LMFDB - Embedded newform 570.2.bc.a.169.10

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			169.10
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.a.199.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.39204 - 1.74992i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-0.187519 + 0.108264i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.39204 - 1.74992i) 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} +(1.67476 - 1.48161i) 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} +(0.445735 + 2.19119i) 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} +(-1.12447 - 4.87192i) 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} +(0.0584672 + 2.23530i) 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} +(-0.0715793 + 0.478851i) q^{35} +(0.173648 - 0.984808i) q^{36} +11.8158i q^{37} +(4.32241 - 0.562862i) q^{38} -5.03322 q^{39} +(2.08050 - 0.819460i) 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} +(-1.96506 - 1.06702i) 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} +(-0.261384 - 4.99316i) 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} +(-2.29393 - 5.82399i) q^{55} -0.216528 q^{56} +(-1.67375 + 4.02474i) q^{57} +5.74965i q^{58} +(1.87994 - 10.6617i) q^{59} +(-0.330577 + 2.21150i) 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} +(11.2508 - 0.294278i) 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} +(-0.153643 + 0.459147i) 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} +(2.19119 - 0.445735i) 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} +(-3.32830 + 2.94446i) 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} +(-1.74992 - 1.39204i) q^{90} +(-1.02411 - 0.372745i) q^{91} +(2.55443 - 3.04425i) q^{92} +(4.73882 + 0.835582i) q^{93} -8.76649 q^{94} +(3.50602 - 9.09438i) 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
$5$	1.39204	−	1.74992i	0.622538	−	0.782590i
$5$	1.39204	−	1.74992i	0.622538	−	0.782590i
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	−0.187519	+	0.108264i	−0.0708755	+	0.0409200i	−0.535019	−	0.844840i	$-0.679696\pi$
$7$	−0.187519	+	0.108264i	−0.0708755	+	0.0409200i	0.464143	+	0.885760i	$0.346362\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	1.67476	−	1.48161i	0.529606	−	0.468527i
$11$	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	$0.0236960\pi$
$13$	3.23529	+	3.85567i	0.897308	+	1.06937i	−0.0999228	+	0.994995i	$0.531860\pi$
$14$	−0.203470	+	0.0740570i	−0.0543796	+	0.0197926i
$15$	0.445735	+	2.19119i	0.115088	+	0.565763i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.95714	−	0.345096i	−0.474676	−	0.0836981i	−0.0688079	−	0.997630i	$-0.521920\pi$
$17$	−1.95714	−	0.345096i	−0.474676	−	0.0836981i	−0.405868	+	0.913932i	$0.633031\pi$
$18$		−	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	$-0.752910\pi$
$23$	1.35918	−	3.73432i	0.283409	−	0.778660i	0.996950	−	0.0780462i	$-0.0248682\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	−1.12447	−	4.87192i	−0.224893	−	0.974383i
$26$	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	$0.765192\pi$
$30$	0.0584672	+	2.23530i	0.0106746	+	0.408109i
$31$	−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
$35$	−0.0715793	+	0.478851i	−0.0120991	+	0.0809406i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$			11.8158i			1.94250i	0.238052	+	0.971252i	$0.423491\pi$
$37$			11.8158i			1.94250i	−0.238052	+	0.971252i	$0.576509\pi$
$38$	4.32241	−	0.562862i	0.701187	−	0.0913083i
$39$	−5.03322			−0.805959
$40$	2.08050	−	0.819460i	0.328956	−	0.129568i
$41$	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	0.948093	−	0.317994i	$-0.103009\pi$
$43$	0.114156	+	0.313642i	0.0174087	+	0.0478299i	−0.930684	+	0.365824i	$0.880787\pi$
$44$	2.14441	−	1.79937i	0.323281	−	0.271265i
$45$	−1.96506	−	1.06702i	−0.292934	−	0.159062i
$46$	1.98699	−	3.44157i	0.292966	−	0.507432i
$47$	−8.63331	+	1.52229i	−1.25930	+	0.222048i	−0.763168	−	0.646200i	$-0.776357\pi$
$47$	−8.63331	+	1.52229i	−1.25930	+	0.222048i	−0.496130	+	0.868248i	$0.665246\pi$
$48$	−0.984808	+	0.173648i	−0.142145	+	0.0250640i
$49$	−3.47656	+	6.02157i	−0.496651	+	0.860225i
$50$	−0.261384	−	4.99316i	−0.0369652	−	0.706140i
$51$	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	$-0.664418\pi$
$53$	3.22788	−	8.86854i	0.443384	−	1.21819i	0.937253	−	0.348651i	$-0.113360\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	−2.29393	−	5.82399i	−0.309314	−	0.785307i
$56$	−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	$-0.193373\pi$
$60$	−0.330577	+	2.21150i	−0.0426774	+	0.285503i
$61$	−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
$65$	11.2508	−	0.294278i	1.39549	−	0.0365007i
$66$	0.486097	+	2.75679i	0.0598344	+	0.339338i
$67$	−8.93005	+	1.57461i	−1.09098	+	0.192369i	−0.690066	−	0.723747i	$-0.742418\pi$
$67$	−8.93005	+	1.57461i	−1.09098	+	0.192369i	−0.400914	+	0.916116i	$0.631307\pi$
$68$	−1.72108	−	0.993665i	−0.208711	−	0.120500i
$69$	1.98699	+	3.44157i	0.239206	+	0.414316i
$70$	−0.153643	+	0.459147i	−0.0183639	+	0.0548785i
$71$	−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	−0.471420	−	0.881909i	$-0.656258\pi$
$73$	4.09217	−	4.87685i	0.478952	−	0.570792i	0.950372	+	0.311116i	$0.100703\pi$
$74$	−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	$0.792533\pi$
$80$	2.19119	−	0.445735i	0.244983	−	0.0498347i
$81$	−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	−0.759873	−	0.650071i	$-0.774739\pi$
$83$	−5.25519	+	3.03408i	−0.576832	+	0.333034i	0.183042	+	0.983105i	$0.441406\pi$
$84$	0.108264	−	0.187519i	0.0118126	−	0.0204600i
$85$	−3.32830	+	2.94446i	−0.361005	+	0.319371i
$86$	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	$0.514173\pi$
$90$	−1.74992	−	1.39204i	−0.184458	−	0.146734i
$91$	−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
$95$	3.50602	−	9.09438i	0.359710	−	0.933064i
$96$	−1.00000			−0.102062
$97$	−10.4677	−	1.84573i	−1.06283	−	0.187406i	−0.385219	−	0.922825i	$-0.625874\pi$
$97$	−10.4677	−	1.84573i	−1.06283	−	0.187406i	−0.677612	+	0.735420i	$0.736985\pi$
$98$	−4.46938	+	5.32640i	−0.451475	+	0.538047i
$99$	−2.63050	−	0.957425i	−0.264376	−	0.0962248i
$100$	0.609641	−	4.96269i	0.0609641	−	0.496269i
$101$	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	0.315092	−	0.949061i	$-0.397965\pi$
$103$	−3.54473	−	2.04655i	−0.349273	−	0.201653i	−0.664365	+	0.747408i	$0.731298\pi$
$104$	0.874009	+	4.95675i	0.0857036	+	0.486049i
$105$	−0.320811	−	0.362633i	−0.0313080	−	0.0353893i
$106$	4.71885	−	8.17329i	0.458335	−	0.793860i
$107$	11.7716	−	6.79632i	1.13800	−	0.657025i	0.192066	−	0.981382i	$-0.438481\pi$
$107$	11.7716	−	6.79632i	1.13800	−	0.657025i	0.945935	+	0.324357i	$0.105148\pi$
$108$	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	$0.952397\pi$
$110$	−1.24776	−	6.13385i	−0.118969	−	0.584840i
$111$	−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	$-0.885174\pi$
$113$		−	7.50410i		−	0.705926i	0.935637	−	0.352963i	$-0.114826\pi$
$114$	−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
$120$	−0.709578	+	2.12050i	−0.0647753	+	0.193574i
$121$	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
$125$	−10.0908	−	4.81416i	−0.902547	−	0.430591i
$126$	0.108264	+	0.187519i	0.00964493	+	0.0167055i
$127$	1.42490	+	1.69813i	0.126439	+	0.150685i	0.825550	−	0.564329i	$-0.190865\pi$
$127$	1.42490	+	1.69813i	0.126439	+	0.150685i	−0.699111	+	0.715013i	$0.746421\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−0.313642	−	0.114156i	−0.0276146	−	0.0100509i
$130$	11.1309	+	1.66387i	0.976248	+	0.145931i
$131$	−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
$135$	2.08050	−	0.819460i	0.179061	−	0.0705279i
$136$	−1.52238	−	1.27743i	−0.130543	−	0.109539i
$137$	3.62376	−	9.95621i	0.309599	−	0.850616i	−0.683136	−	0.730292i	$-0.739384\pi$
$137$	3.62376	−	9.95621i	0.309599	−	0.850616i	0.992735	−	0.120325i	$-0.0383936\pi$
$138$	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	$0.546407\pi$
$140$	−0.231039	+	0.425491i	−0.0195264	+	0.0359606i
$141$	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
$145$	11.2984	+	6.13498i	0.938283	+	0.509482i
$146$	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	$0.796158\pi$
$150$	3.99300	+	3.00931i	0.326027	+	0.245709i
$151$	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
$155$	−10.6416	−	1.59071i	−0.854751	−	0.127769i
$156$	−4.72968	−	1.72146i	−0.378677	−	0.137827i
$157$	3.44643	+	9.46899i	0.275055	+	0.755708i	0.997905	+	0.0647024i	$0.0206098\pi$
$157$	3.44643	+	9.46899i	0.275055	+	0.755708i	−0.722849	+	0.691006i	$0.757168\pi$
$158$	−2.50348	−	2.98353i	−0.199166	−	0.237357i
$159$	4.71885	+	8.17329i	0.374229	+	0.648184i
$160$	2.23530	−	0.0584672i	0.176716	−	0.00462224i
$161$	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	0.0436336	−	0.999048i	$-0.486107\pi$
$163$	−10.2105	−	5.89505i	−0.799750	−	0.461736i	−0.843384	+	0.537312i	$0.819440\pi$
$164$	3.24886	+	5.62719i	0.253693	+	0.439410i
$165$	5.93595	+	1.98634i	0.462113	+	0.154636i
$166$	−5.70221	+	2.07544i	−0.442577	+	0.161085i
$167$	−1.84778	+	5.07675i	−0.142986	+	0.392851i	−0.990427	−	0.138039i	$-0.955920\pi$
$167$	−1.84778	+	5.07675i	−0.142986	+	0.392851i	0.847441	+	0.530890i	$0.178142\pi$
$168$	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	0.346847	−	0.937922i	$-0.387252\pi$
$173$	4.62968	+	0.816338i	0.351988	+	0.0620650i	0.00514142	+	0.999987i	$0.498363\pi$
$174$	−4.40449	−	3.69580i	−0.333903	−	0.280178i
$175$	0.738312	+	0.791837i	0.0558111	+	0.0598572i
$176$	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	$0.274119\pi$
$180$	−1.48161	−	1.67476i	−0.110433	−	0.124829i
$181$	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
$185$	20.6767	+	16.4480i	1.52018	+	1.20928i
$186$	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
$190$	5.03198	−	8.34740i	0.365058	−	0.605584i
$191$	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	$-0.545986\pi$
$193$	11.8861	−	14.1653i	0.855582	−	1.01964i	0.999548	−	0.0300602i	$-0.00956990\pi$
$194$	−9.98813	−	3.63538i	−0.717106	−	0.261005i
$195$	−7.00642	+	8.80774i	−0.501740	+	0.630736i
$196$	−5.32640	+	4.46938i	−0.380457	+	0.319241i
$197$	14.8624	−	8.58079i	1.05890	−	0.611356i	0.133772	−	0.991012i	$-0.457291\pi$
$197$	14.8624	−	8.58079i	1.05890	−	0.611356i	0.925128	+	0.379656i	$0.123958\pi$
$198$	−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	$0.658116\pi$
$200$	1.46214	−	4.78144i	0.103389	−	0.338099i
$201$	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
$205$	14.2378	−	2.89626i	0.994408	−	0.202284i
$206$	−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
$215$	0.707758	+	0.236836i	0.0482687	+	0.0161521i
$216$	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
$220$	−0.163668	−	6.25734i	−0.0110345	−	0.421870i
$221$	−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	0.968185	−	0.250236i	$-0.0805083\pi$
$223$	0.980565	+	2.69408i	0.0656635	+	0.180409i	−0.902521	+	0.430645i	$0.858286\pi$
$224$	−0.203470	−	0.0740570i	−0.0135949	−	0.00494814i
$225$	−4.60264	+	1.95338i	−0.306843	+	0.130226i
$226$	1.30307	−	7.39010i	0.0866792	−	0.491582i
$227$		−	0.156244i		−	0.0103703i	−0.999987	−	0.00518514i	$-0.998350\pi$
$227$		−	0.156244i		−	0.0103703i	0.999987	−	0.00518514i	$-0.00165049\pi$
$228$	−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	$0.193996\pi$
$230$	−3.25652	−	8.26788i	−0.214729	−	0.545168i
$231$	−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	$0.00863116\pi$
$233$	3.83588	+	10.5390i	0.251297	+	0.690433i	−0.748335	+	0.663321i	$0.769147\pi$
$234$	3.85567	−	3.23529i	0.252053	−	0.211497i
$235$	−9.35400	+	17.2267i	−0.610188	+	1.12375i
$236$	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	$0.0722423\pi$
$240$	−1.06702	+	1.96506i	−0.0688757	+	0.126844i
$241$	−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
$245$	5.69780	+	14.4660i	0.364019	+	0.924197i
$246$	−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
$250$	−9.10151	−	6.49327i	−0.575630	−	0.410670i
$251$	−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
$255$	−0.116194	−	4.44229i	−0.00727632	−	0.278187i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−13.2655	+	2.33907i	−0.827481	+	0.145907i	−0.571320	−	0.820727i	$-0.693569\pi$
$257$	−13.2655	+	2.33907i	−0.827481	+	0.145907i	−0.256160	+	0.966634i	$0.582458\pi$
$258$	−0.289054	−	0.166885i	−0.0179957	−	0.0103898i
$259$	−1.27923	−	2.21568i	−0.0794872	−	0.137676i
$260$	10.6729	+	3.57146i	0.661906	+	0.221492i
$261$	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	−0.949708	−	0.313136i	$-0.898620\pi$
$263$	−7.72614	+	9.20766i	−0.476414	+	0.567769i	0.473294	+	0.880905i	$0.343065\pi$
$264$	−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	$0.830482\pi$
$270$	2.19119	−	0.445735i	0.133352	−	0.0271266i
$271$	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
$275$	−13.3848	−	4.09301i	−0.807133	−	0.246818i
$276$	0.690075	+	3.91361i	0.0415376	+	0.235572i
$277$	−7.72742	−	4.46143i	−0.464296	−	0.268061i	0.249553	−	0.968361i	$-0.419716\pi$
$277$	−7.72742	−	4.46143i	−0.464296	−	0.268061i	−0.713849	+	0.700300i	$0.753050\pi$
$278$	−15.2594	+	8.81001i	−0.915197	+	0.528389i
$279$	−3.68615	+	3.09305i	−0.220684	+	0.185176i
$280$	−0.301415	+	0.378908i	−0.0180130	+	0.0226441i
$281$	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	0.581261	−	0.813717i	$-0.302560\pi$
$283$	14.2851	+	2.51884i	0.849160	+	0.149730i	0.267899	+	0.963447i	$0.413671\pi$
$284$	−1.96138			−0.116386
$285$	4.71307	+	8.53153i	0.279178	+	0.505364i
$286$	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
$290$	10.0615	+	8.00373i	0.590829	+	0.469995i
$291$	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	0.990399	−	0.138241i	$-0.0441449\pi$
$293$	23.3801	+	13.4985i	1.36588	+	0.788590i	0.375479	+	0.926831i	$0.377478\pi$
$294$	−1.20740	−	6.84748i	−0.0704168	−	0.399353i
$295$	−16.0402	−	18.1312i	−0.933895	−	1.05564i
$296$	−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
$300$	3.40977	+	3.65697i	0.196863	+	0.211135i
$301$	−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	−0.685638	−	0.727942i	$-0.740477\pi$
$307$	2.63355	−	3.13855i	0.150305	−	0.179126i	0.835943	+	0.548816i	$0.184921\pi$
$308$	−0.207309	+	0.569578i	−0.0118125	+	0.0324547i
$309$	3.84626	−	1.39992i	0.218806	−	0.0796389i
$310$	−10.2037	−	3.41444i	−0.579529	−	0.193927i
$311$	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	−0.622288	−	0.782788i	$-0.713797\pi$
$313$	−16.6182	+	2.93024i	−0.939318	+	0.165627i	−0.317030	+	0.948416i	$0.602686\pi$
$314$	1.74980	+	9.92361i	0.0987469	+	0.560021i
$315$	0.484006	−	0.0126598i	0.0272706	−	0.000713298i
$316$	−1.94736	−	3.37293i	−0.109548	−	0.189742i
$317$	−7.44870	−	8.87702i	−0.418361	−	0.498583i	0.515166	−	0.857090i	$-0.327730\pi$
$317$	−7.44870	−	8.87702i	−0.418361	−	0.498583i	−0.933527	+	0.358507i	$0.883286\pi$
$318$	3.22788	+	8.86854i	0.181011	+	0.497323i
$319$	15.1245	+	5.50486i	0.846808	+	0.308213i
$320$	2.21150	+	0.330577i	0.123626	+	0.0184798i
$321$	−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
$325$	15.1465	−	20.0976i	0.840177	−	1.11482i
$326$	−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
$330$	5.50085	+	2.98693i	0.302812	+	0.164425i
$331$	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
$335$	−9.67552	+	17.8188i	−0.528630	+	0.973546i
$336$	0.165870	−	0.139182i	0.00904896	−	0.00759298i
$337$	7.18317	+	19.7356i	0.391292	+	1.07507i	0.966412	+	0.256998i	$0.0827332\pi$
$337$	7.18317	+	19.7356i	0.391292	+	1.07507i	−0.575120	+	0.818069i	$0.695045\pi$
$338$	−4.21822	+	11.5895i	−0.229441	+	0.630384i
$339$	5.74847	+	4.82354i	0.312214	+	0.261979i
$340$	−4.13464	+	1.62854i	−0.224232	+	0.0883198i
$341$	−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
$345$	8.78845	+	1.31371i	0.473154	+	0.0707277i
$346$	4.41759	+	1.60787i	0.237491	+	0.0864398i
$347$	−4.82645	−	13.2606i	−0.259097	−	0.711864i	−0.999224	−	0.0393962i	$-0.987457\pi$
$347$	−4.82645	−	13.2606i	−0.259097	−	0.711864i	0.740126	−	0.672468i	$-0.234766\pi$
$348$	−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	$0.919833\pi$
$350$	0.589594	+	0.908014i	0.0315151	+	0.0485354i
$351$	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	0.946378	−	0.323062i	$-0.104712\pi$
$353$	21.4146	+	12.3638i	1.13979	+	0.658056i	0.193409	+	0.981118i	$0.438046\pi$
$354$	5.41308	+	9.37572i	0.287702	+	0.498314i
$355$	−1.39175	+	4.15910i	−0.0738665	+	0.220742i
$356$	−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
$365$	−2.83768	−	13.9497i	−0.148531	−	0.730163i
$366$	8.15975	−	2.96991i	0.426517	−	0.155240i
$367$	13.1233	+	15.6398i	0.685033	+	0.816390i	0.990745	−	0.135733i	$-0.0433391\pi$
$367$	13.1233	+	15.6398i	0.685033	+	0.816390i	−0.305712	+	0.952124i	$0.598895\pi$
$368$	3.44157	−	1.98699i	0.179404	−	0.103579i
$369$	3.24886	−	5.62719i	0.169129	−	0.292940i
$370$	17.5064	+	19.7886i	0.910117	+	1.02876i
$371$	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	0.108769	−	0.994067i	$-0.465309\pi$
$373$	19.7775	−	11.4186i	1.02404	−	0.591230i	0.915272	+	0.402837i	$0.131976\pi$
$374$	−4.26164	+	3.57594i	−0.220364	+	0.184908i
$375$	10.1741	−	4.63551i	0.525388	−	0.239377i
$376$	−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	$0.504590\pi$
$380$	6.40505	−	7.34679i	0.328572	−	0.376883i
$381$	−2.21675			−0.113567
$382$	5.73844	+	1.01184i	0.293604	+	0.0517703i
$383$	−6.28115	+	7.48558i	−0.320952	+	0.382496i	−0.902263	−	0.431186i	$-0.858095\pi$
$383$	−6.28115	+	7.48558i	−0.320952	+	0.382496i	0.581311	+	0.813681i	$0.302540\pi$
$384$	−0.939693	−	0.342020i	−0.0479535	−	0.0174536i
$385$	1.06068	+	0.843758i	0.0540575	+	0.0430019i
$386$	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	$-0.236395\pi$
$390$	−8.42943	+	7.45728i	−0.426841	+	0.377614i
$391$	−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
$395$	−8.53409	+	1.73602i	−0.429397	+	0.0873485i
$396$	−2.14441	−	1.79937i	−0.107760	−	0.0904217i
$397$	4.19141	+	0.739059i	0.210361	+	0.0370923i	0.277835	−	0.960629i	$-0.410383\pi$
$397$	4.19141	+	0.739059i	0.210361	+	0.0370923i	−0.0674745	+	0.997721i	$0.521494\pi$
$398$			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
$405$	−0.709578	+	2.12050i	−0.0352592	+	0.105368i
$406$	−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	$0.791215\pi$
$410$	14.5244	−	0.379904i	0.717308	−	0.0187621i
$411$	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
$415$	−2.00600	+	13.4197i	−0.0984706	+	0.658749i
$416$	−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	$0.661621\pi$
$420$	−0.177436	−	0.450487i	−0.00865800	−	0.0219815i
$421$	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
$425$	0.519456	+	9.92306i	0.0251973	+	0.481339i
$426$	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
$430$	0.655880	+	0.356139i	0.0316293	+	0.0171745i
$431$	−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	−0.795042	−	0.606554i	$-0.792551\pi$
$433$	4.24249	−	11.6562i	0.203881	−	0.560159i	0.998923	+	0.0463955i	$0.0147735\pi$
$434$	0.798155	+	0.669732i	0.0383127	+	0.0321481i
$435$	−11.9622	+	4.71161i	−0.573541	+	0.225904i
$436$	−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	$-0.215203\pi$
$440$	0.925393	−	6.19069i	0.0441164	−	0.295130i
$441$	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	$-0.987307\pi$
$443$	−18.2052	−	21.6961i	−0.864954	−	1.03081i	0.134252	−	0.990947i	$-0.457137\pi$
$444$	−5.90790	−	10.2328i	−0.280376	−	0.485626i
$445$	0.746007	+	28.5212i	0.0353641	+	1.35203i
$446$	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	$-0.349038\pi$
$450$	−4.87192	+	1.12447i	−0.229664	+	0.0530079i
$451$	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	$-0.893099\pi$
$457$		−	14.0905i		−	0.659126i	0.944134	−	0.329563i	$-0.106901\pi$
$458$	24.4395	+	4.30934i	1.14198	+	0.201362i
$459$	−1.52238	−	1.27743i	−0.0710588	−	0.0596254i
$460$	−1.77134	−	8.70776i	−0.0825894	−	0.406001i
$461$	−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	$-0.333183\pi$
$463$	32.2849	−	18.6397i	1.50041	−	0.866261i	1.00000		0.000470819i	$-0.000149866\pi$
$464$	−2.87483	+	4.97934i	−0.133460	+	0.231160i
$465$	8.05882	−	7.12942i	0.373719	−	0.330619i
$466$	1.94753	+	11.0450i	0.0902175	+	0.511649i
$467$	−17.3392	−	10.0108i	−0.802364	−	0.463245i	0.0419332	−	0.999120i	$-0.486648\pi$
$467$	−17.3392	−	10.0108i	−0.802364	−	0.463245i	−0.844297	+	0.535875i	$0.819982\pi$
$468$	4.35889	−	2.51661i	0.201490	−	0.116330i
$469$	1.50408	−	1.26207i	0.0694519	−	0.0582771i
$470$	−12.2033	+	15.3407i	−0.562895	+	0.707613i
$471$	−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
$475$	−11.0340	−	18.7950i	−0.506273	−	0.862373i
$476$	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	$0.761007\pi$
$480$	−1.39204	+	1.74992i	−0.0635375	+	0.0798727i
$481$	−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
$485$	−17.8013	+	15.7483i	−0.808314	+	0.715093i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	0.675159	−	0.389803i	0.0305944	−	0.0176637i	−0.484625	−	0.874722i	$-0.661044\pi$
$487$	0.675159	−	0.389803i	0.0305944	−	0.0176637i	0.515219	+	0.857058i	$0.327711\pi$
$488$	−5.58160	−	6.65189i	−0.252667	−	0.301117i
$489$	11.0791	−	4.03245i	0.501013	−	0.182354i
$490$	3.09925	+	15.2356i	0.140010	+	0.688275i
$491$	−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	$0.252142\pi$
$500$	−7.83569	−	7.97508i	−0.350423	−	0.356656i
$501$	−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	−0.0757474	−	0.997127i	$-0.524134\pi$
$503$	4.35345	−	0.767631i	0.194111	−	0.0342270i	0.269858	+	0.962900i	$0.413023\pi$
$504$	0.0375997	+	0.213239i	0.00167482	+	0.00949840i
$505$	−0.381131	−	14.5713i	−0.0169601	−	0.648415i
$506$	−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	$0.439300\pi$
$510$	0.656966	−	4.39497i	0.0290910	−	0.194613i
$511$	−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
$515$	−8.51571	+	3.35413i	−0.375247	+	0.147801i
$516$	−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
$520$	9.89059	+	5.37053i	0.433731	+	0.235513i
$521$	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	−0.696268	−	0.717782i	$-0.745157\pi$
$523$	−25.2716	+	4.45607i	−1.10505	+	0.194850i	−0.408782	+	0.912632i	$0.634046\pi$
$524$	−6.72871	+	11.6545i	−0.293945	+	0.509127i
$525$	−1.08116	+	0.0565969i	−0.0471857	+	0.00247009i
$526$	−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
$530$	−7.73382	−	19.6351i	−0.335936	−	0.852896i
$531$	−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
$535$	4.49342	−	30.0601i	0.194267	−	1.29961i
$536$	−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
$540$	2.23530	−	0.0584672i	0.0961921	−	0.00251603i
$541$	−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
$545$	−14.5225	+	43.3989i	−0.622075	+	1.85900i
$546$	1.02411	−	0.372745i	0.0438278	−	0.0159520i
$547$	−10.7384	+	29.5035i	−0.459140	+	1.26148i	0.466987	+	0.884264i	$0.345340\pi$
$547$	−10.7384	+	29.5035i	−0.459140	+	1.26148i	−0.926127	+	0.377212i	$0.876883\pi$
$548$	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
$555$	−25.8907	+	5.26672i	−1.09900	+	0.223560i
$556$	−16.5574	+	6.02640i	−0.702190	+	0.255576i
$557$	−12.5357	−	14.9394i	−0.531154	−	0.633005i	0.432026	−	0.901861i	$-0.357799\pi$
$557$	−12.5357	−	14.9394i	−0.531154	−	0.633005i	−0.963180	+	0.268856i	$0.913354\pi$
$558$	−4.16725	+	2.40596i	−0.176414	+	0.101853i
$559$	−0.839969	+	1.45487i	−0.0355269	+	0.0615344i
$560$	−0.362633	+	0.320811i	−0.0153240	+	0.0135567i
$561$	−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	−0.999616	−	0.0277126i	$-0.991178\pi$
$563$	−35.0083	+	20.2121i	−1.47542	+	0.851836i	−0.475808	+	0.879549i	$0.657844\pi$
$564$	6.71552	−	5.63499i	0.282774	−	0.237276i
$565$	−13.1316	−	10.4460i	−0.552451	−	0.439466i
$566$	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	$0.428182\pi$
$570$	3.15999	+	9.22033i	0.132357	+	0.386197i
$571$	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
$575$	−19.7217	−	2.42270i	−0.822450	−	0.101034i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	−17.1828	+	9.92050i	−0.715330	+	0.412996i	−0.813031	−	0.582220i	$-0.802184\pi$
$577$	−17.1828	+	9.92050i	−0.715330	+	0.412996i	0.0977014	+	0.995216i	$0.468851\pi$
$578$	−11.3021	−	6.52526i	−0.470105	−	0.271415i
$579$	3.21102	+	18.2106i	0.133445	+	0.756807i
$580$	8.51876	+	9.62928i	0.353722	+	0.399834i
$581$	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
$585$	−2.24348	−	11.0287i	−0.0927566	−	0.455982i
$586$	20.6809	+	17.3533i	0.854319	+	0.716859i
$587$	5.42869	+	0.957225i	0.224066	+	0.0395089i	0.284554	−	0.958660i	$-0.408155\pi$
$587$	5.42869	+	0.957225i	0.224066	+	0.0395089i	−0.0604878	+	0.998169i	$0.519266\pi$
$588$		−	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	$-0.700688\pi$
$593$	9.28489	−	25.5100i	0.381285	−	1.04757i	0.970816	−	0.239826i	$-0.0770902\pi$
$594$	2.63050	−	0.957425i	0.107931	−	0.0392836i
$595$	0.305340	−	0.912476i	0.0125177	−	0.0374079i
$596$	−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	$0.886265\pi$
$600$	2.72295	+	4.19351i	0.111164	+	0.171200i
$601$	−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
$605$	6.99672	+	1.04588i	0.284457	+	0.0425210i
$606$	−1.13196	+	6.41969i	−0.0459829	+	0.260782i
$607$		−	14.2869i		−	0.579888i	−0.957044	−	0.289944i	$-0.906363\pi$
$607$		−	14.2869i		−	0.579888i	0.957044	−	0.289944i	$-0.0936367\pi$
$608$	3.67296	+	2.34721i	0.148958	+	0.0951920i
$609$	1.24496			0.0504484
$610$	−18.0659	+	7.11572i	−0.731466	+	0.288107i
$611$	−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	$0.0334093\pi$
$613$	7.42790	+	20.4080i	0.300010	+	0.824271i	−0.694487	+	0.719506i	$0.744368\pi$
$614$	3.13855	−	2.63355i	0.126661	−	0.106282i
$615$	−6.93319	+	12.7684i	−0.279573	+	0.514873i
$616$	−0.303066	+	0.524926i	−0.0122109	+	0.0211499i
$617$	−23.4553	+	4.13580i	−0.944274	+	0.166501i	−0.624528	−	0.781002i	$-0.714709\pi$
$617$	−23.4553	+	4.13580i	−0.944274	+	0.166501i	−0.319746	+	0.947503i	$0.603598\pi$
$618$	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	$-0.0212953\pi$
$620$	−9.45574	−	5.13441i	−0.379752	−	0.206203i
$621$	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
$625$	−22.4712	+	10.9566i	−0.898846	+	0.438265i
$626$	−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
$630$	0.478851	+	0.0715793i	0.0190779	+	0.00285179i
$631$	−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
$635$	4.95511	−	0.129607i	0.196637	−	0.00514330i
$636$	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
$640$	2.12050	+	0.709578i	0.0838199	+	0.0280485i
$641$	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	$0.475189\pi$
$643$	−23.2648	+	27.7259i	−0.917473	+	1.09340i	−0.995339	+	0.0964383i	$0.969255\pi$
$644$	−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	$-0.762332\pi$
$647$		−	34.5519i		−	1.35837i	0.733965	−	0.679187i	$-0.237668\pi$
$648$	−0.984808	−	0.173648i	−0.0386869	−	0.00682154i
$649$	−23.2157	−	19.4803i	−0.911294	−	0.764667i
$650$	18.4063	−	17.1621i	0.721955	−	0.673154i
$651$	−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	−0.428375	−	0.903601i	$-0.640914\pi$
$653$	3.57699	−	2.06518i	0.139978	−	0.0808165i	0.568354	+	0.822784i	$0.307581\pi$
$654$	10.2332	−	17.7244i	0.400150	−	0.693079i
$655$	19.9387	+	22.5379i	0.779069	+	0.880630i
$656$	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	$0.104047\pi$
$660$	4.89860	+	3.89676i	0.190678	+	0.151681i
$661$	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
$665$	0.327149	+	2.08494i	0.0126863	+	0.0808507i
$666$	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
$670$	−12.6227	+	15.8680i	−0.487659	+	0.613034i
$671$	−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	0.387391	−	0.921915i	$-0.373376\pi$
$673$	−5.63765	−	3.25490i	−0.217315	−	0.125467i	−0.604707	+	0.796448i	$0.706710\pi$
$674$	3.64699	+	20.6831i	0.140477	+	0.796684i
$675$	1.46214	−	4.78144i	0.0562779	−	0.184038i
$676$	−6.16663	+	10.6809i	−0.237178	+	0.410804i
$677$	−20.1132	+	11.6124i	−0.773014	+	0.446300i	−0.833949	−	0.551842i	$-0.813925\pi$
$677$	−20.1132	+	11.6124i	−0.773014	+	0.446300i	0.0609350	+	0.998142i	$0.480592\pi$
$678$	4.82354	+	5.74847i	0.185247	+	0.220769i
$679$	2.16271	−	0.787163i	0.0829973	−	0.0302085i
$680$	−4.35462	+	0.885823i	−0.166992	+	0.0339698i
$681$	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	$-0.718023\pi$
$683$		−	40.4798i		−	1.54892i	0.632626	−	0.774458i	$-0.281977\pi$
$684$	−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
$690$	8.42681	+	2.81985i	0.320803	+	0.107350i
$691$	−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
$695$	1.03019	+	39.3861i	0.0390774	+	1.49400i
$696$	−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
$700$	0.422962	+	0.996601i	0.0159865	+	0.0376680i
$701$	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
$705$	−7.18379	−	18.2387i	−0.270557	−	0.686909i
$706$	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	$0.236582\pi$
$710$	−2.09283	+	3.85423i	−0.0785424	+	0.144647i
$711$	−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
$715$	15.0338	−	27.6869i	0.562234	−	1.03543i
$716$	−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	$0.855319\pi$
$720$	−0.819460	−	2.08050i	−0.0305395	−	0.0775357i
$721$	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
$725$	26.4636	−	11.2313i	0.982832	−	0.417119i
$726$	−2.97299	−	1.08208i	−0.110338	−	0.0401598i
$727$	15.2844	+	41.9934i	0.566865	+	1.55745i	0.809370	+	0.587299i	$0.199809\pi$
$727$	15.2844	+	41.9934i	0.566865	+	1.55745i	−0.242504	+	0.970150i	$0.577969\pi$
$728$	−0.700531	−	0.834860i	−0.0259634	−	0.0309420i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	−0.372218	−	14.2306i	−0.0137764	−	0.526697i
$731$	−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	0.398260	−	0.917272i	$-0.369614\pi$
$733$	−5.33333	−	3.07920i	−0.196991	−	0.113733i	−0.595251	+	0.803540i	$0.702947\pi$
$734$	10.2081	+	17.6810i	0.376790	+	0.652619i
$735$	−14.7440	−	4.93378i	−0.543842	−	0.181985i
$736$	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	0.698206	−	0.715897i	$-0.253982\pi$
$743$	30.2415	+	5.33240i	1.10945	+	0.195627i	0.411248	+	0.911523i	$0.365093\pi$
$744$	3.68615	+	3.09305i	0.135141	+	0.113397i
$745$	−12.3140	+	2.50492i	−0.451149	+	0.0917733i
$746$	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
$750$	10.8245	−	2.79837i	0.395254	−	0.102182i
$751$	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
$755$	13.7673	−	17.3068i	0.501043	−	0.629859i
$756$	−0.203470	−	0.0740570i	−0.00740013	−	0.00269343i
$757$	−4.34085	+	5.17322i	−0.157771	+	0.188024i	−0.839139	−	0.543917i	$-0.816941\pi$
$757$	−4.34085	+	5.17322i	−0.157771	+	0.188024i	0.681368	+	0.731941i	$0.261385\pi$
$758$	−0.552961	−	0.0975019i	−0.0200844	−	0.00354143i
$759$	11.1245			0.403792
$760$	7.58350	−	6.12296i	0.275082	−	0.222103i
$761$	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
$765$	3.47768	+	2.76644i	0.125736	+	0.100021i
$766$	−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	$0.868604\pi$
$770$	0.898054	+	1.01513i	0.0323636	+	0.0365826i
$771$	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	0.496931	−	0.867790i	$-0.334460\pi$
$773$	−12.3436	−	14.7105i	−0.443967	−	0.529099i	−0.940898	+	0.338691i	$0.890016\pi$
$774$	0.313642	−	0.114156i	0.0112736	−	0.00410326i
$775$	−17.5971	+	16.4076i	−0.632106	+	0.589378i
$776$	−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
$785$	21.3676	+	7.15020i	0.762642	+	0.255201i
$786$	−6.72871	−	11.6545i	−0.240005	−	0.415701i
$787$	40.3364	+	23.2883i	1.43784	+	0.830136i	0.997699	−	0.0677931i	$-0.0215958\pi$
$787$	40.3364	+	23.2883i	1.43784	+	0.830136i	0.440139	+	0.897930i	$0.354929\pi$
$788$	16.9009	−	2.98008i	0.602068	−	0.106161i
$789$	−2.08721	−	11.8371i	−0.0743065	−	0.421413i
$790$	−8.70589	+	0.227714i	−0.309742	+	0.00810168i
$791$	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
$795$	20.8714	+	3.11989i	0.740234	+	0.110651i
$796$	−3.83625	+	21.7564i	−0.135972	+	0.771137i
$797$			11.1555i			0.395148i	0.980288	+	0.197574i	$0.0633063\pi$
$797$			11.1555i			0.395148i	−0.980288	+	0.197574i	$0.936694\pi$
$798$	0.0424973	−	0.942867i	0.00150439	−	0.0333771i
$799$	17.4219			0.616343
$800$	3.00931	−	3.99300i	0.106395	−	0.141174i
$801$	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
$805$	1.69090	+	0.918146i	0.0595962	+	0.0323604i
$806$	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	$0.00952666\pi$
$810$	−1.06702	+	1.96506i	−0.0374912	+	0.0690453i
$811$	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
$815$	−24.5293	+	9.66152i	−0.859225	+	0.338428i
$816$	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
$820$	14.3697	+	2.14800i	0.501812	+	0.0750114i
$821$	−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	$0.0856385\pi$
$823$	30.3632	+	36.1854i	1.05839	+	1.26134i	0.0943677	+	0.995537i	$0.469917\pi$
$824$	−2.04655	−	3.54473i	−0.0712950	−	0.123487i
$825$	11.7390	−	7.62241i	0.408700	−	0.265378i
$826$	0.407060	+	2.30855i	0.0141634	+	0.0803248i
$827$	10.5848	−	1.86638i	0.368068	−	0.0649004i	0.0134450	−	0.999910i	$-0.495720\pi$
$827$	10.5848	−	1.86638i	0.368068	−	0.0649004i	0.354623	+	0.935009i	$0.384609\pi$
$828$	−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	$0.663486\pi$
$830$	−4.30584	+	12.8675i	−0.149458	+	0.446638i
$831$	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	$0.662291\pi$
$840$	−0.0965142	−	0.474455i	−0.00333006	−	0.0163702i
$841$	−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
$845$	18.2731	+	20.6552i	0.628615	+	0.710562i
$846$	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
$850$	−1.21156	+	9.86251i	−0.0415561	+	0.338281i
$851$	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	−0.153996	−	0.988072i	$-0.549214\pi$
$853$	−18.5939	−	3.27861i	−0.636644	−	0.112258i	−0.482649	+	0.875814i	$0.660325\pi$
$854$	1.88021			0.0643393
$855$	−9.56503	−	1.87354i	−0.327117	−	0.0640736i
$856$	13.5926			0.464587
$857$	−1.19159	−	0.210110i	−0.0407041	−	0.00717723i	0.153259	−	0.988186i	$-0.451023\pi$
$857$	−1.19159	−	0.210110i	−0.0407041	−	0.00717723i	−0.193963	+	0.981009i	$0.562134\pi$
$858$	−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	$0.687454\pi$
$860$	0.584073	+	0.464621i	0.0199167	+	0.0158434i
$861$	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	0.995317	−	0.0966621i	$-0.0308166\pi$
$863$	41.3998	+	23.9022i	1.40926	+	0.813639i	0.413947	+	0.910301i	$0.364150\pi$
$864$	0.173648	+	0.984808i	0.00590763	+	0.0335038i
$865$	7.87322	−	6.96522i	0.267698	−	0.236825i
$866$	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
$870$	−12.5986	+	2.56282i	−0.427132	+	0.0868878i
$871$	−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	−0.988782	−	0.149368i	$-0.952276\pi$
$877$	−19.8410	+	23.6456i	−0.669982	+	0.798454i	0.318799	+	0.947822i	$0.396720\pi$
$878$	10.7733	−	29.5994i	0.363582	−	0.998932i
$879$	−25.3688	+	9.23351i	−0.855670	+	0.311438i
$880$	1.98634	−	5.93595i	0.0669594	−	0.200101i
$881$	−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	−0.375362	−	0.926878i	$-0.622481\pi$
$883$	−12.2152	+	2.15387i	−0.411075	+	0.0724836i	−0.0357134	+	0.999362i	$0.511370\pi$
$884$	−1.73694	−	9.85070i	−0.0584197	−	0.331315i
$885$	24.1997	−	0.632974i	0.813465	−	0.0212772i
$886$	−14.1611	−	24.5278i	−0.475752	−	0.824026i
$887$	−0.733305	−	0.873919i	−0.0246220	−	0.0293433i	0.753593	−	0.657341i	$-0.228319\pi$
$887$	−0.733305	−	0.873919i	−0.0246220	−	0.0293433i	−0.778215	+	0.627998i	$0.783875\pi$
$888$	−4.04124	−	11.1032i	−0.135615	−	0.372600i
$889$	−0.451042	−	0.164166i	−0.0151275	−	0.00550594i
$890$	−4.21797	+	28.2174i	−0.141387	+	0.945849i
$891$	−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
$895$	7.26224	+	18.4379i	0.242750	+	0.616310i
$896$	−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
$900$	−4.99316	+	0.261384i	−0.166439	+	0.00871279i
$901$	−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
$905$	17.7208	+	9.62227i	0.589058	+	0.319855i
$906$	−7.57620	+	6.35719i	−0.251702	+	0.211203i
$907$	−15.3664	−	42.2187i	−0.510231	−	1.40185i	−0.880997	−	0.473123i	$-0.843127\pi$
$907$	−15.3664	−	42.2187i	−0.510231	−	1.40185i	0.370765	−	0.928727i	$-0.379096\pi$
$908$	0.0534386	−	0.146821i	0.00177342	−	0.00487244i
$909$	−4.99363	−	4.19015i	−0.165628	−	0.138979i
$910$	−2.26740	+	0.893074i	−0.0751635	+	0.0296051i
$911$	−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
$915$	2.87054	−	19.2034i	0.0948973	−	0.634844i
$916$	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	$0.463982\pi$
$920$	−0.232348	−	8.88306i	−0.00766027	−	0.292866i
$921$	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
$925$	57.5656	−	13.2865i	1.89274	−	0.436856i
$926$	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
$935$	2.47970	+	12.1900i	0.0810950	+	0.398655i
$936$	4.72968	−	1.72146i	0.154594	−	0.0562677i
$937$	−13.8432	−	16.4977i	−0.452238	−	0.538956i	0.490962	−	0.871181i	$-0.336645\pi$
$937$	−13.8432	−	16.4977i	−0.452238	−	0.538956i	−0.943200	+	0.332224i	$0.892201\pi$
$938$	1.70039	−	0.981718i	0.0555196	−	0.0320542i
$939$	8.43730	−	14.6138i	0.275341	−	0.476904i
$940$	−14.6818	+	12.9886i	−0.478866	+	0.423640i
$941$	−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
$945$	−0.301415	+	0.378908i	−0.00980503	+	0.0123259i
$946$	0.877984	+	0.319560i	0.0285457	+	0.0103898i
$947$	27.3003	−	32.5353i	0.887142	−	1.05725i	−0.110845	−	0.993838i	$-0.535356\pi$
$947$	27.3003	−	32.5353i	0.887142	−	1.05725i	0.997987	−	0.0634169i	$-0.0201998\pi$
$948$	3.83556	+	0.676312i	0.124573	+	0.0219656i
$949$	32.0429			1.04016
$950$	−7.60262	−	20.4255i	−0.246661	−	0.662690i
$951$	11.5881			0.375771
$952$	0.423775	+	0.0747230i	0.0137346	+	0.00242179i
$953$	8.93942	−	10.6536i	0.289576	−	0.345103i	−0.601570	−	0.798820i	$-0.705458\pi$
$953$	8.93942	−	10.6536i	0.289576	−	0.345103i	0.891146	+	0.453717i	$0.149902\pi$
$954$	−8.86854	−	3.22788i	−0.287129	−	0.104507i
$955$	8.11135	−	10.1967i	0.262477	−	0.329959i
$956$	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
$960$	−1.67476	+	1.48161i	−0.0540526	+	0.0478189i
$961$	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
$965$	−8.24233	−	40.5185i	−0.265330	−	1.30434i
$966$	−0.659165	−	0.553105i	−0.0212083	−	0.0177959i
$967$	44.6853	+	7.87923i	1.43698	+	0.253379i	0.837250	−	0.546821i	$-0.184162\pi$
$967$	44.6853	+	7.87923i	1.43698	+	0.253379i	0.599734	+	0.800200i	$0.295273\pi$
$968$			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
$975$	5.65968	+	24.5214i	0.181255	+	0.785314i
$976$	−4.34171	−	7.52007i	−0.138975	−	0.240712i
$977$	44.7260	+	25.8226i	1.43091	+	0.826138i	0.997190	−	0.0749089i	$-0.0238666\pi$
$977$	44.7260	+	25.8226i	1.43091	+	0.826138i	0.433722	+	0.901047i	$0.357200\pi$
$978$	11.6110	−	2.04733i	0.371278	−	0.0654664i
$979$	6.20232	+	35.1751i	0.198227	+	1.12420i
$980$	0.406529	+	15.5423i	0.0129861	+	0.496481i
$981$	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	$-0.856054\pi$
$983$	−15.4040	−	42.3222i	−0.491312	−	1.34987i	0.408167	−	0.912907i	$-0.366168\pi$
$984$	−6.10586	−	2.22235i	−0.194648	−	0.0708460i
$985$	5.67323	−	37.9528i	0.180764	−	1.20928i
$986$	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
$990$	−5.82399	+	2.29393i	−0.185099	+	0.0729060i
$991$	−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
$995$	43.4123	+	23.5726i	1.37626	+	0.747303i
$996$	3.03408	−	5.25519i	0.0961386	−	0.166517i
$997$	−16.7662	+	2.95633i	−0.530990	+	0.0936279i	−0.432714	−	0.901531i	$-0.642444\pi$
$997$	−16.7662	+	2.95633i	−0.530990	+	0.0936279i	−0.0982764	+	0.995159i	$0.531333\pi$
$998$	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.169.10	yes	60
5.4	even	2	inner	570.2.bc.a.169.5	✓	60
19.9	even	9	inner	570.2.bc.a.199.5	yes	60
95.9	even	18	inner	570.2.bc.a.199.10	yes	60

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

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.39204 - 1.74992i) q^{5} +(-0.766044 + 0.642788i) q^{6} +(-0.187519 + 0.108264i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.642788 + 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.39204 - 1.74992i) 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} +(1.67476 - 1.48161i) 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} +(0.445735 + 2.19119i) 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} +(-1.12447 - 4.87192i) 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} +(0.0584672 + 2.23530i) 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} +(-0.0715793 + 0.478851i) q^{35} +(0.173648 - 0.984808i) q^{36} +11.8158i q^{37} +(4.32241 - 0.562862i) q^{38} -5.03322 q^{39} +(2.08050 - 0.819460i) 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} +(-1.96506 - 1.06702i) 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} +(-0.261384 - 4.99316i) 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} +(-2.29393 - 5.82399i) q^{55} -0.216528 q^{56} +(-1.67375 + 4.02474i) q^{57} +5.74965i q^{58} +(1.87994 - 10.6617i) q^{59} +(-0.330577 + 2.21150i) 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} +(11.2508 - 0.294278i) 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} +(-0.153643 + 0.459147i) 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} +(2.19119 - 0.445735i) 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} +(-3.32830 + 2.94446i) 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} +(-1.74992 - 1.39204i) q^{90} +(-1.02411 - 0.372745i) q^{91} +(2.55443 - 3.04425i) q^{92} +(4.73882 + 0.835582i) q^{93} -8.76649 q^{94} +(3.50602 - 9.09438i) 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

Related objects

Downloads

Learn more