LMFDB - Embedded newform 640.2.bm.a.101.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			101.61
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.61

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41105 - 0.0944946i) q^{2} +(-1.53516 + 0.820563i) q^{3} +(1.98214 - 0.266674i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-2.08866 + 1.30292i) q^{6} +(1.09494 - 0.731615i) q^{7} +(2.77171 - 0.563593i) q^{8} +(0.0166972 - 0.0249891i) q^{9} +O(q^{10})$	\(q+(1.41105 - 0.0944946i) q^{2} +(-1.53516 + 0.820563i) q^{3} +(1.98214 - 0.266674i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-2.08866 + 1.30292i) q^{6} +(1.09494 - 0.731615i) q^{7} +(2.77171 - 0.563593i) q^{8} +(0.0166972 - 0.0249891i) q^{9} +(0.968208 + 1.03081i) q^{10} +(2.79400 - 0.847549i) q^{11} +(-2.82409 + 2.03586i) q^{12} +(0.0512124 + 0.0420289i) q^{13} +(1.47588 - 1.13581i) q^{14} +(-1.60820 - 0.666139i) q^{15} +(3.85777 - 1.05717i) q^{16} +(-2.15192 + 0.891354i) q^{17} +(0.0211993 - 0.0368387i) q^{18} +(0.428359 + 4.34920i) q^{19} +(1.46360 + 1.36304i) q^{20} +(-1.08058 + 2.02162i) q^{21} +(3.86239 - 1.45995i) q^{22} +(5.38872 - 1.07188i) q^{23} +(-3.79256 + 3.13957i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(0.0762349 + 0.0544657i) q^{26} +(0.506729 - 5.14491i) q^{27} +(1.97522 - 1.74216i) q^{28} +(-2.58840 + 8.53281i) q^{29} +(-2.33220 - 0.787991i) q^{30} +(-0.801865 - 0.801865i) q^{31} +(5.34362 - 1.85626i) q^{32} +(-3.59378 + 3.59378i) q^{33} +(-2.95224 + 1.46109i) q^{34} +(1.26017 + 0.382268i) q^{35} +(0.0264322 - 0.0539846i) q^{36} +(5.58663 + 0.550235i) q^{37} +(1.01541 + 6.09648i) q^{38} +(-0.113107 - 0.0224983i) q^{39} +(2.19402 + 1.78502i) q^{40} +(-0.244736 - 1.23037i) q^{41} +(-1.33372 + 2.95472i) q^{42} +(0.489478 + 0.261632i) q^{43} +(5.31208 - 2.42505i) q^{44} +(0.0299094 - 0.00294582i) q^{45} +(7.50248 - 2.02169i) q^{46} +(-3.62958 - 8.76258i) q^{47} +(-5.05484 + 4.78847i) q^{48} +(-2.01515 + 4.86501i) q^{49} +(-0.182604 + 1.40238i) q^{50} +(2.57214 - 3.13416i) q^{51} +(0.112718 + 0.0696502i) q^{52} +(1.23239 + 4.06265i) q^{53} +(0.228856 - 7.30762i) q^{54} +(2.42766 + 1.62211i) q^{55} +(2.62252 - 2.64492i) q^{56} +(-4.22640 - 6.32525i) q^{57} +(-2.84606 + 12.2848i) q^{58} +(0.288482 - 0.236751i) q^{59} +(-3.36533 - 0.891516i) q^{60} +(-5.18465 - 9.69979i) q^{61} +(-1.20725 - 1.05570i) q^{62} -0.0395774i q^{63} +(7.36473 - 3.12423i) q^{64} +0.0662505i q^{65} +(-4.73142 + 5.41060i) q^{66} +(-1.18104 - 2.20958i) q^{67} +(-4.02771 + 2.34065i) q^{68} +(-7.39302 + 6.06730i) q^{69} +(1.81429 + 0.420321i) q^{70} +(-5.01609 - 7.50712i) q^{71} +(0.0321960 - 0.0786728i) q^{72} +(-14.1814 - 9.47568i) q^{73} +(7.93502 + 0.248504i) q^{74} +(-0.505300 - 1.66575i) q^{75} +(2.00889 + 8.50650i) q^{76} +(2.43918 - 2.97214i) q^{77} +(-0.161726 - 0.0210584i) q^{78} +(1.46071 - 3.52646i) q^{79} +(3.26455 + 2.31143i) q^{80} +(3.47831 + 8.39738i) q^{81} +(-0.461599 - 1.71299i) q^{82} +(8.00596 - 0.788518i) q^{83} +(-1.60274 + 4.29529i) q^{84} +(-2.05419 - 1.09799i) q^{85} +(0.715403 + 0.322923i) q^{86} +(-3.02808 - 15.2232i) q^{87} +(7.26647 - 3.92383i) q^{88} +(-7.52623 - 1.49706i) q^{89} +(0.0419254 - 0.00698298i) q^{90} +(0.0868234 + 0.00855136i) q^{91} +(10.3954 - 3.56165i) q^{92} +(1.88898 + 0.573014i) q^{93} +(-5.94954 - 12.0215i) q^{94} +(-3.09023 + 3.09023i) q^{95} +(-6.68016 + 7.23445i) q^{96} +(-6.92117 - 6.92117i) q^{97} +(-2.38377 + 7.05521i) q^{98} +(0.0254723 - 0.0839711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * 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

Display 100 coefficients 10 coefficients

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 $

$2$	1.41105	−	0.0944946i	0.997765	−	0.0668178i
$2$	1.41105	−	0.0944946i	0.997765	−	0.0668178i
$3$	−1.53516	+	0.820563i	−0.886328	+	0.473752i	−0.850723	−	0.525614i	$-0.823836\pi$
$3$	−1.53516	+	0.820563i	−0.886328	+	0.473752i	−0.0356046	+	0.999366i	$0.511336\pi$
$4$	1.98214	−	0.266674i	0.991071	−	0.133337i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	−2.08866	+	1.30292i	−0.852692	+	0.531916i
$7$	1.09494	−	0.731615i	0.413848	−	0.276525i	−0.331167	−	0.943572i	$-0.607442\pi$
$7$	1.09494	−	0.731615i	0.413848	−	0.276525i	0.745015	+	0.667048i	$0.232442\pi$
$8$	2.77171	−	0.563593i	0.979947	−	0.199260i
$9$	0.0166972	−	0.0249891i	0.00556572	−	0.00832970i
$10$	0.968208	+	1.03081i	0.306174	+	0.325971i
$11$	2.79400	−	0.847549i	0.842421	−	0.255546i	0.160559	−	0.987026i	$-0.448670\pi$
$11$	2.79400	−	0.847549i	0.842421	−	0.255546i	0.681862	+	0.731481i	$0.261170\pi$
$12$	−2.82409	+	2.03586i	−0.815245	+	0.587702i
$13$	0.0512124	+	0.0420289i	0.0142038	+	0.0116567i	0.641468	−	0.767149i	$-0.278326\pi$
$13$	0.0512124	+	0.0420289i	0.0142038	+	0.0116567i	−0.627265	+	0.778806i	$0.715826\pi$
$14$	1.47588	−	1.13581i	0.394447	−	0.303559i
$15$	−1.60820	−	0.666139i	−0.415236	−	0.171996i
$16$	3.85777	−	1.05717i	0.964443	−	0.264293i
$17$	−2.15192	+	0.891354i	−0.521917	+	0.216185i	−0.628059	−	0.778166i	$-0.716150\pi$
$17$	−2.15192	+	0.891354i	−0.521917	+	0.216185i	0.106142	+	0.994351i	$0.466150\pi$
$18$	0.0211993	−	0.0368387i	0.00499671	−	0.00868297i
$19$	0.428359	+	4.34920i	0.0982723	+	0.997776i	0.910242	+	0.414076i	$0.135895\pi$
$19$	0.428359	+	4.34920i	0.0982723	+	0.997776i	−0.811970	+	0.583699i	$0.801605\pi$
$20$	1.46360	+	1.36304i	0.327271	+	0.304785i
$21$	−1.08058	+	2.02162i	−0.235801	+	0.441153i
$22$	3.86239	−	1.45995i	0.823464	−	0.311263i
$23$	5.38872	−	1.07188i	1.12363	−	0.223503i	0.401901	−	0.915683i	$-0.368350\pi$
$23$	5.38872	−	1.07188i	1.12363	−	0.223503i	0.721725	+	0.692180i	$0.243350\pi$
$24$	−3.79256	+	3.13957i	−0.774154	+	0.640862i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	0.0762349	+	0.0544657i	0.0149509	+	0.0106816i
$27$	0.506729	−	5.14491i	0.0975200	−	0.990138i
$28$	1.97522	−	1.74216i	0.373282	−	0.329237i
$29$	−2.58840	+	8.53281i	−0.480654	+	1.58450i	0.296397	+	0.955065i	$0.404215\pi$
$29$	−2.58840	+	8.53281i	−0.480654	+	1.58450i	−0.777051	+	0.629438i	$0.783285\pi$
$30$	−2.33220	−	0.787991i	−0.425800	−	0.143867i
$31$	−0.801865	−	0.801865i	−0.144019	−	0.144019i	0.631421	−	0.775440i	$-0.282472\pi$
$31$	−0.801865	−	0.801865i	−0.144019	−	0.144019i	−0.775440	+	0.631421i	$0.782472\pi$
$32$	5.34362	−	1.85626i	0.944628	−	0.328144i
$33$	−3.59378	+	3.59378i	−0.625596	+	0.625596i
$34$	−2.95224	+	1.46109i	−0.506305	+	0.250575i
$35$	1.26017	+	0.382268i	0.213007	+	0.0646151i
$36$	0.0264322	−	0.0539846i	0.00440537	−	0.00899743i
$37$	5.58663	+	0.550235i	0.918436	+	0.0904581i	0.546176	−	0.837670i	$-0.316083\pi$
$37$	5.58663	+	0.550235i	0.918436	+	0.0904581i	0.372260	+	0.928128i	$0.378583\pi$
$38$	1.01541	+	6.09648i	0.164722	+	0.988979i
$39$	−0.113107	−	0.0224983i	−0.0181116	−	0.00360262i
$40$	2.19402	+	1.78502i	0.346904	+	0.282236i
$41$	−0.244736	−	1.23037i	−0.0382214	−	0.192152i	0.956958	−	0.290228i	$-0.0937311\pi$
$41$	−0.244736	−	1.23037i	−0.0382214	−	0.192152i	−0.995179	+	0.0980762i	$0.968731\pi$
$42$	−1.33372	+	2.95472i	−0.205797	+	0.455923i
$43$	0.489478	+	0.261632i	0.0746448	+	0.0398985i	0.508297	−	0.861182i	$-0.330275\pi$
$43$	0.489478	+	0.261632i	0.0746448	+	0.0398985i	−0.433652	+	0.901080i	$0.642775\pi$
$44$	5.31208	−	2.42505i	0.800825	−	0.365590i
$45$	0.0299094	−	0.00294582i	0.00445863	−	0.000439137i
$46$	7.50248	−	2.02169i	1.10618	−	0.298082i
$47$	−3.62958	−	8.76258i	−0.529428	−	1.27815i	−0.931898	−	0.362720i	$-0.881848\pi$
$47$	−3.62958	−	8.76258i	−0.529428	−	1.27815i	0.402470	−	0.915433i	$-0.368152\pi$
$48$	−5.05484	+	4.78847i	−0.729603	+	0.691157i
$49$	−2.01515	+	4.86501i	−0.287879	+	0.695001i
$50$	−0.182604	+	1.40238i	−0.0258241	+	0.198326i
$51$	2.57214	−	3.13416i	0.360171	−	0.438870i
$52$	0.112718	+	0.0696502i	0.0156312	+	0.00965875i
$53$	1.23239	+	4.06265i	0.169282	+	0.558048i	0.999999	+	0.00135334i	$0.000430783\pi$
$53$	1.23239	+	4.06265i	0.169282	+	0.558048i	−0.830717	+	0.556695i	$0.812069\pi$
$54$	0.228856	−	7.30762i	0.0311433	−	0.994441i
$55$	2.42766	+	1.62211i	0.327345	+	0.218725i
$56$	2.62252	−	2.64492i	0.350449	−	0.353443i
$57$	−4.22640	−	6.32525i	−0.559800	−	0.837800i
$58$	−2.84606	+	12.2848i	−0.373707	+	1.61308i
$59$	0.288482	−	0.236751i	0.0375571	−	0.0308223i	−0.615428	−	0.788193i	$-0.711017\pi$
$59$	0.288482	−	0.236751i	0.0375571	−	0.0308223i	0.652985	+	0.757371i	$0.273517\pi$
$60$	−3.36533	−	0.891516i	−0.434462	−	0.115094i
$61$	−5.18465	−	9.69979i	−0.663826	−	1.24193i	−0.958161	−	0.286229i	$-0.907598\pi$
$61$	−5.18465	−	9.69979i	−0.663826	−	1.24193i	0.294335	−	0.955702i	$-0.404902\pi$
$62$	−1.20725	−	1.05570i	−0.153320	−	0.134074i
$63$		−	0.0395774i		−	0.00498629i
$64$	7.36473	−	3.12423i	0.920591	−	0.390529i
$65$			0.0662505i			0.00821737i
$66$	−4.73142	+	5.41060i	−0.582397	+	0.665999i
$67$	−1.18104	−	2.20958i	−0.144287	−	0.269943i	0.799388	−	0.600815i	$-0.205157\pi$
$67$	−1.18104	−	2.20958i	−0.144287	−	0.269943i	−0.943676	+	0.330872i	$0.892657\pi$
$68$	−4.02771	+	2.34065i	−0.488431	+	0.283845i
$69$	−7.39302	+	6.06730i	−0.890015	+	0.730417i
$70$	1.81429	+	0.420321i	0.216849	+	0.0502380i
$71$	−5.01609	−	7.50712i	−0.595301	−	0.890931i	0.404420	−	0.914574i	$-0.367474\pi$
$71$	−5.01609	−	7.50712i	−0.595301	−	0.890931i	−0.999720	+	0.0236428i	$0.992474\pi$
$72$	0.0321960	−	0.0786728i	0.00379434	−	0.00927168i
$73$	−14.1814	−	9.47568i	−1.65980	−	1.10904i	−0.864012	−	0.503472i	$-0.832056\pi$
$73$	−14.1814	−	9.47568i	−1.65980	−	1.10904i	−0.795790	−	0.605572i	$-0.792944\pi$
$74$	7.93502	+	0.248504i	0.922428	+	0.0288880i
$75$	−0.505300	−	1.66575i	−0.0583470	−	0.192344i
$76$	2.00889	+	8.50650i	0.230435	+	0.975763i
$77$	2.43918	−	2.97214i	0.277970	−	0.338707i
$78$	−0.161726	−	0.0210584i	−0.0183118	−	0.00238439i
$79$	1.46071	−	3.52646i	0.164343	−	0.396758i	−0.820159	−	0.572136i	$-0.806115\pi$
$79$	1.46071	−	3.52646i	0.164343	−	0.396758i	0.984501	+	0.175378i	$0.0561148\pi$
$80$	3.26455	+	2.31143i	0.364987	+	0.258426i
$81$	3.47831	+	8.39738i	0.386479	+	0.933042i
$82$	−0.461599	−	1.71299i	−0.0509751	−	0.189168i
$83$	8.00596	−	0.788518i	0.878769	−	0.0865511i	0.351438	−	0.936211i	$-0.385693\pi$
$83$	8.00596	−	0.788518i	0.878769	−	0.0865511i	0.527331	+	0.849660i	$0.323193\pi$
$84$	−1.60274	+	4.29529i	−0.174874	+	0.468655i
$85$	−2.05419	−	1.09799i	−0.222808	−	0.119093i
$86$	0.715403	+	0.322923i	0.0771439	+	0.0348217i
$87$	−3.02808	−	15.2232i	−0.324645	−	1.63210i
$88$	7.26647	−	3.92383i	0.774608	−	0.418282i
$89$	−7.52623	−	1.49706i	−0.797779	−	0.158688i	−0.220663	−	0.975350i	$-0.570822\pi$
$89$	−7.52623	−	1.49706i	−0.797779	−	0.158688i	−0.577116	+	0.816662i	$0.695822\pi$
$90$	0.0419254	−	0.00698298i	0.00441932	−	0.000736071i
$91$	0.0868234	+	0.00855136i	0.00910157	+	0.000896426i
$92$	10.3954	−	3.56165i	1.08379	−	0.371328i
$93$	1.88898	+	0.573014i	0.195878	+	0.0594188i
$94$	−5.94954	−	12.0215i	−0.613649	−	1.23992i
$95$	−3.09023	+	3.09023i	−0.317051	+	0.317051i
$96$	−6.68016	+	7.23445i	−0.681791	+	0.738362i
$97$	−6.92117	−	6.92117i	−0.702738	−	0.702738i	0.262259	−	0.964998i	$-0.415533\pi$
$97$	−6.92117	−	6.92117i	−0.702738	−	0.702738i	−0.964998	+	0.262259i	$0.915533\pi$
$98$	−2.38377	+	7.05521i	−0.240797	+	0.712683i
$99$	0.0254723	−	0.0839711i	0.00256007	−	0.00843941i
$100$	−0.125147	+	1.99608i	−0.0125147	+	0.199608i
$101$	−0.465512	+	4.72642i	−0.0463202	+	0.470297i	0.943844	+	0.330390i	$0.107180\pi$
$101$	−0.465512	+	4.72642i	−0.0463202	+	0.470297i	−0.990165	+	0.139907i	$0.955320\pi$
$102$	3.33326	−	4.66552i	0.330042	−	0.461955i
$103$	1.35741	−	6.82415i	0.133749	−	0.672404i	−0.854487	−	0.519472i	$-0.826129\pi$
$103$	1.35741	−	6.82415i	0.133749	−	0.672404i	0.988237	−	0.152932i	$-0.0488714\pi$
$104$	0.165633	+	0.0876289i	0.0162416	+	0.00859272i
$105$	−2.24824	+	0.447203i	−0.219406	+	0.0436425i
$106$	2.12287	+	5.61616i	0.206191	+	0.545490i
$107$	0.814933	−	1.52463i	0.0787826	−	0.147392i	−0.839445	−	0.543444i	$-0.817120\pi$
$107$	0.814933	−	1.52463i	0.0787826	−	0.147392i	0.918228	+	0.396052i	$0.129620\pi$
$108$	−0.367603	−	10.3331i	−0.0353726	−	0.994299i
$109$	0.535459	+	5.43660i	0.0512877	+	0.520732i	0.986166	+	0.165763i	$0.0530087\pi$
$109$	0.535459	+	5.43660i	0.0512877	+	0.520732i	−0.934878	+	0.354969i	$0.884491\pi$
$110$	3.57883	+	2.05948i	0.341228	+	0.196364i
$111$	−9.02790	+	3.73948i	−0.856890	+	0.354936i
$112$	3.45058	−	3.97994i	0.326049	−	0.376069i
$113$	−3.00845	−	1.24614i	−0.283011	−	0.117227i	0.236662	−	0.971592i	$-0.423946\pi$
$113$	−3.00845	−	1.24614i	−0.283011	−	0.117227i	−0.519674	+	0.854365i	$0.673946\pi$
$114$	−6.56137	−	8.52589i	−0.614529	−	0.798523i
$115$	4.24714	+	3.48554i	0.396048	+	0.325028i
$116$	−2.85510	+	17.6035i	−0.265089	+	1.63444i
$117$	0.00190537		0.000577986i	0.000176151		5.34348e-5i
$118$	0.384691	−	0.361328i	0.0354137	−	0.0332629i
$119$	−1.70409	+	2.55035i	−0.156214	+	0.233791i
$120$	−4.83290	−	0.939972i	−0.441181	−	0.0858073i
$121$	−2.05810	+	1.37518i	−0.187100	+	0.125016i
$122$	−8.23239	−	13.1970i	−0.745326	−	1.19480i
$123$	1.38531	+	1.68800i	0.124909	+	0.152202i
$124$	−1.80325	−	1.37557i	−0.161936	−	0.123530i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−0.00373986	−	0.0558459i	−0.000333173	−	0.00497515i
$127$	−12.0053			−1.06530			−0.532650	−	0.846335i	$-0.678804\pi$
$127$	−12.0053			−1.06530			−0.532650	+	0.846335i	$0.678804\pi$
$128$	10.0968	−	5.10438i	0.892439	−	0.451168i
$129$	−0.966115			−0.0850617
$130$	0.00626032	+	0.0934830i	0.000549066	+	0.00819900i
$131$	−1.41695	+	0.757374i	−0.123799	+	0.0661721i	−0.532134	−	0.846660i	$-0.678610\pi$
$131$	−1.41695	+	0.757374i	−0.123799	+	0.0661721i	0.408335	+	0.912832i	$0.366110\pi$
$132$	−6.16501	+	8.08174i	−0.536595	+	0.703425i
$133$	3.65097	+	4.44872i	0.316579	+	0.385753i
$134$	−1.87531	−	3.00623i	−0.162002	−	0.259698i
$135$	4.29853	−	2.87219i	0.369959	−	0.247198i
$136$	−5.46213	+	3.68338i	−0.468374	+	0.315847i
$137$	9.38553	−	14.0464i	0.801860	−	1.20007i	−0.174657	−	0.984629i	$-0.555882\pi$
$137$	9.38553	−	14.0464i	0.801860	−	1.20007i	0.976517	−	0.215439i	$-0.0691184\pi$
$138$	−9.85862	+	9.25988i	−0.839221	+	0.788253i
$139$	−0.290092	+	0.0879984i	−0.0246053	+	0.00746393i	−0.302563	−	0.953129i	$-0.597842\pi$
$139$	−0.290092	+	0.0879984i	−0.0246053	+	0.00746393i	0.277958	+	0.960593i	$0.410342\pi$
$140$	2.59977	+	0.421655i	0.219721	+	0.0356364i
$141$	12.7622	+	10.4737i	1.07478	+	0.882045i
$142$	−7.78736	−	10.1189i	−0.653501	−	0.849163i
$143$	0.178709	+	0.0740235i	0.0149444	+	0.00619016i
$144$	0.0379961	−	0.114054i	0.00316634	−	0.00950449i
$145$	−8.23801	+	3.41230i	−0.684130	+	0.283376i
$146$	−20.9060	−	12.0306i	−1.73020	−	0.995661i
$147$	−0.898453	−	9.12215i	−0.0741032	−	0.752382i
$148$	11.2202	−	0.399164i	0.922297	−	0.0328111i
$149$	5.68713	−	10.6399i	0.465908	−	0.871652i	−0.533754	−	0.845640i	$-0.679219\pi$
$149$	5.68713	−	10.6399i	0.465908	−	0.871652i	0.999662	−	0.0260123i	$-0.00828092\pi$
$150$	−0.870410	−	2.30271i	−0.0710686	−	0.188016i
$151$	−14.8924	+	2.96228i	−1.21192	+	0.241067i	−0.759363	−	0.650667i	$-0.774489\pi$
$151$	−14.8924	+	2.96228i	−1.21192	+	0.241067i	−0.452560	+	0.891734i	$0.649489\pi$
$152$	3.63847	+	11.8133i	0.295119	+	0.958185i
$153$	−0.0136568	+	0.0686576i	−0.00110409	+	0.00555063i
$154$	3.16095	−	4.42434i	0.254717	−	0.356524i
$155$	0.111152	−	1.12855i	0.00892796	−	0.0906471i
$156$	−0.230193	−	0.0144323i	−0.0184302	−	0.00115551i
$157$	0.689464	−	2.27286i	0.0550252	−	0.181394i	−0.925120	−	0.379675i	$-0.876036\pi$
$157$	0.689464	−	2.27286i	0.0550252	−	0.181394i	0.980145	+	0.198281i	$0.0635359\pi$
$158$	1.72791	−	5.11406i	0.137465	−	0.406853i
$159$	−5.22559	−	5.22559i	−0.414416	−	0.414416i
$160$	4.82487	+	2.95307i	0.381439	+	0.233461i
$161$	5.11611	−	5.11611i	0.403206	−	0.403206i
$162$	5.70159	+	11.5205i	0.447959	+	0.905133i
$163$	−19.4775	−	5.90844i	−1.52560	−	0.462784i	−0.587519	−	0.809211i	$-0.699895\pi$
$163$	−19.4775	−	5.90844i	−1.52560	−	0.462784i	−0.938077	+	0.346426i	$0.887395\pi$
$164$	−0.813209	−	2.37351i	−0.0635010	−	0.185340i
$165$	−5.05789	−	0.498159i	−0.393757	−	0.0387816i
$166$	11.2223	−	1.86916i	0.871022	−	0.145075i
$167$	11.1234	+	2.21258i	0.860755	+	0.171215i	0.605682	−	0.795707i	$-0.292900\pi$
$167$	11.1234	+	2.21258i	0.860755	+	0.171215i	0.255073	+	0.966922i	$0.417900\pi$
$168$	−1.85567	+	6.21233i	−0.143168	+	0.479292i
$169$	−2.53532	−	12.7459i	−0.195024	−	0.980454i
$170$	−3.00232	−	1.35521i	−0.230268	−	0.103940i
$171$	0.115835	+	0.0619151i	0.00885812	+	0.00473477i
$172$	1.03999	+	0.388060i	0.0792982	+	0.0295893i
$173$	−3.37719	+	0.332624i	−0.256763	+	0.0252889i	−0.225579	−	0.974225i	$-0.572428\pi$
$173$	−3.37719	+	0.332624i	−0.256763	+	0.0252889i	−0.0311832	+	0.999514i	$0.509928\pi$
$174$	−5.71130	−	21.1946i	−0.432973	−	1.60676i
$175$	0.503945	+	1.21663i	0.0380947	+	0.0919687i
$176$	9.88259	−	6.22338i	0.744928	−	0.469105i
$177$	−0.248598	+	0.600169i	−0.0186858	+	0.0451115i
$178$	−10.7614	−	1.40124i	−0.806600	−	0.105028i
$179$	9.52794	−	11.6098i	0.712152	−	0.867760i	−0.283685	−	0.958918i	$-0.591557\pi$
$179$	9.52794	−	11.6098i	0.712152	−	0.867760i	0.995836	+	0.0911581i	$0.0290569\pi$
$180$	0.0584991	−	0.0138151i	0.00436026	−	0.00102972i
$181$	7.10092	+	23.4086i	0.527807	+	1.73995i	0.662503	+	0.749059i	$0.269494\pi$
$181$	7.10092	+	23.4086i	0.527807	+	1.73995i	−0.134696	+	0.990887i	$0.543006\pi$
$182$	0.123320	+	0.00386208i	0.00914112	+	0.000286276i
$183$	15.9186	+	10.6365i	1.17674	+	0.786269i
$184$	14.3318	−	6.00799i	1.05656	−	0.442915i
$185$	3.11878	+	4.66759i	0.229297	+	0.343168i
$186$	2.71959	+	0.630056i	0.199410	+	0.0461979i
$187$	−5.25698	+	4.31430i	−0.384429	+	0.315493i
$188$	−9.53109	−	16.4008i	−0.695126	−	1.19615i
$189$	−3.20925	−	6.00409i	−0.233439	−	0.436733i
$190$	−4.06847	+	4.65249i	−0.295158	+	0.337527i
$191$			19.8293i			1.43480i	0.696663	+	0.717398i	$0.254667\pi$
$191$			19.8293i			1.43480i	−0.696663	+	0.717398i	$0.745333\pi$
$192$	−8.74244	+	10.8394i	−0.630932	+	0.782268i
$193$			1.13489i			0.0816910i	0.999165	+	0.0408455i	$0.0130051\pi$
$193$			1.13489i			0.0816910i	−0.999165	+	0.0408455i	$0.986995\pi$
$194$	−10.4202	−	9.11213i	−0.748123	−	0.654213i
$195$	−0.0543627	−	0.101705i	−0.00389300	−	0.00728328i
$196$	−2.69695	+	10.1805i	−0.192639	+	0.727180i
$197$	−8.40366	+	6.89671i	−0.598736	+	0.491370i	−0.884256	−	0.467003i	$-0.845334\pi$
$197$	−8.40366	+	6.89671i	−0.598736	+	0.491370i	0.285520	+	0.958373i	$0.407834\pi$
$198$	0.0280080	−	0.120895i	0.00199044	−	0.00859161i
$199$	10.2545	+	15.3469i	0.726920	+	1.08791i	0.992311	+	0.123771i	$0.0394989\pi$
$199$	10.2545	+	15.3469i	0.726920	+	1.08791i	−0.265391	+	0.964141i	$0.585501\pi$
$200$	0.0120301	+	2.82840i	0.000850656	+	0.199998i
$201$	3.62619	+	2.42294i	0.255772	+	0.170901i
$202$	−0.210241	+	6.71322i	−0.0147925	+	0.472341i
$203$	3.40859	+	11.2366i	0.239236	+	0.788656i
$204$	4.26254	−	6.89827i	0.298438	−	0.482975i
$205$	0.795831	−	0.969723i	0.0555832	−	0.0677284i
$206$	1.27053	−	9.75751i	0.0885220	−	0.679838i
$207$	0.0631910	−	0.152557i	0.00439208	−	0.0106034i
$208$	0.241997	+	0.107998i	0.0167795	+	0.00748829i
$209$	4.88300	+	11.7886i	0.337764	+	0.815434i
$210$	−3.13013	+	0.843474i	−0.215999	+	0.0582052i
$211$	19.4504	−	1.91570i	1.33902	−	0.131882i	0.596991	−	0.802248i	$-0.296363\pi$
$211$	19.4504	−	1.91570i	1.33902	−	0.131882i	0.742031	+	0.670366i	$0.233863\pi$
$212$	3.52618	+	7.72411i	0.242179	+	0.530494i
$213$	13.8606	+	7.40864i	0.949712	+	0.507632i
$214$	1.00584	−	2.22835i	0.0687581	−	0.152327i
$215$	0.108278	+	0.544349i	0.00738448	+	0.0371243i
$216$	−1.49513	−	14.5458i	−0.101730	−	0.989714i
$217$	−1.46465	−	0.291337i	−0.0994269	−	0.0197772i
$218$	1.26929	+	7.62074i	0.0859672	+	0.516142i
$219$	29.5461	+	2.91004i	1.99654	+	0.196642i
$220$	5.24453	+	2.56786i	0.353586	+	0.173125i
$221$	−0.147667	−	0.0447944i	−0.00993319	−	0.00301320i
$222$	−12.3855	+	6.12969i	−0.831259	+	0.411398i
$223$	−8.60443	+	8.60443i	−0.576195	+	0.576195i	−0.933853	−	0.357657i	$-0.883576\pi$
$223$	−8.60443	+	8.60443i	−0.576195	+	0.576195i	0.357657	+	0.933853i	$0.383576\pi$
$224$	4.49287	−	5.94197i	0.300193	−	0.397015i
$225$	0.0212515	+	0.0212515i	0.00141676	+	0.00141676i
$226$	−4.36284	−	1.47409i	−0.290211	−	0.0980549i
$227$	−0.305082	+	1.00572i	−0.0202490	+	0.0667519i	−0.966483	−	0.256732i	$-0.917354\pi$
$227$	−0.305082	+	1.00572i	−0.0202490	+	0.0667519i	0.946234	+	0.323484i	$0.104854\pi$
$228$	−10.0641	−	11.4105i	−0.666511	−	0.755677i
$229$	−1.29415	+	13.1397i	−0.0855195	+	0.868295i	0.852734	+	0.522346i	$0.174943\pi$
$229$	−1.29415	+	13.1397i	−0.0855195	+	0.868295i	−0.938253	+	0.345949i	$0.887557\pi$
$230$	6.32231	+	4.51695i	0.416881	+	0.297839i
$231$	−1.30571	+	6.56423i	−0.0859092	+	0.431894i
$232$	−2.36526	+	25.1093i	−0.155287	+	1.64850i
$233$	22.2073	−	4.41730i	1.45485	−	0.289387i	0.596564	−	0.802566i	$-0.296532\pi$
$233$	22.2073	−	4.41730i	1.45485	−	0.289387i	0.858282	+	0.513179i	$0.171532\pi$
$234$	0.00263395		0.000995616i	0.000172187		6.50855e-5i
$235$	4.47098	−	8.36462i	0.291655	−	0.545648i
$236$	0.508676	−	0.546204i	0.0331120	−	0.0355549i
$237$	0.651255	+	6.61231i	0.0423036	+	0.429516i
$238$	−2.16357	+	3.75971i	−0.140243	+	0.243706i
$239$	−2.85248	+	1.18153i	−0.184511	+	0.0764271i	−0.473026	−	0.881048i	$-0.656838\pi$
$239$	−2.85248	+	1.18153i	−0.184511	+	0.0764271i	0.288515	+	0.957475i	$0.406838\pi$
$240$	−6.90830	−	0.869667i	−0.445929	−	0.0561368i
$241$	17.5624	+	7.27457i	1.13129	+	0.468596i	0.868219	−	0.496180i	$-0.165265\pi$
$241$	17.5624	+	7.27457i	1.13129	+	0.468596i	0.263071	+	0.964776i	$0.415265\pi$
$242$	−2.77413	+	2.13492i	−0.178328	+	0.137238i
$243$	−0.241426	−	0.198134i	−0.0154875	−	0.0127103i
$244$	−12.8634	−	17.8438i	−0.823494	−	1.14233i
$245$	−5.03910	+	1.52859i	−0.321936	+	0.0976583i
$246$	2.11425	+	2.25096i	0.134800	+	0.143516i
$247$	−0.160855	+	0.240736i	−0.0102350	+	0.0153177i
$248$	−2.67446	−	1.77061i	−0.169828	−	0.112434i
$249$	−11.6434	+	7.77990i	−0.737873	+	0.493031i
$250$	−1.19989	+	0.748503i	−0.0758879	+	0.0473395i
$251$	−12.9202	−	15.7434i	−0.815518	−	0.993712i	−0.999941	−	0.0108650i	$-0.996542\pi$
$251$	−12.9202	−	15.7434i	−0.815518	−	0.993712i	0.184423	−	0.982847i	$-0.440958\pi$
$252$	−0.0105543	−	0.0784481i	−0.000664856	−	0.00494176i
$253$	14.1476	−	7.56204i	0.889451	−	0.475421i
$254$	−16.9402	+	1.13444i	−1.06292	+	0.0711810i
$255$	4.05448			0.253902
$256$	13.7648	−	8.15664i	0.860299	−	0.509790i
$257$	22.9495			1.43155			0.715775	−	0.698331i	$-0.246074\pi$
$257$	22.9495			1.43155			0.715775	+	0.698331i	$0.246074\pi$
$258$	−1.36324	+	0.0912927i	−0.0848716	+	0.00568363i
$259$	6.51958	−	3.48479i	0.405107	−	0.216534i
$260$	0.0176673	+	0.131318i	0.00109568	+	0.00814399i
$261$	0.170008	+	0.207156i	0.0105232	+	0.0128226i
$262$	−1.92782	+	1.20259i	−0.119101	+	0.0742962i
$263$	−10.8410	+	7.24373i	−0.668485	+	0.446667i	−0.842947	−	0.537997i	$-0.819181\pi$
$263$	−10.8410	+	7.24373i	−0.668485	+	0.446667i	0.174462	+	0.984664i	$0.444181\pi$
$264$	−7.93547	+	11.9863i	−0.488394	+	0.737707i
$265$	−2.35865	+	3.52997i	−0.144891	+	0.216844i
$266$	5.57209	+	5.93238i	0.341647	+	0.363738i
$267$	12.7824	−	3.87751i	0.782273	−	0.237300i
$268$	−2.93023	−	4.06474i	−0.178992	−	0.248294i
$269$	11.2150	+	9.20387i	0.683788	+	0.561170i	0.910864	−	0.412707i	$-0.135417\pi$
$269$	11.2150	+	9.20387i	0.683788	+	0.561170i	−0.227076	+	0.973877i	$0.572917\pi$
$270$	5.79405	−	4.45900i	0.352615	−	0.271366i
$271$	−28.6212	−	11.8553i	−1.73862	−	0.720158i	−0.998883	−	0.0472586i	$-0.984952\pi$
$271$	−28.6212	−	11.8553i	−1.73862	−	0.720158i	−0.739734	−	0.672900i	$-0.765048\pi$
$272$	−7.35929	+	5.71358i	−0.446223	+	0.346437i
$273$	−0.140305	+	0.0581163i	−0.00849165	+	0.00351736i
$274$	11.9162	−	20.7072i	0.719882	−	1.25097i
$275$	0.286182	+	2.90566i	0.0172574	+	0.175218i
$276$	−13.0360	+	13.9978i	−0.784677	+	0.842567i
$277$	−2.26770	+	4.24256i	−0.136253	+	0.254911i	−0.940789	−	0.338993i	$-0.889914\pi$
$277$	−2.26770	+	4.24256i	−0.136253	+	0.254911i	0.804536	+	0.593903i	$0.202414\pi$
$278$	−0.401020	+	0.151583i	−0.0240516	+	0.00909132i
$279$	−0.0334267	+	0.00664899i	−0.00200121	+	0.000398065i
$280$	3.70826	+	0.349313i	0.221611	+	0.0208755i
$281$	1.10795	−	5.57006i	0.0660950	−	0.332282i	−0.933564	−	0.358412i	$-0.883318\pi$
$281$	1.10795	−	5.57006i	0.0660950	−	0.332282i	0.999659	+	0.0261299i	$0.00831836\pi$
$282$	18.9979	+	13.5730i	1.13131	+	0.808260i
$283$	0.652273	−	6.62263i	0.0387736	−	0.393675i	−0.956138	−	0.292918i	$-0.905374\pi$
$283$	0.652273	−	6.62263i	0.0387736	−	0.393675i	0.994911	−	0.100757i	$-0.0321263\pi$
$284$	−11.9446	−	13.5425i	−0.708779	−	0.803600i
$285$	2.20829	−	7.27974i	0.130808	−	0.431215i
$286$	0.259162	+	0.0875641i	0.0153246	+	0.00517778i
$287$	−1.16813	−	1.16813i	−0.0689525	−	0.0689525i
$288$	0.0428371	−	0.164527i	0.00252420	−	0.00969482i
$289$	−8.18457	+	8.18457i	−0.481446	+	0.481446i
$290$	−11.3018	+	5.59338i	−0.663666	+	0.328455i
$291$	16.3044	+	4.94588i	0.955780	+	0.289933i
$292$	−30.6364	−	15.0003i	−1.79286	−	0.877828i
$293$	−12.3316	−	1.21456i	−0.720419	−	0.0709551i	−0.268838	−	0.963185i	$-0.586640\pi$
$293$	−12.3316	−	1.21456i	−0.720419	−	0.0709551i	−0.451581	+	0.892230i	$0.649140\pi$
$294$	−2.12976	−	12.7869i	−0.124210	−	0.745749i
$295$	0.366022	+	0.0728063i	0.0213106	+	0.00423895i
$296$	15.7946	−	1.62349i	0.918043	−	0.0943636i
$297$	−2.94476	−	14.8043i	−0.170872	−	0.859034i
$298$	7.01943	−	15.5508i	0.406625	−	0.900835i
$299$	0.321019	+	0.171588i	0.0185650	+	0.00992320i
$300$	−1.44579	−	3.16700i	−0.0834726	−	0.182847i
$301$	0.727363	−	0.0716390i	0.0419245	−	0.00412920i
$302$	−20.7340	+	5.58718i	−1.19311	+	0.321506i
$303$	−3.16369	−	7.63782i	−0.181749	−	0.438781i
$304$	6.25036	+	16.3254i	0.358483	+	0.936325i
$305$	4.20894	−	10.1613i	0.241003	−	0.581833i
$306$	−0.0127828	+	0.0981700i	−0.000730741	+	0.00561200i
$307$	4.72638	−	5.75911i	0.269749	−	0.328690i	−0.620464	−	0.784235i	$-0.713056\pi$
$307$	4.72638	−	5.75911i	0.269749	−	0.328690i	0.890213	+	0.455545i	$0.150556\pi$
$308$	4.04220	−	6.54167i	0.230326	−	0.372747i
$309$	3.51580	+	11.5900i	0.200007	+	0.659334i
$310$	0.0502000	−	1.60294i	0.00285117	−	0.0910411i
$311$	8.60080	+	5.74687i	0.487707	+	0.325875i	0.774993	−	0.631970i	$-0.217753\pi$
$311$	8.60080	+	5.74687i	0.487707	+	0.325875i	−0.287287	+	0.957845i	$0.592753\pi$
$312$	−0.326179	+	0.00138734i	−0.0184662	+	7.85428e-5i
$313$	1.98649	+	2.97299i	0.112283	+	0.168043i	0.883355	−	0.468705i	$-0.155279\pi$
$313$	1.98649	+	2.97299i	0.112283	+	0.168043i	−0.771072	+	0.636748i	$0.780279\pi$
$314$	0.758098	−	3.27228i	0.0427819	−	0.184665i
$315$	0.0305938	−	0.0251077i	0.00172376	−	0.00141466i
$316$	1.95492	−	7.37948i	0.109973	−	0.415128i
$317$	2.83000	+	5.29456i	0.158949	+	0.297372i	0.948772	−	0.315963i	$-0.102327\pi$
$317$	2.83000	+	5.29456i	0.158949	+	0.297372i	−0.789823	+	0.613335i	$0.789827\pi$
$318$	−7.86737	−	6.87979i	−0.441180	−	0.385800i
$319$			26.0344i			1.45765i
$320$	7.08719	+	3.71102i	0.396186	+	0.207452i
$321$			3.00927i			0.167961i
$322$	6.73566	−	7.70255i	0.375364	−	0.429246i
$323$	−4.79847	−	8.97731i	−0.266994	−	0.499511i
$324$	9.13386	+	15.7172i	0.507437	+	0.873179i
$325$	−0.0512124	+	0.0420289i	−0.00284075	+	0.00233134i
$326$	−28.0421	−	6.49660i	−1.55311	−	0.359813i
$327$	−5.28309	−	7.90671i	−0.292156	−	0.437242i
$328$	−1.37177	−	3.27230i	−0.0757431	−	0.180682i
$329$	−10.3850	−	6.93904i	−0.572544	−	0.382562i
$330$	−7.18403	−	0.224985i	−0.395468	−	0.0123850i
$331$	4.89494	+	16.1364i	0.269050	+	0.886939i	0.982505	+	0.186238i	$0.0596295\pi$
$331$	4.89494	+	16.1364i	0.269050	+	0.886939i	−0.713455	+	0.700702i	$0.752870\pi$
$332$	15.6587	−	3.69794i	0.859381	−	0.202951i
$333$	0.107031	−	0.130417i	0.00586525	−	0.00714683i
$334$	15.9048	+	2.07097i	0.870272	+	0.113318i
$335$	0.958780	−	2.31470i	0.0523837	−	0.126466i
$336$	−2.03142	+	8.94128i	−0.110823	+	0.487787i
$337$	−10.1367	−	24.4722i	−0.552182	−	1.33309i	−0.915836	−	0.401552i	$-0.868471\pi$
$337$	−10.1367	−	24.4722i	−0.552182	−	1.33309i	0.363654	−	0.931534i	$-0.381529\pi$
$338$	−4.78189	−	17.7456i	−0.260100	−	0.965232i
$339$	5.64100	−	0.555590i	0.306377	−	0.0301755i
$340$	−4.36450	−	1.62857i	−0.236698	−	0.0883214i
$341$	−2.92003	−	1.56079i	−0.158128	−	0.0845213i
$342$	0.169300	+	0.0764197i	0.00915469	+	0.00413230i
$343$	3.15121	+	15.8422i	0.170149	+	0.855398i
$344$	1.50414	+	0.449300i	0.0810980	+	0.0242246i
$345$	−9.38017	−	1.86583i	−0.505011	−	0.100453i
$346$	−4.73396	+	0.788476i	−0.254499	+	0.0423887i
$347$	−23.9581	−	2.35966i	−1.28614	−	0.126673i	−0.568263	−	0.822847i	$-0.692384\pi$
$347$	−23.9581	−	2.35966i	−1.28614	−	0.126673i	−0.717873	+	0.696174i	$0.754884\pi$
$348$	−10.0617	−	29.3670i	−0.539365	−	1.57424i
$349$	−22.7538	−	6.90230i	−1.21798	−	0.369471i	−0.385077	−	0.922884i	$-0.625825\pi$
$349$	−22.7538	−	6.90230i	−1.21798	−	0.369471i	−0.832907	+	0.553413i	$0.813325\pi$
$350$	0.826059	+	1.66911i	0.0441547	+	0.0892178i
$351$	0.242185	−	0.242185i	0.0129269	−	0.0129269i
$352$	13.3568	−	9.71537i	0.711919	−	0.517831i
$353$	−4.00867	−	4.00867i	−0.213360	−	0.213360i	0.592333	−	0.805693i	$-0.298207\pi$
$353$	−4.00867	−	4.00867i	−0.213360	−	0.213360i	−0.805693	+	0.592333i	$0.798207\pi$
$354$	−0.294072	+	0.870362i	−0.0156298	+	0.0462592i
$355$	2.62090	−	8.63996i	0.139103	−	0.458561i
$356$	−15.3173	−	0.960337i	−0.811815	−	0.0508978i
$357$	0.523337	−	5.31353i	0.0276979	−	0.281222i
$358$	12.3474	−	17.2824i	0.652579	−	0.913405i
$359$	6.27335	−	31.5382i	0.331095	−	1.66452i	−0.353374	−	0.935482i	$-0.614966\pi$
$359$	6.27335	−	31.5382i	0.331095	−	1.66452i	0.684468	−	0.729042i	$-0.260034\pi$
$360$	0.0812399	−	0.0250217i	0.00428172	−	0.00131876i
$361$	−0.0971572	+	0.0193258i	−0.00511354	+	0.00101715i
$362$	12.2318	+	32.3598i	0.642887	+	1.70079i
$363$	2.03110	−	3.79992i	0.106605	−	0.199444i
$364$	0.174377	−	0.00620353i	0.00913982	−	0.000325153i
$365$	−1.67176	−	16.9736i	−0.0875038	−	0.888441i
$366$	23.4670	+	13.5044i	1.22664	+	0.705885i
$367$	−10.9929	+	4.55340i	−0.573824	+	0.237686i	−0.650674	−	0.759357i	$-0.725514\pi$
$367$	−10.9929	+	4.55340i	−0.573824	+	0.237686i	0.0768502	+	0.997043i	$0.475514\pi$
$368$	19.6553	−	9.83187i	1.02460	−	0.512522i
$369$	−0.0348323	−	0.0144280i	−0.00181329	−	0.000751091i
$370$	4.84183	+	6.29151i	0.251715	+	0.327080i
$371$	4.32169	+	3.54672i	0.224371	+	0.184137i
$372$	3.89702	+	0.632055i	0.202051	+	0.0327705i
$373$	5.82450	−	1.76684i	0.301581	−	0.0914836i	−0.135868	−	0.990727i	$-0.543382\pi$
$373$	5.82450	−	1.76684i	0.301581	−	0.0914836i	0.437449	+	0.899243i	$0.355882\pi$
$374$	−7.01021	+	6.58446i	−0.362489	+	0.340474i
$375$	0.967084	−	1.44734i	0.0499400	−	0.0747405i
$376$	−14.9987	−	22.2417i	−0.773497	−	1.14703i
$377$	−0.491183	+	0.328198i	−0.0252972	+	0.0169030i
$378$	−5.09578	−	8.16883i	−0.262099	−	0.420159i
$379$	18.5044	+	22.5477i	0.950509	+	1.15820i	0.987299	+	0.158876i	$0.0507870\pi$
$379$	18.5044	+	22.5477i	0.950509	+	1.15820i	−0.0367893	+	0.999323i	$0.511713\pi$
$380$	−5.30119	+	6.94936i	−0.271945	+	0.356495i
$381$	18.4302	−	9.85113i	0.944206	−	0.504688i
$382$	1.87376	+	27.9802i	0.0958699	+	1.43159i
$383$	14.3609			0.733806			0.366903	−	0.930259i	$-0.380418\pi$
$383$	14.3609			0.733806			0.366903	+	0.930259i	$0.380418\pi$
$384$	−11.3118	+	16.1211i	−0.577252	+	0.822677i
$385$	3.84490			0.195954
$386$	0.107241	+	1.60139i	0.00545841	+	0.0815084i
$387$	0.0147108	−	0.00786311i	0.000747794	−	0.000399704i
$388$	−15.5644	−	11.8730i	−0.790165	−	0.602763i
$389$	11.6029	+	14.1381i	0.588288	+	0.716831i	0.979041	−	0.203665i	$-0.0652852\pi$
$389$	11.6029	+	14.1381i	0.588288	+	0.716831i	−0.390753	+	0.920496i	$0.627785\pi$
$390$	−0.0863193	−	0.138375i	−0.00437095	−	0.00700688i
$391$	−10.6407	+	7.10986i	−0.538121	+	0.359561i
$392$	−2.84353	+	14.6201i	−0.143620	+	0.738427i
$393$	1.55378	−	2.32539i	0.0783776	−	0.117300i
$394$	−11.2063	+	10.5257i	−0.564566	+	0.530278i
$395$	3.65266	−	1.10802i	0.183785	−	0.0557506i
$396$	0.0280969	−	0.173235i	0.00141192	−	0.00870540i
$397$	16.8935	+	13.8641i	0.847860	+	0.695821i	0.954414	−	0.298486i	$-0.0964817\pi$
$397$	16.8935	+	13.8641i	0.847860	+	0.695821i	−0.106554	+	0.994307i	$0.533982\pi$
$398$	15.9198	+	20.6863i	0.797987	+	1.03691i
$399$	−9.25529	−	3.83367i	−0.463344	−	0.191923i
$400$	0.284244	+	3.98989i	0.0142122	+	0.199494i
$401$	23.3852	−	9.68645i	1.16780	−	0.483718i	0.287335	−	0.957830i	$-0.407231\pi$
$401$	23.3852	−	9.68645i	1.16780	−	0.483718i	0.880465	+	0.474112i	$0.157231\pi$
$402$	5.34570	+	3.07625i	0.266620	+	0.153429i
$403$	−0.00736390	−	0.0747669i	−0.000366822	−	0.00372440i
$404$	0.337703	+	9.49258i	0.0168013	+	0.472274i
$405$	−4.28465	+	8.01601i	−0.212906	+	0.398319i
$406$	5.87150	+	15.5334i	0.291398	+	0.770908i
$407$	16.0754	−	3.19759i	0.796826	−	0.158499i
$408$	5.36282	−	10.1366i	0.265499	−	0.501837i
$409$	−0.623322	+	3.13365i	−0.0308213	+	0.154949i	−0.993131	−	0.117006i	$-0.962670\pi$
$409$	−0.623322	+	3.13365i	−0.0308213	+	0.154949i	0.962310	+	0.271955i	$0.0876703\pi$
$410$	1.03133	−	1.44353i	0.0509336	−	0.0712910i
$411$	−2.88235	+	29.2650i	−0.142176	+	1.44354i
$412$	0.870753	−	13.8884i	0.0428989	−	0.684234i
$413$	0.142660	−	0.470286i	0.00701982	−	0.0231412i
$414$	0.0747501	−	0.221237i	0.00367376	−	0.0108732i
$415$	5.68846	+	5.68846i	0.279236	+	0.279236i
$416$	0.351676	+	0.129523i	0.0172423	+	0.00635038i
$417$	0.373131	−	0.373131i	0.0182723	−	0.0182723i
$418$	8.00413	+	16.1729i	0.391495	+	0.791043i
$419$	−15.7635	−	4.78179i	−0.770095	−	0.233606i	−0.119299	−	0.992858i	$-0.538065\pi$
$419$	−15.7635	−	4.78179i	−0.770095	−	0.233606i	−0.650796	+	0.759253i	$0.725565\pi$
$420$	−4.33707	+	1.48597i	−0.211628	+	0.0725077i
$421$	−29.0812	−	2.86425i	−1.41733	−	0.139595i	−0.639849	−	0.768501i	$-0.721003\pi$
$421$	−29.0812	−	2.86425i	−1.41733	−	0.139595i	−0.777481	+	0.628906i	$0.783503\pi$
$422$	27.2645	−	4.54111i	1.32722	−	0.221058i
$423$	−0.279573	−	0.0556104i	−0.0135933	−	0.00270387i
$424$	5.70551	+	10.5659i	0.277084	+	0.513126i
$425$	−0.454408	−	2.28446i	−0.0220420	−	0.110813i
$426$	20.2581	+	9.14423i	0.981508	+	0.443040i
$427$	−12.7734	−	6.82752i	−0.618148	−	0.330407i
$428$	1.20873	−	3.23936i	0.0584263	−	0.156580i
$429$	−0.335088	+	0.0330033i	−0.0161782	+	0.00159341i
$430$	0.204224	+	0.757874i	0.00984855	+	0.0365479i
$431$	0.786141	+	1.89791i	0.0378671	+	0.0914193i	0.941682	−	0.336505i	$-0.109245\pi$
$431$	0.786141	+	1.89791i	0.0378671	+	0.0914193i	−0.903815	+	0.427924i	$0.859245\pi$
$432$	−3.48420	−	20.3836i	−0.167634	−	0.980705i
$433$	−11.8233	+	28.5439i	−0.568190	+	1.37173i	0.334889	+	0.942257i	$0.391301\pi$
$433$	−11.8233	+	28.5439i	−0.568190	+	1.37173i	−0.903079	+	0.429474i	$0.858699\pi$
$434$	−2.09423	−	0.272690i	−0.100526	−	0.0130896i
$435$	9.84670	−	11.9982i	0.472113	−	0.575272i
$436$	2.51116	+	10.6333i	0.120263	+	0.509244i
$437$	6.97014	+	22.9775i	0.333427	+	1.09916i
$438$	41.9661	+	1.31427i	2.00522	+	0.0627982i
$439$	30.9263	+	20.6643i	1.47603	+	0.986254i	0.993915	+	0.110149i	$0.0351327\pi$
$439$	30.9263	+	20.6643i	1.47603	+	0.986254i	0.482119	+	0.876106i	$0.339867\pi$
$440$	7.64296	+	3.12780i	0.364364	+	0.149112i
$441$	0.0879248	+	0.131589i	0.00418689	+	0.00626613i
$442$	−0.212599	−	0.0492535i	−0.0101123	−	0.00234275i
$443$	−4.58871	+	3.76585i	−0.218016	+	0.178921i	−0.737062	−	0.675825i	$-0.763787\pi$
$443$	−4.58871	+	3.76585i	−0.218016	+	0.178921i	0.519046	+	0.854746i	$0.326287\pi$
$444$	−16.8974	+	9.81968i	−0.801913	+	0.466021i
$445$	−3.61735	−	6.76758i	−0.171479	−	0.320814i
$446$	−11.3282	+	12.9544i	−0.536408	+	0.613408i
$447$			21.0006i			0.993294i
$448$	5.77820	−	8.80899i	0.272994	−	0.416185i
$449$			6.72934i			0.317577i	0.987313	+	0.158789i	$0.0507589\pi$
$449$			6.72934i			0.317577i	−0.987313	+	0.158789i	$0.949241\pi$
$450$	0.0319951	+	0.0279788i	0.00150826	+	0.00131893i
$451$	−1.72659	−	3.23023i	−0.0813020	−	0.152105i
$452$	−6.29549	−	1.66775i	−0.296115	−	0.0784445i
$453$	20.4315	−	16.7677i	0.959956	−	0.787815i
$454$	−0.335451	+	1.44795i	−0.0157435	+	0.0679558i
$455$	0.0484699	+	0.0725403i	0.00227230	+	0.00340074i
$456$	−15.2792	−	15.1498i	−0.715514	−	0.709453i
$457$	−15.3002	−	10.2232i	−0.715712	−	0.478223i	0.143626	−	0.989632i	$-0.454124\pi$
$457$	−15.3002	−	10.2232i	−0.715712	−	0.478223i	−0.859338	+	0.511409i	$0.829124\pi$
$458$	−0.584479	+	18.6631i	−0.0273109	+	0.872068i
$459$	3.49549	+	11.5231i	0.163156	+	0.537852i
$460$	9.34794	+	5.77623i	0.435850	+	0.269318i
$461$	−3.38446	+	4.12398i	−0.157630	+	0.192073i	−0.845837	−	0.533442i	$-0.820898\pi$
$461$	−3.38446	+	4.12398i	−0.157630	+	0.192073i	0.688206	+	0.725515i	$0.258398\pi$
$462$	−1.22214	+	9.38586i	−0.0568589	+	0.436670i
$463$	−10.3323	+	24.9444i	−0.480182	+	1.15926i	0.479340	+	0.877629i	$0.340876\pi$
$463$	−10.3323	+	24.9444i	−0.480182	+	1.15926i	−0.959522	+	0.281633i	$0.909124\pi$
$464$	−0.964814	+	35.6540i	−0.0447904	+	1.65520i
$465$	0.755407	+	1.82371i	0.0350312	+	0.0845727i
$466$	30.9182	−	8.33151i	1.43226	−	0.385950i
$467$	26.6177	−	2.62161i	1.23172	−	0.121314i	0.538865	−	0.842392i	$-0.318853\pi$
$467$	26.6177	−	2.62161i	1.23172	−	0.121314i	0.692853	+	0.721079i	$0.256353\pi$
$468$	0.00362257	−	0.00165376i	0.000167453	−	7.64452e-5i
$469$	−2.90973	−	1.55528i	−0.134359	−	0.0718163i
$470$	5.51838	−	12.2254i	0.254544	−	0.563916i
$471$	0.806582	+	4.05496i	0.0371653	+	0.186843i
$472$	0.666156	−	0.818791i	0.0306623	−	0.0376879i
$473$	1.58935	+	0.316141i	0.0730782	+	0.0145362i
$474$	1.54378	+	9.26878i	0.0709083	+	0.425729i
$475$	−4.34920	−	0.428359i	−0.199555	−	0.0196545i
$476$	−2.69764	+	5.50960i	−0.123646	+	0.252532i
$477$	0.122099	+	0.0370385i	0.00559055	+	0.00169587i
$478$	−3.91335	+	1.93675i	−0.178992	+	0.0885850i
$479$	17.4273	−	17.4273i	0.796272	−	0.796272i	−0.186233	−	0.982506i	$-0.559628\pi$
$479$	17.4273	−	17.4273i	0.796272	−	0.796272i	0.982506	+	0.186233i	$0.0596280\pi$
$480$	−9.83015	−	0.574350i	−0.448683	−	0.0262154i
$481$	0.262979	+	0.262979i	0.0119908	+	0.0119908i
$482$	25.4688	+	8.60525i	1.16007	+	0.391958i
$483$	−3.65599	+	12.0522i	−0.166353	+	0.548393i
$484$	−3.71271	+	3.27463i	−0.168760	+	0.148847i
$485$	0.959393	−	9.74088i	0.0435638	−	0.442311i
$486$	−0.359388	−	0.256764i	−0.0163022	−	0.0116470i
$487$	4.71372	−	23.6974i	0.213599	−	1.07383i	−0.713968	−	0.700178i	$-0.753104\pi$
$487$	4.71372	−	23.6974i	0.213599	−	1.07383i	0.927567	−	0.373656i	$-0.121896\pi$
$488$	−19.8371	−	23.9630i	−0.897982	−	1.08475i
$489$	34.7494	−	6.91209i	1.57142	−	0.312575i
$490$	−6.96600	+	2.63310i	−0.314692	+	0.118951i
$491$	5.05809	−	9.46301i	0.228268	−	0.427060i	−0.741547	−	0.670901i	$-0.765908\pi$
$491$	5.05809	−	9.46301i	0.228268	−	0.427060i	0.969815	+	0.243841i	$0.0784075\pi$
$492$	3.19602	+	2.97643i	0.144088	+	0.134188i
$493$	−2.03573	−	20.6691i	−0.0916846	−	0.930889i
$494$	−0.204227	+	0.354892i	−0.00918859	+	0.0159673i
$495$	0.0810700	−	0.0335803i	0.00364383	−	0.00150932i
$496$	−3.94112	−	2.24570i	−0.176961	−	0.100835i
$497$	−10.9846	−	4.54999i	−0.492728	−	0.204095i
$498$	−15.6944	+	12.0781i	−0.703281	+	0.541232i
$499$	−24.7558	−	20.3166i	−1.10822	−	0.909496i	−0.111778	−	0.993733i	$-0.535655\pi$
$499$	−24.7558	−	20.3166i	−1.10822	−	0.909496i	−0.996446	+	0.0842374i	$0.973155\pi$
$500$	−1.62238	+	1.16956i	−0.0725552	+	0.0523043i
$501$	−18.8918	+	5.73078i	−0.844025	+	0.256032i
$502$	−19.7188	−	20.9938i	−0.880093	−	0.937000i
$503$	−5.40690	+	8.09200i	−0.241082	+	0.360805i	−0.932204	−	0.361934i	$-0.882117\pi$
$503$	−5.40690	+	8.09200i	−0.241082	+	0.360805i	0.691122	+	0.722738i	$0.257117\pi$
$504$	−0.0223056	−	0.109697i	−0.000993568	−	0.00488630i
$505$	−3.94889	+	2.63857i	−0.175723	+	0.117415i
$506$	19.2484	−	12.0073i	0.855696	−	0.533790i
$507$	14.3509	+	17.4867i	0.637348	+	0.776611i
$508$	−23.7963	+	3.20151i	−1.05579	+	0.142044i
$509$	−33.7093	+	18.0180i	−1.49414	+	0.798633i	−0.997590	−	0.0693777i	$-0.977899\pi$
$509$	−33.7093	+	18.0180i	−1.49414	+	0.798633i	−0.496546	+	0.868010i	$0.665399\pi$
$510$	5.72109	−	0.383127i	0.253334	−	0.0169651i
$511$	−22.4603			−0.993584
$512$	18.6521	−	12.8102i	0.824313	−	0.566134i
$513$	22.5933			0.997519
$514$	32.3829	−	2.16860i	1.42835	−	0.0956529i
$515$	6.13627	−	3.27991i	0.270397	−	0.144530i
$516$	−1.91498	+	0.257638i	−0.0843022	+	0.0113419i
$517$	−17.5677	−	21.4064i	−0.772628	−	0.941451i
$518$	8.87018	−	5.53329i	0.389733	−	0.243119i
$519$	4.91160	−	3.28182i	0.215595	−	0.144056i
$520$	0.0373383	+	0.183627i	0.00163739	+	0.00805258i
$521$	9.75136	−	14.5939i	0.427215	−	0.639372i	−0.553949	−	0.832551i	$-0.686880\pi$
$521$	9.75136	−	14.5939i	0.427215	−	0.639372i	0.981164	+	0.193179i	$0.0618797\pi$
$522$	0.259466	+	0.276243i	0.0113565	+	0.0120908i
$523$	−32.0507	+	9.72248i	−1.40148	+	0.425134i	−0.898428	−	0.439122i	$-0.855290\pi$
$523$	−32.0507	+	9.72248i	−1.40148	+	0.425134i	−0.503052	+	0.864256i	$0.667790\pi$
$524$	−2.60662	+	1.87909i	−0.113871	+	0.0820883i
$525$	−1.77196	−	1.45421i	−0.0773347	−	0.0634670i
$526$	−14.6127	+	11.2457i	−0.637146	+	0.490336i
$527$	2.44029	+	1.01080i	0.106301	+	0.0440313i
$528$	−10.0647	+	17.6632i	−0.438011	+	0.768692i
$529$	6.64011	−	2.75042i	0.288701	−	0.119584i
$530$	−2.99462	+	5.20386i	−0.130078	+	0.226041i
$531$	−0.00109936	−	0.0111620i	−4.77081e−5	−	0.000484388i
$532$	8.42310	+	7.84437i	0.365188	+	0.340097i
$533$	0.0391776	−	0.0732962i	0.00169697	−	0.00317481i
$534$	17.6703	−	6.67925i	0.764669	−	0.289039i
$535$	1.69555	−	0.337265i	0.0733048	−	0.0145812i
$536$	−4.51881	−	5.45867i	−0.195183	−	0.235779i
$537$	−5.10037	+	25.6413i	−0.220097	+	1.10650i
$538$	16.6946	+	11.9274i	0.719756	+	0.514227i
$539$	−1.50699	+	15.3008i	−0.0649108	+	0.659050i
$540$	7.75436	−	6.83939i	0.333695	−	0.294320i
$541$	−5.51235	+	18.1718i	−0.236995	+	0.781266i	0.755082	+	0.655631i	$0.227597\pi$
$541$	−5.51235	+	18.1718i	−0.236995	+	0.781266i	−0.992076	+	0.125636i	$0.959903\pi$
$542$	−41.5063	−	14.0239i	−1.78285	−	0.602379i
$543$	−30.1093	−	30.1093i	−1.29211	−	1.29211i
$544$	−9.84445	+	8.75758i	−0.422077	+	0.375478i
$545$	−3.86286	+	3.86286i	−0.165467	+	0.165467i
$546$	−0.192486	+	0.0952633i	−0.00823765	+	0.00407689i
$547$	−25.8395	−	7.83833i	−1.10482	−	0.335143i	−0.315375	−	0.948967i	$-0.602130\pi$
$547$	−25.8395	−	7.83833i	−1.10482	−	0.335143i	−0.789443	+	0.613824i	$0.789630\pi$
$548$	14.8576	−	30.3449i	0.634687	−	1.29627i
$549$	−0.328958	−	0.0323995i	−0.0140396	−	0.00138278i
$550$	0.678388	+	4.07300i	0.0289265	+	0.173673i
$551$	−38.2197	−	7.60237i	−1.62821	−	0.323872i
$552$	−17.0718	+	20.9834i	−0.726625	+	0.893114i
$553$	−0.980626	−	4.92994i	−0.0417005	−	0.209642i
$554$	−2.79894	+	6.20076i	−0.118916	+	0.263445i
$555$	−8.61789	−	4.60636i	−0.365809	−	0.195529i
$556$	−0.551536	+	0.251785i	−0.0233903	+	0.0106781i
$557$	40.4930	−	3.98821i	1.71574	−	0.168986i	0.808190	−	0.588922i	$-0.200447\pi$
$557$	40.4930	−	3.98821i	1.71574	−	0.168986i	0.907554	+	0.419936i	$0.137947\pi$
$558$	−0.0465386	+	0.0125407i	−0.00197014	+	0.000530891i
$559$	0.0140713	+	0.0339710i	0.000595151	+	0.00143682i
$560$	5.26556	+	0.142489i	0.222511	+	0.00602124i
$561$	4.53019	−	10.9368i	0.191265	−	0.461754i
$562$	1.03704	−	7.96435i	0.0437449	−	0.335956i
$563$	16.8547	−	20.5375i	0.710341	−	0.865553i	−0.285337	−	0.958427i	$-0.592106\pi$
$563$	16.8547	−	20.5375i	0.710341	−	0.865553i	0.995678	+	0.0928746i	$0.0296056\pi$
$564$	28.0896	+	17.3570i	1.18279	+	0.730862i
$565$	−0.945260	−	3.11611i	−0.0397674	−	0.131096i
$566$	0.294588	−	9.40652i	0.0123824	−	0.395386i
$567$	9.95219	+	6.64984i	0.417953	+	0.279267i
$568$	−18.1341	−	17.9805i	−0.760890	−	0.754445i
$569$	−20.6209	−	30.8613i	−0.864472	−	1.29377i	−0.954614	−	0.297845i	$-0.903732\pi$
$569$	−20.6209	−	30.8613i	−0.864472	−	1.29377i	0.0901418	−	0.995929i	$-0.471268\pi$
$570$	2.42811	−	10.4808i	0.101702	−	0.438991i
$571$	20.2600	−	16.6270i	0.847856	−	0.695818i	−0.106557	−	0.994307i	$-0.533983\pi$
$571$	20.2600	−	16.6270i	0.847856	−	0.695818i	0.954413	+	0.298489i	$0.0964826\pi$
$572$	0.373966	+	0.0990682i	0.0156363	+	0.00414225i
$573$	−16.2712	−	30.4412i	−0.679738	−	1.27170i
$574$	−1.75867	−	1.53791i	−0.0734057	−	0.0641912i
$575$			5.49429i			0.229128i
$576$	0.0448985	−	0.236204i	0.00187077	−	0.00984182i
$577$		−	47.2813i		−	1.96835i	−0.177211	−	0.984173i	$-0.556707\pi$
$577$		−	47.2813i		−	1.96835i	0.177211	−	0.984173i	$-0.443293\pi$
$578$	−10.7755	+	12.3223i	−0.448200	+	0.512539i
$579$	−0.931246	−	1.74224i	−0.0387013	−	0.0724050i
$580$	−15.4189	+	8.96052i	−0.640237	+	0.372065i
$581$	8.18915	−	6.72066i	0.339743	−	0.278820i
$582$	23.4737	+	5.43823i	0.973017	+	0.225422i
$583$	6.88660	+	10.3065i	0.285214	+	0.426852i
$584$	−44.6470	−	18.2713i	−1.84751	−	0.756072i
$585$	0.00165554	+	0.00110620i	6.84482e−5	+	4.57356e-5i
$586$	−17.5153	−	0.548533i	−0.723550	−	0.0226597i
$587$	8.33792	+	27.4864i	0.344143	+	1.13449i	0.942766	+	0.333456i	$0.108215\pi$
$587$	8.33792	+	27.4864i	0.344143	+	1.13449i	−0.598623	+	0.801031i	$0.704285\pi$
$588$	−4.21350	−	17.8418i	−0.173762	−	0.735783i
$589$	3.14399	−	3.83096i	0.129546	−	0.157852i
$590$	0.523356	+	0.0681464i	0.0215462	+	0.00280554i
$591$	7.24182	−	17.4833i	0.297889	−	0.719167i
$592$	22.1336	−	3.78334i	0.909686	−	0.155494i
$593$	14.5568	+	35.1431i	0.597774	+	1.44315i	0.875844	+	0.482594i	$0.160305\pi$
$593$	14.5568	+	35.1431i	0.597774	+	1.44315i	−0.278070	+	0.960561i	$0.589695\pi$
$594$	−5.55414	−	20.6114i	−0.227889	−	0.845697i
$595$	−3.05252	+	0.300647i	−0.125141	+	0.0123253i
$596$	8.43532	−	22.6063i	0.345524	−	0.925992i
$597$	−28.3354	−	15.1456i	−1.15969	−	0.619867i
$598$	0.469189	+	0.211785i	0.0191866	+	0.00866055i
$599$	3.14702	+	15.8211i	0.128584	+	0.646433i	0.990289	+	0.139024i	$0.0443966\pi$
$599$	3.14702	+	15.8211i	0.128584	+	0.646433i	−0.861705	+	0.507409i	$0.830603\pi$
$600$	−2.33935	−	4.33219i	−0.0955035	−	0.176861i
$601$	−22.5521	−	4.48588i	−0.919918	−	0.182983i	−0.287652	−	0.957735i	$-0.592875\pi$
$601$	−22.5521	−	4.48588i	−0.919918	−	0.182983i	−0.632265	+	0.774752i	$0.717875\pi$
$602$	1.01958	−	0.169818i	0.0415549	−	0.00692128i
$603$	−0.0749354	−	0.00738049i	−0.00305160	−	0.000300557i
$604$	−28.7288	+	9.84305i	−1.16896	+	0.400508i
$605$	−2.36867	−	0.718527i	−0.0963000	−	0.0292123i
$606$	−5.18587	−	10.4784i	−0.210661	−	0.425657i
$607$	−28.4702	+	28.4702i	−1.15557	+	1.15557i	−0.170152	+	0.985418i	$0.554426\pi$
$607$	−28.4702	+	28.4702i	−1.15557	+	1.15557i	−0.985418	+	0.170152i	$0.945574\pi$
$608$	10.3623	+	22.4453i	0.420245	+	0.910279i
$609$	−14.4531	−	14.4531i	−0.585669	−	0.585669i
$610$	4.97885	−	14.7358i	0.201588	−	0.596636i
$611$	0.182402	−	0.601299i	0.00737920	−	0.0243260i
$612$	−0.00876061	+	0.139731i	−0.000354127	+	0.00564829i
$613$	0.792776	−	8.04919i	0.0320199	−	0.325104i	−0.965810	−	0.259253i	$-0.916524\pi$
$613$	0.792776	−	8.04919i	0.0320199	−	0.325104i	0.997829	−	0.0658511i	$-0.0209762\pi$
$614$	6.12497	−	8.57303i	0.247184	−	0.345979i
$615$	−0.426013	+	2.14171i	−0.0171785	+	0.0863622i
$616$	5.08560	−	9.61262i	0.204905	−	0.387303i
$617$	11.7335	−	2.33394i	0.472373	−	0.0939609i	0.0468376	−	0.998903i	$-0.485086\pi$
$617$	11.7335	−	2.33394i	0.472373	−	0.0939609i	0.425536	+	0.904942i	$0.360086\pi$
$618$	6.05618	+	16.0219i	0.243615	+	0.644497i
$619$	2.60775	−	4.87876i	0.104814	−	0.196094i	−0.824047	−	0.566521i	$-0.808289\pi$
$619$	2.60775	−	4.87876i	0.104814	−	0.196094i	0.928861	+	0.370428i	$0.120789\pi$
$620$	−0.0806347	−	2.26658i	−0.00323837	−	0.0910281i
$621$	−2.78412	−	28.2676i	−0.111723	−	1.13434i
$622$	12.6792	+	7.29641i	0.508391	+	0.292559i
$623$	−9.33604	+	3.86712i	−0.374041	+	0.154933i
$624$	−0.460124	+	0.0327798i	−0.0184197	+	0.00131224i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	3.08397	+	4.00733i	0.123260	+	0.160165i
$627$	−17.1695	−	14.0906i	−0.685683	−	0.562726i
$628$	0.760504	−	4.68899i	0.0303474	−	0.187111i
$629$	−12.5124	+	3.79560i	−0.498903	+	0.151341i
$630$	0.0407969	−	0.0383192i	0.00162539	−	0.00152667i
$631$	−10.0081	+	14.9781i	−0.398415	+	0.596270i	−0.975389	−	0.220493i	$-0.929233\pi$
$631$	−10.0081	+	14.9781i	−0.398415	+	0.596270i	0.576974	+	0.816763i	$0.304233\pi$
$632$	2.06117	−	10.5976i	0.0819889	−	0.421549i
$633$	−28.2876	+	18.9012i	−1.12433	+	0.751255i
$634$	4.49359	+	7.20349i	0.178463	+	0.286087i
$635$	−7.61610	−	9.28025i	−0.302236	−	0.368275i
$636$	−11.7514	−	8.96433i	−0.465973	−	0.355459i
$637$	−0.307672	+	0.164454i	−0.0121904	+	0.00651590i
$638$	2.46011	+	36.7360i	0.0973968	+	1.45439i
$639$	−0.271351			−0.0107345
$640$	10.3511	+	4.56675i	0.409162	+	0.180516i
$641$	35.3665			1.39689			0.698446	−	0.715662i	$-0.253875\pi$
$641$	35.3665			1.39689			0.698446	+	0.715662i	$0.253875\pi$
$642$	0.284360	+	4.24624i	0.0112228	+	0.167586i
$643$	−28.1735	+	15.0590i	−1.11105	+	0.593871i	−0.921648	−	0.388028i	$-0.873156\pi$
$643$	−28.1735	+	15.0590i	−1.11105	+	0.593871i	−0.189407	+	0.981899i	$0.560656\pi$
$644$	8.77653	−	11.5052i	0.345844	−	0.453368i
$645$	−0.612897	−	0.746817i	−0.0241328	−	0.0294059i
$646$	−7.61921	−	12.2140i	−0.299774	−	0.480555i
$647$	16.0540	−	10.7269i	0.631148	−	0.421719i	−0.198427	−	0.980116i	$-0.563583\pi$
$647$	16.0540	−	10.7269i	0.631148	−	0.421719i	0.829574	+	0.558396i	$0.188583\pi$
$648$	14.3736	+	21.3147i	0.564647	+	0.837322i
$649$	0.605359	−	0.905983i	0.0237624	−	0.0355630i
$650$	−0.0682918	+	0.0641443i	−0.00267863	+	0.00251595i
$651$	2.48754	−	0.754587i	0.0974944	−	0.0295746i
$652$	−40.1828	−	6.51722i	−1.57368	−	0.255234i
$653$	22.6290	+	18.5711i	0.885541	+	0.726745i	0.962785	−	0.270268i	$-0.0871122\pi$
$653$	22.6290	+	18.5711i	0.885541	+	0.726745i	−0.0772444	+	0.997012i	$0.524612\pi$
$654$	−8.20186	−	10.6576i	−0.320718	−	0.416744i
$655$	−1.48436	−	0.614842i	−0.0579988	−	0.0240239i
$656$	−2.24485	−	4.48776i	−0.0876466	−	0.175218i
$657$	−0.473577	+	0.196162i	−0.0184760	+	0.00765301i
$658$	−15.3095	−	8.81002i	−0.596826	−	0.343450i
$659$	0.781694	+	7.93667i	0.0304505	+	0.309169i	0.998331	+	0.0577570i	$0.0183949\pi$
$659$	0.781694	+	7.93667i	0.0304505	+	0.309169i	−0.967880	+	0.251412i	$0.919105\pi$
$660$	−10.1583	+	0.361386i	−0.395412	+	0.0140669i
$661$	5.98139	−	11.1904i	0.232649	−	0.435256i	−0.738323	−	0.674447i	$-0.764382\pi$
$661$	5.98139	−	11.1904i	0.232649	−	0.435256i	0.970973	+	0.239191i	$0.0768821\pi$
$662$	8.43183	+	22.3068i	0.327712	+	0.866980i
$663$	0.263450	−	0.0524036i	0.0102316	−	0.00203519i
$664$	21.7458	−	6.69764i	0.843900	−	0.259919i
$665$	−1.12276	+	5.64448i	−0.0435386	+	0.218883i
$666$	0.138702	−	0.194140i	0.00537461	−	0.00752276i
$667$	−4.80198	+	48.7554i	−0.185934	+	1.88781i
$668$	22.6382	+	1.41933i	0.875899	+	0.0549156i
$669$	6.14875	−	20.2697i	0.237724	−	0.783672i
$670$	1.13416	−	3.35676i	0.0438165	−	0.129683i
$671$	−22.7069	−	22.7069i	−0.876592	−	0.876592i
$672$	−2.02154	+	12.8086i	−0.0779826	+	0.494102i
$673$	−0.369088	+	0.369088i	−0.0142273	+	0.0142273i	−0.714185	−	0.699957i	$-0.753202\pi$
$673$	−0.369088	+	0.369088i	−0.0142273	+	0.0142273i	0.699957	+	0.714185i	$0.253202\pi$
$674$	−16.6159	−	33.5737i	−0.640022	−	1.29321i
$675$	4.94719	+	1.50071i	0.190417	+	0.0577625i
$676$	−8.42436	−	24.5881i	−0.324014	−	0.945695i
$677$	3.70582	+	0.364991i	0.142426	+	0.0140278i	0.168979	−	0.985620i	$-0.445953\pi$
$677$	3.70582	+	0.364991i	0.142426	+	0.0140278i	−0.0265528	+	0.999647i	$0.508453\pi$
$678$	7.90725	−	1.31701i	0.303676	−	0.0505795i
$679$	−12.6419	−	2.51463i	−0.485151	−	0.0965026i
$680$	−6.31243	−	1.88557i	−0.242071	−	0.0723084i
$681$	−0.356905	−	1.79428i	−0.0136766	−	0.0687571i
$682$	−4.26780	−	1.92643i	−0.163422	−	0.0737667i
$683$	−23.0233	−	12.3062i	−0.880964	−	0.470885i	−0.0320926	−	0.999485i	$-0.510217\pi$
$683$	−23.0233	−	12.3062i	−0.880964	−	0.470885i	−0.848871	+	0.528600i	$0.822717\pi$
$684$	0.246113	+	0.0918343i	0.00941035	+	0.00351137i
$685$	16.8122	−	1.65585i	0.642360	−	0.0632669i
$686$	5.94352	+	22.0564i	0.226925	+	0.842117i
$687$	−8.79520	−	21.2335i	−0.335558	−	0.810109i
$688$	2.16488	+	0.491853i	0.0825354	+	0.0187517i
$689$	−0.107635	+	0.259854i	−0.00410057	+	0.00989965i
$690$	−13.4122	−	1.74641i	−0.510595	−	0.0664848i
$691$	17.2972	−	21.0767i	0.658016	−	0.801795i	−0.331920	−	0.943307i	$-0.607696\pi$
$691$	17.2972	−	21.0767i	0.658016	−	0.801795i	0.989937	+	0.141512i	$0.0451965\pi$
$692$	−6.60536	+	1.55991i	−0.251098	+	0.0592991i
$693$	−0.0335438	−	0.110579i	−0.00127422	−	0.00420056i
$694$	−34.0291	−	1.06570i	−1.29173	−	0.0404535i
$695$	−0.252056	−	0.168418i	−0.00956103	−	0.00638848i
$696$	−16.9727	−	40.4877i	−0.643347	−	1.53468i
$697$	1.62335	+	2.42951i	0.0614887	+	0.0920243i
$698$	−32.7591	−	7.58939i	−1.23995	−	0.287263i
$699$	−30.4671	+	25.0037i	−1.15237	+	0.945728i
$700$	1.32333	+	2.27715i	0.0500173	+	0.0860681i
$701$	−13.4731	−	25.2064i	−0.508872	−	0.952033i	−0.996860	−	0.0791826i	$-0.974769\pi$
$701$	−13.4731	−	25.2064i	−0.508872	−	0.952033i	0.487988	−	0.872850i	$-0.337731\pi$
$702$	0.318851	−	0.364622i	0.0120343	−	0.0137618i
$703$			24.5331i			0.925283i
$704$	17.9291	−	14.9710i	0.675727	−	0.564243i
$705$			16.5098i			0.621795i
$706$	−6.03525	−	5.27765i	−0.227140	−	0.198627i
$707$	2.94822	+	5.51572i	0.110879	+	0.207440i
$708$	−0.332707	+	1.25591i	−0.0125039	+	0.0472002i
$709$	−11.3981	+	9.35421i	−0.428066	+	0.351305i	−0.823624	−	0.567136i	$-0.808051\pi$
$709$	−11.3981	+	9.35421i	−0.428066	+	0.351305i	0.395558	+	0.918441i	$0.370551\pi$
$710$	2.88180	−	12.4391i	0.108152	−	0.466831i
$711$	−0.0637334	−	0.0953838i	−0.00239019	−	0.00357717i
$712$	−21.7043	+	0.0923151i	−0.813401	+	0.00345965i
$713$	−5.18053	−	3.46152i	−0.194012	−	0.129635i
$714$	0.236356	−	7.54712i	0.00884541	−	0.282444i
$715$	0.0561506	+	0.185104i	0.00209991	+	0.00692249i
$716$	15.7897	−	25.5532i	0.590088	−	0.954967i
$717$	3.40950	−	4.15449i	0.127330	−	0.155152i
$718$	5.87183	−	45.0949i	0.219135	−	1.68293i
$719$	14.9166	−	36.0118i	0.556294	−	1.34301i	−0.356386	−	0.934339i	$-0.615991\pi$
$719$	14.9166	−	36.0118i	0.556294	−	1.34301i	0.912680	−	0.408675i	$-0.134009\pi$
$720$	0.112269	−	0.0429836i	0.00418403	−	0.00160191i
$721$	−3.50637	−	8.46514i	−0.130584	−	0.315258i
$722$	−0.135268	+	0.0364505i	−0.00503414	+	0.00135655i
$723$	−32.9303	+	3.24336i	−1.22469	+	0.120622i
$724$	20.3175	+	44.5055i	0.755093	+	1.65403i
$725$	−7.86388	−	4.20333i	−0.292057	−	0.156108i
$726$	2.50692	−	5.55381i	0.0930404	−	0.206121i
$727$	−4.62163	−	23.2345i	−0.171407	−	0.861720i	−0.966782	−	0.255602i	$-0.917726\pi$
$727$	−4.62163	−	23.2345i	−0.171407	−	0.861720i	0.795375	−	0.606117i	$-0.207274\pi$
$728$	0.245469	−	0.0252312i	0.00909767	−	0.000935129i
$729$	−26.2106	−	5.21362i	−0.970764	−	0.193097i
$730$	−3.96286	−	23.7927i	−0.146672	−	0.880609i
$731$	−1.28652	−	0.126712i	−0.0475838	−	0.00468660i
$732$	34.3893	+	16.8379i	1.27107	+	0.622346i
$733$	8.22598	+	2.49532i	0.303833	+	0.0921669i	0.438520	−	0.898721i	$-0.355503\pi$
$733$	8.22598	+	2.49532i	0.303833	+	0.0921669i	−0.134687	+	0.990888i	$0.543003\pi$
$734$	−15.0813	+	7.46386i	−0.556660	+	0.275496i
$735$	6.48154	−	6.48154i	0.239075	−	0.239075i
$736$	26.8056	−	15.7306i	0.988066	−	0.579838i
$737$	−5.17255	−	5.17255i	−0.190533	−	0.190533i
$738$	−0.0505135	−	0.0170672i	−0.00185943	−	0.000628252i
$739$	4.85677	−	16.0106i	0.178659	−	0.588960i	−0.821174	−	0.570678i	$-0.806680\pi$
$739$	4.85677	−	16.0106i	0.178659	−	0.588960i	0.999833	−	0.0182819i	$-0.00581963\pi$
$740$	7.42659	+	8.42012i	0.273007	+	0.309530i
$741$	0.0493995	−	0.501562i	0.00181474	−	0.0184253i
$742$	6.43328	+	4.59624i	0.236173	+	0.168733i
$743$	−6.66366	+	33.5005i	−0.244466	+	1.22901i	0.642176	+	0.766557i	$0.278032\pi$
$743$	−6.66366	+	33.5005i	−0.244466	+	1.22901i	−0.886642	+	0.462457i	$0.846968\pi$
$744$	5.55863	+	0.523616i	0.203789	+	0.0191967i
$745$	11.8326	−	2.35365i	0.433513	−	0.0862311i
$746$	8.05172	−	3.04349i	0.294794	−	0.111430i
$747$	0.113973	−	0.213228i	0.00417004	−	0.00780159i
$748$	−9.26958	+	9.95344i	−0.338929	+	0.363934i
$749$	−0.223142	−	2.26560i	−0.00815343	−	0.0827832i
$750$	1.22784	−	2.13366i	0.0448344	−	0.0779103i
$751$	29.6409	−	12.2777i	1.08161	−	0.448019i	0.230539	−	0.973063i	$-0.425951\pi$
$751$	29.6409	−	12.2777i	1.08161	−	0.448019i	0.851075	+	0.525044i	$0.175951\pi$
$752$	−23.2656	−	29.9669i	−0.848410	−	1.09278i
$753$	32.7531	+	13.5668i	1.19359	+	0.494401i
$754$	−0.662072	+	0.509518i	−0.0241112	+	0.0185556i
$755$	−11.7375	−	9.63271i	−0.427171	−	0.350570i
$756$	−7.96233	−	11.0451i	−0.289587	−	0.401708i
$757$	−23.7709	+	7.21082i	−0.863967	+	0.262082i	−0.691008	−	0.722847i	$-0.742833\pi$
$757$	−23.7709	+	7.21082i	−0.863967	+	0.262082i	−0.172959	+	0.984929i	$0.555333\pi$
$758$	28.2414	+	30.0675i	1.02577	+	1.09210i
$759$	−15.5137	+	23.2179i	−0.563113	+	0.842758i
$760$	−6.82359	+	10.3068i	−0.247517	+	0.373869i
$761$	5.23034	−	3.49480i	0.189600	−	0.126687i	−0.457147	−	0.889391i	$-0.651129\pi$
$761$	5.23034	−	3.49480i	0.189600	−	0.126687i	0.646747	+	0.762704i	$0.276129\pi$
$762$	25.0751	−	15.6420i	0.908373	−	0.566650i
$763$	4.56380	+	5.56100i	0.165221	+	0.201322i
$764$	5.28795	+	39.3044i	0.191311	+	1.42199i
$765$	−0.0617368	+	0.0329990i	−0.00223210	+	0.00119308i
$766$	20.2639	−	1.35702i	0.732166	−	0.0490313i
$767$	0.0247242			0.000892740
$768$	−14.4382	+	23.8167i	−0.520993	+	0.859410i
$769$	−5.93499			−0.214021			−0.107011	−	0.994258i	$-0.534128\pi$
$769$	−5.93499			−0.214021			−0.107011	+	0.994258i	$0.534128\pi$
$770$	5.42535	−	0.363322i	0.195516	−	0.0130932i
$771$	−35.2312	+	18.8315i	−1.26882	+	0.678199i
$772$	0.302645	+	2.24951i	0.0108924	+	0.0809615i
$773$	−9.79401	−	11.9340i	−0.352266	−	0.429237i	0.566487	−	0.824071i	$-0.308302\pi$
$773$	−9.79401	−	11.9340i	−0.352266	−	0.429237i	−0.918753	+	0.394834i	$0.870802\pi$
$774$	0.0200148	−	0.0124854i	0.000719416	−	0.000448777i
$775$	0.942893	−	0.630021i	0.0338697	−	0.0226310i
$776$	−23.0842	−	15.2827i	−0.828674	−	0.548618i
$777$	−7.14914	+	10.6994i	−0.256474	+	0.383841i
$778$	17.7082	+	18.8532i	0.634870	+	0.675921i
$779$	5.24630	−	1.59145i	0.187968	−	0.0570195i
$780$	−0.134877	−	0.187098i	−0.00482936	−	0.00669917i
$781$	−20.3776	−	16.7235i	−0.729168	−	0.598412i
$782$	−14.3427	+	11.0379i	−0.512893	+	0.394713i
$783$	42.5889	+	17.6409i	1.52200	+	0.630434i
$784$	−2.63085	+	20.8984i	−0.0939589	+	0.746373i
$785$	2.19434	−	0.908923i	0.0783192	−	0.0324409i
$786$	1.97272	−	3.42807i	0.0703647	−	0.122275i
$787$	4.96298	+	50.3900i	0.176911	+	1.79621i	0.517175	+	0.855880i	$0.326984\pi$
$787$	4.96298	+	50.3900i	0.176911	+	1.79621i	−0.340263	+	0.940330i	$0.610516\pi$
$788$	−14.8181	+	15.9113i	−0.527872	+	0.566816i
$789$	10.6988	−	20.0160i	0.380887	−	0.712590i
$790$	5.04939	−	1.90863i	0.179649	−	0.0679062i
$791$	−4.20576	+	0.836579i	−0.149540	+	0.0297453i
$792$	0.0232764	−	0.247099i	0.000827091	−	0.00878029i
$793$	0.142154	−	0.714654i	0.00504802	−	0.0253781i
$794$	25.1477	+	17.9667i	0.892458	+	0.637614i
$795$	0.724356	−	7.35451i	0.0256903	−	0.260838i
$796$	24.4184	+	27.6851i	0.865488	+	0.981273i
$797$	−8.95516	+	29.5212i	−0.317208	+	1.04569i	0.642873	+	0.765973i	$0.277742\pi$
$797$	−8.95516	+	29.5212i	−0.317208	+	1.04569i	−0.960081	+	0.279722i	$0.909758\pi$
$798$	−13.4220	−	4.53493i	−0.475133	−	0.160535i
$799$	15.6211	+	15.6211i	0.552635	+	0.552635i
$800$	0.778106	+	5.60308i	0.0275102	+	0.198099i
$801$	−0.163077	+	0.163077i	−0.00576204	+	0.00576204i
$802$	32.0824	−	15.8779i	1.13287	−	0.560667i
$803$	−47.6537	−	14.4556i	−1.68166	−	0.510127i
$804$	7.83376	+	3.83561i	0.276275	+	0.135271i
$805$	7.20044	+	0.709181i	0.253782	+	0.0249954i
$806$	−0.0174559	−	0.104804i	−0.000614858	−	0.00369157i
$807$	−24.7692	−	4.92689i	−0.871915	−	0.173435i
$808$	1.37351	+	13.3626i	0.0483201	+	0.470096i
$809$	−2.92068	−	14.6832i	−0.102686	−	0.516235i	−0.997554	−	0.0699047i	$-0.977730\pi$
$809$	−2.92068	−	14.6832i	−0.102686	−	0.516235i	0.894868	−	0.446331i	$-0.147270\pi$
$810$	−5.28839	+	11.7159i	−0.185815	+	0.411655i
$811$	−23.2546	−	12.4299i	−0.816581	−	0.436472i	0.00954670	−	0.999954i	$-0.496961\pi$
$811$	−23.2546	−	12.4299i	−0.816581	−	0.436472i	−0.826128	+	0.563483i	$0.809461\pi$
$812$	9.75282	+	21.3636i	0.342257	+	0.749715i
$813$	53.6663	−	5.28567i	1.88216	−	0.185377i
$814$	22.3810	−	6.03100i	0.784455	−	0.211387i
$815$	−7.78911	−	18.8046i	−0.272841	−	0.658696i
$816$	6.60938	−	14.8101i	0.231374	−	0.518456i
$817$	−0.928217	+	2.24091i	−0.0324742	+	0.0783996i
$818$	−0.583427	+	4.48065i	−0.0203991	+	0.156662i
$819$	0.00166340	−	0.00202685i	5.81238e−5	−	7.08240e-5i
$820$	1.31885	−	2.13436i	0.0460562	−	0.0745349i
$821$	8.13415	+	26.8147i	0.283884	+	0.935840i	0.976679	+	0.214705i	$0.0688791\pi$
$821$	8.13415	+	26.8147i	0.283884	+	0.935840i	−0.692795	+	0.721135i	$0.743621\pi$
$822$	−1.30177	+	41.5669i	−0.0454043	+	1.44981i
$823$	13.9155	+	9.29802i	0.485063	+	0.324109i	0.773942	−	0.633257i	$-0.218282\pi$
$823$	13.9155	+	9.29802i	0.485063	+	0.324109i	−0.288879	+	0.957366i	$0.593282\pi$
$824$	−0.0837035	−	19.6796i	−0.00291595	−	0.685571i
$825$	−2.82361	−	4.22583i	−0.0983055	−	0.147125i
$826$	0.156861	−	0.677078i	0.00545788	−	0.0235586i
$827$	−6.60612	+	5.42150i	−0.229717	+	0.188524i	−0.742210	−	0.670168i	$-0.766222\pi$
$827$	−6.60612	+	5.42150i	−0.229717	+	0.188524i	0.512493	+	0.858692i	$0.328722\pi$
$828$	0.0845706	−	0.319240i	0.00293903	−	0.0110944i
$829$	16.2859	+	30.4688i	0.565632	+	1.05822i	0.988384	+	0.151978i	$0.0485643\pi$
$829$	16.2859	+	30.4688i	0.565632	+	1.05822i	−0.422751	+	0.906246i	$0.638936\pi$
$830$	8.56425	+	7.48919i	0.297269	+	0.259954i
$831$		−	8.37382i		−	0.290484i
$832$	0.508473	+	0.149532i	0.0176281	+	0.00518410i
$833$		−	12.2653i		−	0.424968i
$834$	0.491248	−	0.561766i	0.0170105	−	0.0194524i
$835$	5.34627	+	10.0022i	0.185015	+	0.346139i
$836$	12.8225	+	22.0645i	0.443476	+	0.763117i
$837$	−4.53185	+	3.71919i	−0.156644	+	0.128554i
$838$	−22.6949	−	5.25780i	−0.783983	−	0.181628i
$839$	−8.80289	−	13.1745i	−0.303909	−	0.454833i	0.647810	−	0.761802i	$-0.275685\pi$
$839$	−8.80289	−	13.1745i	−0.303909	−	0.454833i	−0.951719	+	0.306969i	$0.900685\pi$
$840$	−5.97943	+	2.50661i	−0.206310	+	0.0864862i
$841$	−41.9964	−	28.0611i	−1.44815	−	0.967624i
$842$	−41.3057	−	1.29359i	−1.42349	−	0.0445800i
$843$	2.86969	+	9.46011i	0.0988374	+	0.325823i
$844$	38.0426	−	8.98410i	1.30948	−	0.309245i
$845$	8.24433	−	10.0457i	0.283614	−	0.345584i
$846$	−0.399747	−	0.0520512i	−0.0137436	−	0.00178956i
$847$	−1.24739	+	3.01147i	−0.0428608	+	0.103475i
$848$	9.04920	+	14.3699i	0.310751	+	0.493466i
$849$	4.43294	+	10.7021i	0.152138	+	0.367294i
$850$	−0.857064	−	3.18056i	−0.0293970	−	0.109092i
$851$	30.6946	−	3.02315i	1.05220	−	0.103632i
$852$	29.4493	+	10.9887i	1.00892	+	0.376467i
$853$	10.9664	+	5.86165i	0.375481	+	0.200699i	0.648333	−	0.761357i	$-0.275467\pi$
$853$	10.9664	+	5.86165i	0.375481	+	0.200699i	−0.272851	+	0.962056i	$0.587967\pi$
$854$	−18.6691	−	8.42698i	−0.638843	−	0.288365i
$855$	0.0256239	+	0.128820i	0.000876320	+	0.00440556i
$856$	1.39949	−	4.68513i	0.0478334	−	0.160134i
$857$	54.3662	+	10.8141i	1.85711	+	0.369403i	0.991371	−	0.131086i	$-0.0418464\pi$
$857$	54.3662	+	10.8141i	1.85711	+	0.369403i	0.865743	+	0.500489i	$0.166846\pi$
$858$	−0.469709	+	0.0782334i	−0.0160356	+	0.00267085i
$859$	46.9775	+	4.62688i	1.60285	+	0.157867i	0.859536	−	0.511075i	$-0.170752\pi$
$859$	46.9775	+	4.62688i	1.60285	+	0.157867i	0.743315	+	0.668942i	$0.233252\pi$
$860$	0.359786	+	1.05010i	0.0122686	+	0.0358082i
$861$	2.75179	+	0.834748i	0.0937809	+	0.0284481i
$862$	1.28863	+	2.60377i	0.0438909	+	0.0886848i
$863$	−11.5186	+	11.5186i	−0.392099	+	0.392099i	−0.875435	−	0.483336i	$-0.839425\pi$
$863$	−11.5186	+	11.5186i	−0.392099	+	0.392099i	0.483336	+	0.875435i	$0.339425\pi$
$864$	−6.84253	−	28.4331i	−0.232788	−	0.967312i
$865$	−2.39959	−	2.39959i	−0.0815884	−	0.0815884i
$866$	−13.9860	+	41.3942i	−0.475264	+	1.40663i
$867$	5.84871	−	19.2806i	0.198633	−	0.654804i
$868$	−2.98084	−	0.186887i	−0.101176	−	0.00634337i
$869$	1.09236	−	11.0909i	0.0370559	−	0.376235i
$870$	12.7605	−	17.8606i	0.432620	−	0.605532i
$871$	0.0323820	−	0.162796i	0.00109722	−	0.00551612i
$872$	4.54817	+	14.7669i	0.154020	+	0.500070i
$873$	−0.288518	+	0.0573897i	−0.00976485	+	0.00194235i
$874$	12.0065	+	31.7638i	0.406125	+	1.07443i
$875$	−0.620769	+	1.16138i	−0.0209858	+	0.0392617i
$876$	59.3406	−	2.11107i	2.00493	−	0.0713264i
$877$	1.33772	+	13.5821i	0.0451717	+	0.458636i	0.990990	+	0.133938i	$0.0427624\pi$
$877$	1.33772	+	13.5821i	0.0451717	+	0.458636i	−0.945818	+	0.324697i	$0.894738\pi$
$878$	45.5914	+	26.2361i	1.53863	+	0.885425i
$879$	19.9276	−	8.25430i	0.672143	−	0.278411i
$880$	11.0802	+	3.69127i	0.373513	+	0.124433i
$881$	6.28138	+	2.60183i	0.211625	+	0.0876579i	0.485978	−	0.873971i	$-0.338464\pi$
$881$	6.28138	+	2.60183i	0.211625	+	0.0876579i	−0.274353	+	0.961629i	$0.588464\pi$
$882$	0.136501	+	0.177370i	0.00459623	+	0.00597237i
$883$	−33.9125	−	27.8313i	−1.14125	−	0.936597i	−0.142661	−	0.989772i	$-0.545566\pi$
$883$	−33.9125	−	27.8313i	−1.14125	−	0.936597i	−0.998585	+	0.0531749i	$0.983066\pi$
$884$	−0.304643	−	0.0494098i	−0.0102463	−	0.00166183i
$885$	−0.621646	+	0.188574i	−0.0208964	+	0.00633885i
$886$	−6.11906	+	5.74743i	−0.205574	+	0.193089i
$887$	21.8464	−	32.6954i	0.733530	−	1.09780i	−0.257773	−	0.966205i	$-0.582989\pi$
$887$	21.8464	−	32.6954i	0.733530	−	1.09780i	0.991303	−	0.131599i	$-0.0420113\pi$
$888$	−22.9152	+	15.4528i	−0.768982	+	0.518562i
$889$	−13.1451	+	8.78328i	−0.440873	+	0.294582i
$890$	−5.74377	−	9.20760i	−0.192532	−	0.308639i
$891$	16.8356	+	20.5142i	0.564013	+	0.687252i
$892$	−14.7606	+	19.3498i	−0.494222	+	0.647879i
$893$	36.5555	−	19.5393i	1.22328	−	0.653858i
$894$	1.98444	+	29.6330i	0.0663697	+	0.991075i
$895$	15.0190			0.502029
$896$	7.32094	−	12.9760i	0.244575	−	0.433496i
$897$	−0.633616			−0.0211558
$898$	0.635887	+	9.49546i	0.0212198	+	0.316868i
$899$	8.91771	−	4.76661i	0.297422	−	0.158975i
$900$	0.0477906	+	0.0364562i	0.00159302	+	0.00121521i
$901$	−6.27327	−	7.64400i	−0.208993	−	0.254659i
$902$	−2.74155	−	4.39487i	−0.0912837	−	0.146333i
$903$	−1.05784	+	0.706824i	−0.0352026	+	0.0235216i
$904$	−9.04086	−	1.75840i	−0.300694	−	0.0584834i
$905$	−13.5903	+	20.3393i	−0.451757	+	0.676102i
$906$	27.2455	−	25.5908i	0.905170	−	0.850197i
$907$	1.05174	−	0.319042i	0.0349224	−	0.0105936i	−0.272775	−	0.962078i	$-0.587942\pi$
$907$	1.05174	−	0.319042i	0.0349224	−	0.0105936i	0.307698	+	0.951484i	$0.400442\pi$
$908$	−0.336516	+	2.07484i	−0.0111677	+	0.0688558i
$909$	0.110336	+	0.0905507i	0.00365962	+	0.00300338i
$910$	0.0752483	+	0.0977781i	0.00249446	+	0.00324131i
$911$	16.3705	+	6.78088i	0.542378	+	0.224660i	0.637015	−	0.770851i	$-0.280169\pi$
$911$	16.3705	+	6.78088i	0.542378	+	0.224660i	−0.0946366	+	0.995512i	$0.530169\pi$
$912$	−22.9913	−	19.9333i	−0.761319	−	0.660059i
$913$	21.7003	−	8.98856i	0.718176	−	0.297478i
$914$	−22.5554	−	12.9798i	−0.746066	−	0.429332i
$915$	1.87655	+	19.0529i	0.0620368	+	0.629870i
$916$	0.938830	+	26.3898i	0.0310198	+	0.871944i
$917$	−0.997365	+	1.86594i	−0.0329359	+	0.0616188i
$918$	6.02119	+	15.9294i	0.198729	+	0.525748i
$919$	6.54715	−	1.30231i	0.215971	−	0.0429592i	−0.0859190	−	0.996302i	$-0.527383\pi$
$919$	6.54715	−	1.30231i	0.215971	−	0.0429592i	0.301890	+	0.953343i	$0.402383\pi$
$920$	13.7363	+	7.26724i	0.452871	+	0.239594i
$921$	−2.53006	+	12.7195i	−0.0833684	+	0.419121i
$922$	−4.38597	+	6.13897i	−0.144444	+	0.202176i
$923$	0.0586298	−	0.595278i	0.00192982	−	0.0195938i
$924$	−0.837586	+	13.3594i	−0.0275546	+	0.439493i
$925$	−1.62956	+	5.37194i	−0.0535796	+	0.176628i
$926$	−12.2223	+	36.1742i	−0.401650	+	1.18876i
$927$	−0.147864	−	0.147864i	−0.00485651	−	0.00485651i
$928$	2.00771	+	50.4008i	0.0659062	+	1.65449i
$929$	−35.7526	+	35.7526i	−1.17301	+	1.17301i	−0.191516	+	0.981490i	$0.561340\pi$
$929$	−35.7526	+	35.7526i	−1.17301	+	1.17301i	−0.981490	+	0.191516i	$0.938660\pi$
$930$	1.23825	+	2.50198i	0.0406038	+	0.0820430i
$931$	−22.0221	−	6.68034i	−0.721746	−	0.218939i
$932$	42.8399	−	14.6778i	1.40327	−	0.480787i
$933$	−17.9193	−	1.76490i	−0.586652	−	0.0577802i
$934$	37.3112	−	6.21446i	1.22086	−	0.203343i
$935$	−6.66999	−	1.32674i	−0.218132	−	0.0433892i
$936$	0.00495537	−	0.00267586i	0.000161971	−	8.74632e-5i
$937$	9.48957	+	47.7073i	0.310011	+	1.55853i	0.750561	+	0.660802i	$0.229784\pi$
$937$	9.48957	+	47.7073i	0.310011	+	1.55853i	−0.440550	+	0.897728i	$0.645216\pi$
$938$	−4.25275	−	1.91963i	−0.138857	−	0.0626782i
$939$	−5.48911	−	2.93399i	−0.179130	−	0.0957471i
$940$	6.63150	−	17.7722i	0.216296	−	0.579664i
$941$	2.30091	−	0.226619i	0.0750074	−	0.00738758i	−0.0604438	−	0.998172i	$-0.519252\pi$
$941$	2.30091	−	0.226619i	0.0750074	−	0.00738758i	0.135451	+	0.990784i	$0.456752\pi$
$942$	1.52130	+	5.64555i	0.0495667	+	0.183942i
$943$	−2.63763	−	6.36780i	−0.0858930	−	0.207364i
$944$	0.862610	−	1.21831i	0.0280756	−	0.0396525i
$945$	2.60530	−	6.28974i	0.0847503	−	0.204605i
$946$	2.27253	+	0.295906i	0.0738862	+	0.00962075i
$947$	6.86489	−	8.36490i	0.223079	−	0.271823i	−0.649429	−	0.760422i	$-0.724992\pi$
$947$	6.86489	−	8.36490i	0.223079	−	0.271823i	0.872508	+	0.488599i	$0.162492\pi$
$948$	3.05421	+	12.9329i	0.0991961	+	0.420040i
$949$	−0.328008	−	1.08130i	−0.0106476	−	0.0351004i
$950$	−6.17743	−	0.193461i	−0.200422	−	0.00627671i
$951$	−8.68904	−	5.80583i	−0.281762	−	0.188267i
$952$	−3.28588	+	8.02925i	−0.106496	+	0.260230i
$953$	25.2598	+	37.8040i	0.818247	+	1.22459i	0.971649	+	0.236429i	$0.0759770\pi$
$953$	25.2598	+	37.8040i	0.818247	+	1.22459i	−0.153402	+	0.988164i	$0.549023\pi$
$954$	0.175789	+	0.0407255i	0.00569137	+	0.00131854i
$955$	−15.3282	+	12.5796i	−0.496010	+	0.407065i
$956$	−5.33893	+	3.10265i	−0.172673	+	0.100347i
$957$	−21.3629	−	39.9671i	−0.690564	−	1.29195i
$958$	22.9440	−	26.2376i	0.741288	−	0.847698i
$959$		−	22.2466i		−	0.718380i
$960$	−13.9251	+	0.118458i	−0.449432	+	0.00382322i
$961$		−	29.7140i		−	0.958517i
$962$	0.395927	+	0.346227i	0.0127652	+	0.0111628i
$963$	−0.0244921	−	0.0458215i	−0.000789247	−	0.00147658i
$964$	36.7510	+	9.73580i	1.18367	+	0.313569i
$965$	−0.877280	+	0.719965i	−0.0282406	+	0.0231765i
$966$	−4.01992	+	17.3517i	−0.129339	+	0.558282i
$967$	9.85036	+	14.7421i	0.316766	+	0.474074i	0.955349	−	0.295479i	$-0.0954792\pi$
$967$	9.85036	+	14.7421i	0.316766	+	0.474074i	−0.638583	+	0.769553i	$0.720479\pi$
$968$	−4.92940	+	4.97151i	−0.158437	+	0.159790i
$969$	14.7329	+	9.84420i	0.473289	+	0.316241i
$970$	0.433294	−	13.8356i	0.0139122	−	0.444233i
$971$	7.09762	+	23.3977i	0.227773	+	0.750868i	0.994105	+	0.108423i	$0.0345801\pi$
$971$	7.09762	+	23.3977i	0.227773	+	0.750868i	−0.766331	+	0.642445i	$0.777920\pi$
$972$	−0.531379	−	0.328347i	−0.0170440	−	0.0105317i
$973$	−0.253252	+	0.308589i	−0.00811889	+	0.00989289i
$974$	4.41202	−	33.8838i	0.141370	−	1.08571i
$975$	0.0441321	−	0.106544i	0.00141336	−	0.00341215i
$976$	−30.2555	−	31.9385i	−0.968456	−	1.02233i
$977$	6.87366	+	16.5945i	0.219908	+	0.530905i	0.994877	−	0.101095i	$-0.0322345\pi$
$977$	6.87366	+	16.5945i	0.219908	+	0.530905i	−0.774969	+	0.631999i	$0.782235\pi$
$978$	48.3801	−	13.0370i	1.54703	−	0.416876i
$979$	−22.2971	+	2.19607i	−0.712618	+	0.0701868i
$980$	−9.58058	+	4.37369i	−0.306040	+	0.139712i
$981$	0.144796	+	0.0773953i	0.00462299	+	0.00247104i
$982$	6.24302	−	13.8308i	0.199223	−	0.441358i
$983$	−9.92785	−	49.9107i	−0.316649	−	1.59190i	−0.731387	−	0.681963i	$-0.761127\pi$
$983$	−9.92785	−	49.9107i	−0.316649	−	1.59190i	0.414738	−	0.909941i	$-0.363873\pi$
$984$	4.79101	+	3.89790i	0.152732	+	0.124260i
$985$	−10.6625	−	2.12089i	−0.339734	−	0.0675773i
$986$	−4.82564	−	28.9728i	−0.153680	−	0.922682i
$987$	21.6366	+	2.13102i	0.688701	+	0.0678311i
$988$	−0.254639	+	0.520069i	−0.00810115	+	0.0165456i
$989$	2.91810	+	0.885196i	0.0927902	+	0.0281476i
$990$	0.111221	−	0.0550443i	0.00353483	−	0.00174942i
$991$	25.8626	−	25.8626i	0.821551	−	0.821551i	−0.164779	−	0.986330i	$-0.552691\pi$
$991$	25.8626	−	25.8626i	0.821551	−	0.821551i	0.986330	+	0.164779i	$0.0526912\pi$
$992$	−5.77333	−	2.79639i	−0.183304	−	0.0887855i
$993$	−20.7555	−	20.7555i	−0.658656	−	0.658656i
$994$	−15.9299	−	5.38228i	−0.505264	−	0.170716i
$995$	−5.35794	+	17.6628i	−0.169858	+	0.559948i
$996$	−21.0043	+	18.5259i	−0.665545	+	0.587014i
$997$	4.19333	−	42.5756i	0.132804	−	1.34838i	−0.665621	−	0.746290i	$-0.731833\pi$
$997$	4.19333	−	42.5756i	0.132804	−	1.34838i	0.798426	−	0.602094i	$-0.205667\pi$
$998$	−36.8516	−	26.3285i	−1.16652	−	0.833414i
$999$	5.66181	−	28.4639i	0.179132	−	0.900557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.61	✓	1024
128.109	even	32	inner	640.2.bm.a.621.61	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.61	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.61	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41105 - 0.0944946i) q^{2} +(-1.53516 + 0.820563i) q^{3} +(1.98214 - 0.266674i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-2.08866 + 1.30292i) q^{6} +(1.09494 - 0.731615i) q^{7} +(2.77171 - 0.563593i) q^{8} +(0.0166972 - 0.0249891i) q^{9} +O(q^{10})\)	\(q+(1.41105 - 0.0944946i) q^{2} +(-1.53516 + 0.820563i) q^{3} +(1.98214 - 0.266674i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-2.08866 + 1.30292i) q^{6} +(1.09494 - 0.731615i) q^{7} +(2.77171 - 0.563593i) q^{8} +(0.0166972 - 0.0249891i) q^{9} +(0.968208 + 1.03081i) q^{10} +(2.79400 - 0.847549i) q^{11} +(-2.82409 + 2.03586i) q^{12} +(0.0512124 + 0.0420289i) q^{13} +(1.47588 - 1.13581i) q^{14} +(-1.60820 - 0.666139i) q^{15} +(3.85777 - 1.05717i) q^{16} +(-2.15192 + 0.891354i) q^{17} +(0.0211993 - 0.0368387i) q^{18} +(0.428359 + 4.34920i) q^{19} +(1.46360 + 1.36304i) q^{20} +(-1.08058 + 2.02162i) q^{21} +(3.86239 - 1.45995i) q^{22} +(5.38872 - 1.07188i) q^{23} +(-3.79256 + 3.13957i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(0.0762349 + 0.0544657i) q^{26} +(0.506729 - 5.14491i) q^{27} +(1.97522 - 1.74216i) q^{28} +(-2.58840 + 8.53281i) q^{29} +(-2.33220 - 0.787991i) q^{30} +(-0.801865 - 0.801865i) q^{31} +(5.34362 - 1.85626i) q^{32} +(-3.59378 + 3.59378i) q^{33} +(-2.95224 + 1.46109i) q^{34} +(1.26017 + 0.382268i) q^{35} +(0.0264322 - 0.0539846i) q^{36} +(5.58663 + 0.550235i) q^{37} +(1.01541 + 6.09648i) q^{38} +(-0.113107 - 0.0224983i) q^{39} +(2.19402 + 1.78502i) q^{40} +(-0.244736 - 1.23037i) q^{41} +(-1.33372 + 2.95472i) q^{42} +(0.489478 + 0.261632i) q^{43} +(5.31208 - 2.42505i) q^{44} +(0.0299094 - 0.00294582i) q^{45} +(7.50248 - 2.02169i) q^{46} +(-3.62958 - 8.76258i) q^{47} +(-5.05484 + 4.78847i) q^{48} +(-2.01515 + 4.86501i) q^{49} +(-0.182604 + 1.40238i) q^{50} +(2.57214 - 3.13416i) q^{51} +(0.112718 + 0.0696502i) q^{52} +(1.23239 + 4.06265i) q^{53} +(0.228856 - 7.30762i) q^{54} +(2.42766 + 1.62211i) q^{55} +(2.62252 - 2.64492i) q^{56} +(-4.22640 - 6.32525i) q^{57} +(-2.84606 + 12.2848i) q^{58} +(0.288482 - 0.236751i) q^{59} +(-3.36533 - 0.891516i) q^{60} +(-5.18465 - 9.69979i) q^{61} +(-1.20725 - 1.05570i) q^{62} -0.0395774i q^{63} +(7.36473 - 3.12423i) q^{64} +0.0662505i q^{65} +(-4.73142 + 5.41060i) q^{66} +(-1.18104 - 2.20958i) q^{67} +(-4.02771 + 2.34065i) q^{68} +(-7.39302 + 6.06730i) q^{69} +(1.81429 + 0.420321i) q^{70} +(-5.01609 - 7.50712i) q^{71} +(0.0321960 - 0.0786728i) q^{72} +(-14.1814 - 9.47568i) q^{73} +(7.93502 + 0.248504i) q^{74} +(-0.505300 - 1.66575i) q^{75} +(2.00889 + 8.50650i) q^{76} +(2.43918 - 2.97214i) q^{77} +(-0.161726 - 0.0210584i) q^{78} +(1.46071 - 3.52646i) q^{79} +(3.26455 + 2.31143i) q^{80} +(3.47831 + 8.39738i) q^{81} +(-0.461599 - 1.71299i) q^{82} +(8.00596 - 0.788518i) q^{83} +(-1.60274 + 4.29529i) q^{84} +(-2.05419 - 1.09799i) q^{85} +(0.715403 + 0.322923i) q^{86} +(-3.02808 - 15.2232i) q^{87} +(7.26647 - 3.92383i) q^{88} +(-7.52623 - 1.49706i) q^{89} +(0.0419254 - 0.00698298i) q^{90} +(0.0868234 + 0.00855136i) q^{91} +(10.3954 - 3.56165i) q^{92} +(1.88898 + 0.573014i) q^{93} +(-5.94954 - 12.0215i) q^{94} +(-3.09023 + 3.09023i) q^{95} +(-6.68016 + 7.23445i) q^{96} +(-6.92117 - 6.92117i) q^{97} +(-2.38377 + 7.05521i) q^{98} +(0.0254723 - 0.0839711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * 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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