LMFDB - Embedded newform 930.2.be.b.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-0.0950827 - 2.23405i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.582615 + 2.17435i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-0.0950827 - 2.23405i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.582615 + 2.17435i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.51248 + 1.64694i) q^{10} +(-2.30117 - 1.32858i) q^{11} +(0.965926 + 0.258819i) q^{12} +(6.59309 - 1.76661i) q^{13} +(1.94947 - 1.12553i) q^{14} +(-2.18253 - 0.486371i) q^{15} -1.00000 q^{16} +(-5.05958 - 1.35571i) q^{17} +(0.258819 + 0.965926i) q^{18} +(4.50868 - 2.60309i) q^{19} +(2.23405 - 0.0950827i) q^{20} +(1.94947 + 1.12553i) q^{21} +(0.687724 + 2.56662i) q^{22} +(-2.29894 - 2.29894i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.98192 + 0.424838i) q^{25} +(-5.91120 - 3.41283i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.17435 - 0.582615i) q^{28} -9.26804 q^{29} +(1.19937 + 1.88720i) q^{30} +(1.32271 - 5.40837i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.87890 + 1.87890i) q^{33} +(2.61903 + 4.53629i) q^{34} +(4.91299 + 1.09485i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.60697 - 2.03828i) q^{37} +(-5.02878 - 1.34746i) q^{38} -6.82567i q^{39} +(-1.64694 - 1.51248i) q^{40} +(1.28540 - 2.22637i) q^{41} +(-0.582615 - 2.17435i) q^{42} +(0.757850 - 2.82834i) q^{43} +(1.32858 - 2.30117i) q^{44} +(-1.03468 + 1.98228i) q^{45} +3.25120i q^{46} +(5.74626 + 5.74626i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(1.67382 + 0.966382i) q^{49} +(3.82315 + 3.22234i) q^{50} +(-2.61903 + 4.53629i) q^{51} +(1.76661 + 6.59309i) q^{52} +(-8.83301 + 2.36680i) q^{53} +1.00000 q^{54} +(-2.74931 + 5.26724i) q^{55} +(1.12553 + 1.94947i) q^{56} +(-1.34746 - 5.02878i) q^{57} +(6.55349 + 6.55349i) q^{58} +(2.14160 - 1.23646i) q^{59} +(0.486371 - 2.18253i) q^{60} +8.17968i q^{61} +(-4.75959 + 2.88900i) q^{62} +(1.59173 - 1.59173i) q^{63} -1.00000i q^{64} +(-4.57358 - 14.5613i) q^{65} +2.65716 q^{66} +(-1.21580 + 0.325772i) q^{67} +(1.35571 - 5.05958i) q^{68} +(-2.81562 + 1.62560i) q^{69} +(-2.69984 - 4.24818i) q^{70} +(5.65625 - 9.79691i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-13.3228 + 3.56984i) q^{73} +(3.93766 + 6.82022i) q^{74} +(-0.879053 + 4.92212i) q^{75} +(2.60309 + 4.50868i) q^{76} +(4.22949 - 4.22949i) q^{77} +(-4.82648 + 4.82648i) q^{78} +(-3.31449 - 5.74087i) q^{79} +(0.0950827 + 2.23405i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.48320 + 0.665370i) q^{82} +(-4.95738 + 1.32833i) q^{83} +(-1.12553 + 1.94947i) q^{84} +(-2.54764 + 11.4322i) q^{85} +(-2.53582 + 1.46405i) q^{86} +(-2.39874 + 8.95224i) q^{87} +(-2.56662 + 0.687724i) q^{88} +18.0871 q^{89} +(2.13331 - 0.670056i) q^{90} +15.3649i q^{91} +(2.29894 - 2.29894i) q^{92} +(-4.88174 - 2.67743i) q^{93} -8.12644i q^{94} +(-6.24411 - 9.82508i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-5.05912 - 5.05912i) q^{97} +(-0.500236 - 1.86691i) q^{98} +(1.32858 + 2.30117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	−0.0950827	−	2.23405i	−0.0425223	−	0.999096i
$5$	−0.0950827	−	2.23405i	−0.0425223	−	0.999096i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.582615	+	2.17435i	−0.220208	+	0.821827i	0.764060	+	0.645145i	$0.223203\pi$
$7$	−0.582615	+	2.17435i	−0.220208	+	0.821827i	−0.984268	+	0.176682i	$0.943464\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−1.51248	+	1.64694i	−0.478287	+	0.520809i
$11$	−2.30117	−	1.32858i	−0.693829	−	0.400582i	0.111216	−	0.993796i	$-0.464525\pi$
$11$	−2.30117	−	1.32858i	−0.693829	−	0.400582i	−0.805045	+	0.593214i	$0.797859\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	6.59309	−	1.76661i	1.82859	−	0.489970i	0.830813	−	0.556552i	$-0.187876\pi$
$13$	6.59309	−	1.76661i	1.82859	−	0.489970i	0.997781	+	0.0665817i	$0.0212093\pi$
$14$	1.94947	−	1.12553i	0.521017	−	0.300809i
$15$	−2.18253	−	0.486371i	−0.563527	−	0.125580i
$16$	−1.00000			−0.250000
$17$	−5.05958	−	1.35571i	−1.22713	−	0.328808i	−0.413667	−	0.910428i	$-0.635752\pi$
$17$	−5.05958	−	1.35571i	−1.22713	−	0.328808i	−0.813460	+	0.581621i	$0.802419\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	4.50868	−	2.60309i	1.03436	−	0.597189i	0.116131	−	0.993234i	$-0.462951\pi$
$19$	4.50868	−	2.60309i	1.03436	−	0.597189i	0.918231	+	0.396045i	$0.129618\pi$
$20$	2.23405	−	0.0950827i	0.499548	−	0.0212611i
$21$	1.94947	+	1.12553i	0.425409	+	0.245610i
$22$	0.687724	+	2.56662i	0.146623	+	0.547205i
$23$	−2.29894	−	2.29894i	−0.479363	−	0.479363i	0.425565	−	0.904928i	$-0.360075\pi$
$23$	−2.29894	−	2.29894i	−0.479363	−	0.479363i	−0.904928	+	0.425565i	$0.860075\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.98192	+	0.424838i	−0.996384	+	0.0849677i
$26$	−5.91120	−	3.41283i	−1.15928	−	0.669312i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.17435	−	0.582615i	−0.410913	−	0.110104i
$29$	−9.26804			−1.72103			−0.860516	−	0.509424i	$-0.829858\pi$
$29$	−9.26804			−1.72103			−0.860516	+	0.509424i	$0.829858\pi$
$30$	1.19937	+	1.88720i	0.218973	+	0.344554i
$31$	1.32271	−	5.40837i	0.237565	−	0.971372i
$31$	1.32271	−	5.40837i	0.237565	−	0.971372i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.87890	+	1.87890i	−0.327074	+	0.327074i
$34$	2.61903	+	4.53629i	0.449160	+	0.777967i
$35$	4.91299	+	1.09485i	0.830447	+	0.185063i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−7.60697	−	2.03828i	−1.25058	−	0.335091i	−0.428018	−	0.903770i	$-0.640788\pi$
$37$	−7.60697	−	2.03828i	−1.25058	−	0.335091i	−0.822560	+	0.568679i	$0.807455\pi$
$38$	−5.02878	−	1.34746i	−0.815775	−	0.218586i
$39$		−	6.82567i		−	1.09298i
$40$	−1.64694	−	1.51248i	−0.260404	−	0.239143i
$41$	1.28540	−	2.22637i	0.200745	−	0.347701i	−0.748024	−	0.663672i	$-0.768997\pi$
$41$	1.28540	−	2.22637i	0.200745	−	0.347701i	0.948769	+	0.315971i	$0.102330\pi$
$42$	−0.582615	−	2.17435i	−0.0898995	−	0.335509i
$43$	0.757850	−	2.82834i	0.115571	−	0.431317i	−0.883758	−	0.467944i	$-0.844995\pi$
$43$	0.757850	−	2.82834i	0.115571	−	0.431317i	0.999329	+	0.0366272i	$0.0116614\pi$
$44$	1.32858	−	2.30117i	0.200291	−	0.346914i
$45$	−1.03468	+	1.98228i	−0.154241	+	0.295501i
$46$			3.25120i			0.479363i
$47$	5.74626	+	5.74626i	0.838179	+	0.838179i	0.988619	−	0.150440i	$-0.0480692\pi$
$47$	5.74626	+	5.74626i	0.838179	+	0.838179i	−0.150440	+	0.988619i	$0.548069\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	1.67382	+	0.966382i	0.239118	+	0.138055i
$50$	3.82315	+	3.22234i	0.540676	+	0.455708i
$51$	−2.61903	+	4.53629i	−0.366737	+	0.635208i
$52$	1.76661	+	6.59309i	0.244985	+	0.914297i
$53$	−8.83301	+	2.36680i	−1.21331	+	0.325105i	−0.808059	−	0.589102i	$-0.799482\pi$
$53$	−8.83301	+	2.36680i	−1.21331	+	0.325105i	−0.405249	+	0.914206i	$0.632815\pi$
$54$	1.00000			0.136083
$55$	−2.74931	+	5.26724i	−0.370717	+	0.710235i
$56$	1.12553	+	1.94947i	0.150405	+	0.260509i
$57$	−1.34746	−	5.02878i	−0.178475	−	0.666078i
$58$	6.55349	+	6.55349i	0.860516	+	0.860516i
$59$	2.14160	−	1.23646i	0.278813	−	0.160973i	−0.354073	−	0.935218i	$-0.615203\pi$
$59$	2.14160	−	1.23646i	0.278813	−	0.160973i	0.632886	+	0.774245i	$0.281870\pi$
$60$	0.486371	−	2.18253i	0.0627902	−	0.281764i
$61$			8.17968i			1.04730i	0.851933	+	0.523651i	$0.175430\pi$
$61$			8.17968i			1.04730i	−0.851933	+	0.523651i	$0.824570\pi$
$62$	−4.75959	+	2.88900i	−0.604468	+	0.366903i
$63$	1.59173	−	1.59173i	0.200540	−	0.200540i
$64$		−	1.00000i		−	0.125000i
$65$	−4.57358	−	14.5613i	−0.567283	−	1.80611i
$66$	2.65716			0.327074
$67$	−1.21580	+	0.325772i	−0.148534	+	0.0397994i	−0.332320	−	0.943167i	$-0.607831\pi$
$67$	−1.21580	+	0.325772i	−0.148534	+	0.0397994i	0.183786	+	0.982966i	$0.441165\pi$
$68$	1.35571	−	5.05958i	0.164404	−	0.613564i
$69$	−2.81562	+	1.62560i	−0.338961	+	0.195699i
$70$	−2.69984	−	4.24818i	−0.322692	−	0.507755i
$71$	5.65625	−	9.79691i	0.671273	−	1.16268i	−0.306271	−	0.951945i	$-0.599081\pi$
$71$	5.65625	−	9.79691i	0.671273	−	1.16268i	0.977543	−	0.210734i	$-0.0675855\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−13.3228	+	3.56984i	−1.55932	+	0.417818i	−0.932448	−	0.361304i	$-0.882332\pi$
$73$	−13.3228	+	3.56984i	−1.55932	+	0.417818i	−0.626872	+	0.779123i	$0.715665\pi$
$74$	3.93766	+	6.82022i	0.457743	+	0.792834i
$75$	−0.879053	+	4.92212i	−0.101504	+	0.568357i
$76$	2.60309	+	4.50868i	0.298595	+	0.517181i
$77$	4.22949	−	4.22949i	0.481996	−	0.481996i
$78$	−4.82648	+	4.82648i	−0.546491	+	0.546491i
$79$	−3.31449	−	5.74087i	−0.372909	−	0.645898i	0.617102	−	0.786883i	$-0.288306\pi$
$79$	−3.31449	−	5.74087i	−0.372909	−	0.645898i	−0.990012	+	0.140985i	$0.954973\pi$
$80$	0.0950827	+	2.23405i	0.0106306	+	0.249774i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−2.48320	+	0.665370i	−0.274223	+	0.0734779i
$83$	−4.95738	+	1.32833i	−0.544143	+	0.145803i	−0.520411	−	0.853916i	$-0.674221\pi$
$83$	−4.95738	+	1.32833i	−0.544143	+	0.145803i	−0.0237317	+	0.999718i	$0.507555\pi$
$84$	−1.12553	+	1.94947i	−0.122805	+	0.212704i
$85$	−2.54764	+	11.4322i	−0.276330	+	1.24000i
$86$	−2.53582	+	1.46405i	−0.273444	+	0.157873i
$87$	−2.39874	+	8.95224i	−0.257172	+	0.959780i
$88$	−2.56662	+	0.687724i	−0.273603	+	0.0733116i
$89$	18.0871			1.91723			0.958615	−	0.284707i	$-0.0918963\pi$
$89$	18.0871			1.91723			0.958615	+	0.284707i	$0.0918963\pi$
$90$	2.13331	−	0.670056i	0.224871	−	0.0706301i
$91$			15.3649i			1.61068i
$92$	2.29894	−	2.29894i	0.239681	−	0.239681i
$93$	−4.88174	−	2.67743i	−0.506213	−	0.277636i
$94$		−	8.12644i		−	0.838179i
$95$	−6.24411	−	9.82508i	−0.640632	−	1.00803i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−5.05912	−	5.05912i	−0.513676	−	0.513676i	0.401975	−	0.915651i	$-0.368324\pi$
$97$	−5.05912	−	5.05912i	−0.513676	−	0.513676i	−0.915651	+	0.401975i	$0.868324\pi$
$98$	−0.500236	−	1.86691i	−0.0505315	−	0.188586i
$99$	1.32858	+	2.30117i	0.133527	+	0.231276i
$100$	−0.424838	−	4.98192i	−0.0424838	−	0.498192i
$101$	−0.676173			−0.0672817			−0.0336409	−	0.999434i	$-0.510710\pi$
$101$	−0.676173			−0.0672817			−0.0336409	+	0.999434i	$0.510710\pi$
$102$	5.05958	−	1.35571i	0.500973	−	0.134235i
$103$	−3.45040	−	12.8771i	−0.339978	−	1.26882i	−0.898370	−	0.439239i	$-0.855248\pi$
$103$	−3.45040	−	12.8771i	−0.339978	−	1.26882i	0.558392	−	0.829577i	$-0.311419\pi$
$104$	3.41283	−	5.91120i	0.334656	−	0.579641i
$105$	2.32912	−	4.46222i	0.227298	−	0.435468i
$106$	7.91946	+	4.57230i	0.769206	+	0.444101i
$107$	−1.70088	+	6.34778i	−0.164431	+	0.613663i	0.833682	+	0.552245i	$0.186229\pi$
$107$	−1.70088	+	6.34778i	−0.164431	+	0.613663i	−0.998112	+	0.0614177i	$0.980438\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	6.86821i		−	0.657855i	−0.944355	−	0.328927i	$-0.893313\pi$
$109$		−	6.86821i		−	0.657855i	0.944355	−	0.328927i	$-0.106687\pi$
$110$	5.66856	−	1.78045i	0.540476	−	0.169759i
$111$	−3.93766	+	6.82022i	−0.373746	+	0.647347i
$112$	0.582615	−	2.17435i	0.0550520	−	0.205457i
$113$	2.87999	+	10.7483i	0.270927	+	1.01111i	0.958522	+	0.285019i	$0.0919999\pi$
$113$	2.87999	+	10.7483i	0.270927	+	1.01111i	−0.687595	+	0.726095i	$0.741333\pi$
$114$	−2.60309	+	4.50868i	−0.243801	+	0.422276i
$115$	−4.91735	+	5.35453i	−0.458546	+	0.499313i
$116$		−	9.26804i		−	0.860516i
$117$	−6.59309	−	1.76661i	−0.609531	−	0.163323i
$118$	−2.38865	−	0.640037i	−0.219893	−	0.0589202i
$119$	5.89557	−	10.2114i	0.540446	−	0.936080i
$120$	−1.88720	+	1.19937i	−0.172277	+	0.109487i
$121$	−1.96975	−	3.41170i	−0.179068	−	0.310155i
$122$	5.78391	−	5.78391i	0.523651	−	0.523651i
$123$	−1.81783	−	1.81783i	−0.163908	−	0.163908i
$124$	5.40837	+	1.32271i	0.485686	+	0.118783i
$125$	1.42280	+	11.0894i	0.127259	+	0.991869i
$126$	−2.25105			−0.200540
$127$	−5.94544	−	1.59307i	−0.527572	−	0.141363i	−0.0148052	−	0.999890i	$-0.504713\pi$
$127$	−5.94544	−	1.59307i	−0.527572	−	0.141363i	−0.512767	+	0.858528i	$0.671379\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−2.53582	−	1.46405i	−0.223266	−	0.128903i
$130$	−7.06237	+	13.5304i	−0.619411	+	1.18669i
$131$	1.22882	+	2.12837i	0.107362	+	0.185957i	0.914701	−	0.404132i	$-0.132426\pi$
$131$	1.22882	+	2.12837i	0.107362	+	0.185957i	−0.807339	+	0.590088i	$0.799093\pi$
$132$	−1.87890	−	1.87890i	−0.163537	−	0.163537i
$133$	3.03320	+	11.3200i	0.263011	+	0.981572i
$134$	1.09006	+	0.629344i	0.0941665	+	0.0543670i
$135$	1.64694	+	1.51248i	0.141746	+	0.130173i
$136$	−4.53629	+	2.61903i	−0.388984	+	0.224580i
$137$	−4.54319	−	16.9554i	−0.388151	−	1.44860i	−0.833140	−	0.553062i	$-0.813459\pi$
$137$	−4.54319	−	16.9554i	−0.388151	−	1.44860i	0.444989	−	0.895536i	$-0.353207\pi$
$138$	3.14041	+	0.841471i	0.267330	+	0.0716308i
$139$	7.48915			0.635221			0.317611	−	0.948221i	$-0.397120\pi$
$139$	7.48915			0.635221			0.317611	+	0.948221i	$0.397120\pi$
$140$	−1.09485	+	4.91299i	−0.0925313	+	0.415224i
$141$	7.03771	−	4.06322i	0.592682	−	0.342185i
$142$	−10.9270	+	2.92789i	−0.916976	+	0.245703i
$143$	−17.5189	−	4.69417i	−1.46500	−	0.392547i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	0.881230	+	20.7052i	0.0731822	+	1.71947i
$146$	11.9449	+	6.89641i	0.988569	+	0.570751i
$147$	1.36667	−	1.36667i	0.112721	−	0.112721i
$148$	2.03828	−	7.60697i	0.167546	−	0.625289i
$149$	4.39253	−	2.53603i	0.359850	−	0.207759i	−0.309165	−	0.951008i	$-0.600050\pi$
$149$	4.39253	−	2.53603i	0.359850	−	0.207759i	0.669015	+	0.743249i	$0.266716\pi$
$150$	4.10205	−	2.85888i	0.334931	−	0.233427i
$151$		−	6.89249i		−	0.560903i	−0.959868	−	0.280451i	$-0.909516\pi$
$151$		−	6.89249i		−	0.560903i	0.959868	−	0.280451i	$-0.0904841\pi$
$152$	1.34746	−	5.02878i	0.109293	−	0.407888i
$153$	3.70387	+	3.70387i	0.299440	+	0.299440i
$154$	−5.98141			−0.481996
$155$	−12.2083	−	2.44075i	−0.980595	−	0.196045i
$156$	6.82567			0.546491
$157$	8.29772	+	8.29772i	0.662231	+	0.662231i	0.955905	−	0.293675i	$-0.0948783\pi$
$157$	8.29772	+	8.29772i	0.662231	+	0.662231i	−0.293675	+	0.955905i	$0.594878\pi$
$158$	−1.71571	+	6.40311i	−0.136494	+	0.509404i
$159$			9.14461i			0.725215i
$160$	1.51248	−	1.64694i	0.119572	−	0.130202i
$161$	6.33810	−	3.65931i	0.499513	−	0.288394i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	7.09226	−	7.09226i	0.555509	−	0.555509i	−0.372517	−	0.928026i	$-0.621505\pi$
$163$	7.09226	−	7.09226i	0.555509	−	0.555509i	0.928026	+	0.372517i	$0.121505\pi$
$164$	2.22637	+	1.28540i	0.173850	+	0.100373i
$165$	4.37619	+	4.01889i	0.340686	+	0.312870i
$166$	4.44467	+	2.56613i	0.344973	+	0.199170i
$167$	17.0587	+	4.57087i	1.32004	+	0.353704i	0.848994	−	0.528403i	$-0.177209\pi$
$167$	17.0587	+	4.57087i	1.32004	+	0.353704i	0.471049	+	0.882107i	$0.343876\pi$
$168$	2.17435	−	0.582615i	0.167755	−	0.0449497i
$169$	29.0896	−	16.7949i	2.23766	−	1.29191i
$170$	9.88526	−	6.28235i	0.758165	−	0.481834i
$171$	−5.20617			−0.398126
$172$	2.82834	+	0.757850i	0.215659	+	0.0577856i
$173$	−2.65058	−	9.89210i	−0.201520	−	0.752082i	−0.990482	−	0.137641i	$-0.956048\pi$
$173$	−2.65058	−	9.89210i	−0.201520	−	0.752082i	0.788962	−	0.614441i	$-0.210619\pi$
$174$	8.02636	−	4.63402i	0.608476	−	0.351304i
$175$	1.97879	−	11.0799i	0.149583	−	0.837565i
$176$	2.30117	+	1.32858i	0.173457	+	0.100146i
$177$	−0.640037	−	2.38865i	−0.0481081	−	0.179542i
$178$	−12.7895	−	12.7895i	−0.958615	−	0.958615i
$179$	6.16471	+	10.6776i	0.460772	+	0.798081i	0.999000	−	0.0447189i	$-0.0142392\pi$
$179$	6.16471	+	10.6776i	0.460772	+	0.798081i	−0.538228	+	0.842800i	$0.680906\pi$
$180$	−1.98228	−	1.03468i	−0.147751	−	0.0771204i
$181$	9.27251	+	5.35349i	0.689220	+	0.397922i	0.803320	−	0.595548i	$-0.203065\pi$
$181$	9.27251	+	5.35349i	0.689220	+	0.397922i	−0.114099	+	0.993469i	$0.536398\pi$
$182$	10.8646	−	10.8646i	0.805341	−	0.805341i
$183$	7.90097	+	2.11706i	0.584056	+	0.156497i
$184$	−3.25120			−0.239681
$185$	−3.83032	+	17.1881i	−0.281611	+	1.26370i
$186$	1.55869	+	5.34514i	0.114288	+	0.391925i
$187$	9.84177	+	9.84177i	0.719701	+	0.719701i
$188$	−5.74626	+	5.74626i	−0.419089	+	0.419089i
$189$	−1.12553	−	1.94947i	−0.0818700	−	0.141803i
$190$	−2.53213	+	11.3626i	−0.183700	+	0.824332i
$191$	0.470282	−	0.814553i	0.0340284	−	0.0589390i	−0.848510	−	0.529180i	$-0.822500\pi$
$191$	0.470282	−	0.814553i	0.0340284	−	0.0589390i	0.882538	+	0.470241i	$0.155833\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−3.44531	−	0.923168i	−0.247999	−	0.0664511i	0.132678	−	0.991159i	$-0.457642\pi$
$193$	−3.44531	−	0.923168i	−0.247999	−	0.0664511i	−0.380677	+	0.924708i	$0.624309\pi$
$194$			7.15468i			0.513676i
$195$	−15.2489	+	0.649003i	−1.09199	+	0.0464761i
$196$	−0.966382	+	1.67382i	−0.0690273	+	0.119559i
$197$	2.82341	+	10.5371i	0.201160	+	0.750739i	0.990586	+	0.136893i	$0.0437116\pi$
$197$	2.82341	+	10.5371i	0.201160	+	0.750739i	−0.789426	+	0.613846i	$0.789622\pi$
$198$	0.687724	−	2.56662i	0.0488744	−	0.182402i
$199$	9.23765	−	16.0001i	0.654840	−	1.13422i	−0.327094	−	0.944992i	$-0.606069\pi$
$199$	9.23765	−	16.0001i	0.654840	−	1.13422i	0.981934	−	0.189224i	$-0.0605972\pi$
$200$	−3.22234	+	3.82315i	−0.227854	+	0.270338i
$201$			1.25869i			0.0887810i
$202$	0.478126	+	0.478126i	0.0336409	+	0.0336409i
$203$	5.39970	−	20.1519i	0.378985	−	1.41439i
$204$	−4.53629	−	2.61903i	−0.317604	−	0.183369i
$205$	−5.09604	−	2.65995i	−0.355923	−	0.185779i
$206$	−6.66567	+	11.5453i	−0.464419	+	0.804397i
$207$	0.841471	+	3.14041i	0.0584863	+	0.218274i
$208$	−6.59309	+	1.76661i	−0.457148	+	0.122493i
$209$	−13.8336			−0.956893
$210$	−4.80220	+	1.50833i	−0.331383	+	0.104085i
$211$	−8.28255	−	14.3458i	−0.570194	−	0.987605i	−0.996546	−	0.0830476i	$-0.973535\pi$
$211$	−8.28255	−	14.3458i	−0.570194	−	0.987605i	0.426351	−	0.904558i	$-0.359799\pi$
$212$	−2.36680	−	8.83301i	−0.162552	−	0.606654i
$213$	−7.99914	−	7.99914i	−0.548092	−	0.548092i
$214$	5.69126	−	3.28585i	0.389047	−	0.224616i
$215$	−6.39069	−	1.42415i	−0.435841	−	0.0971260i
$216$			1.00000i			0.0680414i
$217$	10.9891	+	6.02702i	0.745985	+	0.409141i
$218$	−4.85655	+	4.85655i	−0.328927	+	0.328927i
$219$			13.7928i			0.932032i
$220$	−5.26724	−	2.74931i	−0.355117	−	0.185358i
$221$	−35.7532			−2.40502
$222$	7.60697	−	2.03828i	0.510546	−	0.136800i
$223$	−5.65241	+	21.0951i	−0.378513	+	1.41263i	0.469629	+	0.882864i	$0.344388\pi$
$223$	−5.65241	+	21.0951i	−0.378513	+	1.41263i	−0.848143	+	0.529768i	$0.822279\pi$
$224$	−1.94947	+	1.12553i	−0.130254	+	0.0752024i
$225$	4.52689	+	2.12304i	0.301792	+	0.141536i
$226$	5.56372	−	9.63665i	0.370093	−	0.641020i
$227$	18.3264	−	4.91054i	1.21636	−	0.325924i	0.407109	−	0.913380i	$-0.366537\pi$
$227$	18.3264	−	4.91054i	1.21636	−	0.325924i	0.809256	+	0.587456i	$0.199870\pi$
$228$	5.02878	−	1.34746i	0.333039	−	0.0892375i
$229$	2.15589	+	3.73410i	0.142465	+	0.246756i	0.928424	−	0.371522i	$-0.121164\pi$
$229$	2.15589	+	3.73410i	0.142465	+	0.246756i	−0.785959	+	0.618278i	$0.787831\pi$
$230$	7.26332	−	0.309133i	0.478929	−	0.0203836i
$231$	−2.99070	−	5.18005i	−0.196774	−	0.340822i
$232$	−6.55349	+	6.55349i	−0.430258	+	0.430258i
$233$	9.58965	−	9.58965i	0.628239	−	0.628239i	−0.319386	−	0.947625i	$-0.603477\pi$
$233$	9.58965	−	9.58965i	0.628239	−	0.628239i	0.947625	+	0.319386i	$0.103477\pi$
$234$	3.41283	+	5.91120i	0.223104	+	0.386427i
$235$	12.2910	−	13.3838i	0.801779	−	0.873062i
$236$	1.23646	+	2.14160i	0.0804864	+	0.139407i
$237$	−6.40311	+	1.71571i	−0.415926	+	0.111447i
$238$	−11.3894	+	3.05177i	−0.738263	+	0.197817i
$239$	10.3693	−	17.9602i	0.670734	−	1.16175i	−0.306962	−	0.951722i	$-0.599313\pi$
$239$	10.3693	−	17.9602i	0.670734	−	1.16175i	0.977696	−	0.210024i	$-0.0673542\pi$
$240$	2.18253	+	0.486371i	0.140882	+	0.0313951i
$241$	4.84177	−	2.79540i	0.311886	−	0.180067i	−0.335884	−	0.941903i	$-0.609035\pi$
$241$	4.84177	−	2.79540i	0.311886	−	0.180067i	0.647770	+	0.761836i	$0.275702\pi$
$242$	−1.01962	+	3.80526i	−0.0655434	+	0.244611i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−8.17968			−0.523651
$245$	1.99979	−	3.83128i	0.127762	−	0.244772i
$246$			2.57079i			0.163908i
$247$	25.1275	−	25.1275i	1.59882	−	1.59882i
$248$	−2.88900	−	4.75959i	−0.183452	−	0.302234i
$249$			5.13226i			0.325244i
$250$	6.83534	−	8.84749i	0.432305	−	0.559564i
$251$	17.1316	−	9.89091i	1.08133	−	0.624309i	0.150078	−	0.988674i	$-0.452047\pi$
$251$	17.1316	−	9.89091i	1.08133	−	0.624309i	0.931256	+	0.364365i	$0.118714\pi$
$252$	1.59173	+	1.59173i	0.100270	+	0.100270i
$253$	2.23593	+	8.34459i	0.140571	+	0.524620i
$254$	3.07758	+	5.33053i	0.193105	+	0.334467i
$255$	10.3833	+	5.41971i	0.650228	+	0.339395i
$256$	1.00000			0.0625000
$257$	22.9806	−	6.15762i	1.43349	−	0.384102i	0.543239	−	0.839578i	$-0.317198\pi$
$257$	22.9806	−	6.15762i	1.43349	−	0.384102i	0.890248	+	0.455476i	$0.150531\pi$
$258$	0.757850	+	2.82834i	0.0471817	+	0.176085i
$259$	8.86387	−	15.3527i	0.550774	−	0.953968i
$260$	14.5613	−	4.57358i	0.903053	−	0.283642i
$261$	8.02636	+	4.63402i	0.496819	+	0.286839i
$262$	0.636082	−	2.37389i	0.0392973	−	0.146660i
$263$	12.0770	+	12.0770i	0.744698	+	0.744698i	0.973478	−	0.228780i	$-0.0734737\pi$
$263$	12.0770	+	12.0770i	0.744698	+	0.744698i	−0.228780	+	0.973478i	$0.573474\pi$
$264$			2.65716i			0.163537i
$265$	6.12740	+	19.5083i	0.376403	+	1.19839i
$266$	5.85968	−	10.1493i	0.359280	−	0.622292i
$267$	4.68129	−	17.4708i	0.286490	−	1.06920i
$268$	−0.325772	−	1.21580i	−0.0198997	−	0.0742668i
$269$	−10.2558	+	17.7636i	−0.625309	+	1.08307i	0.363172	+	0.931722i	$0.381694\pi$
$269$	−10.2558	+	17.7636i	−0.625309	+	1.08307i	−0.988481	+	0.151345i	$0.951640\pi$
$270$	−0.0950827	−	2.23405i	−0.00578655	−	0.135960i
$271$		−	4.34638i		−	0.264024i	−0.991248	−	0.132012i	$-0.957856\pi$
$271$		−	4.34638i		−	0.264024i	0.991248	−	0.132012i	$-0.0421437\pi$
$272$	5.05958	+	1.35571i	0.306782	+	0.0822019i
$273$	14.8414	+	3.97674i	0.898242	+	0.240683i
$274$	−8.77676	+	15.2018i	−0.530224	+	0.918374i
$275$	12.0287	+	5.64126i	0.725356	+	0.340180i
$276$	−1.62560	−	2.81562i	−0.0978495	−	0.169480i
$277$	5.20258	−	5.20258i	0.312593	−	0.312593i	−0.533321	−	0.845913i	$-0.679056\pi$
$277$	5.20258	−	5.20258i	0.312593	−	0.312593i	0.845913	+	0.533321i	$0.179056\pi$
$278$	−5.29563	−	5.29563i	−0.317611	−	0.317611i
$279$	−3.84968	+	4.02243i	−0.230474	+	0.240817i
$280$	4.24818	−	2.69984i	0.253877	−	0.161346i
$281$	−15.5469			−0.927451			−0.463725	−	0.885979i	$-0.653488\pi$
$281$	−15.5469			−0.927451			−0.463725	+	0.885979i	$0.653488\pi$
$282$	−7.84954	−	2.10328i	−0.467433	−	0.125248i
$283$	−11.9165	+	11.9165i	−0.708365	+	0.708365i	−0.966191	−	0.257826i	$-0.916994\pi$
$283$	−11.9165	+	11.9165i	−0.708365	+	0.708365i	0.257826	+	0.966191i	$0.416994\pi$
$284$	9.79691	+	5.65625i	0.581339	+	0.335636i
$285$	−11.1064	+	3.48843i	−0.657886	+	0.206637i
$286$	9.06845	+	15.7070i	0.536229	+	0.928775i
$287$	4.09202	+	4.09202i	0.241544	+	0.241544i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	9.03892	+	5.21862i	0.531701	+	0.306978i
$290$	14.0177	−	15.2639i	0.823146	−	0.896328i
$291$	−6.19614	+	3.57734i	−0.363224	+	0.209707i
$292$	−3.56984	−	13.3228i	−0.208909	−	0.779660i
$293$	18.4652	+	4.94774i	1.07875	+	0.289050i	0.754084	−	0.656779i	$-0.228081\pi$
$293$	18.4652	+	4.94774i	1.07875	+	0.289050i	0.324666	+	0.945829i	$0.394748\pi$
$294$	−1.93276			−0.112721
$295$	−2.96593	−	4.66688i	−0.172683	−	0.271716i
$296$	−6.82022	+	3.93766i	−0.396417	+	0.228872i
$297$	2.56662	−	0.687724i	0.148930	−	0.0399058i
$298$	−4.89923	−	1.31274i	−0.283804	−	0.0760452i
$299$	−19.2185	−	11.0958i	−1.11143	−	0.641686i
$300$	−4.92212	−	0.879053i	−0.284179	−	0.0507522i
$301$	5.70826	+	3.29566i	0.329018	+	0.189959i
$302$	−4.87372	+	4.87372i	−0.280451	+	0.280451i
$303$	−0.175006	+	0.653133i	−0.0100539	+	0.0375215i
$304$	−4.50868	+	2.60309i	−0.258590	+	0.149297i
$305$	18.2738	−	0.777747i	1.04635	−	0.0445336i
$306$		−	5.23806i		−	0.299440i
$307$	7.60554	−	28.3843i	0.434071	−	1.61998i	−0.309209	−	0.950994i	$-0.600064\pi$
$307$	7.60554	−	28.3843i	0.434071	−	1.61998i	0.743280	−	0.668981i	$-0.233269\pi$
$308$	4.22949	+	4.22949i	0.240998	+	0.240998i
$309$	−13.3313			−0.758393
$310$	6.90671	+	10.3584i	0.392275	+	0.588320i
$311$	5.41518			0.307067			0.153533	−	0.988143i	$-0.450935\pi$
$311$	5.41518			0.307067			0.153533	+	0.988143i	$0.450935\pi$
$312$	−4.82648	−	4.82648i	−0.273245	−	0.273245i
$313$	4.80877	−	17.9466i	0.271808	−	1.01440i	−0.686142	−	0.727467i	$-0.740697\pi$
$313$	4.80877	−	17.9466i	0.271808	−	1.01440i	0.957950	−	0.286934i	$-0.0926361\pi$
$314$		−	11.7348i		−	0.662231i
$315$	−3.70735	−	3.40466i	−0.208886	−	0.191831i
$316$	5.74087	−	3.31449i	0.322949	−	0.186455i
$317$	1.52144	−	5.67811i	0.0854528	−	0.318914i	−0.909947	−	0.414725i	$-0.863878\pi$
$317$	1.52144	−	5.67811i	0.0854528	−	0.318914i	0.995400	+	0.0958109i	$0.0305444\pi$
$318$	6.46621	−	6.46621i	0.362607	−	0.362607i
$319$	21.3273	+	12.3133i	1.19410	+	0.689414i
$320$	−2.23405	+	0.0950827i	−0.124887	+	0.00531529i
$321$	5.69126	+	3.28585i	0.317655	+	0.183398i
$322$	−7.06924	−	1.89420i	−0.393953	−	0.105559i
$323$	−26.3410	+	7.05806i	−1.46565	+	0.392721i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−32.0957	+	11.6021i	−1.78035	+	0.643570i
$326$	−10.0300			−0.555509
$327$	−6.63418	−	1.77762i	−0.366871	−	0.0983027i
$328$	−0.665370	−	2.48320i	−0.0367389	−	0.137112i
$329$	−15.8422	+	9.14652i	−0.873411	+	0.504264i
$330$	−0.252650	−	5.93622i	−0.0139079	−	0.326778i
$331$	29.3998	+	16.9740i	1.61596	+	0.932975i	0.987951	+	0.154768i	$0.0494631\pi$
$331$	29.3998	+	16.9740i	1.61596	+	0.932975i	0.628009	+	0.778206i	$0.283870\pi$
$332$	−1.32833	−	4.95738i	−0.0729014	−	0.272072i
$333$	5.56869	+	5.56869i	0.305162	+	0.305162i
$334$	−8.83023	−	15.2944i	−0.483169	−	0.836873i
$335$	0.843392	+	2.68518i	0.0460794	+	0.146707i
$336$	−1.94947	−	1.12553i	−0.106352	−	0.0614025i
$337$	−19.3478	+	19.3478i	−1.05394	+	1.05394i	−0.0554841	+	0.998460i	$0.517670\pi$
$337$	−19.3478	+	19.3478i	−1.05394	+	1.05394i	−0.998460	+	0.0554841i	$0.982330\pi$
$338$	−32.4452	−	8.69366i	−1.76479	−	0.472873i
$339$	11.1274			0.604360
$340$	−11.4322	−	2.54764i	−0.619999	−	0.138165i
$341$	−10.2292	+	10.6882i	−0.553944	+	0.578801i
$342$	3.68132	+	3.68132i	0.199063	+	0.199063i
$343$	−14.2186	+	14.2186i	−0.767732	+	0.767732i
$344$	−1.46405	−	2.53582i	−0.0789365	−	0.136722i
$345$	3.89938	+	6.13565i	0.209935	+	0.330332i
$346$	−5.12053	+	8.86901i	−0.275281	+	0.476801i
$347$	−32.7509	−	8.77558i	−1.75816	−	0.471098i	−0.771824	−	0.635837i	$-0.780655\pi$
$347$	−32.7509	−	8.77558i	−1.75816	−	0.471098i	−0.986337	+	0.164739i	$0.947322\pi$
$348$	−8.95224	−	2.39874i	−0.479890	−	0.128586i
$349$		−	4.48325i		−	0.239983i	−0.992775	−	0.119991i	$-0.961713\pi$
$349$		−	4.48325i		−	0.239983i	0.992775	−	0.119991i	$-0.0382867\pi$
$350$	−9.23393	+	6.43549i	−0.493574	+	0.343991i
$351$	−3.41283	+	5.91120i	−0.182164	+	0.315517i
$352$	−0.687724	−	2.56662i	−0.0366558	−	0.136801i
$353$	3.25740	−	12.1568i	0.173374	−	0.647040i	−0.823449	−	0.567390i	$-0.807953\pi$
$353$	3.25740	−	12.1568i	0.173374	−	0.647040i	0.996823	−	0.0796498i	$-0.0253802\pi$
$354$	−1.23646	+	2.14160i	−0.0657169	+	0.113825i
$355$	−22.4245	−	11.7048i	−1.19017	−	0.621226i
$356$			18.0871i			0.958615i
$357$	−8.33760	−	8.33760i	−0.441272	−	0.441272i
$358$	3.19109	−	11.9093i	0.168654	−	0.629426i
$359$	29.5304	+	17.0494i	1.55856	+	0.899833i	0.997395	+	0.0721272i	$0.0229788\pi$
$359$	29.5304	+	17.0494i	1.55856	+	0.899833i	0.561162	+	0.827706i	$0.310355\pi$
$360$	0.670056	+	2.13331i	0.0353151	+	0.112435i
$361$	4.05212	−	7.01848i	0.213269	−	0.369393i
$362$	−2.77117	−	10.3421i	−0.145649	−	0.543571i
$363$	−3.80526	+	1.01962i	−0.199724	+	0.0535160i
$364$	−15.3649			−0.805341
$365$	9.24196	+	29.4244i	0.483746	+	1.54014i
$366$	−4.08984	−	7.08381i	−0.213779	−	0.370277i
$367$	1.91460	+	7.14537i	0.0999411	+	0.372985i	0.997722	−	0.0674567i	$-0.0214885\pi$
$367$	1.91460	+	7.14537i	0.0999411	+	0.372985i	−0.897781	+	0.440442i	$0.854822\pi$
$368$	2.29894	+	2.29894i	0.119841	+	0.119841i
$369$	−2.22637	+	1.28540i	−0.115900	+	0.0669151i
$370$	14.8623	−	9.44539i	0.772653	−	0.491042i
$371$		−	20.5850i		−	1.06872i
$372$	2.67743	−	4.88174i	0.138818	−	0.253106i
$373$	−18.0881	+	18.0881i	−0.936569	+	0.936569i	−0.998105	−	0.0615361i	$-0.980400\pi$
$373$	−18.0881	+	18.0881i	−0.936569	+	0.936569i	0.0615361	+	0.998105i	$0.480400\pi$
$374$		−	13.9184i		−	0.719701i
$375$	11.0798	+	1.49584i	0.572160	+	0.0772446i
$376$	8.12644			0.419089
$377$	−61.1050	+	16.3730i	−3.14707	+	0.843254i
$378$	−0.582615	+	2.17435i	−0.0299665	+	0.111836i
$379$	−27.5071	+	15.8812i	−1.41294	+	0.815764i	−0.995665	−	0.0930139i	$-0.970350\pi$
$379$	−27.5071	+	15.8812i	−1.41294	+	0.815764i	−0.417280	+	0.908778i	$0.637017\pi$
$380$	9.82508	−	6.24411i	0.504016	−	0.320316i
$381$	−3.07758	+	5.33053i	−0.157669	+	0.273091i
$382$	−0.908516	+	0.243436i	−0.0464837	+	0.0124553i
$383$	11.8956	−	3.18742i	0.607838	−	0.162870i	0.0582451	−	0.998302i	$-0.481450\pi$
$383$	11.8956	−	3.18742i	0.607838	−	0.162870i	0.549593	+	0.835433i	$0.314783\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−9.85103	−	9.04673i	−0.502055	−	0.461064i
$386$	1.78342	+	3.08898i	0.0907739	+	0.157225i
$387$	−2.07049	+	2.07049i	−0.105249	+	0.105249i
$388$	5.05912	−	5.05912i	0.256838	−	0.256838i
$389$	3.70324	+	6.41420i	0.187762	+	0.325213i	0.944504	−	0.328501i	$-0.106543\pi$
$389$	3.70324	+	6.41420i	0.187762	+	0.325213i	−0.756742	+	0.653714i	$0.773210\pi$
$390$	11.2415	+	10.3237i	0.569235	+	0.522758i
$391$	8.51498	+	14.7484i	0.430621	+	0.745857i
$392$	1.86691	−	0.500236i	0.0942931	−	0.0252657i
$393$	2.37389	−	0.636082i	0.119747	−	0.0320861i
$394$	5.45441	−	9.44732i	0.274789	−	0.475949i
$395$	−12.5102	+	7.95058i	−0.629457	+	0.400037i
$396$	−2.30117	+	1.32858i	−0.115638	+	0.0667637i
$397$	5.18242	−	19.3410i	0.260098	−	0.970699i	−0.705085	−	0.709123i	$-0.749091\pi$
$397$	5.18242	−	19.3410i	0.260098	−	0.970699i	0.965183	−	0.261576i	$-0.0842422\pi$
$398$	−17.8458	+	4.78176i	−0.894528	+	0.239688i
$399$	11.7194			0.586702
$400$	4.98192	−	0.424838i	0.249096	−	0.0212419i
$401$			28.6131i			1.42887i	0.699701	+	0.714436i	$0.253317\pi$
$401$			28.6131i			1.42887i	−0.699701	+	0.714436i	$0.746683\pi$
$402$	0.890027	−	0.890027i	0.0443905	−	0.0443905i
$403$	−0.833766	−	37.9946i	−0.0415329	−	1.89264i
$404$		−	0.676173i		−	0.0336409i
$405$	1.88720	−	1.19937i	0.0937757	−	0.0595970i
$406$	−18.0677	+	10.4314i	−0.896687	+	0.517703i
$407$	14.7969	+	14.7969i	0.733455	+	0.733455i
$408$	1.35571	+	5.05958i	0.0671176	+	0.250486i
$409$	−1.30005	−	2.25175i	−0.0642834	−	0.111342i	0.832093	−	0.554637i	$-0.187143\pi$
$409$	−1.30005	−	2.25175i	−0.0642834	−	0.111342i	−0.896376	+	0.443295i	$0.853809\pi$
$410$	1.72258	+	5.48431i	0.0850720	+	0.270851i
$411$	−17.5535			−0.865852
$412$	12.8771	−	3.45040i	0.634408	−	0.169989i
$413$	1.44076	+	5.37698i	0.0708950	+	0.264584i
$414$	1.62560	−	2.81562i	0.0798938	−	0.138380i
$415$	3.43890	+	10.9487i	0.168809	+	0.537451i
$416$	5.91120	+	3.41283i	0.289820	+	0.167328i
$417$	1.93833	−	7.23396i	0.0949206	−	0.354249i
$418$	9.78186	+	9.78186i	0.478446	+	0.478446i
$419$		−	11.4521i		−	0.559472i	−0.960077	−	0.279736i	$-0.909753\pi$
$419$		−	11.4521i		−	0.559472i	0.960077	−	0.279736i	$-0.0902469\pi$
$420$	4.46222	+	2.32912i	0.217734	+	0.113649i
$421$	0.392692	−	0.680163i	0.0191386	−	0.0331491i	−0.856297	−	0.516483i	$-0.827241\pi$
$421$	0.392692	−	0.680163i	0.0191386	−	0.0331491i	0.875436	+	0.483334i	$0.160574\pi$
$422$	−4.28736	+	16.0007i	−0.208706	+	0.778900i
$423$	−2.10328	−	7.84954i	−0.102265	−	0.381658i
$424$	−4.57230	+	7.91946i	−0.222051	+	0.384603i
$425$	25.7823	+	4.60453i	1.25063	+	0.223353i
$426$			11.3125i			0.548092i
$427$	−17.7855	−	4.76561i	−0.860700	−	0.230624i
$428$	−6.34778	−	1.70088i	−0.306832	−	0.0822153i
$429$	−9.06845	+	15.7070i	−0.437829	+	0.758342i
$430$	3.51188	+	5.52592i	0.169358	+	0.266484i
$431$	8.13056	+	14.0825i	0.391635	+	0.678332i	0.992665	−	0.120894i	$-0.0385762\pi$
$431$	8.13056	+	14.0825i	0.391635	+	0.678332i	−0.601030	+	0.799226i	$0.705243\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	9.72100	+	9.72100i	0.467162	+	0.467162i	0.900994	−	0.433832i	$-0.142839\pi$
$433$	9.72100	+	9.72100i	0.467162	+	0.467162i	−0.433832	+	0.900994i	$0.642839\pi$
$434$	−3.50868	−	12.0322i	−0.168422	−	0.577563i
$435$	20.2278	+	4.50770i	0.969848	+	0.216128i
$436$	6.86821			0.328927
$437$	−16.3495	−	4.38085i	−0.782105	−	0.209564i
$438$	9.75299	−	9.75299i	0.466016	−	0.466016i
$439$	13.3697	+	7.71901i	0.638102	+	0.368408i	0.783883	−	0.620909i	$-0.213236\pi$
$439$	13.3697	+	7.71901i	0.638102	+	0.368408i	−0.145781	+	0.989317i	$0.546569\pi$
$440$	1.78045	+	5.66856i	0.0848795	+	0.270238i
$441$	−0.966382	−	1.67382i	−0.0460182	−	0.0797059i
$442$	25.2814	+	25.2814i	1.20251	+	1.20251i
$443$	3.70537	+	13.8286i	0.176047	+	0.657018i	0.996371	+	0.0851181i	$0.0271267\pi$
$443$	3.70537	+	13.8286i	0.176047	+	0.657018i	−0.820323	+	0.571900i	$0.806207\pi$
$444$	−6.82022	−	3.93766i	−0.323673	−	0.186873i
$445$	−1.71977	−	40.4074i	−0.0815250	−	1.91550i
$446$	18.9133	−	10.9196i	0.895573	−	0.517059i
$447$	−1.31274	−	4.89923i	−0.0620906	−	0.231725i
$448$	2.17435	+	0.582615i	0.102728	+	0.0275260i
$449$	−34.4440			−1.62551			−0.812756	−	0.582605i	$-0.802034\pi$
$449$	−34.4440			−1.62551			−0.812756	+	0.582605i	$0.802034\pi$
$450$	−1.69978	−	4.70221i	−0.0801283	−	0.221664i
$451$	−5.91583	+	3.41551i	−0.278566	+	0.160830i
$452$	−10.7483	+	2.87999i	−0.505557	+	0.135464i
$453$	−6.65763	−	1.78391i	−0.312803	−	0.0838153i
$454$	−16.4310	−	9.48643i	−0.771144	−	0.445220i
$455$	34.3260	−	1.46094i	1.60923	−	0.0684899i
$456$	−4.50868	−	2.60309i	−0.211138	−	0.121901i
$457$	−1.23761	+	1.23761i	−0.0578931	+	0.0578931i	−0.735461	−	0.677568i	$-0.763034\pi$
$457$	−1.23761	+	1.23761i	−0.0578931	+	0.0578931i	0.677568	+	0.735461i	$0.263034\pi$
$458$	1.11597	−	4.16485i	0.0521458	−	0.194611i
$459$	4.53629	−	2.61903i	0.211736	−	0.122246i
$460$	−5.35453	−	4.91735i	−0.249656	−	0.229273i
$461$		−	7.07229i		−	0.329389i	−0.986345	−	0.164695i	$-0.947336\pi$
$461$		−	7.07229i		−	0.329389i	0.986345	−	0.164695i	$-0.0526639\pi$
$462$	−1.54810	+	5.77760i	−0.0720242	+	0.268798i
$463$	−15.0904	−	15.0904i	−0.701308	−	0.701308i	0.263383	−	0.964691i	$-0.415162\pi$
$463$	−15.0904	−	15.0904i	−0.701308	−	0.701308i	−0.964691	+	0.263383i	$0.915162\pi$
$464$	9.26804			0.430258
$465$	−5.51732	+	11.1606i	−0.255860	+	0.517561i
$466$	−13.5618			−0.628239
$467$	−0.259170	−	0.259170i	−0.0119929	−	0.0119929i	0.701085	−	0.713078i	$-0.252699\pi$
$467$	−0.259170	−	0.259170i	−0.0119929	−	0.0119929i	−0.713078	+	0.701085i	$0.752699\pi$
$468$	1.76661	−	6.59309i	0.0816617	−	0.304766i
$469$		−	2.83337i		−	0.130833i
$470$	−18.1548	+	0.772684i	−0.837421	+	0.0356413i
$471$	10.1626	−	5.86738i	0.468268	−	0.270354i
$472$	0.640037	−	2.38865i	0.0294601	−	0.109947i
$473$	−5.50161	+	5.50161i	−0.252964	+	0.252964i
$474$	5.74087	+	3.31449i	0.263687	+	0.152240i
$475$	−21.3560	+	14.8838i	−0.979879	+	0.682917i
$476$	10.2114	+	5.89557i	0.468040	+	0.270223i
$477$	8.83301	+	2.36680i	0.404436	+	0.108368i
$478$	−20.0319	+	5.36754i	−0.916240	+	0.245506i
$479$	−2.91282	+	1.68172i	−0.133090	+	0.0768396i	−0.565067	−	0.825045i	$-0.691150\pi$
$479$	−2.91282	+	1.68172i	−0.133090	+	0.0768396i	0.431977	+	0.901885i	$0.357816\pi$
$480$	−1.19937	−	1.88720i	−0.0547434	−	0.0861384i
$481$	−53.7543			−2.45098
$482$	−5.40029	−	1.44700i	−0.245976	−	0.0659092i
$483$	−1.89420	−	7.06924i	−0.0861889	−	0.321661i
$484$	3.41170	−	1.96975i	0.155077	−	0.0895340i
$485$	−10.8213	+	11.7833i	−0.491369	+	0.535054i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	8.43293	+	31.4721i	0.382133	+	1.42614i	0.842638	+	0.538481i	$0.181002\pi$
$487$	8.43293	+	31.4721i	0.382133	+	1.42614i	−0.460505	+	0.887657i	$0.652332\pi$
$488$	5.78391	+	5.78391i	0.261825	+	0.261825i
$489$	−5.01499	−	8.68621i	−0.226786	−	0.392804i
$490$	−4.12319	+	1.29506i	−0.186267	+	0.0585049i
$491$	−26.5611	−	15.3351i	−1.19869	−	0.692062i	−0.238425	−	0.971161i	$-0.576631\pi$
$491$	−26.5611	−	15.3351i	−1.19869	−	0.692062i	−0.960262	+	0.279099i	$0.909964\pi$
$492$	1.81783	−	1.81783i	0.0819539	−	0.0819539i
$493$	46.8923	+	12.5648i	2.11192	+	0.565888i
$494$	−35.5356			−1.59882
$495$	5.01459	−	3.18691i	0.225389	−	0.143241i
$496$	−1.32271	+	5.40837i	−0.0593913	+	0.242843i
$497$	18.0065	+	18.0065i	0.807701	+	0.807701i
$498$	3.62905	−	3.62905i	0.162622	−	0.162622i
$499$	−4.35159	−	7.53718i	−0.194804	−	0.337410i	0.752032	−	0.659126i	$-0.229074\pi$
$499$	−4.35159	−	7.53718i	−0.194804	−	0.337410i	−0.946836	+	0.321716i	$0.895740\pi$
$500$	−11.0894	+	1.42280i	−0.495935	+	0.0636297i
$501$	8.83023	−	15.2944i	0.394506	−	0.683304i
$502$	−19.1078	−	5.11991i	−0.852821	−	0.228513i
$503$	23.3269	+	6.25044i	1.04010	+	0.278693i	0.738154	−	0.674633i	$-0.235698\pi$
$503$	23.3269	+	6.25044i	1.04010	+	0.278693i	0.301943	+	0.953326i	$0.402365\pi$
$504$		−	2.25105i		−	0.100270i
$505$	0.0642924	+	1.51060i	0.00286097	+	0.0672209i
$506$	4.31948	−	7.48155i	0.192024	−	0.332596i
$507$	−8.69366	−	32.4452i	−0.386099	−	1.44094i
$508$	1.59307	−	5.94544i	0.0706813	−	0.263786i
$509$	0.449046	−	0.777770i	0.0199036	−	0.0344740i	−0.855902	−	0.517138i	$-0.826997\pi$
$509$	0.449046	−	0.777770i	0.0199036	−	0.0344740i	0.875806	+	0.482664i	$0.160331\pi$
$510$	−3.50979	−	11.1744i	−0.155416	−	0.494811i
$511$		−	31.0483i		−	1.37350i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.34746	+	5.02878i	−0.0594917	+	0.222026i
$514$	−20.6038	−	11.8956i	−0.908795	−	0.524693i
$515$	−28.4399	+	8.93274i	−1.25321	+	0.393624i
$516$	1.46405	−	2.53582i	0.0644514	−	0.111633i
$517$	−5.58875	−	20.8575i	−0.245793	−	0.917312i
$518$	−17.1237	+	4.58828i	−0.752371	+	0.201597i
$519$	−10.2411			−0.449532
$520$	−13.5304	−	7.06237i	−0.593347	−	0.309706i
$521$	−21.4186	−	37.0982i	−0.938367	−	1.62530i	−0.768517	−	0.639830i	$-0.779005\pi$
$521$	−21.4186	−	37.0982i	−0.938367	−	1.62530i	−0.169850	−	0.985470i	$-0.554328\pi$
$522$	−2.39874	−	8.95224i	−0.104990	−	0.391829i
$523$	−26.2845	−	26.2845i	−1.14934	−	1.14934i	−0.986682	−	0.162658i	$-0.947993\pi$
$523$	−26.2845	−	26.2845i	−1.14934	−	1.14934i	−0.162658	−	0.986682i	$-0.552007\pi$
$524$	−2.12837	+	1.22882i	−0.0929784	+	0.0536811i
$525$	−10.1903	−	4.77907i	−0.444739	−	0.208576i
$526$		−	17.0794i		−	0.744698i
$527$	−14.0245	+	25.5708i	−0.610917	+	1.11388i
$528$	1.87890	−	1.87890i	0.0817685	−	0.0817685i
$529$		−	12.4297i		−	0.540423i
$530$	9.46173	−	18.1272i	0.410991	−	0.787395i
$531$	−2.47291			−0.107315
$532$	−11.3200	+	3.03320i	−0.490786	+	0.131506i
$533$	4.54160	−	16.9495i	0.196718	−	0.734163i
$534$	−15.6639	+	9.04355i	−0.677843	+	0.391353i
$535$	14.3430	+	3.19628i	0.620100	+	0.138187i
$536$	−0.629344	+	1.09006i	−0.0271835	+	0.0470832i
$537$	11.9093	−	3.19109i	0.513924	−	0.137706i
$538$	19.8127	−	5.30881i	0.854188	−	0.228879i
$539$	−2.56783	−	4.44762i	−0.110604	−	0.191572i
$540$	−1.51248	+	1.64694i	−0.0650866	+	0.0708731i
$541$	5.47493	+	9.48285i	0.235385	+	0.407700i	0.959385	−	0.282101i	$-0.0910314\pi$
$541$	5.47493	+	9.48285i	0.235385	+	0.407700i	−0.723999	+	0.689801i	$0.757698\pi$
$542$	−3.07335	+	3.07335i	−0.132012	+	0.132012i
$543$	7.57097	−	7.57097i	0.324902	−	0.324902i
$544$	−2.61903	−	4.53629i	−0.112290	−	0.194492i
$545$	−15.3439	+	0.653048i	−0.657260	+	0.0279735i
$546$	−7.68247	−	13.3064i	−0.328779	−	0.569462i
$547$	16.3169	−	4.37210i	0.697660	−	0.186938i	0.107478	−	0.994207i	$-0.465722\pi$
$547$	16.3169	−	4.37210i	0.697660	−	0.186938i	0.590182	+	0.807270i	$0.299056\pi$
$548$	16.9554	−	4.54319i	0.724299	−	0.194075i
$549$	4.08984	−	7.08381i	0.174550	−	0.302330i
$550$	−4.51658	−	12.4945i	−0.192588	−	0.532768i
$551$	−41.7866	+	24.1255i	−1.78017	+	1.02778i
$552$	−0.841471	+	3.14041i	−0.0358154	+	0.133665i
$553$	14.4137	−	3.86215i	0.612934	−	0.164235i
$554$	−7.35756			−0.312593
$555$	15.6111	+	8.14842i	0.662654	+	0.345881i
$556$			7.48915i			0.317611i
$557$	−18.7392	+	18.7392i	−0.794006	+	0.794006i	−0.982143	−	0.188136i	$-0.939755\pi$
$557$	−18.7392	+	18.7392i	−0.794006	+	0.794006i	0.188136	+	0.982143i	$0.439755\pi$
$558$	5.56642	−	0.122152i	0.235646	−	0.00517109i
$559$		−	19.9863i		−	0.845330i
$560$	−4.91299	−	1.09485i	−0.207612	−	0.0462657i
$561$	12.0537	−	6.95918i	0.508906	−	0.293817i
$562$	10.9933	+	10.9933i	0.463725	+	0.463725i
$563$	5.50970	+	20.5625i	0.232206	+	0.866606i	0.979388	+	0.201986i	$0.0647396\pi$
$563$	5.50970	+	20.5625i	0.232206	+	0.866606i	−0.747182	+	0.664619i	$0.768594\pi$
$564$	4.06322	+	7.03771i	0.171092	+	0.296341i
$565$	23.7383	−	7.45601i	0.998678	−	0.313677i
$566$	16.8525			0.708365
$567$	−2.17435	+	0.582615i	−0.0913141	+	0.0244675i
$568$	−2.92789	−	10.9270i	−0.122851	−	0.458488i
$569$	5.17135	−	8.95705i	0.216794	−	0.375499i	−0.737032	−	0.675858i	$-0.763773\pi$
$569$	5.17135	−	8.95705i	0.216794	−	0.375499i	0.953826	+	0.300359i	$0.0971065\pi$
$570$	10.3201	+	5.38672i	0.432261	+	0.225625i
$571$	19.8778	+	11.4765i	0.831861	+	0.480275i	0.854489	−	0.519469i	$-0.173870\pi$
$571$	19.8778	+	11.4765i	0.831861	+	0.480275i	−0.0226284	+	0.999744i	$0.507203\pi$
$572$	4.69417	−	17.5189i	0.196273	−	0.732502i
$573$	−0.665080	−	0.665080i	−0.0277841	−	0.0277841i
$574$		−	5.78699i		−	0.241544i
$575$	12.4298	+	10.4765i	0.518360	+	0.436899i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.72857	+	32.5755i	−0.363375	+	1.35613i	0.506235	+	0.862395i	$0.331037\pi$
$577$	−8.72857	+	32.5755i	−0.363375	+	1.35613i	−0.869610	+	0.493739i	$0.835630\pi$
$578$	−2.70136	−	10.0816i	−0.112362	−	0.419340i
$579$	−1.78342	+	3.08898i	−0.0741166	+	0.128374i
$580$	−20.7052	+	0.881230i	−0.859737	+	0.0365911i
$581$		−	11.5530i		−	0.479298i
$582$	6.91089	+	1.85177i	0.286466	+	0.0767582i
$583$	23.4707	+	6.28897i	0.972059	+	0.260462i
$584$	−6.89641	+	11.9449i	−0.285375	+	0.494285i
$585$	−3.31980	+	14.8972i	−0.137257	+	0.615925i
$586$	−9.55830	−	16.5555i	−0.394850	−	0.683900i
$587$	−3.13069	+	3.13069i	−0.129217	+	0.129217i	−0.768758	−	0.639540i	$-0.779125\pi$
$587$	−3.13069	+	3.13069i	−0.129217	+	0.129217i	0.639540	+	0.768758i	$0.279125\pi$
$588$	1.36667	+	1.36667i	0.0563606	+	0.0563606i
$589$	−8.11479	−	27.8277i	−0.334364	−	1.14662i
$590$	−1.20275	+	5.39721i	−0.0495165	+	0.222200i
$591$	10.9088			0.448729
$592$	7.60697	+	2.03828i	0.312644	+	0.0837728i
$593$	11.5888	−	11.5888i	0.475897	−	0.475897i	−0.427920	−	0.903817i	$-0.640753\pi$
$593$	11.5888	−	11.5888i	0.475897	−	0.475897i	0.903817	+	0.427920i	$0.140753\pi$
$594$	−2.30117	−	1.32858i	−0.0944181	−	0.0545123i
$595$	−23.3734	−	12.2000i	−0.958214	−	0.500153i
$596$	2.53603	+	4.39253i	0.103880	+	0.179925i
$597$	−13.0640	−	13.0640i	−0.534674	−	0.534674i
$598$	5.74360	+	21.4354i	0.234873	+	0.876560i
$599$	8.05022	+	4.64780i	0.328923	+	0.189904i	0.655363	−	0.755314i	$-0.272516\pi$
$599$	8.05022	+	4.64780i	0.328923	+	0.189904i	−0.326440	+	0.945218i	$0.605849\pi$
$600$	2.85888	+	4.10205i	0.116713	+	0.167465i
$601$	6.04019	−	3.48731i	0.246385	−	0.142250i	−0.371723	−	0.928344i	$-0.621233\pi$
$601$	6.04019	−	3.48731i	0.246385	−	0.142250i	0.618108	+	0.786093i	$0.287900\pi$
$602$	−1.70596	−	6.36673i	−0.0695298	−	0.259489i
$603$	1.21580	+	0.325772i	0.0495112	+	0.0132665i
$604$	6.89249			0.280451
$605$	−7.43461	+	4.72490i	−0.302260	+	0.192095i
$606$	0.585583	−	0.338086i	0.0237877	−	0.0137338i
$607$	−11.4684	+	3.07296i	−0.465490	+	0.124728i	−0.483938	−	0.875102i	$-0.660794\pi$
$607$	−11.4684	+	3.07296i	−0.465490	+	0.124728i	0.0184485	+	0.999830i	$0.494127\pi$
$608$	5.02878	+	1.34746i	0.203944	+	0.0546466i
$609$	−18.0677	−	10.4314i	−0.732142	−	0.422702i
$610$	−13.4715	−	12.3716i	−0.545444	−	0.500910i
$611$	48.0370	+	27.7342i	1.94337	+	1.12201i
$612$	−3.70387	+	3.70387i	−0.149720	+	0.149720i
$613$	−7.69370	+	28.7133i	−0.310746	+	1.15972i	0.617140	+	0.786853i	$0.288291\pi$
$613$	−7.69370	+	28.7133i	−0.310746	+	1.15972i	−0.927886	+	0.372865i	$0.878376\pi$
$614$	−25.4486	+	14.6928i	−1.02702	+	0.592952i
$615$	−3.88826	+	4.23395i	−0.156790	+	0.170729i
$616$		−	5.98141i		−	0.240998i
$617$	9.14762	−	34.1394i	0.368269	−	1.37440i	−0.494665	−	0.869084i	$-0.664709\pi$
$617$	9.14762	−	34.1394i	0.368269	−	1.37440i	0.862934	−	0.505316i	$-0.168624\pi$
$618$	9.42668	+	9.42668i	0.379197	+	0.379197i
$619$	42.4200			1.70500			0.852502	−	0.522725i	$-0.175084\pi$
$619$	42.4200			1.70500			0.852502	+	0.522725i	$0.175084\pi$
$620$	2.44075	−	12.2083i	0.0980227	−	0.490297i
$621$	3.25120			0.130466
$622$	−3.82911	−	3.82911i	−0.153533	−	0.153533i
$623$	−10.5378	+	39.3277i	−0.422189	+	1.57563i
$624$			6.82567i			0.273245i
$625$	24.6390	−	4.23302i	0.985561	−	0.169321i
$626$	−16.0905	+	9.28984i	−0.643105	+	0.371297i
$627$	−3.58041	+	13.3623i	−0.142988	+	0.533638i
$628$	−8.29772	+	8.29772i	−0.331115	+	0.331115i
$629$	35.7247	+	20.6257i	1.42444	+	0.822399i
$630$	0.214036	+	5.02895i	0.00852741	+	0.200358i
$631$	−30.8586	−	17.8162i	−1.22846	−	0.709251i	−0.261752	−	0.965135i	$-0.584300\pi$
$631$	−30.8586	−	17.8162i	−1.22846	−	0.709251i	−0.966708	+	0.255884i	$0.917634\pi$
$632$	−6.40311	−	1.71571i	−0.254702	−	0.0682472i
$633$	−16.0007	+	4.28736i	−0.635969	+	0.170407i
$634$	−5.09085	+	2.93920i	−0.202184	+	0.116731i
$635$	−2.99369	+	13.4338i	−0.118801	+	0.533106i
$636$	−9.14461			−0.362607
$637$	12.7429	+	3.41445i	0.504892	+	0.135285i
$638$	−6.37385	−	23.7875i	−0.252343	−	0.941757i
$639$	−9.79691	+	5.65625i	−0.387560	+	0.223758i
$640$	1.64694	+	1.51248i	0.0651011	+	0.0597858i
$641$	−34.3264	−	19.8183i	−1.35581	−	0.782777i	−0.366754	−	0.930318i	$-0.619531\pi$
$641$	−34.3264	−	19.8183i	−1.35581	−	0.782777i	−0.989056	+	0.147541i	$0.952864\pi$
$642$	−1.70088	−	6.34778i	−0.0671285	−	0.250527i
$643$	−24.1950	−	24.1950i	−0.954158	−	0.954158i	0.0448366	−	0.998994i	$-0.485723\pi$
$643$	−24.1950	−	24.1950i	−0.954158	−	0.954158i	−0.998994	+	0.0448366i	$0.985723\pi$
$644$	3.65931	+	6.33810i	0.144197	+	0.249756i
$645$	−3.02965	+	5.80434i	−0.119292	+	0.228546i
$646$	23.6167	+	13.6351i	0.929187	+	0.536467i
$647$	9.65936	−	9.65936i	0.379749	−	0.379749i	−0.491263	−	0.871011i	$-0.663465\pi$
$647$	9.65936	−	9.65936i	0.379749	−	0.379749i	0.871011	+	0.491263i	$0.163465\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−6.57093			−0.257931
$650$	30.8990	+	14.4912i	1.21196	+	0.568390i
$651$	8.66583	−	9.05470i	0.339641	−	0.354882i
$652$	7.09226	+	7.09226i	0.277754	+	0.277754i
$653$	24.0628	−	24.0628i	0.941650	−	0.941650i	−0.0567389	−	0.998389i	$-0.518070\pi$
$653$	24.0628	−	24.0628i	0.941650	−	0.941650i	0.998389	+	0.0567389i	$0.0180703\pi$
$654$	3.43410	+	5.94804i	0.134284	+	0.232587i
$655$	4.63804	−	2.94760i	0.181223	−	0.115172i
$656$	−1.28540	+	2.22637i	−0.0501863	+	0.0869252i
$657$	13.3228	+	3.56984i	0.519773	+	0.139273i
$658$	17.6697	+	4.73459i	0.688838	+	0.184573i
$659$		−	4.60799i		−	0.179502i	−0.995964	−	0.0897509i	$-0.971393\pi$
$659$		−	4.60799i		−	0.179502i	0.995964	−	0.0897509i	$-0.0286071\pi$
$660$	−4.01889	+	4.37619i	−0.156435	+	0.170343i
$661$	−1.55180	+	2.68780i	−0.0603580	+	0.104543i	−0.894625	−	0.446817i	$-0.852558\pi$
$661$	−1.55180	+	2.68780i	−0.0603580	+	0.104543i	0.834267	+	0.551360i	$0.185891\pi$
$662$	−8.78638	−	32.7912i	−0.341492	−	1.27447i
$663$	−9.25362	+	34.5350i	−0.359381	+	1.34123i
$664$	−2.56613	+	4.44467i	−0.0995851	+	0.172486i
$665$	25.0011	−	7.85264i	0.969500	−	0.304512i
$666$		−	7.87531i		−	0.305162i
$667$	21.3067	+	21.3067i	0.824998	+	0.824998i
$668$	−4.57087	+	17.0587i	−0.176852	+	0.660021i
$669$	18.9133	+	10.9196i	0.731232	+	0.422177i
$670$	1.30234	−	2.49507i	0.0503137	−	0.0963931i
$671$	10.8674	−	18.8228i	0.419530	−	0.726647i
$672$	0.582615	+	2.17435i	0.0224749	+	0.0838773i
$673$	10.7624	−	2.88377i	0.414859	−	0.111161i	−0.0453513	−	0.998971i	$-0.514441\pi$
$673$	10.7624	−	2.88377i	0.414859	−	0.111161i	0.460210	+	0.887810i	$0.347774\pi$
$674$	27.3620			1.05394
$675$	3.22234	−	3.82315i	0.124028	−	0.147153i
$676$	16.7949	+	29.0896i	0.645957	+	1.11883i
$677$	12.2127	+	45.5784i	0.469372	+	1.75172i	0.641973	+	0.766727i	$0.278116\pi$
$677$	12.2127	+	45.5784i	0.469372	+	1.75172i	−0.172601	+	0.984992i	$0.555217\pi$
$678$	−7.86829	−	7.86829i	−0.302180	−	0.302180i
$679$	13.9478	−	8.05278i	0.535268	−	0.309037i
$680$	6.28235	+	9.88526i	0.240917	+	0.379082i
$681$		−	18.9729i		−	0.727042i
$682$	14.7909	−	0.324577i	0.566372	−	0.0124287i
$683$	6.24378	−	6.24378i	0.238912	−	0.238912i	−0.577488	−	0.816399i	$-0.695967\pi$
$683$	6.24378	−	6.24378i	0.238912	−	0.238912i	0.816399	+	0.577488i	$0.195967\pi$
$684$		−	5.20617i		−	0.199063i
$685$	−37.4472	+	11.7619i	−1.43078	+	0.449397i
$686$	20.1081			0.767732
$687$	4.16485	−	1.11597i	0.158899	−	0.0425768i
$688$	−0.757850	+	2.82834i	−0.0288928	+	0.107829i
$689$	−54.0556	+	31.2090i	−2.05936	+	1.18897i
$690$	1.58129	−	7.09584i	0.0601985	−	0.270134i
$691$	17.2140	−	29.8155i	0.654851	−	1.13423i	−0.327080	−	0.944997i	$-0.606065\pi$
$691$	17.2140	−	29.8155i	0.654851	−	1.13423i	0.981931	−	0.189238i	$-0.0606019\pi$
$692$	9.89210	−	2.65058i	0.376041	−	0.100760i
$693$	−5.77760	+	1.54810i	−0.219473	+	0.0588075i
$694$	16.9531	+	29.3637i	0.643532	+	1.11463i
$695$	−0.712089	−	16.7311i	−0.0270111	−	0.634647i
$696$	4.63402	+	8.02636i	0.175652	+	0.304238i
$697$	−9.52187	+	9.52187i	−0.360667	+	0.360667i
$698$	−3.17013	+	3.17013i	−0.119991	+	0.119991i
$699$	−6.78091	−	11.7449i	−0.256477	−	0.444232i
$700$	11.0799	+	1.97879i	0.418783	+	0.0747914i
$701$	−18.1041	−	31.3572i	−0.683782	−	1.18434i	−0.973818	−	0.227329i	$-0.927001\pi$
$701$	−18.1041	−	31.3572i	−0.683782	−	1.18434i	0.290036	−	0.957016i	$-0.406333\pi$
$702$	6.59309	−	1.76661i	0.248840	−	0.0666765i
$703$	−39.6032	+	10.6116i	−1.49366	+	0.400226i
$704$	−1.32858	+	2.30117i	−0.0500728	+	0.0867286i
$705$	−9.74659	−	15.3362i	−0.367078	−	0.577595i
$706$	−10.8995	+	6.29281i	−0.410207	+	0.236833i
$707$	0.393949	−	1.47024i	0.0148160	−	0.0552939i
$708$	2.38865	−	0.640037i	0.0897710	−	0.0240541i
$709$	−14.9203			−0.560343			−0.280172	−	0.959950i	$-0.590391\pi$
$709$	−14.9203			−0.560343			−0.280172	+	0.959950i	$0.590391\pi$
$710$	7.58001	+	24.1331i	0.284473	+	0.905699i
$711$			6.62898i			0.248606i
$712$	12.7895	−	12.7895i	0.479307	−	0.479307i
$713$	−15.4744	+	9.39270i	−0.579519	+	0.351759i
$714$			11.7911i			0.441272i
$715$	−8.82125	+	39.5843i	−0.329896	+	1.48037i
$716$	−10.6776	+	6.16471i	−0.399040	+	0.230386i
$717$	−14.6644	−	14.6644i	−0.547652	−	0.547652i
$718$	−8.82542	−	32.9369i	−0.329362	−	1.22920i
$719$	5.79145	+	10.0311i	0.215985	+	0.374096i	0.953577	−	0.301150i	$-0.0973705\pi$
$719$	5.79145	+	10.0311i	0.215985	+	0.374096i	−0.737592	+	0.675247i	$0.764037\pi$
$720$	1.03468	−	1.98228i	0.0385602	−	0.0738753i
$721$	30.0095			1.11761
$722$	−7.82809	+	2.09753i	−0.291331	+	0.0780620i
$723$	−1.44700	−	5.40029i	−0.0538146	−	0.200839i
$724$	−5.35349	+	9.27251i	−0.198961	+	0.344610i
$725$	46.1726	−	3.93742i	1.71481	−	0.146232i
$726$	3.41170	+	1.96975i	0.126620	+	0.0731042i
$727$	−6.93961	+	25.8990i	−0.257376	+	0.960540i	0.709377	+	0.704829i	$0.248976\pi$
$727$	−6.93961	+	25.8990i	−0.257376	+	0.960540i	−0.966753	+	0.255711i	$0.917690\pi$
$728$	10.8646	+	10.8646i	0.402671	+	0.402671i
$729$		−	1.00000i		−	0.0370370i
$730$	14.2711	−	27.3412i	0.528198	−	1.01194i
$731$	−7.66880	+	13.2828i	−0.283641	+	0.491280i
$732$	−2.11706	+	7.90097i	−0.0782487	+	0.292028i
$733$	1.69553	+	6.32781i	0.0626259	+	0.233723i	0.990144	−	0.140056i	$-0.0447284\pi$
$733$	1.69553	+	6.32781i	0.0626259	+	0.233723i	−0.927518	+	0.373779i	$0.878062\pi$
$734$	3.69871	−	6.40636i	0.136522	−	0.236463i
$735$	−3.18315	−	2.92326i	−0.117412	−	0.107826i
$736$		−	3.25120i		−	0.119841i
$737$	3.23057	+	0.865630i	0.119000	+	0.0318859i
$738$	2.48320	+	0.665370i	0.0914077	+	0.0244926i
$739$	−24.4897	+	42.4174i	−0.900868	+	1.56035i	−0.0744980	+	0.997221i	$0.523735\pi$
$739$	−24.4897	+	42.4174i	−0.900868	+	1.56035i	−0.826370	+	0.563128i	$0.809598\pi$
$740$	−17.1881	−	3.83032i	−0.631848	−	0.140805i
$741$	−17.7678	−	30.7747i	−0.652717	−	1.13054i
$742$	−14.5558	+	14.5558i	−0.534360	+	0.534360i
$743$	16.2282	+	16.2282i	0.595355	+	0.595355i	0.939073	−	0.343718i	$-0.111686\pi$
$743$	16.2282	+	16.2282i	0.595355	+	0.595355i	−0.343718	+	0.939073i	$0.611686\pi$
$744$	−5.34514	+	1.55869i	−0.195962	+	0.0571442i
$745$	−6.08325	−	9.57197i	−0.222873	−	0.350690i
$746$	25.5805			0.936569
$747$	4.95738	+	1.32833i	0.181381	+	0.0486009i
$748$	−9.84177	+	9.84177i	−0.359851	+	0.359851i
$749$	−12.8113	−	7.39663i	−0.468116	−	0.270267i
$750$	−6.77690	−	8.89233i	−0.247457	−	0.324702i
$751$	7.96880	+	13.8024i	0.290786	+	0.503656i	0.973996	−	0.226566i	$-0.0727500\pi$
$751$	7.96880	+	13.8024i	0.290786	+	0.503656i	−0.683210	+	0.730222i	$0.739417\pi$
$752$	−5.74626	−	5.74626i	−0.209545	−	0.209545i
$753$	−5.11991	−	19.1078i	−0.186580	−	0.696326i
$754$	54.7852	+	31.6303i	1.99516	+	1.15191i
$755$	−15.3981	+	0.655357i	−0.560395	+	0.0238509i
$756$	1.94947	−	1.12553i	0.0709015	−	0.0409350i
$757$	6.51761	+	24.3241i	0.236887	+	0.884073i	0.977289	+	0.211909i	$0.0679682\pi$
$757$	6.51761	+	24.3241i	0.236887	+	0.884073i	−0.740403	+	0.672164i	$0.765365\pi$
$758$	30.6802	+	8.22073i	1.11435	+	0.298590i
$759$	8.63895			0.313574
$760$	−11.3626	−	2.53213i	−0.412166	−	0.0918500i
$761$	3.95340	−	2.28250i	0.143311	−	0.0827404i	−0.426630	−	0.904426i	$-0.640299\pi$
$761$	3.95340	−	2.28250i	0.143311	−	0.0827404i	0.569941	+	0.821686i	$0.306966\pi$
$762$	5.94544	−	1.59307i	0.215380	−	0.0577110i
$763$	14.9339	+	4.00152i	0.540643	+	0.144865i
$764$	0.814553	+	0.470282i	0.0294695	+	0.0170142i
$765$	7.92243	−	8.62678i	0.286436	−	0.311902i
$766$	−10.6653	−	6.15763i	−0.385354	−	0.222484i
$767$	11.9355	−	11.9355i	0.430964	−	0.430964i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	16.2455	−	9.37932i	0.585826	−	0.338227i	−0.177619	−	0.984099i	$-0.556840\pi$
$769$	16.2455	−	9.37932i	0.585826	−	0.338227i	0.763445	+	0.645872i	$0.223506\pi$
$770$	0.568729	+	13.3627i	0.0204956	+	0.481560i
$771$		−	23.7912i		−	0.856820i
$772$	0.923168	−	3.44531i	0.0332256	−	0.123999i
$773$	−7.73592	−	7.73592i	−0.278242	−	0.278242i	0.554165	−	0.832407i	$-0.313038\pi$
$773$	−7.73592	−	7.73592i	−0.278242	−	0.278242i	−0.832407	+	0.554165i	$0.813038\pi$
$774$	2.92811			0.105249
$775$	−4.29194	+	27.5060i	−0.154171	+	0.988044i
$776$	−7.15468			−0.256838
$777$	−12.5354	−	12.5354i	−0.449705	−	0.449705i
$778$	1.91694	−	7.15411i	0.0687256	−	0.256487i
$779$		−	13.3840i		−	0.479531i
$780$	−0.649003	−	15.2489i	−0.0232380	−	0.545996i
$781$	−26.0320	+	15.0296i	−0.931497	+	0.537800i
$782$	4.40768	−	16.4497i	0.157618	−	0.588239i
$783$	6.55349	−	6.55349i	0.234203	−	0.234203i
$784$	−1.67382	−	0.966382i	−0.0597794	−	0.0345137i
$785$	17.7485	−	19.3265i	0.633472	−	0.689791i
$786$	−2.12837	−	1.22882i	−0.0759166	−	0.0438304i
$787$	45.0351	+	12.0671i	1.60533	+	0.430146i	0.946646	−	0.322275i	$-0.104447\pi$
$787$	45.0351	+	12.0671i	1.60533	+	0.430146i	0.658682	+	0.752421i	$0.271114\pi$
$788$	−10.5371	+	2.82341i	−0.375369	+	0.100580i
$789$	14.7912	−	8.53971i	0.526581	−	0.304022i
$790$	14.4680	+	3.22414i	0.514747	+	0.114710i
$791$	−25.0484			−0.890620
$792$	2.56662	+	0.687724i	0.0912009	+	0.0244372i
$793$	14.4503	+	53.9294i	0.513146	+	1.91509i
$794$	−17.3407	+	10.0117i	−0.615398	+	0.355300i
$795$	20.4295	−	0.869494i	0.724559	−	0.0308378i
$796$	16.0001	+	9.23765i	0.567108	+	0.327420i
$797$	7.92394	+	29.5725i	0.280680	+	1.04751i	0.951938	+	0.306289i	$0.0990875\pi$
$797$	7.92394	+	29.5725i	0.280680	+	1.04751i	−0.671258	+	0.741224i	$0.734246\pi$
$798$	−8.28684	−	8.28684i	−0.293351	−	0.293351i
$799$	−21.2834	−	36.8639i	−0.752952	−	1.30415i
$800$	−3.82315	−	3.22234i	−0.135169	−	0.113927i
$801$	−15.6639	−	9.04355i	−0.553456	−	0.319538i
$802$	20.2325	−	20.2325i	0.714436	−	0.714436i
$803$	35.4009	+	9.48565i	1.24927	+	0.334741i
$804$	−1.25869			−0.0443905
$805$	−8.77770	−	13.8117i	−0.309373	−	0.486798i
$806$	−26.2767	+	27.4558i	−0.925556	+	0.967088i
$807$	14.5039	+	14.5039i	0.510563	+	0.510563i
$808$	−0.478126	+	0.478126i	−0.0168204	+	0.0168204i
$809$	9.38569	+	16.2565i	0.329983	+	0.571548i	0.982508	−	0.186219i	$-0.0596236\pi$
$809$	9.38569	+	16.2565i	0.329983	+	0.571548i	−0.652525	+	0.757767i	$0.726290\pi$
$810$	−2.18253	−	0.486371i	−0.0766863	−	0.0170893i
$811$	9.77266	−	16.9267i	0.343164	−	0.594378i	−0.641854	−	0.766827i	$-0.721835\pi$
$811$	9.77266	−	16.9267i	0.343164	−	0.594378i	0.985019	+	0.172449i	$0.0551678\pi$
$812$	20.1519	+	5.39970i	0.707195	+	0.189492i
$813$	−4.19828	−	1.12492i	−0.147240	−	0.0394528i
$814$		−	20.9260i		−	0.733455i
$815$	−16.5188	−	15.1701i	−0.578628	−	0.531385i
$816$	2.61903	−	4.53629i	0.0916843	−	0.158802i
$817$	−3.94550	−	14.7248i	−0.138036	−	0.515156i
$818$	−0.672956	+	2.51151i	−0.0235293	+	0.0878127i
$819$	7.68247	−	13.3064i	0.268447	−	0.464964i
$820$	2.65995	−	5.09604i	0.0928893	−	0.177961i
$821$			17.8057i			0.621424i	0.950504	+	0.310712i	$0.100567\pi$
$821$			17.8057i			0.621424i	−0.950504	+	0.310712i	$0.899433\pi$
$822$	12.4122	+	12.4122i	0.432926	+	0.432926i
$823$	6.51267	−	24.3056i	0.227017	−	0.847240i	−0.754569	−	0.656221i	$-0.772154\pi$
$823$	6.51267	−	24.3056i	0.227017	−	0.847240i	0.981586	−	0.191019i	$-0.0611793\pi$
$824$	−11.5453	−	6.66567i	−0.402199	−	0.232209i
$825$	8.56228	−	10.1587i	0.298100	−	0.353682i
$826$	2.78333	−	4.82086i	0.0968443	−	0.167739i
$827$	−3.62942	−	13.5452i	−0.126207	−	0.471012i	0.873673	−	0.486514i	$-0.161732\pi$
$827$	−3.62942	−	13.5452i	−0.126207	−	0.471012i	−0.999880	+	0.0155024i	$0.995065\pi$
$828$	−3.14041	+	0.841471i	−0.109137	+	0.0292432i
$829$	26.2604			0.912060			0.456030	−	0.889964i	$-0.349271\pi$
$829$	26.2604			0.912060			0.456030	+	0.889964i	$0.349271\pi$
$830$	5.31024	−	10.1736i	0.184321	−	0.353130i
$831$	−3.67878	−	6.37183i	−0.127615	−	0.221036i
$832$	−1.76661	−	6.59309i	−0.0612463	−	0.228574i
$833$	−7.15870	−	7.15870i	−0.248034	−	0.248034i
$834$	−6.48579	+	3.74457i	−0.224585	+	0.129664i
$835$	8.58953	−	38.5445i	0.297253	−	1.33389i
$836$		−	13.8336i		−	0.478446i
$837$	2.88900	+	4.75959i	0.0998584	+	0.164515i
$838$	−8.09786	+	8.09786i	−0.279736	+	0.279736i
$839$			16.3284i			0.563719i	0.959456	+	0.281859i	$0.0909512\pi$
$839$			16.3284i			0.563719i	−0.959456	+	0.281859i	$0.909049\pi$
$840$	−1.50833	−	4.80220i	−0.0520424	−	0.165692i
$841$	56.8965			1.96195
$842$	−0.758623	+	0.203272i	−0.0261439	+	0.00700523i
$843$	−4.02384	+	15.0172i	−0.138588	+	0.517218i
$844$	14.3458	−	8.28255i	0.493803	−	0.285097i
$845$	−40.2864	−	63.3905i	−1.38589	−	2.18070i
$846$	−4.06322	+	7.03771i	−0.139696	+	0.241961i
$847$	8.56584	−	2.29521i	0.294326	−	0.0788643i
$848$	8.83301	−	2.36680i	0.303327	−	0.0812762i
$849$	8.42627	+	14.5947i	0.289189	+	0.500890i
$850$	−14.9750	−	21.4868i	−0.513638	−	0.736990i
$851$	12.8021	+	22.1739i	0.438850	+	0.760111i
$852$	7.99914	−	7.99914i	0.274046	−	0.274046i
$853$	−8.10359	+	8.10359i	−0.277461	+	0.277461i	−0.832095	−	0.554633i	$-0.812859\pi$
$853$	−8.10359	+	8.10359i	−0.277461	+	0.277461i	0.554633	+	0.832095i	$0.312859\pi$
$854$	9.20645	+	15.9460i	0.315038	+	0.545662i
$855$	0.495017	+	11.6308i	0.0169292	+	0.397766i
$856$	3.28585	+	5.69126i	0.112308	+	0.194523i
$857$	−28.4232	+	7.61598i	−0.970919	+	0.260157i	−0.709216	−	0.704992i	$-0.750951\pi$
$857$	−28.4232	+	7.61598i	−0.970919	+	0.260157i	−0.261703	+	0.965148i	$0.584284\pi$
$858$	17.5189	−	4.69417i	0.598085	−	0.160256i
$859$	26.0722	−	45.1584i	0.889573	−	1.54079i	0.0491924	−	0.998789i	$-0.484335\pi$
$859$	26.0722	−	45.1584i	0.889573	−	1.54079i	0.840381	−	0.541997i	$-0.182331\pi$
$860$	1.42415	−	6.39069i	0.0485630	−	0.217921i
$861$	5.01168	−	2.89349i	0.170798	−	0.0986100i
$862$	4.20869	−	15.7070i	0.143348	−	0.534984i
$863$	17.1791	−	4.60313i	0.584784	−	0.156692i	0.0457155	−	0.998954i	$-0.485443\pi$
$863$	17.1791	−	4.60313i	0.584784	−	0.156692i	0.539068	+	0.842262i	$0.318777\pi$
$864$	−1.00000			−0.0340207
$865$	−21.8474	+	6.86208i	−0.742833	+	0.233318i
$866$		−	13.7476i		−	0.467162i
$867$	7.38025	−	7.38025i	0.250646	−	0.250646i
$868$	−6.02702	+	10.9891i	−0.204571	+	0.372993i
$869$			17.6143i			0.597523i
$870$	−11.1158	−	17.4906i	−0.376860	−	0.592988i
$871$	−7.44036	+	4.29569i	−0.252107	+	0.145554i
$872$	−4.85655	−	4.85655i	−0.164464	−	0.164464i
$873$	1.85177	+	6.91089i	0.0626728	+	0.233898i
$874$	8.46315	+	14.6586i	0.286270	+	0.495834i
$875$	−24.9413	−	3.36720i	−0.843168	−	0.113832i
$876$	−13.7928			−0.466016
$877$	−43.4947	+	11.6544i	−1.46871	+	0.393540i	−0.902489	−	0.430712i	$-0.858262\pi$
$877$	−43.4947	+	11.6544i	−1.46871	+	0.393540i	−0.566223	+	0.824252i	$0.691596\pi$
$878$	−3.99566	−	14.9120i	−0.134847	−	0.503255i
$879$	9.55830	−	16.5555i	0.322394	−	0.558402i
$880$	2.74931	−	5.26724i	0.0926791	−	0.177559i
$881$	−7.56416	−	4.36717i	−0.254843	−	0.147134i	0.367137	−	0.930167i	$-0.380338\pi$
$881$	−7.56416	−	4.36717i	−0.254843	−	0.147134i	−0.621980	+	0.783033i	$0.713671\pi$
$882$	−0.500236	+	1.86691i	−0.0168438	+	0.0628620i
$883$	−10.4653	−	10.4653i	−0.352185	−	0.352185i	0.508737	−	0.860922i	$-0.330113\pi$
$883$	−10.4653	−	10.4653i	−0.352185	−	0.352185i	−0.860922	+	0.508737i	$0.830113\pi$
$884$		−	35.7532i		−	1.20251i
$885$	−5.27550	+	1.65699i	−0.177334	+	0.0556991i
$886$	7.15822	−	12.3984i	0.240485	−	0.416533i
$887$	0.695006	−	2.59380i	0.0233360	−	0.0870912i	−0.953276	−	0.302101i	$-0.902312\pi$
$887$	0.695006	−	2.59380i	0.0233360	−	0.0870912i	0.976612	+	0.215010i	$0.0689785\pi$
$888$	2.03828	+	7.60697i	0.0684002	+	0.255273i
$889$	6.92780	−	11.9993i	0.232351	−	0.402444i
$890$	−27.3563	+	29.7884i	−0.916985	+	0.998510i
$891$		−	2.65716i		−	0.0890182i
$892$	−21.0951	−	5.65241i	−0.706316	−	0.189257i
$893$	40.8661	+	10.9500i	1.36753	+	0.366429i
$894$	−2.53603	+	4.39253i	−0.0848174	+	0.146908i
$895$	23.2681	−	14.7875i	0.777766	−	0.494292i
$896$	−1.12553	−	1.94947i	−0.0376012	−	0.0651272i
$897$	−15.6918	+	15.6918i	−0.523935	+	0.523935i
$898$	24.3556	+	24.3556i	0.812756	+	0.812756i
$899$	−12.2589	+	50.1250i	−0.408857	+	1.67176i
$900$	−2.12304	+	4.52689i	−0.0707679	+	0.150896i
$901$	47.9000			1.59578
$902$	6.59825	+	1.76800i	0.219698	+	0.0588678i
$903$	4.66077	−	4.66077i	0.155101	−	0.155101i
$904$	9.63665	+	5.56372i	0.320510	+	0.185047i
$905$	11.0783	−	21.2242i	0.368254	−	0.705518i
$906$	3.44624	+	5.96907i	0.114494	+	0.198309i
$907$	−8.22906	−	8.22906i	−0.273241	−	0.273241i	0.557162	−	0.830404i	$-0.311890\pi$
$907$	−8.22906	−	8.22906i	−0.273241	−	0.273241i	−0.830404	+	0.557162i	$0.811890\pi$
$908$	4.91054	+	18.3264i	0.162962	+	0.608182i
$909$	0.585583	+	0.338086i	0.0194226	+	0.0112136i
$910$	−25.3052	−	23.2391i	−0.838858	−	0.770368i
$911$	−2.95892	+	1.70833i	−0.0980333	+	0.0565996i	−0.548215	−	0.836337i	$-0.684693\pi$
$911$	−2.95892	+	1.70833i	−0.0980333	+	0.0565996i	0.450182	+	0.892937i	$0.351359\pi$
$912$	1.34746	+	5.02878i	0.0446188	+	0.166519i
$913$	13.1726	+	3.52958i	0.435948	+	0.116812i
$914$	1.75025			0.0578931
$915$	3.97836	−	17.8524i	0.131520	−	0.590183i
$916$	−3.73410	+	2.15589i	−0.123378	+	0.0712325i
$917$	−5.34375	+	1.43185i	−0.176466	+	0.0472840i
$918$	−5.05958	−	1.35571i	−0.166991	−	0.0447451i
$919$	50.0621	+	28.9034i	1.65140	+	0.953434i	0.976499	+	0.215521i	$0.0691450\pi$
$919$	50.0621	+	28.9034i	1.65140	+	0.953434i	0.674896	+	0.737913i	$0.264188\pi$
$920$	0.309133	+	7.26332i	0.0101918	+	0.239465i
$921$	−25.4486	−	14.6928i	−0.838561	−	0.484143i
$922$	−5.00086	+	5.00086i	−0.164695	+	0.164695i
$923$	19.9848	−	74.5843i	0.657807	−	2.45497i
$924$	5.18005	−	2.99070i	0.170411	−	0.0983869i
$925$	38.7632	+	6.92282i	1.27453	+	0.227621i
$926$			21.3410i			0.701308i
$927$	−3.45040	+	12.8771i	−0.113326	+	0.422939i
$928$	−6.55349	−	6.55349i	−0.215129	−	0.215129i
$929$	−38.4828			−1.26258			−0.631290	−	0.775547i	$-0.717474\pi$
$929$	−38.4828			−1.26258			−0.631290	+	0.775547i	$0.717474\pi$
$930$	11.7931	−	3.99041i	0.386710	−	0.130851i
$931$	10.0623			0.329779
$932$	9.58965	+	9.58965i	0.314119	+	0.314119i
$933$	1.40155	−	5.23066i	0.0458847	−	0.171244i
$934$			0.366521i			0.0119929i
$935$	21.0512	−	22.9227i	0.688447	−	0.749654i
$936$	−5.91120	+	3.41283i	−0.193214	+	0.111552i
$937$	−0.721312	+	2.69197i	−0.0235642	+	0.0879429i	−0.976707	−	0.214579i	$-0.931162\pi$
$937$	−0.721312	+	2.69197i	−0.0235642	+	0.0879429i	0.953142	+	0.302522i	$0.0978286\pi$
$938$	−2.00350	+	2.00350i	−0.0654165	+	0.0654165i
$939$	−16.0905	−	9.28984i	−0.525093	−	0.303162i
$940$	13.3838	+	12.2910i	0.436531	+	0.400890i
$941$	−15.8316	−	9.14039i	−0.516096	−	0.297968i	0.219240	−	0.975671i	$-0.429642\pi$
$941$	−15.8316	−	9.14039i	−0.516096	−	0.297968i	−0.735336	+	0.677703i	$0.762976\pi$
$942$	−11.3349	−	3.03718i	−0.369311	−	0.0989566i
$943$	−8.07336	+	2.16325i	−0.262905	+	0.0704451i
$944$	−2.14160	+	1.23646i	−0.0697033	+	0.0402432i
$945$	−4.24818	+	2.69984i	−0.138193	+	0.0878257i
$946$	7.78046			0.252964
$947$	−32.9194	−	8.82073i	−1.06974	−	0.286635i	−0.319352	−	0.947636i	$-0.603465\pi$
$947$	−32.9194	−	8.82073i	−1.06974	−	0.286635i	−0.750385	+	0.661001i	$0.770132\pi$
$948$	−1.71571	−	6.40311i	−0.0557236	−	0.207963i
$949$	−81.5321	+	47.0726i	−2.64664	+	1.52804i
$950$	25.6254	+	4.57650i	0.831398	+	0.148481i
$951$	−5.09085	−	2.93920i	−0.165082	−	0.0953102i
$952$	−3.05177	−	11.3894i	−0.0989085	−	0.369132i
$953$	1.65003	+	1.65003i	0.0534497	+	0.0534497i	0.733326	−	0.679877i	$-0.237967\pi$
$953$	1.65003	+	1.65003i	0.0534497	+	0.0534497i	−0.679877	+	0.733326i	$0.737967\pi$
$954$	−4.57230	−	7.91946i	−0.148034	−	0.256402i
$955$	−1.86446	−	0.973182i	−0.0603326	−	0.0314914i
$956$	17.9602	+	10.3693i	0.580873	+	0.335367i
$957$	17.4137	−	17.4137i	0.562904	−	0.562904i
$958$	3.24883	+	0.870521i	0.104965	+	0.0281252i
$959$	39.5139			1.27597
$960$	−0.486371	+	2.18253i	−0.0156975	+	0.0704409i
$961$	−27.5009	−	14.3074i	−0.887126	−	0.461528i
$962$	38.0100	+	38.0100i	1.22549	+	1.22549i
$963$	4.64690	−	4.64690i	0.149744	−	0.149744i
$964$	2.79540	+	4.84177i	0.0900336	+	0.155943i
$965$	−1.73481	+	7.78476i	−0.0558455	+	0.250600i
$966$	−3.65931	+	6.33810i	−0.117736	+	0.203925i
$967$	−18.0348	−	4.83241i	−0.579960	−	0.155400i	−0.0430992	−	0.999071i	$-0.513723\pi$
$967$	−18.0348	−	4.83241i	−0.579960	−	0.155400i	−0.536860	+	0.843671i	$0.680390\pi$
$968$	−3.80526	−	1.01962i	−0.122306	−	0.0327717i
$969$			27.2702i			0.876046i
$970$	15.9839	−	0.680287i	0.513212	−	0.0218427i
$971$	9.73594	−	16.8631i	0.312441	−	0.541164i	−0.666449	−	0.745550i	$-0.732187\pi$
$971$	9.73594	−	16.8631i	0.312441	−	0.541164i	0.978890	+	0.204387i	$0.0655200\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−4.36329	+	16.2840i	−0.139881	+	0.522042i
$974$	16.2912	−	28.2171i	0.522003	−	0.904135i
$975$	2.89981	+	34.0049i	0.0928681	+	1.08903i
$976$		−	8.17968i		−	0.261825i
$977$	−14.0601	−	14.0601i	−0.449822	−	0.449822i	0.445473	−	0.895295i	$-0.353035\pi$
$977$	−14.0601	−	14.0601i	−0.449822	−	0.449822i	−0.895295	+	0.445473i	$0.853035\pi$
$978$	−2.59595	+	9.68821i	−0.0830093	+	0.309795i
$979$	−41.6215	−	24.0302i	−1.33023	−	0.768008i
$980$	3.83128	+	1.99979i	0.122386	+	0.0638810i
$981$	−3.43410	+	5.94804i	−0.109642	+	0.189906i
$982$	7.93802	+	29.6251i	0.253312	+	0.945375i
$983$	9.37294	−	2.51147i	0.298950	−	0.0801035i	−0.106226	−	0.994342i	$-0.533877\pi$
$983$	9.37294	−	2.51147i	0.298950	−	0.0801035i	0.405177	+	0.914238i	$0.367210\pi$
$984$	−2.57079			−0.0819539
$985$	23.2719	−	7.30953i	0.741506	−	0.232901i
$986$	−24.2733	−	42.0425i	−0.773018	−	1.33891i
$987$	4.73459	+	17.6697i	0.150704	+	0.562434i
$988$	25.1275	+	25.1275i	0.799411	+	0.799411i
$989$	−8.24444	+	4.75993i	−0.262158	+	0.151357i
$990$	−5.79934	−	1.29237i	−0.184315	−	0.0410741i
$991$		−	49.9264i		−	1.58597i	−0.609244	−	0.792983i	$-0.708527\pi$
$991$		−	49.9264i		−	1.58597i	0.609244	−	0.792983i	$-0.291473\pi$
$992$	4.75959	−	2.88900i	0.151117	−	0.0917258i
$993$	24.0048	−	24.0048i	0.761771	−	0.761771i
$994$		−	25.4650i		−	0.807701i
$995$	−36.6233	−	19.1160i	−1.16104	−	0.606018i
$996$	−5.13226			−0.162622
$997$	2.43570	−	0.652644i	0.0771395	−	0.0206695i	−0.220043	−	0.975490i	$-0.570620\pi$
$997$	2.43570	−	0.652644i	0.0771395	−	0.0206695i	0.297182	+	0.954821i	$0.403953\pi$
$998$	−2.25255	+	8.40663i	−0.0713032	+	0.266107i
$999$	6.82022	−	3.93766i	0.215782	−	0.124582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.4	yes	64
5.3	odd	4		930.2.be.a.223.7	✓	64
31.26	odd	6		930.2.be.a.367.7	yes	64
155.88	even	12	inner	930.2.be.b.553.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.7	✓	64	5.3	odd	4
930.2.be.a.367.7	yes	64	31.26	odd	6
930.2.be.b.37.4	yes	64	1.1	even	1	trivial
930.2.be.b.553.4	yes	64	155.88	even	12	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.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-0.0950827 - 2.23405i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.582615 + 2.17435i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-0.0950827 - 2.23405i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.582615 + 2.17435i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.51248 + 1.64694i) q^{10} +(-2.30117 - 1.32858i) q^{11} +(0.965926 + 0.258819i) q^{12} +(6.59309 - 1.76661i) q^{13} +(1.94947 - 1.12553i) q^{14} +(-2.18253 - 0.486371i) q^{15} -1.00000 q^{16} +(-5.05958 - 1.35571i) q^{17} +(0.258819 + 0.965926i) q^{18} +(4.50868 - 2.60309i) q^{19} +(2.23405 - 0.0950827i) q^{20} +(1.94947 + 1.12553i) q^{21} +(0.687724 + 2.56662i) q^{22} +(-2.29894 - 2.29894i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.98192 + 0.424838i) q^{25} +(-5.91120 - 3.41283i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.17435 - 0.582615i) q^{28} -9.26804 q^{29} +(1.19937 + 1.88720i) q^{30} +(1.32271 - 5.40837i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.87890 + 1.87890i) q^{33} +(2.61903 + 4.53629i) q^{34} +(4.91299 + 1.09485i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.60697 - 2.03828i) q^{37} +(-5.02878 - 1.34746i) q^{38} -6.82567i q^{39} +(-1.64694 - 1.51248i) q^{40} +(1.28540 - 2.22637i) q^{41} +(-0.582615 - 2.17435i) q^{42} +(0.757850 - 2.82834i) q^{43} +(1.32858 - 2.30117i) q^{44} +(-1.03468 + 1.98228i) q^{45} +3.25120i q^{46} +(5.74626 + 5.74626i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(1.67382 + 0.966382i) q^{49} +(3.82315 + 3.22234i) q^{50} +(-2.61903 + 4.53629i) q^{51} +(1.76661 + 6.59309i) q^{52} +(-8.83301 + 2.36680i) q^{53} +1.00000 q^{54} +(-2.74931 + 5.26724i) q^{55} +(1.12553 + 1.94947i) q^{56} +(-1.34746 - 5.02878i) q^{57} +(6.55349 + 6.55349i) q^{58} +(2.14160 - 1.23646i) q^{59} +(0.486371 - 2.18253i) q^{60} +8.17968i q^{61} +(-4.75959 + 2.88900i) q^{62} +(1.59173 - 1.59173i) q^{63} -1.00000i q^{64} +(-4.57358 - 14.5613i) q^{65} +2.65716 q^{66} +(-1.21580 + 0.325772i) q^{67} +(1.35571 - 5.05958i) q^{68} +(-2.81562 + 1.62560i) q^{69} +(-2.69984 - 4.24818i) q^{70} +(5.65625 - 9.79691i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-13.3228 + 3.56984i) q^{73} +(3.93766 + 6.82022i) q^{74} +(-0.879053 + 4.92212i) q^{75} +(2.60309 + 4.50868i) q^{76} +(4.22949 - 4.22949i) q^{77} +(-4.82648 + 4.82648i) q^{78} +(-3.31449 - 5.74087i) q^{79} +(0.0950827 + 2.23405i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.48320 + 0.665370i) q^{82} +(-4.95738 + 1.32833i) q^{83} +(-1.12553 + 1.94947i) q^{84} +(-2.54764 + 11.4322i) q^{85} +(-2.53582 + 1.46405i) q^{86} +(-2.39874 + 8.95224i) q^{87} +(-2.56662 + 0.687724i) q^{88} +18.0871 q^{89} +(2.13331 - 0.670056i) q^{90} +15.3649i q^{91} +(2.29894 - 2.29894i) q^{92} +(-4.88174 - 2.67743i) q^{93} -8.12644i q^{94} +(-6.24411 - 9.82508i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-5.05912 - 5.05912i) q^{97} +(-0.500236 - 1.86691i) q^{98} +(1.32858 + 2.30117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

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