LMFDB - Embedded newform 605.2.m.g.112.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			112.18
Character	$\chi$	$=$	605.112
Dual form			605.2.m.g.578.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05076 + 2.06223i) q^{2} +(0.159862 - 1.00933i) q^{3} +(-1.97313 + 2.71579i) q^{4} +(-1.98733 + 1.02495i) q^{5} +(2.24944 - 0.730888i) q^{6} +(-2.99845 + 0.474908i) q^{7} +(-3.10187 - 0.491288i) q^{8} +(1.85999 + 0.604346i) q^{9} +O(q^{10})$	\(q+(1.05076 + 2.06223i) q^{2} +(0.159862 - 1.00933i) q^{3} +(-1.97313 + 2.71579i) q^{4} +(-1.98733 + 1.02495i) q^{5} +(2.24944 - 0.730888i) q^{6} +(-2.99845 + 0.474908i) q^{7} +(-3.10187 - 0.491288i) q^{8} +(1.85999 + 0.604346i) q^{9} +(-4.20189 - 3.02136i) q^{10} +(2.42569 + 2.42569i) q^{12} +(-3.73187 + 1.90148i) q^{13} +(-4.13002 - 5.68449i) q^{14} +(0.716809 + 2.16971i) q^{15} +(-0.171494 - 0.527805i) q^{16} +(-5.99159 - 3.05287i) q^{17} +(0.708096 + 4.47075i) q^{18} +(-0.593572 + 0.431256i) q^{19} +(1.13773 - 7.41953i) q^{20} +3.10233i q^{21} +(-4.96412 + 4.96412i) q^{23} +(-0.991740 + 3.05226i) q^{24} +(2.89896 - 4.07382i) q^{25} +(-7.84260 - 5.69798i) q^{26} +(2.29913 - 4.51230i) q^{27} +(4.62660 - 9.08021i) q^{28} +(3.92271 + 2.85001i) q^{29} +(-3.72126 + 3.75808i) q^{30} +(0.334876 - 1.03064i) q^{31} +(-3.53313 + 3.53313i) q^{32} -15.5639i q^{34} +(5.47216 - 4.01705i) q^{35} +(-5.31128 + 3.85887i) q^{36} +(-0.0132489 - 0.0836500i) q^{37} +(-1.51305 - 0.770938i) q^{38} +(1.32263 + 4.07065i) q^{39} +(6.66799 - 2.20290i) q^{40} +(3.15212 + 4.33853i) q^{41} +(-6.39773 + 3.25981i) q^{42} +(1.92858 + 1.92858i) q^{43} +(-4.31583 + 0.705353i) q^{45} +(-15.4533 - 5.02107i) q^{46} +(10.0926 + 1.59850i) q^{47} +(-0.560143 + 0.0887179i) q^{48} +(2.10777 - 0.684857i) q^{49} +(11.4473 + 1.69773i) q^{50} +(-4.03916 + 5.55943i) q^{51} +(2.19946 - 13.8869i) q^{52} +(-1.03078 - 2.02302i) q^{53} +11.7212 q^{54} +9.53412 q^{56} +(0.340388 + 0.668049i) q^{57} +(-1.75557 + 11.0842i) q^{58} +(-0.703280 + 0.967982i) q^{59} +(-7.30684 - 2.33444i) q^{60} +(-7.01046 + 2.27784i) q^{61} +(2.47730 - 0.392365i) q^{62} +(-5.86408 - 0.928780i) q^{63} +(-12.0542 - 3.91665i) q^{64} +(5.46754 - 7.60385i) q^{65} +(3.89698 + 3.89698i) q^{67} +(20.1132 - 10.2482i) q^{68} +(4.21684 + 5.80399i) q^{69} +(14.0340 + 7.06390i) q^{70} +(4.29785 + 13.2274i) q^{71} +(-5.47253 - 2.78839i) q^{72} +(0.426034 + 2.68987i) q^{73} +(0.158584 - 0.115218i) q^{74} +(-3.64838 - 3.57725i) q^{75} -2.46294i q^{76} +(-7.00485 + 7.00485i) q^{78} +(-3.20120 + 9.85229i) q^{79} +(0.881788 + 0.873150i) q^{80} +(0.559756 + 0.406686i) q^{81} +(-5.63493 + 11.0592i) q^{82} +(0.779264 - 1.52939i) q^{83} +(-8.42528 - 6.12132i) q^{84} +(15.0363 - 0.0740116i) q^{85} +(-1.95071 + 6.00366i) q^{86} +(3.50368 - 3.50368i) q^{87} -10.9954i q^{89} +(-5.98950 - 8.15909i) q^{90} +(10.2868 - 7.47380i) q^{91} +(-3.68661 - 23.2764i) q^{92} +(-0.986720 - 0.502759i) q^{93} +(7.30837 + 22.4928i) q^{94} +(0.737610 - 1.46543i) q^{95} +(3.00127 + 4.13089i) q^{96} +(-3.97547 + 2.02560i) q^{97} +(3.62710 + 3.62710i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{3} + 4 q^{5}+O(q^{10}) $ 160 * q - 8 * q^3 + 4 * q^5	$ 160 q - 8 q^{3} + 4 q^{5} - 128 q^{12} - 32 q^{15} + 24 q^{16} - 32 q^{20} - 96 q^{23} + 52 q^{25} + 8 q^{26} - 32 q^{27} - 16 q^{31} + 40 q^{36} - 36 q^{37} - 32 q^{38} - 32 q^{42} + 256 q^{45} - 32 q^{47} + 16 q^{48} + 68 q^{53} + 320 q^{56} - 132 q^{58} + 64 q^{60} - 352 q^{67} + 8 q^{70} + 16 q^{75} - 992 q^{78} + 164 q^{80} + 40 q^{81} - 100 q^{82} + 80 q^{86} + 96 q^{91} + 56 q^{92} - 24 q^{93} + 68 q^{97}+O(q^{100}) $ 160 * q - 8 * q^3 + 4 * q^5 - 128 * q^12 - 32 * q^15 + 24 * q^16 - 32 * q^20 - 96 * q^23 + 52 * q^25 + 8 * q^26 - 32 * q^27 - 16 * q^31 + 40 * q^36 - 36 * q^37 - 32 * q^38 - 32 * q^42 + 256 * q^45 - 32 * q^47 + 16 * q^48 + 68 * q^53 + 320 * q^56 - 132 * q^58 + 64 * q^60 - 352 * q^67 + 8 * q^70 + 16 * q^75 - 992 * q^78 + 164 * q^80 + 40 * q^81 - 100 * q^82 + 80 * q^86 + 96 * q^91 + 56 * q^92 - 24 * q^93 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	1.05076	+	2.06223i	0.742999	+	1.45822i	0.883645	+	0.468158i	$0.155082\pi$
$2$	1.05076	+	2.06223i	0.742999	+	1.45822i	−0.140645	+	0.990060i	$0.544918\pi$
$3$	0.159862	−	1.00933i	0.0922961	−	0.582735i	−0.897586	−	0.440840i	$-0.854681\pi$
$3$	0.159862	−	1.00933i	0.0922961	−	0.582735i	0.989882	−	0.141895i	$-0.0453194\pi$
$4$	−1.97313	+	2.71579i	−0.986567	+	1.35789i
$5$	−1.98733	+	1.02495i	−0.888761	+	0.458371i
$5$	−1.98733	+	1.02495i	−0.888761	+	0.458371i
$6$	2.24944	−	0.730888i	0.918331	−	0.298384i
$7$	−2.99845	+	0.474908i	−1.13331	+	0.179498i	−0.694782	−	0.719220i	$-0.744499\pi$
$7$	−2.99845	+	0.474908i	−1.13331	+	0.179498i	−0.438526	+	0.898719i	$0.644499\pi$
$8$	−3.10187	−	0.491288i	−1.09668	−	0.173697i
$9$	1.85999	+	0.604346i	0.619995	+	0.201449i
$10$	−4.20189	−	3.02136i	−1.32875	−	0.955439i
$11$		0			0
$11$		0			0
$12$	2.42569	+	2.42569i	0.700235	+	0.700235i
$13$	−3.73187	+	1.90148i	−1.03503	+	0.527377i	−0.887079	−	0.461617i	$-0.847269\pi$
$13$	−3.73187	+	1.90148i	−1.03503	+	0.527377i	−0.147956	+	0.988994i	$0.547269\pi$
$14$	−4.13002	−	5.68449i	−1.10379	−	1.51924i
$15$	0.716809	+	2.16971i	0.185079	+	0.560218i
$16$	−0.171494	−	0.527805i	−0.0428736	−	0.131951i
$17$	−5.99159	−	3.05287i	−1.45317	−	0.740429i	−0.463816	−	0.885932i	$-0.653520\pi$
$17$	−5.99159	−	3.05287i	−1.45317	−	0.740429i	−0.989358	+	0.145503i	$0.953520\pi$
$18$	0.708096	+	4.47075i	0.166900	+	1.05376i
$19$	−0.593572	+	0.431256i	−0.136175	+	0.0989368i	−0.653787	−	0.756678i	$-0.726821\pi$
$19$	−0.593572	+	0.431256i	−0.136175	+	0.0989368i	0.517612	+	0.855615i	$0.326821\pi$
$20$	1.13773	−	7.41953i	0.254404	−	1.65906i
$21$			3.10233i			0.676985i
$22$		0			0
$23$	−4.96412	+	4.96412i	−1.03509	+	1.03509i	−0.0357287	+	0.999362i	$0.511375\pi$
$23$	−4.96412	+	4.96412i	−1.03509	+	1.03509i	−0.999362	+	0.0357287i	$0.988625\pi$
$24$	−0.991740	+	3.05226i	−0.202438	+	0.623040i
$25$	2.89896	−	4.07382i	0.579793	−	0.814764i
$26$	−7.84260	−	5.69798i	−1.53806	−	1.11747i
$27$	2.29913	−	4.51230i	0.442468	−	0.868393i
$28$	4.62660	−	9.08021i	0.874345	−	1.71600i
$29$	3.92271	+	2.85001i	0.728428	+	0.529234i	0.889066	−	0.457779i	$-0.151355\pi$
$29$	3.92271	+	2.85001i	0.728428	+	0.529234i	−0.160637	+	0.987013i	$0.551355\pi$
$30$	−3.72126	+	3.75808i	−0.679406	+	0.686128i
$31$	0.334876	−	1.03064i	0.0601455	−	0.185109i	−0.916469	−	0.400105i	$-0.868974\pi$
$31$	0.334876	−	1.03064i	0.0601455	−	0.185109i	0.976615	+	0.214996i	$0.0689738\pi$
$32$	−3.53313	+	3.53313i	−0.624575	+	0.624575i
$33$		0			0
$34$		−	15.5639i		−	2.66918i
$35$	5.47216	−	4.01705i	0.924963	−	0.679006i
$36$	−5.31128	+	3.85887i	−0.885213	+	0.643145i
$37$	−0.0132489	−	0.0836500i	−0.00217810	−	0.0137520i	0.986575	−	0.163307i	$-0.0522160\pi$
$37$	−0.0132489	−	0.0836500i	−0.00217810	−	0.0137520i	−0.988753	+	0.149555i	$0.952216\pi$
$38$	−1.51305	−	0.770938i	−0.245449	−	0.125063i
$39$	1.32263	+	4.07065i	0.211791	+	0.651826i
$40$	6.66799	−	2.20290i	1.05430	−	0.348310i
$41$	3.15212	+	4.33853i	0.492279	+	0.677564i	0.980806	−	0.194985i	$-0.0624657\pi$
$41$	3.15212	+	4.33853i	0.492279	+	0.677564i	−0.488527	+	0.872549i	$0.662466\pi$
$42$	−6.39773	+	3.25981i	−0.987192	+	0.502999i
$43$	1.92858	+	1.92858i	0.294106	+	0.294106i	0.838700	−	0.544594i	$-0.183316\pi$
$43$	1.92858	+	1.92858i	0.294106	+	0.294106i	−0.544594	+	0.838700i	$0.683316\pi$
$44$		0			0
$45$	−4.31583	+	0.705353i	−0.643366	+	0.105148i
$46$	−15.4533	−	5.02107i	−2.27846	−	0.740316i
$47$	10.0926	+	1.59850i	1.47215	+	0.233166i	0.840383	−	0.541992i	$-0.182330\pi$
$47$	10.0926	+	1.59850i	1.47215	+	0.233166i	0.631767	+	0.775158i	$0.282330\pi$
$48$	−0.560143	+	0.0887179i	−0.0808496	+	0.0128053i
$49$	2.10777	−	0.684857i	0.301110	−	0.0978367i
$50$	11.4473	+	1.69773i	1.61889	+	0.240095i
$51$	−4.03916	+	5.55943i	−0.565596	+	0.778476i
$52$	2.19946	−	13.8869i	0.305010	−	1.92576i
$53$	−1.03078	−	2.02302i	−0.141589	−	0.277884i	0.809312	−	0.587379i	$-0.199840\pi$
$53$	−1.03078	−	2.02302i	−0.141589	−	0.277884i	−0.950901	+	0.309495i	$0.899840\pi$
$54$	11.7212			1.59506
$55$		0			0
$56$	9.53412			1.27405
$57$	0.340388	+	0.668049i	0.0450855	+	0.0884853i
$58$	−1.75557	+	11.0842i	−0.230517	+	1.45543i
$59$	−0.703280	+	0.967982i	−0.0915593	+	0.126021i	−0.852339	−	0.522989i	$-0.824817\pi$
$59$	−0.703280	+	0.967982i	−0.0915593	+	0.126021i	0.760780	+	0.649010i	$0.224817\pi$
$60$	−7.30684	−	2.33444i	−0.943309	−	0.301375i
$61$	−7.01046	+	2.27784i	−0.897597	+	0.291647i	−0.721245	−	0.692680i	$-0.756430\pi$
$61$	−7.01046	+	2.27784i	−0.897597	+	0.291647i	−0.176352	+	0.984327i	$0.556430\pi$
$62$	2.47730	−	0.392365i	0.314617	−	0.0498305i
$63$	−5.86408	−	0.928780i	−0.738805	−	0.117015i
$64$	−12.0542	−	3.91665i	−1.50678	−	0.489582i
$65$	5.46754	−	7.60385i	0.678165	−	0.943141i
$66$		0			0
$67$	3.89698	+	3.89698i	0.476092	+	0.476092i	0.903879	−	0.427787i	$-0.140707\pi$
$67$	3.89698	+	3.89698i	0.476092	+	0.476092i	−0.427787	+	0.903879i	$0.640707\pi$
$68$	20.1132	−	10.2482i	2.43908	−	1.24277i
$69$	4.21684	+	5.80399i	0.507648	+	0.698718i
$70$	14.0340	+	7.06390i	1.67739	+	0.844297i
$71$	4.29785	+	13.2274i	0.510061	+	1.56981i	0.792092	+	0.610402i	$0.208992\pi$
$71$	4.29785	+	13.2274i	0.510061	+	1.56981i	−0.282030	+	0.959406i	$0.591008\pi$
$72$	−5.47253	−	2.78839i	−0.644944	−	0.328615i
$73$	0.426034	+	2.68987i	0.0498635	+	0.314826i	0.999996	+	0.00297784i	$0.000947879\pi$
$73$	0.426034	+	2.68987i	0.0498635	+	0.314826i	−0.950132	+	0.311848i	$0.899052\pi$
$74$	0.158584	−	0.115218i	0.0184351	−	0.0133939i
$75$	−3.64838	−	3.57725i	−0.421279	−	0.413065i
$76$		−	2.46294i		−	0.282519i
$77$		0			0
$78$	−7.00485	+	7.00485i	−0.793143	+	0.793143i
$79$	−3.20120	+	9.85229i	−0.360164	+	1.10847i	0.592791	+	0.805356i	$0.298026\pi$
$79$	−3.20120	+	9.85229i	−0.360164	+	1.10847i	−0.952955	+	0.303113i	$0.901974\pi$
$80$	0.881788	+	0.873150i	0.0985869	+	0.0976211i
$81$	0.559756	+	0.406686i	0.0621951	+	0.0451874i
$82$	−5.63493	+	11.0592i	−0.622273	+	1.22128i
$83$	0.779264	−	1.52939i	0.0855353	−	0.167873i	−0.844276	−	0.535908i	$-0.819969\pi$
$83$	0.779264	−	1.52939i	0.0855353	−	0.167873i	0.929812	+	0.368035i	$0.119969\pi$
$84$	−8.42528	−	6.12132i	−0.919273	−	0.667891i
$85$	15.0363	−	0.0740116i	1.63092	−	0.00802769i
$86$	−1.95071	+	6.00366i	−0.210350	+	0.647391i
$87$	3.50368	−	3.50368i	0.375634	−	0.375634i
$88$		0			0
$89$		−	10.9954i		−	1.16551i	−0.812647	−	0.582756i	$-0.801974\pi$
$89$		−	10.9954i		−	1.16551i	0.812647	−	0.582756i	$-0.198026\pi$
$90$	−5.98950	−	8.15909i	−0.631349	−	0.860043i
$91$	10.2868	−	7.47380i	1.07835	−	0.783467i
$92$	−3.68661	−	23.2764i	−0.384356	−	2.42673i
$93$	−0.986720	−	0.502759i	−0.102318	−	0.0521337i
$94$	7.30837	+	22.4928i	0.753800	+	2.31996i
$95$	0.737610	−	1.46543i	0.0756772	−	0.150350i
$96$	3.00127	+	4.13089i	0.306316	+	0.421608i
$97$	−3.97547	+	2.02560i	−0.403648	+	0.205669i	−0.644015	−	0.765013i	$-0.722732\pi$
$97$	−3.97547	+	2.02560i	−0.403648	+	0.205669i	0.240366	+	0.970682i	$0.422732\pi$
$98$	3.62710	+	3.62710i	0.366392	+	0.366392i
$99$		0			0
$100$	5.34358	+	15.9112i	0.534358	+	1.59112i
$101$	13.1641	+	4.27727i	1.30987	+	0.425604i	0.879006	−	0.476811i	$-0.158207\pi$
$101$	13.1641	+	4.27727i	1.30987	+	0.425604i	0.430868	+	0.902415i	$0.358207\pi$
$102$	−15.7090	−	2.48807i	−1.55543	−	0.246355i
$103$	8.30625	−	1.31558i	0.818439	−	0.129628i	0.266844	−	0.963740i	$-0.414019\pi$
$103$	8.30625	−	1.31558i	0.818439	−	0.129628i	0.551596	+	0.834112i	$0.314019\pi$
$104$	12.5100	−	4.06473i	1.22670	−	0.398580i
$105$	−3.17973	−	6.16536i	−0.310310	−	0.601678i
$106$	3.08884	−	4.25143i	0.300015	−	0.412935i
$107$	−0.442911	+	2.79643i	−0.0428178	+	0.270341i	−0.999804	−	0.0197920i	$-0.993700\pi$
$107$	−0.442911	+	2.79643i	−0.0428178	+	0.270341i	0.956986	+	0.290133i	$0.0936996\pi$
$108$	7.71795	+	15.1473i	0.742660	+	1.45755i
$109$	−3.06400			−0.293478			−0.146739	−	0.989175i	$-0.546878\pi$
$109$	−3.06400			−0.293478			−0.146739	+	0.989175i	$0.546878\pi$
$110$		0			0
$111$	−0.0865481			−0.00821478
$112$	0.764876	+	1.50115i	0.0722740	+	0.141846i
$113$	1.17845	−	7.44046i	0.110860	−	0.699939i	−0.868177	−	0.496255i	$-0.834708\pi$
$113$	1.17845	−	7.44046i	0.110860	−	0.699939i	0.979037	−	0.203685i	$-0.0652918\pi$
$114$	−1.02001	+	1.40392i	−0.0955324	+	0.131489i
$115$	4.77738	−	14.9533i	0.445493	−	1.39440i
$116$	−15.4801	+	5.02978i	−1.43729	+	0.467003i
$117$	−8.09038	+	1.28139i	−0.747956	+	0.118465i
$118$	−2.73518	−	0.433210i	−0.251794	−	0.0398803i
$119$	19.4153	+	6.30842i	1.77980	+	0.578292i
$120$	−1.15749	−	7.08233i	−0.105664	−	0.646526i
$121$		0			0
$122$	−12.0637	−	12.0637i	−1.09220	−	1.09220i
$123$	4.88289	−	2.48796i	0.440276	−	0.224332i
$124$	2.13825	+	2.94305i	0.192020	+	0.264294i
$125$	−1.58574	+	11.0673i	−0.141833	+	0.989891i
$126$	−4.24638	−	13.0690i	−0.378298	−	1.16428i
$127$	−2.04684	−	1.04292i	−0.181627	−	0.0925438i	0.360813	−	0.932638i	$-0.382499\pi$
$127$	−2.04684	−	1.04292i	−0.181627	−	0.0925438i	−0.542440	+	0.840095i	$0.682499\pi$
$128$	−3.02576	−	19.1039i	−0.267442	−	1.68856i
$129$	2.25487	−	1.63826i	0.198531	−	0.144241i
$130$	21.4260	+	3.28552i	1.87918	+	0.288159i
$131$			2.05576i			0.179613i	0.995959	+	0.0898063i	$0.0286248\pi$
$131$			2.05576i			0.179613i	−0.995959	+	0.0898063i	$0.971375\pi$
$132$		0			0
$133$	1.57499	−	1.57499i	0.136569	−	0.136569i
$134$	−3.94169	+	12.1313i	−0.340510	+	1.04798i
$135$	0.0557386	+	11.3239i	0.00479721	+	0.974608i
$136$	17.0853	+	12.4132i	1.46505	+	1.06442i
$137$	2.28123	−	4.47717i	0.194899	−	0.382511i	−0.772788	−	0.634664i	$-0.781139\pi$
$137$	2.28123	−	4.47717i	0.194899	−	0.382511i	0.967687	+	0.252153i	$0.0811386\pi$
$138$	−7.53828	+	14.7947i	−0.641701	+	1.25941i
$139$	1.58424	+	1.15102i	0.134373	+	0.0976279i	0.652941	−	0.757408i	$-0.273535\pi$
$139$	1.58424	+	1.15102i	0.134373	+	0.0976279i	−0.518568	+	0.855036i	$0.673535\pi$
$140$	0.112164	+	22.7874i	0.00947960	+	1.92589i
$141$	3.22682	−	9.93114i	0.271748	−	0.836353i
$142$	−22.7620	+	22.7620i	−1.91015	+	1.91015i
$143$		0			0
$144$		−	1.08535i		−	0.0904460i
$145$	−10.7168	−	1.64335i	−0.889984	−	0.136473i
$146$	−5.09948	+	3.70499i	−0.422036	+	0.306627i
$147$	−0.354292	−	2.23691i	−0.0292215	−	0.184497i
$148$	0.253317	+	0.129072i	0.0208226	+	0.0106096i
$149$	−3.31203	−	10.1934i	−0.271332	−	0.835075i	−0.990167	−	0.139893i	$-0.955324\pi$
$149$	−3.31203	−	10.1934i	−0.271332	−	0.835075i	0.718834	−	0.695181i	$-0.244676\pi$
$150$	3.54354	−	11.2826i	0.289329	−	0.921223i
$151$	−10.8233	−	14.8970i	−0.880786	−	1.21230i	−0.976203	−	0.216860i	$-0.930418\pi$
$151$	−10.8233	−	14.8970i	−0.880786	−	1.21230i	0.0954168	−	0.995437i	$-0.469582\pi$
$152$	2.05306	−	1.04608i	0.166525	−	0.0848486i
$153$	−9.29928	−	9.29928i	−0.751802	−	0.751802i
$154$		0			0
$155$	0.390845	+	2.39146i	0.0313935	+	0.192086i
$156$	−13.6648	−	4.43995i	−1.09406	−	0.355480i
$157$	−17.4002	−	2.75591i	−1.38868	−	0.219946i	−0.583087	−	0.812410i	$-0.698155\pi$
$157$	−17.4002	−	2.75591i	−1.38868	−	0.219946i	−0.805597	+	0.592464i	$0.798155\pi$
$158$	−23.6814	+	3.75077i	−1.88399	+	0.298395i
$159$	−2.20667	+	0.716992i	−0.175001	+	0.0568611i
$160$	3.40022	−	10.6428i	0.268811	−	0.841385i
$161$	12.5272	−	17.2422i	0.987279	−	1.35887i
$162$	−0.250513	+	1.58168i	−0.0196821	+	0.124268i
$163$	6.34464	+	12.4521i	0.496950	+	0.975320i	0.994183	+	0.107703i	$0.0343495\pi$
$163$	6.34464	+	12.4521i	0.496950	+	0.975320i	−0.497233	+	0.867617i	$0.665650\pi$
$164$	−18.0021			−1.40573
$165$		0			0
$166$	3.97278			0.308348
$167$	0.682572	+	1.33962i	0.0528190	+	0.103663i	0.915907	−	0.401390i	$-0.131473\pi$
$167$	0.682572	+	1.33962i	0.0528190	+	0.103663i	−0.863088	+	0.505053i	$0.831473\pi$
$168$	1.52414	−	9.62304i	0.117590	−	0.742434i
$169$	2.67002	−	3.67496i	0.205386	−	0.282689i
$170$	15.9522	+	30.9306i	1.22348	+	2.37227i
$171$	−1.36466	+	0.443406i	−0.104358	+	0.0339081i
$172$	−9.04297	+	1.43227i	−0.689520	+	0.109209i
$173$	−2.59032	−	0.410267i	−0.196939	−	0.0311920i	0.0571858	−	0.998364i	$-0.481787\pi$
$173$	−2.59032	−	0.410267i	−0.196939	−	0.0311920i	−0.254124	+	0.967172i	$0.581787\pi$
$174$	10.9069	+	3.54388i	0.826853	+	0.268661i
$175$	−6.75771	+	13.5919i	−0.510835	+	1.02745i
$176$		0			0
$177$	0.864582	+	0.864582i	0.0649860	+	0.0649860i
$178$	22.6751	−	11.5535i	1.69957	−	0.865974i
$179$	−2.82001	−	3.88141i	−0.210777	−	0.290110i	0.690518	−	0.723315i	$-0.257383\pi$
$179$	−2.82001	−	3.88141i	−0.210777	−	0.290110i	−0.901295	+	0.433205i	$0.857383\pi$
$180$	6.60012	−	13.1126i	0.491944	−	0.977358i
$181$	−0.294046	−	0.904981i	−0.0218563	−	0.0672667i	0.939533	−	0.342457i	$-0.111259\pi$
$181$	−0.294046	−	0.904981i	−0.0218563	−	0.0672667i	−0.961390	+	0.275190i	$0.911259\pi$
$182$	26.2217	+	13.3606i	1.94368	+	0.990354i
$183$	1.17838	+	7.43998i	0.0871081	+	0.549979i
$184$	17.8369	−	12.9592i	1.31495	−	0.955368i
$185$	0.112067	+	0.152661i	0.00823931	+	0.0112238i
$186$		−	2.56313i		−	0.187937i
$187$		0			0
$188$	−24.2552	+	24.2552i	−1.76899	+	1.76899i
$189$	−4.75091	+	14.6218i	−0.345578	+	1.06358i
$190$	3.79710	−	0.0186901i	0.275471	−	0.00135592i
$191$	−8.50884	−	6.18204i	−0.615678	−	0.447316i	0.235731	−	0.971818i	$-0.424252\pi$
$191$	−8.50884	−	6.18204i	−0.615678	−	0.447316i	−0.851409	+	0.524502i	$0.824252\pi$
$192$	−5.88019	+	11.5405i	−0.424366	+	0.832865i
$193$	−5.79383	+	11.3710i	−0.417049	+	0.818504i	0.582933	+	0.812520i	$0.301905\pi$
$193$	−5.79383	+	11.3710i	−0.417049	+	0.818504i	−0.999982	+	0.00598418i	$0.998095\pi$
$194$	−8.35453	−	6.06992i	−0.599821	−	0.435795i
$195$	−6.80071	−	6.73409i	−0.487009	−	0.482238i
$196$	−2.29899	+	7.07557i	−0.164214	+	0.505398i
$197$	7.07191	−	7.07191i	0.503853	−	0.503853i	−0.408780	−	0.912633i	$-0.634046\pi$
$197$	7.07191	−	7.07191i	0.503853	−	0.503853i	0.912633	+	0.408780i	$0.134046\pi$
$198$		0			0
$199$			19.7573i			1.40056i	0.713870	+	0.700278i	$0.246941\pi$
$199$			19.7573i			1.40056i	−0.713870	+	0.700278i	$0.753059\pi$
$200$	−10.9936	+	11.2122i	−0.777367	+	0.792825i
$201$	4.55630	−	3.31035i	0.321377	−	0.233494i
$202$	5.01156	+	31.6418i	0.352612	+	2.22631i
$203$	−13.1155	−	6.68270i	−0.920530	−	0.469034i
$204$	−7.12842	−	21.9390i	−0.499089	−	1.53604i
$205$	−10.7111	−	5.39132i	−0.748094	−	0.376546i
$206$	11.4409	+	15.7471i	0.797126	+	1.09715i
$207$	−12.2332	+	6.23314i	−0.850269	+	0.433233i
$208$	1.64361	+	1.64361i	0.113964	+	0.113964i
$209$		0			0
$210$	9.37328	−	13.0357i	0.646817	−	0.899546i
$211$	14.8192	+	4.81504i	1.02019	+	0.331481i	0.770906	−	0.636949i	$-0.219804\pi$
$211$	14.8192	+	4.81504i	1.02019	+	0.331481i	0.249287	+	0.968430i	$0.419804\pi$
$212$	7.52798	+	1.19231i	0.517024	+	0.0818885i
$213$	14.0379	−	2.22338i	0.961858	−	0.152343i
$214$	−6.23228	+	2.02499i	−0.426030	+	0.138426i
$215$	−5.80942	−	1.85603i	−0.396199	−	0.126580i
$216$	−9.34845	+	12.8670i	−0.636081	+	0.875491i
$217$	−0.514649	+	3.24936i	−0.0349366	+	0.220581i
$218$	−3.21953	−	6.31869i	−0.218054	−	0.427955i
$219$	2.78306			0.188062
$220$		0			0
$221$	28.1648			1.89457
$222$	−0.0909413	−	0.178482i	−0.00610358	−	0.0119790i
$223$	−3.26369	+	20.6061i	−0.218553	+	1.37989i	0.597481	+	0.801883i	$0.296168\pi$
$223$	−3.26369	+	20.6061i	−0.218553	+	1.37989i	−0.816034	+	0.578004i	$0.803832\pi$
$224$	8.91601	−	12.2718i	0.595726	−	0.819946i
$225$	7.85403	−	5.82527i	0.523602	−	0.388351i
$226$	16.5822	−	5.38789i	1.10303	−	0.358397i
$227$	−6.60577	+	1.04625i	−0.438440	+	0.0694421i	−0.371753	−	0.928332i	$-0.621243\pi$
$227$	−6.60577	+	1.04625i	−0.438440	+	0.0694421i	−0.0666876	+	0.997774i	$0.521243\pi$
$228$	−2.48591	−	0.393730i	−0.164634	−	0.0260754i
$229$	−27.0374	−	8.78500i	−1.78668	−	0.580529i	−0.787333	−	0.616528i	$-0.788539\pi$
$229$	−27.0374	−	8.78500i	−1.78668	−	0.580529i	−0.999352	+	0.0359988i	$0.988539\pi$
$230$	35.8571	−	5.86027i	2.36434	−	0.386414i
$231$		0			0
$232$	−10.7676	−	10.7676i	−0.706925	−	0.706925i
$233$	−22.1399	+	11.2808i	−1.45043	+	0.739032i	−0.988968	−	0.148127i	$-0.952676\pi$
$233$	−22.1399	+	11.2808i	−1.45043	+	0.739032i	−0.461464	+	0.887159i	$0.652676\pi$
$234$	−11.1436	−	15.3378i	−0.728478	−	1.00266i
$235$	−21.6956	+	7.16759i	−1.41527	+	0.467562i
$236$	−1.24117	−	3.81992i	−0.0807931	−	0.248656i
$237$	9.43243	+	4.80606i	0.612702	+	0.312187i
$238$	7.39141	+	46.6675i	0.479114	+	3.02501i
$239$	10.8680	−	7.89607i	0.702993	−	0.510754i	−0.177913	−	0.984046i	$-0.556935\pi$
$239$	10.8680	−	7.89607i	0.702993	−	0.510754i	0.880906	+	0.473292i	$0.156935\pi$
$240$	1.02226	−	0.750429i	0.0659864	−	0.0484400i
$241$		−	10.8836i		−	0.701075i	−0.936549	−	0.350537i	$-0.885999\pi$
$241$		−	10.8836i		−	0.701075i	0.936549	−	0.350537i	$-0.114001\pi$
$242$		0			0
$243$	11.2429	−	11.2429i	0.721233	−	0.721233i
$244$	7.64646	−	23.5334i	0.489515	−	1.50657i
$245$	−3.48690	+	3.52139i	−0.222770	+	0.224974i
$246$	10.2615	+	7.45541i	0.654249	+	0.475340i
$247$	1.39511	−	2.73806i	0.0887688	−	0.174218i
$248$	−1.54508	+	3.03240i	−0.0981129	+	0.192558i
$249$	−1.41908	−	1.03102i	−0.0899306	−	0.0653384i
$250$	−24.4896	+	8.35891i	−1.54886	+	0.528664i
$251$	2.14060	−	6.58808i	0.135113	−	0.415836i	−0.860494	−	0.509460i	$-0.829845\pi$
$251$	2.14060	−	6.58808i	0.135113	−	0.415836i	0.995608	+	0.0936240i	$0.0298451\pi$
$252$	14.0930	−	14.0930i	0.887775	−	0.887775i
$253$		0			0
$254$		−	5.31691i		−	0.333612i
$255$	2.32902	−	15.1884i	0.145849	−	0.951132i
$256$	15.7094	−	11.4136i	0.981841	−	0.713349i
$257$	−1.93781	−	12.2349i	−0.120877	−	0.763189i	−0.971435	−	0.237307i	$-0.923735\pi$
$257$	−1.93781	−	12.2349i	−0.120877	−	0.763189i	0.850557	−	0.525882i	$-0.176265\pi$
$258$	5.74781	+	2.92865i	0.357843	+	0.182330i
$259$	0.0794521	+	0.244528i	0.00493691	+	0.0151943i
$260$	9.86224	+	29.8521i	0.611630	+	1.85135i
$261$	5.57379	+	7.67166i	0.345009	+	0.474864i
$262$	−4.23946	+	2.16011i	−0.261914	+	0.133452i
$263$	10.5123	+	10.5123i	0.648216	+	0.648216i	0.952562	−	0.304346i	$-0.0984378\pi$
$263$	10.5123	+	10.5123i	0.648216	+	0.648216i	−0.304346	+	0.952562i	$0.598438\pi$
$264$		0			0
$265$	4.12200	+	2.96392i	0.253212	+	0.182072i
$266$	4.90293	+	1.59306i	0.300618	+	0.0976768i
$267$	−11.0980	−	1.75774i	−0.679184	−	0.107572i
$268$	−18.2726	+	2.89410i	−1.11618	+	0.176785i
$269$	−6.77570	+	2.20156i	−0.413121	+	0.134231i	−0.508201	−	0.861238i	$-0.669689\pi$
$269$	−6.77570	+	2.20156i	−0.413121	+	0.134231i	0.0950798	+	0.995470i	$0.469689\pi$
$270$	−23.2940	+	12.0137i	−1.41763	+	0.731128i
$271$	14.9482	−	20.5745i	0.908040	−	1.24981i	−0.0597909	−	0.998211i	$-0.519043\pi$
$271$	14.9482	−	20.5745i	0.908040	−	1.24981i	0.967831	−	0.251600i	$-0.0809566\pi$
$272$	−0.583795	+	3.68594i	−0.0353978	+	0.223493i
$273$	−5.89904	−	11.5775i	−0.357026	−	0.700703i
$274$	11.6300			0.702594
$275$		0			0
$276$	−24.0828			−1.44961
$277$	1.39998	+	2.74761i	0.0841166	+	0.165088i	0.929233	−	0.369494i	$-0.120469\pi$
$277$	1.39998	+	2.74761i	0.0841166	+	0.165088i	−0.845117	+	0.534582i	$0.820469\pi$
$278$	−0.709009	+	4.47651i	−0.0425235	+	0.268483i
$279$	1.24573	−	1.71460i	0.0745798	−	0.102650i
$280$	−18.9475	+	9.77198i	−1.13233	+	0.583987i
$281$	27.1520	−	8.82221i	1.61975	−	0.526289i	0.647868	−	0.761753i	$-0.275661\pi$
$281$	27.1520	−	8.82221i	1.61975	−	0.526289i	0.971883	+	0.235464i	$0.0756608\pi$
$282$	23.8709	−	3.78078i	1.42149	−	0.225142i
$283$	−26.3050	−	4.16631i	−1.56367	−	0.247661i	−0.686245	−	0.727370i	$-0.740742\pi$
$283$	−26.3050	−	4.16631i	−1.56367	−	0.247661i	−0.877428	+	0.479709i	$0.840742\pi$
$284$	−44.4032	−	14.4275i	−2.63484	−	0.856112i
$285$	−1.36118	−	0.978755i	−0.0806293	−	0.0579764i
$286$		0			0
$287$	−11.5119	−	11.5119i	−0.679525	−	0.679525i
$288$	−8.70681	+	4.43634i	−0.513054	+	0.261414i
$289$	16.5868	+	22.8298i	0.975693	+	1.34293i
$290$	−7.87185	−	23.8274i	−0.462251	−	1.39919i
$291$	1.40897	+	4.33637i	0.0825953	+	0.254202i
$292$	−8.14574	−	4.15046i	−0.476693	−	0.242887i
$293$	−2.38377	−	15.0505i	−0.139261	−	0.879260i	−0.954082	−	0.299547i	$-0.903165\pi$
$293$	−2.38377	−	15.0505i	−0.139261	−	0.879260i	0.814821	−	0.579713i	$-0.196835\pi$
$294$	4.24076	−	3.08109i	0.247326	−	0.179693i
$295$	0.405519	−	2.64453i	0.0236102	−	0.153970i
$296$			0.265981i			0.0154598i
$297$		0			0
$298$	17.5410	−	17.5410i	1.01612	−	1.01612i
$299$	9.08626	−	27.9646i	0.525472	−	1.61724i
$300$	16.9138	−	2.84983i	0.976518	−	0.164535i
$301$	−6.69865	−	4.86686i	−0.386104	−	0.280521i
$302$	19.3483	−	37.9732i	1.11337	−	2.18511i
$303$	6.42159	−	12.6031i	0.368910	−	0.724028i
$304$	0.329413	+	0.239333i	0.0188931	+	0.0137267i
$305$	11.5974	−	11.7122i	0.664067	−	0.670637i
$306$	9.40597	−	28.9486i	0.537703	−	1.65488i
$307$	16.7363	−	16.7363i	0.955194	−	0.955194i	−0.0438445	−	0.999038i	$-0.513961\pi$
$307$	16.7363	−	16.7363i	0.955194	−	0.955194i	0.999038	+	0.0438445i	$0.0139606\pi$
$308$		0			0
$309$		−	8.59403i		−	0.488897i
$310$	−4.52105	+	3.31886i	−0.256779	+	0.188499i
$311$	0.394195	−	0.286400i	0.0223528	−	0.0162402i	−0.576553	−	0.817060i	$-0.695602\pi$
$311$	0.394195	−	0.286400i	0.0223528	−	0.0162402i	0.598906	+	0.800820i	$0.295602\pi$
$312$	−2.10278	−	13.2764i	−0.119046	−	0.751629i
$313$	−4.42373	−	2.25400i	−0.250044	−	0.127404i	0.324477	−	0.945894i	$-0.394812\pi$
$313$	−4.42373	−	2.25400i	−0.250044	−	0.127404i	−0.574521	+	0.818490i	$0.694812\pi$
$314$	−12.6001	−	38.7790i	−0.711062	−	2.18842i
$315$	12.6058	−	4.16459i	0.710258	−	0.234648i
$316$	−20.4403	−	28.1337i	−1.14986	−	1.58264i
$317$	22.9649	−	11.7012i	1.28984	−	0.657206i	0.331666	−	0.943397i	$-0.392389\pi$
$317$	22.9649	−	11.7012i	1.28984	−	0.657206i	0.958173	+	0.286191i	$0.0923892\pi$
$318$	−3.79729	−	3.79729i	−0.212941	−	0.212941i
$319$		0			0
$320$	27.9701	−	4.57126i	1.56358	−	0.255541i
$321$	2.75171	+	0.894084i	0.153585	+	0.0499029i
$322$	48.7204	+	7.71655i	2.71508	+	0.430027i
$323$	4.87301	−	0.771809i	0.271141	−	0.0429446i
$324$	−2.20895	+	0.717730i	−0.122719	+	0.0398739i
$325$	−3.07226	+	20.7153i	−0.170418	+	1.14908i
$326$	−19.0123	+	26.1682i	−1.05300	+	1.44932i
$327$	−0.489816	+	3.09258i	−0.0270869	+	0.171020i
$328$	−7.64602	−	15.0062i	−0.422181	−	0.828576i
$329$	−31.0212			−1.71025
$330$		0			0
$331$	−30.1887			−1.65932			−0.829660	−	0.558270i	$-0.811465\pi$
$331$	−30.1887			−1.65932			−0.829660	+	0.558270i	$0.811465\pi$
$332$	2.61591	+	5.13401i	0.143567	+	0.281766i
$333$	0.0259109	−	0.163595i	0.00141991	−	0.00896494i
$334$	−2.04539	+	2.81524i	−0.111919	+	0.154043i
$335$	−11.7388	−	3.75039i	−0.641359	−	0.204906i
$336$	1.63743	−	0.532032i	0.0893290	−	0.0290247i
$337$	13.4344	−	2.12779i	0.731816	−	0.115908i	0.220605	−	0.975363i	$-0.429197\pi$
$337$	13.4344	−	2.12779i	0.731816	−	0.115908i	0.511211	+	0.859455i	$0.329197\pi$
$338$	10.3842	+	1.64469i	0.564824	+	0.0894594i
$339$	−7.32146	−	2.37889i	−0.397647	−	0.129203i
$340$	−29.4676	+	40.9814i	−1.59811	+	2.22253i
$341$		0			0
$342$	−2.34834	−	2.34834i	−0.126984	−	0.126984i
$343$	12.9398	−	6.59315i	0.698683	−	0.355997i
$344$	−5.03472	−	6.92970i	−0.271454	−	0.373624i
$345$	−14.3290	−	7.21239i	−0.771450	−	0.388302i
$346$	−1.87574	−	5.77294i	−0.100841	−	0.310355i
$347$	−21.6038	−	11.0077i	−1.15975	−	0.590924i	−0.235189	−	0.971950i	$-0.575571\pi$
$347$	−21.6038	−	11.0077i	−1.15975	−	0.590924i	−0.924564	+	0.381026i	$0.875571\pi$
$348$	2.60202	+	16.4285i	0.139483	+	0.880660i
$349$	−8.50807	+	6.18147i	−0.455427	+	0.330887i	−0.791735	−	0.610865i	$-0.790822\pi$
$349$	−8.50807	+	6.18147i	−0.455427	+	0.330887i	0.336308	+	0.941752i	$0.390822\pi$
$350$	−35.1304	+	0.345846i	−1.87780	+	0.0184862i
$351$			21.2111i			1.13216i
$352$		0			0
$353$	7.93178	−	7.93178i	0.422166	−	0.422166i	−0.463783	−	0.885949i	$-0.653508\pi$
$353$	7.93178	−	7.93178i	0.422166	−	0.422166i	0.885949	+	0.463783i	$0.153508\pi$
$354$	−0.874501	+	2.69144i	−0.0464792	+	0.143048i
$355$	−22.0987	−	21.8822i	−1.17288	−	1.16139i
$356$	29.8612	+	21.6954i	1.58264	+	1.14986i
$357$	9.47101	−	18.5879i	0.501259	−	0.983777i
$358$	5.04121	−	9.89393i	0.266436	−	0.522911i
$359$	26.4641	+	19.2273i	1.39672	+	1.01478i	0.995090	+	0.0989776i	$0.0315572\pi$
$359$	26.4641	+	19.2273i	1.39672	+	1.01478i	0.401633	+	0.915801i	$0.368443\pi$
$360$	13.7337	−	0.0675999i	0.723828	−	0.00356283i
$361$	−5.70498	+	17.5581i	−0.300262	+	0.924111i
$362$	1.55731	−	1.55731i	0.0818504	−	0.0818504i
$363$		0			0
$364$			42.6836i			2.23723i
$365$	−3.60365	−	4.90900i	−0.188624	−	0.256949i
$366$	−14.1048	+	10.2477i	−0.737268	+	0.535657i
$367$	4.59482	+	29.0105i	0.239848	+	1.51434i	0.754135	+	0.656720i	$0.228057\pi$
$367$	4.59482	+	29.0105i	0.239848	+	1.51434i	−0.514287	+	0.857618i	$0.671943\pi$
$368$	3.47140	+	1.76877i	0.180959	+	0.0922034i
$369$	3.24094	+	9.97457i	0.168716	+	0.519256i
$370$	−0.197067	+	0.391518i	−0.0102450	+	0.0203540i
$371$	4.05150	+	5.57641i	0.210343	+	0.289513i
$372$	3.31232	−	1.68771i	0.171736	−	0.0875037i
$373$	22.9546	+	22.9546i	1.18854	+	1.18854i	0.977470	+	0.211074i	$0.0676963\pi$
$373$	22.9546	+	22.9546i	1.18854	+	1.18854i	0.211074	+	0.977470i	$0.432304\pi$
$374$		0			0
$375$	10.9170	+	3.36977i	0.563753	+	0.174014i
$376$	−30.5205	−	9.91670i	−1.57397	−	0.511415i
$377$	−20.0583	−	3.17692i	−1.03305	−	0.163620i
$378$	−35.1456	+	5.56651i	−1.80769	+	0.286310i
$379$	−24.9062	+	8.09250i	−1.27934	+	0.415684i	−0.868349	−	0.495954i	$-0.834818\pi$
$379$	−24.9062	+	8.09250i	−1.27934	+	0.415684i	−0.410994	+	0.911638i	$0.634818\pi$
$380$	2.52439	+	4.89468i	0.129498	+	0.251092i
$381$	−1.37985	+	1.89920i	−0.0706920	+	0.0972992i
$382$	3.80804	−	24.0430i	0.194836	−	1.23015i
$383$	15.7736	+	30.9574i	0.805993	+	1.58185i	0.813277	+	0.581877i	$0.197681\pi$
$383$	15.7736	+	30.9574i	0.805993	+	1.58185i	−0.00728423	+	0.999973i	$0.502319\pi$
$384$	−19.7658			−1.00867
$385$		0			0
$386$	−29.5376			−1.50342
$387$	2.42160	+	4.75266i	0.123097	+	0.241592i
$388$	2.34303	−	14.7933i	0.118949	−	0.751018i
$389$	10.0316	−	13.8073i	0.508621	−	0.700056i	−0.475065	−	0.879951i	$-0.657576\pi$
$389$	10.0316	−	13.8073i	0.508621	−	0.700056i	0.983686	+	0.179894i	$0.0575756\pi$
$390$	6.74135	−	21.1006i	0.341361	−	1.06847i
$391$	44.8977	−	14.5882i	2.27058	−	0.737755i
$392$	−6.87450	+	1.08881i	−0.347215	+	0.0549934i
$393$	2.07493	+	0.328637i	0.104667	+	0.0165775i
$394$	22.0148	+	7.15304i	1.10909	+	0.360365i
$395$	−3.73624	−	22.8608i	−0.187990	−	1.15025i
$396$		0			0
$397$	3.11088	+	3.11088i	0.156130	+	0.156130i	0.780850	−	0.624719i	$-0.214787\pi$
$397$	3.11088	+	3.11088i	0.156130	+	0.156130i	−0.624719	+	0.780850i	$0.714787\pi$
$398$	−40.7441	+	20.7601i	−2.04232	+	1.04061i
$399$	−1.33790	−	1.84146i	−0.0669787	−	0.0921883i
$400$	−2.64734	−	0.831451i	−0.132367	−	0.0415725i
$401$	8.02685	+	24.7041i	0.400842	+	1.23366i	0.924318	+	0.381624i	$0.124635\pi$
$401$	8.02685	+	24.7041i	0.400842	+	1.23366i	−0.523476	+	0.852041i	$0.675365\pi$
$402$	11.6143	+	5.91778i	0.579268	+	0.295152i
$403$	0.710035	+	4.48298i	0.0353694	+	0.223313i
$404$	−37.5906	+	27.3112i	−1.87020	+	1.35878i
$405$	−1.52925	−	0.234500i	−0.0759891	−	0.0116524i
$406$		−	34.0692i		−	1.69083i
$407$		0			0
$408$	15.2602	−	15.2602i	0.755495	−	0.755495i
$409$	−1.78160	+	5.48319i	−0.0880943	+	0.271126i	−0.985393	−	0.170298i	$-0.945527\pi$
$409$	−1.78160	+	5.48319i	−0.0880943	+	0.271126i	0.897298	+	0.441425i	$0.145527\pi$
$410$	−0.136609	−	27.7537i	−0.00674665	−	1.37066i
$411$	−4.15425	−	3.01824i	−0.204914	−	0.148879i
$412$	−12.8165	+	25.1538i	−0.631425	+	1.23924i
$413$	1.64905	−	3.23644i	0.0811444	−	0.159255i
$414$	−25.7084	−	18.6782i	−1.26350	−	0.917985i
$415$	0.0188919	+	3.83811i	0.000927369	+	0.188406i
$416$	6.46700	−	19.9034i	0.317071	−	0.975844i
$417$	1.41501	−	1.41501i	0.0692933	−	0.0692933i
$418$		0			0
$419$			15.1605i			0.740637i	0.928905	+	0.370318i	$0.120751\pi$
$419$			15.1605i			0.740637i	−0.928905	+	0.370318i	$0.879249\pi$
$420$	23.0179	+	3.52962i	1.12316	+	0.172228i
$421$	6.06758	−	4.40836i	0.295716	−	0.214850i	−0.430027	−	0.902816i	$-0.641496\pi$
$421$	6.06758	−	4.40836i	0.295716	−	0.214850i	0.725743	+	0.687966i	$0.241496\pi$
$422$	5.64165	+	35.6200i	0.274631	+	1.73395i
$423$	17.8060	+	9.07259i	0.865755	+	0.441124i
$424$	2.20347	+	6.78157i	0.107010	+	0.329342i
$425$	−29.8062	+	15.5585i	−1.44581	+	0.754698i
$426$	19.3355	+	26.6131i	0.936810	+	1.28941i
$427$	19.9388	−	10.1593i	0.964904	−	0.491643i
$428$	−6.72059	−	6.72059i	−0.324852	−	0.324852i
$429$		0			0
$430$	−2.27674	−	13.9306i	−0.109794	−	0.671794i
$431$	1.83055	+	0.594783i	0.0881747	+	0.0286497i	0.352772	−	0.935709i	$-0.385239\pi$
$431$	1.83055	+	0.594783i	0.0881747	+	0.0286497i	−0.264597	+	0.964359i	$0.585239\pi$
$432$	−2.77590	−	0.439660i	−0.133556	−	0.0211531i
$433$	2.36499	−	0.374577i	0.113654	−	0.0180010i	−0.0993484	−	0.995053i	$-0.531676\pi$
$433$	2.36499	−	0.374577i	0.113654	−	0.0180010i	0.213002	+	0.977052i	$0.431676\pi$
$434$	−7.24172	+	2.35298i	−0.347614	+	0.112946i
$435$	−3.37188	+	10.5541i	−0.161669	+	0.506029i
$436$	6.04569	−	8.32118i	0.289536	−	0.398512i
$437$	0.805760	−	5.08737i	0.0385447	−	0.243362i
$438$	2.92433	+	5.73932i	0.139730	+	0.274235i
$439$	−4.93496			−0.235533			−0.117767	−	0.993041i	$-0.537573\pi$
$439$	−4.93496			−0.235533			−0.117767	+	0.993041i	$0.537573\pi$
$440$		0			0
$441$	4.33432			0.206396
$442$	29.5945	+	58.0824i	1.40766	+	2.76270i
$443$	−1.96876	+	12.4303i	−0.0935386	+	0.590580i	0.895744	+	0.444569i	$0.146643\pi$
$443$	−1.96876	+	12.4303i	−0.0935386	+	0.590580i	−0.989283	+	0.146010i	$0.953357\pi$
$444$	0.170771	−	0.235046i	0.00810444	−	0.0111548i
$445$	11.2697	+	21.8515i	0.534236	+	1.03586i
$446$	−45.9239	+	14.9216i	−2.17456	+	0.706558i
$447$	−10.8179	+	1.71339i	−0.511670	+	0.0810406i
$448$	38.0040	+	6.01925i	1.79552	+	0.284383i
$449$	14.2710	+	4.63693i	0.673490	+	0.218830i	0.625743	−	0.780029i	$-0.284796\pi$
$449$	14.2710	+	4.63693i	0.673490	+	0.218830i	0.0477472	+	0.998859i	$0.484796\pi$
$450$	20.2658	+	10.0759i	0.955337	+	0.474981i
$451$		0			0
$452$	17.8815	+	17.8815i	0.841073	+	0.841073i
$453$	−16.7661	+	8.54277i	−0.787741	+	0.401374i
$454$	−9.09869	−	12.5233i	−0.427023	−	0.587746i
$455$	−12.7830	+	25.3963i	−0.599277	+	1.19060i
$456$	−0.727635	−	2.23943i	−0.0340747	−	0.104871i
$457$	0.798807	+	0.407012i	0.0373666	+	0.0190392i	0.472574	−	0.881291i	$-0.343325\pi$
$457$	0.798807	+	0.407012i	0.0373666	+	0.0190392i	−0.435207	+	0.900330i	$0.643325\pi$
$458$	−10.2932	−	64.9884i	−0.480968	−	3.03671i
$459$	−27.5509	+	20.0169i	−1.28597	+	0.934309i
$460$	31.1836	+	42.4792i	1.45394	+	1.98060i
$461$		−	4.51026i		−	0.210064i	−0.994469	−	0.105032i	$-0.966506\pi$
$461$		−	4.51026i		−	0.210064i	0.994469	−	0.105032i	$-0.0334945\pi$
$462$		0			0
$463$	−16.0636	+	16.0636i	−0.746539	+	0.746539i	−0.973827	−	0.227289i	$-0.927014\pi$
$463$	−16.0636	+	16.0636i	−0.746539	+	0.746539i	0.227289	+	0.973827i	$0.427014\pi$
$464$	0.831530	−	2.55918i	0.0386028	−	0.118807i
$465$	2.47624	−	0.0121885i	0.114833	−	0.000565230i
$466$	−46.5274	−	33.8041i	−2.15534	−	1.56595i
$467$	−8.55843	+	16.7969i	−0.396037	+	0.777266i	−0.999802	−	0.0198961i	$-0.993666\pi$
$467$	−8.55843	+	16.7969i	−0.396037	+	0.777266i	0.603765	+	0.797162i	$0.293666\pi$
$468$	12.4834	−	24.5001i	0.577047	−	1.13252i
$469$	−13.5356	−	9.83420i	−0.625017	−	0.454101i
$470$	−37.5781	−	37.2100i	−1.73335	−	1.71637i
$471$	−5.56323	+	17.1219i	−0.256340	+	0.788934i
$472$	2.65704	−	2.65704i	0.122300	−	0.122300i
$473$		0			0
$474$			24.5019i			1.12541i
$475$	0.0361131	+	3.66830i	0.00165698	+	0.168313i
$476$	−55.4414	+	40.2805i	−2.54115	+	1.84625i
$477$	−0.694634	−	4.38575i	−0.0318051	−	0.200809i
$478$	27.7032	+	14.1155i	1.26711	+	0.645627i
$479$	5.22360	+	16.0766i	0.238672	+	0.734558i	0.996613	+	0.0822345i	$0.0262056\pi$
$479$	5.22360	+	16.0766i	0.238672	+	0.734558i	−0.757941	+	0.652324i	$0.773794\pi$
$480$	−10.1985	−	5.13331i	−0.465494	−	0.234302i
$481$	0.208502	+	0.286979i	0.00950688	+	0.0130851i
$482$	22.4445	−	11.4361i	1.02232	−	0.520898i
$483$	−15.4004	−	15.4004i	−0.700740	−	0.700740i
$484$		0			0
$485$	5.82444	−	8.10020i	0.264474	−	0.367811i
$486$	34.9991	+	11.3719i	1.58759	+	0.515839i
$487$	−10.6463	−	1.68621i	−0.482429	−	0.0764093i	−0.0895172	−	0.995985i	$-0.528532\pi$
$487$	−10.6463	−	1.68621i	−0.482429	−	0.0764093i	−0.392912	+	0.919576i	$0.628532\pi$
$488$	22.8646	−	3.62140i	1.03503	−	0.163933i
$489$	13.5824	−	4.41321i	0.614220	−	0.199572i
$490$	−10.9258	−	3.49065i	−0.493578	−	0.157692i
$491$	−15.9405	+	21.9402i	−0.719384	+	0.990147i	0.280160	+	0.959953i	$0.409612\pi$
$491$	−15.9405	+	21.9402i	−0.719384	+	0.990147i	−0.999544	+	0.0301935i	$0.990388\pi$
$492$	−2.87784	+	18.1700i	−0.129743	+	0.819166i
$493$	−14.8025	−	29.0516i	−0.666673	−	1.30842i
$494$	7.11244			0.320004
$495$		0			0
$496$	−0.601407			−0.0270040
$497$	−19.1687	−	37.6207i	−0.859834	−	1.68752i
$498$	0.635095	−	4.00983i	0.0284593	−	0.179685i
$499$	13.3659	−	18.3965i	0.598338	−	0.823542i	−0.397217	−	0.917725i	$-0.630024\pi$
$499$	13.3659	−	18.3965i	0.598338	−	0.823542i	0.995555	+	0.0941829i	$0.0300239\pi$
$500$	−26.9276	−	26.1438i	−1.20424	−	1.16919i
$501$	1.46123	−	0.474784i	0.0652831	−	0.0212118i
$502$	15.8354	−	2.50808i	0.706769	−	0.111941i
$503$	5.94278	+	0.941243i	0.264975	+	0.0419680i	0.287508	−	0.957778i	$-0.407173\pi$
$503$	5.94278	+	0.941243i	0.264975	+	0.0419680i	−0.0225330	+	0.999746i	$0.507173\pi$
$504$	17.7333	+	5.76191i	0.789905	+	0.256656i
$505$	−30.5453	+	4.99215i	−1.35925	+	0.222148i
$506$		0			0
$507$	−3.28240	−	3.28240i	−0.145777	−	0.145777i
$508$	6.87102	−	3.50096i	0.304852	−	0.155330i
$509$	−17.7848	−	24.4787i	−0.788300	−	1.08500i	−0.994318	−	0.106453i	$-0.966051\pi$
$509$	−17.7848	−	24.4787i	−0.788300	−	1.08500i	0.206018	−	0.978548i	$-0.433949\pi$
$510$	33.7692	−	11.1563i	1.49532	−	0.494011i
$511$	−2.55488	−	7.86312i	−0.113021	−	0.347844i
$512$	5.57658	+	2.84141i	0.246452	+	0.125574i
$513$	0.581253	+	3.66989i	0.0256630	+	0.162030i
$514$	23.1949	−	16.8521i	1.02309	−	0.743315i
$515$	−15.1589	+	11.1280i	−0.667979	+	0.490357i
$516$			9.35627i			0.411887i
$517$		0			0
$518$	−0.420789	+	0.420789i	−0.0184884	+	0.0184884i
$519$	−0.828186	+	2.54890i	−0.0363533	+	0.111884i
$520$	−20.6953	+	20.9000i	−0.907548	+	0.916527i
$521$	31.0761	+	22.5781i	1.36147	+	0.989164i	0.998350	+	0.0574212i	$0.0182878\pi$
$521$	31.0761	+	22.5781i	1.36147	+	0.989164i	0.363118	+	0.931743i	$0.381712\pi$
$522$	−9.96403	+	19.5555i	−0.436114	+	0.855921i
$523$	−8.47399	+	16.6311i	−0.370542	+	0.727229i	−0.998706	−	0.0508515i	$-0.983806\pi$
$523$	−8.47399	+	16.6311i	−0.370542	+	0.727229i	0.628164	+	0.778081i	$0.283806\pi$
$524$	−5.58301	−	4.05629i	−0.243895	−	0.177200i
$525$	12.6384	+	8.99355i	0.551583	+	0.392511i
$526$	−10.6329	+	32.7247i	−0.463616	+	1.42686i
$527$	−5.15285	+	5.15285i	−0.224462	+	0.224462i
$528$		0			0
$529$		−	26.2849i		−	1.14282i
$530$	−1.78106	+	11.6149i	−0.0773642	+	0.504518i
$531$	−1.89309	+	1.37541i	−0.0821530	+	0.0596877i
$532$	1.16967	+	7.38501i	0.0507117	+	0.320181i
$533$	−20.0130	−	10.1971i	−0.866858	−	0.441686i
$534$	−8.03641	−	24.7335i	−0.347770	−	1.07032i
$535$	−1.98599	−	6.01139i	−0.0858616	−	0.259895i
$536$	−10.1734	−	14.0025i	−0.439424	−	0.604815i
$537$	−4.36841	+	2.22582i	−0.188511	+	0.0960512i
$538$	−11.6597	−	11.6597i	−0.502687	−	0.502687i
$539$		0			0
$540$	−30.8633	−	22.1922i	−1.32815	−	0.955002i
$541$	−28.9135	−	9.39457i	−1.24309	−	0.403904i	−0.387650	−	0.921807i	$-0.626713\pi$
$541$	−28.9135	−	9.39457i	−1.24309	−	0.403904i	−0.855440	+	0.517903i	$0.826713\pi$
$542$	58.1364	+	9.20789i	2.49717	+	0.395513i
$543$	−0.960428	+	0.152117i	−0.0412159	+	0.00652796i
$544$	31.9553	−	10.3829i	1.37007	−	0.445163i
$545$	6.08919	−	3.14044i	0.260832	−	0.134522i
$546$	17.6770	−	24.3304i	0.756508	−	1.04124i
$547$	−6.68388	+	42.2004i	−0.285782	+	1.80436i	0.259106	+	0.965849i	$0.416572\pi$
$547$	−6.68388	+	42.2004i	−0.285782	+	1.80436i	−0.544888	+	0.838509i	$0.683428\pi$
$548$	7.65787	+	15.0294i	0.327128	+	0.642025i
$549$	−14.4160			−0.615258
$550$		0			0
$551$	−3.55750			−0.151554
$552$	−10.2287	−	20.0749i	−0.435361	−	0.854445i
$553$	4.91972	−	31.0619i	0.209208	−	1.32089i
$554$	−4.19517	+	5.77416i	−0.178236	+	0.245321i
$555$	0.172000	−	0.0887073i	0.00730098	−	0.00376542i
$556$	−6.25183	+	2.03134i	−0.265137	+	0.0861481i
$557$	−2.24528	+	0.355617i	−0.0951354	+	0.0150680i	−0.203821	−	0.979008i	$-0.565336\pi$
$557$	−2.24528	+	0.355617i	−0.0951354	+	0.0150680i	0.108685	+	0.994076i	$0.465336\pi$
$558$	4.84486	+	0.767351i	0.205099	+	0.0324846i
$559$	−10.8644	−	3.53005i	−0.459514	−	0.149305i
$560$	−3.05866	−	2.19933i	−0.129252	−	0.0929386i
$561$		0			0
$562$	46.7237	+	46.7237i	1.97092	+	1.97092i
$563$	6.52128	−	3.32276i	0.274839	−	0.140037i	−0.311139	−	0.950364i	$-0.600710\pi$
$563$	6.52128	−	3.32276i	0.274839	−	0.140037i	0.585978	+	0.810327i	$0.300710\pi$
$564$	20.6039	+	28.3588i	0.867581	+	1.19412i
$565$	5.28411	+	15.9945i	0.222304	+	0.672894i
$566$	−19.0484	−	58.6249i	−0.800663	−	2.46419i
$567$	−1.87154	−	0.953596i	−0.0785972	−	0.0400473i
$568$	−6.83291	−	43.1413i	−0.286702	−	1.81017i
$569$	21.7128	−	15.7752i	0.910246	−	0.661333i	−0.0308309	−	0.999525i	$-0.509815\pi$
$569$	21.7128	−	15.7752i	0.910246	−	0.661333i	0.941077	+	0.338192i	$0.109815\pi$
$570$	0.588147	−	3.83550i	0.0246348	−	0.160652i
$571$			26.2105i			1.09687i	0.836192	+	0.548437i	$0.184777\pi$
$571$			26.2105i			1.09687i	−0.836192	+	0.548437i	$0.815223\pi$
$572$		0			0
$573$	−7.59993	+	7.59993i	−0.317492	+	0.317492i
$574$	11.6440	−	35.8364i	0.486009	−	1.49578i
$575$	5.83213	+	34.6137i	0.243217	+	1.44349i
$576$	−20.0537	−	14.5698i	−0.835569	−	0.607077i
$577$	5.13241	−	10.0729i	0.213665	−	0.419341i	−0.759153	−	0.650912i	$-0.774387\pi$
$577$	5.13241	−	10.0729i	0.213665	−	0.419341i	0.972818	+	0.231571i	$0.0743866\pi$
$578$	−29.6515	+	58.1944i	−1.23334	+	2.42057i
$579$	10.5509	+	7.66565i	0.438479	+	0.318574i
$580$	25.6087	−	25.8621i	1.06334	−	1.07386i
$581$	−1.61026	+	4.95588i	−0.0668050	+	0.205605i
$582$	−7.46210	+	7.46210i	−0.309314	+	0.309314i
$583$		0			0
$584$		−	8.55294i		−	0.353923i
$585$	14.7649	−	10.8388i	0.610454	−	0.448128i
$586$	28.5329	−	20.7303i	1.17868	−	0.856362i
$587$	−5.85736	−	36.9819i	−0.241759	−	1.52641i	−0.747815	−	0.663907i	$-0.768897\pi$
$587$	−5.85736	−	36.9819i	−0.241759	−	1.52641i	0.506056	−	0.862501i	$-0.331103\pi$
$588$	6.77404	+	3.45155i	0.279357	+	0.142339i
$589$	0.245697	+	0.756178i	0.0101238	+	0.0311578i
$590$	5.87973	−	1.94249i	0.242065	−	0.0799710i
$591$	−6.00734	−	8.26839i	−0.247109	−	0.340116i
$592$	−0.0418788	+	0.0213383i	−0.00172121	+	0.000876999i
$593$	19.3337	+	19.3337i	0.793940	+	0.793940i	0.982132	−	0.188192i	$-0.0602627\pi$
$593$	19.3337	+	19.3337i	0.793940	+	0.793940i	−0.188192	+	0.982132i	$0.560263\pi$
$594$		0			0
$595$	−45.0504	+	7.36278i	−1.84689	+	0.301844i
$596$	34.2182	+	11.1182i	1.40163	+	0.455417i
$597$	19.9415	+	3.15843i	0.816152	+	0.129266i
$598$	67.2171	−	10.6461i	2.74871	−	0.435353i
$599$	−1.08354	+	0.352062i	−0.0442721	+	0.0143849i	−0.331069	−	0.943606i	$-0.607409\pi$
$599$	−1.08354	+	0.352062i	−0.0442721	+	0.0143849i	0.286797	+	0.957991i	$0.407409\pi$
$600$	9.55935	+	12.8886i	0.390259	+	0.526173i
$601$	15.7542	−	21.6838i	0.642627	−	0.884500i	−0.356125	−	0.934438i	$-0.615902\pi$
$601$	15.7542	−	21.6838i	0.642627	−	0.884500i	0.998752	+	0.0499379i	$0.0159024\pi$
$602$	2.99791	−	18.9281i	0.122186	−	0.771451i
$603$	4.89321	+	9.60346i	0.199267	+	0.391083i
$604$	61.8128			2.51513
$605$		0			0
$606$	32.7380			1.32989
$607$	−6.57177	−	12.8978i	−0.266740	−	0.523506i	0.718321	−	0.695711i	$-0.244911\pi$
$607$	−6.57177	−	12.8978i	−0.266740	−	0.523506i	−0.985061	+	0.172205i	$0.944911\pi$
$608$	0.573487	−	3.62085i	0.0232580	−	0.146845i
$609$	−8.84169	+	12.1695i	−0.358284	+	0.493135i
$610$	36.3393	+	11.6099i	1.47134	+	0.470072i
$611$	−40.7036	+	13.2254i	−1.64669	+	0.535043i
$612$	43.6036	−	6.90613i	1.76257	−	0.279164i
$613$	25.5057	+	4.03971i	1.03017	+	0.163162i	0.648560	−	0.761163i	$-0.275371\pi$
$613$	25.5057	+	4.03971i	1.03017	+	0.163162i	0.381605	+	0.924325i	$0.375371\pi$
$614$	52.1001	+	16.9284i	2.10259	+	0.683173i
$615$	−7.15389	+	9.94911i	−0.288473	+	0.401187i
$616$		0			0
$617$	−33.8317	−	33.8317i	−1.36201	−	1.36201i	−0.871348	−	0.490665i	$-0.836754\pi$
$617$	−33.8317	−	33.8317i	−1.36201	−	1.36201i	−0.490665	−	0.871348i	$-0.663246\pi$
$618$	17.7229	−	9.03026i	0.712919	−	0.363250i
$619$	20.8406	+	28.6846i	0.837654	+	1.15293i	0.986450	+	0.164064i	$0.0524604\pi$
$619$	20.8406	+	28.6846i	0.837654	+	1.15293i	−0.148795	+	0.988868i	$0.547540\pi$
$620$	−7.26588	−	3.65721i	−0.291805	−	0.146877i
$621$	10.9864	+	33.8128i	0.440870	+	1.35686i
$622$	1.00483	+	0.511985i	0.0402899	+	0.0205287i
$623$	5.22181	+	32.9692i	0.209207	+	1.32088i
$624$	1.92168	−	1.39619i	0.0769290	−	0.0558922i
$625$	−8.19202	−	23.6197i	−0.327681	−	0.944788i
$626$		−	11.4912i		−	0.459280i
$627$		0			0
$628$	41.8173	−	41.8173i	1.66869	−	1.66869i
$629$	−0.175991	+	0.541643i	−0.00701721	+	0.0215967i
$630$	21.8340	+	21.6202i	0.869889	+	0.861367i
$631$	−11.9250	−	8.66400i	−0.474726	−	0.344909i	0.324554	−	0.945867i	$-0.394786\pi$
$631$	−11.9250	−	8.66400i	−0.474726	−	0.344909i	−0.799280	+	0.600959i	$0.794786\pi$
$632$	14.7700	−	28.9878i	0.587520	−	1.15307i
$633$	7.22896	−	14.1876i	0.287325	−	0.563908i
$634$	48.2612	+	35.0638i	1.91670	+	1.39256i
$635$	5.13668	−	0.0252837i	0.203843	−	0.00100335i
$636$	2.40687	−	7.40758i	0.0954385	−	0.293730i
$637$	−6.56369	+	6.56369i	−0.260063	+	0.260063i
$638$		0			0
$639$			27.2002i			1.07602i
$640$	25.5937	+	34.8645i	1.01168	+	1.37814i
$641$	14.0157	−	10.1830i	0.553585	−	0.402203i	−0.275520	−	0.961295i	$-0.588850\pi$
$641$	14.0157	−	10.1830i	0.553585	−	0.402203i	0.829106	+	0.559092i	$0.188850\pi$
$642$	1.04757	+	6.61412i	0.0413445	+	0.261039i
$643$	18.0053	+	9.17415i	0.710059	+	0.361793i	0.771423	−	0.636322i	$-0.219545\pi$
$643$	18.0053	+	9.17415i	0.710059	+	0.361793i	−0.0613644	+	0.998115i	$0.519545\pi$
$644$	22.1083	+	68.0422i	0.871187	+	2.68124i
$645$	−2.80205	+	5.56690i	−0.110330	+	0.219196i
$646$	6.71201	+	9.23829i	0.264080	+	0.363476i
$647$	−30.4288	+	15.5042i	−1.19628	+	0.609534i	−0.934627	−	0.355628i	$-0.884267\pi$
$647$	−30.4288	+	15.5042i	−1.19628	+	0.609534i	−0.261651	+	0.965163i	$0.584267\pi$
$648$	−1.53649	−	1.53649i	−0.0603590	−	0.0603590i
$649$		0			0
$650$	−45.9480	+	15.4311i	−1.80223	+	0.605258i
$651$	3.19740	+	1.03890i	0.125316	+	0.0407176i
$652$	−46.3360	−	7.33889i	−1.81466	−	0.287413i
$653$	36.4080	−	5.76646i	1.42476	−	0.225659i	0.604021	−	0.796969i	$-0.293564\pi$
$653$	36.4080	−	5.76646i	1.42476	−	0.225659i	0.820735	+	0.571309i	$0.193564\pi$
$654$	−6.89229	+	2.23944i	−0.269510	+	0.0875691i
$655$	−2.10705	−	4.08548i	−0.0823292	−	0.159633i
$656$	1.74933	−	2.40774i	0.0682997	−	0.0940064i
$657$	−0.833196	+	5.26059i	−0.0325061	+	0.205235i
$658$	−32.5958	−	63.9729i	−1.27072	−	2.49392i
$659$	42.3793			1.65086			0.825432	−	0.564501i	$-0.190931\pi$
$659$	42.3793			1.65086			0.825432	+	0.564501i	$0.190931\pi$
$660$		0			0
$661$	1.78019			0.0692412			0.0346206	−	0.999401i	$-0.488978\pi$
$661$	1.78019			0.0692412			0.0346206	+	0.999401i	$0.488978\pi$
$662$	−31.7210	−	62.2560i	−1.23287	−	2.41965i
$663$	4.50247	−	28.4275i	0.174861	−	1.10403i
$664$	−3.16855	+	4.36113i	−0.122964	+	0.169245i
$665$	−1.51574	+	4.74431i	−0.0587780	+	0.183976i
$666$	0.364596	−	0.118465i	0.0141278	−	0.00459041i
$667$	−33.6206	+	5.32498i	−1.30179	+	0.206184i
$668$	−4.98494	−	0.789536i	−0.192873	−	0.0305481i
$669$	20.2765	+	6.58825i	0.783936	+	0.254716i
$670$	−4.60049	−	28.1489i	−0.177732	−	1.08749i
$671$		0			0
$672$	−10.9610	−	10.9610i	−0.422828	−	0.422828i
$673$	−7.96361	+	4.05766i	−0.306974	+	0.156411i	−0.600691	−	0.799481i	$-0.705108\pi$
$673$	−7.96361	+	4.05766i	−0.306974	+	0.156411i	0.293717	+	0.955893i	$0.405108\pi$
$674$	18.5043	+	25.4690i	0.712759	+	0.981028i
$675$	−11.7172	−	22.4472i	−0.450995	−	0.863995i
$676$	4.71211	+	14.5024i	0.181235	+	0.557784i
$677$	10.5245	+	5.36250i	0.404489	+	0.206097i	0.644385	−	0.764701i	$-0.277113\pi$
$677$	10.5245	+	5.36250i	0.404489	+	0.206097i	−0.239896	+	0.970799i	$0.577113\pi$
$678$	−2.78728	−	17.5982i	−0.107045	−	0.675854i
$679$	10.9583	−	7.96166i	0.420540	−	0.305540i
$680$	−46.6770	−	7.15758i	−1.78998	−	0.274481i
$681$			6.83463i			0.261904i
$682$		0			0
$683$	12.1989	−	12.1989i	0.466779	−	0.466779i	−0.434090	−	0.900869i	$-0.642930\pi$
$683$	12.1989	−	12.1989i	0.466779	−	0.466779i	0.900869	+	0.434090i	$0.142930\pi$
$684$	1.48847	−	4.58104i	0.0569130	−	0.175160i
$685$	0.0553047	+	11.2358i	0.00211308	+	0.429297i
$686$	27.1932	+	19.7570i	1.03824	+	0.754327i
$687$	−13.1892	+	25.8852i	−0.503199	+	0.987583i
$688$	0.687174	−	1.34866i	0.0261983	−	0.0514170i
$689$	7.69349	+	5.58965i	0.293099	+	0.212949i
$690$	−0.182753	−	37.1283i	−0.00695728	−	1.41345i
$691$	3.78707	−	11.6554i	0.144067	−	0.443392i	−0.852823	−	0.522200i	$-0.825111\pi$
$691$	3.78707	−	11.6554i	0.144067	−	0.443392i	0.996890	+	0.0788078i	$0.0251114\pi$
$692$	6.22526	−	6.22526i	0.236649	−	0.236649i
$693$		0			0
$694$		−	56.1185i		−	2.13023i
$695$	−4.32813	−	0.663688i	−0.164175	−	0.0251751i
$696$	−12.5893	+	9.14666i	−0.477196	+	0.346703i
$697$	−5.64129	−	35.6177i	−0.213679	−	1.34912i
$698$	−21.6876	−	11.0504i	−0.820887	−	0.418263i
$699$	7.84673	+	24.1497i	0.296790	+	0.913427i
$700$	−23.5788	−	45.1711i	−0.891195	−	1.70731i
$701$	−4.87736	−	6.71312i	−0.184215	−	0.253551i	0.706914	−	0.707299i	$-0.250087\pi$
$701$	−4.87736	−	6.71312i	−0.184215	−	0.253551i	−0.891130	+	0.453748i	$0.850087\pi$
$702$	−43.7422	+	22.2878i	−1.65094	+	0.841197i
$703$	0.0439387	+	0.0439387i	0.00165718	+	0.00165718i
$704$		0			0
$705$	3.76614	+	23.0438i	0.141841	+	0.867879i
$706$	24.6916	+	8.02278i	0.929279	+	0.301941i
$707$	−41.5031	−	6.57345i	−1.56089	−	0.247220i
$708$	−4.05396	+	0.642084i	−0.152357	+	0.0241310i
$709$	−35.8297	+	11.6418i	−1.34561	+	0.437216i	−0.891214	−	0.453583i	$-0.850145\pi$
$709$	−35.8297	+	11.6418i	−1.34561	+	0.437216i	−0.454397	+	0.890799i	$0.650145\pi$
$710$	21.9058	−	68.5656i	0.822109	−	2.57322i
$711$	−11.9084	+	16.3905i	−0.446599	+	0.614691i
$712$	−5.40192	+	34.1063i	−0.202445	+	1.27819i
$713$	3.45387	+	6.77859i	0.129348	+	0.253860i
$714$	48.2843			1.80700
$715$		0			0
$716$	16.1053			0.601884
$717$	−6.23233	−	12.2316i	−0.232751	−	0.456799i
$718$	−11.8437	+	74.7784i	−0.442004	+	2.79071i
$719$	−29.5803	+	40.7138i	−1.10316	+	1.51837i	−0.272027	+	0.962290i	$0.587694\pi$
$719$	−29.5803	+	40.7138i	−1.10316	+	1.51837i	−0.831131	+	0.556077i	$0.812306\pi$
$720$	1.11243	+	2.15695i	0.0414578	+	0.0803849i
$721$	−24.2811	+	7.88941i	−0.904276	+	0.293817i
$722$	−42.2035	+	6.68437i	−1.57065	+	0.248767i
$723$	−10.9851	−	1.73987i	−0.408541	−	0.0647065i
$724$	3.03793	+	0.987083i	0.112904	+	0.0366847i
$725$	22.9822	−	7.71832i	0.853538	−	0.286651i
$726$		0			0
$727$	12.0396	+	12.0396i	0.446524	+	0.446524i	0.894197	−	0.447673i	$-0.147747\pi$
$727$	12.0396	+	12.0396i	0.446524	+	0.446524i	−0.447673	+	0.894197i	$0.647747\pi$
$728$	−35.5801	+	18.1290i	−1.31869	+	0.671905i
$729$	−8.33039	−	11.4658i	−0.308533	−	0.424659i
$730$	6.33693	−	12.5897i	0.234540	−	0.465967i
$731$	−5.66756	−	17.4430i	−0.209622	−	0.645152i
$732$	−22.5305	−	11.4799i	−0.832751	−	0.424308i
$733$	−2.91045	−	18.3758i	−0.107500	−	0.678727i	−0.981306	−	0.192453i	$-0.938356\pi$
$733$	−2.91045	−	18.3758i	−0.107500	−	0.678727i	0.873806	−	0.486274i	$-0.161644\pi$
$734$	−54.9984	+	39.9587i	−2.03003	+	1.47490i
$735$	2.99681	+	4.08235i	0.110539	+	0.150580i
$736$		−	35.0778i		−	1.29298i
$737$		0			0
$738$	−17.1644	+	17.1644i	−0.631832	+	0.631832i
$739$	0.526220	−	1.61954i	0.0193573	−	0.0595757i	−0.940911	−	0.338653i	$-0.890029\pi$
$739$	0.526220	−	1.61954i	0.0193573	−	0.0595757i	0.960269	+	0.279078i	$0.0900287\pi$
$740$	−0.635717	+	0.00312913i	−0.0233694	+	0.000115029i
$741$	−2.54057	−	1.84583i	−0.0933302	−	0.0678083i
$742$	−7.24270	+	14.2146i	−0.265888	+	0.521834i
$743$	5.74772	−	11.2805i	0.210864	−	0.413843i	−0.761215	−	0.648500i	$-0.775397\pi$
$743$	5.74772	−	11.2805i	0.210864	−	0.413843i	0.972078	+	0.234657i	$0.0753967\pi$
$744$	2.81368	+	2.04426i	0.103155	+	0.0749461i
$745$	17.0298	+	16.8630i	0.623923	+	0.617811i
$746$	−23.2180	+	71.4575i	−0.850070	+	2.61625i
$747$	2.37370	−	2.37370i	0.0868492	−	0.0868492i
$748$		0			0
$749$		−	8.59530i		−	0.314065i
$750$	4.52193	+	26.0543i	0.165117	+	0.951367i
$751$	26.9646	−	19.5909i	0.983953	−	0.714883i	0.0253641	−	0.999678i	$-0.491925\pi$
$751$	26.9646	−	19.5909i	0.983953	−	0.714883i	0.958588	+	0.284795i	$0.0919255\pi$
$752$	−0.887117	−	5.60103i	−0.0323498	−	0.204249i
$753$	−6.30733	−	3.21374i	−0.229852	−	0.117115i
$754$	−14.5249	−	44.7030i	−0.528966	−	1.62799i
$755$	36.7780	+	18.5119i	1.33849	+	0.673717i
$756$	−30.3355	−	41.7532i	−1.10329	−	1.51855i
$757$	−21.5600	+	10.9854i	−0.783612	+	0.399270i	−0.799548	−	0.600603i	$-0.794927\pi$
$757$	−21.5600	+	10.9854i	−0.783612	+	0.399270i	0.0159356	+	0.999873i	$0.494927\pi$
$758$	−42.8590	−	42.8590i	−1.55671	−	1.55671i
$759$		0			0
$760$	−3.00792	+	4.18319i	−0.109109	+	0.151740i
$761$	14.7154	+	4.78133i	0.533434	+	0.173323i	0.563333	−	0.826230i	$-0.309519\pi$
$761$	14.7154	+	4.78133i	0.533434	+	0.173323i	−0.0298994	+	0.999553i	$0.509519\pi$
$762$	−5.36649	−	0.849969i	−0.194408	−	0.0307911i
$763$	9.18726	−	1.45512i	0.332601	−	0.0526789i
$764$	33.5782	−	10.9102i	1.21482	−	0.394718i
$765$	28.0120	+	8.94946i	1.01278	+	0.323569i
$766$	−47.2671	+	65.0576i	−1.70783	+	2.35063i
$767$	0.783949	−	4.94966i	0.0283068	−	0.178722i
$768$	−9.00869	−	17.6806i	−0.325073	−	0.637992i
$769$	16.4515			0.593255			0.296627	−	0.954993i	$-0.404138\pi$
$769$	16.4515			0.593255			0.296627	+	0.954993i	$0.404138\pi$
$770$		0			0
$771$	−12.6587			−0.455894
$772$	−19.4493	−	38.1714i	−0.699995	−	1.37382i
$773$	3.63664	−	22.9609i	0.130801	−	0.825844i	−0.831831	−	0.555030i	$-0.812707\pi$
$773$	3.63664	−	22.9609i	0.130801	−	0.825844i	0.962631	−	0.270815i	$-0.0872931\pi$
$774$	−7.25657	+	9.98782i	−0.260832	+	0.359005i
$775$	−3.22786	−	4.35202i	−0.115948	−	0.156329i
$776$	13.3266	−	4.33006i	0.478396	−	0.155440i
$777$	0.259510	−	0.0411024i	0.00930988	−	0.00147454i
$778$	39.0146	+	6.17930i	1.39874	+	0.221539i
$779$	−3.74203	−	1.21586i	−0.134072	−	0.0435627i
$780$	31.7071	−	5.18202i	1.13530	−	0.185546i
$781$		0			0
$782$	77.2609	+	77.2609i	2.76284	+	2.76284i
$783$	21.8789	−	11.1479i	0.781889	−	0.398393i
$784$	−0.722941	−	0.995043i	−0.0258193	−	0.0355373i
$785$	37.4045	−	12.3573i	1.33502	−	0.441053i
$786$	1.50253	+	4.62431i	0.0535935	+	0.164944i
$787$	13.1933	+	6.72230i	0.470289	+	0.239624i	0.673040	−	0.739606i	$-0.264988\pi$
$787$	13.1933	+	6.72230i	0.470289	+	0.239624i	−0.202751	+	0.979230i	$0.564988\pi$
$788$	5.25197	+	33.1596i	0.187094	+	1.18126i
$789$	12.2908	−	8.92982i	0.437566	−	0.317910i
$790$	43.2184	−	31.7262i	1.53764	−	1.12877i
$791$			22.8695i			0.813146i
$792$		0			0
$793$	21.8309	−	21.8309i	0.775237	−	0.775237i
$794$	−3.14657	+	9.68413i	−0.111667	+	0.343677i
$795$	3.65051	−	3.68663i	0.129470	−	0.130751i
$796$	−53.6565	−	38.9838i	−1.90181	−	1.38174i
$797$	−8.49513	+	16.6726i	−0.300913	+	0.590575i	−0.991110	−	0.133047i	$-0.957524\pi$
$797$	−8.49513	+	16.6726i	−0.300913	+	0.590575i	0.690197	+	0.723622i	$0.257524\pi$
$798$	2.39171	−	4.69399i	0.0846655	−	0.166165i
$799$	−55.5904	−	40.3888i	−1.96665	−	1.42885i
$800$	4.15092	+	24.6358i	0.146757	+	0.871006i
$801$	6.64503	−	20.4513i	0.234791	−	0.722612i
$802$	−42.5113	+	42.5113i	−1.50113	+	1.50113i
$803$		0			0
$804$			18.9057i			0.666753i
$805$	−7.22329	+	47.1056i	−0.254588	+	1.66025i
$806$	−8.49888	+	6.17480i	−0.299360	+	0.217498i
$807$	1.13892	+	7.19083i	0.0400917	+	0.253129i
$808$	−38.7319	−	19.7349i	−1.36258	−	0.694271i
$809$	−5.15790	−	15.8744i	−0.181342	−	0.558114i	0.818524	−	0.574472i	$-0.194793\pi$
$809$	−5.15790	−	15.8744i	−0.181342	−	0.558114i	−0.999866	+	0.0163584i	$0.994793\pi$
$810$	−1.12328	−	3.40007i	−0.0394682	−	0.119466i
$811$	13.3970	+	18.4394i	0.470433	+	0.647495i	0.976631	−	0.214922i	$-0.0689496\pi$
$811$	13.3970	+	18.4394i	0.470433	+	0.647495i	−0.506198	+	0.862417i	$0.668950\pi$
$812$	44.0275	−	22.4331i	1.54506	−	0.787249i
$813$	−18.3767	−	18.3767i	−0.644499	−	0.644499i
$814$		0			0
$815$	−25.3716	−	18.2434i	−0.888728	−	0.639039i
$816$	3.62699	+	1.17848i	0.126970	+	0.0412551i
$817$	−1.97646	−	0.313041i	−0.0691477	−	0.0109519i
$818$	−13.1796	+	2.08745i	−0.460816	+	0.0729860i
$819$	23.6501	−	7.68437i	0.826400	−	0.268514i
$820$	35.7761	−	18.4512i	1.24936	−	0.644344i
$821$	1.22091	−	1.68044i	0.0426100	−	0.0586476i	−0.787180	−	0.616723i	$-0.788460\pi$
$821$	1.22091	−	1.68044i	0.0426100	−	0.0586476i	0.829790	+	0.558075i	$0.188460\pi$
$822$	1.85919	−	11.7385i	0.0648467	−	0.409426i
$823$	−10.8005	−	21.1972i	−0.376482	−	0.738888i	0.622563	−	0.782569i	$-0.286091\pi$
$823$	−10.8005	−	21.1972i	−0.376482	−	0.738888i	−0.999046	+	0.0436815i	$0.986091\pi$
$824$	−26.4113			−0.920080
$825$		0			0
$826$	8.40705			0.292519
$827$	4.43872	+	8.71147i	0.154349	+	0.302928i	0.955213	−	0.295919i	$-0.0956259\pi$
$827$	4.43872	+	8.71147i	0.154349	+	0.302928i	−0.800864	+	0.598847i	$0.795626\pi$
$828$	7.20993	−	45.5217i	0.250562	−	1.58199i
$829$	−28.4732	+	39.1900i	−0.988916	+	1.36113i	−0.0570307	+	0.998372i	$0.518163\pi$
$829$	−28.4732	+	39.1900i	−0.988916	+	1.36113i	−0.931885	+	0.362753i	$0.881837\pi$
$830$	−7.89523	+	4.07189i	−0.274047	+	0.141337i
$831$	2.99704	−	0.973798i	0.103966	−	0.0337807i
$832$	52.4322	−	8.30445i	1.81776	−	0.287905i
$833$	−14.7197	−	2.33137i	−0.510007	−	0.0807771i
$834$	4.40491	+	1.43124i	0.152530	+	0.0495599i
$835$	−2.72954	−	1.96267i	−0.0944596	−	0.0679211i
$836$		0			0
$837$	−3.88064	−	3.88064i	−0.134135	−	0.134135i
$838$	−31.2644	+	15.9300i	−1.08001	+	0.550293i
$839$	−5.22001	−	7.18473i	−0.180215	−	0.248045i	0.709347	−	0.704860i	$-0.248990\pi$
$839$	−5.22001	−	7.18473i	−0.180215	−	0.248045i	−0.889562	+	0.456815i	$0.848990\pi$
$840$	6.83415	+	20.6863i	0.235800	+	0.713746i
$841$	−1.69644	−	5.22110i	−0.0584979	−	0.180038i
$842$	15.4666	+	7.88064i	0.533015	+	0.271585i
$843$	−4.56393	−	28.8155i	−0.157190	−	0.992460i
$844$	−42.3168	+	30.7450i	−1.45661	+	1.05829i
$845$	−1.53956	+	10.0400i	−0.0529624	+	0.345386i
$846$			46.2531i			1.59022i
$847$		0			0
$848$	−0.890989	+	0.890989i	−0.0305967	+	0.0305967i
$849$	−8.41033	+	25.8843i	−0.288642	+	0.888348i
$850$	−63.4044	−	45.1191i	−2.17475	−	1.54757i
$851$	0.481017	+	0.349480i	0.0164891	+	0.0119800i
$852$	−21.6604	+	42.5109i	−0.742072	+	1.45640i
$853$	11.1264	−	21.8367i	0.380959	−	0.747675i	−0.618308	−	0.785936i	$-0.712182\pi$
$853$	11.1264	−	21.8367i	0.380959	−	0.747675i	0.999268	+	0.0382607i	$0.0121817\pi$
$854$	41.9017	+	30.4433i	1.43385	+	1.04175i
$855$	2.25757	−	2.27990i	0.0772073	−	0.0779711i
$856$	2.74771	−	8.45657i	0.0939147	−	0.289040i
$857$	−13.2386	+	13.2386i	−0.452221	+	0.452221i	−0.896091	−	0.443870i	$-0.853605\pi$
$857$	−13.2386	+	13.2386i	−0.452221	+	0.452221i	0.443870	+	0.896091i	$0.353605\pi$
$858$		0			0
$859$		−	9.57133i		−	0.326569i	−0.986579	−	0.163285i	$-0.947791\pi$
$859$		−	9.57133i		−	0.326569i	0.986579	−	0.163285i	$-0.0522089\pi$
$860$	16.5034	−	12.1150i	0.562760	−	0.413117i
$861$	−13.4596	+	9.77894i	−0.458701	+	0.333266i
$862$	0.696892	+	4.40000i	0.0237362	+	0.149865i
$863$	31.7865	+	16.1960i	1.08203	+	0.551319i	0.901733	−	0.432294i	$-0.142296\pi$
$863$	31.7865	+	16.1960i	1.08203	+	0.551319i	0.180292	+	0.983613i	$0.442296\pi$
$864$	7.81941	+	24.0657i	0.266022	+	0.818731i
$865$	5.56833	−	1.83961i	0.189329	−	0.0625486i
$866$	3.25750	+	4.48356i	0.110694	+	0.152358i
$867$	25.6943	−	13.0919i	0.872623	−	0.444624i
$868$	−7.80911	−	7.80911i	−0.265059	−	0.265059i
$869$		0			0
$870$	−25.3080	+	4.13619i	−0.858021	+	0.140230i
$871$	−21.9531	−	7.13299i	−0.743852	−	0.241692i
$872$	9.50414	+	1.50531i	0.321851	+	0.0509762i
$873$	−8.61849	+	1.36503i	−0.291692	+	0.0461994i
$874$	11.3380	−	3.68394i	0.383513	−	0.124611i
$875$	−0.501179	−	33.9379i	−0.0169429	−	1.14731i
$876$	−5.49136	+	7.55821i	−0.185536	+	0.255368i
$877$	−1.79523	+	11.3346i	−0.0606206	+	0.382743i	0.938661	+	0.344842i	$0.112067\pi$
$877$	−1.79523	+	11.3346i	−0.0606206	+	0.382743i	−0.999281	+	0.0379018i	$0.987933\pi$
$878$	−5.18546	−	10.1770i	−0.175001	−	0.343459i
$879$	−15.5719			−0.525228
$880$		0			0
$881$	−16.7047			−0.562795			−0.281397	−	0.959591i	$-0.590798\pi$
$881$	−16.7047			−0.562795			−0.281397	+	0.959591i	$0.590798\pi$
$882$	4.55432	+	8.93837i	0.153352	+	0.300970i
$883$	−1.35531	+	8.55707i	−0.0456097	+	0.287968i	−0.999942	−	0.0107792i	$-0.996569\pi$
$883$	−1.35531	+	8.55707i	−0.0456097	+	0.287968i	0.954332	+	0.298747i	$0.0965688\pi$
$884$	−55.5730	+	76.4896i	−1.86912	+	2.57262i
$885$	−2.60436	−	0.832059i	−0.0875447	−	0.0279694i
$886$	−27.7028	+	9.00118i	−0.930693	+	0.302401i
$887$	18.2132	−	2.88469i	0.611541	−	0.0968585i	0.157021	−	0.987595i	$-0.449811\pi$
$887$	18.2132	−	2.88469i	0.611541	−	0.0968585i	0.454520	+	0.890737i	$0.349811\pi$
$888$	0.268461	+	0.0425201i	0.00900897	+	0.00142688i
$889$	6.63263	+	2.15507i	0.222451	+	0.0722788i
$890$	−33.2211	+	46.2015i	−1.11357	+	1.54868i
$891$		0			0
$892$	−49.5221	−	49.5221i	−1.65812	−	1.65812i
$893$	−6.68003	+	3.40364i	−0.223539	+	0.113899i
$894$	−14.9004	−	20.5087i	−0.498345	−	0.685914i
$895$	9.58252	+	4.82328i	0.320308	+	0.161224i
$896$	18.1452	+	55.8451i	0.606188	+	1.86565i
$897$	−26.7729	−	13.6415i	−0.893921	−	0.455476i
$898$	5.43297	+	34.3024i	0.181301	+	1.14469i
$899$	4.25096	−	3.08851i	0.141778	−	0.103007i
$900$	0.323139	+	32.8239i	0.0107713	+	1.09413i
$901$			15.2680i			0.508650i
$902$		0			0
$903$	−5.98310	+	5.98310i	−0.199105	+	0.199105i
$904$	−7.31082	+	22.5004i	−0.243154	+	0.748352i
$905$	1.51193	+	1.49711i	0.0502581	+	0.0497658i
$906$	−35.2343	−	25.5992i	−1.17058	−	0.850478i
$907$	20.7743	−	40.7719i	0.689801	−	1.35381i	−0.234489	−	0.972119i	$-0.575342\pi$
$907$	20.7743	−	40.7719i	0.689801	−	1.35381i	0.924290	−	0.381692i	$-0.124658\pi$
$908$	10.1927	−	20.0043i	0.338256	−	0.663865i
$909$	21.9000	+	15.9113i	0.726378	+	0.527745i
$910$	−65.8050	+	0.323905i	−2.18142	+	0.0107374i
$911$	8.11054	−	24.9617i	0.268714	−	0.827018i	−0.722100	−	0.691789i	$-0.756823\pi$
$911$	8.11054	−	24.9617i	0.268714	−	0.827018i	0.990814	−	0.135229i	$-0.0431770\pi$
$912$	0.294225	−	0.294225i	0.00974277	−	0.00974277i
$913$		0			0
$914$			2.07500i			0.0686348i
$915$	−9.96741	−	13.5779i	−0.329513	−	0.448872i
$916$	77.2067	−	56.0940i	2.55098	−	1.85340i
$917$	−0.976297	−	6.16410i	−0.0322402	−	0.203556i
$918$	−70.2289	−	35.7834i	−2.31790	−	1.18103i
$919$	11.0781	+	34.0949i	0.365432	+	1.12469i	0.949710	+	0.313131i	$0.101378\pi$
$919$	11.0781	+	34.0949i	0.365432	+	1.12469i	−0.584277	+	0.811554i	$0.698622\pi$
$920$	−22.1652	+	44.0362i	−0.730765	+	1.45183i
$921$	−14.2169	−	19.5679i	−0.468464	−	0.644785i
$922$	9.30121	−	4.73920i	0.306319	−	0.156077i
$923$	−41.1908	−	41.1908i	−1.35581	−	1.35581i
$924$		0			0
$925$	−0.379183	−	0.188525i	−0.0124675	−	0.00619866i
$926$	−50.0059	−	16.2479i	−1.64329	−	0.533939i
$927$	16.2446	+	2.57289i	0.533542	+	0.0845048i
$928$	−23.9289	+	3.78997i	−0.785505	+	0.124412i
$929$	26.1207	−	8.48713i	0.856992	−	0.278454i	0.152620	−	0.988285i	$-0.451229\pi$
$929$	26.1207	−	8.48713i	0.856992	−	0.278454i	0.704372	+	0.709831i	$0.251229\pi$
$930$	2.62707	+	5.09378i	0.0861450	+	0.167032i
$931$	−0.955767	+	1.31550i	−0.0313240	+	0.0431138i
$932$	13.0486	−	82.3858i	0.427422	−	2.69864i
$933$	−0.226054	−	0.443656i	−0.00740067	−	0.0145246i
$934$	−43.6319			−1.42768
$935$		0			0
$936$	25.7249			0.840843
$937$	16.5478	+	32.4768i	0.540591	+	1.06097i	0.986171	+	0.165728i	$0.0529975\pi$
$937$	16.5478	+	32.4768i	0.540591	+	1.06097i	−0.445580	+	0.895242i	$0.647003\pi$
$938$	6.05772	−	38.2470i	0.197792	−	1.24881i
$939$	−2.98221	+	4.10466i	−0.0973208	+	0.133951i
$940$	23.3427	−	73.0633i	0.761356	−	2.38306i
$941$	−11.0683	+	3.59630i	−0.360816	+	0.117236i	−0.483814	−	0.875171i	$-0.660749\pi$
$941$	−11.0683	+	3.59630i	−0.360816	+	0.117236i	0.122999	+	0.992407i	$0.460749\pi$
$942$	−41.1549	+	6.51830i	−1.34090	+	0.212378i
$943$	−37.1845	−	5.88944i	−1.21089	−	0.191787i
$944$	0.631514	+	0.205191i	0.0205540	+	0.00667841i
$945$	−5.54495	−	33.9277i	−0.180377	−	1.10367i
$946$		0			0
$947$	19.6094	+	19.6094i	0.637221	+	0.637221i	0.949869	−	0.312648i	$-0.101216\pi$
$947$	19.6094	+	19.6094i	0.637221	+	0.637221i	−0.312648	+	0.949869i	$0.601216\pi$
$948$	−31.6637	+	16.1335i	−1.02839	+	0.523990i
$949$	−6.70465	−	9.22816i	−0.217642	−	0.299559i
$950$	−7.52694	+	3.92898i	−0.244206	+	0.127473i
$951$	−8.13913	−	25.0497i	−0.263929	−	0.812291i
$952$	−57.1245	−	29.1064i	−1.85142	−	0.943344i
$953$	−0.481778	−	3.04183i	−0.0156063	−	0.0985344i	0.978656	−	0.205507i	$-0.0658843\pi$
$953$	−0.481778	−	3.04183i	−0.0156063	−	0.0985344i	−0.994262	+	0.106973i	$0.965884\pi$
$954$	8.31453	−	6.04086i	0.269193	−	0.195580i
$955$	23.2461	+	3.56463i	0.752228	+	0.115349i
$956$			45.0952i			1.45848i
$957$		0			0
$958$	−27.6649	+	27.6649i	−0.893813	+	0.893813i
$959$	−4.71392	+	14.5080i	−0.152220	+	0.468486i
$960$	−0.142555	−	28.9617i	−0.00460095	−	0.934735i
$961$	24.1294	+	17.5311i	0.778369	+	0.565518i
$962$	−0.372731	+	0.731525i	−0.0120173	+	0.0235853i
$963$	−2.51382	+	4.93365i	−0.0810067	+	0.158985i
$964$	29.5576	+	21.4748i	0.951985	+	0.691657i
$965$	−0.140462	−	28.5363i	−0.00452162	−	0.918618i
$966$	15.5770	−	47.9412i	0.501183	−	1.54248i
$967$	8.85124	−	8.85124i	0.284637	−	0.284637i	−0.550318	−	0.834955i	$-0.685494\pi$
$967$	8.85124	−	8.85124i	0.284637	−	0.284637i	0.834955	+	0.550318i	$0.185494\pi$
$968$		0			0
$969$		−	5.04184i		−	0.161967i
$970$	22.8246	+	3.49998i	0.732853	+	0.112378i
$971$	−30.6142	+	22.2425i	−0.982455	+	0.713795i	−0.958256	−	0.285912i	$-0.907704\pi$
$971$	−30.6142	+	22.2425i	−0.982455	+	0.713795i	−0.0241990	+	0.999707i	$0.507704\pi$
$972$	8.34957	+	52.7171i	0.267813	+	1.69090i
$973$	−5.29688	−	2.69890i	−0.169810	−	0.0865226i
$974$	−7.70934	−	23.7269i	−0.247023	−	0.760260i
$975$	20.4174	+	6.41249i	0.653879	+	0.205364i
$976$	2.40451	+	3.30952i	0.0769664	+	0.105935i
$977$	21.6636	−	11.0381i	0.693079	−	0.353141i	−0.0717070	−	0.997426i	$-0.522845\pi$
$977$	21.6636	−	11.0381i	0.693079	−	0.353141i	0.764786	+	0.644284i	$0.222845\pi$
$978$	23.3729	+	23.3729i	0.747384	+	0.747384i
$979$		0			0
$980$	−2.68324	−	16.4179i	−0.0857128	−	0.524449i
$981$	−5.69900	−	1.85172i	−0.181955	−	0.0591208i
$982$	−61.9954	−	9.81910i	−1.97835	−	0.313340i
$983$	−14.7415	+	2.33483i	−0.470182	+	0.0744695i	−0.387030	−	0.922067i	$-0.626499\pi$
$983$	−14.7415	+	2.33483i	−0.470182	+	0.0744695i	−0.0831525	+	0.996537i	$0.526499\pi$
$984$	−16.3684	+	5.31842i	−0.521806	+	0.169545i
$985$	−6.80588	+	21.3026i	−0.216853	+	0.678756i
$986$	44.3573	−	61.0525i	1.41262	−	1.94431i
$987$	−4.95909	+	31.3105i	−0.157850	+	0.996624i
$988$	4.68324	+	9.19138i	0.148994	+	0.292417i
$989$	−19.1474			−0.608852
$990$		0			0
$991$	53.6555			1.70442			0.852212	−	0.523197i	$-0.175261\pi$
$991$	53.6555			1.70442			0.852212	+	0.523197i	$0.175261\pi$
$992$	2.45823	+	4.82456i	0.0780490	+	0.153180i
$993$	−4.82601	+	30.4702i	−0.153149	+	0.966943i
$994$	57.4410	−	79.0607i	1.82192	−	2.50765i
$995$	−20.2502	−	39.2642i	−0.641974	−	1.24476i
$996$	5.60008	−	1.81958i	0.177445	−	0.0576554i
$997$	11.7550	−	1.86180i	0.372283	−	0.0589639i	0.0325104	−	0.999471i	$-0.489650\pi$
$997$	11.7550	−	1.86180i	0.372283	−	0.0589639i	0.339773	+	0.940508i	$0.389650\pi$
$998$	51.9822	+	8.23318i	1.64547	+	0.260617i
$999$	−0.407915	−	0.132540i	−0.0129059	−	0.00419337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.g.112.18		160
5.3	odd	4	inner	605.2.m.g.233.18		160
11.2	odd	10	inner	605.2.m.g.602.3		160
11.3	even	5	inner	605.2.m.g.282.18		160
11.4	even	5		605.2.e.c.362.3	✓	40
11.5	even	5	inner	605.2.m.g.457.3		160
11.6	odd	10	inner	605.2.m.g.457.18		160
11.7	odd	10		605.2.e.c.362.18	yes	40
11.8	odd	10	inner	605.2.m.g.282.3		160
11.9	even	5	inner	605.2.m.g.602.18		160
11.10	odd	2	inner	605.2.m.g.112.3		160
55.3	odd	20	inner	605.2.m.g.403.3		160
55.8	even	20	inner	605.2.m.g.403.18		160
55.13	even	20	inner	605.2.m.g.118.18		160
55.18	even	20		605.2.e.c.483.3	yes	40
55.28	even	20	inner	605.2.m.g.578.18		160
55.38	odd	20	inner	605.2.m.g.578.3		160
55.43	even	4	inner	605.2.m.g.233.3		160
55.48	odd	20		605.2.e.c.483.18	yes	40
55.53	odd	20	inner	605.2.m.g.118.3		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.3	✓	40	11.4	even	5
605.2.e.c.362.18	yes	40	11.7	odd	10
605.2.e.c.483.3	yes	40	55.18	even	20
605.2.e.c.483.18	yes	40	55.48	odd	20
605.2.m.g.112.3		160	11.10	odd	2	inner
605.2.m.g.112.18		160	1.1	even	1	trivial
605.2.m.g.118.3		160	55.53	odd	20	inner
605.2.m.g.118.18		160	55.13	even	20	inner
605.2.m.g.233.3		160	55.43	even	4	inner
605.2.m.g.233.18		160	5.3	odd	4	inner
605.2.m.g.282.3		160	11.8	odd	10	inner
605.2.m.g.282.18		160	11.3	even	5	inner
605.2.m.g.403.3		160	55.3	odd	20	inner
605.2.m.g.403.18		160	55.8	even	20	inner
605.2.m.g.457.3		160	11.5	even	5	inner
605.2.m.g.457.18		160	11.6	odd	10	inner
605.2.m.g.578.3		160	55.38	odd	20	inner
605.2.m.g.578.18		160	55.28	even	20	inner
605.2.m.g.602.3		160	11.2	odd	10	inner
605.2.m.g.602.18		160	11.9	even	5	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05076 + 2.06223i) q^{2} +(0.159862 - 1.00933i) q^{3} +(-1.97313 + 2.71579i) q^{4} +(-1.98733 + 1.02495i) q^{5} +(2.24944 - 0.730888i) q^{6} +(-2.99845 + 0.474908i) q^{7} +(-3.10187 - 0.491288i) q^{8} +(1.85999 + 0.604346i) q^{9} +O(q^{10})\)	\(q+(1.05076 + 2.06223i) q^{2} +(0.159862 - 1.00933i) q^{3} +(-1.97313 + 2.71579i) q^{4} +(-1.98733 + 1.02495i) q^{5} +(2.24944 - 0.730888i) q^{6} +(-2.99845 + 0.474908i) q^{7} +(-3.10187 - 0.491288i) q^{8} +(1.85999 + 0.604346i) q^{9} +(-4.20189 - 3.02136i) q^{10} +(2.42569 + 2.42569i) q^{12} +(-3.73187 + 1.90148i) q^{13} +(-4.13002 - 5.68449i) q^{14} +(0.716809 + 2.16971i) q^{15} +(-0.171494 - 0.527805i) q^{16} +(-5.99159 - 3.05287i) q^{17} +(0.708096 + 4.47075i) q^{18} +(-0.593572 + 0.431256i) q^{19} +(1.13773 - 7.41953i) q^{20} +3.10233i q^{21} +(-4.96412 + 4.96412i) q^{23} +(-0.991740 + 3.05226i) q^{24} +(2.89896 - 4.07382i) q^{25} +(-7.84260 - 5.69798i) q^{26} +(2.29913 - 4.51230i) q^{27} +(4.62660 - 9.08021i) q^{28} +(3.92271 + 2.85001i) q^{29} +(-3.72126 + 3.75808i) q^{30} +(0.334876 - 1.03064i) q^{31} +(-3.53313 + 3.53313i) q^{32} -15.5639i q^{34} +(5.47216 - 4.01705i) q^{35} +(-5.31128 + 3.85887i) q^{36} +(-0.0132489 - 0.0836500i) q^{37} +(-1.51305 - 0.770938i) q^{38} +(1.32263 + 4.07065i) q^{39} +(6.66799 - 2.20290i) q^{40} +(3.15212 + 4.33853i) q^{41} +(-6.39773 + 3.25981i) q^{42} +(1.92858 + 1.92858i) q^{43} +(-4.31583 + 0.705353i) q^{45} +(-15.4533 - 5.02107i) q^{46} +(10.0926 + 1.59850i) q^{47} +(-0.560143 + 0.0887179i) q^{48} +(2.10777 - 0.684857i) q^{49} +(11.4473 + 1.69773i) q^{50} +(-4.03916 + 5.55943i) q^{51} +(2.19946 - 13.8869i) q^{52} +(-1.03078 - 2.02302i) q^{53} +11.7212 q^{54} +9.53412 q^{56} +(0.340388 + 0.668049i) q^{57} +(-1.75557 + 11.0842i) q^{58} +(-0.703280 + 0.967982i) q^{59} +(-7.30684 - 2.33444i) q^{60} +(-7.01046 + 2.27784i) q^{61} +(2.47730 - 0.392365i) q^{62} +(-5.86408 - 0.928780i) q^{63} +(-12.0542 - 3.91665i) q^{64} +(5.46754 - 7.60385i) q^{65} +(3.89698 + 3.89698i) q^{67} +(20.1132 - 10.2482i) q^{68} +(4.21684 + 5.80399i) q^{69} +(14.0340 + 7.06390i) q^{70} +(4.29785 + 13.2274i) q^{71} +(-5.47253 - 2.78839i) q^{72} +(0.426034 + 2.68987i) q^{73} +(0.158584 - 0.115218i) q^{74} +(-3.64838 - 3.57725i) q^{75} -2.46294i q^{76} +(-7.00485 + 7.00485i) q^{78} +(-3.20120 + 9.85229i) q^{79} +(0.881788 + 0.873150i) q^{80} +(0.559756 + 0.406686i) q^{81} +(-5.63493 + 11.0592i) q^{82} +(0.779264 - 1.52939i) q^{83} +(-8.42528 - 6.12132i) q^{84} +(15.0363 - 0.0740116i) q^{85} +(-1.95071 + 6.00366i) q^{86} +(3.50368 - 3.50368i) q^{87} -10.9954i q^{89} +(-5.98950 - 8.15909i) q^{90} +(10.2868 - 7.47380i) q^{91} +(-3.68661 - 23.2764i) q^{92} +(-0.986720 - 0.502759i) q^{93} +(7.30837 + 22.4928i) q^{94} +(0.737610 - 1.46543i) q^{95} +(3.00127 + 4.13089i) q^{96} +(-3.97547 + 2.02560i) q^{97} +(3.62710 + 3.62710i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{3} + 4 q^{5}+O(q^{10}) \) 160 * q - 8 * q^3 + 4 * q^5	\( 160 q - 8 q^{3} + 4 q^{5} - 128 q^{12} - 32 q^{15} + 24 q^{16} - 32 q^{20} - 96 q^{23} + 52 q^{25} + 8 q^{26} - 32 q^{27} - 16 q^{31} + 40 q^{36} - 36 q^{37} - 32 q^{38} - 32 q^{42} + 256 q^{45} - 32 q^{47} + 16 q^{48} + 68 q^{53} + 320 q^{56} - 132 q^{58} + 64 q^{60} - 352 q^{67} + 8 q^{70} + 16 q^{75} - 992 q^{78} + 164 q^{80} + 40 q^{81} - 100 q^{82} + 80 q^{86} + 96 q^{91} + 56 q^{92} - 24 q^{93} + 68 q^{97}+O(q^{100}) \) 160 * q - 8 * q^3 + 4 * q^5 - 128 * q^12 - 32 * q^15 + 24 * q^16 - 32 * q^20 - 96 * q^23 + 52 * q^25 + 8 * q^26 - 32 * q^27 - 16 * q^31 + 40 * q^36 - 36 * q^37 - 32 * q^38 - 32 * q^42 + 256 * q^45 - 32 * q^47 + 16 * q^48 + 68 * q^53 + 320 * q^56 - 132 * q^58 + 64 * q^60 - 352 * q^67 + 8 * q^70 + 16 * q^75 - 992 * q^78 + 164 * q^80 + 40 * q^81 - 100 * q^82 + 80 * q^86 + 96 * q^91 + 56 * q^92 - 24 * q^93 + 68 * q^97

Introduction

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