LMFDB - Embedded newform 990.2.o.a.329.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.17
Character	$\chi$	$=$	990.329
Dual form			990.2.o.a.659.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.353989 - 1.69549i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.45625 - 1.69686i) q^{5} +(1.15431 + 1.29134i) q^{6} +(1.23806 + 2.14438i) q^{7} +1.00000i q^{8} +(-2.74938 + 1.20037i) q^{9} +(2.10958 + 0.741395i) q^{10} +(3.29655 + 0.364386i) q^{11} +(-1.64533 - 0.541182i) q^{12} +(2.71959 - 4.71047i) q^{13} +(-2.14438 - 1.23806i) q^{14} +(-2.36151 + 3.06974i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.57186i q^{17} +(1.78085 - 2.41424i) q^{18} +6.61333i q^{19} +(-2.19765 + 0.412724i) q^{20} +(3.19752 - 2.85821i) q^{21} +(-3.03709 + 1.33271i) q^{22} +(2.70928 - 4.69261i) q^{23} +(1.69549 - 0.353989i) q^{24} +(-0.758650 + 4.94211i) q^{25} +5.43919i q^{26} +(3.00847 + 4.23664i) q^{27} +2.47612 q^{28} +(-1.38639 - 2.40129i) q^{29} +(0.510260 - 3.83922i) q^{30} +(0.527450 - 0.913571i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.549128 - 5.71826i) q^{33} +(3.28593 + 5.69140i) q^{34} +(1.83578 - 5.22357i) q^{35} +(-0.335140 + 2.98122i) q^{36} -6.20405i q^{37} +(-3.30667 - 5.72731i) q^{38} +(-8.94928 - 2.94359i) q^{39} +(1.69686 - 1.45625i) q^{40} +(1.87077 - 3.24027i) q^{41} +(-1.34003 + 4.07404i) q^{42} +(0.330840 + 0.573031i) q^{43} +(1.96384 - 2.67270i) q^{44} +(6.04066 + 2.91727i) q^{45} +5.41856i q^{46} +(4.34462 + 7.52510i) q^{47} +(-1.29134 + 1.15431i) q^{48} +(0.434422 - 0.752440i) q^{49} +(-1.81405 - 4.65932i) q^{50} +(-11.1425 + 2.32637i) q^{51} +(-2.71959 - 4.71047i) q^{52} -12.4342 q^{53} +(-4.72373 - 2.16480i) q^{54} +(-4.18230 - 6.12441i) q^{55} +(-2.14438 + 1.23806i) q^{56} +(11.2128 - 2.34105i) q^{57} +(2.40129 + 1.38639i) q^{58} +(-11.9694 - 6.91054i) q^{59} +(1.47771 + 3.57999i) q^{60} +(-11.3561 + 6.55647i) q^{61} +1.05490i q^{62} +(-5.97795 - 4.40959i) q^{63} -1.00000 q^{64} +(-11.9534 + 2.24488i) q^{65} +(3.33469 + 4.67759i) q^{66} +(-11.6848 - 6.74621i) q^{67} +(-5.69140 - 3.28593i) q^{68} +(-8.91533 - 2.93243i) q^{69} +(1.02195 + 5.44164i) q^{70} -7.36969i q^{71} +(-1.20037 - 2.74938i) q^{72} +4.44550 q^{73} +(3.10202 + 5.37286i) q^{74} +(8.64786 - 0.463169i) q^{75} +(5.72731 + 3.30667i) q^{76} +(3.29994 + 7.52018i) q^{77} +(9.22210 - 1.92541i) q^{78} +(4.19028 - 2.41926i) q^{79} +(-0.741395 + 2.10958i) q^{80} +(6.11822 - 6.60056i) q^{81} +3.74154i q^{82} +(6.50905 - 3.75800i) q^{83} +(-0.876518 - 4.19824i) q^{84} +(-11.1515 + 9.57030i) q^{85} +(-0.573031 - 0.330840i) q^{86} +(-3.58060 + 3.20063i) q^{87} +(-0.364386 + 3.29655i) q^{88} +0.836570i q^{89} +(-6.69000 + 0.493902i) q^{90} +13.4681 q^{91} +(-2.70928 - 4.69261i) q^{92} +(-1.73566 - 0.570894i) q^{93} +(-7.52510 - 4.34462i) q^{94} +(11.2219 - 9.63069i) q^{95} +(0.541182 - 1.64533i) q^{96} +(10.3774 - 5.99140i) q^{97} +0.868843i q^{98} +(-9.50087 + 2.95524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.353989	−	1.69549i	−0.204376	−	0.978893i
$3$	−0.353989	−	1.69549i	−0.204376	−	0.978893i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.45625	−	1.69686i	−0.651257	−	0.758858i
$5$	−1.45625	−	1.69686i	−0.651257	−	0.758858i
$6$	1.15431	+	1.29134i	0.471245	+	0.527189i
$7$	1.23806	+	2.14438i	0.467942	+	0.810500i	0.999329	−	0.0366297i	$-0.0116622\pi$
$7$	1.23806	+	2.14438i	0.467942	+	0.810500i	−0.531387	+	0.847129i	$0.678329\pi$
$8$			1.00000i			0.353553i
$9$	−2.74938	+	1.20037i	−0.916461	+	0.400124i
$10$	2.10958	+	0.741395i	0.667108	+	0.234450i
$11$	3.29655	+	0.364386i	0.993946	+	0.109867i
$11$	3.29655	+	0.364386i	0.993946	+	0.109867i
$12$	−1.64533	−	0.541182i	−0.474967	−	0.156226i
$13$	2.71959	−	4.71047i	0.754280	−	1.30645i	−0.191452	−	0.981502i	$-0.561320\pi$
$13$	2.71959	−	4.71047i	0.754280	−	1.30645i	0.945732	−	0.324949i	$-0.105347\pi$
$14$	−2.14438	−	1.23806i	−0.573110	−	0.330885i
$15$	−2.36151	+	3.06974i	−0.609739	+	0.792602i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	6.57186i		−	1.59391i	−0.604038	−	0.796955i	$-0.706443\pi$
$17$		−	6.57186i		−	1.59391i	0.604038	−	0.796955i	$-0.293557\pi$
$18$	1.78085	−	2.41424i	0.419750	−	0.569043i
$19$			6.61333i			1.51720i	0.651555	+	0.758601i	$0.274117\pi$
$19$			6.61333i			1.51720i	−0.651555	+	0.758601i	$0.725883\pi$
$20$	−2.19765	+	0.412724i	−0.491409	+	0.0922879i
$21$	3.19752	−	2.85821i	0.697756	−	0.623712i
$22$	−3.03709	+	1.33271i	−0.647509	+	0.284134i
$23$	2.70928	−	4.69261i	0.564924	−	0.978476i	−0.432133	−	0.901810i	$-0.642239\pi$
$23$	2.70928	−	4.69261i	0.564924	−	0.978476i	0.997057	−	0.0766666i	$-0.0244277\pi$
$24$	1.69549	−	0.353989i	0.346091	−	0.0722577i
$25$	−0.758650	+	4.94211i	−0.151730	+	0.988422i
$26$			5.43919i			1.06671i
$27$	3.00847	+	4.23664i	0.578980	+	0.815341i
$28$	2.47612			0.467942
$29$	−1.38639	−	2.40129i	−0.257445	−	0.445908i	0.708112	−	0.706101i	$-0.249547\pi$
$29$	−1.38639	−	2.40129i	−0.257445	−	0.445908i	−0.965557	+	0.260192i	$0.916214\pi$
$30$	0.510260	−	3.83922i	0.0931602	−	0.700943i
$31$	0.527450	−	0.913571i	0.0947329	−	0.164082i	−0.814764	−	0.579792i	$-0.803134\pi$
$31$	0.527450	−	0.913571i	0.0947329	−	0.164082i	0.909497	+	0.415710i	$0.136467\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.549128	−	5.71826i	−0.0955909	−	0.995421i
$34$	3.28593	+	5.69140i	0.563532	+	0.976067i
$35$	1.83578	−	5.22357i	0.310303	−	0.882945i
$36$	−0.335140	+	2.98122i	−0.0558567	+	0.496870i
$37$		−	6.20405i		−	1.01994i	−0.860192	−	0.509970i	$-0.829657\pi$
$37$		−	6.20405i		−	1.01994i	0.860192	−	0.509970i	$-0.170343\pi$
$38$	−3.30667	−	5.72731i	−0.536412	−	0.929093i
$39$	−8.94928	−	2.94359i	−1.43303	−	0.471352i
$40$	1.69686	−	1.45625i	0.268297	−	0.230254i
$41$	1.87077	−	3.24027i	0.292165	−	0.506045i	−0.682156	−	0.731206i	$-0.738958\pi$
$41$	1.87077	−	3.24027i	0.292165	−	0.506045i	0.974321	+	0.225162i	$0.0722910\pi$
$42$	−1.34003	+	4.07404i	−0.206771	+	0.628638i
$43$	0.330840	+	0.573031i	0.0504526	+	0.0873864i	0.890149	−	0.455670i	$-0.150600\pi$
$43$	0.330840	+	0.573031i	0.0504526	+	0.0873864i	−0.839696	+	0.543056i	$0.817267\pi$
$44$	1.96384	−	2.67270i	0.296060	−	0.402925i
$45$	6.04066	+	2.91727i	0.900488	+	0.434880i
$46$			5.41856i			0.798923i
$47$	4.34462	+	7.52510i	0.633728	+	1.09765i	0.986783	+	0.162046i	$0.0518093\pi$
$47$	4.34462	+	7.52510i	0.633728	+	1.09765i	−0.353056	+	0.935602i	$0.614857\pi$
$48$	−1.29134	+	1.15431i	−0.186389	+	0.166610i
$49$	0.434422	−	0.752440i	0.0620602	−	0.107491i
$50$	−1.81405	−	4.65932i	−0.256545	−	0.658927i
$51$	−11.1425	+	2.32637i	−1.56027	+	0.325757i
$52$	−2.71959	−	4.71047i	−0.377140	−	0.653225i
$53$	−12.4342			−1.70797			−0.853984	−	0.520299i	$-0.825821\pi$
$53$	−12.4342			−1.70797			−0.853984	+	0.520299i	$0.825821\pi$
$54$	−4.72373	−	2.16480i	−0.642818	−	0.294592i
$55$	−4.18230	−	6.12441i	−0.563941	−	0.825815i
$56$	−2.14438	+	1.23806i	−0.286555	+	0.165443i
$57$	11.2128	−	2.34105i	1.48518	−	0.310079i
$58$	2.40129	+	1.38639i	0.315305	+	0.182041i
$59$	−11.9694	−	6.91054i	−1.55828	−	0.899675i	−0.997421	−	0.0717663i	$-0.977136\pi$
$59$	−11.9694	−	6.91054i	−1.55828	−	0.899675i	−0.560862	−	0.827909i	$-0.689530\pi$
$60$	1.47771	+	3.57999i	0.190772	+	0.462175i
$61$	−11.3561	+	6.55647i	−1.45400	+	0.839470i	−0.998705	−	0.0508683i	$-0.983801\pi$
$61$	−11.3561	+	6.55647i	−1.45400	+	0.839470i	−0.455299	+	0.890338i	$0.650468\pi$
$62$			1.05490i			0.133973i
$63$	−5.97795	−	4.40959i	−0.753151	−	0.555557i
$64$	−1.00000			−0.125000
$65$	−11.9534	+	2.24488i	−1.48264	+	0.278444i
$66$	3.33469	+	4.67759i	0.410472	+	0.575772i
$67$	−11.6848	−	6.74621i	−1.42752	−	0.824180i	−0.430597	−	0.902544i	$-0.641697\pi$
$67$	−11.6848	−	6.74621i	−1.42752	−	0.824180i	−0.996925	+	0.0783639i	$0.975030\pi$
$68$	−5.69140	−	3.28593i	−0.690183	−	0.398478i
$69$	−8.91533	−	2.93243i	−1.07328	−	0.353023i
$70$	1.02195	+	5.44164i	0.122147	+	0.650400i
$71$		−	7.36969i		−	0.874621i	−0.899310	−	0.437311i	$-0.855931\pi$
$71$		−	7.36969i		−	0.874621i	0.899310	−	0.437311i	$-0.144069\pi$
$72$	−1.20037	−	2.74938i	−0.141465	−	0.324018i
$73$	4.44550			0.520307			0.260153	−	0.965567i	$-0.416227\pi$
$73$	4.44550			0.520307			0.260153	+	0.965567i	$0.416227\pi$
$74$	3.10202	+	5.37286i	0.360603	+	0.624583i
$75$	8.64786	−	0.463169i	0.998569	−	0.0534822i
$76$	5.72731	+	3.30667i	0.656968	+	0.379301i
$77$	3.29994	+	7.52018i	0.376063	+	0.857004i
$78$	9.22210	−	1.92541i	1.04420	−	0.218010i
$79$	4.19028	−	2.41926i	0.471443	−	0.272188i	−0.245400	−	0.969422i	$-0.578919\pi$
$79$	4.19028	−	2.41926i	0.471443	−	0.272188i	0.716844	+	0.697234i	$0.245586\pi$
$80$	−0.741395	+	2.10958i	−0.0828904	+	0.235858i
$81$	6.11822	−	6.60056i	0.679802	−	0.733396i
$82$			3.74154i			0.413184i
$83$	6.50905	−	3.75800i	0.714461	−	0.412494i	−0.0982494	−	0.995162i	$-0.531324\pi$
$83$	6.50905	−	3.75800i	0.714461	−	0.412494i	0.812711	+	0.582667i	$0.197991\pi$
$84$	−0.876518	−	4.19824i	−0.0956360	−	0.458065i
$85$	−11.1515	+	9.57030i	−1.20955	+	1.03804i
$86$	−0.573031	−	0.330840i	−0.0617915	−	0.0356754i
$87$	−3.58060	+	3.20063i	−0.383881	+	0.343144i
$88$	−0.364386	+	3.29655i	−0.0388437	+	0.351413i
$89$			0.836570i			0.0886763i	0.999017	+	0.0443381i	$0.0141179\pi$
$89$			0.836570i			0.0886763i	−0.999017	+	0.0443381i	$0.985882\pi$
$90$	−6.69000	+	0.493902i	−0.705188	+	0.0520619i
$91$	13.4681			1.41184
$92$	−2.70928	−	4.69261i	−0.282462	−	0.489238i
$93$	−1.73566	−	0.570894i	−0.179980	−	0.0591989i
$94$	−7.52510	−	4.34462i	−0.776155	−	0.448113i
$95$	11.2219	−	9.63069i	1.15134	−	0.988088i
$96$	0.541182	−	1.64533i	0.0552342	−	0.167926i
$97$	10.3774	−	5.99140i	1.05367	−	0.608335i	0.129993	−	0.991515i	$-0.458504\pi$
$97$	10.3774	−	5.99140i	1.05367	−	0.608335i	0.923674	+	0.383180i	$0.125171\pi$
$98$			0.868843i			0.0877664i
$99$	−9.50087	+	2.95524i	−0.954873	+	0.297013i
$100$	3.90067	+	3.12806i	0.390067	+	0.312806i
$101$	−3.42432	−	5.93109i	−0.340732	−	0.590165i	0.643837	−	0.765163i	$-0.277342\pi$
$101$	−3.42432	−	5.93109i	−0.340732	−	0.590165i	−0.984569	+	0.174998i	$0.944008\pi$
$102$	8.48654	−	7.58596i	0.840292	−	0.751122i
$103$	−3.17923	−	1.83553i	−0.313259	−	0.180860i	0.335125	−	0.942174i	$-0.391221\pi$
$103$	−3.17923	−	1.83553i	−0.313259	−	0.180860i	−0.648384	+	0.761314i	$0.724555\pi$
$104$	4.71047	+	2.71959i	0.461900	+	0.266678i
$105$	−9.50637	−	1.26346i	−0.927726	−	0.123301i
$106$	10.7683	−	6.21710i	1.04591	−	0.603858i
$107$		−	2.58804i		−	0.250196i	−0.992144	−	0.125098i	$-0.960076\pi$
$107$		−	2.58804i		−	0.250196i	0.992144	−	0.125098i	$-0.0399245\pi$
$108$	5.17327	−	0.487093i	0.497798	−	0.0468705i
$109$			4.50470i			0.431472i	0.976452	+	0.215736i	$0.0692150\pi$
$109$			4.50470i			0.431472i	−0.976452	+	0.215736i	$0.930785\pi$
$110$	6.68418	+	3.21274i	0.637312	+	0.306323i
$111$	−10.5189	+	2.19617i	−0.998411	+	0.208451i
$112$	1.23806	−	2.14438i	0.116986	−	0.202625i
$113$	−0.996555	+	1.72608i	−0.0937480	+	0.162376i	−0.909085	−	0.416610i	$-0.863218\pi$
$113$	−0.996555	+	1.72608i	−0.0937480	+	0.162376i	0.815337	+	0.578986i	$0.196551\pi$
$114$	−8.54009	+	7.63383i	−0.799852	+	0.714974i
$115$	−11.9081	+	2.23637i	−1.11043	+	0.208543i
$116$	−2.77277			−0.257445
$117$	−1.82289	+	16.2154i	−0.168526	+	1.49912i
$118$	13.8211			1.27233
$119$	14.0926	−	8.13635i	1.29186	−	0.745858i
$120$	−3.06974	−	2.36151i	−0.280227	−	0.215575i
$121$	10.7344	+	2.40243i	0.975859	+	0.218403i
$122$	6.55647	−	11.3561i	0.593595	−	1.02814i
$123$	−6.15608	−	2.02485i	−0.555075	−	0.182575i
$124$	−0.527450	−	0.913571i	−0.0473664	−	0.0820411i
$125$	9.49084	−	5.90965i	0.848887	−	0.528575i
$126$	7.38185	+	0.829846i	0.657628	+	0.0739285i
$127$	−9.10368			−0.807821			−0.403910	−	0.914799i	$-0.632349\pi$
$127$	−9.10368			−0.807821			−0.403910	+	0.914799i	$0.632349\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	0.854456	−	0.763783i	0.0752307	−	0.0672473i
$130$	9.22952	−	7.92084i	0.809483	−	0.694703i
$131$	−2.43368	+	4.21525i	−0.212631	+	0.368288i	−0.952537	−	0.304422i	$-0.901537\pi$
$131$	−2.43368	+	4.21525i	−0.212631	+	0.368288i	0.739906	+	0.672710i	$0.234870\pi$
$132$	−5.22672	−	2.38357i	−0.454928	−	0.207463i
$133$	−14.1815	+	8.18769i	−1.22969	+	0.709963i
$134$	13.4924			1.16557
$135$	2.80787	−	11.2746i	0.241663	−	0.970360i
$136$	6.57186			0.563532
$137$	−2.71986	−	4.71093i	−0.232373	−	0.402482i	0.726133	−	0.687554i	$-0.241316\pi$
$137$	−2.71986	−	4.71093i	−0.232373	−	0.402482i	−0.958506	+	0.285072i	$0.907982\pi$
$138$	9.18712	−	1.91811i	0.782059	−	0.163280i
$139$	18.5789	+	10.7265i	1.57584	+	0.909814i	0.995430	+	0.0954917i	$0.0304423\pi$
$139$	18.5789	+	10.7265i	1.57584	+	0.909814i	0.580413	+	0.814322i	$0.302891\pi$
$140$	−3.60586	−	4.20162i	−0.304750	−	0.355102i
$141$	11.2208	−	10.0301i	0.944961	−	0.844684i
$142$	3.68485	+	6.38234i	0.309225	+	0.535594i
$143$	10.6817	−	14.5373i	0.893249	−	1.21567i
$144$	2.41424	+	1.78085i	0.201187	+	0.148404i
$145$	−2.05572	+	5.84938i	−0.170718	+	0.485765i
$146$	−3.84992	+	2.22275i	−0.318621	+	0.183956i
$147$	−1.42954	−	0.470203i	−0.117906	−	0.0387817i
$148$	−5.37286	−	3.10202i	−0.441647	−	0.254985i
$149$	−0.368057	+	0.637494i	−0.0301524	+	0.0522256i	−0.880708	−	0.473660i	$-0.842933\pi$
$149$	−0.368057	+	0.637494i	−0.0301524	+	0.0522256i	0.850555	+	0.525885i	$0.176266\pi$
$150$	−7.25768	+	4.72505i	−0.592587	+	0.385798i
$151$	−3.49802	+	2.01958i	−0.284665	+	0.164351i	−0.635533	−	0.772073i	$-0.719220\pi$
$151$	−3.49802	+	2.01958i	−0.284665	+	0.164351i	0.350869	+	0.936425i	$0.385886\pi$
$152$	−6.61333			−0.536412
$153$	7.88867	+	18.0686i	0.637761	+	1.46076i
$154$	−6.61792	−	4.86270i	−0.533287	−	0.391848i
$155$	−2.31830	+	0.435383i	−0.186210	+	0.0349708i
$156$	−7.02386	+	6.27850i	−0.562359	+	0.502683i
$157$	9.26317	+	5.34809i	0.739281	+	0.426824i	0.821808	−	0.569765i	$-0.192966\pi$
$157$	9.26317	+	5.34809i	0.739281	+	0.426824i	−0.0825265	+	0.996589i	$0.526299\pi$
$158$	−2.41926	+	4.19028i	−0.192466	+	0.333361i
$159$	4.40157	+	21.0821i	0.349067	+	1.67192i
$160$	−0.412724	−	2.19765i	−0.0326287	−	0.173739i
$161$	13.4170			1.05741
$162$	−1.99825	+	8.77536i	−0.156998	+	0.689458i
$163$		−	11.9850i		−	0.938736i	−0.883003	−	0.469368i	$-0.844482\pi$
$163$		−	11.9850i		−	0.938736i	0.883003	−	0.469368i	$-0.155518\pi$
$164$	−1.87077	−	3.24027i	−0.146083	−	0.253022i
$165$	−8.90340	+	9.25902i	−0.693128	+	0.720814i
$166$	−3.75800	+	6.50905i	−0.291678	+	0.505200i
$167$	−5.74198	−	3.31514i	−0.444328	−	0.256533i	0.261104	−	0.965311i	$-0.415914\pi$
$167$	−5.74198	−	3.31514i	−0.444328	−	0.256533i	−0.705432	+	0.708778i	$0.749247\pi$
$168$	2.85821	+	3.19752i	0.220515	+	0.246694i
$169$	−8.29238	−	14.3628i	−0.637875	−	1.10483i
$170$	4.87234	−	13.8639i	0.373692	−	1.06331i
$171$	−7.93845	−	18.1826i	−0.607068	−	1.39046i
$172$	0.661679			0.0504526
$173$	0.994669	−	0.574273i	0.0756233	−	0.0436611i	−0.461712	−	0.887030i	$-0.652764\pi$
$173$	0.994669	−	0.574273i	0.0756233	−	0.0436611i	0.537335	+	0.843369i	$0.319431\pi$
$174$	1.50057	−	4.56213i	0.113758	−	0.345854i
$175$	−11.5370	+	4.49179i	−0.872116	+	0.339547i
$176$	−1.33271	−	3.03709i	−0.100456	−	0.228929i
$177$	−7.47972	+	22.7403i	−0.562210	+	1.70926i
$178$	−0.418285	−	0.724491i	−0.0313518	−	0.0543029i
$179$			9.36347i			0.699859i	0.936776	+	0.349929i	$0.113794\pi$
$179$			9.36347i			0.699859i	−0.936776	+	0.349929i	$0.886206\pi$
$180$	5.54676	−	3.77273i	0.413431	−	0.281203i
$181$	9.43766			0.701495			0.350748	−	0.936470i	$-0.385927\pi$
$181$	9.43766			0.701495			0.350748	+	0.936470i	$0.385927\pi$
$182$	−11.6637	+	6.73403i	−0.864570	+	0.499160i
$183$	15.1364	+	16.9333i	1.11891	+	1.25175i
$184$	4.69261	+	2.70928i	0.345944	+	0.199731i
$185$	−10.5274	+	9.03467i	−0.773989	+	0.664242i
$186$	1.78858	−	0.373423i	0.131145	−	0.0273807i
$187$	2.39470	−	21.6644i	0.175118	−	1.58426i
$188$	8.68923			0.633728
$189$	−5.36030	+	11.6965i	−0.389905	+	0.850796i
$190$	−4.90309	+	13.9514i	−0.355707	+	1.01214i
$191$	22.4274	−	12.9484i	1.62279	−	0.936916i	0.636616	−	0.771181i	$-0.280334\pi$
$191$	22.4274	−	12.9484i	1.62279	−	0.936916i	0.986170	−	0.165735i	$-0.0529996\pi$
$192$	0.353989	+	1.69549i	0.0255470	+	0.122362i
$193$	6.48628	−	11.2346i	0.466893	−	0.808682i	−0.532392	−	0.846498i	$-0.678707\pi$
$193$	6.48628	−	11.2346i	0.466893	−	0.808682i	0.999285	+	0.0378159i	$0.0120400\pi$
$194$	−5.99140	+	10.3774i	−0.430158	+	0.745055i
$195$	8.03756	+	19.4723i	0.575582	+	1.39444i
$196$	−0.434422	−	0.752440i	−0.0310301	−	0.0537457i
$197$			9.55969i			0.681100i	0.940226	+	0.340550i	$0.110613\pi$
$197$			9.55969i			0.681100i	−0.940226	+	0.340550i	$0.889387\pi$
$198$	6.75037	−	7.30975i	0.479728	−	0.519481i
$199$	5.53098			0.392080			0.196040	−	0.980596i	$-0.437192\pi$
$199$	5.53098			0.392080			0.196040	+	0.980596i	$0.437192\pi$
$200$	−4.94211	−	0.758650i	−0.349460	−	0.0536446i
$201$	−7.30185	+	22.1995i	−0.515033	+	1.56583i
$202$	5.93109	+	3.42432i	0.417310	+	0.240934i
$203$	3.43285	−	5.94587i	0.240939	−	0.417319i
$204$	−3.55657	+	10.8129i	−0.249010	+	0.757055i
$205$	−8.22258	+	1.54422i	−0.574290	+	0.107853i
$206$	3.67106			0.255775
$207$	−1.81597	+	16.1539i	−0.126219	+	1.12277i
$208$	−5.43919			−0.377140
$209$	−2.40981	+	21.8012i	−0.166690	+	1.50802i
$210$	8.86449	−	3.65899i	0.611708	−	0.252494i
$211$	15.3754	+	8.87697i	1.05848	+	0.611116i	0.925013	−	0.379937i	$-0.124054\pi$
$211$	15.3754	+	8.87697i	1.05848	+	0.611116i	0.133471	+	0.991053i	$0.457388\pi$
$212$	−6.21710	+	10.7683i	−0.426992	+	0.739572i
$213$	−12.4952	+	2.60879i	−0.856160	+	0.178751i
$214$	1.29402	+	2.24131i	0.0884575	+	0.153213i
$215$	0.490566	−	1.39587i	0.0334563	−	0.0951973i
$216$	−4.23664	+	3.00847i	−0.288267	+	0.204701i
$217$	2.61206			0.177318
$218$	−2.25235	−	3.90118i	−0.152548	−	0.264222i
$219$	−1.57366	−	7.53731i	−0.106338	−	0.509324i
$220$	−7.39504	+	0.559772i	−0.498574	+	0.0377398i
$221$	−30.9566	−	17.8728i	−2.08237	−	1.20225i
$222$	8.01156	−	7.16139i	0.537701	−	0.480641i
$223$	13.1419	−	7.58750i	0.880050	−	0.508097i	0.00937487	−	0.999956i	$-0.497016\pi$
$223$	13.1419	−	7.58750i	0.880050	−	0.508097i	0.870675	+	0.491859i	$0.163683\pi$
$224$			2.47612i			0.165443i
$225$	−3.84655	−	14.4984i	−0.256436	−	0.966561i
$226$		−	1.99311i		−	0.132580i
$227$	−21.7160	+	12.5377i	−1.44134	+	0.832158i	−0.997939	−	0.0641651i	$-0.979562\pi$
$227$	−21.7160	+	12.5377i	−1.44134	+	0.832158i	−0.443401	+	0.896323i	$0.646228\pi$
$228$	3.57902	−	10.8811i	0.237026	−	0.720621i
$229$	12.2726	−	21.2567i	0.810993	−	1.40468i	−0.101177	−	0.994868i	$-0.532261\pi$
$229$	12.2726	−	21.2567i	0.810993	−	1.40468i	0.912170	−	0.409813i	$-0.134406\pi$
$230$	9.19452	−	7.89079i	0.606269	−	0.520304i
$231$	11.5823	−	8.25708i	0.762057	−	0.543276i
$232$	2.40129	−	1.38639i	0.157652	−	0.0910206i
$233$			15.3695i			1.00689i	0.864027	+	0.503446i	$0.167935\pi$
$233$			15.3695i			1.00689i	−0.864027	+	0.503446i	$0.832065\pi$
$234$	−6.52904	−	14.9544i	−0.426817	−	0.977600i
$235$	6.44215	−	18.3306i	0.420240	−	1.19576i
$236$	−11.9694	+	6.91054i	−0.779142	+	0.449838i
$237$	−5.58515	−	6.24819i	−0.362794	−	0.405864i
$238$	−8.13635	+	14.0926i	−0.527401	+	0.913486i
$239$	−1.64421	+	2.84786i	−0.106355	+	0.184213i	−0.914291	−	0.405058i	$-0.867251\pi$
$239$	−1.64421	+	2.84786i	−0.106355	+	0.184213i	0.807936	+	0.589270i	$0.200585\pi$
$240$	3.83922	+	0.510260i	0.247821	+	0.0329371i
$241$	−20.5730	+	11.8779i	−1.32523	+	0.765120i	−0.984557	−	0.175064i	$-0.943987\pi$
$241$	−20.5730	+	11.8779i	−1.32523	+	0.765120i	−0.340669	+	0.940183i	$0.610654\pi$
$242$	−10.4975	+	3.28665i	−0.674806	+	0.211274i
$243$	−13.3570	−	8.03686i	−0.856850	−	0.515565i
$244$			13.1129i			0.839470i
$245$	−1.90941	+	0.358593i	−0.121988	+	0.0229096i
$246$	6.34375	−	1.32446i	0.404462	−	0.0844447i
$247$	31.1519	+	17.9856i	1.98215	+	1.14439i
$248$	0.913571	+	0.527450i	0.0580118	+	0.0334931i
$249$	−8.67580	−	9.70575i	−0.549806	−	0.615077i
$250$	−5.26449	+	9.86332i	−0.332955	+	0.623811i
$251$			17.2664i			1.08985i	0.838486	+	0.544924i	$0.183441\pi$
$251$			17.2664i			1.08985i	−0.838486	+	0.544924i	$0.816559\pi$
$252$	−6.80780	+	2.97226i	−0.428851	+	0.187235i
$253$	10.6412	−	14.4822i	0.669006	−	0.910487i
$254$	7.88401	−	4.55184i	0.494687	−	0.285608i
$255$	20.1739	+	15.5195i	1.26334	+	0.971870i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.77203	+	15.1936i	−0.547184	+	0.947751i	0.451282	+	0.892382i	$0.350967\pi$
$257$	−8.77203	+	15.1936i	−0.547184	+	0.947751i	−0.998466	+	0.0553693i	$0.982366\pi$
$258$	−0.358089	+	1.08868i	−0.0222937	+	0.0677785i
$259$	13.3038	−	7.68098i	0.826660	−	0.477273i
$260$	−4.03258	+	11.4744i	−0.250090	+	0.711613i
$261$	6.69414	+	4.93789i	0.414357	+	0.305648i
$262$		−	4.86736i		−	0.300706i
$263$	25.5703	−	14.7630i	1.57673	−	0.910325i	0.581418	−	0.813605i	$-0.302498\pi$
$263$	25.5703	−	14.7630i	1.57673	−	0.910325i	0.995312	−	0.0967205i	$-0.0308353\pi$
$264$	5.71826	−	0.549128i	0.351934	−	0.0337965i
$265$	18.1074	+	21.0991i	1.11233	+	1.29611i
$266$	8.18769	−	14.1815i	0.502020	−	0.869523i
$267$	1.41840	−	0.296137i	0.0868045	−	0.0181233i
$268$	−11.6848	+	6.74621i	−0.713761	+	0.412090i
$269$			12.2089i			0.744390i	0.928155	+	0.372195i	$0.121395\pi$
$269$			12.2089i			0.744390i	−0.928155	+	0.372195i	$0.878605\pi$
$270$	3.20559	+	11.1680i	0.195086	+	0.679663i
$271$		−	3.08928i		−	0.187661i	−0.995588	−	0.0938303i	$-0.970089\pi$
$271$		−	3.08928i		−	0.187661i	0.995588	−	0.0938303i	$-0.0299111\pi$
$272$	−5.69140	+	3.28593i	−0.345092	+	0.199239i
$273$	−4.76755	−	22.8350i	−0.288545	−	1.38204i
$274$	4.71093	+	2.71986i	0.284598	+	0.164313i
$275$	−4.30176	+	16.0155i	−0.259406	+	0.965768i
$276$	−6.99722	+	6.25469i	−0.421183	+	0.376488i
$277$	−9.74793	−	16.8839i	−0.585697	−	1.01446i	−0.994788	−	0.101963i	$-0.967488\pi$
$277$	−9.74793	−	16.8839i	−0.585697	−	1.01446i	0.409092	−	0.912493i	$-0.365846\pi$
$278$	−21.4531			−1.28667
$279$	−0.353539	+	3.14489i	−0.0211659	+	0.188280i
$280$	5.22357	+	1.83578i	0.312168	+	0.109709i
$281$	−9.06378	−	15.6989i	−0.540700	−	0.936519i	−0.998864	−	0.0476518i	$-0.984826\pi$
$281$	−9.06378	−	15.6989i	−0.540700	−	0.936519i	0.458164	−	0.888868i	$-0.348507\pi$
$282$	−4.70246	+	14.2967i	−0.280027	+	0.851355i
$283$	−7.77843	+	13.4726i	−0.462380	+	0.800865i	−0.999079	−	0.0429083i	$-0.986338\pi$
$283$	−7.77843	+	13.4726i	−0.462380	+	0.800865i	0.536699	+	0.843774i	$0.319671\pi$
$284$	−6.38234	−	3.68485i	−0.378722	−	0.218655i
$285$	−20.3012	−	15.6174i	−1.20254	−	0.925097i
$286$	−1.98197	+	17.9305i	−0.117196	+	1.06025i
$287$	9.26449			0.546865
$288$	−2.98122	−	0.335140i	−0.175670	−	0.0197483i
$289$	−26.1894			−1.54055
$290$	−1.14439	−	6.09357i	−0.0672009	−	0.357827i
$291$	−13.8319	−	15.4739i	−0.810838	−	0.907098i
$292$	2.22275	−	3.84992i	0.130077	−	0.225299i
$293$	0.242168	+	0.139816i	0.0141476	+	0.00816811i	0.507057	−	0.861912i	$-0.330733\pi$
$293$	0.242168	+	0.139816i	0.0141476	+	0.00816811i	−0.492910	+	0.870081i	$0.664067\pi$
$294$	1.47312	−	0.307561i	0.0859139	−	0.0179373i
$295$	5.70429	+	30.3739i	0.332117	+	1.76844i
$296$	6.20405			0.360603
$297$	8.37379	+	15.0625i	0.485897	+	0.874016i
$298$		−	0.736115i		−	0.0426420i
$299$	−14.7363	−	25.5240i	−0.852221	−	1.47609i
$300$	3.92281	−	7.72085i	0.226484	−	0.445764i
$301$	−0.819198	+	1.41889i	−0.0472178	+	0.0817836i
$302$	2.01958	−	3.49802i	0.116214	−	0.201288i
$303$	−8.84394	+	7.90544i	−0.508071	+	0.454156i
$304$	5.72731	−	3.30667i	0.328484	−	0.189650i
$305$	27.6628	+	9.72186i	1.58397	+	0.556672i
$306$	−15.8661	−	11.7035i	−0.907003	−	0.669045i
$307$	−1.02772			−0.0586549			−0.0293275	−	0.999570i	$-0.509337\pi$
$307$	−1.02772			−0.0586549			−0.0293275	+	0.999570i	$0.509337\pi$
$308$	8.16264	+	0.902263i	0.465109	+	0.0514112i
$309$	−1.98671	+	6.04011i	−0.113020	+	0.343610i
$310$	1.79002	−	1.53620i	0.101666	−	0.0872505i
$311$	−0.0509806	−	0.0294337i	−0.00289084	−	0.00166903i	0.498554	−	0.866859i	$-0.333865\pi$
$311$	−0.0509806	−	0.0294337i	−0.00289084	−	0.00166903i	−0.501445	+	0.865190i	$0.667198\pi$
$312$	2.94359	−	8.94928i	0.166648	−	0.506653i
$313$	11.4955	−	6.63695i	0.649766	−	0.375143i	−0.138601	−	0.990348i	$-0.544260\pi$
$313$	11.4955	−	6.63695i	0.649766	−	0.375143i	0.788367	+	0.615206i	$0.210927\pi$
$314$	−10.6962			−0.603621
$315$	1.22296	+	16.5652i	0.0689060	+	0.933344i
$316$		−	4.83852i		−	0.272188i
$317$	4.38173	+	7.58938i	0.246103	+	0.426262i	0.962441	−	0.271491i	$-0.0875167\pi$
$317$	4.38173	+	7.58938i	0.246103	+	0.426262i	−0.716338	+	0.697753i	$0.754183\pi$
$318$	−14.3529	−	16.0568i	−0.804871	−	0.900422i
$319$	−3.69529	−	8.42114i	−0.206896	−	0.471494i
$320$	1.45625	+	1.69686i	0.0814071	+	0.0948572i
$321$	−4.38801	+	0.916140i	−0.244915	+	0.0511339i
$322$	−11.6194	+	6.70849i	−0.647526	+	0.373850i
$323$	43.4619			2.41828
$324$	−2.65714	−	8.59881i	−0.147619	−	0.477712i
$325$	21.2165	+	17.0141i	1.17688	+	0.943774i
$326$	5.99249	+	10.3793i	0.331893	+	0.574856i
$327$	7.63768	−	1.59461i	0.422365	−	0.0881824i
$328$	3.24027	+	1.87077i	0.178914	+	0.103296i
$329$	−10.7578	+	18.6330i	−0.593096	+	1.02727i
$330$	3.08106	−	12.4702i	0.169607	−	0.686465i
$331$	−7.50151	−	12.9930i	−0.412320	−	0.714160i	0.582823	−	0.812599i	$-0.301948\pi$
$331$	−7.50151	−	12.9930i	−0.412320	−	0.714160i	−0.995143	+	0.0984395i	$0.968615\pi$
$332$		−	7.51601i		−	0.412494i
$333$	7.44716	+	17.0573i	0.408102	+	0.934735i
$334$	6.63027			0.362792
$335$	5.56864	+	29.6516i	0.304248	+	1.62004i
$336$	−4.07404	−	1.34003i	−0.222257	−	0.0731047i
$337$	−7.26369	+	12.5811i	−0.395679	+	0.685335i	−0.993188	−	0.116527i	$-0.962824\pi$
$337$	−7.26369	+	12.5811i	−0.395679	+	0.685335i	0.597509	+	0.801862i	$0.296157\pi$
$338$	14.3628	+	8.29238i	0.781235	+	0.451046i
$339$	3.27933	+	1.07864i	0.178109	+	0.0585834i
$340$	2.71237	+	14.4426i	0.147099	+	0.783262i
$341$	2.07166	−	2.81943i	0.112187	−	0.152681i
$342$	15.9662	+	11.7774i	0.863353	+	0.636846i
$343$	19.4842			1.05205
$344$	−0.573031	+	0.330840i	−0.0308958	+	0.0178377i
$345$	8.00708	+	19.3984i	0.431087	+	1.04438i
$346$	−0.574273	+	0.994669i	−0.0308731	+	0.0534737i
$347$	2.27135	+	1.31136i	0.121932	+	0.0703977i	0.559726	−	0.828678i	$-0.310906\pi$
$347$	2.27135	+	1.31136i	0.121932	+	0.0703977i	−0.437793	+	0.899076i	$0.644240\pi$
$348$	0.981530	+	4.70121i	0.0526156	+	0.252011i
$349$	−0.624531	+	0.360573i	−0.0334304	+	0.0193010i	−0.516622	−	0.856214i	$-0.672811\pi$
$349$	−0.624531	+	0.360573i	−0.0334304	+	0.0193010i	0.483192	+	0.875515i	$0.339477\pi$
$350$	7.74546	−	9.65851i	0.414012	−	0.516269i
$351$	28.1384	−	2.64939i	1.50192	−	0.141414i
$352$	2.67270	+	1.96384i	0.142455	+	0.104673i
$353$	7.93237	+	13.7393i	0.422197	+	0.731267i	0.996154	−	0.0876185i	$-0.0279256\pi$
$353$	7.93237	+	13.7393i	0.422197	+	0.731267i	−0.573957	+	0.818886i	$0.694592\pi$
$354$	−4.89251	−	23.4335i	−0.260034	−	1.24548i
$355$	−12.5053	+	10.7321i	−0.663713	+	0.569603i
$356$	0.724491	+	0.418285i	0.0383979	+	0.0221691i
$357$	−18.7837	−	21.0137i	−0.994140	−	1.11216i
$358$	−4.68173	−	8.10900i	−0.247437	−	0.428574i
$359$	14.6862			0.775107			0.387554	−	0.921847i	$-0.373320\pi$
$359$	14.6862			0.775107			0.387554	+	0.921847i	$0.373320\pi$
$360$	−2.91727	+	6.04066i	−0.153753	+	0.318371i
$361$	−24.7361			−1.30190
$362$	−8.17325	+	4.71883i	−0.429576	+	0.248016i
$363$	0.273429	−	19.0506i	0.0143513	−	0.999897i
$364$	6.73403	−	11.6637i	0.352959	−	0.611343i
$365$	−6.47378	−	7.54338i	−0.338853	−	0.394839i
$366$	−21.5752	−	7.09649i	−1.12775	−	0.370940i
$367$	−8.67612	+	5.00916i	−0.452890	+	0.261476i	−0.709050	−	0.705158i	$-0.750876\pi$
$367$	−8.67612	+	5.00916i	−0.452890	+	0.261476i	0.256160	+	0.966634i	$0.417543\pi$
$368$	−5.41856			−0.282462
$369$	−1.25394	+	11.1544i	−0.0652774	+	0.580672i
$370$	4.59965	−	13.0879i	0.239124	−	0.680410i
$371$	−15.3943	−	26.6637i	−0.799231	−	1.38431i
$372$	−1.36224	+	1.21768i	−0.0706289	+	0.0631339i
$373$	2.24162	−	3.88260i	0.116067	−	0.201033i	−0.802139	−	0.597137i	$-0.796305\pi$
$373$	2.24162	−	3.88260i	0.116067	−	0.201033i	0.918206	+	0.396104i	$0.129638\pi$
$374$	8.75836	+	19.9593i	0.452884	+	1.03207i
$375$	−13.3794	−	13.9997i	−0.690910	−	0.722941i
$376$	−7.52510	+	4.34462i	−0.388077	+	0.224057i
$377$	−15.0816			−0.776743
$378$	−1.20610	−	12.8096i	−0.0620350	−	0.658856i
$379$	9.13129			0.469043			0.234522	−	0.972111i	$-0.424648\pi$
$379$	9.13129			0.469043			0.234522	+	0.972111i	$0.424648\pi$
$380$	−2.72948	−	14.5338i	−0.140019	−	0.745567i
$381$	3.22260	+	15.4352i	0.165099	+	0.790770i
$382$	−12.9484	+	22.4274i	−0.662500	+	1.14748i
$383$	−7.56879	+	13.1095i	−0.386747	+	0.669865i	−0.992010	−	0.126160i	$-0.959735\pi$
$383$	−7.56879	+	13.1095i	−0.386747	+	0.669865i	0.605263	+	0.796026i	$0.293068\pi$
$384$	−1.15431	−	1.29134i	−0.0589056	−	0.0658986i
$385$	7.95513	−	16.5508i	0.405431	−	0.843508i
$386$			12.9726i			0.660286i
$387$	−1.59746	−	1.17835i	−0.0812032	−	0.0598990i
$388$		−	11.9828i		−	0.608335i
$389$	20.9035	−	12.0686i	1.05985	−	0.611904i	0.134458	−	0.990919i	$-0.457071\pi$
$389$	20.9035	−	12.0686i	1.05985	−	0.611904i	0.925390	+	0.379016i	$0.123737\pi$
$390$	−16.6969	−	12.8447i	−0.845479	−	0.650416i
$391$	−30.8392	−	17.8050i	−1.55960	−	0.900438i
$392$	0.752440	+	0.434422i	0.0380040	+	0.0219416i
$393$	8.00842	+	2.63413i	0.403971	+	0.132874i
$394$	−4.77984	−	8.27893i	−0.240805	−	0.417087i
$395$	−10.2073	−	3.58725i	−0.513583	−	0.180494i
$396$	−2.19112	+	9.70562i	−0.110108	+	0.487726i
$397$		−	12.1341i		−	0.608991i	−0.952514	−	0.304495i	$-0.901512\pi$
$397$		−	12.1341i		−	0.608991i	0.952514	−	0.304495i	$-0.0984878\pi$
$398$	−4.78997	+	2.76549i	−0.240099	+	0.138621i
$399$	18.9023	+	21.1463i	0.946296	+	1.05864i
$400$	4.65932	−	1.81405i	0.232966	−	0.0907023i
$401$	10.7993	+	6.23499i	0.539292	+	0.311360i	0.744792	−	0.667297i	$-0.232549\pi$
$401$	10.7993	+	6.23499i	0.539292	+	0.311360i	−0.205500	+	0.978657i	$0.565882\pi$
$402$	−4.77617	−	22.8763i	−0.238214	−	1.14096i
$403$	−2.86890	−	4.96908i	−0.142910	−	0.247528i
$404$	−6.84863			−0.340732
$405$	−20.1099	−	0.769653i	−0.999268	−	0.0382444i
$406$			6.86570i			0.340739i
$407$	2.26067	−	20.4519i	0.112057	−	1.01376i
$408$	−2.32637	−	11.1425i	−0.115172	−	0.551638i
$409$	22.9939	+	13.2756i	1.13698	+	0.656434i	0.945680	−	0.325099i	$-0.105397\pi$
$409$	22.9939	+	13.2756i	1.13698	+	0.656434i	0.191297	+	0.981532i	$0.438731\pi$
$410$	6.34886	−	5.44863i	0.313548	−	0.269089i
$411$	−7.02454	+	6.27911i	−0.346495	+	0.309726i
$412$	−3.17923	+	1.83553i	−0.156629	+	0.0904300i
$413$		−	34.2226i		−	1.68398i
$414$	−6.50428	−	14.8977i	−0.319668	−	0.732182i
$415$	−15.8556	−	5.57233i	−0.778322	−	0.273535i
$416$	4.71047	−	2.71959i	0.230950	−	0.133339i
$417$	11.6100	−	35.2975i	0.568546	−	1.72853i
$418$	−8.81362	−	20.0853i	−0.431088	−	0.982402i
$419$	22.6429	+	13.0729i	1.10618	+	0.638652i	0.937837	−	0.347076i	$-0.112826\pi$
$419$	22.6429	+	13.0729i	1.10618	+	0.638652i	0.168342	+	0.985729i	$0.446159\pi$
$420$	−5.84737	+	7.60102i	−0.285323	+	0.370892i
$421$	1.82766	+	3.16560i	0.0890747	+	0.154282i	0.907120	−	0.420872i	$-0.138276\pi$
$421$	1.82766	+	3.16560i	0.0890747	+	0.154282i	−0.818046	+	0.575153i	$0.804942\pi$
$422$	−17.7539			−0.864249
$423$	−20.9779	−	15.4742i	−1.01998	−	0.752383i
$424$		−	12.4342i		−	0.603858i
$425$	32.4789	+	4.98574i	1.57546	+	0.241844i
$426$	9.51681	−	8.50690i	0.461091	−	0.412161i
$427$	−28.1191	−	16.2346i	−1.36078	−	0.785647i
$428$	−2.24131	−	1.29402i	−0.108338	−	0.0625489i
$429$	−28.4291	−	12.9647i	−1.37257	−	0.625941i
$430$	0.273091	+	1.45414i	0.0131696	+	0.0701248i
$431$	−12.4008			−0.597326			−0.298663	−	0.954359i	$-0.596541\pi$
$431$	−12.4008			−0.597326			−0.298663	+	0.954359i	$0.596541\pi$
$432$	2.16480	−	4.72373i	0.104154	−	0.227271i
$433$			14.2995i			0.687192i	0.939118	+	0.343596i	$0.111645\pi$
$433$			14.2995i			0.687192i	−0.939118	+	0.343596i	$0.888355\pi$
$434$	−2.26211	+	1.30603i	−0.108585	+	0.0626914i
$435$	10.6453	+	1.41483i	0.510402	+	0.0678360i
$436$	3.90118	+	2.25235i	0.186833	+	0.107868i
$437$	31.0338	+	17.9174i	1.48455	+	0.857103i
$438$	5.13148	+	5.74067i	0.245192	+	0.274300i
$439$	8.35802	−	4.82551i	0.398907	−	0.230309i	−0.287106	−	0.957899i	$-0.592693\pi$
$439$	8.35802	−	4.82551i	0.398907	−	0.230309i	0.686012	+	0.727590i	$0.259360\pi$
$440$	6.12441	−	4.18230i	0.291970	−	0.199383i
$441$	−0.291184	+	2.59021i	−0.0138659	+	0.123344i
$442$	35.7456			1.70024
$443$	−13.7249	−	23.7722i	−0.652090	−	1.12945i	−0.982615	−	0.185655i	$-0.940559\pi$
$443$	−13.7249	−	23.7722i	−0.652090	−	1.12945i	0.330525	−	0.943797i	$-0.392774\pi$
$444$	−3.35752	+	10.2077i	−0.159341	+	0.484437i
$445$	1.41954	−	1.21826i	0.0672927	−	0.0577510i
$446$	−7.58750	+	13.1419i	−0.359279	+	0.622289i
$447$	1.21115	+	0.398372i	0.0572856	+	0.0188424i
$448$	−1.23806	−	2.14438i	−0.0584928	−	0.101312i
$449$		−	9.31577i		−	0.439638i	−0.975541	−	0.219819i	$-0.929453\pi$
$449$		−	9.31577i		−	0.439638i	0.975541	−	0.219819i	$-0.0705468\pi$
$450$	10.5804	+	10.6327i	0.498766	+	0.501231i
$451$	7.34779	−	10.0000i	0.345994	−	0.470882i
$452$	0.996555	+	1.72608i	0.0468740	+	0.0811881i
$453$	4.66245	+	5.21595i	0.219061	+	0.245067i
$454$	12.5377	−	21.7160i	0.588425	−	1.01918i
$455$	−19.6129	−	22.8534i	−0.919468	−	1.07138i
$456$	2.34105	+	11.2128i	0.109630	+	0.525090i
$457$	−15.5593	−	26.9495i	−0.727833	−	1.26064i	−0.957797	−	0.287445i	$-0.907194\pi$
$457$	−15.5593	−	26.9495i	−0.727833	−	1.26064i	0.229964	−	0.973199i	$-0.426139\pi$
$458$			24.5451i			1.14692i
$459$	27.8426	−	19.7713i	1.29958	−	0.922843i
$460$	−4.01729	+	11.4309i	−0.187307	+	0.532968i
$461$	−8.56675	−	14.8380i	−0.398993	−	0.691076i	0.594609	−	0.804015i	$-0.297307\pi$
$461$	−8.56675	−	14.8380i	−0.398993	−	0.691076i	−0.993602	+	0.112939i	$0.963974\pi$
$462$	−5.90200	+	12.9420i	−0.274586	+	0.602115i
$463$	9.33178	+	5.38771i	0.433685	+	0.250388i	0.700915	−	0.713245i	$-0.252775\pi$
$463$	9.33178	+	5.38771i	0.433685	+	0.250388i	−0.267230	+	0.963633i	$0.586108\pi$
$464$	−1.38639	+	2.40129i	−0.0643613	+	0.111477i
$465$	1.55884	+	3.77654i	0.0722895	+	0.175133i
$466$	−7.68476	−	13.3104i	−0.355990	−	0.616592i
$467$	−21.7898			−1.00831			−0.504156	−	0.863613i	$-0.668196\pi$
$467$	−21.7898			−1.00831			−0.504156	+	0.863613i	$0.668196\pi$
$468$	13.1315	+	9.68638i	0.607005	+	0.447753i
$469$		−	33.4088i		−	1.54267i
$470$	3.58626	+	19.0959i	0.165422	+	0.880827i
$471$	5.78859	−	17.5988i	0.266724	−	0.810910i
$472$	6.91054	−	11.9694i	0.318083	−	0.550936i
$473$	0.881824	+	2.00958i	0.0405463	+	0.0924005i
$474$	7.96098	+	2.61852i	0.365660	+	0.120273i
$475$	−32.6838	−	5.01720i	−1.49964	−	0.230205i
$476$		−	16.2727i		−	0.745858i
$477$	34.1864	−	14.9257i	1.56529	−	0.683399i
$478$		−	3.28842i		−	0.150409i
$479$	19.7306	+	34.1744i	0.901513	+	1.56147i	0.825530	+	0.564358i	$0.190876\pi$
$479$	19.7306	+	34.1744i	0.901513	+	1.56147i	0.0759832	+	0.997109i	$0.475790\pi$
$480$	−3.57999	+	1.47771i	−0.163404	+	0.0674481i
$481$	−29.2240	−	16.8725i	−1.33250	−	0.769319i
$482$	11.8779	−	20.5730i	0.541021	−	0.937076i
$483$	−4.74947	−	22.7484i	−0.216108	−	1.03509i
$484$	7.44779	−	8.09509i	0.338536	−	0.367958i
$485$	−25.2787	−	8.88399i	−1.14785	−	0.403401i
$486$	15.5859	+	0.281638i	0.706991	+	0.0127754i
$487$		−	36.6600i		−	1.66123i	−0.556851	−	0.830613i	$-0.687990\pi$
$487$		−	36.6600i		−	1.66123i	0.556851	−	0.830613i	$-0.312010\pi$
$488$	−6.55647	−	11.3561i	−0.296797	−	0.514068i
$489$	−20.3204	+	4.24255i	−0.918922	+	0.191855i
$490$	1.47430	−	1.26526i	0.0666022	−	0.0571585i
$491$	−2.60620	+	4.51406i	−0.117616	+	0.203717i	−0.918822	−	0.394671i	$-0.870859\pi$
$491$	−2.60620	+	4.51406i	−0.117616	+	0.203717i	0.801206	+	0.598388i	$0.204192\pi$
$492$	−4.83161	+	4.31889i	−0.217826	+	0.194711i
$493$	−15.7809	+	9.11113i	−0.710738	+	0.410345i
$494$	−35.9711			−1.61842
$495$	18.8503	+	11.8180i	0.847258	+	0.531181i
$496$	−1.05490			−0.0473664
$497$	15.8034	−	9.12411i	0.708880	−	0.409272i
$498$	12.3663	+	4.06753i	0.554149	+	0.182270i
$499$	−13.7057	+	23.7390i	−0.613552	+	1.06270i	0.377084	+	0.926179i	$0.376927\pi$
$499$	−13.7057	+	23.7390i	−0.613552	+	1.06270i	−0.990637	+	0.136525i	$0.956407\pi$
$500$	−0.372483	−	11.1741i	−0.0166580	−	0.499722i
$501$	−3.58819	+	10.9090i	−0.160308	+	0.487379i
$502$	−8.63321	−	14.9532i	−0.385319	−	0.667392i
$503$		−	8.66800i		−	0.386487i	−0.981151	−	0.193244i	$-0.938099\pi$
$503$		−	8.66800i		−	0.386487i	0.981151	−	0.193244i	$-0.0619008\pi$
$504$	4.40959	−	5.97795i	0.196419	−	0.266279i
$505$	−5.07754	+	14.4477i	−0.225947	+	0.642916i
$506$	−1.97445	+	17.8625i	−0.0877749	+	0.794086i
$507$	−21.4166	+	19.1439i	−0.951146	+	0.850212i
$508$	−4.55184	+	7.88401i	−0.201955	+	0.349797i
$509$	26.7428	+	15.4400i	1.18535	+	0.684364i	0.957247	−	0.289272i	$-0.0934132\pi$
$509$	26.7428	+	15.4400i	1.18535	+	0.684364i	0.228107	+	0.973636i	$0.426747\pi$
$510$	−25.2308	−	3.35335i	−1.11724	−	0.148489i
$511$	5.50379	+	9.53285i	0.243473	+	0.421708i
$512$		−	1.00000i		−	0.0441942i
$513$	−28.0183	+	19.8960i	−1.23704	+	0.878430i
$514$		−	17.5441i		−	0.773835i
$515$	1.51513	+	8.06769i	0.0667648	+	0.355505i
$516$	−0.234227	−	1.12187i	−0.0103113	−	0.0493877i
$517$	11.5802	+	26.3900i	0.509296	+	1.16063i
$518$	−7.68098	+	13.3038i	−0.337483	+	0.584537i
$519$	−1.32578	−	1.48317i	−0.0581951	−	0.0651038i
$520$	−2.24488	−	11.9534i	−0.0984447	−	0.524192i
$521$			19.4043i			0.850116i	0.905166	+	0.425058i	$0.139746\pi$
$521$			19.4043i			0.850116i	−0.905166	+	0.425058i	$0.860254\pi$
$522$	−8.26624	−	0.929266i	−0.361804	−	0.0406729i
$523$	−22.8291			−0.998245			−0.499123	−	0.866531i	$-0.666344\pi$
$523$	−22.8291			−0.998245			−0.499123	+	0.866531i	$0.666344\pi$
$524$	2.43368	+	4.21525i	0.106316	+	0.184144i
$525$	11.6998	+	17.9709i	0.510620	+	0.784313i
$526$	−14.7630	+	25.5703i	−0.643697	+	1.11492i
$527$	−6.00386	−	3.46633i	−0.261532	−	0.150996i
$528$	−4.67759	+	3.33469i	−0.203566	+	0.145124i
$529$	−3.18038	−	5.50858i	−0.138277	−	0.239503i
$530$	−26.2310	−	9.21865i	−1.13940	−	0.400433i
$531$	41.2037	+	4.63199i	1.78809	+	0.201011i
$532$			16.3754i			0.709963i
$533$	−10.1755	−	17.6244i	−0.440748	−	0.763398i
$534$	−1.08030	+	0.965661i	−0.0467492	+	0.0417882i
$535$	−4.39154	+	3.76885i	−0.189863	+	0.162942i
$536$	6.74621	−	11.6848i	0.291392	−	0.504705i
$537$	15.8757	−	3.31457i	0.685086	−	0.143034i
$538$	−6.10445	−	10.5732i	−0.263182	−	0.455844i
$539$	1.70627	−	2.32216i	0.0734943	−	0.100022i
$540$	−8.36012	−	8.06897i	−0.359762	−	0.347233i
$541$		−	33.3302i		−	1.43298i	−0.697600	−	0.716488i	$-0.745749\pi$
$541$		−	33.3302i		−	1.43298i	0.697600	−	0.716488i	$-0.254251\pi$
$542$	1.54464	+	2.67540i	0.0663480	+	0.114918i
$543$	−3.34083	−	16.0015i	−0.143369	−	0.686689i
$544$	3.28593	−	5.69140i	0.140883	−	0.244017i
$545$	7.64383	−	6.55999i	0.327426	−	0.280999i
$546$	15.5463	+	17.3919i	0.665321	+	0.744305i
$547$	19.8122	+	34.3157i	0.847107	+	1.46723i	0.883779	+	0.467905i	$0.154991\pi$
$547$	19.8122	+	34.3157i	0.847107	+	1.46723i	−0.0366717	+	0.999327i	$0.511676\pi$
$548$	−5.43971			−0.232373
$549$	23.3522	−	31.6578i	0.996647	−	1.35112i
$550$	−4.28229	−	16.0207i	−0.182598	−	0.683124i
$551$	15.8805	−	9.16862i	0.676533	−	0.390596i
$552$	2.93243	−	8.91533i	0.124812	−	0.379462i
$553$	10.3756	+	5.99037i	0.441216	+	0.254736i
$554$	16.8839	+	9.74793i	0.717329	+	0.414150i
$555$	19.0448	+	14.6509i	0.808406	+	0.621897i
$556$	18.5789	−	10.7265i	0.787922	−	0.454907i
$557$			18.3623i			0.778034i	0.921231	+	0.389017i	$0.127185\pi$
$557$			18.3623i			0.778034i	−0.921231	+	0.389017i	$0.872815\pi$
$558$	−1.26627	−	2.90033i	−0.0536056	−	0.122781i
$559$	3.59900			0.152221
$560$	−5.44164	+	1.02195i	−0.229951	+	0.0431854i
$561$	−37.5796	+	3.60879i	−1.58661	+	0.152363i
$562$	15.6989	+	9.06378i	0.662219	+	0.382332i
$563$	−20.8691	−	12.0488i	−0.879526	−	0.507795i	−0.00902385	−	0.999959i	$-0.502872\pi$
$563$	−20.8691	−	12.0488i	−0.879526	−	0.507795i	−0.870502	+	0.492165i	$0.836206\pi$
$564$	−3.07589	−	14.7325i	−0.129519	−	0.620351i
$565$	4.38015	−	0.822604i	0.184274	−	0.0346072i
$566$		−	15.5569i		−	0.653904i
$567$	21.7288	+	4.94791i	0.912525	+	0.207793i
$568$	7.36969			0.309225
$569$	20.9736	+	36.3273i	0.879259	+	1.52292i	0.852155	+	0.523289i	$0.175295\pi$
$569$	20.9736	+	36.3273i	0.879259	+	1.52292i	0.0271038	+	0.999633i	$0.491372\pi$
$570$	25.3901	+	3.37452i	1.06347	+	0.141343i
$571$	14.2995	+	8.25581i	0.598414	+	0.345495i	0.768418	−	0.639949i	$-0.221044\pi$
$571$	14.2995	+	8.25581i	0.598414	+	0.345495i	−0.170003	+	0.985444i	$0.554378\pi$
$572$	−7.24884	−	16.5193i	−0.303089	−	0.690706i
$573$	−29.8930	−	33.4418i	−1.24880	−	1.39705i
$574$	−8.02328	+	4.63224i	−0.334885	+	0.193346i
$575$	21.1360	+	16.9496i	0.881432	+	0.706847i
$576$	2.74938	−	1.20037i	0.114558	−	0.0500155i
$577$			16.7764i			0.698411i	0.937046	+	0.349206i	$0.113548\pi$
$577$			16.7764i			0.698411i	−0.937046	+	0.349206i	$0.886452\pi$
$578$	22.6807	−	13.0947i	0.943391	−	0.544667i
$579$	−21.3442	−	7.02052i	−0.887034	−	0.291763i
$580$	4.03786	+	4.70500i	0.167663	+	0.195364i
$581$	16.1172	+	9.30526i	0.668653	+	0.386047i
$582$	19.7157	+	6.48488i	0.817243	+	0.268807i
$583$	−40.9899	−	4.53085i	−1.69763	−	0.187649i
$584$			4.44550i			0.183956i
$585$	30.1698	−	20.5206i	1.24737	−	0.848422i
$586$	−0.279631			−0.0115515
$587$	1.17889	+	2.04190i	0.0486580	+	0.0842781i	0.889329	−	0.457269i	$-0.151172\pi$
$587$	1.17889	+	2.04190i	0.0486580	+	0.0842781i	−0.840671	+	0.541547i	$0.817839\pi$
$588$	−1.12198	+	1.00291i	−0.0462695	+	0.0413595i
$589$	6.04175	+	3.48820i	0.248946	+	0.143729i
$590$	−20.1270	−	23.4524i	−0.828615	−	0.965520i
$591$	16.2084	−	3.38403i	0.666723	−	0.139200i
$592$	−5.37286	+	3.10202i	−0.220823	+	0.127492i
$593$			25.2808i			1.03816i	0.854726	+	0.519080i	$0.173725\pi$
$593$			25.2808i			1.03816i	−0.854726	+	0.519080i	$0.826275\pi$
$594$	−14.7832	−	8.85763i	−0.606561	−	0.363433i
$595$	−34.3286	−	12.0645i	−1.40733	−	0.494596i
$596$	0.368057	+	0.637494i	0.0150762	+	0.0261128i
$597$	−1.95790	−	9.37772i	−0.0801317	−	0.383805i
$598$	25.5240	+	14.7363i	1.04375	+	0.602611i
$599$	11.6337	+	6.71674i	0.475341	+	0.274438i	0.718473	−	0.695555i	$-0.244841\pi$
$599$	11.6337	+	6.71674i	0.475341	+	0.274438i	−0.243132	+	0.969993i	$0.578175\pi$
$600$	0.463169	+	8.64786i	0.0189088	+	0.353047i
$601$	36.1881	−	20.8932i	1.47614	−	0.852251i	0.476505	−	0.879172i	$-0.341903\pi$
$601$	36.1881	−	20.8932i	1.47614	−	0.852251i	0.999638	+	0.0269206i	$0.00857012\pi$
$602$		−	1.63840i		−	0.0667760i
$603$	40.2239	+	4.52185i	1.63804	+	0.184144i
$604$			4.03916i			0.164351i
$605$	−11.5555	−	21.7134i	−0.469797	−	0.882774i
$606$	3.70636	−	11.2683i	0.150560	−	0.457743i
$607$	5.94720	−	10.3009i	0.241389	−	0.418099i	−0.719721	−	0.694263i	$-0.755730\pi$
$607$	5.94720	−	10.3009i	0.241389	−	0.418099i	0.961110	+	0.276165i	$0.0890636\pi$
$608$	−3.30667	+	5.72731i	−0.134103	+	0.232273i
$609$	−11.2964	−	3.71560i	−0.457752	−	0.150564i
$610$	−28.8176	+	5.41203i	−1.16679	+	0.219127i
$611$	47.2624			1.91203
$612$	19.5922	+	2.20249i	0.791967	+	0.0890305i
$613$	19.2840			0.778871			0.389436	−	0.921054i	$-0.372670\pi$
$613$	19.2840			0.778871			0.389436	+	0.921054i	$0.372670\pi$
$614$	0.890030	−	0.513859i	0.0359187	−	0.0207377i
$615$	5.52892	+	13.3947i	0.222948	+	0.540126i
$616$	−7.52018	+	3.29994i	−0.302997	+	0.132958i
$617$	11.4284	−	19.7945i	0.460089	−	0.796898i	−0.538876	−	0.842385i	$-0.681151\pi$
$617$	11.4284	−	19.7945i	0.460089	−	0.796898i	0.998965	+	0.0454874i	$0.0144841\pi$
$618$	−1.29951	−	6.22425i	−0.0522741	−	0.250376i
$619$	7.63885	+	13.2309i	0.307031	+	0.531794i	0.977711	−	0.209953i	$-0.0673311\pi$
$619$	7.63885	+	13.2309i	0.307031	+	0.531794i	−0.670680	+	0.741747i	$0.733998\pi$
$620$	−0.782098	+	2.22540i	−0.0314098	+	0.0893742i
$621$	28.0317	−	2.63934i	1.12487	−	0.105913i
$622$	0.0588673			0.00236036
$623$	−1.79392	+	1.03572i	−0.0718721	+	0.0414954i
$624$	1.92541	+	9.22210i	0.0770782	+	0.369179i
$625$	−23.8489	−	7.49866i	−0.953956	−	0.299946i
$626$	−6.63695	+	11.4955i	−0.265266	+	0.459454i
$627$	37.8167	−	3.63156i	1.51025	−	0.145031i
$628$	9.26317	−	5.34809i	0.369641	−	0.213412i
$629$	−40.7721			−1.62569
$630$	−9.34172	−	13.7344i	−0.372183	−	0.547192i
$631$	−31.1161			−1.23871			−0.619356	−	0.785110i	$-0.712606\pi$
$631$	−31.1161			−1.23871			−0.619356	+	0.785110i	$0.712606\pi$
$632$	2.41926	+	4.19028i	0.0962330	+	0.166680i
$633$	9.60812	−	29.2112i	0.381889	−	1.16104i
$634$	−7.58938	−	4.38173i	−0.301413	−	0.174021i
$635$	13.2573	+	15.4476i	0.526098	+	0.613021i
$636$	20.4584	+	6.72917i	0.811228	+	0.266829i
$637$	−2.36290	−	4.09266i	−0.0936215	−	0.162157i
$638$	7.41078	+	5.44528i	0.293396	+	0.215581i
$639$	8.84636	+	20.2621i	0.349957	+	0.801557i
$640$	−2.10958	−	0.741395i	−0.0833885	−	0.0293062i
$641$	−24.1340	+	13.9337i	−0.953234	+	0.550350i	−0.894084	−	0.447899i	$-0.852172\pi$
$641$	−24.1340	+	13.9337i	−0.953234	+	0.550350i	−0.0591499	+	0.998249i	$0.518839\pi$
$642$	3.34206	−	2.98740i	0.131900	−	0.117903i
$643$	3.77376	+	2.17878i	0.148822	+	0.0859227i	0.572562	−	0.819861i	$-0.305950\pi$
$643$	3.77376	+	2.17878i	0.148822	+	0.0859227i	−0.423740	+	0.905784i	$0.639283\pi$
$644$	6.70849	−	11.6194i	0.264352	−	0.457870i
$645$	−2.54034	−	0.337628i	−0.100026	−	0.0132941i
$646$	−37.6391	+	21.7309i	−1.48089	+	0.854993i
$647$	6.09542			0.239636			0.119818	−	0.992796i	$-0.461769\pi$
$647$	6.09542			0.239636			0.119818	+	0.992796i	$0.461769\pi$
$648$	6.60056	+	6.11822i	0.259295	+	0.240346i
$649$	−36.9396	−	27.1424i	−1.45001	−	1.06543i
$650$	−26.8811	−	4.12644i	−1.05436	−	0.161852i
$651$	−0.924640	−	4.42872i	−0.0362395	−	0.173575i
$652$	−10.3793	−	5.99249i	−0.406485	−	0.234684i
$653$	−5.12234	+	8.87215i	−0.200453	+	0.347194i	−0.948674	−	0.316255i	$-0.897575\pi$
$653$	−5.12234	+	8.87215i	−0.200453	+	0.347194i	0.748222	+	0.663449i	$0.230908\pi$
$654$	−5.81712	+	5.19982i	−0.227467	+	0.203329i
$655$	10.6967	−	2.00888i	0.417956	−	0.0784933i
$656$	−3.74154			−0.146083
$657$	−12.2224	+	5.33625i	−0.476841	+	0.208187i
$658$		−	21.5156i		−	0.838764i
$659$	−10.3111	−	17.8593i	−0.401662	−	0.695699i	0.592264	−	0.805744i	$-0.298234\pi$
$659$	−10.3111	−	17.8593i	−0.401662	−	0.695699i	−0.993927	+	0.110044i	$0.964901\pi$
$660$	3.56685	+	12.3401i	0.138840	+	0.480337i
$661$	0.963515	−	1.66886i	0.0374764	−	0.0649110i	−0.846679	−	0.532104i	$-0.821401\pi$
$661$	0.963515	−	1.66886i	0.0374764	−	0.0649110i	0.884155	+	0.467193i	$0.154735\pi$
$662$	12.9930	+	7.50151i	0.504987	+	0.291555i
$663$	−19.3449	+	58.8134i	−0.751293	+	2.28412i
$664$	3.75800	+	6.50905i	0.145839	+	0.252600i
$665$	34.5452	+	12.1406i	1.33961	+	0.470793i
$666$	−14.9781	−	11.0485i	−0.580389	−	0.428120i
$667$	−15.0244			−0.581748
$668$	−5.74198	+	3.31514i	−0.222164	+	0.128266i
$669$	−17.5167	−	19.5962i	−0.677233	−	0.757631i
$670$	−19.6484	−	22.8947i	−0.759083	−	0.884499i
$671$	−39.8251	+	17.4757i	−1.53743	+	0.674642i
$672$	4.19824	−	0.876518i	0.161950	−	0.0338124i
$673$	2.48624	+	4.30629i	0.0958373	+	0.165995i	0.909958	−	0.414701i	$-0.136114\pi$
$673$	2.48624	+	4.30629i	0.0958373	+	0.165995i	−0.814120	+	0.580696i	$0.802780\pi$
$674$		−	14.5274i		−	0.559574i
$675$	−23.2203	+	11.6541i	−0.893750	+	0.448565i
$676$	−16.5848			−0.637875
$677$	−13.7423	+	7.93412i	−0.528159	+	0.304933i	−0.740267	−	0.672313i	$-0.765301\pi$
$677$	−13.7423	+	7.93412i	−0.528159	+	0.304933i	0.212107	+	0.977246i	$0.431967\pi$
$678$	−3.37930	+	0.705539i	−0.129781	+	0.0270961i
$679$	25.6957	+	14.8354i	0.986110	+	0.569331i
$680$	−9.57030	−	11.1515i	−0.367004	−	0.427641i
$681$	28.9448	+	32.3810i	1.10917	+	1.24084i
$682$	−0.384391	+	3.47753i	−0.0147191	+	0.133162i
$683$	25.3762			0.970994			0.485497	−	0.874238i	$-0.338639\pi$
$683$	25.3762			0.970994			0.485497	+	0.874238i	$0.338639\pi$
$684$	−19.7158	−	2.21639i	−0.753853	−	0.0847458i
$685$	−4.03297	+	11.4755i	−0.154092	+	0.438457i
$686$	−16.8738	+	9.74209i	−0.644244	+	0.371955i
$687$	−40.3849	−	13.2834i	−1.54078	−	0.506792i
$688$	0.330840	−	0.573031i	0.0126131	−	0.0218466i
$689$	−33.8160	+	58.5710i	−1.28829	+	2.23138i
$690$	−16.6335	−	12.7960i	−0.633228	−	0.487134i
$691$	1.91017	+	3.30851i	0.0726663	+	0.125862i	0.900069	−	0.435747i	$-0.143516\pi$
$691$	1.91017	+	3.30851i	0.0726663	+	0.125862i	−0.827403	+	0.561609i	$0.810183\pi$
$692$		−	1.14855i		−	0.0436611i
$693$	−18.0998	−	16.7147i	−0.687554	−	0.634940i
$694$	−2.62273			−0.0995574
$695$	−8.85421	−	47.1464i	−0.335859	−	1.78836i
$696$	−3.20063	−	3.58060i	−0.121320	−	0.135722i
$697$	−21.2946	−	12.2944i	−0.806590	−	0.465685i
$698$	0.360573	−	0.624531i	0.0136479	−	0.0236388i
$699$	26.0589	−	5.44064i	0.985638	−	0.205784i
$700$	−1.87851	+	12.2372i	−0.0710008	+	0.462524i
$701$	−50.8242			−1.91960			−0.959801	−	0.280681i	$-0.909440\pi$
$701$	−50.8242			−1.91960			−0.959801	+	0.280681i	$0.909440\pi$
$702$	−23.0439	+	16.3636i	−0.869735	+	0.617606i
$703$	41.0294			1.54745
$704$	−3.29655	−	0.364386i	−0.124243	−	0.0137333i
$705$	−33.3599	−	4.43376i	−1.25641	−	0.166985i
$706$	−13.7393	−	7.93237i	−0.517084	−	0.298539i
$707$	8.47901	−	14.6861i	0.318886	−	0.552326i
$708$	15.9538	+	17.8478i	0.599580	+	0.670760i
$709$	−2.59901	−	4.50161i	−0.0976077	−	0.169061i	0.813086	−	0.582143i	$-0.197786\pi$
$709$	−2.59901	−	4.50161i	−0.0976077	−	0.169061i	−0.910694	+	0.413082i	$0.864452\pi$
$710$	5.46385	−	15.5470i	0.205055	−	0.583467i
$711$	−8.61668	+	11.6814i	−0.323151	+	0.438085i
$712$	−0.836570			−0.0313518
$713$	−2.85802	−	4.95024i	−0.107034	−	0.185388i
$714$	26.7740	+	8.80650i	1.00199	+	0.329575i
$715$	−40.2230	+	3.04470i	−1.50426	+	0.113865i
$716$	8.10900	+	4.68173i	0.303048	+	0.174965i
$717$	5.41055	+	1.77964i	0.202061	+	0.0664617i
$718$	−12.7186	+	7.34309i	−0.474654	+	0.274042i
$719$			39.0596i			1.45668i	0.685218	+	0.728338i	$0.259707\pi$
$719$			39.0596i			1.45668i	−0.685218	+	0.728338i	$0.740293\pi$
$720$	−0.493902	−	6.69000i	−0.0184067	−	0.249321i
$721$		−	9.08997i		−	0.338528i
$722$	21.4221	−	12.3681i	0.797249	−	0.460292i
$723$	27.4214	+	30.6768i	1.01981	+	1.14088i
$724$	4.71883	−	8.17325i	0.175374	−	0.303756i
$725$	12.9192	−	5.02993i	0.479808	−	0.186807i
$726$	9.28850	+	16.6350i	0.344729	+	0.617383i
$727$	−10.0973	+	5.82968i	−0.374488	+	0.216211i	−0.675417	−	0.737436i	$-0.736037\pi$
$727$	−10.0973	+	5.82968i	−0.374488	+	0.216211i	0.300929	+	0.953646i	$0.402703\pi$
$728$			13.4681i			0.499160i
$729$	−8.89821	+	25.4916i	−0.329563	+	0.944133i
$730$	9.37815	+	3.29587i	0.347101	+	0.121986i
$731$	3.76588	−	2.17423i	0.139286	−	0.0804169i
$732$	22.2329	−	4.64184i	0.821751	−	0.171567i
$733$	−19.8809	+	34.4347i	−0.734316	+	1.27187i	0.220706	+	0.975340i	$0.429164\pi$
$733$	−19.8809	+	34.4347i	−0.734316	+	1.27187i	−0.955023	+	0.296533i	$0.904170\pi$
$734$	5.00916	−	8.67612i	0.184892	−	0.320241i
$735$	1.28390	+	3.11045i	0.0473574	+	0.114731i
$736$	4.69261	−	2.70928i	0.172972	−	0.0998653i
$737$	−36.0612	−	26.4970i	−1.32833	−	0.976028i
$738$	−4.49123	−	10.2869i	−0.165325	−	0.378667i
$739$			14.2640i			0.524711i	0.964971	+	0.262356i	$0.0844993\pi$
$739$			14.2640i			0.524711i	−0.964971	+	0.262356i	$0.915501\pi$
$740$	2.56056	+	13.6343i	0.0941281	+	0.501207i
$741$	19.4669	−	59.1845i	0.715136	−	2.17420i
$742$	26.6637	+	15.3943i	0.978854	+	0.565141i
$743$	−9.35968	−	5.40381i	−0.343373	−	0.198247i	0.318389	−	0.947960i	$-0.396858\pi$
$743$	−9.35968	−	5.40381i	−0.343373	−	0.198247i	−0.661763	+	0.749713i	$0.730191\pi$
$744$	0.570894	−	1.73566i	0.0209300	−	0.0636325i
$745$	1.61772	−	0.303812i	0.0592687	−	0.0111308i
$746$			4.48324i			0.164143i
$747$	−13.3849	+	18.1455i	−0.489727	+	0.663908i
$748$	−17.5646	−	12.9061i	−0.642226	−	0.471893i
$749$	5.54975	−	3.20415i	0.202784	−	0.117077i
$750$	18.5868	+	5.43438i	0.678692	+	0.198436i
$751$	−17.8004	+	30.8311i	−0.649544	+	1.12504i	0.333687	+	0.942684i	$0.391707\pi$
$751$	−17.8004	+	30.8311i	−0.649544	+	1.12504i	−0.983232	+	0.182360i	$0.941626\pi$
$752$	4.34462	−	7.52510i	0.158432	−	0.274412i
$753$	29.2751	−	6.11213i	1.06684	−	0.222738i
$754$	13.0611	−	7.54081i	0.475656	−	0.274620i
$755$	8.52095	+	2.99461i	0.310109	+	0.108985i
$756$	7.44933	+	10.4904i	0.270929	+	0.381533i
$757$		−	17.7627i		−	0.645597i	−0.946468	−	0.322798i	$-0.895376\pi$
$757$		−	17.7627i		−	0.645597i	0.946468	−	0.322798i	$-0.104624\pi$
$758$	−7.90793	+	4.56565i	−0.287229	+	0.165832i
$759$	−28.3213	−	12.9155i	−1.02800	−	0.468803i
$760$	9.63069	+	11.2219i	0.349342	+	0.407060i
$761$	−3.51966	+	6.09624i	−0.127588	+	0.220988i	−0.922741	−	0.385419i	$-0.874057\pi$
$761$	−3.51966	+	6.09624i	−0.127588	+	0.220988i	0.795154	+	0.606408i	$0.207390\pi$
$762$	−10.5085	−	11.7560i	−0.380681	−	0.425874i
$763$	−9.65979	+	5.57708i	−0.349708	+	0.201904i
$764$		−	25.8969i		−	0.936916i
$765$	19.1719	−	39.6984i	0.693160	−	1.43530i
$766$		−	15.1376i		−	0.546943i
$767$	−65.1038	+	37.5877i	−2.35076	+	1.35721i
$768$	1.64533	+	0.541182i	0.0593709	+	0.0195282i
$769$	−9.58581	−	5.53437i	−0.345673	−	0.199574i	0.317105	−	0.948391i	$-0.397289\pi$
$769$	−9.58581	−	5.53437i	−0.345673	−	0.199574i	−0.662778	+	0.748816i	$0.730623\pi$
$770$	1.38606	+	18.3110i	0.0499501	+	0.659882i
$771$	28.8658	+	9.49453i	1.03958	+	0.341937i
$772$	−6.48628	−	11.2346i	−0.233446	−	0.404341i
$773$	7.47378			0.268813			0.134407	−	0.990926i	$-0.457087\pi$
$773$	7.47378			0.268813			0.134407	+	0.990926i	$0.457087\pi$
$774$	1.97261	+	0.221755i	0.0709041	+	0.00797083i
$775$	4.11482	+	3.29980i	0.147809	+	0.118532i
$776$	5.99140	+	10.3774i	0.215079	+	0.372527i
$777$	−17.7324	−	19.8376i	−0.636148	−	0.711669i
$778$	−12.0686	+	20.9035i	−0.432681	+	0.749426i
$779$	21.4290	+	12.3720i	0.767772	+	0.443273i
$780$	20.8823	+	2.77540i	0.747705	+	0.0993752i
$781$	2.68541	−	24.2945i	0.0960917	−	0.869327i
$782$	35.6100			1.27341
$783$	6.00250	−	13.0978i	0.214512	−	0.468078i
$784$	−0.868843			−0.0310301
$785$	−4.41458	−	23.5065i	−0.157563	−	0.838982i
$786$	−8.25256	+	1.72299i	−0.294359	+	0.0614570i
$787$	2.07804	−	3.59927i	0.0740740	−	0.128300i	−0.826609	−	0.562776i	$-0.809733\pi$
$787$	2.07804	−	3.59927i	0.0740740	−	0.128300i	0.900683	+	0.434476i	$0.143067\pi$
$788$	8.27893	+	4.77984i	0.294925	+	0.170275i
$789$	−34.0821	−	38.1282i	−1.21336	−	1.35740i
$790$	10.6334	−	1.99697i	0.378318	−	0.0710491i
$791$	−4.93517			−0.175475
$792$	−2.95524	−	9.50087i	−0.105010	−	0.337599i
$793$			71.3237i			2.53278i
$794$	6.06703	+	10.5084i	0.215311	+	0.372929i
$795$	29.3635	−	38.1697i	1.04142	−	1.35374i
$796$	2.76549	−	4.78997i	0.0980201	−	0.169776i
$797$	14.0270	−	24.2955i	0.496862	−	0.860591i	−0.503131	−	0.864210i	$-0.667819\pi$
$797$	14.0270	−	24.2955i	0.496862	−	0.860591i	0.999993	+	0.00361925i	$0.00115205\pi$
$798$	−26.9430	−	8.86207i	−0.953771	−	0.313714i
$799$	49.4539	−	28.5522i	1.74955	−	1.01010i
$800$	−3.12806	+	3.90067i	−0.110594	+	0.137909i
$801$	−1.00419	−	2.30005i	−0.0354815	−	0.0812684i
$802$	−12.4700			−0.440330
$803$	14.6548	+	1.61988i	0.517157	+	0.0571643i
$804$	15.5744	+	17.4233i	0.549267	+	0.614474i
$805$	−19.5385	−	22.7667i	−0.688643	−	0.802421i
$806$	4.96908	+	2.86890i	0.175028	+	0.101053i
$807$	20.7001	−	4.32182i	0.728678	−	0.152135i
$808$	5.93109	−	3.42432i	0.208655	−	0.120467i
$809$	−50.8806			−1.78887			−0.894433	−	0.447202i	$-0.852421\pi$
$809$	−50.8806			−1.78887			−0.894433	+	0.447202i	$0.852421\pi$
$810$	17.8005	−	9.38841i	0.625446	−	0.329875i
$811$		−	29.3567i		−	1.03085i	−0.856933	−	0.515427i	$-0.827633\pi$
$811$		−	29.3567i		−	1.03085i	0.856933	−	0.515427i	$-0.172367\pi$
$812$	−3.43285	−	5.94587i	−0.120469	−	0.208659i
$813$	−5.23785	+	1.09357i	−0.183700	+	0.0383533i
$814$	8.26817	+	18.8422i	0.289799	+	0.660420i
$815$	−20.3368	+	17.4532i	−0.712367	+	0.611358i
$816$	7.58596	+	8.48654i	0.265562	+	0.297088i
$817$	−3.78965	+	2.18795i	−0.132583	+	0.0765468i
$818$	−26.5511			−0.928338
$819$	−37.0289	+	16.1667i	−1.29389	+	0.564909i
$820$	−2.77396	+	7.89308i	−0.0968707	+	0.275638i
$821$	17.8357	+	30.8923i	0.622470	+	1.07815i	0.989024	+	0.147753i	$0.0472041\pi$
$821$	17.8357	+	30.8923i	0.622470	+	1.07815i	−0.366554	+	0.930397i	$0.619463\pi$
$822$	2.94388	−	8.95014i	0.102679	−	0.312172i
$823$	11.9729	+	6.91258i	0.417350	+	0.240957i	0.693943	−	0.720030i	$-0.255872\pi$
$823$	11.9729	+	6.91258i	0.417350	+	0.240957i	−0.276593	+	0.960987i	$0.589205\pi$
$824$	1.83553	−	3.17923i	0.0639437	−	0.110754i
$825$	28.6768	+	1.62430i	0.998400	+	0.0565510i
$826$	17.1113	+	29.6376i	0.595378	+	1.03123i
$827$			8.28824i			0.288210i	0.989562	+	0.144105i	$0.0460304\pi$
$827$			8.28824i			0.288210i	−0.989562	+	0.144105i	$0.953970\pi$
$828$	13.0817	+	9.64964i	0.454621	+	0.335348i
$829$	37.0760			1.28770			0.643851	−	0.765151i	$-0.277336\pi$
$829$	37.0760			1.28770			0.643851	+	0.765151i	$0.277336\pi$
$830$	16.5175	−	3.10204i	0.573332	−	0.107673i
$831$	−25.1759	+	22.5043i	−0.873341	+	0.780664i
$832$	−2.71959	+	4.71047i	−0.0942849	+	0.163306i
$833$	−4.94493	−	2.85496i	−0.171332	−	0.0989185i
$834$	7.59416	+	36.3735i	0.262964	+	1.25951i
$835$	2.73647	+	14.5710i	0.0946996	+	0.504251i
$836$	17.6755	+	12.9875i	0.611318	+	0.449183i
$837$	5.45729	−	0.513835i	0.188631	−	0.0177607i
$838$	−26.1458			−0.903191
$839$	5.69442	−	3.28768i	0.196593	−	0.113503i	−0.398472	−	0.917180i	$-0.630459\pi$
$839$	5.69442	−	3.28768i	0.196593	−	0.113503i	0.595065	+	0.803677i	$0.297126\pi$
$840$	1.26346	−	9.50637i	0.0435936	−	0.328001i
$841$	10.6559	−	18.4565i	0.367444	−	0.636431i
$842$	−3.16560	−	1.82766i	−0.109094	−	0.0629853i
$843$	−23.4089	+	20.9248i	−0.806246	+	0.720689i
$844$	15.3754	−	8.87697i	0.529242	−	0.305558i
$845$	−12.2959	+	34.9869i	−0.422990	+	1.20359i
$846$	25.9045	+	2.91211i	0.890616	+	0.100120i
$847$	8.13814	+	25.9931i	0.279630	+	0.893133i
$848$	6.21710	+	10.7683i	0.213496	+	0.369786i
$849$	25.5962	+	8.41910i	0.878460	+	0.288943i
$850$	−30.6204	+	11.9217i	−1.05027	+	0.408909i
$851$	−29.1132	−	16.8085i	−0.997986	−	0.576188i
$852$	−3.98835	+	12.1256i	−0.136638	+	0.415416i
$853$	7.76911	+	13.4565i	0.266009	+	0.460741i	0.967828	−	0.251615i	$-0.0809615\pi$
$853$	7.76911	+	13.4565i	0.266009	+	0.460741i	−0.701818	+	0.712356i	$0.747628\pi$
$854$	32.4692			1.11107
$855$	−19.2928	+	39.9489i	−0.659801	+	1.36622i
$856$	2.58804			0.0884575
$857$	−10.1190	+	5.84219i	−0.345657	+	0.199565i	−0.662771	−	0.748822i	$-0.730620\pi$
$857$	−10.1190	+	5.84219i	−0.345657	+	0.199565i	0.317114	+	0.948388i	$0.397286\pi$
$858$	31.1027	−	2.98681i	1.06183	−	0.101968i
$859$	19.7580	−	34.2219i	0.674135	−	1.16764i	−0.302586	−	0.953122i	$-0.597850\pi$
$859$	19.7580	−	34.2219i	0.674135	−	1.16764i	0.976721	−	0.214514i	$-0.0688167\pi$
$860$	−0.963573	−	1.12278i	−0.0328576	−	0.0382863i
$861$	−3.27953	−	15.7079i	−0.111766	−	0.535322i
$862$	10.7394	−	6.20040i	0.365786	−	0.211187i
$863$	35.5158			1.20897			0.604485	−	0.796616i	$-0.293379\pi$
$863$	35.5158			1.20897			0.604485	+	0.796616i	$0.293379\pi$
$864$	0.487093	+	5.17327i	0.0165712	+	0.175998i
$865$	−2.42295	−	0.851525i	−0.0823828	−	0.0289527i
$866$	−7.14977	−	12.3838i	−0.242959	−	0.420817i
$867$	9.27075	+	44.4038i	0.314851	+	1.50803i
$868$	1.30603	−	2.26211i	0.0443295	−	0.0767810i
$869$	14.6950	−	6.44832i	0.498494	−	0.218744i
$870$	−9.92650	+	4.09736i	−0.336540	+	0.138914i
$871$	−63.5557	+	36.6939i	−2.15350	+	1.24332i
$872$	−4.50470			−0.152548
$873$	−21.3396	+	28.9294i	−0.722236	+	0.979112i
$874$	−35.8347			−1.21213
$875$	24.4227	+	13.0355i	0.825640	+	0.440680i
$876$	−7.31433	−	2.40583i	−0.247128	−	0.0812854i
$877$	5.91076	−	10.2377i	0.199592	−	0.345704i	−0.748804	−	0.662791i	$-0.769372\pi$
$877$	5.91076	−	10.2377i	0.199592	−	0.345704i	0.948396	+	0.317088i	$0.102705\pi$
$878$	−4.82551	+	8.35802i	−0.162853	+	0.282070i
$879$	0.151331	−	0.460086i	0.00510428	−	0.0155183i
$880$	−3.21274	+	6.68418i	−0.108302	+	0.225324i
$881$		−	4.87452i		−	0.164227i	−0.996623	−	0.0821133i	$-0.973833\pi$
$881$		−	4.87452i		−	0.164227i	0.996623	−	0.0821133i	$-0.0261669\pi$
$882$	−1.04293	−	2.38878i	−0.0351174	−	0.0804345i
$883$		−	23.3185i		−	0.784730i	−0.919810	−	0.392365i	$-0.871657\pi$
$883$		−	23.3185i		−	0.784730i	0.919810	−	0.392365i	$-0.128343\pi$
$884$	−30.9566	+	17.8728i	−1.04118	+	0.601127i
$885$	49.4794	−	20.4236i	1.66323	−	0.686532i
$886$	23.7722	+	13.7249i	0.798643	+	0.461097i
$887$	38.8949	+	22.4560i	1.30596	+	0.753998i	0.981420	−	0.191872i	$-0.0614560\pi$
$887$	38.8949	+	22.4560i	1.30596	+	0.753998i	0.324544	+	0.945871i	$0.394789\pi$
$888$	−2.19617	−	10.5189i	−0.0736985	−	0.352992i
$889$	−11.2709	−	19.5217i	−0.378013	−	0.654738i
$890$	−0.620229	+	1.76481i	−0.0207901	+	0.0591567i
$891$	22.5742	−	19.5297i	0.756262	−	0.654268i
$892$		−	15.1750i		−	0.508097i
$893$	−49.7660	+	28.7324i	−1.66535	+	0.961493i
$894$	−1.24808	+	0.260577i	−0.0417419	+	0.00871499i
$895$	15.8885	−	13.6356i	0.531093	−	0.455787i
$896$	2.14438	+	1.23806i	0.0716387	+	0.0413606i
$897$	−38.0592	+	34.0204i	−1.27076	+	1.13591i
$898$	4.65789	+	8.06770i	0.155436	+	0.269222i
$899$	−2.92500			−0.0975541
$900$	−14.4793	−	3.91800i	−0.482642	−	0.130600i
$901$			81.7158i			2.72235i
$902$	−1.36337	+	12.3342i	−0.0453951	+	0.410682i
$903$	2.69571	+	0.886671i	0.0897075	+	0.0295066i
$904$	−1.72608	−	0.996555i	−0.0574087	−	0.0331449i
$905$	−13.7436	−	16.0144i	−0.456853	−	0.532335i
$906$	−6.64577	−	2.18592i	−0.220791	−	0.0726225i
$907$	−2.55579	+	1.47559i	−0.0848638	+	0.0489961i	−0.541831	−	0.840487i	$-0.682269\pi$
$907$	−2.55579	+	1.47559i	−0.0848638	+	0.0489961i	0.456968	+	0.889483i	$0.348936\pi$
$908$			25.0755i			0.832158i
$909$	16.5343	+	12.1964i	0.548407	+	0.404529i
$910$	28.4120	+	9.98515i	0.941848	+	0.331005i
$911$	−2.85746	+	1.64975i	−0.0946718	+	0.0546588i	−0.546588	−	0.837401i	$-0.684074\pi$
$911$	−2.85746	+	1.64975i	−0.0946718	+	0.0546588i	0.451917	+	0.892060i	$0.350740\pi$
$912$	−7.63383	−	8.54009i	−0.252781	−	0.282791i
$913$	22.8268	−	10.0166i	0.755456	−	0.331502i
$914$	26.9495	+	15.5593i	0.891410	+	0.514656i
$915$	6.69100	−	50.3435i	0.221198	−	1.66431i
$916$	−12.2726	−	21.2567i	−0.405497	−	0.702341i
$917$	−12.0521			−0.397997
$918$	−14.2268	+	31.0437i	−0.469553	+	1.02459i
$919$		−	38.2488i		−	1.26171i	−0.775900	−	0.630856i	$-0.782704\pi$
$919$		−	38.2488i		−	1.26171i	0.775900	−	0.630856i	$-0.217296\pi$
$920$	−2.23637	−	11.9081i	−0.0737309	−	0.392598i
$921$	0.363801	+	1.74249i	0.0119876	+	0.0574169i
$922$	14.8380	+	8.56675i	0.488665	+	0.282131i
$923$	−34.7147	−	20.0426i	−1.14265	−	0.659709i
$924$	−1.35970	−	14.1591i	−0.0447310	−	0.465799i
$925$	30.6611	+	4.70670i	1.00813	+	0.154755i
$926$	−10.7754			−0.354102
$927$	10.9442	+	1.23032i	0.359456	+	0.0404089i
$928$		−	2.77277i		−	0.0910206i
$929$	5.38715	−	3.11027i	0.176747	−	0.102045i	−0.409017	−	0.912527i	$-0.634128\pi$
$929$	5.38715	−	3.11027i	0.176747	−	0.102045i	0.585763	+	0.810482i	$0.300795\pi$
$930$	−3.23827	−	2.49116i	−0.106187	−	0.0816883i
$931$	4.97614	+	2.87297i	0.163086	+	0.0941579i
$932$	13.3104	+	7.68476i	0.435997	+	0.251723i
$933$	−0.0318579	+	0.0968564i	−0.00104298	+	0.00317093i
$934$	18.8705	−	10.8949i	0.617462	−	0.356492i
$935$	−40.2488	+	27.4855i	−1.31628	+	0.898871i
$936$	−16.2154	−	1.82289i	−0.530018	−	0.0595830i
$937$	13.4721			0.440115			0.220057	−	0.975487i	$-0.429376\pi$
$937$	13.4721			0.440115			0.220057	+	0.975487i	$0.429376\pi$
$938$	16.7044	+	28.9329i	0.545418	+	0.944692i
$939$	−15.3222	−	17.1412i	−0.500021	−	0.559381i
$940$	−12.6537	−	14.7444i	−0.412719	−	0.480909i
$941$	14.6369	−	25.3519i	0.477150	−	0.826448i	−0.522507	−	0.852635i	$-0.675003\pi$
$941$	14.6369	−	25.3519i	0.477150	−	0.826448i	0.999657	+	0.0261872i	$0.00833660\pi$
$942$	3.78633	+	18.1353i	0.123365	+	0.590880i
$943$	−10.1369	−	17.5576i	−0.330102	−	0.571753i
$944$			13.8211i			0.449838i
$945$	27.6533	−	7.93742i	0.899561	−	0.258204i
$946$	−1.76847	−	1.29943i	−0.0574980	−	0.0422482i
$947$	−13.9564	−	24.1732i	−0.453522	−	0.785523i	0.545080	−	0.838384i	$-0.316499\pi$
$947$	−13.9564	−	24.1732i	−0.453522	−	0.785523i	−0.998602	+	0.0528610i	$0.983166\pi$
$948$	−8.20367	+	1.71278i	−0.266443	+	0.0556286i
$949$	12.0900	−	20.9404i	0.392457	−	0.679755i
$950$	30.8136	−	11.9969i	0.999725	−	0.389230i
$951$	11.3166	−	10.1157i	0.366967	−	0.328026i
$952$	8.13635	+	14.0926i	0.263701	+	0.456743i
$953$			44.5167i			1.44204i	0.692915	+	0.721019i	$0.256326\pi$
$953$			44.5167i			1.44204i	−0.692915	+	0.721019i	$0.743674\pi$
$954$	−22.1434	+	30.0192i	−0.716921	+	0.971907i
$955$	−54.6316	−	19.1998i	−1.76784	−	0.621291i
$956$	1.64421	+	2.84786i	0.0531776	+	0.0921063i
$957$	−12.9699	+	9.24632i	−0.419257	+	0.298891i
$958$	−34.1744	−	19.7306i	−1.10412	−	0.637466i
$959$	6.73469	−	11.6648i	0.217474	−	0.376677i
$960$	2.36151	−	3.06974i	0.0762174	−	0.0990753i
$961$	14.9436	+	25.8831i	0.482051	+	0.834937i
$962$	33.7450			1.08798
$963$	3.10661	+	7.11553i	0.100109	+	0.229295i
$964$			23.7557i			0.765120i
$965$	−28.5091	+	5.35409i	−0.917742	+	0.172354i
$966$	15.4873	+	17.3259i	0.498297	+	0.557453i
$967$	−14.1475	+	24.5042i	−0.454953	+	0.788001i	−0.998685	−	0.0512572i	$-0.983677\pi$
$967$	−14.1475	+	24.5042i	−0.454953	+	0.788001i	0.543733	+	0.839258i	$0.317011\pi$
$968$	−2.40243	+	10.7344i	−0.0772171	+	0.345018i
$969$	−15.3850	−	73.6893i	−0.494239	−	2.36724i
$970$	26.3340	−	4.94559i	0.845534	−	0.158793i
$971$		−	34.4577i		−	1.10580i	−0.833248	−	0.552899i	$-0.813521\pi$
$971$		−	34.4577i		−	1.10580i	0.833248	−	0.552899i	$-0.186479\pi$
$972$	−13.6386	+	7.54905i	−0.437459	+	0.242136i
$973$			53.1204i			1.70296i
$974$	18.3300	+	31.7485i	0.587332	+	1.01729i
$975$	21.3369	−	41.9952i	0.683328	−	1.34492i
$976$	11.3561	+	6.55647i	0.363501	+	0.209868i
$977$	−17.2251	+	29.8348i	−0.551081	+	0.954499i	0.447116	+	0.894476i	$0.352451\pi$
$977$	−17.2251	+	29.8348i	−0.551081	+	0.954499i	−0.998197	+	0.0600237i	$0.980882\pi$
$978$	15.4767	−	13.8344i	0.494891	−	0.442375i
$979$	−0.304835	+	2.75779i	−0.00974256	+	0.0881394i
$980$	−0.644156	+	1.83290i	−0.0205768	+	0.0585497i
$981$	−5.40731	−	12.3851i	−0.172642	−	0.395427i
$982$		−	5.21239i		−	0.166334i
$983$	6.57684	+	11.3914i	0.209768	+	0.363330i	0.951642	−	0.307211i	$-0.0993956\pi$
$983$	6.57684	+	11.3914i	0.209768	+	0.363330i	−0.741873	+	0.670540i	$0.766062\pi$
$984$	2.02485	−	6.15608i	0.0645500	−	0.196249i
$985$	16.2214	−	13.9213i	0.516858	−	0.443571i
$986$	9.11113	−	15.7809i	0.290158	−	0.502568i
$987$	35.4003	+	11.6438i	1.12680	+	0.370628i
$988$	31.1519	−	17.9856i	0.991075	−	0.572197i
$989$	3.58535			0.114007
$990$	−22.2339	−	0.809571i	−0.706639	−	0.0257299i
$991$	51.2799			1.62896			0.814480	−	0.580191i	$-0.197022\pi$
$991$	51.2799			1.62896			0.814480	+	0.580191i	$0.197022\pi$
$992$	0.913571	−	0.527450i	0.0290059	−	0.0167466i
$993$	−19.3741	+	17.3181i	−0.614818	+	0.549574i
$994$	−9.12411	+	15.8034i	−0.289399	+	0.501254i
$995$	−8.05450	−	9.38528i	−0.255345	−	0.297533i
$996$	−12.7433	+	2.66058i	−0.403788	+	0.0843038i
$997$	11.7285	+	20.3144i	0.371446	+	0.643364i	0.989788	−	0.142545i	$-0.0455286\pi$
$997$	11.7285	+	20.3144i	0.371446	+	0.643364i	−0.618342	+	0.785909i	$0.712195\pi$
$998$		−	27.4114i		−	0.867694i
$999$	26.2843	−	18.6647i	0.831599	−	0.590525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.329.17	✓	144
5.4	even	2	inner	990.2.o.a.329.56	yes	144
9.2	odd	6	inner	990.2.o.a.659.20	yes	144
11.10	odd	2	inner	990.2.o.a.329.53	yes	144
45.29	odd	6	inner	990.2.o.a.659.53	yes	144
55.54	odd	2	inner	990.2.o.a.329.20	yes	144
99.65	even	6	inner	990.2.o.a.659.56	yes	144
495.164	even	6	inner	990.2.o.a.659.17	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.17	✓	144	1.1	even	1	trivial
990.2.o.a.329.20	yes	144	55.54	odd	2	inner
990.2.o.a.329.53	yes	144	11.10	odd	2	inner
990.2.o.a.329.56	yes	144	5.4	even	2	inner
990.2.o.a.659.17	yes	144	495.164	even	6	inner
990.2.o.a.659.20	yes	144	9.2	odd	6	inner
990.2.o.a.659.53	yes	144	45.29	odd	6	inner
990.2.o.a.659.56	yes	144	99.65	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.353989 - 1.69549i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.45625 - 1.69686i) q^{5} +(1.15431 + 1.29134i) q^{6} +(1.23806 + 2.14438i) q^{7} +1.00000i q^{8} +(-2.74938 + 1.20037i) q^{9} +(2.10958 + 0.741395i) q^{10} +(3.29655 + 0.364386i) q^{11} +(-1.64533 - 0.541182i) q^{12} +(2.71959 - 4.71047i) q^{13} +(-2.14438 - 1.23806i) q^{14} +(-2.36151 + 3.06974i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.57186i q^{17} +(1.78085 - 2.41424i) q^{18} +6.61333i q^{19} +(-2.19765 + 0.412724i) q^{20} +(3.19752 - 2.85821i) q^{21} +(-3.03709 + 1.33271i) q^{22} +(2.70928 - 4.69261i) q^{23} +(1.69549 - 0.353989i) q^{24} +(-0.758650 + 4.94211i) q^{25} +5.43919i q^{26} +(3.00847 + 4.23664i) q^{27} +2.47612 q^{28} +(-1.38639 - 2.40129i) q^{29} +(0.510260 - 3.83922i) q^{30} +(0.527450 - 0.913571i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.549128 - 5.71826i) q^{33} +(3.28593 + 5.69140i) q^{34} +(1.83578 - 5.22357i) q^{35} +(-0.335140 + 2.98122i) q^{36} -6.20405i q^{37} +(-3.30667 - 5.72731i) q^{38} +(-8.94928 - 2.94359i) q^{39} +(1.69686 - 1.45625i) q^{40} +(1.87077 - 3.24027i) q^{41} +(-1.34003 + 4.07404i) q^{42} +(0.330840 + 0.573031i) q^{43} +(1.96384 - 2.67270i) q^{44} +(6.04066 + 2.91727i) q^{45} +5.41856i q^{46} +(4.34462 + 7.52510i) q^{47} +(-1.29134 + 1.15431i) q^{48} +(0.434422 - 0.752440i) q^{49} +(-1.81405 - 4.65932i) q^{50} +(-11.1425 + 2.32637i) q^{51} +(-2.71959 - 4.71047i) q^{52} -12.4342 q^{53} +(-4.72373 - 2.16480i) q^{54} +(-4.18230 - 6.12441i) q^{55} +(-2.14438 + 1.23806i) q^{56} +(11.2128 - 2.34105i) q^{57} +(2.40129 + 1.38639i) q^{58} +(-11.9694 - 6.91054i) q^{59} +(1.47771 + 3.57999i) q^{60} +(-11.3561 + 6.55647i) q^{61} +1.05490i q^{62} +(-5.97795 - 4.40959i) q^{63} -1.00000 q^{64} +(-11.9534 + 2.24488i) q^{65} +(3.33469 + 4.67759i) q^{66} +(-11.6848 - 6.74621i) q^{67} +(-5.69140 - 3.28593i) q^{68} +(-8.91533 - 2.93243i) q^{69} +(1.02195 + 5.44164i) q^{70} -7.36969i q^{71} +(-1.20037 - 2.74938i) q^{72} +4.44550 q^{73} +(3.10202 + 5.37286i) q^{74} +(8.64786 - 0.463169i) q^{75} +(5.72731 + 3.30667i) q^{76} +(3.29994 + 7.52018i) q^{77} +(9.22210 - 1.92541i) q^{78} +(4.19028 - 2.41926i) q^{79} +(-0.741395 + 2.10958i) q^{80} +(6.11822 - 6.60056i) q^{81} +3.74154i q^{82} +(6.50905 - 3.75800i) q^{83} +(-0.876518 - 4.19824i) q^{84} +(-11.1515 + 9.57030i) q^{85} +(-0.573031 - 0.330840i) q^{86} +(-3.58060 + 3.20063i) q^{87} +(-0.364386 + 3.29655i) q^{88} +0.836570i q^{89} +(-6.69000 + 0.493902i) q^{90} +13.4681 q^{91} +(-2.70928 - 4.69261i) q^{92} +(-1.73566 - 0.570894i) q^{93} +(-7.52510 - 4.34462i) q^{94} +(11.2219 - 9.63069i) q^{95} +(0.541182 - 1.64533i) q^{96} +(10.3774 - 5.99140i) q^{97} +0.868843i q^{98} +(-9.50087 + 2.95524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

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