LMFDB - Embedded newform 310.2.n.a.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(39,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("310.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.n (of order $10$, degree $4$, 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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	310.109
Dual form			310.2.n.a.219.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(0.913834 - 1.25778i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.22372 + 0.234651i) q^{5} -1.55471 q^{6} +(-2.79616 - 0.908529i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.180122 + 0.554358i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.913834 - 1.25778i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.22372 + 0.234651i) q^{5} -1.55471 q^{6} +(-2.79616 - 0.908529i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.180122 + 0.554358i) q^{9} +(-1.11723 - 1.93695i) q^{10} +(1.65278 - 5.08673i) q^{11} +(0.913834 + 1.25778i) q^{12} +(2.00343 - 2.75749i) q^{13} +(0.908529 + 2.79616i) q^{14} +(2.32725 - 2.58253i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.80814 - 1.56226i) q^{17} +(0.342612 - 0.471565i) q^{18} +(-5.22960 + 3.79953i) q^{19} +(-0.910334 + 2.04237i) q^{20} +(-3.69796 + 2.68673i) q^{21} +(-5.08673 + 1.65278i) q^{22} +(-6.10655 + 1.98414i) q^{23} +(0.480431 - 1.47861i) q^{24} +(4.88988 + 1.04360i) q^{25} -3.40844 q^{26} +(5.29771 + 1.72133i) q^{27} +(1.72812 - 2.37856i) q^{28} +(1.65316 - 1.20109i) q^{29} +(-3.45724 - 0.364813i) q^{30} +(1.69296 - 5.30414i) q^{31} +1.00000i q^{32} +(-4.88764 - 6.72726i) q^{33} +(-4.09005 - 2.97159i) q^{34} +(-6.00470 - 2.67644i) q^{35} -0.582886 q^{36} +0.355184i q^{37} +(6.14776 + 1.99753i) q^{38} +(-1.63752 - 5.03977i) q^{39} +(2.18740 - 0.464002i) q^{40} +(-5.98905 + 4.35130i) q^{41} +(4.34722 + 1.41250i) q^{42} +(2.16858 + 2.98479i) q^{43} +(4.32703 + 3.14377i) q^{44} +(0.270460 + 1.27500i) q^{45} +(5.19454 + 3.77405i) q^{46} +(-7.46139 + 10.2697i) q^{47} +(-1.47861 + 0.480431i) q^{48} +(1.32999 + 0.966295i) q^{49} +(-2.02991 - 4.56941i) q^{50} +(2.42885 - 7.47525i) q^{51} +(2.00343 + 2.75749i) q^{52} +(0.0123555 - 0.00401453i) q^{53} +(-1.72133 - 5.29771i) q^{54} +(4.86892 - 10.9236i) q^{55} -2.94006 q^{56} +10.0498i q^{57} +(-1.94341 - 0.631453i) q^{58} +(7.58927 + 5.51393i) q^{59} +(1.73697 + 3.01139i) q^{60} +6.91322 q^{61} +(-5.28623 + 1.74806i) q^{62} -1.71372i q^{63} +(0.809017 - 0.587785i) q^{64} +(5.10212 - 5.66178i) q^{65} +(-2.56959 + 7.90837i) q^{66} +8.83439i q^{67} +5.05558i q^{68} +(-3.08475 + 9.49389i) q^{69} +(1.36419 + 6.43108i) q^{70} +(3.09697 + 9.53148i) q^{71} +(0.342612 + 0.471565i) q^{72} +(3.22181 + 1.04683i) q^{73} +(0.287350 - 0.208772i) q^{74} +(5.78116 - 5.19674i) q^{75} +(-1.99753 - 6.14776i) q^{76} +(-9.24288 + 12.7217i) q^{77} +(-3.11475 + 4.28708i) q^{78} +(-3.26876 - 10.0602i) q^{79} +(-1.66110 - 1.49691i) q^{80} +(5.59159 - 4.06253i) q^{81} +(7.04055 + 2.28761i) q^{82} +(5.25598 + 7.23423i) q^{83} +(-1.41250 - 4.34722i) q^{84} +(11.0585 - 2.34580i) q^{85} +(1.14009 - 3.50883i) q^{86} -3.17692i q^{87} -5.34850i q^{88} +(-2.84661 + 8.76096i) q^{89} +(0.872527 - 0.968235i) q^{90} +(-8.10718 + 5.89021i) q^{91} -6.42080i q^{92} +(-5.12438 - 6.97648i) q^{93} +12.6941 q^{94} +(-12.5207 + 7.22196i) q^{95} +(1.25778 + 0.913834i) q^{96} +(2.24610 + 0.729803i) q^{97} -1.64396i q^{98} +3.11757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 16 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9}+O(q^{10}) $ 64 * q + 16 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9	$ 64 q + 16 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{15} - 16 q^{16} + 16 q^{19} - 4 q^{20} + 32 q^{21} - 4 q^{24} - 8 q^{25} - 48 q^{26} - 40 q^{29} - 8 q^{30} - 60 q^{31} - 20 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} - 4 q^{44} - 22 q^{45} + 36 q^{46} + 32 q^{49} + 20 q^{50} - 4 q^{51} - 40 q^{54} + 32 q^{59} + 14 q^{60} - 64 q^{61} + 16 q^{64} + 48 q^{65} - 4 q^{66} - 20 q^{70} - 20 q^{71} - 4 q^{74} + 62 q^{75} + 24 q^{76} - 116 q^{79} - 6 q^{80} - 116 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{86} + 60 q^{89} - 82 q^{90} + 28 q^{91} + 16 q^{94} - 90 q^{95} + 4 q^{96} + 16 q^{99}+O(q^{100}) $ 64 * q + 16 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^15 - 16 * q^16 + 16 * q^19 - 4 * q^20 + 32 * q^21 - 4 * q^24 - 8 * q^25 - 48 * q^26 - 40 * q^29 - 8 * q^30 - 60 * q^31 - 20 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 - 4 * q^44 - 22 * q^45 + 36 * q^46 + 32 * q^49 + 20 * q^50 - 4 * q^51 - 40 * q^54 + 32 * q^59 + 14 * q^60 - 64 * q^61 + 16 * q^64 + 48 * q^65 - 4 * q^66 - 20 * q^70 - 20 * q^71 - 4 * q^74 + 62 * q^75 + 24 * q^76 - 116 * q^79 - 6 * q^80 - 116 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^86 + 60 * q^89 - 82 * q^90 + 28 * q^91 + 16 * q^94 - 90 * q^95 + 4 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.913834	−	1.25778i	0.527602	−	0.726182i	−0.459160	−	0.888353i	$-0.651850\pi$
$3$	0.913834	−	1.25778i	0.527602	−	0.726182i	0.986763	+	0.162171i	$0.0518497\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.22372	+	0.234651i	0.994479	+	0.104939i
$5$	2.22372	+	0.234651i	0.994479	+	0.104939i
$6$	−1.55471			−0.634706
$7$	−2.79616	−	0.908529i	−1.05685	−	0.343392i	−0.271497	−	0.962439i	$-0.587519\pi$
$7$	−2.79616	−	0.908529i	−1.05685	−	0.343392i	−0.785353	+	0.619048i	$0.787519\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.180122	+	0.554358i	0.0600406	+	0.184786i
$10$	−1.11723	−	1.93695i	−0.353301	−	0.612518i
$11$	1.65278	−	5.08673i	0.498331	−	1.53371i	−0.313369	−	0.949632i	$-0.601458\pi$
$11$	1.65278	−	5.08673i	0.498331	−	1.53371i	0.811700	−	0.584075i	$-0.198542\pi$
$12$	0.913834	+	1.25778i	0.263801	+	0.363091i
$13$	2.00343	−	2.75749i	0.555652	−	0.764789i	−0.435114	−	0.900376i	$-0.643292\pi$
$13$	2.00343	−	2.75749i	0.555652	−	0.764789i	0.990766	+	0.135586i	$0.0432918\pi$
$14$	0.908529	+	2.79616i	0.242815	+	0.747306i
$15$	2.32725	−	2.58253i	0.600894	−	0.666807i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.80814	−	1.56226i	1.16615	−	0.378903i	0.338942	−	0.940807i	$-0.389931\pi$
$17$	4.80814	−	1.56226i	1.16615	−	0.378903i	0.827203	+	0.561904i	$0.189931\pi$
$18$	0.342612	−	0.471565i	0.0807544	−	0.111149i
$19$	−5.22960	+	3.79953i	−1.19975	+	0.871671i	−0.994260	−	0.106988i	$-0.965879\pi$
$19$	−5.22960	+	3.79953i	−1.19975	+	0.871671i	−0.205492	+	0.978659i	$0.565879\pi$
$20$	−0.910334	+	2.04237i	−0.203557	+	0.456689i
$21$	−3.69796	+	2.68673i	−0.806962	+	0.586292i
$22$	−5.08673	+	1.65278i	−1.08449	+	0.352373i
$23$	−6.10655	+	1.98414i	−1.27330	+	0.413721i	−0.866217	−	0.499668i	$-0.833455\pi$
$23$	−6.10655	+	1.98414i	−1.27330	+	0.413721i	−0.407086	+	0.913390i	$0.633455\pi$
$24$	0.480431	−	1.47861i	0.0980675	−	0.301821i
$25$	4.88988	+	1.04360i	0.977976	+	0.208719i
$26$	−3.40844			−0.668450
$27$	5.29771	+	1.72133i	1.01954	+	0.331270i
$28$	1.72812	−	2.37856i	0.326585	−	0.449505i
$29$	1.65316	−	1.20109i	0.306985	−	0.223038i	−0.423617	−	0.905841i	$-0.639240\pi$
$29$	1.65316	−	1.20109i	0.306985	−	0.223038i	0.730602	+	0.682804i	$0.239240\pi$
$30$	−3.45724	−	0.364813i	−0.631202	−	0.0666055i
$31$	1.69296	−	5.30414i	0.304064	−	0.952652i
$31$	1.69296	−	5.30414i	0.304064	−	0.952652i
$32$			1.00000i			0.176777i
$33$	−4.88764	−	6.72726i	−0.850829	−	1.17107i
$34$	−4.09005	−	2.97159i	−0.701437	−	0.509624i
$35$	−6.00470	−	2.67644i	−1.01498	−	0.452401i
$36$	−0.582886			−0.0971477
$37$			0.355184i			0.0583920i	0.999574	+	0.0291960i	$0.00929469\pi$
$37$			0.355184i			0.0583920i	−0.999574	+	0.0291960i	$0.990705\pi$
$38$	6.14776	+	1.99753i	0.997299	+	0.324042i
$39$	−1.63752	−	5.03977i	−0.262213	−	0.807009i
$40$	2.18740	−	0.464002i	0.345858	−	0.0733651i
$41$	−5.98905	+	4.35130i	−0.935332	+	0.679558i	−0.947292	−	0.320370i	$-0.896193\pi$
$41$	−5.98905	+	4.35130i	−0.935332	+	0.679558i	0.0119605	+	0.999928i	$0.496193\pi$
$42$	4.34722	+	1.41250i	0.670790	+	0.217953i
$43$	2.16858	+	2.98479i	0.330705	+	0.455176i	0.941698	−	0.336460i	$-0.109230\pi$
$43$	2.16858	+	2.98479i	0.330705	+	0.455176i	−0.610993	+	0.791636i	$0.709230\pi$
$44$	4.32703	+	3.14377i	0.652324	+	0.473941i
$45$	0.270460	+	1.27500i	0.0403178	+	0.190066i
$46$	5.19454	+	3.77405i	0.765893	+	0.556454i
$47$	−7.46139	+	10.2697i	−1.08835	+	1.49799i	−0.238378	+	0.971172i	$0.576616\pi$
$47$	−7.46139	+	10.2697i	−1.08835	+	1.49799i	−0.849977	+	0.526820i	$0.823384\pi$
$48$	−1.47861	+	0.480431i	−0.213420	+	0.0693442i
$49$	1.32999	+	0.966295i	0.189999	+	0.138042i
$50$	−2.02991	−	4.56941i	−0.287073	−	0.646211i
$51$	2.42885	−	7.47525i	0.340108	−	1.04674i
$52$	2.00343	+	2.75749i	0.277826	+	0.382395i
$53$	0.0123555	−	0.00401453i	0.00169715	−	0.000551438i	−0.308168	−	0.951332i	$-0.599716\pi$
$53$	0.0123555	−	0.00401453i	0.00169715	−	0.000551438i	0.309865	+	0.950780i	$0.399716\pi$
$54$	−1.72133	−	5.29771i	−0.234243	−	0.720927i
$55$	4.86892	−	10.9236i	0.656526	−	1.47294i
$56$	−2.94006			−0.392882
$57$			10.0498i			1.33113i
$58$	−1.94341	−	0.631453i	−0.255182	−	0.0829138i
$59$	7.58927	+	5.51393i	0.988039	+	0.717853i	0.959491	−	0.281740i	$-0.0909115\pi$
$59$	7.58927	+	5.51393i	0.988039	+	0.717853i	0.0285485	+	0.999592i	$0.490912\pi$
$60$	1.73697	+	3.01139i	0.224242	+	0.388769i
$61$	6.91322			0.885147			0.442573	−	0.896732i	$-0.354066\pi$
$61$	6.91322			0.885147			0.442573	+	0.896732i	$0.354066\pi$
$62$	−5.28623	+	1.74806i	−0.671352	+	0.222004i
$63$		−	1.71372i		−	0.215909i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	5.10212	−	5.66178i	0.632840	−	0.702257i
$66$	−2.56959	+	7.90837i	−0.316294	+	0.973453i
$67$			8.83439i			1.07929i	0.841892	+	0.539646i	$0.181442\pi$
$67$			8.83439i			1.07929i	−0.841892	+	0.539646i	$0.818558\pi$
$68$			5.05558i			0.613079i
$69$	−3.08475	+	9.49389i	−0.371361	+	1.14293i
$70$	1.36419	+	6.43108i	0.163052	+	0.768661i
$71$	3.09697	+	9.53148i	0.367542	+	1.13118i	0.948374	+	0.317155i	$0.102728\pi$
$71$	3.09697	+	9.53148i	0.367542	+	1.13118i	−0.580831	+	0.814024i	$0.697272\pi$
$72$	0.342612	+	0.471565i	0.0403772	+	0.0555745i
$73$	3.22181	+	1.04683i	0.377084	+	0.122522i	0.491426	−	0.870919i	$-0.336476\pi$
$73$	3.22181	+	1.04683i	0.377084	+	0.122522i	−0.114342	+	0.993441i	$0.536476\pi$
$74$	0.287350	−	0.208772i	0.0334038	−	0.0242693i
$75$	5.78116	−	5.19674i	0.667550	−	0.600068i
$76$	−1.99753	−	6.14776i	−0.229132	−	0.705197i
$77$	−9.24288	+	12.7217i	−1.05332	+	1.44978i
$78$	−3.11475	+	4.28708i	−0.352676	+	0.485417i
$79$	−3.26876	−	10.0602i	−0.367764	−	1.13186i	−0.948232	−	0.317579i	$-0.897130\pi$
$79$	−3.26876	−	10.0602i	−0.367764	−	1.13186i	0.580467	−	0.814283i	$-0.302870\pi$
$80$	−1.66110	−	1.49691i	−0.185717	−	0.167359i
$81$	5.59159	−	4.06253i	0.621288	−	0.451392i
$82$	7.04055	+	2.28761i	0.777498	+	0.252625i
$83$	5.25598	+	7.23423i	0.576919	+	0.794060i	0.993353	−	0.115105i	$-0.0367206\pi$
$83$	5.25598	+	7.23423i	0.576919	+	0.794060i	−0.416435	+	0.909166i	$0.636721\pi$
$84$	−1.41250	−	4.34722i	−0.154116	−	0.474320i
$85$	11.0585	−	2.34580i	1.19947	−	0.254437i
$86$	1.14009	−	3.50883i	0.122939	−	0.378367i
$87$		−	3.17692i		−	0.340602i
$88$		−	5.34850i		−	0.570152i
$89$	−2.84661	+	8.76096i	−0.301740	+	0.928660i	0.679134	+	0.734015i	$0.262356\pi$
$89$	−2.84661	+	8.76096i	−0.301740	+	0.928660i	−0.980874	+	0.194645i	$0.937644\pi$
$90$	0.872527	−	0.968235i	0.0919724	−	0.102061i
$91$	−8.10718	+	5.89021i	−0.849863	+	0.617462i
$92$		−	6.42080i		−	0.669415i
$93$	−5.12438	−	6.97648i	−0.531374	−	0.723427i
$94$	12.6941			1.30929
$95$	−12.5207	+	7.22196i	−1.28460	+	0.740957i
$96$	1.25778	+	0.913834i	0.128372	+	0.0932678i
$97$	2.24610	+	0.729803i	0.228057	+	0.0741003i	0.420816	−	0.907146i	$-0.361744\pi$
$97$	2.24610	+	0.729803i	0.228057	+	0.0741003i	−0.192759	+	0.981246i	$0.561744\pi$
$98$		−	1.64396i		−	0.166065i
$99$	3.11757			0.313328
$100$	−2.50357	+	4.32806i	−0.250357	+	0.432806i
$101$	−2.83781	−	8.73389i	−0.282373	−	0.869055i	−0.987174	−	0.159649i	$-0.948964\pi$
$101$	−2.83781	−	8.73389i	−0.282373	−	0.869055i	0.704801	−	0.709405i	$-0.251036\pi$
$102$	−7.47525	+	2.42885i	−0.740160	+	0.240492i
$103$	−0.510935	−	0.703242i	−0.0503439	−	0.0692925i	0.783103	−	0.621892i	$-0.213636\pi$
$103$	−0.510935	−	0.703242i	−0.0503439	−	0.0692925i	−0.833447	+	0.552600i	$0.813636\pi$
$104$	1.05327	−	3.24162i	0.103281	−	0.317867i
$105$	−8.85368	+	5.10680i	−0.864031	+	0.498373i
$106$	−0.0105102	−	0.00763609i	−0.00102084	−	0.000741683i
$107$	14.1285	−	4.59061i	1.36585	−	0.443791i	0.467858	−	0.883804i	$-0.345026\pi$
$107$	14.1285	−	4.59061i	1.36585	−	0.443791i	0.897992	+	0.440012i	$0.145026\pi$
$108$	−3.27416	+	4.50650i	−0.315056	+	0.433638i
$109$	4.97303	+	3.61312i	0.476330	+	0.346074i	0.799903	−	0.600129i	$-0.204884\pi$
$109$	4.97303	+	3.61312i	0.476330	+	0.346074i	−0.323573	+	0.946203i	$0.604884\pi$
$110$	−11.6993	+	2.48171i	−1.11548	+	0.236622i
$111$	0.446745	+	0.324580i	0.0424032	+	0.0308077i
$112$	1.72812	+	2.37856i	0.163292	+	0.224753i
$113$	−15.9660	−	5.18768i	−1.50196	−	0.488016i	−0.561370	−	0.827565i	$-0.689725\pi$
$113$	−15.9660	−	5.18768i	−1.50196	−	0.488016i	−0.940588	+	0.339549i	$0.889725\pi$
$114$	8.13049	−	5.90715i	0.761490	−	0.553255i
$115$	−14.0448	+	2.97926i	−1.30969	+	0.277818i
$116$	0.631453	+	1.94341i	0.0586289	+	0.180441i
$117$	1.88950	+	0.613935i	0.174684	+	0.0567583i
$118$		−	9.38086i		−	0.863578i
$119$	−14.8637			−1.36255
$120$	1.41530	−	3.17529i	0.129199	−	0.289863i
$121$	−14.2439	−	10.3488i	−1.29490	−	0.940802i
$122$	−4.06349	−	5.59291i	−0.367891	−	0.506358i
$123$			11.5093i			1.03776i
$124$	4.52138	+	3.24917i	0.406032	+	0.291784i
$125$	10.6288	+	3.46808i	0.950673	+	0.310195i
$126$	−1.38643	+	1.00730i	−0.123513	+	0.0897375i
$127$	4.78506	−	6.58607i	0.424605	−	0.584419i	−0.542099	−	0.840315i	$-0.682370\pi$
$127$	4.78506	−	6.58607i	0.424605	−	0.584419i	0.966704	+	0.255895i	$0.0823702\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	5.73594			0.505022
$130$	−7.57943	−	0.799794i	−0.664760	−	0.0701466i
$131$	−0.688733	+	2.11970i	−0.0601749	+	0.185199i	−0.976625	−	0.214949i	$-0.931041\pi$
$131$	−0.688733	+	2.11970i	−0.0601749	+	0.185199i	0.916450	+	0.400148i	$0.131041\pi$
$132$	7.90837	−	2.56959i	0.688335	−	0.223654i
$133$	18.0748	−	5.87286i	1.56728	−	0.509241i
$134$	7.14717	−	5.19272i	0.617421	−	0.448583i
$135$	11.3767	+	5.07087i	0.979152	+	0.436431i
$136$	4.09005	−	2.97159i	0.350719	−	0.254812i
$137$	−9.57644	+	13.1808i	−0.818171	+	1.12612i	0.171840	+	0.985125i	$0.445029\pi$
$137$	−9.57644	+	13.1808i	−0.818171	+	1.12612i	−0.990011	+	0.140990i	$0.954971\pi$
$138$	9.49389	−	3.08475i	0.808174	−	0.262592i
$139$	−10.7169	−	7.78627i	−0.908994	−	0.660423i	0.0317661	−	0.999495i	$-0.489887\pi$
$139$	−10.7169	−	7.78627i	−0.908994	−	0.660423i	−0.940760	+	0.339072i	$0.889887\pi$
$140$	4.40100	−	4.88375i	0.371952	−	0.412752i
$141$	6.09862	+	18.7696i	0.513597	+	1.58069i
$142$	5.89078	−	8.10796i	0.494343	−	0.680405i
$143$	−10.7154	−	14.7484i	−0.896063	−	1.23333i
$144$	0.180122	−	0.554358i	0.0150102	−	0.0461965i
$145$	3.95802	−	2.28298i	0.328695	−	0.189591i
$146$	−1.04683	−	3.22181i	−0.0866361	−	0.266639i
$147$	2.43078	−	0.789809i	0.200487	−	0.0651423i
$148$	−0.337801	−	0.109758i	−0.0277670	−	0.00902206i
$149$	−21.1121			−1.72957			−0.864784	−	0.502144i	$-0.832545\pi$
$149$	−21.1121			−1.72957			−0.864784	+	0.502144i	$0.832545\pi$
$150$	−7.60233	−	1.62249i	−0.620727	−	0.132476i
$151$	−2.39010	+	7.35597i	−0.194504	+	0.598620i	0.805478	+	0.592625i	$0.201908\pi$
$151$	−2.39010	+	7.35597i	−0.194504	+	0.598620i	−0.999982	+	0.00599537i	$0.998092\pi$
$152$	−3.79953	+	5.22960i	−0.308182	+	0.424176i
$153$	1.73210	+	2.38403i	0.140032	+	0.192738i
$154$	15.7249			1.26715
$155$	5.00928	−	11.3977i	0.402355	−	0.915484i
$156$	5.29913			0.424270
$157$	−2.43353	−	3.34947i	−0.194217	−	0.267317i	0.700791	−	0.713366i	$-0.252830\pi$
$157$	−2.43353	−	3.34947i	−0.194217	−	0.267317i	−0.895008	+	0.446050i	$0.852830\pi$
$158$	−6.21755	+	8.55773i	−0.494642	+	0.680816i
$159$	0.00624142	−	0.0192091i	0.000494977	−	0.00152338i
$160$	−0.234651	+	2.22372i	−0.0185508	+	0.175801i
$161$	18.8776			1.48776
$162$	−6.57331	−	2.13580i	−0.516448	−	0.167804i
$163$	12.5207	−	4.06824i	0.980701	−	0.318649i	0.225573	−	0.974226i	$-0.427575\pi$
$163$	12.5207	−	4.06824i	0.980701	−	0.318649i	0.755128	+	0.655577i	$0.227575\pi$
$164$	−2.28761	−	7.04055i	−0.178633	−	0.549774i
$165$	−9.29020	−	16.1064i	−0.723241	−	1.25389i
$166$	2.76323	−	8.50435i	0.214468	−	0.660066i
$167$	−13.1925	−	18.1580i	−1.02087	−	1.40511i	−0.911592	−	0.411096i	$-0.865146\pi$
$167$	−13.1925	−	18.1580i	−1.02087	−	1.40511i	−0.109278	−	0.994011i	$-0.534854\pi$
$168$	−2.68673	+	3.69796i	−0.207285	+	0.285304i
$169$	0.427225	+	1.31486i	0.0328635	+	0.101143i
$170$	−8.39784	−	7.56773i	−0.644085	−	0.580418i
$171$	−3.04826	−	2.21469i	−0.233106	−	0.169362i
$172$	−3.50883	+	1.14009i	−0.267546	+	0.0869310i
$173$	−6.66402	+	9.17224i	−0.506656	+	0.697353i	−0.983351	−	0.181716i	$-0.941835\pi$
$173$	−6.66402	+	9.17224i	−0.506656	+	0.697353i	0.476695	+	0.879069i	$0.341835\pi$
$174$	−2.57019	+	1.86735i	−0.194845	+	0.141563i
$175$	−12.7248	−	7.36066i	−0.961902	−	0.556414i
$176$	−4.32703	+	3.14377i	−0.326162	+	0.236971i
$177$	13.8707	−	4.50685i	1.04258	−	0.338756i
$178$	8.76096	−	2.84661i	0.656662	−	0.213362i
$179$	2.79983	−	8.61700i	0.209269	−	0.644065i	−0.790242	−	0.612795i	$-0.790045\pi$
$179$	2.79983	−	8.61700i	0.209269	−	0.644065i	0.999511	−	0.0312694i	$-0.00995498\pi$
$180$	−1.29618	−	0.136775i	−0.0966114	−	0.0101946i
$181$	−10.3658			−0.770487			−0.385243	−	0.922815i	$-0.625882\pi$
$181$	−10.3658			−0.770487			−0.385243	+	0.922815i	$0.625882\pi$
$182$	9.53056	+	3.09667i	0.706452	+	0.229540i
$183$	6.31753	−	8.69533i	0.467005	−	0.642778i
$184$	−5.19454	+	3.77405i	−0.382947	+	0.278227i
$185$	−0.0833444	+	0.789831i	−0.00612760	+	0.0580696i
$186$	−2.63205	+	8.24638i	−0.192991	+	0.604654i
$187$		−	27.0398i		−	1.97734i
$188$	−7.46139	−	10.2697i	−0.544177	−	0.748996i
$189$	−13.2494	−	9.62624i	−0.963751	−	0.700206i
$190$	13.2022	+	5.88453i	0.957788	+	0.426908i
$191$	18.5318			1.34092			0.670458	−	0.741948i	$-0.266098\pi$
$191$	18.5318			1.34092			0.670458	+	0.741948i	$0.266098\pi$
$192$		−	1.55471i		−	0.112201i
$193$	5.63993	+	1.83252i	0.405971	+	0.131908i	0.504882	−	0.863188i	$-0.331536\pi$
$193$	5.63993	+	1.83252i	0.405971	+	0.131908i	−0.0989110	+	0.995096i	$0.531536\pi$
$194$	−0.729803	−	2.24610i	−0.0523968	−	0.161261i
$195$	−2.45880	−	11.5913i	−0.176079	−	0.830070i
$196$	−1.32999	+	0.966295i	−0.0949994	+	0.0690211i
$197$	−0.129723	−	0.0421496i	−0.00924238	−	0.00300303i	0.304392	−	0.952547i	$-0.401547\pi$
$197$	−0.129723	−	0.0421496i	−0.00924238	−	0.00300303i	−0.313635	+	0.949544i	$0.601547\pi$
$198$	−1.83246	−	2.52217i	−0.130227	−	0.179243i
$199$	−2.39975	−	1.74352i	−0.170114	−	0.123595i	0.499471	−	0.866331i	$-0.333528\pi$
$199$	−2.39975	−	1.74352i	−0.170114	−	0.123595i	−0.669584	+	0.742736i	$0.733528\pi$
$200$	4.97304	−	0.518536i	0.351647	−	0.0366660i
$201$	11.1118	+	8.07316i	0.783763	+	0.569437i
$202$	−5.39784	+	7.42949i	−0.379791	+	0.522737i
$203$	−5.71375	+	1.85651i	−0.401026	+	0.130301i
$204$	6.35882	+	4.61996i	0.445207	+	0.323462i
$205$	−14.3390	+	8.27074i	−1.00148	+	0.577653i
$206$	−0.268615	+	0.826711i	−0.0187153	+	0.0575997i
$207$	−2.19984	−	3.02783i	−0.152900	−	0.210449i
$208$	−3.24162	+	1.05327i	−0.224766	+	0.0730309i
$209$	10.6838	+	32.8813i	0.739013	+	2.27445i
$210$	9.33556	+	4.16108i	0.644215	+	0.287142i
$211$	−9.09369			−0.626035			−0.313018	−	0.949747i	$-0.601340\pi$
$211$	−9.09369			−0.626035			−0.313018	+	0.949747i	$0.601340\pi$
$212$			0.0129913i			0.000892246i
$213$	14.8187	+	4.81487i	1.01536	+	0.329910i
$214$	−12.0184	−	8.73187i	−0.821560	−	0.596898i
$215$	4.12193	+	7.14620i	0.281113	+	0.487367i
$216$	5.57034			0.379014
$217$	−9.55275	+	13.2931i	−0.648483	+	0.902398i
$218$		−	6.14700i		−	0.416328i
$219$	4.26088	−	3.09571i	0.287924	−	0.209189i
$220$	8.88442	+	8.00621i	0.598988	+	0.539779i
$221$	5.32487	−	16.3883i	0.358189	−	1.10239i
$222$		−	0.552208i		−	0.0370618i
$223$		−	4.83197i		−	0.323573i	−0.986826	−	0.161786i	$-0.948274\pi$
$223$		−	4.83197i		−	0.323573i	0.986826	−	0.161786i	$-0.0517256\pi$
$224$	0.908529	−	2.79616i	0.0607036	−	0.186827i
$225$	0.302248	+	2.89872i	0.0201498	+	0.193248i
$226$	5.18768	+	15.9660i	0.345079	+	1.06204i
$227$	−1.30664	−	1.79844i	−0.0867250	−	0.119367i	0.763450	−	0.645867i	$-0.223504\pi$
$227$	−1.30664	−	1.79844i	−0.0867250	−	0.119367i	−0.850175	+	0.526500i	$0.823504\pi$
$228$	−9.55797	−	3.10557i	−0.632992	−	0.205672i
$229$	−16.4789	+	11.9726i	−1.08896	+	0.791173i	−0.979223	−	0.202788i	$-0.935000\pi$
$229$	−16.4789	+	11.9726i	−1.08896	+	0.791173i	−0.109733	+	0.993961i	$0.535000\pi$
$230$	10.6656	+	9.61135i	0.703271	+	0.633754i
$231$	7.55474	+	23.2511i	0.497065	+	1.52981i
$232$	1.20109	−	1.65316i	0.0788557	−	0.108536i
$233$	7.45074	−	10.2551i	0.488114	−	0.671831i	−0.491925	−	0.870638i	$-0.663706\pi$
$233$	7.45074	−	10.2551i	0.488114	−	0.671831i	0.980039	+	0.198806i	$0.0637065\pi$
$234$	−0.613935	−	1.88950i	−0.0401342	−	0.123520i
$235$	−19.0018	+	21.0862i	−1.23954	+	1.37551i
$236$	−7.58927	+	5.51393i	−0.494020	+	0.358926i
$237$	−15.6407	−	5.08197i	−1.01597	−	0.330109i
$238$	8.73667	+	12.0250i	0.566314	+	0.779464i
$239$	−0.0999939	−	0.307750i	−0.00646807	−	0.0199067i	0.947770	−	0.318953i	$-0.103331\pi$
$239$	−0.0999939	−	0.307750i	−0.00646807	−	0.0199067i	−0.954238	+	0.299047i	$0.903331\pi$
$240$	−3.40076	+	0.721386i	−0.219518	+	0.0465653i
$241$	0.552133	−	1.69929i	0.0355660	−	0.109461i	−0.931697	−	0.363235i	$-0.881672\pi$
$241$	0.552133	−	1.69929i	0.0355660	−	0.109461i	0.967263	+	0.253774i	$0.0816721\pi$
$242$			17.6065i			1.13179i
$243$			5.96553i			0.382689i
$244$	−2.13630	+	6.57486i	−0.136763	+	0.420912i
$245$	2.73079	+	2.46085i	0.174464	+	0.157218i
$246$	9.31121	−	6.76499i	0.593661	−	0.431320i
$247$			22.0326i			1.40190i
$248$	−0.0289725	−	5.56769i	−0.00183975	−	0.353549i
$249$	13.9022			0.881016
$250$	−3.44174	−	10.6374i	−0.217675	−	0.672769i
$251$	2.52091	+	1.83155i	0.159118	+	0.115606i	0.664495	−	0.747292i	$-0.268647\pi$
$251$	2.52091	+	1.83155i	0.159118	+	0.115606i	−0.505377	+	0.862899i	$0.668647\pi$
$252$	1.62985	+	0.529569i	0.102671	+	0.0333597i
$253$			34.3417i			2.15904i
$254$	−8.14083			−0.510801
$255$	7.15517	−	16.0529i	0.448074	−	1.00527i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.48703	+	0.483166i	−0.0927586	+	0.0301391i	−0.355029	−	0.934855i	$-0.615529\pi$
$257$	−1.48703	+	0.483166i	−0.0927586	+	0.0301391i	0.262270	+	0.964995i	$0.415529\pi$
$258$	−3.37150	−	4.64048i	−0.209901	−	0.288903i
$259$	0.322695	−	0.993154i	0.0200513	−	0.0617116i
$260$	3.80803	+	6.60199i	0.236164	+	0.409438i
$261$	0.963607	+	0.700102i	0.0596458	+	0.0433352i
$262$	2.11970	−	0.688733i	0.130956	−	0.0425501i
$263$	1.49385	−	2.05611i	0.0921150	−	0.126785i	−0.760472	−	0.649371i	$-0.775032\pi$
$263$	1.49385	−	2.05611i	0.0921150	−	0.126785i	0.852587	+	0.522585i	$0.175032\pi$
$264$	−6.72726	−	4.88764i	−0.414034	−	0.300814i
$265$	0.0284171	−	0.00602798i	0.00174565	−	0.000370296i
$266$	−15.3753	−	11.1708i	−0.942723	−	0.684928i
$267$	8.41807	+	11.5865i	0.515178	+	0.709081i
$268$	−8.40200	−	2.72998i	−0.513234	−	0.166760i
$269$	−4.75866	+	3.45737i	−0.290141	+	0.210799i	−0.723328	−	0.690504i	$-0.757389\pi$
$269$	−4.75866	+	3.45737i	−0.290141	+	0.210799i	0.433188	+	0.901304i	$0.357389\pi$
$270$	−2.58465	−	12.1845i	−0.157297	−	0.741527i
$271$	−2.15810	−	6.64195i	−0.131095	−	0.403470i	0.863867	−	0.503720i	$-0.168036\pi$
$271$	−2.15810	−	6.64195i	−0.131095	−	0.403470i	−0.994962	+	0.100250i	$0.968036\pi$
$272$	−4.80814	−	1.56226i	−0.291536	−	0.0947259i
$273$			15.5798i			0.942930i
$274$	16.2924			0.984261
$275$	13.3904	−	23.1486i	0.807470	−	1.39592i
$276$	−8.07599	−	5.86755i	−0.486117	−	0.353185i
$277$	−16.2619	−	22.3826i	−0.977082	−	1.34484i	−0.938387	−	0.345587i	$-0.887680\pi$
$277$	−16.2619	−	22.3826i	−0.977082	−	1.34484i	−0.0386953	−	0.999251i	$-0.512320\pi$
$278$			13.2468i			0.794490i
$279$	3.24533	−	0.0168877i	0.194293	−	0.00101104i
$280$	−6.53788	−	0.689888i	−0.390713	−	0.0412287i
$281$	7.42619	−	5.39544i	0.443009	−	0.321865i	−0.343820	−	0.939035i	$-0.611721\pi$
$281$	7.42619	−	5.39544i	0.443009	−	0.321865i	0.786829	+	0.617171i	$0.211721\pi$
$282$	11.6003	−	15.9664i	0.690786	−	0.950785i
$283$	11.8133	+	3.83837i	0.702226	+	0.228167i	0.638300	−	0.769787i	$-0.279638\pi$
$283$	11.8133	+	3.83837i	0.702226	+	0.228167i	0.0639260	+	0.997955i	$0.479638\pi$
$284$	−10.0220			−0.594696
$285$	−2.35820	+	22.3481i	−0.139688	+	1.32378i
$286$	−5.63340	+	17.3378i	−0.333110	+	1.02521i
$287$	20.6996	−	6.72572i	1.22186	−	0.397007i
$288$	−0.554358	+	0.180122i	−0.0326659	+	0.0106138i
$289$	6.92426	−	5.03077i	0.407309	−	0.295928i
$290$	−4.17343	−	1.86020i	−0.245073	−	0.109235i
$291$	2.97050	−	2.15819i	0.174134	−	0.126516i
$292$	−1.99119	+	2.74063i	−0.116525	+	0.160383i
$293$	−13.5113	+	4.39009i	−0.789339	+	0.256472i	−0.675822	−	0.737064i	$-0.736211\pi$
$293$	−13.5113	+	4.39009i	−0.789339	+	0.256472i	−0.113516	+	0.993536i	$0.536211\pi$
$294$	−2.06775	−	1.50231i	−0.120593	−	0.0876162i
$295$	15.5826	+	14.0423i	0.907253	+	0.817573i
$296$	0.109758	+	0.337801i	0.00637956	+	0.0196343i
$297$	17.5119	−	24.1030i	1.01614	−	1.39860i
$298$	12.4094	+	17.0800i	0.718855	+	0.989419i
$299$	−6.76282	+	20.8138i	−0.391104	+	1.20369i
$300$	3.15592	+	7.10409i	0.182207	+	0.410155i
$301$	−3.35193	−	10.3162i	−0.193202	−	0.594615i
$302$	7.35597	−	2.39010i	0.423289	−	0.137535i
$303$	−13.5786	−	4.41197i	−0.780072	−	0.253461i
$304$	6.46414			0.370744
$305$	15.3731	+	1.62219i	0.880259	+	0.0928865i
$306$	0.910620	−	2.80260i	0.0520567	−	0.160214i
$307$	1.01439	−	1.39618i	0.0578942	−	0.0796845i	−0.779088	−	0.626914i	$-0.784318\pi$
$307$	1.01439	−	1.39618i	0.0578942	−	0.0796845i	0.836982	+	0.547230i	$0.184318\pi$
$308$	−9.24288	−	12.7217i	−0.526662	−	0.724888i
$309$	−1.35144			−0.0768805
$310$	−12.1653	+	2.64679i	−0.690943	+	0.150328i
$311$	−20.4188			−1.15784			−0.578922	−	0.815383i	$-0.696526\pi$
$311$	−20.4188			−1.15784			−0.578922	+	0.815383i	$0.696526\pi$
$312$	−3.11475	−	4.28708i	−0.176338	−	0.242708i
$313$	12.4946	−	17.1974i	0.706238	−	0.972053i	−0.293632	−	0.955919i	$-0.594864\pi$
$313$	12.4946	−	17.1974i	0.706238	−	0.972053i	0.999870	−	0.0161344i	$-0.00513596\pi$
$314$	−1.27938	+	3.93754i	−0.0721998	+	0.222208i
$315$	0.402126	−	3.81084i	0.0226573	−	0.214717i
$316$	10.5779			0.595055
$317$	21.0684	+	6.84555i	1.18332	+	0.384484i	0.833599	−	0.552369i	$-0.186276\pi$
$317$	21.0684	+	6.84555i	1.18332	+	0.384484i	0.349722	+	0.936854i	$0.386276\pi$
$318$	−0.0192091	+	0.00624142i	−0.00107719	+	0.000350001i
$319$	−3.37733	−	10.3943i	−0.189094	−	0.581971i
$320$	1.93695	−	1.11723i	0.108279	−	0.0624553i
$321$	7.13706	−	21.9656i	0.398352	−	1.22600i
$322$	−11.0959	−	15.2723i	−0.618353	−	0.851090i
$323$	−19.2088	+	26.4386i	−1.06881	+	1.47109i
$324$	2.13580	+	6.57331i	0.118655	+	0.365184i
$325$	12.6742	−	11.3930i	0.703040	−	0.631970i
$326$	−10.6508	−	7.73825i	−0.589892	−	0.428582i
$327$	9.08904	−	2.95321i	0.502625	−	0.163313i
$328$	−4.35130	+	5.98905i	−0.240260	+	0.330690i
$329$	30.1936	−	21.9369i	1.66463	−	1.20942i
$330$	−7.56975	+	16.9831i	−0.416701	+	0.934887i
$331$	9.31710	−	6.76927i	0.512114	−	0.372073i	−0.301511	−	0.953463i	$-0.597491\pi$
$331$	9.31710	−	6.76927i	0.512114	−	0.372073i	0.813625	+	0.581390i	$0.197491\pi$
$332$	−8.50435	+	2.76323i	−0.466737	+	0.151652i
$333$	−0.196899	+	0.0639765i	−0.0107900	+	0.00350589i
$334$	−6.93573	+	21.3460i	−0.379506	+	1.16800i
$335$	−2.07300	+	19.6452i	−0.113260	+	1.07333i
$336$	4.57093			0.249365
$337$	−14.8607	−	4.82852i	−0.809511	−	0.263026i	−0.125121	−	0.992142i	$-0.539932\pi$
$337$	−14.8607	−	4.82852i	−0.809511	−	0.263026i	−0.684391	+	0.729115i	$0.739932\pi$
$338$	0.812630	−	1.11849i	0.0442012	−	0.0608378i
$339$	−21.1153	+	15.3411i	−1.14682	+	0.833217i
$340$	−1.18630	+	11.2422i	−0.0643359	+	0.609694i
$341$	−24.1826	−	17.3782i	−1.30956	−	0.941081i
$342$			3.76786i			0.203743i
$343$	9.25591	+	12.7397i	0.499772	+	0.687877i
$344$	2.98479	+	2.16858i	0.160929	+	0.116922i
$345$	−9.08738	+	20.3879i	−0.489248	+	1.09765i
$346$	11.3375			0.609508
$347$		−	18.9925i		−	1.01957i	−0.860301	−	0.509786i	$-0.829724\pi$
$347$		−	18.9925i		−	1.01957i	0.860301	−	0.509786i	$-0.170276\pi$
$348$	3.02143	+	0.981724i	0.161966	+	0.0526259i
$349$	−3.15305	−	9.70410i	−0.168779	−	0.519449i	0.830516	−	0.556995i	$-0.188046\pi$
$349$	−3.15305	−	9.70410i	−0.168779	−	0.519449i	−0.999295	+	0.0375465i	$0.988046\pi$
$350$	1.52453	+	14.6210i	0.0814894	+	0.781527i
$351$	15.3601	−	11.1598i	0.819863	−	0.595666i
$352$	5.08673	+	1.65278i	0.271124	+	0.0880934i
$353$	−0.581176	−	0.799921i	−0.0309329	−	0.0425755i	0.793270	−	0.608869i	$-0.208377\pi$
$353$	−0.581176	−	0.799921i	−0.0309329	−	0.0425755i	−0.824203	+	0.566294i	$0.808377\pi$
$354$	−11.7991	−	8.57255i	−0.627115	−	0.455626i
$355$	4.65022	+	21.9221i	0.246808	+	1.16350i
$356$	−7.45252	−	5.41457i	−0.394983	−	0.286972i
$357$	−13.5830	+	18.6953i	−0.718886	+	0.989462i
$358$	−8.61700	+	2.79983i	−0.455422	+	0.147976i
$359$	2.68385	+	1.94993i	0.141648	+	0.102913i	0.656353	−	0.754454i	$-0.272098\pi$
$359$	2.68385	+	1.94993i	0.141648	+	0.102913i	−0.514704	+	0.857368i	$0.672098\pi$
$360$	0.651221	+	1.12902i	0.0343223	+	0.0595048i
$361$	7.04098	−	21.6699i	0.370578	−	1.14052i
$362$	6.09289	+	8.38614i	0.320235	+	0.440766i
$363$	−26.0332	+	8.45869i	−1.36639	+	0.443966i
$364$	−3.09667	−	9.53056i	−0.162309	−	0.499537i
$365$	6.91876	+	3.08386i	0.362145	+	0.161416i
$366$	−10.7480			−0.561808
$367$		−	6.80095i		−	0.355006i	−0.984120	−	0.177503i	$-0.943198\pi$
$367$		−	6.80095i		−	0.355006i	0.984120	−	0.177503i	$-0.0568020\pi$
$368$	6.10655	+	1.98414i	0.318326	+	0.103430i
$369$	−3.49093	−	2.53631i	−0.181731	−	0.132035i
$370$	0.687976	−	0.396824i	0.0357662	−	0.0206299i
$371$	−0.0381952			−0.00198300
$372$	8.21854	−	2.71773i	0.426112	−	0.140908i
$373$		−	3.31546i		−	0.171668i	−0.996309	−	0.0858339i	$-0.972645\pi$
$373$		−	3.31546i		−	0.171668i	0.996309	−	0.0858339i	$-0.0273554\pi$
$374$	−21.8756	+	15.8936i	−1.13116	+	0.821837i
$375$	14.0751	−	10.1995i	0.726835	−	0.526702i
$376$	−3.92268	+	12.0728i	−0.202297	+	0.622606i
$377$		−	6.96489i		−	0.358710i
$378$			16.3771i			0.842349i
$379$	−1.51574	+	4.66497i	−0.0778583	+	0.239623i	−0.982409	−	0.186743i	$-0.940207\pi$
$379$	−1.51574	+	4.66497i	−0.0778583	+	0.239623i	0.904550	+	0.426367i	$0.140207\pi$
$380$	−2.99937	−	14.1396i	−0.153864	−	0.725348i
$381$	−3.91111	−	12.0371i	−0.200372	−	0.616682i
$382$	−10.8927	−	14.9926i	−0.557321	−	0.767086i
$383$	33.8784	+	11.0078i	1.73111	+	0.562470i	0.993609	−	0.112880i	$-0.0360077\pi$
$383$	33.8784	+	11.0078i	1.73111	+	0.562470i	0.737497	+	0.675351i	$0.236008\pi$
$384$	−1.25778	+	0.913834i	−0.0641860	+	0.0466339i
$385$	−23.5388	+	26.1207i	−1.19965	+	1.33124i
$386$	−1.83252	−	5.63993i	−0.0932731	−	0.287065i
$387$	−1.26403	+	1.73979i	−0.0642545	+	0.0884387i
$388$	−1.38817	+	1.91065i	−0.0704735	+	0.0969985i
$389$	2.60954	+	8.03133i	0.132309	+	0.407204i	0.995162	−	0.0982506i	$-0.0313247\pi$
$389$	2.60954	+	8.03133i	0.132309	+	0.407204i	−0.862853	+	0.505455i	$0.831325\pi$
$390$	−7.93230	+	8.80240i	−0.401668	+	0.445727i
$391$	−26.2614	+	19.0800i	−1.32810	+	0.964918i
$392$	1.56350	+	0.508011i	0.0789686	+	0.0256584i
$393$	2.03674	+	2.80333i	0.102740	+	0.141409i
$394$	0.0421496	+	0.129723i	0.00212346	+	0.00653535i
$395$	−4.90818	−	23.1381i	−0.246957	−	1.16421i
$396$	−0.963382	+	2.96498i	−0.0484118	+	0.148996i
$397$		−	24.8554i		−	1.24746i	−0.781641	−	0.623728i	$-0.785617\pi$
$397$		−	24.8554i		−	1.24746i	0.781641	−	0.623728i	$-0.214383\pi$
$398$			2.96625i			0.148685i
$399$	9.13057	−	28.1010i	0.457100	−	1.40681i
$400$	−3.34258	−	3.71849i	−0.167129	−	0.185924i
$401$	−16.7097	+	12.1403i	−0.834443	+	0.606258i	−0.920813	−	0.390005i	$-0.872473\pi$
$401$	−16.7097	+	12.1403i	−0.834443	+	0.606258i	0.0863698	+	0.996263i	$0.472473\pi$
$402$		−	13.7349i		−	0.685034i
$403$	−11.2344	−	15.2948i	−0.559624	−	0.761887i
$404$	9.18336			0.456889
$405$	13.3874	−	7.72186i	0.665226	−	0.383702i
$406$	4.86040	+	3.53129i	0.241218	+	0.175255i
$407$	1.80673	+	0.587041i	0.0895561	+	0.0290985i
$408$		−	7.85994i		−	0.389125i
$409$	26.0254			1.28687			0.643436	−	0.765500i	$-0.277508\pi$
$409$	26.0254			1.28687			0.643436	+	0.765500i	$0.277508\pi$
$410$	15.1194	+	6.73908i	0.746695	+	0.332820i
$411$	7.82738	+	24.0902i	0.386096	+	1.18828i
$412$	0.826711	−	0.268615i	0.0407291	−	0.0132337i
$413$	−16.2113	−	22.3129i	−0.797706	−	1.09795i
$414$	−1.15653	+	3.55942i	−0.0568402	+	0.174936i
$415$	9.99031	+	17.3202i	0.490405	+	0.850217i
$416$	2.75749	+	2.00343i	0.135197	+	0.0982263i
$417$	−19.5869	+	6.36417i	−0.959175	+	0.311655i
$418$	20.3218	−	27.9705i	0.993970	−	1.36808i
$419$	27.6167	+	20.0647i	1.34917	+	0.980227i	0.999053	+	0.0435193i	$0.0138570\pi$
$419$	27.6167	+	20.0647i	1.34917	+	0.980227i	0.350114	+	0.936707i	$0.386143\pi$
$420$	−2.12092	−	9.99844i	−0.103490	−	0.487874i
$421$	−15.6793	−	11.3917i	−0.764161	−	0.555196i	0.136023	−	0.990706i	$-0.456568\pi$
$421$	−15.6793	−	11.3917i	−0.764161	−	0.555196i	−0.900184	+	0.435510i	$0.856568\pi$
$422$	5.34514	+	7.35695i	0.260197	+	0.358131i
$423$	−7.03706	−	2.28648i	−0.342153	−	0.111172i
$424$	0.0105102	−	0.00763609i	0.000510419	−	0.000370841i
$425$	25.1416	−	2.62150i	1.21955	−	0.127161i
$426$	−4.81487	−	14.8187i	−0.233281	−	0.717966i
$427$	−19.3305	−	6.28086i	−0.935468	−	0.303952i
$428$			14.8555i			0.718069i
$429$	−28.3424			−1.36838
$430$	3.35859	−	7.53514i	0.161966	−	0.363377i
$431$	19.7299	+	14.3346i	0.950356	+	0.690474i	0.950891	−	0.309526i	$-0.100170\pi$
$431$	19.7299	+	14.3346i	0.950356	+	0.690474i	−0.000534778		1.00000i	$0.500170\pi$
$432$	−3.27416	−	4.50650i	−0.157528	−	0.216819i
$433$		−	25.3442i		−	1.21797i	−0.793183	−	0.608983i	$-0.791578\pi$
$433$		−	25.3442i		−	1.21797i	0.793183	−	0.608983i	$-0.208422\pi$
$434$	16.3693	−	0.0851808i	0.785754	−	0.00408881i
$435$	0.745468	−	7.06460i	0.0357425	−	0.338721i
$436$	−4.97303	+	3.61312i	−0.238165	+	0.173037i
$437$	24.3960	−	33.5782i	1.16702	−	1.60626i
$438$	−5.00897	−	1.62751i	−0.239338	−	0.0777655i
$439$	4.40648			0.210310			0.105155	−	0.994456i	$-0.466466\pi$
$439$	4.40648			0.210310			0.105155	+	0.994456i	$0.466466\pi$
$440$	1.25503	−	11.8936i	0.0598313	−	0.567004i
$441$	−0.296113	+	0.911342i	−0.0141006	+	0.0433972i
$442$	−16.3883	+	5.32487i	−0.779510	+	0.253278i
$443$	−19.0058	+	6.17535i	−0.902991	+	0.293400i	−0.723471	−	0.690355i	$-0.757454\pi$
$443$	−19.0058	+	6.17535i	−0.902991	+	0.293400i	−0.179520	+	0.983754i	$0.557454\pi$
$444$	−0.446745	+	0.324580i	−0.0212016	+	0.0154039i
$445$	−8.38583	+	18.8140i	−0.397527	+	0.891868i
$446$	−3.90915	+	2.84016i	−0.185104	+	0.134486i
$447$	−19.2929	+	26.5544i	−0.912524	+	1.25598i
$448$	−2.79616	+	0.908529i	−0.132106	+	0.0429240i
$449$	−13.7206	−	9.96857i	−0.647513	−	0.470446i	0.214910	−	0.976634i	$-0.431054\pi$
$449$	−13.7206	−	9.96857i	−0.647513	−	0.470446i	−0.862423	+	0.506188i	$0.831054\pi$
$450$	2.16746	−	1.94835i	0.102175	−	0.0918459i
$451$	12.2353	+	37.6564i	0.576138	+	1.77317i
$452$	9.86755	−	13.5815i	0.464131	−	0.638821i
$453$	7.06807	+	9.72836i	0.332087	+	0.457078i
$454$	−0.686943	+	2.11419i	−0.0322398	+	0.0992240i
$455$	−19.4103	+	11.1958i	−0.909967	+	0.524869i
$456$	3.10557	+	9.55797i	0.145432	+	0.447593i
$457$	8.60981	−	2.79750i	0.402750	−	0.130861i	−0.100636	−	0.994923i	$-0.532088\pi$
$457$	8.60981	−	2.79750i	0.402750	−	0.130861i	0.503385	+	0.864062i	$0.332088\pi$
$458$	19.3721	+	6.29438i	0.905199	+	0.294117i
$459$	28.1613			1.31446
$460$	1.50665	−	14.2781i	0.0702478	−	0.665719i
$461$	−7.64604	+	23.5321i	−0.356112	+	1.09600i	0.599250	+	0.800562i	$0.295465\pi$
$461$	−7.64604	+	23.5321i	−0.356112	+	1.09600i	−0.955362	+	0.295438i	$0.904535\pi$
$462$	14.3700	−	19.7786i	0.668551	−	0.920182i
$463$	−12.0003	−	16.5170i	−0.557700	−	0.767608i	0.433332	−	0.901234i	$-0.357338\pi$
$463$	−12.0003	−	16.5170i	−0.557700	−	0.767608i	−0.991032	+	0.133626i	$0.957338\pi$
$464$	−2.04342			−0.0948635
$465$	−9.75817	−	16.7162i	−0.452524	−	0.775194i
$466$	−12.6760			−0.587202
$467$	−13.4114	−	18.4592i	−0.620606	−	0.854191i	0.376791	−	0.926298i	$-0.377028\pi$
$467$	−13.4114	−	18.4592i	−0.620606	−	0.854191i	−0.997397	+	0.0721073i	$0.977028\pi$
$468$	−1.16777	+	1.60730i	−0.0539803	+	0.0742976i
$469$	8.02630	−	24.7024i	0.370620	−	1.14065i
$470$	28.2281	+	2.97867i	1.30206	+	0.137396i
$471$	−6.43676			−0.296590
$472$	8.92173	+	2.89884i	0.410656	+	0.133430i
$473$	18.7670	−	6.09777i	0.862907	−	0.280376i
$474$	5.08197	+	15.6407i	0.233422	+	0.718400i
$475$	−29.5373	+	13.1216i	−1.35526	+	0.602061i
$476$	4.59314	−	14.1362i	0.210526	−	0.647933i
$477$	0.00445098	+	0.00612624i	0.000203796	+	0.000280501i
$478$	−0.190200	+	0.261787i	−0.00869953	+	0.0119739i
$479$	−6.09166	−	18.7482i	−0.278335	−	0.856628i	−0.988318	−	0.152408i	$-0.951297\pi$
$479$	−6.09166	−	18.7482i	−0.278335	−	0.856628i	0.709982	−	0.704219i	$-0.248703\pi$
$480$	2.58253	+	2.32725i	0.117876	+	0.106224i
$481$	0.979417	+	0.711588i	0.0446575	+	0.0324456i
$482$	−1.69929	+	0.552133i	−0.0774005	+	0.0251490i
$483$	17.2509	−	23.7439i	0.784945	−	1.08038i
$484$	14.2439	−	10.3488i	0.647452	−	0.470401i
$485$	4.82346	+	2.14993i	0.219022	+	0.0976232i
$486$	4.82621	−	3.50645i	0.218921	−	0.159056i
$487$	10.1598	−	3.30113i	0.460387	−	0.149589i	−0.0696355	−	0.997572i	$-0.522184\pi$
$487$	10.1598	−	3.30113i	0.460387	−	0.149589i	0.530022	+	0.847984i	$0.322184\pi$
$488$	6.57486	−	2.13630i	0.297630	−	0.0967058i
$489$	6.32492	−	19.4661i	0.286023	−	0.880287i
$490$	0.385757	−	3.65571i	0.0174267	−	0.165148i
$491$	1.00598			0.0453993			0.0226997	−	0.999742i	$-0.492774\pi$
$491$	1.00598			0.0453993			0.0226997	+	0.999742i	$0.492774\pi$
$492$	−10.9460	−	3.55657i	−0.493483	−	0.160342i
$493$	6.07222	−	8.35770i	0.273479	−	0.376412i
$494$	17.8248	−	12.9505i	0.801975	−	0.582669i
$495$	6.93261	+	0.731541i	0.311598	+	0.0328803i
$496$	−4.48733	+	3.29604i	−0.201487	+	0.147997i
$497$		−	29.4653i		−	1.32170i
$498$	−8.17150	−	11.2471i	−0.366174	−	0.503995i
$499$	3.64812	+	2.65052i	0.163312	+	0.118653i	0.666440	−	0.745559i	$-0.267817\pi$
$499$	3.64812	+	2.65052i	0.163312	+	0.118653i	−0.503127	+	0.864212i	$0.667817\pi$
$500$	−6.58284	+	9.03694i	−0.294393	+	0.404144i
$501$	−34.8946			−1.55898
$502$		−	3.11601i		−	0.139075i
$503$	−10.2019	−	3.31480i	−0.454880	−	0.147800i	0.0726103	−	0.997360i	$-0.476867\pi$
$503$	−10.2019	−	3.31480i	−0.454880	−	0.147800i	−0.527491	+	0.849561i	$0.676867\pi$
$504$	−0.529569	−	1.62985i	−0.0235889	−	0.0725991i
$505$	−4.26109	−	20.0876i	−0.189616	−	0.893888i
$506$	27.7830	−	20.1855i	1.23511	−	0.897356i
$507$	2.04423	+	0.664209i	0.0907873	+	0.0294986i
$508$	4.78506	+	6.58607i	0.212303	+	0.292210i
$509$	−14.2288	−	10.3378i	−0.630679	−	0.458215i	0.225957	−	0.974137i	$-0.427449\pi$
$509$	−14.2288	−	10.3378i	−0.630679	−	0.458215i	−0.856635	+	0.515923i	$0.827449\pi$
$510$	−17.1928	+	3.64702i	−0.761310	+	0.161493i
$511$	−8.05763	−	5.85421i	−0.356448	−	0.258975i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−34.2451	+	11.1269i	−1.51196	+	0.491265i
$514$	1.26495	+	0.919037i	0.0557944	+	0.0405370i
$515$	−0.971162	−	1.68371i	−0.0427945	−	0.0741930i
$516$	−1.77250	+	5.45521i	−0.0780301	+	0.240152i
$517$	39.9072	+	54.9276i	1.75512	+	2.41571i
$518$	−0.993154	+	0.322695i	−0.0436367	+	0.0141784i
$519$	5.44689	+	16.7638i	0.239092	+	0.735849i
$520$	3.10282	−	6.96131i	0.136068	−	0.305274i
$521$	40.3070			1.76588			0.882941	−	0.469484i	$-0.155560\pi$
$521$	40.3070			1.76588			0.882941	+	0.469484i	$0.155560\pi$
$522$		−	1.19108i		−	0.0521323i
$523$	27.2127	+	8.84195i	1.18993	+	0.386632i	0.836047	−	0.548658i	$-0.184861\pi$
$523$	27.2127	+	8.84195i	1.18993	+	0.386632i	0.353883	+	0.935290i	$0.384861\pi$
$524$	−1.80313	−	1.31005i	−0.0787700	−	0.0572297i
$525$	−20.8864	+	9.27859i	−0.911559	+	0.404951i
$526$	−2.54150			−0.110815
$527$	−0.146472	−	28.1479i	−0.00638044	−	1.22614i
$528$			8.31535i			0.361879i
$529$	14.7457	−	10.7134i	0.641118	−	0.465800i
$530$	−0.0215799	−	0.0194468i	−0.000937371	−	0.000844714i
$531$	−1.68970	+	5.20035i	−0.0733266	+	0.225676i
$532$			19.0050i			0.823970i
$533$			25.2322i			1.09293i
$534$	4.42564	−	13.6207i	0.191516	−	0.589427i
$535$	32.4949	−	6.89299i	1.40488	−	0.298010i
$536$	2.72998	+	8.40200i	0.117917	+	0.362911i
$537$	−8.27974	−	11.3961i	−0.357297	−	0.491778i
$538$	5.59414	+	1.81765i	0.241180	+	0.0783643i
$539$	7.11346	−	5.16823i	0.306398	−	0.222611i
$540$	−8.33828	+	9.25291i	−0.358822	+	0.398182i
$541$	−10.4608	−	32.1951i	−0.449745	−	1.38417i	−0.877195	−	0.480134i	$-0.840588\pi$
$541$	−10.4608	−	32.1951i	−0.449745	−	1.38417i	0.427450	−	0.904039i	$-0.359412\pi$
$542$	−4.10495	+	5.64998i	−0.176323	+	0.242687i
$543$	−9.47265	+	13.0380i	−0.406510	+	0.559514i
$544$	1.56226	+	4.80814i	0.0669813	+	0.206147i
$545$	10.2108	+	9.20149i	0.437383	+	0.394149i
$546$	12.6043	−	9.15755i	0.539414	−	0.391907i
$547$	−0.0250160	−	0.00812819i	−0.00106961	−	0.000347536i	0.308482	−	0.951230i	$-0.400179\pi$
$547$	−0.0250160	−	0.00812819i	−0.00106961	−	0.000347536i	−0.309552	+	0.950883i	$0.600179\pi$
$548$	−9.57644	−	13.1808i	−0.409085	−	0.563058i
$549$	1.24522	+	3.83240i	0.0531447	+	0.163563i
$550$	−26.5983	+	2.77339i	−1.13416	+	0.118258i
$551$	−4.08180	+	12.5625i	−0.173890	+	0.535180i
$552$			9.98247i			0.424882i
$553$			31.0998i			1.32250i
$554$	−8.54938	+	26.3123i	−0.363228	+	1.11790i
$555$	0.917275	+	0.826604i	0.0389361	+	0.0350874i
$556$	10.7169	−	7.78627i	0.454497	−	0.330211i
$557$			41.4365i			1.75572i	0.478915	+	0.877861i	$0.341030\pi$
$557$			41.4365i			1.75572i	−0.478915	+	0.877861i	$0.658970\pi$
$558$	−1.92122	−	2.61560i	−0.0813317	−	0.110727i
$559$	12.5751			0.531871
$560$	3.28474	+	5.69476i	0.138805	+	0.240648i
$561$	−34.0102	−	24.7098i	−1.43591	−	1.04325i
$562$	−8.73000	−	2.83655i	−0.368253	−	0.119653i
$563$		−	24.6828i		−	1.04026i	−0.854088	−	0.520129i	$-0.825884\pi$
$563$		−	24.6828i		−	1.04026i	0.854088	−	0.520129i	$-0.174116\pi$
$564$	−19.7356			−0.831017
$565$	−34.2867	−	15.2824i	−1.44245	−	0.642935i
$566$	−3.83837	−	11.8133i	−0.161339	−	0.496549i
$567$	−19.3259	+	6.27937i	−0.811613	+	0.263709i
$568$	5.89078	+	8.10796i	0.247172	+	0.340203i
$569$	−9.51559	+	29.2860i	−0.398914	+	1.22773i	0.526956	+	0.849892i	$0.323333\pi$
$569$	−9.51559	+	29.2860i	−0.398914	+	1.22773i	−0.925871	+	0.377840i	$0.876667\pi$
$570$	19.4661	−	11.2280i	0.815344	−	0.470290i
$571$	15.7852	+	11.4686i	0.660591	+	0.479948i	0.866863	−	0.498547i	$-0.166133\pi$
$571$	15.7852	+	11.4686i	0.660591	+	0.479948i	−0.206271	+	0.978495i	$0.566133\pi$
$572$	17.3378	−	5.63340i	0.724930	−	0.235544i
$573$	16.9350	−	23.3090i	0.707470	−	0.973749i
$574$	−17.6082	−	12.7931i	−0.734951	−	0.533973i
$575$	−31.9309	+	3.32942i	−1.33161	+	0.138846i
$576$	0.471565	+	0.342612i	0.0196485	+	0.0142755i
$577$	−5.13946	−	7.07386i	−0.213959	−	0.294489i	0.688525	−	0.725212i	$-0.258258\pi$
$577$	−5.13946	−	7.07386i	−0.213959	−	0.294489i	−0.902484	+	0.430724i	$0.858258\pi$
$578$	−8.13996	−	2.64483i	−0.338578	−	0.110010i
$579$	7.45888	−	5.41919i	0.309981	−	0.225214i
$580$	0.948152	+	4.46978i	0.0393699	+	0.185597i
$581$	−8.12407	−	25.0033i	−0.337043	−	1.03731i
$582$	−3.49203	−	1.13463i	−0.144749	−	0.0470319i
$583$		−	0.0694840i		−	0.00287773i
$584$	3.38761			0.140180
$585$	4.05765	+	1.80859i	0.167763	+	0.0747761i
$586$	11.4934	+	8.35044i	0.474788	+	0.344954i
$587$	20.2708	+	27.9003i	0.836665	+	1.15157i	0.986646	+	0.162881i	$0.0520787\pi$
$587$	20.2708	+	27.9003i	0.836665	+	1.15157i	−0.149981	+	0.988689i	$0.547921\pi$
$588$			2.55587i			0.105402i
$589$	11.2997	+	34.1710i	0.465597	+	1.40799i
$590$	2.20123	−	20.8604i	0.0906231	−	0.858810i
$591$	−0.171560	+	0.124646i	−0.00705705	+	0.00512725i
$592$	0.208772	−	0.287350i	0.00858048	−	0.0118100i
$593$	10.9460	+	3.55656i	0.449496	+	0.146050i	0.525013	−	0.851094i	$-0.324061\pi$
$593$	10.9460	+	3.55656i	0.449496	+	0.146050i	−0.0755164	+	0.997145i	$0.524061\pi$
$594$	−29.7930			−1.22242
$595$	−33.0527	−	3.48778i	−1.35503	−	0.142985i
$596$	6.52399	−	20.0788i	0.267233	−	0.822458i
$597$	−4.38594	+	1.42508i	−0.179505	+	0.0583246i
$598$	20.8138	−	6.76282i	0.851140	−	0.276552i
$599$	−21.0528	+	15.2957i	−0.860193	+	0.624967i	−0.927937	−	0.372736i	$-0.878420\pi$
$599$	−21.0528	+	15.2957i	−0.860193	+	0.624967i	0.0677445	+	0.997703i	$0.478420\pi$
$600$	3.89233	−	6.72887i	0.158904	−	0.274705i
$601$	18.5663	−	13.4892i	0.757334	−	0.550236i	−0.140757	−	0.990044i	$-0.544954\pi$
$601$	18.5663	−	13.4892i	0.757334	−	0.550236i	0.898092	+	0.439809i	$0.144954\pi$
$602$	−6.37575	+	8.77547i	−0.259856	+	0.357661i
$603$	−4.89741	+	1.59127i	−0.199438	+	0.0648014i
$604$	−6.25736	−	4.54624i	−0.254608	−	0.184984i
$605$	−29.2462	−	26.3553i	−1.18903	−	1.07149i
$606$	4.41197	+	13.5786i	0.179224	+	0.551595i
$607$	−20.5205	+	28.2441i	−0.832902	+	1.14639i	0.154474	+	0.987997i	$0.450632\pi$
$607$	−20.5205	+	28.2441i	−0.832902	+	1.14639i	−0.987376	+	0.158394i	$0.949368\pi$
$608$	−3.79953	−	5.22960i	−0.154091	−	0.212088i
$609$	−2.88633	+	8.88320i	−0.116960	+	0.359966i
$610$	−7.72368	−	13.3906i	−0.312723	−	0.542168i
$611$	13.3702	+	41.1493i	0.540902	+	1.66472i
$612$	−2.80260	+	0.910620i	−0.113288	+	0.0368096i
$613$	−14.6373	−	4.75595i	−0.591195	−	0.192091i	−0.00188568	−	0.999998i	$-0.500600\pi$
$613$	−14.6373	−	4.75595i	−0.591195	−	0.192091i	−0.589310	+	0.807907i	$0.700600\pi$
$614$	−1.72578			−0.0696468
$615$	−2.70067	+	25.5935i	−0.108901	+	1.03203i
$616$	−4.85927	+	14.9553i	−0.195786	+	0.602566i
$617$	3.45076	−	4.74957i	0.138922	−	0.191210i	−0.733887	−	0.679272i	$-0.762296\pi$
$617$	3.45076	−	4.74957i	0.138922	−	0.191210i	0.872809	+	0.488061i	$0.162296\pi$
$618$	0.794355	+	1.09334i	0.0319536	+	0.0439804i
$619$	−32.8884			−1.32190			−0.660949	−	0.750431i	$-0.729846\pi$
$619$	−32.8884			−1.32190			−0.660949	+	0.750431i	$0.729846\pi$
$620$	9.29188	+	8.28619i	0.373171	+	0.332781i
$621$	−35.7660			−1.43524
$622$	12.0019	+	16.5191i	0.481231	+	0.662357i
$623$	15.9192	−	21.9109i	0.637788	−	0.877840i
$624$	−1.63752	+	5.03977i	−0.0655533	+	0.201752i
$625$	22.8218	+	10.2061i	0.912872	+	0.408245i
$626$	−21.2571			−0.849605
$627$	51.1208	+	16.6102i	2.04157	+	0.663346i
$628$	3.93754	−	1.27938i	0.157125	−	0.0510530i
$629$	0.554890	+	1.70778i	0.0221249	+	0.0680935i
$630$	−3.31940	+	1.91463i	−0.132248	+	0.0762806i
$631$	−9.83548	+	30.2705i	−0.391544	+	1.20505i	0.540076	+	0.841616i	$0.318395\pi$
$631$	−9.83548	+	30.2705i	−0.391544	+	1.20505i	−0.931620	+	0.363433i	$0.881605\pi$
$632$	−6.21755	−	8.55773i	−0.247321	−	0.340408i
$633$	−8.31012	+	11.4379i	−0.330298	+	0.454616i
$634$	−6.84555	−	21.0684i	−0.271871	−	0.836734i
$635$	12.1861	−	13.5228i	0.483589	−	0.536635i
$636$	0.0163402	+	0.0118719i	0.000647933	+	0.000470751i
$637$	5.32909	−	1.73153i	0.211146	−	0.0686056i
$638$	−6.42405	+	8.84195i	−0.254331	+	0.350056i
$639$	−4.72602	+	3.43366i	−0.186959	+	0.135833i
$640$	−2.04237	−	0.910334i	−0.0807319	−	0.0359841i
$641$	−13.6731	+	9.93411i	−0.540056	+	0.392374i	−0.824106	−	0.566436i	$-0.808322\pi$
$641$	−13.6731	+	9.93411i	−0.540056	+	0.392374i	0.284050	+	0.958810i	$0.408322\pi$
$642$	−21.9656	+	7.13706i	−0.866913	+	0.281677i
$643$	26.7375	−	8.68754i	1.05442	−	0.342603i	0.270021	−	0.962854i	$-0.412969\pi$
$643$	26.7375	−	8.68754i	1.05442	−	0.342603i	0.784403	+	0.620251i	$0.212969\pi$
$644$	−5.83349	+	17.9536i	−0.229872	+	0.707472i
$645$	12.7551	+	1.34594i	0.502233	+	0.0529965i
$646$	32.6800			1.28578
$647$	−16.9311	−	5.50123i	−0.665629	−	0.216276i	−0.0433360	−	0.999061i	$-0.513799\pi$
$647$	−16.9311	−	5.50123i	−0.665629	−	0.216276i	−0.622293	+	0.782785i	$0.713799\pi$
$648$	4.06253	−	5.59159i	0.159591	−	0.219658i
$649$	40.5912	−	29.4913i	1.59335	−	1.15763i
$650$	−16.6669	−	3.55704i	−0.653728	−	0.139519i
$651$	7.99029	+	24.1630i	0.313164	+	0.947024i
$652$			13.1651i			0.515585i
$653$	7.82413	+	10.7690i	0.306182	+	0.421423i	0.934186	−	0.356787i	$-0.116128\pi$
$653$	7.82413	+	10.7690i	0.306182	+	0.421423i	−0.628004	+	0.778210i	$0.716128\pi$
$654$	−7.73160	−	5.61734i	−0.302330	−	0.219655i
$655$	−2.02894	+	4.55202i	−0.0792773	+	0.177862i
$656$	7.40287			0.289033
$657$			1.97459i			0.0770361i
$658$	−35.4947	−	11.5329i	−1.38373	−	0.449600i
$659$	−10.4838	−	32.2659i	−0.408391	−	1.25690i	−0.918030	−	0.396511i	$-0.870221\pi$
$659$	−10.4838	−	32.2659i	−0.408391	−	1.25690i	0.509639	−	0.860389i	$-0.329779\pi$
$660$	18.1890	−	3.85834i	0.708005	−	0.150186i
$661$	−2.53891	+	1.84462i	−0.0987521	+	0.0717476i	−0.636066	−	0.771635i	$-0.719439\pi$
$661$	−2.53891	+	1.84462i	−0.0987521	+	0.0717476i	0.537313	+	0.843383i	$0.319439\pi$
$662$	−10.9529	−	3.55882i	−0.425697	−	0.138317i
$663$	−15.7469	−	21.6737i	−0.611557	−	0.841736i
$664$	7.23423	+	5.25598i	0.280743	+	0.203971i
$665$	41.5714	−	8.81833i	1.61207	−	0.341960i
$666$	0.167493	+	0.121690i	0.00649021	+	0.00471541i
$667$	−7.71199	+	10.6146i	−0.298609	+	0.411001i
$668$	21.3460	−	6.93573i	0.825901	−	0.268352i
$669$	−6.07758	−	4.41562i	−0.234973	−	0.170718i
$670$	17.1118	−	9.87008i	0.661086	−	0.381314i
$671$	11.4260	−	35.1656i	0.441096	−	1.35755i
$672$	−2.68673	−	3.69796i	−0.103643	−	0.142652i
$673$	−14.6214	+	4.75077i	−0.563612	+	0.183129i	−0.576946	−	0.816782i	$-0.695756\pi$
$673$	−14.6214	+	4.75077i	−0.563612	+	0.183129i	0.0133338	+	0.999911i	$0.495756\pi$
$674$	4.82852	+	14.8607i	0.185988	+	0.572411i
$675$	24.1088	+	13.9458i	0.927947	+	0.536773i
$676$	−1.38253			−0.0531742
$677$		−	12.5099i		−	0.480795i	−0.970675	−	0.240397i	$-0.922722\pi$
$677$		−	12.5099i		−	0.480795i	0.970675	−	0.240397i	$-0.0772778\pi$
$678$	24.8225	+	8.06532i	0.953302	+	0.309747i
$679$	−5.61743	−	4.08130i	−0.215577	−	0.156626i
$680$	9.79242	−	5.64826i	0.375522	−	0.216601i
$681$	−3.45610			−0.132438
$682$	0.154959	+	29.7788i	0.00593370	+	1.14029i
$683$			24.3572i			0.932002i	0.884784	+	0.466001i	$0.154306\pi$
$683$			24.3572i			0.932002i	−0.884784	+	0.466001i	$0.845694\pi$
$684$	3.04826	−	2.21469i	0.116553	−	0.0846809i
$685$	−24.3882	+	27.0634i	−0.931827	+	1.03404i
$686$	4.86612	−	14.9764i	0.185789	−	0.571800i
$687$			31.6679i			1.20820i
$688$		−	3.68940i		−	0.140657i
$689$	0.0136833	−	0.0421128i	0.000521292	−	0.00160437i
$690$	21.8356	−	4.63188i	0.831268	−	0.176333i
$691$	−11.1752	−	34.3936i	−0.425123	−	1.30839i	−0.902877	−	0.429900i	$-0.858549\pi$
$691$	−11.1752	−	34.3936i	−0.425123	−	1.30839i	0.477754	−	0.878494i	$-0.341451\pi$
$692$	−6.66402	−	9.17224i	−0.253328	−	0.348676i
$693$	−8.71724	−	2.83240i	−0.331140	−	0.107594i
$694$	−15.3653	+	11.1635i	−0.583258	+	0.423762i
$695$	−22.0043	−	19.8292i	−0.834671	−	0.752165i
$696$	−0.981724	−	3.02143i	−0.0372121	−	0.114527i
$697$	−21.9983	+	30.2781i	−0.833246	+	1.14686i
$698$	−5.99746	+	8.25480i	−0.227007	+	0.312449i
$699$	−6.08992	−	18.7428i	−0.230342	−	0.708919i
$700$	10.9326	−	9.82740i	0.413212	−	0.371441i
$701$	−7.70516	+	5.59812i	−0.291020	+	0.211438i	−0.723710	−	0.690105i	$-0.757565\pi$
$701$	−7.70516	+	5.59812i	−0.291020	+	0.211438i	0.432690	+	0.901543i	$0.357565\pi$
$702$	−18.0569	−	5.86705i	−0.681515	−	0.221438i
$703$	−1.34953	−	1.85747i	−0.0508986	−	0.0700559i
$704$	−1.65278	−	5.08673i	−0.0622914	−	0.191713i
$705$	9.15733	+	43.1695i	0.344885	+	1.62586i
$706$	−0.305542	+	0.940363i	−0.0114992	+	0.0353910i
$707$			26.9996i			1.01543i
$708$			14.5845i			0.548119i
$709$	−2.10205	+	6.46945i	−0.0789442	+	0.242965i	−0.982738	−	0.185003i	$-0.940771\pi$
$709$	−2.10205	+	6.46945i	−0.0789442	+	0.242965i	0.903794	+	0.427968i	$0.140771\pi$
$710$	15.0020	−	16.6476i	0.563015	−	0.624772i
$711$	4.98818	−	3.62413i	0.187072	−	0.135915i
$712$			9.21182i			0.345228i
$713$	0.186026	+	35.7490i	0.00696674	+	1.33881i
$714$	23.1087			0.864821
$715$	−20.3672	−	35.3108i	−0.761692	−	1.32055i
$716$	7.33006	+	5.32560i	0.273937	+	0.199027i
$717$	−0.478460	−	0.155461i	−0.0178684	−	0.00580581i
$718$		−	3.31742i		−	0.123805i
$719$	36.5730			1.36394			0.681971	−	0.731379i	$-0.261123\pi$
$719$	36.5730			1.36394			0.681971	+	0.731379i	$0.261123\pi$
$720$	0.530621	−	1.19047i	0.0197751	−	0.0443663i
$721$	0.789743	+	2.43058i	0.0294116	+	0.0905195i
$722$	−21.6699	+	7.04098i	−0.806471	+	0.262038i
$723$	−1.63278	−	2.24733i	−0.0607238	−	0.0835792i
$724$	3.20322	−	9.85850i	0.119047	−	0.366388i
$725$	9.33723	−	4.14797i	0.346776	−	0.154052i
$726$	22.1451	+	16.0894i	0.821884	+	0.597133i
$727$	−10.5108	+	3.41517i	−0.389824	+	0.126662i	−0.497370	−	0.867539i	$-0.665701\pi$
$727$	−10.5108	+	3.41517i	−0.389824	+	0.126662i	0.107546	+	0.994200i	$0.465701\pi$
$728$	−5.89021	+	8.10718i	−0.218306	+	0.300472i
$729$	24.2781	+	17.6391i	0.899189	+	0.653299i
$730$	−1.57186	−	7.41004i	−0.0581770	−	0.274258i
$731$	15.0898	+	10.9634i	0.558118	+	0.405496i
$732$	6.31753	+	8.69533i	0.233503	+	0.321389i
$733$	−42.1920	−	13.7090i	−1.55840	−	0.506354i	−0.602017	−	0.798483i	$-0.705636\pi$
$733$	−42.1920	−	13.7090i	−1.55840	−	0.506354i	−0.956379	+	0.292129i	$0.905636\pi$
$734$	−5.50208	+	3.99750i	−0.203085	+	0.147550i
$735$	5.59071	−	1.18593i	0.206216	−	0.0437437i
$736$	−1.98414	−	6.10655i	−0.0731363	−	0.225090i
$737$	44.9381	+	14.6013i	1.65532	+	0.537845i
$738$			4.31503i			0.158839i
$739$	−25.4303			−0.935471			−0.467735	−	0.883869i	$-0.654930\pi$
$739$	−25.4303			−0.935471			−0.467735	+	0.883869i	$0.654930\pi$
$740$	−0.725420	−	0.323337i	−0.0266670	−	0.0118861i
$741$	27.7123	+	20.1342i	1.01804	+	0.739647i
$742$	0.0224506	+	0.0309006i	0.000824187	+	0.00113440i
$743$			36.8646i			1.35243i	0.736704	+	0.676216i	$0.236381\pi$
$743$			36.8646i			1.35243i	−0.736704	+	0.676216i	$0.763619\pi$
$744$	−7.02943	−	5.05150i	−0.257711	−	0.185197i
$745$	−46.9474	−	4.95397i	−1.72002	−	0.181499i
$746$	−2.68226	+	1.94878i	−0.0982045	+	0.0713498i
$747$	−3.06364	+	4.21674i	−0.112093	+	0.154282i
$748$	25.7163	+	8.35575i	0.940283	+	0.305516i
$749$	−43.6762			−1.59589
$750$	−16.5247	−	5.39185i	−0.603398	−	0.196883i
$751$	−0.982658	+	3.02431i	−0.0358577	+	0.110359i	−0.967383	−	0.253317i	$-0.918478\pi$
$751$	−0.982658	+	3.02431i	−0.0358577	+	0.110359i	0.931526	+	0.363676i	$0.118478\pi$
$752$	12.0728	−	3.92268i	0.440249	−	0.143046i
$753$	4.60738	−	1.49703i	0.167902	−	0.0545548i
$754$	−5.63471	+	4.09386i	−0.205204	+	0.149090i
$755$	−7.04100	+	15.7968i	−0.256248	+	0.574904i
$756$	13.2494	−	9.62624i	0.481875	−	0.350103i
$757$	13.4822	−	18.5566i	0.490018	−	0.674452i	−0.490373	−	0.871513i	$-0.663140\pi$
$757$	13.4822	−	18.5566i	0.490018	−	0.674452i	0.980391	+	0.197060i	$0.0631395\pi$
$758$	4.66497	−	1.51574i	0.169439	−	0.0550541i
$759$	43.1944	+	31.3826i	1.56786	+	1.13912i
$760$	−9.67622	+	10.7376i	−0.350993	+	0.389494i
$761$	−5.82506	−	17.9277i	−0.211158	−	0.649878i	−0.999404	−	0.0345178i	$-0.989010\pi$
$761$	−5.82506	−	17.9277i	−0.211158	−	0.649878i	0.788246	−	0.615360i	$-0.210990\pi$
$762$	−7.43937	+	10.2394i	−0.269500	+	0.370935i
$763$	−10.6228	−	14.6210i	−0.384571	−	0.529316i
$764$	−5.72665	+	17.6248i	−0.207183	+	0.637643i
$765$	3.29230	+	5.70787i	0.119033	+	0.206368i
$766$	−11.0078	−	33.8784i	−0.397726	−	1.22408i
$767$	30.4092	−	9.88054i	1.09801	−	0.356766i
$768$	1.47861	+	0.480431i	0.0533549	+	0.0173361i
$769$	43.8253			1.58038			0.790190	−	0.612862i	$-0.209982\pi$
$769$	43.8253			1.58038			0.790190	+	0.612862i	$0.209982\pi$
$770$	34.9679	+	3.68987i	1.26015	+	0.132974i
$771$	−0.751182	+	2.31190i	−0.0270532	+	0.0832611i
$772$	−3.48567	+	4.79761i	−0.125452	+	0.172670i
$773$	1.99118	+	2.74063i	0.0716179	+	0.0985736i	0.843323	−	0.537407i	$-0.180596\pi$
$773$	1.99118	+	2.74063i	0.0716179	+	0.0985736i	−0.771705	+	0.635980i	$0.780596\pi$
$774$	2.15050			0.0772983
$775$	13.8137	−	24.1698i	0.496204	−	0.868206i
$776$	2.36169			0.0847798
$777$	−0.954284	−	1.31346i	−0.0342347	−	0.0471201i
$778$	4.96363	−	6.83185i	0.177955	−	0.244934i
$779$	14.7874	−	45.5111i	0.529815	−	1.63060i
$780$	11.7838	+	1.24344i	0.421927	+	0.0445225i
$781$	53.6027			1.91805
$782$	30.8721	+	10.0310i	1.10398	+	0.358706i
$783$	10.8255	−	3.51740i	0.386870	−	0.125702i
$784$	−0.508011	−	1.56350i	−0.0181433	−	0.0558392i
$785$	−4.62554	−	8.01932i	−0.165093	−	0.286222i
$786$	1.07078	−	3.29552i	0.0381934	−	0.117547i
$787$	−25.7388	−	35.4264i	−0.917488	−	1.26281i	−0.964544	−	0.263922i	$-0.914984\pi$
$787$	−25.7388	−	35.4264i	−0.917488	−	1.26281i	0.0470558	−	0.998892i	$-0.485016\pi$
$788$	0.0801732	−	0.110349i	0.00285605	−	0.00393102i
$789$	−1.22101	−	3.75789i	−0.0434692	−	0.133785i
$790$	−15.8342	+	17.5711i	−0.563355	+	0.625150i
$791$	39.9305	+	29.0112i	1.41976	+	1.03152i
$792$	2.96498	−	0.963382i	0.105356	−	0.0342323i
$793$	13.8502	−	19.0631i	0.491833	−	0.676951i
$794$	−20.1084	+	14.6096i	−0.713622	+	0.518477i
$795$	0.0183866	−	0.0412512i	0.000652106	−	0.00146303i
$796$	2.39975	−	1.74352i	0.0850568	−	0.0617974i
$797$	−31.5021	+	10.2357i	−1.11586	+	0.362565i	−0.808187	−	0.588926i	$-0.799551\pi$
$797$	−31.5021	+	10.2357i	−1.11586	+	0.362565i	−0.307675	+	0.951492i	$0.599551\pi$
$798$	−28.1010	+	9.13057i	−0.994765	+	0.323219i
$799$	−19.8314	+	61.0348i	−0.701585	+	2.15926i
$800$	−1.04360	+	4.88988i	−0.0368967	+	0.172883i
$801$	−5.36945			−0.189720
$802$	19.6434	+	6.38254i	0.693634	+	0.225375i
$803$	10.6499	−	14.6583i	0.375826	−	0.517279i
$804$	−11.1118	+	8.07316i	−0.391881	+	0.284718i
$805$	41.9784	+	4.42964i	1.47955	+	0.156124i
$806$	−5.77034	+	18.0788i	−0.203252	+	0.636800i
$807$			9.14483i			0.321913i
$808$	−5.39784	−	7.42949i	−0.189895	−	0.261369i
$809$	−36.4854	−	26.5082i	−1.28276	−	0.931979i	−0.283126	−	0.959083i	$-0.591372\pi$
$809$	−36.4854	−	26.5082i	−1.28276	−	0.931979i	−0.999633	+	0.0271037i	$0.991372\pi$
$810$	−14.1160	−	6.29185i	−0.495987	−	0.221073i
$811$	10.5524			0.370546			0.185273	−	0.982687i	$-0.440683\pi$
$811$	10.5524			0.370546			0.185273	+	0.982687i	$0.440683\pi$
$812$		−	6.00779i		−	0.210832i
$813$	−10.3263	−	3.35521i	−0.362158	−	0.117672i
$814$	−0.587041	−	1.80673i	−0.0205758	−	0.0633257i
$815$	28.7973	−	6.10862i	1.00872	−	0.213976i
$816$	−6.35882	+	4.61996i	−0.222603	+	0.161731i
$817$	−22.6816	−	7.36969i	−0.793528	−	0.257833i
$818$	−15.2973	−	21.0550i	−0.534859	−	0.736170i
$819$	−4.72557	−	3.43332i	−0.165125	−	0.119970i
$820$	−3.43494	−	16.1930i	−0.119953	−	0.565484i
$821$	30.0234	+	21.8132i	1.04782	+	0.761287i	0.971797	−	0.235818i	$-0.0757771\pi$
$821$	30.0234	+	21.8132i	1.04782	+	0.761287i	0.0760251	+	0.997106i	$0.475777\pi$
$822$	14.8886	−	20.4923i	0.519298	−	0.714753i
$823$	−0.371597	+	0.120739i	−0.0129530	+	0.00420870i	−0.315486	−	0.948930i	$-0.602168\pi$
$823$	−0.371597	+	0.120739i	−0.0129530	+	0.00420870i	0.302533	+	0.953139i	$0.402168\pi$
$824$	−0.703242	−	0.510935i	−0.0244986	−	0.0177993i
$825$	−16.8794	−	37.9962i	−0.587666	−	1.32286i
$826$	−8.52278	+	26.2304i	−0.296545	+	0.912673i
$827$	−5.96763	−	8.21374i	−0.207515	−	0.285620i	0.692555	−	0.721365i	$-0.256485\pi$
$827$	−5.96763	−	8.21374i	−0.207515	−	0.285620i	−0.900070	+	0.435745i	$0.856485\pi$
$828$	3.55942	−	1.15653i	0.123699	−	0.0401921i
$829$	−2.65979	−	8.18600i	−0.0923784	−	0.284312i	0.894183	−	0.447701i	$-0.147757\pi$
$829$	−2.65979	−	8.18600i	−0.0923784	−	0.284312i	−0.986562	+	0.163390i	$0.947757\pi$
$830$	8.14021	−	18.2629i	0.282551	−	0.633915i
$831$	−43.0131			−1.49211
$832$		−	3.40844i		−	0.118166i
$833$	7.90438	+	2.56829i	0.273871	+	0.0889860i
$834$	16.6616	+	12.1054i	0.576944	+	0.419175i
$835$	−25.0758	−	43.4739i	−0.867783	−	1.50448i
$836$	−34.5735			−1.19575
$837$	18.0990	−	25.1856i	0.625591	−	0.870543i
$838$		−	34.1362i		−	1.17921i
$839$	3.26107	−	2.36931i	0.112585	−	0.0817976i	−0.530068	−	0.847955i	$-0.677834\pi$
$839$	3.26107	−	2.36931i	0.112585	−	0.0817976i	0.642653	+	0.766157i	$0.277834\pi$
$840$	−6.84226	+	7.59280i	−0.236081	+	0.261976i
$841$	−7.67117	+	23.6094i	−0.264523	+	0.814118i
$842$			19.3807i			0.667902i
$843$		−	14.2711i		−	0.491522i
$844$	2.81010	−	8.64861i	0.0967278	−	0.297697i
$845$	0.641496	+	3.02414i	0.0220681	+	0.104034i
$846$	2.28648	+	7.03706i	0.0786108	+	0.241939i
$847$	30.4262	+	41.8780i	1.04546	+	1.43895i
$848$	−0.0123555	−	0.00401453i	−0.000424288	−	0.000137860i
$849$	15.6232	−	11.3509i	0.536187	−	0.389563i
$850$	−16.8987	−	18.7991i	−0.579620	−	0.644803i
$851$	−0.704735	−	2.16895i	−0.0241580	−	0.0743507i
$852$	−9.15844	+	12.6055i	−0.313763	+	0.431858i
$853$	6.52227	−	8.97714i	0.223318	−	0.307371i	−0.682626	−	0.730768i	$-0.739162\pi$
$853$	6.52227	−	8.97714i	0.223318	−	0.307371i	0.905945	+	0.423396i	$0.139162\pi$
$854$	6.28086	+	19.3305i	0.214926	+	0.661476i
$855$	−6.25881	−	5.64014i	−0.214047	−	0.192889i
$856$	12.0184	−	8.73187i	0.410780	−	0.298449i
$857$	−35.5504	−	11.5510i	−1.21438	−	0.394576i	−0.369348	−	0.929291i	$-0.620419\pi$
$857$	−35.5504	−	11.5510i	−1.21438	−	0.394576i	−0.845032	+	0.534715i	$0.820419\pi$
$858$	16.6592	+	22.9295i	0.568737	+	0.782799i
$859$	−17.3986	−	53.5472i	−0.593631	−	1.82701i	−0.561426	−	0.827527i	$-0.689747\pi$
$859$	−17.3986	−	53.5472i	−0.593631	−	1.82701i	−0.0322055	−	0.999481i	$-0.510253\pi$
$860$	−8.07019	+	1.71189i	−0.275191	+	0.0583749i
$861$	10.4565	−	32.1819i	0.356357	−	1.09676i
$862$		−	24.3875i		−	0.830642i
$863$		−	18.0253i		−	0.613587i	−0.951776	−	0.306793i	$-0.900744\pi$
$863$		−	18.0253i		−	0.613587i	0.951776	−	0.306793i	$-0.0992561\pi$
$864$	−1.72133	+	5.29771i	−0.0585608	+	0.180232i
$865$	−16.9712	+	18.8328i	−0.577038	+	0.640334i
$866$	−20.5039	+	14.8970i	−0.696751	+	0.506219i
$867$		−	13.3065i		−	0.451913i
$868$	−9.69057	−	13.1930i	−0.328919	−	0.447800i
$869$	−56.5761			−1.91921
$870$	−6.15355	+	3.54937i	−0.208625	+	0.120335i
$871$	24.3607	+	17.6991i	0.825431	+	0.599711i
$872$	5.84615	+	1.89953i	0.197976	+	0.0643261i
$873$			1.37660i			0.0465908i
$874$	−41.5050			−1.40393
$875$	−26.5691	−	19.3539i	−0.898201	−	0.654283i
$876$	1.62751	+	5.00897i	0.0549885	+	0.169237i
$877$	−27.0680	+	8.79493i	−0.914022	+	0.296984i	−0.728012	−	0.685564i	$-0.759556\pi$
$877$	−27.0680	+	8.79493i	−0.914022	+	0.296984i	−0.186010	+	0.982548i	$0.559556\pi$
$878$	−2.59006	−	3.56491i	−0.0874103	−	0.120310i
$879$	−6.82530	+	21.0061i	−0.230212	+	0.708519i
$880$	−10.3598	+	5.97553i	−0.349229	+	0.201435i
$881$	−8.05484	−	5.85218i	−0.271374	−	0.197165i	0.443772	−	0.896140i	$-0.353640\pi$
$881$	−8.05484	−	5.85218i	−0.271374	−	0.197165i	−0.715146	+	0.698975i	$0.753640\pi$
$882$	0.911342	−	0.296113i	0.0306865	−	0.00997064i
$883$	−27.0686	+	37.2567i	−0.910929	+	1.25379i	0.0559188	+	0.998435i	$0.482191\pi$
$883$	−27.0686	+	37.2567i	−0.910929	+	1.25379i	−0.966848	+	0.255352i	$0.917809\pi$
$884$	13.9407	+	10.1285i	0.468876	+	0.340658i
$885$	31.9020	−	6.76722i	1.07238	−	0.227478i
$886$	16.1673	+	11.7462i	0.543150	+	0.394622i
$887$	18.7871	+	25.8583i	0.630811	+	0.868236i	0.998084	−	0.0618767i	$-0.0197086\pi$
$887$	18.7871	+	25.8583i	0.630811	+	0.868236i	−0.367273	+	0.930113i	$0.619709\pi$
$888$	0.525181	+	0.170642i	0.0176239	+	0.00572636i
$889$	−19.3635	+	14.0684i	−0.649429	+	0.471838i
$890$	20.1499	−	4.27430i	0.675426	−	0.143275i
$891$	−11.4233	−	35.1573i	−0.382695	−	1.17782i
$892$	4.59548	+	1.49316i	0.153868	+	0.0499947i
$893$		−	82.0562i		−	2.74591i
$894$	32.8231			1.09777
$895$	8.24803	−	18.5048i	0.275701	−	0.618548i
$896$	2.37856	+	1.72812i	0.0794621	+	0.0577326i
$897$	19.9992	+	27.5265i	0.667754	+	0.919084i
$898$			16.9595i			0.565947i
$899$	−3.57204	−	10.8020i	−0.119134	−	0.360267i
$900$	−2.85024	−	0.608298i	−0.0950081	−	0.0202766i
$901$	0.0531350	−	0.0386049i	0.00177018	−	0.00128611i
$902$	23.2729	−	32.0324i	0.774904	−	1.06656i
$903$	−16.0386	−	5.21127i	−0.533732	−	0.173420i
$904$	−16.7877			−0.558350
$905$	−23.0507	−	2.43235i	−0.766232	−	0.0808542i
$906$	3.71590	−	11.4364i	0.123453	−	0.379948i
$907$	−14.9239	+	4.84907i	−0.495540	+	0.161011i	−0.546116	−	0.837709i	$-0.683894\pi$
$907$	−14.9239	+	4.84907i	−0.495540	+	0.161011i	0.0505761	+	0.998720i	$0.483894\pi$
$908$	2.11419	−	0.686943i	0.0701620	−	0.0227970i
$909$	4.33055	−	3.14633i	0.143635	−	0.104357i
$910$	20.4667	+	9.12248i	0.678464	+	0.302407i
$911$	0.451978	−	0.328381i	0.0149747	−	0.0108797i	−0.580273	−	0.814422i	$-0.697054\pi$
$911$	0.451978	−	0.328381i	0.0149747	−	0.0108797i	0.595247	+	0.803542i	$0.297054\pi$
$912$	5.90715	−	8.13049i	0.195605	−	0.269228i
$913$	45.4855	−	14.7791i	1.50535	−	0.489118i
$914$	−7.32394	−	5.32115i	−0.242254	−	0.176008i
$915$	16.0888	−	17.8536i	0.531879	−	0.590221i
$916$	−6.29438	−	19.3721i	−0.207972	−	0.640072i
$917$	3.85162	−	5.30130i	0.127192	−	0.175064i
$918$	−16.5528	−	22.7829i	−0.546323	−	0.751949i
$919$	−0.377395	+	1.16150i	−0.0124491	+	0.0383144i	−0.957088	−	0.289797i	$-0.906412\pi$
$919$	−0.377395	+	1.16150i	−0.0124491	+	0.0383144i	0.944639	+	0.328112i	$0.106412\pi$
$920$	−12.4368	+	7.17354i	−0.410029	+	0.236505i
$921$	−0.829118	−	2.55176i	−0.0273204	−	0.0840834i
$922$	23.5321	−	7.64604i	0.774989	−	0.251809i
$923$	32.4875	+	10.5558i	1.06934	+	0.347449i
$924$	−24.4476			−0.804269
$925$	−0.370669	+	1.73681i	−0.0121875	+	0.0571059i
$926$	−6.30891	+	19.4168i	−0.207324	+	0.638077i
$927$	0.297817	−	0.409910i	0.00978160	−	0.0134632i
$928$	1.20109	+	1.65316i	0.0394278	+	0.0542678i
$929$	26.8844			0.882048			0.441024	−	0.897495i	$-0.354615\pi$
$929$	26.8844			0.882048			0.441024	+	0.897495i	$0.354615\pi$
$930$	−7.78797	+	17.7200i	−0.255378	+	0.581063i
$931$	−10.6268			−0.348279
$932$	7.45074	+	10.2551i	0.244057	+	0.335916i
$933$	−18.6594	+	25.6824i	−0.610881	+	0.840805i
$934$	−7.05080	+	21.7001i	−0.230709	+	0.710050i
$935$	6.34491	−	60.1289i	0.207501	−	1.96643i
$936$	1.98673			0.0649384
$937$	39.0463	+	12.6869i	1.27559	+	0.414463i	0.867023	−	0.498268i	$-0.166030\pi$
$937$	39.0463	+	12.6869i	1.27559	+	0.414463i	0.408562	+	0.912730i	$0.366030\pi$
$938$	−24.7024	+	8.02630i	−0.806562	+	0.262068i
$939$	−10.2126	−	31.4311i	−0.333275	−	1.02571i
$940$	−14.1822	−	24.5878i	−0.462574	−	0.801966i
$941$	−7.05567	+	21.7151i	−0.230008	+	0.707892i	0.767736	+	0.640766i	$0.221383\pi$
$941$	−7.05567	+	21.7151i	−0.230008	+	0.707892i	−0.997744	+	0.0671264i	$0.978617\pi$
$942$	3.78343	+	5.20745i	0.123271	+	0.169668i
$943$	27.9388	−	38.4545i	0.909813	−	1.25225i
$944$	−2.89884	−	8.92173i	−0.0943494	−	0.290377i
$945$	−27.2041	−	24.5151i	−0.884950	−	0.797475i
$946$	−15.9642	−	11.5986i	−0.519040	−	0.377104i
$947$	−28.4545	+	9.24543i	−0.924647	+	0.300436i	−0.732372	−	0.680905i	$-0.761587\pi$
$947$	−28.4545	+	9.24543i	−0.924647	+	0.300436i	−0.192275	+	0.981341i	$0.561587\pi$
$948$	9.66647	−	13.3048i	0.313952	−	0.432118i
$949$	9.34129	−	6.78684i	0.303231	−	0.220310i
$950$	27.9772	+	16.1835i	0.907700	+	0.525061i
$951$	27.8633	−	20.2438i	0.903528	−	0.656452i
$952$	−14.1362	+	4.59314i	−0.458158	+	0.148864i
$953$	−38.9803	+	12.6655i	−1.26269	+	0.410274i	−0.862454	−	0.506136i	$-0.831074\pi$
$953$	−38.9803	+	12.6655i	−1.26269	+	0.410274i	−0.400241	+	0.916410i	$0.631074\pi$
$954$	0.00234002	−	0.00720183i	7.57608e−5	−	0.000233168i
$955$	41.2096	+	4.34851i	1.33351	+	0.140714i
$956$	0.323587			0.0104656
$957$	−16.1601	−	5.25075i	−0.522383	−	0.169733i
$958$	−11.5870	+	15.9482i	−0.374360	+	0.515262i
$959$	38.7525	−	28.1553i	1.25138	−	0.909183i
$960$	0.364813	−	3.45724i	0.0117743	−	0.111582i
$961$	−25.2678	−	17.9594i	−0.815090	−	0.579334i
$962$		−	1.21063i		−	0.0390321i
$963$	5.08969	+	7.00535i	0.164013	+	0.225744i
$964$	1.44550	+	1.05022i	0.0465565	+	0.0338253i
$965$	12.1116	+	5.39844i	0.389887	+	0.173782i
$966$	−29.3491			−0.944291
$967$			28.9027i			0.929447i	0.885456	+	0.464724i	$0.153846\pi$
$967$			28.9027i			0.929447i	−0.885456	+	0.464724i	$0.846154\pi$
$968$	−16.7448	−	5.44070i	−0.538197	−	0.174871i
$969$	15.7005	+	48.3210i	0.504371	+	1.55230i
$970$	−1.09583	−	5.16596i	−0.0351849	−	0.165869i
$971$	−26.1068	+	18.9677i	−0.837806	+	0.608702i	−0.921757	−	0.387768i	$-0.873246\pi$
$971$	−26.1068	+	18.9677i	−0.837806	+	0.608702i	0.0839510	+	0.996470i	$0.473246\pi$
$972$	−5.67355	−	1.84345i	−0.181979	−	0.0591287i
$973$	22.8921	+	31.5083i	0.733887	+	1.01011i
$974$	−8.64248	−	6.27913i	−0.276923	−	0.201196i
$975$	−2.74779	−	26.3528i	−0.0879996	−	0.843964i
$976$	−5.59291	−	4.06349i	−0.179025	−	0.130069i
$977$	−25.7694	+	35.4685i	−0.824435	+	1.13474i	0.164499	+	0.986377i	$0.447399\pi$
$977$	−25.7694	+	35.4685i	−0.824435	+	1.13474i	−0.988933	+	0.148360i	$0.952601\pi$
$978$	−19.4661	+	6.32492i	−0.622457	+	0.202249i
$979$	39.8598	+	28.9599i	1.27393	+	0.925561i
$980$	−3.18427	+	1.83669i	−0.101718	+	0.0586708i
$981$	−1.10721	+	3.40764i	−0.0353505	+	0.108798i
$982$	−0.591301	−	0.813856i	−0.0188692	−	0.0259712i
$983$	1.77616	−	0.577109i	0.0566507	−	0.0184069i	−0.280555	−	0.959838i	$-0.590518\pi$
$983$	1.77616	−	0.577109i	0.0566507	−	0.0184069i	0.337205	+	0.941431i	$0.390518\pi$
$984$	3.55657	+	10.9460i	0.113379	+	0.348945i
$985$	−0.278577	−	0.124169i	−0.00887622	−	0.00395634i
$986$	−10.3307			−0.328996
$987$		−	58.0237i		−	1.84692i
$988$	−20.9543	−	6.80846i	−0.666645	−	0.216606i
$989$	−19.1648	−	13.9240i	−0.609404	−	0.442758i
$990$	−3.48306	−	6.03859i	−0.110699	−	0.191919i
$991$	−14.9877			−0.476099			−0.238049	−	0.971253i	$-0.576508\pi$
$991$	−14.9877			−0.476099			−0.238049	+	0.971253i	$0.576508\pi$
$992$	5.30414	+	1.69296i	0.168407	+	0.0537514i
$993$		−	17.9049i		−	0.568195i
$994$	−23.8379	+	17.3193i	−0.756092	+	0.549333i
$995$	−4.92725	−	4.44020i	−0.156204	−	0.140764i
$996$	−4.29601	+	13.2218i	−0.136124	+	0.418948i
$997$			27.4934i			0.870725i	0.900255	+	0.435362i	$0.143380\pi$
$997$			27.4934i			0.870725i	−0.900255	+	0.435362i	$0.856620\pi$
$998$		−	4.50933i		−	0.142740i
$999$	−0.611389	+	1.88166i	−0.0193435	+	0.0595332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.n.a.109.6	✓	64
5.4	even	2	inner	310.2.n.a.109.11	yes	64
31.2	even	5	inner	310.2.n.a.219.11	yes	64
155.64	even	10	inner	310.2.n.a.219.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.n.a.109.6	✓	64	1.1	even	1	trivial
310.2.n.a.109.11	yes	64	5.4	even	2	inner
310.2.n.a.219.6	yes	64	155.64	even	10	inner
310.2.n.a.219.11	yes	64	31.2	even	5	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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.913834 - 1.25778i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.22372 + 0.234651i) q^{5} -1.55471 q^{6} +(-2.79616 - 0.908529i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.180122 + 0.554358i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.913834 - 1.25778i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.22372 + 0.234651i) q^{5} -1.55471 q^{6} +(-2.79616 - 0.908529i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.180122 + 0.554358i) q^{9} +(-1.11723 - 1.93695i) q^{10} +(1.65278 - 5.08673i) q^{11} +(0.913834 + 1.25778i) q^{12} +(2.00343 - 2.75749i) q^{13} +(0.908529 + 2.79616i) q^{14} +(2.32725 - 2.58253i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.80814 - 1.56226i) q^{17} +(0.342612 - 0.471565i) q^{18} +(-5.22960 + 3.79953i) q^{19} +(-0.910334 + 2.04237i) q^{20} +(-3.69796 + 2.68673i) q^{21} +(-5.08673 + 1.65278i) q^{22} +(-6.10655 + 1.98414i) q^{23} +(0.480431 - 1.47861i) q^{24} +(4.88988 + 1.04360i) q^{25} -3.40844 q^{26} +(5.29771 + 1.72133i) q^{27} +(1.72812 - 2.37856i) q^{28} +(1.65316 - 1.20109i) q^{29} +(-3.45724 - 0.364813i) q^{30} +(1.69296 - 5.30414i) q^{31} +1.00000i q^{32} +(-4.88764 - 6.72726i) q^{33} +(-4.09005 - 2.97159i) q^{34} +(-6.00470 - 2.67644i) q^{35} -0.582886 q^{36} +0.355184i q^{37} +(6.14776 + 1.99753i) q^{38} +(-1.63752 - 5.03977i) q^{39} +(2.18740 - 0.464002i) q^{40} +(-5.98905 + 4.35130i) q^{41} +(4.34722 + 1.41250i) q^{42} +(2.16858 + 2.98479i) q^{43} +(4.32703 + 3.14377i) q^{44} +(0.270460 + 1.27500i) q^{45} +(5.19454 + 3.77405i) q^{46} +(-7.46139 + 10.2697i) q^{47} +(-1.47861 + 0.480431i) q^{48} +(1.32999 + 0.966295i) q^{49} +(-2.02991 - 4.56941i) q^{50} +(2.42885 - 7.47525i) q^{51} +(2.00343 + 2.75749i) q^{52} +(0.0123555 - 0.00401453i) q^{53} +(-1.72133 - 5.29771i) q^{54} +(4.86892 - 10.9236i) q^{55} -2.94006 q^{56} +10.0498i q^{57} +(-1.94341 - 0.631453i) q^{58} +(7.58927 + 5.51393i) q^{59} +(1.73697 + 3.01139i) q^{60} +6.91322 q^{61} +(-5.28623 + 1.74806i) q^{62} -1.71372i q^{63} +(0.809017 - 0.587785i) q^{64} +(5.10212 - 5.66178i) q^{65} +(-2.56959 + 7.90837i) q^{66} +8.83439i q^{67} +5.05558i q^{68} +(-3.08475 + 9.49389i) q^{69} +(1.36419 + 6.43108i) q^{70} +(3.09697 + 9.53148i) q^{71} +(0.342612 + 0.471565i) q^{72} +(3.22181 + 1.04683i) q^{73} +(0.287350 - 0.208772i) q^{74} +(5.78116 - 5.19674i) q^{75} +(-1.99753 - 6.14776i) q^{76} +(-9.24288 + 12.7217i) q^{77} +(-3.11475 + 4.28708i) q^{78} +(-3.26876 - 10.0602i) q^{79} +(-1.66110 - 1.49691i) q^{80} +(5.59159 - 4.06253i) q^{81} +(7.04055 + 2.28761i) q^{82} +(5.25598 + 7.23423i) q^{83} +(-1.41250 - 4.34722i) q^{84} +(11.0585 - 2.34580i) q^{85} +(1.14009 - 3.50883i) q^{86} -3.17692i q^{87} -5.34850i q^{88} +(-2.84661 + 8.76096i) q^{89} +(0.872527 - 0.968235i) q^{90} +(-8.10718 + 5.89021i) q^{91} -6.42080i q^{92} +(-5.12438 - 6.97648i) q^{93} +12.6941 q^{94} +(-12.5207 + 7.22196i) q^{95} +(1.25778 + 0.913834i) q^{96} +(2.24610 + 0.729803i) q^{97} -1.64396i q^{98} +3.11757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9}+O(q^{10}) \) 64 * q + 16 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9	\( 64 q + 16 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{15} - 16 q^{16} + 16 q^{19} - 4 q^{20} + 32 q^{21} - 4 q^{24} - 8 q^{25} - 48 q^{26} - 40 q^{29} - 8 q^{30} - 60 q^{31} - 20 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} - 4 q^{44} - 22 q^{45} + 36 q^{46} + 32 q^{49} + 20 q^{50} - 4 q^{51} - 40 q^{54} + 32 q^{59} + 14 q^{60} - 64 q^{61} + 16 q^{64} + 48 q^{65} - 4 q^{66} - 20 q^{70} - 20 q^{71} - 4 q^{74} + 62 q^{75} + 24 q^{76} - 116 q^{79} - 6 q^{80} - 116 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{86} + 60 q^{89} - 82 q^{90} + 28 q^{91} + 16 q^{94} - 90 q^{95} + 4 q^{96} + 16 q^{99}+O(q^{100}) \) 64 * q + 16 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^15 - 16 * q^16 + 16 * q^19 - 4 * q^20 + 32 * q^21 - 4 * q^24 - 8 * q^25 - 48 * q^26 - 40 * q^29 - 8 * q^30 - 60 * q^31 - 20 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 - 4 * q^44 - 22 * q^45 + 36 * q^46 + 32 * q^49 + 20 * q^50 - 4 * q^51 - 40 * q^54 + 32 * q^59 + 14 * q^60 - 64 * q^61 + 16 * q^64 + 48 * q^65 - 4 * q^66 - 20 * q^70 - 20 * q^71 - 4 * q^74 + 62 * q^75 + 24 * q^76 - 116 * q^79 - 6 * q^80 - 116 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^86 + 60 * q^89 - 82 * q^90 + 28 * q^91 + 16 * q^94 - 90 * q^95 + 4 * q^96 + 16 * q^99

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