LMFDB - Embedded newform 950.2.r.b.11.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(11,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("950.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.r (of order $15$, degree $8$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$25$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	950.11
Dual form			950.2.r.b.691.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 - 0.994522i) q^{2} +(0.525231 + 0.583328i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-1.47087 - 1.68420i) q^{5} +(0.525231 - 0.583328i) q^{6} -3.06829 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.249181 - 2.37080i) q^{9} +O(q^{10})$	\(q+(-0.104528 - 0.994522i) q^{2} +(0.525231 + 0.583328i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-1.47087 - 1.68420i) q^{5} +(0.525231 - 0.583328i) q^{6} -3.06829 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.249181 - 2.37080i) q^{9} +(-1.52123 + 1.63886i) q^{10} +(3.96238 - 2.87884i) q^{11} +(-0.635034 - 0.461379i) q^{12} +(-0.491604 + 4.67730i) q^{13} +(0.320724 + 3.05148i) q^{14} +(0.209896 - 1.74259i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-3.48808 - 0.741415i) q^{17} -2.38386 q^{18} +(-0.409596 + 4.33961i) q^{19} +(1.78889 + 1.34159i) q^{20} +(-1.61156 - 1.78982i) q^{21} +(-3.27725 - 3.63975i) q^{22} +(-7.83409 - 3.48796i) q^{23} +(-0.392472 + 0.679782i) q^{24} +(-0.673082 + 4.95449i) q^{25} +4.70306 q^{26} +(3.41893 - 2.48400i) q^{27} +(3.00124 - 0.637933i) q^{28} +(-2.20647 + 0.469000i) q^{29} +(-1.75499 - 0.0265959i) q^{30} +(2.08669 + 6.42217i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.76047 + 0.799312i) q^{33} +(-0.372749 + 3.54647i) q^{34} +(4.51306 + 5.16762i) q^{35} +(0.249181 + 2.37080i) q^{36} +(-3.29621 - 2.39483i) q^{37} +(4.35865 - 0.0462611i) q^{38} +(-2.98660 + 2.16989i) q^{39} +(1.14725 - 1.91933i) q^{40} +(-6.70639 + 2.98588i) q^{41} +(-1.61156 + 1.78982i) q^{42} +(-4.69880 + 8.13855i) q^{43} +(-3.27725 + 3.63975i) q^{44} +(-4.35943 + 3.06747i) q^{45} +(-2.64997 + 8.15576i) q^{46} +(-10.5543 + 2.24339i) q^{47} +(0.717083 + 0.319266i) q^{48} +2.41440 q^{49} +(4.99770 + 0.151509i) q^{50} +(-1.39956 - 2.42411i) q^{51} +(-0.491604 - 4.67730i) q^{52} +(4.66374 - 0.991309i) q^{53} +(-2.82777 - 3.14056i) q^{54} +(-10.6767 - 2.43906i) q^{55} +(-0.948154 - 2.91812i) q^{56} +(-2.74655 + 2.04037i) q^{57} +(0.697070 + 2.14536i) q^{58} +(9.27050 - 4.12749i) q^{59} +(0.156996 + 1.74815i) q^{60} +(-1.38662 - 0.617364i) q^{61} +(6.16887 - 2.74656i) q^{62} +(-0.764561 + 7.27431i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(8.60060 - 6.05173i) q^{65} +(0.401857 - 3.82342i) q^{66} +(6.71097 - 7.45328i) q^{67} +3.56601 q^{68} +(-2.08008 - 6.40183i) q^{69} +(4.66757 - 5.02850i) q^{70} +(-11.0193 - 12.2382i) q^{71} +(2.33177 - 0.495633i) q^{72} +(0.956298 + 9.09857i) q^{73} +(-2.03717 + 3.52848i) q^{74} +(-3.24361 + 2.20962i) q^{75} +(-0.501611 - 4.32994i) q^{76} +(-12.1577 + 8.83310i) q^{77} +(2.47019 + 2.74343i) q^{78} +(1.25452 + 1.39329i) q^{79} +(-2.02873 - 0.940340i) q^{80} +(-3.75059 - 0.797212i) q^{81} +(3.67053 + 6.35754i) q^{82} +(-3.33086 - 10.2513i) q^{83} +(1.94847 + 1.41564i) q^{84} +(3.88182 + 6.96516i) q^{85} +(8.58513 + 3.82235i) q^{86} +(-1.43249 - 1.04076i) q^{87} +(3.96238 + 2.87884i) q^{88} +(-3.58830 - 1.59761i) q^{89} +(3.50635 + 4.01491i) q^{90} +(1.50838 - 14.3513i) q^{91} +(8.38808 + 1.78294i) q^{92} +(-2.65024 + 4.59035i) q^{93} +(3.33433 + 10.2620i) q^{94} +(7.91125 - 5.69316i) q^{95} +(0.242561 - 0.746527i) q^{96} +(1.52039 + 1.68857i) q^{97} +(-0.252374 - 2.40118i) q^{98} +(-5.83780 - 10.1114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9}+O(q^{10}) $ 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9} - 4 q^{10} + 14 q^{11} + 8 q^{13} + q^{14} - 4 q^{15} + 25 q^{16} - 5 q^{17} + 184 q^{18} + 24 q^{19} - 2 q^{20} + 32 q^{21} + 8 q^{22} + 11 q^{23} - 23 q^{25} + 64 q^{26} - 36 q^{27} + 6 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 100 q^{32} + 12 q^{33} + 2 q^{35} + 13 q^{36} + 8 q^{37} + 2 q^{38} - 52 q^{39} + q^{40} + 14 q^{41} + 32 q^{42} - 10 q^{43} + 8 q^{44} - 52 q^{45} + 8 q^{46} - 22 q^{47} + 204 q^{49} - 34 q^{50} - 10 q^{51} + 8 q^{52} - 18 q^{53} - 12 q^{54} + 10 q^{55} - 12 q^{56} + 34 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 16 q^{61} - 4 q^{62} - 21 q^{63} - 50 q^{64} + 96 q^{65} - 18 q^{66} - 54 q^{67} - 20 q^{68} - 20 q^{69} - 3 q^{70} - 5 q^{71} + 33 q^{72} - 16 q^{73} - 4 q^{74} + 56 q^{75} + 14 q^{76} - 116 q^{77} - 34 q^{78} + q^{80} + 57 q^{81} - 36 q^{82} - 72 q^{83} + 76 q^{84} - 5 q^{85} - 112 q^{87} + 14 q^{88} - 4 q^{89} - 49 q^{90} - 64 q^{91} - 4 q^{92} - 124 q^{93} + 44 q^{94} + 41 q^{95} + 13 q^{97} + 43 q^{98} - 28 q^{99}+O(q^{100}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9 - 4 * q^10 + 14 * q^11 + 8 * q^13 + q^14 - 4 * q^15 + 25 * q^16 - 5 * q^17 + 184 * q^18 + 24 * q^19 - 2 * q^20 + 32 * q^21 + 8 * q^22 + 11 * q^23 - 23 * q^25 + 64 * q^26 - 36 * q^27 + 6 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 100 * q^32 + 12 * q^33 + 2 * q^35 + 13 * q^36 + 8 * q^37 + 2 * q^38 - 52 * q^39 + q^40 + 14 * q^41 + 32 * q^42 - 10 * q^43 + 8 * q^44 - 52 * q^45 + 8 * q^46 - 22 * q^47 + 204 * q^49 - 34 * q^50 - 10 * q^51 + 8 * q^52 - 18 * q^53 - 12 * q^54 + 10 * q^55 - 12 * q^56 + 34 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 16 * q^61 - 4 * q^62 - 21 * q^63 - 50 * q^64 + 96 * q^65 - 18 * q^66 - 54 * q^67 - 20 * q^68 - 20 * q^69 - 3 * q^70 - 5 * q^71 + 33 * q^72 - 16 * q^73 - 4 * q^74 + 56 * q^75 + 14 * q^76 - 116 * q^77 - 34 * q^78 + q^80 + 57 * q^81 - 36 * q^82 - 72 * q^83 + 76 * q^84 - 5 * q^85 - 112 * q^87 + 14 * q^88 - 4 * q^89 - 49 * q^90 - 64 * q^91 - 4 * q^92 - 124 * q^93 + 44 * q^94 + 41 * q^95 + 13 * q^97 + 43 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$3$	0.525231	+	0.583328i	0.303242	+	0.336784i	0.875436	−	0.483334i	$-0.160574\pi$
$3$	0.525231	+	0.583328i	0.303242	+	0.336784i	−0.572194	+	0.820118i	$0.693908\pi$
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	−1.47087	−	1.68420i	−0.657793	−	0.753199i
$5$	−1.47087	−	1.68420i	−0.657793	−	0.753199i
$6$	0.525231	−	0.583328i	0.214425	−	0.238143i
$7$	−3.06829			−1.15970			−0.579852	−	0.814722i	$-0.696890\pi$
$7$	−3.06829			−1.15970			−0.579852	+	0.814722i	$0.696890\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.249181	−	2.37080i	0.0830605	−	0.790267i
$10$	−1.52123	+	1.63886i	−0.481055	+	0.518253i
$11$	3.96238	−	2.87884i	1.19470	−	0.868002i	0.200949	−	0.979602i	$-0.435598\pi$
$11$	3.96238	−	2.87884i	1.19470	−	0.868002i	0.993753	+	0.111600i	$0.0355975\pi$
$12$	−0.635034	−	0.461379i	−0.183318	−	0.133189i
$13$	−0.491604	+	4.67730i	−0.136346	+	1.29725i	0.685724	+	0.727862i	$0.259486\pi$
$13$	−0.491604	+	4.67730i	−0.136346	+	1.29725i	−0.822070	+	0.569387i	$0.807181\pi$
$14$	0.320724	+	3.05148i	0.0857170	+	0.815543i
$15$	0.209896	−	1.74259i	0.0541950	−	0.449936i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−3.48808	−	0.741415i	−0.845984	−	0.179819i	−0.235526	−	0.971868i	$-0.575681\pi$
$17$	−3.48808	−	0.741415i	−0.845984	−	0.179819i	−0.610458	+	0.792049i	$0.709015\pi$
$18$	−2.38386			−0.561882
$19$	−0.409596	+	4.33961i	−0.0939677	+	0.995575i
$19$	−0.409596	+	4.33961i	−0.0939677	+	0.995575i
$20$	1.78889	+	1.34159i	0.400009	+	0.299988i
$21$	−1.61156	−	1.78982i	−0.351671	−	0.390570i
$22$	−3.27725	−	3.63975i	−0.698711	−	0.775998i
$23$	−7.83409	−	3.48796i	−1.63352	−	0.727290i	−0.634560	−	0.772874i	$-0.718819\pi$
$23$	−7.83409	−	3.48796i	−1.63352	−	0.727290i	−0.998961	+	0.0455838i	$0.985485\pi$
$24$	−0.392472	+	0.679782i	−0.0801131	+	0.138760i
$25$	−0.673082	+	4.95449i	−0.134616	+	0.990898i
$26$	4.70306			0.922346
$27$	3.41893	−	2.48400i	0.657974	−	0.478046i
$28$	3.00124	−	0.637933i	0.567181	−	0.120558i
$29$	−2.20647	+	0.469000i	−0.409732	+	0.0870912i	−0.408166	−	0.912908i	$-0.633832\pi$
$29$	−2.20647	+	0.469000i	−0.409732	+	0.0870912i	−0.00156551	+	0.999999i	$0.500498\pi$
$30$	−1.75499	−	0.0265959i	−0.320416	−	0.00485572i
$31$	2.08669	+	6.42217i	0.374781	+	1.15346i	0.943627	+	0.331012i	$0.107390\pi$
$31$	2.08669	+	6.42217i	0.374781	+	1.15346i	−0.568846	+	0.822444i	$0.692610\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.76047	+	0.799312i	0.654613	+	0.139142i
$34$	−0.372749	+	3.54647i	−0.0639260	+	0.608215i
$35$	4.51306	+	5.16762i	0.762846	+	0.873488i
$36$	0.249181	+	2.37080i	0.0415302	+	0.395134i
$37$	−3.29621	−	2.39483i	−0.541893	−	0.393708i	0.282895	−	0.959151i	$-0.408705\pi$
$37$	−3.29621	−	2.39483i	−0.541893	−	0.393708i	−0.824788	+	0.565443i	$0.808705\pi$
$38$	4.35865	−	0.0462611i	0.707067	−	0.00750455i
$39$	−2.98660	+	2.16989i	−0.478239	+	0.347461i
$40$	1.14725	−	1.91933i	0.181396	−	0.303472i
$41$	−6.70639	+	2.98588i	−1.04736	+	0.466316i	−0.856956	−	0.515390i	$-0.827647\pi$
$41$	−6.70639	+	2.98588i	−1.04736	+	0.466316i	−0.190406	+	0.981705i	$0.560980\pi$
$42$	−1.61156	+	1.78982i	−0.248669	+	0.276175i
$43$	−4.69880	+	8.13855i	−0.716560	+	1.24112i	0.245795	+	0.969322i	$0.420951\pi$
$43$	−4.69880	+	8.13855i	−0.716560	+	1.24112i	−0.962355	+	0.271796i	$0.912382\pi$
$44$	−3.27725	+	3.63975i	−0.494064	+	0.548713i
$45$	−4.35943	+	3.06747i	−0.649865	+	0.457271i
$46$	−2.64997	+	8.15576i	−0.390716	+	1.20250i
$47$	−10.5543	+	2.24339i	−1.53951	+	0.327232i	−0.898039	−	0.439917i	$-0.855008\pi$
$47$	−10.5543	+	2.24339i	−1.53951	+	0.327232i	−0.641469	+	0.767149i	$0.721675\pi$
$48$	0.717083	+	0.319266i	0.103502	+	0.0460821i
$49$	2.41440			0.344915
$50$	4.99770	+	0.151509i	0.706782	+	0.0214267i
$51$	−1.39956	−	2.42411i	−0.195978	−	0.339443i
$52$	−0.491604	−	4.67730i	−0.0681732	−	0.648624i
$53$	4.66374	−	0.991309i	0.640615	−	0.136167i	0.123859	−	0.992300i	$-0.460473\pi$
$53$	4.66374	−	0.991309i	0.640615	−	0.136167i	0.516756	+	0.856133i	$0.327140\pi$
$54$	−2.82777	−	3.14056i	−0.384811	−	0.427376i
$55$	−10.6767	−	2.43906i	−1.43964	−	0.328882i
$56$	−0.948154	−	2.91812i	−0.126702	−	0.389950i
$57$	−2.74655	+	2.04037i	−0.363789	+	0.270253i
$58$	0.697070	+	2.14536i	0.0915298	+	0.281700i
$59$	9.27050	−	4.12749i	1.20692	−	0.537354i	0.298094	−	0.954537i	$-0.403649\pi$
$59$	9.27050	−	4.12749i	1.20692	−	0.537354i	0.908823	+	0.417183i	$0.136983\pi$
$60$	0.156996	+	1.74815i	0.0202681	+	0.225686i
$61$	−1.38662	−	0.617364i	−0.177539	−	0.0790453i	0.316043	−	0.948745i	$-0.397646\pi$
$61$	−1.38662	−	0.617364i	−0.177539	−	0.0790453i	−0.493581	+	0.869700i	$0.664312\pi$
$62$	6.16887	−	2.74656i	0.783448	−	0.348813i
$63$	−0.764561	+	7.27431i	−0.0963256	+	0.916477i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	8.60060	−	6.05173i	1.06677	−	0.750625i
$66$	0.401857	−	3.82342i	0.0494652	−	0.470630i
$67$	6.71097	−	7.45328i	0.819875	−	0.910563i	−0.177415	−	0.984136i	$-0.556773\pi$
$67$	6.71097	−	7.45328i	0.819875	−	0.910563i	0.997290	+	0.0735727i	$0.0234401\pi$
$68$	3.56601			0.432442
$69$	−2.08008	−	6.40183i	−0.250412	−	0.770689i
$70$	4.66757	−	5.02850i	0.557882	−	0.601020i
$71$	−11.0193	−	12.2382i	−1.30775	−	1.45240i	−0.811661	−	0.584129i	$-0.801436\pi$
$71$	−11.0193	−	12.2382i	−1.30775	−	1.45240i	−0.496087	−	0.868273i	$-0.665230\pi$
$72$	2.33177	−	0.495633i	0.274802	−	0.0584109i
$73$	0.956298	+	9.09857i	0.111926	+	1.06491i	0.895944	+	0.444168i	$0.146501\pi$
$73$	0.956298	+	9.09857i	0.111926	+	1.06491i	−0.784017	+	0.620739i	$0.786833\pi$
$74$	−2.03717	+	3.52848i	−0.236816	+	0.410177i
$75$	−3.24361	+	2.20962i	−0.374540	+	0.255145i
$76$	−0.501611	−	4.32994i	−0.0575387	−	0.496678i
$77$	−12.1577	+	8.83310i	−1.38550	+	1.00663i
$78$	2.47019	+	2.74343i	0.279694	+	0.310632i
$79$	1.25452	+	1.39329i	0.141145	+	0.156757i	0.809572	−	0.587020i	$-0.199699\pi$
$79$	1.25452	+	1.39329i	0.141145	+	0.156757i	−0.668428	+	0.743777i	$0.733032\pi$
$80$	−2.02873	−	0.940340i	−0.226819	−	0.105133i
$81$	−3.75059	−	0.797212i	−0.416732	−	0.0885791i
$82$	3.67053	+	6.35754i	0.405342	+	0.702073i
$83$	−3.33086	−	10.2513i	−0.365610	−	1.12523i	−0.949598	−	0.313469i	$-0.898509\pi$
$83$	−3.33086	−	10.2513i	−0.365610	−	1.12523i	0.583989	−	0.811762i	$-0.301491\pi$
$84$	1.94847	+	1.41564i	0.212595	+	0.154459i
$85$	3.88182	+	6.96516i	0.421043	+	0.755478i
$86$	8.58513	+	3.82235i	0.925758	+	0.412174i
$87$	−1.43249	−	1.04076i	−0.153579	−	0.111582i
$88$	3.96238	+	2.87884i	0.422391	+	0.306885i
$89$	−3.58830	−	1.59761i	−0.380359	−	0.169347i	0.207646	−	0.978204i	$-0.433420\pi$
$89$	−3.58830	−	1.59761i	−0.380359	−	0.169347i	−0.588005	+	0.808857i	$0.700086\pi$
$90$	3.50635	+	4.01491i	0.369602	+	0.423208i
$91$	1.50838	−	14.3513i	0.158121	−	1.50442i
$92$	8.38808	+	1.78294i	0.874518	+	0.185885i
$93$	−2.65024	+	4.59035i	−0.274817	+	0.475997i
$94$	3.33433	+	10.2620i	0.343910	+	1.05845i
$95$	7.91125	−	5.69316i	0.811677	−	0.584106i
$96$	0.242561	−	0.746527i	0.0247563	−	0.0761921i
$97$	1.52039	+	1.68857i	0.154372	+	0.171448i	0.815370	−	0.578940i	$-0.196533\pi$
$97$	1.52039	+	1.68857i	0.154372	+	0.171448i	−0.660998	+	0.750388i	$0.729867\pi$
$98$	−0.252374	−	2.40118i	−0.0254936	−	0.242555i
$99$	−5.83780	−	10.1114i	−0.586721	−	1.01623i
$100$	−0.371723	−	4.98616i	−0.0371723	−	0.498616i
$101$	2.71031	+	4.69439i	0.269686	+	0.467109i	0.968781	−	0.247919i	$-0.0797468\pi$
$101$	2.71031	+	4.69439i	0.269686	+	0.467109i	−0.699095	+	0.715029i	$0.746413\pi$
$102$	−2.26454	+	1.64528i	−0.224222	+	0.162907i
$103$	1.16583	−	3.58805i	0.114872	−	0.353541i	−0.877048	−	0.480403i	$-0.840491\pi$
$103$	1.16583	−	3.58805i	0.114872	−	0.353541i	0.991920	+	0.126862i	$0.0404905\pi$
$104$	−4.60029	+	0.977821i	−0.451095	+	0.0958832i
$105$	−0.644023	+	5.34679i	−0.0628502	+	0.521793i
$106$	−1.47337	−	4.53458i	−0.143107	−	0.440437i
$107$	−7.27318			−0.703125			−0.351563	−	0.936164i	$-0.614350\pi$
$107$	−7.27318			−0.703125			−0.351563	+	0.936164i	$0.614350\pi$
$108$	−2.82777	+	3.14056i	−0.272102	+	0.302200i
$109$	−0.113612	+	0.0505834i	−0.0108821	+	0.00484501i	−0.412170	−	0.911107i	$-0.635229\pi$
$109$	−0.113612	+	0.0505834i	−0.0108821	+	0.00484501i	0.401288	+	0.915952i	$0.368563\pi$
$110$	−1.30968	+	10.8732i	−0.124873	+	1.03671i
$111$	−0.334296	−	3.18061i	−0.0317299	−	0.301890i
$112$	−2.80302	+	1.24799i	−0.264861	+	0.117924i
$113$	4.61346	+	3.35187i	0.433998	+	0.315318i	0.783245	−	0.621713i	$-0.213563\pi$
$113$	4.61346	+	3.35187i	0.433998	+	0.315318i	−0.349248	+	0.937030i	$0.613563\pi$
$114$	2.31628	+	2.51823i	0.216940	+	0.235853i
$115$	5.64849	+	18.3245i	0.526725	+	1.70877i
$116$	2.06075	−	0.917503i	0.191335	−	0.0851880i
$117$	10.9664	+	2.33099i	1.01385	+	0.215500i
$118$	−5.07391	−	8.78827i	−0.467091	−	0.809026i
$119$	10.7024	+	2.27488i	0.981092	+	0.208537i
$120$	1.72217	−	0.338868i	0.157212	−	0.0309343i
$121$	4.01356	−	12.3525i	0.364869	−	1.12295i
$122$	−0.469040	+	1.44356i	−0.0424649	+	0.130694i
$123$	−5.26415	−	2.34375i	−0.474652	−	0.211329i
$124$	−3.37634	−	5.84798i	−0.303204	−	0.525165i
$125$	9.33438	−	6.15380i	0.834893	−	0.550413i
$126$	7.31438			0.651617
$127$	−5.78198	−	2.57430i	−0.513068	−	0.228432i	0.133837	−	0.991003i	$-0.457270\pi$
$127$	−5.78198	−	2.57430i	−0.513068	−	0.228432i	−0.646905	+	0.762571i	$0.723937\pi$
$128$	0.669131	+	0.743145i	0.0591433	+	0.0656853i
$129$	−7.21540	+	1.53368i	−0.635280	+	0.135033i
$130$	−6.91759	−	7.92091i	−0.606713	−	0.694710i
$131$	9.10128	+	1.93454i	0.795183	+	0.169021i	0.587553	−	0.809186i	$-0.300092\pi$
$131$	9.10128	+	1.93454i	0.795183	+	0.169021i	0.207630	+	0.978207i	$0.433425\pi$
$132$	−3.84448			−0.334619
$133$	1.25676	−	13.3152i	0.108975	−	1.15457i
$134$	−8.11394	−	5.89512i	−0.700938	−	0.509261i
$135$	−9.21237	−	2.10454i	−0.792875	−	0.181130i
$136$	−0.372749	−	3.54647i	−0.0319630	−	0.304108i
$137$	−0.623269	+	5.93001i	−0.0532495	+	0.506635i	0.935095	+	0.354398i	$0.115314\pi$
$137$	−0.623269	+	5.93001i	−0.0532495	+	0.506635i	−0.988344	+	0.152237i	$0.951352\pi$
$138$	−6.14933	+	2.73786i	−0.523466	+	0.233062i
$139$	10.1200	+	4.50573i	0.858371	+	0.382171i	0.788241	−	0.615367i	$-0.210992\pi$
$139$	10.1200	+	4.50573i	0.858371	+	0.382171i	0.0701296	+	0.997538i	$0.477659\pi$
$140$	−5.48884	−	4.11638i	−0.463892	−	0.347898i
$141$	−6.85209	−	4.97834i	−0.577050	−	0.419252i
$142$	−11.0193	+	12.2382i	−0.924718	+	1.02700i
$143$	11.5173	+	19.9485i	0.963121	+	1.66817i
$144$	−0.736654	−	2.26719i	−0.0613878	−	0.188932i
$145$	4.03533	+	3.02631i	0.335116	+	0.251321i
$146$	8.94876	−	1.90212i	0.740605	−	0.157420i
$147$	1.26812	+	1.40839i	0.104593	+	0.116162i
$148$	3.72209	+	1.65718i	0.305954	+	0.136220i
$149$	−0.169299	+	0.293234i	−0.0138695	+	0.0240227i	−0.872877	−	0.487941i	$-0.837748\pi$
$149$	−0.169299	+	0.293234i	−0.0138695	+	0.0240227i	0.859007	+	0.511963i	$0.171082\pi$
$150$	2.53657	+	2.99488i	0.207110	+	0.244531i
$151$	−5.69378			−0.463354			−0.231677	−	0.972793i	$-0.574421\pi$
$151$	−5.69378			−0.463354			−0.231677	+	0.972793i	$0.574421\pi$
$152$	−4.25379	+	0.951465i	−0.345028	+	0.0771740i
$153$	−2.62691	+	8.08481i	−0.212373	+	0.653618i
$154$	10.0555	+	11.1678i	0.810299	+	0.899928i
$155$	7.74699	−	12.9606i	0.622253	−	1.04102i
$156$	2.47019	−	2.74343i	0.197774	−	0.219650i
$157$	5.51096	−	9.54526i	0.439823	−	0.761795i	−0.557853	−	0.829940i	$-0.688375\pi$
$157$	5.51096	−	9.54526i	0.439823	−	0.761795i	0.997675	+	0.0681449i	$0.0217080\pi$
$158$	1.25452	−	1.39329i	0.0998043	−	0.110844i
$159$	3.02780	+	2.19983i	0.240120	+	0.174458i
$160$	−0.723128	+	2.11591i	−0.0571683	+	0.167278i
$161$	24.0373	+	10.7021i	1.89440	+	0.843442i
$162$	−0.400802	+	3.81337i	−0.0314900	+	0.299607i
$163$	−17.1636	−	12.4701i	−1.34436	−	0.976731i	−0.999272	−	0.0381592i	$-0.987851\pi$
$163$	−17.1636	−	12.4701i	−1.34436	−	0.976731i	−0.345083	−	0.938572i	$-0.612149\pi$
$164$	5.93904	−	4.31496i	0.463761	−	0.336942i
$165$	−4.18496	−	7.50908i	−0.325798	−	0.584581i
$166$	−9.84701	+	4.38417i	−0.764277	+	0.340278i
$167$	10.5566	−	11.7243i	0.816894	−	0.907253i	−0.180185	−	0.983633i	$-0.557669\pi$
$167$	10.5566	−	11.7243i	0.816894	−	0.907253i	0.997079	+	0.0763798i	$0.0243362\pi$
$168$	1.20422	−	2.08577i	0.0929075	−	0.160921i
$169$	−8.91950	−	1.89590i	−0.686116	−	0.145838i
$170$	6.52125	−	4.58862i	0.500157	−	0.351931i
$171$	10.1863	+	2.05242i	0.778966	+	0.156953i
$172$	2.90402	−	8.93764i	0.221429	−	0.681489i
$173$	2.20783	+	21.0061i	0.167858	+	1.59706i	0.676736	+	0.736225i	$0.263394\pi$
$173$	2.20783	+	21.0061i	0.167858	+	1.59706i	−0.508878	+	0.860838i	$0.669940\pi$
$174$	−0.885327	+	1.53343i	−0.0671164	+	0.116249i
$175$	2.06521	−	15.2018i	0.156115	−	1.14915i
$176$	2.44888	−	4.24159i	0.184592	−	0.319722i
$177$	7.27683	+	3.23985i	0.546960	+	0.243522i
$178$	−1.21378	+	3.73564i	−0.0909768	+	0.279998i
$179$	−3.68823	+	11.3512i	−0.275671	+	0.848429i	0.713370	+	0.700788i	$0.247168\pi$
$179$	−3.68823	+	11.3512i	−0.275671	+	0.848429i	−0.989041	+	0.147641i	$0.952832\pi$
$180$	3.62640	−	3.90681i	0.270296	−	0.291197i
$181$	−1.06266	+	1.18020i	−0.0789868	+	0.0877238i	−0.781343	−	0.624102i	$-0.785465\pi$
$181$	−1.06266	+	1.18020i	−0.0789868	+	0.0877238i	0.702356	+	0.711826i	$0.252132\pi$
$182$	−14.4304			−1.06965
$183$	−0.368171	−	1.13311i	−0.0272160	−	0.0837622i
$184$	0.896381	−	8.52850i	0.0660821	−	0.628729i
$185$	0.814904	+	9.07397i	0.0599130	+	0.667132i
$186$	4.84223	+	2.15590i	0.355049	+	0.158078i
$187$	−15.9555	+	7.10385i	−1.16678	+	0.519485i
$188$	9.85727	−	4.38874i	0.718915	−	0.320082i
$189$	−10.4903	+	7.62163i	−0.763056	+	0.554392i
$190$	−6.48893	−	7.27281i	−0.470756	−	0.527625i
$191$	−16.7512	−	12.1705i	−1.21208	−	0.880625i	−0.216659	−	0.976247i	$-0.569516\pi$
$191$	−16.7512	−	12.1705i	−1.21208	−	0.880625i	−0.995418	+	0.0956224i	$0.969516\pi$
$192$	−0.767792	−	0.163199i	−0.0554106	−	0.0117779i
$193$	6.62041	−	11.4669i	0.476547	−	0.825404i	−0.523091	−	0.852277i	$-0.675221\pi$
$193$	6.62041	−	11.4669i	0.476547	−	0.825404i	0.999639	+	0.0268721i	$0.00855470\pi$
$194$	1.52039	−	1.68857i	0.109158	−	0.121232i
$195$	8.04745	+	1.83841i	0.576290	+	0.131652i
$196$	−2.36164	+	0.501982i	−0.168689	+	0.0358559i
$197$	7.35789	−	22.6453i	0.524228	−	1.61341i	−0.241609	−	0.970374i	$-0.577675\pi$
$197$	7.35789	−	22.6453i	0.524228	−	1.61341i	0.765837	−	0.643035i	$-0.222325\pi$
$198$	−9.44576	+	6.86275i	−0.671281	+	0.487714i
$199$	−5.24407	−	9.08300i	−0.371742	−	0.643877i	0.618091	−	0.786106i	$-0.287906\pi$
$199$	−5.24407	−	9.08300i	−0.371742	−	0.643877i	−0.989834	+	0.142230i	$0.954573\pi$
$200$	−4.91999	+	0.890882i	−0.347896	+	0.0629949i
$201$	7.87251			0.555284
$202$	4.38537	−	3.18616i	0.308554	−	0.224177i
$203$	6.77010	−	1.43903i	0.475168	−	0.101000i
$204$	1.87298	+	2.08015i	0.131135	+	0.145640i
$205$	14.8930	+	6.90308i	1.04018	+	0.482132i
$206$	−3.69025	−	0.784387i	−0.257112	−	0.0546509i
$207$	−10.2214	+	17.7039i	−0.710435	+	1.23051i
$208$	1.45333	+	4.47288i	0.100770	+	0.310138i
$209$	10.8701	+	18.3743i	0.751898	+	1.27098i
$210$	5.38481	+	0.0816038i	0.371587	+	0.00563120i
$211$	−0.200052	−	1.90337i	−0.0137722	−	0.131033i	0.985475	−	0.169818i	$-0.0543180\pi$
$211$	−0.200052	−	1.90337i	−0.0137722	−	0.131033i	−0.999248	+	0.0387847i	$0.987651\pi$
$212$	−4.35573	+	1.93929i	−0.299152	+	0.133191i
$213$	1.35119	−	12.8557i	0.0925820	−	0.880859i
$214$	0.760255	+	7.23334i	0.0519699	+	0.494461i
$215$	20.6183	−	4.05703i	1.40616	−	0.276687i
$216$	3.41893	+	2.48400i	0.232629	+	0.169015i
$217$	−6.40257	−	19.7051i	−0.434635	−	1.33767i
$218$	0.0621820	+	0.107702i	0.00421150	+	0.00729453i
$219$	−4.80517	+	5.33668i	−0.324703	+	0.360620i
$220$	10.9505	+	0.165948i	0.738282	+	0.0111882i
$221$	5.18257	−	15.9503i	0.348617	−	1.07293i
$222$	−3.12824	+	0.664929i	−0.209954	+	0.0446271i
$223$	0.148686	+	1.41465i	0.00995675	+	0.0947322i	0.998372	−	0.0570438i	$-0.0181675\pi$
$223$	0.148686	+	1.41465i	0.00995675	+	0.0947322i	−0.988415	+	0.151776i	$0.951501\pi$
$224$	1.53414	+	2.65722i	0.102504	+	0.177543i
$225$	11.5784	+	2.83031i	0.771893	+	0.188687i
$226$	2.85127	−	4.93855i	0.189664	−	0.328508i
$227$	0.102460	−	0.0744418i	0.00680054	−	0.00494088i	−0.584380	−	0.811480i	$-0.698662\pi$
$227$	0.102460	−	0.0744418i	0.00680054	−	0.00494088i	0.591180	+	0.806539i	$0.298662\pi$
$228$	2.26231	−	2.56682i	0.149825	−	0.169992i
$229$	3.56298	−	10.9657i	0.235448	−	0.724635i	−0.761613	−	0.648032i	$-0.775592\pi$
$229$	3.56298	−	10.9657i	0.235448	−	0.724635i	0.997062	−	0.0766036i	$-0.0244076\pi$
$230$	17.6337	−	7.53298i	1.16273	−	0.496710i
$231$	−11.5382	−	2.45252i	−0.759158	−	0.161364i
$232$	−1.12788	−	1.95355i	−0.0740492	−	0.128257i
$233$	7.42703	+	1.57866i	0.486561	+	0.103422i	0.444659	−	0.895700i	$-0.353325\pi$
$233$	7.42703	+	1.57866i	0.486561	+	0.103422i	0.0419022	+	0.999122i	$0.486658\pi$
$234$	1.17191	−	11.1500i	0.0766105	−	0.728900i
$235$	19.3024	+	14.4759i	1.25915	+	0.944304i
$236$	−8.20976	+	5.96474i	−0.534410	+	0.388272i
$237$	−0.153830	+	1.46359i	−0.00999233	+	0.0950706i
$238$	1.14370	−	10.8816i	0.0741353	−	0.705350i
$239$	−14.7016	+	10.6813i	−0.950966	+	0.690917i	−0.951035	−	0.309083i	$-0.899978\pi$
$239$	−14.7016	+	10.6813i	−0.950966	+	0.690917i	6.91366e−5		1.00000i	$0.499978\pi$
$240$	−0.517027	−	1.67731i	−0.0333740	−	0.108270i
$241$	0.392817	−	3.73740i	0.0253036	−	0.240747i	−0.974558	−	0.224134i	$-0.928045\pi$
$241$	0.392817	−	3.73740i	0.0253036	−	0.240747i	0.999862	−	0.0166136i	$-0.00528853\pi$
$242$	−12.7043	−	2.70039i	−0.816664	−	0.173587i
$243$	−7.84394	−	13.5861i	−0.503189	−	0.871549i
$244$	1.48468	+	0.315578i	0.0950468	+	0.0202028i
$245$	−3.55127	−	4.06634i	−0.226882	−	0.259789i
$246$	−1.78066	+	5.48030i	−0.113530	+	0.349411i
$247$	−20.0963	−	4.04917i	−1.27870	−	0.257642i
$248$	−5.46303	+	3.96912i	−0.346902	+	0.252039i
$249$	4.23042	−	7.32731i	0.268092	−	0.464349i
$250$	−7.09580	−	8.64000i	−0.448778	−	0.546442i
$251$	−11.1336	−	19.2839i	−0.702746	−	1.21719i	−0.967499	−	0.252875i	$-0.918624\pi$
$251$	−11.1336	−	19.2839i	−0.702746	−	1.21719i	0.264753	−	0.964316i	$-0.414710\pi$
$252$	−0.764561	−	7.27431i	−0.0481628	−	0.458238i
$253$	−41.0829	+	8.73244i	−2.58286	+	0.549004i
$254$	−1.95582	+	6.01939i	−0.122719	+	0.377690i
$255$	−2.02412	+	5.92269i	−0.126755	+	0.370893i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−6.65252	−	11.5225i	−0.414973	−	0.718754i	0.580453	−	0.814294i	$-0.302876\pi$
$257$	−6.65252	−	11.5225i	−0.414973	−	0.718754i	−0.995426	+	0.0955401i	$0.969542\pi$
$258$	2.27949	+	7.01556i	0.141915	+	0.436770i
$259$	10.1137	+	7.34805i	0.628436	+	0.456585i
$260$	−7.15443	+	7.70766i	−0.443699	+	0.478009i
$261$	0.562095	+	5.34798i	0.0347928	+	0.331032i
$262$	0.972597	−	9.25364i	0.0600872	−	0.571692i
$263$	1.01499	−	0.451905i	0.0625872	−	0.0278656i	−0.375204	−	0.926942i	$-0.622427\pi$
$263$	1.01499	−	0.451905i	0.0625872	−	0.0278656i	0.437792	+	0.899077i	$0.355761\pi$
$264$	0.401857	+	3.82342i	0.0247326	+	0.235315i
$265$	−8.52933	−	6.39661i	−0.523953	−	0.392940i
$266$	−13.3736	+	0.141943i	−0.819989	+	0.00870306i
$267$	−0.952752	−	2.93227i	−0.0583075	−	0.179452i
$268$	−5.01469	+	8.68570i	−0.306321	+	0.530564i
$269$	3.71946	+	0.790595i	0.226779	+	0.0482034i	0.319900	−	0.947451i	$-0.396351\pi$
$269$	3.71946	+	0.790595i	0.226779	+	0.0482034i	−0.0931204	+	0.995655i	$0.529684\pi$
$270$	−1.13005	+	9.38189i	−0.0687729	+	0.570964i
$271$	−15.3412	−	17.0381i	−0.931909	−	1.03499i	−0.999305	−	0.0372636i	$-0.988136\pi$
$271$	−15.3412	−	17.0381i	−0.931909	−	1.03499i	0.0673964	−	0.997726i	$-0.478531\pi$
$272$	−3.48808	+	0.741415i	−0.211496	+	0.0449549i
$273$	9.16376	−	6.65786i	0.554616	−	0.402952i
$274$	5.96267			0.360218
$275$	11.5962	+	21.5693i	0.699275	+	1.30067i
$276$	3.36564	+	5.82946i	0.202588	+	0.350892i
$277$	−5.25976	+	3.82144i	−0.316028	+	0.229608i	−0.734479	−	0.678632i	$-0.762573\pi$
$277$	−5.25976	+	3.82144i	−0.316028	+	0.229608i	0.418451	+	0.908240i	$0.362573\pi$
$278$	3.42322	−	10.5356i	0.205311	−	0.631882i
$279$	15.7457	−	3.34684i	0.942668	−	0.200370i
$280$	−3.52009	+	5.88905i	−0.210366	+	0.351938i
$281$	−2.66211	+	2.95657i	−0.158808	+	0.176374i	−0.817298	−	0.576215i	$-0.804529\pi$
$281$	−2.66211	+	2.95657i	−0.158808	+	0.176374i	0.658490	+	0.752590i	$0.271196\pi$
$282$	−4.23483	+	7.33493i	−0.252180	+	0.436789i
$283$	−20.9237	−	4.44747i	−1.24378	−	0.264374i	−0.461412	−	0.887186i	$-0.652657\pi$
$283$	−20.9237	−	4.44747i	−1.24378	−	0.264374i	−0.782372	+	0.622812i	$0.785990\pi$
$284$	13.3229	+	9.67968i	0.790571	+	0.574383i
$285$	7.47621	+	1.62463i	0.442853	+	0.0962347i
$286$	18.6353	−	13.5393i	1.10193	−	0.800598i
$287$	20.5771	−	9.16153i	1.21463	−	0.540788i
$288$	−2.17777	+	0.969604i	−0.128326	+	0.0571345i
$289$	−3.91325	−	1.74229i	−0.230191	−	0.102488i
$290$	2.58793	−	4.32956i	0.151968	−	0.254240i
$291$	−0.186431	+	1.77377i	−0.0109288	+	0.103980i
$292$	−2.82710	−	8.70092i	−0.165443	−	0.509183i
$293$	−32.3944			−1.89250			−0.946251	−	0.323432i	$-0.895163\pi$
$293$	−32.3944			−1.89250			−0.946251	+	0.323432i	$0.895163\pi$
$294$	1.26812	−	1.40839i	0.0739581	−	0.0821388i
$295$	−20.5872	−	9.54240i	−1.19864	−	0.555580i
$296$	1.25904	−	3.87492i	0.0731802	−	0.225225i
$297$	6.39608	−	19.6851i	0.371138	−	1.14225i
$298$	0.309324	+	0.137720i	0.0179187	+	0.00797790i
$299$	20.1655	−	34.9277i	1.16620	−	2.01992i
$300$	2.71333	−	2.83572i	0.156654	−	0.163720i
$301$	14.4173	−	24.9714i	0.830998	−	1.43933i
$302$	0.595162	+	5.66259i	0.0342478	+	0.325846i
$303$	−1.31483	+	4.04664i	−0.0755351	+	0.232473i
$304$	1.39089	+	4.13103i	0.0797733	+	0.236931i
$305$	0.999775	+	3.24342i	0.0572469	+	0.185717i
$306$	8.31510	+	1.76743i	0.475343	+	0.101037i
$307$	−13.9899	+	24.2313i	−0.798448	+	1.38295i	0.122179	+	0.992508i	$0.461012\pi$
$307$	−13.9899	+	24.2313i	−0.798448	+	1.38295i	−0.920627	+	0.390444i	$0.872322\pi$
$308$	10.0555	−	11.1678i	0.572968	−	0.636345i
$309$	2.70534	−	1.20449i	0.153901	−	0.0685212i
$310$	−13.6994	−	6.34980i	−0.778072	−	0.360645i
$311$	−3.78170	+	2.74756i	−0.214440	+	0.155800i	−0.689821	−	0.723980i	$-0.742311\pi$
$311$	−3.78170	+	2.74756i	−0.214440	+	0.155800i	0.475380	+	0.879781i	$0.342311\pi$
$312$	−2.98660	−	2.16989i	−0.169083	−	0.122846i
$313$	0.186683	−	1.77617i	0.0105520	−	0.100395i	−0.987978	−	0.154593i	$-0.950593\pi$
$313$	0.186683	−	1.77617i	0.0105520	−	0.100395i	0.998530	+	0.0541976i	$0.0172601\pi$
$314$	−10.0690	−	4.48302i	−0.568228	−	0.252991i
$315$	13.3760	−	9.41189i	0.753651	−	0.530300i
$316$	−1.51679	−	1.10201i	−0.0853260	−	0.0619929i
$317$	−12.8497	+	14.2710i	−0.721711	+	0.801542i	−0.986673	−	0.162717i	$-0.947974\pi$
$317$	−12.8497	+	14.2710i	−0.721711	+	0.801542i	0.264961	+	0.964259i	$0.414641\pi$
$318$	1.87128	−	3.24116i	0.104936	−	0.181755i
$319$	−7.39271	+	8.21043i	−0.413912	+	0.459696i
$320$	2.17991	+	0.497993i	0.121861	+	0.0278387i
$321$	−3.82010	−	4.24265i	−0.213217	−	0.236802i
$322$	8.13087	−	25.0242i	0.453116	−	1.39455i
$323$	4.64616	−	14.8332i	0.258519	−	0.825344i
$324$	3.83438			0.213021
$325$	−22.8427	−	5.58385i	−1.26709	−	0.309736i
$326$	−10.6077	+	18.3730i	−0.587505	+	1.01759i
$327$	−0.0891793	−	0.0397052i	−0.00493163	−	0.00219570i
$328$	−4.91212	−	5.45547i	−0.271227	−	0.301228i
$329$	32.3837	−	6.88338i	1.78537	−	0.379493i
$330$	−7.03049	+	4.94694i	−0.387016	+	0.272320i
$331$	3.21548	+	9.89623i	0.176739	+	0.543946i	0.999709	−	0.0241392i	$-0.00768449\pi$
$331$	3.21548	+	9.89623i	0.176739	+	0.543946i	−0.822970	+	0.568085i	$0.807684\pi$
$332$	5.38945	+	9.33480i	0.295784	+	0.512314i
$333$	−6.49903	+	7.21791i	−0.356145	+	0.395539i
$334$	−12.7635	−	9.27325i	−0.698389	−	0.507410i
$335$	−22.4238	−	0.339820i	−1.22514	−	0.0185663i
$336$	−2.20022	−	0.979600i	−0.120032	−	0.0534416i
$337$	23.1529	−	10.3083i	1.26122	−	0.561530i	0.336321	−	0.941747i	$-0.390817\pi$
$337$	23.1529	−	10.3083i	1.26122	−	0.561530i	0.924897	+	0.380217i	$0.124151\pi$
$338$	−0.953171	+	9.06882i	−0.0518457	+	0.493279i
$339$	0.467889	+	4.45167i	0.0254122	+	0.241781i
$340$	−5.24513	−	6.00588i	−0.284457	−	0.325715i
$341$	26.7566	+	19.4398i	1.44895	+	1.05273i
$342$	0.976419	−	10.3450i	0.0527987	−	0.559395i
$343$	14.0699			0.759706
$344$	−9.19223	−	1.95387i	−0.495612	−	0.105346i
$345$	−7.72245	+	12.9195i	−0.415763	+	0.695564i
$346$	20.6602	−	4.39147i	1.11070	−	0.236087i
$347$	12.0636	+	13.3980i	0.647610	+	0.719244i	0.974141	−	0.225943i	$-0.0725462\pi$
$347$	12.0636	+	13.3980i	0.647610	+	0.719244i	−0.326530	+	0.945187i	$0.605880\pi$
$348$	1.61757	+	0.720190i	0.0867110	+	0.0386062i
$349$	9.27832			0.496657			0.248328	−	0.968676i	$-0.420119\pi$
$349$	9.27832			0.496657			0.248328	+	0.968676i	$0.420119\pi$
$350$	−15.3344	−	0.464875i	−0.819658	−	0.0248486i
$351$	9.93765	+	17.2125i	0.530432	+	0.918736i
$352$	−4.47433	−	1.99210i	−0.238483	−	0.106179i
$353$	−5.26366	+	16.1999i	−0.280156	+	0.862233i	0.707652	+	0.706561i	$0.249754\pi$
$353$	−5.26366	+	16.1999i	−0.280156	+	0.862233i	−0.987809	+	0.155672i	$0.950246\pi$
$354$	2.46147	−	7.57563i	0.130826	−	0.402640i
$355$	−4.40360	+	36.5594i	−0.233719	+	1.94037i
$356$	3.84205	+	0.816652i	0.203628	+	0.0432825i
$357$	4.29426	+	7.43787i	0.227276	+	0.393654i
$358$	11.6745	+	2.48150i	0.617019	+	0.131151i
$359$	−0.0522181	+	0.0232490i	−0.00275596	+	0.00122703i	−0.408114	−	0.912931i	$-0.633813\pi$
$359$	−0.0522181	+	0.0232490i	−0.00275596	+	0.00122703i	0.405358	+	0.914158i	$0.367147\pi$
$360$	−4.26447	−	3.19816i	−0.224758	−	0.168558i
$361$	−18.6645	−	3.55497i	−0.982340	−	0.187104i
$362$	1.28482	+	0.933473i	0.0675284	+	0.0490622i
$363$	9.31357	−	4.14667i	0.488836	−	0.217644i
$364$	1.50838	+	14.3513i	0.0790607	+	0.752212i
$365$	13.9172	−	14.9934i	0.728462	−	0.784791i
$366$	−1.08842	+	0.484597i	−0.0568927	+	0.0253303i
$367$	−2.60995	+	2.89864i	−0.136238	+	0.151308i	−0.807403	−	0.590000i	$-0.799128\pi$
$367$	−2.60995	+	2.89864i	−0.136238	+	0.151308i	0.671165	+	0.741308i	$0.265794\pi$
$368$	−8.57548			−0.447028
$369$	5.40782	+	16.6435i	0.281520	+	0.866428i
$370$	8.93909	−	1.75893i	0.464721	−	0.0914423i
$371$	−14.3097	+	3.04162i	−0.742924	+	0.157913i
$372$	1.63794	−	5.04105i	0.0849231	−	0.261366i
$373$	−2.74242	+	1.99248i	−0.141997	+	0.103167i	−0.656516	−	0.754312i	$-0.727971\pi$
$373$	−2.74242	+	1.99248i	−0.141997	+	0.103167i	0.514519	+	0.857479i	$0.327971\pi$
$374$	8.73274	+	15.1256i	0.451559	+	0.782124i
$375$	8.49239	+	2.21284i	0.438545	+	0.114270i
$376$	−5.39506	−	9.34452i	−0.278229	−	0.481907i
$377$	−1.10894	−	10.5509i	−0.0571135	−	0.543399i
$378$	8.67642	+	9.63614i	0.446267	+	0.495629i
$379$	0.258163	−	0.794544i	0.0132609	−	0.0408130i	−0.944207	−	0.329352i	$-0.893170\pi$
$379$	0.258163	−	0.794544i	0.0132609	−	0.0408130i	0.957468	+	0.288539i	$0.0931696\pi$
$380$	−6.55470	+	7.21360i	−0.336249	+	0.370050i
$381$	−1.53521	−	4.72489i	−0.0786512	−	0.242064i
$382$	−10.3528	+	17.9316i	−0.529697	+	0.917462i
$383$	4.89624	+	1.04073i	0.250186	+	0.0531787i	0.331298	−	0.943526i	$-0.392514\pi$
$383$	4.89624	+	1.04073i	0.250186	+	0.0531787i	−0.0811113	+	0.996705i	$0.525847\pi$
$384$	−0.0820491	+	0.780645i	−0.00418705	+	0.0398371i
$385$	32.7592	+	7.48373i	1.66956	+	0.381406i
$386$	−12.0961	−	5.38553i	−0.615675	−	0.274116i
$387$	18.1241	+	13.1679i	0.921297	+	0.669362i
$388$	−1.83824	−	1.33556i	−0.0933225	−	0.0678027i
$389$	15.4550	+	6.88102i	0.783601	+	0.348882i	0.759231	−	0.650821i	$-0.225575\pi$
$389$	15.4550	+	6.88102i	0.783601	+	0.348882i	0.0243703	+	0.999703i	$0.492242\pi$
$390$	0.987156	−	8.19553i	0.0499866	−	0.414997i
$391$	24.7399	+	17.9746i	1.25115	+	0.909015i
$392$	0.746091	+	2.29623i	0.0376833	+	0.115977i
$393$	3.65180	+	6.32511i	0.184209	+	0.319060i
$394$	−23.2903	−	4.95051i	−1.17335	−	0.249403i
$395$	0.501341	−	4.16221i	0.0252252	−	0.209424i
$396$	7.81250	+	8.67666i	0.392593	+	0.436019i
$397$	23.2324	+	25.8022i	1.16600	+	1.29497i	0.947726	+	0.319085i	$0.103376\pi$
$397$	23.2324	+	25.8022i	1.16600	+	1.29497i	0.218273	+	0.975888i	$0.429958\pi$
$398$	−8.48508	+	6.16478i	−0.425319	+	0.309012i
$399$	8.42721	−	6.26044i	0.421888	−	0.313414i
$400$	1.40028	+	4.79992i	0.0700141	+	0.239996i
$401$	11.8298	−	20.4898i	0.590751	−	1.02321i	−0.403380	−	0.915032i	$-0.632165\pi$
$401$	11.8298	−	20.4898i	0.590751	−	1.02321i	0.994131	−	0.108179i	$-0.0345019\pi$
$402$	−0.822902	−	7.82939i	−0.0410426	−	0.390494i
$403$	−31.0642	+	6.60290i	−1.54742	+	0.328914i
$404$	−3.62710	−	4.02830i	−0.180455	−	0.200416i
$405$	4.17396	+	7.48935i	0.207406	+	0.372149i
$406$	−2.13881	−	6.58259i	−0.106148	−	0.326689i
$407$	−19.9552			−0.989140
$408$	1.87298	−	2.08015i	0.0927262	−	0.102983i
$409$	2.64775	−	25.1916i	0.130923	−	1.24565i	−0.709887	−	0.704315i	$-0.751254\pi$
$409$	2.64775	−	25.1916i	0.130923	−	1.24565i	0.840810	−	0.541331i	$-0.182079\pi$
$410$	5.30852	−	15.5330i	0.262169	−	0.767122i
$411$	−3.78650	+	2.75105i	−0.186774	+	0.135699i
$412$	−0.394354	+	3.75203i	−0.0194284	+	0.184849i
$413$	−28.4446	+	12.6643i	−1.39967	+	0.623171i
$414$	18.6754	+	8.31481i	0.917845	+	0.408651i
$415$	−12.3661	+	20.6882i	−0.607027	+	1.01555i
$416$	4.29646	−	1.91291i	0.210651	−	0.0937880i
$417$	2.68704	+	8.26985i	0.131585	+	0.404976i
$418$	17.1375	−	12.7312i	0.838220	−	0.622701i
$419$	−5.69813	−	17.5370i	−0.278372	−	0.856741i	−0.988307	−	0.152474i	$-0.951276\pi$
$419$	−5.69813	−	17.5370i	−0.278372	−	0.856741i	0.709936	−	0.704267i	$-0.248724\pi$
$420$	−0.481710	−	5.36385i	−0.0235050	−	0.261729i
$421$	2.16993	+	2.40995i	0.105756	+	0.117454i	0.793699	−	0.608311i	$-0.208153\pi$
$421$	2.16993	+	2.40995i	0.105756	+	0.117454i	−0.687943	+	0.725765i	$0.741486\pi$
$422$	−1.87203	+	0.397913i	−0.0911291	+	0.0193701i
$423$	2.68870	+	25.5812i	0.130729	+	1.24380i
$424$	2.38397	+	4.12915i	0.115776	+	0.200529i
$425$	6.02110	−	16.7826i	0.292066	−	0.814077i
$426$	−12.9265			−0.626292
$427$	4.25456	+	1.89425i	0.205892	+	0.0916692i
$428$	7.11425	−	1.51218i	0.343880	−	0.0730940i
$429$	−5.58728	+	17.1959i	−0.269756	+	0.830225i
$430$	−6.19000	−	20.0813i	−0.298508	−	0.968405i
$431$	−21.4895	+	23.8665i	−1.03511	+	1.14961i	−0.0465322	+	0.998917i	$0.514817\pi$
$431$	−21.4895	+	23.8665i	−1.03511	+	1.14961i	−0.988581	+	0.150692i	$0.951850\pi$
$432$	2.11302	−	3.65985i	0.101663	−	0.176085i
$433$	−23.2282	+	25.7976i	−1.11628	+	1.23975i	−0.148238	+	0.988952i	$0.547360\pi$
$433$	−23.2282	+	25.7976i	−1.11628	+	1.23975i	−0.968039	+	0.250800i	$0.919307\pi$
$434$	−18.9279	+	8.42724i	−0.908568	+	0.404520i
$435$	0.354147	+	3.94343i	0.0169800	+	0.189073i
$436$	0.100613	−	0.0730993i	0.00481847	−	0.00350082i
$437$	18.3452	−	32.5682i	0.877570	−	1.55795i
$438$	5.80972	+	4.22101i	0.277599	+	0.201688i
$439$	−2.84854	−	27.1020i	−0.135953	−	1.29351i	−0.823478	−	0.567348i	$-0.807970\pi$
$439$	−2.84854	−	27.1020i	−0.135953	−	1.29351i	0.687525	−	0.726161i	$-0.258697\pi$
$440$	−0.979598	−	10.9078i	−0.0467005	−	0.520011i
$441$	0.601624	−	5.72407i	0.0286488	−	0.272575i
$442$	−16.4047	−	3.48692i	−0.780290	−	0.165856i
$443$	−13.7352	−	23.7901i	−0.652580	−	1.13030i	−0.982495	−	0.186291i	$-0.940353\pi$
$443$	−13.7352	−	23.7901i	−0.652580	−	1.13030i	0.329915	−	0.944011i	$-0.392980\pi$
$444$	0.988276	+	3.04160i	0.0469015	+	0.144348i
$445$	2.58721	+	8.39330i	0.122646	+	0.397881i
$446$	1.39136	−	0.295743i	0.0658829	−	0.0140038i
$447$	−0.259972	+	0.0552588i	−0.0122963	+	0.00261365i
$448$	2.48230	−	1.80350i	0.117278	−	0.0852072i
$449$	23.4076			1.10467			0.552337	−	0.833621i	$-0.313736\pi$
$449$	23.4076			1.10467			0.552337	+	0.833621i	$0.313736\pi$
$450$	1.60453	−	11.8108i	0.0756384	−	0.556767i
$451$	−17.9774	+	31.1378i	−0.846523	+	1.46622i
$452$	−5.20954	−	2.31944i	−0.245036	−	0.109097i
$453$	−2.99055	−	3.32134i	−0.140508	−	0.156050i
$454$	−0.0847441	−	0.0941178i	−0.00397724	−	0.00441717i
$455$	−26.3891	+	18.5685i	−1.23714	+	0.870504i
$456$	−2.78924	−	1.98161i	−0.130618	−	0.0927976i
$457$	7.30263			0.341602			0.170801	−	0.985306i	$-0.445364\pi$
$457$	7.30263			0.341602			0.170801	+	0.985306i	$0.445364\pi$
$458$	−11.2781	−	2.39723i	−0.526990	−	0.112015i
$459$	−13.7672	+	6.12955i	−0.642598	+	0.286103i
$460$	−9.33494	−	16.7497i	−0.435244	−	0.780959i
$461$	3.27564	+	31.1656i	0.152562	+	1.45153i	0.756237	+	0.654298i	$0.227036\pi$
$461$	3.27564	+	31.1656i	0.152562	+	1.45153i	−0.603675	+	0.797230i	$0.706298\pi$
$462$	−1.23302	+	11.7314i	−0.0573651	+	0.545792i
$463$	5.41010	+	3.93067i	0.251429	+	0.182674i	0.706360	−	0.707853i	$-0.250336\pi$
$463$	5.41010	+	3.93067i	0.251429	+	0.182674i	−0.454931	+	0.890527i	$0.650336\pi$
$464$	−1.82495	+	1.32591i	−0.0847214	+	0.0615537i
$465$	11.6292	−	2.28826i	0.539293	−	0.106116i
$466$	0.793680	−	7.55136i	0.0367665	−	0.349810i
$467$	−11.1137	−	34.2045i	−0.514282	−	1.58280i	−0.784584	−	0.620022i	$-0.787124\pi$
$467$	−11.1137	−	34.2045i	−0.514282	−	1.58280i	0.270302	−	0.962775i	$-0.412876\pi$
$468$	−11.2114			−0.518249
$469$	−20.5912	+	22.8688i	−0.950813	+	1.05598i
$470$	12.3790	−	20.7098i	0.570998	−	0.955271i
$471$	8.46254	−	1.79877i	0.389933	−	0.0828829i
$472$	6.79022	+	7.54130i	0.312545	+	0.347117i
$473$	4.81116	+	45.7751i	0.221217	+	2.10474i
$474$	1.47166			0.0675954
$475$	−21.2249	−	4.95025i	−0.973864	−	0.227133i
$476$	−10.9415			−0.501505
$477$	−1.18808	−	11.3038i	−0.0543985	−	0.517567i
$478$	12.1595	+	13.5045i	0.556164	+	0.617683i
$479$	10.1339	−	2.15403i	0.463031	−	0.0984203i	0.0295114	−	0.999564i	$-0.490605\pi$
$479$	10.1339	−	2.15403i	0.463031	−	0.0984203i	0.433520	+	0.901144i	$0.357272\pi$
$480$	−1.61408	+	0.689522i	−0.0736723	+	0.0314722i
$481$	12.8218	−	14.2400i	0.584623	−	0.649289i
$482$	−3.75799			−0.171172
$483$	6.38229	+	19.6427i	0.290404	+	0.893772i
$484$	−1.35763	+	12.9170i	−0.0617105	+	0.587136i
$485$	0.607589	−	5.04431i	0.0275892	−	0.229050i
$486$	−12.6918	+	9.22111i	−0.575710	+	0.418278i
$487$	20.2796	+	14.7340i	0.918958	+	0.667662i	0.943264	−	0.332043i	$-0.107738\pi$
$487$	20.2796	+	14.7340i	0.918958	+	0.667662i	−0.0243065	+	0.999705i	$0.507738\pi$
$488$	0.158658	−	1.50953i	0.00718212	−	0.0683333i
$489$	−1.74070	−	16.5617i	−0.0787172	−	0.748944i
$490$	−3.67286	+	3.95687i	−0.165923	+	0.178753i
$491$	−37.0665	+	16.5031i	−1.67279	+	0.744773i	−0.672801	+	0.739824i	$0.734909\pi$
$491$	−37.0665	+	16.5031i	−1.67279	+	0.744773i	−0.999988	+	0.00494985i	$0.998424\pi$
$492$	5.63640	+	1.19805i	0.254109	+	0.0540125i
$493$	8.04408			0.362287
$494$	−1.92635	+	20.4095i	−0.0866707	+	0.918265i
$495$	−8.44295	+	24.7046i	−0.379482	+	1.11039i
$496$	4.51842	+	5.01821i	0.202883	+	0.225324i
$497$	33.8104	+	37.5502i	1.51660	+	1.68436i
$498$	−7.72936	−	3.44133i	−0.346361	−	0.154210i
$499$	−6.35489	+	11.0070i	−0.284484	+	0.492741i	−0.972484	−	0.232970i	$-0.925156\pi$
$499$	−6.35489	+	11.0070i	−0.284484	+	0.492741i	0.688000	+	0.725711i	$0.258489\pi$
$500$	−7.85096	+	7.96006i	−0.351105	+	0.355984i
$501$	12.3838			0.553265
$502$	−18.0145	+	13.0883i	−0.804028	+	0.584160i
$503$	13.5688	−	2.88414i	0.605003	−	0.128597i	0.104782	−	0.994495i	$-0.466586\pi$
$503$	13.5688	−	2.88414i	0.605003	−	0.128597i	0.500221	+	0.865898i	$0.333252\pi$
$504$	−7.15454	+	1.52074i	−0.318689	+	0.0677393i
$505$	3.91980	−	11.4696i	0.174429	−	0.510388i
$506$	12.9789	+	39.9450i	0.576984	+	1.77577i
$507$	−3.57887	−	6.19878i	−0.158943	−	0.275297i
$508$	6.19086	+	1.31591i	0.274675	+	0.0583839i
$509$	−4.36812	+	41.5599i	−0.193613	+	1.84211i	0.278336	+	0.960484i	$0.410217\pi$
$509$	−4.36812	+	41.5599i	−0.193613	+	1.84211i	−0.471950	+	0.881625i	$0.656450\pi$
$510$	6.10183	+	1.39394i	0.270193	+	0.0617248i
$511$	−2.93420	−	27.9170i	−0.129801	−	1.23498i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	9.37922	+	15.8543i	0.414103	+	0.699984i
$514$	−10.7640	+	7.82050i	−0.474780	+	0.344948i
$515$	−7.75778	+	3.31406i	−0.341849	+	0.146035i
$516$	6.73885	−	3.00033i	0.296662	−	0.132082i
$517$	−35.3619	+	39.2734i	−1.55521	+	1.72724i
$518$	6.25062	−	10.8264i	0.274637	−	0.475684i
$519$	−11.0938	+	12.3209i	−0.486965	+	0.540829i
$520$	8.41327	+	6.30957i	0.368946	+	0.276693i
$521$	4.11464	−	12.6636i	0.180266	−	0.554801i	−0.819569	−	0.572981i	$-0.805787\pi$
$521$	4.11464	−	12.6636i	0.180266	−	0.554801i	0.999835	+	0.0181794i	$0.00578701\pi$
$522$	5.25993	−	1.11803i	0.230221	−	0.0489349i
$523$	−21.1767	−	9.42849i	−0.925994	−	0.412279i	−0.112367	−	0.993667i	$-0.535843\pi$
$523$	−21.1767	−	9.42849i	−0.925994	−	0.412279i	−0.813627	+	0.581388i	$0.802510\pi$
$524$	−9.30461			−0.406474
$525$	9.95235	−	6.77976i	0.434356	−	0.295893i
$526$	−0.555525	−	0.962197i	−0.0242220	−	0.0419538i
$527$	−2.51705	−	23.9482i	−0.109645	−	1.04320i
$528$	3.76047	−	0.799312i	0.163653	−	0.0347856i
$529$	33.8171	+	37.5576i	1.47031	+	1.63294i
$530$	−5.47001	+	9.15123i	−0.237602	+	0.397504i
$531$	−7.47543	−	23.0070i	−0.324406	−	0.998419i
$532$	1.53909	+	13.2855i	0.0667279	+	0.576000i
$533$	−10.6689	−	32.8356i	−0.462123	−	1.42227i
$534$	−2.81662	+	1.25404i	−0.121887	+	0.0542675i
$535$	10.6979	+	12.2495i	0.462511	+	0.529593i
$536$	9.16230	+	4.07932i	0.395751	+	0.176200i
$537$	−8.55865	+	3.81055i	−0.369333	+	0.164438i
$538$	0.397475	−	3.78172i	0.0171364	−	0.163042i
$539$	9.56677	−	6.95067i	0.412070	−	0.299386i
$540$	9.44862	+	0.143188i	0.406604	+	0.00616185i
$541$	3.01956	−	28.7292i	0.129821	−	1.23517i	−0.714618	−	0.699515i	$-0.753400\pi$
$541$	3.01956	−	28.7292i	0.129821	−	1.23517i	0.844439	−	0.535651i	$-0.179934\pi$
$542$	−15.3412	+	17.0381i	−0.658959	+	0.731848i
$543$	−1.24659			−0.0534961
$544$	1.10196	+	3.39148i	0.0472460	+	0.145408i
$545$	0.252301	+	0.116944i	0.0108074	+	0.00500935i
$546$	−7.57926	−	8.41762i	−0.324363	−	0.360241i
$547$	19.3877	−	4.12099i	0.828959	−	0.176201i	0.226156	−	0.974091i	$-0.427384\pi$
$547$	19.3877	−	4.12099i	0.828959	−	0.176201i	0.602803	+	0.797890i	$0.294051\pi$
$548$	−0.623269	−	5.93001i	−0.0266247	−	0.253317i
$549$	−1.80917	+	3.13357i	−0.0772134	+	0.133738i
$550$	20.2390	−	13.7872i	0.862992	−	0.587890i
$551$	−1.13152	−	9.76734i	−0.0482043	−	0.416103i
$552$	5.44572	−	3.95655i	0.231785	−	0.168402i
$553$	−3.84923	−	4.27501i	−0.163686	−	0.181792i
$554$	4.35030	+	4.83150i	0.184826	+	0.205271i
$555$	−4.86509	+	5.24129i	−0.206512	+	0.222480i
$556$	−10.8357	−	2.30320i	−0.459535	−	0.0976773i
$557$	19.2817	+	33.3969i	0.816992	+	1.41507i	0.907888	+	0.419212i	$0.137694\pi$
$557$	19.2817	+	33.3969i	0.816992	+	1.41507i	−0.0908962	+	0.995860i	$0.528973\pi$
$558$	−4.97438	−	15.3096i	−0.210582	−	0.648106i
$559$	−35.7565	−	25.9786i	−1.51234	−	1.09878i
$560$	6.22474	+	2.88523i	0.263043	+	0.121923i
$561$	−12.5242	−	5.57613i	−0.528772	−	0.235425i
$562$	3.21864	+	2.33848i	0.135770	+	0.0986428i
$563$	19.6989	+	14.3121i	0.830208	+	0.603181i	0.919618	−	0.392814i	$-0.128498\pi$
$563$	19.6989	+	14.3121i	0.830208	+	0.603181i	−0.0894103	+	0.995995i	$0.528498\pi$
$564$	7.73741	+	3.44492i	0.325804	+	0.145057i
$565$	−1.14056	−	12.7002i	−0.0479838	−	0.534300i
$566$	−2.23598	+	21.2739i	−0.0939853	+	0.894211i
$567$	11.5079	+	2.44608i	0.483286	+	0.102726i
$568$	8.23403	−	14.2618i	0.345492	−	0.598410i
$569$	1.14712	+	3.53049i	0.0480899	+	0.148006i	0.972218	−	0.234077i	$-0.0752069\pi$
$569$	1.14712	+	3.53049i	0.0480899	+	0.148006i	−0.924128	+	0.382083i	$0.875207\pi$
$570$	0.834251	−	7.60508i	0.0349429	−	0.318542i
$571$	0.980534	−	3.01777i	0.0410341	−	0.126290i	−0.928441	−	0.371480i	$-0.878850\pi$
$571$	0.980534	−	3.01777i	0.0410341	−	0.126290i	0.969475	+	0.245190i	$0.0788504\pi$
$572$	−15.4131	−	17.1180i	−0.644454	−	0.715738i
$573$	−1.69888	−	16.1638i	−0.0709717	−	0.675251i
$574$	−11.2622	−	19.5068i	−0.470077	−	0.814197i
$575$	22.5540	−	36.4662i	0.940569	−	1.52075i
$576$	1.19193	+	2.06448i	0.0496638	+	0.0860202i
$577$	34.7393	−	25.2396i	1.44622	−	1.05074i	0.459521	−	0.888167i	$-0.348021\pi$
$577$	34.7393	−	25.2396i	1.44622	−	1.05074i	0.986697	−	0.162571i	$-0.0519788\pi$
$578$	−1.32370	+	4.07393i	−0.0550587	+	0.169453i
$579$	10.1662	−	2.16089i	0.422493	−	0.0898036i
$580$	−4.57635	−	2.12119i	−0.190023	−	0.0880775i
$581$	10.2201	+	31.4541i	0.423999	+	1.30494i
$582$	1.78354			0.0739302
$583$	15.6257	−	17.3541i	0.647150	−	0.718733i
$584$	−8.35774	+	3.72111i	−0.345846	+	0.153980i
$585$	−12.2044	−	21.8983i	−0.504588	−	0.905384i
$586$	3.38614	+	32.2170i	0.139880	+	1.33087i
$587$	13.6167	−	6.06257i	0.562023	−	0.250229i	−0.106004	−	0.994366i	$-0.533806\pi$
$587$	13.6167	−	6.06257i	0.562023	−	0.250229i	0.668027	+	0.744137i	$0.267139\pi$
$588$	−1.53323	−	1.11395i	−0.0632292	−	0.0459387i
$589$	−28.7244	+	6.42493i	−1.18357	+	0.264735i
$590$	−7.33817	+	21.4719i	−0.302108	+	0.883985i
$591$	17.0742	−	7.60193i	0.702339	−	0.312701i
$592$	−3.98530	−	0.847102i	−0.163795	−	0.0348157i
$593$	−0.275291	−	0.476817i	−0.0113048	−	0.0195805i	0.860318	−	0.509758i	$-0.170265\pi$
$593$	−0.275291	−	0.476817i	−0.0113048	−	0.0195805i	−0.871622	+	0.490178i	$0.836932\pi$
$594$	−20.2458	−	4.30339i	−0.830697	−	0.176570i
$595$	−11.9106	−	21.3711i	−0.488285	−	0.876131i
$596$	0.104632	−	0.322025i	0.00428591	−	0.0131907i
$597$	2.54402	−	7.82968i	0.104120	−	0.320448i
$598$	−36.8442	−	16.4041i	−1.50667	−	0.670813i
$599$	−2.39568	−	4.14943i	−0.0978847	−	0.169541i	0.812924	−	0.582370i	$-0.197874\pi$
$599$	−2.39568	−	4.14943i	−0.0978847	−	0.169541i	−0.910809	+	0.412828i	$0.864541\pi$
$600$	−3.10381	−	2.40205i	−0.126712	−	0.0980633i
$601$	19.5921			0.799179			0.399590	−	0.916694i	$-0.369153\pi$
$601$	19.5921			0.799179			0.399590	+	0.916694i	$0.369153\pi$
$602$	−26.3417	−	11.7281i	−1.07361	−	0.478000i
$603$	−15.9980	−	17.7676i	−0.651489	−	0.723552i
$604$	5.56936	−	1.18380i	0.226614	−	0.0481683i
$605$	−26.7075	+	11.4092i	−1.08581	+	0.463850i
$606$	4.16191	+	0.884641i	0.169066	+	0.0359361i
$607$	−38.7306			−1.57203			−0.786014	−	0.618209i	$-0.787859\pi$
$607$	−38.7306			−1.57203			−0.786014	+	0.618209i	$0.787859\pi$
$608$	3.96301	−	1.81509i	0.160721	−	0.0736114i
$609$	4.39529	+	3.19336i	0.178106	+	0.129402i
$610$	3.12114	−	1.33333i	0.126371	−	0.0539848i
$611$	−5.30446	−	50.4686i	−0.214596	−	2.04174i
$612$	0.888583	−	8.45430i	0.0359188	−	0.341745i
$613$	−33.5476	+	14.9364i	−1.35497	+	0.603274i	−0.950342	−	0.311206i	$-0.899267\pi$
$613$	−33.5476	+	14.9364i	−1.35497	+	0.603274i	−0.404632	+	0.914480i	$0.632600\pi$
$614$	25.5609	+	11.3804i	1.03155	+	0.459277i
$615$	3.79553	+	12.3132i	0.153050	+	0.496518i
$616$	−12.1577	−	8.83310i	−0.489849	−	0.355896i
$617$	2.03809	−	2.26353i	0.0820503	−	0.0911261i	−0.700722	−	0.713435i	$-0.747138\pi$
$617$	2.03809	−	2.26353i	0.0820503	−	0.0911261i	0.782772	+	0.622309i	$0.213805\pi$
$618$	−1.48068	−	2.56461i	−0.0595616	−	0.103164i
$619$	1.30530	+	4.01729i	0.0524643	+	0.161468i	0.973856	−	0.227167i	$-0.0729464\pi$
$619$	1.30530	+	4.01729i	0.0524643	+	0.161468i	−0.921391	+	0.388636i	$0.872946\pi$
$620$	−4.88304	+	14.2881i	−0.196108	+	0.573822i
$621$	−35.4483	+	7.53477i	−1.42249	+	0.302360i
$622$	3.12781	+	3.47378i	0.125414	+	0.139286i
$623$	11.0099	+	4.90194i	0.441104	+	0.196392i
$624$	−1.84582	+	3.19706i	−0.0738920	+	0.127985i
$625$	−24.0939	−	6.66955i	−0.963757	−	0.266782i
$626$	−1.78596			−0.0713811
$627$	−5.00898	+	15.9916i	−0.200039	+	0.638642i
$628$	−3.40596	+	10.4825i	−0.135913	+	0.418296i
$629$	9.72188	+	10.7972i	0.387637	+	0.430514i
$630$	−10.7585	−	12.3189i	−0.428629	−	0.490797i
$631$	1.67487	−	1.86013i	0.0666754	−	0.0740505i	−0.708884	−	0.705325i	$-0.750801\pi$
$631$	1.67487	−	1.86013i	0.0666754	−	0.0740505i	0.775560	+	0.631274i	$0.217468\pi$
$632$	−0.937426	+	1.62367i	−0.0372888	+	0.0645861i
$633$	1.00522	−	1.11640i	0.0399537	−	0.0443731i
$634$	15.5360	+	11.2876i	0.617014	+	0.448287i
$635$	4.16889	+	13.5245i	0.165437	+	0.536703i
$636$	−3.41900	−	1.52224i	−0.135572	−	0.0603607i
$637$	−1.18693	+	11.2929i	−0.0470278	+	0.447440i
$638$	8.93820	+	6.49398i	0.353867	+	0.257099i
$639$	−31.7600	+	23.0750i	−1.25641	+	0.912834i
$640$	0.267403	−	2.22002i	0.0105700	−	0.0877541i
$641$	−30.1163	+	13.4086i	−1.18952	+	0.529610i	−0.903490	−	0.428610i	$-0.859003\pi$
$641$	−30.1163	+	13.4086i	−1.18952	+	0.529610i	−0.286033	+	0.958220i	$0.592337\pi$
$642$	−3.82010	+	4.24265i	−0.150767	+	0.167444i
$643$	−1.13154	+	1.95989i	−0.0446237	+	0.0772905i	−0.887475	−	0.460857i	$-0.847542\pi$
$643$	−1.13154	+	1.95989i	−0.0446237	+	0.0772905i	0.842851	+	0.538147i	$0.180876\pi$
$644$	−25.7371	−	5.47058i	−1.01418	−	0.215571i
$645$	13.1959	+	9.89635i	0.519590	+	0.389669i
$646$	−15.2376	−	3.07021i	−0.599517	−	0.120796i
$647$	7.08602	−	21.8085i	0.278580	−	0.857382i	−0.709670	−	0.704535i	$-0.751156\pi$
$647$	7.08602	−	21.8085i	0.278580	−	0.857382i	0.988250	−	0.152847i	$-0.0488442\pi$
$648$	−0.400802	−	3.81337i	−0.0157450	−	0.149803i
$649$	24.8508	−	43.0429i	0.975481	−	1.68958i
$650$	−3.16554	+	23.3013i	−0.124163	+	0.913951i
$651$	8.13170	−	14.0845i	0.318706	−	0.552016i
$652$	19.3812	+	8.62906i	0.759026	+	0.337940i
$653$	3.18587	−	9.80509i	0.124673	−	0.383703i	−0.869169	−	0.494516i	$-0.835345\pi$
$653$	3.18587	−	9.80509i	0.124673	−	0.383703i	0.993841	+	0.110813i	$0.0353454\pi$
$654$	−0.0301659	+	0.0928411i	−0.00117958	+	0.00363037i
$655$	−10.1287	−	18.1739i	−0.395759	−	0.710112i
$656$	−4.91212	+	5.45547i	−0.191786	+	0.213000i
$657$	21.8092			0.850858
$658$	−10.2307	−	31.4868i	−0.398834	−	1.22748i
$659$	2.26057	−	21.5078i	0.0880591	−	0.837827i	−0.857960	−	0.513716i	$-0.828268\pi$
$659$	2.26057	−	21.5078i	0.0880591	−	0.837827i	0.946019	−	0.324110i	$-0.105065\pi$
$660$	5.65473	+	6.47488i	0.220110	+	0.252035i
$661$	11.0361	+	4.91357i	0.429253	+	0.191116i	0.609979	−	0.792418i	$-0.291178\pi$
$661$	11.0361	+	4.91357i	0.429253	+	0.191116i	−0.180726	+	0.983534i	$0.557845\pi$
$662$	9.50590	−	4.23230i	0.369457	−	0.164493i
$663$	12.0263	−	5.35446i	0.467063	−	0.207950i
$664$	8.72031	−	6.33568i	0.338414	−	0.245872i
$665$	−24.2740	+	17.4683i	−0.941306	+	0.677391i
$666$	7.85770	+	5.70895i	0.304480	+	0.221217i
$667$	18.9216	+	4.02190i	0.732646	+	0.155729i
$668$	−7.88830	+	13.6629i	−0.305207	+	0.528635i
$669$	−0.747112	+	0.829752i	−0.0288850	+	0.0320801i
$670$	2.00597	+	22.3365i	0.0774973	+	0.862934i
$671$	−7.27161	+	1.54563i	−0.280717	+	0.0596683i
$672$	−0.744248	+	2.29056i	−0.0287100	+	0.0883603i
$673$	15.9159	−	11.5635i	0.613511	−	0.445742i	−0.237138	−	0.971476i	$-0.576209\pi$
$673$	15.9159	−	11.5635i	0.613511	−	0.445742i	0.850649	+	0.525734i	$0.176209\pi$
$674$	−12.6720	−	21.9485i	−0.488107	−	0.845426i
$675$	10.0057	+	18.6110i	0.385121	+	0.716338i
$676$	9.11877			0.350722
$677$	−11.3443	+	8.24213i	−0.435998	+	0.316771i	−0.784043	−	0.620707i	$-0.786846\pi$
$677$	−11.3443	+	8.24213i	−0.435998	+	0.316771i	0.348045	+	0.937478i	$0.386846\pi$
$678$	4.37837	−	0.930652i	0.168150	−	0.0357415i
$679$	−4.66500	−	5.18101i	−0.179026	−	0.198829i
$680$	−5.42472	+	5.84419i	−0.208028	+	0.224114i
$681$	0.0972394	+	0.0206689i	0.00372622	+	0.000792033i
$682$	16.5365	−	28.6421i	0.633216	−	1.09676i
$683$	8.36033	+	25.7305i	0.319899	+	0.984549i	0.973691	+	0.227874i	$0.0731774\pi$
$683$	8.36033	+	25.7305i	0.319899	+	0.984549i	−0.653791	+	0.756675i	$0.726823\pi$
$684$	−10.3904	+	0.110280i	−0.397288	+	0.00421667i
$685$	10.9041	−	7.67256i	0.416624	−	0.293154i
$686$	−1.47071	−	13.9929i	−0.0561520	−	0.534250i
$687$	8.26800	−	3.68115i	0.315444	−	0.140445i
$688$	−0.982316	+	9.34611i	−0.0374504	+	0.356317i
$689$	2.34393	+	22.3010i	0.0892968	+	0.849602i
$690$	13.6560	+	6.32969i	0.519874	+	0.240967i
$691$	24.6245	+	17.8908i	0.936761	+	0.680597i	0.947639	−	0.319344i	$-0.103462\pi$
$691$	24.6245	+	17.8908i	0.936761	+	0.680597i	−0.0108775	+	0.999941i	$0.503462\pi$
$692$	−6.52700	−	20.0880i	−0.248119	−	0.763632i
$693$	17.9121	+	31.0246i	0.680423	+	1.17853i
$694$	12.0636	−	13.3980i	0.457929	−	0.508582i
$695$	−7.29670	−	23.6716i	−0.276779	−	0.897913i
$696$	0.547162	−	1.68399i	0.0207401	−	0.0638315i
$697$	25.6062	−	5.44277i	0.969904	−	0.206159i
$698$	−0.969848	−	9.22749i	−0.0367093	−	0.349266i
$699$	2.98003	+	5.16156i	0.112715	+	0.195228i
$700$	1.14055	+	15.2990i	0.0431089	+	0.578248i
$701$	−13.7963	+	23.8959i	−0.521079	+	0.902535i	0.478620	+	0.878022i	$0.341137\pi$
$701$	−13.7963	+	23.8959i	−0.521079	+	0.902535i	−0.999700	+	0.0245134i	$0.992196\pi$
$702$	16.0795	−	11.6824i	0.606880	−	0.440924i
$703$	11.7428	−	13.3233i	0.442887	−	0.502500i
$704$	−1.51349	+	4.65805i	−0.0570419	+	0.175557i
$705$	1.69401	+	18.8628i	0.0638000	+	0.710414i
$706$	16.6613	+	3.54148i	0.627058	+	0.133285i
$707$	−8.31601	−	14.4038i	−0.312756	−	0.541709i
$708$	−7.79142	−	1.65612i	−0.292819	−	0.0622407i
$709$	−0.725795	+	6.90548i	−0.0272578	+	0.259341i	0.972403	+	0.233306i	$0.0749545\pi$
$709$	−0.725795	+	6.90548i	−0.0272578	+	0.259341i	−0.999661	+	0.0260342i	$0.991712\pi$
$710$	36.8195	+	0.557978i	1.38181	+	0.0209405i
$711$	3.61581	−	2.62704i	0.135603	−	0.0985217i
$712$	0.410575	−	3.90636i	0.0153870	−	0.146397i
$713$	6.05297	−	57.5902i	0.226685	−	2.15677i
$714$	6.94825	−	5.04820i	0.260032	−	0.188924i
$715$	16.6569	−	48.7390i	0.622932	−	1.82273i
$716$	1.24759	−	11.8700i	0.0466245	−	0.443602i
$717$	−13.9524	−	2.96568i	−0.521063	−	0.110755i
$718$	0.0285799	+	0.0495018i	0.00106659	+	0.00184739i
$719$	−36.0237	−	7.65708i	−1.34346	−	0.285561i	−0.520597	−	0.853803i	$-0.674290\pi$
$719$	−36.0237	−	7.65708i	−1.34346	−	0.285561i	−0.822862	+	0.568242i	$0.807624\pi$
$720$	−2.73488	+	4.57541i	−0.101923	+	0.170516i
$721$	−3.57709	+	11.0092i	−0.133218	+	0.410003i
$722$	−1.58453	+	18.9338i	−0.0589701	+	0.704644i
$723$	2.38645	−	1.73386i	0.0887530	−	0.0644828i
$724$	0.794060	−	1.37535i	0.0295110	−	0.0511145i
$725$	−0.838520	−	11.2476i	−0.0311419	−	0.417726i
$726$	−5.09749	−	8.82911i	−0.189186	−	0.327679i
$727$	5.28953	+	50.3265i	0.196178	+	1.86651i	0.441763	+	0.897132i	$0.354353\pi$
$727$	5.28953	+	50.3265i	0.196178	+	1.86651i	−0.245585	+	0.969375i	$0.578980\pi$
$728$	14.1150	−	3.00024i	0.523137	−	0.111196i
$729$	0.250608	−	0.771293i	0.00928179	−	0.0285664i
$730$	−16.3660	−	12.2738i	−0.605734	−	0.454273i
$731$	22.4238	−	24.9042i	0.829375	−	0.921115i
$732$	0.595713	+	1.03181i	0.0220182	+	0.0381366i
$733$	0.712652	+	2.19332i	0.0263224	+	0.0810121i	0.963355	−	0.268231i	$-0.0864389\pi$
$733$	0.712652	+	2.19332i	0.0263224	+	0.0810121i	−0.937032	+	0.349243i	$0.886439\pi$
$734$	3.15558	+	2.29266i	0.116475	+	0.0846237i
$735$	0.506774	−	4.20732i	0.0186927	−	0.155189i
$736$	0.896381	+	8.52850i	0.0330411	+	0.314365i
$737$	5.13460	−	48.8525i	0.189136	−	1.79951i
$738$	15.9871	−	7.11792i	0.588493	−	0.262014i
$739$	−0.469278	−	4.46488i	−0.0172627	−	0.164243i	0.982494	−	0.186293i	$-0.0596474\pi$
$739$	−0.469278	−	4.46488i	−0.0172627	−	0.164243i	−0.999757	+	0.0220499i	$0.992981\pi$
$740$	−2.68368	−	8.70626i	−0.0986541	−	0.320048i
$741$	−8.19320	−	13.8495i	−0.300985	−	0.508773i
$742$	4.52074	+	13.9134i	0.165961	+	0.510777i
$743$	−3.97643	+	6.88737i	−0.145881	+	0.252673i	−0.929701	−	0.368315i	$-0.879935\pi$
$743$	−3.97643	+	6.88737i	−0.145881	+	0.252673i	0.783820	+	0.620988i	$0.213268\pi$
$744$	−5.18465	−	1.10203i	−0.190078	−	0.0404024i
$745$	0.742882	−	0.146176i	0.0272171	−	0.00535546i
$746$	2.26823	+	2.51912i	0.0830458	+	0.0922317i
$747$	−25.1339	+	5.34237i	−0.919601	+	0.195467i
$748$	14.1299	−	10.2660i	0.516639	−	0.375360i
$749$	22.3162			0.815417
$750$	1.31302	−	8.67717i	0.0479447	−	0.316846i
$751$	18.5479	+	32.1258i	0.676821	+	1.17229i	0.975933	+	0.218070i	$0.0699761\pi$
$751$	18.5479	+	32.1258i	0.676821	+	1.17229i	−0.299112	+	0.954218i	$0.596691\pi$
$752$	−8.72939	+	6.34227i	−0.318328	+	0.231279i
$753$	5.40116	−	16.6231i	0.196829	−	0.605778i
$754$	−10.3772	+	2.20574i	−0.377914	+	0.0803282i
$755$	8.37482	+	9.58949i	0.304791	+	0.348997i
$756$	8.67642	−	9.63614i	0.315558	−	0.350463i
$757$	21.6949	−	37.5767i	0.788515	−	1.36575i	−0.138362	−	0.990382i	$-0.544184\pi$
$757$	21.6949	−	37.5767i	0.788515	−	1.36575i	0.926877	−	0.375366i	$-0.122483\pi$
$758$	−0.817177	−	0.173696i	−0.0296812	−	0.00630893i
$759$	−26.6719	−	19.3782i	−0.968127	−	0.703386i
$760$	7.85923	+	5.76476i	0.285084	+	0.209110i
$761$	−40.8646	+	29.6899i	−1.48134	+	1.07626i	−0.504218	+	0.863576i	$0.668219\pi$
$761$	−40.8646	+	29.6899i	−1.48134	+	1.07626i	−0.977122	+	0.212680i	$0.931781\pi$
$762$	−4.53853	+	2.02069i	−0.164414	+	0.0732017i
$763$	0.348595	−	0.155205i	0.0126200	−	0.00561878i
$764$	18.9156	+	8.42175i	0.684341	+	0.304688i
$765$	17.4803	−	7.46745i	0.632002	−	0.269986i
$766$	0.523231	−	4.97821i	0.0189051	−	0.179870i
$767$	14.7481	+	45.3900i	0.532523	+	1.63894i
$768$	0.784945			0.0283243
$769$	7.40974	−	8.22935i	0.267202	−	0.296758i	−0.594580	−	0.804036i	$-0.702682\pi$
$769$	7.40974	−	8.22935i	0.267202	−	0.296758i	0.861782	+	0.507278i	$0.169348\pi$
$770$	4.01847	−	33.3620i	0.144816	−	1.20228i
$771$	3.22729	−	9.93257i	0.116228	−	0.357713i
$772$	−4.09164	+	12.5928i	−0.147261	+	0.453224i
$773$	23.6048	+	10.5095i	0.849006	+	0.378002i	0.784660	−	0.619926i	$-0.212837\pi$
$773$	23.6048	+	10.5095i	0.849006	+	0.378002i	0.0643456	+	0.997928i	$0.479504\pi$
$774$	11.2013	−	19.4012i	0.402622	−	0.697361i
$775$	−33.2231	+	6.01584i	−1.19341	+	0.216095i
$776$	−1.13609	+	1.96777i	−0.0407834	+	0.0706389i
$777$	1.02572	+	9.75903i	0.0367973	+	0.350103i
$778$	5.22784	−	16.0896i	0.187427	−	0.576841i
$779$	−10.2106	−	30.3261i	−0.365834	−	1.08655i
$780$	−8.25382	−	0.125082i	−0.295534	−	0.00447865i
$781$	−78.8942	−	16.7695i	−2.82306	−	0.600059i
$782$	15.2901	−	26.4832i	0.546773	−	0.947039i
$783$	−6.37879	+	7.08436i	−0.227959	+	0.253174i
$784$	2.20567	−	0.982026i	0.0787738	−	0.0350723i
$785$	−24.1821	+	4.75827i	−0.863095	+	0.169830i
$786$	5.90874	−	4.29295i	0.210758	−	0.153125i
$787$	8.09588	+	5.88200i	0.288587	+	0.209671i	0.722654	−	0.691210i	$-0.242922\pi$
$787$	8.09588	+	5.88200i	0.288587	+	0.209671i	−0.434067	+	0.900881i	$0.642922\pi$
$788$	−2.48889	+	23.6802i	−0.0886630	+	0.843572i
$789$	0.796715	+	0.354720i	0.0283638	+	0.0126284i
$790$	−4.19182	−	0.0635246i	−0.149138	−	0.00226010i
$791$	−14.1554	−	10.2845i	−0.503309	−	0.365675i
$792$	7.81250	−	8.67666i	0.277605	−	0.308312i
$793$	3.56926	−	6.18214i	0.126748	−	0.219534i
$794$	23.2324	−	25.8022i	0.824486	−	0.915684i
$795$	−0.748547	−	8.33509i	−0.0265482	−	0.295615i
$796$	7.01794	+	7.79421i	0.248744	+	0.276258i
$797$	1.84164	−	5.66799i	0.0652343	−	0.200770i	−0.913127	−	0.407676i	$-0.866339\pi$
$797$	1.84164	−	5.66799i	0.0652343	−	0.200770i	0.978361	+	0.206906i	$0.0663393\pi$
$798$	−7.10703	−	7.72665i	−0.251586	−	0.273520i
$799$	38.4777			1.36124
$800$	4.62725	−	1.89434i	0.163598	−	0.0669750i
$801$	−4.68176	+	8.10905i	−0.165422	+	0.286519i
$802$	−21.6141	−	9.62321i	−0.763220	−	0.339807i
$803$	29.9825	+	33.2989i	1.05806	+	1.17509i
$804$	−7.70048	+	1.63679i	−0.271575	+	0.0577250i
$805$	−17.3312	−	56.2250i	−0.610845	−	1.98167i
$806$	9.81383	+	30.2039i	0.345677	+	1.06389i
$807$	1.49240	+	2.58491i	0.0525348	+	0.0909930i
$808$	−3.62710	+	4.02830i	−0.127601	+	0.141715i
$809$	9.41325	+	6.83913i	0.330952	+	0.240451i	0.740835	−	0.671687i	$-0.234430\pi$
$809$	9.41325	+	6.83913i	0.330952	+	0.240451i	−0.409882	+	0.912138i	$0.634430\pi$
$810$	7.01203	−	4.93395i	0.246377	−	0.173361i
$811$	−44.4135	−	19.7741i	−1.55957	−	0.694364i	−0.567889	−	0.823105i	$-0.692240\pi$
$811$	−44.4135	−	19.7741i	−1.55957	−	0.694364i	−0.991678	+	0.128741i	$0.958907\pi$
$812$	−6.32297	+	2.81517i	−0.221893	+	0.0987929i
$813$	1.88114	−	17.8978i	0.0659745	−	0.627705i
$814$	2.08588	+	19.8458i	0.0731101	+	0.695596i
$815$	4.24326	+	47.2488i	0.148635	+	1.65505i
$816$	−2.26454	−	1.64528i	−0.0792746	−	0.0575964i
$817$	−33.3936	−	23.7245i	−1.16829	−	0.830014i
$818$	−25.3304			−0.885657
$819$	−33.6482	−	7.15215i	−1.17576	−	0.249916i
$820$	−16.0028	−	3.65580i	−0.558843	−	0.127666i
$821$	−27.1339	+	5.76749i	−0.946979	+	0.201287i	−0.655419	−	0.755266i	$-0.727508\pi$
$821$	−27.1339	+	5.76749i	−0.946979	+	0.201287i	−0.291561	+	0.956552i	$0.594174\pi$
$822$	3.13178	+	3.47819i	0.109233	+	0.121316i
$823$	2.71688	+	1.20963i	0.0947044	+	0.0421651i	0.453542	−	0.891235i	$-0.350160\pi$
$823$	2.71688	+	1.20963i	0.0947044	+	0.0421651i	−0.358838	+	0.933400i	$0.616827\pi$
$824$	3.77270			0.131428
$825$	−6.49129	+	18.0932i	−0.225998	+	0.629924i
$826$	15.5682	+	26.9650i	0.541688	+	0.938231i
$827$	−16.9527	−	7.54782i	−0.589502	−	0.262463i	0.0902332	−	0.995921i	$-0.471239\pi$
$827$	−16.9527	−	7.54782i	−0.589502	−	0.262463i	−0.679735	+	0.733457i	$0.737905\pi$
$828$	6.31716	−	19.4422i	0.219536	−	0.675663i
$829$	2.86266	−	8.81036i	0.0994243	−	0.305997i	−0.888957	−	0.457990i	$-0.848569\pi$
$829$	2.86266	−	8.81036i	0.0994243	−	0.305997i	0.988381	+	0.151994i	$0.0485694\pi$
$830$	21.8675	+	10.1358i	0.759033	+	0.351820i
$831$	−4.99174	−	1.06103i	−0.173161	−	0.0368066i
$832$	−2.35153	−	4.07297i	−0.0815246	−	0.141205i
$833$	−8.42163	−	1.79007i	−0.291792	−	0.0620224i
$834$	7.94367	−	3.53675i	0.275067	−	0.122468i
$835$	−35.2735	−	0.534549i	−1.22069	−	0.0184988i
$836$	−14.4528	−	15.7128i	−0.499859	−	0.543439i
$837$	23.0869	+	16.7736i	0.798001	+	0.579782i
$838$	−16.8454	+	7.50004i	−0.581913	+	0.259084i
$839$	5.65010	+	53.7571i	0.195063	+	1.85590i	0.455276	+	0.890350i	$0.349541\pi$
$839$	5.65010	+	53.7571i	0.195063	+	1.85590i	−0.260213	+	0.965551i	$0.583793\pi$
$840$	−5.28411	+	1.03975i	−0.182319	+	0.0358746i
$841$	−21.8443	+	9.72569i	−0.753250	+	0.335369i
$842$	2.16993	−	2.40995i	0.0747808	−	0.0830524i
$843$	−3.12287			−0.107557
$844$	0.591414	+	1.82018i	0.0203573	+	0.0626533i
$845$	9.92635	+	17.8109i	0.341477	+	0.612713i
$846$	25.1601	−	5.34794i	0.865021	−	0.183866i
$847$	−12.3148	+	37.9009i	−0.423140	+	1.30229i
$848$	3.85734	−	2.80252i	0.132462	−	0.0962390i
$849$	−8.39543	−	14.5413i	−0.288130	−	0.499057i
$850$	−17.3201	−	4.23385i	−0.594074	−	0.145220i
$851$	17.4697	+	30.2584i	0.598853	+	1.03724i
$852$	1.35119	+	12.8557i	0.0462910	+	0.440429i
$853$	9.79860	+	10.8824i	0.335498	+	0.372608i	0.887162	−	0.461458i	$-0.152674\pi$
$853$	9.79860	+	10.8824i	0.335498	+	0.372608i	−0.551664	+	0.834066i	$0.686007\pi$
$854$	1.43915	−	4.42925i	0.0492468	−	0.151566i
$855$	−11.5260	−	20.1746i	−0.394182	−	0.689958i
$856$	−2.24754	−	6.91721i	−0.0768192	−	0.236425i
$857$	−8.62829	+	14.9446i	−0.294737	+	0.510499i	−0.974924	−	0.222540i	$-0.928565\pi$
$857$	−8.62829	+	14.9446i	−0.294737	+	0.510499i	0.680187	+	0.733039i	$0.261899\pi$
$858$	17.6857	+	3.75921i	0.603780	+	0.128337i
$859$	2.71963	−	25.8755i	0.0927926	−	0.882862i	−0.844790	−	0.535099i	$-0.820274\pi$
$859$	2.71963	−	25.8755i	0.0927926	−	0.882862i	0.937582	−	0.347764i	$-0.113059\pi$
$860$	−19.3242	+	8.25516i	−0.658951	+	0.281499i
$861$	16.1519	+	7.19130i	0.550456	+	0.245079i
$862$	25.9820	+	18.8770i	0.884951	+	0.642955i
$863$	32.2132	+	23.4043i	1.09655	+	0.796690i	0.980493	−	0.196553i	$-0.0629746\pi$
$863$	32.2132	+	23.4043i	1.09655	+	0.796690i	0.116056	+	0.993243i	$0.462975\pi$
$864$	−3.86067	−	1.71888i	−0.131343	−	0.0584776i
$865$	32.1311	−	34.6157i	1.09249	−	1.17697i
$866$	28.0842	+	20.4044i	0.954341	+	0.693370i
$867$	−1.03903	−	3.19781i	−0.0352874	−	0.108603i
$868$	10.3596	+	17.9433i	0.351627	+	0.609036i
$869$	8.98193	+	1.90917i	0.304691	+	0.0647641i
$870$	3.88481	−	0.764407i	0.131707	−	0.0259158i
$871$	31.5621	+	35.0532i	1.06944	+	1.18773i
$872$	−0.0832158	−	0.0924205i	−0.00281804	−	0.00312975i
$873$	4.38211	−	3.18379i	0.148312	−	0.107755i
$874$	−34.3074	−	14.8404i	−1.16047	−	0.501984i
$875$	−28.6406	+	18.8817i	−0.968229	+	0.638316i
$876$	3.59061	−	6.21911i	0.121315	−	0.210124i
$877$	−3.17218	−	30.1812i	−0.107117	−	1.01915i	−0.907612	−	0.419809i	$-0.862097\pi$
$877$	−3.17218	−	30.1812i	−0.107117	−	1.01915i	0.800496	−	0.599339i	$-0.204570\pi$
$878$	−26.6558	+	5.66586i	−0.899589	+	0.191214i
$879$	−17.0145	−	18.8966i	−0.573886	−	0.637365i
$880$	−10.7457	+	2.11441i	−0.362237	+	0.0712768i
$881$	7.57607	+	23.3167i	0.255244	+	0.785561i	0.993781	+	0.111348i	$0.0355169\pi$
$881$	7.57607	+	23.3167i	0.255244	+	0.785561i	−0.738537	+	0.674213i	$0.764483\pi$
$882$	−5.75560			−0.193801
$883$	3.39308	−	3.76840i	0.114186	−	0.126817i	−0.683342	−	0.730099i	$-0.739474\pi$
$883$	3.39308	−	3.76840i	0.114186	−	0.126817i	0.797528	+	0.603282i	$0.206141\pi$
$884$	−1.75306	+	16.6793i	−0.0589619	+	0.560985i
$885$	−5.24670	−	17.0211i	−0.176366	−	0.572157i
$886$	−22.2240	+	16.1467i	−0.746631	+	0.542459i
$887$	3.40476	−	32.3942i	0.114321	−	1.08769i	−0.775490	−	0.631360i	$-0.782497\pi$
$887$	3.40476	−	32.3942i	0.114321	−	1.08769i	0.889811	−	0.456330i	$-0.150836\pi$
$888$	2.92164	−	1.30080i	0.0980437	−	0.0436519i
$889$	17.7408	+	7.89871i	0.595007	+	0.264914i
$890$	8.07689	−	3.45038i	0.270738	−	0.115657i
$891$	−17.1563	+	7.63848i	−0.574758	+	0.255899i
$892$	−0.439560	−	1.35283i	−0.0147175	−	0.0452960i
$893$	−5.41244	−	46.7206i	−0.181121	−	1.56344i
$894$	0.0821306	+	0.252772i	0.00274686	+	0.00845396i
$895$	24.5426	−	10.4844i	0.820370	−	0.350456i
$896$	−2.05309	−	2.28018i	−0.0685888	−	0.0761756i
$897$	30.9658	−	6.58199i	1.03392	−	0.219766i
$898$	−2.44676	−	23.2794i	−0.0816495	−	0.776843i
$899$	−7.61623	−	13.1917i	−0.254015	−	0.439968i
$900$	−11.9138	−	0.361178i	−0.397128	−	0.0120393i
$901$	−17.0025			−0.566435
$902$	32.8463	+	14.6241i	1.09366	+	0.486930i
$903$	22.1389	−	4.70577i	0.736737	−	0.156598i
$904$	−1.76218	+	5.42345i	−0.0586094	+	0.180381i
$905$	3.55073	+	0.0538094i	0.118030	+	0.00178868i
$906$	−2.99055	+	3.32134i	−0.0993544	+	0.110344i
$907$	16.7727	−	29.0512i	0.556928	−	0.964628i	−0.440823	−	0.897594i	$-0.645313\pi$
$907$	16.7727	−	29.0512i	0.556928	−	0.964628i	0.997751	−	0.0670336i	$-0.0213535\pi$
$908$	−0.0847441	+	0.0941178i	−0.00281233	+	0.00312341i
$909$	11.8048	−	5.25585i	0.391542	−	0.174326i
$910$	21.2252	+	24.3036i	0.703608	+	0.805658i
$911$	6.67974	−	4.85312i	0.221310	−	0.160791i	−0.471606	−	0.881809i	$-0.656326\pi$
$911$	6.67974	−	4.85312i	0.221310	−	0.160791i	0.692916	+	0.721018i	$0.256326\pi$
$912$	−1.67920	+	2.98109i	−0.0556040	+	0.0987138i
$913$	−42.7101	−	31.0307i	−1.41350	−	1.02697i
$914$	−0.763332	−	7.26262i	−0.0252488	−	0.240226i
$915$	−1.36686	+	2.28674i	−0.0451871	+	0.0755972i
$916$	−1.20522	+	11.4669i	−0.0398215	+	0.378876i
$917$	−27.9254	−	5.93572i	−0.922177	−	0.196015i
$918$	7.53504	+	13.0511i	0.248693	+	0.430749i
$919$	−8.29062	−	25.5159i	−0.273482	−	0.841692i	−0.989617	−	0.143730i	$-0.954090\pi$
$919$	−8.29062	−	25.5159i	−0.273482	−	0.841692i	0.716135	−	0.697962i	$-0.245910\pi$
$920$	−15.6822	+	11.0346i	−0.517026	+	0.363801i
$921$	−21.4827	+	4.56629i	−0.707880	+	0.150464i
$922$	30.6525	−	6.51539i	1.00949	−	0.214573i
$923$	62.6586	−	45.5241i	2.06243	−	1.49844i
$924$	11.7960			0.388059
$925$	14.0838	−	14.7191i	0.463072	−	0.483961i
$926$	3.34363	−	5.79133i	0.109878	−	0.190315i
$927$	−8.21605	−	3.65802i	−0.269850	−	0.120145i
$928$	1.50940	+	1.67636i	0.0495486	+	0.0550293i
$929$	−21.8763	−	24.2961i	−0.717740	−	0.797130i	0.268354	−	0.963320i	$-0.413520\pi$
$929$	−21.8763	−	24.2961i	−0.717740	−	0.797130i	−0.986094	+	0.166190i	$0.946854\pi$
$930$	−3.49131	−	11.3263i	−0.114485	−	0.371405i
$931$	−0.988928	+	10.4776i	−0.0324108	+	0.343388i
$932$	−7.59296			−0.248716
$933$	−3.58900	−	0.762864i	−0.117498	−	0.0249751i
$934$	−32.8555	+	14.6282i	−1.07506	+	0.478649i
$935$	35.4328	+	16.4235i	1.15878	+	0.537105i
$936$	1.17191	+	11.1500i	0.0383052	+	0.364450i
$937$	−2.13939	+	20.3549i	−0.0698908	+	0.664967i	0.902353	+	0.430997i	$0.141838\pi$
$937$	−2.13939	+	20.3549i	−0.0698908	+	0.664967i	−0.972244	+	0.233969i	$0.924829\pi$
$938$	24.8959	+	18.0879i	0.812881	+	0.590592i
$939$	1.13414	−	0.824002i	0.0370113	−	0.0268903i
$940$	−21.8903	−	10.1464i	−0.713982	−	0.330938i
$941$	4.19875	−	39.9484i	0.136875	−	1.30228i	−0.683287	−	0.730150i	$-0.739450\pi$
$941$	4.19875	−	39.9484i	0.136875	−	1.30228i	0.820162	−	0.572131i	$-0.193883\pi$
$942$	−2.67349	−	8.22816i	−0.0871071	−	0.268088i
$943$	62.9530			2.05003
$944$	6.79022	−	7.54130i	0.221003	−	0.245449i
$945$	28.2662	+	6.45733i	0.919500	+	0.210057i
$946$	45.0214	−	9.56960i	1.46377	−	0.311135i
$947$	−8.40912	−	9.33928i	−0.273260	−	0.303486i	0.590858	−	0.806776i	$-0.298789\pi$
$947$	−8.40912	−	9.33928i	−0.273260	−	0.303486i	−0.864118	+	0.503290i	$0.832123\pi$
$948$	−0.153830	−	1.46359i	−0.00499616	−	0.0475353i
$949$	−43.0268			−1.39671
$950$	−2.70453	+	21.6260i	−0.0877465	+	0.701641i
$951$	−15.0738			−0.488800
$952$	1.14370	+	10.8816i	0.0370676	+	0.352675i
$953$	7.05009	+	7.82992i	0.228375	+	0.253636i	0.846432	−	0.532498i	$-0.178746\pi$
$953$	7.05009	+	7.82992i	0.228375	+	0.253636i	−0.618057	+	0.786134i	$0.712080\pi$
$954$	−11.1177	+	2.36314i	−0.359949	+	0.0765096i
$955$	4.14132	+	46.1137i	0.134010	+	1.49220i
$956$	12.1595	−	13.5045i	0.393268	−	0.436768i
$957$	−8.67225			−0.280334
$958$	−3.20152	−	9.85325i	−0.103436	−	0.318344i
$959$	1.91237	−	18.1950i	0.0617537	−	0.587547i
$960$	0.854462	+	1.53316i	0.0275776	+	0.0494826i
$961$	−11.8105	+	8.58082i	−0.380984	+	0.276801i
$962$	−15.5023	−	11.2631i	−0.499813	−	0.363135i
$963$	−1.81234	+	17.2433i	−0.0584019	+	0.555657i
$964$	0.392817	+	3.73740i	0.0126518	+	0.120374i
$965$	−29.0503	+	5.71618i	−0.935163	+	0.184010i
$966$	18.8679	−	8.40054i	0.607065	−	0.270283i
$967$	−23.7992	−	5.05868i	−0.765332	−	0.162676i	−0.191325	−	0.981527i	$-0.561278\pi$
$967$	−23.7992	−	5.05868i	−0.765332	−	0.162676i	−0.574007	+	0.818850i	$0.694612\pi$
$968$	12.9881			0.417455
$969$	11.0929	−	5.08064i	0.356357	−	0.163214i
$970$	−5.08018	−	0.0769873i	−0.163115	−	0.00247191i
$971$	31.7466	+	35.2582i	1.01880	+	1.13149i	0.991267	+	0.131868i	$0.0420975\pi$
$971$	31.7466	+	35.2582i	1.01880	+	1.13149i	0.0275300	+	0.999621i	$0.491236\pi$
$972$	10.4972	+	11.6584i	0.336699	+	0.373942i
$973$	−31.0512	−	13.8249i	−0.995456	−	0.443206i
$974$	12.5335	−	21.7087i	0.401599	−	0.695590i
$975$	−8.74049	−	16.2576i	−0.279920	−	0.520660i
$976$	−1.51785			−0.0485851
$977$	−6.56769	+	4.77170i	−0.210119	+	0.152660i	−0.687868	−	0.725836i	$-0.741453\pi$
$977$	−6.56769	+	4.77170i	−0.210119	+	0.152660i	0.477749	+	0.878497i	$0.341453\pi$
$978$	−16.2890	+	3.46233i	−0.520864	+	0.110713i
$979$	−18.8175	+	3.99977i	−0.601409	+	0.127833i
$980$	4.31911	+	3.23913i	0.137969	+	0.103470i
$981$	0.0916132	+	0.281956i	0.00292498	+	0.00900218i
$982$	20.2872	+	35.1384i	0.647390	+	1.12131i
$983$	−8.78659	−	1.86765i	−0.280249	−	0.0595687i	0.0656429	−	0.997843i	$-0.479090\pi$
$983$	−8.78659	−	1.86765i	−0.280249	−	0.0595687i	−0.345892	+	0.938274i	$0.612424\pi$
$984$	0.602327	−	5.73076i	0.0192015	−	0.182690i
$985$	−48.9617	+	20.9161i	−1.56005	+	0.666441i
$986$	−0.840836	−	8.00002i	−0.0267777	−	0.254772i
$987$	21.0242	+	15.2750i	0.669208	+	0.486208i
$988$	20.4990	−	0.217569i	0.652160	−	0.00692179i
$989$	65.1977	−	47.3689i	2.07317	−	1.50624i
$990$	25.4517	+	5.81437i	0.808910	+	0.184793i
$991$	51.6242	−	22.9846i	1.63990	−	0.730130i	0.640610	−	0.767866i	$-0.278681\pi$
$991$	51.6242	−	22.9846i	1.63990	−	0.730130i	0.999288	+	0.0377363i	$0.0120147\pi$
$992$	4.51842	−	5.01821i	0.143460	−	0.159328i
$993$	−4.08388	+	7.07348i	−0.129598	+	0.224470i
$994$	33.8104	−	37.5502i	1.07240	−	1.19102i
$995$	−7.58427	+	22.1920i	−0.240437	+	0.703533i
$996$	−2.61454	+	8.04674i	−0.0828450	+	0.254971i
$997$	8.18316	−	1.73938i	0.259163	−	0.0550869i	−0.0764975	−	0.997070i	$-0.524374\pi$
$997$	8.18316	−	1.73938i	0.259163	−	0.0550869i	0.335661	+	0.941983i	$0.391040\pi$
$998$	11.6110	+	5.16953i	0.367539	+	0.163639i
$999$	−17.2183			−0.544762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.r.b.11.17	✓	200
19.7	even	3	inner	950.2.r.b.311.9	yes	200
25.16	even	5	inner	950.2.r.b.391.9	yes	200
475.216	even	15	inner	950.2.r.b.691.17	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.r.b.11.17	✓	200	1.1	even	1	trivial
950.2.r.b.311.9	yes	200	19.7	even	3	inner
950.2.r.b.391.9	yes	200	25.16	even	5	inner
950.2.r.b.691.17	yes	200	475.216	even	15	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.r (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 - 0.994522i) q^{2} +(0.525231 + 0.583328i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-1.47087 - 1.68420i) q^{5} +(0.525231 - 0.583328i) q^{6} -3.06829 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.249181 - 2.37080i) q^{9} +O(q^{10})\)	\(q+(-0.104528 - 0.994522i) q^{2} +(0.525231 + 0.583328i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-1.47087 - 1.68420i) q^{5} +(0.525231 - 0.583328i) q^{6} -3.06829 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.249181 - 2.37080i) q^{9} +(-1.52123 + 1.63886i) q^{10} +(3.96238 - 2.87884i) q^{11} +(-0.635034 - 0.461379i) q^{12} +(-0.491604 + 4.67730i) q^{13} +(0.320724 + 3.05148i) q^{14} +(0.209896 - 1.74259i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-3.48808 - 0.741415i) q^{17} -2.38386 q^{18} +(-0.409596 + 4.33961i) q^{19} +(1.78889 + 1.34159i) q^{20} +(-1.61156 - 1.78982i) q^{21} +(-3.27725 - 3.63975i) q^{22} +(-7.83409 - 3.48796i) q^{23} +(-0.392472 + 0.679782i) q^{24} +(-0.673082 + 4.95449i) q^{25} +4.70306 q^{26} +(3.41893 - 2.48400i) q^{27} +(3.00124 - 0.637933i) q^{28} +(-2.20647 + 0.469000i) q^{29} +(-1.75499 - 0.0265959i) q^{30} +(2.08669 + 6.42217i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.76047 + 0.799312i) q^{33} +(-0.372749 + 3.54647i) q^{34} +(4.51306 + 5.16762i) q^{35} +(0.249181 + 2.37080i) q^{36} +(-3.29621 - 2.39483i) q^{37} +(4.35865 - 0.0462611i) q^{38} +(-2.98660 + 2.16989i) q^{39} +(1.14725 - 1.91933i) q^{40} +(-6.70639 + 2.98588i) q^{41} +(-1.61156 + 1.78982i) q^{42} +(-4.69880 + 8.13855i) q^{43} +(-3.27725 + 3.63975i) q^{44} +(-4.35943 + 3.06747i) q^{45} +(-2.64997 + 8.15576i) q^{46} +(-10.5543 + 2.24339i) q^{47} +(0.717083 + 0.319266i) q^{48} +2.41440 q^{49} +(4.99770 + 0.151509i) q^{50} +(-1.39956 - 2.42411i) q^{51} +(-0.491604 - 4.67730i) q^{52} +(4.66374 - 0.991309i) q^{53} +(-2.82777 - 3.14056i) q^{54} +(-10.6767 - 2.43906i) q^{55} +(-0.948154 - 2.91812i) q^{56} +(-2.74655 + 2.04037i) q^{57} +(0.697070 + 2.14536i) q^{58} +(9.27050 - 4.12749i) q^{59} +(0.156996 + 1.74815i) q^{60} +(-1.38662 - 0.617364i) q^{61} +(6.16887 - 2.74656i) q^{62} +(-0.764561 + 7.27431i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(8.60060 - 6.05173i) q^{65} +(0.401857 - 3.82342i) q^{66} +(6.71097 - 7.45328i) q^{67} +3.56601 q^{68} +(-2.08008 - 6.40183i) q^{69} +(4.66757 - 5.02850i) q^{70} +(-11.0193 - 12.2382i) q^{71} +(2.33177 - 0.495633i) q^{72} +(0.956298 + 9.09857i) q^{73} +(-2.03717 + 3.52848i) q^{74} +(-3.24361 + 2.20962i) q^{75} +(-0.501611 - 4.32994i) q^{76} +(-12.1577 + 8.83310i) q^{77} +(2.47019 + 2.74343i) q^{78} +(1.25452 + 1.39329i) q^{79} +(-2.02873 - 0.940340i) q^{80} +(-3.75059 - 0.797212i) q^{81} +(3.67053 + 6.35754i) q^{82} +(-3.33086 - 10.2513i) q^{83} +(1.94847 + 1.41564i) q^{84} +(3.88182 + 6.96516i) q^{85} +(8.58513 + 3.82235i) q^{86} +(-1.43249 - 1.04076i) q^{87} +(3.96238 + 2.87884i) q^{88} +(-3.58830 - 1.59761i) q^{89} +(3.50635 + 4.01491i) q^{90} +(1.50838 - 14.3513i) q^{91} +(8.38808 + 1.78294i) q^{92} +(-2.65024 + 4.59035i) q^{93} +(3.33433 + 10.2620i) q^{94} +(7.91125 - 5.69316i) q^{95} +(0.242561 - 0.746527i) q^{96} +(1.52039 + 1.68857i) q^{97} +(-0.252374 - 2.40118i) q^{98} +(-5.83780 - 10.1114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9}+O(q^{10}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9} - 4 q^{10} + 14 q^{11} + 8 q^{13} + q^{14} - 4 q^{15} + 25 q^{16} - 5 q^{17} + 184 q^{18} + 24 q^{19} - 2 q^{20} + 32 q^{21} + 8 q^{22} + 11 q^{23} - 23 q^{25} + 64 q^{26} - 36 q^{27} + 6 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 100 q^{32} + 12 q^{33} + 2 q^{35} + 13 q^{36} + 8 q^{37} + 2 q^{38} - 52 q^{39} + q^{40} + 14 q^{41} + 32 q^{42} - 10 q^{43} + 8 q^{44} - 52 q^{45} + 8 q^{46} - 22 q^{47} + 204 q^{49} - 34 q^{50} - 10 q^{51} + 8 q^{52} - 18 q^{53} - 12 q^{54} + 10 q^{55} - 12 q^{56} + 34 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 16 q^{61} - 4 q^{62} - 21 q^{63} - 50 q^{64} + 96 q^{65} - 18 q^{66} - 54 q^{67} - 20 q^{68} - 20 q^{69} - 3 q^{70} - 5 q^{71} + 33 q^{72} - 16 q^{73} - 4 q^{74} + 56 q^{75} + 14 q^{76} - 116 q^{77} - 34 q^{78} + q^{80} + 57 q^{81} - 36 q^{82} - 72 q^{83} + 76 q^{84} - 5 q^{85} - 112 q^{87} + 14 q^{88} - 4 q^{89} - 49 q^{90} - 64 q^{91} - 4 q^{92} - 124 q^{93} + 44 q^{94} + 41 q^{95} + 13 q^{97} + 43 q^{98} - 28 q^{99}+O(q^{100}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9 - 4 * q^10 + 14 * q^11 + 8 * q^13 + q^14 - 4 * q^15 + 25 * q^16 - 5 * q^17 + 184 * q^18 + 24 * q^19 - 2 * q^20 + 32 * q^21 + 8 * q^22 + 11 * q^23 - 23 * q^25 + 64 * q^26 - 36 * q^27 + 6 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 100 * q^32 + 12 * q^33 + 2 * q^35 + 13 * q^36 + 8 * q^37 + 2 * q^38 - 52 * q^39 + q^40 + 14 * q^41 + 32 * q^42 - 10 * q^43 + 8 * q^44 - 52 * q^45 + 8 * q^46 - 22 * q^47 + 204 * q^49 - 34 * q^50 - 10 * q^51 + 8 * q^52 - 18 * q^53 - 12 * q^54 + 10 * q^55 - 12 * q^56 + 34 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 16 * q^61 - 4 * q^62 - 21 * q^63 - 50 * q^64 + 96 * q^65 - 18 * q^66 - 54 * q^67 - 20 * q^68 - 20 * q^69 - 3 * q^70 - 5 * q^71 + 33 * q^72 - 16 * q^73 - 4 * q^74 + 56 * q^75 + 14 * q^76 - 116 * q^77 - 34 * q^78 + q^80 + 57 * q^81 - 36 * q^82 - 72 * q^83 + 76 * q^84 - 5 * q^85 - 112 * q^87 + 14 * q^88 - 4 * q^89 - 49 * q^90 - 64 * q^91 - 4 * q^92 - 124 * q^93 + 44 * q^94 + 41 * q^95 + 13 * q^97 + 43 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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