LMFDB - Embedded newform 950.2.w.a.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, 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:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	950.37
Dual form			950.2.w.a.873.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(-1.00551 + 1.97343i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.74220 - 1.40169i) q^{5} +(0.684420 - 2.10643i) q^{6} +(-1.24411 - 1.24411i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-1.12001 - 1.54156i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.00551 + 1.97343i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.74220 - 1.40169i) q^{5} +(0.684420 - 2.10643i) q^{6} +(-1.24411 - 1.24411i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-1.12001 - 1.54156i) q^{9} +(-1.50148 + 1.65697i) q^{10} +(-0.307616 - 0.223496i) q^{11} +(-0.346476 + 2.18756i) q^{12} +(-0.429072 - 0.0679584i) q^{13} +(1.42341 + 1.03417i) q^{14} +(1.01433 + 4.84752i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.50933 - 0.769040i) q^{17} +(1.34737 + 1.34737i) q^{18} +(-0.284917 - 4.34958i) q^{19} +(1.22379 - 1.87146i) q^{20} +(3.70613 - 1.20419i) q^{21} +(0.338791 + 0.172623i) q^{22} +(-4.31528 + 0.683474i) q^{23} -2.21483i q^{24} +(1.07053 - 4.88405i) q^{25} +0.434421 q^{26} +(-2.39435 + 0.379228i) q^{27} +(-1.56767 - 0.798768i) q^{28} +(-2.32165 - 7.14530i) q^{29} +(-1.76016 - 4.62917i) q^{30} +(-3.00296 - 0.975720i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.750365 - 0.382330i) q^{33} +(-1.37044 + 0.995682i) q^{34} +(-3.91135 - 0.423635i) q^{35} +(-1.54156 - 1.12001i) q^{36} +(0.0275644 - 0.174035i) q^{37} +(0.961833 + 4.25146i) q^{38} +(0.565548 - 0.778410i) q^{39} +(-0.915960 + 2.03986i) q^{40} +(-0.974243 - 1.34093i) q^{41} +(-3.47212 + 1.76913i) q^{42} +(-2.98283 + 2.98283i) q^{43} +(-0.361624 - 0.117499i) q^{44} +(-4.11206 - 1.11580i) q^{45} +(4.15524 - 1.35012i) q^{46} +(2.17733 - 4.27324i) q^{47} +(0.346476 + 2.18756i) q^{48} -3.90438i q^{49} +(-0.293321 + 4.99139i) q^{50} +3.75182i q^{51} +(-0.429072 + 0.0679584i) q^{52} +(-0.410877 + 0.806392i) q^{53} +(2.30555 - 0.749118i) q^{54} +(-0.849201 + 0.0418067i) q^{55} +(1.67332 + 0.543696i) q^{56} +(8.87006 + 3.81129i) q^{57} +(3.41084 + 6.69415i) q^{58} +(5.49093 - 3.98939i) q^{59} +(2.46265 + 4.29682i) q^{60} +(4.15016 + 3.01526i) q^{61} +(3.11862 + 0.493941i) q^{62} +(-0.524455 + 3.31128i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.842787 + 0.483029i) q^{65} +(-0.681317 + 0.495006i) q^{66} +(-2.95956 - 5.80847i) q^{67} +(1.19781 - 1.19781i) q^{68} +(2.99028 - 9.20314i) q^{69} +(3.92946 - 0.193450i) q^{70} +(8.79015 - 2.85609i) q^{71} +(1.69779 + 0.865065i) q^{72} +(1.46344 - 0.231786i) q^{73} +0.176204i q^{74} +(8.56189 + 7.02359i) q^{75} +(-1.61507 - 4.04865i) q^{76} +(0.104654 + 0.660762i) q^{77} +(-0.436815 + 0.857298i) q^{78} +(-1.48533 - 4.57137i) q^{79} +(0.585579 - 2.15803i) q^{80} +(3.42564 - 10.5430i) q^{81} +(1.17202 + 1.17202i) q^{82} +(-1.78343 - 3.50018i) q^{83} +(3.15262 - 2.29051i) q^{84} +(1.55159 - 3.45543i) q^{85} +(2.47949 - 3.41273i) q^{86} +(16.4352 + 2.60308i) q^{87} +(0.375553 + 0.0594818i) q^{88} +(0.691971 + 0.502746i) q^{89} +(4.23599 + 0.458797i) q^{90} +(0.449265 + 0.618361i) q^{91} +(-3.89287 + 1.98352i) q^{92} +(4.94502 - 4.94502i) q^{93} +(-1.48204 + 4.56124i) q^{94} +(-6.59314 - 7.17848i) q^{95} +(-0.684420 - 2.10643i) q^{96} +(-2.55695 - 1.30283i) q^{97} +(0.610780 + 3.85631i) q^{98} +0.724525i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

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 $

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	−1.00551	+	1.97343i	−0.580532	+	1.13936i	0.394831	+	0.918754i	$0.370803\pi$
$3$	−1.00551	+	1.97343i	−0.580532	+	1.13936i	−0.975363	+	0.220605i	$0.929197\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	1.74220	−	1.40169i	0.779136	−	0.626854i
$5$	1.74220	−	1.40169i	0.779136	−	0.626854i
$6$	0.684420	−	2.10643i	0.279413	−	0.859946i
$7$	−1.24411	−	1.24411i	−0.470229	−	0.470229i	0.431759	−	0.901989i	$-0.357893\pi$
$7$	−1.24411	−	1.24411i	−0.470229	−	0.470229i	−0.901989	+	0.431759i	$0.857893\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	−1.12001	−	1.54156i	−0.373336	−	0.513853i
$10$	−1.50148	+	1.65697i	−0.474810	+	0.523981i
$11$	−0.307616	−	0.223496i	−0.0927497	−	0.0673866i	0.540444	−	0.841380i	$-0.318256\pi$
$11$	−0.307616	−	0.223496i	−0.0927497	−	0.0673866i	−0.633194	+	0.773993i	$0.718256\pi$
$12$	−0.346476	+	2.18756i	−0.100019	+	0.631495i
$13$	−0.429072	−	0.0679584i	−0.119003	−	0.0188483i	0.0966487	−	0.995319i	$-0.469188\pi$
$13$	−0.429072	−	0.0679584i	−0.119003	−	0.0188483i	−0.215652	+	0.976470i	$0.569188\pi$
$14$	1.42341	+	1.03417i	0.380424	+	0.276394i
$15$	1.01433	+	4.84752i	0.261898	+	1.25163i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	1.50933	−	0.769040i	0.366065	−	0.186519i	−0.261276	−	0.965264i	$-0.584143\pi$
$17$	1.50933	−	0.769040i	0.366065	−	0.186519i	0.627341	+	0.778745i	$0.284143\pi$
$18$	1.34737	+	1.34737i	0.317578	+	0.317578i
$19$	−0.284917	−	4.34958i	−0.0653644	−	0.997861i
$19$	−0.284917	−	4.34958i	−0.0653644	−	0.997861i
$20$	1.22379	−	1.87146i	0.273647	−	0.418470i
$21$	3.70613	−	1.20419i	0.808743	−	0.262777i
$22$	0.338791	+	0.172623i	0.0722306	+	0.0368033i
$23$	−4.31528	+	0.683474i	−0.899799	+	0.142514i	−0.589162	−	0.808015i	$-0.700542\pi$
$23$	−4.31528	+	0.683474i	−0.899799	+	0.142514i	−0.310637	+	0.950529i	$0.600542\pi$
$24$		−	2.21483i		−	0.452100i
$25$	1.07053	−	4.88405i	0.214107	−	0.976810i
$26$	0.434421			0.0851969
$27$	−2.39435	+	0.379228i	−0.460793	+	0.0729825i
$28$	−1.56767	−	0.798768i	−0.296262	−	0.150953i
$29$	−2.32165	−	7.14530i	−0.431119	−	1.32685i	−0.897011	−	0.442008i	$-0.854266\pi$
$29$	−2.32165	−	7.14530i	−0.431119	−	1.32685i	0.465892	−	0.884842i	$-0.345734\pi$
$30$	−1.76016	−	4.62917i	−0.321360	−	0.845166i
$31$	−3.00296	−	0.975720i	−0.539347	−	0.175245i	0.0266604	−	0.999645i	$-0.491513\pi$
$31$	−3.00296	−	0.975720i	−0.539347	−	0.175245i	−0.566008	+	0.824400i	$0.691513\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.750365	−	0.382330i	0.130622	−	0.0665551i
$34$	−1.37044	+	0.995682i	−0.235028	+	0.170758i
$35$	−3.91135	−	0.423635i	−0.661138	−	0.0716074i
$36$	−1.54156	−	1.12001i	−0.256926	−	0.186668i
$37$	0.0275644	−	0.174035i	0.00453157	−	0.0286112i	−0.985319	−	0.170724i	$-0.945389\pi$
$37$	0.0275644	−	0.174035i	0.00453157	−	0.0286112i	0.989851	+	0.142112i	$0.0453895\pi$
$38$	0.961833	+	4.25146i	0.156030	+	0.689677i
$39$	0.565548	−	0.778410i	0.0905602	−	0.124645i
$40$	−0.915960	+	2.03986i	−0.144826	+	0.322530i
$41$	−0.974243	−	1.34093i	−0.152151	−	0.209418i	0.726137	−	0.687550i	$-0.241314\pi$
$41$	−0.974243	−	1.34093i	−0.152151	−	0.209418i	−0.878288	+	0.478132i	$0.841314\pi$
$42$	−3.47212	+	1.76913i	−0.535760	+	0.272983i
$43$	−2.98283	+	2.98283i	−0.454878	+	0.454878i	−0.896970	−	0.442092i	$-0.854236\pi$
$43$	−2.98283	+	2.98283i	−0.454878	+	0.454878i	0.442092	+	0.896970i	$0.354236\pi$
$44$	−0.361624	−	0.117499i	−0.0545169	−	0.0177136i
$45$	−4.11206	−	1.11580i	−0.612990	−	0.166334i
$46$	4.15524	−	1.35012i	0.612656	−	0.199064i
$47$	2.17733	−	4.27324i	0.317596	−	0.623317i	−0.675925	−	0.736971i	$-0.736256\pi$
$47$	2.17733	−	4.27324i	0.317596	−	0.623317i	0.993520	+	0.113654i	$0.0362556\pi$
$48$	0.346476	+	2.18756i	0.0500095	+	0.315747i
$49$		−	3.90438i		−	0.557769i
$50$	−0.293321	+	4.99139i	−0.0414818	+	0.705889i
$51$			3.75182i			0.525360i
$52$	−0.429072	+	0.0679584i	−0.0595016	+	0.00942413i
$53$	−0.410877	+	0.806392i	−0.0564383	+	0.110766i	−0.917503	−	0.397729i	$-0.869798\pi$
$53$	−0.410877	+	0.806392i	−0.0564383	+	0.110766i	0.861064	+	0.508496i	$0.169798\pi$
$54$	2.30555	−	0.749118i	0.313745	−	0.101942i
$55$	−0.849201	+	0.0418067i	−0.114506	+	0.00563722i
$56$	1.67332	+	0.543696i	0.223607	+	0.0726544i
$57$	8.87006	+	3.81129i	1.17487	+	0.504817i
$58$	3.41084	+	6.69415i	0.447865	+	0.878984i
$59$	5.49093	−	3.98939i	0.714858	−	0.519375i	−0.169879	−	0.985465i	$-0.554338\pi$
$59$	5.49093	−	3.98939i	0.714858	−	0.519375i	0.884737	+	0.466090i	$0.154338\pi$
$60$	2.46265	+	4.29682i	0.317927	+	0.554718i
$61$	4.15016	+	3.01526i	0.531373	+	0.386065i	0.820871	−	0.571113i	$-0.193488\pi$
$61$	4.15016	+	3.01526i	0.531373	+	0.386065i	−0.289498	+	0.957179i	$0.593488\pi$
$62$	3.11862	+	0.493941i	0.396065	+	0.0627306i
$63$	−0.524455	+	3.31128i	−0.0660751	+	0.417182i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−0.842787	+	0.483029i	−0.104535	+	0.0599124i
$66$	−0.681317	+	0.495006i	−0.0838643	+	0.0609310i
$67$	−2.95956	−	5.80847i	−0.361568	−	0.709617i	0.636531	−	0.771251i	$-0.280369\pi$
$67$	−2.95956	−	5.80847i	−0.361568	−	0.709617i	−0.998099	+	0.0616341i	$0.980369\pi$
$68$	1.19781	−	1.19781i	0.145255	−	0.145255i
$69$	2.99028	−	9.20314i	0.359988	−	1.10793i
$70$	3.92946	−	0.193450i	0.469661	−	0.0231217i
$71$	8.79015	−	2.85609i	1.04320	−	0.338956i	0.263203	−	0.964740i	$-0.415221\pi$
$71$	8.79015	−	2.85609i	1.04320	−	0.338956i	0.779996	+	0.625785i	$0.215221\pi$
$72$	1.69779	+	0.865065i	0.200086	+	0.101949i
$73$	1.46344	−	0.231786i	0.171282	−	0.0271285i	−0.0702041	−	0.997533i	$-0.522365\pi$
$73$	1.46344	−	0.231786i	0.171282	−	0.0271285i	0.241486	+	0.970404i	$0.422365\pi$
$74$			0.176204i			0.0204833i
$75$	8.56189	+	7.02359i	0.988642	+	0.811015i
$76$	−1.61507	−	4.04865i	−0.185261	−	0.464412i
$77$	0.104654	+	0.660762i	0.0119265	+	0.0753008i
$78$	−0.436815	+	0.857298i	−0.0494596	+	0.0970699i
$79$	−1.48533	−	4.57137i	−0.167112	−	0.514319i	0.832073	−	0.554666i	$-0.187154\pi$
$79$	−1.48533	−	4.57137i	−0.167112	−	0.514319i	−0.999186	+	0.0403466i	$0.987154\pi$
$80$	0.585579	−	2.15803i	0.0654697	−	0.241275i
$81$	3.42564	−	10.5430i	0.380626	−	1.17145i
$82$	1.17202	+	1.17202i	0.129428	+	0.129428i
$83$	−1.78343	−	3.50018i	−0.195757	−	0.384195i	0.772174	−	0.635411i	$-0.219169\pi$
$83$	−1.78343	−	3.50018i	−0.195757	−	0.384195i	−0.967931	+	0.251217i	$0.919169\pi$
$84$	3.15262	−	2.29051i	0.343979	−	0.249915i
$85$	1.55159	−	3.45543i	0.168294	−	0.374794i
$86$	2.47949	−	3.41273i	0.267370	−	0.368004i
$87$	16.4352	+	2.60308i	1.76204	+	0.279079i
$88$	0.375553	+	0.0594818i	0.0400341	+	0.00634078i
$89$	0.691971	+	0.502746i	0.0733488	+	0.0532910i	0.623855	−	0.781540i	$-0.285565\pi$
$89$	0.691971	+	0.502746i	0.0733488	+	0.0532910i	−0.550507	+	0.834831i	$0.685565\pi$
$90$	4.23599	+	0.458797i	0.446512	+	0.0483614i
$91$	0.449265	+	0.618361i	0.0470958	+	0.0648218i
$92$	−3.89287	+	1.98352i	−0.405860	+	0.206796i
$93$	4.94502	−	4.94502i	0.512775	−	0.512775i
$94$	−1.48204	+	4.56124i	−0.152860	+	0.470456i
$95$	−6.59314	−	7.17848i	−0.676442	−	0.736496i
$96$	−0.684420	−	2.10643i	−0.0698533	−	0.214986i
$97$	−2.55695	−	1.30283i	−0.259619	−	0.132283i	0.319337	−	0.947641i	$-0.396540\pi$
$97$	−2.55695	−	1.30283i	−0.259619	−	0.132283i	−0.578956	+	0.815359i	$0.696540\pi$
$98$	0.610780	+	3.85631i	0.0616981	+	0.389546i
$99$			0.724525i			0.0728175i
$100$	−0.491116	−	4.97582i	−0.0491116	−	0.497582i
$101$	15.4490			1.53723			0.768617	−	0.639709i	$-0.220945\pi$
$101$	15.4490			1.53723			0.768617	+	0.639709i	$0.220945\pi$
$102$	−0.586914	−	3.70563i	−0.0581132	−	0.366912i
$103$	−6.96950	+	13.6784i	−0.686725	+	1.34777i	0.239534	+	0.970888i	$0.423005\pi$
$103$	−6.96950	+	13.6784i	−0.686725	+	1.34777i	−0.926259	+	0.376886i	$0.876995\pi$
$104$	0.413159	−	0.134243i	0.0405135	−	0.0131636i
$105$	4.76892	−	7.29279i	0.465399	−	0.711703i
$106$	0.279671	−	0.860739i	0.0271641	−	0.0836024i
$107$	−0.234711	+	0.234711i	−0.0226903	+	0.0226903i	−0.718361	−	0.695671i	$-0.755107\pi$
$107$	−0.234711	+	0.234711i	−0.0226903	+	0.0226903i	0.695671	+	0.718361i	$0.255107\pi$
$108$	−2.15998	+	1.10056i	−0.207844	+	0.105902i
$109$	6.55527	−	4.76269i	0.627881	−	0.456183i	−0.227784	−	0.973712i	$-0.573148\pi$
$109$	6.55527	−	4.76269i	0.627881	−	0.456183i	0.855666	+	0.517529i	$0.173148\pi$
$110$	0.832206	−	0.174136i	0.0793478	−	0.0166033i
$111$	0.315729	+	0.229391i	0.0299677	+	0.0217728i
$112$	−1.73778	−	0.275237i	−0.164204	−	0.0260074i
$113$	7.34131	+	1.16275i	0.690612	+	0.109382i	0.491869	−	0.870669i	$-0.336314\pi$
$113$	7.34131	+	1.16275i	0.690612	+	0.109382i	0.198743	+	0.980052i	$0.436314\pi$
$114$	−9.35707	−	2.37678i	−0.876370	−	0.222606i
$115$	−6.56008	+	7.23944i	−0.611730	+	0.675081i
$116$	−4.41604	−	6.07816i	−0.410019	−	0.564343i
$117$	0.375802	+	0.737554i	0.0347429	+	0.0681869i
$118$	−4.79925	+	4.79925i	−0.441807	+	0.441807i
$119$	−2.83454	−	0.920997i	−0.259841	−	0.0844276i
$120$	−3.10450	−	3.85868i	−0.283401	−	0.352248i
$121$	−3.35451	−	10.3241i	−0.304955	−	0.938556i
$122$	−4.57075	−	2.32891i	−0.413816	−	0.210850i
$123$	3.62584	−	0.574277i	0.326931	−	0.0517808i
$124$	−3.15750			−0.283552
$125$	−4.98083	−	10.0096i	−0.445499	−	0.895282i
$126$		−	3.35255i		−	0.298669i
$127$	−0.821648	+	0.130136i	−0.0729094	+	0.0115477i	−0.192783	−	0.981241i	$-0.561751\pi$
$127$	−0.821648	+	0.130136i	−0.0729094	+	0.0115477i	0.119873	+	0.992789i	$0.461751\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	−2.88713	−	8.88568i	−0.254198	−	0.782340i
$130$	0.756849	−	0.608923i	0.0663800	−	0.0534061i
$131$	0.735450	−	2.26348i	0.0642566	−	0.197761i	−0.913774	−	0.406223i	$-0.866846\pi$
$131$	0.735450	−	2.26348i	0.0642566	−	0.197761i	0.978031	+	0.208462i	$0.0668456\pi$
$132$	0.595493	−	0.595493i	0.0518310	−	0.0518310i
$133$	−5.05688	+	5.76582i	−0.438487	+	0.499960i
$134$	3.83177	+	5.27398i	0.331014	+	0.455602i
$135$	−3.63988	+	4.01683i	−0.313271	+	0.345714i
$136$	−0.995682	+	1.37044i	−0.0853790	+	0.117514i
$137$	15.8491	+	2.51025i	1.35408	+	0.214465i	0.790939	−	0.611896i	$-0.209593\pi$
$137$	15.8491	+	2.51025i	1.35408	+	0.214465i	0.563141	+	0.826361i	$0.309593\pi$
$138$	−1.51378	+	9.55762i	−0.128861	+	0.813599i
$139$	−6.77870	+	9.33009i	−0.574962	+	0.791368i	−0.993132	−	0.117001i	$-0.962672\pi$
$139$	−6.77870	+	9.33009i	−0.574962	+	0.791368i	0.418170	+	0.908369i	$0.362672\pi$
$140$	−3.85082	+	0.805771i	−0.325454	+	0.0681001i
$141$	6.24361	+	8.59359i	0.525807	+	0.723711i
$142$	−8.23514	+	4.19601i	−0.691078	+	0.352122i
$143$	0.116801	+	0.116801i	0.00976740	+	0.00976740i
$144$	−1.81221	−	0.588823i	−0.151017	−	0.0490686i
$145$	−14.0603	−	9.19433i	−1.16764	−	0.763547i
$146$	−1.40916	+	0.457864i	−0.116623	+	0.0378931i
$147$	7.70501	+	3.92590i	0.635499	+	0.323803i
$148$	−0.0275644	−	0.174035i	−0.00226578	−	0.0143056i
$149$			11.9641i			0.980133i	0.871685	+	0.490067i	$0.163028\pi$
$149$			11.9641i			0.980133i	−0.871685	+	0.490067i	$0.836972\pi$
$150$	−9.55521	−	5.59775i	−0.780179	−	0.457054i
$151$			1.69611i			0.138027i	0.997616	+	0.0690136i	$0.0219852\pi$
$151$			1.69611i			0.138027i	−0.997616	+	0.0690136i	$0.978015\pi$
$152$	2.22853	+	3.74615i	0.180758	+	0.303853i
$153$	−2.87597	−	1.46538i	−0.232509	−	0.118469i
$154$	−0.206732	−	0.636255i	−0.0166589	−	0.0512709i
$155$	−6.59941	+	2.50931i	−0.530078	+	0.201553i
$156$	0.297326	−	0.915076i	0.0238052	−	0.0732647i
$157$	−3.76861	−	3.76861i	−0.300768	−	0.300768i	0.540546	−	0.841314i	$-0.318218\pi$
$157$	−3.76861	−	3.76861i	−0.300768	−	0.300768i	−0.841314	+	0.540546i	$0.818218\pi$
$158$	2.18216	+	4.28273i	0.173603	+	0.340716i
$159$	−1.17821	−	1.62167i	−0.0934385	−	0.128607i
$160$	−0.240779	+	2.22307i	−0.0190352	+	0.175749i
$161$	6.21900	+	4.51837i	0.490126	+	0.356098i
$162$	−1.73417	+	10.9491i	−0.136249	+	0.860243i
$163$	0.165756	−	1.04654i	0.0129830	−	0.0819713i	−0.980346	−	0.197285i	$-0.936787\pi$
$163$	0.165756	−	1.04654i	0.0129830	−	0.0819713i	0.993329	+	0.115314i	$0.0367874\pi$
$164$	−1.34093	−	0.974243i	−0.104709	−	0.0760756i
$165$	0.771379	−	1.71787i	0.0600518	−	0.133736i
$166$	2.30902	+	3.17810i	0.179215	+	0.246668i
$167$	0.956202	+	1.87665i	0.0739931	+	0.145220i	0.925040	−	0.379871i	$-0.124032\pi$
$167$	0.956202	+	1.87665i	0.0739931	+	0.145220i	−0.851046	+	0.525090i	$0.824032\pi$
$168$	−2.75549	+	2.75549i	−0.212591	+	0.212591i
$169$	−12.1842	−	3.95890i	−0.937250	−	0.304531i
$170$	−0.991944	+	3.65561i	−0.0760786	+	0.280372i
$171$	−6.38602	+	5.31077i	−0.488351	+	0.406125i
$172$	−1.91510	+	3.75859i	−0.146025	+	0.286590i
$173$	−1.04837	−	6.61914i	−0.0797059	−	0.503244i	−0.994952	−	0.100349i	$-0.968004\pi$
$173$	−1.04837	−	6.61914i	−0.0797059	−	0.503244i	0.915246	−	0.402895i	$-0.131996\pi$
$174$	−16.6400			−1.26148
$175$	−7.40816	+	4.74443i	−0.560004	+	0.358645i
$176$	−0.380234			−0.0286612
$177$	2.35159	+	14.8473i	0.176756	+	1.11599i
$178$	−0.762098	−	0.388309i	−0.0571217	−	0.0291050i
$179$	−0.775770	−	2.38757i	−0.0579838	−	0.178456i	0.917870	−	0.396882i	$-0.129908\pi$
$179$	−0.775770	−	2.38757i	−0.0579838	−	0.178456i	−0.975853	+	0.218426i	$0.929908\pi$
$180$	−4.25561	+	0.209506i	−0.317194	+	0.0156157i
$181$	−14.1097	−	4.58452i	−1.04877	−	0.340765i	−0.266582	−	0.963812i	$-0.585894\pi$
$181$	−14.1097	−	4.58452i	−1.04877	−	0.340765i	−0.782184	+	0.623047i	$0.785894\pi$
$182$	−0.540467	−	0.540467i	−0.0400621	−	0.0400621i
$183$	−10.1234	+	5.15815i	−0.748346	+	0.381301i
$184$	3.53466	−	2.56808i	0.260578	−	0.189321i
$185$	−0.195920	−	0.341841i	−0.0144043	−	0.0251326i
$186$	−4.11057	+	5.65771i	−0.301402	+	0.414844i
$187$	−0.636170	−	0.100759i	−0.0465214	−	0.00736826i
$188$	0.750255	−	4.73693i	0.0547180	−	0.345476i
$189$	3.45064	+	2.50703i	0.250997	+	0.182360i
$190$	7.63493	+	6.05870i	0.553896	+	0.439545i
$191$	−16.0040	+	11.6276i	−1.15801	+	0.841340i	−0.989525	−	0.144365i	$-0.953886\pi$
$191$	−16.0040	+	11.6276i	−1.15801	+	0.841340i	−0.168481	+	0.985705i	$0.553886\pi$
$192$	1.00551	+	1.97343i	0.0725665	+	0.142420i
$193$	−17.9899	−	17.9899i	−1.29494	−	1.29494i	−0.931691	−	0.363252i	$-0.881667\pi$
$193$	−17.9899	−	17.9899i	−1.29494	−	1.29494i	−0.363252	−	0.931691i	$-0.618333\pi$
$194$	2.72928	+	0.886797i	0.195951	+	0.0636683i
$195$	−0.105790	−	2.14887i	−0.00757580	−	0.153884i
$196$	−1.20652	−	3.71329i	−0.0861800	−	0.265235i
$197$	7.73350	−	15.1778i	0.550989	−	1.08138i	−0.432707	−	0.901535i	$-0.642441\pi$
$197$	7.73350	−	15.1778i	0.550989	−	1.08138i	0.983696	−	0.179842i	$-0.0575585\pi$
$198$	−0.113341	−	0.715605i	−0.00805477	−	0.0508558i
$199$			21.5427i			1.52712i	0.645735	+	0.763562i	$0.276551\pi$
$199$			21.5427i			1.52712i	−0.645735	+	0.763562i	$0.723449\pi$
$200$	1.26346	+	4.83773i	0.0893401	+	0.342079i
$201$	14.4385			1.01841
$202$	−15.2588	+	2.41676i	−1.07361	+	0.170043i
$203$	−6.00115	+	11.7779i	−0.421198	+	0.826648i
$204$	1.15938	+	3.56819i	0.0811726	+	0.249824i
$205$	−3.57690	−	0.970586i	−0.249821	−	0.0677887i
$206$	4.74392	−	14.6003i	0.330525	−	1.01725i
$207$	5.88676	+	5.88676i	0.409158	+	0.409158i
$208$	−0.387072	+	0.197223i	−0.0268386	+	0.0136749i
$209$	−0.884469	+	1.40168i	−0.0611800	+	0.0969561i
$210$	−3.56936	+	7.94902i	−0.246309	+	0.548535i
$211$	−3.78731	+	5.21278i	−0.260729	+	0.358863i	−0.919233	−	0.393715i	$-0.871190\pi$
$211$	−3.78731	+	5.21278i	−0.260729	+	0.358863i	0.658504	+	0.752577i	$0.271190\pi$
$212$	−0.141579	+	0.893892i	−0.00972366	+	0.0613928i
$213$	−3.20231	+	20.2186i	−0.219418	+	1.38535i
$214$	0.195104	−	0.268538i	0.0133370	−	0.0183569i
$215$	−1.01569	+	9.37770i	−0.0692696	+	0.639554i
$216$	1.96122	−	1.42491i	0.133444	−	0.0969527i
$217$	2.52211	+	4.94991i	0.171212	+	0.336022i
$218$	−5.72952	+	5.72952i	−0.388052	+	0.388052i
$219$	−1.01409	+	3.12105i	−0.0685259	+	0.210901i
$220$	−0.794720	+	0.302178i	−0.0535800	+	0.0203729i
$221$	−0.699872	+	0.227402i	−0.0470785	+	0.0152967i
$222$	−0.347727	−	0.177176i	−0.0233379	−	0.0118912i
$223$	−3.24009	−	20.4571i	−0.216973	−	1.36991i	−0.820079	−	0.572251i	$-0.806070\pi$
$223$	−3.24009	−	20.4571i	−0.216973	−	1.36991i	0.603106	−	0.797661i	$-0.293930\pi$
$224$	1.75944			0.117557
$225$	−8.72805	+	3.81988i	−0.581870	+	0.254659i
$226$	−7.43282			−0.494424
$227$	16.3407	−	2.58811i	1.08457	−	0.171779i	0.411539	−	0.911392i	$-0.364992\pi$
$227$	16.3407	−	2.58811i	1.08457	−	0.171779i	0.673032	+	0.739613i	$0.264992\pi$
$228$	9.61368	+	0.883749i	0.636682	+	0.0585277i
$229$	−16.4833	+	5.35574i	−1.08924	+	0.353917i	−0.797955	−	0.602718i	$-0.794085\pi$
$229$	−16.4833	+	5.35574i	−1.08924	+	0.353917i	−0.291290	+	0.956635i	$0.594085\pi$
$230$	5.34682	−	8.17653i	0.352559	−	0.539144i
$231$	−1.40920	−	0.457876i	−0.0927184	−	0.0301260i
$232$	5.31250	+	5.31250i	0.348783	+	0.348783i
$233$	−0.858553	−	1.68501i	−0.0562457	−	0.110388i	0.861173	−	0.508313i	$-0.169731\pi$
$233$	−0.858553	−	1.68501i	−0.0562457	−	0.110388i	−0.917418	+	0.397924i	$0.869731\pi$
$234$	−0.486554	−	0.669685i	−0.0318071	−	0.0437787i
$235$	−2.19642	−	10.4968i	−0.143278	−	0.684735i
$236$	3.98939	−	5.49093i	0.259687	−	0.357429i
$237$	10.5148	+	1.66538i	0.683008	+	0.108178i
$238$	2.94371	+	0.466238i	0.190813	+	0.0302217i
$239$	−8.01697	+	11.0344i	−0.518575	+	0.713757i	−0.985336	−	0.170627i	$-0.945421\pi$
$239$	−8.01697	+	11.0344i	−0.518575	+	0.713757i	0.466761	+	0.884383i	$0.345421\pi$
$240$	3.66991	+	3.32552i	0.236892	+	0.214662i
$241$	3.14878	+	4.33392i	0.202831	+	0.279172i	0.898299	−	0.439384i	$-0.144803\pi$
$241$	3.14878	+	4.33392i	0.202831	+	0.279172i	−0.695469	+	0.718556i	$0.744803\pi$
$242$	4.92826	+	9.67225i	0.316800	+	0.621756i
$243$	12.2189	+	12.2189i	0.783842	+	0.783842i
$244$	4.87880	+	1.58522i	0.312333	+	0.101483i
$245$	−5.47273	−	6.80222i	−0.349640	−	0.434578i
$246$	−3.49137	+	1.13441i	−0.222601	+	0.0723276i
$247$	−0.173340	+	1.88565i	−0.0110294	+	0.119981i
$248$	3.11862	−	0.493941i	0.198033	−	0.0313653i
$249$	8.70061			0.551379
$250$	6.48535	+	9.10715i	0.410170	+	0.575987i
$251$	16.6688			1.05213			0.526063	−	0.850445i	$-0.323668\pi$
$251$	16.6688			1.05213			0.526063	+	0.850445i	$0.323668\pi$
$252$	0.524455	+	3.31128i	0.0330376	+	0.208591i
$253$	1.48020	+	0.754202i	0.0930597	+	0.0474163i
$254$	0.791174	−	0.257068i	0.0496427	−	0.0161299i
$255$	5.25889	+	6.53643i	0.329324	+	0.409327i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	1.56451	−	1.56451i	0.0975912	−	0.0975912i	−0.656626	−	0.754217i	$-0.728017\pi$
$257$	1.56451	−	1.56451i	0.0975912	−	0.0975912i	0.754217	+	0.656626i	$0.228017\pi$
$258$	4.24161	+	8.32463i	0.264071	+	0.518269i
$259$	−0.250812	+	0.182225i	−0.0155847	+	0.0113229i
$260$	−0.652274	+	0.719823i	−0.0404523	+	0.0446415i
$261$	−8.41463	+	11.5817i	−0.520853	+	0.716892i
$262$	−0.372309	+	2.35067i	−0.0230013	+	0.145225i
$263$	0.476742	−	3.01003i	0.0293972	−	0.185606i	−0.968620	−	0.248546i	$-0.920047\pi$
$263$	0.476742	−	3.01003i	0.0293972	−	0.185606i	0.998017	+	0.0629392i	$0.0200474\pi$
$264$	−0.495006	+	0.681317i	−0.0304655	+	0.0419322i
$265$	0.414480	+	1.98082i	0.0254613	+	0.121681i
$266$	4.09265	−	6.48590i	0.250937	−	0.397676i
$267$	−1.68792	+	0.860037i	−0.103299	+	0.0526334i
$268$	−4.60963	−	4.60963i	−0.281578	−	0.281578i
$269$	−7.15138	+	22.0097i	−0.436027	+	1.34195i	0.456003	+	0.889978i	$0.349281\pi$
$269$	−7.15138	+	22.0097i	−0.436027	+	1.34195i	−0.892030	+	0.451976i	$0.850719\pi$
$270$	2.96670	−	4.53678i	0.180548	−	0.276099i
$271$	−4.75210	−	14.6255i	−0.288669	−	0.888433i	−0.985275	−	0.170979i	$-0.945307\pi$
$271$	−4.75210	−	14.6255i	−0.288669	−	0.888433i	0.696605	−	0.717455i	$-0.254693\pi$
$272$	0.769040	−	1.50933i	0.0466299	−	0.0915163i
$273$	−1.67203	+	0.264824i	−0.101196	+	0.0160279i
$274$	−16.0467			−0.969414
$275$	−1.42088	+	1.26315i	−0.0856823	+	0.0761710i
$276$		−	9.67676i		−	0.582472i
$277$	1.43617	+	9.06763i	0.0862912	+	0.544821i	0.992525	+	0.122044i	$0.0389448\pi$
$277$	1.43617	+	9.06763i	0.0862912	+	0.544821i	−0.906234	+	0.422778i	$0.861055\pi$
$278$	5.23570	−	10.2756i	0.314016	−	0.616292i
$279$	1.85921	+	5.72205i	0.111308	+	0.342570i
$280$	3.67736	−	1.39825i	0.219764	−	0.0835616i
$281$	18.4011	+	5.97888i	1.09772	+	0.356670i	0.801224	−	0.598364i	$-0.204182\pi$
$281$	18.4011	+	5.97888i	1.09772	+	0.356670i	0.296494	+	0.955035i	$0.404182\pi$
$282$	−7.51107	−	7.51107i	−0.447278	−	0.447278i
$283$	−7.04484	−	13.8263i	−0.418772	−	0.821886i	−0.999967	−	0.00812207i	$-0.997415\pi$
$283$	−7.04484	−	13.8263i	−0.418772	−	0.821886i	0.581195	−	0.813764i	$-0.302585\pi$
$284$	7.47735	−	5.43261i	0.443699	−	0.322366i
$285$	20.7957	−	5.79304i	1.23183	−	0.343150i
$286$	−0.133635	−	0.0970914i	−0.00790199	−	0.00574113i
$287$	−0.456200	+	2.88033i	−0.0269286	+	0.170021i
$288$	1.88201	+	0.298081i	0.110899	+	0.0175646i
$289$	−8.30571	+	11.4318i	−0.488571	+	0.672460i
$290$	15.3255	+	6.88162i	0.899943	+	0.404103i
$291$	5.14209	−	3.73595i	0.301435	−	0.219005i
$292$	1.32019	−	0.672668i	0.0772580	−	0.0393649i
$293$	−16.1136	−	16.1136i	−0.941369	−	0.941369i	0.0570050	−	0.998374i	$-0.481845\pi$
$293$	−16.1136	−	16.1136i	−0.941369	−	0.941369i	−0.998374	+	0.0570050i	$0.981845\pi$
$294$	−8.22430	−	2.67224i	−0.479651	−	0.155848i
$295$	3.97442	−	14.6469i	0.231400	−	0.852776i
$296$	0.0544501	+	0.167580i	0.00316485	+	0.00974041i
$297$	0.821297	+	0.418472i	0.0476565	+	0.0242822i
$298$	−1.87159	−	11.8168i	−0.108418	−	0.684526i
$299$	1.89802			0.109765
$300$	10.3132	+	4.03406i	0.595436	+	0.232907i
$301$	7.42194			0.427794
$302$	−0.265330	−	1.67523i	−0.0152680	−	0.0963984i
$303$	−15.5342	+	30.4875i	−0.892415	+	1.75146i
$304$	−2.78712	−	3.35141i	−0.159852	−	0.192217i
$305$	11.4569	−	0.564029i	0.656019	−	0.0322962i
$306$	3.06980	+	0.997439i	0.175489	+	0.0570198i
$307$	15.5919	−	15.5919i	0.889876	−	0.889876i	−0.104635	−	0.994511i	$-0.533367\pi$
$307$	15.5919	−	15.5919i	0.889876	−	0.889876i	0.994511	+	0.104635i	$0.0333674\pi$
$308$	0.303719	+	0.596082i	0.0173060	+	0.0339649i
$309$	−19.9855	−	27.5076i	−1.13693	−	1.56485i
$310$	6.12562	−	3.51079i	0.347912	−	0.199400i
$311$	−10.7186	−	7.78750i	−0.607794	−	0.441588i	0.240843	−	0.970564i	$-0.422576\pi$
$311$	−10.7186	−	7.78750i	−0.607794	−	0.441588i	−0.848637	+	0.528976i	$0.822576\pi$
$312$	−0.150516	+	0.950322i	−0.00852130	+	0.0538014i
$313$	−4.74385	+	29.9515i	−0.268138	+	1.69296i	0.374853	+	0.927084i	$0.377693\pi$
$313$	−4.74385	+	29.9515i	−0.268138	+	1.69296i	−0.642991	+	0.765874i	$0.722307\pi$
$314$	4.31176	+	3.13268i	0.243327	+	0.176787i
$315$	3.72768	+	6.50404i	0.210031	+	0.366461i
$316$	−2.82526	−	3.88864i	−0.158933	−	0.218753i
$317$	11.6753	+	22.9141i	0.655750	+	1.28698i	0.944164	+	0.329476i	$0.106872\pi$
$317$	11.6753	+	22.9141i	0.655750	+	1.28698i	−0.288414	+	0.957506i	$0.593128\pi$
$318$	1.41739	+	1.41739i	0.0794835	+	0.0794835i
$319$	−0.882771	+	2.71689i	−0.0494257	+	0.152117i
$320$	−0.109950	−	2.23336i	−0.00614638	−	0.124849i
$321$	−0.227180	−	0.699189i	−0.0126800	−	0.0390249i
$322$	−6.84927	−	3.48988i	−0.381695	−	0.194483i
$323$	−3.77503	−	6.34581i	−0.210048	−	0.353091i
$324$		−	11.0856i		−	0.615866i
$325$	−0.791249	+	2.02286i	−0.0438906	+	0.112208i
$326$			1.05958i			0.0586850i
$327$	2.80741	+	17.7253i	0.155250	+	0.980211i
$328$	1.47683	+	0.752481i	0.0815441	+	0.0415488i
$329$	−8.02522	+	2.60755i	−0.442445	+	0.143759i
$330$	−0.493148	+	1.81740i	−0.0271469	+	0.100044i
$331$	13.8820	+	4.51054i	0.763025	+	0.247922i	0.664577	−	0.747220i	$-0.268612\pi$
$331$	13.8820	+	4.51054i	0.763025	+	0.247922i	0.0984487	+	0.995142i	$0.468612\pi$
$332$	−2.77776	−	2.77776i	−0.152449	−	0.152449i
$333$	−0.299157	+	0.152428i	−0.0163937	+	0.00835302i
$334$	−1.23800	−	1.70396i	−0.0677405	−	0.0932367i
$335$	−13.2978	−	5.97114i	−0.726537	−	0.326238i
$336$	2.29051	−	3.15262i	0.124958	−	0.171990i
$337$	−1.25170	+	7.90293i	−0.0681845	+	0.430500i	0.929856	+	0.367924i	$0.119931\pi$
$337$	−1.25170	+	7.90293i	−0.0681845	+	0.430500i	−0.998040	+	0.0625757i	$0.980069\pi$
$338$	12.6536	+	2.00413i	0.688262	+	0.109010i
$339$	−9.67637	+	13.3184i	−0.525548	+	0.723355i
$340$	0.407868	−	3.76578i	0.0221198	−	0.204228i
$341$	0.705688	+	0.971297i	0.0382152	+	0.0525987i
$342$	5.47660	−	6.24438i	0.296141	−	0.337658i
$343$	−13.5662	+	13.5662i	−0.732509	+	0.732509i
$344$	1.30355	−	4.01190i	0.0702825	−	0.216307i
$345$	−7.69027	−	20.2252i	−0.414030	−	1.08889i
$346$	2.07092	+	6.37364i	0.111333	+	0.342649i
$347$	16.3767	−	32.1410i	0.879145	−	1.72542i	0.216805	−	0.976215i	$-0.430436\pi$
$347$	16.3767	−	32.1410i	0.879145	−	1.72542i	0.662340	−	0.749204i	$-0.269564\pi$
$348$	16.4352	−	2.60308i	0.881018	−	0.139540i
$349$		−	15.4292i		−	0.825907i	−0.910752	−	0.412953i	$-0.864497\pi$
$349$		−	15.4292i		−	0.825907i	0.910752	−	0.412953i	$-0.135503\pi$
$350$	6.57476	−	5.84491i	0.351436	−	0.312424i
$351$	1.05312			0.0562115
$352$	0.375553	−	0.0594818i	0.0200170	−	0.00317039i
$353$	−6.79035	−	3.45985i	−0.361414	−	0.184149i	0.263849	−	0.964564i	$-0.415008\pi$
$353$	−6.79035	−	3.45985i	−0.361414	−	0.184149i	−0.625262	+	0.780415i	$0.715008\pi$
$354$	−4.64527	−	14.2967i	−0.246893	−	0.759860i
$355$	11.3109	−	17.2970i	0.600318	−	0.918027i
$356$	0.813461	+	0.264309i	0.0431133	+	0.0140084i
$357$	4.66768	−	4.66768i	0.247040	−	0.247040i
$358$	1.13972	+	2.23682i	0.0602359	+	0.118220i
$359$	−1.83116	−	2.52038i	−0.0966451	−	0.133021i	0.757956	−	0.652306i	$-0.226198\pi$
$359$	−1.83116	−	2.52038i	−0.0966451	−	0.133021i	−0.854601	+	0.519285i	$0.826198\pi$
$360$	4.17044	−	0.872650i	0.219801	−	0.0459927i
$361$	−18.8376	+	2.47854i	−0.991455	+	0.130449i
$362$	14.6532	+	2.32083i	0.770153	+	0.121980i
$363$	23.7469	+	3.76114i	1.24639	+	0.197409i
$364$	0.618361	+	0.449265i	0.0324109	+	0.0235479i
$365$	2.22471	−	2.45510i	0.116447	−	0.128506i
$366$	9.19189	−	6.67830i	0.480468	−	0.349080i
$367$	−30.3579	+	15.4681i	−1.58467	+	0.807429i	−0.999993	−	0.00383758i	$-0.998778\pi$
$367$	−30.3579	+	15.4681i	−1.58467	+	0.807429i	−0.584676	+	0.811267i	$0.698778\pi$
$368$	−3.08940	+	3.08940i	−0.161046	+	0.161046i
$369$	−0.975963	+	3.00370i	−0.0508066	+	0.156367i
$370$	0.246984	+	0.306984i	0.0128401	+	0.0159593i
$371$	1.51442	−	0.492064i	0.0786246	−	0.0255467i
$372$	3.17490	−	6.23109i	0.164611	−	0.323067i
$373$	−4.52614	−	28.5769i	−0.234355	−	1.47966i	−0.771533	−	0.636189i	$-0.780510\pi$
$373$	−4.52614	−	28.5769i	−0.234355	−	1.47966i	0.537178	−	0.843469i	$-0.319490\pi$
$374$	0.644100			0.0333056
$375$	24.7614	+	0.235411i	1.27867	+	0.0121566i
$376$			4.79597i			0.247333i
$377$	0.510572	+	3.22363i	0.0262958	+	0.166025i
$378$	−3.80034	−	1.93637i	−0.195468	−	0.0995961i
$379$	9.29791	+	28.6160i	0.477602	+	1.46991i	0.842417	+	0.538827i	$0.181132\pi$
$379$	9.29791	+	28.6160i	0.477602	+	1.46991i	−0.364815	+	0.931080i	$0.618868\pi$
$380$	−8.48872	−	4.78974i	−0.435462	−	0.245709i
$381$	0.569362	−	1.75232i	0.0291693	−	0.0897738i
$382$	13.9880	−	13.9880i	0.715687	−	0.715687i
$383$	−12.7435	+	6.49313i	−0.651161	+	0.331783i	−0.748177	−	0.663500i	$-0.769070\pi$
$383$	−12.7435	+	6.49313i	−0.651161	+	0.331783i	0.0970154	+	0.995283i	$0.469070\pi$
$384$	−1.30184	−	1.79183i	−0.0664345	−	0.0914392i
$385$	1.10851	+	1.00449i	0.0564950	+	0.0511934i
$386$	20.5827	+	14.9542i	1.04763	+	0.761148i
$387$	7.93900	+	1.25741i	0.403562	+	0.0639180i
$388$	−2.83440	−	0.448926i	−0.143895	−	0.0227907i
$389$	−10.8956	+	14.9965i	−0.552430	+	0.760355i	−0.990339	−	0.138664i	$-0.955719\pi$
$389$	−10.8956	+	14.9965i	−0.552430	+	0.760355i	0.437909	+	0.899019i	$0.355719\pi$
$390$	0.440645	+	2.10587i	0.0223129	+	0.106635i
$391$	−5.98755	+	4.35021i	−0.302803	+	0.219999i
$392$	1.77255	+	3.47883i	0.0895274	+	0.175707i
$393$	3.72732	+	3.72732i	0.188018	+	0.188018i
$394$	−5.26395	+	16.2008i	−0.265194	+	0.816182i
$395$	−8.99538	−	5.88228i	−0.452606	−	0.295969i
$396$	0.223891	+	0.689064i	0.0112509	+	0.0346268i
$397$	−6.98540	+	13.7096i	−0.350587	+	0.688066i	−0.997202	−	0.0747501i	$-0.976184\pi$
$397$	−6.98540	+	13.7096i	−0.350587	+	0.688066i	0.646615	+	0.762817i	$0.276184\pi$
$398$	−3.37003	−	21.2775i	−0.168924	−	1.06654i
$399$	−6.29367	−	15.7770i	−0.315078	−	0.789838i
$400$	−2.00469	−	4.58052i	−0.100235	−	0.229026i
$401$			24.3696i			1.21696i	0.793570	+	0.608479i	$0.208220\pi$
$401$			24.3696i			1.21696i	−0.793570	+	0.608479i	$0.791780\pi$
$402$	−14.2607	+	2.25867i	−0.711259	+	0.112652i
$403$	1.22218	+	0.622731i	0.0608810	+	0.0310204i
$404$	14.6929	−	4.77401i	0.730999	−	0.237516i
$405$	−8.80990	−	23.1698i	−0.437767	−	1.15131i
$406$	4.08480	−	12.5717i	0.202725	−	0.623923i
$407$	−0.0473754	+	0.0473754i	−0.00234831	+	0.00234831i
$408$	−1.70329	−	3.34290i	−0.0843255	−	0.165498i
$409$	13.6814	−	9.94011i	0.676501	−	0.491507i	−0.195694	−	0.980665i	$-0.562696\pi$
$409$	13.6814	−	9.94011i	0.676501	−	0.491507i	0.872195	+	0.489158i	$0.162696\pi$
$410$	3.68469	+	0.399086i	0.181974	+	0.0197095i
$411$	−20.8902	+	28.7530i	−1.03044	+	1.41828i
$412$	−2.40153	+	15.1626i	−0.118315	+	0.747010i
$413$	−11.7946	−	1.86808i	−0.580373	−	0.0919220i
$414$	−6.73518	−	4.89340i	−0.331016	−	0.240497i
$415$	−8.01326	−	3.59820i	−0.393356	−	0.176629i
$416$	0.351454	−	0.255346i	0.0172314	−	0.0125194i
$417$	−11.5962	−	22.7588i	−0.567868	−	1.11450i
$418$	0.654309	−	1.52278i	0.0320033	−	0.0744817i
$419$	−13.2697	−	4.31159i	−0.648268	−	0.210635i	−0.0336176	−	0.999435i	$-0.510703\pi$
$419$	−13.2697	−	4.31159i	−0.648268	−	0.210635i	−0.614650	+	0.788800i	$0.710703\pi$
$420$	2.28191	−	8.40953i	0.111346	−	0.410343i
$421$	−6.03717	+	1.96160i	−0.294234	+	0.0956023i	−0.452414	−	0.891808i	$-0.649437\pi$
$421$	−6.03717	+	1.96160i	−0.294234	+	0.0956023i	0.158181	+	0.987410i	$0.449437\pi$
$422$	2.92522	−	5.74107i	0.142397	−	0.279471i
$423$	−9.02607	+	1.42959i	−0.438863	+	0.0695090i
$424$		−	0.905035i		−	0.0439524i
$425$	−2.14024	−	8.19490i	−0.103817	−	0.397511i
$426$		−	20.4706i		−	0.991803i
$427$	−1.41193	−	8.91457i	−0.0683281	−	0.431406i
$428$	−0.150694	+	0.295753i	−0.00728405	+	0.0142958i
$429$	−0.347943	+	0.113054i	−0.0167989	+	0.00545828i
$430$	−0.463808	−	9.42113i	−0.0223668	−	0.454327i
$431$	−9.58917	−	3.11571i	−0.461894	−	0.150078i	0.0688207	−	0.997629i	$-0.478076\pi$
$431$	−9.58917	−	3.11571i	−0.461894	−	0.150078i	−0.530715	+	0.847551i	$0.678076\pi$
$432$	−1.71417	+	1.71417i	−0.0824729	+	0.0824729i
$433$	8.20574	−	4.18103i	0.394343	−	0.200928i	−0.245564	−	0.969380i	$-0.578973\pi$
$433$	8.20574	−	4.18103i	0.394343	−	0.200928i	0.639906	+	0.768453i	$0.278973\pi$
$434$	−3.26539	−	4.49443i	−0.156744	−	0.215739i
$435$	32.2821	−	18.5019i	1.54781	−	0.887100i
$436$	4.76269	−	6.55527i	0.228091	−	0.313941i
$437$	4.20232	+	18.5749i	0.201024	+	0.888559i
$438$	0.513366	−	3.24126i	0.0245296	−	0.154874i
$439$	24.5365	+	17.8268i	1.17106	+	0.850828i	0.991136	−	0.132851i	$-0.0424133\pi$
$439$	24.5365	+	17.8268i	1.17106	+	0.850828i	0.179929	+	0.983680i	$0.442413\pi$
$440$	0.737664	−	0.422779i	0.0351668	−	0.0201552i
$441$	−6.01883	+	4.37294i	−0.286611	+	0.208235i
$442$	0.655682	−	0.334087i	0.0311876	−	0.0158909i
$443$	23.7261	−	23.7261i	1.12726	−	1.12726i	0.136639	−	0.990621i	$-0.456370\pi$
$443$	23.7261	−	23.7261i	1.12726	−	1.12726i	0.990621	−	0.136639i	$-0.0436299\pi$
$444$	0.371162	+	0.120598i	0.0176146	+	0.00572332i
$445$	1.91025	−	0.0940427i	0.0905544	−	0.00445805i
$446$	6.40041	+	19.6984i	0.303068	+	0.932747i
$447$	−23.6102	−	12.0300i	−1.11672	−	0.568999i
$448$	−1.73778	+	0.275237i	−0.0821022	+	0.0130037i
$449$	2.82503			0.133321			0.0666606	−	0.997776i	$-0.478766\pi$
$449$	2.82503			0.133321			0.0666606	+	0.997776i	$0.478766\pi$
$450$	8.02304	−	5.13822i	0.378210	−	0.242218i
$451$			0.630232i			0.0296764i
$452$	7.34131	−	1.16275i	0.345306	−	0.0546911i
$453$	−3.34715	−	1.70546i	−0.157263	−	0.0801293i
$454$	−15.7347	+	5.11250i	−0.738464	+	0.239941i
$455$	1.64946	+	0.447579i	0.0773279	+	0.0209828i
$456$	−9.63357	+	0.631043i	−0.451133	+	0.0295513i
$457$	7.38631	+	7.38631i	0.345517	+	0.345517i	0.858437	−	0.512920i	$-0.171436\pi$
$457$	7.38631	+	7.38631i	0.345517	+	0.345517i	−0.512920	+	0.858437i	$0.671436\pi$
$458$	15.4425	−	7.86835i	0.721581	−	0.367664i
$459$	−3.32221	+	2.41373i	−0.155068	+	0.112663i
$460$	−4.00190	+	8.91229i	−0.186589	+	0.415538i
$461$	−7.14850	−	5.19369i	−0.332939	−	0.241894i	0.408738	−	0.912652i	$-0.365969\pi$
$461$	−7.14850	−	5.19369i	−0.332939	−	0.241894i	−0.741677	+	0.670758i	$0.765969\pi$
$462$	1.46348	+	0.231792i	0.0680870	+	0.0107839i
$463$	0.0425230	−	0.268480i	0.00197621	−	0.0124773i	−0.986681	−	0.162670i	$-0.947989\pi$
$463$	0.0425230	−	0.268480i	0.00197621	−	0.0124773i	0.988657	+	0.150193i	$0.0479894\pi$
$464$	−6.07816	−	4.41604i	−0.282171	−	0.205009i
$465$	1.68384	−	15.5466i	0.0780863	−	0.720957i
$466$	1.11158	+	1.52995i	0.0514928	+	0.0708737i
$467$	15.6822	−	7.99050i	0.725687	−	0.369756i	−0.0517978	−	0.998658i	$-0.516495\pi$
$467$	15.6822	−	7.99050i	0.725687	−	0.369756i	0.777485	+	0.628901i	$0.216495\pi$
$468$	0.585326	+	0.585326i	0.0270567	+	0.0270567i
$469$	−3.54435	+	10.9084i	−0.163663	+	0.503703i
$470$	3.81144	+	10.0240i	0.175808	+	0.462371i
$471$	11.2265	−	3.64770i	0.517289	−	0.168077i
$472$	−3.08131	+	6.04741i	−0.141829	+	0.278354i
$473$	1.58422	−	0.250916i	0.0728424	−	0.0115371i
$474$	−10.6458			−0.488980
$475$	−21.5486	−	3.26482i	−0.988716	−	0.149800i
$476$	−2.98041			−0.136607
$477$	1.70328	−	0.269774i	0.0779881	−	0.0123521i
$478$	6.19210	−	12.1527i	0.283220	−	0.555851i
$479$	17.3026	−	5.62196i	0.790577	−	0.256874i	0.114227	−	0.993455i	$-0.463561\pi$
$479$	17.3026	−	5.62196i	0.790577	−	0.256874i	0.676350	+	0.736580i	$0.263561\pi$
$480$	−4.14496	−	2.71048i	−0.189190	−	0.123716i
$481$	−0.0236543	+	0.0728004i	−0.00107854	+	0.00331941i
$482$	−3.78799	−	3.78799i	−0.172538	−	0.172538i
$483$	−15.1700	+	7.72948i	−0.690257	+	0.351704i
$484$	−6.38066	−	8.78222i	−0.290030	−	0.399192i
$485$	−6.28090	+	1.31426i	−0.285201	+	0.0596773i
$486$	−13.9799	−	10.1570i	−0.634141	−	0.460731i
$487$	−2.05571	+	12.9792i	−0.0931531	+	0.588146i	0.896318	+	0.443413i	$0.146232\pi$
$487$	−2.05571	+	12.9792i	−0.0931531	+	0.588146i	−0.989471	+	0.144733i	$0.953768\pi$
$488$	−5.06672	−	0.802489i	−0.229360	−	0.0363270i
$489$	1.89860	+	1.37941i	0.0858577	+	0.0623793i
$490$	6.46945	+	5.86235i	0.292260	+	0.264834i
$491$	13.8066	−	10.0311i	0.623085	−	0.452697i	−0.230913	−	0.972974i	$-0.574171\pi$
$491$	13.8066	−	10.0311i	0.623085	−	0.452697i	0.853998	+	0.520277i	$0.174171\pi$
$492$	3.27092	−	1.66662i	0.147464	−	0.0751369i
$493$	−8.99914	−	8.99914i	−0.405301	−	0.405301i
$494$	−0.123774	−	1.88955i	−0.00556885	−	0.0850147i
$495$	1.01556	+	1.26227i	0.0456460	+	0.0567348i
$496$	−3.00296	+	0.975720i	−0.134837	+	0.0438111i
$497$	−14.4892	−	7.38262i	−0.649930	−	0.331156i
$498$	−8.59349	+	1.36108i	−0.385084	+	0.0609913i
$499$		−	26.7339i		−	1.19677i	−0.801207	−	0.598387i	$-0.795808\pi$
$499$		−	26.7339i		−	1.19677i	0.801207	−	0.598387i	$-0.204192\pi$
$500$	−7.83018	−	7.98049i	−0.350176	−	0.356899i
$501$	−4.66491			−0.208413
$502$	−16.4636	+	2.60758i	−0.734806	+	0.116382i
$503$	17.5538	+	8.94411i	0.782686	+	0.398798i	0.799200	−	0.601065i	$-0.205257\pi$
$503$	17.5538	+	8.94411i	0.782686	+	0.398798i	−0.0165141	+	0.999864i	$0.505257\pi$
$504$	−1.03600	−	3.18847i	−0.0461469	−	0.142026i
$505$	26.9153	−	21.6547i	1.19772	−	0.963622i
$506$	−1.57996	−	0.513361i	−0.0702380	−	0.0228217i
$507$	20.0640	−	20.0640i	0.891074	−	0.891074i
$508$	−0.741219	+	0.377670i	−0.0328863	+	0.0167564i
$509$	6.53586	−	4.74858i	0.289697	−	0.210477i	−0.433439	−	0.901183i	$-0.642700\pi$
$509$	6.53586	−	4.74858i	0.289697	−	0.210477i	0.723136	+	0.690706i	$0.242700\pi$
$510$	−6.21667	−	5.63329i	−0.275279	−	0.249446i
$511$	−2.10904	−	1.53231i	−0.0932986	−	0.0677854i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	2.33167	+	10.3064i	0.102946	+	0.455037i
$514$	−1.30050	+	1.78999i	−0.0573627	+	0.0789529i
$515$	7.03061	+	33.5996i	0.309806	+	1.48058i
$516$	−5.49165	−	7.55861i	−0.241756	−	0.332749i
$517$	−1.62483	+	0.827894i	−0.0714601	+	0.0364107i
$518$	0.219218	−	0.219218i	0.00963187	−	0.00963187i
$519$	14.1165	+	4.58674i	0.619647	+	0.201335i
$520$	0.531638	−	0.812999i	0.0233139	−	0.0356524i
$521$	21.8033	−	7.08432i	0.955219	−	0.310370i	0.210385	−	0.977619i	$-0.432528\pi$
$521$	21.8033	−	7.08432i	0.955219	−	0.310370i	0.744835	+	0.667249i	$0.232528\pi$
$522$	6.49925	−	12.7555i	0.284464	−	0.558293i
$523$	3.01517	+	19.0370i	0.131844	+	0.832430i	0.961630	+	0.274349i	$0.0884623\pi$
$523$	3.01517	+	19.0370i	0.131844	+	0.832430i	−0.829786	+	0.558081i	$0.811538\pi$
$524$		−	2.37997i		−	0.103969i
$525$	−1.91381	−	19.3900i	−0.0835254	−	0.846251i
$526$			3.04755i			0.132880i
$527$	−5.28281	+	0.836714i	−0.230123	+	0.0364479i
$528$	0.382330	−	0.750365i	0.0166388	−	0.0326554i
$529$	−3.71976	+	1.20862i	−0.161729	+	0.0525488i
$530$	−0.719245	−	1.89159i	−0.0312420	−	0.0821656i
$531$	−12.2998	−	3.99644i	−0.533764	−	0.173431i
$532$	−3.02765	+	7.04628i	−0.131265	+	0.305495i
$533$	0.326893	+	0.641564i	0.0141593	+	0.0277892i
$534$	1.53260	−	1.11350i	0.0663220	−	0.0481857i
$535$	−0.0799220	+	0.737905i	−0.00345533	+	0.0319024i
$536$	5.27398	+	3.83177i	0.227801	+	0.165507i
$537$	5.49175	+	0.869808i	0.236986	+	0.0375350i
$538$	3.62026	−	22.8574i	0.156081	−	0.985454i
$539$	−0.872614	+	1.20105i	−0.0375862	+	0.0517329i
$540$	−2.22047	+	4.94502i	−0.0955537	+	0.212800i
$541$	7.24321	−	5.26250i	0.311410	−	0.226253i	−0.421091	−	0.907018i	$-0.638353\pi$
$541$	7.24321	−	5.26250i	0.311410	−	0.226253i	0.732501	+	0.680766i	$0.238353\pi$
$542$	6.98152	+	13.7020i	0.299882	+	0.588551i
$543$	23.2347	−	23.2347i	0.997096	−	0.997096i
$544$	−0.523461	+	1.61105i	−0.0224432	+	0.0690731i
$545$	4.74481	−	17.4860i	0.203245	−	0.749019i
$546$	1.61002	−	0.523127i	0.0689024	−	0.0223878i
$547$	32.9425	+	16.7850i	1.40852	+	0.717676i	0.982365	−	0.186975i	$-0.0598684\pi$
$547$	32.9425	+	16.7850i	1.40852	+	0.717676i	0.426153	+	0.904651i	$0.359868\pi$
$548$	15.8491	−	2.51025i	0.677040	−	0.107233i
$549$		−	9.77482i		−	0.417179i
$550$	1.20579	−	1.46988i	0.0514149	−	0.0626757i
$551$	−30.4176	+	12.1340i	−1.29583	+	0.516926i
$552$	1.51378	+	9.55762i	0.0644307	+	0.406799i
$553$	−3.83937	+	7.53519i	−0.163267	+	0.320429i
$554$	−2.83698	−	8.73133i	−0.120532	−	0.370959i
$555$	0.871598	−	0.0429093i	0.0369973	−	0.00182140i
$556$	−3.56378	+	10.9682i	−0.151138	+	0.465154i
$557$	−0.465492	−	0.465492i	−0.0197235	−	0.0197235i	0.697176	−	0.716900i	$-0.254439\pi$
$557$	−0.465492	−	0.465492i	−0.0197235	−	0.0197235i	−0.716900	+	0.697176i	$0.754439\pi$
$558$	−2.73144	−	5.36075i	−0.115631	−	0.226939i
$559$	1.48256	−	1.07714i	0.0627056	−	0.0455583i
$560$	−3.41335	+	1.95630i	−0.144240	+	0.0826689i
$561$	0.838518	−	1.15412i	0.0354022	−	0.0487270i
$562$	−19.1099	−	3.02671i	−0.806101	−	0.127674i
$563$	34.5285	+	5.46877i	1.45520	+	0.230481i	0.833390	−	0.552685i	$-0.186397\pi$
$563$	34.5285	+	5.46877i	1.45520	+	0.230481i	0.621812	+	0.783167i	$0.286397\pi$
$564$	8.59359	+	6.24361i	0.361855	+	0.262903i
$565$	14.4198	−	8.26449i	0.606648	−	0.347690i
$566$	9.12101	+	12.5540i	0.383385	+	0.527684i
$567$	−17.3786	+	8.85481i	−0.729831	+	0.371867i
$568$	−6.53544	+	6.53544i	−0.274221	+	0.274221i
$569$	−10.2064	+	31.4121i	−0.427875	+	1.31686i	0.472340	+	0.881416i	$0.343409\pi$
$569$	−10.2064	+	31.4121i	−0.427875	+	1.31686i	−0.900215	+	0.435446i	$0.856591\pi$
$570$	−19.6334	+	8.97488i	−0.822353	+	0.375916i
$571$	−11.8234	−	36.3887i	−0.494794	−	1.52282i	−0.817278	−	0.576243i	$-0.804518\pi$
$571$	−11.8234	−	36.3887i	−0.494794	−	1.52282i	0.322485	−	0.946575i	$-0.395482\pi$
$572$	0.147178	+	0.0749909i	0.00615382	+	0.00313553i
$573$	−6.85397	−	43.2743i	−0.286329	−	1.80781i
$574$		−	2.91623i		−	0.121721i
$575$	−1.28154	+	21.8078i	−0.0534439	+	0.909446i
$576$	−1.90547			−0.0793946
$577$	1.18416	+	7.47649i	0.0492972	+	0.311250i	0.999999	+	0.00114469i	$0.000364366\pi$
$577$	1.18416	+	7.47649i	0.0492972	+	0.311250i	−0.950702	+	0.310105i	$0.899636\pi$
$578$	6.41512	−	12.5904i	0.266834	−	0.523691i
$579$	53.5909	−	17.4127i	2.22716	−	0.723648i
$580$	−16.2133	−	4.39946i	−0.673221	−	0.182678i
$581$	−2.13582	+	6.57339i	−0.0886089	+	0.272710i
$582$	−4.49435	+	4.49435i	−0.186297	+	0.186297i
$583$	0.306618	−	0.156230i	0.0126988	−	0.00647037i
$584$	−1.19870	+	0.870909i	−0.0496027	+	0.0360385i
$585$	1.68854	+	0.758209i	0.0698127	+	0.0313481i
$586$	18.4360	+	13.3945i	0.761583	+	0.553323i
$587$	−32.4985	−	5.14725i	−1.34136	−	0.212450i	−0.555839	−	0.831290i	$-0.687603\pi$
$587$	−32.4985	−	5.14725i	−1.34136	−	0.212450i	−0.785517	+	0.618840i	$0.787603\pi$
$588$	8.54107	+	1.35277i	0.352228	+	0.0557874i
$589$	−3.38838	+	13.3396i	−0.139616	+	0.549648i
$590$	−1.63420	+	15.0883i	−0.0672792	+	0.621176i
$591$	22.1762	+	30.5230i	0.912209	+	1.25555i
$592$	−0.0799951	−	0.156999i	−0.00328778	−	0.00645263i
$593$	11.4924	−	11.4924i	0.471937	−	0.471937i	−0.430604	−	0.902541i	$-0.641699\pi$
$593$	11.4924	−	11.4924i	0.471937	−	0.471937i	0.902541	+	0.430604i	$0.141699\pi$
$594$	−0.876649	−	0.284840i	−0.0359693	−	0.0116871i
$595$	−6.22928	+	2.36858i	−0.255376	+	0.0971022i
$596$	3.69710	+	11.3785i	0.151439	+	0.466081i
$597$	−42.5130	−	21.6615i	−1.73994	−	0.886545i
$598$	−1.87465	+	0.296915i	−0.0766601	+	0.0121418i
$599$	21.8903			0.894414			0.447207	−	0.894430i	$-0.352419\pi$
$599$	21.8903			0.894414			0.447207	+	0.894430i	$0.352419\pi$
$600$	−10.8173	−	2.37105i	−0.441616	−	0.0967978i
$601$		−	15.6719i		−	0.639269i	−0.947541	−	0.319634i	$-0.896440\pi$
$601$		−	15.6719i		−	0.639269i	0.947541	−	0.319634i	$-0.103560\pi$
$602$	−7.33057	+	1.16105i	−0.298772	+	0.0473208i
$603$	−5.63936	+	11.0679i	−0.229652	+	0.450718i
$604$	0.524126	+	1.61309i	0.0213264	+	0.0656359i
$605$	−20.3154	−	13.2847i	−0.825940	−	0.540101i
$606$	10.5736	−	32.5422i	0.429524	−	1.32194i
$607$	10.9426	−	10.9426i	0.444147	−	0.444147i	−0.449256	−	0.893403i	$-0.648311\pi$
$607$	10.9426	−	10.9426i	0.444147	−	0.444147i	0.893403	+	0.449256i	$0.148311\pi$
$608$	3.27708	+	2.87415i	0.132903	+	0.116562i
$609$	−17.2087	−	23.6857i	−0.697330	−	0.959792i
$610$	−11.2276	+	2.34933i	−0.454592	+	0.0951218i
$611$	−1.22463	+	1.68556i	−0.0495434	+	0.0681906i
$612$	−3.18804	−	0.504936i	−0.128869	−	0.0204108i
$613$	−5.24426	+	33.1110i	−0.211814	+	1.33734i	0.621011	+	0.783802i	$0.286722\pi$
$613$	−5.24426	+	33.1110i	−0.211814	+	1.33734i	−0.832825	+	0.553537i	$0.813278\pi$
$614$	−12.9608	+	17.8390i	−0.523056	+	0.719925i
$615$	5.51199	−	6.08281i	0.222265	−	0.245283i
$616$	−0.393227	−	0.541231i	−0.0158436	−	0.0218068i
$617$	−14.0916	+	7.18002i	−0.567306	+	0.289057i	−0.714024	−	0.700122i	$-0.753129\pi$
$617$	−14.0916	+	7.18002i	−0.567306	+	0.289057i	0.146718	+	0.989178i	$0.453129\pi$
$618$	24.0425	+	24.0425i	0.967133	+	0.967133i
$619$	42.1554	+	13.6971i	1.69437	+	0.550533i	0.987611	−	0.156924i	$-0.0501577\pi$
$619$	42.1554	+	13.6971i	1.69437	+	0.550533i	0.706756	+	0.707457i	$0.250158\pi$
$620$	−5.50100	+	4.42583i	−0.220925	+	0.177746i
$621$	10.0731	−	3.27295i	0.404220	−	0.131339i
$622$	11.8048	+	6.01487i	0.473331	+	0.241174i
$623$	−0.235416	−	1.48636i	−0.00943175	−	0.0595497i
$624$		−	0.962168i		−	0.0385175i
$625$	−22.7079	−	10.4571i	−0.908316	−	0.418284i
$626$		−	30.3248i		−	1.21202i
$627$	−1.87677	−	3.15484i	−0.0749508	−	0.125992i
$628$	−4.74873	−	2.41960i	−0.189495	−	0.0965525i
$629$	−0.0922361	−	0.283874i	−0.00367769	−	0.0113188i
$630$	−4.69924	−	5.84083i	−0.187222	−	0.232704i
$631$	−3.99581	+	12.2978i	−0.159071	+	0.489569i	−0.998551	−	0.0538214i	$-0.982860\pi$
$631$	−3.99581	+	12.2978i	−0.159071	+	0.489569i	0.839480	+	0.543391i	$0.182860\pi$
$632$	3.39879	+	3.39879i	0.135197	+	0.135197i
$633$	−6.47886	−	12.7155i	−0.257512	−	0.505395i
$634$	−15.1161	−	20.8055i	−0.600337	−	0.826294i
$635$	−1.24907	+	1.37842i	−0.0495677	+	0.0547009i
$636$	−1.62167	−	1.17821i	−0.0643035	−	0.0467192i
$637$	−0.265335	+	1.67526i	−0.0105130	+	0.0663763i
$638$	0.446887	−	2.82154i	0.0176924	−	0.111706i
$639$	−14.2479	−	10.3517i	−0.563637	−	0.409506i
$640$	0.457971	+	2.18867i	0.0181029	+	0.0865147i
$641$	19.9475	+	27.4553i	0.787877	+	1.08442i	0.994369	+	0.105972i	$0.0337953\pi$
$641$	19.9475	+	27.4553i	0.787877	+	1.08442i	−0.206492	+	0.978448i	$0.566205\pi$
$642$	0.333761	+	0.655042i	0.0131725	+	0.0258524i
$643$	17.8815	−	17.8815i	0.705176	−	0.705176i	−0.260341	−	0.965517i	$-0.583835\pi$
$643$	17.8815	−	17.8815i	0.705176	−	0.705176i	0.965517	+	0.260341i	$0.0838349\pi$
$644$	7.31088	+	2.37545i	0.288089	+	0.0936058i
$645$	−17.4849	−	11.4338i	−0.688468	−	0.450205i
$646$	4.72126	+	5.67714i	0.185755	+	0.223364i
$647$	10.6055	−	20.8145i	0.416946	−	0.818302i	−0.583037	−	0.812445i	$-0.698136\pi$
$647$	10.6055	−	20.8145i	0.416946	−	0.818302i	0.999983	−	0.00585649i	$-0.00186419\pi$
$648$	1.73417	+	10.9491i	0.0681246	+	0.430122i
$649$	−2.58071			−0.101302
$650$	0.465062	−	2.12173i	0.0182412	−	0.0832212i
$651$	−12.3043			−0.482244
$652$	−0.165756	−	1.04654i	−0.00649149	−	0.0409856i
$653$	−9.40484	−	4.79200i	−0.368040	−	0.187526i	0.260183	−	0.965559i	$-0.416217\pi$
$653$	−9.40484	−	4.79200i	−0.368040	−	0.187526i	−0.628222	+	0.778034i	$0.716217\pi$
$654$	−5.54569	−	17.0679i	−0.216854	−	0.667407i
$655$	−1.89140	−	4.97432i	−0.0739030	−	0.194363i
$656$	−1.57636	−	0.512190i	−0.0615465	−	0.0199977i
$657$	−1.99637	−	1.99637i	−0.0778859	−	0.0778859i
$658$	7.51850	−	3.83087i	0.293102	−	0.149343i
$659$	−1.78440	+	1.29645i	−0.0695105	+	0.0505023i	−0.621998	−	0.783019i	$-0.713679\pi$
$659$	−1.78440	+	1.29645i	−0.0695105	+	0.0505023i	0.552487	+	0.833521i	$0.313679\pi$
$660$	0.202773	−	1.87217i	0.00789292	−	0.0728739i
$661$	23.7180	−	32.6451i	0.922524	−	1.26975i	−0.0401811	−	0.999192i	$-0.512794\pi$
$661$	23.7180	−	32.6451i	0.922524	−	1.26975i	0.962705	−	0.270553i	$-0.0872065\pi$
$662$	−14.4167	−	2.28338i	−0.560322	−	0.0887463i
$663$	0.254968	−	1.60980i	0.00990213	−	0.0625196i
$664$	3.17810	+	2.30902i	0.123334	+	0.0896075i
$665$	−0.728224	+	17.1334i	−0.0282393	+	0.664405i
$666$	0.271629	−	0.197350i	0.0105254	−	0.00764716i
$667$	14.9022	+	29.2472i	0.577016	+	1.13246i
$668$	1.48932	+	1.48932i	0.0576235	+	0.0576235i
$669$	43.6286	+	14.1758i	1.68678	+	0.548068i
$670$	14.0682	+	3.81738i	0.543502	+	0.147478i
$671$	−0.602755	−	1.85509i	−0.0232691	−	0.0716149i
$672$	−1.76913	+	3.47212i	−0.0682458	+	0.133940i
$673$	1.09651	+	6.92308i	0.0422673	+	0.266865i	0.999767	−	0.0215678i	$-0.00686578\pi$
$673$	1.09651	+	6.92308i	0.0422673	+	0.266865i	−0.957500	+	0.288433i	$0.906866\pi$
$674$		−	8.00144i		−	0.308204i
$675$	−0.711067	+	12.1001i	−0.0273690	+	0.465733i
$676$	−12.8113			−0.492741
$677$	−15.5818	+	2.46791i	−0.598857	+	0.0948496i	−0.448501	−	0.893782i	$-0.648042\pi$
$677$	−15.5818	+	2.46791i	−0.598857	+	0.0948496i	−0.150356	+	0.988632i	$0.548042\pi$
$678$	7.47378	−	14.6681i	0.287029	−	0.563326i
$679$	1.56026	+	4.80200i	0.0598774	+	0.184284i
$680$	0.186250	+	3.78322i	0.00714237	+	0.145080i
$681$	−11.3233	+	34.8496i	−0.433910	+	1.33544i
$682$	−0.848944	−	0.848944i	−0.0325078	−	0.0325078i
$683$	−3.80986	+	1.94122i	−0.145780	+	0.0742787i	−0.525359	−	0.850881i	$-0.676069\pi$
$683$	−3.80986	+	1.94122i	−0.145780	+	0.0742787i	0.379579	+	0.925159i	$0.376069\pi$
$684$	−4.43234	+	7.02423i	−0.169475	+	0.268578i
$685$	31.1309	−	17.8421i	1.18945	−	0.681713i
$686$	11.2770	−	15.5215i	0.430558	−	0.592612i
$687$	6.00495	−	37.9138i	0.229103	−	1.44650i
$688$	−0.659897	+	4.16643i	−0.0251583	+	0.158844i
$689$	0.231097	−	0.318078i	0.00880410	−	0.0121178i
$690$	10.7595	+	18.7731i	0.409607	+	0.714682i
$691$	−28.4666	+	20.6822i	−1.08292	+	0.786788i	−0.978190	−	0.207713i	$-0.933398\pi$
$691$	−28.4666	+	20.6822i	−1.08292	+	0.786788i	−0.104731	+	0.994501i	$0.533398\pi$
$692$	−3.04248	−	5.97121i	−0.115658	−	0.226991i
$693$	0.901389	−	0.901389i	0.0342409	−	0.0342409i
$694$	−11.1471	+	34.3072i	−0.423137	+	1.30228i
$695$	1.26801	+	25.7565i	0.0480984	+	0.977001i
$696$	−15.8256	+	5.14206i	−0.599869	+	0.194909i
$697$	−2.50168	−	1.27467i	−0.0947578	−	0.0482815i
$698$	2.41366	+	15.2393i	0.0913584	+	0.576814i
$699$	4.18852			0.158424
$700$	−5.57947	+	6.80147i	−0.210884	+	0.257071i
$701$	10.1248			0.382407			0.191203	−	0.981550i	$-0.438761\pi$
$701$	10.1248			0.382407			0.191203	+	0.981550i	$0.438761\pi$
$702$	−1.04016	+	0.164745i	−0.0392582	+	0.00621788i
$703$	−0.764832	−	0.0703081i	−0.0288462	−	0.00265172i
$704$	−0.361624	+	0.117499i	−0.0136292	+	0.00442841i
$705$	22.9232	+	6.22017i	0.863337	+	0.234265i
$706$	7.24799	+	2.35501i	0.272782	+	0.0886321i
$707$	−19.2203	−	19.2203i	−0.722853	−	0.722853i
$708$	6.82457	+	13.3940i	0.256483	+	0.503376i
$709$	23.2959	+	32.0640i	0.874896	+	1.20419i	0.977809	+	0.209500i	$0.0671836\pi$
$709$	23.2959	+	32.0640i	0.874896	+	1.20419i	−0.102913	+	0.994690i	$0.532816\pi$
$710$	−8.46577	+	18.8534i	−0.317715	+	0.707556i
$711$	−5.38345	+	7.40968i	−0.201895	+	0.277885i
$712$	−0.844793	−	0.133802i	−0.0316599	−	0.00501444i
$713$	13.6255	+	2.15807i	0.510279	+	0.0808202i
$714$	−3.88003	+	5.34040i	−0.145206	+	0.199859i
$715$	0.367210	+	0.0397722i	0.0137329	+	0.00148740i
$716$	−1.47560	−	2.03099i	−0.0551458	−	0.0759017i
$717$	−13.7145	−	26.9161i	−0.512176	−	1.00520i
$718$	2.20289	+	2.20289i	0.0822113	+	0.0822113i
$719$	24.5053	+	7.96227i	0.913895	+	0.296943i	0.727960	−	0.685619i	$-0.240469\pi$
$719$	24.5053	+	7.96227i	0.913895	+	0.296943i	0.185935	+	0.982562i	$0.440469\pi$
$720$	−3.98258	+	1.51431i	−0.148422	+	0.0564349i
$721$	25.6883	−	8.34663i	0.956682	−	0.310845i
$722$	18.2180	−	5.39488i	0.678004	−	0.200777i
$723$	−11.7188	+	1.85608i	−0.435827	+	0.0690283i
$724$	−14.8358			−0.551369
$725$	−37.3834	+	3.68976i	−1.38839	+	0.137034i
$726$	−24.0429			−0.892316
$727$	1.55974	+	9.84780i	0.0578475	+	0.365235i	0.999583	+	0.0288800i	$0.00919408\pi$
$727$	1.55974	+	9.84780i	0.0578475	+	0.365235i	−0.941735	+	0.336355i	$0.890806\pi$
$728$	−0.681028	−	0.347001i	−0.0252406	−	0.0128607i
$729$	−4.77023	+	1.54994i	−0.176675	+	0.0574053i
$730$	−1.81326	+	2.77290i	−0.0671117	+	0.102630i
$731$	−2.20815	+	6.79598i	−0.0816713	+	0.251358i
$732$	−8.03401	+	8.03401i	−0.296945	+	0.296945i
$733$	−5.81969	−	11.4218i	−0.214955	−	0.421874i	0.758200	−	0.652022i	$-0.226079\pi$
$733$	−5.81969	−	11.4218i	−0.214955	−	0.421874i	−0.973156	+	0.230148i	$0.926079\pi$
$734$	27.5644	−	20.0267i	1.01742	−	0.739199i
$735$	18.9266	−	3.96032i	0.698117	−	0.146079i
$736$	2.56808	−	3.53466i	0.0946606	−	0.130289i
$737$	−0.387761	+	2.44823i	−0.0142834	+	0.0901817i
$738$	0.494064	−	3.11940i	0.0181868	−	0.114827i
$739$	−23.5736	+	32.4463i	−0.867170	+	1.19356i	0.112642	+	0.993636i	$0.464069\pi$
$739$	−23.5736	+	32.4463i	−0.867170	+	1.19356i	−0.979812	+	0.199922i	$0.935931\pi$
$740$	−0.291966	−	0.264567i	−0.0107329	−	0.00972569i
$741$	−3.54689	−	2.23811i	−0.130298	−	0.0822191i
$742$	−1.41880	+	0.722912i	−0.0520856	+	0.0265390i
$743$	19.3267	+	19.3267i	0.709027	+	0.709027i	0.966331	−	0.257304i	$-0.0828340\pi$
$743$	19.3267	+	19.3267i	0.709027	+	0.709027i	−0.257304	+	0.966331i	$0.582834\pi$
$744$	−2.16105	+	6.65104i	−0.0792281	+	0.243839i
$745$	16.7699	+	20.8438i	0.614401	+	0.763657i
$746$	8.94084	+	27.5171i	0.327347	+	1.00747i
$747$	−3.39827	+	6.66949i	−0.124336	+	0.244024i
$748$	−0.636170	+	0.100759i	−0.0232607	+	0.00368413i
$749$	0.584012			0.0213393
$750$	−24.4934	+	3.64103i	−0.894373	+	0.132952i
$751$		−	6.86670i		−	0.250569i	−0.992121	−	0.125285i	$-0.960016\pi$
$751$		−	6.86670i		−	0.250569i	0.992121	−	0.125285i	$-0.0399844\pi$
$752$	−0.750255	−	4.73693i	−0.0273590	−	0.172738i
$753$	−16.7607	+	32.8947i	−0.610794	+	1.19875i
$754$	−1.00857	−	3.10407i	−0.0367301	−	0.113043i
$755$	2.37742	+	2.95496i	0.0865230	+	0.107542i
$756$	4.05647	+	1.31803i	0.147532	+	0.0479361i
$757$	−6.44154	−	6.44154i	−0.234122	−	0.234122i	0.580289	−	0.814411i	$-0.302940\pi$
$757$	−6.44154	−	6.44154i	−0.234122	−	0.234122i	−0.814411	+	0.580289i	$0.802940\pi$
$758$	−13.6600	−	26.8092i	−0.496153	−	0.973754i
$759$	−2.97673	+	2.16272i	−0.108048	+	0.0785017i
$760$	9.13349	+	3.40285i	0.331306	+	0.123434i
$761$	3.30855	+	2.40380i	0.119935	+	0.0871377i	0.646136	−	0.763223i	$-0.276384\pi$
$761$	3.30855	+	2.40380i	0.119935	+	0.0871377i	−0.526201	+	0.850360i	$0.676384\pi$
$762$	−0.288230	+	1.81981i	−0.0104415	+	0.0659247i
$763$	−14.0808	−	2.23018i	−0.509759	−	0.0807378i
$764$	−11.6276	+	16.0040i	−0.420670	+	0.579003i
$765$	−7.06454	+	1.47823i	−0.255419	+	0.0534455i
$766$	11.5708	−	8.40670i	0.418071	−	0.303747i
$767$	−2.62712	+	1.33858i	−0.0948598	+	0.0483335i
$768$	1.56612	+	1.56612i	0.0565125	+	0.0565125i
$769$	22.5447	+	7.32523i	0.812984	+	0.264155i	0.685861	−	0.727732i	$-0.259426\pi$
$769$	22.5447	+	7.32523i	0.812984	+	0.264155i	0.127123	+	0.991887i	$0.459426\pi$
$770$	−1.25200	−	0.818711i	−0.0451190	−	0.0295043i
$771$	1.51431	+	4.66057i	0.0545366	+	0.167846i
$772$	−22.6686	−	11.5502i	−0.815862	−	0.415702i
$773$	5.08181	+	32.0853i	0.182780	+	1.15403i	0.893003	+	0.450050i	$0.148594\pi$
$773$	5.08181	+	32.0853i	0.182780	+	1.15403i	−0.710223	+	0.703977i	$0.751406\pi$
$774$	−8.03796			−0.288919
$775$	−7.98024	+	13.6221i	−0.286659	+	0.489319i
$776$	2.86974			0.103018
$777$	−0.107415	−	0.678189i	−0.00385348	−	0.0243299i
$778$	8.41551	−	16.5164i	0.301711	−	0.592140i
$779$	−5.55490	+	4.61960i	−0.199025	+	0.165514i
$780$	−0.764650	−	2.01101i	−0.0273789	−	0.0720056i
$781$	−3.34232	−	1.08598i	−0.119598	−	0.0388596i
$782$	5.23331	−	5.23331i	0.187143	−	0.187143i
$783$	8.26854	+	16.2279i	0.295494	+	0.579939i
$784$	−2.29494	−	3.15871i	−0.0819621	−	0.112811i
$785$	−11.8481	−	1.28326i	−0.422877	−	0.0458015i
$786$	−4.26451	−	3.09835i	−0.152110	−	0.110514i
$787$	2.75171	−	17.3736i	0.0980878	−	0.619302i	−0.888850	−	0.458199i	$-0.848495\pi$
$787$	2.75171	−	17.3736i	0.0980878	−	0.619302i	0.986938	−	0.161103i	$-0.0515053\pi$
$788$	2.66478	−	16.8248i	0.0949289	−	0.599357i
$789$	5.46071	+	3.96744i	0.194406	+	0.141244i
$790$	9.80482	+	4.40267i	0.348840	+	0.156640i
$791$	−7.68680	−	10.5800i	−0.273311	−	0.376181i
$792$	−0.328928	−	0.645557i	−0.0116879	−	0.0229389i
$793$	−1.57580	−	1.57580i	−0.0559585	−	0.0559585i
$794$	4.75474	−	14.6336i	0.168740	−	0.519327i
$795$	−4.32577	−	1.17379i	−0.153419	−	0.0416301i
$796$	6.65707	+	20.4884i	0.235954	+	0.726190i
$797$	−34.2254	−	17.4387i	−1.21232	−	0.617710i	−0.273423	−	0.961894i	$-0.588156\pi$
$797$	−34.2254	−	17.4387i	−1.21232	−	0.617710i	−0.938902	+	0.344184i	$0.888156\pi$
$798$	8.68425	+	14.5982i	0.307419	+	0.516771i
$799$		−	8.12416i		−	0.287412i
$800$	2.69656	+	4.21053i	0.0953379	+	0.148865i
$801$		−	1.62979i		−	0.0575859i
$802$	−3.81224	−	24.0695i	−0.134615	−	0.849925i
$803$	−0.501980	−	0.255772i	−0.0177145	−	0.00902598i
$804$	13.7318	−	4.46173i	0.484283	−	0.157353i
$805$	17.1681	−	0.845197i	0.605096	−	0.0297893i
$806$	−1.30455	−	0.423873i	−0.0459507	−	0.0149303i
$807$	−36.2437	−	36.2437i	−1.27584	−	1.27584i
$808$	−13.7652	+	7.01371i	−0.484257	+	0.246741i
$809$	18.2740	+	25.1520i	0.642480	+	0.884298i	0.998745	−	0.0500872i	$-0.0159499\pi$
$809$	18.2740	+	25.1520i	0.642480	+	0.884298i	−0.356265	+	0.934385i	$0.615950\pi$
$810$	12.3260	+	21.5063i	0.433091	+	0.755655i
$811$	9.27482	−	12.7657i	0.325683	−	0.448264i	−0.614509	−	0.788910i	$-0.710646\pi$
$811$	9.27482	−	12.7657i	0.325683	−	0.448264i	0.940192	+	0.340646i	$0.110646\pi$
$812$	−2.06786	+	13.0559i	−0.0725675	+	0.458173i
$813$	33.6406	+	5.32814i	1.17983	+	0.186866i
$814$	0.0393810	−	0.0542033i	0.00138030	−	0.00189982i
$815$	−1.17814	−	2.05562i	−0.0412686	−	0.0720052i
$816$	2.20527	+	3.03529i	0.0771997	+	0.106256i
$817$	13.8239	+	12.1242i	0.483638	+	0.424172i
$818$	−11.9580	+	11.9580i	−0.418101	+	0.418101i
$819$	0.450058	−	1.38514i	0.0157263	−	0.0484006i
$820$	−3.70176	+	0.182240i	−0.129271	+	0.00636409i
$821$	−3.53826	−	10.8897i	−0.123486	−	0.380052i	0.870136	−	0.492812i	$-0.164031\pi$
$821$	−3.53826	−	10.8897i	−0.123486	−	0.380052i	−0.993622	+	0.112760i	$0.964031\pi$
$822$	16.1351	−	31.6669i	0.562776	−	1.10451i
$823$	11.4334	−	1.81088i	0.398544	−	0.0631232i	0.0460547	−	0.998939i	$-0.485335\pi$
$823$	11.4334	−	1.81088i	0.398544	−	0.0631232i	0.352490	+	0.935816i	$0.385335\pi$
$824$		−	15.3516i		−	0.534800i
$825$	−1.06403	−	4.07412i	−0.0370447	−	0.141843i
$826$	11.9416			0.415501
$827$	−49.0085	+	7.76219i	−1.70419	+	0.269918i	−0.931203	−	0.364500i	$-0.881240\pi$
$827$	−49.0085	+	7.76219i	−1.70419	+	0.269918i	−0.772990	+	0.634418i	$0.781240\pi$
$828$	7.41776	+	3.77954i	0.257785	+	0.131348i
$829$	−7.55123	−	23.2403i	−0.262265	−	0.807169i	−0.992311	−	0.123771i	$-0.960501\pi$
$829$	−7.55123	−	23.2403i	−0.262265	−	0.807169i	0.730046	−	0.683398i	$-0.239499\pi$
$830$	8.47749	+	2.30035i	0.294258	+	0.0798465i
$831$	−19.3384	−	6.28343i	−0.670842	−	0.217970i
$832$	−0.307182	+	0.307182i	−0.0106496	+	0.0106496i
$833$	−3.00262	−	5.89298i	−0.104035	−	0.204180i
$834$	15.0137	+	20.6646i	0.519881	+	0.715555i
$835$	4.29638	+	1.92921i	0.148682	+	0.0667630i
$836$	−0.408038	+	1.60639i	−0.0141123	+	0.0555582i
$837$	7.56016	+	1.19741i	0.261317	+	0.0413886i
$838$	13.7808	+	2.18267i	0.476051	+	0.0753990i
$839$	−30.3224	−	22.0305i	−1.04684	−	0.760577i	−0.0752346	−	0.997166i	$-0.523971\pi$
$839$	−30.3224	−	22.0305i	−1.04684	−	0.760577i	−0.971610	+	0.236589i	$0.923971\pi$
$840$	−0.938280	+	8.66296i	−0.0323737	+	0.298901i
$841$	−22.2038	+	16.1320i	−0.765648	+	0.556276i
$842$	5.65598	−	2.88187i	0.194918	−	0.0993157i
$843$	−30.3014	+	30.3014i	−1.04364	+	1.04364i
$844$	−1.99110	+	6.12799i	−0.0685366	+	0.210934i
$845$	−26.7766	+	10.1813i	−0.921142	+	0.350248i
$846$	8.69131	−	2.82398i	0.298813	−	0.0970904i
$847$	−8.67096	+	17.0177i	−0.297938	+	0.584736i
$848$	0.141579	+	0.893892i	0.00486183	+	0.0306964i
$849$	34.3688			1.17953
$850$	3.39586	+	7.75920i	0.116477	+	0.266138i
$851$			0.769850i			0.0263901i
$852$	3.20231	+	20.2186i	0.109709	+	0.692677i
$853$	24.4027	+	12.4338i	0.835532	+	0.425725i	0.818761	−	0.574134i	$-0.194661\pi$
$853$	24.4027	+	12.4338i	0.835532	+	0.425725i	0.0167711	+	0.999859i	$0.494661\pi$
$854$	2.78909	+	8.58394i	0.0954408	+	0.293737i
$855$	−3.68167	+	18.2036i	−0.125911	+	0.622552i
$856$	0.102572	−	0.315685i	0.00350585	−	0.0107899i
$857$	−1.35017	+	1.35017i	−0.0461209	+	0.0461209i	−0.729791	−	0.683670i	$-0.760383\pi$
$857$	−1.35017	+	1.35017i	−0.0461209	+	0.0461209i	0.683670	+	0.729791i	$0.260383\pi$
$858$	0.325974	−	0.166092i	0.0111286	−	0.00567029i
$859$	−13.1738	−	18.1322i	−0.449486	−	0.618664i	0.522801	−	0.852455i	$-0.324887\pi$
$859$	−13.1738	−	18.1322i	−0.449486	−	0.618664i	−0.972287	+	0.233791i	$0.924887\pi$
$860$	1.93189	+	9.23259i	0.0658768	+	0.314829i
$861$	−5.22541	−	3.79648i	−0.178082	−	0.129384i
$862$	9.95851	+	1.57727i	0.339188	+	0.0537221i
$863$	−30.4239	−	4.81867i	−1.03564	−	0.164029i	−0.384609	−	0.923080i	$-0.625664\pi$
$863$	−30.4239	−	4.81867i	−1.03564	−	0.164029i	−0.651032	+	0.759050i	$0.725664\pi$
$864$	1.42491	−	1.96122i	0.0484763	−	0.0667219i
$865$	−11.1044	−	10.0624i	−0.377562	−	0.342131i
$866$	−7.45065	+	5.41322i	−0.253183	+	0.183949i
$867$	−14.2084	−	27.8856i	−0.482542	−	0.947043i
$868$	3.92827	+	3.92827i	0.133334	+	0.133334i
$869$	−0.564772	+	1.73819i	−0.0191586	+	0.0589641i
$870$	−28.9903	+	23.3242i	−0.982864	+	0.790764i
$871$	0.875132	+	2.69338i	0.0296527	+	0.0912617i
$872$	−3.67858	+	7.21962i	−0.124572	+	0.244487i
$873$	0.855414	+	5.40087i	0.0289514	+	0.182792i
$874$	−7.05634	−	17.6889i	−0.238684	−	0.598334i
$875$	−6.25629	+	18.6497i	−0.211501	+	0.630475i
$876$			3.28167i			0.110877i
$877$	−8.13597	+	1.28861i	−0.274732	+	0.0435133i	−0.292280	−	0.956333i	$-0.594414\pi$
$877$	−8.13597	+	1.28861i	−0.274732	+	0.0435133i	0.0175480	+	0.999846i	$0.494414\pi$
$878$	−27.0232	−	13.7690i	−0.911988	−	0.464681i
$879$	48.0016	−	15.5966i	1.61905	−	0.526062i
$880$	−0.662445	+	0.532970i	−0.0223310	+	0.0179664i
$881$	2.03599	−	6.26613i	0.0685942	−	0.211111i	−0.910884	−	0.412664i	$-0.864599\pi$
$881$	2.03599	−	6.26613i	0.0685942	−	0.211111i	0.979478	+	0.201552i	$0.0645985\pi$
$882$	5.26065	−	5.26065i	0.177135	−	0.177135i
$883$	−11.2733	−	22.1251i	−0.379376	−	0.744568i	0.619816	−	0.784747i	$-0.287207\pi$
$883$	−11.2733	−	22.1251i	−0.379376	−	0.744568i	−0.999193	+	0.0401789i	$0.987207\pi$
$884$	−0.595347	+	0.432545i	−0.0200237	+	0.0145481i
$885$	24.9083	+	22.5709i	0.837283	+	0.758711i
$886$	−19.7224	+	27.1455i	−0.662587	+	0.911972i
$887$	−0.925548	+	5.84368i	−0.0310769	+	0.196212i	−0.998342	−	0.0575551i	$-0.981670\pi$
$887$	−0.925548	+	5.84368i	−0.0310769	+	0.196212i	0.967265	+	0.253767i	$0.0816695\pi$
$888$	−0.385458	−	0.0610505i	−0.0129351	−	0.00204872i
$889$	1.18412	+	0.860316i	0.0397142	+	0.0288541i
$890$	−1.87202	+	0.391713i	−0.0627502	+	0.0131303i
$891$	−3.41011	+	2.47759i	−0.114243	+	0.0830023i
$892$	−9.40312	−	18.4547i	−0.314840	−	0.617908i
$893$	−19.2072	−	8.25293i	−0.642743	−	0.276174i
$894$	25.2014	+	8.18844i	0.842861	+	0.273862i
$895$	−4.69818	−	3.07225i	−0.157043	−	0.102694i
$896$	1.67332	−	0.543696i	0.0559018	−	0.0181636i
$897$	−1.90848	+	3.74560i	−0.0637222	+	0.125062i
$898$	−2.79025	+	0.441932i	−0.0931117	+	0.0147474i
$899$			23.7223i			0.791184i
$900$	−7.12046	+	6.33004i	−0.237349	+	0.211001i
$901$			1.53309i			0.0510746i
$902$	−0.0985899	−	0.622472i	−0.00328269	−	0.0207261i
$903$	−7.46285	+	14.6467i	−0.248348	+	0.487410i
$904$	−7.06903	+	2.29687i	−0.235112	+	0.0763926i
$905$	−31.0080	+	11.7903i	−1.03074	+	0.391922i
$906$	3.57273	+	1.16085i	0.118696	+	0.0385667i
$907$	12.4212	−	12.4212i	0.412439	−	0.412439i	−0.470148	−	0.882587i	$-0.655800\pi$
$907$	12.4212	−	12.4212i	0.412439	−	0.412439i	0.882587	+	0.470148i	$0.155800\pi$
$908$	14.7412	−	7.51100i	0.489203	−	0.249261i
$909$	−17.3030	−	23.8156i	−0.573905	−	0.789912i
$910$	−1.69917	−	0.184036i	−0.0563269	−	0.00610073i
$911$	9.72048	−	13.3791i	0.322054	−	0.443269i	−0.617039	−	0.786933i	$-0.711668\pi$
$911$	9.72048	−	13.3791i	0.322054	−	0.443269i	0.939093	+	0.343663i	$0.111668\pi$
$912$	9.41625	−	2.13030i	0.311803	−	0.0705412i
$913$	−0.233665	+	1.47530i	−0.00773318	+	0.0488254i
$914$	−8.45084	−	6.13990i	−0.279529	−	0.203090i
$915$	−10.4069	+	23.1764i	−0.344043	+	0.766190i
$916$	−14.0215	+	10.1872i	−0.463283	+	0.336595i
$917$	−3.73100	+	1.90104i	−0.123209	+	0.0627779i
$918$	2.90372	−	2.90372i	0.0958371	−	0.0958371i
$919$	41.9159	+	13.6193i	1.38268	+	0.449260i	0.903549	−	0.428484i	$-0.140952\pi$
$919$	41.9159	+	13.6193i	1.38268	+	0.449260i	0.479130	+	0.877744i	$0.340952\pi$
$920$	2.55844	−	9.42860i	0.0843492	−	0.310852i
$921$	15.0916	+	46.4473i	0.497286	+	1.53049i
$922$	7.87297	+	4.01148i	0.259282	+	0.132111i
$923$	−3.96571	+	0.628106i	−0.130533	+	0.0206744i
$924$	−1.48172			−0.0487449
$925$	−0.820487	−	0.320937i	−0.0269774	−	0.0105523i
$926$			0.271826i			0.00893276i
$927$	28.8920	−	4.57604i	0.948937	−	0.150297i
$928$	6.69415	+	3.41084i	0.219746	+	0.111966i
$929$	−38.7527	+	12.5915i	−1.27144	+	0.413115i	−0.865556	−	0.500812i	$-0.833035\pi$
$929$	−38.7527	+	12.5915i	−1.27144	+	0.413115i	−0.405880	+	0.913926i	$0.633035\pi$
$930$	0.768914	+	15.6186i	0.0252137	+	0.512155i
$931$	−16.9824	+	1.11242i	−0.556576	+	0.0364582i
$932$	−1.33723	−	1.33723i	−0.0438024	−	0.0438024i
$933$	26.1457	−	13.3219i	0.855972	−	0.436140i
$934$	−14.2392	+	10.3454i	−0.465920	+	0.338511i
$935$	−1.24957	+	0.716169i	−0.0408653	+	0.0234212i
$936$	−0.669685	−	0.486554i	−0.0218893	−	0.0159035i
$937$	−52.5982	−	8.33074i	−1.71831	−	0.272153i	−0.781987	−	0.623295i	$-0.785793\pi$
$937$	−52.5982	−	8.33074i	−1.71831	−	0.272153i	−0.936322	+	0.351142i	$0.885793\pi$
$938$	1.79427	−	11.3285i	0.0585849	−	0.369890i
$939$	−54.3371	−	39.4782i	−1.77322	−	1.28832i
$940$	−5.33260	−	9.30431i	−0.173930	−	0.303473i
$941$	−16.6941	−	22.9775i	−0.544212	−	0.749044i	0.445000	−	0.895530i	$-0.353204\pi$
$941$	−16.6941	−	22.9775i	−0.544212	−	0.749044i	−0.989213	+	0.146487i	$0.953204\pi$
$942$	−10.5176	+	5.35900i	−0.342683	+	0.174606i
$943$	5.12063	+	5.12063i	0.166751	+	0.166751i
$944$	2.09735	−	6.45498i	0.0682629	−	0.210092i
$945$	9.52579	−	0.468961i	0.309874	−	0.0152553i
$946$	−1.52546	+	0.495653i	−0.0495971	+	0.0161151i
$947$	16.3854	−	32.1582i	0.532455	−	1.04500i	−0.455496	−	0.890238i	$-0.650538\pi$
$947$	16.3854	−	32.1582i	0.532455	−	1.04500i	0.987951	−	0.154764i	$-0.0494618\pi$
$948$	10.5148	−	1.66538i	0.341504	−	0.0540889i
$949$	−0.643672			−0.0208945
$950$	21.7940	−	0.146311i	0.707091	−	0.00474697i
$951$	−56.9589			−1.84702
$952$	2.94371	−	0.466238i	0.0954063	−	0.0151109i
$953$	10.8213	−	21.2381i	0.350538	−	0.687969i	−0.646660	−	0.762778i	$-0.723835\pi$
$953$	10.8213	−	21.2381i	0.350538	−	0.687969i	0.997198	+	0.0748092i	$0.0238348\pi$
$954$	−1.64011	+	0.532905i	−0.0531006	+	0.0172534i
$955$	−11.5839	+	42.6901i	−0.374846	+	1.38142i
$956$	−4.21477	+	12.9717i	−0.136315	+	0.419536i
$957$	−4.47395	−	4.47395i	−0.144622	−	0.144622i
$958$	−16.2101	+	8.25948i	−0.523726	+	0.266852i
$959$	−16.5950	−	22.8410i	−0.535880	−	0.737576i
$960$	4.51794	+	2.02869i	0.145816	+	0.0654758i
$961$	−17.0138	−	12.3613i	−0.548832	−	0.398750i
$962$	0.0119746	−	0.0756044i	0.000386075	−	0.00243758i
$963$	0.624698	+	0.0989424i	0.0201306	+	0.00318838i
$964$	4.33392	+	3.14878i	0.139586	+	0.101415i
$965$	−56.5583	−	6.12579i	−1.82068	−	0.197196i
$966$	13.7740	−	10.0074i	0.443172	−	0.321984i
$967$	−26.0542	+	13.2753i	−0.837847	+	0.426904i	−0.819605	−	0.572929i	$-0.805807\pi$
$967$	−26.0542	+	13.2753i	−0.837847	+	0.426904i	−0.0182420	+	0.999834i	$0.505807\pi$
$968$	7.67594	+	7.67594i	0.246714	+	0.246714i
$969$	16.3188	−	1.06896i	0.524237	−	0.0343399i
$970$	5.99797	−	2.28062i	0.192583	−	0.0732264i
$971$	−26.3031	+	8.54639i	−0.844106	+	0.274267i	−0.698975	−	0.715146i	$-0.746360\pi$
$971$	−26.3031	+	8.54639i	−0.844106	+	0.274267i	−0.145131	+	0.989413i	$0.546360\pi$
$972$	15.3967	+	7.84501i	0.493849	+	0.251629i
$973$	20.0411	−	3.17420i	0.642488	−	0.101760i
$974$		−	13.1410i		−	0.421066i
$975$	−3.19636	−	3.59548i	−0.102365	−	0.115148i
$976$	5.12988			0.164203
$977$	−10.4602	+	1.65674i	−0.334652	+	0.0530037i	−0.321499	−	0.946910i	$-0.604187\pi$
$977$	−10.4602	+	1.65674i	−0.334652	+	0.0530037i	−0.0131528	+	0.999913i	$0.504187\pi$
$978$	−2.09101	−	1.06542i	−0.0668632	−	0.0340685i
$979$	−0.100500	−	0.309306i	−0.00321198	−	0.00988545i
$980$	−7.30688	−	4.77813i	−0.233410	−	0.152632i
$981$	−14.6839	−	4.77109i	−0.468821	−	0.152329i
$982$	−12.0674	+	12.0674i	−0.385087	+	0.385087i
$983$	2.79739	−	1.42534i	0.0892229	−	0.0454613i	−0.408810	−	0.912620i	$-0.634056\pi$
$983$	2.79739	−	1.42534i	0.0892229	−	0.0454613i	0.498033	+	0.867158i	$0.334056\pi$
$984$	−2.96993	+	2.15778i	−0.0946780	+	0.0687876i
$985$	−7.80130	−	37.2828i	−0.248570	−	1.18793i
$986$	10.2961	+	7.48057i	0.327895	+	0.238230i
$987$	2.92364	−	18.4591i	0.0930603	−	0.587560i
$988$	0.417840	+	1.84692i	0.0132933	+	0.0587584i
$989$	10.8331	−	14.9105i	0.344472	−	0.474125i
$990$	−1.20052	−	1.08786i	−0.0381550	−	0.0345745i
$991$	−19.9232	−	27.4219i	−0.632880	−	0.871085i	0.365330	−	0.930878i	$-0.380956\pi$
$991$	−19.9232	−	27.4219i	−0.632880	−	0.871085i	−0.998211	+	0.0597928i	$0.980956\pi$
$992$	2.81335	−	1.43347i	0.0893240	−	0.0455128i
$993$	−22.8598	+	22.8598i	−0.725433	+	0.725433i
$994$	15.4657	+	5.02512i	0.490543	+	0.159387i
$995$	30.1962	+	37.5318i	0.957284	+	1.18984i
$996$	8.27477	−	2.68864i	0.262196	−	0.0851927i
$997$	−11.5374	+	22.6434i	−0.365393	+	0.717125i	−0.998372	−	0.0570447i	$-0.981832\pi$
$997$	−11.5374	+	22.6434i	−0.365393	+	0.717125i	0.632978	+	0.774170i	$0.281832\pi$
$998$	4.18211	+	26.4048i	0.132382	+	0.835828i
$999$			0.427154i			0.0135146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.37.5	✓	400
19.18	odd	2	inner	950.2.w.a.37.46	yes	400
25.23	odd	20	inner	950.2.w.a.873.46	yes	400
475.398	even	20	inner	950.2.w.a.873.5	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.37.5	✓	400	1.1	even	1	trivial
950.2.w.a.37.46	yes	400	19.18	odd	2	inner
950.2.w.a.873.5	yes	400	475.398	even	20	inner
950.2.w.a.873.46	yes	400	25.23	odd	20	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.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.00551 + 1.97343i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.74220 - 1.40169i) q^{5} +(0.684420 - 2.10643i) q^{6} +(-1.24411 - 1.24411i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-1.12001 - 1.54156i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(-1.00551 + 1.97343i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.74220 - 1.40169i) q^{5} +(0.684420 - 2.10643i) q^{6} +(-1.24411 - 1.24411i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-1.12001 - 1.54156i) q^{9} +(-1.50148 + 1.65697i) q^{10} +(-0.307616 - 0.223496i) q^{11} +(-0.346476 + 2.18756i) q^{12} +(-0.429072 - 0.0679584i) q^{13} +(1.42341 + 1.03417i) q^{14} +(1.01433 + 4.84752i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.50933 - 0.769040i) q^{17} +(1.34737 + 1.34737i) q^{18} +(-0.284917 - 4.34958i) q^{19} +(1.22379 - 1.87146i) q^{20} +(3.70613 - 1.20419i) q^{21} +(0.338791 + 0.172623i) q^{22} +(-4.31528 + 0.683474i) q^{23} -2.21483i q^{24} +(1.07053 - 4.88405i) q^{25} +0.434421 q^{26} +(-2.39435 + 0.379228i) q^{27} +(-1.56767 - 0.798768i) q^{28} +(-2.32165 - 7.14530i) q^{29} +(-1.76016 - 4.62917i) q^{30} +(-3.00296 - 0.975720i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.750365 - 0.382330i) q^{33} +(-1.37044 + 0.995682i) q^{34} +(-3.91135 - 0.423635i) q^{35} +(-1.54156 - 1.12001i) q^{36} +(0.0275644 - 0.174035i) q^{37} +(0.961833 + 4.25146i) q^{38} +(0.565548 - 0.778410i) q^{39} +(-0.915960 + 2.03986i) q^{40} +(-0.974243 - 1.34093i) q^{41} +(-3.47212 + 1.76913i) q^{42} +(-2.98283 + 2.98283i) q^{43} +(-0.361624 - 0.117499i) q^{44} +(-4.11206 - 1.11580i) q^{45} +(4.15524 - 1.35012i) q^{46} +(2.17733 - 4.27324i) q^{47} +(0.346476 + 2.18756i) q^{48} -3.90438i q^{49} +(-0.293321 + 4.99139i) q^{50} +3.75182i q^{51} +(-0.429072 + 0.0679584i) q^{52} +(-0.410877 + 0.806392i) q^{53} +(2.30555 - 0.749118i) q^{54} +(-0.849201 + 0.0418067i) q^{55} +(1.67332 + 0.543696i) q^{56} +(8.87006 + 3.81129i) q^{57} +(3.41084 + 6.69415i) q^{58} +(5.49093 - 3.98939i) q^{59} +(2.46265 + 4.29682i) q^{60} +(4.15016 + 3.01526i) q^{61} +(3.11862 + 0.493941i) q^{62} +(-0.524455 + 3.31128i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.842787 + 0.483029i) q^{65} +(-0.681317 + 0.495006i) q^{66} +(-2.95956 - 5.80847i) q^{67} +(1.19781 - 1.19781i) q^{68} +(2.99028 - 9.20314i) q^{69} +(3.92946 - 0.193450i) q^{70} +(8.79015 - 2.85609i) q^{71} +(1.69779 + 0.865065i) q^{72} +(1.46344 - 0.231786i) q^{73} +0.176204i q^{74} +(8.56189 + 7.02359i) q^{75} +(-1.61507 - 4.04865i) q^{76} +(0.104654 + 0.660762i) q^{77} +(-0.436815 + 0.857298i) q^{78} +(-1.48533 - 4.57137i) q^{79} +(0.585579 - 2.15803i) q^{80} +(3.42564 - 10.5430i) q^{81} +(1.17202 + 1.17202i) q^{82} +(-1.78343 - 3.50018i) q^{83} +(3.15262 - 2.29051i) q^{84} +(1.55159 - 3.45543i) q^{85} +(2.47949 - 3.41273i) q^{86} +(16.4352 + 2.60308i) q^{87} +(0.375553 + 0.0594818i) q^{88} +(0.691971 + 0.502746i) q^{89} +(4.23599 + 0.458797i) q^{90} +(0.449265 + 0.618361i) q^{91} +(-3.89287 + 1.98352i) q^{92} +(4.94502 - 4.94502i) q^{93} +(-1.48204 + 4.56124i) q^{94} +(-6.59314 - 7.17848i) q^{95} +(-0.684420 - 2.10643i) q^{96} +(-2.55695 - 1.30283i) q^{97} +(0.610780 + 3.85631i) q^{98} +0.724525i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

Modular forms

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Database

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