LMFDB - Embedded newform 185.2.p.a.103.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.p (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	185.103
Dual form			185.2.p.a.97.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29225 - 2.23824i) q^{2} +(-0.642284 - 2.39703i) q^{3} +(-2.33980 + 4.05266i) q^{4} +(-0.420021 - 2.19627i) q^{5} +(-4.53514 + 4.53514i) q^{6} +(-0.287588 - 1.07329i) q^{7} +6.92543 q^{8} +(-2.73517 + 1.57915i) q^{9} +(-4.37299 + 3.77822i) q^{10} -1.13579i q^{11} +(11.2172 + 3.00564i) q^{12} +(-1.96744 + 3.40771i) q^{13} +(-2.03065 + 2.03065i) q^{14} +(-4.99475 + 2.41743i) q^{15} +(-4.26976 - 7.39544i) q^{16} +(6.66627 - 3.84877i) q^{17} +(7.06904 + 4.08131i) q^{18} +(6.44768 - 1.72765i) q^{19} +(9.88348 + 3.43663i) q^{20} +(-2.38800 + 1.37871i) q^{21} +(-2.54216 + 1.46772i) q^{22} -2.90461 q^{23} +(-4.44809 - 16.6005i) q^{24} +(-4.64717 + 1.84495i) q^{25} +10.1697 q^{26} +(0.277785 + 0.277785i) q^{27} +(5.02258 + 1.34580i) q^{28} +(-5.98715 + 5.98715i) q^{29} +(11.8652 + 8.05553i) q^{30} +(-2.00251 - 2.00251i) q^{31} +(-4.10973 + 7.11827i) q^{32} +(-2.72252 + 0.729498i) q^{33} +(-17.2289 - 9.94713i) q^{34} +(-2.23644 + 1.08242i) q^{35} -14.7796i q^{36} +(-6.08209 - 0.0901489i) q^{37} +(-12.1989 - 12.1989i) q^{38} +(9.43206 + 2.52731i) q^{39} +(-2.90882 - 15.2101i) q^{40} +(2.72061 + 1.57074i) q^{41} +(6.17178 + 3.56328i) q^{42} -3.89038 q^{43} +(4.60296 + 2.65752i) q^{44} +(4.61707 + 5.34389i) q^{45} +(3.75348 + 6.50121i) q^{46} +(0.267107 - 0.267107i) q^{47} +(-14.9847 + 14.9847i) q^{48} +(4.99293 - 2.88267i) q^{49} +(10.1347 + 8.01732i) q^{50} +(-13.5073 - 13.5073i) q^{51} +(-9.20687 - 15.9468i) q^{52} +(0.908138 - 3.38922i) q^{53} +(0.262782 - 0.980717i) q^{54} +(-2.49449 + 0.477055i) q^{55} +(-1.99167 - 7.43301i) q^{56} +(-8.28247 - 14.3457i) q^{57} +(21.1375 + 5.66378i) q^{58} +(0.528916 - 1.97394i) q^{59} +(1.88973 - 25.8983i) q^{60} +(-4.38730 + 1.17557i) q^{61} +(-1.89436 + 7.06985i) q^{62} +(2.48149 + 2.48149i) q^{63} +4.16413 q^{64} +(8.31061 + 2.88972i) q^{65} +(5.15096 + 5.15096i) q^{66} +(8.91454 - 2.38864i) q^{67} +36.0215i q^{68} +(1.86559 + 6.96246i) q^{69} +(5.31275 + 3.60693i) q^{70} +(4.58524 - 7.94186i) q^{71} +(-18.9422 + 10.9363i) q^{72} +(-0.472207 + 0.472207i) q^{73} +(7.65779 + 13.7297i) q^{74} +(7.40722 + 9.95443i) q^{75} +(-8.08472 + 30.1726i) q^{76} +(-1.21903 + 0.326639i) q^{77} +(-6.53183 - 24.3771i) q^{78} +(12.9021 - 3.45711i) q^{79} +(-14.4490 + 12.4838i) q^{80} +(-4.25001 + 7.36124i) q^{81} -8.11916i q^{82} +(2.38683 - 8.90779i) q^{83} -12.9037i q^{84} +(-11.2529 - 13.0243i) q^{85} +(5.02733 + 8.70760i) q^{86} +(18.1968 + 10.5060i) q^{87} -7.86582i q^{88} +(-0.295261 - 0.0791150i) q^{89} +(5.99450 - 17.2397i) q^{90} +(4.22328 + 1.13162i) q^{91} +(6.79623 - 11.7714i) q^{92} +(-3.51391 + 6.08628i) q^{93} +(-0.943018 - 0.252681i) q^{94} +(-6.50253 - 13.4352i) q^{95} +(19.7024 + 5.27923i) q^{96} +15.1628i q^{97} +(-12.9042 - 7.45024i) q^{98} +(1.79358 + 3.10658i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100})$ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$ .

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	−1.29225	−	2.23824i	−0.913757	−	1.58267i	−0.808712	−	0.588205i	$-0.799835\pi$
$2$	−1.29225	−	2.23824i	−0.913757	−	1.58267i	−0.105045	−	0.994467i	$-0.533499\pi$
$3$	−0.642284	−	2.39703i	−0.370823	−	1.38393i	−0.859353	−	0.511382i	$-0.829134\pi$
$3$	−0.642284	−	2.39703i	−0.370823	−	1.38393i	0.488531	−	0.872547i	$-0.337533\pi$
$4$	−2.33980	+	4.05266i	−1.16990	+	2.02633i
$5$	−0.420021	−	2.19627i	−0.187839	−	0.982200i
$5$	−0.420021	−	2.19627i	−0.187839	−	0.982200i
$6$	−4.53514	+	4.53514i	−1.85146	+	1.85146i
$7$	−0.287588	−	1.07329i	−0.108698	−	0.405666i	0.890041	−	0.455881i	$-0.150676\pi$
$7$	−0.287588	−	1.07329i	−0.108698	−	0.405666i	−0.998738	+	0.0502154i	$0.984009\pi$
$8$	6.92543			2.44851
$9$	−2.73517	+	1.57915i	−0.911724	+	0.526384i
$10$	−4.37299	+	3.77822i	−1.38286	+	1.19478i
$11$		−	1.13579i		−	0.342453i	−0.985232	−	0.171227i	$-0.945227\pi$
$11$		−	1.13579i		−	0.342453i	0.985232	−	0.171227i	$-0.0547730\pi$
$12$	11.2172	+	3.00564i	3.23812	+	0.867652i
$13$	−1.96744	+	3.40771i	−0.545671	+	0.945129i	0.452894	+	0.891565i	$0.350392\pi$
$13$	−1.96744	+	3.40771i	−0.545671	+	0.945129i	−0.998564	+	0.0535649i	$0.982942\pi$
$14$	−2.03065	+	2.03065i	−0.542713	+	0.542713i
$15$	−4.99475	+	2.41743i	−1.28964	+	0.624178i
$16$	−4.26976	−	7.39544i	−1.06744	−	1.84886i
$17$	6.66627	−	3.84877i	1.61681	−	0.933464i	0.629069	−	0.777349i	$-0.283436\pi$
$17$	6.66627	−	3.84877i	1.61681	−	0.933464i	0.987739	−	0.156115i	$-0.0498971\pi$
$18$	7.06904	+	4.08131i	1.66619	+	0.961974i
$19$	6.44768	−	1.72765i	1.47920	−	0.396350i	0.573124	−	0.819469i	$-0.305731\pi$
$19$	6.44768	−	1.72765i	1.47920	−	0.396350i	0.906074	+	0.423119i	$0.139065\pi$
$20$	9.88348	+	3.43663i	2.21001	+	0.768454i
$21$	−2.38800	+	1.37871i	−0.521105	+	0.300860i
$22$	−2.54216	+	1.46772i	−0.541991	+	0.312919i
$23$	−2.90461			−0.605654			−0.302827	−	0.953046i	$-0.597930\pi$
$23$	−2.90461			−0.605654			−0.302827	+	0.953046i	$0.597930\pi$
$24$	−4.44809	−	16.6005i	−0.907963	−	3.38856i
$25$	−4.64717	+	1.84495i	−0.929433	+	0.368991i
$26$	10.1697			1.99444
$27$	0.277785	+	0.277785i	0.0534598	+	0.0534598i
$28$	5.02258	+	1.34580i	0.949179	+	0.254332i
$29$	−5.98715	+	5.98715i	−1.11179	+	1.11179i	−0.118876	+	0.992909i	$0.537929\pi$
$29$	−5.98715	+	5.98715i	−1.11179	+	1.11179i	−0.992909	+	0.118876i	$0.962071\pi$
$30$	11.8652	+	8.05553i	2.16629	+	1.47073i
$31$	−2.00251	−	2.00251i	−0.359662	−	0.359662i	0.504026	−	0.863688i	$-0.331852\pi$
$31$	−2.00251	−	2.00251i	−0.359662	−	0.359662i	−0.863688	+	0.504026i	$0.831852\pi$
$32$	−4.10973	+	7.11827i	−0.726505	+	1.25834i
$33$	−2.72252	+	0.729498i	−0.473931	+	0.126989i
$34$	−17.2289	−	9.94713i	−2.95474	−	1.70592i
$35$	−2.23644	+	1.08242i	−0.378027	+	0.182963i
$36$		−	14.7796i		−	2.46327i
$37$	−6.08209	−	0.0901489i	−0.999890	−	0.0148204i
$37$	−6.08209	−	0.0901489i	−0.999890	−	0.0148204i
$38$	−12.1989	−	12.1989i	−1.97892	−	1.97892i
$39$	9.43206	+	2.52731i	1.51034	+	0.404694i
$40$	−2.90882	−	15.2101i	−0.459925	−	2.40493i
$41$	2.72061	+	1.57074i	0.424888	+	0.245309i	0.697166	−	0.716909i	$-0.254444\pi$
$41$	2.72061	+	1.57074i	0.424888	+	0.245309i	−0.272279	+	0.962218i	$0.587777\pi$
$42$	6.17178	+	3.56328i	0.952327	+	0.549826i
$43$	−3.89038			−0.593277			−0.296639	−	0.954990i	$-0.595866\pi$
$43$	−3.89038			−0.593277			−0.296639	+	0.954990i	$0.595866\pi$
$44$	4.60296	+	2.65752i	0.693923	+	0.400637i
$45$	4.61707	+	5.34389i	0.688272	+	0.796620i
$46$	3.75348	+	6.50121i	0.553420	+	0.958552i
$47$	0.267107	−	0.267107i	0.0389616	−	0.0389616i	−0.687358	−	0.726319i	$-0.741229\pi$
$47$	0.267107	−	0.267107i	0.0389616	−	0.0389616i	0.726319	+	0.687358i	$0.241229\pi$
$48$	−14.9847	+	14.9847i	−2.16286	+	2.16286i
$49$	4.99293	−	2.88267i	0.713276	−	0.411810i
$50$	10.1347	+	8.01732i	1.43327	+	1.13382i
$51$	−13.5073	−	13.5073i	−1.89140	−	1.89140i
$52$	−9.20687	−	15.9468i	−1.27676	−	2.21142i
$53$	0.908138	−	3.38922i	0.124742	−	0.465545i	−0.875088	−	0.483964i	$-0.839197\pi$
$53$	0.908138	−	3.38922i	0.124742	−	0.465545i	0.999830	+	0.0184192i	$0.00586333\pi$
$54$	0.262782	−	0.980717i	0.0357601	−	0.133459i
$55$	−2.49449	+	0.477055i	−0.336357	+	0.0643260i
$56$	−1.99167	−	7.43301i	−0.266148	−	0.993277i
$57$	−8.28247	−	14.3457i	−1.09704	−	1.90013i
$58$	21.1375	+	5.66378i	2.77549	+	0.743691i
$59$	0.528916	−	1.97394i	0.0688590	−	0.256985i	−0.922912	−	0.385011i	$-0.874198\pi$
$59$	0.528916	−	1.97394i	0.0688590	−	0.256985i	0.991771	+	0.128026i	$0.0408642\pi$
$60$	1.88973	−	25.8983i	0.243963	−	3.34346i
$61$	−4.38730	+	1.17557i	−0.561736	+	0.150517i	−0.528504	−	0.848931i	$-0.677247\pi$
$61$	−4.38730	+	1.17557i	−0.561736	+	0.150517i	−0.0332320	+	0.999448i	$0.510580\pi$
$62$	−1.89436	+	7.06985i	−0.240584	+	0.897871i
$63$	2.48149	+	2.48149i	0.312639	+	0.312639i
$64$	4.16413			0.520517
$65$	8.31061	+	2.88972i	1.03080	+	0.358426i
$66$	5.15096	+	5.15096i	0.634040	+	0.634040i
$67$	8.91454	−	2.38864i	1.08908	−	0.291819i	0.330772	−	0.943711i	$-0.392691\pi$
$67$	8.91454	−	2.38864i	1.08908	−	0.291819i	0.758312	+	0.651891i	$0.226024\pi$
$68$			36.0215i			4.36825i
$69$	1.86559	+	6.96246i	0.224590	+	0.838182i
$70$	5.31275	+	3.60693i	0.634995	+	0.431110i
$71$	4.58524	−	7.94186i	0.544168	−	0.942526i	−0.454491	−	0.890751i	$-0.650179\pi$
$71$	4.58524	−	7.94186i	0.544168	−	0.942526i	0.998659	−	0.0517747i	$-0.0164878\pi$
$72$	−18.9422	+	10.9363i	−2.23237	+	1.28886i
$73$	−0.472207	+	0.472207i	−0.0552677	+	0.0552677i	−0.734200	−	0.678933i	$-0.762443\pi$
$73$	−0.472207	+	0.472207i	−0.0552677	+	0.0552677i	0.678933	+	0.734200i	$0.262443\pi$
$74$	7.65779	+	13.7297i	0.890200	+	1.59604i
$75$	7.40722	+	9.95443i	0.855312	+	1.14944i
$76$	−8.08472	+	30.1726i	−0.927382	+	3.46103i
$77$	−1.21903	+	0.326639i	−0.138922	+	0.0372239i
$78$	−6.53183	−	24.3771i	−0.739584	−	2.76016i
$79$	12.9021	−	3.45711i	1.45160	−	0.388955i	0.555020	−	0.831837i	$-0.312710\pi$
$79$	12.9021	−	3.45711i	1.45160	−	0.388955i	0.896580	+	0.442882i	$0.146044\pi$
$80$	−14.4490	+	12.4838i	−1.61544	+	1.39573i
$81$	−4.25001	+	7.36124i	−0.472224	+	0.817915i
$82$		−	8.11916i		−	0.896611i
$83$	2.38683	−	8.90779i	0.261989	−	0.977757i	−0.702078	−	0.712100i	$-0.747744\pi$
$83$	2.38683	−	8.90779i	0.261989	−	0.977757i	0.964068	−	0.265657i	$-0.0855889\pi$
$84$		−	12.9037i		−	1.40791i
$85$	−11.2529	−	13.0243i	−1.22055	−	1.41269i
$86$	5.02733	+	8.70760i	0.542111	+	0.938964i
$87$	18.1968	+	10.5060i	1.95091	+	1.12636i
$88$		−	7.86582i		−	0.838500i
$89$	−0.295261	−	0.0791150i	−0.0312976	−	0.00838618i	0.243136	−	0.969992i	$-0.421824\pi$
$89$	−0.295261	−	0.0791150i	−0.0312976	−	0.00838618i	−0.274434	+	0.961606i	$0.588490\pi$
$90$	5.99450	−	17.2397i	0.631876	−	1.81723i
$91$	4.22328	+	1.13162i	0.442720	+	0.118627i
$92$	6.79623	−	11.7714i	0.708556	−	1.22725i
$93$	−3.51391	+	6.08628i	−0.364376	+	0.631118i
$94$	−0.943018	−	0.252681i	−0.0972649	−	0.0260620i
$95$	−6.50253	−	13.4352i	−0.667146	−	1.37842i
$96$	19.7024	+	5.27923i	2.01086	+	0.538809i
$97$			15.1628i			1.53955i	0.638313	+	0.769777i	$0.279633\pi$
$97$			15.1628i			1.53955i	−0.638313	+	0.769777i	$0.720367\pi$
$98$	−12.9042	−	7.45024i	−1.30352	−	0.752588i
$99$	1.79358	+	3.10658i	0.180262	+	0.312223i
$100$	3.39649	−	23.1502i	0.339649	−	2.31502i
$101$		−	12.6408i		−	1.25780i	−0.777485	−	0.628901i	$-0.783505\pi$
$101$		−	12.6408i		−	1.25780i	0.777485	−	0.628901i	$-0.216495\pi$
$102$	−12.7778	+	47.6872i	−1.26519	+	4.72174i
$103$		−	6.06845i		−	0.597942i	−0.954262	−	0.298971i	$-0.903357\pi$
$103$		−	6.06845i		−	0.597942i	0.954262	−	0.298971i	$-0.0966434\pi$
$104$	−13.6254	+	23.5999i	−1.33608	+	2.31416i
$105$	4.03104	+	4.66560i	0.393389	+	0.455316i
$106$	−8.75941	+	2.34708i	−0.850789	+	0.227968i
$107$	−0.870997	−	3.25060i	−0.0842024	−	0.314248i	0.910960	−	0.412496i	$-0.135343\pi$
$107$	−0.870997	−	3.25060i	−0.0842024	−	0.314248i	−0.995162	+	0.0982480i	$0.968676\pi$
$108$	−1.77573	+	0.475806i	−0.170870	+	0.0457845i
$109$	−1.10052	+	4.10719i	−0.105410	+	0.393397i	−0.998391	−	0.0566973i	$-0.981943\pi$
$109$	−1.10052	+	4.10719i	−0.105410	+	0.393397i	0.892981	+	0.450094i	$0.148610\pi$
$110$	4.29126	+	4.96680i	0.409156	+	0.473565i
$111$	3.69034	+	14.6369i	0.350272	+	1.38927i
$112$	−6.70953	+	6.70953i	−0.633991	+	0.633991i
$113$	−6.69547	+	3.86563i	−0.629857	+	0.363648i	−0.780697	−	0.624910i	$-0.785136\pi$
$113$	−6.69547	+	3.86563i	−0.629857	+	0.363648i	0.150840	+	0.988558i	$0.451802\pi$
$114$	−21.4060	+	37.0763i	−2.00486	+	3.47251i
$115$	1.22000	+	6.37930i	0.113765	+	0.594873i
$116$	−10.2551	−	38.2726i	−0.952164	−	3.55352i
$117$		−	12.4276i		−	1.14893i
$118$	−5.10164	+	1.36698i	−0.469644	+	0.125841i
$119$	−6.04799	−	6.04799i	−0.554418	−	0.554418i
$120$	−34.5908	+	16.7417i	−3.15770	+	1.52830i
$121$	9.70998			0.882726
$122$	8.30068	+	8.30068i	0.751508	+	0.751508i
$123$	2.01773	−	7.53026i	0.181932	−	0.678981i
$124$	12.8010	−	3.43002i	1.14956	−	0.308025i
$125$	6.00391	+	9.43149i	0.537006	+	0.843578i
$126$	2.34747	−	8.76087i	0.209129	−	0.780480i
$127$	13.0613	+	3.49977i	1.15901	+	0.310555i	0.786569	−	0.617503i	$-0.211856\pi$
$127$	13.0613	+	3.49977i	1.15901	+	0.310555i	0.372437	+	0.928057i	$0.378522\pi$
$128$	2.83838	+	4.91622i	0.250880	+	0.434537i
$129$	2.49873	+	9.32538i	0.220001	+	0.821054i
$130$	−4.27148	−	22.3353i	−0.374634	−	1.95894i
$131$	−1.02256	+	3.81625i	−0.0893416	+	0.333428i	−0.996101	−	0.0882212i	$-0.971882\pi$
$131$	−1.02256	+	3.81625i	−0.0893416	+	0.333428i	0.906759	+	0.421649i	$0.138548\pi$
$132$	3.41377	−	12.7403i	0.297130	−	1.10890i
$133$	−3.70854	−	6.42339i	−0.321571	−	0.556978i
$134$	−16.8661	−	16.8661i	−1.45701	−	1.45701i
$135$	0.493415	−	0.726766i	0.0424664	−	0.0625501i
$136$	46.1668	−	26.6544i	3.95877	−	2.28560i
$137$	1.85613	−	1.85613i	0.158580	−	0.158580i	−0.623357	−	0.781937i	$-0.714232\pi$
$137$	1.85613	−	1.85613i	0.158580	−	0.158580i	0.781937	+	0.623357i	$0.214232\pi$
$138$	13.1728	−	13.1728i	1.12135	−	1.12135i
$139$	−1.35441	−	2.34591i	−0.114880	−	0.198978i	0.802852	−	0.596178i	$-0.203315\pi$
$139$	−1.35441	−	2.34591i	−0.114880	−	0.198978i	−0.917732	+	0.397201i	$0.869982\pi$
$140$	0.846140	−	11.5962i	0.0715118	−	0.980057i
$141$	−0.811824	−	0.468707i	−0.0683679	−	0.0394722i
$142$	−23.7010			−1.98895
$143$	3.87044	+	2.23460i	0.323662	+	0.186867i
$144$	23.3571	+	13.4852i	1.94642	+	1.12377i
$145$	15.6641	+	10.6346i	1.30083	+	0.883159i
$146$	1.66712	+	0.446704i	0.137972	+	0.0369695i
$147$	−10.1167	−	10.1167i	−0.834414	−	0.834414i
$148$	14.5963	−	24.4377i	1.19980	−	2.00877i
$149$		−	13.0492i		−	1.06903i	−0.845158	−	0.534517i	$-0.820494\pi$
$149$		−	13.0492i		−	1.06903i	0.845158	−	0.534517i	$-0.179506\pi$
$150$	12.7084	−	29.4427i	1.03764	−	2.40399i
$151$	4.79718	+	2.76965i	0.390389	+	0.225391i	0.682329	−	0.731046i	$-0.260967\pi$
$151$	4.79718	+	2.76965i	0.390389	+	0.225391i	−0.291940	+	0.956437i	$0.594301\pi$
$152$	44.6529	−	11.9647i	3.62183	−	0.970467i
$153$	−12.1556	+	21.0541i	−0.982722	+	1.70212i
$154$	2.30638	+	2.30638i	0.185854	+	0.185854i
$155$	−3.55696	+	5.23915i	−0.285702	+	0.420819i
$156$	−32.3115	+	32.3115i	−2.58699	+	2.58699i
$157$	−10.2265	−	2.74019i	−0.816167	−	0.218691i	−0.173497	−	0.984834i	$-0.555507\pi$
$157$	−10.2265	−	2.74019i	−0.816167	−	0.218691i	−0.642670	+	0.766143i	$0.722173\pi$
$158$	−24.4105	−	24.4105i	−1.94200	−	1.94200i
$159$	−8.70735			−0.690538
$160$	17.3598	+	6.03625i	1.37241	+	0.477207i
$161$	0.835331	+	3.11750i	0.0658333	+	0.245693i
$162$	21.9683			1.72599
$163$	2.56535	−	1.48110i	0.200934	−	0.116009i	−0.396157	−	0.918183i	$-0.629657\pi$
$163$	2.56535	−	1.48110i	0.200934	−	0.116009i	0.597091	+	0.802174i	$0.296323\pi$
$164$	−12.7314	+	7.35047i	−0.994154	+	0.573975i
$165$	2.74569	+	5.67298i	0.213752	+	0.441641i
$166$	−23.0221	+	6.16876i	−1.78686	+	0.478789i
$167$	−5.04911	−	2.91511i	−0.390712	−	0.225578i	0.291757	−	0.956493i	$-0.405760\pi$
$167$	−5.04911	−	2.91511i	−0.390712	−	0.225578i	−0.682469	+	0.730915i	$0.739094\pi$
$168$	−16.5380	+	9.54820i	−1.27593	+	0.736659i
$169$	−1.24167	−	2.15063i	−0.0955131	−	0.165433i
$170$	−14.6100	+	42.0173i	−1.12054	+	3.22258i
$171$	−14.9073	+	14.9073i	−1.13999	+	1.13999i
$172$	9.10273	−	15.7664i	0.694077	−	1.20218i
$173$	−0.339866	−	0.0910668i	−0.0258395	−	0.00692368i	0.245876	−	0.969301i	$-0.420924\pi$
$173$	−0.339866	−	0.0910668i	−0.0258395	−	0.00692368i	−0.271716	+	0.962378i	$0.587591\pi$
$174$		−	54.3051i		−	4.11686i
$175$	3.31664	+	4.45718i	0.250714	+	0.336931i
$176$	−8.39965	+	4.84954i	−0.633148	+	0.365548i
$177$	−5.07132			−0.381184
$178$	0.204472	+	0.763101i	0.0153258	+	0.0571968i
$179$	1.08892	−	1.08892i	0.0813893	−	0.0813893i	−0.665240	−	0.746629i	$-0.731671\pi$
$179$	1.08892	−	1.08892i	0.0813893	−	0.0813893i	0.746629	+	0.665240i	$0.231671\pi$
$180$	−32.4600	+	6.20775i	−2.41942	+	0.462698i
$181$	7.17266	−	12.4234i	0.533140	−	0.923426i	−0.466111	−	0.884726i	$-0.654345\pi$
$181$	7.17266	−	12.4234i	0.533140	−	0.923426i	0.999251	−	0.0386992i	$-0.0123214\pi$
$182$	−2.92468	−	10.9150i	−0.216791	−	0.809077i
$183$	5.63578	+	9.76145i	0.416609	+	0.721587i
$184$	−20.1157			−1.48295
$185$	2.35661	+	13.3958i	0.173262	+	0.984876i
$186$	18.1634			1.33180
$187$	−4.37139	−	7.57147i	−0.319668	−	0.553681i
$188$	0.457516	+	1.70747i	0.0333678	+	0.124530i
$189$	0.218257	−	0.378032i	0.0158759	−	0.0274978i
$190$	−21.6682	+	31.9158i	−1.57198	+	2.31541i
$191$	10.7939	−	10.7939i	0.781022	−	0.781022i	−0.198981	−	0.980003i	$-0.563763\pi$
$191$	10.7939	−	10.7939i	0.781022	−	0.781022i	0.980003	+	0.198981i	$0.0637633\pi$
$192$	−2.67455	−	9.98157i	−0.193019	−	0.720358i
$193$	−6.01184			−0.432741			−0.216371	−	0.976311i	$-0.569422\pi$
$193$	−6.01184			−0.432741			−0.216371	+	0.976311i	$0.569422\pi$
$194$	33.9381	−	19.5941i	2.43661	−	1.40678i
$195$	1.58899	−	21.7768i	0.113790	−	1.55947i
$196$			26.9795i			1.92711i
$197$	8.58205	+	2.29955i	0.611445	+	0.163836i	0.551236	−	0.834349i	$-0.314156\pi$
$197$	8.58205	+	2.29955i	0.611445	+	0.163836i	0.0602095	+	0.998186i	$0.480823\pi$
$198$	4.63550	−	8.02893i	0.329431	−	0.570591i
$199$	−15.0785	+	15.0785i	−1.06889	+	1.06889i	−0.0714408	+	0.997445i	$0.522760\pi$
$199$	−15.0785	+	15.0785i	−1.06889	+	1.06889i	−0.997445	+	0.0714408i	$0.977240\pi$
$200$	−32.1836	+	12.7771i	−2.27573	+	0.903477i
$201$	−11.4513	−	19.8343i	−0.807714	−	1.39900i
$202$	−28.2930	+	16.3350i	−1.99069	+	1.14933i
$203$	8.14778	+	4.70412i	0.571862	+	0.330165i
$204$	86.3448	−	23.1360i	6.04534	−	1.61985i
$205$	2.30706	−	6.63493i	0.161132	−	0.463403i
$206$	−13.5826	+	7.84194i	−0.946347	+	0.546374i
$207$	7.94462	−	4.58683i	0.552189	−	0.318806i
$208$	33.6020			2.32988
$209$	−1.96224	−	7.32320i	−0.135731	−	0.506556i
$210$	5.23363	−	15.0515i	0.361155	−	1.03865i
$211$	−27.5995			−1.90003			−0.950013	−	0.312210i	$-0.898931\pi$
$211$	−27.5995			−1.90003			−0.950013	+	0.312210i	$0.898931\pi$
$212$	11.6105	+	11.6105i	0.797411	+	0.797411i
$213$	−21.9819	−	5.89005i	−1.50618	−	0.403579i
$214$	−6.15008	+	6.15008i	−0.420411	+	0.420411i
$215$	1.63404	+	8.54431i	0.111441	+	0.582717i
$216$	1.92378	+	1.92378i	0.130897	+	0.130897i
$217$	−1.57338	+	2.72518i	−0.106808	+	0.184997i
$218$	10.6150	−	2.84428i	0.718938	−	0.192639i
$219$	1.43519	+	0.828607i	0.0969811	+	0.0559921i
$220$	3.90329	−	11.2255i	0.263159	−	0.756826i
$221$			30.2890i			2.03746i
$222$	27.9920	−	27.1743i	1.87870	−	1.82382i
$223$	13.1885	+	13.1885i	0.883166	+	0.883166i	0.993855	−	0.110690i	$-0.0353059\pi$
$223$	13.1885	+	13.1885i	0.883166	+	0.883166i	−0.110690	+	0.993855i	$0.535306\pi$
$224$	8.82189	+	2.36382i	0.589437	+	0.157939i
$225$	9.79733	−	12.3848i	0.653156	−	0.825657i
$226$	17.3044	+	9.99070i	1.15107	+	0.664572i
$227$	3.11283	+	1.79719i	0.206606	+	0.119284i	0.599733	−	0.800200i	$-0.295273\pi$
$227$	3.11283	+	1.79719i	0.206606	+	0.119284i	−0.393127	+	0.919484i	$0.628607\pi$
$228$	77.5175			5.13372
$229$	17.6716	+	10.2027i	1.16777	+	0.674215i	0.953155	−	0.302483i	$-0.0978154\pi$
$229$	17.6716	+	10.2027i	1.16777	+	0.674215i	0.214620	+	0.976698i	$0.431149\pi$
$230$	12.7019	−	10.9743i	0.837535	−	0.723622i
$231$	1.56593	+	2.71227i	0.103031	+	0.178454i
$232$	−41.4636	+	41.4636i	−2.72222	+	2.72222i
$233$	11.0421	−	11.0421i	0.723393	−	0.723393i	−0.245902	−	0.969295i	$-0.579084\pi$
$233$	11.0421	−	11.0421i	0.723393	−	0.723393i	0.969295	+	0.245902i	$0.0790842\pi$
$234$	−27.8159	+	16.0595i	−1.81838	+	1.04984i
$235$	−0.698829	−	0.474448i	−0.0455866	−	0.0309496i
$236$	6.76215	+	6.76215i	0.440178	+	0.440178i
$237$	−16.5736	−	28.7064i	−1.07657	−	1.86468i
$238$	−5.72134	+	21.3523i	−0.370859	+	1.38407i
$239$	1.49500	−	5.57943i	0.0967037	−	0.360903i	−0.900569	−	0.434714i	$-0.856849\pi$
$239$	1.49500	−	5.57943i	0.0967037	−	0.360903i	0.997272	+	0.0738108i	$0.0235161\pi$
$240$	39.2043	+	26.6166i	2.53063	+	1.71809i
$241$	2.24164	+	8.36590i	0.144396	+	0.538895i	0.999782	+	0.0209022i	$0.00665385\pi$
$241$	2.24164	+	8.36590i	0.144396	+	0.538895i	−0.855385	+	0.517993i	$0.826679\pi$
$242$	−12.5477	−	21.7333i	−0.806597	−	1.39707i
$243$	21.5132	+	5.76446i	1.38008	+	0.369790i
$244$	5.50122	−	20.5308i	0.352179	−	1.31435i
$245$	−8.42824	−	9.75502i	−0.538461	−	0.623225i
$246$	−19.4619	+	5.21480i	−1.24085	+	0.332484i
$247$	−6.79811	+	25.3709i	−0.432553	+	1.61431i
$248$	−13.8683	−	13.8683i	−0.880636	−	0.880636i
$249$	−22.8853			−1.45030
$250$	13.3514	−	25.6260i	0.844415	−	1.62073i
$251$	2.48414	+	2.48414i	0.156798	+	0.156798i	0.781146	−	0.624348i	$-0.214635\pi$
$251$	2.48414	+	2.48414i	0.156798	+	0.156798i	−0.624348	+	0.781146i	$0.714635\pi$
$252$	−15.8628	+	4.25044i	−0.999266	+	0.267752i
$253$			3.29903i			0.207408i
$254$	−9.04514	−	33.7569i	−0.567543	−	2.11810i
$255$	−23.9922	+	35.3389i	−1.50245	+	2.21301i
$256$	11.4999	−	19.9184i	0.718745	−	1.24490i
$257$	−2.27579	+	1.31393i	−0.141960	+	0.0819604i	−0.569298	−	0.822132i	$-0.692785\pi$
$257$	−2.27579	+	1.31393i	−0.141960	+	0.0819604i	0.427338	+	0.904092i	$0.359451\pi$
$258$	17.6434	−	17.6434i	1.09843	−	1.09843i
$259$	1.65238	+	6.55379i	0.102674	+	0.407232i
$260$	−31.1562	+	26.9187i	−1.93223	+	1.66943i
$261$	6.92126	−	25.8305i	0.428415	−	1.59887i
$262$	9.86308	−	2.64280i	0.609343	−	0.163273i
$263$	−0.384224	−	1.43394i	−0.0236923	−	0.0884208i	0.953067	−	0.302758i	$-0.0979075\pi$
$263$	−0.384224	−	1.43394i	−0.0236923	−	0.0884208i	−0.976760	+	0.214337i	$0.931241\pi$
$264$	−18.8547	+	5.05209i	−1.16042	+	0.310935i
$265$	−7.82505	−	0.570971i	−0.480689	−	0.0350745i
$266$	−9.58471	+	16.6012i	−0.587676	+	1.01788i
$267$			0.758566i			0.0464235i
$268$	−11.1779	+	41.7166i	−0.682800	+	2.54824i
$269$			16.7444i			1.02092i	0.859901	+	0.510461i	$0.170525\pi$
$269$			16.7444i			1.02092i	−0.859901	+	0.510461i	$0.829475\pi$
$270$	−2.26429	−	0.165218i	−0.137800	−	0.0100549i
$271$	1.74829	+	3.02812i	0.106201	+	0.183945i	0.914228	−	0.405200i	$-0.132798\pi$
$271$	1.74829	+	3.02812i	0.106201	+	0.183945i	−0.808027	+	0.589145i	$0.799465\pi$
$272$	−56.9267	−	32.8667i	−3.45169	−	1.99283i
$273$		−	10.8502i		−	0.656683i
$274$	−6.55303	−	1.75588i	−0.395883	−	0.106076i
$275$	2.09548	+	5.27820i	0.126362	+	0.318287i
$276$	−32.5816	−	8.73021i	−1.96118	−	0.525497i
$277$	−10.3266	+	17.8861i	−0.620463	+	1.07467i	0.368937	+	0.929455i	$0.379722\pi$
$277$	−10.3266	+	17.8861i	−0.620463	+	1.07467i	−0.989400	+	0.145219i	$0.953611\pi$
$278$	−3.50047	+	6.06299i	−0.209944	+	0.363634i
$279$	8.63950	+	2.31495i	0.517233	+	0.138592i
$280$	−15.4883	+	7.49625i	−0.925604	+	0.447986i
$281$	−0.545820	−	0.146252i	−0.0325609	−	0.00872467i	0.242502	−	0.970151i	$-0.422032\pi$
$281$	−0.545820	−	0.146252i	−0.0325609	−	0.00872467i	−0.275063	+	0.961426i	$0.588699\pi$
$282$			2.42274i			0.144272i
$283$	10.0364	+	5.79452i	0.596602	+	0.344448i	0.767704	−	0.640805i	$-0.221399\pi$
$283$	10.0364	+	5.79452i	0.596602	+	0.344448i	−0.171102	+	0.985253i	$0.554733\pi$
$284$	21.4571	+	37.1648i	1.27325	+	2.20533i
$285$	−28.0281	+	24.2160i	−1.66024	+	1.43443i
$286$		−	11.5506i		−	0.683002i
$287$	0.903453	−	3.37173i	0.0533292	−	0.199027i
$288$		−	25.9596i		−	1.52968i
$289$	21.1261	−	36.5915i	1.24271	−	2.15244i
$290$	3.56098	−	48.8025i	0.209108	−	2.86578i
$291$	36.3459	−	9.73885i	2.13063	−	0.570901i
$292$	−0.808823	−	3.01857i	−0.0473328	−	0.176648i
$293$	−26.6267	+	7.13460i	−1.55555	+	0.416808i	−0.931251	−	0.364380i	$-0.881281\pi$
$293$	−26.6267	+	7.13460i	−1.55555	+	0.416808i	−0.624297	+	0.781187i	$0.714614\pi$
$294$	−9.57034	+	35.7170i	−0.558153	+	2.08306i
$295$	−4.55745	−	0.332544i	−0.265345	−	0.0193614i
$296$	−42.1211	−	0.624320i	−2.44824	−	0.0362879i
$297$	0.315505	−	0.315505i	0.0183075	−	0.0183075i
$298$	−29.2072	+	16.8628i	−1.69193	+	0.976836i
$299$	5.71466	−	9.89809i	0.330487	−	0.572421i
$300$	−57.6734	+	6.72750i	−3.32977	+	0.388412i
$301$	1.11883	+	4.17551i	0.0644880	+	0.240673i
$302$		−	14.3163i		−	0.823810i
$303$	−30.3003	+	8.11895i	−1.74071	+	0.466422i
$304$	−40.3068	−	40.3068i	−2.31175	−	2.31175i
$305$	4.42462	+	9.14190i	0.253353	+	0.523464i
$306$	62.8321			3.59187
$307$	−8.94227	−	8.94227i	−0.510362	−	0.510362i	0.404275	−	0.914637i	$-0.367524\pi$
$307$	−8.94227	−	8.94227i	−0.510362	−	0.510362i	−0.914637	+	0.404275i	$0.867524\pi$
$308$	1.52854	−	5.70459i	0.0870967	−	0.325049i
$309$	−14.5463	+	3.89767i	−0.827510	+	0.221731i
$310$	16.3229	+	1.19104i	0.927080	+	0.0676463i
$311$	6.22810	−	23.2436i	0.353163	−	1.31802i	−0.529617	−	0.848237i	$-0.677664\pi$
$311$	6.22810	−	23.2436i	0.353163	−	1.31802i	0.882780	−	0.469786i	$-0.155669\pi$
$312$	65.3211	+	17.5027i	3.69808	+	0.990897i
$313$	1.93946	+	3.35924i	0.109625	+	0.189876i	0.915618	−	0.402049i	$-0.131702\pi$
$313$	1.93946	+	3.35924i	0.109625	+	0.189876i	−0.805994	+	0.591924i	$0.798368\pi$
$314$	7.08202	+	26.4304i	0.399661	+	1.49156i
$315$	4.40774	−	6.49229i	0.248348	−	0.365799i
$316$	−16.1779	+	60.3768i	−0.910079	+	3.39646i
$317$	1.31291	−	4.89983i	0.0737401	−	0.275202i	−0.919205	−	0.393780i	$-0.871167\pi$
$317$	1.31291	−	4.89983i	0.0737401	−	0.275202i	0.992945	+	0.118578i	$0.0378337\pi$
$318$	11.2520	+	19.4891i	0.630983	+	1.09290i
$319$	6.80013	+	6.80013i	0.380734	+	0.380734i
$320$	−1.74902	−	9.14554i	−0.0977733	−	0.511251i
$321$	−7.23238	+	4.17562i	−0.403672	+	0.233060i
$322$	5.89824	−	5.89824i	0.328696	−	0.328696i
$323$	36.3326	−	36.3326i	2.02160	−	2.02160i
$324$	−19.8884	−	34.4477i	−1.10491	−	1.91376i
$325$	2.85596	−	19.4660i	0.158420	−	1.07978i
$326$	−6.63013	−	3.82790i	−0.367209	−	0.212008i
$327$	10.5519			0.583522
$328$	18.8414	+	10.8781i	1.04034	+	0.600642i
$329$	−0.363501	−	0.209867i	−0.0200404	−	0.0115704i
$330$	9.14937	−	13.4764i	0.503656	−	0.741851i
$331$	19.9596	+	5.34816i	1.09708	+	0.293961i	0.761575	−	0.648077i	$-0.224427\pi$
$331$	19.9596	+	5.34816i	1.09708	+	0.293961i	0.335504	+	0.942039i	$0.391093\pi$
$332$	30.5155	+	30.5155i	1.67476	+	1.67476i
$333$	16.7779	−	9.35798i	0.919425	−	0.512814i
$334$			15.0682i			0.824493i
$335$	−8.99039	−	18.5754i	−0.491197	−	1.01488i
$336$	20.3924	+	11.7736i	1.11250	+	0.642300i
$337$	25.6887	−	6.88327i	1.39935	−	0.374956i	0.521241	−	0.853410i	$-0.325469\pi$
$337$	25.6887	−	6.88327i	1.39935	−	0.374956i	0.878112	+	0.478454i	$0.158803\pi$
$338$	−3.20909	+	5.55830i	−0.174551	+	0.302332i
$339$	13.5664	+	13.5664i	0.736828	+	0.736828i
$340$	79.1128	−	15.1298i	4.29049	−	0.820527i
$341$	−2.27443	+	2.27443i	−0.123167	+	0.123167i
$342$	52.6299	+	14.1021i	2.84590	+	0.762557i
$343$	−10.0298	−	10.0298i	−0.541557	−	0.541557i
$344$	−26.9426			−1.45265
$345$	14.5078	−	7.02170i	0.781075	−	0.378035i
$346$	0.235362	+	0.878382i	0.0126531	+	0.0472221i
$347$	−33.1904			−1.78175			−0.890877	−	0.454244i	$-0.849909\pi$
$347$	−33.1904			−1.78175			−0.890877	+	0.454244i	$0.849909\pi$
$348$	−85.1541	+	49.1637i	−4.56474	+	2.63545i
$349$	18.0845	−	10.4411i	0.968042	−	0.558899i	0.0694032	−	0.997589i	$-0.477890\pi$
$349$	18.0845	−	10.4411i	0.968042	−	0.558899i	0.898639	+	0.438689i	$0.144557\pi$
$350$	5.69030	−	13.1832i	0.304159	−	0.704672i
$351$	−1.49314	+	0.400086i	−0.0796979	+	0.0213550i
$352$	8.08485	+	4.66779i	0.430924	+	0.248794i
$353$	9.50935	−	5.49023i	0.506132	−	0.292215i	−0.225110	−	0.974333i	$-0.572274\pi$
$353$	9.50935	−	5.49023i	0.506132	−	0.292215i	0.731242	+	0.682118i	$0.238941\pi$
$354$	6.55339	+	11.3508i	0.348309	+	0.603289i
$355$	−19.3683	−	6.73465i	−1.02796	−	0.357438i
$356$	1.01148	−	1.01148i	0.0536083	−	0.0536083i
$357$	−10.6127	+	18.3818i	−0.561685	+	0.972866i
$358$	−3.84440	−	1.03010i	−0.203183	−	0.0544427i
$359$			25.5608i			1.34905i	0.738253	+	0.674524i	$0.235651\pi$
$359$			25.5608i			1.34905i	−0.738253	+	0.674524i	$0.764349\pi$
$360$	31.9752	+	37.0087i	1.68524	+	1.95053i
$361$	22.1333	−	12.7787i	1.16491	−	0.672561i
$362$	−37.0754			−1.94864
$363$	−6.23656	−	23.2752i	−0.327335	−	1.22163i
$364$	−14.4677	+	14.4677i	−0.758316	+	0.758316i
$365$	1.23543	+	0.838756i	0.0646654	+	0.0439025i
$366$	14.5656	−	25.2284i	0.761358	−	1.31871i
$367$	4.05783	+	15.1440i	0.211817	+	0.790512i	0.987263	+	0.159098i	$0.0508586\pi$
$367$	4.05783	+	15.1440i	0.211817	+	0.790512i	−0.775446	+	0.631414i	$0.782475\pi$
$368$	12.4020	+	21.4809i	0.646499	+	1.11977i
$369$	−9.92178			−0.516507
$370$	26.9376	−	22.5853i	1.40042	−	1.17415i
$371$	−3.89878			−0.202415
$372$	−16.4437	−	28.4814i	−0.852569	−	1.47669i
$373$	−5.74496	−	21.4405i	−0.297463	−	1.11015i	−0.939242	−	0.343256i	$-0.888470\pi$
$373$	−5.74496	−	21.4405i	−0.297463	−	1.11015i	0.641779	−	0.766889i	$-0.278197\pi$
$374$	−11.2978	+	19.5684i	−0.584197	+	1.01186i
$375$	18.7514	−	20.4493i	0.968318	−	1.05600i
$376$	1.84983	−	1.84983i	0.0953978	−	0.0953978i
$377$	−8.62310	−	32.1818i	−0.444112	−	1.65745i
$378$	−1.12817			−0.0580267
$379$	−10.4699	+	6.04477i	−0.537800	+	0.310499i	−0.744187	−	0.667971i	$-0.767163\pi$
$379$	−10.4699	+	6.04477i	−0.537800	+	0.310499i	0.206387	+	0.978470i	$0.433829\pi$
$380$	69.6628	+	5.08309i	3.57363	+	0.260757i
$381$		−	33.5563i		−	1.71914i
$382$	−38.1078	−	10.2110i	−1.94977	−	0.522438i
$383$	−16.2251	+	28.1027i	−0.829065	+	1.43598i	0.0697080	+	0.997567i	$0.477793\pi$
$383$	−16.2251	+	28.1027i	−0.829065	+	1.43598i	−0.898773	+	0.438415i	$0.855540\pi$
$384$	9.96131	−	9.96131i	0.508336	−	0.508336i
$385$	1.22940	+	2.54012i	0.0626562	+	0.129457i
$386$	7.76878	+	13.4559i	0.395420	+	0.684888i
$387$	10.6409	−	6.14350i	0.540905	−	0.312292i
$388$	−61.4499	−	35.4781i	−3.11964	−	1.80113i
$389$	−4.69136	+	1.25705i	−0.237861	+	0.0637347i	−0.375780	−	0.926709i	$-0.622625\pi$
$389$	−4.69136	+	1.25705i	−0.237861	+	0.0637347i	0.137919	+	0.990444i	$0.455959\pi$
$390$	−50.7951	+	24.5845i	−2.57211	+	1.24489i
$391$	−19.3629	+	11.1792i	−0.979226	+	0.565356i
$392$	34.5782	−	19.9637i	1.74646	−	1.00832i
$393$	9.80447			0.494570
$394$	−5.94318	−	22.1802i	−0.299413	−	1.11742i
$395$	−13.0119	−	26.8844i	−0.654699	−	1.35270i
$396$	−16.7865			−0.843555
$397$	8.38681	+	8.38681i	0.420922	+	0.420922i	0.885521	−	0.464599i	$-0.153802\pi$
$397$	8.38681	+	8.38681i	0.420922	+	0.420922i	−0.464599	+	0.885521i	$0.653802\pi$
$398$	53.2344	+	14.2641i	2.66840	+	0.714995i
$399$	−13.0151	+	13.0151i	−0.651572	+	0.651572i
$400$	33.4865	+	26.4903i	1.67433	+	1.32452i
$401$	17.3473	+	17.3473i	0.866283	+	0.866283i	0.992059	−	0.125776i	$-0.0401419\pi$
$401$	17.3473	+	17.3473i	0.866283	+	0.866283i	−0.125776	+	0.992059i	$0.540142\pi$
$402$	−29.5959	+	51.2616i	−1.47611	+	2.55669i
$403$	10.7638	−	2.88416i	0.536184	−	0.143670i
$404$	51.2287	+	29.5769i	2.54872	+	1.47151i
$405$	17.9523	+	6.24229i	0.892058	+	0.310182i
$406$		−	24.3156i		−	1.20676i
$407$	−0.102390	+	6.90797i	−0.00507529	+	0.342415i
$408$	−93.5437	−	93.5437i	−4.63110	−	4.63110i
$409$	28.0626	+	7.51935i	1.38761	+	0.371808i	0.873878	−	0.486146i	$-0.161598\pi$
$409$	28.0626	+	7.51935i	1.38761	+	0.371808i	0.513728	+	0.857953i	$0.328264\pi$
$410$	−17.8318	+	3.41021i	−0.880651	+	0.168418i
$411$	−5.64136	−	3.25704i	−0.278268	−	0.160658i
$412$	24.5934	+	14.1990i	1.21163	+	0.699534i
$413$	−2.27072			−0.111735
$414$	−20.5328	−	11.8546i	−1.00913	−	0.582623i
$415$	−20.5664	−	1.50067i	−1.00956	−	0.0736649i
$416$	−16.1713	−	28.0096i	−0.792865	−	1.37328i
$417$	−4.75331	+	4.75331i	−0.232771	+	0.232771i
$418$	−13.8553	+	13.8553i	−0.677687	+	0.677687i
$419$	11.6353	−	6.71763i	0.568420	−	0.328178i	−0.188098	−	0.982150i	$-0.560232\pi$
$419$	11.6353	−	6.71763i	0.568420	−	0.328178i	0.756518	+	0.653973i	$0.226899\pi$
$420$	−28.3399	+	5.41982i	−1.38285	+	0.264460i
$421$	7.93609	+	7.93609i	0.386781	+	0.386781i	0.873538	−	0.486756i	$-0.161820\pi$
$421$	7.93609	+	7.93609i	0.386781	+	0.386781i	−0.486756	+	0.873538i	$0.661820\pi$
$422$	35.6653	+	61.7742i	1.73616	+	3.00712i
$423$	−0.308781	+	1.15239i	−0.0150135	+	0.0560310i
$424$	6.28924	−	23.4718i	0.305433	−	1.13989i
$425$	−23.8785	+	30.1848i	−1.15828	+	1.46418i
$426$	15.2228	+	56.8122i	0.737546	+	2.75256i
$427$	2.52346	+	4.37077i	0.122119	+	0.211516i
$428$	15.2116	+	4.07592i	0.735278	+	0.197017i
$429$	2.87049	−	10.7128i	0.138589	−	0.517220i
$430$	17.0126	−	14.6987i	0.820421	−	0.708836i
$431$	−7.77927	+	2.08445i	−0.374714	+	0.100404i	−0.441261	−	0.897379i	$-0.645469\pi$
$431$	−7.77927	+	2.08445i	−0.374714	+	0.100404i	0.0665465	+	0.997783i	$0.478802\pi$
$432$	0.868269	−	3.24042i	0.0417746	−	0.155905i
$433$	25.2127	+	25.2127i	1.21165	+	1.21165i	0.970485	+	0.241163i	$0.0775287\pi$
$433$	25.2127	+	25.2127i	1.21165	+	1.21165i	0.241163	+	0.970485i	$0.422471\pi$
$434$	8.13280			0.390387
$435$	15.4308	−	44.3778i	0.739851	−	2.12775i
$436$	−14.0700	−	14.0700i	−0.673832	−	0.673832i
$437$	−18.7280	+	5.01815i	−0.895882	+	0.240051i
$438$		−	4.28306i		−	0.204652i
$439$	−7.66147	−	28.5930i	−0.365662	−	1.36467i	−0.866521	−	0.499140i	$-0.833649\pi$
$439$	−7.66147	−	28.5930i	−0.365662	−	1.36467i	0.500859	−	0.865529i	$-0.333017\pi$
$440$	−17.2754	+	3.30381i	−0.823574	+	0.157503i
$441$	−9.10435	+	15.7692i	−0.433540	+	0.750914i
$442$	67.7939	−	39.1408i	3.22463	−	1.86174i
$443$	10.6816	−	10.6816i	0.507499	−	0.507499i	−0.406259	−	0.913758i	$-0.633167\pi$
$443$	10.6816	−	10.6816i	0.507499	−	0.507499i	0.913758	+	0.406259i	$0.133167\pi$
$444$	−67.9530	−	19.2918i	−3.22491	−	0.915547i
$445$	−0.0497418	+	0.681702i	−0.00235799	+	0.0323158i
$446$	12.4762	−	46.5617i	0.590764	−	2.20476i
$447$	−31.2794	+	8.38130i	−1.47947	+	0.396422i
$448$	−1.19755	−	4.46933i	−0.0565790	−	0.211156i
$449$	−16.0064	+	4.28889i	−0.755387	+	0.202405i	−0.615906	−	0.787819i	$-0.711210\pi$
$449$	−16.0064	+	4.28889i	−0.755387	+	0.202405i	−0.139481	+	0.990225i	$0.544543\pi$
$450$	−40.3808	−	5.92448i	−1.90357	−	0.279283i
$451$	1.78403	−	3.09004i	0.0840069	−	0.145504i
$452$		−	36.1793i		−	1.70173i
$453$	3.55780	−	13.2779i	0.167160	−	0.623850i
$454$		−	9.28968i		−	0.435986i
$455$	0.711483	−	9.75075i	0.0333549	−	0.457122i
$456$	−57.3597	−	99.3499i	−2.68611	−	4.65249i
$457$	−13.5730	−	7.83638i	−0.634919	−	0.366571i	0.147736	−	0.989027i	$-0.452801\pi$
$457$	−13.5730	−	7.83638i	−0.634919	−	0.366571i	−0.782655	+	0.622456i	$0.786135\pi$
$458$		−	52.7378i		−	2.46427i
$459$	2.92093	+	0.782660i	0.136337	+	0.0365314i
$460$	−28.7077	−	9.98208i	−1.33850	−	0.465417i
$461$	15.2926	+	4.09763i	0.712246	+	0.190846i	0.596709	−	0.802457i	$-0.296474\pi$
$461$	15.2926	+	4.09763i	0.712246	+	0.190846i	0.115537	+	0.993303i	$0.463141\pi$
$462$	4.04713	−	7.00984i	0.188290	−	0.326127i
$463$	−0.197140	+	0.341457i	−0.00916189	+	0.0158689i	−0.870570	−	0.492045i	$-0.836250\pi$
$463$	−0.197140	+	0.341457i	−0.00916189	+	0.0158689i	0.861408	+	0.507913i	$0.169583\pi$
$464$	69.8412	+	18.7139i	3.24230	+	0.868771i
$465$	14.8430	+	5.16113i	0.688328	+	0.239342i
$466$	−38.9840	−	10.4457i	−1.80590	−	0.483889i
$467$			23.4749i			1.08629i	0.839639	+	0.543144i	$0.182766\pi$
$467$			23.4749i			1.08629i	−0.839639	+	0.543144i	$0.817234\pi$
$468$	50.3647	+	29.0781i	2.32811	+	1.34414i
$469$	−5.12742	−	8.88095i	−0.236762	−	0.410084i
$470$	−0.158867	+	2.17725i	−0.00732801	+	0.100429i
$471$			26.2734i			1.21061i
$472$	3.66297	−	13.6704i	0.168602	−	0.629231i
$473$			4.41865i			0.203170i
$474$	−42.8344	+	74.1914i	−1.96745	+	3.40772i
$475$	−26.7760	+	19.9243i	−1.22857	+	0.914191i
$476$	38.6616	−	10.3593i	1.77205	−	0.474819i
$477$	2.86818	+	10.7042i	0.131325	+	0.490111i
$478$	−14.4200	+	3.86383i	−0.659555	+	0.176727i
$479$	1.20655	−	4.50291i	0.0551288	−	0.205743i	−0.932868	−	0.360219i	$-0.882702\pi$
$479$	1.20655	−	4.50291i	0.0551288	−	0.205743i	0.987997	+	0.154475i	$0.0493687\pi$
$480$	3.31920	−	45.4890i	0.151500	−	2.07628i
$481$	12.2734	−	20.5487i	0.559618	−	0.936939i
$482$	15.8281	−	15.8281i	0.720951	−	0.720951i
$483$	6.93623	−	4.00463i	0.315609	−	0.182217i
$484$	−22.7195	+	39.3513i	−1.03270	+	1.78869i
$485$	33.3016	−	6.36871i	1.51215	−	0.289188i
$486$	−14.8982	−	55.6008i	−0.675796	−	2.52211i
$487$		−	0.580115i		−	0.0262875i	−0.999914	−	0.0131438i	$-0.995816\pi$
$487$		−	0.580115i		−	0.0262875i	0.999914	−	0.0131438i	$-0.00418391\pi$
$488$	−30.3839	+	8.14135i	−1.37542	+	0.368541i
$489$	−5.19794	−	5.19794i	−0.235059	−	0.235059i
$490$	−10.9427	+	31.4703i	−0.494340	+	1.42168i
$491$	−25.7023			−1.15993			−0.579965	−	0.814641i	$-0.696934\pi$
$491$	−25.7023			−1.15993			−0.579965	+	0.814641i	$0.696934\pi$
$492$	25.7965	+	25.7965i	1.16300	+	1.16300i
$493$	−16.8688	+	62.9551i	−0.759731	+	2.83535i
$494$	65.5709	−	17.5697i	2.95017	−	0.790497i
$495$	6.06953	−	5.24401i	0.272805	−	0.235701i
$496$	−6.25922	+	23.3597i	−0.281047	+	1.04888i
$497$	−9.84259	−	2.63731i	−0.441501	−	0.118300i
$498$	29.5735	+	51.2227i	1.32522	+	2.29535i
$499$	−8.07968	−	30.1538i	−0.361696	−	1.34987i	−0.871845	−	0.489783i	$-0.837076\pi$
$499$	−8.07968	−	30.1538i	−0.361696	−	1.34987i	0.510148	−	0.860086i	$-0.329590\pi$
$500$	−52.2706	+	2.26398i	−2.33761	+	0.101248i
$501$	−3.74465	+	13.9752i	−0.167299	+	0.624367i
$502$	2.34997	−	8.77022i	0.104884	−	0.391434i
$503$	−0.774181	−	1.34092i	−0.0345190	−	0.0597887i	0.848250	−	0.529596i	$-0.177657\pi$
$503$	−0.774181	−	1.34092i	−0.0345190	−	0.0597887i	−0.882769	+	0.469808i	$0.844323\pi$
$504$	17.1854	+	17.1854i	0.765499	+	0.765499i
$505$	−27.7625	+	5.30938i	−1.23541	+	0.236264i
$506$	7.38400	−	4.26316i	0.328259	−	0.189520i
$507$	−4.35764	+	4.35764i	−0.193530	+	0.193530i
$508$	−44.7444	+	44.7444i	−1.98521	+	1.98521i
$509$	4.45266	+	7.71223i	0.197361	+	0.341839i	0.947672	−	0.319246i	$-0.103430\pi$
$509$	4.45266	+	7.71223i	0.197361	+	0.341839i	−0.750311	+	0.661085i	$0.770096\pi$
$510$	110.101	+	8.03372i	4.87534	+	0.355739i
$511$	0.642617	+	0.371015i	0.0284277	+	0.0164127i
$512$	−48.0894			−2.12527
$513$	2.27099	+	1.31115i	0.100267	+	0.0578889i
$514$	5.88175	+	3.39583i	0.259433	+	0.149784i
$515$	−13.3279	+	2.54888i	−0.587299	+	0.112317i
$516$	−43.6391	−	11.6931i	−1.92111	−	0.514759i
$517$	−0.303377	−	0.303377i	−0.0133425	−	0.0133425i
$518$	12.5336	−	12.1675i	0.550697	−	0.534610i
$519$			0.873161i			0.0383275i
$520$	57.5546	+	20.0126i	2.52393	+	0.877609i
$521$	2.58292	+	1.49125i	0.113160	+	0.0653329i	0.555512	−	0.831509i	$-0.312522\pi$
$521$	2.58292	+	1.49125i	0.113160	+	0.0653329i	−0.442352	+	0.896842i	$0.645856\pi$
$522$	−66.7587	+	17.8880i	−2.92195	+	0.782934i
$523$	−8.55694	+	14.8210i	−0.374169	+	0.648079i	−0.990202	−	0.139641i	$-0.955405\pi$
$523$	−8.55694	+	14.8210i	−0.374169	+	0.648079i	0.616034	+	0.787720i	$0.288739\pi$
$524$	−13.0734	−	13.0734i	−0.571113	−	0.571113i
$525$	8.55379	−	10.8129i	0.373318	−	0.471912i
$526$	−2.71300	+	2.71300i	−0.118292	+	0.118292i
$527$	−21.0565	−	5.64208i	−0.917237	−	0.245773i
$528$	17.0195	+	17.0195i	0.740678	+	0.740678i
$529$	−14.5632			−0.633184
$530$	8.83393	+	18.2522i	0.383722	+	0.792823i
$531$	1.67048	+	6.23430i	0.0724925	+	0.270546i
$532$	34.7091			1.50483
$533$	−10.7053	+	6.18070i	−0.463698	+	0.267716i
$534$	1.69785	−	0.980254i	0.0734732	−	0.0424198i
$535$	−6.77335	+	3.27826i	−0.292838	+	0.141732i
$536$	61.7370	−	16.5424i	2.66663	−	0.714522i
$537$	−3.30956	−	1.91078i	−0.142818	−	0.0824561i
$538$	37.4779	−	21.6379i	1.61579	−	0.932874i
$539$	−3.27410	−	5.67091i	−0.141026	−	0.244263i
$540$	1.79084	+	3.70013i	0.0770656	+	0.159228i
$541$	12.7602	−	12.7602i	0.548605	−	0.548605i	−0.377433	−	0.926037i	$-0.623193\pi$
$541$	12.7602	−	12.7602i	0.548605	−	0.548605i	0.926037	+	0.377433i	$0.123193\pi$
$542$	4.51844	−	7.82616i	0.194083	−	0.336162i
$543$	−34.3863	−	9.21377i	−1.47566	−	0.395401i
$544$			63.2697i			2.71267i
$545$	9.48271	+	0.691925i	0.406195	+	0.0296388i
$546$	−24.2853	+	14.0211i	−1.03931	+	0.600048i
$547$	26.2958			1.12433			0.562163	−	0.827026i	$-0.309969\pi$
$547$	26.2958			1.12433			0.562163	+	0.827026i	$0.309969\pi$
$548$	3.17928	+	11.8652i	0.135812	+	0.506857i
$549$	10.1436	−	10.1436i	0.432918	−	0.432918i
$550$	9.10598	−	11.5109i	0.388280	−	0.490827i
$551$	−28.2595	+	48.9469i	−1.20389	+	2.08521i
$552$	12.9200	+	48.2180i	0.549911	+	2.05230i
$553$	−7.42097	−	12.8535i	−0.315572	−	0.546586i
$554$	53.3779			2.26781
$555$	30.5965	−	14.2528i	1.29875	−	0.604996i
$556$	12.6762			0.537592
$557$	15.4347	+	26.7336i	0.653988	+	1.13274i	0.982147	+	0.188117i	$0.0602385\pi$
$557$	15.4347	+	26.7336i	0.653988	+	1.13274i	−0.328159	+	0.944623i	$0.606428\pi$
$558$	−5.98296	−	22.3287i	−0.253279	−	0.945250i
$559$	7.65411	−	13.2573i	0.323734	−	0.560724i
$560$	17.5541	+	11.9178i	0.741794	+	0.503618i
$561$	−15.3414	+	15.3414i	−0.647715	+	0.647715i
$562$	0.377988	+	1.41067i	0.0159444	+	0.0595055i
$563$	19.7690			0.833165			0.416582	−	0.909098i	$-0.363228\pi$
$563$	19.7690			0.833165			0.416582	+	0.909098i	$0.363228\pi$
$564$	3.79902	−	2.19336i	0.159968	−	0.0923573i
$565$	11.3022	+	13.0814i	0.475487	+	0.550338i
$566$		−	29.9518i		−	1.25897i
$567$	9.12300	+	2.44450i	0.383130	+	0.102659i
$568$	31.7547	−	55.0008i	1.33240	−	2.30778i
$569$	5.64528	−	5.64528i	0.236662	−	0.236662i	−0.578804	−	0.815467i	$-0.696480\pi$
$569$	5.64528	−	5.64528i	0.236662	−	0.236662i	0.815467	+	0.578804i	$0.196480\pi$
$570$	90.4203	+	31.4405i	3.78729	+	1.31690i
$571$	−18.2648	−	31.6356i	−0.764360	−	1.32391i	−0.940585	−	0.339560i	$-0.889722\pi$
$571$	−18.2648	−	31.6356i	−0.764360	−	1.32391i	0.176225	−	0.984350i	$-0.443611\pi$
$572$	−18.1121	+	10.4571i	−0.757307	+	0.437231i
$573$	−32.8062	−	18.9407i	−1.37050	−	0.791258i
$574$	−8.71423	+	2.33497i	−0.363725	+	0.0974597i
$575$	13.4982	−	5.35888i	0.562915	−	0.223481i
$576$	−11.3896	+	6.57580i	−0.474567	+	0.273992i
$577$	−11.8892	+	6.86425i	−0.494955	+	0.285763i	−0.726628	−	0.687031i	$-0.758914\pi$
$577$	−11.8892	+	6.86425i	−0.494955	+	0.285763i	0.231673	+	0.972794i	$0.425580\pi$
$578$	−109.201			−4.54214
$579$	3.86130	+	14.4106i	0.160470	+	0.598883i
$580$	−79.7495	+	38.5982i	−3.31142	+	1.60270i
$581$	−10.2471			−0.425120
$582$	−68.7657	−	68.7657i	−2.85043	−	2.85043i
$583$	−3.84943	−	1.03145i	−0.159427	−	0.0427184i
$584$	−3.27024	+	3.27024i	−0.135324	+	0.135324i
$585$	−27.2943	+	5.21984i	−1.12848	+	0.215814i
$586$	50.3772	+	50.3772i	2.08106	+	2.08106i
$587$	5.80144	−	10.0484i	0.239451	−	0.414742i	−0.721106	−	0.692825i	$-0.756366\pi$
$587$	5.80144	−	10.0484i	0.239451	−	0.414742i	0.960557	+	0.278083i	$0.0896992\pi$
$588$	64.6709	−	17.3285i	2.66698	−	0.714616i
$589$	−16.3712	−	9.45192i	−0.674564	−	0.389460i
$590$	5.14504	+	10.6304i	0.211818	+	0.437646i
$591$		−	22.0484i		−	0.906951i
$592$	25.3024	+	45.3647i	1.03992	+	1.86448i
$593$	−13.3104	−	13.3104i	−0.546594	−	0.546594i	0.378860	−	0.925454i	$-0.376316\pi$
$593$	−13.3104	−	13.3104i	−0.546594	−	0.546594i	−0.925454	+	0.378860i	$0.876316\pi$
$594$	−1.11389	−	0.298465i	−0.0457033	−	0.0122462i
$595$	−10.7427	+	15.8233i	−0.440408	+	0.648691i
$596$	52.8840	+	30.5326i	2.16621	+	1.25066i
$597$	45.8283	+	26.4590i	1.87563	+	1.08289i
$598$	−29.5390			−1.20794
$599$	−9.11903	−	5.26487i	−0.372593	−	0.215117i	0.301997	−	0.953309i	$-0.402347\pi$
$599$	−9.11903	−	5.26487i	−0.372593	−	0.215117i	−0.674591	+	0.738192i	$0.735680\pi$
$600$	51.2982	+	68.9388i	2.09424	+	2.81441i
$601$	3.24164	+	5.61468i	0.132229	+	0.229028i	0.924536	−	0.381096i	$-0.124453\pi$
$601$	3.24164	+	5.61468i	0.132229	+	0.229028i	−0.792306	+	0.610123i	$0.791120\pi$
$602$	7.89999	−	7.89999i	0.321980	−	0.321980i
$603$	−20.6108	+	20.6108i	−0.839335	+	0.839335i
$604$	−22.4489	+	12.9609i	−0.913433	+	0.527371i
$605$	−4.07839	−	21.3257i	−0.165810	−	0.867013i
$606$	57.3277	+	57.3277i	2.32878	+	2.32878i
$607$	2.41737	+	4.18700i	0.0981179	+	0.169945i	0.910906	−	0.412615i	$-0.135384\pi$
$607$	2.41737	+	4.18700i	0.0981179	+	0.169945i	−0.812788	+	0.582560i	$0.802051\pi$
$608$	−14.2004	+	52.9965i	−0.575901	+	2.14929i
$609$	6.04276	−	22.5519i	0.244865	−	0.913849i
$610$	14.7440	−	21.7170i	0.596969	−	0.879294i
$611$	0.384706	+	1.43574i	0.0155635	+	0.0580839i
$612$	−56.8834	−	98.5250i	−2.29938	−	3.98264i
$613$	16.1062	+	4.31564i	0.650523	+	0.174307i	0.568965	−	0.822361i	$-0.307344\pi$
$613$	16.1062	+	4.31564i	0.650523	+	0.174307i	0.0815578	+	0.996669i	$0.474010\pi$
$614$	−8.45930	+	31.5705i	−0.341390	+	1.27408i
$615$	−17.3859	−	1.26860i	−0.701069	−	0.0511549i
$616$	−8.44232	+	2.26211i	−0.340151	+	0.0911431i
$617$	−4.71086	+	17.5812i	−0.189652	+	0.707791i	0.803935	+	0.594718i	$0.202736\pi$
$617$	−4.71086	+	17.5812i	−0.189652	+	0.707791i	−0.993587	+	0.113073i	$0.963930\pi$
$618$	27.5213	+	27.5213i	1.10707	+	1.10707i
$619$	−22.6457			−0.910209			−0.455104	−	0.890438i	$-0.650398\pi$
$619$	−22.6457			−0.910209			−0.455104	+	0.890438i	$0.650398\pi$
$620$	−12.9099	−	26.6737i	−0.518475	−	1.07124i
$621$	−0.806859	−	0.806859i	−0.0323781	−	0.0323781i
$622$	−60.0729	+	16.0965i	−2.40870	+	0.645410i
$623$			0.339654i			0.0136079i
$624$	−21.5820	−	80.5453i	−0.863973	−	3.22439i
$625$	18.1923	−	17.1476i	0.727692	−	0.685904i
$626$	5.01252	−	8.68194i	0.200341	−	0.347000i
$627$	−16.2936	+	9.40714i	−0.650705	+	0.375685i
$628$	35.0332	−	35.0332i	1.39798	−	1.39798i
$629$	−40.8918	+	22.8076i	−1.63046	+	0.909400i
$630$	−20.2272	−	1.47592i	−0.805870	−	0.0588020i
$631$	8.69983	−	32.4682i	0.346335	−	1.29254i	−0.544710	−	0.838624i	$-0.683360\pi$
$631$	8.69983	−	32.4682i	0.346335	−	1.29254i	0.891045	−	0.453915i	$-0.149973\pi$
$632$	89.3527	−	23.9420i	3.55426	−	0.952361i
$633$	17.7267	+	66.1569i	0.704573	+	2.62950i
$634$	−12.6636	+	3.39320i	−0.502935	+	0.134761i
$635$	2.20040	−	30.1561i	0.0873204	−	1.19671i
$636$	20.3735	−	35.2879i	0.807862	−	1.39926i
$637$			22.6860i			0.898850i
$638$	6.43286	−	24.0078i	0.254679	−	0.950476i
$639$			28.9632i			1.14576i
$640$	9.60515	−	8.29876i	0.379677	−	0.328037i
$641$	0.402097	+	0.696452i	0.0158819	+	0.0275082i	0.873857	−	0.486183i	$-0.161611\pi$
$641$	0.402097	+	0.696452i	0.0158819	+	0.0275082i	−0.857975	+	0.513691i	$0.828278\pi$
$642$	18.6921	+	10.7919i	0.737716	+	0.425921i
$643$			28.1085i			1.10849i	0.832353	+	0.554245i	$0.186993\pi$
$643$			28.1085i			1.10849i	−0.832353	+	0.554245i	$0.813007\pi$
$644$	−14.5887	−	3.90902i	−0.574874	−	0.154037i
$645$	19.4315	−	9.40472i	0.765114	−	0.370311i
$646$	−128.272	−	34.3703i	−5.04678	−	1.35228i
$647$	8.44655	−	14.6299i	0.332068	−	0.575159i	−0.650849	−	0.759207i	$-0.725587\pi$
$647$	8.44655	−	14.6299i	0.332068	−	0.575159i	0.982917	+	0.184048i	$0.0589202\pi$
$648$	−29.4332	+	50.9798i	−1.15624	+	2.00267i
$649$	−2.24198	−	0.600736i	−0.0880054	−	0.0235810i
$650$	−47.2602	+	18.7626i	−1.85370	+	0.735930i
$651$	7.54291	+	2.02112i	0.295630	+	0.0792138i
$652$			13.8620i			0.542877i
$653$	2.32328	+	1.34135i	0.0909170	+	0.0524910i	0.544769	−	0.838586i	$-0.316617\pi$
$653$	2.32328	+	1.34135i	0.0909170	+	0.0524910i	−0.453852	+	0.891077i	$0.649951\pi$
$654$	−13.6357	−	23.6177i	−0.533197	−	0.923524i
$655$	8.81100	+	0.642913i	0.344274	+	0.0251207i
$656$		−	26.8268i		−	1.04741i
$657$	0.545881	−	2.03726i	0.0212969	−	0.0794809i
$658$			1.08480i			0.0422899i
$659$	−8.22980	+	14.2544i	−0.320587	+	0.555274i	−0.980609	−	0.195973i	$-0.937214\pi$
$659$	−8.22980	+	14.2544i	−0.320587	+	0.555274i	0.660022	+	0.751246i	$0.270547\pi$
$660$	−29.4150	−	2.14633i	−1.14498	−	0.0835457i
$661$	6.24798	−	1.67414i	0.243018	−	0.0651165i	−0.135254	−	0.990811i	$-0.543185\pi$
$661$	6.24798	−	1.67414i	0.243018	−	0.0651165i	0.378272	+	0.925694i	$0.376518\pi$
$662$	−13.8223	−	51.5855i	−0.537218	−	2.00493i
$663$	72.6037	−	19.4541i	2.81970	−	0.755535i
$664$	16.5299	−	61.6903i	0.641483	−	2.39405i
$665$	−12.5498	+	10.8429i	−0.486660	+	0.420470i
$666$	−42.6266	−	25.4602i	−1.65175	−	0.986562i
$667$	17.3903	−	17.3903i	0.673357	−	0.673357i
$668$	23.6279	−	13.6416i	0.914190	−	0.527808i
$669$	23.1425	−	40.0840i	0.894740	−	1.54974i
$670$	−29.9584	+	44.1266i	−1.15739	+	1.70476i
$671$	1.33520	+	4.98304i	0.0515449	+	0.192368i
$672$		−	22.6646i		−	0.874306i
$673$	22.8099	−	6.11188i	0.879255	−	0.235596i	0.209169	−	0.977879i	$-0.432924\pi$
$673$	22.8099	−	6.11188i	0.879255	−	0.235596i	0.670086	+	0.742284i	$0.266257\pi$
$674$	−48.6025	−	48.6025i	−1.87210	−	1.87210i
$675$	−1.80342	−	0.778414i	−0.0694135	−	0.0299612i
$676$	11.6211			0.446964
$677$	34.3238	+	34.3238i	1.31917	+	1.31917i	0.914433	+	0.404737i	$0.132637\pi$
$677$	34.3238	+	34.3238i	1.31917	+	1.31917i	0.404737	+	0.914433i	$0.367363\pi$
$678$	12.8337	−	47.8961i	0.492876	−	1.83944i
$679$	16.2742	−	4.36065i	0.624545	−	0.167346i
$680$	−77.9312	−	90.1991i	−2.98852	−	3.45898i
$681$	2.30862	−	8.61588i	0.0884664	−	0.330161i
$682$	8.02985	+	2.15159i	0.307479	+	0.0823887i
$683$	20.1951	+	34.9789i	0.772744	+	1.33843i	0.936054	+	0.351857i	$0.114450\pi$
$683$	20.1951	+	34.9789i	0.772744	+	1.33843i	−0.163310	+	0.986575i	$0.552217\pi$
$684$	−25.5340	−	95.2943i	−0.976318	−	3.64367i
$685$	−4.85616	−	3.29694i	−0.185544	−	0.125969i
$686$	−9.48807	+	35.4100i	−0.362256	+	1.35196i
$687$	13.1061	−	48.9126i	0.500028	−	1.86613i
$688$	16.6110	+	28.7711i	0.633288	+	1.09689i
$689$	9.76276	+	9.76276i	0.371932	+	0.371932i
$690$	−34.4639	−	23.3982i	−1.31202	−	0.890754i
$691$	−0.790949	+	0.456655i	−0.0300891	+	0.0173720i	−0.514969	−	0.857209i	$-0.672197\pi$
$691$	−0.790949	+	0.456655i	−0.0300891	+	0.0173720i	0.484880	+	0.874581i	$0.338863\pi$
$692$	1.16428	−	1.16428i	0.0442594	−	0.0442594i
$693$	2.81845	−	2.81845i	0.107064	−	0.107064i
$694$	42.8902	+	74.2880i	1.62809	+	2.81993i
$695$	−4.58336	+	3.95998i	−0.173857	+	0.150211i
$696$	126.021	+	72.7583i	4.77681	+	2.75789i
$697$	24.1818			0.915949
$698$	−46.7393	−	26.9850i	−1.76911	−	1.02140i
$699$	−33.5605	−	19.3762i	−1.26937	−	0.732874i
$700$	−25.8237	+	3.01229i	−0.976044	+	0.113854i
$701$	2.64686	+	0.709224i	0.0999706	+	0.0267870i	0.308458	−	0.951238i	$-0.400187\pi$
$701$	2.64686	+	0.709224i	0.0999706	+	0.0267870i	−0.208487	+	0.978025i	$0.566854\pi$
$702$	2.82499	+	2.82499i	0.106622	+	0.106622i
$703$	−39.3711	+	9.92648i	−1.48491	+	0.374384i
$704$		−	4.72957i		−	0.178252i
$705$	−0.688422	+	1.97985i	−0.0259275	+	0.0745654i
$706$	−24.5769	−	14.1895i	−0.924962	−	0.534027i
$707$	−13.5672	+	3.63533i	−0.510248	+	0.136720i
$708$	11.8659	−	20.5523i	0.445947	−	0.772404i
$709$	6.01796	+	6.01796i	0.226009	+	0.226009i	0.811023	−	0.585014i	$-0.198911\pi$
$709$	6.01796	+	6.01796i	0.226009	+	0.226009i	−0.585014	+	0.811023i	$0.698911\pi$
$710$	9.95492	+	52.0538i	0.373602	+	1.95354i
$711$	−29.8302	+	29.8302i	−1.11872	+	1.11872i
$712$	−2.04481	−	0.547906i	−0.0766326	−	0.0205336i
$713$	5.81653	+	5.81653i	0.217831	+	0.217831i
$714$	54.8570			2.05297
$715$	3.28211	−	9.43909i	0.122744	−	0.353002i
$716$	1.86515	+	6.96085i	0.0697041	+	0.260139i
$717$	−14.3343			−0.535324
$718$	57.2111	−	33.0309i	2.13510	−	1.23270i
$719$	−34.2686	+	19.7850i	−1.27800	+	0.737855i	−0.976481	−	0.215604i	$-0.930828\pi$
$719$	−34.2686	+	19.7850i	−1.27800	+	0.737855i	−0.301522	+	0.953459i	$0.597495\pi$
$720$	19.8066	−	56.9624i	0.738150	−	2.12286i
$721$	−6.51322	+	1.74521i	−0.242565	+	0.0649951i
$722$	−57.2033	−	33.0264i	−2.12889	−	1.22911i
$723$	18.6136	−	10.7466i	0.692247	−	0.399669i
$724$	33.5653	+	58.1367i	1.24744	+	2.16063i
$725$	16.7772	−	38.8693i	0.623091	−	1.44357i
$726$	−44.0362	+	44.0362i	−1.63434	+	1.63434i
$727$	22.1721	−	38.4032i	0.822318	−	1.42430i	−0.0816344	−	0.996662i	$-0.526014\pi$
$727$	22.1721	−	38.4032i	0.822318	−	1.42430i	0.903952	−	0.427634i	$-0.140653\pi$
$728$	29.2480	+	7.83699i	1.08400	+	0.290458i
$729$		−	29.7703i		−	1.10261i
$730$	0.280855	−	3.84907i	0.0103949	−	0.142460i
$731$	−25.9343	+	14.9732i	−0.959216	+	0.553803i
$732$	−52.7465			−1.94956
$733$	−8.47421	−	31.6262i	−0.313002	−	1.16814i	−0.925835	−	0.377928i	$-0.876637\pi$
$733$	−8.47421	−	31.6262i	−0.313002	−	1.16814i	0.612833	−	0.790213i	$-0.290030\pi$
$734$	28.6522	−	28.6522i	1.05757	−	1.05757i
$735$	−17.9698	+	26.4683i	−0.662826	+	0.976297i
$736$	11.9372	−	20.6758i	0.440011	−	0.762121i
$737$	−2.71299	−	10.1250i	−0.0999344	−	0.372960i
$738$	12.8214	+	22.2073i	0.471962	+	0.817462i
$739$	0.0586148			0.00215618			0.00107809	−	0.999999i	$-0.499657\pi$
$739$	0.0586148			0.00215618			0.00107809	+	0.999999i	$0.499657\pi$
$740$	−59.8025	−	21.7929i	−2.19838	−	0.801123i
$741$	65.1812			2.39449
$742$	5.03819	+	8.72641i	0.184958	+	0.320356i
$743$	−2.69091	−	10.0426i	−0.0987198	−	0.368427i	0.898837	−	0.438282i	$-0.144413\pi$
$743$	−2.69091	−	10.0426i	−0.0987198	−	0.368427i	−0.997557	+	0.0698550i	$0.977746\pi$
$744$	−24.3354	+	42.1501i	−0.892178	+	1.54530i
$745$	−28.6595	+	5.48094i	−1.05000	+	0.200806i
$746$	−40.5650	+	40.5650i	−1.48519	+	1.48519i
$747$	7.53835	+	28.1335i	0.275814	+	1.02935i
$748$	40.9128			1.49592
$749$	−3.23836	+	1.86967i	−0.118327	+	0.0683161i
$750$	−70.0018	−	15.5446i	−2.55610	−	0.567607i
$751$			20.6505i			0.753549i	0.926305	+	0.376774i	$0.122967\pi$
$751$			20.6505i			0.753549i	−0.926305	+	0.376774i	$0.877033\pi$
$752$	−3.11586	−	0.834892i	−0.113624	−	0.0304454i
$753$	4.35905	−	7.55010i	0.158853	−	0.275141i
$754$	−60.8874	+	60.8874i	−2.21739	+	2.21739i
$755$	4.06798	−	11.6992i	0.148049	−	0.425777i
$756$	1.02136	+	1.76904i	0.0371464	+	0.0643395i
$757$	38.3557	−	22.1447i	1.39406	−	0.804863i	0.400301	−	0.916384i	$-0.368906\pi$
$757$	38.3557	−	22.1447i	1.39406	−	0.804863i	0.993762	+	0.111521i	$0.0355722\pi$
$758$	27.0593	+	15.6227i	0.982837	+	0.567441i
$759$	7.90788	−	2.11891i	0.287038	−	0.0769116i
$760$	−45.0329	−	93.0443i	−1.63351	−	3.37507i
$761$	7.58351	−	4.37834i	0.274902	−	0.158715i	−0.356211	−	0.934405i	$-0.615932\pi$
$761$	7.58351	−	4.37834i	0.274902	−	0.158715i	0.631113	+	0.775691i	$0.282598\pi$
$762$	−75.1070	+	43.3631i	−2.72084	+	1.57088i
$763$	4.72470			0.171046
$764$	18.4885	+	68.9999i	0.668889	+	2.49633i
$765$	51.3460	+	17.8538i	1.85642	+	0.645504i
$766$	83.8674			3.03025
$767$	5.68601	+	5.68601i	0.205310	+	0.205310i
$768$	−55.1314	−	14.7724i	−1.98938	−	0.533054i
$769$	−6.24542	+	6.24542i	−0.225216	+	0.225216i	−0.810690	−	0.585475i	$-0.800908\pi$
$769$	−6.24542	+	6.24542i	−0.225216	+	0.225216i	0.585475	+	0.810690i	$0.300908\pi$
$770$	4.09670	−	6.03416i	0.147635	−	0.217456i
$771$	4.61122	+	4.61122i	0.166069	+	0.166069i
$772$	14.0665	−	24.3639i	0.506265	−	0.876877i
$773$	5.24421	−	1.40518i	0.188621	−	0.0505409i	−0.163272	−	0.986581i	$-0.552205\pi$
$773$	5.24421	−	1.40518i	0.188621	−	0.0505409i	0.351893	+	0.936040i	$0.385538\pi$
$774$	−27.5012	−	15.8778i	−0.988512	−	0.570717i
$775$	13.0006	+	5.61147i	0.466994	+	0.201570i
$776$			105.009i			3.76961i
$777$	14.6484	−	8.17020i	0.525507	−	0.293104i
$778$	8.87596	+	8.87596i	0.318219	+	0.318219i
$779$	20.2553	+	5.42739i	0.725722	+	0.194457i
$780$	84.5362	+	57.3932i	3.02688	+	2.05501i
$781$	−9.02028	−	5.20786i	−0.322771	−	0.186352i
$782$	50.0434	+	28.8926i	1.78955	+	1.03320i
$783$	−3.32628			−0.118872
$784$	−42.6372	−	24.6166i	−1.52276	−	0.879165i
$785$	−1.72284	+	23.6111i	−0.0614906	+	0.842718i
$786$	−12.6698	−	21.9447i	−0.451916	−	0.782742i
$787$	−4.68846	+	4.68846i	−0.167125	+	0.167125i	−0.785715	−	0.618589i	$-0.787705\pi$
$787$	−4.68846	+	4.68846i	−0.167125	+	0.167125i	0.618589	+	0.785715i	$0.287705\pi$
$788$	−29.3996	+	29.3996i	−1.04732	+	1.04732i
$789$	−3.19043	+	1.84200i	−0.113582	+	0.0655769i
$790$	−43.3591	+	63.8650i	−1.54265	+	2.27221i
$791$	6.07449	+	6.07449i	0.215984	+	0.215984i
$792$	12.4213	+	21.5144i	0.441373	+	0.764480i
$793$	4.62574	−	17.2635i	0.164265	−	0.613045i
$794$	7.93384	−	29.6095i	0.281562	−	1.05080i
$795$	3.65727	+	19.1237i	0.129710	+	0.678246i
$796$	−25.8273	−	96.3887i	−0.915423	−	3.41641i
$797$	22.9918	+	39.8230i	0.814411	+	1.41060i	0.909750	+	0.415157i	$0.136273\pi$
$797$	22.9918	+	39.8230i	0.814411	+	1.41060i	−0.0953388	+	0.995445i	$0.530393\pi$
$798$	45.9498	+	12.3122i	1.62660	+	0.435847i
$799$	0.752574	−	2.80864i	0.0266241	−	0.0993627i
$800$	5.96574	−	40.6620i	0.210921	−	1.43762i
$801$	0.932525	−	0.249869i	0.0329492	−	0.00882870i
$802$	16.4104	−	61.2444i	0.579471	−	2.16261i
$803$	0.536328	+	0.536328i	0.0189266	+	0.0189266i
$804$	107.175			3.77979
$805$	6.49599	−	3.14402i	0.228954	−	0.110812i
$806$	−20.3650	−	20.3650i	−0.717325	−	0.717325i
$807$	40.1368	−	10.7546i	1.41288	−	0.378581i
$808$		−	87.5427i		−	3.07974i
$809$	0.951632	+	3.55154i	0.0334576	+	0.124865i	0.980635	−	0.195845i	$-0.0627450\pi$
$809$	0.951632	+	3.55154i	0.0334576	+	0.124865i	−0.947177	+	0.320711i	$0.896078\pi$
$810$	−9.22712	−	48.2481i	−0.324208	−	1.69527i
$811$	−12.8941	+	22.3332i	−0.452773	+	0.784226i	−0.998557	−	0.0536998i	$-0.982899\pi$
$811$	−12.8941	+	22.3332i	−0.452773	+	0.784226i	0.545784	+	0.837926i	$0.316232\pi$
$812$	−38.1284	+	22.0135i	−1.33805	+	0.772521i
$813$	6.13562	−	6.13562i	0.215185	−	0.215185i
$814$	15.5940	−	8.69763i	0.546569	−	0.304852i
$815$	−4.33040	−	5.01209i	−0.151687	−	0.175566i
$816$	−42.2194	+	157.565i	−1.47798	+	5.51588i
$817$	−25.0839	+	6.72122i	−0.877575	+	0.235146i
$818$	−19.4337	−	72.5276i	−0.679484	−	2.53587i
$819$	−13.3384	+	3.57402i	−0.466082	+	0.124886i
$820$	21.4910	+	24.8742i	0.750499	+	0.868643i
$821$	5.60192	−	9.70282i	0.195509	−	0.338631i	−0.751559	−	0.659666i	$-0.770698\pi$
$821$	5.60192	−	9.70282i	0.195509	−	0.338631i	0.947067	+	0.321036i	$0.104031\pi$
$822$			16.8356i			0.587209i
$823$	10.2219	−	38.1487i	0.356314	−	1.32978i	−0.522510	−	0.852633i	$-0.675004\pi$
$823$	10.2219	−	38.1487i	0.356314	−	1.32978i	0.878823	−	0.477147i	$-0.158329\pi$
$824$		−	42.0267i		−	1.46407i
$825$	11.3061	−	8.41303i	0.393629	−	0.292904i
$826$	2.93433	+	5.08242i	0.102099	+	0.176840i
$827$	−40.4142	−	23.3332i	−1.40534	−	0.811373i	−0.410406	−	0.911903i	$-0.634613\pi$
$827$	−40.4142	−	23.3332i	−1.40534	−	0.811373i	−0.994934	+	0.100530i	$0.967946\pi$
$828$			42.9291i			1.49189i
$829$	18.9445	+	5.07616i	0.657969	+	0.176302i	0.572329	−	0.820024i	$-0.306040\pi$
$829$	18.9445	+	5.07616i	0.657969	+	0.176302i	0.0856396	+	0.996326i	$0.472707\pi$
$830$	23.2180	+	47.9717i	0.805909	+	1.66512i
$831$	49.5063	+	13.2652i	1.71735	+	0.460163i
$832$	−8.19270	+	14.1902i	−0.284031	+	0.491955i
$833$	22.1895	−	38.4333i	0.768820	−	1.33164i
$834$	16.7815	+	4.49659i	0.581096	+	0.155704i
$835$	−4.28162	+	12.3136i	−0.148171	+	0.426130i
$836$	34.2697	+	9.18254i	1.18524	+	0.317585i
$837$		−	1.11254i		−	0.0384550i
$838$	−30.0713	−	17.3617i	−1.03880	−	0.599749i
$839$	17.1911	+	29.7759i	0.593503	+	1.02798i	0.993756	+	0.111572i	$0.0355887\pi$
$839$	17.1911	+	29.7759i	0.593503	+	1.02798i	−0.400254	+	0.916404i	$0.631078\pi$
$840$	27.9167	+	32.3113i	0.963216	+	1.11485i
$841$		−	42.6918i		−	1.47213i
$842$	7.50747	−	28.0182i	0.258724	−	0.965572i
$843$			1.40229i			0.0482973i
$844$	64.5774	−	111.851i	2.22284	−	3.85008i
$845$	−4.20184	+	3.63035i	−0.144548	+	0.124888i
$846$	2.97834	−	0.798043i	0.102397	−	0.0274373i
$847$	−2.79247	−	10.4216i	−0.0959504	−	0.358092i
$848$	−28.9423	+	7.75506i	−0.993882	+	0.266310i
$849$	7.44345	−	27.7793i	0.255459	−	0.953384i
$850$	98.4177	+	14.4394i	3.37570	+	0.495266i
$851$	17.6661	+	0.261848i	0.605587	+	0.00897603i
$852$	75.3038	−	75.3038i	2.57987	−	2.57987i
$853$	−49.0980	+	28.3467i	−1.68108	+	0.970574i	−0.720139	+	0.693830i	$0.755922\pi$
$853$	−49.0980	+	28.3467i	−1.68108	+	0.970574i	−0.960944	+	0.276744i	$0.910745\pi$
$854$	6.52188	−	11.2962i	0.223174	−	0.386549i
$855$	39.0017	+	26.4790i	1.33383	+	0.905562i
$856$	−6.03203	−	22.5118i	−0.206170	−	0.769439i
$857$			23.8014i			0.813039i	0.913642	+	0.406519i	$0.133258\pi$
$857$			23.8014i			0.813039i	−0.913642	+	0.406519i	$0.866742\pi$
$858$	−27.6872	+	7.41877i	−0.945227	+	0.253273i
$859$	30.4686	+	30.4686i	1.03958	+	1.03958i	0.999184	+	0.0403928i	$0.0128609\pi$
$859$	30.4686	+	30.4686i	1.03958	+	1.03958i	0.0403928	+	0.999184i	$0.487139\pi$
$860$	−38.4505	−	13.3698i	−1.31115	−	0.455906i
$861$	−8.66244			−0.295215
$862$	14.7182	+	14.7182i	0.501305	+	0.501305i
$863$	−12.5149	+	46.7061i	−0.426011	+	1.58990i	0.335693	+	0.941971i	$0.391029\pi$
$863$	−12.5149	+	46.7061i	−0.426011	+	1.58990i	−0.761705	+	0.647924i	$0.775637\pi$
$864$	−3.11898	+	0.835727i	−0.106110	+	0.0284320i
$865$	−0.0572562	+	0.784686i	−0.00194677	+	0.0266801i
$866$	23.8510	−	89.0132i	0.810491	−	3.02479i
$867$	−101.280	−	27.1379i	−3.43965	−	0.921651i
$868$	−7.36282	−	12.7528i	−0.249910	−	0.432857i
$869$	−3.92654	−	14.6541i	−0.133199	−	0.497105i
$870$	−119.269	+	22.8093i	−4.04358	+	0.773307i
$871$	−9.39904	+	35.0777i	−0.318474	+	1.18856i
$872$	−7.62156	+	28.4440i	−0.258098	+	0.963237i
$873$	−23.9444	−	41.4730i	−0.810397	−	1.40365i
$874$	35.4330	+	35.4330i	1.19854	+	1.19854i
$875$	8.39609	−	9.15633i	0.283840	−	0.309540i
$876$	−6.71612	+	3.87755i	−0.226917	+	0.131010i
$877$	31.7665	−	31.7665i	1.07268	−	1.07268i	0.0755336	−	0.997143i	$-0.475934\pi$
$877$	31.7665	−	31.7665i	1.07268	−	1.07268i	0.997143	−	0.0755336i	$-0.0240660\pi$
$878$	−54.0974	+	54.0974i	−1.82570	+	1.82570i
$879$	34.2038	+	59.2426i	1.15366	+	1.99820i
$880$	14.1789	+	16.4110i	0.477971	+	0.553214i
$881$	−48.1673	−	27.8094i	−1.62280	−	0.936922i	−0.986168	−	0.165752i	$-0.946995\pi$
$881$	−48.1673	−	27.8094i	−1.62280	−	0.936922i	−0.636629	−	0.771170i	$-0.719672\pi$
$882$	47.0603			1.58460
$883$	−1.40662	−	0.812113i	−0.0473366	−	0.0273298i	0.476145	−	0.879367i	$-0.342034\pi$
$883$	−1.40662	−	0.812113i	−0.0473366	−	0.0273298i	−0.523482	+	0.852037i	$0.675367\pi$
$884$	−122.751	−	70.8703i	−4.12856	−	2.38363i
$885$	2.13006	+	11.1380i	0.0716011	+	0.374398i
$886$	−37.7113	−	10.1047i	−1.26693	−	0.339474i
$887$	−27.5442	−	27.5442i	−0.924845	−	0.924845i	0.0725215	−	0.997367i	$-0.476895\pi$
$887$	−27.5442	−	27.5442i	−0.924845	−	0.924845i	−0.997367	+	0.0725215i	$0.976895\pi$
$888$	25.5572	+	101.367i	0.857643	+	3.40165i
$889$		−	15.0251i		−	0.503926i
$890$	1.59009	−	0.769594i	0.0532999	−	0.0257968i
$891$	8.36081	+	4.82712i	0.280098	+	0.161714i
$892$	−84.3068	+	22.5900i	−2.82280	+	0.756367i
$893$	1.26075	−	2.18369i	0.0421895	−	0.0730744i
$894$	59.1801	+	59.1801i	1.97928	+	1.97928i
$895$	−2.84891	−	1.93418i	−0.0952287	−	0.0646525i
$896$	4.46026	−	4.46026i	0.149007	−	0.149007i
$897$	−27.3965	−	7.34087i	−0.914742	−	0.245104i
$898$	30.2837	+	30.2837i	1.01058	+	1.01058i
$899$	23.9787			0.799734
$900$	27.2677	+	68.6834i	0.908924	+	2.28945i
$901$	−6.99043	−	26.0886i	−0.232885	−	0.869139i
$902$	−9.22165			−0.307047
$903$	9.29025	−	5.36373i	0.309160	−	0.178494i
$904$	−46.3690	+	26.7712i	−1.54221	+	0.890396i
$905$	−30.2978	−	10.5350i	−1.00713	−	0.350195i
$906$	−34.3167	+	9.19512i	−1.14009	+	0.305487i
$907$	18.3302	+	10.5829i	0.608643	+	0.351400i	0.772434	−	0.635095i	$-0.219039\pi$
$907$	18.3302	+	10.5829i	0.608643	+	0.351400i	−0.163791	+	0.986495i	$0.552372\pi$
$908$	−14.5668	+	8.41017i	−0.483417	+	0.279101i
$909$	19.9617	+	34.5747i	0.662087	+	1.14677i
$910$	−22.7439	+	11.0079i	−0.753953	+	0.364909i
$911$	−33.4304	+	33.4304i	−1.10760	+	1.10760i	−0.114134	+	0.993465i	$0.536409\pi$
$911$	−33.4304	+	33.4304i	−1.10760	+	1.10760i	−0.993465	+	0.114134i	$0.963591\pi$
$912$	−70.7283	+	122.505i	−2.34205	+	4.05655i
$913$	−10.1174	−	2.71094i	−0.334836	−	0.0897190i
$914$			40.5062i			1.33982i
$915$	19.0716	−	16.4777i	0.630488	−	0.544735i
$916$	−82.6964	+	47.7448i	−2.73236	+	1.57753i
$917$	4.39003			0.144971
$918$	−2.02278	−	7.54911i	−0.0667617	−	0.249158i
$919$	−12.1260	+	12.1260i	−0.399998	+	0.399998i	−0.878232	−	0.478234i	$-0.841277\pi$
$919$	−12.1260	+	12.1260i	−0.399998	+	0.399998i	0.478234	+	0.878232i	$0.341277\pi$
$920$	8.44901	+	44.1794i	0.278556	+	1.45655i
$921$	−15.6915	+	27.1784i	−0.517051	+	0.895559i
$922$	−10.5903	−	39.5236i	−0.348773	−	1.30164i
$923$	18.0424	+	31.2503i	0.593873	+	1.02862i
$924$	−14.6559			−0.482143
$925$	28.4308	−	10.8022i	0.934800	−	0.355176i
$926$	1.01902			0.0334869
$927$	9.58301	+	16.5983i	0.314747	+	0.545158i
$928$	−18.0125	−	67.2237i	−0.591290	−	2.20673i
$929$	−8.11478	+	14.0552i	−0.266237	+	0.461136i	−0.967887	−	0.251386i	$-0.919114\pi$
$929$	−8.11478	+	14.0552i	−0.266237	+	0.461136i	0.701650	+	0.712522i	$0.252447\pi$
$930$	−7.62900	−	39.8916i	−0.250165	−	1.30810i
$931$	27.2126	−	27.2126i	0.891855	−	0.891855i
$932$	18.9135	+	70.5863i	0.619534	+	2.31213i
$933$	−59.7159			−1.95501
$934$	52.5424	−	30.3354i	1.71924	−	0.992603i
$935$	−14.7929	+	12.7809i	−0.483779	+	0.417980i
$936$		−	86.0663i		−	2.81317i
$937$	36.6527	+	9.82105i	1.19739	+	0.320840i	0.801803	−	0.597589i	$-0.203874\pi$
$937$	36.6527	+	9.82105i	1.19739	+	0.320840i	0.395587	+	0.918428i	$0.370541\pi$
$938$	−13.2518	+	22.9528i	−0.432686	+	0.749435i
$939$	6.80654	−	6.80654i	0.222123	−	0.222123i
$940$	3.55790	−	1.72200i	0.116046	−	0.0561655i
$941$	−19.6844	−	34.0944i	−0.641693	−	1.11144i	−0.985055	−	0.172241i	$-0.944899\pi$
$941$	−19.6844	−	34.0944i	−0.641693	−	1.11144i	0.343362	−	0.939203i	$-0.388434\pi$
$942$	58.8060	−	33.9517i	1.91600	−	1.10621i
$943$	−7.90232	−	4.56241i	−0.257335	−	0.148572i
$944$	−16.8565	+	4.51669i	−0.548632	+	0.147006i
$945$	−0.921932	−	0.320569i	−0.0299904	−	0.0104281i
$946$	9.88999	−	5.70999i	0.321551	−	0.185648i
$947$	21.7482	−	12.5563i	0.706720	−	0.408025i	−0.103125	−	0.994668i	$-0.532884\pi$
$947$	21.7482	−	12.5563i	0.706720	−	0.408025i	0.809846	+	0.586643i	$0.199551\pi$
$948$	155.116			5.03794
$949$	−0.680106	−	2.53819i	−0.0220772	−	0.0823931i
$950$	79.1966	+	34.1838i	2.56948	+	1.10907i
$951$	−12.5883			−0.408204
$952$	−41.8849	−	41.8849i	−1.35750	−	1.35750i
$953$	−21.7502	−	5.82794i	−0.704558	−	0.188786i	−0.111286	−	0.993788i	$-0.535497\pi$
$953$	−21.7502	−	5.82794i	−0.704558	−	0.188786i	−0.593271	+	0.805003i	$0.702164\pi$
$954$	20.2521	−	20.2521i	0.655686	−	0.655686i
$955$	−28.2400	−	19.1727i	−0.913826	−	0.620413i
$956$	19.1135	+	19.1135i	0.618175	+	0.618175i
$957$	11.9325	−	20.6678i	0.385724	−	0.668094i
$958$	−11.6378	+	3.11833i	−0.375999	+	0.100749i
$959$	−2.52596	−	1.45837i	−0.0815676	−	0.0470931i
$960$	−20.7988	+	10.0665i	−0.671279	+	0.324895i
$961$		−	22.9799i		−	0.741286i
$962$	−61.8530	−	0.916787i	−1.99422	−	0.0295584i
$963$	7.51552	+	7.51552i	0.242184	+	0.242184i
$964$	−39.1491	−	10.4900i	−1.26091	−	0.337859i
$965$	2.52510	+	13.2036i	0.0812857	+	0.425039i
$966$	−17.9266	−	10.3500i	−0.576780	−	0.333004i
$967$	13.3242	+	7.69271i	0.428476	+	0.247381i	0.698697	−	0.715417i	$-0.253763\pi$
$967$	13.3242	+	7.69271i	0.428476	+	0.247381i	−0.270221	+	0.962798i	$0.587097\pi$
$968$	67.2458			2.16136
$969$	−110.426	−	63.7547i	−3.54741	−	2.04810i
$970$	−57.2886	−	66.3070i	−1.83943	−	2.12899i
$971$	−24.3855	−	42.2370i	−0.782569	−	1.35545i	−0.930441	−	0.366442i	$-0.880576\pi$
$971$	−24.3855	−	42.2370i	−0.782569	−	1.35545i	0.147872	−	0.989007i	$-0.452758\pi$
$972$	−73.6982	+	73.6982i	−2.36387	+	2.36387i
$973$	−2.12833	+	2.12833i	−0.0682313	+	0.0682313i
$974$	−1.29844	+	0.749652i	−0.0416046	+	0.0240204i
$975$	−48.4951	+	5.65687i	−1.55309	+	0.181165i
$976$	27.4266	+	27.4266i	0.877903	+	0.877903i
$977$	8.97973	+	15.5533i	0.287287	+	0.497596i	0.973161	−	0.230124i	$-0.0739133\pi$
$977$	8.97973	+	15.5533i	0.287287	+	0.497596i	−0.685874	+	0.727720i	$0.740580\pi$
$978$	−4.91720	+	18.3512i	−0.157235	+	0.586808i
$979$	−0.0898579	+	0.335354i	−0.00287187	+	0.0107180i
$980$	59.2542	−	11.3320i	1.89281	−	0.361986i
$981$	−3.47577	−	12.9717i	−0.110973	−	0.414156i
$982$	33.2138	+	57.5279i	1.05989	+	1.83579i
$983$	1.27882	+	0.342659i	0.0407881	+	0.0109291i	0.279155	−	0.960246i	$-0.409946\pi$
$983$	1.27882	+	0.342659i	0.0407881	+	0.0109291i	−0.238367	+	0.971175i	$0.576612\pi$
$984$	13.9736	−	52.1503i	0.445463	−	1.66249i
$985$	1.44579	−	19.8143i	0.0460667	−	0.631336i
$986$	162.707	−	43.5972i	5.18165	−	1.38842i
$987$	−0.269588	+	1.00612i	−0.00858110	+	0.0320251i
$988$	−86.9133	−	86.9133i	−2.76508	−	2.76508i
$989$	11.3001			0.359321
$990$	−19.5807	−	6.80848i	−0.622314	−	0.216388i
$991$	15.6624	+	15.6624i	0.497531	+	0.497531i	0.910669	−	0.413137i	$-0.135567\pi$
$991$	15.6624	+	15.6624i	0.497531	+	0.497531i	−0.413137	+	0.910669i	$0.635567\pi$
$992$	22.4842	−	6.02463i	0.713875	−	0.191282i
$993$		−	51.2789i		−	1.62729i
$994$	6.81612	+	25.4381i	0.216194	+	0.806848i
$995$	39.4496	+	26.7831i	1.25064	+	0.849081i
$996$	53.5471	−	92.7464i	1.69671	−	2.93878i
$997$	−33.6572	+	19.4320i	−1.06593	+	0.615417i	−0.927068	−	0.374894i	$-0.877679\pi$
$997$	−33.6572	+	19.4320i	−1.06593	+	0.615417i	−0.138867	+	0.990311i	$0.544346\pi$
$998$	−57.0504	+	57.0504i	−1.80590	+	1.80590i
$999$	−1.66448	−	1.71456i	−0.0526617	−	0.0542463i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.103.1	yes	68
5.2	odd	4		185.2.u.a.177.17	yes	68
5.3	odd	4		925.2.y.b.732.1		68
5.4	even	2		925.2.t.b.843.17		68
37.23	odd	12		185.2.u.a.23.17	yes	68
185.23	even	12		925.2.t.b.282.17		68
185.97	even	12	inner	185.2.p.a.97.1	✓	68
185.134	odd	12		925.2.y.b.393.1		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.1	✓	68	185.97	even	12	inner
185.2.p.a.103.1	yes	68	1.1	even	1	trivial
185.2.u.a.23.17	yes	68	37.23	odd	12
185.2.u.a.177.17	yes	68	5.2	odd	4
925.2.t.b.282.17		68	185.23	even	12
925.2.t.b.843.17		68	5.4	even	2
925.2.y.b.393.1		68	185.134	odd	12
925.2.y.b.732.1		68	5.3	odd	4

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.p.a.103.1

Level	$185$
Weight	$2$
Character	185.103
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$68$
Inner twists	$2$