LMFDB - Embedded newform 570.2.bc.a.169.5

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			169.5
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.a.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.19119 + 0.445735i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(0.187519 - 0.108264i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.19119 + 0.445735i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(0.187519 - 0.108264i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(-2.08050 - 0.819460i) q^{10} +(1.39966 - 2.42428i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-3.23529 - 3.85567i) q^{13} +(-0.203470 + 0.0740570i) q^{14} +(1.74992 - 1.39204i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.95714 + 0.345096i) q^{17} +1.00000i q^{18} +(4.15900 - 1.30489i) q^{19} +(1.90660 + 1.16829i) q^{20} +(0.0375997 - 0.213239i) q^{21} +(-1.79937 + 2.14441i) q^{22} +(-1.35918 + 3.73432i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(4.60264 + 1.95338i) q^{25} +(2.51661 + 4.35889i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(0.213239 - 0.0375997i) q^{28} +(0.998416 + 5.66230i) q^{29} +(-1.96506 + 1.06702i) q^{30} +(-2.40596 - 4.16725i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-0.957425 - 2.63050i) q^{33} +(-1.86748 - 0.679707i) q^{34} +(0.459147 - 0.153643i) q^{35} +(0.173648 - 0.984808i) q^{36} -11.8158i q^{37} +(-4.32241 + 0.562862i) q^{38} -5.03322 q^{39} +(-1.67476 - 1.48161i) q^{40} +(4.97755 + 4.17666i) q^{41} +(-0.0740570 + 0.203470i) q^{42} +(-0.114156 - 0.313642i) q^{43} +(2.14441 - 1.79937i) q^{44} +(0.0584672 - 2.23530i) q^{45} +(1.98699 - 3.44157i) q^{46} +(8.63331 - 1.52229i) q^{47} +(0.984808 - 0.173648i) q^{48} +(-3.47656 + 6.02157i) q^{49} +(-4.19351 - 2.72295i) q^{50} +(1.52238 - 1.27743i) q^{51} +(-1.72146 - 4.72968i) q^{52} +(-3.22788 + 8.86854i) q^{53} +(0.766044 + 0.642788i) q^{54} +(4.14752 - 4.68819i) q^{55} -0.216528 q^{56} +(1.67375 - 4.02474i) q^{57} -5.74965i q^{58} +(1.87994 - 10.6617i) q^{59} +(2.12050 - 0.709578i) q^{60} +(-8.15975 - 2.96991i) q^{61} +(1.64578 + 4.52173i) q^{62} +(-0.139182 - 0.165870i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-5.37053 - 9.89059i) q^{65} +(0.486097 + 2.75679i) q^{66} +(8.93005 - 1.57461i) q^{67} +(1.72108 + 0.993665i) q^{68} +(1.98699 + 3.44157i) q^{69} +(-0.478851 + 0.0715793i) q^{70} +(-1.84309 + 0.670831i) q^{71} +(-0.342020 + 0.939693i) q^{72} +(-4.09217 + 4.87685i) q^{73} +(-2.05179 + 11.6363i) q^{74} +(4.45490 - 2.27022i) q^{75} +(4.35448 + 0.196267i) q^{76} -0.606132i q^{77} +(4.95675 + 0.874009i) q^{78} +(-2.98353 - 2.50348i) q^{79} +(1.39204 + 1.74992i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-4.17666 - 4.97755i) q^{82} +(5.25519 - 3.03408i) q^{83} +(0.108264 - 0.187519i) q^{84} +(4.13464 + 1.62854i) q^{85} +(0.0579586 + 0.328700i) q^{86} +(4.97934 + 2.87483i) q^{87} +(-2.42428 + 1.39966i) q^{88} +(-9.77428 + 8.20159i) q^{89} +(-0.445735 + 2.19119i) q^{90} +(-1.02411 - 0.372745i) q^{91} +(-2.55443 + 3.04425i) q^{92} +(-4.73882 - 0.835582i) q^{93} -8.76649 q^{94} +(9.69480 - 1.00545i) q^{95} -1.00000 q^{96} +(10.4677 + 1.84573i) q^{97} +(4.46938 - 5.32640i) q^{98} +(-2.63050 - 0.957425i) 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
$5$	2.19119	+	0.445735i	0.979931	+	0.199339i
$5$	2.19119	+	0.445735i	0.979931	+	0.199339i
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	0.187519	−	0.108264i	0.0708755	−	0.0409200i	−0.464143	−	0.885760i	$-0.653638\pi$
$7$	0.187519	−	0.108264i	0.0708755	−	0.0409200i	0.535019	+	0.844840i	$0.320304\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	−2.08050	−	0.819460i	−0.657912	−	0.259136i
$11$	1.39966	−	2.42428i	0.422014	−	0.730949i	−0.574123	−	0.818769i	$-0.694657\pi$
$11$	1.39966	−	2.42428i	0.422014	−	0.730949i	0.996136	+	0.0878200i	$0.0279900\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−3.23529	−	3.85567i	−0.897308	−	1.06937i	−0.997230	−	0.0743743i	$-0.976304\pi$
$13$	−3.23529	−	3.85567i	−0.897308	−	1.06937i	0.0999228	−	0.994995i	$-0.468140\pi$
$14$	−0.203470	+	0.0740570i	−0.0543796	+	0.0197926i
$15$	1.74992	−	1.39204i	0.451828	−	0.359422i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	1.95714	+	0.345096i	0.474676	+	0.0836981i	0.405868	−	0.913932i	$-0.366969\pi$
$17$	1.95714	+	0.345096i	0.474676	+	0.0836981i	0.0688079	+	0.997630i	$0.478080\pi$
$18$			1.00000i			0.235702i
$19$	4.15900	−	1.30489i	0.954140	−	0.299362i
$19$	4.15900	−	1.30489i	0.954140	−	0.299362i
$20$	1.90660	+	1.16829i	0.426328	+	0.261237i
$21$	0.0375997	−	0.213239i	0.00820493	−	0.0465325i
$22$	−1.79937	+	2.14441i	−0.383627	+	0.457189i
$23$	−1.35918	+	3.73432i	−0.283409	+	0.778660i	0.713541	+	0.700614i	$0.247090\pi$
$23$	−1.35918	+	3.73432i	−0.283409	+	0.778660i	−0.996950	+	0.0780462i	$0.975132\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	4.60264	+	1.95338i	0.920528	+	0.390677i
$26$	2.51661	+	4.35889i	0.493547	+	0.854849i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	0.213239	−	0.0375997i	0.0402983	−	0.00710568i
$29$	0.998416	+	5.66230i	0.185401	+	1.05146i	0.925439	+	0.378897i	$0.123697\pi$
$29$	0.998416	+	5.66230i	0.185401	+	1.05146i	−0.740037	+	0.672566i	$0.765192\pi$
$30$	−1.96506	+	1.06702i	−0.358770	+	0.194810i
$31$	−2.40596	−	4.16725i	−0.432124	−	0.748460i	0.564932	−	0.825137i	$-0.308902\pi$
$31$	−2.40596	−	4.16725i	−0.432124	−	0.748460i	−0.997056	+	0.0766769i	$0.975569\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	−0.957425	−	2.63050i	−0.166666	−	0.457912i
$34$	−1.86748	−	0.679707i	−0.320270	−	0.116569i
$35$	0.459147	−	0.153643i	0.0776100	−	0.0259705i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$		−	11.8158i		−	1.94250i	−0.238052	−	0.971252i	$-0.576509\pi$
$37$		−	11.8158i		−	1.94250i	0.238052	−	0.971252i	$-0.423491\pi$
$38$	−4.32241	+	0.562862i	−0.701187	+	0.0913083i
$39$	−5.03322			−0.805959
$40$	−1.67476	−	1.48161i	−0.264803	−	0.234264i
$41$	4.97755	+	4.17666i	0.777362	+	0.652284i	0.942583	−	0.333972i	$-0.108389\pi$
$41$	4.97755	+	4.17666i	0.777362	+	0.652284i	−0.165221	+	0.986257i	$0.552834\pi$
$42$	−0.0740570	+	0.203470i	−0.0114272	+	0.0313961i
$43$	−0.114156	−	0.313642i	−0.0174087	−	0.0478299i	0.930684	−	0.365824i	$-0.119213\pi$
$43$	−0.114156	−	0.313642i	−0.0174087	−	0.0478299i	−0.948093	+	0.317994i	$0.896991\pi$
$44$	2.14441	−	1.79937i	0.323281	−	0.271265i
$45$	0.0584672	−	2.23530i	0.00871577	−	0.333219i
$46$	1.98699	−	3.44157i	0.292966	−	0.507432i
$47$	8.63331	−	1.52229i	1.25930	−	0.222048i	0.496130	−	0.868248i	$-0.334754\pi$
$47$	8.63331	−	1.52229i	1.25930	−	0.222048i	0.763168	+	0.646200i	$0.223643\pi$
$48$	0.984808	−	0.173648i	0.142145	−	0.0250640i
$49$	−3.47656	+	6.02157i	−0.496651	+	0.860225i
$50$	−4.19351	−	2.72295i	−0.593052	−	0.385083i
$51$	1.52238	−	1.27743i	0.213176	−	0.178876i
$52$	−1.72146	−	4.72968i	−0.238724	−	0.655888i
$53$	−3.22788	+	8.86854i	−0.443384	+	1.21819i	0.493869	+	0.869536i	$0.335582\pi$
$53$	−3.22788	+	8.86854i	−0.443384	+	1.21819i	−0.937253	+	0.348651i	$0.886640\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	4.14752	−	4.68819i	0.559251	−	0.632156i
$56$	−0.216528			−0.0289348
$57$	1.67375	−	4.02474i	0.221694	−	0.533090i
$58$		−	5.74965i		−	0.754966i
$59$	1.87994	−	10.6617i	0.244748	−	1.38803i	−0.576331	−	0.817216i	$-0.695516\pi$
$59$	1.87994	−	10.6617i	0.244748	−	1.38803i	0.821078	−	0.570816i	$-0.193373\pi$
$60$	2.12050	−	0.709578i	0.273755	−	0.0916061i
$61$	−8.15975	−	2.96991i	−1.04475	−	0.380258i	−0.238070	−	0.971248i	$-0.576515\pi$
$61$	−8.15975	−	2.96991i	−1.04475	−	0.380258i	−0.806679	+	0.590990i	$0.798737\pi$
$62$	1.64578	+	4.52173i	0.209014	+	0.574261i
$63$	−0.139182	−	0.165870i	−0.0175352	−	0.0208977i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−5.37053	−	9.89059i	−0.666132	−	1.22678i
$66$	0.486097	+	2.75679i	0.0598344	+	0.339338i
$67$	8.93005	−	1.57461i	1.09098	−	0.192369i	0.400914	−	0.916116i	$-0.368693\pi$
$67$	8.93005	−	1.57461i	1.09098	−	0.192369i	0.690066	+	0.723747i	$0.257582\pi$
$68$	1.72108	+	0.993665i	0.208711	+	0.120500i
$69$	1.98699	+	3.44157i	0.239206	+	0.414316i
$70$	−0.478851	+	0.0715793i	−0.0572337	+	0.00855536i
$71$	−1.84309	+	0.670831i	−0.218735	+	0.0796130i	−0.449063	−	0.893500i	$-0.648242\pi$
$71$	−1.84309	+	0.670831i	−0.218735	+	0.0796130i	0.230328	+	0.973113i	$0.426020\pi$
$72$	−0.342020	+	0.939693i	−0.0403075	+	0.110744i
$73$	−4.09217	+	4.87685i	−0.478952	+	0.570792i	−0.950372	−	0.311116i	$-0.899297\pi$
$73$	−4.09217	+	4.87685i	−0.478952	+	0.570792i	0.471420	+	0.881909i	$0.343742\pi$
$74$	−2.05179	+	11.6363i	−0.238516	+	1.35269i
$75$	4.45490	−	2.27022i	0.514407	−	0.262142i
$76$	4.35448	+	0.196267i	0.499493	+	0.0225134i
$77$		−	0.606132i		−	0.0690752i
$78$	4.95675	+	0.874009i	0.561241	+	0.0989620i
$79$	−2.98353	−	2.50348i	−0.335674	−	0.281664i	0.459333	−	0.888264i	$-0.348088\pi$
$79$	−2.98353	−	2.50348i	−0.335674	−	0.281664i	−0.795007	+	0.606600i	$0.792533\pi$
$80$	1.39204	+	1.74992i	0.155634	+	0.195647i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−4.17666	−	4.97755i	−0.461235	−	0.549678i
$83$	5.25519	−	3.03408i	0.576832	−	0.333034i	−0.183042	−	0.983105i	$-0.558594\pi$
$83$	5.25519	−	3.03408i	0.576832	−	0.333034i	0.759873	+	0.650071i	$0.225261\pi$
$84$	0.108264	−	0.187519i	0.0118126	−	0.0204600i
$85$	4.13464	+	1.62854i	0.448465	+	0.176640i
$86$	0.0579586	+	0.328700i	0.00624984	+	0.0354446i
$87$	4.97934	+	2.87483i	0.533842	+	0.308214i
$88$	−2.42428	+	1.39966i	−0.258430	+	0.149204i
$89$	−9.77428	+	8.20159i	−1.03607	+	0.869367i	−0.991561	−	0.129642i	$-0.958617\pi$
$89$	−9.77428	+	8.20159i	−1.03607	+	0.869367i	−0.0445104	+	0.999009i	$0.514173\pi$
$90$	−0.445735	+	2.19119i	−0.0469846	+	0.230972i
$91$	−1.02411	−	0.372745i	−0.107356	−	0.0390743i
$92$	−2.55443	+	3.04425i	−0.266317	+	0.317385i
$93$	−4.73882	−	0.835582i	−0.491393	−	0.0866459i
$94$	−8.76649			−0.904194
$95$	9.69480	−	1.00545i	0.994665	−	0.103157i
$96$	−1.00000			−0.102062
$97$	10.4677	+	1.84573i	1.06283	+	0.187406i	0.677612	−	0.735420i	$-0.263015\pi$
$97$	10.4677	+	1.84573i	1.06283	+	0.187406i	0.385219	+	0.922825i	$0.374126\pi$
$98$	4.46938	−	5.32640i	0.451475	−	0.538047i
$99$	−2.63050	−	0.957425i	−0.264376	−	0.0962248i
$100$	3.65697	+	3.40977i	0.365697	+	0.340977i
$101$	4.99363	−	4.19015i	0.496885	−	0.416936i	−0.359601	−	0.933106i	$-0.617087\pi$
$101$	4.99363	−	4.19015i	0.496885	−	0.416936i	0.856486	+	0.516170i	$0.172643\pi$
$102$	−1.72108	+	0.993665i	−0.170412	+	0.0983875i
$103$	3.54473	+	2.04655i	0.349273	+	0.201653i	0.664365	−	0.747408i	$-0.268702\pi$
$103$	3.54473	+	2.04655i	0.349273	+	0.201653i	−0.315092	+	0.949061i	$0.602035\pi$
$104$	0.874009	+	4.95675i	0.0857036	+	0.486049i
$105$	0.177436	−	0.450487i	0.0173160	−	0.0439630i
$106$	4.71885	−	8.17329i	0.458335	−	0.793860i
$107$	−11.7716	+	6.79632i	−1.13800	+	0.657025i	−0.945935	−	0.324357i	$-0.894852\pi$
$107$	−11.7716	+	6.79632i	−1.13800	+	0.657025i	−0.192066	+	0.981382i	$0.561519\pi$
$108$	−0.642788	−	0.766044i	−0.0618523	−	0.0737127i
$109$	−19.2321	+	6.99992i	−1.84210	+	0.670471i	−0.853264	+	0.521479i	$0.825380\pi$
$109$	−19.2321	+	6.99992i	−1.84210	+	0.670471i	−0.988838	+	0.148991i	$0.952397\pi$
$110$	−4.89860	+	3.89676i	−0.467063	+	0.371542i
$111$	−9.05142	−	7.59505i	−0.859123	−	0.720890i
$112$	0.213239	+	0.0375997i	0.0201491	+	0.00355284i
$113$			7.50410i			0.705926i	0.935637	+	0.352963i	$0.114826\pi$
$113$			7.50410i			0.705926i	−0.935637	+	0.352963i	$0.885174\pi$
$114$	−2.34721	+	3.67296i	−0.219836	+	0.344004i
$115$	−4.64275	+	7.57678i	−0.432938	+	0.706538i
$116$	−0.998416	+	5.66230i	−0.0927006	+	0.525731i
$117$	−3.23529	+	3.85567i	−0.299103	+	0.356457i
$118$	−3.70276	+	10.1733i	−0.340867	+	0.936524i
$119$	0.404362	−	0.147176i	0.0370678	−	0.0134916i
$120$	−2.21150	+	0.330577i	−0.201881	+	0.0301775i
$121$	1.58190	+	2.73992i	0.143809	+	0.249084i
$122$	7.52007	+	4.34171i	0.680835	+	0.393080i
$123$	6.39901	−	1.12832i	0.576979	−	0.101737i
$124$	−0.835582	−	4.73882i	−0.0750375	−	0.425559i
$125$	9.21457	+	6.33179i	0.824177	+	0.566333i
$126$	0.108264	+	0.187519i	0.00964493	+	0.0167055i
$127$	−1.42490	−	1.69813i	−0.126439	−	0.150685i	0.699111	−	0.715013i	$-0.253579\pi$
$127$	−1.42490	−	1.69813i	−0.126439	−	0.150685i	−0.825550	+	0.564329i	$0.809135\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	−0.313642	−	0.114156i	−0.0276146	−	0.0100509i
$130$	3.57146	+	10.6729i	0.313238	+	0.936076i
$131$	−2.33686	+	13.2530i	−0.204172	+	1.15792i	0.694565	+	0.719430i	$0.255597\pi$
$131$	−2.33686	+	13.2530i	−0.204172	+	1.15792i	−0.898737	+	0.438487i	$0.855514\pi$
$132$		−	2.79932i		−	0.243650i
$133$	0.638618	−	0.694961i	0.0553752	−	0.0602608i
$134$	−9.06781			−0.783340
$135$	−1.67476	−	1.48161i	−0.144140	−	0.127517i
$136$	−1.52238	−	1.27743i	−0.130543	−	0.109539i
$137$	−3.62376	+	9.95621i	−0.309599	+	0.850616i	0.683136	+	0.730292i	$0.260616\pi$
$137$	−3.62376	+	9.95621i	−0.309599	+	0.850616i	−0.992735	+	0.120325i	$0.961606\pi$
$138$	−1.35918	−	3.73432i	−0.115701	−	0.317887i
$139$	−13.4977	+	11.3259i	−1.14486	+	0.960653i	−0.999587	−	0.0287385i	$-0.990851\pi$
$139$	−13.4977	+	11.3259i	−1.14486	+	0.960653i	−0.145275	+	0.989391i	$0.546407\pi$
$140$	0.484006	+	0.0126598i	0.0409060	+	0.00106995i
$141$	4.38325	−	7.59200i	0.369136	−	0.639362i
$142$	1.93158	−	0.340590i	0.162095	−	0.0285817i
$143$	−13.8755	+	2.44663i	−1.16033	+	0.204598i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−0.336166	+	12.8522i	−0.0279171	+	1.06732i
$146$	4.87685	−	4.09217i	0.403611	−	0.338670i
$147$	2.37811	+	6.53379i	0.196143	+	0.538898i
$148$	4.04124	−	11.1032i	0.332188	−	0.912679i
$149$	−4.30498	−	3.61231i	−0.352678	−	0.295932i	0.449186	−	0.893438i	$-0.351714\pi$
$149$	−4.30498	−	3.61231i	−0.352678	−	0.295932i	−0.801864	+	0.597506i	$0.796158\pi$
$150$	−4.78144	+	1.46214i	−0.390403	+	0.119383i
$151$	9.89003			0.804839			0.402419	−	0.915455i	$-0.368169\pi$
$151$	9.89003			0.804839			0.402419	+	0.915455i	$0.368169\pi$
$152$	−4.25424	−	0.949432i	−0.345065	−	0.0770091i
$153$		−	1.98733i		−	0.160666i
$154$	−0.105254	+	0.596924i	−0.00848159	+	0.0481015i
$155$	−3.41444	−	10.2037i	−0.274254	−	0.819578i
$156$	−4.72968	−	1.72146i	−0.378677	−	0.137827i
$157$	−3.44643	−	9.46899i	−0.275055	−	0.755708i	−0.997905	−	0.0647024i	$-0.979390\pi$
$157$	−3.44643	−	9.46899i	−0.275055	−	0.755708i	0.722849	−	0.691006i	$-0.242832\pi$
$158$	2.50348	+	2.98353i	0.199166	+	0.237357i
$159$	4.71885	+	8.17329i	0.374229	+	0.648184i
$160$	−1.06702	−	1.96506i	−0.0843552	−	0.155352i
$161$	0.149421	+	0.847406i	0.0117760	+	0.0667850i
$162$	0.984808	−	0.173648i	0.0773738	−	0.0136431i
$163$	10.2105	+	5.89505i	0.799750	+	0.461736i	0.843384	−	0.537312i	$-0.180560\pi$
$163$	10.2105	+	5.89505i	0.799750	+	0.461736i	−0.0436336	+	0.999048i	$0.513893\pi$
$164$	3.24886	+	5.62719i	0.253693	+	0.439410i
$165$	−0.925393	−	6.19069i	−0.0720417	−	0.481945i
$166$	−5.70221	+	2.07544i	−0.442577	+	0.161085i
$167$	1.84778	−	5.07675i	0.142986	−	0.392851i	−0.847441	−	0.530890i	$-0.821858\pi$
$167$	1.84778	−	5.07675i	0.142986	−	0.392851i	0.990427	+	0.138039i	$0.0440800\pi$
$168$	−0.139182	+	0.165870i	−0.0107381	+	0.0127972i
$169$	−2.14165	+	12.1459i	−0.164742	+	0.934299i
$170$	−3.78904	−	2.32177i	−0.290606	−	0.178072i
$171$	−2.00727	−	3.86922i	−0.153500	−	0.295887i
$172$		−	0.333770i		−	0.0254497i
$173$	−4.62968	−	0.816338i	−0.351988	−	0.0620650i	−0.00514142	−	0.999987i	$-0.501637\pi$
$173$	−4.62968	−	0.816338i	−0.351988	−	0.0620650i	−0.346847	+	0.937922i	$0.612748\pi$
$174$	−4.40449	−	3.69580i	−0.333903	−	0.280178i
$175$	1.07456	−	0.132004i	0.0812293	−	0.00997859i
$176$	2.63050	−	0.957425i	0.198282	−	0.0721686i
$177$	−6.95892	−	8.29331i	−0.523064	−	0.623364i
$178$	11.0500	−	6.37971i	0.828231	−	0.478179i
$179$	−4.43111	+	7.67491i	−0.331197	+	0.573650i	−0.982747	−	0.184956i	$-0.940786\pi$
$179$	−4.43111	+	7.67491i	−0.331197	+	0.573650i	0.651550	+	0.758606i	$0.274119\pi$
$180$	0.819460	−	2.08050i	0.0610789	−	0.155071i
$181$	1.56594	+	8.88091i	0.116396	+	0.660113i	0.986050	+	0.166451i	$0.0532308\pi$
$181$	1.56594	+	8.88091i	0.116396	+	0.660113i	−0.869654	+	0.493662i	$0.835658\pi$
$182$	0.943823	+	0.544916i	0.0699608	+	0.0403919i
$183$	−7.52007	+	4.34171i	−0.555899	+	0.320949i
$184$	3.04425	−	2.55443i	0.224425	−	0.188315i
$185$	5.26672	−	25.8907i	0.387217	−	1.90352i
$186$	4.52173	+	1.64578i	0.331550	+	0.120674i
$187$	3.57594	−	4.26164i	0.261499	−	0.311642i
$188$	8.63331	+	1.52229i	0.629649	+	0.111024i
$189$	−0.216528			−0.0157501
$190$	−9.72210	−	0.693310i	−0.705316	−	0.0502980i
$191$	5.82697			0.421625			0.210812	−	0.977527i	$-0.432389\pi$
$191$	5.82697			0.421625			0.210812	+	0.977527i	$0.432389\pi$
$192$	0.984808	+	0.173648i	0.0710724	+	0.0125320i
$193$	−11.8861	+	14.1653i	−0.855582	+	1.01964i	0.143966	+	0.989583i	$0.454014\pi$
$193$	−11.8861	+	14.1653i	−0.855582	+	1.01964i	−0.999548	+	0.0300602i	$0.990430\pi$
$194$	−9.98813	−	3.63538i	−0.717106	−	0.261005i
$195$	−11.0287	−	2.24348i	−0.789784	−	0.160659i
$196$	−5.32640	+	4.46938i	−0.380457	+	0.319241i
$197$	−14.8624	+	8.58079i	−1.05890	+	0.611356i	−0.925128	−	0.379656i	$-0.876042\pi$
$197$	−14.8624	+	8.58079i	−1.05890	+	0.611356i	−0.133772	+	0.991012i	$0.542709\pi$
$198$	2.42428	+	1.39966i	0.172286	+	0.0994696i
$199$	3.83625	+	21.7564i	0.271944	+	1.54227i	0.748504	+	0.663131i	$0.230773\pi$
$199$	3.83625	+	21.7564i	0.271944	+	1.54227i	−0.476559	+	0.879142i	$0.658116\pi$
$200$	−3.00931	−	3.99300i	−0.212790	−	0.282348i
$201$	4.53391	−	7.85296i	0.319797	−	0.553905i
$202$	−5.64538	+	3.25936i	−0.397208	+	0.229328i
$203$	0.800246	+	0.953695i	0.0561662	+	0.0669363i
$204$	1.86748	−	0.679707i	0.130750	−	0.0475890i
$205$	9.04507	+	11.3705i	0.631735	+	0.794152i
$206$	−3.13550	−	2.63100i	−0.218461	−	0.183310i
$207$	3.91361	+	0.690075i	0.272015	+	0.0479635i
$208$		−	5.03322i		−	0.348991i
$209$	2.65777	−	11.9090i	0.183842	−	0.823763i
$210$	−0.252967	+	0.412832i	−0.0174564	+	0.0284881i
$211$	2.87341	−	16.2959i	0.197814	−	1.12186i	−0.710541	−	0.703656i	$-0.751550\pi$
$211$	2.87341	−	16.2959i	0.197814	−	1.12186i	0.908355	−	0.418201i	$-0.137339\pi$
$212$	−6.06644	+	7.22970i	−0.416645	+	0.496538i
$213$	−0.670831	+	1.84309i	−0.0459646	+	0.126287i
$214$	12.7729	−	4.64896i	0.873137	−	0.317796i
$215$	−0.110337	−	0.738132i	−0.00752492	−	0.0503402i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−0.902327	−	0.520959i	−0.0612539	−	0.0353650i
$218$	20.1555	−	3.55395i	1.36510	−	0.240704i
$219$	1.10549	+	6.26956i	0.0747023	+	0.423658i
$220$	5.50085	−	2.98693i	0.370867	−	0.201379i
$221$	−5.00133	−	8.66256i	−0.336426	−	0.582707i
$222$	7.59505	+	9.05142i	0.509746	+	0.607492i
$223$	−0.980565	−	2.69408i	−0.0656635	−	0.180409i	0.902521	−	0.430645i	$-0.141714\pi$
$223$	−0.980565	−	2.69408i	−0.0656635	−	0.180409i	−0.968185	+	0.250236i	$0.919492\pi$
$224$	−0.203470	−	0.0740570i	−0.0135949	−	0.00494814i
$225$	1.12447	−	4.87192i	0.0749644	−	0.324794i
$226$	1.30307	−	7.39010i	0.0866792	−	0.491582i
$227$			0.156244i			0.0103703i	0.999987	+	0.00518514i	$0.00165049\pi$
$227$			0.156244i			0.0103703i	−0.999987	+	0.00518514i	$0.998350\pi$
$228$	2.94935	−	3.20957i	0.195326	−	0.212559i
$229$	24.8165			1.63992			0.819959	−	0.572422i	$-0.193996\pi$
$229$	24.8165			1.63992			0.819959	+	0.572422i	$0.193996\pi$
$230$	5.88791	−	6.65547i	0.388237	−	0.438849i
$231$	−0.464324	−	0.389614i	−0.0305503	−	0.0256347i
$232$	1.96650	−	5.40290i	0.129107	−	0.354718i
$233$	−3.83588	−	10.5390i	−0.251297	−	0.690433i	−0.999632	−	0.0271123i	$-0.991369\pi$
$233$	−3.83588	−	10.5390i	−0.251297	−	0.690433i	0.748335	−	0.663321i	$-0.230853\pi$
$234$	3.85567	−	3.23529i	0.252053	−	0.211497i
$235$	19.5958	+	0.512552i	1.27829	+	0.0334352i
$236$	5.41308	−	9.37572i	0.352361	−	0.610307i
$237$	−3.83556	+	0.676312i	−0.249146	+	0.0439312i
$238$	−0.423775	+	0.0747230i	−0.0274693	+	0.00484357i
$239$	4.51903	−	7.82718i	0.292311	−	0.506298i	−0.682044	−	0.731311i	$-0.738909\pi$
$239$	4.51903	−	7.82718i	0.292311	−	0.506298i	0.974356	+	0.225012i	$0.0722423\pi$
$240$	2.23530	+	0.0584672i	0.144288	+	0.00377404i
$241$	−20.0523	+	16.8259i	−1.29168	+	1.08385i	−0.300164	+	0.953887i	$0.597042\pi$
$241$	−20.0523	+	16.8259i	−1.29168	+	1.08385i	−0.991519	+	0.129963i	$0.958514\pi$
$242$	−1.08208	−	2.97299i	−0.0695588	−	0.191111i
$243$	−0.342020	+	0.939693i	−0.0219406	+	0.0602813i
$244$	−6.65189	−	5.58160i	−0.425844	−	0.357325i
$245$	−10.3018	+	11.6448i	−0.658160	+	0.743959i
$246$	−6.49772			−0.414280
$247$	−18.4868	−	11.8140i	−1.17629	−	0.751708i
$248$			4.81193i			0.305558i
$249$	1.05373	−	5.97598i	0.0667772	−	0.378712i
$250$	−7.97508	−	7.83569i	−0.504388	−	0.495573i
$251$	−3.29802	−	1.20038i	−0.208169	−	0.0757673i	0.235831	−	0.971794i	$-0.424219\pi$
$251$	−3.29802	−	1.20038i	−0.208169	−	0.0757673i	−0.444000	+	0.896027i	$0.646441\pi$
$252$	−0.0740570	−	0.203470i	−0.00466515	−	0.0128174i
$253$	7.15067	+	8.52183i	0.449559	+	0.535763i
$254$	1.10837	+	1.91976i	0.0695456	+	0.120457i
$255$	3.90523	−	2.12052i	0.244555	−	0.132792i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	13.2655	−	2.33907i	0.827481	−	0.145907i	0.256160	−	0.966634i	$-0.417542\pi$
$257$	13.2655	−	2.33907i	0.827481	−	0.145907i	0.571320	+	0.820727i	$0.306431\pi$
$258$	0.289054	+	0.166885i	0.0179957	+	0.0103898i
$259$	−1.27923	−	2.21568i	−0.0794872	−	0.137676i
$260$	−1.66387	−	11.1309i	−0.103189	−	0.690312i
$261$	5.40290	−	1.96650i	0.334431	−	0.121723i
$262$	4.60271	−	12.6458i	0.284356	−	0.781262i
$263$	7.72614	−	9.20766i	0.476414	−	0.567769i	−0.473294	−	0.880905i	$-0.656935\pi$
$263$	7.72614	−	9.20766i	0.476414	−	0.567769i	0.949708	+	0.313136i	$0.101380\pi$
$264$	−0.486097	+	2.75679i	−0.0299172	+	0.169669i
$265$	−11.0259	+	17.9939i	−0.677318	+	1.10536i
$266$	−0.749595	+	0.573508i	−0.0459606	+	0.0351641i
$267$			12.7594i			0.780863i
$268$	8.93005	+	1.57461i	0.545490	+	0.0961846i
$269$	−8.38250	−	7.03375i	−0.511090	−	0.428855i	0.350423	−	0.936592i	$-0.386038\pi$
$269$	−8.38250	−	7.03375i	−0.511090	−	0.428855i	−0.861512	+	0.507736i	$0.830482\pi$
$270$	1.39204	+	1.74992i	0.0847167	+	0.106497i
$271$	1.64228	−	0.597739i	0.0997611	−	0.0363101i	−0.291657	−	0.956523i	$-0.594207\pi$
$271$	1.64228	−	0.597739i	0.0997611	−	0.0363101i	0.391419	+	0.920213i	$0.371984\pi$
$272$	1.27743	+	1.52238i	0.0774556	+	0.0923080i
$273$	−0.943823	+	0.544916i	−0.0571227	+	0.0329798i
$274$	5.29759	−	9.17569i	0.320039	−	0.554324i
$275$	11.1777	−	8.42404i	0.674040	−	0.507988i
$276$	0.690075	+	3.91361i	0.0415376	+	0.235572i
$277$	7.72742	+	4.46143i	0.464296	+	0.268061i	0.713849	−	0.700300i	$-0.246950\pi$
$277$	7.72742	+	4.46143i	0.464296	+	0.268061i	−0.249553	+	0.968361i	$0.580284\pi$
$278$	15.2594	−	8.81001i	0.915197	−	0.528389i
$279$	−3.68615	+	3.09305i	−0.220684	+	0.185176i
$280$	−0.474455	−	0.0965142i	−0.0283541	−	0.00576783i
$281$	24.9608	+	9.08500i	1.48904	+	0.541965i	0.953196	−	0.302353i	$-0.0977722\pi$
$281$	24.9608	+	9.08500i	1.48904	+	0.541965i	0.535842	+	0.844318i	$0.319994\pi$
$282$	−5.63499	+	6.71552i	−0.335559	+	0.399903i
$283$	−14.2851	−	2.51884i	−0.849160	−	0.149730i	−0.267899	−	0.963447i	$-0.586329\pi$
$283$	−14.2851	−	2.51884i	−0.849160	−	0.149730i	−0.581261	+	0.813717i	$0.697440\pi$
$284$	−1.96138			−0.116386
$285$	5.46148	−	8.07293i	0.323510	−	0.478199i
$286$	14.0896			0.833135
$287$	1.38557	+	0.244313i	0.0817873	+	0.0144213i
$288$	−0.642788	+	0.766044i	−0.0378766	+	0.0451396i
$289$	−12.2635	−	4.46354i	−0.721381	−	0.262561i
$290$	2.56282	−	12.5986i	0.150494	−	0.739814i
$291$	8.14240	−	6.83229i	0.477316	−	0.400516i
$292$	−5.51336	+	3.18314i	−0.322645	+	0.186279i
$293$	−23.3801	−	13.4985i	−1.36588	−	0.788590i	−0.375479	−	0.926831i	$-0.622522\pi$
$293$	−23.3801	−	13.4985i	−1.36588	−	0.788590i	−0.990399	+	0.138241i	$0.955855\pi$
$294$	−1.20740	−	6.84748i	−0.0704168	−	0.399353i
$295$	8.87160	−	22.5238i	0.516524	−	1.31139i
$296$	−5.90790	+	10.2328i	−0.343390	+	0.594768i
$297$	−2.42428	+	1.39966i	−0.140671	+	0.0812166i
$298$	3.61231	+	4.30498i	0.209256	+	0.249381i
$299$	18.7956	−	6.84106i	1.08698	−	0.395629i
$300$	4.96269	−	0.609641i	0.286521	−	0.0351976i
$301$	−0.0553625	−	0.0464547i	−0.00319104	−	0.00267760i
$302$	−9.73977	−	1.71739i	−0.560461	−	0.0988244i
$303$		−	6.51872i		−	0.374491i
$304$	4.02474	+	1.67375i	0.230835	+	0.0959961i
$305$	−16.5558	−	10.1447i	−0.947982	−	0.580885i
$306$	−0.345096	+	1.95714i	−0.0197278	+	0.111882i
$307$	−2.63355	+	3.13855i	−0.150305	+	0.179126i	−0.835943	−	0.548816i	$-0.815079\pi$
$307$	−2.63355	+	3.13855i	−0.150305	+	0.179126i	0.685638	+	0.727942i	$0.259523\pi$
$308$	0.207309	−	0.569578i	0.0118125	−	0.0324547i
$309$	3.84626	−	1.39992i	0.218806	−	0.0796389i
$310$	1.59071	+	10.6416i	0.0903465	+	0.604400i
$311$	5.81542	+	10.0726i	0.329762	+	0.571164i	0.982464	−	0.186450i	$-0.0596982\pi$
$311$	5.81542	+	10.0726i	0.329762	+	0.571164i	−0.652703	+	0.757614i	$0.726365\pi$
$312$	4.35889	+	2.51661i	0.246774	+	0.142475i
$313$	16.6182	−	2.93024i	0.939318	−	0.165627i	0.317030	−	0.948416i	$-0.397314\pi$
$313$	16.6182	−	2.93024i	0.939318	−	0.165627i	0.622288	+	0.782788i	$0.286203\pi$
$314$	1.74980	+	9.92361i	0.0987469	+	0.560021i
$315$	−0.231039	−	0.425491i	−0.0130176	−	0.0239737i
$316$	−1.94736	−	3.37293i	−0.109548	−	0.189742i
$317$	7.44870	+	8.87702i	0.418361	+	0.498583i	0.933527	−	0.358507i	$-0.116714\pi$
$317$	7.44870	+	8.87702i	0.418361	+	0.498583i	−0.515166	+	0.857090i	$0.672270\pi$
$318$	−3.22788	−	8.86854i	−0.181011	−	0.497323i
$319$	15.1245	+	5.50486i	0.846808	+	0.308213i
$320$	0.709578	+	2.12050i	0.0396666	+	0.118539i
$321$	−2.36034	+	13.3861i	−0.131741	+	0.747141i
$322$		−	0.860479i		−	0.0479526i
$323$	8.59004	−	1.11859i	0.477963	−	0.0622402i
$324$	−1.00000			−0.0555556
$325$	−7.35928	−	24.0660i	−0.408219	−	1.33494i
$326$	−9.03174	−	7.57853i	−0.500222	−	0.419736i
$327$	−6.99992	+	19.2321i	−0.387096	+	1.06354i
$328$	−2.22235	−	6.10586i	−0.122709	−	0.337140i
$329$	1.45410	−	1.22013i	0.0801671	−	0.0672682i
$330$	−0.163668	+	6.25734i	−0.00900965	+	0.344455i
$331$	14.1914	−	24.5803i	0.780032	−	1.35106i	−0.151890	−	0.988397i	$-0.548536\pi$
$331$	14.1914	−	24.5803i	0.780032	−	1.35106i	0.931922	−	0.362658i	$-0.118131\pi$
$332$	5.97598	−	1.05373i	0.327974	−	0.0578307i
$333$	−11.6363	+	2.05179i	−0.637665	+	0.112437i
$334$	−2.70128	+	4.67876i	−0.147808	+	0.256010i
$335$	20.2693	+	0.530169i	1.10743	+	0.0289662i
$336$	0.165870	−	0.139182i	0.00904896	−	0.00759298i
$337$	−7.18317	−	19.7356i	−0.391292	−	1.07507i	−0.966412	−	0.256998i	$-0.917267\pi$
$337$	−7.18317	−	19.7356i	−0.391292	−	1.07507i	0.575120	−	0.818069i	$-0.304955\pi$
$338$	4.21822	−	11.5895i	0.229441	−	0.630384i
$339$	5.74847	+	4.82354i	0.312214	+	0.261979i
$340$	3.32830	+	2.94446i	0.180502	+	0.159686i
$341$	−13.4701			−0.729449
$342$	1.30489	+	4.15900i	0.0705603	+	0.224893i
$343$			3.02124i			0.163132i
$344$	−0.0579586	+	0.328700i	−0.00312492	+	0.0177223i
$345$	2.81985	+	8.42681i	0.151816	+	0.453684i
$346$	4.41759	+	1.60787i	0.237491	+	0.0864398i
$347$	4.82645	+	13.2606i	0.259097	+	0.711864i	0.999224	+	0.0393962i	$0.0125435\pi$
$347$	4.82645	+	13.2606i	0.259097	+	0.711864i	−0.740126	+	0.672468i	$0.765234\pi$
$348$	3.69580	+	4.40449i	0.198116	+	0.236105i
$349$	−5.01442	−	8.68522i	−0.268416	−	0.464909i	0.700037	−	0.714106i	$-0.253167\pi$
$349$	−5.01442	−	8.68522i	−0.268416	−	0.464909i	−0.968453	+	0.249197i	$0.919833\pi$
$350$	−1.08116	−	0.0565969i	−0.0577904	−	0.00302523i
$351$	0.874009	+	4.95675i	0.0466511	+	0.264572i
$352$	−2.75679	+	0.486097i	−0.146938	+	0.0259091i
$353$	−21.4146	−	12.3638i	−1.13979	−	0.658056i	−0.193409	−	0.981118i	$-0.561954\pi$
$353$	−21.4146	−	12.3638i	−1.13979	−	0.658056i	−0.946378	+	0.323062i	$0.895288\pi$
$354$	5.41308	+	9.37572i	0.287702	+	0.498314i
$355$	−4.33758	+	0.648388i	−0.230215	+	0.0344129i
$356$	−11.9899	+	4.36398i	−0.635465	+	0.231290i
$357$	0.147176	−	0.404362i	0.00778936	−	0.0214011i
$358$	5.69653	−	6.78886i	0.301071	−	0.358802i
$359$	1.50249	−	8.52106i	0.0792985	−	0.449724i	−0.919143	−	0.393923i	$-0.871118\pi$
$359$	1.50249	−	8.52106i	0.0792985	−	0.449724i	0.998442	−	0.0558012i	$-0.0177713\pi$
$360$	−1.16829	+	1.90660i	−0.0615741	+	0.100486i
$361$	15.5945	−	10.8541i	0.820765	−	0.571266i
$362$		−	9.01791i		−	0.473971i
$363$	3.11573	+	0.549387i	0.163533	+	0.0288353i
$364$	−0.834860	−	0.700531i	−0.0437586	−	0.0367178i
$365$	−11.1405	+	8.86210i	−0.583121	+	0.463863i
$366$	8.15975	−	2.96991i	0.426517	−	0.155240i
$367$	−13.1233	−	15.6398i	−0.685033	−	0.816390i	0.305712	−	0.952124i	$-0.401105\pi$
$367$	−13.1233	−	15.6398i	−0.685033	−	0.816390i	−0.990745	+	0.135733i	$0.956661\pi$
$368$	−3.44157	+	1.98699i	−0.179404	+	0.103579i
$369$	3.24886	−	5.62719i	0.169129	−	0.292940i
$370$	−9.68257	+	24.5828i	−0.503373	+	1.27800i
$371$	0.354855	+	2.01248i	0.0184231	+	0.104483i
$372$	−4.16725	−	2.40596i	−0.216062	−	0.124743i
$373$	−19.7775	+	11.4186i	−1.02404	+	0.591230i	−0.915272	−	0.402837i	$-0.868024\pi$
$373$	−19.7775	+	11.4186i	−1.02404	+	0.591230i	−0.108769	+	0.994067i	$0.534691\pi$
$374$	−4.26164	+	3.57594i	−0.220364	+	0.184908i
$375$	10.7735	−	2.98877i	0.556339	−	0.154340i
$376$	−8.23781	−	2.99832i	−0.424832	−	0.154626i
$377$	18.6018	−	22.1687i	0.958040	−	1.14175i
$378$	0.213239	+	0.0375997i	0.0109678	+	0.00193392i
$379$	−0.561491			−0.0288419			−0.0144209	−	0.999896i	$-0.504590\pi$
$379$	−0.561491			−0.0288419			−0.0144209	+	0.999896i	$0.504590\pi$
$380$	9.45401	+	2.37100i	0.484981	+	0.121630i
$381$	−2.21675			−0.113567
$382$	−5.73844	−	1.01184i	−0.293604	−	0.0517703i
$383$	6.28115	−	7.48558i	0.320952	−	0.382496i	−0.581311	−	0.813681i	$-0.697460\pi$
$383$	6.28115	−	7.48558i	0.320952	−	0.382496i	0.902263	+	0.431186i	$0.141905\pi$
$384$	−0.939693	−	0.342020i	−0.0479535	−	0.0174536i
$385$	0.270174	−	1.32815i	0.0137694	−	0.0676889i
$386$	14.1653	−	11.8861i	0.720996	−	0.604988i
$387$	−0.289054	+	0.166885i	−0.0146934	+	0.00848325i
$388$	9.20511	+	5.31457i	0.467319	+	0.269807i
$389$	−3.68552	−	20.9016i	−0.186863	−	1.05975i	−0.923538	−	0.383507i	$-0.874716\pi$
$389$	−3.68552	−	20.9016i	−0.186863	−	1.05975i	0.736674	−	0.676248i	$-0.236395\pi$
$390$	10.4716	+	4.12452i	0.530251	+	0.208853i
$391$	−3.94881	+	6.83954i	−0.199700	+	0.345890i
$392$	6.02157	−	3.47656i	0.304135	−	0.175593i
$393$	8.65026	+	10.3090i	0.436348	+	0.520019i
$394$	16.1266	−	5.86961i	0.812447	−	0.295706i
$395$	−5.42160	−	6.81547i	−0.272790	−	0.342924i
$396$	−2.14441	−	1.79937i	−0.107760	−	0.0904217i
$397$	−4.19141	−	0.739059i	−0.210361	−	0.0370923i	0.0674745	−	0.997721i	$-0.478506\pi$
$397$	−4.19141	−	0.739059i	−0.210361	−	0.0370923i	−0.277835	+	0.960629i	$0.589617\pi$
$398$		−	22.0921i		−	1.10738i
$399$	−0.121875	−	0.935922i	−0.00610140	−	0.0468547i
$400$	2.27022	+	4.45490i	0.113511	+	0.222745i
$401$	−5.37136	+	30.4625i	−0.268233	+	1.52122i	0.491436	+	0.870914i	$0.336472\pi$
$401$	−5.37136	+	30.4625i	−0.268233	+	1.52122i	−0.759669	+	0.650310i	$0.774639\pi$
$402$	−5.82868	+	6.94635i	−0.290708	+	0.346452i
$403$	−8.28355	+	22.7589i	−0.412633	+	1.13370i
$404$	6.12560	−	2.22953i	0.304760	−	0.110923i
$405$	−2.21150	+	0.330577i	−0.109890	+	0.0164265i
$406$	−0.622480	−	1.07817i	−0.0308932	−	0.0535086i
$407$	−28.6449	−	16.5381i	−1.41987	−	0.819764i
$408$	−1.95714	+	0.345096i	−0.0968928	+	0.0170848i
$409$	3.25200	+	18.4430i	0.160801	+	0.911948i	0.953289	+	0.302060i	$0.0976743\pi$
$409$	3.25200	+	18.4430i	0.160801	+	0.911948i	−0.792488	+	0.609888i	$0.791215\pi$
$410$	−6.93319	−	12.7684i	−0.342406	−	0.630588i
$411$	5.29759	+	9.17569i	0.261311	+	0.452604i
$412$	2.63100	+	3.13550i	0.129620	+	0.154475i
$413$	−0.801752	−	2.20280i	−0.0394516	−	0.108392i
$414$	−3.73432	−	1.35918i	−0.183532	−	0.0668002i
$415$	12.8675	−	4.30584i	0.631642	−	0.211365i
$416$	−0.874009	+	4.95675i	−0.0428518	+	0.243025i
$417$			17.6200i			0.862856i
$418$	−4.68537	+	11.2666i	−0.229169	+	0.551065i
$419$	−19.9049			−0.972420			−0.486210	−	0.873842i	$-0.661621\pi$
$419$	−19.9049			−0.972420			−0.486210	+	0.873842i	$0.661621\pi$
$420$	0.320811	−	0.362633i	0.0156540	−	0.0176947i
$421$	7.13586	+	5.98770i	0.347780	+	0.291822i	0.799898	−	0.600136i	$-0.204887\pi$
$421$	7.13586	+	5.98770i	0.347780	+	0.291822i	−0.452118	+	0.891958i	$0.649331\pi$
$422$	−5.65951	+	15.5494i	−0.275501	+	0.756932i
$423$	−2.99832	−	8.23781i	−0.145783	−	0.400536i
$424$	7.22970	−	6.06644i	0.351105	−	0.294612i
$425$	8.33390	+	5.41139i	0.404253	+	0.262491i
$426$	0.980690	−	1.69860i	0.0475146	−	0.0822977i
$427$	−1.85164	+	0.326494i	−0.0896072	+	0.0158002i
$428$	−13.3861	+	2.36034i	−0.647043	+	0.114091i
$429$	−7.04480	+	12.2019i	−0.340126	+	0.589116i
$430$	−0.0195146	+	0.746078i	−0.000941078	+	0.0359791i
$431$	−28.3264	+	23.7687i	−1.36443	+	1.14490i	−0.389848	+	0.920879i	$0.627473\pi$
$431$	−28.3264	+	23.7687i	−1.36443	+	1.14490i	−0.974585	+	0.224017i	$0.928083\pi$
$432$	−0.342020	−	0.939693i	−0.0164555	−	0.0452110i
$433$	−4.24249	+	11.6562i	−0.203881	+	0.560159i	−0.998923	−	0.0463955i	$-0.985227\pi$
$433$	−4.24249	+	11.6562i	−0.203881	+	0.560159i	0.795042	+	0.606554i	$0.207449\pi$
$434$	0.798155	+	0.669732i	0.0383127	+	0.0321481i
$435$	9.62928	+	8.51876i	0.461689	+	0.408443i
$436$	−20.4664			−0.980162
$437$	−0.779961	+	17.3046i	−0.0373106	+	0.827792i
$438$		−	6.36628i		−	0.304193i
$439$	5.46975	−	31.0205i	0.261057	−	1.48053i	−0.518975	−	0.854789i	$-0.673686\pi$
$439$	5.46975	−	31.0205i	0.261057	−	1.48053i	0.780032	−	0.625739i	$-0.215203\pi$
$440$	−5.93595	+	1.98634i	−0.282985	+	0.0946949i
$441$	6.53379	+	2.37811i	0.311133	+	0.113243i
$442$	3.42111	+	9.39942i	0.162726	+	0.447085i
$443$	18.2052	+	21.6961i	0.864954	+	1.03081i	0.999205	+	0.0398642i	$0.0126925\pi$
$443$	18.2052	+	21.6961i	0.864954	+	1.03081i	−0.134252	+	0.990947i	$0.542863\pi$
$444$	−5.90790	−	10.2328i	−0.280376	−	0.485626i
$445$	−25.0731	+	13.6145i	−1.18858	+	0.645390i
$446$	0.497846	+	2.82342i	0.0235737	+	0.133693i
$447$	−5.53438	+	0.975861i	−0.261767	+	0.0461566i
$448$	0.187519	+	0.108264i	0.00885943	+	0.00511500i
$449$	−11.4869	−	19.8960i	−0.542102	−	0.938949i	−0.998783	−	0.0493182i	$-0.984295\pi$
$449$	−11.4869	−	19.8960i	−0.542102	−	0.938949i	0.456681	−	0.889631i	$-0.349038\pi$
$450$	−1.95338	+	4.60264i	−0.0920833	+	0.216971i
$451$	17.0923	−	6.22108i	0.804844	−	0.292939i
$452$	−2.56655	+	7.05155i	−0.120721	+	0.331677i
$453$	6.35719	−	7.57620i	0.298687	−	0.355961i
$454$	0.0271315	−	0.153870i	0.00127334	−	0.00722150i
$455$	−2.07787	−	1.27324i	−0.0974121	−	0.0596902i
$456$	−3.46188	+	2.64866i	−0.162117	+	0.124035i
$457$			14.0905i			0.659126i	0.944134	+	0.329563i	$0.106901\pi$
$457$			14.0905i			0.659126i	−0.944134	+	0.329563i	$0.893099\pi$
$458$	−24.4395	−	4.30934i	−1.14198	−	0.201362i
$459$	−1.52238	−	1.27743i	−0.0710588	−	0.0596254i
$460$	−6.95417	+	5.53193i	−0.324240	+	0.257928i
$461$	−7.43181	+	2.70496i	−0.346134	+	0.125982i	−0.509236	−	0.860627i	$-0.670072\pi$
$461$	−7.43181	+	2.70496i	−0.346134	+	0.125982i	0.163103	+	0.986609i	$0.447850\pi$
$462$	0.389614	+	0.464324i	0.0181265	+	0.0216023i
$463$	−32.2849	+	18.6397i	−1.50041	+	0.866261i	−0.500408	+	0.865790i	$0.666817\pi$
$463$	−32.2849	+	18.6397i	−1.50041	+	0.866261i	−1.00000		0.000470819i	$0.999850\pi$
$464$	−2.87483	+	4.97934i	−0.133460	+	0.231160i
$465$	−10.0112	−	3.94318i	−0.464259	−	0.182861i
$466$	1.94753	+	11.0450i	0.0902175	+	0.511649i
$467$	17.3392	+	10.0108i	0.802364	+	0.463245i	0.844297	−	0.535875i	$-0.180018\pi$
$467$	17.3392	+	10.0108i	0.802364	+	0.463245i	−0.0419332	+	0.999120i	$0.513352\pi$
$468$	−4.35889	+	2.51661i	−0.201490	+	0.116330i
$469$	1.50408	−	1.26207i	0.0694519	−	0.0582771i
$470$	−19.2091	−	3.90753i	−0.886048	−	0.180241i
$471$	−9.46899	−	3.44643i	−0.436308	−	0.158803i
$472$	−6.95892	+	8.29331i	−0.320310	+	0.381731i
$473$	−0.920136	−	0.162245i	−0.0423079	−	0.00746003i
$474$	3.89472			0.178891
$475$	21.6913	+	2.11818i	0.995266	+	0.0971889i
$476$	0.430313			0.0197234
$477$	9.29432	+	1.63884i	0.425558	+	0.0750373i
$478$	−5.80955	+	6.92355i	−0.265722	+	0.316676i
$479$	−18.6617	−	6.79229i	−0.852673	−	0.310348i	−0.121543	−	0.992586i	$-0.538784\pi$
$479$	−18.6617	−	6.79229i	−0.852673	−	0.310348i	−0.731130	+	0.682238i	$0.761007\pi$
$480$	−2.19119	−	0.445735i	−0.100014	−	0.0203449i
$481$	−45.5578	+	38.2275i	−2.07726	+	1.74302i
$482$	22.6695	−	13.0882i	1.03257	−	0.596152i
$483$	0.745197	+	0.430239i	0.0339076	+	0.0195766i
$484$	0.549387	+	3.11573i	0.0249721	+	0.141624i
$485$	22.1140	+	8.71016i	1.00414	+	0.395508i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−0.675159	+	0.389803i	−0.0305944	+	0.0176637i	−0.515219	−	0.857058i	$-0.672289\pi$
$487$	−0.675159	+	0.389803i	−0.0305944	+	0.0176637i	0.484625	+	0.874722i	$0.338956\pi$
$488$	5.58160	+	6.65189i	0.252667	+	0.301117i
$489$	11.0791	−	4.03245i	0.501013	−	0.182354i
$490$	12.1674	−	9.67899i	0.549668	−	0.437252i
$491$	−18.6379	−	15.6390i	−0.841116	−	0.705780i	0.116698	−	0.993167i	$-0.462769\pi$
$491$	−18.6379	−	15.6390i	−0.841116	−	0.705780i	−0.957814	+	0.287387i	$0.907213\pi$
$492$	6.39901	+	1.12832i	0.288490	+	0.0508685i
$493$			11.4265i			0.514622i
$494$	16.1544	+	14.8447i	0.726822	+	0.667896i
$495$	−5.33718	−	3.27041i	−0.239888	−	0.146994i
$496$	0.835582	−	4.73882i	0.0375188	−	0.212779i
$497$	−0.272988	+	0.325334i	−0.0122452	+	0.0145932i
$498$	−2.07544	+	5.70221i	−0.0930025	+	0.255522i
$499$	17.4860	−	6.36439i	0.782782	−	0.284909i	0.0804499	−	0.996759i	$-0.474364\pi$
$499$	17.4860	−	6.36439i	0.782782	−	0.284909i	0.702332	+	0.711849i	$0.252142\pi$
$500$	6.49327	+	9.10151i	0.290388	+	0.407032i
$501$	−2.70128	−	4.67876i	−0.120684	−	0.209031i
$502$	3.03947	+	1.75484i	0.135658	+	0.0783223i
$503$	−4.35345	+	0.767631i	−0.194111	+	0.0342270i	−0.269858	−	0.962900i	$-0.586977\pi$
$503$	−4.35345	+	0.767631i	−0.194111	+	0.0342270i	0.0757474	+	0.997127i	$0.475866\pi$
$504$	0.0375997	+	0.213239i	0.00167482	+	0.00949840i
$505$	12.8097	−	6.95559i	0.570024	−	0.309520i
$506$	−5.56223	−	9.63407i	−0.247271	−	0.428286i
$507$	7.92766	+	9.44782i	0.352080	+	0.419593i
$508$	−0.758173	−	2.08306i	−0.0336385	−	0.0924210i
$509$	21.7911	+	7.93130i	0.965872	+	0.351549i	0.776332	−	0.630324i	$-0.217078\pi$
$509$	21.7911	+	7.93130i	0.965872	+	0.351549i	0.189540	+	0.981873i	$0.439300\pi$
$510$	−4.21412	+	1.41016i	−0.186605	+	0.0624431i
$511$	−0.239370	+	1.35754i	−0.0105891	+	0.0600539i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.25424	−	0.949432i	−0.187829	−	0.0419185i
$514$	−13.4702			−0.594144
$515$	6.85496	+	6.06440i	0.302066	+	0.267229i
$516$	−0.255683	−	0.214543i	−0.0112558	−	0.00944475i
$517$	8.39326	−	23.0603i	0.369135	−	1.01419i
$518$	0.875042	+	2.40416i	0.0384471	+	0.105633i
$519$	−3.60126	+	3.02181i	−0.158078	+	0.132643i
$520$	−0.294278	+	11.2508i	−0.0129049	+	0.493379i
$521$	21.6132	−	37.4351i	0.946891	−	1.64006i	0.194971	−	0.980809i	$-0.437539\pi$
$521$	21.6132	−	37.4351i	0.946891	−	1.64006i	0.751920	−	0.659255i	$-0.229128\pi$
$522$	−5.66230	+	0.998416i	−0.247832	+	0.0436995i
$523$	25.2716	−	4.45607i	1.10505	−	0.194850i	0.408782	−	0.912632i	$-0.365954\pi$
$523$	25.2716	−	4.45607i	1.10505	−	0.194850i	0.696268	+	0.717782i	$0.254843\pi$
$524$	−6.72871	+	11.6545i	−0.293945	+	0.509127i
$525$	0.589594	−	0.908014i	0.0257320	−	0.0396290i
$526$	−9.20766	+	7.72614i	−0.401473	+	0.336876i
$527$	−3.27070	−	8.98617i	−0.142474	−	0.391444i
$528$	0.957425	−	2.63050i	0.0416666	−	0.114478i
$529$	5.52123	+	4.63287i	0.240054	+	0.201429i
$530$	13.9830	−	15.8059i	0.607384	−	0.686564i
$531$	−10.8262			−0.469815
$532$	0.837795	−	0.434630i	0.0363230	−	0.0188436i
$533$		−	32.7044i		−	1.41659i
$534$	2.21565	−	12.5656i	0.0958805	−	0.543765i
$535$	−28.8231	+	9.64503i	−1.24613	+	0.416991i
$536$	−8.52096	−	3.10137i	−0.368049	−	0.133959i
$537$	3.03106	+	8.32777i	0.130800	+	0.359370i
$538$	7.03375	+	8.38250i	0.303246	+	0.361395i
$539$	9.73201	+	16.8563i	0.419187	+	0.726054i
$540$	−1.06702	−	1.96506i	−0.0459171	−	0.0845629i
$541$	−1.84361	−	10.4557i	−0.0792631	−	0.449524i	−0.998448	−	0.0556966i	$-0.982262\pi$
$541$	−1.84361	−	10.4557i	−0.0792631	−	0.449524i	0.919185	−	0.393827i	$-0.128849\pi$
$542$	−1.72112	+	0.303480i	−0.0739285	+	0.0130356i
$543$	7.80974	+	4.50896i	0.335148	+	0.193498i
$544$	−0.993665	−	1.72108i	−0.0426030	−	0.0737906i
$545$	−45.2614	+	6.76573i	−1.93878	+	0.289812i
$546$	1.02411	−	0.372745i	0.0438278	−	0.0159520i
$547$	10.7384	−	29.5035i	0.459140	−	1.26148i	−0.466987	−	0.884264i	$-0.654660\pi$
$547$	10.7384	−	29.5035i	0.459140	−	1.26148i	0.926127	−	0.377212i	$-0.123117\pi$
$548$	−6.81045	+	8.11638i	−0.290928	+	0.346714i
$549$	−1.50786	+	8.55151i	−0.0643539	+	0.364969i
$550$	−12.4707	+	6.35507i	−0.531752	+	0.270981i
$551$	11.5411	+	22.2467i	0.491667	+	0.947740i
$552$		−	3.97398i		−	0.169144i
$553$	−0.830505	−	0.146441i	−0.0353167	−	0.00622728i
$554$	−6.83531	−	5.73550i	−0.290404	−	0.243678i
$555$	−16.4480	−	20.6767i	−0.698180	−	0.877679i
$556$	−16.5574	+	6.02640i	−0.702190	+	0.255576i
$557$	12.5357	+	14.9394i	0.531154	+	0.633005i	0.963180	−	0.268856i	$-0.0866457\pi$
$557$	12.5357	+	14.9394i	0.531154	+	0.633005i	−0.432026	+	0.901861i	$0.642201\pi$
$558$	4.16725	−	2.40596i	0.176414	−	0.101853i
$559$	−0.839969	+	1.45487i	−0.0355269	+	0.0615344i
$560$	0.450487	+	0.177436i	0.0190365	+	0.00749804i
$561$	−0.966036	−	5.47866i	−0.0407861	−	0.231309i
$562$	−23.0040	−	13.2814i	−0.970366	−	0.560241i
$563$	35.0083	−	20.2121i	1.47542	−	0.851836i	0.475808	−	0.879549i	$-0.342156\pi$
$563$	35.0083	−	20.2121i	1.47542	−	0.851836i	0.999616	+	0.0277126i	$0.00882233\pi$
$564$	6.71552	−	5.63499i	0.282774	−	0.237276i
$565$	−3.34484	+	16.4429i	−0.140719	+	0.691759i
$566$	13.6307	+	4.96116i	0.572939	+	0.208533i
$567$	−0.139182	+	0.165870i	−0.00584508	+	0.00696589i
$568$	1.93158	+	0.340590i	0.0810474	+	0.0142908i
$569$	10.6728			0.447425			0.223713	−	0.974655i	$-0.428182\pi$
$569$	10.6728			0.447425			0.223713	+	0.974655i	$0.428182\pi$
$570$	−6.78035	+	7.00191i	−0.283998	+	0.293278i
$571$	40.4489			1.69274			0.846368	−	0.532599i	$-0.178785\pi$
$571$	40.4489			1.69274			0.846368	+	0.532599i	$0.178785\pi$
$572$	−13.8755	−	2.44663i	−0.580166	−	0.102299i
$573$	3.74550	−	4.46372i	0.156471	−	0.186474i
$574$	−1.32209	−	0.481202i	−0.0551830	−	0.0200850i
$575$	−13.5504	+	14.5327i	−0.565090	+	0.606057i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	17.1828	−	9.92050i	0.715330	−	0.412996i	−0.0977014	−	0.995216i	$-0.531149\pi$
$577$	17.1828	−	9.92050i	0.715330	−	0.412996i	0.813031	+	0.582220i	$0.197816\pi$
$578$	11.3021	+	6.52526i	0.470105	+	0.271415i
$579$	3.21102	+	18.2106i	0.133445	+	0.756807i
$580$	−4.71161	+	11.9622i	−0.195639	+	0.496701i
$581$	0.656964	−	1.13790i	0.0272555	−	0.0472079i
$582$	−9.20511	+	5.31457i	−0.381564	+	0.220296i
$583$	16.9819	+	20.2383i	0.703319	+	0.838183i
$584$	5.98235	−	2.17740i	0.247551	−	0.0901013i
$585$	−8.80774	+	7.00642i	−0.364155	+	0.289680i
$586$	20.6809	+	17.3533i	0.854319	+	0.716859i
$587$	−5.42869	−	0.957225i	−0.224066	−	0.0395089i	0.0604878	−	0.998169i	$-0.480734\pi$
$587$	−5.42869	−	0.957225i	−0.224066	−	0.0395089i	−0.284554	+	0.958660i	$0.591845\pi$
$588$			6.95312i			0.286742i
$589$	−15.4442	−	14.1921i	−0.636367	−	0.584774i
$590$	−12.6480	+	20.6411i	−0.520711	+	0.849780i
$591$	−2.98008	+	16.9009i	−0.122584	+	0.695208i
$592$	7.59505	−	9.05142i	0.312155	−	0.372011i
$593$	−9.28489	+	25.5100i	−0.381285	+	1.04757i	0.589531	+	0.807746i	$0.299312\pi$
$593$	−9.28489	+	25.5100i	−0.381285	+	1.04757i	−0.970816	+	0.239826i	$0.922910\pi$
$594$	2.63050	−	0.957425i	0.107931	−	0.0392836i
$595$	0.951635	−	0.142252i	0.0390132	−	0.00583175i
$596$	−2.80988	−	4.86685i	−0.115097	−	0.199354i
$597$	19.1323	+	11.0460i	0.783033	+	0.452084i
$598$	−19.6980	+	3.47330i	−0.805513	+	0.142034i
$599$	1.54494	+	8.76181i	0.0631247	+	0.357998i	0.999966	+	0.00824330i	$0.00262395\pi$
$599$	1.54494	+	8.76181i	0.0631247	+	0.357998i	−0.936841	+	0.349755i	$0.886265\pi$
$600$	−4.99316	−	0.261384i	−0.203845	−	0.0106709i
$601$	−16.8816	−	29.2398i	−0.688616	−	1.19272i	−0.972286	−	0.233796i	$-0.924885\pi$
$601$	−16.8816	−	29.2398i	−0.688616	−	1.19272i	0.283670	−	0.958922i	$-0.408448\pi$
$602$	0.0464547	+	0.0553625i	0.00189335	+	0.00225641i
$603$	−3.10137	−	8.52096i	−0.126298	−	0.347000i
$604$	9.29358	+	3.38259i	0.378151	+	0.137636i
$605$	2.24496	+	6.70880i	0.0912704	+	0.272752i
$606$	−1.13196	+	6.41969i	−0.0459829	+	0.260782i
$607$			14.2869i			0.579888i	0.957044	+	0.289944i	$0.0936367\pi$
$607$			14.2869i			0.579888i	−0.957044	+	0.289944i	$0.906363\pi$
$608$	−3.67296	−	2.34721i	−0.148958	−	0.0951920i
$609$	1.24496			0.0504484
$610$	14.5427	+	12.8655i	0.588815	+	0.520908i
$611$	−33.8007	−	28.3621i	−1.36743	−	1.14741i
$612$	0.679707	−	1.86748i	0.0274755	−	0.0754884i
$613$	−7.42790	−	20.4080i	−0.300010	−	0.824271i	−0.994497	−	0.104766i	$-0.966591\pi$
$613$	−7.42790	−	20.4080i	−0.300010	−	0.824271i	0.694487	−	0.719506i	$-0.255632\pi$
$614$	3.13855	−	2.63355i	0.126661	−	0.106282i
$615$	14.5244	+	0.379904i	0.585680	+	0.0153192i
$616$	−0.303066	+	0.524926i	−0.0122109	+	0.0211499i
$617$	23.4553	−	4.13580i	0.944274	−	0.166501i	0.319746	−	0.947503i	$-0.396402\pi$
$617$	23.4553	−	4.13580i	0.944274	−	0.166501i	0.624528	+	0.781002i	$0.285291\pi$
$618$	−4.03092	+	0.710760i	−0.162147	+	0.0285910i
$619$	13.8524	−	23.9931i	0.556776	−	0.964365i	−0.440987	−	0.897514i	$-0.645371\pi$
$619$	13.8524	−	23.9931i	0.556776	−	0.964365i	0.997763	−	0.0668511i	$-0.0212953\pi$
$620$	0.281340	−	10.7561i	0.0112989	−	0.431976i
$621$	3.04425	−	2.55443i	0.122161	−	0.102506i
$622$	−3.97798	−	10.9294i	−0.159502	−	0.438229i
$623$	−0.944923	+	2.59616i	−0.0378576	+	0.104013i
$624$	−3.85567	−	3.23529i	−0.154350	−	0.129515i
$625$	17.3686	+	17.9814i	0.694744	+	0.719257i
$626$	−16.8746			−0.674444
$627$	−7.41444	−	9.69092i	−0.296104	−	0.387018i
$628$		−	10.0767i		−	0.402104i
$629$	4.07759	−	23.1251i	0.162584	−	0.922060i
$630$	0.153643	+	0.459147i	0.00612130	+	0.0182928i
$631$	−24.8426	−	9.04198i	−0.988970	−	0.359956i	−0.203649	−	0.979044i	$-0.565280\pi$
$631$	−24.8426	−	9.04198i	−0.988970	−	0.359956i	−0.785321	+	0.619088i	$0.787502\pi$
$632$	1.33207	+	3.65984i	0.0529871	+	0.145581i
$633$	−10.6364	−	12.6760i	−0.422759	−	0.503825i
$634$	−5.79406	−	10.0356i	−0.230112	−	0.398565i
$635$	−2.36531	−	4.35605i	−0.0938645	−	0.172865i
$636$	1.63884	+	9.29432i	0.0649842	+	0.368544i
$637$	34.4649	−	6.07708i	1.36555	−	0.240783i
$638$	−13.9388	−	8.04756i	−0.551842	−	0.318606i
$639$	0.980690	+	1.69860i	0.0387955	+	0.0671958i
$640$	−0.330577	−	2.21150i	−0.0130672	−	0.0874171i
$641$	16.3383	−	5.94665i	0.645324	−	0.234879i	0.00143632	−	0.999999i	$-0.499543\pi$
$641$	16.3383	−	5.94665i	0.645324	−	0.234879i	0.643887	+	0.765120i	$0.277321\pi$
$642$	4.64896	−	12.7729i	0.183480	−	0.504106i
$643$	23.2648	−	27.7259i	0.917473	−	1.09340i	−0.0778656	−	0.996964i	$-0.524811\pi$
$643$	23.2648	−	27.7259i	0.917473	−	1.09340i	0.995339	−	0.0964383i	$-0.0307450\pi$
$644$	−0.149421	+	0.847406i	−0.00588800	+	0.0333925i
$645$	−0.636365	−	0.389939i	−0.0250569	−	0.0153538i
$646$	−8.65378	−	0.390047i	−0.340479	−	0.0153462i
$647$			34.5519i			1.35837i	0.733965	+	0.679187i	$0.237668\pi$
$647$			34.5519i			1.35837i	−0.733965	+	0.679187i	$0.762332\pi$
$648$	0.984808	+	0.173648i	0.0386869	+	0.00682154i
$649$	−23.2157	−	19.4803i	−0.911294	−	0.764667i
$650$	3.06845	+	24.9783i	0.120355	+	0.979730i
$651$	−0.979082	+	0.356357i	−0.0383733	+	0.0139667i
$652$	7.57853	+	9.03174i	0.296798	+	0.353710i
$653$	−3.57699	+	2.06518i	−0.139978	+	0.0808165i	−0.568354	−	0.822784i	$-0.692419\pi$
$653$	−3.57699	+	2.06518i	−0.139978	+	0.0808165i	0.428375	+	0.903601i	$0.359086\pi$
$654$	10.2332	−	17.7244i	0.400150	−	0.693079i
$655$	−11.0278	+	27.9982i	−0.430892	+	1.09398i
$656$	1.12832	+	6.39901i	0.0440534	+	0.249839i
$657$	5.51336	+	3.18314i	0.215097	+	0.124186i
$658$	−1.64388	+	0.949096i	−0.0640852	+	0.0369996i
$659$	20.4161	−	17.1311i	0.795298	−	0.667335i	−0.151752	−	0.988419i	$-0.548492\pi$
$659$	20.4161	−	17.1311i	0.795298	−	0.667335i	0.947051	+	0.321084i	$0.104047\pi$
$660$	1.24776	−	6.13385i	0.0485689	−	0.238760i
$661$	15.0105	+	5.46336i	0.583839	+	0.212500i	0.617018	−	0.786949i	$-0.288341\pi$
$661$	15.0105	+	5.46336i	0.583839	+	0.212500i	−0.0331784	+	0.999449i	$0.510563\pi$
$662$	−18.2442	+	21.7425i	−0.709079	+	0.845048i
$663$	−9.85070	−	1.73694i	−0.382569	−	0.0674573i
$664$	−6.06817			−0.235491
$665$	1.70910	−	1.23814i	0.0662762	−	0.0480130i
$666$	11.8158			0.457853
$667$	−22.5019	−	3.96769i	−0.871277	−	0.153630i
$668$	3.47270	−	4.13860i	0.134363	−	0.160127i
$669$	−2.69408	−	0.980565i	−0.104159	−	0.0379108i
$670$	−19.8693	−	4.04184i	−0.767619	−	0.156150i
$671$	−18.6208	+	15.6247i	−0.718848	+	0.603185i
$672$	−0.187519	+	0.108264i	−0.00723370	+	0.00417638i
$673$	5.63765	+	3.25490i	0.217315	+	0.125467i	0.604707	−	0.796448i	$-0.293290\pi$
$673$	5.63765	+	3.25490i	0.217315	+	0.125467i	−0.387391	+	0.921915i	$0.626624\pi$
$674$	3.64699	+	20.6831i	0.140477	+	0.796684i
$675$	−3.00931	−	3.99300i	−0.115828	−	0.153691i
$676$	−6.16663	+	10.6809i	−0.237178	+	0.410804i
$677$	20.1132	−	11.6124i	0.773014	−	0.446300i	−0.0609350	−	0.998142i	$-0.519408\pi$
$677$	20.1132	−	11.6124i	0.773014	−	0.446300i	0.833949	+	0.551842i	$0.186075\pi$
$678$	−4.82354	−	5.74847i	−0.185247	−	0.220769i
$679$	2.16271	−	0.787163i	0.0829973	−	0.0302085i
$680$	−2.76644	−	3.47768i	−0.106088	−	0.133363i
$681$	0.119690	+	0.100432i	0.00458653	+	0.00384855i
$682$	13.2655	+	2.33906i	0.507962	+	0.0895674i
$683$			40.4798i			1.54892i	0.632626	+	0.774458i	$0.281977\pi$
$683$			40.4798i			1.54892i	−0.632626	+	0.774458i	$0.718023\pi$
$684$	−0.562862	−	4.32241i	−0.0215216	−	0.165271i
$685$	−12.3782	+	20.2007i	−0.472947	+	0.771830i
$686$	0.524633	−	2.97534i	0.0200306	−	0.113599i
$687$	15.9517	−	19.0105i	0.608596	−	0.725297i
$688$	0.114156	−	0.313642i	0.00435216	−	0.0119575i
$689$	44.6373	−	16.2466i	1.70054	−	0.618947i
$690$	−1.31371	−	8.78845i	−0.0500121	−	0.334571i
$691$	−6.47610	−	11.2169i	−0.246362	−	0.426712i	0.716151	−	0.697945i	$-0.245902\pi$
$691$	−6.47610	−	11.2169i	−0.246362	−	0.426712i	−0.962514	+	0.271233i	$0.912569\pi$
$692$	−4.07128	−	2.35055i	−0.154767	−	0.0893546i
$693$	−0.596924	+	0.105254i	−0.0226753	+	0.00399826i
$694$	−2.45045	−	13.8972i	−0.0930179	−	0.527531i
$695$	−34.6245	+	18.8009i	−1.31338	+	0.713158i
$696$	−2.87483	−	4.97934i	−0.108970	−	0.188742i
$697$	8.30039	+	9.89202i	0.314400	+	0.374687i
$698$	3.43006	+	9.42402i	0.129830	+	0.356704i
$699$	−10.5390	−	3.83588i	−0.398622	−	0.145086i
$700$	1.05491	+	0.243479i	0.0398717	+	0.00920263i
$701$	1.19332	−	6.76764i	0.0450710	−	0.255610i	−0.953944	−	0.299985i	$-0.903018\pi$
$701$	1.19332	−	6.76764i	0.0450710	−	0.255610i	0.999015	+	0.0443746i	$0.0141295\pi$
$702$		−	5.03322i		−	0.189966i
$703$	−15.4183	−	49.1419i	−0.581512	−	1.85342i
$704$	2.79932			0.105503
$705$	12.9886	−	14.6818i	0.489177	−	0.552947i
$706$	18.9424	+	15.8945i	0.712905	+	0.598199i
$707$	0.482757	−	1.32636i	0.0181559	−	0.0498830i
$708$	−3.70276	−	10.1733i	−0.139158	−	0.382334i
$709$	5.26501	−	4.41786i	0.197731	−	0.165916i	−0.538546	−	0.842596i	$-0.681026\pi$
$709$	5.26501	−	4.41786i	0.197731	−	0.165916i	0.736278	+	0.676680i	$0.236582\pi$
$710$	4.38428	+	0.114676i	0.164539	+	0.00430372i
$711$	−1.94736	+	3.37293i	−0.0730318	+	0.126495i
$712$	12.5656	−	2.21565i	0.470915	−	0.0830349i
$713$	18.8320	−	3.32059i	0.705264	−	0.124357i
$714$	−0.215156	+	0.372662i	−0.00805202	+	0.0139465i
$715$	−31.4945	−	0.823779i	−1.17783	−	0.0308076i
$716$	−6.78886	+	5.69653i	−0.253712	+	0.212889i
$717$	−3.09120	−	8.49299i	−0.115443	−	0.317177i
$718$	−2.95933	+	8.13070i	−0.110441	+	0.303435i
$719$	−16.6816	−	13.9975i	−0.622118	−	0.522019i	0.276350	−	0.961057i	$-0.410875\pi$
$719$	−16.6816	−	13.9975i	−0.622118	−	0.522019i	−0.898469	+	0.439038i	$0.855319\pi$
$720$	1.48161	−	1.67476i	0.0552165	−	0.0624146i
$721$	0.886272			0.0330065
$722$	−17.2424	+	7.98120i	−0.641696	+	0.297030i
$723$			26.1764i			0.973512i
$724$	−1.56594	+	8.88091i	−0.0581978	+	0.330056i
$725$	−6.46529	+	28.0118i	−0.240115	+	1.04033i
$726$	−2.97299	−	1.08208i	−0.110338	−	0.0401598i
$727$	−15.2844	−	41.9934i	−0.566865	−	1.55745i	−0.809370	−	0.587299i	$-0.800191\pi$
$727$	−15.2844	−	41.9934i	−0.566865	−	1.55745i	0.242504	−	0.970150i	$-0.422031\pi$
$728$	0.700531	+	0.834860i	0.0259634	+	0.0309420i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	12.5101	−	6.79293i	0.463021	−	0.251418i
$731$	−0.115183	−	0.653235i	−0.00426019	−	0.0241608i
$732$	−8.55151	+	1.50786i	−0.316073	+	0.0557322i
$733$	5.33333	+	3.07920i	0.196991	+	0.113733i	0.595251	−	0.803540i	$-0.297053\pi$
$733$	5.33333	+	3.07920i	0.196991	+	0.113733i	−0.398260	+	0.917272i	$0.630386\pi$
$734$	10.2081	+	17.6810i	0.376790	+	0.652619i
$735$	2.29854	+	15.3768i	0.0847830	+	0.567182i
$736$	3.73432	−	1.35918i	0.137649	−	0.0501001i
$737$	8.68175	−	23.8529i	0.319796	−	0.878633i
$738$	−4.17666	+	4.97755i	−0.153745	+	0.183226i
$739$	6.41364	−	36.3736i	0.235930	−	1.33802i	−0.604717	−	0.796440i	$-0.706714\pi$
$739$	6.41364	−	36.3736i	0.235930	−	1.33802i	0.840647	−	0.541583i	$-0.182175\pi$
$740$	13.8042	−	22.5279i	0.507453	−	0.828144i
$741$	−20.9331	+	6.56779i	−0.768998	+	0.241274i
$742$		−	2.04353i		−	0.0750202i
$743$	−30.2415	−	5.33240i	−1.10945	−	0.195627i	−0.411248	−	0.911523i	$-0.634907\pi$
$743$	−30.2415	−	5.33240i	−1.10945	−	0.195627i	−0.698206	+	0.715897i	$0.746018\pi$
$744$	3.68615	+	3.09305i	0.135141	+	0.113397i
$745$	−7.82291	−	9.83415i	−0.286609	−	0.360295i
$746$	21.4599	−	7.81075i	0.785701	−	0.285972i
$747$	−3.90054	−	4.64849i	−0.142713	−	0.170079i
$748$	4.81785	−	2.78159i	0.176158	−	0.101705i
$749$	−1.47159	+	2.54888i	−0.0537709	+	0.0931339i
$750$	−11.1288	+	1.07258i	−0.406365	+	0.0391650i
$751$	6.68271	+	37.8996i	0.243856	+	1.38297i	0.823135	+	0.567845i	$0.192223\pi$
$751$	6.68271	+	37.8996i	0.243856	+	1.38297i	−0.579279	+	0.815129i	$0.696666\pi$
$752$	7.59200	+	4.38325i	0.276852	+	0.159841i
$753$	−3.03947	+	1.75484i	−0.110764	+	0.0639499i
$754$	−22.1687	+	18.6018i	−0.807338	+	0.677437i
$755$	21.6709	+	4.40833i	0.788686	+	0.160436i
$756$	−0.203470	−	0.0740570i	−0.00740013	−	0.00269343i
$757$	4.34085	−	5.17322i	0.157771	−	0.188024i	−0.681368	−	0.731941i	$-0.738615\pi$
$757$	4.34085	−	5.17322i	0.157771	−	0.188024i	0.839139	+	0.543917i	$0.183059\pi$
$758$	0.552961	+	0.0975019i	0.0200844	+	0.00354143i
$759$	11.1245			0.403792
$760$	−8.89866	−	3.97665i	−0.322788	−	0.144248i
$761$	29.2125			1.05895			0.529476	−	0.848325i	$-0.322389\pi$
$761$	29.2125			1.05895			0.529476	+	0.848325i	$0.322389\pi$
$762$	2.18307	+	0.384934i	0.0790843	+	0.0139447i
$763$	−2.84854	+	3.39476i	−0.103124	+	0.122899i
$764$	5.47556	+	1.99294i	0.198099	+	0.0721020i
$765$	0.885823	−	4.35462i	0.0320270	−	0.157442i
$766$	−7.48558	+	6.28115i	−0.270465	+	0.226947i
$767$	−47.1900	+	27.2452i	−1.70393	+	0.983766i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	2.27300	+	12.8908i	0.0819663	+	0.464854i	0.997970	+	0.0636845i	$0.0202851\pi$
$769$	2.27300	+	12.8908i	0.0819663	+	0.464854i	−0.916004	+	0.401170i	$0.868604\pi$
$770$	−0.496701	+	1.26106i	−0.0178999	+	0.0454454i
$771$	6.73508	−	11.6655i	0.242558	−	0.420123i
$772$	−16.0141	+	9.24576i	−0.576361	+	0.332762i
$773$	12.3436	+	14.7105i	0.443967	+	0.529099i	0.940898	−	0.338691i	$-0.109984\pi$
$773$	12.3436	+	14.7105i	0.443967	+	0.529099i	−0.496931	+	0.867790i	$0.665540\pi$
$774$	0.313642	−	0.114156i	0.0112736	−	0.00410326i
$775$	−2.93355	−	23.8801i	−0.105376	−	0.857799i
$776$	−8.14240	−	6.83229i	−0.292295	−	0.245265i
$777$	−2.51958	−	0.444270i	−0.0903895	−	0.0159381i
$778$			21.2241i			0.760920i
$779$	26.1517	+	10.8756i	0.936981	+	0.389657i
$780$	−9.59631	−	5.88023i	−0.343603	−	0.210546i
$781$	−0.953421	+	5.40712i	−0.0341161	+	0.193482i
$782$	5.07649	−	6.04992i	0.181535	−	0.216345i
$783$	1.96650	−	5.40290i	0.0702768	−	0.193084i
$784$	−6.53379	+	2.37811i	−0.233350	+	0.0849323i
$785$	−3.33113	−	22.2846i	−0.118893	−	0.795371i
$786$	−6.72871	−	11.6545i	−0.240005	−	0.415701i
$787$	−40.3364	−	23.2883i	−1.43784	−	0.830136i	−0.440139	−	0.897930i	$-0.645071\pi$
$787$	−40.3364	−	23.2883i	−1.43784	−	0.830136i	−0.997699	+	0.0677931i	$0.978404\pi$
$788$	−16.9009	+	2.98008i	−0.602068	+	0.106161i
$789$	−2.08721	−	11.8371i	−0.0743065	−	0.421413i
$790$	4.15574	+	7.65338i	0.147855	+	0.272295i
$791$	0.812424	+	1.40716i	0.0288865	+	0.0500329i
$792$	1.79937	+	2.14441i	0.0639378	+	0.0761981i
$793$	14.9482	+	41.0698i	0.530825	+	1.45843i
$794$	3.99940	+	1.45566i	0.141933	+	0.0516595i
$795$	6.69678	+	20.0126i	0.237510	+	0.709774i
$796$	−3.83625	+	21.7564i	−0.135972	+	0.771137i
$797$		−	11.1555i		−	0.395148i	−0.980288	−	0.197574i	$-0.936694\pi$
$797$		−	11.1555i		−	0.395148i	0.980288	−	0.197574i	$-0.0633063\pi$
$798$	−0.0424973	+	0.942867i	−0.00150439	+	0.0333771i
$799$	17.4219			0.616343
$800$	−1.46214	−	4.78144i	−0.0516945	−	0.169049i
$801$	9.77428	+	8.20159i	0.345357	+	0.289789i
$802$	10.5795	−	29.0670i	0.373575	−	1.02639i
$803$	6.09523	+	16.7465i	0.215096	+	0.590972i
$804$	6.94635	−	5.82868i	0.244979	−	0.205562i
$805$	−0.0503098	+	1.92343i	−0.00177319	+	0.0677921i
$806$	12.1097	−	20.9747i	0.426547	−	0.738801i
$807$	−10.7763	+	1.90016i	−0.379345	+	0.0668887i
$808$	−6.41969	+	1.13196i	−0.225844	+	0.0398224i
$809$	13.4780	−	23.3446i	0.473861	−	0.820751i	−0.525691	−	0.850675i	$-0.676193\pi$
$809$	13.4780	−	23.3446i	0.473861	−	0.820751i	0.999552	+	0.0299244i	$0.00952666\pi$
$810$	2.23530	+	0.0584672i	0.0785406	+	0.00205433i
$811$	27.9047	−	23.4148i	0.979866	−	0.822205i	−0.00420330	−	0.999991i	$-0.501338\pi$
$811$	27.9047	−	23.4148i	0.979866	−	0.822205i	0.984069	+	0.177786i	$0.0568935\pi$
$812$	0.425802	+	1.16988i	0.0149427	+	0.0410548i
$813$	0.597739	−	1.64228i	0.0209636	−	0.0575971i
$814$	25.3379	+	21.2610i	0.888092	+	0.745197i
$815$	19.7456	+	17.4684i	0.691658	+	0.611891i
$816$	1.98733			0.0695705
$817$	−0.884043	−	1.15547i	−0.0309287	−	0.0404249i
$818$		−	18.7275i		−	0.654792i
$819$	−0.189247	+	1.07328i	−0.00661284	+	0.0375033i
$820$	4.61064	+	13.7784i	0.161011	+	0.481162i
$821$	−12.8375	−	4.67245i	−0.448030	−	0.163070i	0.108144	−	0.994135i	$-0.465509\pi$
$821$	−12.8375	−	4.67245i	−0.448030	−	0.163070i	−0.556175	+	0.831066i	$0.687731\pi$
$822$	−3.62376	−	9.95621i	−0.126393	−	0.347263i
$823$	−30.3632	−	36.1854i	−1.05839	−	1.26134i	−0.964026	−	0.265807i	$-0.914362\pi$
$823$	−30.3632	−	36.1854i	−1.05839	−	1.26134i	−0.0943677	−	0.995537i	$-0.530083\pi$
$824$	−2.04655	−	3.54473i	−0.0712950	−	0.123487i
$825$	0.731697	−	13.9775i	0.0254744	−	0.486633i
$826$	0.407060	+	2.30855i	0.0141634	+	0.0803248i
$827$	−10.5848	+	1.86638i	−0.368068	+	0.0649004i	−0.354623	−	0.935009i	$-0.615391\pi$
$827$	−10.5848	+	1.86638i	−0.368068	+	0.0649004i	−0.0134450	+	0.999910i	$0.504280\pi$
$828$	3.44157	+	1.98699i	0.119603	+	0.0690527i
$829$	14.6446	+	25.3653i	0.508629	+	0.880972i	0.999950	+	0.00999323i	$0.00318100\pi$
$829$	14.6446	+	25.3653i	0.508629	+	0.880972i	−0.491321	+	0.870979i	$0.663486\pi$
$830$	−13.4197	+	2.00600i	−0.465806	+	0.0696292i
$831$	8.38475	−	3.05180i	0.290864	−	0.105866i
$832$	1.72146	−	4.72968i	0.0596809	−	0.163972i
$833$	−8.88213	+	10.5853i	−0.307747	+	0.366759i
$834$	3.05968	−	17.3523i	0.105948	−	0.600862i
$835$	6.31174	−	10.3005i	0.218427	−	0.356464i
$836$	6.57060	−	10.2818i	0.227249	−	0.355603i
$837$			4.81193i			0.166325i
$838$	19.6025	+	3.45646i	0.677159	+	0.119401i
$839$	8.30616	+	6.96970i	0.286760	+	0.240621i	0.774808	−	0.632196i	$-0.217846\pi$
$839$	8.30616	+	6.96970i	0.286760	+	0.240621i	−0.488048	+	0.872817i	$0.662291\pi$
$840$	−0.378908	+	0.301415i	−0.0130736	+	0.0103998i
$841$	−3.81373	+	1.38808i	−0.131508	+	0.0478650i
$842$	−5.98770	−	7.13586i	−0.206350	−	0.245918i
$843$	23.0040	−	13.2814i	0.792300	−	0.457435i
$844$	8.27365	−	14.3304i	0.284791	−	0.493272i
$845$	−10.1066	+	25.6594i	−0.347678	+	0.882709i
$846$	1.52229	+	8.63331i	0.0523372	+	0.296819i
$847$	0.593271	+	0.342525i	0.0203850	+	0.0117693i
$848$	−8.17329	+	4.71885i	−0.280672	+	0.162046i
$849$	−11.1118	+	9.32392i	−0.381357	+	0.319996i
$850$	−7.26761	−	6.77635i	−0.249277	−	0.232427i
$851$	44.1240	+	16.0598i	1.51255	+	0.550524i
$852$	−1.26075	+	1.50250i	−0.0431926	+	0.0514749i
$853$	18.5939	+	3.27861i	0.636644	+	0.112258i	0.482649	−	0.875814i	$-0.339675\pi$
$853$	18.5939	+	3.27861i	0.636644	+	0.112258i	0.153996	+	0.988072i	$0.450786\pi$
$854$	1.88021			0.0643393
$855$	−2.67366	−	9.37292i	−0.0914372	−	0.320547i
$856$	13.5926			0.464587
$857$	1.19159	+	0.210110i	0.0407041	+	0.00717723i	0.193963	−	0.981009i	$-0.437866\pi$
$857$	1.19159	+	0.210110i	0.0407041	+	0.00717723i	−0.153259	+	0.988186i	$0.548977\pi$
$858$	9.05662	−	10.7933i	0.309188	−	0.368476i
$859$	−13.0846	−	4.76241i	−0.446441	−	0.162491i	0.109009	−	0.994041i	$-0.465232\pi$
$859$	−13.0846	−	4.76241i	−0.446441	−	0.162491i	−0.555451	+	0.831549i	$0.687454\pi$
$860$	0.148773	−	0.731355i	0.00507312	−	0.0249390i
$861$	1.07778	−	0.904363i	0.0367306	−	0.0308206i
$862$	32.0234	−	18.4887i	1.09072	−	0.629729i
$863$	−41.3998	−	23.9022i	−1.40926	−	0.813639i	−0.413947	−	0.910301i	$-0.635850\pi$
$863$	−41.3998	−	23.9022i	−1.40926	−	0.813639i	−0.995317	+	0.0966621i	$0.969183\pi$
$864$	0.173648	+	0.984808i	0.00590763	+	0.0335038i
$865$	−9.78065	−	3.85237i	−0.332552	−	0.130984i
$866$	6.20211	−	10.7424i	0.210756	−	0.365040i
$867$	−11.3021	+	6.52526i	−0.383839	+	0.221609i
$868$	−0.669732	−	0.798155i	−0.0227322	−	0.0270911i
$869$	−10.2451	+	3.72891i	−0.347541	+	0.126494i
$870$	−8.00373	−	10.0615i	−0.271352	−	0.341115i
$871$	−34.9625	−	29.3370i	−1.18466	−	0.994046i
$872$	20.1555	+	3.55395i	0.682550	+	0.120352i
$873$		−	10.6291i		−	0.359742i
$874$	3.77303	−	16.9063i	0.127625	−	0.571864i
$875$	2.41341	+	0.189724i	0.0815882	+	0.00641383i
$876$	−1.10549	+	6.26956i	−0.0373511	+	0.211829i
$877$	19.8410	−	23.6456i	0.669982	−	0.798454i	−0.318799	−	0.947822i	$-0.603280\pi$
$877$	19.8410	−	23.6456i	0.669982	−	0.798454i	0.988782	+	0.149368i	$0.0477241\pi$
$878$	−10.7733	+	29.5994i	−0.363582	+	0.998932i
$879$	−25.3688	+	9.23351i	−0.855670	+	0.311438i
$880$	6.19069	−	0.925393i	0.208688	−	0.0311950i
$881$	−5.29599	−	9.17293i	−0.178427	−	0.309044i	0.762915	−	0.646499i	$-0.223767\pi$
$881$	−5.29599	−	9.17293i	−0.178427	−	0.309044i	−0.941342	+	0.337455i	$0.890434\pi$
$882$	−6.02157	−	3.47656i	−0.202757	−	0.117062i
$883$	12.2152	−	2.15387i	0.411075	−	0.0724836i	0.0357134	−	0.999362i	$-0.488630\pi$
$883$	12.2152	−	2.15387i	0.411075	−	0.0724836i	0.375362	+	0.926878i	$0.377519\pi$
$884$	−1.73694	−	9.85070i	−0.0584197	−	0.331315i
$885$	−11.5517	−	21.2741i	−0.388306	−	0.715120i
$886$	−14.1611	−	24.5278i	−0.475752	−	0.824026i
$887$	0.733305	+	0.873919i	0.0246220	+	0.0293433i	0.778215	−	0.627998i	$-0.216125\pi$
$887$	0.733305	+	0.873919i	0.0246220	+	0.0293433i	−0.753593	+	0.657341i	$0.771681\pi$
$888$	4.04124	+	11.1032i	0.135615	+	0.372600i
$889$	−0.451042	−	0.164166i	−0.0151275	−	0.00550594i
$890$	27.0563	−	9.05379i	0.906928	−	0.303484i
$891$	−0.486097	+	2.75679i	−0.0162849	+	0.0923561i
$892$		−	2.86698i		−	0.0959936i
$893$	33.9195	−	17.5967i	1.13507	−	0.588851i
$894$	5.61976			0.187953
$895$	−13.1304	+	14.8421i	−0.438901	+	0.496117i
$896$	−0.165870	−	0.139182i	−0.00554133	−	0.00464973i
$897$	6.84106	−	18.7956i	0.228416	−	0.627568i
$898$	7.85753	+	21.5884i	0.262209	+	0.720414i
$899$	21.1941	−	17.7839i	0.706862	−	0.593128i
$900$	2.72295	−	4.19351i	0.0907649	−	0.139784i
$901$	−9.37791	+	16.2430i	−0.312424	+	0.541133i
$902$	−17.9129	+	3.15853i	−0.596434	+	0.105167i
$903$	−0.0711727	+	0.0125497i	−0.00236848	+	0.000417627i
$904$	3.75205	−	6.49874i	0.124791	−	0.216145i
$905$	−0.527252	+	20.1578i	−0.0175264	+	0.670067i
$906$	−7.57620	+	6.35719i	−0.251702	+	0.211203i
$907$	15.3664	+	42.2187i	0.510231	+	1.40185i	0.880997	+	0.473123i	$0.156873\pi$
$907$	15.3664	+	42.2187i	0.510231	+	1.40185i	−0.370765	+	0.928727i	$0.620904\pi$
$908$	−0.0534386	+	0.146821i	−0.00177342	+	0.00487244i
$909$	−4.99363	−	4.19015i	−0.165628	−	0.138979i
$910$	1.82521	+	1.61471i	0.0605050	+	0.0535271i
$911$	−31.5904			−1.04664			−0.523318	−	0.852137i	$-0.675306\pi$
$911$	−31.5904			−1.04664			−0.523318	+	0.852137i	$0.675306\pi$
$912$	3.86922	−	2.00727i	0.128123	−	0.0664673i
$913$		−	16.9868i		−	0.562180i
$914$	2.44679	−	13.8764i	0.0809326	−	0.458992i
$915$	−18.4132	+	6.16157i	−0.608720	+	0.203695i
$916$	23.3199	+	8.48773i	0.770510	+	0.280443i
$917$	0.996615	+	2.73818i	0.0329111	+	0.0904226i
$918$	1.27743	+	1.52238i	0.0421615	+	0.0502461i
$919$	27.7972	+	48.1461i	0.916944	+	1.58819i	0.804030	+	0.594588i	$0.202685\pi$
$919$	27.7972	+	48.1461i	0.916944	+	1.58819i	0.112913	+	0.993605i	$0.463982\pi$
$920$	7.80913	−	4.24031i	0.257459	−	0.139799i
$921$	0.711450	+	4.03484i	0.0234431	+	0.132952i
$922$	7.78861	−	1.37334i	0.256504	−	0.0452286i
$923$	8.54944	+	4.93602i	0.281408	+	0.162471i
$924$	−0.303066	−	0.524926i	−0.00997014	−	0.0172688i
$925$	23.0808	−	54.3839i	0.758891	−	1.78813i
$926$	35.0312	−	12.7503i	1.15120	−	0.419001i
$927$	1.39992	−	3.84626i	0.0459795	−	0.126328i
$928$	3.69580	−	4.40449i	0.121321	−	0.144584i
$929$	−4.75464	+	26.9649i	−0.155995	+	0.884690i	0.801876	+	0.597491i	$0.203835\pi$
$929$	−4.75464	+	26.9649i	−0.155995	+	0.884690i	−0.957871	+	0.287200i	$0.907276\pi$
$930$	9.17440	+	5.62171i	0.300840	+	0.184343i
$931$	−6.60151	+	29.5802i	−0.216356	+	0.969453i
$932$		−	11.2154i		−	0.367372i
$933$	11.4541	+	2.01967i	0.374991	+	0.0661211i
$934$	−15.3374	−	12.8696i	−0.501857	−	0.421108i
$935$	9.73514	−	7.74415i	0.318373	−	0.253261i
$936$	4.72968	−	1.72146i	0.154594	−	0.0562677i
$937$	13.8432	+	16.4977i	0.452238	+	0.538956i	0.943200	−	0.332224i	$-0.107799\pi$
$937$	13.8432	+	16.4977i	0.452238	+	0.538956i	−0.490962	+	0.871181i	$0.663355\pi$
$938$	−1.70039	+	0.981718i	−0.0555196	+	0.0320542i
$939$	8.43730	−	14.6138i	0.275341	−	0.476904i
$940$	18.2387	+	7.18379i	0.594881	+	0.234309i
$941$	−4.98409	−	28.2662i	−0.162477	−	0.921451i	−0.951628	−	0.307252i	$-0.900590\pi$
$941$	−4.98409	−	28.2662i	−0.162477	−	0.921451i	0.789151	−	0.614199i	$-0.210521\pi$
$942$	8.72667	+	5.03835i	0.284330	+	0.164158i
$943$	−22.3624	+	12.9109i	−0.728219	+	0.420437i
$944$	8.29331	−	6.95892i	0.269924	−	0.226493i
$945$	−0.474455	−	0.0965142i	−0.0154340	−	0.00313961i
$946$	0.877984	+	0.319560i	0.0285457	+	0.0103898i
$947$	−27.3003	+	32.5353i	−0.887142	+	1.05725i	0.110845	+	0.993838i	$0.464644\pi$
$947$	−27.3003	+	32.5353i	−0.887142	+	1.05725i	−0.997987	+	0.0634169i	$0.979800\pi$
$948$	−3.83556	−	0.676312i	−0.124573	−	0.0219656i
$949$	32.0429			1.04016
$950$	−20.9940	−	5.85266i	−0.681134	−	0.189885i
$951$	11.5881			0.375771
$952$	−0.423775	−	0.0747230i	−0.0137346	−	0.00242179i
$953$	−8.93942	+	10.6536i	−0.289576	+	0.345103i	−0.891146	−	0.453717i	$-0.850098\pi$
$953$	−8.93942	+	10.6536i	−0.289576	+	0.345103i	0.601570	+	0.798820i	$0.294542\pi$
$954$	−8.86854	−	3.22788i	−0.287129	−	0.104507i
$955$	12.7680	+	2.59728i	0.413163	+	0.0840462i
$956$	6.92355	−	5.80955i	0.223924	−	0.187894i
$957$	13.9388	−	8.04756i	0.450577	−	0.260141i
$958$	17.1987	+	9.92966i	0.555664	+	0.320813i
$959$	0.398376	+	2.25930i	0.0128642	+	0.0729566i
$960$	2.08050	+	0.819460i	0.0671479	+	0.0264480i
$961$	3.92268	−	6.79428i	0.126538	−	0.219170i
$962$	51.5038	−	29.7357i	1.66055	−	0.958718i
$963$	8.73718	+	10.4126i	0.281552	+	0.335540i
$964$	−24.5978	+	8.95287i	−0.792242	+	0.288353i
$965$	−32.3588	+	25.7409i	−1.04167	+	0.828628i
$966$	−0.659165	−	0.553105i	−0.0212083	−	0.0177959i
$967$	−44.6853	−	7.87923i	−1.43698	−	0.253379i	−0.599734	−	0.800200i	$-0.704727\pi$
$967$	−44.6853	−	7.87923i	−1.43698	−	0.253379i	−0.837250	+	0.546821i	$0.815838\pi$
$968$		−	3.16379i		−	0.101688i
$969$	4.66468	−	7.29937i	0.149851	−	0.234490i
$970$	−20.2655	−	12.4179i	−0.650686	−	0.398714i
$971$	−8.17533	+	46.3646i	−0.262359	+	1.48791i	0.514093	+	0.857734i	$0.328129\pi$
$971$	−8.17533	+	46.3646i	−0.262359	+	1.48791i	−0.776452	+	0.630176i	$0.782983\pi$
$972$	−0.642788	+	0.766044i	−0.0206174	+	0.0245709i
$973$	−1.30489	+	3.58514i	−0.0418327	+	0.114934i
$974$	0.732590	−	0.266641i	0.0234737	−	0.00854373i
$975$	−23.1661	−	9.83180i	−0.741908	−	0.314869i
$976$	−4.34171	−	7.52007i	−0.138975	−	0.240712i
$977$	−44.7260	−	25.8226i	−1.43091	−	0.826138i	−0.433722	−	0.901047i	$-0.642800\pi$
$977$	−44.7260	−	25.8226i	−1.43091	−	0.826138i	−0.997190	+	0.0749089i	$0.976133\pi$
$978$	−11.6110	+	2.04733i	−0.371278	+	0.0654664i
$979$	6.20232	+	35.1751i	0.198227	+	1.12420i
$980$	−13.6633	+	7.41910i	−0.436458	+	0.236994i
$981$	10.2332	+	17.7244i	0.326721	+	0.565897i
$982$	15.6390	+	18.6379i	0.499062	+	0.594759i
$983$	15.4040	+	42.3222i	0.491312	+	1.34987i	0.899480	+	0.436963i	$0.143946\pi$
$983$	15.4040	+	42.3222i	0.491312	+	1.34987i	−0.408167	+	0.912907i	$0.633832\pi$
$984$	−6.10586	−	2.22235i	−0.194648	−	0.0708460i
$985$	−36.3910	+	12.1775i	−1.15952	+	0.388007i
$986$	1.98418	−	11.2529i	0.0631892	−	0.358364i
$987$		−	1.89819i		−	0.0604201i
$988$	−13.3313	−	17.4244i	−0.424124	−	0.554344i
$989$	1.32640			0.0421770
$990$	4.68819	+	4.14752i	0.149001	+	0.131817i
$991$	−16.0959	−	13.5061i	−0.511303	−	0.429034i	0.350284	−	0.936643i	$-0.386085\pi$
$991$	−16.0959	−	13.5061i	−0.511303	−	0.429034i	−0.861587	+	0.507609i	$0.830529\pi$
$992$	−1.64578	+	4.52173i	−0.0522534	+	0.143565i
$993$	−9.70752	−	26.6712i	−0.308059	−	0.846384i
$994$	0.325334	−	0.272988i	0.0103190	−	0.00865865i
$995$	−1.29166	+	49.3825i	−0.0409484	+	1.56553i
$996$	3.03408	−	5.25519i	0.0961386	−	0.166517i
$997$	16.7662	−	2.95633i	0.530990	−	0.0936279i	0.0982764	−	0.995159i	$-0.468667\pi$
$997$	16.7662	−	2.95633i	0.530990	−	0.0936279i	0.432714	+	0.901531i	$0.357556\pi$
$998$	−18.3255	+	3.23129i	−0.580085	+	0.102285i
$999$	−5.90790	+	10.2328i	−0.186918	+	0.323751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.a.169.5	✓	60
5.4	even	2	inner	570.2.bc.a.169.10	yes	60
19.9	even	9	inner	570.2.bc.a.199.10	yes	60
95.9	even	18	inner	570.2.bc.a.199.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.a.169.5	✓	60	1.1	even	1	trivial
570.2.bc.a.169.10	yes	60	5.4	even	2	inner
570.2.bc.a.199.5	yes	60	95.9	even	18	inner
570.2.bc.a.199.10	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)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.19119 + 0.445735i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(0.187519 - 0.108264i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.19119 + 0.445735i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(0.187519 - 0.108264i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(-2.08050 - 0.819460i) q^{10} +(1.39966 - 2.42428i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-3.23529 - 3.85567i) q^{13} +(-0.203470 + 0.0740570i) q^{14} +(1.74992 - 1.39204i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.95714 + 0.345096i) q^{17} +1.00000i q^{18} +(4.15900 - 1.30489i) q^{19} +(1.90660 + 1.16829i) q^{20} +(0.0375997 - 0.213239i) q^{21} +(-1.79937 + 2.14441i) q^{22} +(-1.35918 + 3.73432i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(4.60264 + 1.95338i) q^{25} +(2.51661 + 4.35889i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(0.213239 - 0.0375997i) q^{28} +(0.998416 + 5.66230i) q^{29} +(-1.96506 + 1.06702i) q^{30} +(-2.40596 - 4.16725i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-0.957425 - 2.63050i) q^{33} +(-1.86748 - 0.679707i) q^{34} +(0.459147 - 0.153643i) q^{35} +(0.173648 - 0.984808i) q^{36} -11.8158i q^{37} +(-4.32241 + 0.562862i) q^{38} -5.03322 q^{39} +(-1.67476 - 1.48161i) q^{40} +(4.97755 + 4.17666i) q^{41} +(-0.0740570 + 0.203470i) q^{42} +(-0.114156 - 0.313642i) q^{43} +(2.14441 - 1.79937i) q^{44} +(0.0584672 - 2.23530i) q^{45} +(1.98699 - 3.44157i) q^{46} +(8.63331 - 1.52229i) q^{47} +(0.984808 - 0.173648i) q^{48} +(-3.47656 + 6.02157i) q^{49} +(-4.19351 - 2.72295i) q^{50} +(1.52238 - 1.27743i) q^{51} +(-1.72146 - 4.72968i) q^{52} +(-3.22788 + 8.86854i) q^{53} +(0.766044 + 0.642788i) q^{54} +(4.14752 - 4.68819i) q^{55} -0.216528 q^{56} +(1.67375 - 4.02474i) q^{57} -5.74965i q^{58} +(1.87994 - 10.6617i) q^{59} +(2.12050 - 0.709578i) q^{60} +(-8.15975 - 2.96991i) q^{61} +(1.64578 + 4.52173i) q^{62} +(-0.139182 - 0.165870i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-5.37053 - 9.89059i) q^{65} +(0.486097 + 2.75679i) q^{66} +(8.93005 - 1.57461i) q^{67} +(1.72108 + 0.993665i) q^{68} +(1.98699 + 3.44157i) q^{69} +(-0.478851 + 0.0715793i) q^{70} +(-1.84309 + 0.670831i) q^{71} +(-0.342020 + 0.939693i) q^{72} +(-4.09217 + 4.87685i) q^{73} +(-2.05179 + 11.6363i) q^{74} +(4.45490 - 2.27022i) q^{75} +(4.35448 + 0.196267i) q^{76} -0.606132i q^{77} +(4.95675 + 0.874009i) q^{78} +(-2.98353 - 2.50348i) q^{79} +(1.39204 + 1.74992i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-4.17666 - 4.97755i) q^{82} +(5.25519 - 3.03408i) q^{83} +(0.108264 - 0.187519i) q^{84} +(4.13464 + 1.62854i) q^{85} +(0.0579586 + 0.328700i) q^{86} +(4.97934 + 2.87483i) q^{87} +(-2.42428 + 1.39966i) q^{88} +(-9.77428 + 8.20159i) q^{89} +(-0.445735 + 2.19119i) q^{90} +(-1.02411 - 0.372745i) q^{91} +(-2.55443 + 3.04425i) q^{92} +(-4.73882 - 0.835582i) q^{93} -8.76649 q^{94} +(9.69480 - 1.00545i) q^{95} -1.00000 q^{96} +(10.4677 + 1.84573i) q^{97} +(4.46938 - 5.32640i) q^{98} +(-2.63050 - 0.957425i) 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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