LMFDB - Embedded newform 930.2.be.a.37.16

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			37.16
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.60244 + 1.55955i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.784034 - 2.92605i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.60244 + 1.55955i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.784034 - 2.92605i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.0303243 + 2.23586i) q^{10} +(-3.64807 - 2.10621i) q^{11} +(0.965926 + 0.258819i) q^{12} +(5.40883 - 1.44929i) q^{13} +(2.62343 - 1.51464i) q^{14} +(1.92115 - 1.14419i) q^{15} -1.00000 q^{16} +(0.605346 + 0.162202i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(6.62616 - 3.82561i) q^{19} +(-1.55955 + 1.60244i) q^{20} +(-2.62343 - 1.51464i) q^{21} +(-1.09026 - 4.06889i) q^{22} +(0.0248139 + 0.0248139i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.135602 + 4.99816i) q^{25} +(4.84942 + 2.79982i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.92605 + 0.784034i) q^{28} +0.154463 q^{29} +(2.16753 + 0.549393i) q^{30} +(-5.01084 + 2.42724i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.97864 + 2.97864i) q^{33} +(0.313350 + 0.542739i) q^{34} +(5.81969 - 3.46607i) q^{35} +(0.500000 - 0.866025i) q^{36} +(10.7328 + 2.87586i) q^{37} +(7.39052 + 1.98028i) q^{38} -5.59963i q^{39} +(-2.23586 + 0.0303243i) q^{40} +(0.596464 - 1.03311i) q^{41} +(-0.784034 - 2.92605i) q^{42} +(-2.17721 + 8.12547i) q^{43} +(2.10621 - 3.64807i) q^{44} +(-0.607975 - 2.15183i) q^{45} +0.0350922i q^{46} +(-6.98492 - 6.98492i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-1.88490 - 1.08825i) q^{49} +(-3.43835 + 3.63012i) q^{50} +(0.313350 - 0.542739i) q^{51} +(1.44929 + 5.40883i) q^{52} +(-5.92187 + 1.58676i) q^{53} -1.00000 q^{54} +(-2.56105 - 9.06442i) q^{55} +(1.51464 + 2.62343i) q^{56} +(-1.98028 - 7.39052i) q^{57} +(0.109222 + 0.109222i) q^{58} +(-7.05360 + 4.07240i) q^{59} +(1.14419 + 1.92115i) q^{60} +7.54724i q^{61} +(-5.25952 - 1.82688i) q^{62} +(-2.14202 + 2.14202i) q^{63} -1.00000i q^{64} +(10.9275 + 6.11295i) q^{65} -4.21243 q^{66} +(11.4819 - 3.07656i) q^{67} +(-0.162202 + 0.605346i) q^{68} +(0.0303908 - 0.0175461i) q^{69} +(6.56603 + 1.66426i) q^{70} +(6.46667 - 11.2006i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-6.36206 + 1.70471i) q^{73} +(5.55573 + 9.62280i) q^{74} +(4.86295 + 1.16264i) q^{75} +(3.82561 + 6.62616i) q^{76} +(-9.02310 + 9.02310i) q^{77} +(3.95954 - 3.95954i) q^{78} +(-1.83804 - 3.18357i) q^{79} +(-1.60244 - 1.55955i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.15228 - 0.308753i) q^{82} +(-6.90813 + 1.85103i) q^{83} +(1.51464 - 2.62343i) q^{84} +(0.717066 + 1.20399i) q^{85} +(-7.28509 + 4.20605i) q^{86} +(0.0399781 - 0.149200i) q^{87} +(4.06889 - 1.09026i) q^{88} +4.49754 q^{89} +(1.09167 - 1.95148i) q^{90} -16.9628i q^{91} +(-0.0248139 + 0.0248139i) q^{92} +(1.04764 + 5.46831i) q^{93} -9.87817i q^{94} +(16.5842 + 4.20353i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-3.56033 - 3.56033i) q^{97} +(-0.563318 - 2.10233i) q^{98} +(2.10621 + 3.64807i) 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
$5$	1.60244	+	1.55955i	0.716631	+	0.697452i
$5$	1.60244	+	1.55955i	0.716631	+	0.697452i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	0.784034	−	2.92605i	0.296337	−	1.10594i	−0.643813	−	0.765183i	$-0.722649\pi$
$7$	0.784034	−	2.92605i	0.296337	−	1.10594i	0.940150	−	0.340761i	$-0.110685\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	0.0303243	+	2.23586i	0.00958939	+	0.707042i
$11$	−3.64807	−	2.10621i	−1.09993	−	0.635047i	−0.163731	−	0.986505i	$-0.552353\pi$
$11$	−3.64807	−	2.10621i	−1.09993	−	0.635047i	−0.936204	+	0.351458i	$0.885686\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	5.40883	−	1.44929i	1.50014	−	0.401961i	0.586992	−	0.809592i	$-0.300312\pi$
$13$	5.40883	−	1.44929i	1.50014	−	0.401961i	0.913147	+	0.407631i	$0.133645\pi$
$14$	2.62343	−	1.51464i	0.701140	−	0.404804i
$15$	1.92115	−	1.14419i	0.496039	−	0.295429i
$16$	−1.00000			−0.250000
$17$	0.605346	+	0.162202i	0.146818	+	0.0393398i	0.331480	−	0.943462i	$-0.392452\pi$
$17$	0.605346	+	0.162202i	0.146818	+	0.0393398i	−0.184661	+	0.982802i	$0.559119\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	6.62616	−	3.82561i	1.52014	−	0.877656i	0.520426	−	0.853907i	$-0.325773\pi$
$19$	6.62616	−	3.82561i	1.52014	−	0.877656i	0.999718	−	0.0237491i	$-0.00756030\pi$
$20$	−1.55955	+	1.60244i	−0.348726	+	0.358316i
$21$	−2.62343	−	1.51464i	−0.572479	−	0.330521i
$22$	−1.09026	−	4.06889i	−0.232443	−	0.867491i
$23$	0.0248139	+	0.0248139i	0.00517407	+	0.00517407i	0.709689	−	0.704515i	$-0.248835\pi$
$23$	0.0248139	+	0.0248139i	0.00517407	+	0.00517407i	−0.704515	+	0.709689i	$0.748835\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	0.135602	+	4.99816i	0.0271204	+	0.999632i
$26$	4.84942	+	2.79982i	0.951050	+	0.549089i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	2.92605	+	0.784034i	0.552972	+	0.148168i
$29$	0.154463			0.0286831			0.0143416	−	0.999897i	$-0.495435\pi$
$29$	0.154463			0.0286831			0.0143416	+	0.999897i	$0.495435\pi$
$30$	2.16753	+	0.549393i	0.395734	+	0.100305i
$31$	−5.01084	+	2.42724i	−0.899973	+	0.435946i
$31$	−5.01084	+	2.42724i	−0.899973	+	0.435946i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.97864	+	2.97864i	−0.518514	+	0.518514i
$34$	0.313350	+	0.542739i	0.0537391	+	0.0930789i
$35$	5.81969	−	3.46607i	0.983708	−	0.585873i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	10.7328	+	2.87586i	1.76447	+	0.472788i	0.987615	−	0.156895i	$-0.0501484\pi$
$37$	10.7328	+	2.87586i	1.76447	+	0.472788i	0.776852	+	0.629683i	$0.216815\pi$
$38$	7.39052	+	1.98028i	1.19890	+	0.321244i
$39$		−	5.59963i		−	0.896659i
$40$	−2.23586	+	0.0303243i	−0.353521	+	0.00479469i
$41$	0.596464	−	1.03311i	0.0931521	−	0.161344i	−0.815684	−	0.578498i	$-0.803639\pi$
$41$	0.596464	−	1.03311i	0.0931521	−	0.161344i	0.908836	+	0.417154i	$0.136972\pi$
$42$	−0.784034	−	2.92605i	−0.120979	−	0.451500i
$43$	−2.17721	+	8.12547i	−0.332022	+	1.23912i	0.575040	+	0.818125i	$0.304986\pi$
$43$	−2.17721	+	8.12547i	−0.332022	+	1.23912i	−0.907062	+	0.420997i	$0.861680\pi$
$44$	2.10621	−	3.64807i	0.317524	−	0.549967i
$45$	−0.607975	−	2.15183i	−0.0906315	−	0.320776i
$46$			0.0350922i			0.00517407i
$47$	−6.98492	−	6.98492i	−1.01886	−	1.01886i	−0.999819	−	0.0190365i	$-0.993940\pi$
$47$	−6.98492	−	6.98492i	−1.01886	−	1.01886i	−0.0190365	−	0.999819i	$-0.506060\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	−1.88490	−	1.08825i	−0.269271	−	0.155464i
$50$	−3.43835	+	3.63012i	−0.486256	+	0.513376i
$51$	0.313350	−	0.542739i	0.0438778	−	0.0759986i
$52$	1.44929	+	5.40883i	0.200981	+	0.750070i
$53$	−5.92187	+	1.58676i	−0.813432	+	0.217958i	−0.641473	−	0.767146i	$-0.721676\pi$
$53$	−5.92187	+	1.58676i	−0.813432	+	0.217958i	−0.171959	+	0.985104i	$0.555010\pi$
$54$	−1.00000			−0.136083
$55$	−2.56105	−	9.06442i	−0.345332	−	1.22225i
$56$	1.51464	+	2.62343i	0.202402	+	0.350570i
$57$	−1.98028	−	7.39052i	−0.262295	−	0.978898i
$58$	0.109222	+	0.109222i	0.0143416	+	0.0143416i
$59$	−7.05360	+	4.07240i	−0.918300	+	0.530181i	−0.883092	−	0.469199i	$-0.844543\pi$
$59$	−7.05360	+	4.07240i	−0.918300	+	0.530181i	−0.0352080	+	0.999380i	$0.511209\pi$
$60$	1.14419	+	1.92115i	0.147715	+	0.248020i
$61$			7.54724i			0.966325i	0.875531	+	0.483162i	$0.160512\pi$
$61$			7.54724i			0.966325i	−0.875531	+	0.483162i	$0.839488\pi$
$62$	−5.25952	−	1.82688i	−0.667959	−	0.232013i
$63$	−2.14202	+	2.14202i	−0.269869	+	0.269869i
$64$		−	1.00000i		−	0.125000i
$65$	10.9275	+	6.11295i	1.35540	+	0.758218i
$66$	−4.21243			−0.518514
$67$	11.4819	−	3.07656i	1.40274	−	0.375862i	0.523409	−	0.852081i	$-0.324660\pi$
$67$	11.4819	−	3.07656i	1.40274	−	0.375862i	0.879326	+	0.476220i	$0.157993\pi$
$68$	−0.162202	+	0.605346i	−0.0196699	+	0.0734090i
$69$	0.0303908	−	0.0175461i	0.00365862	−	0.00211230i
$70$	6.56603	+	1.66426i	0.784790	+	0.198917i
$71$	6.46667	−	11.2006i	0.767453	−	1.32927i	−0.171487	−	0.985186i	$-0.554857\pi$
$71$	6.46667	−	11.2006i	0.767453	−	1.32927i	0.938940	−	0.344081i	$-0.111809\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−6.36206	+	1.70471i	−0.744623	+	0.199521i	−0.611132	−	0.791529i	$-0.709285\pi$
$73$	−6.36206	+	1.70471i	−0.744623	+	0.199521i	−0.133491	+	0.991050i	$0.542619\pi$
$74$	5.55573	+	9.62280i	0.645840	+	1.11863i
$75$	4.86295	+	1.16264i	0.561525	+	0.134250i
$76$	3.82561	+	6.62616i	0.438828	+	0.760072i
$77$	−9.02310	+	9.02310i	−1.02828	+	1.02828i
$78$	3.95954	−	3.95954i	0.448329	−	0.448329i
$79$	−1.83804	−	3.18357i	−0.206795	−	0.358180i	0.743908	−	0.668282i	$-0.232970\pi$
$79$	−1.83804	−	3.18357i	−0.206795	−	0.358180i	−0.950703	+	0.310102i	$0.899637\pi$
$80$	−1.60244	−	1.55955i	−0.179158	−	0.174363i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.15228	−	0.308753i	0.127248	−	0.0340960i
$83$	−6.90813	+	1.85103i	−0.758266	+	0.203177i	−0.617181	−	0.786821i	$-0.711726\pi$
$83$	−6.90813	+	1.85103i	−0.758266	+	0.203177i	−0.141084	+	0.989998i	$0.545059\pi$
$84$	1.51464	−	2.62343i	0.165260	−	0.286239i
$85$	0.717066	+	1.20399i	0.0777768	+	0.130591i
$86$	−7.28509	+	4.20605i	−0.785572	+	0.453550i
$87$	0.0399781	−	0.149200i	0.00428610	−	0.0159959i
$88$	4.06889	−	1.09026i	0.433745	−	0.116222i
$89$	4.49754			0.476738			0.238369	−	0.971175i	$-0.423387\pi$
$89$	4.49754			0.476738			0.238369	+	0.971175i	$0.423387\pi$
$90$	1.09167	−	1.95148i	0.115072	−	0.205704i
$91$		−	16.9628i		−	1.77819i
$92$	−0.0248139	+	0.0248139i	−0.00258703	+	0.00258703i
$93$	1.04764	+	5.46831i	0.108635	+	0.567038i
$94$		−	9.87817i		−	1.01886i
$95$	16.5842	+	4.20353i	1.70151	+	0.431273i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−3.56033	−	3.56033i	−0.361497	−	0.361497i	0.502867	−	0.864364i	$-0.332279\pi$
$97$	−3.56033	−	3.56033i	−0.361497	−	0.361497i	−0.864364	+	0.502867i	$0.832279\pi$
$98$	−0.563318	−	2.10233i	−0.0569038	−	0.212368i
$99$	2.10621	+	3.64807i	0.211682	+	0.366645i
$100$	−4.99816	+	0.135602i	−0.499816	+	0.0135602i
$101$	7.71981			0.768150			0.384075	−	0.923302i	$-0.374520\pi$
$101$	7.71981			0.768150			0.384075	+	0.923302i	$0.374520\pi$
$102$	0.605346	−	0.162202i	0.0599382	−	0.0160604i
$103$	3.04092	+	11.3489i	0.299630	+	1.11824i	0.937470	+	0.348066i	$0.113162\pi$
$103$	3.04092	+	11.3489i	0.299630	+	1.11824i	−0.637840	+	0.770169i	$0.720172\pi$
$104$	−2.79982	+	4.84942i	−0.274544	+	0.475525i
$105$	−1.84172	−	6.51848i	−0.179734	−	0.636138i
$106$	−5.30941	−	3.06539i	−0.515695	−	0.297737i
$107$	−2.04240	+	7.62233i	−0.197446	+	0.736879i	0.794174	+	0.607690i	$0.207904\pi$
$107$	−2.04240	+	7.62233i	−0.197446	+	0.736879i	−0.991620	+	0.129188i	$0.958763\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	6.96538i		−	0.667162i	−0.942721	−	0.333581i	$-0.891743\pi$
$109$		−	6.96538i		−	0.667162i	0.942721	−	0.333581i	$-0.108257\pi$
$110$	4.59858	−	8.22045i	0.438457	−	0.783789i
$111$	5.55573	−	9.62280i	0.527326	−	0.913356i
$112$	−0.784034	+	2.92605i	−0.0740842	+	0.276486i
$113$	1.38910	+	5.18420i	0.130676	+	0.487688i	0.999978	−	0.00659211i	$-0.00209835\pi$
$113$	1.38910	+	5.18420i	0.130676	+	0.487688i	−0.869303	+	0.494280i	$0.835432\pi$
$114$	3.82561	−	6.62616i	0.358301	−	0.620596i
$115$	0.00106415	+	0.0784614i	9.92323e−5	+	0.00731656i
$116$			0.154463i			0.0143416i
$117$	−5.40883	−	1.44929i	−0.500046	−	0.133987i
$118$	−7.86727	−	2.10803i	−0.724241	−	0.194060i
$119$	0.949224	−	1.64410i	0.0870152	−	0.150715i
$120$	−0.549393	+	2.16753i	−0.0501525	+	0.197867i
$121$	3.37227	+	5.84095i	0.306570	+	0.530995i
$122$	−5.33670	+	5.33670i	−0.483162	+	0.483162i
$123$	−0.843528	−	0.843528i	−0.0760583	−	0.0760583i
$124$	−2.42724	−	5.01084i	−0.217973	−	0.449986i
$125$	−7.57759	+	8.22071i	−0.677761	+	0.735283i
$126$	−3.02927			−0.269869
$127$	−18.8945	−	5.06278i	−1.67662	−	0.449249i	−0.709736	−	0.704467i	$-0.751186\pi$
$127$	−18.8945	−	5.06278i	−1.67662	−	0.449249i	−0.966883	+	0.255218i	$0.917853\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	7.28509	+	4.20605i	0.641417	+	0.370322i
$130$	3.40443	+	12.0494i	0.298589	+	1.05681i
$131$	−0.195216	−	0.338125i	−0.0170561	−	0.0295421i	0.857371	−	0.514698i	$-0.172096\pi$
$131$	−0.195216	−	0.338125i	−0.0170561	−	0.0295421i	−0.874427	+	0.485156i	$0.838763\pi$
$132$	−2.97864	−	2.97864i	−0.259257	−	0.259257i
$133$	−5.99882	−	22.3879i	−0.520163	−	1.94128i
$134$	10.2944	+	5.94346i	0.889299	+	0.513437i
$135$	−2.23586	+	0.0303243i	−0.192432	+	0.00260990i
$136$	−0.542739	+	0.313350i	−0.0465395	+	0.0268696i
$137$	0.0155478	+	0.0580251i	0.00132834	+	0.00495741i	0.966587	−	0.256339i	$-0.0825165\pi$
$137$	0.0155478	+	0.0580251i	0.00132834	+	0.00495741i	−0.965258	+	0.261297i	$0.915850\pi$
$138$	0.0338965	+	0.00908254i	0.00288546	+	0.000773157i
$139$	−16.0979			−1.36541			−0.682703	−	0.730696i	$-0.739196\pi$
$139$	−16.0979			−1.36541			−0.682703	+	0.730696i	$0.739196\pi$
$140$	3.46607	+	5.81969i	0.292937	+	0.491854i
$141$	−8.55474	+	4.93908i	−0.720439	+	0.415946i
$142$	12.4926	−	3.34740i	1.04836	−	0.280907i
$143$	−22.7843	−	6.10503i	−1.90532	−	0.510529i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	0.247518	+	0.240894i	0.0205552	+	0.0200051i
$146$	−5.70407	−	3.29324i	−0.472072	−	0.272551i
$147$	−1.53901	+	1.53901i	−0.126936	+	0.126936i
$148$	−2.87586	+	10.7328i	−0.236394	+	0.882234i
$149$	−14.2744	+	8.24130i	−1.16940	+	0.675154i	−0.953539	−	0.301270i	$-0.902589\pi$
$149$	−14.2744	+	8.24130i	−1.16940	+	0.675154i	−0.215862	+	0.976424i	$0.569256\pi$
$150$	2.61652	+	4.26073i	0.213638	+	0.347887i
$151$			5.26477i			0.428441i	0.976785	+	0.214221i	$0.0687212\pi$
$151$			5.26477i			0.428441i	−0.976785	+	0.214221i	$0.931279\pi$
$152$	−1.98028	+	7.39052i	−0.160622	+	0.599450i
$153$	−0.443144	−	0.443144i	−0.0358261	−	0.0358261i
$154$	−12.7606			−1.02828
$155$	−11.8150	−	3.92515i	−0.949000	−	0.315276i
$156$	5.59963			0.448329
$157$	−8.80542	−	8.80542i	−0.702749	−	0.702749i	0.262251	−	0.965000i	$-0.415535\pi$
$157$	−8.80542	−	8.80542i	−0.702749	−	0.702749i	−0.965000	+	0.262251i	$0.915535\pi$
$158$	0.951437	−	3.55081i	0.0756923	−	0.282487i
$159$			6.13078i			0.486202i
$160$	−0.0303243	−	2.23586i	−0.00239735	−	0.176760i
$161$	0.0920619	−	0.0531520i	0.00725549	−	0.00418896i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	12.6240	−	12.6240i	0.988786	−	0.988786i	−0.0111517	−	0.999938i	$-0.503550\pi$
$163$	12.6240	−	12.6240i	0.988786	−	0.988786i	0.999938	+	0.0111517i	$0.00354975\pi$
$164$	1.03311	+	0.596464i	0.0806721	+	0.0465760i
$165$	−9.41841	+	0.127739i	−0.733222	+	0.00994447i
$166$	−6.19366	−	3.57591i	−0.480721	−	0.277545i
$167$	−21.8877	−	5.86479i	−1.69372	−	0.453831i	−0.722375	−	0.691502i	$-0.756949\pi$
$167$	−21.8877	−	5.86479i	−1.69372	−	0.453831i	−0.971346	+	0.237671i	$0.923616\pi$
$168$	2.92605	−	0.784034i	0.225750	−	0.0604895i
$169$	15.8966	−	9.17793i	1.22282	−	0.705995i
$170$	−0.344305	+	1.35839i	−0.0264070	+	0.104184i
$171$	−7.65123			−0.585104
$172$	−8.12547	−	2.17721i	−0.619561	−	0.166011i
$173$	0.210334	+	0.784977i	0.0159914	+	0.0596807i	0.973460	−	0.228855i	$-0.0734982\pi$
$173$	0.210334	+	0.784977i	0.0159914	+	0.0596807i	−0.957469	+	0.288536i	$0.906832\pi$
$174$	0.133769	−	0.0772317i	0.0101410	−	0.00585492i
$175$	14.7312	+	3.52195i	1.11357	+	0.266234i
$176$	3.64807	+	2.10621i	0.274984	+	0.158762i
$177$	2.10803	+	7.86727i	0.158449	+	0.591340i
$178$	3.18024	+	3.18024i	0.238369	+	0.238369i
$179$	12.7518	+	22.0869i	0.953118	+	1.65085i	0.738617	+	0.674125i	$0.235479\pi$
$179$	12.7518	+	22.0869i	0.953118	+	1.65085i	0.214501	+	0.976724i	$0.431188\pi$
$180$	2.15183	−	0.607975i	0.160388	−	0.0453158i
$181$	−2.20695	−	1.27418i	−0.164041	−	0.0947093i	0.415732	−	0.909487i	$-0.363525\pi$
$181$	−2.20695	−	1.27418i	−0.164041	−	0.0947093i	−0.579773	+	0.814778i	$0.696859\pi$
$182$	11.9945	−	11.9945i	0.889093	−	0.889093i
$183$	7.29007	+	1.95337i	0.538898	+	0.144397i
$184$	−0.0350922			−0.00258703
$185$	12.7136	+	21.3468i	0.934726	+	1.56945i
$186$	−3.12589	+	4.60747i	−0.229201	+	0.337836i
$187$	−1.86671	−	1.86671i	−0.136508	−	0.136508i
$188$	6.98492	−	6.98492i	0.509428	−	0.509428i
$189$	1.51464	+	2.62343i	0.110174	+	0.190826i
$190$	8.75448	+	14.6992i	0.635116	+	1.06639i
$191$	−8.36215	+	14.4837i	−0.605064	+	1.04800i	0.386977	+	0.922089i	$0.373519\pi$
$191$	−8.36215	+	14.4837i	−0.605064	+	1.04800i	−0.992041	+	0.125912i	$0.959814\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−12.9215	−	3.46230i	−0.930109	−	0.249222i	−0.238208	−	0.971214i	$-0.576560\pi$
$193$	−12.9215	−	3.46230i	−0.930109	−	0.249222i	−0.691901	+	0.721992i	$0.743227\pi$
$194$		−	5.03507i		−	0.361497i
$195$	8.73291	−	8.97305i	0.625377	−	0.642573i
$196$	1.08825	−	1.88490i	0.0777320	−	0.134636i
$197$	−1.49220	−	5.56897i	−0.106315	−	0.396773i	0.892176	−	0.451688i	$-0.149178\pi$
$197$	−1.49220	−	5.56897i	−0.106315	−	0.396773i	−0.998491	+	0.0549150i	$0.982511\pi$
$198$	−1.09026	+	4.06889i	−0.0774812	+	0.289164i
$199$	0.451994	−	0.782877i	0.0320410	−	0.0554967i	−0.849560	−	0.527492i	$-0.823133\pi$
$199$	0.451994	−	0.782877i	0.0320410	−	0.0554967i	0.881601	+	0.471995i	$0.156466\pi$
$200$	−3.63012	−	3.43835i	−0.256688	−	0.243128i
$201$		−	11.8869i		−	0.838439i
$202$	5.45873	+	5.45873i	0.384075	+	0.384075i
$203$	0.121104	−	0.451968i	0.00849987	−	0.0317219i
$204$	0.542739	+	0.313350i	0.0379993	+	0.0219389i
$205$	2.56698	−	0.725270i	0.179286	−	0.0506551i
$206$	−5.87460	+	10.1751i	−0.409303	+	0.708933i
$207$	−0.00908254	−	0.0338965i	−0.000631280	−	0.00235597i
$208$	−5.40883	+	1.44929i	−0.375035	+	0.100490i
$209$	−32.2302			−2.22941
$210$	3.30697	−	5.91155i	0.228202	−	0.407936i
$211$	6.80387	+	11.7847i	0.468398	+	0.811289i	0.999348	−	0.0361142i	$-0.0114980\pi$
$211$	6.80387	+	11.7847i	0.468398	+	0.811289i	−0.530950	+	0.847403i	$0.678165\pi$
$212$	−1.58676	−	5.92187i	−0.108979	−	0.406716i
$213$	−9.14525	−	9.14525i	−0.626622	−	0.626622i
$214$	−6.83400	+	3.94561i	−0.467162	+	0.269716i
$215$	−16.1609	+	9.62506i	−1.10217	+	0.656424i
$216$		−	1.00000i		−	0.0680414i
$217$	3.17358	+	16.5650i	0.215437	+	1.12451i
$218$	4.92527	−	4.92527i	0.333581	−	0.333581i
$219$			6.58649i			0.445074i
$220$	9.06442	−	2.56105i	0.611123	−	0.172666i
$221$	3.50929			0.236061
$222$	10.7328	−	2.87586i	0.720341	−	0.193015i
$223$	−5.85340	+	21.8452i	−0.391973	+	1.46286i	0.434903	+	0.900477i	$0.356783\pi$
$223$	−5.85340	+	21.8452i	−0.391973	+	1.46286i	−0.826876	+	0.562385i	$0.809884\pi$
$224$	−2.62343	+	1.51464i	−0.175285	+	0.101201i
$225$	2.38165	−	4.39634i	0.158776	−	0.293089i
$226$	−2.68354	+	4.64802i	−0.178506	+	0.309182i
$227$	7.47021	−	2.00164i	0.495816	−	0.132853i	−0.00224175	−	0.999997i	$-0.500714\pi$
$227$	7.47021	−	2.00164i	0.495816	−	0.132853i	0.498057	+	0.867144i	$0.334047\pi$
$228$	7.39052	−	1.98028i	0.489449	−	0.131147i
$229$	5.06914	+	8.78001i	0.334978	+	0.580199i	0.983481	−	0.181013i	$-0.0579377\pi$
$229$	5.06914	+	8.78001i	0.334978	+	0.580199i	−0.648502	+	0.761213i	$0.724604\pi$
$230$	−0.0547281	+	0.0562330i	−0.00360866	+	0.00370790i
$231$	6.38030	+	11.0510i	0.419793	+	0.727102i
$232$	−0.109222	+	0.109222i	−0.00717078	+	0.00717078i
$233$	−10.4783	+	10.4783i	−0.686454	+	0.686454i	−0.961446	−	0.274992i	$-0.911325\pi$
$233$	−10.4783	+	10.4783i	−0.686454	+	0.686454i	0.274992	+	0.961446i	$0.411325\pi$
$234$	−2.79982	−	4.84942i	−0.183030	−	0.317017i
$235$	−0.299549	−	22.0862i	−0.0195404	−	1.44075i
$236$	−4.07240	−	7.05360i	−0.265091	−	0.459150i
$237$	−3.55081	+	0.951437i	−0.230650	+	0.0618025i
$238$	1.83376	−	0.491354i	0.118865	−	0.0318498i
$239$	−4.69381	+	8.12992i	−0.303617	+	0.525881i	−0.976953	−	0.213457i	$-0.931528\pi$
$239$	−4.69381	+	8.12992i	−0.303617	+	0.525881i	0.673335	+	0.739337i	$0.264861\pi$
$240$	−1.92115	+	1.14419i	−0.124010	+	0.0738573i
$241$	10.0892	−	5.82501i	0.649903	−	0.375222i	−0.138516	−	0.990360i	$-0.544233\pi$
$241$	10.0892	−	5.82501i	0.649903	−	0.375222i	0.788419	+	0.615139i	$0.210900\pi$
$242$	−1.74562	+	6.51473i	−0.112213	+	0.418783i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−7.54724			−0.483162
$245$	−1.32325	−	4.68345i	−0.0845396	−	0.299214i
$246$		−	1.19293i		−	0.0760583i
$247$	30.2953	−	30.2953i	1.92764	−	1.92764i
$248$	1.82688	−	5.25952i	0.116007	−	0.333980i
$249$			7.15182i			0.453228i
$250$	−11.1711	+	0.454753i	−0.706522	+	0.0287611i
$251$	4.33037	−	2.50014i	0.273330	−	0.157807i	−0.357070	−	0.934078i	$-0.616224\pi$
$251$	4.33037	−	2.50014i	0.273330	−	0.157807i	0.630400	+	0.776270i	$0.282891\pi$
$252$	−2.14202	−	2.14202i	−0.134935	−	0.134935i
$253$	−0.0382595	−	0.142786i	−0.00240536	−	0.00897691i
$254$	−9.78054	−	16.9404i	−0.613685	−	1.06293i
$255$	1.34855	−	0.381018i	0.0844496	−	0.0238603i
$256$	1.00000			0.0625000
$257$	−3.37736	+	0.904960i	−0.210674	+	0.0564499i	−0.362612	−	0.931940i	$-0.618115\pi$
$257$	−3.37736	+	0.904960i	−0.210674	+	0.0564499i	0.151939	+	0.988390i	$0.451448\pi$
$258$	2.17721	+	8.12547i	0.135547	+	0.505869i
$259$	16.8298	−	29.1501i	1.04575	−	1.81130i
$260$	−6.11295	+	10.9275i	−0.379109	+	0.677698i
$261$	−0.133769	−	0.0772317i	−0.00828011	−	0.00478052i
$262$	0.101051	−	0.377129i	0.00624298	−	0.0232991i
$263$	5.19672	+	5.19672i	0.320444	+	0.320444i	0.848937	−	0.528494i	$-0.177243\pi$
$263$	5.19672	+	5.19672i	0.320444	+	0.320444i	−0.528494	+	0.848937i	$0.677243\pi$
$264$		−	4.21243i		−	0.259257i
$265$	−11.9641	−	6.69278i	−0.734946	−	0.411134i
$266$	11.5888	−	20.0724i	0.710556	−	1.23072i
$267$	1.16405	−	4.34429i	0.0712386	−	0.265866i
$268$	3.07656	+	11.4819i	0.187931	+	0.701368i
$269$	12.2401	−	21.2005i	0.746294	−	1.29262i	−0.203293	−	0.979118i	$-0.565165\pi$
$269$	12.2401	−	21.2005i	0.746294	−	1.29262i	0.949588	−	0.313502i	$-0.101502\pi$
$270$	−1.60244	−	1.55955i	−0.0975211	−	0.0949112i
$271$		−	0.367557i		−	0.0223275i	−0.999938	−	0.0111638i	$-0.996446\pi$
$271$		−	0.367557i		−	0.0223275i	0.999938	−	0.0111638i	$-0.00355361\pi$
$272$	−0.605346	−	0.162202i	−0.0367045	−	0.00983495i
$273$	−16.3848	−	4.39030i	−0.991654	−	0.265713i
$274$	−0.0300360	+	0.0520238i	−0.00181454	+	0.00314288i
$275$	10.0325	−	18.5192i	0.604983	−	1.11675i
$276$	0.0175461	+	0.0303908i	0.00105615	+	0.00182931i
$277$	−14.2606	+	14.2606i	−0.856837	+	0.856837i	−0.990964	−	0.134127i	$-0.957177\pi$
$277$	−14.2606	+	14.2606i	−0.856837	+	0.856837i	0.134127	+	0.990964i	$0.457177\pi$
$278$	−11.3829	−	11.3829i	−0.682703	−	0.682703i
$279$	5.55313	+	0.403363i	0.332457	+	0.0241487i
$280$	−1.66426	+	6.56603i	−0.0994586	+	0.392395i
$281$	20.7663			1.23882			0.619408	−	0.785070i	$-0.287373\pi$
$281$	20.7663			1.23882			0.619408	+	0.785070i	$0.287373\pi$
$282$	−9.54158	−	2.55666i	−0.568193	−	0.152247i
$283$	−11.6340	+	11.6340i	−0.691568	+	0.691568i	−0.962577	−	0.271009i	$-0.912643\pi$
$283$	−11.6340	+	11.6340i	−0.691568	+	0.691568i	0.271009	+	0.962577i	$0.412643\pi$
$284$	11.2006	+	6.46667i	0.664633	+	0.383726i
$285$	8.35261	−	14.9312i	0.494766	−	0.884447i
$286$	−11.7940	−	20.4278i	−0.697395	−	1.20792i
$287$	−2.55528	−	2.55528i	−0.150833	−	0.150833i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−14.3823	−	8.30362i	−0.846017	−	0.488448i
$290$	0.00468400	+	0.345359i	0.000275054	+	0.0202802i
$291$	−4.36050	+	2.51754i	−0.255617	+	0.147581i
$292$	−1.70471	−	6.36206i	−0.0997605	−	0.372311i
$293$	−26.1620	−	7.01008i	−1.52840	−	0.409533i	−0.605902	−	0.795539i	$-0.707188\pi$
$293$	−26.1620	−	7.01008i	−1.52840	−	0.409533i	−0.922496	+	0.386006i	$0.873854\pi$
$294$	−2.17650			−0.126936
$295$	−17.6541	−	4.47469i	−1.02786	−	0.260527i
$296$	−9.62280	+	5.55573i	−0.559314	+	0.322920i
$297$	4.06889	−	1.09026i	0.236101	−	0.0632631i
$298$	−15.9210	−	4.26601i	−0.922277	−	0.247123i
$299$	0.170177	+	0.0982517i	0.00984159	+	0.00568205i
$300$	−1.16264	+	4.86295i	−0.0671249	+	0.280762i
$301$	22.0685	+	12.7413i	1.27201	+	0.734395i
$302$	−3.72276	+	3.72276i	−0.214221	+	0.214221i
$303$	1.99803	−	7.45676i	0.114784	−	0.428380i
$304$	−6.62616	+	3.82561i	−0.380036	+	0.219414i
$305$	−11.7703	+	12.0940i	−0.673966	+	0.692498i
$306$		−	0.626701i		−	0.0358261i
$307$	5.69085	−	21.2385i	0.324794	−	1.21215i	−0.589725	−	0.807604i	$-0.700764\pi$
$307$	5.69085	−	21.2385i	0.324794	−	1.21215i	0.914519	−	0.404543i	$-0.132570\pi$
$308$	−9.02310	−	9.02310i	−0.514139	−	0.514139i
$309$	11.7492			0.668388
$310$	−5.57893	−	11.1299i	−0.316862	−	0.632138i
$311$	33.7360			1.91299			0.956496	−	0.291745i	$-0.0942358\pi$
$311$	33.7360			1.91299			0.956496	+	0.291745i	$0.0942358\pi$
$312$	3.95954	+	3.95954i	0.224165	+	0.224165i
$313$	−7.76251	+	28.9701i	−0.438763	+	1.63749i	0.293134	+	0.956071i	$0.405302\pi$
$313$	−7.76251	+	28.9701i	−0.438763	+	1.63749i	−0.731897	+	0.681415i	$0.761365\pi$
$314$		−	12.4527i		−	0.702749i
$315$	−6.77304	+	0.0918606i	−0.381617	+	0.00517576i
$316$	3.18357	−	1.83804i	0.179090	−	0.103398i
$317$	6.70985	−	25.0415i	0.376863	−	1.40647i	−0.473741	−	0.880664i	$-0.657097\pi$
$317$	6.70985	−	25.0415i	0.376863	−	1.40647i	0.850604	−	0.525807i	$-0.176237\pi$
$318$	−4.33511	+	4.33511i	−0.243101	+	0.243101i
$319$	−0.563493	−	0.325333i	−0.0315496	−	0.0182151i
$320$	1.55955	−	1.60244i	0.0871815	−	0.0895789i
$321$	6.83400	+	3.94561i	0.381437	+	0.220223i
$322$	0.102682	+	0.0275135i	0.00572223	+	0.00153327i
$323$	4.63164	−	1.24104i	0.257711	−	0.0690536i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	7.97724	+	26.8377i	0.442498	+	1.48869i
$326$	17.8530			0.988786
$327$	−6.72804	−	1.80277i	−0.372061	−	0.0996935i
$328$	0.308753	+	1.15228i	0.0170480	+	0.0636240i
$329$	−25.9147	+	14.9618i	−1.42872	+	0.824873i
$330$	−6.75015	−	6.56950i	−0.371583	−	0.361639i
$331$	−15.7769	−	9.10879i	−0.867176	−	0.500665i	−0.000767496	−	1.00000i	$-0.500244\pi$
$331$	−15.7769	−	9.10879i	−0.867176	−	0.500665i	−0.866409	+	0.499335i	$0.833578\pi$
$332$	−1.85103	−	6.90813i	−0.101588	−	0.379133i
$333$	−7.85698	−	7.85698i	−0.430560	−	0.430560i
$334$	−11.3299	−	19.6240i	−0.619945	−	1.07378i
$335$	23.1970	+	12.9766i	1.26739	+	0.708987i
$336$	2.62343	+	1.51464i	0.143120	+	0.0826302i
$337$	−0.688043	+	0.688043i	−0.0374801	+	0.0374801i	−0.725598	−	0.688118i	$-0.758437\pi$
$337$	−0.688043	+	0.688043i	−0.0374801	+	0.0374801i	0.688118	+	0.725598i	$0.258437\pi$
$338$	17.7304	+	4.75085i	0.964407	+	0.258412i
$339$	5.36707			0.291499
$340$	−1.20399	+	0.717066i	−0.0652954	+	0.0388884i
$341$	23.3922	+	1.69914i	1.26676	+	0.0920136i
$342$	−5.41023	−	5.41023i	−0.292552	−	0.292552i
$343$	10.3320	−	10.3320i	0.557878	−	0.557878i
$344$	−4.20605	−	7.28509i	−0.226775	−	0.392786i
$345$	0.0760633	+	0.0192794i	0.00409511	+	0.00103797i
$346$	−0.406334	+	0.703791i	−0.0218447	+	0.0378361i
$347$	25.3607	+	6.79538i	1.36143	+	0.364795i	0.864343	−	0.502903i	$-0.167735\pi$
$347$	25.3607	+	6.79538i	1.36143	+	0.364795i	0.497091	+	0.867698i	$0.334401\pi$
$348$	0.149200	+	0.0399781i	0.00799797	+	0.00214305i
$349$		−	4.15705i		−	0.222522i	−0.993791	−	0.111261i	$-0.964511\pi$
$349$		−	4.15705i		−	0.222522i	0.993791	−	0.111261i	$-0.0354889\pi$
$350$	7.92614	+	12.9069i	0.423670	+	0.689904i
$351$	−2.79982	+	4.84942i	−0.149443	+	0.258843i
$352$	1.09026	+	4.06889i	0.0581109	+	0.216873i
$353$	−2.96818	+	11.0774i	−0.157981	+	0.589591i	0.840851	+	0.541266i	$0.182055\pi$
$353$	−2.96818	+	11.0774i	−0.157981	+	0.589591i	−0.998832	+	0.0483249i	$0.984612\pi$
$354$	−4.07240	+	7.05360i	−0.216446	+	0.374895i
$355$	27.8303	−	7.86315i	1.47708	−	0.417332i
$356$			4.49754i			0.238369i
$357$	−1.34241	−	1.34241i	−0.0710476	−	0.0710476i
$358$	−6.60084	+	24.6347i	−0.348865	+	1.30198i
$359$	9.64823	+	5.57041i	0.509214	+	0.293995i	0.732510	−	0.680756i	$-0.238348\pi$
$359$	9.64823	+	5.57041i	0.509214	+	0.293995i	−0.223297	+	0.974751i	$0.571682\pi$
$360$	1.95148	+	1.09167i	0.102852	+	0.0575360i
$361$	19.7706	−	34.2437i	1.04056	−	1.80230i
$362$	−0.659565	−	2.46153i	−0.0346660	−	0.129375i
$363$	6.51473	−	1.74562i	0.341935	−	0.0916212i
$364$	16.9628			0.889093
$365$	−12.8534	−	7.19027i	−0.672776	−	0.376356i
$366$	3.77362	+	6.53610i	0.197250	+	0.341647i
$367$	2.96472	+	11.0645i	0.154757	+	0.577562i	0.999126	+	0.0417998i	$0.0133092\pi$
$367$	2.96472	+	11.0645i	0.154757	+	0.577562i	−0.844369	+	0.535763i	$0.820024\pi$
$368$	−0.0248139	−	0.0248139i	−0.00129352	−	0.00129352i
$369$	−1.03311	+	0.596464i	−0.0537814	+	0.0310507i
$370$	−6.10455	+	24.0844i	−0.317360	+	1.25209i
$371$			18.5718i			0.964199i
$372$	−5.46831	+	1.04764i	−0.283519	+	0.0543175i
$373$	−1.09401	+	1.09401i	−0.0566455	+	0.0566455i	−0.734862	−	0.678217i	$-0.762753\pi$
$373$	−1.09401	+	1.09401i	−0.0566455	+	0.0566455i	0.678217	+	0.734862i	$0.262753\pi$
$374$		−	2.63993i		−	0.136508i
$375$	5.97937	+	9.44707i	0.308773	+	0.487845i
$376$	9.87817			0.509428
$377$	0.835466	−	0.223862i	0.0430287	−	0.0115295i
$378$	−0.784034	+	2.92605i	−0.0403263	+	0.150500i
$379$	17.9959	−	10.3899i	0.924386	−	0.533694i	0.0393542	−	0.999225i	$-0.487470\pi$
$379$	17.9959	−	10.3899i	0.924386	−	0.533694i	0.885032	+	0.465531i	$0.154137\pi$
$380$	−4.20353	+	16.5842i	−0.215636	+	0.850753i
$381$	−9.78054	+	16.9404i	−0.501072	+	0.867882i
$382$	−16.1544	+	4.32857i	−0.826533	+	0.221469i
$383$	19.5981	−	5.25130i	1.00142	−	0.268329i	0.279378	−	0.960181i	$-0.409872\pi$
$383$	19.5981	−	5.25130i	1.00142	−	0.268329i	0.722039	+	0.691852i	$0.243205\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−28.5309	+	0.386956i	−1.45407	+	0.0197211i
$386$	−6.68865	−	11.5851i	−0.340443	−	0.589665i
$387$	5.94825	−	5.94825i	0.302367	−	0.302367i
$388$	3.56033	−	3.56033i	0.180749	−	0.180749i
$389$	1.34175	+	2.32398i	0.0680295	+	0.117831i	0.898034	−	0.439926i	$-0.144995\pi$
$389$	1.34175	+	2.32398i	0.0680295	+	0.117831i	−0.830004	+	0.557757i	$0.811662\pi$
$390$	12.5200	−	0.169805i	0.633975	−	0.00859841i
$391$	0.0109962	+	0.0190459i	0.000556100	+	0.000963193i
$392$	2.10233	−	0.563318i	0.106184	−	0.0284519i
$393$	−0.377129	+	0.101051i	−0.0190236	+	0.00509737i
$394$	2.88271	−	4.99300i	0.145229	−	0.251544i
$395$	2.01961	−	7.96798i	0.101617	−	0.400912i
$396$	−3.64807	+	2.10621i	−0.183322	+	0.105841i
$397$	−3.48748	+	13.0154i	−0.175031	+	0.653226i	0.821515	+	0.570187i	$0.193129\pi$
$397$	−3.48748	+	13.0154i	−0.175031	+	0.653226i	−0.996546	+	0.0830391i	$0.973537\pi$
$398$	0.873186	−	0.233969i	0.0437689	−	0.0117278i
$399$	−23.1777			−1.16033
$400$	−0.135602	−	4.99816i	−0.00678010	−	0.249908i
$401$		−	3.66156i		−	0.182849i	−0.995812	−	0.0914247i	$-0.970858\pi$
$401$		−	3.66156i		−	0.182849i	0.995812	−	0.0914247i	$-0.0291421\pi$
$402$	8.40532	−	8.40532i	0.419219	−	0.419219i
$403$	−23.5850	+	20.3907i	−1.17485	+	1.01573i
$404$			7.71981i			0.384075i
$405$	−0.549393	+	2.16753i	−0.0272995	+	0.107705i
$406$	0.405224	−	0.233956i	0.0201109	−	0.0116110i
$407$	−33.0970	−	33.0970i	−1.64056	−	1.64056i
$408$	0.162202	+	0.605346i	0.00803020	+	0.0299691i
$409$	−3.41089	−	5.90784i	−0.168658	−	0.292124i	0.769290	−	0.638899i	$-0.220610\pi$
$409$	−3.41089	−	5.90784i	−0.168658	−	0.292124i	−0.937948	+	0.346775i	$0.887277\pi$
$410$	2.32797	+	1.30228i	0.114970	+	0.0643152i
$411$	0.0600720			0.00296313
$412$	−11.3489	+	3.04092i	−0.559118	+	0.149815i
$413$	6.38579	+	23.8321i	0.314224	+	1.17270i
$414$	0.0175461	−	0.0303908i	0.000862344	−	0.00149362i
$415$	−13.9566	−	7.80743i	−0.685103	−	0.383252i
$416$	−4.84942	−	2.79982i	−0.237763	−	0.137272i
$417$	−4.16644	+	15.5494i	−0.204032	+	0.761456i
$418$	−22.7902	−	22.7902i	−1.11471	−	1.11471i
$419$		−	6.42908i		−	0.314081i	−0.987592	−	0.157040i	$-0.949805\pi$
$419$		−	6.42908i		−	0.314081i	0.987592	−	0.157040i	$-0.0501953\pi$
$420$	6.51848	−	1.84172i	0.318069	−	0.0898668i
$421$	−4.42759	+	7.66881i	−0.215787	+	0.373755i	−0.953516	−	0.301343i	$-0.902565\pi$
$421$	−4.42759	+	7.66881i	−0.215787	+	0.373755i	0.737728	+	0.675098i	$0.235899\pi$
$422$	−3.52194	+	13.1441i	−0.171446	+	0.639844i
$423$	2.55666	+	9.54158i	0.124309	+	0.463927i
$424$	3.06539	−	5.30941i	0.148868	−	0.257848i
$425$	−0.728626	+	3.04761i	−0.0353435	+	0.147831i
$426$		−	12.9333i		−	0.626622i
$427$	22.0836	+	5.91729i	1.06870	+	0.286358i
$428$	−7.62233	−	2.04240i	−0.368439	−	0.0987231i
$429$	−11.7940	+	20.4278i	−0.569421	+	0.986266i
$430$	−18.2334	−	4.62155i	−0.879295	−	0.222871i
$431$	8.42837	+	14.5984i	0.405980	+	0.703178i	0.994435	−	0.105352i	$-0.0335969\pi$
$431$	8.42837	+	14.5984i	0.405980	+	0.703178i	−0.588455	+	0.808530i	$0.700264\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	13.1004	+	13.1004i	0.629566	+	0.629566i	0.947959	−	0.318393i	$-0.103143\pi$
$433$	13.1004	+	13.1004i	0.629566	+	0.629566i	−0.318393	+	0.947959i	$0.603143\pi$
$434$	−9.46917	+	13.9573i	−0.454535	+	0.669972i
$435$	0.296748	−	0.176736i	0.0142280	−	0.00847384i
$436$	6.96538			0.333581
$437$	0.259350	+	0.0694925i	0.0124064	+	0.00332428i
$438$	−4.65735	+	4.65735i	−0.222537	+	0.222537i
$439$	12.5585	+	7.25068i	0.599386	+	0.346056i	0.768800	−	0.639489i	$-0.220854\pi$
$439$	12.5585	+	7.25068i	0.599386	+	0.346056i	−0.169414	+	0.985545i	$0.554187\pi$
$440$	8.22045	+	4.59858i	0.391895	+	0.219229i
$441$	1.08825	+	1.88490i	0.0518213	+	0.0897572i
$442$	2.48144	+	2.48144i	0.118030	+	0.118030i
$443$	10.6208	+	39.6375i	0.504611	+	1.88323i	0.467645	+	0.883916i	$0.345102\pi$
$443$	10.6208	+	39.6375i	0.504611	+	1.88323i	0.0369652	+	0.999317i	$0.488231\pi$
$444$	9.62280	+	5.55573i	0.456678	+	0.263663i
$445$	7.20701	+	7.01414i	0.341645	+	0.332502i
$446$	−19.5859	+	11.3079i	−0.927417	+	0.535445i
$447$	4.26601	+	15.9210i	0.201775	+	0.753036i
$448$	−2.92605	−	0.784034i	−0.138243	−	0.0370421i
$449$	16.8232			0.793935			0.396968	−	0.917833i	$-0.370063\pi$
$449$	16.8232			0.793935			0.396968	+	0.917833i	$0.370063\pi$
$450$	4.79276	−	1.42460i	0.225933	−	0.0671563i
$451$	−4.35189	+	2.51256i	−0.204922	+	0.118312i
$452$	−5.18420	+	1.38910i	−0.243844	+	0.0653378i
$453$	5.08538	+	1.36262i	0.238932	+	0.0640217i
$454$	6.69761	+	3.86687i	0.314334	+	0.181481i
$455$	26.4544	−	27.1818i	1.24020	−	1.27430i
$456$	6.62616	+	3.82561i	0.310298	+	0.179151i
$457$	−13.2079	+	13.2079i	−0.617840	+	0.617840i	−0.944977	−	0.327137i	$-0.893916\pi$
$457$	−13.2079	+	13.2079i	−0.617840	+	0.617840i	0.327137	+	0.944977i	$0.393916\pi$
$458$	−2.62398	+	9.79283i	−0.122611	+	0.457589i
$459$	−0.542739	+	0.313350i	−0.0253329	+	0.0146259i
$460$	−0.0784614	+	0.00106415i	−0.00365828	+	4.96161e-5i
$461$			8.70636i			0.405495i	0.979231	+	0.202748i	$0.0649871\pi$
$461$			8.70636i			0.405495i	−0.979231	+	0.202748i	$0.935013\pi$
$462$	−3.30268	+	12.3258i	−0.153655	+	0.573448i
$463$	−14.3952	−	14.3952i	−0.669001	−	0.669001i	0.288484	−	0.957485i	$-0.406849\pi$
$463$	−14.3952	−	14.3952i	−0.669001	−	0.669001i	−0.957485	+	0.288484i	$0.906849\pi$
$464$	−0.154463			−0.00717078
$465$	−6.84934	+	10.3965i	−0.317631	+	0.482125i
$466$	−14.8185			−0.686454
$467$	1.35068	+	1.35068i	0.0625020	+	0.0625020i	0.737667	−	0.675165i	$-0.235928\pi$
$467$	1.35068	+	1.35068i	0.0625020	+	0.0625020i	−0.675165	+	0.737667i	$0.735928\pi$
$468$	1.44929	−	5.40883i	0.0669935	−	0.250023i
$469$		−	36.0087i		−	1.66273i
$470$	15.4055	−	15.8291i	0.710603	−	0.730143i
$471$	−10.7844	+	6.22637i	−0.496918	+	0.286896i
$472$	2.10803	−	7.86727i	0.0970299	−	0.362120i
$473$	25.0566	−	25.0566i	1.15210	−	1.15210i
$474$	−3.18357	−	1.83804i	−0.146226	−	0.0844238i
$475$	20.0195	+	32.5998i	0.918560	+	1.49578i
$476$	1.64410	+	0.949224i	0.0753574	+	0.0435076i
$477$	5.92187	+	1.58676i	0.271144	+	0.0726528i
$478$	−9.06774	+	2.42969i	−0.414749	+	0.111132i
$479$	30.3020	−	17.4949i	1.38453	−	0.799361i	0.391842	−	0.920032i	$-0.371838\pi$
$479$	30.3020	−	17.4949i	1.38453	−	0.799361i	0.992693	+	0.120671i	$0.0385046\pi$
$480$	−2.16753	−	0.549393i	−0.0989336	−	0.0250762i
$481$	62.2200			2.83699
$482$	11.2530	+	3.01525i	0.512562	+	0.137341i
$483$	−0.0275135	−	0.102682i	−0.00125191	−	0.00467218i
$484$	−5.84095	+	3.37227i	−0.265498	+	0.153285i
$485$	−0.152685	−	11.2577i	−0.00693307	−	0.511187i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	6.28372	+	23.4511i	0.284742	+	1.06267i	0.949027	+	0.315194i	$0.102069\pi$
$487$	6.28372	+	23.4511i	0.284742	+	1.06267i	−0.664285	+	0.747479i	$0.731264\pi$
$488$	−5.33670	−	5.33670i	−0.241581	−	0.241581i
$489$	−8.92650	−	15.4612i	−0.403670	−	0.699177i
$490$	2.37601	−	4.24738i	0.107337	−	0.191877i
$491$	−31.3581	−	18.1046i	−1.41517	−	0.817048i	−0.419300	−	0.907848i	$-0.637724\pi$
$491$	−31.3581	−	18.1046i	−1.41517	−	0.817048i	−0.995869	+	0.0907993i	$0.971058\pi$
$492$	0.843528	−	0.843528i	0.0380292	−	0.0380292i
$493$	0.0935039	+	0.0250543i	0.00421120	+	0.00112839i
$494$	42.8440			1.92764
$495$	−2.31428	+	9.13055i	−0.104019	+	0.410388i
$496$	5.01084	−	2.42724i	0.224993	−	0.108986i
$497$	−27.7035	−	27.7035i	−1.24267	−	1.24267i
$498$	−5.05710	+	5.05710i	−0.226614	+	0.226614i
$499$	−17.8297	−	30.8820i	−0.798168	−	1.38247i	−0.920808	−	0.390016i	$-0.872469\pi$
$499$	−17.8297	−	30.8820i	−0.798168	−	1.38247i	0.122640	−	0.992451i	$-0.460864\pi$
$500$	−8.22071	−	7.57759i	−0.367641	−	0.338880i
$501$	−11.3299	+	19.6240i	−0.506183	+	0.876734i
$502$	4.82990	+	1.29417i	0.215569	+	0.0577615i
$503$	15.3138	+	4.10331i	0.682807	+	0.182958i	0.583517	−	0.812101i	$-0.301676\pi$
$503$	15.3138	+	4.10331i	0.682807	+	0.182958i	0.0992902	+	0.995059i	$0.468343\pi$
$504$		−	3.02927i		−	0.134935i
$505$	12.3705	+	12.0394i	0.550480	+	0.535748i
$506$	0.0739117	−	0.128019i	0.00328578	−	0.00569113i
$507$	−4.75085	−	17.7304i	−0.210993	−	0.787435i
$508$	5.06278	−	18.8945i	0.224624	−	0.838310i
$509$	19.6597	−	34.0517i	0.871403	−	1.50931i	0.0108566	−	0.999941i	$-0.496544\pi$
$509$	19.6597	−	34.0517i	0.871403	−	1.50931i	0.860546	−	0.509373i	$-0.170122\pi$
$510$	1.22299	+	0.684150i	0.0541550	+	0.0302947i
$511$			19.9523i			0.882637i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.98028	+	7.39052i	−0.0874316	+	0.326299i
$514$	−3.02806	−	1.74825i	−0.133562	−	0.0771119i
$515$	−12.8262	+	22.9283i	−0.565192	+	1.01034i
$516$	−4.20605	+	7.28509i	−0.185161	+	0.320708i
$517$	10.7697	+	40.1932i	0.473653	+	1.76770i
$518$	32.5127	−	8.71175i	1.42853	−	0.382772i
$519$	0.812668			0.0356722
$520$	−12.0494	+	3.40443i	−0.528403	+	0.149294i
$521$	2.95644	+	5.12070i	0.129524	+	0.224342i	0.923492	−	0.383617i	$-0.125322\pi$
$521$	2.95644	+	5.12070i	0.129524	+	0.224342i	−0.793968	+	0.607959i	$0.791988\pi$
$522$	−0.0399781	−	0.149200i	−0.00174979	−	0.00653032i
$523$	7.81273	+	7.81273i	0.341627	+	0.341627i	0.856979	−	0.515352i	$-0.172339\pi$
$523$	7.81273	+	7.81273i	0.341627	+	0.341627i	−0.515352	+	0.856979i	$0.672339\pi$
$524$	0.338125	−	0.195216i	0.0147710	−	0.00852807i
$525$	7.21466	−	13.3177i	0.314873	−	0.581232i
$526$			7.34928i			0.320444i
$527$	−3.42700	+	0.656555i	−0.149282	+	0.0286000i
$528$	2.97864	−	2.97864i	0.129629	−	0.129629i
$529$		−	22.9988i		−	0.999946i
$530$	−3.72736	−	13.1924i	−0.161906	−	0.573040i
$531$	8.14480			0.353454
$532$	22.3879	−	5.99882i	0.970638	−	0.260082i
$533$	1.72890	−	6.45235i	0.0748870	−	0.279482i
$534$	3.89498	−	2.24877i	0.168552	−	0.0973137i
$535$	−15.1602	+	9.02908i	−0.655434	+	0.390361i
$536$	−5.94346	+	10.2944i	−0.256718	+	0.444649i
$537$	24.6347	−	6.60084i	1.06306	−	0.284847i
$538$	23.6461	−	6.33596i	1.01946	−	0.273163i
$539$	4.58417	+	7.94001i	0.197454	+	0.342000i
$540$	−0.0303243	−	2.23586i	−0.00130495	−	0.0962162i
$541$	17.7177	+	30.6879i	0.761743	+	1.31938i	0.941951	+	0.335749i	$0.108989\pi$
$541$	17.7177	+	30.6879i	0.761743	+	1.31938i	−0.180208	+	0.983628i	$0.557677\pi$
$542$	0.259902	−	0.259902i	0.0111638	−	0.0111638i
$543$	−1.80197	+	1.80197i	−0.0773298	+	0.0773298i
$544$	−0.313350	−	0.542739i	−0.0134348	−	0.0232697i
$545$	10.8629	−	11.1616i	0.465314	−	0.478109i
$546$	−8.48141	−	14.6902i	−0.362971	−	0.628684i
$547$	−1.51560	+	0.406104i	−0.0648024	+	0.0173637i	−0.291075	−	0.956700i	$-0.594013\pi$
$547$	−1.51560	+	0.406104i	−0.0648024	+	0.0173637i	0.226272	+	0.974064i	$0.427346\pi$
$548$	−0.0580251	+	0.0155478i	−0.00247871	+	0.000664168i
$549$	3.77362	−	6.53610i	0.161054	−	0.278954i
$550$	20.1891	−	6.00103i	0.860868	−	0.255885i
$551$	1.02350	−	0.590917i	0.0436025	−	0.0251739i
$552$	−0.00908254	+	0.0338965i	−0.000386578	+	0.00144273i
$553$	−10.7564	+	2.88216i	−0.457408	+	0.122562i
$554$	−20.1676			−0.856837
$555$	23.9099	−	6.75548i	1.01492	−	0.286754i
$556$		−	16.0979i		−	0.682703i
$557$	−11.1562	+	11.1562i	−0.472704	+	0.472704i	−0.902789	−	0.430085i	$-0.858484\pi$
$557$	−11.1562	+	11.1562i	−0.472704	+	0.472704i	0.430085	+	0.902789i	$0.358484\pi$
$558$	3.64144	+	4.21188i	0.154154	+	0.178303i
$559$			47.1047i			1.99231i
$560$	−5.81969	+	3.46607i	−0.245927	+	0.146468i
$561$	−2.28625	+	1.31997i	−0.0965254	+	0.0557290i
$562$	14.6840	+	14.6840i	0.619408	+	0.619408i
$563$	−11.2938	−	42.1490i	−0.475976	−	1.77637i	−0.617648	−	0.786454i	$-0.711915\pi$
$563$	−11.2938	−	42.1490i	−0.475976	−	1.77637i	0.141672	−	0.989914i	$-0.454752\pi$
$564$	−4.93908	−	8.55474i	−0.207973	−	0.360220i
$565$	−5.85907	+	10.4737i	−0.246493	+	0.440632i
$566$	−16.4529			−0.691568
$567$	2.92605	−	0.784034i	0.122883	−	0.0329263i
$568$	3.34740	+	12.4926i	0.140454	+	0.524180i
$569$	11.8746	−	20.5674i	0.497808	−	0.862229i	−0.502188	−	0.864758i	$-0.667472\pi$
$569$	11.8746	−	20.5674i	0.497808	−	0.862229i	0.999997	+	0.00252889i	$0.000804973\pi$
$570$	16.4641	−	4.65175i	0.689606	−	0.194840i
$571$	−15.9995	−	9.23734i	−0.669560	−	0.386571i	0.126350	−	0.991986i	$-0.459674\pi$
$571$	−15.9995	−	9.23734i	−0.669560	−	0.386571i	−0.795910	+	0.605415i	$0.793007\pi$
$572$	6.10503	−	22.7843i	0.255264	−	0.952659i
$573$	11.8259	+	11.8259i	0.494033	+	0.494033i
$574$		−	3.61371i		−	0.150833i
$575$	−0.120659	+	0.127389i	−0.00503184	+	0.00531249i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	10.1562	−	37.9036i	0.422810	−	1.57795i	−0.345850	−	0.938290i	$-0.612409\pi$
$577$	10.1562	−	37.9036i	0.422810	−	1.57795i	0.768660	−	0.639658i	$-0.220924\pi$
$578$	−4.29827	−	16.0414i	−0.178785	−	0.667233i
$579$	−6.68865	+	11.5851i	−0.277971	+	0.481460i
$580$	−0.240894	+	0.247518i	−0.0100026	+	0.0102776i
$581$			21.6648i			0.898808i
$582$	−4.86350	−	1.30317i	−0.201599	−	0.0540182i
$583$	24.9455	+	6.68412i	1.03314	+	0.276828i
$584$	3.29324	−	5.70407i	0.136275	−	0.236036i
$585$	−6.40706	−	10.7577i	−0.264899	−	0.444778i
$586$	−13.5424	−	23.4562i	−0.559432	−	0.968965i
$587$	6.00802	−	6.00802i	0.247977	−	0.247977i	−0.572163	−	0.820140i	$-0.693895\pi$
$587$	6.00802	−	6.00802i	0.247977	−	0.247977i	0.820140	+	0.572163i	$0.193895\pi$
$588$	−1.53901	−	1.53901i	−0.0634679	−	0.0634679i
$589$	−23.9169	+	35.2528i	−0.985478	+	1.45257i
$590$	−9.31922	−	15.6474i	−0.383666	−	0.644193i
$591$	−5.76542			−0.237158
$592$	−10.7328	−	2.87586i	−0.441117	−	0.118197i
$593$	−28.5271	+	28.5271i	−1.17147	+	1.17147i	−0.189607	+	0.981860i	$0.560721\pi$
$593$	−28.5271	+	28.5271i	−1.17147	+	1.17147i	−0.981860	+	0.189607i	$0.939279\pi$
$594$	3.64807	+	2.10621i	0.149682	+	0.0864190i
$595$	4.08513	−	1.15421i	0.167474	−	0.0473179i
$596$	−8.24130	−	14.2744i	−0.337577	−	0.584700i
$597$	−0.639217	−	0.639217i	−0.0261614	−	0.0261614i
$598$	0.0508588	+	0.189808i	0.00207977	+	0.00776182i
$599$	27.4119	+	15.8263i	1.12002	+	0.646645i	0.941406	−	0.337274i	$-0.109505\pi$
$599$	27.4119	+	15.8263i	1.12002	+	0.646645i	0.178615	+	0.983919i	$0.442838\pi$
$600$	−4.26073	+	2.61652i	−0.173944	+	0.106819i
$601$	−5.20702	+	3.00628i	−0.212399	+	0.122629i	−0.602426	−	0.798175i	$-0.705799\pi$
$601$	−5.20702	+	3.00628i	−0.212399	+	0.122629i	0.390027	+	0.920803i	$0.372466\pi$
$602$	6.59537	+	24.6143i	0.268807	+	1.00320i
$603$	−11.4819	−	3.07656i	−0.467579	−	0.125287i
$604$	−5.26477			−0.214221
$605$	−3.70541	+	14.6190i	−0.150646	+	0.594346i
$606$	6.68555	−	3.85990i	0.271582	−	0.156798i
$607$	20.6830	−	5.54198i	0.839495	−	0.224942i	0.186644	−	0.982428i	$-0.440239\pi$
$607$	20.6830	−	5.54198i	0.839495	−	0.224942i	0.652852	+	0.757486i	$0.273572\pi$
$608$	−7.39052	−	1.98028i	−0.299725	−	0.0803111i
$609$	−0.405224	−	0.233956i	−0.0164205	−	0.00948037i
$610$	−16.8746	+	0.228865i	−0.683232	+	0.00926647i
$611$	−47.9034	−	27.6570i	−1.93796	−	1.11888i
$612$	0.443144	−	0.443144i	0.0179130	−	0.0179130i
$613$	6.39942	−	23.8830i	0.258470	−	0.964624i	−0.707657	−	0.706556i	$-0.750248\pi$
$613$	6.39942	−	23.8830i	0.258470	−	0.964624i	0.966127	−	0.258067i	$-0.0830856\pi$
$614$	19.0420	−	10.9939i	0.768471	−	0.443677i
$615$	−0.0361747	−	2.66722i	−0.00145871	−	0.107553i
$616$		−	12.7606i		−	0.514139i
$617$	−1.16705	+	4.35549i	−0.0469836	+	0.175345i	−0.985431	−	0.170078i	$-0.945598\pi$
$617$	−1.16705	+	4.35549i	−0.0469836	+	0.175345i	0.938447	+	0.345423i	$0.112265\pi$
$618$	8.30794	+	8.30794i	0.334194	+	0.334194i
$619$	−47.6465			−1.91508			−0.957538	−	0.288308i	$-0.906907\pi$
$619$	−47.6465			−1.91508			−0.957538	+	0.288308i	$0.906907\pi$
$620$	3.92515	−	11.8150i	0.157638	−	0.474500i
$621$	−0.0350922			−0.00140820
$622$	23.8549	+	23.8549i	0.956496	+	0.956496i
$623$	3.52622	−	13.1600i	0.141275	−	0.527245i
$624$			5.59963i			0.224165i
$625$	−24.9632	+	1.35552i	−0.998529	+	0.0542208i
$626$	−25.9739	+	14.9960i	−1.03812	+	0.599362i
$627$	−8.34180	+	31.1320i	−0.333139	+	1.24329i
$628$	8.80542	−	8.80542i	0.351374	−	0.351374i
$629$	6.03061	+	3.48178i	0.240456	+	0.138828i
$630$	−4.85422	−	4.72431i	−0.193397	−	0.188221i
$631$	4.73335	+	2.73280i	0.188432	+	0.108791i	0.591248	−	0.806490i	$-0.298635\pi$
$631$	4.73335	+	2.73280i	0.188432	+	0.108791i	−0.402816	+	0.915281i	$0.631969\pi$
$632$	3.55081	+	0.951437i	0.141244	+	0.0378461i
$633$	13.1441	−	3.52194i	0.522430	−	0.139985i
$634$	22.4516	−	12.9624i	0.891667	−	0.514804i
$635$	−22.3816	−	37.5798i	−0.888188	−	1.49131i
$636$	−6.13078			−0.243101
$637$	−11.7723	−	3.15438i	−0.466435	−	0.124981i
$638$	−0.168405	−	0.628495i	−0.00666721	−	0.0248824i
$639$	−11.2006	+	6.46667i	−0.443089	+	0.255818i
$640$	2.23586	−	0.0303243i	0.0883802	−	0.00119867i
$641$	−15.9513	−	9.20947i	−0.630037	−	0.363752i	0.150729	−	0.988575i	$-0.451838\pi$
$641$	−15.9513	−	9.20947i	−0.630037	−	0.363752i	−0.780767	+	0.624823i	$0.785171\pi$
$642$	2.04240	+	7.62233i	0.0806070	+	0.300830i
$643$	−24.4737	−	24.4737i	−0.965148	−	0.965148i	0.0342643	−	0.999413i	$-0.489091\pi$
$643$	−24.4737	−	24.4737i	−0.965148	−	0.965148i	−0.999413	+	0.0342643i	$0.989091\pi$
$644$	0.0531520	+	0.0920619i	0.00209448	+	0.00362775i
$645$	5.11434	+	18.1014i	0.201377	+	0.712742i
$646$	4.15262	+	2.39751i	0.163382	+	0.0943289i
$647$	−10.7459	+	10.7459i	−0.422466	+	0.422466i	−0.886052	−	0.463586i	$-0.846562\pi$
$647$	−10.7459	+	10.7459i	−0.422466	+	0.422466i	0.463586	+	0.886052i	$0.346562\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	34.3094			1.34676
$650$	−13.3363	+	24.6179i	−0.523094	+	0.965592i
$651$	16.8220	+	1.22190i	0.659305	+	0.0478900i
$652$	12.6240	+	12.6240i	0.494393	+	0.494393i
$653$	−3.97724	+	3.97724i	−0.155641	+	0.155641i	−0.780632	−	0.624991i	$-0.785103\pi$
$653$	−3.97724	+	3.97724i	−0.155641	+	0.155641i	0.624991	+	0.780632i	$0.285103\pi$
$654$	−3.48269	−	6.03219i	−0.136184	−	0.235877i
$655$	0.214501	−	0.846273i	0.00838124	−	0.0330666i
$656$	−0.596464	+	1.03311i	−0.0232880	+	0.0403360i
$657$	6.36206	+	1.70471i	0.248208	+	0.0665070i
$658$	−28.9040	−	7.74482i	−1.12680	−	0.301924i
$659$			24.2340i			0.944025i	0.881592	+	0.472012i	$0.156472\pi$
$659$			24.2340i			0.944025i	−0.881592	+	0.472012i	$0.843528\pi$
$660$	−0.127739	−	9.41841i	−0.00497223	−	0.366611i
$661$	4.61908	−	8.00047i	0.179661	−	0.311182i	−0.762103	−	0.647455i	$-0.775833\pi$
$661$	4.61908	−	8.00047i	0.179661	−	0.311182i	0.941765	+	0.336273i	$0.109167\pi$
$662$	−4.71506	−	17.5968i	−0.183256	−	0.683920i
$663$	0.908272	−	3.38972i	0.0352744	−	0.131646i
$664$	3.57591	−	6.19366i	0.138772	−	0.240361i
$665$	25.3023	−	45.2306i	0.981182	−	1.75397i
$666$		−	11.1115i		−	0.430560i
$667$	0.00383285	+	0.00383285i	0.000148408	+	0.000148408i
$668$	5.86479	−	21.8877i	0.226916	−	0.846860i
$669$	19.5859	+	11.3079i	0.757233	+	0.437189i
$670$	7.22695	+	25.5786i	0.279201	+	0.988188i
$671$	15.8961	−	27.5329i	0.613662	−	1.06289i
$672$	0.784034	+	2.92605i	0.0302448	+	0.112875i
$673$	−5.50307	+	1.47454i	−0.212128	+	0.0568394i	−0.363318	−	0.931665i	$-0.618356\pi$
$673$	−5.50307	+	1.47454i	−0.212128	+	0.0568394i	0.151190	+	0.988505i	$0.451689\pi$
$674$	−0.973040			−0.0374801
$675$	−3.63012	−	3.43835i	−0.139723	−	0.132342i
$676$	9.17793	+	15.8966i	0.352997	+	0.611410i
$677$	−1.49874	−	5.59336i	−0.0576012	−	0.214970i	0.931126	−	0.364697i	$-0.118827\pi$
$677$	−1.49874	−	5.59336i	−0.0576012	−	0.214970i	−0.988727	+	0.149726i	$0.952161\pi$
$678$	3.79509	+	3.79509i	0.145750	+	0.145750i
$679$	−13.2091	+	7.62630i	−0.506920	+	0.292671i
$680$	−1.35839	−	0.344305i	−0.0520919	−	0.0132035i
$681$		−	7.73374i		−	0.296357i
$682$	15.3393	+	17.7422i	0.587372	+	0.679385i
$683$	−8.38124	+	8.38124i	−0.320699	+	0.320699i	−0.849035	−	0.528336i	$-0.822816\pi$
$683$	−8.38124	+	8.38124i	−0.320699	+	0.320699i	0.528336	+	0.849035i	$0.322816\pi$
$684$		−	7.65123i		−	0.292552i
$685$	−0.0655787	+	0.117229i	−0.00250563	+	0.00447909i
$686$	14.6117			0.557878
$687$	9.79283	−	2.62398i	0.373620	−	0.100111i
$688$	2.17721	−	8.12547i	0.0830054	−	0.309780i
$689$	−29.7307	+	17.1650i	−1.13265	+	0.653936i
$690$	0.0401523	+	0.0674175i	0.00152857	+	0.00256654i
$691$	0.0559218	−	0.0968593i	0.00212736	−	0.00368470i	−0.864960	−	0.501841i	$-0.832656\pi$
$691$	0.0559218	−	0.0968593i	0.00212736	−	0.00368470i	0.867087	+	0.498157i	$0.165990\pi$
$692$	−0.784977	+	0.210334i	−0.0298404	+	0.00799570i
$693$	12.3258	−	3.30268i	0.468218	−	0.125459i
$694$	13.1277	+	22.7378i	0.498320	+	0.863115i
$695$	−25.7958	−	25.1055i	−0.978492	−	0.952305i
$696$	0.0772317	+	0.133769i	0.00292746	+	0.00507051i
$697$	0.528639	−	0.528639i	0.0200236	−	0.0200236i
$698$	2.93947	−	2.93947i	0.111261	−	0.111261i
$699$	7.40925	+	12.8332i	0.280244	+	0.485396i
$700$	−3.52195	+	14.7312i	−0.133117	+	0.556787i
$701$	−10.2690	−	17.7864i	−0.387853	−	0.671781i	0.604307	−	0.796751i	$-0.293450\pi$
$701$	−10.2690	−	17.7864i	−0.387853	−	0.671781i	−0.992161	+	0.124970i	$0.960117\pi$
$702$	−5.40883	+	1.44929i	−0.204143	+	0.0547000i
$703$	82.1194	−	22.0038i	3.09719	−	0.829890i
$704$	−2.10621	+	3.64807i	−0.0793809	+	0.137492i
$705$	−21.4112	−	5.42699i	−0.806392	−	0.204392i
$706$	−9.93174	+	5.73409i	−0.373786	+	0.215805i
$707$	6.05259	−	22.5886i	0.227631	−	0.849531i
$708$	−7.86727	+	2.10803i	−0.295670	+	0.0792246i
$709$	24.1122			0.905551			0.452775	−	0.891625i	$-0.350434\pi$
$709$	24.1122			0.905551			0.452775	+	0.891625i	$0.350434\pi$
$710$	25.2391	+	14.1189i	0.947207	+	0.529874i
$711$			3.67607i			0.137863i
$712$	−3.18024	+	3.18024i	−0.119184	+	0.119184i
$713$	−0.184568	−	0.0641091i	−0.00691213	−	0.00240091i
$714$		−	1.89845i		−	0.0710476i
$715$	−26.9893	−	45.3162i	−1.00934	−	1.69473i
$716$	−22.0869	+	12.7518i	−0.825424	+	0.476559i
$717$	6.63805	+	6.63805i	0.247903	+	0.247903i
$718$	2.88345	+	10.7612i	0.107610	+	0.401604i
$719$	11.7783	+	20.4007i	0.439258	+	0.760818i	0.997632	−	0.0687716i	$-0.0219080\pi$
$719$	11.7783	+	20.4007i	0.439258	+	0.760818i	−0.558374	+	0.829589i	$0.688575\pi$
$720$	0.607975	+	2.15183i	0.0226579	+	0.0801939i
$721$	35.5915			1.32550
$722$	38.1939	−	10.2340i	1.42143	−	0.380871i
$723$	−3.01525	−	11.2530i	−0.112138	−	0.418505i
$724$	1.27418	−	2.20695i	0.0473546	−	0.0820206i
$725$	0.0209455	+	0.772033i	0.000777898	+	0.0286726i
$726$	5.84095	+	3.37227i	0.216778	+	0.125157i
$727$	4.35863	−	16.2666i	0.161653	−	0.603296i	−0.836791	−	0.547523i	$-0.815571\pi$
$727$	4.35863	−	16.2666i	0.161653	−	0.603296i	0.998443	−	0.0557732i	$-0.0177624\pi$
$728$	11.9945	+	11.9945i	0.444546	+	0.444546i
$729$		−	1.00000i		−	0.0370370i
$730$	−4.00442	−	14.1730i	−0.148210	−	0.524566i
$731$	−2.63593	+	4.56557i	−0.0974936	+	0.168864i
$732$	−1.95337	+	7.29007i	−0.0721986	+	0.269449i
$733$	−5.00185	−	18.6672i	−0.184748	−	0.689488i	−0.994684	−	0.102970i	$-0.967165\pi$
$733$	−5.00185	−	18.6672i	−0.184748	−	0.689488i	0.809937	−	0.586517i	$-0.199501\pi$
$734$	−5.72741	+	9.92016i	−0.211403	+	0.366160i
$735$	−4.86634	+	0.0660007i	−0.179498	+	0.00243447i
$736$		−	0.0350922i		−	0.00129352i
$737$	−48.3666	−	12.9598i	−1.78161	−	0.477380i
$738$	−1.15228	−	0.308753i	−0.0424160	−	0.0113653i
$739$	−3.82393	+	6.62323i	−0.140665	+	0.243640i	−0.927747	−	0.373209i	$-0.878258\pi$
$739$	−3.82393	+	6.62323i	−0.140665	+	0.243640i	0.787082	+	0.616848i	$0.211591\pi$
$740$	−21.3468	+	12.7136i	−0.784723	+	0.467363i
$741$	−21.4220	−	37.1040i	−0.786958	−	1.36305i
$742$	−13.1322	+	13.1322i	−0.482100	+	0.482100i
$743$	29.3053	+	29.3053i	1.07511	+	1.07511i	0.996940	+	0.0781669i	$0.0249067\pi$
$743$	29.3053	+	29.3053i	1.07511	+	1.07511i	0.0781669	+	0.996940i	$0.475093\pi$
$744$	−4.60747	−	3.12589i	−0.168918	−	0.114601i
$745$	−35.7265	−	9.05542i	−1.30892	−	0.331765i
$746$	−1.54716			−0.0566455
$747$	6.90813	+	1.85103i	0.252755	+	0.0677256i
$748$	1.86671	−	1.86671i	0.0682538	−	0.0682538i
$749$	20.7020	+	11.9523i	0.756436	+	0.436729i
$750$	−2.45203	+	10.9081i	−0.0895356	+	0.398309i
$751$	3.26579	+	5.65651i	0.119170	+	0.206409i	0.919439	−	0.393232i	$-0.128643\pi$
$751$	3.26579	+	5.65651i	0.119170	+	0.206409i	−0.800269	+	0.599641i	$0.795310\pi$
$752$	6.98492	+	6.98492i	0.254714	+	0.254714i
$753$	−1.29417	−	4.82990i	−0.0471621	−	0.176011i
$754$	0.749058	+	0.432469i	0.0272791	+	0.0157496i
$755$	−8.21068	+	8.43646i	−0.298817	+	0.307034i
$756$	−2.62343	+	1.51464i	−0.0954131	+	0.0550868i
$757$	12.4110	+	46.3184i	0.451085	+	1.68347i	0.699349	+	0.714780i	$0.253473\pi$
$757$	12.4110	+	46.3184i	0.451085	+	1.68347i	−0.248264	+	0.968692i	$0.579860\pi$
$758$	20.0718	+	5.37822i	0.729040	+	0.195346i
$759$	−0.147823			−0.00536565
$760$	−14.6992	+	8.75448i	−0.533195	+	0.317558i
$761$	8.85264	−	5.11107i	0.320908	−	0.185276i	−0.330889	−	0.943670i	$-0.607349\pi$
$761$	8.85264	−	5.11107i	0.320908	−	0.185276i	0.651797	+	0.758393i	$0.274015\pi$
$762$	−18.8945	+	5.06278i	−0.684477	+	0.183405i
$763$	−20.3811	−	5.46109i	−0.737844	−	0.197705i
$764$	−14.4837	−	8.36215i	−0.524001	−	0.302532i
$765$	−0.0190043	−	1.40122i	−0.000687101	−	0.0506611i
$766$	17.5712	+	10.1447i	0.634873	+	0.366544i
$767$	−32.2496	+	32.2496i	−1.16447	+	1.16447i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−5.06236	+	2.92275i	−0.182553	+	0.105397i	−0.588492	−	0.808503i	$-0.700278\pi$
$769$	−5.06236	+	2.92275i	−0.182553	+	0.105397i	0.405938	+	0.913900i	$0.366945\pi$
$770$	−20.4480	−	19.9008i	−0.736896	−	0.717175i
$771$			3.49650i			0.125923i
$772$	3.46230	−	12.9215i	0.124611	−	0.465054i
$773$	−16.0800	−	16.0800i	−0.578357	−	0.578357i	0.356094	−	0.934450i	$-0.384108\pi$
$773$	−16.0800	−	16.0800i	−0.578357	−	0.578357i	−0.934450	+	0.356094i	$0.884108\pi$
$774$	8.41210			0.302367
$775$	−12.8112	−	24.7158i	−0.460193	−	0.887819i
$776$	5.03507			0.180749
$777$	−23.8009	−	23.8009i	−0.853854	−	0.853854i
$778$	−0.694541	+	2.59206i	−0.0249005	+	0.0929300i
$779$		−	9.12736i		−	0.327022i
$780$	8.97305	+	8.73291i	0.321287	+	0.312688i
$781$	−47.1817	+	27.2404i	−1.68830	+	0.974738i
$782$	−0.00569203	+	0.0212429i	−0.000203547	+	0.000759646i
$783$	−0.109222	+	0.109222i	−0.00390328	+	0.00390328i
$784$	1.88490	+	1.08825i	0.0673179	+	0.0388660i
$785$	−0.377621	−	27.8426i	−0.0134779	−	0.993745i
$786$	−0.338125	−	0.195216i	−0.0120605	−	0.00696314i
$787$	−12.9992	−	3.48312i	−0.463371	−	0.124160i	0.0195782	−	0.999808i	$-0.493768\pi$
$787$	−12.9992	−	3.48312i	−0.463371	−	0.124160i	−0.482949	+	0.875649i	$0.660434\pi$
$788$	5.56897	−	1.49220i	0.198386	−	0.0531575i
$789$	6.36466	−	3.67464i	0.226588	−	0.130821i
$790$	7.06229	−	4.20613i	0.251265	−	0.149648i
$791$	16.2583			0.578080
$792$	−4.06889	−	1.09026i	−0.144582	−	0.0387406i
$793$	10.9381	+	40.8217i	0.388425	+	1.44962i
$794$	−11.6693	+	6.73729i	−0.414129	+	0.239097i
$795$	−9.56126	+	9.82418i	−0.339103	+	0.348428i
$796$	0.782877	+	0.451994i	0.0277483	+	0.0160205i
$797$	1.35478	+	5.05610i	0.0479887	+	0.179096i	0.985760	−	0.168156i	$-0.0537813\pi$
$797$	1.35478	+	5.05610i	0.0479887	+	0.179096i	−0.937772	+	0.347253i	$0.887115\pi$
$798$	−16.3891	−	16.3891i	−0.580167	−	0.580167i
$799$	−3.09533	−	5.36126i	−0.109505	−	0.189668i
$800$	3.43835	−	3.63012i	0.121564	−	0.128344i
$801$	−3.89498	−	2.24877i	−0.137622	−	0.0794563i
$802$	2.58911	−	2.58911i	0.0914247	−	0.0914247i
$803$	26.7997	+	7.18096i	0.945742	+	0.253411i
$804$	11.8869			0.419219
$805$	0.230416	+	0.0584026i	0.00812111	+	0.00205842i
$806$	−31.0955	−	2.25869i	−1.09529	−	0.0795588i
$807$	−17.3102	−	17.3102i	−0.609347	−	0.609347i
$808$	−5.45873	+	5.45873i	−0.192037	+	0.192037i
$809$	−12.8150	−	22.1963i	−0.450552	−	0.780380i	0.547868	−	0.836565i	$-0.315440\pi$
$809$	−12.8150	−	22.1963i	−0.450552	−	0.780380i	−0.998420	+	0.0561851i	$0.982106\pi$
$810$	−1.92115	+	1.14419i	−0.0675024	+	0.0402028i
$811$	20.6168	−	35.7094i	0.723955	−	1.25393i	−0.235448	−	0.971887i	$-0.575656\pi$
$811$	20.6168	−	35.7094i	0.723955	−	1.25393i	0.959403	−	0.282040i	$-0.0910110\pi$
$812$	0.451968	+	0.121104i	0.0158610	+	0.00424993i
$813$	−0.355033	−	0.0951309i	−0.0124516	−	0.00333639i
$814$		−	46.8062i		−	1.64056i
$815$	39.9168	−	0.541380i	1.39823	−	0.0189637i
$816$	−0.313350	+	0.542739i	−0.0109695	+	0.0189997i
$817$	16.6583	+	62.1698i	0.582801	+	2.17504i
$818$	1.76561	−	6.58934i	0.0617330	−	0.230391i
$819$	−8.48141	+	14.6902i	−0.296364	+	0.513318i
$820$	0.725270	+	2.56698i	0.0253275	+	0.0896428i
$821$		−	35.5485i		−	1.24065i	−0.784345	−	0.620325i	$-0.787001\pi$
$821$		−	35.5485i		−	1.24065i	0.784345	−	0.620325i	$-0.212999\pi$
$822$	0.0424773	+	0.0424773i	0.00148157	+	0.00148157i
$823$	−7.75909	+	28.9573i	−0.270465	+	1.00939i	0.688355	+	0.725374i	$0.258333\pi$
$823$	−7.75909	+	28.9573i	−0.270465	+	1.00939i	−0.958820	+	0.284015i	$0.908333\pi$
$824$	−10.1751	−	5.87460i	−0.354467	−	0.204651i
$825$	−15.2916	−	14.4838i	−0.532386	−	0.504261i
$826$	−12.3364	+	21.3673i	−0.429238	+	0.743463i
$827$	−11.1730	−	41.6982i	−0.388523	−	1.44999i	−0.832537	−	0.553969i	$-0.813113\pi$
$827$	−11.1730	−	41.6982i	−0.388523	−	1.44999i	0.444014	−	0.896020i	$-0.353554\pi$
$828$	0.0338965	−	0.00908254i	0.00117798	−	0.000315640i
$829$	−36.6155			−1.27171			−0.635854	−	0.771809i	$-0.719352\pi$
$829$	−36.6155			−1.27171			−0.635854	+	0.771809i	$0.719352\pi$
$830$	−4.34813	−	15.3895i	−0.150926	−	0.534177i
$831$	10.0838	+	17.4656i	0.349802	+	0.605875i
$832$	−1.44929	−	5.40883i	−0.0502451	−	0.187517i
$833$	−0.964502	−	0.964502i	−0.0334180	−	0.0334180i
$834$	−13.9412	+	8.04895i	−0.482744	+	0.278712i
$835$	−25.9272	−	43.5329i	−0.897247	−	1.50652i
$836$		−	32.2302i		−	1.11471i
$837$	1.82688	−	5.25952i	0.0631461	−	0.181796i
$838$	4.54604	−	4.54604i	0.157040	−	0.157040i
$839$		−	22.1133i		−	0.763435i	−0.924279	−	0.381718i	$-0.875333\pi$
$839$		−	22.1133i		−	0.763435i	0.924279	−	0.381718i	$-0.124667\pi$
$840$	5.91155	+	3.30697i	0.203968	+	0.114101i
$841$	−28.9761			−0.999177
$842$	−8.55344	+	2.29189i	−0.294771	+	0.0789837i
$843$	5.37472	−	20.0587i	0.185115	−	0.690859i
$844$	−11.7847	+	6.80387i	−0.405645	+	0.234199i
$845$	39.7868	+	10.0846i	1.36871	+	0.346920i
$846$	−4.93908	+	8.55474i	−0.169809	+	0.294118i
$847$	19.7349	−	5.28795i	0.678099	−	0.181696i
$848$	5.92187	−	1.58676i	0.203358	−	0.0544896i
$849$	8.22646	+	14.2486i	0.282331	+	0.489012i
$850$	−2.67020	+	1.63977i	−0.0915873	+	0.0562437i
$851$	0.194963	+	0.337685i	0.00668324	+	0.0115757i
$852$	9.14525	−	9.14525i	0.313311	−	0.313311i
$853$	−36.7868	+	36.7868i	−1.25956	+	1.25956i	−0.308251	+	0.951305i	$0.599744\pi$
$853$	−36.7868	+	36.7868i	−1.25956	+	1.25956i	−0.951305	+	0.308251i	$0.900256\pi$
$854$	11.4313	+	19.7996i	0.391172	+	0.677529i
$855$	−12.2606	−	11.9325i	−0.419304	−	0.408082i
$856$	−3.94561	−	6.83400i	−0.134858	−	0.233581i
$857$	39.5088	−	10.5863i	1.34959	−	0.361622i	0.489609	−	0.871942i	$-0.337140\pi$
$857$	39.5088	−	10.5863i	1.34959	−	0.361622i	0.859985	+	0.510320i	$0.170473\pi$
$858$	−22.7843	+	6.10503i	−0.777843	+	0.208422i
$859$	0.0805822	−	0.139572i	0.00274943	−	0.00476215i	−0.864647	−	0.502379i	$-0.832458\pi$
$859$	0.0805822	−	0.139572i	0.00274943	−	0.00476215i	0.867397	+	0.497617i	$0.165791\pi$
$860$	−9.62506	−	16.1609i	−0.328212	−	0.551083i
$861$	−3.12956	+	1.80685i	−0.106655	+	0.0615774i
$862$	−4.36284	+	16.2824i	−0.148599	+	0.554579i
$863$	13.8882	−	3.72132i	0.472758	−	0.126675i	−0.0145703	−	0.999894i	$-0.504638\pi$
$863$	13.8882	−	3.72132i	0.472758	−	0.126675i	0.487329	+	0.873219i	$0.337971\pi$
$864$	1.00000			0.0340207
$865$	−0.887165	+	1.58590i	−0.0301645	+	0.0539223i
$866$			18.5268i			0.629566i
$867$	−11.7431	+	11.7431i	−0.398816	+	0.398816i
$868$	−16.5650	+	3.17358i	−0.562253	+	0.107718i
$869$			15.4852i			0.525299i
$870$	0.334803	+	0.0848611i	0.0113509	+	0.00287706i
$871$	57.6447	−	33.2812i	1.95322	−	1.12769i
$872$	4.92527	+	4.92527i	0.166791	+	0.166791i
$873$	1.30317	+	4.86350i	0.0441057	+	0.164605i
$874$	0.134249	+	0.232527i	0.00454105	+	0.00786533i
$875$	18.1131	+	28.6178i	0.612336	+	0.967457i
$876$	−6.58649			−0.222537
$877$	1.20312	−	0.322374i	0.0406263	−	0.0108858i	−0.238449	−	0.971155i	$-0.576639\pi$
$877$	1.20312	−	0.322374i	0.0406263	−	0.0108858i	0.279075	+	0.960269i	$0.409972\pi$
$878$	3.75323	+	14.0072i	0.126665	+	0.472721i
$879$	−13.5424	+	23.4562i	−0.456775	+	0.791157i
$880$	2.56105	+	9.06442i	0.0863330	+	0.305562i
$881$	33.4336	+	19.3029i	1.12641	+	0.650331i	0.943029	−	0.332712i	$-0.107964\pi$
$881$	33.4336	+	19.3029i	1.12641	+	0.650331i	0.183377	+	0.983043i	$0.441297\pi$
$882$	−0.563318	+	2.10233i	−0.0189679	+	0.0707892i
$883$	−16.9351	−	16.9351i	−0.569910	−	0.569910i	0.362193	−	0.932103i	$-0.382028\pi$
$883$	−16.9351	−	16.9351i	−0.569910	−	0.569910i	−0.932103	+	0.362193i	$0.882028\pi$
$884$			3.50929i			0.118030i
$885$	−8.89143	+	15.8944i	−0.298882	+	0.534283i
$886$	−20.5179	+	35.5380i	−0.689311	+	1.19392i
$887$	−8.53531	+	31.8542i	−0.286588	+	1.06956i	0.661084	+	0.750312i	$0.270097\pi$
$887$	−8.53531	+	31.8542i	−0.286588	+	1.06956i	−0.947671	+	0.319248i	$0.896570\pi$
$888$	2.87586	+	10.7328i	0.0965074	+	0.360170i
$889$	−29.6279	+	51.3171i	−0.993688	+	1.72112i
$890$	0.136385	+	10.0559i	0.00457162	+	0.337074i
$891$		−	4.21243i		−	0.141122i
$892$	−21.8452	−	5.85340i	−0.731431	−	0.195986i
$893$	−73.0048	−	19.5616i	−2.44301	−	0.654603i
$894$	−8.24130	+	14.2744i	−0.275630	+	0.477406i
$895$	−14.0115	+	55.2799i	−0.468354	+	1.84780i
$896$	−1.51464	−	2.62343i	−0.0506005	−	0.0876426i
$897$	0.138949	−	0.138949i	0.00463937	−	0.00463937i
$898$	11.8958	+	11.8958i	0.396968	+	0.396968i
$899$	−0.773991	+	0.374920i	−0.0258140	+	0.0125043i
$900$	4.39634	+	2.38165i	0.146545	+	0.0793882i
$901$	−3.84216			−0.128001
$902$	−4.85390	−	1.30060i	−0.161617	−	0.0433052i
$903$	18.0189	−	18.0189i	0.599631	−	0.599631i
$904$	−4.64802	−	2.68354i	−0.154591	−	0.0892531i
$905$	−1.54934	−	5.48365i	−0.0515019	−	0.182283i
$906$	2.63239	+	4.55943i	0.0874552	+	0.151477i
$907$	−15.2026	−	15.2026i	−0.504795	−	0.504795i	0.408129	−	0.912924i	$-0.366181\pi$
$907$	−15.2026	−	15.2026i	−0.504795	−	0.504795i	−0.912924	+	0.408129i	$0.866181\pi$
$908$	2.00164	+	7.47021i	0.0664267	+	0.247908i
$909$	−6.68555	−	3.85990i	−0.221746	−	0.128025i
$910$	37.9265	−	0.514386i	1.25725	−	0.0170517i
$911$	16.6136	−	9.59188i	0.550434	−	0.317793i	−0.198863	−	0.980027i	$-0.563725\pi$
$911$	16.6136	−	9.59188i	0.550434	−	0.317793i	0.749297	+	0.662234i	$0.230392\pi$
$912$	1.98028	+	7.39052i	0.0655737	+	0.244724i
$913$	29.1000	+	7.79732i	0.963070	+	0.258054i
$914$	−18.6788			−0.617840
$915$	8.63550	+	14.4994i	0.285481	+	0.479335i
$916$	−8.78001	+	5.06914i	−0.290100	+	0.167489i
$917$	−1.14243	+	0.306112i	−0.0377263	+	0.0101087i
$918$	−0.605346	−	0.162202i	−0.0199794	−	0.00535347i
$919$	−25.9145	−	14.9617i	−0.854841	−	0.493543i	0.00744045	−	0.999972i	$-0.497632\pi$
$919$	−25.9145	−	14.9617i	−0.854841	−	0.493543i	−0.862281	+	0.506430i	$0.830965\pi$
$920$	−0.0562330	−	0.0547281i	−0.00185395	−	0.00180433i
$921$	−19.0420	−	10.9939i	−0.627454	−	0.362261i
$922$	−6.15632	+	6.15632i	−0.202748	+	0.202748i
$923$	18.7442	−	69.9542i	0.616972	−	2.30257i
$924$	−11.0510	+	6.38030i	−0.363551	+	0.209896i
$925$	−12.9186	+	54.0344i	−0.424761	+	1.77664i
$926$		−	20.3579i		−	0.669001i
$927$	3.04092	−	11.3489i	0.0998768	−	0.372745i
$928$	−0.109222	−	0.109222i	−0.00358539	−	0.00358539i
$929$	−16.2835			−0.534243			−0.267121	−	0.963663i	$-0.586072\pi$
$929$	−16.2835			−0.534243			−0.267121	+	0.963663i	$0.586072\pi$
$930$	−12.1946	+	2.50820i	−0.399878	+	0.0822470i
$931$	−16.6529			−0.545775
$932$	−10.4783	−	10.4783i	−0.343227	−	0.343227i
$933$	8.73152	−	32.5865i	0.285857	−	1.06683i
$934$			1.91015i			0.0625020i
$935$	−0.0800541	−	5.90252i	−0.00261805	−	0.193033i
$936$	4.84942	−	2.79982i	0.158508	−	0.0915148i
$937$	1.45735	−	5.43890i	0.0476095	−	0.177681i	−0.938027	−	0.346563i	$-0.887349\pi$
$937$	1.45735	−	5.43890i	0.0476095	−	0.177681i	0.985636	+	0.168881i	$0.0540155\pi$
$938$	25.4620	−	25.4620i	0.831365	−	0.831365i
$939$	25.9739	+	14.9960i	0.847625	+	0.489377i
$940$	22.0862	−	0.299549i	0.720373	−	0.00977020i
$941$	−19.8391	−	11.4541i	−0.646736	−	0.373393i	0.140469	−	0.990085i	$-0.455139\pi$
$941$	−19.8391	−	11.4541i	−0.646736	−	0.373393i	−0.787204	+	0.616692i	$0.788472\pi$
$942$	−12.0284	−	3.22301i	−0.391907	−	0.105011i
$943$	0.0404361	−	0.0108348i	0.00131678	−	0.000352830i
$944$	7.05360	−	4.07240i	0.229575	−	0.132545i
$945$	−1.66426	+	6.56603i	−0.0541384	+	0.213593i
$946$	35.4354			1.15210
$947$	49.5803	+	13.2850i	1.61114	+	0.431705i	0.948383	−	0.317127i	$-0.102718\pi$
$947$	49.5803	+	13.2850i	1.61114	+	0.431705i	0.662761	+	0.748831i	$0.269385\pi$
$948$	−0.951437	−	3.55081i	−0.0309012	−	0.115325i
$949$	−31.9407	+	18.4410i	−1.03684	+	0.598619i
$950$	−8.89560	+	37.2075i	−0.288611	+	1.20717i
$951$	−22.4516	−	12.9624i	−0.728043	−	0.420336i
$952$	0.491354	+	1.83376i	0.0159249	+	0.0594325i
$953$	−6.59878	−	6.59878i	−0.213755	−	0.213755i	0.592105	−	0.805861i	$-0.298297\pi$
$953$	−6.59878	−	6.59878i	−0.213755	−	0.213755i	−0.805861	+	0.592105i	$0.798297\pi$
$954$	3.06539	+	5.30941i	0.0992456	+	0.171898i
$955$	−35.9878	+	10.1680i	−1.16454	+	0.329027i
$956$	−8.12992	−	4.69381i	−0.262940	−	0.151809i
$957$	−0.460090	+	0.460090i	−0.0148726	+	0.0148726i
$958$	33.7975	+	9.05602i	1.09195	+	0.292587i
$959$	0.181974			0.00587626
$960$	−1.14419	−	1.92115i	−0.0369287	−	0.0620049i
$961$	19.2170	−	24.3250i	0.619902	−	0.784679i
$962$	43.9962	+	43.9962i	1.41849	+	1.41849i
$963$	5.57994	−	5.57994i	0.179811	−	0.179811i
$964$	5.82501	+	10.0892i	0.187611	+	0.324951i
$965$	−15.3062	−	25.6998i	−0.492724	−	0.827307i
$966$	0.0531520	−	0.0920619i	0.00171014	−	0.00296204i
$967$	31.4869	+	8.43689i	1.01255	+	0.271312i	0.726695	−	0.686960i	$-0.241055\pi$
$967$	31.4869	+	8.43689i	1.01255	+	0.271312i	0.285856	+	0.958273i	$0.407722\pi$
$968$	−6.51473	−	1.74562i	−0.209391	−	0.0561063i
$969$		−	4.79503i		−	0.154038i
$970$	7.85245	−	8.06838i	0.252127	−	0.259060i
$971$	−12.5746	+	21.7798i	−0.403537	+	0.698947i	−0.994150	−	0.108008i	$-0.965553\pi$
$971$	−12.5746	+	21.7798i	−0.403537	+	0.698947i	0.590613	+	0.806955i	$0.298886\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−12.6213	+	47.1033i	−0.404620	+	1.51006i
$974$	−12.1392	+	21.0257i	−0.388965	+	0.673708i
$975$	27.9879	−	0.759321i	0.896329	−	0.0243177i
$976$		−	7.54724i		−	0.241581i
$977$	−14.6867	−	14.6867i	−0.469868	−	0.469868i	0.432004	−	0.901872i	$-0.357807\pi$
$977$	−14.6867	−	14.6867i	−0.469868	−	0.469868i	−0.901872	+	0.432004i	$0.857807\pi$
$978$	4.62070	−	17.2447i	0.147754	−	0.551424i
$979$	−16.4073	−	9.47277i	−0.524380	−	0.302751i
$980$	4.68345	−	1.32325i	0.149607	−	0.0422698i
$981$	−3.48269	+	6.03219i	−0.111194	+	0.192593i
$982$	−9.37162	−	34.9754i	−0.299060	−	1.11611i
$983$	−52.5787	+	14.0884i	−1.67700	+	0.449351i	−0.966985	−	0.254834i	$-0.917979\pi$
$983$	−52.5787	+	14.0884i	−1.67700	+	0.449351i	−0.710017	+	0.704185i	$0.751313\pi$
$984$	1.19293			0.0380292
$985$	6.29394	−	11.2511i	0.200541	−	0.358489i
$986$	0.0484012	+	0.0838333i	0.00154141	+	0.00266980i
$987$	7.74482	+	28.9040i	0.246520	+	0.920026i
$988$	30.2953	+	30.2953i	0.963822	+	0.963822i
$989$	−0.255650	+	0.147600i	−0.00812920	+	0.00469340i
$990$	−8.09271	+	4.81983i	−0.257203	+	0.153184i
$991$		−	23.4242i		−	0.744095i	−0.928214	−	0.372047i	$-0.878656\pi$
$991$		−	23.4242i		−	0.744095i	0.928214	−	0.372047i	$-0.121344\pi$
$992$	5.25952	+	1.82688i	0.166990	+	0.0580034i
$993$	−12.8818	+	12.8818i	−0.408791	+	0.408791i
$994$		−	39.1786i		−	1.24267i
$995$	1.94523	−	0.549602i	0.0616679	−	0.0174236i
$996$	−7.15182			−0.226614
$997$	39.4657	−	10.5748i	1.24989	−	0.334907i	0.427596	−	0.903970i	$-0.359361\pi$
$997$	39.4657	−	10.5748i	1.24989	−	0.334907i	0.822294	+	0.569063i	$0.192694\pi$
$998$	9.22934	−	34.4444i	0.292150	−	1.09032i
$999$	−9.62280	+	5.55573i	−0.304452	+	0.175775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.16	✓	64
5.3	odd	4		930.2.be.b.223.10	yes	64
31.26	odd	6		930.2.be.b.367.10	yes	64
155.88	even	12	inner	930.2.be.a.553.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.16	✓	64	1.1	even	1	trivial
930.2.be.a.553.16	yes	64	155.88	even	12	inner
930.2.be.b.223.10	yes	64	5.3	odd	4
930.2.be.b.367.10	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.60244 + 1.55955i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.784034 - 2.92605i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.60244 + 1.55955i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.784034 - 2.92605i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.0303243 + 2.23586i) q^{10} +(-3.64807 - 2.10621i) q^{11} +(0.965926 + 0.258819i) q^{12} +(5.40883 - 1.44929i) q^{13} +(2.62343 - 1.51464i) q^{14} +(1.92115 - 1.14419i) q^{15} -1.00000 q^{16} +(0.605346 + 0.162202i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(6.62616 - 3.82561i) q^{19} +(-1.55955 + 1.60244i) q^{20} +(-2.62343 - 1.51464i) q^{21} +(-1.09026 - 4.06889i) q^{22} +(0.0248139 + 0.0248139i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.135602 + 4.99816i) q^{25} +(4.84942 + 2.79982i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.92605 + 0.784034i) q^{28} +0.154463 q^{29} +(2.16753 + 0.549393i) q^{30} +(-5.01084 + 2.42724i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.97864 + 2.97864i) q^{33} +(0.313350 + 0.542739i) q^{34} +(5.81969 - 3.46607i) q^{35} +(0.500000 - 0.866025i) q^{36} +(10.7328 + 2.87586i) q^{37} +(7.39052 + 1.98028i) q^{38} -5.59963i q^{39} +(-2.23586 + 0.0303243i) q^{40} +(0.596464 - 1.03311i) q^{41} +(-0.784034 - 2.92605i) q^{42} +(-2.17721 + 8.12547i) q^{43} +(2.10621 - 3.64807i) q^{44} +(-0.607975 - 2.15183i) q^{45} +0.0350922i q^{46} +(-6.98492 - 6.98492i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-1.88490 - 1.08825i) q^{49} +(-3.43835 + 3.63012i) q^{50} +(0.313350 - 0.542739i) q^{51} +(1.44929 + 5.40883i) q^{52} +(-5.92187 + 1.58676i) q^{53} -1.00000 q^{54} +(-2.56105 - 9.06442i) q^{55} +(1.51464 + 2.62343i) q^{56} +(-1.98028 - 7.39052i) q^{57} +(0.109222 + 0.109222i) q^{58} +(-7.05360 + 4.07240i) q^{59} +(1.14419 + 1.92115i) q^{60} +7.54724i q^{61} +(-5.25952 - 1.82688i) q^{62} +(-2.14202 + 2.14202i) q^{63} -1.00000i q^{64} +(10.9275 + 6.11295i) q^{65} -4.21243 q^{66} +(11.4819 - 3.07656i) q^{67} +(-0.162202 + 0.605346i) q^{68} +(0.0303908 - 0.0175461i) q^{69} +(6.56603 + 1.66426i) q^{70} +(6.46667 - 11.2006i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-6.36206 + 1.70471i) q^{73} +(5.55573 + 9.62280i) q^{74} +(4.86295 + 1.16264i) q^{75} +(3.82561 + 6.62616i) q^{76} +(-9.02310 + 9.02310i) q^{77} +(3.95954 - 3.95954i) q^{78} +(-1.83804 - 3.18357i) q^{79} +(-1.60244 - 1.55955i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.15228 - 0.308753i) q^{82} +(-6.90813 + 1.85103i) q^{83} +(1.51464 - 2.62343i) q^{84} +(0.717066 + 1.20399i) q^{85} +(-7.28509 + 4.20605i) q^{86} +(0.0399781 - 0.149200i) q^{87} +(4.06889 - 1.09026i) q^{88} +4.49754 q^{89} +(1.09167 - 1.95148i) q^{90} -16.9628i q^{91} +(-0.0248139 + 0.0248139i) q^{92} +(1.04764 + 5.46831i) q^{93} -9.87817i q^{94} +(16.5842 + 4.20353i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-3.56033 - 3.56033i) q^{97} +(-0.563318 - 2.10233i) q^{98} +(2.10621 + 3.64807i) 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

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