$	5.45242	+	34.4252i	0.174438	+	1.10136i	−0.732708	+	0.680543i	$0.761744\pi$
$978$	8.32145	−	16.3318i	0.266091	−	0.522232i
$979$	0.201702	+	0.620775i	0.00644643	+	0.0198401i
$980$	−8.76145	−	11.1076i	−0.279874	−	0.354820i
$981$	19.8430	+	6.44737i	0.633537	+	0.205849i
$982$	−7.35486	−	7.35486i	−0.234703	−	0.234703i
$983$	−25.5346	−	50.1144i	−0.814426	−	1.59840i	−0.801131	−	0.598489i	$-0.795768\pi$
$983$	−25.5346	−	50.1144i	−0.814426	−	1.59840i	−0.0132948	−	0.999912i	$-0.504232\pi$
$984$	−0.509495	+	0.370170i	−0.0162421	+	0.0118006i
$985$	−20.3423	−	2.40206i	−0.648160	−	0.0765359i
$986$	−38.4259	−	27.9181i	−1.22373	−	0.889092i
$987$	39.5020	+	6.25651i	1.25736	+	0.199147i
$988$	14.0712	−	9.08304i	0.447663	−	0.288970i
$989$	0.0963039	−	0.132551i	0.00306229	−	0.00421488i
$990$	17.7281	−	9.93456i	0.563436	−	0.315741i
$991$	−23.9135	−	32.9142i	−0.759639	−	1.04555i	−0.997244	−	0.0741912i	$-0.976362\pi$
$991$	−23.9135	−	32.9142i	−0.759639	−	1.04555i	0.237605	−	0.971362i	$-0.423638\pi$
$992$	2.17086	+	4.26056i	0.0689250	+	0.135273i
$993$	−3.17326	−	3.17326i	−0.100700	−	0.100700i
$994$	31.0039	+	10.0738i	0.983384	+	0.319521i
$995$	16.4324	+	44.5045i	0.520941	+	1.41089i
$996$	6.32298	−	2.05446i	0.200351	−	0.0650981i
$997$	20.0800	+	10.2313i	0.635941	+	0.324028i	0.742068	−	0.670325i	$-0.233845\pi$
$997$	20.0800	+	10.2313i	0.635941	+	0.324028i	−0.106127	+	0.994353i	$0.533845\pi$
$998$	−37.0047	+	5.86097i	−1.17136	+	0.185526i
$999$		−	30.7362i		−	0.972450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.113.10	✓	400
19.18	odd	2	inner	950.2.w.a.113.41	yes	400
25.2	odd	20	inner	950.2.w.a.227.41	yes	400
475.227	even	20	inner	950.2.w.a.227.10	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.113.10	✓	400	1.1	even	1	trivial
950.2.w.a.113.41	yes	400	19.18	odd	2	inner
950.2.w.a.227.10	yes	400	475.227	even	20	inner
950.2.w.a.227.41	yes	400	25.2	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)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.833741 - 0.424812i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-2.09765 + 0.774512i) q^{5} +(-0.289156 + 0.889931i) q^{6} +(2.58136 - 2.58136i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-1.24870 - 1.71868i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.833741 - 0.424812i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-2.09765 + 0.774512i) q^{5} +(-0.289156 + 0.889931i) q^{6} +(2.58136 - 2.58136i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-1.24870 - 1.71868i) q^{9} +(1.09312 + 1.95066i) q^{10} +(3.46098 + 2.51455i) q^{11} +(0.924209 + 0.146380i) q^{12} +(0.601065 - 3.79498i) q^{13} +(-2.95339 - 2.14576i) q^{14} +(2.07792 + 0.245364i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.28152 + 4.47773i) q^{17} +(-1.50219 + 1.50219i) q^{18} +(-1.76197 - 3.98691i) q^{19} +(1.75565 - 1.38481i) q^{20} +(-3.24877 + 1.05559i) q^{21} +(1.94217 - 3.81173i) q^{22} +(0.419531 + 2.64881i) q^{23} -0.935729i q^{24} +(3.80026 - 3.24931i) q^{25} -3.84228 q^{26} +(0.750113 + 4.73603i) q^{27} +(-1.65733 + 3.25270i) q^{28} +(-2.92060 - 8.98867i) q^{29} +(-0.0827147 - 2.09072i) q^{30} +(-4.54771 - 1.47764i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.81735 - 3.56675i) q^{33} +(4.06570 - 2.95390i) q^{34} +(-3.41549 + 7.41407i) q^{35} +(1.71868 + 1.24870i) q^{36} +(-6.33105 - 1.00274i) q^{37} +(-3.66219 + 2.36397i) q^{38} +(-2.11328 + 2.90869i) q^{39} +(-1.64241 - 1.51740i) q^{40} +(-0.395595 - 0.544490i) q^{41} +(1.55081 + 3.04365i) q^{42} +(-0.0431995 - 0.0431995i) q^{43} +(-4.06863 - 1.32198i) q^{44} +(3.95047 + 2.63806i) q^{45} +(2.55057 - 0.828732i) q^{46} +(-10.4320 - 5.31537i) q^{47} +(-0.924209 + 0.146380i) q^{48} -6.32680i q^{49} +(-3.80380 - 3.24517i) q^{50} -4.70249i q^{51} +(0.601065 + 3.79498i) q^{52} +(-4.61679 - 2.35237i) q^{53} +(4.56037 - 1.48176i) q^{54} +(-9.20747 - 2.59407i) q^{55} +(3.47192 + 1.12809i) q^{56} +(-0.224658 + 4.07256i) q^{57} +(-8.42113 + 4.29078i) q^{58} +(10.3201 - 7.49798i) q^{59} +(-2.05204 + 0.408757i) q^{60} +(-6.46404 - 4.69640i) q^{61} +(-0.748029 + 4.72287i) q^{62} +(-7.65987 - 1.21320i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(1.67843 + 8.42606i) q^{65} +(-3.23854 + 2.35294i) q^{66} +(-4.99046 + 2.54277i) q^{67} +(-3.55355 - 3.55355i) q^{68} +(0.775468 - 2.38665i) q^{69} +(7.85709 + 2.21362i) q^{70} +(-8.49285 + 2.75949i) q^{71} +(0.964462 - 1.89286i) q^{72} +(0.0348056 + 0.219754i) q^{73} +6.40997i q^{74} +(-4.54878 + 1.09469i) q^{75} +(2.90776 + 3.24730i) q^{76} +(15.4250 - 2.44308i) q^{77} +(3.20347 + 1.63225i) q^{78} +(0.951427 + 2.92819i) q^{79} +(-1.24179 + 1.85956i) q^{80} +(-0.582915 + 1.79403i) q^{81} +(-0.475901 + 0.475901i) q^{82} +(6.33062 - 3.22561i) q^{83} +(2.76357 - 2.00785i) q^{84} +(-8.25388 - 7.62565i) q^{85} +(-0.0359097 + 0.0494255i) q^{86} +(-1.38348 + 8.73493i) q^{87} +(-0.669228 + 4.22534i) q^{88} +(0.123437 + 0.0896820i) q^{89} +(1.98760 - 4.31452i) q^{90} +(-8.24462 - 11.3477i) q^{91} +(-1.21753 - 2.38953i) q^{92} +(3.16389 + 3.16389i) q^{93} +(-3.61800 + 11.1351i) q^{94} +(6.78391 + 6.99847i) q^{95} +(0.289156 + 0.889931i) q^{96} +(6.22905 - 12.2252i) q^{97} +(-6.24891 + 0.989730i) q^{98} -9.08824i 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

Modular forms

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Database

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