LMFDB - Embedded newform 966.2.l.c.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.454222 - 1.67143i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.02138 - 3.50113i) q^{5} +(-1.22908 + 1.22039i) q^{6} +(2.64571 + 0.0151948i) q^{7} -1.00000i q^{8} +(-2.58737 - 1.51840i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.454222 - 1.67143i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.02138 - 3.50113i) q^{5} +(-1.22908 + 1.22039i) q^{6} +(2.64571 + 0.0151948i) q^{7} -1.00000i q^{8} +(-2.58737 - 1.51840i) q^{9} +(-3.50113 + 2.02138i) q^{10} +(-4.36781 + 2.52176i) q^{11} +(1.67461 - 0.442348i) q^{12} -0.407478i q^{13} +(-2.28365 - 1.33601i) q^{14} +(-4.93375 - 4.96889i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.316710 - 0.548557i) q^{17} +(1.48152 + 2.60866i) q^{18} +(-5.54253 - 3.19998i) q^{19} +4.04276 q^{20} +(1.22714 - 4.41522i) q^{21} +5.04352 q^{22} +(0.866025 + 0.500000i) q^{23} +(-1.67143 - 0.454222i) q^{24} +(-5.67196 - 9.82412i) q^{25} +(-0.203739 + 0.352886i) q^{26} +(-3.71314 + 3.63491i) q^{27} +(1.30969 + 2.29885i) q^{28} -2.33239i q^{29} +(1.78831 + 6.77006i) q^{30} +(-4.47097 + 2.58132i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.23099 + 8.44594i) q^{33} +0.633419i q^{34} +(5.40118 - 9.23226i) q^{35} +(0.0212915 - 2.99992i) q^{36} +(1.82672 - 3.16396i) q^{37} +(3.19998 + 5.54253i) q^{38} +(-0.681071 - 0.185085i) q^{39} +(-3.50113 - 2.02138i) q^{40} +9.25865 q^{41} +(-3.27034 + 3.21012i) q^{42} +10.5834 q^{43} +(-4.36781 - 2.52176i) q^{44} +(-10.5462 + 5.98944i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.64632 + 2.85152i) q^{47} +(1.22039 + 1.22908i) q^{48} +(6.99954 + 0.0804020i) q^{49} +11.3439i q^{50} +(-1.06073 + 0.280192i) q^{51} +(0.352886 - 0.203739i) q^{52} +(5.44908 - 3.14603i) q^{53} +(5.03313 - 1.29136i) q^{54} +20.3897i q^{55} +(0.0151948 - 2.64571i) q^{56} +(-7.86609 + 7.81045i) q^{57} +(-1.16619 + 2.01991i) q^{58} +(1.38089 + 2.39177i) q^{59} +(1.83631 - 6.75720i) q^{60} +(-13.2213 - 7.63330i) q^{61} +5.16264 q^{62} +(-6.82234 - 4.05656i) q^{63} -1.00000 q^{64} +(-1.42663 - 0.823667i) q^{65} +(2.29088 - 8.42989i) q^{66} +(0.427367 + 0.740221i) q^{67} +(0.316710 - 0.548557i) q^{68} +(1.22908 - 1.22039i) q^{69} +(-9.29369 + 5.29478i) q^{70} -13.9280i q^{71} +(-1.51840 + 2.58737i) q^{72} +(7.94013 - 4.58424i) q^{73} +(-3.16396 + 1.82672i) q^{74} +(-18.9967 + 5.01796i) q^{75} -6.39996i q^{76} +(-11.5943 + 6.60547i) q^{77} +(0.497282 + 0.500824i) q^{78} +(7.07821 - 12.2598i) q^{79} +(2.02138 + 3.50113i) q^{80} +(4.38892 + 7.85732i) q^{81} +(-8.01822 - 4.62932i) q^{82} -9.22214 q^{83} +(4.43726 - 1.14488i) q^{84} -2.56076 q^{85} +(-9.16546 - 5.29168i) q^{86} +(-3.89843 - 1.05942i) q^{87} +(2.52176 + 4.36781i) q^{88} +(-6.19702 + 10.7335i) q^{89} +(12.1280 + 0.0860763i) q^{90} +(0.00619154 - 1.07807i) q^{91} +1.00000i q^{92} +(2.28368 + 8.64542i) q^{93} +(2.85152 - 1.64632i) q^{94} +(-22.4071 + 12.9368i) q^{95} +(-0.442348 - 1.67461i) q^{96} -2.81141i q^{97} +(-6.02158 - 3.56940i) q^{98} +(15.1302 + 0.107384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.454222	−	1.67143i	0.262245	−	0.965001i
$3$	0.454222	−	1.67143i	0.262245	−	0.965001i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.02138	−	3.50113i	0.903989	−	1.56575i	0.0817199	−	0.996655i	$-0.473959\pi$
$5$	2.02138	−	3.50113i	0.903989	−	1.56575i	0.822269	−	0.569099i	$-0.192708\pi$
$6$	−1.22908	+	1.22039i	−0.501771	+	0.498223i
$7$	2.64571	+	0.0151948i	0.999984	+	0.00574309i
$7$	2.64571	+	0.0151948i	0.999984	+	0.00574309i
$8$		−	1.00000i		−	0.353553i
$9$	−2.58737	−	1.51840i	−0.862455	−	0.506134i
$10$	−3.50113	+	2.02138i	−1.10716	+	0.639217i
$11$	−4.36781	+	2.52176i	−1.31695	+	0.760339i	−0.983236	−	0.182337i	$-0.941634\pi$
$11$	−4.36781	+	2.52176i	−1.31695	+	0.760339i	−0.333709	+	0.942676i	$0.608300\pi$
$12$	1.67461	−	0.442348i	0.483419	−	0.127695i
$13$		−	0.407478i		−	0.113014i	−0.998402	−	0.0565070i	$-0.982004\pi$
$13$		−	0.407478i		−	0.113014i	0.998402	−	0.0565070i	$-0.0179963\pi$
$14$	−2.28365	−	1.33601i	−0.610332	−	0.357064i
$15$	−4.93375	−	4.96889i	−1.27389	−	1.28296i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.316710	−	0.548557i	−0.0768134	−	0.133045i	0.825060	−	0.565045i	$-0.191141\pi$
$17$	−0.316710	−	0.548557i	−0.0768134	−	0.133045i	−0.901873	+	0.432000i	$0.857808\pi$
$18$	1.48152	+	2.60866i	0.349198	+	0.614866i
$19$	−5.54253	−	3.19998i	−1.27154	−	0.734126i	−0.296265	−	0.955106i	$-0.595741\pi$
$19$	−5.54253	−	3.19998i	−1.27154	−	0.734126i	−0.975278	+	0.220980i	$0.929074\pi$
$20$	4.04276			0.903989
$21$	1.22714	−	4.41522i	0.267783	−	0.963479i
$22$	5.04352			1.07528
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$	−1.67143	−	0.454222i	−0.341179	−	0.0927176i
$25$	−5.67196	−	9.82412i	−1.13439	−	1.96482i
$26$	−0.203739	+	0.352886i	−0.0399565	+	0.0692066i
$27$	−3.71314	+	3.63491i	−0.714594	+	0.699539i
$28$	1.30969	+	2.29885i	0.247509	+	0.434441i
$29$		−	2.33239i		−	0.433114i	−0.976270	−	0.216557i	$-0.930517\pi$
$29$		−	2.33239i		−	0.433114i	0.976270	−	0.216557i	$-0.0694827\pi$
$30$	1.78831	+	6.77006i	0.326499	+	1.23604i
$31$	−4.47097	+	2.58132i	−0.803011	+	0.463618i	−0.844523	−	0.535520i	$-0.820116\pi$
$31$	−4.47097	+	2.58132i	−0.803011	+	0.463618i	0.0415122	+	0.999138i	$0.486782\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.23099	+	8.44594i	0.388365	+	1.47025i
$34$			0.633419i			0.108631i
$35$	5.40118	−	9.23226i	0.912966	−	1.56054i
$36$	0.0212915	−	2.99992i	0.00354858	−	0.499987i
$37$	1.82672	−	3.16396i	0.300310	−	0.520153i	−0.675896	−	0.736997i	$-0.736243\pi$
$37$	1.82672	−	3.16396i	0.300310	−	0.520153i	0.976206	+	0.216844i	$0.0695765\pi$
$38$	3.19998	+	5.54253i	0.519105	+	0.899117i
$39$	−0.681071	−	0.185085i	−0.109059	−	0.0296374i
$40$	−3.50113	−	2.02138i	−0.553578	−	0.319608i
$41$	9.25865			1.44596			0.722979	−	0.690870i	$-0.242772\pi$
$41$	9.25865			1.44596			0.722979	+	0.690870i	$0.242772\pi$
$42$	−3.27034	+	3.21012i	−0.504624	+	0.495333i
$43$	10.5834			1.61395			0.806973	−	0.590588i	$-0.201104\pi$
$43$	10.5834			1.61395			0.806973	+	0.590588i	$0.201104\pi$
$44$	−4.36781	−	2.52176i	−0.658473	−	0.380169i
$45$	−10.5462	+	5.98944i	−1.57213	+	0.892854i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−1.64632	+	2.85152i	−0.240141	+	0.415937i	−0.960754	−	0.277401i	$-0.910527\pi$
$47$	−1.64632	+	2.85152i	−0.240141	+	0.415937i	0.720613	+	0.693337i	$0.243860\pi$
$48$	1.22039	+	1.22908i	0.176148	+	0.177403i
$49$	6.99954	+	0.0804020i	0.999934	+	0.0114860i
$50$			11.3439i			1.60427i
$51$	−1.06073	+	0.280192i	−0.148532	+	0.0392347i
$52$	0.352886	−	0.203739i	0.0489365	−	0.0282535i
$53$	5.44908	−	3.14603i	0.748488	−	0.432140i	−0.0766590	−	0.997057i	$-0.524425\pi$
$53$	5.44908	−	3.14603i	0.748488	−	0.432140i	0.825147	+	0.564917i	$0.191092\pi$
$54$	5.03313	−	1.29136i	0.684922	−	0.175731i
$55$			20.3897i			2.74935i
$56$	0.0151948	−	2.64571i	0.00203049	−	0.353548i
$57$	−7.86609	+	7.81045i	−1.04189	+	1.03452i
$58$	−1.16619	+	2.01991i	−0.153129	+	0.265227i
$59$	1.38089	+	2.39177i	0.179777	+	0.311382i	0.941804	−	0.336163i	$-0.109129\pi$
$59$	1.38089	+	2.39177i	0.179777	+	0.311382i	−0.762027	+	0.647545i	$0.775796\pi$
$60$	1.83631	−	6.75720i	0.237067	−	0.872350i
$61$	−13.2213	−	7.63330i	−1.69281	−	0.977344i	−0.952234	−	0.305370i	$-0.901220\pi$
$61$	−13.2213	−	7.63330i	−1.69281	−	0.977344i	−0.740575	−	0.671974i	$-0.765447\pi$
$62$	5.16264			0.655655
$63$	−6.82234	−	4.05656i	−0.859534	−	0.511079i
$64$	−1.00000			−0.125000
$65$	−1.42663	−	0.823667i	−0.176952	−	0.102163i
$66$	2.29088	−	8.42989i	0.281987	−	1.03765i
$67$	0.427367	+	0.740221i	0.0522112	+	0.0904324i	0.890950	−	0.454102i	$-0.150040\pi$
$67$	0.427367	+	0.740221i	0.0522112	+	0.0904324i	−0.838739	+	0.544534i	$0.816706\pi$
$68$	0.316710	−	0.548557i	0.0384067	−	0.0665223i
$69$	1.22908	−	1.22039i	0.147964	−	0.146918i
$70$	−9.29369	+	5.29478i	−1.11081	+	0.632848i
$71$		−	13.9280i		−	1.65295i	−0.562977	−	0.826473i	$-0.690344\pi$
$71$		−	13.9280i		−	1.65295i	0.562977	−	0.826473i	$-0.309656\pi$
$72$	−1.51840	+	2.58737i	−0.178945	+	0.304924i
$73$	7.94013	−	4.58424i	0.929322	−	0.536544i	0.0427250	−	0.999087i	$-0.486396\pi$
$73$	7.94013	−	4.58424i	0.929322	−	0.536544i	0.886597	+	0.462542i	$0.153063\pi$
$74$	−3.16396	+	1.82672i	−0.367803	+	0.212351i
$75$	−18.9967	+	5.01796i	−2.19355	+	0.579424i
$76$		−	6.39996i		−	0.734126i
$77$	−11.5943	+	6.60547i	−1.32129	+	0.752763i
$78$	0.497282	+	0.500824i	0.0563061	+	0.0567071i
$79$	7.07821	−	12.2598i	0.796360	−	1.37934i	−0.125611	−	0.992080i	$-0.540089\pi$
$79$	7.07821	−	12.2598i	0.796360	−	1.37934i	0.921972	−	0.387257i	$-0.126577\pi$
$80$	2.02138	+	3.50113i	0.225997	+	0.391439i
$81$	4.38892	+	7.85732i	0.487657	+	0.873035i
$82$	−8.01822	−	4.62932i	−0.885465	−	0.511223i
$83$	−9.22214			−1.01226			−0.506131	−	0.862457i	$-0.668925\pi$
$83$	−9.22214			−1.01226			−0.506131	+	0.862457i	$0.668925\pi$
$84$	4.43726	−	1.14488i	0.484144	−	0.124916i
$85$	−2.56076			−0.277754
$86$	−9.16546	−	5.29168i	−0.988337	−	0.570616i
$87$	−3.89843	−	1.05942i	−0.417956	−	0.113582i
$88$	2.52176	+	4.36781i	0.268820	+	0.465610i
$89$	−6.19702	+	10.7335i	−0.656882	+	1.13775i	0.324536	+	0.945873i	$0.394792\pi$
$89$	−6.19702	+	10.7335i	−0.656882	+	1.13775i	−0.981418	+	0.191880i	$0.938541\pi$
$90$	12.1280	+	0.0860763i	1.27840	+	0.00907324i
$91$	0.00619154	−	1.07807i	0.000649050	−	0.113012i
$92$			1.00000i			0.104257i
$93$	2.28368	+	8.64542i	0.236807	+	0.896488i
$94$	2.85152	−	1.64632i	0.294112	−	0.169805i
$95$	−22.4071	+	12.9368i	−2.29892	+	1.32728i
$96$	−0.442348	−	1.67461i	−0.0451470	−	0.170914i
$97$		−	2.81141i		−	0.285456i	−0.989762	−	0.142728i	$-0.954413\pi$
$97$		−	2.81141i		−	0.285456i	0.989762	−	0.142728i	$-0.0455874\pi$
$98$	−6.02158	−	3.56940i	−0.608271	−	0.360564i
$99$	15.1302	+	0.107384i	1.52064	+	0.0107925i
$100$	5.67196	−	9.82412i	0.567196	−	0.982412i
$101$	4.20929	+	7.29071i	0.418840	+	0.725453i	0.995823	−	0.0913035i	$-0.0291033\pi$
$101$	4.20929	+	7.29071i	0.418840	+	0.725453i	−0.576983	+	0.816756i	$0.695770\pi$
$102$	1.05872	+	0.287713i	0.104829	+	0.0284878i
$103$	9.63339	+	5.56184i	0.949206	+	0.548024i	0.892834	−	0.450385i	$-0.148713\pi$
$103$	9.63339	+	5.56184i	0.949206	+	0.548024i	0.0563719	+	0.998410i	$0.482047\pi$
$104$	−0.407478			−0.0399565
$105$	−12.9778	−	13.2212i	−1.26650	−	1.29026i
$106$	−6.29205			−0.611138
$107$	6.76335	+	3.90482i	0.653838	+	0.377493i	0.789925	−	0.613204i	$-0.210119\pi$
$107$	6.76335	+	3.90482i	0.653838	+	0.377493i	−0.136087	+	0.990697i	$0.543453\pi$
$108$	−5.00450	−	1.39822i	−0.481558	−	0.134544i
$109$	2.48688	+	4.30740i	0.238200	+	0.412574i	0.960198	−	0.279321i	$-0.0901093\pi$
$109$	2.48688	+	4.30740i	0.238200	+	0.412574i	−0.721998	+	0.691895i	$0.756776\pi$
$110$	10.1949	−	17.6580i	0.972042	−	1.68363i
$111$	−4.45862	−	4.49037i	−0.423193	−	0.426207i
$112$	−1.33601	+	2.28365i	−0.126241	+	0.215785i
$113$			13.1590i			1.23790i	0.785431	+	0.618949i	$0.212441\pi$
$113$			13.1590i			1.23790i	−0.785431	+	0.618949i	$0.787559\pi$
$114$	10.7175	−	2.83101i	1.00378	−	0.265148i
$115$	3.50113	−	2.02138i	0.326482	−	0.188495i
$116$	2.01991	−	1.16619i	0.187544	−	0.108278i
$117$	−0.618714	+	1.05429i	−0.0572002	+	0.0974694i
$118$		−	2.76178i		−	0.254242i
$119$	−0.829586	−	1.45613i	−0.0760480	−	0.133484i
$120$	−4.96889	+	4.93375i	−0.453596	+	0.450388i
$121$	7.21853	−	12.5029i	0.656230	−	1.13662i
$122$	7.63330	+	13.2213i	0.691086	+	1.19700i
$123$	4.20548	−	15.4752i	0.379195	−	1.39535i
$124$	−4.47097	−	2.58132i	−0.401505	−	0.231809i
$125$	−25.6469			−2.29393
$126$	3.88004	+	6.92425i	0.345661	+	0.616862i
$127$	−6.74581			−0.598594			−0.299297	−	0.954160i	$-0.596752\pi$
$127$	−6.74581			−0.598594			−0.299297	+	0.954160i	$0.596752\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	4.80719	−	17.6894i	0.423250	−	1.55746i
$130$	0.823667	+	1.42663i	0.0722404	+	0.125124i
$131$	0.476912	−	0.826036i	0.0416680	−	0.0721711i	−0.844439	−	0.535651i	$-0.820066\pi$
$131$	0.476912	−	0.826036i	0.0416680	−	0.0721711i	0.886107	+	0.463480i	$0.153399\pi$
$132$	−6.19890	+	6.15506i	−0.539545	+	0.535729i
$133$	−14.6153	−	8.55043i	−1.26731	−	0.741416i
$134$		−	0.854734i		−	0.0738378i
$135$	5.22064	+	20.3477i	0.449321	+	1.75125i
$136$	−0.548557	+	0.316710i	−0.0470384	+	0.0271576i
$137$	12.9111	−	7.45424i	1.10307	−	0.636859i	0.166045	−	0.986118i	$-0.446900\pi$
$137$	12.9111	−	7.45424i	1.10307	−	0.636859i	0.937026	+	0.349260i	$0.113567\pi$
$138$	−1.67461	+	0.442348i	−0.142553	+	0.0376552i
$139$			16.9359i			1.43649i	0.695792	+	0.718243i	$0.255053\pi$
$139$			16.9359i			1.43649i	−0.695792	+	0.718243i	$0.744947\pi$
$140$	10.6960	+	0.0614289i	0.903974	+	0.00519169i
$141$	4.01832	+	4.04694i	0.338404	+	0.340814i
$142$	−6.96398	+	12.0620i	−0.584405	+	1.01222i
$143$	1.02756	+	1.77979i	0.0859289	+	0.148833i
$144$	2.60866	−	1.48152i	0.217388	−	0.123460i
$145$	−8.16601	−	4.71465i	−0.678150	−	0.391530i
$146$	−9.16847			−0.758788
$147$	3.31373	−	11.6627i	0.273312	−	0.961925i
$148$	3.65343			0.300310
$149$	−9.52881	−	5.50146i	−0.780631	−	0.450697i	0.0560231	−	0.998429i	$-0.482158\pi$
$149$	−9.52881	−	5.50146i	−0.780631	−	0.450697i	−0.836654	+	0.547732i	$0.815491\pi$
$150$	18.9606	+	5.15265i	1.54812	+	0.420712i
$151$	−0.264804	−	0.458655i	−0.0215495	−	0.0373248i	0.855050	−	0.518546i	$-0.173527\pi$
$151$	−0.264804	−	0.458655i	−0.0215495	−	0.0373248i	−0.876599	+	0.481221i	$0.840193\pi$
$152$	−3.19998	+	5.54253i	−0.259553	+	0.449558i
$153$	−0.0134864	+	1.90021i	−0.00109031	+	0.153623i
$154$	13.3437	+	0.0766352i	1.07526	+	0.00617544i
$155$			20.8713i			1.67642i
$156$	−0.180247	−	0.682367i	−0.0144313	−	0.0546331i
$157$	2.93219	−	1.69290i	0.234014	−	0.135108i	−0.378408	−	0.925639i	$-0.623528\pi$
$157$	2.93219	−	1.69290i	0.234014	−	0.135108i	0.612423	+	0.790531i	$0.290195\pi$
$158$	−12.2598	+	7.07821i	−0.975338	+	0.563112i
$159$	−2.78328	−	10.5368i	−0.220728	−	0.835619i
$160$		−	4.04276i		−	0.319608i
$161$	2.28365	+	1.33601i	0.179977	+	0.105293i
$162$	0.127746	−	8.99909i	0.0100366	−	0.707036i
$163$	4.12228	−	7.14000i	0.322882	−	0.559248i	−0.658199	−	0.752844i	$-0.728682\pi$
$163$	4.12228	−	7.14000i	0.322882	−	0.559248i	0.981081	+	0.193596i	$0.0620150\pi$
$164$	4.62932	+	8.01822i	0.361489	+	0.626118i
$165$	34.0800	+	9.26146i	2.65313	+	0.721004i
$166$	7.98661	+	4.61107i	0.619881	+	0.357888i
$167$	4.68173			0.362283			0.181142	−	0.983457i	$-0.442021\pi$
$167$	4.68173			0.362283			0.181142	+	0.983457i	$0.442021\pi$
$168$	−4.41522	−	1.22714i	−0.340641	−	0.0946755i
$169$	12.8340			0.987228
$170$	2.21769	+	1.28038i	0.170089	+	0.0982008i
$171$	9.48169	+	16.6953i	0.725083	+	1.27672i
$172$	5.29168	+	9.16546i	0.403487	+	0.698859i
$173$	1.99397	−	3.45366i	0.151599	−	0.262577i	−0.780217	−	0.625509i	$-0.784891\pi$
$173$	1.99397	−	3.45366i	0.151599	−	0.262577i	0.931815	+	0.362933i	$0.118225\pi$
$174$	2.84643	+	2.86670i	0.215787	+	0.217324i
$175$	−14.8571	−	26.0779i	−1.12309	−	1.97131i
$176$		−	5.04352i		−	0.380169i
$177$	4.62491	−	1.22167i	0.347630	−	0.0918262i
$178$	10.7335	−	6.19702i	0.804513	−	0.464486i
$179$	17.6724	−	10.2031i	1.32089	−	0.762619i	0.337023	−	0.941496i	$-0.390580\pi$
$179$	17.6724	−	10.2031i	1.32089	−	0.762619i	0.983871	+	0.178877i	$0.0572465\pi$
$180$	−10.4601	−	6.13853i	−0.779650	−	0.457539i
$181$			4.56195i			0.339087i	0.985523	+	0.169543i	$0.0542293\pi$
$181$			4.56195i			0.339087i	−0.985523	+	0.169543i	$0.945771\pi$
$182$	−0.544395	+	0.930537i	−0.0403533	+	0.0689760i
$183$	−18.7639	+	18.6312i	−1.38707	+	1.37726i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−7.38498	−	12.7912i	−0.542954	−	0.940424i
$186$	2.34498	−	8.62899i	0.171942	−	0.632708i
$187$	2.76666	+	1.59733i	0.202318	+	0.116808i
$188$	−3.29265			−0.240141
$189$	−9.87912	+	9.56049i	−0.718600	+	0.695424i
$190$	25.8735			1.87706
$191$	3.90107	+	2.25229i	0.282272	+	0.162970i	0.634451	−	0.772963i	$-0.281226\pi$
$191$	3.90107	+	2.25229i	0.282272	+	0.162970i	−0.352180	+	0.935932i	$0.614559\pi$
$192$	−0.454222	+	1.67143i	−0.0327806	+	0.120625i
$193$	−2.07842	−	3.59992i	−0.149608	−	0.259128i	0.781475	−	0.623937i	$-0.214468\pi$
$193$	−2.07842	−	3.59992i	−0.149608	−	0.259128i	−0.931082	+	0.364809i	$0.881134\pi$
$194$	−1.40571	+	2.43476i	−0.100924	+	0.174805i
$195$	−2.02471	+	2.01039i	−0.144993	+	0.143967i
$196$	3.43014	+	6.10198i	0.245010	+	0.435856i
$197$		−	23.6112i		−	1.68223i	−0.540859	−	0.841113i	$-0.681901\pi$
$197$		−	23.6112i		−	1.68223i	0.540859	−	0.841113i	$-0.318099\pi$
$198$	−13.0494	−	7.65808i	−0.927382	−	0.544236i
$199$	−0.186904	+	0.107909i	−0.0132493	+	0.00764949i	−0.506610	−	0.862175i	$-0.669102\pi$
$199$	−0.186904	+	0.107909i	−0.0132493	+	0.00764949i	0.493361	+	0.869825i	$0.335768\pi$
$200$	−9.82412	+	5.67196i	−0.694670	+	0.401068i
$201$	1.43135	−	0.378090i	0.100960	−	0.0266684i
$202$		−	8.41859i		−	0.592330i
$203$	0.0354402	−	6.17082i	0.00248741	−	0.433107i
$204$	−0.773019	−	0.778525i	−0.0541222	−	0.0545077i
$205$	18.7152	−	32.4158i	1.30713	−	2.26401i
$206$	−5.56184	−	9.63339i	−0.387512	−	0.671190i
$207$	−1.48152	−	2.60866i	−0.102973	−	0.181314i
$208$	0.352886	+	0.203739i	0.0244682	+	0.0141267i
$209$	32.2783			2.23274
$210$	4.62847	+	17.9388i	0.319395	+	1.23789i
$211$	−4.99265			−0.343708			−0.171854	−	0.985122i	$-0.554976\pi$
$211$	−4.99265			−0.343708			−0.171854	+	0.985122i	$0.554976\pi$
$212$	5.44908	+	3.14603i	0.374244	+	0.216070i
$213$	−23.2796	−	6.32639i	−1.59509	−	0.433477i
$214$	−3.90482	−	6.76335i	−0.266928	−	0.462333i
$215$	21.3930	−	37.0537i	1.45899	−	2.52704i
$216$	3.63491	+	3.71314i	0.247324	+	0.252647i
$217$	−11.8681	+	6.76148i	−0.805660	+	0.458999i
$218$		−	4.97376i		−	0.336865i
$219$	−4.05566	−	15.3536i	−0.274056	−	1.03750i
$220$	−17.6580	+	10.1949i	−1.19050	+	0.687338i
$221$	−0.223525	+	0.129052i	−0.0150359	+	0.00868098i
$222$	1.61609	+	6.11808i	0.108465	+	0.410619i
$223$			28.8447i			1.93158i	0.259318	+	0.965792i	$0.416502\pi$
$223$			28.8447i			1.93158i	−0.259318	+	0.965792i	$0.583498\pi$
$224$	2.29885	−	1.30969i	0.153598	−	0.0875077i
$225$	−0.241529	+	34.0309i	−0.0161019	+	2.26873i
$226$	6.57952	−	11.3961i	0.437663	−	0.758055i
$227$	7.13282	+	12.3544i	0.473422	+	0.819991i	0.999537	−	0.0304226i	$-0.00968531\pi$
$227$	7.13282	+	12.3544i	0.473422	+	0.819991i	−0.526115	+	0.850413i	$0.676352\pi$
$228$	−10.6971	−	2.90700i	−0.708432	−	0.192521i
$229$	3.77791	+	2.18118i	0.249652	+	0.144136i	0.619605	−	0.784914i	$-0.287293\pi$
$229$	3.77791	+	2.18118i	0.249652	+	0.144136i	−0.369953	+	0.929050i	$0.620626\pi$
$230$	−4.04276			−0.266572
$231$	5.77421	+	22.3794i	0.379915	+	1.47246i
$232$	−2.33239			−0.153129
$233$	3.28785	+	1.89824i	0.215394	+	0.124358i	0.603816	−	0.797124i	$-0.293646\pi$
$233$	3.28785	+	1.89824i	0.215394	+	0.124358i	−0.388422	+	0.921482i	$0.626980\pi$
$234$	1.06297	−	0.603687i	0.0694885	−	0.0394643i
$235$	6.65570	+	11.5280i	0.434170	+	0.752004i
$236$	−1.38089	+	2.39177i	−0.0898883	+	0.155691i
$237$	−17.2764	−	17.3994i	−1.12222	−	1.13021i
$238$	−0.00962468	+	1.67584i	−0.000623875	+	0.108629i
$239$			23.2581i			1.50444i	0.658910	+	0.752222i	$0.271018\pi$
$239$			23.2581i			1.50444i	−0.658910	+	0.752222i	$0.728982\pi$
$240$	6.77006	−	1.78831i	0.437005	−	0.115435i
$241$	3.18843	−	1.84084i	0.205385	−	0.118579i	−0.393780	−	0.919205i	$-0.628833\pi$
$241$	3.18843	−	1.84084i	0.205385	−	0.118579i	0.599165	+	0.800626i	$0.295499\pi$
$242$	−12.5029	+	7.21853i	−0.803714	+	0.464025i
$243$	15.1265	−	3.76681i	0.970366	−	0.241641i
$244$		−	15.2666i		−	0.977344i
$245$	14.4302	−	24.3438i	0.921913	−	1.55527i
$246$	−11.3796	+	11.2992i	−0.725540	+	0.720409i
$247$	−1.30392	+	2.25846i	−0.0829665	+	0.143702i
$248$	2.58132	+	4.47097i	0.163914	+	0.283907i
$249$	−4.18890	+	15.4142i	−0.265461	+	0.976834i
$250$	22.2109	+	12.8235i	1.40474	+	0.811027i
$251$	−5.14115			−0.324506			−0.162253	−	0.986749i	$-0.551876\pi$
$251$	−5.14115			−0.324506			−0.162253	+	0.986749i	$0.551876\pi$
$252$	0.101914	−	7.93660i	0.00641999	−	0.499959i
$253$	−5.04352			−0.317083
$254$	5.84204	+	3.37290i	0.366562	+	0.211635i
$255$	−1.16315	+	4.28014i	−0.0728396	+	0.268033i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.27167	+	2.20259i	−0.0793243	+	0.137394i	−0.902959	−	0.429728i	$-0.858610\pi$
$257$	−1.27167	+	2.20259i	−0.0793243	+	0.137394i	0.823634	+	0.567121i	$0.191943\pi$
$258$	−13.0078	+	12.9158i	−0.809832	+	0.804105i
$259$	4.88103	−	8.34317i	0.303293	−	0.518419i
$260$		−	1.64733i		−	0.102163i
$261$	−3.54150	+	6.03474i	−0.219214	+	0.373541i
$262$	−0.826036	+	0.476912i	−0.0510327	+	0.0294637i
$263$	−10.0393	+	5.79621i	−0.619051	+	0.357410i	−0.776500	−	0.630118i	$-0.783007\pi$
$263$	−10.0393	+	5.79621i	−0.619051	+	0.357410i	0.157448	+	0.987527i	$0.449673\pi$
$264$	8.44594	−	2.23099i	0.519812	−	0.137308i
$265$		−	25.4373i		−	1.56260i
$266$	8.38200	+	14.7125i	0.513933	+	0.902083i
$267$	15.1256	+	15.2333i	0.925670	+	0.932263i
$268$	−0.427367	+	0.740221i	−0.0261056	+	0.0452162i
$269$	−11.2389	−	19.4664i	−0.685250	−	1.18689i	−0.973358	−	0.229290i	$-0.926360\pi$
$269$	−11.2389	−	19.4664i	−0.685250	−	1.18689i	0.288108	−	0.957598i	$-0.406974\pi$
$270$	5.65266	−	20.2320i	0.344010	−	1.23128i
$271$	−0.0326978	−	0.0188781i	−0.00198625	−	0.00114676i	0.499007	−	0.866598i	$-0.333698\pi$
$271$	−0.0326978	−	0.0188781i	−0.00198625	−	0.00114676i	−0.500993	+	0.865451i	$0.667032\pi$
$272$	0.633419			0.0384067
$273$	−1.79910	−	0.500030i	−0.108887	−	0.0302632i
$274$	−14.9085			−0.900654
$275$	49.5481	+	28.6066i	2.98786	+	1.72504i
$276$	1.67143	+	0.454222i	0.100608	+	0.0273409i
$277$	−6.22441	−	10.7810i	−0.373989	−	0.647767i	0.616187	−	0.787600i	$-0.288677\pi$
$277$	−6.22441	−	10.7810i	−0.373989	−	0.647767i	−0.990175	+	0.139833i	$0.955343\pi$
$278$	8.46796	−	14.6669i	0.507875	−	0.879665i
$279$	15.4875	+	0.109920i	0.927213	+	0.00658074i
$280$	−9.23226	−	5.40118i	−0.551733	−	0.322782i
$281$		−	1.81393i		−	0.108210i	−0.998535	−	0.0541051i	$-0.982769\pi$
$281$		−	1.81393i		−	0.108210i	0.998535	−	0.0541051i	$-0.0172306\pi$
$282$	−1.45650	−	5.51391i	−0.0867331	−	0.328349i
$283$	12.6915	−	7.32742i	0.754429	−	0.435570i	−0.0728631	−	0.997342i	$-0.523214\pi$
$283$	12.6915	−	7.32742i	0.754429	−	0.435570i	0.827292	+	0.561772i	$0.189880\pi$
$284$	12.0620	−	6.96398i	0.715746	−	0.413236i
$285$	11.4451	+	43.3281i	0.677949	+	2.56654i
$286$		−	2.05512i		−	0.121522i
$287$	24.4957	+	0.140683i	1.44593	+	0.00830427i
$288$	−2.99992	−	0.0212915i	−0.176772	−	0.00125461i
$289$	8.29939	−	14.3750i	0.488199	−	0.845586i
$290$	4.71465	+	8.16601i	0.276854	+	0.479525i
$291$	−4.69909	−	1.27701i	−0.275465	−	0.0748594i
$292$	7.94013	+	4.58424i	0.464661	+	0.268272i
$293$	15.9520			0.931927			0.465963	−	0.884804i	$-0.345708\pi$
$293$	15.9520			0.931927			0.465963	+	0.884804i	$0.345708\pi$
$294$	−8.70114	+	8.44335i	−0.507461	+	0.492426i
$295$	11.1652			0.650064
$296$	−3.16396	−	1.82672i	−0.183902	−	0.106176i
$297$	7.05194	−	25.2403i	0.409195	−	1.46459i
$298$	5.50146	+	9.52881i	0.318691	+	0.551989i
$299$	0.203739	−	0.352886i	0.0117825	−	0.0204079i
$300$	−13.8440	−	13.9426i	−0.799284	−	0.804977i
$301$	28.0005	+	0.160812i	1.61392	+	0.00926905i
$302$			0.529609i			0.0304756i
$303$	14.0979	−	3.72395i	0.809902	−	0.213935i
$304$	5.54253	−	3.19998i	0.317886	−	0.183531i
$305$	−53.4504	+	30.8596i	−3.06056	+	1.76702i
$306$	0.961785	−	1.63889i	0.0549816	−	0.0936890i
$307$		−	3.05221i		−	0.174199i	−0.996200	−	0.0870994i	$-0.972240\pi$
$307$		−	3.05221i		−	0.174199i	0.996200	−	0.0870994i	$-0.0277598\pi$
$308$	−11.5176	−	6.73820i	−0.656278	−	0.383945i
$309$	13.6719	−	13.5752i	0.777769	−	0.772268i
$310$	10.4357	−	18.0751i	0.592705	−	1.02660i
$311$	7.24775	+	12.5535i	0.410982	+	0.711842i	0.994997	−	0.0999008i	$-0.0318526\pi$
$311$	7.24775	+	12.5535i	0.410982	+	0.711842i	−0.584015	+	0.811743i	$0.698519\pi$
$312$	−0.185085	+	0.681071i	−0.0104784	+	0.0385580i
$313$	0.806859	+	0.465840i	0.0456064	+	0.0263309i	0.522630	−	0.852560i	$-0.324951\pi$
$313$	0.806859	+	0.465840i	0.0456064	+	0.0263309i	−0.477023	+	0.878891i	$0.658284\pi$
$314$	−3.38580			−0.191072
$315$	−27.9931	+	15.6861i	−1.57723	+	0.883810i
$316$	14.1564			0.796360
$317$	−27.9919	−	16.1611i	−1.57218	−	0.907698i	−0.995902	−	0.0904441i	$-0.971171\pi$
$317$	−27.9919	−	16.1611i	−1.57218	−	0.907698i	−0.576278	−	0.817254i	$-0.695495\pi$
$318$	−2.85799	+	10.5167i	−0.160268	+	0.589749i
$319$	5.88172	+	10.1874i	0.329313	+	0.570387i
$320$	−2.02138	+	3.50113i	−0.112999	+	0.195719i
$321$	9.59870	−	9.53082i	0.535747	−	0.531958i
$322$	−1.30969	−	2.29885i	−0.0729864	−	0.128110i
$323$			4.05386i			0.225563i
$324$	−4.61018	+	7.72957i	−0.256121	+	0.429421i
$325$	−4.00311	+	2.31120i	−0.222052	+	0.128202i
$326$	−7.14000	+	4.12228i	−0.395448	+	0.228312i
$327$	8.32912	−	2.20013i	0.460601	−	0.121668i
$328$		−	9.25865i		−	0.511223i
$329$	−4.39902	+	7.51927i	−0.242526	+	0.414551i
$330$	−24.8834	−	25.0607i	−1.36979	−	1.37954i
$331$	−7.42444	+	12.8595i	−0.408084	+	0.706822i	−0.994675	−	0.103061i	$-0.967136\pi$
$331$	−7.42444	+	12.8595i	−0.408084	+	0.706822i	0.586591	+	0.809883i	$0.300470\pi$
$332$	−4.61107	−	7.98661i	−0.253065	−	0.438322i
$333$	−9.53055	+	5.41264i	−0.522271	+	0.296611i
$334$	−4.05450	−	2.34086i	−0.221852	−	0.128086i
$335$	3.45548			0.188793
$336$	3.21012	+	3.27034i	0.175127	+	0.178412i
$337$	−24.8358			−1.35289			−0.676447	−	0.736491i	$-0.736481\pi$
$337$	−24.8358			−1.35289			−0.676447	+	0.736491i	$0.736481\pi$
$338$	−11.1145	−	6.41698i	−0.604551	−	0.349038i
$339$	21.9944	+	5.97713i	1.19457	+	0.324633i
$340$	−1.28038	−	2.21769i	−0.0694384	−	0.120271i
$341$	13.0189	−	22.5494i	0.705014	−	1.22112i
$342$	0.136265	−	19.1994i	0.00736834	−	1.03818i
$343$	18.5175	+	0.319077i	0.999852	+	0.0172285i
$344$		−	10.5834i		−	0.570616i
$345$	−1.78831	−	6.77006i	−0.0962792	−	0.364488i
$346$	−3.45366	+	1.99397i	−0.185670	+	0.107196i
$347$	−3.54358	+	2.04588i	−0.190229	+	0.109829i	−0.592090	−	0.805872i	$-0.701697\pi$
$347$	−3.54358	+	2.04588i	−0.190229	+	0.109829i	0.401861	+	0.915701i	$0.368364\pi$
$348$	−1.03173	−	3.90585i	−0.0553064	−	0.209376i
$349$			16.1981i			0.867066i	0.901138	+	0.433533i	$0.142733\pi$
$349$			16.1981i			0.867066i	−0.901138	+	0.433533i	$0.857267\pi$
$350$	−0.172369	+	30.0127i	−0.00921348	+	1.60425i
$351$	1.48114	+	1.51302i	0.0790577	+	0.0807591i
$352$	−2.52176	+	4.36781i	−0.134410	+	0.232805i
$353$	2.33704	+	4.04787i	0.124388	+	0.215446i	0.921494	−	0.388394i	$-0.126970\pi$
$353$	2.33704	+	4.04787i	0.124388	+	0.215446i	−0.797106	+	0.603840i	$0.793637\pi$
$354$	−4.61613	−	1.25446i	−0.245344	−	0.0666738i
$355$	−48.7637	−	28.1537i	−2.58811	−	1.49424i
$356$	−12.3940			−0.656882
$357$	−2.81065	+	0.725188i	−0.148755	+	0.0383810i
$358$	−20.4063			−1.07851
$359$	19.4262	+	11.2157i	1.02527	+	0.591942i	0.915627	−	0.402028i	$-0.131695\pi$
$359$	19.4262	+	11.2157i	1.02527	+	0.591942i	0.109647	+	0.993971i	$0.465028\pi$
$360$	5.98944	+	10.5462i	0.315671	+	0.555832i
$361$	10.9798	+	19.0175i	0.577882	+	1.00092i
$362$	2.28097	−	3.95076i	0.119885	−	0.207647i
$363$	−17.6189	−	17.7444i	−0.924750	−	0.931337i
$364$	0.936729	−	0.533671i	0.0490979	−	0.0279720i
$365$		−	37.0659i		−	1.94012i
$366$	25.5656	−	6.75315i	1.33634	−	0.352993i
$367$	19.7850	−	11.4229i	1.03277	−	0.596269i	0.114991	−	0.993367i	$-0.463316\pi$
$367$	19.7850	−	11.4229i	1.03277	−	0.596269i	0.917776	+	0.397098i	$0.129983\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	−23.9555	−	14.0583i	−1.24707	−	0.731848i
$370$			14.7700i			0.767853i
$371$	14.4645	−	8.24067i	0.750958	−	0.427834i
$372$	−6.34531	+	6.30043i	−0.328989	+	0.326662i
$373$	0.0552069	−	0.0956212i	0.00285850	−	0.00495108i	−0.864593	−	0.502473i	$-0.832423\pi$
$373$	0.0552069	−	0.0956212i	0.00285850	−	0.00495108i	0.867451	+	0.497522i	$0.165757\pi$
$374$	−1.59733	−	2.76666i	−0.0825960	−	0.143060i
$375$	−11.6494	+	42.8671i	−0.601572	+	2.21365i
$376$	2.85152	+	1.64632i	0.147056	+	0.0849027i
$377$	−0.950396			−0.0489479
$378$	13.3358	−	3.34007i	0.685920	−	0.171795i
$379$	−36.5656			−1.87825			−0.939125	−	0.343575i	$-0.888362\pi$
$379$	−36.5656			−1.87825			−0.939125	+	0.343575i	$0.888362\pi$
$380$	−22.4071	−	12.9368i	−1.14946	−	0.663642i
$381$	−3.06409	+	11.2752i	−0.156978	+	0.577644i
$382$	−2.25229	−	3.90107i	−0.115237	−	0.199596i
$383$	1.62144	−	2.80841i	0.0828516	−	0.143503i	−0.821622	−	0.570033i	$-0.806931\pi$
$383$	1.62144	−	2.80841i	0.0828516	−	0.143503i	0.904474	+	0.426529i	$0.140264\pi$
$384$	1.22908	−	1.22039i	0.0627214	−	0.0622778i
$385$	−0.309818	+	53.9453i	−0.0157898	+	2.74931i
$386$			4.15683i			0.211577i
$387$	−27.3830	−	16.0698i	−1.39196	−	0.816873i
$388$	2.43476	−	1.40571i	0.123606	−	0.0713640i
$389$	17.1825	−	9.92034i	0.871189	−	0.502981i	0.00344580	−	0.999994i	$-0.498903\pi$
$389$	17.1825	−	9.92034i	0.871189	−	0.502981i	0.867743	+	0.497013i	$0.165570\pi$
$390$	2.75865	−	0.728695i	0.139690	−	0.0368989i
$391$		−	0.633419i		−	0.0320334i
$392$	0.0804020	−	6.99954i	0.00406091	−	0.353530i
$393$	−1.16404	−	1.17233i	−0.0587180	−	0.0591362i
$394$	−11.8056	+	20.4479i	−0.594757	+	1.03015i
$395$	−28.6155	−	49.5635i	−1.43980	−	2.49381i
$396$	7.47209	+	13.1568i	0.375487	+	0.661154i
$397$	−18.7627	−	10.8327i	−0.941675	−	0.543676i	−0.0511901	−	0.998689i	$-0.516301\pi$
$397$	−18.7627	−	10.8327i	−0.941675	−	0.543676i	−0.890485	+	0.455013i	$0.849635\pi$
$398$	0.215819			0.0108180
$399$	−20.9300	+	20.5447i	−1.04781	+	1.02852i
$400$	11.3439			0.567196
$401$	22.1051	+	12.7624i	1.10387	+	0.637322i	0.937236	−	0.348696i	$-0.113375\pi$
$401$	22.1051	+	12.7624i	1.10387	+	0.637322i	0.166638	+	0.986018i	$0.446709\pi$
$402$	−1.42863	−	0.388239i	−0.0712535	−	0.0193636i
$403$	1.05183	+	1.82182i	0.0523953	+	0.0907514i
$404$	−4.20929	+	7.29071i	−0.209420	+	0.362726i
$405$	36.3812	+	0.516445i	1.80780	+	0.0256623i
$406$	−3.11610	+	5.32637i	−0.154650	+	0.264343i
$407$			18.4261i			0.913350i
$408$	0.280192	+	1.06073i	0.0138716	+	0.0525141i
$409$	−6.82441	+	3.94008i	−0.337445	+	0.194824i	−0.659142	−	0.752019i	$-0.729080\pi$
$409$	−6.82441	+	3.94008i	−0.337445	+	0.194824i	0.321696	+	0.946843i	$0.395747\pi$
$410$	−32.4158	+	18.7152i	−1.60090	+	0.924280i
$411$	−6.59473	−	24.9659i	−0.325294	−	1.23148i
$412$			11.1237i			0.548024i
$413$	3.61709	+	6.34891i	0.177985	+	0.312410i
$414$	−0.0212915	+	2.99992i	−0.00104642	+	0.147438i
$415$	−18.6415	+	32.2879i	−0.915073	+	1.58495i
$416$	−0.203739	−	0.352886i	−0.00998911	−	0.0173017i
$417$	28.3072	+	7.69267i	1.38621	+	0.376712i
$418$	−27.9538	−	16.1392i	−1.36727	−	0.789392i
$419$	−12.3891			−0.605246			−0.302623	−	0.953110i	$-0.597862\pi$
$419$	−12.3891			−0.605246			−0.302623	+	0.953110i	$0.597862\pi$
$420$	4.96101	−	17.8497i	0.242073	−	0.870974i
$421$	7.62310			0.371527			0.185764	−	0.982594i	$-0.440524\pi$
$421$	7.62310			0.371527			0.185764	+	0.982594i	$0.440524\pi$
$422$	4.32377	+	2.49633i	0.210478	+	0.121519i
$423$	8.58939	−	4.87814i	0.417631	−	0.237183i
$424$	−3.14603	−	5.44908i	−0.152785	−	0.264631i
$425$	−3.59273	+	6.22279i	−0.174273	+	0.301850i
$426$	16.9976	+	17.1186i	0.823535	+	0.829400i
$427$	−34.8636	−	20.3964i	−1.68717	−	0.987049i
$428$			7.80964i			0.377493i
$429$	3.44153	−	0.909078i	0.166159	−	0.0438907i
$430$	−37.0537	+	21.3930i	−1.78689	+	1.03166i
$431$	−14.6175	+	8.43944i	−0.704102	+	0.406514i	−0.808873	−	0.587983i	$-0.799922\pi$
$431$	−14.6175	+	8.43944i	−0.704102	+	0.406514i	0.104771	+	0.994496i	$0.466589\pi$
$432$	−1.29136	−	5.03313i	−0.0621304	−	0.242157i
$433$			13.2320i			0.635891i	0.948109	+	0.317945i	$0.102993\pi$
$433$			13.2320i			0.635891i	−0.948109	+	0.317945i	$0.897007\pi$
$434$	13.6588	+	0.0784452i	0.655645	+	0.00376549i
$435$	−11.5894	+	11.5074i	−0.555669	+	0.551739i
$436$	−2.48688	+	4.30740i	−0.119100	+	0.206287i
$437$	−3.19998	−	5.54253i	−0.153076	−	0.265135i
$438$	−4.16452	+	15.3245i	−0.198989	+	0.732232i
$439$	−4.95987	−	2.86358i	−0.236722	−	0.136671i	0.376947	−	0.926235i	$-0.376974\pi$
$439$	−4.95987	−	2.86358i	−0.236722	−	0.136671i	−0.613669	+	0.789563i	$0.710307\pi$
$440$	20.3897			0.972042
$441$	−17.9883	−	10.8361i	−0.856585	−	0.516006i
$442$	0.258104			0.0122768
$443$	11.2952	+	6.52126i	0.536649	+	0.309835i	0.743720	−	0.668491i	$-0.233060\pi$
$443$	11.2952	+	6.52126i	0.536649	+	0.309835i	−0.207071	+	0.978326i	$0.566393\pi$
$444$	1.65947	−	6.10646i	0.0787549	−	0.289800i
$445$	25.0531	+	43.3932i	1.18763	+	2.05703i
$446$	14.4224	−	24.9802i	0.682918	−	1.18285i
$447$	−13.5235	+	13.4279i	−0.639640	+	0.635116i
$448$	−2.64571	−	0.0151948i	−0.124998	−	0.000717887i
$449$			3.12676i			0.147561i	0.997275	+	0.0737804i	$0.0235064\pi$
$449$			3.12676i			0.147561i	−0.997275	+	0.0737804i	$0.976494\pi$
$450$	17.2246	−	29.3508i	0.811976	−	1.38361i
$451$	−40.4400	+	23.3481i	−1.90425	+	1.09942i
$452$	−11.3961	+	6.57952i	−0.536026	+	0.309475i
$453$	−0.886890	+	0.234271i	−0.0416697	+	0.0110070i
$454$		−	14.2656i		−	0.669520i
$455$	−3.76194	−	2.20086i	−0.176362	−	0.103178i
$456$	7.81045	+	7.86609i	0.365758	+	0.368363i
$457$	2.76125	−	4.78263i	0.129166	−	0.223722i	−0.794188	−	0.607673i	$-0.792103\pi$
$457$	2.76125	−	4.78263i	0.129166	−	0.223722i	0.923354	+	0.383950i	$0.125437\pi$
$458$	−2.18118	−	3.77791i	−0.101920	−	0.176530i
$459$	3.16995	+	0.885659i	0.147960	+	0.0413390i
$460$	3.50113	+	2.02138i	0.163241	+	0.0942473i
$461$	−6.42400			−0.299196			−0.149598	−	0.988747i	$-0.547798\pi$
$461$	−6.42400			−0.299196			−0.149598	+	0.988747i	$0.547798\pi$
$462$	6.18908	−	22.2682i	0.287942	−	1.03601i
$463$	22.6375			1.05205			0.526027	−	0.850468i	$-0.323681\pi$
$463$	22.6375			1.05205			0.526027	+	0.850468i	$0.323681\pi$
$464$	2.01991	+	1.16619i	0.0937719	+	0.0541392i
$465$	34.8849	+	9.48020i	1.61775	+	0.439634i
$466$	−1.89824	−	3.28785i	−0.0879342	−	0.152307i
$467$	17.5522	−	30.4014i	0.812221	−	1.40681i	−0.0990861	−	0.995079i	$-0.531592\pi$
$467$	17.5522	−	30.4014i	0.812221	−	1.40681i	0.911307	−	0.411728i	$-0.135075\pi$
$468$	−1.22240	−	0.00867579i	−0.0565055	−	0.000401039i
$469$	1.11944	+	1.96490i	0.0516910	+	0.0907308i
$470$		−	13.3114i		−	0.614009i
$471$	−1.49770	−	5.66991i	−0.0690105	−	0.261256i
$472$	2.39177	−	1.38089i	0.110090	−	0.0635606i
$473$	−46.2261	+	26.6887i	−2.12548	+	1.22715i
$474$	6.26206	+	23.7065i	0.287626	+	1.08888i
$475$			72.6006i			3.33114i
$476$	0.846257	−	1.44651i	0.0387881	−	0.0663007i
$477$	−18.8757	−	0.133967i	−0.864258	−	0.00613393i
$478$	11.6291	−	20.1421i	0.531901	−	0.921280i
$479$	−2.97924	−	5.16020i	−0.136125	−	0.235775i	0.789902	−	0.613234i	$-0.210132\pi$
$479$	−2.97924	−	5.16020i	−0.136125	−	0.235775i	−0.926027	+	0.377458i	$0.876798\pi$
$480$	−6.75720	−	1.83631i	−0.308422	−	0.0838157i
$481$	−1.28924	−	0.744346i	−0.0587845	−	0.0339392i
$482$	−3.68168			−0.167696
$483$	3.27034	−	3.21012i	0.148806	−	0.146066i
$484$	14.4371			0.656230
$485$	−9.84314	−	5.68294i	−0.446954	−	0.258049i
$486$	−14.9833	−	4.30110i	−0.679658	−	0.195102i
$487$	−11.4687	−	19.8645i	−0.519699	−	0.900144i	−0.999738	−	0.0228973i	$-0.992711\pi$
$487$	−11.4687	−	19.8645i	−0.519699	−	0.900144i	0.480039	−	0.877247i	$-0.340622\pi$
$488$	−7.63330	+	13.2213i	−0.345543	+	0.598498i
$489$	−10.0616	−	10.1333i	−0.455001	−	0.458242i
$490$	−24.6688	+	13.8672i	−1.11442	+	0.626458i
$491$			11.3982i			0.514392i	0.966359	+	0.257196i	$0.0827986\pi$
$491$			11.3982i			0.514392i	−0.966359	+	0.257196i	$0.917201\pi$
$492$	15.5046	−	4.09554i	0.699004	−	0.184641i
$493$	−1.27945	+	0.738691i	−0.0576235	+	0.0332689i
$494$	2.25846	−	1.30392i	0.101613	−	0.0586661i
$495$	30.9598	−	52.7557i	1.39154	−	2.37119i
$496$		−	5.16264i		−	0.231809i
$497$	0.211633	−	36.8493i	0.00949302	−	1.65292i
$498$	11.3348	−	11.2546i	0.507924	−	0.504332i
$499$	−7.29590	+	12.6369i	−0.326609	+	0.565704i	−0.981837	−	0.189728i	$-0.939239\pi$
$499$	−7.29590	+	12.6369i	−0.326609	+	0.565704i	0.655227	+	0.755432i	$0.272573\pi$
$500$	−12.8235	−	22.2109i	−0.573483	−	0.993301i
$501$	2.12654	−	7.82519i	0.0950070	−	0.349604i
$502$	4.45236	+	2.57057i	0.198719	+	0.114730i
$503$	−38.8305			−1.73137			−0.865684	−	0.500591i	$-0.833116\pi$
$503$	−38.8305			−1.73137			−0.865684	+	0.500591i	$0.833116\pi$
$504$	−4.05656	+	6.82234i	−0.180694	+	0.303891i
$505$	34.0343			1.51451
$506$	4.36781	+	2.52176i	0.194173	+	0.112106i
$507$	5.82947	−	21.4511i	0.258896	−	0.952676i
$508$	−3.37290	−	5.84204i	−0.149648	−	0.259199i
$509$	10.0919	−	17.4797i	0.447316	−	0.774775i	−0.550894	−	0.834575i	$-0.685713\pi$
$509$	10.0919	−	17.4797i	0.447316	−	0.774775i	0.998210	+	0.0598005i	$0.0190465\pi$
$510$	3.14739	−	3.12513i	0.139369	−	0.138383i
$511$	21.0769	−	12.0079i	0.932388	−	0.531198i
$512$			1.00000i			0.0441942i
$513$	32.2118	−	8.26463i	1.42219	−	0.364892i
$514$	2.20259	−	1.27167i	0.0971520	−	0.0560908i
$515$	38.9455	−	22.4852i	1.71614	−	0.990816i
$516$	17.7230	−	4.68153i	0.780213	−	0.206093i
$517$		−	16.6065i		−	0.730354i
$518$	−8.39868	+	4.78488i	−0.369017	+	0.210236i
$519$	−4.86685	−	4.90151i	−0.213631	−	0.215152i
$520$	−0.823667	+	1.42663i	−0.0361202	+	0.0625620i
$521$	11.9952	+	20.7763i	0.525520	+	0.910228i	0.999558	+	0.0297235i	$0.00946267\pi$
$521$	11.9952	+	20.7763i	0.525520	+	0.910228i	−0.474038	+	0.880504i	$0.657204\pi$
$522$	6.08440	−	3.45549i	0.266307	−	0.151243i
$523$	−29.8197	−	17.2164i	−1.30392	−	0.752821i	−0.322849	−	0.946450i	$-0.604641\pi$
$523$	−29.8197	−	17.2164i	−1.30392	−	0.752821i	−0.981075	+	0.193629i	$0.937974\pi$
$524$	0.953824			0.0416680
$525$	−50.3359	+	12.9874i	−2.19684	+	0.566817i
$526$	11.5924			0.505453
$527$	2.83200	+	1.63506i	0.123364	+	0.0712242i
$528$	−8.42989	−	2.29088i	−0.366864	−	0.0996976i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−12.7186	+	22.0293i	−0.552462	+	0.956893i
$531$	0.0588023	−	8.28513i	0.00255180	−	0.359544i
$532$	0.0972461	−	16.9324i	0.00421615	−	0.734114i
$533$		−	3.77269i		−	0.163413i
$534$	−5.48248	−	20.7552i	−0.237250	−	0.898166i
$535$	27.3426	−	15.7863i	1.18212	−	0.682499i
$536$	0.740221	−	0.427367i	0.0319727	−	0.0184594i
$537$	−9.02668	−	34.1726i	−0.389530	−	1.47466i
$538$			22.4779i			0.969090i
$539$	−30.7754	+	17.3000i	−1.32559	+	0.745162i
$540$	−15.0113	+	14.6951i	−0.645985	+	0.632376i
$541$	−18.6466	+	32.2969i	−0.801682	+	1.38855i	0.116827	+	0.993152i	$0.462728\pi$
$541$	−18.6466	+	32.2969i	−0.801682	+	1.38855i	−0.918509	+	0.395401i	$0.870606\pi$
$542$	0.0188781	+	0.0326978i	0.000810882	+	0.00140449i
$543$	7.62498	+	2.07214i	0.327219	+	0.0889239i
$544$	−0.548557	−	0.316710i	−0.0235192	−	0.0135788i
$545$	20.1077			0.861320
$546$	1.30805	+	1.33259i	0.0559795	+	0.0570296i
$547$	−1.51166			−0.0646340			−0.0323170	−	0.999478i	$-0.510289\pi$
$547$	−1.51166			−0.0646340			−0.0323170	+	0.999478i	$0.510289\pi$
$548$	12.9111	+	7.45424i	0.551536	+	0.318429i
$549$	22.6178	+	39.8253i	0.965305	+	1.69970i
$550$	−28.6066	−	49.5481i	−1.21979	−	2.11274i
$551$	−7.46360	+	12.9273i	−0.317960	+	0.550723i
$552$	−1.22039	−	1.22908i	−0.0519433	−	0.0523133i
$553$	18.9131	−	32.3283i	0.804269	−	1.37474i
$554$			12.4488i			0.528900i
$555$	−24.7340	+	6.53346i	−1.04990	+	0.277330i
$556$	−14.6669	+	8.46796i	−0.622017	+	0.359122i
$557$	24.3274	−	14.0455i	1.03079	−	0.595125i	0.113577	−	0.993529i	$-0.463769\pi$
$557$	24.3274	−	14.0455i	1.03079	−	0.595125i	0.917210	+	0.398404i	$0.130436\pi$
$558$	−13.3576	−	7.83895i	−0.565473	−	0.331849i
$559$		−	4.31248i		−	0.182398i
$560$	5.29478	+	9.29369i	0.223745	+	0.392730i
$561$	3.92651	−	3.89874i	0.165777	−	0.164605i
$562$	−0.906967	+	1.57091i	−0.0382581	+	0.0662649i
$563$	−18.6520	−	32.3063i	−0.786090	−	1.36155i	−0.928346	−	0.371717i	$-0.878769\pi$
$563$	−18.6520	−	32.3063i	−0.786090	−	1.36155i	0.142256	−	0.989830i	$-0.454564\pi$
$564$	−1.49559	+	5.50344i	−0.0629758	+	0.231737i
$565$	46.0716	+	26.5994i	1.93825	+	1.11905i
$566$	−14.6548			−0.615989
$567$	11.4924	+	20.8549i	0.482635	+	0.875821i
$568$	−13.9280			−0.584405
$569$	−24.9914	−	14.4288i	−1.04769	−	0.604886i	−0.125690	−	0.992070i	$-0.540115\pi$
$569$	−24.9914	−	14.4288i	−1.04769	−	0.604886i	−0.922003	+	0.387184i	$0.873448\pi$
$570$	11.7523	−	43.2458i	0.492250	−	1.81137i
$571$	−6.13745	−	10.6304i	−0.256844	−	0.444867i	0.708551	−	0.705660i	$-0.249349\pi$
$571$	−6.13745	−	10.6304i	−0.256844	−	0.444867i	−0.965395	+	0.260793i	$0.916016\pi$
$572$	−1.02756	+	1.77979i	−0.0429644	+	0.0744166i
$573$	5.53649	−	5.49734i	0.231290	−	0.229655i
$574$	−21.1435	−	12.3697i	−0.882514	−	0.516300i
$575$		−	11.3439i		−	0.473074i
$576$	2.58737	+	1.51840i	0.107807	+	0.0632667i
$577$	−26.8367	+	15.4942i	−1.11723	+	0.645031i	−0.940691	−	0.339264i	$-0.889822\pi$
$577$	−26.8367	+	15.4942i	−1.11723	+	0.645031i	−0.176535	+	0.984294i	$0.556489\pi$
$578$	−14.3750	+	8.29939i	−0.597920	+	0.345209i
$579$	−6.96108	+	1.83877i	−0.289293	+	0.0764165i
$580$		−	9.42929i		−	0.391530i
$581$	−24.3991	−	0.140129i	−1.01224	−	0.00581351i
$582$	3.43102	+	3.45546i	0.142221	+	0.143234i
$583$	−15.8670	+	27.4825i	−0.657146	+	1.13821i
$584$	−4.58424	−	7.94013i	−0.189697	−	0.328565i
$585$	2.44056	+	4.29733i	0.100905	+	0.177673i
$586$	−13.8148	−	7.97601i	−0.570686	−	0.329486i
$587$	47.2582			1.95055			0.975277	−	0.220985i	$-0.0709272\pi$
$587$	47.2582			1.95055			0.975277	+	0.220985i	$0.0709272\pi$
$588$	11.7571	−	2.96159i	0.484854	−	0.122134i
$589$	33.0407			1.36142
$590$	−9.66936	−	5.58261i	−0.398081	−	0.229832i
$591$	−39.4645	−	10.7247i	−1.62335	−	0.441156i
$592$	1.82672	+	3.16396i	0.0750776	+	0.130038i
$593$	−17.7607	+	30.7625i	−0.729346	+	1.26326i	0.227814	+	0.973705i	$0.426842\pi$
$593$	−17.7607	+	30.7625i	−0.729346	+	1.26326i	−0.957160	+	0.289560i	$0.906491\pi$
$594$	−18.7273	+	18.3327i	−0.768390	+	0.752201i
$595$	−6.77503	−	0.0389103i	−0.277749	−	0.00159517i
$596$		−	11.0029i		−	0.450697i
$597$	0.0954669	+	0.361413i	0.00390720	+	0.0147916i
$598$	−0.352886	+	0.203739i	−0.0144306	+	0.00833150i
$599$	29.7447	−	17.1731i	1.21534	−	0.701674i	0.251419	−	0.967878i	$-0.419103\pi$
$599$	29.7447	−	17.1731i	1.21534	−	0.701674i	0.963917	+	0.266204i	$0.0857695\pi$
$600$	5.01796	+	18.9967i	0.204857	+	0.775536i
$601$			7.95412i			0.324455i	0.986753	+	0.162228i	$0.0518679\pi$
$601$			7.95412i			0.324455i	−0.986753	+	0.162228i	$0.948132\pi$
$602$	−24.1687	−	14.1395i	−0.985043	−	0.576283i
$603$	0.0181985	−	2.56414i	0.000741102	−	0.104420i
$604$	0.264804	−	0.458655i	0.0107747	−	0.0186624i
$605$	−29.1828	−	50.5461i	−1.18645	−	2.05499i
$606$	−14.0711	−	3.82391i	−0.571599	−	0.155336i
$607$	−6.75145	−	3.89795i	−0.274033	−	0.158213i	0.356686	−	0.934224i	$-0.383907\pi$
$607$	−6.75145	−	3.89795i	−0.274033	−	0.158213i	−0.630719	+	0.776011i	$0.717240\pi$
$608$	−6.39996			−0.259553
$609$	−10.2980	−	2.86216i	−0.417296	−	0.115980i
$610$	61.7192			2.49894
$611$	1.16193	+	0.670840i	0.0470066	+	0.0271393i
$612$	−1.65237	+	0.938426i	−0.0667933	+	0.0379336i
$613$	−16.7856	−	29.0735i	−0.677963	−	1.17427i	−0.975593	−	0.219585i	$-0.929530\pi$
$613$	−16.7856	−	29.0735i	−0.677963	−	1.17427i	0.297630	−	0.954681i	$-0.403804\pi$
$614$	−1.52611	+	2.64329i	−0.0615886	+	0.106675i
$615$	−45.6798	−	46.0052i	−1.84199	−	1.85511i
$616$	6.60547	+	11.5943i	0.266142	+	0.467147i
$617$		−	15.3067i		−	0.616225i	−0.951350	−	0.308113i	$-0.900303\pi$
$617$		−	15.3067i		−	0.616225i	0.951350	−	0.308113i	$-0.0996974\pi$
$618$	−18.6279	+	4.92054i	−0.749322	+	0.197933i
$619$	32.2210	−	18.6028i	1.29507	−	0.747709i	0.315521	−	0.948918i	$-0.397821\pi$
$619$	32.2210	−	18.6028i	1.29507	−	0.747709i	0.979548	+	0.201210i	$0.0644873\pi$
$620$	−18.0751	+	10.4357i	−0.725913	+	0.419106i
$621$	−5.03313	+	1.29136i	−0.201973	+	0.0518203i
$622$		−	14.4955i		−	0.581216i
$623$	−16.5586	+	28.3037i	−0.663406	+	1.13396i
$624$	0.500824	−	0.497282i	0.0200490	−	0.0199072i
$625$	−23.4824	+	40.6727i	−0.939297	+	1.62691i
$626$	−0.465840	−	0.806859i	−0.0186187	−	0.0322486i
$627$	14.6615	−	53.9510i	0.585524	−	2.15459i
$628$	2.93219	+	1.69290i	0.117007	+	0.0675541i
$629$	−2.31415			−0.0922714
$630$	32.0858	+	0.412015i	1.27833	+	0.0164151i
$631$	−41.2498			−1.64213			−0.821064	−	0.570836i	$-0.806619\pi$
$631$	−41.2498			−1.64213			−0.821064	+	0.570836i	$0.806619\pi$
$632$	−12.2598	−	7.07821i	−0.487669	−	0.281556i
$633$	−2.26777	+	8.34488i	−0.0901359	+	0.331679i
$634$	16.1611	+	27.9919i	0.641839	+	1.11170i
$635$	−13.6358	+	23.6180i	−0.541122	+	0.937251i
$636$	7.73346	−	7.67877i	0.306652	−	0.304483i
$637$	0.0327620	−	2.85215i	0.00129808	−	0.113006i
$638$		−	11.7634i		−	0.465719i
$639$	−21.1482	+	36.0367i	−0.836612	+	1.42559i
$640$	3.50113	−	2.02138i	0.138394	−	0.0799021i
$641$	6.80986	−	3.93168i	0.268973	−	0.155292i	−0.359448	−	0.933165i	$-0.617035\pi$
$641$	6.80986	−	3.93168i	0.268973	−	0.155292i	0.628421	+	0.777873i	$0.283702\pi$
$642$	−13.0781	+	3.45458i	−0.516153	+	0.136341i
$643$			50.1629i			1.97823i	0.147142	+	0.989115i	$0.452992\pi$
$643$			50.1629i			1.97823i	−0.147142	+	0.989115i	$0.547008\pi$
$644$	−0.0151948	+	2.64571i	−0.000598759	+	0.104255i
$645$	−52.2156	−	52.5875i	−2.05599	−	2.07063i
$646$	2.02693	−	3.51075i	0.0797485	−	0.138128i
$647$	11.1790	+	19.3626i	0.439492	+	0.761223i	0.997650	−	0.0685118i	$-0.0218251\pi$
$647$	11.1790	+	19.3626i	0.439492	+	0.761223i	−0.558158	+	0.829735i	$0.688492\pi$
$648$	7.85732	−	4.38892i	0.308665	−	0.172413i
$649$	−12.0629	−	6.96454i	−0.473512	−	0.273382i
$650$	4.62239			0.181305
$651$	5.91059	+	22.9079i	0.231654	+	0.897833i
$652$	8.24456			0.322882
$653$	27.3772	+	15.8062i	1.07135	+	0.618545i	0.928550	−	0.371207i	$-0.121056\pi$
$653$	27.3772	+	15.8062i	1.07135	+	0.618545i	0.142801	+	0.989751i	$0.454389\pi$
$654$	−8.31330	−	2.25919i	−0.325076	−	0.0883413i
$655$	−1.92804	−	3.33947i	−0.0753348	−	0.130484i
$656$	−4.62932	+	8.01822i	−0.180745	+	0.313059i
$657$	−27.5047	−	0.195210i	−1.07306	−	0.00761588i
$658$	7.56930	−	4.31237i	0.295082	−	0.168114i
$659$			5.54816i			0.216125i	0.994144	+	0.108063i	$0.0344647\pi$
$659$			5.54816i			0.216125i	−0.994144	+	0.108063i	$0.965535\pi$
$660$	9.01936	+	34.1449i	0.351078	+	1.32909i
$661$	16.5880	−	9.57708i	0.645198	−	0.372505i	−0.141416	−	0.989950i	$-0.545166\pi$
$661$	16.5880	−	9.57708i	0.645198	−	0.372505i	0.786614	+	0.617445i	$0.211832\pi$
$662$	12.8595	−	7.42444i	0.499799	−	0.288559i
$663$	0.114172	+	0.432225i	0.00443407	+	0.0167862i
$664$			9.22214i			0.357888i
$665$	−59.4793	+	33.8864i	−2.30651	+	1.31406i
$666$	10.9600	+	0.0777869i	0.424692	+	0.00301418i
$667$	1.16619	−	2.01991i	0.0451552	−	0.0782112i
$668$	2.34086	+	4.05450i	0.0905708	+	0.156873i
$669$	48.2119	+	13.1019i	1.86398	+	0.506548i
$670$	−2.99254	−	1.72774i	−0.115612	−	0.0667485i
$671$	76.9973			2.97245
$672$	−1.14488	−	4.43726i	−0.0441646	−	0.171171i
$673$	44.0223			1.69694			0.848468	−	0.529247i	$-0.177526\pi$
$673$	44.0223			1.69694			0.848468	+	0.529247i	$0.177526\pi$
$674$	21.5085	+	12.4179i	0.828475	+	0.478320i
$675$	56.7706	+	15.8613i	2.18510	+	0.610501i
$676$	6.41698	+	11.1145i	0.246807	+	0.427482i
$677$	−9.82051	+	17.0096i	−0.377433	+	0.653733i	−0.990688	−	0.136152i	$-0.956526\pi$
$677$	−9.82051	+	17.0096i	−0.377433	+	0.653733i	0.613255	+	0.789885i	$0.289860\pi$
$678$	−16.0592	−	16.1736i	−0.616749	−	0.621142i
$679$	0.0427189	−	7.43818i	0.00163940	−	0.285451i
$680$			2.56076i			0.0982008i
$681$	23.8894	−	6.31038i	0.915445	−	0.241814i
$682$	−22.5494	+	13.0189i	−0.863462	+	0.498520i
$683$	12.6673	−	7.31347i	0.484701	−	0.279842i	−0.237673	−	0.971345i	$-0.576385\pi$
$683$	12.6673	−	7.31347i	0.484701	−	0.279842i	0.722373	+	0.691503i	$0.243051\pi$
$684$	−9.71771	+	16.5590i	−0.371566	+	0.633151i
$685$		−	60.2714i		−	2.30285i
$686$	−15.8771	−	9.53508i	−0.606190	−	0.364051i
$687$	5.36170	−	5.32378i	0.204562	−	0.203115i
$688$	−5.29168	+	9.16546i	−0.201743	+	0.349430i
$689$	−1.28194	−	2.22038i	−0.0488378	−	0.0845896i
$690$	−1.83631	+	6.75720i	−0.0699071	+	0.257242i
$691$	17.3233	+	10.0016i	0.659009	+	0.380479i	0.791899	−	0.610652i	$-0.209092\pi$
$691$	17.3233	+	10.0016i	0.659009	+	0.380479i	−0.132890	+	0.991131i	$0.542426\pi$
$692$	3.98794			0.151599
$693$	40.0284	+	0.514006i	1.52055	+	0.0195255i
$694$	4.09177			0.155321
$695$	59.2949	+	34.2339i	2.24919	+	1.29857i
$696$	−1.05942	+	3.89843i	−0.0401573	+	0.147770i
$697$	−2.93230	−	5.07890i	−0.111069	−	0.192377i
$698$	8.09906	−	14.0280i	0.306554	−	0.530967i
$699$	4.66619	−	4.63319i	0.176491	−	0.175243i
$700$	15.1556	−	25.9056i	0.572828	−	0.979138i
$701$		−	1.01932i		−	0.0384990i	−0.999815	−	0.0192495i	$-0.993872\pi$
$701$		−	1.01932i		−	0.0384990i	0.999815	−	0.0192495i	$-0.00612769\pi$
$702$	−0.526198	−	2.05089i	−0.0198601	−	0.0774058i
$703$	−20.2493	+	11.6909i	−0.763715	+	0.440931i
$704$	4.36781	−	2.52176i	0.164618	−	0.0950423i
$705$	22.2914	−	5.88827i	0.839544	−	0.221765i
$706$		−	4.67408i		−	0.175911i
$707$	11.0258	+	19.3530i	0.414667	+	0.727846i
$708$	3.37045	+	3.39446i	0.126669	+	0.127572i
$709$	4.04252	−	7.00185i	0.151820	−	0.262960i	−0.780077	−	0.625684i	$-0.784820\pi$
$709$	4.04252	−	7.00185i	0.151820	−	0.262960i	0.931897	+	0.362724i	$0.118153\pi$
$710$	28.1537	+	48.7637i	1.05659	+	1.83007i
$711$	−36.9292	+	20.9731i	−1.38495	+	0.786551i
$712$	10.7335	+	6.19702i	0.402257	+	0.232243i
$713$	−5.16264			−0.193342
$714$	2.79668	+	0.777291i	0.104663	+	0.0290894i
$715$	8.30836			0.310715
$716$	17.6724	+	10.2031i	0.660447	+	0.381310i
$717$	38.8744	+	10.5644i	1.45179	+	0.394533i
$718$	−11.2157	−	19.4262i	−0.418566	−	0.724978i
$719$	−7.92167	+	13.7207i	−0.295428	+	0.511697i	−0.975084	−	0.221834i	$-0.928796\pi$
$719$	−7.92167	+	13.7207i	−0.295428	+	0.511697i	0.679656	+	0.733531i	$0.262129\pi$
$720$	0.0860763	−	12.1280i	0.00320787	−	0.451983i
$721$	25.4026	+	14.8614i	0.946043	+	0.553467i
$722$		−	21.9595i		−	0.817248i
$723$	−1.62858	−	6.16539i	−0.0605677	−	0.229293i
$724$	−3.95076	+	2.28097i	−0.146829	+	0.0847717i
$725$	−22.9137	+	13.2292i	−0.850993	+	0.491321i
$726$	6.38620	+	24.1765i	0.237014	+	0.897274i
$727$			28.9513i			1.07375i	0.843663	+	0.536873i	$0.180394\pi$
$727$			28.9513i			1.07375i	−0.843663	+	0.536873i	$0.819606\pi$
$728$	−1.07807	−	0.00619154i	−0.0399558	−	0.000229474i
$729$	0.574831	−	26.9939i	0.0212900	−	0.999773i
$730$	−18.5330	+	32.1001i	−0.685936	+	1.18808i
$731$	−3.35185	−	5.80558i	−0.123973	−	0.214727i
$732$	−25.5171	−	6.93442i	−0.943138	−	0.256304i
$733$	−23.8917	−	13.7939i	−0.882460	−	0.509489i	−0.0109913	−	0.999940i	$-0.503499\pi$
$733$	−23.8917	−	13.7939i	−0.882460	−	0.509489i	−0.871469	+	0.490451i	$0.836832\pi$
$734$	−22.8457			−0.843251
$735$	−34.1345	−	35.1766i	−1.25907	−	1.29751i
$736$	1.00000			0.0368605
$737$	−3.73332	−	2.15543i	−0.137519	−	0.0793964i
$738$	13.7169	+	24.1526i	0.504926	+	0.889071i
$739$	−5.23164	−	9.06147i	−0.192449	−	0.333332i	0.753612	−	0.657319i	$-0.228310\pi$
$739$	−5.23164	−	9.06147i	−0.192449	−	0.333332i	−0.946061	+	0.323988i	$0.894976\pi$
$740$	7.38498	−	12.7912i	0.271477	−	0.470212i
$741$	3.18258	+	3.20525i	0.116915	+	0.117748i
$742$	−16.6469	−	0.0956065i	−0.611128	−	0.00350982i
$743$			12.6450i			0.463901i	0.972728	+	0.231950i	$0.0745107\pi$
$743$			12.6450i			0.463901i	−0.972728	+	0.231950i	$0.925489\pi$
$744$	8.64542	−	2.28368i	0.316956	−	0.0837238i
$745$	−38.5227	+	22.2411i	−1.41136	+	0.814851i
$746$	−0.0956212	+	0.0552069i	−0.00350094	+	0.00202127i
$747$	23.8610	+	14.0029i	0.873030	+	0.512340i
$748$			3.19466i			0.116808i
$749$	17.8345	+	10.4338i	0.651659	+	0.381242i
$750$	31.5222	−	31.2993i	1.15103	−	1.14289i
$751$	−1.77884	+	3.08104i	−0.0649108	+	0.112429i	−0.896654	−	0.442731i	$-0.854010\pi$
$751$	−1.77884	+	3.08104i	−0.0649108	+	0.112429i	0.831744	+	0.555160i	$0.187343\pi$
$752$	−1.64632	−	2.85152i	−0.0600353	−	0.103984i
$753$	−2.33522	+	8.59307i	−0.0851002	+	0.313149i
$754$	0.823067	+	0.475198i	0.0299744	+	0.0173057i
$755$	−2.14108			−0.0779219
$756$	−13.2192	−	3.77532i	−0.480777	−	0.137307i
$757$	−8.94460			−0.325097			−0.162548	−	0.986701i	$-0.551971\pi$
$757$	−8.94460			−0.325097			−0.162548	+	0.986701i	$0.551971\pi$
$758$	31.6668	+	18.2828i	1.15019	+	0.664062i
$759$	−2.29088	+	8.42989i	−0.0831535	+	0.305986i
$760$	12.9368	+	22.4071i	0.469265	+	0.812792i
$761$	2.73722	−	4.74100i	0.0992241	−	0.171861i	−0.812140	−	0.583463i	$-0.801697\pi$
$761$	2.73722	−	4.74100i	0.0992241	−	0.171861i	0.911364	+	0.411602i	$0.135031\pi$
$762$	8.29116	−	8.23252i	0.300357	−	0.298233i
$763$	6.51411	+	11.4339i	0.235826	+	0.413935i
$764$			4.50457i			0.162970i
$765$	6.62563	+	3.88827i	0.239550	+	0.140581i
$766$	−2.80841	+	1.62144i	−0.101472	+	0.0585849i
$767$	0.974593	−	0.562682i	0.0351905	−	0.0203173i
$768$	−1.67461	+	0.442348i	−0.0604274	+	0.0159619i
$769$			35.0762i			1.26488i	0.774609	+	0.632440i	$0.217947\pi$
$769$			35.0762i			1.26488i	−0.774609	+	0.632440i	$0.782053\pi$
$770$	27.2409	−	46.5631i	0.981696	−	1.67802i
$771$	3.10386	+	3.12597i	0.111783	+	0.112579i
$772$	2.07842	−	3.59992i	0.0748038	−	0.129564i
$773$	2.89868	+	5.02066i	0.104258	+	0.180581i	0.913435	−	0.406985i	$-0.133420\pi$
$773$	2.89868	+	5.02066i	0.104258	+	0.180581i	−0.809177	+	0.587565i	$0.800086\pi$
$774$	15.6795	+	27.6083i	0.563588	+	0.992361i
$775$	50.7183	+	29.2823i	1.82186	+	1.05185i
$776$	−2.81141			−0.100924
$777$	−11.7280	−	11.9480i	−0.420738	−	0.428631i
$778$	−19.8407			−0.711323
$779$	−51.3163	−	29.6275i	−1.83860	−	1.06152i
$780$	−2.75341	−	0.748255i	−0.0985877	−	0.0267918i
$781$	35.1230	+	60.8348i	1.25680	+	2.17684i
$782$	−0.316710	+	0.548557i	−0.0113255	+	0.0196164i
$783$	8.47803	+	8.66049i	0.302980	+	0.309501i
$784$	−3.56940	+	6.02158i	−0.127479	+	0.215056i
$785$		−	13.6880i		−	0.488545i
$786$	0.421922	+	1.59729i	0.0150495	+	0.0569733i
$787$	−27.9400	+	16.1312i	−0.995954	+	0.575014i	−0.907049	−	0.421026i	$-0.861670\pi$
$787$	−27.9400	+	16.1312i	−0.995954	+	0.575014i	−0.0889051	+	0.996040i	$0.528337\pi$
$788$	20.4479	−	11.8056i	0.728426	−	0.420557i
$789$	5.12788	+	19.4128i	0.182557	+	0.691114i
$790$			57.2310i			2.03619i
$791$	−0.199949	+	34.8150i	−0.00710937	+	1.23788i
$792$	0.107384	−	15.1302i	0.00381572	−	0.537627i
$793$	−3.11040	+	5.38737i	−0.110453	+	0.191311i
$794$	10.8327	+	18.7627i	0.384437	+	0.665865i
$795$	−42.5166	−	11.5542i	−1.50791	−	0.409784i
$796$	−0.186904	−	0.107909i	−0.00662465	−	0.00382474i
$797$	−33.9296			−1.20185			−0.600924	−	0.799306i	$-0.705201\pi$
$797$	−33.9296			−1.20185			−0.600924	+	0.799306i	$0.705201\pi$
$798$	28.3983	−	7.32717i	1.00529	−	0.259379i
$799$	2.08563			0.0737842
$800$	−9.82412	−	5.67196i	−0.347335	−	0.200534i
$801$	32.3318	−	18.3621i	1.14239	−	0.648791i
$802$	−12.7624	−	22.1051i	−0.450655	−	0.780557i
$803$	−23.1207	+	40.0462i	−0.815911	+	1.41320i
$804$	1.04311	+	1.05054i	0.0367876	+	0.0370497i
$805$	9.29369	−	5.29478i	0.327560	−	0.186617i
$806$		−	2.10366i		−	0.0740982i
$807$	−37.6417	+	9.94304i	−1.32505	+	0.350012i
$808$	7.29071	−	4.20929i	0.256486	−	0.148082i
$809$	−27.6119	+	15.9418i	−0.970784	+	0.560482i	−0.899475	−	0.436972i	$-0.856051\pi$
$809$	−27.6119	+	15.9418i	−0.970784	+	0.560482i	−0.0713087	+	0.997454i	$0.522718\pi$
$810$	−31.2488	−	18.6378i	−1.09797	−	0.654867i
$811$			27.7808i			0.975516i	0.872979	+	0.487758i	$0.162185\pi$
$811$			27.7808i			0.975516i	−0.872979	+	0.487758i	$0.837815\pi$
$812$	5.36181	−	3.05472i	0.188163	−	0.107200i
$813$	−0.0464054	+	0.0460773i	−0.00162751	+	0.00161600i
$814$	9.21307	−	15.9575i	0.322918	−	0.559310i
$815$	−16.6654	−	28.8653i	−0.583763	−	1.01111i
$816$	0.287713	−	1.05872i	0.0100720	−	0.0370625i
$817$	−58.6586	−	33.8665i	−2.05220	−	1.18484i
$818$	7.88015			0.275523
$819$	−1.65296	+	2.77995i	−0.0577590	+	0.0971393i
$820$	37.4305			1.30713
$821$	12.2442	+	7.06917i	0.427324	+	0.246716i	0.698206	−	0.715897i	$-0.253982\pi$
$821$	12.2442	+	7.06917i	0.427324	+	0.246716i	−0.270882	+	0.962613i	$0.587315\pi$
$822$	−6.77176	+	24.9185i	−0.236192	+	0.869132i
$823$	24.5581	+	42.5359i	0.856042	+	1.48271i	0.875675	+	0.482901i	$0.160417\pi$
$823$	24.5581	+	42.5359i	0.856042	+	1.48271i	−0.0196328	+	0.999807i	$0.506250\pi$
$824$	5.56184	−	9.63339i	0.193756	−	0.335595i
$825$	70.3198	−	69.8225i	2.44822	−	2.43091i
$826$	0.0419647	−	7.30686i	0.00146014	−	0.254238i
$827$		−	20.0182i		−	0.696099i	−0.937476	−	0.348050i	$-0.886844\pi$
$827$		−	20.0182i		−	0.696099i	0.937476	−	0.348050i	$-0.113156\pi$
$828$	1.51840	−	2.58737i	0.0527681	−	0.0899172i
$829$	28.5518	−	16.4844i	0.991645	−	0.572526i	0.0858793	−	0.996306i	$-0.472630\pi$
$829$	28.5518	−	16.4844i	0.991645	−	0.572526i	0.905766	+	0.423779i	$0.139297\pi$
$830$	32.2879	−	18.6415i	1.12073	−	0.647054i
$831$	−20.8470	+	5.50671i	−0.723173	+	0.191026i
$832$			0.407478i			0.0141267i
$833$	−2.17272	−	3.86511i	−0.0752802	−	0.133918i
$834$	−20.6685	−	20.8157i	−0.715690	−	0.720787i
$835$	9.46356	−	16.3914i	0.327500	−	0.567246i
$836$	16.1392	+	27.9538i	0.558184	+	0.966804i
$837$	7.21849	−	25.8364i	0.249508	−	0.893036i
$838$	10.7293	+	6.19454i	0.370636	+	0.213987i
$839$	8.17906			0.282373			0.141186	−	0.989983i	$-0.454908\pi$
$839$	8.17906			0.282373			0.141186	+	0.989983i	$0.454908\pi$
$840$	−13.2212	+	12.9778i	−0.456175	+	0.447775i
$841$	23.5600			0.812412
$842$	−6.60180	−	3.81155i	−0.227513	−	0.131355i
$843$	−3.03187	−	0.823928i	−0.104423	−	0.0283776i
$844$	−2.49633	−	4.32377i	−0.0859271	−	0.148830i
$845$	25.9423	−	44.9334i	0.892443	−	1.54576i
$846$	−9.87770	−	0.0701053i	−0.339602	−	0.00241027i
$847$	19.2881	−	32.9692i	0.662747	−	1.13284i
$848$			6.29205i			0.216070i
$849$	−6.48254	−	24.5412i	−0.222480	−	0.842251i
$850$	6.22279	−	3.59273i	0.213440	−	0.123230i
$851$	3.16396	−	1.82672i	0.108459	−	0.0626190i
$852$	−6.16101	−	23.3240i	−0.211073	−	0.799066i
$853$			31.1646i			1.06705i	0.845783	+	0.533527i	$0.179134\pi$
$853$			31.1646i			1.06705i	−0.845783	+	0.533527i	$0.820866\pi$
$854$	19.9946	+	35.0956i	0.684200	+	1.20095i
$855$	77.6186	+	0.550885i	2.65450	+	0.0188399i
$856$	3.90482	−	6.76335i	0.133464	−	0.231166i
$857$	8.18639	+	14.1792i	0.279642	+	0.484354i	0.971296	−	0.237875i	$-0.0764509\pi$
$857$	8.18639	+	14.1792i	0.279642	+	0.484354i	−0.691654	+	0.722229i	$0.743118\pi$
$858$	−3.43499	−	0.933480i	−0.117269	−	0.0318685i
$859$	1.48350	+	0.856499i	0.0506164	+	0.0292234i	0.525095	−	0.851044i	$-0.324030\pi$
$859$	1.48350	+	0.856499i	0.0506164	+	0.0292234i	−0.474478	+	0.880267i	$0.657363\pi$
$860$	42.7860			1.45899
$861$	11.3616	−	40.8789i	0.387203	−	1.39315i
$862$	16.8789			0.574897
$863$	27.3859	+	15.8112i	0.932226	+	0.538221i	0.887515	−	0.460779i	$-0.152430\pi$
$863$	27.3859	+	15.8112i	0.932226	+	0.538221i	0.0447111	+	0.999000i	$0.485763\pi$
$864$	−1.39822	+	5.00450i	−0.0475684	+	0.170256i
$865$	−8.06114	−	13.9623i	−0.274087	−	0.474733i
$866$	6.61601	−	11.4593i	0.224821	−	0.389402i
$867$	−20.2570	−	20.4013i	−0.687964	−	0.692864i
$868$	−11.7897	−	6.89735i	−0.400167	−	0.234111i
$869$			71.3981i			2.42201i
$870$	15.7904	−	4.17103i	0.535345	−	0.141411i
$871$	0.301624	−	0.174142i	0.0102201	−	0.00590059i
$872$	4.30740	−	2.48688i	0.145867	−	0.0842164i
$873$	−4.26885	+	7.27415i	−0.144479	+	0.246193i
$874$			6.39996i			0.216482i
$875$	−67.8543	−	0.389700i	−2.29389	−	0.0131743i
$876$	11.2688	−	11.1891i	0.380738	−	0.378045i
$877$	−1.73936	+	3.01267i	−0.0587342	+	0.101731i	−0.893897	−	0.448272i	$-0.852040\pi$
$877$	−1.73936	+	3.01267i	−0.0587342	+	0.101731i	0.835163	+	0.550002i	$0.185373\pi$
$878$	2.86358	+	4.95987i	0.0966412	+	0.167387i
$879$	7.24575	−	26.6627i	0.244393	−	0.899310i
$880$	−17.6580	−	10.1949i	−0.595252	−	0.343669i
$881$	11.3547			0.382549			0.191274	−	0.981537i	$-0.438738\pi$
$881$	11.3547			0.382549			0.191274	+	0.981537i	$0.438738\pi$
$882$	10.1602	+	18.3785i	0.342113	+	0.618837i
$883$	1.10444			0.0371673			0.0185837	−	0.999827i	$-0.494084\pi$
$883$	1.10444			0.0371673			0.0185837	+	0.999827i	$0.494084\pi$
$884$	−0.223525	−	0.129052i	−0.00751795	−	0.00434049i
$885$	5.07149	−	18.6619i	0.170476	−	0.627313i
$886$	−6.52126	−	11.2952i	−0.219086	−	0.379468i
$887$	−9.28162	+	16.0762i	−0.311646	+	0.539787i	−0.978719	−	0.205205i	$-0.934214\pi$
$887$	−9.28162	+	16.0762i	−0.311646	+	0.539787i	0.667073	+	0.744993i	$0.267547\pi$
$888$	−4.49037	+	4.45862i	−0.150687	+	0.149621i
$889$	−17.8474	−	0.102501i	−0.598584	−	0.00343778i
$890$		−	50.1061i		−	1.67956i
$891$	−38.9842	−	23.2515i	−1.30602	−	0.778955i
$892$	−24.9802	+	14.4224i	−0.836400	+	0.482896i
$893$	18.2496	−	10.5364i	0.610700	−	0.352588i
$894$	18.4256	−	4.86712i	0.616246	−	0.162781i
$895$		−	82.4978i		−	2.75760i
$896$	2.28365	+	1.33601i	0.0762915	+	0.0446331i
$897$	−0.497282	−	0.500824i	−0.0166038	−	0.0167220i
$898$	1.56338	−	2.70785i	0.0521706	−	0.0903621i
$899$	6.02064	+	10.4281i	0.200800	+	0.347795i
$900$	−29.5924	+	16.8063i	−0.986413	+	0.560209i
$901$	−3.45155	−	1.99275i	−0.114988	−	0.0663883i
$902$	46.6961			1.55481
$903$	12.9872	−	46.7278i	0.432187	−	1.55500i
$904$	13.1590			0.437663
$905$	15.9720	+	9.22143i	0.530927	+	0.306531i
$906$	0.885205	+	0.240560i	0.0294090	+	0.00799207i
$907$	−12.4121	−	21.4984i	−0.412137	−	0.713842i	0.582986	−	0.812482i	$-0.301884\pi$
$907$	−12.4121	−	21.4984i	−0.412137	−	0.713842i	−0.995123	+	0.0986400i	$0.968551\pi$
$908$	−7.13282	+	12.3544i	−0.236711	+	0.409995i
$909$	0.179244	−	25.2551i	0.00594515	−	0.837660i
$910$	2.15750	+	3.78697i	0.0715206	+	0.125537i
$911$			4.43043i			0.146787i	0.997303	+	0.0733933i	$0.0233828\pi$
$911$			4.43043i			0.146787i	−0.997303	+	0.0733933i	$0.976617\pi$
$912$	−2.83101	−	10.7175i	−0.0937441	−	0.354890i
$913$	40.2806	−	23.2560i	1.33309	−	0.769662i
$914$	−4.78263	+	2.76125i	−0.158195	+	0.0913341i
$915$	27.3014	+	103.356i	0.902555	+	3.41684i
$916$			4.36236i			0.144136i
$917$	1.27432	−	2.17820i	0.0420818	−	0.0719306i
$918$	−2.30242	−	2.35198i	−0.0759913	−	0.0776268i
$919$	29.0284	−	50.2786i	0.957557	−	1.65854i	0.229152	−	0.973391i	$-0.426405\pi$
$919$	29.0284	−	50.2786i	0.957557	−	1.65854i	0.728405	−	0.685147i	$-0.240262\pi$
$920$	−2.02138	−	3.50113i	−0.0666429	−	0.115429i
$921$	−5.10156	−	1.38638i	−0.168102	−	0.0456828i
$922$	5.56335	+	3.21200i	0.183219	+	0.105782i
$923$	−5.67533			−0.186806
$924$	−16.4940	+	16.1903i	−0.542613	+	0.532622i
$925$	−41.4442			−1.36268
$926$	−19.6047	−	11.3188i	−0.644249	−	0.371957i
$927$	−16.4800	−	29.0179i	−0.541274	−	0.953072i
$928$	−1.16619	−	2.01991i	−0.0382822	−	0.0663068i
$929$	−17.6573	+	30.5834i	−0.579318	+	1.00341i	0.416240	+	0.909255i	$0.363348\pi$
$929$	−17.6573	+	30.5834i	−0.579318	+	1.00341i	−0.995558	+	0.0941533i	$0.969986\pi$
$930$	−25.4712	−	25.6526i	−0.835232	−	0.841181i
$931$	−38.5379	−	22.8440i	−1.26303	−	0.748682i
$932$			3.79648i			0.124358i
$933$	24.2743	−	6.41205i	0.794706	−	0.209921i
$934$	−30.4014	+	17.5522i	−0.994763	+	0.574327i
$935$	11.1849	−	6.45763i	0.365787	−	0.211187i
$936$	1.05429	+	0.618714i	0.0344606	+	0.0202233i
$937$		−	23.4330i		−	0.765523i	−0.923847	−	0.382761i	$-0.874973\pi$
$937$		−	23.4330i		−	0.765523i	0.923847	−	0.382761i	$-0.125027\pi$
$938$	0.0129875	−	2.26138i	0.000424057	−	0.0738365i
$939$	1.14511	−	1.13701i	0.0373694	−	0.0371051i
$940$	−6.65570	+	11.5280i	−0.217085	+	0.376002i
$941$	18.1566	+	31.4482i	0.591889	+	1.02518i	0.993978	+	0.109582i	$0.0349511\pi$
$941$	18.1566	+	31.4482i	0.591889	+	1.02518i	−0.402088	+	0.915601i	$0.631716\pi$
$942$	−1.53790	+	5.65913i	−0.0501077	+	0.184385i
$943$	8.01822	+	4.62932i	0.261109	+	0.150752i
$944$	−2.76178			−0.0898883
$945$	13.5031	+	53.9135i	0.439256	+	1.75381i
$946$	53.3773			1.73545
$947$	−25.8048	−	14.8984i	−0.838542	−	0.484132i	0.0182264	−	0.999834i	$-0.494198\pi$
$947$	−25.8048	−	14.8984i	−0.838542	−	0.484132i	−0.856768	+	0.515701i	$0.827531\pi$
$948$	6.43015	−	23.6615i	0.208842	−	0.768489i
$949$	−1.86797	−	3.23543i	−0.0606370	−	0.105026i
$950$	36.3003	−	62.8740i	1.17774	−	2.03990i
$951$	−39.7267	+	39.4457i	−1.28823	+	1.27912i
$952$	−1.45613	+	0.829586i	−0.0471936	+	0.0268870i
$953$			10.3275i			0.334541i	0.985911	+	0.167270i	$0.0534953\pi$
$953$			10.3275i			0.334541i	−0.985911	+	0.167270i	$0.946505\pi$
$954$	16.2798	+	9.55386i	0.527079	+	0.309318i
$955$	15.7711	−	9.10545i	0.510341	−	0.294646i
$956$	−20.1421	+	11.6291i	−0.651444	+	0.376111i
$957$	19.6992	−	5.20354i	0.636785	−	0.168206i
$958$			5.95848i			0.192510i
$959$	34.2723	−	19.5256i	1.10671	−	0.630513i
$960$	4.93375	+	4.96889i	0.159236	+	0.160370i
$961$	−2.17359	+	3.76478i	−0.0701159	+	0.121444i
$962$	0.744346	+	1.28924i	0.0239987	+	0.0415669i
$963$	−11.5702	−	20.3727i	−0.372843	−	0.656500i
$964$	3.18843	+	1.84084i	0.102692	+	0.0592895i
$965$	−16.8051			−0.540975
$966$	−4.43726	+	1.14488i	−0.142766	+	0.0368358i
$967$	−6.69432			−0.215275			−0.107637	−	0.994190i	$-0.534329\pi$
$967$	−6.69432			−0.215275			−0.107637	+	0.994190i	$0.534329\pi$
$968$	−12.5029	−	7.21853i	−0.401857	−	0.232012i
$969$	6.77575	+	1.84135i	0.217668	+	0.0591527i
$970$	5.68294	+	9.84314i	0.182468	+	0.316044i
$971$	17.2456	−	29.8703i	0.553439	−	0.958585i	−0.444584	−	0.895737i	$-0.646648\pi$
$971$	17.2456	−	29.8703i	0.553439	−	0.958585i	0.998023	−	0.0628476i	$-0.0200182\pi$
$972$	10.8254	+	11.2165i	0.347225	+	0.359771i
$973$	−0.257338	+	44.8075i	−0.00824988	+	1.43646i
$974$			22.9375i			0.734965i
$975$	2.04471	+	7.74071i	0.0654830	+	0.247901i
$976$	13.2213	−	7.63330i	0.423202	−	0.244336i
$977$	34.3030	−	19.8048i	1.09745	−	0.633613i	0.161900	−	0.986807i	$-0.448238\pi$
$977$	34.3030	−	19.8048i	1.09745	−	0.633613i	0.935550	+	0.353194i	$0.114904\pi$
$978$	3.64697	+	13.8064i	0.116617	+	0.441482i
$979$		−	62.5095i		−	1.99781i
$980$	28.2975	+	0.325046i	0.903929	+	0.0103832i
$981$	0.105899	−	14.9209i	0.00338108	−	0.476388i
$982$	5.69908	−	9.87110i	0.181865	−	0.314999i
$983$	16.3441	+	28.3089i	0.521297	+	0.902913i	0.999693	+	0.0247687i	$0.00788492\pi$
$983$	16.3441	+	28.3089i	0.521297	+	0.902913i	−0.478396	+	0.878144i	$0.658782\pi$
$984$	−15.4752	−	4.20548i	−0.493331	−	0.134066i
$985$	−82.6659	−	47.7272i	−2.63395	−	1.52071i
$986$	1.47738			0.0470494
$987$	10.5698	+	10.7681i	0.336441	+	0.342752i
$988$	−2.60784			−0.0829665
$989$	9.16546	+	5.29168i	0.291445	+	0.168266i
$990$	−53.1898	+	30.2079i	−1.69048	+	0.960069i
$991$	8.09964	+	14.0290i	0.257294	+	0.445645i	0.965516	−	0.260344i	$-0.0838359\pi$
$991$	8.09964	+	14.0290i	0.257294	+	0.445645i	−0.708222	+	0.705989i	$0.750503\pi$
$992$	−2.58132	+	4.47097i	−0.0819569	+	0.141954i
$993$	18.1214	+	18.2505i	0.575066	+	0.579162i
$994$	−18.6079	+	31.8066i	−0.590208	+	1.00885i
$995$			0.872503i			0.0276602i
$996$	−15.4435	+	4.07940i	−0.489347	+	0.129261i
$997$	−24.2415	+	13.9958i	−0.767737	+	0.443253i	−0.832067	−	0.554676i	$-0.812842\pi$
$997$	−24.2415	+	13.9958i	−0.767737	+	0.443253i	0.0643300	+	0.997929i	$0.479509\pi$
$998$	12.6369	−	7.29590i	0.400013	−	0.230948i
$999$	4.71788	+	18.3882i	0.149267	+	0.581777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.47.10	✓	56
3.2	odd	2	inner	966.2.l.c.47.27	yes	56
7.3	odd	6	inner	966.2.l.c.185.27	yes	56
21.17	even	6	inner	966.2.l.c.185.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.10	✓	56	1.1	even	1	trivial
966.2.l.c.47.27	yes	56	3.2	odd	2	inner
966.2.l.c.185.10	yes	56	21.17	even	6	inner
966.2.l.c.185.27	yes	56	7.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.454222 - 1.67143i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.02138 - 3.50113i) q^{5} +(-1.22908 + 1.22039i) q^{6} +(2.64571 + 0.0151948i) q^{7} -1.00000i q^{8} +(-2.58737 - 1.51840i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.454222 - 1.67143i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.02138 - 3.50113i) q^{5} +(-1.22908 + 1.22039i) q^{6} +(2.64571 + 0.0151948i) q^{7} -1.00000i q^{8} +(-2.58737 - 1.51840i) q^{9} +(-3.50113 + 2.02138i) q^{10} +(-4.36781 + 2.52176i) q^{11} +(1.67461 - 0.442348i) q^{12} -0.407478i q^{13} +(-2.28365 - 1.33601i) q^{14} +(-4.93375 - 4.96889i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.316710 - 0.548557i) q^{17} +(1.48152 + 2.60866i) q^{18} +(-5.54253 - 3.19998i) q^{19} +4.04276 q^{20} +(1.22714 - 4.41522i) q^{21} +5.04352 q^{22} +(0.866025 + 0.500000i) q^{23} +(-1.67143 - 0.454222i) q^{24} +(-5.67196 - 9.82412i) q^{25} +(-0.203739 + 0.352886i) q^{26} +(-3.71314 + 3.63491i) q^{27} +(1.30969 + 2.29885i) q^{28} -2.33239i q^{29} +(1.78831 + 6.77006i) q^{30} +(-4.47097 + 2.58132i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.23099 + 8.44594i) q^{33} +0.633419i q^{34} +(5.40118 - 9.23226i) q^{35} +(0.0212915 - 2.99992i) q^{36} +(1.82672 - 3.16396i) q^{37} +(3.19998 + 5.54253i) q^{38} +(-0.681071 - 0.185085i) q^{39} +(-3.50113 - 2.02138i) q^{40} +9.25865 q^{41} +(-3.27034 + 3.21012i) q^{42} +10.5834 q^{43} +(-4.36781 - 2.52176i) q^{44} +(-10.5462 + 5.98944i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.64632 + 2.85152i) q^{47} +(1.22039 + 1.22908i) q^{48} +(6.99954 + 0.0804020i) q^{49} +11.3439i q^{50} +(-1.06073 + 0.280192i) q^{51} +(0.352886 - 0.203739i) q^{52} +(5.44908 - 3.14603i) q^{53} +(5.03313 - 1.29136i) q^{54} +20.3897i q^{55} +(0.0151948 - 2.64571i) q^{56} +(-7.86609 + 7.81045i) q^{57} +(-1.16619 + 2.01991i) q^{58} +(1.38089 + 2.39177i) q^{59} +(1.83631 - 6.75720i) q^{60} +(-13.2213 - 7.63330i) q^{61} +5.16264 q^{62} +(-6.82234 - 4.05656i) q^{63} -1.00000 q^{64} +(-1.42663 - 0.823667i) q^{65} +(2.29088 - 8.42989i) q^{66} +(0.427367 + 0.740221i) q^{67} +(0.316710 - 0.548557i) q^{68} +(1.22908 - 1.22039i) q^{69} +(-9.29369 + 5.29478i) q^{70} -13.9280i q^{71} +(-1.51840 + 2.58737i) q^{72} +(7.94013 - 4.58424i) q^{73} +(-3.16396 + 1.82672i) q^{74} +(-18.9967 + 5.01796i) q^{75} -6.39996i q^{76} +(-11.5943 + 6.60547i) q^{77} +(0.497282 + 0.500824i) q^{78} +(7.07821 - 12.2598i) q^{79} +(2.02138 + 3.50113i) q^{80} +(4.38892 + 7.85732i) q^{81} +(-8.01822 - 4.62932i) q^{82} -9.22214 q^{83} +(4.43726 - 1.14488i) q^{84} -2.56076 q^{85} +(-9.16546 - 5.29168i) q^{86} +(-3.89843 - 1.05942i) q^{87} +(2.52176 + 4.36781i) q^{88} +(-6.19702 + 10.7335i) q^{89} +(12.1280 + 0.0860763i) q^{90} +(0.00619154 - 1.07807i) q^{91} +1.00000i q^{92} +(2.28368 + 8.64542i) q^{93} +(2.85152 - 1.64632i) q^{94} +(-22.4071 + 12.9368i) q^{95} +(-0.442348 - 1.67461i) q^{96} -2.81141i q^{97} +(-6.02158 - 3.56940i) q^{98} +(15.1302 + 0.107384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

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