LMFDB - Embedded newform 735.2.y.e.263.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(128,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.128"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.8
Character	$\chi$	$=$	735.263
Dual form			735.2.y.e.422.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.689408 - 2.57291i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-4.41251 - 2.54756i) q^{4} +(2.03083 - 0.935797i) q^{5} +(1.64624 - 4.30991i) q^{6} +(-5.82966 + 5.82966i) q^{8} +(2.93649 + 0.614017i) q^{9} +(-1.00765 - 5.87029i) q^{10} +(-1.27225 - 0.734536i) q^{11} +(-7.14817 - 5.17539i) q^{12} +(-2.80707 - 2.80707i) q^{13} +(3.66560 - 1.25036i) q^{15} +(5.88503 + 10.1932i) q^{16} +(-2.02374 + 0.542259i) q^{17} +(3.60425 - 7.13201i) q^{18} +(3.85667 - 2.22665i) q^{19} +(-11.3451 - 1.04446i) q^{20} +(-2.76700 + 2.76700i) q^{22} +(-4.62404 - 1.23901i) q^{23} +(-11.0825 + 9.00486i) q^{24} +(3.24857 - 3.80090i) q^{25} +(-9.15753 + 5.28710i) q^{26} +(4.94975 + 1.58114i) q^{27} +2.00000 q^{29} +(-0.689964 - 10.2932i) q^{30} +(1.70783 - 2.95805i) q^{31} +(14.3563 - 3.84676i) q^{32} +(-2.06102 - 1.49222i) q^{33} +5.58072i q^{34} +(-11.3930 - 10.1903i) q^{36} +(4.03131 + 1.08019i) q^{37} +(-3.07014 - 11.4579i) q^{38} +(-4.33597 - 5.33639i) q^{39} +(-6.38369 + 17.2945i) q^{40} +5.16373i q^{41} +(8.75139 + 8.75139i) q^{43} +(3.74256 + 6.48230i) q^{44} +(6.53812 - 1.50100i) q^{45} +(-6.37569 + 11.0430i) q^{46} +(0.0927452 - 0.346130i) q^{47} +(8.32269 + 18.6101i) q^{48} +(-7.53976 - 10.9786i) q^{50} +(-3.58324 + 0.573612i) q^{51} +(5.23503 + 19.5374i) q^{52} +(2.80532 + 10.4696i) q^{53} +(7.48052 - 11.6452i) q^{54} +(-3.27111 - 0.301149i) q^{55} +(7.04129 - 3.14896i) q^{57} +(1.37882 - 5.14581i) q^{58} +(-1.00423 + 1.73938i) q^{59} +(-19.3598 - 3.82112i) q^{60} +(-2.56401 - 4.44099i) q^{61} +(-6.43339 - 6.43339i) q^{62} -16.0493i q^{64} +(-8.32753 - 3.07384i) q^{65} +(-5.26021 + 4.27407i) q^{66} +(2.75763 + 10.2916i) q^{67} +(10.3112 + 2.76288i) q^{68} +(-7.74578 - 2.95862i) q^{69} +3.29486i q^{71} +(-20.6983 + 13.5392i) q^{72} +(2.35872 - 0.632017i) q^{73} +(5.55843 - 9.62748i) q^{74} +(6.27413 - 5.96953i) q^{75} -22.6901 q^{76} +(-16.7193 + 7.47709i) q^{78} +(-2.90965 + 1.67989i) q^{79} +(21.4903 + 15.1934i) q^{80} +(8.24597 + 3.60611i) q^{81} +(13.2858 + 3.55991i) q^{82} +(-1.29103 + 1.29103i) q^{83} +(-3.60243 + 2.99504i) q^{85} +(28.5498 - 16.4832i) q^{86} +(3.44572 + 0.356394i) q^{87} +(11.6989 - 3.13471i) q^{88} +(-3.56473 - 6.17430i) q^{89} +(0.645513 - 17.8568i) q^{90} +(17.2472 + 17.2472i) q^{92} +(3.46947 - 4.79198i) q^{93} +(-0.826620 - 0.477249i) q^{94} +(5.74857 - 8.13102i) q^{95} +(25.4194 - 4.06918i) q^{96} +(1.57010 - 1.57010i) q^{97} +(-3.28495 - 2.93815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 56 q^{8} + 32 q^{9} + 8 q^{15} + 48 q^{16} + 28 q^{18} + 16 q^{22} + 16 q^{23} - 8 q^{25} + 64 q^{29} - 64 q^{30} + 52 q^{32} - 80 q^{36} + 24 q^{37} - 8 q^{39} + 48 q^{43} - 8 q^{44} - 88 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) $ 32 * q - 4 * q^2 - 56 * q^8 + 32 * q^9 + 8 * q^15 + 48 * q^16 + 28 * q^18 + 16 * q^22 + 16 * q^23 - 8 * q^25 + 64 * q^29 - 64 * q^30 + 52 * q^32 - 80 * q^36 + 24 * q^37 - 8 * q^39 + 48 * q^43 - 8 * q^44 - 88 * q^46 - 104 * q^50 - 40 * q^51 - 8 * q^53 - 8 * q^58 - 28 * q^60 - 112 * q^65 - 16 * q^67 + 4 * q^72 - 8 * q^74 + 16 * q^81 + 48 * q^85 + 80 * q^88 + 160 * q^92 - 16 * q^93 + 72 * q^95 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.689408	−	2.57291i	0.487485	−	1.81932i	−0.0811149	−	0.996705i	$-0.525848\pi$
$2$	0.689408	−	2.57291i	0.487485	−	1.81932i	0.568600	−	0.822614i	$-0.307485\pi$
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$4$	−4.41251	−	2.54756i	−2.20625	−	1.27378i
$5$	2.03083	−	0.935797i	0.908216	−	0.418501i
$5$	2.03083	−	0.935797i	0.908216	−	0.418501i
$6$	1.64624	−	4.30991i	0.672074	−	1.75951i
$7$		0			0
$7$		0			0
$8$	−5.82966	+	5.82966i	−2.06110	+	2.06110i
$9$	2.93649	+	0.614017i	0.978831	+	0.204672i
$10$	−1.00765	−	5.87029i	−0.318645	−	1.85635i
$11$	−1.27225	−	0.734536i	−0.383599	−	0.221471i	0.295784	−	0.955255i	$-0.404419\pi$
$11$	−1.27225	−	0.734536i	−0.383599	−	0.221471i	−0.679383	+	0.733784i	$0.737753\pi$
$12$	−7.14817	−	5.17539i	−2.06350	−	1.49401i
$13$	−2.80707	−	2.80707i	−0.778540	−	0.778540i	0.201042	−	0.979583i	$-0.435567\pi$
$13$	−2.80707	−	2.80707i	−0.778540	−	0.778540i	−0.979583	+	0.201042i	$0.935567\pi$
$14$		0			0
$15$	3.66560	−	1.25036i	0.946453	−	0.322841i
$16$	5.88503	+	10.1932i	1.47126	+	2.54829i
$17$	−2.02374	+	0.542259i	−0.490828	+	0.131517i	−0.495740	−	0.868471i	$-0.665103\pi$
$17$	−2.02374	+	0.542259i	−0.490828	+	0.131517i	0.00491193	+	0.999988i	$0.498436\pi$
$18$	3.60425	−	7.13201i	0.849529	−	1.68103i
$19$	3.85667	−	2.22665i	0.884782	−	0.510829i	0.0125497	−	0.999921i	$-0.496005\pi$
$19$	3.85667	−	2.22665i	0.884782	−	0.510829i	0.872232	+	0.489092i	$0.162672\pi$
$20$	−11.3451	−	1.04446i	−2.53684	−	0.233549i
$21$		0			0
$22$	−2.76700	+	2.76700i	−0.589925	+	0.589925i
$23$	−4.62404	−	1.23901i	−0.964178	−	0.258351i	−0.257810	−	0.966196i	$-0.583001\pi$
$23$	−4.62404	−	1.23901i	−0.964178	−	0.258351i	−0.706368	+	0.707845i	$0.749668\pi$
$24$	−11.0825	+	9.00486i	−2.26221	+	1.83811i
$25$	3.24857	−	3.80090i	0.649713	−	0.760179i
$26$	−9.15753	+	5.28710i	−1.79594	+	1.03689i
$27$	4.94975	+	1.58114i	0.952579	+	0.304290i
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−0.689964	−	10.2932i	−0.125970	−	1.87928i
$31$	1.70783	−	2.95805i	0.306736	−	0.531281i	−0.670911	−	0.741538i	$-0.734097\pi$
$31$	1.70783	−	2.95805i	0.306736	−	0.531281i	0.977646	+	0.210257i	$0.0674300\pi$
$32$	14.3563	−	3.84676i	2.53786	−	0.680018i
$33$	−2.06102	−	1.49222i	−0.358778	−	0.259761i
$34$			5.58072i			0.957086i
$35$		0			0
$36$	−11.3930	−	10.1903i	−1.89884	−	1.69838i
$37$	4.03131	+	1.08019i	0.662743	+	0.177581i	0.574483	−	0.818516i	$-0.305203\pi$
$37$	4.03131	+	1.08019i	0.662743	+	0.177581i	0.0882592	+	0.996098i	$0.471870\pi$
$38$	−3.07014	−	11.4579i	−0.498043	−	1.85872i
$39$	−4.33597	−	5.33639i	−0.694311	−	0.854507i
$40$	−6.38369	+	17.2945i	−1.00935	+	2.73449i
$41$			5.16373i			0.806439i	0.915103	+	0.403219i	$0.132109\pi$
$41$			5.16373i			0.806439i	−0.915103	+	0.403219i	$0.867891\pi$
$42$		0			0
$43$	8.75139	+	8.75139i	1.33457	+	1.33457i	0.901227	+	0.433347i	$0.142668\pi$
$43$	8.75139	+	8.75139i	1.33457	+	1.33457i	0.433347	+	0.901227i	$0.357332\pi$
$44$	3.74256	+	6.48230i	0.564212	+	0.977243i
$45$	6.53812	−	1.50100i	0.974645	−	0.223755i
$46$	−6.37569	+	11.0430i	−0.940045	+	1.62821i
$47$	0.0927452	−	0.346130i	0.0135283	−	0.0504882i	−0.958832	−	0.283975i	$-0.908347\pi$
$47$	0.0927452	−	0.346130i	0.0135283	−	0.0504882i	0.972360	+	0.233487i	$0.0750135\pi$
$48$	8.32269	+	18.6101i	1.20128	+	2.68614i
$49$		0			0
$50$	−7.53976	−	10.9786i	−1.06628	−	1.55261i
$51$	−3.58324	+	0.573612i	−0.501754	+	0.0803217i
$52$	5.23503	+	19.5374i	0.725967	+	2.70935i
$53$	2.80532	+	10.4696i	0.385341	+	1.43811i	0.837629	+	0.546239i	$0.183941\pi$
$53$	2.80532	+	10.4696i	0.385341	+	1.43811i	−0.452289	+	0.891872i	$0.649392\pi$
$54$	7.48052	−	11.6452i	1.01797	−	1.58471i
$55$	−3.27111	−	0.301149i	−0.441077	−	0.0406069i
$56$		0			0
$57$	7.04129	−	3.14896i	0.932642	−	0.417090i
$58$	1.37882	−	5.14581i	0.181047	−	0.675678i
$59$	−1.00423	+	1.73938i	−0.130739	+	0.226447i	−0.923962	−	0.382485i	$-0.875068\pi$
$59$	−1.00423	+	1.73938i	−0.130739	+	0.226447i	0.793222	+	0.608932i	$0.208402\pi$
$60$	−19.3598	−	3.82112i	−2.49935	−	0.493304i
$61$	−2.56401	−	4.44099i	−0.328287	−	0.568611i	0.653885	−	0.756594i	$-0.273138\pi$
$61$	−2.56401	−	4.44099i	−0.328287	−	0.568611i	−0.982172	+	0.187984i	$0.939805\pi$
$62$	−6.43339	−	6.43339i	−0.817042	−	0.817042i
$63$		0			0
$64$		−	16.0493i		−	2.00616i
$65$	−8.32753	−	3.07384i	−1.03290	−	0.381263i
$66$	−5.26021	+	4.27407i	−0.647488	+	0.526102i
$67$	2.75763	+	10.2916i	0.336898	+	1.25732i	0.901796	+	0.432161i	$0.142249\pi$
$67$	2.75763	+	10.2916i	0.336898	+	1.25732i	−0.564898	+	0.825161i	$0.691085\pi$
$68$	10.3112	+	2.76288i	1.25042	+	0.335048i
$69$	−7.74578	−	2.95862i	−0.932482	−	0.356176i
$70$		0			0
$71$			3.29486i			0.391028i	0.980701	+	0.195514i	$0.0626375\pi$
$71$			3.29486i			0.391028i	−0.980701	+	0.195514i	$0.937363\pi$
$72$	−20.6983	+	13.5392i	−2.43931	+	1.59562i
$73$	2.35872	−	0.632017i	0.276067	−	0.0739720i	−0.118129	−	0.992998i	$-0.537690\pi$
$73$	2.35872	−	0.632017i	0.276067	−	0.0739720i	0.394196	+	0.919026i	$0.371023\pi$
$74$	5.55843	−	9.62748i	0.646154	−	1.11917i
$75$	6.27413	−	5.96953i	0.724475	−	0.689302i
$76$	−22.6901			−2.60274
$77$		0			0
$78$	−16.7193	+	7.47709i	−1.89309	+	0.846614i
$79$	−2.90965	+	1.67989i	−0.327361	+	0.189002i	−0.654669	−	0.755916i	$-0.727192\pi$
$79$	−2.90965	+	1.67989i	−0.327361	+	0.189002i	0.327308	+	0.944918i	$0.393859\pi$
$80$	21.4903	+	15.1934i	2.40268	+	1.69868i
$81$	8.24597	+	3.60611i	0.916219	+	0.400679i
$82$	13.2858	+	3.55991i	1.46717	+	0.393127i
$83$	−1.29103	+	1.29103i	−0.141709	+	0.141709i	−0.774402	−	0.632694i	$-0.781949\pi$
$83$	−1.29103	+	1.29103i	−0.141709	+	0.141709i	0.632694	+	0.774402i	$0.281949\pi$
$84$		0			0
$85$	−3.60243	+	2.99504i	−0.390738	+	0.324858i
$86$	28.5498	−	16.4832i	3.07860	−	1.77743i
$87$	3.44572	+	0.356394i	0.369420	+	0.0382094i
$88$	11.6989	−	3.13471i	1.24711	−	0.334162i
$89$	−3.56473	−	6.17430i	−0.377861	−	0.654474i	0.612890	−	0.790168i	$-0.290007\pi$
$89$	−3.56473	−	6.17430i	−0.377861	−	0.654474i	−0.990751	+	0.135694i	$0.956674\pi$
$90$	0.645513	−	17.8568i	0.0680430	−	1.88227i
$91$		0			0
$92$	17.2472	+	17.2472i	1.79814	+	1.79814i
$93$	3.46947	−	4.79198i	0.359767	−	0.496905i
$94$	−0.826620	−	0.477249i	−0.0852593	−	0.0492245i
$95$	5.74857	−	8.13102i	0.589791	−	0.834225i
$96$	25.4194	−	4.06918i	2.59436	−	0.415309i
$97$	1.57010	−	1.57010i	0.159420	−	0.159420i	−0.622890	−	0.782310i	$-0.714042\pi$
$97$	1.57010	−	1.57010i	0.159420	−	0.159420i	0.782310	+	0.622890i	$0.214042\pi$
$98$		0			0
$99$	−3.28495	−	2.93815i	−0.330150	−	0.295295i
$100$	−24.0174	+	8.49556i	−2.40174	+	0.849556i
$101$	13.4629	+	7.77281i	1.33961	+	0.773423i	0.986749	−	0.162253i	$-0.0518760\pi$
$101$	13.4629	+	7.77281i	1.33961	+	0.773423i	0.352859	+	0.935676i	$0.385209\pi$
$102$	−0.994467	+	9.61480i	−0.0984670	+	0.952007i
$103$	4.03772	−	15.0690i	0.397848	−	1.48479i	−0.419027	−	0.907974i	$-0.637629\pi$
$103$	4.03772	−	15.0690i	0.397848	−	1.48479i	0.816875	−	0.576815i	$-0.195705\pi$
$104$	32.7285			3.20929
$105$		0			0
$106$	28.8713			2.80423
$107$	−3.73913	+	13.9546i	−0.361476	+	1.34905i	0.510660	+	0.859783i	$0.329401\pi$
$107$	−3.73913	+	13.9546i	−0.361476	+	1.34905i	−0.872136	+	0.489263i	$0.837266\pi$
$108$	−17.8128	−	19.5866i	−1.71403	−	1.88472i
$109$	−4.12569	−	2.38197i	−0.395169	−	0.228151i	0.289228	−	0.957260i	$-0.406601\pi$
$109$	−4.12569	−	2.38197i	−0.395169	−	0.228151i	−0.684397	+	0.729109i	$0.739935\pi$
$110$	−3.02996	+	8.20865i	−0.288895	+	0.782664i
$111$	6.75289	+	2.57937i	0.640956	+	0.244823i
$112$		0			0
$113$	3.28990	−	3.28990i	0.309488	−	0.309488i	−0.535223	−	0.844711i	$-0.679772\pi$
$113$	3.28990	−	3.28990i	0.309488	−	0.309488i	0.844711	+	0.535223i	$0.179772\pi$
$114$	−3.24766	−	20.2875i	−0.304171	−	1.90010i
$115$	−10.5501	+	1.81094i	−0.983802	+	0.168871i
$116$	−8.82502	−	5.09513i	−0.819382	−	0.473071i
$117$	−6.51934	−	9.96651i	−0.602713	−	0.921404i
$118$	3.78293	+	3.78293i	0.348246	+	0.348246i
$119$		0			0
$120$	−14.0800	+	28.6584i	−1.28532	+	2.61614i
$121$	−4.42091	−	7.65725i	−0.401901	−	0.696113i
$122$	−13.1939	+	3.53529i	−1.19452	+	0.320070i
$123$	−0.920160	+	8.89638i	−0.0829681	+	0.802159i
$124$	−15.0716	+	8.70161i	−1.35347	+	0.781428i
$125$	3.04043	−	10.7590i	0.271944	−	0.962313i
$126$		0			0
$127$	−11.3312	+	11.3312i	−1.00548	+	1.00548i	−0.00549599	+	0.999985i	$0.501749\pi$
$127$	−11.3312	+	11.3312i	−1.00548	+	1.00548i	−0.999985	+	0.00549599i	$0.998251\pi$
$128$	−12.5807	−	3.37100i	−1.11199	−	0.297957i
$129$	13.5179	+	16.6369i	1.19019	+	1.46480i
$130$	−13.6498	+	19.3068i	−1.19716	+	1.69332i
$131$	−0.436883	+	0.252235i	−0.0381706	+	0.0220378i	−0.518964	−	0.854796i	$-0.673682\pi$
$131$	−0.436883	+	0.252235i	−0.0381706	+	0.0220378i	0.480793	+	0.876834i	$0.340349\pi$
$132$	5.29277	+	11.8350i	0.460677	+	1.03010i
$133$		0			0
$134$	28.3805			2.45170
$135$	11.5317	−	1.42093i	0.992494	−	0.122294i
$136$	8.63652	−	14.9589i	0.740575	−	1.28271i
$137$	−11.3916	+	3.05236i	−0.973248	+	0.260781i	−0.710199	−	0.704001i	$-0.751395\pi$
$137$	−11.3916	+	3.05236i	−0.973248	+	0.260781i	−0.263049	+	0.964782i	$0.584728\pi$
$138$	−12.9523	+	17.8895i	−1.10257	+	1.52285i
$139$			7.63765i			0.647817i	0.946088	+	0.323909i	$0.104997\pi$
$139$			7.63765i			0.647817i	−0.946088	+	0.323909i	$0.895003\pi$
$140$		0			0
$141$	0.221466	−	0.579806i	0.0186508	−	0.0488285i
$142$	8.47736	+	2.27150i	0.711404	+	0.190620i
$143$	1.50941	+	5.63319i	0.126223	+	0.471071i
$144$	11.0226	+	33.5457i	0.918547	+	2.79547i
$145$	4.06167	−	1.87159i	0.337303	−	0.155427i
$146$		−	6.50448i		−	0.538315i
$147$		0			0
$148$	−15.0363	−	15.0363i	−1.23598	−	1.23598i
$149$	−3.33119	−	5.76980i	−0.272902	−	0.472680i	0.696702	−	0.717361i	$-0.254650\pi$
$149$	−3.33119	−	5.76980i	−0.272902	−	0.472680i	−0.969604	+	0.244681i	$0.921317\pi$
$150$	−11.0336	−	20.2582i	−0.900889	−	1.65407i
$151$	1.13029	−	1.95772i	0.0919818	−	0.159317i	−0.816363	−	0.577539i	$-0.804013\pi$
$151$	1.13029	−	1.95772i	0.0919818	−	0.159317i	0.908345	+	0.418222i	$0.137347\pi$
$152$	−9.50248	+	35.4637i	−0.770753	+	2.87649i
$153$	−6.27564	+	0.349729i	−0.507356	+	0.0282740i
$154$		0			0
$155$	0.700185	−	7.60549i	0.0562402	−	0.610888i
$156$	5.53771	+	34.5930i	0.443372	+	2.76966i
$157$	−4.15209	−	15.4958i	−0.331373	−	1.23670i	−0.907748	−	0.419516i	$-0.862200\pi$
$157$	−4.15209	−	15.4958i	−0.331373	−	1.23670i	0.576375	−	0.817186i	$-0.304467\pi$
$158$	2.31626	+	8.64439i	0.184271	+	0.687711i
$159$	2.96752	+	18.5376i	0.235340	+	1.47012i
$160$	25.5555	−	21.2467i	2.02034	−	1.67970i
$161$		0			0
$162$	14.9630	−	18.7300i	1.17561	−	1.47157i
$163$	−1.71477	+	6.39962i	−0.134311	+	0.501257i	0.865688	+	0.500583i	$0.166881\pi$
$163$	−1.71477	+	6.39962i	−0.134311	+	0.501257i	−1.00000		0.000673502i	$0.999786\pi$
$164$	13.1549	−	22.7850i	1.02723	−	1.77921i
$165$	−5.58201	−	1.10174i	−0.434559	−	0.0857703i
$166$	2.43164	+	4.21173i	0.188732	+	0.326894i
$167$	12.2531	+	12.2531i	0.948177	+	0.948177i	0.998722	−	0.0505450i	$-0.0160958\pi$
$167$	12.2531	+	12.2531i	0.948177	+	0.948177i	−0.0505450	+	0.998722i	$0.516096\pi$
$168$		0			0
$169$			2.75924i			0.212249i
$170$	5.22242	+	11.3335i	0.400542	+	0.869241i
$171$	12.6923	−	4.17048i	0.970604	−	0.318925i
$172$	−16.3209	−	60.9103i	−1.24445	−	4.64437i
$173$	−20.5004	−	5.49305i	−1.55861	−	0.417629i	−0.626389	−	0.779511i	$-0.715468\pi$
$173$	−20.5004	−	5.49305i	−1.55861	−	0.417629i	−0.932224	+	0.361882i	$0.882134\pi$
$174$	3.29247	−	8.61981i	0.249602	−	0.653466i
$175$		0			0
$176$		−	17.2911i		−	1.30336i
$177$	−2.04010	+	2.81775i	−0.153343	+	0.211795i
$178$	−18.3434	+	4.91511i	−1.37490	+	0.368403i
$179$	8.85329	−	15.3343i	0.661726	−	1.14614i	−0.318436	−	0.947944i	$-0.603158\pi$
$179$	8.85329	−	15.3343i	0.661726	−	1.14614i	0.980162	−	0.198198i	$-0.0635091\pi$
$180$	−32.6734	−	10.0331i	−2.43533	−	0.747824i
$181$	−0.580226			−0.0431278			−0.0215639	−	0.999767i	$-0.506865\pi$
$181$	−0.580226			−0.0431278			−0.0215639	+	0.999767i	$0.506865\pi$
$182$		0			0
$183$	−3.62605	−	8.10810i	−0.268046	−	0.599368i
$184$	34.1796	−	19.7336i	2.51975	−	1.45478i
$185$	9.19775	−	1.57881i	0.676232	−	0.116076i
$186$	−9.93742	−	12.2302i	−0.728647	−	0.896765i
$187$	2.97302	+	0.796617i	0.217408	+	0.0582544i
$188$	−1.29103	+	1.29103i	−0.0941577	+	0.0941577i
$189$		0			0
$190$	−16.9572	−	20.3961i	−1.23021	−	1.47969i
$191$	−2.94668	+	1.70126i	−0.213214	+	0.123099i	−0.602804	−	0.797889i	$-0.705950\pi$
$191$	−2.94668	+	1.70126i	−0.213214	+	0.123099i	0.389590	+	0.920988i	$0.372617\pi$
$192$	2.85994	−	27.6507i	0.206398	−	1.99552i
$193$	19.1698	−	5.13653i	1.37987	−	0.369736i	0.508798	−	0.860886i	$-0.330090\pi$
$193$	19.1698	−	5.13653i	1.37987	−	0.369736i	0.871075	+	0.491150i	$0.163423\pi$
$194$	−2.95729	−	5.12217i	−0.212321	−	0.367750i
$195$	−13.7994	−	6.77973i	−0.988197	−	0.485507i
$196$		0			0
$197$	−10.7101	−	10.7101i	−0.763063	−	0.763063i	0.213812	−	0.976875i	$-0.431412\pi$
$197$	−10.7101	−	10.7101i	−0.763063	−	0.763063i	−0.976875	+	0.213812i	$0.931412\pi$
$198$	−9.82424	+	6.42628i	−0.698178	+	0.456696i
$199$	−9.55941	−	5.51913i	−0.677648	−	0.391240i	0.121320	−	0.992613i	$-0.461287\pi$
$199$	−9.55941	−	5.51913i	−0.677648	−	0.391240i	−0.798968	+	0.601373i	$0.794621\pi$
$200$	3.21990	+	41.0960i	0.227681	+	2.90593i
$201$	2.91708	+	18.2224i	0.205755	+	1.28531i
$202$	29.2801	−	29.2801i	2.06014	−	2.06014i
$203$		0			0
$204$	17.2724	+	6.59747i	1.20931	+	0.461915i
$205$	4.83220	+	10.4867i	0.337496	+	0.732421i
$206$	−35.9874	−	20.7773i	−2.50736	−	1.44762i
$207$	−12.8177	−	6.47757i	−0.890890	−	0.450222i
$208$	12.0932	−	45.1326i	0.838515	−	3.12938i
$209$	−6.54223			−0.452535
$210$		0			0
$211$	−10.4117			−0.716772			−0.358386	−	0.933573i	$-0.616673\pi$
$211$	−10.4117			−0.716772			−0.358386	+	0.933573i	$0.616673\pi$
$212$	14.2935	−	53.3439i	0.981679	−	3.66368i
$213$	−0.587134	+	5.67658i	−0.0402298	+	0.388953i
$214$	33.3262	+	19.2409i	2.27813	+	1.31528i
$215$	25.9621	+	9.58308i	1.77060	+	0.653561i
$216$	−38.0729	+	19.6379i	−2.59053	+	1.33619i
$217$		0			0
$218$	−8.97285	+	8.97285i	−0.607718	+	0.607718i
$219$	4.17637	−	0.668560i	0.282213	−	0.0451771i
$220$	13.6666	+	9.66219i	0.921403	+	0.651425i
$221$	7.20292	+	4.15861i	0.484521	+	0.279738i
$222$	11.2920	−	15.5963i	0.757868	−	1.04676i
$223$	5.40780	+	5.40780i	0.362133	+	0.362133i	0.864598	−	0.502465i	$-0.167573\pi$
$223$	5.40780	+	5.40780i	0.362133	+	0.362133i	−0.502465	+	0.864598i	$0.667573\pi$
$224$		0			0
$225$	11.8732	−	9.16663i	0.791547	−	0.611108i
$226$	−6.19652	−	10.7327i	−0.412187	−	0.713928i
$227$	−13.2868	+	3.56017i	−0.881873	+	0.236297i	−0.671215	−	0.741263i	$-0.734227\pi$
$227$	−13.2868	+	3.56017i	−0.881873	+	0.236297i	−0.210658	+	0.977560i	$0.567561\pi$
$228$	−39.0919	−	4.04332i	−2.58893	−	0.267775i
$229$	−19.0061	+	10.9732i	−1.25596	+	0.725126i	−0.972286	−	0.233796i	$-0.924885\pi$
$229$	−19.0061	+	10.9732i	−1.25596	+	0.725126i	−0.283670	+	0.958922i	$0.591552\pi$
$230$	−2.61394	+	28.3929i	−0.172358	+	1.87217i
$231$		0			0
$232$	−11.6593	+	11.6593i	−0.765472	+	0.765472i
$233$	−10.8802	−	2.91533i	−0.712783	−	0.190990i	−0.115834	−	0.993269i	$-0.536954\pi$
$233$	−10.8802	−	2.91533i	−0.712783	−	0.190990i	−0.596949	+	0.802279i	$0.703621\pi$
$234$	−30.1374	+	9.90266i	−1.97014	+	0.647357i
$235$	−0.135557	−	0.789722i	−0.00884278	−	0.0515158i
$236$	8.86234	−	5.11667i	0.576889	−	0.333067i
$237$	−5.31227	+	2.37572i	−0.345069	+	0.154320i
$238$		0			0
$239$	−22.1980			−1.43587			−0.717935	−	0.696110i	$-0.754912\pi$
$239$	−22.1980			−1.43587			−0.717935	+	0.696110i	$0.754912\pi$
$240$	34.3173	+	30.0057i	2.21517	+	1.93686i
$241$	6.80665	−	11.7895i	0.438455	−	0.759426i	−0.559116	−	0.829090i	$-0.688859\pi$
$241$	6.80665	−	11.7895i	0.438455	−	0.759426i	0.997571	+	0.0696637i	$0.0221926\pi$
$242$	−22.7492	+	6.09562i	−1.46237	+	0.391842i
$243$	13.5640	+	7.68223i	0.870134	+	0.492815i
$244$			26.1279i			1.67267i
$245$		0			0
$246$	22.2552	+	8.50072i	1.41894	+	0.541986i
$247$	−17.0763	−	4.57558i	−1.08654	−	0.291137i
$248$	7.28836	+	27.2005i	0.462811	+	1.72723i
$249$	−2.45431	+	1.99420i	−0.155536	+	0.126377i
$250$	−25.5858	−	15.2401i	−1.61819	−	0.963866i
$251$		−	24.2900i		−	1.53317i	−0.642141	−	0.766587i	$-0.721954\pi$
$251$		−	24.2900i		−	1.53317i	0.642141	−	0.766587i	$-0.278046\pi$
$252$		0			0
$253$	4.97285	+	4.97285i	0.312641	+	0.312641i
$254$	21.3423	+	36.9659i	1.33913	+	2.31945i
$255$	−6.74018	+	4.51810i	−0.422087	+	0.282934i
$256$	−1.29720	+	2.24682i	−0.0810752	+	0.140426i
$257$	6.77944	−	25.3012i	0.422890	−	1.57825i	−0.345598	−	0.938383i	$-0.612324\pi$
$257$	6.77944	−	25.3012i	0.422890	−	1.57825i	0.768488	−	0.639864i	$-0.221009\pi$
$258$	52.1245	−	23.3108i	3.24513	−	1.45127i
$259$		0			0
$260$	28.9145	+	34.7782i	1.79320	+	2.15686i
$261$	5.87298	+	1.22803i	0.363529	+	0.0760134i
$262$	0.347785	+	1.29795i	0.0214862	+	0.0801877i
$263$	0.288266	+	1.07582i	0.0177753	+	0.0663382i	0.974244	−	0.225497i	$-0.0724007\pi$
$263$	0.288266	+	1.07582i	0.0177753	+	0.0663382i	−0.956469	+	0.291835i	$0.905734\pi$
$264$	20.7142	−	3.31596i	1.27487	−	0.204083i
$265$	15.4946	+	18.6368i	0.951824	+	1.14485i
$266$		0			0
$267$	−5.04129	−	11.2727i	−0.308522	−	0.689876i
$268$	14.0505	−	52.4371i	0.858270	−	3.20311i
$269$	14.2540	−	24.6886i	0.869080	−	1.50529i	0.00614101	−	0.999981i	$-0.498045\pi$
$269$	14.2540	−	24.6886i	0.869080	−	1.50529i	0.862939	−	0.505309i	$-0.168621\pi$
$270$	4.29415	−	30.6497i	0.261334	−	1.86528i
$271$	8.65303	+	14.9875i	0.525634	+	0.910425i	0.999554	+	0.0298574i	$0.00950533\pi$
$271$	8.65303	+	14.9875i	0.525634	+	0.910425i	−0.473920	+	0.880568i	$0.657161\pi$
$272$	−17.4371	−	17.4371i	−1.05728	−	1.05728i
$273$		0			0
$274$			31.4138i			1.89778i
$275$	−6.92490	+	2.44952i	−0.417587	+	0.147711i
$276$	26.6410	+	32.7878i	1.60360	+	1.97359i
$277$	5.59484	+	20.8802i	0.336161	+	1.25457i	0.902605	+	0.430470i	$0.141652\pi$
$277$	5.59484	+	20.8802i	0.336161	+	1.25457i	−0.566444	+	0.824100i	$0.691681\pi$
$278$	19.6510	+	5.26546i	1.17859	+	0.315801i
$279$	6.83132	−	7.63765i	0.408981	−	0.457254i
$280$		0			0
$281$			32.2337i			1.92290i	0.274976	+	0.961451i	$0.411330\pi$
$281$			32.2337i			1.92290i	−0.274976	+	0.961451i	$0.588670\pi$
$282$	−1.33911	−	0.969534i	−0.0797426	−	0.0577349i
$283$	−1.04625	+	0.280341i	−0.0621930	+	0.0166646i	−0.289781	−	0.957093i	$-0.593583\pi$
$283$	−1.04625	+	0.280341i	−0.0621930	+	0.0166646i	0.227588	+	0.973757i	$0.426916\pi$
$284$	8.39386	−	14.5386i	0.498084	−	0.862707i
$285$	11.3529	−	12.9842i	0.672488	−	0.769120i
$286$	15.5343			0.918561
$287$		0			0
$288$	44.5192	−	2.48097i	2.62332	−	0.146192i
$289$	−10.9210	+	6.30522i	−0.642410	+	0.370895i
$290$	−2.01529	−	11.7406i	−0.118342	−	0.689430i
$291$	2.98486	−	2.42528i	0.174975	−	0.142172i
$292$	−12.0180	−	3.22021i	−0.703299	−	0.188448i
$293$	0.775387	−	0.775387i	0.0452986	−	0.0452986i	−0.684095	−	0.729393i	$-0.739802\pi$
$293$	0.775387	−	0.775387i	0.0452986	−	0.0452986i	0.729393	+	0.684095i	$0.239802\pi$
$294$		0			0
$295$	−0.411718	+	4.47214i	−0.0239712	+	0.260378i
$296$	−29.7983	+	17.2040i	−1.73199	+	0.999965i
$297$	−5.13593	−	5.64738i	−0.298017	−	0.327694i
$298$	−17.1417	+	4.59310i	−0.992992	+	0.266071i
$299$	9.50200	+	16.4579i	0.549515	+	0.951788i
$300$	−42.8924	+	10.3568i	−2.47639	+	0.597952i
$301$		0			0
$302$	−4.25780	−	4.25780i	−0.245009	−	0.245009i
$303$	21.8096	+	15.7905i	1.25293	+	0.907141i
$304$	45.3933	+	26.2078i	2.60348	+	1.50312i
$305$	−9.36294	−	6.61952i	−0.536120	−	0.379033i
$306$	−3.42666	+	16.3877i	−0.195889	+	0.936825i
$307$	−17.3087	+	17.3087i	−0.987862	+	0.987862i	−0.999927	−	0.0120650i	$-0.996160\pi$
$307$	−17.3087	+	17.3087i	−0.987862	+	0.987862i	0.0120650	+	0.999927i	$0.496160\pi$
$308$		0			0
$309$	9.64166	−	25.2422i	0.548495	−	1.43598i
$310$	−19.0855	−	7.04479i	−1.08398	−	0.400117i
$311$	−0.173147	−	0.0999662i	−0.00981824	−	0.00566856i	0.495083	−	0.868846i	$-0.335138\pi$
$311$	−0.173147	−	0.0999662i	−0.00981824	−	0.00566856i	−0.504901	+	0.863177i	$0.668471\pi$
$312$	56.3866	+	5.83212i	3.19226	+	0.330179i
$313$	−8.13762	+	30.3700i	−0.459966	+	1.71661i	0.213099	+	0.977031i	$0.431644\pi$
$313$	−8.13762	+	30.3700i	−0.459966	+	1.71661i	−0.673064	+	0.739584i	$0.735022\pi$
$314$	−42.7318			−2.41149
$315$		0			0
$316$	17.1185			0.962990
$317$	−0.0160768	+	0.0599993i	−0.000902962	+	0.00336990i	−0.966376	−	0.257134i	$-0.917222\pi$
$317$	−0.0160768	+	0.0599993i	−0.000902962	+	0.00336990i	0.965473	+	0.260504i	$0.0838886\pi$
$318$	49.7412	+	5.14478i	2.78935	+	0.288505i
$319$	−2.54451	−	1.46907i	−0.142465	−	0.0822523i
$320$	−15.0189	−	32.5935i	−0.839582	−	1.82203i
$321$	−8.92868	+	23.3756i	−0.498350	+	1.30470i
$322$		0			0
$323$	−6.59747	+	6.59747i	−0.367093	+	0.367093i
$324$	−27.1986	−	36.9191i	−1.51103	−	2.05106i
$325$	−19.7883	+	1.55043i	−1.09766	+	0.0860022i
$326$	15.2834	+	8.82389i	0.846471	+	0.488710i
$327$	−6.68352	−	4.83898i	−0.369599	−	0.267596i
$328$	−30.1028	−	30.1028i	−1.66215	−	1.66215i
$329$		0			0
$330$	−6.68295	+	13.6024i	−0.367884	+	0.748789i
$331$	4.50072	+	7.79547i	0.247382	+	0.428478i	0.962799	−	0.270220i	$-0.0870965\pi$
$331$	4.50072	+	7.79547i	0.247382	+	0.428478i	−0.715417	+	0.698698i	$0.753763\pi$
$332$	8.98563	−	2.40769i	0.493151	−	0.132139i
$333$	11.1746	+	5.64725i	0.612367	+	0.309467i
$334$	39.9736	−	23.0788i	2.18726	−	1.26281i
$335$	15.2312	+	18.3200i	0.832167	+	1.00093i
$336$		0			0
$337$	0.205859	−	0.205859i	0.0112139	−	0.0112139i	−0.701478	−	0.712691i	$-0.747476\pi$
$337$	0.205859	−	0.205859i	0.0112139	−	0.0112139i	0.712691	+	0.701478i	$0.247476\pi$
$338$	7.09927	+	1.90224i	0.386149	+	0.103468i
$339$	6.25429	−	5.08179i	0.339687	−	0.276005i
$340$	23.5258	−	4.03825i	1.27587	−	0.219005i
$341$	−4.34559	+	2.50893i	−0.235327	+	0.135866i
$342$	−1.98009	−	35.5312i	−0.107071	−	1.92131i
$343$		0			0
$344$	−102.035			−5.50137
$345$	−18.4991	+	1.24001i	−0.995956	+	0.0667597i
$346$	−28.2662	+	48.9585i	−1.51960	+	2.63203i
$347$	−17.7061	+	4.74434i	−0.950514	+	0.254689i	−0.700580	−	0.713574i	$-0.747075\pi$
$347$	−17.7061	+	4.74434i	−0.950514	+	0.254689i	−0.249934	+	0.968263i	$0.580409\pi$
$348$	−14.2963	−	10.3508i	−0.766364	−	0.554860i
$349$			1.81144i			0.0969639i	0.998824	+	0.0484820i	$0.0154383\pi$
$349$			1.81144i			0.0969639i	−0.998824	+	0.0484820i	$0.984562\pi$
$350$		0			0
$351$	−9.45591	−	18.3326i	−0.504719	−	0.978523i
$352$	−21.0905	−	5.65117i	−1.12413	−	0.301209i
$353$	4.87044	+	18.1767i	0.259227	+	0.967450i	0.965690	+	0.259699i	$0.0836233\pi$
$353$	4.87044	+	18.1767i	0.259227	+	0.967450i	−0.706462	+	0.707751i	$0.749710\pi$
$354$	5.84334	+	7.19156i	0.310570	+	0.382227i
$355$	3.08332	+	6.69131i	0.163646	+	0.355138i
$356$			36.3255i			1.92525i
$357$		0			0
$358$	−33.3503	−	33.3503i	−1.76262	−	1.76262i
$359$	−7.18800	−	12.4500i	−0.379368	−	0.657085i	0.611602	−	0.791165i	$-0.290525\pi$
$359$	−7.18800	−	12.4500i	−0.379368	−	0.657085i	−0.990970	+	0.134080i	$0.957192\pi$
$360$	−29.3647	+	46.8653i	−1.54766	+	2.47002i
$361$	0.415956	−	0.720457i	0.0218924	−	0.0379188i
$362$	−0.400012	+	1.49287i	−0.0210242	+	0.0784633i
$363$	−6.25211	−	13.9802i	−0.328151	−	0.733768i
$364$		0			0
$365$	4.19873	−	3.49081i	0.219771	−	0.182717i
$366$	−23.3612	+	3.73970i	−1.22111	+	0.195477i
$367$	4.78509	+	17.8582i	0.249780	+	0.932191i	0.970920	+	0.239402i	$0.0769514\pi$
$367$	4.78509	+	17.8582i	0.249780	+	0.932191i	−0.721141	+	0.692789i	$0.756382\pi$
$368$	−14.5832	−	54.4252i	−0.760201	−	2.83711i
$369$	−3.17061	+	15.1632i	−0.165056	+	0.789367i
$370$	2.27887	−	24.7534i	0.118473	−	1.28687i
$371$		0			0
$372$	−27.5169	+	12.3059i	−1.42669	+	0.638033i
$373$	0.0864069	−	0.322475i	0.00447398	−	0.0166971i	−0.963653	−	0.267158i	$-0.913915\pi$
$373$	0.0864069	−	0.322475i	0.00447398	−	0.0166971i	0.968127	+	0.250461i	$0.0805821\pi$
$374$	4.09924	−	7.10010i	0.211967	−	0.367137i
$375$	7.15545	−	17.9944i	0.369506	−	0.929228i
$376$	1.47715	+	2.55849i	0.0761780	+	0.131944i
$377$	−5.61413	−	5.61413i	−0.289143	−	0.289143i
$378$		0			0
$379$		−	29.4032i		−	1.51034i	−0.655527	−	0.755172i	$-0.727554\pi$
$379$		−	29.4032i		−	1.51034i	0.655527	−	0.755172i	$-0.272446\pi$
$380$	−46.0799	+	21.2334i	−2.36385	+	1.08925i
$381$	−21.5412	+	17.5029i	−1.10359	+	0.896699i
$382$	2.34573	+	8.75439i	0.120018	+	0.447913i
$383$	−18.2404	−	4.88750i	−0.932041	−	0.249740i	−0.239316	−	0.970942i	$-0.576923\pi$
$383$	−18.2404	−	4.88750i	−0.932041	−	0.249740i	−0.692725	+	0.721202i	$0.743590\pi$
$384$	−21.0741	−	8.04960i	−1.07544	−	0.410780i
$385$		0			0
$386$		−	52.8633i		−	2.69067i
$387$	20.3249	+	31.0719i	1.03317	+	1.57947i
$388$	−10.9280	+	2.92816i	−0.554787	+	0.148655i
$389$	−2.16457	+	3.74914i	−0.109748	+	0.190089i	−0.915668	−	0.401935i	$-0.868338\pi$
$389$	−2.16457	+	3.74914i	−0.109748	+	0.190089i	0.805920	+	0.592024i	$0.201671\pi$
$390$	−26.9570	+	30.8306i	−1.36502	+	1.56117i
$391$	10.0297			0.507223
$392$		0			0
$393$	−0.797636	+	0.356713i	−0.0402354	+	0.0179938i
$394$	−34.9397	+	20.1724i	−1.76024	+	1.01627i
$395$	−4.33698	+	6.13442i	−0.218217	+	0.308656i
$396$	7.00974	+	21.3332i	0.352253	+	1.07203i
$397$	−8.87752	−	2.37872i	−0.445550	−	0.119385i	0.0290665	−	0.999577i	$-0.490747\pi$
$397$	−8.87752	−	2.37872i	−0.445550	−	0.119385i	−0.474616	+	0.880193i	$0.657413\pi$
$398$	−20.7905	+	20.7905i	−1.04213	+	1.04213i
$399$		0			0
$400$	57.8611	+	10.7448i	2.89305	+	0.537240i
$401$	25.5964	−	14.7781i	1.27822	−	0.737982i	0.301701	−	0.953403i	$-0.402446\pi$
$401$	25.5964	−	14.7781i	1.27822	−	0.737982i	0.976521	+	0.215421i	$0.0691123\pi$
$402$	48.8956	+	5.05732i	2.43869	+	0.252236i
$403$	−13.0974	+	3.50945i	−0.652430	+	0.174818i
$404$	−39.6034	−	68.5952i	−1.97034	−	3.41274i
$405$	20.1208	−	0.393144i	0.999809	−	0.0195355i
$406$		0			0
$407$	−4.33541	−	4.33541i	−0.214898	−	0.214898i
$408$	17.5451	−	24.2331i	0.868614	−	1.19972i
$409$	−7.17263	−	4.14112i	−0.354664	−	0.204765i	0.312074	−	0.950058i	$-0.398976\pi$
$409$	−7.17263	−	4.14112i	−0.354664	−	0.204765i	−0.666737	+	0.745293i	$0.732310\pi$
$410$	30.3126	−	5.20321i	1.49703	−	0.256968i
$411$	−20.1700	+	3.22885i	−0.994913	+	0.159267i
$412$	−56.2056	+	56.2056i	−2.76905	+	2.76905i
$413$		0			0
$414$	−25.5028	+	28.5130i	−1.25339	+	1.40134i
$415$	−1.41372	+	3.83000i	−0.0693968	+	0.188007i
$416$	−51.0972	−	29.5010i	−2.50525	−	1.44641i
$417$	−1.36101	+	13.1586i	−0.0666488	+	0.644380i
$418$	−4.51026	+	16.8325i	−0.220604	+	0.823306i
$419$	20.3953			0.996374			0.498187	−	0.867070i	$-0.333999\pi$
$419$	20.3953			0.996374			0.498187	+	0.867070i	$0.333999\pi$
$420$		0			0
$421$	−31.3149			−1.52619			−0.763097	−	0.646285i	$-0.776322\pi$
$421$	−31.3149			−1.52619			−0.763097	+	0.646285i	$0.776322\pi$
$422$	−7.17792	+	26.7884i	−0.349416	+	1.30404i
$423$	0.484875	−	0.959460i	0.0235754	−	0.0466505i
$424$	−77.3883	−	44.6802i	−3.75831	−	2.16986i
$425$	−4.51317	+	9.45358i	−0.218921	+	0.458566i
$426$	14.2005	+	5.42412i	0.688018	+	0.262799i
$427$		0			0
$428$	52.0493	−	52.0493i	2.51590	−	2.51590i
$429$	1.59668	+	9.97418i	0.0770886	+	0.481558i
$430$	42.5549	−	60.1915i	2.05218	−	2.90269i
$431$	31.0605	+	17.9328i	1.49613	+	0.863793i	0.999990	−	0.00444774i	$-0.00141576\pi$
$431$	31.0605	+	17.9328i	1.49613	+	0.863793i	0.496143	+	0.868241i	$0.334749\pi$
$432$	13.0126	+	59.7587i	0.626069	+	2.87514i
$433$	10.4546	+	10.4546i	0.502418	+	0.502418i	0.912189	−	0.409771i	$-0.134391\pi$
$433$	10.4546	+	10.4546i	0.502418	+	0.502418i	−0.409771	+	0.912189i	$0.634391\pi$
$434$		0			0
$435$	7.33119	−	2.50072i	0.351504	−	0.119900i
$436$	12.1364	+	21.0209i	0.581229	+	1.00672i
$437$	−20.5922	+	5.51767i	−0.985060	+	0.263946i
$438$	1.15908	−	11.2063i	0.0553829	−	0.535458i
$439$	17.2345	−	9.95036i	0.822559	−	0.474905i	−0.0287391	−	0.999587i	$-0.509149\pi$
$439$	17.2345	−	9.95036i	0.822559	−	0.474905i	0.851298	+	0.524682i	$0.175816\pi$
$440$	20.8251	−	17.3139i	0.992797	−	0.825407i
$441$		0			0
$442$	15.6655	−	15.6655i	0.745130	−	0.745130i
$443$	4.86424	+	1.30337i	0.231107	+	0.0619249i	0.372514	−	0.928027i	$-0.378496\pi$
$443$	4.86424	+	1.30337i	0.231107	+	0.0619249i	−0.141407	+	0.989952i	$0.545163\pi$
$444$	−23.2261	−	28.5849i	−1.10226	−	1.35658i
$445$	−13.0173	−	9.20310i	−0.617077	−	0.436269i
$446$	17.6419	−	10.1856i	0.835370	−	0.482301i
$447$	−4.71102	−	10.5342i	−0.222824	−	0.498249i
$448$		0			0
$449$	29.7534			1.40415			0.702076	−	0.712102i	$-0.252257\pi$
$449$	29.7534			1.40415			0.702076	+	0.712102i	$0.252257\pi$
$450$	−15.3994	−	36.8682i	−0.725934	−	1.73798i
$451$	3.79295	−	6.56957i	0.178603	−	0.309349i
$452$	−22.8980	+	6.13549i	−1.07703	+	0.288589i
$453$	2.29619	−	3.17147i	0.107885	−	0.149008i
$454$			36.6400i			1.71960i
$455$		0			0
$456$	−22.6910	+	59.4057i	−1.06260	+	2.78193i
$457$	−1.94643	−	0.521544i	−0.0910500	−	0.0243968i	0.213006	−	0.977051i	$-0.431674\pi$
$457$	−1.94643	−	0.521544i	−0.0910500	−	0.0243968i	−0.304056	+	0.952654i	$0.598341\pi$
$458$	15.1300	+	56.4658i	0.706977	+	2.63847i
$459$	−10.8744	−	0.515765i	−0.507572	−	0.0240739i
$460$	51.1659	+	18.8862i	2.38562	+	0.880576i
$461$		−	29.6537i		−	1.38111i	−0.723280	−	0.690555i	$-0.757366\pi$
$461$		−	29.6537i		−	1.38111i	0.723280	−	0.690555i	$-0.242634\pi$
$462$		0			0
$463$	6.74148	+	6.74148i	0.313303	+	0.313303i	0.846188	−	0.532885i	$-0.178892\pi$
$463$	6.74148	+	6.74148i	0.313303	+	0.313303i	−0.532885	+	0.846188i	$0.678892\pi$
$464$	11.7701	+	20.3863i	0.546411	+	0.946412i
$465$	2.56160	−	12.9784i	0.118791	−	0.601860i
$466$	−15.0017	+	25.9838i	−0.694943	+	1.20368i
$467$	−7.86464	+	29.3512i	−0.363932	+	1.35821i	0.504931	+	0.863160i	$0.331518\pi$
$467$	−7.86464	+	29.3512i	−0.363932	+	1.35821i	−0.868863	+	0.495053i	$0.835149\pi$
$468$	3.37633	+	60.5858i	0.156071	+	2.80058i
$469$		0			0
$470$	−2.12533	−	0.195665i	−0.0980344	−	0.00902534i
$471$	−4.39217	−	27.4370i	−0.202380	−	1.26423i
$472$	−4.28566	−	15.9943i	−0.197263	−	0.736197i
$473$	−4.70578	−	17.5622i	−0.216372	−	0.807511i
$474$	2.45018	+	15.3058i	0.112541	+	0.703020i
$475$	4.06539	−	21.8922i	0.186533	−	1.00449i
$476$		0			0
$477$	1.80929	+	32.4664i	0.0828418	+	1.48654i
$478$	−15.3035	+	57.1134i	−0.699965	+	2.61230i
$479$	−8.38965	+	14.5313i	−0.383333	+	0.663952i	−0.991536	−	0.129829i	$-0.958557\pi$
$479$	−8.38965	+	14.5313i	−0.383333	+	0.663952i	0.608204	+	0.793781i	$0.291890\pi$
$480$	47.8146	−	32.0512i	2.18243	−	1.46293i
$481$	−8.28399	−	14.3483i	−0.377718	−	0.654226i
$482$	−25.6406	−	25.6406i	−1.16790	−	1.16790i
$483$		0			0
$484$			45.0502i			2.04774i
$485$	1.71932	−	4.65792i	0.0780703	−	0.211505i
$486$	29.1168	−	29.6028i	1.32077	−	1.34281i
$487$	1.93769	+	7.23154i	0.0878049	+	0.327692i	0.995831	−	0.0912222i	$-0.0290774\pi$
$487$	1.93769	+	7.23154i	0.0878049	+	0.327692i	−0.908026	+	0.418915i	$0.862411\pi$
$488$	40.8368	+	10.9422i	1.84859	+	0.495329i
$489$	−4.09470	+	10.7201i	−0.185169	+	0.484779i
$490$		0			0
$491$			35.2820i			1.59226i	0.605129	+	0.796128i	$0.293122\pi$
$491$			35.2820i			1.59226i	−0.605129	+	0.796128i	$0.706878\pi$
$492$	26.7243	−	36.9112i	1.20482	−	1.66408i
$493$	−4.04747	+	1.08452i	−0.182289	+	0.0488442i
$494$	−23.5451	+	40.7813i	−1.05934	+	1.83484i
$495$	−9.42069	−	2.89284i	−0.423428	−	0.130023i
$496$	40.2025			1.80515
$497$		0			0
$498$	3.43886	+	7.68953i	0.154099	+	0.344576i
$499$	16.3625	−	9.44688i	0.732485	−	0.422901i	−0.0868454	−	0.996222i	$-0.527679\pi$
$499$	16.3625	−	9.44688i	0.732485	−	0.422901i	0.819331	+	0.573321i	$0.194345\pi$
$500$	−40.8251	+	39.7284i	−1.82575	+	1.77671i
$501$	18.9270	+	23.2939i	0.845595	+	1.04070i
$502$	−62.4960	−	16.7457i	−2.78933	−	0.747399i
$503$	15.2696	−	15.2696i	0.680836	−	0.680836i	−0.279353	−	0.960189i	$-0.590120\pi$
$503$	15.2696	−	15.2696i	0.680836	−	0.680836i	0.960189	+	0.279353i	$0.0901199\pi$
$504$		0			0
$505$	34.6147	+	3.18673i	1.54033	+	0.141808i
$506$	16.2230	−	9.36636i	0.721201	−	0.416385i
$507$	−0.491689	+	4.75379i	−0.0218367	+	0.211123i
$508$	78.8659	−	21.1321i	3.49911	−	0.937584i
$509$	−3.36179	−	5.82279i	−0.149009	−	0.258091i	0.781853	−	0.623463i	$-0.214275\pi$
$509$	−3.36179	−	5.82279i	−0.149009	−	0.258091i	−0.930861	+	0.365373i	$0.880942\pi$
$510$	6.97790	+	20.4567i	0.308987	+	0.905837i
$511$		0			0
$512$	−13.5329	−	13.5329i	−0.598076	−	0.598076i
$513$	22.6102	−	4.92343i	0.998265	−	0.217375i
$514$	−60.4238	−	34.8857i	−2.66518	−	1.53874i
$515$	−5.90156	−	34.3810i	−0.260054	−	1.51501i
$516$	−17.2645	−	107.848i	−0.760029	−	4.74775i
$517$	−0.372240	+	0.372240i	−0.0163711	+	0.0163711i
$518$		0			0
$519$	−34.3404	−	13.1169i	−1.50738	−	0.575766i
$520$	66.4661	−	30.6272i	2.91473	−	1.34309i
$521$	4.06805	+	2.34869i	0.178224	+	0.102898i	0.586458	−	0.809979i	$-0.300522\pi$
$521$	4.06805	+	2.34869i	0.178224	+	0.102898i	−0.408234	+	0.912877i	$0.633855\pi$
$522$	7.20850	−	14.2640i	0.315507	−	0.624319i
$523$	−1.07047	+	3.99503i	−0.0468082	+	0.174691i	−0.985373	−	0.170413i	$-0.945490\pi$
$523$	−1.07047	+	3.99503i	−0.0468082	+	0.174691i	0.938564	+	0.345104i	$0.112156\pi$
$524$	2.57033			0.112286
$525$		0			0
$526$	2.96673			0.129355
$527$	−1.85217	+	6.91240i	−0.0806819	+	0.301109i
$528$	3.08122	−	29.7901i	0.134093	−	1.29645i
$529$	−0.0720150	−	0.0415779i	−0.00313109	−	0.00180773i
$530$	58.6328	−	27.0177i	2.54685	−	1.17357i
$531$	−4.01692	+	4.49105i	−0.174319	+	0.194895i
$532$		0			0
$533$	14.4949	−	14.4949i	0.627845	−	0.627845i
$534$	−32.4790	+	5.19930i	−1.40550	+	0.224996i
$535$	5.46516	+	31.8386i	0.236279	+	1.37650i
$536$	−76.0727	−	43.9206i	−3.28584	−	1.89708i
$537$	17.9855	−	24.8413i	0.776132	−	1.07198i
$538$	−53.6946	−	53.6946i	−2.31494	−	2.31494i
$539$		0			0
$540$	−54.5038	−	23.1080i	−2.34547	−	0.994408i
$541$	10.7563	+	18.6305i	0.462451	+	0.800989i	0.999082	−	0.0428277i	$-0.0136366\pi$
$541$	10.7563	+	18.6305i	0.462451	+	0.800989i	−0.536631	+	0.843817i	$0.680303\pi$
$542$	44.5269	−	11.9309i	1.91259	−	0.512478i
$543$	−0.999648	−	0.103394i	−0.0428990	−	0.00443708i
$544$	−26.9675	+	15.5697i	−1.15622	+	0.667544i
$545$	−10.6076	−	0.976570i	−0.454380	−	0.0418316i
$546$		0			0
$547$	−11.8220	+	11.8220i	−0.505472	+	0.505472i	−0.913133	−	0.407661i	$-0.866344\pi$
$547$	−11.8220	+	11.8220i	−0.505472	+	0.505472i	0.407661	+	0.913133i	$0.366344\pi$
$548$	58.0415	+	15.5522i	2.47941	+	0.664356i
$549$	−4.80234	−	14.6153i	−0.204959	−	0.623765i
$550$	1.52829	+	19.5058i	0.0651666	+	0.831731i
$551$	7.71335	−	4.45330i	0.328600	−	0.189717i
$552$	62.4031	−	27.9075i	2.65605	−	1.18782i
$553$		0			0
$554$	57.5799			2.44634
$555$	16.1278	−	1.08106i	0.684586	−	0.0458883i
$556$	19.4574	−	33.7012i	0.825178	−	1.42925i
$557$	12.6257	−	3.38304i	0.534968	−	0.143344i	0.0187865	−	0.999824i	$-0.494020\pi$
$557$	12.6257	−	3.38304i	0.534968	−	0.143344i	0.516181	+	0.856479i	$0.327353\pi$
$558$	−14.9414	−	22.8418i	−0.632519	−	0.966971i
$559$		−	49.1315i		−	2.07804i
$560$		0			0
$561$	4.98014	+	1.90224i	0.210261	+	0.0803127i
$562$	82.9343	+	22.2222i	3.49837	+	0.937386i
$563$	−4.21270	−	15.7220i	−0.177544	−	0.662604i	−0.996104	−	0.0881829i	$-0.971894\pi$
$563$	−4.21270	−	15.7220i	−0.177544	−	0.662604i	0.818560	−	0.574421i	$-0.194773\pi$
$564$	−2.45431	+	1.99420i	−0.103345	+	0.0839710i
$565$	3.60256	−	9.75993i	0.151561	−	0.410603i
$566$			2.88517i			0.121273i
$567$		0			0
$568$	−19.2079	−	19.2079i	−0.805946	−	0.805946i
$569$	−12.9622	−	22.4512i	−0.543404	−	0.941203i	−0.998705	−	0.0508658i	$-0.983802\pi$
$569$	−12.9622	−	22.4512i	−0.543404	−	0.941203i	0.455302	−	0.890337i	$-0.349531\pi$
$570$	−25.5804	−	38.1614i	−1.07145	−	1.59840i
$571$	4.70514	−	8.14954i	0.196904	−	0.341048i	−0.750619	−	0.660735i	$-0.770245\pi$
$571$	4.70514	−	8.14954i	0.196904	−	0.341048i	0.947523	+	0.319688i	$0.103578\pi$
$572$	7.69063	−	28.7018i	0.321562	−	1.20008i
$573$	−5.37987	+	2.40595i	−0.224747	+	0.100510i
$574$		0			0
$575$	−19.7308	+	13.5505i	−0.822832	+	0.565094i
$576$	9.85455	−	47.1287i	0.410606	−	1.96369i
$577$	−3.07588	−	11.4793i	−0.128051	−	0.477891i	0.871879	−	0.489720i	$-0.162901\pi$
$577$	−3.07588	−	11.4793i	−0.128051	−	0.477891i	−0.999930	+	0.0118294i	$0.996235\pi$
$578$	8.69374	+	32.4455i	0.361612	+	1.34955i
$579$	33.9422	−	5.43353i	1.41059	−	0.225810i
$580$	−22.6901	−	2.08892i	−0.942157	−	0.0867378i
$581$		0			0
$582$	−4.18223	−	9.35176i	−0.173359	−	0.387643i
$583$	4.12122	−	15.3806i	0.170684	−	0.637000i
$584$	−10.0661	+	17.4350i	−0.416538	+	0.721465i
$585$	−22.5663	−	14.1395i	−0.933003	−	0.584598i
$586$	−1.46044	−	2.52956i	−0.0603302	−	0.104495i
$587$	9.88318	+	9.88318i	0.407922	+	0.407922i	0.881013	−	0.473091i	$-0.156862\pi$
$587$	9.88318	+	9.88318i	0.407922	+	0.407922i	−0.473091	+	0.881013i	$0.656862\pi$
$588$		0			0
$589$		−	15.2110i		−	0.626758i
$590$	11.2225	+	4.14244i	0.462025	+	0.170542i
$591$	−16.5435	−	20.3605i	−0.680508	−	0.837519i
$592$	12.7138	+	47.4487i	0.522536	+	1.95013i
$593$	−39.2616	−	10.5201i	−1.61228	−	0.432009i	−0.663559	−	0.748124i	$-0.730955\pi$
$593$	−39.2616	−	10.5201i	−1.61228	−	0.432009i	−0.948721	+	0.316114i	$0.897622\pi$
$594$	−18.0709	+	9.32092i	−0.741459	+	0.382442i
$595$		0			0
$596$			33.9457i			1.39047i
$597$	−15.4860	−	11.2121i	−0.633801	−	0.458882i
$598$	48.8955	−	13.1015i	1.99949	−	0.535761i
$599$	−6.25861	+	10.8402i	−0.255720	+	0.442920i	−0.965091	−	0.261915i	$-0.915646\pi$
$599$	−6.25861	+	10.8402i	−0.255720	+	0.442920i	0.709371	+	0.704835i	$0.248979\pi$
$600$	−1.77575	+	71.3764i	−0.0724948	+	2.91393i
$601$	−26.6977			−1.08902			−0.544512	−	0.838753i	$-0.683285\pi$
$601$	−26.6977			−1.08902			−0.544512	+	0.838753i	$0.683285\pi$
$602$		0			0
$603$	1.77853	+	31.9145i	0.0724275	+	1.29966i
$604$	−9.97484	+	5.75898i	−0.405870	+	0.234329i
$605$	−16.1438	−	11.4135i	−0.656337	−	0.464025i
$606$	55.6632	−	45.2279i	2.26116	−	1.83726i
$607$	−24.8573	−	6.66049i	−1.00893	−	0.270341i	−0.283745	−	0.958900i	$-0.591577\pi$
$607$	−24.8573	−	6.66049i	−1.00893	−	0.270341i	−0.725181	+	0.688559i	$0.758244\pi$
$608$	46.8022	−	46.8022i	1.89808	−	1.89808i
$609$		0			0
$610$	−23.4863	+	19.5264i	−0.950932	+	0.790601i
$611$	−1.23195	+	0.711267i	−0.0498394	+	0.0287748i
$612$	28.5823	+	14.4444i	1.15537	+	0.583881i
$613$	−5.03137	+	1.34815i	−0.203215	+	0.0544513i	−0.358991	−	0.933341i	$-0.616879\pi$
$613$	−5.03137	+	1.34815i	−0.203215	+	0.0544513i	0.155776	+	0.987792i	$0.450212\pi$
$614$	32.6010	+	56.4666i	1.31567	+	2.27880i
$615$	6.45651	+	18.9281i	0.260352	+	0.763256i
$616$		0			0
$617$	−12.9502	−	12.9502i	−0.521357	−	0.521357i	0.396624	−	0.917981i	$-0.370182\pi$
$617$	−12.9502	−	12.9502i	−0.521357	−	0.521357i	−0.917981	+	0.396624i	$0.870182\pi$
$618$	−58.2987	−	42.2093i	−2.34512	−	1.69791i
$619$	31.5296	+	18.2036i	1.26728	+	0.731665i	0.974473	−	0.224506i	$-0.0720768\pi$
$619$	31.5296	+	18.2036i	1.26728	+	0.731665i	0.292808	+	0.956171i	$0.405410\pi$
$620$	−22.4650	+	31.7755i	−0.902218	+	1.27614i
$621$	−20.9288	−	13.4440i	−0.839843	−	0.539490i
$622$	−0.376572	+	0.376572i	−0.0150992	+	0.0150992i
$623$		0			0
$624$	28.8774	−	75.6021i	1.15602	−	3.02651i
$625$	−3.89363	−	24.6949i	−0.155745	−	0.987797i
$626$	72.5290	+	41.8747i	2.89884	+	1.67365i
$627$	−11.2713	−	1.16581i	−0.450134	−	0.0465578i
$628$	−21.1554	+	78.9532i	−0.844194	+	3.15058i
$629$	−8.74404			−0.348648
$630$		0			0
$631$	36.2436			1.44284			0.721418	−	0.692500i	$-0.243491\pi$
$631$	36.2436			1.44284			0.721418	+	0.692500i	$0.243491\pi$
$632$	7.16911	−	26.7555i	0.285172	−	1.06428i
$633$	−17.9379	−	1.85534i	−0.712969	−	0.0737430i
$634$	0.143289	+	0.0827280i	0.00569074	+	0.00328555i
$635$	−12.4081	+	33.6155i	−0.492399	+	1.33399i
$636$	34.1314	−	89.3571i	1.35340	−	3.54324i
$637$		0			0
$638$	−5.53399	+	5.53399i	−0.219093	+	0.219093i
$639$	−2.02310	+	9.67533i	−0.0800326	+	0.382750i
$640$	−28.7039	+	4.92708i	−1.13462	+	0.194760i
$641$	−32.7179	−	18.8897i	−1.29228	−	0.746098i	−0.313222	−	0.949680i	$-0.601408\pi$
$641$	−32.7179	−	18.8897i	−1.29228	−	0.746098i	−0.979058	+	0.203582i	$0.934742\pi$
$642$	53.9877	+	39.0880i	2.13072	+	1.54268i
$643$	25.4445	+	25.4445i	1.00343	+	1.00343i	0.999994	+	0.00343779i	$0.00109428\pi$
$643$	25.4445	+	25.4445i	1.00343	+	1.00343i	0.00343779	+	0.999994i	$0.498906\pi$
$644$		0			0
$645$	43.0214	+	21.1367i	1.69397	+	0.832256i
$646$	12.4263	+	21.5230i	0.488907	+	0.846812i
$647$	−32.4469	+	8.69412i	−1.27562	+	0.341801i	−0.832181	−	0.554504i	$-0.812908\pi$
$647$	−32.4469	+	8.69412i	−1.27562	+	0.341801i	−0.443438	+	0.896305i	$0.646241\pi$
$648$	−69.0936	+	27.0488i	−2.71425	+	1.06258i
$649$	2.55527	−	1.47529i	0.100303	−	0.0579100i
$650$	−9.65312	+	51.9823i	−0.378627	+	2.03891i
$651$		0			0
$652$	23.8699	−	23.8699i	0.934816	−	0.934816i
$653$	−27.6149	−	7.39939i	−1.08065	−	0.289560i	−0.325790	−	0.945442i	$-0.605630\pi$
$653$	−27.6149	−	7.39939i	−1.08065	−	0.289560i	−0.754864	+	0.655882i	$0.772297\pi$
$654$	−17.0579	+	13.8600i	−0.667017	+	0.541970i
$655$	−0.651196	+	0.921080i	−0.0254443	+	0.0359896i
$656$	−52.6347	+	30.3887i	−2.05504	+	1.18648i
$657$	7.31443	−	0.407619i	0.285363	−	0.0159027i
$658$		0			0
$659$	4.61265			0.179683			0.0898416	−	0.995956i	$-0.471364\pi$
$659$	4.61265			0.179683			0.0898416	+	0.995956i	$0.471364\pi$
$660$	21.8239	+	19.0819i	0.849494	+	0.742764i
$661$	−6.15692	+	10.6641i	−0.239476	+	0.414785i	−0.960564	−	0.278058i	$-0.910309\pi$
$661$	−6.15692	+	10.6641i	−0.239476	+	0.414785i	0.721088	+	0.692844i	$0.243642\pi$
$662$	23.1598	−	6.20566i	0.900133	−	0.241190i
$663$	11.6686	+	8.44823i	0.453170	+	0.328102i
$664$		−	15.0525i		−	0.584150i
$665$		0			0
$666$	22.2337	−	24.8581i	0.861539	−	0.963230i
$667$	−9.24807	−	2.47801i	−0.358087	−	0.0959491i
$668$	−22.8514	−	85.2828i	−0.884149	−	3.29969i
$669$	8.35323	+	10.2805i	0.322955	+	0.397469i
$670$	57.6361	−	26.5584i	2.22668	−	1.02604i
$671$			7.53343i			0.290825i
$672$		0			0
$673$	2.70658	+	2.70658i	0.104331	+	0.104331i	0.757345	−	0.653015i	$-0.226496\pi$
$673$	2.70658	+	2.70658i	0.104331	+	0.104331i	−0.653015	+	0.757345i	$0.726496\pi$
$674$	−0.387735	−	0.671577i	−0.0149350	−	0.0258682i
$675$	22.0893	−	13.6770i	0.850219	−	0.526430i
$676$	7.02934	−	12.1752i	0.270359	−	0.468276i
$677$	9.04100	−	33.7415i	0.347474	−	1.29679i	−0.542222	−	0.840235i	$-0.682417\pi$
$677$	9.04100	−	33.7415i	0.347474	−	1.29679i	0.889696	−	0.456554i	$-0.150917\pi$
$678$	−8.76321	−	19.5951i	−0.336549	−	0.752546i
$679$		0			0
$680$	3.54084	−	38.4610i	0.135785	−	1.47491i
$681$	−23.5256	+	3.76602i	−0.901504	+	0.144314i
$682$	3.45935	+	12.9105i	0.132465	+	0.494367i
$683$	5.16805	+	19.2874i	0.197750	+	0.738013i	0.991538	+	0.129818i	$0.0414393\pi$
$683$	5.16805	+	19.2874i	0.197750	+	0.738013i	−0.793788	+	0.608195i	$0.791894\pi$
$684$	−66.6294	−	13.9321i	−2.54764	−	0.532708i
$685$	−20.2780	+	16.8590i	−0.774783	+	0.644151i
$686$		0			0
$687$	−34.7002	+	15.5184i	−1.32389	+	0.592063i
$688$	−37.7022	+	140.707i	−1.43738	+	5.36439i
$689$	21.5141	−	37.2636i	0.819624	−	1.41963i
$690$	−9.56298	+	48.4512i	−0.364056	+	1.84451i
$691$	18.2704	+	31.6453i	0.695040	+	1.20385i	0.970167	+	0.242437i	$0.0779468\pi$
$691$	18.2704	+	31.6453i	0.695040	+	1.20385i	−0.275127	+	0.961408i	$0.588720\pi$
$692$	76.4641	+	76.4641i	2.90673	+	2.90673i
$693$		0			0
$694$			48.8269i			1.85344i
$695$	7.14729	+	15.5108i	0.271112	+	0.588358i
$696$	−22.1650	+	18.0097i	−0.840164	+	0.682657i
$697$	−2.80007	−	10.4500i	−0.106060	−	0.395823i
$698$	4.66065	+	1.24882i	0.176408	+	0.0472685i
$699$	−18.2255	−	6.96152i	−0.689352	−	0.263309i
$700$		0			0
$701$		−	9.92733i		−	0.374950i	−0.982269	−	0.187475i	$-0.939970\pi$
$701$		−	9.92733i		−	0.374950i	0.982269	−	0.187475i	$-0.0600304\pi$
$702$	−53.6871	+	11.6905i	−2.02629	+	0.441229i
$703$	17.9526	−	4.81039i	0.677096	−	0.181427i
$704$	−11.7888	+	20.4188i	−0.444307	+	0.769563i
$705$	−0.0928200	−	1.38474i	−0.00349580	−	0.0521522i
$706$	50.1247			1.88647
$707$		0			0
$708$	16.1803	−	7.23607i	0.608094	−	0.271948i
$709$	26.7462	−	15.4419i	1.00447	−	0.579934i	0.0949055	−	0.995486i	$-0.469745\pi$
$709$	26.7462	−	15.4419i	1.00447	−	0.579934i	0.909569	+	0.415553i	$0.136412\pi$
$710$	19.3418	−	3.32005i	0.725884	−	0.124599i
$711$	−9.57565	+	3.14640i	−0.359115	+	0.117999i
$712$	56.7752	+	15.2129i	2.12774	+	0.570127i
$713$	−11.5621	+	11.5621i	−0.433005	+	0.433005i
$714$		0			0
$715$	8.33689	+	10.0276i	0.311782	+	0.375010i
$716$	−78.1304	+	45.1086i	−2.91987	+	1.68579i
$717$	−38.2440	−	3.95562i	−1.42825	−	0.147725i
$718$	−36.9881	+	9.91093i	−1.38038	+	0.369873i
$719$	−17.9143	−	31.0285i	−0.668092	−	1.15717i	−0.978437	−	0.206545i	$-0.933778\pi$
$719$	−17.9143	−	31.0285i	−0.668092	−	1.15717i	0.310345	−	0.950624i	$-0.399555\pi$
$720$	53.7769	+	57.8108i	2.00415	+	2.15448i
$721$		0			0
$722$	−1.56691	−	1.56691i	−0.0583142	−	0.0583142i
$723$	13.8277	−	19.0987i	0.514259	−	0.710287i
$724$	2.56025	+	1.47816i	0.0951510	+	0.0549355i
$725$	6.49713	−	7.60179i	0.241297	−	0.282323i
$726$	−40.2799	+	6.44807i	−1.49493	+	0.239310i
$727$	−0.694750	+	0.694750i	−0.0257668	+	0.0257668i	−0.719873	−	0.694106i	$-0.755800\pi$
$727$	−0.694750	+	0.694750i	−0.0257668	+	0.0257668i	0.694106	+	0.719873i	$0.255800\pi$
$728$		0			0
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	−6.08688	−	13.2095i	−0.225285	−	0.488906i
$731$	−22.4560	−	12.9650i	−0.830566	−	0.479527i
$732$	−4.65591	+	45.0147i	−0.172087	+	1.66379i
$733$	10.1120	−	37.7386i	0.373496	−	1.39391i	−0.482034	−	0.876153i	$-0.660102\pi$
$733$	10.1120	−	37.7386i	0.373496	−	1.39391i	0.855530	−	0.517754i	$-0.173232\pi$
$734$	49.2464			1.81772
$735$		0			0
$736$	−71.1503			−2.62263
$737$	4.05116	−	15.1191i	0.149226	−	0.556921i
$738$	36.8277	+	18.6113i	1.35565	+	0.685093i
$739$	−10.1780	−	5.87629i	−0.374405	−	0.216163i	0.300976	−	0.953632i	$-0.402688\pi$
$739$	−10.1780	−	5.87629i	−0.374405	−	0.216163i	−0.675381	+	0.737469i	$0.736021\pi$
$740$	−44.6072	−	16.4653i	−1.63980	−	0.605277i
$741$	−28.6047	−	10.9260i	−1.05082	−	0.401378i
$742$		0			0
$743$	2.23518	−	2.23518i	0.0820008	−	0.0820008i	−0.664917	−	0.746918i	$-0.731533\pi$
$743$	2.23518	−	2.23518i	0.0820008	−	0.0820008i	0.746918	+	0.664917i	$0.231533\pi$
$744$	7.70977	+	48.1614i	0.282654	+	1.76568i
$745$	−12.1645	−	8.60017i	−0.445671	−	0.315086i
$746$	−0.770128	−	0.444633i	−0.0281964	−	0.0162792i
$747$	−4.58380	+	2.99838i	−0.167712	+	0.109705i
$748$	−11.0890	−	11.0890i	−0.405455	−	0.405455i
$749$		0			0
$750$	−41.3649	−	30.8158i	−1.51043	−	1.12523i
$751$	−22.1980	−	38.4481i	−0.810017	−	1.40299i	−0.912852	−	0.408292i	$-0.866125\pi$
$751$	−22.1980	−	38.4481i	−0.810017	−	1.40299i	0.102835	−	0.994698i	$-0.467209\pi$
$752$	4.07397	−	1.09162i	0.148562	−	0.0398071i
$753$	4.32841	−	41.8483i	0.157736	−	1.52504i
$754$	−18.3151	+	10.5742i	−0.666995	+	0.385090i
$755$	0.463402	−	5.03353i	0.0168649	−	0.183189i
$756$		0			0
$757$	18.9607	−	18.9607i	0.689140	−	0.689140i	−0.272902	−	0.962042i	$-0.587983\pi$
$757$	18.9607	−	18.9607i	0.689140	−	0.689140i	0.962042	+	0.272902i	$0.0879835\pi$
$758$	−75.6518	−	20.2708i	−2.74780	−	0.736270i
$759$	7.68138	+	9.45368i	0.278817	+	0.343147i
$760$	13.8889	+	80.9133i	0.503804	+	2.93503i
$761$	−0.211049	+	0.121849i	−0.00765051	+	0.00441702i	−0.503820	−	0.863808i	$-0.668073\pi$
$761$	−0.211049	+	0.121849i	−0.00765051	+	0.00441702i	0.496170	+	0.868225i	$0.334739\pi$
$762$	30.1825	+	67.4902i	1.09340	+	2.44491i
$763$		0			0
$764$	17.3363			0.627206
$765$	−12.4175	+	6.58297i	−0.448956	+	0.238008i
$766$	−25.1502	+	43.5614i	−0.908712	+	1.57394i
$767$	7.70148	−	2.06361i	0.278084	−	0.0745125i
$768$	−2.63528	+	3.63980i	−0.0950924	+	0.131340i
$769$		−	41.4408i		−	1.49439i	−0.664604	−	0.747196i	$-0.731400\pi$
$769$		−	41.4408i		−	1.49439i	0.664604	−	0.747196i	$-0.268600\pi$
$770$		0			0
$771$	16.1886	−	42.3824i	0.583019	−	1.52636i
$772$	−97.6726	−	26.1713i	−3.51531	−	0.941925i
$773$	−7.97687	−	29.7701i	−0.286908	−	1.07076i	−0.947434	−	0.319952i	$-0.896333\pi$
$773$	−7.97687	−	29.7701i	−0.286908	−	1.07076i	0.660525	−	0.750804i	$-0.270334\pi$
$774$	93.9571	−	30.8728i	3.37722	−	1.10970i
$775$	−5.69524	−	16.1007i	−0.204579	−	0.578355i
$776$			18.3063i			0.657159i
$777$		0			0
$778$	8.15392	+	8.15392i	0.292332	+	0.292332i
$779$	11.4978	+	19.9148i	0.411952	+	0.713522i
$780$	43.6182	+	65.0705i	1.56178	+	2.32990i
$781$	2.42019	−	4.19190i	0.0866014	−	0.149998i
$782$	6.91455	−	25.8054i	0.247264	−	0.922801i
$783$	9.89949	+	3.16228i	0.353779	+	0.113011i
$784$		0			0
$785$	−22.9332	−	27.5839i	−0.818520	−	0.984512i
$786$	0.367894	+	2.29816i	0.0131223	+	0.0819727i
$787$	2.12871	+	7.94447i	0.0758805	+	0.283190i	0.993432	−	0.114428i	$-0.0365036\pi$
$787$	2.12871	+	7.94447i	0.0758805	+	0.283190i	−0.917551	+	0.397618i	$0.869837\pi$
$788$	19.9737	+	74.5430i	0.711535	+	2.65549i
$789$	0.304934	+	1.90486i	0.0108559	+	0.0678149i
$790$	12.7933	+	15.3878i	0.455166	+	0.547472i
$791$		0			0
$792$	36.2785	−	2.02173i	1.28910	−	0.0718392i
$793$	−5.26882	+	19.6635i	−0.187101	+	0.698271i
$794$	−12.2405	+	21.2011i	−0.434398	+	0.752399i
$795$	23.3739	+	34.8697i	0.828988	+	1.23670i
$796$	28.1206	+	48.7064i	0.996710	+	1.72635i
$797$	−30.4739	−	30.4739i	−1.07944	−	1.07944i	−0.996559	−	0.0828804i	$-0.973588\pi$
$797$	−30.4739	−	30.4739i	−1.07944	−	1.07944i	−0.0828804	−	0.996559i	$-0.526412\pi$
$798$		0			0
$799$			0.750767i			0.0265602i
$800$	32.0163	−	67.0633i	1.13195	−	2.37105i
$801$	−6.67668	−	20.3196i	−0.235909	−	0.717957i
$802$	−20.3762	−	76.0452i	−0.719510	−	2.68525i
$803$	−3.46513	−	0.928479i	−0.122282	−	0.0327653i
$804$	33.5511	−	87.8380i	1.18326	−	3.09781i
$805$		0			0
$806$			36.1179i			1.27220i
$807$	28.9570	−	39.9950i	1.01934	−	1.40789i
$808$	−123.797	+	33.1713i	−4.35516	+	1.16696i
$809$	3.71153	−	6.42857i	0.130491	−	0.226016i	−0.793375	−	0.608733i	$-0.791678\pi$
$809$	3.71153	−	6.42857i	0.130491	−	0.226016i	0.923866	+	0.382717i	$0.125011\pi$
$810$	12.8599	−	52.0399i	0.451851	−	1.82850i
$811$	−43.7407			−1.53594			−0.767972	−	0.640483i	$-0.778734\pi$
$811$	−43.7407			−1.53594			−0.767972	+	0.640483i	$0.778734\pi$
$812$		0			0
$813$	12.2372	+	27.3633i	0.429179	+	0.959673i
$814$	−14.1435	+	8.16574i	−0.495728	+	0.286209i
$815$	2.50633	+	14.6012i	0.0877928	+	0.511459i
$816$	−26.9344	−	33.1489i	−0.942893	−	1.16044i
$817$	53.2375	+	14.2650i	1.86255	+	0.499068i
$818$	−15.5996	+	15.5996i	−0.545426	+	0.545426i
$819$		0			0
$820$	5.39332	−	58.5828i	0.188343	−	2.04580i
$821$	13.9974	−	8.08141i	0.488513	−	0.282043i	−0.235444	−	0.971888i	$-0.575655\pi$
$821$	13.9974	−	8.08141i	0.488513	−	0.282043i	0.723957	+	0.689845i	$0.242321\pi$
$822$	−5.59784	+	54.1215i	−0.195247	+	1.88771i
$823$	2.23059	−	0.597684i	0.0777534	−	0.0208339i	−0.219733	−	0.975560i	$-0.570519\pi$
$823$	2.23059	−	0.597684i	0.0777534	−	0.0208339i	0.297486	+	0.954726i	$0.403852\pi$
$824$	64.3084	+	111.385i	2.24029	+	3.88030i
$825$	−12.3671	+	2.98618i	−0.430568	+	0.103965i
$826$		0			0
$827$	17.2207	+	17.2207i	0.598823	+	0.598823i	0.939999	−	0.341176i	$-0.110825\pi$
$827$	17.2207	+	17.2207i	0.598823	+	0.598823i	−0.341176	+	0.939999i	$0.610825\pi$
$828$	40.0561	+	61.2362i	1.39204	+	2.12810i
$829$	36.4104	+	21.0215i	1.26458	+	0.730108i	0.973958	−	0.226729i	$-0.0728031\pi$
$829$	36.4104	+	21.0215i	1.26458	+	0.730108i	0.290626	+	0.956837i	$0.406136\pi$
$830$	8.87959	+	6.27780i	0.308215	+	0.217906i
$831$	5.91833	+	36.9707i	0.205305	+	1.28250i
$832$	−45.0515	+	45.0515i	−1.56188	+	1.56188i
$833$		0			0
$834$	32.9176	+	12.5734i	1.13984	+	0.435381i
$835$	36.3506	+	13.4176i	1.25796	+	0.464336i
$836$	28.8676	+	16.6667i	0.998408	+	0.576431i
$837$	13.1304	−	11.9413i	0.453854	−	0.412751i
$838$	14.0607	−	52.4751i	0.485717	−	1.81272i
$839$	2.18571			0.0754590			0.0377295	−	0.999288i	$-0.487987\pi$
$839$	2.18571			0.0754590			0.0377295	+	0.999288i	$0.487987\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−21.5887	+	80.5702i	−0.743996	+	2.77663i
$843$	−5.74395	+	55.5342i	−0.197832	+	1.91270i
$844$	45.9418	+	26.5245i	1.58138	+	0.913011i
$845$	2.58209	+	5.60356i	0.0888267	+	0.192768i
$846$	−2.13432	−	1.90900i	−0.0733795	−	0.0656326i
$847$		0			0
$848$	−90.2090	+	90.2090i	−3.09779	+	3.09779i
$849$	−1.85249	+	0.296551i	−0.0635775	+	0.0101776i
$850$	21.2117	+	18.1293i	0.727557	+	0.621831i
$851$	−17.3025	−	9.98963i	−0.593124	−	0.342440i
$852$	17.0522	−	23.5522i	0.584198	−	0.806885i
$853$	−26.6624	−	26.6624i	−0.912902	−	0.912902i	0.0835974	−	0.996500i	$-0.473359\pi$
$853$	−26.6624	−	26.6624i	−0.912902	−	0.912902i	−0.996500	+	0.0835974i	$0.973359\pi$
$854$		0			0
$855$	21.8732	−	20.3470i	0.748048	−	0.695852i
$856$	−59.5529	−	103.149i	−2.03548	−	3.52555i
$857$	41.0630	−	11.0028i	1.40268	−	0.375848i	0.523376	−	0.852102i	$-0.324672\pi$
$857$	41.0630	−	11.0028i	1.40268	−	0.375848i	0.879308	+	0.476254i	$0.158006\pi$
$858$	26.7634	+	2.76816i	0.913687	+	0.0945035i
$859$	2.40002	−	1.38565i	0.0818878	−	0.0472779i	−0.458497	−	0.888696i	$-0.651612\pi$
$859$	2.40002	−	1.38565i	0.0818878	−	0.0472779i	0.540385	+	0.841418i	$0.318279\pi$
$860$	−90.1446	−	108.426i	−3.07391	−	3.69728i
$861$		0			0
$862$	67.5528	−	67.5528i	2.30086	−	2.30086i
$863$	37.0184	+	9.91905i	1.26012	+	0.337649i	0.826238	−	0.563321i	$-0.190476\pi$
$863$	37.0184	+	9.91905i	1.26012	+	0.337649i	0.433883	+	0.900969i	$0.357143\pi$
$864$	77.1424	+	3.65882i	2.62444	+	0.124476i
$865$	−46.7732	+	8.02870i	−1.59034	+	0.272984i
$866$	34.1063	−	19.6913i	1.15898	−	0.669137i
$867$	−19.9389	+	8.91693i	−0.677159	+	0.302835i
$868$		0			0
$869$	4.93576			0.167434
$870$	−1.37993	−	20.5865i	−0.0467840	−	0.697947i
$871$	21.1484	−	36.6301i	0.716587	−	1.24116i
$872$	37.9374	−	10.1653i	1.28472	−	0.344240i
$873$	5.57466	−	3.64652i	0.188674	−	0.123416i
$874$			56.7858i			1.92081i
$875$		0			0
$876$	−20.1315	−	7.68953i	−0.680179	−	0.259805i
$877$	−42.4319	−	11.3696i	−1.43282	−	0.383924i	−0.542808	−	0.839857i	$-0.682639\pi$
$877$	−42.4319	−	11.3696i	−1.43282	−	0.383924i	−0.890014	+	0.455933i	$0.849306\pi$
$878$	−13.7197	−	51.2027i	−0.463018	−	1.72801i
$879$	1.47405	−	1.19771i	0.0497186	−	0.0403978i
$880$	−16.1809	−	35.1153i	−0.545459	−	1.18374i
$881$			19.6090i			0.660643i	0.943868	+	0.330322i	$0.107157\pi$
$881$			19.6090i			0.660643i	−0.943868	+	0.330322i	$0.892843\pi$
$882$		0			0
$883$	−11.4231	−	11.4231i	−0.384417	−	0.384417i	0.488274	−	0.872691i	$-0.337627\pi$
$883$	−11.4231	−	11.4231i	−0.384417	−	0.384417i	−0.872691	+	0.488274i	$0.837627\pi$
$884$	−21.1886	−	36.6998i	−0.712651	−	1.23435i
$885$	−1.50625	+	7.63150i	−0.0506322	+	0.256530i
$886$	6.70689	−	11.6167i	0.225322	−	0.390270i
$887$	−6.91381	+	25.8027i	−0.232143	+	0.866369i	0.747273	+	0.664517i	$0.231363\pi$
$887$	−6.91381	+	25.8027i	−0.232143	+	0.866369i	−0.979416	+	0.201852i	$0.935304\pi$
$888$	−54.4040	+	24.3302i	−1.82568	+	0.816468i
$889$		0			0
$890$	−32.6529	+	27.1475i	−1.09453	+	0.909986i
$891$	−7.84215	−	10.6449i	−0.262722	−	0.356616i
$892$	−10.0853	−	37.6387i	−0.337679	−	1.26024i
$893$	−0.413022	−	1.54142i	−0.0138213	−	0.0515817i
$894$	−30.3512	+	4.85867i	−1.01510	+	0.162498i
$895$	3.62971	−	39.4264i	0.121328	−	1.31788i
$896$		0			0
$897$	13.4379	+	30.0480i	0.448677	+	1.00327i
$898$	20.5123	−	76.5528i	0.684503	−	2.55460i
$899$	3.41566	−	5.91610i	0.113919	−	0.197313i
$900$	−75.7432	+	10.2001i	−2.52477	+	0.340003i
$901$	−11.3545	−	19.6665i	−0.378272	−	0.655186i
$902$	−14.2880	−	14.2880i	−0.475739	−	0.475739i
$903$		0			0
$904$			38.3580i			1.27577i
$905$	−1.17834	+	0.542974i	−0.0391694	+	0.0180491i
$906$	−6.57687	−	8.09432i	−0.218502	−	0.268916i
$907$	1.56728	+	5.84916i	0.0520406	+	0.194218i	0.987052	−	0.160399i	$-0.0512780\pi$
$907$	1.56728	+	5.84916i	0.0520406	+	0.194218i	−0.935012	+	0.354617i	$0.884611\pi$
$908$	67.6977	+	18.1395i	2.24663	+	0.601982i
$909$	34.7611	+	31.0912i	1.15295	+	1.03123i
$910$		0			0
$911$		−	5.05822i		−	0.167586i	−0.996483	−	0.0837931i	$-0.973297\pi$
$911$		−	5.05822i		−	0.167586i	0.996483	−	0.0837931i	$-0.0267035\pi$
$912$	73.5361	+	53.2413i	2.43502	+	1.76300i
$913$	2.59082	−	0.694208i	0.0857436	−	0.0229749i
$914$	−2.68376	+	4.64842i	−0.0887710	+	0.153756i
$915$	−14.9514	−	13.0730i	−0.494280	−	0.432178i
$916$	111.819			3.69461
$917$		0			0
$918$	−8.82389	+	27.6232i	−0.291232	+	0.911700i
$919$	28.6385	−	16.5344i	0.944696	−	0.545420i	0.0532664	−	0.998580i	$-0.483037\pi$
$919$	28.6385	−	16.5344i	0.944696	−	0.545420i	0.891429	+	0.453160i	$0.149703\pi$
$920$	50.9464	−	72.0607i	1.67965	−	2.37577i
$921$	−32.9049	+	26.7362i	−1.08425	+	0.880987i
$922$	−76.2962	−	20.4435i	−2.51268	−	0.673271i
$923$	9.24889	−	9.24889i	0.304431	−	0.304431i
$924$		0			0
$925$	17.2016	−	11.8135i	0.565586	−	0.388426i
$926$	21.9928	−	12.6976i	0.722728	−	0.417267i
$927$	21.1093	−	41.7706i	0.693321	−	1.37193i
$928$	28.7126	−	7.69353i	0.942538	−	0.252552i
$929$	−13.1172	−	22.7196i	−0.430361	−	0.745406i	0.566544	−	0.824032i	$-0.308280\pi$
$929$	−13.1172	−	22.7196i	−0.430361	−	0.745406i	−0.996904	+	0.0786254i	$0.974947\pi$
$930$	−31.6263	−	15.5382i	−1.03707	−	0.509517i
$931$		0			0
$932$	40.5818	+	40.5818i	1.32930	+	1.32930i
$933$	−0.280494	−	0.203082i	−0.00918294	−	0.00664860i
$934$	70.0960	+	40.4699i	2.29361	+	1.32422i
$935$	6.78317	−	1.16434i	0.221833	−	0.0380781i
$936$	96.1070	+	20.0958i	3.14135	+	0.656853i
$937$	0.973827	−	0.973827i	0.0318135	−	0.0318135i	−0.691021	−	0.722835i	$-0.742839\pi$
$937$	0.973827	−	0.973827i	0.0318135	−	0.0318135i	0.722835	+	0.691021i	$0.242839\pi$
$938$		0			0
$939$	−19.4318	+	50.8732i	−0.634134	+	1.66018i
$940$	−1.41372	+	3.83000i	−0.0461105	+	0.124921i
$941$	10.8470	+	6.26252i	0.353602	+	0.204152i	0.666271	−	0.745710i	$-0.267890\pi$
$941$	10.8470	+	6.26252i	0.353602	+	0.204152i	−0.312668	+	0.949862i	$0.601223\pi$
$942$	−73.6209	−	7.61468i	−2.39870	−	0.248100i
$943$	6.39789	−	23.8773i	0.208344	−	0.777550i
$944$	−23.6397			−0.769406
$945$		0			0
$946$	−48.4301			−1.57460
$947$	−6.83474	+	25.5076i	−0.222099	+	0.828885i	0.761447	+	0.648227i	$0.224489\pi$
$947$	−6.83474	+	25.5076i	−0.222099	+	0.828885i	−0.983546	+	0.180658i	$0.942177\pi$
$948$	29.4928	+	3.05046i	0.957880	+	0.0990744i
$949$	−8.39520	−	4.84697i	−0.272520	−	0.157339i
$950$	−53.5240	−	25.5526i	−1.73655	−	0.829034i
$951$	−0.0383897	+	0.100506i	−0.00124487	+	0.00325912i
$952$		0			0
$953$	−1.55049	+	1.55049i	−0.0502251	+	0.0502251i	−0.731773	−	0.681548i	$-0.761307\pi$
$953$	−1.55049	+	1.55049i	−0.0502251	+	0.0502251i	0.681548	+	0.731773i	$0.261307\pi$
$954$	84.7804	+	17.7275i	2.74487	+	0.573948i
$955$	−4.39217	+	6.21248i	−0.142127	+	0.201031i
$956$	97.9489	+	56.5508i	3.16789	+	1.82898i
$957$	−4.12205	−	2.98443i	−0.133247	−	0.0964729i
$958$	31.6038	+	31.6038i	1.02107	+	1.02107i
$959$		0			0
$960$	−20.0674	−	58.8303i	−0.647673	−	1.89874i
$961$	9.66663	+	16.7431i	0.311827	+	0.540100i
$962$	−42.6279	+	11.4221i	−1.37438	+	0.368263i
$963$	−19.5483	+	38.6818i	−0.629936	+	1.24650i
$964$	−60.0688	+	34.6807i	−1.93469	+	1.11699i
$965$	34.1239	−	28.3705i	1.09849	−	0.913279i
$966$		0			0
$967$	−10.0727	+	10.0727i	−0.323915	+	0.323915i	−0.850267	−	0.526352i	$-0.823560\pi$
$967$	−10.0727	+	10.0727i	−0.323915	+	0.323915i	0.526352	+	0.850267i	$0.323560\pi$
$968$	70.4116	+	18.8667i	2.26311	+	0.606400i
$969$	−12.5422	+	10.1909i	−0.402912	+	0.327378i
$970$	−10.7991	−	7.63485i	−0.346737	−	0.245140i
$971$	31.5916	−	18.2394i	1.01382	−	0.585331i	0.101514	−	0.994834i	$-0.467631\pi$
$971$	31.5916	−	18.2394i	1.01382	−	0.585331i	0.912309	+	0.409504i	$0.134298\pi$
$972$	−40.2805	−	68.4532i	−1.29200	−	2.19564i
$973$		0			0
$974$	19.9419			0.638980
$975$	−34.3688	−	0.855051i	−1.10068	−	0.0273835i
$976$	30.1785	−	52.2707i	0.965991	−	1.67314i
$977$	−20.9383	+	5.61039i	−0.669874	+	0.179492i	−0.577698	−	0.816251i	$-0.696049\pi$
$977$	−20.9383	+	5.61039i	−0.669874	+	0.179492i	−0.0921759	+	0.995743i	$0.529382\pi$
$978$	24.7588	+	17.9258i	0.791700	+	0.573204i
$979$			10.4737i			0.334741i
$980$		0			0
$981$	−10.6525	−	9.52786i	−0.340107	−	0.304201i
$982$	90.7773	+	24.3237i	2.89682	+	0.776201i
$983$	−0.440668	−	1.64460i	−0.0140551	−	0.0524545i	0.958542	−	0.284951i	$-0.0919773\pi$
$983$	−0.440668	−	1.64460i	−0.0140551	−	0.0524545i	−0.972597	+	0.232496i	$0.925311\pi$
$984$	−46.4986	−	57.2271i	−1.48232	−	1.82433i
$985$	−31.7729	−	11.7279i	−1.01237	−	0.373683i
$986$			11.1614i			0.355453i
$987$		0			0
$988$	63.6927	+	63.6927i	2.02634	+	2.02634i
$989$	−29.6237	−	51.3098i	−0.941979	−	1.63156i
$990$	−13.9377	+	22.2442i	−0.442969	+	0.706967i
$991$	4.11480	−	7.12704i	0.130711	−	0.226398i	−0.793240	−	0.608909i	$-0.791607\pi$
$991$	4.11480	−	7.12704i	0.130711	−	0.226398i	0.923951	+	0.382511i	$0.124941\pi$
$992$	13.1392	−	49.0363i	0.417171	−	1.55690i
$993$	6.36498	+	14.2325i	0.201986	+	0.451655i
$994$		0			0
$995$	−24.5783	−	2.26276i	−0.779186	−	0.0717342i
$996$	15.9100	−	2.54690i	0.504129	−	0.0807018i
$997$	10.8852	+	40.6240i	0.344736	+	1.28657i	0.892920	+	0.450216i	$0.148653\pi$
$997$	10.8852	+	40.6240i	0.344736	+	1.28657i	−0.548183	+	0.836358i	$0.684680\pi$
$998$	−13.0255	−	48.6119i	−0.412315	−	1.53878i
$999$	18.2460	+	11.7207i	0.577279	+	0.370827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.y.e.263.8		32
3.2	odd	2		735.2.y.f.263.2		32
5.2	odd	4		735.2.y.f.557.8		32
7.2	even	3	inner	735.2.y.e.128.1		32
7.3	odd	6		735.2.j.d.638.8	yes	16
7.4	even	3		735.2.j.d.638.7	yes	16
7.5	odd	6	inner	735.2.y.e.128.2		32
7.6	odd	2	inner	735.2.y.e.263.7		32
15.2	even	4	inner	735.2.y.e.557.1		32
21.2	odd	6		735.2.y.f.128.8		32
21.5	even	6		735.2.y.f.128.7		32
21.11	odd	6		735.2.j.c.638.1	yes	16
21.17	even	6		735.2.j.c.638.2	yes	16
21.20	even	2		735.2.y.f.263.1		32
35.2	odd	12		735.2.y.f.422.2		32
35.12	even	12		735.2.y.f.422.1		32
35.17	even	12		735.2.j.c.197.2	yes	16
35.27	even	4		735.2.y.f.557.7		32
35.32	odd	12		735.2.j.c.197.1	✓	16
105.2	even	12	inner	735.2.y.e.422.8		32
105.17	odd	12		735.2.j.d.197.8	yes	16
105.32	even	12		735.2.j.d.197.7	yes	16
105.47	odd	12	inner	735.2.y.e.422.7		32
105.62	odd	4	inner	735.2.y.e.557.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.j.c.197.1	✓	16	35.32	odd	12
735.2.j.c.197.2	yes	16	35.17	even	12
735.2.j.c.638.1	yes	16	21.11	odd	6
735.2.j.c.638.2	yes	16	21.17	even	6
735.2.j.d.197.7	yes	16	105.32	even	12
735.2.j.d.197.8	yes	16	105.17	odd	12
735.2.j.d.638.7	yes	16	7.4	even	3
735.2.j.d.638.8	yes	16	7.3	odd	6
735.2.y.e.128.1		32	7.2	even	3	inner
735.2.y.e.128.2		32	7.5	odd	6	inner
735.2.y.e.263.7		32	7.6	odd	2	inner
735.2.y.e.263.8		32	1.1	even	1	trivial
735.2.y.e.422.7		32	105.47	odd	12	inner
735.2.y.e.422.8		32	105.2	even	12	inner
735.2.y.e.557.1		32	15.2	even	4	inner
735.2.y.e.557.2		32	105.62	odd	4	inner
735.2.y.f.128.7		32	21.5	even	6
735.2.y.f.128.8		32	21.2	odd	6
735.2.y.f.263.1		32	21.20	even	2
735.2.y.f.263.2		32	3.2	odd	2
735.2.y.f.422.1		32	35.12	even	12
735.2.y.f.422.2		32	35.2	odd	12
735.2.y.f.557.7		32	35.27	even	4
735.2.y.f.557.8		32	5.2	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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.689408 - 2.57291i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-4.41251 - 2.54756i) q^{4} +(2.03083 - 0.935797i) q^{5} +(1.64624 - 4.30991i) q^{6} +(-5.82966 + 5.82966i) q^{8} +(2.93649 + 0.614017i) q^{9} +(-1.00765 - 5.87029i) q^{10} +(-1.27225 - 0.734536i) q^{11} +(-7.14817 - 5.17539i) q^{12} +(-2.80707 - 2.80707i) q^{13} +(3.66560 - 1.25036i) q^{15} +(5.88503 + 10.1932i) q^{16} +(-2.02374 + 0.542259i) q^{17} +(3.60425 - 7.13201i) q^{18} +(3.85667 - 2.22665i) q^{19} +(-11.3451 - 1.04446i) q^{20} +(-2.76700 + 2.76700i) q^{22} +(-4.62404 - 1.23901i) q^{23} +(-11.0825 + 9.00486i) q^{24} +(3.24857 - 3.80090i) q^{25} +(-9.15753 + 5.28710i) q^{26} +(4.94975 + 1.58114i) q^{27} +2.00000 q^{29} +(-0.689964 - 10.2932i) q^{30} +(1.70783 - 2.95805i) q^{31} +(14.3563 - 3.84676i) q^{32} +(-2.06102 - 1.49222i) q^{33} +5.58072i q^{34} +(-11.3930 - 10.1903i) q^{36} +(4.03131 + 1.08019i) q^{37} +(-3.07014 - 11.4579i) q^{38} +(-4.33597 - 5.33639i) q^{39} +(-6.38369 + 17.2945i) q^{40} +5.16373i q^{41} +(8.75139 + 8.75139i) q^{43} +(3.74256 + 6.48230i) q^{44} +(6.53812 - 1.50100i) q^{45} +(-6.37569 + 11.0430i) q^{46} +(0.0927452 - 0.346130i) q^{47} +(8.32269 + 18.6101i) q^{48} +(-7.53976 - 10.9786i) q^{50} +(-3.58324 + 0.573612i) q^{51} +(5.23503 + 19.5374i) q^{52} +(2.80532 + 10.4696i) q^{53} +(7.48052 - 11.6452i) q^{54} +(-3.27111 - 0.301149i) q^{55} +(7.04129 - 3.14896i) q^{57} +(1.37882 - 5.14581i) q^{58} +(-1.00423 + 1.73938i) q^{59} +(-19.3598 - 3.82112i) q^{60} +(-2.56401 - 4.44099i) q^{61} +(-6.43339 - 6.43339i) q^{62} -16.0493i q^{64} +(-8.32753 - 3.07384i) q^{65} +(-5.26021 + 4.27407i) q^{66} +(2.75763 + 10.2916i) q^{67} +(10.3112 + 2.76288i) q^{68} +(-7.74578 - 2.95862i) q^{69} +3.29486i q^{71} +(-20.6983 + 13.5392i) q^{72} +(2.35872 - 0.632017i) q^{73} +(5.55843 - 9.62748i) q^{74} +(6.27413 - 5.96953i) q^{75} -22.6901 q^{76} +(-16.7193 + 7.47709i) q^{78} +(-2.90965 + 1.67989i) q^{79} +(21.4903 + 15.1934i) q^{80} +(8.24597 + 3.60611i) q^{81} +(13.2858 + 3.55991i) q^{82} +(-1.29103 + 1.29103i) q^{83} +(-3.60243 + 2.99504i) q^{85} +(28.5498 - 16.4832i) q^{86} +(3.44572 + 0.356394i) q^{87} +(11.6989 - 3.13471i) q^{88} +(-3.56473 - 6.17430i) q^{89} +(0.645513 - 17.8568i) q^{90} +(17.2472 + 17.2472i) q^{92} +(3.46947 - 4.79198i) q^{93} +(-0.826620 - 0.477249i) q^{94} +(5.74857 - 8.13102i) q^{95} +(25.4194 - 4.06918i) q^{96} +(1.57010 - 1.57010i) q^{97} +(-3.28495 - 2.93815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 56 q^{8} + 32 q^{9} + 8 q^{15} + 48 q^{16} + 28 q^{18} + 16 q^{22} + 16 q^{23} - 8 q^{25} + 64 q^{29} - 64 q^{30} + 52 q^{32} - 80 q^{36} + 24 q^{37} - 8 q^{39} + 48 q^{43} - 8 q^{44} - 88 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 32 * q - 4 * q^2 - 56 * q^8 + 32 * q^9 + 8 * q^15 + 48 * q^16 + 28 * q^18 + 16 * q^22 + 16 * q^23 - 8 * q^25 + 64 * q^29 - 64 * q^30 + 52 * q^32 - 80 * q^36 + 24 * q^37 - 8 * q^39 + 48 * q^43 - 8 * q^44 - 88 * q^46 - 104 * q^50 - 40 * q^51 - 8 * q^53 - 8 * q^58 - 28 * q^60 - 112 * q^65 - 16 * q^67 + 4 * q^72 - 8 * q^74 + 16 * q^81 + 48 * q^85 + 80 * q^88 + 160 * q^92 - 16 * q^93 + 72 * q^95 - 80 * q^99

Introduction

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Modular forms

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Database

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