LMFDB - Embedded newform 640.2.bm.a.101.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.23
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.501270 - 1.32240i) q^{2} +(-2.51853 + 1.34618i) q^{3} +(-1.49746 + 1.32575i) q^{4} +(0.634393 + 0.773010i) q^{5} +(3.04265 + 2.65570i) q^{6} +(1.35015 - 0.902145i) q^{7} +(2.50380 + 1.31567i) q^{8} +(2.86409 - 4.28642i) q^{9} +(0.704223 - 1.22641i) q^{10} +(-1.04813 + 0.317945i) q^{11} +(1.98669 - 5.35481i) q^{12} +(-2.64302 - 2.16907i) q^{13} +(-1.86978 - 1.33322i) q^{14} +(-2.63836 - 1.09284i) q^{15} +(0.484759 - 3.97052i) q^{16} +(5.73537 - 2.37567i) q^{17} +(-7.10402 - 1.63881i) q^{18} +(0.629445 + 6.39086i) q^{19} +(-1.97480 - 0.316502i) q^{20} +(-2.18596 + 4.08964i) q^{21} +(0.945843 + 1.22666i) q^{22} +(-4.91663 + 0.977978i) q^{23} +(-8.07704 + 0.0570126i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-1.54350 + 4.58241i) q^{26} +(-0.603272 + 6.12513i) q^{27} +(-0.825779 + 3.14089i) q^{28} +(-1.03398 + 3.40858i) q^{29} +(-0.122643 + 4.03676i) q^{30} +(5.21639 + 5.21639i) q^{31} +(-5.49359 + 1.34926i) q^{32} +(2.21173 - 2.21173i) q^{33} +(-6.01654 - 6.39358i) q^{34} +(1.55390 + 0.471369i) q^{35} +(1.39387 + 10.2158i) q^{36} +(2.05496 + 0.202396i) q^{37} +(8.13572 - 4.03592i) q^{38} +(9.57651 + 1.90489i) q^{39} +(0.571366 + 2.77012i) q^{40} +(0.612269 + 3.07809i) q^{41} +(6.50387 + 0.840688i) q^{42} +(-6.01279 - 3.21390i) q^{43} +(1.14801 - 1.86567i) q^{44} +(5.13041 - 0.505301i) q^{45} +(3.75783 + 6.01149i) q^{46} +(2.39259 + 5.77623i) q^{47} +(4.12417 + 10.6525i) q^{48} +(-1.66973 + 4.03109i) q^{49} +(1.39478 - 0.233651i) q^{50} +(-11.2466 + 13.7041i) q^{51} +(6.83347 - 0.255900i) q^{52} +(1.46530 + 4.83046i) q^{53} +(8.40224 - 2.27258i) q^{54} +(-0.910699 - 0.608510i) q^{55} +(4.56744 - 0.482429i) q^{56} +(-10.1886 - 15.2483i) q^{57} +(5.02579 - 0.341285i) q^{58} +(-2.88403 + 2.36687i) q^{59} +(5.39967 - 1.86132i) q^{60} +(2.41850 + 4.52470i) q^{61} +(4.28331 - 9.51295i) q^{62} -8.37115i q^{63} +(4.53802 + 6.58835i) q^{64} -3.41913i q^{65} +(-4.03345 - 1.81611i) q^{66} +(4.86355 + 9.09906i) q^{67} +(-5.43893 + 11.1612i) q^{68} +(11.0662 - 9.08176i) q^{69} +(-0.155584 - 2.29115i) q^{70} +(-4.22630 - 6.32510i) q^{71} +(12.8106 - 6.96412i) q^{72} +(-6.47451 - 4.32613i) q^{73} +(-0.762442 - 2.81893i) q^{74} +(-0.828976 - 2.73277i) q^{75} +(-9.41527 - 8.73556i) q^{76} +(-1.12830 + 1.37484i) q^{77} +(-2.28140 - 13.6188i) q^{78} +(-6.20419 + 14.9782i) q^{79} +(3.37678 - 2.14415i) q^{80} +(-0.807729 - 1.95003i) q^{81} +(3.76353 - 2.35261i) q^{82} +(-8.72092 + 0.858936i) q^{83} +(-2.14847 - 9.02210i) q^{84} +(5.47490 + 2.92639i) q^{85} +(-1.23602 + 9.56232i) q^{86} +(-1.98446 - 9.97655i) q^{87} +(-3.04261 - 0.582917i) q^{88} +(9.45919 + 1.88155i) q^{89} +(-3.23992 - 6.53113i) q^{90} +(-5.52530 - 0.544195i) q^{91} +(6.06589 - 7.98271i) q^{92} +(-20.1599 - 6.11544i) q^{93} +(6.43912 - 6.05940i) q^{94} +(-4.54089 + 4.54089i) q^{95} +(12.0194 - 10.7935i) q^{96} +(-11.6742 - 11.6742i) q^{97} +(6.16768 + 0.187383i) q^{98} +(-1.63908 + 5.40333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.501270	−	1.32240i	−0.354451	−	0.935075i
$2$	−0.501270	−	1.32240i	−0.354451	−	0.935075i
$3$	−2.51853	+	1.34618i	−1.45408	+	0.777220i	−0.993866	−	0.110590i	$-0.964726\pi$
$3$	−2.51853	+	1.34618i	−1.45408	+	0.777220i	−0.460210	+	0.887810i	$0.652226\pi$
$4$	−1.49746	+	1.32575i	−0.748729	+	0.662876i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	3.04265	+	2.65570i	1.24216	+	1.08418i
$7$	1.35015	−	0.902145i	0.510311	−	0.340979i	−0.273609	−	0.961841i	$-0.588217\pi$
$7$	1.35015	−	0.902145i	0.510311	−	0.340979i	0.783920	+	0.620862i	$0.213217\pi$
$8$	2.50380	+	1.31567i	0.885227	+	0.465160i
$9$	2.86409	−	4.28642i	0.954697	−	1.42881i
$10$	0.704223	−	1.22641i	0.222695	−	0.387823i
$11$	−1.04813	+	0.317945i	−0.316022	+	0.0958642i	−0.444311	−	0.895873i	$-0.646551\pi$
$11$	−1.04813	+	0.317945i	−0.316022	+	0.0958642i	0.128289	+	0.991737i	$0.459051\pi$
$12$	1.98669	−	5.35481i	0.573508	−	1.54580i
$13$	−2.64302	−	2.16907i	−0.733042	−	0.601592i	0.192027	−	0.981390i	$-0.438494\pi$
$13$	−2.64302	−	2.16907i	−0.733042	−	0.601592i	−0.925070	+	0.379797i	$0.875994\pi$
$14$	−1.86978	−	1.33322i	−0.499721	−	0.356318i
$15$	−2.63836	−	1.09284i	−0.681221	−	0.282171i
$16$	0.484759	−	3.97052i	0.121190	−	0.992629i
$17$	5.73537	−	2.37567i	1.39103	−	0.576184i	0.443624	−	0.896213i	$-0.353692\pi$
$17$	5.73537	−	2.37567i	1.39103	−	0.576184i	0.947408	+	0.320028i	$0.103692\pi$
$18$	−7.10402	−	1.63881i	−1.67443	−	0.386271i
$19$	0.629445	+	6.39086i	0.144405	+	1.46616i	0.745242	+	0.666794i	$0.232334\pi$
$19$	0.629445	+	6.39086i	0.144405	+	1.46616i	−0.600838	+	0.799371i	$0.705166\pi$
$20$	−1.97480	−	0.316502i	−0.441578	−	0.0707719i
$21$	−2.18596	+	4.08964i	−0.477015	+	0.892433i
$22$	0.945843	+	1.22666i	0.201654	+	0.261525i
$23$	−4.91663	+	0.977978i	−1.02519	+	0.203923i	−0.678919	−	0.734213i	$-0.737551\pi$
$23$	−4.91663	+	0.977978i	−1.02519	+	0.203923i	−0.346269	+	0.938135i	$0.612551\pi$
$24$	−8.07704	+	0.0570126i	−1.64872	+	0.0116376i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−1.54350	+	4.58241i	−0.302706	+	0.898684i
$27$	−0.603272	+	6.12513i	−0.116100	+	1.17878i
$28$	−0.825779	+	3.14089i	−0.156058	+	0.593573i
$29$	−1.03398	+	3.40858i	−0.192005	+	0.632957i	0.807090	+	0.590429i	$0.201041\pi$
$29$	−1.03398	+	3.40858i	−0.192005	+	0.632957i	−0.999095	+	0.0425285i	$0.986459\pi$
$30$	−0.122643	+	4.03676i	−0.0223914	+	0.737008i
$31$	5.21639	+	5.21639i	0.936892	+	0.936892i	0.998124	−	0.0612317i	$-0.0195029\pi$
$31$	5.21639	+	5.21639i	0.936892	+	0.936892i	−0.0612317	+	0.998124i	$0.519503\pi$
$32$	−5.49359	+	1.34926i	−0.971138	+	0.238517i
$33$	2.21173	−	2.21173i	0.385012	−	0.385012i
$34$	−6.01654	−	6.39358i	−1.03183	−	1.09649i
$35$	1.55390	+	0.471369i	0.262656	+	0.0796760i
$36$	1.39387	+	10.2158i	0.232312	+	1.70263i
$37$	2.05496	+	0.202396i	0.337833	+	0.0332737i	0.265512	−	0.964108i	$-0.414459\pi$
$37$	2.05496	+	0.202396i	0.337833	+	0.0332737i	0.0723218	+	0.997381i	$0.476959\pi$
$38$	8.13572	−	4.03592i	1.31979	−	0.654713i
$39$	9.57651	+	1.90489i	1.53347	+	0.305026i
$40$	0.571366	+	2.77012i	0.0903408	+	0.437994i
$41$	0.612269	+	3.07809i	0.0956204	+	0.480716i	0.998688	+	0.0512169i	$0.0163100\pi$
$41$	0.612269	+	3.07809i	0.0956204	+	0.480716i	−0.903067	+	0.429499i	$0.858690\pi$
$42$	6.50387	+	0.840688i	1.00357	+	0.129721i
$43$	−6.01279	−	3.21390i	−0.916942	−	0.490116i	−0.0557781	−	0.998443i	$-0.517764\pi$
$43$	−6.01279	−	3.21390i	−0.916942	−	0.490116i	−0.861164	+	0.508327i	$0.830264\pi$
$44$	1.14801	−	1.86567i	0.173069	−	0.281260i
$45$	5.13041	−	0.505301i	0.764796	−	0.0753258i
$46$	3.75783	+	6.01149i	0.554062	+	0.886347i
$47$	2.39259	+	5.77623i	0.348996	+	0.842550i	0.996739	+	0.0806913i	$0.0257128\pi$
$47$	2.39259	+	5.77623i	0.348996	+	0.842550i	−0.647744	+	0.761858i	$0.724287\pi$
$48$	4.12417	+	10.6525i	0.595272	+	1.53755i
$49$	−1.66973	+	4.03109i	−0.238533	+	0.575870i
$50$	1.39478	−	0.233651i	0.197251	−	0.0330433i
$51$	−11.2466	+	13.7041i	−1.57485	+	1.91895i
$52$	6.83347	−	0.255900i	0.947631	−	0.0354870i
$53$	1.46530	+	4.83046i	0.201275	+	0.663515i	0.998230	+	0.0594758i	$0.0189429\pi$
$53$	1.46530	+	4.83046i	0.201275	+	0.663515i	−0.796955	+	0.604039i	$0.793557\pi$
$54$	8.40224	−	2.27258i	1.14340	−	0.309258i
$55$	−0.910699	−	0.608510i	−0.122799	−	0.0820514i
$56$	4.56744	−	0.482429i	0.610350	−	0.0644673i
$57$	−10.1886	−	15.2483i	−1.34951	−	2.01968i
$58$	5.02579	−	0.341285i	0.659919	−	0.0448129i
$59$	−2.88403	+	2.36687i	−0.375469	+	0.308140i	−0.803135	−	0.595797i	$-0.796836\pi$
$59$	−2.88403	+	2.36687i	−0.375469	+	0.308140i	0.427666	+	0.903937i	$0.359336\pi$
$60$	5.39967	−	1.86132i	0.697094	−	0.240296i
$61$	2.41850	+	4.52470i	0.309658	+	0.579329i	0.987823	−	0.155580i	$-0.0497247\pi$
$61$	2.41850	+	4.52470i	0.309658	+	0.579329i	−0.678166	+	0.734909i	$0.737225\pi$
$62$	4.28331	−	9.51295i	0.543981	−	1.20815i
$63$		−	8.37115i		−	1.05467i
$64$	4.53802	+	6.58835i	0.567252	+	0.823544i
$65$		−	3.41913i		−	0.424091i
$66$	−4.03345	−	1.81611i	−0.496483	−	0.223547i
$67$	4.86355	+	9.09906i	0.594177	+	1.11163i	0.981819	+	0.189817i	$0.0607896\pi$
$67$	4.86355	+	9.09906i	0.594177	+	1.11163i	−0.387642	+	0.921810i	$0.626710\pi$
$68$	−5.43893	+	11.1612i	−0.659567	+	1.35349i
$69$	11.0662	−	9.08176i	1.33221	−	1.09332i
$70$	−0.155584	−	2.29115i	−0.0185959	−	0.273845i
$71$	−4.22630	−	6.32510i	−0.501569	−	0.750651i	0.491154	−	0.871073i	$-0.336575\pi$
$71$	−4.22630	−	6.32510i	−0.501569	−	0.750651i	−0.992723	+	0.120422i	$0.961575\pi$
$72$	12.8106	−	6.96412i	1.50975	−	0.820730i
$73$	−6.47451	−	4.32613i	−0.757785	−	0.506335i	0.115642	−	0.993291i	$-0.463107\pi$
$73$	−6.47451	−	4.32613i	−0.757785	−	0.506335i	−0.873427	+	0.486955i	$0.838107\pi$
$74$	−0.762442	−	2.81893i	−0.0886321	−	0.327693i
$75$	−0.828976	−	2.73277i	−0.0957220	−	0.315553i
$76$	−9.41527	−	8.73556i	−1.08001	−	1.00204i
$77$	−1.12830	+	1.37484i	−0.128582	+	0.156677i
$78$	−2.28140	−	13.6188i	−0.258318	−	1.54202i
$79$	−6.20419	+	14.9782i	−0.698026	+	1.68518i	0.0299234	+	0.999552i	$0.490474\pi$
$79$	−6.20419	+	14.9782i	−0.698026	+	1.68518i	−0.727949	+	0.685631i	$0.759526\pi$
$80$	3.37678	−	2.14415i	0.377535	−	0.239723i
$81$	−0.807729	−	1.95003i	−0.0897477	−	0.216670i
$82$	3.76353	−	2.35261i	0.415613	−	0.259803i
$83$	−8.72092	+	0.858936i	−0.957246	+	0.0942805i	−0.564560	−	0.825392i	$-0.690954\pi$
$83$	−8.72092	+	0.858936i	−0.957246	+	0.0942805i	−0.392686	+	0.919673i	$0.628454\pi$
$84$	−2.14847	−	9.02210i	−0.234417	−	0.984392i
$85$	5.47490	+	2.92639i	0.593836	+	0.317412i
$86$	−1.23602	+	9.56232i	−0.133284	+	1.03113i
$87$	−1.98446	−	9.97655i	−0.212756	−	1.06960i
$88$	−3.04261	−	0.582917i	−0.324343	−	0.0621392i
$89$	9.45919	+	1.88155i	1.00267	+	0.199444i	0.669014	−	0.743250i	$-0.266717\pi$
$89$	9.45919	+	1.88155i	1.00267	+	0.199444i	0.333659	+	0.942694i	$0.391717\pi$
$90$	−3.23992	−	6.53113i	−0.341518	−	0.688442i
$91$	−5.52530	−	0.544195i	−0.579209	−	0.0570471i
$92$	6.06589	−	7.98271i	0.632412	−	0.832256i
$93$	−20.1599	−	6.11544i	−2.09048	−	0.634141i
$94$	6.43912	−	6.05940i	0.664145	−	0.624980i
$95$	−4.54089	+	4.54089i	−0.465885	+	0.465885i
$96$	12.0194	−	10.7935i	1.22673	−	1.10161i
$97$	−11.6742	−	11.6742i	−1.18533	−	1.18533i	−0.978343	−	0.206990i	$-0.933633\pi$
$97$	−11.6742	−	11.6742i	−1.18533	−	1.18533i	−0.206990	−	0.978343i	$-0.566367\pi$
$98$	6.16768	+	0.187383i	0.623029	+	0.0189285i
$99$	−1.63908	+	5.40333i	−0.164734	+	0.543055i
$100$	−1.00814	−	1.72733i	−0.100814	−	0.172733i
$101$	0.407936	−	4.14184i	0.0405911	−	0.412129i	−0.953321	−	0.301957i	$-0.902360\pi$
$101$	0.407936	−	4.14184i	0.0405911	−	0.412129i	0.993913	−	0.110171i	$-0.0351400\pi$
$102$	23.7598	+	8.00307i	2.35257	+	0.792422i
$103$	−1.45844	+	7.33209i	−0.143705	+	0.722452i	0.839990	+	0.542603i	$0.182561\pi$
$103$	−1.45844	+	7.33209i	−0.143705	+	0.722452i	−0.983694	+	0.179849i	$0.942439\pi$
$104$	−3.76381	−	8.90827i	−0.369072	−	0.873527i
$105$	−4.54809	+	0.904672i	−0.443848	+	0.0882869i
$106$	5.65327	−	4.35907i	0.549094	−	0.423391i
$107$	3.06796	−	5.73975i	0.296591	−	0.554882i	−0.688849	−	0.724904i	$-0.741884\pi$
$107$	3.06796	−	5.73975i	0.296591	−	0.554882i	0.985440	+	0.170022i	$0.0543839\pi$
$108$	−7.21703	−	9.97191i	−0.694459	−	0.959548i
$109$	1.01556	+	10.3112i	0.0972730	+	0.987630i	0.912662	+	0.408716i	$0.134023\pi$
$109$	1.01556	+	10.3112i	0.0972730	+	0.987630i	−0.815389	+	0.578914i	$0.803477\pi$
$110$	−0.348185	+	1.50933i	−0.0331981	+	0.143909i
$111$	−5.44795	+	2.25662i	−0.517097	+	0.214188i
$112$	−2.92748	−	5.79814i	−0.276621	−	0.547872i
$113$	15.2477	+	6.31581i	1.43438	+	0.594142i	0.958430	−	0.285328i	$-0.0921026\pi$
$113$	15.2477	+	6.31581i	1.43438	+	0.594142i	0.475955	+	0.879470i	$0.342103\pi$
$114$	−15.0570	+	21.1168i	−1.41022	+	1.97777i
$115$	−3.87506	−	3.18018i	−0.361352	−	0.296554i
$116$	−2.97059	−	6.47501i	−0.275812	−	0.601189i
$117$	−16.8674	+	5.11667i	−1.55939	+	0.473036i
$118$	4.57561	+	2.62739i	0.421219	+	0.241871i
$119$	5.60044	−	8.38166i	0.513392	−	0.768345i
$120$	−5.16809	−	6.20747i	−0.471780	−	0.566662i
$121$	−8.14869	+	5.44478i	−0.740790	+	0.494980i
$122$	4.77112	−	5.46631i	0.431957	−	0.494897i
$123$	−5.68569	−	6.92804i	−0.512662	−	0.624680i
$124$	−14.7270	−	0.895680i	−1.32252	−	0.0804345i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−11.0700	+	4.19620i	−0.986191	+	0.373827i
$127$	−5.13449			−0.455612			−0.227806	−	0.973707i	$-0.573155\pi$
$127$	−5.13449			−0.455612			−0.227806	+	0.973707i	$0.573155\pi$
$128$	6.43763	−	9.30359i	0.569012	−	0.822329i
$129$	19.4699			1.71423
$130$	−4.52144	+	1.71390i	−0.396556	+	0.150319i
$131$	10.8460	−	5.79733i	0.947623	−	0.506515i	0.0762244	−	0.997091i	$-0.475713\pi$
$131$	10.8460	−	5.79733i	0.947623	−	0.506515i	0.871399	+	0.490576i	$0.163213\pi$
$132$	−0.379764	+	6.24417i	−0.0330543	+	0.543485i
$133$	6.61533	+	8.06080i	0.573622	+	0.698960i
$134$	9.59460	−	10.9926i	0.828848	−	0.949617i
$135$	−5.11750	+	3.41940i	−0.440444	+	0.294295i
$136$	17.4858	+	1.59767i	1.49940	+	0.136999i
$137$	5.30587	−	7.94080i	0.453311	−	0.678428i	−0.532473	−	0.846447i	$-0.678737\pi$
$137$	5.30587	−	7.94080i	0.453311	−	0.678428i	0.985784	+	0.168019i	$0.0537371\pi$
$138$	−17.5568	−	10.0814i	−1.49453	−	0.858188i
$139$	−9.11364	+	2.76459i	−0.773009	+	0.234490i	−0.652058	−	0.758169i	$-0.726094\pi$
$139$	−9.11364	+	2.76459i	−0.773009	+	0.234490i	−0.120951	+	0.992659i	$0.538594\pi$
$140$	−2.95181	+	1.35423i	−0.249474	+	0.114453i
$141$	−13.8017	−	11.3268i	−1.16231	−	0.953885i
$142$	−6.24577	+	8.75942i	−0.524133	+	0.735074i
$143$	3.45987	+	1.43312i	0.289328	+	0.119844i
$144$	−15.6309	−	13.4498i	−1.30257	−	1.12082i
$145$	−3.29082	+	1.36310i	−0.273288	+	0.113199i
$146$	−2.47538	+	10.7304i	−0.204864	+	0.888056i
$147$	−1.22131	−	12.4002i	−0.100732	−	1.02275i
$148$	−3.34554	+	2.42129i	−0.275002	+	0.199029i
$149$	4.73359	−	8.85592i	0.387791	−	0.725505i	−0.609968	−	0.792426i	$-0.708818\pi$
$149$	4.73359	−	8.85592i	0.387791	−	0.725505i	0.997758	+	0.0669212i	$0.0213176\pi$
$150$	−3.19826	+	2.46609i	−0.261137	+	0.201355i
$151$	8.79574	−	1.74958i	0.715787	−	0.142379i	0.176256	−	0.984344i	$-0.443601\pi$
$151$	8.79574	−	1.74958i	0.715787	−	0.142379i	0.539531	+	0.841965i	$0.318601\pi$
$152$	−6.83227	+	16.8296i	−0.554170	+	1.36506i
$153$	6.24353	−	31.3883i	0.504759	−	2.53760i
$154$	2.38366	+	0.802894i	0.192081	+	0.0646990i
$155$	−0.723082	+	7.34157i	−0.0580793	+	0.589689i
$156$	−16.8658	+	9.84360i	−1.35035	+	0.788119i
$157$	−6.75765	+	22.2770i	−0.539319	+	1.77790i	0.0846063	+	0.996414i	$0.473037\pi$
$157$	−6.75765	+	22.2770i	−0.539319	+	1.77790i	−0.623926	+	0.781484i	$0.714463\pi$
$158$	22.9171	+	0.696255i	1.82319	+	0.0553911i
$159$	−10.1931	−	10.1931i	−0.808366	−	0.808366i
$160$	−4.52808	−	3.39064i	−0.357977	−	0.268054i
$161$	−5.75593	+	5.75593i	−0.453631	+	0.453631i
$162$	−2.17382	+	2.04563i	−0.170792	+	0.160720i
$163$	16.5918	+	5.03308i	1.29957	+	0.394221i	0.862889	−	0.505393i	$-0.168653\pi$
$163$	16.5918	+	5.03308i	1.29957	+	0.394221i	0.436684	+	0.899615i	$0.356153\pi$
$164$	−4.99763	−	3.79759i	−0.390249	−	0.296542i
$165$	3.11279	+	0.306583i	0.242331	+	0.0238675i
$166$	5.50739	+	11.1019i	0.427456	+	0.861678i
$167$	6.51535	+	1.29598i	0.504173	+	0.100286i	0.440623	−	0.897692i	$-0.354758\pi$
$167$	6.51535	+	1.29598i	0.504173	+	0.100286i	0.0635504	+	0.997979i	$0.479758\pi$
$168$	−10.8538	+	7.36363i	−0.837390	+	0.568117i
$169$	−0.255483	−	1.28440i	−0.0196526	−	0.0988002i
$170$	1.12545	−	8.70689i	0.0863181	−	0.667788i
$171$	29.1967	+	15.6060i	2.23273	+	1.19342i
$172$	13.2647	−	3.15879i	1.01143	−	0.240855i
$173$	18.7771	−	1.84938i	1.42760	−	0.140606i	0.645499	−	0.763761i	$-0.276649\pi$
$173$	18.7771	−	1.84938i	1.42760	−	0.140606i	0.782099	+	0.623155i	$0.214149\pi$
$174$	−12.1982	+	7.62518i	−0.924743	+	0.578064i
$175$	0.621408	+	1.50021i	0.0469740	+	0.113405i
$176$	0.754320	+	4.31573i	0.0568590	+	0.325310i
$177$	4.07730	−	9.84347i	0.306469	−	0.739881i
$178$	−2.25345	−	13.4520i	−0.168903	−	1.00827i
$179$	8.11007	−	9.88215i	0.606175	−	0.738626i	−0.375995	−	0.926622i	$-0.622699\pi$
$179$	8.11007	−	9.88215i	0.606175	−	0.738626i	0.982170	+	0.187995i	$0.0601990\pi$
$180$	−7.01266	+	7.55832i	−0.522693	+	0.563364i
$181$	−3.25712	−	10.7373i	−0.242100	−	0.798097i	−0.990817	−	0.135208i	$-0.956830\pi$
$181$	−3.25712	−	10.7373i	−0.242100	−	0.798097i	0.748717	−	0.662890i	$-0.230670\pi$
$182$	2.05003	+	7.57942i	0.151958	+	0.561824i
$183$	−12.1822	−	8.13987i	−0.900532	−	0.601716i
$184$	−13.5969	−	4.02001i	−1.00238	−	0.296359i
$185$	1.14720	+	1.71690i	0.0843438	+	0.126229i
$186$	2.01852	+	29.7248i	0.148005	+	2.17953i
$187$	−5.25606	+	4.31354i	−0.384361	+	0.315437i
$188$	−11.2407	−	5.47767i	−0.819809	−	0.399500i
$189$	4.71124	+	8.81411i	0.342692	+	0.641132i
$190$	8.28106	+	3.72864i	0.600771	+	0.270504i
$191$		−	12.4750i		−	0.902661i	−0.892357	−	0.451331i	$-0.850950\pi$
$191$		−	12.4750i		−	0.902661i	0.892357	−	0.451331i	$-0.149050\pi$
$192$	−20.2983	−	10.4840i	−1.46490	−	0.756616i
$193$			21.1428i			1.52189i	0.648815	+	0.760946i	$0.275265\pi$
$193$			21.1428i			1.52189i	−0.648815	+	0.760946i	$0.724735\pi$
$194$	−9.58596	+	21.2898i	−0.688232	+	1.52852i
$195$	4.60278	+	8.61119i	0.329612	+	0.616660i
$196$	−2.84387	−	8.25003i	−0.203134	−	0.589288i
$197$	−20.8313	+	17.0958i	−1.48417	+	1.21802i	−0.564436	+	0.825477i	$0.690906\pi$
$197$	−20.8313	+	17.0958i	−1.48417	+	1.21802i	−0.919731	+	0.392548i	$0.871594\pi$
$198$	7.96696	−	0.541010i	0.566187	−	0.0384479i
$199$	−5.18604	−	7.76146i	−0.367629	−	0.550196i	0.600827	−	0.799379i	$-0.294838\pi$
$199$	−5.18604	−	7.76146i	−0.367629	−	0.550196i	−0.968456	+	0.249183i	$0.919838\pi$
$200$	−1.77886	+	2.19901i	−0.125784	+	0.155494i
$201$	−24.4980	−	16.3691i	−1.72796	−	1.15458i
$202$	−5.68164	+	1.53673i	−0.399758	+	0.108124i
$203$	1.67900	+	5.53491i	0.117842	+	0.388474i
$204$	−1.32684	−	35.4315i	−0.0928976	−	2.48070i
$205$	−1.99097	+	2.42601i	−0.139056	+	0.169440i
$206$	10.4270	−	1.74671i	0.726483	−	0.121699i
$207$	−9.88965	+	23.8757i	−0.687378	+	1.65948i
$208$	−9.89357	+	9.44269i	−0.685995	+	0.654732i
$209$	−2.69168	−	6.49830i	−0.186188	−	0.449497i
$210$	3.47615	+	5.56089i	0.239877	+	0.383738i
$211$	7.54150	−	0.742773i	0.519178	−	0.0511346i	0.164965	−	0.986299i	$-0.447249\pi$
$211$	7.54150	−	0.742773i	0.519178	−	0.0511346i	0.354213	+	0.935165i	$0.384749\pi$
$212$	−8.59823	−	5.29078i	−0.590529	−	0.363372i
$213$	19.1588	+	10.2406i	1.31274	+	0.701675i
$214$	−9.12809	−	1.17989i	−0.623983	−	0.0806559i
$215$	−1.33009	−	6.68683i	−0.0907116	−	0.456038i
$216$	−9.56913	+	14.5424i	−0.651097	+	0.989484i
$217$	11.7489	+	2.33700i	0.797566	+	0.158646i
$218$	13.1264	−	6.51164i	0.889029	−	0.441024i
$219$	22.1301	+	2.17962i	1.49541	+	0.147285i
$220$	2.17047	−	0.296144i	0.146333	−	0.0199660i
$221$	−20.3117	−	6.16149i	−1.36631	−	0.414467i
$222$	5.71503	+	6.07317i	0.383568	+	0.407605i
$223$	1.74101	−	1.74101i	0.116586	−	0.116586i	−0.646407	−	0.762993i	$-0.723729\pi$
$223$	1.74101	−	1.74101i	0.116586	−	0.116586i	0.762993	+	0.646407i	$0.223729\pi$
$224$	−6.19997	+	6.77772i	−0.414253	+	0.452855i
$225$	3.64530	+	3.64530i	0.243020	+	0.243020i
$226$	0.708782	−	23.3294i	0.0471475	−	1.55185i
$227$	7.62513	−	25.1367i	0.506098	−	1.66838i	−0.215845	−	0.976428i	$-0.569251\pi$
$227$	7.62513	−	25.1367i	0.506098	−	1.66838i	0.721943	−	0.691953i	$-0.243249\pi$
$228$	35.4724	+	9.32611i	2.34921	+	0.617637i
$229$	−0.627379	+	6.36988i	−0.0414583	+	0.420934i	0.951946	+	0.306267i	$0.0990800\pi$
$229$	−0.627379	+	6.36988i	−0.0414583	+	0.420934i	−0.993404	+	0.114667i	$0.963420\pi$
$230$	−2.26301	+	6.71849i	−0.149218	+	0.443004i
$231$	0.990876	−	4.98147i	0.0651949	−	0.327757i
$232$	−7.07345	+	7.17402i	−0.464395	+	0.470997i
$233$	−13.9156	+	2.76798i	−0.911640	+	0.181337i	−0.628561	−	0.777760i	$-0.716356\pi$
$233$	−13.9156	+	2.76798i	−0.911640	+	0.181337i	−0.283079	+	0.959097i	$0.591356\pi$
$234$	15.2214	+	19.7405i	0.995052	+	1.29048i
$235$	−2.94724	+	5.51390i	−0.192257	+	0.359687i
$236$	1.18084	−	7.36780i	0.0768661	−	0.479603i
$237$	−4.53801	−	46.0752i	−0.294775	−	2.99291i
$238$	−13.8912	−	3.20453i	−0.900432	−	0.207719i
$239$	2.72978	−	1.13071i	0.176575	−	0.0731396i	−0.292645	−	0.956221i	$-0.594535\pi$
$239$	2.72978	−	1.13071i	0.176575	−	0.0731396i	0.469219	+	0.883082i	$0.344535\pi$
$240$	−5.61812	+	9.94587i	−0.362648	+	0.642003i
$241$	23.4546	+	9.71521i	1.51084	+	0.625812i	0.975732	−	0.218970i	$-0.0702696\pi$
$241$	23.4546	+	9.71521i	1.51084	+	0.625812i	0.535111	+	0.844782i	$0.320270\pi$
$242$	11.2848	+	8.04648i	0.725417	+	0.517247i
$243$	−9.61370	−	7.88976i	−0.616719	−	0.506128i
$244$	−9.62025	−	3.56921i	−0.615873	−	0.228495i
$245$	−4.17534	+	1.26658i	−0.266753	+	0.0809185i
$246$	−6.31154	+	10.9915i	−0.402409	+	0.700795i
$247$	12.1986	−	18.2565i	0.776179	−	1.16163i
$248$	6.19774	+	19.9239i	0.393557	+	1.26517i
$249$	20.8077	−	13.9032i	1.31863	−	0.881082i
$250$	1.06545	+	0.929952i	0.0673852	+	0.0588153i
$251$	15.6000	+	19.0087i	0.984664	+	1.19982i	0.979831	+	0.199829i	$0.0640385\pi$
$251$	15.6000	+	19.0087i	0.984664	+	1.19982i	0.00483340	+	0.999988i	$0.498461\pi$
$252$	11.0981	+	12.5354i	0.699113	+	0.789659i
$253$	4.84230	−	2.58826i	0.304433	−	0.162723i
$254$	2.57376	+	6.78982i	0.161492	+	0.426031i
$255$	−17.7282			−1.11018
$256$	−15.5300	−	3.84949i	−0.970626	−	0.240593i
$257$	−8.17338			−0.509841			−0.254921	−	0.966962i	$-0.582049\pi$
$257$	−8.17338			−0.509841			−0.254921	+	0.966962i	$0.582049\pi$
$258$	−9.75968	−	25.7469i	−0.607611	−	1.60293i
$259$	2.95711	−	1.58061i	0.183746	−	0.0982141i
$260$	4.53292	+	5.12000i	0.281120	+	0.317529i
$261$	11.6492	+	14.1946i	0.721066	+	0.878621i
$262$	−13.1032	−	11.4367i	−0.809515	−	0.706563i
$263$	19.9374	−	13.3217i	1.22939	−	0.821453i	0.240581	−	0.970629i	$-0.422662\pi$
$263$	19.9374	−	13.3217i	1.22939	−	0.821453i	0.988811	+	0.149176i	$0.0476622\pi$
$264$	8.44763	−	2.62781i	0.519916	−	0.161731i
$265$	−2.80442	+	4.19711i	−0.172274	+	0.257826i
$266$	7.34350	−	12.7887i	0.450259	−	0.784127i
$267$	−26.3562	+	7.99507i	−1.61297	+	0.489290i
$268$	−19.3461	−	7.17759i	−1.18175	−	0.438441i
$269$	−17.3639	−	14.2502i	−1.05870	−	0.868849i	−0.0670378	−	0.997750i	$-0.521355\pi$
$269$	−17.3639	−	14.2502i	−1.05870	−	0.868849i	−0.991657	+	0.128902i	$0.958855\pi$
$270$	7.08705	+	5.05331i	0.431304	+	0.307535i
$271$	−22.4359	−	9.29326i	−1.36288	−	0.564525i	−0.423034	−	0.906114i	$-0.639035\pi$
$271$	−22.4359	−	9.29326i	−1.36288	−	0.564525i	−0.939850	+	0.341589i	$0.889035\pi$
$272$	−6.65236	−	23.9240i	−0.403359	−	1.45061i
$273$	14.6483	−	6.06751i	0.886553	−	0.367222i
$274$	−13.1605	−	3.03598i	−0.795057	−	0.183410i
$275$	−0.107357	−	1.09001i	−0.00647387	−	0.0657303i
$276$	−4.53093	+	28.2705i	−0.272730	+	1.70169i
$277$	−11.5781	+	21.6611i	−0.695660	+	1.30149i	0.247415	+	0.968910i	$0.420419\pi$
$277$	−11.5781	+	21.6611i	−0.695660	+	1.30149i	−0.943075	+	0.332579i	$0.892081\pi$
$278$	8.22427	+	10.6660i	0.493259	+	0.639706i
$279$	37.2999	−	7.41940i	2.23308	−	0.444188i
$280$	3.27048	+	3.22463i	0.195448	+	0.192709i
$281$	−1.07224	+	5.39052i	−0.0639645	+	0.321571i	−0.999499	−	0.0316653i	$-0.989919\pi$
$281$	−1.07224	+	5.39052i	−0.0639645	+	0.321571i	0.935534	+	0.353237i	$0.114919\pi$
$282$	−8.06008	+	23.9291i	−0.479971	+	1.42495i
$283$	1.77585	−	18.0305i	0.105563	−	1.07180i	−0.785790	−	0.618493i	$-0.787743\pi$
$283$	1.77585	−	18.0305i	0.105563	−	1.07180i	0.891353	−	0.453309i	$-0.149757\pi$
$284$	14.7142	+	3.86855i	0.873128	+	0.229556i
$285$	5.32351	−	17.5493i	0.315337	−	1.03953i
$286$	0.160830	−	5.29369i	0.00951007	−	0.313022i
$287$	3.60354	+	3.60354i	0.212710	+	0.212710i
$288$	−9.95066	+	27.4122i	−0.586349	+	1.61528i
$289$	15.2299	−	15.2299i	0.895876	−	0.895876i
$290$	3.45215	+	3.66848i	0.202717	+	0.215421i
$291$	45.1174	+	13.6862i	2.64483	+	0.802300i
$292$	15.4307	−	2.10541i	0.903013	−	0.123210i
$293$	17.3250	+	1.70637i	1.01214	+	0.0996870i	0.590467	−	0.807062i	$-0.298944\pi$
$293$	17.3250	+	1.70637i	1.01214	+	0.0996870i	0.421672	+	0.906749i	$0.361444\pi$
$294$	−15.7858	+	7.83090i	−0.920644	+	0.456707i
$295$	−3.65922	−	0.727865i	−0.213048	−	0.0423779i
$296$	4.87892	+	3.21041i	0.283582	+	0.186601i
$297$	−1.31515	−	6.61171i	−0.0763128	−	0.383650i
$298$	−14.0838	−	1.82047i	−0.815854	−	0.105457i
$299$	15.1161	+	8.07970i	0.874184	+	0.467261i
$300$	4.86433	+	2.99319i	0.280842	+	0.172812i
$301$	−11.0176	+	1.08514i	−0.635044	+	0.0625464i
$302$	−6.72268	−	10.7544i	−0.386847	−	0.618848i
$303$	4.54828	+	10.9805i	0.261292	+	0.630815i
$304$	25.6802	+	0.598806i	1.47286	+	0.0343439i
$305$	−1.96336	+	4.73997i	−0.112422	+	0.271410i
$306$	−44.6375	+	7.47760i	−2.55175	+	0.427466i
$307$	15.0479	−	18.3359i	0.858827	−	1.04648i	−0.139589	−	0.990210i	$-0.544578\pi$
$307$	15.0479	−	18.3359i	0.858827	−	1.04648i	0.998415	−	0.0562738i	$-0.0179220\pi$
$308$	−0.133113	−	3.55461i	−0.00758482	−	0.202542i
$309$	−6.19720	−	20.4294i	−0.352547	−	1.16219i
$310$	10.0709	−	2.72391i	0.571990	−	0.154707i
$311$	6.89885	+	4.60966i	0.391198	+	0.261390i	0.735578	−	0.677440i	$-0.236911\pi$
$311$	6.89885	+	4.60966i	0.391198	+	0.261390i	−0.344380	+	0.938830i	$0.611911\pi$
$312$	21.4715	+	17.3690i	1.21558	+	0.983326i
$313$	−4.44737	−	6.65596i	−0.251380	−	0.376217i	0.684222	−	0.729274i	$-0.260142\pi$
$313$	−4.44737	−	6.65596i	−0.251380	−	0.376217i	−0.935602	+	0.353057i	$0.885142\pi$
$314$	32.8464	−	2.23049i	1.85363	−	0.125874i
$315$	6.47099	−	5.31060i	0.364599	−	0.299218i
$316$	−10.5669	−	30.6545i	−0.594436	−	1.72445i
$317$	4.49685	+	8.41302i	0.252568	+	0.472522i	0.975970	−	0.217905i	$-0.0699225\pi$
$317$	4.49685	+	8.41302i	0.252568	+	0.472522i	−0.723402	+	0.690428i	$0.757422\pi$
$318$	−8.36982	+	18.5888i	−0.469356	+	1.04241i
$319$		−	3.90137i		−	0.218435i
$320$	−2.21398	+	7.68754i	−0.123765	+	0.429747i
$321$			18.5858i			1.03736i
$322$	10.4969	+	4.72634i	0.584969	+	0.263389i
$323$	18.7927	+	35.1586i	1.04565	+	1.95628i
$324$	3.79480	+	1.84924i	0.210822	+	0.102736i
$325$	2.64302	−	2.16907i	0.146608	−	0.120318i
$326$	−1.66126	−	24.4639i	−0.0920089	−	1.35493i
$327$	−16.4384	−	24.6019i	−0.909048	−	1.36049i
$328$	−2.51675	+	8.51245i	−0.138964	+	0.470022i
$329$	8.44136	+	5.64034i	0.465388	+	0.310962i
$330$	−1.15492	−	4.27002i	−0.0635765	−	0.235057i
$331$	−0.441757	−	1.45628i	−0.0242812	−	0.0800442i	0.943962	−	0.330053i	$-0.107067\pi$
$331$	−0.441757	−	1.45628i	−0.0242812	−	0.0800442i	−0.968244	+	0.250009i	$0.919567\pi$
$332$	11.9205	−	12.8480i	0.654221	−	0.705126i
$333$	6.75315	−	8.22874i	0.370070	−	0.450932i
$334$	−1.55215	−	9.26551i	−0.0849296	−	0.506986i
$335$	−3.94827	+	9.53196i	−0.215717	+	0.520786i
$336$	15.1783	+	10.6619i	0.828045	+	0.581653i
$337$	7.25482	+	17.5147i	0.395195	+	0.954086i	0.988789	+	0.149321i	$0.0477087\pi$
$337$	7.25482	+	17.5147i	0.395195	+	0.954086i	−0.593594	+	0.804765i	$0.702291\pi$
$338$	−1.57042	+	0.981682i	−0.0854196	+	0.0533965i
$339$	−46.9042	+	4.61966i	−2.54748	+	0.250905i
$340$	−12.0781	+	2.87621i	−0.655027	+	0.155984i
$341$	−7.12596	−	3.80891i	−0.385893	−	0.206264i
$342$	6.00183	−	46.4323i	0.324542	−	2.51077i
$343$	3.59977	+	18.0972i	0.194369	+	0.977159i
$344$	−10.8264	−	15.9578i	−0.583719	−	0.860388i
$345$	14.0406	+	2.79285i	0.755920	+	0.150362i
$346$	−11.8580	−	23.9037i	−0.637491	−	1.28507i
$347$	−0.561784	−	0.0553309i	−0.0301581	−	0.00297032i	0.0829268	−	0.996556i	$-0.473573\pi$
$347$	−0.561784	−	0.0553309i	−0.0301581	−	0.00297032i	−0.113085	+	0.993585i	$0.536073\pi$
$348$	16.1981	+	12.3086i	0.868309	+	0.659808i
$349$	23.2598	+	7.05579i	1.24507	+	0.377688i	0.842996	−	0.537919i	$-0.180790\pi$
$349$	23.2598	+	7.05579i	1.24507	+	0.377688i	0.402074	+	0.915607i	$0.368290\pi$
$350$	1.67238	−	1.57376i	0.0893924	−	0.0841209i
$351$	14.8803	−	14.8803i	0.794252	−	0.794252i
$352$	5.32898	−	3.16085i	0.284036	−	0.168474i
$353$	8.66549	+	8.66549i	0.461217	+	0.461217i	0.899054	−	0.437837i	$-0.144255\pi$
$353$	8.66549	+	8.66549i	0.461217	+	0.461217i	−0.437837	+	0.899054i	$0.644255\pi$
$354$	−15.0608	−	0.457568i	−0.800472	−	0.0243195i
$355$	2.20823	−	7.27957i	0.117201	−	0.386360i
$356$	−16.6592	+	9.72301i	−0.882937	+	0.515318i
$357$	−2.82165	+	28.6487i	−0.149338	+	1.51625i
$358$	−17.1334	−	5.77109i	−0.905530	−	0.305012i
$359$	−3.20146	+	16.0948i	−0.168967	+	0.849453i	0.799568	+	0.600575i	$0.205062\pi$
$359$	−3.20146	+	16.0948i	−0.168967	+	0.849453i	−0.968535	+	0.248878i	$0.919938\pi$
$360$	13.5103	+	5.48475i	0.712056	+	0.289072i
$361$	−21.8120	+	4.33868i	−1.14800	+	0.228352i
$362$	−12.5663	+	9.68949i	−0.660468	+	0.509268i
$363$	13.1931	−	24.6825i	0.692457	−	1.29550i
$364$	8.99538	−	6.51028i	0.471486	−	0.341231i
$365$	−0.763243	−	7.74934i	−0.0399500	−	0.405619i
$366$	−4.65757	+	20.1899i	−0.243455	+	1.05534i
$367$	−23.3491	+	9.67152i	−1.21881	+	0.504849i	−0.897032	−	0.441965i	$-0.854282\pi$
$367$	−23.3491	+	9.67152i	−1.21881	+	0.504849i	−0.321782	+	0.946814i	$0.604282\pi$
$368$	1.49970	+	19.9956i	0.0781772	+	1.04234i
$369$	14.9476	+	6.19148i	0.778139	+	0.322316i
$370$	1.69537	−	2.37768i	0.0881381	−	0.123610i
$371$	6.33616	+	5.19995i	0.328957	+	0.269968i
$372$	38.2961	−	17.5694i	1.98556	−	0.910932i
$373$	−22.5571	+	6.84263i	−1.16796	+	0.354298i	−0.813946	−	0.580941i	$-0.802685\pi$
$373$	−22.5571	+	6.84263i	−1.16796	+	0.354298i	−0.354018	+	0.935239i	$0.615185\pi$
$374$	8.33890	+	4.78834i	0.431194	+	0.247599i
$375$	1.58656	−	2.37446i	0.0819297	−	0.122616i
$376$	−1.60905	+	17.6104i	−0.0829803	+	0.908186i
$377$	10.1263	−	6.76617i	0.521530	−	0.348475i
$378$	9.29414	−	10.6484i	0.478039	−	0.547693i
$379$	7.05547	+	8.59711i	0.362415	+	0.441604i	0.922012	−	0.387161i	$-0.126544\pi$
$379$	7.05547	+	8.59711i	0.362415	+	0.441604i	−0.559597	+	0.828765i	$0.689044\pi$
$380$	0.779693	−	12.8199i	0.0399974	−	0.657646i
$381$	12.9314	−	6.91197i	0.662495	−	0.354111i
$382$	−16.4969	+	6.25335i	−0.844056	+	0.319949i
$383$	−30.5629			−1.56169			−0.780847	−	0.624723i	$-0.785212\pi$
$383$	−30.5629			−1.56169			−0.780847	+	0.624723i	$0.785212\pi$
$384$	−3.68905	+	32.0977i	−0.188256	+	1.63798i
$385$	−1.77855			−0.0906432
$386$	27.9591	−	10.5982i	1.42308	−	0.539437i
$387$	−30.9973	+	16.5684i	−1.57568	+	0.842220i
$388$	32.9586	+	2.00451i	1.67322	+	0.101764i
$389$	−2.25556	−	2.74841i	−0.114361	−	0.139350i	0.712683	−	0.701486i	$-0.247480\pi$
$389$	−2.25556	−	2.74841i	−0.114361	−	0.139350i	−0.827045	+	0.562136i	$0.809980\pi$
$390$	9.08016	−	10.4032i	0.459792	−	0.526787i
$391$	−25.8753	+	17.2894i	−1.30857	+	0.874360i
$392$	−9.48426	+	7.89621i	−0.479027	+	0.398819i
$393$	−19.5119	+	29.2015i	−0.984243	+	1.47302i
$394$	33.0495	+	18.9776i	1.66501	+	0.956077i
$395$	−15.5142	+	4.70619i	−0.780606	+	0.236794i
$396$	−4.70902	−	10.2643i	−0.236637	−	0.515799i
$397$	−14.4706	−	11.8757i	−0.726258	−	0.596024i	0.196910	−	0.980422i	$-0.436909\pi$
$397$	−14.4706	−	11.8757i	−0.726258	−	0.596024i	−0.923168	+	0.384397i	$0.874409\pi$
$398$	−7.66412	+	10.7486i	−0.384167	+	0.538778i
$399$	−27.5123	−	11.3960i	−1.37734	−	0.570511i
$400$	3.79965	+	1.25005i	0.189983	+	0.0625027i
$401$	8.43709	−	3.49476i	0.421328	−	0.174520i	−0.161938	−	0.986801i	$-0.551774\pi$
$401$	8.43709	−	3.49476i	0.421328	−	0.174520i	0.583266	+	0.812281i	$0.301774\pi$
$402$	−9.36625	+	40.6014i	−0.467146	+	2.02501i
$403$	−2.47231	−	25.1018i	−0.123154	−	1.25041i
$404$	4.88019	+	6.74305i	0.242799	+	0.335479i
$405$	0.994977	−	1.86147i	0.0494408	−	0.0924972i
$406$	6.47771	−	4.99478i	0.321483	−	0.247887i
$407$	−2.21821	+	0.441229i	−0.109953	+	0.0218709i
$408$	−46.1894	+	19.5154i	−2.28672	+	0.966155i
$409$	3.43752	−	17.2816i	0.169974	−	0.854519i	−0.797843	−	0.602865i	$-0.794026\pi$
$409$	3.43752	−	17.2816i	0.169974	−	0.854519i	0.967817	−	0.251654i	$-0.0809744\pi$
$410$	4.20615	+	1.41677i	0.207727	+	0.0699692i
$411$	−2.67324	+	27.1418i	−0.131861	+	1.33881i
$412$	−7.53658	−	12.9130i	−0.371301	−	0.636179i
$413$	−1.75864	+	5.79745i	−0.0865369	+	0.285274i
$414$	36.5305	+	1.10985i	1.79538	+	0.0545462i
$415$	−6.19646	−	6.19646i	−0.304172	−	0.304172i
$416$	17.4463	+	8.34987i	0.855375	+	0.409386i
$417$	19.2314	−	19.2314i	0.941764	−	0.941764i
$418$	−7.24406	+	6.81687i	−0.354319	+	0.333424i
$419$	−28.8878	−	8.76303i	−1.41126	−	0.428102i	−0.509552	−	0.860440i	$-0.670189\pi$
$419$	−28.8878	−	8.76303i	−1.41126	−	0.428102i	−0.901712	+	0.432338i	$0.857689\pi$
$420$	5.61120	−	7.38435i	0.273799	−	0.360320i
$421$	−10.6647	−	1.05038i	−0.519766	−	0.0511924i	−0.165267	−	0.986249i	$-0.552849\pi$
$421$	−10.6647	−	1.05038i	−0.519766	−	0.0511924i	−0.354499	+	0.935056i	$0.615349\pi$
$422$	−4.76256	−	9.60051i	−0.231838	−	0.467346i
$423$	31.6119	+	6.28800i	1.53702	+	0.305733i
$424$	−2.68647	+	14.0224i	−0.130467	+	0.680986i
$425$	1.21111	+	6.08864i	0.0587473	+	0.295342i
$426$	3.93839	−	30.4688i	0.190816	−	1.47622i
$427$	7.34729	+	3.92721i	0.355560	+	0.190051i
$428$	3.01535	+	12.6624i	0.145752	+	0.612060i
$429$	−10.6430	+	1.04825i	−0.513851	+	0.0506099i
$430$	−8.17589	+	5.11081i	−0.394277	+	0.246465i
$431$	1.54067	+	3.71951i	0.0742116	+	0.179163i	0.956632	−	0.291299i	$-0.0940874\pi$
$431$	1.54067	+	3.71951i	0.0742116	+	0.179163i	−0.882420	+	0.470462i	$0.844087\pi$
$432$	24.0275	+	5.36452i	1.15602	+	0.258100i
$433$	7.03247	−	16.9779i	0.337959	−	0.815905i	−0.659953	−	0.751307i	$-0.729424\pi$
$433$	7.03247	−	16.9779i	0.337959	−	0.815905i	0.997911	−	0.0645974i	$-0.0205763\pi$
$434$	−2.79892	−	16.7081i	−0.134353	−	0.802016i
$435$	6.45305	−	7.86307i	0.309400	−	0.377005i
$436$	−15.1908	−	14.0941i	−0.727508	−	0.674987i
$437$	−9.34487	−	30.8059i	−0.447026	−	1.47365i
$438$	−8.21080	−	30.3573i	−0.392327	−	1.45053i
$439$	−15.5318	−	10.3780i	−0.741293	−	0.495316i	0.126670	−	0.991945i	$-0.459571\pi$
$439$	−15.5318	−	10.3780i	−0.741293	−	0.495316i	−0.867963	+	0.496629i	$0.834571\pi$
$440$	−1.47961	−	2.72177i	−0.0705376	−	0.129755i
$441$	12.4967	+	18.7026i	0.595079	+	0.890598i
$442$	2.03372	+	29.9487i	0.0967341	+	1.42451i
$443$	−4.72507	+	3.87776i	−0.224495	+	0.184238i	−0.739917	−	0.672698i	$-0.765135\pi$
$443$	−4.72507	+	3.87776i	−0.224495	+	0.184238i	0.515422	+	0.856936i	$0.327635\pi$
$444$	5.16636	−	10.6018i	0.245185	−	0.503140i
$445$	4.54639	+	8.50570i	0.215520	+	0.403209i
$446$	−3.17501	−	1.42959i	−0.150341	−	0.0676928i
$447$			28.6762i			1.35634i
$448$	12.0707	+	4.80135i	0.570286	+	0.226842i
$449$			22.6218i			1.06759i	0.845614	+	0.533795i	$0.179234\pi$
$449$			22.6218i			1.06759i	−0.845614	+	0.533795i	$0.820766\pi$
$450$	2.99325	−	6.64780i	0.141103	−	0.313380i
$451$	−1.62040	−	3.03155i	−0.0763016	−	0.142750i
$452$	−31.2060	+	10.7570i	−1.46781	+	0.505969i
$453$	−19.7971	+	16.2471i	−0.930150	+	0.763354i
$454$	−37.0629	+	2.51682i	−1.73945	+	0.118120i
$455$	−3.08455	−	4.61635i	−0.144606	−	0.216418i
$456$	−5.44841	−	51.5834i	−0.255145	−	2.41561i
$457$	31.6860	+	21.1719i	1.48221	+	0.990380i	0.992987	+	0.118221i	$0.0377191\pi$
$457$	31.6860	+	21.1719i	1.48221	+	0.990380i	0.489222	+	0.872159i	$0.337281\pi$
$458$	8.73799	−	2.36339i	0.408299	−	0.110434i
$459$	11.0913	+	36.5631i	0.517697	+	1.70662i
$460$	10.0189	−	0.375188i	0.467133	−	0.0174932i
$461$	8.63648	−	10.5236i	0.402241	−	0.490132i	−0.532015	−	0.846735i	$-0.678565\pi$
$461$	8.63648	−	10.5236i	0.402241	−	0.490132i	0.934256	+	0.356603i	$0.116065\pi$
$462$	−7.08417	+	1.18673i	−0.329585	+	0.0552117i
$463$	−3.10821	+	7.50387i	−0.144451	+	0.348735i	−0.979501	−	0.201439i	$-0.935438\pi$
$463$	−3.10821	+	7.50387i	−0.144451	+	0.348735i	0.835051	+	0.550173i	$0.185438\pi$
$464$	13.0326	+	5.75778i	0.605023	+	0.267298i
$465$	−8.06200	−	19.4634i	−0.373867	−	0.902594i
$466$	10.6358	+	17.0144i	0.492695	+	0.788177i
$467$	−38.7601	+	3.81753i	−1.79360	+	0.176654i	−0.939294	−	0.343113i	$-0.888519\pi$
$467$	−38.7601	+	3.81753i	−1.79360	+	0.176654i	−0.854308	+	0.519767i	$0.826019\pi$
$468$	18.4748	−	30.0240i	0.853997	−	1.38786i
$469$	14.7752	+	7.89752i	0.682256	+	0.364673i
$470$	8.76892	+	1.13347i	0.404480	+	0.0522829i
$471$	−12.9696	−	65.2024i	−0.597606	−	3.00437i
$472$	−10.3351	+	2.13171i	−0.475710	+	0.0981201i
$473$	7.32401	+	1.45684i	0.336758	+	0.0669854i
$474$	−58.6548	+	29.0971i	−2.69411	+	1.33648i
$475$	−6.39086	−	0.629445i	−0.293233	−	0.0288809i
$476$	2.72558	+	19.9760i	0.124927	+	0.915598i
$477$	24.9021	+	7.55398i	1.14019	+	0.345873i
$478$	−2.86360	−	3.04305i	−0.130978	−	0.139186i
$479$	14.8429	−	14.8429i	0.678191	−	0.678191i	−0.281399	−	0.959591i	$-0.590799\pi$
$479$	14.8429	−	14.8429i	0.678191	−	0.678191i	0.959591	+	0.281399i	$0.0907986\pi$
$480$	15.9686	+	2.44381i	0.728862	+	0.111544i
$481$	−4.99229	−	4.99229i	−0.227629	−	0.227629i
$482$	1.09027	−	35.8862i	0.0496606	−	1.63457i
$483$	6.74796	−	22.2451i	0.307043	−	1.01219i
$484$	4.98388	−	18.9565i	0.226540	−	0.861658i
$485$	1.61824	−	16.4303i	0.0734805	−	0.746060i
$486$	−5.61432	+	16.6680i	−0.254671	+	0.756076i
$487$	0.234310	−	1.17796i	0.0106176	−	0.0533784i	−0.975113	−	0.221707i	$-0.928837\pi$
$487$	0.234310	−	1.17796i	0.0106176	−	0.0533784i	0.985731	+	0.168329i	$0.0538371\pi$
$488$	0.102427	+	14.5109i	0.00463663	+	0.656878i
$489$	−48.5626	+	9.65970i	−2.19608	+	0.436827i
$490$	3.76788	+	4.88655i	0.170216	+	0.220752i
$491$	13.5769	−	25.4006i	0.612717	−	1.14631i	−0.363923	−	0.931429i	$-0.618563\pi$
$491$	13.5769	−	25.4006i	0.612717	−	1.14631i	0.976640	−	0.214883i	$-0.0689370\pi$
$492$	17.6990	+	2.83662i	0.797930	+	0.127885i
$493$	2.16739	+	22.0059i	0.0976143	+	0.991094i
$494$	−30.2571	−	6.97995i	−1.36133	−	0.314043i
$495$	−5.21665	+	2.16081i	−0.234471	+	0.0971211i
$496$	23.2405	−	18.1831i	1.04353	−	0.816445i
$497$	−11.4123	−	4.72713i	−0.511912	−	0.212041i
$498$	−28.8158	−	20.5467i	−1.29127	−	0.920719i
$499$	−4.90929	−	4.02895i	−0.219770	−	0.180361i	0.518066	−	0.855341i	$-0.326652\pi$
$499$	−4.90929	−	4.02895i	−0.219770	−	0.180361i	−0.737836	+	0.674980i	$0.764152\pi$
$500$	0.695684	−	1.87511i	0.0311119	−	0.0838573i
$501$	−18.1538	+	5.50689i	−0.811051	+	0.246030i
$502$	17.3172	−	30.1579i	0.772903	−	1.34601i
$503$	−22.5662	+	33.7727i	−1.00618	+	1.50585i	−0.150318	+	0.988638i	$0.548030\pi$
$503$	−22.5662	+	33.7727i	−1.00618	+	1.50585i	−0.855858	+	0.517211i	$0.826970\pi$
$504$	11.0137	−	20.9597i	0.490588	−	0.933618i
$505$	3.46048	−	2.31222i	0.153989	−	0.102892i
$506$	−5.85001	−	5.10602i	−0.260064	−	0.226990i
$507$	2.37249	+	2.89088i	0.105366	+	0.128389i
$508$	7.68868	−	6.80706i	0.341130	−	0.302015i
$509$	−0.251686	+	0.134529i	−0.0111558	+	0.00596289i	−0.476965	−	0.878922i	$-0.658263\pi$
$509$	−0.251686	+	0.134529i	−0.0111558	+	0.00596289i	0.465809	+	0.884885i	$0.345763\pi$
$510$	8.88660	+	23.4437i	0.393505	+	1.03810i
$511$	−12.6444			−0.559355
$512$	2.69418	+	22.4665i	0.119067	+	0.992886i
$513$	−39.5246			−1.74505
$514$	4.09707	+	10.8084i	0.180714	+	0.476740i
$515$	−6.59301	+	3.52403i	−0.290523	+	0.155288i
$516$	−29.1554	+	25.8123i	−1.28349	+	1.13632i
$517$	−4.34426	−	5.29350i	−0.191061	−	0.232808i
$518$	−3.57249	−	3.11815i	−0.156966	−	0.137004i
$519$	−44.8012	+	29.9352i	−1.96655	+	1.31401i
$520$	4.49845	−	8.56081i	0.197270	−	0.375416i
$521$	6.76521	−	10.1249i	0.296389	−	0.443578i	−0.653149	−	0.757230i	$-0.726552\pi$
$521$	6.76521	−	10.1249i	0.296389	−	0.443578i	0.949538	+	0.313652i	$0.101552\pi$
$522$	12.9314	−	22.5201i	0.565994	−	0.985678i
$523$	40.4249	−	12.2627i	1.76766	−	0.536213i	0.772544	−	0.634962i	$-0.218984\pi$
$523$	40.4249	−	12.2627i	1.76766	−	0.536213i	0.995112	+	0.0987492i	$0.0314842\pi$
$524$	−8.55566	+	23.0604i	−0.373756	+	1.00740i
$525$	−3.58460	−	2.94180i	−0.156445	−	0.128391i
$526$	−27.6106	−	19.6873i	−1.20388	−	0.858408i
$527$	42.3104	+	17.5255i	1.84307	+	0.763424i
$528$	−7.70955	−	9.85386i	−0.335515	−	0.428834i
$529$	1.96756	−	0.814991i	0.0855462	−	0.0354344i
$530$	6.95600	+	1.60467i	0.302149	+	0.0697022i
$531$	1.88523	+	19.1411i	0.0818121	+	0.830652i
$532$	−20.5928	−	3.30042i	−0.892812	−	0.143091i
$533$	5.05835	−	9.46350i	0.219101	−	0.409910i
$534$	23.7842	+	30.8456i	1.02924	+	1.33482i
$535$	6.38318	−	1.26969i	0.275969	−	0.0548936i
$536$	0.205977	+	29.1811i	0.00889686	+	1.26043i
$537$	−7.12229	+	35.8062i	−0.307350	+	1.54515i
$538$	−10.1404	+	30.1051i	−0.437183	+	1.29792i
$539$	0.468422	−	4.75597i	0.0201764	−	0.204854i
$540$	3.12996	−	11.9050i	0.134692	−	0.512308i
$541$	7.93477	−	26.1574i	0.341143	−	1.12460i	−0.603739	−	0.797182i	$-0.706323\pi$
$541$	7.93477	−	26.1574i	0.341143	−	1.12460i	0.944881	−	0.327414i	$-0.106177\pi$
$542$	−1.04292	+	34.3276i	−0.0447973	+	1.47449i
$543$	22.6576	+	22.6576i	0.972329	+	0.972329i
$544$	−28.3024	+	20.7894i	−1.21345	+	0.891340i
$545$	−7.32637	+	7.32637i	−0.313827	+	0.313827i
$546$	−15.3664	−	16.3293i	−0.657620	−	0.698831i
$547$	3.82790	+	1.16118i	0.163669	+	0.0496485i	0.371056	−	0.928611i	$-0.378996\pi$
$547$	3.82790	+	1.16118i	0.163669	+	0.0496485i	−0.207387	+	0.978259i	$0.566496\pi$
$548$	2.58222	+	18.9253i	0.110307	+	0.808448i
$549$	26.3216	+	2.59245i	1.12338	+	0.110643i
$550$	−1.38761	+	0.688359i	−0.0591681	+	0.0293517i
$551$	−22.4346	−	4.46252i	−0.955746	−	0.190110i
$552$	39.6560	−	8.17948i	1.68787	−	0.348142i
$553$	5.13592	+	25.8200i	0.218402	+	1.09798i
$554$	34.4483	+	4.45277i	1.46357	+	0.189180i
$555$	−5.20053	−	2.77974i	−0.220750	−	0.117993i
$556$	9.98212	−	16.2223i	0.423336	−	0.687979i
$557$	−23.3635	+	2.30110i	−0.989944	+	0.0975009i	−0.580006	−	0.814612i	$-0.696950\pi$
$557$	−23.3635	+	2.30110i	−0.989944	+	0.0975009i	−0.409938	+	0.912113i	$0.634450\pi$
$558$	−28.5087	−	45.6060i	−1.20687	−	1.93066i
$559$	8.92075	+	21.5366i	0.377307	+	0.910901i
$560$	2.62485	−	5.94127i	0.110920	−	0.251065i
$561$	7.43075	−	17.9394i	0.313726	−	0.757403i
$562$	7.66588	−	1.28418i	0.323365	−	0.0541697i
$563$	25.6728	−	31.2824i	1.08198	−	1.31840i	0.137254	−	0.990536i	$-0.456172\pi$
$563$	25.6728	−	31.2824i	1.08198	−	1.31840i	0.944726	−	0.327861i	$-0.106328\pi$
$564$	35.6839	−	1.33629i	1.50257	−	0.0562682i
$565$	4.79086	+	15.7934i	0.201553	+	0.664431i
$566$	−24.7336	+	6.68977i	−1.03963	+	0.281192i
$567$	−2.84977	−	1.90416i	−0.119679	−	0.0799670i
$568$	−2.26005	−	21.3972i	−0.0948294	−	0.897807i
$569$	−6.19280	−	9.26818i	−0.259616	−	0.388542i	0.678648	−	0.734464i	$-0.262566\pi$
$569$	−6.19280	−	9.26818i	−0.259616	−	0.388542i	−0.938263	+	0.345922i	$0.887566\pi$
$570$	−25.8756	+	1.75713i	−1.08381	+	0.0735979i
$571$	−0.544826	+	0.447127i	−0.0228003	+	0.0187117i	−0.645724	−	0.763571i	$-0.723445\pi$
$571$	−0.544826	+	0.447127i	−0.0228003	+	0.0187117i	0.622924	+	0.782282i	$0.285945\pi$
$572$	−7.08097	+	2.44088i	−0.296070	+	0.102059i
$573$	16.7937	+	31.4188i	0.701566	+	1.31254i
$574$	2.95896	−	6.57164i	0.123504	−	0.274295i
$575$		−	5.01295i		−	0.209054i
$576$	41.2377	−	0.582190i	1.71824	−	0.0242579i
$577$			6.91222i			0.287760i	0.989595	+	0.143880i	$0.0459579\pi$
$577$			6.91222i			0.287760i	−0.989595	+	0.143880i	$0.954042\pi$
$578$	−27.7742	−	12.5056i	−1.15525	−	0.520166i
$579$	−28.4621	−	53.2489i	−1.18285	−	2.21295i
$580$	3.12072	−	6.40400i	0.129581	−	0.265912i
$581$	−10.9997	+	9.02723i	−0.456345	+	0.374513i
$582$	−4.51740	−	66.5235i	−0.187252	−	2.75749i
$583$	−3.07165	−	4.59704i	−0.127215	−	0.190390i
$584$	−10.5191	−	19.3501i	−0.435284	−	0.800713i
$585$	−14.6558	−	9.79270i	−0.605943	−	0.404878i
$586$	−6.42802	−	23.7659i	−0.265539	−	0.981759i
$587$	−4.28968	−	14.1412i	−0.177054	−	0.583668i	−0.999882	−	0.0153778i	$-0.995105\pi$
$587$	−4.28968	−	14.1412i	−0.177054	−	0.583668i	0.822828	−	0.568291i	$-0.192395\pi$
$588$	18.2685	+	16.9496i	0.753379	+	0.698990i
$589$	−30.0538	+	36.6207i	−1.23835	+	1.50893i
$590$	0.871732	+	5.20380i	0.0358887	+	0.214237i
$591$	29.4502	−	71.0991i	1.21142	−	2.92463i
$592$	1.79978	−	8.06114i	0.0739704	−	0.331311i
$593$	−4.50871	−	10.8850i	−0.185151	−	0.446993i	0.803864	−	0.594814i	$-0.202774\pi$
$593$	−4.50871	−	10.8850i	−0.185151	−	0.446993i	−0.989014	+	0.147821i	$0.952774\pi$
$594$	−8.08405	+	5.05340i	−0.331693	+	0.207344i
$595$	10.0320	−	0.988065i	0.411272	−	0.0405067i
$596$	4.65241	+	19.5369i	0.190570	+	0.800264i
$597$	23.5096	+	12.5661i	0.962184	+	0.514298i
$598$	3.10734	−	24.0395i	0.127069	−	0.983049i
$599$	3.60028	+	18.0998i	0.147103	+	0.739538i	0.981963	+	0.189075i	$0.0605489\pi$
$599$	3.60028	+	18.0998i	0.147103	+	0.739538i	−0.834859	+	0.550463i	$0.814451\pi$
$600$	1.51984	−	7.93296i	0.0620470	−	0.323862i
$601$	−32.2330	−	6.41154i	−1.31481	−	0.261532i	−0.512628	−	0.858611i	$-0.671328\pi$
$601$	−32.2330	−	6.41154i	−1.31481	−	0.261532i	−0.802183	+	0.597079i	$0.796328\pi$
$602$	6.95777	+	14.0257i	0.283578	+	0.571644i
$603$	52.9320	+	5.21335i	2.15556	+	0.212304i
$604$	−10.8517	+	14.2809i	−0.441551	+	0.581082i
$605$	−9.37834	−	2.84489i	−0.381284	−	0.115661i
$606$	12.2407	−	11.5188i	0.497244	−	0.467920i
$607$	25.7441	−	25.7441i	1.04492	−	1.04492i	0.0459766	−	0.998943i	$-0.485360\pi$
$607$	25.7441	−	25.7441i	1.04492	−	1.04492i	0.998943	−	0.0459766i	$-0.0146400\pi$
$608$	−12.0808	−	34.2595i	−0.489942	−	1.38941i
$609$	−11.6796	−	11.6796i	−0.473282	−	0.473282i
$610$	7.25229	+	0.220335i	0.293636	+	0.00892110i
$611$	6.20538	−	20.4564i	0.251043	−	0.827578i
$612$	32.2638	+	55.2801i	1.30418	+	2.23456i
$613$	−0.408814	+	4.15076i	−0.0165119	+	0.167648i	−0.999904	−	0.0138450i	$-0.995593\pi$
$613$	−0.408814	+	4.15076i	−0.0165119	+	0.167648i	0.983392	+	0.181493i	$0.0580929\pi$
$614$	−31.7903	−	10.7080i	−1.28295	−	0.432140i
$615$	1.74848	−	8.79020i	0.0705055	−	0.354455i
$616$	−4.63387	+	1.95784i	−0.186704	+	0.0788838i
$617$	−4.26224	+	0.847811i	−0.171591	+	0.0341316i	−0.280138	−	0.959960i	$-0.590380\pi$
$617$	−4.26224	+	0.847811i	−0.171591	+	0.0341316i	0.108547	+	0.994091i	$0.465380\pi$
$618$	−23.9093	+	18.4358i	−0.961774	+	0.741597i
$619$	7.99192	−	14.9518i	0.321222	−	0.600965i	−0.668542	−	0.743674i	$-0.733081\pi$
$619$	7.99192	−	14.9518i	0.321222	−	0.600965i	0.989765	+	0.142709i	$0.0455814\pi$
$620$	−8.65032	−	11.9523i	−0.347405	−	0.480017i
$621$	−3.02418	−	30.7050i	−0.121356	−	1.23215i
$622$	2.63761	−	11.4337i	0.105759	−	0.458449i
$623$	14.4688	−	5.99318i	0.579680	−	0.240112i
$624$	12.2057	−	37.1003i	0.488619	−	1.48520i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	−6.57248	+	9.21761i	−0.262689	+	0.368410i
$627$	15.5270	+	12.7427i	0.620089	+	0.508894i
$628$	−19.4145	−	42.3178i	−0.774723	−	1.68867i
$629$	12.2668	−	3.72109i	0.489109	−	0.148370i
$630$	−10.2664	−	5.89516i	−0.409024	−	0.234869i
$631$	−9.34612	+	13.9875i	−0.372063	+	0.556832i	−0.969502	−	0.245082i	$-0.921185\pi$
$631$	−9.34612	+	13.9875i	−0.372063	+	0.556832i	0.597439	+	0.801914i	$0.296185\pi$
$632$	−35.2405	+	29.3398i	−1.40179	+	1.16708i
$633$	−17.9936	+	12.0229i	−0.715182	+	0.477869i
$634$	8.87120	−	10.1638i	0.352320	−	0.403656i
$635$	−3.25728	−	3.96901i	−0.129261	−	0.157505i
$636$	28.7773	+	1.75021i	1.14109	+	0.0694002i
$637$	13.1569	−	7.03248i	0.521293	−	0.278637i
$638$	−5.15915	+	1.95564i	−0.204253	+	0.0774244i
$639$	−39.2165			−1.55138
$640$	11.2758	−	0.925779i	0.445714	−	0.0365946i
$641$	36.2106			1.43023			0.715116	−	0.699006i	$-0.246374\pi$
$641$	36.2106			1.43023			0.715116	+	0.699006i	$0.246374\pi$
$642$	24.5778	−	9.31649i	0.970007	−	0.367693i
$643$	−5.08993	+	2.72063i	−0.200727	+	0.107291i	−0.568698	−	0.822546i	$-0.692553\pi$
$643$	−5.08993	+	2.72063i	−0.200727	+	0.107291i	0.367971	+	0.929837i	$0.380053\pi$
$644$	0.988322	−	16.2502i	0.0389453	−	0.640348i
$645$	12.3516	+	15.0505i	0.486343	+	0.592611i
$646$	37.0734	−	42.4753i	1.45863	−	1.67117i
$647$	26.1325	−	17.4612i	1.02738	−	0.686471i	0.0768266	−	0.997044i	$-0.475521\pi$
$647$	26.1325	−	17.4612i	1.02738	−	0.686471i	0.950549	+	0.310574i	$0.100521\pi$
$648$	0.543208	−	5.94519i	0.0213392	−	0.233549i
$649$	2.27030	−	3.39774i	0.0891169	−	0.133373i
$650$	−4.19324	−	2.40783i	−0.164472	−	0.0944428i
$651$	−32.7360	+	9.93035i	−1.28302	+	0.389201i
$652$	−31.5182	+	14.4599i	−1.23435	+	0.566292i
$653$	−16.0324	−	13.1574i	−0.627396	−	0.514890i	0.266110	−	0.963943i	$-0.414262\pi$
$653$	−16.0324	−	13.1574i	−0.627396	−	0.514890i	−0.893505	+	0.449052i	$0.851762\pi$
$654$	−24.2933	+	34.0703i	−0.949943	+	1.33225i
$655$	11.3621	+	4.70632i	0.443952	+	0.183891i
$656$	12.5184	−	0.938896i	0.488761	−	0.0366577i
$657$	−37.0872	+	15.3620i	−1.44691	+	0.599330i
$658$	3.22736	−	13.9902i	0.125816	−	0.545393i
$659$	−2.28411	−	23.1909i	−0.0889761	−	0.903390i	−0.931260	−	0.364355i	$-0.881289\pi$
$659$	−2.28411	−	23.1909i	−0.0889761	−	0.903390i	0.842284	−	0.539034i	$-0.181211\pi$
$660$	−5.06773	+	3.66770i	−0.197261	+	0.142765i
$661$	24.1993	−	45.2737i	0.941243	−	1.76094i	0.420063	−	0.907495i	$-0.362008\pi$
$661$	24.1993	−	45.2737i	0.941243	−	1.76094i	0.521180	−	0.853447i	$-0.325492\pi$
$662$	−1.70433	+	1.31416i	−0.0662409	+	0.0510765i
$663$	59.4503	−	11.8254i	2.30886	−	0.459260i
$664$	−22.9655	−	9.32327i	−0.891235	−	0.361813i
$665$	−2.03436	+	10.2274i	−0.0788893	+	0.396603i
$666$	−14.2668	−	4.80552i	−0.552827	−	0.186210i
$667$	1.75018	−	17.7699i	0.0677674	−	0.688054i
$668$	−11.4746	+	6.69707i	−0.443966	+	0.259117i
$669$	−2.04107	+	6.72850i	−0.0789123	+	0.260139i
$670$	14.5842	+	0.443088i	0.563435	+	0.0171180i
$671$	−3.97351	−	3.97351i	−0.153395	−	0.153395i
$672$	6.49078	−	25.4162i	0.250387	−	0.980452i
$673$	−15.9132	+	15.9132i	−0.613410	+	0.613410i	−0.943833	−	0.330423i	$-0.892809\pi$
$673$	−15.9132	+	15.9132i	−0.613410	+	0.613410i	0.330423	+	0.943833i	$0.392809\pi$
$674$	19.5247	−	18.3733i	0.752064	−	0.707714i
$675$	−5.88974	−	1.78663i	−0.226696	−	0.0687676i
$676$	2.08538	+	1.58463i	0.0802068	+	0.0609473i
$677$	−33.7975	−	3.32877i	−1.29895	−	0.127935i	−0.575206	−	0.818009i	$-0.695078\pi$
$677$	−33.7975	−	3.32877i	−1.29895	−	0.127935i	−0.723739	+	0.690074i	$0.757578\pi$
$678$	29.6206	+	59.7101i	1.13757	+	2.29315i
$679$	−26.2937	−	5.23015i	−1.00906	−	0.200715i
$680$	9.85787	+	14.5303i	0.378032	+	0.557210i
$681$	14.6345	+	73.5724i	0.560794	+	2.81930i
$682$	−1.46485	+	11.3326i	−0.0560921	+	0.433949i
$683$	18.2885	+	9.77542i	0.699791	+	0.374046i	0.782605	−	0.622519i	$-0.213891\pi$
$683$	18.2885	+	9.77542i	0.699791	+	0.374046i	−0.0828138	+	0.996565i	$0.526391\pi$
$684$	−64.4104	+	15.3383i	−2.46279	+	0.586476i
$685$	9.50433	−	0.936094i	0.363142	−	0.0357663i
$686$	22.1273	−	13.8319i	0.844822	−	0.528105i
$687$	−6.99496	−	16.8873i	−0.266875	−	0.644292i
$688$	−15.6756	+	22.3159i	−0.597627	+	0.850787i
$689$	6.60478	−	15.9454i	0.251622	−	0.607470i
$690$	−3.34487	−	19.9672i	−0.127337	−	0.760138i
$691$	−11.9584	+	14.5714i	−0.454920	+	0.554322i	−0.949074	−	0.315052i	$-0.897978\pi$
$691$	−11.9584	+	14.5714i	−0.454920	+	0.554322i	0.494154	+	0.869374i	$0.335478\pi$
$692$	−25.6661	+	27.6632i	−0.975679	+	1.05160i
$693$	2.66157	+	8.77402i	0.101105	+	0.333297i
$694$	0.208436	+	0.770636i	0.00791211	+	0.0292529i
$695$	−7.91869	−	5.29110i	−0.300373	−	0.200703i
$696$	8.15718	−	27.5902i	0.309197	−	1.04580i
$697$	10.8241	+	16.1994i	0.409992	+	0.613597i
$698$	−2.32890	−	34.2955i	−0.0881501	−	1.29811i
$699$	31.3207	−	25.7042i	1.18466	−	0.972222i
$700$	−2.91944	−	1.42267i	−0.110345	−	0.0537719i
$701$	8.41779	+	15.7486i	0.317935	+	0.594815i	0.989229	−	0.146376i	$-0.0467610\pi$
$701$	8.41779	+	15.7486i	0.317935	+	0.594815i	−0.671294	+	0.741192i	$0.734261\pi$
$702$	−27.1367	−	12.2186i	−1.02421	−	0.461161i
$703$			13.2604i			0.500124i
$704$	−6.85115	−	5.46258i	−0.258212	−	0.205879i
$705$		−	17.8545i		−	0.672439i
$706$	7.11545	−	15.8029i	0.267794	−	0.594752i
$707$	−3.18576	−	5.96014i	−0.119813	−	0.224154i
$708$	6.94443	+	20.1457i	0.260988	+	0.757121i
$709$	13.5440	−	11.1153i	0.508655	−	0.417442i	−0.344747	−	0.938696i	$-0.612035\pi$
$709$	13.5440	−	11.1153i	0.508655	−	0.417442i	0.853402	+	0.521253i	$0.174535\pi$
$710$	−10.7334	+	0.728870i	−0.402817	+	0.0273540i
$711$	46.4336	+	69.4928i	1.74140	+	2.60618i
$712$	21.2084	+	17.1562i	0.794819	+	0.642956i
$713$	−30.7486	−	20.5455i	−1.15154	−	0.769437i
$714$	39.2993	−	10.6294i	1.47074	−	0.397795i
$715$	1.08710	+	3.58368i	0.0406551	+	0.134022i
$716$	0.956799	+	25.5500i	0.0357573	+	0.954850i
$717$	−5.35289	+	6.52252i	−0.199907	+	0.243588i
$718$	22.8885	−	3.83426i	0.854193	−	0.143093i
$719$	4.43469	−	10.7063i	0.165386	−	0.399277i	−0.819359	−	0.573281i	$-0.805670\pi$
$719$	4.43469	−	10.7063i	0.165386	−	0.399277i	0.984745	+	0.174003i	$0.0556704\pi$
$720$	0.480705	−	20.6153i	0.0179148	−	0.768287i
$721$	4.64548	+	11.2152i	0.173007	+	0.417675i
$722$	16.6711	+	26.6693i	0.620436	+	0.992527i
$723$	−72.1497	+	7.10612i	−2.68327	+	0.264280i
$724$	19.1124	+	11.7605i	0.710307	+	0.437076i
$725$	−3.14136	−	1.67909i	−0.116667	−	0.0623600i
$726$	−39.2533	−	5.07387i	−1.45683	−	0.188309i
$727$	−8.82744	−	44.3785i	−0.327392	−	1.64591i	−0.697255	−	0.716823i	$-0.745596\pi$
$727$	−8.82744	−	44.3785i	−0.327392	−	1.64591i	0.369864	−	0.929086i	$-0.379404\pi$
$728$	−13.1183	−	8.63204i	−0.486195	−	0.319925i
$729$	41.0439	+	8.16414i	1.52015	+	0.302376i
$730$	−9.86509	+	4.89381i	−0.365123	+	0.181128i
$731$	−42.1208	−	4.14853i	−1.55789	−	0.153439i
$732$	29.0337	−	3.96144i	1.07312	−	0.146419i
$733$	−18.6812	−	5.66689i	−0.690006	−	0.209311i	−0.0742406	−	0.997240i	$-0.523653\pi$
$733$	−18.6812	−	5.66689i	−0.690006	−	0.209311i	−0.615766	+	0.787929i	$0.711153\pi$
$734$	24.4938	+	26.0287i	0.904082	+	0.960738i
$735$	8.81069	−	8.81069i	0.324987	−	0.324987i
$736$	25.6904	−	12.0064i	0.946960	−	0.442562i
$737$	−7.99062	−	7.99062i	−0.294338	−	0.294338i
$738$	0.694829	−	22.8702i	0.0255770	−	0.841863i
$739$	−6.55748	+	21.6171i	−0.241221	+	0.795198i	0.749820	+	0.661641i	$0.230140\pi$
$739$	−6.55748	+	21.6171i	−0.241221	+	0.795198i	−0.991041	+	0.133557i	$0.957360\pi$
$740$	−3.99407	−	1.05009i	−0.146825	−	0.0386021i
$741$	−6.14598	+	62.4012i	−0.225778	+	2.29237i
$742$	3.70027	−	10.9855i	0.135841	−	0.403290i
$743$	−3.73530	+	18.7786i	−0.137035	+	0.688921i	0.849789	+	0.527123i	$0.176729\pi$
$743$	−3.73530	+	18.7786i	−0.137035	+	0.688921i	−0.986824	+	0.161798i	$0.948271\pi$
$744$	−42.4304	−	41.8356i	−1.55557	−	1.53377i
$745$	9.84867	−	1.95902i	0.360827	−	0.0717730i
$746$	20.3559	+	26.3994i	0.745281	+	0.966552i
$747$	−21.2958	+	39.8416i	−0.779172	+	1.45773i
$748$	2.15204	−	13.4276i	0.0786865	−	0.490961i
$749$	−1.03586	−	10.5173i	−0.0378496	−	0.384293i
$750$	−3.93527	−	0.907818i	−0.143696	−	0.0331488i
$751$	−15.2098	+	6.30010i	−0.555013	+	0.229894i	−0.642518	−	0.766270i	$-0.722110\pi$
$751$	−15.2098	+	6.30010i	−0.555013	+	0.229894i	0.0875057	+	0.996164i	$0.472110\pi$
$752$	24.0945	−	6.69975i	0.878634	−	0.244315i
$753$	−64.8784	−	26.8735i	−2.36430	−	0.979325i
$754$	−14.0235	−	9.99928i	−0.510707	−	0.364152i
$755$	6.93240	+	5.68928i	0.252296	+	0.207054i
$756$	−18.7402	−	6.95282i	−0.681575	−	0.252872i
$757$	−30.5405	+	9.26437i	−1.11001	+	0.336719i	−0.791482	−	0.611193i	$-0.790690\pi$
$757$	−30.5405	+	9.26437i	−1.11001	+	0.336719i	−0.318533	+	0.947912i	$0.603190\pi$
$758$	7.83209	−	13.6396i	0.284474	−	0.495412i
$759$	−8.71122	+	13.0373i	−0.316197	+	0.473223i
$760$	−17.3438	+	5.39516i	−0.629125	+	0.195703i
$761$	3.14059	−	2.09848i	0.113846	−	0.0760697i	−0.497344	−	0.867554i	$-0.665691\pi$
$761$	3.14059	−	2.09848i	0.113846	−	0.0760697i	0.611190	+	0.791484i	$0.290691\pi$
$762$	−15.6225	−	13.6356i	−0.565942	−	0.493967i
$763$	10.6733	+	13.0055i	0.386400	+	0.470830i
$764$	16.5388	+	18.6808i	0.598353	+	0.675848i
$765$	28.2244	−	15.0862i	1.02045	−	0.545444i
$766$	15.3203	+	40.4163i	0.553544	+	1.46030i
$767$	12.7565			0.460609
$768$	44.2950	−	11.2112i	1.59836	−	0.404549i
$769$	33.0855			1.19309			0.596547	−	0.802578i	$-0.296539\pi$
$769$	33.0855			1.19309			0.596547	+	0.802578i	$0.296539\pi$
$770$	0.891532	+	2.35194i	0.0321286	+	0.0847582i
$771$	20.5849	−	11.0029i	0.741349	−	0.396259i
$772$	−28.0301	−	31.6605i	−1.00883	−	1.13949i
$773$	−16.9379	−	20.6389i	−0.609215	−	0.742330i	0.373465	−	0.927644i	$-0.378170\pi$
$773$	−16.9379	−	20.6389i	−0.609215	−	0.742330i	−0.982679	+	0.185314i	$0.940670\pi$
$774$	37.4480	+	32.6855i	1.34604	+	1.17485i
$775$	−6.13383	+	4.09849i	−0.220334	+	0.147222i
$776$	−13.8704	−	44.5892i	−0.497919	−	1.60066i
$777$	−5.31978	+	7.96162i	−0.190846	+	0.285622i
$778$	−2.50384	+	4.36043i	−0.0897669	+	0.156329i
$779$	−19.2862	+	5.85042i	−0.691001	+	0.209613i
$780$	−18.3088	−	6.79275i	−0.655559	−	0.243219i
$781$	6.44073	+	5.28577i	0.230467	+	0.189140i
$782$	35.8339	+	25.5508i	1.28142	+	0.913695i
$783$	−20.2542	−	8.38957i	−0.723826	−	0.299819i
$784$	15.1961	+	8.58380i	0.542717	+	0.306564i
$785$	−21.5074	+	8.90864i	−0.767631	+	0.317963i
$786$	48.3967	+	11.1645i	1.72625	+	0.398226i
$787$	−0.827535	−	8.40211i	−0.0294984	−	0.299503i	−0.998602	−	0.0528503i	$-0.983169\pi$
$787$	−0.827535	−	8.40211i	−0.0294984	−	0.299503i	0.969104	−	0.246652i	$-0.0793306\pi$
$788$	8.52917	−	53.2174i	0.303839	−	1.89579i
$789$	−32.2795	+	60.3906i	−1.14918	+	2.14996i
$790$	14.0003	+	18.1569i	0.498107	+	0.645992i
$791$	26.2846	−	5.22832i	0.934571	−	0.185898i
$792$	−11.2129	+	11.3724i	−0.398434	+	0.404099i
$793$	3.42225	−	17.2048i	0.121528	−	0.610960i
$794$	−8.45070	+	25.0887i	−0.299904	+	0.890366i
$795$	1.41294	−	14.3458i	0.0501118	−	0.508794i
$796$	18.0557	+	4.74705i	0.639966	+	0.168255i
$797$	10.2074	−	33.6492i	0.361564	−	1.19192i	−0.567929	−	0.823078i	$-0.692255\pi$
$797$	10.2074	−	33.6492i	0.361564	−	1.19192i	0.929493	−	0.368840i	$-0.120245\pi$
$798$	−1.27889	+	42.0945i	−0.0452723	+	1.49013i
$799$	27.4448	+	27.4448i	0.970928	+	0.970928i
$800$	−0.251585	−	5.65126i	−0.00889488	−	0.199802i
$801$	35.1571	−	35.1571i	1.24222	−	1.24222i
$802$	−8.85071	−	9.40536i	−0.312529	−	0.332115i
$803$	8.16158	+	2.47579i	0.288016	+	0.0873687i
$804$	58.3861	−	7.96636i	2.05912	−	0.280952i
$805$	−8.10092	−	0.797871i	−0.285520	−	0.0281213i
$806$	−31.9552	+	15.8521i	−1.12557	+	0.558367i
$807$	62.9149	+	12.5146i	2.21471	+	0.440533i
$808$	6.47069	−	9.83363i	0.227638	−	0.345946i
$809$	−7.24881	−	36.4422i	−0.254855	−	1.28124i	−0.870088	−	0.492896i	$-0.835938\pi$
$809$	−7.24881	−	36.4422i	−0.254855	−	1.28124i	0.615233	−	0.788345i	$-0.289062\pi$
$810$	−2.96035	−	0.382654i	−0.104016	−	0.0134451i
$811$	37.5024	+	20.0454i	1.31689	+	0.703891i	0.972050	−	0.234772i	$-0.0754343\pi$
$811$	37.5024	+	20.0454i	1.31689	+	0.703891i	0.344837	+	0.938663i	$0.387934\pi$
$812$	−9.85215	−	6.06236i	−0.345743	−	0.212747i
$813$	69.0160	−	6.79749i	2.42050	−	0.238398i
$814$	1.69540	+	2.71217i	0.0594237	+	0.0950616i
$815$	6.63513	+	16.0186i	0.232418	+	0.561108i
$816$	48.9604	+	51.2982i	1.71396	+	1.79580i
$817$	16.7549	−	40.4499i	0.586180	−	1.41516i
$818$	−24.5762	+	4.11697i	−0.859287	+	0.143946i
$819$	−18.1576	+	22.1251i	−0.634479	+	0.773115i
$820$	−0.234889	−	6.27238i	−0.00820266	−	0.219041i
$821$	−0.349493	−	1.15212i	−0.0121974	−	0.0402094i	0.950630	−	0.310325i	$-0.100438\pi$
$821$	−0.349493	−	1.15212i	−0.0121974	−	0.0402094i	−0.962828	+	0.270116i	$0.912938\pi$
$822$	37.2323	−	10.0703i	1.29862	−	0.351242i
$823$	−22.3249	−	14.9170i	−0.778197	−	0.519975i	0.101885	−	0.994796i	$-0.467513\pi$
$823$	−22.3249	−	14.9170i	−0.778197	−	0.519975i	−0.880082	+	0.474822i	$0.842513\pi$
$824$	−13.2983	+	16.4392i	−0.463267	+	0.572688i
$825$	1.73774	+	2.60072i	0.0605005	+	0.0905453i
$826$	8.54807	−	0.580472i	0.297425	−	0.0201972i
$827$	−26.9156	+	22.0890i	−0.935946	+	0.768111i	−0.972905	−	0.231206i	$-0.925733\pi$
$827$	−26.9156	+	22.0890i	−0.935946	+	0.768111i	0.0369590	+	0.999317i	$0.488233\pi$
$828$	−16.8440	−	48.8641i	−0.585369	−	1.69815i
$829$	11.5690	+	21.6440i	0.401807	+	0.751727i	0.998720	−	0.0505784i	$-0.0161065\pi$
$829$	11.5690	+	21.6440i	0.401807	+	0.751727i	−0.596914	+	0.802306i	$0.703606\pi$
$830$	−5.08807	+	11.3003i	−0.176610	+	0.392238i
$831$		−	70.1405i		−	2.43315i
$832$	2.29653	−	27.2564i	0.0796178	−	0.944947i
$833$			27.0865i			0.938492i
$834$	−35.0716	−	15.7914i	−1.21443	−	0.546810i
$835$	3.13149	+	5.85860i	0.108370	+	0.202745i
$836$	12.6458	+	6.16242i	0.437365	+	0.213132i
$837$	−35.0980	+	28.8042i	−1.21316	+	0.995618i
$838$	2.89241	+	42.5938i	0.0999165	+	1.47138i
$839$	21.2644	+	31.8245i	0.734130	+	1.09870i	0.991208	+	0.132312i	$0.0422401\pi$
$839$	21.2644	+	31.8245i	0.734130	+	1.09870i	−0.257078	+	0.966391i	$0.582760\pi$
$840$	−12.5778	−	3.71868i	−0.433974	−	0.128307i
$841$	13.5633	+	9.06272i	0.467701	+	0.312508i
$842$	3.95687	+	14.6295i	0.136363	+	0.504165i
$843$	−4.55616	−	15.0196i	−0.156922	−	0.517304i
$844$	−10.3083	+	11.1104i	−0.354828	+	0.382437i
$845$	0.830779	−	1.01231i	0.0285797	−	0.0348244i
$846$	−7.53087	−	44.9554i	−0.258917	−	1.54560i
$847$	−6.09001	+	14.7026i	−0.209255	+	0.505187i
$848$	19.8897	−	3.47641i	0.683017	−	0.119380i
$849$	19.7999	+	47.8011i	0.679529	+	1.64053i
$850$	7.44450	−	4.65361i	0.255344	−	0.159618i
$851$	−10.3014	+	1.01460i	−0.353128	+	0.0347801i
$852$	−42.2660	+	10.0650i	−1.44801	+	0.344821i
$853$	−3.08544	−	1.64920i	−0.105643	−	0.0564676i	0.417729	−	0.908572i	$-0.362826\pi$
$853$	−3.08544	−	1.64920i	−0.105643	−	0.0564676i	−0.523372	+	0.852104i	$0.675326\pi$
$854$	1.51035	−	11.6846i	0.0516831	−	0.399839i
$855$	6.45862	+	32.4697i	0.220880	+	1.11044i
$856$	15.2332	−	10.3348i	0.520659	−	0.353235i
$857$	0.793417	+	0.157821i	0.0271026	+	0.00539105i	0.208623	−	0.977996i	$-0.433102\pi$
$857$	0.793417	+	0.157821i	0.0271026	+	0.00539105i	−0.181520	+	0.983387i	$0.558102\pi$
$858$	6.72123	+	13.5488i	0.229459	+	0.462550i
$859$	−5.87499	−	0.578636i	−0.200452	−	0.0197428i	−0.00270732	−	0.999996i	$-0.500862\pi$
$859$	−5.87499	−	0.578636i	−0.200452	−	0.0197428i	−0.197745	+	0.980254i	$0.563362\pi$
$860$	10.8568	+	8.24987i	0.370215	+	0.281318i
$861$	−13.9267	−	4.22461i	−0.474619	−	0.143974i
$862$	4.14637	−	3.90186i	0.141226	−	0.132898i
$863$	12.8573	−	12.8573i	0.437667	−	0.437667i	−0.453559	−	0.891226i	$-0.649846\pi$
$863$	12.8573	−	12.8573i	0.437667	−	0.437667i	0.891226	+	0.453559i	$0.149846\pi$
$864$	−4.95024	−	34.4629i	−0.168411	−	1.17245i
$865$	13.3417	+	13.3417i	0.453630	+	0.453630i
$866$	−25.9766	−	0.789207i	−0.882722	−	0.0268184i
$867$	−17.8548	+	58.8592i	−0.606379	+	1.99896i
$868$	−20.6917	+	12.0766i	−0.702323	+	0.409905i
$869$	1.74051	−	17.6717i	0.0590427	−	0.599470i
$870$	−13.6328	−	4.59197i	−0.462195	−	0.155682i
$871$	6.88205	−	34.5984i	0.233189	−	1.17232i
$872$	−11.0233	+	27.1532i	−0.373297	+	0.919524i
$873$	−83.4763	+	16.6045i	−2.82524	+	0.561976i
$874$	−36.0533	+	27.7997i	−1.21952	+	0.940338i
$875$	−0.765462	+	1.43208i	−0.0258773	+	0.0484131i
$876$	−36.0285	+	26.0751i	−1.21729	+	0.880996i
$877$	1.29893	+	13.1883i	0.0438618	+	0.445336i	0.991885	+	0.127136i	$0.0405785\pi$
$877$	1.29893	+	13.1883i	0.0438618	+	0.445336i	−0.948023	+	0.318200i	$0.896922\pi$
$878$	−5.93822	+	25.7414i	−0.200405	+	0.868729i
$879$	−45.9308	+	19.0251i	−1.54921	+	0.641702i
$880$	−2.85757	+	3.32097i	−0.0963286	+	0.111950i
$881$	12.9953	+	5.38281i	0.437821	+	0.181352i	0.590696	−	0.806894i	$-0.298853\pi$
$881$	12.9953	+	5.38281i	0.437821	+	0.181352i	−0.152875	+	0.988246i	$0.548853\pi$
$882$	18.4680	−	25.9005i	0.621850	−	0.872117i
$883$	−23.9403	−	19.6473i	−0.805656	−	0.661184i	0.138618	−	0.990346i	$-0.455734\pi$
$883$	−23.9403	−	19.6473i	−0.805656	−	0.661184i	−0.944274	+	0.329162i	$0.893234\pi$
$884$	38.5845	−	17.7017i	1.29774	−	0.595374i
$885$	10.1957	−	3.09284i	0.342725	−	0.103965i
$886$	7.49646	+	4.30460i	0.251849	+	0.144616i
$887$	6.30891	−	9.44195i	0.211832	−	0.317030i	−0.710304	−	0.703895i	$-0.751442\pi$
$887$	6.30891	−	9.44195i	0.211832	−	0.317030i	0.922136	+	0.386866i	$0.126442\pi$
$888$	−16.6095	−	1.51760i	−0.557380	−	0.0509274i
$889$	−6.93235	+	4.63205i	−0.232504	+	0.155354i
$890$	8.96893	−	10.2758i	0.300639	−	0.344445i
$891$	1.46661	+	1.78706i	0.0491331	+	0.0598689i
$892$	−0.298939	+	4.91523i	−0.0100092	+	0.164574i
$893$	−35.4091	+	18.9266i	−1.18492	+	0.633353i
$894$	37.9213	−	14.3745i	1.26828	−	0.480756i
$895$	12.7840			0.427321
$896$	0.298617	−	18.3690i	0.00997608	−	0.613664i
$897$	−48.9471			−1.63430
$898$	29.9150	−	11.3396i	0.998275	−	0.378408i
$899$	−23.1741	+	12.3868i	−0.772901	+	0.413124i
$900$	−10.2914	−	0.625915i	−0.343048	−	0.0208638i
$901$	19.8796	+	24.2234i	0.662287	+	0.806999i
$902$	−3.19665	+	3.66243i	−0.106437	+	0.121946i
$903$	26.2874	−	17.5647i	0.874790	−	0.584516i
$904$	29.8677	+	35.8745i	0.993385	+	1.19317i
$905$	6.23375	−	9.32946i	0.207217	−	0.310122i
$906$	31.4087	+	18.0354i	1.04349	+	0.599188i
$907$	−0.498493	+	0.151216i	−0.0165522	+	0.00502105i	−0.298550	−	0.954394i	$-0.596503\pi$
$907$	−0.498493	+	0.151216i	−0.0165522	+	0.00502105i	0.281998	+	0.959415i	$0.409003\pi$
$908$	21.9067	+	47.7502i	0.727000	+	1.58464i
$909$	−16.5853	−	13.6112i	−0.550099	−	0.451455i
$910$	−4.55845	+	6.39303i	−0.151111	+	0.211927i
$911$	4.20639	+	1.74234i	0.139364	+	0.0577264i	0.451275	−	0.892385i	$-0.350969\pi$
$911$	4.20639	+	1.74234i	0.139364	+	0.0577264i	−0.311911	+	0.950111i	$0.600969\pi$
$912$	−65.4825	+	33.0621i	−2.16834	+	1.09480i
$913$	8.86753	−	3.67305i	0.293472	−	0.121560i
$914$	12.1144	−	52.5143i	0.400709	−	1.73702i
$915$	−1.43609	−	14.5808i	−0.0474755	−	0.482027i
$916$	−7.50542	−	10.3704i	−0.247986	−	0.342647i
$917$	9.41380	−	17.6120i	0.310871	−	0.581599i
$918$	42.7911	−	32.9950i	1.41232	−	1.08900i
$919$	53.3713	−	10.6162i	1.76056	−	0.350196i	0.794250	−	0.607591i	$-0.207864\pi$
$919$	53.3713	−	10.6162i	1.76056	−	0.350196i	0.966306	+	0.257395i	$0.0828641\pi$
$920$	−5.51831	−	13.0608i	−0.181933	−	0.430603i
$921$	−13.2151	+	66.4367i	−0.435452	+	2.18916i
$922$	−18.2455	−	6.14569i	−0.600885	−	0.202397i
$923$	−2.54940	+	25.8845i	−0.0839146	+	0.851999i
$924$	5.12041	+	8.77320i	0.168449	+	0.288617i
$925$	−0.599410	+	1.97599i	−0.0197085	+	0.0649701i
$926$	11.4811	+	0.348813i	0.377293	+	0.0114627i
$927$	27.2513	+	27.2513i	0.895049	+	0.895049i
$928$	1.08122	−	20.1204i	0.0354927	−	0.660486i
$929$	28.9981	−	28.9981i	0.951397	−	0.951397i	−0.0474757	−	0.998872i	$-0.515118\pi$
$929$	28.9981	−	28.9981i	0.951397	−	0.951397i	0.998872	+	0.0474757i	$0.0151177\pi$
$930$	−21.6971	+	20.4176i	−0.711475	+	0.669518i
$931$	−26.8131	−	8.13367i	−0.878765	−	0.266570i
$932$	17.1683	−	22.5936i	0.562368	−	0.740077i
$933$	−23.5805	−	2.32247i	−0.771989	−	0.0760343i
$934$	24.4775	+	49.3425i	0.800929	+	1.61454i
$935$	−6.66882	−	1.32651i	−0.218094	−	0.0433815i
$936$	−48.9644	−	9.38084i	−1.60045	−	0.306622i
$937$	8.20133	+	41.2309i	0.267926	+	1.34695i	0.846962	+	0.531653i	$0.178429\pi$
$937$	8.20133	+	41.2309i	0.267926	+	1.34695i	−0.579037	+	0.815302i	$0.696571\pi$
$938$	3.03727	−	23.4975i	0.0991704	−	0.767219i
$939$	20.1610	+	10.7763i	0.657930	+	0.351671i
$940$	−2.89670	−	12.1641i	−0.0944799	−	0.396751i
$941$	−26.6180	+	2.62165i	−0.867724	+	0.0854633i	−0.522074	−	0.852900i	$-0.674841\pi$
$941$	−26.6180	+	2.62165i	−0.867724	+	0.0854633i	−0.345650	+	0.938364i	$0.612341\pi$
$942$	−79.7221	+	49.8349i	−2.59749	+	1.62371i
$943$	−6.02060	−	14.5350i	−0.196058	−	0.473325i
$944$	7.99962	+	12.5985i	0.260365	+	0.410045i
$945$	−3.82462	+	9.23345i	−0.124415	+	0.300364i
$946$	−1.74479	−	10.4155i	−0.0567280	−	0.338637i
$947$	7.42783	−	9.05083i	0.241372	−	0.294113i	−0.638208	−	0.769864i	$-0.720324\pi$
$947$	7.42783	−	9.05083i	0.241372	−	0.294113i	0.879580	+	0.475752i	$0.157824\pi$
$948$	67.8798	+	62.9794i	2.20463	+	2.04547i
$949$	7.72859	+	25.4777i	0.250881	+	0.827043i
$950$	2.37117	+	8.76677i	0.0769309	+	0.284432i
$951$	−22.6509	−	15.1349i	−0.734507	−	0.490782i
$952$	25.0499	−	13.6176i	0.811872	−	0.441350i
$953$	−16.9015	−	25.2949i	−0.547494	−	0.819383i	0.449782	−	0.893138i	$-0.351502\pi$
$953$	−16.9015	−	25.2949i	−0.547494	−	0.819383i	−0.997276	+	0.0737554i	$0.976502\pi$
$954$	−2.49334	−	36.7170i	−0.0807247	−	1.18876i
$955$	9.64333	−	7.91407i	0.312051	−	0.256093i
$956$	−2.58868	+	5.31220i	−0.0837240	+	0.171809i
$957$	5.25196	+	9.82573i	0.169772	+	0.317621i
$958$	−27.0685	−	12.1879i	−0.874545	−	0.393774i
$959$		−	15.5080i		−	0.500778i
$960$	−4.77287	−	22.3418i	−0.154044	−	0.721077i
$961$			23.4215i			0.755533i
$962$	−4.09930	+	9.10427i	−0.132167	+	0.293533i
$963$	−15.8160	−	29.5897i	−0.509665	−	0.953515i
$964$	−48.0022	+	16.5469i	−1.54605	+	0.532939i
$965$	−16.3436	+	13.4129i	−0.526120	+	0.431775i
$966$	−32.7993	+	2.22729i	−1.05530	+	0.0716620i
$967$	−3.31090	−	4.95511i	−0.106471	−	0.159345i	0.774408	−	0.632687i	$-0.218048\pi$
$967$	−3.31090	−	4.95511i	−0.106471	−	0.159345i	−0.880879	+	0.473341i	$0.843048\pi$
$968$	−27.5662	+	2.91164i	−0.886012	+	0.0935836i
$969$	−94.6600	−	63.2498i	−3.04092	−	2.03188i
$970$	−22.5385	+	6.09604i	−0.723667	+	0.195732i
$971$	−1.22205	−	4.02855i	−0.0392173	−	0.129282i	0.935146	−	0.354263i	$-0.115268\pi$
$971$	−1.22205	−	4.02855i	−0.0392173	−	0.129282i	−0.974363	+	0.224981i	$0.927768\pi$
$972$	24.8560	−	0.930808i	0.797256	−	0.0298557i
$973$	−9.81076	+	11.9544i	−0.314519	+	0.383242i
$974$	−1.67518	+	0.280624i	−0.0536762	+	0.00899176i
$975$	−3.73657	+	9.02088i	−0.119666	+	0.288899i
$976$	19.1378	−	7.40932i	0.612586	−	0.237167i
$977$	9.32506	+	22.5127i	0.298335	+	0.720245i	0.999970	+	0.00770844i	$0.00245370\pi$
$977$	9.32506	+	22.5127i	0.298335	+	0.720245i	−0.701635	+	0.712536i	$0.747546\pi$
$978$	37.1169	+	59.3768i	1.18687	+	1.89866i
$979$	−10.5127	+	1.03541i	−0.335986	+	0.0330917i
$980$	4.57323	−	7.43211i	0.146086	−	0.237410i
$981$	47.1066	+	25.1790i	1.50400	+	0.803903i
$982$	−40.3953	−	5.22148i	−1.28907	−	0.166624i
$983$	0.196819	+	0.989475i	0.00627754	+	0.0315593i	0.983797	−	0.179285i	$-0.0573786\pi$
$983$	0.196819	+	0.989475i	0.00627754	+	0.0315593i	−0.977520	+	0.210845i	$0.932379\pi$
$984$	−5.12081	−	24.8269i	−0.163246	−	0.791453i
$985$	−26.4305	−	5.25734i	−0.842144	−	0.167513i
$986$	28.0140	−	13.8970i	0.892148	−	0.442571i
$987$	−28.8528	−	2.84175i	−0.918395	−	0.0904540i
$988$	5.93671	+	43.5107i	0.188872	+	1.38426i
$989$	32.7058	+	9.92119i	1.03998	+	0.315476i
$990$	5.47239	+	5.81533i	0.173924	+	0.184823i
$991$	−14.6745	+	14.6745i	−0.466149	+	0.466149i	−0.900665	−	0.434515i	$-0.856920\pi$
$991$	−14.6745	+	14.6745i	−0.466149	+	0.466149i	0.434515	+	0.900665i	$0.356920\pi$
$992$	−35.6950	−	21.6185i	−1.13332	−	0.686387i
$993$	3.07300	+	3.07300i	0.0975187	+	0.0975187i
$994$	−0.530495	+	17.4612i	−0.0168263	+	0.553834i
$995$	2.70970	−	8.93269i	0.0859033	−	0.283185i
$996$	−12.7263	+	48.4053i	−0.403250	+	1.53378i
$997$	−3.66435	+	37.2047i	−0.116051	+	1.17829i	0.744037	+	0.668139i	$0.232909\pi$
$997$	−3.66435	+	37.2047i	−0.116051	+	1.17829i	−0.860088	+	0.510147i	$0.829591\pi$
$998$	−2.86699	+	8.51161i	−0.0907529	+	0.269430i
$999$	−2.47940	+	12.4648i	−0.0784448	+	0.394369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.23	✓	1024
128.109	even	32	inner	640.2.bm.a.621.23	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.23	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.23	yes	1024	128.109	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.501270 - 1.32240i) q^{2} +(-2.51853 + 1.34618i) q^{3} +(-1.49746 + 1.32575i) q^{4} +(0.634393 + 0.773010i) q^{5} +(3.04265 + 2.65570i) q^{6} +(1.35015 - 0.902145i) q^{7} +(2.50380 + 1.31567i) q^{8} +(2.86409 - 4.28642i) q^{9} +(0.704223 - 1.22641i) q^{10} +(-1.04813 + 0.317945i) q^{11} +(1.98669 - 5.35481i) q^{12} +(-2.64302 - 2.16907i) q^{13} +(-1.86978 - 1.33322i) q^{14} +(-2.63836 - 1.09284i) q^{15} +(0.484759 - 3.97052i) q^{16} +(5.73537 - 2.37567i) q^{17} +(-7.10402 - 1.63881i) q^{18} +(0.629445 + 6.39086i) q^{19} +(-1.97480 - 0.316502i) q^{20} +(-2.18596 + 4.08964i) q^{21} +(0.945843 + 1.22666i) q^{22} +(-4.91663 + 0.977978i) q^{23} +(-8.07704 + 0.0570126i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-1.54350 + 4.58241i) q^{26} +(-0.603272 + 6.12513i) q^{27} +(-0.825779 + 3.14089i) q^{28} +(-1.03398 + 3.40858i) q^{29} +(-0.122643 + 4.03676i) q^{30} +(5.21639 + 5.21639i) q^{31} +(-5.49359 + 1.34926i) q^{32} +(2.21173 - 2.21173i) q^{33} +(-6.01654 - 6.39358i) q^{34} +(1.55390 + 0.471369i) q^{35} +(1.39387 + 10.2158i) q^{36} +(2.05496 + 0.202396i) q^{37} +(8.13572 - 4.03592i) q^{38} +(9.57651 + 1.90489i) q^{39} +(0.571366 + 2.77012i) q^{40} +(0.612269 + 3.07809i) q^{41} +(6.50387 + 0.840688i) q^{42} +(-6.01279 - 3.21390i) q^{43} +(1.14801 - 1.86567i) q^{44} +(5.13041 - 0.505301i) q^{45} +(3.75783 + 6.01149i) q^{46} +(2.39259 + 5.77623i) q^{47} +(4.12417 + 10.6525i) q^{48} +(-1.66973 + 4.03109i) q^{49} +(1.39478 - 0.233651i) q^{50} +(-11.2466 + 13.7041i) q^{51} +(6.83347 - 0.255900i) q^{52} +(1.46530 + 4.83046i) q^{53} +(8.40224 - 2.27258i) q^{54} +(-0.910699 - 0.608510i) q^{55} +(4.56744 - 0.482429i) q^{56} +(-10.1886 - 15.2483i) q^{57} +(5.02579 - 0.341285i) q^{58} +(-2.88403 + 2.36687i) q^{59} +(5.39967 - 1.86132i) q^{60} +(2.41850 + 4.52470i) q^{61} +(4.28331 - 9.51295i) q^{62} -8.37115i q^{63} +(4.53802 + 6.58835i) q^{64} -3.41913i q^{65} +(-4.03345 - 1.81611i) q^{66} +(4.86355 + 9.09906i) q^{67} +(-5.43893 + 11.1612i) q^{68} +(11.0662 - 9.08176i) q^{69} +(-0.155584 - 2.29115i) q^{70} +(-4.22630 - 6.32510i) q^{71} +(12.8106 - 6.96412i) q^{72} +(-6.47451 - 4.32613i) q^{73} +(-0.762442 - 2.81893i) q^{74} +(-0.828976 - 2.73277i) q^{75} +(-9.41527 - 8.73556i) q^{76} +(-1.12830 + 1.37484i) q^{77} +(-2.28140 - 13.6188i) q^{78} +(-6.20419 + 14.9782i) q^{79} +(3.37678 - 2.14415i) q^{80} +(-0.807729 - 1.95003i) q^{81} +(3.76353 - 2.35261i) q^{82} +(-8.72092 + 0.858936i) q^{83} +(-2.14847 - 9.02210i) q^{84} +(5.47490 + 2.92639i) q^{85} +(-1.23602 + 9.56232i) q^{86} +(-1.98446 - 9.97655i) q^{87} +(-3.04261 - 0.582917i) q^{88} +(9.45919 + 1.88155i) q^{89} +(-3.23992 - 6.53113i) q^{90} +(-5.52530 - 0.544195i) q^{91} +(6.06589 - 7.98271i) q^{92} +(-20.1599 - 6.11544i) q^{93} +(6.43912 - 6.05940i) q^{94} +(-4.54089 + 4.54089i) q^{95} +(12.0194 - 10.7935i) q^{96} +(-11.6742 - 11.6742i) q^{97} +(6.16768 + 0.187383i) q^{98} +(-1.63908 + 5.40333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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