LMFDB - Embedded newform 230.2.l.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	230.17
Dual form			230.2.l.a.203.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.936950 - 0.349464i) q^{2} +(-1.76120 + 0.961687i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-1.99344 + 1.01301i) q^{5} +(-1.31408 + 1.51653i) q^{6} +(2.41169 + 3.22164i) q^{7} +(0.479249 - 0.877679i) q^{8} +(0.555057 - 0.863686i) q^{9} +(-1.51374 + 1.64578i) q^{10} +(-4.30959 + 1.96812i) q^{11} +(-0.701254 + 1.88014i) q^{12} +(1.19161 + 0.892027i) q^{13} +(3.38548 + 2.17572i) q^{14} +(2.53665 - 3.70118i) q^{15} +(0.142315 - 0.989821i) q^{16} +(0.0907664 + 1.26908i) q^{17} +(0.218233 - 1.00320i) q^{18} +(3.13937 + 3.62302i) q^{19} +(-0.843161 + 2.07101i) q^{20} +(-7.34568 - 3.35466i) q^{21} +(-3.35008 + 3.35008i) q^{22} +(4.79353 - 0.148532i) q^{23} +2.00666i q^{24} +(2.94762 - 4.03876i) q^{25} +(1.42821 + 0.419360i) q^{26} +(0.282489 - 3.94971i) q^{27} +(3.93236 + 0.855433i) q^{28} +(-7.98668 - 6.92050i) q^{29} +(1.08328 - 4.35429i) q^{30} +(1.06616 - 0.313053i) q^{31} +(-0.212565 - 0.977147i) q^{32} +(5.69733 - 7.61074i) q^{33} +(0.528542 + 1.15734i) q^{34} +(-8.07113 - 3.97908i) q^{35} +(-0.146110 - 1.01622i) q^{36} +(1.32802 - 0.288894i) q^{37} +(4.20754 + 2.29749i) q^{38} +(-2.95651 - 0.425082i) q^{39} +(-0.0662559 + 2.23509i) q^{40} +(-1.96187 + 1.26082i) q^{41} +(-8.05487 - 0.576096i) q^{42} +(-2.53560 - 4.64360i) q^{43} +(-1.96812 + 4.30959i) q^{44} +(-0.231550 + 2.28399i) q^{45} +(4.43939 - 1.81433i) q^{46} +(9.20268 + 9.20268i) q^{47} +(0.701254 + 1.88014i) q^{48} +(-2.59060 + 8.82277i) q^{49} +(1.35037 - 4.81420i) q^{50} +(-1.38032 - 2.14781i) q^{51} +(1.48471 - 0.106189i) q^{52} +(7.32042 - 5.48000i) q^{53} +(-1.11561 - 3.79940i) q^{54} +(6.59719 - 8.28901i) q^{55} +(3.98337 - 0.572722i) q^{56} +(-9.01326 - 3.36177i) q^{57} +(-9.90159 - 3.69310i) q^{58} +(10.3086 - 1.48216i) q^{59} +(-0.506689 - 4.45832i) q^{60} +(1.27306 + 4.33565i) q^{61} +(0.889539 - 0.665901i) q^{62} +(4.12111 - 0.294748i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(-3.27904 - 0.571091i) q^{65} +(2.67843 - 9.12189i) q^{66} +(3.73192 + 10.0057i) q^{67} +(0.899668 + 0.899668i) q^{68} +(-8.29952 + 4.87147i) q^{69} +(-8.95279 - 0.907633i) q^{70} +(-1.02618 + 2.24701i) q^{71} +(-0.492028 - 0.901083i) q^{72} +(-7.87517 - 0.563243i) q^{73} +(1.14333 - 0.734775i) q^{74} +(-1.30732 + 9.94774i) q^{75} +(4.74515 + 0.682249i) q^{76} +(-16.7340 - 9.13746i) q^{77} +(-2.91865 + 0.634914i) q^{78} +(-0.376097 - 2.61582i) q^{79} +(0.719004 + 2.11732i) q^{80} +(4.58035 + 10.0296i) q^{81} +(-1.39756 + 1.86693i) q^{82} +(2.63492 + 12.1125i) q^{83} +(-7.74833 + 2.27512i) q^{84} +(-1.46653 - 2.43789i) q^{85} +(-3.99850 - 3.46472i) q^{86} +(20.7215 + 4.50769i) q^{87} +(-0.337986 + 4.72566i) q^{88} +(-3.70010 - 1.08645i) q^{89} +(0.581220 + 2.22090i) q^{90} +5.99023i q^{91} +(3.52544 - 3.25135i) q^{92} +(-1.57666 + 1.57666i) q^{93} +(11.8385 + 5.40644i) q^{94} +(-9.92830 - 4.04207i) q^{95} +(1.31408 + 1.51653i) q^{96} +(0.437154 - 2.00956i) q^{97} +(0.655981 + 9.17181i) q^{98} +(-0.692229 + 4.81456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

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 $

$2$	0.936950	−	0.349464i	0.662524	−	0.247108i
$2$	0.936950	−	0.349464i	0.662524	−	0.247108i
$3$	−1.76120	+	0.961687i	−1.01683	+	0.555231i	−0.899067	−	0.437811i	$-0.855754\pi$
$3$	−1.76120	+	0.961687i	−1.01683	+	0.555231i	−0.117762	+	0.993042i	$0.537572\pi$
$4$	0.755750	−	0.654861i	0.377875	−	0.327430i
$5$	−1.99344	+	1.01301i	−0.891494	+	0.453032i
$5$	−1.99344	+	1.01301i	−0.891494	+	0.453032i
$6$	−1.31408	+	1.51653i	−0.536471	+	0.619120i
$7$	2.41169	+	3.22164i	0.911534	+	1.21767i	0.975563	+	0.219719i	$0.0705139\pi$
$7$	2.41169	+	3.22164i	0.911534	+	1.21767i	−0.0640296	+	0.997948i	$0.520395\pi$
$8$	0.479249	−	0.877679i	0.169440	−	0.310306i
$9$	0.555057	−	0.863686i	0.185019	−	0.287895i
$10$	−1.51374	+	1.64578i	−0.478688	+	0.520440i
$11$	−4.30959	+	1.96812i	−1.29939	+	0.593412i	−0.940445	−	0.339946i	$-0.889591\pi$
$11$	−4.30959	+	1.96812i	−1.29939	+	0.593412i	−0.358946	+	0.933358i	$0.616864\pi$
$12$	−0.701254	+	1.88014i	−0.202435	+	0.542748i
$13$	1.19161	+	0.892027i	0.330493	+	0.247404i	0.751618	−	0.659599i	$-0.229274\pi$
$13$	1.19161	+	0.892027i	0.330493	+	0.247404i	−0.421125	+	0.907003i	$0.638365\pi$
$14$	3.38548	+	2.17572i	0.904808	+	0.581485i
$15$	2.53665	−	3.70118i	0.654959	−	0.955641i
$16$	0.142315	−	0.989821i	0.0355787	−	0.247455i
$17$	0.0907664	+	1.26908i	0.0220141	+	0.307797i	0.996515	+	0.0834137i	$0.0265823\pi$
$17$	0.0907664	+	1.26908i	0.0220141	+	0.307797i	−0.974501	+	0.224384i	$0.927963\pi$
$18$	0.218233	−	1.00320i	0.0514381	−	0.236457i
$19$	3.13937	+	3.62302i	0.720220	+	0.831178i	0.991334	−	0.131369i	$-0.0419373\pi$
$19$	3.13937	+	3.62302i	0.720220	+	0.831178i	−0.271114	+	0.962547i	$0.587392\pi$
$20$	−0.843161	+	2.07101i	−0.188537	+	0.463092i
$21$	−7.34568	−	3.35466i	−1.60296	−	0.732047i
$22$	−3.35008	+	3.35008i	−0.714240	+	0.714240i
$23$	4.79353	−	0.148532i	0.999520	−	0.0309710i
$23$	4.79353	−	0.148532i	0.999520	−	0.0309710i
$24$			2.00666i			0.409607i
$25$	2.94762	−	4.03876i	0.589523	−	0.807751i
$26$	1.42821	+	0.419360i	0.280095	+	0.0822433i
$27$	0.282489	−	3.94971i	0.0543650	−	0.760123i
$28$	3.93236	+	0.855433i	0.743147	+	0.161662i
$29$	−7.98668	−	6.92050i	−1.48309	−	1.28510i	−0.867914	−	0.496714i	$-0.834540\pi$
$29$	−7.98668	−	6.92050i	−1.48309	−	1.28510i	−0.615175	−	0.788390i	$-0.710915\pi$
$30$	1.08328	−	4.35429i	0.197779	−	0.794981i
$31$	1.06616	−	0.313053i	0.191488	−	0.0562260i	−0.184582	−	0.982817i	$-0.559093\pi$
$31$	1.06616	−	0.313053i	0.191488	−	0.0562260i	0.376071	+	0.926591i	$0.377275\pi$
$32$	−0.212565	−	0.977147i	−0.0375766	−	0.172737i
$33$	5.69733	−	7.61074i	0.991778	−	1.32486i
$34$	0.528542	+	1.15734i	0.0906441	+	0.198483i
$35$	−8.07113	−	3.97908i	−1.36427	−	0.672588i
$36$	−0.146110	−	1.01622i	−0.0243516	−	0.169369i
$37$	1.32802	−	0.288894i	0.218326	−	0.0474938i	−0.102072	−	0.994777i	$-0.532547\pi$
$37$	1.32802	−	0.288894i	0.218326	−	0.0474938i	0.320397	+	0.947283i	$0.396184\pi$
$38$	4.20754	+	2.29749i	0.682554	+	0.372703i
$39$	−2.95651	−	0.425082i	−0.473421	−	0.0680677i
$40$	−0.0662559	+	2.23509i	−0.0104760	+	0.353398i
$41$	−1.96187	+	1.26082i	−0.306393	+	0.196907i	−0.684797	−	0.728734i	$-0.740109\pi$
$41$	−1.96187	+	1.26082i	−0.306393	+	0.196907i	0.378404	+	0.925640i	$0.376473\pi$
$42$	−8.05487	−	0.576096i	−1.24289	−	0.0888935i
$43$	−2.53560	−	4.64360i	−0.386675	−	0.708142i	0.609753	−	0.792592i	$-0.291269\pi$
$43$	−2.53560	−	4.64360i	−0.386675	−	0.708142i	−0.996428	+	0.0844494i	$0.973087\pi$
$44$	−1.96812	+	4.30959i	−0.296706	+	0.649695i
$45$	−0.231550	+	2.28399i	−0.0345175	+	0.340477i
$46$	4.43939	−	1.81433i	0.654552	−	0.267509i
$47$	9.20268	+	9.20268i	1.34235	+	1.34235i	0.893716	+	0.448633i	$0.148089\pi$
$47$	9.20268	+	9.20268i	1.34235	+	1.34235i	0.448633	+	0.893716i	$0.351911\pi$
$48$	0.701254	+	1.88014i	0.101217	+	0.271374i
$49$	−2.59060	+	8.82277i	−0.370085	+	1.26040i
$50$	1.35037	−	4.81420i	0.190971	−	0.680831i
$51$	−1.38032	−	2.14781i	−0.193283	−	0.300754i
$52$	1.48471	−	0.106189i	0.205892	−	0.0147257i
$53$	7.32042	−	5.48000i	1.00554	−	0.752736i	0.0364201	−	0.999337i	$-0.488405\pi$
$53$	7.32042	−	5.48000i	1.00554	−	0.752736i	0.969117	+	0.246601i	$0.0793137\pi$
$54$	−1.11561	−	3.79940i	−0.151815	−	0.517033i
$55$	6.59719	−	8.28901i	0.889564	−	1.11769i
$56$	3.98337	−	0.572722i	0.532300	−	0.0765332i
$57$	−9.01326	−	3.36177i	−1.19384	−	0.445278i
$58$	−9.90159	−	3.69310i	−1.30014	−	0.484928i
$59$	10.3086	−	1.48216i	1.34207	−	0.192961i	0.566417	−	0.824119i	$-0.308329\pi$
$59$	10.3086	−	1.48216i	1.34207	−	0.192961i	0.775654	+	0.631158i	$0.217420\pi$
$60$	−0.506689	−	4.45832i	−0.0654133	−	0.575566i
$61$	1.27306	+	4.33565i	0.162999	+	0.555123i	0.999969	+	0.00787442i	$0.00250653\pi$
$61$	1.27306	+	4.33565i	0.162999	+	0.555123i	−0.836970	+	0.547248i	$0.815675\pi$
$62$	0.889539	−	0.665901i	0.112972	−	0.0845695i
$63$	4.12111	−	0.294748i	0.519212	−	0.0371347i
$64$	−0.540641	−	0.841254i	−0.0675801	−	0.105157i
$65$	−3.27904	−	0.571091i	−0.406714	−	0.0708351i
$66$	2.67843	−	9.12189i	0.329692	−	1.12283i
$67$	3.73192	+	10.0057i	0.455927	+	1.22239i	0.938116	+	0.346320i	$0.112569\pi$
$67$	3.73192	+	10.0057i	0.455927	+	1.22239i	−0.482190	+	0.876067i	$0.660158\pi$
$68$	0.899668	+	0.899668i	0.109101	+	0.109101i
$69$	−8.29952	+	4.87147i	−0.999145	+	0.586456i
$70$	−8.95279	−	0.907633i	−1.07006	−	0.108483i
$71$	−1.02618	+	2.24701i	−0.121785	+	0.266671i	−0.960699	−	0.277592i	$-0.910464\pi$
$71$	−1.02618	+	2.24701i	−0.121785	+	0.266671i	0.838914	+	0.544264i	$0.183191\pi$
$72$	−0.492028	−	0.901083i	−0.0579861	−	0.106194i
$73$	−7.87517	−	0.563243i	−0.921719	−	0.0659226i	−0.397592	−	0.917563i	$-0.630154\pi$
$73$	−7.87517	−	0.563243i	−0.921719	−	0.0659226i	−0.524127	+	0.851640i	$0.675608\pi$
$74$	1.14333	−	0.734775i	0.132910	−	0.0854159i
$75$	−1.30732	+	9.94774i	−0.150956	+	1.14867i
$76$	4.74515	+	0.682249i	0.544306	+	0.0782594i
$77$	−16.7340	−	9.13746i	−1.90702	−	1.04131i
$78$	−2.91865	+	0.634914i	−0.330473	+	0.0718899i
$79$	−0.376097	−	2.61582i	−0.0423143	−	0.294302i	−0.999979	−	0.00641770i	$-0.997957\pi$
$79$	−0.376097	−	2.61582i	−0.0423143	−	0.294302i	0.957665	−	0.287884i	$-0.0929519\pi$
$80$	0.719004	+	2.11732i	0.0803871	+	0.236723i
$81$	4.58035	+	10.0296i	0.508927	+	1.11440i
$82$	−1.39756	+	1.86693i	−0.154335	+	0.206168i
$83$	2.63492	+	12.1125i	0.289220	+	1.32952i	0.860786	+	0.508968i	$0.169973\pi$
$83$	2.63492	+	12.1125i	0.289220	+	1.32952i	−0.571565	+	0.820556i	$0.693664\pi$
$84$	−7.74833	+	2.27512i	−0.845412	+	0.248235i
$85$	−1.46653	−	2.43789i	−0.159068	−	0.264426i
$86$	−3.99850	−	3.46472i	−0.431169	−	0.373610i
$87$	20.7215	+	4.50769i	2.22158	+	0.483275i
$88$	−0.337986	+	4.72566i	−0.0360294	+	0.503757i
$89$	−3.70010	−	1.08645i	−0.392210	−	0.115163i	0.0796804	−	0.996820i	$-0.474610\pi$
$89$	−3.70010	−	1.08645i	−0.392210	−	0.115163i	−0.471890	+	0.881657i	$0.656428\pi$
$90$	0.581220	+	2.22090i	0.0612660	+	0.234103i
$91$			5.99023i			0.627947i
$92$	3.52544	−	3.25135i	0.367553	−	0.338976i
$93$	−1.57666	+	1.57666i	−0.163492	+	0.163492i
$94$	11.8385	+	5.40644i	1.22104	+	0.557632i
$95$	−9.92830	−	4.04207i	−1.01862	−	0.414707i
$96$	1.31408	+	1.51653i	0.134118	+	0.154780i
$97$	0.437154	−	2.00956i	0.0443862	−	0.204040i	−0.949613	−	0.313424i	$-0.898524\pi$
$97$	0.437154	−	2.00956i	0.0443862	−	0.204040i	0.994000	+	0.109383i	$0.0348876\pi$
$98$	0.655981	+	9.17181i	0.0662641	+	0.926493i
$99$	−0.692229	+	4.81456i	−0.0695716	+	0.483881i
$100$	−0.417164	−	4.98257i	−0.0417164	−	0.498257i
$101$	1.64350	+	1.05622i	0.163535	+	0.105097i	0.619848	−	0.784722i	$-0.287194\pi$
$101$	1.64350	+	1.05622i	0.163535	+	0.105097i	−0.456314	+	0.889819i	$0.650830\pi$
$102$	−2.04387	−	1.53002i	−0.202373	−	0.151495i
$103$	3.68856	−	9.88940i	0.363444	−	0.974432i	−0.618588	−	0.785716i	$-0.712295\pi$
$103$	3.68856	−	9.88940i	0.363444	−	0.974432i	0.982032	−	0.188716i	$-0.0604325\pi$
$104$	1.35399	−	0.618347i	0.132770	−	0.0606339i
$105$	18.0415	−	0.753941i	1.76067	−	0.0735771i
$106$	4.94380	−	7.69271i	0.480185	−	0.747182i
$107$	−0.208930	+	0.382627i	−0.0201980	+	0.0369899i	−0.887583	−	0.460648i	$-0.847617\pi$
$107$	−0.208930	+	0.382627i	−0.0201980	+	0.0369899i	0.867385	+	0.497638i	$0.165799\pi$
$108$	−2.37302	−	3.16999i	−0.228344	−	0.305032i
$109$	3.36003	−	3.87768i	0.321833	−	0.371415i	−0.571661	−	0.820490i	$-0.693701\pi$
$109$	3.36003	−	3.87768i	0.321833	−	0.371415i	0.893494	+	0.449075i	$0.148246\pi$
$110$	3.28452	−	10.0719i	0.313167	−	0.960315i
$111$	−2.06109	+	1.78594i	−0.195630	+	0.169514i
$112$	3.53207	−	1.92866i	0.333749	−	0.182241i
$113$	1.55201	−	0.578869i	0.146001	−	0.0544554i	−0.275402	−	0.961329i	$-0.588811\pi$
$113$	1.55201	−	0.578869i	0.146001	−	0.0544554i	0.421402	+	0.906874i	$0.361538\pi$
$114$	−9.61979			−0.900976
$115$	−9.40516	+	5.15199i	−0.877035	+	0.480426i
$116$	−10.5679			−0.981204
$117$	1.43184	−	0.534050i	0.132374	−	0.0493729i
$118$	9.14072	−	4.99121i	0.841472	−	0.459478i
$119$	−3.86962	+	3.35305i	−0.354728	+	0.307373i
$120$	−2.03276	−	4.00015i	−0.185565	−	0.365162i
$121$	7.49560	−	8.65039i	0.681418	−	0.786399i
$122$	2.70795	+	3.61740i	0.245166	+	0.327504i
$123$	2.24273	−	4.10726i	0.202220	−	0.370339i
$124$	0.600745	−	0.934777i	0.0539485	−	0.0839455i
$125$	−1.78459	+	11.0370i	−0.159619	+	0.987179i
$126$	3.75827	−	1.71635i	0.334814	−	0.152904i
$127$	−3.78541	+	10.1491i	−0.335901	+	0.900584i	0.653702	+	0.756752i	$0.273215\pi$
$127$	−3.78541	+	10.1491i	−0.335901	+	0.900584i	−0.989602	+	0.143832i	$0.954058\pi$
$128$	−0.800541	−	0.599278i	−0.0707585	−	0.0529692i
$129$	8.93138	+	5.73985i	0.786364	+	0.505366i
$130$	−3.27187	+	0.610823i	−0.286962	+	0.0535727i
$131$	0.345748	−	2.40473i	0.0302082	−	0.210103i	−0.969127	−	0.246562i	$-0.920699\pi$
$131$	0.345748	−	2.40473i	0.0302082	−	0.210103i	0.999335	+	0.0364598i	$0.0116081\pi$
$132$	−0.678221	−	9.48277i	−0.0590316	−	0.825369i
$133$	−4.10090	+	18.8515i	−0.355593	+	1.63463i
$134$	6.99325	+	8.07064i	0.604124	+	0.697197i
$135$	3.43798	+	8.15969i	0.295894	+	0.702274i
$136$	1.15734	+	0.528542i	0.0992415	+	0.0453221i
$137$	12.0719	−	12.0719i	1.03137	−	1.03137i	0.0318826	−	0.999492i	$-0.489850\pi$
$137$	12.0719	−	12.0719i	1.03137	−	1.03137i	0.999492	−	0.0318826i	$-0.0101503\pi$
$138$	−6.07383	+	7.46471i	−0.517039	+	0.635438i
$139$		−	10.0328i		−	0.850974i	−0.904965	−	0.425487i	$-0.860103\pi$
$139$		−	10.0328i		−	0.850974i	0.904965	−	0.425487i	$-0.139897\pi$
$140$	−8.70550	+	2.27827i	−0.735749	+	0.192549i
$141$	−25.0579	−	7.35765i	−2.11025	−	0.619626i
$142$	−0.176225	+	2.46395i	−0.0147885	+	0.206770i
$143$	−6.89097	−	1.49904i	−0.576252	−	0.125356i
$144$	−0.775902	−	0.672323i	−0.0646585	−	0.0560269i
$145$	22.9315	+	5.70501i	1.90436	+	0.473775i
$146$	−7.57547	+	2.22436i	−0.626950	+	0.184089i
$147$	−3.92219	−	18.0300i	−0.323496	−	1.48709i
$148$	0.814467	−	1.08800i	0.0669488	−	0.0894331i
$149$	−0.0863664	−	0.189116i	−0.00707541	−	0.0154930i	0.906061	−	0.423146i	$-0.139074\pi$
$149$	−0.0863664	−	0.189116i	−0.00707541	−	0.0154930i	−0.913137	+	0.407653i	$0.866347\pi$
$150$	2.25149	+	9.77739i	0.183833	+	0.798321i
$151$	−1.84700	−	12.8461i	−0.150306	−	1.04540i	−0.915706	−	0.401849i	$-0.868368\pi$
$151$	−1.84700	−	12.8461i	−0.150306	−	1.04540i	0.765400	−	0.643555i	$-0.222541\pi$
$152$	4.68439	−	1.01903i	0.379954	−	0.0826539i
$153$	1.14647	+	0.626018i	0.0926864	+	0.0506106i
$154$	−18.8721	−	2.71340i	−1.52076	−	0.218652i
$155$	−1.80820	+	1.70409i	−0.145238	+	0.136876i
$156$	−2.51275	+	1.61485i	−0.201181	+	0.129291i
$157$	6.83149	+	0.488598i	0.545213	+	0.0389944i	0.341229	−	0.939980i	$-0.389157\pi$
$157$	6.83149	+	0.488598i	0.545213	+	0.0389944i	0.203983	+	0.978974i	$0.434611\pi$
$158$	−1.26652	−	2.31945i	−0.100759	−	0.184526i
$159$	−7.62267	+	16.6913i	−0.604517	+	1.32371i
$160$	1.41360	+	1.73255i	0.111755	+	0.136970i
$161$	12.0390	+	15.0848i	0.948809	+	1.18885i
$162$	7.79653	+	7.79653i	0.612553	+	0.612553i
$163$	6.90845	+	18.5223i	0.541111	+	1.45078i	0.863588	+	0.504198i	$0.168212\pi$
$163$	6.90845	+	18.5223i	0.541111	+	1.45078i	−0.322476	+	0.946577i	$0.604515\pi$
$164$	−0.657023	+	2.23762i	−0.0513049	+	0.174728i
$165$	−3.64752	+	20.9430i	−0.283959	+	1.63041i
$166$	6.70169	+	10.4280i	0.520152	+	0.809372i
$167$	−10.4008	+	0.743879i	−0.804837	+	0.0575631i	−0.467694	−	0.883890i	$-0.654915\pi$
$167$	−10.4008	+	0.743879i	−0.804837	+	0.0575631i	−0.337143	+	0.941453i	$0.609461\pi$
$168$	−6.46473	+	4.83943i	−0.498764	+	0.373370i
$169$	−3.03830	−	10.3475i	−0.233716	−	0.795963i
$170$	−2.22602	−	1.77168i	−0.170728	−	0.135882i
$171$	4.87168	−	0.700442i	0.372547	−	0.0535641i
$172$	−4.95719	−	1.84893i	−0.377982	−	0.140980i
$173$	−10.0463	−	3.74709i	−0.763809	−	0.284886i	−0.0627881	−	0.998027i	$-0.519999\pi$
$173$	−10.0463	−	3.74709i	−0.763809	−	0.284886i	−0.701021	+	0.713141i	$0.747272\pi$
$174$	20.9903	−	3.01795i	1.59127	−	0.228790i
$175$	20.1202	−	0.244072i	1.52094	−	0.0184501i
$176$	1.33477	+	4.54582i	0.100612	+	0.342654i
$177$	−16.7302	+	12.5241i	−1.25752	+	0.941367i
$178$	−3.84648	+	0.275106i	−0.288306	+	0.0206201i
$179$	−11.9930	−	18.6615i	−0.896400	−	1.39483i	−0.918650	−	0.395073i	$-0.870719\pi$
$179$	−11.9930	−	18.6615i	−0.896400	−	1.39483i	0.0222499	−	0.999752i	$-0.492917\pi$
$180$	1.32070	+	1.87775i	0.0984391	+	0.139960i
$181$	−0.648890	+	2.20992i	−0.0482316	+	0.164262i	−0.980087	−	0.198568i	$-0.936371\pi$
$181$	−0.648890	+	2.20992i	−0.0482316	+	0.164262i	0.931856	+	0.362829i	$0.118189\pi$
$182$	2.09337	+	5.61255i	0.155171	+	0.416030i
$183$	−6.41165	−	6.41165i	−0.473963	−	0.473963i
$184$	2.16693	−	4.27837i	0.159748	−	0.315405i
$185$	−2.35468	+	1.92119i	−0.173120	+	0.141249i
$186$	−0.926267	+	2.02824i	−0.0679172	+	0.148718i
$187$	−2.88887	−	5.29058i	−0.211255	−	0.386885i
$188$	12.9814	+	0.928448i	0.946766	+	0.0677140i
$189$	13.4058	−	8.61541i	0.975132	−	0.626679i
$190$	−10.7149	−	0.317627i	−0.777339	−	0.0230431i
$191$	−20.6384	−	2.96735i	−1.49334	−	0.214710i	−0.653244	−	0.757147i	$-0.726593\pi$
$191$	−20.6384	−	2.96735i	−1.49334	−	0.214710i	−0.840096	+	0.542437i	$0.817502\pi$
$192$	1.76120	+	0.961687i	0.127104	+	0.0694038i
$193$	9.76004	−	2.12317i	0.702543	−	0.152829i	0.152916	−	0.988239i	$-0.451134\pi$
$193$	9.76004	−	2.12317i	0.702543	−	0.152829i	0.549627	+	0.835410i	$0.314770\pi$
$194$	−0.292679	−	2.03563i	−0.0210132	−	0.146150i
$195$	6.32425	−	2.14760i	0.452889	−	0.153793i
$196$	3.81984	+	8.36428i	0.272846	+	0.597449i
$197$	−6.51435	+	8.70215i	−0.464128	+	0.620002i	−0.970146	−	0.242520i	$-0.922026\pi$
$197$	−6.51435	+	8.70215i	−0.464128	+	0.620002i	0.506018	+	0.862523i	$0.331117\pi$
$198$	1.03393	+	4.75291i	0.0734783	+	0.337774i
$199$	−14.4203	+	4.23419i	−1.02223	+	0.300154i	−0.749548	−	0.661950i	$-0.769729\pi$
$199$	−14.4203	+	4.23419i	−1.02223	+	0.300154i	−0.272683	+	0.962104i	$0.587911\pi$
$200$	−2.13209	−	4.52263i	−0.150762	−	0.319798i
$201$	−16.1950	−	14.0330i	−1.14231	−	0.989814i
$202$	1.90899	+	0.415275i	0.134316	+	0.0292187i
$203$	3.03396	−	42.4203i	0.212942	−	2.97732i
$204$	−2.44969	−	0.719295i	−0.171513	−	0.0503607i
$205$	2.63365	−	4.50077i	0.183942	−	0.314347i
$206$		−	10.5549i		−	0.735394i
$207$	2.53240	−	4.22255i	0.176014	−	0.293487i
$208$	1.05253	−	1.05253i	0.0729799	−	0.0729799i
$209$	−20.6599	−	9.43508i	−1.42908	−	0.652638i
$210$	16.6405	−	7.01126i	1.14830	−	0.483823i
$211$	−1.58462	−	1.82875i	−0.109090	−	0.125896i	0.698579	−	0.715533i	$-0.253816\pi$
$211$	−1.58462	−	1.82875i	−0.109090	−	0.125896i	−0.807668	+	0.589637i	$0.799271\pi$
$212$	1.94377	−	8.93536i	0.133499	−	0.613683i
$213$	−0.353623	−	4.94429i	−0.0242298	−	0.338777i
$214$	−0.0620426	+	0.431516i	−0.00424114	+	0.0294978i
$215$	9.75858	+	6.68815i	0.665530	+	0.456128i
$216$	−3.33120	−	2.14083i	−0.226659	−	0.145665i
$217$	3.57980	+	2.67980i	0.243013	+	0.181917i
$218$	1.79307	−	4.80741i	0.121442	−	0.325599i
$219$	14.4114	−	6.58147i	0.973833	−	0.444734i
$220$	−0.442325	−	10.5847i	−0.0298215	−	0.713617i
$221$	−1.02390	+	1.59321i	−0.0688747	+	0.107171i
$222$	−1.30701	+	2.39361i	−0.0877209	+	0.160649i
$223$	−0.146047	−	0.195096i	−0.00978005	−	0.0130646i	0.795625	−	0.605790i	$-0.207143\pi$
$223$	−0.146047	−	0.195096i	−0.00978005	−	0.0130646i	−0.805405	+	0.592725i	$0.798052\pi$
$224$	2.63538	−	3.04139i	0.176083	−	0.203211i
$225$	−1.85212	−	4.78756i	−0.123475	−	0.319170i
$226$	1.25186	−	1.08474i	0.0832725	−	0.0721560i
$227$	1.92574	−	1.05154i	0.127816	−	0.0697929i	−0.414069	−	0.910246i	$-0.635893\pi$
$227$	1.92574	−	1.05154i	0.127816	−	0.0697929i	0.541885	+	0.840453i	$0.317711\pi$
$228$	−9.01326	+	3.36177i	−0.596918	+	0.222639i
$229$	26.7809			1.76973			0.884865	−	0.465847i	$-0.154250\pi$
$229$	26.7809			1.76973			0.884865	+	0.465847i	$0.154250\pi$
$230$	−7.01172	+	8.11392i	−0.462339	+	0.535016i
$231$	38.2593			2.51728
$232$	−9.90159	+	3.69310i	−0.650071	+	0.242464i
$233$	6.03535	−	3.29555i	0.395389	−	0.215899i	−0.269239	−	0.963074i	$-0.586772\pi$
$233$	6.03535	−	3.29555i	0.395389	−	0.215899i	0.664628	+	0.747175i	$0.268590\pi$
$234$	1.15493	−	1.00076i	0.0755004	−	0.0654214i
$235$	−27.6674	−	9.02258i	−1.80482	−	0.588568i
$236$	6.82015	−	7.87087i	0.443954	−	0.512350i
$237$	3.17798	+	4.24528i	0.206432	+	0.275761i
$238$	−2.45387	+	4.49393i	−0.159061	+	0.291298i
$239$	14.0294	−	21.8302i	0.907488	−	1.41208i	−0.00365694	−	0.999993i	$-0.501164\pi$
$239$	14.0294	−	21.8302i	0.907488	−	1.41208i	0.911145	−	0.412086i	$-0.135200\pi$
$240$	−3.30251	−	3.03756i	−0.213176	−	0.196074i
$241$	12.3882	−	5.65750i	0.797994	−	0.364432i	0.0256782	−	0.999670i	$-0.491825\pi$
$241$	12.3882	−	5.65750i	0.797994	−	0.364432i	0.772316	+	0.635239i	$0.219098\pi$
$242$	4.00000	−	10.7244i	0.257130	−	0.689392i
$243$	−8.20225	−	6.14013i	−0.526175	−	0.393889i
$244$	3.80136	+	2.44299i	0.243357	+	0.156396i
$245$	−3.77336	−	20.2120i	−0.241071	−	1.29130i
$246$	0.665988	−	4.63205i	0.0424619	−	0.295329i
$247$	0.509063	+	7.11763i	0.0323909	+	0.452884i
$248$	0.236197	−	1.08578i	0.0149985	−	0.0689470i
$249$	−16.2891	−	18.7986i	−1.03228	−	1.19131i
$250$	2.18496	+	10.9648i	0.138189	+	0.693472i
$251$	20.1541	+	9.20408i	1.27212	+	0.580957i	0.933030	−	0.359798i	$-0.117155\pi$
$251$	20.1541	+	9.20408i	1.27212	+	0.580957i	0.339087	+	0.940755i	$0.389882\pi$
$252$	2.92151	−	2.92151i	0.184038	−	0.184038i
$253$	−20.3658	+	10.0744i	−1.28039	+	0.633371i
$254$			10.8320i			0.679662i
$255$	4.92734	+	2.88327i	0.308562	+	0.180557i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	1.83980	−	25.7238i	0.114764	−	1.60461i	−0.535257	−	0.844689i	$-0.679785\pi$
$257$	1.83980	−	25.7238i	0.114764	−	1.60461i	0.650020	−	0.759917i	$-0.274760\pi$
$258$	10.3741	+	2.25675i	0.645865	+	0.140499i
$259$	4.13349	+	3.58169i	0.256843	+	0.222556i
$260$	−2.85212	+	1.71571i	−0.176881	+	0.106404i
$261$	−10.4102	+	3.05671i	−0.644375	+	0.189206i
$262$	−0.516419	−	2.37394i	−0.0319045	−	0.146663i
$263$	−12.1287	+	16.2020i	−0.747885	+	0.999057i	0.251627	+	0.967824i	$0.419034\pi$
$263$	−12.1287	+	16.2020i	−0.747885	+	0.999057i	−0.999512	+	0.0312332i	$0.990057\pi$
$264$	−3.94935	−	8.64787i	−0.243066	−	0.532239i
$265$	−9.04153	+	18.3397i	−0.555417	+	1.12660i
$266$	2.74560	+	19.0960i	0.168343	+	1.17085i
$267$	7.56144	−	1.64489i	0.462753	−	0.100666i
$268$	9.37272	+	5.11789i	0.572530	+	0.312625i
$269$	5.60877	+	0.806420i	0.341973	+	0.0491683i	0.311162	−	0.950357i	$-0.399282\pi$
$269$	5.60877	+	0.806420i	0.341973	+	0.0491683i	0.0308112	+	0.999525i	$0.490191\pi$
$270$	6.07273	+	6.44376i	0.369575	+	0.392155i
$271$	−17.4653	+	11.2243i	−1.06094	+	0.681825i	−0.950078	−	0.312011i	$-0.898997\pi$
$271$	−17.4653	+	11.2243i	−1.06094	+	0.681825i	−0.110862	+	0.993836i	$0.535361\pi$
$272$	1.26908	+	0.0907664i	0.0769493	+	0.00550352i
$273$	−5.76073	−	10.5500i	−0.348655	−	0.638515i
$274$	7.09208	−	15.5295i	0.428448	−	0.938171i
$275$	−4.75424	+	23.2067i	−0.286692	+	1.39942i
$276$	−3.08222	+	9.11664i	−0.185528	+	0.548757i
$277$	−8.34177	−	8.34177i	−0.501208	−	0.501208i	0.410605	−	0.911813i	$-0.365318\pi$
$277$	−8.34177	−	8.34177i	−0.501208	−	0.501208i	−0.911813	+	0.410605i	$0.865318\pi$
$278$	−3.50612	−	9.40026i	−0.210283	−	0.563790i
$279$	0.321401	−	1.09459i	0.0192418	−	0.0655315i
$280$	−7.36044	+	5.17689i	−0.439870	+	0.309378i
$281$	10.1548	+	15.8012i	0.605785	+	0.942620i	0.999724	+	0.0234836i	$0.00747574\pi$
$281$	10.1548	+	15.8012i	0.605785	+	0.942620i	−0.393939	+	0.919137i	$0.628888\pi$
$282$	−26.0492	+	1.86307i	−1.55121	+	0.110944i
$283$	−5.14866	+	3.85424i	−0.306056	+	0.229111i	−0.741255	−	0.671224i	$-0.765769\pi$
$283$	−5.14866	+	3.85424i	−0.306056	+	0.229111i	0.435199	+	0.900334i	$0.356678\pi$
$284$	0.695948	+	2.37018i	0.0412969	+	0.140644i
$285$	21.3729	−	2.42904i	1.26602	−	0.143884i
$286$	−6.98035	+	1.00362i	−0.412757	+	0.0593455i
$287$	−8.79334	−	3.27975i	−0.519054	−	0.193597i
$288$	−0.961934	−	0.358783i	−0.0566825	−	0.0211415i
$289$	15.2246	−	2.18897i	0.895567	−	0.128763i
$290$	23.4794	−	2.66844i	1.37876	−	0.156696i
$291$	1.16266	+	3.95965i	0.0681562	+	0.232119i
$292$	−6.32050	+	4.73147i	−0.369879	+	0.276888i
$293$	−24.2374	+	1.73349i	−1.41596	+	0.101272i	−0.758234	−	0.651982i	$-0.773938\pi$
$293$	−24.2374	+	1.73349i	−1.41596	+	0.101272i	−0.657730	+	0.753254i	$0.728483\pi$
$294$	−9.97573	−	15.5225i	−0.581796	−	0.905293i
$295$	−19.0482	+	13.3974i	−1.10903	+	0.780025i
$296$	0.382898	−	1.30403i	0.0222555	−	0.0757952i
$297$	6.55612	+	17.5776i	0.380424	+	1.01996i
$298$	−0.147010	−	0.147010i	−0.00851607	−	0.00851607i
$299$	5.84451	+	4.09897i	0.337997	+	0.237049i
$300$	5.52638	+	8.37411i	0.319066	+	0.483480i
$301$	8.84494	−	19.3677i	0.509814	−	1.11634i
$302$	−6.21981	−	11.3907i	−0.357910	−	0.655463i
$303$	−3.91029	−	0.279669i	−0.224640	−	0.0160666i
$304$	4.03292	−	2.59180i	0.231304	−	0.148650i
$305$	−6.92983	−	7.35323i	−0.396801	−	0.421045i
$306$	1.29295	+	0.185899i	0.0739132	+	0.0106271i
$307$	−23.2229	−	12.6806i	−1.32540	−	0.723722i	−0.348476	−	0.937318i	$-0.613301\pi$
$307$	−23.2229	−	12.6806i	−1.32540	−	0.723722i	−0.976922	+	0.213595i	$0.931483\pi$
$308$	−18.6305	+	4.05281i	−1.06157	+	0.230930i
$309$	3.01423	+	20.9644i	0.171474	+	1.19263i
$310$	−1.09868	+	2.22855i	−0.0624008	+	0.126573i
$311$	3.80114	+	8.32333i	0.215543	+	0.471973i	0.986259	−	0.165206i	$-0.0528287\pi$
$311$	3.80114	+	8.32333i	0.215543	+	0.471973i	−0.770716	+	0.637178i	$0.780101\pi$
$312$	−1.78999	+	2.39115i	−0.101338	+	0.135372i
$313$	0.185974	+	0.854907i	0.0105119	+	0.0483222i	0.982104	−	0.188339i	$-0.0603104\pi$
$313$	0.185974	+	0.854907i	0.0105119	+	0.0483222i	−0.971592	+	0.236661i	$0.923947\pi$
$314$	6.57151	−	1.92957i	0.370852	−	0.108892i
$315$	−7.91662	+	4.76230i	−0.446051	+	0.268325i
$316$	−1.99723	−	1.73061i	−0.112353	−	0.0973544i
$317$	−5.71180	−	1.24253i	−0.320807	−	0.0697872i	0.0492784	−	0.998785i	$-0.484308\pi$
$317$	−5.71180	−	1.24253i	−0.320807	−	0.0697872i	−0.370085	+	0.928998i	$0.620671\pi$
$318$	−1.30904	+	18.3028i	−0.0734074	+	1.02637i
$319$	48.0398	+	14.1057i	2.68971	+	0.789770i
$320$	1.92994	+	1.12931i	0.107887	+	0.0631306i
$321$		−	0.874807i		−	0.0488270i
$322$	16.5516	+	9.92652i	0.922383	+	0.553183i
$323$	−4.31296	+	4.31296i	−0.239979	+	0.239979i
$324$	10.0296	+	4.58035i	0.557198	+	0.254464i
$325$	7.11509	−	2.18327i	0.394674	−	0.121106i
$326$	12.9457	+	14.9402i	0.716998	+	0.827460i
$327$	−2.18857	+	10.0607i	−0.121028	+	0.556357i
$328$	0.166369	+	2.32614i	0.00918618	+	0.128440i
$329$	−7.45372	+	51.8418i	−0.410937	+	2.85813i
$330$	3.90129	+	20.8972i	0.214759	+	1.15036i
$331$	−14.5979	−	9.38149i	−0.802373	−	0.515654i	0.0740166	−	0.997257i	$-0.476418\pi$
$331$	−14.5979	−	9.38149i	−0.802373	−	0.515654i	−0.876389	+	0.481603i	$0.840055\pi$
$332$	9.92337	+	7.42854i	0.544616	+	0.407694i
$333$	0.487615	−	1.30735i	0.0267211	−	0.0716422i
$334$	−9.48505	+	4.33168i	−0.518999	+	0.237019i
$335$	−17.5752	−	16.1652i	−0.960237	−	0.883201i
$336$	−4.36591	+	6.79350i	−0.238180	+	0.370616i
$337$	9.36405	−	17.1490i	0.510092	−	0.934164i	−0.488025	−	0.872830i	$-0.662283\pi$
$337$	9.36405	−	17.1490i	0.510092	−	0.934164i	0.998117	−	0.0613344i	$-0.0195356\pi$
$338$	−6.46282	−	8.63332i	−0.351531	−	0.469591i
$339$	−2.17670	+	2.51205i	−0.118222	+	0.136436i
$340$	−2.70481	−	0.882061i	−0.146689	−	0.0478365i
$341$	−3.97859	+	3.44747i	−0.215453	+	0.186691i
$342$	4.31974	−	2.35876i	0.233585	−	0.127547i
$343$	−8.27736	+	3.08729i	−0.446935	+	0.166698i
$344$	−5.29077			−0.285259
$345$	11.6098	−	18.1185i	0.625048	−	0.975468i
$346$	−10.7224			−0.576439
$347$	31.0872	−	11.5949i	1.66885	−	0.622449i	0.675476	−	0.737382i	$-0.263938\pi$
$347$	31.0872	−	11.5949i	1.66885	−	0.622449i	0.993373	+	0.114934i	$0.0366655\pi$
$348$	18.6122	−	10.1630i	0.997717	−	0.544795i
$349$	−8.99832	+	7.79709i	−0.481669	+	0.417369i	−0.861555	−	0.507665i	$-0.830509\pi$
$349$	−8.99832	+	7.79709i	−0.481669	+	0.417369i	0.379885	+	0.925034i	$0.375963\pi$
$350$	18.7663	−	7.25996i	1.00310	−	0.388061i
$351$	3.85987	−	4.45453i	0.206025	−	0.237765i
$352$	2.83922	+	3.79275i	0.151331	+	0.202154i
$353$	−6.99666	+	12.8134i	−0.372395	+	0.681990i	−0.994926	−	0.100605i	$-0.967922\pi$
$353$	−6.99666	+	12.8134i	−0.372395	+	0.681990i	0.622532	+	0.782594i	$0.286104\pi$
$354$	−11.2986	+	17.5810i	−0.600516	+	0.934421i
$355$	−0.230627	−	5.51881i	−0.0122404	−	0.292908i
$356$	−3.50782	+	1.60197i	−0.185914	+	0.0849042i
$357$	3.59059	−	9.62675i	0.190034	−	0.509502i
$358$	−17.7584	−	13.2938i	−0.938559	−	0.702597i
$359$	−9.74006	−	6.25955i	−0.514061	−	0.330367i	0.257758	−	0.966210i	$-0.417016\pi$
$359$	−9.74006	−	6.25955i	−0.514061	−	0.330367i	−0.771819	+	0.635843i	$0.780653\pi$
$360$	1.89364	+	1.29782i	0.0998034	+	0.0684014i
$361$	−0.566684	+	3.94137i	−0.0298255	+	0.207441i
$362$	0.164309	+	2.29734i	0.00863590	+	0.120746i
$363$	−4.88228	+	22.4435i	−0.256253	+	1.17798i
$364$	3.92277	+	4.52712i	0.205609	+	0.237285i
$365$	16.2693	−	6.85484i	0.851572	−	0.358799i
$366$	−8.24804	−	3.76675i	−0.431132	−	0.196891i
$367$	−14.1268	+	14.1268i	−0.737413	+	0.737413i	−0.972077	−	0.234664i	$-0.924601\pi$
$367$	−14.1268	+	14.1268i	−0.737413	+	0.737413i	0.234664	+	0.972077i	$0.424601\pi$
$368$	0.535170	−	4.76588i	0.0278977	−	0.248439i
$369$			2.39427i			0.124641i
$370$	−1.53483	+	2.62294i	−0.0797920	+	0.136360i
$371$	35.3092	+	10.3677i	1.83316	+	0.538265i
$372$	−0.159068	+	2.22406i	−0.00824728	+	0.115312i
$373$	−2.42661	−	0.527877i	−0.125645	−	0.0273324i	0.149303	−	0.988791i	$-0.452297\pi$
$373$	−2.42661	−	0.527877i	−0.125645	−	0.0273324i	−0.274948	+	0.961459i	$0.588661\pi$
$374$	−4.55560	−	3.94745i	−0.235564	−	0.204118i
$375$	−7.47112	−	21.1546i	−0.385807	−	1.09242i
$376$	12.4874	−	3.66662i	0.643987	−	0.189092i
$377$	−3.34373	−	15.3709i	−0.172211	−	0.791640i
$378$	9.54982	−	12.7571i	0.491190	−	0.656153i
$379$	−6.21472	−	13.6083i	−0.319229	−	0.699014i	0.680192	−	0.733034i	$-0.261896\pi$
$379$	−6.21472	−	13.6083i	−0.319229	−	0.699014i	−0.999421	+	0.0340201i	$0.989169\pi$
$380$	−10.1503	+	3.44687i	−0.520700	+	0.176820i
$381$	−3.09338	−	21.5149i	−0.158479	−	1.10224i
$382$	−20.3741	+	4.43212i	−1.04243	+	0.226767i
$383$	27.9260	+	15.2488i	1.42695	+	0.779175i	0.992584	−	0.121561i	$-0.0387899\pi$
$383$	27.9260	+	15.2488i	1.42695	+	0.779175i	0.434368	+	0.900735i	$0.356972\pi$
$384$	1.98623	+	0.285577i	0.101359	+	0.0145733i
$385$	42.6146	+	1.26325i	2.17184	+	0.0643811i
$386$	8.40270	−	5.40008i	0.427686	−	0.274857i
$387$	−5.41801	−	0.387504i	−0.275413	−	0.0196979i
$388$	−0.985605	−	1.80500i	−0.0500365	−	0.0916351i
$389$	−14.7210	+	32.2344i	−0.746382	+	1.63435i	0.0263798	+	0.999652i	$0.491602\pi$
$389$	−14.7210	+	32.2344i	−0.746382	+	1.63435i	−0.772762	+	0.634696i	$0.781125\pi$
$390$	5.17499	−	4.22230i	0.262046	−	0.213804i
$391$	0.623591	+	6.06989i	0.0315363	+	0.306968i
$392$	6.50202	+	6.50202i	0.328401	+	0.328401i
$393$	1.70367	+	4.56772i	0.0859388	+	0.230411i
$394$	−3.06253	+	10.4300i	−0.154288	+	0.525456i
$395$	3.39958	+	4.83348i	0.171051	+	0.243199i
$396$	2.62971	+	4.09191i	0.132148	+	0.205626i
$397$	14.5034	−	1.03731i	0.727906	−	0.0520609i	0.297532	−	0.954712i	$-0.403836\pi$
$397$	14.5034	−	1.03731i	0.727906	−	0.0520609i	0.430374	+	0.902651i	$0.358382\pi$
$398$	−12.0314	+	9.00662i	−0.603081	+	0.451461i
$399$	−10.9068	−	37.1451i	−0.546022	−	1.85958i
$400$	−3.57816	−	3.49239i	−0.178908	−	0.174619i
$401$	−6.71092	+	0.964885i	−0.335127	+	0.0481840i	−0.307824	−	0.951443i	$-0.599601\pi$
$401$	−6.71092	+	0.964885i	−0.335127	+	0.0481840i	−0.0273029	+	0.999627i	$0.508692\pi$
$402$	−20.0779	−	7.48868i	−1.00140	−	0.373501i
$403$	1.54970	+	0.578008i	0.0771961	+	0.0287926i
$404$	1.93375	−	0.278032i	0.0962078	−	0.0138326i
$405$	−19.2907	−	15.3534i	−0.958563	−	0.762916i
$406$	−11.9817	−	40.8060i	−0.594643	−	2.02517i
$407$	−5.15466	+	3.85873i	−0.255507	+	0.191270i
$408$	−2.54661	+	0.182137i	−0.126076	+	0.00901712i
$409$	1.02498	+	1.59490i	0.0506819	+	0.0788626i	0.865670	−	0.500615i	$-0.166893\pi$
$409$	1.02498	+	1.59490i	0.0506819	+	0.0788626i	−0.814988	+	0.579478i	$0.803256\pi$
$410$	0.894744	−	5.13736i	0.0441882	−	0.253716i
$411$	−9.65165	+	32.8705i	−0.476081	+	1.62138i
$412$	−3.68856	−	9.88940i	−0.181722	−	0.487216i
$413$	29.6363	+	29.6363i	1.45831	+	1.45831i
$414$	0.897101	−	4.84130i	0.0440901	−	0.237937i
$415$	−17.5227	−	21.4764i	−0.860156	−	1.05424i
$416$	0.618347	−	1.35399i	0.0303170	−	0.0663849i
$417$	9.64845	+	17.6698i	0.472487	+	0.865295i
$418$	−22.6546	−	1.62029i	−1.10807	−	0.0792508i
$419$	−10.3753	+	6.66780i	−0.506867	+	0.325743i	−0.768958	−	0.639300i	$-0.779224\pi$
$419$	−10.3753	+	6.66780i	−0.506867	+	0.325743i	0.262091	+	0.965043i	$0.415588\pi$
$420$	13.1411	−	12.3845i	0.641221	−	0.604300i
$421$	−18.3998	−	2.64549i	−0.896751	−	0.128933i	−0.321499	−	0.946910i	$-0.604187\pi$
$421$	−18.3998	−	2.64549i	−0.896751	−	0.128933i	−0.575252	+	0.817976i	$0.695096\pi$
$422$	−2.12379	−	1.15968i	−0.103385	−	0.0564523i
$423$	13.0562	−	2.84021i	0.634816	−	0.138096i
$424$	−1.30138	−	9.05126i	−0.0632004	−	0.439568i
$425$	5.39305	+	3.37418i	0.261601	+	0.163672i
$426$	−2.05918	−	4.50898i	−0.0997676	−	0.218461i
$427$	−10.8977	+	14.5576i	−0.527376	+	0.704491i
$428$	0.0926685	+	0.425990i	0.00447930	+	0.0205910i
$429$	13.5780	−	3.98685i	0.655551	−	0.192487i
$430$	11.4806	+	2.85619i	0.553642	+	0.137738i
$431$	19.2191	+	16.6534i	0.925750	+	0.802167i	0.980538	−	0.196331i	$-0.0629028\pi$
$431$	19.2191	+	16.6534i	0.925750	+	0.802167i	−0.0547879	+	0.998498i	$0.517448\pi$
$432$	−3.86931	−	0.841717i	−0.186162	−	0.0404971i
$433$	1.93256	−	27.0207i	0.0928727	−	1.29853i	−0.710773	−	0.703422i	$-0.751655\pi$
$433$	1.93256	−	27.0207i	0.0928727	−	1.29853i	0.803645	−	0.595108i	$-0.202891\pi$
$434$	4.29059	+	1.25983i	0.205955	+	0.0604738i
$435$	−45.8734	+	12.0053i	−2.19946	+	0.575610i
$436$		−	5.13091i		−	0.245726i
$437$	15.5868	+	16.9008i	0.745617	+	0.808473i
$438$	11.2028	−	11.2028i	0.535289	−	0.535289i
$439$	−19.8620	−	9.07065i	−0.947959	−	0.432919i	−0.119417	−	0.992844i	$-0.538102\pi$
$439$	−19.8620	−	9.07065i	−0.947959	−	0.432919i	−0.828543	+	0.559926i	$0.810830\pi$
$440$	−4.11339	−	9.76271i	−0.196098	−	0.465419i
$441$	6.18217	+	7.13460i	0.294389	+	0.339743i
$442$	−0.402568	+	1.85058i	−0.0191482	+	0.0880229i
$443$	1.67356	+	23.3994i	0.0795132	+	1.11174i	0.867959	+	0.496636i	$0.165432\pi$
$443$	1.67356	+	23.3994i	0.0795132	+	1.11174i	−0.788446	+	0.615104i	$0.789114\pi$
$444$	−0.388122	+	2.69945i	−0.0184195	+	0.128110i
$445$	8.47652	−	1.58248i	0.401826	−	0.0750165i
$446$	−0.205018	−	0.131757i	−0.00970789	−	0.00623888i
$447$	0.333979	+	0.250013i	0.0157967	+	0.0118252i
$448$	1.40636	−	3.77060i	0.0664442	−	0.178144i
$449$	32.3026	−	14.7521i	1.52445	−	0.696194i	0.535515	−	0.844526i	$-0.320118\pi$
$449$	32.3026	−	14.7521i	1.52445	−	0.696194i	0.988938	+	0.148332i	$0.0473904\pi$
$450$	−3.40842	−	3.83845i	−0.160675	−	0.180946i
$451$	5.97342	−	9.29482i	0.281277	−	0.437676i
$452$	0.793851	−	1.45383i	0.0373396	−	0.0683824i
$453$	15.6069	+	20.8484i	0.733276	+	0.979542i
$454$	1.43685	−	1.65821i	0.0674348	−	0.0778239i
$455$	−6.06818	−	11.9412i	−0.284480	−	0.559811i
$456$	−7.27016	+	6.29963i	−0.340456	+	0.295007i
$457$	−0.353056	+	0.192783i	−0.0165153	+	0.00901801i	−0.487485	−	0.873131i	$-0.662086\pi$
$457$	−0.353056	+	0.192783i	−0.0165153	+	0.00901801i	0.470970	+	0.882149i	$0.343904\pi$
$458$	25.0923	−	9.35896i	1.17249	−	0.437315i
$459$	5.03814			0.235160
$460$	−3.73411	+	10.0527i	−0.174104	+	0.468709i
$461$	−17.1932			−0.800766			−0.400383	−	0.916348i	$-0.631123\pi$
$461$	−17.1932			−0.800766			−0.400383	+	0.916348i	$0.631123\pi$
$462$	35.8470	−	13.3703i	1.66775	−	0.622040i
$463$	−4.08469	+	2.23041i	−0.189832	+	0.103656i	−0.571354	−	0.820704i	$-0.693582\pi$
$463$	−4.08469	+	2.23041i	−0.189832	+	0.103656i	0.381522	+	0.924360i	$0.375400\pi$
$464$	−7.98668	+	6.92050i	−0.370772	+	0.321276i
$465$	1.54581	−	4.74017i	0.0716851	−	0.219820i
$466$	4.50314	−	5.19690i	0.208604	−	0.240742i
$467$	−1.51830	−	2.02822i	−0.0702587	−	0.0938547i	0.764035	−	0.645174i	$-0.223215\pi$
$467$	−1.51830	−	2.02822i	−0.0702587	−	0.0938547i	−0.834294	+	0.551320i	$0.814124\pi$
$468$	0.732386	−	1.34127i	0.0338546	−	0.0620000i
$469$	−23.2344	+	36.1535i	−1.07287	+	1.66941i
$470$	−29.0761	+	1.21507i	−1.34118	+	0.0560469i
$471$	−12.5015	+	5.70924i	−0.576039	+	0.263068i
$472$	3.63955	−	9.75800i	0.167524	−	0.449149i
$473$	20.0666	+	15.0216i	0.922662	+	0.690696i
$474$	4.46118	+	2.86703i	0.204909	+	0.131687i
$475$	23.8861	−	1.99986i	1.09597	−	0.0917599i
$476$	−0.728687	+	5.06813i	−0.0333993	+	0.232297i
$477$	−0.669745	−	9.36426i	−0.0306655	−	0.428760i
$478$	5.51599	−	25.3566i	0.252295	−	1.15978i
$479$	−23.7808	−	27.4445i	−1.08657	−	1.25397i	−0.965241	−	0.261360i	$-0.915829\pi$
$479$	−23.7808	−	27.4445i	−1.08657	−	1.25397i	−0.121331	−	0.992612i	$-0.538716\pi$
$480$	−4.15580	−	1.69193i	−0.189686	−	0.0772258i
$481$	1.84018	+	0.840384i	0.0839052	+	0.0383182i
$482$	9.63003	−	9.63003i	0.438636	−	0.438636i
$483$	−35.7100	−	14.9896i	−1.62486	−	0.682051i
$484$		−	11.4461i		−	0.520277i
$485$	1.16427	+	4.44879i	0.0528668	+	0.202009i
$486$	−9.83085	−	2.88660i	−0.445936	−	0.130939i
$487$	−1.36226	+	19.0468i	−0.0617298	+	0.863095i	0.868400	+	0.495864i	$0.165149\pi$
$487$	−1.36226	+	19.0468i	−0.0617298	+	0.863095i	−0.930130	+	0.367231i	$0.880306\pi$
$488$	4.41542	+	0.960516i	0.199877	+	0.0434805i
$489$	−29.9798	−	25.9776i	−1.35573	−	1.17475i
$490$	−10.5988	−	17.6189i	−0.478805	−	0.795943i
$491$	33.1580	−	9.73608i	1.49640	−	0.439383i	0.571823	−	0.820377i	$-0.306236\pi$
$491$	33.1580	−	9.73608i	1.49640	−	0.439383i	0.924578	+	0.380994i	$0.124418\pi$
$492$	−0.994738	−	4.57274i	−0.0448463	−	0.206155i
$493$	8.05775	−	10.7639i	0.362903	−	0.484781i
$494$	2.96432	+	6.49096i	0.133371	+	0.292042i
$495$	−3.49728	−	10.2988i	−0.157191	−	0.462895i
$496$	−0.158136	−	1.09986i	−0.00710053	−	0.0493853i
$497$	−9.71389	+	2.11313i	−0.435727	+	0.0947867i
$498$	−21.8315	−	11.9209i	−0.978294	−	0.534189i
$499$	7.16424	+	1.03006i	0.320715	+	0.0461119i	0.300792	−	0.953690i	$-0.402749\pi$
$499$	7.16424	+	1.03006i	0.320715	+	0.0461119i	0.0199229	+	0.999802i	$0.493658\pi$
$500$	5.87899	+	9.50986i	0.262916	+	0.425294i
$501$	17.6025	−	11.3124i	0.786421	−	0.505402i
$502$	22.0999	+	1.58062i	0.986367	+	0.0705464i
$503$	−10.8106	−	19.7982i	−0.482022	−	0.882757i	−0.999632	−	0.0271402i	$-0.991360\pi$
$503$	−10.8106	−	19.7982i	−0.482022	−	0.882757i	0.517610	−	0.855617i	$-0.326822\pi$
$504$	1.71635	−	3.75827i	0.0764521	−	0.167407i
$505$	−4.34619	−	0.440616i	−0.193403	−	0.0196072i
$506$	−15.5611	+	16.5563i	−0.691777	+	0.736018i
$507$	15.3021	+	15.3021i	0.679592	+	0.679592i
$508$	3.78541	+	10.1491i	0.167950	+	0.450292i
$509$	−2.03892	+	6.94393i	−0.0903737	+	0.307784i	−0.992258	−	0.124193i	$-0.960366\pi$
$509$	−2.03892	+	6.94393i	−0.0903737	+	0.307784i	0.901884	+	0.431977i	$0.142184\pi$
$510$	5.62427	+	0.979546i	0.249047	+	0.0433750i
$511$	−17.1779	−	26.7294i	−0.759906	−	1.18244i
$512$	−0.997452	+	0.0713392i	−0.0440816	+	0.00315278i
$513$	15.1967	−	11.3761i	0.670952	−	0.502268i
$514$	−7.26574	−	24.7448i	−0.320478	−	1.09145i
$515$	2.66516	+	23.4505i	0.117441	+	1.03335i
$516$	10.5087	−	1.51092i	0.462619	−	0.0665146i
$517$	−57.7718	−	21.5478i	−2.54080	−	0.947670i
$518$	5.12455	+	1.91136i	0.225160	+	0.0839802i
$519$	21.2971	−	3.06206i	0.934840	−	0.134410i
$520$	−2.07271	+	2.60425i	−0.0908943	+	0.114204i
$521$	−4.48212	−	15.2647i	−0.196365	−	0.668759i	−0.997525	−	0.0703085i	$-0.977602\pi$
$521$	−4.48212	−	15.2647i	−0.196365	−	0.668759i	0.801160	−	0.598450i	$-0.204217\pi$
$522$	−8.68563	+	6.50198i	−0.380159	+	0.284584i
$523$	22.9496	−	1.64139i	1.00351	−	0.0717728i	0.440101	−	0.897948i	$-0.354943\pi$
$523$	22.9496	−	1.64139i	1.00351	−	0.0717728i	0.563413	+	0.826175i	$0.309488\pi$
$524$	−1.31347	−	2.04379i	−0.0573790	−	0.0892835i
$525$	−35.2009	+	19.7792i	−1.53629	+	0.863234i
$526$	−5.70193	+	19.4190i	−0.248616	+	0.846708i
$527$	0.494062	+	1.32463i	0.0215217	+	0.0577018i
$528$	−6.72246	−	6.72246i	−0.292558	−	0.292558i
$529$	22.9559	−	1.42398i	0.998082	−	0.0619124i
$530$	−2.06238	+	20.3431i	−0.0895841	+	0.883647i
$531$	4.44177	−	9.72611i	0.192756	−	0.422077i
$532$	9.24587	+	16.9326i	0.400859	+	0.734119i
$533$	−3.46247	−	0.247641i	−0.149976	−	0.0107265i
$534$	6.50986	−	4.18363i	0.281709	−	0.181044i
$535$	0.0288845	−	0.974393i	0.00124878	−	0.0421267i
$536$	10.5703	+	1.51978i	0.456567	+	0.0656444i
$537$	39.0686	+	21.3331i	1.68593	+	0.920590i
$538$	5.53695	−	1.20449i	0.238715	−	0.0519293i
$539$	−6.19989	−	43.1211i	−0.267048	−	1.85736i
$540$	7.94171	+	3.91528i	0.341757	+	0.168487i
$541$	−0.183364	−	0.401511i	−0.00788343	−	0.0172623i	0.905649	−	0.424027i	$-0.139384\pi$
$541$	−0.183364	−	0.401511i	−0.00788343	−	0.0172623i	−0.913533	+	0.406765i	$0.866657\pi$
$542$	−12.4416	+	16.6200i	−0.534413	+	0.713892i
$543$	−0.982424	−	4.51613i	−0.0421599	−	0.193806i
$544$	1.22078	−	0.358455i	0.0523407	−	0.0153686i
$545$	−2.76989	+	11.1337i	−0.118649	+	0.476915i
$546$	−9.08436	−	7.87165i	−0.388775	−	0.336875i
$547$	12.8245	+	2.78979i	0.548335	+	0.119283i	0.478194	−	0.878254i	$-0.341292\pi$
$547$	12.8245	+	2.78979i	0.548335	+	0.119283i	0.0701407	+	0.997537i	$0.477655\pi$
$548$	1.21792	−	17.0288i	0.0520271	−	0.727434i
$549$	4.45126	+	1.30701i	0.189975	+	0.0557817i
$550$	3.65541	+	23.4049i	0.155867	+	0.997989i
$551$		−	50.6619i		−	2.15827i
$552$	0.298052	+	9.61896i	0.0126860	+	0.409410i
$553$	7.52019	−	7.52019i	0.319791	−	0.319791i
$554$	−10.7310	−	4.90067i	−0.455915	−	0.208210i
$555$	2.29948	−	5.64808i	0.0976073	−	0.239747i
$556$	−6.57011	−	7.58231i	−0.278635	−	0.321562i
$557$	5.93298	−	27.2735i	0.251389	−	1.15561i	−0.662313	−	0.749228i	$-0.730425\pi$
$557$	5.93298	−	27.2735i	0.251389	−	1.15561i	0.913701	−	0.406387i	$-0.133211\pi$
$558$	−0.0813839	−	1.13790i	−0.00344525	−	0.0481709i
$559$	1.12078	−	7.79518i	0.0474038	−	0.329701i
$560$	−5.08722	+	7.42269i	−0.214974	+	0.313666i
$561$	10.1758	+	6.53957i	0.429621	+	0.276101i
$562$	15.0365	+	11.2562i	0.634276	+	0.474813i
$563$	2.03899	−	5.46675i	0.0859332	−	0.230396i	−0.886874	−	0.462011i	$-0.847128\pi$
$563$	2.03899	−	5.46675i	0.0859332	−	0.230396i	0.972808	+	0.231615i	$0.0744009\pi$
$564$	−23.7557	+	10.8489i	−1.00030	+	0.456820i
$565$	−2.50744	+	2.72614i	−0.105489	+	0.114690i
$566$	−3.47712	+	5.41050i	−0.146154	+	0.227420i
$567$	−21.2653	+	38.9444i	−0.893058	+	1.63551i
$568$	1.48036	+	1.97753i	0.0621146	+	0.0829753i
$569$	−18.1953	+	20.9984i	−0.762785	+	0.880301i	−0.995742	−	0.0921864i	$-0.970614\pi$
$569$	−18.1953	+	20.9984i	−0.762785	+	0.880301i	0.232957	+	0.972487i	$0.425160\pi$
$570$	19.1765	−	9.74496i	0.803215	−	0.408171i
$571$	11.3507	−	9.83548i	0.475014	−	0.411602i	−0.384175	−	0.923260i	$-0.625514\pi$
$571$	11.3507	−	9.83548i	0.475014	−	0.411602i	0.859189	+	0.511658i	$0.170969\pi$
$572$	−6.18951	+	3.37973i	−0.258796	+	0.141314i
$573$	39.2020	−	14.6216i	1.63769	−	0.610825i
$574$	−9.38507			−0.391725
$575$	13.5296	−	19.7977i	0.564223	−	0.825622i
$576$	−1.02667			−0.0427777
$577$	−32.5823	+	12.1526i	−1.35642	+	0.505918i	−0.919325	−	0.393499i	$-0.871264\pi$
$577$	−32.5823	+	12.1526i	−1.35642	+	0.505918i	−0.437092	+	0.899417i	$0.643992\pi$
$578$	13.4998	−	7.37142i	0.561516	−	0.306611i
$579$	−15.1476	+	13.1254i	−0.629511	+	0.545474i
$580$	21.0665	−	10.7054i	0.874738	−	0.444517i
$581$	−32.6677	+	37.7005i	−1.35528	+	1.56408i
$582$	2.47311	+	3.30368i	0.102514	+	0.136942i
$583$	−20.7627	+	38.0241i	−0.859904	+	1.57480i
$584$	−4.26851	+	6.64194i	−0.176632	+	0.274845i
$585$	−2.31330	+	2.51507i	−0.0956430	+	0.103985i
$586$	−22.1034	+	10.0943i	−0.913084	+	0.416992i
$587$	5.02161	−	13.4635i	0.207264	−	0.555696i	−0.791173	−	0.611593i	$-0.790529\pi$
$587$	5.02161	−	13.4635i	0.207264	−	0.555696i	0.998437	+	0.0558968i	$0.0178018\pi$
$588$	−14.7713	−	11.0577i	−0.609159	−	0.456011i
$589$	4.48127	+	2.87994i	0.184648	+	0.118666i
$590$	−13.1653	+	19.2093i	−0.542008	+	0.790836i
$591$	3.10431	−	21.5910i	0.127694	−	0.888134i
$592$	−0.0969558	−	1.35562i	−0.00398486	−	0.0557156i
$593$	1.41801	−	6.51849i	0.0582308	−	0.267682i	−0.938822	−	0.344403i	$-0.888081\pi$
$593$	1.41801	−	6.51849i	0.0582308	−	0.267682i	0.997053	+	0.0767206i	$0.0244450\pi$
$594$	12.2855	+	14.1782i	0.504080	+	0.581740i
$595$	4.31719	−	10.6041i	0.176988	−	0.434725i
$596$	−0.189116	−	0.0863664i	−0.00774649	−	0.00353770i
$597$	21.3251	−	21.3251i	0.872779	−	0.872779i
$598$	6.90845	+	1.79808i	0.282508	+	0.0735290i
$599$			6.14352i			0.251018i	0.992093	+	0.125509i	$0.0400563\pi$
$599$			6.14352i			0.251018i	−0.992093	+	0.125509i	$0.959944\pi$
$600$	8.10439	+	5.91485i	0.330860	+	0.241473i
$601$	−8.99265	−	2.64048i	−0.366818	−	0.107707i	0.0931287	−	0.995654i	$-0.470313\pi$
$601$	−8.99265	−	2.64048i	−0.366818	−	0.107707i	−0.459946	+	0.887947i	$0.652131\pi$
$602$	1.51894	−	21.2376i	0.0619074	−	0.865578i
$603$	10.7132	+	2.33051i	0.436275	+	0.0949057i
$604$	−9.80830	−	8.49894i	−0.399094	−	0.345817i
$605$	−6.17910	+	24.8372i	−0.251216	+	1.00977i
$606$	−3.76148	+	1.10447i	−0.152800	+	0.0448660i
$607$	−5.55466	−	25.5344i	−0.225457	−	1.03641i	−0.941149	−	0.337992i	$-0.890252\pi$
$607$	−5.55466	−	25.5344i	−0.225457	−	1.03641i	0.715692	−	0.698416i	$-0.246111\pi$
$608$	2.87290	−	3.83775i	0.116512	−	0.155641i
$609$	35.4517	+	77.6284i	1.43658	+	3.14566i
$610$	−9.06260	−	4.46788i	−0.366934	−	0.180899i
$611$	2.75695	+	19.1750i	0.111534	+	0.775739i
$612$	1.27640	−	0.277663i	0.0515953	−	0.0112239i
$613$	10.5979	+	5.78687i	0.428044	+	0.233730i	0.678804	−	0.734320i	$-0.262499\pi$
$613$	10.5979	+	5.78687i	0.428044	+	0.233730i	−0.250760	+	0.968049i	$0.580680\pi$
$614$	−26.1901	−	3.76557i	−1.05695	−	0.151966i
$615$	−0.310057	+	10.4595i	−0.0125027	+	0.421768i
$616$	−16.0395	+	10.3080i	−0.646250	+	0.415320i
$617$	28.4197	+	2.03262i	1.14413	+	0.0818300i	0.630507	−	0.776184i	$-0.282847\pi$
$617$	28.4197	+	2.03262i	1.14413	+	0.0818300i	0.513626	+	0.858014i	$0.328302\pi$
$618$	10.1505	+	18.5893i	0.408313	+	0.747770i
$619$	−8.00922	+	17.5377i	−0.321918	+	0.704901i	−0.999534	−	0.0305140i	$-0.990286\pi$
$619$	−8.00922	+	17.5377i	−0.321918	+	0.704901i	0.677617	+	0.735415i	$0.263013\pi$
$620$	−0.250610	+	2.47199i	−0.0100647	+	0.0992773i
$621$	0.767462	−	18.9750i	0.0307972	−	0.761442i
$622$	6.47018	+	6.47018i	0.259431	+	0.259431i
$623$	−5.42336	−	14.5406i	−0.217282	−	0.582556i
$624$	−0.841511	+	2.86592i	−0.0336874	+	0.114729i
$625$	−7.62312	−	23.8094i	−0.304925	−	0.952376i
$626$	0.473007	+	0.736014i	0.0189052	+	0.0294170i
$627$	45.4599	−	3.25135i	1.81549	−	0.129847i
$628$	5.48286	−	4.10442i	0.218790	−	0.163784i
$629$	0.487169	+	1.65915i	0.0194247	+	0.0661545i
$630$	−5.75322	+	7.22861i	−0.229214	+	0.287995i
$631$	−37.0353	+	5.32488i	−1.47435	+	0.211980i	−0.832148	−	0.554553i	$-0.812889\pi$
$631$	−37.0353	+	5.32488i	−1.47435	+	0.211980i	−0.642205	+	0.766533i	$0.721980\pi$
$632$	−2.47609	−	0.923534i	−0.0984936	−	0.0367362i
$633$	4.54952	+	1.69688i	0.180827	+	0.0674450i
$634$	−5.78589	+	0.831885i	−0.229787	+	0.0330384i
$635$	−2.73514	−	24.0662i	−0.108541	−	0.955039i
$636$	5.16966	+	17.6063i	0.204990	+	0.698133i
$637$	−10.9571	+	8.20240i	−0.434137	+	0.324991i
$638$	49.9403	−	3.57180i	1.97715	−	0.141409i
$639$	1.37113	+	2.13351i	0.0542409	+	0.0844005i
$640$	2.20291	+	0.383667i	0.0870775	+	0.0151658i
$641$	2.72895	−	9.29394i	0.107787	−	0.367088i	−0.887881	−	0.460074i	$-0.847823\pi$
$641$	2.72895	−	9.29394i	0.107787	−	0.367088i	0.995667	+	0.0929856i	$0.0296411\pi$
$642$	−0.305714	−	0.819651i	−0.0120656	−	0.0323490i
$643$	−21.6346	−	21.6346i	−0.853186	−	0.853186i	0.137338	−	0.990524i	$-0.456145\pi$
$643$	−21.6346	−	21.6346i	−0.853186	−	0.853186i	−0.990524	+	0.137338i	$0.956145\pi$
$644$	18.9770	+	3.51646i	0.747797	+	0.138568i
$645$	−23.6187	−	2.39446i	−0.929986	−	0.0942819i
$646$	−2.53380	+	5.54825i	−0.0996910	+	0.218293i
$647$	−9.34360	−	17.1115i	−0.367335	−	0.672724i	0.627000	−	0.779020i	$-0.284283\pi$
$647$	−9.34360	−	17.1115i	−0.367335	−	0.672724i	−0.994335	+	0.106296i	$0.966101\pi$
$648$	10.9979	+	0.786583i	0.432037	+	0.0308999i
$649$	−41.5090	+	26.6762i	−1.62937	+	1.04713i
$650$	5.90351	−	4.53208i	0.231555	−	0.177763i
$651$	−8.88187	−	1.27702i	−0.348108	−	0.0500504i
$652$	17.3506	+	9.47412i	0.679500	+	0.371035i
$653$	39.8310	−	8.66471i	1.55871	−	0.339076i	0.651132	−	0.758964i	$-0.274294\pi$
$653$	39.8310	−	8.66471i	1.55871	−	0.339076i	0.907576	+	0.419888i	$0.137931\pi$
$654$	1.46527	+	10.1912i	0.0572966	+	0.398506i
$655$	1.74679	+	5.14394i	0.0682528	+	0.200990i
$656$	0.968782	+	2.12134i	0.0378246	+	0.0828243i
$657$	−4.85763	+	6.48904i	−0.189514	+	0.253162i
$658$	11.1331	+	51.1779i	0.434013	+	1.99512i
$659$	−13.3060	+	3.90698i	−0.518326	+	0.152194i	−0.530424	−	0.847732i	$-0.677967\pi$
$659$	−13.3060	+	3.90698i	−0.518326	+	0.152194i	0.0120977	+	0.999927i	$0.496149\pi$
$660$	10.9581	+	18.2163i	0.426545	+	0.709069i
$661$	−19.1917	−	16.6297i	−0.746471	−	0.646821i	0.196192	−	0.980565i	$-0.437142\pi$
$661$	−19.1917	−	16.6297i	−0.746471	−	0.646821i	−0.942664	+	0.333744i	$0.891688\pi$
$662$	−16.9560	−	3.68855i	−0.659013	−	0.143360i
$663$	0.271112	−	3.79064i	0.0105291	−	0.147216i
$664$	11.8937	+	3.49231i	0.461565	+	0.135528i
$665$	−10.9219	−	41.7337i	−0.423534	−	1.61836i
$666$		−	1.39532i		−	0.0540676i
$667$	−39.3123	−	31.9873i	−1.52218	−	1.23856i
$668$	−7.37325	+	7.37325i	−0.285280	+	0.285280i
$669$	0.444840	+	0.203152i	0.0171985	+	0.00785430i
$670$	−22.1163	−	9.00410i	−0.854426	−	0.347859i
$671$	−14.0195	−	16.1793i	−0.541216	−	0.624596i
$672$	−1.71656	+	7.89090i	−0.0662177	+	0.304398i
$673$	−1.82073	−	25.4571i	−0.0701838	−	0.981298i	−0.903524	−	0.428538i	$-0.859029\pi$
$673$	−1.82073	−	25.4571i	−0.0701838	−	0.981298i	0.833340	−	0.552760i	$-0.186426\pi$
$674$	2.78069	−	19.3401i	0.107108	−	0.744954i
$675$	−15.1193	−	12.7831i	−0.581941	−	0.492023i
$676$	−9.07238	−	5.83046i	−0.348938	−	0.224249i
$677$	34.7974	+	26.0490i	1.33737	+	1.00115i	0.998172	+	0.0604321i	$0.0192479\pi$
$677$	34.7974	+	26.0490i	1.33737	+	1.00115i	0.339202	+	0.940714i	$0.389843\pi$
$678$	−1.16159	+	3.11435i	−0.0446106	+	0.119606i
$679$	7.52838	−	3.43809i	0.288913	−	0.131942i
$680$	−2.84252	+	0.118787i	−0.109006	+	0.00455526i
$681$	−2.38037	+	3.70393i	−0.0912160	+	0.141935i
$682$	−2.52298	+	4.62048i	−0.0966097	+	0.176927i
$683$	25.0218	+	33.4252i	0.957433	+	1.27898i	0.960295	+	0.278985i	$0.0899980\pi$
$683$	25.0218	+	33.4252i	0.957433	+	1.27898i	−0.00286216	+	0.999996i	$0.500911\pi$
$684$	3.22308	−	3.71963i	0.123237	−	0.142224i
$685$	−11.8357	+	36.2937i	−0.452218	+	1.38671i
$686$	−6.67657	+	5.78528i	−0.254913	+	0.220883i
$687$	−47.1665	+	25.7548i	−1.79951	+	0.982608i
$688$	−4.95719	+	1.84893i	−0.188991	+	0.0704900i
$689$	13.6114			0.518553
$690$	4.54598	−	21.0333i	0.173063	−	0.800725i
$691$	10.5242			0.400358			0.200179	−	0.979759i	$-0.435848\pi$
$691$	10.5242			0.400358			0.200179	+	0.979759i	$0.435848\pi$
$692$	−10.0463	+	3.74709i	−0.381904	+	0.142443i
$693$	−17.1802	+	9.38111i	−0.652623	+	0.356359i
$694$	25.0751	−	21.7277i	0.951839	−	0.824774i
$695$	10.1634	+	19.9999i	0.385519	+	0.758638i
$696$	13.8871	−	16.0265i	0.526388	−	0.607484i
$697$	−1.77815	−	2.37533i	−0.0673523	−	0.0899722i
$698$	−5.70617	+	10.4501i	−0.215982	+	0.395541i
$699$	−7.46017	+	11.6082i	−0.282169	+	0.439064i
$700$	15.0460	−	13.3604i	0.568685	−	0.504974i
$701$	19.6587	−	8.97784i	0.742499	−	0.339088i	−0.00799218	−	0.999968i	$-0.502544\pi$
$701$	19.6587	−	8.97784i	0.742499	−	0.339088i	0.750492	+	0.660880i	$0.229817\pi$
$702$	2.05981	−	5.52255i	0.0777424	−	0.208435i
$703$	5.21582	+	3.90451i	0.196718	+	0.147261i
$704$	3.98563	+	2.56141i	0.150214	+	0.0965368i
$705$	57.4047	−	10.7169i	2.16199	−	0.403620i
$706$	−2.07768	+	14.4506i	−0.0781947	+	0.543856i
$707$	0.560874	+	7.84205i	0.0210939	+	0.294931i
$708$	−4.44232	+	20.4210i	−0.166953	+	0.767469i
$709$	4.46376	+	5.15145i	0.167640	+	0.193467i	0.833353	−	0.552741i	$-0.186418\pi$
$709$	4.46376	+	5.15145i	0.167640	+	0.193467i	−0.665713	+	0.746208i	$0.731873\pi$
$710$	−2.14471	−	5.09025i	−0.0804897	−	0.191034i
$711$	−2.46800	−	1.12710i	−0.0925572	−	0.0422694i
$712$	−2.72682	+	2.72682i	−0.102192	+	0.102192i
$713$	5.06418	−	1.65899i	0.189655	−	0.0621297i
$714$		−	10.2746i		−	0.384516i
$715$	15.2553	−	3.99239i	0.570515	−	0.149307i
$716$	−21.2844	−	6.24966i	−0.795435	−	0.233561i
$717$	−3.71477	+	51.9393i	−0.138731	+	1.93971i
$718$	−11.3134	−	2.46109i	−0.422214	−	0.0918469i
$719$	31.7879	+	27.5444i	1.18549	+	1.02723i	0.998997	+	0.0447759i	$0.0142574\pi$
$719$	31.7879	+	27.5444i	1.18549	+	1.02723i	0.186492	+	0.982456i	$0.440288\pi$
$720$	2.22779	+	0.554239i	0.0830247	+	0.0206553i
$721$	40.7558	−	11.9670i	1.51782	−	0.445673i
$722$	0.846414	+	3.89090i	0.0315003	+	0.144804i
$723$	−16.3773	+	21.8776i	−0.609080	+	0.813635i
$724$	0.956789	+	2.09508i	0.0355588	+	0.0778629i
$725$	−51.4919	+	11.8573i	−1.91236	+	0.440369i
$726$	3.26874	+	22.7346i	0.121314	+	0.843760i
$727$	34.8579	−	7.58287i	1.29281	−	0.281233i	0.486995	−	0.873405i	$-0.338093\pi$
$727$	34.8579	−	7.58287i	1.29281	−	0.281233i	0.805812	+	0.592172i	$0.201729\pi$
$728$	5.25750	+	2.87081i	0.194856	+	0.106399i
$729$	−12.3905	−	1.78148i	−0.458907	−	0.0659809i
$730$	12.8480	−	12.1082i	0.475524	−	0.448143i
$731$	5.66295	−	3.63936i	0.209452	−	0.134607i
$732$	−9.04434	−	0.646864i	−0.334289	−	0.0239088i
$733$	−13.5082	−	24.7384i	−0.498937	−	0.913735i	−0.998863	−	0.0476668i	$-0.984821\pi$
$733$	−13.5082	−	24.7384i	−0.498937	−	0.913735i	0.499926	−	0.866068i	$-0.333360\pi$
$734$	−8.29929	+	18.1729i	−0.306332	+	0.670774i
$735$	26.0832	+	31.9685i	0.962095	+	1.17918i
$736$	−1.16408	−	4.65241i	−0.0429084	−	0.171490i
$737$	−35.7755	−	35.7755i	−1.31781	−	1.31781i
$738$	0.836711	+	2.24331i	0.0307997	+	0.0825773i
$739$	−6.06188	+	20.6449i	−0.222990	+	0.759434i	0.769664	+	0.638449i	$0.220424\pi$
$739$	−6.06188	+	20.6449i	−0.222990	+	0.759434i	−0.992654	+	0.120985i	$0.961395\pi$
$740$	−0.521435	+	2.99393i	−0.0191683	+	0.110059i
$741$	−7.74149	−	12.0460i	−0.284391	−	0.442521i
$742$	36.7061	−	2.62527i	1.34752	−	0.0963767i
$743$	−11.9885	+	8.97450i	−0.439817	+	0.329243i	−0.796132	−	0.605123i	$-0.793124\pi$
$743$	−11.9885	+	8.97450i	−0.439817	+	0.329243i	0.356315	+	0.934366i	$0.384033\pi$
$744$	0.628190	+	2.13942i	0.0230306	+	0.0784349i
$745$	0.363743	+	0.289501i	0.0133265	+	0.0106065i
$746$	−2.45809	+	0.353419i	−0.0899969	+	0.0129396i
$747$	11.9240	+	4.44741i	0.436275	+	0.162722i
$748$	−5.64786	−	2.10654i	−0.206506	−	0.0770228i
$749$	−1.73656	+	0.249680i	−0.0634526	+	0.00912310i
$750$	−14.3928	−	17.2099i	−0.525552	−	0.628416i
$751$	2.35793	+	8.03036i	0.0860419	+	0.293032i	0.991261	−	0.131913i	$-0.0421118\pi$
$751$	2.35793	+	8.03036i	0.0860419	+	0.293032i	−0.905219	+	0.424944i	$0.860294\pi$
$752$	10.4187	−	7.79933i	0.379930	−	0.284412i
$753$	−44.3469	+	3.17175i	−1.61609	+	0.115585i
$754$	−8.50447	−	13.2332i	−0.309715	−	0.481925i
$755$	16.6952	+	23.7370i	0.607599	+	0.863878i
$756$	4.48956	−	15.2901i	0.163284	−	0.556094i
$757$	−9.69539	−	25.9944i	−0.352385	−	0.944781i	−0.985341	−	0.170593i	$-0.945432\pi$
$757$	−9.69539	−	25.9944i	−0.352385	−	0.944781i	0.632956	−	0.774187i	$-0.281841\pi$
$758$	−10.5785	−	10.5785i	−0.384229	−	0.384229i
$759$	26.1799	−	37.3286i	0.950270	−	1.35494i
$760$	−8.30577	+	6.77671i	−0.301282	+	0.245817i
$761$	−8.35745	+	18.3003i	−0.302957	+	0.663384i	−0.998480	−	0.0551205i	$-0.982446\pi$
$761$	−8.35745	+	18.3003i	−0.302957	+	0.663384i	0.695522	+	0.718504i	$0.255173\pi$
$762$	−10.4170	−	19.0774i	−0.377369	−	0.691100i
$763$	20.5959	+	1.47305i	0.745621	+	0.0533278i
$764$	−17.5406	+	11.2727i	−0.634598	+	0.407832i
$765$	−2.91958	−	0.0865467i	−0.105558	−	0.00312910i
$766$	31.4942	+	4.52818i	1.13793	+	0.163610i
$767$	13.6060	+	7.42944i	0.491284	+	0.268262i
$768$	1.96080	−	0.426545i	0.0707542	−	0.0153916i
$769$	−0.480760	−	3.34376i	−0.0173366	−	0.120579i	0.979315	−	0.202340i	$-0.0648546\pi$
$769$	−0.480760	−	3.34376i	−0.0173366	−	0.120579i	−0.996652	+	0.0817611i	$0.973946\pi$
$770$	40.3692	−	13.7087i	1.45480	−	0.494026i
$771$	21.4980	+	47.0740i	0.774231	+	1.69533i
$772$	5.98577	−	7.99605i	0.215432	−	0.287784i
$773$	−8.67571	−	39.8816i	−0.312044	−	1.43444i	−0.819656	−	0.572856i	$-0.805836\pi$
$773$	−8.67571	−	39.8816i	−0.312044	−	1.43444i	0.507613	−	0.861585i	$-0.330528\pi$
$774$	−5.21182	+	1.53033i	−0.187335	+	0.0550066i
$775$	1.87829	−	5.22873i	0.0674701	−	0.187822i
$776$	−1.55425	−	1.34676i	−0.0557942	−	0.0483459i
$777$	−10.7244	−	2.33294i	−0.384735	−	0.0836939i
$778$	−2.52803	+	35.3464i	−0.0906342	+	1.26723i
$779$	−10.7270	−	3.14973i	−0.384335	−	0.112851i
$780$	3.37317	−	5.76455i	0.120779	−	0.206404i
$781$		−	11.7033i		−	0.418779i
$782$	2.70548	+	5.46926i	0.0967479	+	0.195580i
$783$	−29.5901	+	29.5901i	−1.05747	+	1.05747i
$784$	8.36428	+	3.81984i	0.298724	+	0.136423i
$785$	−14.1131	+	5.94639i	−0.503719	+	0.212236i
$786$	3.19251	+	3.68435i	0.113873	+	0.131416i
$787$	−9.30112	+	42.7566i	−0.331549	+	1.52411i	0.445854	+	0.895105i	$0.352900\pi$
$787$	−9.30112	+	42.7566i	−0.331549	+	1.52411i	−0.777404	+	0.629002i	$0.783464\pi$
$788$	0.775481	+	10.8426i	0.0276253	+	0.386253i
$789$	5.77973	−	40.1989i	0.205764	−	1.43112i
$790$	4.87436	+	3.34070i	0.173422	+	0.118857i
$791$	5.60787	+	3.60396i	0.199393	+	0.128142i
$792$	3.89388	+	2.91493i	0.138363	+	0.103577i
$793$	−2.35053	+	6.30200i	−0.0834696	+	0.223791i
$794$	13.2265	−	6.04033i	0.469390	−	0.214363i
$795$	−1.71315	−	40.9950i	−0.0607593	−	1.45394i
$796$	−8.12536	+	12.6433i	−0.287996	+	0.448130i
$797$	−14.4220	+	26.4120i	−0.510854	+	0.935559i	0.487205	+	0.873288i	$0.338016\pi$
$797$	−14.4220	+	26.4120i	−0.510854	+	0.935559i	−0.998059	+	0.0622719i	$0.980165\pi$
$798$	−23.2000	−	30.9915i	−0.821270	−	1.09709i
$799$	−10.8436	+	12.5142i	−0.383621	+	0.442722i
$800$	−4.57302	−	2.02175i	−0.161681	−	0.0714798i
$801$	−2.99212	+	2.59269i	−0.105721	+	0.0916080i
$802$	−5.95060	+	3.24928i	−0.210123	+	0.114736i
$803$	35.0473	−	13.0720i	1.23679	−	0.461300i
$804$	−21.4290			−0.755744
$805$	−39.2802	−	17.8750i	−1.38445	−	0.630013i
$806$	1.65398			0.0582591
$807$	−10.6537	+	3.97362i	−0.375028	+	0.139878i
$808$	1.71467	−	0.936279i	0.0603217	−	0.0329382i
$809$	25.1846	−	21.8226i	0.885442	−	0.767240i	−0.0880124	−	0.996119i	$-0.528052\pi$
$809$	25.1846	−	21.8226i	0.885442	−	0.767240i	0.973455	+	0.228879i	$0.0735061\pi$
$810$	−23.4399	−	7.64395i	−0.823594	−	0.268581i
$811$	10.0184	−	11.5619i	0.351794	−	0.405992i	−0.552080	−	0.833791i	$-0.686166\pi$
$811$	10.0184	−	11.5619i	0.351794	−	0.405992i	0.903874	+	0.427800i	$0.140711\pi$
$812$	−25.4865	−	34.0460i	−0.894401	−	1.19478i
$813$	19.9656	−	36.5643i	0.700224	−	1.28237i
$814$	−3.48117	+	5.41680i	−0.122015	+	0.189859i
$815$	−32.5349	−	29.9247i	−1.13965	−	1.04822i
$816$	−2.32239	+	1.06060i	−0.0813000	+	0.0371285i
$817$	8.86369	−	23.7645i	0.310101	−	0.831414i
$818$	1.51771	+	1.13615i	0.0530656	+	0.0397244i
$819$	5.17368	+	3.32492i	0.180783	+	0.116182i
$820$	−0.956993	−	5.12613i	−0.0334196	−	0.179012i
$821$	4.39238	−	30.5497i	0.153295	−	1.06619i	−0.757352	−	0.653007i	$-0.773507\pi$
$821$	4.39238	−	30.5497i	0.153295	−	1.06619i	0.910647	−	0.413185i	$-0.135584\pi$
$822$	2.44395	+	34.1709i	0.0852426	+	1.19185i
$823$	3.09623	−	14.2331i	0.107928	−	0.496136i	−0.891170	−	0.453669i	$-0.850115\pi$
$823$	3.09623	−	14.2331i	0.107928	−	0.496136i	0.999098	−	0.0424668i	$-0.0135217\pi$
$824$	−6.91198	−	7.97685i	−0.240790	−	0.277887i
$825$	−13.9444	−	45.4437i	−0.485482	−	1.58215i
$826$	38.1245	+	17.4109i	1.32652	+	0.605802i
$827$	12.5303	−	12.5303i	0.435721	−	0.435721i	−0.454848	−	0.890569i	$-0.650307\pi$
$827$	12.5303	−	12.5303i	0.435721	−	0.435721i	0.890569	+	0.454848i	$0.150307\pi$
$828$	−0.851322	−	4.84956i	−0.0295855	−	0.168534i
$829$		−	40.9155i		−	1.42105i	−0.703671	−	0.710526i	$-0.748457\pi$
$829$		−	40.9155i		−	1.42105i	0.703671	−	0.710526i	$-0.251543\pi$
$830$	−23.9231	−	13.9988i	−0.830384	−	0.485905i
$831$	22.7137	+	6.66934i	0.787929	+	0.231357i
$832$	0.106189	−	1.48471i	0.00368143	−	0.0514731i
$833$	−11.4319	−	2.48687i	−0.396093	−	0.0861648i
$834$	15.2151	+	13.1839i	0.526855	+	0.456523i
$835$	19.9798	−	12.0190i	0.691429	−	0.415934i
$836$	−21.7924	+	6.39883i	−0.753706	+	0.221308i
$837$	−0.935292	−	4.29947i	−0.0323284	−	0.148611i
$838$	−7.39098	+	9.87319i	−0.255317	+	0.341064i
$839$	3.56158	+	7.79878i	0.122960	+	0.269244i	0.961095	−	0.276219i	$-0.0890814\pi$
$839$	3.56158	+	7.79878i	0.122960	+	0.269244i	−0.838135	+	0.545462i	$0.816354\pi$
$840$	7.98465	−	16.1960i	0.275497	−	0.558814i
$841$	11.7666	+	81.8388i	0.405746	+	2.82203i
$842$	−18.1642	+	3.95138i	−0.625979	+	0.136173i
$843$	−33.0805	−	18.0633i	−1.13935	−	0.622133i
$844$	−2.39515	−	0.344371i	−0.0824445	−	0.0118537i
$845$	16.5388	+	17.5493i	0.568953	+	0.603715i
$846$	11.2405	−	7.22382i	0.386456	−	0.248360i
$847$	45.9455	+	3.28609i	1.57871	+	0.112911i
$848$	−4.38242	−	8.02580i	−0.150493	−	0.275607i
$849$	5.36124	−	11.7395i	0.183997	−	0.402898i
$850$	6.23217	+	1.27676i	0.213762	+	0.0437924i
$851$	6.32301	−	1.58207i	0.216750	−	0.0542328i
$852$	−3.50507	−	3.50507i	−0.120082	−	0.120082i
$853$	4.10003	+	10.9926i	0.140382	+	0.376380i	0.988047	−	0.154153i	$-0.0492648\pi$
$853$	4.10003	+	10.9926i	0.140382	+	0.376380i	−0.847665	+	0.530532i	$0.821992\pi$
$854$	−5.12322	+	17.4481i	−0.175313	+	0.597061i
$855$	−9.00185	+	6.33136i	−0.307857	+	0.216528i
$856$	0.235694	+	0.366747i	0.00805585	+	0.0125352i
$857$	−7.56860	+	0.541317i	−0.258539	+	0.0184910i	−0.200007	−	0.979795i	$-0.564096\pi$
$857$	−7.56860	+	0.541317i	−0.258539	+	0.0184910i	−0.0585318	+	0.998286i	$0.518642\pi$
$858$	11.3286	−	8.48050i	0.386753	−	0.289519i
$859$	6.23301	+	21.2277i	0.212667	+	0.724279i	0.994862	+	0.101244i	$0.0322823\pi$
$859$	6.23301	+	21.2277i	0.212667	+	0.724279i	−0.782194	+	0.623035i	$0.785900\pi$
$860$	11.7549	−	1.33594i	0.400837	−	0.0455553i
$861$	18.6409	−	2.68016i	0.635280	−	0.0913395i
$862$	23.8271	+	8.88704i	0.811553	+	0.302694i
$863$	−19.9243	−	7.43137i	−0.678230	−	0.252967i	−0.0133432	−	0.999911i	$-0.504247\pi$
$863$	−19.9243	−	7.43137i	−0.678230	−	0.252967i	−0.664887	+	0.746944i	$0.731520\pi$
$864$	−3.91950	+	0.563539i	−0.133344	+	0.0191720i
$865$	23.8226	−	2.70745i	0.809994	−	0.0920561i
$866$	−7.63205	−	25.9924i	−0.259348	−	0.883256i
$867$	−24.7085	+	18.4966i	−0.839145	+	0.628176i
$868$	4.46033	−	0.319009i	0.151393	−	0.0108279i
$869$	6.76908	+	10.5329i	0.229625	+	0.357304i
$870$	−38.7857	+	27.2795i	−1.31496	+	0.924861i
$871$	−4.47834	+	15.2518i	−0.151743	+	0.516788i
$872$	−1.79307	−	4.80741i	−0.0607210	−	0.162799i
$873$	−1.49299	−	1.49299i	−0.0505299	−	0.0505299i
$874$	20.5102	+	10.3881i	0.693769	+	0.351384i
$875$	−39.8611	+	20.8685i	−1.34755	+	0.705484i
$876$	6.58147	−	14.4114i	0.222367	−	0.486916i
$877$	−1.91153	−	3.50070i	−0.0645476	−	0.118210i	0.843413	−	0.537266i	$-0.180543\pi$
$877$	−1.91153	−	3.50070i	−0.0645476	−	0.118210i	−0.907960	+	0.419056i	$0.862361\pi$
$878$	−21.7795	−	1.55770i	−0.735023	−	0.0525699i
$879$	41.0198	−	26.3618i	1.38356	−	0.889162i
$880$	−7.26576	−	7.70969i	−0.244929	−	0.259893i
$881$	−23.4396	−	3.37010i	−0.789699	−	0.113542i	−0.264348	−	0.964427i	$-0.585157\pi$
$881$	−23.4396	−	3.37010i	−0.789699	−	0.113542i	−0.525351	+	0.850886i	$0.676066\pi$
$882$	8.28567	+	4.52432i	0.278993	+	0.152342i
$883$	36.8660	−	8.01972i	1.24064	−	0.269885i	0.456081	−	0.889938i	$-0.349253\pi$
$883$	36.8660	−	8.01972i	1.24064	−	0.269885i	0.784560	+	0.620053i	$0.212889\pi$
$884$	0.269524	+	1.87458i	0.00906507	+	0.0630490i
$885$	20.6636	−	41.9139i	0.694601	−	1.40892i
$886$	9.74530	+	21.3392i	0.327400	+	0.716905i
$887$	12.7889	−	17.0839i	0.429408	−	0.573622i	−0.532695	−	0.846307i	$-0.678821\pi$
$887$	12.7889	−	17.0839i	0.429408	−	0.573622i	0.962103	+	0.272685i	$0.0879118\pi$
$888$	0.579710	+	2.66488i	0.0194538	+	0.0894276i
$889$	−41.8259	+	12.2812i	−1.40280	+	0.411898i
$890$	7.38906	−	4.44494i	0.247682	−	0.148995i
$891$	−39.4789	−	34.2086i	−1.32259	−	1.14603i
$892$	−0.238136	−	0.0518033i	−0.00797339	−	0.00173450i
$893$	−4.45093	+	62.2321i	−0.148945	+	2.08252i
$894$	0.400292	+	0.117536i	0.0133878	+	0.00393100i
$895$	42.8117	+	25.0515i	1.43104	+	0.837380i
$896$		−	4.02433i		−	0.134443i
$897$	−14.2353	−	1.59851i	−0.475302	−	0.0533727i
$898$	25.1106	−	25.1106i	0.837950	−	0.837950i
$899$	−10.6816	−	4.87811i	−0.356251	−	0.162694i
$900$	−4.53492	−	2.40531i	−0.151164	−	0.0801770i
$901$	7.61901	+	8.79280i	0.253826	+	0.292931i
$902$	2.34859	−	10.7963i	0.0781994	−	0.359477i
$903$	3.04799	+	42.6165i	0.101431	+	1.41819i
$904$	0.235737	−	1.63959i	0.00784050	−	0.0545319i
$905$	−0.945146	−	5.06267i	−0.0314177	−	0.168289i
$906$	21.9086	+	14.0798i	0.727866	+	0.467771i
$907$	5.07098	+	3.79609i	0.168379	+	0.126047i	0.680144	−	0.733078i	$-0.261917\pi$
$907$	5.07098	+	3.79609i	0.168379	+	0.126047i	−0.511765	+	0.859126i	$0.671008\pi$
$908$	0.766771	−	2.05579i	0.0254462	−	0.0682239i
$909$	1.82448	−	0.833211i	0.0605141	−	0.0276359i
$910$	−9.85859	−	9.06767i	−0.326809	−	0.300590i
$911$	−3.71384	+	5.77884i	−0.123045	+	0.191462i	−0.897311	−	0.441398i	$-0.854483\pi$
$911$	−3.71384	+	5.77884i	−0.123045	+	0.191462i	0.774266	+	0.632860i	$0.218119\pi$
$912$	−4.61028	+	8.44309i	−0.152662	+	0.279579i
$913$	−35.1944	−	47.0143i	−1.16477	−	1.55594i
$914$	−0.263425	+	0.304008i	−0.00871332	+	0.0100557i
$915$	19.2763	+	6.28618i	0.637256	+	0.207815i
$916$	20.2396	−	17.5377i	0.668736	−	0.579463i
$917$	8.58103	−	4.68560i	0.283371	−	0.154732i
$918$	4.72049	−	1.76065i	0.155799	−	0.0581101i
$919$	−51.9330			−1.71311			−0.856556	−	0.516054i	$-0.827400\pi$
$919$	−51.9330			−1.71311			−0.856556	+	0.516054i	$0.827400\pi$
$920$	0.0143820	+	10.7238i	0.000474162	+	0.353553i
$921$	53.0949			1.74954
$922$	−16.1091	+	6.00840i	−0.530526	+	0.197876i
$923$	−3.22720	+	1.76218i	−0.106224	+	0.0580029i
$924$	28.9144	−	25.0545i	0.951215	−	0.824233i
$925$	2.74773	−	6.21511i	0.0903448	−	0.204352i
$926$	−3.04770	+	3.51724i	−0.100154	+	0.115584i
$927$	−6.49398	−	8.67494i	−0.213290	−	0.284922i
$928$	−5.06465	+	9.27522i	−0.166255	+	0.304474i
$929$	−8.21304	+	12.7797i	−0.269461	+	0.419290i	−0.949443	−	0.313939i	$-0.898351\pi$
$929$	−8.21304	+	12.7797i	−0.269461	+	0.419290i	0.679982	+	0.733229i	$0.261988\pi$
$930$	−0.208173	−	4.98150i	−0.00682627	−	0.163350i
$931$	−40.0979	+	18.3121i	−1.31416	+	0.600155i
$932$	2.40309	−	6.44293i	0.0787157	−	0.211045i
$933$	−14.6990	−	11.0035i	−0.481224	−	0.360240i
$934$	−2.13136	−	1.36974i	−0.0697404	−	0.0448194i
$935$	11.1182	+	7.62000i	0.363605	+	0.249201i
$936$	0.217485	−	1.51264i	0.00710872	−	0.0494422i
$937$	0.263903	+	3.68984i	0.00862132	+	0.120542i	0.999940	−	0.0109379i	$-0.00348171\pi$
$937$	0.263903	+	3.68984i	0.00862132	+	0.120542i	−0.991319	+	0.131480i	$0.958027\pi$
$938$	−9.13515	+	41.9936i	−0.298273	+	1.37114i
$939$	−1.14969	−	1.32681i	−0.0375187	−	0.0432989i
$940$	−26.8182	+	11.2995i	−0.874713	+	0.368549i
$941$	−25.8107	−	11.7873i	−0.841404	−	0.384256i	−0.0523861	−	0.998627i	$-0.516683\pi$
$941$	−25.8107	−	11.7873i	−0.841404	−	0.384256i	−0.789017	+	0.614371i	$0.789410\pi$
$942$	−9.71810	+	9.71810i	−0.316633	+	0.316633i
$943$	−9.21702	+	6.33517i	−0.300148	+	0.206302i
$944$		−	10.4147i		−	0.338968i
$945$	−17.9962	+	30.7546i	−0.585418	+	1.00045i
$946$	24.0509	+	7.06198i	0.781962	+	0.229605i
$947$	1.14730	−	16.0413i	0.0372821	−	0.521272i	−0.944157	−	0.329497i	$-0.893121\pi$
$947$	1.14730	−	16.0413i	0.0372821	−	0.521272i	0.981439	−	0.191776i	$-0.0614246\pi$
$948$	5.18183	+	1.12724i	0.168298	+	0.0366110i
$949$	−8.88170	−	7.69603i	−0.288312	−	0.249824i
$950$	21.6812	−	10.2211i	0.703432	−	0.331617i
$951$	11.2545	−	3.30463i	0.364954	−	0.107160i
$952$	1.08839	+	5.00323i	0.0352748	+	0.162156i
$953$	−16.4115	+	21.9232i	−0.531620	+	0.710161i	−0.983295	−	0.182021i	$-0.941736\pi$
$953$	−16.4115	+	21.9232i	−0.531620	+	0.710161i	0.451674	+	0.892183i	$0.350827\pi$
$954$	−3.89999	−	8.53979i	−0.126267	−	0.276486i
$955$	44.1474	−	14.9917i	1.42857	−	0.485119i
$956$	−3.69302	−	25.6855i	−0.119441	−	0.830728i
$957$	−98.1729	+	21.3562i	−3.17348	+	0.690348i
$958$	−31.8723	−	17.4036i	−1.02975	−	0.562284i
$959$	68.0052	+	9.77767i	2.19600	+	0.315737i
$960$	−4.48505	−	0.132953i	−0.144754	−	0.00429103i
$961$	−25.0402	+	16.0923i	−0.807747	+	0.519108i
$962$	2.01785	+	0.144319i	0.0650579	+	0.00465304i
$963$	0.214501	+	0.392830i	0.00691221	+	0.0126588i
$964$	5.65750	−	12.3882i	0.182216	−	0.398997i
$965$	−17.3053	+	14.1194i	−0.557076	+	0.454521i
$966$	−38.6968	−	1.56513i	−1.24505	−	0.0503571i
$967$	29.0133	+	29.0133i	0.933004	+	0.933004i	0.997893	−	0.0648887i	$-0.0206692\pi$
$967$	29.0133	+	29.0133i	0.933004	+	0.933004i	−0.0648887	+	0.997893i	$0.520669\pi$
$968$	−4.00000	−	10.7244i	−0.128565	−	0.344696i
$969$	3.44826	−	11.7437i	0.110774	−	0.377262i
$970$	2.64556	+	3.76142i	0.0849437	+	0.120772i
$971$	31.5809	+	49.1408i	1.01348	+	1.57700i	0.799950	+	0.600067i	$0.204859\pi$
$971$	31.5809	+	49.1408i	1.01348	+	1.57700i	0.213529	+	0.976937i	$0.431504\pi$
$972$	−10.2198	+	0.730933i	−0.327799	+	0.0234447i
$973$	32.3222	−	24.1961i	1.03620	−	0.775691i
$974$	5.37982	+	18.3220i	0.172381	+	0.587075i
$975$	−10.4315	+	10.6877i	−0.334074	+	0.342279i
$976$	4.47269	−	0.643076i	0.143167	−	0.0205844i
$977$	−4.05767	−	1.51343i	−0.129816	−	0.0484190i	0.283716	−	0.958908i	$-0.408433\pi$
$977$	−4.05767	−	1.51343i	−0.129816	−	0.0484190i	−0.413533	+	0.910489i	$0.635705\pi$
$978$	−37.1678	−	13.8629i	−1.18850	−	0.443286i
$979$	18.0842	−	2.60012i	0.577974	−	0.0831000i
$980$	−16.0877	−	12.8042i	−0.513904	−	0.409014i
$981$	−1.48409	−	5.05435i	−0.0473834	−	0.161373i
$982$	27.6650	−	20.7098i	0.882826	−	0.660875i
$983$	−47.6979	+	3.41142i	−1.52133	+	0.108807i	−0.806810	−	0.590812i	$-0.798808\pi$
$983$	−47.6979	+	3.41142i	−1.52133	+	0.108807i	−0.714516	+	0.699619i	$0.753353\pi$
$984$	−2.53003	−	3.93680i	−0.0806543	−	0.125501i
$985$	4.17059	−	23.9463i	0.132886	−	0.762993i
$986$	3.78811	−	12.9011i	0.120638	−	0.410855i
$987$	−36.7281	−	98.4718i	−1.16907	−	3.13439i
$988$	5.04578	+	5.04578i	0.160528	+	0.160528i
$989$	−12.8442	−	21.8826i	−0.408421	−	0.695827i
$990$	−6.87583	−	8.42725i	−0.218528	−	0.267836i
$991$	7.14791	−	15.6517i	0.227061	−	0.497194i	−0.761472	−	0.648197i	$-0.775523\pi$
$991$	7.14791	−	15.6517i	0.227061	−	0.497194i	0.988533	+	0.151004i	$0.0482505\pi$
$992$	−0.532528	−	0.975252i	−0.0169078	−	0.0309643i
$993$	34.7319	+	2.48407i	1.10218	+	0.0788296i
$994$	−8.36296	+	5.37455i	−0.265257	+	0.170470i
$995$	24.4568	−	23.0486i	0.775333	−	0.730689i
$996$	−24.6210	−	3.53996i	−0.780145	−	0.112168i
$997$	−2.03222	−	1.10968i	−0.0643610	−	0.0351438i	0.446746	−	0.894661i	$-0.352583\pi$
$997$	−2.03222	−	1.10968i	−0.0643610	−	0.0351438i	−0.511107	+	0.859517i	$0.670765\pi$
$998$	7.07250	−	1.53853i	0.223876	−	0.0487013i
$999$	−0.765895	−	5.32692i	−0.0242319	−	0.168536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.17.8	✓	240
5.3	odd	4	inner	230.2.l.a.63.2	yes	240
23.19	odd	22	inner	230.2.l.a.157.2	yes	240
115.88	even	44	inner	230.2.l.a.203.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.8	✓	240	1.1	even	1	trivial
230.2.l.a.63.2	yes	240	5.3	odd	4	inner
230.2.l.a.157.2	yes	240	23.19	odd	22	inner
230.2.l.a.203.8	yes	240	115.88	even	44	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.936950 - 0.349464i) q^{2} +(-1.76120 + 0.961687i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-1.99344 + 1.01301i) q^{5} +(-1.31408 + 1.51653i) q^{6} +(2.41169 + 3.22164i) q^{7} +(0.479249 - 0.877679i) q^{8} +(0.555057 - 0.863686i) q^{9} +(-1.51374 + 1.64578i) q^{10} +(-4.30959 + 1.96812i) q^{11} +(-0.701254 + 1.88014i) q^{12} +(1.19161 + 0.892027i) q^{13} +(3.38548 + 2.17572i) q^{14} +(2.53665 - 3.70118i) q^{15} +(0.142315 - 0.989821i) q^{16} +(0.0907664 + 1.26908i) q^{17} +(0.218233 - 1.00320i) q^{18} +(3.13937 + 3.62302i) q^{19} +(-0.843161 + 2.07101i) q^{20} +(-7.34568 - 3.35466i) q^{21} +(-3.35008 + 3.35008i) q^{22} +(4.79353 - 0.148532i) q^{23} +2.00666i q^{24} +(2.94762 - 4.03876i) q^{25} +(1.42821 + 0.419360i) q^{26} +(0.282489 - 3.94971i) q^{27} +(3.93236 + 0.855433i) q^{28} +(-7.98668 - 6.92050i) q^{29} +(1.08328 - 4.35429i) q^{30} +(1.06616 - 0.313053i) q^{31} +(-0.212565 - 0.977147i) q^{32} +(5.69733 - 7.61074i) q^{33} +(0.528542 + 1.15734i) q^{34} +(-8.07113 - 3.97908i) q^{35} +(-0.146110 - 1.01622i) q^{36} +(1.32802 - 0.288894i) q^{37} +(4.20754 + 2.29749i) q^{38} +(-2.95651 - 0.425082i) q^{39} +(-0.0662559 + 2.23509i) q^{40} +(-1.96187 + 1.26082i) q^{41} +(-8.05487 - 0.576096i) q^{42} +(-2.53560 - 4.64360i) q^{43} +(-1.96812 + 4.30959i) q^{44} +(-0.231550 + 2.28399i) q^{45} +(4.43939 - 1.81433i) q^{46} +(9.20268 + 9.20268i) q^{47} +(0.701254 + 1.88014i) q^{48} +(-2.59060 + 8.82277i) q^{49} +(1.35037 - 4.81420i) q^{50} +(-1.38032 - 2.14781i) q^{51} +(1.48471 - 0.106189i) q^{52} +(7.32042 - 5.48000i) q^{53} +(-1.11561 - 3.79940i) q^{54} +(6.59719 - 8.28901i) q^{55} +(3.98337 - 0.572722i) q^{56} +(-9.01326 - 3.36177i) q^{57} +(-9.90159 - 3.69310i) q^{58} +(10.3086 - 1.48216i) q^{59} +(-0.506689 - 4.45832i) q^{60} +(1.27306 + 4.33565i) q^{61} +(0.889539 - 0.665901i) q^{62} +(4.12111 - 0.294748i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(-3.27904 - 0.571091i) q^{65} +(2.67843 - 9.12189i) q^{66} +(3.73192 + 10.0057i) q^{67} +(0.899668 + 0.899668i) q^{68} +(-8.29952 + 4.87147i) q^{69} +(-8.95279 - 0.907633i) q^{70} +(-1.02618 + 2.24701i) q^{71} +(-0.492028 - 0.901083i) q^{72} +(-7.87517 - 0.563243i) q^{73} +(1.14333 - 0.734775i) q^{74} +(-1.30732 + 9.94774i) q^{75} +(4.74515 + 0.682249i) q^{76} +(-16.7340 - 9.13746i) q^{77} +(-2.91865 + 0.634914i) q^{78} +(-0.376097 - 2.61582i) q^{79} +(0.719004 + 2.11732i) q^{80} +(4.58035 + 10.0296i) q^{81} +(-1.39756 + 1.86693i) q^{82} +(2.63492 + 12.1125i) q^{83} +(-7.74833 + 2.27512i) q^{84} +(-1.46653 - 2.43789i) q^{85} +(-3.99850 - 3.46472i) q^{86} +(20.7215 + 4.50769i) q^{87} +(-0.337986 + 4.72566i) q^{88} +(-3.70010 - 1.08645i) q^{89} +(0.581220 + 2.22090i) q^{90} +5.99023i q^{91} +(3.52544 - 3.25135i) q^{92} +(-1.57666 + 1.57666i) q^{93} +(11.8385 + 5.40644i) q^{94} +(-9.92830 - 4.04207i) q^{95} +(1.31408 + 1.51653i) q^{96} +(0.437154 - 2.00956i) q^{97} +(0.655981 + 9.17181i) q^{98} +(-0.692229 + 4.81456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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