LMFDB - Embedded newform 570.2.bc.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.a.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.14282 - 0.639010i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-0.495802 + 0.286252i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.14282 - 0.639010i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-0.495802 + 0.286252i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(1.99930 + 1.00140i) q^{10} +(-3.23142 + 5.59698i) q^{11} +(0.866025 - 0.500000i) q^{12} +(1.31467 + 1.56676i) q^{13} +(0.537977 - 0.195808i) q^{14} +(-1.86689 + 1.23075i) q^{15} +(0.766044 + 0.642788i) q^{16} +(2.95864 + 0.521688i) q^{17} +1.00000i q^{18} +(3.15729 + 3.00525i) q^{19} +(-1.79504 - 1.33336i) q^{20} +(-0.0994141 + 0.563806i) q^{21} +(4.15423 - 4.95082i) q^{22} +(-0.0536445 + 0.147387i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(4.18333 + 2.73856i) q^{25} +(-1.02263 - 1.77125i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(-0.563806 + 0.0994141i) q^{28} +(0.874739 + 4.96089i) q^{29} +(2.05224 - 0.887867i) q^{30} +(-0.161126 - 0.279078i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(2.21042 + 6.07308i) q^{33} +(-2.82310 - 1.02752i) q^{34} +(1.24533 - 0.296562i) q^{35} +(0.173648 - 0.984808i) q^{36} -7.38565i q^{37} +(-2.58747 - 3.50785i) q^{38} +2.04526 q^{39} +(1.53623 + 1.62481i) q^{40} +(0.234480 + 0.196752i) q^{41} +(0.195808 - 0.537977i) q^{42} +(2.29619 + 6.30873i) q^{43} +(-4.95082 + 4.15423i) q^{44} +(-0.257205 + 2.22123i) q^{45} +(0.0784231 - 0.135833i) q^{46} +(-5.30368 + 0.935182i) q^{47} +(0.984808 - 0.173648i) q^{48} +(-3.33612 + 5.77833i) q^{49} +(-3.64423 - 3.42339i) q^{50} +(2.30141 - 1.93111i) q^{51} +(0.699522 + 1.92192i) q^{52} +(0.269736 - 0.741094i) q^{53} +(0.766044 + 0.642788i) q^{54} +(10.5009 - 9.92840i) q^{55} +0.572503 q^{56} +(4.33162 - 0.486886i) q^{57} -5.03742i q^{58} +(-0.510726 + 2.89647i) q^{59} +(-2.17524 + 0.518010i) q^{60} +(4.40213 + 1.60224i) q^{61} +(0.110217 + 0.302818i) q^{62} +(0.367998 + 0.438563i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-1.81592 - 4.19737i) q^{65} +(-1.12226 - 6.36465i) q^{66} +(-8.73266 + 1.53980i) q^{67} +(2.60178 + 1.50214i) q^{68} +(0.0784231 + 0.135833i) q^{69} +(-1.27791 + 0.0758075i) q^{70} +(10.9468 - 3.98431i) q^{71} +(-0.342020 + 0.939693i) q^{72} +(-8.85170 + 10.5490i) q^{73} +(-1.28251 + 7.27345i) q^{74} +(4.78686 - 1.44431i) q^{75} +(1.93903 + 3.90387i) q^{76} -3.70000i q^{77} +(-2.01419 - 0.355156i) q^{78} +(8.45792 + 7.09704i) q^{79} +(-1.23075 - 1.86689i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.196752 - 0.234480i) q^{82} +(-8.38761 + 4.84259i) q^{83} +(-0.286252 + 0.495802i) q^{84} +(-6.00646 - 3.00848i) q^{85} +(-1.16581 - 6.61162i) q^{86} +(4.36254 + 2.51871i) q^{87} +(5.59698 - 3.23142i) q^{88} +(1.12976 - 0.947980i) q^{89} +(0.639010 - 2.14282i) q^{90} +(-1.10031 - 0.400478i) q^{91} +(-0.100819 + 0.120151i) q^{92} +(-0.317356 - 0.0559584i) q^{93} +5.38550 q^{94} +(-4.84511 - 8.45724i) q^{95} -1.00000 q^{96} +(-1.94645 - 0.343212i) q^{97} +(4.28883 - 5.11123i) q^{98} +(6.07308 + 2.21042i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{5}+O(q^{10}) $ 60 * q - 6 * q^5	$ 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−2.14282	−	0.639010i	−0.958297	−	0.285774i
$5$	−2.14282	−	0.639010i	−0.958297	−	0.285774i
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	−0.495802	+	0.286252i	−0.187396	+	0.108193i	−0.590763	−	0.806845i	$-0.701173\pi$
$7$	−0.495802	+	0.286252i	−0.187396	+	0.108193i	0.403367	+	0.915038i	$0.367840\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	1.99930	+	1.00140i	0.632234	+	0.316670i
$11$	−3.23142	+	5.59698i	−0.974309	+	1.68755i	−0.292114	+	0.956383i	$0.594359\pi$
$11$	−3.23142	+	5.59698i	−0.974309	+	1.68755i	−0.682195	+	0.731170i	$0.738975\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	1.31467	+	1.56676i	0.364624	+	0.434542i	0.916899	−	0.399120i	$-0.130684\pi$
$13$	1.31467	+	1.56676i	0.364624	+	0.434542i	−0.552275	+	0.833662i	$0.686240\pi$
$14$	0.537977	−	0.195808i	0.143780	−	0.0523318i
$15$	−1.86689	+	1.23075i	−0.482028	+	0.317777i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	2.95864	+	0.521688i	0.717575	+	0.126528i	0.520501	−	0.853861i	$-0.325745\pi$
$17$	2.95864	+	0.521688i	0.717575	+	0.126528i	0.197074	+	0.980389i	$0.436856\pi$
$18$			1.00000i			0.235702i
$19$	3.15729	+	3.00525i	0.724332	+	0.689452i
$19$	3.15729	+	3.00525i	0.724332	+	0.689452i
$20$	−1.79504	−	1.33336i	−0.401382	−	0.298148i
$21$	−0.0994141	+	0.563806i	−0.0216939	+	0.123032i
$22$	4.15423	−	4.95082i	0.885685	−	1.05552i
$23$	−0.0536445	+	0.147387i	−0.0111857	+	0.0307324i	−0.945160	−	0.326608i	$-0.894094\pi$
$23$	−0.0536445	+	0.147387i	−0.0111857	+	0.0307324i	0.933974	+	0.357341i	$0.116316\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	4.18333	+	2.73856i	0.836667	+	0.547712i
$26$	−1.02263	−	1.77125i	−0.200555	−	0.347371i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	−0.563806	+	0.0994141i	−0.106549	+	0.0187875i
$29$	0.874739	+	4.96089i	0.162435	+	0.921215i	0.951670	+	0.307123i	$0.0993663\pi$
$29$	0.874739	+	4.96089i	0.162435	+	0.921215i	−0.789235	+	0.614092i	$0.789523\pi$
$30$	2.05224	−	0.887867i	0.374686	−	0.162102i
$31$	−0.161126	−	0.279078i	−0.0289391	−	0.0501239i	0.851193	−	0.524853i	$-0.175880\pi$
$31$	−0.161126	−	0.279078i	−0.0289391	−	0.0501239i	−0.880132	+	0.474729i	$0.842546\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	2.21042	+	6.07308i	0.384785	+	1.05719i
$34$	−2.82310	−	1.02752i	−0.484158	−	0.176219i
$35$	1.24533	−	0.296562i	0.210499	−	0.0501282i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$		−	7.38565i		−	1.21419i	−0.794628	−	0.607097i	$-0.792334\pi$
$37$		−	7.38565i		−	1.21419i	0.794628	−	0.607097i	$-0.207666\pi$
$38$	−2.58747	−	3.50785i	−0.419742	−	0.569049i
$39$	2.04526			0.327504
$40$	1.53623	+	1.62481i	0.242899	+	0.256905i
$41$	0.234480	+	0.196752i	0.0366196	+	0.0307275i	0.660914	−	0.750462i	$-0.270169\pi$
$41$	0.234480	+	0.196752i	0.0366196	+	0.0307275i	−0.624294	+	0.781189i	$0.714613\pi$
$42$	0.195808	−	0.537977i	0.0302138	−	0.0830117i
$43$	2.29619	+	6.30873i	0.350166	+	0.962073i	0.982317	+	0.187228i	$0.0599502\pi$
$43$	2.29619	+	6.30873i	0.350166	+	0.962073i	−0.632151	+	0.774846i	$0.717828\pi$
$44$	−4.95082	+	4.15423i	−0.746364	+	0.626274i
$45$	−0.257205	+	2.22123i	−0.0383419	+	0.331121i
$46$	0.0784231	−	0.135833i	0.0115629	−	0.0200274i
$47$	−5.30368	+	0.935182i	−0.773621	+	0.136410i	−0.546503	−	0.837457i	$-0.684041\pi$
$47$	−5.30368	+	0.935182i	−0.773621	+	0.136410i	−0.227118	+	0.973867i	$0.572930\pi$
$48$	0.984808	−	0.173648i	0.142145	−	0.0250640i
$49$	−3.33612	+	5.77833i	−0.476589	+	0.825476i
$50$	−3.64423	−	3.42339i	−0.515372	−	0.484140i
$51$	2.30141	−	1.93111i	0.322262	−	0.270410i
$52$	0.699522	+	1.92192i	0.0970062	+	0.266522i
$53$	0.269736	−	0.741094i	0.0370511	−	0.101797i	−0.919788	−	0.392417i	$-0.871639\pi$
$53$	0.269736	−	0.741094i	0.0370511	−	0.101797i	0.956839	+	0.290620i	$0.0938614\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	10.5009	−	9.92840i	1.41594	−	1.33875i
$56$	0.572503			0.0765040
$57$	4.33162	−	0.486886i	0.573737	−	0.0644897i
$58$		−	5.03742i		−	0.661446i
$59$	−0.510726	+	2.89647i	−0.0664908	+	0.377088i	0.933345	+	0.358980i	$0.116875\pi$
$59$	−0.510726	+	2.89647i	−0.0664908	+	0.377088i	−0.999836	+	0.0181081i	$0.994236\pi$
$60$	−2.17524	+	0.518010i	−0.280822	+	0.0668748i
$61$	4.40213	+	1.60224i	0.563635	+	0.205146i	0.608094	−	0.793865i	$-0.291934\pi$
$61$	4.40213	+	1.60224i	0.563635	+	0.205146i	−0.0444595	+	0.999011i	$0.514157\pi$
$62$	0.110217	+	0.302818i	0.0139975	+	0.0384579i
$63$	0.367998	+	0.438563i	0.0463634	+	0.0552537i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−1.81592	−	4.19737i	−0.225237	−	0.520620i
$66$	−1.12226	−	6.36465i	−0.138141	−	0.783435i
$67$	−8.73266	+	1.53980i	−1.06686	+	0.188117i	−0.679400	−	0.733768i	$-0.737760\pi$
$67$	−8.73266	+	1.53980i	−1.06686	+	0.188117i	−0.387464	+	0.921885i	$0.626649\pi$
$68$	2.60178	+	1.50214i	0.315512	+	0.182161i
$69$	0.0784231	+	0.135833i	0.00944103	+	0.0163523i
$70$	−1.27791	+	0.0758075i	−0.152739	+	0.00906073i
$71$	10.9468	−	3.98431i	1.29915	−	0.472851i	0.402428	−	0.915452i	$-0.368166\pi$
$71$	10.9468	−	3.98431i	1.29915	−	0.472851i	0.896719	+	0.442601i	$0.145944\pi$
$72$	−0.342020	+	0.939693i	−0.0403075	+	0.110744i
$73$	−8.85170	+	10.5490i	−1.03601	+	1.23467i	−0.0644433	+	0.997921i	$0.520527\pi$
$73$	−8.85170	+	10.5490i	−1.03601	+	1.23467i	−0.971570	+	0.236751i	$0.923917\pi$
$74$	−1.28251	+	7.27345i	−0.149088	+	0.845521i
$75$	4.78686	−	1.44431i	0.552738	−	0.166774i
$76$	1.93903	+	3.90387i	0.222421	+	0.447804i
$77$		−	3.70000i		−	0.421654i
$78$	−2.01419	−	0.355156i	−0.228062	−	0.0402135i
$79$	8.45792	+	7.09704i	0.951591	+	0.798480i	0.979565	−	0.201129i	$-0.0644611\pi$
$79$	8.45792	+	7.09704i	0.951591	+	0.798480i	−0.0279738	+	0.999609i	$0.508906\pi$
$80$	−1.23075	−	1.86689i	−0.137602	−	0.208724i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−0.196752	−	0.234480i	−0.0217276	−	0.0258939i
$83$	−8.38761	+	4.84259i	−0.920660	+	0.531543i	−0.883846	−	0.467779i	$-0.845054\pi$
$83$	−8.38761	+	4.84259i	−0.920660	+	0.531543i	−0.0368145	+	0.999322i	$0.511721\pi$
$84$	−0.286252	+	0.495802i	−0.0312326	+	0.0540965i
$85$	−6.00646	−	3.00848i	−0.651492	−	0.326315i
$86$	−1.16581	−	6.61162i	−0.125712	−	0.712949i
$87$	4.36254	+	2.51871i	0.467713	+	0.270034i
$88$	5.59698	−	3.23142i	0.596640	−	0.344470i
$89$	1.12976	−	0.947980i	0.119754	−	0.100486i	−0.580944	−	0.813944i	$-0.697316\pi$
$89$	1.12976	−	0.947980i	0.119754	−	0.100486i	0.700698	+	0.713458i	$0.252872\pi$
$90$	0.639010	−	2.14282i	0.0673575	−	0.225873i
$91$	−1.10031	−	0.400478i	−0.115343	−	0.0419815i
$92$	−0.100819	+	0.120151i	−0.0105111	+	0.0125266i
$93$	−0.317356	−	0.0559584i	−0.0329083	−	0.00580262i
$94$	5.38550			0.555472
$95$	−4.84511	−	8.45724i	−0.497098	−	0.867695i
$96$	−1.00000			−0.102062
$97$	−1.94645	−	0.343212i	−0.197633	−	0.0348479i	0.0739555	−	0.997262i	$-0.476438\pi$
$97$	−1.94645	−	0.343212i	−0.197633	−	0.0348479i	−0.271588	+	0.962414i	$0.587549\pi$
$98$	4.28883	−	5.11123i	0.433238	−	0.516312i
$99$	6.07308	+	2.21042i	0.610368	+	0.222156i
$100$	2.99440	+	4.00419i	0.299440	+	0.400419i
$101$	−4.22046	+	3.54139i	−0.419951	+	0.352381i	−0.828145	−	0.560514i	$-0.810603\pi$
$101$	−4.22046	+	3.54139i	−0.419951	+	0.352381i	0.408193	+	0.912896i	$0.366159\pi$
$102$	−2.60178	+	1.50214i	−0.257615	+	0.148734i
$103$	7.94695	+	4.58817i	0.783036	+	0.452086i	0.837505	−	0.546429i	$-0.184013\pi$
$103$	7.94695	+	4.58817i	0.783036	+	0.452086i	−0.0544691	+	0.998515i	$0.517347\pi$
$104$	−0.355156	−	2.01419i	−0.0348260	−	0.197508i
$105$	0.573304	−	1.14461i	0.0559487	−	0.111702i
$106$	−0.394328	+	0.682996i	−0.0383005	+	0.0663384i
$107$	−7.01790	+	4.05178i	−0.678446	+	0.391701i	−0.799269	−	0.600973i	$-0.794780\pi$
$107$	−7.01790	+	4.05178i	−0.678446	+	0.391701i	0.120824	+	0.992674i	$0.461446\pi$
$108$	−0.642788	−	0.766044i	−0.0618523	−	0.0737127i
$109$	−9.48639	+	3.45277i	−0.908632	+	0.330715i	−0.753706	−	0.657211i	$-0.771736\pi$
$109$	−9.48639	+	3.45277i	−0.908632	+	0.330715i	−0.154925	+	0.987926i	$0.549514\pi$
$110$	−12.0654	+	7.95411i	−1.15039	+	0.758395i
$111$	−5.65774	−	4.74741i	−0.537009	−	0.450604i
$112$	−0.563806	−	0.0994141i	−0.0532746	−	0.00939375i
$113$			1.82176i			0.171377i	0.996322	+	0.0856884i	$0.0273090\pi$
$113$			1.82176i			0.171377i	−0.996322	+	0.0856884i	$0.972691\pi$
$114$	−4.35036	−	0.272689i	−0.407449	−	0.0255396i
$115$	0.209132	−	0.281544i	0.0195017	−	0.0262542i
$116$	−0.874739	+	4.96089i	−0.0812175	+	0.460607i
$117$	1.31467	−	1.56676i	0.121541	−	0.144847i
$118$	1.00593	−	2.76378i	0.0926037	−	0.254427i
$119$	−1.61623	+	0.588261i	−0.148160	+	0.0539258i
$120$	2.23214	−	0.132414i	0.203766	−	0.0120877i
$121$	−15.3841	−	26.6461i	−1.39856	−	2.42237i
$122$	−4.05702	−	2.34232i	−0.367306	−	0.212064i
$123$	0.301441	−	0.0531522i	0.0271800	−	0.00479257i
$124$	−0.0559584	−	0.317356i	−0.00502522	−	0.0284994i
$125$	−7.21415	−	8.54143i	−0.645253	−	0.763969i
$126$	−0.286252	−	0.495802i	−0.0255013	−	0.0441696i
$127$	−5.44980	−	6.49482i	−0.483591	−	0.576322i	0.467984	−	0.883737i	$-0.344980\pi$
$127$	−5.44980	−	6.49482i	−0.483591	−	0.576322i	−0.951575	+	0.307415i	$0.900536\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	6.30873	+	2.29619i	0.555453	+	0.202168i
$130$	1.05947	+	4.44894i	0.0929215	+	0.390198i
$131$	0.197560	−	1.12042i	0.0172609	−	0.0978915i	−0.974960	−	0.222379i	$-0.928618\pi$
$131$	0.197560	−	1.12042i	0.0172609	−	0.0978915i	0.992221	+	0.124488i	$0.0397288\pi$
$132$			6.46284i			0.562518i
$133$	−2.42565	−	0.586231i	−0.210330	−	0.0508327i
$134$	8.86738			0.766025
$135$	1.53623	+	1.62481i	0.132218	+	0.139841i
$136$	−2.30141	−	1.93111i	−0.197344	−	0.165592i
$137$	7.97650	−	21.9153i	0.681479	−	1.87235i	0.259491	−	0.965746i	$-0.416445\pi$
$137$	7.97650	−	21.9153i	0.681479	−	1.87235i	0.421988	−	0.906601i	$-0.361332\pi$
$138$	−0.0536445	−	0.147387i	−0.00456653	−	0.0125464i
$139$	14.1335	−	11.8594i	1.19879	−	1.00590i	0.199126	−	0.979974i	$-0.436190\pi$
$139$	14.1335	−	11.8594i	1.19879	−	1.00590i	0.999664	−	0.0259298i	$-0.00825464\pi$
$140$	1.27166	+	0.147251i	0.107475	+	0.0124450i
$141$	−2.69275	+	4.66398i	−0.226770	+	0.392778i
$142$	−11.4724	+	2.02289i	−0.962740	+	0.169757i
$143$	−13.0174	+	2.29532i	−1.08857	+	0.191944i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	1.29565	−	11.1893i	0.107598	−	0.929217i
$146$	10.5490	−	8.85170i	0.873046	−	0.732572i
$147$	2.28204	+	6.26985i	0.188220	+	0.517129i
$148$	2.52604	−	6.94024i	0.207639	−	0.570485i
$149$	1.29358	+	1.08544i	0.105974	+	0.0889229i	0.694235	−	0.719748i	$-0.255743\pi$
$149$	1.29358	+	1.08544i	0.105974	+	0.0889229i	−0.588261	+	0.808671i	$0.700187\pi$
$150$	−4.96493	+	0.591135i	−0.405385	+	0.0482659i
$151$	−11.2991			−0.919509			−0.459755	−	0.888046i	$-0.652063\pi$
$151$	−11.2991			−0.919509			−0.459755	+	0.888046i	$0.652063\pi$
$152$	−1.23167	−	4.18127i	−0.0999014	−	0.339146i
$153$		−	3.00428i		−	0.242882i
$154$	−0.642497	+	3.64378i	−0.0517739	+	0.293624i
$155$	0.166930	+	0.700975i	0.0134081	+	0.0563036i
$156$	1.92192	+	0.699522i	0.153877	+	0.0560065i
$157$	−0.917542	−	2.52092i	−0.0732278	−	0.201192i	0.897679	−	0.440651i	$-0.145252\pi$
$157$	−0.917542	−	2.52092i	−0.0732278	−	0.201192i	−0.970907	+	0.239459i	$0.923030\pi$
$158$	−7.09704	−	8.45792i	−0.564610	−	0.672876i
$159$	−0.394328	−	0.682996i	−0.0312722	−	0.0541651i
$160$	0.887867	+	2.05224i	0.0701920	+	0.162244i
$161$	−0.0155927	−	0.0884307i	−0.00122888	−	0.00696932i
$162$	0.984808	−	0.173648i	0.0773738	−	0.0136431i
$163$	−14.6771	−	8.47382i	−1.14960	−	0.663721i	−0.200809	−	0.979630i	$-0.564357\pi$
$163$	−14.6771	−	8.47382i	−1.14960	−	0.663721i	−0.948789	+	0.315909i	$0.897690\pi$
$164$	0.153046	+	0.265083i	0.0119509	+	0.0206995i
$165$	−0.855771	−	14.4260i	−0.0666217	−	1.12306i
$166$	9.10109	−	3.31253i	0.706382	−	0.257102i
$167$	2.30438	−	6.33124i	0.178318	−	0.489926i	−0.818043	−	0.575157i	$-0.804941\pi$
$167$	2.30438	−	6.33124i	0.178318	−	0.489926i	0.996361	+	0.0852315i	$0.0271630\pi$
$168$	0.367998	−	0.438563i	0.0283917	−	0.0338359i
$169$	1.53104	−	8.68295i	0.117772	−	0.667919i
$170$	5.39279	+	4.00578i	0.413608	+	0.307230i
$171$	2.41134	−	3.63118i	0.184399	−	0.277683i
$172$			6.71362i			0.511908i
$173$	18.9980	+	3.34986i	1.44439	+	0.254685i	0.840253	−	0.542194i	$-0.182406\pi$
$173$	18.9980	+	3.34986i	1.44439	+	0.254685i	0.604139	+	0.796879i	$0.293517\pi$
$174$	−3.85889	−	3.23799i	−0.292542	−	0.245472i
$175$	−2.85802	−	0.160300i	−0.216046	−	0.0121175i
$176$	−6.07308	+	2.21042i	−0.457776	+	0.166617i
$177$	1.89054	+	2.25305i	0.142101	+	0.169350i
$178$	−1.27721	+	0.737398i	−0.0957310	+	0.0552703i
$179$	−8.27312	+	14.3295i	−0.618362	+	1.07103i	0.371422	+	0.928464i	$0.378870\pi$
$179$	−8.27312	+	14.3295i	−0.618362	+	1.07103i	−0.989785	+	0.142571i	$0.954463\pi$
$180$	−1.00140	+	1.99930i	−0.0746398	+	0.149019i
$181$	−4.61244	−	26.1584i	−0.342840	−	1.94434i	−0.328677	−	0.944442i	$-0.606603\pi$
$181$	−4.61244	−	26.1584i	−0.342840	−	1.94434i	−0.0141625	−	0.999900i	$-0.504508\pi$
$182$	1.01405	+	0.585460i	0.0751661	+	0.0433972i
$183$	4.05702	−	2.34232i	0.299904	−	0.173149i
$184$	0.120151	−	0.100819i	0.00885766	−	0.00743246i
$185$	−4.71950	+	15.8261i	−0.346985	+	1.16356i
$186$	0.302818	+	0.110217i	0.0222037	+	0.00808147i
$187$	−12.4805	+	14.8736i	−0.912663	+	1.08767i
$188$	−5.30368	−	0.935182i	−0.386811	−	0.0682052i
$189$	0.572503			0.0416435
$190$	3.30292	+	9.17010i	0.239619	+	0.665269i
$191$	5.31545			0.384613			0.192306	−	0.981335i	$-0.438403\pi$
$191$	5.31545			0.384613			0.192306	+	0.981335i	$0.438403\pi$
$192$	0.984808	+	0.173648i	0.0710724	+	0.0125320i
$193$	6.59528	−	7.85995i	0.474739	−	0.565772i	−0.474529	−	0.880240i	$-0.657382\pi$
$193$	6.59528	−	7.85995i	0.474739	−	0.565772i	0.949268	+	0.314468i	$0.101826\pi$
$194$	1.85729	+	0.675997i	0.133345	+	0.0485337i
$195$	−4.38263	−	1.30694i	−0.313846	−	0.0935922i
$196$	−5.11123	+	4.28883i	−0.365088	+	0.306345i
$197$	6.86331	−	3.96253i	0.488990	−	0.282319i	−0.235165	−	0.971955i	$-0.575563\pi$
$197$	6.86331	−	3.96253i	0.488990	−	0.282319i	0.724156	+	0.689637i	$0.242230\pi$
$198$	−5.59698	−	3.23142i	−0.397760	−	0.229647i
$199$	3.83434	+	21.7456i	0.271809	+	1.54151i	0.748919	+	0.662662i	$0.230573\pi$
$199$	3.83434	+	21.7456i	0.271809	+	1.54151i	−0.477110	+	0.878844i	$0.658316\pi$
$200$	−2.25359	−	4.46333i	−0.159353	−	0.315605i
$201$	−4.43369	+	7.67937i	−0.312728	+	0.541661i
$202$	4.77130	−	2.75471i	0.335707	−	0.193821i
$203$	−1.85376	−	2.20923i	−0.130109	−	0.155057i
$204$	2.82310	−	1.02752i	0.197656	−	0.0719411i
$205$	−0.376721	−	0.571438i	−0.0263113	−	0.0399110i
$206$	−7.02949	−	5.89844i	−0.489768	−	0.410964i
$207$	0.154463	+	0.0272361i	0.0107359	+	0.00189304i
$208$			2.04526i			0.141814i
$209$	−27.0229	+	7.96007i	−1.86921	+	0.550609i
$210$	−0.763352	+	1.02766i	−0.0526763	+	0.0709155i
$211$	−4.37543	+	24.8143i	−0.301217	+	1.70829i	0.339580	+	0.940577i	$0.389715\pi$
$211$	−4.37543	+	24.8143i	−0.301217	+	1.70829i	−0.640797	+	0.767710i	$0.721396\pi$
$212$	0.506938	−	0.604145i	0.0348166	−	0.0414929i
$213$	3.98431	−	10.9468i	0.273001	−	0.750063i
$214$	7.61486	−	2.77158i	0.520541	−	0.189462i
$215$	−0.888977	−	14.9858i	−0.0606277	−	1.02202i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	0.159773	+	0.0922451i	0.0108461	+	0.00626200i
$218$	9.94184	−	1.75301i	0.673346	−	0.118729i
$219$	2.39128	+	13.5616i	0.161587	+	0.916408i
$220$	13.2633	−	5.73814i	0.894211	−	0.386865i
$221$	3.07227	+	5.32133i	0.206663	+	0.357952i
$222$	4.74741	+	5.65774i	0.318625	+	0.379723i
$223$	8.70389	+	23.9137i	0.582855	+	1.60138i	0.783277	+	0.621672i	$0.213546\pi$
$223$	8.70389	+	23.9137i	0.582855	+	1.60138i	−0.200422	+	0.979710i	$0.564231\pi$
$224$	0.537977	+	0.195808i	0.0359451	+	0.0130829i
$225$	1.97053	−	4.59533i	0.131369	−	0.306355i
$226$	0.316346	−	1.79408i	0.0210430	−	0.119341i
$227$			14.0544i			0.932821i	0.884568	+	0.466411i	$0.154453\pi$
$227$			14.0544i			0.932821i	−0.884568	+	0.466411i	$0.845547\pi$
$228$	4.23692	+	1.02398i	0.280597	+	0.0678146i
$229$	−5.31966			−0.351533			−0.175766	−	0.984432i	$-0.556240\pi$
$229$	−5.31966			−0.351533			−0.175766	+	0.984432i	$0.556240\pi$
$230$	−0.254845	+	0.240952i	−0.0168040	+	0.0158879i
$231$	−2.83436	−	2.37831i	−0.186487	−	0.156481i
$232$	1.72290	−	4.73363i	0.113114	−	0.310778i
$233$	−3.44526	−	9.46576i	−0.225706	−	0.620123i	0.774212	−	0.632927i	$-0.218147\pi$
$233$	−3.44526	−	9.46576i	−0.225706	−	0.620123i	−0.999918	+	0.0128038i	$0.995924\pi$
$234$	−1.56676	+	1.31467i	−0.102423	+	0.0859427i
$235$	11.9624	+	1.38518i	0.780342	+	0.0903591i
$236$	−1.47058	+	2.54711i	−0.0957264	+	0.165803i
$237$	10.8733	−	1.91726i	0.706297	−	0.124539i
$238$	1.69383	−	0.298668i	0.109795	−	0.0193598i
$239$	6.16476	−	10.6777i	0.398765	−	0.690681i	−0.594809	−	0.803867i	$-0.702772\pi$
$239$	6.16476	−	10.6777i	0.398765	−	0.690681i	0.993574	+	0.113186i	$0.0361055\pi$
$240$	−2.22123	−	0.257205i	−0.143380	−	0.0166025i
$241$	5.71549	−	4.79586i	0.368167	−	0.308929i	−0.439869	−	0.898062i	$-0.644975\pi$
$241$	5.71549	−	4.79586i	0.368167	−	0.308929i	0.808036	+	0.589133i	$0.200531\pi$
$242$	10.5234	+	28.9127i	0.676468	+	1.85858i
$243$	−0.342020	+	0.939693i	−0.0219406	+	0.0602813i
$244$	3.58865	+	3.01123i	0.229740	+	0.192774i
$245$	10.8411	−	10.2501i	0.692613	−	0.654854i
$246$	−0.306091			−0.0195157
$247$	−0.557720	+	8.89764i	−0.0354869	+	0.566143i
$248$			0.322252i			0.0204630i
$249$	−1.68181	+	9.53804i	−0.106581	+	0.604449i
$250$	5.62135	+	9.66439i	0.355525	+	0.611230i
$251$	29.4307	+	10.7119i	1.85765	+	0.676129i	0.980691	+	0.195564i	$0.0626538\pi$
$251$	29.4307	+	10.7119i	1.85765	+	0.676129i	0.876959	+	0.480565i	$0.159568\pi$
$252$	0.195808	+	0.537977i	0.0123347	+	0.0338894i
$253$	−0.651575	−	0.776517i	−0.0409642	−	0.0488192i
$254$	4.23919	+	7.34249i	0.265990	+	0.460709i
$255$	−6.16551	+	2.66740i	−0.386099	+	0.167039i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	11.4098	−	2.01186i	0.711724	−	0.125496i	0.193947	−	0.981012i	$-0.437871\pi$
$257$	11.4098	−	2.01186i	0.711724	−	0.125496i	0.517777	+	0.855516i	$0.326760\pi$
$258$	−5.81416	−	3.35681i	−0.361974	−	0.208986i
$259$	2.11416	+	3.66182i	0.131367	+	0.227535i
$260$	−0.270822	−	4.56532i	−0.0167957	−	0.283129i
$261$	4.73363	−	1.72290i	0.293004	−	0.106645i
$262$	−0.389118	+	1.06909i	−0.0240398	+	0.0660487i
$263$	8.90660	−	10.6145i	0.549204	−	0.654516i	−0.418021	−	0.908438i	$-0.637276\pi$
$263$	8.90660	−	10.6145i	0.549204	−	0.654516i	0.967225	+	0.253921i	$0.0817204\pi$
$264$	1.12226	−	6.36465i	0.0690703	−	0.391717i
$265$	−1.05156	+	1.41566i	−0.0645969	+	0.0869636i
$266$	2.28700	+	0.998534i	0.140225	+	0.0612241i
$267$		−	1.47480i		−	0.0902560i
$268$	−8.73266	−	1.53980i	−0.533432	−	0.0940585i
$269$	7.47693	+	6.27389i	0.455876	+	0.382526i	0.841611	−	0.540084i	$-0.181608\pi$
$269$	7.47693	+	6.27389i	0.455876	+	0.382526i	−0.385735	+	0.922610i	$0.626052\pi$
$270$	−1.23075	−	1.86689i	−0.0749008	−	0.113615i
$271$	−6.87014	+	2.50053i	−0.417332	+	0.151896i	−0.542147	−	0.840284i	$-0.682388\pi$
$271$	−6.87014	+	2.50053i	−0.417332	+	0.151896i	0.124815	+	0.992180i	$0.460166\pi$
$272$	1.93111	+	2.30141i	0.117091	+	0.139544i
$273$	−1.01405	+	0.585460i	−0.0613729	+	0.0354337i
$274$	−11.6609	+	20.1972i	−0.704459	+	1.22016i
$275$	−28.8458	+	14.5646i	−1.73947	+	0.878278i
$276$	0.0272361	+	0.154463i	0.00163942	+	0.00929760i
$277$	−10.6243	−	6.13394i	−0.638352	−	0.368553i	0.145627	−	0.989340i	$-0.453480\pi$
$277$	−10.6243	−	6.13394i	−0.638352	−	0.368553i	−0.783979	+	0.620787i	$0.786813\pi$
$278$	−15.9782	+	9.22500i	−0.958307	+	0.553279i
$279$	−0.246859	+	0.207139i	−0.0147791	+	0.0124011i
$280$	−1.22677	−	0.365835i	−0.0733135	−	0.0218628i
$281$	12.1555	+	4.42424i	0.725136	+	0.263928i	0.678104	−	0.734966i	$-0.262802\pi$
$281$	12.1555	+	4.42424i	0.725136	+	0.263928i	0.0470314	+	0.998893i	$0.485024\pi$
$282$	3.46173	−	4.12553i	0.206143	−	0.245672i
$283$	22.7188	+	4.00594i	1.35049	+	0.238128i	0.801649	−	0.597796i	$-0.203957\pi$
$283$	22.7188	+	4.00594i	1.35049	+	0.238128i	0.548845	+	0.835924i	$0.315068\pi$
$284$	11.6493			0.691262
$285$	−9.59300	−	1.72464i	−0.568240	−	0.102159i
$286$	13.2182			0.781609
$287$	−0.172576	−	0.0304298i	−0.0101868	−	0.00179622i
$288$	−0.642788	+	0.766044i	−0.0378766	+	0.0451396i
$289$	−7.49340	−	2.72737i	−0.440788	−	0.160434i
$290$	−3.21896	+	10.7943i	−0.189024	+	0.633862i
$291$	−1.51407	+	1.27046i	−0.0887565	+	0.0744756i
$292$	−11.9259	+	6.88540i	−0.697909	+	0.402938i
$293$	26.7907	+	15.4676i	1.56513	+	0.903628i	0.996724	+	0.0808793i	$0.0257728\pi$
$293$	26.7907	+	15.4676i	1.56513	+	0.903628i	0.568406	+	0.822749i	$0.307560\pi$
$294$	−1.15862	−	6.57087i	−0.0675722	−	0.383221i
$295$	2.94526	−	5.88025i	0.171480	−	0.342361i
$296$	−3.69283	+	6.39616i	−0.214641	+	0.371769i
$297$	5.59698	−	3.23142i	0.324770	−	0.187506i
$298$	−1.08544	−	1.29358i	−0.0628780	−	0.0749350i
$299$	−0.301446	+	0.109717i	−0.0174331	+	0.00634511i
$300$	4.99215	+	0.279998i	0.288222	+	0.0161657i
$301$	−2.94434	−	2.47060i	−0.169709	−	0.142403i
$302$	11.1275	+	1.96207i	0.640313	+	0.112905i
$303$			5.50942i			0.316508i
$304$	0.486886	+	4.33162i	0.0279248	+	0.248436i
$305$	−8.40911	−	6.24632i	−0.481504	−	0.357663i
$306$	−0.521688	+	2.95864i	−0.0298229	+	0.169134i
$307$	5.82709	−	6.94446i	0.332570	−	0.396341i	−0.573683	−	0.819077i	$-0.694486\pi$
$307$	5.82709	−	6.94446i	0.332570	−	0.396341i	0.906253	+	0.422736i	$0.138930\pi$
$308$	1.26547	−	3.47686i	0.0721070	−	0.198112i
$309$	8.62294	−	3.13850i	0.490542	−	0.178543i
$310$	−0.0426707	−	0.719312i	−0.00242353	−	0.0408542i
$311$	−14.2785	−	24.7312i	−0.809662	−	1.40238i	−0.913098	−	0.407740i	$-0.866317\pi$
$311$	−14.2785	−	24.7312i	−0.809662	−	1.40238i	0.103436	−	0.994636i	$-0.467016\pi$
$312$	−1.77125	−	1.02263i	−0.100277	−	0.0578951i
$313$	−14.6146	+	2.57695i	−0.826067	+	0.145658i	−0.570671	−	0.821179i	$-0.693317\pi$
$313$	−14.6146	+	2.57695i	−0.826067	+	0.145658i	−0.255396	+	0.966837i	$0.582206\pi$
$314$	0.465848	+	2.64196i	0.0262893	+	0.149094i
$315$	−0.508307	−	1.17491i	−0.0286398	−	0.0661989i
$316$	5.52052	+	9.56182i	0.310553	+	0.537894i
$317$	16.1341	+	19.2278i	0.906179	+	1.07994i	0.996464	+	0.0840259i	$0.0267778\pi$
$317$	16.1341	+	19.2278i	0.906179	+	1.07994i	−0.0902847	+	0.995916i	$0.528778\pi$
$318$	0.269736	+	0.741094i	0.0151260	+	0.0415585i
$319$	−30.5927	−	11.1348i	−1.71286	−	0.623430i
$320$	−0.518010	−	2.17524i	−0.0289576	−	0.121600i
$321$	−1.40717	+	7.98046i	−0.0785406	+	0.445426i
$322$			0.0897949i			0.00500408i
$323$	7.77347	+	10.5386i	0.432528	+	0.586381i
$324$	−1.00000			−0.0555556
$325$	1.20903	+	10.1546i	0.0670647	+	0.563276i
$326$	12.9826	+	10.8937i	0.719042	+	0.603348i
$327$	−3.45277	+	9.48639i	−0.190938	+	0.524599i
$328$	−0.104689	−	0.287632i	−0.00578051	−	0.0158818i
$329$	2.36188	−	1.98185i	0.130215	−	0.109263i
$330$	−1.66228	+	14.3554i	−0.0915053	+	0.790240i
$331$	−9.22456	+	15.9774i	−0.507027	+	0.878197i	0.492939	+	0.870064i	$0.335922\pi$
$331$	−9.22456	+	15.9774i	−0.507027	+	0.878197i	−0.999967	+	0.00813375i	$0.997411\pi$
$332$	−9.53804	+	1.68181i	−0.523468	+	0.0923015i
$333$	−7.27345	+	1.28251i	−0.398583	+	0.0702809i
$334$	−3.36878	+	5.83490i	−0.184332	+	0.319272i
$335$	19.6965	+	2.28074i	1.07613	+	0.124610i
$336$	−0.438563	+	0.367998i	−0.0239256	+	0.0200759i
$337$	−11.5772	−	31.8082i	−0.630652	−	1.73270i	−0.679275	−	0.733884i	$-0.737706\pi$
$337$	−11.5772	−	31.8082i	−0.630652	−	1.73270i	0.0486235	−	0.998817i	$-0.484517\pi$
$338$	−3.01556	+	8.28517i	−0.164025	+	0.450654i
$339$	1.39555	+	1.17101i	0.0757959	+	0.0636003i
$340$	−4.61526	−	4.88138i	−0.250298	−	0.264730i
$341$	2.08266			0.112782
$342$	−3.00525	+	3.15729i	−0.162505	+	0.170727i
$343$		−	7.82740i		−	0.422640i
$344$	1.16581	−	6.61162i	0.0628561	−	0.356475i
$345$	−0.0812479	−	0.341178i	−0.00437424	−	0.0183684i
$346$	−18.1277	−	6.59794i	−0.974551	−	0.354707i
$347$	7.35360	+	20.2038i	0.394762	+	1.08460i	0.964801	+	0.262982i	$0.0847058\pi$
$347$	7.35360	+	20.2038i	0.394762	+	1.08460i	−0.570039	+	0.821618i	$0.693072\pi$
$348$	3.23799	+	3.85889i	0.173575	+	0.206858i
$349$	3.50353	+	6.06829i	0.187540	+	0.324828i	0.944429	−	0.328714i	$-0.106615\pi$
$349$	3.50353	+	6.06829i	0.187540	+	0.324828i	−0.756890	+	0.653543i	$0.773282\pi$
$350$	2.78677	+	0.654155i	0.148959	+	0.0349661i
$351$	−0.355156	−	2.01419i	−0.0189568	−	0.107510i
$352$	6.36465	−	1.12226i	0.339237	−	0.0598167i
$353$	−12.0093	−	6.93360i	−0.639193	−	0.369038i	0.145111	−	0.989415i	$-0.453646\pi$
$353$	−12.0093	−	6.93360i	−0.639193	−	0.369038i	−0.784304	+	0.620377i	$0.786979\pi$
$354$	−1.47058	−	2.54711i	−0.0781603	−	0.135378i
$355$	−26.0030	+	1.54254i	−1.38010	+	0.0818694i
$356$	1.38585	−	0.504410i	0.0734501	−	0.0267337i
$357$	−0.588261	+	1.61623i	−0.0311341	+	0.0855401i
$358$	10.6357	−	12.6752i	0.562115	−	0.669903i
$359$	4.95743	−	28.1150i	0.261643	−	1.48385i	−0.516783	−	0.856116i	$-0.672871\pi$
$359$	4.95743	−	28.1150i	0.261643	−	1.48385i	0.778427	−	0.627736i	$-0.216018\pi$
$360$	1.33336	−	1.79504i	0.0702742	−	0.0946067i
$361$	0.936947	+	18.9769i	0.0493130	+	0.998783i
$362$			26.5620i			1.39607i
$363$	−30.3008	−	5.34285i	−1.59038	−	0.280427i
$364$	−0.896977	−	0.752653i	−0.0470144	−	0.0394497i
$365$	25.7085	−	16.9484i	1.34565	−	0.887118i
$366$	−4.40213	+	1.60224i	−0.230103	+	0.0837506i
$367$	−14.2486	−	16.9808i	−0.743769	−	0.886389i	0.252938	−	0.967483i	$-0.418603\pi$
$367$	−14.2486	−	16.9808i	−0.743769	−	0.886389i	−0.996706	+	0.0810937i	$0.974159\pi$
$368$	−0.135833	+	0.0784231i	−0.00708077	+	0.00408809i
$369$	0.153046	−	0.265083i	0.00796724	−	0.0137997i
$370$	7.39598	−	14.7661i	0.384499	−	0.767655i
$371$	0.0784035	+	0.444648i	0.00407051	+	0.0230850i
$372$	−0.279078	−	0.161126i	−0.0144695	−	0.00835399i
$373$	26.8531	−	15.5036i	1.39040	−	0.802747i	0.397039	−	0.917802i	$-0.370038\pi$
$373$	26.8531	−	15.5036i	1.39040	−	0.802747i	0.993359	+	0.115055i	$0.0367043\pi$
$374$	14.8736	−	12.4805i	0.769098	−	0.645350i
$375$	−11.1803	+	0.0360362i	−0.577347	+	0.00186090i
$376$	5.06071	+	1.84195i	0.260986	+	0.0949913i
$377$	−6.62255	+	7.89245i	−0.341079	+	0.406482i
$378$	−0.563806	−	0.0994141i	−0.0289990	−	0.00511331i
$379$	31.4277			1.61433			0.807165	−	0.590326i	$-0.201001\pi$
$379$	31.4277			1.61433			0.807165	+	0.590326i	$0.201001\pi$
$380$	−1.66037	−	9.60433i	−0.0851751	−	0.492692i
$381$	−8.47838			−0.434361
$382$	−5.23470	−	0.923019i	−0.267831	−	0.0472258i
$383$	−0.925805	+	1.10333i	−0.0473064	+	0.0563776i	−0.789179	−	0.614163i	$-0.789494\pi$
$383$	−0.925805	+	1.10333i	−0.0473064	+	0.0563776i	0.741872	+	0.670541i	$0.233938\pi$
$384$	−0.939693	−	0.342020i	−0.0479535	−	0.0174536i
$385$	−2.36433	+	7.92841i	−0.120498	+	0.404069i
$386$	−7.85995	+	6.59528i	−0.400061	+	0.335691i
$387$	5.81416	−	3.35681i	0.295550	−	0.170636i
$388$	−1.71168	−	0.988241i	−0.0868976	−	0.0501703i
$389$	−3.62043	−	20.5325i	−0.183563	−	1.04104i	−0.927788	−	0.373108i	$-0.878292\pi$
$389$	−3.62043	−	20.5325i	−0.183563	−	1.04104i	0.744225	−	0.667929i	$-0.232819\pi$
$390$	4.08910	+	2.04812i	0.207059	+	0.103711i
$391$	−0.235605	+	0.408080i	−0.0119150	+	0.0206375i
$392$	5.77833	−	3.33612i	0.291850	−	0.168500i
$393$	−0.731302	−	0.871532i	−0.0368893	−	0.0439630i
$394$	−7.44713	+	2.71053i	−0.375181	+	0.136555i
$395$	−13.5887	−	20.6124i	−0.683722	−	1.03712i
$396$	4.95082	+	4.15423i	0.248788	+	0.208758i
$397$	−35.1112	−	6.19105i	−1.76218	−	0.310720i	−0.803521	−	0.595276i	$-0.797043\pi$
$397$	−35.1112	−	6.19105i	−1.76218	−	0.310720i	−0.958659	+	0.284556i	$0.908154\pi$
$398$		−	22.0811i		−	1.10682i
$399$	−2.00826	+	1.48133i	−0.100539	+	0.0741594i
$400$	1.44431	+	4.78686i	0.0722153	+	0.239343i
$401$	−1.63506	+	9.27288i	−0.0816510	+	0.463066i	0.916378	+	0.400314i	$0.131099\pi$
$401$	−1.63506	+	9.27288i	−0.0816510	+	0.463066i	−0.998029	+	0.0627520i	$0.980012\pi$
$402$	5.69984	−	6.79281i	0.284282	−	0.338794i
$403$	0.225422	−	0.619342i	0.0112291	−	0.0308516i
$404$	−5.17716	+	1.88433i	−0.257573	+	0.0937490i
$405$	2.23214	−	0.132414i	0.110916	−	0.00657971i
$406$	1.44197	+	2.49757i	0.0715638	+	0.123952i
$407$	41.3374	+	23.8661i	2.04902	+	1.18300i
$408$	−2.95864	+	0.521688i	−0.146474	+	0.0258274i
$409$	−3.89152	−	22.0699i	−0.192423	−	1.09129i	−0.916041	−	0.401086i	$-0.868633\pi$
$409$	−3.89152	−	22.0699i	−0.192423	−	1.09129i	0.723617	−	0.690202i	$-0.242478\pi$
$410$	0.271768	+	0.628173i	0.0134217	+	0.0310233i
$411$	−11.6609	−	20.1972i	−0.575188	−	0.996255i
$412$	5.89844	+	7.02949i	0.290595	+	0.346318i
$413$	−0.575900	−	1.58227i	−0.0283382	−	0.0778585i
$414$	−0.147387	−	0.0536445i	−0.00724368	−	0.00263649i
$415$	21.0676	−	5.01702i	1.03417	−	0.246276i
$416$	0.355156	−	2.01419i	0.0174130	−	0.0987539i
$417$		−	18.4500i		−	0.903500i
$418$	27.9946	−	3.14667i	1.36926	−	0.153909i
$419$	−13.4514			−0.657143			−0.328571	−	0.944479i	$-0.606567\pi$
$419$	−13.4514			−0.657143			−0.328571	+	0.944479i	$0.606567\pi$
$420$	0.930207	−	0.879496i	0.0453895	−	0.0429150i
$421$	24.6267	+	20.6642i	1.20023	+	1.00711i	0.999623	+	0.0274407i	$0.00873575\pi$
$421$	24.6267	+	20.6642i	1.20023	+	1.00711i	0.200607	+	0.979672i	$0.435709\pi$
$422$	8.61792	−	23.6775i	0.419514	−	1.15260i
$423$	1.84195	+	5.06071i	0.0895586	+	0.246060i
$424$	−0.604145	+	0.506938i	−0.0293399	+	0.0246191i
$425$	10.9483	+	10.2848i	0.531070	+	0.498886i
$426$	−5.82467	+	10.0886i	−0.282206	+	0.488796i
$427$	−2.64123	+	0.465720i	−0.127818	+	0.0225378i
$428$	−7.98046	+	1.40717i	−0.385750	+	0.0680181i
$429$	−6.60911	+	11.4473i	−0.319091	+	0.552681i
$430$	−1.72678	+	14.9125i	−0.0832726	+	0.719143i
$431$	13.7491	−	11.5369i	0.662272	−	0.555712i	−0.248495	−	0.968633i	$-0.579936\pi$
$431$	13.7491	−	11.5369i	0.662272	−	0.555712i	0.910767	+	0.412921i	$0.135492\pi$
$432$	−0.342020	−	0.939693i	−0.0164555	−	0.0452110i
$433$	−9.07472	+	24.9326i	−0.436103	+	1.19818i	0.505904	+	0.862590i	$0.331159\pi$
$433$	−9.07472	+	24.9326i	−0.436103	+	1.19818i	−0.942007	+	0.335593i	$0.891063\pi$
$434$	−0.141328	−	0.118588i	−0.00678395	−	0.00569241i
$435$	−7.73864	−	8.18484i	−0.371039	−	0.392433i
$436$	−10.0952			−0.483473
$437$	−0.612307	+	0.304129i	−0.0292906	+	0.0145484i
$438$		−	13.7708i		−	0.657995i
$439$	1.17941	−	6.68874i	0.0562900	−	0.319236i	−0.943641	−	0.330970i	$-0.892624\pi$
$439$	1.17941	−	6.68874i	0.0562900	−	0.319236i	0.999931	+	0.0117340i	$0.00373513\pi$
$440$	−14.0582	+	3.34782i	−0.670199	+	0.159601i
$441$	6.26985	+	2.28204i	0.298565	+	0.108669i
$442$	−2.10156	−	5.77398i	−0.0999609	−	0.274640i
$443$	21.4008	+	25.5045i	1.01678	+	1.21176i	0.977152	+	0.212541i	$0.0681738\pi$
$443$	21.4008	+	25.5045i	1.01678	+	1.21176i	0.0396310	+	0.999214i	$0.487382\pi$
$444$	−3.69283	−	6.39616i	−0.175254	−	0.303549i
$445$	−3.02664	+	1.30942i	−0.143476	+	0.0620725i
$446$	−4.41908	−	25.0618i	−0.209249	−	1.18671i
$447$	1.66299	−	0.293231i	0.0786569	−	0.0138693i
$448$	−0.495802	−	0.286252i	−0.0234245	−	0.0135241i
$449$	1.89302	+	3.27880i	0.0893371	+	0.154736i	0.907231	−	0.420633i	$-0.138192\pi$
$449$	1.89302	+	3.27880i	0.0893371	+	0.154736i	−0.817894	+	0.575369i	$0.804858\pi$
$450$	−2.73856	+	4.18333i	−0.129097	+	0.197204i
$451$	−1.85892	+	0.676591i	−0.0875330	+	0.0318594i
$452$	−0.623079	+	1.71190i	−0.0293072	+	0.0805208i
$453$	−7.26293	+	8.65563i	−0.341242	+	0.406677i
$454$	2.44052	−	13.8409i	0.114539	−	0.649583i
$455$	2.10184	+	1.56126i	0.0985359	+	0.0731929i
$456$	−3.99474	−	1.74415i	−0.187071	−	0.0816775i
$457$			7.22193i			0.337827i	0.985631	+	0.168914i	$0.0540259\pi$
$457$			7.22193i			0.337827i	−0.985631	+	0.168914i	$0.945974\pi$
$458$	5.23884	+	0.923748i	0.244795	+	0.0431639i
$459$	−2.30141	−	1.93111i	−0.107421	−	0.0901367i
$460$	0.292814	−	0.193038i	0.0136525	−	0.00900043i
$461$	−14.2894	+	5.20092i	−0.665524	+	0.242231i	−0.652620	−	0.757686i	$-0.726330\pi$
$461$	−14.2894	+	5.20092i	−0.665524	+	0.242231i	−0.0129048	+	0.999917i	$0.504108\pi$
$462$	2.37831	+	2.83436i	0.110649	+	0.131866i
$463$	10.2252	−	5.90355i	0.475207	−	0.274361i	−0.243210	−	0.969974i	$-0.578200\pi$
$463$	10.2252	−	5.90355i	0.475207	−	0.274361i	0.718417	+	0.695613i	$0.244867\pi$
$464$	−2.51871	+	4.36254i	−0.116928	+	0.202526i
$465$	0.644278	+	0.322702i	0.0298777	+	0.0149650i
$466$	1.74920	+	9.92022i	0.0810302	+	0.459545i
$467$	17.4184	+	10.0565i	0.806026	+	0.465359i	0.845574	−	0.533859i	$-0.179259\pi$
$467$	17.4184	+	10.0565i	0.806026	+	0.465359i	−0.0395481	+	0.999218i	$0.512592\pi$
$468$	1.77125	−	1.02263i	0.0818761	−	0.0472712i
$469$	3.88890	−	3.26318i	0.179573	−	0.150680i
$470$	−11.5401	−	3.44139i	−0.532307	−	0.158739i
$471$	−2.52092	−	0.917542i	−0.116158	−	0.0422781i
$472$	1.89054	−	2.25305i	0.0870190	−	0.103705i
$473$	−42.7298	−	7.53442i	−1.96472	−	0.346433i
$474$	−11.0410			−0.507132
$475$	4.97793	+	21.2184i	0.228403	+	0.973567i
$476$	−1.71996			−0.0788342
$477$	−0.776674	−	0.136949i	−0.0355615	−	0.00627044i
$478$	−7.92526	+	9.44496i	−0.362493	+	0.432002i
$479$	−2.75040	−	1.00106i	−0.125669	−	0.0457397i	0.278420	−	0.960459i	$-0.410189\pi$
$479$	−2.75040	−	1.00106i	−0.125669	−	0.0457397i	−0.404089	+	0.914720i	$0.632411\pi$
$480$	2.14282	+	0.639010i	0.0978058	+	0.0291667i
$481$	11.5716	−	9.70970i	0.527618	−	0.442724i
$482$	−6.46145	+	3.73052i	−0.294311	+	0.169921i
$483$	−0.0777647	−	0.0448975i	−0.00353842	−	0.00204291i
$484$	−5.34285	−	30.3008i	−0.242857	−	1.37731i
$485$	3.95158	+	1.97924i	0.179432	+	0.0898729i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	8.40502	−	4.85264i	0.380868	−	0.219894i	−0.297328	−	0.954775i	$-0.596095\pi$
$487$	8.40502	−	4.85264i	0.380868	−	0.219894i	0.678196	+	0.734881i	$0.262762\pi$
$488$	−3.01123	−	3.58865i	−0.136312	−	0.162450i
$489$	−15.9256	+	5.79644i	−0.720180	+	0.262124i
$490$	−12.4563	+	8.21183i	−0.562719	+	0.370973i
$491$	18.7113	+	15.7006i	0.844428	+	0.708559i	0.958555	−	0.284907i	$-0.0919627\pi$
$491$	18.7113	+	15.7006i	0.844428	+	0.708559i	−0.114127	+	0.993466i	$0.536407\pi$
$492$	0.301441	+	0.0531522i	0.0135900	+	0.00239629i
$493$			15.1338i			0.681593i
$494$	2.09431	−	8.66562i	0.0942273	−	0.389884i
$495$	−11.6010	−	8.61729i	−0.521427	−	0.387318i
$496$	0.0559584	−	0.317356i	0.00251261	−	0.0142497i
$497$	−4.28694	+	5.10897i	−0.192295	+	0.229169i
$498$	3.31253	−	9.10109i	0.148438	−	0.407830i
$499$	10.9391	−	3.98149i	0.489699	−	0.178236i	−0.0853559	−	0.996351i	$-0.527203\pi$
$499$	10.9391	−	3.98149i	0.489699	−	0.178236i	0.575055	+	0.818114i	$0.304981\pi$
$500$	−3.85774	−	10.4937i	−0.172524	−	0.469293i
$501$	−3.36878	−	5.83490i	−0.150506	−	0.260684i
$502$	−27.1235	−	15.6598i	−1.21058	−	0.698929i
$503$	−28.4595	+	5.01818i	−1.26895	+	0.223750i	−0.767281	−	0.641312i	$-0.778391\pi$
$503$	−28.4595	+	5.01818i	−1.26895	+	0.223750i	−0.501666	+	0.865061i	$0.667280\pi$
$504$	−0.0994141	−	0.563806i	−0.00442826	−	0.0251139i
$505$	11.3067	−	4.89163i	0.503139	−	0.217675i
$506$	0.506836	+	0.877865i	0.0225316	+	0.0390259i
$507$	−5.66739	−	6.75413i	−0.251698	−	0.299962i
$508$	−2.89978	−	7.96707i	−0.128657	−	0.353482i
$509$	−20.3032	−	7.38976i	−0.899924	−	0.327546i	−0.149702	−	0.988731i	$-0.547831\pi$
$509$	−20.3032	−	7.38976i	−0.899924	−	0.327546i	−0.750222	+	0.661186i	$0.770054\pi$
$510$	6.53503	−	1.55625i	0.289376	−	0.0689118i
$511$	1.36901	−	7.76406i	0.0605616	−	0.343462i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.23167	−	4.18127i	−0.0543795	−	0.184607i
$514$	−11.5858			−0.511029
$515$	−14.0970	−	14.9098i	−0.621187	−	0.657004i
$516$	5.14293	+	4.31543i	0.226405	+	0.189976i
$517$	11.9042	−	32.7066i	0.523547	−	1.43843i
$518$	−1.44617	−	3.97331i	−0.0635409	−	0.174577i
$519$	14.7778	−	12.4001i	0.648675	−	0.544303i
$520$	−0.526053	+	4.54299i	−0.0230689	+	0.199223i
$521$	18.5148	−	32.0686i	0.811149	−	1.40495i	−0.100912	−	0.994895i	$-0.532176\pi$
$521$	18.5148	−	32.0686i	0.811149	−	1.40495i	0.912061	−	0.410055i	$-0.134491\pi$
$522$	−4.96089	+	0.874739i	−0.217132	+	0.0382863i
$523$	−26.5180	+	4.67584i	−1.15955	+	0.204460i	−0.720142	−	0.693826i	$-0.755924\pi$
$523$	−26.5180	+	4.67584i	−1.15955	+	0.204460i	−0.439410	+	0.898287i	$0.644812\pi$
$524$	0.568852	−	0.985281i	0.0248504	−	0.0430422i
$525$	−1.95990	+	2.08633i	−0.0855370	+	0.0910551i
$526$	−10.6145	+	8.90660i	−0.462813	+	0.388346i
$527$	−0.331121	−	0.909749i	−0.0144239	−	0.0396293i
$528$	−2.21042	+	6.07308i	−0.0961962	+	0.264297i
$529$	17.6002	+	14.7683i	0.765225	+	0.642100i
$530$	1.28141	−	1.21156i	0.0556610	−	0.0526266i
$531$	2.94115			0.127635
$532$	−2.07886	−	1.38050i	−0.0901301	−	0.0598522i
$533$			0.626038i			0.0271167i
$534$	−0.256096	+	1.45239i	−0.0110823	+	0.0628511i
$535$	17.6272	−	4.19773i	0.762090	−	0.181484i
$536$	8.33261	+	3.03282i	0.359914	+	0.130998i
$537$	5.65915	+	15.5484i	0.244210	+	0.670962i
$538$	−6.27389	−	7.47693i	−0.270486	−	0.322353i
$539$	−21.5608	−	37.3444i	−0.928690	−	1.60854i
$540$	0.887867	+	2.05224i	0.0382077	+	0.0883144i
$541$	−5.54887	−	31.4692i	−0.238565	−	1.35297i	−0.834975	−	0.550288i	$-0.814518\pi$
$541$	−5.54887	−	31.4692i	−0.238565	−	1.35297i	0.596410	−	0.802680i	$-0.296593\pi$
$542$	7.19998	−	1.26955i	0.309266	−	0.0545319i
$543$	−23.0034	−	13.2810i	−0.987168	−	0.569942i
$544$	−1.50214	−	2.60178i	−0.0644037	−	0.111550i
$545$	22.5340	−	1.33675i	0.965249	−	0.0572600i
$546$	1.10031	−	0.400478i	0.0470887	−	0.0171389i
$547$	−9.33255	+	25.6410i	−0.399031	+	1.09633i	0.563726	+	0.825962i	$0.309367\pi$
$547$	−9.33255	+	25.6410i	−0.399031	+	1.09633i	−0.962757	+	0.270367i	$0.912855\pi$
$548$	14.9909	−	17.8655i	0.640380	−	0.763176i
$549$	0.813480	−	4.61348i	0.0347185	−	0.196898i
$550$	30.9367	−	9.33431i	1.31914	−	0.398016i
$551$	−12.1469	+	18.2918i	−0.517476	+	0.779256i
$552$		−	0.156846i		−	0.00667582i
$553$	−6.22500	−	1.09764i	−0.264714	−	0.0466762i
$554$	9.39774	+	7.88564i	0.399272	+	0.335029i
$555$	9.08986	+	13.7882i	0.385843	+	0.585276i
$556$	17.3373	−	6.31027i	0.735266	−	0.267615i
$557$	−17.5346	−	20.8970i	−0.742966	−	0.885433i	0.253678	−	0.967289i	$-0.418360\pi$
$557$	−17.5346	−	20.8970i	−0.742966	−	0.885433i	−0.996644	+	0.0818560i	$0.973915\pi$
$558$	0.279078	−	0.161126i	0.0118143	−	0.00682100i
$559$	−6.86556	+	11.8915i	−0.290382	+	0.502957i
$560$	1.14461	+	0.573304i	0.0483684	+	0.0242265i
$561$	3.37158	+	19.1212i	0.142348	+	0.807297i
$562$	−11.2026	−	6.46780i	−0.472552	−	0.272828i
$563$	−23.2741	+	13.4373i	−0.980886	+	0.566315i	−0.902537	−	0.430612i	$-0.858298\pi$
$563$	−23.2741	+	13.4373i	−0.980886	+	0.566315i	−0.0783482	+	0.996926i	$0.524965\pi$
$564$	−4.12553	+	3.46173i	−0.173716	+	0.145765i
$565$	1.16412	−	3.90370i	0.0489750	−	0.164230i
$566$	−21.6780	−	7.89016i	−0.911196	−	0.331648i
$567$	0.367998	−	0.438563i	0.0154545	−	0.0184179i
$568$	−11.4724	−	2.02289i	−0.481370	−	0.0848785i
$569$	7.45629			0.312584			0.156292	−	0.987711i	$-0.450046\pi$
$569$	7.45629			0.312584			0.156292	+	0.987711i	$0.450046\pi$
$570$	9.14778	+	3.36424i	0.383158	+	0.140913i
$571$	12.4848			0.522473			0.261237	−	0.965275i	$-0.415870\pi$
$571$	12.4848			0.522473			0.261237	+	0.965275i	$0.415870\pi$
$572$	−13.0174	−	2.29532i	−0.544285	−	0.0959721i
$573$	3.41671	−	4.07187i	0.142735	−	0.170105i
$574$	0.164670	+	0.0599350i	0.00687320	+	0.00250164i
$575$	−0.628042	+	0.469661i	−0.0261912	+	0.0195862i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	−12.1507	+	7.01519i	−0.505839	+	0.292046i	−0.731122	−	0.682247i	$-0.761003\pi$
$577$	−12.1507	+	7.01519i	−0.505839	+	0.292046i	0.225283	+	0.974293i	$0.427669\pi$
$578$	6.90595	+	3.98715i	0.287250	+	0.165844i
$579$	−1.78171	−	10.1046i	−0.0740452	−	0.419931i
$580$	5.04446	−	10.0713i	0.209460	−	0.418189i
$581$	2.77240	−	4.80193i	0.115018	−	0.199218i
$582$	1.71168	−	0.988241i	0.0709516	−	0.0409639i
$583$	3.27626	+	3.90449i	0.135689	+	0.161708i
$584$	12.9403	−	4.70989i	0.535474	−	0.194897i
$585$	−3.81828	+	2.51720i	−0.157866	+	0.104073i
$586$	−23.6978	−	19.8848i	−0.978946	−	0.821433i
$587$	−30.1534	−	5.31686i	−1.24456	−	0.219450i	−0.487693	−	0.873015i	$-0.662162\pi$
$587$	−30.1534	−	5.31686i	−1.24456	−	0.219450i	−0.756871	+	0.653565i	$0.773273\pi$
$588$			6.67224i			0.275159i
$589$	0.329979	−	1.36535i	0.0135965	−	0.0562584i
$590$	−3.92161	+	5.27947i	−0.161450	+	0.217352i
$591$	1.37617	−	7.80467i	0.0566082	−	0.321041i
$592$	4.74741	−	5.65774i	0.195117	−	0.232532i
$593$	−15.8989	+	43.6820i	−0.652891	+	1.79380i	−0.0461077	+	0.998936i	$0.514682\pi$
$593$	−15.8989	+	43.6820i	−0.652891	+	1.79380i	−0.606783	+	0.794867i	$0.707540\pi$
$594$	−6.07308	+	2.21042i	−0.249182	+	0.0906947i
$595$	3.83920	−	0.227747i	0.157392	−	0.00933671i
$596$	0.844324	+	1.46241i	0.0345849	+	0.0599027i
$597$	19.1228	+	11.0405i	0.782643	+	0.451859i
$598$	0.315918	−	0.0557049i	0.0129189	−	0.00227794i
$599$	0.134166	+	0.760896i	0.00548189	+	0.0310894i	0.987426	−	0.158082i	$-0.0505310\pi$
$599$	0.134166	+	0.760896i	0.00548189	+	0.0310894i	−0.981944	+	0.189171i	$0.939420\pi$
$600$	−4.86769	−	1.14262i	−0.198723	−	0.0466474i
$601$	−1.40041	−	2.42557i	−0.0571237	−	0.0989412i	0.836049	−	0.548654i	$-0.184860\pi$
$601$	−1.40041	−	2.42557i	−0.0571237	−	0.0989412i	−0.893173	+	0.449713i	$0.851526\pi$
$602$	2.47060	+	2.94434i	0.100694	+	0.120002i
$603$	3.03282	+	8.33261i	0.123506	+	0.339330i
$604$	−10.6177	−	3.86453i	−0.432028	−	0.157245i
$605$	15.9383	+	66.9283i	0.647983	+	2.72102i
$606$	0.956700	−	5.42572i	0.0388633	−	0.220405i
$607$		−	22.8681i		−	0.928188i	−0.885786	−	0.464094i	$-0.846380\pi$
$607$		−	22.8681i		−	0.928188i	0.885786	−	0.464094i	$-0.153620\pi$
$608$	0.272689	−	4.35036i	0.0110590	−	0.176430i
$609$	−2.88394			−0.116863
$610$	7.19669	+	7.61165i	0.291386	+	0.308187i
$611$	−8.43780	−	7.08016i	−0.341357	−	0.286432i
$612$	1.02752	−	2.82310i	0.0415352	−	0.114117i
$613$	13.0659	+	35.8983i	0.527728	+	1.44992i	0.861740	+	0.507351i	$0.169375\pi$
$613$	13.0659	+	35.8983i	0.527728	+	1.44992i	−0.334012	+	0.942569i	$0.608403\pi$
$614$	−6.94446	+	5.82709i	−0.280255	+	0.235162i
$615$	−0.679898	−	0.0787283i	−0.0274161	−	0.00317463i
$616$	−1.85000	+	3.20429i	−0.0745385	+	0.129105i
$617$	−7.54717	+	1.33077i	−0.303838	+	0.0535748i	−0.323488	−	0.946232i	$-0.604856\pi$
$617$	−7.54717	+	1.33077i	−0.303838	+	0.0535748i	0.0196508	+	0.999807i	$0.493745\pi$
$618$	−9.03694	+	1.59346i	−0.363519	+	0.0640982i
$619$	−2.84877	+	4.93421i	−0.114502	+	0.198323i	−0.917580	−	0.397550i	$-0.869860\pi$
$619$	−2.84877	+	4.93421i	−0.114502	+	0.198323i	0.803079	+	0.595873i	$0.203194\pi$
$620$	−0.0828849	+	0.715794i	−0.00332874	+	0.0287470i
$621$	0.120151	−	0.100819i	0.00482150	−	0.00404572i
$622$	9.76710	+	26.8349i	0.391625	+	1.07598i
$623$	−0.288776	+	0.793406i	−0.0115696	+	0.0317871i
$624$	1.56676	+	1.31467i	0.0627207	+	0.0526289i
$625$	10.0006	+	22.9126i	0.400022	+	0.916505i
$626$	14.8401			0.593128
$627$	−11.2722	+	25.8173i	−0.450168	+	1.03105i
$628$		−	2.68271i		−	0.107052i
$629$	3.85300	−	21.8515i	0.153629	−	0.871275i
$630$	0.296562	+	1.24533i	0.0118153	+	0.0496152i
$631$	38.2110	+	13.9077i	1.52116	+	0.553656i	0.961437	−	0.275026i	$-0.0886866\pi$
$631$	38.2110	+	13.9077i	1.52116	+	0.553656i	0.559720	+	0.828682i	$0.310909\pi$
$632$	−3.77626	−	10.3752i	−0.150211	−	0.412703i
$633$	16.1964	+	19.3021i	0.643749	+	0.767190i
$634$	−12.5501	−	21.7374i	−0.498427	−	0.863301i
$635$	7.52767	+	17.3997i	0.298727	+	0.690485i
$636$	−0.136949	−	0.776674i	−0.00543036	−	0.0307971i
$637$	−13.4392	+	2.36969i	−0.532479	+	0.0938905i
$638$	28.1944	+	16.2780i	1.11623	+	0.644453i
$639$	−5.82467	−	10.0886i	−0.230421	−	0.399100i
$640$	0.132414	+	2.23214i	0.00523413	+	0.0882332i
$641$	−31.4347	+	11.4413i	−1.24159	+	0.451903i	−0.877553	−	0.479479i	$-0.840826\pi$
$641$	−31.4347	+	11.4413i	−1.24159	+	0.451903i	−0.364041	+	0.931383i	$0.618603\pi$
$642$	2.77158	−	7.61486i	0.109386	−	0.300535i
$643$	20.6525	−	24.6127i	0.814455	−	0.970630i	−0.185473	−	0.982649i	$-0.559382\pi$
$643$	20.6525	−	24.6127i	0.814455	−	0.970630i	0.999928	+	0.0120195i	$0.00382602\pi$
$644$	0.0155927	−	0.0884307i	0.000614439	−	0.00348466i
$645$	−12.0512	−	8.95166i	−0.474515	−	0.352471i
$646$	−5.82537	−	11.7283i	−0.229196	−	0.461444i
$647$		−	20.9365i		−	0.823100i	−0.911387	−	0.411550i	$-0.864988\pi$
$647$		−	20.9365i		−	0.823100i	0.911387	−	0.411550i	$-0.135012\pi$
$648$	0.984808	+	0.173648i	0.0386869	+	0.00682154i
$649$	−14.5611	−	12.2182i	−0.571574	−	0.479608i
$650$	0.572669	−	10.2103i	0.0224619	−	0.400480i
$651$	0.173364	−	0.0630994i	0.00679467	−	0.00247306i
$652$	−10.8937	−	12.9826i	−0.426632	−	0.508440i
$653$	14.5837	−	8.41988i	0.570703	−	0.329496i	−0.186727	−	0.982412i	$-0.559788\pi$
$653$	14.5837	−	8.41988i	0.570703	−	0.329496i	0.757430	+	0.652916i	$0.226455\pi$
$654$	5.04760	−	8.74271i	0.197377	−	0.341867i
$655$	−1.13929	+	2.27461i	−0.0445159	+	0.0888764i
$656$	0.0531522	+	0.301441i	0.00207525	+	0.0117693i
$657$	11.9259	+	6.88540i	0.465272	+	0.268625i
$658$	−2.67014	+	1.54161i	−0.104093	+	0.0600981i
$659$	22.9133	−	19.2265i	0.892575	−	0.748959i	−0.0761500	−	0.997096i	$-0.524263\pi$
$659$	22.9133	−	19.2265i	0.892575	−	0.748959i	0.968725	+	0.248137i	$0.0798183\pi$
$660$	4.12982	−	13.8487i	0.160753	−	0.539059i
$661$	−4.35222	−	1.58408i	−0.169282	−	0.0616135i	0.255989	−	0.966680i	$-0.417599\pi$
$661$	−4.35222	−	1.58408i	−0.169282	−	0.0616135i	−0.425271	+	0.905066i	$0.639821\pi$
$662$	11.8589	−	14.1328i	0.460908	−	0.549288i
$663$	6.05120	+	1.06699i	0.235009	+	0.0414384i
$664$	9.68518			0.375858
$665$	4.82312	+	2.80620i	0.187032	+	0.108820i
$666$	7.38565			0.286188
$667$	−0.778097	−	0.137199i	−0.0301280	−	0.00531239i
$668$	4.33082	−	5.16127i	0.167565	−	0.199696i
$669$	23.9137	+	8.70389i	0.924558	+	0.336512i
$670$	−19.0012	−	5.66634i	−0.734079	−	0.218910i
$671$	−23.1928	+	19.4611i	−0.895350	+	0.751288i
$672$	0.495802	−	0.286252i	0.0191260	−	0.0110424i
$673$	12.4469	+	7.18624i	0.479794	+	0.277009i	0.720331	−	0.693631i	$-0.243990\pi$
$673$	12.4469	+	7.18624i	0.479794	+	0.277009i	−0.240537	+	0.970640i	$0.577323\pi$
$674$	5.87791	+	33.3353i	0.226409	+	1.28403i
$675$	−2.25359	−	4.46333i	−0.0867408	−	0.171794i
$676$	4.40845	−	7.63565i	0.169556	−	0.293679i
$677$	−15.5629	+	8.98524i	−0.598130	+	0.345331i	−0.768306	−	0.640083i	$-0.778900\pi$
$677$	−15.5629	+	8.98524i	−0.598130	+	0.345331i	0.170175	+	0.985414i	$0.445567\pi$
$678$	−1.17101	−	1.39555i	−0.0449722	−	0.0535958i
$679$	1.06330	−	0.387010i	0.0408058	−	0.0148521i
$680$	3.69750	+	5.60865i	0.141793	+	0.215082i
$681$	10.7663	+	9.03398i	0.412564	+	0.346183i
$682$	−2.05102	−	0.361650i	−0.0785376	−	0.0138483i
$683$		−	23.6970i		−	0.906739i	−0.891323	−	0.453369i	$-0.850222\pi$
$683$		−	23.6970i		−	0.906739i	0.891323	−	0.453369i	$-0.149778\pi$
$684$	3.50785	−	2.58747i	0.134126	−	0.0989343i
$685$	−31.0963	+	41.8633i	−1.18813	+	1.59952i
$686$	−1.35921	+	7.70848i	−0.0518950	+	0.294311i
$687$	−3.41941	+	4.07509i	−0.130459	+	0.155474i
$688$	−2.29619	+	6.30873i	−0.0875415	+	0.240518i
$689$	1.51573	−	0.551681i	0.0577448	−	0.0210174i
$690$	0.0207686	+	0.350103i	0.000790649	+	0.0133282i
$691$	6.08692	+	10.5428i	0.231557	+	0.401069i	0.958267	−	0.285876i	$-0.0922846\pi$
$691$	6.08692	+	10.5428i	0.231557	+	0.401069i	−0.726709	+	0.686945i	$0.758951\pi$
$692$	16.7066	+	9.64554i	0.635088	+	0.366668i
$693$	−3.64378	+	0.642497i	−0.138416	+	0.0244065i
$694$	−3.73352	−	21.1738i	−0.141722	−	0.803748i
$695$	−37.8638	+	16.3811i	−1.43626	+	0.621372i
$696$	−2.51871	−	4.36254i	−0.0954715	−	0.165361i
$697$	0.591097	+	0.704442i	0.0223894	+	0.0266827i
$698$	−2.39656	−	6.58449i	−0.0907110	−	0.249226i
$699$	−9.46576	−	3.44526i	−0.358028	−	0.130312i
$700$	−2.63084	−	1.12813i	−0.0994363	−	0.0426395i
$701$	2.89429	−	16.4143i	0.109316	−	0.619961i	−0.880093	−	0.474802i	$-0.842520\pi$
$701$	2.89429	−	16.4143i	0.109316	−	0.619961i	0.989408	−	0.145159i	$-0.0463693\pi$
$702$			2.04526i			0.0771935i
$703$	22.1957	−	23.3186i	0.837128	−	0.879479i
$704$	−6.46284			−0.243577
$705$	8.75040	−	8.27336i	0.329559	−	0.311593i
$706$	10.6229	+	8.91366i	0.399798	+	0.335470i
$707$	1.07879	−	2.96394i	0.0405719	−	0.111470i
$708$	1.00593	+	2.76378i	0.0378053	+	0.103869i
$709$	13.4680	−	11.3010i	0.505801	−	0.424417i	−0.353848	−	0.935303i	$-0.615127\pi$
$709$	13.4680	−	11.3010i	0.505801	−	0.424417i	0.859649	+	0.510886i	$0.170683\pi$
$710$	25.8758	+	2.99627i	0.971103	+	0.112448i
$711$	5.52052	−	9.56182i	0.207036	−	0.358596i
$712$	−1.45239	+	0.256096i	−0.0544306	+	0.00959759i
$713$	0.0497761	−	0.00877687i	0.00186413	−	0.000328696i
$714$	0.859980	−	1.48953i	0.0321839	−	0.0557442i
$715$	29.3606	+	3.39979i	1.09803	+	0.127145i
$716$	−12.6752	+	10.6357i	−0.473693	+	0.397476i
$717$	−4.21694	−	11.5860i	−0.157485	−	0.432686i
$718$	−9.76423	+	26.8270i	−0.364398	+	1.00117i
$719$	−25.1096	−	21.0694i	−0.936428	−	0.785757i	0.0405318	−	0.999178i	$-0.487095\pi$
$719$	−25.1096	−	21.0694i	−0.936428	−	0.785757i	−0.976960	+	0.213421i	$0.931539\pi$
$720$	−1.62481	+	1.53623i	−0.0605530	+	0.0572519i
$721$	−5.25349			−0.195650
$722$	2.37259	−	18.8513i	0.0882986	−	0.701572i
$723$		−	7.46104i		−	0.277479i
$724$	4.61244	−	26.1584i	0.171420	−	0.972171i
$725$	−9.92639	+	23.1486i	−0.368657	+	0.859717i
$726$	28.9127	+	10.5234i	1.07305	+	0.390559i
$727$	8.48929	+	23.3241i	0.314850	+	0.865044i	0.991659	+	0.128886i	$0.0411400\pi$
$727$	8.48929	+	23.3241i	0.314850	+	0.865044i	−0.676809	+	0.736158i	$0.736638\pi$
$728$	0.752653	+	0.896977i	0.0278952	+	0.0332442i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	−28.2610	+	12.2266i	−1.04599	+	0.452528i
$731$	3.50241	+	19.8632i	0.129541	+	0.734665i
$732$	4.61348	−	0.813480i	0.170519	−	0.0300671i
$733$	2.83348	+	1.63591i	0.104657	+	0.0604237i	0.551415	−	0.834231i	$-0.314088\pi$
$733$	2.83348	+	1.63591i	0.104657	+	0.0604237i	−0.446758	+	0.894655i	$0.647421\pi$
$734$	11.0834	+	19.1970i	0.409096	+	0.708575i
$735$	−0.883498	−	14.8934i	−0.0325883	−	0.549351i
$736$	0.147387	−	0.0536445i	0.00543276	−	0.00197736i
$737$	19.6006	−	53.8523i	0.721999	−	1.98368i
$738$	−0.196752	+	0.234480i	−0.00724253	+	0.00863131i
$739$	−0.807436	+	4.57920i	−0.0297020	+	0.168449i	−0.996051	−	0.0887877i	$-0.971701\pi$
$739$	−0.807436	+	4.57920i	−0.0297020	+	0.168449i	0.966349	+	0.257236i	$0.0828119\pi$
$740$	−9.84773	+	13.2575i	−0.362010	+	0.487356i
$741$	6.45749	+	6.14653i	0.237222	+	0.225798i
$742$		−	0.451508i		−	0.0165754i
$743$	46.5346	+	8.20531i	1.70719	+	0.301024i	0.940197	−	0.340632i	$-0.110641\pi$
$743$	46.5346	+	8.20531i	1.70719	+	0.301024i	0.766993	+	0.641656i	$0.221752\pi$
$744$	0.246859	+	0.207139i	0.00905030	+	0.00759410i
$745$	−2.07830	−	3.15251i	−0.0761429	−	0.115499i
$746$	−29.1373	+	10.6051i	−1.06679	+	0.388280i
$747$	6.22551	+	7.41928i	0.227780	+	0.271457i
$748$	−16.8149	+	9.70809i	−0.614814	+	0.354963i
$749$	2.31966	−	4.01777i	0.0847585	−	0.146806i
$750$	11.0167	+	1.90595i	0.402272	+	0.0695953i
$751$	−1.94953	−	11.0563i	−0.0711394	−	0.403452i	−0.999496	−	0.0317597i	$-0.989889\pi$
$751$	−1.94953	−	11.0563i	−0.0711394	−	0.403452i	0.928356	−	0.371692i	$-0.121222\pi$
$752$	−4.66398	−	2.69275i	−0.170078	−	0.0981945i
$753$	27.1235	−	15.6598i	0.988435	−	0.570673i
$754$	7.89245	−	6.62255i	0.287426	−	0.241179i
$755$	24.2120	+	7.22025i	0.881163	+	0.262772i
$756$	0.537977	+	0.195808i	0.0195660	+	0.00712145i
$757$	2.85651	−	3.40426i	0.103822	−	0.123730i	−0.711631	−	0.702553i	$-0.752043\pi$
$757$	2.85651	−	3.40426i	0.103822	−	0.123730i	0.815453	+	0.578823i	$0.196488\pi$
$758$	−30.9502	−	5.45735i	−1.12416	−	0.198220i
$759$	−1.01367			−0.0367939
$760$	−0.0326314	+	9.74674i	−0.00118367	+	0.353551i
$761$	29.2828			1.06150			0.530750	−	0.847529i	$-0.321910\pi$
$761$	29.2828			1.06150			0.530750	+	0.847529i	$0.321910\pi$
$762$	8.34957	+	1.47226i	0.302473	+	0.0533342i
$763$	3.71502	−	4.42738i	0.134493	−	0.160282i
$764$	4.99489	+	1.81799i	0.180709	+	0.0657727i
$765$	−1.91976	+	6.43762i	−0.0694092	+	0.232753i
$766$	1.10333	−	0.925805i	0.0398650	−	0.0334507i
$767$	−5.20952	+	3.00772i	−0.188105	+	0.108602i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−6.39296	−	36.2563i	−0.230536	−	1.30743i	−0.851814	−	0.523844i	$-0.824497\pi$
$769$	−6.39296	−	36.2563i	−0.230536	−	1.30743i	0.621278	−	0.783590i	$-0.286614\pi$
$770$	3.70517	−	7.39740i	0.133525	−	0.266584i
$771$	5.79291	−	10.0336i	0.208627	−	0.361352i
$772$	8.88580	−	5.13022i	0.319807	−	0.184641i
$773$	−2.46528	−	2.93801i	−0.0886700	−	0.105673i	0.719885	−	0.694093i	$-0.244194\pi$
$773$	−2.46528	−	2.93801i	−0.0886700	−	0.105673i	−0.808555	+	0.588420i	$0.799750\pi$
$774$	−6.30873	+	2.29619i	−0.226763	+	0.0825349i
$775$	0.0902298	−	1.60873i	0.00324115	−	0.0577873i
$776$	1.51407	+	1.27046i	0.0543520	+	0.0456068i
$777$	4.16407	+	0.734238i	0.149385	+	0.0263407i
$778$			20.8492i			0.747480i
$779$	0.149032	+	1.32587i	0.00533962	+	0.0475043i
$780$	−3.67132	−	2.72707i	−0.131454	−	0.0976448i
$781$	−13.0736	+	74.1441i	−0.467810	+	2.65308i
$782$	0.302888	−	0.360968i	0.0108312	−	0.0129082i
$783$	1.72290	−	4.73363i	0.0615714	−	0.169166i
$784$	−6.26985	+	2.28204i	−0.223923	+	0.0815014i
$785$	0.355229	+	5.98820i	0.0126787	+	0.213728i
$786$	0.568852	+	0.985281i	0.0202903	+	0.0351438i
$787$	−0.642579	−	0.370993i	−0.0229055	−	0.0132245i	0.488504	−	0.872562i	$-0.337543\pi$
$787$	−0.642579	−	0.370993i	−0.0229055	−	0.0132245i	−0.511409	+	0.859337i	$0.670876\pi$
$788$	7.80467	−	1.37617i	0.278030	−	0.0490241i
$789$	−2.40611	−	13.6457i	−0.0856596	−	0.485800i
$790$	9.80297	+	22.6589i	0.348774	+	0.806166i
$791$	−0.521482	−	0.903233i	−0.0185418	−	0.0321153i
$792$	−4.15423	−	4.95082i	−0.147614	−	0.175920i
$793$	3.27701	+	9.00351i	0.116370	+	0.319724i
$794$	33.5027	+	12.1940i	1.18897	+	0.432748i
$795$	0.408531	+	1.71551i	0.0144891	+	0.0608430i
$796$	−3.83434	+	21.7456i	−0.135904	+	0.770753i
$797$		−	37.9181i		−	1.34313i	−0.740946	−	0.671564i	$-0.765623\pi$
$797$		−	37.9181i		−	1.34313i	0.740946	−	0.671564i	$-0.234377\pi$
$798$	2.23498	−	1.11010i	0.0791173	−	0.0392970i
$799$	−16.1795			−0.572391
$800$	−0.591135	−	4.96493i	−0.0208998	−	0.175537i
$801$	−1.12976	−	0.947980i	−0.0399181	−	0.0334952i
$802$	3.22044	−	8.84808i	0.113718	−	0.312437i
$803$	−30.4393	−	83.6312i	−1.07418	−	2.95128i
$804$	−6.79281	+	5.69984i	−0.239564	+	0.201018i
$805$	−0.0230957	+	0.199455i	−0.000814018	+	0.00702986i
$806$	−0.329545	+	0.570789i	−0.0116077	+	0.0201052i
$807$	9.61215	−	1.69488i	0.338364	−	0.0596627i
$808$	5.42572	−	0.956700i	0.190876	−	0.0336566i
$809$	7.99947	−	13.8555i	0.281247	−	0.487133i	−0.690445	−	0.723384i	$-0.742585\pi$
$809$	7.99947	−	13.8555i	0.281247	−	0.487133i	0.971692	+	0.236251i	$0.0759188\pi$
$810$	−2.22123	−	0.257205i	−0.0780459	−	0.00903727i
$811$	−11.1508	+	9.35664i	−0.391558	+	0.328556i	−0.817220	−	0.576326i	$-0.804486\pi$
$811$	−11.1508	+	9.35664i	−0.391558	+	0.328556i	0.425662	+	0.904882i	$0.360041\pi$
$812$	−0.986366	−	2.71002i	−0.0346146	−	0.0951030i
$813$	−2.50053	+	6.87014i	−0.0876973	+	0.240946i
$814$	−36.5651	−	30.6817i	−1.28160	−	1.07539i
$815$	26.0355	+	27.5367i	0.911983	+	0.964567i
$816$	3.00428			0.105171
$817$	−11.7096	+	26.8191i	−0.409666	+	0.938283i
$818$			22.4104i			0.783561i
$819$	−0.203328	+	1.15313i	−0.00710486	+	0.0402937i
$820$	−0.158558	−	0.665822i	−0.00553710	−	0.0232515i
$821$	−31.4502	−	11.4470i	−1.09762	−	0.399501i	−0.271182	−	0.962528i	$-0.587415\pi$
$821$	−31.4502	−	11.4470i	−1.09762	−	0.399501i	−0.826439	+	0.563027i	$0.809637\pi$
$822$	7.97650	+	21.9153i	0.278212	+	0.764382i
$823$	−6.43079	−	7.66391i	−0.224163	−	0.267147i	0.642227	−	0.766514i	$-0.278010\pi$
$823$	−6.43079	−	7.66391i	−0.224163	−	0.267147i	−0.866391	+	0.499367i	$0.833566\pi$
$824$	−4.58817	−	7.94695i	−0.159837	−	0.276845i
$825$	−7.38458	+	31.4591i	−0.257098	+	1.09527i
$826$	0.292392	+	1.65824i	0.0101736	+	0.0576975i
$827$	−24.6250	+	4.34205i	−0.856295	+	0.150988i	−0.584526	−	0.811375i	$-0.698720\pi$
$827$	−24.6250	+	4.34205i	−0.856295	+	0.150988i	−0.271769	+	0.962363i	$0.587609\pi$
$828$	0.135833	+	0.0784231i	0.00472051	+	0.00272539i
$829$	23.6005	+	40.8773i	0.819680	+	1.41973i	0.905918	+	0.423453i	$0.139182\pi$
$829$	23.6005	+	40.8773i	0.819680	+	1.41973i	−0.0862377	+	0.996275i	$0.527484\pi$
$830$	−21.6187	+	1.28245i	−0.750397	+	0.0445146i
$831$	−11.5280	+	4.19586i	−0.399903	+	0.145553i
$832$	−0.699522	+	1.92192i	−0.0242515	+	0.0666306i
$833$	−12.8849	+	15.3556i	−0.446434	+	0.532039i
$834$	−3.20381	+	18.1697i	−0.110939	+	0.629165i
$835$	−8.98359	+	12.0942i	−0.310890	+	0.418536i
$836$	−28.1157	−	1.76234i	−0.972401	−	0.0609519i
$837$			0.322252i			0.0111387i
$838$	13.2470	+	2.33581i	0.457611	+	0.0806891i
$839$	−0.601629	−	0.504827i	−0.0207705	−	0.0174285i	0.632343	−	0.774688i	$-0.282093\pi$
$839$	−0.601629	−	0.504827i	−0.0207705	−	0.0174285i	−0.653114	+	0.757260i	$0.726538\pi$
$840$	−1.06880	+	0.704606i	−0.0368770	+	0.0243112i
$841$	3.40580	−	1.23961i	0.117441	−	0.0427452i
$842$	−20.6642	−	24.6267i	−0.712136	−	0.848691i
$843$	11.2026	−	6.46780i	0.385837	−	0.222763i
$844$	−12.5986	+	21.8213i	−0.433660	+	0.751121i
$845$	−8.82922	+	17.6276i	−0.303734	+	0.606409i
$846$	−0.935182	−	5.30368i	−0.0321522	−	0.182344i
$847$	15.2550	+	8.80747i	0.524167	+	0.302628i
$848$	0.682996	−	0.394328i	0.0234542	−	0.0135413i
$849$	17.6721	−	14.8287i	0.606505	−	0.508918i
$850$	−8.99603	−	12.0297i	−0.308561	−	0.412616i
$851$	1.08855	+	0.396200i	0.0373150	+	0.0135816i
$852$	7.48806	−	8.92392i	0.256537	−	0.305728i
$853$	−9.85205	−	1.73718i	−0.337328	−	0.0594800i	0.00241862	−	0.999997i	$-0.499230\pi$
$853$	−9.85205	−	1.73718i	−0.337328	−	0.0594800i	−0.339746	+	0.940517i	$0.610341\pi$
$854$	2.68197			0.0917753
$855$	−7.48741	+	6.24009i	−0.256064	+	0.213406i
$856$	8.10357			0.276974
$857$	24.5951	+	4.33679i	0.840154	+	0.148142i	0.577135	−	0.816649i	$-0.304171\pi$
$857$	24.5951	+	4.33679i	0.840154	+	0.148142i	0.263019	+	0.964791i	$0.415282\pi$
$858$	8.49650	−	10.1257i	0.290066	−	0.345687i
$859$	22.0912	+	8.04054i	0.753742	+	0.274340i	0.690179	−	0.723638i	$-0.257532\pi$
$859$	22.0912	+	8.04054i	0.753742	+	0.274340i	0.0635623	+	0.997978i	$0.479754\pi$
$860$	4.29007	−	14.3861i	0.146290	−	0.490560i
$861$	−0.134240	+	0.112641i	−0.00457490	+	0.00383880i
$862$	−15.5436	+	8.97410i	−0.529417	+	0.305659i
$863$	23.3129	+	13.4597i	0.793581	+	0.458174i	0.841222	−	0.540691i	$-0.181837\pi$
$863$	23.3129	+	13.4597i	0.793581	+	0.458174i	−0.0476409	+	0.998865i	$0.515170\pi$
$864$	0.173648	+	0.984808i	0.00590763	+	0.0335038i
$865$	−38.5687	−	19.3181i	−1.31137	−	0.656833i
$866$	13.2663	−	22.9780i	0.450809	−	0.780824i
$867$	−6.90595	+	3.98715i	−0.234538	+	0.135411i
$868$	0.118588	+	0.141328i	0.00402514	+	0.00479697i
$869$	−67.0531	+	24.4053i	−2.27462	+	0.827894i
$870$	6.19979	+	9.40429i	0.210192	+	0.318835i
$871$	−13.8931	−	11.6577i	−0.470749	−	0.395005i
$872$	9.94184	+	1.75301i	0.336673	+	0.0593646i
$873$			1.97648i			0.0668938i
$874$	0.655816	−	0.193182i	0.0221833	−	0.00653449i
$875$	6.02179	+	2.16980i	0.203574	+	0.0733525i
$876$	−2.39128	+	13.5616i	−0.0807937	+	0.458204i
$877$	−1.59340	+	1.89894i	−0.0538054	+	0.0641227i	−0.792276	−	0.610163i	$-0.791104\pi$
$877$	−1.59340	+	1.89894i	−0.0538054	+	0.0641227i	0.738471	+	0.674286i	$0.235548\pi$
$878$	−2.32298	+	6.38232i	−0.0783966	+	0.215393i
$879$	29.0696	−	10.5805i	0.980494	−	0.356871i
$880$	14.4260	−	0.855771i	0.486300	−	0.0288480i
$881$	0.947433	+	1.64100i	0.0319198	+	0.0552867i	0.881544	−	0.472102i	$-0.156505\pi$
$881$	0.947433	+	1.64100i	0.0319198	+	0.0552867i	−0.849624	+	0.527389i	$0.823171\pi$
$882$	−5.77833	−	3.33612i	−0.194566	−	0.112333i
$883$	36.0670	−	6.35958i	1.21375	−	0.214017i	0.470117	−	0.882604i	$-0.344212\pi$
$883$	36.0670	−	6.35958i	1.21375	−	0.214017i	0.743634	+	0.668587i	$0.233101\pi$
$884$	1.06699	+	6.05120i	0.0358867	+	0.203524i
$885$	−2.61135	−	6.03595i	−0.0877796	−	0.202896i
$886$	−16.6469	−	28.8332i	−0.559263	−	0.968671i
$887$	−9.78089	−	11.6564i	−0.328410	−	0.391384i	0.576422	−	0.817152i	$-0.304448\pi$
$887$	−9.78089	−	11.6564i	−0.328410	−	0.391384i	−0.904832	+	0.425768i	$0.860004\pi$
$888$	2.52604	+	6.94024i	0.0847684	+	0.232899i
$889$	4.56117	+	1.66013i	0.152977	+	0.0556790i
$890$	3.20803	−	0.763959i	0.107533	−	0.0256080i
$891$	1.12226	−	6.36465i	0.0375971	−	0.213224i
$892$			25.4485i			0.852078i
$893$	−19.5557	−	12.9862i	−0.654407	−	0.434568i
$894$	−1.68865			−0.0564768
$895$	26.8845	−	25.4188i	0.898648	−	0.849658i
$896$	0.438563	+	0.367998i	0.0146514	+	0.0122939i
$897$	−0.109717	+	0.301446i	−0.00366335	+	0.0100650i
$898$	−1.29490	−	3.55771i	−0.0432114	−	0.118722i
$899$	1.24353	−	1.04345i	0.0414742	−	0.0348010i
$900$	3.42339	−	3.64423i	0.114113	−	0.121474i
$901$	1.18467	−	2.05191i	0.0394671	−	0.0683590i
$902$	1.94817	−	0.343514i	0.0648668	−	0.0114378i
$903$	−3.78517	+	0.667428i	−0.125963	+	0.0222106i
$904$	0.910881	−	1.57769i	0.0302954	−	0.0524732i
$905$	−6.83188	+	59.0002i	−0.227099	+	1.96123i
$906$	8.65563	−	7.26293i	0.287564	−	0.241295i
$907$	−12.0998	−	33.2439i	−0.401768	−	1.10385i	−0.961412	−	0.275114i	$-0.911284\pi$
$907$	−12.0998	−	33.2439i	−0.401768	−	1.10385i	0.559644	−	0.828733i	$-0.310938\pi$
$908$	−4.80688	+	13.2068i	−0.159522	+	0.438283i
$909$	4.22046	+	3.54139i	0.139984	+	0.117460i
$910$	−1.79880	−	1.90252i	−0.0596297	−	0.0630679i
$911$	−38.2348			−1.26677			−0.633387	−	0.773835i	$-0.718336\pi$
$911$	−38.2348			−1.26677			−0.633387	+	0.773835i	$0.718336\pi$
$912$	3.63118	+	2.41134i	0.120240	+	0.0798473i
$913$		−	62.5937i		−	2.07155i
$914$	1.25407	−	7.11221i	0.0414811	−	0.235251i
$915$	−10.1902	+	2.42669i	−0.336878	+	0.0802240i
$916$	−4.99884	−	1.81943i	−0.165166	−	0.0601156i
$917$	0.222771	+	0.612059i	0.00735655	+	0.0202120i
$918$	1.93111	+	2.30141i	0.0637362	+	0.0759579i
$919$	13.5744	+	23.5116i	0.447780	+	0.775577i	0.998241	−	0.0592833i	$-0.0188815\pi$
$919$	13.5744	+	23.5116i	0.447780	+	0.775577i	−0.550461	+	0.834861i	$0.685548\pi$
$920$	−0.321886	+	0.139258i	−0.0106123	+	0.00459122i
$921$	−1.57418	−	8.92762i	−0.0518710	−	0.294175i
$922$	14.9755	−	2.64058i	0.493190	−	0.0869628i
$923$	20.6339	+	11.9130i	0.679174	+	0.392121i
$924$	−1.85000	−	3.20429i	−0.0608604	−	0.105413i
$925$	20.2261	−	30.8967i	0.665029	−	1.01588i
$926$	−11.0950	+	4.03826i	−0.364606	+	0.132706i
$927$	3.13850	−	8.62294i	0.103082	−	0.283215i
$928$	3.23799	−	3.85889i	0.106292	−	0.126674i
$929$	−4.43914	+	25.1756i	−0.145644	+	0.825986i	0.821205	+	0.570634i	$0.193302\pi$
$929$	−4.43914	+	25.1756i	−0.145644	+	0.825986i	−0.966848	+	0.255352i	$0.917809\pi$
$930$	−0.578453	−	0.429677i	−0.0189682	−	0.0140897i
$931$	−27.8984	+	8.21798i	−0.914334	+	0.269333i
$932$		−	10.0733i		−	0.329960i
$933$	−28.1232	−	4.95889i	−0.920714	−	0.162347i
$934$	−15.4074	−	12.9284i	−0.504147	−	0.423030i
$935$	36.2478	−	23.8964i	1.18543	−	0.781495i
$936$	−1.92192	+	0.699522i	−0.0628199	+	0.0228646i
$937$	−4.79954	−	5.71987i	−0.156794	−	0.186860i	0.681929	−	0.731419i	$-0.261142\pi$
$937$	−4.79954	−	5.71987i	−0.156794	−	0.186860i	−0.838723	+	0.544559i	$0.816697\pi$
$938$	−4.39647	+	2.53830i	−0.143550	+	0.0828785i
$939$	−7.42003	+	12.8519i	−0.242144	+	0.419405i
$940$	10.7672	+	5.39303i	0.351188	+	0.175901i
$941$	10.1445	+	57.5324i	0.330702	+	1.87550i	0.466129	+	0.884717i	$0.345648\pi$
$941$	10.1445	+	57.5324i	0.330702	+	1.87550i	−0.135427	+	0.990787i	$0.543241\pi$
$942$	2.32330	+	1.34136i	0.0756971	+	0.0437037i
$943$	−0.0415772	+	0.0240046i	−0.00135394	+	0.000781698i
$944$	−2.25305	+	1.89054i	−0.0733307	+	0.0615317i
$945$	−1.22677	−	0.365835i	−0.0399068	−	0.0119006i
$946$	40.7723	+	14.8399i	1.32562	+	0.482487i
$947$	−36.2137	+	43.1578i	−1.17679	+	1.40244i	−0.279985	+	0.960004i	$0.590330\pi$
$947$	−36.2137	+	43.1578i	−1.17679	+	1.40244i	−0.896801	+	0.442435i	$0.854115\pi$
$948$	10.8733	+	1.91726i	0.353148	+	0.0622696i
$949$	−28.1649			−0.914273
$950$	−1.21777	−	21.7604i	−0.0395096	−	0.706002i
$951$	25.1001			0.813928
$952$	1.69383	+	0.298668i	0.0548973	+	0.00967988i
$953$	21.7935	−	25.9725i	0.705960	−	0.841331i	−0.287227	−	0.957863i	$-0.592733\pi$
$953$	21.7935	−	25.9725i	0.705960	−	0.841331i	0.993187	+	0.116532i	$0.0371778\pi$
$954$	0.741094	+	0.269736i	0.0239938	+	0.00873303i
$955$	−11.3900	−	3.39663i	−0.368573	−	0.109912i
$956$	9.44496	−	7.92526i	0.305472	−	0.256321i
$957$	−28.1944	+	16.2780i	−0.911394	+	0.526194i
$958$	2.53478	+	1.46346i	0.0818950	+	0.0472821i
$959$	2.31851	+	13.1489i	0.0748686	+	0.424601i
$960$	−1.99930	−	1.00140i	−0.0645271	−	0.0323200i
$961$	15.4481	−	26.7569i	0.498325	−	0.863124i
$962$	−13.0818	+	7.55281i	−0.421776	+	0.243512i
$963$	5.20887	+	6.20769i	0.167854	+	0.200040i
$964$	7.01108	−	2.55183i	0.225812	−	0.0821888i
$965$	−19.1551	+	12.6280i	−0.616624	+	0.406509i
$966$	0.0687869	+	0.0577191i	0.00221318	+	0.00185708i
$967$	30.8538	+	5.44035i	0.992191	+	0.174950i	0.646101	−	0.763252i	$-0.276398\pi$
$967$	30.8538	+	5.44035i	0.992191	+	0.174950i	0.346089	+	0.938202i	$0.387509\pi$
$968$			30.7683i			0.988930i
$969$	13.0697	+	0.819233i	0.419859	+	0.0263176i
$970$	−3.54785	−	2.63536i	−0.113915	−	0.0846163i
$971$	−4.03492	+	22.8832i	−0.129487	+	0.734356i	0.849055	+	0.528305i	$0.177172\pi$
$971$	−4.03492	+	22.8832i	−0.129487	+	0.734356i	−0.978541	+	0.206051i	$0.933939\pi$
$972$	−0.642788	+	0.766044i	−0.0206174	+	0.0245709i
$973$	−3.61265	+	9.92568i	−0.115816	+	0.318203i
$974$	−9.11998	+	3.31940i	−0.292223	+	0.106361i
$975$	8.55602	+	5.60108i	0.274012	+	0.179378i
$976$	2.34232	+	4.05702i	0.0749759	+	0.129862i
$977$	13.9476	+	8.05262i	0.446222	+	0.257626i	0.706233	−	0.707979i	$-0.250393\pi$
$977$	13.9476	+	8.05262i	0.446222	+	0.257626i	−0.260011	+	0.965606i	$0.583726\pi$
$978$	16.6902	−	2.94293i	0.533693	−	0.0941045i
$979$	1.65510	+	9.38656i	0.0528973	+	0.299996i
$980$	13.6930	−	5.92406i	0.437408	−	0.189237i
$981$	5.04760	+	8.74271i	0.161158	+	0.279133i
$982$	−15.7006	−	18.7113i	−0.501027	−	0.597101i
$983$	−14.6007	−	40.1150i	−0.465689	−	1.27947i	−0.921148	−	0.389213i	$-0.872747\pi$
$983$	−14.6007	−	40.1150i	−0.465689	−	1.27947i	0.455459	−	0.890257i	$-0.349475\pi$
$984$	−0.287632	−	0.104689i	−0.00916937	−	0.00333738i
$985$	−17.2389	+	4.10526i	−0.549277	+	0.130805i
$986$	2.62796	−	14.9039i	0.0836913	−	0.474637i
$987$		−	3.08321i		−	0.0981398i
$988$	−3.56726	+	8.17029i	−0.113490	+	0.259932i
$989$	−1.05300			−0.0334836
$990$	9.92840	+	10.5009i	0.315545	+	0.333739i
$991$	30.6303	+	25.7019i	0.973004	+	0.816447i	0.983019	−	0.183503i	$-0.0587436\pi$
$991$	30.6303	+	25.7019i	0.973004	+	0.816447i	−0.0100152	+	0.999950i	$0.503188\pi$
$992$	−0.110217	+	0.302818i	−0.00349938	+	0.00961447i
$993$	6.30997	+	17.3365i	0.200241	+	0.550157i
$994$	5.10897	−	4.28694i	0.162047	−	0.135973i
$995$	5.67937	−	49.0470i	0.180048	−	1.55490i
$996$	−4.84259	+	8.38761i	−0.153443	+	0.265772i
$997$	55.7121	−	9.82355i	1.76442	−	0.311115i	0.805038	−	0.593224i	$-0.202145\pi$
$997$	55.7121	−	9.82355i	1.76442	−	0.311115i	0.959382	+	0.282109i	$0.0910339\pi$
$998$	−11.4642	+	2.02146i	−0.362894	+	0.0639881i
$999$	−3.69283	+	6.39616i	−0.116836	+	0.202366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.a.169.1	✓	60
5.4	even	2	inner	570.2.bc.a.169.7	yes	60
19.9	even	9	inner	570.2.bc.a.199.7	yes	60
95.9	even	18	inner	570.2.bc.a.199.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.a.169.1	✓	60	1.1	even	1	trivial
570.2.bc.a.169.7	yes	60	5.4	even	2	inner
570.2.bc.a.199.1	yes	60	95.9	even	18	inner
570.2.bc.a.199.7	yes	60	19.9	even	9	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.14282 - 0.639010i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-0.495802 + 0.286252i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.14282 - 0.639010i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-0.495802 + 0.286252i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(1.99930 + 1.00140i) q^{10} +(-3.23142 + 5.59698i) q^{11} +(0.866025 - 0.500000i) q^{12} +(1.31467 + 1.56676i) q^{13} +(0.537977 - 0.195808i) q^{14} +(-1.86689 + 1.23075i) q^{15} +(0.766044 + 0.642788i) q^{16} +(2.95864 + 0.521688i) q^{17} +1.00000i q^{18} +(3.15729 + 3.00525i) q^{19} +(-1.79504 - 1.33336i) q^{20} +(-0.0994141 + 0.563806i) q^{21} +(4.15423 - 4.95082i) q^{22} +(-0.0536445 + 0.147387i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(4.18333 + 2.73856i) q^{25} +(-1.02263 - 1.77125i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(-0.563806 + 0.0994141i) q^{28} +(0.874739 + 4.96089i) q^{29} +(2.05224 - 0.887867i) q^{30} +(-0.161126 - 0.279078i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(2.21042 + 6.07308i) q^{33} +(-2.82310 - 1.02752i) q^{34} +(1.24533 - 0.296562i) q^{35} +(0.173648 - 0.984808i) q^{36} -7.38565i q^{37} +(-2.58747 - 3.50785i) q^{38} +2.04526 q^{39} +(1.53623 + 1.62481i) q^{40} +(0.234480 + 0.196752i) q^{41} +(0.195808 - 0.537977i) q^{42} +(2.29619 + 6.30873i) q^{43} +(-4.95082 + 4.15423i) q^{44} +(-0.257205 + 2.22123i) q^{45} +(0.0784231 - 0.135833i) q^{46} +(-5.30368 + 0.935182i) q^{47} +(0.984808 - 0.173648i) q^{48} +(-3.33612 + 5.77833i) q^{49} +(-3.64423 - 3.42339i) q^{50} +(2.30141 - 1.93111i) q^{51} +(0.699522 + 1.92192i) q^{52} +(0.269736 - 0.741094i) q^{53} +(0.766044 + 0.642788i) q^{54} +(10.5009 - 9.92840i) q^{55} +0.572503 q^{56} +(4.33162 - 0.486886i) q^{57} -5.03742i q^{58} +(-0.510726 + 2.89647i) q^{59} +(-2.17524 + 0.518010i) q^{60} +(4.40213 + 1.60224i) q^{61} +(0.110217 + 0.302818i) q^{62} +(0.367998 + 0.438563i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-1.81592 - 4.19737i) q^{65} +(-1.12226 - 6.36465i) q^{66} +(-8.73266 + 1.53980i) q^{67} +(2.60178 + 1.50214i) q^{68} +(0.0784231 + 0.135833i) q^{69} +(-1.27791 + 0.0758075i) q^{70} +(10.9468 - 3.98431i) q^{71} +(-0.342020 + 0.939693i) q^{72} +(-8.85170 + 10.5490i) q^{73} +(-1.28251 + 7.27345i) q^{74} +(4.78686 - 1.44431i) q^{75} +(1.93903 + 3.90387i) q^{76} -3.70000i q^{77} +(-2.01419 - 0.355156i) q^{78} +(8.45792 + 7.09704i) q^{79} +(-1.23075 - 1.86689i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.196752 - 0.234480i) q^{82} +(-8.38761 + 4.84259i) q^{83} +(-0.286252 + 0.495802i) q^{84} +(-6.00646 - 3.00848i) q^{85} +(-1.16581 - 6.61162i) q^{86} +(4.36254 + 2.51871i) q^{87} +(5.59698 - 3.23142i) q^{88} +(1.12976 - 0.947980i) q^{89} +(0.639010 - 2.14282i) q^{90} +(-1.10031 - 0.400478i) q^{91} +(-0.100819 + 0.120151i) q^{92} +(-0.317356 - 0.0559584i) q^{93} +5.38550 q^{94} +(-4.84511 - 8.45724i) q^{95} -1.00000 q^{96} +(-1.94645 - 0.343212i) q^{97} +(4.28883 - 5.11123i) q^{98} +(6.07308 + 2.21042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{5}+O(q^{10}) \) 60 * q - 6 * q^5	\( 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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