LMFDB - Embedded newform 930.2.be.a.37.15

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			37.15
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.20229 - 1.88534i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.614903 - 2.29485i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.20229 - 1.88534i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.614903 - 2.29485i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.18328 - 0.482987i) q^{10} +(-1.25412 - 0.724067i) q^{11} +(0.965926 + 0.258819i) q^{12} +(0.0156000 - 0.00418001i) q^{13} +(2.05750 - 1.18790i) q^{14} +(-1.50992 - 1.64928i) q^{15} -1.00000 q^{16} +(4.54726 + 1.21843i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-0.111562 + 0.0644102i) q^{19} +(1.88534 + 1.20229i) q^{20} +(-2.05750 - 1.18790i) q^{21} +(-0.374805 - 1.39879i) q^{22} +(-4.84571 - 4.84571i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.10900 - 4.53345i) q^{25} +(0.0139866 + 0.00807515i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.29485 + 0.614903i) q^{28} +4.76154 q^{29} +(0.0985454 - 2.23390i) q^{30} +(3.55757 - 4.28296i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.02398 + 1.02398i) q^{33} +(2.35383 + 4.07696i) q^{34} +(-3.58727 - 3.91837i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-8.93188 - 2.39329i) q^{37} +(-0.124431 - 0.0333412i) q^{38} -0.0161503i q^{39} +(0.482987 + 2.18328i) q^{40} +(-2.12652 + 3.68323i) q^{41} +(-0.614903 - 2.29485i) q^{42} +(0.846818 - 3.16037i) q^{43} +(0.724067 - 1.25412i) q^{44} +(-1.98388 + 1.03160i) q^{45} -6.85287i q^{46} +(3.51963 + 3.51963i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(1.17396 + 0.677784i) q^{49} +(1.71435 - 4.69692i) q^{50} +(2.35383 - 4.07696i) q^{51} +(0.00418001 + 0.0156000i) q^{52} +(11.0631 - 2.96436i) q^{53} -1.00000 q^{54} +(-2.87293 + 1.49390i) q^{55} +(1.18790 + 2.05750i) q^{56} +(0.0333412 + 0.124431i) q^{57} +(3.36691 + 3.36691i) q^{58} +(-10.4304 + 6.02199i) q^{59} +(1.64928 - 1.50992i) q^{60} +7.91452i q^{61} +(5.54409 - 0.512929i) q^{62} +(-1.67995 + 1.67995i) q^{63} -1.00000i q^{64} +(0.0108750 - 0.0344368i) q^{65} -1.44813 q^{66} +(5.92494 - 1.58758i) q^{67} +(-1.21843 + 4.54726i) q^{68} +(-5.93476 + 3.42643i) q^{69} +(0.234124 - 5.30729i) q^{70} +(-0.242566 + 0.420136i) q^{71} +(0.965926 - 0.258819i) q^{72} +(2.88344 - 0.772616i) q^{73} +(-4.62348 - 8.00811i) q^{74} +(-4.92482 + 0.863790i) q^{75} +(-0.0644102 - 0.111562i) q^{76} +(-2.43278 + 2.43278i) q^{77} +(0.0114200 - 0.0114200i) q^{78} +(3.94138 + 6.82668i) q^{79} +(-1.20229 + 1.88534i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-4.10811 + 1.10077i) q^{82} +(13.8853 - 3.72056i) q^{83} +(1.18790 - 2.05750i) q^{84} +(7.76429 - 7.10821i) q^{85} +(2.83351 - 1.63593i) q^{86} +(1.23238 - 4.59929i) q^{87} +(1.39879 - 0.374805i) q^{88} -2.63366 q^{89} +(-2.13227 - 0.673362i) q^{90} -0.0383699i q^{91} +(4.84571 - 4.84571i) q^{92} +(-3.21625 - 4.54486i) q^{93} +4.97750i q^{94} +(-0.0126947 + 0.287771i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(6.26451 + 6.26451i) q^{97} +(0.350847 + 1.30938i) q^{98} +(0.724067 + 1.25412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * 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
$5$	1.20229	−	1.88534i	0.537681	−	0.843149i
$5$	1.20229	−	1.88534i	0.537681	−	0.843149i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	0.614903	−	2.29485i	0.232411	−	0.867371i	−0.746887	−	0.664951i	$-0.768453\pi$
$7$	0.614903	−	2.29485i	0.232411	−	0.867371i	0.979299	−	0.202420i	$-0.0648807\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	2.18328	−	0.482987i	0.690415	−	0.152734i
$11$	−1.25412	−	0.724067i	−0.378132	−	0.218314i	0.298873	−	0.954293i	$-0.403389\pi$
$11$	−1.25412	−	0.724067i	−0.378132	−	0.218314i	−0.677005	+	0.735978i	$0.736722\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	0.0156000	−	0.00418001i	0.00432666	−	0.00115933i	−0.256655	−	0.966503i	$-0.582620\pi$
$13$	0.0156000	−	0.00418001i	0.00432666	−	0.00115933i	0.260982	+	0.965344i	$0.415954\pi$
$14$	2.05750	−	1.18790i	0.549891	−	0.317480i
$15$	−1.50992	−	1.64928i	−0.389860	−	0.425843i
$16$	−1.00000			−0.250000
$17$	4.54726	+	1.21843i	1.10287	+	0.295514i	0.763934	−	0.645295i	$-0.223265\pi$
$17$	4.54726	+	1.21843i	1.10287	+	0.295514i	0.338939	+	0.940808i	$0.389932\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−0.111562	+	0.0644102i	−0.0255940	+	0.0147767i	−0.512742	−	0.858542i	$-0.671370\pi$
$19$	−0.111562	+	0.0644102i	−0.0255940	+	0.0147767i	0.487148	+	0.873319i	$0.338037\pi$
$20$	1.88534	+	1.20229i	0.421574	+	0.268840i
$21$	−2.05750	−	1.18790i	−0.448984	−	0.259221i
$22$	−0.374805	−	1.39879i	−0.0799086	−	0.298223i
$23$	−4.84571	−	4.84571i	−1.01040	−	1.01040i	−0.999945	−	0.0104550i	$-0.996672\pi$
$23$	−4.84571	−	4.84571i	−1.01040	−	1.01040i	−0.0104550	−	0.999945i	$-0.503328\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−2.10900	−	4.53345i	−0.421799	−	0.906689i
$26$	0.0139866	+	0.00807515i	0.00274299	+	0.00158367i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	2.29485	+	0.614903i	0.433685	+	0.116206i
$29$	4.76154			0.884195			0.442098	−	0.896967i	$-0.354234\pi$
$29$	4.76154			0.884195			0.442098	+	0.896967i	$0.354234\pi$
$30$	0.0985454	−	2.23390i	0.0179918	−	0.407852i
$31$	3.55757	−	4.28296i	0.638958	−	0.769242i
$31$	3.55757	−	4.28296i	0.638958	−	0.769242i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.02398	+	1.02398i	−0.178253	+	0.178253i
$34$	2.35383	+	4.07696i	0.403679	+	0.699193i
$35$	−3.58727	−	3.91837i	−0.606359	−	0.662326i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−8.93188	−	2.39329i	−1.46839	−	0.393455i	−0.566013	−	0.824397i	$-0.691515\pi$
$37$	−8.93188	−	2.39329i	−1.46839	−	0.393455i	−0.902380	+	0.430942i	$0.858181\pi$
$38$	−0.124431	−	0.0333412i	−0.0201854	−	0.00540865i
$39$		−	0.0161503i		−	0.00258612i
$40$	0.482987	+	2.18328i	0.0763670	+	0.345207i
$41$	−2.12652	+	3.68323i	−0.332106	+	0.575225i	−0.982925	−	0.184009i	$-0.941093\pi$
$41$	−2.12652	+	3.68323i	−0.332106	+	0.575225i	0.650819	+	0.759233i	$0.274426\pi$
$42$	−0.614903	−	2.29485i	−0.0948815	−	0.354103i
$43$	0.846818	−	3.16037i	0.129139	−	0.481952i	−0.870815	−	0.491611i	$-0.836408\pi$
$43$	0.846818	−	3.16037i	0.129139	−	0.481952i	0.999953	+	0.00965959i	$0.00307479\pi$
$44$	0.724067	−	1.25412i	0.109157	−	0.189066i
$45$	−1.98388	+	1.03160i	−0.295740	+	0.153783i
$46$		−	6.85287i		−	1.01040i
$47$	3.51963	+	3.51963i	0.513390	+	0.513390i	0.915564	−	0.402173i	$-0.131745\pi$
$47$	3.51963	+	3.51963i	0.513390	+	0.513390i	−0.402173	+	0.915564i	$0.631745\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	1.17396	+	0.677784i	0.167708	+	0.0968264i
$50$	1.71435	−	4.69692i	0.242445	−	0.664244i
$51$	2.35383	−	4.07696i	0.329603	−	0.570889i
$52$	0.00418001	+	0.0156000i	0.000579663	+	0.00216333i
$53$	11.0631	−	2.96436i	1.51964	−	0.407186i	0.600017	−	0.799987i	$-0.295161\pi$
$53$	11.0631	−	2.96436i	1.51964	−	0.407186i	0.919624	+	0.392801i	$0.128494\pi$
$54$	−1.00000			−0.136083
$55$	−2.87293	+	1.49390i	−0.387385	+	0.201438i
$56$	1.18790	+	2.05750i	0.158740	+	0.274946i
$57$	0.0333412	+	0.124431i	0.00441615	+	0.0164813i
$58$	3.36691	+	3.36691i	0.442098	+	0.442098i
$59$	−10.4304	+	6.02199i	−1.35792	+	0.783996i	−0.989343	−	0.145601i	$-0.953488\pi$
$59$	−10.4304	+	6.02199i	−1.35792	+	0.783996i	−0.368577	+	0.929597i	$0.620155\pi$
$60$	1.64928	−	1.50992i	0.212922	−	0.194930i
$61$			7.91452i			1.01335i	0.862137	+	0.506675i	$0.169126\pi$
$61$			7.91452i			1.01335i	−0.862137	+	0.506675i	$0.830874\pi$
$62$	5.54409	−	0.512929i	0.704100	−	0.0651421i
$63$	−1.67995	+	1.67995i	−0.211653	+	0.211653i
$64$		−	1.00000i		−	0.125000i
$65$	0.0108750	−	0.0344368i	0.00134888	−	0.00427136i
$66$	−1.44813			−0.178253
$67$	5.92494	−	1.58758i	0.723847	−	0.193954i	0.121960	−	0.992535i	$-0.461082\pi$
$67$	5.92494	−	1.58758i	0.723847	−	0.193954i	0.601888	+	0.798581i	$0.294416\pi$
$68$	−1.21843	+	4.54726i	−0.147757	+	0.551436i
$69$	−5.93476	+	3.42643i	−0.714461	+	0.412494i
$70$	0.234124	−	5.30729i	0.0279832	−	0.634343i
$71$	−0.242566	+	0.420136i	−0.0287872	+	0.0498609i	−0.880060	−	0.474862i	$-0.842498\pi$
$71$	−0.242566	+	0.420136i	−0.0287872	+	0.0498609i	0.851273	+	0.524723i	$0.175831\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	2.88344	−	0.772616i	0.337482	−	0.0904279i	−0.0860984	−	0.996287i	$-0.527440\pi$
$73$	2.88344	−	0.772616i	0.337482	−	0.0904279i	0.423580	+	0.905859i	$0.360773\pi$
$74$	−4.62348	−	8.00811i	−0.537469	−	0.930923i
$75$	−4.92482	+	0.863790i	−0.568669	+	0.0997419i
$76$	−0.0644102	−	0.111562i	−0.00738836	−	0.0127970i
$77$	−2.43278	+	2.43278i	−0.277242	+	0.277242i
$78$	0.0114200	−	0.0114200i	0.00129306	−	0.00129306i
$79$	3.94138	+	6.82668i	0.443440	+	0.768061i	0.997942	−	0.0641213i	$-0.0204245\pi$
$79$	3.94138	+	6.82668i	0.443440	+	0.768061i	−0.554502	+	0.832183i	$0.687091\pi$
$80$	−1.20229	+	1.88534i	−0.134420	+	0.210787i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−4.10811	+	1.10077i	−0.453665	+	0.121559i
$83$	13.8853	−	3.72056i	1.52411	−	0.408385i	0.603019	−	0.797727i	$-0.293964\pi$
$83$	13.8853	−	3.72056i	1.52411	−	0.408385i	0.921093	+	0.389342i	$0.127298\pi$
$84$	1.18790	−	2.05750i	0.129611	−	0.224492i
$85$	7.76429	−	7.10821i	0.842155	−	0.770993i
$86$	2.83351	−	1.63593i	0.305545	−	0.176407i
$87$	1.23238	−	4.59929i	0.132125	−	0.493096i
$88$	1.39879	−	0.374805i	0.149111	−	0.0399543i
$89$	−2.63366			−0.279168			−0.139584	−	0.990210i	$-0.544577\pi$
$89$	−2.63366			−0.279168			−0.139584	+	0.990210i	$0.544577\pi$
$90$	−2.13227	−	0.673362i	−0.224761	−	0.0709786i
$91$		−	0.0383699i		−	0.00402226i
$92$	4.84571	−	4.84571i	0.505200	−	0.505200i
$93$	−3.21625	−	4.54486i	−0.333510	−	0.471280i
$94$			4.97750i			0.513390i
$95$	−0.0126947	+	0.287771i	−0.00130244	+	0.0295247i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	6.26451	+	6.26451i	0.636065	+	0.636065i	0.949582	−	0.313518i	$-0.101508\pi$
$97$	6.26451	+	6.26451i	0.636065	+	0.636065i	−0.313518	+	0.949582i	$0.601508\pi$
$98$	0.350847	+	1.30938i	0.0354409	+	0.132267i
$99$	0.724067	+	1.25412i	0.0727714	+	0.126044i
$100$	4.53345	−	2.10900i	0.453345	−	0.210900i
$101$	2.43374			0.242167			0.121083	−	0.992642i	$-0.461363\pi$
$101$	2.43374			0.242167			0.121083	+	0.992642i	$0.461363\pi$
$102$	4.54726	−	1.21843i	0.450246	−	0.120643i
$103$	−2.96223	−	11.0552i	−0.291877	−	1.08930i	−0.943666	−	0.330900i	$-0.892648\pi$
$103$	−2.96223	−	11.0552i	−0.291877	−	1.08930i	0.651788	−	0.758401i	$-0.274019\pi$
$104$	−0.00807515	+	0.0139866i	−0.000791834	+	0.00137150i
$105$	−4.71331	+	2.45089i	−0.459972	+	0.239182i
$106$	9.91895	+	5.72671i	0.963413	+	0.556227i
$107$	−3.67402	+	13.7116i	−0.355181	+	1.32555i	0.525076	+	0.851056i	$0.324037\pi$
$107$	−3.67402	+	13.7116i	−0.355181	+	1.32555i	−0.880257	+	0.474498i	$0.842630\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	5.28563i		−	0.506272i	−0.967431	−	0.253136i	$-0.918538\pi$
$109$		−	5.28563i		−	0.506272i	0.967431	−	0.253136i	$-0.0814620\pi$
$110$	−3.08781	−	0.975118i	−0.294412	−	0.0929739i
$111$	−4.62348	+	8.00811i	−0.438841	+	0.760096i
$112$	−0.614903	+	2.29485i	−0.0581028	+	0.216843i
$113$	4.11374	+	15.3527i	0.386988	+	1.44426i	0.835009	+	0.550237i	$0.185463\pi$
$113$	4.11374	+	15.3527i	0.386988	+	1.44426i	−0.448020	+	0.894023i	$0.647871\pi$
$114$	−0.0644102	+	0.111562i	−0.00603257	+	0.0104487i
$115$	−14.9617	+	3.30985i	−1.39519	+	0.308645i
$116$			4.76154i			0.442098i
$117$	−0.0156000	−	0.00418001i	−0.00144222	−	0.000386442i
$118$	−11.6336	−	3.11721i	−1.07096	−	0.286962i
$119$	5.59224	−	9.68605i	0.512640	−	0.887919i
$120$	2.23390	+	0.0985454i	0.203926	+	0.00899592i
$121$	−4.45145	−	7.71015i	−0.404678	−	0.700922i
$122$	−5.59641	+	5.59641i	−0.506675	+	0.506675i
$123$	3.00735	+	3.00735i	0.271163	+	0.271163i
$124$	4.28296	+	3.55757i	0.384621	+	0.319479i
$125$	−11.0827	−	1.47435i	−0.991267	−	0.131870i
$126$	−2.37580			−0.211653
$127$	−3.59869	−	0.964266i	−0.319332	−	0.0855648i	0.0955926	−	0.995421i	$-0.469525\pi$
$127$	−3.59869	−	0.964266i	−0.319332	−	0.0855648i	−0.414925	+	0.909856i	$0.636192\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−2.83351	−	1.63593i	−0.249477	−	0.144035i
$130$	0.0320403	−	0.0166607i	0.00281012	−	0.00146124i
$131$	8.97854	+	15.5513i	0.784458	+	1.35872i	0.929322	+	0.369270i	$0.120392\pi$
$131$	8.97854	+	15.5513i	0.784458	+	1.35872i	−0.144864	+	0.989452i	$0.546274\pi$
$132$	−1.02398	−	1.02398i	−0.0891265	−	0.0891265i
$133$	0.0792120	+	0.295623i	0.00686855	+	0.0256338i
$134$	5.31216	+	3.06698i	0.458901	+	0.264946i
$135$	0.482987	+	2.18328i	0.0415689	+	0.187907i
$136$	−4.07696	+	2.35383i	−0.349597	+	0.201840i
$137$	5.72592	+	21.3694i	0.489198	+	1.82571i	0.560361	+	0.828248i	$0.310662\pi$
$137$	5.72592	+	21.3694i	0.489198	+	1.82571i	−0.0711628	+	0.997465i	$0.522671\pi$
$138$	−6.61936	−	1.77365i	−0.563478	−	0.150983i
$139$	−8.88181			−0.753345			−0.376673	−	0.926346i	$-0.622932\pi$
$139$	−8.88181			−0.753345			−0.376673	+	0.926346i	$0.622932\pi$
$140$	3.91837	−	3.58727i	0.331163	−	0.303180i
$141$	4.31064	−	2.48875i	0.363022	−	0.209591i
$142$	−0.468601	+	0.125561i	−0.0393241	+	0.0105369i
$143$	−0.0225909	−	0.00605321i	−0.00188914	−	0.000506195i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	5.72475	−	8.97710i	0.475415	−	0.745508i
$146$	2.58522	+	1.49258i	0.213955	+	0.123527i
$147$	0.958532	−	0.958532i	0.0790584	−	0.0790584i
$148$	2.39329	−	8.93188i	0.196727	−	0.734196i
$149$	−0.886493	+	0.511817i	−0.0726244	+	0.0419297i	−0.535872	−	0.844299i	$-0.680017\pi$
$149$	−0.886493	+	0.511817i	−0.0726244	+	0.0419297i	0.463248	+	0.886229i	$0.346684\pi$
$150$	−4.09317	−	2.87158i	−0.334206	−	0.234464i
$151$		−	4.99185i		−	0.406231i	−0.979155	−	0.203116i	$-0.934893\pi$
$151$		−	4.99185i		−	0.406231i	0.979155	−	0.203116i	$-0.0651067\pi$
$152$	0.0333412	−	0.124431i	0.00270433	−	0.0100927i
$153$	−3.32882	−	3.32882i	−0.269120	−	0.269120i
$154$	−3.44048			−0.277242
$155$	−3.79759	−	11.8566i	−0.305030	−	0.952343i
$156$	0.0161503			0.00129306
$157$	−5.88081	−	5.88081i	−0.469340	−	0.469340i	0.432361	−	0.901701i	$-0.357681\pi$
$157$	−5.88081	−	5.88081i	−0.469340	−	0.469340i	−0.901701	+	0.432361i	$0.857681\pi$
$158$	−2.04021	+	7.61417i	−0.162310	+	0.605751i
$159$		−	11.4534i		−	0.908315i
$160$	−2.18328	+	0.482987i	−0.172604	+	0.0381835i
$161$	−14.0998	+	8.14053i	−1.11122	+	0.641563i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−4.14730	+	4.14730i	−0.324842	+	0.324842i	−0.850621	−	0.525779i	$-0.823774\pi$
$163$	−4.14730	+	4.14730i	−0.324842	+	0.324842i	0.525779	+	0.850621i	$0.323774\pi$
$164$	−3.68323	−	2.12652i	−0.287612	−	0.166053i
$165$	0.699430	+	3.16168i	0.0544505	+	0.246137i
$166$	12.4492	+	7.18757i	0.966249	+	0.557864i
$167$	−4.19413	−	1.12381i	−0.324552	−	0.0869634i	0.0928646	−	0.995679i	$-0.470398\pi$
$167$	−4.19413	−	1.12381i	−0.324552	−	0.0869634i	−0.417416	+	0.908715i	$0.637064\pi$
$168$	2.29485	−	0.614903i	0.177051	−	0.0474408i
$169$	−11.2581	+	6.49987i	−0.866008	+	0.499990i
$170$	10.5164	+	0.463919i	0.806574	+	0.0355810i
$171$	0.128820			0.00985114
$172$	3.16037	+	0.846818i	0.240976	+	0.0645693i
$173$	5.55939	+	20.7479i	0.422672	+	1.57743i	0.768954	+	0.639304i	$0.220777\pi$
$173$	5.55939	+	20.7479i	0.422672	+	1.57743i	−0.346282	+	0.938131i	$0.612556\pi$
$174$	4.12361	−	2.38077i	0.312610	−	0.180486i
$175$	−11.7004	+	2.05219i	−0.884467	+	0.155131i
$176$	1.25412	+	0.724067i	0.0945329	+	0.0545786i
$177$	3.11721	+	11.6336i	0.234304	+	0.874434i
$178$	−1.86228	−	1.86228i	−0.139584	−	0.139584i
$179$	−3.22793	−	5.59093i	−0.241267	−	0.417886i	0.719809	−	0.694172i	$-0.244229\pi$
$179$	−3.22793	−	5.59093i	−0.241267	−	0.417886i	−0.961075	+	0.276287i	$0.910896\pi$
$180$	−1.03160	−	1.98388i	−0.0768913	−	0.147870i
$181$	−14.1432	−	8.16557i	−1.05125	−	0.606942i	−0.128254	−	0.991741i	$-0.540937\pi$
$181$	−14.1432	−	8.16557i	−1.05125	−	0.606942i	−0.923000	+	0.384799i	$0.874271\pi$
$182$	0.0271316	−	0.0271316i	0.00201113	−	0.00201113i
$183$	7.64484	+	2.04843i	0.565123	+	0.151424i
$184$	6.85287			0.505200
$185$	−15.2509	+	13.9622i	−1.12127	+	1.02652i
$186$	0.939464	−	5.48793i	0.0688848	−	0.402395i
$187$	−4.82058	−	4.82058i	−0.352516	−	0.352516i
$188$	−3.51963	+	3.51963i	−0.256695	+	0.256695i
$189$	1.18790	+	2.05750i	0.0864071	+	0.149661i
$190$	−0.212462	+	0.194509i	−0.0154136	+	0.0141111i
$191$	−8.30077	+	14.3773i	−0.600622	+	1.04031i	0.392105	+	0.919921i	$0.371747\pi$
$191$	−8.30077	+	14.3773i	−0.600622	+	1.04031i	−0.992727	+	0.120388i	$0.961586\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	18.5390	+	4.96750i	1.33446	+	0.357568i	0.854377	−	0.519653i	$-0.173939\pi$
$193$	18.5390	+	4.96750i	1.33446	+	0.357568i	0.480086	+	0.877221i	$0.340605\pi$
$194$			8.85935i			0.636065i
$195$	−0.0304488	−	0.0194174i	−0.00218048	−	0.00139051i
$196$	−0.677784	+	1.17396i	−0.0484132	+	0.0838541i
$197$	6.68212	+	24.9380i	0.476081	+	1.77676i	0.617242	+	0.786774i	$0.288250\pi$
$197$	6.68212	+	24.9380i	0.476081	+	1.77676i	−0.141160	+	0.989987i	$0.545083\pi$
$198$	−0.374805	+	1.39879i	−0.0266362	+	0.0994076i
$199$	4.47445	−	7.74997i	0.317185	−	0.549381i	−0.662714	−	0.748872i	$-0.730596\pi$
$199$	4.47445	−	7.74997i	0.317185	−	0.549381i	0.979900	+	0.199491i	$0.0639290\pi$
$200$	4.69692	+	1.71435i	0.332122	+	0.121223i
$201$		−	6.13395i		−	0.432656i
$202$	1.72092	+	1.72092i	0.121083	+	0.121083i
$203$	2.92788	−	10.9270i	0.205497	−	0.766925i
$204$	4.07696	+	2.35383i	0.285444	+	0.164801i
$205$	4.38745	+	8.43752i	0.306433	+	0.589302i
$206$	5.72259	−	9.91182i	0.398712	−	0.690589i
$207$	1.77365	+	6.61936i	0.123277	+	0.460078i
$208$	−0.0156000	+	0.00418001i	−0.00108167	+	0.000289831i
$209$	0.186549			0.0129039
$210$	−5.06585	−	1.59977i	−0.349577	−	0.110395i
$211$	−6.50646	−	11.2695i	−0.447923	−	0.775826i	0.550327	−	0.834949i	$-0.314503\pi$
$211$	−6.50646	−	11.2695i	−0.447923	−	0.775826i	−0.998251	+	0.0591231i	$0.981170\pi$
$212$	2.96436	+	11.0631i	0.203593	+	0.759820i
$213$	0.343039	+	0.343039i	0.0235047	+	0.0235047i
$214$	−12.2935	+	7.09766i	−0.840367	+	0.485186i
$215$	−4.94024	−	5.39622i	−0.336922	−	0.368019i
$216$		−	1.00000i		−	0.0680414i
$217$	−7.64118	−	10.7977i	−0.518717	−	0.732994i
$218$	3.73751	−	3.73751i	0.253136	−	0.253136i
$219$		−	2.98516i		−	0.201718i
$220$	−1.49390	−	2.87293i	−0.100719	−	0.193693i
$221$	0.0760303			0.00511435
$222$	−8.93188	+	2.39329i	−0.599469	+	0.160627i
$223$	0.321997	−	1.20171i	0.0215625	−	0.0804723i	−0.954306	−	0.298831i	$-0.903403\pi$
$223$	0.321997	−	1.20171i	0.0215625	−	0.0804723i	0.975869	+	0.218358i	$0.0700701\pi$
$224$	−2.05750	+	1.18790i	−0.137473	+	0.0793699i
$225$	−0.440280	+	4.98058i	−0.0293520	+	0.332039i
$226$	−7.94714	+	13.7649i	−0.528636	+	0.915624i
$227$	−1.45350	+	0.389463i	−0.0964719	+	0.0258496i	−0.306732	−	0.951796i	$-0.599236\pi$
$227$	−1.45350	+	0.389463i	−0.0964719	+	0.0258496i	0.210260	+	0.977645i	$0.432569\pi$
$228$	−0.124431	+	0.0333412i	−0.00824064	+	0.00220807i
$229$	8.74542	+	15.1475i	0.577914	+	1.00098i	0.995718	+	0.0924390i	$0.0294663\pi$
$229$	8.74542	+	15.1475i	0.577914	+	1.00098i	−0.417805	+	0.908537i	$0.637200\pi$
$230$	−12.9200	−	8.23914i	−0.851918	−	0.543273i
$231$	1.72024	+	2.97954i	0.113183	+	0.196039i
$232$	−3.36691	+	3.36691i	−0.221049	+	0.221049i
$233$	14.9264	−	14.9264i	0.977859	−	0.977859i	−0.0219016	−	0.999760i	$-0.506972\pi$
$233$	14.9264	−	14.9264i	0.977859	−	0.977859i	0.999760	+	0.0219016i	$0.00697205\pi$
$234$	−0.00807515	−	0.0139866i	−0.000527889	−	0.000914331i
$235$	10.8673	−	2.40407i	0.708904	−	0.156824i
$236$	−6.02199	−	10.4304i	−0.391998	−	0.678960i
$237$	7.61417	−	2.04021i	0.494593	−	0.132526i
$238$	10.8034	−	2.89476i	0.700279	−	0.187639i
$239$	8.53893	−	14.7899i	0.552338	−	0.956677i	−0.445768	−	0.895149i	$-0.647069\pi$
$239$	8.53893	−	14.7899i	0.552338	−	0.956677i	0.998105	−	0.0615282i	$-0.0195974\pi$
$240$	1.50992	+	1.64928i	0.0974649	+	0.106461i
$241$	7.03836	−	4.06360i	0.453381	−	0.261759i	−0.255876	−	0.966710i	$-0.582364\pi$
$241$	7.03836	−	4.06360i	0.453381	−	0.261759i	0.709257	+	0.704950i	$0.249031\pi$
$242$	2.30424	−	8.59955i	0.148122	−	0.552800i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−7.91452			−0.506675
$245$	2.68929	−	1.39841i	0.171812	−	0.0893412i
$246$			4.25303i			0.271163i
$247$	−0.00147113	+	0.00147113i	−9.36056e−5	+	9.36056e-5i
$248$	0.512929	+	5.54409i	0.0325710	+	0.352050i
$249$		−	14.3751i		−	0.910988i
$250$	−6.79413	−	8.87918i	−0.429698	−	0.561569i
$251$	16.6427	−	9.60865i	1.05048	−	0.606493i	0.127694	−	0.991814i	$-0.459243\pi$
$251$	16.6427	−	9.60865i	1.05048	−	0.606493i	0.922783	+	0.385321i	$0.125909\pi$
$252$	−1.67995	−	1.67995i	−0.105827	−	0.105827i
$253$	2.56849	+	9.58572i	0.161479	+	0.602649i
$254$	−1.86282	−	3.22650i	−0.116884	−	0.202448i
$255$	−4.85645	−	9.33946i	−0.304123	−	0.584860i
$256$	1.00000			0.0625000
$257$	−3.04126	+	0.814904i	−0.189709	+	0.0508323i	−0.352422	−	0.935841i	$-0.614642\pi$
$257$	−3.04126	+	0.814904i	−0.189709	+	0.0508323i	0.162714	+	0.986673i	$0.447975\pi$
$258$	−0.846818	−	3.16037i	−0.0527206	−	0.196756i
$259$	−10.9845	+	19.0257i	−0.682542	+	1.18220i
$260$	0.0344368	+	0.0108750i	0.00213568	+	0.000674439i
$261$	−4.12361	−	2.38077i	−0.255245	−	0.147366i
$262$	−4.64763	+	17.3452i	−0.287132	+	1.07159i
$263$	−7.18314	−	7.18314i	−0.442931	−	0.442931i	0.450065	−	0.892996i	$-0.351401\pi$
$263$	−7.18314	−	7.18314i	−0.442931	−	0.442931i	−0.892996	+	0.450065i	$0.851401\pi$
$264$		−	1.44813i		−	0.0891265i
$265$	7.71230	−	24.4218i	0.473763	−	1.50022i
$266$	−0.153026	+	0.265049i	−0.00938262	+	0.0162512i
$267$	−0.681643	+	2.54392i	−0.0417158	+	0.155686i
$268$	1.58758	+	5.92494i	0.0969771	+	0.361924i
$269$	−5.95616	+	10.3164i	−0.363153	+	0.629000i	−0.988478	−	0.151365i	$-0.951633\pi$
$269$	−5.95616	+	10.3164i	−0.363153	+	0.629000i	0.625325	+	0.780365i	$0.284967\pi$
$270$	−1.20229	+	1.88534i	−0.0731691	+	0.114738i
$271$		−	13.1910i		−	0.801297i	−0.916232	−	0.400648i	$-0.868785\pi$
$271$		−	13.1910i		−	0.801297i	0.916232	−	0.400648i	$-0.131215\pi$
$272$	−4.54726	−	1.21843i	−0.275718	−	0.0738784i
$273$	−0.0370625	−	0.00993086i	−0.00224312	−	0.000601043i
$274$	−11.0616	+	19.1593i	−0.668257	+	1.15746i
$275$	−0.637584	+	7.21254i	−0.0384478	+	0.434933i
$276$	−3.42643	−	5.93476i	−0.206247	−	0.357230i
$277$	0.624877	−	0.624877i	0.0375452	−	0.0375452i	−0.688085	−	0.725630i	$-0.741548\pi$
$277$	0.624877	−	0.624877i	0.0375452	−	0.0375452i	0.725630	+	0.688085i	$0.241548\pi$
$278$	−6.28039	−	6.28039i	−0.376673	−	0.376673i
$279$	−5.22242	+	1.93037i	−0.312658	+	0.115568i
$280$	5.30729	+	0.234124i	0.317171	+	0.0139916i
$281$	−23.1111			−1.37870			−0.689348	−	0.724431i	$-0.742103\pi$
$281$	−23.1111			−1.37870			−0.689348	+	0.724431i	$0.742103\pi$
$282$	4.80790	+	1.28827i	0.286306	+	0.0767155i
$283$	−4.70017	+	4.70017i	−0.279396	+	0.279396i	−0.832868	−	0.553472i	$-0.813303\pi$
$283$	−4.70017	+	4.70017i	−0.279396	+	0.279396i	0.553472	+	0.832868i	$0.313303\pi$
$284$	−0.420136	−	0.242566i	−0.0249305	−	0.0143936i
$285$	0.274680	+	0.0867428i	0.0162706	+	0.00513820i
$286$	−0.0116939	−	0.0202544i	−0.000691475	−	0.00119767i
$287$	7.14486	+	7.14486i	0.421748	+	0.421748i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	4.47055	+	2.58107i	0.262974	+	0.151828i
$290$	10.3958	−	2.29976i	0.610461	−	0.135047i
$291$	7.67243	−	4.42968i	0.449766	−	0.259672i
$292$	0.772616	+	2.88344i	0.0452139	+	0.168741i
$293$	6.66151	+	1.78495i	0.389170	+	0.104278i	0.448098	−	0.893985i	$-0.352102\pi$
$293$	6.66151	+	1.78495i	0.389170	+	0.104278i	−0.0589282	+	0.998262i	$0.518768\pi$
$294$	1.35557			0.0790584
$295$	−1.18688	+	26.9050i	−0.0691027	+	1.56647i
$296$	8.00811	−	4.62348i	0.465462	−	0.268734i
$297$	1.39879	−	0.374805i	0.0811660	−	0.0217484i
$298$	−0.988755	−	0.264936i	−0.0572770	−	0.0153473i
$299$	−0.0958481	−	0.0553380i	−0.00554304	−	0.00320028i
$300$	−0.863790	−	4.92482i	−0.0498710	−	0.284335i
$301$	−6.73185	−	3.88664i	−0.388018	−	0.224022i
$302$	3.52977	−	3.52977i	0.203116	−	0.203116i
$303$	0.629899	−	2.35082i	0.0361868	−	0.135051i
$304$	0.111562	−	0.0644102i	0.00639850	−	0.00369418i
$305$	14.9215	+	9.51555i	0.854405	+	0.544859i
$306$		−	4.70767i		−	0.269120i
$307$	−3.08651	+	11.5190i	−0.176156	+	0.657424i	0.820195	+	0.572083i	$0.193865\pi$
$307$	−3.08651	+	11.5190i	−0.176156	+	0.657424i	−0.996352	+	0.0853410i	$0.972802\pi$
$308$	−2.43278	−	2.43278i	−0.138621	−	0.138621i
$309$	−11.4452			−0.651094
$310$	5.69856	−	11.0692i	0.323656	−	0.628686i
$311$	−14.8920			−0.844447			−0.422224	−	0.906492i	$-0.638750\pi$
$311$	−14.8920			−0.844447			−0.422224	+	0.906492i	$0.638750\pi$
$312$	0.0114200	+	0.0114200i	0.000646530	+	0.000646530i
$313$	2.37768	−	8.87362i	0.134394	−	0.501567i	−0.865605	−	0.500727i	$-0.833066\pi$
$313$	2.37768	−	8.87362i	0.134394	−	0.501567i	1.00000		0.000839747i	$-0.000267300\pi$
$314$		−	8.31672i		−	0.469340i
$315$	1.14748	+	5.18705i	0.0646533	+	0.292257i
$316$	−6.82668	+	3.94138i	−0.384031	+	0.221720i
$317$	2.18867	−	8.16823i	0.122928	−	0.458774i	−0.876829	−	0.480802i	$-0.840346\pi$
$317$	2.18867	−	8.16823i	0.122928	−	0.458774i	0.999757	+	0.0220281i	$0.00701233\pi$
$318$	8.09879	−	8.09879i	0.454157	−	0.454157i
$319$	−5.97154	−	3.44767i	−0.334342	−	0.193032i
$320$	−1.88534	−	1.20229i	−0.105394	−	0.0672101i
$321$	12.2935	+	7.09766i	0.686157	+	0.396153i
$322$	−15.7263	−	4.21385i	−0.876392	−	0.234828i
$323$	−0.585780	+	0.156959i	−0.0325937	+	0.00873344i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−0.0518501	−	0.0619061i	−0.00287613	−	0.00343393i
$326$	−5.86517			−0.324842
$327$	−5.10553	−	1.36802i	−0.282336	−	0.0756518i
$328$	−1.10077	−	4.10811i	−0.0607796	−	0.226833i
$329$	10.2412	−	5.91278i	0.564617	−	0.325982i
$330$	−1.74108	+	2.73022i	−0.0958431	+	0.150294i
$331$	−25.6403	−	14.8034i	−1.40932	−	0.813671i	−0.413996	−	0.910279i	$-0.635867\pi$
$331$	−25.6403	−	14.8034i	−1.40932	−	0.813671i	−0.995323	+	0.0966080i	$0.969201\pi$
$332$	3.72056	+	13.8853i	0.204192	+	0.762056i
$333$	6.53859	+	6.53859i	0.358313	+	0.358313i
$334$	−2.17104	−	3.76036i	−0.118794	−	0.205758i
$335$	4.13037	−	13.0793i	0.225666	−	0.714596i
$336$	2.05750	+	1.18790i	0.112246	+	0.0648053i
$337$	−8.71093	+	8.71093i	−0.474515	+	0.474515i	−0.903372	−	0.428858i	$-0.858916\pi$
$337$	−8.71093	+	8.71093i	−0.474515	+	0.474515i	0.428858	+	0.903372i	$0.358916\pi$
$338$	−12.5568	−	3.36458i	−0.682999	−	0.183009i
$339$	15.8943			0.863259
$340$	7.10821	+	7.76429i	0.385497	+	0.421078i
$341$	−7.56276	+	2.79543i	−0.409547	+	0.151381i
$342$	0.0910898	+	0.0910898i	0.00492557	+	0.00492557i
$343$	14.0369	−	14.0369i	0.757921	−	0.757921i
$344$	1.63593	+	2.83351i	0.0882033	+	0.152773i
$345$	−0.675319	+	15.3086i	−0.0363579	+	0.824187i
$346$	−10.7399	+	18.6021i	−0.577381	+	1.00005i
$347$	−4.97933	−	1.33421i	−0.267304	−	0.0716240i	0.122677	−	0.992447i	$-0.460852\pi$
$347$	−4.97933	−	1.33421i	−0.267304	−	0.0716240i	−0.389982	+	0.920823i	$0.627519\pi$
$348$	4.59929	+	1.23238i	0.246548	+	0.0660623i
$349$			8.10988i			0.434112i	0.976159	+	0.217056i	$0.0696454\pi$
$349$			8.10988i			0.434112i	−0.976159	+	0.217056i	$0.930355\pi$
$350$	−9.72455	−	6.82231i	−0.519799	−	0.364668i
$351$	−0.00807515	+	0.0139866i	−0.000431020	+	0.000746548i
$352$	0.374805	+	1.39879i	0.0199771	+	0.0745557i
$353$	4.17374	−	15.5766i	0.222146	−	0.829059i	−0.761382	−	0.648303i	$-0.775479\pi$
$353$	4.17374	−	15.5766i	0.222146	−	0.829059i	0.983528	−	0.180756i	$-0.0578544\pi$
$354$	−6.02199	+	10.4304i	−0.320065	+	0.554369i
$355$	0.500464	+	0.962443i	0.0265618	+	0.0510812i
$356$		−	2.63366i		−	0.139584i
$357$	−7.90863	−	7.90863i	−0.418569	−	0.418569i
$358$	1.67090	−	6.23587i	0.0883097	−	0.329576i
$359$	11.2520	+	6.49634i	0.593858	+	0.342864i	0.766621	−	0.642099i	$-0.221936\pi$
$359$	11.2520	+	6.49634i	0.593858	+	0.342864i	−0.172764	+	0.984963i	$0.555270\pi$
$360$	0.673362	−	2.13227i	0.0354893	−	0.112381i
$361$	−9.49170	+	16.4401i	−0.499563	+	0.865269i
$362$	−4.22681	−	15.7747i	−0.222156	−	0.829098i
$363$	−8.59955	+	2.30424i	−0.451359	+	0.120941i
$364$	0.0383699			0.00201113
$365$	2.01009	−	6.36517i	0.105213	−	0.333168i
$366$	3.95726	+	6.85417i	0.206849	+	0.358273i
$367$	−4.73840	−	17.6840i	−0.247343	−	0.923095i	−0.972191	−	0.234187i	$-0.924757\pi$
$367$	−4.73840	−	17.6840i	−0.247343	−	0.923095i	0.724849	−	0.688908i	$-0.241910\pi$
$368$	4.84571	+	4.84571i	0.252600	+	0.252600i
$369$	3.68323	−	2.12652i	0.191742	−	0.110702i
$370$	−20.6568	−	0.911246i	−1.07389	−	0.0473734i
$371$		−	27.2110i		−	1.41273i
$372$	4.54486	−	3.21625i	0.235640	−	0.166755i
$373$	14.1294	−	14.1294i	0.731592	−	0.731592i	−0.239343	−	0.970935i	$-0.576932\pi$
$373$	14.1294	−	14.1294i	0.731592	−	0.731592i	0.970935	+	0.239343i	$0.0769320\pi$
$374$		−	6.81733i		−	0.352516i
$375$	−4.29253	+	10.3235i	−0.221665	+	0.533102i
$376$	−4.97750			−0.256695
$377$	0.0742799	−	0.0199033i	0.00382561	−	0.00102507i
$378$	−0.614903	+	2.29485i	−0.0316272	+	0.118034i
$379$	−0.438587	+	0.253218i	−0.0225287	+	0.0130069i	−0.511222	−	0.859449i	$-0.670807\pi$
$379$	−0.438587	+	0.253218i	−0.0225287	+	0.0130069i	0.488693	+	0.872456i	$0.337474\pi$
$380$	−0.287771	−	0.0126947i	−0.0147624	−	0.000651222i
$381$	−1.86282	+	3.22650i	−0.0954351	+	0.165298i
$382$	−16.0358	+	4.29679i	−0.820465	+	0.219843i
$383$	9.83787	−	2.63605i	0.502692	−	0.134696i	0.00144276	−	0.999999i	$-0.499541\pi$
$383$	9.83787	−	2.63605i	0.502692	−	0.134696i	0.501249	+	0.865303i	$0.332874\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	1.66171	+	7.51153i	0.0846884	+	0.382823i
$386$	9.59647	+	16.6216i	0.488448	+	0.846016i
$387$	−2.31355	+	2.31355i	−0.117604	+	0.117604i
$388$	−6.26451	+	6.26451i	−0.318032	+	0.318032i
$389$	6.91724	+	11.9810i	0.350718	+	0.607461i	0.986375	−	0.164510i	$-0.0526043\pi$
$389$	6.91724	+	11.9810i	0.350718	+	0.607461i	−0.635658	+	0.771971i	$0.719271\pi$
$390$	−0.00780039	−	0.0352607i	−0.000394988	−	0.00178549i
$391$	−16.1305	−	27.9389i	−0.815755	−	1.41293i
$392$	−1.30938	+	0.350847i	−0.0661336	+	0.0177205i
$393$	17.3452	−	4.64763i	0.874950	−	0.234442i
$394$	−12.9089	+	22.3588i	−0.650339	+	1.12642i
$395$	17.6093	+	0.776810i	0.886019	+	0.0390856i
$396$	−1.25412	+	0.724067i	−0.0630219	+	0.0363857i
$397$	0.979778	−	3.65658i	0.0491737	−	0.183519i	−0.936971	−	0.349408i	$-0.886383\pi$
$397$	0.979778	−	3.65658i	0.0491737	−	0.183519i	0.986144	+	0.165889i	$0.0530494\pi$
$398$	8.64397	−	2.31615i	0.433283	−	0.116098i
$399$	0.306052			0.0153217
$400$	2.10900	+	4.53345i	0.105450	+	0.226672i
$401$		−	29.3221i		−	1.46427i	−0.681157	−	0.732137i	$-0.738523\pi$
$401$		−	29.3221i		−	1.46427i	0.681157	−	0.732137i	$-0.261477\pi$
$402$	4.33736	−	4.33736i	0.216328	−	0.216328i
$403$	0.0375952	−	0.0816848i	0.00187275	−	0.00406901i
$404$			2.43374i			0.121083i
$405$	2.23390	+	0.0985454i	0.111003	+	0.00489676i
$406$	9.79688	−	5.65623i	0.486211	−	0.280714i
$407$	9.46875	+	9.46875i	0.469349	+	0.469349i
$408$	1.21843	+	4.54726i	0.0603215	+	0.225123i
$409$	6.00173	+	10.3953i	0.296766	+	0.514015i	0.975394	−	0.220468i	$-0.0707584\pi$
$409$	6.00173	+	10.3953i	0.296766	+	0.514015i	−0.678628	+	0.734482i	$0.737425\pi$
$410$	−2.86383	+	9.06862i	−0.141435	+	0.447867i
$411$	22.1233			1.09126
$412$	11.0552	−	2.96223i	0.544651	−	0.145939i
$413$	7.40587	+	27.6391i	0.364419	+	1.36003i
$414$	−3.42643	+	5.93476i	−0.168400	+	0.291677i
$415$	9.67968	−	30.6517i	0.475157	−	1.50463i
$416$	−0.0139866	−	0.00807515i	−0.000685748	−	0.000395917i
$417$	−2.29878	+	8.57917i	−0.112572	+	0.420124i
$418$	0.131910	+	0.131910i	0.00645194	+	0.00645194i
$419$		−	1.12470i		−	0.0549450i	−0.999623	−	0.0274725i	$-0.991254\pi$
$419$		−	1.12470i		−	0.0549450i	0.999623	−	0.0274725i	$-0.00874586\pi$
$420$	−2.45089	−	4.71331i	−0.119591	−	0.229986i
$421$	−6.25280	+	10.8302i	−0.304743	+	0.527830i	−0.977204	−	0.212302i	$-0.931904\pi$
$421$	−6.25280	+	10.8302i	−0.304743	+	0.527830i	0.672461	+	0.740132i	$0.265237\pi$
$422$	3.36799	−	12.5695i	0.163951	−	0.611875i
$423$	−1.28827	−	4.80790i	−0.0626379	−	0.233768i
$424$	−5.72671	+	9.91895i	−0.278113	+	0.481707i
$425$	−4.06644	−	23.1844i	−0.197251	−	1.12461i
$426$			0.485131i			0.0235047i
$427$	18.1626	+	4.86666i	0.878951	+	0.235514i
$428$	−13.7116	−	3.67402i	−0.662777	−	0.177590i
$429$	−0.0116939	+	0.0202544i	−0.000564587	+	0.000977893i
$430$	0.322426	−	7.30898i	0.0155488	−	0.352470i
$431$	−2.49987	−	4.32990i	−0.120415	−	0.208564i	0.799517	−	0.600644i	$-0.205089\pi$
$431$	−2.49987	−	4.32990i	−0.120415	−	0.208564i	−0.919931	+	0.392080i	$0.871756\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	19.9954	+	19.9954i	0.960916	+	0.960916i	0.999264	−	0.0383481i	$-0.0122096\pi$
$433$	19.9954	+	19.9954i	0.960916	+	0.960916i	−0.0383481	+	0.999264i	$0.512210\pi$
$434$	2.23198	−	13.0382i	0.107138	−	0.625855i
$435$	−7.18954	−	7.85313i	−0.344712	−	0.376529i
$436$	5.28563			0.253136
$437$	0.852709	+	0.228483i	0.0407906	+	0.0109298i
$438$	2.11083	−	2.11083i	0.100859	−	0.100859i
$439$	27.3144	+	15.7700i	1.30364	+	0.752660i	0.981027	−	0.193870i	$-0.0621039\pi$
$439$	27.3144	+	15.7700i	1.30364	+	0.752660i	0.322618	+	0.946529i	$0.395437\pi$
$440$	0.975118	−	3.08781i	0.0464869	−	0.147206i
$441$	−0.677784	−	1.17396i	−0.0322755	−	0.0559027i
$442$	0.0537615	+	0.0537615i	0.00255718	+	0.00255718i
$443$	6.54982	+	24.4443i	0.311191	+	1.16138i	0.927483	+	0.373864i	$0.121967\pi$
$443$	6.54982	+	24.4443i	0.311191	+	1.16138i	−0.616292	+	0.787518i	$0.711366\pi$
$444$	−8.00811	−	4.62348i	−0.380048	−	0.219421i
$445$	−3.16643	+	4.96535i	−0.150103	+	0.235380i
$446$	1.07742	−	0.622050i	0.0510174	−	0.0294549i
$447$	0.264936	+	0.988755i	0.0125310	+	0.0467665i
$448$	−2.29485	−	0.614903i	−0.108421	−	0.0290514i
$449$	−9.72150			−0.458786			−0.229393	−	0.973334i	$-0.573674\pi$
$449$	−9.72150			−0.458786			−0.229393	+	0.973334i	$0.573674\pi$
$450$	−3.83313	+	3.21048i	−0.180695	+	0.151343i
$451$	5.33381	−	3.07948i	0.251160	−	0.145007i
$452$	−15.3527	+	4.11374i	−0.722130	+	0.193494i
$453$	−4.82176	−	1.29199i	−0.226546	−	0.0607028i
$454$	−1.30317	−	0.752385i	−0.0611607	−	0.0353112i
$455$	−0.0723402	−	0.0461318i	−0.00339136	−	0.00216269i
$456$	−0.111562	−	0.0644102i	−0.00522436	−	0.00301628i
$457$	25.5756	−	25.5756i	1.19638	−	1.19638i	0.221132	−	0.975244i	$-0.429025\pi$
$457$	25.5756	−	25.5756i	1.19638	−	1.19638i	0.975244	−	0.221132i	$-0.0709751\pi$
$458$	−4.52696	+	16.8949i	−0.211531	+	0.789445i
$459$	−4.07696	+	2.35383i	−0.190296	+	0.109868i
$460$	−3.30985	−	14.9617i	−0.154322	−	0.697595i
$461$		−	2.95878i		−	0.137804i	−0.997623	−	0.0689020i	$-0.978050\pi$
$461$		−	2.95878i		−	0.137804i	0.997623	−	0.0689020i	$-0.0219496\pi$
$462$	−0.890461	+	3.32325i	−0.0414280	+	0.154611i
$463$	10.0177	+	10.0177i	0.465561	+	0.465561i	0.900473	−	0.434912i	$-0.143220\pi$
$463$	10.0177	+	10.0177i	0.465561	+	0.465561i	−0.434912	+	0.900473i	$0.643220\pi$
$464$	−4.76154			−0.221049
$465$	−12.4355	+	0.599486i	−0.576681	+	0.0278005i
$466$	21.1091			0.977859
$467$	18.3090	+	18.3090i	0.847240	+	0.847240i	0.989788	−	0.142548i	$-0.0455296\pi$
$467$	18.3090	+	18.3090i	0.847240	+	0.847240i	−0.142548	+	0.989788i	$0.545530\pi$
$468$	0.00418001	−	0.0156000i	0.000193221	−	0.000721110i
$469$		−	14.5731i		−	0.672921i
$470$	9.38427	+	5.98440i	0.432864	+	0.276040i
$471$	−7.20249	+	4.15836i	−0.331873	+	0.191607i
$472$	3.11721	−	11.6336i	0.143481	−	0.535479i
$473$	−3.35033	+	3.35033i	−0.154048	+	0.154048i
$474$	6.82668	+	3.94138i	0.313560	+	0.181034i
$475$	0.527283	+	0.369918i	0.0241934	+	0.0169730i
$476$	9.68605	+	5.59224i	0.443959	+	0.256320i
$477$	−11.0631	−	2.96436i	−0.506547	−	0.135729i
$478$	16.4960	−	4.42008i	0.754507	−	0.202170i
$479$	26.1712	−	15.1099i	1.19579	−	0.690391i	0.236178	−	0.971710i	$-0.424105\pi$
$479$	26.1712	−	15.1099i	1.19579	−	0.690391i	0.959614	+	0.281319i	$0.0907719\pi$
$480$	−0.0985454	+	2.23390i	−0.00449796	+	0.101963i
$481$	−0.149341			−0.00680938
$482$	7.85027	+	2.10347i	0.357570	+	0.0958106i
$483$	4.21385	+	15.7263i	0.191737	+	0.715571i
$484$	7.71015	−	4.45145i	0.350461	−	0.202339i
$485$	19.3425	−	4.27895i	0.878297	−	0.194297i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−5.57605	−	20.8101i	−0.252675	−	0.942997i	−0.969369	−	0.245609i	$-0.921012\pi$
$487$	−5.57605	−	20.8101i	−0.252675	−	0.942997i	0.716694	−	0.697388i	$-0.245654\pi$
$488$	−5.59641	−	5.59641i	−0.253338	−	0.253338i
$489$	2.93258	+	5.07939i	0.132616	+	0.229698i
$490$	2.89044	+	0.912789i	0.130577	+	0.0412356i
$491$	−26.8077	−	15.4774i	−1.20982	−	0.698487i	−0.247097	−	0.968991i	$-0.579476\pi$
$491$	−26.8077	−	15.4774i	−1.20982	−	0.698487i	−0.962719	+	0.270504i	$0.912810\pi$
$492$	−3.00735	+	3.00735i	−0.135582	+	0.135582i
$493$	21.6519	+	5.80162i	0.975154	+	0.261292i
$494$	−0.00208049			−9.36056e−5
$495$	3.23498	+	0.142707i	0.145401	+	0.00641420i
$496$	−3.55757	+	4.28296i	−0.159739	+	0.192310i
$497$	0.814994	+	0.814994i	0.0365575	+	0.0365575i
$498$	10.1648	−	10.1648i	0.455494	−	0.455494i
$499$	1.14154	+	1.97721i	0.0511025	+	0.0885122i	0.890445	−	0.455091i	$-0.150393\pi$
$499$	1.14154	+	1.97721i	0.0511025	+	0.0885122i	−0.839343	+	0.543603i	$0.817060\pi$
$500$	1.47435	−	11.0827i	0.0659351	−	0.495634i
$501$	−2.17104	+	3.76036i	−0.0969950	+	0.168000i
$502$	18.5625	+	4.97380i	0.828484	+	0.221992i
$503$	−24.6440	−	6.60335i	−1.09882	−	0.294429i	−0.336538	−	0.941670i	$-0.609256\pi$
$503$	−24.6440	−	6.60335i	−1.09882	−	0.294429i	−0.762285	+	0.647241i	$0.775923\pi$
$504$		−	2.37580i		−	0.105827i
$505$	2.92607	−	4.58843i	0.130208	−	0.204182i
$506$	−4.96193	+	8.59432i	−0.220585	+	0.382064i
$507$	3.36458	+	12.5568i	0.149426	+	0.557666i
$508$	0.964266	−	3.59869i	0.0427824	−	0.159666i
$509$	4.94390	−	8.56309i	0.219135	−	0.379552i	−0.735409	−	0.677623i	$-0.763010\pi$
$509$	4.94390	−	8.56309i	0.219135	−	0.379552i	0.954544	+	0.298071i	$0.0963433\pi$
$510$	3.16997	−	10.0380i	0.140368	−	0.444491i
$511$		−	7.09215i		−	0.313738i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.0333412	−	0.124431i	0.00147205	−	0.00549376i
$514$	−2.72672	−	1.57427i	−0.120271	−	0.0694382i
$515$	−24.4042	−	7.70676i	−1.07538	−	0.339600i
$516$	1.63593	−	2.83351i	0.0720177	−	0.124738i
$517$	−1.86559	−	6.96248i	−0.0820486	−	0.306209i
$518$	−21.2204	+	5.68598i	−0.932370	+	0.249828i
$519$	21.4798			0.942859
$520$	0.0166607	+	0.0320403i	0.000730621	+	0.00140506i
$521$	−10.6716	−	18.4838i	−0.467532	−	0.809789i	0.531780	−	0.846883i	$-0.321523\pi$
$521$	−10.6716	−	18.4838i	−0.467532	−	0.809789i	−0.999312	+	0.0370934i	$0.988190\pi$
$522$	−1.23238	−	4.59929i	−0.0539396	−	0.201306i
$523$	−8.98568	−	8.98568i	−0.392916	−	0.392916i	0.482809	−	0.875726i	$-0.339616\pi$
$523$	−8.98568	−	8.98568i	−0.392916	−	0.392916i	−0.875726	+	0.482809i	$0.839616\pi$
$524$	−15.5513	+	8.97854i	−0.679361	+	0.392229i
$525$	−1.04602	+	11.8329i	−0.0456520	+	0.516428i
$526$		−	10.1585i		−	0.442931i
$527$	21.3957	−	15.1411i	0.932010	−	0.659555i
$528$	1.02398	−	1.02398i	0.0445632	−	0.0445632i
$529$			23.9618i			1.04182i
$530$	22.7222	−	11.8154i	0.986991	−	0.513228i
$531$	12.0440			0.522664
$532$	−0.295623	+	0.0792120i	−0.0128169	+	0.00343428i
$533$	−0.0177777	+	0.0663473i	−0.000770038	+	0.00287382i
$534$	−2.28082	+	1.31683i	−0.0987008	+	0.0569849i
$535$	21.4338	+	23.4121i	0.926664	+	1.01219i
$536$	−3.06698	+	5.31216i	−0.132473	+	0.229450i
$537$	−6.23587	+	1.67090i	−0.269098	+	0.0721045i
$538$	−11.5064	+	3.08313i	−0.496077	+	0.132923i
$539$	−0.981522	−	1.70005i	−0.0422772	−	0.0732262i
$540$	−2.18328	+	0.482987i	−0.0939535	+	0.0207845i
$541$	10.2969	+	17.8347i	0.442697	+	0.766774i	0.997889	−	0.0649484i	$-0.0206883\pi$
$541$	10.2969	+	17.8347i	0.442697	+	0.766774i	−0.555191	+	0.831723i	$0.687355\pi$
$542$	9.32745	−	9.32745i	0.400648	−	0.400648i
$543$	−11.5479	+	11.5479i	−0.495566	+	0.495566i
$544$	−2.35383	−	4.07696i	−0.100920	−	0.174798i
$545$	−9.96520	−	6.35487i	−0.426862	−	0.272213i
$546$	−0.0191850	−	0.0332293i	−0.000821040	−	0.00142208i
$547$	20.8810	−	5.59506i	0.892809	−	0.239227i	0.216883	−	0.976198i	$-0.430411\pi$
$547$	20.8810	−	5.59506i	0.892809	−	0.239227i	0.675925	+	0.736970i	$0.263744\pi$
$548$	−21.3694	+	5.72592i	−0.912857	+	0.244599i
$549$	3.95726	−	6.85417i	0.168892	−	0.292529i
$550$	−5.55088	+	4.64920i	−0.236690	+	0.198242i
$551$	−0.531205	+	0.306692i	−0.0226301	+	0.0130655i
$552$	1.77365	−	6.61936i	0.0754917	−	0.281739i
$553$	18.0898	−	4.84713i	0.769255	−	0.206121i
$554$	0.883709			0.0375452
$555$	9.53921	+	18.3449i	0.404917	+	0.778697i
$556$		−	8.88181i		−	0.376673i
$557$	8.62612	−	8.62612i	0.365500	−	0.365500i	−0.500333	−	0.865833i	$-0.666789\pi$
$557$	8.62612	−	8.62612i	0.365500	−	0.365500i	0.865833	+	0.500333i	$0.166789\pi$
$558$	−5.05779	−	2.32783i	−0.214113	−	0.0985451i
$559$		−	0.0528414i		−	0.00223495i
$560$	3.58727	+	3.91837i	0.151590	+	0.165581i
$561$	−5.90398	+	3.40867i	−0.249266	+	0.143914i
$562$	−16.3420	−	16.3420i	−0.689348	−	0.689348i
$563$	−10.5741	−	39.4632i	−0.445646	−	1.66317i	−0.714225	−	0.699916i	$-0.753221\pi$
$563$	−10.5741	−	39.4632i	−0.445646	−	1.66317i	0.268579	−	0.963258i	$-0.413446\pi$
$564$	2.48875	+	4.31064i	0.104795	+	0.181511i
$565$	33.8909	+	10.7026i	1.42580	+	0.450262i
$566$	−6.64704			−0.279396
$567$	2.29485	−	0.614903i	0.0963745	−	0.0258235i
$568$	−0.125561	−	0.468601i	−0.00526843	−	0.0196620i
$569$	−16.3989	+	28.4038i	−0.687480	+	1.19075i	0.285171	+	0.958477i	$0.407950\pi$
$569$	−16.3989	+	28.4038i	−0.687480	+	1.19075i	−0.972651	+	0.232273i	$0.925384\pi$
$570$	0.132892	+	0.255565i	0.00556622	+	0.0107044i
$571$	16.7384	+	9.66394i	0.700482	+	0.404423i	0.807527	−	0.589831i	$-0.200806\pi$
$571$	16.7384	+	9.66394i	0.700482	+	0.404423i	−0.107045	+	0.994254i	$0.534139\pi$
$572$	0.00605321	−	0.0225909i	0.000253097	−	0.000944572i
$573$	11.7391	+	11.7391i	0.490406	+	0.490406i
$574$			10.1044i			0.421748i
$575$	−11.7482	+	32.1873i	−0.489933	+	1.34231i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	11.0054	−	41.0727i	0.458160	−	1.70988i	−0.220466	−	0.975395i	$-0.570758\pi$
$577$	11.0054	−	41.0727i	0.458160	−	1.70988i	0.678626	−	0.734484i	$-0.262576\pi$
$578$	1.33606	+	4.98625i	0.0555729	+	0.207401i
$579$	9.59647	−	16.6216i	0.398816	−	0.690769i
$580$	8.97710	+	5.72475i	0.372754	+	0.237707i
$581$		−	34.1525i		−	1.41688i
$582$	8.55748	+	2.29297i	0.354719	+	0.0950467i
$583$	−16.0209	−	4.29279i	−0.663519	−	0.177789i
$584$	−1.49258	+	2.58522i	−0.0617634	+	0.106977i
$585$	−0.0266364	+	0.0243857i	−0.00110128	+	0.00100822i
$586$	3.44825	+	5.97255i	0.142446	+	0.246724i
$587$	−1.88396	+	1.88396i	−0.0777594	+	0.0777594i	−0.744917	−	0.667157i	$-0.767511\pi$
$587$	−1.88396	+	1.88396i	−0.0777594	+	0.0777594i	0.667157	+	0.744917i	$0.267511\pi$
$588$	0.958532	+	0.958532i	0.0395292	+	0.0395292i
$589$	−0.121022	+	0.706958i	−0.00498663	+	0.0291297i
$590$	−19.8639	+	18.1854i	−0.817786	+	0.748683i
$591$	25.8177			1.06200
$592$	8.93188	+	2.39329i	0.367098	+	0.0983636i
$593$	15.1310	−	15.1310i	0.621357	−	0.621357i	−0.324521	−	0.945878i	$-0.605203\pi$
$593$	15.1310	−	15.1310i	0.621357	−	0.621357i	0.945878	+	0.324521i	$0.105203\pi$
$594$	1.25412	+	0.724067i	0.0514572	+	0.0297088i
$595$	−11.5380	−	22.1887i	−0.473011	−	0.909648i
$596$	−0.511817	−	0.886493i	−0.0209648	−	0.0363122i
$597$	−6.32783	−	6.32783i	−0.258981	−	0.258981i
$598$	−0.0286450	−	0.106905i	−0.00117138	−	0.00437166i
$599$	−17.3332	−	10.0073i	−0.708214	−	0.408888i	0.102185	−	0.994765i	$-0.467417\pi$
$599$	−17.3332	−	10.0073i	−0.708214	−	0.408888i	−0.810400	+	0.585878i	$0.800750\pi$
$600$	2.87158	−	4.09317i	0.117232	−	0.167103i
$601$	−22.4932	+	12.9864i	−0.917516	+	0.529728i	−0.882842	−	0.469671i	$-0.844373\pi$
$601$	−22.4932	+	12.9864i	−0.917516	+	0.529728i	−0.0346740	+	0.999399i	$0.511039\pi$
$602$	−2.01187	−	7.50841i	−0.0819978	−	0.306020i
$603$	−5.92494	−	1.58758i	−0.241282	−	0.0646514i
$604$	4.99185			0.203116
$605$	−19.8882	−	0.877341i	−0.808569	−	0.0356690i
$606$	2.10768	−	1.21687i	0.0856188	−	0.0494320i
$607$	−21.5732	+	5.78052i	−0.875628	+	0.234624i	−0.668520	−	0.743694i	$-0.733072\pi$
$607$	−21.5732	+	5.78052i	−0.875628	+	0.234624i	−0.207108	+	0.978318i	$0.566405\pi$
$608$	0.124431	+	0.0333412i	0.00504634	+	0.00135216i
$609$	−9.79688	−	5.65623i	−0.396990	−	0.229202i
$610$	3.82261	+	17.2796i	0.154773	+	0.699632i
$611$	0.0696182	+	0.0401941i	0.00281645	+	0.00162608i
$612$	3.32882	−	3.32882i	0.134560	−	0.134560i
$613$	4.90442	−	18.3036i	0.198088	−	0.739274i	−0.793358	−	0.608755i	$-0.791669\pi$
$613$	4.90442	−	18.3036i	0.198088	−	0.739274i	0.991446	−	0.130519i	$-0.0416642\pi$
$614$	−10.3277	+	5.96268i	−0.416790	+	0.240634i
$615$	9.28557	−	2.05416i	0.374430	−	0.0828317i
$616$		−	3.44048i		−	0.138621i
$617$	−5.25473	+	19.6109i	−0.211548	+	0.789506i	0.775806	+	0.630972i	$0.217344\pi$
$617$	−5.25473	+	19.6109i	−0.211548	+	0.789506i	−0.987353	+	0.158535i	$0.949323\pi$
$618$	−8.09297	−	8.09297i	−0.325547	−	0.325547i
$619$	−40.9798			−1.64712			−0.823558	−	0.567232i	$-0.808014\pi$
$619$	−40.9798			−1.64712			−0.823558	+	0.567232i	$0.808014\pi$
$620$	11.8566	−	3.79759i	0.476171	−	0.152515i
$621$	6.85287			0.274996
$622$	−10.5302	−	10.5302i	−0.422224	−	0.422224i
$623$	−1.61945	+	6.04386i	−0.0648818	+	0.242142i
$624$			0.0161503i			0.000646530i
$625$	−16.1043	+	19.1220i	−0.644171	+	0.764881i
$626$	7.95587	−	4.59333i	0.317981	−	0.183586i
$627$	0.0482825	−	0.180193i	0.00192822	−	0.00719620i
$628$	5.88081	−	5.88081i	0.234670	−	0.234670i
$629$	−37.6995	−	21.7658i	−1.50318	−	0.867860i
$630$	−2.85640	+	4.47919i	−0.113802	+	0.178455i
$631$	3.17739	+	1.83447i	0.126490	+	0.0730291i	0.561910	−	0.827198i	$-0.310067\pi$
$631$	3.17739	+	1.83447i	0.126490	+	0.0730291i	−0.435420	+	0.900227i	$0.643400\pi$
$632$	−7.61417	−	2.04021i	−0.302875	−	0.0811552i
$633$	−12.5695	+	3.36799i	−0.499593	+	0.133866i
$634$	7.32344	−	4.22819i	0.290851	−	0.167923i
$635$	−6.14464	+	5.62542i	−0.243842	+	0.223238i
$636$	11.4534			0.454157
$637$	0.0211469	+	0.00566629i	0.000837869	+	0.000224506i
$638$	−1.78465	−	6.66039i	−0.0706548	−	0.263687i
$639$	0.420136	−	0.242566i	0.0166203	−	0.00959574i
$640$	−0.482987	−	2.18328i	−0.0190917	−	0.0863018i
$641$	30.3941	+	17.5480i	1.20049	+	0.693105i	0.960665	−	0.277710i	$-0.0895753\pi$
$641$	30.3941	+	17.5480i	1.20049	+	0.693105i	0.239829	+	0.970815i	$0.422909\pi$
$642$	3.67402	+	13.7116i	0.145002	+	0.541155i
$643$	−22.5663	−	22.5663i	−0.889926	−	0.889926i	0.104589	−	0.994516i	$-0.466647\pi$
$643$	−22.5663	−	22.5663i	−0.889926	−	0.889926i	−0.994516	+	0.104589i	$0.966647\pi$
$644$	−8.14053	−	14.0998i	−0.320782	−	0.555610i
$645$	−6.49097	+	3.37526i	−0.255582	+	0.132901i
$646$	−0.525196	−	0.303222i	−0.0206636	−	0.0119301i
$647$	25.1982	−	25.1982i	0.990644	−	0.990644i	−0.00931269	−	0.999957i	$-0.502964\pi$
$647$	25.1982	−	25.1982i	0.990644	−	0.990644i	0.999957	+	0.00931269i	$0.00296436\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	17.4413			0.684630
$650$	0.00711066	−	0.0804378i	0.000278903	−	0.00315503i
$651$	−12.4074	+	4.58617i	−0.486286	+	0.179746i
$652$	−4.14730	−	4.14730i	−0.162421	−	0.162421i
$653$	−19.4627	+	19.4627i	−0.761634	+	0.761634i	−0.976618	−	0.214984i	$-0.931030\pi$
$653$	−19.4627	+	19.4627i	−0.761634	+	0.761634i	0.214984	+	0.976618i	$0.431030\pi$
$654$	−2.64282	−	4.57749i	−0.103342	−	0.178994i
$655$	40.1142	+	1.76959i	1.56739	+	0.0691435i
$656$	2.12652	−	3.68323i	0.0830265	−	0.143806i
$657$	−2.88344	−	0.772616i	−0.112494	−	0.0301426i
$658$	11.4226	+	3.06068i	0.445300	+	0.119318i
$659$			15.4862i			0.603257i	0.953426	+	0.301628i	$0.0975302\pi$
$659$			15.4862i			0.603257i	−0.953426	+	0.301628i	$0.902470\pi$
$660$	−3.16168	+	0.699430i	−0.123068	+	0.0272253i
$661$	−10.0496	+	17.4065i	−0.390885	+	0.677033i	−0.992567	−	0.121703i	$-0.961164\pi$
$661$	−10.0496	+	17.4065i	−0.390885	+	0.677033i	0.601681	+	0.798736i	$0.294498\pi$
$662$	−7.66282	−	28.5980i	−0.297824	−	1.11149i
$663$	0.0196781	−	0.0734396i	0.000764234	−	0.00285216i
$664$	−7.18757	+	12.4492i	−0.278932	+	0.483124i
$665$	0.652585	+	0.206084i	0.0253062	+	0.00799158i
$666$			9.24696i			0.358313i
$667$	−23.0730	−	23.0730i	−0.893391	−	0.893391i
$668$	1.12381	−	4.19413i	0.0434817	−	0.162276i
$669$	−1.07742	−	0.622050i	−0.0416556	−	0.0240498i
$670$	12.1690	−	6.32782i	0.470131	−	0.244465i
$671$	5.73064	−	9.92576i	0.221229	−	0.383180i
$672$	0.614903	+	2.29485i	0.0237204	+	0.0885257i
$673$	14.0669	−	3.76920i	0.542238	−	0.145292i	0.0227041	−	0.999742i	$-0.492772\pi$
$673$	14.0669	−	3.76920i	0.542238	−	0.145292i	0.519533	+	0.854450i	$0.326106\pi$
$674$	−12.3191			−0.474515
$675$	4.69692	+	1.71435i	0.180784	+	0.0659852i
$676$	−6.49987	−	11.2581i	−0.249995	−	0.433004i
$677$	3.23165	+	12.0607i	0.124202	+	0.463529i	0.999810	−	0.0194937i	$-0.00620543\pi$
$677$	3.23165	+	12.0607i	0.124202	+	0.463529i	−0.875608	+	0.483023i	$0.839539\pi$
$678$	11.2390	+	11.2390i	0.431629	+	0.431629i
$679$	18.2282	−	10.5240i	0.699533	−	0.403875i
$680$	−0.463919	+	10.5164i	−0.0177905	+	0.403287i
$681$			1.50477i			0.0576629i
$682$	−7.32435	−	3.37101i	−0.280464	−	0.129083i
$683$	0.0361743	−	0.0361743i	0.00138417	−	0.00138417i	−0.706414	−	0.707799i	$-0.749688\pi$
$683$	0.0361743	−	0.0361743i	0.00138417	−	0.00138417i	0.707799	+	0.706414i	$0.249688\pi$
$684$			0.128820i			0.00492557i
$685$	47.1728	+	14.8970i	1.80238	+	0.569184i
$686$	19.8512			0.757921
$687$	16.8949	−	4.52696i	0.644579	−	0.172714i
$688$	−0.846818	+	3.16037i	−0.0322846	+	0.120488i
$689$	0.160194	−	0.0924881i	0.00610291	−	0.00352351i
$690$	−11.3023	+	10.3473i	−0.430272	+	0.393914i
$691$	−3.32852	+	5.76516i	−0.126623	+	0.219317i	−0.922366	−	0.386317i	$-0.873747\pi$
$691$	−3.32852	+	5.76516i	−0.126623	+	0.219317i	0.795743	+	0.605634i	$0.207080\pi$
$692$	−20.7479	+	5.55939i	−0.788717	+	0.211336i
$693$	3.32325	−	0.890461i	0.126240	−	0.0338258i
$694$	−2.57749	−	4.46434i	−0.0978402	−	0.169464i
$695$	−10.6785	+	16.7452i	−0.405059	+	0.635182i
$696$	2.38077	+	4.12361i	0.0902428	+	0.156305i
$697$	−14.1576	+	14.1576i	−0.536257	+	0.536257i
$698$	−5.73455	+	5.73455i	−0.217056	+	0.217056i
$699$	−10.5545	−	18.2810i	−0.399209	−	0.691450i
$700$	−2.05219	−	11.7004i	−0.0775657	−	0.442233i
$701$	7.76699	+	13.4528i	0.293355	+	0.508106i	0.974601	−	0.223949i	$-0.0718948\pi$
$701$	7.76699	+	13.4528i	0.293355	+	0.508106i	−0.681246	+	0.732055i	$0.738562\pi$
$702$	−0.0156000	+	0.00418001i	−0.000588784	+	0.000157764i
$703$	1.15061	−	0.308305i	0.0433960	−	0.0116279i
$704$	−0.724067	+	1.25412i	−0.0272893	+	0.0472664i
$705$	0.490510	−	11.1192i	0.0184737	−	0.418774i
$706$	13.9656	−	8.06305i	0.525602	−	0.303457i
$707$	1.49651	−	5.58507i	0.0562822	−	0.210048i
$708$	−11.6336	+	3.11721i	−0.437217	+	0.117152i
$709$	−1.31850			−0.0495172			−0.0247586	−	0.999693i	$-0.507882\pi$
$709$	−1.31850			−0.0495172			−0.0247586	+	0.999693i	$0.507882\pi$
$710$	−0.326669	+	1.03443i	−0.0122597	+	0.0388215i
$711$		−	7.88277i		−	0.295627i
$712$	1.86228	−	1.86228i	0.0697920	−	0.0697920i
$713$	−37.9929	+	3.51504i	−1.42285	+	0.131639i
$714$		−	11.1845i		−	0.418569i
$715$	−0.0385731	+	0.0353137i	−0.00144255	+	0.00132066i
$716$	5.59093	−	3.22793i	0.208943	−	0.120633i
$717$	−12.0759	−	12.0759i	−0.450982	−	0.450982i
$718$	3.36275	+	12.5500i	0.125497	+	0.468361i
$719$	−11.0120	−	19.0733i	−0.410677	−	0.711314i	0.584287	−	0.811547i	$-0.301374\pi$
$719$	−11.0120	−	19.0733i	−0.410677	−	0.711314i	−0.994964	+	0.100233i	$0.968041\pi$
$720$	1.98388	−	1.03160i	0.0739349	−	0.0384456i
$721$	−27.1915			−1.01266
$722$	−18.3366	+	4.91327i	−0.682416	+	0.182853i
$723$	−2.10347	−	7.85027i	−0.0782290	−	0.291955i
$724$	8.16557	−	14.1432i	0.303471	−	0.525627i
$725$	−10.0421	−	21.5862i	−0.372953	−	0.801690i
$726$	−7.71015	−	4.45145i	−0.286150	−	0.165209i
$727$	−11.2161	+	41.8592i	−0.415984	+	1.55247i	0.366874	+	0.930271i	$0.380428\pi$
$727$	−11.2161	+	41.8592i	−0.415984	+	1.55247i	−0.782858	+	0.622201i	$0.786239\pi$
$728$	0.0271316	+	0.0271316i	0.00100556	+	0.00100556i
$729$		−	1.00000i		−	0.0370370i
$730$	5.92221	−	3.07951i	0.219191	−	0.113978i
$731$	7.70140	−	13.3392i	0.284847	−	0.493369i
$732$	−2.04843	+	7.64484i	−0.0757121	+	0.282561i
$733$	9.50328	+	35.4667i	0.351012	+	1.30999i	0.885430	+	0.464773i	$0.153864\pi$
$733$	9.50328	+	35.4667i	0.351012	+	1.30999i	−0.534418	+	0.845220i	$0.679469\pi$
$734$	9.15389	−	15.8550i	0.337876	−	0.585219i
$735$	−0.654722	−	2.95959i	−0.0241498	−	0.109166i
$736$			6.85287i			0.252600i
$737$	−8.58011	−	2.29903i	−0.316052	−	0.0846860i
$738$	4.10811	+	1.10077i	0.151222	+	0.0405197i
$739$	9.42009	−	16.3161i	0.346524	−	0.600197i	−0.639106	−	0.769119i	$-0.720695\pi$
$739$	9.42009	−	16.3161i	0.346524	−	0.600197i	0.985629	+	0.168922i	$0.0540287\pi$
$740$	−13.9622	−	15.2509i	−0.513260	−	0.560633i
$741$	0.00104024	+	0.00180176i	3.82143e−5	+	6.61892e-5i
$742$	19.2411	−	19.2411i	0.706363	−	0.706363i
$743$	−13.8826	−	13.8826i	−0.509303	−	0.509303i	0.405009	−	0.914313i	$-0.367268\pi$
$743$	−13.8826	−	13.8826i	−0.509303	−	0.509303i	−0.914313	+	0.405009i	$0.867268\pi$
$744$	5.48793	+	0.939464i	0.201197	+	0.0344424i
$745$	−0.100874	+	2.28669i	−0.00369575	+	0.0837779i
$746$	19.9820			0.731592
$747$	−13.8853	−	3.72056i	−0.508037	−	0.136128i
$748$	4.82058	−	4.82058i	0.176258	−	0.176258i
$749$	29.2069	+	16.8626i	1.06720	+	0.616147i
$750$	−10.3351	+	4.26452i	−0.377384	+	0.155718i
$751$	−5.67296	−	9.82586i	−0.207009	−	0.358551i	0.743762	−	0.668445i	$-0.233040\pi$
$751$	−5.67296	−	9.82586i	−0.207009	−	0.358551i	−0.950771	+	0.309894i	$0.899706\pi$
$752$	−3.51963	−	3.51963i	−0.128348	−	0.128348i
$753$	−4.97380	−	18.5625i	−0.181255	−	0.676455i
$754$	0.0665976	+	0.0384501i	0.00242534	+	0.00140027i
$755$	−9.41132	−	6.00165i	−0.342513	−	0.218423i
$756$	−2.05750	+	1.18790i	−0.0748307	+	0.0432035i
$757$	4.96356	+	18.5243i	0.180404	+	0.673276i	0.995568	+	0.0940459i	$0.0299800\pi$
$757$	4.96356	+	18.5243i	0.180404	+	0.673276i	−0.815164	+	0.579230i	$0.803353\pi$
$758$	−0.489180	−	0.131075i	−0.0177678	−	0.00476087i
$759$	9.92387			0.360214
$760$	−0.194509	−	0.212462i	−0.00705557	−	0.00770679i
$761$	−35.4152	+	20.4470i	−1.28380	+	0.741203i	−0.977541	−	0.210744i	$-0.932411\pi$
$761$	−35.4152	+	20.4470i	−1.28380	+	0.741203i	−0.306261	+	0.951948i	$0.599078\pi$
$762$	−3.59869	+	0.964266i	−0.130367	+	0.0349317i
$763$	−12.1297	−	3.25015i	−0.439125	−	0.117663i
$764$	−14.3773	−	8.30077i	−0.520154	−	0.300311i
$765$	−10.2782	+	2.27374i	−0.371608	+	0.0822074i
$766$	8.82039	+	5.09246i	0.318694	+	0.183998i
$767$	−0.137542	+	0.137542i	−0.00496636	+	0.00496636i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	0.0461985	−	0.0266727i	0.00166596	−	0.000961842i	−0.499167	−	0.866506i	$-0.666361\pi$
$769$	0.0461985	−	0.0266727i	0.00166596	−	0.000961842i	0.500833	+	0.865544i	$0.333027\pi$
$770$	−4.13645	+	6.48646i	−0.149067	+	0.233756i
$771$			3.14855i			0.113392i
$772$	−4.96750	+	18.5390i	−0.178784	+	0.667232i
$773$	−36.5683	−	36.5683i	−1.31527	−	1.31527i	−0.917472	−	0.397799i	$-0.869774\pi$
$773$	−36.5683	−	36.5683i	−1.31527	−	1.31527i	−0.397799	−	0.917472i	$-0.630226\pi$
$774$	−3.27185			−0.117604
$775$	−26.9194	−	7.09530i	−0.966975	−	0.254871i
$776$	−8.85935			−0.318032
$777$	15.5344	+	15.5344i	0.557293	+	0.557293i
$778$	−3.58063	+	13.3631i	−0.128372	+	0.479089i
$779$		−	0.547877i		−	0.0196297i
$780$	0.0194174	−	0.0304488i	0.000695253	−	0.00109024i
$781$	0.608413	−	0.351267i	0.0217707	−	0.0125693i
$782$	8.34977	−	31.1618i	0.298587	−	1.11434i
$783$	−3.36691	+	3.36691i	−0.120324	+	0.120324i
$784$	−1.17396	−	0.677784i	−0.0419270	−	0.0242066i
$785$	−18.1578	+	4.01687i	−0.648078	+	0.143368i
$786$	15.5513	+	8.97854i	0.554696	+	0.320254i
$787$	−39.2315	−	10.5120i	−1.39845	−	0.374714i	−0.520663	−	0.853762i	$-0.674315\pi$
$787$	−39.2315	−	10.5120i	−1.39845	−	0.374714i	−0.877789	+	0.479048i	$0.840982\pi$
$788$	−24.9380	+	6.68212i	−0.888380	+	0.238041i
$789$	−8.79752	+	5.07925i	−0.313200	+	0.180826i
$790$	11.9024	+	13.0009i	0.423467	+	0.462552i
$791$	37.7616			1.34265
$792$	−1.39879	−	0.374805i	−0.0497038	−	0.0133181i
$793$	0.0330827	+	0.123466i	0.00117480	+	0.00438442i
$794$	3.27840	−	1.89279i	0.116346	−	0.0671725i
$795$	−21.5936	−	13.7703i	−0.765844	−	0.488383i
$796$	7.74997	+	4.47445i	0.274691	+	0.158593i
$797$	−12.4931	−	46.6249i	−0.442528	−	1.65154i	−0.722382	−	0.691495i	$-0.756953\pi$
$797$	−12.4931	−	46.6249i	−0.442528	−	1.65154i	0.279854	−	0.960043i	$-0.409714\pi$
$798$	0.216411	+	0.216411i	0.00766087	+	0.00766087i
$799$	11.7162	+	20.2931i	0.414490	+	0.717918i
$800$	−1.71435	+	4.69692i	−0.0606113	+	0.166061i
$801$	2.28082	+	1.31683i	0.0805888	+	0.0465280i
$802$	20.7338	−	20.7338i	0.732137	−	0.732137i
$803$	−4.17561	−	1.11885i	−0.147354	−	0.0394834i
$804$	6.13395			0.216328
$805$	−1.60442	+	36.3702i	−0.0565485	+	1.28188i
$806$	0.0843437	−	0.0311760i	0.00297088	−	0.00109813i
$807$	8.42328	+	8.42328i	0.296513	+	0.296513i
$808$	−1.72092	+	1.72092i	−0.0605416	+	0.0605416i
$809$	−3.57196	−	6.18682i	−0.125583	−	0.217517i	0.796377	−	0.604800i	$-0.206747\pi$
$809$	−3.57196	−	6.18682i	−0.125583	−	0.217517i	−0.921961	+	0.387283i	$0.873414\pi$
$810$	1.50992	+	1.64928i	0.0530532	+	0.0579500i
$811$	−22.9139	+	39.6881i	−0.804618	+	1.39364i	0.111931	+	0.993716i	$0.464296\pi$
$811$	−22.9139	+	39.6881i	−0.804618	+	1.39364i	−0.916549	+	0.399923i	$0.869037\pi$
$812$	10.9270	+	2.92788i	0.383463	+	0.102748i
$813$	−12.7415	−	3.41408i	−0.446865	−	0.119737i
$814$			13.3908i			0.469349i
$815$	2.83280	+	12.8053i	0.0992287	+	0.448551i
$816$	−2.35383	+	4.07696i	−0.0824007	+	0.142722i
$817$	0.109087	+	0.407120i	0.00381649	+	0.0142433i
$818$	−3.10672	+	11.5945i	−0.108624	+	0.405390i
$819$	−0.0191850	+	0.0332293i	−0.000670377	+	0.00116113i
$820$	−8.43752	+	4.38745i	−0.294651	+	0.153216i
$821$		−	33.4305i		−	1.16673i	−0.812209	−	0.583366i	$-0.801735\pi$
$821$		−	33.4305i		−	1.16673i	0.812209	−	0.583366i	$-0.198265\pi$
$822$	15.6435	+	15.6435i	0.545630	+	0.545630i
$823$	0.886971	−	3.31022i	0.0309179	−	0.115387i	−0.948742	−	0.316050i	$-0.897643\pi$
$823$	0.886971	−	3.31022i	0.0309179	−	0.115387i	0.979660	+	0.200663i	$0.0643098\pi$
$824$	9.91182	+	5.72259i	0.345295	+	0.199356i
$825$	6.80176	+	2.48260i	0.236807	+	0.0864331i
$826$	−14.3070	+	24.7805i	−0.497806	+	0.862225i
$827$	13.0535	+	48.7162i	0.453914	+	1.69403i	0.691262	+	0.722604i	$0.257055\pi$
$827$	13.0535	+	48.7162i	0.453914	+	1.69403i	−0.237348	+	0.971425i	$0.576278\pi$
$828$	−6.61936	+	1.77365i	−0.230039	+	0.0616387i
$829$	−7.38536			−0.256504			−0.128252	−	0.991742i	$-0.540937\pi$
$829$	−7.38536			−0.256504			−0.128252	+	0.991742i	$0.540937\pi$
$830$	28.5186	−	14.8295i	0.989895	−	0.514738i
$831$	−0.441855	−	0.765314i	−0.0153278	−	0.0265485i
$832$	−0.00418001	−	0.0156000i	−0.000144916	−	0.000540833i
$833$	4.51245	+	4.51245i	0.156347	+	0.156347i
$834$	−7.69187	+	4.44090i	−0.266348	+	0.153776i
$835$	−7.16134	+	6.55620i	−0.247828	+	0.226887i
$836$			0.186549i			0.00645194i
$837$	0.512929	+	5.54409i	0.0177294	+	0.191632i
$838$	0.795280	−	0.795280i	0.0274725	−	0.0274725i
$839$		−	0.373679i		−	0.0129008i	−0.999979	−	0.00645041i	$-0.997947\pi$
$839$		−	0.373679i		−	0.0129008i	0.999979	−	0.00645041i	$-0.00205324\pi$
$840$	1.59977	−	5.06585i	0.0551975	−	0.174789i
$841$	−6.32777			−0.218199
$842$	−12.0795	+	3.23669i	−0.416287	+	0.111544i
$843$	−5.98160	+	22.3237i	−0.206017	+	0.768867i
$844$	11.2695	−	6.50646i	0.387913	−	0.223962i
$845$	−1.28106	+	29.0401i	−0.0440699	+	0.999008i
$846$	2.48875	−	4.31064i	0.0855650	−	0.148203i
$847$	−20.4308	+	5.47442i	−0.702011	+	0.188103i
$848$	−11.0631	+	2.96436i	−0.379910	+	0.101797i
$849$	3.32352	+	5.75650i	0.114063	+	0.197563i
$850$	13.5185	−	19.2693i	0.463679	−	0.660931i
$851$	31.6841	+	54.8785i	1.08612	+	1.88121i
$852$	−0.343039	+	0.343039i	−0.0117523	+	0.0117523i
$853$	−17.7832	+	17.7832i	−0.608884	+	0.608884i	−0.942654	−	0.333770i	$-0.891679\pi$
$853$	−17.7832	+	17.7832i	−0.608884	+	0.608884i	0.333770	+	0.942654i	$0.391679\pi$
$854$	9.40166	+	16.2842i	0.321718	+	0.557232i
$855$	0.154880	−	0.242870i	0.00529677	−	0.00830598i
$856$	−7.09766	−	12.2935i	−0.242593	−	0.420184i
$857$	−24.9347	+	6.68124i	−0.851754	+	0.228227i	−0.658181	−	0.752859i	$-0.728674\pi$
$857$	−24.9347	+	6.68124i	−0.851754	+	0.228227i	−0.193572	+	0.981086i	$0.562007\pi$
$858$	−0.0225909	+	0.00605321i	−0.000771240	+	0.000206653i
$859$	7.21136	−	12.4904i	0.246048	−	0.426168i	−0.716378	−	0.697713i	$-0.754201\pi$
$859$	7.21136	−	12.4904i	0.246048	−	0.426168i	0.962426	+	0.271545i	$0.0875345\pi$
$860$	5.39622	−	4.94024i	0.184010	−	0.168461i
$861$	8.75063	−	5.05218i	0.298221	−	0.172178i
$862$	1.29403	−	4.82938i	0.0440748	−	0.164489i
$863$	21.3316	−	5.71579i	0.726137	−	0.194568i	0.123229	−	0.992378i	$-0.460675\pi$
$863$	21.3316	−	5.71579i	0.726137	−	0.194568i	0.602908	+	0.797811i	$0.294009\pi$
$864$	1.00000			0.0340207
$865$	45.8008	+	14.4637i	1.55727	+	0.491781i
$866$			28.2777i			0.960916i
$867$	3.65019	−	3.65019i	0.123967	−	0.123967i
$868$	10.7977	−	7.64118i	0.366497	−	0.259358i
$869$		−	11.4153i		−	0.387238i
$870$	0.469227	−	10.6368i	0.0159083	−	0.360620i
$871$	0.0857930	−	0.0495326i	0.00290698	−	0.00167835i
$872$	3.73751	+	3.73751i	0.126568	+	0.126568i
$873$	−2.29297	−	8.55748i	−0.0776053	−	0.289627i
$874$	0.441395	+	0.764518i	0.0149304	+	0.0258602i
$875$	−10.1982	+	24.5265i	−0.344762	+	0.829148i
$876$	2.98516			0.100859
$877$	−53.2171	+	14.2595i	−1.79701	+	0.481508i	−0.993505	−	0.113785i	$-0.963703\pi$
$877$	−53.2171	+	14.2595i	−1.79701	+	0.481508i	−0.803509	+	0.595293i	$0.797036\pi$
$878$	8.16314	+	30.4652i	0.275493	+	1.02815i
$879$	3.44825	−	5.97255i	0.116307	−	0.201449i
$880$	2.87293	−	1.49390i	0.0968464	−	0.0503594i
$881$	−15.0806	−	8.70681i	−0.508080	−	0.293340i	0.223964	−	0.974597i	$-0.428100\pi$
$881$	−15.0806	−	8.70681i	−0.508080	−	0.293340i	−0.732044	+	0.681257i	$0.761433\pi$
$882$	0.350847	−	1.30938i	0.0118136	−	0.0440891i
$883$	−13.7831	−	13.7831i	−0.463839	−	0.463839i	0.436072	−	0.899912i	$-0.356369\pi$
$883$	−13.7831	−	13.7831i	−0.463839	−	0.463839i	−0.899912	+	0.436072i	$0.856369\pi$
$884$			0.0760303i			0.00255718i
$885$	25.6810	+	8.10996i	0.863258	+	0.272613i
$886$	−12.6533	+	21.9161i	−0.425095	+	0.736287i
$887$	7.61094	−	28.4044i	0.255550	−	0.953726i	−0.712233	−	0.701943i	$-0.752316\pi$
$887$	7.61094	−	28.4044i	0.255550	−	0.953726i	0.967784	−	0.251784i	$-0.0810171\pi$
$888$	−2.39329	−	8.93188i	−0.0803136	−	0.299734i
$889$	−4.42569	+	7.66551i	−0.148433	+	0.257093i
$890$	−5.75003	+	1.27203i	−0.192742	+	0.0426384i
$891$		−	1.44813i		−	0.0485143i
$892$	1.20171	+	0.321997i	0.0402362	+	0.0107812i
$893$	−0.619355	−	0.165956i	−0.0207259	−	0.00555350i
$894$	−0.511817	+	0.886493i	−0.0171177	+	0.0296488i
$895$	−14.4217	−	0.636194i	−0.482064	−	0.0212656i
$896$	−1.18790	−	2.05750i	−0.0396850	−	0.0687364i
$897$	−0.0782597	+	0.0782597i	−0.00261301	+	0.00261301i
$898$	−6.87414	−	6.87414i	−0.229393	−	0.229393i
$899$	16.9395	−	20.3935i	0.564963	−	0.680160i
$900$	−4.98058	−	0.440280i	−0.166019	−	0.0146760i
$901$	53.9189			1.79630
$902$	5.94910	+	1.59406i	0.198083	+	0.0530763i
$903$	−5.49653	+	5.49653i	−0.182913	+	0.182913i
$904$	−13.7649	−	7.94714i	−0.457812	−	0.264318i
$905$	−32.3991	+	16.8473i	−1.07698	+	0.560023i
$906$	−2.49593	−	4.32307i	−0.0829216	−	0.143624i
$907$	9.03204	+	9.03204i	0.299904	+	0.299904i	0.840976	−	0.541072i	$-0.181981\pi$
$907$	9.03204	+	9.03204i	0.299904	+	0.299904i	−0.541072	+	0.840976i	$0.681981\pi$
$908$	−0.389463	−	1.45350i	−0.0129248	−	0.0482359i
$909$	−2.10768	−	1.21687i	−0.0699074	−	0.0403611i
$910$	−0.0185322	−	0.0837724i	−0.000614336	−	0.00277703i
$911$	−3.25654	+	1.88017i	−0.107894	+	0.0622927i	−0.552976	−	0.833197i	$-0.686508\pi$
$911$	−3.25654	+	1.88017i	−0.107894	+	0.0622927i	0.445082	+	0.895490i	$0.353175\pi$
$912$	−0.0333412	−	0.124431i	−0.00110404	−	0.00412032i
$913$	−20.1078	−	5.38787i	−0.665471	−	0.178312i
$914$	36.1693			1.19638
$915$	13.0533	−	11.9503i	0.431529	−	0.395065i
$916$	−15.1475	+	8.74542i	−0.500488	+	0.288957i
$917$	41.2087	−	11.0418i	1.36083	−	0.364634i
$918$	−4.54726	−	1.21843i	−0.150082	−	0.0402143i
$919$	31.4924	+	18.1821i	1.03884	+	0.599773i	0.919504	−	0.393081i	$-0.128591\pi$
$919$	31.4924	+	18.1821i	1.03884	+	0.599773i	0.119333	+	0.992854i	$0.461924\pi$
$920$	8.23914	−	12.9200i	0.271636	−	0.425959i
$921$	10.3277	+	5.96268i	0.340308	+	0.196477i
$922$	2.09217	−	2.09217i	0.0689020	−	0.0689020i
$923$	−0.00202785	+	0.00756804i	−6.67475e−5	+	0.000249105i
$924$	−2.97954	+	1.72024i	−0.0980197	+	0.0565917i
$925$	7.98744	+	45.5396i	0.262625	+	1.49733i
$926$			14.1671i			0.465561i
$927$	−2.96223	+	11.0552i	−0.0972925	+	0.363100i
$928$	−3.36691	−	3.36691i	−0.110524	−	0.110524i
$929$	−45.7395			−1.50066			−0.750332	−	0.661061i	$-0.770106\pi$
$929$	−45.7395			−1.50066			−0.750332	+	0.661061i	$0.770106\pi$
$930$	−9.21710	−	8.36930i	−0.302241	−	0.274440i
$931$	−0.174625			−0.00572310
$932$	14.9264	+	14.9264i	0.488929	+	0.488929i
$933$	−3.85433	+	14.3846i	−0.126185	+	0.470929i
$934$			25.8928i			0.847240i
$935$	−14.8842	+	3.29268i	−0.486764	+	0.107682i
$936$	0.0139866	−	0.00807515i	0.000457165	−	0.000263945i
$937$	−0.0737171	+	0.275116i	−0.00240823	+	0.00898765i	−0.967119	−	0.254322i	$-0.918148\pi$
$937$	−0.0737171	+	0.275116i	−0.00240823	+	0.00898765i	0.964711	+	0.263310i	$0.0848142\pi$
$938$	10.3047	−	10.3047i	0.336461	−	0.336461i
$939$	−7.95587	−	4.59333i	−0.259630	−	0.149898i
$940$	2.40407	+	10.8673i	0.0784121	+	0.354452i
$941$	0.876874	+	0.506264i	0.0285853	+	0.0165037i	0.514225	−	0.857656i	$-0.328080\pi$
$941$	0.876874	+	0.506264i	0.0285853	+	0.0165037i	−0.485639	+	0.874159i	$0.661413\pi$
$942$	−8.03334	−	2.15253i	−0.261740	−	0.0701331i
$943$	28.1524	−	7.54340i	0.916767	−	0.245647i
$944$	10.4304	−	6.02199i	0.339480	−	0.195999i
$945$	5.30729	+	0.234124i	0.172646	+	0.00761606i
$946$	−4.73808			−0.154048
$947$	−19.1474	−	5.13052i	−0.622206	−	0.166720i	−0.0660756	−	0.997815i	$-0.521048\pi$
$947$	−19.1474	−	5.13052i	−0.622206	−	0.166720i	−0.556130	+	0.831095i	$0.687715\pi$
$948$	2.04021	+	7.61417i	0.0662630	+	0.247297i
$949$	0.0417522	−	0.0241056i	0.00135533	−	0.000782502i
$950$	0.111274	+	0.634417i	0.00361020	+	0.0205832i
$951$	−7.32344	−	4.22819i	−0.237479	−	0.137108i
$952$	2.89476	+	10.8034i	0.0938196	+	0.350140i
$953$	−7.88283	−	7.88283i	−0.255350	−	0.255350i	0.567810	−	0.823160i	$-0.307791\pi$
$953$	−7.88283	−	7.88283i	−0.255350	−	0.255350i	−0.823160	+	0.567810i	$0.807791\pi$
$954$	−5.72671	−	9.91895i	−0.185409	−	0.321138i
$955$	17.1262	+	32.9355i	0.554192	+	1.06577i
$956$	14.7899	+	8.53893i	0.478338	+	0.276169i
$957$	−4.87574	+	4.87574i	−0.157610	+	0.157610i
$958$	29.1902	+	7.82148i	0.943091	+	0.252701i
$959$	52.5605			1.69727
$960$	−1.64928	+	1.50992i	−0.0532304	+	0.0487325i
$961$	−5.68745	−	30.4738i	−0.183466	−	0.983026i
$962$	−0.105600	−	0.105600i	−0.00340469	−	0.00340469i
$963$	10.0376	−	10.0376i	0.323457	−	0.323457i
$964$	4.06360	+	7.03836i	0.130880	+	0.226690i
$965$	31.6546	−	28.9798i	1.01900	−	0.932893i
$966$	−8.14053	+	14.0998i	−0.261917	+	0.453654i
$967$	36.4322	+	9.76199i	1.17158	+	0.313924i	0.791582	−	0.611062i	$-0.209258\pi$
$967$	36.4322	+	9.76199i	1.17158	+	0.313924i	0.379999	+	0.924987i	$0.375924\pi$
$968$	8.59955	+	2.30424i	0.276400	+	0.0740612i
$969$			0.606444i			0.0194818i
$970$	16.7029	+	10.6515i	0.536297	+	0.342000i
$971$	−24.3768	+	42.2218i	−0.782287	+	1.35496i	0.148319	+	0.988940i	$0.452614\pi$
$971$	−24.3768	+	42.2218i	−0.782287	+	1.35496i	−0.930606	+	0.366022i	$0.880720\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−5.46145	+	20.3824i	−0.175086	+	0.653430i
$974$	10.7721	−	18.6578i	0.345161	−	0.597836i
$975$	−0.0732165	+	0.0340609i	−0.00234481	+	0.00109082i
$976$		−	7.91452i		−	0.253338i
$977$	20.6585	+	20.6585i	0.660924	+	0.660924i	0.955598	−	0.294674i	$-0.0952111\pi$
$977$	20.6585	+	20.6585i	0.660924	+	0.660924i	−0.294674	+	0.955598i	$0.595211\pi$
$978$	−1.51802	+	5.66532i	−0.0485408	+	0.181157i
$979$	3.30293	+	1.90695i	0.105562	+	0.0609464i
$980$	1.39841	+	2.68929i	0.0446706	+	0.0859062i
$981$	−2.64282	+	4.57749i	−0.0843786	+	0.146148i
$982$	−8.01172	−	29.9001i	−0.255664	−	0.954151i
$983$	29.0063	−	7.77221i	0.925157	−	0.247895i	0.235369	−	0.971906i	$-0.424370\pi$
$983$	29.0063	−	7.77221i	0.925157	−	0.247895i	0.689788	+	0.724011i	$0.257704\pi$
$984$	−4.25303			−0.135582
$985$	55.0504	+	17.3847i	1.75405	+	0.553922i
$986$	11.2079	+	19.4126i	0.356931	+	0.618223i
$987$	−3.06068	−	11.4226i	−0.0974225	−	0.363586i
$988$	−0.00147113	−	0.00147113i	−4.68028e−5	−	4.68028e-5i
$989$	−19.4177	+	11.2108i	−0.617446	+	0.356482i
$990$	2.18657	+	2.38838i	0.0694936	+	0.0759078i
$991$			23.2179i			0.737540i	0.929521	+	0.368770i	$0.120221\pi$
$991$			23.2179i			0.737540i	−0.929521	+	0.368770i	$0.879779\pi$
$992$	−5.54409	+	0.512929i	−0.176025	+	0.0162855i
$993$	−20.9352	+	20.9352i	−0.664359	+	0.664359i
$994$			1.15257i			0.0365575i
$995$	−9.23173	−	17.7536i	−0.292665	−	0.562826i
$996$	14.3751			0.455494
$997$	−41.9080	+	11.2292i	−1.32724	+	0.355632i	−0.851685	−	0.524054i	$-0.824419\pi$
$997$	−41.9080	+	11.2292i	−1.32724	+	0.355632i	−0.475554	+	0.879687i	$0.657752\pi$
$998$	−0.590907	+	2.20529i	−0.0187048	+	0.0698074i
$999$	8.00811	−	4.62348i	0.253365	−	0.146280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.15	✓	64
5.3	odd	4		930.2.be.b.223.14	yes	64
31.26	odd	6		930.2.be.b.367.14	yes	64
155.88	even	12	inner	930.2.be.a.553.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.15	✓	64	1.1	even	1	trivial
930.2.be.a.553.15	yes	64	155.88	even	12	inner
930.2.be.b.223.14	yes	64	5.3	odd	4
930.2.be.b.367.14	yes	64	31.26	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.20229 - 1.88534i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.614903 - 2.29485i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.20229 - 1.88534i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.614903 - 2.29485i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.18328 - 0.482987i) q^{10} +(-1.25412 - 0.724067i) q^{11} +(0.965926 + 0.258819i) q^{12} +(0.0156000 - 0.00418001i) q^{13} +(2.05750 - 1.18790i) q^{14} +(-1.50992 - 1.64928i) q^{15} -1.00000 q^{16} +(4.54726 + 1.21843i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-0.111562 + 0.0644102i) q^{19} +(1.88534 + 1.20229i) q^{20} +(-2.05750 - 1.18790i) q^{21} +(-0.374805 - 1.39879i) q^{22} +(-4.84571 - 4.84571i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.10900 - 4.53345i) q^{25} +(0.0139866 + 0.00807515i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.29485 + 0.614903i) q^{28} +4.76154 q^{29} +(0.0985454 - 2.23390i) q^{30} +(3.55757 - 4.28296i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.02398 + 1.02398i) q^{33} +(2.35383 + 4.07696i) q^{34} +(-3.58727 - 3.91837i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-8.93188 - 2.39329i) q^{37} +(-0.124431 - 0.0333412i) q^{38} -0.0161503i q^{39} +(0.482987 + 2.18328i) q^{40} +(-2.12652 + 3.68323i) q^{41} +(-0.614903 - 2.29485i) q^{42} +(0.846818 - 3.16037i) q^{43} +(0.724067 - 1.25412i) q^{44} +(-1.98388 + 1.03160i) q^{45} -6.85287i q^{46} +(3.51963 + 3.51963i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(1.17396 + 0.677784i) q^{49} +(1.71435 - 4.69692i) q^{50} +(2.35383 - 4.07696i) q^{51} +(0.00418001 + 0.0156000i) q^{52} +(11.0631 - 2.96436i) q^{53} -1.00000 q^{54} +(-2.87293 + 1.49390i) q^{55} +(1.18790 + 2.05750i) q^{56} +(0.0333412 + 0.124431i) q^{57} +(3.36691 + 3.36691i) q^{58} +(-10.4304 + 6.02199i) q^{59} +(1.64928 - 1.50992i) q^{60} +7.91452i q^{61} +(5.54409 - 0.512929i) q^{62} +(-1.67995 + 1.67995i) q^{63} -1.00000i q^{64} +(0.0108750 - 0.0344368i) q^{65} -1.44813 q^{66} +(5.92494 - 1.58758i) q^{67} +(-1.21843 + 4.54726i) q^{68} +(-5.93476 + 3.42643i) q^{69} +(0.234124 - 5.30729i) q^{70} +(-0.242566 + 0.420136i) q^{71} +(0.965926 - 0.258819i) q^{72} +(2.88344 - 0.772616i) q^{73} +(-4.62348 - 8.00811i) q^{74} +(-4.92482 + 0.863790i) q^{75} +(-0.0644102 - 0.111562i) q^{76} +(-2.43278 + 2.43278i) q^{77} +(0.0114200 - 0.0114200i) q^{78} +(3.94138 + 6.82668i) q^{79} +(-1.20229 + 1.88534i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-4.10811 + 1.10077i) q^{82} +(13.8853 - 3.72056i) q^{83} +(1.18790 - 2.05750i) q^{84} +(7.76429 - 7.10821i) q^{85} +(2.83351 - 1.63593i) q^{86} +(1.23238 - 4.59929i) q^{87} +(1.39879 - 0.374805i) q^{88} -2.63366 q^{89} +(-2.13227 - 0.673362i) q^{90} -0.0383699i q^{91} +(4.84571 - 4.84571i) q^{92} +(-3.21625 - 4.54486i) q^{93} +4.97750i q^{94} +(-0.0126947 + 0.287771i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(6.26451 + 6.26451i) q^{97} +(0.350847 + 1.30938i) q^{98} +(0.724067 + 1.25412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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