LMFDB - Embedded newform 912.2.bq.a.733.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(277,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 8]))

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

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

chi := DirichletCharacter("912.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bq (of order $12$, degree $4$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$80$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			733.20
Character	$\chi$	$=$	912.733
Dual form			912.2.bq.a.805.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.956029 + 1.04212i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.172017 - 1.99259i) q^{4} +(1.08198 + 4.03799i) q^{5} +(-0.653733 + 1.25405i) q^{6} -1.09440i q^{7} +(2.24096 + 1.72571i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.956029 + 1.04212i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.172017 - 1.99259i) q^{4} +(1.08198 + 4.03799i) q^{5} +(-0.653733 + 1.25405i) q^{6} -1.09440i q^{7} +(2.24096 + 1.72571i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-5.24246 - 2.73289i) q^{10} +(-3.68173 + 3.68173i) q^{11} +(-0.681875 - 1.88017i) q^{12} +(-0.262678 + 0.980329i) q^{13} +(1.14050 + 1.04628i) q^{14} +(2.09022 + 3.62036i) q^{15} +(-3.94082 + 0.685516i) q^{16} +(-1.38165 + 2.39309i) q^{17} +(-0.306887 + 1.38051i) q^{18} +(-0.823158 - 4.28047i) q^{19} +(7.85994 - 2.85054i) q^{20} +(-0.283252 - 1.05711i) q^{21} +(-0.316953 - 7.35664i) q^{22} +(-2.47715 + 1.43018i) q^{23} +(2.61125 + 1.08691i) q^{24} +(-10.8046 + 6.23803i) q^{25} +(-0.770489 - 1.21096i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.18070 + 0.188255i) q^{28} +(-1.22454 + 4.57004i) q^{29} +(-5.77115 - 1.28292i) q^{30} +8.18786 q^{31} +(3.05315 - 4.76217i) q^{32} +(-2.60338 + 4.50918i) q^{33} +(-1.17298 - 3.72771i) q^{34} +(4.41919 - 1.18412i) q^{35} +(-1.14527 - 1.63962i) q^{36} +(0.714297 - 0.714297i) q^{37} +(5.24771 + 3.23443i) q^{38} +1.01491i q^{39} +(-4.54374 + 10.9162i) q^{40} +(-3.45105 - 1.99246i) q^{41} +(1.37243 + 0.715448i) q^{42} +(0.292517 + 1.09169i) q^{43} +(7.96950 + 6.70286i) q^{44} +(2.95602 + 2.95602i) q^{45} +(0.877809 - 3.94878i) q^{46} +(-5.67266 - 9.82534i) q^{47} +(-3.62912 + 1.68212i) q^{48} +5.80228 q^{49} +(3.82874 - 17.2234i) q^{50} +(-0.715196 + 2.66915i) q^{51} +(1.99858 + 0.354777i) q^{52} +(6.34769 + 1.70086i) q^{53} +(0.0608734 + 1.41290i) q^{54} +(-18.8504 - 10.8833i) q^{55} +(1.88862 - 2.45252i) q^{56} +(-1.90298 - 3.92157i) q^{57} +(-3.59183 - 5.64521i) q^{58} +(2.35790 + 8.79979i) q^{59} +(6.85435 - 4.78771i) q^{60} +(-2.03845 + 7.60759i) q^{61} +(-7.82784 + 8.53271i) q^{62} +(-0.547202 - 0.947781i) q^{63} +(2.04384 + 7.73452i) q^{64} -4.24277 q^{65} +(-2.21019 - 7.02393i) q^{66} +(-2.80015 + 10.4503i) q^{67} +(5.00612 + 2.34141i) q^{68} +(-2.02258 + 2.02258i) q^{69} +(-2.99089 + 5.73737i) q^{70} +(-10.3899 - 5.99864i) q^{71} +(2.80359 + 0.374028i) q^{72} +(5.34922 + 3.08837i) q^{73} +(0.0614925 + 1.42727i) q^{74} +(-8.82190 + 8.82190i) q^{75} +(-8.38762 + 2.37653i) q^{76} +(4.02930 + 4.02930i) q^{77} +(-1.05766 - 0.970285i) q^{78} +(4.08050 - 7.06763i) q^{79} +(-7.03199 - 15.1713i) q^{80} +(0.500000 - 0.866025i) q^{81} +(5.37568 - 1.69154i) q^{82} +(3.56884 + 3.56884i) q^{83} +(-2.05767 + 0.746246i) q^{84} +(-11.1582 - 2.98983i) q^{85} +(-1.41732 - 0.738849i) q^{86} +4.73126i q^{87} +(-14.6042 + 1.89702i) q^{88} +(-4.39337 + 2.53651i) q^{89} +(-5.90655 + 0.254478i) q^{90} +(1.07288 + 0.287476i) q^{91} +(3.27588 + 4.68993i) q^{92} +(7.90887 - 2.11917i) q^{93} +(15.6624 + 3.48173i) q^{94} +(16.3939 - 7.95527i) q^{95} +(1.71658 - 5.39012i) q^{96} +(-8.63993 + 14.9648i) q^{97} +(-5.54715 + 6.04666i) q^{98} +(-1.34761 + 5.02934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 24 q^{8}+O(q^{10}) $ 320 * q + 24 * q^8	$ 320 q + 24 q^{8} - 8 q^{10} + 16 q^{15} - 4 q^{16} + 8 q^{19} - 8 q^{24} - 40 q^{26} - 40 q^{28} + 96 q^{31} - 60 q^{32} + 28 q^{34} - 48 q^{35} - 4 q^{36} - 16 q^{38} + 20 q^{40} + 56 q^{44} - 104 q^{46} - 320 q^{49} + 88 q^{50} + 8 q^{51} + 16 q^{52} + 4 q^{54} + 56 q^{56} + 56 q^{58} - 48 q^{60} - 32 q^{61} - 24 q^{62} - 72 q^{64} - 48 q^{66} + 48 q^{67} + 32 q^{68} + 64 q^{69} + 48 q^{70} + 40 q^{74} - 56 q^{76} - 24 q^{78} + 48 q^{79} + 16 q^{80} + 160 q^{81} + 80 q^{82} + 80 q^{83} - 16 q^{85} - 64 q^{86} + 24 q^{92} + 128 q^{94} + 48 q^{95} + 40 q^{96} + 4 q^{98}+O(q^{100}) $ 320 * q + 24 * q^8 - 8 * q^10 + 16 * q^15 - 4 * q^16 + 8 * q^19 - 8 * q^24 - 40 * q^26 - 40 * q^28 + 96 * q^31 - 60 * q^32 + 28 * q^34 - 48 * q^35 - 4 * q^36 - 16 * q^38 + 20 * q^40 + 56 * q^44 - 104 * q^46 - 320 * q^49 + 88 * q^50 + 8 * q^51 + 16 * q^52 + 4 * q^54 + 56 * q^56 + 56 * q^58 - 48 * q^60 - 32 * q^61 - 24 * q^62 - 72 * q^64 - 48 * q^66 + 48 * q^67 + 32 * q^68 + 64 * q^69 + 48 * q^70 + 40 * q^74 - 56 * q^76 - 24 * q^78 + 48 * q^79 + 16 * q^80 + 160 * q^81 + 80 * q^82 + 80 * q^83 - 16 * q^85 - 64 * q^86 + 24 * q^92 + 128 * q^94 + 48 * q^95 + 40 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−0.956029	+	1.04212i	−0.676015	+	0.736888i
$2$	−0.956029	+	1.04212i	−0.676015	+	0.736888i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.172017	−	1.99259i	−0.0860083	−	0.996294i
$5$	1.08198	+	4.03799i	0.483875	+	1.80584i	0.585075	+	0.810979i	$0.301065\pi$
$5$	1.08198	+	4.03799i	0.483875	+	1.80584i	−0.101201	+	0.994866i	$0.532268\pi$
$6$	−0.653733	+	1.25405i	−0.266886	+	0.511962i
$7$		−	1.09440i		−	0.413646i	−0.978378	−	0.206823i	$-0.933688\pi$
$7$		−	1.09440i		−	0.413646i	0.978378	−	0.206823i	$-0.0663124\pi$
$8$	2.24096	+	1.72571i	0.792300	+	0.610131i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−5.24246	−	2.73289i	−1.65781	−	0.864216i
$11$	−3.68173	+	3.68173i	−1.11008	+	1.11008i	−0.116946	+	0.993138i	$0.537310\pi$
$11$	−3.68173	+	3.68173i	−1.11008	+	1.11008i	−0.993138	+	0.116946i	$0.962690\pi$
$12$	−0.681875	−	1.88017i	−0.196840	−	0.542759i
$13$	−0.262678	+	0.980329i	−0.0728539	+	0.271894i	−0.992738	−	0.120296i	$-0.961616\pi$
$13$	−0.262678	+	0.980329i	−0.0728539	+	0.271894i	0.919884	+	0.392190i	$0.128282\pi$
$14$	1.14050	+	1.04628i	0.304811	+	0.279630i
$15$	2.09022	+	3.62036i	0.539692	+	0.934774i
$16$	−3.94082	+	0.685516i	−0.985205	+	0.171379i
$17$	−1.38165	+	2.39309i	−0.335100	+	0.580410i	−0.983504	−	0.180886i	$-0.942103\pi$
$17$	−1.38165	+	2.39309i	−0.335100	+	0.580410i	0.648404	+	0.761296i	$0.275437\pi$
$18$	−0.306887	+	1.38051i	−0.0723339	+	0.325390i
$19$	−0.823158	−	4.28047i	−0.188845	−	0.982007i
$19$	−0.823158	−	4.28047i	−0.188845	−	0.982007i
$20$	7.85994	−	2.85054i	1.75754	−	0.637399i
$21$	−0.283252	−	1.05711i	−0.0618107	−	0.230681i
$22$	−0.316953	−	7.35664i	−0.0675746	−	1.56844i
$23$	−2.47715	+	1.43018i	−0.516522	+	0.298214i	−0.735510	−	0.677514i	$-0.763058\pi$
$23$	−2.47715	+	1.43018i	−0.516522	+	0.298214i	0.218989	+	0.975727i	$0.429724\pi$
$24$	2.61125	+	1.08691i	0.533020	+	0.221864i
$25$	−10.8046	+	6.23803i	−2.16092	+	1.24761i
$26$	−0.770489	−	1.21096i	−0.151105	−	0.237490i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.18070	+	0.188255i	−0.412113	+	0.0355769i
$29$	−1.22454	+	4.57004i	−0.227391	+	0.848636i	0.754041	+	0.656827i	$0.228102\pi$
$29$	−1.22454	+	4.57004i	−0.227391	+	0.848636i	−0.981432	+	0.191809i	$0.938565\pi$
$30$	−5.77115	−	1.28292i	−1.05366	−	0.234228i
$31$	8.18786			1.47058			0.735292	−	0.677751i	$-0.237045\pi$
$31$	8.18786			1.47058			0.735292	+	0.677751i	$0.237045\pi$
$32$	3.05315	−	4.76217i	0.539726	−	0.841841i
$33$	−2.60338	+	4.50918i	−0.453190	+	0.784948i
$34$	−1.17298	−	3.72771i	−0.201165	−	0.639297i
$35$	4.41919	−	1.18412i	0.746980	−	0.200153i
$36$	−1.14527	−	1.63962i	−0.190878	−	0.273271i
$37$	0.714297	−	0.714297i	0.117430	−	0.117430i	−0.645950	−	0.763380i	$-0.723539\pi$
$37$	0.714297	−	0.714297i	0.117430	−	0.117430i	0.763380	+	0.645950i	$0.223539\pi$
$38$	5.24771	+	3.23443i	0.851291	+	0.524693i
$39$			1.01491i			0.162516i
$40$	−4.54374	+	10.9162i	−0.718428	+	1.72600i
$41$	−3.45105	−	1.99246i	−0.538963	−	0.311170i	0.205696	−	0.978616i	$-0.434054\pi$
$41$	−3.45105	−	1.99246i	−0.538963	−	0.311170i	−0.744658	+	0.667446i	$0.767388\pi$
$42$	1.37243	+	0.715448i	0.211771	+	0.110396i
$43$	0.292517	+	1.09169i	0.0446085	+	0.166481i	0.984637	−	0.174616i	$-0.0558683\pi$
$43$	0.292517	+	1.09169i	0.0446085	+	0.166481i	−0.940028	+	0.341097i	$0.889202\pi$
$44$	7.96950	+	6.70286i	1.20145	+	1.01049i
$45$	2.95602	+	2.95602i	0.440657	+	0.440657i
$46$	0.877809	−	3.94878i	0.129426	−	0.582216i
$47$	−5.67266	−	9.82534i	−0.827443	−	1.43317i	−0.900038	−	0.435812i	$-0.856461\pi$
$47$	−5.67266	−	9.82534i	−0.827443	−	1.43317i	0.0725945	−	0.997362i	$-0.476872\pi$
$48$	−3.62912	+	1.68212i	−0.523818	+	0.242793i
$49$	5.80228			0.828897
$50$	3.82874	−	17.2234i	0.541465	−	2.43575i
$51$	−0.715196	+	2.66915i	−0.100147	+	0.373755i
$52$	1.99858	+	0.354777i	0.277153	+	0.0491987i
$53$	6.34769	+	1.70086i	0.871922	+	0.233631i	0.666919	−	0.745130i	$-0.267613\pi$
$53$	6.34769	+	1.70086i	0.871922	+	0.233631i	0.205003	+	0.978761i	$0.434279\pi$
$54$	0.0608734	+	1.41290i	0.00828383	+	0.192272i
$55$	−18.8504	−	10.8833i	−2.54178	−	1.46750i
$56$	1.88862	−	2.45252i	0.252378	−	0.327732i
$57$	−1.90298	−	3.92157i	−0.252055	−	0.519424i
$58$	−3.59183	−	5.64521i	−0.471630	−	0.741252i
$59$	2.35790	+	8.79979i	0.306972	+	1.14563i	0.931235	+	0.364420i	$0.118733\pi$
$59$	2.35790	+	8.79979i	0.306972	+	1.14563i	−0.624263	+	0.781214i	$0.714601\pi$
$60$	6.85435	−	4.78771i	0.884892	−	0.618091i
$61$	−2.03845	+	7.60759i	−0.260997	+	0.974053i	0.703659	+	0.710538i	$0.251548\pi$
$61$	−2.03845	+	7.60759i	−0.260997	+	0.974053i	−0.964655	+	0.263515i	$0.915118\pi$
$62$	−7.82784	+	8.53271i	−0.994136	+	1.08366i
$63$	−0.547202	−	0.947781i	−0.0689409	−	0.119409i
$64$	2.04384	+	7.73452i	0.255480	+	0.966814i
$65$	−4.24277			−0.526251
$66$	−2.21019	−	7.02393i	−0.272056	−	0.864587i
$67$	−2.80015	+	10.4503i	−0.342092	+	1.27671i	0.553880	+	0.832596i	$0.313146\pi$
$67$	−2.80015	+	10.4503i	−0.342092	+	1.27671i	−0.895973	+	0.444109i	$0.853520\pi$
$68$	5.00612	+	2.34141i	0.607081	+	0.283938i
$69$	−2.02258	+	2.02258i	−0.243491	+	0.243491i
$70$	−2.99089	+	5.73737i	−0.357479	+	0.685747i
$71$	−10.3899	−	5.99864i	−1.23306	−	0.711908i	−0.265393	−	0.964140i	$-0.585502\pi$
$71$	−10.3899	−	5.99864i	−1.23306	−	0.711908i	−0.967667	+	0.252233i	$0.918835\pi$
$72$	2.80359	+	0.374028i	0.330406	+	0.0440796i
$73$	5.34922	+	3.08837i	0.626078	+	0.361466i	0.779232	−	0.626736i	$-0.215610\pi$
$73$	5.34922	+	3.08837i	0.626078	+	0.361466i	−0.153153	+	0.988202i	$0.548943\pi$
$74$	0.0614925	+	1.42727i	0.00714835	+	0.165917i
$75$	−8.82190	+	8.82190i	−1.01867	+	1.01867i
$76$	−8.38762	+	2.37653i	−0.962126	+	0.272606i
$77$	4.02930	+	4.02930i	0.459181	+	0.459181i
$78$	−1.05766	−	0.970285i	−0.119756	−	0.109863i
$79$	4.08050	−	7.06763i	0.459092	−	0.795171i	−0.539821	−	0.841780i	$-0.681508\pi$
$79$	4.08050	−	7.06763i	0.459092	−	0.795171i	0.998913	+	0.0466088i	$0.0148414\pi$
$80$	−7.03199	−	15.1713i	−0.786200	−	1.69620i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	5.37568	−	1.69154i	0.593644	−	0.186800i
$83$	3.56884	+	3.56884i	0.391731	+	0.391731i	0.875304	−	0.483573i	$-0.160661\pi$
$83$	3.56884	+	3.56884i	0.391731	+	0.391731i	−0.483573	+	0.875304i	$0.660661\pi$
$84$	−2.05767	+	0.746246i	−0.224510	+	0.0814222i
$85$	−11.1582	−	2.98983i	−1.21028	−	0.324293i
$86$	−1.41732	−	0.738849i	−0.152834	−	0.0796722i
$87$			4.73126i			0.507244i
$88$	−14.6042	+	1.89702i	−1.55682	+	0.202223i
$89$	−4.39337	+	2.53651i	−0.465697	+	0.268870i	−0.714437	−	0.699700i	$-0.753317\pi$
$89$	−4.39337	+	2.53651i	−0.465697	+	0.268870i	0.248740	+	0.968570i	$0.419984\pi$
$90$	−5.90655	+	0.254478i	−0.622605	+	0.0268243i
$91$	1.07288	+	0.287476i	0.112468	+	0.0301357i
$92$	3.27588	+	4.68993i	0.341534	+	0.488959i
$93$	7.90887	−	2.11917i	0.820111	−	0.219748i
$94$	15.6624	+	3.48173i	1.61545	+	0.359113i
$95$	16.3939	−	7.95527i	1.68197	−	0.816194i
$96$	1.71658	−	5.39012i	0.175197	−	0.550127i
$97$	−8.63993	+	14.9648i	−0.877252	+	1.51945i	−0.0229086	+	0.999738i	$0.507293\pi$
$97$	−8.63993	+	14.9648i	−0.877252	+	1.51945i	−0.854344	+	0.519708i	$0.826041\pi$
$98$	−5.54715	+	6.04666i	−0.560347	+	0.610805i
$99$	−1.34761	+	5.02934i	−0.135440	+	0.505468i
$100$	14.2884	+	20.4560i	1.42884	+	2.04560i
$101$	−9.19445	−	2.46364i	−0.914882	−	0.245142i	−0.229485	−	0.973312i	$-0.573704\pi$
$101$	−9.19445	−	2.46364i	−0.914882	−	0.245142i	−0.685396	+	0.728170i	$0.740371\pi$
$102$	−2.09782	−	3.29710i	−0.207715	−	0.326462i
$103$			5.04125i			0.496730i	0.968667	+	0.248365i	$0.0798932\pi$
$103$			5.04125i			0.496730i	−0.968667	+	0.248365i	$0.920107\pi$
$104$	−2.28042	+	1.74357i	−0.223613	+	0.170972i
$105$	3.96214	−	2.28754i	0.386665	−	0.223241i
$106$	−7.84107	+	4.98897i	−0.761592	+	0.484571i
$107$	10.5902	−	10.5902i	1.02380	−	1.02380i	0.0240858	−	0.999710i	$-0.492332\pi$
$107$	10.5902	−	10.5902i	1.02380	−	1.02380i	0.999710	−	0.0240858i	$-0.00766751\pi$
$108$	−1.53061	−	1.28734i	−0.147283	−	0.123874i
$109$	9.25694	−	2.48039i	0.886654	−	0.237578i	0.213378	−	0.976970i	$-0.431553\pi$
$109$	9.25694	−	2.48039i	0.886654	−	0.237578i	0.673276	+	0.739392i	$0.264887\pi$
$110$	29.3631	−	9.23957i	2.79966	−	0.880958i
$111$	0.505085	−	0.874832i	0.0479405	−	0.0830354i
$112$	0.750231	+	4.31285i	0.0708902	+	0.407526i
$113$	−8.91743			−0.838881			−0.419441	−	0.907783i	$-0.637774\pi$
$113$	−8.91743			−0.838881			−0.419441	+	0.907783i	$0.637774\pi$
$114$	5.90603	+	1.76601i	0.553151	+	0.165402i
$115$	−8.45529	−	8.45529i	−0.788460	−	0.788460i
$116$	9.31686	+	1.65388i	0.865049	+	0.153559i
$117$	0.262678	+	0.980329i	0.0242846	+	0.0906314i
$118$	−11.4246	−	5.95565i	−1.05172	−	0.548262i
$119$	2.61901	+	1.51208i	0.240084	+	0.138613i
$120$	−1.56360	+	11.7202i	−0.142737	+	1.06990i
$121$		−	16.1103i		−	1.46457i
$122$	−5.97919	−	9.39738i	−0.541330	−	0.850799i
$123$	−3.84914	−	1.03137i	−0.347065	−	0.0929959i
$124$	−1.40845	−	16.3150i	−0.126482	−	1.46513i
$125$	−22.0993	−	22.0993i	−1.97662	−	1.97662i
$126$	1.51084	+	0.335858i	0.134596	+	0.0299206i
$127$	4.91697	+	8.51645i	0.436311	+	0.755712i	0.997402	−	0.0720418i	$-0.0229515\pi$
$127$	4.91697	+	8.51645i	0.436311	+	0.755712i	−0.561091	+	0.827754i	$0.689618\pi$
$128$	−10.0142	−	5.26450i	−0.885142	−	0.465321i
$129$	0.565100	+	0.978782i	0.0497543	+	0.0861769i
$130$	4.05621	−	4.42147i	0.355754	−	0.387788i
$131$	13.6324	−	3.65278i	1.19107	−	0.319145i	0.391759	−	0.920068i	$-0.371867\pi$
$131$	13.6324	−	3.65278i	1.19107	−	0.319145i	0.799307	+	0.600923i	$0.205200\pi$
$132$	9.43277	+	4.41181i	0.821017	+	0.383999i
$133$	−4.68456	+	0.900867i	−0.406203	+	0.0781151i
$134$	−8.21340	−	12.9089i	−0.709530	−	1.11516i
$135$	3.62036	+	2.09022i	0.311591	+	0.179897i
$136$	−7.22602	+	2.97850i	−0.619626	+	0.255404i
$137$	6.79525	−	3.92324i	0.580557	−	0.335185i	−0.180798	−	0.983520i	$-0.557868\pi$
$137$	6.79525	−	3.92324i	0.580557	−	0.335185i	0.761355	+	0.648335i	$0.224535\pi$
$138$	−0.174120	−	4.04142i	−0.0148221	−	0.344029i
$139$	−12.7954	−	3.42852i	−1.08529	−	0.290803i	−0.328530	−	0.944493i	$-0.606553\pi$
$139$	−12.7954	−	3.42852i	−1.08529	−	0.290803i	−0.756762	+	0.653690i	$0.773220\pi$
$140$	−3.11964	−	8.60194i	−0.263657	−	0.726997i
$141$	−8.02236	−	8.02236i	−0.675605	−	0.675605i
$142$	16.1844	−	5.09267i	1.35816	−	0.427367i
$143$	−2.64220	−	4.57642i	−0.220952	−	0.382699i
$144$	−3.07009	+	2.56408i	−0.255841	+	0.213674i
$145$	−19.7787			−1.64253
$146$	−8.33245	+	2.62194i	−0.689598	+	0.216993i
$147$	5.60457	−	1.50174i	0.462257	−	0.123862i
$148$	−1.54617	−	1.30043i	−0.127095	−	0.106895i
$149$	−0.542326	−	2.02399i	−0.0444291	−	0.165812i	0.940147	−	0.340770i	$-0.110688\pi$
$149$	−0.542326	−	2.02399i	−0.0444291	−	0.165812i	−0.984576	+	0.174958i	$0.944021\pi$
$150$	−0.759460	−	17.6275i	−0.0620097	−	1.43928i
$151$			0.315570i			0.0256808i	0.999918	+	0.0128404i	$0.00408733\pi$
$151$			0.315570i			0.0256808i	−0.999918	+	0.0128404i	$0.995913\pi$
$152$	5.54219	−	11.0129i	0.449531	−	0.893265i
$153$			2.76330i			0.223400i
$154$	−8.05113	+	0.346875i	−0.648779	+	0.0279519i
$155$	8.85908	+	33.0625i	0.711578	+	2.65565i
$156$	2.02230	−	0.174581i	0.161914	−	0.0139777i
$157$	18.0697	−	4.84177i	1.44212	−	0.386415i	0.548845	−	0.835924i	$-0.315068\pi$
$157$	18.0697	−	4.84177i	1.44212	−	0.386415i	0.893276	+	0.449509i	$0.148401\pi$
$158$	3.46423	+	11.0092i	0.275599	+	0.875847i
$159$	6.57161			0.521163
$160$	22.5330	+	7.17604i	1.78139	+	0.567316i
$161$	1.56520	+	2.71100i	0.123355	+	0.213657i
$162$	0.424485	+	1.34900i	0.0333507	+	0.105988i
$163$	6.11419	+	6.11419i	0.478901	+	0.478901i	0.904780	−	0.425879i	$-0.140035\pi$
$163$	6.11419	+	6.11419i	0.478901	+	0.478901i	−0.425879	+	0.904780i	$0.640035\pi$
$164$	−3.37652	+	7.21925i	−0.263662	+	0.563729i
$165$	−21.0248	−	5.63359i	−1.63678	−	0.438574i
$166$	−7.13107	+	0.307235i	−0.553478	+	0.0238460i
$167$	−2.81451	+	1.62496i	−0.217793	+	0.125743i	−0.604928	−	0.796280i	$-0.706798\pi$
$167$	−2.81451	+	1.62496i	−0.217793	+	0.125743i	0.387135	+	0.922023i	$0.373465\pi$
$168$	1.18951	−	2.85776i	0.0917729	−	0.220481i
$169$	10.3663	+	5.98498i	0.797407	+	0.460383i
$170$	13.7833	−	8.76979i	1.05713	−	0.672612i
$171$	−2.85311	−	3.29542i	−0.218183	−	0.252007i
$172$	2.12497	−	0.770655i	0.162027	−	0.0587619i
$173$	−4.56587	+	1.22342i	−0.347137	+	0.0930150i	−0.428175	−	0.903696i	$-0.640843\pi$
$173$	−4.56587	+	1.22342i	−0.347137	+	0.0930150i	0.0810379	+	0.996711i	$0.474177\pi$
$174$	−4.93053	−	4.52322i	−0.373782	−	0.342904i
$175$	6.82692	+	11.8246i	0.516066	+	0.893853i
$176$	11.9852	−	17.0329i	0.903415	−	1.28391i
$177$	4.55511	+	7.88967i	0.342383	+	0.593024i
$178$	1.55685	−	7.00339i	0.116691	−	0.524926i
$179$	8.67560	+	8.67560i	0.648444	+	0.648444i	0.952617	−	0.304173i	$-0.0983799\pi$
$179$	8.67560	+	8.67560i	0.648444	+	0.648444i	−0.304173	+	0.952617i	$0.598380\pi$
$180$	5.38164	−	6.39861i	0.401124	−	0.476924i
$181$	10.5071	+	2.81538i	0.780989	+	0.209265i	0.627221	−	0.778842i	$-0.284192\pi$
$181$	10.5071	+	2.81538i	0.780989	+	0.209265i	0.153768	+	0.988107i	$0.450859\pi$
$182$	−1.32528	+	0.843226i	−0.0982366	+	0.0625041i
$183$			7.87596i			0.582208i
$184$	−8.01929	−	1.06986i	−0.591190	−	0.0788710i
$185$	3.65718	+	2.11147i	0.268881	+	0.155239i
$186$	−5.35268	+	10.2680i	−0.392478	+	0.752883i
$187$	−3.72385	−	13.8976i	−0.272315	−	1.01629i
$188$	−18.6021	+	12.9934i	−1.35670	+	0.947642i
$189$	−0.773860	−	0.773860i	−0.0562900	−	0.0562900i
$190$	−7.38268	+	24.6898i	−0.535596	+	1.79119i
$191$	19.5759			1.41646			0.708231	−	0.705981i	$-0.249493\pi$
$191$	19.5759			1.41646			0.708231	+	0.705981i	$0.249493\pi$
$192$	3.97604	+	6.94198i	0.286946	+	0.500995i
$193$	−3.17564	+	5.50036i	−0.228587	+	0.395925i	−0.957390	−	0.288799i	$-0.906744\pi$
$193$	−3.17564	+	5.50036i	−0.228587	+	0.395925i	0.728802	+	0.684724i	$0.240077\pi$
$194$	−7.33505	−	23.3106i	−0.526626	−	1.67360i
$195$	−4.09820	+	1.09811i	−0.293478	+	0.0786373i
$196$	−0.998088	−	11.5616i	−0.0712920	−	0.825826i
$197$	1.92290	−	1.92290i	0.137001	−	0.137001i	−0.635280	−	0.772282i	$-0.719115\pi$
$197$	1.92290	−	1.92290i	0.137001	−	0.137001i	0.772282	+	0.635280i	$0.219115\pi$
$198$	−3.95281	−	6.21256i	−0.280914	−	0.441507i
$199$	10.1887	−	5.88245i	0.722258	−	0.416996i	−0.0933254	−	0.995636i	$-0.529750\pi$
$199$	10.1887	−	5.88245i	0.722258	−	0.416996i	0.815583	+	0.578640i	$0.196416\pi$
$200$	−34.9777	−	4.66640i	−2.47330	−	0.329964i
$201$			10.8189i			0.763109i
$202$	11.3576	−	7.22638i	0.799116	−	0.508446i
$203$	5.00147	+	1.34014i	0.351034	+	0.0940594i
$204$	5.44154	+	0.965954i	0.380984	+	0.0676303i
$205$	4.31160	−	16.0911i	0.301135	−	1.12385i
$206$	−5.25358	−	4.81959i	−0.366034	−	0.335796i
$207$	−1.43018	+	2.47715i	−0.0994046	+	0.172174i
$208$	0.363137	−	4.04337i	0.0251790	−	0.280357i
$209$	18.7902	+	12.7289i	1.29974	+	0.880476i
$210$	−1.40403	+	6.31597i	−0.0968875	+	0.435843i
$211$	8.74513	−	2.34325i	0.602040	−	0.161316i	0.0550898	−	0.998481i	$-0.482455\pi$
$211$	8.74513	−	2.34325i	0.602040	−	0.161316i	0.546950	+	0.837165i	$0.315789\pi$
$212$	2.29720	−	12.9409i	0.157773	−	0.888785i
$213$	−11.5885	−	3.10512i	−0.794030	−	0.212760i
$214$	0.911692	+	21.1608i	0.0623220	+	1.44652i
$215$	−4.09173	+	2.36236i	−0.279054	+	0.161112i
$216$	2.80486	−	0.364338i	0.190847	−	0.0247901i
$217$		−	8.96082i		−	0.608300i
$218$	−6.26504	+	12.0181i	−0.424322	+	0.813971i
$219$	5.96627	+	1.59866i	0.403163	+	0.108027i
$220$	−18.4433	+	39.4331i	−1.24345	+	2.65858i
$221$	−1.98309	−	1.98309i	−0.133397	−	0.133397i
$222$	0.428802	+	1.36272i	0.0287793	+	0.0914599i
$223$	12.9783	−	22.4790i	0.869088	−	1.50530i	0.00615792	−	0.999981i	$-0.498040\pi$
$223$	12.9783	−	22.4790i	0.869088	−	1.50530i	0.862930	−	0.505323i	$-0.168627\pi$
$224$	−5.21174	−	3.34138i	−0.348224	−	0.223255i
$225$	−6.23803	+	10.8046i	−0.415868	+	0.720305i
$226$	8.52532	−	9.29301i	0.567096	−	0.618162i
$227$	13.1798	+	13.1798i	0.874775	+	0.874775i	0.992988	−	0.118213i	$-0.0377166\pi$
$227$	13.1798	+	13.1798i	0.874775	+	0.874775i	−0.118213	+	0.992988i	$0.537717\pi$
$228$	−7.48673	+	4.46642i	−0.495820	+	0.295796i
$229$	−5.40485	+	5.40485i	−0.357162	+	0.357162i	−0.862766	−	0.505604i	$-0.831270\pi$
$229$	−5.40485	+	5.40485i	−0.357162	+	0.357162i	0.505604	+	0.862766i	$0.331270\pi$
$230$	16.8949	−	0.727899i	1.11402	−	0.0479962i
$231$	4.93486	+	2.84915i	0.324690	+	0.187460i
$232$	−10.6307	+	8.12810i	−0.697942	+	0.533636i
$233$	9.29077	+	5.36403i	0.608659	+	0.351409i	0.772440	−	0.635087i	$-0.219036\pi$
$233$	9.29077	+	5.36403i	0.608659	+	0.351409i	−0.163782	+	0.986497i	$0.552369\pi$
$234$	−1.27275	−	0.663481i	−0.0832020	−	0.0433731i
$235$	33.5370	−	33.5370i	2.18771	−	2.18771i
$236$	17.1288	−	6.21203i	1.11499	−	0.404368i
$237$	2.11222	−	7.88292i	0.137204	−	0.512051i
$238$	−4.07962	+	1.28372i	−0.264442	+	0.0832109i
$239$	5.84709			0.378217			0.189109	−	0.981956i	$-0.439440\pi$
$239$	5.84709			0.378217			0.189109	+	0.981956i	$0.439440\pi$
$240$	−10.7190	−	12.8343i	−0.691908	−	0.828452i
$241$	−9.38504	−	16.2554i	−0.604544	−	1.04710i	−0.992123	−	0.125264i	$-0.960022\pi$
$241$	−9.38504	−	16.2554i	−0.604544	−	1.04710i	0.387580	−	0.921836i	$-0.373311\pi$
$242$	16.7888	+	15.4019i	1.07923	+	0.990073i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	15.5095	+	2.75316i	0.992891	+	0.176253i
$245$	6.27793	+	23.4296i	0.401082	+	1.49686i
$246$	4.75470	−	3.02523i	0.303149	−	0.192882i
$247$	4.41249	+	0.317420i	0.280760	+	0.0201970i
$248$	18.3487	+	14.1299i	1.16514	+	0.897249i
$249$	4.37092	+	2.52355i	0.276996	+	0.159924i
$250$	44.1577	−	1.90249i	2.79278	−	0.120324i
$251$	17.4684	+	4.68064i	1.10260	+	0.295440i	0.763821	−	0.645428i	$-0.223321\pi$
$251$	17.4684	+	4.68064i	1.10260	+	0.295440i	0.338775	+	0.940868i	$0.389988\pi$
$252$	−1.79441	+	1.25338i	−0.113037	+	0.0789556i
$253$	3.85465	−	14.3858i	0.242340	−	0.904425i
$254$	−13.5759	−	3.01791i	−0.851828	−	0.189360i
$255$	−11.5518			−0.723403
$256$	15.0601	−	5.40299i	0.941258	−	0.337687i
$257$	6.20487	+	10.7472i	0.387049	+	0.670389i	0.992051	−	0.125835i	$-0.0401610\pi$
$257$	6.20487	+	10.7472i	0.387049	+	0.670389i	−0.605002	+	0.796224i	$0.706828\pi$
$258$	−1.56026	−	0.346843i	−0.0971374	−	0.0215935i
$259$	−0.781729	−	0.781729i	−0.0485743	−	0.0485743i
$260$	0.729827	+	8.45410i	0.0452619	+	0.524301i
$261$	1.22454	+	4.57004i	0.0757971	+	0.282879i
$262$	−9.22631	+	17.6987i	−0.570004	+	1.09343i
$263$	−2.23288	−	1.28915i	−0.137685	−	0.0794926i	0.429575	−	0.903031i	$-0.358663\pi$
$263$	−2.23288	−	1.28915i	−0.137685	−	0.0794926i	−0.567260	+	0.823539i	$0.691997\pi$
$264$	−13.6156	+	5.61224i	−0.837984	+	0.345409i
$265$			27.4722i			1.68760i
$266$	3.53977	−	5.74311i	0.217037	−	0.352133i
$267$	−3.58717	+	3.58717i	−0.219531	+	0.219531i
$268$	21.3048	+	3.78192i	1.30140	+	0.231017i
$269$	−15.1126	+	4.04941i	−0.921432	+	0.246897i	−0.688197	−	0.725524i	$-0.741598\pi$
$269$	−15.1126	+	4.04941i	−0.921432	+	0.246897i	−0.233234	+	0.972421i	$0.574931\pi$
$270$	−5.63943	+	1.77453i	−0.343205	+	0.107995i
$271$	−13.4243	+	23.2516i	−0.815468	+	1.41243i	0.0935231	+	0.995617i	$0.470187\pi$
$271$	−13.4243	+	23.2516i	−0.815468	+	1.41243i	−0.908991	+	0.416815i	$0.863146\pi$
$272$	3.80434	−	10.3779i	0.230672	−	0.629252i
$273$	1.11072			0.0672240
$274$	−2.40798	+	10.8322i	−0.145471	+	0.654396i
$275$	16.8128	−	62.7463i	1.01385	−	3.78375i
$276$	4.37810	+	3.68226i	0.263531	+	0.221646i
$277$	20.3263	−	20.3263i	1.22129	−	1.22129i	0.254117	−	0.967173i	$-0.418215\pi$
$277$	20.3263	−	20.3263i	1.22129	−	1.22129i	0.967173	−	0.254117i	$-0.0817849\pi$
$278$	15.8057	−	10.0566i	0.947963	−	0.603152i
$279$	7.09090	−	4.09393i	0.424521	−	0.245097i
$280$	11.9467	+	4.97268i	0.713952	+	0.297175i
$281$	−11.3026	+	6.52556i	−0.674257	+	0.389282i	−0.797688	−	0.603071i	$-0.793944\pi$
$281$	−11.3026	+	6.52556i	−0.674257	+	0.389282i	0.123431	+	0.992353i	$0.460610\pi$
$282$	16.0298	−	0.690629i	0.954564	−	0.0411264i
$283$	3.91520	+	14.6117i	0.232735	+	0.868578i	0.979157	+	0.203105i	$0.0651033\pi$
$283$	3.91520	+	14.6117i	0.232735	+	0.868578i	−0.746422	+	0.665473i	$0.768230\pi$
$284$	−10.1656	+	21.7348i	−0.603216	+	1.28972i
$285$	13.7763	−	11.9272i	0.816036	−	0.706509i
$286$	7.29518	+	1.62171i	0.431373	+	0.0958938i
$287$	−2.18056	+	3.77684i	−0.128714	+	0.222940i
$288$	0.263021	−	5.65074i	0.0154987	−	0.332973i
$289$	4.68207	+	8.10959i	0.275416	+	0.477035i
$290$	18.9090	−	20.6118i	1.11038	−	1.21036i
$291$	−4.47236	+	16.6911i	−0.262174	+	0.978448i
$292$	5.23370	−	11.1900i	0.306279	−	0.654847i
$293$	17.1872	−	17.1872i	1.00409	−	1.00409i	0.00409401	−	0.999992i	$-0.498697\pi$
$293$	17.1872	−	17.1872i	1.00409	−	1.00409i	0.999992	−	0.00409401i	$-0.00130317\pi$
$294$	−3.79315	+	7.27633i	−0.221221	+	0.424364i
$295$	−32.9823	+	19.0423i	−1.92030	+	1.10869i
$296$	2.83339	−	0.368043i	0.164687	−	0.0213921i
$297$			5.20676i			0.302127i
$298$	2.62771	+	1.36982i	0.152219	+	0.0793518i
$299$	−0.751356	−	2.80410i	−0.0434521	−	0.162165i
$300$	19.0959	+	16.0609i	1.10250	+	0.927277i
$301$	1.19475	−	0.320132i	0.0688641	−	0.0184521i
$302$	−0.328861	−	0.301695i	−0.0189238	−	0.0173606i
$303$	−9.51879			−0.546840
$304$	6.17825	+	16.3043i	0.354347	+	0.935114i
$305$	−32.9250			−1.88528
$306$	−2.87969	−	2.64180i	−0.164621	−	0.151022i
$307$	−21.0153	+	5.63103i	−1.19941	+	0.321380i	−0.802597	−	0.596521i	$-0.796549\pi$
$307$	−21.0153	+	5.63103i	−1.19941	+	0.321380i	−0.396809	+	0.917901i	$0.629883\pi$
$308$	7.33563	−	8.72184i	0.417986	−	0.496973i
$309$	1.30477	+	4.86948i	0.0742259	+	0.277015i
$310$	−42.9246	−	22.3765i	−2.43795	−	1.27090i
$311$		−	12.8217i		−	0.727049i	−0.931585	−	0.363525i	$-0.881573\pi$
$311$		−	12.8217i		−	0.727049i	0.931585	−	0.363525i	$-0.118427\pi$
$312$	−1.75144	+	2.27438i	−0.0991560	+	0.128761i
$313$	−18.6599	+	10.7733i	−1.05472	+	0.608943i	−0.923967	−	0.382471i	$-0.875073\pi$
$313$	−18.6599	+	10.7733i	−1.05472	+	0.608943i	−0.130754	+	0.991415i	$0.541740\pi$
$314$	−12.2295	+	23.4596i	−0.690150	+	1.32390i
$315$	3.23507	−	3.23507i	0.182276	−	0.182276i
$316$	−14.7848	−	6.91501i	−0.831710	−	0.389000i
$317$	−5.66755	+	21.1516i	−0.318321	+	1.18799i	0.602536	+	0.798092i	$0.294157\pi$
$317$	−5.66755	+	21.1516i	−0.318321	+	1.18799i	−0.920857	+	0.389900i	$0.872510\pi$
$318$	−6.28265	+	6.84839i	−0.352314	+	0.384039i
$319$	−12.3173	−	21.3341i	−0.689634	−	1.19448i
$320$	−29.0205	+	16.6216i	−1.62230	+	0.929174i
$321$	7.48842	−	12.9703i	0.417963	−	0.723933i
$322$	−4.32156	−	0.960677i	−0.240831	−	0.0535364i
$323$	11.3809	+	3.94423i	0.633249	+	0.219463i
$324$	−1.81164	−	0.847324i	−0.100647	−	0.0470735i
$325$	−3.27719	−	12.2306i	−0.181786	−	0.678434i
$326$	−12.2171	+	0.526359i	−0.676640	+	0.0291523i
$327$	8.29954	−	4.79174i	0.458966	−	0.264984i
$328$	−4.29525	−	10.4205i	−0.237166	−	0.575378i
$329$	−10.7529	+	6.20818i	−0.592826	+	0.342268i
$330$	25.9712	−	16.5245i	1.42967	−	0.909642i
$331$	10.7840	−	10.7840i	0.592745	−	0.592745i	−0.345627	−	0.938372i	$-0.612334\pi$
$331$	10.7840	−	10.7840i	0.592745	−	0.592745i	0.938372	+	0.345627i	$0.112334\pi$
$332$	6.49733	−	7.72513i	0.356588	−	0.423972i
$333$	0.261451	−	0.975748i	0.0143274	−	0.0534707i
$334$	0.997356	−	4.48655i	0.0545729	−	0.245493i
$335$	−45.2279			−2.47106
$336$	1.84091	+	3.97172i	0.100430	+	0.216675i
$337$	13.5463	−	23.4628i	0.737912	−	1.27810i	−0.215521	−	0.976499i	$-0.569145\pi$
$337$	13.5463	−	23.4628i	0.737912	−	1.27810i	0.953434	−	0.301603i	$-0.0975216\pi$
$338$	−16.1475	+	5.08107i	−0.878309	+	0.276374i
$339$	−8.61357	+	2.30800i	−0.467825	+	0.125353i
$340$	−4.03811	+	22.7480i	−0.218997	+	1.23368i
$341$	−30.1455	+	30.1455i	−1.63247	+	1.63247i
$342$	6.16187	+	0.177238i	0.333196	+	0.00958393i
$343$		−	14.0109i		−	0.756515i
$344$	−1.22842	+	2.95124i	−0.0662320	+	0.159120i
$345$	−10.3556	−	5.97879i	−0.557525	−	0.321887i
$346$	3.09016	−	5.92780i	0.166128	−	0.318680i
$347$	−5.88036	−	21.9458i	−0.315674	−	1.17811i	−0.923360	−	0.383935i	$-0.874569\pi$
$347$	−5.88036	−	21.9458i	−0.315674	−	1.17811i	0.607686	−	0.794178i	$-0.292098\pi$
$348$	9.42745	−	0.813854i	0.505364	−	0.0436272i
$349$	−17.3151	−	17.3151i	−0.926858	−	0.926858i	0.0706437	−	0.997502i	$-0.477495\pi$
$349$	−17.3151	−	17.3151i	−0.926858	−	0.926858i	−0.997502	+	0.0706437i	$0.977495\pi$
$350$	−18.8493	−	4.19018i	−1.00754	−	0.223975i
$351$	0.507456	+	0.878939i	0.0270860	+	0.0469143i
$352$	6.29215	+	28.7739i	0.335373	+	1.53366i
$353$	37.3535			1.98812			0.994062	−	0.108817i	$-0.0347062\pi$
$353$	37.3535			1.98812			0.994062	+	0.108817i	$0.0347062\pi$
$354$	−12.5768	−	2.79580i	−0.668448	−	0.148595i
$355$	12.9808	−	48.4449i	0.688948	−	2.57119i
$356$	5.80996	+	8.31786i	0.307927	+	0.440846i
$357$	2.92112	+	0.782713i	0.154602	+	0.0414256i
$358$	−17.3351	+	0.746865i	−0.916189	+	0.0394730i
$359$	−8.54782	−	4.93509i	−0.451137	−	0.260464i	0.257174	−	0.966365i	$-0.417209\pi$
$359$	−8.54782	−	4.93509i	−0.451137	−	0.260464i	−0.708310	+	0.705901i	$0.750542\pi$
$360$	1.52309	+	11.7256i	0.0802741	+	0.617991i
$361$	−17.6448	+	7.04701i	−0.928675	+	0.370895i
$362$	−12.9791	+	8.25808i	−0.682165	+	0.434035i
$363$	−4.16965	−	15.5614i	−0.218850	−	0.816760i
$364$	0.388269	−	2.18725i	0.0203508	−	0.114643i
$365$	−6.68309	+	24.9416i	−0.349809	+	1.30550i
$366$	−8.20767	−	7.52965i	−0.429022	−	0.393581i
$367$	1.46243	+	2.53300i	0.0763381	+	0.132221i	0.901667	−	0.432430i	$-0.142344\pi$
$367$	1.46243	+	2.53300i	0.0763381	+	0.132221i	−0.825329	+	0.564652i	$0.809010\pi$
$368$	8.78159	−	7.33422i	0.457772	−	0.382323i
$369$	−3.98492			−0.207447
$370$	−5.69677	+	1.79258i	−0.296161	+	0.0931918i
$371$	1.86142	−	6.94693i	0.0966404	−	0.360667i
$372$	−5.58310	−	15.3946i	−0.289470	−	0.798172i
$373$	19.8144	−	19.8144i	1.02595	−	1.02595i	0.0262958	−	0.999654i	$-0.491629\pi$
$373$	19.8144	−	19.8144i	1.02595	−	1.02595i	0.999654	−	0.0262958i	$-0.00837119\pi$
$374$	18.0430	+	9.40582i	0.932983	+	0.486363i
$375$	−27.0660	−	15.6266i	−1.39768	−	0.806953i
$376$	4.24347	−	31.8076i	0.218840	−	1.64035i
$377$	−4.15849	−	2.40090i	−0.214173	−	0.123653i
$378$	1.54629	−	0.0666201i	0.0795323	−	0.00342657i
$379$	−18.4467	+	18.4467i	−0.947542	+	0.947542i	−0.998691	−	0.0511494i	$-0.983712\pi$
$379$	−18.4467	+	18.4467i	−0.947542	+	0.947542i	0.0511494	+	0.998691i	$0.483712\pi$
$380$	−18.6716	−	31.2978i	−0.957833	−	1.60554i
$381$	6.95365	+	6.95365i	0.356246	+	0.356246i
$382$	−18.7151	+	20.4004i	−0.957549	+	1.04377i
$383$	0.658800	−	1.14108i	0.0336631	−	0.0583062i	−0.848703	−	0.528870i	$-0.822616\pi$
$383$	0.658800	−	1.14108i	0.0336631	−	0.0583062i	0.882366	+	0.470564i	$0.155949\pi$
$384$	−11.0356	−	2.49324i	−0.563156	−	0.127233i
$385$	−11.9107	+	20.6299i	−0.607024	+	1.05140i
$386$	−2.69602	−	8.56790i	−0.137224	−	0.436094i
$387$	0.799172	+	0.799172i	0.0406242	+	0.0406242i
$388$	31.3049	+	14.6416i	1.58927	+	0.743317i
$389$	−15.0604	−	4.03542i	−0.763593	−	0.204604i	−0.144054	−	0.989570i	$-0.546014\pi$
$389$	−15.0604	−	4.03542i	−0.763593	−	0.204604i	−0.619539	+	0.784966i	$0.712680\pi$
$390$	2.77364	−	5.32063i	0.140449	−	0.269421i
$391$		−	7.90406i		−	0.399726i
$392$	13.0027	+	10.0131i	0.656736	+	0.505736i
$393$	12.2224	−	7.05663i	0.616541	−	0.355960i
$394$	0.165539	+	3.84224i	0.00833972	+	0.193569i
$395$	32.9541	+	8.83001i	1.65810	+	0.444286i
$396$	10.2532	+	1.82010i	0.515244	+	0.0914634i
$397$	9.52896	−	2.55328i	0.478245	−	0.128145i	−0.0116404	−	0.999932i	$-0.503705\pi$
$397$	9.52896	−	2.55328i	0.478245	−	0.128145i	0.489885	+	0.871787i	$0.337039\pi$
$398$	−3.61049	+	16.2416i	−0.180978	+	0.814118i
$399$	−4.29177	+	2.08262i	−0.214857	+	0.104262i
$400$	38.3026	−	31.9897i	1.91513	−	1.59948i
$401$	5.09435	−	8.82367i	0.254400	−	0.440633i	−0.710333	−	0.703866i	$-0.751455\pi$
$401$	5.09435	−	8.82367i	0.254400	−	0.440633i	0.964732	+	0.263233i	$0.0847888\pi$
$402$	−11.2746	−	10.3432i	−0.562326	−	0.515873i
$403$	−2.15077	+	8.02680i	−0.107138	+	0.399843i
$404$	−3.32743	+	18.7445i	−0.165546	+	0.932576i
$405$	4.03799	+	1.08198i	0.200649	+	0.0537639i
$406$	−6.17814	+	3.93091i	−0.306616	+	0.195088i
$407$			5.25970i			0.260714i
$408$	−6.20891	+	4.74724i	−0.307387	+	0.235023i
$409$	25.0781	−	14.4789i	1.24003	−	0.715934i	0.270933	−	0.962598i	$-0.412668\pi$
$409$	25.0781	−	14.4789i	1.24003	−	0.715934i	0.969101	+	0.246664i	$0.0793344\pi$
$410$	12.6468	+	19.8767i	0.624581	+	0.981642i
$411$	5.54830	−	5.54830i	0.273677	−	0.273677i
$412$	10.0451	−	0.867179i	0.494889	−	0.0427228i
$413$	9.63052	−	2.58049i	0.473887	−	0.126978i
$414$	−1.21418	−	3.85865i	−0.0596739	−	0.189642i
$415$	−10.5496	+	18.2724i	−0.517857	+	0.896955i
$416$	3.86650	+	4.24401i	0.189571	+	0.208080i
$417$	−13.2468			−0.648698
$418$	−31.2290	+	7.41239i	−1.52746	+	0.362552i
$419$	0.119344	+	0.119344i	0.00583034	+	0.00583034i	0.710016	−	0.704186i	$-0.248688\pi$
$419$	0.119344	+	0.119344i	0.00583034	+	0.00583034i	−0.704186	+	0.710016i	$0.748688\pi$
$420$	−5.23968	−	7.50142i	−0.255670	−	0.366032i
$421$	−6.04655	−	22.5660i	−0.294691	−	1.09980i	−0.941463	−	0.337117i	$-0.890548\pi$
$421$	−6.04655	−	22.5660i	−0.294691	−	1.09980i	0.646772	−	0.762683i	$-0.276119\pi$
$422$	−5.91866	+	11.3537i	−0.288116	+	0.552688i
$423$	−9.82534	−	5.67266i	−0.477725	−	0.275814i
$424$	11.2898	+	14.7658i	0.548279	+	0.717093i
$425$		−	34.4751i		−	1.67229i
$426$	14.3148	−	9.10797i	0.693556	−	0.441282i
$427$	8.32578	+	2.23089i	0.402913	+	0.107960i
$428$	−22.9237	−	19.2803i	−1.10806	−	0.931947i
$429$	−3.73663	−	3.73663i	−0.180406	−	0.180406i
$430$	1.44996	−	6.52256i	0.0699232	−	0.314546i
$431$	1.27001	+	2.19973i	0.0611744	+	0.105957i	0.894991	−	0.446085i	$-0.147182\pi$
$431$	1.27001	+	2.19973i	0.0611744	+	0.105957i	−0.833816	+	0.552042i	$0.813849\pi$
$432$	−2.30185	+	3.27131i	−0.110748	+	0.157391i
$433$	10.9665	+	18.9945i	0.527015	+	0.912816i	0.999504	+	0.0314799i	$0.0100220\pi$
$433$	10.9665	+	18.9945i	0.527015	+	0.912816i	−0.472490	+	0.881336i	$0.656645\pi$
$434$	9.33823	+	8.56681i	0.448249	+	0.411220i
$435$	−19.1048	+	5.11911i	−0.916004	+	0.245443i
$436$	−6.53474	−	18.0186i	−0.312957	−	0.862934i
$437$	8.16094	+	9.42610i	0.390391	+	0.450911i
$438$	−7.36992	+	4.68919i	−0.352148	+	0.224058i
$439$	−32.6717	−	18.8630i	−1.55933	−	0.900282i	−0.997321	−	0.0731538i	$-0.976694\pi$
$439$	−32.6717	−	18.8630i	−1.55933	−	0.900282i	−0.562013	−	0.827128i	$-0.689973\pi$
$440$	−23.4616	−	56.9193i	−1.11849	−	2.71352i
$441$	5.02492	−	2.90114i	0.239282	−	0.138150i
$442$	3.96250	−	0.170720i	0.188477	−	0.00812033i
$443$	−22.8130	−	6.11272i	−1.08388	−	0.290424i	−0.327694	−	0.944784i	$-0.606272\pi$
$443$	−22.8130	−	6.11272i	−1.08388	−	0.290424i	−0.756183	+	0.654360i	$0.772938\pi$
$444$	−1.83006	−	0.855940i	−0.0868510	−	0.0406211i
$445$	−14.9960	−	14.9960i	−0.710876	−	0.710876i
$446$	11.0182	+	35.0154i	0.521725	+	1.65803i
$447$	−1.04769	−	1.81466i	−0.0495542	−	0.0858304i
$448$	8.46468	−	2.23678i	0.399918	−	0.105678i
$449$	−36.5524			−1.72501			−0.862506	−	0.506046i	$-0.831106\pi$
$449$	−36.5524			−1.72501			−0.862506	+	0.506046i	$0.831106\pi$
$450$	−5.29590	−	16.8302i	−0.249651	−	0.793385i
$451$	20.0415	−	5.37011i	0.943719	−	0.252869i
$452$	1.53394	+	17.7688i	0.0721507	+	0.835773i
$453$	0.0816756	+	0.304818i	0.00383746	+	0.0143216i
$454$	−26.3352	+	1.13462i	−1.23597	+	0.0532506i
$455$			4.64330i			0.217681i
$456$	2.50299	−	12.0721i	0.117213	−	0.565327i
$457$		−	17.6985i		−	0.827900i	−0.910300	−	0.413950i	$-0.864149\pi$
$457$		−	17.6985i		−	0.827900i	0.910300	−	0.413950i	$-0.135851\pi$
$458$	−0.465293	−	10.7997i	−0.0217417	−	0.504636i
$459$	0.715196	+	2.66915i	0.0333825	+	0.124585i
$460$	−15.3935	+	18.3024i	−0.717724	+	0.853352i
$461$	8.39887	−	2.25047i	0.391175	−	0.104815i	−0.0578703	−	0.998324i	$-0.518431\pi$
$461$	8.39887	−	2.25047i	0.391175	−	0.104815i	0.449045	+	0.893509i	$0.351764\pi$
$462$	−7.68702	+	2.41884i	−0.357632	+	0.112535i
$463$	15.7479			0.731869			0.365934	−	0.930641i	$-0.380749\pi$
$463$	15.7479			0.731869			0.365934	+	0.930641i	$0.380749\pi$
$464$	1.69285	−	18.8492i	0.0785887	−	0.875051i
$465$	17.1144	+	29.6430i	0.793662	+	1.37466i
$466$	−14.4722	+	4.55390i	−0.670412	+	0.210956i
$467$	−2.40851	−	2.40851i	−0.111453	−	0.111453i	0.649181	−	0.760634i	$-0.275112\pi$
$467$	−2.40851	−	2.40851i	−0.111453	−	0.111453i	−0.760634	+	0.649181i	$0.775112\pi$
$468$	1.90821	−	0.692043i	0.0882069	−	0.0319897i
$469$	11.4368	+	3.06449i	0.528104	+	0.141505i
$470$	2.88713	+	67.0118i	0.133173	+	3.09102i
$471$	16.2009	−	9.35357i	0.746497	−	0.430990i
$472$	−9.90194	+	23.7891i	−0.455774	+	1.09498i
$473$	−5.09628	−	2.94234i	−0.234327	−	0.135289i
$474$	6.19558	+	9.73749i	0.284573	+	0.447258i
$475$	35.5956	+	41.1138i	1.63324	+	1.88643i
$476$	2.56245	−	5.47871i	0.117450	−	0.251116i
$477$	6.34769	−	1.70086i	0.290641	−	0.0778770i
$478$	−5.58999	+	6.09336i	−0.255680	+	0.278704i
$479$	−10.3324	−	17.8962i	−0.472099	−	0.817700i	0.527391	−	0.849623i	$-0.323170\pi$
$479$	−10.3324	−	17.8962i	−0.472099	−	0.817700i	−0.999490	+	0.0319230i	$0.989837\pi$
$480$	23.6225	+	1.09954i	1.07822	+	0.0501871i
$481$	0.512616	+	0.887877i	0.0233733	+	0.0404837i
$482$	25.9124	+	5.76029i	1.18028	+	0.262374i
$483$	2.21352	+	2.21352i	0.100719	+	0.100719i
$484$	−32.1012	+	2.77124i	−1.45915	+	0.125965i
$485$	−69.7760	−	18.6964i	−3.16836	−	0.848960i
$486$	0.759169	+	1.19317i	0.0344366	+	0.0541234i
$487$			30.7337i			1.39268i	0.717714	+	0.696338i	$0.245189\pi$
$487$			30.7337i			1.39268i	−0.717714	+	0.696338i	$0.754811\pi$
$488$	−17.6966	+	13.5306i	−0.801088	+	0.612500i
$489$	7.48833	+	4.32339i	0.338634	+	0.195510i
$490$	−30.4182	−	15.8570i	−1.37416	−	0.716347i
$491$	−7.22056	−	26.9475i	−0.325859	−	1.21612i	−0.913445	−	0.406962i	$-0.866588\pi$
$491$	−7.22056	−	26.9475i	−0.325859	−	1.21612i	0.587586	−	0.809162i	$-0.300079\pi$
$492$	−1.39299	+	7.84717i	−0.0628008	+	0.353778i
$493$	−9.24465	−	9.24465i	−0.416358	−	0.416358i
$494$	−4.54926	+	4.29487i	−0.204681	+	0.193235i
$495$	−21.7665			−0.978332
$496$	−32.2669	+	5.61291i	−1.44883	+	0.252027i
$497$	−6.56493	+	11.3708i	−0.294477	+	0.510050i
$498$	−6.80856	+	2.14242i	−0.305099	+	0.0960042i
$499$	4.39876	−	1.17865i	0.196916	−	0.0527634i	−0.159013	−	0.987276i	$-0.550831\pi$
$499$	4.39876	−	1.17865i	0.196916	−	0.0527634i	0.355929	+	0.934513i	$0.384165\pi$
$500$	−40.2334	+	47.8363i	−1.79929	+	2.13931i
$501$	−2.29804	+	2.29804i	−0.102669	+	0.102669i
$502$	−21.5781	+	13.7293i	−0.963077	+	0.612768i
$503$	16.9457	−	9.78363i	0.755573	−	0.436230i	−0.0721309	−	0.997395i	$-0.522980\pi$
$503$	16.9457	−	9.78363i	0.755573	−	0.436230i	0.827704	+	0.561165i	$0.189647\pi$
$504$	0.409338	−	3.06826i	0.0182334	−	0.136671i
$505$		−	39.7927i		−	1.77075i
$506$	11.3065	+	17.7702i	0.502635	+	0.789982i
$507$	11.5621	+	3.09805i	0.513490	+	0.137589i
$508$	16.1240	−	11.2625i	0.715386	−	0.499691i
$509$	−7.22916	+	26.9796i	−0.320427	+	1.19585i	0.598403	+	0.801195i	$0.295802\pi$
$509$	−7.22916	+	26.9796i	−0.320427	+	1.19585i	−0.918830	+	0.394654i	$0.870864\pi$
$510$	11.0439	−	12.0384i	0.489031	−	0.533067i
$511$	3.37992	−	5.85420i	0.149519	−	0.258975i
$512$	−8.76738	+	20.8598i	−0.387467	+	0.921884i
$513$	−3.60881	−	2.44469i	−0.159333	−	0.107936i
$514$	−17.1318	−	3.80839i	−0.755653	−	0.167981i
$515$	−20.3565	+	5.45452i	−0.897017	+	0.240355i
$516$	1.85310	−	1.29438i	0.0815783	−	0.0569818i
$517$	57.0595	+	15.2891i	2.50947	+	0.672412i
$518$	1.56201	−	0.0672976i	0.0686308	−	0.00295688i
$519$	−4.09365	+	2.36347i	−0.179691	+	0.103745i
$520$	−9.50790	−	7.32180i	−0.416949	−	0.321082i
$521$		−	6.12772i		−	0.268460i	−0.990950	−	0.134230i	$-0.957144\pi$
$521$		−	6.12772i		−	0.268460i	0.990950	−	0.134230i	$-0.0428561\pi$
$522$	−5.93322	−	3.09298i	−0.259690	−	0.135376i
$523$	15.8751	+	4.25371i	0.694168	+	0.186002i	0.588617	−	0.808412i	$-0.299673\pi$
$523$	15.8751	+	4.25371i	0.694168	+	0.186002i	0.105551	+	0.994414i	$0.466339\pi$
$524$	−9.62348	−	26.5354i	−0.420404	−	1.15920i
$525$	9.65472	+	9.65472i	0.421366	+	0.421366i
$526$	3.47814	−	1.09445i	0.151654	−	0.0477204i
$527$	−11.3128	+	19.5943i	−0.492792	+	0.853542i
$528$	7.16833	−	19.5545i	0.311961	−	0.851002i
$529$	−7.40915	+	12.8330i	−0.322137	+	0.557958i
$530$	−28.6293	−	26.2642i	−1.24358	−	1.14085i
$531$	6.44189	+	6.44189i	0.279554	+	0.279554i
$532$	2.60088	+	9.17944i	0.112762	+	0.397979i
$533$	2.85978	−	2.85978i	0.123871	−	0.123871i
$534$	−0.308813	−	7.16770i	−0.0133636	−	0.310177i
$535$	54.2216	+	31.3049i	2.34421	+	1.35343i
$536$	−24.3092	+	18.5865i	−1.05000	+	0.802813i
$537$	10.6254	+	6.13457i	0.458519	+	0.264726i
$538$	10.2281	−	19.6205i	0.440966	−	0.845898i
$539$	−21.3624	+	21.3624i	−0.920146	+	0.920146i
$540$	3.54218	−	7.57345i	0.152431	−	0.325909i
$541$	−11.9549	+	44.6162i	−0.513981	+	1.91820i	−0.142369	+	0.989814i	$0.545472\pi$
$541$	−11.9549	+	44.6162i	−0.513981	+	1.91820i	−0.371612	+	0.928388i	$0.621195\pi$
$542$	−11.3968	−	36.2189i	−0.489536	−	1.55573i
$543$	10.8778			0.466810
$544$	7.17792	+	13.8861i	0.307751	+	0.595363i
$545$	20.0316	+	34.6957i	0.858058	+	1.48620i
$546$	−1.06188	+	1.15750i	−0.0454444	+	0.0495365i
$547$	4.78061	−	17.8415i	0.204404	−	0.762847i	−0.785226	−	0.619209i	$-0.787453\pi$
$547$	4.78061	−	17.8415i	0.204404	−	0.762847i	0.989630	−	0.143638i	$-0.0458800\pi$
$548$	−8.98630	−	12.8653i	−0.383876	−	0.549577i
$549$	2.03845	+	7.60759i	0.0869989	+	0.324684i
$550$	49.3155	+	77.5082i	2.10282	+	3.30496i
$551$	20.5699	+	1.47973i	0.876308	+	0.0630388i
$552$	−8.02294	+	1.04214i	−0.341479	+	0.0443565i
$553$	−7.73484	−	4.46571i	−0.328919	−	0.189901i
$554$	1.74985	+	40.6150i	0.0743442	+	1.72557i
$555$	4.07905	+	1.09298i	0.173146	+	0.0463944i
$556$	−4.63061	+	26.0858i	−0.196382	+	1.10628i
$557$	10.0600	−	37.5444i	0.426256	−	1.59081i	−0.334909	−	0.942251i	$-0.608705\pi$
$557$	10.0600	−	37.5444i	0.426256	−	1.59081i	0.761165	−	0.648559i	$-0.224628\pi$
$558$	−2.51275	+	11.3035i	−0.106373	+	0.478514i
$559$	−1.14705			−0.0485151
$560$	−16.6035	+	7.69583i	−0.701626	+	0.325208i
$561$	−7.19393	−	12.4602i	−0.303728	−	0.526072i
$562$	4.00522	−	18.0173i	0.168950	−	0.760012i
$563$	−1.60516	−	1.60516i	−0.0676494	−	0.0676494i	0.672473	−	0.740122i	$-0.265232\pi$
$563$	−1.60516	−	1.60516i	−0.0676494	−	0.0676494i	−0.740122	+	0.672473i	$0.765232\pi$
$564$	−14.6053	+	17.3652i	−0.614993	+	0.731209i
$565$	−9.64845	−	36.0085i	−0.405913	−	1.51489i
$566$	−18.9702	−	9.88915i	−0.797377	−	0.415672i
$567$	−0.947781	−	0.547202i	−0.0398031	−	0.0229803i
$568$	−12.9316	−	31.3728i	−0.542597	−	1.31637i
$569$			26.7694i			1.12223i	0.827737	+	0.561117i	$0.189628\pi$
$569$			26.7694i			1.12223i	−0.827737	+	0.561117i	$0.810372\pi$
$570$	−0.740932	+	25.7593i	−0.0310342	+	1.07894i
$571$	−6.79401	+	6.79401i	−0.284321	+	0.284321i	−0.834829	−	0.550509i	$-0.814434\pi$
$571$	−6.79401	+	6.79401i	−0.284321	+	0.284321i	0.550509	+	0.834829i	$0.314434\pi$
$572$	−8.66442	+	6.05203i	−0.362278	+	0.253048i
$573$	18.9089	−	5.06662i	0.789929	−	0.211661i
$574$	−1.85123	−	5.88316i	−0.0772688	−	0.245558i
$575$	17.8430	−	30.9051i	0.744106	−	1.28883i
$576$	5.63727	+	5.67637i	0.234886	+	0.236515i
$577$	−0.906597			−0.0377421			−0.0188711	−	0.999822i	$-0.506007\pi$
$577$	−0.906597			−0.0377421			−0.0188711	+	0.999822i	$0.506007\pi$
$578$	−12.9273	−	2.87373i	−0.537706	−	0.119532i
$579$	−1.64383	+	6.13486i	−0.0683153	+	0.254956i
$580$	3.40227	+	39.4109i	0.141271	+	1.63645i
$581$	3.90575	−	3.90575i	0.162038	−	0.162038i
$582$	−13.1183	−	20.6179i	−0.543773	−	0.854638i
$583$	−29.6326	+	17.1084i	−1.22726	+	0.708557i
$584$	6.65776	+	16.1521i	0.275500	+	0.668380i
$585$	−3.67435	+	2.12139i	−0.151916	+	0.0877085i
$586$	1.47961	+	34.3425i	0.0611221	+	1.41868i
$587$	−3.51898	−	13.1330i	−0.145244	−	0.542057i	−0.999744	−	0.0226068i	$-0.992803\pi$
$587$	−3.51898	−	13.1330i	−0.145244	−	0.542057i	0.854501	−	0.519450i	$-0.173863\pi$
$588$	−3.95643	−	10.9093i	−0.163160	−	0.449891i
$589$	−6.73991	−	35.0479i	−0.277713	−	1.44412i
$590$	11.6877	−	52.5764i	0.481174	−	2.16454i
$591$	1.35970	−	2.35506i	0.0559304	−	0.0968744i
$592$	−2.32526	+	3.30458i	−0.0955674	+	0.135817i
$593$	11.9095	+	20.6278i	0.489064	+	0.847083i	0.999921	−	0.0125825i	$-0.00400525\pi$
$593$	11.9095	+	20.6278i	0.489064	+	0.847083i	−0.510857	+	0.859666i	$0.670672\pi$
$594$	−5.42605	−	4.97781i	−0.222634	−	0.204242i
$595$	−3.27208	+	12.2116i	−0.134142	+	0.500626i
$596$	−3.93969	+	1.42879i	−0.161376	+	0.0585256i
$597$	8.31904	−	8.31904i	0.340476	−	0.340476i
$598$	3.64052	+	1.89780i	0.148872	+	0.0776068i
$599$	−38.2100	+	22.0605i	−1.56122	+	0.901369i	−0.564083	+	0.825718i	$0.690770\pi$
$599$	−38.2100	+	22.0605i	−1.56122	+	0.901369i	−0.997134	+	0.0756510i	$0.975897\pi$
$600$	−34.9936	+	4.54550i	−1.42861	+	0.185569i
$601$			45.3446i			1.84964i	0.380402	+	0.924821i	$0.375786\pi$
$601$			45.3446i			1.84964i	−0.380402	+	0.924821i	$0.624214\pi$
$602$	−0.808599	+	1.55112i	−0.0329560	+	0.0632190i
$603$	2.80015	+	10.4503i	0.114031	+	0.425568i
$604$	0.628802	−	0.0542833i	0.0255856	−	0.00220876i
$605$	65.0533	−	17.4310i	2.64479	−	0.708670i
$606$	9.10024	−	9.91970i	0.369672	−	0.402960i
$607$	−6.23145			−0.252927			−0.126463	−	0.991971i	$-0.540363\pi$
$607$	−6.23145			−0.252927			−0.126463	+	0.991971i	$0.540363\pi$
$608$	−22.8975	−	9.14890i	−0.928618	−	0.371037i
$609$	5.17790			0.209819
$610$	31.4772	−	34.3117i	1.27448	−	1.38924i
$611$	11.1222	−	2.98017i	0.449954	−	0.120565i
$612$	5.50613	−	0.475334i	0.222572	−	0.0192142i
$613$	8.83538	+	32.9741i	0.356858	+	1.33181i	0.878131	+	0.478421i	$0.158791\pi$
$613$	8.83538	+	32.9741i	0.356858	+	1.33181i	−0.521273	+	0.853390i	$0.674543\pi$
$614$	14.2230	−	27.2838i	0.573995	−	1.10109i
$615$		−	16.6587i		−	0.671745i
$616$	2.07611	+	15.9829i	0.0836487	+	0.643970i
$617$	24.3168	−	14.0393i	0.978958	−	0.565202i	0.0770029	−	0.997031i	$-0.475465\pi$
$617$	24.3168	−	14.0393i	0.978958	−	0.565202i	0.901956	+	0.431829i	$0.142132\pi$
$618$	−6.32197	−	3.29564i	−0.254307	−	0.132570i
$619$	−23.0496	+	23.0496i	−0.926442	+	0.926442i	−0.997474	−	0.0710317i	$-0.977371\pi$
$619$	−23.0496	+	23.0496i	−0.926442	+	0.926442i	0.0710317	+	0.997474i	$0.477371\pi$
$620$	64.3561	−	23.3398i	2.58460	−	0.937349i
$621$	−0.740317	+	2.76290i	−0.0297079	+	0.110871i
$622$	13.3617	+	12.2579i	0.535754	+	0.491496i
$623$	2.77597	+	4.80812i	0.111217	+	0.192633i
$624$	−0.695738	−	3.99958i	−0.0278518	−	0.160111i
$625$	34.1358	−	59.1250i	1.36543	−	2.36500i
$626$	6.61238	−	29.7454i	0.264284	−	1.18887i
$627$	21.4444	+	7.43191i	0.856407	+	0.296802i
$628$	−12.7559	−	35.1727i	−0.509017	−	1.40354i
$629$	0.722469	+	2.69629i	0.0288067	+	0.107508i
$630$	0.278501	+	6.46415i	0.0110957	+	0.257538i
$631$	−0.184328	+	0.106422i	−0.00733798	+	0.00423658i	−0.503665	−	0.863899i	$-0.668015\pi$
$631$	−0.184328	+	0.106422i	−0.00733798	+	0.00423658i	0.496327	+	0.868136i	$0.334682\pi$
$632$	21.3410	−	8.79655i	0.848898	−	0.349908i
$633$	7.84067	−	4.52681i	0.311639	−	0.179925i
$634$	−16.6241	−	26.1278i	−0.660227	−	1.03767i
$635$	−29.0693	+	29.0693i	−1.15358	+	1.15358i
$636$	−1.13043	−	13.0945i	−0.0448243	−	0.519232i
$637$	−1.52413	+	5.68814i	−0.0603884	+	0.225372i
$638$	34.0083	+	7.56001i	1.34640	+	0.299304i
$639$	−11.9973			−0.474605
$640$	10.4228	−	46.1335i	0.411999	−	1.82359i
$641$	−8.85029	+	15.3291i	−0.349565	+	0.605465i	−0.986172	−	0.165724i	$-0.947004\pi$
$641$	−8.85029	+	15.3291i	−0.349565	+	0.605465i	0.636607	+	0.771188i	$0.280337\pi$
$642$	6.35745	+	20.2038i	0.250909	+	0.797381i
$643$	−23.5365	+	6.30658i	−0.928188	+	0.248707i	−0.691082	−	0.722777i	$-0.742866\pi$
$643$	−23.5365	+	6.30658i	−0.928188	+	0.248707i	−0.237106	+	0.971484i	$0.576199\pi$
$644$	5.13267	−	3.58513i	0.202256	−	0.141274i
$645$	−3.34089	+	3.34089i	−0.131547	+	0.131547i
$646$	−14.9908	+	8.08941i	−0.589805	+	0.318274i
$647$			10.6941i			0.420428i	0.977655	+	0.210214i	$0.0674161\pi$
$647$			10.6941i			0.420428i	−0.977655	+	0.210214i	$0.932584\pi$
$648$	2.61499	−	1.07788i	0.102727	−	0.0423430i
$649$	−41.0796	−	23.7173i	−1.61252	−	0.930986i
$650$	15.8788	+	8.27763i	0.622820	+	0.324675i
$651$	−2.31923	−	8.65549i	−0.0908979	−	0.339235i
$652$	11.1313	−	13.2348i	0.435937	−	0.518315i
$653$	−7.35114	−	7.35114i	−0.287672	−	0.287672i	0.548487	−	0.836159i	$-0.315204\pi$
$653$	−7.35114	−	7.35114i	−0.287672	−	0.287672i	−0.836159	+	0.548487i	$0.815204\pi$
$654$	−2.94105	+	13.2301i	−0.115004	+	0.517339i
$655$	29.4998	+	51.0952i	1.15265	+	1.99645i
$656$	14.9658	+	5.48619i	0.584317	+	0.214200i
$657$	6.17674			0.240978
$658$	3.81042	−	17.1410i	0.148546	−	0.668225i
$659$	−5.51909	+	20.5975i	−0.214993	+	0.802365i	0.771176	+	0.636622i	$0.219669\pi$
$659$	−5.51909	+	20.5975i	−0.214993	+	0.802365i	−0.986169	+	0.165743i	$0.946998\pi$
$660$	−7.60881	+	42.8629i	−0.296172	+	1.66844i
$661$	−5.31114	−	1.42311i	−0.206579	−	0.0553528i	0.154045	−	0.988064i	$-0.450770\pi$
$661$	−5.31114	−	1.42311i	−0.206579	−	0.0553528i	−0.360625	+	0.932711i	$0.617436\pi$
$662$	0.928378	+	21.5481i	0.0360824	+	0.837491i
$663$	−2.42878	−	1.40225i	−0.0943258	−	0.0544591i
$664$	1.83885	+	14.1564i	0.0713614	+	0.549376i
$665$	−8.70628	−	17.9415i	−0.337615	−	0.695741i
$666$	0.766889	+	1.20531i	0.0297164	+	0.0467047i
$667$	−3.50263	−	13.0720i	−0.135622	−	0.506150i
$668$	3.72201	+	5.32864i	0.144009	+	0.206171i
$669$	6.71804	−	25.0721i	0.259734	−	0.969342i
$670$	43.2392	−	47.1327i	1.67047	−	1.82090i
$671$	−20.5041	−	35.5141i	−0.791552	−	1.37101i
$672$	−5.89896	−	1.87863i	−0.227557	−	0.0724696i
$673$	−38.1318			−1.46987			−0.734937	−	0.678136i	$-0.762788\pi$
$673$	−38.1318			−1.46987			−0.734937	+	0.678136i	$0.762788\pi$
$674$	11.5004	+	36.5480i	0.442978	+	1.40777i
$675$	−3.22904	+	12.0509i	−0.124286	+	0.463841i
$676$	10.1424	−	21.6853i	0.390093	−	0.834048i
$677$	10.8766	−	10.8766i	0.418020	−	0.418020i	−0.466501	−	0.884521i	$-0.654486\pi$
$677$	10.8766	−	10.8766i	0.418020	−	0.418020i	0.884521	+	0.466501i	$0.154486\pi$
$678$	5.82962	−	11.1829i	0.223885	−	0.429476i
$679$	16.3775	+	9.45557i	0.628512	+	0.362872i
$680$	−19.8455	−	25.9559i	−0.761042	−	0.995365i
$681$	16.1419	+	9.31954i	0.618559	+	0.357125i
$682$	−2.59517	−	60.2352i	−0.0993741	−	2.30652i
$683$	−19.7466	+	19.7466i	−0.755582	+	0.755582i	−0.975515	−	0.219933i	$-0.929416\pi$
$683$	−19.7466	+	19.7466i	−0.755582	+	0.755582i	0.219933	+	0.975515i	$0.429416\pi$
$684$	−6.07563	+	6.25194i	−0.232307	+	0.239049i
$685$	23.1943	+	23.1943i	0.886209	+	0.886209i
$686$	14.6010	+	13.3948i	0.557467	+	0.511415i
$687$	−3.82180	+	6.61956i	−0.145811	+	0.252552i
$688$	−1.90113	−	4.10163i	−0.0724798	−	0.156373i
$689$	−3.33480	+	5.77604i	−0.127046	+	0.220050i
$690$	16.1308	−	5.07582i	0.614090	−	0.193233i
$691$	−33.2473	−	33.2473i	−1.26479	−	1.26479i	−0.948746	−	0.316040i	$-0.897646\pi$
$691$	−33.2473	−	33.2473i	−1.26479	−	1.26479i	−0.316040	−	0.948746i	$-0.602354\pi$
$692$	3.22318	+	8.88745i	0.122527	+	0.337850i
$693$	5.50413	+	1.47483i	0.209084	+	0.0560240i
$694$	28.4919	+	14.8528i	1.08154	+	0.563805i
$695$		−	55.3773i		−	2.10058i
$696$	−8.16479	+	10.6026i	−0.309485	+	0.401890i
$697$	9.53629	−	5.50578i	0.361213	−	0.208546i
$698$	34.5982	−	1.49063i	1.30956	−	0.0564210i
$699$	10.3625	+	2.77663i	0.391946	+	0.105022i
$700$	22.3872	−	15.6373i	0.846155	−	0.591033i
$701$	24.0804	−	6.45234i	0.909506	−	0.243701i	0.226412	−	0.974032i	$-0.427301\pi$
$701$	24.0804	−	6.45234i	0.909506	−	0.243701i	0.683094	+	0.730330i	$0.260634\pi$
$702$	−1.40110	−	0.311463i	−0.0528811	−	0.0117554i
$703$	−3.64551	−	2.46955i	−0.137493	−	0.0931408i
$704$	−36.0013	−	20.9515i	−1.35685	−	0.789641i
$705$	23.7142	−	41.0742i	0.893129	−	1.54694i
$706$	−35.7110	+	38.9267i	−1.34400	+	1.46502i
$707$	−2.69622	+	10.0624i	−0.101402	+	0.378437i
$708$	14.9373	−	10.4336i	0.561379	−	0.392119i
$709$	3.44652	+	0.923493i	0.129437	+	0.0346825i	0.322956	−	0.946414i	$-0.395323\pi$
$709$	3.44652	+	0.923493i	0.129437	+	0.0346825i	−0.193519	+	0.981097i	$0.561990\pi$
$710$	38.0753	+	59.8422i	1.42894	+	2.24584i
$711$		−	8.16100i		−	0.306061i
$712$	−14.2227	−	1.89746i	−0.533018	−	0.0711102i
$713$	−20.2826	+	11.7101i	−0.759588	+	0.438548i
$714$	−3.60836	+	2.29586i	−0.135039	+	0.0859203i
$715$	15.6208	−	15.6208i	0.584183	−	0.584183i
$716$	15.7945	−	18.7792i	0.590270	−	0.701813i
$717$	5.64786	−	1.51334i	0.210923	−	0.0565167i
$718$	13.3149	−	4.18974i	0.496908	−	0.156360i
$719$	11.3693	−	19.6923i	0.424005	−	0.734398i	−0.572322	−	0.820029i	$-0.693957\pi$
$719$	11.3693	−	19.6923i	0.424005	−	0.734398i	0.996327	+	0.0856311i	$0.0272906\pi$
$720$	−13.6755	−	9.62273i	−0.509657	−	0.358618i
$721$	5.51717			0.205470
$722$	9.52516	−	25.1251i	0.354490	−	0.935060i
$723$	−13.2725	−	13.2725i	−0.493608	−	0.493608i
$724$	3.80249	−	21.4207i	0.141318	−	0.796093i
$725$	−15.2774	−	57.0161i	−0.567389	−	2.11753i
$726$	20.2031	+	10.5318i	0.749806	+	0.390873i
$727$	−26.7707	−	15.4561i	−0.992871	−	0.573235i	−0.0867400	−	0.996231i	$-0.527645\pi$
$727$	−26.7707	−	15.4561i	−0.992871	−	0.573235i	−0.906131	+	0.422996i	$0.860978\pi$
$728$	1.90817	+	2.49570i	0.0707216	+	0.0924967i
$729$		−	1.00000i		−	0.0370370i
$730$	−19.6029	−	30.8095i	−0.725535	−	1.14031i
$731$	−3.01667	−	0.808314i	−0.111576	−	0.0298966i
$732$	15.6936	−	1.35480i	0.580050	−	0.0500747i
$733$	25.0918	+	25.0918i	0.926788	+	0.926788i	0.997497	−	0.0707089i	$-0.0225262\pi$
$733$	25.0918	+	25.0918i	0.926788	+	0.926788i	−0.0707089	+	0.997497i	$0.522526\pi$
$734$	−4.03781	−	0.897600i	−0.149038	−	0.0331310i
$735$	12.1280	+	21.0064i	0.447349	+	0.774832i
$736$	−0.752337	+	16.1632i	−0.0277315	+	0.595783i
$737$	−28.1658	−	48.7845i	−1.03750	−	1.79700i
$738$	3.80970	−	4.15276i	0.140237	−	0.152865i
$739$	3.25408	−	0.871929i	0.119703	−	0.0320744i	−0.198470	−	0.980107i	$-0.563597\pi$
$739$	3.25408	−	0.871929i	0.119703	−	0.0320744i	0.318173	+	0.948033i	$0.396931\pi$
$740$	3.57820	−	7.65047i	0.131537	−	0.281237i
$741$	4.34430	−	0.835433i	0.159592	−	0.0306904i
$742$	5.45994	+	8.58129i	0.200441	+	0.315029i
$743$	25.6803	+	14.8265i	0.942118	+	0.543932i	0.890624	−	0.454741i	$-0.150268\pi$
$743$	25.6803	+	14.8265i	0.942118	+	0.543932i	0.0514943	+	0.998673i	$0.483602\pi$
$744$	21.3806	+	8.89943i	0.783850	+	0.326269i
$745$	7.58607	−	4.37982i	0.277932	−	0.160464i
$746$	1.70578	+	39.5920i	0.0624531	+	1.44957i
$747$	4.87513	+	1.30629i	0.178372	+	0.0477945i
$748$	−27.0516	+	9.81072i	−0.989106	+	0.358715i
$749$	−11.5900	−	11.5900i	−0.423489	−	0.423489i
$750$	42.1607	−	13.2665i	1.53949	−	0.484425i
$751$	−3.53829	−	6.12849i	−0.129114	−	0.223632i	0.794220	−	0.607631i	$-0.207880\pi$
$751$	−3.53829	−	6.12849i	−0.129114	−	0.223632i	−0.923334	+	0.383999i	$0.874547\pi$
$752$	29.0904	+	34.8312i	1.06082	+	1.27016i
$753$	18.0846			0.659040
$754$	6.47766	−	2.03830i	0.235902	−	0.0742304i
$755$	−1.27427	+	0.341440i	−0.0463755	+	0.0124263i
$756$	−1.40887	+	1.67510i	−0.0512400	+	0.0609229i
$757$	−7.50903	−	28.0241i	−0.272920	−	1.01855i	−0.957222	−	0.289354i	$-0.906560\pi$
$757$	−7.50903	−	28.0241i	−0.272920	−	1.01855i	0.684302	−	0.729199i	$-0.260107\pi$
$758$	−1.58804	−	36.8591i	−0.0576801	−	1.33878i
$759$		−	14.8932i		−	0.540590i
$760$	50.4666	+	10.4636i	1.83061	+	0.379554i
$761$		−	15.3530i		−	0.556546i	−0.960502	−	0.278273i	$-0.910238\pi$
$761$		−	15.3530i		−	0.556546i	0.960502	−	0.278273i	$-0.0897619\pi$
$762$	−13.8944	+	0.598626i	−0.503341	+	0.0216859i
$763$	−2.71455	−	10.1308i	−0.0982731	−	0.366760i
$764$	−3.36738	−	39.0067i	−0.121827	−	1.41121i
$765$	−11.1582	+	2.98983i	−0.403426	+	0.108098i
$766$	0.559302	+	1.77745i	0.0202084	+	0.0642218i
$767$	−9.24605			−0.333856
$768$	13.1486	−	9.11674i	0.474458	−	0.328972i
$769$	−25.2653	−	43.7607i	−0.911089	−	1.57805i	−0.812529	−	0.582920i	$-0.801910\pi$
$769$	−25.2653	−	43.7607i	−0.911089	−	1.57805i	−0.0985593	−	0.995131i	$-0.531423\pi$
$770$	−10.1118	−	32.1351i	−0.364404	−	1.15807i
$771$	8.77502	+	8.77502i	0.316024	+	0.316024i
$772$	11.5062	+	5.38159i	0.414118	+	0.193688i
$773$	17.0524	+	4.56918i	0.613333	+	0.164342i	0.552095	−	0.833781i	$-0.313829\pi$
$773$	17.0524	+	4.56918i	0.613333	+	0.164342i	0.0612377	+	0.998123i	$0.480495\pi$
$774$	−1.59686	+	0.0687991i	−0.0573980	+	0.00247293i
$775$	−88.4664	+	51.0761i	−3.17781	+	1.83471i
$776$	−45.1867	+	18.6256i	−1.62211	+	0.668618i
$777$	−0.957419	−	0.552766i	−0.0343472	−	0.0198304i
$778$	18.6036	−	11.8367i	0.666970	−	0.424367i
$779$	−5.68791	+	16.4122i	−0.203791	+	0.588028i
$780$	2.89304	+	7.97714i	0.103587	+	0.285627i
$781$	60.3384	−	16.1676i	2.15908	−	0.578523i
$782$	8.23696	+	7.55652i	0.294553	+	0.270220i
$783$	2.36563	+	4.09739i	0.0845407	+	0.146429i
$784$	−22.8658	+	3.97756i	−0.816634	+	0.142056i
$785$	39.1020	+	67.7267i	1.39561	+	2.41727i
$786$	−4.33118	+	19.4836i	−0.154488	+	0.694956i
$787$	17.0582	+	17.0582i	0.608060	+	0.608060i	0.942439	−	0.334379i	$-0.108527\pi$
$787$	17.0582	+	17.0582i	0.608060	+	0.608060i	−0.334379	+	0.942439i	$0.608527\pi$
$788$	−4.16232	−	3.50078i	−0.148277	−	0.124710i
$789$	−2.49045	−	0.667314i	−0.0886624	−	0.0237570i
$790$	−40.7070	+	25.9002i	−1.44829	+	0.921489i
$791$			9.75926i			0.346999i
$792$	−11.6991	+	8.94499i	−0.415710	+	0.317846i
$793$	−6.92249	−	3.99670i	−0.245825	−	0.141927i
$794$	−6.44915	+	12.3713i	−0.228872	+	0.439041i
$795$	7.11033	+	26.5361i	0.252177	+	0.941139i
$796$	−13.4739	−	19.2900i	−0.477571	−	0.683716i
$797$	20.6290	+	20.6290i	0.730717	+	0.730717i	0.970762	−	0.240045i	$-0.0771622\pi$
$797$	20.6290	+	20.6290i	0.730717	+	0.730717i	−0.240045	+	0.970762i	$0.577162\pi$
$798$	1.93272	−	6.46358i	0.0684177	−	0.228808i
$799$	31.3506			1.10910
$800$	−3.28147	+	70.4989i	−0.116017	+	2.49251i
$801$	−2.53651	+	4.39337i	−0.0896233	+	0.155232i
$802$	4.32495	+	13.7446i	0.152719	+	0.485339i
$803$	−31.0649	+	8.32382i	−1.09626	+	0.293741i
$804$	21.5577	−	1.86103i	0.760281	−	0.0656336i
$805$	−9.25349	+	9.25349i	−0.326143	+	0.326143i
$806$	−6.30866	−	9.91521i	−0.222213	−	0.349248i
$807$	−13.5496	+	7.82286i	−0.476968	+	0.275378i
$808$	−16.3529	−	21.3879i	−0.575292	−	0.752424i
$809$		−	4.31181i		−	0.151595i	−0.997123	−	0.0757976i	$-0.975850\pi$
$809$		−	4.31181i		−	0.151595i	0.997123	−	0.0757976i	$-0.0241503\pi$
$810$	−4.98798	+	3.17366i	−0.175260	+	0.111511i
$811$	−16.0208	−	4.29276i	−0.562567	−	0.150739i	−0.0336815	−	0.999433i	$-0.510723\pi$
$811$	−16.0208	−	4.29276i	−0.562567	−	0.150739i	−0.528885	+	0.848693i	$0.677390\pi$
$812$	1.81001	−	10.1964i	0.0635190	−	0.357824i
$813$	−6.94893	+	25.9338i	−0.243710	+	0.909537i
$814$	−5.48123	−	5.02843i	−0.192117	−	0.176246i
$815$	−18.0736	+	31.3045i	−0.633092	+	1.09655i
$816$	0.988715	−	11.0089i	0.0346119	−	0.385389i
$817$	4.43215	−	2.15074i	0.155061	−	0.0752450i
$818$	−8.88675	+	39.9766i	−0.310718	+	1.39775i
$819$	1.07288	−	0.287476i	0.0374893	−	0.0100452i
$820$	−32.8046	−	5.82330i	−1.14559	−	0.203359i
$821$	−9.64670	−	2.58483i	−0.336672	−	0.0902111i	0.0865223	−	0.996250i	$-0.472425\pi$
$821$	−9.64670	−	2.58483i	−0.336672	−	0.0902111i	−0.423194	+	0.906039i	$0.639091\pi$
$822$	0.477642	+	11.0863i	0.0166597	+	0.386679i
$823$	1.19896	−	0.692220i	0.0417931	−	0.0241293i	−0.478958	−	0.877838i	$-0.658985\pi$
$823$	1.19896	−	0.692220i	0.0417931	−	0.0241293i	0.520751	+	0.853709i	$0.325652\pi$
$824$	−8.69975	+	11.2973i	−0.303070	+	0.393559i
$825$		−	64.9598i		−	2.26161i
$826$	−6.51788	+	12.5031i	−0.226786	+	0.435040i
$827$	−10.1574	−	2.72166i	−0.353207	−	0.0946416i	0.0778528	−	0.996965i	$-0.475194\pi$
$827$	−10.1574	−	2.72166i	−0.353207	−	0.0946416i	−0.431060	+	0.902323i	$0.641860\pi$
$828$	5.18196	+	2.42366i	0.180085	+	0.0842279i
$829$	29.5127	+	29.5127i	1.02502	+	1.02502i	0.999679	+	0.0253387i	$0.00806644\pi$
$829$	29.5127	+	29.5127i	1.02502	+	1.02502i	0.0253387	+	0.999679i	$0.491934\pi$
$830$	−8.95626	−	28.4628i	−0.310876	−	0.987957i
$831$	14.3729	−	24.8946i	0.498590	−	0.863583i
$832$	−8.11924	−	0.0280558i	−0.281484	−	0.000972659i
$833$	−8.01674	+	13.8854i	−0.277763	+	0.481100i
$834$	12.6643	−	13.8047i	0.438529	−	0.478018i
$835$	−9.60679	−	9.60679i	−0.332457	−	0.332457i
$836$	22.1312	−	39.6307i	0.765424	−	1.37066i
$837$	5.78969	−	5.78969i	0.200121	−	0.200121i
$838$	−0.238467	+	0.0102741i	−0.00823770	+	0.000354913i
$839$	41.9031	+	24.1928i	1.44666	+	0.835227i	0.998280	−	0.0586179i	$-0.0186694\pi$
$839$	41.9031	+	24.1928i	1.44666	+	0.835227i	0.448376	+	0.893845i	$0.352003\pi$
$840$	12.8266	+	1.71121i	0.442561	+	0.0590424i
$841$	5.72893	+	3.30760i	0.197549	+	0.114055i
$842$	29.2971	+	15.2726i	1.00965	+	0.526327i
$843$	−9.22853	+	9.22853i	−0.317848	+	0.317848i
$844$	−6.17344	−	17.0224i	−0.212499	−	0.585934i
$845$	−12.9512	+	48.3346i	−0.445535	+	1.66276i
$846$	15.3049	−	4.81593i	0.526193	−	0.165575i
$847$	−17.6312			−0.605814
$848$	−26.1811	−	2.35133i	−0.899062	−	0.0807451i
$849$	7.56359	+	13.1005i	0.259582	+	0.449609i
$850$	35.9271	+	32.9592i	1.23229	+	1.13049i
$851$	−0.747846	+	2.79100i	−0.0256358	+	0.0956742i
$852$	−4.19383	+	23.6252i	−0.143678	+	0.809386i
$853$	1.13935	+	4.25213i	0.0390108	+	0.145590i	0.982684	−	0.185288i	$-0.0593218\pi$
$853$	1.13935	+	4.25213i	0.0390108	+	0.145590i	−0.943674	+	0.330878i	$0.892655\pi$
$854$	−10.2845	+	6.54364i	−0.351929	+	0.223919i
$855$	10.2199	−	15.0864i	0.349512	−	0.515944i
$856$	42.0080	−	5.45664i	1.43580	−	0.186504i
$857$	0.948269	+	0.547484i	0.0323923	+	0.0187017i	0.516109	−	0.856523i	$-0.327380\pi$
$857$	0.948269	+	0.547484i	0.0323923	+	0.0187017i	−0.483716	+	0.875225i	$0.660713\pi$
$858$	7.46634	−	0.321679i	0.254897	−	0.0109819i
$859$	−32.5682	−	8.72662i	−1.11121	−	0.297748i	−0.343890	−	0.939010i	$-0.611745\pi$
$859$	−32.5682	−	8.72662i	−1.11121	−	0.297748i	−0.767322	+	0.641262i	$0.778411\pi$
$860$	5.41107	+	7.74678i	0.184516	+	0.264163i
$861$	−1.12874	+	4.21251i	−0.0384673	+	0.143562i
$862$	−3.50654	−	0.779501i	−0.119433	−	0.0265499i
$863$	33.1570			1.12868			0.564339	−	0.825543i	$-0.309131\pi$
$863$	33.1570			1.12868			0.564339	+	0.825543i	$0.309131\pi$
$864$	−1.20846	−	5.52627i	−0.0411126	−	0.188007i
$865$	−9.88033	−	17.1132i	−0.335941	−	0.581867i
$866$	−30.2787	−	6.73093i	−1.02891	−	0.228726i
$867$	6.62145	+	6.62145i	0.224876	+	0.224876i
$868$	−17.8552	+	1.54141i	−0.606046	+	0.0523188i
$869$	10.9978	+	41.0444i	0.373076	+	1.39234i
$870$	12.9300	−	24.8034i	0.438369	−	0.840915i
$871$	−9.50918	−	5.49013i	−0.322206	−	0.186026i
$872$	25.0249	+	10.4163i	0.847450	+	0.352742i
$873$			17.2799i			0.584835i
$874$	−17.6252	−	0.506965i	−0.596181	−	0.0171484i
$875$	−24.1856	+	24.1856i	−0.817622	+	0.817622i
$876$	2.15917	−	12.1633i	0.0729516	−	0.410961i
$877$	25.0841	−	6.72127i	0.847031	−	0.226961i	0.190901	−	0.981609i	$-0.438859\pi$
$877$	25.0841	−	6.72127i	0.847031	−	0.226961i	0.656130	+	0.754648i	$0.272192\pi$
$878$	50.8925	−	16.0141i	1.71754	−	0.540451i
$879$	12.1532	−	21.0499i	0.409916	−	0.709996i
$880$	81.7465	+	29.9667i	2.75567	+	1.01018i
$881$	−28.6433			−0.965019			−0.482509	−	0.875891i	$-0.660275\pi$
$881$	−28.6433			−0.965019			−0.482509	+	0.875891i	$0.660275\pi$
$882$	−1.78064	+	8.01013i	−0.0599574	+	0.269715i
$883$	8.87237	−	33.1121i	0.298579	−	1.11431i	−0.639754	−	0.768580i	$-0.720964\pi$
$883$	8.87237	−	33.1121i	0.298579	−	1.11431i	0.938333	−	0.345733i	$-0.112370\pi$
$884$	−3.61035	+	4.29260i	−0.121429	+	0.144376i
$885$	−26.9299	+	26.9299i	−0.905239	+	0.905239i
$886$	28.1801	−	17.9299i	0.946727	−	0.602366i
$887$	27.9317	−	16.1264i	0.937856	−	0.541471i	0.0485683	−	0.998820i	$-0.484534\pi$
$887$	27.9317	−	16.1264i	0.937856	−	0.541471i	0.889288	+	0.457349i	$0.151201\pi$
$888$	2.64158	−	1.08884i	0.0886458	−	0.0365390i
$889$	9.32043	−	5.38115i	0.312597	−	0.180478i
$890$	29.9641	−	1.29097i	1.00440	−	0.0432735i
$891$	1.34761	+	5.02934i	0.0451466	+	0.168489i
$892$	−47.0239	−	21.9936i	−1.57448	−	0.736399i
$893$	−37.3876	+	32.3695i	−1.25113	+	1.08320i
$894$	2.89271	+	0.643047i	0.0967468	+	0.0215067i
$895$	−25.6452	+	44.4188i	−0.857224	+	1.48476i
$896$	−5.76149	+	10.9596i	−0.192478	+	0.366135i
$897$	−1.45151	−	2.51409i	−0.0484645	−	0.0839429i
$898$	34.9451	−	38.0918i	1.16613	−	1.27114i
$899$	−10.0264	+	37.4189i	−0.334398	+	1.24799i
$900$	22.6021	+	10.5713i	0.753404	+	0.352375i
$901$	−12.8406	+	12.8406i	−0.427783	+	0.427783i
$902$	−13.5640	+	26.0196i	−0.451632	+	0.866358i
$903$	1.07118	−	0.618447i	0.0356467	−	0.0205806i
$904$	−19.9836	−	15.3889i	−0.664646	−	0.511828i
$905$			45.4739i			1.51160i
$906$	−0.395740	−	0.206299i	−0.0131476	−	0.00685382i
$907$	6.09600	+	22.7506i	0.202414	+	0.755420i	0.990222	+	0.139499i	$0.0445493\pi$
$907$	6.09600	+	22.7506i	0.202414	+	0.755420i	−0.787808	+	0.615921i	$0.788784\pi$
$908$	23.9948	−	28.5291i	0.796296	−	0.946772i
$909$	−9.19445	+	2.46364i	−0.304961	+	0.0817139i
$910$	−4.83887	−	4.43913i	−0.160407	−	0.147156i
$911$	3.98161			0.131917			0.0659583	−	0.997822i	$-0.478990\pi$
$911$	3.98161			0.131917			0.0659583	+	0.997822i	$0.478990\pi$
$912$	10.1876	+	14.1497i	0.337345	+	0.468542i
$913$	−26.2790			−0.869709
$914$	18.4439	+	16.9203i	0.610069	+	0.559672i
$915$	−31.8031	+	8.52161i	−1.05138	+	0.281716i
$916$	11.6994	+	9.83992i	0.386558	+	0.325120i
$917$	−3.99762	−	14.9193i	−0.132013	−	0.492679i
$918$	−3.46531	−	1.80646i	−0.114372	−	0.0596222i
$919$		−	2.10441i		−	0.0694179i	−0.999397	−	0.0347090i	$-0.988950\pi$
$919$		−	2.10441i		−	0.0694179i	0.999397	−	0.0347090i	$-0.0110504\pi$
$920$	−4.35661	−	33.5394i	−0.143633	−	1.10576i
$921$	−18.8418	+	10.8783i	−0.620859	+	0.358453i
$922$	−5.68431	+	10.9041i	−0.187203	+	0.359108i
$923$	8.60985	−	8.60985i	0.283397	−	0.283397i
$924$	4.82830	−	10.3233i	0.158839	−	0.339610i
$925$	−3.26188	+	12.1735i	−0.107250	+	0.400262i
$926$	−15.0555	+	16.4112i	−0.494754	+	0.539306i
$927$	2.52063	+	4.36585i	0.0827883	+	0.143393i
$928$	18.0246	+	19.7845i	0.591687	+	0.649458i
$929$	−3.22383	+	5.58384i	−0.105771	+	0.183200i	−0.914053	−	0.405595i	$-0.867064\pi$
$929$	−3.22383	+	5.58384i	−0.105771	+	0.183200i	0.808282	+	0.588795i	$0.200398\pi$
$930$	−47.2534	−	10.5044i	−1.54950	−	0.344452i
$931$	−4.77620	−	24.8365i	−0.156534	−	0.813983i
$932$	9.09014	−	19.4354i	0.297757	−	0.636627i
$933$	−3.31849	−	12.3848i	−0.108642	−	0.405459i
$934$	4.81256	−	0.207344i	0.157472	−	0.00678450i
$935$	52.0893	−	30.0738i	1.70350	−	0.983517i
$936$	−1.10311	+	2.65019i	−0.0360564	+	0.0866241i
$937$	6.72844	−	3.88467i	0.219808	−	0.126906i	−0.386053	−	0.922477i	$-0.626162\pi$
$937$	6.72844	−	3.88467i	0.219808	−	0.126906i	0.605862	+	0.795570i	$0.292829\pi$
$938$	−14.1275	+	8.98877i	−0.461279	+	0.293494i
$939$	−15.2358	+	15.2358i	−0.497200	+	0.497200i
$940$	−72.5943	−	61.0565i	−2.36777	−	1.99144i
$941$	6.48654	−	24.2081i	0.211455	−	0.789161i	−0.775929	−	0.630820i	$-0.782719\pi$
$941$	6.48654	−	24.2081i	0.211455	−	0.789161i	0.987384	−	0.158341i	$-0.0506147\pi$
$942$	−5.74098	+	25.8255i	−0.187051	+	0.841440i
$943$	11.3983			0.371181
$944$	−15.3244	−	33.0620i	−0.498768	−	1.07608i
$945$	2.28754	−	3.96214i	0.0744137	−	0.128888i
$946$	7.93845	−	2.49796i	0.258101	−	0.0812156i
$947$	8.43599	−	2.26042i	0.274133	−	0.0734537i	−0.119134	−	0.992878i	$-0.538012\pi$
$947$	8.43599	−	2.26042i	0.274133	−	0.0734537i	0.393266	+	0.919425i	$0.371345\pi$
$948$	−16.0708	−	2.85280i	−0.521954	−	0.0926546i
$949$	−4.43274	+	4.43274i	−0.143893	+	0.143893i
$950$	−76.8758	−	2.21123i	−2.49418	−	0.0717417i
$951$			21.8977i			0.710083i
$952$	3.25968	+	7.90818i	0.105647	+	0.256306i
$953$	−23.6970	−	13.6815i	−0.767621	−	0.443186i	0.0644046	−	0.997924i	$-0.479485\pi$
$953$	−23.6970	−	13.6815i	−0.767621	−	0.443186i	−0.832025	+	0.554738i	$0.812819\pi$
$954$	−4.29608	+	8.24111i	−0.139091	+	0.266816i
$955$	21.1807	+	79.0473i	0.685390	+	2.55791i
$956$	−1.00580	−	11.6509i	−0.0325298	−	0.376815i
$957$	−17.4192	−	17.4192i	−0.563084	−	0.563084i
$958$	28.5280	+	6.34175i	0.921699	+	0.204893i
$959$	−4.29361	−	7.43674i	−0.138648	−	0.240145i
$960$	−23.7297	+	23.5663i	−0.765873	+	0.760598i
$961$	36.0411			1.16262
$962$	−1.41535	−	0.314630i	−0.0456326	−	0.0101441i
$963$	3.87629	−	14.4665i	0.124912	−	0.466177i
$964$	−30.7759	+	21.4967i	−0.991225	+	0.692363i
$965$	−25.6464	−	6.87193i	−0.825587	−	0.221215i
$966$	−4.42294	+	0.190558i	−0.142306	+	0.00613110i
$967$	−48.5166	−	28.0111i	−1.56019	−	0.900775i	−0.997237	−	0.0742848i	$-0.976333\pi$
$967$	−48.5166	−	28.0111i	−1.56019	−	0.900775i	−0.562951	−	0.826490i	$-0.690334\pi$
$968$	27.8017	−	36.1026i	0.893582	−	1.16038i
$969$	12.0139	+	0.864243i	0.385943	+	0.0277635i
$970$	86.1917	−	54.8404i	2.76745	−	1.76082i
$971$	−9.22813	−	34.4399i	−0.296145	−	1.10523i	−0.940304	−	0.340336i	$-0.889459\pi$
$971$	−9.22813	−	34.4399i	−0.296145	−	1.10523i	0.644159	−	0.764892i	$-0.277208\pi$
$972$	−1.96921	−	0.349565i	−0.0631626	−	0.0112123i
$973$	−3.75218	+	14.0033i	−0.120289	+	0.448926i
$974$	−32.0281	−	29.3823i	−1.02625	−	0.941470i
$975$	−6.33104	−	10.9657i	−0.202756	−	0.351183i
$976$	2.81803	−	31.3776i	0.0902030	−	1.00437i
$977$	39.9700			1.27875			0.639377	−	0.768893i	$-0.279192\pi$
$977$	39.9700			1.27875			0.639377	+	0.768893i	$0.279192\pi$
$978$	−11.6645	+	3.67043i	−0.372991	+	0.117367i
$979$	6.83645	−	25.5140i	0.218494	−	0.815431i
$980$	45.6056	−	16.5396i	1.45682	−	0.528339i
$981$	6.77655	−	6.77655i	0.216358	−	0.216358i
$982$	34.9855	+	18.2379i	1.11643	+	0.581996i
$983$	−12.6302	−	7.29205i	−0.402841	−	0.232580i	0.284868	−	0.958567i	$-0.408050\pi$
$983$	−12.6302	−	7.29205i	−0.402841	−	0.232580i	−0.687709	+	0.725986i	$0.741384\pi$
$984$	−6.84593	−	8.95378i	−0.218240	−	0.285436i
$985$	9.84520	+	5.68413i	0.313694	+	0.181111i
$986$	18.4722	−	0.795854i	0.588273	−	0.0253451i
$987$	−8.77970	+	8.77970i	−0.279461	+	0.279461i
$988$	−0.126533	−	8.84689i	−0.00402555	−	0.281457i
$989$	−2.28592	−	2.28592i	−0.0726882	−	0.0726882i
$990$	20.8094	−	22.6833i	0.661367	−	0.720921i
$991$	−1.31056	+	2.26996i	−0.0416314	+	0.0721076i	−0.886090	−	0.463513i	$-0.846589\pi$
$991$	−1.31056	+	2.26996i	−0.0416314	+	0.0721076i	0.844459	+	0.535620i	$0.179922\pi$
$992$	24.9988	−	38.9920i	0.793712	−	1.23800i
$993$	7.62547	−	13.2077i	0.241987	−	0.419134i
$994$	−5.57343	−	17.7122i	−0.176779	−	0.561798i
$995$	34.7772	+	34.7772i	1.10251	+	1.10251i
$996$	4.27653	−	9.14354i	0.135507	−	0.289724i
$997$	47.1411	+	12.6314i	1.49297	+	0.400041i	0.910740	−	0.412981i	$-0.135512\pi$
$997$	47.1411	+	12.6314i	1.49297	+	0.400041i	0.582233	+	0.813022i	$0.302179\pi$
$998$	−2.97706	+	5.71085i	−0.0942372	+	0.180774i
$999$		−	1.01017i		−	0.0319603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bq.a.733.20	yes	320
16.5	even	4	inner	912.2.bq.a.277.35	✓	320
19.7	even	3	inner	912.2.bq.a.349.35	yes	320
304.197	even	12	inner	912.2.bq.a.805.20	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bq.a.277.35	✓	320	16.5	even	4	inner
912.2.bq.a.349.35	yes	320	19.7	even	3	inner
912.2.bq.a.733.20	yes	320	1.1	even	1	trivial
912.2.bq.a.805.20	yes	320	304.197	even	12	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.956029 + 1.04212i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.172017 - 1.99259i) q^{4} +(1.08198 + 4.03799i) q^{5} +(-0.653733 + 1.25405i) q^{6} -1.09440i q^{7} +(2.24096 + 1.72571i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.956029 + 1.04212i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.172017 - 1.99259i) q^{4} +(1.08198 + 4.03799i) q^{5} +(-0.653733 + 1.25405i) q^{6} -1.09440i q^{7} +(2.24096 + 1.72571i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-5.24246 - 2.73289i) q^{10} +(-3.68173 + 3.68173i) q^{11} +(-0.681875 - 1.88017i) q^{12} +(-0.262678 + 0.980329i) q^{13} +(1.14050 + 1.04628i) q^{14} +(2.09022 + 3.62036i) q^{15} +(-3.94082 + 0.685516i) q^{16} +(-1.38165 + 2.39309i) q^{17} +(-0.306887 + 1.38051i) q^{18} +(-0.823158 - 4.28047i) q^{19} +(7.85994 - 2.85054i) q^{20} +(-0.283252 - 1.05711i) q^{21} +(-0.316953 - 7.35664i) q^{22} +(-2.47715 + 1.43018i) q^{23} +(2.61125 + 1.08691i) q^{24} +(-10.8046 + 6.23803i) q^{25} +(-0.770489 - 1.21096i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.18070 + 0.188255i) q^{28} +(-1.22454 + 4.57004i) q^{29} +(-5.77115 - 1.28292i) q^{30} +8.18786 q^{31} +(3.05315 - 4.76217i) q^{32} +(-2.60338 + 4.50918i) q^{33} +(-1.17298 - 3.72771i) q^{34} +(4.41919 - 1.18412i) q^{35} +(-1.14527 - 1.63962i) q^{36} +(0.714297 - 0.714297i) q^{37} +(5.24771 + 3.23443i) q^{38} +1.01491i q^{39} +(-4.54374 + 10.9162i) q^{40} +(-3.45105 - 1.99246i) q^{41} +(1.37243 + 0.715448i) q^{42} +(0.292517 + 1.09169i) q^{43} +(7.96950 + 6.70286i) q^{44} +(2.95602 + 2.95602i) q^{45} +(0.877809 - 3.94878i) q^{46} +(-5.67266 - 9.82534i) q^{47} +(-3.62912 + 1.68212i) q^{48} +5.80228 q^{49} +(3.82874 - 17.2234i) q^{50} +(-0.715196 + 2.66915i) q^{51} +(1.99858 + 0.354777i) q^{52} +(6.34769 + 1.70086i) q^{53} +(0.0608734 + 1.41290i) q^{54} +(-18.8504 - 10.8833i) q^{55} +(1.88862 - 2.45252i) q^{56} +(-1.90298 - 3.92157i) q^{57} +(-3.59183 - 5.64521i) q^{58} +(2.35790 + 8.79979i) q^{59} +(6.85435 - 4.78771i) q^{60} +(-2.03845 + 7.60759i) q^{61} +(-7.82784 + 8.53271i) q^{62} +(-0.547202 - 0.947781i) q^{63} +(2.04384 + 7.73452i) q^{64} -4.24277 q^{65} +(-2.21019 - 7.02393i) q^{66} +(-2.80015 + 10.4503i) q^{67} +(5.00612 + 2.34141i) q^{68} +(-2.02258 + 2.02258i) q^{69} +(-2.99089 + 5.73737i) q^{70} +(-10.3899 - 5.99864i) q^{71} +(2.80359 + 0.374028i) q^{72} +(5.34922 + 3.08837i) q^{73} +(0.0614925 + 1.42727i) q^{74} +(-8.82190 + 8.82190i) q^{75} +(-8.38762 + 2.37653i) q^{76} +(4.02930 + 4.02930i) q^{77} +(-1.05766 - 0.970285i) q^{78} +(4.08050 - 7.06763i) q^{79} +(-7.03199 - 15.1713i) q^{80} +(0.500000 - 0.866025i) q^{81} +(5.37568 - 1.69154i) q^{82} +(3.56884 + 3.56884i) q^{83} +(-2.05767 + 0.746246i) q^{84} +(-11.1582 - 2.98983i) q^{85} +(-1.41732 - 0.738849i) q^{86} +4.73126i q^{87} +(-14.6042 + 1.89702i) q^{88} +(-4.39337 + 2.53651i) q^{89} +(-5.90655 + 0.254478i) q^{90} +(1.07288 + 0.287476i) q^{91} +(3.27588 + 4.68993i) q^{92} +(7.90887 - 2.11917i) q^{93} +(15.6624 + 3.48173i) q^{94} +(16.3939 - 7.95527i) q^{95} +(1.71658 - 5.39012i) q^{96} +(-8.63993 + 14.9648i) q^{97} +(-5.54715 + 6.04666i) q^{98} +(-1.34761 + 5.02934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 24 q^{8}+O(q^{10}) \) 320 * q + 24 * q^8	\( 320 q + 24 q^{8} - 8 q^{10} + 16 q^{15} - 4 q^{16} + 8 q^{19} - 8 q^{24} - 40 q^{26} - 40 q^{28} + 96 q^{31} - 60 q^{32} + 28 q^{34} - 48 q^{35} - 4 q^{36} - 16 q^{38} + 20 q^{40} + 56 q^{44} - 104 q^{46} - 320 q^{49} + 88 q^{50} + 8 q^{51} + 16 q^{52} + 4 q^{54} + 56 q^{56} + 56 q^{58} - 48 q^{60} - 32 q^{61} - 24 q^{62} - 72 q^{64} - 48 q^{66} + 48 q^{67} + 32 q^{68} + 64 q^{69} + 48 q^{70} + 40 q^{74} - 56 q^{76} - 24 q^{78} + 48 q^{79} + 16 q^{80} + 160 q^{81} + 80 q^{82} + 80 q^{83} - 16 q^{85} - 64 q^{86} + 24 q^{92} + 128 q^{94} + 48 q^{95} + 40 q^{96} + 4 q^{98}+O(q^{100}) \) 320 * q + 24 * q^8 - 8 * q^10 + 16 * q^15 - 4 * q^16 + 8 * q^19 - 8 * q^24 - 40 * q^26 - 40 * q^28 + 96 * q^31 - 60 * q^32 + 28 * q^34 - 48 * q^35 - 4 * q^36 - 16 * q^38 + 20 * q^40 + 56 * q^44 - 104 * q^46 - 320 * q^49 + 88 * q^50 + 8 * q^51 + 16 * q^52 + 4 * q^54 + 56 * q^56 + 56 * q^58 - 48 * q^60 - 32 * q^61 - 24 * q^62 - 72 * q^64 - 48 * q^66 + 48 * q^67 + 32 * q^68 + 64 * q^69 + 48 * q^70 + 40 * q^74 - 56 * q^76 - 24 * q^78 + 48 * q^79 + 16 * q^80 + 160 * q^81 + 80 * q^82 + 80 * q^83 - 16 * q^85 - 64 * q^86 + 24 * q^92 + 128 * q^94 + 48 * q^95 + 40 * q^96 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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