LMFDB - Embedded newform 640.2.bm.a.341.48

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			341.48
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998032 - 1.00196i) q^{2} +(1.57969 - 1.92485i) q^{3} +(-0.00786299 - 1.99998i) q^{4} +(0.956940 - 0.290285i) q^{5} +(-0.352055 - 3.50385i) q^{6} +(1.57166 + 0.312622i) q^{7} +(-2.01176 - 1.98817i) q^{8} +(-0.624379 - 3.13897i) q^{9} +O(q^{10})$	\(q+(0.998032 - 1.00196i) q^{2} +(1.57969 - 1.92485i) q^{3} +(-0.00786299 - 1.99998i) q^{4} +(0.956940 - 0.290285i) q^{5} +(-0.352055 - 3.50385i) q^{6} +(1.57166 + 0.312622i) q^{7} +(-2.01176 - 1.98817i) q^{8} +(-0.624379 - 3.13897i) q^{9} +(0.664203 - 1.24853i) q^{10} +(-0.747739 - 0.0736458i) q^{11} +(-3.86210 - 3.14421i) q^{12} +(-1.27611 + 4.20676i) q^{13} +(1.88180 - 1.26274i) q^{14} +(0.952910 - 2.30053i) q^{15} +(-3.99988 + 0.0314517i) q^{16} +(0.465593 + 1.12404i) q^{17} +(-3.76828 - 2.50718i) q^{18} +(2.40905 - 1.28766i) q^{19} +(-0.588089 - 1.91158i) q^{20} +(3.08448 - 2.53136i) q^{21} +(-0.820058 + 0.675706i) q^{22} +(-2.14642 + 3.21234i) q^{23} +(-7.00488 + 0.731656i) q^{24} +(0.831470 - 0.555570i) q^{25} +(2.94143 + 5.47710i) q^{26} +(-0.440224 - 0.235305i) q^{27} +(0.612882 - 3.14575i) q^{28} +(0.496248 + 5.03849i) q^{29} +(-1.35401 - 3.25078i) q^{30} +(-0.858217 - 0.858217i) q^{31} +(-3.96049 + 4.03912i) q^{32} +(-1.32295 + 1.32295i) q^{33} +(1.59092 + 0.655322i) q^{34} +(1.59473 - 0.157067i) q^{35} +(-6.27297 + 1.27343i) q^{36} +(-0.0179195 + 0.0335250i) q^{37} +(1.11411 - 3.69890i) q^{38} +(6.08155 + 9.10168i) q^{39} +(-2.50227 - 1.31858i) q^{40} +(0.0467971 + 0.0312689i) q^{41} +(0.542072 - 5.61692i) q^{42} +(-3.70480 - 4.51431i) q^{43} +(-0.141411 + 1.49604i) q^{44} +(-1.50869 - 2.82256i) q^{45} +(1.07645 + 5.35665i) q^{46} +(6.11489 - 2.53287i) q^{47} +(-6.25801 + 7.74885i) q^{48} +(-4.09478 - 1.69611i) q^{49} +(0.273172 - 1.38758i) q^{50} +(2.89910 + 0.879433i) q^{51} +(8.42349 + 2.51912i) q^{52} +(-0.251964 + 2.55824i) q^{53} +(-0.675125 + 0.206247i) q^{54} +(-0.736919 + 0.146582i) q^{55} +(-2.54025 - 3.75365i) q^{56} +(1.32698 - 6.67116i) q^{57} +(5.54365 + 4.53135i) q^{58} +(2.01062 + 6.62812i) q^{59} +(-4.60851 - 1.88772i) q^{60} +(-10.4228 - 8.55374i) q^{61} +(-1.71643 + 0.00337408i) q^{62} -5.12858i q^{63} +(0.0943539 + 7.99944i) q^{64} +4.39605i q^{65} +(0.00520118 + 2.64589i) q^{66} +(-2.11259 - 1.73376i) q^{67} +(2.24440 - 0.940017i) q^{68} +(2.79261 + 9.20602i) q^{69} +(1.43422 - 1.75462i) q^{70} +(-1.41168 + 7.09699i) q^{71} +(-4.98470 + 7.55622i) q^{72} +(-7.51418 + 1.49466i) q^{73} +(0.0157066 + 0.0514137i) q^{74} +(0.244070 - 2.47808i) q^{75} +(-2.59425 - 4.80793i) q^{76} +(-1.15217 - 0.349506i) q^{77} +(15.1891 + 2.99028i) q^{78} +(13.4238 + 5.56031i) q^{79} +(-3.81851 + 1.19120i) q^{80} +(7.72218 - 3.19863i) q^{81} +(0.0780353 - 0.0156817i) q^{82} +(-7.06351 - 13.2149i) q^{83} +(-5.08694 - 6.14900i) q^{84} +(0.771836 + 0.940485i) q^{85} +(-8.22068 - 0.793353i) q^{86} +(10.4823 + 7.00402i) q^{87} +(1.35785 + 1.63479i) q^{88} +(-1.08026 - 1.61672i) q^{89} +(-4.33382 - 1.30535i) q^{90} +(-3.32073 + 6.21265i) q^{91} +(6.44150 + 4.26754i) q^{92} +(-3.00765 + 0.296228i) q^{93} +(3.56501 - 8.65478i) q^{94} +(1.93152 - 1.93152i) q^{95} +(1.51838 + 14.0039i) q^{96} +(5.02939 + 5.02939i) q^{97} +(-5.78617 + 2.41005i) q^{98} +(0.235701 + 2.39311i) 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

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 $

$2$	0.998032	−	1.00196i	0.705715	−	0.708495i
$2$	0.998032	−	1.00196i	0.705715	−	0.708495i
$3$	1.57969	−	1.92485i	0.912032	−	1.11131i	−0.0813764	−	0.996683i	$-0.525932\pi$
$3$	1.57969	−	1.92485i	0.912032	−	1.11131i	0.993408	−	0.114631i	$-0.0365684\pi$
$4$	−0.00786299	−	1.99998i	−0.00393149	−	0.999992i
$5$	0.956940	−	0.290285i	0.427957	−	0.129819i
$5$	0.956940	−	0.290285i	0.427957	−	0.129819i
$6$	−0.352055	−	3.50385i	−0.143726	−	1.43044i
$7$	1.57166	+	0.312622i	0.594031	+	0.118160i	0.482945	−	0.875651i	$-0.339567\pi$
$7$	1.57166	+	0.312622i	0.594031	+	0.118160i	0.111086	+	0.993811i	$0.464567\pi$
$8$	−2.01176	−	1.98817i	−0.711264	−	0.702925i
$9$	−0.624379	−	3.13897i	−0.208126	−	1.04632i
$10$	0.664203	−	1.24853i	0.210039	−	0.394821i
$11$	−0.747739	−	0.0736458i	−0.225452	−	0.0222051i	−0.0153395	−	0.999882i	$-0.504883\pi$
$11$	−0.747739	−	0.0736458i	−0.225452	−	0.0222051i	−0.210112	+	0.977677i	$0.567383\pi$
$12$	−3.86210	−	3.14421i	−1.11489	−	0.907656i
$13$	−1.27611	+	4.20676i	−0.353928	+	1.16675i	0.581594	+	0.813479i	$0.302429\pi$
$13$	−1.27611	+	4.20676i	−0.353928	+	1.16675i	−0.935523	+	0.353267i	$0.885071\pi$
$14$	1.88180	−	1.26274i	0.502933	−	0.337481i
$15$	0.952910	−	2.30053i	0.246040	−	0.593994i
$16$	−3.99988	+	0.0314517i	−0.999969	+	0.00786293i
$17$	0.465593	+	1.12404i	0.112923	+	0.272620i	0.970230	−	0.242185i	$-0.0778642\pi$
$17$	0.465593	+	1.12404i	0.112923	+	0.272620i	−0.857307	+	0.514805i	$0.827864\pi$
$18$	−3.76828	−	2.50718i	−0.888192	−	0.590949i
$19$	2.40905	−	1.28766i	0.552673	−	0.295410i	−0.171322	−	0.985215i	$-0.554804\pi$
$19$	2.40905	−	1.28766i	0.552673	−	0.295410i	0.723995	+	0.689805i	$0.242304\pi$
$20$	−0.588089	−	1.91158i	−0.131501	−	0.427443i
$21$	3.08448	−	2.53136i	0.673088	−	0.552389i
$22$	−0.820058	+	0.675706i	−0.174837	+	0.144061i
$23$	−2.14642	+	3.21234i	−0.447559	+	0.669819i	−0.984816	−	0.173599i	$-0.944460\pi$
$23$	−2.14642	+	3.21234i	−0.447559	+	0.669819i	0.537258	+	0.843418i	$0.319460\pi$
$24$	−7.00488	+	0.731656i	−1.42987	+	0.149349i
$25$	0.831470	−	0.555570i	0.166294	−	0.111114i
$26$	2.94143	+	5.47710i	0.576861	+	1.07415i
$27$	−0.440224	−	0.235305i	−0.0847212	−	0.0452844i
$28$	0.612882	−	3.14575i	0.115824	−	0.594491i
$29$	0.496248	+	5.03849i	0.0921509	+	0.935624i	0.924452	+	0.381299i	$0.124523\pi$
$29$	0.496248	+	5.03849i	0.0921509	+	0.935624i	−0.832301	+	0.554324i	$0.812977\pi$
$30$	−1.35401	−	3.25078i	−0.247207	−	0.593509i
$31$	−0.858217	−	0.858217i	−0.154140	−	0.154140i	0.625824	−	0.779964i	$-0.284763\pi$
$31$	−0.858217	−	0.858217i	−0.154140	−	0.154140i	−0.779964	+	0.625824i	$0.784763\pi$
$32$	−3.96049	+	4.03912i	−0.700123	+	0.714022i
$33$	−1.32295	+	1.32295i	−0.230296	+	0.230296i
$34$	1.59092	+	0.655322i	0.272841	+	0.112387i
$35$	1.59473	−	0.157067i	0.269559	−	0.0265492i
$36$	−6.27297	+	1.27343i	−1.04550	+	0.212238i
$37$	−0.0179195	+	0.0335250i	−0.00294594	+	0.00551148i	−0.883390	−	0.468639i	$-0.844745\pi$
$37$	−0.0179195	+	0.0335250i	−0.00294594	+	0.00551148i	0.880444	+	0.474150i	$0.157245\pi$
$38$	1.11411	−	3.69890i	0.180733	−	0.600041i
$39$	6.08155	+	9.10168i	0.973827	+	1.45743i
$40$	−2.50227	−	1.31858i	−0.395644	−	0.208485i
$41$	0.0467971	+	0.0312689i	0.00730849	+	0.00488337i	0.559219	−	0.829020i	$-0.311101\pi$
$41$	0.0467971	+	0.0312689i	0.00730849	+	0.00488337i	−0.551911	+	0.833903i	$0.686101\pi$
$42$	0.542072	−	5.61692i	0.0836435	−	0.866709i
$43$	−3.70480	−	4.51431i	−0.564976	−	0.688425i	0.409655	−	0.912240i	$-0.365649\pi$
$43$	−3.70480	−	4.51431i	−0.564976	−	0.688425i	−0.974632	+	0.223815i	$0.928149\pi$
$44$	−0.141411	+	1.49604i	−0.0213185	+	0.225537i
$45$	−1.50869	−	2.82256i	−0.224902	−	0.420762i
$46$	1.07645	+	5.35665i	0.158715	+	0.789795i
$47$	6.11489	−	2.53287i	0.891948	−	0.369457i	0.110829	−	0.993839i	$-0.464649\pi$
$47$	6.11489	−	2.53287i	0.891948	−	0.369457i	0.781119	+	0.624383i	$0.214649\pi$
$48$	−6.25801	+	7.74885i	−0.903265	+	1.11845i
$49$	−4.09478	−	1.69611i	−0.584969	−	0.242302i
$50$	0.273172	−	1.38758i	0.0386324	−	0.196233i
$51$	2.89910	+	0.879433i	0.405956	+	0.123145i
$52$	8.42349	+	2.51912i	1.16813	+	0.349339i
$53$	−0.251964	+	2.55824i	−0.0346100	+	0.351401i	0.962247	+	0.272178i	$0.0877439\pi$
$53$	−0.251964	+	2.55824i	−0.0346100	+	0.351401i	−0.996857	+	0.0792229i	$0.974756\pi$
$54$	−0.675125	+	0.206247i	−0.0918728	+	0.0280667i
$55$	−0.736919	+	0.146582i	−0.0993662	+	0.0197652i
$56$	−2.54025	−	3.75365i	−0.339455	−	0.501602i
$57$	1.32698	−	6.67116i	0.175762	−	0.883616i
$58$	5.54365	+	4.53135i	0.727917	+	0.594995i
$59$	2.01062	+	6.62812i	0.261760	+	0.862908i	0.985036	+	0.172349i	$0.0551356\pi$
$59$	2.01062	+	6.62812i	0.261760	+	0.862908i	−0.723276	+	0.690559i	$0.757364\pi$
$60$	−4.60851	−	1.88772i	−0.594956	−	0.243703i
$61$	−10.4228	−	8.55374i	−1.33450	−	1.09519i	−0.987549	−	0.157310i	$-0.949718\pi$
$61$	−10.4228	−	8.55374i	−1.33450	−	1.09519i	−0.346948	−	0.937884i	$-0.612782\pi$
$62$	−1.71643	+	0.00337408i	−0.217987	+	0.000428509i
$63$		−	5.12858i		−	0.646140i
$64$	0.0943539	+	7.99944i	0.0117942	+	0.999930i
$65$			4.39605i			0.545263i
$66$	0.00520118	+	2.64589i	0.000640220	+	0.325687i
$67$	−2.11259	−	1.73376i	−0.258094	−	0.211812i	0.496444	−	0.868069i	$-0.334639\pi$
$67$	−2.11259	−	1.73376i	−0.258094	−	0.211812i	−0.754538	+	0.656257i	$0.772139\pi$
$68$	2.24440	−	0.940017i	0.272174	−	0.113994i
$69$	2.79261	+	9.20602i	0.336191	+	1.10827i
$70$	1.43422	−	1.75462i	0.171422	−	0.209718i
$71$	−1.41168	+	7.09699i	−0.167536	+	0.842258i	0.802003	+	0.597320i	$0.203768\pi$
$71$	−1.41168	+	7.09699i	−0.167536	+	0.842258i	−0.969539	+	0.244938i	$0.921232\pi$
$72$	−4.98470	+	7.55622i	−0.587452	+	0.890509i
$73$	−7.51418	+	1.49466i	−0.879468	+	0.174937i	−0.614117	−	0.789215i	$-0.710488\pi$
$73$	−7.51418	+	1.49466i	−0.879468	+	0.174937i	−0.265351	+	0.964152i	$0.585488\pi$
$74$	0.0157066	+	0.0514137i	0.00182586	+	0.00597672i
$75$	0.244070	−	2.47808i	0.0281828	−	0.286144i
$76$	−2.59425	−	4.80793i	−0.297580	−	0.551507i
$77$	−1.15217	−	0.349506i	−0.131301	−	0.0398299i
$78$	15.1891	+	2.99028i	1.71983	+	0.338582i
$79$	13.4238	+	5.56031i	1.51029	+	0.625583i	0.975618	−	0.219475i	$-0.0704346\pi$
$79$	13.4238	+	5.56031i	1.51029	+	0.625583i	0.534674	+	0.845059i	$0.320435\pi$
$80$	−3.81851	+	1.19120i	−0.426923	+	0.133180i
$81$	7.72218	−	3.19863i	0.858020	−	0.355404i
$82$	0.0780353	−	0.0156817i	0.00861756	−	0.00173176i
$83$	−7.06351	−	13.2149i	−0.775321	−	1.45052i	−0.889438	−	0.457056i	$-0.848904\pi$
$83$	−7.06351	−	13.2149i	−0.775321	−	1.45052i	0.114117	−	0.993467i	$-0.463596\pi$
$84$	−5.08694	−	6.14900i	−0.555031	−	0.670911i
$85$	0.771836	+	0.940485i	0.0837174	+	0.102010i
$86$	−8.22068	−	0.793353i	−0.886459	−	0.0855494i
$87$	10.4823	+	7.00402i	1.12382	+	0.750910i
$88$	1.35785	+	1.63479i	0.144747	+	0.174269i
$89$	−1.08026	−	1.61672i	−0.114507	−	0.171372i	0.769789	−	0.638298i	$-0.220361\pi$
$89$	−1.08026	−	1.61672i	−0.114507	−	0.171372i	−0.884296	+	0.466926i	$0.845361\pi$
$90$	−4.33382	−	1.30535i	−0.456824	−	0.137596i
$91$	−3.32073	+	6.21265i	−0.348107	+	0.651263i
$92$	6.44150	+	4.26754i	0.671573	+	0.444922i
$93$	−3.00765	+	0.296228i	−0.311879	+	0.0307174i
$94$	3.56501	−	8.65478i	0.367703	−	0.892672i
$95$	1.93152	−	1.93152i	0.198170	−	0.198170i
$96$	1.51838	+	14.0039i	0.154969	+	1.42927i
$97$	5.02939	+	5.02939i	0.510657	+	0.510657i	0.914728	−	0.404071i	$-0.132405\pi$
$97$	5.02939	+	5.02939i	0.510657	+	0.510657i	−0.404071	+	0.914728i	$0.632405\pi$
$98$	−5.78617	+	2.41005i	−0.584491	+	0.243451i
$99$	0.235701	+	2.39311i	0.0236888	+	0.240516i
$100$	−1.11767	−	1.65856i	−0.111767	−	0.165856i
$101$	−4.42607	−	2.36578i	−0.440410	−	0.235404i	0.236261	−	0.971690i	$-0.424078\pi$
$101$	−4.42607	−	2.36578i	−0.440410	−	0.235404i	−0.676671	+	0.736285i	$0.736578\pi$
$102$	3.77456	−	2.02709i	0.373737	−	0.200712i
$103$	16.6964	−	11.1562i	1.64515	−	1.09925i	0.741520	−	0.670930i	$-0.234105\pi$
$103$	16.6964	−	11.1562i	1.64515	−	1.09925i	0.903626	−	0.428321i	$-0.140895\pi$
$104$	10.9310	−	5.92587i	1.07187	−	0.581080i
$105$	2.21684	−	3.31774i	0.216342	−	0.323778i
$106$	2.31179	+	2.80566i	0.224541	+	0.272510i
$107$	2.94137	−	2.41392i	0.284353	−	0.233362i	−0.481394	−	0.876504i	$-0.659869\pi$
$107$	2.94137	−	2.41392i	0.284353	−	0.233362i	0.765747	+	0.643142i	$0.222369\pi$
$108$	−0.467144	+	0.882292i	−0.0449510	+	0.0848985i
$109$	0.812363	−	0.434217i	0.0778102	−	0.0415904i	−0.432033	−	0.901858i	$-0.642204\pi$
$109$	0.812363	−	0.434217i	0.0778102	−	0.0415904i	0.509843	+	0.860267i	$0.329704\pi$
$110$	−0.588599	+	0.884661i	−0.0561207	+	0.0843491i
$111$	0.0362235	+	0.0874513i	0.00343818	+	0.00830051i
$112$	−6.29627	−	1.20102i	−0.594942	−	0.113486i
$113$	3.52141	−	8.50145i	0.331267	−	0.799749i	−0.667226	−	0.744856i	$-0.732518\pi$
$113$	3.52141	−	8.50145i	0.331267	−	0.799749i	0.998492	−	0.0548929i	$-0.0174817\pi$
$114$	−5.35989	−	7.98761i	−0.502000	−	0.748108i
$115$	−1.12150	+	3.69709i	−0.104580	+	0.344755i
$116$	10.0730	−	1.03211i	0.935254	−	0.0958286i
$117$	14.0017	+	1.37904i	1.29445	+	0.127493i
$118$	8.64780	+	4.60051i	0.796095	+	0.423512i
$119$	0.380353	+	1.91216i	0.0348669	+	0.175288i
$120$	−6.49087	+	2.73356i	−0.592532	+	0.249539i
$121$	−10.2349	−	2.03586i	−0.930450	−	0.185078i
$122$	−18.9728	+	1.90632i	−1.71772	+	0.172590i
$123$	0.134113	−	0.0406826i	0.0120925	−	0.00366823i
$124$	−1.70967	+	1.72317i	−0.153533	+	0.154745i
$125$	0.634393	−	0.773010i	0.0567419	−	0.0691402i
$126$	−5.13865	−	5.11848i	−0.457787	−	0.455991i
$127$	9.20844			0.817117			0.408559	−	0.912732i	$-0.366032\pi$
$127$	9.20844			0.817117			0.408559	+	0.912732i	$0.366032\pi$
$128$	8.10932	+	7.88916i	0.716770	+	0.697310i
$129$	−14.5418			−1.28033
$130$	4.40469	+	4.38740i	0.386317	+	0.384801i
$131$	−10.5355	+	12.8376i	−0.920494	+	1.12163i	0.0717629	+	0.997422i	$0.477137\pi$
$131$	−10.5355	+	12.8376i	−0.920494	+	1.12163i	−0.992257	+	0.124203i	$0.960363\pi$
$132$	2.65628	+	2.63548i	0.231199	+	0.229389i
$133$	4.18875	−	1.27064i	0.363210	−	0.110179i
$134$	−3.84559	+	0.386392i	−0.332209	+	0.0333792i
$135$	−0.489574	−	0.0973822i	−0.0421358	−	0.00838133i
$136$	1.29812	−	3.18698i	0.111313	−	0.273281i
$137$	−2.05093	−	10.3107i	−0.175223	−	0.880905i	−0.963934	−	0.266141i	$-0.914251\pi$
$137$	−2.05093	−	10.3107i	−0.175223	−	0.880905i	0.788711	−	0.614764i	$-0.210749\pi$
$138$	12.0112	+	6.38980i	1.02246	+	0.543936i
$139$	−4.13524	−	0.407286i	−0.350747	−	0.0345455i	−0.0788900	−	0.996883i	$-0.525138\pi$
$139$	−4.13524	−	0.407286i	−0.350747	−	0.0345455i	−0.271856	+	0.962338i	$0.587638\pi$
$140$	−0.326672	−	3.18821i	−0.0276088	−	0.269453i
$141$	4.78420	−	15.7714i	0.402902	−	1.32819i
$142$	5.70203	+	8.49748i	0.478504	+	0.713093i
$143$	1.26400	−	3.05158i	0.105701	−	0.255186i
$144$	2.59617	+	12.5358i	0.216347	+	1.04465i
$145$	1.93747	+	4.67748i	0.160899	+	0.388443i
$146$	−6.00179	+	9.02066i	−0.496712	+	0.746555i
$147$	−9.73323	+	5.20252i	−0.802784	+	0.429097i
$148$	0.0671904	+	0.0355751i	0.00552301	+	0.00292425i
$149$	9.79150	−	8.03567i	0.802151	−	0.658308i	−0.141246	−	0.989975i	$-0.545111\pi$
$149$	9.79150	−	8.03567i	0.802151	−	0.658308i	0.943397	+	0.331667i	$0.107611\pi$
$150$	−2.23936	−	2.71776i	−0.182843	−	0.221904i
$151$	−7.67644	+	11.4886i	−0.624700	+	0.934930i	0.375268	+	0.926916i	$0.377551\pi$
$151$	−7.67644	+	11.4886i	−0.624700	+	0.934930i	−0.999968	+	0.00801343i	$0.997449\pi$
$152$	−7.40651	−	2.19913i	−0.600747	−	0.178373i
$153$	3.23762	−	2.16331i	0.261746	−	0.174893i
$154$	−1.50009	+	0.805611i	−0.120881	+	0.0649180i
$155$	−1.07039	−	0.572135i	−0.0859757	−	0.0459550i
$156$	18.1554	−	12.2346i	1.45359	−	0.979549i
$157$	−0.705787	−	7.16597i	−0.0563279	−	0.571907i	−0.981381	−	0.192070i	$-0.938480\pi$
$157$	−0.705787	−	7.16597i	−0.0563279	−	0.571907i	0.925053	−	0.379837i	$-0.124020\pi$
$158$	18.9686	−	7.90076i	1.50906	−	0.628551i
$159$	4.52620	+	4.52620i	0.358951	+	0.358951i
$160$	−2.61746	+	5.01487i	−0.206928	+	0.396460i
$161$	−4.37768	+	4.37768i	−0.345009	+	0.345009i
$162$	4.50207	−	10.9297i	0.353716	−	0.858717i
$163$	−2.90493	+	0.286111i	−0.227532	+	0.0224099i	−0.211140	−	0.977456i	$-0.567718\pi$
$163$	−2.90493	+	0.286111i	−0.227532	+	0.0224099i	−0.0163913	+	0.999866i	$0.505218\pi$
$164$	0.0621693	−	0.0938394i	0.00485460	−	0.00732763i
$165$	−0.881951	+	1.65002i	−0.0686598	+	0.128453i
$166$	−20.2905	−	6.11151i	−1.57485	−	0.474345i
$167$	12.7800	+	19.1266i	0.988946	+	1.48006i	0.873545	+	0.486744i	$0.161816\pi$
$167$	12.7800	+	19.1266i	0.988946	+	1.48006i	0.115402	+	0.993319i	$0.463184\pi$
$168$	−11.2380	−	1.03997i	−0.867031	−	0.0802354i
$169$	−5.25929	−	3.51414i	−0.404561	−	0.270319i
$170$	1.71265	+	0.165283i	0.131354	+	0.0126766i
$171$	−5.54608	−	6.75792i	−0.424120	−	0.516791i
$172$	−8.99942	+	7.44503i	−0.686199	+	0.567678i
$173$	−3.41656	−	6.39194i	−0.259756	−	0.485970i	0.717909	−	0.696137i	$-0.245099\pi$
$173$	−3.41656	−	6.39194i	−0.259756	−	0.485970i	−0.977666	+	0.210167i	$0.932599\pi$
$174$	17.4794	−	3.51260i	1.32511	−	0.266290i
$175$	1.48047	−	0.613231i	0.111913	−	0.0463559i
$176$	2.99318	+	0.271057i	0.225619	+	0.0204317i
$177$	15.9343	+	6.60020i	1.19770	+	0.496102i
$178$	−2.69802	−	0.531159i	−0.202225	−	0.0398120i
$179$	6.01123	+	1.82349i	0.449300	+	0.136294i	0.506822	−	0.862051i	$-0.330820\pi$
$179$	6.01123	+	1.82349i	0.449300	+	0.136294i	−0.0575223	+	0.998344i	$0.518320\pi$
$180$	−5.63320	+	3.03955i	−0.419874	+	0.226554i
$181$	1.91295	−	19.4225i	0.142188	−	1.44366i	−0.613999	−	0.789307i	$-0.710440\pi$
$181$	1.91295	−	19.4225i	0.142188	−	1.44366i	0.756187	−	0.654355i	$-0.227060\pi$
$182$	2.91065	+	9.52768i	0.215752	+	0.706239i
$183$	−32.9294	+	6.55006i	−2.43421	+	0.484194i
$184$	10.7047	−	2.19501i	0.789165	−	0.161818i
$185$	−0.00741608	+	0.0372832i	−0.000545241	+	0.00274111i
$186$	−2.70492	+	3.30920i	−0.198335	+	0.242643i
$187$	−0.265361	−	0.874778i	−0.0194051	−	0.0639701i
$188$	−5.11378	−	12.2098i	−0.372961	−	0.890488i
$189$	−0.618320	−	0.507442i	−0.0449762	−	0.0369110i
$190$	−0.00759379	−	3.86304i	−0.000550911	−	0.280254i
$191$			18.7110i			1.35388i	0.736037	+	0.676941i	$0.236695\pi$
$191$			18.7110i			1.35388i	−0.736037	+	0.676941i	$0.763305\pi$
$192$	15.5468	+	12.4550i	1.12199	+	0.898861i
$193$		−	3.50862i		−	0.252556i	−0.991995	−	0.126278i	$-0.959697\pi$
$193$		−	3.50862i		−	0.252556i	0.991995	−	0.126278i	$-0.0403032\pi$
$194$	10.0588	−	0.0197731i	0.722177	−	0.00141962i
$195$	8.46175	+	6.94438i	0.605959	+	0.497298i
$196$	−3.36000	+	8.20283i	−0.240000	+	0.585917i
$197$	5.83095	+	19.2221i	0.415438	+	1.36952i	0.876181	+	0.481982i	$0.160083\pi$
$197$	5.83095	+	19.2221i	0.415438	+	1.36952i	−0.460743	+	0.887534i	$0.652417\pi$
$198$	2.63305	+	2.15224i	0.187122	+	0.152953i
$199$	−3.23280	+	16.2524i	−0.229167	+	1.15210i	0.679209	+	0.733945i	$0.262323\pi$
$199$	−3.23280	+	16.2524i	−0.229167	+	1.15210i	−0.908376	+	0.418155i	$0.862677\pi$
$200$	−2.77729	−	0.535430i	−0.196384	−	0.0378606i
$201$	−6.67445	+	1.32763i	−0.470779	+	0.0936438i
$202$	−6.78779	+	2.07363i	−0.477587	+	0.145900i
$203$	−0.795211	+	8.07392i	−0.0558129	+	0.566678i
$204$	1.73606	−	5.80508i	0.121548	−	0.406437i
$205$	0.0538589	+	0.0163379i	0.00376167	+	0.00114109i
$206$	5.48547	−	27.8634i	0.382190	−	1.94134i
$207$	11.4236	+	4.73181i	0.793995	+	0.328883i
$208$	4.97196	−	16.8667i	0.344743	−	1.16949i
$209$	−1.89617	+	0.785418i	−0.131161	+	0.0543285i
$210$	−1.11177	−	5.53241i	−0.0767198	−	0.381773i
$211$	−11.4436	−	21.4094i	−0.787807	−	1.47388i	−0.878364	−	0.477993i	$-0.841365\pi$
$211$	−11.4436	−	21.4094i	−0.787807	−	1.47388i	0.0905565	−	0.995891i	$-0.471135\pi$
$212$	5.11841	+	0.483809i	0.351534	+	0.0332282i
$213$	11.4307	+	13.9283i	0.783215	+	0.954351i
$214$	0.516921	−	5.35631i	0.0353360	−	0.366150i
$215$	−4.85570	−	3.24448i	−0.331156	−	0.221272i
$216$	0.417799	+	1.34862i	0.0284276	+	0.0917618i
$217$	−1.08053	−	1.61712i	−0.0733509	−	0.109777i
$218$	0.375695	−	1.24732i	0.0254452	−	0.0844792i
$219$	−8.99303	+	16.8248i	−0.607693	+	1.13691i
$220$	0.298957	+	1.47267i	0.0201557	+	0.0992877i
$221$	−5.32272	+	0.524242i	−0.358045	+	0.0352643i
$222$	0.123775	+	0.0509846i	0.00830725	+	0.00342186i
$223$	−3.40984	+	3.40984i	−0.228339	+	0.228339i	−0.811999	−	0.583659i	$-0.801620\pi$
$223$	−3.40984	+	3.40984i	−0.228339	+	0.228339i	0.583659	+	0.811999i	$0.301620\pi$
$224$	−7.48726	+	5.10998i	−0.500264	+	0.341425i
$225$	−2.26307	−	2.26307i	−0.150871	−	0.150871i
$226$	−5.00366	−	12.0130i	−0.332838	−	0.799096i
$227$	1.03975	+	10.5568i	0.0690108	+	0.700678i	0.965985	+	0.258596i	$0.0832600\pi$
$227$	1.03975	+	10.5568i	0.0690108	+	0.700678i	−0.896975	+	0.442082i	$0.854240\pi$
$228$	−13.3526	−	2.60147i	−0.884300	−	0.172287i
$229$	−13.3337	−	7.12701i	−0.881116	−	0.470966i	−0.0321921	−	0.999482i	$-0.510249\pi$
$229$	−13.3337	−	7.12701i	−0.881116	−	0.470966i	−0.848924	+	0.528516i	$0.822749\pi$
$230$	2.58506	+	4.81351i	0.170454	+	0.317394i
$231$	−2.49281	+	1.66564i	−0.164015	+	0.109591i
$232$	9.01904	−	11.1228i	0.592129	−	0.730251i
$233$	−9.44542	+	14.1361i	−0.618790	+	0.926085i	0.381209	+	0.924489i	$0.375508\pi$
$233$	−9.44542	+	14.1361i	−0.618790	+	0.926085i	−0.999999	+	0.00159587i	$0.999492\pi$
$234$	15.3559	−	12.6528i	1.00384	−	0.827141i
$235$	5.11633	−	4.19886i	0.333752	−	0.273904i
$236$	13.2403	−	4.07332i	0.861872	−	0.265151i
$237$	31.9081	−	17.0552i	2.07265	−	1.10786i
$238$	2.29552	+	1.52730i	0.148797	+	0.0990002i
$239$	−3.56797	−	8.61383i	−0.230793	−	0.557183i	0.765478	−	0.643462i	$-0.222502\pi$
$239$	−3.56797	−	8.61383i	−0.230793	−	0.557183i	−0.996271	+	0.0862790i	$0.972502\pi$
$240$	−3.73916	+	9.23179i	−0.241362	+	0.595910i
$241$	−7.23973	+	17.4783i	−0.466352	+	1.12587i	0.499391	+	0.866376i	$0.333557\pi$
$241$	−7.23973	+	17.4783i	−0.466352	+	1.12587i	−0.965744	+	0.259498i	$0.916443\pi$
$242$	−12.2547	+	8.22320i	−0.787760	+	0.528607i
$243$	6.47642	−	21.3499i	0.415463	−	1.36960i
$244$	−17.0254	+	20.9126i	−1.08994	+	1.33879i
$245$	−4.41082	−	0.434428i	−0.281797	−	0.0277546i
$246$	0.0930863	−	0.174979i	0.00593496	−	0.0111562i
$247$	2.34268	+	11.7775i	0.149061	+	0.749383i
$248$	0.0202444	+	3.43281i	0.00128552	+	0.217983i
$249$	−36.5948	−	7.27917i	−2.31910	−	0.461299i
$250$	−0.141384	−	1.40713i	−0.00894188	−	0.0889946i
$251$	27.2558	−	8.26794i	1.72037	−	0.521868i	0.732989	−	0.680241i	$-0.238125\pi$
$251$	27.2558	−	8.26794i	1.72037	−	0.521868i	0.987379	+	0.158373i	$0.0506249\pi$
$252$	−10.2571	+	0.0403259i	−0.646135	+	0.00254029i
$253$	1.84153	−	2.24391i	0.115776	−	0.141074i
$254$	9.19032	−	9.22653i	0.576652	−	0.578924i
$255$	3.02955			0.189718
$256$	15.9980	−	0.251606i	0.999876	−	0.0157254i
$257$	−23.1059			−1.44131			−0.720653	−	0.693296i	$-0.756158\pi$
$257$	−23.1059			−1.44131			−0.720653	+	0.693296i	$0.756158\pi$
$258$	−14.5132	+	14.5703i	−0.903551	+	0.907110i
$259$	−0.0386440	+	0.0470878i	−0.00240122	+	0.00292589i
$260$	8.79204	−	0.0345661i	0.545259	−	0.00214370i
$261$	15.5058	−	4.70363i	0.959784	−	0.291147i
$262$	2.34799	+	23.3685i	0.145059	+	1.44371i
$263$	−11.7819	−	2.34357i	−0.726503	−	0.144511i	−0.182035	−	0.983292i	$-0.558268\pi$
$263$	−11.7819	−	2.34357i	−0.726503	−	0.144511i	−0.544468	+	0.838782i	$0.683268\pi$
$264$	5.29170	−	0.0312069i	0.325682	−	0.00192065i
$265$	0.501502	+	2.52122i	0.0308070	+	0.154877i
$266$	2.90737	−	5.46511i	0.178262	−	0.335088i
$267$	−4.81841	−	0.474572i	−0.294882	−	0.0290433i
$268$	−3.45087	+	4.23878i	−0.210796	+	0.258924i
$269$	−4.68113	+	15.4316i	−0.285414	+	0.940882i	0.690612	+	0.723226i	$0.257341\pi$
$269$	−4.68113	+	15.4316i	−0.285414	+	0.940882i	−0.976025	+	0.217657i	$0.930159\pi$
$270$	−0.586184	+	0.393344i	−0.0356740	+	0.0239382i
$271$	8.72379	−	21.0611i	0.529933	−	1.27937i	−0.401634	−	0.915800i	$-0.631558\pi$
$271$	8.72379	−	21.0611i	0.529933	−	1.27937i	0.931567	−	0.363571i	$-0.118442\pi$
$272$	−1.89767	−	4.48138i	−0.115063	−	0.271724i
$273$	6.71272	+	16.2059i	0.406273	+	0.980829i
$274$	−12.3779	−	8.23548i	−0.747775	−	0.497524i
$275$	−0.662637	+	0.354187i	−0.0399585	+	0.0213583i
$276$	18.3899	−	5.65757i	1.10694	−	0.340546i
$277$	−4.72823	+	3.88035i	−0.284092	+	0.233148i	−0.765636	−	0.643273i	$-0.777576\pi$
$277$	−4.72823	+	3.88035i	−0.284092	+	0.233148i	0.481545	+	0.876421i	$0.340076\pi$
$278$	−4.53519	+	3.73688i	−0.272003	+	0.224123i
$279$	−2.15806	+	3.22977i	−0.129200	+	0.193361i
$280$	−3.52050	−	2.85462i	−0.210390	−	0.170596i
$281$	−20.4678	+	13.6761i	−1.22101	+	0.815851i	−0.987671	−	0.156546i	$-0.949964\pi$
$281$	−20.4678	+	13.6761i	−1.22101	+	0.815851i	−0.233336	+	0.972396i	$0.574964\pi$
$282$	−11.0276	−	20.5339i	−0.656683	−	1.22278i
$283$	4.67992	+	2.50147i	0.278192	+	0.148697i	0.604593	−	0.796535i	$-0.293336\pi$
$283$	4.67992	+	2.50147i	0.278192	+	0.148697i	−0.326401	+	0.945232i	$0.605836\pi$
$284$	14.2050	+	2.76753i	0.842910	+	0.164223i
$285$	−0.666698	−	6.76910i	−0.0394918	−	0.400967i
$286$	−1.79605	−	4.31206i	−0.106203	−	0.254977i
$287$	0.0637738	+	0.0637738i	0.00376445	+	0.00376445i
$288$	15.1515	+	9.90991i	0.892811	+	0.583947i
$289$	10.9741	−	10.9741i	0.645537	−	0.645537i
$290$	6.62033	+	2.72699i	0.388759	+	0.160135i
$291$	17.6257	−	1.73598i	1.03324	−	0.101765i
$292$	3.04839	+	15.0165i	0.178393	+	0.878773i
$293$	−11.9194	+	22.2996i	−0.696338	+	1.30276i	0.246383	+	0.969173i	$0.420758\pi$
$293$	−11.9194	+	22.2996i	−0.696338	+	1.30276i	−0.942721	+	0.333583i	$0.891742\pi$
$294$	−4.50134	+	14.9446i	−0.262524	+	0.871589i
$295$	3.84808	+	5.75907i	0.224044	+	0.335306i
$296$	0.102703	−	0.0318172i	0.00596950	−	0.00184934i
$297$	0.311843	+	0.208367i	0.0180950	+	0.0120907i
$298$	1.72078	−	17.8306i	0.0996819	−	1.03290i
$299$	−10.7745	−	13.1287i	−0.623104	−	0.759255i
$300$	−4.95805	−	0.468651i	−0.286253	−	0.0270576i
$301$	−4.41140	−	8.25315i	−0.254269	−	0.475704i
$302$	3.84983	+	19.1575i	0.221533	+	1.10239i
$303$	−11.5456	+	4.78234i	−0.663276	+	0.274738i
$304$	−9.59538	+	5.22625i	−0.550333	+	0.299746i
$305$	−12.4570	−	5.15985i	−0.713285	−	0.295452i
$306$	1.06369	−	5.40303i	0.0608072	−	0.308871i
$307$	−3.66399	−	1.11146i	−0.209115	−	0.0634344i	0.183989	−	0.982928i	$-0.441099\pi$
$307$	−3.66399	−	1.11146i	−0.209115	−	0.0634344i	−0.393104	+	0.919494i	$0.628599\pi$
$308$	−0.689947	+	2.30706i	−0.0393134	+	0.131457i
$309$	4.90107	−	49.7614i	0.278812	−	2.83083i
$310$	−1.64154	+	0.501482i	−0.0932333	+	0.0284823i
$311$	−20.2064	+	4.01931i	−1.14580	+	0.227914i	−0.731249	−	0.682111i	$-0.761062\pi$
$311$	−20.2064	+	4.01931i	−1.14580	+	0.227914i	−0.414554	+	0.910025i	$0.636062\pi$
$312$	5.86108	−	30.4015i	0.331818	−	1.72115i
$313$	5.06333	−	25.4551i	0.286196	−	1.43881i	−0.523535	−	0.852004i	$-0.675387\pi$
$313$	5.06333	−	25.4551i	0.286196	−	1.43881i	0.809731	−	0.586801i	$-0.199613\pi$
$314$	−7.88444	−	6.44470i	−0.444945	−	0.363695i
$315$	−1.48875	−	4.90774i	−0.0838814	−	0.276520i
$316$	11.0150	−	26.8910i	0.619641	−	1.51274i
$317$	−15.5105	−	12.7291i	−0.871154	−	0.714937i	0.0885138	−	0.996075i	$-0.471788\pi$
$317$	−15.5105	−	12.7291i	−0.871154	−	0.714937i	−0.959667	+	0.281138i	$0.909288\pi$
$318$	9.05239	−	0.0177948i	0.507633	−	0.000997881i
$319$		−	3.80402i		−	0.212984i
$320$	2.41241	+	7.62760i	0.134858	+	0.426396i
$321$		−	9.47493i		−	0.528839i
$322$	0.0172109	+	8.75534i	0.000959123	+	0.487916i
$323$	2.56902	+	2.10834i	0.142944	+	0.117311i
$324$	−6.45793	−	15.4191i	−0.358774	−	0.856616i
$325$	1.27611	+	4.20676i	0.0707857	+	0.233349i
$326$	−2.61254	+	3.19618i	−0.144695	+	0.177020i
$327$	0.447474	−	2.24960i	0.0247454	−	0.124403i
$328$	−0.0319768	−	0.155946i	−0.00176562	−	0.00861069i
$329$	10.4023	−	2.06915i	0.573500	−	0.114076i
$330$	0.773039	+	2.53045i	0.0425544	+	0.139297i
$331$	2.43590	−	24.7321i	0.133889	−	1.35940i	−0.659968	−	0.751294i	$-0.729430\pi$
$331$	2.43590	−	24.7321i	0.133889	−	1.35940i	0.793857	−	0.608104i	$-0.208070\pi$
$332$	−26.3741	+	14.2308i	−1.44746	+	0.781018i
$333$	0.116422	+	0.0353163i	0.00637991	+	0.00193532i
$334$	31.9190	+	6.28389i	1.74653	+	0.343839i
$335$	−2.52490	−	1.04585i	−0.137950	−	0.0571408i
$336$	−12.2579	+	10.2222i	−0.668724	+	0.557664i
$337$	16.9110	−	7.00475i	0.921199	−	0.381573i	0.128866	−	0.991662i	$-0.458866\pi$
$337$	16.9110	−	7.00475i	0.921199	−	0.381573i	0.792333	+	0.610089i	$0.208866\pi$
$338$	−8.76998	+	1.76239i	−0.477024	+	0.0958612i
$339$	−10.8013	−	20.2078i	−0.586646	−	1.09754i
$340$	1.87489	−	1.55106i	0.101680	−	0.0841178i
$341$	0.578518	+	0.704926i	0.0313285	+	0.0381739i
$342$	−12.3064	−	1.18765i	−0.665452	−	0.0642207i
$343$	−15.2321	−	10.1777i	−0.822454	−	0.549546i
$344$	−1.52205	+	16.4475i	−0.0820637	+	0.886788i
$345$	5.34473	+	7.99896i	0.287751	+	0.430649i
$346$	−9.81433	−	2.95609i	−0.527621	−	0.158920i
$347$	6.63685	−	12.4167i	0.356285	−	0.666562i	−0.638380	−	0.769721i	$-0.720395\pi$
$347$	6.63685	−	12.4167i	0.356285	−	0.666562i	0.994665	+	0.103159i	$0.0328951\pi$
$348$	13.9255	−	21.0194i	0.746486	−	1.12676i
$349$	−9.38168	+	0.924014i	−0.502190	+	0.0494614i	−0.345941	−	0.938256i	$-0.612440\pi$
$349$	−9.38168	+	0.924014i	−0.502190	+	0.0494614i	−0.156249	+	0.987718i	$0.549940\pi$
$350$	0.863122	−	2.09540i	0.0461358	−	0.112004i
$351$	1.55164	−	1.55164i	0.0828206	−	0.0828206i
$352$	3.25888	−	2.72853i	0.173699	−	0.145431i
$353$	16.9704	+	16.9704i	0.903245	+	0.903245i	0.995715	−	0.0924701i	$-0.0294762\pi$
$353$	16.9704	+	16.9704i	0.903245	+	0.903245i	−0.0924701	+	0.995715i	$0.529476\pi$
$354$	22.5161	−	9.37838i	1.19672	−	0.498455i
$355$	0.709255	+	7.20119i	0.0376434	+	0.382199i
$356$	−3.22492	+	2.17321i	−0.170920	+	0.115180i
$357$	4.28147	+	2.28849i	0.226599	+	0.121120i
$358$	7.82646	−	4.20313i	0.413641	−	0.222142i
$359$	−7.14994	+	4.77744i	−0.377359	+	0.252143i	−0.729757	−	0.683707i	$-0.760367\pi$
$359$	−7.14994	+	4.77744i	−0.377359	+	0.252143i	0.352397	+	0.935851i	$0.385367\pi$
$360$	−2.57661	+	8.67783i	−0.135799	+	0.457362i
$361$	−6.41041	+	9.59385i	−0.337390	+	0.504940i
$362$	−17.5514	−	21.3010i	−0.922483	−	1.11955i
$363$	−20.0867	+	16.4847i	−1.05428	+	0.865225i
$364$	12.4513	+	6.59256i	0.652626	+	0.345544i
$365$	−6.75674	+	3.61155i	−0.353664	+	0.189037i
$366$	−26.3016	+	39.5312i	−1.37481	+	2.06633i
$367$	−5.17872	−	12.5025i	−0.270327	−	0.652628i	0.729170	−	0.684332i	$-0.239906\pi$
$367$	−5.17872	−	12.5025i	−0.270327	−	0.652628i	−0.999497	+	0.0317050i	$0.989906\pi$
$368$	8.48436	−	12.9165i	0.442278	−	0.673317i
$369$	0.0689327	−	0.166418i	0.00358849	−	0.00866339i
$370$	0.0299549	+	0.0446405i	0.00155728	+	0.00232075i
$371$	−1.19576	+	3.94190i	−0.0620809	+	0.204653i
$372$	0.616100	+	6.01293i	0.0319433	+	0.311756i
$373$	−8.43667	−	0.830940i	−0.436834	−	0.0430244i	−0.122790	−	0.992433i	$-0.539184\pi$
$373$	−8.43667	−	0.830940i	−0.436834	−	0.0430244i	−0.314044	+	0.949408i	$0.601684\pi$
$374$	−1.14133	−	0.607174i	−0.0590170	−	0.0313962i
$375$	−0.485789	−	2.44223i	−0.0250860	−	0.126116i
$376$	−17.3375	−	7.06191i	−0.894111	−	0.364190i
$377$	−21.8290	−	4.34205i	−1.12425	−	0.223627i
$378$	−1.12554	+	0.113091i	−0.0578917	+	0.00581676i
$379$	−22.3588	+	6.78246i	−1.14849	+	0.348391i	−0.806455	−	0.591295i	$-0.798617\pi$
$379$	−22.3588	+	6.78246i	−1.14849	+	0.348391i	−0.342037	+	0.939686i	$0.611117\pi$
$380$	−3.87821	−	3.84783i	−0.198948	−	0.197390i
$381$	14.5464	−	17.7249i	0.745237	−	0.908074i
$382$	18.7478	+	18.6742i	0.959220	+	0.955456i
$383$	30.9758			1.58279			0.791394	−	0.611307i	$-0.209356\pi$
$383$	30.9758			1.58279			0.791394	+	0.611307i	$0.209356\pi$
$384$	27.9957	−	3.14685i	1.42865	−	0.160587i
$385$	−1.20401			−0.0613620
$386$	−3.51551	−	3.50172i	−0.178935	−	0.178233i
$387$	−11.8571	+	14.4479i	−0.602728	+	0.734427i
$388$	10.0192	−	10.0982i	0.508646	−	0.512661i
$389$	−29.5140	+	8.95297i	−1.49642	+	0.453934i	−0.929182	−	0.369621i	$-0.879487\pi$
$389$	−29.5140	+	8.95297i	−1.49642	+	0.453934i	−0.567236	+	0.823555i	$0.691987\pi$
$390$	15.4031	−	1.54765i	0.779967	−	0.0783685i
$391$	−4.61015	−	0.917017i	−0.233146	−	0.0463755i
$392$	4.86555	+	11.5533i	0.245747	+	0.583530i
$393$	8.06763	+	40.5587i	0.406958	+	2.04592i
$394$	25.0793	+	13.3418i	1.26348	+	0.672153i
$395$	14.4598	+	1.42417i	0.727552	+	0.0716576i
$396$	4.78433	−	0.490215i	0.240421	−	0.0246342i
$397$	1.78330	−	5.87874i	0.0895011	−	0.295046i	−0.900750	−	0.434337i	$-0.856983\pi$
$397$	1.78330	−	5.87874i	0.0895011	−	0.295046i	0.990251	+	0.139292i	$0.0444826\pi$
$398$	13.0578	+	19.4595i	0.654531	+	0.975418i
$399$	4.17110	−	10.0699i	0.208816	−	0.504127i
$400$	−3.30830	+	2.24836i	−0.165415	+	0.112418i
$401$	7.87311	+	19.0074i	0.393164	+	0.949183i	0.989246	+	0.146259i	$0.0467234\pi$
$401$	7.87311	+	19.0074i	0.393164	+	0.949183i	−0.596082	+	0.802924i	$0.703277\pi$
$402$	−5.33108	+	8.01257i	−0.265890	+	0.399631i
$403$	4.70549	−	2.51514i	0.234397	−	0.125288i
$404$	−4.69673	+	8.87067i	−0.233671	+	0.441332i
$405$	6.46115	−	5.30253i	0.321057	−	0.263485i
$406$	7.29613	+	8.85480i	0.362101	+	0.439456i
$407$	0.0158681	−	0.0237482i	0.000786551	−	0.00117716i
$408$	−4.08383	−	7.53312i	−0.202180	−	0.372945i
$409$	−23.7718	+	15.8838i	−1.17544	+	0.785402i	−0.980713	−	0.195456i	$-0.937381\pi$
$409$	−23.7718	+	15.8838i	−1.17544	+	0.785402i	−0.194725	+	0.980858i	$0.562381\pi$
$410$	0.0701230	−	0.0376589i	0.00346313	−	0.00185984i
$411$	−23.0865	−	12.3400i	−1.13877	−	0.608686i
$412$	−22.4435	−	33.3049i	−1.10571	−	1.64081i
$413$	1.08791	+	11.0457i	0.0535324	+	0.543524i
$414$	16.1422	−	6.72353i	0.793347	−	0.330444i
$415$	−10.5954	−	10.5954i	−0.520110	−	0.520110i
$416$	−11.9376	−	21.8152i	−0.585289	−	1.06958i
$417$	−7.31634	+	7.31634i	−0.358283	+	0.358283i
$418$	−1.10548	+	2.68376i	−0.0540706	+	0.131267i
$419$	22.0880	−	2.17547i	1.07907	−	0.106279i	0.457171	−	0.889379i	$-0.348863\pi$
$419$	22.0880	−	2.17547i	1.07907	−	0.106279i	0.621896	+	0.783100i	$0.286363\pi$
$420$	−6.65286	−	4.40757i	−0.324626	−	0.215067i
$421$	10.9747	−	20.5323i	0.534876	−	1.00068i	−0.458816	−	0.888531i	$-0.651726\pi$
$421$	10.9747	−	20.5323i	0.534876	−	1.00068i	0.993691	−	0.112150i	$-0.0357738\pi$
$422$	−32.8725	−	9.90124i	−1.60021	−	0.481985i
$423$	−11.7686	−	17.6129i	−0.572209	−	0.856371i
$424$	5.59310	−	4.64561i	0.271625	−	0.225611i
$425$	1.01161	+	0.675936i	0.0490703	+	0.0327877i
$426$	25.3638	+	2.44778i	1.22888	+	0.118596i
$427$	−13.7069	−	16.7019i	−0.663325	−	0.808263i
$428$	−4.85093	−	5.86371i	−0.234478	−	0.283433i
$429$	−3.87711	−	7.25356i	−0.187188	−	0.350205i
$430$	−8.09700	+	1.62715i	−0.390472	+	0.0784680i
$431$	−25.7987	+	10.6862i	−1.24268	+	0.514736i	−0.904552	−	0.426364i	$-0.859794\pi$
$431$	−25.7987	+	10.6862i	−1.24268	+	0.514736i	−0.338130	+	0.941099i	$0.609794\pi$
$432$	1.76824	+	0.927344i	0.0850746	+	0.0446169i
$433$	12.1854	+	5.04735i	0.585592	+	0.242560i	0.655753	−	0.754976i	$-0.272351\pi$
$433$	12.1854	+	5.04735i	0.585592	+	0.242560i	−0.0701610	+	0.997536i	$0.522351\pi$
$434$	−2.69870	−	0.531291i	−0.129542	−	0.0255028i
$435$	12.0641	+	3.65959i	0.578427	+	0.175464i
$436$	−0.874815	−	1.62130i	−0.0418960	−	0.0776461i
$437$	−1.03441	+	10.5025i	−0.0494825	+	0.502404i
$438$	7.88248	+	25.8024i	0.376640	+	1.23288i
$439$	4.66763	−	0.928449i	0.222774	−	0.0443125i	−0.0824412	−	0.996596i	$-0.526272\pi$
$439$	4.66763	−	0.928449i	0.222774	−	0.0443125i	0.305215	+	0.952283i	$0.401272\pi$
$440$	1.77394	+	1.17023i	0.0845691	+	0.0557887i
$441$	−2.76735	+	13.9124i	−0.131778	+	0.662495i
$442$	−4.78697	+	5.85638i	−0.227693	+	0.278560i
$443$	−7.54782	−	24.8818i	−0.358608	−	1.18217i	−0.931868	−	0.362798i	$-0.881821\pi$
$443$	−7.54782	−	24.8818i	−0.358608	−	1.18217i	0.573260	−	0.819374i	$-0.305679\pi$
$444$	0.174616	−	0.0731341i	0.00828693	−	0.00347079i
$445$	−1.50305	−	1.23352i	−0.0712513	−	0.0584745i
$446$	0.0134058	+	6.81966i	0.000634782	+	0.322920i
$447$		−	31.5410i		−	1.49184i
$448$	−2.35251	+	12.6019i	−0.111146	+	0.595383i
$449$		−	22.5229i		−	1.06292i	−0.847083	−	0.531460i	$-0.821643\pi$
$449$		−	22.5229i		−	1.06292i	0.847083	−	0.531460i	$-0.178357\pi$
$450$	−4.52613	+	0.00889726i	−0.213364	+	0.000419421i
$451$	−0.0326892	−	0.0268273i	−0.00153927	−	0.00126325i
$452$	−17.0304	−	6.97593i	−0.801045	−	0.328120i
$453$	9.98751	+	32.9244i	0.469254	+	1.54692i
$454$	11.6152	+	9.49422i	0.545129	+	0.445586i
$455$	−1.37430	+	6.90909i	−0.0644284	+	0.323903i
$456$	−15.9330	+	10.7825i	−0.746129	+	0.504937i
$457$	26.0279	−	5.17726i	1.21753	−	0.242182i	0.455804	−	0.890080i	$-0.349352\pi$
$457$	26.0279	−	5.17726i	1.21753	−	0.242182i	0.761727	+	0.647898i	$0.224352\pi$
$458$	−20.4485	+	6.24690i	−0.955494	+	0.291898i
$459$	0.0595268	−	0.604386i	0.00277847	−	0.0282103i
$460$	7.40294	+	2.21391i	0.345164	+	0.103224i
$461$	−2.39155	−	0.725469i	−0.111386	−	0.0337884i	0.234100	−	0.972213i	$-0.424786\pi$
$461$	−2.39155	−	0.725469i	−0.111386	−	0.0337884i	−0.345485	+	0.938424i	$0.612286\pi$
$462$	−0.818990	+	4.16006i	−0.0381029	+	0.193544i
$463$	−6.24861	−	2.58826i	−0.290397	−	0.120287i	0.232729	−	0.972542i	$-0.425234\pi$
$463$	−6.24861	−	2.58826i	−0.290397	−	0.120287i	−0.523126	+	0.852255i	$0.675234\pi$
$464$	−2.14340	−	20.1377i	−0.0995048	−	0.934870i
$465$	−2.79215	+	1.15655i	−0.129483	+	0.0536336i
$466$	4.73700	+	23.5722i	0.219437	+	1.09196i
$467$	−0.857113	−	1.60354i	−0.0396624	−	0.0742032i	0.861309	−	0.508081i	$-0.169645\pi$
$467$	−0.857113	−	1.60354i	−0.0396624	−	0.0742032i	−0.900972	+	0.433878i	$0.857145\pi$
$468$	2.64797	−	28.0139i	0.122402	−	1.29494i
$469$	−2.77825	−	3.38531i	−0.128288	−	0.156319i
$470$	0.899153	−	9.31697i	0.0414748	−	0.429760i
$471$	−14.9084	−	9.96145i	−0.686941	−	0.458999i
$472$	9.13296	−	17.3316i	0.420378	−	0.797754i
$473$	2.43776	+	3.64836i	0.112088	+	0.167752i
$474$	14.7566	−	48.9924i	0.677792	−	2.25030i
$475$	1.28766	−	2.40905i	0.0590820	−	0.110535i
$476$	3.82130	−	0.775735i	0.175149	−	0.0355557i
$477$	8.18754	−	0.806402i	0.374882	−	0.0369226i
$478$	−12.1917	−	5.02191i	−0.557635	−	0.229697i
$479$	2.13649	−	2.13649i	0.0976185	−	0.0976185i	−0.656611	−	0.754229i	$-0.728011\pi$
$479$	2.13649	−	2.13649i	0.0976185	−	0.0976185i	0.754229	+	0.656611i	$0.228011\pi$
$480$	5.51812	+	12.9601i	0.251866	+	0.591547i
$481$	−0.118164	−	0.118164i	−0.00538784	−	0.00538784i
$482$	10.2871	+	24.6978i	0.468565	+	1.12496i
$483$	1.51103	+	15.3417i	0.0687542	+	0.698073i
$484$	−3.99121	+	20.4857i	−0.181419	+	0.931170i
$485$	6.27278	+	3.35287i	0.284832	+	0.152246i
$486$	−14.9282	−	27.7970i	−0.677155	−	1.26090i
$487$	35.7838	−	23.9100i	1.62152	−	1.08346i	0.687536	−	0.726151i	$-0.258693\pi$
$487$	35.7838	−	23.9100i	1.62152	−	1.08346i	0.933984	−	0.357314i	$-0.116307\pi$
$488$	3.96180	+	37.9303i	0.179342	+	1.71702i
$489$	−4.03816	+	6.04353i	−0.182612	+	0.273298i
$490$	−4.83742	+	3.98591i	−0.218532	+	0.180065i
$491$	4.84618	−	3.97716i	0.218705	−	0.179487i	−0.518661	−	0.854980i	$-0.673569\pi$
$491$	4.84618	−	3.97716i	0.218705	−	0.179487i	0.737366	+	0.675493i	$0.236069\pi$
$492$	−0.0824192	−	0.267903i	−0.00371574	−	0.0120780i
$493$	−5.43241	+	2.90369i	−0.244664	+	0.130775i
$494$	14.1387	+	9.40701i	0.636129	+	0.423241i
$495$	0.920234	+	2.22164i	0.0413615	+	0.0998554i
$496$	3.45975	+	3.40577i	0.155347	+	0.152924i
$497$	−4.43736	+	10.7127i	−0.199043	+	0.480531i
$498$	−43.8163	+	29.4019i	−1.96346	+	1.31753i
$499$	−0.685614	+	2.26017i	−0.0306923	+	0.101179i	−0.970948	−	0.239289i	$-0.923086\pi$
$499$	−0.685614	+	2.26017i	−0.0306923	+	0.101179i	0.940256	+	0.340468i	$0.110586\pi$
$500$	−1.55100	−	1.26270i	−0.0693627	−	0.0564696i
$501$	57.0043	+	5.61444i	2.54677	+	0.250834i
$502$	18.9179	−	35.5610i	0.844349	−	1.58716i
$503$	1.24801	+	6.27418i	0.0556461	+	0.279752i	0.998583	−	0.0532203i	$-0.0169486\pi$
$503$	1.24801	+	6.27418i	0.0556461	+	0.279752i	−0.942937	+	0.332972i	$0.891949\pi$
$504$	−10.1965	+	10.3175i	−0.454188	+	0.459576i
$505$	−4.92224	−	0.979093i	−0.219037	−	0.0435691i
$506$	−0.410412	−	4.08465i	−0.0182450	−	0.181585i
$507$	−15.0722	+	4.57211i	−0.669381	+	0.203055i
$508$	−0.0724059	−	18.4167i	−0.00321249	−	0.817111i
$509$	16.7338	−	20.3902i	0.741713	−	0.903780i	−0.256312	−	0.966594i	$-0.582508\pi$
$509$	16.7338	−	20.3902i	0.741713	−	0.903780i	0.998025	+	0.0628141i	$0.0200075\pi$
$510$	3.02359	−	3.03550i	0.133887	−	0.134414i
$511$	−12.2770			−0.543102
$512$	15.7144	−	16.2805i	0.694487	−	0.719505i
$513$	−1.36351			−0.0602005
$514$	−23.0604	+	23.1513i	−1.01715	+	1.02116i
$515$	12.7390	−	15.5225i	0.561348	−	0.684004i
$516$	0.114342	+	29.0834i	0.00503362	+	1.28032i
$517$	−4.75887	+	1.44359i	−0.209295	+	0.0634889i
$518$	0.00861235	+	0.0857150i	0.000378405	+	0.00376610i
$519$	−17.7006	−	3.52087i	−0.776971	−	0.154549i
$520$	8.74011	−	8.84380i	0.383279	−	0.387826i
$521$	8.54623	+	42.9648i	0.374417	+	1.88232i	0.463172	+	0.886268i	$0.346711\pi$
$521$	8.54623	+	42.9648i	0.374417	+	1.88232i	−0.0887549	+	0.996053i	$0.528289\pi$
$522$	10.7624	−	20.2306i	0.471058	−	0.885470i
$523$	20.4364	+	2.01281i	0.893620	+	0.0880139i	0.534393	−	0.845236i	$-0.320540\pi$
$523$	20.4364	+	2.01281i	0.893620	+	0.0880139i	0.359227	+	0.933250i	$0.383040\pi$
$524$	25.7578	+	20.9700i	1.12524	+	0.916077i
$525$	1.15830	−	3.81840i	0.0505523	−	0.166648i
$526$	−14.1069	+	9.46609i	−0.615090	+	0.412741i
$527$	0.565091	−	1.36425i	0.0246157	−	0.0594277i
$528$	5.25002	−	5.33324i	0.228478	−	0.232100i
$529$	3.08970	+	7.45920i	0.134335	+	0.324313i
$530$	3.02669	+	2.01377i	0.131471	+	0.0874727i
$531$	19.5501	−	10.4497i	0.848400	−	0.453479i
$532$	−2.57420	−	8.36744i	−0.111606	−	0.362774i
$533$	−0.191259	+	0.156962i	−0.00828434	+	0.00679878i
$534$	−5.28443	+	4.35423i	−0.228680	+	0.188426i
$535$	2.11399	−	3.16381i	0.0913957	−	0.136783i
$536$	0.803016	+	7.68809i	0.0346850	+	0.332075i
$537$	13.0058	−	8.69019i	0.561241	−	0.375009i
$538$	10.7900	+	20.0916i	0.465190	+	0.866209i
$539$	2.93691	+	1.56981i	0.126502	+	0.0676166i
$540$	−0.190913	+	0.979905i	−0.00821561	+	0.0421684i
$541$	1.51320	+	15.3638i	0.0650577	+	0.660542i	0.971312	+	0.237809i	$0.0764293\pi$
$541$	1.51320	+	15.3638i	0.0650577	+	0.660542i	−0.906254	+	0.422733i	$0.861071\pi$
$542$	−12.3958	−	29.7606i	−0.532447	−	1.27833i
$543$	−34.3636	−	34.3636i	−1.47468	−	1.47468i
$544$	−6.38411	−	2.57117i	−0.273717	−	0.110238i
$545$	0.651336	−	0.651336i	0.0279002	−	0.0279002i
$546$	22.9373	+	9.44815i	0.981625	+	0.404344i
$547$	25.5508	−	2.51653i	1.09247	−	0.107599i	0.464303	−	0.885676i	$-0.346305\pi$
$547$	25.5508	−	2.51653i	1.09247	−	0.107599i	0.628168	+	0.778077i	$0.283805\pi$
$548$	−20.6052	+	4.18290i	−0.880209	+	0.178685i
$549$	−20.3421	+	38.0575i	−0.868181	+	1.62425i
$550$	−0.306451	+	1.01743i	−0.0130671	+	0.0433833i
$551$	7.68335	+	11.4989i	0.327322	+	0.489871i
$552$	12.6851	−	24.0725i	0.539912	−	1.02459i
$553$	19.3593	+	12.9355i	0.823241	+	0.550072i
$554$	−0.830947	+	8.61023i	−0.0353036	+	0.365814i
$555$	0.0600495	+	0.0731705i	0.00254896	+	0.00310592i
$556$	−0.782050	+	8.27362i	−0.0331663	+	0.350880i
$557$	−3.95729	−	7.40356i	−0.167676	−	0.313699i	0.784024	−	0.620731i	$-0.213164\pi$
$557$	−3.95729	−	7.40356i	−0.167676	−	0.313699i	−0.951699	+	0.307032i	$0.900664\pi$
$558$	1.08229	+	5.38571i	0.0458172	+	0.227995i
$559$	23.7183	−	9.82446i	1.00318	−	0.415530i
$560$	−6.37379	+	0.678407i	−0.269342	+	0.0286679i
$561$	−2.10300	−	0.871093i	−0.0887889	−	0.0367776i
$562$	−6.72452	+	34.1572i	−0.283657	+	1.44084i
$563$	7.41015	+	2.24784i	0.312300	+	0.0947353i	0.442544	−	0.896747i	$-0.354076\pi$
$563$	7.41015	+	2.24784i	0.312300	+	0.0947353i	−0.130244	+	0.991482i	$0.541576\pi$
$564$	−31.5801	−	9.44431i	−1.32976	−	0.397677i
$565$	0.901944	−	9.15759i	0.0379451	−	0.385263i
$566$	7.17709	−	2.19256i	0.301676	−	0.0921603i
$567$	13.1366	−	2.61303i	0.551685	−	0.109737i
$568$	16.9500	−	11.4708i	0.711206	−	0.481303i
$569$	−4.81183	+	24.1907i	−0.201723	+	1.01413i	0.738678	+	0.674059i	$0.235450\pi$
$569$	−4.81183	+	24.1907i	−0.201723	+	1.01413i	−0.940400	+	0.340069i	$0.889550\pi$
$570$	−7.44778	−	6.08777i	−0.311953	−	0.254989i
$571$	1.26293	+	4.16334i	0.0528522	+	0.174230i	0.979393	−	0.201964i	$-0.0647325\pi$
$571$	1.26293	+	4.16334i	0.0528522	+	0.174230i	−0.926541	+	0.376194i	$0.877232\pi$
$572$	−6.11305	−	2.50400i	−0.255599	−	0.104697i
$573$	36.0160	+	29.5575i	1.50459	+	1.23478i
$574$	0.127547		0.000250727i	0.00532372		1.04651e-5i
$575$			3.86345i			0.161117i
$576$	25.0511	−	5.29086i	1.04379	−	0.220452i
$577$		−	38.5192i		−	1.60358i	−0.597608	−	0.801789i	$-0.703882\pi$
$577$		−	38.5192i		−	1.60358i	0.597608	−	0.801789i	$-0.296118\pi$
$578$	−0.0431448	−	21.9482i	−0.00179459	−	0.912925i
$579$	−6.75358	−	5.54252i	−0.280669	−	0.230339i
$580$	9.33965	−	3.91170i	0.387808	−	0.162424i
$581$	−6.97015	−	22.9775i	−0.289171	−	0.953268i
$582$	15.8516	−	19.3929i	0.657071	−	0.803860i
$583$	0.376807	−	1.89434i	0.0156057	−	0.0784554i
$584$	18.0884	+	11.9326i	0.748502	+	0.493773i
$585$	13.7991	−	2.74480i	0.570521	−	0.113484i
$586$	10.4475	+	34.1985i	0.431580	+	1.41273i
$587$	4.03163	−	40.9338i	0.166403	−	1.68952i	−0.442892	−	0.896575i	$-0.646048\pi$
$587$	4.03163	−	40.9338i	0.166403	−	1.68952i	0.609295	−	0.792944i	$-0.291452\pi$
$588$	10.4815	+	19.4254i	0.432250	+	0.801090i
$589$	−3.17258	−	0.962390i	−0.130724	−	0.0396546i
$590$	9.61089	+	1.89209i	0.395674	+	0.0778962i
$591$	46.2107	+	19.1411i	1.90085	+	0.787360i
$592$	0.0706213	−	0.134659i	0.00290252	−	0.00553447i
$593$	20.8695	−	8.64441i	0.857006	−	0.354984i	0.0894702	−	0.995989i	$-0.471483\pi$
$593$	20.8695	−	8.64441i	0.857006	−	0.354984i	0.767536	+	0.641006i	$0.221483\pi$
$594$	0.520006	−	0.104499i	0.0213361	−	0.00428763i
$595$	0.919046	+	1.71941i	0.0376772	+	0.0704891i
$596$	−16.1482	−	19.5197i	−0.661457	−	0.799556i
$597$	26.1766	+	31.8963i	1.07134	+	1.30543i
$598$	−23.9078	−	2.30727i	−0.977663	−	0.0943513i
$599$	−11.2173	−	7.49515i	−0.458326	−	0.306244i	0.304889	−	0.952388i	$-0.401380\pi$
$599$	−11.2173	−	7.49515i	−0.458326	−	0.306244i	−0.763215	+	0.646144i	$0.776380\pi$
$600$	−5.41786	+	4.50005i	−0.221183	+	0.183714i
$601$	20.8347	+	31.1813i	0.849863	+	1.27191i	0.960565	+	0.278056i	$0.0896902\pi$
$601$	20.8347	+	31.1813i	0.849863	+	1.27191i	−0.110702	+	0.993854i	$0.535310\pi$
$602$	−12.6721	−	3.81685i	−0.516475	−	0.155563i
$603$	−4.12315	+	7.71386i	−0.167907	+	0.314133i
$604$	23.0374	+	15.2624i	0.937379	+	0.621020i
$605$	−10.3852	+	1.02285i	−0.422219	+	0.0415849i
$606$	−6.73113	+	16.3412i	−0.273434	+	0.663815i
$607$	−14.0821	+	14.0821i	−0.571576	+	0.571576i	−0.932569	−	0.360993i	$-0.882438\pi$
$607$	−14.0821	+	14.0821i	−0.571576	+	0.571576i	0.360993	+	0.932569i	$0.382438\pi$
$608$	−4.33998	+	14.8302i	−0.176010	+	0.601444i
$609$	14.2849	+	14.2849i	0.578854	+	0.578854i
$610$	−17.6024	+	7.33175i	−0.712702	+	0.296854i
$611$	2.85192	+	28.9561i	0.115377	+	1.17144i
$612$	−4.35204	−	6.45818i	−0.175921	−	0.261056i
$613$	0.689617	+	0.368608i	0.0278534	+	0.0148879i	0.485265	−	0.874367i	$-0.338723\pi$
$613$	0.689617	+	0.368608i	0.0278534	+	0.0148879i	−0.457411	+	0.889255i	$0.651223\pi$
$614$	−4.77043	+	2.56192i	−0.192519	+	0.103391i
$615$	0.116528	−	0.0778617i	0.00469887	−	0.00313969i
$616$	1.62300	+	2.99382i	0.0653927	+	0.120625i
$617$	−3.04364	+	4.55512i	−0.122532	+	0.183382i	−0.887665	−	0.460491i	$-0.847673\pi$
$617$	−3.04364	+	4.55512i	−0.122532	+	0.183382i	0.765132	+	0.643873i	$0.222673\pi$
$618$	−44.9677	−	54.5742i	−1.80887	−	2.19530i
$619$	−19.2894	+	15.8304i	−0.775307	+	0.636278i	−0.936509	−	0.350643i	$-0.885963\pi$
$619$	−19.2894	+	15.8304i	−0.775307	+	0.636278i	0.161202	+	0.986921i	$0.448463\pi$
$620$	−1.13584	+	2.14526i	−0.0456166	+	0.0861557i
$621$	1.70078	−	0.909087i	0.0682500	−	0.0364804i
$622$	−16.1395	+	24.2575i	−0.647134	+	0.972638i
$623$	−1.19237	−	2.87864i	−0.0477713	−	0.115330i
$624$	−24.6117	−	36.2143i	−0.985256	−	1.44973i
$625$	0.382683	−	0.923880i	0.0153073	−	0.0369552i
$626$	−20.4517	−	30.4783i	−0.817414	−	1.21816i
$627$	−1.48353	+	4.89055i	−0.0592466	+	0.195310i
$628$	−14.3263	+	1.46791i	−0.571681	+	0.0585759i
$629$	−0.0460266	−	0.00453323i	−0.00183520	−	0.000180752i
$630$	−6.40320	−	3.40641i	−0.255109	−	0.135715i
$631$	6.33450	+	31.8457i	0.252173	+	1.26776i	0.874510	+	0.485008i	$0.161183\pi$
$631$	6.33450	+	31.8457i	0.252173	+	1.26776i	−0.622337	+	0.782749i	$0.713817\pi$
$632$	−15.9506	−	37.8747i	−0.634479	−	1.50658i
$633$	−59.2872	−	11.7929i	−2.35645	−	0.468728i
$634$	−28.2340	+	2.83686i	−1.12132	+	0.112666i
$635$	8.81193	−	2.67307i	0.349691	−	0.106078i
$636$	9.01674	−	9.08792i	0.357537	−	0.360360i
$637$	12.3605	−	15.0613i	0.489742	−	0.596752i
$638$	−3.81149	−	3.79653i	−0.150898	−	0.150306i
$639$	23.1586			0.916142
$640$	10.0502	+	5.19545i	0.397271	+	0.205368i
$641$	0.424644			0.0167724			0.00838622	−	0.999965i	$-0.497331\pi$
$641$	0.424644			0.0167724			0.00838622	+	0.999965i	$0.497331\pi$
$642$	−9.49353	−	9.45628i	−0.374680	−	0.373210i
$643$	−7.60656	+	9.26862i	−0.299973	+	0.365519i	−0.901082	−	0.433649i	$-0.857226\pi$
$643$	−7.60656	+	9.26862i	−0.299973	+	0.365519i	0.601109	+	0.799167i	$0.294726\pi$
$644$	8.78971	+	8.72087i	0.346363	+	0.343650i
$645$	−13.9156	+	4.22126i	−0.547927	+	0.166212i
$646$	4.67644	−	0.469873i	0.183992	−	0.0184869i
$647$	21.9362	+	4.36338i	0.862400	+	0.171542i	0.606424	−	0.795141i	$-0.292603\pi$
$647$	21.9362	+	4.36338i	0.862400	+	0.171542i	0.255976	+	0.966683i	$0.417603\pi$
$648$	−21.8946	−	8.91814i	−0.860101	−	0.350337i
$649$	−1.01528	−	5.10418i	−0.0398534	−	0.200356i
$650$	5.48862	+	2.91987i	0.215281	+	0.114527i
$651$	−4.81961	−	0.474690i	−0.188895	−	0.0186046i
$652$	0.595059	+	5.80757i	0.0233043	+	0.227442i
$653$	−3.57408	+	11.7822i	−0.139865	+	0.461072i	−0.998688	−	0.0511992i	$-0.983696\pi$
$653$	−3.57408	+	11.7822i	−0.139865	+	0.461072i	0.858824	+	0.512271i	$0.171196\pi$
$654$	−1.80743	−	2.69353i	−0.0706760	−	0.105325i
$655$	−6.35532	+	15.3431i	−0.248323	+	0.599505i
$656$	−0.188166	−	0.123600i	−0.00734666	−	0.00482576i
$657$	9.38339	+	22.6535i	0.366081	+	0.883798i
$658$	8.30865	−	12.4879i	0.323905	−	0.486827i
$659$	3.49177	−	1.86639i	0.136020	−	0.0727043i	−0.401983	−	0.915647i	$-0.631679\pi$
$659$	3.49177	−	1.86639i	0.136020	−	0.0727043i	0.538003	+	0.842943i	$0.319179\pi$
$660$	3.30694	+	1.75092i	0.128722	+	0.0681543i
$661$	−32.8107	+	26.9270i	−1.27619	+	1.04734i	−0.280008	+	0.959998i	$0.590337\pi$
$661$	−32.8107	+	26.9270i	−1.27619	+	1.04734i	−0.996178	+	0.0873417i	$0.972163\pi$
$662$	−22.3495	−	27.1241i	−0.868640	−	1.05421i
$663$	−7.39913	+	11.0736i	−0.287358	+	0.430062i
$664$	−12.0634	+	40.6287i	−0.468150	+	1.57670i
$665$	3.63953	−	2.43186i	0.141135	−	0.0943034i
$666$	0.151579	−	0.0814042i	0.00587357	−	0.00315435i
$667$	−17.2505	−	9.22057i	−0.667941	−	0.357022i
$668$	38.1525	−	25.7102i	1.47616	−	0.994758i
$669$	1.17696	+	11.9499i	0.0455040	+	0.462010i
$670$	−3.56784	+	1.48607i	−0.137838	+	0.0574119i
$671$	7.16355	+	7.16355i	0.276546	+	0.276546i
$672$	−1.99156	+	22.4840i	−0.0768260	+	0.867340i
$673$	22.6353	−	22.6353i	0.872526	−	0.872526i	−0.120221	−	0.992747i	$-0.538360\pi$
$673$	22.6353	−	22.6353i	0.872526	−	0.872526i	0.992747	+	0.120221i	$0.0383604\pi$
$674$	9.85918	−	23.9351i	0.379761	−	0.921947i
$675$	−0.496761	+	0.0489267i	−0.0191203	+	0.00188319i
$676$	−6.98688	+	10.5461i	−0.268726	+	0.405620i
$677$	−21.1860	+	39.6363i	−0.814245	+	1.52335i	0.0374438	+	0.999299i	$0.488078\pi$
$677$	−21.1860	+	39.6363i	−0.814245	+	1.52335i	−0.851689	+	0.524047i	$0.824422\pi$
$678$	−31.0275	−	9.34554i	−1.19161	−	0.358913i
$679$	6.33218	+	9.47678i	0.243007	+	0.363685i
$680$	0.317096	−	3.42657i	0.0121601	−	0.131403i
$681$	21.9627	+	14.6750i	0.841614	+	0.562348i
$682$	1.28369	+	0.123885i	0.0491550	+	0.00474380i
$683$	−14.6178	−	17.8119i	−0.559336	−	0.681552i	0.414174	−	0.910198i	$-0.364070\pi$
$683$	−14.6178	−	17.8119i	−0.559336	−	0.681552i	−0.973510	+	0.228645i	$0.926570\pi$
$684$	−13.4721	+	11.1452i	−0.515120	+	0.426148i
$685$	−4.95567	−	9.27140i	−0.189346	−	0.354242i
$686$	−25.3998	+	5.10426i	−0.969770	+	0.194882i
$687$	−34.7815	+	14.4070i	−1.32700	+	0.549660i
$688$	14.9607	+	17.9402i	0.570372	+	0.683962i
$689$	−10.4404	−	4.32454i	−0.397746	−	0.164752i
$690$	13.3489	+	2.62799i	0.508183	+	0.100046i
$691$	14.8297	+	4.49853i	0.564147	+	0.171132i	0.559461	−	0.828857i	$-0.311008\pi$
$691$	14.8297	+	4.49853i	0.564147	+	0.171132i	0.00468655	+	0.999989i	$0.498508\pi$
$692$	−12.7569	+	6.88333i	−0.484945	+	0.261665i
$693$	−0.377698	+	3.83483i	−0.0143476	+	0.145673i
$694$	−5.81727	−	19.0421i	−0.220821	−	0.722830i
$695$	−4.07541	+	0.810649i	−0.154589	+	0.0307497i
$696$	−7.16259	−	34.9309i	−0.271497	−	1.32405i
$697$	−0.0133590	+	0.0671605i	−0.000506010	+	0.00254388i
$698$	−8.43739	+	10.3223i	−0.319360	+	0.390705i
$699$	12.2891	+	40.5116i	0.464815	+	1.53229i
$700$	−1.23809	−	2.95609i	−0.0467955	−	0.111730i
$701$	32.9854	+	27.0705i	1.24584	+	1.02244i	0.998568	+	0.0534914i	$0.0170350\pi$
$701$	32.9854	+	27.0705i	1.24584	+	1.02244i	0.247275	+	0.968945i	$0.420465\pi$
$702$	−0.00610029	−	3.10328i	−0.000230241	−	0.117126i
$703$			0.103837i			0.00391630i
$704$	0.518574	−	5.98844i	0.0195445	−	0.225698i
$705$		−	16.4811i		−	0.620712i
$706$	33.9408	−	0.0667193i	1.27738	−	0.00251101i
$707$	−6.21667	−	5.10189i	−0.233802	−	0.191876i
$708$	13.0750	−	31.9203i	0.491389	−	1.19964i
$709$	−1.73549	−	5.72116i	−0.0651779	−	0.214863i	0.918302	−	0.395881i	$-0.129561\pi$
$709$	−1.73549	−	5.72116i	−0.0651779	−	0.214863i	−0.983480	+	0.181018i	$0.942061\pi$
$710$	7.92319	+	6.47637i	0.297352	+	0.243054i
$711$	9.07209	−	45.6085i	0.340230	−	1.71045i
$712$	−1.04109	+	5.40018i	−0.0390167	+	0.202380i
$713$	4.59897	−	0.914792i	0.172233	−	0.0342592i
$714$	6.56603	−	2.00589i	0.245727	−	0.0750684i
$715$	0.323751	−	3.28710i	0.0121076	−	0.122931i
$716$	3.59968	−	12.0367i	0.134526	−	0.449832i
$717$	−22.2166	−	6.73934i	−0.829695	−	0.251685i
$718$	−2.34905	+	11.9320i	−0.0876658	+	0.445299i
$719$	21.3138	+	8.82845i	0.794869	+	0.329246i	0.742899	−	0.669403i	$-0.233450\pi$
$719$	21.3138	+	8.82845i	0.794869	+	0.329246i	0.0519697	+	0.998649i	$0.483450\pi$
$720$	6.12334	+	11.2424i	0.228203	+	0.418980i
$721$	29.7287	−	12.3140i	1.10716	−	0.458599i
$722$	3.21490	+	15.9980i	0.119646	+	0.595383i
$723$	22.2066	+	41.5456i	0.825871	+	1.54510i
$724$	−38.8597	−	3.67315i	−1.44421	−	0.136511i
$725$	3.21185	+	3.91365i	0.119285	+	0.145349i
$726$	−3.53008	+	36.5785i	−0.131013	+	1.35755i
$727$	13.9001	+	9.28773i	0.515525	+	0.344463i	0.785962	−	0.618275i	$-0.212168\pi$
$727$	13.9001	+	9.28773i	0.515525	+	0.344463i	−0.270437	+	0.962738i	$0.587168\pi$
$728$	19.0323	−	5.89618i	0.705385	−	0.218527i
$729$	−16.9336	−	25.3429i	−0.627171	−	0.938628i
$730$	−3.12480	+	10.3745i	−0.115654	+	0.383976i
$731$	3.34934	−	6.26617i	0.123880	−	0.231763i
$732$	13.3589	+	65.8067i	0.493761	+	2.43229i
$733$	2.89899	−	0.285525i	0.107077	−	0.0105461i	−0.0443369	−	0.999017i	$-0.514118\pi$
$733$	2.89899	−	0.285525i	0.107077	−	0.0105461i	0.151413	+	0.988471i	$0.451618\pi$
$734$	−17.6956	−	7.28905i	−0.653158	−	0.269044i
$735$	−7.80391	+	7.80391i	−0.287852	+	0.287852i
$736$	−4.47416	−	21.3921i	−0.164920	−	0.788522i
$737$	1.45198	+	1.45198i	0.0534844	+	0.0534844i
$738$	−0.0979480	−	0.235159i	−0.00360552	−	0.00865632i
$739$	0.219366	+	2.22726i	0.00806952	+	0.0819312i	0.998376	−	0.0569685i	$-0.0181434\pi$
$739$	0.219366	+	2.22726i	0.00806952	+	0.0819312i	−0.990306	+	0.138900i	$0.955643\pi$
$740$	0.0746241	+	0.0145389i	0.00274324	+	0.000534460i
$741$	26.3706	+	14.0954i	0.968748	+	0.517807i
$742$	2.75623	+	5.13226i	0.101185	+	0.188411i
$743$	36.4624	−	24.3634i	1.33768	−	0.893808i	0.338785	−	0.940864i	$-0.389984\pi$
$743$	36.4624	−	24.3634i	1.33768	−	0.893808i	0.998892	+	0.0470561i	$0.0149840\pi$
$744$	6.63963	+	5.38379i	0.243420	+	0.197379i
$745$	7.03724	−	10.5320i	0.257825	−	0.385862i
$746$	−9.25264	+	7.62394i	−0.338763	+	0.279132i
$747$	−37.0708	+	30.4232i	−1.35635	+	1.11313i
$748$	−1.74745	+	0.537596i	−0.0638933	+	0.0196565i
$749$	5.37747	−	2.87432i	0.196488	−	0.105025i
$750$	−2.93186	−	1.95068i	−0.107056	−	0.0712287i
$751$	−8.20530	−	19.8093i	−0.299416	−	0.722853i	−0.999957	−	0.00924174i	$-0.997058\pi$
$751$	−8.20530	−	19.8093i	−0.299416	−	0.722853i	0.700542	−	0.713611i	$-0.252942\pi$
$752$	−24.3791	+	10.3235i	−0.889015	+	0.376459i
$753$	27.1409	−	65.5240i	0.989071	−	2.38783i
$754$	−26.1366	+	17.5383i	−0.951839	+	0.638708i
$755$	−4.01093	+	13.2223i	−0.145973	+	0.481208i
$756$	−1.01001	+	1.24062i	−0.0367339	+	0.0451209i
$757$	23.7842	+	2.34254i	0.864451	+	0.0851409i	0.520515	−	0.853852i	$-0.325740\pi$
$757$	23.7842	+	2.34254i	0.864451	+	0.0851409i	0.343935	+	0.938993i	$0.388240\pi$
$758$	−15.5190	+	29.1718i	−0.563675	+	1.05957i
$759$	−1.41016	−	7.08936i	−0.0511856	−	0.257327i
$760$	−7.72596	+	0.0455625i	−0.280250	+	0.00165273i
$761$	6.29238	+	1.25163i	0.228098	+	0.0453716i	0.307816	−	0.951446i	$-0.400402\pi$
$761$	6.29238	+	1.25163i	0.228098	+	0.0453716i	−0.0797176	+	0.996817i	$0.525402\pi$
$762$	−3.24188	−	32.2650i	−0.117441	−	1.16884i
$763$	1.41250	−	0.428478i	0.0511360	−	0.0155119i
$764$	37.4218	−	0.147125i	1.35387	−	0.00532278i
$765$	2.47023	−	3.00999i	0.0893115	−	0.108826i
$766$	30.9148	−	31.0366i	1.11700	−	1.12140i
$767$	−30.4487			−1.09944
$768$	24.7875	−	31.1913i	0.894443	−	1.12552i
$769$	36.0112			1.29860			0.649299	−	0.760533i	$-0.275062\pi$
$769$	36.0112			1.29860			0.649299	+	0.760533i	$0.275062\pi$
$770$	−1.20164	+	1.20637i	−0.0433041	+	0.0434747i
$771$	−36.5000	+	44.4754i	−1.31452	+	1.60174i
$772$	−7.01719	+	0.0275882i	−0.252554	+	0.000992923i
$773$	24.4991	−	7.43171i	0.881170	−	0.267300i	0.182897	−	0.983132i	$-0.441452\pi$
$773$	24.4991	−	7.43171i	0.881170	−	0.267300i	0.698273	+	0.715832i	$0.253952\pi$
$774$	2.64251	+	26.2998i	0.0949832	+	0.945326i
$775$	−1.19038	−	0.236781i	−0.0427597	−	0.00850544i
$776$	−0.118638	−	20.1172i	−0.00425884	−	0.722166i
$777$	0.0295918	+	0.148768i	0.00106160	+	0.00533702i
$778$	−20.4854	+	38.5073i	−0.734436	+	1.38055i
$779$	0.153000	+	0.0150692i	0.00548180	+	0.000539910i
$780$	13.8221	−	16.9780i	0.494911	−	0.607909i
$781$	1.57823	−	5.20273i	0.0564736	−	0.186168i
$782$	−5.51990	+	3.70400i	−0.197391	+	0.132455i
$783$	0.967119	−	2.33483i	0.0345620	−	0.0834401i
$784$	16.4320	+	6.65546i	0.586856	+	0.237695i
$785$	−2.75557	−	6.65253i	−0.0983504	−	0.237439i
$786$	48.6901	+	32.3954i	1.73672	+	1.15551i
$787$	20.2717	−	10.8355i	0.722609	−	0.386242i	−0.0687178	−	0.997636i	$-0.521891\pi$
$787$	20.2717	−	10.8355i	0.722609	−	0.386242i	0.791327	+	0.611394i	$0.209391\pi$
$788$	38.3980	−	11.8130i	1.36787	−	0.420819i
$789$	−23.1227	+	18.9763i	−0.823191	+	0.675575i
$790$	15.8583	−	13.0668i	0.564214	−	0.464897i
$791$	8.19220	−	12.2605i	0.291281	−	0.435933i
$792$	4.28374	−	5.28297i	0.152216	−	0.187722i
$793$	49.2841	−	32.9306i	1.75013	−	1.16940i
$794$	−4.11050	−	7.65398i	−0.145876	−	0.271629i
$795$	5.64519	+	3.01742i	0.200214	+	0.107017i
$796$	32.5299	+	6.33775i	1.15299	+	0.224636i
$797$	4.08838	+	41.5100i	0.144818	+	1.47036i	0.743158	+	0.669116i	$0.233327\pi$
$797$	4.08838	+	41.5100i	0.144818	+	1.47036i	−0.598340	+	0.801242i	$0.704173\pi$
$798$	−5.92681	−	14.2294i	−0.209807	−	0.503716i
$799$	5.69409	+	5.69409i	0.201443	+	0.201443i
$800$	−1.04901	+	5.55874i	−0.0370882	+	0.196531i
$801$	−4.40033	+	4.40033i	−0.155478	+	0.155478i
$802$	26.9023	+	11.0814i	0.949954	+	0.391298i
$803$	5.72872	−	0.564229i	0.202162	−	0.0199112i
$804$	2.70772	+	13.3384i	0.0954940	+	0.470407i
$805$	−2.91840	+	5.45995i	−0.102860	+	0.192438i
$806$	2.17615	−	7.22492i	0.0766518	−	0.254487i
$807$	22.3089	+	33.3876i	0.785310	+	1.17530i
$808$	4.20061	+	13.5592i	0.147777	+	0.477010i
$809$	−45.9472	−	30.7009i	−1.61542	−	1.07939i	−0.939576	−	0.342339i	$-0.888781\pi$
$809$	−45.9472	−	30.7009i	−1.61542	−	1.07939i	−0.675841	−	0.737048i	$-0.736219\pi$
$810$	1.13550	−	11.7659i	0.0398972	−	0.413413i
$811$	−17.4878	−	21.3090i	−0.614080	−	0.748259i	0.369401	−	0.929270i	$-0.379563\pi$
$811$	−17.4878	−	21.3090i	−0.614080	−	0.748259i	−0.983481	+	0.181011i	$0.942063\pi$
$812$	16.1540	+	1.52693i	0.566893	+	0.0535846i
$813$	−26.7587	−	50.0619i	−0.938467	−	1.75575i
$814$	−0.00795803	−	0.0396007i	−0.000278929	−	0.00138800i
$815$	−2.69679	+	1.11705i	−0.0944645	+	0.0391285i
$816$	−11.6237	−	3.42644i	−0.406911	−	0.119949i
$817$	−14.7379	−	6.10465i	−0.515615	−	0.213575i
$818$	−7.81001	+	39.6710i	−0.273071	+	1.38706i
$819$	21.5747	+	6.54461i	0.753881	+	0.228687i
$820$	0.0322521	−	0.107846i	0.00112629	−	0.00376613i
$821$	0.851767	−	8.64814i	0.0297269	−	0.301822i	−0.968813	−	0.247795i	$-0.920294\pi$
$821$	0.851767	−	8.64814i	0.0297269	−	0.301822i	0.998539	−	0.0540274i	$-0.0172058\pi$
$822$	−35.4052	+	10.8161i	−1.23490	+	0.377255i
$823$	−6.77637	+	1.34790i	−0.236210	+	0.0469850i	−0.311775	−	0.950156i	$-0.600924\pi$
$823$	−6.77637	+	1.34790i	−0.236210	+	0.0469850i	0.0755659	+	0.997141i	$0.475924\pi$
$824$	−55.7696	−	10.7518i	−1.94283	−	0.374555i
$825$	−0.365001	+	1.83498i	−0.0127077	+	0.0638859i
$826$	12.1532	+	9.93393i	0.422863	+	0.345646i
$827$	−5.25901	−	17.3366i	−0.182874	−	0.602854i	−0.999664	−	0.0259191i	$-0.991749\pi$
$827$	−5.25901	−	17.3366i	−0.182874	−	0.602854i	0.816790	−	0.576934i	$-0.195751\pi$
$828$	9.37372	−	22.8842i	0.325759	−	0.795282i
$829$	−28.7611	−	23.6036i	−0.998913	−	0.819787i	−0.0152639	−	0.999883i	$-0.504859\pi$
$829$	−28.7611	−	23.6036i	−0.998913	−	0.819787i	−0.983649	+	0.180097i	$0.942359\pi$
$830$	−21.1908	+	0.0416560i	−0.735545	+	0.00144590i
$831$			15.2309i			0.528353i
$832$	−33.7722	−	9.81122i	−1.17084	−	0.340143i
$833$		−	5.39240i		−	0.186836i
$834$	0.0287642	+	14.6327i	0.000996023	+	0.506688i
$835$	17.7819	+	14.5932i	0.615367	+	0.505019i
$836$	1.58573	+	3.78613i	0.0548437	+	0.130946i
$837$	0.175865	+	0.579750i	0.00607879	+	0.0200391i
$838$	19.8647	−	24.3025i	0.686216	−	0.839517i
$839$	2.35143	−	11.8214i	0.0811802	−	0.408121i	−0.918732	−	0.394881i	$-0.870786\pi$
$839$	2.35143	−	11.8214i	0.0811802	−	0.408121i	0.999912	−	0.0132392i	$-0.00421429\pi$
$840$	−11.0560	+	2.26703i	−0.381468	+	0.0782201i
$841$	3.30269	−	0.656945i	0.113886	−	0.0226533i
$842$	−9.61946	−	31.4882i	−0.331508	−	1.08515i
$843$	−6.00812	+	61.0015i	−0.206931	+	2.10100i
$844$	−42.7285	+	23.0553i	−1.47078	+	0.793596i
$845$	−6.05293	−	1.83613i	−0.208227	−	0.0631650i
$846$	−29.3930	−	5.78658i	−1.01055	−	0.198947i
$847$	−15.4494	−	6.39934i	−0.530847	−	0.219884i
$848$	0.927365	−	10.2406i	0.0318458	−	0.351662i
$849$	12.2078	−	5.05662i	0.418969	−	0.173543i
$850$	1.68688	−	0.338990i	0.0578596	−	0.0116273i
$851$	−0.0692310	−	0.129522i	−0.00237321	−	0.00443996i
$852$	27.7665	−	22.9706i	0.951264	−	0.786961i
$853$	−16.9137	−	20.6094i	−0.579115	−	0.705654i	0.398235	−	0.917284i	$-0.369623\pi$
$853$	−16.9137	−	20.6094i	−0.579115	−	0.705654i	−0.977350	+	0.211630i	$0.932123\pi$
$854$	−30.4147	−	2.93523i	−1.04077	−	0.100441i
$855$	−7.26899	−	4.85698i	−0.248594	−	0.166105i
$856$	−10.7166	−	0.991718i	−0.366286	−	0.0338962i
$857$	−4.67108	−	6.99076i	−0.159561	−	0.238800i	0.743071	−	0.669212i	$-0.233368\pi$
$857$	−4.67108	−	6.99076i	−0.159561	−	0.238800i	−0.902632	+	0.430412i	$0.858368\pi$
$858$	−11.1373	−	3.35456i	−0.380220	−	0.114523i
$859$	−4.88167	+	9.13296i	−0.166560	+	0.311613i	−0.951329	−	0.308176i	$-0.900282\pi$
$859$	−4.88167	+	9.13296i	−0.166560	+	0.311613i	0.784769	+	0.619788i	$0.212782\pi$
$860$	−6.45072	+	9.73684i	−0.219968	+	0.332024i
$861$	0.223498	−	0.0220126i	0.00761678	−	0.000750187i
$862$	−15.0408	+	36.5146i	−0.512292	+	1.24369i
$863$	−10.7664	+	10.7664i	−0.366494	+	0.366494i	−0.866197	−	0.499703i	$-0.833443\pi$
$863$	−10.7664	+	10.7664i	−0.366494	+	0.366494i	0.499703	+	0.866197i	$0.333443\pi$
$864$	2.69393	−	0.846196i	0.0916493	−	0.0287882i
$865$	−5.12493	−	5.12493i	−0.174253	−	0.174253i
$866$	17.2187	−	7.17189i	0.585114	−	0.243711i
$867$	−3.78790	−	38.4592i	−0.128644	−	1.30614i
$868$	−3.22572	+	2.17375i	−0.109488	+	0.0737819i
$869$	−9.62797	−	5.14626i	−0.326607	−	0.174575i
$870$	15.7071	−	8.43536i	0.532520	−	0.285985i
$871$	9.98939	−	6.67469i	0.338477	−	0.226163i
$872$	−2.49758	−	0.741576i	−0.0845786	−	0.0251129i
$873$	12.6468	−	18.9273i	0.428031	−	0.640593i
$874$	9.49078	+	11.5183i	0.321030	+	0.389612i
$875$	1.23871	−	1.01658i	0.0418760	−	0.0343668i
$876$	33.7200	+	17.8536i	1.13929	+	0.603218i
$877$	24.3083	−	12.9931i	0.820834	−	0.438745i	−0.00682435	−	0.999977i	$-0.502172\pi$
$877$	24.3083	−	12.9931i	0.820834	−	0.438745i	0.827659	+	0.561232i	$0.189672\pi$
$878$	3.72817	−	5.60342i	0.125820	−	0.189106i
$879$	24.0945	+	58.1694i	0.812689	+	1.96200i
$880$	2.94298	−	0.609489i	0.0992077	−	0.0205459i
$881$	−15.6680	+	37.8258i	−0.527867	+	1.27438i	0.405051	+	0.914294i	$0.367254\pi$
$881$	−15.6680	+	37.8258i	−0.527867	+	1.27438i	−0.932918	+	0.360090i	$0.882746\pi$
$882$	11.1778	+	16.6578i	0.376377	+	0.560897i
$883$	5.42800	−	17.8937i	0.182667	−	0.602172i	−0.817007	−	0.576628i	$-0.804368\pi$
$883$	5.42800	−	17.8937i	0.182667	−	0.602172i	0.999674	−	0.0255439i	$-0.00813177\pi$
$884$	1.09033	+	10.6412i	0.0366717	+	0.357903i
$885$	17.1641	+	1.69052i	0.576965	+	0.0568261i
$886$	−32.4637	−	17.2702i	−1.09064	−	0.580205i
$887$	3.85930	+	19.4020i	0.129583	+	0.651456i	0.989908	+	0.141711i	$0.0452603\pi$
$887$	3.85930	+	19.4020i	0.129583	+	0.651456i	−0.860326	+	0.509745i	$0.829740\pi$
$888$	0.100995	−	0.247950i	0.00338917	−	0.00832064i
$889$	14.4725	+	2.87876i	0.485393	+	0.0965506i
$890$	−2.73603	+	0.274907i	−0.0917121	+	0.00921492i
$891$	−6.00974	+	1.82303i	−0.201334	+	0.0610739i
$892$	6.84643	+	6.79281i	0.229235	+	0.227440i
$893$	11.4696	−	13.9757i	0.383814	−	0.467679i
$894$	−31.6030	−	31.4790i	−1.05696	−	1.05281i
$895$	6.28171			0.209975
$896$	10.2788	+	14.9342i	0.343389	+	0.498917i
$897$	−42.2912			−1.41206
$898$	−22.5671	−	22.4786i	−0.753075	−	0.750120i
$899$	3.89823	−	4.75000i	0.130013	−	0.158421i
$900$	−4.50831	+	4.54390i	−0.150277	+	0.151463i
$901$	−2.99287	+	0.907878i	−0.0997071	+	0.0302458i
$902$	−0.0595049	+	0.00597885i	−0.00198130	+	0.000199074i
$903$	−22.8547	−	4.54609i	−0.760557	−	0.151284i
$904$	−23.9866	+	10.1017i	−0.797781	+	0.335977i
$905$	−3.80747	−	19.1415i	−0.126565	−	0.636284i
$906$	42.9569	+	22.8525i	1.42715	+	0.759224i
$907$	19.8794	+	1.95795i	0.660085	+	0.0650127i	0.422512	−	0.906357i	$-0.361148\pi$
$907$	19.8794	+	1.95795i	0.660085	+	0.0650127i	0.237572	+	0.971370i	$0.423648\pi$
$908$	21.1052	−	2.16250i	0.700402	−	0.0717650i
$909$	−4.66257	+	15.3704i	−0.154648	+	0.509805i
$910$	5.55106	+	8.27250i	0.184016	+	0.274231i
$911$	9.32028	−	22.5011i	0.308795	−	0.745496i	−0.690950	−	0.722902i	$-0.742808\pi$
$911$	9.32028	−	22.5011i	0.308795	−	0.745496i	0.999745	−	0.0225936i	$-0.00719239\pi$
$912$	−5.09792	+	26.7255i	−0.168809	+	0.884971i
$913$	4.30844	+	10.4015i	0.142588	+	0.344239i
$914$	20.7892	−	31.2460i	0.687646	−	1.03353i
$915$	−29.6101	+	15.8269i	−0.978878	+	0.523221i
$916$	−14.1491	+	26.7232i	−0.467498	+	0.882961i
$917$	−20.5716	+	16.8827i	−0.679333	+	0.557514i
$918$	−0.546163	−	0.662840i	−0.0180261	−	0.0218770i
$919$	0.235392	−	0.352289i	0.00776486	−	0.0116209i	−0.827567	−	0.561367i	$-0.810276\pi$
$919$	0.235392	−	0.352289i	0.00776486	−	0.0116209i	0.835332	+	0.549746i	$0.185276\pi$
$920$	9.60663	−	5.20792i	0.316721	−	0.171700i
$921$	−7.92736	+	5.29689i	−0.261215	+	0.174538i
$922$	−3.11374	+	1.67221i	−0.102545	+	0.0550711i
$923$	−28.0539	−	14.9951i	−0.923405	−	0.493571i
$924$	3.35086	+	4.97248i	0.110235	+	0.163583i
$925$	0.00372598	+	0.0378305i	0.000122510	+	0.00124386i
$926$	−8.82965	+	3.67771i	−0.290160	+	0.120857i
$927$	−45.4438	−	45.4438i	−1.49257	−	1.49257i
$928$	−22.3164	−	17.9505i	−0.732573	−	0.589254i
$929$	38.0179	−	38.0179i	1.24733	−	1.24733i	0.290429	−	0.956897i	$-0.406202\pi$
$929$	38.0179	−	38.0179i	1.24733	−	1.24733i	0.956897	−	0.290429i	$-0.0937979\pi$
$930$	−1.62784	+	3.95191i	−0.0533790	+	0.129588i
$931$	−12.0485	+	1.18668i	−0.394875	+	0.0388918i
$932$	28.3462	+	18.7795i	0.928511	+	0.615144i
$933$	−24.1832	+	45.2437i	−0.791724	+	1.48121i
$934$	−2.46212	−	0.741594i	−0.0805630	−	0.0242657i
$935$	−0.507869	−	0.760080i	−0.0166091	−	0.0248573i
$936$	−25.4262	−	30.6120i	−0.831081	−	1.00058i
$937$	−0.891560	−	0.595722i	−0.0291260	−	0.0194614i	0.540922	−	0.841073i	$-0.318075\pi$
$937$	−0.891560	−	0.595722i	−0.0291260	−	0.0194614i	−0.570048	+	0.821611i	$0.693075\pi$
$938$	−6.16475	−	0.594941i	−0.201286	−	0.0194255i
$939$	−40.9988	−	49.9572i	−1.33794	−	1.63029i
$940$	−8.43789	−	10.1996i	−0.275214	−	0.332673i
$941$	−1.54971	−	2.89930i	−0.0505191	−	0.0945146i	0.855395	−	0.517977i	$-0.173315\pi$
$941$	−1.54971	−	2.89930i	−0.0505191	−	0.0945146i	−0.905914	+	0.423462i	$0.860815\pi$
$942$	−24.8600	+	4.99579i	−0.809984	+	0.162772i
$943$	−0.200892	+	0.0832123i	−0.00654195	+	0.00270977i
$944$	−8.25069	−	26.4484i	−0.268537	−	0.860823i
$945$	−0.738998	−	0.306103i	−0.0240396	−	0.00995754i
$946$	6.08849	+	1.19864i	0.197954	+	0.0389711i
$947$	−6.75364	−	2.04870i	−0.219464	−	0.0665736i	0.178638	−	0.983915i	$-0.442831\pi$
$947$	−6.75364	−	2.04870i	−0.219464	−	0.0665736i	−0.398102	+	0.917341i	$0.630331\pi$
$948$	−34.3611	−	63.6816i	−1.11600	−	2.06828i
$949$	3.30121	−	33.5177i	0.107162	−	1.08803i
$950$	−1.12865	−	3.69449i	−0.0366182	−	0.119865i
$951$	−49.0033	+	9.74736i	−1.58904	+	0.316080i
$952$	3.03653	−	4.60302i	0.0984144	−	0.149185i
$953$	4.37480	−	21.9936i	0.141714	−	0.712442i	−0.842952	−	0.537989i	$-0.819184\pi$
$953$	4.37480	−	21.9936i	0.141714	−	0.712442i	0.984665	−	0.174453i	$-0.0558158\pi$
$954$	7.36344	−	9.00843i	0.238400	−	0.291659i
$955$	5.43153	+	17.9053i	0.175760	+	0.579403i
$956$	−17.1995	+	7.20361i	−0.556271	+	0.232981i
$957$	−7.32217	−	6.00915i	−0.236692	−	0.194248i
$958$	−0.00839959	−	4.27296i	−0.000271379	−	0.138053i
$959$		−	16.8461i		−	0.543989i
$960$	18.4928	+	7.40568i	0.596854	+	0.239017i
$961$		−	29.5269i		−	0.952482i
$962$	−0.236328		0.000464564i	−0.00761954		1.49781e-5i
$963$	−9.41373	−	7.72565i	−0.303353	−	0.248956i
$964$	35.0132	+	14.3419i	1.12770	+	0.461922i
$965$	−1.01850	−	3.35754i	−0.0327866	−	0.108083i
$966$	16.8799	+	13.7976i	0.543103	+	0.443929i
$967$	7.88979	−	39.6647i	0.253719	−	1.27553i	−0.618255	−	0.785977i	$-0.712160\pi$
$967$	7.88979	−	39.6647i	0.253719	−	1.27553i	0.871974	−	0.489552i	$-0.162840\pi$
$968$	16.5426	+	24.4445i	0.531700	+	0.785675i
$969$	8.11648	−	1.61447i	0.260739	−	0.0518642i
$970$	9.61989	−	2.93883i	0.308876	−	0.0943600i
$971$	4.59443	−	46.6480i	0.147442	−	1.49701i	−0.582126	−	0.813099i	$-0.697779\pi$
$971$	4.59443	−	46.6480i	0.147442	−	1.49701i	0.729568	−	0.683908i	$-0.239721\pi$
$972$	−42.7504	−	12.7849i	−1.37122	−	0.410075i
$973$	−6.37186	−	1.93288i	−0.204272	−	0.0619653i
$974$	11.7565	−	59.7170i	0.376702	−	1.91346i
$975$	10.1132	+	4.18904i	0.323883	+	0.134157i
$976$	41.9588	+	33.8861i	1.34307	+	1.08467i
$977$	−10.4200	+	4.31612i	−0.333367	+	0.138085i	−0.543087	−	0.839676i	$-0.682745\pi$
$977$	−10.4200	+	4.31612i	−0.333367	+	0.138085i	0.209720	+	0.977761i	$0.432745\pi$
$978$	2.02519	+	10.0777i	0.0647583	+	0.322250i
$979$	0.688684	+	1.28844i	0.0220105	+	0.0411787i
$980$	−0.834166	+	8.82498i	−0.0266465	+	0.281904i
$981$	−1.87021	−	2.27886i	−0.0597113	−	0.0727585i
$982$	0.851677	−	8.82503i	0.0271781	−	0.281618i
$983$	−26.9540	−	18.0101i	−0.859700	−	0.574433i	0.0457181	−	0.998954i	$-0.485442\pi$
$983$	−26.9540	−	18.0101i	−0.859700	−	0.574433i	−0.905418	+	0.424521i	$0.860442\pi$
$984$	−0.350687	−	0.184795i	−0.0111795	−	0.00589106i
$985$	11.1597	+	16.7017i	0.355579	+	0.532162i
$986$	−2.51234	+	8.34106i	−0.0800091	+	0.265633i
$987$	12.4496	−	23.2916i	0.396275	−	0.741379i
$988$	23.5363	−	4.77794i	0.748791	−	0.152007i
$989$	22.4535	−	2.21148i	0.713980	−	0.0703209i
$990$	3.14443	+	1.29523i	0.0999365	+	0.0411651i
$991$	28.5527	−	28.5527i	0.907005	−	0.907005i	−0.0890241	−	0.996029i	$-0.528375\pi$
$991$	28.5527	−	28.5527i	0.907005	−	0.907005i	0.996029	+	0.0890241i	$0.0283748\pi$
$992$	6.86540	−	0.0674805i	0.217977	−	0.00214251i
$993$	−43.7576	−	43.7576i	−1.38861	−	1.38861i
$994$	6.30514	+	15.1377i	0.199987	+	0.480139i
$995$	1.62422	+	16.4910i	0.0514912	+	0.522799i
$996$	−14.2705	+	73.2464i	−0.452177	+	2.32090i
$997$	−21.2000	−	11.3317i	−0.671412	−	0.358877i	0.100203	−	0.994967i	$-0.468051\pi$
$997$	−21.2000	−	11.3317i	−0.671412	−	0.358877i	−0.771615	+	0.636090i	$0.780551\pi$
$998$	1.58034	+	2.94268i	0.0500248	+	0.0931489i
$999$	0.0157772	−	0.0105420i	0.000499168	−	0.000333533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.341.48	✓	1024
128.125	even	32	inner	640.2.bm.a.381.48	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.48	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.48	yes	1024	128.125	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)

\(f(q)\)	\(=\)	\(q+(0.998032 - 1.00196i) q^{2} +(1.57969 - 1.92485i) q^{3} +(-0.00786299 - 1.99998i) q^{4} +(0.956940 - 0.290285i) q^{5} +(-0.352055 - 3.50385i) q^{6} +(1.57166 + 0.312622i) q^{7} +(-2.01176 - 1.98817i) q^{8} +(-0.624379 - 3.13897i) q^{9} +O(q^{10})\)	\(q+(0.998032 - 1.00196i) q^{2} +(1.57969 - 1.92485i) q^{3} +(-0.00786299 - 1.99998i) q^{4} +(0.956940 - 0.290285i) q^{5} +(-0.352055 - 3.50385i) q^{6} +(1.57166 + 0.312622i) q^{7} +(-2.01176 - 1.98817i) q^{8} +(-0.624379 - 3.13897i) q^{9} +(0.664203 - 1.24853i) q^{10} +(-0.747739 - 0.0736458i) q^{11} +(-3.86210 - 3.14421i) q^{12} +(-1.27611 + 4.20676i) q^{13} +(1.88180 - 1.26274i) q^{14} +(0.952910 - 2.30053i) q^{15} +(-3.99988 + 0.0314517i) q^{16} +(0.465593 + 1.12404i) q^{17} +(-3.76828 - 2.50718i) q^{18} +(2.40905 - 1.28766i) q^{19} +(-0.588089 - 1.91158i) q^{20} +(3.08448 - 2.53136i) q^{21} +(-0.820058 + 0.675706i) q^{22} +(-2.14642 + 3.21234i) q^{23} +(-7.00488 + 0.731656i) q^{24} +(0.831470 - 0.555570i) q^{25} +(2.94143 + 5.47710i) q^{26} +(-0.440224 - 0.235305i) q^{27} +(0.612882 - 3.14575i) q^{28} +(0.496248 + 5.03849i) q^{29} +(-1.35401 - 3.25078i) q^{30} +(-0.858217 - 0.858217i) q^{31} +(-3.96049 + 4.03912i) q^{32} +(-1.32295 + 1.32295i) q^{33} +(1.59092 + 0.655322i) q^{34} +(1.59473 - 0.157067i) q^{35} +(-6.27297 + 1.27343i) q^{36} +(-0.0179195 + 0.0335250i) q^{37} +(1.11411 - 3.69890i) q^{38} +(6.08155 + 9.10168i) q^{39} +(-2.50227 - 1.31858i) q^{40} +(0.0467971 + 0.0312689i) q^{41} +(0.542072 - 5.61692i) q^{42} +(-3.70480 - 4.51431i) q^{43} +(-0.141411 + 1.49604i) q^{44} +(-1.50869 - 2.82256i) q^{45} +(1.07645 + 5.35665i) q^{46} +(6.11489 - 2.53287i) q^{47} +(-6.25801 + 7.74885i) q^{48} +(-4.09478 - 1.69611i) q^{49} +(0.273172 - 1.38758i) q^{50} +(2.89910 + 0.879433i) q^{51} +(8.42349 + 2.51912i) q^{52} +(-0.251964 + 2.55824i) q^{53} +(-0.675125 + 0.206247i) q^{54} +(-0.736919 + 0.146582i) q^{55} +(-2.54025 - 3.75365i) q^{56} +(1.32698 - 6.67116i) q^{57} +(5.54365 + 4.53135i) q^{58} +(2.01062 + 6.62812i) q^{59} +(-4.60851 - 1.88772i) q^{60} +(-10.4228 - 8.55374i) q^{61} +(-1.71643 + 0.00337408i) q^{62} -5.12858i q^{63} +(0.0943539 + 7.99944i) q^{64} +4.39605i q^{65} +(0.00520118 + 2.64589i) q^{66} +(-2.11259 - 1.73376i) q^{67} +(2.24440 - 0.940017i) q^{68} +(2.79261 + 9.20602i) q^{69} +(1.43422 - 1.75462i) q^{70} +(-1.41168 + 7.09699i) q^{71} +(-4.98470 + 7.55622i) q^{72} +(-7.51418 + 1.49466i) q^{73} +(0.0157066 + 0.0514137i) q^{74} +(0.244070 - 2.47808i) q^{75} +(-2.59425 - 4.80793i) q^{76} +(-1.15217 - 0.349506i) q^{77} +(15.1891 + 2.99028i) q^{78} +(13.4238 + 5.56031i) q^{79} +(-3.81851 + 1.19120i) q^{80} +(7.72218 - 3.19863i) q^{81} +(0.0780353 - 0.0156817i) q^{82} +(-7.06351 - 13.2149i) q^{83} +(-5.08694 - 6.14900i) q^{84} +(0.771836 + 0.940485i) q^{85} +(-8.22068 - 0.793353i) q^{86} +(10.4823 + 7.00402i) q^{87} +(1.35785 + 1.63479i) q^{88} +(-1.08026 - 1.61672i) q^{89} +(-4.33382 - 1.30535i) q^{90} +(-3.32073 + 6.21265i) q^{91} +(6.44150 + 4.26754i) q^{92} +(-3.00765 + 0.296228i) q^{93} +(3.56501 - 8.65478i) q^{94} +(1.93152 - 1.93152i) q^{95} +(1.51838 + 14.0039i) q^{96} +(5.02939 + 5.02939i) q^{97} +(-5.78617 + 2.41005i) q^{98} +(0.235701 + 2.39311i) 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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