LMFDB - Embedded newform 680.2.co.a.99.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(99,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.co (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			99.13
Character	$\chi$	$=$	680.99
Dual form			680.2.co.a.419.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31885 - 0.510535i) q^{2} +(-0.821426 - 0.163392i) q^{3} +(1.47871 + 1.34663i) q^{4} +(-1.70342 - 1.44857i) q^{5} +(0.999917 + 0.634856i) q^{6} +(-3.51029 - 2.34550i) q^{7} +(-1.26268 - 2.53094i) q^{8} +(-2.12359 - 0.879621i) q^{9} +(1.50701 + 2.78010i) q^{10} +(-0.146226 + 0.0290862i) q^{11} +(-0.994620 - 1.34777i) q^{12} +(-1.47133 - 1.47133i) q^{13} +(3.43207 + 4.88547i) q^{14} +(1.16255 + 1.46822i) q^{15} +(0.373151 + 3.98256i) q^{16} +(1.48653 + 3.84581i) q^{17} +(2.35161 + 2.24425i) q^{18} +(5.17597 - 2.14396i) q^{19} +(-0.568173 - 4.43590i) q^{20} +(2.50021 + 2.50021i) q^{21} +(0.207699 + 0.0362934i) q^{22} +(-0.872501 - 4.38636i) q^{23} +(0.623666 + 2.28529i) q^{24} +(0.803303 + 4.93505i) q^{25} +(1.18929 + 2.69162i) q^{26} +(3.68977 + 2.46542i) q^{27} +(-2.03216 - 8.19538i) q^{28} +(-1.73169 + 1.15708i) q^{29} +(-0.783651 - 2.52988i) q^{30} +(-0.677420 + 3.40562i) q^{31} +(1.54111 - 5.44288i) q^{32} +0.124866 q^{33} +(0.00292394 - 5.83095i) q^{34} +(2.58189 + 9.08026i) q^{35} +(-1.95565 - 4.16041i) q^{36} +(-2.16031 + 10.8606i) q^{37} +(-7.92087 + 0.185033i) q^{38} +(0.968184 + 1.44899i) q^{39} +(-1.51535 + 6.14034i) q^{40} +(-9.05140 - 6.04795i) q^{41} +(-2.02094 - 4.57383i) q^{42} +(-0.245522 + 0.592742i) q^{43} +(-0.255394 - 0.153903i) q^{44} +(2.34319 + 4.57454i) q^{45} +(-1.08870 + 6.23038i) q^{46} +(-0.855982 - 0.855982i) q^{47} +(0.344202 - 3.33235i) q^{48} +(4.14196 + 9.99958i) q^{49} +(1.46008 - 6.91868i) q^{50} +(-0.592697 - 3.40194i) q^{51} +(-0.194322 - 4.15700i) q^{52} +(5.61555 - 2.32604i) q^{53} +(-3.60755 - 5.13527i) q^{54} +(0.291218 + 0.162272i) q^{55} +(-1.50393 + 11.8459i) q^{56} +(-4.60199 + 0.915392i) q^{57} +(2.87456 - 0.641918i) q^{58} +(1.53944 - 3.71653i) q^{59} +(-0.258077 + 3.73660i) q^{60} +(10.5179 + 7.02785i) q^{61} +(2.63210 - 4.14564i) q^{62} +(5.39127 + 8.06861i) q^{63} +(-4.81127 + 6.39153i) q^{64} +(0.374976 + 4.63761i) q^{65} +(-0.164679 - 0.0637487i) q^{66} +7.15571 q^{67} +(-2.98076 + 7.68863i) q^{68} +3.74563i q^{69} +(1.23068 - 13.2936i) q^{70} +(-12.3082 - 2.44825i) q^{71} +(0.455159 + 6.48536i) q^{72} +(2.35512 + 3.52469i) q^{73} +(8.39383 - 13.2205i) q^{74} +(0.146492 - 4.18503i) q^{75} +(10.5409 + 3.79986i) q^{76} +(0.581517 + 0.240872i) q^{77} +(-0.537125 - 2.40529i) q^{78} +(-0.955563 - 4.80394i) q^{79} +(5.13337 - 7.32451i) q^{80} +(2.24794 + 2.24794i) q^{81} +(8.84971 + 12.5974i) q^{82} +(2.53694 - 1.05083i) q^{83} +(0.330209 + 7.06394i) q^{84} +(3.03873 - 8.70437i) q^{85} +(0.626421 - 0.656387i) q^{86} +(1.61151 - 0.667510i) q^{87} +(0.258252 + 0.333362i) q^{88} +(-8.87873 + 8.87873i) q^{89} +(-0.754841 - 7.22939i) q^{90} +(1.71378 + 8.61578i) q^{91} +(4.61665 - 7.66108i) q^{92} +(1.11290 - 2.68678i) q^{93} +(0.691899 + 1.56592i) q^{94} +(-11.9225 - 3.84568i) q^{95} +(-2.15523 + 4.21912i) q^{96} +(-8.90994 + 5.95343i) q^{97} +(-0.357469 - 15.3025i) q^{98} +(0.336110 + 0.0668563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) $ 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$	$-1$	$-1$

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 $

$2$	−1.31885	−	0.510535i	−0.932565	−	0.361003i
$2$	−1.31885	−	0.510535i	−0.932565	−	0.361003i
$3$	−0.821426	−	0.163392i	−0.474251	−	0.0943343i	−0.0478228	−	0.998856i	$-0.515228\pi$
$3$	−0.821426	−	0.163392i	−0.474251	−	0.0943343i	−0.426428	+	0.904521i	$0.640228\pi$
$4$	1.47871	+	1.34663i	0.739354	+	0.673317i
$5$	−1.70342	−	1.44857i	−0.761794	−	0.647819i
$5$	−1.70342	−	1.44857i	−0.761794	−	0.647819i
$6$	0.999917	+	0.634856i	0.408215	+	0.259179i
$7$	−3.51029	−	2.34550i	−1.32676	−	0.886515i	−0.328447	−	0.944522i	$-0.606525\pi$
$7$	−3.51029	−	2.34550i	−1.32676	−	0.886515i	−0.998316	+	0.0580075i	$0.981525\pi$
$8$	−1.26268	−	2.53094i	−0.446426	−	0.894821i
$9$	−2.12359	−	0.879621i	−0.707865	−	0.293207i
$10$	1.50701	+	2.78010i	0.476558	+	0.879143i
$11$	−0.146226	+	0.0290862i	−0.0440888	+	0.00876981i	−0.217085	−	0.976153i	$-0.569655\pi$
$11$	−0.146226	+	0.0290862i	−0.0440888	+	0.00876981i	0.172997	+	0.984922i	$0.444655\pi$
$12$	−0.994620	−	1.34777i	−0.287122	−	0.389068i
$13$	−1.47133	−	1.47133i	−0.408073	−	0.408073i	0.472993	−	0.881066i	$-0.343174\pi$
$13$	−1.47133	−	1.47133i	−0.408073	−	0.408073i	−0.881066	+	0.472993i	$0.843174\pi$
$14$	3.43207	+	4.88547i	0.917258	+	1.30570i
$15$	1.16255	+	1.46822i	0.300170	+	0.379092i
$16$	0.373151	+	3.98256i	0.0932876	+	0.995639i
$17$	1.48653	+	3.84581i	0.360535	+	0.932746i
$17$	1.48653	+	3.84581i	0.360535	+	0.932746i
$18$	2.35161	+	2.24425i	0.554281	+	0.528976i
$19$	5.17597	−	2.14396i	1.18745	−	0.491858i	0.300526	−	0.953774i	$-0.402838\pi$
$19$	5.17597	−	2.14396i	1.18745	−	0.491858i	0.886924	+	0.461916i	$0.152838\pi$
$20$	−0.568173	−	4.43590i	−0.127047	−	0.991897i
$21$	2.50021	+	2.50021i	0.545590	+	0.545590i
$22$	0.207699	+	0.0362934i	0.0442816	+	0.00773778i
$23$	−0.872501	−	4.38636i	−0.181929	−	0.914619i	−0.958609	−	0.284724i	$-0.908098\pi$
$23$	−0.872501	−	4.38636i	−0.181929	−	0.914619i	0.776680	−	0.629895i	$-0.216902\pi$
$24$	0.623666	+	2.28529i	0.127305	+	0.466483i
$25$	0.803303	+	4.93505i	0.160661	+	0.987010i
$26$	1.18929	+	2.69162i	0.233239	+	0.527870i
$27$	3.68977	+	2.46542i	0.710096	+	0.474471i
$28$	−2.03216	−	8.19538i	−0.384041	−	1.54878i
$29$	−1.73169	+	1.15708i	−0.321566	+	0.214864i	−0.705867	−	0.708344i	$-0.749443\pi$
$29$	−1.73169	+	1.15708i	−0.321566	+	0.214864i	0.384301	+	0.923208i	$0.374443\pi$
$30$	−0.783651	−	2.52988i	−0.143074	−	0.461890i
$31$	−0.677420	+	3.40562i	−0.121668	+	0.611667i	0.871049	+	0.491197i	$0.163440\pi$
$31$	−0.677420	+	3.40562i	−0.121668	+	0.611667i	−0.992717	+	0.120471i	$0.961560\pi$
$32$	1.54111	−	5.44288i	0.272432	−	0.962175i
$33$	0.124866			0.0217364
$34$	0.00292394	−	5.83095i	0.000501452	−	1.00000i
$35$	2.58189	+	9.08026i	0.436419	+	1.53484i
$36$	−1.95565	−	4.16041i	−0.325941	−	0.693401i
$37$	−2.16031	+	10.8606i	−0.355152	+	1.78547i	0.228581	+	0.973525i	$0.426592\pi$
$37$	−2.16031	+	10.8606i	−0.355152	+	1.78547i	−0.583733	+	0.811946i	$0.698408\pi$
$38$	−7.92087	+	0.185033i	−1.28494	+	0.0300162i
$39$	0.968184	+	1.44899i	0.155034	+	0.232024i
$40$	−1.51535	+	6.14034i	−0.239598	+	0.970872i
$41$	−9.05140	−	6.04795i	−1.41359	−	0.944531i	−0.999410	−	0.0343369i	$-0.989068\pi$
$41$	−9.05140	−	6.04795i	−1.41359	−	0.944531i	−0.414181	−	0.910195i	$-0.635932\pi$
$42$	−2.02094	−	4.57383i	−0.311838	−	0.705757i
$43$	−0.245522	+	0.592742i	−0.0374417	+	0.0903923i	−0.941494	−	0.337029i	$-0.890578\pi$
$43$	−0.245522	+	0.592742i	−0.0374417	+	0.0903923i	0.904053	+	0.427421i	$0.140578\pi$
$44$	−0.255394	−	0.153903i	−0.0385021	−	0.0232018i
$45$	2.34319	+	4.57454i	0.349302	+	0.681932i
$46$	−1.08870	+	6.23038i	−0.160520	+	0.918619i
$47$	−0.855982	−	0.855982i	−0.124858	−	0.124858i	0.641917	−	0.766774i	$-0.278140\pi$
$47$	−0.855982	−	0.855982i	−0.124858	−	0.124858i	−0.766774	+	0.641917i	$0.778140\pi$
$48$	0.344202	−	3.33235i	0.0496812	−	0.480983i
$49$	4.14196	+	9.99958i	0.591709	+	1.42851i
$50$	1.46008	−	6.91868i	0.206487	−	0.978449i
$51$	−0.592697	−	3.40194i	−0.0829942	−	0.476366i
$52$	−0.194322	−	4.15700i	−0.0269476	−	0.576473i
$53$	5.61555	−	2.32604i	0.771355	−	0.319505i	0.0379336	−	0.999280i	$-0.487922\pi$
$53$	5.61555	−	2.32604i	0.771355	−	0.319505i	0.733421	+	0.679775i	$0.237922\pi$
$54$	−3.60755	−	5.13527i	−0.490925	−	0.698822i
$55$	0.291218	+	0.162272i	0.0392678	+	0.0218808i
$56$	−1.50393	+	11.8459i	−0.200971	+	1.58298i
$57$	−4.60199	+	0.915392i	−0.609548	+	0.121247i
$58$	2.87456	−	0.641918i	0.377448	−	0.0842880i
$59$	1.53944	−	3.71653i	0.200417	−	0.483851i	−0.791433	−	0.611256i	$-0.790665\pi$
$59$	1.53944	−	3.71653i	0.200417	−	0.483851i	0.991851	+	0.127405i	$0.0406648\pi$
$60$	−0.258077	+	3.73660i	−0.0333176	+	0.482393i
$61$	10.5179	+	7.02785i	1.34668	+	0.899824i	0.999282	−	0.0378935i	$-0.0120648\pi$
$61$	10.5179	+	7.02785i	1.34668	+	0.899824i	0.347400	+	0.937717i	$0.387065\pi$
$62$	2.63210	−	4.14564i	0.334277	−	0.526497i
$63$	5.39127	+	8.06861i	0.679236	+	1.01655i
$64$	−4.81127	+	6.39153i	−0.601409	+	0.798942i
$65$	0.374976	+	4.63761i	0.0465101	+	0.575225i
$66$	−0.164679	−	0.0637487i	−0.0202706	−	0.00784692i
$67$	7.15571			0.874210			0.437105	−	0.899411i	$-0.356004\pi$
$67$	7.15571			0.874210			0.437105	+	0.899411i	$0.356004\pi$
$68$	−2.98076	+	7.68863i	−0.361471	+	0.932384i
$69$			3.74563i			0.450921i
$70$	1.23068	−	13.2936i	0.147094	−	1.58889i
$71$	−12.3082	−	2.44825i	−1.46071	−	0.290553i	−0.600144	−	0.799892i	$-0.704890\pi$
$71$	−12.3082	−	2.44825i	−1.46071	−	0.290553i	−0.860566	+	0.509339i	$0.829890\pi$
$72$	0.455159	+	6.48536i	0.0536410	+	0.764307i
$73$	2.35512	+	3.52469i	0.275646	+	0.412533i	0.943302	−	0.331937i	$-0.107702\pi$
$73$	2.35512	+	3.52469i	0.275646	+	0.412533i	−0.667656	+	0.744470i	$0.732702\pi$
$74$	8.39383	−	13.2205i	0.975763	−	1.53686i
$75$	0.146492	−	4.18503i	0.0169155	−	0.483246i
$76$	10.5409	+	3.79986i	1.20912	+	0.435873i
$77$	0.581517	+	0.240872i	0.0662700	+	0.0274499i
$78$	−0.537125	−	2.40529i	−0.0608174	−	0.272345i
$79$	−0.955563	−	4.80394i	−0.107509	−	0.540485i	−0.996574	−	0.0827042i	$-0.973644\pi$
$79$	−0.955563	−	4.80394i	−0.107509	−	0.540485i	0.889065	−	0.457781i	$-0.151356\pi$
$80$	5.13337	−	7.32451i	0.573928	−	0.818906i
$81$	2.24794	+	2.24794i	0.249771	+	0.249771i
$82$	8.84971	+	12.5974i	0.977287	+	1.39115i
$83$	2.53694	−	1.05083i	0.278465	−	0.115344i	−0.239080	−	0.971000i	$-0.576846\pi$
$83$	2.53694	−	1.05083i	0.278465	−	0.115344i	0.517545	+	0.855656i	$0.326846\pi$
$84$	0.330209	+	7.06394i	0.0360288	+	0.770739i
$85$	3.03873	−	8.70437i	0.329597	−	0.944122i
$86$	0.626421	−	0.656387i	0.0675487	−	0.0707801i
$87$	1.61151	−	0.667510i	0.172772	−	0.0715646i
$88$	0.258252	+	0.333362i	0.0275298	+	0.0355365i
$89$	−8.87873	+	8.87873i	−0.941143	+	0.941143i	−0.998362	−	0.0572184i	$-0.981777\pi$
$89$	−8.87873	+	8.87873i	−0.941143	+	0.941143i	0.0572184	+	0.998362i	$0.481777\pi$
$90$	−0.754841	−	7.22939i	−0.0795672	−	0.762045i
$91$	1.71378	+	8.61578i	0.179653	+	0.903179i
$92$	4.61665	−	7.66108i	0.481319	−	0.798723i
$93$	1.11290	−	2.68678i	0.115402	−	0.278606i
$94$	0.691899	+	1.56592i	0.0713639	+	0.161512i
$95$	−11.9225	−	3.84568i	−1.22323	−	0.394558i
$96$	−2.15523	+	4.21912i	−0.219967	+	0.430613i
$97$	−8.90994	+	5.95343i	−0.904668	+	0.604480i	−0.918498	−	0.395425i	$-0.870597\pi$
$97$	−8.90994	+	5.95343i	−0.904668	+	0.604480i	0.0138307	+	0.999904i	$0.495597\pi$
$98$	−0.357469	−	15.3025i	−0.0361098	−	1.54579i
$99$	0.336110	+	0.0668563i	0.0337803	+	0.00671932i
$100$	−5.45786	+	8.37925i	−0.545786	+	0.837925i
$101$	−1.50701			−0.149953			−0.0749767	−	0.997185i	$-0.523888\pi$
$101$	−1.50701			−0.149953			−0.0749767	+	0.997185i	$0.523888\pi$
$102$	−0.955132	+	4.78922i	−0.0945722	+	0.474203i
$103$	9.73621			0.959337			0.479668	−	0.877450i	$-0.340757\pi$
$103$	9.73621			0.959337			0.479668	+	0.877450i	$0.340757\pi$
$104$	−1.86602	+	5.58165i	−0.182978	+	0.547326i
$105$	−0.637192	−	7.88063i	−0.0621836	−	0.769071i
$106$	−8.59356	+	0.200747i	−0.834680	+	0.0194982i
$107$	5.85894	+	8.76852i	0.566405	+	0.847685i	0.998534	−	0.0541266i	$-0.0172375\pi$
$107$	5.85894	+	8.76852i	0.566405	+	0.847685i	−0.432129	+	0.901812i	$0.642237\pi$
$108$	2.13606	+	8.61441i	0.205543	+	0.828922i
$109$	0.703133	−	1.05231i	0.0673480	−	0.100793i	−0.796267	−	0.604945i	$-0.793195\pi$
$109$	0.703133	−	1.05231i	0.0673480	−	0.100793i	0.863615	+	0.504152i	$0.168195\pi$
$110$	−0.301226	−	0.362689i	−0.0287208	−	0.0345811i
$111$	3.54907	−	8.56820i	0.336862	−	0.813258i
$112$	8.03121	−	14.8551i	0.758878	−	1.40368i
$113$	−0.331935	−	1.66875i	−0.0312258	−	0.156983i	0.962027	−	0.272956i	$-0.0880014\pi$
$113$	−0.331935	−	1.66875i	−0.0312258	−	0.156983i	−0.993252	+	0.115973i	$0.963001\pi$
$114$	6.53665	+	1.14222i	0.612213	+	0.106978i
$115$	−4.86770	+	8.73571i	−0.453915	+	0.814609i
$116$	−4.11882	−	0.620973i	−0.382423	−	0.0576559i
$117$	1.83029	+	4.41871i	0.169210	+	0.408510i
$118$	−3.92770	+	4.11559i	−0.361574	+	0.378871i
$119$	3.80221	−	16.9865i	0.348548	−	1.55715i
$120$	2.24803	−	4.79624i	0.205216	−	0.437835i
$121$	−10.1421	+	4.20101i	−0.922013	+	0.381910i
$122$	−10.2835	−	14.6384i	−0.931028	−	1.32530i
$123$	6.44687	+	6.44687i	0.581295	+	0.581295i
$124$	−5.58783	+	4.12368i	−0.501802	+	0.370317i
$125$	5.78039	−	9.57012i	0.517014	−	0.855977i
$126$	−2.99094	−	13.3937i	−0.266455	−	1.19320i
$127$	−1.98017	+	4.78056i	−0.175712	+	0.424206i	−0.987059	−	0.160359i	$-0.948735\pi$
$127$	−1.98017	+	4.78056i	−0.175712	+	0.424206i	0.811347	+	0.584565i	$0.198735\pi$
$128$	9.60842	−	5.97312i	0.849273	−	0.527954i
$129$	0.298527	−	0.446777i	0.0262838	−	0.0393366i
$130$	1.87313	−	6.30773i	0.164284	−	0.553225i
$131$	−2.40330	−	3.59679i	−0.209977	−	0.314253i	0.711500	−	0.702686i	$-0.248016\pi$
$131$	−2.40330	−	3.59679i	−0.209977	−	0.314253i	−0.921477	+	0.388434i	$0.873016\pi$
$132$	0.184641	+	0.168149i	0.0160709	+	0.0146355i
$133$	−23.1978	−	4.61433i	−2.01150	−	0.400113i
$134$	−9.43728	−	3.65325i	−0.815257	−	0.315592i
$135$	−2.71390	−	9.54454i	−0.233576	−	0.821463i
$136$	7.85648	−	8.61833i	0.673688	−	0.739016i
$137$		−	3.70115i		−	0.316211i	−0.987422	−	0.158105i	$-0.949461\pi$
$137$		−	3.70115i		−	0.316211i	0.987422	−	0.158105i	$-0.0505385\pi$
$138$	1.91228	−	4.93991i	0.162784	−	0.420513i
$139$	1.92302	−	9.66765i	0.163108	−	0.819999i	−0.809423	−	0.587226i	$-0.800220\pi$
$139$	1.92302	−	9.66765i	0.163108	−	0.819999i	0.972531	−	0.232773i	$-0.0747800\pi$
$140$	−8.40994	+	16.9039i	−0.710769	+	1.42864i
$141$	0.563266	+	0.842987i	0.0474355	+	0.0709923i
$142$	14.9827	+	9.51261i	1.25732	+	0.798281i
$143$	0.257942	+	0.172351i	0.0215702	+	0.0144127i
$144$	2.71072	−	8.78557i	0.225894	−	0.732130i
$145$	4.62590	+	0.537476i	0.384160	+	0.0446349i
$146$	−1.30656	−	5.85089i	−0.108132	−	0.484223i
$147$	−1.76847	−	8.89068i	−0.145861	−	0.733291i
$148$	−17.8197	+	13.1505i	−1.46477	+	1.08096i
$149$	6.94573	−	6.94573i	0.569016	−	0.569016i	−0.362837	−	0.931853i	$-0.618192\pi$
$149$	6.94573	−	6.94573i	0.569016	−	0.569016i	0.931853	+	0.362837i	$0.118192\pi$
$150$	−2.32981	+	5.44462i	−0.190228	+	0.444552i
$151$	−0.0408501	+	0.0169206i	−0.00332433	+	0.00137698i	−0.384345	−	0.923190i	$-0.625573\pi$
$151$	−0.0408501	+	0.0169206i	−0.00332433	+	0.00137698i	0.381021	+	0.924567i	$0.375573\pi$
$152$	−11.9618	−	10.3929i	−0.970232	−	0.842977i
$153$	0.226079	−	9.47452i	0.0182774	−	0.765969i
$154$	−0.643957	−	0.614558i	−0.0518915	−	0.0495225i
$155$	6.08720	−	4.81992i	0.488936	−	0.387145i
$156$	−0.519599	+	3.44642i	−0.0416012	+	0.275935i
$157$	−13.1440	+	13.1440i	−1.04900	+	1.04900i	−0.0502657	+	0.998736i	$0.516007\pi$
$157$	−13.1440	+	13.1440i	−1.04900	+	1.04900i	−0.998736	+	0.0502657i	$0.983993\pi$
$158$	−1.19234	+	6.82350i	−0.0948575	+	0.542849i
$159$	−4.99281	+	0.993132i	−0.395956	+	0.0787605i
$160$	−10.5095	+	7.03914i	−0.830853	+	0.556493i
$161$	−7.22547	+	17.4438i	−0.569447	+	1.37477i
$162$	−1.81703	−	4.11234i	−0.142760	−	0.323096i
$163$	−18.1234	−	12.1097i	−1.41953	−	0.948502i	−0.999153	−	0.0411542i	$-0.986897\pi$
$163$	−18.1234	−	12.1097i	−1.41953	−	0.948502i	−0.420381	−	0.907348i	$-0.638103\pi$
$164$	−5.23999	−	21.1321i	−0.409174	−	1.65014i
$165$	−0.212700	−	0.180877i	−0.0165587	−	0.0140813i
$166$	−3.88232	+	0.0906915i	−0.301326	+	0.00703902i
$167$	−14.5257	−	2.88934i	−1.12403	−	0.223584i	−0.402132	−	0.915582i	$-0.631731\pi$
$167$	−14.5257	−	2.88934i	−1.12403	−	0.223584i	−0.721899	+	0.691998i	$0.756731\pi$
$168$	3.17090	−	9.48483i	0.244640	−	0.731770i
$169$		−	8.67039i		−	0.666953i
$170$	−8.45151	+	9.92834i	−0.648201	+	0.761469i
$171$	−12.8775			−0.984770
$172$	−1.16126	+	0.545863i	−0.0885453	+	0.0416217i
$173$	−2.36713	+	11.9004i	−0.179970	+	0.904769i	0.780238	+	0.625483i	$0.215098\pi$
$173$	−2.36713	+	11.9004i	−0.179970	+	0.904769i	−0.960208	+	0.279286i	$0.909902\pi$
$174$	−2.46612	+	0.0576089i	−0.186956	+	0.00436732i
$175$	8.75532	−	19.2076i	0.661840	−	1.45196i
$176$	−0.170402	−	0.571500i	−0.0128445	−	0.0430784i
$177$	−1.87178	+	2.80132i	−0.140692	+	0.210560i
$178$	16.2426	−	7.17677i	1.21743	−	0.537921i
$179$	−9.64299	−	3.99426i	−0.720751	−	0.298545i	−0.00800595	−	0.999968i	$-0.502548\pi$
$179$	−9.64299	−	3.99426i	−0.720751	−	0.298545i	−0.712745	+	0.701423i	$0.752548\pi$
$180$	−2.69534	+	9.91982i	−0.200899	+	0.739380i
$181$	3.85368	+	19.3738i	0.286442	+	1.44004i	0.809187	+	0.587552i	$0.199908\pi$
$181$	3.85368	+	19.3738i	0.286442	+	1.44004i	−0.522745	+	0.852489i	$0.675092\pi$
$182$	2.13844	−	12.2378i	0.158512	−	0.907128i
$183$	−7.49140	−	7.49140i	−0.553780	−	0.553780i
$184$	−9.99990	+	7.74682i	−0.737203	+	0.571103i
$185$	19.4122	−	15.3708i	1.42722	−	1.13009i
$186$	−2.83944	+	2.97527i	−0.208198	+	0.218158i
$187$	−0.329229	−	0.519120i	−0.0240756	−	0.0379618i
$188$	−0.113052	−	2.41844i	−0.00824515	−	0.176383i
$189$	−7.16949	−	17.3087i	−0.521504	−	1.25902i
$190$	13.7606	+	11.1587i	0.998301	+	0.809540i
$191$	15.8798	+	15.8798i	1.14902	+	1.14902i	0.986745	+	0.162278i	$0.0518843\pi$
$191$	15.8798	+	15.8798i	1.14902	+	1.14902i	0.162278	+	0.986745i	$0.448116\pi$
$192$	4.99643	−	4.46405i	0.360586	−	0.322165i
$193$	14.8987	−	2.96353i	1.07243	−	0.213319i	0.372863	−	0.927887i	$-0.378376\pi$
$193$	14.8987	−	2.96353i	1.07243	−	0.213319i	0.699567	+	0.714567i	$0.253376\pi$
$194$	14.7903	−	3.30282i	1.06188	−	0.237129i
$195$	0.449733	−	3.87072i	0.0322060	−	0.277188i
$196$	−7.34103	+	20.3642i	−0.524359	+	1.45458i
$197$	3.16439	−	4.73585i	0.225454	−	0.337415i	−0.701447	−	0.712721i	$-0.747462\pi$
$197$	3.16439	−	4.73585i	0.225454	−	0.337415i	0.926901	+	0.375306i	$0.122462\pi$
$198$	−0.409144	−	0.259769i	−0.0290766	−	0.0184610i
$199$	10.7811	−	7.20369i	0.764251	−	0.510656i	−0.111297	−	0.993787i	$-0.535500\pi$
$199$	10.7811	−	7.20369i	0.764251	−	0.510656i	0.875548	+	0.483131i	$0.160500\pi$
$200$	11.4760	−	8.26451i	0.811474	−	0.584389i
$201$	−5.87789	−	1.16919i	−0.414595	−	0.0824680i
$202$	1.98752	+	0.769384i	0.139841	+	0.0541337i
$203$	8.79264			0.617123
$204$	3.70474	−	5.82861i	0.259384	−	0.408085i
$205$	6.65750	+	23.4138i	0.464980	+	1.63529i
$206$	−12.8406	−	4.97068i	−0.894644	−	0.346324i
$207$	−2.00550	+	10.0823i	−0.139392	+	0.700770i
$208$	5.31062	−	6.40867i	0.368225	−	0.444361i
$209$	−0.694502	+	0.464052i	−0.0480397	+	0.0320991i
$210$	−3.18298	+	10.7186i	−0.219647	+	0.739656i
$211$	−1.12513	−	0.751785i	−0.0774569	−	0.0517550i	0.516239	−	0.856445i	$-0.327332\pi$
$211$	−1.12513	−	0.751785i	−0.0774569	−	0.0517550i	−0.593696	+	0.804690i	$0.702332\pi$
$212$	11.4361	+	4.12256i	0.785432	+	0.283139i
$213$	9.71023	+	4.02211i	0.665334	+	0.275590i
$214$	−3.25040	−	14.5555i	−0.222193	−	0.994995i
$215$	1.27685	−	0.654035i	0.0870807	−	0.0446048i
$216$	1.58083	−	12.4516i	0.107562	−	0.847225i
$217$	10.3658	−	10.3658i	0.703677	−	0.703677i
$218$	−1.46457	+	1.02886i	−0.0991930	+	0.0696835i
$219$	−1.35865	−	3.28008i	−0.0918092	−	0.221647i
$220$	0.212105	+	0.632118i	0.0143001	+	0.0426174i
$221$	3.47128	−	7.84561i	0.233503	−	0.527753i
$222$	−9.05504	+	9.48821i	−0.607735	+	0.636807i
$223$	16.4637	−	6.81950i	1.10249	−	0.456667i	0.244146	−	0.969738i	$-0.421492\pi$
$223$	16.4637	−	6.81950i	1.10249	−	0.456667i	0.858346	+	0.513071i	$0.171492\pi$
$224$	−18.1760	+	15.4914i	−1.21444	+	1.03506i
$225$	2.63508	−	11.1866i	0.175672	−	0.745776i
$226$	−0.414185	+	2.37029i	−0.0275512	+	0.157669i
$227$	−18.7030	+	3.72026i	−1.24136	+	0.246922i	−0.771736	−	0.635943i	$-0.780611\pi$
$227$	−18.7030	+	3.72026i	−1.24136	+	0.246922i	−0.469627	+	0.882865i	$0.655611\pi$
$228$	−8.03769	−	4.84360i	−0.532309	−	0.320775i
$229$	−13.3320	−	5.52231i	−0.881005	−	0.364924i	−0.104119	−	0.994565i	$-0.533202\pi$
$229$	−13.3320	−	5.52231i	−0.881005	−	0.364924i	−0.776887	+	0.629641i	$0.783202\pi$
$230$	10.8796	−	9.03592i	0.717382	−	0.595811i
$231$	−0.438317	−	0.292874i	−0.0288391	−	0.0192697i
$232$	5.11506	+	2.92177i	0.335820	+	0.191824i
$233$	−21.6192	+	14.4455i	−1.41632	+	0.946355i	−0.417022	+	0.908897i	$0.636926\pi$
$233$	−21.6192	+	14.4455i	−1.41632	+	0.946355i	−0.999298	+	0.0374580i	$0.988074\pi$
$234$	−0.157962	−	6.76203i	−0.0103263	−	0.442048i
$235$	0.218152	+	2.69805i	0.0142307	+	0.176001i
$236$	7.28118	−	3.42260i	0.473964	−	0.222792i
$237$			4.10221i			0.266467i
$238$	−13.6867	+	20.4614i	−0.887180	+	1.32632i
$239$			13.2308i			0.855829i	0.903819	+	0.427915i	$0.140752\pi$
$239$			13.2308i			0.855829i	−0.903819	+	0.427915i	$0.859248\pi$
$240$	−5.41345	+	5.17780i	−0.349437	+	0.334226i
$241$	−2.40111	+	12.0712i	−0.154669	+	0.777574i	0.823101	+	0.567895i	$0.192242\pi$
$241$	−2.40111	+	12.0712i	−0.154669	+	0.777574i	−0.977770	+	0.209679i	$0.932758\pi$
$242$	15.5207	−	0.362565i	0.997707	−	0.0233066i
$243$	−8.87550	−	13.2831i	−0.569363	−	0.852113i
$244$	6.08898	+	24.5559i	0.389807	+	1.57203i
$245$	7.42955	−	23.0334i	0.474657	−	1.47155i
$246$	−5.21107	−	11.7938i	−0.332246	−	0.751944i
$247$	−10.7700	−	4.46109i	−0.685280	−	0.283852i
$248$	9.47477	−	2.58571i	0.601648	−	0.164193i
$249$	−2.25561	+	0.448668i	−0.142943	+	0.0284332i
$250$	−12.5093	+	9.67041i	−0.791159	+	0.611611i
$251$	19.2684	+	19.2684i	1.21621	+	1.21621i	0.968949	+	0.247260i	$0.0795301\pi$
$251$	19.2684	+	19.2684i	1.21621	+	1.21621i	0.247260	+	0.968949i	$0.420470\pi$
$252$	−2.89335	+	19.1912i	−0.182264	+	1.20893i
$253$	0.255165	+	0.616022i	0.0160421	+	0.0387290i
$254$	5.05219	−	5.29387i	0.317002	−	0.332167i
$255$	−3.91832	+	6.65350i	−0.245375	+	0.416658i
$256$	−15.7215	+	2.97219i	−0.982595	+	0.185762i
$257$	−7.21315	−	17.4141i	−0.449944	−	1.08626i	−0.972343	−	0.233559i	$-0.924963\pi$
$257$	−7.21315	−	17.4141i	−0.449944	−	1.08626i	0.522399	−	0.852701i	$-0.325037\pi$
$258$	−0.621807	+	0.436822i	−0.0387120	+	0.0271953i
$259$	33.0568	−	33.0568i	2.05405	−	2.05405i
$260$	−5.69069	+	7.36263i	−0.352921	+	0.456611i
$261$	4.69519	−	0.933932i	0.290625	−	0.0578089i
$262$	1.33329	+	5.97058i	0.0823710	+	0.368864i
$263$	1.95760	−	4.72607i	0.120711	−	0.291422i	−0.851961	−	0.523605i	$-0.824587\pi$
$263$	1.95760	−	4.72607i	0.120711	−	0.291422i	0.972672	+	0.232183i	$0.0745868\pi$
$264$	−0.157667	−	0.316029i	−0.00970370	−	0.0194502i
$265$	−12.9351	−	4.17228i	−0.794595	−	0.256301i
$266$	28.2385	+	17.9289i	1.73141	+	1.09929i
$267$	8.74393	−	5.84251i	0.535120	−	0.357556i
$268$	10.5812	+	9.63613i	0.646350	+	0.588621i
$269$	−2.89616	+	14.5600i	−0.176582	+	0.887737i	0.786307	+	0.617837i	$0.211991\pi$
$269$	−2.89616	+	14.5600i	−0.176582	+	0.887737i	−0.962888	+	0.269900i	$0.913009\pi$
$270$	−1.29361	+	13.9733i	−0.0787263	+	0.850389i
$271$	−30.6738			−1.86330			−0.931649	−	0.363360i	$-0.881630\pi$
$271$	−30.6738			−1.86330			−0.931649	+	0.363360i	$0.881630\pi$
$272$	−14.7615	+	7.35524i	−0.895045	+	0.445977i
$273$		−	7.35724i		−	0.445281i
$274$	−1.88957	+	4.88124i	−0.114153	+	0.294887i
$275$	−0.261005	−	0.698268i	−0.0157392	−	0.0421071i
$276$	−5.04400	+	5.53869i	−0.303613	+	0.333390i
$277$	1.64013	−	1.09590i	0.0985461	−	0.0658464i	−0.505321	−	0.862932i	$-0.668626\pi$
$277$	1.64013	−	1.09590i	0.0985461	−	0.0658464i	0.603867	+	0.797085i	$0.293626\pi$
$278$	−7.47184	+	11.7684i	−0.448131	+	0.705820i
$279$	4.43422	−	6.63628i	0.265470	−	0.397304i
$280$	19.7215	−	18.0001i	1.17858	−	1.07571i
$281$	16.8736	+	6.98926i	1.00659	+	0.416944i	0.824210	−	0.566284i	$-0.191619\pi$
$281$	16.8736	+	6.98926i	1.00659	+	0.416944i	0.182382	+	0.983228i	$0.441619\pi$
$282$	−0.312486	−	1.39934i	−0.0186083	−	0.0833293i
$283$	−1.13742	−	5.71818i	−0.0676124	−	0.339910i	0.932142	−	0.362094i	$-0.117938\pi$
$283$	−1.13742	−	5.71818i	−0.0676124	−	0.339910i	−0.999754	+	0.0221837i	$0.992938\pi$
$284$	−14.9033	−	20.1948i	−0.884347	−	1.19834i
$285$	9.16514	+	5.10699i	0.542896	+	0.302512i
$286$	−0.252194	−	0.358993i	−0.0149125	−	0.0212277i
$287$	17.5875	+	42.4601i	1.03816	+	2.50634i
$288$	−8.06037	+	10.2029i	−0.474962	+	0.601211i
$289$	−12.5805	+	11.4338i	−0.740029	+	0.672575i
$290$	−5.82645	−	3.07053i	−0.342141	−	0.180308i
$291$	8.29161	−	3.43450i	0.486063	−	0.201334i
$292$	−1.26393	+	8.38346i	−0.0739660	+	0.490605i
$293$	13.7235	−	13.7235i	0.801736	−	0.801736i	−0.181631	−	0.983367i	$-0.558138\pi$
$293$	13.7235	−	13.7235i	0.801736	−	0.801736i	0.983367	+	0.181631i	$0.0581377\pi$
$294$	−2.20667	+	12.6283i	−0.128696	+	0.736497i
$295$	−8.00595	+	4.10084i	−0.466125	+	0.238760i
$296$	30.2152	−	8.24588i	1.75623	−	0.479282i
$297$	−0.611250	−	0.253188i	−0.0354683	−	0.0146915i
$298$	−12.7064	+	5.61430i	−0.736061	+	0.325228i
$299$	−5.17004	+	7.73751i	−0.298991	+	0.447472i
$300$	5.85233	−	5.99117i	0.337884	−	0.345900i
$301$	2.25213	−	1.50482i	0.129810	−	0.0867365i
$302$	0.0625135	−	0.00146032i	0.00359725	−	8.40321e-5i
$303$	1.23790	+	0.246234i	0.0711156	+	0.0141458i
$304$	10.4699	+	19.8136i	0.600487	+	1.13639i
$305$	−7.73615	−	27.2073i	−0.442971	−	1.55789i
$306$	−5.13524	+	12.3800i	−0.293562	+	0.707718i
$307$		−	2.90077i		−	0.165556i	−0.996568	−	0.0827778i	$-0.973621\pi$
$307$		−	2.90077i		−	0.165556i	0.996568	−	0.0827778i	$-0.0263792\pi$
$308$	0.535526	+	1.13927i	0.0305144	+	0.0649159i
$309$	−7.99758	−	1.59082i	−0.454966	−	0.0904984i
$310$	−10.4888	+	3.24900i	−0.595725	+	0.184531i
$311$	7.49899	+	11.2230i	0.425228	+	0.636399i	0.980788	−	0.195078i	$-0.0624958\pi$
$311$	7.49899	+	11.2230i	0.425228	+	0.636399i	−0.555559	+	0.831477i	$0.687496\pi$
$312$	2.44479	−	4.28003i	0.138409	−	0.242309i
$313$	−2.41684	+	3.61705i	−0.136608	+	0.204448i	−0.893466	−	0.449132i	$-0.851733\pi$
$313$	−2.41684	+	3.61705i	−0.136608	+	0.204448i	0.756858	+	0.653579i	$0.226733\pi$
$314$	24.0453	−	10.6244i	1.35695	−	0.599569i
$315$	2.50431	−	21.5539i	0.141102	−	1.21442i
$316$	5.05615	−	8.39041i	0.284431	−	0.471998i
$317$	−11.7599	+	2.33919i	−0.660502	+	0.131382i	−0.513949	−	0.857821i	$-0.671818\pi$
$317$	−11.7599	+	2.33919i	−0.660502	+	0.131382i	−0.146553	+	0.989203i	$0.546818\pi$
$318$	7.09178	+	1.23922i	0.397687	+	0.0694920i
$319$	0.219563	−	0.219563i	0.0122932	−	0.0122932i
$320$	17.4542	−	3.91804i	0.975719	−	0.219025i
$321$	−3.37998	−	8.16000i	−0.188652	−	0.455447i
$322$	18.4350	−	19.3169i	1.02734	−	1.07649i
$323$	15.9395	+	16.7187i	0.886896	+	0.930256i
$324$	0.296892	+	6.35121i	0.0164940	+	0.352845i
$325$	6.07915	−	8.44299i	0.337211	−	0.468333i
$326$	17.7195	+	25.2234i	0.981395	+	1.39700i
$327$	−0.749512	+	0.749512i	−0.0414481	+	0.0414481i
$328$	−3.87794	+	30.5452i	−0.214123	+	1.68657i
$329$	0.997037	+	5.01244i	0.0549684	+	0.276345i
$330$	0.188175	+	0.347140i	0.0103587	+	0.0191095i
$331$	−3.20756	+	7.74373i	−0.176303	+	0.425634i	−0.987186	−	0.159575i	$-0.948988\pi$
$331$	−3.20756	+	7.74373i	−0.176303	+	0.425634i	0.810882	+	0.585209i	$0.198988\pi$
$332$	5.16648	+	1.86245i	0.283548	+	0.102215i
$333$	14.1408	−	21.1632i	0.774913	−	1.15974i
$334$	17.6820	+	11.2265i	0.967517	+	0.614285i
$335$	−12.1892	−	10.3655i	−0.665968	−	0.566330i
$336$	−9.02426	+	10.8902i	−0.492314	+	0.594107i
$337$	5.57629	−	28.0339i	0.303760	−	1.52710i	−0.463691	−	0.885997i	$-0.653475\pi$
$337$	5.57629	−	28.0339i	0.303760	−	1.52710i	0.767451	−	0.641108i	$-0.221525\pi$
$338$	−4.42654	+	11.4349i	−0.240772	+	0.621977i
$339$			1.42499i			0.0773949i
$340$	16.2150	−	8.77916i	0.879382	−	0.476117i
$341$		−	0.517694i		−	0.0280347i
$342$	16.9835	+	6.57444i	0.918361	+	0.355505i
$343$	3.14912	−	15.8317i	0.170036	−	0.854831i
$344$	1.81021	−	0.127045i	0.0975998	−	0.00684980i
$345$	5.42580	−	6.38040i	0.292115	−	0.343509i
$346$	9.19745	−	14.4863i	0.494458	−	0.778786i
$347$	−18.4767	+	27.6523i	−0.991879	+	1.48445i	−0.121183	+	0.992630i	$0.538669\pi$
$347$	−18.4767	+	27.6523i	−0.991879	+	1.48445i	−0.870696	+	0.491821i	$0.836331\pi$
$348$	3.28185	+	1.18307i	0.175925	+	0.0634190i
$349$	−11.6475	+	28.1195i	−0.623475	+	1.50520i	0.224123	+	0.974561i	$0.428048\pi$
$349$	−11.6475	+	28.1195i	−0.623475	+	1.50520i	−0.847597	+	0.530640i	$0.821952\pi$
$350$	−21.3531	+	20.8619i	−1.14137	+	1.11512i
$351$	−1.80141	−	9.05631i	−0.0961522	−	0.483390i
$352$	−0.0670375	+	0.840716i	−0.00357311	+	0.0448103i
$353$	−15.0774	+	15.0774i	−0.802491	+	0.802491i	−0.983484	−	0.180994i	$-0.942069\pi$
$353$	−15.0774	+	15.0774i	−0.802491	+	0.802491i	0.180994	+	0.983484i	$0.442069\pi$
$354$	3.89877	−	2.73890i	0.207217	−	0.145571i
$355$	17.4196	+	21.9996i	0.924535	+	1.16762i
$356$	−25.0854	+	1.17264i	−1.32953	+	0.0621497i
$357$	−5.89869	+	13.3319i	−0.312192	+	0.705601i
$358$	10.6784	+	10.1909i	0.564371	+	0.538606i
$359$	12.0598	+	29.1149i	0.636491	+	1.53663i	0.831323	+	0.555790i	$0.187584\pi$
$359$	12.0598	+	29.1149i	0.636491	+	1.53663i	−0.194832	+	0.980837i	$0.562416\pi$
$360$	8.61916	−	11.7066i	0.454269	−	0.616994i
$361$	8.75910	−	8.75910i	0.461005	−	0.461005i
$362$	4.80858	−	27.5184i	0.252733	−	1.44634i
$363$	9.01743	−	1.79368i	0.473292	−	0.0941437i
$364$	−9.06812	+	15.0481i	−0.475298	+	0.788732i
$365$	1.09398	−	9.41558i	0.0572615	−	0.492834i
$366$	6.05538	+	13.7046i	0.316520	+	0.716352i
$367$	−11.3447	+	16.9785i	−0.592188	+	0.886271i	−0.999637	−	0.0269566i	$-0.991418\pi$
$367$	−11.3447	+	16.9785i	−0.592188	+	0.886271i	0.407449	+	0.913228i	$0.366418\pi$
$368$	17.1434	−	5.11156i	0.893659	−	0.266458i
$369$	13.9016	+	20.8052i	0.723688	+	1.08308i
$370$	−33.4491	+	10.3611i	−1.73894	+	0.538650i
$371$	−25.1679	−	5.00620i	−1.30665	−	0.259909i
$372$	5.26377	−	2.47429i	0.272914	−	0.128286i
$373$			2.60552i			0.134909i	0.997722	+	0.0674544i	$0.0214877\pi$
$373$			2.60552i			0.134909i	−0.997722	+	0.0674544i	$0.978512\pi$
$374$	0.169172	+	0.852722i	0.00874770	+	0.0440932i
$375$	−6.31184	+	6.91668i	−0.325942	+	0.357176i
$376$	−1.08560	+	3.24727i	−0.0559856	+	0.167465i
$377$	4.25032	+	0.845441i	0.218903	+	0.0435424i
$378$	0.618757	+	26.4878i	0.0318254	+	1.36238i
$379$	25.9773	−	17.3575i	1.33437	−	0.891594i	0.335636	−	0.941992i	$-0.391049\pi$
$379$	25.9773	−	17.3575i	1.33437	−	0.891594i	0.998729	+	0.0503975i	$0.0160488\pi$
$380$	−12.4512	−	21.7419i	−0.638734	−	1.11534i
$381$	2.40767	−	3.60333i	0.123349	−	0.184604i
$382$	−12.8358	−	29.0502i	−0.656738	−	1.48634i
$383$	−11.8358	−	4.90255i	−0.604782	−	0.250509i	0.0592138	−	0.998245i	$-0.481141\pi$
$383$	−11.8358	−	4.90255i	−0.604782	−	0.250509i	−0.663996	+	0.747737i	$0.731141\pi$
$384$	−8.86857	+	3.33654i	−0.452572	+	0.170267i
$385$	−0.641650	−	1.25267i	−0.0327015	−	0.0638422i
$386$	−21.1620	−	3.69786i	−1.07712	−	0.188216i
$387$	1.04278	−	1.04278i	0.0530073	−	0.0530073i
$388$	−21.1923	−	3.19505i	−1.07588	−	0.162204i
$389$	9.90996	−	4.10484i	0.502455	−	0.208124i	−0.117036	−	0.993128i	$-0.537339\pi$
$389$	9.90996	−	4.10484i	0.502455	−	0.208124i	0.619491	+	0.785004i	$0.287339\pi$
$390$	−2.56927	+	4.87528i	−0.130100	+	0.246870i
$391$	15.5721	−	9.87591i	0.787515	−	0.499446i
$392$	20.0783	−	23.1093i	1.01411	−	1.16720i
$393$	1.38645	+	3.34718i	0.0699370	+	0.168843i
$394$	−6.59116	+	4.63032i	−0.332058	+	0.233272i
$395$	−5.33110	+	9.56734i	−0.268237	+	0.481385i
$396$	0.406977	+	0.551478i	0.0204513	+	0.0277128i
$397$	0.508135	+	2.55457i	0.0255026	+	0.128210i	0.991439	−	0.130568i	$-0.0416801\pi$
$397$	0.508135	+	2.55457i	0.0255026	+	0.128210i	−0.965937	+	0.258778i	$0.916680\pi$
$398$	−17.8963	+	3.99643i	−0.897062	+	0.200323i
$399$	18.3013	+	7.58066i	0.916213	+	0.379508i
$400$	−19.3544	+	5.04072i	−0.967718	+	0.252036i
$401$	16.9023	−	25.2961i	0.844062	−	1.26323i	−0.118714	−	0.992928i	$-0.537877\pi$
$401$	16.9023	−	25.2961i	0.844062	−	1.26323i	0.962776	−	0.270300i	$-0.0871228\pi$
$402$	7.15512	+	4.54285i	0.356865	+	0.226577i
$403$	6.00749	−	4.01407i	0.299254	−	0.199955i
$404$	−2.22843	−	2.02940i	−0.110869	−	0.100966i
$405$	−0.572901	−	7.08549i	−0.0284677	−	0.352081i
$406$	−11.5961	−	4.48896i	−0.575507	−	0.222783i
$407$		−	1.65094i		−	0.0818339i
$408$	−7.86169	+	5.79564i	−0.389212	+	0.286927i
$409$	16.7526			0.828361			0.414181	−	0.910195i	$-0.364068\pi$
$409$	16.7526			0.828361			0.414181	+	0.910195i	$0.364068\pi$
$410$	3.17335	−	34.2781i	0.156721	−	1.69287i
$411$	−0.604738	+	3.04022i	−0.0298295	+	0.149963i
$412$	14.3970	+	13.1111i	0.709289	+	0.645938i
$413$	−14.1210	+	9.43533i	−0.694847	+	0.464282i
$414$	7.79232	−	12.2731i	0.382972	−	0.603192i
$415$	−5.84369	−	1.88491i	−0.286855	−	0.0925267i
$416$	−10.2757	+	5.74079i	−0.503810	+	0.281465i
$417$	−3.15923	+	7.62706i	−0.154708	+	0.373499i
$418$	1.15286	−	0.257444i	0.0563880	−	0.0125920i
$419$	−25.9825	+	5.16825i	−1.26933	+	0.252485i	−0.783403	−	0.621514i	$-0.786518\pi$
$419$	−25.9825	+	5.16825i	−1.26933	+	0.252485i	−0.485927	+	0.874000i	$0.661518\pi$
$420$	9.67011	−	12.5112i	0.471853	−	0.610484i
$421$	−21.0817	+	21.0817i	−1.02746	+	1.02746i	−0.0278482	+	0.999612i	$0.508866\pi$
$421$	−21.0817	+	21.0817i	−1.02746	+	1.02746i	−0.999612	+	0.0278482i	$0.991134\pi$
$422$	1.10005	+	1.56591i	0.0535498	+	0.0762271i
$423$	1.06482	+	2.57070i	0.0517732	+	0.124992i
$424$	−12.9777	−	11.2755i	−0.630252	−	0.547589i
$425$	−17.7851	+	10.4254i	−0.862705	+	0.505707i
$426$	−10.7529	−	10.2620i	−0.520978	−	0.497193i
$427$	−20.4371	−	49.3395i	−0.989020	−	2.38771i
$428$	−3.14434	+	20.8559i	−0.151987	+	1.00811i
$429$	−0.183719	−	0.183719i	−0.00887005	−	0.00887005i
$430$	−2.01788	+	0.210693i	−0.0973109	+	0.0101605i
$431$	−7.98564	+	1.58844i	−0.384655	+	0.0765126i	−0.383630	−	0.923487i	$-0.625326\pi$
$431$	−7.98564	+	1.58844i	−0.384655	+	0.0765126i	−0.00102474	+	0.999999i	$0.500326\pi$
$432$	−8.44185	+	15.6147i	−0.406159	+	0.751262i
$433$	1.73795	+	0.719882i	0.0835204	+	0.0345953i	0.424053	−	0.905638i	$-0.360607\pi$
$433$	1.73795	+	0.719882i	0.0835204	+	0.0345953i	−0.340532	+	0.940233i	$0.610607\pi$
$434$	−18.9630	+	8.37879i	−0.910254	+	0.402195i
$435$	−3.71202	−	1.19733i	−0.177978	−	0.0574077i
$436$	2.45681	−	0.609200i	0.117660	−	0.0291754i
$437$	−13.9202	−	20.8331i	−0.665894	−	0.996581i
$438$	0.117257	+	5.01956i	0.00560277	+	0.239844i
$439$	−5.80962	+	29.2069i	−0.277278	+	1.39397i	0.551398	+	0.834242i	$0.314095\pi$
$439$	−5.80962	+	29.2069i	−0.277278	+	1.39397i	−0.828676	+	0.559728i	$0.810905\pi$
$440$	0.0429847	−	0.941953i	0.00204921	−	0.0449058i
$441$		−	24.8784i		−	1.18469i
$442$	−8.58354	+	8.57494i	−0.408277	+	0.407868i
$443$			2.80589i			0.133312i	0.997776	+	0.0666559i	$0.0212330\pi$
$443$			2.80589i			0.133312i	−0.997776	+	0.0666559i	$0.978767\pi$
$444$	16.7863	−	7.89057i	0.796641	−	0.374470i
$445$	27.9857	−	2.26279i	1.32665	−	0.107267i
$446$	−25.1947	+	0.588551i	−1.19300	+	0.0278687i
$447$	−6.84028	+	4.57053i	−0.323534	+	0.216179i
$448$	31.8803	−	11.1513i	1.50620	−	0.526849i
$449$	−9.63053	−	6.43491i	−0.454493	−	0.303682i	0.307172	−	0.951654i	$-0.400617\pi$
$449$	−9.63053	−	6.43491i	−0.454493	−	0.303682i	−0.761664	+	0.647972i	$0.775617\pi$
$450$	−9.18645	+	13.4081i	−0.433053	+	0.632066i
$451$	1.49946	+	0.621098i	0.0706069	+	0.0292463i
$452$	1.75636	−	2.91459i	0.0826124	−	0.137091i
$453$	0.0363200	−	0.00722450i	0.00170646	−	0.000339437i
$454$	26.5657	+	4.64210i	1.24679	+	0.217865i
$455$	9.56123	−	17.1588i	0.448238	−	0.804419i
$456$	8.12764	+	10.4915i	0.380612	+	0.491309i
$457$	−1.94889	+	0.807258i	−0.0911654	+	0.0377619i	−0.427800	−	0.903873i	$-0.640711\pi$
$457$	−1.94889	+	0.807258i	−0.0911654	+	0.0377619i	0.336635	+	0.941635i	$0.390711\pi$
$458$	14.7636	+	14.0895i	0.689856	+	0.658361i
$459$	−3.99662	+	17.8551i	−0.186546	+	0.833403i
$460$	−18.9617	+	6.36254i	−0.884094	+	0.296655i
$461$	−5.59071	−	13.4972i	−0.260385	−	0.628626i	0.738577	−	0.674169i	$-0.235498\pi$
$461$	−5.59071	−	13.4972i	−0.260385	−	0.628626i	−0.998962	+	0.0455434i	$0.985498\pi$
$462$	0.428550	+	0.610032i	0.0199379	+	0.0283812i
$463$	−26.4748	+	26.4748i	−1.23039	+	1.23039i	−0.266572	+	0.963815i	$0.585891\pi$
$463$	−26.4748	+	26.4748i	−1.23039	+	1.23039i	−0.963815	+	0.266572i	$0.914109\pi$
$464$	−5.25431	−	6.46478i	−0.243925	−	0.300120i
$465$	−5.78772	+	2.96461i	−0.268399	+	0.137481i
$466$	35.8873	−	8.01400i	1.66245	−	0.371241i
$467$	−19.9102	−	8.24708i	−0.921335	−	0.381629i	−0.128950	−	0.991651i	$-0.541161\pi$
$467$	−19.9102	−	8.24708i	−0.921335	−	0.381629i	−0.792385	+	0.610022i	$0.791161\pi$
$468$	−3.24393	+	8.99872i	−0.149951	+	0.415966i
$469$	−25.1186	−	16.7837i	−1.15987	−	0.775000i
$470$	1.08974	−	3.66968i	0.0502659	−	0.169270i
$471$	12.9444	−	8.64917i	0.596447	−	0.398533i
$472$	−11.3501	+	0.796579i	−0.522431	+	0.0366655i
$473$	0.0186611	−	0.0938155i	0.000858037	−	0.00431364i
$474$	2.09432	−	5.41019i	0.0961955	−	0.248498i
$475$	14.7384	+	23.8214i	0.676245	+	1.09300i
$476$	28.4970	−	19.9979i	1.30616	−	0.916603i
$477$	−13.9712			−0.639696
$478$	6.75479	−	17.4494i	0.308957	−	0.798116i
$479$	19.4071	+	3.86032i	0.886734	+	0.176382i	0.617386	−	0.786661i	$-0.288192\pi$
$479$	19.4071	+	3.86032i	0.886734	+	0.176382i	0.269348	+	0.963043i	$0.413192\pi$
$480$	9.78296	−	4.06496i	0.446529	−	0.185539i
$481$	19.1580	−	12.8010i	0.873530	−	0.583674i
$482$	9.32946	−	14.6942i	0.424945	−	0.669302i
$483$	8.78537	−	13.1482i	0.399748	−	0.598266i
$484$	−20.6545	−	7.44569i	−0.938840	−	0.338440i
$485$	23.8014	+	2.76544i	1.08076	+	0.125572i
$486$	4.92391	+	22.0496i	0.223353	+	1.00019i
$487$	18.6641	−	3.71253i	0.845753	−	0.168231i	0.246851	−	0.969053i	$-0.420604\pi$
$487$	18.6641	−	3.71253i	0.845753	−	0.168231i	0.598901	+	0.800823i	$0.295604\pi$
$488$	4.50624	−	35.4941i	0.203988	−	1.60674i
$489$	12.9084	+	12.9084i	0.583739	+	0.583739i
$490$	−21.5578	+	26.5845i	−0.973883	+	1.20096i
$491$	−2.15157	−	5.19435i	−0.0970990	−	0.234418i	0.867865	−	0.496800i	$-0.165492\pi$
$491$	−2.15157	−	5.19435i	−0.0970990	−	0.234418i	−0.964964	+	0.262382i	$0.915492\pi$
$492$	0.851456	+	18.2146i	0.0383866	+	0.821179i
$493$	−7.02410	−	4.93972i	−0.316349	−	0.222474i
$494$	11.9264	+	11.3820i	0.536596	+	0.512098i
$495$	−0.475691	−	0.600762i	−0.0213807	−	0.0270022i
$496$	−13.8158	−	1.42705i	−0.620350	−	0.0640766i
$497$	37.4628	+	37.4628i	1.68044	+	1.68044i
$498$	3.20386	+	0.559843i	0.143568	+	0.0250872i
$499$	4.13698	+	20.7980i	0.185197	+	0.931048i	0.955864	+	0.293810i	$0.0949232\pi$
$499$	4.13698	+	20.7980i	0.185197	+	0.931048i	−0.770667	+	0.637238i	$0.780077\pi$
$500$	21.4349	−	6.36733i	0.958600	−	0.284756i
$501$	11.4597	+	4.74676i	0.511981	+	0.212069i
$502$	−15.5748	−	35.2492i	−0.695138	−	1.57325i
$503$	2.72537	−	4.07881i	0.121518	−	0.181865i	−0.765723	−	0.643170i	$-0.777619\pi$
$503$	2.72537	−	4.07881i	0.121518	−	0.181865i	0.887242	+	0.461305i	$0.152619\pi$
$504$	13.6137	−	23.8330i	0.606401	−	1.06161i
$505$	2.56708	+	2.18301i	0.114234	+	0.0971427i
$506$	−0.0220218	−	0.942709i	−0.000978988	−	0.0419085i
$507$	−1.41667	+	7.12209i	−0.0629166	+	0.316303i
$508$	−9.36576	+	4.40248i	−0.415539	+	0.195328i
$509$	−16.9210			−0.750011			−0.375006	−	0.927023i	$-0.622359\pi$
$509$	−16.9210			−0.750011			−0.375006	+	0.927023i	$0.622359\pi$
$510$	8.56450	−	6.77450i	0.379243	−	0.299980i
$511$		−	17.8966i		−	0.791698i
$512$	22.2517	+	4.10654i	0.983394	+	0.181485i
$513$	24.3839	+	4.85026i	1.07658	+	0.214144i
$514$	0.622525	+	26.6491i	0.0274584	+	1.17544i
$515$	−16.5849	−	14.1036i	−0.730817	−	0.621477i
$516$	1.04308	−	0.258646i	0.0459190	−	0.0113863i
$517$	0.150064	+	0.100270i	0.00659981	+	0.00440985i
$518$	−60.4735	+	26.7201i	−2.65705	+	1.17402i
$519$	3.88885	−	9.38852i	0.170702	−	0.412110i
$520$	11.2640	−	6.80487i	0.493960	−	0.298413i
$521$	4.85617	−	0.965953i	0.212753	−	0.0423192i	−0.0875630	−	0.996159i	$-0.527908\pi$
$521$	4.85617	−	0.965953i	0.212753	−	0.0423192i	0.300316	+	0.953840i	$0.402908\pi$
$522$	−6.66904	−	1.16535i	−0.291896	−	0.0510060i
$523$	−23.9417	+	23.9417i	−1.04690	+	1.04690i	−0.0480535	+	0.998845i	$0.515302\pi$
$523$	−23.9417	+	23.9417i	−1.04690	+	1.04690i	−0.998845	+	0.0480535i	$0.984698\pi$
$524$	1.28979	−	8.55496i	0.0563446	−	0.373725i
$525$	−10.3302	+	14.3471i	−0.450848	+	0.626157i
$526$	−4.99460	+	5.23353i	−0.217775	+	0.228193i
$527$	−14.1044	+	2.45731i	−0.614395	+	0.107042i
$528$	0.0465940	+	0.497287i	0.00202774	+	0.0216417i
$529$	2.77033	−	1.14751i	0.120449	−	0.0498916i
$530$	14.9293	+	12.1064i	0.648486	+	0.525868i
$531$	−6.53827	+	6.53827i	−0.283737	+	0.283737i
$532$	−28.0889	−	38.0622i	−1.21781	−	1.65020i
$533$	4.41906	+	22.2161i	0.191411	+	0.962286i
$534$	−14.5147	+	3.24128i	−0.628113	+	0.140264i
$535$	2.72154	−	23.4236i	0.117663	−	1.01269i
$536$	−9.03539	−	18.1107i	−0.390270	−	0.782261i
$537$	7.26838	+	4.85658i	0.313654	+	0.209577i
$538$	11.2530	−	17.7238i	0.485150	−	0.764125i
$539$	−0.896512	−	1.34172i	−0.0386155	−	0.0577922i
$540$	8.83994	−	17.7682i	0.380410	−	0.764622i
$541$	8.10356	−	40.7393i	0.348399	−	1.75152i	−0.267370	−	0.963594i	$-0.586155\pi$
$541$	8.10356	−	40.7393i	0.348399	−	1.75152i	0.615769	−	0.787927i	$-0.288845\pi$
$542$	40.4539	+	15.6600i	1.73765	+	0.672656i
$543$		−	16.5438i		−	0.709962i
$544$	23.2232	−	2.16418i	0.995686	−	0.0927884i
$545$	−2.72208	+	0.773999i	−0.116601	+	0.0331545i
$546$	−3.75613	+	9.70307i	−0.160748	+	0.415253i
$547$	28.9893	+	5.76633i	1.23949	+	0.246551i	0.770953	−	0.636892i	$-0.219780\pi$
$547$	28.9893	+	5.76633i	1.23949	+	0.246551i	0.468540	+	0.883442i	$0.344780\pi$
$548$	4.98410	−	5.47292i	0.212910	−	0.233791i
$549$	−16.1539	−	24.1761i	−0.689433	−	1.03181i
$550$	−0.0122644	+	1.05416i	−0.000522955	+	0.0449495i
$551$	−6.48245	+	9.70167i	−0.276162	+	0.413305i
$552$	9.47995	−	4.72954i	0.403494	−	0.201303i
$553$	−7.91333	+	19.1045i	−0.336509	+	0.812405i
$554$	−2.72258	+	0.607980i	−0.115671	+	0.0258306i
$555$	−18.4572	+	9.45422i	−0.783464	+	0.401309i
$556$	15.8624	−	11.7060i	0.672714	−	0.496446i
$557$	23.5275	+	23.5275i	0.996893	+	0.996893i	0.999995	−	0.00310218i	$-0.000987457\pi$
$557$	23.5275	+	23.5275i	0.996893	+	0.996893i	−0.00310218	+	0.999995i	$0.500987\pi$
$558$	−9.23611	+	6.48840i	−0.390996	+	0.274676i
$559$	1.23336	−	0.510874i	0.0521656	−	0.0216077i
$560$	−35.1992	+	13.6708i	−1.48744	+	0.577698i
$561$	0.185617	+	0.480212i	0.00783676	+	0.0202746i
$562$	−18.6854	−	17.8323i	−0.788194	−	0.752210i
$563$	7.04019	+	16.9965i	0.296709	+	0.716318i	0.999985	+	0.00540181i	$0.00171946\pi$
$563$	7.04019	+	16.9965i	0.296709	+	0.716318i	−0.703277	+	0.710916i	$0.748281\pi$
$564$	−0.302290	+	2.00504i	−0.0127287	+	0.0844276i
$565$	−1.85187	+	3.32342i	−0.0779089	+	0.139817i
$566$	−1.41926	+	8.12209i	−0.0596558	+	0.341397i
$567$	−2.61838	−	13.1635i	−0.109961	−	0.552814i
$568$	9.34494	+	34.2425i	0.392105	+	1.43678i
$569$	−7.10357	+	17.1495i	−0.297797	+	0.718946i	0.702179	+	0.712001i	$0.252211\pi$
$569$	−7.10357	+	17.1495i	−0.297797	+	0.718946i	−0.999976	+	0.00694533i	$0.997789\pi$
$570$	−9.48010	−	11.4145i	−0.397078	−	0.478099i
$571$	18.1549	−	27.1708i	0.759761	−	1.13706i	−0.226844	−	0.973931i	$-0.572841\pi$
$571$	18.1549	−	27.1708i	0.759761	−	1.13706i	0.986604	−	0.163131i	$-0.0521594\pi$
$572$	0.149326	+	0.602210i	0.00624364	+	0.0251797i
$573$	−10.4495	−	15.6387i	−0.436533	−	0.653318i
$574$	−1.51788	−	64.9774i	−0.0633550	−	2.71210i
$575$	20.9460	−	7.82941i	0.873509	−	0.326509i
$576$	15.8393	−	9.34093i	0.659971	−	0.389205i
$577$	−16.2906			−0.678185			−0.339092	−	0.940753i	$-0.610120\pi$
$577$	−16.2906			−0.678185			−0.339092	+	0.940753i	$0.610120\pi$
$578$	22.4291	−	8.65661i	0.932926	−	0.360068i
$579$	−12.7224			−0.528724
$580$	6.11657	+	7.02417i	0.253977	+	0.291663i
$581$	−11.3701	−	2.26166i	−0.471712	−	0.0938293i
$582$	−12.6888	+	0.296411i	−0.525967	+	0.0122866i
$583$	−0.753484	+	0.503462i	−0.0312061	+	0.0208512i
$584$	5.94698	−	10.4112i	0.246088	−	0.430819i
$585$	3.28305	−	10.1782i	0.135737	−	0.420818i
$586$	−25.1055	+	11.0928i	−1.03710	+	0.458241i
$587$	−0.600119	+	1.44882i	−0.0247696	+	0.0597990i	−0.935780	−	0.352583i	$-0.885303\pi$
$587$	−0.600119	+	1.44882i	−0.0247696	+	0.0597990i	0.911011	+	0.412382i	$0.135303\pi$
$588$	9.35745	−	15.5282i	0.385895	−	0.640372i
$589$	3.79520	+	19.0797i	0.156378	+	0.786167i
$590$	12.6522	−	1.32106i	0.520884	−	0.0543870i
$591$	−3.37311	+	3.37311i	−0.138751	+	0.138751i
$592$	−44.0591	−	4.55091i	−1.81082	−	0.187041i
$593$	19.6112	−	8.12322i	0.805335	−	0.333581i	0.0582442	−	0.998302i	$-0.481450\pi$
$593$	19.6112	−	8.12322i	0.805335	−	0.333581i	0.747091	+	0.664722i	$0.231450\pi$
$594$	0.676883	+	0.645981i	0.0277728	+	0.0265049i
$595$	−31.0829	+	23.4275i	−1.27427	+	0.960434i
$596$	19.6241	−	0.917341i	0.803832	−	0.0375757i
$597$	−10.0329	+	4.15576i	−0.410619	+	0.170084i
$598$	10.7688	−	7.56509i	0.440367	−	0.309360i
$599$	−21.3552	−	21.3552i	−0.872549	−	0.872549i	0.120201	−	0.992750i	$-0.461646\pi$
$599$	−21.3552	−	21.3552i	−0.872549	−	0.872549i	−0.992750	+	0.120201i	$0.961646\pi$
$600$	−10.7770	+	4.91360i	−0.439970	+	0.200597i
$601$	−0.481617	−	2.42125i	−0.0196456	−	0.0987649i	0.969719	−	0.244225i	$-0.0785337\pi$
$601$	−0.481617	−	2.42125i	−0.0196456	−	0.0987649i	−0.989364	+	0.145460i	$0.953534\pi$
$602$	−3.73847	+	0.834838i	−0.152369	+	0.0340255i
$603$	−15.1958	−	6.29432i	−0.618822	−	0.256325i
$604$	−0.0831912	−	0.0299894i	−0.00338500	−	0.00122025i
$605$	23.3618	+	7.53547i	0.949793	+	0.306361i
$606$	−1.50689	−	0.956737i	−0.0612132	−	0.0388648i
$607$	2.13016	+	3.18802i	0.0864607	+	0.129398i	0.872179	−	0.489187i	$-0.162706\pi$
$607$	2.13016	+	3.18802i	0.0864607	+	0.129398i	−0.785718	+	0.618585i	$0.787706\pi$
$608$	−3.69258	−	31.4763i	−0.149754	−	1.27653i
$609$	−7.22251	−	1.43665i	−0.292671	−	0.0582159i
$610$	−3.68750	+	39.8318i	−0.149303	+	1.61274i
$611$			2.51886i			0.101902i
$612$	13.0930	−	13.7056i	0.529254	−	0.554016i
$613$	4.89291			0.197623			0.0988114	−	0.995106i	$-0.468496\pi$
$613$	4.89291			0.197623			0.0988114	+	0.995106i	$0.468496\pi$
$614$	−1.48094	+	3.82566i	−0.0597660	+	0.154391i
$615$	−1.64302	−	20.3205i	−0.0662531	−	0.819401i
$616$	−0.124639	−	1.77593i	−0.00502185	−	0.0715541i
$617$	16.7269	+	25.0336i	0.673401	+	1.00782i	0.998077	+	0.0619906i	$0.0197449\pi$
$617$	16.7269	+	25.0336i	0.673401	+	1.00782i	−0.324676	+	0.945825i	$0.605255\pi$
$618$	9.73540	+	6.18109i	0.391615	+	0.248640i
$619$	−40.6046	−	27.1312i	−1.63204	−	1.09049i	−0.922623	−	0.385702i	$-0.873959\pi$
$619$	−40.6046	−	27.1312i	−1.63204	−	1.09049i	−0.709415	−	0.704791i	$-0.751041\pi$
$620$	15.4919	+	1.06998i	0.622168	+	0.0429715i
$621$	7.59491	−	18.3357i	0.304773	−	0.735788i
$622$	−4.16025	−	18.6299i	−0.166811	−	0.746992i
$623$	51.9919	−	10.3418i	2.08301	−	0.414337i
$624$	−5.40941	+	4.39654i	−0.216550	+	0.176002i
$625$	−23.7094	+	7.92868i	−0.948376	+	0.317147i
$626$	5.03407	−	3.53645i	0.201202	−	0.141345i
$627$	0.646305	−	0.267708i	0.0258109	−	0.0106912i
$628$	−37.1362	+	1.73596i	−1.48189	+	0.0692722i
$629$	−44.9791	+	7.83642i	−1.79343	+	0.312459i
$630$	−14.3068	+	27.1477i	−0.569997	+	1.08159i
$631$	0.940969	+	2.27170i	0.0374594	+	0.0904349i	0.941502	−	0.337007i	$-0.109415\pi$
$631$	0.940969	+	2.27170i	0.0374594	+	0.0904349i	−0.904043	+	0.427442i	$0.859415\pi$
$632$	−10.9519	+	8.48431i	−0.435643	+	0.337488i
$633$	0.801373	+	0.801373i	0.0318517	+	0.0318517i
$634$	16.7037	+	2.91882i	0.663390	+	0.115921i
$635$	10.2980	−	5.27490i	0.408665	−	0.209328i
$636$	−8.72030	−	5.25494i	−0.345782	−	0.208372i
$637$	8.61847	−	20.8068i	0.341476	−	0.824397i
$638$	−0.401664	+	0.177475i	−0.0159020	+	0.00702630i
$639$	23.9840	+	16.0256i	0.948793	+	0.633963i
$640$	−25.0197	−	3.74370i	−0.988990	−	0.147983i
$641$	−24.2840	−	36.3435i	−0.959159	−	1.43548i	−0.899328	−	0.437274i	$-0.855944\pi$
$641$	−24.2840	−	36.3435i	−0.959159	−	1.43548i	−0.0598306	−	0.998209i	$-0.519056\pi$
$642$	0.291707	+	12.4874i	0.0115127	+	0.492838i
$643$	−1.56495	+	7.86753i	−0.0617156	+	0.310265i	−0.999297	−	0.0375019i	$-0.988060\pi$
$643$	−1.56495	+	7.86753i	−0.0617156	+	0.310265i	0.937581	+	0.347767i	$0.113060\pi$
$644$	−34.1748	+	16.0642i	−1.34668	+	0.633020i
$645$	−1.15571	+	0.328614i	−0.0455059	+	0.0129392i
$646$	−12.4862	−	30.1871i	−0.491262	−	1.18770i
$647$	−31.9538			−1.25623			−0.628116	−	0.778120i	$-0.716174\pi$
$647$	−31.9538			−1.25623			−0.628116	+	0.778120i	$0.716174\pi$
$648$	2.85096	−	8.52783i	0.111996	−	0.335005i
$649$	−0.117006	+	0.588229i	−0.00459289	+	0.0230900i
$650$	−12.3279	+	8.03138i	−0.483540	+	0.315017i
$651$	−10.2084	+	6.82106i	−0.400100	+	0.267338i
$652$	−10.4919	−	42.3122i	−0.410895	−	1.65707i
$653$	16.2989	+	10.8906i	0.637827	+	0.426182i	0.831993	−	0.554786i	$-0.187200\pi$
$653$	16.2989	+	10.8906i	0.637827	+	0.426182i	−0.194166	+	0.980969i	$0.562200\pi$
$654$	1.37114	−	0.605838i	0.0536159	−	0.0236901i
$655$	−1.11636	+	9.60819i	−0.0436198	+	0.375423i
$656$	20.7088	−	38.3045i	0.808542	−	1.49554i
$657$	−1.90093	−	9.55661i	−0.0741623	−	0.372839i
$658$	1.24409	−	7.11966i	0.0484998	−	0.277553i
$659$	−0.117786	−	0.117786i	−0.00458829	−	0.00458829i	0.704809	−	0.709397i	$-0.251033\pi$
$659$	−0.117786	−	0.117786i	−0.00458829	−	0.00458829i	−0.709397	+	0.704809i	$0.751033\pi$
$660$	−0.0709457	−	0.553894i	−0.00276156	−	0.0215603i
$661$	−0.591995	+	0.245212i	−0.0230259	+	0.00953765i	−0.394167	−	0.919039i	$-0.628967\pi$
$661$	−0.591995	+	0.245212i	−0.0230259	+	0.00953765i	0.371141	+	0.928577i	$0.378967\pi$
$662$	8.18372	−	8.57521i	0.318069	−	0.333285i
$663$	−4.13331	+	5.87741i	−0.160524	+	0.228260i
$664$	−5.86294	−	5.09396i	−0.227526	−	0.197684i
$665$	32.8315	+	41.4637i	1.27315	+	1.60789i
$666$	−29.4541	+	20.6917i	−1.14133	+	0.801785i
$667$	6.58626	+	6.58626i	0.255021	+	0.255021i
$668$	−17.5883	−	23.8333i	−0.680513	−	0.922137i
$669$	−14.6380	+	2.91168i	−0.565937	+	0.112572i
$670$	10.7837	+	19.8936i	0.416611	+	0.768556i
$671$	−1.74241	−	0.721728i	−0.0672649	−	0.0278620i
$672$	17.4614	−	9.75524i	0.673589	−	0.376317i
$673$	−6.30339	−	4.21179i	−0.242978	−	0.162353i	0.428119	−	0.903722i	$-0.359176\pi$
$673$	−6.30339	−	4.21179i	−0.242978	−	0.162353i	−0.671097	+	0.741370i	$0.734176\pi$
$674$	−21.6666	+	34.1255i	−0.834565	+	1.31447i
$675$	−9.20299	+	20.1897i	−0.354223	+	0.777101i
$676$	11.6758	−	12.8210i	0.449071	−	0.493114i
$677$	−12.7301	−	2.53218i	−0.489259	−	0.0973197i	−0.0557050	−	0.998447i	$-0.517741\pi$
$677$	−12.7301	−	2.53218i	−0.489259	−	0.0973197i	−0.433554	+	0.901128i	$0.642741\pi$
$678$	0.727509	−	1.87934i	0.0279398	−	0.0721758i
$679$	45.2402			1.73616
$680$	−25.8672	+	3.30002i	−0.991960	+	0.126550i
$681$	15.9710			0.612011
$682$	−0.264301	+	0.682758i	−0.0101206	+	0.0261442i
$683$	−3.38441	−	0.673201i	−0.129501	−	0.0257593i	0.129914	−	0.991525i	$-0.458530\pi$
$683$	−3.38441	−	0.673201i	−0.129501	−	0.0257593i	−0.259415	+	0.965766i	$0.583530\pi$
$684$	−19.0421	−	17.3413i	−0.728093	−	0.663062i
$685$	−5.36137	+	6.30462i	−0.204847	+	0.240887i
$686$	−12.2358	+	19.2718i	−0.467166	+	0.735801i
$687$	10.0490	+	6.71451i	0.383393	+	0.256175i
$688$	−2.45224	−	0.756622i	−0.0934909	−	0.0288459i
$689$	−11.6847	−	4.83995i	−0.445150	−	0.184387i
$690$	−10.4132	+	5.64470i	−0.396424	+	0.214890i
$691$	−26.8908	+	5.34892i	−1.02298	+	0.203482i	−0.677948	−	0.735110i	$-0.737130\pi$
$691$	−26.8908	+	5.34892i	−1.02298	+	0.203482i	−0.345028	+	0.938593i	$0.612130\pi$
$692$	−19.5258	+	14.4095i	−0.742258	+	0.547768i
$693$	−1.02303	−	1.02303i	−0.0388617	−	0.0388617i
$694$	38.4853	−	27.0361i	1.46088	−	1.02628i
$695$	−17.2800	+	13.6825i	−0.655466	+	0.519006i
$696$	−3.72425	−	3.23578i	−0.141167	−	0.122652i
$697$	9.80413	−	43.8004i	0.371358	−	1.65906i
$698$	29.7172	−	31.1388i	1.12481	−	1.17862i
$699$	20.1188	−	8.33350i	0.760965	−	0.315202i
$700$	38.8121	−	16.6122i	1.46696	−	0.627881i
$701$	−11.8550	−	11.8550i	−0.447756	−	0.447756i	0.446852	−	0.894608i	$-0.352545\pi$
$701$	−11.8550	−	11.8550i	−0.447756	−	0.447756i	−0.894608	+	0.446852i	$0.852545\pi$
$702$	−2.24778	+	12.8636i	−0.0848370	+	0.485503i
$703$	12.1030	+	60.8457i	0.456472	+	2.29484i
$704$	0.517627	−	1.07455i	0.0195088	−	0.0404986i
$705$	0.261643	−	2.25189i	0.00985406	−	0.0848111i
$706$	27.5824	−	12.1872i	1.03808	−	0.458673i
$707$	5.29005	+	3.53470i	0.198953	+	0.132936i
$708$	−6.54018	+	1.62173i	−0.245795	+	0.0609482i
$709$	27.1264	−	18.1253i	1.01875	−	0.680708i	0.0702663	−	0.997528i	$-0.477615\pi$
$709$	27.1264	−	18.1253i	1.01875	−	0.680708i	0.948486	+	0.316820i	$0.102615\pi$
$710$	−11.7421	−	37.9074i	−0.440675	−	1.42264i
$711$	−2.19642	+	11.0421i	−0.0823722	+	0.414113i
$712$	33.6825	+	11.2605i	1.26230	+	0.422004i
$713$	15.5293			0.581578
$714$	14.5859	−	14.5713i	0.545863	−	0.545316i
$715$	−0.189722	−	0.667233i	−0.00709519	−	0.0249531i
$716$	−8.88036	−	18.8919i	−0.331875	−	0.706024i
$717$	2.16181	−	10.8681i	0.0807341	−	0.405878i
$718$	−1.04081	−	44.5550i	−0.0388427	−	1.66278i
$719$	23.3651	+	34.9683i	0.871370	+	1.30410i	0.951606	+	0.307322i	$0.0994327\pi$
$719$	23.3651	+	34.9683i	0.871370	+	1.30410i	−0.0802357	+	0.996776i	$0.525567\pi$
$720$	−17.3440	+	11.0389i	−0.646372	+	0.411395i
$721$	−34.1769	−	22.8363i	−1.27281	−	0.850466i
$722$	−16.0237	+	7.08007i	−0.596342	+	0.263493i
$723$	3.94467	−	9.52327i	0.146704	−	0.354174i
$724$	−20.3909	+	33.8376i	−0.757822	+	1.25757i
$725$	−7.10130	−	7.61648i	−0.263736	−	0.282869i
$726$	−12.8083	−	2.23813i	−0.475362	−	0.0830649i
$727$	−1.66737	−	1.66737i	−0.0618393	−	0.0618393i	0.675511	−	0.737350i	$-0.263923\pi$
$727$	−1.66737	−	1.66737i	−0.0618393	−	0.0618393i	−0.737350	+	0.675511i	$0.763923\pi$
$728$	19.6420	−	15.2165i	0.727981	−	0.563960i
$729$	1.47048	+	3.55006i	0.0544623	+	0.131484i
$730$	−6.24978	+	11.8592i	−0.231315	+	0.438928i
$731$	−2.64455	−	0.0631037i	−0.0978120	−	0.00233398i
$732$	−0.989410	−	21.1658i	−0.0365696	−	0.782309i
$733$	13.1430	−	5.44402i	0.485449	−	0.201080i	−0.126516	−	0.991965i	$-0.540379\pi$
$733$	13.1430	−	5.44402i	0.485449	−	0.201080i	0.611965	+	0.790885i	$0.290379\pi$
$734$	23.6300	−	16.6002i	0.872200	−	0.612724i
$735$	−9.86631	+	17.7063i	−0.363924	+	0.653108i
$736$	−25.2191	−	2.01093i	−0.929587	−	0.0741240i
$737$	−1.04635	+	0.208132i	−0.0385429	+	0.00766665i
$738$	−7.71226	−	34.5361i	−0.283892	−	1.27129i
$739$	1.25112	−	3.02047i	0.0460232	−	0.111110i	−0.899196	−	0.437546i	$-0.855848\pi$
$739$	1.25112	−	3.02047i	0.0460232	−	0.111110i	0.945219	+	0.326436i	$0.105848\pi$
$740$	49.4039	+	3.41220i	1.81612	+	0.125435i
$741$	8.11787	+	5.42419i	0.298217	+	0.199262i
$742$	30.6367	+	19.4515i	1.12471	+	0.714087i
$743$	−22.8736	−	34.2328i	−0.839152	−	1.25588i	−0.964583	−	0.263778i	$-0.915031\pi$
$743$	−22.8736	−	34.2328i	−0.839152	−	1.25588i	0.125431	−	0.992102i	$-0.459969\pi$
$744$	−8.20531	+	0.575869i	−0.300821	+	0.0211124i
$745$	−21.8929	+	1.77016i	−0.802093	+	0.0648536i
$746$	1.33021	−	3.43628i	0.0487025	−	0.125811i
$747$	−6.31177			−0.230935
$748$	0.212232	−	1.21098i	0.00775998	−	0.0442777i
$749$		−	44.5222i		−	1.62680i
$750$	11.8556	−	5.89961i	0.432904	−	0.215423i
$751$	−22.7911	−	4.53343i	−0.831659	−	0.165427i	−0.239141	−	0.970985i	$-0.576866\pi$
$751$	−22.7911	−	4.53343i	−0.831659	−	0.165427i	−0.592518	+	0.805557i	$0.701866\pi$
$752$	3.08959	−	3.72841i	0.112666	−	0.135961i
$753$	−12.6793	−	18.9758i	−0.462058	−	0.691518i
$754$	−5.17389	−	3.28495i	−0.188422	−	0.119631i
$755$	0.0940956	+	0.0303510i	0.00342449	+	0.00110459i
$756$	12.7069	−	35.2492i	0.462145	−	1.28200i
$757$	28.5322	+	11.8184i	1.03702	+	0.429548i	0.835242	−	0.549883i	$-0.185328\pi$
$757$	28.5322	+	11.8184i	1.03702	+	0.429548i	0.201779	+	0.979431i	$0.435328\pi$
$758$	−43.1217	+	9.62951i	−1.56625	+	0.349759i
$759$	−0.108946	−	0.547709i	−0.00395449	−	0.0198806i
$760$	5.32121	+	35.0310i	0.193021	+	1.27071i
$761$	34.4931	+	34.4931i	1.25038	+	1.25038i	0.955552	+	0.294824i	$0.0952609\pi$
$761$	34.4931	+	34.4931i	1.25038	+	1.25038i	0.294824	+	0.955552i	$0.404739\pi$
$762$	−5.01498	+	3.52304i	−0.181673	+	0.127626i
$763$	−4.93640	+	2.04472i	−0.178710	+	0.0740240i
$764$	2.09729	+	44.8659i	0.0758773	+	1.62319i
$765$	−14.1096	+	15.8116i	−0.510133	+	0.571670i
$766$	13.1067	+	12.5083i	0.473564	+	0.451944i
$767$	−7.73324	+	3.20321i	−0.279231	+	0.115661i
$768$	13.3997	+	0.127336i	0.483520	+	0.00459483i
$769$	−22.9471	+	22.9471i	−0.827494	+	0.827494i	−0.987170	−	0.159675i	$-0.948955\pi$
$769$	−22.9471	+	22.9471i	−0.827494	+	0.827494i	0.159675	+	0.987170i	$0.448955\pi$
$770$	0.206703	+	1.97967i	0.00744905	+	0.0713423i
$771$	3.07975	+	15.4830i	0.110915	+	0.557605i
$772$	26.0216	+	15.6809i	0.936536	+	0.564367i
$773$	2.97340	−	7.17843i	0.106946	−	0.258190i	−0.861343	−	0.508024i	$-0.830376\pi$
$773$	2.97340	−	7.17843i	0.106946	−	0.258190i	0.968289	+	0.249834i	$0.0803761\pi$
$774$	−1.90764	+	0.842887i	−0.0685685	+	0.0302969i
$775$	−17.3511	−	0.607355i	−0.623269	−	0.0218168i
$776$	26.3182	+	15.0332i	0.944768	+	0.539660i
$777$	−32.5549	+	21.7525i	−1.16790	+	0.780367i
$778$	−15.1654	+	0.354265i	−0.543705	+	0.0127010i
$779$	−59.8164	−	11.8982i	−2.14314	−	0.426298i
$780$	5.87748	−	5.11804i	0.210447	−	0.183255i
$781$	1.87098			0.0669491
$782$	−25.5792	+	5.07469i	−0.914711	+	0.181470i
$783$	−9.24222			−0.330290
$784$	−38.2783	+	20.2269i	−1.36708	+	0.722391i
$785$	41.4296	−	3.34981i	1.47869	−	0.119560i
$786$	−0.119656	−	5.12224i	−0.00426799	−	0.182704i
$787$	27.6142	+	41.3276i	0.984340	+	1.47317i	0.877897	+	0.478850i	$0.158946\pi$
$787$	27.6142	+	41.3276i	0.984340	+	1.47317i	0.106443	+	0.994319i	$0.466054\pi$
$788$	11.0567	−	2.74165i	0.393877	−	0.0976673i
$789$	−2.38023	+	3.56226i	−0.0847384	+	0.126820i
$790$	11.9154	−	9.89613i	0.423930	−	0.352088i
$791$	−2.74886	+	6.63635i	−0.0977384	+	0.235961i
$792$	−0.255190	−	0.935090i	−0.00906780	−	0.0332270i
$793$	−5.13504	−	25.8156i	−0.182350	−	0.916738i
$794$	0.634045	−	3.62850i	0.0225014	−	0.128771i
$795$	9.94349	+	5.54070i	0.352659	+	0.196508i
$796$	25.6428	+	3.86603i	0.908886	+	0.137028i
$797$	−9.89962	−	23.8998i	−0.350662	−	0.846574i	−0.996539	−	0.0831318i	$-0.973508\pi$
$797$	−9.89962	−	23.8998i	−0.350662	−	0.846574i	0.645876	−	0.763442i	$-0.276492\pi$
$798$	−20.2664	−	19.3412i	−0.717424	−	0.684671i
$799$	2.01950	−	4.56438i	0.0714449	−	0.161476i
$800$	28.0989	+	3.23316i	0.993445	+	0.114309i
$801$	26.6647	−	11.0449i	0.942152	−	0.390252i
$802$	−35.2061	+	24.7324i	−1.24317	+	0.873333i
$803$	−0.446899	−	0.446899i	−0.0157707	−	0.0157707i
$804$	−7.11722	−	9.64426i	−0.251005	−	0.340127i
$805$	37.5766	−	19.2476i	1.32440	−	0.678390i
$806$	−9.97227	+	2.22691i	−0.351258	+	0.0784395i
$807$	4.75796	−	11.4867i	0.167488	−	0.404352i
$808$	1.90288	+	3.81416i	0.0669431	+	0.134182i
$809$	4.42300	−	6.61949i	0.155504	−	0.232729i	−0.745535	−	0.666467i	$-0.767806\pi$
$809$	4.42300	−	6.61949i	0.155504	−	0.232729i	0.901039	+	0.433738i	$0.142806\pi$
$810$	−2.86183	+	9.63716i	−0.100554	+	0.338615i
$811$	16.6547	+	24.9255i	0.584826	+	0.875254i	0.999396	−	0.0347635i	$-0.0110678\pi$
$811$	16.6547	+	24.9255i	0.584826	+	0.875254i	−0.414569	+	0.910018i	$0.636068\pi$
$812$	13.0017	+	11.8405i	0.456272	+	0.415519i
$813$	25.1962	+	5.01184i	0.883670	+	0.175773i
$814$	−0.842862	+	2.17733i	−0.0295423	+	0.0763154i
$815$	13.3301	+	46.8808i	0.466935	+	1.64216i
$816$	13.3272	−	3.62988i	0.466547	−	0.127071i
$817$			3.59440i			0.125752i
$818$	−22.0941	−	8.55278i	−0.772500	−	0.299041i
$819$	3.93924	−	19.8039i	0.137648	−	0.692004i
$820$	−21.6853	+	43.5874i	−0.757285	+	1.52214i
$821$	−3.28387	−	4.91466i	−0.114608	−	0.171523i	0.769731	−	0.638368i	$-0.220390\pi$
$821$	−3.28387	−	4.91466i	−0.114608	−	0.171523i	−0.884339	+	0.466846i	$0.845390\pi$
$822$	2.34970	−	3.70084i	0.0819551	−	0.129082i
$823$	−38.6872	−	25.8499i	−1.34855	−	0.901072i	−0.349198	−	0.937049i	$-0.613546\pi$
$823$	−38.6872	−	25.8499i	−1.34855	−	0.901072i	−0.999353	+	0.0359767i	$0.988546\pi$
$824$	−12.2937	−	24.6417i	−0.428272	−	0.858435i
$825$	0.100306	+	0.616222i	0.00349219	+	0.0214541i
$826$	23.4404	−	5.23449i	0.815597	−	0.182131i
$827$	6.98843	+	35.1332i	0.243011	+	1.22170i	0.888840	+	0.458218i	$0.151512\pi$
$827$	6.98843	+	35.1332i	0.243011	+	1.22170i	−0.645828	+	0.763483i	$0.723488\pi$
$828$	−16.5427	+	12.2081i	−0.574900	+	0.424262i
$829$	−10.4495	+	10.4495i	−0.362927	+	0.362927i	−0.864889	−	0.501962i	$-0.832612\pi$
$829$	−10.4495	+	10.4495i	−0.362927	+	0.362927i	0.501962	+	0.864889i	$0.332612\pi$
$830$	6.74461	+	5.46932i	0.234109	+	0.189843i
$831$	−1.52631	+	0.632219i	−0.0529471	+	0.0219314i
$832$	16.4830	−	2.32509i	0.571445	−	0.0806079i
$833$	−32.2993	+	30.7938i	−1.11911	+	1.06694i
$834$	8.06042	−	8.44601i	0.279110	−	0.292462i
$835$	20.5580	+	25.9632i	0.711438	+	0.898493i
$836$	−1.65187	−	0.249044i	−0.0571312	−	0.00861338i
$837$	−10.8958	+	10.8958i	−0.376615	+	0.376615i
$838$	36.9055	+	6.44888i	1.27488	+	0.222773i
$839$	40.8876	−	8.13305i	1.41160	−	0.280784i	0.570335	−	0.821412i	$-0.306813\pi$
$839$	40.8876	−	8.13305i	1.41160	−	0.280784i	0.841262	+	0.540628i	$0.181813\pi$
$840$	−19.1408	+	11.5634i	−0.660420	+	0.398976i
$841$	−9.43790	+	22.7851i	−0.325445	+	0.785693i
$842$	38.5665	−	17.0406i	1.32909	−	0.587257i
$843$	−12.7184	−	8.49816i	−0.438045	−	0.292692i
$844$	−0.651352	−	2.62680i	−0.0224205	−	0.0904183i
$845$	−12.5596	+	14.7693i	−0.432065	+	0.508081i
$846$	−0.0918982	−	3.93398i	−0.00315953	−	0.135253i
$847$	45.4553	+	9.04161i	1.56186	+	0.310674i
$848$	11.3590	+	21.4963i	0.390070	+	0.738185i
$849$			4.88291i			0.167581i
$850$	28.7784	−	4.66959i	0.987090	−	0.160166i
$851$	49.5234			1.69764
$852$	8.94228	+	19.0237i	0.306357	+	0.651740i
$853$	2.35930	−	11.8610i	0.0807808	−	0.406113i	−0.919145	−	0.393920i	$-0.871119\pi$
$853$	2.35930	−	11.8610i	0.0807808	−	0.406113i	0.999926	−	0.0121928i	$-0.00388120\pi$
$854$	1.76381	+	75.5050i	0.0603562	+	2.58373i
$855$	21.9359	+	18.6540i	0.750192	+	0.637953i
$856$	14.7946	−	25.9005i	0.505669	−	0.885259i
$857$	−23.3238	+	34.9066i	−0.796726	+	1.19239i	0.181202	+	0.983446i	$0.442001\pi$
$857$	−23.3238	+	34.9066i	−0.796726	+	1.19239i	−0.977929	+	0.208939i	$0.932999\pi$
$858$	0.148502	+	0.336093i	0.00506978	+	0.0114740i
$859$	32.3046	+	13.3810i	1.10222	+	0.456554i	0.858252	−	0.513229i	$-0.171551\pi$
$859$	32.3046	+	13.3810i	1.10222	+	0.456554i	0.243968	+	0.969783i	$0.421551\pi$
$860$	2.76884	+	0.752329i	0.0944166	+	0.0256542i
$861$	−7.50924	−	37.7515i	−0.255914	−	1.28657i
$862$	11.3428	+	1.98204i	0.386337	+	0.0675086i
$863$	5.28847	+	5.28847i	0.180022	+	0.180022i	0.791365	−	0.611344i	$-0.209371\pi$
$863$	5.28847	+	5.28847i	0.180022	+	0.180022i	−0.611344	+	0.791365i	$0.709371\pi$
$864$	19.1054	−	16.2835i	0.649977	−	0.553976i
$865$	21.2707	−	16.8424i	0.723227	−	0.572660i
$866$	−1.92456	−	1.83670i	−0.0653992	−	0.0624135i
$867$	12.2021	−	7.33646i	0.414406	−	0.249159i
$868$	29.2870	−	1.36904i	0.994064	−	0.0464683i
$869$	0.279456	+	0.674667i	0.00947991	+	0.0228865i
$870$	4.28430	+	3.47421i	0.145251	+	0.117787i
$871$	−10.5284	−	10.5284i	−0.356741	−	0.356741i
$872$	−3.55117	−	0.450848i	−0.120258	−	0.0152676i
$873$	24.1579	−	4.80530i	0.817620	−	0.162635i
$874$	7.72259	+	34.5824i	0.261221	+	1.16977i
$875$	−42.7375	+	20.0360i	−1.44479	+	0.677339i
$876$	2.40802	−	6.67988i	0.0813593	−	0.225692i
$877$	17.8409	−	26.7008i	0.602446	−	0.901623i	−0.397426	−	0.917634i	$-0.630097\pi$
$877$	17.8409	−	26.7008i	0.602446	−	0.901623i	0.999872	+	0.0160106i	$0.00509656\pi$
$878$	22.5732	−	35.5534i	0.761807	−	1.19987i
$879$	−13.5152	+	9.03054i	−0.455855	+	0.304593i
$880$	−0.537590	+	1.22034i	−0.0181222	+	0.0411378i
$881$	15.0664	+	2.99690i	0.507601	+	0.100968i	0.442246	−	0.896894i	$-0.354182\pi$
$881$	15.0664	+	2.99690i	0.507601	+	0.100968i	0.0653552	+	0.997862i	$0.479182\pi$
$882$	−12.7013	+	32.8108i	−0.427675	+	1.10480i
$883$	20.5616			0.691953			0.345977	−	0.938243i	$-0.387548\pi$
$883$	20.5616			0.691953			0.345977	+	0.938243i	$0.387548\pi$
$884$	15.6982	−	6.92682i	0.527987	−	0.232974i
$885$	7.24634	−	2.06043i	0.243583	−	0.0692607i
$886$	1.43250	−	3.70053i	0.0481259	−	0.124322i
$887$	−5.27254	+	26.5068i	−0.177034	+	0.890012i	0.785502	+	0.618859i	$0.212405\pi$
$887$	−5.27254	+	26.5068i	−0.177034	+	0.890012i	−0.962536	+	0.271153i	$0.912595\pi$
$888$	−26.1669	+	1.83646i	−0.878104	+	0.0616275i
$889$	18.1638	−	12.1366i	0.609193	−	0.407050i
$890$	−38.0640	−	11.3034i	−1.27591	−	0.378891i
$891$	−0.394092	−	0.263324i	−0.0132026	−	0.00882167i
$892$	33.5284	+	12.0866i	1.12261	+	0.404688i
$893$	−6.26573	−	2.59535i	−0.209675	−	0.0868500i
$894$	11.3547	−	2.53562i	0.379758	−	0.0848037i
$895$	10.6401	+	20.7724i	0.355661	+	0.694346i
$896$	−47.7383	−	1.56917i	−1.59482	−	0.0524223i
$897$	5.51105	−	5.51105i	0.184009	−	0.184009i
$898$	9.41593	+	13.4034i	0.314214	+	0.447277i
$899$	−2.76748	−	6.68130i	−0.0923008	−	0.222834i
$900$	18.9608	−	12.9933i	0.632028	−	0.433109i
$901$	17.2931	+	18.1386i	0.576118	+	0.604284i
$902$	−1.66047	−	1.58466i	−0.0552875	−	0.0527634i
$903$	−2.09583	+	0.868122i	−0.0697449	+	0.0288893i
$904$	−3.80437	+	2.94721i	−0.126532	+	0.0980227i
$905$	21.4998	−	38.5840i	0.714676	−	1.28258i
$906$	−0.0515888	−	0.00901465i	−0.00171392	−	0.000299492i
$907$	−7.55436	+	1.50266i	−0.250838	+	0.0498949i	−0.318908	−	0.947786i	$-0.603316\pi$
$907$	−7.55436	+	1.50266i	−0.250838	+	0.0498949i	0.0680695	+	0.997681i	$0.478316\pi$
$908$	−32.6661	−	19.6850i	−1.08406	−	0.653268i
$909$	3.20029	+	1.32560i	0.106147	+	0.0439674i
$910$	−21.3700	+	17.7485i	−0.708408	+	0.588358i
$911$	−19.4516	−	12.9971i	−0.644460	−	0.430614i	0.189923	−	0.981799i	$-0.439176\pi$
$911$	−19.4516	−	12.9971i	−0.644460	−	0.430614i	−0.834383	+	0.551185i	$0.814176\pi$
$912$	−5.36283	−	17.9861i	−0.177581	−	0.595579i
$913$	−0.340402	+	0.227449i	−0.0112657	+	0.00752747i
$914$	2.98242	−	0.0696698i	0.0986498	−	0.00230447i
$915$	1.90923	+	23.6128i	0.0631171	+	0.780616i
$916$	−12.2776	−	26.1192i	−0.405665	−	0.863004i
$917$			18.2627i			0.603087i
$918$	14.3866	−	21.5077i	0.474827	−	0.709858i
$919$		−	26.7862i		−	0.883595i	−0.897115	−	0.441797i	$-0.854341\pi$
$919$		−	26.7862i		−	0.883595i	0.897115	−	0.441797i	$-0.145659\pi$
$920$	28.2559	+	1.28942i	0.931568	+	0.0425108i
$921$	−0.473962	+	2.38277i	−0.0156176	+	0.0785148i
$922$	0.482502	+	20.6549i	0.0158903	+	0.680234i
$923$	14.5072	+	21.7115i	0.477509	+	0.714643i
$924$	−0.253748	−	1.02333i	−0.00834770	−	0.0336650i
$925$	−55.3329	−	1.93687i	−1.81934	−	0.0636838i
$926$	48.4324	−	21.3998i	1.59159	−	0.703242i
$927$	−20.6758	−	8.56418i	−0.679081	−	0.281284i
$928$	3.62912	+	11.2086i	0.119132	+	0.367939i
$929$	−49.4886	+	9.84390i	−1.62367	+	0.322968i	−0.921302	−	0.388847i	$-0.872874\pi$
$929$	−49.4886	+	9.84390i	−1.62367	+	0.322968i	−0.702367	+	0.711815i	$0.747874\pi$
$930$	9.14665	−	0.955028i	0.299931	−	0.0313166i
$931$	42.8773	+	42.8773i	1.40525	+	1.40525i
$932$	−51.4212	−	7.75251i	−1.68436	−	0.253942i
$933$	−4.32611	−	10.4442i	−0.141631	−	0.341927i
$934$	22.0481	+	21.0415i	0.721435	+	0.688499i
$935$	−0.191165	+	1.36119i	−0.00625176	+	0.0445157i
$936$	8.87240	−	10.2118i	0.290004	−	0.333782i
$937$	−6.42317	−	15.5069i	−0.209836	−	0.506588i	0.783561	−	0.621314i	$-0.213401\pi$
$937$	−6.42317	−	15.5069i	−0.209836	−	0.506588i	−0.993397	+	0.114726i	$0.963401\pi$
$938$	24.5589	+	34.9591i	0.801876	+	1.14145i
$939$	2.57625	−	2.57625i	0.0840728	−	0.0840728i
$940$	−3.31070	+	4.28339i	−0.107983	+	0.139709i
$941$	−17.6358	+	3.50799i	−0.574912	+	0.114357i	−0.473979	−	0.880536i	$-0.657183\pi$
$941$	−17.6358	+	3.50799i	−0.574912	+	0.114357i	−0.100933	+	0.994893i	$0.532183\pi$
$942$	−21.4874	+	4.79835i	−0.700097	+	0.156339i
$943$	−18.6311	+	44.9796i	−0.606713	+	1.46474i
$944$	15.3757	+	4.74407i	0.500437	+	0.154406i
$945$	−12.8601	+	39.8695i	−0.418340	+	1.29696i
$946$	−0.0725072	+	0.114201i	−0.00235741	+	0.00371300i
$947$	29.6190	−	19.7908i	0.962488	−	0.643114i	0.0281885	−	0.999603i	$-0.491026\pi$
$947$	29.6190	−	19.7908i	0.962488	−	0.643114i	0.934300	+	0.356489i	$0.116026\pi$
$948$	−5.52418	+	6.06597i	−0.179417	+	0.197014i
$949$	1.72081	−	8.65112i	0.0558600	−	0.280827i
$950$	−7.27601	−	38.9413i	−0.236065	−	1.26342i
$951$	10.0421			0.325637
$952$	−47.7928	+	11.8254i	−1.54897	+	0.383265i
$953$		−	14.5462i		−	0.471197i	−0.971850	−	0.235599i	$-0.924295\pi$
$953$		−	14.5462i		−	0.471197i	0.971850	−	0.235599i	$-0.0757051\pi$
$954$	18.4258	+	7.13278i	0.596558	+	0.230932i
$955$	−4.04706	−	50.0531i	−0.130960	−	1.61968i
$956$	−17.8171	+	19.5645i	−0.576245	+	0.632761i
$957$	−0.216230	+	0.144480i	−0.00698971	+	0.00467038i
$958$	−23.6242	−	14.9992i	−0.763262	−	0.484602i
$959$	−8.68104	+	12.9921i	−0.280325	+	0.419536i
$960$	−14.9775	+	0.366508i	−0.483397	+	0.0118290i
$961$	17.5009	+	7.24912i	0.564546	+	0.233843i
$962$	−31.8018	+	7.10167i	−1.02533	+	0.228967i
$963$	−4.72903	−	23.7744i	−0.152391	−	0.766121i
$964$	−19.8060	+	14.6163i	−0.637909	+	0.470761i
$965$	−29.6716	−	16.5336i	−0.955163	−	0.532235i
$966$	−18.2992	+	12.8553i	−0.588767	+	0.413611i
$967$	−9.65400	−	23.3068i	−0.310452	−	0.749497i	−0.999688	−	0.0249604i	$-0.992054\pi$
$967$	−9.65400	−	23.3068i	−0.310452	−	0.749497i	0.689237	−	0.724536i	$-0.257946\pi$
$968$	23.4388	+	20.3646i	0.753351	+	0.654542i
$969$	−10.3614	−	16.3376i	−0.332856	−	0.524839i
$970$	−29.9785	−	15.7986i	−0.962550	−	0.507263i
$971$	−45.9175	+	19.0196i	−1.47356	+	0.610369i	−0.967668	−	0.252226i	$-0.918837\pi$
$971$	−45.9175	+	19.0196i	−1.47356	+	0.610369i	−0.505894	+	0.862596i	$0.668837\pi$
$972$	4.76325	−	31.5939i	0.152781	−	1.01337i
$973$	−29.4258	+	29.4258i	−0.943347	+	0.943347i
$974$	−26.5105	−	4.63245i	−0.849451	−	0.148433i
$975$	−6.37309	+	5.94202i	−0.204102	+	0.190297i
$976$	−24.0640	+	44.5106i	−0.770271	+	1.42475i
$977$	0.986530	+	0.408634i	0.0315619	+	0.0130734i	0.398409	−	0.917208i	$-0.369563\pi$
$977$	0.986530	+	0.408634i	0.0315619	+	0.0130734i	−0.366847	+	0.930281i	$0.619563\pi$
$978$	−10.4340	−	23.6144i	−0.333643	−	0.755105i
$979$	1.04005	−	1.55655i	0.0332402	−	0.0497475i
$980$	42.0037	−	24.0548i	1.34176	−	0.768403i
$981$	−2.41881	+	1.61620i	−0.0772266	+	0.0516012i
$982$	0.185689	+	7.94900i	0.00592559	+	0.253663i
$983$	15.4761	+	3.07839i	0.493612	+	0.0981855i	0.435618	−	0.900131i	$-0.356530\pi$
$983$	15.4761	+	3.07839i	0.493612	+	0.0981855i	0.0579935	+	0.998317i	$0.481530\pi$
$984$	8.17627	−	24.4570i	0.260650	−	0.779660i
$985$	−12.2505	+	3.48332i	−0.390333	+	0.110988i
$986$	6.74180	+	10.1008i	0.214703	+	0.321674i
$987$		−	4.28026i		−	0.136242i
$988$	−9.91825	−	21.0999i	−0.315541	−	0.671278i
$989$	2.81420	+	0.559779i	0.0894863	+	0.0177999i
$990$	0.320653	+	1.03517i	0.0101910	+	0.0328998i
$991$	0.152114	+	0.227655i	0.00483206	+	0.00723169i	0.833878	−	0.551949i	$-0.186116\pi$
$991$	0.152114	+	0.227655i	0.00483206	+	0.00723169i	−0.829046	+	0.559181i	$0.811116\pi$
$992$	17.4924	+	8.93554i	0.555385	+	0.283704i
$993$	3.90003	−	5.83681i	0.123764	−	0.185226i
$994$	−30.2816	−	68.5338i	−0.960473	−	2.17376i
$995$	−28.7998	−	3.34620i	−0.913015	−	0.106082i
$996$	−3.93958	−	2.37403i	−0.124830	−	0.0752240i
$997$	15.5614	−	3.09535i	0.492833	−	0.0980306i	0.0575839	−	0.998341i	$-0.481660\pi$
$997$	15.5614	−	3.09535i	0.492833	−	0.0980306i	0.435249	+	0.900310i	$0.356660\pi$
$998$	5.16208	−	29.5415i	0.163403	−	0.935119i
$999$	−34.7470	+	34.7470i	−1.09935	+	1.09935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.co.a.99.13	✓	832
5.4	even	2	inner	680.2.co.a.99.92	yes	832
8.3	odd	2	inner	680.2.co.a.99.67	yes	832
17.11	odd	16	inner	680.2.co.a.419.38	yes	832
40.19	odd	2	inner	680.2.co.a.99.38	yes	832
85.79	odd	16	inner	680.2.co.a.419.67	yes	832
136.11	even	16	inner	680.2.co.a.419.92	yes	832
680.419	even	16	inner	680.2.co.a.419.13	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.13	✓	832	1.1	even	1	trivial
680.2.co.a.99.38	yes	832	40.19	odd	2	inner
680.2.co.a.99.67	yes	832	8.3	odd	2	inner
680.2.co.a.99.92	yes	832	5.4	even	2	inner
680.2.co.a.419.13	yes	832	680.419	even	16	inner
680.2.co.a.419.38	yes	832	17.11	odd	16	inner
680.2.co.a.419.67	yes	832	85.79	odd	16	inner
680.2.co.a.419.92	yes	832	136.11	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.co (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31885 - 0.510535i) q^{2} +(-0.821426 - 0.163392i) q^{3} +(1.47871 + 1.34663i) q^{4} +(-1.70342 - 1.44857i) q^{5} +(0.999917 + 0.634856i) q^{6} +(-3.51029 - 2.34550i) q^{7} +(-1.26268 - 2.53094i) q^{8} +(-2.12359 - 0.879621i) q^{9} +(1.50701 + 2.78010i) q^{10} +(-0.146226 + 0.0290862i) q^{11} +(-0.994620 - 1.34777i) q^{12} +(-1.47133 - 1.47133i) q^{13} +(3.43207 + 4.88547i) q^{14} +(1.16255 + 1.46822i) q^{15} +(0.373151 + 3.98256i) q^{16} +(1.48653 + 3.84581i) q^{17} +(2.35161 + 2.24425i) q^{18} +(5.17597 - 2.14396i) q^{19} +(-0.568173 - 4.43590i) q^{20} +(2.50021 + 2.50021i) q^{21} +(0.207699 + 0.0362934i) q^{22} +(-0.872501 - 4.38636i) q^{23} +(0.623666 + 2.28529i) q^{24} +(0.803303 + 4.93505i) q^{25} +(1.18929 + 2.69162i) q^{26} +(3.68977 + 2.46542i) q^{27} +(-2.03216 - 8.19538i) q^{28} +(-1.73169 + 1.15708i) q^{29} +(-0.783651 - 2.52988i) q^{30} +(-0.677420 + 3.40562i) q^{31} +(1.54111 - 5.44288i) q^{32} +0.124866 q^{33} +(0.00292394 - 5.83095i) q^{34} +(2.58189 + 9.08026i) q^{35} +(-1.95565 - 4.16041i) q^{36} +(-2.16031 + 10.8606i) q^{37} +(-7.92087 + 0.185033i) q^{38} +(0.968184 + 1.44899i) q^{39} +(-1.51535 + 6.14034i) q^{40} +(-9.05140 - 6.04795i) q^{41} +(-2.02094 - 4.57383i) q^{42} +(-0.245522 + 0.592742i) q^{43} +(-0.255394 - 0.153903i) q^{44} +(2.34319 + 4.57454i) q^{45} +(-1.08870 + 6.23038i) q^{46} +(-0.855982 - 0.855982i) q^{47} +(0.344202 - 3.33235i) q^{48} +(4.14196 + 9.99958i) q^{49} +(1.46008 - 6.91868i) q^{50} +(-0.592697 - 3.40194i) q^{51} +(-0.194322 - 4.15700i) q^{52} +(5.61555 - 2.32604i) q^{53} +(-3.60755 - 5.13527i) q^{54} +(0.291218 + 0.162272i) q^{55} +(-1.50393 + 11.8459i) q^{56} +(-4.60199 + 0.915392i) q^{57} +(2.87456 - 0.641918i) q^{58} +(1.53944 - 3.71653i) q^{59} +(-0.258077 + 3.73660i) q^{60} +(10.5179 + 7.02785i) q^{61} +(2.63210 - 4.14564i) q^{62} +(5.39127 + 8.06861i) q^{63} +(-4.81127 + 6.39153i) q^{64} +(0.374976 + 4.63761i) q^{65} +(-0.164679 - 0.0637487i) q^{66} +7.15571 q^{67} +(-2.98076 + 7.68863i) q^{68} +3.74563i q^{69} +(1.23068 - 13.2936i) q^{70} +(-12.3082 - 2.44825i) q^{71} +(0.455159 + 6.48536i) q^{72} +(2.35512 + 3.52469i) q^{73} +(8.39383 - 13.2205i) q^{74} +(0.146492 - 4.18503i) q^{75} +(10.5409 + 3.79986i) q^{76} +(0.581517 + 0.240872i) q^{77} +(-0.537125 - 2.40529i) q^{78} +(-0.955563 - 4.80394i) q^{79} +(5.13337 - 7.32451i) q^{80} +(2.24794 + 2.24794i) q^{81} +(8.84971 + 12.5974i) q^{82} +(2.53694 - 1.05083i) q^{83} +(0.330209 + 7.06394i) q^{84} +(3.03873 - 8.70437i) q^{85} +(0.626421 - 0.656387i) q^{86} +(1.61151 - 0.667510i) q^{87} +(0.258252 + 0.333362i) q^{88} +(-8.87873 + 8.87873i) q^{89} +(-0.754841 - 7.22939i) q^{90} +(1.71378 + 8.61578i) q^{91} +(4.61665 - 7.66108i) q^{92} +(1.11290 - 2.68678i) q^{93} +(0.691899 + 1.56592i) q^{94} +(-11.9225 - 3.84568i) q^{95} +(-2.15523 + 4.21912i) q^{96} +(-8.90994 + 5.95343i) q^{97} +(-0.357469 - 15.3025i) q^{98} +(0.336110 + 0.0668563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) \) 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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