LMFDB - Embedded newform 418.2.f.g.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} + \cdots + 16 $ x^16 - x^15 + 7x^14 - 13x^13 + 51x^12 - 74x^11 + 332x^10 - 614x^9 + 1832x^8 - 2960x^7 + 5348x^6 - 6872x^5 + 8232x^4 - 6344x^3 + 3984x^2 - 400x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.2
Root			$-0.494109 + 1.52071i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.g.267.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.494109 + 1.52071i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-3.03200 + 2.20287i) q^{5} +(-1.29359 + 0.939851i) q^{6} +(-0.259070 - 0.797336i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.358634 + 0.260563i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.494109 + 1.52071i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-3.03200 + 2.20287i) q^{5} +(-1.29359 + 0.939851i) q^{6} +(-0.259070 - 0.797336i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.358634 + 0.260563i) q^{9} -3.74775 q^{10} +(3.31587 - 0.0707159i) q^{11} -1.59897 q^{12} +(-3.59386 - 2.61109i) q^{13} +(0.259070 - 0.797336i) q^{14} +(-1.85180 - 5.69925i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.06727 + 2.95504i) q^{17} +(0.136986 + 0.421600i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-3.03200 - 2.20287i) q^{20} +1.34053 q^{21} +(2.72416 + 1.89181i) q^{22} -6.07470 q^{23} +(-1.29359 - 0.939851i) q^{24} +(2.79526 - 8.60292i) q^{25} +(-1.37273 - 4.22483i) q^{26} +(-4.45423 + 3.23618i) q^{27} +(0.678255 - 0.492781i) q^{28} +(0.862275 + 2.65381i) q^{29} +(1.85180 - 5.69925i) q^{30} +(5.99324 + 4.35434i) q^{31} -1.00000 q^{32} +(-1.53086 + 5.07742i) q^{33} -5.02742 q^{34} +(2.54193 + 1.84682i) q^{35} +(-0.136986 + 0.421600i) q^{36} +(2.52769 + 7.77942i) q^{37} +(0.809017 - 0.587785i) q^{38} +(5.74647 - 4.17506i) q^{39} +(-1.15812 - 3.56432i) q^{40} +(1.97251 - 6.07075i) q^{41} +(1.08451 + 0.787941i) q^{42} +9.55796 q^{43} +(1.09192 + 3.13173i) q^{44} -1.66137 q^{45} +(-4.91454 - 3.57062i) q^{46} +(-2.52645 + 7.77563i) q^{47} +(-0.494109 - 1.52071i) q^{48} +(5.09449 - 3.70136i) q^{49} +(7.31808 - 5.31690i) q^{50} +(-2.48409 - 7.64525i) q^{51} +(1.37273 - 4.22483i) q^{52} +(10.8122 + 7.85551i) q^{53} -5.50573 q^{54} +(-9.89793 + 7.51885i) q^{55} +0.838369 q^{56} +(1.29359 + 0.939851i) q^{57} +(-0.862275 + 2.65381i) q^{58} +(2.25216 + 6.93145i) q^{59} +(4.84807 - 3.52233i) q^{60} +(-6.68721 + 4.85854i) q^{61} +(2.28921 + 7.04548i) q^{62} +(0.114845 - 0.353456i) q^{63} +(-0.809017 - 0.587785i) q^{64} +16.6485 q^{65} +(-4.22293 + 3.20790i) q^{66} -7.32824 q^{67} +(-4.06727 - 2.95504i) q^{68} +(3.00156 - 9.23787i) q^{69} +(0.970931 + 2.98822i) q^{70} +(-10.0464 + 7.29914i) q^{71} +(-0.358634 + 0.260563i) q^{72} +(-2.33579 - 7.18882i) q^{73} +(-2.52769 + 7.77942i) q^{74} +(11.7014 + 8.50156i) q^{75} +1.00000 q^{76} +(-0.915428 - 2.62554i) q^{77} +7.10303 q^{78} +(-7.26918 - 5.28137i) q^{79} +(1.15812 - 3.56432i) q^{80} +(-2.30947 - 7.10781i) q^{81} +(5.16409 - 3.75193i) q^{82} +(1.05726 - 0.768144i) q^{83} +(0.414245 + 1.27492i) q^{84} +(5.82235 - 17.9194i) q^{85} +(7.73256 + 5.61803i) q^{86} -4.46174 q^{87} +(-0.957406 + 3.17543i) q^{88} +10.4914 q^{89} +(-1.34407 - 0.976526i) q^{90} +(-1.15086 + 3.54197i) q^{91} +(-1.87719 - 5.77739i) q^{92} +(-9.58301 + 6.96246i) q^{93} +(-6.61434 + 4.80560i) q^{94} +(1.15812 + 3.56432i) q^{95} +(0.494109 - 1.52071i) q^{96} +(-6.56639 - 4.77076i) q^{97} +6.29714 q^{98} +(1.20761 + 0.838633i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.494109	+	1.52071i	−0.285274	+	0.877983i	0.701043	+	0.713119i	$0.252718\pi$
$3$	−0.494109	+	1.52071i	−0.285274	+	0.877983i	−0.986316	+	0.164863i	$0.947282\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−3.03200	+	2.20287i	−1.35595	+	0.985155i	−0.357259	+	0.934006i	$0.616289\pi$
$5$	−3.03200	+	2.20287i	−1.35595	+	0.985155i	−0.998691	+	0.0511495i	$0.983711\pi$
$6$	−1.29359	+	0.939851i	−0.528107	+	0.383692i
$7$	−0.259070	−	0.797336i	−0.0979193	−	0.301365i	0.890084	−	0.455796i	$-0.150645\pi$
$7$	−0.259070	−	0.797336i	−0.0979193	−	0.301365i	−0.988004	+	0.154431i	$0.950645\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.358634	+	0.260563i	0.119545	+	0.0868544i
$10$	−3.74775			−1.18514
$11$	3.31587	−	0.0707159i	0.999773	−	0.0213217i
$11$	3.31587	−	0.0707159i	0.999773	−	0.0213217i
$12$	−1.59897			−0.461583
$13$	−3.59386	−	2.61109i	−0.996757	−	0.724186i	−0.0353667	−	0.999374i	$-0.511260\pi$
$13$	−3.59386	−	2.61109i	−0.996757	−	0.724186i	−0.961390	+	0.275188i	$0.911260\pi$
$14$	0.259070	−	0.797336i	0.0692394	−	0.213097i
$15$	−1.85180	−	5.69925i	−0.478132	−	1.47154i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.06727	+	2.95504i	−0.986458	+	0.716704i	−0.959143	−	0.282923i	$-0.908696\pi$
$17$	−4.06727	+	2.95504i	−0.986458	+	0.716704i	−0.0273154	+	0.999627i	$0.508696\pi$
$18$	0.136986	+	0.421600i	0.0322880	+	0.0993721i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−3.03200	−	2.20287i	−0.677975	−	0.492578i
$21$	1.34053			0.292527
$22$	2.72416	+	1.89181i	0.580793	+	0.403335i
$23$	−6.07470			−1.26666			−0.633332	−	0.773880i	$-0.718313\pi$
$23$	−6.07470			−1.26666			−0.633332	+	0.773880i	$0.718313\pi$
$24$	−1.29359	−	0.939851i	−0.264054	−	0.191846i
$25$	2.79526	−	8.60292i	0.559052	−	1.72058i
$26$	−1.37273	−	4.22483i	−0.269215	−	0.828558i
$27$	−4.45423	+	3.23618i	−0.857216	+	0.622804i
$28$	0.678255	−	0.492781i	0.128178	−	0.0931268i
$29$	0.862275	+	2.65381i	0.160121	+	0.492800i	0.998644	−	0.0520657i	$-0.0165805\pi$
$29$	0.862275	+	2.65381i	0.160121	+	0.492800i	−0.838523	+	0.544866i	$0.816581\pi$
$30$	1.85180	−	5.69925i	0.338090	−	1.04054i
$31$	5.99324	+	4.35434i	1.07642	+	0.782063i	0.977055	−	0.212988i	$-0.0683195\pi$
$31$	5.99324	+	4.35434i	1.07642	+	0.782063i	0.0993629	+	0.995051i	$0.468320\pi$
$32$	−1.00000			−0.176777
$33$	−1.53086	+	5.07742i	−0.266489	+	0.883865i
$34$	−5.02742			−0.862196
$35$	2.54193	+	1.84682i	0.429665	+	0.312170i
$36$	−0.136986	+	0.421600i	−0.0228310	+	0.0702667i
$37$	2.52769	+	7.77942i	0.415549	+	1.27893i	0.911759	+	0.410726i	$0.134725\pi$
$37$	2.52769	+	7.77942i	0.415549	+	1.27893i	−0.496210	+	0.868203i	$0.665275\pi$
$38$	0.809017	−	0.587785i	0.131240	−	0.0953514i
$39$	5.74647	−	4.17506i	0.920172	−	0.668544i
$40$	−1.15812	−	3.56432i	−0.183115	−	0.563569i
$41$	1.97251	−	6.07075i	0.308054	−	0.948092i	−0.670466	−	0.741940i	$-0.733906\pi$
$41$	1.97251	−	6.07075i	0.308054	−	0.948092i	0.978520	−	0.206152i	$-0.0660941\pi$
$42$	1.08451	+	0.787941i	0.167343	+	0.121582i
$43$	9.55796			1.45758			0.728788	−	0.684739i	$-0.240084\pi$
$43$	9.55796			1.45758			0.728788	+	0.684739i	$0.240084\pi$
$44$	1.09192	+	3.13173i	0.164612	+	0.472126i
$45$	−1.66137			−0.247662
$46$	−4.91454	−	3.57062i	−0.724609	−	0.526459i
$47$	−2.52645	+	7.77563i	−0.368521	+	1.13419i	0.579225	+	0.815167i	$0.303355\pi$
$47$	−2.52645	+	7.77563i	−0.368521	+	1.13419i	−0.947747	+	0.319024i	$0.896645\pi$
$48$	−0.494109	−	1.52071i	−0.0713185	−	0.219496i
$49$	5.09449	−	3.70136i	0.727785	−	0.528766i
$50$	7.31808	−	5.31690i	1.03493	−	0.751923i
$51$	−2.48409	−	7.64525i	−0.347843	−	1.07055i
$52$	1.37273	−	4.22483i	0.190364	−	0.585879i
$53$	10.8122	+	7.85551i	1.48517	+	1.07904i	0.975846	+	0.218460i	$0.0701034\pi$
$53$	10.8122	+	7.85551i	1.48517	+	1.07904i	0.509321	+	0.860577i	$0.329897\pi$
$54$	−5.50573			−0.749234
$55$	−9.89793	+	7.51885i	−1.33464	+	1.01384i
$56$	0.838369			0.112032
$57$	1.29359	+	0.939851i	0.171341	+	0.124486i
$58$	−0.862275	+	2.65381i	−0.113222	+	0.348462i
$59$	2.25216	+	6.93145i	0.293207	+	0.902398i	0.983818	+	0.179171i	$0.0573416\pi$
$59$	2.25216	+	6.93145i	0.293207	+	0.902398i	−0.690611	+	0.723226i	$0.742658\pi$
$60$	4.84807	−	3.52233i	0.625883	−	0.454731i
$61$	−6.68721	+	4.85854i	−0.856210	+	0.622073i	−0.926851	−	0.375429i	$-0.877495\pi$
$61$	−6.68721	+	4.85854i	−0.856210	+	0.622073i	0.0706414	+	0.997502i	$0.477495\pi$
$62$	2.28921	+	7.04548i	0.290730	+	0.894776i
$63$	0.114845	−	0.353456i	0.0144691	−	0.0445313i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	16.6485			2.06499
$66$	−4.22293	+	3.20790i	−0.519806	+	0.394865i
$67$	−7.32824			−0.895287			−0.447643	−	0.894212i	$-0.647737\pi$
$67$	−7.32824			−0.895287			−0.447643	+	0.894212i	$0.647737\pi$
$68$	−4.06727	−	2.95504i	−0.493229	−	0.358352i
$69$	3.00156	−	9.23787i	0.361346	−	1.11211i
$70$	0.970931	+	2.98822i	0.116048	+	0.357160i
$71$	−10.0464	+	7.29914i	−1.19229	+	0.866248i	−0.993504	−	0.113795i	$-0.963699\pi$
$71$	−10.0464	+	7.29914i	−1.19229	+	0.866248i	−0.198784	+	0.980043i	$0.563699\pi$
$72$	−0.358634	+	0.260563i	−0.0422655	+	0.0307077i
$73$	−2.33579	−	7.18882i	−0.273383	−	0.841388i	−0.989643	−	0.143553i	$-0.954147\pi$
$73$	−2.33579	−	7.18882i	−0.273383	−	0.841388i	0.716259	−	0.697834i	$-0.245853\pi$
$74$	−2.52769	+	7.77942i	−0.293838	+	0.904339i
$75$	11.7014	+	8.50156i	1.35116	+	0.981675i
$76$	1.00000			0.114708
$77$	−0.915428	−	2.62554i	−0.104323	−	0.299208i
$78$	7.10303			0.804260
$79$	−7.26918	−	5.28137i	−0.817846	−	0.594200i	0.0982484	−	0.995162i	$-0.468676\pi$
$79$	−7.26918	−	5.28137i	−0.817846	−	0.594200i	−0.916095	+	0.400962i	$0.868676\pi$
$80$	1.15812	−	3.56432i	0.129482	−	0.398504i
$81$	−2.30947	−	7.10781i	−0.256608	−	0.789757i
$82$	5.16409	−	3.75193i	0.570278	−	0.414331i
$83$	1.05726	−	0.768144i	0.116049	−	0.0843148i	−0.528247	−	0.849091i	$-0.677150\pi$
$83$	1.05726	−	0.768144i	0.116049	−	0.0843148i	0.644296	+	0.764776i	$0.277150\pi$
$84$	0.414245	+	1.27492i	0.0451979	+	0.139105i
$85$	5.82235	−	17.9194i	0.631523	−	1.94363i
$86$	7.73256	+	5.61803i	0.833823	+	0.605808i
$87$	−4.46174			−0.478348
$88$	−0.957406	+	3.17543i	−0.102060	+	0.338502i
$89$	10.4914			1.11209			0.556044	−	0.831153i	$-0.312319\pi$
$89$	10.4914			1.11209			0.556044	+	0.831153i	$0.312319\pi$
$90$	−1.34407	−	0.976526i	−0.141678	−	0.102935i
$91$	−1.15086	+	3.54197i	−0.120642	+	0.371299i
$92$	−1.87719	−	5.77739i	−0.195710	−	0.602334i
$93$	−9.58301	+	6.96246i	−0.993712	+	0.721974i
$94$	−6.61434	+	4.80560i	−0.682217	+	0.495660i
$95$	1.15812	+	3.56432i	0.118821	+	0.365692i
$96$	0.494109	−	1.52071i	0.0504298	−	0.155207i
$97$	−6.56639	−	4.77076i	−0.666715	−	0.484397i	0.202209	−	0.979342i	$-0.435188\pi$
$97$	−6.56639	−	4.77076i	−0.666715	−	0.484397i	−0.868924	+	0.494945i	$0.835188\pi$
$98$	6.29714			0.636107
$99$	1.20761	+	0.838633i	0.121370	+	0.0842858i
$100$	9.04565			0.904565
$101$	9.93957	+	7.22152i	0.989024	+	0.718568i	0.959707	−	0.281002i	$-0.0906667\pi$
$101$	9.93957	+	7.22152i	0.989024	+	0.718568i	0.0293172	+	0.999570i	$0.490667\pi$
$102$	2.48409	−	7.64525i	0.245962	−	0.756993i
$103$	1.54400	+	4.75196i	0.152135	+	0.468224i	0.997859	−	0.0653961i	$-0.0208311\pi$
$103$	1.54400	+	4.75196i	0.152135	+	0.468224i	−0.845724	+	0.533620i	$0.820831\pi$
$104$	3.59386	−	2.61109i	0.352407	−	0.256039i
$105$	−4.06447	+	2.95301i	−0.396652	+	0.288184i
$106$	4.12988	+	12.7105i	0.401130	+	1.23455i
$107$	−1.08411	+	3.33653i	−0.104804	+	0.322555i	−0.989685	−	0.143264i	$-0.954240\pi$
$107$	−1.08411	+	3.33653i	−0.104804	+	0.322555i	0.884880	+	0.465819i	$0.154240\pi$
$108$	−4.45423	−	3.23618i	−0.428608	−	0.311402i
$109$	−4.66438			−0.446767			−0.223383	−	0.974731i	$-0.571710\pi$
$109$	−4.66438			−0.446767			−0.223383	+	0.974731i	$0.571710\pi$
$110$	−12.4271	+	0.265026i	−1.18487	+	0.0252692i
$111$	−13.0792			−1.24142
$112$	0.678255	+	0.492781i	0.0640890	+	0.0465634i
$113$	5.40531	−	16.6358i	0.508489	−	1.56497i	−0.286336	−	0.958129i	$-0.592437\pi$
$113$	5.40531	−	16.6358i	0.508489	−	1.56497i	0.794825	−	0.606839i	$-0.207563\pi$
$114$	0.494109	+	1.52071i	0.0462775	+	0.142428i
$115$	18.4185	−	13.3818i	1.71753	−	1.24786i
$116$	−2.25747	+	1.64015i	−0.209600	+	0.152284i
$117$	−0.608527	−	1.87285i	−0.0562584	−	0.173145i
$118$	−2.25216	+	6.93145i	−0.207328	+	0.638091i
$119$	3.40987	+	2.47742i	0.312582	+	0.227104i
$120$	5.99254			0.547042
$121$	10.9900	−	0.468970i	0.999091	−	0.0426336i
$122$	−8.26585			−0.748355
$123$	8.25722	+	5.99922i	0.744528	+	0.540932i
$124$	−2.28921	+	7.04548i	−0.205577	+	0.632702i
$125$	4.68534	+	14.4200i	0.419070	+	1.28976i
$126$	0.300668	−	0.218448i	0.0267856	−	0.0194609i
$127$	0.969791	−	0.704594i	0.0860550	−	0.0625227i	−0.543926	−	0.839133i	$-0.683063\pi$
$127$	0.969791	−	0.704594i	0.0860550	−	0.0625227i	0.629981	+	0.776611i	$0.283063\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−4.72267	+	14.5349i	−0.415808	+	1.27973i
$130$	13.4689	+	9.78572i	1.18130	+	0.858265i
$131$	8.60188			0.751550			0.375775	−	0.926711i	$-0.377377\pi$
$131$	8.60188			0.751550			0.375775	+	0.926711i	$0.377377\pi$
$132$	−5.30198	+	0.113073i	−0.461478	+	0.00984171i
$133$	−0.838369			−0.0726958
$134$	−5.92867	−	4.30743i	−0.512159	−	0.372105i
$135$	6.37629	−	19.6242i	0.548783	−	1.68898i
$136$	−1.55356	−	4.78136i	−0.133217	−	0.409998i
$137$	−4.89825	+	3.55879i	−0.418486	+	0.304048i	−0.777028	−	0.629466i	$-0.783274\pi$
$137$	−4.89825	+	3.55879i	−0.418486	+	0.304048i	0.358542	+	0.933513i	$0.383274\pi$
$138$	7.85820	−	5.70932i	0.668934	−	0.486009i
$139$	−1.21538	−	3.74055i	−0.103087	−	0.317269i	0.886190	−	0.463323i	$-0.153343\pi$
$139$	−1.21538	−	3.74055i	−0.103087	−	0.317269i	−0.989277	+	0.146053i	$0.953343\pi$
$140$	−0.970931	+	2.98822i	−0.0820586	+	0.252551i
$141$	−10.5761	−	7.68401i	−0.890671	−	0.647110i
$142$	−12.4180			−1.04210
$143$	−12.1014	−	8.40390i	−1.01197	−	0.702769i
$144$	−0.443297			−0.0369414
$145$	−8.46043	−	6.14686i	−0.702600	−	0.510469i
$146$	2.33579	−	7.18882i	0.193311	−	0.594951i
$147$	3.11147	+	9.57612i	0.256630	+	0.789825i
$148$	−6.61757	+	4.80794i	−0.543961	+	0.395211i
$149$	17.4219	−	12.6577i	1.42725	−	1.03696i	0.436734	−	0.899591i	$-0.356135\pi$
$149$	17.4219	−	12.6577i	1.42725	−	1.03696i	0.990520	−	0.137370i	$-0.0438649\pi$
$150$	4.46953	+	13.7558i	0.364936	+	1.12316i
$151$	0.0402109	−	0.123756i	0.00327232	−	0.0100712i	−0.949407	−	0.314048i	$-0.898315\pi$
$151$	0.0402109	−	0.123756i	0.00327232	−	0.0100712i	0.952679	+	0.303977i	$0.0983146\pi$
$152$	0.809017	+	0.587785i	0.0656199	+	0.0476757i
$153$	−2.22864			−0.180175
$154$	0.802659	−	2.66218i	0.0646801	−	0.214525i
$155$	−27.7635			−2.23002
$156$	5.74647	+	4.17506i	0.460086	+	0.334272i
$157$	0.716145	−	2.20407i	0.0571546	−	0.175904i	−0.918404	−	0.395645i	$-0.870521\pi$
$157$	0.716145	−	2.20407i	0.0571546	−	0.175904i	0.975558	+	0.219741i	$0.0705212\pi$
$158$	−2.77658	−	8.54543i	−0.220893	−	0.679838i
$159$	−17.2883	+	12.5607i	−1.37105	+	0.996130i
$160$	3.03200	−	2.20287i	0.239700	−	0.174152i
$161$	1.57377	+	4.84358i	0.124031	+	0.381728i
$162$	2.30947	−	7.10781i	0.181449	−	0.558443i
$163$	14.6263	+	10.6266i	1.14562	+	0.832341i	0.987892	−	0.155142i	$-0.0495835\pi$
$163$	14.6263	+	10.6266i	1.14562	+	0.832341i	0.157727	+	0.987483i	$0.449583\pi$
$164$	6.38316			0.498441
$165$	−6.54335	−	18.7670i	−0.509399	−	1.46101i
$166$	1.30685			0.101431
$167$	−6.48860	−	4.71424i	−0.502103	−	0.364799i	0.307717	−	0.951478i	$-0.400435\pi$
$167$	−6.48860	−	4.71424i	−0.502103	−	0.364799i	−0.809820	+	0.586679i	$0.800435\pi$
$168$	−0.414245	+	1.27492i	−0.0319597	+	0.0983619i
$169$	2.08080	+	6.40405i	0.160062	+	0.492619i
$170$	15.2431	−	11.0748i	1.16909	−	0.849397i
$171$	0.358634	−	0.260563i	0.0274255	−	0.0199258i
$172$	2.95357	+	9.09016i	0.225208	+	0.693119i
$173$	0.724872	−	2.23093i	0.0551110	−	0.169614i	−0.919712	−	0.392593i	$-0.871578\pi$
$173$	0.724872	−	2.23093i	0.0551110	−	0.169614i	0.974823	+	0.222979i	$0.0715781\pi$
$174$	−3.60962	−	2.62254i	−0.273645	−	0.198814i
$175$	−7.58359			−0.573265
$176$	−2.64103	+	2.00623i	−0.199075	+	0.151225i
$177$	−11.6535			−0.875933
$178$	8.48773	+	6.16670i	0.636183	+	0.462214i
$179$	−4.11566	+	12.6667i	−0.307619	+	0.946754i	0.671068	+	0.741396i	$0.265836\pi$
$179$	−4.11566	+	12.6667i	−0.307619	+	0.946754i	−0.978687	+	0.205358i	$0.934164\pi$
$180$	−0.513390	−	1.58005i	−0.0382659	−	0.117770i
$181$	0.762737	−	0.554161i	0.0566938	−	0.0411905i	−0.559077	−	0.829115i	$-0.688845\pi$
$181$	0.762737	−	0.554161i	0.0566938	−	0.0411905i	0.615771	+	0.787925i	$0.288845\pi$
$182$	−3.01298	+	2.18906i	−0.223337	+	0.162264i
$183$	−4.08423	−	12.5700i	−0.301915	−	0.929198i
$184$	1.87719	−	5.77739i	0.138388	−	0.425915i
$185$	−24.8010	−	18.0190i	−1.82341	−	1.32478i
$186$	−11.8452			−0.868536
$187$	−13.2776	+	10.0862i	−0.970952	+	0.737574i
$188$	−8.17578			−0.596280
$189$	3.73428	+	2.71312i	0.271629	+	0.197350i
$190$	−1.15812	+	3.56432i	−0.0840188	+	0.258583i
$191$	−5.02080	−	15.4524i	−0.363292	−	1.11810i	−0.951044	−	0.309057i	$-0.899987\pi$
$191$	−5.02080	−	15.4524i	−0.363292	−	1.11810i	0.587751	−	0.809042i	$-0.300013\pi$
$192$	1.29359	−	0.939851i	0.0933571	−	0.0678279i
$193$	11.0333	−	8.01615i	0.794194	−	0.577015i	−0.115011	−	0.993364i	$-0.536690\pi$
$193$	11.0333	−	8.01615i	0.794194	−	0.577015i	0.909205	+	0.416349i	$0.136690\pi$
$194$	−2.50814	−	7.71925i	−0.180074	−	0.554210i
$195$	−8.22615	+	25.3175i	−0.589087	+	1.81302i
$196$	5.09449	+	3.70136i	0.363892	+	0.264383i
$197$	14.9289			1.06364			0.531821	−	0.846857i	$-0.321508\pi$
$197$	14.9289			1.06364			0.531821	+	0.846857i	$0.321508\pi$
$198$	0.484042	+	1.38828i	0.0343994	+	0.0986611i
$199$	7.43443			0.527013			0.263506	−	0.964658i	$-0.415121\pi$
$199$	7.43443			0.527013			0.263506	+	0.964658i	$0.415121\pi$
$200$	7.31808	+	5.31690i	0.517467	+	0.375962i
$201$	3.62095	−	11.1441i	0.255402	−	0.786046i
$202$	3.79658	+	11.6847i	0.267126	+	0.822130i
$203$	1.89259	−	1.37505i	0.132834	−	0.0965094i
$204$	6.50344	−	4.72503i	0.455332	−	0.330818i
$205$	7.39246	+	22.7517i	0.516312	+	1.58905i
$206$	−1.54400	+	4.75196i	−0.107576	+	0.331085i
$207$	−2.17860	−	1.58284i	−0.151423	−	0.110015i
$208$	4.44225			0.308015
$209$	0.957406	−	3.17543i	0.0662251	−	0.219649i
$210$	−5.02396			−0.346686
$211$	−3.00721	−	2.18487i	−0.207025	−	0.150412i	0.479442	−	0.877574i	$-0.340839\pi$
$211$	−3.00721	−	2.18487i	−0.207025	−	0.150412i	−0.686467	+	0.727161i	$0.740839\pi$
$212$	−4.12988	+	12.7105i	−0.283642	+	0.872959i
$213$	−6.13586	−	18.8842i	−0.420422	−	1.29393i
$214$	−2.83823	+	2.06209i	−0.194017	+	0.140962i
$215$	−28.9797	+	21.0550i	−1.97640	+	1.43594i
$216$	−1.70136	−	5.23626i	−0.115763	−	0.356282i
$217$	1.91921	−	5.90671i	0.130284	−	0.400973i
$218$	−3.77356	−	2.74166i	−0.255578	−	0.185688i
$219$	12.0862			0.816713
$220$	−10.2095	−	7.09003i	−0.688323	−	0.478010i
$221$	22.3331			1.50229
$222$	−10.5813	−	7.68776i	−0.710170	−	0.515968i
$223$	5.54760	−	17.0737i	0.371495	−	1.14334i	−0.574319	−	0.818632i	$-0.694733\pi$
$223$	5.54760	−	17.0737i	0.371495	−	1.14334i	0.945813	−	0.324711i	$-0.105267\pi$
$224$	0.259070	+	0.797336i	0.0173099	+	0.0532743i
$225$	3.24408	−	2.35696i	0.216272	−	0.157131i
$226$	14.1513	−	10.2815i	0.941330	−	0.683916i
$227$	5.50395	+	16.9394i	0.365310	+	1.12431i	0.949787	+	0.312898i	$0.101300\pi$
$227$	5.50395	+	16.9394i	0.365310	+	1.12431i	−0.584476	+	0.811411i	$0.698700\pi$
$228$	−0.494109	+	1.52071i	−0.0327232	+	0.100712i
$229$	−5.30819	−	3.85662i	−0.350775	−	0.254853i	0.398419	−	0.917203i	$-0.369559\pi$
$229$	−5.30819	−	3.85662i	−0.350775	−	0.254853i	−0.749194	+	0.662351i	$0.769559\pi$
$230$	22.7665			1.50118
$231$	4.44501	−	0.0947965i	0.292460	−	0.00623715i
$232$	−2.79038			−0.183198
$233$	1.97401	+	1.43420i	0.129322	+	0.0939579i	0.650566	−	0.759450i	$-0.274532\pi$
$233$	1.97401	+	1.43420i	0.129322	+	0.0939579i	−0.521244	+	0.853408i	$0.674532\pi$
$234$	0.608527	−	1.87285i	0.0397807	−	0.122432i
$235$	−9.46852	−	29.1411i	−0.617658	−	1.90096i
$236$	−5.89624	+	4.28387i	−0.383813	+	0.278856i
$237$	11.6232	−	8.44474i	0.755008	−	0.548545i
$238$	1.30246	+	4.00855i	0.0844256	+	0.259835i
$239$	−2.20105	+	6.77412i	−0.142374	+	0.438182i	−0.996664	−	0.0816150i	$-0.973992\pi$
$239$	−2.20105	+	6.77412i	−0.142374	+	0.438182i	0.854290	+	0.519796i	$0.173992\pi$
$240$	4.84807	+	3.52233i	0.312941	+	0.227365i
$241$	−15.1545			−0.976184			−0.488092	−	0.872792i	$-0.662307\pi$
$241$	−15.1545			−0.976184			−0.488092	+	0.872792i	$0.662307\pi$
$242$	9.16675	+	6.08035i	0.589261	+	0.390860i
$243$	−4.56712			−0.292981
$244$	−6.68721	−	4.85854i	−0.428105	−	0.311036i
$245$	−7.29284	+	22.4450i	−0.465922	+	1.43396i
$246$	3.15398	+	9.70694i	0.201090	+	0.618892i
$247$	−3.59386	+	2.61109i	−0.228672	+	0.166140i
$248$	−5.99324	+	4.35434i	−0.380571	+	0.276501i
$249$	0.645724	+	1.98733i	0.0409211	+	0.125942i
$250$	−4.68534	+	14.4200i	−0.296327	+	0.912001i
$251$	14.1283	+	10.2648i	0.891769	+	0.647908i	0.936339	−	0.351098i	$-0.114192\pi$
$251$	14.1283	+	10.2648i	0.891769	+	0.647908i	−0.0445700	+	0.999006i	$0.514192\pi$
$252$	0.371646			0.0234115
$253$	−20.1429	+	0.429578i	−1.26638	+	0.0270074i
$254$	1.19873			0.0752149
$255$	24.3733	+	17.7082i	1.52631	+	1.10893i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−3.55482	−	10.9406i	−0.221743	−	0.682456i	−0.998606	−	0.0527856i	$-0.983190\pi$
$257$	−3.55482	−	10.9406i	−0.221743	−	0.682456i	0.776863	−	0.629670i	$-0.216810\pi$
$258$	−12.3641	+	8.98306i	−0.769757	+	0.559261i
$259$	5.54796	−	4.03083i	0.344734	−	0.250464i
$260$	5.14466	+	15.8336i	0.319058	+	0.981960i
$261$	−0.382244	+	1.17643i	−0.0236603	+	0.0728189i
$262$	6.95907	+	5.05606i	0.429933	+	0.312364i
$263$	17.1790			1.05930			0.529651	−	0.848216i	$-0.322323\pi$
$263$	17.1790			1.05930			0.529651	+	0.848216i	$0.322323\pi$
$264$	−4.35585	−	3.02495i	−0.268084	−	0.186173i
$265$	−50.0872			−3.07683
$266$	−0.678255	−	0.492781i	−0.0415865	−	0.0302143i
$267$	−5.18390	+	15.9544i	−0.317250	+	0.976394i
$268$	−2.26455	−	6.96957i	−0.138329	−	0.425734i
$269$	−8.90943	+	6.47308i	−0.543218	+	0.394671i	−0.825279	−	0.564726i	$-0.808982\pi$
$269$	−8.90943	+	6.47308i	−0.543218	+	0.394671i	0.282061	+	0.959397i	$0.408982\pi$
$270$	16.6933	−	12.1284i	1.01592	−	0.738112i
$271$	2.44037	+	7.51068i	0.148242	+	0.456241i	0.997414	−	0.0718755i	$-0.0228984\pi$
$271$	2.44037	+	7.51068i	0.148242	+	0.456241i	−0.849172	+	0.528117i	$0.822898\pi$
$272$	1.55356	−	4.78136i	0.0941983	−	0.289913i
$273$	−4.81766	−	3.50024i	−0.291578	−	0.211844i
$274$	−6.05457			−0.365770
$275$	8.66035	−	28.7239i	0.522239	−	1.73211i
$276$	9.71327			0.584670
$277$	−6.20926	−	4.51130i	−0.373079	−	0.271057i	0.385408	−	0.922746i	$-0.374061\pi$
$277$	−6.20926	−	4.51130i	−0.373079	−	0.271057i	−0.758486	+	0.651689i	$0.774061\pi$
$278$	1.21538	−	3.74055i	0.0728935	−	0.224343i
$279$	1.01480	+	3.12324i	0.0607545	+	0.186983i
$280$	−2.54193	+	1.84682i	−0.151909	+	0.110369i
$281$	−13.3512	+	9.70020i	−0.796465	+	0.578666i	−0.909875	−	0.414883i	$-0.863823\pi$
$281$	−13.3512	+	9.70020i	−0.796465	+	0.578666i	0.113410	+	0.993548i	$0.463823\pi$
$282$	−4.03972	−	12.4330i	−0.240562	−	0.740374i
$283$	2.23456	−	6.87727i	0.132831	−	0.408811i	−0.862415	−	0.506201i	$-0.831049\pi$
$283$	2.23456	−	6.87727i	0.132831	−	0.408811i	0.995246	+	0.0973897i	$0.0310493\pi$
$284$	−10.0464	−	7.29914i	−0.596144	−	0.433124i
$285$	−5.99254			−0.354968
$286$	−4.85056	−	13.9119i	−0.286820	−	0.822630i
$287$	−5.35145			−0.315886
$288$	−0.358634	−	0.260563i	−0.0211327	−	0.0153538i
$289$	2.55711	−	7.86997i	0.150418	−	0.462939i
$290$	−3.23159	−	9.94583i	−0.189766	−	0.584039i
$291$	10.4994	−	7.62830i	0.615489	−	0.447179i
$292$	6.11517	−	4.44293i	0.357863	−	0.260003i
$293$	−0.578042	−	1.77903i	−0.0337696	−	0.103932i	0.932751	−	0.360521i	$-0.117401\pi$
$293$	−0.578042	−	1.77903i	−0.0337696	−	0.103932i	−0.966521	+	0.256589i	$0.917401\pi$
$294$	−3.11147	+	9.57612i	−0.181465	+	0.558491i
$295$	−22.0977	−	16.0549i	−1.28657	−	0.934751i
$296$	−8.17976			−0.475439
$297$	−14.5408	+	11.0458i	−0.843742	+	0.640940i
$298$	21.5346			1.24747
$299$	21.8316	+	15.8616i	1.26256	+	0.917301i
$300$	−4.46953	+	13.7558i	−0.258049	+	0.794192i
$301$	−2.47618	−	7.62091i	−0.142725	−	0.439262i
$302$	0.105274	−	0.0764857i	0.00605781	−	0.00440126i
$303$	−15.8931	+	11.5470i	−0.913033	+	0.663357i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	9.57284	−	29.4622i	0.548139	−	1.68700i
$306$	−1.80301	−	1.30996i	−0.103071	−	0.0748855i
$307$	3.18323			0.181676			0.0908382	−	0.995866i	$-0.471045\pi$
$307$	3.18323			0.181676			0.0908382	+	0.995866i	$0.471045\pi$
$308$	2.21416	−	1.68196i	0.126163	−	0.0958386i
$309$	−7.98926			−0.454493
$310$	−22.4612	−	16.3190i	−1.27571	−	0.926857i
$311$	5.58071	−	17.1757i	0.316453	−	0.973942i	−0.658699	−	0.752406i	$-0.728893\pi$
$311$	5.58071	−	17.1757i	0.316453	−	0.973942i	0.975152	−	0.221536i	$-0.0711070\pi$
$312$	2.19496	+	6.75538i	0.124265	+	0.382448i
$313$	9.52771	−	6.92228i	0.538538	−	0.391271i	−0.285004	−	0.958526i	$-0.591995\pi$
$313$	9.52771	−	6.92228i	0.538538	−	0.391271i	0.823542	+	0.567256i	$0.191995\pi$
$314$	1.87489	−	1.36219i	0.105806	−	0.0768727i
$315$	0.430410	+	1.32467i	0.0242509	+	0.0746365i
$316$	2.77658	−	8.54543i	0.156195	−	0.480718i
$317$	−4.98270	−	3.62014i	−0.279856	−	0.203328i	0.438998	−	0.898488i	$-0.355333\pi$
$317$	−4.98270	−	3.62014i	−0.279856	−	0.203328i	−0.718855	+	0.695160i	$0.755333\pi$
$318$	−21.3696			−1.19835
$319$	3.04686	+	8.73872i	0.170591	+	0.489274i
$320$	3.74775			0.209506
$321$	−4.53824	−	3.29722i	−0.253300	−	0.184033i
$322$	−1.57377	+	4.84358i	−0.0877031	+	0.269922i
$323$	1.55356	+	4.78136i	0.0864423	+	0.266042i
$324$	6.04627	−	4.39287i	0.335904	−	0.244048i
$325$	−32.5088	+	23.6190i	−1.80326	+	1.31015i
$326$	5.58674	+	17.1942i	0.309421	+	0.952300i
$327$	2.30471	−	7.09317i	0.127451	−	0.392253i
$328$	5.16409	+	3.75193i	0.285139	+	0.207166i
$329$	6.85432			0.377891
$330$	5.73729	−	19.0289i	0.315828	−	1.04751i
$331$	4.75415			0.261312			0.130656	−	0.991428i	$-0.458292\pi$
$331$	4.75415			0.261312			0.130656	+	0.991428i	$0.458292\pi$
$332$	1.05726	+	0.768144i	0.0580247	+	0.0421574i
$333$	−1.12051	+	3.44859i	−0.0614038	+	0.188982i
$334$	−2.47842	−	7.62780i	−0.135613	−	0.417375i
$335$	22.2192	−	16.1432i	1.21396	−	0.881996i
$336$	−1.08451	+	0.787941i	−0.0591648	+	0.0429857i
$337$	10.1683	+	31.2949i	0.553905	+	1.70474i	0.698819	+	0.715299i	$0.253709\pi$
$337$	10.1683	+	31.2949i	0.553905	+	1.70474i	−0.144914	+	0.989444i	$0.546291\pi$
$338$	−2.08080	+	6.40405i	−0.113181	+	0.348335i
$339$	22.6275	+	16.4398i	1.22896	+	0.892889i
$340$	18.8415			1.02183
$341$	20.1807	+	14.0146i	1.09285	+	0.758934i
$342$	0.443297			0.0239707
$343$	−9.01884	−	6.55257i	−0.486972	−	0.353806i
$344$	−2.95357	+	9.09016i	−0.159246	+	0.490109i
$345$	11.2491	+	34.6212i	0.605632	+	1.86394i
$346$	1.89774	−	1.37879i	0.102023	−	0.0741242i
$347$	−24.6814	+	17.9321i	−1.32497	+	0.962647i	−0.325113	+	0.945675i	$0.605403\pi$
$347$	−24.6814	+	17.9321i	−1.32497	+	0.962647i	−0.999856	+	0.0169716i	$0.994597\pi$
$348$	−1.37875	−	4.24336i	−0.0739089	−	0.227468i
$349$	5.85862	−	18.0310i	0.313605	−	0.965176i	−0.662720	−	0.748867i	$-0.730598\pi$
$349$	5.85862	−	18.0310i	0.313605	−	0.965176i	0.976325	−	0.216309i	$-0.0694018\pi$
$350$	−6.13525	−	4.45752i	−0.327943	−	0.238265i
$351$	24.4578			1.30546
$352$	−3.31587	+	0.0707159i	−0.176737	+	0.00376917i
$353$	2.16128			0.115033			0.0575167	−	0.998345i	$-0.481682\pi$
$353$	2.16128			0.115033			0.0575167	+	0.998345i	$0.481682\pi$
$354$	−9.42791	−	6.84978i	−0.501088	−	0.364062i
$355$	14.3816	−	44.2619i	0.763294	−	2.34918i
$356$	3.24203	+	9.97793i	0.171827	+	0.528829i
$357$	−5.45228	+	3.96131i	−0.288565	+	0.209655i
$358$	−10.7749	+	7.82845i	−0.569473	+	0.413746i
$359$	3.39322	+	10.4432i	0.179087	+	0.551174i	0.999797	−	0.0201723i	$-0.00642149\pi$
$359$	3.39322	+	10.4432i	0.179087	+	0.551174i	−0.820709	+	0.571346i	$0.806421\pi$
$360$	0.513390	−	1.58005i	0.0270580	−	0.0832761i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	0.942795			0.0495522
$363$	−4.71709	+	16.9443i	−0.247583	+	0.889347i
$364$	−3.72425			−0.195204
$365$	22.9182	+	16.6510i	1.19959	+	0.871554i
$366$	4.08423	−	12.5700i	0.213486	−	0.657042i
$367$	5.63691	+	17.3486i	0.294244	+	0.905590i	0.983474	+	0.181048i	$0.0579489\pi$
$367$	5.63691	+	17.3486i	0.294244	+	0.905590i	−0.689230	+	0.724542i	$0.742051\pi$
$368$	4.91454	−	3.57062i	0.256188	−	0.186132i
$369$	2.28922	−	1.66322i	0.119172	−	0.0865836i
$370$	−9.47314	−	29.1553i	−0.492485	−	1.51571i
$371$	3.46237	−	10.6561i	0.179757	−	0.553235i
$372$	−9.58301	−	6.96246i	−0.496856	−	0.360987i
$373$	−3.49137			−0.180776			−0.0903881	−	0.995907i	$-0.528811\pi$
$373$	−3.49137			−0.180776			−0.0903881	+	0.995907i	$0.528811\pi$
$374$	−16.6703	+	0.355519i	−0.862000	+	0.0183834i
$375$	−24.2437			−1.25194
$376$	−6.61434	−	4.80560i	−0.341109	−	0.247830i
$377$	3.83045	−	11.7889i	0.197278	−	0.607159i
$378$	1.42637	+	4.38991i	0.0733645	+	0.225793i
$379$	−24.0129	+	17.4464i	−1.23346	+	0.896160i	−0.997145	−	0.0755172i	$-0.975939\pi$
$379$	−24.0129	+	17.4464i	−1.23346	+	0.896160i	−0.236314	+	0.971677i	$0.575939\pi$
$380$	−3.03200	+	2.20287i	−0.155538	+	0.113005i
$381$	0.592302	+	1.82292i	0.0303445	+	0.0933909i
$382$	5.02080	−	15.4524i	0.256886	−	0.790615i
$383$	−9.89115	−	7.18634i	−0.505414	−	0.367205i	0.305667	−	0.952138i	$-0.401121\pi$
$383$	−9.89115	−	7.18634i	−0.505414	−	0.367205i	−0.811081	+	0.584934i	$0.801121\pi$
$384$	1.59897			0.0815971
$385$	8.55931	+	5.94406i	0.436223	+	0.302937i
$386$	13.6379			0.694151
$387$	3.42782	+	2.49045i	0.174246	+	0.126597i
$388$	2.50814	−	7.71925i	0.127331	−	0.391885i
$389$	−6.54845	−	20.1540i	−0.332019	−	1.02185i	−0.968172	−	0.250287i	$-0.919475\pi$
$389$	−6.54845	−	20.1540i	−0.332019	−	1.02185i	0.636152	−	0.771564i	$-0.280525\pi$
$390$	−21.5363	+	15.6471i	−1.09054	+	0.792320i
$391$	24.7075	−	17.9510i	1.24951	−	0.907822i
$392$	1.94592	+	5.98893i	0.0982839	+	0.302487i
$393$	−4.25026	+	13.0810i	−0.214397	+	0.659847i
$394$	12.0778	+	8.77500i	0.608468	+	0.442078i
$395$	33.6743			1.69434
$396$	−0.424415	+	1.40766i	−0.0213276	+	0.0707375i
$397$	31.6829			1.59012			0.795060	−	0.606531i	$-0.207440\pi$
$397$	31.6829			1.59012			0.795060	+	0.606531i	$0.207440\pi$
$398$	6.01458	+	4.36985i	0.301484	+	0.219041i
$399$	0.414245	−	1.27492i	0.0207382	−	0.0638256i
$400$	2.79526	+	8.60292i	0.139763	+	0.430146i
$401$	9.15010	−	6.64794i	0.456934	−	0.331982i	−0.335393	−	0.942078i	$-0.608869\pi$
$401$	9.15010	−	6.64794i	0.456934	−	0.331982i	0.792327	+	0.610096i	$0.208869\pi$
$402$	9.47976	−	6.88745i	0.472807	−	0.343515i
$403$	−10.1693	−	31.2978i	−0.506567	−	1.55905i
$404$	−3.79658	+	11.6847i	−0.188887	+	0.581334i
$405$	22.6599	+	16.4634i	1.12598	+	0.818073i
$406$	2.33937			0.116101
$407$	8.93161	+	25.6168i	0.442723	+	1.26978i
$408$	8.03870			0.397975
$409$	32.1532	+	23.3607i	1.58987	+	1.15511i	0.904122	+	0.427274i	$0.140526\pi$
$409$	32.1532	+	23.3607i	1.58987	+	1.15511i	0.685751	+	0.727836i	$0.259474\pi$
$410$	−7.39246	+	22.7517i	−0.365088	+	1.12362i
$411$	−2.99162	−	9.20725i	−0.147566	−	0.454160i
$412$	−4.04226	+	2.93687i	−0.199148	+	0.144689i
$413$	4.94322	−	3.59146i	0.243240	−	0.176724i
$414$	−0.832151	−	2.56110i	−0.0408980	−	0.125871i
$415$	−1.51348	+	4.65802i	−0.0742939	+	0.228653i
$416$	3.59386	+	2.61109i	0.176203	+	0.128019i
$417$	6.28882			0.307965
$418$	2.64103	−	2.00623i	0.129177	−	0.0981279i
$419$	12.6037			0.615732			0.307866	−	0.951430i	$-0.400385\pi$
$419$	12.6037			0.615732			0.307866	+	0.951430i	$0.400385\pi$
$420$	−4.06447	−	2.95301i	−0.198326	−	0.144092i
$421$	−1.00814	+	3.10274i	−0.0491337	+	0.151218i	−0.972613	−	0.232430i	$-0.925332\pi$
$421$	−1.00814	+	3.10274i	−0.0491337	+	0.151218i	0.923479	+	0.383648i	$0.125332\pi$
$422$	−1.14865	−	3.53519i	−0.0559155	−	0.172090i
$423$	−2.93212	+	2.13031i	−0.142564	+	0.103579i
$424$	−10.8122	+	7.85551i	−0.525086	+	0.381497i
$425$	14.0529	+	43.2505i	0.681668	+	2.09796i
$426$	6.13586	−	18.8842i	0.297283	−	0.914944i
$427$	5.60635	+	4.07325i	0.271310	+	0.197118i
$428$	−3.50824			−0.169577
$429$	18.7593	−	14.2503i	0.905708	−	0.688012i
$430$	−35.8209			−1.72744
$431$	−2.59001	−	1.88175i	−0.124756	−	0.0906408i	0.523657	−	0.851929i	$-0.324567\pi$
$431$	−2.59001	−	1.88175i	−0.124756	−	0.0906408i	−0.648414	+	0.761288i	$0.724567\pi$
$432$	1.70136	−	5.23626i	0.0818569	−	0.251930i
$433$	−1.06774	−	3.28617i	−0.0513123	−	0.157923i	0.922117	−	0.386912i	$-0.126458\pi$
$433$	−1.06774	−	3.28617i	−0.0513123	−	0.157923i	−0.973429	+	0.228989i	$0.926458\pi$
$434$	5.02455	−	3.65055i	0.241186	−	0.175232i
$435$	13.5280	−	9.82864i	0.648616	−	0.471247i
$436$	−1.44137	−	4.43609i	−0.0690293	−	0.212450i
$437$	−1.87719	+	5.77739i	−0.0897980	+	0.276370i
$438$	9.77798	+	7.10412i	0.467210	+	0.339448i
$439$	14.3937			0.686974			0.343487	−	0.939157i	$-0.388392\pi$
$439$	14.3937			0.686974			0.343487	+	0.939157i	$0.388392\pi$
$440$	−4.09223	−	11.7369i	−0.195089	−	0.559537i
$441$	2.79150			0.132929
$442$	18.0678	+	13.1271i	0.859400	+	0.624391i
$443$	0.393741	−	1.21181i	0.0187072	−	0.0575749i	−0.941267	−	0.337663i	$-0.890364\pi$
$443$	0.393741	−	1.21181i	0.0187072	−	0.0575749i	0.959974	+	0.280088i	$0.0903636\pi$
$444$	−4.04169	−	12.4391i	−0.191810	−	0.590331i
$445$	−31.8099	+	23.1113i	−1.50793	+	1.09558i
$446$	14.5238	−	10.5522i	0.687722	−	0.499659i
$447$	10.6404	+	32.7479i	0.503275	+	1.54892i
$448$	−0.259070	+	0.797336i	−0.0122399	+	0.0376706i
$449$	−14.7890	−	10.7449i	−0.697937	−	0.507081i	0.181322	−	0.983424i	$-0.441962\pi$
$449$	−14.7890	−	10.7449i	−0.697937	−	0.507081i	−0.879260	+	0.476343i	$0.841962\pi$
$450$	4.00990			0.189029
$451$	6.11128	−	20.2693i	0.287769	−	0.954444i
$452$	17.4920			0.822753
$453$	0.168329	+	0.122298i	0.00790879	+	0.00574608i
$454$	−5.50395	+	16.9394i	−0.258313	+	0.795007i
$455$	−4.31312	−	13.2744i	−0.202202	−	0.622315i
$456$	−1.29359	+	0.939851i	−0.0605781	+	0.0440125i
$457$	15.0969	−	10.9685i	0.706203	−	0.513086i	−0.175744	−	0.984436i	$-0.556233\pi$
$457$	15.0969	−	10.9685i	0.706203	−	0.513086i	0.881946	+	0.471350i	$0.156233\pi$
$458$	−2.02755	−	6.24015i	−0.0947410	−	0.291583i
$459$	8.55347	−	26.3249i	0.399242	−	1.22874i
$460$	18.4185	+	13.3818i	0.858766	+	0.623930i
$461$	−34.0250			−1.58470			−0.792351	−	0.610066i	$-0.791143\pi$
$461$	−34.0250			−1.58470			−0.792351	+	0.610066i	$0.791143\pi$
$462$	3.65181	+	2.53602i	0.169898	+	0.117986i
$463$	21.0000			0.975955			0.487977	−	0.872856i	$-0.337735\pi$
$463$	21.0000			0.975955			0.487977	+	0.872856i	$0.337735\pi$
$464$	−2.25747	−	1.64015i	−0.104800	−	0.0761418i
$465$	13.7182	−	42.2203i	0.636167	−	1.95792i
$466$	0.754006	+	2.32059i	0.0349287	+	0.107499i
$467$	−3.36590	+	2.44547i	−0.155755	+	0.113163i	−0.662933	−	0.748679i	$-0.730689\pi$
$467$	−3.36590	+	2.44547i	−0.155755	+	0.113163i	0.507178	+	0.861841i	$0.330689\pi$
$468$	1.59315	−	1.15749i	0.0736432	−	0.0535049i
$469$	1.89853	+	5.84307i	0.0876659	+	0.269808i
$470$	9.46852	−	29.1411i	0.436750	−	1.34418i
$471$	2.99789	+	2.17810i	0.138136	+	0.100361i
$472$	−7.28815			−0.335465
$473$	31.6930	−	0.675900i	1.45724	−	0.0310779i
$474$	14.3671			0.659901
$475$	−7.31808	−	5.31690i	−0.335777	−	0.243956i
$476$	−1.30246	+	4.00855i	−0.0596979	+	0.183731i
$477$	1.83076	+	5.63451i	0.0838249	+	0.257987i
$478$	−5.76241	+	4.18664i	−0.263567	+	0.191492i
$479$	−27.3944	+	19.9032i	−1.25168	+	0.909400i	−0.998318	−	0.0579705i	$-0.981537\pi$
$479$	−27.3944	+	19.9032i	−1.25168	+	0.909400i	−0.253364	+	0.967371i	$0.581537\pi$
$480$	1.85180	+	5.69925i	0.0845226	+	0.260134i
$481$	11.2286	−	34.5581i	0.511981	−	1.57572i
$482$	−12.2602	−	8.90756i	−0.558437	−	0.405728i
$483$	−8.14330			−0.370533
$484$	3.84211	+	10.3072i	0.174642	+	0.468509i
$485$	30.4186			1.38124
$486$	−3.69488	−	2.68449i	−0.167603	−	0.121771i
$487$	2.24994	−	6.92461i	0.101955	−	0.313784i	−0.887049	−	0.461675i	$-0.847249\pi$
$487$	2.24994	−	6.92461i	0.101955	−	0.313784i	0.989004	+	0.147891i	$0.0472485\pi$
$488$	−2.55429	−	7.86129i	−0.115627	−	0.355864i
$489$	−23.3870	+	16.9916i	−1.05760	+	0.768388i
$490$	−19.0929	+	13.8718i	−0.862529	+	0.626664i
$491$	−9.01211	−	27.7364i	−0.406711	−	1.25173i	−0.919458	−	0.393188i	$-0.871372\pi$
$491$	−9.01211	−	27.7364i	−0.406711	−	1.25173i	0.512747	−	0.858540i	$-0.328628\pi$
$492$	−3.15398	+	9.70694i	−0.142192	+	0.437623i
$493$	−11.3492	−	8.24570i	−0.511144	−	0.371368i
$494$	−4.44225			−0.199866
$495$	−5.50887	+	0.117485i	−0.247605	+	0.00528056i
$496$	−7.40805			−0.332631
$497$	8.42259	+	6.11937i	0.377805	+	0.274491i
$498$	−0.645724	+	1.98733i	−0.0289356	+	0.0890545i
$499$	−1.66839	−	5.13479i	−0.0746876	−	0.229865i	0.906743	−	0.421685i	$-0.138561\pi$
$499$	−1.66839	−	5.13479i	−0.0746876	−	0.229865i	−0.981430	+	0.191820i	$0.938561\pi$
$500$	−12.2664	+	8.91205i	−0.548570	+	0.398559i
$501$	10.3751	−	7.53793i	0.463524	−	0.336770i
$502$	5.39652	+	16.6088i	0.240858	+	0.741286i
$503$	5.73010	−	17.6354i	0.255492	−	0.786325i	−0.738240	−	0.674538i	$-0.764343\pi$
$503$	5.73010	−	17.6354i	0.255492	−	0.786325i	0.993732	−	0.111786i	$-0.0356572\pi$
$504$	0.300668	+	0.218448i	0.0133928	+	0.00973045i
$505$	−46.0448			−2.04897
$506$	−16.5485	−	11.4922i	−0.735670	−	0.510890i
$507$	−10.7669			−0.478173
$508$	0.969791	+	0.704594i	0.0430275	+	0.0312613i
$509$	2.21819	−	6.82688i	0.0983194	−	0.302596i	−0.889785	−	0.456380i	$-0.849146\pi$
$509$	2.21819	−	6.82688i	0.0983194	−	0.302596i	0.988105	+	0.153784i	$0.0491459\pi$
$510$	9.30977	+	28.6525i	0.412243	+	1.26875i
$511$	−5.12677	+	3.72482i	−0.226795	+	0.164776i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	1.70136	+	5.23626i	0.0751170	+	0.231186i
$514$	3.55482	−	10.9406i	0.156796	−	0.482569i
$515$	−15.1494	−	11.0067i	−0.667561	−	0.485012i
$516$	−15.2829			−0.672792
$517$	−7.82753	+	25.9616i	−0.344255	+	1.14179i
$518$	6.85766			0.301308
$519$	3.03443	+	2.20464i	0.133197	+	0.0967730i
$520$	−5.14466	+	15.8336i	−0.225608	+	0.694351i
$521$	−1.14273	−	3.51695i	−0.0500637	−	0.154080i	0.922899	−	0.385042i	$-0.125813\pi$
$521$	−1.14273	−	3.51695i	−0.0500637	−	0.154080i	−0.972963	+	0.230961i	$0.925813\pi$
$522$	−1.00073	+	0.727071i	−0.0438006	+	0.0318230i
$523$	−22.5219	+	16.3631i	−0.984814	+	0.715509i	−0.958779	−	0.284152i	$-0.908288\pi$
$523$	−22.5219	+	16.3631i	−0.984814	+	0.715509i	−0.0260346	+	0.999661i	$0.508288\pi$
$524$	2.65813	+	8.18087i	0.116121	+	0.357383i
$525$	3.74712	−	11.5324i	0.163538	−	0.503317i
$526$	13.8981	+	10.0976i	0.605986	+	0.440274i
$527$	−37.2434			−1.62235
$528$	−1.74594	−	5.00754i	−0.0759823	−	0.217925i
$529$	13.9020			0.604437
$530$	−40.5214	−	29.4405i	−1.76014	−	1.27881i
$531$	−0.998376	+	3.07269i	−0.0433258	+	0.133343i
$532$	−0.259070	−	0.797336i	−0.0112321	−	0.0345689i
$533$	−22.9402	+	16.6670i	−0.993650	+	0.721929i
$534$	−13.5716	+	9.86036i	−0.587302	+	0.426700i
$535$	−4.06296	−	12.5045i	−0.175657	−	0.540617i
$536$	2.26455	−	6.96957i	0.0978137	−	0.301039i
$537$	−17.2288	−	12.5175i	−0.743477	−	0.540168i
$538$	−11.0127			−0.474790
$539$	16.6309	−	12.6335i	0.716345	−	0.544164i
$540$	20.6341			0.887950
$541$	−30.8354	−	22.4032i	−1.32572	−	0.963191i	−0.999842	−	0.0177784i	$-0.994341\pi$
$541$	−30.8354	−	22.4032i	−1.32572	−	0.963191i	−0.325876	−	0.945412i	$-0.605659\pi$
$542$	−2.44037	+	7.51068i	−0.104823	+	0.322611i
$543$	0.465843	+	1.43372i	0.0199913	+	0.0615267i
$544$	4.06727	−	2.95504i	0.174383	−	0.126696i
$545$	14.1424	−	10.2750i	0.605793	−	0.440135i
$546$	−1.84018	−	5.66350i	−0.0787526	−	0.242375i
$547$	−7.85387	+	24.1717i	−0.335807	+	1.03351i	0.630516	+	0.776176i	$0.282843\pi$
$547$	−7.85387	+	24.1717i	−0.335807	+	1.03351i	−0.966323	+	0.257332i	$0.917157\pi$
$548$	−4.89825	−	3.55879i	−0.209243	−	0.152024i
$549$	−3.66422			−0.156385
$550$	23.8898	−	18.1477i	1.01867	−	0.773819i
$551$	2.79038			0.118874
$552$	7.85820	+	5.70932i	0.334467	+	0.243005i
$553$	−2.32780	+	7.16422i	−0.0989880	+	0.304654i
$554$	−2.37173	−	7.29943i	−0.100765	−	0.310123i
$555$	39.6561	−	28.8118i	1.68331	−	1.22299i
$556$	3.18190	−	2.31179i	0.134943	−	0.0980415i
$557$	2.82563	+	8.69641i	0.119726	+	0.368479i	0.992903	−	0.118924i	$-0.0379444\pi$
$557$	2.82563	+	8.69641i	0.119726	+	0.368479i	−0.873177	+	0.487403i	$0.837944\pi$
$558$	−1.01480	+	3.12324i	−0.0429599	+	0.132217i
$559$	−34.3500	−	24.9567i	−1.45285	−	1.05556i
$560$	−3.14200			−0.132774
$561$	−8.77757	−	25.1750i	−0.370589	−	1.06289i
$562$	−16.5030			−0.696136
$563$	−25.3618	−	18.4264i	−1.06887	−	0.776581i	−0.0931634	−	0.995651i	$-0.529698\pi$
$563$	−25.3618	−	18.4264i	−1.06887	−	0.776581i	−0.975709	+	0.219069i	$0.929698\pi$
$564$	4.03972	−	12.4330i	0.170103	−	0.523523i
$565$	20.2578	+	62.3470i	0.852251	+	2.62296i
$566$	5.85016	−	4.25039i	0.245900	−	0.178657i
$567$	−5.06900	+	3.68285i	−0.212878	+	0.154665i
$568$	−3.83738	−	11.8103i	−0.161013	−	0.495547i
$569$	−12.6165	+	38.8297i	−0.528913	+	1.62783i	0.227533	+	0.973770i	$0.426934\pi$
$569$	−12.6165	+	38.8297i	−0.528913	+	1.62783i	−0.756446	+	0.654056i	$0.773066\pi$
$570$	−4.84807	−	3.52233i	−0.203063	−	0.147534i
$571$	40.1015			1.67820			0.839098	−	0.543980i	$-0.183083\pi$
$571$	40.1015			1.67820			0.839098	+	0.543980i	$0.183083\pi$
$572$	4.25304	−	14.1061i	0.177828	−	0.589805i
$573$	25.9795			1.08531
$574$	−4.32941	−	3.14550i	−0.180706	−	0.131291i
$575$	−16.9804	+	52.2602i	−0.708131	+	2.17940i
$576$	−0.136986	−	0.421600i	−0.00570776	−	0.0175667i
$577$	−16.3114	+	11.8509i	−0.679053	+	0.493361i	−0.873044	−	0.487642i	$-0.837857\pi$
$577$	−16.3114	+	11.8509i	−0.679053	+	0.493361i	0.193990	+	0.981003i	$0.437857\pi$
$578$	6.69460	−	4.86391i	0.278459	−	0.202312i
$579$	6.73860	+	20.7393i	0.280047	+	0.861895i
$580$	3.23159	−	9.94583i	0.134185	−	0.412978i
$581$	−0.886374	−	0.643988i	−0.0367730	−	0.0267171i
$582$	12.9780			0.537957
$583$	36.4073	+	25.2833i	1.50784	+	1.04713i
$584$	7.55877			0.312784
$585$	5.97071	+	4.33798i	0.246859	+	0.179353i
$586$	0.578042	−	1.77903i	0.0238787	−	0.0734910i
$587$	−13.3748	−	41.1635i	−0.552038	−	1.69900i	−0.703639	−	0.710557i	$-0.748443\pi$
$587$	−13.3748	−	41.1635i	−0.552038	−	1.69900i	0.151601	−	0.988442i	$-0.451557\pi$
$588$	−8.14594	+	5.91837i	−0.335933	+	0.244069i
$589$	5.99324	−	4.35434i	0.246947	−	0.179418i
$590$	−8.44055	−	25.9773i	−0.347492	−	1.06947i
$591$	−7.37651	+	22.7026i	−0.303429	+	0.933859i
$592$	−6.61757	−	4.80794i	−0.271980	−	0.197605i
$593$	47.4219			1.94739			0.973693	−	0.227865i	$-0.0731743\pi$
$593$	47.4219			1.94739			0.973693	+	0.227865i	$0.0731743\pi$
$594$	−18.2563	+	0.389343i	−0.749064	+	0.0159749i
$595$	−15.7962			−0.647579
$596$	17.4219	+	12.6577i	0.713627	+	0.518480i
$597$	−3.67342	+	11.3056i	−0.150343	+	0.462708i
$598$	8.33894	+	25.6646i	0.341005	+	1.04950i
$599$	0.894893	−	0.650178i	0.0365644	−	0.0265656i	−0.569353	−	0.822093i	$-0.692806\pi$
$599$	0.894893	−	0.650178i	0.0365644	−	0.0265656i	0.605917	+	0.795528i	$0.292806\pi$
$600$	−11.7014	+	8.50156i	−0.477707	+	0.347075i
$601$	6.40240	+	19.7046i	0.261159	+	0.803766i	0.992553	+	0.121811i	$0.0388701\pi$
$601$	6.40240	+	19.7046i	0.261159	+	0.803766i	−0.731394	+	0.681955i	$0.761130\pi$
$602$	2.47618	−	7.62091i	0.100922	−	0.310605i
$603$	−2.62816	−	1.90947i	−0.107027	−	0.0777596i
$604$	0.130125			0.00529472
$605$	−32.2885	+	25.6315i	−1.31272	+	1.04207i
$606$	−19.6449			−0.798020
$607$	−4.63034	−	3.36414i	−0.187940	−	0.136546i	0.489837	−	0.871814i	$-0.337056\pi$
$607$	−4.63034	−	3.36414i	−0.187940	−	0.136546i	−0.677777	+	0.735268i	$0.737056\pi$
$608$	−0.309017	+	0.951057i	−0.0125323	+	0.0385704i
$609$	1.15590	+	3.55750i	0.0468395	+	0.144157i
$610$	25.0620	−	18.2086i	1.01473	−	0.737246i
$611$	29.3826	−	21.3477i	1.18869	−	0.863635i
$612$	−0.688687	−	2.11956i	−0.0278385	−	0.0856782i
$613$	9.11368	−	28.0490i	0.368098	−	1.13289i	−0.579920	−	0.814673i	$-0.696916\pi$
$613$	9.11368	−	28.0490i	0.368098	−	1.13289i	0.948018	−	0.318216i	$-0.103084\pi$
$614$	2.57529	+	1.87105i	0.103930	+	0.0755096i
$615$	−38.2514			−1.54244
$616$	2.77992	−	0.0592860i	0.112006	−	0.00238870i
$617$	−20.9449			−0.843211			−0.421605	−	0.906779i	$-0.638533\pi$
$617$	−20.9449			−0.843211			−0.421605	+	0.906779i	$0.638533\pi$
$618$	−6.46345	−	4.69597i	−0.259998	−	0.188900i
$619$	−13.6378	+	41.9729i	−0.548151	+	1.68703i	0.165228	+	0.986255i	$0.447164\pi$
$619$	−13.6378	+	41.9729i	−0.548151	+	1.68703i	−0.713379	+	0.700779i	$0.752836\pi$
$620$	−8.57941	−	26.4047i	−0.344557	−	1.06044i
$621$	27.0581	−	19.6589i	1.08580	−	0.788883i
$622$	14.6105	−	10.6151i	0.585827	−	0.425628i
$623$	−2.71801	−	8.36518i	−0.108895	−	0.335144i
$624$	−2.19496	+	6.75538i	−0.0878686	+	0.270432i
$625$	−9.38097	−	6.81567i	−0.375239	−	0.272627i
$626$	11.7769			0.470699
$627$	4.35585	+	3.02495i	0.173956	+	0.120805i
$628$	2.31749			0.0924781
$629$	−33.2693	−	24.1716i	−1.32653	−	0.963784i
$630$	−0.430410	+	1.32467i	−0.0171480	+	0.0527760i
$631$	−11.8254	−	36.3947i	−0.470760	−	1.44885i	−0.851591	−	0.524207i	$-0.824362\pi$
$631$	−11.8254	−	36.3947i	−0.470760	−	1.44885i	0.380831	−	0.924645i	$-0.375638\pi$
$632$	7.26918	−	5.28137i	0.289152	−	0.210081i
$633$	4.80844	−	3.49353i	0.191118	−	0.138855i
$634$	−1.90322	−	5.85752i	−0.0755866	−	0.232632i
$635$	−1.38827	+	4.27265i	−0.0550918	+	0.169555i
$636$	−17.2883	−	12.5607i	−0.685527	−	0.498065i
$637$	−27.9735			−1.10835
$638$	−2.67153	+	8.86067i	−0.105767	+	0.350797i
$639$	−5.50487			−0.217769
$640$	3.03200	+	2.20287i	0.119850	+	0.0870762i
$641$	−13.2456	+	40.7658i	−0.523171	+	1.61015i	0.244735	+	0.969590i	$0.421299\pi$
$641$	−13.2456	+	40.7658i	−0.523171	+	1.61015i	−0.767905	+	0.640563i	$0.778701\pi$
$642$	−1.73345	−	5.33502i	−0.0684139	−	0.210556i
$643$	−24.0858	+	17.4994i	−0.949852	+	0.690108i	−0.950772	−	0.309892i	$-0.899707\pi$
$643$	−24.0858	+	17.4994i	−0.949852	+	0.690108i	0.000919804		1.00000i	$0.499707\pi$
$644$	−4.12020	+	2.99350i	−0.162358	+	0.117960i
$645$	−17.6994	−	54.4732i	−0.696914	−	2.14488i
$646$	−1.55356	+	4.78136i	−0.0611240	+	0.188120i
$647$	1.46637	+	1.06538i	0.0576488	+	0.0418843i	0.616236	−	0.787561i	$-0.288657\pi$
$647$	1.46637	+	1.06538i	0.0576488	+	0.0418843i	−0.558588	+	0.829445i	$0.688657\pi$
$648$	7.47360			0.293591
$649$	7.95805	+	22.8245i	0.312381	+	0.895941i
$650$	−40.1831			−1.57611
$651$	8.03409	+	5.83711i	0.314881	+	0.228774i
$652$	−5.58674	+	17.1942i	−0.218794	+	0.673378i
$653$	5.54316	+	17.0601i	0.216920	+	0.667613i	0.999012	+	0.0444486i	$0.0141531\pi$
$653$	5.54316	+	17.0601i	0.216920	+	0.667613i	−0.782091	+	0.623164i	$0.785847\pi$
$654$	6.03381	−	4.38382i	0.235941	−	0.171421i
$655$	−26.0809	+	18.9489i	−1.01906	+	0.740393i
$656$	1.97251	+	6.07075i	0.0770134	+	0.237023i
$657$	1.03545	−	3.18678i	0.0403966	−	0.124328i
$658$	5.54526	+	4.02887i	0.216177	+	0.157062i
$659$	−28.4253			−1.10729			−0.553646	−	0.832752i	$-0.686764\pi$
$659$	−28.4253			−1.10729			−0.553646	+	0.832752i	$0.686764\pi$
$660$	15.8265	−	12.0224i	0.616045	−	0.467972i
$661$	22.7419			0.884556			0.442278	−	0.896878i	$-0.354171\pi$
$661$	22.7419			0.884556			0.442278	+	0.896878i	$0.354171\pi$
$662$	3.84619	+	2.79442i	0.149486	+	0.108608i
$663$	−11.0350	+	33.9622i	−0.428563	+	1.31898i
$664$	0.403837	+	1.24288i	0.0156719	+	0.0482332i
$665$	2.54193	−	1.84682i	0.0985718	−	0.0716166i
$666$	−2.93355	+	2.13135i	−0.113673	+	0.0825880i
$667$	−5.23807	−	16.1211i	−0.202819	−	0.624212i
$668$	2.47842	−	7.62780i	0.0958931	−	0.295129i
$669$	23.2231	+	16.8726i	0.897857	+	0.652331i
$670$	27.4644			1.06104
$671$	−21.8304	+	16.5832i	−0.842752	+	0.640187i
$672$	−1.34053			−0.0517119
$673$	−37.2922	−	27.0944i	−1.43751	−	1.04441i	−0.988556	−	0.150856i	$-0.951797\pi$
$673$	−37.2922	−	27.0944i	−1.43751	−	1.04441i	−0.448953	−	0.893555i	$-0.648203\pi$
$674$	−10.1683	+	31.2949i	−0.391670	+	1.20544i
$675$	15.3899	+	47.3653i	0.592359	+	1.82309i
$676$	−5.44761	+	3.95792i	−0.209524	+	0.152228i
$677$	25.1391	−	18.2646i	0.966172	−	0.701965i	0.0115963	−	0.999933i	$-0.496309\pi$
$677$	25.1391	−	18.2646i	0.966172	−	0.701965i	0.954576	+	0.297967i	$0.0963087\pi$
$678$	8.64293	+	26.6002i	0.331930	+	1.02157i
$679$	−2.10274	+	6.47158i	−0.0806959	+	0.248356i
$680$	15.2431	+	11.0748i	0.584547	+	0.424698i
$681$	−28.4795			−1.09134
$682$	8.08897	+	23.2000i	0.309743	+	0.888374i
$683$	−39.9779			−1.52971			−0.764856	−	0.644201i	$-0.777190\pi$
$683$	−39.9779			−1.52971			−0.764856	+	0.644201i	$0.777190\pi$
$684$	0.358634	+	0.260563i	0.0137127	+	0.00996288i
$685$	7.01192	−	21.5805i	0.267912	−	0.824547i
$686$	−3.44489	−	10.6023i	−0.131527	−	0.404797i
$687$	8.48763	−	6.16662i	0.323823	−	0.235271i
$688$	−7.73256	+	5.61803i	−0.294801	+	0.214185i
$689$	−18.3460	−	56.4632i	−0.698927	−	2.15108i
$690$	−11.2491	+	34.6212i	−0.428247	+	1.31801i
$691$	−5.21196	−	3.78671i	−0.198272	−	0.144053i	0.484219	−	0.874947i	$-0.339104\pi$
$691$	−5.21196	−	3.78671i	−0.198272	−	0.144053i	−0.682492	+	0.730893i	$0.739104\pi$
$692$	2.34574			0.0891715
$693$	0.355816	−	1.18014i	0.0135163	−	0.0448297i
$694$	−30.5079			−1.15807
$695$	11.9250	+	8.66400i	0.452340	+	0.328644i
$696$	1.37875	−	4.24336i	0.0522615	−	0.160844i
$697$	9.91662	+	30.5202i	0.375619	+	1.15604i
$698$	15.3381	−	11.1438i	0.580554	−	0.421797i
$699$	−3.15639	+	2.29325i	−0.119386	+	0.0867387i
$700$	−2.34346	−	7.21242i	−0.0885744	−	0.272604i
$701$	−10.9495	+	33.6991i	−0.413557	+	1.27280i	0.499978	+	0.866038i	$0.333342\pi$
$701$	−10.9495	+	33.6991i	−0.413557	+	1.27280i	−0.913535	+	0.406760i	$0.866658\pi$
$702$	19.7868	+	14.3760i	0.746805	+	0.542585i
$703$	8.17976			0.308506
$704$	−2.72416	−	1.89181i	−0.102671	−	0.0713003i
$705$	48.9937			1.84521
$706$	1.74851	+	1.27037i	0.0658062	+	0.0478110i
$707$	3.18293	−	9.79606i	0.119707	−	0.368419i
$708$	−3.60114	−	11.0832i	−0.135339	−	0.416531i
$709$	24.2799	−	17.6404i	0.911850	−	0.662498i	−0.0296317	−	0.999561i	$-0.509433\pi$
$709$	24.2799	−	17.6404i	0.911850	−	0.662498i	0.941482	+	0.337063i	$0.109433\pi$
$710$	37.6514	−	27.3554i	1.41303	−	1.02663i
$711$	−1.23085	−	3.78816i	−0.0461604	−	0.142067i
$712$	−3.24203	+	9.97793i	−0.121500	+	0.373939i
$713$	−36.4072	−	26.4514i	−1.36346	−	0.990611i
$714$	−6.73939			−0.252215
$715$	55.2042	−	1.17731i	2.06452	−	0.0440290i
$716$	−13.3186			−0.497738
$717$	−9.21392	−	6.69431i	−0.344100	−	0.250003i
$718$	−3.39322	+	10.4432i	−0.126634	+	0.389739i
$719$	5.46922	+	16.8325i	0.203967	+	0.627747i	0.999754	+	0.0221702i	$0.00705756\pi$
$719$	5.46922	+	16.8325i	0.203967	+	0.627747i	−0.795787	+	0.605577i	$0.792942\pi$
$720$	1.34407	−	0.976526i	0.0500906	−	0.0363930i
$721$	3.38890	−	2.46218i	0.126209	−	0.0916964i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	7.48795	−	23.0455i	0.278480	−	0.857073i
$724$	0.762737	+	0.554161i	0.0283469	+	0.0205952i
$725$	25.2408			0.937420
$726$	−13.7758	+	10.9356i	−0.511269	+	0.405859i
$727$	−18.2854			−0.678167			−0.339084	−	0.940756i	$-0.610117\pi$
$727$	−18.2854			−0.678167			−0.339084	+	0.940756i	$0.610117\pi$
$728$	−3.01298	−	2.18906i	−0.111668	−	0.0811319i
$729$	9.18506	−	28.2687i	0.340187	−	1.04699i
$730$	8.75396	+	26.9419i	0.323998	+	0.997165i
$731$	−38.8748	+	28.2442i	−1.43784	+	1.04465i
$732$	10.6926	−	7.76866i	0.395212	−	0.287138i
$733$	−2.17422	−	6.69155i	−0.0803066	−	0.247158i	0.902840	−	0.429976i	$-0.141478\pi$
$733$	−2.17422	−	6.69155i	−0.0803066	−	0.247158i	−0.983147	+	0.182818i	$0.941478\pi$
$734$	−5.63691	+	17.3486i	−0.208062	+	0.640349i
$735$	−30.5290	−	22.1806i	−1.12608	−	0.818143i
$736$	6.07470			0.223917
$737$	−24.2995	+	0.518223i	−0.895083	+	0.0190890i
$738$	2.82963			0.104160
$739$	7.77003	+	5.64526i	0.285825	+	0.207664i	0.721454	−	0.692462i	$-0.243474\pi$
$739$	7.77003	+	5.64526i	0.285825	+	0.207664i	−0.435629	+	0.900126i	$0.643474\pi$
$740$	9.47314	−	29.1553i	0.348240	−	1.07177i
$741$	−2.19496	−	6.75538i	−0.0806337	−	0.248165i
$742$	9.06459	−	6.58581i	0.332772	−	0.241773i
$743$	10.2860	−	7.47318i	0.377355	−	0.274165i	−0.382899	−	0.923790i	$-0.625074\pi$
$743$	10.2860	−	7.47318i	0.377355	−	0.274165i	0.760254	+	0.649626i	$0.225074\pi$
$744$	−3.66038	−	11.2655i	−0.134196	−	0.413013i
$745$	−24.9396	+	76.7563i	−0.913717	+	2.81213i
$746$	−2.82458	−	2.05217i	−0.103415	−	0.0751355i
$747$	0.579320			0.0211962
$748$	−13.6955	−	9.51093i	−0.500757	−	0.347754i
$749$	2.94120			0.107469
$750$	−19.6136	−	14.2501i	−0.716187	−	0.520340i
$751$	6.08880	−	18.7394i	0.222183	−	0.683810i	−0.776382	−	0.630263i	$-0.782947\pi$
$751$	6.08880	−	18.7394i	0.222183	−	0.683810i	0.998565	−	0.0535473i	$-0.0170528\pi$
$752$	−2.52645	−	7.77563i	−0.0921303	−	0.283548i
$753$	−22.5907	+	16.4131i	−0.823250	+	0.598126i
$754$	10.0282	−	7.28594i	0.365207	−	0.265338i
$755$	0.150701	+	0.463809i	0.00548455	+	0.0168797i
$756$	−1.42637	+	4.38991i	−0.0518766	+	0.159660i
$757$	0.960600	+	0.697917i	0.0349136	+	0.0253662i	0.605105	−	0.796146i	$-0.293131\pi$
$757$	0.960600	+	0.697917i	0.0349136	+	0.0253662i	−0.570192	+	0.821512i	$0.693131\pi$
$758$	−29.6815			−1.07808
$759$	9.29954	−	30.8438i	0.337552	−	1.11956i
$760$	−3.74775			−0.135945
$761$	31.0198	+	22.5372i	1.12447	+	0.816972i	0.984880	−	0.173238i	$-0.0554230\pi$
$761$	31.0198	+	22.5372i	1.12447	+	0.816972i	0.139585	+	0.990210i	$0.455423\pi$
$762$	−0.592302	+	1.82292i	−0.0214568	+	0.0660373i
$763$	1.20840	+	3.71908i	0.0437471	+	0.134640i
$764$	13.1446	−	9.55012i	0.475556	−	0.345511i
$765$	6.75722	−	4.90941i	0.244308	−	0.177500i
$766$	−3.77808	−	11.6277i	−0.136508	−	0.420128i
$767$	10.0047	−	30.7912i	0.361248	−	1.11181i
$768$	1.29359	+	0.939851i	0.0466785	+	0.0339139i
$769$	31.3585			1.13082			0.565409	−	0.824811i	$-0.308718\pi$
$769$	31.3585			1.13082			0.565409	+	0.824811i	$0.308718\pi$
$770$	3.43080	+	9.83989i	0.123637	+	0.354605i
$771$	18.3939			0.662442
$772$	11.0333	+	8.01615i	0.397097	+	0.288508i
$773$	−5.99549	+	18.4522i	−0.215643	+	0.663681i	0.783464	+	0.621437i	$0.213451\pi$
$773$	−5.99549	+	18.4522i	−0.215643	+	0.663681i	−0.999107	+	0.0422440i	$0.986549\pi$
$774$	1.30931	+	4.02964i	0.0470621	+	0.144842i
$775$	54.2127	−	39.3879i	1.94738	−	1.41485i
$776$	6.56639	−	4.77076i	0.235719	−	0.171260i
$777$	3.38843	+	10.4285i	0.121559	+	0.374121i
$778$	6.54845	−	20.1540i	0.234773	−	0.722558i
$779$	−5.16409	−	3.75193i	−0.185023	−	0.134427i
$780$	−26.6204			−0.953163
$781$	−32.7964	+	24.9134i	−1.17355	+	0.891473i
$782$	30.5401			1.09211
$783$	−12.4290	−	9.03019i	−0.444176	−	0.322713i
$784$	−1.94592	+	5.98893i	−0.0694972	+	0.213890i
$785$	2.68393	+	8.26030i	0.0957937	+	0.294823i
$786$	−11.1273	+	8.08448i	−0.396899	+	0.288364i
$787$	8.30469	−	6.03371i	0.296030	−	0.215079i	−0.429849	−	0.902901i	$-0.641433\pi$
$787$	8.30469	−	6.03371i	0.296030	−	0.215079i	0.725879	+	0.687822i	$0.241433\pi$
$788$	4.61329	+	14.1982i	0.164342	+	0.505792i
$789$	−8.48829	+	26.1243i	−0.302191	+	0.930049i
$790$	27.2431	+	19.7933i	0.969265	+	0.704212i
$791$	−14.6647			−0.521417
$792$	−1.17076	+	0.889355i	−0.0416011	+	0.0316019i
$793$	36.7190			1.30393
$794$	25.6320	+	18.6227i	0.909646	+	0.660896i
$795$	24.7485	−	76.1681i	0.877739	−	2.70140i
$796$	2.29737	+	7.07056i	0.0814280	+	0.250610i
$797$	−5.14012	+	3.73452i	−0.182073	+	0.132283i	−0.675088	−	0.737737i	$-0.735894\pi$
$797$	−5.14012	+	3.73452i	−0.182073	+	0.132283i	0.493016	+	0.870020i	$0.335894\pi$
$798$	1.08451	−	0.787941i	0.0383912	−	0.0278928i
$799$	−12.7016	−	39.0914i	−0.449349	−	1.38295i
$800$	−2.79526	+	8.60292i	−0.0988273	+	0.304159i
$801$	3.76258	+	2.73368i	0.132944	+	0.0965897i
$802$	11.3101			0.399375
$803$	−8.25354	−	23.6720i	−0.291261	−	0.835367i
$804$	11.7176			0.413249
$805$	−15.4415	−	11.2189i	−0.544241	−	0.395414i
$806$	10.1693	−	31.2978i	0.358197	−	1.10242i
$807$	−5.44145	−	16.7471i	−0.191548	−	0.589525i
$808$	−9.93957	+	7.22152i	−0.349673	+	0.254052i
$809$	−12.6239	+	9.17178i	−0.443832	+	0.322463i	−0.787156	−	0.616754i	$-0.788447\pi$
$809$	−12.6239	+	9.17178i	−0.443832	+	0.322463i	0.343324	+	0.939217i	$0.388447\pi$
$810$	8.65532	+	26.6383i	0.304117	+	0.935975i
$811$	−0.723424	+	2.22647i	−0.0254029	+	0.0781819i	−0.962954	−	0.269665i	$-0.913087\pi$
$811$	−0.723424	+	2.22647i	−0.0254029	+	0.0781819i	0.937551	+	0.347847i	$0.113087\pi$
$812$	1.89259	+	1.37505i	0.0664169	+	0.0482547i
$813$	−12.6274			−0.442861
$814$	−7.83135	+	25.9743i	−0.274489	+	0.910398i
$815$	−67.7559			−2.37339
$816$	6.50344	+	4.72503i	0.227666	+	0.165409i
$817$	2.95357	−	9.09016i	0.103332	−	0.318025i
$818$	12.2814	+	37.7983i	0.429410	+	1.32159i
$819$	−1.33564	+	0.970402i	−0.0466712	+	0.0339086i
$820$	−19.3537	+	14.0613i	−0.675861	+	0.491042i
$821$	−15.5177	−	47.7584i	−0.541570	−	1.66678i	−0.729009	−	0.684504i	$-0.760019\pi$
$821$	−15.5177	−	47.7584i	−0.541570	−	1.66678i	0.187439	−	0.982276i	$-0.439981\pi$
$822$	2.99162	−	9.20725i	0.104345	−	0.321140i
$823$	32.5353	+	23.6383i	1.13411	+	0.823980i	0.986288	−	0.165034i	$-0.0527735\pi$
$823$	32.5353	+	23.6383i	1.13411	+	0.823980i	0.147823	+	0.989014i	$0.452773\pi$
$824$	−4.99650			−0.174061
$825$	39.4015	+	27.3626i	1.37178	+	0.952643i
$826$	6.11016			0.212600
$827$	21.1504	+	15.3667i	0.735472	+	0.534352i	0.891290	−	0.453434i	$-0.149801\pi$
$827$	21.1504	+	15.3667i	0.735472	+	0.534352i	−0.155817	+	0.987786i	$0.549801\pi$
$828$	0.832151	−	2.56110i	0.0289192	−	0.0890042i
$829$	−8.68049	−	26.7158i	−0.301486	−	0.927878i	−0.980965	−	0.194184i	$-0.937794\pi$
$829$	−8.68049	−	26.7158i	−0.301486	−	0.927878i	0.679479	−	0.733695i	$-0.262206\pi$
$830$	−3.96235	+	2.87882i	−0.137535	+	0.0999251i
$831$	9.92843	−	7.21342i	0.344413	−	0.250231i
$832$	1.37273	+	4.22483i	0.0475909	+	0.146470i
$833$	−9.78298	+	30.1089i	−0.338960	+	1.04321i
$834$	5.08776	+	3.69647i	0.176175	+	0.127998i
$835$	30.0583			1.04021
$836$	3.31587	−	0.0707159i	0.114682	−	0.00244576i
$837$	−40.7867			−1.40979
$838$	10.1966	+	7.40828i	0.352237	+	0.255915i
$839$	2.46370	−	7.58250i	0.0850565	−	0.261777i	−0.899478	−	0.436965i	$-0.856053\pi$
$839$	2.46370	−	7.58250i	0.0850565	−	0.261777i	0.984535	+	0.175188i	$0.0560533\pi$
$840$	−1.55249	−	4.77807i	−0.0535660	−	0.164859i
$841$	17.1623	−	12.4691i	0.591803	−	0.429970i
$842$	−2.63935	+	1.91760i	−0.0909578	+	0.0660847i
$843$	−8.15426	−	25.0962i	−0.280848	−	0.864360i
$844$	1.14865	−	3.53519i	0.0395382	−	0.121686i
$845$	−20.4163	−	14.8333i	−0.702342	−	0.510281i
$846$	−3.62429			−0.124606
$847$	−3.22111	−	8.64123i	−0.110679	−	0.296916i
$848$	−13.3646			−0.458942
$849$	9.35422	+	6.79624i	0.321036	+	0.233246i
$850$	−14.0529	+	43.2505i	−0.482012	+	1.48348i
$851$	−15.3549	−	47.2577i	−0.526361	−	1.61997i
$852$	16.0639	−	11.6711i	0.550340	−	0.399845i
$853$	21.0754	−	15.3122i	0.721609	−	0.524279i	−0.165289	−	0.986245i	$-0.552856\pi$
$853$	21.0754	−	15.3122i	0.721609	−	0.524279i	0.886898	+	0.461966i	$0.152856\pi$
$854$	2.14144	+	6.59066i	0.0732784	+	0.225528i
$855$	−0.513390	+	1.58005i	−0.0175576	+	0.0540367i
$856$	−2.83823	−	2.06209i	−0.0970085	−	0.0704808i
$857$	33.7585			1.15317			0.576584	−	0.817038i	$-0.304385\pi$
$857$	33.7585			1.15317			0.576584	+	0.817038i	$0.304385\pi$
$858$	23.5527	−	0.502297i	0.804077	−	0.0171481i
$859$	9.57479			0.326688			0.163344	−	0.986569i	$-0.447772\pi$
$859$	9.57479			0.326688			0.163344	+	0.986569i	$0.447772\pi$
$860$	−28.9797	−	21.0550i	−0.988200	−	0.717969i
$861$	2.64420	−	8.13800i	0.0901140	−	0.277342i
$862$	−0.989295	−	3.04474i	−0.0336955	−	0.103704i
$863$	18.4597	−	13.4118i	0.628377	−	0.456542i	−0.227461	−	0.973787i	$-0.573042\pi$
$863$	18.4597	−	13.4118i	0.628377	−	0.456542i	0.855837	+	0.517245i	$0.173042\pi$
$864$	4.45423	−	3.23618i	0.151536	−	0.110097i
$865$	2.71664	+	8.36097i	0.0923686	+	0.284281i
$866$	1.06774	−	3.28617i	0.0362833	−	0.111668i
$867$	10.7045	+	7.77724i	0.363542	+	0.264129i
$868$	6.21068			0.210804
$869$	−24.4771	−	16.9983i	−0.830330	−	0.576627i
$870$	16.7215			0.566911
$871$	26.3367	+	19.1347i	0.892383	+	0.648354i
$872$	1.44137	−	4.43609i	0.0488111	−	0.150225i
$873$	−1.11185	−	3.42192i	−0.0376304	−	0.115814i
$874$	−4.91454	+	3.57062i	−0.166237	+	0.120778i
$875$	10.2838	−	7.47159i	0.347654	−	0.252586i
$876$	3.73485	+	11.4947i	0.126189	+	0.388370i
$877$	10.4646	−	32.2069i	0.353366	−	1.08755i	−0.603585	−	0.797299i	$-0.706262\pi$
$877$	10.4646	−	32.2069i	0.353366	−	1.08755i	0.956951	−	0.290250i	$-0.0937383\pi$
$878$	11.6448	+	8.46041i	0.392991	+	0.285525i
$879$	2.99100			0.100884
$880$	3.58812	−	11.9007i	0.120955	−	0.401174i
$881$	−10.2923			−0.346757			−0.173379	−	0.984855i	$-0.555468\pi$
$881$	−10.2923			−0.346757			−0.173379	+	0.984855i	$0.555468\pi$
$882$	2.25837	+	1.64080i	0.0760433	+	0.0552487i
$883$	−7.54942	+	23.2347i	−0.254058	+	0.781910i	0.739956	+	0.672656i	$0.234846\pi$
$883$	−7.54942	+	23.2347i	−0.254058	+	0.781910i	−0.994014	+	0.109255i	$0.965154\pi$
$884$	6.90130	+	21.2400i	0.232116	+	0.714379i
$885$	35.3335	−	25.6713i	1.18772	−	0.862930i
$886$	1.03083	−	0.748940i	0.0346313	−	0.0251611i
$887$	1.30830	+	4.02652i	0.0439283	+	0.135197i	0.970615	−	0.240637i	$-0.0773562\pi$
$887$	1.30830	+	4.02652i	0.0439283	+	0.135197i	−0.926687	+	0.375834i	$0.877356\pi$
$888$	4.04169	−	12.4391i	0.135630	−	0.417427i
$889$	−0.813043	−	0.590710i	−0.0272686	−	0.0198118i
$890$	−39.3192			−1.31798
$891$	−8.16054	−	23.4053i	−0.273388	−	0.784106i
$892$	17.9524			0.601091
$893$	6.61434	+	4.80560i	0.221341	+	0.160813i
$894$	−10.6404	+	32.7479i	−0.355869	+	1.09525i
$895$	−15.4245	−	47.4717i	−0.515583	−	1.58680i
$896$	−0.678255	+	0.492781i	−0.0226589	+	0.0164627i
$897$	−34.9081	+	25.3622i	−1.16555	+	0.846820i
$898$	−5.64891	−	17.3855i	−0.188506	−	0.580163i
$899$	−6.38778	+	19.6596i	−0.213044	+	0.655683i
$900$	3.24408	+	2.35696i	0.108136	+	0.0785654i
$901$	−67.1894			−2.23840
$902$	16.8581	−	12.8061i	0.561314	−	0.426396i
$903$	12.8127			0.426380
$904$	14.1513	+	10.2815i	0.470665	+	0.341958i
$905$	−1.09187	+	3.36043i	−0.0362950	+	0.111704i
$906$	0.0642960	+	0.197883i	0.00213609	+	0.00657422i
$907$	−29.7046	+	21.5816i	−0.986324	+	0.716606i	−0.959113	−	0.283023i	$-0.908663\pi$
$907$	−29.7046	+	21.5816i	−0.986324	+	0.716606i	−0.0272112	+	0.999630i	$0.508663\pi$
$908$	−14.4095	+	10.4691i	−0.478197	+	0.347431i
$909$	1.68301	+	5.17977i	0.0558219	+	0.171802i
$910$	4.31312	−	13.2744i	0.142979	−	0.440043i
$911$	23.8001	+	17.2918i	0.788531	+	0.572902i	0.907527	−	0.419993i	$-0.137968\pi$
$911$	23.8001	+	17.2918i	0.788531	+	0.572902i	−0.118996	+	0.992895i	$0.537968\pi$
$912$	−1.59897			−0.0529472
$913$	3.45142	−	2.62183i	0.114225	−	0.0867700i
$914$	18.6608			0.617244
$915$	40.0734	+	29.1150i	1.32479	+	0.962513i
$916$	2.02755	−	6.24015i	0.0669920	−	0.206180i
$917$	−2.22849	−	6.85859i	−0.0735912	−	0.226491i
$918$	22.3933	−	16.2697i	0.739088	−	0.536979i
$919$	27.4242	−	19.9248i	0.904640	−	0.657259i	−0.0350139	−	0.999387i	$-0.511148\pi$
$919$	27.4242	−	19.9248i	0.904640	−	0.657259i	0.939653	+	0.342128i	$0.111148\pi$
$920$	7.03523	+	21.6522i	0.231945	+	0.713853i
$921$	−1.57286	+	4.84077i	−0.0518275	+	0.159509i
$922$	−27.5268	−	19.9994i	−0.906546	−	0.658645i
$923$	55.1641			1.81575
$924$	1.46374	+	4.19816i	0.0481535	+	0.138109i
$925$	73.9913			2.43282
$926$	16.9894	+	12.3435i	0.558306	+	0.405633i
$927$	−0.684452	+	2.10653i	−0.0224804	+	0.0691874i
$928$	−0.862275	−	2.65381i	−0.0283056	−	0.0871156i
$929$	25.6918	−	18.6662i	0.842920	−	0.612417i	−0.0802650	−	0.996774i	$-0.525577\pi$
$929$	25.6918	−	18.6662i	0.842920	−	0.612417i	0.923185	+	0.384357i	$0.125577\pi$
$930$	35.9147	−	26.0936i	1.17769	−	0.855642i
$931$	−1.94592	−	5.98893i	−0.0637750	−	0.196279i
$932$	−0.754006	+	2.32059i	−0.0246983	+	0.0760135i
$933$	23.3617	+	16.9733i	0.764828	+	0.555680i
$934$	−4.16048			−0.136135
$935$	18.0390	−	59.8300i	0.589938	−	1.95665i
$936$	1.96924			0.0643665
$937$	16.3708	+	11.8941i	0.534810	+	0.388562i	0.822154	−	0.569265i	$-0.192772\pi$
$937$	16.3708	+	11.8941i	0.534810	+	0.388562i	−0.287344	+	0.957828i	$0.592772\pi$
$938$	−1.89853	+	5.84307i	−0.0619891	+	0.190783i
$939$	5.81907	+	17.9092i	0.189898	+	0.584446i
$940$	24.7889	−	18.0102i	0.808525	−	0.587428i
$941$	−29.7380	+	21.6059i	−0.969430	+	0.704332i	−0.955322	−	0.295568i	$-0.904491\pi$
$941$	−29.7380	+	21.6059i	−0.969430	+	0.704332i	−0.0141084	+	0.999900i	$0.504491\pi$
$942$	1.14509	+	3.52424i	0.0373092	+	0.114826i
$943$	−11.9824	+	36.8780i	−0.390200	+	1.20091i
$944$	−5.89624	−	4.28387i	−0.191906	−	0.139428i
$945$	−17.2990			−0.562736
$946$	26.0374	+	18.0818i	0.846550	+	0.587892i
$947$	30.2362			0.982544			0.491272	−	0.871006i	$-0.336532\pi$
$947$	30.2362			0.982544			0.491272	+	0.871006i	$0.336532\pi$
$948$	11.6232	+	8.44474i	0.377504	+	0.274273i
$949$	−10.3762	+	31.9346i	−0.336825	+	1.03664i
$950$	−2.79526	−	8.60292i	−0.0906902	−	0.279116i
$951$	7.96719	−	5.78850i	0.258354	−	0.187705i
$952$	−3.40987	+	2.47742i	−0.110515	+	0.0802936i
$953$	−4.89834	−	15.0756i	−0.158673	−	0.488345i	0.839842	−	0.542832i	$-0.182648\pi$
$953$	−4.89834	−	15.0756i	−0.158673	−	0.488345i	−0.998515	+	0.0544866i	$0.982648\pi$
$954$	−1.83076	+	5.63451i	−0.0592732	+	0.182424i
$955$	49.2628	+	35.7915i	1.59411	+	1.15819i
$956$	−7.12273			−0.230366
$957$	−14.7945	+	0.315516i	−0.478240	+	0.0101992i
$958$	−33.8613			−1.09401
$959$	4.10654	+	2.98358i	0.132607	+	0.0963448i
$960$	−1.85180	+	5.69925i	−0.0597665	+	0.183942i
$961$	7.37909	+	22.7105i	0.238035	+	0.732597i
$962$	29.3969	−	21.3581i	0.947795	−	0.688613i
$963$	−1.25818	+	0.914118i	−0.0405441	+	0.0294570i
$964$	−4.68298	−	14.4127i	−0.150829	−	0.464203i
$965$	−15.7943	+	48.6099i	−0.508437	+	1.56481i
$966$	−6.58807	−	4.78651i	−0.211968	−	0.154003i
$967$	23.6222			0.759639			0.379820	−	0.925061i	$-0.375986\pi$
$967$	23.6222			0.759639			0.379820	+	0.925061i	$0.375986\pi$
$968$	−2.95008	+	10.5970i	−0.0948191	+	0.340601i
$969$	−8.03870			−0.258240
$970$	24.6092	+	17.8796i	0.790153	+	0.574080i
$971$	0.349604	−	1.07597i	0.0112193	−	0.0345295i	−0.945290	−	0.326231i	$-0.894221\pi$
$971$	0.349604	−	1.07597i	0.0112193	−	0.0345295i	0.956509	+	0.291701i	$0.0942213\pi$
$972$	−1.41132	−	4.34359i	−0.0452681	−	0.139321i
$973$	−2.66760	+	1.93813i	−0.0855195	+	0.0621335i
$974$	5.89043	−	4.27965i	0.188741	−	0.137129i
$975$	−19.8548	−	61.1068i	−0.635863	−	1.95698i
$976$	2.55429	−	7.86129i	0.0817608	−	0.251634i
$977$	−29.7957	−	21.6479i	−0.953250	−	0.692577i	−0.00167706	−	0.999999i	$-0.500534\pi$
$977$	−29.7957	−	21.6479i	−0.953250	−	0.692577i	−0.951573	+	0.307422i	$0.900534\pi$
$978$	−28.9079			−0.924373
$979$	34.7882	−	0.741910i	1.11183	−	0.0237116i
$980$	−23.6001			−0.753878
$981$	−1.67281	−	1.21537i	−0.0534087	−	0.0388037i
$982$	9.01211	−	27.7364i	0.287588	−	0.885105i
$983$	8.50546	+	26.1771i	0.271282	+	0.834920i	0.990179	+	0.139804i	$0.0446472\pi$
$983$	8.50546	+	26.1771i	0.271282	+	0.834920i	−0.718897	+	0.695117i	$0.755353\pi$
$984$	−8.25722	+	5.99922i	−0.263231	+	0.191248i
$985$	−45.2644	+	32.8865i	−1.44224	+	1.04785i
$986$	−4.33502	−	13.3418i	−0.138055	−	0.424890i
$987$	−3.38678	+	10.4234i	−0.107802	+	0.331781i
$988$	−3.59386	−	2.61109i	−0.114336	−	0.0830699i
$989$	−58.0618			−1.84626
$990$	−4.52583	−	3.14299i	−0.143840	−	0.0998907i
$991$	7.71442			0.245057			0.122528	−	0.992465i	$-0.460900\pi$
$991$	7.71442			0.245057			0.122528	+	0.992465i	$0.460900\pi$
$992$	−5.99324	−	4.35434i	−0.190286	−	0.138251i
$993$	−2.34907	+	7.22969i	−0.0745454	+	0.229427i
$994$	3.21714	+	9.90135i	0.102042	+	0.314052i
$995$	−22.5412	+	16.3771i	−0.714603	+	0.519189i
$996$	−1.69053	+	1.22824i	−0.0535664	+	0.0389183i
$997$	13.7324	+	42.2640i	0.434909	+	1.33851i	0.893180	+	0.449700i	$0.148469\pi$
$997$	13.7324	+	42.2640i	0.434909	+	1.33851i	−0.458270	+	0.888813i	$0.651531\pi$
$998$	1.66839	−	5.13479i	0.0528121	−	0.162539i
$999$	−36.4345	−	26.4712i	−1.15274	−	0.837513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.g.191.2	✓	16
11.3	even	5	inner	418.2.f.g.267.2	yes	16
11.5	even	5		4598.2.a.bw.1.3		8
11.6	odd	10		4598.2.a.bz.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.g.191.2	✓	16	1.1	even	1	trivial
418.2.f.g.267.2	yes	16	11.3	even	5	inner
4598.2.a.bw.1.3		8	11.5	even	5
4598.2.a.bz.1.3		8	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.494109 + 1.52071i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-3.03200 + 2.20287i) q^{5} +(-1.29359 + 0.939851i) q^{6} +(-0.259070 - 0.797336i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.358634 + 0.260563i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.494109 + 1.52071i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-3.03200 + 2.20287i) q^{5} +(-1.29359 + 0.939851i) q^{6} +(-0.259070 - 0.797336i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.358634 + 0.260563i) q^{9} -3.74775 q^{10} +(3.31587 - 0.0707159i) q^{11} -1.59897 q^{12} +(-3.59386 - 2.61109i) q^{13} +(0.259070 - 0.797336i) q^{14} +(-1.85180 - 5.69925i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.06727 + 2.95504i) q^{17} +(0.136986 + 0.421600i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-3.03200 - 2.20287i) q^{20} +1.34053 q^{21} +(2.72416 + 1.89181i) q^{22} -6.07470 q^{23} +(-1.29359 - 0.939851i) q^{24} +(2.79526 - 8.60292i) q^{25} +(-1.37273 - 4.22483i) q^{26} +(-4.45423 + 3.23618i) q^{27} +(0.678255 - 0.492781i) q^{28} +(0.862275 + 2.65381i) q^{29} +(1.85180 - 5.69925i) q^{30} +(5.99324 + 4.35434i) q^{31} -1.00000 q^{32} +(-1.53086 + 5.07742i) q^{33} -5.02742 q^{34} +(2.54193 + 1.84682i) q^{35} +(-0.136986 + 0.421600i) q^{36} +(2.52769 + 7.77942i) q^{37} +(0.809017 - 0.587785i) q^{38} +(5.74647 - 4.17506i) q^{39} +(-1.15812 - 3.56432i) q^{40} +(1.97251 - 6.07075i) q^{41} +(1.08451 + 0.787941i) q^{42} +9.55796 q^{43} +(1.09192 + 3.13173i) q^{44} -1.66137 q^{45} +(-4.91454 - 3.57062i) q^{46} +(-2.52645 + 7.77563i) q^{47} +(-0.494109 - 1.52071i) q^{48} +(5.09449 - 3.70136i) q^{49} +(7.31808 - 5.31690i) q^{50} +(-2.48409 - 7.64525i) q^{51} +(1.37273 - 4.22483i) q^{52} +(10.8122 + 7.85551i) q^{53} -5.50573 q^{54} +(-9.89793 + 7.51885i) q^{55} +0.838369 q^{56} +(1.29359 + 0.939851i) q^{57} +(-0.862275 + 2.65381i) q^{58} +(2.25216 + 6.93145i) q^{59} +(4.84807 - 3.52233i) q^{60} +(-6.68721 + 4.85854i) q^{61} +(2.28921 + 7.04548i) q^{62} +(0.114845 - 0.353456i) q^{63} +(-0.809017 - 0.587785i) q^{64} +16.6485 q^{65} +(-4.22293 + 3.20790i) q^{66} -7.32824 q^{67} +(-4.06727 - 2.95504i) q^{68} +(3.00156 - 9.23787i) q^{69} +(0.970931 + 2.98822i) q^{70} +(-10.0464 + 7.29914i) q^{71} +(-0.358634 + 0.260563i) q^{72} +(-2.33579 - 7.18882i) q^{73} +(-2.52769 + 7.77942i) q^{74} +(11.7014 + 8.50156i) q^{75} +1.00000 q^{76} +(-0.915428 - 2.62554i) q^{77} +7.10303 q^{78} +(-7.26918 - 5.28137i) q^{79} +(1.15812 - 3.56432i) q^{80} +(-2.30947 - 7.10781i) q^{81} +(5.16409 - 3.75193i) q^{82} +(1.05726 - 0.768144i) q^{83} +(0.414245 + 1.27492i) q^{84} +(5.82235 - 17.9194i) q^{85} +(7.73256 + 5.61803i) q^{86} -4.46174 q^{87} +(-0.957406 + 3.17543i) q^{88} +10.4914 q^{89} +(-1.34407 - 0.976526i) q^{90} +(-1.15086 + 3.54197i) q^{91} +(-1.87719 - 5.77739i) q^{92} +(-9.58301 + 6.96246i) q^{93} +(-6.61434 + 4.80560i) q^{94} +(1.15812 + 3.56432i) q^{95} +(0.494109 - 1.52071i) q^{96} +(-6.56639 - 4.77076i) q^{97} +6.29714 q^{98} +(1.20761 + 0.838633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

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