LMFDB - Embedded newform 119.2.p.a.62.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,2,Mod(6,119)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("119.6"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	119.p (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.950219784053$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			62.7
Character	$\chi$	$=$	119.62
Dual form			119.2.p.a.48.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309497 + 0.128198i) q^{2} +(-2.47536 + 0.492379i) q^{3} +(-1.33486 - 1.33486i) q^{4} +(1.11993 - 1.67609i) q^{5} +(-0.829238 - 0.164946i) q^{6} +(0.495002 - 2.59903i) q^{7} +(-0.498405 - 1.20326i) q^{8} +(3.11332 - 1.28958i) q^{9} +(0.561487 - 0.375173i) q^{10} +(-4.33958 - 0.863197i) q^{11} +(3.96151 + 2.64700i) q^{12} +(-0.719092 - 0.719092i) q^{13} +(0.486393 - 0.740935i) q^{14} +(-1.94695 + 4.70036i) q^{15} +3.33925i q^{16} +(3.58606 + 2.03474i) q^{17} +1.12889 q^{18} +(0.887763 - 2.14325i) q^{19} +(-3.73230 + 0.742400i) q^{20} +(0.0544034 + 6.67727i) q^{21} +(-1.23243 - 0.823483i) q^{22} +(-0.185582 + 0.932984i) q^{23} +(1.82619 + 2.73309i) q^{24} +(0.358372 + 0.865186i) q^{25} +(-0.130371 - 0.314743i) q^{26} +(-0.776096 + 0.518571i) q^{27} +(-4.13010 + 2.80859i) q^{28} +(2.17325 - 3.25249i) q^{29} +(-1.20515 + 1.20515i) q^{30} +(-0.730122 - 3.67057i) q^{31} +(-1.42490 + 3.44000i) q^{32} +11.1670 q^{33} +(0.849027 + 1.08947i) q^{34} +(-3.80185 - 3.74040i) q^{35} +(-5.87725 - 2.43444i) q^{36} +(-1.93327 - 9.71922i) q^{37} +(0.549520 - 0.549520i) q^{38} +(2.13408 + 1.42594i) q^{39} +(-2.57495 - 0.512189i) q^{40} +(0.475427 + 0.711527i) q^{41} +(-0.839174 + 2.07357i) q^{42} +(6.12887 - 2.53866i) q^{43} +(4.64049 + 6.94498i) q^{44} +(1.32524 - 6.66245i) q^{45} +(-0.177044 + 0.264965i) q^{46} +(7.22797 + 7.22797i) q^{47} +(-1.64418 - 8.26585i) q^{48} +(-6.50995 - 2.57305i) q^{49} +0.313715i q^{50} +(-9.87865 - 3.27101i) q^{51} +1.91977i q^{52} +(11.9124 + 4.93428i) q^{53} +(-0.306679 + 0.0610023i) q^{54} +(-6.30683 + 6.30683i) q^{55} +(-3.37401 + 0.699757i) q^{56} +(-1.14224 + 5.74242i) q^{57} +(1.08958 - 0.728032i) q^{58} +(-5.38700 + 2.23137i) q^{59} +(8.87323 - 3.67541i) q^{60} +(-8.76818 + 5.85871i) q^{61} +(0.244589 - 1.22963i) q^{62} +(-1.81056 - 8.72996i) q^{63} +(3.84042 - 3.84042i) q^{64} +(-2.01060 + 0.399933i) q^{65} +(3.45617 + 1.43159i) q^{66} -10.5514i q^{67} +(-2.07080 - 7.50298i) q^{68} -2.40085i q^{69} +(-0.697151 - 1.64503i) q^{70} +(1.33343 + 6.70358i) q^{71} +(-3.10339 - 3.10339i) q^{72} +(8.14005 - 12.1824i) q^{73} +(0.647642 - 3.25591i) q^{74} +(-1.31310 - 1.96519i) q^{75} +(-4.04598 + 1.67590i) q^{76} +(-4.39158 + 10.8514i) q^{77} +(0.477687 + 0.714910i) q^{78} +(-4.04186 - 0.803976i) q^{79} +(5.59690 + 3.73973i) q^{80} +(-5.48271 + 5.48271i) q^{81} +(0.0559271 + 0.281164i) q^{82} +(-2.28169 - 0.945109i) q^{83} +(8.84059 - 8.98583i) q^{84} +(7.42655 - 3.73181i) q^{85} +2.22232 q^{86} +(-3.77810 + 9.12114i) q^{87} +(1.12422 + 5.65185i) q^{88} +(9.96197 - 9.96197i) q^{89} +(1.26427 - 1.89212i) q^{90} +(-2.22490 + 1.51299i) q^{91} +(1.49313 - 0.997677i) q^{92} +(3.61463 + 8.72648i) q^{93} +(1.31043 + 3.16365i) q^{94} +(-2.59805 - 3.88826i) q^{95} +(1.83334 - 9.21683i) q^{96} +(-4.35295 - 2.90855i) q^{97} +(-1.68495 - 1.63091i) q^{98} +(-14.6237 + 2.90883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 16 q^{2} - 16 q^{4} - 8 q^{7} - 16 q^{8} - 16 q^{9} + 8 q^{14} - 64 q^{15} + 32 q^{18} + 16 q^{21} - 48 q^{22} - 16 q^{23} - 56 q^{28} - 16 q^{29} + 112 q^{30} + 16 q^{32} - 48 q^{35} - 48 q^{36}+ \cdots + 128 q^{99}+O(q^{100}) $ 80 * q - 16 * q^2 - 16 * q^4 - 8 * q^7 - 16 * q^8 - 16 * q^9 + 8 * q^14 - 64 * q^15 + 32 * q^18 + 16 * q^21 - 48 * q^22 - 16 * q^23 - 56 * q^28 - 16 * q^29 + 112 * q^30 + 16 * q^32 - 48 * q^35 - 48 * q^36 + 48 * q^37 - 8 * q^42 - 16 * q^43 - 16 * q^44 + 16 * q^46 + 24 * q^49 - 48 * q^51 + 16 * q^53 + 112 * q^56 - 16 * q^57 - 48 * q^58 + 48 * q^60 + 112 * q^63 + 48 * q^64 - 32 * q^65 + 64 * q^70 + 16 * q^71 - 80 * q^72 - 80 * q^74 + 40 * q^77 + 112 * q^78 - 16 * q^79 - 64 * q^81 + 112 * q^85 + 48 * q^86 - 112 * q^88 - 72 * q^91 + 256 * q^92 + 48 * q^93 - 48 * q^95 - 144 * q^98 + 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{7}{16}\right)$

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 $

$2$	0.309497	+	0.128198i	0.218848	+	0.0906497i	0.489414	−	0.872052i	$-0.337211\pi$
$2$	0.309497	+	0.128198i	0.218848	+	0.0906497i	−0.270566	+	0.962701i	$0.587211\pi$
$3$	−2.47536	+	0.492379i	−1.42915	+	0.284275i	−0.848205	−	0.529669i	$-0.822316\pi$
$3$	−2.47536	+	0.492379i	−1.42915	+	0.284275i	−0.580944	+	0.813944i	$0.697316\pi$
$4$	−1.33486	−	1.33486i	−0.667430	−	0.667430i
$5$	1.11993	−	1.67609i	0.500848	−	0.749571i	−0.491787	−	0.870715i	$-0.663656\pi$
$5$	1.11993	−	1.67609i	0.500848	−	0.749571i	0.992635	+	0.121144i	$0.0386562\pi$
$6$	−0.829238	−	0.164946i	−0.338535	−	0.0673388i
$7$	0.495002	−	2.59903i	0.187093	−	0.982342i
$7$	0.495002	−	2.59903i	0.187093	−	0.982342i
$8$	−0.498405	−	1.20326i	−0.176213	−	0.425415i
$9$	3.11332	−	1.28958i	1.03777	−	0.429860i
$10$	0.561487	−	0.375173i	0.177558	−	0.118640i
$11$	−4.33958	−	0.863197i	−1.30843	−	0.260264i	−0.508869	−	0.860844i	$-0.669936\pi$
$11$	−4.33958	−	0.863197i	−1.30843	−	0.260264i	−0.799565	+	0.600580i	$0.794936\pi$
$12$	3.96151	+	2.64700i	1.14359	+	0.764122i
$13$	−0.719092	−	0.719092i	−0.199440	−	0.199440i	0.600320	−	0.799760i	$-0.295040\pi$
$13$	−0.719092	−	0.719092i	−0.199440	−	0.199440i	−0.799760	+	0.600320i	$0.795040\pi$
$14$	0.486393	−	0.740935i	0.129994	−	0.198023i
$15$	−1.94695	+	4.70036i	−0.502701	+	1.21363i
$16$			3.33925i			0.834814i
$17$	3.58606	+	2.03474i	0.869748	+	0.493497i
$17$	3.58606	+	2.03474i	0.869748	+	0.493497i
$18$	1.12889			0.266081
$19$	0.887763	−	2.14325i	0.203667	−	0.491695i	−0.788735	−	0.614733i	$-0.789264\pi$
$19$	0.887763	−	2.14325i	0.203667	−	0.491695i	0.992402	+	0.123038i	$0.0392637\pi$
$20$	−3.73230	+	0.742400i	−0.834567	+	0.166006i
$21$	0.0544034	+	6.67727i	0.0118718	+	1.45710i
$22$	−1.23243	−	0.823483i	−0.262755	−	0.175567i
$23$	−0.185582	+	0.932984i	−0.0386965	+	0.194541i	−0.995298	−	0.0968582i	$-0.969121\pi$
$23$	−0.185582	+	0.932984i	−0.0386965	+	0.194541i	0.956602	+	0.291399i	$0.0941207\pi$
$24$	1.82619	+	2.73309i	0.372769	+	0.557889i
$25$	0.358372	+	0.865186i	0.0716744	+	0.173037i
$26$	−0.130371	−	0.314743i	−0.0255678	−	0.0617262i
$27$	−0.776096	+	0.518571i	−0.149360	+	0.0997990i
$28$	−4.13010	+	2.80859i	−0.780516	+	0.530773i
$29$	2.17325	−	3.25249i	0.403562	−	0.603972i	−0.572910	−	0.819618i	$-0.694186\pi$
$29$	2.17325	−	3.25249i	0.403562	−	0.603972i	0.976472	+	0.215646i	$0.0691856\pi$
$30$	−1.20515	+	1.20515i	−0.220030	+	0.220030i
$31$	−0.730122	−	3.67057i	−0.131134	−	0.659254i	−0.989302	−	0.145885i	$-0.953397\pi$
$31$	−0.730122	−	3.67057i	−0.131134	−	0.659254i	0.858168	−	0.513369i	$-0.171603\pi$
$32$	−1.42490	+	3.44000i	−0.251888	+	0.608112i
$33$	11.1670			1.94393
$34$	0.849027	+	1.08947i	0.145607	+	0.186843i
$35$	−3.80185	−	3.74040i	−0.642631	−	0.632243i
$36$	−5.87725	−	2.43444i	−0.979542	−	0.405740i
$37$	−1.93327	−	9.71922i	−0.317828	−	1.59783i	−0.727838	−	0.685749i	$-0.759475\pi$
$37$	−1.93327	−	9.71922i	−0.317828	−	1.59783i	0.410010	−	0.912081i	$-0.365525\pi$
$38$	0.549520	−	0.549520i	0.0891440	−	0.0891440i
$39$	2.13408	+	1.42594i	0.341726	+	0.228334i
$40$	−2.57495	−	0.512189i	−0.407135	−	0.0809842i
$41$	0.475427	+	0.711527i	0.0742492	+	0.111122i	0.866736	−	0.498768i	$-0.166214\pi$
$41$	0.475427	+	0.711527i	0.0742492	+	0.111122i	−0.792487	+	0.609889i	$0.791214\pi$
$42$	−0.839174	+	2.07357i	−0.129487	+	0.319959i
$43$	6.12887	−	2.53866i	0.934644	−	0.387142i	0.137205	−	0.990543i	$-0.456188\pi$
$43$	6.12887	−	2.53866i	0.934644	−	0.387142i	0.797438	+	0.603401i	$0.206188\pi$
$44$	4.64049	+	6.94498i	0.699580	+	1.04700i
$45$	1.32524	−	6.66245i	0.197556	−	0.993179i
$46$	−0.177044	+	0.264965i	−0.0261037	+	0.0390669i
$47$	7.22797	+	7.22797i	1.05431	+	1.05431i	0.998438	+	0.0558698i	$0.0177932\pi$
$47$	7.22797	+	7.22797i	1.05431	+	1.05431i	0.0558698	+	0.998438i	$0.482207\pi$
$48$	−1.64418	−	8.26585i	−0.237317	−	1.19307i
$49$	−6.50995	−	2.57305i	−0.929992	−	0.367579i
$50$			0.313715i			0.0443661i
$51$	−9.87865	−	3.27101i	−1.38329	−	0.458033i
$52$			1.91977i			0.266225i
$53$	11.9124	+	4.93428i	1.63629	+	0.677776i	0.995916	−	0.0902836i	$-0.0287773\pi$
$53$	11.9124	+	4.93428i	1.63629	+	0.677776i	0.640379	+	0.768059i	$0.278777\pi$
$54$	−0.306679	+	0.0610023i	−0.0417338	+	0.00830136i
$55$	−6.30683	+	6.30683i	−0.850412	+	0.850412i
$56$	−3.37401	+	0.699757i	−0.450872	+	0.0935090i
$57$	−1.14224	+	5.74242i	−0.151293	+	0.760603i
$58$	1.08958	−	0.728032i	0.143068	−	0.0955952i
$59$	−5.38700	+	2.23137i	−0.701327	+	0.290499i	−0.704710	−	0.709495i	$-0.748923\pi$
$59$	−5.38700	+	2.23137i	−0.701327	+	0.290499i	0.00338321	+	0.999994i	$0.498923\pi$
$60$	8.87323	−	3.67541i	1.14553	−	0.474494i
$61$	−8.76818	+	5.85871i	−1.12265	+	0.750131i	−0.971184	−	0.238332i	$-0.923399\pi$
$61$	−8.76818	+	5.85871i	−1.12265	+	0.750131i	−0.151466	+	0.988462i	$0.548399\pi$
$62$	0.244589	−	1.22963i	0.0310628	−	0.156163i
$63$	−1.81056	−	8.72996i	−0.228109	−	1.09987i
$64$	3.84042	−	3.84042i	0.480052	−	0.480052i
$65$	−2.01060	+	0.399933i	−0.249384	+	0.0496055i
$66$	3.45617	+	1.43159i	0.425425	+	0.176217i
$67$		−	10.5514i		−	1.28905i	−0.764582	−	0.644526i	$-0.777055\pi$
$67$		−	10.5514i		−	1.28905i	0.764582	−	0.644526i	$-0.222945\pi$
$68$	−2.07080	−	7.50298i	−0.251121	−	0.909870i
$69$		−	2.40085i		−	0.289028i
$70$	−0.697151	−	1.64503i	−0.0833255	−	0.196619i
$71$	1.33343	+	6.70358i	0.158249	+	0.795569i	0.975621	+	0.219460i	$0.0704296\pi$
$71$	1.33343	+	6.70358i	0.158249	+	0.795569i	−0.817373	+	0.576109i	$0.804570\pi$
$72$	−3.10339	−	3.10339i	−0.365738	−	0.365738i
$73$	8.14005	−	12.1824i	0.952721	−	1.42585i	0.0484800	−	0.998824i	$-0.484562\pi$
$73$	8.14005	−	12.1824i	0.952721	−	1.42585i	0.904241	−	0.427023i	$-0.140438\pi$
$74$	0.647642	−	3.25591i	0.0752868	−	0.378492i
$75$	−1.31310	−	1.96519i	−0.151624	−	0.226921i
$76$	−4.04598	+	1.67590i	−0.464105	+	0.192239i
$77$	−4.39158	+	10.8514i	−0.500467	+	1.23664i
$78$	0.477687	+	0.714910i	0.0540875	+	0.0809476i
$79$	−4.04186	−	0.803976i	−0.454745	−	0.0904544i	−0.0375969	−	0.999293i	$-0.511970\pi$
$79$	−4.04186	−	0.803976i	−0.454745	−	0.0904544i	−0.417148	+	0.908839i	$0.636970\pi$
$80$	5.59690	+	3.73973i	0.625752	+	0.418114i
$81$	−5.48271	+	5.48271i	−0.609190	+	0.609190i
$82$	0.0559271	+	0.281164i	0.00617611	+	0.0310494i
$83$	−2.28169	−	0.945109i	−0.250448	−	0.103739i	0.253928	−	0.967223i	$-0.418277\pi$
$83$	−2.28169	−	0.945109i	−0.250448	−	0.103739i	−0.504376	+	0.863484i	$0.668277\pi$
$84$	8.84059	−	8.98583i	0.964588	−	0.980435i
$85$	7.42655	−	3.73181i	0.805522	−	0.404771i
$86$	2.22232			0.239639
$87$	−3.77810	+	9.12114i	−0.405055	+	0.977889i
$88$	1.12422	+	5.65185i	0.119843	+	0.602490i
$89$	9.96197	−	9.96197i	1.05597	−	1.05597i	0.0576289	−	0.998338i	$-0.481646\pi$
$89$	9.96197	−	9.96197i	1.05597	−	1.05597i	0.998338	−	0.0576289i	$-0.0183540\pi$
$90$	1.26427	−	1.89212i	0.133266	−	0.199447i
$91$	−2.22490	+	1.51299i	−0.233232	+	0.158605i
$92$	1.49313	−	0.997677i	0.155669	−	0.104015i
$93$	3.61463	+	8.72648i	0.374819	+	0.904894i
$94$	1.31043	+	3.16365i	0.135160	+	0.326305i
$95$	−2.59805	−	3.88826i	−0.266555	−	0.398927i
$96$	1.83334	−	9.21683i	0.187115	−	0.940688i
$97$	−4.35295	−	2.90855i	−0.441975	−	0.295318i	0.314601	−	0.949224i	$-0.398129\pi$
$97$	−4.35295	−	2.90855i	−0.441975	−	0.295318i	−0.756576	+	0.653906i	$0.773129\pi$
$98$	−1.68495	−	1.63091i	−0.170206	−	0.164747i
$99$	−14.6237	+	2.90883i	−1.46973	+	0.292348i
$100$	0.676526	−	1.63328i	0.0676526	−	0.163328i
$101$	−13.3542			−1.32880			−0.664398	−	0.747379i	$-0.731312\pi$
$101$	−13.3542			−1.32880			−0.664398	+	0.747379i	$0.731312\pi$
$102$	−2.63808	−	2.27879i	−0.261209	−	0.225634i
$103$			14.6476i			1.44327i	0.692276	+	0.721633i	$0.256608\pi$
$103$			14.6476i			1.44327i	−0.692276	+	0.721633i	$0.743392\pi$
$104$	−0.506853	+	1.22365i	−0.0497010	+	0.119989i
$105$	11.2526	+	7.38688i	1.09815	+	0.720886i
$106$	3.05429	+	3.05429i	0.296659	+	0.296659i
$107$	0.310987	+	0.207795i	0.0300642	+	0.0200883i	0.570512	−	0.821290i	$-0.306745\pi$
$107$	0.310987	+	0.207795i	0.0300642	+	0.0200883i	−0.540447	+	0.841378i	$0.681745\pi$
$108$	1.72820	+	0.343760i	0.166296	+	0.0330783i
$109$	−9.50043	+	6.34798i	−0.909976	+	0.608026i	−0.919998	−	0.391923i	$-0.871810\pi$
$109$	−9.50043	+	6.34798i	−0.909976	+	0.608026i	0.0100221	+	0.999950i	$0.496810\pi$
$110$	−2.76047	+	1.14342i	−0.263200	+	0.109021i
$111$	9.57109	+	23.1066i	0.908447	+	2.19319i
$112$	8.67883	+	1.65294i	0.820073	+	0.156188i
$113$	1.10240	+	0.219281i	0.103705	+	0.0206282i	0.246670	−	0.969100i	$-0.420664\pi$
$113$	1.10240	+	0.219281i	0.103705	+	0.0206282i	−0.142965	+	0.989728i	$0.545664\pi$
$114$	−1.08969	+	1.63083i	−0.102059	+	0.152741i
$115$	1.35593	+	1.35593i	0.126441	+	0.126441i
$116$	−7.24260	+	1.44064i	−0.672458	+	0.133760i
$117$	−3.16609	−	1.31144i	−0.292705	−	0.121242i
$118$	−1.95332			−0.179817
$119$	7.06346	−	8.31309i	0.647507	−	0.762060i
$120$	6.62611			0.604878
$121$	7.92421	+	3.28232i	0.720383	+	0.298392i
$122$	−3.46480	+	0.689192i	−0.313688	+	0.0623965i
$123$	−1.52719	−	1.52719i	−0.137702	−	0.137702i
$124$	−3.92509	+	5.87431i	−0.352483	+	0.527529i
$125$	11.7369	+	2.33462i	1.04978	+	0.208815i
$126$	0.558800	−	2.93401i	0.0497819	−	0.261382i
$127$	2.61124	+	6.30409i	0.231710	+	0.559398i	0.996379	−	0.0850259i	$-0.0270973\pi$
$127$	2.61124	+	6.30409i	0.231710	+	0.559398i	−0.764669	+	0.644424i	$0.777097\pi$
$128$	8.56094	−	3.54606i	0.756687	−	0.313430i
$129$	−13.9212	+	9.30182i	−1.22569	+	0.818980i
$130$	−0.673545	−	0.133976i	−0.0590738	−	0.0117505i
$131$	6.02470	+	4.02558i	0.526381	+	0.351716i	0.790193	−	0.612858i	$-0.209980\pi$
$131$	6.02470	+	4.02558i	0.526381	+	0.351716i	−0.263813	+	0.964574i	$0.584980\pi$
$132$	−14.9064	−	14.9064i	−1.29744	−	1.29744i
$133$	−5.13093	−	3.36824i	−0.444908	−	0.292063i
$134$	1.35266	−	3.26561i	0.116852	−	0.282106i
$135$			1.88157i			0.161940i
$136$	0.661003	−	5.32908i	0.0566805	−	0.456964i
$137$	−8.26733			−0.706326			−0.353163	−	0.935562i	$-0.614894\pi$
$137$	−8.26733			−0.706326			−0.353163	+	0.935562i	$0.614894\pi$
$138$	0.307784	−	0.743055i	0.0262003	−	0.0632531i
$139$	20.1083	−	3.99980i	1.70557	−	0.339258i	0.756419	−	0.654088i	$-0.226947\pi$
$139$	20.1083	−	3.99980i	1.70557	−	0.339258i	0.949148	+	0.314829i	$0.101947\pi$
$140$	0.0820284	+	10.0679i	0.00693267	+	0.850889i
$141$	−21.4507	−	14.3329i	−1.80648	−	1.20705i
$142$	−0.446694	+	2.24568i	−0.0374857	+	0.188454i
$143$	2.49984	+	3.74128i	0.209047	+	0.312861i
$144$	4.30623	+	10.3962i	0.358853	+	0.866347i
$145$	−3.01760	−	7.28512i	−0.250598	−	0.604996i
$146$	4.08109	−	2.72690i	0.337753	−	0.225680i
$147$	17.3814	+	3.16386i	1.43359	+	0.260951i
$148$	−10.3932	+	15.5544i	−0.854312	+	1.27857i
$149$	0.288666	−	0.288666i	0.0236484	−	0.0236484i	−0.695184	−	0.718832i	$-0.744677\pi$
$149$	0.288666	−	0.288666i	0.0236484	−	0.0236484i	0.718832	+	0.695184i	$0.244677\pi$
$150$	−0.154467	−	0.776558i	−0.0126122	−	0.0634057i
$151$	3.66571	−	8.84981i	0.298311	−	0.720187i	−0.701659	−	0.712513i	$-0.747557\pi$
$151$	3.66571	−	8.84981i	0.298311	−	0.720187i	0.999971	−	0.00767447i	$-0.00244288\pi$
$152$	−3.02134			−0.245063
$153$	13.7885	+	1.71029i	1.11474	+	0.138268i
$154$	−2.75031	+	2.79550i	−0.221627	+	0.225268i
$155$	−6.96991	−	2.88703i	−0.559836	−	0.231892i
$156$	−0.945257	−	4.75213i	−0.0756811	−	0.380475i
$157$	12.8092	−	12.8092i	1.02229	−	1.02229i	0.0225409	−	0.999746i	$-0.492824\pi$
$157$	12.8092	−	12.8092i	1.02229	−	1.02229i	0.999746	−	0.0225409i	$-0.00717558\pi$
$158$	−1.14788	−	0.766987i	−0.0913202	−	0.0610182i
$159$	−31.9170	−	6.34869i	−2.53118	−	0.503484i
$160$	4.16998	+	6.24082i	0.329666	+	0.493380i
$161$	2.33299	+	0.944163i	0.183866	+	0.0744104i
$162$	−2.39976	+	0.994012i	−0.188543	+	0.0780970i
$163$	0.674796	+	1.00990i	0.0528541	+	0.0791018i	0.856955	−	0.515390i	$-0.172353\pi$
$163$	0.674796	+	1.00990i	0.0528541	+	0.0791018i	−0.804101	+	0.594492i	$0.797353\pi$
$164$	0.315160	−	1.58442i	0.0246099	−	0.123722i
$165$	12.5063	−	18.7170i	0.973614	−	1.45712i
$166$	−0.585017	−	0.585017i	−0.0454061	−	0.0454061i
$167$	−1.21609	−	6.11371i	−0.0941040	−	0.473093i	−0.998885	−	0.0472151i	$-0.984965\pi$
$167$	−1.21609	−	6.11371i	−0.0941040	−	0.473093i	0.904781	−	0.425878i	$-0.140035\pi$
$168$	8.00735	−	3.39344i	0.617780	−	0.261810i
$169$		−	11.9658i		−	0.920447i
$170$	2.77691	−	0.202915i	0.212979	−	0.0155629i
$171$		−	7.81746i		−	0.597816i
$172$	−11.5699	−	4.79242i	−0.882199	−	0.365419i
$173$	−14.1607	+	2.81674i	−1.07662	+	0.214153i	−0.701389	−	0.712779i	$-0.747436\pi$
$173$	−14.1607	+	2.81674i	−1.07662	+	0.214153i	−0.375230	+	0.926932i	$0.622436\pi$
$174$	−2.33862	+	2.33862i	−0.177291	+	0.177291i
$175$	2.42604	−	0.503152i	0.183392	−	0.0380347i
$176$	2.88243	−	14.4910i	0.217272	−	1.09230i
$177$	12.2361	−	8.17588i	0.919719	−	0.614537i
$178$	4.36031	−	1.80610i	0.326819	−	0.135373i
$179$	−6.44165	+	2.66822i	−0.481472	+	0.199432i	−0.610199	−	0.792248i	$-0.708911\pi$
$179$	−6.44165	+	2.66822i	−0.481472	+	0.199432i	0.128728	+	0.991680i	$0.458911\pi$
$180$	−10.6624	+	7.12442i	−0.794732	+	0.531023i
$181$	−1.46307	+	7.35534i	−0.108749	+	0.546718i	0.887546	+	0.460719i	$0.152408\pi$
$181$	−1.46307	+	7.35534i	−0.108749	+	0.546718i	−0.996295	+	0.0859995i	$0.972592\pi$
$182$	−0.882562	+	0.183040i	−0.0654198	+	0.0135678i
$183$	18.8197	−	18.8197i	1.39119	−	1.39119i
$184$	1.21511	−	0.241701i	0.0895794	−	0.0178184i
$185$	−18.4554	−	7.64450i	−1.35687	−	0.562035i
$186$			3.16421i			0.232011i
$187$	−13.8056	−	11.9254i	−1.00957	−	0.872072i
$188$		−	19.2967i		−	1.40735i
$189$	0.963614	+	2.27379i	0.0700926	+	0.165394i
$190$	−0.305623	−	1.53647i	−0.0221722	−	0.111467i
$191$	2.66439	+	2.66439i	0.192788	+	0.192788i	0.796900	−	0.604111i	$-0.206472\pi$
$191$	2.66439	+	2.66439i	0.192788	+	0.192788i	−0.604111	+	0.796900i	$0.706472\pi$
$192$	−7.61546	+	11.3973i	−0.549599	+	0.822532i
$193$	−4.05029	+	20.3622i	−0.291546	+	1.46570i	0.506047	+	0.862506i	$0.331106\pi$
$193$	−4.05029	+	20.3622i	−0.291546	+	1.46570i	−0.797593	+	0.603195i	$0.793894\pi$
$194$	−0.974356	−	1.45823i	−0.0699547	−	0.104695i
$195$	4.78003	−	1.97995i	0.342305	−	0.141787i
$196$	5.25520	+	12.1245i	0.375372	+	0.866038i
$197$	11.7306	+	17.5561i	0.835771	+	1.25082i	0.965795	+	0.259308i	$0.0834946\pi$
$197$	11.7306	+	17.5561i	0.835771	+	1.25082i	−0.130024	+	0.991511i	$0.541505\pi$
$198$	−4.89889	−	0.974451i	−0.348149	−	0.0692512i
$199$	11.5410	+	7.71146i	0.818121	+	0.546651i	0.892746	−	0.450561i	$-0.148776\pi$
$199$	11.5410	+	7.71146i	0.818121	+	0.546651i	−0.0746248	+	0.997212i	$0.523776\pi$
$200$	0.862427	−	0.862427i	0.0609828	−	0.0609828i
$201$	5.19527	+	26.1184i	0.366446	+	1.84225i
$202$	−4.13310	−	1.71199i	−0.290804	−	0.120455i
$203$	−7.37757	−	7.25833i	−0.517804	−	0.509435i
$204$	8.82027	+	17.5529i	0.617543	+	1.22895i
$205$	1.72503			0.120481
$206$	−1.87779	+	4.53338i	−0.130832	+	0.315855i
$207$	0.625380	+	3.14400i	0.0434669	+	0.218523i
$208$	2.40123	−	2.40123i	0.166495	−	0.166495i
$209$	−5.70257	+	8.53450i	−0.394455	+	0.590343i
$210$	2.53568	+	3.72879i	0.174979	+	0.257311i
$211$	−2.83065	+	1.89138i	−0.194870	+	0.130208i	−0.649177	−	0.760637i	$-0.724887\pi$
$211$	−2.83065	+	1.89138i	−0.194870	+	0.130208i	0.454308	+	0.890845i	$0.349887\pi$
$212$	−9.31482	−	22.4880i	−0.639744	−	1.54448i
$213$	−6.60141	−	15.9372i	−0.452321	−	1.09200i
$214$	0.0696107	+	0.104180i	0.00475849	+	0.00712158i
$215$	2.60887	−	13.1157i	0.177923	−	0.894481i
$216$	1.01078	+	0.675384i	0.0687751	+	0.0459541i
$217$	−9.90135	+	0.0806718i	−0.672148	+	0.00547636i
$218$	−3.75415	+	0.746748i	−0.254263	+	0.0505761i
$219$	−14.1512	+	34.1639i	−0.956246	+	2.30858i
$220$	16.8375			1.13518
$221$	−1.11554	−	4.04187i	−0.0750395	−	0.271886i
$222$			8.37844i			0.562324i
$223$	1.86869	−	4.51141i	0.125137	−	0.302107i	−0.848879	−	0.528587i	$-0.822722\pi$
$223$	1.86869	−	4.51141i	0.125137	−	0.302107i	0.974016	+	0.226481i	$0.0727220\pi$
$224$	8.23536	+	5.40616i	0.550248	+	0.361214i
$225$	2.23145	+	2.23145i	0.148764	+	0.148764i
$226$	0.313078	+	0.209192i	0.0208257	+	0.0139153i
$227$	−2.65461	−	0.528034i	−0.176192	−	0.0350468i	0.106206	−	0.994344i	$-0.466130\pi$
$227$	−2.65461	−	0.528034i	−0.176192	−	0.0350468i	−0.282398	+	0.959297i	$0.591130\pi$
$228$	9.19006	−	6.14060i	0.608627	−	0.406671i
$229$	−12.5990	+	5.21868i	−0.832565	+	0.344860i	−0.757918	−	0.652350i	$-0.773783\pi$
$229$	−12.5990	+	5.21868i	−0.832565	+	0.344860i	−0.0746476	+	0.997210i	$0.523783\pi$
$230$	0.245829	+	0.593484i	0.0162095	+	0.0391332i
$231$	5.52771	−	29.0235i	0.363696	−	1.90961i
$232$	−4.99674	−	0.993913i	−0.328052	−	0.0652536i
$233$	−0.246802	+	0.369366i	−0.0161686	+	0.0241980i	−0.839466	−	0.543412i	$-0.817132\pi$
$233$	−0.246802	+	0.369366i	−0.0161686	+	0.0241980i	0.823297	+	0.567610i	$0.192132\pi$
$234$	−0.811772	−	0.811772i	−0.0530672	−	0.0530672i
$235$	20.2096	−	4.01993i	1.31833	−	0.262231i
$236$	10.1694	+	4.21232i	0.661975	+	0.274199i
$237$	10.4009			0.675612
$238$	3.25184	−	1.66736i	0.210786	−	0.108079i
$239$	6.21322			0.401900			0.200950	−	0.979602i	$-0.435597\pi$
$239$	6.21322			0.401900			0.200950	+	0.979602i	$0.435597\pi$
$240$	−15.6957	−	6.50137i	−1.01315	−	0.419662i
$241$	8.59997	−	1.71064i	0.553973	−	0.110192i	0.0898377	−	0.995956i	$-0.471365\pi$
$241$	8.59997	−	1.71064i	0.553973	−	0.110192i	0.464135	+	0.885764i	$0.346365\pi$
$242$	2.03174	+	2.03174i	0.130605	+	0.130605i
$243$	12.4278	−	18.5995i	0.797245	−	1.19316i
$244$	19.5248	+	3.88373i	1.24995	+	0.248630i
$245$	−11.6034	+	8.02964i	−0.741311	+	0.512995i
$246$	−0.276879	−	0.668445i	−0.0176532	−	0.0426185i
$247$	−2.17958	+	0.902810i	−0.138683	+	0.0574444i
$248$	−4.05274	+	2.70796i	−0.257349	+	0.171955i
$249$	6.11336	+	1.21602i	0.387419	+	0.0770623i
$250$	3.33325	+	2.22721i	0.210813	+	0.140861i
$251$	9.03734	+	9.03734i	0.570432	+	0.570432i	0.932249	−	0.361817i	$-0.117843\pi$
$251$	9.03734	+	9.03734i	0.570432	+	0.570432i	−0.361817	+	0.932249i	$0.617843\pi$
$252$	−9.23643	+	14.0701i	−0.581841	+	0.886334i
$253$	1.61070	−	3.88857i	0.101264	−	0.244472i
$254$			2.28586i			0.143427i
$255$	−16.5459	+	12.8942i	−1.03614	+	0.807468i
$256$	−7.75815			−0.484885
$257$	−0.513388	+	1.23943i	−0.0320243	+	0.0773134i	−0.939083	−	0.343692i	$-0.888323\pi$
$257$	−0.513388	+	1.23943i	−0.0320243	+	0.0773134i	0.907058	+	0.421005i	$0.138323\pi$
$258$	−5.50103	+	1.09422i	−0.342479	+	0.0681234i
$259$	−26.2176	+	0.213609i	−1.62908	+	0.0132730i
$260$	3.21772	+	2.15001i	0.199554	+	0.133338i
$261$	2.57166	−	12.9286i	0.159182	−	0.800261i
$262$	1.34856	+	2.01826i	0.0833142	+	0.124688i
$263$	−1.20208	−	2.90207i	−0.0741232	−	0.178949i	0.882475	−	0.470359i	$-0.155876\pi$
$263$	−1.20208	−	2.90207i	−0.0741232	−	0.178949i	−0.956598	+	0.291410i	$0.905876\pi$
$264$	−5.56571	−	13.4368i	−0.342546	−	0.826979i
$265$	21.6114	−	14.4403i	1.32758	−	0.887058i
$266$	−1.15621	−	1.70024i	−0.0708917	−	0.104248i
$267$	−19.7544	+	29.5645i	−1.20895	+	1.80932i
$268$	−14.0846	+	14.0846i	−0.860352	+	0.860352i
$269$	−1.37736	−	6.92445i	−0.0839791	−	0.422191i	−0.999788	−	0.0205777i	$-0.993449\pi$
$269$	−1.37736	−	6.92445i	−0.0839791	−	0.422191i	0.915809	−	0.401614i	$-0.131551\pi$
$270$	−0.241214	+	0.582341i	−0.0146798	+	0.0354402i
$271$	1.36091			0.0826693			0.0413347	−	0.999145i	$-0.486839\pi$
$271$	1.36091			0.0826693			0.0413347	+	0.999145i	$0.486839\pi$
$272$	−6.79451	+	11.9748i	−0.411978	+	0.726077i
$273$	4.76245	−	4.84069i	0.288236	−	0.292972i
$274$	−2.55872	−	1.05985i	−0.154578	−	0.0640282i
$275$	−0.808359	−	4.06390i	−0.0487459	−	0.245062i
$276$	−3.20479	+	3.20479i	−0.192906	+	0.192906i
$277$	16.7979	+	11.2240i	1.00929	+	0.674384i	0.946186	−	0.323623i	$-0.104901\pi$
$277$	16.7979	+	11.2240i	1.00929	+	0.674384i	0.0631007	+	0.998007i	$0.479901\pi$
$278$	6.73624	+	1.33992i	0.404013	+	0.0803632i
$279$	−7.00660	−	10.4861i	−0.419474	−	0.627787i
$280$	−2.60580	+	6.43884i	−0.155726	+	0.384794i
$281$	9.10111	−	3.76980i	0.542927	−	0.224888i	−0.0943276	−	0.995541i	$-0.530070\pi$
$281$	9.10111	−	3.76980i	0.542927	−	0.224888i	0.637254	+	0.770654i	$0.280070\pi$
$282$	−4.80149	−	7.18593i	−0.285924	−	0.427916i
$283$	−2.77576	+	13.9547i	−0.165002	+	0.829520i	0.806270	+	0.591548i	$0.201483\pi$
$283$	−2.77576	+	13.9547i	−0.165002	+	0.829520i	−0.971272	+	0.237973i	$0.923517\pi$
$284$	7.16841	−	10.7283i	0.425367	−	0.636606i
$285$	8.34561	+	8.34561i	0.494351	+	0.494351i
$286$	0.294070	+	1.47839i	0.0173887	+	0.0874190i
$287$	2.08462	−	0.883443i	0.123051	−	0.0521480i
$288$			12.5473i			0.739359i
$289$	8.71967	+	14.5934i	0.512922	+	0.858436i
$290$		−	2.64158i		−	0.155119i
$291$	12.2072	+	5.05640i	0.715600	+	0.296411i
$292$	−27.1277	+	5.39603i	−1.58753	+	0.315779i
$293$	−18.6006	+	18.6006i	−1.08666	+	1.08666i	−0.0907866	+	0.995870i	$0.528938\pi$
$293$	−18.6006	+	18.6006i	−1.08666	+	1.08666i	−0.995870	+	0.0907866i	$0.971062\pi$
$294$	4.97388	+	3.20746i	0.290083	+	0.187063i
$295$	−2.29308	+	11.5281i	−0.133508	+	0.671191i
$296$	−10.7312	+	7.17033i	−0.623736	+	0.416767i
$297$	3.81556	−	1.58046i	0.221401	−	0.0917075i
$298$	0.126348	−	0.0523350i	0.00731913	−	0.00303168i
$299$	0.804352	−	0.537451i	0.0465169	−	0.0310816i
$300$	−0.870452	+	4.37606i	−0.0502556	+	0.252652i
$301$	−3.56426	−	17.1858i	−0.205441	−	0.990571i
$302$	2.26905	−	2.26905i	0.130569	−	0.130569i
$303$	33.0565	−	6.57535i	1.89905	−	0.377744i
$304$	7.15685	+	2.96447i	0.410474	+	0.170024i
$305$			21.2576i			1.21721i
$306$	4.04825	+	2.29699i	0.231423	+	0.131310i
$307$			5.73107i			0.327090i	0.986536	+	0.163545i	$0.0522928\pi$
$307$			5.73107i			0.327090i	−0.986536	+	0.163545i	$0.947707\pi$
$308$	20.3473	−	8.62301i	1.15939	−	0.491341i
$309$	−7.21215	−	36.2579i	−0.410285	−	2.06264i
$310$	−1.78706	−	1.78706i	−0.101498	−	0.101498i
$311$	1.13717	−	1.70189i	0.0644830	−	0.0965056i	−0.797827	−	0.602887i	$-0.794017\pi$
$311$	1.13717	−	1.70189i	0.0644830	−	0.0965056i	0.862310	+	0.506381i	$0.169017\pi$
$312$	0.652142	−	3.27854i	0.0369202	−	0.185611i
$313$	8.85417	+	13.2512i	0.500467	+	0.749002i	0.992588	−	0.121525i	$-0.0387783\pi$
$313$	8.85417	+	13.2512i	0.500467	+	0.749002i	−0.492121	+	0.870527i	$0.663778\pi$
$314$	5.60653	−	2.32230i	0.316395	−	0.131055i
$315$	−16.6599	−	6.74228i	−0.938681	−	0.379884i
$316$	4.32212	+	6.46851i	0.243138	+	0.363882i
$317$	−26.6501	−	5.30104i	−1.49682	−	0.297736i	−0.622321	−	0.782762i	$-0.713810\pi$
$317$	−26.6501	−	5.30104i	−1.49682	−	0.297736i	−0.874500	+	0.485026i	$0.838810\pi$
$318$	−9.06434	−	6.05660i	−0.508303	−	0.339637i
$319$	−12.2385	+	12.2385i	−0.685226	+	0.685226i
$320$	−2.13590	−	10.7379i	−0.119400	−	0.600266i
$321$	−0.872117	−	0.361243i	−0.0486768	−	0.0201626i
$322$	0.601015	+	0.591301i	0.0334933	+	0.0329519i
$323$	7.54453	−	5.87945i	0.419789	−	0.327142i
$324$	14.6373			0.813184
$325$	0.364446	−	0.879851i	0.0202158	−	0.0488053i
$326$	0.0793800	+	0.399070i	0.00439645	+	0.0221024i
$327$	20.3913	−	20.3913i	1.12764	−	1.12764i
$328$	0.619194	−	0.926689i	0.0341893	−	0.0511678i
$329$	22.3636	−	15.2079i	1.23294	−	0.838437i
$330$	6.27015	−	4.18958i	0.345160	−	0.230629i
$331$	−3.13132	−	7.55968i	−0.172113	−	0.415517i	0.814160	−	0.580641i	$-0.197198\pi$
$331$	−3.13132	−	7.55968i	−0.172113	−	0.415517i	−0.986273	+	0.165123i	$0.947198\pi$
$332$	1.78415	+	4.30733i	0.0979182	+	0.236395i
$333$	−18.5526	−	27.7659i	−1.01668	−	1.52156i
$334$	0.407388	−	2.04808i	0.0222913	−	0.112066i
$335$	−17.6850	−	11.8168i	−0.966237	−	0.645619i
$336$	−22.2971	+	0.181667i	−1.21641	+	0.00991073i
$337$	10.1119	−	2.01138i	0.550829	−	0.109567i	0.0881739	−	0.996105i	$-0.471897\pi$
$337$	10.1119	−	2.01138i	0.550829	−	0.109567i	0.462655	+	0.886538i	$0.346897\pi$
$338$	1.53399	−	3.70339i	0.0834382	−	0.201438i
$339$	−2.83680			−0.154074
$340$	−14.8948	−	4.93196i	−0.807786	−	0.267473i
$341$			16.5590i			0.896720i
$342$	1.00218	−	2.41948i	0.0541918	−	0.130831i
$343$	−9.90988	+	15.6459i	−0.535083	+	0.844799i
$344$	−6.10932	−	6.10932i	−0.329392	−	0.329392i
$345$	−4.02404	−	2.68878i	−0.216647	−	0.144759i
$346$	−4.74380	−	0.943601i	−0.255029	−	0.0507283i
$347$	16.9416	−	11.3200i	0.909474	−	0.607691i	−0.0103826	−	0.999946i	$-0.503305\pi$
$347$	16.9416	−	11.3200i	0.909474	−	0.607691i	0.919856	+	0.392255i	$0.128305\pi$
$348$	17.2187	−	7.13221i	0.923018	−	0.382327i
$349$	−9.93559	−	23.9866i	−0.531840	−	1.28398i	−0.930303	−	0.366791i	$-0.880456\pi$
$349$	−9.93559	−	23.9866i	−0.531840	−	1.28398i	0.398463	−	0.917184i	$-0.369544\pi$
$350$	0.815357	+	0.155290i	0.0435827	+	0.00830058i
$351$	0.930984	+	0.185184i	0.0496923	+	0.00988441i
$352$	9.15286	−	13.6982i	0.487849	−	0.730117i
$353$	13.4642	+	13.4642i	0.716629	+	0.716629i	0.967913	−	0.251284i	$-0.0808528\pi$
$353$	13.4642	+	13.4642i	0.716629	+	0.716629i	−0.251284	+	0.967913i	$0.580853\pi$
$354$	4.83516	−	0.961773i	0.256986	−	0.0511177i
$355$	12.7292	+	5.27260i	0.675594	+	0.279840i
$356$	−26.5957			−1.40957
$357$	−13.3914	+	24.0558i	−0.708748	+	1.27317i
$358$	−2.33573			−0.123447
$359$	8.42132	+	3.48822i	0.444460	+	0.184101i	0.593678	−	0.804703i	$-0.297675\pi$
$359$	8.42132	+	3.48822i	0.444460	+	0.184101i	−0.149217	+	0.988804i	$0.547675\pi$
$360$	−8.67714	+	1.72599i	−0.457326	+	0.0909677i
$361$	9.62964	+	9.62964i	0.506823	+	0.506823i
$362$	−1.39576	+	2.08890i	−0.0733593	+	0.109790i
$363$	−21.2314	−	4.22319i	−1.11436	−	0.221660i
$364$	4.98955	+	0.950291i	0.261524	+	0.0498088i
$365$	−11.3026	−	27.2870i	−0.591607	−	1.42826i
$366$	8.23728	−	3.41199i	0.430569	−	0.178348i
$367$	14.3722	−	9.60319i	0.750222	−	0.501282i	−0.120709	−	0.992688i	$-0.538517\pi$
$367$	14.3722	−	9.60319i	0.750222	−	0.501282i	0.870931	+	0.491406i	$0.163517\pi$
$368$	−3.11547	−	0.619706i	−0.162405	−	0.0323044i
$369$	2.39773	+	1.60211i	0.124821	+	0.0834025i
$370$	−4.73190	−	4.73190i	−0.246000	−	0.246000i
$371$	18.7210	−	28.5183i	0.971947	−	1.48059i
$372$	6.82361	−	16.4737i	0.353788	−	0.854119i
$373$			14.1872i			0.734584i	0.930106	+	0.367292i	$0.119715\pi$
$373$			14.1872i			0.734584i	−0.930106	+	0.367292i	$0.880285\pi$
$374$	−2.74399	−	5.46073i	−0.141889	−	0.282368i
$375$	−30.2026			−1.55965
$376$	5.09464	−	12.2996i	0.262736	−	0.634301i
$377$	−3.90160	+	0.776077i	−0.200943	+	0.0399700i
$378$	0.00674020	+	0.827266i	0.000346678	+	0.0425500i
$379$	−5.56998	−	3.72174i	−0.286111	−	0.191173i	0.404230	−	0.914657i	$-0.367539\pi$
$379$	−5.56998	−	3.72174i	−0.286111	−	0.191173i	−0.690341	+	0.723484i	$0.742539\pi$
$380$	−1.72225	+	8.65832i	−0.0883494	+	0.444162i
$381$	−9.56776	−	14.3192i	−0.490171	−	0.733593i
$382$	0.483052	+	1.16619i	0.0247151	+	0.0596675i
$383$	−9.09883	−	21.9665i	−0.464929	−	1.12244i	−0.966349	−	0.257234i	$-0.917189\pi$
$383$	−9.09883	−	21.9665i	−0.464929	−	1.12244i	0.501421	−	0.865204i	$-0.332811\pi$
$384$	−19.4454	+	12.9930i	−0.992318	+	0.663046i
$385$	13.2698	+	19.5135i	0.676290	+	0.994502i
$386$	−3.86394	+	5.78280i	−0.196669	+	0.294337i
$387$	15.8073	−	15.8073i	0.803531	−	0.803531i
$388$	1.92807	+	9.69308i	0.0978831	+	0.492092i
$389$	3.24875	−	7.84318i	0.164718	−	0.397665i	−0.819871	−	0.572549i	$-0.805955\pi$
$389$	3.24875	−	7.84318i	0.164718	−	0.397665i	0.984589	+	0.174883i	$0.0559548\pi$
$390$	1.73323			0.0877656
$391$	−2.56389	+	2.96813i	−0.129661	+	0.150105i
$392$	0.148549	+	9.11556i	0.00750285	+	0.460405i
$393$	−16.8954	−	6.99830i	−0.852260	−	0.353018i
$394$	1.37993	+	6.93740i	0.0695201	+	0.349501i
$395$	−5.87414	+	5.87414i	−0.295560	+	0.295560i
$396$	23.4034	+	15.6377i	1.17607	+	0.785823i
$397$	1.70637	+	0.339418i	0.0856401	+	0.0170349i	0.237724	−	0.971333i	$-0.423599\pi$
$397$	1.70637	+	0.339418i	0.0856401	+	0.0170349i	−0.152084	+	0.988368i	$0.548599\pi$
$398$	2.58332	+	3.86621i	0.129490	+	0.193796i
$399$	14.3593	+	5.81123i	0.718866	+	0.290925i
$400$	−2.88908	+	1.19670i	−0.144454	+	0.0598348i
$401$	−0.535755	−	0.801814i	−0.0267543	−	0.0400407i	0.817851	−	0.575429i	$-0.195165\pi$
$401$	−0.535755	−	0.801814i	−0.0267543	−	0.0400407i	−0.844606	+	0.535389i	$0.820165\pi$
$402$	−1.74040	+	8.74959i	−0.0868033	+	0.436390i
$403$	−2.11445	+	3.16450i	−0.105328	+	0.157635i
$404$	17.8260	+	17.8260i	0.886878	+	0.886878i
$405$	3.04928	+	15.3298i	0.151520	+	0.761743i
$406$	−1.35284	−	3.19222i	−0.0671401	−	0.158427i
$407$			43.8462i			2.17337i
$408$	0.987708	+	13.5168i	0.0488988	+	0.669183i
$409$		−	10.9872i		−	0.543281i	−0.962399	−	0.271641i	$-0.912434\pi$
$409$		−	10.9872i		−	0.543281i	0.962399	−	0.271641i	$-0.0875662\pi$
$410$	0.533892	+	0.221145i	0.0263670	+	0.0109216i
$411$	20.4646	−	4.07066i	1.00944	−	0.200791i
$412$	19.5524	−	19.5524i	0.963279	−	0.963279i
$413$	3.13282	+	15.1055i	0.154156	+	0.743294i
$414$	−0.209501	+	1.05323i	−0.0102964	+	0.0517635i
$415$	−4.13943	+	2.76588i	−0.203196	+	0.135772i
$416$	3.49831	−	1.44905i	0.171519	−	0.0710454i
$417$	−47.8059	+	19.8019i	−2.34107	+	0.969701i
$418$	−2.85903	+	1.91035i	−0.139840	+	0.0934381i
$419$	−4.51126	+	22.6796i	−0.220390	+	1.10797i	0.699150	+	0.714975i	$0.253562\pi$
$419$	−4.51126	+	22.6796i	−0.220390	+	1.10797i	−0.919539	+	0.392998i	$0.871438\pi$
$420$	−5.16025	−	24.8811i	−0.251795	−	1.21408i
$421$	2.85847	−	2.85847i	0.139313	−	0.139313i	−0.634011	−	0.773324i	$-0.718593\pi$
$421$	2.85847	−	2.85847i	0.139313	−	0.139313i	0.773324	+	0.634011i	$0.218593\pi$
$422$	−1.11855	+	0.222493i	−0.0544501	+	0.0108308i
$423$	31.8240	+	13.1819i	1.54734	+	0.640928i
$424$		−	16.7930i		−	0.815538i
$425$	−0.475286	+	3.83181i	−0.0230547	+	0.185870i
$426$		−	5.77881i		−	0.279984i
$427$	10.8867	+	25.6889i	0.526845	+	1.24317i
$428$	−0.137747	−	0.692500i	−0.00665825	−	0.0334733i
$429$	−8.03013	−	8.03013i	−0.387698	−	0.387698i
$430$	2.48884	−	3.72481i	0.120023	−	0.179626i
$431$	0.806657	−	4.05534i	0.0388553	−	0.195339i	−0.956482	−	0.291790i	$-0.905749\pi$
$431$	0.806657	−	4.05534i	0.0388553	−	0.195339i	0.995338	+	0.0964511i	$0.0307491\pi$
$432$	−1.73164	−	2.59158i	−0.0833136	−	0.124688i
$433$	−13.3279	+	5.52060i	−0.640499	+	0.265303i	−0.679206	−	0.733947i	$-0.737676\pi$
$433$	−13.3279	+	5.52060i	−0.640499	+	0.265303i	0.0387077	+	0.999251i	$0.487676\pi$
$434$	−3.07478	−	1.24437i	−0.147594	−	0.0597315i
$435$	11.0567	+	16.5475i	0.530127	+	0.793391i
$436$	21.1554	+	4.20807i	1.01316	+	0.201530i
$437$	1.83486	+	1.22602i	0.0877735	+	0.0586483i
$438$	−8.75949	+	8.75949i	−0.418544	+	0.418544i
$439$	1.45468	+	7.31318i	0.0694282	+	0.349039i	0.999848	−	0.0174575i	$-0.00555719\pi$
$439$	1.45468	+	7.31318i	0.0694282	+	0.349039i	−0.930419	+	0.366496i	$0.880557\pi$
$440$	10.7321	+	4.44537i	0.511632	+	0.211925i
$441$	−23.5857	+	0.384357i	−1.12313	+	0.0183027i
$442$	0.172903	−	1.39396i	0.00822413	−	0.0663039i
$443$	−2.24379			−0.106606			−0.0533029	−	0.998578i	$-0.516975\pi$
$443$	−2.24379			−0.106606			−0.0533029	+	0.998578i	$0.516975\pi$
$444$	18.0681	−	43.6202i	0.857473	−	2.07012i
$445$	−5.54048	−	27.8539i	−0.262644	−	1.32040i
$446$	1.15671	−	1.15671i	0.0547717	−	0.0547717i
$447$	−0.572418	+	0.856685i	−0.0270745	+	0.0405198i
$448$	−8.08036	−	11.8824i	−0.381761	−	0.561390i
$449$	−26.9497	+	18.0072i	−1.27184	+	0.849814i	−0.993846	−	0.110770i	$-0.964668\pi$
$449$	−26.9497	+	18.0072i	−1.27184	+	0.849814i	−0.277990	+	0.960584i	$0.589668\pi$
$450$	0.404561	+	0.976696i	0.0190712	+	0.0460419i
$451$	−1.44897	−	3.49812i	−0.0682292	−	0.164720i
$452$	−1.17884	−	1.76426i	−0.0554479	−	0.0829837i
$453$	−4.71648	+	23.7114i	−0.221600	+	1.11406i
$454$	−0.753901	−	0.503740i	−0.0353823	−	0.0236417i
$455$	0.0441889	+	5.42357i	0.00207161	+	0.254261i
$456$	7.47891	−	1.48765i	0.350232	−	0.0696654i
$457$	6.33128	−	15.2851i	0.296165	−	0.715005i	−0.703825	−	0.710374i	$-0.748526\pi$
$457$	6.33128	−	15.2851i	0.296165	−	0.715005i	0.999989	−	0.00463088i	$-0.00147406\pi$
$458$	−4.56838			−0.213466
$459$	−3.83829	+	0.280473i	−0.179156	+	0.0130913i
$460$		−	3.61995i		−	0.168781i
$461$	−2.02862	+	4.89753i	−0.0944823	+	0.228101i	−0.964054	−	0.265706i	$-0.914395\pi$
$461$	−2.02862	+	4.89753i	−0.0944823	+	0.228101i	0.869572	+	0.493807i	$0.164395\pi$
$462$	5.43157	−	8.27406i	0.252699	−	0.384944i
$463$	−17.1634	−	17.1634i	−0.797649	−	0.797649i	0.185076	−	0.982724i	$-0.440747\pi$
$463$	−17.1634	−	17.1634i	−0.797649	−	0.797649i	−0.982724	+	0.185076i	$0.940747\pi$
$464$	10.8609	+	7.25702i	0.504204	+	0.336899i
$465$	18.6745	+	3.71459i	0.866010	+	0.172260i
$466$	−0.123737	+	0.0826782i	−0.00573199	+	0.00382999i
$467$	31.9575	−	13.2372i	1.47882	−	0.612545i	0.509966	−	0.860195i	$-0.329658\pi$
$467$	31.9575	−	13.2372i	1.47882	−	0.612545i	0.968850	+	0.247649i	$0.0796581\pi$
$468$	2.47570	+	5.97687i	0.114439	+	0.276281i
$469$	−27.4233	−	5.22294i	−1.26629	−	0.241173i
$470$	6.77015	+	1.34667i	0.312284	+	0.0621171i
$471$	−25.4004	+	38.0144i	−1.17039	+	1.75161i
$472$	5.36981	+	5.36981i	0.247166	+	0.247166i
$473$	−28.7881	+	5.72631i	−1.32368	+	0.263296i
$474$	3.21905	+	1.33338i	0.147856	+	0.0612440i
$475$	2.17246			0.0996793
$476$	−20.5255	+	1.66808i	−0.940787	+	0.0764562i
$477$	43.4503			1.98945
$478$	1.92297	+	0.796522i	0.0879548	+	0.0364321i
$479$	2.49088	−	0.495467i	0.113811	−	0.0226385i	−0.137856	−	0.990452i	$-0.544021\pi$
$479$	2.49088	−	0.495467i	0.113811	−	0.0226385i	0.251667	+	0.967814i	$0.419021\pi$
$480$	−13.3950	−	13.3950i	−0.611397	−	0.611397i
$481$	−5.59881	+	8.37922i	−0.255284	+	0.382059i
$482$	2.88097	+	0.573060i	0.131225	+	0.0261022i
$483$	−6.23988	−	1.18842i	−0.283924	−	0.0540751i
$484$	−6.19628	−	14.9591i	−0.281649	−	0.679961i
$485$	−9.74999	+	4.03858i	−0.442724	+	0.183382i
$486$	6.23080	−	4.16329i	0.282635	−	0.188850i
$487$	7.51717	+	1.49526i	0.340636	+	0.0677566i	0.362444	−	0.932006i	$-0.381942\pi$
$487$	7.51717	+	1.49526i	0.340636	+	0.0677566i	−0.0218084	+	0.999762i	$0.506942\pi$
$488$	11.4196	+	7.63035i	0.516942	+	0.345410i
$489$	−2.16762	−	2.16762i	−0.0980231	−	0.0980231i
$490$	−4.62059	+	0.997624i	−0.208737	+	0.0450681i
$491$	−8.38519	+	20.2436i	−0.378418	+	0.913582i	0.613845	+	0.789427i	$0.289622\pi$
$491$	−8.38519	+	20.2436i	−0.378418	+	0.913582i	−0.992263	+	0.124155i	$0.960378\pi$
$492$			4.07718i			0.183813i
$493$	14.4114	−	7.24164i	0.649055	−	0.326147i
$494$	−0.790311			−0.0355578
$495$	−11.5020	+	27.7683i	−0.516977	+	1.24809i
$496$	12.2570	−	2.43806i	0.550354	−	0.109472i
$497$	18.0829	−	0.147331i	0.811128	−	0.00660871i
$498$	1.73618	+	1.16008i	0.0778000	+	0.0519843i
$499$	5.21588	−	26.2220i	0.233495	−	1.17386i	−0.669035	−	0.743231i	$-0.733293\pi$
$499$	5.21588	−	26.2220i	0.233495	−	1.17386i	0.902530	−	0.430627i	$-0.141707\pi$
$500$	−12.5507	−	18.7835i	−0.561287	−	0.840025i
$501$	6.02053	+	14.5348i	0.268977	+	0.649368i
$502$	1.63846	+	3.95560i	0.0731282	+	0.176547i
$503$	20.5674	−	13.7427i	0.917056	−	0.612757i	−0.00492696	−	0.999988i	$-0.501568\pi$
$503$	20.5674	−	13.7427i	0.917056	−	0.612757i	0.921983	+	0.387231i	$0.126568\pi$
$504$	−9.60199	+	6.52963i	−0.427707	+	0.290853i
$505$	−14.9558	+	22.3829i	−0.665524	+	0.996027i
$506$	0.997013	−	0.997013i	0.0443227	−	0.0443227i
$507$	5.89172	+	29.6197i	0.261660	+	1.31546i
$508$	4.92944	−	11.9007i	0.218709	−	0.528009i
$509$	−7.79768			−0.345626			−0.172813	−	0.984955i	$-0.555286\pi$
$509$	−7.79768			−0.345626			−0.172813	+	0.984955i	$0.555286\pi$
$510$	−6.77393	+	1.86958i	−0.299954	+	0.0827864i
$511$	−27.6332	−	27.1866i	−1.22242	−	1.20266i
$512$	−19.5230	−	8.08669i	−0.862803	−	0.357385i
$513$	0.422437	+	2.12374i	0.0186511	+	0.0937652i
$514$	−0.317784	+	0.317784i	−0.0140169	+	0.0140169i
$515$	24.5507	+	16.4042i	1.08183	+	0.722857i
$516$	30.9994	+	6.16617i	1.36467	+	0.271450i
$517$	−25.1272	−	37.6056i	−1.10509	−	1.65389i
$518$	−8.14165	−	3.29493i	−0.357723	−	0.144771i
$519$	33.6659	−	13.9449i	1.47777	−	0.612113i
$520$	1.48331	+	2.21993i	0.0650476	+	0.0973506i
$521$	3.27619	−	16.4705i	0.143532	−	0.721586i	−0.840247	−	0.542204i	$-0.817590\pi$
$521$	3.27619	−	16.4705i	0.143532	−	0.721586i	0.983779	−	0.179382i	$-0.0574099\pi$
$522$	2.45334	−	3.67169i	0.107380	−	0.160705i
$523$	−13.2089	−	13.2089i	−0.577585	−	0.577585i	0.356652	−	0.934237i	$-0.383918\pi$
$523$	−13.2089	−	13.2089i	−0.577585	−	0.577585i	−0.934237	+	0.356652i	$0.883918\pi$
$524$	−2.66855	−	13.4157i	−0.116576	−	0.586068i
$525$	−5.75758	+	2.44001i	−0.251282	+	0.106491i
$526$		−	1.05229i		−	0.0458818i
$527$	4.85040	−	14.6485i	0.211287	−	0.638099i
$528$			37.2896i			1.62282i
$529$	20.4132	+	8.45543i	0.887531	+	0.367627i
$530$	8.53987	−	1.69869i	0.370948	−	0.0737862i
$531$	−13.8939	+	13.8939i	−0.602945	+	0.602945i
$532$	2.35295	+	11.3452i	0.102013	+	0.491877i
$533$	0.169777	−	0.853529i	0.00735387	−	0.0369704i
$534$	−9.90404	+	6.61767i	−0.428590	+	0.286374i
$535$	0.696566	−	0.288527i	0.0301152	−	0.0124741i
$536$	−12.6960	+	5.25885i	−0.548383	+	0.227148i
$537$	14.6316	−	9.77653i	0.631401	−	0.421889i
$538$	0.461412	−	2.31967i	0.0198929	−	0.100008i
$539$	26.0294	+	16.7853i	1.12117	+	0.722996i
$540$	2.51163	−	2.51163i	0.108084	−	0.108084i
$541$	−22.9783	+	4.57066i	−0.987913	+	0.196508i	−0.662499	−	0.749063i	$-0.730504\pi$
$541$	−22.9783	+	4.57066i	−0.987913	+	0.196508i	−0.325415	+	0.945571i	$0.605504\pi$
$542$	0.421198	+	0.174466i	0.0180920	+	0.00749395i
$543$		−	18.9275i		−	0.812256i
$544$	−12.1093	+	9.43677i	−0.519181	+	0.404598i
$545$			23.0329i			0.986620i
$546$	2.09453	−	0.887644i	0.0896376	−	0.0379877i
$547$	−1.59327	−	8.00989i	−0.0681231	−	0.342478i	0.931659	−	0.363333i	$-0.118361\pi$
$547$	−1.59327	−	8.00989i	−0.0681231	−	0.342478i	−0.999783	+	0.0208549i	$0.993361\pi$
$548$	11.0357	+	11.0357i	0.471423	+	0.471423i
$549$	−19.7429	+	29.5473i	−0.842605	+	1.26105i
$550$	0.270798	−	1.36139i	0.0115469	−	0.0580501i
$551$	−5.04157	−	7.54525i	−0.214778	−	0.321438i
$552$	−2.88883	+	1.19659i	−0.122957	+	0.0509304i
$553$	−4.09029	+	10.1070i	−0.173937	+	0.429792i
$554$	3.76001	+	5.62725i	0.159747	+	0.239079i
$555$	49.4478	+	9.83578i	2.09894	+	0.417506i
$556$	−32.1810	−	21.5026i	−1.36478	−	0.911915i
$557$	26.5176	−	26.5176i	1.12359	−	1.12359i	0.132388	−	0.991198i	$-0.457736\pi$
$557$	26.5176	−	26.5176i	1.12359	−	1.12359i	0.991198	−	0.132388i	$-0.0422644\pi$
$558$	−0.824224	−	4.14366i	−0.0348922	−	0.175415i
$559$	−6.23275	−	2.58169i	−0.263617	−	0.109194i
$560$	12.4902	−	12.6954i	0.527805	−	0.536477i
$561$	40.0457	+	22.7220i	1.69073	+	0.959325i
$562$	3.30005			0.139204
$563$	−10.1757	+	24.5662i	−0.428853	+	1.03534i	0.550799	+	0.834638i	$0.314323\pi$
$563$	−10.1757	+	24.5662i	−0.428853	+	1.03534i	−0.979652	+	0.200705i	$0.935677\pi$
$564$	9.50127	+	47.7661i	0.400076	+	2.01132i
$565$	1.60214	−	1.60214i	0.0674027	−	0.0674027i
$566$	−2.64805	+	3.96309i	−0.111306	+	0.166581i
$567$	11.5358	+	16.9637i	0.484458	+	0.712409i
$568$	7.40154	−	4.94555i	0.310562	−	0.207511i
$569$	−3.08609	−	7.45049i	−0.129376	−	0.312341i	0.845897	−	0.533347i	$-0.179066\pi$
$569$	−3.08609	−	7.45049i	−0.129376	−	0.312341i	−0.975272	+	0.221006i	$0.929066\pi$
$570$	1.51305	+	3.65283i	0.0633748	+	0.153000i
$571$	−9.81310	−	14.6863i	−0.410665	−	0.614604i	0.567265	−	0.823535i	$-0.308002\pi$
$571$	−9.81310	−	14.6863i	−0.410665	−	0.614604i	−0.977930	+	0.208931i	$0.933002\pi$
$572$	1.65714	−	8.33102i	0.0692886	−	0.348337i
$573$	−7.90721	−	5.28343i	−0.330328	−	0.220718i
$574$	0.758439	−	0.00617943i	0.0316566	−	0.000257924i
$575$	−0.873713	+	0.173792i	−0.0364363	+	0.00724764i
$576$	7.00392	−	16.9090i	0.291830	−	0.704540i
$577$	0.231238			0.00962655			0.00481327	−	0.999988i	$-0.498468\pi$
$577$	0.231238			0.00962655			0.00481327	+	0.999988i	$0.498468\pi$
$578$	0.827868	+	5.63446i	0.0344348	+	0.234363i
$579$		−	52.3979i		−	2.17758i
$580$	−5.69655	+	13.7527i	−0.236536	+	0.571049i
$581$	−3.58581	+	5.46237i	−0.148765	+	0.226617i
$582$	3.12988	+	3.12988i	0.129738	+	0.129738i
$583$	−47.4356	−	31.6955i	−1.96458	−	1.31269i
$584$	−18.7156	−	3.72277i	−0.774459	−	0.154049i
$585$	−5.74389	+	3.83794i	−0.237480	+	0.158679i
$586$	−8.14138	+	3.37227i	−0.336317	+	0.139307i
$587$	−6.02142	−	14.5370i	−0.248531	−	0.600006i	0.749549	−	0.661949i	$-0.230270\pi$
$587$	−6.02142	−	14.5370i	−0.248531	−	0.600006i	−0.998080	+	0.0619427i	$0.980270\pi$
$588$	−18.9784	−	27.4250i	−0.782655	−	1.13099i
$589$	−8.51513	−	1.69376i	−0.350860	−	0.0697903i
$590$	−2.18758	+	3.27394i	−0.0900612	+	0.134786i
$591$	−37.6817	−	37.6817i	−1.55002	−	1.55002i
$592$	32.4550	−	6.45569i	1.33389	−	0.265327i
$593$	−5.81177	−	2.40732i	−0.238661	−	0.0988566i	0.260147	−	0.965569i	$-0.416229\pi$
$593$	−5.81177	−	2.40732i	−0.238661	−	0.0988566i	−0.498808	+	0.866712i	$0.666229\pi$
$594$	1.38352			0.0567664
$595$	−6.02293	−	21.1491i	−0.246916	−	0.867028i
$596$	−0.770657			−0.0315674
$597$	−32.3651	−	13.4061i	−1.32462	−	0.548674i
$598$	0.317845	−	0.0632233i	0.0129976	−	0.00258539i
$599$	4.16595	+	4.16595i	0.170216	+	0.170216i	0.787074	−	0.616858i	$-0.211595\pi$
$599$	4.16595	+	4.16595i	0.170216	+	0.170216i	−0.616858	+	0.787074i	$0.711595\pi$
$600$	−1.71017	+	2.55946i	−0.0698175	+	0.104489i
$601$	−15.6877	−	3.12047i	−0.639914	−	0.127287i	−0.135539	−	0.990772i	$-0.543277\pi$
$601$	−15.6877	−	3.12047i	−0.639914	−	0.127287i	−0.504374	+	0.863485i	$0.668277\pi$
$602$	1.10005	−	5.77588i	0.0448348	−	0.235407i
$603$	−13.6068	−	32.8497i	−0.554112	−	1.33774i
$604$	−16.7065	+	6.92004i	−0.679776	+	0.281573i
$605$	14.3760	−	9.60575i	0.584469	−	0.390529i
$606$	11.0738	+	2.20272i	0.449844	+	0.0894796i
$607$	−7.99187	−	5.34000i	−0.324380	−	0.216744i	0.382708	−	0.923869i	$-0.374992\pi$
$607$	−7.99187	−	5.34000i	−0.324380	−	0.216744i	−0.707088	+	0.707126i	$0.749992\pi$
$608$	6.10781	+	6.10781i	0.247705	+	0.247705i
$609$	21.8360	+	14.3344i	0.884839	+	0.580859i
$610$	−2.72518	+	6.57917i	−0.110339	+	0.266383i
$611$		−	10.3951i		−	0.420543i
$612$	−16.1227	−	20.6887i	−0.651723	−	0.836292i
$613$	26.9195			1.08727			0.543635	−	0.839322i	$-0.317048\pi$
$613$	26.9195			1.08727			0.543635	+	0.839322i	$0.317048\pi$
$614$	−0.734712	+	1.77375i	−0.0296506	+	0.0715828i
$615$	−4.27006	+	0.849369i	−0.172186	+	0.0342498i
$616$	15.2459	−	0.124216i	0.614273	−	0.00500482i
$617$	−30.0466	−	20.0765i	−1.20963	−	0.808249i	−0.223578	−	0.974686i	$-0.571774\pi$
$617$	−30.0466	−	20.0765i	−1.20963	−	0.808249i	−0.986052	+	0.166438i	$0.946774\pi$
$618$	2.41605	−	12.1463i	0.0971879	−	0.488597i
$619$	26.8791	+	40.2275i	1.08036	+	1.61688i	0.734521	+	0.678586i	$0.237407\pi$
$619$	26.8791	+	40.2275i	1.08036	+	1.61688i	0.345842	+	0.938293i	$0.387593\pi$
$620$	5.45007	+	13.1576i	0.218880	+	0.528423i
$621$	−0.339789	−	0.820323i	−0.0136353	−	0.0329184i
$622$	0.570130	−	0.380949i	0.0228601	−	0.0152747i
$623$	−20.9603	−	30.8227i	−0.839757	−	1.23489i
$624$	−4.76159	+	7.12622i	−0.190616	+	0.285277i
$625$	13.7466	−	13.7466i	0.549865	−	0.549865i
$626$	1.04156	+	5.23630i	0.0416293	+	0.209284i
$627$	9.91369	−	23.9338i	0.395915	−	0.955822i
$628$	−34.1970			−1.36461
$629$	12.8433	−	38.7874i	0.512094	−	1.54656i
$630$	−4.29186	−	4.22249i	−0.170992	−	0.168228i
$631$	−25.3433	−	10.4976i	−1.00890	−	0.417901i	−0.183848	−	0.982955i	$-0.558856\pi$
$631$	−25.3433	−	10.4976i	−1.00890	−	0.417901i	−0.825054	+	0.565053i	$0.808856\pi$
$632$	1.04709	+	5.26410i	0.0416512	+	0.209395i
$633$	6.07559	−	6.07559i	0.241483	−	0.241483i
$634$	−7.56856	−	5.05715i	−0.300586	−	0.200845i
$635$	13.4907	+	2.68346i	0.535360	+	0.106490i
$636$	34.1301	+	51.0793i	1.35335	+	2.02543i
$637$	2.83099	+	6.53151i	0.112168	+	0.258788i
$638$	−5.35674	+	2.21884i	−0.212076	+	0.0878446i
$639$	12.7962	+	19.1508i	0.506209	+	0.757596i
$640$	3.64413	−	18.3203i	0.144047	−	0.724172i
$641$	13.3853	−	20.0325i	0.528686	−	0.791234i	−0.466977	−	0.884269i	$-0.654657\pi$
$641$	13.3853	−	20.0325i	0.528686	−	0.791234i	0.995663	+	0.0930352i	$0.0296569\pi$
$642$	−0.223607	−	0.223607i	−0.00882508	−	0.00882508i
$643$	5.73102	+	28.8118i	0.226009	+	1.13623i	0.912497	+	0.409084i	$0.134152\pi$
$643$	5.73102	+	28.8118i	0.226009	+	1.13623i	−0.686487	+	0.727142i	$0.740848\pi$
$644$	−1.85389	−	4.37454i	−0.0730536	−	0.172381i
$645$			33.7505i			1.32893i
$646$	3.08874	−	0.852482i	0.121525	−	0.0335405i
$647$			41.2572i			1.62199i	0.585054	+	0.810994i	$0.301073\pi$
$647$			41.2572i			1.62199i	−0.585054	+	0.810994i	$0.698927\pi$
$648$	9.32972	+	3.86450i	0.366506	+	0.151812i
$649$	25.3034	−	5.03317i	0.993247	−	0.197569i
$650$	0.225590	−	0.225590i	0.00884838	−	0.00884838i
$651$	24.4697	−	5.07491i	0.959042	−	0.198901i
$652$	0.447322	−	2.24884i	0.0175185	−	0.0880713i
$653$	−24.6838	+	16.4932i	−0.965952	+	0.645429i	−0.935208	−	0.354099i	$-0.884788\pi$
$653$	−24.6838	+	16.4932i	−0.965952	+	0.645429i	−0.0307440	+	0.999527i	$0.509788\pi$
$654$	8.92519	−	3.69694i	0.349003	−	0.144562i
$655$	13.4945	−	5.58960i	0.527273	−	0.218404i
$656$	−2.37597	+	1.58757i	−0.0927660	+	0.0619842i
$657$	9.63235	−	48.4251i	0.375794	−	1.88924i
$658$	8.87109	−	1.83983i	0.345831	−	0.0717240i
$659$	33.7265	−	33.7265i	1.31380	−	1.31380i	0.395205	−	0.918593i	$-0.370674\pi$
$659$	33.7265	−	33.7265i	1.31380	−	1.31380i	0.918593	−	0.395205i	$-0.129326\pi$
$660$	−41.6787	+	8.29042i	−1.62234	+	0.322704i
$661$	−11.9584	−	4.95334i	−0.465129	−	0.192663i	0.137796	−	0.990461i	$-0.455998\pi$
$661$	−11.9584	−	4.95334i	−0.465129	−	0.192663i	−0.602925	+	0.797798i	$0.705998\pi$
$662$		−	2.74113i		−	0.106537i
$663$	4.75150	+	9.45581i	0.184533	+	0.367233i
$664$			3.21651i			0.124825i
$665$	−11.3918	+	4.82773i	−0.441753	+	0.187211i
$666$	−2.18244	−	10.9719i	−0.0845680	−	0.425152i
$667$	2.63121	+	2.63121i	0.101881	+	0.101881i
$668$	−6.53763	+	9.78425i	−0.252948	+	0.378564i
$669$	−2.40435	+	12.0875i	−0.0929574	+	0.467329i
$670$	−3.95859	−	5.92444i	−0.152934	−	0.228881i
$671$	43.1075	−	17.8557i	1.66415	−	0.689311i
$672$	−23.0473	−	9.32726i	−0.889070	−	0.359807i
$673$	10.4270	+	15.6051i	0.401930	+	0.601531i	0.976131	−	0.217184i	$-0.0696871\pi$
$673$	10.4270	+	15.6051i	0.401930	+	0.601531i	−0.574201	+	0.818715i	$0.694687\pi$
$674$	3.38745	+	0.673806i	0.130480	+	0.0259540i
$675$	−0.726792	−	0.485627i	−0.0279742	−	0.0186918i
$676$	−15.9727	+	15.9727i	−0.614334	+	0.614334i
$677$	−0.260841	−	1.31134i	−0.0100249	−	0.0503988i	0.975449	−	0.220225i	$-0.0706793\pi$
$677$	−0.260841	−	1.31134i	−0.0100249	−	0.0503988i	−0.985474	+	0.169827i	$0.945679\pi$
$678$	−0.877982	−	0.363672i	−0.0337187	−	0.0139667i
$679$	−9.71413	+	9.87373i	−0.372794	+	0.378919i
$680$	−8.19175	−	7.07609i	−0.314139	−	0.271356i
$681$	6.83109			0.261768
$682$	−2.12283	+	5.12497i	−0.0812874	+	0.196245i
$683$	9.91476	+	49.8449i	0.379378	+	1.90726i	0.418880	+	0.908042i	$0.362423\pi$
$683$	9.91476	+	49.8449i	0.379378	+	1.90726i	−0.0395022	+	0.999219i	$0.512577\pi$
$684$	−10.4352	+	10.4352i	−0.399000	+	0.399000i
$685$	−9.25883	+	13.8568i	−0.353762	+	0.529442i
$686$	−5.07285	+	3.57194i	−0.193683	+	0.136377i
$687$	28.6175	−	19.1216i	1.09182	−	0.729534i
$688$	8.47723	+	20.4658i	0.323191	+	0.780253i
$689$	−5.01791	−	12.1143i	−0.191167	−	0.461519i
$690$	−0.900734	−	1.34804i	−0.0342903	−	0.0513191i
$691$	−3.43393	+	17.2635i	−0.130633	+	0.656735i	0.858867	+	0.512199i	$0.171169\pi$
$691$	−3.43393	+	17.2635i	−0.130633	+	0.656735i	−0.989500	+	0.144536i	$0.953831\pi$
$692$	22.6625	+	15.1426i	0.861500	+	0.575636i
$693$	0.321399	+	39.4473i	0.0122089	+	1.49848i
$694$	6.69459	−	1.33164i	0.254123	−	0.0505482i
$695$	15.8159	−	38.1829i	0.599931	−	1.44836i
$696$	12.8581			0.487385
$697$	0.257138	+	3.51895i	0.00973980	+	0.133290i
$698$		−	8.69752i		−	0.329206i
$699$	0.429056	−	1.03583i	0.0162284	−	0.0391788i
$700$	−3.91006	−	2.56679i	−0.147787	−	0.0970155i
$701$	19.4751	+	19.4751i	0.735565	+	0.735565i	0.971716	−	0.236152i	$-0.0758862\pi$
$701$	19.4751	+	19.4751i	0.735565	+	0.735565i	−0.236152	+	0.971716i	$0.575886\pi$
$702$	0.264397	+	0.176664i	0.00997902	+	0.00666777i
$703$	−22.5470	−	4.48488i	−0.850376	−	0.169150i
$704$	−19.9808	+	13.3508i	−0.753056	+	0.503176i
$705$	−48.0466	+	19.9015i	−1.80954	+	0.749535i
$706$	2.44106	+	5.89324i	0.0918704	+	0.221795i
$707$	−6.61037	+	34.7081i	−0.248609	+	1.30533i
$708$	−27.2471	−	5.41978i	−1.02401	−	0.203688i
$709$	−8.64429	+	12.9371i	−0.324643	+	0.485863i	−0.957511	−	0.288397i	$-0.906878\pi$
$709$	−8.64429	+	12.9371i	−0.324643	+	0.485863i	0.632868	+	0.774260i	$0.281878\pi$
$710$	3.26371	+	3.26371i	0.122485	+	0.122485i
$711$	−13.6204	+	2.70926i	−0.510805	+	0.101605i
$712$	−16.9519	−	7.02171i	−0.635300	−	0.263150i
$713$	3.56008			0.133326
$714$	−7.22851	+	5.72845i	−0.270520	+	0.214382i
$715$	9.07038			0.339213
$716$	12.1604	+	5.03700i	0.454456	+	0.188242i
$717$	−15.3799	+	3.05926i	−0.574374	+	0.114250i
$718$	2.15919	+	2.15919i	0.0805803	+	0.0805803i
$719$	−11.4301	+	17.1063i	−0.426269	+	0.637957i	−0.980985	−	0.194083i	$-0.937827\pi$
$719$	−11.4301	+	17.1063i	−0.426269	+	0.637957i	0.554716	+	0.832040i	$0.312827\pi$
$720$	22.2476	+	4.42533i	0.829120	+	0.164922i
$721$	38.0695	+	7.25057i	1.41778	+	0.270025i
$722$	1.74585	+	4.21485i	0.0649737	+	0.156860i
$723$	−20.4457	+	8.46890i	−0.760385	+	0.314962i
$724$	11.7713	−	7.86536i	0.437478	−	0.292314i
$725$	3.59284	+	0.714661i	0.133435	+	0.0265418i
$726$	−6.02966	−	4.02889i	−0.223782	−	0.149526i
$727$	5.81725	+	5.81725i	0.215750	+	0.215750i	0.806705	−	0.590955i	$-0.201249\pi$
$727$	5.81725	+	5.81725i	0.215750	+	0.215750i	−0.590955	+	0.806705i	$0.701249\pi$
$728$	2.92942	+	1.92304i	0.108571	+	0.0712725i
$729$	−12.7036	+	30.6692i	−0.470503	+	1.13590i
$730$		−	9.89421i		−	0.366201i
$731$	27.1440	+	3.36686i	1.00396	+	0.124528i
$732$	−50.2432			−1.85704
$733$	5.64482	−	13.6278i	0.208496	−	0.503354i	−0.784691	−	0.619888i	$-0.787178\pi$
$733$	5.64482	−	13.6278i	0.208496	−	0.503354i	0.993187	+	0.116533i	$0.0371782\pi$
$734$	5.67926	−	1.12968i	0.209625	−	0.0416971i
$735$	24.7688	−	25.5895i	0.913612	−	0.943882i
$736$	−2.94503	−	1.96781i	−0.108555	−	0.0725344i
$737$	−9.10790	+	45.7885i	−0.335494	+	1.68664i
$738$	0.536702	+	0.803232i	0.0197563	+	0.0295674i
$739$	−4.14512	−	10.0072i	−0.152481	−	0.368121i	0.829119	−	0.559073i	$-0.188843\pi$
$739$	−4.14512	−	10.0072i	−0.152481	−	0.368121i	−0.981599	+	0.190951i	$0.938843\pi$
$740$	14.4311	+	34.8398i	0.530498	+	1.28074i
$741$	4.95070	−	3.30796i	0.181869	−	0.121521i
$742$	9.45009	−	6.42633i	0.346924	−	0.235918i
$743$	−10.0900	+	15.1007i	−0.370165	+	0.553992i	−0.969057	−	0.246839i	$-0.920608\pi$
$743$	−10.0900	+	15.1007i	−0.370165	+	0.553992i	0.598891	+	0.800830i	$0.295608\pi$
$744$	8.69865	−	8.69865i	0.318908	−	0.318908i
$745$	−0.160545	−	0.807117i	−0.00588193	−	0.0295705i
$746$	−1.81877	+	4.39089i	−0.0665898	+	0.160762i
$747$	−8.32244			−0.304502
$748$	2.50984	+	34.3473i	0.0917689	+	1.25586i
$749$	0.694004	−	0.705406i	0.0253584	−	0.0257750i
$750$	−9.34762	−	3.87191i	−0.341327	−	0.141382i
$751$	1.64768	+	8.28343i	0.0601246	+	0.302267i	0.999133	−	0.0416269i	$-0.0132541\pi$
$751$	1.64768	+	8.28343i	0.0601246	+	0.302267i	−0.939009	+	0.343893i	$0.888254\pi$
$752$	−24.1360	+	24.1360i	−0.880151	+	0.880151i
$753$	−26.8205	−	17.9209i	−0.977392	−	0.653072i
$754$	−1.30703	−	0.259984i	−0.0475991	−	0.00946805i
$755$	−10.7278	−	16.0552i	−0.390423	−	0.584310i
$756$	1.74891	−	4.32148i	0.0636071	−	0.157171i
$757$	−0.111359	+	0.0461265i	−0.00404742	+	0.00167649i	−0.384706	−	0.923039i	$-0.625697\pi$
$757$	−0.111359	+	0.0461265i	−0.00404742	+	0.00167649i	0.380659	+	0.924716i	$0.375697\pi$
$758$	−1.24677	−	1.86593i	−0.0452849	−	0.0677737i
$759$	−2.07240	+	10.4187i	−0.0752235	+	0.378174i
$760$	−3.38369	+	5.06405i	−0.122739	+	0.183692i
$761$	−33.0119	−	33.0119i	−1.19668	−	1.19668i	−0.975155	−	0.221524i	$-0.928897\pi$
$761$	−33.0119	−	33.0119i	−1.19668	−	1.19668i	−0.221524	−	0.975155i	$-0.571103\pi$
$762$	−1.12551	−	5.65831i	−0.0407729	−	0.204979i
$763$	11.7959	+	27.8342i	0.427040	+	1.00767i
$764$		−	7.11317i		−	0.257346i
$765$	18.3088	−	21.1954i	0.661955	−	0.766322i
$766$		−	7.96503i		−	0.287788i
$767$	5.47830	+	2.26919i	0.197810	+	0.0819356i
$768$	19.2042	−	3.81995i	0.692972	−	0.137841i
$769$	20.2281	−	20.2281i	0.729443	−	0.729443i	−0.241066	−	0.970509i	$-0.577497\pi$
$769$	20.2281	−	20.2281i	0.729443	−	0.729443i	0.970509	+	0.241066i	$0.0774970\pi$
$770$	1.60536	+	7.74055i	0.0578531	+	0.278950i
$771$	0.660550	−	3.32081i	0.0237891	−	0.119596i
$772$	32.5872	−	21.7741i	1.17284	−	0.783666i
$773$	−12.5053	+	5.17987i	−0.449785	+	0.186307i	−0.596065	−	0.802936i	$-0.703270\pi$
$773$	−12.5053	+	5.17987i	−0.449785	+	0.186307i	0.146280	+	0.989243i	$0.453270\pi$
$774$	6.91879	−	2.86586i	0.248691	−	0.103011i
$775$	2.91407	−	1.94712i	0.104677	−	0.0699427i
$776$	−1.33020	+	6.68735i	−0.0477513	+	0.240062i
$777$	64.7927	−	13.4377i	2.32442	−	0.482076i
$778$	2.01096	−	2.01096i	0.0720964	−	0.0720964i
$779$	1.94704	−	0.387291i	0.0697601	−	0.0138762i
$780$	−9.02362	−	3.73771i	−0.323098	−	0.133831i
$781$		−	30.2418i		−	1.08214i
$782$	−1.17402	+	0.589942i	−0.0419830	+	0.0210963i
$783$			3.65123i			0.130484i
$784$	8.59208	−	21.7384i	0.306860	−	0.776370i
$785$	−7.12402	−	35.8149i	−0.254267	−	1.27829i
$786$	−4.33191	−	4.33191i	−0.154514	−	0.154514i
$787$	27.2024	−	40.7113i	0.969663	−	1.45120i	0.0788207	−	0.996889i	$-0.474885\pi$
$787$	27.2024	−	40.7113i	0.969663	−	1.45120i	0.890842	−	0.454314i	$-0.150115\pi$
$788$	7.77620	−	39.0936i	0.277016	−	1.39265i
$789$	4.40448	+	6.59178i	0.156804	+	0.234673i
$790$	−2.57108	+	1.06498i	−0.0914750	+	0.0378902i
$791$	1.11561	−	2.75663i	0.0396664	−	0.0980144i
$792$	10.7886	+	16.1463i	0.383356	+	0.573732i
$793$	10.5181	+	2.09217i	0.373508	+	0.0742953i
$794$	0.484604	+	0.323802i	0.0171979	+	0.0114913i
$795$	−46.3858	+	46.3858i	−1.64513	+	1.64513i
$796$	−5.11192	−	25.6994i	−0.181187	−	0.910890i
$797$	−5.31334	−	2.20086i	−0.188208	−	0.0779584i	0.286589	−	0.958054i	$-0.407479\pi$
$797$	−5.31334	−	2.20086i	−0.188208	−	0.0779584i	−0.474797	+	0.880095i	$0.657479\pi$
$798$	3.69919	+	3.63940i	0.130950	+	0.128833i
$799$	11.2129	+	40.6270i	0.396684	+	1.43728i
$800$	−3.48689			−0.123280
$801$	18.1681	−	43.8616i	0.641937	−	1.54977i
$802$	−0.0630238	−	0.316842i	−0.00222545	−	0.0111881i
$803$	−45.8403	+	45.8403i	−1.61767	+	1.61767i
$804$	27.9294	−	41.7993i	0.984994	−	1.47415i
$805$	4.19529	−	2.85292i	0.147865	−	0.100552i
$806$	−1.06010	+	0.708337i	−0.0373405	+	0.0249501i
$807$	6.81892	+	16.4623i	0.240037	+	0.579501i
$808$	6.65582	+	16.0686i	0.234151	+	0.565290i
$809$	−30.6042	−	45.8025i	−1.07599	−	1.61033i	−0.745482	−	0.666526i	$-0.767780\pi$
$809$	−30.6042	−	45.8025i	−1.07599	−	1.61033i	−0.330506	−	0.943804i	$-0.607220\pi$
$810$	−1.02150	+	5.13544i	−0.0358919	+	0.180441i
$811$	18.2766	+	12.2120i	0.641779	+	0.428823i	0.833418	−	0.552643i	$-0.186381\pi$
$811$	18.2766	+	12.2120i	0.641779	+	0.428823i	−0.191640	+	0.981465i	$0.561381\pi$
$812$	0.159178	+	19.5369i	0.00558604	+	0.685610i
$813$	−3.36874	+	0.670083i	−0.118147	+	0.0235008i
$814$	−5.62099	+	13.5703i	−0.197016	+	0.475638i
$815$	2.44842			0.0857643
$816$	10.9227	−	32.9873i	0.382372	−	1.15479i
$817$		−	15.3894i		−	0.538408i
$818$	1.40853	−	3.40050i	0.0492483	−	0.118896i
$819$	−4.97569	+	7.57960i	−0.173865	+	0.264853i
$820$	−2.30267	−	2.30267i	−0.0804128	−	0.0804128i
$821$	45.2328	+	30.2236i	1.57864	+	1.05481i	0.963965	+	0.266028i	$0.0857112\pi$
$821$	45.2328	+	30.2236i	1.57864	+	1.05481i	0.614671	+	0.788784i	$0.289289\pi$
$822$	6.85559	+	1.36366i	0.239116	+	0.0475631i
$823$	−31.0122	+	20.7217i	−1.08102	+	0.722314i	−0.962675	−	0.270659i	$-0.912758\pi$
$823$	−31.0122	+	20.7217i	−1.08102	+	0.722314i	−0.118344	+	0.992973i	$0.537758\pi$
$824$	17.6248	−	7.30042i	0.613988	−	0.254322i
$825$	4.00196	+	9.66158i	0.139330	+	0.336373i
$826$	−0.966896	+	5.07674i	−0.0336426	+	0.176642i
$827$	−33.6889	−	6.70114i	−1.17148	−	0.233021i	−0.429260	−	0.903181i	$-0.641226\pi$
$827$	−33.6889	−	6.70114i	−1.17148	−	0.233021i	−0.742217	+	0.670159i	$0.766226\pi$
$828$	3.36200	−	5.03159i	0.116838	−	0.174860i
$829$	18.1274	+	18.1274i	0.629589	+	0.629589i	0.947965	−	0.318376i	$-0.103137\pi$
$829$	18.1274	+	18.1274i	0.629589	+	0.629589i	−0.318376	+	0.947965i	$0.603137\pi$
$830$	−1.63572	+	0.325365i	−0.0567767	+	0.0112936i
$831$	−47.1072	−	19.5124i	−1.63413	−	0.676879i
$832$	−5.52322			−0.191483
$833$	−18.1096	−	22.4732i	−0.627459	−	0.778649i
$834$	−17.3344			−0.600240
$835$	−11.6091	−	4.80864i	−0.401749	−	0.166410i
$836$	19.0045	−	3.78023i	0.657284	−	0.130742i
$837$	2.47010	+	2.47010i	0.0853790	+	0.0853790i
$838$	−4.30371	+	6.44095i	−0.148669	+	0.222499i
$839$	−42.6085	−	8.47535i	−1.47101	−	0.292602i	−0.606445	−	0.795126i	$-0.707405\pi$
$839$	−42.6085	−	8.47535i	−1.47101	−	0.292602i	−0.864563	+	0.502524i	$0.832405\pi$
$840$	3.27994	−	17.2215i	0.113169	−	0.594197i
$841$	5.24211	+	12.6556i	0.180763	+	0.436399i
$842$	1.25114	−	0.518239i	0.0431171	−	0.0178597i
$843$	−20.6723	+	13.8128i	−0.711993	+	0.475738i
$844$	6.30324	+	1.25379i	0.216966	+	0.0431573i
$845$	−20.0558	−	13.4009i	−0.689941	−	0.461004i
$846$	8.15955	+	8.15955i	0.280531	+	0.280531i
$847$	12.4533	−	18.9705i	0.427902	−	0.651835i
$848$	−16.4768	+	39.7786i	−0.565816	+	1.36600i
$849$		−	35.9096i		−	1.23241i
$850$	−0.638329	+	1.12500i	−0.0218945	+	0.0385873i
$851$	9.42666			0.323142
$852$	−12.4620	+	30.0859i	−0.426941	+	1.03073i
$853$	−4.01867	+	0.799362i	−0.137596	+	0.0273696i	−0.263408	−	0.964685i	$-0.584847\pi$
$853$	−4.01867	+	0.799362i	−0.137596	+	0.0273696i	0.125812	+	0.992054i	$0.459847\pi$
$854$	0.0761494	+	9.34628i	0.00260578	+	0.319823i
$855$	−13.1028	−	8.75500i	−0.448106	−	0.299415i
$856$	0.0950329	−	0.477763i	0.00324816	−	0.0163296i
$857$	−27.3686	−	40.9600i	−0.934894	−	1.39917i	−0.916807	−	0.399332i	$-0.869242\pi$
$857$	−27.3686	−	40.9600i	−0.934894	−	1.39917i	−0.0180876	−	0.999836i	$-0.505758\pi$
$858$	−1.45586	−	3.51475i	−0.0497021	−	0.119992i
$859$	13.6096	+	32.8565i	0.464354	+	1.12105i	0.966592	+	0.256320i	$0.0825101\pi$
$859$	13.6096	+	32.8565i	0.464354	+	1.12105i	−0.502238	+	0.864729i	$0.667490\pi$
$860$	−20.9901	+	14.0251i	−0.715755	+	0.478252i
$861$	−4.72519	+	3.21326i	−0.161034	+	0.109508i
$862$	0.769545	−	1.15171i	0.0262108	−	0.0392272i
$863$	22.0107	−	22.0107i	0.749254	−	0.749254i	−0.225085	−	0.974339i	$-0.572266\pi$
$863$	22.0107	−	22.0107i	0.749254	−	0.749254i	0.974339	+	0.225085i	$0.0722661\pi$
$864$	−0.678029	−	3.40868i	−0.0230670	−	0.115966i
$865$	−11.1379	+	26.8892i	−0.378699	+	0.914261i
$866$	−4.83268			−0.164221
$867$	−28.7698	−	31.8305i	−0.977073	−	1.08102i
$868$	13.3246	+	13.1092i	0.452266	+	0.444956i
$869$	16.8460	+	6.97784i	0.571462	+	0.236707i
$870$	1.30066	+	6.53884i	0.0440964	+	0.221688i
$871$	−7.58739	+	7.58739i	−0.257089	+	0.257089i
$872$	12.3733	+	8.26758i	0.419013	+	0.279976i
$873$	−17.3029	−	3.44177i	−0.585615	−	0.116486i
$874$	0.410713	+	0.614675i	0.0138926	+	0.0207917i
$875$	11.8775	−	29.3490i	0.401534	−	0.992177i
$876$	64.4938	−	26.7142i	2.17904	−	0.902590i
$877$	20.2765	+	30.3459i	0.684688	+	1.02471i	0.997199	+	0.0747939i	$0.0238299\pi$
$877$	20.2765	+	30.3459i	0.684688	+	1.02471i	−0.312511	+	0.949914i	$0.601170\pi$
$878$	−0.487315	+	2.44990i	−0.0164461	+	0.0826800i
$879$	36.8845	−	55.2016i	1.24408	−	1.86190i
$880$	−21.0601	−	21.0601i	−0.709936	−	0.709936i
$881$	4.79213	+	24.0916i	0.161451	+	0.811668i	0.973608	+	0.228229i	$0.0732934\pi$
$881$	4.79213	+	24.0916i	0.161451	+	0.811668i	−0.812157	+	0.583439i	$0.801707\pi$
$882$	−7.34898	−	2.90468i	−0.247453	−	0.0978057i
$883$		−	0.405556i		−	0.0136480i	−0.999977	−	0.00682402i	$-0.997828\pi$
$883$		−	0.405556i		−	0.0136480i	0.999977	−	0.00682402i	$-0.00217217\pi$
$884$	−3.90624	+	6.88442i	−0.131381	+	0.231548i
$885$		−	29.6652i		−	0.997184i
$886$	−0.694448	−	0.287650i	−0.0233304	−	0.00966378i
$887$	−42.8651	+	8.52639i	−1.43927	+	0.286288i	−0.852186	−	0.523239i	$-0.824723\pi$
$887$	−42.8651	+	8.52639i	−1.43927	+	0.286288i	−0.587082	+	0.809528i	$0.699723\pi$
$888$	23.0329	−	23.0329i	0.772935	−	0.772935i
$889$	17.6771	−	3.66616i	0.592872	−	0.122959i
$890$	1.85605	−	9.33098i	0.0622149	−	0.312775i
$891$	28.5254	−	19.0600i	0.955635	−	0.638535i
$892$	−8.51654	+	3.52767i	−0.285155	+	0.118115i
$893$	21.9081	−	9.07462i	0.733125	−	0.303670i
$894$	−0.286987	+	0.191759i	−0.00959829	+	0.00641337i
$895$	−2.74201	+	13.7850i	−0.0916553	+	0.460783i
$896$	−4.97864	−	24.0055i	−0.166325	−	0.801966i
$897$	−1.72643	+	1.72643i	−0.0576438	+	0.0576438i
$898$	−10.6494	+	2.11829i	−0.355374	+	0.0706882i
$899$	−13.5252	−	5.60234i	−0.451092	−	0.186848i
$900$		−	5.95735i		−	0.198578i
$901$	32.6786	+	41.9333i	1.08868	+	1.39700i
$902$		−	1.26841i		−	0.0422335i
$903$	17.2847	+	40.7860i	0.575200	+	1.35727i
$904$	−0.285590	−	1.43576i	−0.00949859	−	0.0477526i
$905$	10.6897	+	10.6897i	0.355338	+	0.355338i
$906$	−4.49949	+	6.73396i	−0.149485	+	0.223721i
$907$	−4.13812	+	20.8037i	−0.137404	+	0.690776i	0.849256	+	0.527981i	$0.177051\pi$
$907$	−4.13812	+	20.8037i	−0.137404	+	0.690776i	−0.986660	+	0.162795i	$0.947949\pi$
$908$	2.83868	+	4.24838i	0.0942048	+	0.140987i
$909$	−41.5760	+	17.2213i	−1.37899	+	0.571196i
$910$	−0.681615	+	1.68425i	−0.0225953	+	0.0558322i
$911$	−19.3806	−	29.0052i	−0.642109	−	0.960984i	−0.999633	−	0.0270803i	$-0.991379\pi$
$911$	−19.3806	−	29.0052i	−0.642109	−	0.960984i	0.357524	−	0.933904i	$-0.383621\pi$
$912$	−19.1754	−	3.81423i	−0.634961	−	0.126302i
$913$	9.08579	+	6.07093i	0.300696	+	0.200919i
$914$	3.91903	−	3.91903i	0.129630	−	0.129630i
$915$	−10.4668	−	52.6202i	−0.346022	−	1.73957i
$916$	23.7841	+	9.85170i	0.785849	+	0.325509i
$917$	13.4448	−	13.6657i	0.443988	−	0.451282i
$918$	−1.22389	−	0.405255i	−0.0403945	−	0.0133754i
$919$	−19.5712			−0.645596			−0.322798	−	0.946468i	$-0.604623\pi$
$919$	−19.5712			−0.645596			−0.322798	+	0.946468i	$0.604623\pi$
$920$	0.955728	−	2.30733i	0.0315094	−	0.0760705i
$921$	−2.82186	−	14.1865i	−0.0929835	−	0.467460i
$922$	−1.25571	+	1.25571i	−0.0413545	+	0.0413545i
$923$	3.86164	−	5.77935i	0.127107	−	0.190230i
$924$	−46.1210	+	31.3636i	−1.51727	+	1.03179i
$925$	7.71611	−	5.15574i	0.253704	−	0.169520i
$926$	−3.11170	−	7.51232i	−0.102257	−	0.246870i
$927$	18.8892	+	45.6025i	0.620402	+	1.49778i
$928$	8.09193	+	12.1104i	0.265631	+	0.397544i
$929$	−0.954249	+	4.79734i	−0.0313079	+	0.157395i	−0.993277	−	0.115764i	$-0.963069\pi$
$929$	−0.954249	+	4.79734i	−0.0313079	+	0.157395i	0.961969	+	0.273159i	$0.0880685\pi$
$930$	5.30351	+	3.54369i	0.173909	+	0.116202i
$931$	−11.2940	+	11.6682i	−0.370145	+	0.382409i
$932$	0.822498	−	0.163605i	0.0269418	−	0.00535906i
$933$	−1.97692	+	4.77272i	−0.0647216	+	0.156252i
$934$	11.5877			0.379162
$935$	−35.4494	+	9.78391i	−1.15932	+	0.319968i
$936$			4.46324i			0.145886i
$937$	19.6376	−	47.4093i	0.641531	−	1.54879i	−0.183082	−	0.983098i	$-0.558608\pi$
$937$	19.6376	−	47.4093i	0.641531	−	1.54879i	0.824614	−	0.565696i	$-0.191392\pi$
$938$	−7.81787	−	5.13210i	−0.255263	−	0.167569i
$939$	−28.4418	−	28.4418i	−0.928165	−	0.928165i
$940$	−32.3430	−	21.6109i	−1.05491	−	0.704869i
$941$	36.3976	+	7.23994i	1.18653	+	0.236015i	0.748617	−	0.663003i	$-0.230718\pi$
$941$	36.3976	+	7.23994i	1.18653	+	0.236015i	0.437912	+	0.899018i	$0.355718\pi$
$942$	−12.7347	+	8.50907i	−0.414920	+	0.277240i
$943$	−0.752074	+	0.311519i	−0.0244909	+	0.0101445i
$944$	−7.45110	−	17.9886i	−0.242513	−	0.585477i
$945$	4.89027	+	0.931382i	0.159080	+	0.0302978i
$946$	−9.64394	−	1.91830i	−0.313552	−	0.0623693i
$947$	−4.75953	+	7.12313i	−0.154664	+	0.231471i	−0.900707	−	0.434426i	$-0.856951\pi$
$947$	−4.75953	+	7.12313i	−0.154664	+	0.231471i	0.746043	+	0.665897i	$0.231951\pi$
$948$	−13.8838	−	13.8838i	−0.450923	−	0.450923i
$949$	−14.6137	+	2.90685i	−0.474382	+	0.0943605i
$950$	0.672370	+	0.278505i	0.0218146	+	0.00903589i
$951$	68.5788			2.22382
$952$	−13.5232	−	4.35587i	−0.438291	−	0.141175i
$953$	44.0920			1.42828			0.714140	−	0.700003i	$-0.246818\pi$
$953$	44.0920			1.42828			0.714140	+	0.700003i	$0.246818\pi$
$954$	13.4477	+	5.57024i	0.435387	+	0.180343i
$955$	7.44969	−	1.48184i	0.241066	−	0.0479511i
$956$	−8.29378	−	8.29378i	−0.268240	−	0.268240i
$957$	24.2687	−	36.3207i	0.784497	−	1.17408i
$958$	0.834438	+	0.165980i	0.0269595	+	0.00536257i
$959$	−4.09234	+	21.4871i	−0.132149	+	0.693853i
$960$	10.5742	+	25.5284i	0.341282	+	0.823927i
$961$	15.7002	−	6.50325i	0.506459	−	0.209782i
$962$	−2.80702	+	1.87559i	−0.0905018	+	0.0604714i
$963$	1.23617	+	0.245889i	0.0398350	+	0.00792367i
$964$	−13.7632	−	9.19629i	−0.443284	−	0.296193i
$965$	29.5929	+	29.5929i	0.952628	+	0.952628i
$966$	−1.77887	−	1.16775i	−0.0572343	−	0.0375718i
$967$	5.82350	−	14.0592i	0.187271	−	0.452112i	−0.802161	−	0.597107i	$-0.796317\pi$
$967$	5.82350	−	14.0592i	0.187271	−	0.452112i	0.989432	+	0.144995i	$0.0463166\pi$
$968$		−	11.1708i		−	0.359043i
$969$	−15.7805	+	18.2685i	−0.506942	+	0.586869i
$970$	−3.53533			−0.113513
$971$	12.9125	−	31.1735i	0.414381	−	1.00041i	−0.569566	−	0.821946i	$-0.692889\pi$
$971$	12.9125	−	31.1735i	0.414381	−	1.00041i	0.983947	−	0.178460i	$-0.0571114\pi$
$972$	−41.4172	+	8.23838i	−1.32846	+	0.264246i
$973$	−0.441941	−	54.2421i	−0.0141680	−	1.73892i
$974$	2.13486	+	1.42647i	0.0684052	+	0.0457069i
$975$	−0.468914	+	2.35739i	−0.0150173	+	0.0754969i
$976$	−19.5637	−	29.2792i	−0.626219	−	0.937203i
$977$	14.7980	+	35.7255i	0.473430	+	1.14296i	0.962638	+	0.270793i	$0.0872859\pi$
$977$	14.7980	+	35.7255i	0.473430	+	1.14296i	−0.489208	+	0.872167i	$0.662714\pi$
$978$	−0.392988	−	0.948756i	−0.0125664	−	0.0303379i
$979$	−51.8300	+	34.6317i	−1.65649	+	1.10683i
$980$	26.2073	+	4.77041i	0.837161	+	0.152385i
$981$	−21.3916	+	32.0148i	−0.682982	+	1.02216i
$982$	−5.19039	+	5.19039i	−0.165632	+	0.165632i
$983$	−6.00007	−	30.1644i	−0.191372	−	0.962094i	−0.950399	−	0.311034i	$-0.899325\pi$
$983$	−6.00007	−	30.1644i	−0.191372	−	0.962094i	0.759026	−	0.651060i	$-0.225675\pi$
$984$	−1.07644	+	2.59876i	−0.0343158	+	0.0828456i
$985$	42.5631			1.35617
$986$	5.38864	−	0.393761i	0.171609	−	0.0125399i
$987$	−47.8698	+	48.6563i	−1.52371	+	1.54875i
$988$	4.11455	+	1.70430i	0.130901	+	0.0542211i
$989$	1.23112	+	6.18927i	0.0391474	+	0.196807i
$990$	−7.11968	+	7.11968i	−0.226278	+	0.226278i
$991$	−11.6492	−	7.78373i	−0.370048	−	0.247258i	0.356616	−	0.934251i	$-0.383930\pi$
$991$	−11.6492	−	7.78373i	−0.370048	−	0.247258i	−0.726664	+	0.686993i	$0.758930\pi$
$992$	13.6671	+	2.71856i	0.433932	+	0.0863144i
$993$	11.4734	+	17.1711i	0.364096	+	0.544909i
$994$	5.61549	+	2.27259i	0.178113	+	0.0720822i
$995$	25.8502	−	10.7075i	0.819508	−	0.339451i
$996$	−6.53726	−	9.78370i	−0.207141	−	0.310008i
$997$	−3.38436	+	17.0143i	−0.107184	+	0.538849i	0.889462	+	0.457010i	$0.151080\pi$
$997$	−3.38436	+	17.0143i	−0.107184	+	0.538849i	−0.996646	+	0.0818395i	$0.973920\pi$
$998$	4.97591	−	7.44697i	0.157510	−	0.235730i
$999$	6.54051	+	6.54051i	0.206933	+	0.206933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.2.p.a.62.7	yes	80
7.2	even	3		833.2.bc.f.521.4		160
7.3	odd	6		833.2.bc.f.215.3		160
7.4	even	3		833.2.bc.f.215.4		160
7.5	odd	6		833.2.bc.f.521.3		160
7.6	odd	2	inner	119.2.p.a.62.8	yes	80
17.14	odd	16	inner	119.2.p.a.48.8	yes	80
119.31	even	48		833.2.bc.f.558.4		160
119.48	even	16	inner	119.2.p.a.48.7	✓	80
119.65	odd	48		833.2.bc.f.31.3		160
119.82	even	48		833.2.bc.f.31.4		160
119.116	odd	48		833.2.bc.f.558.3		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.p.a.48.7	✓	80	119.48	even	16	inner
119.2.p.a.48.8	yes	80	17.14	odd	16	inner
119.2.p.a.62.7	yes	80	1.1	even	1	trivial
119.2.p.a.62.8	yes	80	7.6	odd	2	inner
833.2.bc.f.31.3		160	119.65	odd	48
833.2.bc.f.31.4		160	119.82	even	48
833.2.bc.f.215.3		160	7.3	odd	6
833.2.bc.f.215.4		160	7.4	even	3
833.2.bc.f.521.3		160	7.5	odd	6
833.2.bc.f.521.4		160	7.2	even	3
833.2.bc.f.558.3		160	119.116	odd	48
833.2.bc.f.558.4		160	119.31	even	48

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	119.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309497 + 0.128198i) q^{2} +(-2.47536 + 0.492379i) q^{3} +(-1.33486 - 1.33486i) q^{4} +(1.11993 - 1.67609i) q^{5} +(-0.829238 - 0.164946i) q^{6} +(0.495002 - 2.59903i) q^{7} +(-0.498405 - 1.20326i) q^{8} +(3.11332 - 1.28958i) q^{9} +(0.561487 - 0.375173i) q^{10} +(-4.33958 - 0.863197i) q^{11} +(3.96151 + 2.64700i) q^{12} +(-0.719092 - 0.719092i) q^{13} +(0.486393 - 0.740935i) q^{14} +(-1.94695 + 4.70036i) q^{15} +3.33925i q^{16} +(3.58606 + 2.03474i) q^{17} +1.12889 q^{18} +(0.887763 - 2.14325i) q^{19} +(-3.73230 + 0.742400i) q^{20} +(0.0544034 + 6.67727i) q^{21} +(-1.23243 - 0.823483i) q^{22} +(-0.185582 + 0.932984i) q^{23} +(1.82619 + 2.73309i) q^{24} +(0.358372 + 0.865186i) q^{25} +(-0.130371 - 0.314743i) q^{26} +(-0.776096 + 0.518571i) q^{27} +(-4.13010 + 2.80859i) q^{28} +(2.17325 - 3.25249i) q^{29} +(-1.20515 + 1.20515i) q^{30} +(-0.730122 - 3.67057i) q^{31} +(-1.42490 + 3.44000i) q^{32} +11.1670 q^{33} +(0.849027 + 1.08947i) q^{34} +(-3.80185 - 3.74040i) q^{35} +(-5.87725 - 2.43444i) q^{36} +(-1.93327 - 9.71922i) q^{37} +(0.549520 - 0.549520i) q^{38} +(2.13408 + 1.42594i) q^{39} +(-2.57495 - 0.512189i) q^{40} +(0.475427 + 0.711527i) q^{41} +(-0.839174 + 2.07357i) q^{42} +(6.12887 - 2.53866i) q^{43} +(4.64049 + 6.94498i) q^{44} +(1.32524 - 6.66245i) q^{45} +(-0.177044 + 0.264965i) q^{46} +(7.22797 + 7.22797i) q^{47} +(-1.64418 - 8.26585i) q^{48} +(-6.50995 - 2.57305i) q^{49} +0.313715i q^{50} +(-9.87865 - 3.27101i) q^{51} +1.91977i q^{52} +(11.9124 + 4.93428i) q^{53} +(-0.306679 + 0.0610023i) q^{54} +(-6.30683 + 6.30683i) q^{55} +(-3.37401 + 0.699757i) q^{56} +(-1.14224 + 5.74242i) q^{57} +(1.08958 - 0.728032i) q^{58} +(-5.38700 + 2.23137i) q^{59} +(8.87323 - 3.67541i) q^{60} +(-8.76818 + 5.85871i) q^{61} +(0.244589 - 1.22963i) q^{62} +(-1.81056 - 8.72996i) q^{63} +(3.84042 - 3.84042i) q^{64} +(-2.01060 + 0.399933i) q^{65} +(3.45617 + 1.43159i) q^{66} -10.5514i q^{67} +(-2.07080 - 7.50298i) q^{68} -2.40085i q^{69} +(-0.697151 - 1.64503i) q^{70} +(1.33343 + 6.70358i) q^{71} +(-3.10339 - 3.10339i) q^{72} +(8.14005 - 12.1824i) q^{73} +(0.647642 - 3.25591i) q^{74} +(-1.31310 - 1.96519i) q^{75} +(-4.04598 + 1.67590i) q^{76} +(-4.39158 + 10.8514i) q^{77} +(0.477687 + 0.714910i) q^{78} +(-4.04186 - 0.803976i) q^{79} +(5.59690 + 3.73973i) q^{80} +(-5.48271 + 5.48271i) q^{81} +(0.0559271 + 0.281164i) q^{82} +(-2.28169 - 0.945109i) q^{83} +(8.84059 - 8.98583i) q^{84} +(7.42655 - 3.73181i) q^{85} +2.22232 q^{86} +(-3.77810 + 9.12114i) q^{87} +(1.12422 + 5.65185i) q^{88} +(9.96197 - 9.96197i) q^{89} +(1.26427 - 1.89212i) q^{90} +(-2.22490 + 1.51299i) q^{91} +(1.49313 - 0.997677i) q^{92} +(3.61463 + 8.72648i) q^{93} +(1.31043 + 3.16365i) q^{94} +(-2.59805 - 3.88826i) q^{95} +(1.83334 - 9.21683i) q^{96} +(-4.35295 - 2.90855i) q^{97} +(-1.68495 - 1.63091i) q^{98} +(-14.6237 + 2.90883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 16 q^{2} - 16 q^{4} - 8 q^{7} - 16 q^{8} - 16 q^{9} + 8 q^{14} - 64 q^{15} + 32 q^{18} + 16 q^{21} - 48 q^{22} - 16 q^{23} - 56 q^{28} - 16 q^{29} + 112 q^{30} + 16 q^{32} - 48 q^{35} - 48 q^{36}+ \cdots + 128 q^{99}+O(q^{100}) \) 80 * q - 16 * q^2 - 16 * q^4 - 8 * q^7 - 16 * q^8 - 16 * q^9 + 8 * q^14 - 64 * q^15 + 32 * q^18 + 16 * q^21 - 48 * q^22 - 16 * q^23 - 56 * q^28 - 16 * q^29 + 112 * q^30 + 16 * q^32 - 48 * q^35 - 48 * q^36 + 48 * q^37 - 8 * q^42 - 16 * q^43 - 16 * q^44 + 16 * q^46 + 24 * q^49 - 48 * q^51 + 16 * q^53 + 112 * q^56 - 16 * q^57 - 48 * q^58 + 48 * q^60 + 112 * q^63 + 48 * q^64 - 32 * q^65 + 64 * q^70 + 16 * q^71 - 80 * q^72 - 80 * q^74 + 40 * q^77 + 112 * q^78 - 16 * q^79 - 64 * q^81 + 112 * q^85 + 48 * q^86 - 112 * q^88 - 72 * q^91 + 256 * q^92 + 48 * q^93 - 48 * q^95 - 144 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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