LMFDB - Embedded newform 935.2.p.a.373.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(373,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2, 2]))

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

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

chi := DirichletCharacter("935.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.46601258899$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$104$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			373.17
Character	$\chi$	$=$	935.373
Dual form			935.2.p.a.747.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34748 - 1.34748i) q^{2} +(-1.68194 + 1.68194i) q^{3} +1.63139i q^{4} +(-1.41767 - 1.72923i) q^{5} +4.53276 q^{6} +(-2.13197 + 2.13197i) q^{7} +(-0.496689 + 0.496689i) q^{8} -2.65785i q^{9} +O(q^{10})$	\(q+(-1.34748 - 1.34748i) q^{2} +(-1.68194 + 1.68194i) q^{3} +1.63139i q^{4} +(-1.41767 - 1.72923i) q^{5} +4.53276 q^{6} +(-2.13197 + 2.13197i) q^{7} +(-0.496689 + 0.496689i) q^{8} -2.65785i q^{9} +(-0.419818 + 4.24037i) q^{10} +(-0.358401 + 3.29720i) q^{11} +(-2.74391 - 2.74391i) q^{12} +(-2.53373 + 2.53373i) q^{13} +5.74557 q^{14} +(5.29289 + 0.524023i) q^{15} +4.60134 q^{16} +(-3.66054 - 1.89749i) q^{17} +(-3.58140 + 3.58140i) q^{18} +0.718712 q^{19} +(2.82105 - 2.31277i) q^{20} -7.17171i q^{21} +(4.92585 - 3.95997i) q^{22} +(-0.976407 + 0.976407i) q^{23} -1.67080i q^{24} +(-0.980442 + 4.90293i) q^{25} +6.82828 q^{26} +(-0.575471 - 0.575471i) q^{27} +(-3.47809 - 3.47809i) q^{28} +6.69937i q^{29} +(-6.42594 - 7.83816i) q^{30} +0.961272i q^{31} +(-5.20683 - 5.20683i) q^{32} +(-4.94289 - 6.14851i) q^{33} +(2.37568 + 7.48932i) q^{34} +(6.70909 + 0.664235i) q^{35} +4.33601 q^{36} +(7.75105 + 7.75105i) q^{37} +(-0.968449 - 0.968449i) q^{38} -8.52316i q^{39} +(1.56303 + 0.154748i) q^{40} -8.17170 q^{41} +(-9.66372 + 9.66372i) q^{42} +(2.85739 - 2.85739i) q^{43} +(-5.37904 - 0.584694i) q^{44} +(-4.59603 + 3.76795i) q^{45} +2.63137 q^{46} +(4.65328 - 4.65328i) q^{47} +(-7.73919 + 7.73919i) q^{48} -2.09062i q^{49} +(7.92772 - 5.28547i) q^{50} +(9.34827 - 2.96535i) q^{51} +(-4.13350 - 4.13350i) q^{52} +(-5.97993 - 5.97993i) q^{53} +1.55087i q^{54} +(6.20970 - 4.05458i) q^{55} -2.11785i q^{56} +(-1.20883 + 1.20883i) q^{57} +(9.02725 - 9.02725i) q^{58} -10.1755i q^{59} +(-0.854889 + 8.63478i) q^{60} -8.98258 q^{61} +(1.29529 - 1.29529i) q^{62} +(5.66647 + 5.66647i) q^{63} +4.82949i q^{64} +(7.97336 + 0.789404i) q^{65} +(-1.62455 + 14.9454i) q^{66} +(-7.90816 + 7.90816i) q^{67} +(3.09555 - 5.97178i) q^{68} -3.28452i q^{69} +(-8.14531 - 9.93539i) q^{70} -11.6659i q^{71} +(1.32013 + 1.32013i) q^{72} +(-5.22520 - 5.22520i) q^{73} -20.8887i q^{74} +(-6.59740 - 9.89549i) q^{75} +1.17250i q^{76} +(-6.26545 - 7.79365i) q^{77} +(-11.4848 + 11.4848i) q^{78} -13.6232i q^{79} +(-6.52317 - 7.95676i) q^{80} +9.90938 q^{81} +(11.0112 + 11.0112i) q^{82} +(2.01894 - 2.01894i) q^{83} +11.6999 q^{84} +(1.90824 + 9.01990i) q^{85} -7.70054 q^{86} +(-11.2679 - 11.2679i) q^{87} +(-1.45967 - 1.81570i) q^{88} +4.99533i q^{89} +(11.2703 + 1.11582i) q^{90} -10.8037i q^{91} +(-1.59290 - 1.59290i) q^{92} +(-1.61680 - 1.61680i) q^{93} -12.5404 q^{94} +(-1.01889 - 1.24282i) q^{95} +17.5152 q^{96} +(-0.539134 - 0.539134i) q^{97} +(-2.81707 + 2.81707i) q^{98} +(8.76348 + 0.952578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q+O(q^{10}) $ 208 * q	$ 208 q - 8 q^{15} - 184 q^{16} - 48 q^{25} - 32 q^{26} + 4 q^{33} + 280 q^{36} - 80 q^{38} - 64 q^{42} - 8 q^{53} + 48 q^{55} + 128 q^{60} - 48 q^{66} + 56 q^{67} - 112 q^{70} - 84 q^{77} - 192 q^{81} - 112 q^{86} + 112 q^{93}+O(q^{100}) $ 208 * q - 8 * q^15 - 184 * q^16 - 48 * q^25 - 32 * q^26 + 4 * q^33 + 280 * q^36 - 80 * q^38 - 64 * q^42 - 8 * q^53 + 48 * q^55 + 128 * q^60 - 48 * q^66 + 56 * q^67 - 112 * q^70 - 84 * q^77 - 192 * q^81 - 112 * q^86 + 112 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/935\mathbb{Z}\right)^\times$.

$n$	$496$	$562$	$596$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.34748	−	1.34748i	−0.952811	−	0.952811i	0.0461249	−	0.998936i	$-0.485313\pi$
$2$	−1.34748	−	1.34748i	−0.952811	−	0.952811i	−0.998936	+	0.0461249i	$0.985313\pi$
$3$	−1.68194	+	1.68194i	−0.971069	+	0.971069i	−0.999593	−	0.0285238i	$-0.990919\pi$
$3$	−1.68194	+	1.68194i	−0.971069	+	0.971069i	0.0285238	+	0.999593i	$0.490919\pi$
$4$			1.63139i			0.815697i
$5$	−1.41767	−	1.72923i	−0.634000	−	0.773333i
$5$	−1.41767	−	1.72923i	−0.634000	−	0.773333i
$6$	4.53276			1.85049
$7$	−2.13197	+	2.13197i	−0.805810	+	0.805810i	−0.983997	−	0.178186i	$-0.942977\pi$
$7$	−2.13197	+	2.13197i	−0.805810	+	0.805810i	0.178186	+	0.983997i	$0.442977\pi$
$8$	−0.496689	+	0.496689i	−0.175606	+	0.175606i
$9$		−	2.65785i		−	0.885951i
$10$	−0.419818	+	4.24037i	−0.132758	+	1.34092i
$11$	−0.358401	+	3.29720i	−0.108062	+	0.994144i
$11$	−0.358401	+	3.29720i	−0.108062	+	0.994144i
$12$	−2.74391	−	2.74391i	−0.792098	−	0.792098i
$13$	−2.53373	+	2.53373i	−0.702729	+	0.702729i	−0.964995	−	0.262266i	$-0.915530\pi$
$13$	−2.53373	+	2.53373i	−0.702729	+	0.702729i	0.262266	+	0.964995i	$0.415530\pi$
$14$	5.74557			1.53557
$15$	5.29289	+	0.524023i	1.36662	+	0.135302i
$16$	4.60134			1.15034
$17$	−3.66054	−	1.89749i	−0.887811	−	0.460208i
$17$	−3.66054	−	1.89749i	−0.887811	−	0.460208i
$18$	−3.58140	+	3.58140i	−0.844144	+	0.844144i
$19$	0.718712			0.164884			0.0824419	−	0.996596i	$-0.473728\pi$
$19$	0.718712			0.164884			0.0824419	+	0.996596i	$0.473728\pi$
$20$	2.82105	−	2.31277i	0.630805	−	0.517152i
$21$		−	7.17171i		−	1.56500i
$22$	4.92585	−	3.95997i	1.05019	−	0.844269i
$23$	−0.976407	+	0.976407i	−0.203595	+	0.203595i	−0.801538	−	0.597943i	$-0.795985\pi$
$23$	−0.976407	+	0.976407i	−0.203595	+	0.203595i	0.597943	+	0.801538i	$0.295985\pi$
$24$		−	1.67080i		−	0.341051i
$25$	−0.980442	+	4.90293i	−0.196088	+	0.980586i
$26$	6.82828			1.33914
$27$	−0.575471	−	0.575471i	−0.110749	−	0.110749i
$28$	−3.47809	−	3.47809i	−0.657297	−	0.657297i
$29$			6.69937i			1.24404i	0.783001	+	0.622021i	$0.213688\pi$
$29$			6.69937i			1.24404i	−0.783001	+	0.622021i	$0.786312\pi$
$30$	−6.42594	−	7.83816i	−1.17321	−	1.43105i
$31$			0.961272i			0.172649i	0.996267	+	0.0863247i	$0.0275123\pi$
$31$			0.961272i			0.172649i	−0.996267	+	0.0863247i	$0.972488\pi$
$32$	−5.20683	−	5.20683i	−0.920446	−	0.920446i
$33$	−4.94289	−	6.14851i	−0.860447	−	1.07032i
$34$	2.37568	+	7.48932i	0.407425	+	1.28441i
$35$	6.70909	+	0.664235i	1.13404	+	0.112276i
$36$	4.33601			0.722668
$37$	7.75105	+	7.75105i	1.27426	+	1.27426i	0.943828	+	0.330436i	$0.107196\pi$
$37$	7.75105	+	7.75105i	1.27426	+	1.27426i	0.330436	+	0.943828i	$0.392804\pi$
$38$	−0.968449	−	0.968449i	−0.157103	−	0.157103i
$39$		−	8.52316i		−	1.36480i
$40$	1.56303	+	0.154748i	0.247136	+	0.0244678i
$41$	−8.17170			−1.27620			−0.638102	−	0.769952i	$-0.720280\pi$
$41$	−8.17170			−1.27620			−0.638102	+	0.769952i	$0.720280\pi$
$42$	−9.66372	+	9.66372i	−1.49114	+	1.49114i
$43$	2.85739	−	2.85739i	0.435748	−	0.435748i	−0.454830	−	0.890578i	$-0.650300\pi$
$43$	2.85739	−	2.85739i	0.435748	−	0.435748i	0.890578	+	0.454830i	$0.150300\pi$
$44$	−5.37904	−	0.584694i	−0.810920	−	0.0881459i
$45$	−4.59603	+	3.76795i	−0.685135	+	0.561693i
$46$	2.63137			0.387975
$47$	4.65328	−	4.65328i	0.678750	−	0.678750i	−0.280967	−	0.959717i	$-0.590655\pi$
$47$	4.65328	−	4.65328i	0.678750	−	0.678750i	0.959717	+	0.280967i	$0.0906552\pi$
$48$	−7.73919	+	7.73919i	−1.11706	+	1.11706i
$49$		−	2.09062i		−	0.298660i
$50$	7.92772	−	5.28547i	1.12115	−	0.747478i
$51$	9.34827	−	2.96535i	1.30902	−	0.415232i
$52$	−4.13350	−	4.13350i	−0.573214	−	0.573214i
$53$	−5.97993	−	5.97993i	−0.821406	−	0.821406i	0.164904	−	0.986310i	$-0.447269\pi$
$53$	−5.97993	−	5.97993i	−0.821406	−	0.821406i	−0.986310	+	0.164904i	$0.947269\pi$
$54$			1.55087i			0.211046i
$55$	6.20970	−	4.05458i	0.837316	−	0.546719i
$56$		−	2.11785i		−	0.283010i
$57$	−1.20883	+	1.20883i	−0.160114	+	0.160114i
$58$	9.02725	−	9.02725i	1.18534	−	1.18534i
$59$		−	10.1755i		−	1.32474i	−0.749178	−	0.662368i	$-0.769551\pi$
$59$		−	10.1755i		−	1.32474i	0.749178	−	0.662368i	$-0.230449\pi$
$60$	−0.854889	+	8.63478i	−0.110366	+	1.11475i
$61$	−8.98258			−1.15010			−0.575051	−	0.818118i	$-0.695018\pi$
$61$	−8.98258			−1.15010			−0.575051	+	0.818118i	$0.695018\pi$
$62$	1.29529	−	1.29529i	0.164502	−	0.164502i
$63$	5.66647	+	5.66647i	0.713908	+	0.713908i
$64$			4.82949i			0.603686i
$65$	7.97336	+	0.789404i	0.988974	+	0.0979135i
$66$	−1.62455	+	14.9454i	−0.199968	+	1.83965i
$67$	−7.90816	+	7.90816i	−0.966136	+	0.966136i	−0.999445	−	0.0333093i	$-0.989395\pi$
$67$	−7.90816	+	7.90816i	−0.966136	+	0.966136i	0.0333093	+	0.999445i	$0.489395\pi$
$68$	3.09555	−	5.97178i	0.375390	−	0.724185i
$69$		−	3.28452i		−	0.395410i
$70$	−8.14531	−	9.93539i	−0.973551	−	1.18751i
$71$		−	11.6659i		−	1.38449i	−0.721664	−	0.692243i	$-0.756622\pi$
$71$		−	11.6659i		−	1.38449i	0.721664	−	0.692243i	$-0.243378\pi$
$72$	1.32013	+	1.32013i	0.155578	+	0.155578i
$73$	−5.22520	−	5.22520i	−0.611564	−	0.611564i	0.331790	−	0.943353i	$-0.392348\pi$
$73$	−5.22520	−	5.22520i	−0.611564	−	0.611564i	−0.943353	+	0.331790i	$0.892348\pi$
$74$		−	20.8887i		−	2.42827i
$75$	−6.59740	−	9.89549i	−0.761802	−	1.14263i
$76$			1.17250i			0.134495i
$77$	−6.26545	−	7.79365i	−0.714014	−	0.888169i
$78$	−11.4848	+	11.4848i	−1.30039	+	1.30039i
$79$		−	13.6232i		−	1.53273i	−0.642405	−	0.766365i	$-0.722063\pi$
$79$		−	13.6232i		−	1.53273i	0.642405	−	0.766365i	$-0.277937\pi$
$80$	−6.52317	−	7.95676i	−0.729313	−	0.889593i
$81$	9.90938			1.10104
$82$	11.0112	+	11.0112i	1.21598	+	1.21598i
$83$	2.01894	−	2.01894i	0.221607	−	0.221607i	−0.587568	−	0.809175i	$-0.699914\pi$
$83$	2.01894	−	2.01894i	0.221607	−	0.221607i	0.809175	+	0.587568i	$0.199914\pi$
$84$	11.6999			1.27656
$85$	1.90824	+	9.01990i	0.206978	+	0.978346i
$86$	−7.70054			−0.830370
$87$	−11.2679	−	11.2679i	−1.20805	−	1.20805i
$88$	−1.45967	−	1.81570i	−0.155601	−	0.193554i
$89$			4.99533i			0.529504i	0.964317	+	0.264752i	$0.0852901\pi$
$89$			4.99533i			0.529504i	−0.964317	+	0.264752i	$0.914710\pi$
$90$	11.2703	+	1.11582i	1.18799	+	0.117617i
$91$		−	10.8037i		−	1.13253i
$92$	−1.59290	−	1.59290i	−0.166072	−	0.166072i
$93$	−1.61680	−	1.61680i	−0.167655	−	0.167655i
$94$	−12.5404			−1.29344
$95$	−1.01889	−	1.24282i	−0.104536	−	0.127510i
$96$	17.5152			1.78763
$97$	−0.539134	−	0.539134i	−0.0547407	−	0.0547407i	0.679206	−	0.733947i	$-0.262324\pi$
$97$	−0.539134	−	0.539134i	−0.0547407	−	0.0547407i	−0.733947	+	0.679206i	$0.762324\pi$
$98$	−2.81707	+	2.81707i	−0.284567	+	0.284567i
$99$	8.76348	+	0.952578i	0.880763	+	0.0957377i
$100$	−7.99861	−	1.59949i	−0.799861	−	0.159949i
$101$			9.80532i			0.975666i	0.872937	+	0.487833i	$0.162212\pi$
$101$			9.80532i			0.975666i	−0.872937	+	0.487833i	$0.837788\pi$
$102$	−16.5923	−	8.60084i	−1.64289	−	0.851610i
$103$	7.34707	+	7.34707i	0.723928	+	0.723928i	0.969403	−	0.245475i	$-0.0789438\pi$
$103$	7.34707	+	7.34707i	0.723928	+	0.723928i	−0.245475	+	0.969403i	$0.578944\pi$
$104$		−	2.51695i		−	0.246807i
$105$	−12.4015	+	10.1671i	−1.21026	+	0.992207i
$106$			16.1156i			1.56529i
$107$	10.4253	−	10.4253i	1.00786	−	1.00786i	0.00788704	−	0.999969i	$-0.497489\pi$
$107$	10.4253	−	10.4253i	1.00786	−	1.00786i	0.999969	−	0.00788704i	$-0.00251055\pi$
$108$	0.938819	−	0.938819i	0.0903379	−	0.0903379i
$109$		−	6.28066i		−	0.601578i	−0.953691	−	0.300789i	$-0.902750\pi$
$109$		−	6.28066i		−	0.601578i	0.953691	−	0.300789i	$-0.0972500\pi$
$110$	−13.8309	−	2.90398i	−1.31872	−	0.276884i
$111$	−26.0736			−2.47480
$112$	−9.80994	+	9.80994i	−0.926952	+	0.926952i
$113$	−1.08922	+	1.08922i	−0.102465	+	0.102465i	−0.756481	−	0.654016i	$-0.773083\pi$
$113$	−1.08922	+	1.08922i	−0.102465	+	0.102465i	0.654016	+	0.756481i	$0.273083\pi$
$114$	3.25775			0.305116
$115$	3.07265	+	0.304208i	0.286526	+	0.0283676i
$116$	−10.9293			−1.01476
$117$	6.73427	+	6.73427i	0.622584	+	0.622584i
$118$	−13.7113	+	13.7113i	−1.26222	+	1.26222i
$119$	11.8496	−	3.75878i	1.08625	−	0.344567i
$120$	−2.88919	+	2.36864i	−0.263746	+	0.216226i
$121$	−10.7431	−	2.36344i	−0.976645	−	0.214859i
$122$	12.1038	+	12.1038i	1.09583	+	1.09583i
$123$	13.7443	−	13.7443i	1.23928	−	1.23928i
$124$	−1.56821			−0.140830
$125$	9.86821	−	5.25532i	0.882640	−	0.470050i
$126$		−	15.2709i		−	1.36044i
$127$	6.12688	+	6.12688i	0.543672	+	0.543672i	0.924603	−	0.380931i	$-0.124396\pi$
$127$	6.12688	+	6.12688i	0.543672	+	0.543672i	−0.380931	+	0.924603i	$0.624396\pi$
$128$	−3.90602	+	3.90602i	−0.345247	+	0.345247i
$129$			9.61192i			0.846282i
$130$	−9.68022	−	11.8076i	−0.849012	−	1.03560i
$131$	6.88000			0.601108			0.300554	−	0.953765i	$-0.402828\pi$
$131$	6.88000			0.601108			0.300554	+	0.953765i	$0.402828\pi$
$132$	10.0306	−	8.06380i	0.873056	−	0.701864i
$133$	−1.53228	+	1.53228i	−0.132865	+	0.132865i
$134$	21.3121			1.84109
$135$	−0.179293	+	1.81094i	−0.0154311	+	0.155861i
$136$	2.76061	−	0.875689i	0.236720	−	0.0750897i
$137$	4.05517	−	4.05517i	0.346457	−	0.346457i	−0.512331	−	0.858788i	$-0.671218\pi$
$137$	4.05517	−	4.05517i	0.346457	−	0.346457i	0.858788	+	0.512331i	$0.171218\pi$
$138$	−4.42582	+	4.42582i	−0.376751	+	0.376751i
$139$			18.8151i			1.59588i	0.602740	+	0.797938i	$0.294076\pi$
$139$			18.8151i			1.59588i	−0.602740	+	0.797938i	$0.705924\pi$
$140$	−1.08363	+	10.9452i	−0.0915833	+	0.925036i
$141$			15.6531i			1.31823i
$142$	−15.7195	+	15.7195i	−1.31915	+	1.31915i
$143$	−7.44612	−	9.26230i	−0.622676	−	0.774552i
$144$		−	12.2297i		−	1.01914i
$145$	11.5847	−	9.49747i	0.962059	−	0.788722i
$146$			14.0817i			1.16541i
$147$	3.51630	+	3.51630i	0.290020	+	0.290020i
$148$	−12.6450	+	12.6450i	−1.03941	+	1.03941i
$149$	6.16676			0.505201			0.252600	−	0.967571i	$-0.418714\pi$
$149$	6.16676			0.505201			0.252600	+	0.967571i	$0.418714\pi$
$150$	−4.44410	+	22.2238i	−0.362860	+	1.81457i
$151$			12.4141i			1.01024i	0.863049	+	0.505121i	$0.168552\pi$
$151$			12.4141i			1.01024i	−0.863049	+	0.505121i	$0.831448\pi$
$152$	−0.356976	+	0.356976i	−0.0289546	+	0.0289546i
$153$	−5.04324	+	9.72918i	−0.407722	+	0.786557i
$154$	−2.05922	+	18.9443i	−0.165937	+	1.52658i
$155$	1.66226	−	1.36276i	0.133516	−	0.109460i
$156$	13.9046			1.11326
$157$	0.0762818	−	0.0762818i	0.00608795	−	0.00608795i	−0.704056	−	0.710144i	$-0.748630\pi$
$157$	0.0762818	−	0.0762818i	0.00608795	−	0.00608795i	0.710144	+	0.704056i	$0.248630\pi$
$158$	−18.3570	+	18.3570i	−1.46040	+	1.46040i
$159$	20.1158			1.59528
$160$	−1.62223	+	16.3853i	−0.128249	+	1.29537i
$161$		−	4.16335i		−	0.328118i
$162$	−13.3527	−	13.3527i	−1.04908	−	1.04908i
$163$	3.70831	−	3.70831i	0.290457	−	0.290457i	−0.546804	−	0.837261i	$-0.684156\pi$
$163$	3.70831	−	3.70831i	0.290457	−	0.290457i	0.837261	+	0.546804i	$0.184156\pi$
$164$		−	13.3313i		−	1.04100i
$165$	−3.62479	+	17.2639i	−0.282190	+	1.34399i
$166$	−5.44096			−0.422300
$167$	2.36264	−	2.36264i	0.182827	−	0.182827i	−0.609760	−	0.792586i	$-0.708734\pi$
$167$	2.36264	−	2.36264i	0.182827	−	0.182827i	0.792586	+	0.609760i	$0.208734\pi$
$168$	3.56211	+	3.56211i	0.274823	+	0.274823i
$169$			0.160470i			0.0123439i
$170$	9.58280	−	14.7254i	0.734967	−	1.12939i
$171$		−	1.91023i		−	0.146079i
$172$	4.66153	+	4.66153i	0.355438	+	0.355438i
$173$	−2.39142	−	2.39142i	−0.181816	−	0.181816i	0.610331	−	0.792147i	$-0.291037\pi$
$173$	−2.39142	−	2.39142i	−0.181816	−	0.181816i	−0.792147	+	0.610331i	$0.791037\pi$
$174$			30.3666i			2.30209i
$175$	−8.36264	−	12.5432i	−0.632156	−	0.948176i
$176$	−1.64913	+	15.1716i	−0.124308	+	1.14360i
$177$	17.1146	+	17.1146i	1.28641	+	1.28641i
$178$	6.73110	−	6.73110i	0.504517	−	0.504517i
$179$			1.84015i			0.137539i	0.997633	+	0.0687697i	$0.0219074\pi$
$179$			1.84015i			0.137539i	−0.997633	+	0.0687697i	$0.978093\pi$
$180$	−6.14701	−	7.49793i	−0.458171	−	0.558863i
$181$		−	25.6772i		−	1.90857i	−0.298894	−	0.954286i	$-0.596618\pi$
$181$		−	25.6772i		−	1.90857i	0.298894	−	0.954286i	$-0.403382\pi$
$182$	−14.5577	+	14.5577i	−1.07909	+	1.07909i
$183$	15.1082	−	15.1082i	1.11683	−	1.11683i
$184$		−	0.969941i		−	0.0715050i
$185$	2.41491	−	24.3917i	0.177547	−	1.79331i
$186$			4.35721i			0.319486i
$187$	7.56834	−	11.3895i	0.553452	−	0.832881i
$188$	7.59133	+	7.59133i	0.553655	+	0.553655i
$189$	2.45378			0.178486
$190$	−0.301729	+	3.04760i	−0.0218897	+	0.221096i
$191$	−8.17272			−0.591357			−0.295678	−	0.955288i	$-0.595546\pi$
$191$	−8.17272			−0.591357			−0.295678	+	0.955288i	$0.595546\pi$
$192$	−8.12292	−	8.12292i	−0.586221	−	0.586221i
$193$	−5.78079	−	5.78079i	−0.416111	−	0.416111i	0.467750	−	0.883861i	$-0.345065\pi$
$193$	−5.78079	−	5.78079i	−0.416111	−	0.416111i	−0.883861	+	0.467750i	$0.845065\pi$
$194$			1.45294i			0.104315i
$195$	−14.7385	+	12.0830i	−1.05544	+	0.865281i
$196$	3.41063			0.243616
$197$	−14.9229	+	14.9229i	−1.06321	+	1.06321i	−0.0653493	+	0.997862i	$0.520816\pi$
$197$	−14.9229	+	14.9229i	−1.06321	+	1.06321i	−0.997862	+	0.0653493i	$0.979184\pi$
$198$	−10.5250	−	13.0922i	−0.747981	−	0.930421i
$199$	−22.3500			−1.58435			−0.792174	−	0.610295i	$-0.791051\pi$
$199$	−22.3500			−1.58435			−0.792174	+	0.610295i	$0.791051\pi$
$200$	−1.94826	−	2.92221i	−0.137763	−	0.206631i
$201$		−	26.6021i		−	1.87637i
$202$	13.2125	−	13.2125i	0.929625	−	0.929625i
$203$	−14.2829	−	14.2829i	−1.00246	−	1.00246i
$204$	4.83766	+	15.2507i	0.338704	+	1.06776i
$205$	11.5847	+	14.1307i	0.809114	+	0.986931i
$206$		−	19.8000i		−	1.37953i
$207$	2.59515	+	2.59515i	0.180375	+	0.180375i
$208$	−11.6585	+	11.6585i	−0.808374	+	0.808374i
$209$	−0.257587	+	2.36974i	−0.0178177	+	0.163918i
$210$	30.4107	+	3.01082i	2.09854	+	0.207766i
$211$	8.88434			0.611623			0.305812	−	0.952092i	$-0.401072\pi$
$211$	8.88434			0.611623			0.305812	+	0.952092i	$0.401072\pi$
$212$	9.75561	−	9.75561i	0.670018	−	0.670018i
$213$	19.6213	+	19.6213i	1.34443	+	1.34443i
$214$	−28.0958			−1.92059
$215$	−8.99189	−	0.890244i	−0.613242	−	0.0607142i
$216$	0.571660			0.0388965
$217$	−2.04941	−	2.04941i	−0.139123	−	0.139123i
$218$	−8.46305	+	8.46305i	−0.573190	+	0.573190i
$219$	17.5770			1.18774
$220$	6.61461	+	10.1305i	0.445957	+	0.682996i
$221$	14.0825	−	4.46709i	0.947292	−	0.300489i
$222$	35.1336	+	35.1336i	2.35801	+	2.35801i
$223$	12.9761	+	12.9761i	0.868945	+	0.868945i	0.992356	−	0.123410i	$-0.0393831\pi$
$223$	12.9761	+	12.9761i	0.868945	+	0.868945i	−0.123410	+	0.992356i	$0.539383\pi$
$224$	22.2016			1.48341
$225$	13.0313	+	2.60587i	0.868751	+	0.173725i
$226$	2.93541			0.195260
$227$	7.89900	−	7.89900i	0.524275	−	0.524275i	−0.394585	−	0.918860i	$-0.629111\pi$
$227$	7.89900	−	7.89900i	0.524275	−	0.524275i	0.918860	+	0.394585i	$0.129111\pi$
$228$	−1.97208	−	1.97208i	−0.130604	−	0.130604i
$229$		−	7.98733i		−	0.527817i	−0.964548	−	0.263909i	$-0.914988\pi$
$229$		−	7.98733i		−	0.527817i	0.964548	−	0.263909i	$-0.0850118\pi$
$230$	−3.73041	−	4.55024i	−0.245976	−	0.300034i
$231$	23.6466	+	2.57035i	1.55583	+	0.169117i
$232$	−3.32750	−	3.32750i	−0.218461	−	0.218461i
$233$	19.7277	+	19.7277i	1.29241	+	1.29241i	0.933295	+	0.359112i	$0.116920\pi$
$233$	19.7277	+	19.7277i	1.29241	+	1.29241i	0.359112	+	0.933295i	$0.383080\pi$
$234$		−	18.1486i		−	1.18641i
$235$	−14.6434	−	1.44977i	−0.955228	−	0.0945725i
$236$	16.6002			1.08058
$237$	22.9134	+	22.9134i	1.48839	+	1.48839i
$238$	−21.0319	−	10.9021i	−1.36330	−	0.706681i
$239$	10.2416			0.662471			0.331236	−	0.943548i	$-0.392534\pi$
$239$	10.2416			0.662471			0.331236	+	0.943548i	$0.392534\pi$
$240$	24.3544	+	2.41121i	1.57207	+	0.155643i
$241$	11.1626			0.719046			0.359523	−	0.933136i	$-0.382939\pi$
$241$	11.1626			0.719046			0.359523	+	0.933136i	$0.382939\pi$
$242$	11.2914	+	17.6608i	0.725839	+	1.13528i
$243$	−14.9406	+	14.9406i	−0.958438	+	0.958438i
$244$		−	14.6541i		−	0.938134i
$245$	−3.61516	+	2.96381i	−0.230964	+	0.189351i
$246$	−37.0403			−2.36160
$247$	−1.82102	+	1.82102i	−0.115869	+	0.115869i
$248$	−0.477453	−	0.477453i	−0.0303183	−	0.0303183i
$249$			6.79148i			0.430392i
$250$	−20.3786	−	6.21577i	−1.28886	−	0.393120i
$251$	16.2785			1.02749			0.513746	−	0.857942i	$-0.328257\pi$
$251$	16.2785			1.02749			0.513746	+	0.857942i	$0.328257\pi$
$252$	−9.24425	+	9.24425i	−0.582333	+	0.582333i
$253$	−2.86947	−	3.56936i	−0.180402	−	0.224404i
$254$		−	16.5117i		−	1.03603i
$255$	−18.3805	−	11.9614i	−1.15103	−	0.749051i
$256$	20.1855			1.26160
$257$	−21.2079	+	21.2079i	−1.32291	+	1.32291i	−0.411500	+	0.911410i	$0.634995\pi$
$257$	−21.2079	+	21.2079i	−1.32291	+	1.32291i	−0.911410	+	0.411500i	$0.865005\pi$
$258$	12.9519	−	12.9519i	0.806347	−	0.806347i
$259$	−33.0501			−2.05363
$260$	−1.28783	+	13.0077i	−0.0798678	+	0.806703i
$261$	17.8059			1.10216
$262$	−9.27064	−	9.27064i	−0.572742	−	0.572742i
$263$	14.9915	−	14.9915i	0.924418	−	0.924418i	−0.0729198	−	0.997338i	$-0.523232\pi$
$263$	14.9915	−	14.9915i	0.924418	−	0.924418i	0.997338	+	0.0729198i	$0.0232317\pi$
$264$	5.50898	+	0.598818i	0.339054	+	0.0368547i
$265$	−1.86310	+	18.8182i	−0.114449	+	1.15599i
$266$	4.12941			0.253191
$267$	−8.40185	−	8.40185i	−0.514185	−	0.514185i
$268$	−12.9013	−	12.9013i	−0.788074	−	0.788074i
$269$	−20.1051			−1.22583			−0.612914	−	0.790150i	$-0.710003\pi$
$269$	−20.1051			−1.22583			−0.612914	+	0.790150i	$0.710003\pi$
$270$	2.68180	−	2.19861i	0.163209	−	0.133803i
$271$			1.86780i			0.113461i	0.998390	+	0.0567303i	$0.0180675\pi$
$271$			1.86780i			0.113461i	−0.998390	+	0.0567303i	$0.981932\pi$
$272$	−16.8434	−	8.73098i	−1.02128	−	0.529393i
$273$	18.1711	+	18.1711i	1.09977	+	1.09977i
$274$	−10.9285			−0.660215
$275$	−15.8146	−	4.98993i	−0.953654	−	0.300904i
$276$	5.35834			0.322534
$277$	10.7956	−	10.7956i	0.648643	−	0.648643i	−0.304022	−	0.952665i	$-0.598330\pi$
$277$	10.7956	−	10.7956i	0.648643	−	0.648643i	0.952665	+	0.304022i	$0.0983297\pi$
$278$	25.3529	−	25.3529i	1.52057	−	1.52057i
$279$	2.55492			0.152959
$280$	−3.66225	+	3.00241i	−0.218861	+	0.179428i
$281$			7.57696i			0.452004i	0.974127	+	0.226002i	$0.0725655\pi$
$281$			7.57696i			0.452004i	−0.974127	+	0.226002i	$0.927434\pi$
$282$	21.0922	−	21.0922i	1.25602	−	1.25602i
$283$	9.72291	+	9.72291i	0.577967	+	0.577967i	0.934343	−	0.356376i	$-0.115988\pi$
$283$	9.72291	+	9.72291i	0.577967	+	0.577967i	−0.356376	+	0.934343i	$0.615988\pi$
$284$	19.0317			1.12932
$285$	3.80406	+	0.376622i	0.225333	+	0.0223092i
$286$	−2.44726	+	22.5142i	−0.144710	+	1.33129i
$287$	17.4218	−	17.4218i	1.02838	−	1.02838i
$288$	−13.8390	+	13.8390i	−0.815470	+	0.815470i
$289$	9.79910	+	13.8916i	0.576417	+	0.817155i
$290$	−28.4078	−	2.81252i	−1.66816	−	0.165157i
$291$	1.81358			0.106314
$292$	8.52437	−	8.52437i	0.498851	−	0.498851i
$293$	18.3613	−	18.3613i	1.07268	−	1.07268i	0.0755352	−	0.997143i	$-0.475933\pi$
$293$	18.3613	−	18.3613i	1.07268	−	1.07268i	0.997143	−	0.0755352i	$-0.0240665\pi$
$294$		−	9.47628i		−	0.552668i
$295$	−17.5957	+	14.4255i	−1.02446	+	0.839883i
$296$	−7.69972			−0.447537
$297$	2.10369	−	1.69119i	0.122069	−	0.0981331i
$298$	−8.30957	−	8.30957i	−0.481361	−	0.481361i
$299$		−	4.94790i		−	0.286144i
$300$	16.1434	−	10.7630i	0.932042	−	0.621399i
$301$			12.1838i			0.702260i
$302$	16.7277	−	16.7277i	0.962569	−	0.962569i
$303$	−16.4920	−	16.4920i	−0.947439	−	0.947439i
$304$	3.30704			0.189672
$305$	12.7343	+	15.5329i	0.729164	+	0.889412i
$306$	19.9055	−	6.31420i	1.13792	−	0.360959i
$307$	5.70548	+	5.70548i	0.325629	+	0.325629i	0.850922	−	0.525293i	$-0.176044\pi$
$307$	5.70548	+	5.70548i	0.325629	+	0.325629i	−0.525293	+	0.850922i	$0.676044\pi$
$308$	12.7145	−	10.2214i	0.724477	−	0.582419i
$309$	−24.7147			−1.40597
$310$	−4.07615	−	0.403560i	−0.231509	−	0.0229206i
$311$			9.86730i			0.559523i	0.960069	+	0.279762i	$0.0902554\pi$
$311$			9.86730i			0.559523i	−0.960069	+	0.279762i	$0.909745\pi$
$312$	4.23336	+	4.23336i	0.239667	+	0.239667i
$313$	−1.19141	+	1.19141i	−0.0673427	+	0.0673427i	−0.739976	−	0.672633i	$-0.765163\pi$
$313$	−1.19141	+	1.19141i	−0.0673427	+	0.0673427i	0.672633	+	0.739976i	$0.265163\pi$
$314$	−0.205576			−0.0116013
$315$	1.76544	−	17.8318i	0.0994712	−	1.00471i
$316$	22.2248			1.25024
$317$	−0.860732	−	0.860732i	−0.0483436	−	0.0483436i	0.682522	−	0.730865i	$-0.260883\pi$
$317$	−0.860732	−	0.860732i	−0.0483436	−	0.0483436i	−0.730865	+	0.682522i	$0.760883\pi$
$318$	−27.1056	−	27.1056i	−1.52000	−	1.52000i
$319$	−22.0892	−	2.40106i	−1.23676	−	0.134434i
$320$	8.35128	−	6.84661i	0.466851	−	0.382737i
$321$			35.0696i			1.95740i
$322$	−5.61002	+	5.61002i	−0.312634	+	0.312634i
$323$	−2.63087	−	1.36375i	−0.146386	−	0.0758809i
$324$			16.1661i			0.898116i
$325$	−9.93851	−	14.9069i	−0.551289	−	0.826883i
$326$	−9.99372			−0.553501
$327$	10.5637	+	10.5637i	0.584174	+	0.584174i
$328$	4.05879	−	4.05879i	0.224109	−	0.224109i
$329$			19.8413i			1.09389i
$330$	28.1471	−	18.3784i	1.54945	−	1.01170i
$331$	32.4128			1.78157			0.890784	−	0.454427i	$-0.150156\pi$
$331$	32.4128			1.78157			0.890784	+	0.454427i	$0.150156\pi$
$332$	3.29369	+	3.29369i	0.180765	+	0.180765i
$333$	20.6011	−	20.6011i	1.12894	−	1.12894i
$334$	−6.36722			−0.348399
$335$	24.8861	+	2.46386i	1.35967	+	0.134615i
$336$		−	32.9995i		−	1.80027i
$337$	−4.43160	+	4.43160i	−0.241404	+	0.241404i	−0.817431	−	0.576027i	$-0.804602\pi$
$337$	−4.43160	+	4.43160i	−0.241404	+	0.241404i	0.576027	+	0.817431i	$0.304602\pi$
$338$	0.216230	−	0.216230i	0.0117614	−	0.0117614i
$339$		−	3.66402i		−	0.199002i
$340$	−14.7150	+	3.11310i	−0.798033	+	0.168831i
$341$	−3.16951	−	0.344521i	−0.171638	−	0.0186569i
$342$	−2.57399	+	2.57399i	−0.139186	+	0.139186i
$343$	−10.4667	−	10.4667i	−0.565147	−	0.565147i
$344$			2.83847i			0.153040i
$345$	−5.67967	+	4.65635i	−0.305783	+	0.250690i
$346$			6.44477i			0.346473i
$347$	12.0163	−	12.0163i	0.645070	−	0.645070i	−0.306728	−	0.951797i	$-0.599234\pi$
$347$	12.0163	−	12.0163i	0.645070	−	0.645070i	0.951797	+	0.306728i	$0.0992341\pi$
$348$	18.3825	−	18.3825i	0.985403	−	0.985403i
$349$	1.30809			0.0700205			0.0350103	−	0.999387i	$-0.488854\pi$
$349$	1.30809			0.0700205			0.0350103	+	0.999387i	$0.488854\pi$
$350$	−5.63320	+	28.1702i	−0.301107	+	1.50576i
$351$	2.91617			0.155654
$352$	19.0341	−	15.3018i	1.01452	−	0.815591i
$353$	−19.6328	−	19.6328i	−1.04495	−	1.04495i	−0.998941	−	0.0460100i	$-0.985349\pi$
$353$	−19.6328	−	19.6328i	−1.04495	−	1.04495i	−0.0460100	−	0.998941i	$-0.514651\pi$
$354$		−	46.1231i		−	2.45141i
$355$	−20.1730	+	16.5384i	−1.07067	+	0.877765i
$356$	−8.14935			−0.431915
$357$	−13.6082	+	26.2523i	−0.720223	+	1.38942i
$358$	2.47956	−	2.47956i	0.131049	−	0.131049i
$359$	−31.3287			−1.65347			−0.826734	−	0.562593i	$-0.809804\pi$
$359$	−31.3287			−1.65347			−0.826734	+	0.562593i	$0.809804\pi$
$360$	0.411297	−	4.15429i	0.0216772	−	0.218951i
$361$	−18.4835			−0.972813
$362$	−34.5995	+	34.5995i	−1.81851	+	1.81851i
$363$	22.0444	−	14.0941i	1.15703	−	0.739748i
$364$	17.6250			0.923803
$365$	−1.62796	+	16.4432i	−0.0852112	+	0.860674i
$366$	−40.7159			−2.12825
$367$	9.24984	+	9.24984i	0.482838	+	0.482838i	0.906037	−	0.423199i	$-0.139093\pi$
$367$	9.24984	+	9.24984i	0.482838	+	0.482838i	−0.423199	+	0.906037i	$0.639093\pi$
$368$	−4.49278	+	4.49278i	−0.234203	+	0.234203i
$369$			21.7192i			1.13065i
$370$	−36.1213	+	29.6133i	−1.87786	+	1.53952i
$371$	25.4981			1.32379
$372$	2.63764	−	2.63764i	0.136755	−	0.136755i
$373$	23.3472	−	23.3472i	1.20887	−	1.20887i	0.237480	−	0.971392i	$-0.423679\pi$
$373$	23.3472	−	23.3472i	1.20887	−	1.20887i	0.971392	−	0.237480i	$-0.0763215\pi$
$374$	−25.5452	+	5.14890i	−1.32091	+	0.266243i
$375$	−7.75862	+	25.4369i	−0.400653	+	1.31356i
$376$			4.62246i			0.238385i
$377$	−16.9744	−	16.9744i	−0.874224	−	0.874224i
$378$	−3.30641	−	3.30641i	−0.170063	−	0.170063i
$379$	−16.8344			−0.864725			−0.432362	−	0.901700i	$-0.642320\pi$
$379$	−16.8344			−0.864725			−0.432362	+	0.901700i	$0.642320\pi$
$380$	2.02752	−	1.66222i	0.104010	−	0.0852700i
$381$	−20.6101			−1.05589
$382$	11.0126	+	11.0126i	0.563451	+	0.563451i
$383$	−18.4902	−	18.4902i	−0.944803	−	0.944803i	0.0537512	−	0.998554i	$-0.482882\pi$
$383$	−18.4902	−	18.4902i	−0.944803	−	0.944803i	−0.998554	+	0.0537512i	$0.982882\pi$
$384$		−	13.1394i		−	0.670518i
$385$	−4.59466	+	21.8832i	−0.234166	+	1.11527i
$386$			15.5790i			0.792949i
$387$	−7.59452	−	7.59452i	−0.386051	−	0.386051i
$388$	0.879539	−	0.879539i	0.0446518	−	0.0446518i
$389$			7.70054i			0.390433i	0.980760	+	0.195216i	$0.0625409\pi$
$389$			7.70054i			0.390433i	−0.980760	+	0.195216i	$0.937459\pi$
$390$	36.1413	+	3.57818i	1.83009	+	0.181188i
$391$	5.42690	−	1.72146i	0.274450	−	0.0870579i
$392$	1.03839	+	1.03839i	0.0524465	+	0.0524465i
$393$	−11.5717	+	11.5717i	−0.583718	+	0.583718i
$394$	40.2165			2.02608
$395$	−23.5576	+	19.3132i	−1.18531	+	0.971751i
$396$	−1.55403	+	14.2967i	−0.0780930	+	0.718436i
$397$	−5.92144	−	5.92144i	−0.297189	−	0.297189i	0.542723	−	0.839912i	$-0.317393\pi$
$397$	−5.92144	−	5.92144i	−0.297189	−	0.297189i	−0.839912	+	0.542723i	$0.817393\pi$
$398$	30.1161	+	30.1161i	1.50958	+	1.50958i
$399$		−	5.15439i		−	0.258042i
$400$	−4.51135	+	22.5601i	−0.225567	+	1.12800i
$401$		−	10.7671i		−	0.537683i	−0.963184	−	0.268841i	$-0.913359\pi$
$401$		−	10.7671i		−	0.537683i	0.963184	−	0.268841i	$-0.0866408\pi$
$402$	−35.8458	+	35.8458i	−1.78783	+	1.78783i
$403$	−2.43560	−	2.43560i	−0.121326	−	0.121326i
$404$	−15.9963			−0.795848
$405$	−14.0482	−	17.1355i	−0.698060	−	0.851472i
$406$			38.4917i			1.91031i
$407$	−28.3348	+	22.7788i	−1.40450	+	1.12910i
$408$	−3.17032	+	6.11604i	−0.156954	+	0.302789i
$409$	−25.7150			−1.27152			−0.635762	−	0.771885i	$-0.719314\pi$
$409$	−25.7150			−1.27152			−0.635762	+	0.771885i	$0.719314\pi$
$410$	3.43063	−	34.6510i	0.169427	−	1.71129i
$411$			13.6411i			0.672867i
$412$	−11.9860	+	11.9860i	−0.590506	+	0.590506i
$413$	21.6939	+	21.6939i	1.06749	+	1.06749i
$414$		−	6.99381i		−	0.343727i
$415$	−6.35339	−	0.629018i	−0.311876	−	0.0308773i
$416$	26.3854			1.29365
$417$	−31.6459	−	31.6459i	−1.54971	−	1.54971i
$418$	3.54027	−	2.84608i	0.173160	−	0.139206i
$419$	2.62320			0.128152			0.0640758	−	0.997945i	$-0.479590\pi$
$419$	2.62320			0.128152			0.0640758	+	0.997945i	$0.479590\pi$
$420$	−16.5865	−	20.2317i	−0.809340	−	0.987207i
$421$	17.4940			0.852607			0.426304	−	0.904580i	$-0.359816\pi$
$421$	17.4940			0.852607			0.426304	+	0.904580i	$0.359816\pi$
$422$	−11.9715	−	11.9715i	−0.582761	−	0.582761i
$423$	−12.3677	−	12.3677i	−0.601340	−	0.601340i
$424$	5.94032			0.288488
$425$	12.8922	−	16.0870i	0.625363	−	0.780334i
$426$		−	52.8787i		−	2.56198i
$427$	19.1506	−	19.1506i	0.926764	−	0.926764i
$428$	17.0078	+	17.0078i	0.822105	+	0.822105i
$429$	28.1026	+	3.05471i	1.35681	+	0.147483i
$430$	10.9168	+	13.3160i	0.526455	+	0.642153i
$431$	−17.7415			−0.854579			−0.427290	−	0.904115i	$-0.640531\pi$
$431$	−17.7415			−0.854579			−0.427290	+	0.904115i	$0.640531\pi$
$432$	−2.64794	−	2.64794i	−0.127399	−	0.127399i
$433$	−18.1951	−	18.1951i	−0.874400	−	0.874400i	0.118549	−	0.992948i	$-0.462176\pi$
$433$	−18.1951	−	18.1951i	−0.874400	−	0.874400i	−0.992948	+	0.118549i	$0.962176\pi$
$434$			5.52306i			0.265115i
$435$	−3.51063	+	35.4590i	−0.168322	+	1.70013i
$436$	10.2462			0.490705
$437$	−0.701756	+	0.701756i	−0.0335695	+	0.0335695i
$438$	−23.6846	−	23.6846i	−1.13169	−	1.13169i
$439$			5.43130i			0.259222i	0.991565	+	0.129611i	$0.0413728\pi$
$439$			5.43130i			0.259222i	−0.991565	+	0.129611i	$0.958627\pi$
$440$	−1.07043	+	5.09815i	−0.0510305	+	0.243045i
$441$	−5.55657			−0.264598
$442$	−24.9952	−	12.9566i	−1.18890	−	0.616281i
$443$	9.16368	+	9.16368i	0.435380	+	0.435380i	0.890454	−	0.455074i	$-0.150387\pi$
$443$	9.16368	+	9.16368i	0.435380	+	0.435380i	−0.455074	+	0.890454i	$0.650387\pi$
$444$		−	42.5363i		−	2.01869i
$445$	8.63805	−	7.08171i	0.409483	−	0.335705i
$446$		−	34.9701i		−	1.65588i
$447$	−10.3721	+	10.3721i	−0.490585	+	0.490585i
$448$	−10.2963	−	10.2963i	−0.486457	−	0.486457i
$449$	−11.1704			−0.527164			−0.263582	−	0.964637i	$-0.584904\pi$
$449$	−11.1704			−0.527164			−0.263582	+	0.964637i	$0.584904\pi$
$450$	−14.0480	−	21.0707i	−0.662229	−	0.993282i
$451$	2.92875	−	26.9437i	0.137909	−	1.26873i
$452$	−1.77695	−	1.77695i	−0.0835808	−	0.0835808i
$453$	−20.8797	−	20.8797i	−0.981014	−	0.981014i
$454$	−21.2875			−0.999070
$455$	−18.6820	+	15.3160i	−0.875825	+	0.718025i
$456$		−	1.20083i		−	0.0562338i
$457$	−26.6045	−	26.6045i	−1.24450	−	1.24450i	−0.958113	−	0.286392i	$-0.907544\pi$
$457$	−26.6045	−	26.6045i	−1.24450	−	1.24450i	−0.286392	−	0.958113i	$-0.592456\pi$
$458$	−10.7627	+	10.7627i	−0.502910	+	0.502910i
$459$	1.01459	+	3.19848i	0.0473568	+	0.149292i
$460$	−0.496283	+	5.01270i	−0.0231393	+	0.233718i
$461$		−	11.4711i		−	0.534264i	−0.963660	−	0.267132i	$-0.913924\pi$
$461$		−	11.4711i		−	0.534264i	0.963660	−	0.267132i	$-0.0860760\pi$
$462$	−28.3998	−	35.3267i	−1.32128	−	1.64355i
$463$	−3.53359	−	3.53359i	−0.164220	−	0.164220i	0.620213	−	0.784433i	$-0.287046\pi$
$463$	−3.53359	−	3.53359i	−0.164220	−	0.164220i	−0.784433	+	0.620213i	$0.787046\pi$
$464$			30.8261i			1.43107i
$465$	−0.503729	+	5.08790i	−0.0233599	+	0.235946i
$466$		−	53.1654i		−	2.46284i
$467$	−25.4839	+	25.4839i	−1.17925	+	1.17925i	−0.199317	+	0.979935i	$0.563872\pi$
$467$	−25.4839	+	25.4839i	−1.17925	+	1.17925i	−0.979935	+	0.199317i	$0.936128\pi$
$468$	−10.9862	+	10.9862i	−0.507839	+	0.507839i
$469$		−	33.7200i		−	1.55704i
$470$	17.7781	+	21.6851i	0.820042	+	1.00026i
$471$			0.256603i			0.0118236i
$472$	5.05406	+	5.05406i	0.232632	+	0.232632i
$473$	8.39730	+	10.4455i	0.386108	+	0.480284i
$474$		−	61.7507i		−	2.83630i
$475$	−0.704655	+	3.52380i	−0.0323318	+	0.161683i
$476$	6.13206	+	19.3313i	0.281062	+	0.886049i
$477$	−15.8938	+	15.8938i	−0.727726	+	0.727726i
$478$	−13.8003	−	13.8003i	−0.631210	−	0.631210i
$479$		−	22.8288i		−	1.04308i	−0.853228	−	0.521538i	$-0.825358\pi$
$479$		−	22.8288i		−	1.04308i	0.853228	−	0.521538i	$-0.174642\pi$
$480$	−24.8307	−	30.2877i	−1.13336	−	1.38244i
$481$	−39.2781			−1.79093
$482$	−15.0414	−	15.0414i	−0.685115	−	0.685115i
$483$	7.00251	+	7.00251i	0.318625	+	0.318625i
$484$	3.85571	−	17.5262i	0.175259	−	0.796646i
$485$	−0.167972	+	1.69660i	−0.00762720	+	0.0770384i
$486$	40.2642			1.82642
$487$	15.6432	+	15.6432i	0.708863	+	0.708863i	0.966296	−	0.257433i	$-0.0828768\pi$
$487$	15.6432	+	15.6432i	0.708863	+	0.708863i	−0.257433	+	0.966296i	$0.582877\pi$
$488$	4.46155	−	4.46155i	0.201965	−	0.201965i
$489$			12.4743i			0.564108i
$490$	8.86501	+	0.877682i	0.400480	+	0.0396496i
$491$			2.27014i			0.102450i	0.998687	+	0.0512251i	$0.0163126\pi$
$491$			2.27014i			0.102450i	−0.998687	+	0.0512251i	$0.983687\pi$
$492$	22.4224	+	22.4224i	1.01088	+	1.01088i
$493$	12.7120	−	24.5233i	0.572518	−	1.10447i
$494$	4.90757			0.220802
$495$	−10.7765	−	16.5045i	−0.484367	−	0.741821i
$496$			4.42314i			0.198605i
$497$	24.8714	+	24.8714i	1.11563	+	1.11563i
$498$	9.15137	−	9.15137i	0.410083	−	0.410083i
$499$	−38.4327			−1.72048			−0.860241	−	0.509887i	$-0.829687\pi$
$499$	−38.4327			−1.72048			−0.860241	+	0.509887i	$0.829687\pi$
$500$	8.57349	+	16.0989i	0.383418	+	0.719967i
$501$			7.94766i			0.355075i
$502$	−21.9350	−	21.9350i	−0.979006	−	0.979006i
$503$	−28.9416	−	28.9416i	−1.29044	−	1.29044i	−0.934513	−	0.355930i	$-0.884164\pi$
$503$	−28.9416	−	28.9416i	−1.29044	−	1.29044i	−0.355930	−	0.934513i	$-0.615836\pi$
$504$	−5.62895			−0.250733
$505$	16.9556	−	13.9007i	0.754515	−	0.618572i
$506$	−0.943088	+	8.67618i	−0.0419254	+	0.385703i
$507$	−0.269902	−	0.269902i	−0.0119868	−	0.0119868i
$508$	−9.99535	+	9.99535i	−0.443472	+	0.443472i
$509$		−	25.9596i		−	1.15064i	−0.817929	−	0.575319i	$-0.804878\pi$
$509$		−	25.9596i		−	1.15064i	0.817929	−	0.575319i	$-0.195122\pi$
$510$	8.64961	+	40.8850i	0.383011	+	1.81042i
$511$	22.2800			0.985609
$512$	−19.3875	−	19.3875i	−0.856816	−	0.856816i
$513$	−0.413598	−	0.413598i	−0.0182608	−	0.0182608i
$514$	57.1542			2.52097
$515$	2.28904	−	23.1204i	0.100867	−	1.01881i
$516$	−15.6808			−0.690310
$517$	13.6751	+	17.0105i	0.601429	+	0.748123i
$518$	44.5342	+	44.5342i	1.95672	+	1.95672i
$519$	8.04445			0.353112
$520$	−4.35237	+	3.56819i	−0.190864	+	0.156476i
$521$		−	11.0459i		−	0.483928i	−0.970285	−	0.241964i	$-0.922208\pi$
$521$		−	11.0459i		−	0.483928i	0.970285	−	0.241964i	$-0.0777916\pi$
$522$	−23.9931	−	23.9931i	−1.05015	−	1.05015i
$523$	12.5202	−	12.5202i	0.547469	−	0.547469i	−0.378239	−	0.925708i	$-0.623470\pi$
$523$	12.5202	−	12.5202i	0.547469	−	0.547469i	0.925708	+	0.378239i	$0.123470\pi$
$524$			11.2240i			0.490322i
$525$	35.1624	+	7.03144i	1.53461	+	0.306877i
$526$	−40.4015			−1.76159
$527$	1.82400	−	3.51877i	0.0794546	−	0.153280i
$528$	−22.7439	−	28.2914i	−0.989803	−	1.23123i
$529$			21.0933i			0.917098i
$530$	27.8676	−	22.8466i	1.21049	−	0.992393i
$531$	−27.0450			−1.17365
$532$	−2.49974	−	2.49974i	−0.108378	−	0.108378i
$533$	20.7048	−	20.7048i	0.896826	−	0.896826i
$534$			22.6426i			0.979842i
$535$	−32.8074	−	3.24811i	−1.41839	−	0.140428i
$536$		−	7.85579i		−	0.339318i
$537$	−3.09503	−	3.09503i	−0.133560	−	0.133560i
$538$	27.0911	+	27.0911i	1.16798	+	1.16798i
$539$	6.89321	+	0.749282i	0.296911	+	0.0322739i
$540$	−2.95436	−	0.292497i	−0.127136	−	0.0125871i
$541$	38.1534			1.64034			0.820171	−	0.572118i	$-0.193878\pi$
$541$	38.1534			1.64034			0.820171	+	0.572118i	$0.193878\pi$
$542$	2.51682	−	2.51682i	0.108106	−	0.108106i
$543$	43.1876	+	43.1876i	1.85336	+	1.85336i
$544$	9.17992	+	28.9397i	0.393586	+	1.24078i
$545$	−10.8607	+	8.90388i	−0.465220	+	0.381401i
$546$		−	48.9704i		−	2.09574i
$547$	12.9807	−	12.9807i	0.555013	−	0.555013i	−0.372870	−	0.927884i	$-0.621626\pi$
$547$	12.9807	−	12.9807i	0.555013	−	0.555013i	0.927884	+	0.372870i	$0.121626\pi$
$548$	6.61558	+	6.61558i	0.282603	+	0.282603i
$549$			23.8744i			1.01893i
$550$	14.5860	+	28.0336i	0.621947	+	1.19536i
$551$			4.81492i			0.205122i
$552$	1.63138	+	1.63138i	0.0694363	+	0.0694363i
$553$	29.0443	+	29.0443i	1.23509	+	1.23509i
$554$	−29.0936			−1.23607
$555$	36.9637	+	45.0872i	1.56902	+	1.91384i
$556$	−30.6948			−1.30175
$557$	9.82885	+	9.82885i	0.416462	+	0.416462i	0.883982	−	0.467521i	$-0.154853\pi$
$557$	9.82885	+	9.82885i	0.416462	+	0.416462i	−0.467521	+	0.883982i	$0.654853\pi$
$558$	−3.44270	−	3.44270i	−0.145741	−	0.145741i
$559$			14.4797i			0.612425i
$560$	30.8708	+	3.05637i	1.30453	+	0.129155i
$561$	6.42694	+	31.8859i	0.271345	+	1.34623i
$562$	10.2098	−	10.2098i	0.430674	−	0.430674i
$563$	−2.50113	+	2.50113i	−0.105410	+	0.105410i	−0.757845	−	0.652435i	$-0.773748\pi$
$563$	−2.50113	+	2.50113i	−0.105410	+	0.105410i	0.652435	+	0.757845i	$0.273748\pi$
$564$	−25.5363			−1.07527
$565$	3.42767	+	0.339357i	0.144203	+	0.0142769i
$566$		−	26.2028i		−	1.10139i
$567$	−21.1265	+	21.1265i	−0.887231	+	0.887231i
$568$	5.79432	+	5.79432i	0.243124	+	0.243124i
$569$	−25.2206			−1.05730			−0.528651	−	0.848839i	$-0.677302\pi$
$569$	−25.2206			−1.05730			−0.528651	+	0.848839i	$0.677302\pi$
$570$	−4.61840	−	5.63338i	−0.193444	−	0.235956i
$571$	5.87717			0.245952			0.122976	−	0.992410i	$-0.460756\pi$
$571$	5.87717			0.245952			0.122976	+	0.992410i	$0.460756\pi$
$572$	15.1105	−	12.1475i	0.631800	−	0.507915i
$573$	13.7460	−	13.7460i	0.574249	−	0.574249i
$574$	−46.9511			−1.95970
$575$	−3.82995	−	5.74457i	−0.159720	−	0.239565i
$576$	12.8361			0.534837
$577$	14.2068	−	14.2068i	0.591438	−	0.591438i	−0.346581	−	0.938020i	$-0.612658\pi$
$577$	14.2068	−	14.2068i	0.591438	−	0.591438i	0.938020	+	0.346581i	$0.112658\pi$
$578$	5.51462	−	31.9227i	0.229378	−	1.32781i
$579$	19.4459			0.808145
$580$	15.4941	+	18.8992i	0.643358	+	0.784748i
$581$			8.60865i			0.357147i
$582$	−2.44376	−	2.44376i	−0.101297	−	0.101297i
$583$	21.8602	−	17.5738i	0.905359	−	0.727833i
$584$	5.19060			0.214789
$585$	2.09812	−	21.1920i	0.0867466	−	0.876182i
$586$	−49.4829			−2.04412
$587$	16.3136	−	16.3136i	0.673334	−	0.673334i	−0.285149	−	0.958483i	$-0.592043\pi$
$587$	16.3136	−	16.3136i	0.673334	−	0.673334i	0.958483	+	0.285149i	$0.0920430\pi$
$588$	−5.73648	+	5.73648i	−0.236568	+	0.236568i
$589$			0.690877i			0.0284671i
$590$	43.1479	+	4.27186i	1.77637	+	0.175870i
$591$		−	50.1988i		−	2.06490i
$592$	35.6652	+	35.6652i	1.46583	+	1.46583i
$593$	−20.8005	+	20.8005i	−0.854172	+	0.854172i	−0.990644	−	0.136472i	$-0.956424\pi$
$593$	−20.8005	+	20.8005i	−0.854172	+	0.854172i	0.136472	+	0.990644i	$0.456424\pi$
$594$	−5.11353	−	0.555833i	−0.209811	−	0.0228061i
$595$	−23.2985	−	15.1619i	−0.955146	−	0.621576i
$596$			10.0604i			0.412091i
$597$	37.5914	−	37.5914i	1.53851	−	1.53851i
$598$	−6.66718	+	6.66718i	−0.272641	+	0.272641i
$599$			37.5864i			1.53574i	0.640606	+	0.767870i	$0.278683\pi$
$599$			37.5864i			1.53574i	−0.640606	+	0.767870i	$0.721317\pi$
$600$	8.19183	+	1.63812i	0.334430	+	0.0668762i
$601$	−0.0812898			−0.00331588			−0.00165794	−	0.999999i	$-0.500528\pi$
$601$	−0.0812898			−0.00331588			−0.00165794	+	0.999999i	$0.500528\pi$
$602$	16.4173	−	16.4173i	0.669121	−	0.669121i
$603$	21.0187	+	21.0187i	0.855949	+	0.855949i
$604$	−20.2522			−0.824051
$605$	11.1432	+	21.9278i	0.453036	+	0.891492i
$606$			44.4451i			1.80546i
$607$	8.71360	−	8.71360i	0.353674	−	0.353674i	−0.507801	−	0.861475i	$-0.669541\pi$
$607$	8.71360	−	8.71360i	0.353674	−	0.353674i	0.861475	+	0.507801i	$0.169541\pi$
$608$	−3.74221	−	3.74221i	−0.151767	−	0.151767i
$609$	48.0459			1.94692
$610$	3.77105	−	38.0894i	0.152685	−	1.54220i
$611$			23.5803i			0.953955i
$612$	−15.8721	−	8.22751i	−0.641592	−	0.332577i
$613$	−14.3340	+	14.3340i	−0.578944	+	0.578944i	−0.934612	−	0.355668i	$-0.884253\pi$
$613$	−14.3340	+	14.3340i	−0.578944	+	0.578944i	0.355668	+	0.934612i	$0.384253\pi$
$614$		−	15.3760i		−	0.620526i
$615$	−43.2519	−	4.28216i	−1.74408	−	0.172673i
$616$	6.98300	+	0.759042i	0.281353	+	0.0305827i
$617$	−12.2658	−	12.2658i	−0.493802	−	0.493802i	0.415700	−	0.909502i	$-0.363537\pi$
$617$	−12.2658	−	12.2658i	−0.493802	−	0.493802i	−0.909502	+	0.415700i	$0.863537\pi$
$618$	33.3025	+	33.3025i	1.33962	+	1.33962i
$619$	11.3612			0.456643			0.228322	−	0.973586i	$-0.426676\pi$
$619$	11.3612			0.456643			0.228322	+	0.973586i	$0.426676\pi$
$620$	2.22320	+	2.71179i	0.0892860	+	0.108908i
$621$	1.12379			0.0450960
$622$	13.2960	−	13.2960i	0.533120	−	0.533120i
$623$	−10.6499	−	10.6499i	−0.426680	−	0.426680i
$624$		−	39.2180i		−	1.56997i
$625$	−23.0775	−	9.61408i	−0.923099	−	0.384563i
$626$	3.21081			0.128330
$627$	−3.55252	−	4.41901i	−0.141874	−	0.176478i
$628$	0.124446	+	0.124446i	0.00496592	+	0.00496592i
$629$	−13.6655	−	43.0805i	−0.544880	−	1.71773i
$630$	−26.4068	+	21.6490i	−1.05207	+	0.862518i
$631$	−10.7843			−0.429317			−0.214658	−	0.976689i	$-0.568864\pi$
$631$	−10.7843			−0.429317			−0.214658	+	0.976689i	$0.568864\pi$
$632$	6.76649	+	6.76649i	0.269157	+	0.269157i
$633$	−14.9429	+	14.9429i	−0.593928	+	0.593928i
$634$			2.31964i			0.0921245i
$635$	1.90888	−	19.2806i	0.0757517	−	0.765128i
$636$			32.8167i			1.30127i
$637$	5.29706	+	5.29706i	0.209877	+	0.209877i
$638$	26.5293	+	33.0001i	1.05031	+	1.30649i
$639$	−31.0062			−1.22659
$640$	12.2918	+	1.21696i	0.485878	+	0.0481044i
$641$			32.3397i			1.27734i	0.769481	+	0.638670i	$0.220515\pi$
$641$			32.3397i			1.27734i	−0.769481	+	0.638670i	$0.779485\pi$
$642$	47.2556	−	47.2556i	1.86503	−	1.86503i
$643$	−9.27950	+	9.27950i	−0.365948	+	0.365948i	−0.865997	−	0.500049i	$-0.833315\pi$
$643$	−9.27950	+	9.27950i	−0.365948	+	0.365948i	0.500049	+	0.865997i	$0.333315\pi$
$644$	6.79206			0.267645
$645$	16.6212	−	13.6265i	0.654458	−	0.536543i
$646$	1.70743	+	5.38266i	0.0671778	+	0.211778i
$647$	6.60233	−	6.60233i	0.259564	−	0.259564i	−0.565312	−	0.824877i	$-0.691244\pi$
$647$	6.60233	−	6.60233i	0.259564	−	0.259564i	0.824877	+	0.565312i	$0.191244\pi$
$648$	−4.92188	+	4.92188i	−0.193350	+	0.193350i
$649$	33.5507	+	3.64691i	1.31698	+	0.143154i
$650$	−6.69473	+	33.4786i	−0.262589	+	1.31314i
$651$	6.89396			0.270196
$652$	6.04971	+	6.04971i	0.236925	+	0.236925i
$653$	1.39111	−	1.39111i	0.0544384	−	0.0544384i	−0.679364	−	0.733802i	$-0.737744\pi$
$653$	1.39111	−	1.39111i	0.0544384	−	0.0544384i	0.733802	+	0.679364i	$0.237744\pi$
$654$		−	28.4687i		−	1.11321i
$655$	−9.75354	−	11.8971i	−0.381102	−	0.464857i
$656$	−37.6008			−1.46806
$657$	−13.8878	+	13.8878i	−0.541816	+	0.541816i
$658$	26.7358	−	26.7358i	1.04227	−	1.04227i
$659$	39.2812			1.53018			0.765089	−	0.643924i	$-0.222695\pi$
$659$	39.2812			1.53018			0.765089	+	0.643924i	$0.222695\pi$
$660$	−28.1642	−	5.91346i	−1.09629	−	0.230181i
$661$	27.1538			1.05616			0.528081	−	0.849194i	$-0.322912\pi$
$661$	27.1538			1.05616			0.528081	+	0.849194i	$0.322912\pi$
$662$	−43.6755	−	43.6755i	−1.69750	−	1.69750i
$663$	−16.1726	+	31.1993i	−0.628090	+	1.21168i
$664$			2.00557i			0.0778312i
$665$	4.82191	+	0.477394i	0.186985	+	0.0185125i
$666$	−55.5192			−2.15132
$667$	−6.54131	−	6.54131i	−0.253281	−	0.253281i
$668$	3.85440	+	3.85440i	0.149131	+	0.149131i
$669$	−43.6502			−1.68761
$670$	−30.2135	−	36.8535i	−1.16725	−	1.42378i
$671$	3.21937	−	29.6174i	0.124282	−	1.14337i
$672$	−37.3419	+	37.3419i	−1.44049	+	1.44049i
$673$	−29.3133	−	29.3133i	−1.12995	−	1.12995i	−0.990185	−	0.139760i	$-0.955367\pi$
$673$	−29.3133	−	29.3133i	−1.12995	−	1.12995i	−0.139760	−	0.990185i	$-0.544633\pi$
$674$	11.9430			0.460025
$675$	3.38571	−	2.25728i	0.130316	−	0.0868827i
$676$	−0.261791			−0.0100689
$677$	20.1100	−	20.1100i	0.772889	−	0.772889i	−0.205722	−	0.978610i	$-0.565954\pi$
$677$	20.1100	−	20.1100i	0.772889	−	0.772889i	0.978610	+	0.205722i	$0.0659542\pi$
$678$	−4.93718	+	4.93718i	−0.189611	+	0.189611i
$679$	2.29884			0.0882213
$680$	−5.42789	−	3.53228i	−0.208150	−	0.135457i
$681$			26.5713i			1.01821i
$682$	3.80661	+	4.73508i	0.145763	+	0.181315i
$683$	−8.07947	+	8.07947i	−0.309153	+	0.309153i	−0.844581	−	0.535428i	$-0.820150\pi$
$683$	−8.07947	+	8.07947i	−0.309153	+	0.309153i	0.535428	+	0.844581i	$0.320150\pi$
$684$	3.11634			0.119156
$685$	−12.7612	−	1.26342i	−0.487580	−	0.0482729i
$686$			28.2072i			1.07696i
$687$	13.4342	+	13.4342i	0.512547	+	0.512547i
$688$	13.1478	−	13.1478i	0.501256	−	0.501256i
$689$	30.3030			1.15445
$690$	13.9276	+	1.37890i	0.530214	+	0.0524939i
$691$			15.6686i			0.596060i	0.954556	+	0.298030i	$0.0963296\pi$
$691$			15.6686i			0.596060i	−0.954556	+	0.298030i	$0.903670\pi$
$692$	3.90135	−	3.90135i	0.148307	−	0.148307i
$693$	−20.7144	+	16.6526i	−0.786874	+	0.632581i
$694$	−32.3834			−1.22926
$695$	32.5355	−	26.6735i	1.23414	−	1.01178i
$696$	11.1933			0.424282
$697$	29.9128	+	15.5057i	1.13303	+	0.587319i
$698$	−1.76262	−	1.76262i	−0.0667163	−	0.0667163i
$699$	−66.3618			−2.51003
$700$	20.4629	−	13.6428i	0.773425	−	0.515648i
$701$			21.9618i			0.829488i	0.909938	+	0.414744i	$0.136129\pi$
$701$			21.9618i			0.829488i	−0.909938	+	0.414744i	$0.863871\pi$
$702$	−3.92947	−	3.92947i	−0.148308	−	0.148308i
$703$	5.57077	+	5.57077i	0.210106	+	0.210106i
$704$	−15.9238	−	1.73090i	−0.600151	−	0.0652356i
$705$	27.0677	−	22.1909i	1.01943	−	0.835756i
$706$			52.9097i			1.99128i
$707$	−20.9047	−	20.9047i	−0.786202	−	0.786202i
$708$	−27.9206	+	27.9206i	−1.04932	+	1.04932i
$709$	−36.8760			−1.38491			−0.692453	−	0.721463i	$-0.743470\pi$
$709$	−36.8760			−1.38491			−0.692453	+	0.721463i	$0.743470\pi$
$710$	49.4677	+	4.89756i	1.85649	+	0.183802i
$711$	−36.2085			−1.35792
$712$	−2.48112	−	2.48112i	−0.0929841	−	0.0929841i
$713$	−0.938593	−	0.938593i	−0.0351506	−	0.0351506i
$714$	53.7112	−	17.0377i	2.01009	−	0.637618i
$715$	−5.46049	+	26.0069i	−0.204211	+	0.972602i
$716$	−3.00201			−0.112190
$717$	−17.2257	+	17.2257i	−0.643306	+	0.643306i
$718$	42.2148	+	42.2148i	1.57544	+	1.57544i
$719$	26.9655			1.00564			0.502822	−	0.864390i	$-0.332295\pi$
$719$	26.9655			1.00564			0.502822	+	0.864390i	$0.332295\pi$
$720$	−21.1479	+	17.3376i	−0.788135	+	0.646135i
$721$	−31.3275			−1.16670
$722$	24.9060	+	24.9060i	0.926907	+	0.926907i
$723$	−18.7748	+	18.7748i	−0.698244	+	0.698244i
$724$	41.8897			1.55682
$725$	−32.8465	−	6.56834i	−1.21989	−	0.243942i
$726$	−48.6959	−	10.7129i	−1.80727	−	0.397594i
$727$	2.60619	−	2.60619i	0.0966582	−	0.0966582i	−0.657124	−	0.753782i	$-0.728227\pi$
$727$	2.60619	−	2.60619i	0.0966582	−	0.0966582i	0.753782	+	0.657124i	$0.228227\pi$
$728$	5.36606	+	5.36606i	0.198879	+	0.198879i
$729$		−	20.5302i		−	0.760378i
$730$	24.3504	−	19.9632i	0.901250	−	0.738869i
$731$	−15.8814	+	5.03773i	−0.587396	+	0.186327i
$732$	24.6474	+	24.6474i	0.910993	+	0.910993i
$733$	−7.26255	+	7.26255i	−0.268248	+	0.268248i	−0.828394	−	0.560146i	$-0.810745\pi$
$733$	−7.26255	+	7.26255i	−0.268248	+	0.268248i	0.560146	+	0.828394i	$0.310745\pi$
$734$		−	24.9279i		−	0.920106i
$735$	1.09553	−	11.0654i	0.0404094	−	0.408155i
$736$	10.1680			0.374796
$737$	−23.2405	−	28.9091i	−0.856076	−	1.06488i
$738$	29.2661	−	29.2661i	1.07730	−	1.07730i
$739$	−35.7050			−1.31343			−0.656715	−	0.754138i	$-0.728055\pi$
$739$	−35.7050			−1.31343			−0.656715	+	0.754138i	$0.728055\pi$
$740$	39.7925	+	3.93966i	1.46280	+	0.144825i
$741$		−	6.12569i		−	0.225033i
$742$	−34.3581	−	34.3581i	−1.26133	−	1.26133i
$743$	3.23192	+	3.23192i	0.118568	+	0.118568i	0.763901	−	0.645333i	$-0.223282\pi$
$743$	3.23192	+	3.23192i	0.118568	+	0.118568i	−0.645333	+	0.763901i	$0.723282\pi$
$744$	1.60610			0.0588823
$745$	−8.74241	−	10.6637i	−0.320297	−	0.390688i
$746$	−62.9197			−2.30365
$747$	−5.36605	−	5.36605i	−0.196333	−	0.196333i
$748$	18.5807	+	12.3469i	0.679379	+	0.451449i
$749$			44.4531i			1.62428i
$750$	44.7302	−	23.8211i	1.63332	−	0.869823i
$751$		−	42.8915i		−	1.56513i	−0.622566	−	0.782567i	$-0.713910\pi$
$751$		−	42.8915i		−	1.56513i	0.622566	−	0.782567i	$-0.286090\pi$
$752$	21.4113	−	21.4113i	0.780791	−	0.780791i
$753$	−27.3795	+	27.3795i	−0.997766	+	0.997766i
$754$			45.7452i			1.66594i
$755$	21.4667	−	17.5990i	0.781253	−	0.640493i
$756$			4.00308i			0.145590i
$757$	−33.5448	+	33.5448i	−1.21921	+	1.21921i	−0.251298	+	0.967910i	$0.580858\pi$
$757$	−33.5448	+	33.5448i	−1.21921	+	1.21921i	−0.967910	+	0.251298i	$0.919142\pi$
$758$	22.6840	+	22.6840i	0.823919	+	0.823919i
$759$	10.8297	+	1.17718i	0.393094	+	0.0427288i
$760$	1.12337	+	0.111219i	0.0407488	+	0.00403434i
$761$		−	33.3953i		−	1.21058i	−0.796005	−	0.605290i	$-0.793057\pi$
$761$		−	33.3953i		−	1.21058i	0.796005	−	0.605290i	$-0.206943\pi$
$762$	27.7717	+	27.7717i	1.00606	+	1.00606i
$763$	13.3902	+	13.3902i	0.484758	+	0.484758i
$764$		−	13.3329i		−	0.482368i
$765$	23.9736	−	5.07183i	0.866766	−	0.183373i
$766$			49.8302i			1.80044i
$767$	25.7819	+	25.7819i	0.930931	+	0.930931i
$768$	−33.9509	+	33.9509i	−1.22510	+	1.22510i
$769$	11.1125			0.400728			0.200364	−	0.979722i	$-0.435788\pi$
$769$	11.1125			0.400728			0.200364	+	0.979722i	$0.435788\pi$
$770$	35.6783	−	23.2959i	1.28576	−	0.839525i
$771$		−	71.3407i		−	2.56927i
$772$	9.43075	−	9.43075i	0.339420	−	0.339420i
$773$	6.18746	+	6.18746i	0.222547	+	0.222547i	0.809570	−	0.587023i	$-0.199700\pi$
$773$	6.18746	+	6.18746i	0.222547	+	0.222547i	−0.587023	+	0.809570i	$0.699700\pi$
$774$			20.4669i			0.735667i
$775$	−4.71305	−	0.942471i	−0.169298	−	0.0338545i
$776$	0.535563			0.0192256
$777$	55.5883	−	55.5883i	1.99422	−	1.99422i
$778$	10.3763	−	10.3763i	0.372009	−	0.372009i
$779$	−5.87310			−0.210426
$780$	−19.7121	−	24.0442i	−0.705807	−	0.860921i
$781$	38.4648	+	4.18107i	1.37638	+	0.149611i
$782$	−9.63225	−	4.99300i	−0.344449	−	0.178549i
$783$	3.85529	−	3.85529i	0.137777	−	0.137777i
$784$		−	9.61967i		−	0.343560i
$785$	−0.240051	−	0.0237663i	−0.00856778	−	0.000848254i
$786$	31.1854			1.11234
$787$	−23.1792	+	23.1792i	−0.826248	+	0.826248i	−0.986996	−	0.160748i	$-0.948609\pi$
$787$	−23.1792	+	23.1792i	−0.826248	+	0.826248i	0.160748	+	0.986996i	$0.448609\pi$
$788$	−24.3451	−	24.3451i	−0.867259	−	0.867259i
$789$			50.4298i			1.79535i
$790$	57.7674	+	5.71927i	2.05527	+	0.203483i
$791$		−	4.64439i		−	0.165135i
$792$	−4.82586	+	3.87959i	−0.171479	+	0.137855i
$793$	22.7594	−	22.7594i	0.808210	−	0.808210i
$794$			15.9580i			0.566329i
$795$	−28.5175	−	34.7847i	−1.01141	−	1.23369i
$796$		−	36.4616i		−	1.29235i
$797$	7.28148	−	7.28148i	0.257923	−	0.257923i	−0.566286	−	0.824209i	$-0.691620\pi$
$797$	7.28148	−	7.28148i	0.257923	−	0.257923i	0.824209	+	0.566286i	$0.191620\pi$
$798$	−6.94543	+	6.94543i	−0.245866	+	0.245866i
$799$	−25.8630	+	8.20398i	−0.914969	+	0.290236i
$800$	30.6337	−	20.4237i	1.08307	−	0.722088i
$801$	13.2769			0.469115
$802$	−14.5084	+	14.5084i	−0.512310	+	0.512310i
$803$	19.1013	−	15.3558i	0.674069	−	0.541896i
$804$	43.3985			1.53055
$805$	−7.19937	+	5.90224i	−0.253744	+	0.208027i
$806$			6.56383i			0.231201i
$807$	33.8155	−	33.8155i	1.19036	−	1.19036i
$808$	−4.87019	−	4.87019i	−0.171333	−	0.171333i
$809$			23.4210i			0.823440i	0.911310	+	0.411720i	$0.135072\pi$
$809$			23.4210i			0.823440i	−0.911310	+	0.411720i	$0.864928\pi$
$810$	−4.16014	+	42.0194i	−0.146172	+	1.47641i
$811$	35.0963			1.23240			0.616199	−	0.787591i	$-0.288672\pi$
$811$	35.0963			1.23240			0.616199	+	0.787591i	$0.288672\pi$
$812$	23.3010	−	23.3010i	0.817705	−	0.817705i
$813$	−3.14153	−	3.14153i	−0.110178	−	0.110178i
$814$	68.8744	+	7.48655i	2.41405	+	0.262403i
$815$	−11.6696	−	1.15535i	−0.408770	−	0.0404703i
$816$	43.0146	−	13.6446i	1.50581	−	0.477657i
$817$	2.05364	−	2.05364i	0.0718478	−	0.0718478i
$818$	34.6504	+	34.6504i	1.21152	+	1.21152i
$819$	−28.7146			−1.00337
$820$	−23.0527	+	18.8993i	−0.805037	+	0.659991i
$821$	−43.9946			−1.53542			−0.767711	−	0.640796i	$-0.778605\pi$
$821$	−43.9946			−1.53542			−0.767711	+	0.640796i	$0.778605\pi$
$822$	18.3811	−	18.3811i	0.641115	−	0.641115i
$823$	11.7504	−	11.7504i	0.409594	−	0.409594i	−0.472003	−	0.881597i	$-0.656469\pi$
$823$	11.7504	−	11.7504i	0.409594	−	0.409594i	0.881597	+	0.472003i	$0.156469\pi$
$824$	−7.29841			−0.254252
$825$	34.9919	−	18.2064i	1.21826	−	0.633866i
$826$		−	58.4641i		−	2.03423i
$827$	−4.06422	+	4.06422i	−0.141327	+	0.141327i	−0.774231	−	0.632904i	$-0.781863\pi$
$827$	−4.06422	+	4.06422i	−0.141327	+	0.141327i	0.632904	+	0.774231i	$0.281863\pi$
$828$	−4.23371	+	4.23371i	−0.147131	+	0.147131i
$829$		−	50.8161i		−	1.76492i	−0.470390	−	0.882459i	$-0.655887\pi$
$829$		−	50.8161i		−	1.76492i	0.470390	−	0.882459i	$-0.344113\pi$
$830$	7.71346	+	9.40864i	0.267738	+	0.326579i
$831$			36.3150i			1.25975i
$832$	−12.2366	−	12.2366i	−0.424228	−	0.424228i
$833$	−3.96693	+	7.65280i	−0.137446	+	0.265154i
$834$			85.2843i			2.95315i
$835$	−7.43499	−	0.736102i	−0.257298	−	0.0254739i
$836$	−3.86598	−	0.420226i	−0.133708	−	0.0145338i
$837$	0.553184	−	0.553184i	0.0191208	−	0.0191208i
$838$	−3.53470	−	3.53470i	−0.122104	−	0.122104i
$839$	−25.5436			−0.881862			−0.440931	−	0.897541i	$-0.645352\pi$
$839$	−25.5436			−0.881862			−0.440931	+	0.897541i	$0.645352\pi$
$840$	1.10981	−	11.2096i	0.0382919	−	0.386767i
$841$	−15.8816			−0.547640
$842$	−23.5728	−	23.5728i	−0.812373	−	0.812373i
$843$	−12.7440	−	12.7440i	−0.438927	−	0.438927i
$844$			14.4939i			0.498899i
$845$	0.277490	−	0.227494i	0.00954593	−	0.00782602i
$846$			33.3305i			1.14593i
$847$	27.9428	−	17.8652i	0.960126	−	0.613855i
$848$	−27.5157	−	27.5157i	−0.944892	−	0.944892i
$849$	−32.7067			−1.12249
$850$	−39.0488	+	4.30494i	−1.33936	+	0.147658i
$851$	−15.1364			−0.518868
$852$	−32.0101	+	32.0101i	−1.09665	+	1.09665i
$853$	−4.09714	−	4.09714i	−0.140283	−	0.140283i	0.633478	−	0.773761i	$-0.281627\pi$
$853$	−4.09714	−	4.09714i	−0.140283	−	0.140283i	−0.773761	+	0.633478i	$0.781627\pi$
$854$	−51.6101			−1.76606
$855$	−3.30322	+	2.70807i	−0.112968	+	0.0926141i
$856$			10.3563i			0.353971i
$857$	−8.33808	+	8.33808i	−0.284823	+	0.284823i	−0.835029	−	0.550206i	$-0.814549\pi$
$857$	−8.33808	+	8.33808i	−0.284823	+	0.284823i	0.550206	+	0.835029i	$0.314549\pi$
$858$	−33.7514	−	41.9838i	−1.15226	−	1.43330i
$859$		−	22.2072i		−	0.757700i	−0.925458	−	0.378850i	$-0.876320\pi$
$859$		−	22.2072i		−	0.757700i	0.925458	−	0.378850i	$-0.123680\pi$
$860$	1.45234	−	14.6693i	0.0495243	−	0.500220i
$861$			58.6050i			1.99725i
$862$	23.9063	+	23.9063i	0.814252	+	0.814252i
$863$	−22.9006	−	22.9006i	−0.779546	−	0.779546i	0.200208	−	0.979753i	$-0.435838\pi$
$863$	−22.9006	−	22.9006i	−0.779546	−	0.779546i	−0.979753	+	0.200208i	$0.935838\pi$
$864$			5.99276i			0.203878i
$865$	−0.745067	+	7.52554i	−0.0253330	+	0.255876i
$866$			49.0349i			1.66627i
$867$	−39.8464	−	6.88342i	−1.35326	−	0.233773i
$868$	3.34339	−	3.34339i	0.113482	−	0.113482i
$869$	44.9185	+	4.88257i	1.52375	+	0.165630i
$870$	52.5107	−	43.0498i	1.78028	−	1.45952i
$871$		−	40.0742i		−	1.35786i
$872$	3.11953	+	3.11953i	0.105641	+	0.105641i
$873$	−1.43294	+	1.43294i	−0.0484976	+	0.0484976i
$874$	1.89120			0.0639708
$875$	−9.83457	+	32.2430i	−0.332469	+	1.09001i
$876$			28.6750i			0.968837i
$877$	−7.94557	+	7.94557i	−0.268303	+	0.268303i	−0.828416	−	0.560113i	$-0.810758\pi$
$877$	−7.94557	+	7.94557i	−0.268303	+	0.268303i	0.560113	+	0.828416i	$0.310758\pi$
$878$	7.31855	−	7.31855i	0.246989	−	0.246989i
$879$			61.7652i			2.08329i
$880$	28.5730	−	18.6565i	0.963194	−	0.628911i
$881$		−	24.0036i		−	0.808701i	−0.914604	−	0.404351i	$-0.867498\pi$
$881$		−	24.0036i		−	0.808701i	0.914604	−	0.404351i	$-0.132502\pi$
$882$	7.48735	+	7.48735i	0.252112	+	0.252112i
$883$	2.50288	+	2.50288i	0.0842285	+	0.0842285i	0.747966	−	0.663737i	$-0.231031\pi$
$883$	2.50288	+	2.50288i	0.0842285	+	0.0842285i	−0.663737	+	0.747966i	$0.731031\pi$
$884$	7.28759	+	22.9741i	0.245108	+	0.772703i
$885$	5.33220	−	53.8578i	0.179240	−	1.81041i
$886$		−	24.6957i		−	0.829669i
$887$	−9.49888	+	9.49888i	−0.318941	+	0.318941i	−0.848360	−	0.529419i	$-0.822410\pi$
$887$	−9.49888	+	9.49888i	−0.318941	+	0.318941i	0.529419	+	0.848360i	$0.322410\pi$
$888$	12.9505	−	12.9505i	0.434589	−	0.434589i
$889$	−26.1247			−0.876194
$890$	−21.1820	−	2.09713i	−0.710024	−	0.0702960i
$891$	−3.55153	+	32.6732i	−0.118981	+	1.09459i
$892$	−21.1692	+	21.1692i	−0.708796	+	0.708796i
$893$	3.34437	−	3.34437i	0.111915	−	0.111915i
$894$	27.9524			0.934869
$895$	3.18204	−	2.60872i	0.106364	−	0.0872000i
$896$		−	16.6551i		−	0.556407i
$897$	8.32207	+	8.32207i	0.277866	+	0.277866i
$898$	15.0519	+	15.0519i	0.502288	+	0.502288i
$899$	−6.43991			−0.214783
$900$	−4.25120	+	21.2591i	−0.141707	+	0.708638i
$901$	10.5429	+	33.2366i	0.351236	+	1.10727i
$902$	−40.2525	+	32.3597i	−1.34026	+	1.07746i
$903$	−20.4924	−	20.4924i	−0.681943	−	0.681943i
$904$		−	1.08201i		−	0.0359871i
$905$	−44.4017	+	36.4017i	−1.47596	+	1.21003i
$906$			56.2699i			1.86944i
$907$	9.48251	+	9.48251i	0.314862	+	0.314862i	0.846790	−	0.531928i	$-0.178532\pi$
$907$	9.48251	+	9.48251i	0.314862	+	0.314862i	−0.531928	+	0.846790i	$0.678532\pi$
$908$	12.8864	+	12.8864i	0.427650	+	0.427650i
$909$	26.0611			0.864392
$910$	45.8115	+	4.53558i	1.51864	+	0.150353i
$911$			10.4387i			0.345849i	0.984935	+	0.172924i	$0.0553217\pi$
$911$			10.4387i			0.345849i	−0.984935	+	0.172924i	$0.944678\pi$
$912$	−5.56225	+	5.56225i	−0.184184	+	0.184184i
$913$	5.93327	+	7.38045i	0.196362	+	0.244257i
$914$			71.6979i			2.37155i
$915$	−47.5438	−	4.70708i	−1.57175	−	0.155611i
$916$	13.0305			0.430539
$917$	−14.6680	+	14.6680i	−0.484379	+	0.484379i
$918$	2.94275	−	5.67701i	0.0971252	−	0.187369i
$919$	3.99226			0.131692			0.0658462	−	0.997830i	$-0.479025\pi$
$919$	3.99226			0.131692			0.0658462	+	0.997830i	$0.479025\pi$
$920$	−1.67725	+	1.37505i	−0.0552972	+	0.0453342i
$921$	−19.1926			−0.632417
$922$	−15.4571	+	15.4571i	−0.509053	+	0.509053i
$923$	29.5582	+	29.5582i	0.972919	+	0.972919i
$924$	−4.19325	+	38.5769i	−0.137948	+	1.26909i
$925$	−45.6023	+	30.4034i	−1.49939	+	0.999658i
$926$			9.52287i			0.312941i
$927$	19.5274	−	19.5274i	0.641365	−	0.641365i
$928$	34.8825	−	34.8825i	1.14507	−	1.14507i
$929$	36.4331			1.19533			0.597666	−	0.801745i	$-0.296095\pi$
$929$	36.4331			1.19533			0.597666	+	0.801745i	$0.296095\pi$
$930$	7.53460	−	6.17707i	0.247069	−	0.202554i
$931$		−	1.50256i		−	0.0492443i
$932$	−32.1837	+	32.1837i	−1.05421	+	1.05421i
$933$	−16.5962	−	16.5962i	−0.543336	−	0.543336i
$934$	68.6779			2.24721
$935$	−30.4244	+	3.05912i	−0.994983	+	0.100044i
$936$	−6.68967			−0.218659
$937$	18.4788	+	18.4788i	0.603675	+	0.603675i	0.941286	−	0.337611i	$-0.109619\pi$
$937$	18.4788	+	18.4788i	0.603675	+	0.603675i	−0.337611	+	0.941286i	$0.609619\pi$
$938$	−45.4369	+	45.4369i	−1.48357	+	1.48357i
$939$		−	4.00777i		−	0.130789i
$940$	2.36514	−	23.8891i	0.0771425	−	0.779176i
$941$	−5.77120			−0.188136			−0.0940678	−	0.995566i	$-0.529987\pi$
$941$	−5.77120			−0.188136			−0.0940678	+	0.995566i	$0.529987\pi$
$942$	0.345767	−	0.345767i	0.0112657	−	0.0112657i
$943$	7.97890	−	7.97890i	0.259829	−	0.259829i
$944$		−	46.8209i		−	1.52389i
$945$	−3.47864	−	4.24313i	−0.113160	−	0.138029i
$946$	2.75988	−	25.3902i	0.0897315	−	0.825508i
$947$	8.61955	+	8.61955i	0.280098	+	0.280098i	0.833148	−	0.553050i	$-0.186536\pi$
$947$	8.61955	+	8.61955i	0.280098	+	0.280098i	−0.553050	+	0.833148i	$0.686536\pi$
$948$	−37.3808	+	37.3808i	−1.21407	+	1.21407i
$949$	26.4785			0.859527
$950$	5.69775	−	3.79873i	0.184859	−	0.123247i
$951$	2.89540			0.0938899
$952$	−4.01860	+	7.75249i	−0.130244	+	0.251260i
$953$	−2.42711	+	2.42711i	−0.0786217	+	0.0786217i	−0.745324	−	0.666702i	$-0.767705\pi$
$953$	−2.42711	+	2.42711i	−0.0786217	+	0.0786217i	0.666702	+	0.745324i	$0.267705\pi$
$954$	42.8330			1.38677
$955$	11.5862	+	14.1325i	0.374920	+	0.457316i
$956$			16.7080i			0.540376i
$957$	41.1912	−	33.1143i	1.33152	−	1.07043i
$958$	−30.7614	+	30.7614i	−0.993855	+	0.993855i
$959$			17.2910i			0.558356i
$960$	−2.53077	+	25.5620i	−0.0816801	+	0.825009i
$961$	30.0760			0.970192
$962$	52.9263	+	52.9263i	1.70641	+	1.70641i
$963$	−27.7090	−	27.7090i	−0.892911	−	0.892911i
$964$			18.2106i			0.586524i
$965$	−1.80106	+	18.1915i	−0.0579781	+	0.585606i
$966$		−	18.8715i		−	0.607179i
$967$	−27.6116	−	27.6116i	−0.887928	−	0.887928i	0.106396	−	0.994324i	$-0.466069\pi$
$967$	−27.6116	−	27.6116i	−0.887928	−	0.887928i	−0.994324	+	0.106396i	$0.966069\pi$
$968$	6.50987	−	4.16208i	0.209235	−	0.133774i
$969$	6.71872	−	2.13123i	0.215836	−	0.0684651i
$970$	2.51246	−	2.05979i	0.0806703	−	0.0661358i
$971$	−22.9513			−0.736542			−0.368271	−	0.929718i	$-0.620050\pi$
$971$	−22.9513			−0.736542			−0.368271	+	0.929718i	$0.620050\pi$
$972$	−24.3740	−	24.3740i	−0.781795	−	0.781795i
$973$	−40.1133	−	40.1133i	−1.28597	−	1.28597i
$974$		−	42.1578i		−	1.35082i
$975$	41.7884	+	8.35646i	1.33830	+	0.267621i
$976$	−41.3319			−1.32300
$977$	−20.4596	+	20.4596i	−0.654561	+	0.654561i	−0.954088	−	0.299527i	$-0.903171\pi$
$977$	−20.4596	+	20.4596i	−0.654561	+	0.654561i	0.299527	+	0.954088i	$0.403171\pi$
$978$	16.8089	−	16.8089i	0.537488	−	0.537488i
$979$	−16.4706	−	1.79033i	−0.526403	−	0.0572193i
$980$	−4.83513	−	5.89774i	−0.154453	−	0.188397i
$981$	−16.6931			−0.532969
$982$	3.05897	−	3.05897i	0.0976156	−	0.0976156i
$983$	17.5503	−	17.5503i	0.559768	−	0.559768i	−0.369473	−	0.929241i	$-0.620462\pi$
$983$	17.5503	−	17.5503i	0.559768	−	0.559768i	0.929241	+	0.369473i	$0.120462\pi$
$984$			13.6533i			0.435251i
$985$	46.9607	+	4.64936i	1.49629	+	0.148141i
$986$	−50.1737	+	15.9155i	−1.59786	+	0.506854i
$987$	−33.3720	−	33.3720i	−1.06224	−	1.06224i
$988$	−2.97080	−	2.97080i	−0.0945137	−	0.0945137i
$989$			5.57995i			0.177432i
$990$	−7.71835	+	36.7605i	−0.245305	+	1.16832i
$991$		−	29.8423i		−	0.947971i	−0.880533	−	0.473985i	$-0.842815\pi$
$991$		−	29.8423i		−	0.947971i	0.880533	−	0.473985i	$-0.157185\pi$
$992$	5.00518	−	5.00518i	0.158915	−	0.158915i
$993$	−54.5164	+	54.5164i	−1.73003	+	1.73003i
$994$		−	67.0273i		−	2.12598i
$995$	31.6848	+	38.6482i	1.00448	+	1.22523i
$996$	−11.0796			−0.351070
$997$	33.8217	−	33.8217i	1.07114	−	1.07114i	0.0738761	−	0.997267i	$-0.476463\pi$
$997$	33.8217	−	33.8217i	1.07114	−	1.07114i	0.997267	−	0.0738761i	$-0.0235369\pi$
$998$	51.7872	+	51.7872i	1.63929	+	1.63929i
$999$		−	8.92100i		−	0.282248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.p.a.373.17	✓	208
5.2	odd	4	inner	935.2.p.a.747.88	yes	208
11.10	odd	2	inner	935.2.p.a.373.87	yes	208
17.16	even	2	inner	935.2.p.a.373.18	yes	208
55.32	even	4	inner	935.2.p.a.747.18	yes	208
85.67	odd	4	inner	935.2.p.a.747.87	yes	208
187.186	odd	2	inner	935.2.p.a.373.88	yes	208
935.747	even	4	inner	935.2.p.a.747.17	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.p.a.373.17	✓	208	1.1	even	1	trivial
935.2.p.a.373.18	yes	208	17.16	even	2	inner
935.2.p.a.373.87	yes	208	11.10	odd	2	inner
935.2.p.a.373.88	yes	208	187.186	odd	2	inner
935.2.p.a.747.17	yes	208	935.747	even	4	inner
935.2.p.a.747.18	yes	208	55.32	even	4	inner
935.2.p.a.747.87	yes	208	85.67	odd	4	inner
935.2.p.a.747.88	yes	208	5.2	odd	4	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:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34748 - 1.34748i) q^{2} +(-1.68194 + 1.68194i) q^{3} +1.63139i q^{4} +(-1.41767 - 1.72923i) q^{5} +4.53276 q^{6} +(-2.13197 + 2.13197i) q^{7} +(-0.496689 + 0.496689i) q^{8} -2.65785i q^{9} +O(q^{10})\)	\(q+(-1.34748 - 1.34748i) q^{2} +(-1.68194 + 1.68194i) q^{3} +1.63139i q^{4} +(-1.41767 - 1.72923i) q^{5} +4.53276 q^{6} +(-2.13197 + 2.13197i) q^{7} +(-0.496689 + 0.496689i) q^{8} -2.65785i q^{9} +(-0.419818 + 4.24037i) q^{10} +(-0.358401 + 3.29720i) q^{11} +(-2.74391 - 2.74391i) q^{12} +(-2.53373 + 2.53373i) q^{13} +5.74557 q^{14} +(5.29289 + 0.524023i) q^{15} +4.60134 q^{16} +(-3.66054 - 1.89749i) q^{17} +(-3.58140 + 3.58140i) q^{18} +0.718712 q^{19} +(2.82105 - 2.31277i) q^{20} -7.17171i q^{21} +(4.92585 - 3.95997i) q^{22} +(-0.976407 + 0.976407i) q^{23} -1.67080i q^{24} +(-0.980442 + 4.90293i) q^{25} +6.82828 q^{26} +(-0.575471 - 0.575471i) q^{27} +(-3.47809 - 3.47809i) q^{28} +6.69937i q^{29} +(-6.42594 - 7.83816i) q^{30} +0.961272i q^{31} +(-5.20683 - 5.20683i) q^{32} +(-4.94289 - 6.14851i) q^{33} +(2.37568 + 7.48932i) q^{34} +(6.70909 + 0.664235i) q^{35} +4.33601 q^{36} +(7.75105 + 7.75105i) q^{37} +(-0.968449 - 0.968449i) q^{38} -8.52316i q^{39} +(1.56303 + 0.154748i) q^{40} -8.17170 q^{41} +(-9.66372 + 9.66372i) q^{42} +(2.85739 - 2.85739i) q^{43} +(-5.37904 - 0.584694i) q^{44} +(-4.59603 + 3.76795i) q^{45} +2.63137 q^{46} +(4.65328 - 4.65328i) q^{47} +(-7.73919 + 7.73919i) q^{48} -2.09062i q^{49} +(7.92772 - 5.28547i) q^{50} +(9.34827 - 2.96535i) q^{51} +(-4.13350 - 4.13350i) q^{52} +(-5.97993 - 5.97993i) q^{53} +1.55087i q^{54} +(6.20970 - 4.05458i) q^{55} -2.11785i q^{56} +(-1.20883 + 1.20883i) q^{57} +(9.02725 - 9.02725i) q^{58} -10.1755i q^{59} +(-0.854889 + 8.63478i) q^{60} -8.98258 q^{61} +(1.29529 - 1.29529i) q^{62} +(5.66647 + 5.66647i) q^{63} +4.82949i q^{64} +(7.97336 + 0.789404i) q^{65} +(-1.62455 + 14.9454i) q^{66} +(-7.90816 + 7.90816i) q^{67} +(3.09555 - 5.97178i) q^{68} -3.28452i q^{69} +(-8.14531 - 9.93539i) q^{70} -11.6659i q^{71} +(1.32013 + 1.32013i) q^{72} +(-5.22520 - 5.22520i) q^{73} -20.8887i q^{74} +(-6.59740 - 9.89549i) q^{75} +1.17250i q^{76} +(-6.26545 - 7.79365i) q^{77} +(-11.4848 + 11.4848i) q^{78} -13.6232i q^{79} +(-6.52317 - 7.95676i) q^{80} +9.90938 q^{81} +(11.0112 + 11.0112i) q^{82} +(2.01894 - 2.01894i) q^{83} +11.6999 q^{84} +(1.90824 + 9.01990i) q^{85} -7.70054 q^{86} +(-11.2679 - 11.2679i) q^{87} +(-1.45967 - 1.81570i) q^{88} +4.99533i q^{89} +(11.2703 + 1.11582i) q^{90} -10.8037i q^{91} +(-1.59290 - 1.59290i) q^{92} +(-1.61680 - 1.61680i) q^{93} -12.5404 q^{94} +(-1.01889 - 1.24282i) q^{95} +17.5152 q^{96} +(-0.539134 - 0.539134i) q^{97} +(-2.81707 + 2.81707i) q^{98} +(8.76348 + 0.952578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q+O(q^{10}) \) 208 * q	\( 208 q - 8 q^{15} - 184 q^{16} - 48 q^{25} - 32 q^{26} + 4 q^{33} + 280 q^{36} - 80 q^{38} - 64 q^{42} - 8 q^{53} + 48 q^{55} + 128 q^{60} - 48 q^{66} + 56 q^{67} - 112 q^{70} - 84 q^{77} - 192 q^{81} - 112 q^{86} + 112 q^{93}+O(q^{100}) \) 208 * q - 8 * q^15 - 184 * q^16 - 48 * q^25 - 32 * q^26 + 4 * q^33 + 280 * q^36 - 80 * q^38 - 64 * q^42 - 8 * q^53 + 48 * q^55 + 128 * q^60 - 48 * q^66 + 56 * q^67 - 112 * q^70 - 84 * q^77 - 192 * q^81 - 112 * q^86 + 112 * q^93

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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