LMFDB - Embedded newform 930.2.be.b.37.2

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			37.2
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.90333 - 1.17360i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.365018 + 1.36227i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.90333 - 1.17360i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.365018 + 1.36227i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.515994 + 2.17572i) q^{10} +(4.76949 + 2.75367i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-1.59299 + 0.426840i) q^{13} +(1.22137 - 0.705160i) q^{14} +(-1.62623 + 1.53472i) q^{15} -1.00000 q^{16} +(5.00634 + 1.34144i) q^{17} +(0.258819 + 0.965926i) q^{18} +(1.58505 - 0.915126i) q^{19} +(1.17360 - 1.90333i) q^{20} +(1.22137 + 0.705160i) q^{21} +(-1.42540 - 5.31968i) q^{22} +(-1.29889 - 1.29889i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.24532 + 4.46750i) q^{25} +(1.42824 + 0.824592i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.36227 - 0.365018i) q^{28} +8.56947 q^{29} +(2.23513 + 0.0647049i) q^{30} +(-3.92867 - 3.94532i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.89428 - 3.89428i) q^{33} +(-2.59147 - 4.48856i) q^{34} +(2.29351 - 2.16445i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-6.11479 - 1.63845i) q^{37} +(-1.76789 - 0.473704i) q^{38} +1.64918i q^{39} +(-2.17572 + 0.515994i) q^{40} +(3.95985 - 6.85866i) q^{41} +(-0.365018 - 1.36227i) q^{42} +(1.92231 - 7.17416i) q^{43} +(-2.75367 + 4.76949i) q^{44} +(1.06153 + 1.96803i) q^{45} +1.83691i q^{46} +(1.09254 + 1.09254i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(4.33965 + 2.50550i) q^{49} +(1.57132 - 4.74668i) q^{50} +(2.59147 - 4.48856i) q^{51} +(-0.426840 - 1.59299i) q^{52} +(1.21471 - 0.325481i) q^{53} +1.00000 q^{54} +(-5.84620 - 10.8386i) q^{55} +(0.705160 + 1.22137i) q^{56} +(-0.473704 - 1.76789i) q^{57} +(-6.05953 - 6.05953i) q^{58} +(3.20296 - 1.84923i) q^{59} +(-1.53472 - 1.62623i) q^{60} +3.67820i q^{61} +(-0.0117750 + 5.56775i) q^{62} +(0.997247 - 0.997247i) q^{63} -1.00000i q^{64} +(3.53292 + 1.05712i) q^{65} -5.50734 q^{66} +(-6.11665 + 1.63895i) q^{67} +(-1.34144 + 5.00634i) q^{68} +(-1.59081 + 0.918457i) q^{69} +(-3.15225 - 0.0912547i) q^{70} +(0.861959 - 1.49296i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(11.1271 - 2.98150i) q^{73} +(3.16525 + 5.48237i) q^{74} +(4.89640 - 1.01254i) q^{75} +(0.915126 + 1.58505i) q^{76} +(-5.49218 + 5.49218i) q^{77} +(1.16615 - 1.16615i) q^{78} +(6.16709 + 10.6817i) q^{79} +(1.90333 + 1.17360i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-7.64984 + 2.04977i) q^{82} +(-0.111997 + 0.0300095i) q^{83} +(-0.705160 + 1.22137i) q^{84} +(-7.95438 - 8.42865i) q^{85} +(-6.43217 + 3.71362i) q^{86} +(2.21794 - 8.27747i) q^{87} +(5.31968 - 1.42540i) q^{88} +6.11279 q^{89} +(0.640995 - 2.14222i) q^{90} -2.32588i q^{91} +(1.29889 - 1.29889i) q^{92} +(-4.82770 + 2.77368i) q^{93} -1.54508i q^{94} +(-4.09086 - 0.118426i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-5.78447 - 5.78447i) q^{97} +(-1.29694 - 4.84025i) q^{98} +(-2.75367 - 4.76949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	−1.90333	−	1.17360i	−0.851194	−	0.524851i
$5$	−1.90333	−	1.17360i	−0.851194	−	0.524851i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.365018	+	1.36227i	−0.137964	+	0.514888i	0.862004	+	0.506901i	$0.169209\pi$
$7$	−0.365018	+	1.36227i	−0.137964	+	0.514888i	−0.999968	+	0.00798689i	$0.997458\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	0.515994	+	2.17572i	0.163172	+	0.688023i
$11$	4.76949	+	2.75367i	1.43806	+	0.830262i	0.997715	−	0.0675677i	$-0.0215239\pi$
$11$	4.76949	+	2.75367i	1.43806	+	0.830262i	0.440342	+	0.897830i	$0.354857\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−1.59299	+	0.426840i	−0.441816	+	0.118384i	−0.472867	−	0.881134i	$-0.656781\pi$
$13$	−1.59299	+	0.426840i	−0.441816	+	0.118384i	0.0310516	+	0.999518i	$0.490114\pi$
$14$	1.22137	−	0.705160i	0.326426	−	0.188462i
$15$	−1.62623	+	1.53472i	−0.419891	+	0.396264i
$16$	−1.00000			−0.250000
$17$	5.00634	+	1.34144i	1.21422	+	0.325348i	0.808414	−	0.588614i	$-0.200326\pi$
$17$	5.00634	+	1.34144i	1.21422	+	0.325348i	0.405801	+	0.913962i	$0.366993\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	1.58505	−	0.915126i	0.363634	−	0.209944i	−0.307040	−	0.951697i	$-0.599338\pi$
$19$	1.58505	−	0.915126i	0.363634	−	0.209944i	0.670674	+	0.741752i	$0.266005\pi$
$20$	1.17360	−	1.90333i	0.262425	−	0.425597i
$21$	1.22137	+	0.705160i	0.266526	+	0.153879i
$22$	−1.42540	−	5.31968i	−0.303897	−	1.13416i
$23$	−1.29889	−	1.29889i	−0.270838	−	0.270838i	0.558599	−	0.829438i	$-0.311339\pi$
$23$	−1.29889	−	1.29889i	−0.270838	−	0.270838i	−0.829438	+	0.558599i	$0.811339\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.24532	+	4.46750i	0.449063	+	0.893500i
$26$	1.42824	+	0.824592i	0.280100	+	0.161716i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.36227	−	0.365018i	−0.257444	−	0.0689819i
$29$	8.56947			1.59131			0.795655	−	0.605750i	$-0.207127\pi$
$29$	8.56947			1.59131			0.795655	+	0.605750i	$0.207127\pi$
$30$	2.23513	+	0.0647049i	0.408077	+	0.0118134i
$31$	−3.92867	−	3.94532i	−0.705610	−	0.708601i
$31$	−3.92867	−	3.94532i	−0.705610	−	0.708601i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.89428	−	3.89428i	0.677906	−	0.677906i
$34$	−2.59147	−	4.48856i	−0.444434	−	0.769781i
$35$	2.29351	−	2.16445i	0.387673	−	0.365859i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−6.11479	−	1.63845i	−1.00527	−	0.269360i	−0.281616	−	0.959527i	$-0.590870\pi$
$37$	−6.11479	−	1.63845i	−1.00527	−	0.269360i	−0.723650	+	0.690167i	$0.757537\pi$
$38$	−1.76789	−	0.473704i	−0.286789	−	0.0768450i
$39$			1.64918i			0.264081i
$40$	−2.17572	+	0.515994i	−0.344011	+	0.0815859i
$41$	3.95985	−	6.85866i	0.618424	−	1.07114i	−0.371349	−	0.928493i	$-0.621105\pi$
$41$	3.95985	−	6.85866i	0.618424	−	1.07114i	0.989773	−	0.142649i	$-0.0455619\pi$
$42$	−0.365018	−	1.36227i	−0.0563235	−	0.210202i
$43$	1.92231	−	7.17416i	0.293149	−	1.09405i	−0.649527	−	0.760339i	$-0.725033\pi$
$43$	1.92231	−	7.17416i	0.293149	−	1.09405i	0.942676	−	0.333710i	$-0.108300\pi$
$44$	−2.75367	+	4.76949i	−0.415131	+	0.719028i
$45$	1.06153	+	1.96803i	0.158244	+	0.293377i
$46$			1.83691i			0.270838i
$47$	1.09254	+	1.09254i	0.159363	+	0.159363i	0.782284	−	0.622922i	$-0.214054\pi$
$47$	1.09254	+	1.09254i	0.159363	+	0.159363i	−0.622922	+	0.782284i	$0.714054\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	4.33965	+	2.50550i	0.619950	+	0.357928i
$50$	1.57132	−	4.74668i	0.222218	−	0.671282i
$51$	2.59147	−	4.48856i	0.362878	−	0.628524i
$52$	−0.426840	−	1.59299i	−0.0591921	−	0.220908i
$53$	1.21471	−	0.325481i	0.166854	−	0.0447083i	−0.174425	−	0.984670i	$-0.555807\pi$
$53$	1.21471	−	0.325481i	0.166854	−	0.0447083i	0.341279	+	0.939962i	$0.389140\pi$
$54$	1.00000			0.136083
$55$	−5.84620	−	10.8386i	−0.788302	−	1.46148i
$56$	0.705160	+	1.22137i	0.0942310	+	0.163213i
$57$	−0.473704	−	1.76789i	−0.0627437	−	0.234163i
$58$	−6.05953	−	6.05953i	−0.795655	−	0.795655i
$59$	3.20296	−	1.84923i	0.416990	−	0.240749i	−0.276799	−	0.960928i	$-0.589273\pi$
$59$	3.20296	−	1.84923i	0.416990	−	0.240749i	0.693789	+	0.720179i	$0.255940\pi$
$60$	−1.53472	−	1.62623i	−0.198132	−	0.209945i
$61$			3.67820i			0.470945i	0.971881	+	0.235473i	$0.0756638\pi$
$61$			3.67820i			0.470945i	−0.971881	+	0.235473i	$0.924336\pi$
$62$	−0.0117750	+	5.56775i	−0.00149543	+	0.707105i
$63$	0.997247	−	0.997247i	0.125641	−	0.125641i
$64$		−	1.00000i		−	0.125000i
$65$	3.53292	+	1.05712i	0.438205	+	0.131119i
$66$	−5.50734			−0.677906
$67$	−6.11665	+	1.63895i	−0.747267	+	0.200230i	−0.612306	−	0.790621i	$-0.709758\pi$
$67$	−6.11665	+	1.63895i	−0.747267	+	0.200230i	−0.134962	+	0.990851i	$0.543091\pi$
$68$	−1.34144	+	5.00634i	−0.162674	+	0.607108i
$69$	−1.59081	+	0.918457i	−0.191512	+	0.110569i
$70$	−3.15225	−	0.0912547i	−0.376766	−	0.0109070i
$71$	0.861959	−	1.49296i	0.102296	−	0.177181i	−0.810334	−	0.585968i	$-0.800715\pi$
$71$	0.861959	−	1.49296i	0.102296	−	0.177181i	0.912630	+	0.408786i	$0.134048\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	11.1271	−	2.98150i	1.30233	−	0.348958i	0.459998	−	0.887920i	$-0.347850\pi$
$73$	11.1271	−	2.98150i	1.30233	−	0.348958i	0.842330	+	0.538962i	$0.181183\pi$
$74$	3.16525	+	5.48237i	0.367953	+	0.637313i
$75$	4.89640	−	1.01254i	0.565388	−	0.116918i
$76$	0.915126	+	1.58505i	0.104972	+	0.181817i
$77$	−5.49218	+	5.49218i	−0.625892	+	0.625892i
$78$	1.16615	−	1.16615i	0.132040	−	0.132040i
$79$	6.16709	+	10.6817i	0.693852	+	1.20179i	0.970566	+	0.240835i	$0.0774212\pi$
$79$	6.16709	+	10.6817i	0.693852	+	1.20179i	−0.276714	+	0.960952i	$0.589245\pi$
$80$	1.90333	+	1.17360i	0.212799	+	0.131213i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−7.64984	+	2.04977i	−0.844783	+	0.226359i
$83$	−0.111997	+	0.0300095i	−0.0122933	+	0.00329397i	−0.264960	−	0.964259i	$-0.585359\pi$
$83$	−0.111997	+	0.0300095i	−0.0122933	+	0.00329397i	0.252667	+	0.967553i	$0.418692\pi$
$84$	−0.705160	+	1.22137i	−0.0769393	+	0.133263i
$85$	−7.95438	−	8.42865i	−0.862774	−	0.914216i
$86$	−6.43217	+	3.71362i	−0.693599	+	0.400450i
$87$	2.21794	−	8.27747i	0.237788	−	0.887438i
$88$	5.31968	−	1.42540i	0.567080	−	0.151949i
$89$	6.11279			0.647954			0.323977	−	0.946065i	$-0.394980\pi$
$89$	6.11279			0.647954			0.323977	+	0.946065i	$0.394980\pi$
$90$	0.640995	−	2.14222i	0.0675668	−	0.225810i
$91$		−	2.32588i		−	0.243818i
$92$	1.29889	−	1.29889i	0.135419	−	0.135419i
$93$	−4.82770	+	2.77368i	−0.500609	+	0.287617i
$94$		−	1.54508i		−	0.159363i
$95$	−4.09086	−	0.118426i	−0.419713	−	0.0121503i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−5.78447	−	5.78447i	−0.587324	−	0.587324i	0.349582	−	0.936906i	$-0.386324\pi$
$97$	−5.78447	−	5.78447i	−0.587324	−	0.587324i	−0.936906	+	0.349582i	$0.886324\pi$
$98$	−1.29694	−	4.84025i	−0.131011	−	0.488939i
$99$	−2.75367	−	4.76949i	−0.276754	−	0.479352i
$100$	−4.46750	+	2.24532i	−0.446750	+	0.224532i
$101$	1.61451			0.160650			0.0803250	−	0.996769i	$-0.474404\pi$
$101$	1.61451			0.160650			0.0803250	+	0.996769i	$0.474404\pi$
$102$	−5.00634	+	1.34144i	−0.495701	+	0.132823i
$103$	1.94487	+	7.25834i	0.191633	+	0.715185i	0.993113	+	0.117163i	$0.0373800\pi$
$103$	1.94487	+	7.25834i	0.191633	+	0.715185i	−0.801479	+	0.598022i	$0.795953\pi$
$104$	−0.824592	+	1.42824i	−0.0808579	+	0.140050i
$105$	−1.49710	−	2.77556i	−0.146102	−	0.270867i
$106$	−1.08908	−	0.628781i	−0.105781	−	0.0610727i
$107$	−0.0147139	+	0.0549131i	−0.00142245	+	0.00530865i	−0.966633	−	0.256164i	$-0.917541\pi$
$107$	−0.0147139	+	0.0549131i	−0.00142245	+	0.00530865i	0.965211	+	0.261472i	$0.0842080\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	10.4813i		−	1.00393i	−0.864888	−	0.501964i	$-0.832611\pi$
$109$		−	10.4813i		−	1.00393i	0.864888	−	0.501964i	$-0.167389\pi$
$110$	−3.53017	+	11.7980i	−0.336589	+	1.12489i
$111$	−3.16525	+	5.48237i	−0.300432	+	0.520364i
$112$	0.365018	−	1.36227i	0.0344909	−	0.128722i
$113$	−3.20155	−	11.9484i	−0.301177	−	1.12401i	−0.936187	−	0.351503i	$-0.885671\pi$
$113$	−3.20155	−	11.9484i	−0.301177	−	1.12401i	0.635010	−	0.772504i	$-0.280996\pi$
$114$	−0.915126	+	1.58505i	−0.0857094	+	0.148453i
$115$	0.947838	+	3.99661i	0.0883863	+	0.372686i
$116$			8.56947i			0.795655i
$117$	1.59299	+	0.426840i	0.147272	+	0.0394614i
$118$	−3.57244	−	0.957232i	−0.328870	−	0.0881204i
$119$	−3.65480	+	6.33031i	−0.335035	+	0.580298i
$120$	−0.0647049	+	2.23513i	−0.00590672	+	0.204039i
$121$	9.66539	+	16.7409i	0.878671	+	1.52190i
$122$	2.60088	−	2.60088i	0.235473	−	0.235473i
$123$	−5.60007	−	5.60007i	−0.504941	−	0.504941i
$124$	3.94532	−	3.92867i	0.354300	−	0.352805i
$125$	0.969490	−	11.1382i	0.0867138	−	0.996233i
$126$	−1.41032			−0.125641
$127$	14.3322	+	3.84029i	1.27177	+	0.340771i	0.830710	−	0.556705i	$-0.187935\pi$
$127$	14.3322	+	3.84029i	1.27177	+	0.340771i	0.441064	+	0.897476i	$0.354601\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−6.43217	−	3.71362i	−0.566321	−	0.326966i
$130$	−1.75066	−	3.24565i	−0.153543	−	0.284662i
$131$	−4.01261	−	6.95005i	−0.350584	−	0.607228i	0.635768	−	0.771880i	$-0.280683\pi$
$131$	−4.01261	−	6.95005i	−0.350584	−	0.607228i	−0.986352	+	0.164652i	$0.947350\pi$
$132$	3.89428	+	3.89428i	0.338953	+	0.338953i
$133$	0.668075	+	2.49329i	0.0579294	+	0.216196i
$134$	5.48403	+	3.16621i	0.473748	+	0.273519i
$135$	2.17572	−	0.515994i	0.187256	−	0.0444097i
$136$	4.48856	−	2.59147i	0.384891	−	0.222217i
$137$	1.83157	+	6.83553i	0.156482	+	0.583998i	0.998974	+	0.0452896i	$0.0144211\pi$
$137$	1.83157	+	6.83553i	0.156482	+	0.583998i	−0.842492	+	0.538709i	$0.818912\pi$
$138$	1.77432	+	0.475429i	0.151040	+	0.0404712i
$139$	21.5923			1.83143			0.915716	−	0.401827i	$-0.131625\pi$
$139$	21.5923			1.83143			0.915716	+	0.401827i	$0.131625\pi$
$140$	2.16445	+	2.29351i	0.182930	+	0.193837i
$141$	1.33808	−	0.772539i	0.112686	−	0.0650595i
$142$	−1.66518	+	0.446183i	−0.139739	+	0.0374428i
$143$	−8.77313	−	2.35075i	−0.733646	−	0.196580i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−16.3105	−	10.0571i	−1.35451	−	0.835200i
$146$	−9.97628	−	5.75981i	−0.825643	−	0.476685i
$147$	3.54331	−	3.54331i	0.292247	−	0.292247i
$148$	1.63845	−	6.11479i	0.134680	−	0.502633i
$149$	5.20693	−	3.00622i	0.426568	−	0.246279i	−0.271315	−	0.962490i	$-0.587459\pi$
$149$	5.20693	−	3.00622i	0.426568	−	0.246279i	0.697883	+	0.716211i	$0.254125\pi$
$150$	−4.17825	−	2.74631i	−0.341153	−	0.224235i
$151$			16.9926i			1.38284i	0.722455	+	0.691418i	$0.243014\pi$
$151$			16.9926i			1.38284i	−0.722455	+	0.691418i	$0.756986\pi$
$152$	0.473704	−	1.76789i	0.0384225	−	0.143395i
$153$	−3.66489	−	3.66489i	−0.296289	−	0.296289i
$154$	7.76711			0.625892
$155$	2.84731	+	12.1199i	0.228701	+	0.973497i
$156$	−1.64918			−0.132040
$157$	−11.4947	−	11.4947i	−0.917379	−	0.917379i	0.0794594	−	0.996838i	$-0.474681\pi$
$157$	−11.4947	−	11.4947i	−0.917379	−	0.917379i	−0.996838	+	0.0794594i	$0.974681\pi$
$158$	3.19232	−	11.9139i	0.253968	−	0.947820i
$159$		−	1.25756i		−	0.0997312i
$160$	−0.515994	−	2.17572i	−0.0407929	−	0.172006i
$161$	2.24356	−	1.29532i	0.176817	−	0.102085i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−0.570334	+	0.570334i	−0.0446720	+	0.0446720i	−0.729090	−	0.684418i	$-0.760056\pi$
$163$	−0.570334	+	0.570334i	−0.0446720	+	0.0446720i	0.684418	+	0.729090i	$0.260056\pi$
$164$	6.85866	+	3.95985i	0.535571	+	0.309212i
$165$	−11.9824	+	2.84176i	−0.932830	+	0.221230i
$166$	0.100414	+	0.0579739i	0.00779362	+	0.00449965i
$167$	13.1852	+	3.53295i	1.02030	+	0.273388i	0.729926	−	0.683526i	$-0.239554\pi$
$167$	13.1852	+	3.53295i	1.02030	+	0.273388i	0.290372	+	0.956914i	$0.406221\pi$
$168$	1.36227	−	0.365018i	0.105101	−	0.0281617i
$169$	−8.90291	+	5.14010i	−0.684839	+	0.395392i
$170$	−0.335362	+	11.5846i	−0.0257211	+	0.888495i
$171$	−1.83025			−0.139963
$172$	7.17416	+	1.92231i	0.547024	+	0.146575i
$173$	0.969755	+	3.61918i	0.0737291	+	0.275161i	0.992942	−	0.118600i	$-0.0378406\pi$
$173$	0.969755	+	3.61918i	0.0737291	+	0.275161i	−0.919213	+	0.393761i	$0.871174\pi$
$174$	−7.42138	+	4.28473i	−0.562613	+	0.324825i
$175$	−6.90550	+	1.42800i	−0.522007	+	0.107947i
$176$	−4.76949	−	2.75367i	−0.359514	−	0.207566i
$177$	−0.957232	−	3.57244i	−0.0719500	−	0.268521i
$178$	−4.32239	−	4.32239i	−0.323977	−	0.323977i
$179$	9.09197	+	15.7478i	0.679566	+	1.17704i	0.975112	+	0.221714i	$0.0711651\pi$
$179$	9.09197	+	15.7478i	0.679566	+	1.17704i	−0.295546	+	0.955328i	$0.595502\pi$
$180$	−1.96803	+	1.06153i	−0.146689	+	0.0791218i
$181$	−13.6285	−	7.86840i	−1.01300	−	0.584854i	−0.100929	−	0.994894i	$-0.532181\pi$
$181$	−13.6285	−	7.86840i	−1.01300	−	0.584854i	−0.912068	+	0.410040i	$0.865515\pi$
$182$	−1.64464	+	1.64464i	−0.121909	+	0.121909i
$183$	3.55287	+	0.951988i	0.262636	+	0.0703730i
$184$	−1.83691			−0.135419
$185$	9.71556	+	10.2948i	0.714302	+	0.756892i
$186$	5.37499	+	1.45241i	0.394113	+	0.106496i
$187$	20.1838	+	20.1838i	1.47599	+	1.47599i
$188$	−1.09254	+	1.09254i	−0.0796813	+	0.0796813i
$189$	−0.705160	−	1.22137i	−0.0512929	−	0.0888418i
$190$	2.80893	+	2.97641i	0.203781	+	0.215932i
$191$	−3.56841	+	6.18066i	−0.258201	+	0.447217i	−0.965760	−	0.259437i	$-0.916463\pi$
$191$	−3.56841	+	6.18066i	−0.258201	+	0.447217i	0.707559	+	0.706654i	$0.249796\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−20.6245	−	5.52631i	−1.48458	−	0.397792i	−0.576678	−	0.816972i	$-0.695651\pi$
$193$	−20.6245	−	5.52631i	−1.48458	−	0.397792i	−0.907904	+	0.419179i	$0.862318\pi$
$194$			8.18047i			0.587324i
$195$	1.93549	−	3.13894i	0.138603	−	0.224784i
$196$	−2.50550	+	4.33965i	−0.178964	+	0.309975i
$197$	0.196708	+	0.734126i	0.0140149	+	0.0523043i	0.972579	−	0.232572i	$-0.0747141\pi$
$197$	0.196708	+	0.734126i	0.0140149	+	0.0523043i	−0.958564	+	0.284876i	$0.908047\pi$
$198$	−1.42540	+	5.31968i	−0.101299	+	0.378053i
$199$	−5.59973	+	9.69902i	−0.396954	+	0.687545i	−0.993349	−	0.115147i	$-0.963266\pi$
$199$	−5.59973	+	9.69902i	−0.396954	+	0.687545i	0.596394	+	0.802692i	$0.296600\pi$
$200$	4.74668	+	1.57132i	0.335641	+	0.111109i
$201$			6.33242i			0.446654i
$202$	−1.14163	−	1.14163i	−0.0803250	−	0.0803250i
$203$	−3.12801	+	11.6739i	−0.219543	+	0.819346i
$204$	4.48856	+	2.59147i	0.314262	+	0.181439i
$205$	−15.5862	+	8.40699i	−1.08859	+	0.587170i
$206$	3.75719	−	6.50765i	0.261776	−	0.453409i
$207$	0.475429	+	1.77432i	0.0330446	+	0.123324i
$208$	1.59299	−	0.426840i	0.110454	−	0.0295961i
$209$	10.0798			0.697236
$210$	−0.904008	+	3.02122i	−0.0623825	+	0.208484i
$211$	2.26979	+	3.93139i	0.156259	+	0.270648i	0.933517	−	0.358534i	$-0.116723\pi$
$211$	2.26979	+	3.93139i	0.156259	+	0.270648i	−0.777258	+	0.629182i	$0.783390\pi$
$212$	0.325481	+	1.21471i	0.0223541	+	0.0834268i
$213$	−1.21899	−	1.21899i	−0.0835241	−	0.0835241i
$214$	0.0492337	−	0.0284251i	0.00336555	−	0.00194310i
$215$	−12.0784	+	11.3987i	−0.823739	+	0.777388i
$216$			1.00000i			0.0680414i
$217$	6.80861	−	3.91178i	0.462198	−	0.265549i
$218$	−7.41142	+	7.41142i	−0.501964	+	0.501964i
$219$		−	11.5196i		−	0.778424i
$220$	10.8386	−	5.84620i	0.730740	−	0.394151i
$221$	−8.54763			−0.574976
$222$	6.11479	−	1.63845i	0.410398	−	0.109966i
$223$	3.13152	−	11.6870i	0.209702	−	0.782619i	−0.778263	−	0.627939i	$-0.783899\pi$
$223$	3.13152	−	11.6870i	0.209702	−	0.782619i	0.987965	−	0.154680i	$-0.0494346\pi$
$224$	−1.22137	+	0.705160i	−0.0816064	+	0.0471155i
$225$	0.289248	−	4.99163i	0.0192832	−	0.332775i
$226$	−6.18492	+	10.7126i	−0.411415	+	0.712592i
$227$	17.9798	−	4.81768i	1.19336	−	0.319761i	0.393149	−	0.919475i	$-0.371386\pi$
$227$	17.9798	−	4.81768i	1.19336	−	0.319761i	0.800214	+	0.599714i	$0.204719\pi$
$228$	1.76789	−	0.473704i	0.117081	−	0.0313718i
$229$	14.9754	+	25.9381i	0.989600	+	1.71404i	0.619372	+	0.785097i	$0.287387\pi$
$229$	14.9754	+	25.9381i	0.989600	+	1.71404i	0.370228	+	0.928941i	$0.379279\pi$
$230$	2.15581	−	3.49625i	0.142150	−	0.230536i
$231$	3.88356	+	6.72652i	0.255519	+	0.442572i
$232$	6.05953	−	6.05953i	0.397828	−	0.397828i
$233$	−4.63191	+	4.63191i	−0.303446	+	0.303446i	−0.842361	−	0.538914i	$-0.818835\pi$
$233$	−4.63191	+	4.63191i	−0.303446	+	0.303446i	0.538914	+	0.842361i	$0.318835\pi$
$234$	−0.824592	−	1.42824i	−0.0539053	−	0.0933667i
$235$	−0.797252	−	3.36166i	−0.0520070	−	0.219290i
$236$	1.84923	+	3.20296i	0.120375	+	0.208495i
$237$	11.9139	−	3.19232i	0.773892	−	0.207364i
$238$	7.06054	−	1.89187i	0.457667	−	0.122631i
$239$	−14.6461	+	25.3678i	−0.947378	+	1.64091i	−0.196460	+	0.980512i	$0.562944\pi$
$239$	−14.6461	+	25.3678i	−0.947378	+	1.64091i	−0.750918	+	0.660395i	$0.770389\pi$
$240$	1.62623	−	1.53472i	0.104973	−	0.0990660i
$241$	−17.0275	+	9.83082i	−1.09684	+	0.633259i	−0.935388	−	0.353622i	$-0.884950\pi$
$241$	−17.0275	+	9.83082i	−1.09684	+	0.633259i	−0.161448	+	0.986881i	$0.551616\pi$
$242$	5.00317	−	18.6721i	0.321616	−	1.20029i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−3.67820			−0.235473
$245$	−5.31932	−	9.86181i	−0.339839	−	0.630048i
$246$			7.91969i			0.504941i
$247$	−2.13435	+	2.13435i	−0.135805	+	0.135805i
$248$	−5.56775	−	0.0117750i	−0.353553	−	0.000747713i
$249$			0.115948i			0.00734790i
$250$	−8.56145	+	7.19038i	−0.541474	+	0.454760i
$251$	2.47386	−	1.42828i	0.156149	−	0.0901525i	−0.419890	−	0.907575i	$-0.637931\pi$
$251$	2.47386	−	1.42828i	0.156149	−	0.0901525i	0.576038	+	0.817423i	$0.304598\pi$
$252$	0.997247	+	0.997247i	0.0628207	+	0.0628207i
$253$	−2.61835	−	9.77180i	−0.164614	−	0.614348i
$254$	−7.41887	−	12.8499i	−0.465501	−	0.806272i
$255$	−10.2002	+	5.50185i	−0.638761	+	0.344539i
$256$	1.00000			0.0625000
$257$	−7.46671	+	2.00070i	−0.465760	+	0.124800i	−0.484064	−	0.875032i	$-0.660840\pi$
$257$	−7.46671	+	2.00070i	−0.465760	+	0.124800i	0.0183041	+	0.999832i	$0.494173\pi$
$258$	1.92231	+	7.17416i	0.119678	+	0.446643i
$259$	4.46401	−	7.73190i	0.277380	−	0.480437i
$260$	−1.05712	+	3.53292i	−0.0655597	+	0.219103i
$261$	−7.42138	−	4.28473i	−0.459372	−	0.265218i
$262$	−2.07708	+	7.75177i	−0.128322	+	0.478906i
$263$	−14.7396	−	14.7396i	−0.908882	−	0.908882i	0.0872999	−	0.996182i	$-0.472176\pi$
$263$	−14.7396	−	14.7396i	−0.908882	−	0.908882i	−0.996182	+	0.0872999i	$0.972176\pi$
$264$		−	5.50734i		−	0.338953i
$265$	−2.69398	−	0.806091i	−0.165490	−	0.0495178i
$266$	1.29062	−	2.23542i	0.0791331	−	0.137063i
$267$	1.58211	−	5.90450i	0.0968233	−	0.361349i
$268$	−1.63895	−	6.11665i	−0.100115	−	0.373634i
$269$	−2.72975	+	4.72807i	−0.166436	+	0.288275i	−0.937164	−	0.348888i	$-0.886559\pi$
$269$	−2.72975	+	4.72807i	−0.166436	+	0.288275i	0.770728	+	0.637164i	$0.219893\pi$
$270$	−1.90333	−	1.17360i	−0.115833	−	0.0714231i
$271$		−	20.0039i		−	1.21515i	−0.794263	−	0.607574i	$-0.792143\pi$
$271$		−	20.0039i		−	1.21515i	0.794263	−	0.607574i	$-0.207857\pi$
$272$	−5.00634	−	1.34144i	−0.303554	−	0.0813370i
$273$	−2.24663	−	0.601982i	−0.135972	−	0.0364336i
$274$	3.53833	−	6.12857i	0.213758	−	0.370240i
$275$	−1.59299	+	27.4906i	−0.0960607	+	1.65774i
$276$	−0.918457	−	1.59081i	−0.0552846	−	0.0957558i
$277$	−7.36520	+	7.36520i	−0.442532	+	0.442532i	−0.892862	−	0.450330i	$-0.851306\pi$
$277$	−7.36520	+	7.36520i	−0.442532	+	0.442532i	0.450330	+	0.892862i	$0.351306\pi$
$278$	−15.2680	−	15.2680i	−0.915716	−	0.915716i
$279$	1.42967	+	5.38108i	0.0855919	+	0.322157i
$280$	0.0912547	−	3.15225i	0.00545351	−	0.188383i
$281$	21.1775			1.26334			0.631671	−	0.775236i	$-0.282369\pi$
$281$	21.1775			1.26334			0.631671	+	0.775236i	$0.282369\pi$
$282$	−1.49243	−	0.399896i	−0.0888730	−	0.0238134i
$283$	−5.40267	+	5.40267i	−0.321156	+	0.321156i	−0.849210	−	0.528055i	$-0.822922\pi$
$283$	−5.40267	+	5.40267i	−0.321156	+	0.321156i	0.528055	+	0.849210i	$0.322922\pi$
$284$	1.49296	+	0.861959i	0.0885907	+	0.0511479i
$285$	−1.17318	+	3.92081i	−0.0694933	+	0.232249i
$286$	4.54131	+	7.86578i	0.268533	+	0.465113i
$287$	7.89789	+	7.89789i	0.466198	+	0.466198i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	8.54151	+	4.93144i	0.502441	+	0.290085i
$290$	4.42180	+	18.6447i	0.259657	+	1.09486i
$291$	−7.08450	+	4.09024i	−0.415301	+	0.239774i
$292$	2.98150	+	11.1271i	0.174479	+	0.651164i
$293$	18.3769	+	4.92408i	1.07359	+	0.287668i	0.751968	−	0.659200i	$-0.229105\pi$
$293$	18.3769	+	4.92408i	1.07359	+	0.287668i	0.321623	+	0.946868i	$0.395772\pi$
$294$	−5.01100			−0.292247
$295$	−8.26655	−	0.239309i	−0.481297	−	0.0139331i
$296$	−5.48237	+	3.16525i	−0.318656	+	0.183976i
$297$	−5.31968	+	1.42540i	−0.308679	+	0.0827103i
$298$	−5.80757	−	1.55613i	−0.336424	−	0.0901444i
$299$	2.62355	+	1.51471i	0.151724	+	0.0875977i
$300$	1.01254	+	4.89640i	0.0584588	+	0.282694i
$301$	9.07142	+	5.23739i	0.522868	+	0.301878i
$302$	12.0156	−	12.0156i	0.691418	−	0.691418i
$303$	0.417867	−	1.55950i	0.0240058	−	0.0895909i
$304$	−1.58505	+	0.915126i	−0.0909086	+	0.0524861i
$305$	4.31674	−	7.00082i	0.247176	−	0.400866i
$306$			5.18294i			0.296289i
$307$	−4.98996	+	18.6228i	−0.284792	+	1.06286i	0.664199	+	0.747556i	$0.268773\pi$
$307$	−4.98996	+	18.6228i	−0.284792	+	1.06286i	−0.948991	+	0.315303i	$0.897894\pi$
$308$	−5.49218	−	5.49218i	−0.312946	−	0.312946i
$309$	7.51439			0.427478
$310$	6.55674	−	10.5834i	0.372398	−	0.601099i
$311$	−21.3413			−1.21016			−0.605078	−	0.796166i	$-0.706858\pi$
$311$	−21.3413			−1.21016			−0.605078	+	0.796166i	$0.706858\pi$
$312$	1.16615	+	1.16615i	0.0660202	+	0.0660202i
$313$	−5.43604	+	20.2876i	−0.307263	+	1.14672i	0.623717	+	0.781651i	$0.285622\pi$
$313$	−5.43604	+	20.2876i	−0.307263	+	1.14672i	−0.930980	+	0.365071i	$0.881045\pi$
$314$			16.2560i			0.917379i
$315$	−3.06846	+	0.727718i	−0.172888	+	0.0410022i
$316$	−10.6817	+	6.16709i	−0.600894	+	0.346926i
$317$	1.09927	−	4.10255i	0.0617414	−	0.230422i	−0.928160	−	0.372182i	$-0.878610\pi$
$317$	1.09927	−	4.10255i	0.0617414	−	0.230422i	0.989901	+	0.141760i	$0.0452763\pi$
$318$	−0.889231	+	0.889231i	−0.0498656	+	0.0498656i
$319$	40.8720	+	23.5975i	2.28839	+	1.32121i
$320$	−1.17360	+	1.90333i	−0.0656063	+	0.106399i
$321$	0.0492337	+	0.0284251i	0.00274796	+	0.00158654i
$322$	−2.50236	−	0.670507i	−0.139451	−	0.0373659i
$323$	9.16286	−	2.45518i	0.509835	−	0.136610i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−5.48368	−	6.15829i	−0.304180	−	0.341600i
$326$	0.806574			0.0446720
$327$	−10.1242	−	2.71277i	−0.559869	−	0.150016i
$328$	−2.04977	−	7.64984i	−0.113179	−	0.422392i
$329$	−1.88712	+	1.08953i	−0.104040	+	0.0600676i
$330$	10.4823	+	6.46342i	0.577030	+	0.355800i
$331$	−14.0795	−	8.12878i	−0.773877	−	0.446798i	0.0603787	−	0.998176i	$-0.480769\pi$
$331$	−14.0795	−	8.12878i	−0.773877	−	0.446798i	−0.834256	+	0.551377i	$0.814102\pi$
$332$	−0.0300095	−	0.111997i	−0.00164699	−	0.00614664i
$333$	4.47634	+	4.47634i	0.245302	+	0.245302i
$334$	−6.82514	−	11.8215i	−0.373455	−	0.646843i
$335$	13.5655	+	4.05905i	0.741160	+	0.221769i
$336$	−1.22137	−	0.705160i	−0.0666314	−	0.0384696i
$337$	22.6011	−	22.6011i	1.23116	−	1.23116i	0.267644	−	0.963518i	$-0.413755\pi$
$337$	22.6011	−	22.6011i	1.23116	−	1.23116i	0.963518	−	0.267644i	$-0.0862450\pi$
$338$	9.92990	+	2.66071i	0.540115	+	0.144723i
$339$	−12.3698			−0.671838
$340$	8.42865	−	7.95438i	0.457108	−	0.431387i
$341$	−7.87366	−	29.6354i	−0.426382	−	1.60485i
$342$	1.29418	+	1.29418i	0.0699815	+	0.0699815i
$343$	−11.9779	+	11.9779i	−0.646748	+	0.646748i
$344$	−3.71362	−	6.43217i	−0.200225	−	0.346799i
$345$	4.10575	+	0.118857i	0.221046	+	0.00639907i
$346$	1.87342	−	3.24486i	0.100716	−	0.174445i
$347$	−9.35605	−	2.50695i	−0.502259	−	0.134580i	−0.00121079	−	0.999999i	$-0.500385\pi$
$347$	−9.35605	−	2.50695i	−0.502259	−	0.134580i	−0.501048	+	0.865419i	$0.667052\pi$
$348$	8.27747	+	2.21794i	0.443719	+	0.118894i
$349$		−	27.6329i		−	1.47916i	−0.673071	−	0.739578i	$-0.735025\pi$
$349$		−	27.6329i		−	1.47916i	0.673071	−	0.739578i	$-0.264975\pi$
$350$	5.89267	+	3.87318i	0.314977	+	0.207030i
$351$	0.824592	−	1.42824i	0.0440135	−	0.0762336i
$352$	1.42540	+	5.31968i	0.0759743	+	0.283540i
$353$	−0.276676	+	1.03257i	−0.0147260	+	0.0549581i	−0.972898	−	0.231235i	$-0.925723\pi$
$353$	−0.276676	+	1.03257i	−0.0147260	+	0.0549581i	0.958172	+	0.286193i	$0.0923900\pi$
$354$	−1.84923	+	3.20296i	−0.0982855	+	0.170236i
$355$	−3.39273	+	1.82999i	−0.180067	+	0.0971258i
$356$			6.11279i			0.323977i
$357$	5.16867	+	5.16867i	0.273555	+	0.273555i
$358$	4.70635	−	17.5643i	0.248738	−	0.928304i
$359$	−25.4293	−	14.6816i	−1.34211	−	0.774866i	−0.354992	−	0.934869i	$-0.615516\pi$
$359$	−25.4293	−	14.6816i	−1.34211	−	0.774866i	−0.987117	+	0.160003i	$0.948850\pi$
$360$	2.14222	+	0.640995i	0.112905	+	0.0337834i
$361$	−7.82509	+	13.5534i	−0.411847	+	0.713339i
$362$	4.07298	+	15.2006i	0.214071	+	0.798925i
$363$	18.6721	−	5.00317i	0.980031	−	0.262598i
$364$	2.32588			0.121909
$365$	−24.6776	−	7.38402i	−1.29169	−	0.386497i
$366$	−1.83910	−	3.18541i	−0.0961313	−	0.166504i
$367$	2.85716	+	10.6630i	0.149142	+	0.556607i	0.999536	+	0.0304598i	$0.00969714\pi$
$367$	2.85716	+	10.6630i	0.149142	+	0.556607i	−0.850394	+	0.526147i	$0.823636\pi$
$368$	1.29889	+	1.29889i	0.0677096	+	0.0677096i
$369$	−6.85866	+	3.95985i	−0.357047	+	0.206141i
$370$	0.409614	−	14.1495i	0.0212948	−	0.735597i
$371$			1.77357i			0.0920790i
$372$	−2.77368	−	4.82770i	−0.143809	−	0.250305i
$373$	−10.1478	+	10.1478i	−0.525434	+	0.525434i	−0.919208	−	0.393773i	$-0.871170\pi$
$373$	−10.1478	+	10.1478i	−0.525434	+	0.525434i	0.393773	+	0.919208i	$0.371170\pi$
$374$		−	28.5442i		−	1.47599i
$375$	−10.5078	−	3.81924i	−0.542619	−	0.197225i
$376$	1.54508			0.0796813
$377$	−13.6511	+	3.65779i	−0.703066	+	0.188386i
$378$	−0.365018	+	1.36227i	−0.0187745	+	0.0700674i
$379$	−0.779872	+	0.450259i	−0.0400593	+	0.0231283i	−0.519896	−	0.854230i	$-0.674029\pi$
$379$	−0.779872	+	0.450259i	−0.0400593	+	0.0231283i	0.479837	+	0.877358i	$0.340696\pi$
$380$	0.118426	−	4.09086i	0.00607514	−	0.209856i
$381$	7.41887	−	12.8499i	0.380080	−	0.658318i
$382$	6.89363	−	1.84714i	0.352709	−	0.0945081i
$383$	31.0337	−	8.31545i	1.58575	−	0.424900i	0.645048	−	0.764142i	$-0.276837\pi$
$383$	31.0337	−	8.31545i	1.58575	−	0.424900i	0.940699	+	0.339243i	$0.110171\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	16.8990	−	4.00779i	0.861255	−	0.204256i
$386$	10.6760	+	18.4914i	0.543395	+	0.941187i
$387$	−5.25185	+	5.25185i	−0.266966	+	0.266966i
$388$	5.78447	−	5.78447i	0.293662	−	0.293662i
$389$	−17.6888	−	30.6380i	−0.896860	−	1.55341i	−0.831485	−	0.555547i	$-0.812509\pi$
$389$	−17.6888	−	30.6380i	−0.896860	−	1.55341i	−0.0653750	−	0.997861i	$-0.520824\pi$
$390$	−3.58816	+	0.850970i	−0.181694	+	0.0430905i
$391$	−4.76031	−	8.24510i	−0.240739	−	0.416973i
$392$	4.84025	−	1.29694i	0.244470	−	0.0655054i
$393$	−7.75177	+	2.07708i	−0.391025	+	0.104775i
$394$	0.380012	−	0.658199i	0.0191447	−	0.0331596i
$395$	0.798082	−	27.5685i	0.0401559	−	1.38712i
$396$	4.76949	−	2.75367i	0.239676	−	0.138377i
$397$	7.21159	−	26.9140i	0.361939	−	1.35078i	−0.509583	−	0.860421i	$-0.670200\pi$
$397$	7.21159	−	26.9140i	0.361939	−	1.35078i	0.871523	−	0.490355i	$-0.163133\pi$
$398$	10.8178	−	2.89863i	0.542250	−	0.145295i
$399$	2.58124			0.129224
$400$	−2.24532	−	4.46750i	−0.112266	−	0.223375i
$401$		−	3.14917i		−	0.157262i	−0.996904	−	0.0786310i	$-0.974945\pi$
$401$		−	3.14917i		−	0.157262i	0.996904	−	0.0786310i	$-0.0250549\pi$
$402$	4.47769	−	4.47769i	0.223327	−	0.223327i
$403$	7.94235	+	4.60794i	0.395637	+	0.229538i
$404$			1.61451i			0.0803250i
$405$	0.0647049	−	2.23513i	0.00321521	−	0.111065i
$406$	10.4665	−	6.04285i	0.519445	−	0.299902i
$407$	−24.6527	−	24.6527i	−1.22199	−	1.22199i
$408$	−1.34144	−	5.00634i	−0.0664114	−	0.247851i
$409$	−16.8080	−	29.1124i	−0.831104	−	1.43951i	−0.897163	−	0.441699i	$-0.854376\pi$
$409$	−16.8080	−	29.1124i	−0.831104	−	1.43951i	0.0660593	−	0.997816i	$-0.478957\pi$
$410$	16.9658	+	5.07648i	0.837879	+	0.250710i
$411$	7.07666			0.349066
$412$	−7.25834	+	1.94487i	−0.357593	+	0.0958167i
$413$	1.35000	+	5.03829i	0.0664294	+	0.247918i
$414$	0.918457	−	1.59081i	0.0451397	−	0.0781843i
$415$	0.248386	+	0.0743220i	0.0121928	+	0.00364832i
$416$	−1.42824	−	0.824592i	−0.0700250	−	0.0404290i
$417$	5.58849	−	20.8565i	0.273669	−	1.02135i
$418$	−7.12751	−	7.12751i	−0.348618	−	0.348618i
$419$		−	28.4319i		−	1.38899i	−0.719499	−	0.694494i	$-0.755628\pi$
$419$		−	28.4319i		−	1.38899i	0.719499	−	0.694494i	$-0.244372\pi$
$420$	2.77556	−	1.49710i	0.135433	−	0.0730509i
$421$	3.30102	−	5.71753i	0.160882	−	0.278656i	−0.774303	−	0.632815i	$-0.781900\pi$
$421$	3.30102	−	5.71753i	0.160882	−	0.278656i	0.935185	+	0.354159i	$0.115233\pi$
$422$	1.17493	−	4.38489i	0.0571946	−	0.213453i
$423$	−0.399896	−	1.49243i	−0.0194436	−	0.0725645i
$424$	0.628781	−	1.08908i	0.0305363	−	0.0528905i
$425$	5.24791	+	25.3778i	0.254561	+	1.23100i
$426$			1.72392i			0.0835241i
$427$	−5.01068	−	1.34261i	−0.242484	−	0.0649734i
$428$	−0.0549131	−	0.0147139i	−0.00265433	−	0.000711224i
$429$	−4.54131	+	7.86578i	−0.219256	+	0.379763i
$430$	16.6008	+	0.480578i	0.800564	+	0.0231755i
$431$	−8.65159	−	14.9850i	−0.416732	−	0.721802i	0.578876	−	0.815415i	$-0.303491\pi$
$431$	−8.65159	−	14.9850i	−0.416732	−	0.721802i	−0.995609	+	0.0936138i	$0.970158\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	7.93499	+	7.93499i	0.381331	+	0.381331i	0.871582	−	0.490250i	$-0.163095\pi$
$433$	7.93499	+	7.93499i	0.381331	+	0.381331i	−0.490250	+	0.871582i	$0.663095\pi$
$434$	−7.58046	−	2.04837i	−0.363874	−	0.0983249i
$435$	−13.9359	+	13.1518i	−0.668177	+	0.630579i
$436$	10.4813			0.501964
$437$	−3.24746	−	0.870154i	−0.155347	−	0.0416251i
$438$	−8.14560	+	8.14560i	−0.389212	+	0.389212i
$439$	33.9294	+	19.5891i	1.61936	+	0.934939i	0.987085	+	0.160196i	$0.0512127\pi$
$439$	33.9294	+	19.5891i	1.61936	+	0.934939i	0.632277	+	0.774743i	$0.282121\pi$
$440$	−11.7980	−	3.53017i	−0.562445	−	0.168294i
$441$	−2.50550	−	4.33965i	−0.119309	−	0.206650i
$442$	6.04408	+	6.04408i	0.287488	+	0.287488i
$443$	5.91713	+	22.0830i	0.281131	+	1.04920i	0.951620	+	0.307277i	$0.0994177\pi$
$443$	5.91713	+	22.0830i	0.281131	+	1.04920i	−0.670489	+	0.741919i	$0.733916\pi$
$444$	−5.48237	−	3.16525i	−0.260182	−	0.150216i
$445$	−11.6346	−	7.17398i	−0.551535	−	0.340079i
$446$	−10.4783	+	6.04963i	−0.496160	+	0.286458i
$447$	−1.55613	−	5.80757i	−0.0736026	−	0.274689i
$448$	1.36227	+	0.365018i	0.0643610	+	0.0172455i
$449$	−39.2256			−1.85117			−0.925585	−	0.378540i	$-0.876426\pi$
$449$	−39.2256			−1.85117			−0.925585	+	0.378540i	$0.876426\pi$
$450$	−3.73414	+	3.32508i	−0.176029	+	0.156746i
$451$	37.7729	−	21.8082i	1.77866	−	1.02691i
$452$	11.9484	−	3.20155i	0.562003	−	0.150588i
$453$	16.4136	+	4.39800i	0.771177	+	0.206636i
$454$	−16.1203	−	9.30704i	−0.756562	−	0.436801i
$455$	−2.72966	+	4.42691i	−0.127968	+	0.207537i
$456$	−1.58505	−	0.915126i	−0.0742265	−	0.0428547i
$457$	−24.4419	+	24.4419i	−1.14334	+	1.14334i	−0.155507	+	0.987835i	$0.549701\pi$
$457$	−24.4419	+	24.4419i	−1.14334	+	1.14334i	−0.987835	+	0.155507i	$0.950299\pi$
$458$	7.75182	−	28.9302i	0.362219	−	1.35182i
$459$	−4.48856	+	2.59147i	−0.209508	+	0.120959i
$460$	−3.99661	+	0.947838i	−0.186343	+	0.0441932i
$461$		−	23.6921i		−	1.10345i	−0.834025	−	0.551726i	$-0.813969\pi$
$461$		−	23.6921i		−	1.10345i	0.834025	−	0.551726i	$-0.186031\pi$
$462$	2.01028	−	7.50245i	0.0935265	−	0.349046i
$463$	−4.43981	−	4.43981i	−0.206336	−	0.206336i	0.596372	−	0.802708i	$-0.296608\pi$
$463$	−4.43981	−	4.43981i	−0.206336	−	0.206336i	−0.802708	+	0.596372i	$0.796608\pi$
$464$	−8.56947			−0.397828
$465$	12.4439	+	0.386580i	0.577072	+	0.0179272i
$466$	6.55050			0.303446
$467$	−4.88003	−	4.88003i	−0.225821	−	0.225821i	0.585123	−	0.810944i	$-0.301046\pi$
$467$	−4.88003	−	4.88003i	−0.225821	−	0.225821i	−0.810944	+	0.585123i	$0.801046\pi$
$468$	−0.426840	+	1.59299i	−0.0197307	+	0.0736360i
$469$		−	8.93074i		−	0.412383i
$470$	−1.81331	+	2.94079i	−0.0836416	+	0.135649i
$471$	−14.0781	+	8.12800i	−0.648685	+	0.374518i
$472$	0.957232	−	3.57244i	0.0440602	−	0.164435i
$473$	28.9237	−	28.9237i	1.32991	−	1.32991i
$474$	−10.6817	−	6.16709i	−0.490628	−	0.283264i
$475$	7.64726	+	5.02644i	0.350880	+	0.230629i
$476$	−6.33031	−	3.65480i	−0.290149	−	0.167518i
$477$	−1.21471	−	0.325481i	−0.0556179	−	0.0149028i
$478$	28.2941	−	7.58138i	1.29414	−	0.346764i
$479$	−11.3072	+	6.52820i	−0.516638	+	0.298281i	−0.735558	−	0.677462i	$-0.763080\pi$
$479$	−11.3072	+	6.52820i	−0.516638	+	0.298281i	0.218920	+	0.975743i	$0.429747\pi$
$480$	−2.23513	−	0.0647049i	−0.102019	−	0.00295336i
$481$	10.4402			0.476030
$482$	18.9917	+	5.08881i	0.865048	+	0.231789i
$483$	−0.670507	−	2.50236i	−0.0305091	−	0.113862i
$484$	−16.7409	+	9.66539i	−0.760952	+	0.439336i
$485$	4.22108	+	17.7984i	0.191669	+	0.808184i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	5.19146	+	19.3748i	0.235248	+	0.877956i	0.978037	+	0.208431i	$0.0668356\pi$
$487$	5.19146	+	19.3748i	0.235248	+	0.877956i	−0.742790	+	0.669525i	$0.766498\pi$
$488$	2.60088	+	2.60088i	0.117736	+	0.117736i
$489$	0.403287	+	0.698514i	0.0182373	+	0.0315879i
$490$	−3.21202	+	10.7347i	−0.145104	+	0.484943i
$491$	26.9808	+	15.5774i	1.21763	+	0.702997i	0.964410	−	0.264413i	$-0.0851781\pi$
$491$	26.9808	+	15.5774i	1.21763	+	0.702997i	0.253217	+	0.967410i	$0.418511\pi$
$492$	5.60007	−	5.60007i	0.252471	−	0.252471i
$493$	42.9016	+	11.4955i	1.93219	+	0.517730i
$494$	3.01842			0.135805
$495$	−0.356352	+	12.3096i	−0.0160168	+	0.553277i
$496$	3.92867	+	3.94532i	0.176402	+	0.177150i
$497$	1.71917	+	1.71917i	0.0771154	+	0.0771154i
$498$	0.0819875	−	0.0819875i	0.00367395	−	0.00367395i
$499$	−0.204707	−	0.354563i	−0.00916394	−	0.0158724i	0.861407	−	0.507915i	$-0.169584\pi$
$499$	−0.204707	−	0.354563i	−0.00916394	−	0.0158724i	−0.870571	+	0.492043i	$0.836250\pi$
$500$	11.1382	+	0.969490i	0.498117	+	0.0433569i
$501$	6.82514	−	11.8215i	0.304925	−	0.528145i
$502$	−2.75923	−	0.739334i	−0.123151	−	0.0329981i
$503$	−21.9342	−	5.87724i	−0.977996	−	0.262053i	−0.265796	−	0.964029i	$-0.585635\pi$
$503$	−21.9342	−	5.87724i	−0.977996	−	0.262053i	−0.712200	+	0.701976i	$0.752301\pi$
$504$		−	1.41032i		−	0.0628207i
$505$	−3.07295	−	1.89479i	−0.136744	−	0.0843173i
$506$	−5.05826	+	8.76115i	−0.224867	+	0.389481i
$507$	2.66071	+	9.92990i	0.118166	+	0.441002i
$508$	−3.84029	+	14.3322i	−0.170385	+	0.635887i
$509$	18.5441	−	32.1193i	0.821951	−	1.42366i	−0.0822762	−	0.996610i	$-0.526219\pi$
$509$	18.5441	−	32.1193i	0.821951	−	1.42366i	0.904227	−	0.427052i	$-0.140448\pi$
$510$	11.1030	+	3.32224i	0.491650	+	0.147111i
$511$			16.2464i			0.718697i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.473704	+	1.76789i	−0.0209146	+	0.0780542i
$514$	6.69447	+	3.86505i	0.295280	+	0.170480i
$515$	4.81668	−	16.0975i	0.212248	−	0.709341i
$516$	3.71362	−	6.43217i	0.163483	−	0.283161i
$517$	2.20236	+	8.21932i	0.0968597	+	0.361485i
$518$	−8.62381	+	2.31074i	−0.378909	+	0.101528i
$519$	3.74685			0.164468
$520$	3.24565	−	1.75066i	0.142331	−	0.0767714i
$521$	−8.88646	−	15.3918i	−0.389323	−	0.674327i	0.603036	−	0.797714i	$-0.293958\pi$
$521$	−8.88646	−	15.3918i	−0.389323	−	0.674327i	−0.992359	+	0.123387i	$0.960624\pi$
$522$	2.21794	+	8.27747i	0.0970767	+	0.362295i
$523$	−31.7235	−	31.7235i	−1.38717	−	1.38717i	−0.831202	−	0.555971i	$-0.812347\pi$
$523$	−31.7235	−	31.7235i	−1.38717	−	1.38717i	−0.555971	−	0.831202i	$-0.687653\pi$
$524$	6.95005	−	4.01261i	0.303614	−	0.175292i
$525$	−0.407932	+	7.03979i	−0.0178036	+	0.307242i
$526$			20.8449i			0.908882i
$527$	−14.3758	−	25.0217i	−0.626220	−	1.08996i
$528$	−3.89428	+	3.89428i	−0.169477	+	0.169477i
$529$		−	19.6257i		−	0.853293i
$530$	1.33494	+	2.47493i	0.0579861	+	0.107504i
$531$	−3.69846			−0.160500
$532$	−2.49329	+	0.668075i	−0.108098	+	0.0289647i
$533$	−3.38044	+	12.6160i	−0.146423	+	0.546459i
$534$	−5.29383	+	3.05639i	−0.229086	+	0.132263i
$535$	0.0924516	−	0.0872494i	0.00399703	−	0.00377212i
$536$	−3.16621	+	5.48403i	−0.136759	+	0.236874i
$537$	17.5643	−	4.70635i	0.757957	−	0.203094i
$538$	5.27347	−	1.41302i	0.227356	−	0.0609197i
$539$	13.7986	+	23.8999i	0.594349	+	1.02944i
$540$	0.515994	+	2.17572i	0.0222049	+	0.0936280i
$541$	12.4565	+	21.5753i	0.535547	+	0.927594i	0.999137	+	0.0415444i	$0.0132278\pi$
$541$	12.4565	+	21.5753i	0.535547	+	0.927594i	−0.463590	+	0.886050i	$0.653439\pi$
$542$	−14.1449	+	14.1449i	−0.607574	+	0.607574i
$543$	−11.1276	+	11.1276i	−0.477531	+	0.477531i
$544$	2.59147	+	4.48856i	0.111108	+	0.192445i
$545$	−12.3009	+	19.9494i	−0.526913	+	0.854538i
$546$	1.16294	+	2.01427i	0.0497692	+	0.0862028i
$547$	−8.89087	+	2.38230i	−0.380146	+	0.101860i	−0.443832	−	0.896110i	$-0.646381\pi$
$547$	−8.89087	+	2.38230i	−0.380146	+	0.101860i	0.0636855	+	0.997970i	$0.479715\pi$
$548$	−6.83553	+	1.83157i	−0.291999	+	0.0782410i
$549$	1.83910	−	3.18541i	0.0784909	−	0.135950i
$550$	20.5652	−	18.3124i	0.876902	−	0.780842i
$551$	13.5830	−	7.84215i	0.578655	−	0.334087i
$552$	−0.475429	+	1.77432i	−0.0202356	+	0.0755202i
$553$	−16.8024	+	4.50220i	−0.714512	+	0.191453i
$554$	10.4160			0.442532
$555$	12.4586	−	6.72001i	0.528839	−	0.285249i
$556$			21.5923i			0.915716i
$557$	3.75563	−	3.75563i	0.159131	−	0.159131i	−0.623051	−	0.782182i	$-0.714107\pi$
$557$	3.75563	−	3.75563i	0.159131	−	0.159131i	0.782182	+	0.623051i	$0.214107\pi$
$558$	2.79407	−	4.81593i	0.118283	−	0.203874i
$559$			12.2489i			0.518072i
$560$	−2.29351	+	2.16445i	−0.0969183	+	0.0914648i
$561$	24.7200	−	14.2721i	1.04368	−	0.602569i
$562$	−14.9747	−	14.9747i	−0.631671	−	0.631671i
$563$	−4.74453	−	17.7068i	−0.199958	−	0.746254i	−0.990927	−	0.134398i	$-0.957090\pi$
$563$	−4.74453	−	17.7068i	−0.199958	−	0.746254i	0.790969	−	0.611856i	$-0.209577\pi$
$564$	0.772539	+	1.33808i	0.0325298	+	0.0563432i
$565$	−7.92901	+	26.4990i	−0.333576	+	1.11482i
$566$	7.64054			0.321156
$567$	−1.36227	+	0.365018i	−0.0572098	+	0.0153293i
$568$	−0.446183	−	1.66518i	−0.0187214	−	0.0698693i
$569$	4.26917	−	7.39443i	0.178973	−	0.309990i	−0.762556	−	0.646922i	$-0.776056\pi$
$569$	4.26917	−	7.39443i	0.178973	−	0.309990i	0.941529	+	0.336932i	$0.109389\pi$
$570$	3.60200	−	1.94287i	0.150871	−	0.0813778i
$571$	32.8736	+	18.9796i	1.37572	+	0.794272i	0.991641	−	0.129029i	$-0.0411860\pi$
$571$	32.8736	+	18.9796i	1.37572	+	0.794272i	0.384078	+	0.923301i	$0.374519\pi$
$572$	2.35075	−	8.77313i	0.0982900	−	0.366823i
$573$	5.04649	+	5.04649i	0.210820	+	0.210820i
$574$		−	11.1693i		−	0.466198i
$575$	2.88638	−	8.71924i	0.120370	−	0.363618i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	5.97242	−	22.2894i	0.248635	−	0.927919i	−0.722886	−	0.690967i	$-0.757185\pi$
$577$	5.97242	−	22.2894i	0.248635	−	0.927919i	0.971521	−	0.236952i	$-0.0761483\pi$
$578$	−2.55270	−	9.52681i	−0.106178	−	0.396263i
$579$	−10.6760	+	18.4914i	−0.443680	+	0.768476i
$580$	10.0571	−	16.3105i	0.417600	−	0.677257i
$581$		−	0.163524i		−	0.00678410i
$582$	7.90173	+	2.11726i	0.327537	+	0.0877633i
$583$	6.68983	+	1.79254i	0.277065	+	0.0742392i
$584$	5.75981	−	9.97628i	0.238343	−	0.412822i
$585$	−2.53104	−	2.68195i	−0.104646	−	0.110885i
$586$	−9.51259	−	16.4763i	−0.392961	−	0.680629i
$587$	−20.6376	+	20.6376i	−0.851803	+	0.851803i	−0.990355	−	0.138552i	$-0.955755\pi$
$587$	−20.6376	+	20.6376i	−0.851803	+	0.851803i	0.138552	+	0.990355i	$0.455755\pi$
$588$	3.54331	+	3.54331i	0.146124	+	0.146124i
$589$	−9.83759	−	2.65828i	−0.405351	−	0.109533i
$590$	5.67612	+	6.01455i	0.233682	+	0.247615i
$591$	0.760023			0.0312632
$592$	6.11479	+	1.63845i	0.251316	+	0.0673400i
$593$	0.362009	−	0.362009i	0.0148659	−	0.0148659i	−0.699635	−	0.714501i	$-0.746654\pi$
$593$	0.362009	−	0.362009i	0.0148659	−	0.0148659i	0.714501	+	0.699635i	$0.246654\pi$
$594$	4.76949	+	2.75367i	0.195695	+	0.112984i
$595$	14.3856	−	7.75937i	0.589750	−	0.318103i
$596$	3.00622	+	5.20693i	0.123140	+	0.213284i
$597$	7.91921	+	7.91921i	0.324112	+	0.324112i
$598$	−0.784069	−	2.92619i	−0.0320630	−	0.119661i
$599$	18.0441	+	10.4178i	0.737263	+	0.425659i	0.821073	−	0.570823i	$-0.193376\pi$
$599$	18.0441	+	10.4178i	0.737263	+	0.425659i	−0.0838105	+	0.996482i	$0.526709\pi$
$600$	2.74631	−	4.17825i	0.112118	−	0.170576i
$601$	−40.9968	+	23.6695i	−1.67230	+	0.965500i	−0.705947	+	0.708265i	$0.749478\pi$
$601$	−40.9968	+	23.6695i	−1.67230	+	0.965500i	−0.966349	+	0.257235i	$0.917188\pi$
$602$	−2.71107	−	10.1179i	−0.110495	−	0.412373i
$603$	6.11665	+	1.63895i	0.249089	+	0.0667432i
$604$	−16.9926			−0.691418
$605$	1.25080	−	43.2068i	0.0508521	−	1.75661i
$606$	−1.39821	+	0.807256i	−0.0567984	+	0.0327925i
$607$	−8.20283	+	2.19794i	−0.332943	+	0.0892117i	−0.421418	−	0.906867i	$-0.638467\pi$
$607$	−8.20283	+	2.19794i	−0.332943	+	0.0892117i	0.0884750	+	0.996078i	$0.471801\pi$
$608$	1.76789	+	0.473704i	0.0716973	+	0.0192112i
$609$	10.4665	+	6.04285i	0.424125	+	0.244869i
$610$	−8.00273	+	1.89793i	−0.324021	+	0.0768450i
$611$	−2.20674	−	1.27406i	−0.0892750	−	0.0515429i
$612$	3.66489	−	3.66489i	0.148145	−	0.148145i
$613$	5.83611	−	21.7807i	0.235718	−	0.879713i	−0.742105	−	0.670283i	$-0.766173\pi$
$613$	5.83611	−	21.7807i	0.235718	−	0.879713i	0.977824	−	0.209430i	$-0.0671608\pi$
$614$	16.6967	−	9.63987i	0.673826	−	0.389033i
$615$	4.08652	+	17.2310i	0.164784	+	0.694822i
$616$			7.76711i			0.312946i
$617$	−5.91970	+	22.0926i	−0.238318	+	0.889415i	0.738307	+	0.674465i	$0.235626\pi$
$617$	−5.91970	+	22.0926i	−0.238318	+	0.889415i	−0.976625	+	0.214950i	$0.931041\pi$
$618$	−5.31347	−	5.31347i	−0.213739	−	0.213739i
$619$	31.4352			1.26349			0.631743	−	0.775178i	$-0.282340\pi$
$619$	31.4352			1.26349			0.631743	+	0.775178i	$0.282340\pi$
$620$	−12.1199	+	2.84731i	−0.486748	+	0.114351i
$621$	1.83691			0.0737128
$622$	15.0906	+	15.0906i	0.605078	+	0.605078i
$623$	−2.23128	+	8.32723i	−0.0893942	+	0.333624i
$624$		−	1.64918i		−	0.0660202i
$625$	−14.9171	+	20.0619i	−0.596684	+	0.802476i
$626$	18.1893	−	10.5016i	0.726992	−	0.419729i
$627$	2.60885	−	9.73636i	0.104187	−	0.388833i
$628$	11.4947	−	11.4947i	0.458689	−	0.458689i
$629$	−28.4148	−	16.4053i	−1.13297	−	0.654122i
$630$	2.68430	+	1.65515i	0.106945	+	0.0659429i
$631$	−24.7806	−	14.3071i	−0.986499	−	0.569555i	−0.0822727	−	0.996610i	$-0.526218\pi$
$631$	−24.7806	−	14.3071i	−0.986499	−	0.569555i	−0.904226	+	0.427055i	$0.859551\pi$
$632$	11.9139	+	3.19232i	0.473910	+	0.126984i
$633$	4.38489	−	1.17493i	0.174284	−	0.0466992i
$634$	−3.67824	+	2.12363i	−0.146082	+	0.0843403i
$635$	−22.7718	−	24.1296i	−0.903673	−	0.957553i
$636$	1.25756			0.0498656
$637$	−7.98247	−	2.13890i	−0.316277	−	0.0847461i
$638$	−12.2150	−	45.5868i	−0.483595	−	1.80480i
$639$	−1.49296	+	0.861959i	−0.0590605	+	0.0340986i
$640$	2.17572	−	0.515994i	0.0860028	−	0.0203965i
$641$	4.80381	+	2.77348i	0.189739	+	0.109546i	0.591860	−	0.806040i	$-0.298394\pi$
$641$	4.80381	+	2.77348i	0.189739	+	0.109546i	−0.402121	+	0.915586i	$0.631727\pi$
$642$	−0.0147139	−	0.0549131i	−0.000580712	−	0.00216725i
$643$	−33.1894	−	33.1894i	−1.30886	−	1.30886i	−0.922236	−	0.386628i	$-0.873640\pi$
$643$	−33.1894	−	33.1894i	−1.30886	−	1.30886i	−0.386628	−	0.922236i	$-0.626360\pi$
$644$	1.29532	+	2.24356i	0.0510427	+	0.0884086i
$645$	7.88423	+	14.6170i	0.310441	+	0.575545i
$646$	−8.21520	−	4.74305i	−0.323223	−	0.186613i
$647$	−24.3573	+	24.3573i	−0.957582	+	0.957582i	−0.999136	−	0.0415539i	$-0.986769\pi$
$647$	−24.3573	+	24.3573i	−0.957582	+	0.957582i	0.0415539	+	0.999136i	$0.486769\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	20.3687			0.799541
$650$	−0.477023	+	8.23211i	−0.0187104	+	0.322890i
$651$	−2.01629	−	7.58905i	−0.0790246	−	0.297438i
$652$	−0.570334	−	0.570334i	−0.0223360	−	0.0223360i
$653$	−22.4963	+	22.4963i	−0.880350	+	0.880350i	−0.993570	−	0.113220i	$-0.963883\pi$
$653$	−22.4963	+	22.4963i	−0.880350	+	0.880350i	0.113220	+	0.993570i	$0.463883\pi$
$654$	5.24066	+	9.07709i	0.204926	+	0.354942i
$655$	−0.519271	+	17.9374i	−0.0202896	+	0.700873i
$656$	−3.95985	+	6.85866i	−0.154606	+	0.267785i
$657$	−11.1271	−	2.98150i	−0.434109	−	0.116319i
$658$	2.10481	+	0.563981i	0.0820539	+	0.0219863i
$659$			14.3760i			0.560010i	0.959998	+	0.280005i	$0.0903362\pi$
$659$			14.3760i			0.560010i	−0.959998	+	0.280005i	$0.909664\pi$
$660$	−2.84176	−	11.9824i	−0.110615	−	0.466415i
$661$	10.8085	−	18.7209i	0.420403	−	0.728159i	−0.575576	−	0.817748i	$-0.695222\pi$
$661$	10.8085	−	18.7209i	0.420403	−	0.728159i	0.995979	+	0.0895893i	$0.0285555\pi$
$662$	4.20777	+	15.7036i	0.163540	+	0.610338i
$663$	−2.21229	+	8.25637i	−0.0859182	+	0.320651i
$664$	−0.0579739	+	0.100414i	−0.00224983	+	0.00389681i
$665$	1.65456	−	5.52960i	0.0641612	−	0.214429i
$666$		−	6.33050i		−	0.245302i
$667$	−11.1308	−	11.1308i	−0.430988	−	0.430988i
$668$	−3.53295	+	13.1852i	−0.136694	+	0.510149i
$669$	−10.4783	−	6.04963i	−0.405113	−	0.233892i
$670$	−6.72205	−	12.4624i	−0.259695	−	0.481465i
$671$	−10.1285	+	17.5432i	−0.391008	+	0.677246i
$672$	0.365018	+	1.36227i	0.0140809	+	0.0525505i
$673$	−27.3534	+	7.32933i	−1.05440	+	0.282525i	−0.744068	−	0.668104i	$-0.767106\pi$
$673$	−27.3534	+	7.32933i	−1.05440	+	0.282525i	−0.310329	+	0.950629i	$0.600439\pi$
$674$	−31.9628			−1.23116
$675$	−4.74668	−	1.57132i	−0.182700	−	0.0604801i
$676$	−5.14010	−	8.90291i	−0.197696	−	0.342419i
$677$	−6.77613	−	25.2889i	−0.260428	−	0.971930i	−0.964990	−	0.262288i	$-0.915523\pi$
$677$	−6.77613	−	25.2889i	−0.260428	−	0.971930i	0.704562	−	0.709643i	$-0.251144\pi$
$678$	8.74680	+	8.74680i	0.335919	+	0.335919i
$679$	9.99141	−	5.76854i	0.383435	−	0.221376i
$680$	−11.5846	−	0.335362i	−0.444247	−	0.0128605i
$681$		−	18.6141i		−	0.713293i
$682$	−15.3879	+	26.5229i	−0.589233	+	1.01562i
$683$	−20.4303	+	20.4303i	−0.781744	+	0.781744i	−0.980125	−	0.198381i	$-0.936432\pi$
$683$	−20.4303	+	20.4303i	−0.781744	+	0.781744i	0.198381	+	0.980125i	$0.436432\pi$
$684$		−	1.83025i		−	0.0699815i
$685$	4.53610	−	15.1598i	0.173316	−	0.579226i
$686$	16.9394			0.646748
$687$	28.9302	−	7.75182i	1.10376	−	0.295751i
$688$	−1.92231	+	7.17416i	−0.0732873	+	0.273512i
$689$	−1.79610	+	1.03698i	−0.0684258	+	0.0395057i
$690$	−2.81916	−	2.98725i	−0.107323	−	0.113723i
$691$	−14.0746	+	24.3779i	−0.535423	+	0.927379i	0.463720	+	0.885982i	$0.346514\pi$
$691$	−14.0746	+	24.3779i	−0.535423	+	0.927379i	−0.999143	+	0.0413975i	$0.986819\pi$
$692$	−3.61918	+	0.969755i	−0.137580	+	0.0368646i
$693$	7.50245	−	2.01028i	0.284995	−	0.0763641i
$694$	4.84305	+	8.38840i	0.183840	+	0.318419i
$695$	−41.0971	−	25.3407i	−1.55890	−	0.961228i
$696$	−4.28473	−	7.42138i	−0.162412	−	0.281307i
$697$	29.0248	−	29.0248i	1.09939	−	1.09939i
$698$	−19.5394	+	19.5394i	−0.739578	+	0.739578i
$699$	3.27525	+	5.67290i	0.123881	+	0.214569i
$700$	−1.42800	−	6.90550i	−0.0539733	−	0.261003i
$701$	−18.3529	−	31.7881i	−0.693179	−	1.20062i	−0.970791	−	0.239928i	$-0.922876\pi$
$701$	−18.3529	−	31.7881i	−0.693179	−	1.20062i	0.277612	−	0.960693i	$-0.410457\pi$
$702$	−1.59299	+	0.426840i	−0.0601235	+	0.0161101i
$703$	−11.1916	+	2.99878i	−0.422100	+	0.113101i
$704$	2.75367	−	4.76949i	0.103783	−	0.179757i
$705$	−3.45345	−	0.0999742i	−0.130065	−	0.00376524i
$706$	0.925776	−	0.534497i	0.0348420	−	0.0201161i
$707$	−0.589326	+	2.19939i	−0.0221639	+	0.0827167i
$708$	3.57244	−	0.957232i	0.134261	−	0.0359750i
$709$	19.2014			0.721124			0.360562	−	0.932735i	$-0.382585\pi$
$709$	19.2014			0.721124			0.360562	+	0.932735i	$0.382585\pi$
$710$	3.69302	+	1.10502i	0.138597	+	0.0414708i
$711$		−	12.3342i		−	0.462568i
$712$	4.32239	−	4.32239i	0.161989	−	0.161989i
$713$	−0.0216297	+	10.2275i	−0.000810037	+	0.383022i
$714$		−	7.30961i		−	0.273555i
$715$	13.9393	+	14.7704i	0.521300	+	0.552382i
$716$	−15.7478	+	9.09197i	−0.588521	+	0.339783i
$717$	20.7127	+	20.7127i	0.773531	+	0.773531i
$718$	7.59977	+	28.3627i	0.283621	+	1.05849i
$719$	10.9079	+	18.8931i	0.406796	+	0.704592i	0.994529	−	0.104463i	$-0.0333125\pi$
$719$	10.9079	+	18.8931i	0.406796	+	0.704592i	−0.587732	+	0.809055i	$0.699979\pi$
$720$	−1.06153	−	1.96803i	−0.0395609	−	0.0733443i
$721$	−10.5977			−0.394679
$722$	15.1169	−	4.05056i	0.562593	−	0.150746i
$723$	5.08881	+	18.9917i	0.189255	+	0.706308i
$724$	7.86840	−	13.6285i	0.292427	−	0.506498i
$725$	19.2412	+	38.2841i	0.714599	+	1.42184i
$726$	−16.7409	−	9.66539i	−0.621315	−	0.358716i
$727$	−1.52673	+	5.69783i	−0.0566233	+	0.211321i	−0.988441	−	0.151605i	$-0.951556\pi$
$727$	−1.52673	+	5.69783i	−0.0566233	+	0.211321i	0.931818	+	0.362926i	$0.118222\pi$
$728$	−1.64464	−	1.64464i	−0.0609546	−	0.0609546i
$729$		−	1.00000i		−	0.0370370i
$730$	12.2284	+	22.6710i	0.452594	+	0.839091i
$731$	19.2475	−	33.3376i	0.711893	−	1.23303i
$732$	−0.951988	+	3.55287i	−0.0351865	+	0.131318i
$733$	7.49240	+	27.9620i	0.276738	+	1.03280i	0.954668	+	0.297674i	$0.0962108\pi$
$733$	7.49240	+	27.9620i	0.276738	+	1.03280i	−0.677930	+	0.735127i	$0.737123\pi$
$734$	5.51960	−	9.56023i	0.203732	−	0.352874i
$735$	−10.9025	+	2.58565i	−0.402145	+	0.0953730i
$736$		−	1.83691i		−	0.0677096i
$737$	−33.6864	−	9.02625i	−1.24086	−	0.332486i
$738$	7.64984	+	2.04977i	0.281594	+	0.0754530i
$739$	−20.0676	+	34.7582i	−0.738200	+	1.27860i	0.215105	+	0.976591i	$0.430991\pi$
$739$	−20.0676	+	34.7582i	−0.738200	+	1.27860i	−0.953305	+	0.302010i	$0.902343\pi$
$740$	−10.2948	+	9.71556i	−0.378446	+	0.357151i
$741$	1.50921	+	2.61403i	0.0554423	+	0.0960289i
$742$	1.25410	−	1.25410i	0.0460395	−	0.0460395i
$743$	21.6259	+	21.6259i	0.793378	+	0.793378i	0.982042	−	0.188663i	$-0.0604155\pi$
$743$	21.6259	+	21.6259i	0.793378	+	0.793378i	−0.188663	+	0.982042i	$0.560416\pi$
$744$	−1.45241	+	5.37499i	−0.0532481	+	0.197057i
$745$	−13.4386	−	0.389034i	−0.492352	−	0.0142531i
$746$	14.3512			0.525434
$747$	0.111997	+	0.0300095i	0.00409776	+	0.00109799i
$748$	−20.1838	+	20.1838i	−0.737993	+	0.737993i
$749$	−0.0694354	−	0.0400885i	−0.00253711	−	0.00146480i
$750$	4.72951	+	10.1307i	0.172697	+	0.369922i
$751$	2.38477	+	4.13054i	0.0870215	+	0.150726i	0.906251	−	0.422740i	$-0.138932\pi$
$751$	2.38477	+	4.13054i	0.0870215	+	0.150726i	−0.819229	+	0.573466i	$0.805598\pi$
$752$	−1.09254	−	1.09254i	−0.0398407	−	0.0398407i
$753$	−0.739334	−	2.75923i	−0.0269428	−	0.100552i
$754$	12.2392	+	7.06632i	0.445726	+	0.257340i
$755$	19.9425	−	32.3425i	0.725783	−	1.17706i
$756$	1.22137	−	0.705160i	0.0444209	−	0.0256464i
$757$	0.655749	+	2.44729i	0.0238336	+	0.0889483i	0.976818	−	0.214070i	$-0.0686722\pi$
$757$	0.655749	+	2.44729i	0.0238336	+	0.0889483i	−0.952985	+	0.303019i	$0.902006\pi$
$758$	0.869834	+	0.233071i	0.0315938	+	0.00846553i
$759$	−10.1165			−0.367206
$760$	−2.97641	+	2.80893i	−0.107966	+	0.101891i
$761$	31.7609	−	18.3372i	1.15133	−	0.664722i	0.202120	−	0.979361i	$-0.435217\pi$
$761$	31.7609	−	18.3372i	1.15133	−	0.664722i	0.949211	+	0.314639i	$0.101883\pi$
$762$	−14.3322	+	3.84029i	−0.519199	+	0.139119i
$763$	14.2783	+	3.82587i	0.516911	+	0.138506i
$764$	−6.18066	−	3.56841i	−0.223608	−	0.129100i
$765$	2.67437	+	11.2766i	0.0966920	+	0.407707i
$766$	−27.8240	−	16.0642i	−1.00532	−	0.580424i
$767$	−4.31296	+	4.31296i	−0.155732	+	0.155732i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−21.3342	+	12.3173i	−0.769332	+	0.444174i	−0.832636	−	0.553820i	$-0.813170\pi$
$769$	−21.3342	+	12.3173i	−0.769332	+	0.444174i	0.0633040	+	0.997994i	$0.479836\pi$
$770$	−14.7834	−	9.11550i	−0.532755	−	0.328500i
$771$			7.73010i			0.278393i
$772$	5.52631	−	20.6245i	0.198896	−	0.742291i
$773$	−2.70562	−	2.70562i	−0.0973144	−	0.0973144i	0.656774	−	0.754088i	$-0.271921\pi$
$773$	−2.70562	−	2.70562i	−0.0973144	−	0.0973144i	−0.754088	+	0.656774i	$0.771921\pi$
$774$	7.42723			0.266966
$775$	8.80461	−	26.4098i	0.316271	−	0.948669i
$776$	−8.18047			−0.293662
$777$	−6.31307	−	6.31307i	−0.226480	−	0.226480i
$778$	−9.15642	+	34.1722i	−0.328274	+	1.22513i
$779$		−	14.4950i		−	0.519339i
$780$	3.13894	+	1.93549i	0.112392	+	0.0693015i
$781$	8.22222	−	4.74710i	0.294214	−	0.169865i
$782$	−2.46412	+	9.19621i	−0.0881167	+	0.328856i
$783$	−6.05953	+	6.05953i	−0.216550	+	0.216550i
$784$	−4.33965	−	2.50550i	−0.154987	−	0.0894821i
$785$	8.38800	+	35.3685i	0.299381	+	1.26235i
$786$	6.95005	+	4.01261i	0.247900	+	0.143125i
$787$	8.20482	+	2.19847i	0.292470	+	0.0783671i	0.402071	−	0.915609i	$-0.368291\pi$
$787$	8.20482	+	2.19847i	0.292470	+	0.0783671i	−0.109601	+	0.993976i	$0.534957\pi$
$788$	−0.734126	+	0.196708i	−0.0261522	+	0.00700745i
$789$	−18.0522	+	10.4225i	−0.642677	+	0.371050i
$790$	−20.0582	+	18.9296i	−0.713640	+	0.673484i
$791$	17.4455			0.620289
$792$	−5.31968	−	1.42540i	−0.189027	−	0.0506495i
$793$	−1.57000	−	5.85933i	−0.0557525	−	0.208071i
$794$	−24.1305	+	13.9317i	−0.856358	+	0.494418i
$795$	−1.47588	+	2.39355i	−0.0523440	+	0.0848906i
$796$	−9.69902	−	5.59973i	−0.343773	−	0.198477i
$797$	4.38370	+	16.3602i	0.155279	+	0.579508i	0.999081	+	0.0428543i	$0.0136451\pi$
$797$	4.38370	+	16.3602i	0.155279	+	0.579508i	−0.843803	+	0.536654i	$0.819688\pi$
$798$	−1.82521	−	1.82521i	−0.0646119	−	0.0646119i
$799$	4.00403	+	6.93518i	0.141652	+	0.245349i
$800$	−1.57132	+	4.74668i	−0.0555546	+	0.167820i
$801$	−5.29383	−	3.05639i	−0.187048	−	0.107992i
$802$	−2.22680	+	2.22680i	−0.0786310	+	0.0786310i
$803$	61.2807	+	16.4201i	2.16255	+	0.579453i
$804$	−6.33242			−0.223327
$805$	−5.79042	−	0.167627i	−0.204085	−	0.00590808i
$806$	−2.35778	−	8.87440i	−0.0830494	−	0.312587i
$807$	3.86045	+	3.86045i	0.135894	+	0.135894i
$808$	1.14163	−	1.14163i	0.0401625	−	0.0401625i
$809$	−19.2180	−	33.2865i	−0.675667	−	1.17029i	−0.976273	−	0.216542i	$-0.930522\pi$
$809$	−19.2180	−	33.2865i	−0.675667	−	1.17029i	0.300606	−	0.953748i	$-0.402811\pi$
$810$	−1.62623	+	1.53472i	−0.0571399	+	0.0539247i
$811$	−0.278883	+	0.483040i	−0.00979292	+	0.0169618i	−0.870880	−	0.491495i	$-0.836451\pi$
$811$	−0.278883	+	0.483040i	−0.00979292	+	0.0169618i	0.861087	+	0.508457i	$0.169784\pi$
$812$	−11.6739	−	3.12801i	−0.409673	−	0.109772i
$813$	−19.3222	−	5.17738i	−0.677661	−	0.181579i
$814$			34.8642i			1.22199i
$815$	1.75488	−	0.416188i	0.0614707	−	0.0145784i
$816$	−2.59147	+	4.48856i	−0.0907196	+	0.157131i
$817$	−3.51831	−	13.1305i	−0.123090	−	0.459379i
$818$	−8.70048	+	32.4706i	−0.304205	+	1.13531i
$819$	−1.16294	+	2.01427i	−0.0406364	+	0.0703843i
$820$	−8.40699	−	15.5862i	−0.293585	−	0.544294i
$821$		−	17.5931i		−	0.614002i	−0.951709	−	0.307001i	$-0.900674\pi$
$821$		−	17.5931i		−	0.614002i	0.951709	−	0.307001i	$-0.0993255\pi$
$822$	−5.00395	−	5.00395i	−0.174533	−	0.174533i
$823$	−8.77439	+	32.7465i	−0.305856	+	1.14147i	0.626350	+	0.779542i	$0.284548\pi$
$823$	−8.77439	+	32.7465i	−0.305856	+	1.14147i	−0.932206	+	0.361928i	$0.882119\pi$
$824$	6.50765	+	3.75719i	0.226705	+	0.130888i
$825$	26.1416	+	8.65379i	0.910132	+	0.301286i
$826$	2.60801	−	4.51720i	0.0907442	−	0.157174i
$827$	5.22111	+	19.4854i	0.181556	+	0.677575i	0.995342	+	0.0964106i	$0.0307362\pi$
$827$	5.22111	+	19.4854i	0.181556	+	0.677575i	−0.813786	+	0.581165i	$0.802597\pi$
$828$	−1.77432	+	0.475429i	−0.0616620	+	0.0165223i
$829$	−3.80263			−0.132071			−0.0660354	−	0.997817i	$-0.521035\pi$
$829$	−3.80263			−0.132071			−0.0660354	+	0.997817i	$0.521035\pi$
$830$	−0.123082	−	0.228189i	−0.00427224	−	0.00792056i
$831$	5.20798	+	9.02049i	0.180663	+	0.312917i
$832$	0.426840	+	1.59299i	0.0147980	+	0.0552270i
$833$	18.3648	+	18.3648i	0.636301	+	0.636301i
$834$	−18.6994	+	10.7961i	−0.647509	+	0.373839i
$835$	−20.9494	−	22.1985i	−0.724984	−	0.768210i
$836$			10.0798i			0.348618i
$837$	5.56775	+	0.0117750i	0.192450	+	0.000407003i
$838$	−20.1044	+	20.1044i	−0.694494	+	0.694494i
$839$			2.69302i			0.0929734i	0.998919	+	0.0464867i	$0.0148025\pi$
$839$			2.69302i			0.0929734i	−0.998919	+	0.0464867i	$0.985197\pi$
$840$	−3.02122	−	0.904008i	−0.104242	−	0.0311912i
$841$	44.4358			1.53227
$842$	−6.37708	+	1.70873i	−0.219769	+	0.0588869i
$843$	5.48114	−	20.4559i	0.188780	−	0.704538i
$844$	−3.93139	+	2.26979i	−0.135324	+	0.0781293i
$845$	22.9776	+	0.665179i	0.790453	+	0.0228828i
$846$	−0.772539	+	1.33808i	−0.0265604	+	0.0460040i
$847$	−26.3336	+	7.05608i	−0.904834	+	0.242450i
$848$	−1.21471	+	0.325481i	−0.0417134	+	0.0111771i
$849$	3.82027	+	6.61690i	0.131111	+	0.227091i
$850$	14.2340	−	21.6556i	0.488221	−	0.742782i
$851$	5.81429	+	10.0706i	0.199311	+	0.345217i
$852$	1.21899	−	1.21899i	0.0417621	−	0.0417621i
$853$	27.5868	−	27.5868i	0.944554	−	0.944554i	−0.0539872	−	0.998542i	$-0.517193\pi$
$853$	27.5868	−	27.5868i	0.944554	−	0.944554i	0.998542	+	0.0539872i	$0.0171930\pi$
$854$	2.59372	+	4.49246i	0.0887553	+	0.153729i
$855$	3.48357	+	2.14799i	0.119136	+	0.0734596i
$856$	0.0284251	+	0.0492337i	0.000971551	+	0.00168277i
$857$	34.6108	−	9.27393i	1.18228	−	0.316791i	0.386450	−	0.922310i	$-0.373701\pi$
$857$	34.6108	−	9.27393i	1.18228	−	0.316791i	0.795831	+	0.605519i	$0.207034\pi$
$858$	8.77313	−	2.35075i	0.299510	−	0.0802534i
$859$	20.0489	−	34.7257i	0.684060	−	1.18483i	−0.289671	−	0.957126i	$-0.593546\pi$
$859$	20.0489	−	34.7257i	0.684060	−	1.18483i	0.973731	−	0.227701i	$-0.0731207\pi$
$860$	−11.3987	−	12.0784i	−0.388694	−	0.411870i
$861$	9.67290	−	5.58465i	0.329652	−	0.190324i
$862$	−4.47839	+	16.7136i	−0.152535	+	0.569267i
$863$	8.89787	−	2.38418i	0.302887	−	0.0811583i	−0.104175	−	0.994559i	$-0.533220\pi$
$863$	8.89787	−	2.38418i	0.302887	−	0.0811583i	0.407062	+	0.913401i	$0.366553\pi$
$864$	−1.00000			−0.0340207
$865$	2.40171	−	8.02659i	0.0816605	−	0.272912i
$866$		−	11.2218i		−	0.381331i
$867$	6.97411	−	6.97411i	0.236853	−	0.236853i
$868$	3.91178	+	6.80861i	0.132774	+	0.231099i
$869$			67.9285i			2.30432i
$870$	19.1539	+	0.554487i	0.649378	+	0.0187989i
$871$	9.04418	−	5.22166i	0.306450	−	0.176929i
$872$	−7.41142	−	7.41142i	−0.250982	−	0.250982i
$873$	2.11726	+	7.90173i	0.0716585	+	0.267433i
$874$	1.68101	+	2.91159i	0.0568610	+	0.0984861i
$875$	14.8193	+	5.38635i	0.500985	+	0.182092i
$876$	11.5196			0.389212
$877$	−31.4130	+	8.41710i	−1.06074	+	0.284225i	−0.746684	−	0.665179i	$-0.768355\pi$
$877$	−31.4130	+	8.41710i	−1.06074	+	0.284225i	−0.314058	+	0.949404i	$0.601689\pi$
$878$	−10.1401	−	37.8433i	−0.342211	−	1.27715i
$879$	9.51259	−	16.4763i	0.320852	−	0.555731i
$880$	5.84620	+	10.8386i	0.197075	+	0.365370i
$881$	8.12275	+	4.68967i	0.273662	+	0.157999i	0.630551	−	0.776148i	$-0.282829\pi$
$881$	8.12275	+	4.68967i	0.273662	+	0.157999i	−0.356888	+	0.934147i	$0.616162\pi$
$882$	−1.29694	+	4.84025i	−0.0436703	+	0.162980i
$883$	−34.9601	−	34.9601i	−1.17650	−	1.17650i	−0.980629	−	0.195873i	$-0.937246\pi$
$883$	−34.9601	−	34.9601i	−1.17650	−	1.17650i	−0.195873	−	0.980629i	$-0.562754\pi$
$884$		−	8.54763i		−	0.287488i
$885$	−2.37069	+	7.92294i	−0.0796900	+	0.266327i
$886$	11.4310	−	19.7991i	0.384032	−	0.665164i
$887$	−8.69864	+	32.4638i	−0.292072	+	1.09003i	0.651443	+	0.758697i	$0.274164\pi$
$887$	−8.69864	+	32.4638i	−0.292072	+	1.09003i	−0.943515	+	0.331330i	$0.892503\pi$
$888$	1.63845	+	6.11479i	0.0549829	+	0.205199i
$889$	−10.4630	+	18.1224i	−0.350917	+	0.607807i
$890$	3.15416	+	13.2997i	0.105728	+	0.445807i
$891$			5.50734i			0.184503i
$892$	11.6870	+	3.13152i	0.391309	+	0.104851i
$893$	2.73153	+	0.731910i	0.0914070	+	0.0244924i
$894$	−3.00622	+	5.20693i	−0.100543	+	0.174146i
$895$	1.17659	−	40.6435i	0.0393291	−	1.35856i
$896$	−0.705160	−	1.22137i	−0.0235578	−	0.0408032i
$897$	2.14212	−	2.14212i	0.0715232	−	0.0715232i
$898$	27.7367	+	27.7367i	0.925585	+	0.925585i
$899$	−33.6666	−	33.8093i	−1.12284	−	1.12760i
$900$	4.99163	+	0.289248i	0.166388	+	0.00964160i
$901$	6.51787			0.217142
$902$	−42.1302	−	11.2888i	−1.40278	−	0.375875i
$903$	7.40679	−	7.40679i	0.246482	−	0.246482i
$904$	−10.7126	−	6.18492i	−0.356296	−	0.205708i
$905$	16.7051	+	30.9706i	0.555296	+	1.02950i
$906$	−8.49629	−	14.7160i	−0.282270	−	0.488907i
$907$	25.9074	+	25.9074i	0.860242	+	0.860242i	0.991366	−	0.131124i	$-0.0418587\pi$
$907$	25.9074	+	25.9074i	0.860242	+	0.860242i	−0.131124	+	0.991366i	$0.541859\pi$
$908$	4.81768	+	17.9798i	0.159880	+	0.596681i
$909$	−1.39821	−	0.807256i	−0.0463757	−	0.0267750i
$910$	5.06046	−	1.20014i	0.167753	−	0.0397843i
$911$	−9.89443	+	5.71255i	−0.327817	+	0.189265i	−0.654872	−	0.755740i	$-0.727277\pi$
$911$	−9.89443	+	5.71255i	−0.327817	+	0.189265i	0.327054	+	0.945006i	$0.393944\pi$
$912$	0.473704	+	1.76789i	0.0156859	+	0.0585406i
$913$	−0.616806	−	0.165273i	−0.0204133	−	0.00546972i
$914$	34.5660			1.14334
$915$	−5.64502	−	5.98160i	−0.186619	−	0.197746i
$916$	−25.9381	+	14.9754i	−0.857019	+	0.494800i
$917$	10.9325	−	2.92935i	0.361022	−	0.0967356i
$918$	5.00634	+	1.34144i	0.165234	+	0.0442742i
$919$	−5.04783	−	2.91437i	−0.166513	−	0.0961360i	0.414428	−	0.910082i	$-0.363982\pi$
$919$	−5.04783	−	2.91437i	−0.166513	−	0.0961360i	−0.580940	+	0.813946i	$0.697315\pi$
$920$	3.49625	+	2.15581i	0.115268	+	0.0710748i
$921$	16.6967	+	9.63987i	0.550176	+	0.317645i
$922$	−16.7529	+	16.7529i	−0.551726	+	0.551726i
$923$	−0.735838	+	2.74618i	−0.0242204	+	0.0903917i
$924$	−6.72652	+	3.88356i	−0.221286	+	0.127760i
$925$	−6.40986	−	30.9967i	−0.210755	−	1.01916i
$926$			6.27884i			0.206336i
$927$	1.94487	−	7.25834i	0.0638778	−	0.238395i
$928$	6.05953	+	6.05953i	0.198914	+	0.198914i
$929$	−39.8102			−1.30613			−0.653065	−	0.757302i	$-0.726517\pi$
$929$	−39.8102			−1.30613			−0.653065	+	0.757302i	$0.726517\pi$
$930$	−8.52581	−	9.07252i	−0.279572	−	0.297500i
$931$	9.17139			0.300580
$932$	−4.63191	−	4.63191i	−0.151723	−	0.151723i
$933$	−5.52355	+	20.6142i	−0.180833	+	0.674877i
$934$			6.90141i			0.225821i
$935$	−14.7287	−	62.1042i	−0.481679	−	2.03102i
$936$	1.42824	−	0.824592i	0.0466833	−	0.0269526i
$937$	−12.0253	+	44.8789i	−0.392849	+	1.46613i	0.432565	+	0.901603i	$0.357609\pi$
$937$	−12.0253	+	44.8789i	−0.392849	+	1.46613i	−0.825414	+	0.564528i	$0.809058\pi$
$938$	−6.31499	+	6.31499i	−0.206192	+	0.206192i
$939$	18.1893	+	10.5016i	0.593587	+	0.342708i
$940$	3.36166	−	0.797252i	0.109645	−	0.0260035i
$941$	8.21638	+	4.74373i	0.267846	+	0.154641i	0.627909	−	0.778287i	$-0.283911\pi$
$941$	8.21638	+	4.74373i	0.267846	+	0.154641i	−0.360062	+	0.932928i	$0.617245\pi$
$942$	15.7021	+	4.20736i	0.511601	+	0.137083i
$943$	−14.0521	+	3.76525i	−0.457599	+	0.122613i
$944$	−3.20296	+	1.84923i	−0.104248	+	0.0601873i
$945$	−0.0912547	+	3.15225i	−0.00296851	+	0.102543i
$946$	−40.9043			−1.32991
$947$	−11.8003	−	3.16188i	−0.383458	−	0.102747i	0.0619401	−	0.998080i	$-0.480271\pi$
$947$	−11.8003	−	3.16188i	−0.383458	−	0.102747i	−0.445398	+	0.895333i	$0.646938\pi$
$948$	3.19232	+	11.9139i	0.103682	+	0.386946i
$949$	−16.4527	+	9.49899i	−0.534078	+	0.308350i
$950$	−1.85320	−	8.96166i	−0.0601256	−	0.290755i
$951$	−3.67824	−	2.12363i	−0.119275	−	0.0688636i
$952$	1.89187	+	7.06054i	0.0613157	+	0.228833i
$953$	37.2637	+	37.2637i	1.20709	+	1.20709i	0.971965	+	0.235125i	$0.0755500\pi$
$953$	37.2637	+	37.2637i	1.20709	+	1.20709i	0.235125	+	0.971965i	$0.424450\pi$
$954$	0.628781	+	1.08908i	0.0203576	+	0.0352603i
$955$	14.0455	−	7.57594i	0.454501	−	0.245152i
$956$	−25.3678	−	14.6461i	−0.820453	−	0.473689i
$957$	33.3719	−	33.3719i	1.07876	−	1.07876i
$958$	12.6115	+	3.37924i	0.407459	+	0.109178i
$959$	−9.98036			−0.322283
$960$	1.53472	+	1.62623i	0.0495330	+	0.0524863i
$961$	−0.131121	+	30.9997i	−0.00422969	+	0.999991i
$962$	−7.38231	−	7.38231i	−0.238015	−	0.238015i
$963$	0.0401992	−	0.0401992i	0.00129540	−	0.00129540i
$964$	−9.83082	−	17.0275i	−0.316629	−	0.548418i
$965$	32.7694	+	34.7233i	1.05489	+	1.11778i
$966$	−1.29532	+	2.24356i	−0.0416762	+	0.0721853i
$967$	−35.7296	−	9.57373i	−1.14899	−	0.307870i	−0.366428	−	0.930446i	$-0.619419\pi$
$967$	−35.7296	−	9.57373i	−1.14899	−	0.307870i	−0.782559	+	0.622576i	$0.786086\pi$
$968$	18.6721	+	5.00317i	0.600144	+	0.160808i
$969$		−	9.48609i		−	0.304737i
$970$	9.60062	−	15.5701i	0.308257	−	0.499926i
$971$	−20.0798	+	34.7792i	−0.644391	+	1.11612i	0.340051	+	0.940407i	$0.389556\pi$
$971$	−20.0798	+	34.7792i	−0.644391	+	1.11612i	−0.984442	+	0.175711i	$0.943778\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−7.88156	+	29.4144i	−0.252671	+	0.942981i
$974$	10.0291	−	17.3710i	0.321354	−	0.556602i
$975$	−7.36773	+	3.70294i	−0.235956	+	0.118589i
$976$		−	3.67820i		−	0.117736i
$977$	21.7648	+	21.7648i	0.696318	+	0.696318i	0.963614	−	0.267297i	$-0.0861304\pi$
$977$	21.7648	+	21.7648i	0.696318	+	0.696318i	−0.267297	+	0.963614i	$0.586130\pi$
$978$	0.208757	−	0.779091i	0.00667531	−	0.0249126i
$979$	29.1549	+	16.8326i	0.931795	+	0.537972i
$980$	9.86181	−	5.31932i	0.315024	−	0.169919i
$981$	−5.24066	+	9.07709i	−0.167321	+	0.289809i
$982$	−8.06344	−	30.0932i	−0.257315	−	0.960312i
$983$	−11.4651	+	3.07207i	−0.365681	+	0.0979838i	−0.436980	−	0.899471i	$-0.643952\pi$
$983$	−11.4651	+	3.07207i	−0.365681	+	0.0979838i	0.0712996	+	0.997455i	$0.477285\pi$
$984$	−7.91969			−0.252471
$985$	0.487171	−	1.62814i	0.0155226	−	0.0518769i
$986$	−22.2075	−	38.4646i	−0.707232	−	1.22496i
$987$	0.563981	+	2.10481i	0.0179517	+	0.0669967i
$988$	−2.13435	−	2.13435i	−0.0679027	−	0.0679027i
$989$	−11.8154	+	6.82160i	−0.375706	+	0.216914i
$990$	8.95620	−	8.45224i	0.284647	−	0.268630i
$991$		−	13.1734i		−	0.418468i	−0.977866	−	0.209234i	$-0.932903\pi$
$991$		−	13.1734i		−	0.418468i	0.977866	−	0.209234i	$-0.0670970\pi$
$992$	0.0117750	−	5.56775i	0.000373857	−	0.176776i
$993$	−11.4958	+	11.4958i	−0.364809	+	0.364809i
$994$		−	2.43128i		−	0.0771154i
$995$	22.0409	−	11.8886i	0.698744	−	0.376893i
$996$	−0.115948			−0.00367395
$997$	−57.7159	+	15.4649i	−1.82788	+	0.489779i	−0.997704	−	0.0677203i	$-0.978427\pi$
$997$	−57.7159	+	15.4649i	−1.82788	+	0.489779i	−0.830177	+	0.557500i	$0.811761\pi$
$998$	−0.105964	+	0.395463i	−0.00335423	+	0.0125182i
$999$	5.48237	−	3.16525i	0.173455	−	0.100144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.2	yes	64
5.3	odd	4		930.2.be.a.223.6	✓	64
31.26	odd	6		930.2.be.a.367.6	yes	64
155.88	even	12	inner	930.2.be.b.553.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.6	✓	64	5.3	odd	4
930.2.be.a.367.6	yes	64	31.26	odd	6
930.2.be.b.37.2	yes	64	1.1	even	1	trivial
930.2.be.b.553.2	yes	64	155.88	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.90333 - 1.17360i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.365018 + 1.36227i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.90333 - 1.17360i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.365018 + 1.36227i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.515994 + 2.17572i) q^{10} +(4.76949 + 2.75367i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-1.59299 + 0.426840i) q^{13} +(1.22137 - 0.705160i) q^{14} +(-1.62623 + 1.53472i) q^{15} -1.00000 q^{16} +(5.00634 + 1.34144i) q^{17} +(0.258819 + 0.965926i) q^{18} +(1.58505 - 0.915126i) q^{19} +(1.17360 - 1.90333i) q^{20} +(1.22137 + 0.705160i) q^{21} +(-1.42540 - 5.31968i) q^{22} +(-1.29889 - 1.29889i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.24532 + 4.46750i) q^{25} +(1.42824 + 0.824592i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.36227 - 0.365018i) q^{28} +8.56947 q^{29} +(2.23513 + 0.0647049i) q^{30} +(-3.92867 - 3.94532i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.89428 - 3.89428i) q^{33} +(-2.59147 - 4.48856i) q^{34} +(2.29351 - 2.16445i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-6.11479 - 1.63845i) q^{37} +(-1.76789 - 0.473704i) q^{38} +1.64918i q^{39} +(-2.17572 + 0.515994i) q^{40} +(3.95985 - 6.85866i) q^{41} +(-0.365018 - 1.36227i) q^{42} +(1.92231 - 7.17416i) q^{43} +(-2.75367 + 4.76949i) q^{44} +(1.06153 + 1.96803i) q^{45} +1.83691i q^{46} +(1.09254 + 1.09254i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(4.33965 + 2.50550i) q^{49} +(1.57132 - 4.74668i) q^{50} +(2.59147 - 4.48856i) q^{51} +(-0.426840 - 1.59299i) q^{52} +(1.21471 - 0.325481i) q^{53} +1.00000 q^{54} +(-5.84620 - 10.8386i) q^{55} +(0.705160 + 1.22137i) q^{56} +(-0.473704 - 1.76789i) q^{57} +(-6.05953 - 6.05953i) q^{58} +(3.20296 - 1.84923i) q^{59} +(-1.53472 - 1.62623i) q^{60} +3.67820i q^{61} +(-0.0117750 + 5.56775i) q^{62} +(0.997247 - 0.997247i) q^{63} -1.00000i q^{64} +(3.53292 + 1.05712i) q^{65} -5.50734 q^{66} +(-6.11665 + 1.63895i) q^{67} +(-1.34144 + 5.00634i) q^{68} +(-1.59081 + 0.918457i) q^{69} +(-3.15225 - 0.0912547i) q^{70} +(0.861959 - 1.49296i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(11.1271 - 2.98150i) q^{73} +(3.16525 + 5.48237i) q^{74} +(4.89640 - 1.01254i) q^{75} +(0.915126 + 1.58505i) q^{76} +(-5.49218 + 5.49218i) q^{77} +(1.16615 - 1.16615i) q^{78} +(6.16709 + 10.6817i) q^{79} +(1.90333 + 1.17360i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-7.64984 + 2.04977i) q^{82} +(-0.111997 + 0.0300095i) q^{83} +(-0.705160 + 1.22137i) q^{84} +(-7.95438 - 8.42865i) q^{85} +(-6.43217 + 3.71362i) q^{86} +(2.21794 - 8.27747i) q^{87} +(5.31968 - 1.42540i) q^{88} +6.11279 q^{89} +(0.640995 - 2.14222i) q^{90} -2.32588i q^{91} +(1.29889 - 1.29889i) q^{92} +(-4.82770 + 2.77368i) q^{93} -1.54508i q^{94} +(-4.09086 - 0.118426i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-5.78447 - 5.78447i) q^{97} +(-1.29694 - 4.84025i) q^{98} +(-2.75367 - 4.76949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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