LMFDB - Embedded newform 336.2.u.a.139.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(139,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.u (of order $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.12
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618822 + 1.27164i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.23412 - 1.57383i) q^{4} +(-1.80101 + 1.80101i) q^{5} +(0.461610 + 1.33676i) q^{6} +(-1.67026 - 2.05189i) q^{7} +(2.76504 - 0.595430i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.618822 + 1.27164i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.23412 - 1.57383i) q^{4} +(-1.80101 + 1.80101i) q^{5} +(0.461610 + 1.33676i) q^{6} +(-1.67026 - 2.05189i) q^{7} +(2.76504 - 0.595430i) q^{8} -1.00000i q^{9} +(-1.17573 - 3.40473i) q^{10} +(-4.52322 + 4.52322i) q^{11} +(-1.98552 - 0.240213i) q^{12} +(-2.59667 - 2.59667i) q^{13} +(3.64285 - 0.854209i) q^{14} +2.54701i q^{15} +(-0.953897 + 3.88460i) q^{16} -6.20372i q^{17} +(1.27164 + 0.618822i) q^{18} +(-1.43485 + 1.43485i) q^{19} +(5.05715 + 0.611826i) q^{20} +(-2.63195 - 0.269853i) q^{21} +(-2.95283 - 8.55096i) q^{22} -3.79802 q^{23} +(1.53415 - 2.37621i) q^{24} -1.48727i q^{25} +(4.90889 - 1.69514i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.16803 + 5.16098i) q^{28} +(-1.50697 + 1.50697i) q^{29} +(-3.23887 - 1.57615i) q^{30} -4.03614 q^{31} +(-4.34950 - 3.61688i) q^{32} +6.39680i q^{33} +(7.88887 + 3.83899i) q^{34} +(6.70362 + 0.687319i) q^{35} +(-1.57383 + 1.23412i) q^{36} +(-1.57956 - 1.57956i) q^{37} +(-0.936693 - 2.71253i) q^{38} -3.67224 q^{39} +(-3.90749 + 6.05225i) q^{40} +9.26889 q^{41} +(1.97186 - 3.17990i) q^{42} +(4.81028 - 4.81028i) q^{43} +(12.7010 + 1.53660i) q^{44} +(1.80101 + 1.80101i) q^{45} +(2.35030 - 4.82970i) q^{46} -4.48761 q^{47} +(2.07232 + 3.42133i) q^{48} +(-1.42048 + 6.85436i) q^{49} +(1.89127 + 0.920357i) q^{50} +(-4.38669 - 4.38669i) q^{51} +(-0.882121 + 7.29132i) q^{52} +(6.91789 + 6.91789i) q^{53} +(1.33676 - 0.461610i) q^{54} -16.2927i q^{55} +(-5.84009 - 4.67903i) q^{56} +2.02919i q^{57} +(-0.983772 - 2.84886i) q^{58} +(0.516751 + 0.516751i) q^{59} +(4.00857 - 3.14332i) q^{60} +(-6.02748 - 6.02748i) q^{61} +(2.49765 - 5.13250i) q^{62} +(-2.05189 + 1.67026i) q^{63} +(7.29093 - 3.29278i) q^{64} +9.35325 q^{65} +(-8.13441 - 3.95848i) q^{66} +(6.19917 + 6.19917i) q^{67} +(-9.76361 + 7.65613i) q^{68} +(-2.68560 + 2.68560i) q^{69} +(-5.02236 + 8.09924i) q^{70} -10.5595 q^{71} +(-0.595430 - 2.76504i) q^{72} +3.85786 q^{73} +(2.98609 - 1.03116i) q^{74} +(-1.05166 - 1.05166i) q^{75} +(4.02900 + 0.487437i) q^{76} +(16.8361 + 1.72620i) q^{77} +(2.27246 - 4.66976i) q^{78} +5.09974i q^{79} +(-5.27822 - 8.71417i) q^{80} -1.00000 q^{81} +(-5.73579 + 11.7867i) q^{82} +(-10.0631 + 10.0631i) q^{83} +(2.82344 + 4.47528i) q^{84} +(11.1730 + 11.1730i) q^{85} +(3.14023 + 9.09364i) q^{86} +2.13118i q^{87} +(-9.81364 + 15.2002i) q^{88} +0.264516 q^{89} +(-3.40473 + 1.17573i) q^{90} +(-0.990965 + 9.66517i) q^{91} +(4.68721 + 5.97745i) q^{92} +(-2.85398 + 2.85398i) q^{93} +(2.77703 - 5.70661i) q^{94} -5.16836i q^{95} +(-5.63308 + 0.518040i) q^{96} +7.14810i q^{97} +(-7.83723 - 6.04796i) q^{98} +(4.52322 + 4.52322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−0.618822	+	1.27164i	−0.437573	+	0.899183i
$2$	−0.618822	+	1.27164i	−0.437573	+	0.899183i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.23412	−	1.57383i	−0.617060	−	0.786916i
$5$	−1.80101	+	1.80101i	−0.805436	+	0.805436i	−0.983939	−	0.178503i	$-0.942875\pi$
$5$	−1.80101	+	1.80101i	−0.805436	+	0.805436i	0.178503	+	0.983939i	$0.442875\pi$
$6$	0.461610	+	1.33676i	0.188451	+	0.545728i
$7$	−1.67026	−	2.05189i	−0.631298	−	0.775540i
$7$	−1.67026	−	2.05189i	−0.631298	−	0.775540i
$8$	2.76504	−	0.595430i	0.977590	−	0.210516i
$9$		−	1.00000i		−	0.333333i
$10$	−1.17573	−	3.40473i	−0.371797	−	1.07667i
$11$	−4.52322	+	4.52322i	−1.36380	+	1.36380i	−0.494789	+	0.869013i	$0.664755\pi$
$11$	−4.52322	+	4.52322i	−1.36380	+	1.36380i	−0.869013	+	0.494789i	$0.835245\pi$
$12$	−1.98552	−	0.240213i	−0.573171	−	0.0693436i
$13$	−2.59667	−	2.59667i	−0.720186	−	0.720186i	0.248457	−	0.968643i	$-0.420077\pi$
$13$	−2.59667	−	2.59667i	−0.720186	−	0.720186i	−0.968643	+	0.248457i	$0.920077\pi$
$14$	3.64285	−	0.854209i	0.973592	−	0.228297i
$15$			2.54701i			0.657636i
$16$	−0.953897	+	3.88460i	−0.238474	+	0.971149i
$17$		−	6.20372i		−	1.50462i	−0.658808	−	0.752311i	$-0.728939\pi$
$17$		−	6.20372i		−	1.50462i	0.658808	−	0.752311i	$-0.271061\pi$
$18$	1.27164	+	0.618822i	0.299728	+	0.145858i
$19$	−1.43485	+	1.43485i	−0.329178	+	0.329178i	−0.852274	−	0.523096i	$-0.824777\pi$
$19$	−1.43485	+	1.43485i	−0.329178	+	0.329178i	0.523096	+	0.852274i	$0.324777\pi$
$20$	5.05715	+	0.611826i	1.13081	+	0.136808i
$21$	−2.63195	−	0.269853i	−0.574339	−	0.0588867i
$22$	−2.95283	−	8.55096i	−0.629545	−	1.82307i
$23$	−3.79802			−0.791942			−0.395971	−	0.918263i	$-0.629592\pi$
$23$	−3.79802			−0.791942			−0.395971	+	0.918263i	$0.629592\pi$
$24$	1.53415	−	2.37621i	0.313157	−	0.485043i
$25$		−	1.48727i		−	0.297455i
$26$	4.90889	−	1.69514i	0.962713	−	0.332445i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.16803	+	5.16098i	−0.220737	+	0.975333i
$29$	−1.50697	+	1.50697i	−0.279837	+	0.279837i	−0.833044	−	0.553207i	$-0.813404\pi$
$29$	−1.50697	+	1.50697i	−0.279837	+	0.279837i	0.553207	+	0.833044i	$0.313404\pi$
$30$	−3.23887	−	1.57615i	−0.591335	−	0.287764i
$31$	−4.03614			−0.724912			−0.362456	−	0.932001i	$-0.618062\pi$
$31$	−4.03614			−0.724912			−0.362456	+	0.932001i	$0.618062\pi$
$32$	−4.34950	−	3.61688i	−0.768891	−	0.639380i
$33$			6.39680i			1.11354i
$34$	7.88887	+	3.83899i	1.35293	+	0.658382i
$35$	6.70362	+	0.687319i	1.13312	+	0.116178i
$36$	−1.57383	+	1.23412i	−0.262305	+	0.205687i
$37$	−1.57956	−	1.57956i	−0.259678	−	0.259678i	0.565245	−	0.824923i	$-0.308782\pi$
$37$	−1.57956	−	1.57956i	−0.259678	−	0.259678i	−0.824923	+	0.565245i	$0.808782\pi$
$38$	−0.936693	−	2.71253i	−0.151952	−	0.440030i
$39$	−3.67224			−0.588029
$40$	−3.90749	+	6.05225i	−0.617829	+	0.956944i
$41$	9.26889			1.44756			0.723779	−	0.690032i	$-0.242404\pi$
$41$	9.26889			1.44756			0.723779	+	0.690032i	$0.242404\pi$
$42$	1.97186	−	3.17990i	0.304265	−	0.490669i
$43$	4.81028	−	4.81028i	0.733561	−	0.733561i	−0.237762	−	0.971323i	$-0.576414\pi$
$43$	4.81028	−	4.81028i	0.733561	−	0.733561i	0.971323	+	0.237762i	$0.0764139\pi$
$44$	12.7010	+	1.53660i	1.91475	+	0.231651i
$45$	1.80101	+	1.80101i	0.268479	+	0.268479i
$46$	2.35030	−	4.82970i	0.346532	−	0.712100i
$47$	−4.48761			−0.654585			−0.327292	−	0.944923i	$-0.606136\pi$
$47$	−4.48761			−0.654585			−0.327292	+	0.944923i	$0.606136\pi$
$48$	2.07232	+	3.42133i	0.299113	+	0.493827i
$49$	−1.42048	+	6.85436i	−0.202926	+	0.979194i
$50$	1.89127	+	0.920357i	0.267466	+	0.130158i
$51$	−4.38669	−	4.38669i	−0.614260	−	0.614260i
$52$	−0.882121	+	7.29132i	−0.122328	+	1.01112i
$53$	6.91789	+	6.91789i	0.950245	+	0.950245i	0.998820	−	0.0485746i	$-0.0154679\pi$
$53$	6.91789	+	6.91789i	0.950245	+	0.950245i	−0.0485746	+	0.998820i	$0.515468\pi$
$54$	1.33676	−	0.461610i	0.181909	−	0.0628172i
$55$		−	16.2927i		−	2.19691i
$56$	−5.84009	−	4.67903i	−0.780415	−	0.625262i
$57$			2.02919i			0.268772i
$58$	−0.983772	−	2.84886i	−0.129176	−	0.374074i
$59$	0.516751	+	0.516751i	0.0672753	+	0.0672753i	0.739944	−	0.672669i	$-0.234852\pi$
$59$	0.516751	+	0.516751i	0.0672753	+	0.0672753i	−0.672669	+	0.739944i	$0.734852\pi$
$60$	4.00857	−	3.14332i	0.517504	−	0.405801i
$61$	−6.02748	−	6.02748i	−0.771739	−	0.771739i	0.206671	−	0.978410i	$-0.433737\pi$
$61$	−6.02748	−	6.02748i	−0.771739	−	0.771739i	−0.978410	+	0.206671i	$0.933737\pi$
$62$	2.49765	−	5.13250i	0.317202	−	0.651828i
$63$	−2.05189	+	1.67026i	−0.258513	+	0.210433i
$64$	7.29093	−	3.29278i	0.911366	−	0.411598i
$65$	9.35325			1.16013
$66$	−8.13441	−	3.95848i	−1.00128	−	0.487255i
$67$	6.19917	+	6.19917i	0.757349	+	0.757349i	0.975839	−	0.218490i	$-0.0701132\pi$
$67$	6.19917	+	6.19917i	0.757349	+	0.757349i	−0.218490	+	0.975839i	$0.570113\pi$
$68$	−9.76361	+	7.65613i	−1.18401	+	0.928442i
$69$	−2.68560	+	2.68560i	−0.323309	+	0.323309i
$70$	−5.02236	+	8.09924i	−0.600287	+	0.968044i
$71$	−10.5595			−1.25318			−0.626590	−	0.779349i	$-0.715550\pi$
$71$	−10.5595			−1.25318			−0.626590	+	0.779349i	$0.715550\pi$
$72$	−0.595430	−	2.76504i	−0.0701721	−	0.325863i
$73$	3.85786			0.451529			0.225764	−	0.974182i	$-0.427512\pi$
$73$	3.85786			0.451529			0.225764	+	0.974182i	$0.427512\pi$
$74$	2.98609	−	1.03116i	0.347126	−	0.119870i
$75$	−1.05166	−	1.05166i	−0.121435	−	0.121435i
$76$	4.02900	+	0.487437i	0.462157	+	0.0559129i
$77$	16.8361	+	1.72620i	1.91865	+	0.196718i
$78$	2.27246	−	4.66976i	0.257306	−	0.528746i
$79$			5.09974i			0.573765i	0.957966	+	0.286883i	$0.0926190\pi$
$79$			5.09974i			0.573765i	−0.957966	+	0.286883i	$0.907381\pi$
$80$	−5.27822	−	8.71417i	−0.590123	−	0.974274i
$81$	−1.00000			−0.111111
$82$	−5.73579	+	11.7867i	−0.633412	+	1.30162i
$83$	−10.0631	+	10.0631i	−1.10457	+	1.10457i	−0.110721	+	0.993851i	$0.535316\pi$
$83$	−10.0631	+	10.0631i	−1.10457	+	1.10457i	−0.993851	+	0.110721i	$0.964684\pi$
$84$	2.82344	+	4.47528i	0.308063	+	0.488294i
$85$	11.1730	+	11.1730i	1.21188	+	1.21188i
$86$	3.14023	+	9.09364i	0.338619	+	0.980592i
$87$			2.13118i			0.228486i
$88$	−9.81364	+	15.2002i	−1.04614	+	1.62034i
$89$	0.264516			0.0280386			0.0140193	−	0.999902i	$-0.495537\pi$
$89$	0.264516			0.0280386			0.0140193	+	0.999902i	$0.495537\pi$
$90$	−3.40473	+	1.17573i	−0.358890	+	0.123932i
$91$	−0.990965	+	9.66517i	−0.103881	+	1.01319i
$92$	4.68721	+	5.97745i	0.488675	+	0.623192i
$93$	−2.85398	+	2.85398i	−0.295944	+	0.295944i
$94$	2.77703	−	5.70661i	0.286429	−	0.588591i
$95$		−	5.16836i		−	0.530263i
$96$	−5.63308	+	0.518040i	−0.574924	+	0.0528723i
$97$			7.14810i			0.725780i	0.931832	+	0.362890i	$0.118210\pi$
$97$			7.14810i			0.725780i	−0.931832	+	0.362890i	$0.881790\pi$
$98$	−7.83723	−	6.04796i	−0.791680	−	0.610936i
$99$	4.52322	+	4.52322i	0.454601	+	0.454601i
$100$	−2.34072	+	1.83547i	−0.234072	+	0.183547i
$101$	−0.548004	+	0.548004i	−0.0545285	+	0.0545285i	−0.733845	−	0.679317i	$-0.762276\pi$
$101$	−0.548004	+	0.548004i	−0.0545285	+	0.0545285i	0.679317	+	0.733845i	$0.262276\pi$
$102$	8.29286	−	2.86370i	0.821115	−	0.283548i
$103$			2.18981i			0.215768i	0.994163	+	0.107884i	$0.0344075\pi$
$103$			2.18981i			0.215768i	−0.994163	+	0.107884i	$0.965592\pi$
$104$	−8.72603	−	5.63376i	−0.855658	−	0.552436i
$105$	5.22618	−	4.25417i	0.510023	−	0.415164i
$106$	−13.0780	+	4.51610i	−1.27025	+	0.438643i
$107$	5.39210	−	5.39210i	0.521274	−	0.521274i	−0.396682	−	0.917956i	$-0.629838\pi$
$107$	5.39210	−	5.39210i	0.521274	−	0.521274i	0.917956	+	0.396682i	$0.129838\pi$
$108$	−0.240213	+	1.98552i	−0.0231145	+	0.191057i
$109$	0.576562	−	0.576562i	0.0552247	−	0.0552247i	−0.678955	−	0.734180i	$-0.737567\pi$
$109$	0.576562	−	0.576562i	0.0552247	−	0.0552247i	0.734180	+	0.678955i	$0.237567\pi$
$110$	20.7184	+	10.0823i	1.97543	+	0.961309i
$111$	−2.23384			−0.212026
$112$	9.56400	−	4.53098i	0.903713	−	0.428138i
$113$	−11.7404			−1.10444			−0.552221	−	0.833698i	$-0.686220\pi$
$113$	−11.7404			−1.10444			−0.552221	+	0.833698i	$0.686220\pi$
$114$	−2.58039	−	1.25570i	−0.241676	−	0.117608i
$115$	6.84027	−	6.84027i	0.637858	−	0.637858i
$116$	4.23150	+	0.511936i	0.392885	+	0.0475321i
$117$	−2.59667	+	2.59667i	−0.240062	+	0.240062i
$118$	−0.976897	+	0.337343i	−0.0899306	+	0.0310549i
$119$	−12.7293	+	10.3618i	−1.16690	+	0.949865i
$120$	1.51657	+	7.04260i	0.138443	+	0.642898i
$121$		−	29.9191i		−	2.71991i
$122$	11.3947	−	3.93483i	1.03163	−	0.356242i
$123$	6.55410	−	6.55410i	0.590963	−	0.590963i
$124$	4.98108	+	6.35220i	0.447314	+	0.570445i
$125$	−6.32646	−	6.32646i	−0.565855	−	0.565855i
$126$	−0.854209	−	3.64285i	−0.0760989	−	0.324531i
$127$		−	12.6059i		−	1.11859i	−0.828969	−	0.559295i	$-0.811072\pi$
$127$		−	12.6059i		−	1.11859i	0.828969	−	0.559295i	$-0.188928\pi$
$128$	−0.324561	+	11.3091i	−0.0286874	+	0.999588i
$129$		−	6.80277i		−	0.598950i
$130$	−5.78799	+	11.8939i	−0.507640	+	1.04317i
$131$	−5.45251	+	5.45251i	−0.476388	+	0.476388i	−0.903975	−	0.427586i	$-0.859364\pi$
$131$	−5.45251	+	5.45251i	−0.476388	+	0.476388i	0.427586	+	0.903975i	$0.359364\pi$
$132$	10.0675	−	7.89442i	0.876263	−	0.687121i
$133$	5.34073	+	0.547582i	0.463100	+	0.0474814i
$134$	−11.7193	+	4.04691i	−1.01239	+	0.349600i
$135$	2.54701			0.219212
$136$	−3.69388	−	17.1535i	−0.316748	−	1.47090i
$137$		−	13.0524i		−	1.11515i	−0.830128	−	0.557573i	$-0.811733\pi$
$137$		−	13.0524i		−	1.11515i	0.830128	−	0.557573i	$-0.188267\pi$
$138$	−1.75320	−	5.07702i	−0.149243	−	0.432185i
$139$	−13.9478	−	13.9478i	−1.18304	−	1.18304i	−0.978953	−	0.204085i	$-0.934578\pi$
$139$	−13.9478	−	13.9478i	−1.18304	−	1.18304i	−0.204085	−	0.978953i	$-0.565422\pi$
$140$	−7.19134	−	11.3986i	−0.607779	−	0.963358i
$141$	−3.17322	+	3.17322i	−0.267233	+	0.267233i
$142$	6.53443	−	13.4278i	0.548357	−	1.12684i
$143$	23.4906			1.96438
$144$	3.88460	+	0.953897i	0.323716	+	0.0794914i
$145$		−	5.42813i		−	0.450782i
$146$	−2.38733	+	4.90580i	−0.197577	+	0.406007i
$147$	3.84233	+	5.85120i	0.316910	+	0.482598i
$148$	−0.536597	+	4.43533i	−0.0441080	+	0.364582i
$149$	6.12637	+	6.12637i	0.501892	+	0.501892i	0.912025	−	0.410134i	$-0.134518\pi$
$149$	6.12637	+	6.12637i	0.501892	+	0.501892i	−0.410134	+	0.912025i	$0.634518\pi$
$150$	1.98812	−	0.686540i	0.162329	−	0.0560558i
$151$	7.95142			0.647077			0.323539	−	0.946215i	$-0.395127\pi$
$151$	7.95142			0.647077			0.323539	+	0.946215i	$0.395127\pi$
$152$	−3.11307	+	4.82178i	−0.252504	+	0.391098i
$153$	−6.20372			−0.501541
$154$	−12.6136	+	20.3412i	−1.01643	+	1.63914i
$155$	7.26912	−	7.26912i	0.583870	−	0.583870i
$156$	4.53199	+	5.77949i	0.362849	+	0.462730i
$157$	11.9223	+	11.9223i	0.951506	+	0.951506i	0.998877	−	0.0473717i	$-0.0150845\pi$
$157$	11.9223	+	11.9223i	0.951506	+	0.951506i	−0.0473717	+	0.998877i	$0.515085\pi$
$158$	−6.48501	−	3.15583i	−0.515920	−	0.251064i
$159$	9.78337			0.775872
$160$	14.3475	−	1.31945i	1.13427	−	0.104312i
$161$	6.34367	+	7.79311i	0.499951	+	0.614183i
$162$	0.618822	−	1.27164i	0.0486192	−	0.0999092i
$163$	−1.04533	−	1.04533i	−0.0818768	−	0.0818768i	0.664982	−	0.746859i	$-0.268439\pi$
$163$	−1.04533	−	1.04533i	−0.0818768	−	0.0818768i	−0.746859	+	0.664982i	$0.768439\pi$
$164$	−11.4389	−	14.5877i	−0.893230	−	1.13911i
$165$	−11.5207	−	11.5207i	−0.896885	−	0.896885i
$166$	−6.56937	−	19.0239i	−0.509882	−	1.47654i
$167$		−	15.4439i		−	1.19508i	−0.801839	−	0.597541i	$-0.796145\pi$
$167$		−	15.4439i		−	1.19508i	0.801839	−	0.597541i	$-0.203855\pi$
$168$	−7.43814	+	0.820990i	−0.573865	+	0.0633408i
$169$			0.485362i			0.0373356i
$170$	−21.1220	+	7.29387i	−1.61998	+	0.559415i
$171$	1.43485	+	1.43485i	0.109726	+	0.109726i
$172$	−13.5070	−	1.63411i	−1.02990	−	0.124600i
$173$	−14.6842	−	14.6842i	−1.11642	−	1.11642i	−0.992263	−	0.124152i	$-0.960379\pi$
$173$	−14.6842	−	14.6842i	−1.11642	−	1.11642i	−0.124152	−	0.992263i	$-0.539621\pi$
$174$	−2.71008	−	1.31882i	−0.205451	−	0.0999793i
$175$	−3.05172	+	2.48413i	−0.230688	+	0.187783i
$176$	−13.2562	−	21.8856i	−0.999223	−	1.64969i
$177$	0.730797			0.0549300
$178$	−0.163688	+	0.336368i	−0.0122689	+	0.0252118i
$179$	−16.9529	−	16.9529i	−1.26712	−	1.26712i	−0.947569	−	0.319552i	$-0.896468\pi$
$179$	−16.9529	−	16.9529i	−1.26712	−	1.26712i	−0.319552	−	0.947569i	$-0.603532\pi$
$180$	0.611826	−	5.05715i	0.0456028	−	0.376938i
$181$	0.938465	−	0.938465i	0.0697555	−	0.0697555i	−0.671368	−	0.741124i	$-0.734293\pi$
$181$	0.938465	−	0.938465i	0.0697555	−	0.0697555i	0.741124	+	0.671368i	$0.234293\pi$
$182$	−11.6774	−	7.24116i	−0.865583	−	0.536751i
$183$	−8.52414			−0.630122
$184$	−10.5017	+	2.26146i	−0.774195	+	0.166717i
$185$	5.68961			0.418308
$186$	−1.86312	−	5.39533i	−0.136611	−	0.395605i
$187$	28.0608	+	28.0608i	2.05201	+	2.05201i
$188$	5.53824	+	7.06274i	0.403918	+	0.515103i
$189$	−0.269853	+	2.63195i	−0.0196289	+	0.191446i
$190$	6.57228	+	3.19830i	0.476803	+	0.232029i
$191$			17.1005i			1.23735i	0.785646	+	0.618676i	$0.212330\pi$
$191$			17.1005i			1.23735i	−0.785646	+	0.618676i	$0.787670\pi$
$192$	2.82711	−	7.48381i	0.204029	−	0.540098i
$193$	5.76603			0.415048			0.207524	−	0.978230i	$-0.433460\pi$
$193$	5.76603			0.415048			0.207524	+	0.978230i	$0.433460\pi$
$194$	−9.08979	−	4.42340i	−0.652609	−	0.317582i
$195$	6.61374	−	6.61374i	0.473620	−	0.473620i
$196$	12.5407	−	6.22350i	0.895761	−	0.444536i
$197$	−1.62195	−	1.62195i	−0.115559	−	0.115559i	0.646963	−	0.762522i	$-0.276039\pi$
$197$	−1.62195	−	1.62195i	−0.115559	−	0.115559i	−0.762522	+	0.646963i	$0.776039\pi$
$198$	−8.55096	+	2.95283i	−0.607690	+	0.209848i
$199$		−	22.0946i		−	1.56624i	−0.621868	−	0.783122i	$-0.713626\pi$
$199$		−	22.0946i		−	1.56624i	0.621868	−	0.783122i	$-0.286374\pi$
$200$	−0.885568	−	4.11237i	−0.0626191	−	0.290789i
$201$	8.76695			0.618373
$202$	−0.357745	−	1.03598i	−0.0251709	−	0.0728912i
$203$	5.60915	+	0.575104i	0.393685	+	0.0403644i
$204$	−1.49021	+	12.3176i	−0.104336	+	0.862406i
$205$	−16.6934	+	16.6934i	−1.16592	+	1.16592i
$206$	−2.78464	−	1.35510i	−0.194015	−	0.0944142i
$207$			3.79802i			0.263981i
$208$	12.5640	−	7.61005i	0.871154	−	0.527662i
$209$		−	12.9803i		−	0.897866i
$210$	2.17568	+	9.27838i	0.150136	+	0.640269i
$211$	3.04584	+	3.04584i	0.209684	+	0.209684i	0.804133	−	0.594449i	$-0.202630\pi$
$211$	3.04584	+	3.04584i	0.209684	+	0.209684i	−0.594449	+	0.804133i	$0.702630\pi$
$212$	2.35009	−	19.4251i	0.161405	−	1.33412i
$213$	−7.46668	+	7.46668i	−0.511608	+	0.511608i
$214$	3.52005	+	10.1935i	0.240625	+	0.696817i
$215$			17.3267i			1.18167i
$216$	−2.37621	−	1.53415i	−0.161681	−	0.104386i
$217$	6.74139	+	8.28170i	0.457635	+	0.562198i
$218$	0.376389	+	1.08997i	0.0254923	+	0.0738219i
$219$	2.72792	−	2.72792i	0.184336	−	0.184336i
$220$	−25.6420	+	20.1072i	−1.72879	+	1.35563i
$221$	−16.1090	+	16.1090i	−1.08361	+	1.08361i
$222$	1.38235	−	2.84063i	0.0927770	−	0.190651i
$223$	−8.93656			−0.598436			−0.299218	−	0.954185i	$-0.596726\pi$
$223$	−8.93656			−0.598436			−0.299218	+	0.954185i	$0.596726\pi$
$224$	−0.156646	+	14.9658i	−0.0104664	+	0.999945i
$225$	−1.48727			−0.0991516
$226$	7.26520	−	14.9295i	0.483274	−	0.993096i
$227$	−17.3870	+	17.3870i	−1.15402	+	1.15402i	−0.168277	+	0.985740i	$0.553820\pi$
$227$	−17.3870	+	17.3870i	−1.15402	+	1.15402i	−0.985740	+	0.168277i	$0.946180\pi$
$228$	3.19360	−	2.50426i	0.211501	−	0.165849i
$229$	7.54281	−	7.54281i	0.498443	−	0.498443i	−0.412510	−	0.910953i	$-0.635348\pi$
$229$	7.54281	−	7.54281i	0.498443	−	0.498443i	0.910953	+	0.412510i	$0.135348\pi$
$230$	4.46543	+	12.9312i	0.294442	+	0.852661i
$231$	13.1255	−	10.6843i	0.863595	−	0.702975i
$232$	−3.26954	+	5.06413i	−0.214656	+	0.332476i
$233$			21.1778i			1.38741i	0.720262	+	0.693703i	$0.244022\pi$
$233$			21.1778i			1.38741i	−0.720262	+	0.693703i	$0.755978\pi$
$234$	−1.69514	−	4.90889i	−0.110815	−	0.320904i
$235$	8.08222	−	8.08222i	0.527226	−	0.527226i
$236$	0.175547	−	1.45101i	0.0114271	−	0.0944529i
$237$	3.60606	+	3.60606i	0.234239	+	0.234239i
$238$	−5.29927	−	22.5992i	−0.343501	−	1.46489i
$239$			1.99595i			0.129108i	0.997914	+	0.0645538i	$0.0205624\pi$
$239$			1.99595i			0.129108i	−0.997914	+	0.0645538i	$0.979438\pi$
$240$	−9.89411	−	2.42959i	−0.638662	−	0.156829i
$241$		−	1.36012i		−	0.0876132i	−0.999040	−	0.0438066i	$-0.986051\pi$
$241$		−	1.36012i		−	0.0876132i	0.999040	−	0.0438066i	$-0.0139485\pi$
$242$	38.0462	+	18.5146i	2.44570	+	1.19016i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−2.04761	+	16.9249i	−0.131085	+	1.08350i
$245$	−9.78647	−	14.9031i	−0.625235	−	0.952122i
$246$	4.27861	+	12.3902i	0.272794	+	0.789973i
$247$	7.45167			0.474138
$248$	−11.1601	+	2.40324i	−0.708667	+	0.152606i
$249$			14.2314i			0.901880i
$250$	11.9599	−	4.13001i	0.756410	−	0.261204i
$251$	−0.580793	−	0.580793i	−0.0366593	−	0.0366593i	0.688540	−	0.725199i	$-0.258252\pi$
$251$	−0.580793	−	0.580793i	−0.0366593	−	0.0366593i	−0.725199	+	0.688540i	$0.758252\pi$
$252$	5.16098	+	1.16803i	0.325111	+	0.0735789i
$253$	17.1793	−	17.1793i	1.08005	−	1.08005i
$254$	16.0301	+	7.80079i	1.00582	+	0.489465i
$255$	15.8009			0.989494
$256$	−14.1802	−	7.41101i	−0.886260	−	0.463188i
$257$		−	18.3155i		−	1.14249i	−0.820779	−	0.571246i	$-0.806460\pi$
$257$		−	18.3155i		−	1.14249i	0.820779	−	0.571246i	$-0.193540\pi$
$258$	8.65065	+	4.20970i	0.538566	+	0.262084i
$259$	−0.602807	+	5.87935i	−0.0374566	+	0.365325i
$260$	−11.5430	−	14.7204i	−0.715868	−	0.912923i
$261$	1.50697	+	1.50697i	0.0932790	+	0.0932790i
$262$	−3.55948	−	10.3077i	−0.219906	−	0.636815i
$263$	2.28033			0.140611			0.0703055	−	0.997526i	$-0.477603\pi$
$263$	2.28033			0.140611			0.0703055	+	0.997526i	$0.477603\pi$
$264$	3.80885	+	17.6874i	0.234418	+	1.08859i
$265$	−24.9184			−1.53072
$266$	−4.00128	+	6.45261i	−0.245334	+	0.395635i
$267$	0.187041	−	0.187041i	0.0114467	−	0.0114467i
$268$	2.10594	−	17.4070i	0.128641	−	1.06330i
$269$	−5.53677	−	5.53677i	−0.337583	−	0.337583i	0.517874	−	0.855457i	$-0.326724\pi$
$269$	−5.53677	−	5.53677i	−0.337583	−	0.337583i	−0.855457	+	0.517874i	$0.826724\pi$
$270$	−1.57615	+	3.23887i	−0.0959212	+	0.197112i
$271$	−17.1905			−1.04425			−0.522124	−	0.852869i	$-0.674860\pi$
$271$	−17.1905			−1.04425			−0.522124	+	0.852869i	$0.674860\pi$
$272$	24.0989	+	5.91771i	1.46121	+	0.358814i
$273$	6.13359	+	7.53503i	0.371222	+	0.456041i
$274$	16.5980	+	8.07713i	1.00272	+	0.487958i
$275$	6.72727	+	6.72727i	0.405669	+	0.405669i
$276$	7.54105	+	0.912334i	0.453918	+	0.0549161i
$277$	−1.37433	−	1.37433i	−0.0825758	−	0.0825758i	0.664612	−	0.747188i	$-0.268597\pi$
$277$	−1.37433	−	1.37433i	−0.0825758	−	0.0825758i	−0.747188	+	0.664612i	$0.768597\pi$
$278$	26.3678	−	9.10534i	1.58143	−	0.546102i
$279$			4.03614i			0.241637i
$280$	18.9450	−	2.09107i	1.13218	−	0.124965i
$281$		−	14.2452i		−	0.849798i	−0.905241	−	0.424899i	$-0.860310\pi$
$281$		−	14.2452i		−	0.849798i	0.905241	−	0.424899i	$-0.139690\pi$
$282$	−2.07152	−	5.99883i	−0.123357	−	0.357225i
$283$	4.98832	+	4.98832i	0.296525	+	0.296525i	0.839651	−	0.543126i	$-0.182760\pi$
$283$	4.98832	+	4.98832i	0.296525	+	0.296525i	−0.543126	+	0.839651i	$0.682760\pi$
$284$	13.0317	+	16.6188i	0.773287	+	0.986147i
$285$	−3.65459	−	3.65459i	−0.216479	−	0.216479i
$286$	−14.5365	+	29.8715i	−0.859561	+	1.76634i
$287$	−15.4814	−	19.0187i	−0.913840	−	1.12264i
$288$	−3.61688	+	4.34950i	−0.213127	+	0.256297i
$289$	−21.4861			−1.26389
$290$	6.90261	+	3.35904i	0.405335	+	0.197250i
$291$	5.05447	+	5.05447i	0.296298	+	0.296298i
$292$	−4.76106	−	6.07163i	−0.278620	−	0.355315i
$293$	−19.4035	+	19.4035i	−1.13356	+	1.13356i	−0.143982	+	0.989580i	$0.545991\pi$
$293$	−19.4035	+	19.4035i	−1.13356	+	1.13356i	−0.989580	+	0.143982i	$0.954009\pi$
$294$	−9.81831	+	1.26520i	−0.572616	+	0.0737882i
$295$	−1.86135			−0.108372
$296$	−5.30807	−	3.42704i	−0.308525	−	0.199192i
$297$	6.39680			0.371180
$298$	−11.5816	+	3.99939i	−0.670907	+	0.231678i
$299$	9.86219	+	9.86219i	0.570345	+	0.570345i
$300$	−0.357263	+	2.95301i	−0.0206266	+	0.170492i
$301$	−17.9046	−	1.83575i	−1.03200	−	0.105811i
$302$	−4.92051	+	10.1113i	−0.283143	+	0.581841i
$303$			0.774995i			0.0445223i
$304$	−4.20512	−	6.94252i	−0.241180	−	0.398181i
$305$	21.7111			1.24317
$306$	3.83899	−	7.88887i	0.219461	−	0.450977i
$307$	1.13227	−	1.13227i	0.0646220	−	0.0646220i	−0.674057	−	0.738679i	$-0.735450\pi$
$307$	1.13227	−	1.13227i	0.0646220	−	0.0646220i	0.738679	+	0.674057i	$0.235450\pi$
$308$	−18.0610	−	28.6275i	−1.02912	−	1.63120i
$309$	1.54843	+	1.54843i	0.0880869	+	0.0880869i
$310$	4.74539	+	13.7420i	0.269520	+	0.780492i
$311$			31.9613i			1.81236i	0.422894	+	0.906179i	$0.361014\pi$
$311$			31.9613i			1.81236i	−0.422894	+	0.906179i	$0.638986\pi$
$312$	−10.1539	+	2.18656i	−0.574852	+	0.123790i
$313$	−28.5000			−1.61092			−0.805459	−	0.592652i	$-0.798081\pi$
$313$	−28.5000			−1.61092			−0.805459	+	0.592652i	$0.798081\pi$
$314$	−22.5387	+	7.78308i	−1.27193	+	0.439224i
$315$	0.687319	−	6.70362i	0.0387260	−	0.377706i
$316$	8.02613	−	6.29369i	0.451505	−	0.354047i
$317$	3.11011	−	3.11011i	0.174681	−	0.174681i	−0.614351	−	0.789033i	$-0.710582\pi$
$317$	3.11011	−	3.11011i	0.174681	−	0.174681i	0.789033	+	0.614351i	$0.210582\pi$
$318$	−6.05416	+	12.4409i	−0.339500	+	0.697651i
$319$		−	13.6327i		−	0.763285i
$320$	−7.20070	+	19.0614i	−0.402531	+	1.06556i
$321$		−	7.62559i		−	0.425619i
$322$	−13.8356	+	3.24430i	−0.771028	+	0.180798i
$323$	8.90142	+	8.90142i	0.495288	+	0.495288i
$324$	1.23412	+	1.57383i	0.0685622	+	0.0874351i
$325$	−3.86195	+	3.86195i	−0.214223	+	0.214223i
$326$	1.97616	−	0.682409i	0.109449	−	0.0377951i
$327$		−	0.815382i		−	0.0450907i
$328$	25.6289	−	5.51898i	1.41512	−	0.304735i
$329$	7.49546	+	9.20806i	0.413238	+	0.507657i
$330$	21.7794	−	7.52089i	1.19892	−	0.414011i
$331$	−22.4914	+	22.4914i	−1.23624	+	1.23624i	−0.274714	+	0.961526i	$0.588583\pi$
$331$	−22.4914	+	22.4914i	−1.23624	+	1.23624i	−0.961526	+	0.274714i	$0.911417\pi$
$332$	28.2568	+	3.41858i	1.55079	+	0.187619i
$333$	−1.57956	+	1.57956i	−0.0865594	+	0.0865594i
$334$	19.6390	+	9.55699i	1.07460	+	0.522935i
$335$	−22.3295			−1.21999
$336$	3.55888	−	9.96666i	0.194153	−	0.543726i
$337$	−24.8695			−1.35473			−0.677364	−	0.735648i	$-0.736878\pi$
$337$	−24.8695			−1.35473			−0.677364	+	0.735648i	$0.736878\pi$
$338$	−0.617205	−	0.300353i	−0.0335715	−	0.0163370i
$339$	−8.30171	+	8.30171i	−0.450887	+	0.450887i
$340$	3.79560	−	31.3731i	0.205845	−	1.70145i
$341$	18.2563	−	18.2563i	0.988636	−	0.988636i
$342$	−2.71253	+	0.936693i	−0.146677	+	0.0506506i
$343$	16.4369	−	8.53388i	0.887511	−	0.460786i
$344$	10.4365	−	16.1648i	0.562696	−	0.871549i
$345$		−	9.67360i		−	0.520809i
$346$	27.7598	−	9.58604i	1.49238	−	0.515349i
$347$	−5.93378	+	5.93378i	−0.318542	+	0.318542i	−0.848207	−	0.529665i	$-0.822318\pi$
$347$	−5.93378	+	5.93378i	−0.318542	+	0.318542i	0.529665	+	0.848207i	$0.322318\pi$
$348$	3.35411	−	2.63013i	0.179799	−	0.140990i
$349$	17.9498	+	17.9498i	0.960829	+	0.960829i	0.999261	−	0.0384320i	$-0.0122363\pi$
$349$	17.9498	+	17.9498i	0.960829	+	0.960829i	−0.0384320	+	0.999261i	$0.512236\pi$
$350$	−1.27044	−	5.41791i	−0.0679080	−	0.289599i
$351$			3.67224i			0.196010i
$352$	36.0337	−	3.31380i	1.92060	−	0.176626i
$353$		−	19.0051i		−	1.01154i	−0.862668	−	0.505770i	$-0.831209\pi$
$353$		−	19.0051i		−	1.01154i	0.862668	−	0.505770i	$-0.168791\pi$
$354$	−0.452233	+	0.929308i	−0.0240359	+	0.0493922i
$355$	19.0177	−	19.0177i	1.00936	−	1.00936i
$356$	−0.326444	−	0.416303i	−0.0173015	−	0.0220640i
$357$	−1.67409	+	16.3279i	−0.0886023	+	0.864164i
$358$	32.0488	−	11.0671i	1.69383	−	0.584915i
$359$	8.22606			0.434155			0.217077	−	0.976154i	$-0.430348\pi$
$359$	8.22606			0.434155			0.217077	+	0.976154i	$0.430348\pi$
$360$	6.05225	+	3.90749i	0.318981	+	0.205943i
$361$			14.8824i			0.783284i
$362$	0.612644	+	1.77413i	0.0321998	+	0.0932461i
$363$	−21.1560	−	21.1560i	−1.11040	−	1.11040i
$364$	16.4343	−	10.3684i	0.861393	−	0.543450i
$365$	−6.94805	+	6.94805i	−0.363677	+	0.363677i
$366$	5.27492	−	10.8396i	0.275725	−	0.566595i
$367$	27.2942			1.42474			0.712372	−	0.701802i	$-0.247621\pi$
$367$	27.2942			1.42474			0.712372	+	0.701802i	$0.247621\pi$
$368$	3.62292	−	14.7538i	0.188858	−	0.769093i
$369$		−	9.26889i		−	0.482519i
$370$	−3.52085	+	7.23512i	−0.183040	+	0.376136i
$371$	2.64007	−	25.7494i	0.137066	−	1.33684i
$372$	8.01384	+	0.969533i	0.415498	+	0.0502680i
$373$	12.3883	+	12.3883i	0.641440	+	0.641440i	0.950909	−	0.309469i	$-0.100151\pi$
$373$	12.3883	+	12.3883i	0.641440	+	0.641440i	−0.309469	+	0.950909i	$0.600151\pi$
$374$	−53.0477	+	18.3185i	−2.74303	+	0.947227i
$375$	−8.94696			−0.462019
$376$	−12.4084	+	2.67206i	−0.639916	+	0.137801i
$377$	7.82619			0.403069
$378$	−3.17990	−	1.97186i	−0.163556	−	0.101422i
$379$	−2.83357	+	2.83357i	−0.145551	+	0.145551i	−0.776127	−	0.630576i	$-0.782819\pi$
$379$	−2.83357	+	2.83357i	−0.145551	+	0.145551i	0.630576	+	0.776127i	$0.282819\pi$
$380$	−8.13414	+	6.37838i	−0.417273	+	0.327204i
$381$	−8.91370	−	8.91370i	−0.456663	−	0.456663i
$382$	−21.7457	−	10.5822i	−1.11261	−	0.541431i
$383$	3.10041			0.158424			0.0792118	−	0.996858i	$-0.474760\pi$
$383$	3.10041			0.158424			0.0792118	+	0.996858i	$0.474760\pi$
$384$	7.76721	+	8.22621i	0.396369	+	0.419792i
$385$	−33.4308	+	27.2131i	−1.70379	+	1.38691i
$386$	−3.56814	+	7.33229i	−0.181614	+	0.373204i
$387$	−4.81028	−	4.81028i	−0.244520	−	0.244520i
$388$	11.2499	−	8.82162i	0.571128	−	0.447850i
$389$	−1.89523	−	1.89523i	−0.0960920	−	0.0960920i	0.657427	−	0.753519i	$-0.271645\pi$
$389$	−1.89523	−	1.89523i	−0.0960920	−	0.0960920i	−0.753519	+	0.657427i	$0.771645\pi$
$390$	4.31755	+	12.5030i	0.218628	+	0.633114i
$391$			23.5618i			1.19157i
$392$	0.153603	+	19.7984i	0.00775813	+	0.999970i
$393$			7.71102i			0.388969i
$394$	3.06623	−	1.05883i	0.154474	−	0.0533432i
$395$	−9.18468	−	9.18468i	−0.462131	−	0.462131i
$396$	1.53660	−	12.7010i	0.0772168	−	0.638249i
$397$	−16.4165	−	16.4165i	−0.823923	−	0.823923i	0.162745	−	0.986668i	$-0.447965\pi$
$397$	−16.4165	−	16.4165i	−0.823923	−	0.823923i	−0.986668	+	0.162745i	$0.947965\pi$
$398$	28.0963	+	13.6726i	1.40834	+	0.685346i
$399$	4.16366	−	3.38926i	0.208444	−	0.169675i
$400$	5.77745	+	1.41871i	0.288873	+	0.0709353i
$401$	11.6333			0.580938			0.290469	−	0.956884i	$-0.406189\pi$
$401$	11.6333			0.580938			0.290469	+	0.956884i	$0.406189\pi$
$402$	−5.42518	+	11.1484i	−0.270583	+	0.556030i
$403$	10.4805	+	10.4805i	0.522071	+	0.522071i
$404$	1.53877	+	0.186164i	0.0765567	+	0.00926201i
$405$	1.80101	−	1.80101i	0.0894929	−	0.0894929i
$406$	−4.20239	+	6.77692i	−0.208561	+	0.336333i
$407$	14.2894			0.708300
$408$	−14.7414	−	9.51742i	−0.729806	−	0.471182i
$409$	0.396994			0.0196301			0.00981504	−	0.999952i	$-0.496876\pi$
$409$	0.396994			0.0196301			0.00981504	+	0.999952i	$0.496876\pi$
$410$	−10.8977	−	31.5581i	−0.538198	−	1.55854i
$411$	−9.22947	−	9.22947i	−0.455256	−	0.455256i
$412$	3.44639	−	2.70248i	0.169791	−	0.133142i
$413$	0.197208	−	1.92342i	0.00970395	−	0.0946455i
$414$	−4.82970	−	2.35030i	−0.237367	−	0.115511i
$415$		−	36.2476i		−	1.77933i
$416$	1.90237	+	20.6860i	0.0932713	+	1.01422i
$417$	−19.7252			−0.965946
$418$	16.5062	+	8.03249i	0.807346	+	0.392882i
$419$	11.8396	−	11.8396i	0.578402	−	0.578402i	−0.356061	−	0.934463i	$-0.615880\pi$
$419$	11.8396	−	11.8396i	0.578402	−	0.578402i	0.934463	+	0.356061i	$0.115880\pi$
$420$	−13.1451	−	2.97498i	−0.641414	−	0.145164i
$421$	−1.04319	−	1.04319i	−0.0508420	−	0.0508420i	0.681229	−	0.732071i	$-0.261446\pi$
$421$	−1.04319	−	1.04319i	−0.0508420	−	0.0508420i	−0.732071	+	0.681229i	$0.761446\pi$
$422$	−5.75803	+	1.98837i	−0.280297	+	0.0967923i
$423$			4.48761i			0.218195i
$424$	23.2474	+	15.0091i	1.12899	+	0.728908i
$425$	−9.22662			−0.447557
$426$	−4.87436	−	14.1154i	−0.236164	−	0.683896i
$427$	−2.30026	+	22.4351i	−0.111318	+	1.08571i
$428$	−15.1408	−	1.83177i	−0.731857	−	0.0885418i
$429$	16.6104	−	16.6104i	0.801956	−	0.801956i
$430$	−22.0333	−	10.7222i	−1.06254	−	0.517068i
$431$			12.9393i			0.623266i	0.950202	+	0.311633i	$0.100876\pi$
$431$			12.9393i			0.623266i	−0.950202	+	0.311633i	$0.899124\pi$
$432$	3.42133	−	2.07232i	0.164609	−	0.0997044i
$433$			8.67090i			0.416697i	0.978055	+	0.208348i	$0.0668088\pi$
$433$			8.67090i			0.416697i	−0.978055	+	0.208348i	$0.933191\pi$
$434$	−14.7030	+	3.44770i	−0.705768	+	0.165495i
$435$	−3.83827	−	3.83827i	−0.184031	−	0.184031i
$436$	−1.61896	−	0.195866i	−0.0775341	−	0.00938026i
$437$	5.44959	−	5.44959i	0.260689	−	0.260689i
$438$	1.78083	+	5.15702i	0.0850912	+	0.246412i
$439$			19.6051i			0.935700i	0.883808	+	0.467850i	$0.154971\pi$
$439$			19.6051i			0.935700i	−0.883808	+	0.467850i	$0.845029\pi$
$440$	−9.70119	−	45.0501i	−0.462486	−	2.14768i
$441$	6.85436	+	1.42048i	0.326398	+	0.0676419i
$442$	−10.5162	−	30.4534i	−0.500204	−	1.44852i
$443$	11.6535	−	11.6535i	0.553673	−	0.553673i	−0.373826	−	0.927499i	$-0.621954\pi$
$443$	11.6535	−	11.6535i	0.553673	−	0.553673i	0.927499	+	0.373826i	$0.121954\pi$
$444$	2.75682	+	3.51568i	0.130833	+	0.166847i
$445$	−0.476395	+	0.476395i	−0.0225833	+	0.0225833i
$446$	5.53013	−	11.3641i	0.261859	−	0.538103i
$447$	8.66400			0.409793
$448$	−18.9341	−	9.46036i	−0.894554	−	0.446960i
$449$	−1.15967			−0.0547280			−0.0273640	−	0.999626i	$-0.508711\pi$
$449$	−1.15967			−0.0547280			−0.0273640	+	0.999626i	$0.508711\pi$
$450$	0.920357	−	1.89127i	0.0433860	−	0.0891554i
$451$	−41.9252	+	41.9252i	−1.97418	+	1.97418i
$452$	14.4890	+	18.4774i	0.681507	+	0.869104i
$453$	5.62250	−	5.62250i	0.264168	−	0.264168i
$454$	−11.3505	−	32.8694i	−0.532706	−	1.54264i
$455$	−15.6223	−	19.1918i	−0.732386	−	0.899726i
$456$	1.20824	+	5.61079i	0.0565810	+	0.262749i
$457$			12.4379i			0.581820i	0.956750	+	0.290910i	$0.0939580\pi$
$457$			12.4379i			0.581820i	−0.956750	+	0.290910i	$0.906042\pi$
$458$	4.92406	+	14.2594i	0.230086	+	0.666296i
$459$	−4.38669	+	4.38669i	−0.204753	+	0.204753i
$460$	−19.2071	−	2.32373i	−0.895538	−	0.108344i
$461$	5.93297	+	5.93297i	0.276326	+	0.276326i	0.831641	−	0.555314i	$-0.187402\pi$
$461$	5.93297	+	5.93297i	0.276326	+	0.276326i	−0.555314	+	0.831641i	$0.687402\pi$
$462$	5.46420	+	23.3026i	0.254218	+	1.08413i
$463$			34.3424i			1.59603i	0.602640	+	0.798013i	$0.294116\pi$
$463$			34.3424i			1.59603i	−0.602640	+	0.798013i	$0.705884\pi$
$464$	−4.41647	−	7.29146i	−0.205029	−	0.338497i
$465$		−	10.2801i		−	0.476728i
$466$	−26.9305	−	13.1053i	−1.24753	−	0.607091i
$467$	19.0809	−	19.0809i	0.882959	−	0.882959i	−0.110875	−	0.993834i	$-0.535365\pi$
$467$	19.0809	−	19.0809i	0.882959	−	0.882959i	0.993834	+	0.110875i	$0.0353654\pi$
$468$	7.29132	+	0.882121i	0.337041	+	0.0407761i
$469$	2.36579	−	23.0742i	0.109242	−	1.06547i
$470$	5.27620	+	15.2791i	0.243373	+	0.704773i
$471$	16.8607			0.776901
$472$	1.73653	+	1.12115i	0.0799302	+	0.0516051i
$473$			43.5159i			2.00087i
$474$	−6.81710	+	2.35409i	−0.313120	+	0.108127i
$475$	2.13402	+	2.13402i	0.0979154	+	0.0979154i
$476$	32.0173	+	7.24612i	1.46751	+	0.332125i
$477$	6.91789	−	6.91789i	0.316748	−	0.316748i
$478$	−2.53813	−	1.23514i	−0.116091	−	0.0564940i
$479$	15.0304			0.686758			0.343379	−	0.939197i	$-0.388429\pi$
$479$	15.0304			0.686758			0.343379	+	0.939197i	$0.388429\pi$
$480$	9.21224	−	11.0782i	0.420480	−	0.505650i
$481$			8.20319i			0.374033i
$482$	1.72958	+	0.841673i	0.0787803	+	0.0383371i
$483$	9.99621	+	1.02491i	0.454843	+	0.0466349i
$484$	−47.0876	+	36.9237i	−2.14034	+	1.67835i
$485$	−12.8738	−	12.8738i	−0.584569	−	0.584569i
$486$	−0.461610	−	1.33676i	−0.0209391	−	0.0606365i
$487$	23.2550			1.05379			0.526893	−	0.849932i	$-0.323357\pi$
$487$	23.2550			1.05379			0.526893	+	0.849932i	$0.323357\pi$
$488$	−20.2552	−	13.0773i	−0.916908	−	0.591981i
$489$	−1.47832			−0.0668521
$490$	25.0074	−	3.22249i	1.12972	−	0.145577i
$491$	2.45372	−	2.45372i	0.110735	−	0.110735i	−0.649568	−	0.760303i	$-0.725050\pi$
$491$	2.45372	−	2.45372i	0.110735	−	0.110735i	0.760303	+	0.649568i	$0.225050\pi$
$492$	−18.4036	−	2.22651i	−0.829698	−	0.100379i
$493$	9.34881	+	9.34881i	0.421049	+	0.421049i
$494$	−4.61125	+	9.47581i	−0.207470	+	0.426337i
$495$	−16.2927			−0.732304
$496$	3.85006	−	15.6788i	0.172873	−	0.703997i
$497$	17.6370	+	21.6669i	0.791130	+	0.971891i
$498$	−18.0972	−	8.80671i	−0.810955	−	0.394638i
$499$	−14.0960	−	14.0960i	−0.631025	−	0.631025i	0.317300	−	0.948325i	$-0.397224\pi$
$499$	−14.0960	−	14.0960i	−0.631025	−	0.631025i	−0.948325	+	0.317300i	$0.897224\pi$
$500$	−2.14918	+	17.7644i	−0.0961142	+	0.794447i
$501$	−10.9205	−	10.9205i	−0.487890	−	0.487890i
$502$	1.09796	−	0.379150i	0.0490045	−	0.0169223i
$503$		−	13.4597i		−	0.600140i	−0.953917	−	0.300070i	$-0.902990\pi$
$503$		−	13.4597i		−	0.600140i	0.953917	−	0.300070i	$-0.0970100\pi$
$504$	−4.67903	+	5.84009i	−0.208421	+	0.260138i
$505$		−	1.97392i		−	0.0878384i
$506$	11.2149	+	32.4767i	0.498563	+	1.44377i
$507$	0.343203	+	0.343203i	0.0152422	+	0.0152422i
$508$	−19.8395	+	15.5572i	−0.880237	+	0.690237i
$509$	−14.4875	−	14.4875i	−0.642145	−	0.642145i	0.308937	−	0.951082i	$-0.400027\pi$
$509$	−14.4875	−	14.4875i	−0.642145	−	0.642145i	−0.951082	+	0.308937i	$0.900027\pi$
$510$	−9.77797	+	20.0931i	−0.432976	+	0.889736i
$511$	−6.44362	−	7.91590i	−0.285049	−	0.350179i
$512$	18.1991	−	13.4459i	0.804294	−	0.594231i
$513$	2.02919			0.0895908
$514$	23.2907	+	11.3341i	1.02731	+	0.499924i
$515$	−3.94386	−	3.94386i	−0.173787	−	0.173787i
$516$	−10.7064	+	8.39543i	−0.471324	+	0.369588i
$517$	20.2984	−	20.2984i	0.892724	−	0.892724i
$518$	−7.10337	−	4.40482i	−0.312104	−	0.193537i
$519$	−20.7665			−0.911549
$520$	25.8621	−	5.56921i	1.13413	−	0.244226i
$521$	−26.0056			−1.13932			−0.569662	−	0.821879i	$-0.692926\pi$
$521$	−26.0056			−1.13932			−0.569662	+	0.821879i	$0.692926\pi$
$522$	−2.84886	+	0.983772i	−0.124691	+	0.0430585i
$523$	−0.601049	−	0.601049i	−0.0262820	−	0.0262820i	0.693844	−	0.720126i	$-0.255916\pi$
$523$	−0.601049	−	0.601049i	−0.0262820	−	0.0262820i	−0.720126	+	0.693844i	$0.755916\pi$
$524$	15.3104	+	1.85229i	0.668838	+	0.0809176i
$525$	−0.401345	+	3.91443i	−0.0175161	+	0.170840i
$526$	−1.41111	+	2.89975i	−0.0615275	+	0.126435i
$527$			25.0391i			1.09072i
$528$	−24.8490	−	6.10189i	−1.08141	−	0.265551i
$529$	−8.57505			−0.372828
$530$	15.4200	−	31.6871i	0.669803	−	1.37640i
$531$	0.516751	−	0.516751i	0.0224251	−	0.0224251i
$532$	−5.72929	−	9.08119i	−0.248396	−	0.393719i
$533$	−24.0682	−	24.0682i	−1.04251	−	1.04251i
$534$	0.122103	+	0.353593i	0.00528392	+	0.0153015i
$535$			19.4225i			0.839706i
$536$	20.8321	+	13.4498i	0.899811	+	0.580943i
$537$	−23.9750			−1.03460
$538$	10.4670	−	3.61449i	0.451266	−	0.155832i
$539$	−24.5786	−	37.4289i	−1.05868	−	1.61218i
$540$	−3.14332	−	4.00857i	−0.135267	−	0.172501i
$541$	−8.43386	+	8.43386i	−0.362600	+	0.362600i	−0.864769	−	0.502169i	$-0.832535\pi$
$541$	−8.43386	+	8.43386i	−0.362600	+	0.362600i	0.502169	+	0.864769i	$0.332535\pi$
$542$	10.6379	−	21.8601i	0.456935	−	0.938970i
$543$		−	1.32719i		−	0.0569551i
$544$	−22.4381	+	26.9831i	−0.962026	+	1.15689i
$545$			2.07679i			0.0889599i
$546$	−13.3774	+	3.13686i	−0.572500	+	0.134245i
$547$	−17.1165	−	17.1165i	−0.731848	−	0.731848i	0.239137	−	0.970986i	$-0.423135\pi$
$547$	−17.1165	−	17.1165i	−0.731848	−	0.731848i	−0.970986	+	0.239137i	$0.923135\pi$
$548$	−20.5424	+	16.1083i	−0.877526	+	0.688112i
$549$	−6.02748	+	6.02748i	−0.257246	+	0.257246i
$550$	−12.7176	+	4.39166i	−0.542281	+	0.187261i
$551$		−	4.32455i		−	0.184232i
$552$	−5.82672	+	9.02490i	−0.248002	+	0.384125i
$553$	10.4641	−	8.51787i	0.444978	−	0.362217i
$554$	2.59812	−	0.897186i	0.110384	−	0.0381178i
$555$	4.02316	−	4.02316i	0.170774	−	0.170774i
$556$	−4.73825	+	39.1648i	−0.200947	+	1.66096i
$557$	26.9281	−	26.9281i	1.14098	−	1.14098i	0.152707	−	0.988271i	$-0.451201\pi$
$557$	26.9281	−	26.9281i	1.14098	−	1.14098i	0.988271	−	0.152707i	$-0.0487991\pi$
$558$	−5.13250	−	2.49765i	−0.217276	−	0.105734i
$559$	−24.9814			−1.05660
$560$	−9.06452	+	25.3852i	−0.383046	+	1.07272i
$561$	39.6839			1.67546
$562$	18.1147	+	8.81524i	0.764123	+	0.371848i
$563$	16.0469	−	16.0469i	0.676295	−	0.676295i	−0.282865	−	0.959160i	$-0.591285\pi$
$563$	16.0469	−	16.0469i	0.676295	−	0.676295i	0.959160	+	0.282865i	$0.0912849\pi$
$564$	8.91024	+	1.07798i	0.375189	+	0.0453912i
$565$	21.1445	−	21.1445i	0.889558	−	0.889558i
$566$	−9.43021	+	3.25645i	−0.396381	+	0.136879i
$567$	1.67026	+	2.05189i	0.0701442	+	0.0861712i
$568$	−29.1974	+	6.28743i	−1.22510	+	0.263815i
$569$			3.81256i			0.159831i	0.996802	+	0.0799154i	$0.0254650\pi$
$569$			3.81256i			0.159831i	−0.996802	+	0.0799154i	$0.974535\pi$
$570$	6.90884	−	2.38577i	0.289380	−	0.0999289i
$571$	−6.20325	+	6.20325i	−0.259598	+	0.259598i	−0.824891	−	0.565293i	$-0.808763\pi$
$571$	−6.20325	+	6.20325i	−0.259598	+	0.259598i	0.565293	+	0.824891i	$0.308763\pi$
$572$	−28.9902	−	36.9703i	−1.21214	−	1.54580i
$573$	12.0919	+	12.0919i	0.505147	+	0.505147i
$574$	33.7651	−	7.91757i	1.40933	−	0.330473i
$575$			5.64869i			0.235567i
$576$	−3.29278	−	7.29093i	−0.137199	−	0.303789i
$577$			10.7648i			0.448144i	0.974573	+	0.224072i	$0.0719351\pi$
$577$			10.7648i			0.448144i	−0.974573	+	0.224072i	$0.928065\pi$
$578$	13.2961	−	27.3225i	0.553044	−	1.13647i
$579$	4.07720	−	4.07720i	0.169443	−	0.169443i
$580$	−8.54297	+	6.69896i	−0.354727	+	0.278159i
$581$	37.4565	+	3.84039i	1.55396	+	0.159326i
$582$	−9.55527	+	3.29964i	−0.396079	+	0.136774i
$583$	−62.5823			−2.59189
$584$	10.6672	−	2.29709i	0.441410	−	0.0950542i
$585$		−	9.35325i		−	0.386709i
$586$	−12.6669	−	36.6814i	−0.523264	−	1.51530i
$587$	−26.2489	−	26.2489i	−1.08341	−	1.08341i	−0.996189	−	0.0872210i	$-0.972201\pi$
$587$	−26.2489	−	26.2489i	−1.08341	−	1.08341i	−0.0872210	−	0.996189i	$-0.527799\pi$
$588$	4.46690	−	13.2683i	0.184212	−	0.547174i
$589$	5.79126	−	5.79126i	0.238625	−	0.238625i
$590$	1.15184	−	2.36696i	0.0474206	−	0.0974462i
$591$	−2.29378			−0.0943536
$592$	7.64269	−	4.62922i	0.314113	−	0.190260i
$593$			36.5539i			1.50109i	0.660820	+	0.750545i	$0.270209\pi$
$593$			36.5539i			1.50109i	−0.660820	+	0.750545i	$0.729791\pi$
$594$	−3.95848	+	8.13441i	−0.162418	+	0.333759i
$595$	4.26393	−	41.5874i	0.174804	−	1.70492i
$596$	2.08121	−	17.2026i	0.0852495	−	0.704644i
$597$	−15.6232	−	15.6232i	−0.639417	−	0.639417i
$598$	−18.6441	+	6.43819i	−0.762412	+	0.263277i
$599$	−0.0689795			−0.00281842			−0.00140921	−	0.999999i	$-0.500449\pi$
$599$	−0.0689795			−0.00281842			−0.00140921	+	0.999999i	$0.500449\pi$
$600$	−3.53408	−	2.28170i	−0.144278	−	0.0931499i
$601$	14.1634			0.577738			0.288869	−	0.957369i	$-0.406721\pi$
$601$	14.1634			0.577738			0.288869	+	0.957369i	$0.406721\pi$
$602$	13.4141	−	21.6321i	0.546719	−	0.881659i
$603$	6.19917	−	6.19917i	0.252450	−	0.252450i
$604$	−9.81300	−	12.5142i	−0.399285	−	0.509195i
$605$	53.8845	+	53.8845i	2.19072	+	2.19072i
$606$	−0.985512	−	0.479584i	−0.0400337	−	0.0194818i
$607$	0.622926			0.0252838			0.0126419	−	0.999920i	$-0.495976\pi$
$607$	0.622926			0.0252838			0.0126419	+	0.999920i	$0.495976\pi$
$608$	11.4306	−	1.05120i	0.463571	−	0.0426318i
$609$	4.37293	−	3.55961i	0.177200	−	0.144243i
$610$	−13.4353	+	27.6086i	−0.543979	+	1.11784i
$611$	11.6528	+	11.6528i	0.471423	+	0.471423i
$612$	7.65613	+	9.76361i	0.309481	+	0.394671i
$613$	13.5765	+	13.5765i	0.548349	+	0.548349i	0.925963	−	0.377614i	$-0.123255\pi$
$613$	13.5765	+	13.5765i	0.548349	+	0.548349i	−0.377614	+	0.925963i	$0.623255\pi$
$614$	0.739163	+	2.14051i	0.0298302	+	0.0863839i
$615$			23.6080i			0.951966i
$616$	47.5803	−	5.25171i	1.91707	−	0.211597i
$617$		−	23.0955i		−	0.929790i	−0.885366	−	0.464895i	$-0.846092\pi$
$617$		−	23.0955i		−	0.929790i	0.885366	−	0.464895i	$-0.153908\pi$
$618$	−2.92724	+	1.01084i	−0.117751	+	0.0406618i
$619$	−2.92078	−	2.92078i	−0.117396	−	0.117396i	0.645968	−	0.763364i	$-0.276454\pi$
$619$	−2.92078	−	2.92078i	−0.117396	−	0.117396i	−0.763364	+	0.645968i	$0.776454\pi$
$620$	−20.4113	−	2.46941i	−0.819739	−	0.0991740i
$621$	2.68560	+	2.68560i	0.107770	+	0.107770i
$622$	−40.6431	−	19.7783i	−1.62964	−	0.793039i
$623$	−0.441809	−	0.542756i	−0.0177007	−	0.0217451i
$624$	3.50294	−	14.2652i	0.140230	−	0.571064i
$625$	30.2244			1.20898
$626$	17.6364	−	36.2417i	0.704894	−	1.44851i
$627$	−9.17846	−	9.17846i	−0.366552	−	0.366552i
$628$	4.05017	−	33.4773i	0.161619	−	1.33589i
$629$	−9.79915	+	9.79915i	−0.390718	+	0.390718i
$630$	8.09924	+	5.02236i	0.322681	+	0.200096i
$631$	29.4643			1.17296			0.586478	−	0.809965i	$-0.300514\pi$
$631$	29.4643			1.17296			0.586478	+	0.809965i	$0.300514\pi$
$632$	3.03654	+	14.1010i	0.120787	+	0.560907i
$633$	4.30747			0.171206
$634$	2.03033	+	5.87953i	0.0806345	+	0.233506i
$635$	22.7033	+	22.7033i	0.900953	+	0.900953i
$636$	−12.0738	−	15.3974i	−0.478759	−	0.610546i
$637$	21.4870	−	14.1100i	0.851346	−	0.559058i
$638$	17.3358	+	8.43621i	0.686333	+	0.333993i
$639$			10.5595i			0.417727i
$640$	−19.7832	−	20.9523i	−0.781999	−	0.828210i
$641$	−5.40014			−0.213293			−0.106646	−	0.994297i	$-0.534011\pi$
$641$	−5.40014			−0.213293			−0.106646	+	0.994297i	$0.534011\pi$
$642$	9.69698	+	4.71888i	0.382709	+	0.186239i
$643$	9.28303	−	9.28303i	0.366087	−	0.366087i	−0.499961	−	0.866048i	$-0.666652\pi$
$643$	9.28303	−	9.28303i	0.366087	−	0.366087i	0.866048	+	0.499961i	$0.166652\pi$
$644$	4.43620	−	19.6015i	0.174811	−	0.772407i
$645$	12.2519	+	12.2519i	0.482416	+	0.482416i
$646$	−16.8278	+	5.81098i	−0.662079	+	0.228630i
$647$			21.5623i			0.847703i	0.905732	+	0.423852i	$0.139322\pi$
$647$			21.5623i			0.847703i	−0.905732	+	0.423852i	$0.860678\pi$
$648$	−2.76504	+	0.595430i	−0.108621	+	0.0233907i
$649$	−4.67476			−0.183500
$650$	−2.52114	−	7.30086i	−0.0988873	−	0.286363i
$651$	10.6229	+	1.08916i	0.416345	+	0.0426877i
$652$	−0.355113	+	2.93525i	−0.0139073	+	0.114953i
$653$	31.1997	−	31.1997i	1.22094	−	1.22094i	0.253638	−	0.967299i	$-0.418373\pi$
$653$	31.1997	−	31.1997i	1.22094	−	1.22094i	0.967299	−	0.253638i	$-0.0816273\pi$
$654$	1.03687	+	0.504576i	0.0405448	+	0.0197305i
$655$		−	19.6401i		−	0.767401i
$656$	−8.84157	+	36.0059i	−0.345205	+	1.40579i
$657$		−	3.85786i		−	0.150510i
$658$	−16.3477	+	3.83335i	−0.637298	+	0.149440i
$659$	−8.41759	−	8.41759i	−0.327903	−	0.327903i	0.523886	−	0.851789i	$-0.324482\pi$
$659$	−8.41759	−	8.41759i	−0.327903	−	0.327903i	−0.851789	+	0.523886i	$0.824482\pi$
$660$	−3.91373	+	32.3496i	−0.152342	+	1.25921i
$661$	−30.4079	+	30.4079i	−1.18273	+	1.18273i	−0.203695	+	0.979034i	$0.565295\pi$
$661$	−30.4079	+	30.4079i	−1.18273	+	1.18273i	−0.979034	+	0.203695i	$0.934705\pi$
$662$	−14.6827	−	42.5191i	−0.570661	−	1.65255i
$663$			22.7816i			0.884762i
$664$	−21.8331	+	33.8169i	−0.847289	+	1.31235i
$665$	−10.6049	+	8.63250i	−0.411240	+	0.334754i
$666$	−1.03116	−	2.98609i	−0.0399567	−	0.115709i
$667$	5.72350	−	5.72350i	0.221615	−	0.221615i
$668$	−24.3060	+	19.0596i	−0.940429	+	0.737437i
$669$	−6.31910	+	6.31910i	−0.244310	+	0.244310i
$670$	13.8180	−	28.3950i	0.533836	−	1.09700i
$671$	54.5272			2.10500
$672$	10.4717	+	10.6932i	0.403953	+	0.412499i
$673$	51.5164			1.98581			0.992906	−	0.118898i	$-0.0379361\pi$
$673$	51.5164			1.98581			0.992906	+	0.118898i	$0.0379361\pi$
$674$	15.3898	−	31.6250i	0.592792	−	1.21815i
$675$	−1.05166	+	1.05166i	−0.0404785	+	0.0404785i
$676$	0.763879	−	0.598995i	0.0293800	−	0.0230383i
$677$	−12.8377	+	12.8377i	−0.493393	+	0.493393i	−0.909373	−	0.415981i	$-0.863438\pi$
$677$	−12.8377	+	12.8377i	−0.493393	+	0.493393i	0.415981	+	0.909373i	$0.363438\pi$
$678$	−5.41948	−	15.6940i	−0.208134	−	0.602726i
$679$	14.6671	−	11.9392i	0.562872	−	0.458183i
$680$	37.5464	+	24.2410i	1.43984	+	0.929599i
$681$			24.5890i			0.942251i
$682$	11.9180	+	34.5128i	0.456364	+	1.32157i
$683$	−27.6581	+	27.6581i	−1.05831	+	1.05831i	−0.0601146	+	0.998191i	$0.519147\pi$
$683$	−27.6581	+	27.6581i	−1.05831	+	1.05831i	−0.998191	+	0.0601146i	$0.980853\pi$
$684$	0.487437	−	4.02900i	0.0186376	−	0.154052i
$685$	23.5076	+	23.5076i	0.898178	+	0.898178i
$686$	0.680459	+	26.1828i	0.0259801	+	0.999662i
$687$		−	10.6671i		−	0.406977i
$688$	14.0975	+	23.2745i	0.537462	+	0.887333i
$689$		−	35.9269i		−	1.36871i
$690$	12.3013	+	5.98623i	0.468303	+	0.227892i
$691$	−15.0732	+	15.0732i	−0.573413	+	0.573413i	−0.933081	−	0.359668i	$-0.882890\pi$
$691$	−15.0732	+	15.0732i	−0.573413	+	0.573413i	0.359668	+	0.933081i	$0.382890\pi$
$692$	−4.98839	+	41.2324i	−0.189630	+	1.56742i
$693$	1.72620	−	16.8361i	0.0655727	−	0.639550i
$694$	−3.87366	−	11.2176i	−0.147042	−	0.425813i
$695$	50.2403			1.90572
$696$	1.26897	+	5.89279i	0.0481001	+	0.223366i
$697$		−	57.5016i		−	2.17803i
$698$	−33.9333	+	11.7179i	−1.28439	+	0.443528i
$699$	14.9750	+	14.9750i	0.566406	+	0.566406i
$700$	7.67579	+	1.73718i	0.290117	+	0.0656592i
$701$	−7.57647	+	7.57647i	−0.286159	+	0.286159i	−0.835559	−	0.549400i	$-0.814856\pi$
$701$	−7.57647	+	7.57647i	−0.286159	+	0.286159i	0.549400	+	0.835559i	$0.314856\pi$
$702$	−4.66976	−	2.27246i	−0.176249	−	0.0857686i
$703$	4.53287			0.170961
$704$	−18.0845	+	47.8724i	−0.681585	+	1.80426i
$705$		−	11.4300i		−	0.430478i
$706$	24.1676	+	11.7608i	0.909559	+	0.442622i
$707$	2.03975	+	0.209135i	0.0767127	+	0.00786532i
$708$	−0.901891	−	1.15015i	−0.0338951	−	0.0432253i
$709$	−19.7005	−	19.7005i	−0.739866	−	0.739866i	0.232686	−	0.972552i	$-0.425249\pi$
$709$	−19.7005	−	19.7005i	−0.739866	−	0.739866i	−0.972552	+	0.232686i	$0.925249\pi$
$710$	12.4151	+	35.9522i	0.465929	+	1.34926i
$711$	5.09974			0.191255
$712$	0.731397	−	0.157501i	0.0274103	−	0.00590259i
$713$	15.3293			0.574088
$714$	−19.7272	−	12.2329i	−0.738271	−	0.457804i
$715$	−42.3068	+	42.3068i	−1.58218	+	1.58218i
$716$	−5.75912	+	47.6030i	−0.215228	+	1.77901i
$717$	1.41135	+	1.41135i	0.0527079	+	0.0527079i
$718$	−5.09046	+	10.4606i	−0.189974	+	0.390384i
$719$	−0.0891935			−0.00332636			−0.00166318	−	0.999999i	$-0.500529\pi$
$719$	−0.0891935			−0.00332636			−0.00166318	+	0.999999i	$0.500529\pi$
$720$	−8.71417	+	5.27822i	−0.324758	+	0.196708i
$721$	4.49323	−	3.65754i	0.167337	−	0.136214i
$722$	−18.9250	−	9.20955i	−0.704316	−	0.342744i
$723$	−0.961751	−	0.961751i	−0.0357679	−	0.0357679i
$724$	−2.63516	−	0.318808i	−0.0979351	−	0.0118484i
$725$	2.24127	+	2.24127i	0.0832388	+	0.0832388i
$726$	39.9945	−	13.8109i	1.48433	−	0.512572i
$727$		−	31.1159i		−	1.15403i	−0.816735	−	0.577013i	$-0.804218\pi$
$727$		−	31.1159i		−	1.15403i	0.816735	−	0.577013i	$-0.195782\pi$
$728$	3.01487	+	27.3147i	0.111739	+	1.01235i
$729$			1.00000i			0.0370370i
$730$	−4.53579	−	13.1350i	−0.167877	−	0.486148i
$731$	−29.8416	−	29.8416i	−1.10373	−	1.10373i
$732$	10.5198	+	13.4156i	0.388823	+	0.495854i
$733$	−19.9681	−	19.9681i	−0.737539	−	0.737539i	0.234562	−	0.972101i	$-0.424634\pi$
$733$	−19.9681	−	19.9681i	−0.737539	−	0.737539i	−0.972101	+	0.234562i	$0.924634\pi$
$734$	−16.8902	+	34.7083i	−0.623429	+	1.28110i
$735$	−17.4581	−	3.61798i	−0.643953	−	0.133451i
$736$	16.5195	+	13.7370i	0.608916	+	0.506352i
$737$	−56.0804			−2.06575
$738$	11.7867	+	5.73579i	0.433873	+	0.211137i
$739$	9.59456	+	9.59456i	0.352942	+	0.352942i	0.861203	−	0.508261i	$-0.169712\pi$
$739$	9.59456	+	9.59456i	0.352942	+	0.352942i	−0.508261	+	0.861203i	$0.669712\pi$
$740$	−7.02166	−	8.95449i	−0.258121	−	0.329174i
$741$	5.26912	−	5.26912i	0.193566	−	0.193566i
$742$	31.1101	+	19.2915i	1.14209	+	0.708213i
$743$	20.5150			0.752621			0.376310	−	0.926494i	$-0.377193\pi$
$743$	20.5150			0.752621			0.376310	+	0.926494i	$0.377193\pi$
$744$	−6.19203	+	9.59072i	−0.227011	+	0.351613i
$745$	−22.0673			−0.808484
$746$	−23.4195	+	8.08725i	−0.857449	+	0.296095i
$747$	10.0631	+	10.0631i	0.368191	+	0.368191i
$748$	9.53261	−	78.7933i	0.348547	−	2.88097i
$749$	−20.0702	−	2.05779i	−0.733349	−	0.0751899i
$750$	5.53657	−	11.3773i	0.202167	−	0.415440i
$751$		−	29.9255i		−	1.09200i	−0.837787	−	0.545998i	$-0.816151\pi$
$751$		−	29.9255i		−	1.09200i	0.837787	−	0.545998i	$-0.183849\pi$
$752$	4.28072	−	17.4325i	0.156102	−	0.635699i
$753$	−0.821365			−0.0299322
$754$	−4.84302	+	9.95207i	−0.176372	+	0.362433i
$755$	−14.3206	+	14.3206i	−0.521179	+	0.521179i
$756$	4.47528	−	2.82344i	0.162765	−	0.102688i
$757$	18.3461	+	18.3461i	0.666799	+	0.666799i	0.956974	−	0.290175i	$-0.0937135\pi$
$757$	18.3461	+	18.3461i	0.666799	+	0.666799i	−0.290175	+	0.956974i	$0.593714\pi$
$758$	−1.84980	−	5.35674i	−0.0671876	−	0.194566i
$759$		−	24.2952i		−	0.881859i
$760$	−3.07740	−	14.2908i	−0.111629	−	0.518380i
$761$	29.7121			1.07706			0.538531	−	0.842605i	$-0.318979\pi$
$761$	29.7121			1.07706			0.538531	+	0.842605i	$0.318979\pi$
$762$	16.8510	−	5.81900i	0.610447	−	0.210800i
$763$	−2.14605	−	0.220033i	−0.0776922	−	0.00796574i
$764$	26.9134	−	21.1041i	0.973692	−	0.763520i
$765$	11.1730	−	11.1730i	0.403959	−	0.403959i
$766$	−1.91860	+	3.94260i	−0.0693219	+	0.142452i
$767$		−	2.68366i		−	0.0969014i
$768$	−15.2673	+	4.78651i	−0.550910	+	0.172718i
$769$			26.1826i			0.944168i	0.881554	+	0.472084i	$0.156498\pi$
$769$			26.1826i			0.944168i	−0.881554	+	0.472084i	$0.843502\pi$
$770$	−13.9174	−	59.3519i	−0.501548	−	2.13889i
$771$	−12.9510	−	12.9510i	−0.466420	−	0.466420i
$772$	−7.11597	−	9.07476i	−0.256109	−	0.326608i
$773$	−29.9716	+	29.9716i	−1.07800	+	1.07800i	−0.0813162	+	0.996688i	$0.525912\pi$
$773$	−29.9716	+	29.9716i	−1.07800	+	1.07800i	−0.996688	+	0.0813162i	$0.974088\pi$
$774$	9.09364	−	3.14023i	0.326864	−	0.112873i
$775$			6.00284i			0.215628i
$776$	4.25620	+	19.7648i	0.152789	+	0.709516i
$777$	3.73108	+	4.58358i	0.133852	+	0.164435i
$778$	3.58286	−	1.23724i	0.128452	−	0.0443570i
$779$	−13.2995	+	13.2995i	−0.476504	+	0.476504i
$780$	−18.5711	−	2.24677i	−0.664951	−	0.0804474i
$781$	47.7629	−	47.7629i	1.70909	−	1.70909i
$782$	−29.9621	−	14.5806i	−1.07144	−	0.521400i
$783$	2.13118			0.0761620
$784$	−25.2714	−	12.0563i	−0.902551	−	0.430584i
$785$	−42.9445			−1.53275
$786$	−9.80561	−	4.77174i	−0.349755	−	0.170202i
$787$	10.6861	−	10.6861i	0.380920	−	0.380920i	−0.490514	−	0.871433i	$-0.663191\pi$
$787$	10.6861	−	10.6861i	0.380920	−	0.380920i	0.871433	+	0.490514i	$0.163191\pi$
$788$	−0.550997	+	4.55436i	−0.0196284	+	0.162242i
$789$	1.61243	−	1.61243i	0.0574042	−	0.0574042i
$790$	17.3632	−	5.99590i	0.617757	−	0.213324i
$791$	19.6095	+	24.0899i	0.697232	+	0.856540i
$792$	15.2002	+	9.81364i	0.540114	+	0.348712i
$793$			31.3027i			1.11159i
$794$	31.0348	−	10.7170i	1.10138	−	0.380331i
$795$	−17.6199	+	17.6199i	−0.624915	+	0.624915i
$796$	−34.7732	+	27.2674i	−1.23250	+	0.966467i
$797$	14.9215	+	14.9215i	0.528547	+	0.528547i	0.920139	−	0.391592i	$-0.128076\pi$
$797$	14.9215	+	14.9215i	0.528547	+	0.528547i	−0.391592	+	0.920139i	$0.628076\pi$
$798$	1.73335	+	7.39202i	0.0613599	+	0.261675i
$799$			27.8398i			0.984903i
$800$	−5.37929	+	6.46890i	−0.190187	+	0.228710i
$801$		−	0.264516i		−	0.00934620i
$802$	−7.19892	+	14.7933i	−0.254203	+	0.522369i
$803$	−17.4500	+	17.4500i	−0.615796	+	0.615796i
$804$	−10.8195	−	13.7977i	−0.381573	−	0.486608i
$805$	−25.4605	−	2.61045i	−0.897364	−	0.0920063i
$806$	−19.8130	+	6.84183i	−0.697882	+	0.240993i
$807$	−7.83017			−0.275635
$808$	−1.18896	+	1.84155i	−0.0418274	+	0.0647856i
$809$		−	19.2298i		−	0.676082i	−0.941131	−	0.338041i	$-0.890236\pi$
$809$		−	19.2298i		−	0.676082i	0.941131	−	0.338041i	$-0.109764\pi$
$810$	1.17573	+	3.40473i	0.0413108	+	0.119630i
$811$	0.502502	+	0.502502i	0.0176452	+	0.0176452i	0.715874	−	0.698229i	$-0.246028\pi$
$811$	0.502502	+	0.502502i	0.0176452	+	0.0176452i	−0.698229	+	0.715874i	$0.746028\pi$
$812$	−6.01725	−	9.53762i	−0.211164	−	0.334705i
$813$	−12.1555	+	12.1555i	−0.426313	+	0.426313i
$814$	−8.84259	+	18.1709i	−0.309933	+	0.636891i
$815$	3.76531			0.131893
$816$	21.2250	−	12.8561i	0.743023	−	0.450052i
$817$			13.8041i			0.482944i
$818$	−0.245668	+	0.504832i	−0.00858959	+	0.0176510i
$819$	9.66517	+	0.990965i	0.337728	+	0.0346271i
$820$	46.8742	+	5.67095i	1.63692	+	0.198038i
$821$	3.57175	+	3.57175i	0.124655	+	0.124655i	0.766682	−	0.642027i	$-0.221906\pi$
$821$	3.57175	+	3.57175i	0.124655	+	0.124655i	−0.642027	+	0.766682i	$0.721906\pi$
$822$	17.4479	−	6.02514i	0.608566	−	0.210151i
$823$	30.5512			1.06495			0.532474	−	0.846446i	$-0.321262\pi$
$823$	30.5512			1.06495			0.532474	+	0.846446i	$0.321262\pi$
$824$	1.30388	+	6.05491i	0.0454227	+	0.210933i
$825$	9.51379			0.331228
$826$	2.32386	+	1.44103i	0.0808574	+	0.0501399i
$827$	9.21840	−	9.21840i	0.320555	−	0.320555i	−0.528425	−	0.848980i	$-0.677217\pi$
$827$	9.21840	−	9.21840i	0.320555	−	0.320555i	0.848980	+	0.528425i	$0.177217\pi$
$828$	5.97745	−	4.68721i	0.207731	−	0.162892i
$829$	−3.61659	−	3.61659i	−0.125609	−	0.125609i	0.641507	−	0.767117i	$-0.278309\pi$
$829$	−3.61659	−	3.61659i	−0.125609	−	0.125609i	−0.767117	+	0.641507i	$0.778309\pi$
$830$	46.0938	+	22.4308i	1.59994	+	0.778585i
$831$	−1.94360			−0.0674228
$832$	−27.4824	−	10.3819i	−0.952780	−	0.359926i
$833$	42.5225	+	8.81226i	1.47332	+	0.305327i
$834$	12.2064	−	25.0833i	0.422672	−	0.868563i
$835$	27.8145	+	27.8145i	0.962561	+	0.962561i
$836$	−20.4288	+	16.0192i	−0.706546	+	0.554037i
$837$	2.85398	+	2.85398i	0.0986480	+	0.0986480i
$838$	7.72907	+	22.3823i	0.266996	+	0.773183i
$839$		−	25.3066i		−	0.873681i	−0.899539	−	0.436841i	$-0.856097\pi$
$839$		−	25.3066i		−	0.873681i	0.899539	−	0.436841i	$-0.143903\pi$
$840$	11.9176	−	14.8748i	0.411195	−	0.513229i
$841$			24.4581i			0.843382i
$842$	1.97211	−	0.681010i	0.0679633	−	0.0234692i
$843$	−10.0729	−	10.0729i	−0.346928	−	0.346928i
$844$	1.03471	−	8.55257i	0.0356162	−	0.294392i
$845$	−0.874142	−	0.874142i	−0.0300714	−	0.0300714i
$846$	−5.70661	−	2.77703i	−0.196197	−	0.0954762i
$847$	−61.3905	+	49.9725i	−2.10940	+	1.71708i
$848$	−33.4721	+	20.2742i	−1.14944	+	0.696220i
$849$	7.05455			0.242111
$850$	5.70963	−	11.7329i	0.195839	−	0.402436i
$851$	5.99920	+	5.99920i	0.205650	+	0.205650i
$852$	20.9661	+	2.53653i	0.718286	+	0.0869000i
$853$	−12.8593	+	12.8593i	−0.440296	+	0.440296i	−0.892111	−	0.451816i	$-0.850776\pi$
$853$	−12.8593	+	12.8593i	−0.440296	+	0.440296i	0.451816	+	0.892111i	$0.350776\pi$
$854$	−27.1059	−	16.8084i	−0.927544	−	0.575173i
$855$	−5.16836			−0.176754
$856$	11.6988	−	18.1200i	0.399856	−	0.619330i
$857$	−41.8529			−1.42967			−0.714834	−	0.699295i	$-0.753498\pi$
$857$	−41.8529			−1.42967			−0.714834	+	0.699295i	$0.753498\pi$
$858$	10.8435	+	31.4012i	0.370191	+	1.07202i
$859$	9.11357	+	9.11357i	0.310951	+	0.310951i	0.845278	−	0.534327i	$-0.179435\pi$
$859$	9.11357	+	9.11357i	0.310951	+	0.310951i	−0.534327	+	0.845278i	$0.679435\pi$
$860$	27.2694	−	21.3833i	0.929878	−	0.729163i
$861$	−24.3953	−	2.50124i	−0.831389	−	0.0852420i
$862$	−16.4541	−	8.00715i	−0.560430	−	0.272724i
$863$		−	50.1906i		−	1.70851i	−0.519856	−	0.854254i	$-0.674014\pi$
$863$		−	50.1906i		−	1.70851i	0.519856	−	0.854254i	$-0.325986\pi$
$864$	0.518040	+	5.63308i	0.0176241	+	0.191641i
$865$	52.8926			1.79840
$866$	−11.0262	−	5.36574i	−0.374687	−	0.182335i
$867$	−15.1930	+	15.1930i	−0.515981	+	0.515981i
$868$	4.71432	−	20.8304i	0.160015	−	0.707031i
$869$	−23.0672	−	23.0672i	−0.782502	−	0.782502i
$870$	7.25609	−	2.50568i	0.246004	−	0.0849505i
$871$		−	32.1944i		−	1.09086i
$872$	1.25092	−	1.93752i	0.0423614	−	0.0656128i
$873$	7.14810			0.241927
$874$	3.55758	+	10.3022i	0.120337	+	0.348478i
$875$	−2.41436	+	23.5480i	−0.0816204	+	0.796067i
$876$	−7.65987	−	0.926709i	−0.258803	−	0.0313106i
$877$	−6.62177	+	6.62177i	−0.223601	+	0.223601i	−0.810013	−	0.586412i	$-0.800540\pi$
$877$	−6.62177	+	6.62177i	−0.223601	+	0.223601i	0.586412	+	0.810013i	$0.300540\pi$
$878$	−24.9305	−	12.1320i	−0.841365	−	0.409437i
$879$			27.4406i			0.925550i
$880$	63.2907	+	15.5416i	2.13353	+	0.523907i
$881$			40.4323i			1.36220i	0.732191	+	0.681099i	$0.238498\pi$
$881$			40.4323i			1.36220i	−0.732191	+	0.681099i	$0.761502\pi$
$882$	−6.04796	+	7.83723i	−0.203645	+	0.263893i
$883$	−24.8546	−	24.8546i	−0.836423	−	0.836423i	0.151963	−	0.988386i	$-0.451440\pi$
$883$	−24.8546	−	24.8546i	−0.836423	−	0.836423i	−0.988386	+	0.151963i	$0.951440\pi$
$884$	45.2333	+	5.47243i	1.52136	+	0.184058i
$885$	−1.31617	+	1.31617i	−0.0442426	+	0.0442426i
$886$	7.60756	+	22.0304i	0.255581	+	0.740125i
$887$		−	15.9559i		−	0.535748i	−0.963454	−	0.267874i	$-0.913679\pi$
$887$		−	15.9559i		−	0.535748i	0.963454	−	0.267874i	$-0.0863211\pi$
$888$	−6.17665	+	1.33009i	−0.207275	+	0.0446350i
$889$	−25.8658	+	21.0551i	−0.867512	+	0.706164i
$890$	−0.310998	−	0.900605i	−0.0104247	−	0.0301884i
$891$	4.52322	−	4.52322i	0.151534	−	0.151534i
$892$	11.0288	+	14.0646i	0.369271	+	0.470919i
$893$	6.43905	−	6.43905i	0.215475	−	0.215475i
$894$	−5.36147	+	11.0175i	−0.179314	+	0.368479i
$895$	61.0647			2.04117
$896$	23.7470	−	18.2231i	0.793332	−	0.608790i
$897$	13.9472			0.465685
$898$	0.717626	−	1.47467i	0.0239475	−	0.0492105i
$899$	6.08233	−	6.08233i	0.202857	−	0.202857i
$900$	1.83547	+	2.34072i	0.0611824	+	0.0780240i
$901$	42.9166	−	42.9166i	1.42976	−	1.42976i
$902$	−27.3694	−	79.2579i	−0.911302	−	2.63900i
$903$	−13.9585	+	11.3624i	−0.464510	+	0.378116i
$904$	−32.4627	+	6.99058i	−1.07969	+	0.232503i
$905$			3.38037i			0.112367i
$906$	3.67045	+	10.6291i	0.121943	+	0.353128i
$907$	5.32214	−	5.32214i	0.176719	−	0.176719i	−0.613205	−	0.789924i	$-0.710120\pi$
$907$	5.32214	−	5.32214i	0.176719	−	0.176719i	0.789924	+	0.613205i	$0.210120\pi$
$908$	48.8219	+	5.90659i	1.62021	+	0.196017i
$909$	0.548004	+	0.548004i	0.0181762	+	0.0181762i
$910$	34.0724	−	7.98962i	1.12949	−	0.264853i
$911$		−	19.2821i		−	0.638843i	−0.947613	−	0.319422i	$-0.896511\pi$
$911$		−	19.2821i		−	0.638843i	0.947613	−	0.319422i	$-0.103489\pi$
$912$	−7.88257	−	1.93564i	−0.261018	−	0.0640953i
$913$		−	91.0356i		−	3.01284i
$914$	−15.8165	−	7.69683i	−0.523162	−	0.254589i
$915$	15.3521	−	15.3521i	0.507523	−	0.507523i
$916$	−21.1798	−	2.56239i	−0.699802	−	0.0846637i
$917$	20.2950	+	2.08084i	0.670201	+	0.0687154i
$918$	−2.86370	−	8.29286i	−0.0945161	−	0.273705i
$919$	−44.6669			−1.47342			−0.736712	−	0.676207i	$-0.763623\pi$
$919$	−44.6669			−1.47342			−0.736712	+	0.676207i	$0.763623\pi$
$920$	14.8407	−	22.9865i	0.489285	−	0.757844i
$921$		−	1.60127i		−	0.0527637i
$922$	−11.2160	+	3.87313i	−0.369381	+	0.127555i
$923$	27.4195	+	27.4195i	0.902522	+	0.902522i
$924$	−33.0138	−	7.47165i	−1.08607	−	0.245799i
$925$	−2.34924	+	2.34924i	−0.0772425	+	0.0772425i
$926$	−43.6710	−	21.2518i	−1.43512	−	0.698378i
$927$	2.18981			0.0719227
$928$	12.0051	−	1.10403i	0.394086	−	0.0362417i
$929$		−	6.37514i		−	0.209162i	−0.994516	−	0.104581i	$-0.966650\pi$
$929$		−	6.37514i		−	0.209162i	0.994516	−	0.104581i	$-0.0333501\pi$
$930$	13.0725	+	6.36154i	0.428666	+	0.208603i
$931$	−7.79681	−	11.8732i	−0.255530	−	0.389127i
$932$	33.3303	−	26.1360i	1.09177	−	0.856112i
$933$	22.6000	+	22.6000i	0.739892	+	0.739892i
$934$	12.4563	+	36.0717i	0.407583	+	1.18030i
$935$	−101.076			−3.30552
$936$	−5.63376	+	8.72603i	−0.184145	+	0.285219i
$937$	19.8223			0.647568			0.323784	−	0.946131i	$-0.395045\pi$
$937$	19.8223			0.647568			0.323784	+	0.946131i	$0.395045\pi$
$938$	27.8780	+	17.2872i	0.910249	+	0.564448i
$939$	−20.1526	+	20.1526i	−0.657654	+	0.657654i
$940$	−22.6945	−	2.74563i	−0.740213	−	0.0895527i
$941$	16.6010	+	16.6010i	0.541178	+	0.541178i	0.923874	−	0.382696i	$-0.125004\pi$
$941$	16.6010	+	16.6010i	0.541178	+	0.541178i	−0.382696	+	0.923874i	$0.625004\pi$
$942$	−10.4338	+	21.4407i	−0.339951	+	0.698576i
$943$	−35.2034			−1.14638
$944$	−2.50030	+	1.51444i	−0.0813777	+	0.0492909i
$945$	−4.25417	−	5.22618i	−0.138388	−	0.170008i
$946$	−55.3365	−	26.9286i	−1.79914	−	0.875524i
$947$	−10.3480	−	10.3480i	−0.336265	−	0.336265i	0.518695	−	0.854960i	$-0.326418\pi$
$947$	−10.3480	−	10.3480i	−0.336265	−	0.336265i	−0.854960	+	0.518695i	$0.826418\pi$
$948$	1.22502	−	10.1256i	0.0397869	−	0.328865i
$949$	−10.0176	−	10.0176i	−0.325185	−	0.325185i
$950$	−4.03427	+	1.39312i	−0.130889	+	0.0451987i
$951$		−	4.39836i		−	0.142627i
$952$	−29.0274	+	36.2303i	−0.940784	+	1.17423i
$953$			29.2556i			0.947682i	0.880610	+	0.473841i	$0.157133\pi$
$953$			29.2556i			0.947682i	−0.880610	+	0.473841i	$0.842867\pi$
$954$	4.51610	+	13.0780i	0.146214	+	0.423415i
$955$	−30.7982	−	30.7982i	−0.996607	−	0.996607i
$956$	3.14130	−	2.46325i	0.101597	−	0.0796671i
$957$	−9.63978	−	9.63978i	−0.311610	−	0.311610i
$958$	−9.30115	+	19.1132i	−0.300507	+	0.617521i
$959$	−26.7821	+	21.8009i	−0.864840	+	0.703989i
$960$	8.38675	+	18.5701i	0.270681	+	0.599347i
$961$	−14.7096			−0.474503
$962$	−10.4315	−	5.07631i	−0.336324	−	0.163667i
$963$	−5.39210	−	5.39210i	−0.173758	−	0.173758i
$964$	−2.14060	+	1.67855i	−0.0689442	+	0.0540626i
$965$	−10.3847	+	10.3847i	−0.334294	+	0.334294i
$966$	−7.48918	+	12.0773i	−0.240960	+	0.388581i
$967$	−6.89322			−0.221671			−0.110835	−	0.993839i	$-0.535353\pi$
$967$	−6.89322			−0.221671			−0.110835	+	0.993839i	$0.535353\pi$
$968$	−17.8147	−	82.7275i	−0.572586	−	2.65896i
$969$	12.5885			0.404401
$970$	24.3374	−	8.40422i	0.781427	−	0.269843i
$971$	−1.36810	−	1.36810i	−0.0439045	−	0.0439045i	0.684814	−	0.728718i	$-0.259884\pi$
$971$	−1.36810	−	1.36810i	−0.0439045	−	0.0439045i	−0.728718	+	0.684814i	$0.759884\pi$
$972$	1.98552	+	0.240213i	0.0636856	+	0.00770484i
$973$	−5.32290	+	51.9158i	−0.170644	+	1.66434i
$974$	−14.3907	+	29.5719i	−0.461108	+	0.947546i
$975$			5.46163i			0.174912i
$976$	29.1639	−	17.6647i	0.933514	−	0.565434i
$977$	−29.6235			−0.947740			−0.473870	−	0.880595i	$-0.657143\pi$
$977$	−29.6235			−0.947740			−0.473870	+	0.880595i	$0.657143\pi$
$978$	0.914819	−	1.87989i	0.0292527	−	0.0601123i
$979$	−1.19646	+	1.19646i	−0.0382391	+	0.0382391i
$980$	−11.3773	+	33.7944i	−0.363433	+	1.07952i
$981$	−0.576562	−	0.576562i	−0.0184082	−	0.0184082i
$982$	1.60183	+	4.63866i	0.0511164	+	0.148026i
$983$		−	37.6263i		−	1.20009i	−0.799965	−	0.600046i	$-0.795149\pi$
$983$		−	37.6263i		−	1.20009i	0.799965	−	0.600046i	$-0.204851\pi$
$984$	14.2199	−	22.0249i	0.453312	−	0.702127i
$985$	5.84229			0.186151
$986$	−17.6735	+	6.10304i	−0.562840	+	0.194360i
$987$	11.8112	+	1.21099i	0.375954	+	0.0385464i
$988$	−9.19625	−	11.7277i	−0.292572	−	0.373107i
$989$	−18.2695	+	18.2695i	−0.580938	+	0.580938i
$990$	10.0823	−	20.7184i	0.320436	−	0.658475i
$991$			6.15019i			0.195367i	0.995218	+	0.0976836i	$0.0311433\pi$
$991$			6.15019i			0.195367i	−0.995218	+	0.0976836i	$0.968857\pi$
$992$	17.5552	+	14.5982i	0.557378	+	0.463494i
$993$			31.8077i			1.00939i
$994$	−38.4666	+	9.02000i	−1.22009	+	0.286097i
$995$	39.7926	+	39.7926i	1.26151	+	1.26151i
$996$	22.3979	−	17.5633i	0.709704	−	0.556514i
$997$	38.9462	−	38.9462i	1.23344	−	1.23344i	0.270805	−	0.962634i	$-0.412710\pi$
$997$	38.9462	−	38.9462i	1.23344	−	1.23344i	0.962634	−	0.270805i	$-0.0872898\pi$
$998$	26.6480	−	9.20211i	0.843527	−	0.291288i
$999$			2.23384i			0.0706755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.12	yes	64
4.3	odd	2		1344.2.u.a.1231.4		64
7.6	odd	2	inner	336.2.u.a.139.11	✓	64
16.3	odd	4	inner	336.2.u.a.307.11	yes	64
16.13	even	4		1344.2.u.a.559.29		64
28.27	even	2		1344.2.u.a.1231.29		64
112.13	odd	4		1344.2.u.a.559.4		64
112.83	even	4	inner	336.2.u.a.307.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.11	✓	64	7.6	odd	2	inner
336.2.u.a.139.12	yes	64	1.1	even	1	trivial
336.2.u.a.307.11	yes	64	16.3	odd	4	inner
336.2.u.a.307.12	yes	64	112.83	even	4	inner
1344.2.u.a.559.4		64	112.13	odd	4
1344.2.u.a.559.29		64	16.13	even	4
1344.2.u.a.1231.4		64	4.3	odd	2
1344.2.u.a.1231.29		64	28.27	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.618822 + 1.27164i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.23412 - 1.57383i) q^{4} +(-1.80101 + 1.80101i) q^{5} +(0.461610 + 1.33676i) q^{6} +(-1.67026 - 2.05189i) q^{7} +(2.76504 - 0.595430i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.618822 + 1.27164i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.23412 - 1.57383i) q^{4} +(-1.80101 + 1.80101i) q^{5} +(0.461610 + 1.33676i) q^{6} +(-1.67026 - 2.05189i) q^{7} +(2.76504 - 0.595430i) q^{8} -1.00000i q^{9} +(-1.17573 - 3.40473i) q^{10} +(-4.52322 + 4.52322i) q^{11} +(-1.98552 - 0.240213i) q^{12} +(-2.59667 - 2.59667i) q^{13} +(3.64285 - 0.854209i) q^{14} +2.54701i q^{15} +(-0.953897 + 3.88460i) q^{16} -6.20372i q^{17} +(1.27164 + 0.618822i) q^{18} +(-1.43485 + 1.43485i) q^{19} +(5.05715 + 0.611826i) q^{20} +(-2.63195 - 0.269853i) q^{21} +(-2.95283 - 8.55096i) q^{22} -3.79802 q^{23} +(1.53415 - 2.37621i) q^{24} -1.48727i q^{25} +(4.90889 - 1.69514i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.16803 + 5.16098i) q^{28} +(-1.50697 + 1.50697i) q^{29} +(-3.23887 - 1.57615i) q^{30} -4.03614 q^{31} +(-4.34950 - 3.61688i) q^{32} +6.39680i q^{33} +(7.88887 + 3.83899i) q^{34} +(6.70362 + 0.687319i) q^{35} +(-1.57383 + 1.23412i) q^{36} +(-1.57956 - 1.57956i) q^{37} +(-0.936693 - 2.71253i) q^{38} -3.67224 q^{39} +(-3.90749 + 6.05225i) q^{40} +9.26889 q^{41} +(1.97186 - 3.17990i) q^{42} +(4.81028 - 4.81028i) q^{43} +(12.7010 + 1.53660i) q^{44} +(1.80101 + 1.80101i) q^{45} +(2.35030 - 4.82970i) q^{46} -4.48761 q^{47} +(2.07232 + 3.42133i) q^{48} +(-1.42048 + 6.85436i) q^{49} +(1.89127 + 0.920357i) q^{50} +(-4.38669 - 4.38669i) q^{51} +(-0.882121 + 7.29132i) q^{52} +(6.91789 + 6.91789i) q^{53} +(1.33676 - 0.461610i) q^{54} -16.2927i q^{55} +(-5.84009 - 4.67903i) q^{56} +2.02919i q^{57} +(-0.983772 - 2.84886i) q^{58} +(0.516751 + 0.516751i) q^{59} +(4.00857 - 3.14332i) q^{60} +(-6.02748 - 6.02748i) q^{61} +(2.49765 - 5.13250i) q^{62} +(-2.05189 + 1.67026i) q^{63} +(7.29093 - 3.29278i) q^{64} +9.35325 q^{65} +(-8.13441 - 3.95848i) q^{66} +(6.19917 + 6.19917i) q^{67} +(-9.76361 + 7.65613i) q^{68} +(-2.68560 + 2.68560i) q^{69} +(-5.02236 + 8.09924i) q^{70} -10.5595 q^{71} +(-0.595430 - 2.76504i) q^{72} +3.85786 q^{73} +(2.98609 - 1.03116i) q^{74} +(-1.05166 - 1.05166i) q^{75} +(4.02900 + 0.487437i) q^{76} +(16.8361 + 1.72620i) q^{77} +(2.27246 - 4.66976i) q^{78} +5.09974i q^{79} +(-5.27822 - 8.71417i) q^{80} -1.00000 q^{81} +(-5.73579 + 11.7867i) q^{82} +(-10.0631 + 10.0631i) q^{83} +(2.82344 + 4.47528i) q^{84} +(11.1730 + 11.1730i) q^{85} +(3.14023 + 9.09364i) q^{86} +2.13118i q^{87} +(-9.81364 + 15.2002i) q^{88} +0.264516 q^{89} +(-3.40473 + 1.17573i) q^{90} +(-0.990965 + 9.66517i) q^{91} +(4.68721 + 5.97745i) q^{92} +(-2.85398 + 2.85398i) q^{93} +(2.77703 - 5.70661i) q^{94} -5.16836i q^{95} +(-5.63308 + 0.518040i) q^{96} +7.14810i q^{97} +(-7.83723 - 6.04796i) q^{98} +(4.52322 + 4.52322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

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