LMFDB - Embedded newform 930.2.y.b.29.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.13
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.317374 - 1.70273i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.12610 - 0.692603i) q^{5} +(0.744076 - 1.56408i) q^{6} +(0.896862 - 0.291408i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.79855 + 1.08080i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.317374 - 1.70273i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.12610 - 0.692603i) q^{5} +(0.744076 - 1.56408i) q^{6} +(0.896862 - 0.291408i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.79855 + 1.08080i) q^{9} +(-1.31295 - 1.81002i) q^{10} +(-0.303250 - 0.933309i) q^{11} +(1.52131 - 0.828012i) q^{12} +(-3.72860 + 2.70899i) q^{13} +(0.896862 + 0.291408i) q^{14} +(-0.504544 + 3.83998i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.45582 - 1.12286i) q^{17} +(-2.89935 - 0.770557i) q^{18} +(-0.570734 - 0.414663i) q^{19} +(0.00170408 - 2.23607i) q^{20} +(-0.780829 - 1.43462i) q^{21} +(0.303250 - 0.933309i) q^{22} +(-6.16523 - 2.00321i) q^{23} +(1.71746 + 0.224330i) q^{24} +(4.04060 + 2.94509i) q^{25} -4.60880 q^{26} +(2.72850 + 4.42214i) q^{27} +(0.554291 + 0.762917i) q^{28} +(7.61245 + 5.53077i) q^{29} +(-2.66527 + 2.81004i) q^{30} +(-4.28782 - 3.55171i) q^{31} -1.00000 q^{32} +(-1.49292 + 0.812560i) q^{33} +(-2.13581 - 2.93969i) q^{34} +(-2.10865 - 0.00160698i) q^{35} +(-1.89270 - 2.32759i) q^{36} -6.45332 q^{37} +(-0.218001 - 0.670939i) q^{38} +(5.79602 + 5.48902i) q^{39} +(1.31571 - 1.80801i) q^{40} +(-6.98590 + 9.61527i) q^{41} +(0.211547 - 1.61960i) q^{42} +(3.63860 + 2.64360i) q^{43} +(0.793920 - 0.576816i) q^{44} +(6.69856 - 0.359610i) q^{45} +(-3.81032 - 5.24446i) q^{46} +(4.40233 - 3.19848i) q^{47} +(1.25760 + 1.19099i) q^{48} +(-4.94368 + 3.59179i) q^{49} +(1.53784 + 4.75763i) q^{50} +(-0.815140 + 6.24068i) q^{51} +(-3.72860 - 2.70899i) q^{52} +(-10.9537 - 3.55908i) q^{53} +(-0.391868 + 5.18135i) q^{54} +(-0.00167228 + 2.19434i) q^{55} +0.943017i q^{56} +(-0.524921 + 1.10341i) q^{57} +(2.90770 + 8.94897i) q^{58} +(-6.92673 - 9.53382i) q^{59} +(-3.80795 + 0.706769i) q^{60} -5.56409i q^{61} +(-1.38128 - 5.39371i) q^{62} +(-2.19496 + 1.78485i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(9.80363 - 3.17713i) q^{65} +(-1.68541 - 0.220144i) q^{66} -7.43098i q^{67} -3.63366i q^{68} +(-1.45422 + 11.1335i) q^{69} +(-1.70499 - 1.24073i) q^{70} +(10.7047 + 3.47817i) q^{71} +(-0.163105 - 2.99556i) q^{72} +(-1.51144 - 4.65174i) q^{73} +(-5.22084 - 3.79316i) q^{74} +(3.73229 - 7.81473i) q^{75} +(0.218001 - 0.670939i) q^{76} +(-0.543948 - 0.748680i) q^{77} +(1.46271 + 7.84752i) q^{78} +(0.827918 + 0.269007i) q^{79} +(2.12715 - 0.689362i) q^{80} +(6.66373 - 6.04935i) q^{81} +(-11.3034 + 3.67271i) q^{82} +(-0.736452 + 1.01364i) q^{83} +(1.12312 - 1.18594i) q^{84} +(6.56971 + 4.78083i) q^{85} +(1.38982 + 4.27743i) q^{86} +(7.00139 - 14.7172i) q^{87} +0.981339 q^{88} +(3.56176 + 10.9620i) q^{89} +(5.63062 + 3.64638i) q^{90} +(-2.55462 + 3.51613i) q^{91} -6.48251i q^{92} +(-4.68674 + 8.42820i) q^{93} +5.44158 q^{94} +(0.926242 + 1.27691i) q^{95} +(0.317374 + 1.70273i) q^{96} +(6.43121 - 2.08963i) q^{97} -6.11072 q^{98} +(1.85738 + 2.28415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.317374	−	1.70273i	−0.183236	−	0.983069i
$3$	−0.317374	−	1.70273i	−0.183236	−	0.983069i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.12610	−	0.692603i	−0.950821	−	0.309742i
$5$	−2.12610	−	0.692603i	−0.950821	−	0.309742i
$6$	0.744076	−	1.56408i	0.303768	−	0.638534i
$7$	0.896862	−	0.291408i	0.338982	−	0.110142i	−0.134579	−	0.990903i	$-0.542968\pi$
$7$	0.896862	−	0.291408i	0.338982	−	0.110142i	0.473561	+	0.880761i	$0.342968\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.79855	+	1.08080i	−0.932849	+	0.360267i
$10$	−1.31295	−	1.81002i	−0.415191	−	0.572378i
$11$	−0.303250	−	0.933309i	−0.0914334	−	0.281403i	0.894874	−	0.446318i	$-0.147265\pi$
$11$	−0.303250	−	0.933309i	−0.0914334	−	0.281403i	−0.986308	+	0.164915i	$0.947265\pi$
$12$	1.52131	−	0.828012i	0.439166	−	0.239026i
$13$	−3.72860	+	2.70899i	−1.03413	+	0.751337i	−0.969131	−	0.246548i	$-0.920704\pi$
$13$	−3.72860	+	2.70899i	−1.03413	+	0.751337i	−0.0649967	+	0.997885i	$0.520704\pi$
$14$	0.896862	+	0.291408i	0.239697	+	0.0778821i
$15$	−0.504544	+	3.83998i	−0.130273	+	0.991478i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.45582	−	1.12286i	−0.838159	−	0.272334i	−0.141681	−	0.989912i	$-0.545251\pi$
$17$	−3.45582	−	1.12286i	−0.838159	−	0.272334i	−0.696478	+	0.717578i	$0.745251\pi$
$18$	−2.89935	−	0.770557i	−0.683384	−	0.181622i
$19$	−0.570734	−	0.414663i	−0.130935	−	0.0951302i	0.520390	−	0.853929i	$-0.325787\pi$
$19$	−0.570734	−	0.414663i	−0.130935	−	0.0951302i	−0.651325	+	0.758799i	$0.725787\pi$
$20$	0.00170408	−	2.23607i	0.000381045	−	0.500000i
$21$	−0.780829	−	1.43462i	−0.170391	−	0.313061i
$22$	0.303250	−	0.933309i	0.0646532	−	0.198982i
$23$	−6.16523	−	2.00321i	−1.28554	−	0.417697i	−0.415012	−	0.909816i	$-0.636223\pi$
$23$	−6.16523	−	2.00321i	−1.28554	−	0.417697i	−0.870528	+	0.492119i	$0.836223\pi$
$24$	1.71746	+	0.224330i	0.350575	+	0.0457912i
$25$	4.04060	+	2.94509i	0.808120	+	0.589018i
$26$	−4.60880			−0.903860
$27$	2.72850	+	4.42214i	0.525099	+	0.851041i
$28$	0.554291	+	0.762917i	0.104751	+	0.144178i
$29$	7.61245	+	5.53077i	1.41360	+	1.02704i	0.992787	+	0.119889i	$0.0382540\pi$
$29$	7.61245	+	5.53077i	1.41360	+	1.02704i	0.420810	+	0.907149i	$0.361746\pi$
$30$	−2.66527	+	2.81004i	−0.486609	+	0.513042i
$31$	−4.28782	−	3.55171i	−0.770115	−	0.637905i
$31$	−4.28782	−	3.55171i	−0.770115	−	0.637905i
$32$	−1.00000			−0.176777
$33$	−1.49292	+	0.812560i	−0.259885	+	0.141449i
$34$	−2.13581	−	2.93969i	−0.366289	−	0.504153i
$35$	−2.10865	−	0.00160698i	−0.356427	−	0.000271629i
$36$	−1.89270	−	2.32759i	−0.315450	−	0.387932i
$37$	−6.45332			−1.06092			−0.530459	−	0.847710i	$-0.677981\pi$
$37$	−6.45332			−1.06092			−0.530459	+	0.847710i	$0.677981\pi$
$38$	−0.218001	−	0.670939i	−0.0353645	−	0.108841i
$39$	5.79602	+	5.48902i	0.928106	+	0.878946i
$40$	1.31571	−	1.80801i	0.208031	−	0.285872i
$41$	−6.98590	+	9.61527i	−1.09101	+	1.50165i	−0.244229	+	0.969718i	$0.578535\pi$
$41$	−6.98590	+	9.61527i	−1.09101	+	1.50165i	−0.846785	+	0.531935i	$0.821465\pi$
$42$	0.211547	−	1.61960i	0.0326424	−	0.249909i
$43$	3.63860	+	2.64360i	0.554882	+	0.403145i	0.829582	−	0.558385i	$-0.188579\pi$
$43$	3.63860	+	2.64360i	0.554882	+	0.403145i	−0.274700	+	0.961530i	$0.588579\pi$
$44$	0.793920	−	0.576816i	0.119688	−	0.0869584i
$45$	6.69856	−	0.359610i	0.998562	−	0.0536075i
$46$	−3.81032	−	5.24446i	−0.561802	−	0.773254i
$47$	4.40233	−	3.19848i	0.642146	−	0.466546i	−0.218441	−	0.975850i	$-0.570097\pi$
$47$	4.40233	−	3.19848i	0.642146	−	0.466546i	0.860587	+	0.509304i	$0.170097\pi$
$48$	1.25760	+	1.19099i	0.181519	+	0.171904i
$49$	−4.94368	+	3.59179i	−0.706239	+	0.513113i
$50$	1.53784	+	4.75763i	0.217483	+	0.672831i
$51$	−0.815140	+	6.24068i	−0.114142	+	0.873869i
$52$	−3.72860	−	2.70899i	−0.517064	−	0.375669i
$53$	−10.9537	−	3.55908i	−1.50461	−	0.488877i	−0.563251	−	0.826286i	$-0.690450\pi$
$53$	−10.9537	−	3.55908i	−1.50461	−	0.488877i	−0.941358	+	0.337409i	$0.890450\pi$
$54$	−0.391868	+	5.18135i	−0.0533265	+	0.705093i
$55$	−0.00167228	+	2.19434i	−0.000225491	+	0.295885i
$56$			0.943017i			0.126016i
$57$	−0.524921	+	1.10341i	−0.0695274	+	0.146150i
$58$	2.90770	+	8.94897i	0.381799	+	1.17506i
$59$	−6.92673	−	9.53382i	−0.901783	−	1.24120i	−0.969896	−	0.243520i	$-0.921698\pi$
$59$	−6.92673	−	9.53382i	−0.901783	−	1.24120i	0.0681127	−	0.997678i	$-0.478302\pi$
$60$	−3.80795	+	0.706769i	−0.491604	+	0.0912434i
$61$		−	5.56409i		−	0.712409i	−0.934408	−	0.356204i	$-0.884071\pi$
$61$		−	5.56409i		−	0.712409i	0.934408	−	0.356204i	$-0.115929\pi$
$62$	−1.38128	−	5.39371i	−0.175422	−	0.685001i
$63$	−2.19496	+	1.78485i	−0.276539	+	0.224870i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	9.80363	−	3.17713i	1.21599	−	0.394075i
$66$	−1.68541	−	0.220144i	−0.207460	−	0.0270978i
$67$		−	7.43098i		−	0.907839i	−0.891043	−	0.453919i	$-0.850025\pi$
$67$		−	7.43098i		−	0.907839i	0.891043	−	0.453919i	$-0.149975\pi$
$68$		−	3.63366i		−	0.440646i
$69$	−1.45422	+	11.1335i	−0.175068	+	1.34031i
$70$	−1.70499	−	1.24073i	−0.203785	−	0.148296i
$71$	10.7047	+	3.47817i	1.27041	+	0.412783i	0.865194	−	0.501437i	$-0.167195\pi$
$71$	10.7047	+	3.47817i	1.27041	+	0.412783i	0.405220	+	0.914219i	$0.367195\pi$
$72$	−0.163105	−	2.99556i	−0.0192222	−	0.353030i
$73$	−1.51144	−	4.65174i	−0.176901	−	0.544445i	0.822814	−	0.568310i	$-0.192403\pi$
$73$	−1.51144	−	4.65174i	−0.176901	−	0.544445i	−0.999715	+	0.0238654i	$0.992403\pi$
$74$	−5.22084	−	3.79316i	−0.606911	−	0.440946i
$75$	3.73229	−	7.81473i	0.430968	−	0.902367i
$76$	0.218001	−	0.670939i	0.0250064	−	0.0769619i
$77$	−0.543948	−	0.748680i	−0.0619886	−	0.0853200i
$78$	1.46271	+	7.84752i	0.165620	+	0.888557i
$79$	0.827918	+	0.269007i	0.0931481	+	0.0302656i	0.355220	−	0.934783i	$-0.384406\pi$
$79$	0.827918	+	0.269007i	0.0931481	+	0.0302656i	−0.262072	+	0.965048i	$0.584406\pi$
$80$	2.12715	−	0.689362i	0.237823	−	0.0770730i
$81$	6.66373	−	6.04935i	0.740415	−	0.672150i
$82$	−11.3034	+	3.67271i	−1.24825	+	0.405582i
$83$	−0.736452	+	1.01364i	−0.0808361	+	0.111261i	−0.847520	−	0.530763i	$-0.821905\pi$
$83$	−0.736452	+	1.01364i	−0.0808361	+	0.111261i	0.766684	+	0.642025i	$0.221905\pi$
$84$	1.12312	−	1.18594i	0.122542	−	0.129396i
$85$	6.56971	+	4.78083i	0.712585	+	0.518554i
$86$	1.38982	+	4.27743i	0.149868	+	0.461248i
$87$	7.00139	−	14.7172i	0.750627	−	1.57785i
$88$	0.981339			0.104611
$89$	3.56176	+	10.9620i	0.377546	+	1.16197i	0.941745	+	0.336328i	$0.109185\pi$
$89$	3.56176	+	10.9620i	0.377546	+	1.16197i	−0.564199	+	0.825639i	$0.690815\pi$
$90$	5.63062	+	3.64638i	0.593520	+	0.384363i
$91$	−2.55462	+	3.51613i	−0.267797	+	0.368591i
$92$		−	6.48251i		−	0.675848i
$93$	−4.68674	+	8.42820i	−0.485992	+	0.873963i
$94$	5.44158			0.561256
$95$	0.926242	+	1.27691i	0.0950304	+	0.131008i
$96$	0.317374	+	1.70273i	0.0323919	+	0.173784i
$97$	6.43121	−	2.08963i	0.652990	−	0.212169i	0.0362579	−	0.999342i	$-0.488456\pi$
$97$	6.43121	−	2.08963i	0.652990	−	0.212169i	0.616732	+	0.787173i	$0.288456\pi$
$98$	−6.11072			−0.617276
$99$	1.85738	+	2.28415i	0.186674	+	0.229566i
$100$	−1.55233	+	4.75292i	−0.155233	+	0.475292i
$101$	−16.7291	−	5.43563i	−1.66461	−	0.540865i	−0.682781	−	0.730623i	$-0.739230\pi$
$101$	−16.7291	−	5.43563i	−1.66461	−	0.540865i	−0.981831	+	0.189758i	$0.939230\pi$
$102$	−4.32764	+	4.56969i	−0.428500	+	0.452466i
$103$	−5.32723	+	7.33231i	−0.524908	+	0.722474i	−0.986344	−	0.164700i	$-0.947334\pi$
$103$	−5.32723	+	7.33231i	−0.524908	+	0.722474i	0.461436	+	0.887174i	$0.347334\pi$
$104$	−1.42420	−	4.38323i	−0.139654	−	0.429811i
$105$	0.666495	+	3.59096i	0.0650432	+	0.350442i
$106$	−6.76977	−	9.31779i	−0.657538	−	0.905024i
$107$	−1.63104	+	5.01981i	−0.157678	+	0.485283i	−0.998422	−	0.0561490i	$-0.982118\pi$
$107$	−1.63104	+	5.01981i	−0.157678	+	0.485283i	0.840744	+	0.541432i	$0.182118\pi$
$108$	−3.36255	+	3.96147i	−0.323562	+	0.381193i
$109$	12.8521	−	9.33761i	1.23101	−	0.894381i	0.234044	−	0.972226i	$-0.424804\pi$
$109$	12.8521	−	9.33761i	1.23101	−	0.894381i	0.996965	+	0.0778456i	$0.0248041\pi$
$110$	−1.29115	+	1.77428i	−0.123107	+	0.169170i
$111$	2.04812	+	10.9882i	0.194399	+	1.04296i
$112$	−0.554291	+	0.762917i	−0.0523756	+	0.0720889i
$113$	−3.13703	−	9.65477i	−0.295107	−	0.908245i	−0.983186	−	0.182609i	$-0.941546\pi$
$113$	−3.13703	−	9.65477i	−0.295107	−	0.908245i	0.688079	−	0.725636i	$-0.258454\pi$
$114$	−1.07324	+	0.584135i	−0.100518	+	0.0547092i
$115$	11.7205	+	8.52908i	1.09294	+	0.795341i
$116$	−2.90770	+	8.94897i	−0.269973	+	0.830891i
$117$	7.50678	−	11.6111i	0.694002	−	1.07345i
$118$		−	11.7845i		−	1.08485i
$119$	−3.42660			−0.314116
$120$	−3.49612	−	1.66647i	−0.319151	−	0.152127i
$121$	8.12008	−	5.89959i	0.738189	−	0.536326i
$122$	3.27049	−	4.50144i	0.296096	−	0.407542i
$123$	18.5893	+	8.84343i	1.67614	+	0.797385i
$124$	2.05287	−	5.17549i	0.184353	−	0.464773i
$125$	−6.55094	−	9.06009i	−0.585934	−	0.810359i
$126$	−2.82487	+	0.153811i	−0.251659	+	0.0137026i
$127$	8.00308	−	5.81458i	0.710159	−	0.515960i	−0.173066	−	0.984910i	$-0.555367\pi$
$127$	8.00308	−	5.81458i	0.710159	−	0.515960i	0.883225	+	0.468950i	$0.155367\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	3.34653	−	7.03455i	0.294645	−	0.619358i
$130$	9.79877	+	3.19207i	0.859409	+	0.279963i
$131$	13.7204	−	4.45804i	1.19876	−	0.389500i	0.359455	−	0.933163i	$-0.382963\pi$
$131$	13.7204	−	4.45804i	1.19876	−	0.389500i	0.839304	+	0.543662i	$0.182963\pi$
$132$	−1.23413	−	1.16876i	−0.107417	−	0.101728i
$133$	−0.632706	−	0.205579i	−0.0548626	−	0.0178259i
$134$	4.36782	−	6.01179i	0.377322	−	0.519339i
$135$	−2.73827	−	11.2917i	−0.235672	−	0.971833i
$136$	2.13581	−	2.93969i	0.183144	−	0.252077i
$137$	5.47987	+	7.54239i	0.468177	+	0.644390i	0.976179	−	0.216966i	$-0.0696159\pi$
$137$	5.47987	+	7.54239i	0.468177	+	0.644390i	−0.508002	+	0.861356i	$0.669616\pi$
$138$	−7.72058	+	8.15239i	−0.657219	+	0.693978i
$139$	−4.69726	−	6.46522i	−0.398416	−	0.548373i	0.561929	−	0.827185i	$-0.310059\pi$
$139$	−4.69726	−	6.46522i	−0.398416	−	0.548373i	−0.960346	+	0.278812i	$0.910059\pi$
$140$	−0.650080	−	2.00594i	−0.0549418	−	0.169533i
$141$	−6.84332	−	6.48084i	−0.576311	−	0.545786i
$142$	6.61587	+	9.10596i	0.555191	+	0.764155i
$143$	3.65902	+	2.65843i	0.305982	+	0.222309i
$144$	1.62879	−	2.51933i	0.135733	−	0.209944i
$145$	−12.3542	−	17.0314i	−1.02596	−	1.41438i
$146$	1.51144	−	4.65174i	0.125088	−	0.384981i
$147$	7.68483	+	7.27778i	0.633834	+	0.600261i
$148$	−1.99418	−	6.13747i	−0.163921	−	0.504497i
$149$		−	13.6626i		−	1.11928i	−0.828736	−	0.559640i	$-0.810939\pi$
$149$		−	13.6626i		−	1.11928i	0.828736	−	0.559640i	$-0.189061\pi$
$150$	7.61287	−	4.12846i	0.621588	−	0.337087i
$151$	−18.5324	+	6.02154i	−1.50814	+	0.490026i	−0.942381	−	0.334542i	$-0.891418\pi$
$151$	−18.5324	+	6.02154i	−1.50814	+	0.490026i	−0.565763	+	0.824568i	$0.691418\pi$
$152$	0.570734	−	0.414663i	0.0462927	−	0.0336336i
$153$	10.8849	−	0.592670i	0.879989	−	0.0479145i
$154$		−	0.925419i		−	0.0745724i
$155$	6.65640	+	10.5210i	0.534655	+	0.845070i
$156$	−3.42930	+	7.20854i	−0.274564	+	0.577145i
$157$	4.04898	−	5.57295i	0.323144	−	0.444770i	−0.616280	−	0.787527i	$-0.711361\pi$
$157$	4.04898	−	5.57295i	0.323144	−	0.444770i	0.939424	+	0.342758i	$0.111361\pi$
$158$	0.511682	+	0.704269i	0.0407072	+	0.0560287i
$159$	−2.58371	+	19.7807i	−0.204901	+	1.56871i
$160$	2.12610	+	0.692603i	0.168083	+	0.0547551i
$161$	−6.11312			−0.481781
$162$	8.94679	−	0.977185i	0.702926	−	0.0767749i
$163$	7.17899	+	2.33260i	0.562302	+	0.182703i	0.576357	−	0.817198i	$-0.304474\pi$
$163$	7.17899	+	2.33260i	0.562302	+	0.182703i	−0.0140546	+	0.999901i	$0.504474\pi$
$164$	−11.3034	−	3.67271i	−0.882649	−	0.286790i
$165$	3.73689	−	0.693579i	0.290916	−	0.0539951i
$166$	−1.19160	+	0.387176i	−0.0924865	+	0.0300507i
$167$	−9.27476	+	12.7656i	−0.717703	+	0.987833i	0.281894	+	0.959445i	$0.409037\pi$
$167$	−9.27476	+	12.7656i	−0.717703	+	0.987833i	−0.999597	+	0.0283875i	$0.990963\pi$
$168$	1.60570	−	0.299289i	0.123882	−	0.0230907i
$169$	2.54662	−	7.83770i	0.195894	−	0.602900i
$170$	2.50491	+	7.72935i	0.192118	+	0.592814i
$171$	2.04540	+	0.543603i	0.156415	+	0.0415703i
$172$	−1.38982	+	4.27743i	−0.105973	+	0.326151i
$173$	8.71355	−	6.33077i	0.662479	−	0.481319i	−0.205020	−	0.978758i	$-0.565726\pi$
$173$	8.71355	−	6.33077i	0.662479	−	0.481319i	0.867499	+	0.497438i	$0.165726\pi$
$174$	14.3148	−	7.79118i	1.08520	−	0.590648i
$175$	4.48209	+	1.46387i	0.338814	+	0.110659i
$176$	0.793920	+	0.576816i	0.0598440	+	0.0434792i
$177$	−14.0351	+	14.8201i	−1.05494	+	1.11395i
$178$	−3.56176	+	10.9620i	−0.266965	+	0.821634i
$179$	3.20389	+	9.86056i	0.239470	+	0.737013i	0.996497	+	0.0836292i	$0.0266511\pi$
$179$	3.20389	+	9.86056i	0.239470	+	0.737013i	−0.757027	+	0.653384i	$0.773349\pi$
$180$	2.41198	+	6.25958i	0.179778	+	0.466562i
$181$		−	7.92680i		−	0.589194i	−0.955622	−	0.294597i	$-0.904815\pi$
$181$		−	7.92680i		−	0.589194i	0.955622	−	0.294597i	$-0.0951855\pi$
$182$	−4.13346	+	1.34304i	−0.306392	+	0.0995530i
$183$	−9.47412	+	1.76590i	−0.700347	+	0.130539i
$184$	3.81032	−	5.24446i	0.280901	−	0.386627i
$185$	13.7204	+	4.46959i	1.00874	+	0.328611i
$186$	−8.74562	+	4.06376i	−0.641260	+	0.297969i
$187$			3.56585i			0.260761i
$188$	4.40233	+	3.19848i	0.321073	+	0.233273i
$189$	3.73573	+	3.17094i	0.271735	+	0.230652i
$190$	−0.00120217	+	1.57747i	−8.72149e−5	+	0.114442i
$191$			4.98195i			0.360481i	0.983623	+	0.180241i	$0.0576877\pi$
$191$			4.98195i			0.360481i	−0.983623	+	0.180241i	$0.942312\pi$
$192$	−0.744076	+	1.56408i	−0.0536990	+	0.112878i
$193$	6.74468	−	2.19148i	0.485493	−	0.157746i	−0.0560353	−	0.998429i	$-0.517846\pi$
$193$	6.74468	−	2.19148i	0.485493	−	0.157746i	0.541528	+	0.840683i	$0.317846\pi$
$194$	6.43121	+	2.08963i	0.461734	+	0.150026i
$195$	−8.52120	−	15.6845i	−0.610216	−	1.12319i
$196$	−4.94368	−	3.59179i	−0.353120	−	0.256556i
$197$	8.99819	−	2.92369i	0.641095	−	0.208304i	0.0296112	−	0.999561i	$-0.490573\pi$
$197$	8.99819	−	2.92369i	0.641095	−	0.208304i	0.611483	+	0.791257i	$0.290573\pi$
$198$	0.160062	+	2.93966i	0.0113751	+	0.208913i
$199$	−9.41765	−	12.9623i	−0.667600	−	0.918872i	0.332103	−	0.943243i	$-0.392242\pi$
$199$	−9.41765	−	12.9623i	−0.667600	−	0.918872i	−0.999703	+	0.0243707i	$0.992242\pi$
$200$	−4.04956	+	2.93276i	−0.286347	+	0.207377i
$201$	−12.6529	+	2.35840i	−0.892468	+	0.166349i
$202$	−10.3392	−	14.2307i	−0.727462	−	1.00127i
$203$	8.43903	+	2.74201i	0.592304	+	0.192451i
$204$	−6.18713	+	1.15323i	−0.433186	+	0.0807423i
$205$	21.5123	−	15.6046i	1.50248	−	1.08987i
$206$	−8.61964	+	2.80069i	−0.600559	+	0.195133i
$207$	19.4188	−	1.05733i	1.34970	−	0.0734897i
$208$	1.42420	−	4.38323i	0.0987504	−	0.303922i
$209$	−0.213933	+	0.658418i	−0.0147981	+	0.0455437i
$210$	−1.57151	+	3.29690i	−0.108444	+	0.227508i
$211$	−13.0229			−0.896534			−0.448267	−	0.893900i	$-0.647959\pi$
$211$	−13.0229			−0.896534			−0.448267	+	0.893900i	$0.647959\pi$
$212$		−	11.5174i		−	0.791020i
$213$	2.52497	−	19.3310i	0.173008	−	1.32454i
$214$	−4.27011	+	3.10241i	−0.291898	+	0.212077i
$215$	−5.90507	−	8.14067i	−0.402722	−	0.555189i
$216$	−5.04886	+	1.22844i	−0.343531	+	0.0835846i
$217$	−4.88058	−	1.93589i	−0.331315	−	0.131417i
$218$	15.8861			1.07594
$219$	−7.44094	+	4.04991i	−0.502812	+	0.273668i
$220$	−2.08746	+	0.676498i	−0.140736	+	0.0456095i
$221$	15.9272	−	5.17505i	1.07138	−	0.348112i
$222$	−4.80176	+	10.0935i	−0.322273	+	0.677432i
$223$	−20.6440			−1.38242			−0.691211	−	0.722653i	$-0.742922\pi$
$223$	−20.6440			−1.38242			−0.691211	+	0.722653i	$0.742922\pi$
$224$	−0.896862	+	0.291408i	−0.0599241	+	0.0194705i
$225$	−14.4909	−	3.87488i	−0.966058	−	0.258325i
$226$	3.13703	−	9.65477i	0.208672	−	0.642226i
$227$	17.0903	+	12.4169i	1.13432	+	0.824135i	0.986318	−	0.164851i	$-0.0527143\pi$
$227$	17.0903	+	12.4169i	1.13432	+	0.824135i	0.148006	+	0.988986i	$0.452714\pi$
$228$	−1.21161	−	0.158257i	−0.0802410	−	0.0104809i
$229$	−5.45058	+	7.50208i	−0.360184	+	0.495751i	−0.950200	−	0.311640i	$-0.899122\pi$
$229$	−5.45058	+	7.50208i	−0.360184	+	0.495751i	0.590016	+	0.807392i	$0.299122\pi$
$230$	4.46880	+	13.7893i	0.294664	+	0.909239i
$231$	−1.10216	+	1.16381i	−0.0725169	+	0.0765728i
$232$	−7.61245	+	5.53077i	−0.499782	+	0.363113i
$233$	−10.8631	+	7.89249i	−0.711664	+	0.517054i	−0.883710	−	0.468035i	$-0.844962\pi$
$233$	−10.8631	+	7.89249i	−0.711664	+	0.517054i	0.172046	+	0.985089i	$0.444962\pi$
$234$	12.8979	−	4.98120i	0.843165	−	0.325631i
$235$	−11.5751	+	3.75122i	−0.755074	+	0.244703i
$236$	6.92673	−	9.53382i	0.450892	−	0.620599i
$237$	0.195285	−	1.49509i	0.0126851	−	0.0971167i
$238$	−2.77218	−	2.01411i	−0.179694	−	0.130555i
$239$	−2.38067	+	7.32695i	−0.153993	+	0.473941i	−0.998057	−	0.0623005i	$-0.980156\pi$
$239$	−2.38067	+	7.32695i	−0.153993	+	0.473941i	0.844065	+	0.536241i	$0.180156\pi$
$240$	−1.84890	−	3.40317i	−0.119346	−	0.219674i
$241$	−14.6757	+	4.76842i	−0.945343	+	0.307161i	−0.740822	−	0.671701i	$-0.765564\pi$
$241$	−14.6757	+	4.76842i	−0.945343	+	0.307161i	−0.204521	+	0.978862i	$0.565564\pi$
$242$	10.0370			0.645201
$243$	−12.4153	−	9.42660i	−0.796441	−	0.604717i
$244$	5.29177	−	1.71940i	0.338771	−	0.110073i
$245$	12.9984	−	4.21250i	0.830440	−	0.269127i
$246$	9.84102	+	18.0810i	0.627441	+	1.15280i
$247$	3.25136			0.206879
$248$	4.70288	−	2.98042i	0.298633	−	0.189257i
$249$	1.95968	+	0.932273i	0.124190	+	0.0590804i
$250$	0.0255612	−	11.1803i	0.00161663	−	0.707105i
$251$	5.57405	−	4.04979i	0.351831	−	0.255620i	−0.397806	−	0.917470i	$-0.630228\pi$
$251$	5.57405	−	4.04979i	0.351831	−	0.255620i	0.749637	+	0.661849i	$0.230228\pi$
$252$	−2.37577	−	1.53598i	−0.149660	−	0.0967576i
$253$			6.36154i			0.399946i
$254$	9.89235			0.620701
$255$	6.05538	−	12.7037i	0.379203	−	0.795538i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−7.20787	+	22.1835i	−0.449615	+	1.38377i	0.427728	+	0.903907i	$0.359314\pi$
$257$	−7.20787	+	22.1835i	−0.449615	+	1.38377i	−0.877343	+	0.479864i	$0.840686\pi$
$258$	6.84220	−	3.72403i	0.425977	−	0.231848i
$259$	−5.78774	+	1.88055i	−0.359632	+	0.116852i
$260$	6.05112	+	8.34201i	0.375275	+	0.517350i
$261$	−27.2815	−	7.25057i	−1.68868	−	0.448799i
$262$	13.7204	+	4.45804i	0.847651	+	0.275418i
$263$	−4.77981	−	6.57884i	−0.294736	−	0.405669i	0.635809	−	0.771846i	$-0.280666\pi$
$263$	−4.77981	−	6.57884i	−0.294736	−	0.405669i	−0.930545	+	0.366177i	$0.880666\pi$
$264$	−0.311452	−	1.67095i	−0.0191685	−	0.102840i
$265$	20.8237	+	15.1535i	1.27919	+	0.930875i
$266$	−0.391034	−	0.538212i	−0.0239758	−	0.0329999i
$267$	17.5348	−	9.54375i	1.07311	−	0.584068i
$268$	7.06728	−	2.29630i	0.431703	−	0.140269i
$269$	−12.5751	−	9.13633i	−0.766716	−	0.557052i	0.134247	−	0.990948i	$-0.457138\pi$
$269$	−12.5751	−	9.13633i	−0.766716	−	0.557052i	−0.900963	+	0.433896i	$0.857138\pi$
$270$	4.42178	−	10.7447i	0.269101	−	0.653900i
$271$	−16.4407	−	5.34191i	−0.998703	−	0.324498i	−0.236356	−	0.971667i	$-0.575953\pi$
$271$	−16.4407	−	5.34191i	−0.998703	−	0.324498i	−0.762347	+	0.647168i	$0.775953\pi$
$272$	3.45582	−	1.12286i	0.209540	−	0.0680836i
$273$	6.79778	+	3.23389i	0.411420	+	0.195724i
$274$			9.32291i			0.563218i
$275$	1.52336	−	4.66423i	0.0918622	−	0.281263i
$276$	−11.0379	+	2.05738i	−0.664406	+	0.123840i
$277$	−5.93480	−	4.31188i	−0.356587	−	0.259076i	0.395040	−	0.918664i	$-0.370731\pi$
$277$	−5.93480	−	4.31188i	−0.356587	−	0.259076i	−0.751627	+	0.659588i	$0.770731\pi$
$278$		−	7.99145i		−	0.479295i
$279$	15.8384	+	5.30534i	0.948217	+	0.317622i
$280$	0.653137	−	2.00495i	0.0390324	−	0.119819i
$281$	−3.69421	+	5.08464i	−0.220378	+	0.303324i	−0.904863	−	0.425703i	$-0.860027\pi$
$281$	−3.69421	+	5.08464i	−0.220378	+	0.303324i	0.684485	+	0.729027i	$0.260027\pi$
$282$	−1.72702	−	9.26552i	−0.102842	−	0.551753i
$283$	7.94610	−	2.58184i	0.472346	−	0.153475i	−0.0631642	−	0.998003i	$-0.520119\pi$
$283$	7.94610	−	2.58184i	0.472346	−	0.153475i	0.535511	+	0.844529i	$0.320119\pi$
$284$			11.2556i			0.667896i
$285$	1.88026	−	1.98239i	0.111377	−	0.117427i
$286$	1.39762	+	4.30143i	0.0826430	+	0.254349i
$287$	−3.46342	+	10.6593i	−0.204439	+	0.629200i
$288$	2.79855	−	1.08080i	0.164906	−	0.0636869i
$289$	−3.07144	−	2.23153i	−0.180673	−	0.131266i
$290$	0.0160346	−	21.0403i	0.000941583	−	1.23553i
$291$	−5.59916	−	10.2874i	−0.328228	−	0.603057i
$292$	3.95701	−	2.87493i	0.231566	−	0.168243i
$293$	0.963081	−	2.96406i	0.0562638	−	0.173162i	−0.918975	−	0.394315i	$-0.870982\pi$
$293$	0.963081	−	2.96406i	0.0562638	−	0.173162i	0.975239	+	0.221153i	$0.0709819\pi$
$294$	1.93938	+	10.4049i	0.113107	+	0.606825i
$295$	8.12376	+	25.0673i	0.472983	+	1.45948i
$296$	1.99418	−	6.13747i	0.115910	−	0.356733i
$297$	3.29980	−	3.88754i	0.191474	−	0.225578i
$298$	8.03065	−	11.0532i	0.465203	−	0.640297i
$299$	28.4143	−	9.23238i	1.64324	−	0.533922i
$300$	8.58559	+	1.13474i	0.495689	+	0.0655142i
$301$	4.03369	+	1.31063i	0.232498	+	0.0755432i
$302$	−18.5324	−	6.02154i	−1.06642	−	0.346501i
$303$	−3.94598	+	30.2103i	−0.226691	+	1.73553i
$304$	0.705467			0.0404613
$305$	−3.85371	+	11.8298i	−0.220663	+	0.677373i
$306$	9.15440	+	5.91848i	0.523322	+	0.338337i
$307$	8.30586	+	11.4320i	0.474041	+	0.652461i	0.977346	−	0.211648i	$-0.0678829\pi$
$307$	8.30586	+	11.4320i	0.474041	+	0.652461i	−0.503305	+	0.864109i	$0.667883\pi$
$308$	0.543948	−	0.748680i	0.0309943	−	0.0426600i
$309$	14.1756	+	6.74373i	0.806424	+	0.383637i
$310$	−0.798968	+	12.4242i	−0.0453783	+	0.705649i
$311$			22.1179i			1.25419i	0.778943	+	0.627095i	$0.215756\pi$
$311$			22.1179i			1.25419i	−0.778943	+	0.627095i	$0.784244\pi$
$312$	−7.01143	+	3.81614i	−0.396944	+	0.216047i
$313$	−4.21875	+	3.06510i	−0.238458	+	0.173250i	−0.700596	−	0.713558i	$-0.747082\pi$
$313$	−4.21875	+	3.06510i	−0.238458	+	0.173250i	0.462138	+	0.886808i	$0.347082\pi$
$314$	6.55139	−	2.12868i	0.369716	−	0.120128i
$315$	5.90289	−	2.27454i	0.332590	−	0.128156i
$316$			0.870525i			0.0489708i
$317$	6.08406	+	18.7248i	0.341715	+	1.05169i	0.963319	+	0.268359i	$0.0864813\pi$
$317$	6.08406	+	18.7248i	0.341715	+	1.05169i	−0.621604	+	0.783332i	$0.713519\pi$
$318$	−13.7171	+	14.4843i	−0.769216	+	0.812239i
$319$	2.85344	−	8.78198i	0.159762	−	0.491696i
$320$	1.31295	+	1.81002i	0.0733961	+	0.101183i
$321$	9.06501	+	1.18405i	0.505959	+	0.0660870i
$322$	−4.94561	−	3.59320i	−0.275608	−	0.200241i
$323$	1.50674	+	2.07386i	0.0838375	+	0.115392i
$324$	7.81248	+	4.46823i	0.434027	+	0.248235i
$325$	−23.0440	−	0.0351232i	−1.27825	−	0.00194828i
$326$	4.43686	+	6.10682i	0.245735	+	0.338225i
$327$	−19.9783	−	18.9201i	−1.10480	−	1.04628i
$328$	−6.98590	−	9.61527i	−0.385732	−	0.530914i
$329$	3.01622	−	4.15147i	0.166290	−	0.228878i
$330$	3.43088	+	1.63537i	0.188864	+	0.0900242i
$331$	−0.814000	+	1.12038i	−0.0447415	+	0.0615814i	−0.830802	−	0.556569i	$-0.812118\pi$
$331$	−0.814000	+	1.12038i	−0.0447415	+	0.0615814i	0.786060	+	0.618150i	$0.212118\pi$
$332$	−1.19160	−	0.387176i	−0.0653978	−	0.0212490i
$333$	18.0599	−	6.97476i	0.989677	−	0.382214i
$334$	−15.0069	+	4.87603i	−0.821140	+	0.266805i
$335$	−5.14672	+	15.7990i	−0.281195	+	0.863192i
$336$	1.47496	+	0.701676i	0.0804654	+	0.0382796i
$337$	9.30182	+	28.6281i	0.506703	+	1.55947i	0.797889	+	0.602804i	$0.205950\pi$
$337$	9.30182	+	28.6281i	0.506703	+	1.55947i	−0.291187	+	0.956666i	$0.594050\pi$
$338$	6.66715	−	4.84397i	0.362645	−	0.263477i
$339$	−15.4438	+	8.40567i	−0.838793	+	0.456533i
$340$	−2.51669	+	7.72553i	−0.136486	+	0.418976i
$341$	−2.01456	+	5.07891i	−0.109094	+	0.275039i
$342$	1.33524	+	1.64204i	0.0722014	+	0.0887912i
$343$	−7.26716	+	10.0024i	−0.392390	+	0.540078i
$344$	−3.63860	+	2.64360i	−0.196180	+	0.142533i
$345$	10.8029	−	22.6637i	0.581609	−	1.22017i
$346$	10.7705			0.579028
$347$			18.4789i			0.992001i	0.868322	+	0.496001i	$0.165199\pi$
$347$			18.4789i			0.992001i	−0.868322	+	0.496001i	$0.834801\pi$
$348$	16.1605	+	2.11084i	0.866292	+	0.113153i
$349$	5.43792	−	16.7362i	0.291085	−	0.895868i	−0.693423	−	0.720530i	$-0.743898\pi$
$349$	5.43792	−	16.7362i	0.291085	−	0.895868i	0.984508	−	0.175337i	$-0.0561016\pi$
$350$	2.76564	+	3.81880i	0.147830	+	0.204124i
$351$	−22.1530	−	9.09692i	−1.18244	−	0.485558i
$352$	0.303250	+	0.933309i	0.0161633	+	0.0497455i
$353$	−0.760557	+	1.04682i	−0.0404804	+	0.0557164i	−0.828777	−	0.559578i	$-0.810963\pi$
$353$	−0.760557	+	1.04682i	−0.0404804	+	0.0557164i	0.788297	+	0.615295i	$0.210963\pi$
$354$	−20.0657	+	3.74008i	−1.06648	+	0.198783i
$355$	−20.3503	−	14.8090i	−1.08008	−	0.785983i
$356$	−9.32481	+	6.77487i	−0.494214	+	0.359067i
$357$	1.08752	+	5.83457i	0.0575574	+	0.308798i
$358$	−3.20389	+	9.86056i	−0.169331	+	0.521147i
$359$	17.8694	+	24.5951i	0.943112	+	1.29808i	0.954520	+	0.298147i	$0.0963686\pi$
$359$	17.8694	+	24.5951i	0.943112	+	1.29808i	−0.0114083	+	0.999935i	$0.503631\pi$
$360$	−1.72796	+	6.48183i	−0.0910714	+	0.341623i
$361$	−5.71753	−	17.5967i	−0.300923	−	0.926145i
$362$	4.65926	−	6.41292i	0.244885	−	0.337055i
$363$	−12.6225	−	11.9539i	−0.662508	−	0.627417i
$364$	−4.13346	−	1.34304i	−0.216652	−	0.0703946i
$365$	−0.00833489	+	10.9369i	−0.000436268	+	0.572463i
$366$	−8.70269	−	4.14011i	−0.454897	−	0.216407i
$367$	3.66545			0.191335			0.0956674	−	0.995413i	$-0.469501\pi$
$367$	3.66545			0.191335			0.0956674	+	0.995413i	$0.469501\pi$
$368$	6.16523	−	2.00321i	0.321385	−	0.104424i
$369$	9.15817	−	34.4592i	0.476755	−	1.79387i
$370$	8.47287	+	11.6806i	0.440484	+	0.607246i
$371$	−10.8611			−0.563881
$372$	−9.46397	−	1.85290i	−0.490684	−	0.0960682i
$373$		−	20.1010i		−	1.04079i	−0.853925	−	0.520395i	$-0.825785\pi$
$373$		−	20.1010i		−	1.04079i	0.853925	−	0.520395i	$-0.174215\pi$
$374$	−2.09596	+	2.88484i	−0.108379	+	0.149171i
$375$	−13.3477	+	14.0299i	−0.689274	+	0.724501i
$376$	1.68154	+	5.17525i	0.0867188	+	0.266893i
$377$	−43.3666			−2.23349
$378$	1.15844	+	4.76116i	0.0595836	+	0.244887i
$379$	8.21182	+	25.2734i	0.421813	+	1.29821i	0.906013	+	0.423249i	$0.139111\pi$
$379$	8.21182	+	25.2734i	0.421813	+	1.29821i	−0.484200	+	0.874957i	$0.660889\pi$
$380$	−0.928187	+	1.27549i	−0.0476150	+	0.0654315i
$381$	−12.4406	−	11.7817i	−0.637351	−	0.603592i
$382$	−2.92832	+	4.03048i	−0.149826	+	0.206218i
$383$	22.6828	−	7.37008i	1.15904	−	0.376593i	0.334496	−	0.942397i	$-0.391434\pi$
$383$	22.6828	−	7.37008i	1.15904	−	0.376593i	0.824540	+	0.565804i	$0.191434\pi$
$384$	−1.52131	+	0.828012i	−0.0776342	+	0.0422543i
$385$	0.637949	+	1.96851i	0.0325129	+	0.100324i
$386$	6.74468	+	2.19148i	0.343295	+	0.111543i
$387$	−13.0400	−	3.46563i	−0.662861	−	0.176168i
$388$	3.97470	+	5.47071i	0.201785	+	0.277733i
$389$	3.04870	−	9.38293i	0.154575	−	0.475733i	−0.843543	−	0.537062i	$-0.819534\pi$
$389$	3.04870	−	9.38293i	0.154575	−	0.475733i	0.998118	+	0.0613292i	$0.0195340\pi$
$390$	2.32534	−	17.6977i	0.117748	−	0.896158i
$391$	19.0566	+	13.8454i	0.963733	+	0.700193i
$392$	−1.88832	−	5.81164i	−0.0953744	−	0.293532i
$393$	−11.9453	−	21.9472i	−0.602562	−	1.10709i
$394$	8.99819	+	2.92369i	0.453322	+	0.147293i
$395$	−1.57392	−	1.14535i	−0.0791926	−	0.0576290i
$396$	−1.59840	+	2.47232i	−0.0803225	+	0.124239i
$397$			15.3899i			0.772397i	0.922416	+	0.386198i	$0.126212\pi$
$397$			15.3899i			0.772397i	−0.922416	+	0.386198i	$0.873788\pi$
$398$		−	16.0223i		−	0.803124i
$399$	−0.149239	+	1.14257i	−0.00747132	+	0.0572001i
$400$	−4.99999	−	0.00762089i	−0.250000	−	0.000381045i
$401$	−25.0568	−	18.2048i	−1.25128	−	0.909105i	−0.252980	−	0.967471i	$-0.581411\pi$
$401$	−25.0568	−	18.2048i	−1.25128	−	0.909105i	−0.998295	+	0.0583668i	$0.981411\pi$
$402$	−11.6227	−	5.52921i	−0.579685	−	0.275772i
$403$	25.6091	+	1.62725i	1.27568	+	0.0810592i
$404$		−	17.5901i		−	0.875138i
$405$	−18.3576	+	8.24620i	−0.912195	+	0.409757i
$406$	5.21561	+	7.17867i	0.258846	+	0.356271i
$407$	1.95697	+	6.02294i	0.0970034	+	0.298546i
$408$	−5.68334	−	2.70372i	−0.281367	−	0.133854i
$409$		−	8.48491i		−	0.419552i	−0.977749	−	0.209776i	$-0.932727\pi$
$409$		−	8.48491i		−	0.419552i	0.977749	−	0.209776i	$-0.0672735\pi$
$410$	26.5759	+	0.0202532i	1.31249	+	0.00100024i
$411$	11.1035	−	11.7245i	0.547693	−	0.578326i
$412$	−8.61964	−	2.80069i	−0.424659	−	0.137980i
$413$	−8.99056	−	6.53202i	−0.442396	−	0.321420i
$414$	16.3316	+	10.5587i	0.802654	+	0.518930i
$415$	2.26782	−	1.64503i	0.111323	−	0.0807513i
$416$	3.72860	−	2.70899i	0.182810	−	0.132819i
$417$	−9.51770	+	10.0500i	−0.466084	+	0.492152i
$418$	−0.560084	+	0.406925i	−0.0273946	+	0.0199033i
$419$	−17.0182	−	23.4235i	−0.831393	−	1.14431i	−0.987662	−	0.156600i	$-0.949947\pi$
$419$	−17.0182	−	23.4235i	−0.831393	−	1.14431i	0.156269	−	0.987715i	$-0.450053\pi$
$420$	−3.20925	+	1.74354i	−0.156595	+	0.0850761i
$421$	−19.8791	+	14.4430i	−0.968848	+	0.703909i	−0.955189	−	0.295998i	$-0.904348\pi$
$421$	−19.8791	+	14.4430i	−0.968848	+	0.703909i	−0.0136590	+	0.999907i	$0.504348\pi$
$422$	−10.5358	−	7.65467i	−0.512872	−	0.372624i
$423$	−8.86320	+	13.7091i	−0.430944	+	0.666562i
$424$	6.76977	−	9.31779i	0.328769	−	0.452512i
$425$	−10.6566	−	14.7147i	−0.516923	−	0.713769i
$426$	13.4052	−	14.1550i	0.649486	−	0.685812i
$427$	−1.62142	−	4.99022i	−0.0784661	−	0.241494i
$428$	−5.27814			−0.255129
$429$	3.36530	−	7.07402i	0.162478	−	0.341537i
$430$	0.00766422	−	10.0568i	0.000369601	−	0.484984i
$431$	−6.91711	−	9.52059i	−0.333186	−	0.458591i	0.609250	−	0.792978i	$-0.291471\pi$
$431$	−6.91711	−	9.52059i	−0.333186	−	0.458591i	−0.942436	+	0.334387i	$0.891471\pi$
$432$	−4.80667	−	1.97382i	−0.231261	−	0.0949652i
$433$	−4.00553			−0.192493			−0.0962466	−	0.995358i	$-0.530684\pi$
$433$	−4.00553			−0.192493			−0.0962466	+	0.995358i	$0.530684\pi$
$434$	−2.81059	−	4.43490i	−0.134912	−	0.212882i
$435$	−25.0789	+	26.4411i	−1.20244	+	1.26776i
$436$	12.8521	+	9.33761i	0.615505	+	0.447190i
$437$	2.68806	+	3.69979i	0.128587	+	0.176985i
$438$	−8.40033	−	1.09723i	−0.401383	−	0.0524276i
$439$	−2.70003			−0.128865			−0.0644327	−	0.997922i	$-0.520524\pi$
$439$	−2.70003			−0.128865			−0.0644327	+	0.997922i	$0.520524\pi$
$440$	−2.08642	−	0.679679i	−0.0994664	−	0.0324024i
$441$	9.95309	−	15.3949i	0.473957	−	0.733092i
$442$	15.9272	+	5.17505i	0.757578	+	0.246152i
$443$	1.41564	−	4.35689i	0.0672591	−	0.207002i	−0.911778	−	0.410683i	$-0.865290\pi$
$443$	1.41564	−	4.35689i	0.0672591	−	0.207002i	0.979037	+	0.203681i	$0.0652904\pi$
$444$	−9.81752	+	5.34342i	−0.465919	+	0.253588i
$445$	0.0196414	−	25.7731i	0.000931093	−	1.22176i
$446$	−16.7013	−	12.1342i	−0.790830	−	0.574572i
$447$	−23.2636	+	4.33614i	−1.10033	+	0.205092i
$448$	−0.896862	−	0.291408i	−0.0423728	−	0.0137677i
$449$	−25.0859	+	18.2260i	−1.18388	+	0.860136i	−0.992604	−	0.121401i	$-0.961261\pi$
$449$	−25.0859	+	18.2260i	−1.18388	+	0.860136i	−0.191272	+	0.981537i	$0.561261\pi$
$450$	−9.44576	−	11.6524i	−0.445278	−	0.549298i
$451$	11.0925	+	3.60417i	0.522325	+	0.169714i
$452$	8.21284	−	5.96698i	0.386300	−	0.280663i
$453$	16.1347	+	29.6445i	0.758076	+	1.39282i
$454$	6.52792	+	20.0909i	0.306371	+	0.942912i
$455$	7.86666	−	5.70631i	0.368795	−	0.267516i
$456$	−0.887193	−	0.840201i	−0.0415466	−	0.0393460i
$457$	3.35155	−	10.3150i	0.156779	−	0.482516i	−0.841558	−	0.540167i	$-0.818361\pi$
$457$	3.35155	−	10.3150i	0.156779	−	0.482516i	0.998337	+	0.0576509i	$0.0183610\pi$
$458$	−8.81922	+	2.86554i	−0.412095	+	0.133898i
$459$	−4.46373	−	18.3458i	−0.208349	−	0.856310i
$460$	−4.48981	+	13.7825i	−0.209338	+	0.642611i
$461$	−2.44084	−	7.51214i	−0.113681	−	0.349875i	0.877988	−	0.478682i	$-0.158885\pi$
$461$	−2.44084	−	7.51214i	−0.113681	−	0.349875i	−0.991670	+	0.128807i	$0.958885\pi$
$462$	−1.57573	+	0.293704i	−0.0733098	+	0.0136644i
$463$	−19.3055	−	14.0262i	−0.897201	−	0.651854i	0.0405448	−	0.999178i	$-0.487091\pi$
$463$	−19.3055	−	14.0262i	−0.897201	−	0.651854i	−0.937745	+	0.347323i	$0.887091\pi$
$464$	−9.40951			−0.436825
$465$	15.8019	−	14.6731i	0.732794	−	0.680450i
$466$	−13.4275			−0.622017
$467$	−28.4581	−	20.6761i	−1.31689	−	0.956774i	−0.999965	−	0.00832162i	$-0.997351\pi$
$467$	−28.4581	−	20.6761i	−1.31689	−	0.956774i	−0.316921	−	0.948452i	$-0.602649\pi$
$468$	13.3625	+	3.55135i	0.617683	+	0.164161i
$469$	−2.16545	−	6.66457i	−0.0999911	−	0.307741i
$470$	−11.5693	−	3.76886i	−0.533654	−	0.173844i
$471$	−10.7742	−	5.12560i	−0.496451	−	0.236175i
$472$	11.2077	−	3.64160i	0.515875	−	0.167618i
$473$	1.36389	−	4.19761i	0.0627116	−	0.193006i
$474$	1.03678	−	1.09477i	0.0476210	−	0.0502845i
$475$	−1.08489	−	3.35635i	−0.0497782	−	0.154000i
$476$	−1.05888	−	3.25889i	−0.0485336	−	0.149371i
$477$	34.5012	−	1.87855i	1.57970	−	0.0860131i
$478$	−6.23267	+	4.52830i	−0.285076	+	0.207120i
$479$	−3.09799	−	1.00660i	−0.141551	−	0.0459927i	0.237385	−	0.971416i	$-0.423710\pi$
$479$	−3.09799	−	1.00660i	−0.141551	−	0.0459927i	−0.378936	+	0.925423i	$0.623710\pi$
$480$	0.504544	−	3.83998i	0.0230292	−	0.175270i
$481$	24.0618	−	17.4819i	1.09712	−	0.797108i
$482$	−14.6757	−	4.76842i	−0.668459	−	0.217195i
$483$	1.94015	+	10.4090i	0.0882797	+	0.473624i
$484$	8.12008	+	5.89959i	0.369095	+	0.268163i
$485$	−15.1207	−	0.0115233i	−0.686594	−	0.000523246i
$486$	−4.50336	−	14.9238i	−0.204277	−	0.676957i
$487$	−6.41395	+	19.7401i	−0.290644	+	0.894510i	0.694006	+	0.719969i	$0.255844\pi$
$487$	−6.41395	+	19.7401i	−0.290644	+	0.894510i	−0.984650	+	0.174541i	$0.944156\pi$
$488$	5.29177	+	1.71940i	0.239547	+	0.0778335i
$489$	1.69334	−	12.9642i	0.0765756	−	0.586260i
$490$	12.9920	+	4.23231i	0.586919	+	0.191196i
$491$	20.8218			0.939673			0.469836	−	0.882754i	$-0.344313\pi$
$491$	20.8218			0.939673			0.469836	+	0.882754i	$0.344313\pi$
$492$	−2.66619	+	20.4122i	−0.120201	+	0.920255i
$493$	−20.0969	−	27.6611i	−0.905121	−	1.24579i
$494$	2.63040	+	1.91110i	0.118347	+	0.0859844i
$495$	−2.36697	−	6.14277i	−0.106387	−	0.276097i
$496$	5.55656	+	0.353075i	0.249497	+	0.0158535i
$497$	10.6142			0.476112
$498$	1.03744	+	1.90610i	0.0464887	+	0.0854142i
$499$	4.51499	+	6.21435i	0.202119	+	0.278193i	0.898029	−	0.439936i	$-0.144999\pi$
$499$	4.51499	+	6.21435i	0.202119	+	0.278193i	−0.695910	+	0.718129i	$0.744999\pi$
$500$	6.59230	−	9.03004i	0.294817	−	0.403836i
$501$	24.6799	+	11.7409i	1.10262	+	0.524545i
$502$	6.88991			0.307512
$503$	−8.52106	−	26.2251i	−0.379935	−	1.16932i	−0.940088	−	0.340931i	$-0.889258\pi$
$503$	−8.52106	−	26.2251i	−0.379935	−	1.16932i	0.560153	−	0.828389i	$-0.310742\pi$
$504$	−1.01921	−	2.63908i	−0.0453994	−	0.117554i
$505$	31.8031	+	23.1433i	1.41522	+	1.02987i
$506$	−3.73922	+	5.14659i	−0.166229	+	0.228794i
$507$	−14.1537	−	1.84872i	−0.628588	−	0.0821044i
$508$	8.00308	+	5.81458i	0.355079	+	0.257980i
$509$	−32.7390	+	23.7863i	−1.45113	+	1.05431i	−0.465563	+	0.885015i	$0.654148\pi$
$509$	−32.7390	+	23.7863i	−1.45113	+	1.05431i	−0.985566	+	0.169293i	$0.945852\pi$
$510$	12.3660	−	6.71827i	0.547574	−	0.297490i
$511$	−2.71111	−	3.73152i	−0.119932	−	0.165073i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	0.276450	−	3.65527i	0.0122056	−	0.161384i
$514$	−18.8704	+	13.7102i	−0.832340	+	0.604730i
$515$	16.4046	−	11.8996i	0.722874	−	0.524357i
$516$	7.72439	+	1.00894i	0.340047	+	0.0444161i
$517$	−4.32018	−	3.13879i	−0.190001	−	0.138044i
$518$	−5.78774	−	1.88055i	−0.254299	−	0.0826266i
$519$	−13.5450	−	12.8276i	−0.594560	−	0.563068i
$520$	−0.00785378	+	10.3056i	−0.000344411	+	0.451930i
$521$			39.6484i			1.73703i	0.495666	+	0.868513i	$0.334924\pi$
$521$			39.6484i			1.73703i	−0.495666	+	0.868513i	$0.665076\pi$
$522$	−17.8094	−	21.9015i	−0.779496	−	0.958602i
$523$	−0.814621	−	2.50714i	−0.0356209	−	0.109630i	0.931665	−	0.363318i	$-0.118356\pi$
$523$	−0.814621	−	2.50714i	−0.0356209	−	0.109630i	−0.967286	+	0.253688i	$0.918356\pi$
$524$	8.47969	+	11.6713i	0.370437	+	0.509863i
$525$	1.07008	−	8.09636i	0.0467020	−	0.353354i
$526$		−	8.13190i		−	0.354568i
$527$	10.8298	+	17.0887i	0.471755	+	0.744395i
$528$	0.730190	−	1.53489i	0.0317775	−	0.0667977i
$529$	15.3899	+	11.1814i	0.669125	+	0.486148i
$530$	7.93968	+	24.4993i	0.344877	+	1.06418i
$531$	29.6890	+	19.1944i	1.28839	+	0.832967i
$532$		−	0.665267i		−	0.0288430i
$533$		−	54.7762i		−	2.37262i
$534$	19.7956	+	2.58565i	0.856641	+	0.111892i
$535$	6.94448	−	9.54296i	0.300236	−	0.412578i
$536$	7.06728	+	2.29630i	0.305260	+	0.0991850i
$537$	15.7730	−	8.58483i	0.680655	−	0.370463i
$538$	−4.80325	−	14.7829i	−0.207083	−	0.637336i
$539$	4.85142	+	3.52476i	0.208965	+	0.151822i
$540$	9.89285	−	6.09357i	0.425720	−	0.262225i
$541$	3.33713	−	10.2706i	0.143474	−	0.441569i	−0.853337	−	0.521359i	$-0.825425\pi$
$541$	3.33713	−	10.2706i	0.143474	−	0.441569i	0.996812	+	0.0797905i	$0.0254251\pi$
$542$	−10.1609	−	13.9853i	−0.436449	−	0.600721i
$543$	−13.4972	+	2.51576i	−0.579219	+	0.107962i
$544$	3.45582	+	1.12286i	0.148167	+	0.0481424i
$545$	−33.7921	+	10.9513i	−1.44750	+	0.469101i
$546$	3.59869	+	6.61190i	0.154010	+	0.282963i
$547$	−18.9943	+	6.17162i	−0.812138	+	0.263880i	−0.685503	−	0.728070i	$-0.740418\pi$
$547$	−18.9943	+	6.17162i	−0.812138	+	0.263880i	−0.126635	+	0.991949i	$0.540418\pi$
$548$	−5.47987	+	7.54239i	−0.234088	+	0.322195i
$549$	6.01368	+	15.5714i	0.256658	+	0.664570i
$550$	3.97399	−	2.87803i	0.169451	−	0.122720i
$551$	−2.05128	−	6.31320i	−0.0873876	−	0.268951i
$552$	−10.1392	−	4.82348i	−0.431552	−	0.205301i
$553$	0.820920			0.0349091
$554$	−2.26689	−	6.97677i	−0.0963110	−	0.296415i
$555$	3.25598	−	24.7806i	0.138209	−	1.05188i
$556$	4.69726	−	6.46522i	0.199208	−	0.274186i
$557$			19.7791i			0.838069i	0.907970	+	0.419034i	$0.137631\pi$
$557$			19.7791i			0.838069i	−0.907970	+	0.419034i	$0.862369\pi$
$558$	9.69510	+	13.6017i	0.410426	+	0.575804i
$559$	−20.7284			−0.876716
$560$	1.70688	−	1.23813i	0.0721287	−	0.0523207i
$561$	6.07167	−	1.13171i	0.256346	−	0.0477808i
$562$	−5.97735	+	1.94216i	−0.252139	+	0.0819250i
$563$	−19.7270			−0.831393			−0.415696	−	0.909503i	$-0.636462\pi$
$563$	−19.7270			−0.831393			−0.415696	+	0.909503i	$0.636462\pi$
$564$	4.04895	−	8.51107i	0.170491	−	0.358381i
$565$	−0.0172992	+	22.6997i	−0.000727784	+	0.954985i
$566$	7.94610	+	2.58184i	0.333999	+	0.108523i
$567$	4.21362	−	7.36730i	0.176955	−	0.309398i
$568$	−6.61587	+	9.10596i	−0.277596	+	0.382078i
$569$	−6.63721	−	20.4272i	−0.278246	−	0.856354i	−0.988342	−	0.152249i	$-0.951348\pi$
$569$	−6.63721	−	20.4272i	−0.278246	−	0.856354i	0.710096	−	0.704105i	$-0.248652\pi$
$570$	2.68638	−	0.498602i	0.112520	−	0.0208841i
$571$	25.5853	+	35.2152i	1.07071	+	1.47371i	0.869353	+	0.494192i	$0.164536\pi$
$571$	25.5853	+	35.2152i	1.07071	+	1.47371i	0.201359	+	0.979517i	$0.435464\pi$
$572$	−1.39762	+	4.30143i	−0.0584375	+	0.179852i
$573$	8.48290	−	1.58114i	0.354378	−	0.0660532i
$574$	−9.06736	+	6.58782i	−0.378464	+	0.274970i
$575$	−19.0116	−	26.2513i	−0.792840	−	1.09476i
$576$	2.89935	+	0.770557i	0.120806	+	0.0321066i
$577$	3.01083	−	4.14406i	0.125343	−	0.172519i	−0.741734	−	0.670694i	$-0.765996\pi$
$577$	3.01083	−	4.14406i	0.125343	−	0.172519i	0.867077	+	0.498175i	$0.165996\pi$
$578$	−1.17318	−	3.61069i	−0.0487981	−	0.150185i
$579$	−5.87208	−	10.7888i	−0.244035	−	0.448368i
$580$	12.3801	−	17.0125i	0.514058	−	0.706407i
$581$	−0.365113	+	1.12370i	−0.0151475	+	0.0466191i
$582$	1.51696	−	11.6138i	0.0628800	−	0.481406i
$583$			11.3025i			0.468101i
$584$	4.89113			0.202396
$585$	−24.0021	+	19.4871i	−0.992363	+	0.805694i
$586$	2.52138	−	1.83189i	0.104157	−	0.0756746i
$587$	27.9019	−	38.4036i	1.15163	−	1.58509i	0.413390	−	0.910554i	$-0.364345\pi$
$587$	27.9019	−	38.4036i	1.15163	−	1.58509i	0.738244	−	0.674534i	$-0.235655\pi$
$588$	−4.54684	+	9.55766i	−0.187508	+	0.394151i
$589$	0.974445	+	3.80508i	0.0401513	+	0.156786i
$590$	−8.16195	+	25.0549i	−0.336022	+	1.03149i
$591$	−7.83404	−	14.3935i	−0.322249	−	0.592071i
$592$	5.22084	−	3.79316i	0.214575	−	0.155898i
$593$	−4.03263	−	12.4112i	−0.165600	−	0.509665i	0.833480	−	0.552550i	$-0.186345\pi$
$593$	−4.03263	−	12.4112i	−0.165600	−	0.509665i	−0.999080	+	0.0428847i	$0.986345\pi$
$594$	4.95464	−	1.20551i	0.203291	−	0.0494628i
$595$	7.28530	+	2.37328i	0.298668	+	0.0972949i
$596$	12.9939	−	4.22196i	0.532249	−	0.172938i
$597$	−19.0823	+	20.1496i	−0.780986	+	0.824667i
$598$	28.4143	+	9.23238i	1.16195	+	0.377540i
$599$	−4.23489	+	5.82882i	−0.173033	+	0.238159i	−0.886722	−	0.462304i	$-0.847023\pi$
$599$	−4.23489	+	5.82882i	−0.173033	+	0.238159i	0.713689	+	0.700463i	$0.247023\pi$
$600$	6.27891	+	5.96451i	0.256335	+	0.243500i
$601$	2.33900	−	3.21935i	0.0954097	−	0.131320i	−0.758643	−	0.651506i	$-0.774137\pi$
$601$	2.33900	−	3.21935i	0.0954097	−	0.131320i	0.854053	+	0.520186i	$0.174137\pi$
$602$	2.49296	+	3.43126i	0.101605	+	0.139848i
$603$	8.03142	+	20.7959i	0.327065	+	0.846876i
$604$	−11.4536	−	15.7646i	−0.466042	−	0.641452i
$605$	−21.3502	+	6.91911i	−0.868008	+	0.281302i
$606$	−20.9495	+	22.1212i	−0.851016	+	0.898613i
$607$	18.4545	+	25.4005i	0.749046	+	1.03097i	0.998047	+	0.0624697i	$0.0198977\pi$
$607$	18.4545	+	25.4005i	0.749046	+	1.03097i	−0.249001	+	0.968503i	$0.580102\pi$
$608$	0.570734	+	0.414663i	0.0231463	+	0.0168168i
$609$	1.99056	−	15.2396i	0.0806614	−	0.617540i
$610$	−10.0711	+	7.30537i	−0.407767	+	0.295786i
$611$	−7.74989	+	23.8517i	−0.313527	+	0.964936i
$612$	3.92727	+	10.1690i	0.158750	+	0.411056i
$613$	8.97898	+	27.6344i	0.362657	+	1.11614i	0.951435	+	0.307850i	$0.0996094\pi$
$613$	8.97898	+	27.6344i	0.362657	+	1.11614i	−0.588778	+	0.808295i	$0.700391\pi$
$614$			14.1308i			0.570272i
$615$	−33.3977	−	31.6770i	−1.34673	−	1.27734i
$616$	0.880126	−	0.285970i	0.0354613	−	0.0115221i
$617$	2.80807	−	2.04018i	0.113049	−	0.0821346i	−0.529825	−	0.848107i	$-0.677742\pi$
$617$	2.80807	−	2.04018i	0.113049	−	0.0821346i	0.642873	+	0.765973i	$0.277742\pi$
$618$	7.50446	+	13.7880i	0.301874	+	0.554636i
$619$			9.08380i			0.365109i	0.983196	+	0.182554i	$0.0584366\pi$
$619$			9.08380i			0.365109i	−0.983196	+	0.182554i	$0.941563\pi$
$620$	−7.94916	+	9.58180i	−0.319246	+	0.384814i
$621$	−7.96336	−	32.7293i	−0.319559	−	1.31338i
$622$	−13.0006	+	17.8937i	−0.521275	+	0.717474i
$623$	6.38882	+	8.79345i	0.255963	+	0.352302i
$624$	−7.91544	−	1.03389i	−0.316871	−	0.0413889i
$625$	7.65291	+	23.7999i	0.306116	+	0.951994i
$626$	−5.21466			−0.208420
$627$	1.18900	+	0.155304i	0.0474842	+	0.00620225i
$628$	6.55139	+	2.12868i	0.261429	+	0.0849434i
$629$	22.3015	+	7.24619i	0.889218	+	0.288925i
$630$	6.11248	+	1.62949i	0.243527	+	0.0649206i
$631$	−43.6295	+	14.1761i	−1.73686	+	0.564341i	−0.994413	−	0.105562i	$-0.966336\pi$
$631$	−43.6295	+	14.1761i	−1.73686	+	0.564341i	−0.742449	+	0.669902i	$0.766336\pi$
$632$	−0.511682	+	0.704269i	−0.0203536	+	0.0280143i
$633$	4.13313	+	22.1744i	0.164277	+	0.881354i
$634$	−6.08406	+	18.7248i	−0.241629	+	0.743657i
$635$	−21.0425	+	6.81941i	−0.835048	+	0.270620i
$636$	−19.6110	+	3.65533i	−0.777627	+	0.144943i
$637$	8.70287	−	26.7847i	0.344820	−	1.06125i
$638$	7.47039	−	5.42756i	0.295756	−	0.214879i
$639$	−33.7168	+	1.83585i	−1.33382	+	0.0726250i
$640$	−0.00170408	+	2.23607i	−6.73598e−5	+	0.0883883i
$641$	5.72879	+	4.16221i	0.226273	+	0.164397i	0.695146	−	0.718869i	$-0.255340\pi$
$641$	5.72879	+	4.16221i	0.226273	+	0.164397i	−0.468873	+	0.883266i	$0.655340\pi$
$642$	6.63778	+	6.28619i	0.261972	+	0.248096i
$643$	6.85754	−	21.1053i	0.270435	−	0.832313i	−0.719956	−	0.694019i	$-0.755838\pi$
$643$	6.85754	−	21.1053i	0.270435	−	0.832313i	0.990391	−	0.138294i	$-0.0441619\pi$
$644$	−1.88906	−	5.81392i	−0.0744393	−	0.229101i
$645$	−11.9872	+	12.6383i	−0.471996	+	0.497634i
$646$			2.56343i			0.100857i
$647$	25.6523	−	8.33493i	1.00849	−	0.327680i	0.242240	−	0.970216i	$-0.422118\pi$
$647$	25.6523	−	8.33493i	1.00849	−	0.327680i	0.766255	+	0.642537i	$0.222118\pi$
$648$	3.69407	+	8.20694i	0.145117	+	0.322399i
$649$	−6.79747	+	9.35591i	−0.266824	+	0.367252i
$650$	−18.6223	−	13.5733i	−0.730428	−	0.532390i
$651$	−1.74731	+	8.92469i	−0.0684826	+	0.349786i
$652$			7.54844i			0.295620i
$653$	−20.4768	−	14.8772i	−0.801318	−	0.582192i	0.109982	−	0.993934i	$-0.464921\pi$
$653$	−20.4768	−	14.8772i	−0.801318	−	0.582192i	−0.911301	+	0.411742i	$0.864921\pi$
$654$	−5.04183	−	27.0496i	−0.197151	−	1.05772i
$655$	−32.2586	−	0.0245840i	−1.26045	−	0.000960575i
$656$		−	11.8851i		−	0.464036i
$657$	9.25745	+	11.3845i	0.361168	+	0.444153i
$658$	4.88035	−	1.58572i	0.190256	−	0.0618178i
$659$	10.6129	+	3.44835i	0.413422	+	0.134329i	0.508340	−	0.861156i	$-0.330259\pi$
$659$	10.6129	+	3.44835i	0.413422	+	0.134329i	−0.0949188	+	0.995485i	$0.530259\pi$
$660$	1.81440	+	3.33966i	0.0706252	+	0.129996i
$661$	−4.97026	−	3.61110i	−0.193321	−	0.140456i	0.486914	−	0.873450i	$-0.338122\pi$
$661$	−4.97026	−	3.61110i	−0.193321	−	0.140456i	−0.680235	+	0.732994i	$0.738122\pi$
$662$	−1.31708	+	0.427945i	−0.0511898	+	0.0166326i
$663$	−13.8666	−	25.4772i	−0.538533	−	0.989452i
$664$	−0.736452	−	1.01364i	−0.0285799	−	0.0393368i
$665$	1.20281	+	0.875296i	0.0466431	+	0.0339425i
$666$	18.7104	+	4.97265i	0.725015	+	0.192686i
$667$	−35.8533	−	49.3478i	−1.38824	−	1.91075i
$668$	−15.0069	−	4.87603i	−0.580634	−	0.188659i
$669$	6.55186	+	35.1510i	0.253310	+	1.35902i
$670$	−13.4502	+	9.75649i	−0.519627	+	0.376926i
$671$	−5.19301	+	1.68731i	−0.200474	+	0.0651380i
$672$	0.780829	+	1.43462i	0.0301211	+	0.0553419i
$673$	−3.27789	+	10.0883i	−0.126353	+	0.388876i	−0.994145	−	0.108052i	$-0.965539\pi$
$673$	−3.27789	+	10.0883i	−0.126353	+	0.388876i	0.867792	+	0.496928i	$0.165539\pi$
$674$	−9.30182	+	28.6281i	−0.358293	+	1.10271i
$675$	−1.99882	+	25.9038i	−0.0769348	+	0.997036i
$676$	8.24105			0.316963
$677$			18.2647i			0.701969i	0.936381	+	0.350985i	$0.114153\pi$
$677$			18.2647i			0.701969i	−0.936381	+	0.350985i	$0.885847\pi$
$678$	−17.4350	−	2.27732i	−0.669589	−	0.0874598i
$679$	5.15897	−	3.74821i	0.197983	−	0.143843i
$680$	−6.57699	+	4.77081i	−0.252216	+	0.182952i
$681$	15.7185	−	33.0409i	0.602333	−	1.26613i
$682$	−4.61512	+	2.92480i	−0.176722	+	0.111996i
$683$	17.6043			0.673611			0.336805	−	0.941574i	$-0.390654\pi$
$683$	17.6043			0.673611			0.336805	+	0.941574i	$0.390654\pi$
$684$	0.115065	+	2.11327i	0.00439964	+	0.0808029i
$685$	−6.42686	−	19.8313i	−0.245558	−	0.757713i
$686$	−11.7585	+	3.82057i	−0.448942	+	0.145870i
$687$	14.5039	+	6.89987i	0.553357	+	0.263247i
$688$	−4.49756			−0.171468
$689$	50.4835	−	16.4031i	1.92327	−	0.624908i
$690$	22.0611	−	11.9855i	0.839851	−	0.456280i
$691$	−15.1330	+	46.5747i	−0.575688	+	1.77179i	0.0581366	+	0.998309i	$0.481484\pi$
$691$	−15.1330	+	46.5747i	−0.575688	+	1.77179i	−0.633825	+	0.773477i	$0.718516\pi$
$692$	8.71355	+	6.33077i	0.331240	+	0.240660i
$693$	2.33144	+	1.50732i	0.0885640	+	0.0572582i
$694$	−10.8616	+	14.9498i	−0.412302	+	0.567486i
$695$	5.50900	+	16.9990i	0.208968	+	0.644810i
$696$	11.8334	+	11.2066i	0.448543	+	0.424785i
$697$	34.9386	−	25.3844i	1.32339	−	0.961503i
$698$	14.2367	−	10.3435i	0.538865	−	0.391508i
$699$	16.8864	+	15.9920i	0.638703	+	0.604872i
$700$	−0.00718663	+	4.71508i	−0.000271629	+	0.178213i
$701$	11.0866	−	15.2594i	0.418735	−	0.576340i	−0.546587	−	0.837403i	$-0.684073\pi$
$701$	11.0866	−	15.2594i	0.418735	−	0.576340i	0.965322	+	0.261063i	$0.0840730\pi$
$702$	−12.5751	−	20.3808i	−0.474616	−	0.769222i
$703$	3.68313	+	2.67595i	0.138912	+	0.100925i
$704$	−0.303250	+	0.933309i	−0.0114292	+	0.0351754i
$705$	10.0609	+	18.5186i	0.378916	+	0.697452i
$706$	−1.23061	+	0.399849i	−0.0463145	+	0.0150485i
$707$	−16.5877			−0.623846
$708$	−18.4318	−	8.76852i	−0.692711	−	0.329541i
$709$	−7.17849	+	2.33243i	−0.269594	+	0.0875963i	−0.440694	−	0.897657i	$-0.645268\pi$
$709$	−7.17849	+	2.33243i	−0.269594	+	0.0875963i	0.171101	+	0.985254i	$0.445268\pi$
$710$	−7.75918	−	23.9424i	−0.291197	−	0.898541i
$711$	−2.60771	+	0.141987i	−0.0977968	+	0.00532494i
$712$	−11.5261			−0.431959
$713$	19.3206	+	30.4865i	0.723562	+	1.14173i
$714$	−2.54965	+	5.35949i	−0.0954184	+	0.200574i
$715$	−5.93820	−	8.18634i	−0.222076	−	0.306152i
$716$	−8.38789	+	6.09416i	−0.313470	+	0.227749i
$717$	13.2313	+	1.72824i	0.494134	+	0.0645424i
$718$			30.4013i			1.13457i
$719$	−19.8151			−0.738979			−0.369490	−	0.929235i	$-0.620467\pi$
$719$	−19.8151			−0.738979			−0.369490	+	0.929235i	$0.620467\pi$
$720$	−5.20787	+	4.22824i	−0.194086	+	0.157577i
$721$	−2.64110	+	8.12847i	−0.0983597	+	0.302720i
$722$	5.71753	−	17.5967i	0.212784	−	0.654883i
$723$	12.7770	+	23.4753i	0.475181	+	0.873055i
$724$	7.53883	−	2.44952i	0.280179	−	0.0910355i
$725$	14.4703	+	44.7670i	0.537412	+	1.66260i
$726$	−3.18548	−	17.0902i	−0.118224	−	0.634277i
$727$	7.48239	+	2.43118i	0.277506	+	0.0901673i	0.444464	−	0.895797i	$-0.353394\pi$
$727$	7.48239	+	2.43118i	0.277506	+	0.0901673i	−0.166957	+	0.985964i	$0.553394\pi$
$728$	−2.55462	−	3.51613i	−0.0946805	−	0.130317i
$729$	−12.1106	+	24.1316i	−0.448541	+	0.893762i
$730$	−6.43529	+	8.84323i	−0.238181	+	0.327303i
$731$	−9.60595	−	13.2215i	−0.355289	−	0.489013i
$732$	−4.60713	−	8.46473i	−0.170285	−	0.312865i
$733$	24.4839	−	7.95531i	0.904335	−	0.293836i	0.180310	−	0.983610i	$-0.442290\pi$
$733$	24.4839	−	7.95531i	0.904335	−	0.293836i	0.724025	+	0.689774i	$0.242290\pi$
$734$	2.96541	+	2.15450i	0.109455	+	0.0795239i
$735$	−11.2981	−	20.7958i	−0.416737	−	0.767066i
$736$	6.16523	+	2.00321i	0.227254	+	0.0738391i
$737$	−6.93540	+	2.25345i	−0.255469	+	0.0830068i
$738$	27.6637	−	22.4950i	1.01831	−	0.828053i
$739$		−	13.5598i		−	0.498806i	−0.968400	−	0.249403i	$-0.919766\pi$
$739$		−	13.5598i		−	0.498806i	0.968400	−	0.249403i	$-0.0802344\pi$
$740$	−0.0109970	+	14.4300i	−0.000404257	+	0.530459i
$741$	−1.03190	−	5.53617i	−0.0379077	−	0.203376i
$742$	−8.78683	−	6.38401i	−0.322575	−	0.234364i
$743$		−	20.5602i		−	0.754282i	−0.926156	−	0.377141i	$-0.876907\pi$
$743$		−	20.5602i		−	0.754282i	0.926156	−	0.377141i	$-0.123093\pi$
$744$	−6.56741	−	7.06181i	−0.240773	−	0.258898i
$745$	−9.46273	+	29.0479i	−0.346688	+	1.06423i
$746$	11.8151	−	16.2621i	0.432581	−	0.595396i
$747$	0.965452	−	3.63268i	0.0353241	−	0.132913i
$748$	−3.39133	+	1.10191i	−0.123999	+	0.0402898i
$749$			4.97738i			0.181869i
$750$	−19.0451	+	3.50482i	−0.695429	+	0.127978i
$751$	9.07250	+	27.9223i	0.331060	+	1.01890i	0.968630	+	0.248506i	$0.0799397\pi$
$751$	9.07250	+	27.9223i	0.331060	+	1.01890i	−0.637570	+	0.770393i	$0.720060\pi$
$752$	−1.68154	+	5.17525i	−0.0613195	+	0.188722i
$753$	−8.66474	−	8.20579i	−0.315761	−	0.299035i
$754$	−35.0843	−	25.4902i	−1.27769	−	0.928299i
$755$	43.5722	+	0.0332060i	1.58576	+	0.00120849i
$756$	−1.86134	+	4.53277i	−0.0676963	+	0.164855i
$757$	−3.97187	+	2.88574i	−0.144360	+	0.104884i	−0.657621	−	0.753349i	$-0.728437\pi$
$757$	−3.97187	+	2.88574i	−0.144360	+	0.104884i	0.513261	+	0.858233i	$0.328437\pi$
$758$	−8.21182	+	25.2734i	−0.298267	+	0.917971i
$759$	10.8320	−	2.01899i	0.393175	−	0.0732846i
$760$	−1.50064	+	0.486322i	−0.0544338	+	0.0176408i
$761$	−5.86492	+	18.0504i	−0.212603	+	0.654325i	0.786712	+	0.617320i	$0.211782\pi$
$761$	−5.86492	+	18.0504i	−0.212603	+	0.654325i	−0.999315	+	0.0370051i	$0.988218\pi$
$762$	−3.13958	−	16.8440i	−0.113735	−	0.610192i
$763$	8.80552	−	12.1198i	0.318781	−	0.438765i
$764$	−4.73812	+	1.53951i	−0.171419	+	0.0556974i
$765$	−23.5528	−	6.27882i	−0.851553	−	0.227011i
$766$	22.6828	+	7.37008i	0.819562	+	0.266292i
$767$	51.6540	+	16.7834i	1.86512	+	0.606013i
$768$	−1.71746	−	0.224330i	−0.0619736	−	0.00809482i
$769$	28.1069			1.01356			0.506780	−	0.862075i	$-0.330836\pi$
$769$	28.1069			1.01356			0.506780	+	0.862075i	$0.330836\pi$
$770$	−0.640948	+	1.96753i	−0.0230982	+	0.0709050i
$771$	40.0601	+	5.23254i	1.44273	+	0.188445i
$772$	4.16844	+	5.73737i	0.150026	+	0.206492i
$773$	24.6406	−	33.9148i	0.886260	−	1.21983i	−0.0883876	−	0.996086i	$-0.528171\pi$
$773$	24.6406	−	33.9148i	0.886260	−	1.21983i	0.974647	−	0.223746i	$-0.0718286\pi$
$774$	−8.51255	−	10.4685i	−0.305977	−	0.376282i
$775$	−6.86527	−	26.9790i	−0.246608	−	0.969115i
$776$			6.76217i			0.242748i
$777$	5.03894	+	9.25809i	0.180771	+	0.332132i
$778$	7.98159	−	5.79897i	0.286154	−	0.207903i
$779$	7.97419	−	2.59097i	0.285705	−	0.0928312i
$780$	12.2837	−	12.9509i	0.439827	−	0.463718i
$781$		−	11.0455i		−	0.395241i
$782$	7.27897	+	22.4024i	0.260295	+	0.801107i
$783$	−3.68729	+	48.7540i	−0.131773	+	1.74233i
$784$	1.88832	−	5.81164i	0.0674399	−	0.207559i
$785$	−12.4684	+	9.04430i	−0.445016	+	0.322805i
$786$	3.23630	−	24.7770i	0.115435	−	0.883765i
$787$	−20.6206	−	14.9817i	−0.735044	−	0.534041i	0.156111	−	0.987739i	$-0.450104\pi$
$787$	−20.6206	−	14.9817i	−0.735044	−	0.534041i	−0.891155	+	0.453699i	$0.850104\pi$
$788$	5.56119	+	7.65432i	0.198109	+	0.272674i
$789$	−9.68498	+	10.2267i	−0.344794	+	0.364079i
$790$	−0.600107	−	1.85174i	−0.0213508	−	0.0658819i
$791$	−5.62696	−	7.74485i	−0.200072	−	0.275375i
$792$	−2.74632	+	1.06063i	−0.0975863	+	0.0376880i
$793$	15.0730	+	20.7463i	0.535259	+	0.736721i
$794$	−9.04595	+	12.4507i	−0.321029	+	0.441858i
$795$	19.1934	−	40.2663i	0.680721	−	1.42810i
$796$	9.41765	−	12.9623i	0.333800	−	0.459436i
$797$	−30.7873	−	10.0034i	−1.09054	−	0.354338i	−0.292085	−	0.956392i	$-0.594349\pi$
$797$	−30.7873	−	10.0034i	−1.09054	−	0.354338i	−0.798455	+	0.602054i	$0.794349\pi$
$798$	−0.792323	+	0.836638i	−0.0280479	+	0.0296167i
$799$	−18.8051	+	6.11015i	−0.665277	+	0.216162i
$800$	−4.04060	−	2.94509i	−0.142857	−	0.104125i
$801$	−21.8155	−	26.8280i	−0.770812	−	0.947922i
$802$	−9.57083	−	29.4560i	−0.337958	−	1.04013i
$803$	−3.88316	+	2.82128i	−0.137034	+	0.0995609i
$804$	−6.15294	−	11.3049i	−0.216997	−	0.398691i
$805$	12.9971	+	4.23397i	0.458087	+	0.149228i
$806$	19.7617	+	16.3691i	0.696076	+	0.576577i
$807$	−11.5657	+	24.3115i	−0.407130	+	0.855807i
$808$	10.3392	−	14.2307i	0.363731	−	0.500633i
$809$	22.7476	−	16.5271i	0.799764	−	0.581062i	−0.111081	−	0.993811i	$-0.535431\pi$
$809$	22.7476	−	16.5271i	0.799764	−	0.581062i	0.910845	+	0.412749i	$0.135431\pi$
$810$	−19.6986	−	4.11899i	−0.692137	−	0.144726i
$811$	8.42097			0.295700			0.147850	−	0.989010i	$-0.452765\pi$
$811$	8.42097			0.295700			0.147850	+	0.989010i	$0.452765\pi$
$812$			8.87333i			0.311393i
$813$	−3.87795	+	29.6894i	−0.136006	+	1.04125i
$814$	−1.95697	+	6.02294i	−0.0685918	+	0.211104i
$815$	−13.6477	−	9.93153i	−0.478058	−	0.347886i
$816$	−3.00871	−	5.52794i	−0.105326	−	0.193517i
$817$	−0.980474	−	3.01759i	−0.0343024	−	0.105572i
$818$	4.98731	−	6.86444i	0.174377	−	0.240009i
$819$	3.34898	−	12.6011i	0.117023	−	0.440318i
$820$	21.4885	+	15.6373i	0.750410	+	0.546079i
$821$	18.5299	−	13.4628i	0.646699	−	0.469854i	−0.215446	−	0.976516i	$-0.569121\pi$
$821$	18.5299	−	13.4628i	0.646699	−	0.469854i	0.862145	+	0.506661i	$0.169121\pi$
$822$	15.8744	−	2.95885i	0.553682	−	0.103202i
$823$	−2.16043	+	6.64912i	−0.0753079	+	0.231774i	−0.981624	−	0.190827i	$-0.938883\pi$
$823$	−2.16043	+	6.64912i	−0.0753079	+	0.231774i	0.906316	+	0.422601i	$0.138883\pi$
$824$	−5.32723	−	7.33231i	−0.185583	−	0.255433i
$825$	−8.42537	−	1.11356i	−0.293334	−	0.0387693i
$826$	−3.43409	−	10.5690i	−0.119487	−	0.367744i
$827$	1.05378	−	1.45040i	0.0366435	−	0.0504355i	−0.790302	−	0.612717i	$-0.790076\pi$
$827$	1.05378	−	1.45040i	0.0366435	−	0.0504355i	0.826946	+	0.562282i	$0.190076\pi$
$828$	7.00631	+	18.1416i	0.243486	+	0.630465i
$829$	−26.3434	−	8.55948i	−0.914943	−	0.297283i	−0.186552	−	0.982445i	$-0.559731\pi$
$829$	−26.3434	−	8.55948i	−0.914943	−	0.297283i	−0.728391	+	0.685162i	$0.759731\pi$
$830$	2.80163	+	0.00213509i	0.0972460	+	7.41102e-5i
$831$	−5.45840	+	11.4738i	−0.189350	+	0.398022i
$832$	4.60880			0.159781
$833$	21.1175	−	6.86150i	0.731679	−	0.237737i
$834$	−13.6072	+	2.53628i	−0.471180	+	0.0878242i
$835$	28.5606	−	20.7172i	0.988380	−	0.716950i
$836$	−0.692302			−0.0239438
$837$	4.00684	−	28.6521i	0.138497	−	0.990363i
$838$		−	28.9531i		−	1.00017i
$839$	−8.54887	+	11.7665i	−0.295140	+	0.406225i	−0.930675	−	0.365847i	$-0.880779\pi$
$839$	−8.54887	+	11.7665i	−0.295140	+	0.406225i	0.635535	+	0.772072i	$0.280779\pi$
$840$	−3.62116	−	0.475794i	−0.124942	−	0.0164164i
$841$	18.3985	+	56.6248i	0.634432	+	1.95258i
$842$	−24.5719			−0.846804
$843$	9.83019	+	4.67648i	0.338570	+	0.161067i
$844$	−4.02430	−	12.3855i	−0.138522	−	0.426327i
$845$	−10.8428	+	14.8999i	−0.373004	+	0.512574i
$846$	−15.2285	+	5.88127i	−0.523567	+	0.202202i
$847$	5.56341	−	7.65738i	0.191161	−	0.263111i
$848$	10.9537	−	3.55908i	0.376152	−	0.122219i
$849$	−6.91806	−	12.7106i	−0.237427	−	0.436227i
$850$	0.0276917	−	18.1683i	0.000949819	−	0.623167i
$851$	39.7862	+	12.9273i	1.36385	+	0.443143i
$852$	19.1652	−	3.57223i	0.656588	−	0.122383i
$853$	5.83450	+	8.03050i	0.199770	+	0.274959i	0.897135	−	0.441757i	$-0.145645\pi$
$853$	5.83450	+	8.03050i	0.199770	+	0.274959i	−0.697365	+	0.716716i	$0.745645\pi$
$854$	1.62142	−	4.99022i	0.0554839	−	0.170762i
$855$	−3.97221	−	2.57240i	−0.135847	−	0.0879743i
$856$	−4.27011	−	3.10241i	−0.145949	−	0.106038i
$857$	−0.338206	−	1.04089i	−0.0115529	−	0.0355562i	0.945114	−	0.326741i	$-0.105951\pi$
$857$	−0.338206	−	1.04089i	−0.0115529	−	0.0355562i	−0.956667	+	0.291185i	$0.905951\pi$
$858$	6.88059	−	3.74493i	0.234900	−	0.127850i
$859$	32.8894	+	10.6864i	1.12217	+	0.364616i	0.810596	−	0.585605i	$-0.199143\pi$
$859$	32.8894	+	10.6864i	1.12217	+	0.364616i	0.311576	+	0.950221i	$0.399143\pi$
$860$	5.91747	−	8.13166i	0.201784	−	0.277287i
$861$	19.2491	+	2.51426i	0.656007	+	0.0856859i
$862$		−	11.7681i		−	0.400823i
$863$			12.4196i			0.422769i	0.977403	+	0.211384i	$0.0677972\pi$
$863$			12.4196i			0.422769i	−0.977403	+	0.211384i	$0.932203\pi$
$864$	−2.72850	−	4.42214i	−0.0928253	−	0.150444i
$865$	−22.9106	+	7.42481i	−0.778984	+	0.252451i
$866$	−3.24054	−	2.35439i	−0.110118	−	0.0800054i
$867$	−2.82489	+	5.93804i	−0.0959382	+	0.201667i
$868$	0.332956	−	5.23993i	0.0113012	−	0.177855i
$869$		−	0.854280i		−	0.0289795i
$870$	−35.8309	+	6.65034i	−1.21478	+	0.225468i
$871$	20.1304	+	27.7071i	0.682093	+	0.938821i
$872$	4.90907	+	15.1086i	0.166242	+	0.511641i
$873$	−15.7396	+	12.7988i	−0.532703	+	0.433173i
$874$			4.57319i			0.154691i
$875$	−8.51548	−	6.21665i	−0.287876	−	0.210161i
$876$	−6.15107	−	5.82527i	−0.207826	−	0.196817i
$877$	−44.0964	−	14.3278i	−1.48903	−	0.483815i	−0.552232	−	0.833690i	$-0.686224\pi$
$877$	−44.0964	−	14.3278i	−1.48903	−	0.483815i	−0.936796	+	0.349875i	$0.886224\pi$
$878$	−2.18437	−	1.58704i	−0.0737189	−	0.0535599i
$879$	−5.35263	−	0.699147i	−0.180540	−	0.0235816i
$880$	−1.28845	−	1.77624i	−0.0434336	−	0.0598771i
$881$	34.7560	−	25.2517i	1.17096	−	0.850751i	0.179835	−	0.983697i	$-0.442444\pi$
$881$	34.7560	−	25.2517i	1.17096	−	0.850751i	0.991123	+	0.132946i	$0.0424437\pi$
$882$	17.1011	−	6.60448i	0.575825	−	0.222384i
$883$	−33.9988	+	24.7016i	−1.14415	+	0.831274i	−0.987692	−	0.156411i	$-0.950008\pi$
$883$	−33.9988	+	24.7016i	−1.14415	+	0.831274i	−0.156458	+	0.987685i	$0.550008\pi$
$884$	9.84354	+	13.5485i	0.331074	+	0.455684i
$885$	40.1045	−	21.7882i	1.34810	−	0.732404i
$886$	3.70619	−	2.69271i	0.124512	−	0.0904632i
$887$	43.3627	+	31.5048i	1.45598	+	1.05783i	0.984388	+	0.176011i	$0.0563193\pi$
$887$	43.3627	+	31.5048i	1.45598	+	1.05783i	0.471589	+	0.881819i	$0.343681\pi$
$888$	−11.0833	−	1.44767i	−0.371932	−	0.0485808i
$889$	5.48325	−	7.54704i	0.183902	−	0.253120i
$890$	15.1650	−	20.8394i	0.508331	−	0.698537i
$891$	−7.66669	−	4.38485i	−0.256844	−	0.146898i
$892$	−6.37934	−	19.6336i	−0.213596	−	0.657381i
$893$	−3.83885			−0.128462
$894$	−21.3693	−	10.1660i	−0.714698	−	0.340001i
$895$	0.0176679	−	23.1836i	0.000590574	−	0.774941i
$896$	−0.554291	−	0.762917i	−0.0185176	−	0.0254873i
$897$	−24.7382	−	45.4517i	−0.825984	−	1.51759i
$898$	−31.0079			−1.03475
$899$	−12.9971	−	50.7521i	−0.433479	−	1.69268i
$900$	−0.792697	−	14.9790i	−0.0264232	−	0.499301i
$901$	33.8577	+	24.5991i	1.12796	+	0.819513i
$902$	6.85553	+	9.43583i	0.228264	+	0.314179i
$903$	0.951446	−	7.28423i	0.0316622	−	0.242404i
$904$	10.1516			0.337638
$905$	−5.49013	+	16.8532i	−0.182498	+	0.560218i
$906$	−4.37132	+	33.4666i	−0.145227	+	1.11185i
$907$	45.5742	+	14.8080i	1.51327	+	0.491690i	0.943854	−	0.330362i	$-0.107171\pi$
$907$	45.5742	+	14.8080i	1.51327	+	0.491690i	0.569412	+	0.822052i	$0.307171\pi$
$908$	−6.52792	+	20.0909i	−0.216637	+	0.666739i
$909$	52.6921	−	2.86903i	1.74769	−	0.0951598i
$910$	9.71835	+	0.00740625i	0.322160	+	0.000245515i
$911$	−22.7024	−	16.4943i	−0.752165	−	0.546480i	0.144332	−	0.989529i	$-0.453897\pi$
$911$	−22.7024	−	16.4943i	−0.752165	−	0.546480i	−0.896497	+	0.443050i	$0.853897\pi$
$912$	−0.223897	−	1.20122i	−0.00741397	−	0.0397762i
$913$	1.16937	+	0.379951i	0.0387004	+	0.0125745i
$914$	8.77448	−	6.37503i	0.290234	−	0.210867i
$915$	21.3660	+	2.80733i	0.706338	+	0.0928075i
$916$	−8.81922	−	2.86554i	−0.291395	−	0.0946801i
$917$	11.0062	−	7.99649i	0.363457	−	0.264067i
$918$	7.17218	−	17.4658i	0.236717	−	0.576457i
$919$	4.55964	+	14.0331i	0.150409	+	0.462911i	0.997667	−	0.0682710i	$-0.0217482\pi$
$919$	4.55964	+	14.0331i	0.150409	+	0.462911i	−0.847258	+	0.531181i	$0.821748\pi$
$920$	−11.7335	+	8.51120i	−0.386841	+	0.280606i
$921$	16.8296	−	17.7708i	0.554553	−	0.585569i
$922$	2.44084	−	7.51214i	0.0803848	−	0.247399i
$923$	−49.3358	+	16.0302i	−1.62391	+	0.527640i
$924$	−1.44743	−	0.688582i	−0.0476170	−	0.0226527i
$925$	−26.0753	−	19.0056i	−0.857350	−	0.624900i
$926$	−7.37403	−	22.6949i	−0.242326	−	0.745802i
$927$	6.98374	−	26.2775i	0.229376	−	0.863066i
$928$	−7.61245	−	5.53077i	−0.249891	−	0.181556i
$929$	−24.3619			−0.799287			−0.399644	−	0.916671i	$-0.630866\pi$
$929$	−24.3619			−0.799287			−0.399644	+	0.916671i	$0.630866\pi$
$930$	21.4086	−	2.58271i	0.702017	−	0.0846904i
$931$	4.31091			0.141284
$932$	−10.8631	−	7.89249i	−0.355832	−	0.258527i
$933$	37.6607	−	7.01964i	1.23295	−	0.229813i
$934$	−10.8700	−	33.4546i	−0.355679	−	1.09467i
$935$	2.46972	−	7.58136i	0.0807685	−	0.247937i
$936$	8.72309	+	10.7274i	0.285123	+	0.350636i
$937$	49.3325	−	16.0291i	1.61162	−	0.523648i	0.641678	−	0.766974i	$-0.278239\pi$
$937$	49.3325	−	16.0291i	1.61162	−	0.523648i	0.969944	+	0.243326i	$0.0782386\pi$
$938$	2.16545	−	6.66457i	0.0707044	−	0.217606i
$939$	6.55795	+	6.21059i	0.214011	+	0.202675i
$940$	−7.14452	−	9.84936i	−0.233028	−	0.321251i
$941$	−4.27476	−	13.1563i	−0.139353	−	0.428885i	0.856889	−	0.515502i	$-0.172394\pi$
$941$	−4.27476	−	13.1563i	−0.139353	−	0.428885i	−0.996242	+	0.0866170i	$0.972394\pi$
$942$	−5.70379	−	10.4796i	−0.185840	−	0.341445i
$943$	62.3311	−	45.2862i	2.02978	−	1.47472i
$944$	11.2077	+	3.64160i	0.364779	+	0.118524i
$945$	−5.74634	−	9.32912i	−0.186928	−	0.303476i
$946$	3.57070	−	2.59427i	0.116094	−	0.0843469i
$947$	7.09238	+	2.30445i	0.230471	+	0.0748847i	0.421976	−	0.906607i	$-0.361337\pi$
$947$	7.09238	+	2.30445i	0.230471	+	0.0748847i	−0.191505	+	0.981492i	$0.561337\pi$
$948$	1.48226	−	0.276282i	0.0481417	−	0.00897323i
$949$	18.2371	+	13.2500i	0.592000	+	0.430113i
$950$	1.09512	−	3.35303i	0.0355303	−	0.108787i
$951$	29.9523	−	16.3023i	0.971270	−	0.528637i
$952$	1.05888	−	3.25889i	0.0343185	−	0.105621i
$953$	4.14209	+	1.34585i	0.134176	+	0.0435963i	0.375335	−	0.926889i	$-0.377528\pi$
$953$	4.14209	+	1.34585i	0.134176	+	0.0435963i	−0.241159	+	0.970486i	$0.577528\pi$
$954$	29.0162	+	18.7595i	0.939435	+	0.607361i
$955$	3.45052	−	10.5921i	0.111656	−	0.342753i
$956$	−7.70401			−0.249165
$957$	−15.8589	−	2.07145i	−0.512645	−	0.0669604i
$958$	−1.91467	−	2.63531i	−0.0618601	−	0.0851431i
$959$	7.11260	+	5.16761i	0.229678	+	0.166871i
$960$	2.66527	−	2.81004i	0.0860211	−	0.0906938i
$961$	5.77076	+	30.4581i	0.186154	+	0.982521i
$962$	29.7421			0.958922
$963$	−0.860893	−	15.8110i	−0.0277419	−	0.509502i
$964$	−9.07007	−	12.4839i	−0.292127	−	0.402079i
$965$	−15.8577	−	0.0120850i	−0.510477	−	0.000389029i
$966$	−4.54862	+	9.56141i	−0.146349	+	0.307633i
$967$	4.41748			0.142057			0.0710283	−	0.997474i	$-0.477372\pi$
$967$	4.41748			0.142057			0.0710283	+	0.997474i	$0.477372\pi$
$968$	3.10160	+	9.54573i	0.0996891	+	0.306811i
$969$	3.05300	−	3.22376i	0.0980766	−	0.103562i
$970$	−12.2261	−	8.89703i	−0.392556	−	0.285666i
$971$	34.4062	−	47.3561i	1.10415	−	1.51973i	0.274378	−	0.961622i	$-0.411528\pi$
$971$	34.4062	−	47.3561i	1.10415	−	1.51973i	0.829769	−	0.558106i	$-0.188472\pi$
$972$	5.12869	−	14.7206i	0.164503	−	0.472164i
$973$	−6.09681	−	4.42959i	−0.195455	−	0.142006i
$974$	−16.7919	+	12.2001i	−0.538049	+	0.390915i
$975$	7.25376	+	39.2487i	0.232306	+	1.25696i
$976$	3.27049	+	4.50144i	0.104686	+	0.144088i
$977$	33.0165	−	23.9879i	1.05629	−	0.767442i	0.0828939	−	0.996558i	$-0.473584\pi$
$977$	33.0165	−	23.9879i	1.05629	−	0.767442i	0.973399	+	0.229117i	$0.0735838\pi$
$978$	8.99009	−	9.49290i	0.287471	−	0.303550i
$979$	9.15080	−	6.64844i	0.292461	−	0.212485i
$980$	8.02306	+	11.0605i	0.256287	+	0.353315i
$981$	−25.8751	+	40.0223i	−0.826130	+	1.27781i
$982$	16.8452	+	12.2387i	0.537550	+	0.390553i
$983$	−34.0283	−	11.0565i	−1.08533	−	0.352646i	−0.288892	−	0.957362i	$-0.593287\pi$
$983$	−34.0283	−	11.0565i	−1.08533	−	0.352646i	−0.796441	+	0.604716i	$0.793287\pi$
$984$	−14.1550	+	14.9467i	−0.451245	+	0.476484i
$985$	−21.1560	−	0.0161228i	−0.674087	−	0.000513714i
$986$		−	34.1910i		−	1.08886i
$987$	−8.02609	−	3.81823i	−0.255473	−	0.121535i
$988$	1.00472	+	3.09222i	0.0319645	+	0.0983767i
$989$	−17.1372	−	23.5873i	−0.544930	−	0.750032i
$990$	1.69571	−	6.36087i	0.0538933	−	0.202162i
$991$		−	10.2936i		−	0.326986i	−0.986545	−	0.163493i	$-0.947724\pi$
$991$		−	10.2936i		−	0.326986i	0.986545	−	0.163493i	$-0.0522761\pi$
$992$	4.28782	+	3.55171i	0.136138	+	0.112767i
$993$	2.16603	+	1.03044i	0.0687370	+	0.0327001i
$994$	8.58708	+	6.23888i	0.272366	+	0.197885i
$995$	11.0451	+	34.0818i	0.350155	+	1.08047i
$996$	−0.281070	+	2.15186i	−0.00890603	+	0.0681841i
$997$			13.1437i			0.416266i	0.978101	+	0.208133i	$0.0667386\pi$
$997$			13.1437i			0.416266i	−0.978101	+	0.208133i	$0.933261\pi$
$998$			7.68136i			0.243149i
$999$	−17.6078	−	28.5375i	−0.557088	−	0.902885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.b.29.13	yes	128
3.2	odd	2		930.2.y.a.29.27	yes	128
5.4	even	2		930.2.y.a.29.20	✓	128
15.14	odd	2	inner	930.2.y.b.29.6	yes	128
31.15	odd	10	inner	930.2.y.b.449.6	yes	128
93.77	even	10		930.2.y.a.449.20	yes	128
155.139	odd	10		930.2.y.a.449.27	yes	128
465.449	even	10	inner	930.2.y.b.449.13	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.20	✓	128	5.4	even	2
930.2.y.a.29.27	yes	128	3.2	odd	2
930.2.y.a.449.20	yes	128	93.77	even	10
930.2.y.a.449.27	yes	128	155.139	odd	10
930.2.y.b.29.6	yes	128	15.14	odd	2	inner
930.2.y.b.29.13	yes	128	1.1	even	1	trivial
930.2.y.b.449.6	yes	128	31.15	odd	10	inner
930.2.y.b.449.13	yes	128	465.449	even	10	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.317374 - 1.70273i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.12610 - 0.692603i) q^{5} +(0.744076 - 1.56408i) q^{6} +(0.896862 - 0.291408i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.79855 + 1.08080i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.317374 - 1.70273i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.12610 - 0.692603i) q^{5} +(0.744076 - 1.56408i) q^{6} +(0.896862 - 0.291408i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.79855 + 1.08080i) q^{9} +(-1.31295 - 1.81002i) q^{10} +(-0.303250 - 0.933309i) q^{11} +(1.52131 - 0.828012i) q^{12} +(-3.72860 + 2.70899i) q^{13} +(0.896862 + 0.291408i) q^{14} +(-0.504544 + 3.83998i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.45582 - 1.12286i) q^{17} +(-2.89935 - 0.770557i) q^{18} +(-0.570734 - 0.414663i) q^{19} +(0.00170408 - 2.23607i) q^{20} +(-0.780829 - 1.43462i) q^{21} +(0.303250 - 0.933309i) q^{22} +(-6.16523 - 2.00321i) q^{23} +(1.71746 + 0.224330i) q^{24} +(4.04060 + 2.94509i) q^{25} -4.60880 q^{26} +(2.72850 + 4.42214i) q^{27} +(0.554291 + 0.762917i) q^{28} +(7.61245 + 5.53077i) q^{29} +(-2.66527 + 2.81004i) q^{30} +(-4.28782 - 3.55171i) q^{31} -1.00000 q^{32} +(-1.49292 + 0.812560i) q^{33} +(-2.13581 - 2.93969i) q^{34} +(-2.10865 - 0.00160698i) q^{35} +(-1.89270 - 2.32759i) q^{36} -6.45332 q^{37} +(-0.218001 - 0.670939i) q^{38} +(5.79602 + 5.48902i) q^{39} +(1.31571 - 1.80801i) q^{40} +(-6.98590 + 9.61527i) q^{41} +(0.211547 - 1.61960i) q^{42} +(3.63860 + 2.64360i) q^{43} +(0.793920 - 0.576816i) q^{44} +(6.69856 - 0.359610i) q^{45} +(-3.81032 - 5.24446i) q^{46} +(4.40233 - 3.19848i) q^{47} +(1.25760 + 1.19099i) q^{48} +(-4.94368 + 3.59179i) q^{49} +(1.53784 + 4.75763i) q^{50} +(-0.815140 + 6.24068i) q^{51} +(-3.72860 - 2.70899i) q^{52} +(-10.9537 - 3.55908i) q^{53} +(-0.391868 + 5.18135i) q^{54} +(-0.00167228 + 2.19434i) q^{55} +0.943017i q^{56} +(-0.524921 + 1.10341i) q^{57} +(2.90770 + 8.94897i) q^{58} +(-6.92673 - 9.53382i) q^{59} +(-3.80795 + 0.706769i) q^{60} -5.56409i q^{61} +(-1.38128 - 5.39371i) q^{62} +(-2.19496 + 1.78485i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(9.80363 - 3.17713i) q^{65} +(-1.68541 - 0.220144i) q^{66} -7.43098i q^{67} -3.63366i q^{68} +(-1.45422 + 11.1335i) q^{69} +(-1.70499 - 1.24073i) q^{70} +(10.7047 + 3.47817i) q^{71} +(-0.163105 - 2.99556i) q^{72} +(-1.51144 - 4.65174i) q^{73} +(-5.22084 - 3.79316i) q^{74} +(3.73229 - 7.81473i) q^{75} +(0.218001 - 0.670939i) q^{76} +(-0.543948 - 0.748680i) q^{77} +(1.46271 + 7.84752i) q^{78} +(0.827918 + 0.269007i) q^{79} +(2.12715 - 0.689362i) q^{80} +(6.66373 - 6.04935i) q^{81} +(-11.3034 + 3.67271i) q^{82} +(-0.736452 + 1.01364i) q^{83} +(1.12312 - 1.18594i) q^{84} +(6.56971 + 4.78083i) q^{85} +(1.38982 + 4.27743i) q^{86} +(7.00139 - 14.7172i) q^{87} +0.981339 q^{88} +(3.56176 + 10.9620i) q^{89} +(5.63062 + 3.64638i) q^{90} +(-2.55462 + 3.51613i) q^{91} -6.48251i q^{92} +(-4.68674 + 8.42820i) q^{93} +5.44158 q^{94} +(0.926242 + 1.27691i) q^{95} +(0.317374 + 1.70273i) q^{96} +(6.43121 - 2.08963i) q^{97} -6.11072 q^{98} +(1.85738 + 2.28415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Introduction

L-functions

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