LMFDB - Embedded newform 630.2.cg.a.157.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(157,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.157"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.3
Character	$\chi$	$=$	630.157
Dual form			630.2.cg.a.313.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.64267 + 0.549224i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.99630 - 1.00736i) q^{5} +(1.44454 - 0.955663i) q^{6} +(-2.31389 + 1.28293i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.39671 - 1.80438i) q^{9} +(-1.66756 + 1.48971i) q^{10} -0.166984 q^{11} +(-1.14798 + 1.29697i) q^{12} +(2.26834 - 0.607801i) q^{13} +(1.90300 - 1.83809i) q^{14} +(-2.72600 + 2.75117i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.02386 + 3.82109i) q^{17} +(-1.84803 + 2.36321i) q^{18} +(-2.72986 - 4.72826i) q^{19} +(1.22517 - 1.87055i) q^{20} +(3.09634 - 3.37826i) q^{21} +(0.161294 - 0.0432185i) q^{22} +(1.21416 - 1.21416i) q^{23} +(0.773181 - 1.54990i) q^{24} +(2.97047 - 4.02198i) q^{25} +(-2.03374 + 1.17418i) q^{26} +(-2.94598 + 4.28033i) q^{27} +(-1.36243 + 2.26799i) q^{28} +(0.515067 - 0.297374i) q^{29} +(1.92106 - 3.36297i) q^{30} +(3.71918 - 2.14727i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.274298 - 0.0917113i) q^{33} +(-1.97794 - 3.42590i) q^{34} +(-3.32687 + 4.89203i) q^{35} +(1.17342 - 2.76099i) q^{36} +(0.993252 - 3.70687i) q^{37} +(3.86061 + 3.86061i) q^{38} +(-3.39231 + 2.24424i) q^{39} +(-0.699292 + 2.12391i) q^{40} +(9.70992 + 5.60603i) q^{41} +(-2.11648 + 4.06454i) q^{42} +(9.11376 + 2.44202i) q^{43} +(-0.144612 + 0.0834918i) q^{44} +(2.96690 - 6.01644i) q^{45} +(-0.858541 + 1.48704i) q^{46} +(0.202539 + 0.755886i) q^{47} +(-0.345692 + 1.69720i) q^{48} +(3.70820 - 5.93711i) q^{49} +(-1.82829 + 4.65375i) q^{50} +(-3.78050 - 5.71446i) q^{51} +(1.66054 - 1.66054i) q^{52} +(1.87042 + 6.98049i) q^{53} +(1.73777 - 4.89695i) q^{54} +(-0.333350 + 0.168212i) q^{55} +(0.729004 - 2.54334i) q^{56} +(7.08112 + 6.26765i) q^{57} +(-0.420551 + 0.420551i) q^{58} +(0.526480 + 0.911890i) q^{59} +(-0.985201 + 3.74558i) q^{60} +(4.86034 + 2.80612i) q^{61} +(-3.03670 + 3.03670i) q^{62} +(-3.23083 + 7.24995i) q^{63} -1.00000i q^{64} +(3.91603 - 3.49838i) q^{65} +(-0.241215 + 0.159580i) q^{66} +(3.26215 - 12.1745i) q^{67} +(2.79724 + 2.79724i) q^{68} +(-1.32761 + 2.66130i) q^{69} +(1.94736 - 5.58639i) q^{70} +9.49875 q^{71} +(-0.418836 + 2.97062i) q^{72} +(5.82830 - 1.56169i) q^{73} +3.83763i q^{74} +(-2.67052 + 8.23822i) q^{75} +(-4.72826 - 2.72986i) q^{76} +(0.386382 - 0.214228i) q^{77} +(2.69587 - 3.04577i) q^{78} +(7.50903 + 4.33534i) q^{79} +(0.125756 - 2.23253i) q^{80} +(2.48841 - 8.64915i) q^{81} +(-10.8300 - 2.90189i) q^{82} +(-1.70285 + 6.35513i) q^{83} +(0.992378 - 4.47383i) q^{84} +(5.89314 + 6.59668i) q^{85} -9.43526 q^{86} +(-0.682759 + 0.771374i) q^{87} +(0.118075 - 0.118075i) q^{88} +(7.25597 + 12.5677i) q^{89} +(-1.30864 + 6.57932i) q^{90} +(-4.46894 + 4.31650i) q^{91} +(0.444413 - 1.65857i) q^{92} +(-4.93004 + 5.56991i) q^{93} +(-0.391275 - 0.677709i) q^{94} +(-10.2127 - 6.68910i) q^{95} +(-0.105356 - 1.72884i) q^{96} +(-13.8533 - 3.71198i) q^{97} +(-2.04521 + 6.69456i) q^{98} +(-0.400211 + 0.301302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{11} - 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 12 q^{30} - 60 q^{33} + 48 q^{35} - 16 q^{36} + 12 q^{41} + 4 q^{42} - 36 q^{45} + 12 q^{46} - 16 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) $ 192 * q - 16 * q^11 - 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 + 12 * q^21 - 16 * q^23 - 36 * q^27 + 12 * q^30 - 60 * q^33 + 48 * q^35 - 16 * q^36 + 12 * q^41 + 4 * q^42 - 36 * q^45 + 12 * q^46 - 16 * q^50 + 24 * q^51 - 40 * q^53 + 8 * q^56 - 32 * q^57 + 24 * q^58 + 8 * q^60 + 36 * q^61 - 108 * q^63 - 8 * q^65 + 16 * q^71 - 8 * q^72 + 80 * q^77 - 16 * q^78 + 4 * q^81 - 168 * q^83 - 16 * q^86 + 36 * q^90 + 8 * q^92 - 60 * q^93 + 64 * q^95 - 12 * q^96 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−1.64267	+	0.549224i	−0.948394	+	0.317094i
$3$	−1.64267	+	0.549224i	−0.948394	+	0.317094i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.99630	−	1.00736i	0.892775	−	0.450503i
$5$	1.99630	−	1.00736i	0.892775	−	0.450503i
$6$	1.44454	−	0.955663i	0.589733	−	0.390148i
$7$	−2.31389	+	1.28293i	−0.874569	+	0.484900i
$7$	−2.31389	+	1.28293i	−0.874569	+	0.484900i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.39671	−	1.80438i	0.798902	−	0.601461i
$10$	−1.66756	+	1.48971i	−0.527329	+	0.471089i
$11$	−0.166984			−0.0503474			−0.0251737	−	0.999683i	$-0.508014\pi$
$11$	−0.166984			−0.0503474			−0.0251737	+	0.999683i	$0.508014\pi$
$12$	−1.14798	+	1.29697i	−0.331393	+	0.374404i
$13$	2.26834	−	0.607801i	0.629125	−	0.168574i	0.0698525	−	0.997557i	$-0.477747\pi$
$13$	2.26834	−	0.607801i	0.629125	−	0.168574i	0.559273	+	0.828984i	$0.311080\pi$
$14$	1.90300	−	1.83809i	0.508599	−	0.491250i
$15$	−2.72600	+	2.75117i	−0.703850	+	0.710349i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.02386	+	3.82109i	0.248322	+	0.926752i	0.971684	+	0.236283i	$0.0759291\pi$
$17$	1.02386	+	3.82109i	0.248322	+	0.926752i	−0.723362	+	0.690469i	$0.757404\pi$
$18$	−1.84803	+	2.36321i	−0.435585	+	0.557015i
$19$	−2.72986	−	4.72826i	−0.626273	−	1.08474i	−0.988293	−	0.152567i	$-0.951246\pi$
$19$	−2.72986	−	4.72826i	−0.626273	−	1.08474i	0.362020	−	0.932170i	$-0.382087\pi$
$20$	1.22517	−	1.87055i	0.273957	−	0.418267i
$21$	3.09634	−	3.37826i	0.675677	−	0.737198i
$22$	0.161294	−	0.0432185i	0.0343879	−	0.00921422i
$23$	1.21416	−	1.21416i	0.253170	−	0.253170i	−0.569099	−	0.822269i	$-0.692708\pi$
$23$	1.21416	−	1.21416i	0.253170	−	0.253170i	0.822269	+	0.569099i	$0.192708\pi$
$24$	0.773181	−	1.54990i	0.157825	−	0.316372i
$25$	2.97047	−	4.02198i	0.594093	−	0.804396i
$26$	−2.03374	+	1.17418i	−0.398849	+	0.230276i
$27$	−2.94598	+	4.28033i	−0.566954	+	0.823749i
$28$	−1.36243	+	2.26799i	−0.257475	+	0.428610i
$29$	0.515067	−	0.297374i	0.0956456	−	0.0552210i	−0.451414	−	0.892314i	$-0.649080\pi$
$29$	0.515067	−	0.297374i	0.0956456	−	0.0552210i	0.547060	+	0.837093i	$0.315747\pi$
$30$	1.92106	−	3.36297i	0.350736	−	0.613991i
$31$	3.71918	−	2.14727i	0.667984	−	0.385661i	−0.127328	−	0.991861i	$-0.540640\pi$
$31$	3.71918	−	2.14727i	0.667984	−	0.385661i	0.795312	+	0.606200i	$0.207307\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.274298	−	0.0917113i	0.0477492	−	0.0159649i
$34$	−1.97794	−	3.42590i	−0.339215	−	0.587537i
$35$	−3.32687	+	4.89203i	−0.562344	+	0.826903i
$36$	1.17342	−	2.76099i	0.195570	−	0.460166i
$37$	0.993252	−	3.70687i	0.163290	−	0.609405i	−0.834963	−	0.550307i	$-0.814511\pi$
$37$	0.993252	−	3.70687i	0.163290	−	0.609405i	0.998252	−	0.0590983i	$-0.0188225\pi$
$38$	3.86061	+	3.86061i	0.626273	+	0.626273i
$39$	−3.39231	+	2.24424i	−0.543205	+	0.359366i
$40$	−0.699292	+	2.12391i	−0.110568	+	0.335820i
$41$	9.70992	+	5.60603i	1.51643	+	0.875514i	0.999814	+	0.0193001i	$0.00614379\pi$
$41$	9.70992	+	5.60603i	1.51643	+	0.875514i	0.516621	+	0.856214i	$0.327190\pi$
$42$	−2.11648	+	4.06454i	−0.326580	+	0.627173i
$43$	9.11376	+	2.44202i	1.38984	+	0.372405i	0.874684	−	0.484694i	$-0.161069\pi$
$43$	9.11376	+	2.44202i	1.38984	+	0.372405i	0.515152	+	0.857099i	$0.327736\pi$
$44$	−0.144612	+	0.0834918i	−0.0218011	+	0.0125869i
$45$	2.96690	−	6.01644i	0.442280	−	0.896877i
$46$	−0.858541	+	1.48704i	−0.126585	+	0.219251i
$47$	0.202539	+	0.755886i	0.0295433	+	0.110257i	0.979123	−	0.203269i	$-0.0651564\pi$
$47$	0.202539	+	0.755886i	0.0295433	+	0.110257i	−0.949580	+	0.313526i	$0.898490\pi$
$48$	−0.345692	+	1.69720i	−0.0498963	+	0.244970i
$49$	3.70820	−	5.93711i	0.529743	−	0.848158i
$50$	−1.82829	+	4.65375i	−0.258559	+	0.658139i
$51$	−3.78050	−	5.71446i	−0.529375	−	0.800184i
$52$	1.66054	−	1.66054i	0.230276	−	0.230276i
$53$	1.87042	+	6.98049i	0.256922	+	0.958845i	0.967011	+	0.254733i	$0.0819877\pi$
$53$	1.87042	+	6.98049i	0.256922	+	0.958845i	−0.710090	+	0.704111i	$0.751346\pi$
$54$	1.73777	−	4.89695i	0.236480	−	0.666391i
$55$	−0.333350	+	0.168212i	−0.0449489	+	0.0226817i
$56$	0.729004	−	2.54334i	0.0974172	−	0.339867i
$57$	7.08112	+	6.26765i	0.937918	+	0.830170i
$58$	−0.420551	+	0.420551i	−0.0552210	+	0.0552210i
$59$	0.526480	+	0.911890i	0.0685418	+	0.118718i	0.898260	−	0.439465i	$-0.144832\pi$
$59$	0.526480	+	0.911890i	0.0685418	+	0.118718i	−0.829718	+	0.558183i	$0.811499\pi$
$60$	−0.985201	+	3.74558i	−0.127189	+	0.483552i
$61$	4.86034	+	2.80612i	0.622303	+	0.359287i	0.777765	−	0.628555i	$-0.216353\pi$
$61$	4.86034	+	2.80612i	0.622303	+	0.359287i	−0.155462	+	0.987842i	$0.549687\pi$
$62$	−3.03670	+	3.03670i	−0.385661	+	0.385661i
$63$	−3.23083	+	7.24995i	−0.407047	+	0.913407i
$64$		−	1.00000i		−	0.125000i
$65$	3.91603	−	3.49838i	0.485724	−	0.433921i
$66$	−0.241215	+	0.159580i	−0.0296915	+	0.0196429i
$67$	3.26215	−	12.1745i	0.398535	−	1.48735i	−0.417139	−	0.908843i	$-0.636967\pi$
$67$	3.26215	−	12.1745i	0.398535	−	1.48735i	0.815674	−	0.578511i	$-0.196366\pi$
$68$	2.79724	+	2.79724i	0.339215	+	0.339215i
$69$	−1.32761	+	2.66130i	−0.159826	+	0.320383i
$70$	1.94736	−	5.58639i	0.232754	−	0.667702i
$71$	9.49875			1.12729			0.563647	−	0.826016i	$-0.309398\pi$
$71$	9.49875			1.12729			0.563647	+	0.826016i	$0.309398\pi$
$72$	−0.418836	+	2.97062i	−0.0493603	+	0.350091i
$73$	5.82830	−	1.56169i	0.682151	−	0.182782i	0.0989286	−	0.995095i	$-0.468458\pi$
$73$	5.82830	−	1.56169i	0.682151	−	0.182782i	0.583222	+	0.812313i	$0.301792\pi$
$74$			3.83763i			0.446115i
$75$	−2.67052	+	8.23822i	−0.308365	+	0.951268i
$76$	−4.72826	−	2.72986i	−0.542368	−	0.313137i
$77$	0.386382	−	0.214228i	0.0440323	−	0.0244135i
$78$	2.69587	−	3.04577i	0.305247	−	0.344865i
$79$	7.50903	+	4.33534i	0.844832	+	0.487764i	0.858904	−	0.512137i	$-0.171146\pi$
$79$	7.50903	+	4.33534i	0.844832	+	0.487764i	−0.0140721	+	0.999901i	$0.504479\pi$
$80$	0.125756	−	2.23253i	0.0140600	−	0.249604i
$81$	2.48841	−	8.64915i	0.276490	−	0.961017i
$82$	−10.8300	−	2.90189i	−1.19597	−	0.320460i
$83$	−1.70285	+	6.35513i	−0.186912	+	0.697566i	0.807301	+	0.590140i	$0.200928\pi$
$83$	−1.70285	+	6.35513i	−0.186912	+	0.697566i	−0.994213	+	0.107426i	$0.965739\pi$
$84$	0.992378	−	4.47383i	0.108277	−	0.488135i
$85$	5.89314	+	6.59668i	0.639201	+	0.715510i
$86$	−9.43526			−1.01743
$87$	−0.682759	+	0.771374i	−0.0731995	+	0.0827000i
$88$	0.118075	−	0.118075i	0.0125869	−	0.0125869i
$89$	7.25597	+	12.5677i	0.769131	+	1.33217i	0.938035	+	0.346542i	$0.112644\pi$
$89$	7.25597	+	12.5677i	0.769131	+	1.33217i	−0.168903	+	0.985633i	$0.554023\pi$
$90$	−1.30864	+	6.57932i	−0.137943	+	0.693521i
$91$	−4.46894	+	4.31650i	−0.468472	+	0.452492i
$92$	0.444413	−	1.65857i	0.0463333	−	0.172918i
$93$	−4.93004	+	5.56991i	−0.511221	+	0.577573i
$94$	−0.391275	−	0.677709i	−0.0403570	−	0.0699003i
$95$	−10.2127	−	6.68910i	−1.04780	−	0.686287i
$96$	−0.105356	−	1.72884i	−0.0107528	−	0.176449i
$97$	−13.8533	−	3.71198i	−1.40659	−	0.376894i	−0.525882	−	0.850557i	$-0.676265\pi$
$97$	−13.8533	−	3.71198i	−1.40659	−	0.376894i	−0.880706	+	0.473663i	$0.842931\pi$
$98$	−2.04521	+	6.69456i	−0.206598	+	0.676252i
$99$	−0.400211	+	0.301302i	−0.0402227	+	0.0302820i
$100$	0.561510	−	4.96837i	0.0561510	−	0.496837i
$101$		−	0.945804i		−	0.0941110i	−0.998892	−	0.0470555i	$-0.985016\pi$
$101$		−	0.945804i		−	0.0941110i	0.998892	−	0.0470555i	$-0.0149838\pi$
$102$	5.13069	+	4.54128i	0.508014	+	0.449653i
$103$	−10.4774	−	10.4774i	−1.03237	−	1.03237i	−0.999458	−	0.0329098i	$-0.989523\pi$
$103$	−10.4774	−	10.4774i	−1.03237	−	1.03237i	−0.0329098	−	0.999458i	$-0.510477\pi$
$104$	−1.17418	+	2.03374i	−0.115138	+	0.199425i
$105$	2.77813	−	9.86316i	0.271117	−	0.962546i
$106$	−3.61337	−	6.25854i	−0.350961	−	0.607883i
$107$	2.73094	−	10.1920i	0.264010	−	0.985298i	−0.698844	−	0.715274i	$-0.746302\pi$
$107$	2.73094	−	10.1920i	0.264010	−	0.985298i	0.962854	−	0.270023i	$-0.0870315\pi$
$108$	−0.411130	+	5.17986i	−0.0395610	+	0.498432i
$109$	−16.9426	−	9.78181i	−1.62281	−	0.936927i	−0.986165	−	0.165766i	$-0.946990\pi$
$109$	−16.9426	−	9.78181i	−1.62281	−	0.936927i	−0.636640	−	0.771161i	$-0.719676\pi$
$110$	0.278455	−	0.248758i	0.0265496	−	0.0237181i
$111$	0.404317	+	6.63466i	0.0383761	+	0.629734i
$112$	−0.0459002	+	2.64535i	−0.00433716	+	0.249962i
$113$	−1.07718	−	4.02009i	−0.101333	−	0.378178i	0.896571	−	0.442901i	$-0.146051\pi$
$113$	−1.07718	−	4.02009i	−0.101333	−	0.378178i	−0.997903	+	0.0647222i	$0.979384\pi$
$114$	−8.46203	−	4.22135i	−0.792541	−	0.395366i
$115$	1.20074	−	3.64692i	0.111970	−	0.340077i
$116$	0.297374	−	0.515067i	0.0276105	−	0.0478228i
$117$	4.33985	−	5.54968i	0.401219	−	0.513068i
$118$	−0.744555	−	0.744555i	−0.0685418	−	0.0685418i
$119$	−7.27128	−	7.52807i	−0.666557	−	0.690097i
$120$	−0.0177970	−	3.87294i	−0.00162464	−	0.353550i
$121$	−10.9721			−0.997465
$122$	−5.42101	−	1.45255i	−0.490795	−	0.131508i
$123$	−19.0291	−	3.87591i	−1.71580	−	0.349479i
$124$	2.14727	−	3.71918i	0.192830	−	0.333992i
$125$	1.87839	−	11.0214i	0.168008	−	0.985786i
$126$	1.24432	−	7.83911i	0.110853	−	0.698364i
$127$	8.47664	+	8.47664i	0.752181	+	0.752181i	0.974886	−	0.222705i	$-0.0714888\pi$
$127$	8.47664	+	8.47664i	0.752181	+	0.752181i	−0.222705	+	0.974886i	$0.571489\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−16.3121	+	0.994061i	−1.43620	+	0.0875222i
$130$	−2.87715	+	4.39272i	−0.252343	+	0.385267i
$131$			3.67018i			0.320665i	0.987063	+	0.160332i	$0.0512566\pi$
$131$			3.67018i			0.320665i	−0.987063	+	0.160332i	$0.948743\pi$
$132$	0.191694	−	0.216573i	0.0166848	−	0.0188503i
$133$	12.3826	+	7.43847i	1.07371	+	0.644998i
$134$			12.6040i			1.08882i
$135$	−1.56926	+	11.5125i	−0.135060	+	0.990837i
$136$	−3.42590	−	1.97794i	−0.293769	−	0.169607i
$137$	−14.5440	−	14.5440i	−1.24258	−	1.24258i	−0.958928	−	0.283650i	$-0.908455\pi$
$137$	−14.5440	−	14.5440i	−1.24258	−	1.24258i	−0.283650	−	0.958928i	$-0.591545\pi$
$138$	0.593580	−	2.91423i	0.0505289	−	0.248076i
$139$	−8.69051	+	15.0524i	−0.737120	+	1.27673i	0.216667	+	0.976246i	$0.430481\pi$
$139$	−8.69051	+	15.0524i	−0.737120	+	1.27673i	−0.953787	+	0.300483i	$0.902852\pi$
$140$	−0.435144	+	5.90006i	−0.0367764	+	0.498646i
$141$	−0.747854	−	1.13043i	−0.0629807	−	0.0951993i
$142$	−9.17509	+	2.45846i	−0.769957	+	0.206309i
$143$	−0.378776	+	0.101493i	−0.0316748	+	0.00848725i
$144$	−0.364288	−	2.97780i	−0.0303573	−	0.248150i
$145$	0.728670	−	1.11251i	0.0605127	−	0.0923886i
$146$	−5.22551	+	3.01695i	−0.432466	+	0.249684i
$147$	−2.83054	+	11.7893i	−0.233459	+	0.972367i
$148$	−0.993252	−	3.70687i	−0.0816448	−	0.304703i
$149$		−	19.8054i		−	1.62252i	−0.584687	−	0.811259i	$-0.698783\pi$
$149$		−	19.8054i		−	1.62252i	0.584687	−	0.811259i	$-0.301217\pi$
$150$	0.447315	−	8.64869i	0.0365231	−	0.706163i
$151$	16.8259			1.36927			0.684635	−	0.728887i	$-0.259962\pi$
$151$	16.8259			1.36927			0.684635	+	0.728887i	$0.259962\pi$
$152$	5.27369	+	1.41308i	0.427752	+	0.114616i
$153$	9.34861	+	7.31061i	0.755790	+	0.591028i
$154$	−0.317770	+	0.306931i	−0.0256067	+	0.0247332i
$155$	5.26155	−	8.03314i	0.422618	−	0.645238i
$156$	−1.81571	+	3.63973i	−0.145373	+	0.291411i
$157$	−1.72196	−	0.461398i	−0.137427	−	0.0368236i	0.189450	−	0.981890i	$-0.439330\pi$
$157$	−1.72196	−	0.461398i	−0.137427	−	0.0368236i	−0.326877	+	0.945067i	$0.605996\pi$
$158$	−8.37523	−	2.24414i	−0.666298	−	0.178534i
$159$	−6.90633	−	10.4393i	−0.547707	−	0.827894i
$160$	0.456350	+	2.18901i	0.0360776	+	0.173056i
$161$	−1.25176	+	4.36711i	−0.0986524	+	0.344177i
$162$	−0.165050	+	8.99849i	−0.0129676	+	0.706988i
$163$	1.42458	+	0.381715i	0.111582	+	0.0298982i	0.314178	−	0.949364i	$-0.398271\pi$
$163$	1.42458	+	0.381715i	0.111582	+	0.0298982i	−0.202596	+	0.979262i	$0.564938\pi$
$164$	11.2121			0.875514
$165$	0.455197	−	0.459400i	0.0354370	−	0.0357642i
$166$		−	6.57932i		−	0.510654i
$167$	1.87017	+	6.97959i	0.144718	+	0.540097i	0.999768	+	0.0215500i	$0.00686010\pi$
$167$	1.87017	+	6.97959i	0.144718	+	0.540097i	−0.855049	+	0.518547i	$0.826473\pi$
$168$	0.199349	+	4.57824i	0.0153801	+	0.353219i
$169$	−6.48237	+	3.74260i	−0.498644	+	0.287892i
$170$	−7.39968	−	4.84665i	−0.567530	−	0.371721i
$171$	−15.0743	−	6.40653i	−1.15276	−	0.489920i
$172$	9.11376	−	2.44202i	0.694918	−	0.186203i
$173$	−14.2074	+	3.80687i	−1.08017	+	0.289431i	−0.754666	−	0.656109i	$-0.772201\pi$
$173$	−14.2074	+	3.80687i	−1.08017	+	0.289431i	−0.325505	+	0.945540i	$0.605534\pi$
$174$	0.459848	−	0.921801i	0.0348610	−	0.0698816i
$175$	−1.71344	+	13.1173i	−0.129524	+	0.991576i
$176$	−0.0834918	+	0.144612i	−0.00629343	+	0.0109005i
$177$	−1.36566	−	1.20878i	−0.102649	−	0.0908571i
$178$	−10.2615	−	10.2615i	−0.769131	−	0.769131i
$179$	7.13676	+	4.12041i	0.533426	+	0.307974i	0.742410	−	0.669945i	$-0.233682\pi$
$179$	7.13676	+	4.12041i	0.533426	+	0.307974i	−0.208984	+	0.977919i	$0.567016\pi$
$180$	−0.438806	−	6.69384i	−0.0327067	−	0.498929i
$181$			8.70366i			0.646938i	0.946239	+	0.323469i	$0.104849\pi$
$181$			8.70366i			0.646938i	−0.946239	+	0.323469i	$0.895151\pi$
$182$	3.19947	−	5.32607i	0.237161	−	0.394794i
$183$	−9.52511	−	1.94010i	−0.704116	−	0.143417i
$184$			1.71708i			0.126585i
$185$	−1.75130	−	8.40059i	−0.128758	−	0.617624i
$186$	3.32046	−	6.65611i	0.243468	−	0.488050i
$187$	−0.170968	−	0.638060i	−0.0125024	−	0.0466596i
$188$	0.553347	+	0.553347i	0.0403570	+	0.0403570i
$189$	1.32534	−	13.6837i	0.0964044	−	0.995342i
$190$	11.5960	+	3.81794i	0.841259	+	0.276983i
$191$	0.744998	−	1.29037i	0.0539062	−	0.0933682i	−0.837813	−	0.545957i	$-0.816166\pi$
$191$	0.744998	−	1.29037i	0.0539062	−	0.0933682i	0.891719	+	0.452589i	$0.149499\pi$
$192$	0.549224	+	1.64267i	0.0396368	+	0.118549i
$193$	18.7608	+	5.02694i	1.35043	+	0.361847i	0.860294	−	0.509798i	$-0.170280\pi$
$193$	18.7608	+	5.02694i	1.35043	+	0.361847i	0.490137	+	0.871645i	$0.336947\pi$
$194$	14.3420			1.02969
$195$	−4.51134	+	7.89746i	−0.323064	+	0.565549i
$196$	0.242844	−	6.99579i	0.0173460	−	0.499699i
$197$	7.63439	+	7.63439i	0.543928	+	0.543928i	0.924678	−	0.380750i	$-0.124334\pi$
$197$	7.63439	+	7.63439i	0.543928	+	0.543928i	−0.380750	+	0.924678i	$0.624334\pi$
$198$	0.308591	−	0.394618i	0.0219306	−	0.0280443i
$199$	−5.86400	+	10.1567i	−0.415688	+	0.719993i	−0.995500	−	0.0947573i	$-0.969793\pi$
$199$	−5.86400	+	10.1567i	−0.415688	+	0.719993i	0.579812	+	0.814750i	$0.303126\pi$
$200$	0.743532	+	4.94441i	0.0525757	+	0.349622i
$201$	1.32791	+	21.7903i	0.0936632	+	1.53697i
$202$	0.244792	+	0.913576i	0.0172235	+	0.0642790i
$203$	−0.810302	+	1.34889i	−0.0568720	+	0.0946732i
$204$	−6.13123	−	3.05862i	−0.429272	−	0.214146i
$205$	25.0312	+	1.40999i	1.74826	+	0.0984778i
$206$	12.8321	+	7.40864i	0.894057	+	0.516184i
$207$	0.719176	−	5.10079i	0.0499862	−	0.354530i
$208$	0.607801	−	2.26834i	0.0421434	−	0.157281i
$209$	0.455842	+	0.789541i	0.0315312	+	0.0546137i
$210$	−0.130689	+	10.2461i	−0.00901842	+	0.707049i
$211$	9.53792	−	16.5202i	0.656618	−	1.13730i	−0.324868	−	0.945759i	$-0.605320\pi$
$211$	9.53792	−	16.5202i	0.656618	−	1.13730i	0.981486	−	0.191536i	$-0.0613468\pi$
$212$	5.11008	+	5.11008i	0.350961	+	0.350961i
$213$	−15.6033	+	5.21694i	−1.06912	+	0.357459i
$214$			10.5515i			0.721288i
$215$	20.6538	−	4.30578i	1.40858	−	0.293652i
$216$	−0.943526	−	5.10977i	−0.0641988	−	0.347676i
$217$	−5.85100	+	9.73998i	−0.397192	+	0.661193i
$218$	18.8970	+	5.06344i	1.27987	+	0.342939i
$219$	−8.71623	+	5.76637i	−0.588988	+	0.389655i
$220$	−0.204584	+	0.312351i	−0.0137930	+	0.0210587i
$221$	4.64493	+	8.04525i	0.312452	+	0.541182i
$222$	−2.10772	−	6.30395i	−0.141461	−	0.423093i
$223$	−1.70472	+	6.36209i	−0.114156	+	0.426037i	−0.999222	−	0.0394283i	$-0.987446\pi$
$223$	−1.70472	+	6.36209i	−0.114156	+	0.426037i	0.885066	+	0.465465i	$0.154113\pi$
$224$	−0.640332	−	2.56709i	−0.0427840	−	0.171521i
$225$	−0.137854	−	14.9994i	−0.00919024	−	0.999958i
$226$	2.08095	+	3.60431i	0.138423	+	0.239755i
$227$	13.8129	−	13.8129i	0.916795	−	0.916795i	−0.0799998	−	0.996795i	$-0.525492\pi$
$227$	13.8129	−	13.8129i	0.916795	−	0.916795i	0.996795	+	0.0799998i	$0.0254920\pi$
$228$	9.26626	+	1.88738i	0.613673	+	0.124995i
$229$	−18.1306			−1.19810			−0.599052	−	0.800710i	$-0.704456\pi$
$229$	−18.1306			−1.19810			−0.599052	+	0.800710i	$0.704456\pi$
$230$	−0.215934	+	3.83343i	−0.0142383	+	0.252769i
$231$	−0.517038	+	0.564115i	−0.0340186	+	0.0371160i
$232$	−0.153932	+	0.574483i	−0.0101061	+	0.0377167i
$233$	−11.9228	−	3.19471i	−0.781089	−	0.209292i	−0.153824	−	0.988098i	$-0.549159\pi$
$233$	−11.9228	−	3.19471i	−0.781089	−	0.209292i	−0.627265	+	0.778806i	$0.715826\pi$
$234$	−2.75561	+	6.48381i	−0.180140	+	0.423860i
$235$	1.16578	+	1.30495i	0.0760468	+	0.0851255i
$236$	0.911890	+	0.526480i	0.0593590	+	0.0342709i
$237$	−14.7159	−	2.99738i	−0.955900	−	0.194701i
$238$	8.97193	+	5.38961i	0.581564	+	0.349357i
$239$	−14.3393	−	8.27882i	−0.927535	−	0.535513i	−0.0415039	−	0.999138i	$-0.513215\pi$
$239$	−14.3393	−	8.27882i	−0.927535	−	0.535513i	−0.886031	+	0.463626i	$0.846548\pi$
$240$	1.01958	+	3.73637i	0.0658137	+	0.241182i
$241$		−	6.12886i		−	0.394794i	−0.980324	−	0.197397i	$-0.936751\pi$
$241$		−	6.12886i		−	0.394794i	0.980324	−	0.197397i	$-0.0632488\pi$
$242$	10.5983	−	2.83979i	0.681281	−	0.182549i
$243$	0.662698	+	15.5744i	0.0425121	+	0.999096i
$244$	5.61224			0.359287
$245$	1.42192	−	15.5878i	0.0908433	−	0.995865i
$246$	19.3839	−	1.18126i	1.23587	−	0.0753142i
$247$	−9.06610	−	9.06610i	−0.576862	−	0.576862i
$248$	−1.11151	+	4.14821i	−0.0705809	+	0.263411i
$249$	−0.693170	−	11.3746i	−0.0439279	−	0.720837i
$250$	1.03817	+	11.1320i	0.0656594	+	0.704052i
$251$			13.8250i			0.872626i	0.899795	+	0.436313i	$0.143716\pi$
$251$			13.8250i			0.872626i	−0.899795	+	0.436313i	$0.856284\pi$
$252$	0.826989	+	7.89405i	0.0520954	+	0.497279i
$253$	−0.202745	+	0.202745i	−0.0127465	+	0.0127465i
$254$	−10.3817	−	5.99389i	−0.651407	−	0.376090i
$255$	−13.3035	−	7.59949i	−0.833098	−	0.475899i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.5897	+	10.5897i	−0.660569	+	0.660569i	−0.955514	−	0.294945i	$-0.904699\pi$
$257$	−10.5897	+	10.5897i	−0.660569	+	0.660569i	0.294945	+	0.955514i	$0.404699\pi$
$258$	15.4990	−	5.18207i	0.964925	−	0.322621i
$259$	2.45736	+	9.85156i	0.152693	+	0.612146i
$260$	1.64219	−	4.98771i	0.101844	−	0.309324i
$261$	0.697888	−	1.64210i	0.0431982	−	0.101643i
$262$	−0.949912	−	3.54512i	−0.0586857	−	0.219018i
$263$	−6.73971	+	6.73971i	−0.415588	+	0.415588i	−0.883680	−	0.468092i	$-0.844942\pi$
$263$	−6.73971	+	6.73971i	−0.415588	+	0.415588i	0.468092	+	0.883680i	$0.344942\pi$
$264$	−0.129108	+	0.258808i	−0.00794608	+	0.0159285i
$265$	10.7658	+	12.0510i	0.661336	+	0.740288i
$266$	−13.8859	−	3.98016i	−0.851399	−	0.244039i
$267$	−18.8216	−	16.6594i	−1.15186	−	1.01954i
$268$	−3.26215	−	12.1745i	−0.199268	−	0.743677i
$269$	5.21711	−	9.03630i	0.318093	−	0.550953i	−0.661997	−	0.749506i	$-0.730291\pi$
$269$	5.21711	−	9.03630i	0.318093	−	0.550953i	0.980090	+	0.198553i	$0.0636243\pi$
$270$	−1.46386	−	11.5264i	−0.0890878	−	0.701472i
$271$	0.986098	−	0.569324i	0.0599012	−	0.0345840i	−0.469750	−	0.882799i	$-0.655656\pi$
$271$	0.986098	−	0.569324i	0.0599012	−	0.0345840i	0.529651	+	0.848215i	$0.322323\pi$
$272$	3.82109	+	1.02386i	0.231688	+	0.0620806i
$273$	4.97025	−	9.54502i	0.300813	−	0.577691i
$274$	17.8127	+	10.2842i	1.07610	+	0.621289i
$275$	−0.496019	+	0.671605i	−0.0299111	+	0.0404993i
$276$	0.180905	+	2.96856i	0.0108892	+	0.178687i
$277$	−12.2195	−	12.2195i	−0.734196	−	0.734196i	0.237252	−	0.971448i	$-0.423753\pi$
$277$	−12.2195	−	12.2195i	−0.734196	−	0.734196i	−0.971448	+	0.237252i	$0.923753\pi$
$278$	4.49854	−	16.7888i	0.269805	−	1.00692i
$279$	5.03929	−	11.8572i	0.301694	−	0.709872i
$280$	−1.10673	−	5.81164i	−0.0661398	−	0.347312i
$281$	3.98217	+	6.89732i	0.237556	+	0.411460i	0.960013	−	0.279957i	$-0.0903202\pi$
$281$	3.98217	+	6.89732i	0.237556	+	0.411460i	−0.722456	+	0.691417i	$0.756987\pi$
$282$	1.01495	+	0.898352i	0.0604393	+	0.0534961i
$283$	1.19126	−	4.44586i	0.0708133	−	0.264279i	−0.921438	−	0.388525i	$-0.872985\pi$
$283$	1.19126	−	4.44586i	0.0708133	−	0.264279i	0.992251	+	0.124246i	$0.0396513\pi$
$284$	8.22616	−	4.74938i	0.488133	−	0.281824i
$285$	20.4498	+	5.37892i	1.21134	+	0.318620i
$286$	0.339601	−	0.196069i	0.0200810	−	0.0115938i
$287$	−29.6598	−	0.514635i	−1.75076	−	0.0303779i
$288$	1.12259	+	2.78205i	0.0661490	+	0.163934i
$289$	1.16995	−	0.675473i	0.0688208	−	0.0397337i
$290$	−0.415903	+	1.26319i	−0.0244227	+	0.0741772i
$291$	24.7950	−	1.51101i	1.45351	−	0.0885771i
$292$	4.26661	−	4.26661i	0.249684	−	0.249684i
$293$	−6.58517	+	1.76449i	−0.384710	+	0.103083i	−0.445990	−	0.895038i	$-0.647148\pi$
$293$	−6.58517	+	1.76449i	−0.384710	+	0.103083i	0.0612803	+	0.998121i	$0.480482\pi$
$294$	−0.317208	−	12.1202i	−0.0184999	−	0.706865i
$295$	1.96961	+	1.29006i	0.114675	+	0.0751100i
$296$	1.91882	+	3.32349i	0.111529	+	0.193174i
$297$	0.491930	−	0.714744i	0.0285447	−	0.0414737i
$298$	5.12600	+	19.1305i	0.296941	+	1.10820i
$299$	2.01616	−	3.49210i	0.116598	−	0.201953i
$300$	1.80637	+	8.46977i	0.104291	+	0.489002i
$301$	−24.2212	+	6.04169i	−1.39609	+	0.348237i
$302$	−16.2525	+	4.35485i	−0.935228	+	0.250594i
$303$	0.519458	+	1.55364i	0.0298421	+	0.0892543i
$304$	−5.45972			−0.313137
$305$	12.5295	+	0.705775i	0.717436	+	0.0404126i
$306$	−10.9222	−	4.64191i	−0.624380	−	0.265360i
$307$	13.2330	−	13.2330i	0.755247	−	0.755247i	−0.220206	−	0.975453i	$-0.570673\pi$
$307$	13.2330	−	13.2330i	0.755247	−	0.755247i	0.975453	+	0.220206i	$0.0706730\pi$
$308$	0.227503	−	0.378718i	0.0129632	−	0.0215794i
$309$	22.9653	+	11.4564i	1.30645	+	0.651734i
$310$	−3.00314	+	9.12121i	−0.170567	+	0.518050i
$311$	−24.6871	+	14.2531i	−1.39988	+	0.808219i	−0.994379	−	0.105878i	$-0.966235\pi$
$311$	−24.6871	+	14.2531i	−1.39988	+	0.808219i	−0.405497	+	0.914097i	$0.632901\pi$
$312$	0.811809	−	3.98565i	0.0459596	−	0.225643i
$313$	−2.36746	+	0.634360i	−0.133817	+	0.0358562i	−0.325106	−	0.945678i	$-0.605400\pi$
$313$	−2.36746	+	0.634360i	−0.133817	+	0.0358562i	0.191289	+	0.981534i	$0.438733\pi$
$314$	1.78270			0.100604
$315$	0.853548	+	17.7277i	0.0480920	+	0.998843i
$316$	8.67068			0.487764
$317$	15.8894	−	4.25755i	0.892438	−	0.239128i	0.216672	−	0.976244i	$-0.430480\pi$
$317$	15.8894	−	4.25755i	0.892438	−	0.239128i	0.675766	+	0.737116i	$0.263813\pi$
$318$	9.37290	+	8.29615i	0.525606	+	0.465225i
$319$	−0.0860078	+	0.0496566i	−0.00481551	+	0.00278024i
$320$	−1.00736	−	1.99630i	−0.0563129	−	0.111597i
$321$	1.11167	+	18.2419i	0.0620472	+	1.01817i
$322$	0.0788143	−	4.54229i	0.00439215	−	0.253132i
$323$	15.2721	−	15.2721i	0.849764	−	0.849764i
$324$	−2.16955	−	8.73459i	−0.120531	−	0.485255i
$325$	4.29348	−	10.9287i	0.238159	−	0.606214i
$326$	−1.47483			−0.0816835
$327$	33.2034	+	6.76298i	1.83615	+	0.373993i
$328$	−10.8300	+	2.90189i	−0.597987	+	0.160230i
$329$	−1.43840	−	1.48920i	−0.0793015	−	0.0821020i
$330$	−0.320785	+	0.561560i	−0.0176586	+	0.0309129i
$331$	−3.49272	+	6.04957i	−0.191977	+	0.332514i	−0.945905	−	0.324443i	$-0.894823\pi$
$331$	−3.49272	+	6.04957i	−0.191977	+	0.332514i	0.753928	+	0.656957i	$0.228157\pi$
$332$	1.70285	+	6.35513i	0.0934562	+	0.348783i
$333$	−4.30807	−	10.6765i	−0.236081	−	0.585067i
$334$	−3.61290	−	6.25773i	−0.197689	−	0.342408i
$335$	−5.75182	−	27.5902i	−0.314256	−	1.50741i
$336$	−1.37749	−	4.37064i	−0.0751483	−	0.238438i
$337$	−23.8402	+	6.38796i	−1.29866	+	0.347974i	−0.840943	−	0.541124i	$-0.817999\pi$
$337$	−23.8402	+	6.38796i	−1.29866	+	0.347974i	−0.457716	+	0.889099i	$0.651332\pi$
$338$	5.29283	−	5.29283i	0.287892	−	0.287892i
$339$	3.97738	+	6.01206i	0.216021	+	0.326530i
$340$	8.40195	+	2.76632i	0.455660	+	0.150025i
$341$	−0.621042	+	0.358559i	−0.0336313	+	0.0194170i
$342$	16.2188	+	2.28673i	0.877010	+	0.123652i
$343$	−0.963517	+	18.4952i	−0.0520250	+	0.998646i
$344$	−8.17117	+	4.71763i	−0.440560	+	0.254358i
$345$	0.0305589	+	6.65016i	0.00164524	+	0.358032i
$346$	12.7380	−	7.35431i	0.684801	−	0.395370i
$347$	−5.51873	+	20.5962i	−0.296261	+	1.10566i	0.643949	+	0.765068i	$0.277295\pi$
$347$	−5.51873	+	20.5962i	−0.296261	+	1.10566i	−0.940211	+	0.340594i	$0.889372\pi$
$348$	−0.205600	+	1.00941i	−0.0110213	+	0.0541100i
$349$	11.3424	+	19.6456i	0.607143	+	1.05160i	0.991709	+	0.128505i	$0.0410179\pi$
$349$	11.3424	+	19.6456i	0.607143	+	1.05160i	−0.384566	+	0.923098i	$0.625649\pi$
$350$	−1.73996	−	13.1138i	−0.0930046	−	0.700964i
$351$	−4.08091	+	11.4998i	−0.217823	+	0.613815i
$352$	0.0432185	−	0.161294i	0.00230356	−	0.00859698i
$353$	17.8847	+	17.8847i	0.951907	+	0.951907i	0.998895	−	0.0469883i	$-0.0149624\pi$
$353$	17.8847	+	17.8847i	0.951907	+	0.951907i	−0.0469883	+	0.998895i	$0.514962\pi$
$354$	1.63198	+	0.814128i	0.0867389	+	0.0432704i
$355$	18.9624	−	9.56863i	1.00642	−	0.507850i
$356$	12.5677	+	7.25597i	0.666087	+	0.384566i
$357$	16.0789	+	8.37255i	0.850985	+	0.443122i
$358$	−7.96002	−	2.13288i	−0.420700	−	0.112726i
$359$	−19.6461	+	11.3427i	−1.03688	+	0.598643i	−0.918948	−	0.394379i	$-0.870960\pi$
$359$	−19.6461	+	11.3427i	−1.03688	+	0.598643i	−0.117932	+	0.993022i	$0.537626\pi$
$360$	2.15635	+	6.35218i	0.113649	+	0.334789i
$361$	−5.40428	+	9.36050i	−0.284436	+	0.492658i
$362$	−2.25267	−	8.40709i	−0.118398	−	0.441867i
$363$	18.0235	−	6.02615i	0.945990	−	0.316291i
$364$	−1.71196	+	5.97267i	−0.0897313	+	0.313053i
$365$	10.0619	−	8.98877i	0.526663	−	0.470494i
$366$	9.70268	−	0.591283i	0.507167	−	0.0309068i
$367$	4.80793	−	4.80793i	0.250972	−	0.250972i	−0.570397	−	0.821369i	$-0.693211\pi$
$367$	4.80793	−	4.80793i	0.250972	−	0.250972i	0.821369	+	0.570397i	$0.193211\pi$
$368$	−0.444413	−	1.65857i	−0.0231666	−	0.0864591i
$369$	33.3872	−	4.08442i	1.73807	−	0.212626i
$370$	3.86586	+	7.66108i	0.200977	+	0.398281i
$371$	−13.2834	−	13.7525i	−0.689640	−	0.713995i
$372$	−1.48459	+	7.28870i	−0.0769722	+	0.377902i
$373$	21.2224	−	21.2224i	1.09885	−	1.09885i	0.104309	−	0.994545i	$-0.466737\pi$
$373$	21.2224	−	21.2224i	1.09885	−	1.09885i	0.994545	−	0.104309i	$-0.0332630\pi$
$374$	0.330284	+	0.572069i	0.0170786	+	0.0295810i
$375$	2.96765	+	19.1362i	0.153249	+	0.988188i
$376$	−0.677709	−	0.391275i	−0.0349502	−	0.0201785i
$377$	0.987605	−	0.987605i	0.0508643	−	0.0508643i
$378$	2.26142	+	13.5605i	0.116315	+	0.697475i
$379$			4.98082i			0.255847i	0.991784	+	0.127924i	$0.0408313\pi$
$379$			4.98082i			0.255847i	−0.991784	+	0.127924i	$0.959169\pi$
$380$	−12.1890	−	0.686595i	−0.625282	−	0.0352216i
$381$	−18.5799	−	9.26873i	−0.951876	−	0.474851i
$382$	−0.385639	+	1.43923i	−0.0197310	+	0.0736372i
$383$	−7.29768	−	7.29768i	−0.372894	−	0.372894i	0.495636	−	0.868530i	$-0.334935\pi$
$383$	−7.29768	−	7.29768i	−0.372894	−	0.372894i	−0.868530	+	0.495636i	$0.834935\pi$
$384$	−0.955663	−	1.44454i	−0.0487685	−	0.0737166i
$385$	0.555533	−	0.816888i	0.0283126	−	0.0416325i
$386$	−19.4226			−0.988584
$387$	26.2494	−	10.5919i	1.33433	−	0.538416i
$388$	−13.8533	+	3.71198i	−0.703294	+	0.188447i
$389$			8.77352i			0.444835i	0.974951	+	0.222418i	$0.0713948\pi$
$389$			8.77352i			0.444835i	−0.974951	+	0.222418i	$0.928605\pi$
$390$	2.31361	−	8.79598i	0.117154	−	0.445402i
$391$	5.88255	+	3.39629i	0.297493	+	0.171758i
$392$	1.57607	+	6.82026i	0.0796037	+	0.344475i
$393$	−2.01575	−	6.02888i	−0.101681	−	0.304117i
$394$	−9.35018	−	5.39833i	−0.471055	−	0.271964i
$395$	19.3575	+	1.09039i	0.973983	+	0.0548637i
$396$	−0.195941	+	0.461041i	−0.00984643	+	0.0231682i
$397$	6.07724	+	1.62839i	0.305008	+	0.0817266i	0.408077	−	0.912948i	$-0.366200\pi$
$397$	6.07724	+	1.62839i	0.305008	+	0.0817266i	−0.103069	+	0.994674i	$0.532866\pi$
$398$	3.03543	−	11.3284i	0.152152	−	0.567840i
$399$	−24.4259	−	5.41811i	−1.22282	−	0.271245i
$400$	−1.99790	−	4.58349i	−0.0998952	−	0.229175i
$401$	−8.95892			−0.447387			−0.223694	−	0.974660i	$-0.571812\pi$
$401$	−8.95892			−0.447387			−0.223694	+	0.974660i	$0.571812\pi$
$402$	−6.92241	−	20.7041i	−0.345258	−	1.03263i
$403$	7.13126	−	7.13126i	0.355234	−	0.355234i
$404$	−0.472902	−	0.819090i	−0.0235277	−	0.0407513i
$405$	−3.74516	−	19.7731i	−0.186098	−	0.982531i
$406$	0.433574	−	1.51265i	0.0215179	−	0.0750713i
$407$	−0.165857	+	0.618986i	−0.00822121	+	0.0306820i
$408$	6.71395	+	1.36752i	0.332390	+	0.0677022i
$409$	0.386096	+	0.668737i	0.0190912	+	0.0330669i	0.875413	−	0.483375i	$-0.160589\pi$
$409$	0.386096	+	0.668737i	0.0190912	+	0.0330669i	−0.856322	+	0.516442i	$0.827256\pi$
$410$	−24.5432	+	5.11662i	−1.21210	+	0.252692i
$411$	31.8789	+	15.9030i	1.57247	+	0.784439i
$412$	−14.3124	−	3.83499i	−0.705121	−	0.188936i
$413$	−2.38810	−	1.43458i	−0.117511	−	0.0705911i
$414$	0.625512	+	5.11312i	0.0307422	+	0.251296i
$415$	3.00247	+	14.4022i	0.147385	+	0.706974i
$416$			2.34836i			0.115138i
$417$	6.00848	−	29.4991i	0.294236	−	1.44458i
$418$	−0.644658	−	0.644658i	−0.0315312	−	0.0315312i
$419$	9.61903	−	16.6607i	0.469920	−	0.813926i	−0.529488	−	0.848317i	$-0.677616\pi$
$419$	9.61903	−	16.6607i	0.469920	−	0.813926i	0.999408	+	0.0343913i	$0.0109493\pi$
$420$	−2.52565	−	9.93081i	−0.123239	−	0.484574i
$421$	−11.3336	−	19.6303i	−0.552364	−	0.956723i	−0.998103	−	0.0615599i	$-0.980392\pi$
$421$	−11.3336	−	19.6303i	−0.552364	−	0.956723i	0.445739	−	0.895163i	$-0.352941\pi$
$422$	−4.93719	+	18.4259i	−0.240339	+	0.896956i
$423$	1.84933	+	1.44618i	0.0899177	+	0.0703156i
$424$	−6.25854	−	3.61337i	−0.303942	−	0.175481i
$425$	18.4097	+	7.23249i	0.893002	+	0.350828i
$426$	13.7214	−	9.07761i	0.664803	−	0.439811i
$427$	−14.8464	−	0.257603i	−0.718465	−	0.0124663i
$428$	−2.73094	−	10.1920i	−0.132005	−	0.492649i
$429$	0.566460	−	0.374751i	0.0273490	−	0.0180932i
$430$	−18.8357	+	9.50467i	−0.908336	+	0.458356i
$431$	−12.5020	+	21.6541i	−0.602200	+	1.04304i	0.390287	+	0.920693i	$0.372376\pi$
$431$	−12.5020	+	21.6541i	−0.602200	+	1.04304i	−0.992487	+	0.122348i	$0.960958\pi$
$432$	2.23388	+	4.69146i	0.107478	+	0.225718i
$433$	−23.5662	−	23.5662i	−1.13252	−	1.13252i	−0.989757	−	0.142760i	$-0.954402\pi$
$433$	−23.5662	−	23.5662i	−1.13252	−	1.13252i	−0.142760	−	0.989757i	$-0.545598\pi$
$434$	3.13074	−	10.9225i	0.150280	−	0.524294i
$435$	−0.585947	+	2.22768i	−0.0280940	+	0.106809i
$436$	−19.5636			−0.936927
$437$	−9.05535	−	2.42637i	−0.433176	−	0.116069i
$438$	6.92679	−	7.82581i	0.330975	−	0.373932i
$439$	−19.5029	+	33.7800i	−0.930822	+	1.61223i	−0.148901	+	0.988852i	$0.547574\pi$
$439$	−19.5029	+	33.7800i	−0.930822	+	1.61223i	−0.781921	+	0.623378i	$0.785760\pi$
$440$	0.116770	−	0.354658i	0.00556681	−	0.0169077i
$441$	−1.82534	−	20.9205i	−0.0869209	−	0.996215i
$442$	−6.56892	−	6.56892i	−0.312452	−	0.312452i
$443$	−6.35482	−	23.7165i	−0.301927	−	1.12681i	−0.935559	−	0.353171i	$-0.885103\pi$
$443$	−6.35482	−	23.7165i	−0.301927	−	1.12681i	0.633632	−	0.773635i	$-0.281563\pi$
$444$	3.66748	+	5.54363i	0.174051	+	0.263089i
$445$	27.1453	+	17.7796i	1.28681	+	0.842835i
$446$		−	6.58652i		−	0.311881i
$447$	10.8776	+	32.5336i	0.514492	+	1.53879i
$448$	1.28293	+	2.31389i	0.0606125	+	0.109321i
$449$			10.0900i			0.476178i	0.971243	+	0.238089i	$0.0765210\pi$
$449$			10.0900i			0.476178i	−0.971243	+	0.238089i	$0.923479\pi$
$450$	4.01528	+	14.4526i	0.189282	+	0.681302i
$451$	−1.62140	−	0.936114i	−0.0763486	−	0.0440799i
$452$	−2.94291	−	2.94291i	−0.138423	−	0.138423i
$453$	−27.6393	+	9.24116i	−1.29861	+	0.434188i
$454$	−9.76720	+	16.9173i	−0.458398	+	0.793968i
$455$	−4.57311	+	13.1189i	−0.214391	+	0.615022i
$456$	−9.43901	+	0.575214i	−0.442022	+	0.0269369i
$457$	−5.69274	+	1.52536i	−0.266295	+	0.0713535i	−0.389496	−	0.921028i	$-0.627351\pi$
$457$	−5.69274	+	1.52536i	−0.266295	+	0.0713535i	0.123201	+	0.992382i	$0.460684\pi$
$458$	17.5128	−	4.69254i	0.818320	−	0.219268i
$459$	−19.3718	−	6.87442i	−0.904198	−	0.320870i
$460$	−0.783589	−	3.75870i	−0.0365350	−	0.175250i
$461$	27.8161	−	16.0597i	1.29553	−	0.747973i	0.315898	−	0.948793i	$-0.397694\pi$
$461$	27.8161	−	16.0597i	1.29553	−	0.747973i	0.979628	+	0.200820i	$0.0643608\pi$
$462$	0.353417	−	0.678712i	0.0164424	−	0.0315765i
$463$	−0.618271	−	2.30742i	−0.0287335	−	0.107235i	0.950070	−	0.312037i	$-0.101011\pi$
$463$	−0.618271	−	2.30742i	−0.0287335	−	0.107235i	−0.978803	+	0.204803i	$0.934345\pi$
$464$		−	0.594749i		−	0.0276105i
$465$	−4.23098	+	16.0855i	−0.196207	+	0.745949i
$466$	12.3434			0.571797
$467$	−21.0635	−	5.64396i	−0.974704	−	0.261171i	−0.263891	−	0.964552i	$-0.585006\pi$
$467$	−21.0635	−	5.64396i	−0.974704	−	0.261171i	−0.710813	+	0.703381i	$0.751673\pi$
$468$	0.983579	−	6.97609i	0.0454660	−	0.322470i
$469$	8.07073	+	32.3556i	0.372672	+	1.49404i
$470$	−1.46380	−	0.958759i	−0.0675200	−	0.0442243i
$471$	3.08202	−	0.187819i	0.142012	−	0.00865422i
$472$	−1.01708	−	0.272526i	−0.0468149	−	0.0125440i
$473$	−1.52185	−	0.407778i	−0.0699747	−	0.0187497i
$474$	14.9902	−	0.913508i	0.688525	−	0.0419588i
$475$	−27.1259	−	3.06569i	−1.24462	−	0.140663i
$476$	−10.0612	−	2.88386i	−0.461152	−	0.132181i
$477$	17.0783	+	13.3552i	0.781963	+	0.611495i
$478$	15.9935	+	4.28543i	0.731524	+	0.196011i
$479$	39.2598			1.79383			0.896914	−	0.442205i	$-0.145804\pi$
$479$	39.2598			1.79383			0.896914	+	0.442205i	$0.145804\pi$
$480$	−1.95188	−	3.34517i	−0.0890909	−	0.152685i
$481$		−	9.01214i		−	0.410918i
$482$	1.58626	+	5.92002i	0.0722524	+	0.269650i
$483$	−0.342299	−	7.86120i	−0.0155752	−	0.357697i
$484$	−9.50213	+	5.48606i	−0.431915	+	0.249366i
$485$	−31.3947	+	6.54496i	−1.42556	+	0.297191i
$486$	−4.67106	−	14.8722i	−0.211884	−	0.674615i
$487$	24.8714	−	6.66426i	1.12703	−	0.301987i	0.353304	−	0.935508i	$-0.385058\pi$
$487$	24.8714	−	6.66426i	1.12703	−	0.301987i	0.773725	+	0.633522i	$0.218391\pi$
$488$	−5.42101	+	1.45255i	−0.245397	+	0.0657540i
$489$	−2.54976	+	0.155382i	−0.115304	+	0.00702664i
$490$	2.66094	+	15.4246i	0.120209	+	0.696814i
$491$	17.7582	−	30.7581i	0.801417	−	1.38810i	−0.117266	−	0.993100i	$-0.537413\pi$
$491$	17.7582	−	30.7581i	0.801417	−	1.38810i	0.918683	−	0.394995i	$-0.129254\pi$
$492$	−18.4177	+	6.15792i	−0.830332	+	0.277621i
$493$	1.66365	+	1.66365i	0.0749271	+	0.0749271i
$494$	11.1037	+	6.41070i	0.499577	+	0.288431i
$495$	−0.495424	+	1.00465i	−0.0222676	+	0.0451555i
$496$		−	4.29454i		−	0.192830i
$497$	−21.9791	+	12.1862i	−0.985897	+	0.546626i
$498$	3.61352	+	10.8076i	0.161926	+	0.484301i
$499$			10.2662i			0.459577i	0.973241	+	0.229788i	$0.0738034\pi$
$499$			10.2662i			0.459577i	−0.973241	+	0.229788i	$0.926197\pi$
$500$	−3.88397	−	10.4840i	−0.173697	−	0.468860i
$501$	−6.90543	−	10.4380i	−0.308512	−	0.466335i
$502$	−3.57817	−	13.3539i	−0.159702	−	0.596015i
$503$	−28.0275	−	28.0275i	−1.24968	−	1.24968i	−0.955860	−	0.293824i	$-0.905072\pi$
$503$	−28.0275	−	28.0275i	−1.24968	−	1.24968i	−0.293824	−	0.955860i	$-0.594928\pi$
$504$	−2.84194	−	7.41103i	−0.126590	−	0.330114i
$505$	−0.952761	−	1.88811i	−0.0423973	−	0.0840199i
$506$	0.143362	−	0.248311i	0.00637323	−	0.0110387i
$507$	8.59285	−	9.70812i	0.381622	−	0.431153i
$508$	11.5793	+	3.10267i	0.513749	+	0.137659i
$509$	−30.3638			−1.34585			−0.672927	−	0.739709i	$-0.734963\pi$
$509$	−30.3638			−1.34585			−0.672927	+	0.739709i	$0.734963\pi$
$510$	14.8171	+	3.89734i	0.656112	+	0.172577i
$511$	−11.4825	+	11.0908i	−0.507957	+	0.490630i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	28.2806	+	2.24466i	1.24862	+	0.0991040i
$514$	7.48807	−	12.9697i	0.330285	−	0.572070i
$515$	−31.4705	−	10.3616i	−1.38676	−	0.456587i
$516$	−13.6297	+	9.01693i	−0.600012	+	0.396948i
$517$	−0.0338207	−	0.126220i	−0.00148743	−	0.00555117i
$518$	−4.92339	−	8.87987i	−0.216322	−	0.390159i
$519$	21.2472	−	14.0565i	0.932651	−	0.617011i
$520$	−0.295322	+	5.24278i	−0.0129507	+	0.229911i
$521$	23.8765	+	13.7851i	1.04605	+	0.603936i	0.921540	−	0.388282i	$-0.126931\pi$
$521$	23.8765	+	13.7851i	1.04605	+	0.603936i	0.124508	+	0.992219i	$0.460265\pi$
$522$	−0.249102	+	1.76677i	−0.0109029	+	0.0773295i
$523$	−0.951362	+	3.55053i	−0.0416002	+	0.155254i	−0.983602	−	0.180355i	$-0.942275\pi$
$523$	−0.951362	+	3.55053i	−0.0416002	+	0.155254i	0.942001	+	0.335609i	$0.108942\pi$
$524$	1.83509	+	3.17847i	0.0801662	+	0.138852i
$525$	−4.38973	−	22.4884i	−0.191584	−	0.981476i
$526$	4.76569	−	8.25442i	0.207794	−	0.359910i
$527$	12.0128	+	12.0128i	0.523287	+	0.523287i
$528$	0.0577248	−	0.283405i	0.00251215	−	0.0123336i
$529$			20.0516i			0.871810i
$530$	−13.5180	−	8.85400i	−0.587183	−	0.384593i
$531$	2.90722	+	1.23556i	0.126162	+	0.0536188i
$532$	14.4429	+	0.250602i	0.626179	+	0.0108650i
$533$	25.4328	+	6.81469i	1.10162	+	0.295177i
$534$	22.4921	+	11.2204i	0.973327	+	0.485552i
$535$	−4.81519	−	23.0974i	−0.208179	−	0.998586i
$536$	6.30199	+	10.9154i	0.272205	+	0.471472i
$537$	−13.9863	−	2.84878i	−0.603555	−	0.122934i
$538$	−2.70057	+	10.0787i	−0.116430	+	0.434523i
$539$	−0.619209	+	0.991399i	−0.0266712	+	0.0427026i
$540$	4.39723	+	10.7547i	0.189226	+	0.462810i
$541$	−17.9512	−	31.0923i	−0.771781	−	1.33676i	−0.936586	−	0.350438i	$-0.886033\pi$
$541$	−17.9512	−	31.0923i	−0.771781	−	1.33676i	0.164805	−	0.986326i	$-0.447301\pi$
$542$	−0.805146	+	0.805146i	−0.0345840	+	0.0345840i
$543$	−4.78026	−	14.2972i	−0.205140	−	0.613552i
$544$	−3.95589			−0.169607
$545$	−43.6763	−	2.46025i	−1.87089	−	0.105386i
$546$	−2.33046	+	10.5062i	−0.0997346	+	0.449623i
$547$	−5.32856	+	19.8865i	−0.227833	+	0.850284i	0.753417	+	0.657543i	$0.228404\pi$
$547$	−5.32856	+	19.8865i	−0.227833	+	0.850284i	−0.981250	+	0.192741i	$0.938262\pi$
$548$	−19.8675	−	5.32347i	−0.848697	−	0.227408i
$549$	16.7121	−	2.04447i	0.713256	−	0.0872559i
$550$	0.305294	−	0.777099i	0.0130178	−	0.0331356i
$551$	−2.81213	−	1.62358i	−0.119801	−	0.0691669i
$552$	−0.943062	−	2.82059i	−0.0401394	−	0.120052i
$553$	−22.9370	−	0.397986i	−0.975381	−	0.0169241i
$554$	14.9657	+	8.64046i	0.635832	+	0.367098i
$555$	7.49061	+	12.8375i	0.317959	+	0.544922i
$556$			17.3810i			0.737120i
$557$	−4.33688	+	1.16206i	−0.183759	+	0.0492382i	−0.349525	−	0.936927i	$-0.613657\pi$
$557$	−4.33688	+	1.16206i	−0.183759	+	0.0492382i	0.165766	+	0.986165i	$0.446990\pi$
$558$	−1.79871	+	12.7574i	−0.0761454	+	0.540065i
$559$	22.1574			0.937158
$560$	2.57318	+	5.32717i	0.108737	+	0.225114i
$561$	0.631281	+	0.954220i	0.0266527	+	0.0402872i
$562$	−5.63164	−	5.63164i	−0.237556	−	0.237556i
$563$	−7.30409	+	27.2592i	−0.307831	+	1.14884i	0.622650	+	0.782500i	$0.286056\pi$
$563$	−7.30409	+	27.2592i	−0.307831	+	1.14884i	−0.930481	+	0.366340i	$0.880611\pi$
$564$	−1.21288	−	0.605053i	−0.0510713	−	0.0254773i
$565$	−6.20004	−	6.94022i	−0.260838	−	0.291977i
$566$			4.60269i			0.193465i
$567$	5.33832	+	23.2057i	0.224188	+	0.974546i
$568$	−6.71663	+	6.71663i	−0.281824	+	0.281824i
$569$	33.0433	+	19.0775i	1.38525	+	0.799772i	0.992775	−	0.119992i	$-0.0382868\pi$
$569$	33.0433	+	19.0775i	1.38525	+	0.799772i	0.392472	+	0.919764i	$0.371620\pi$
$570$	−21.1452	+	0.0971667i	−0.885675	+	0.00406987i
$571$	−10.1884	−	17.6468i	−0.426371	−	0.738496i	0.570177	−	0.821522i	$-0.306875\pi$
$571$	−10.1884	−	17.6468i	−0.426371	−	0.738496i	−0.996547	+	0.0830263i	$0.973541\pi$
$572$	−0.277283	+	0.277283i	−0.0115938	+	0.0115938i
$573$	−0.515079	+	2.52883i	−0.0215177	+	0.105643i
$574$	28.7824	−	7.17943i	1.20135	−	0.299664i
$575$	−1.27670	−	8.48995i	−0.0532423	−	0.354055i
$576$	−1.80438	−	2.39671i	−0.0751826	−	0.0998628i
$577$	9.53801	+	35.5963i	0.397073	+	1.48190i	0.818221	+	0.574904i	$0.194960\pi$
$577$	9.53801	+	35.5963i	0.397073	+	1.48190i	−0.421149	+	0.906992i	$0.638373\pi$
$578$	−0.955263	+	0.955263i	−0.0397337	+	0.0397337i
$579$	−33.5786	+	2.04629i	−1.39548	+	0.0850408i
$580$	0.0747935	−	1.32779i	0.00310563	−	0.0551336i
$581$	−4.21295	−	16.8897i	−0.174782	−	0.700704i
$582$	−23.5591	+	7.87695i	−0.976556	+	0.326510i
$583$	−0.312329	−	1.16563i	−0.0129353	−	0.0482754i
$584$	−3.01695	+	5.22551i	−0.124842	+	0.216233i
$585$	3.07316	−	15.4506i	0.127059	−	0.638805i
$586$	5.90410	−	3.40873i	0.243896	−	0.140814i
$587$	−9.32497	−	2.49862i	−0.384883	−	0.103129i	0.0611892	−	0.998126i	$-0.480511\pi$
$587$	−9.32497	−	2.49862i	−0.384883	−	0.103129i	−0.446072	+	0.894997i	$0.647177\pi$
$588$	3.44334	+	11.6251i	0.142001	+	0.479412i
$589$	−20.3057	−	11.7235i	−0.836681	−	0.483058i
$590$	−2.23639	−	0.736327i	−0.0920707	−	0.0303141i
$591$	−16.7337	−	8.34777i	−0.688334	−	0.343381i
$592$	−2.71361	−	2.71361i	−0.111529	−	0.111529i
$593$	3.74179	−	13.9646i	0.153657	−	0.573456i	−0.845560	−	0.533881i	$-0.820733\pi$
$593$	3.74179	−	13.9646i	0.153657	−	0.573456i	0.999217	−	0.0395748i	$-0.0126003\pi$
$594$	−0.290179	+	0.817711i	−0.0119062	+	0.0335511i
$595$	−22.0991	−	7.70355i	−0.905977	−	0.315815i
$596$	−9.90268	−	17.1519i	−0.405630	−	0.702571i
$597$	4.05427	−	19.9048i	0.165930	−	0.814649i
$598$	−1.04364	+	3.89493i	−0.0426777	+	0.159275i
$599$	−5.95949	+	3.44071i	−0.243498	+	0.140584i	−0.616783	−	0.787133i	$-0.711565\pi$
$599$	−5.95949	+	3.44071i	−0.243498	+	0.140584i	0.373285	+	0.927717i	$0.378231\pi$
$600$	−3.93696	−	7.71365i	−0.160726	−	0.314908i
$601$	−33.1921	+	19.1635i	−1.35393	+	0.781693i	−0.988798	−	0.149261i	$-0.952310\pi$
$601$	−33.1921	+	19.1635i	−1.35393	+	0.781693i	−0.365135	+	0.930955i	$0.618977\pi$
$602$	21.8322	−	12.1047i	0.889813	−	0.493352i
$603$	−14.1491	−	35.0649i	−0.576195	−	1.42795i
$604$	14.5716	−	8.41293i	0.592911	−	0.342317i
$605$	−21.9037	+	11.0528i	−0.890512	+	0.449361i
$606$	−0.903869	−	1.36626i	−0.0367172	−	0.0555003i
$607$	23.5261	−	23.5261i	0.954895	−	0.954895i	−0.0441309	−	0.999026i	$-0.514052\pi$
$607$	23.5261	−	23.5261i	0.954895	−	0.954895i	0.999026	+	0.0441309i	$0.0140519\pi$
$608$	5.27369	−	1.41308i	0.213876	−	0.0573080i
$609$	0.590216	−	2.66081i	0.0239167	−	0.107821i
$610$	−12.2852	+	2.56114i	−0.497414	+	0.103698i
$611$	0.918856	+	1.59150i	0.0371729	+	0.0643854i
$612$	11.7514	+	1.65687i	0.475024	+	0.0669750i
$613$	0.455255	+	1.69904i	0.0183876	+	0.0686234i	0.974510	−	0.224344i	$-0.0720239\pi$
$613$	0.455255	+	1.69904i	0.0183876	+	0.0686234i	−0.956122	+	0.292967i	$0.905357\pi$
$614$	−9.35714	+	16.2070i	−0.377624	+	0.654063i
$615$	−41.8924	+	11.4316i	−1.68926	+	0.460967i
$616$	−0.121732	+	0.424695i	−0.00490471	+	0.0171115i
$617$	5.90574	−	1.58244i	0.237756	−	0.0637066i	−0.137973	−	0.990436i	$-0.544059\pi$
$617$	5.90574	−	1.58244i	0.237756	−	0.0637066i	0.375730	+	0.926729i	$0.377392\pi$
$618$	−25.1479	−	5.12221i	−1.01160	−	0.206045i
$619$	−3.29602			−0.132478			−0.0662392	−	0.997804i	$-0.521100\pi$
$619$	−3.29602			−0.132478			−0.0662392	+	0.997804i	$0.521100\pi$
$620$	0.540066	−	9.58768i	0.0216896	−	0.385051i
$621$	1.62011	+	8.77389i	0.0650128	+	0.352084i
$622$	20.1569	−	20.1569i	0.808219	−	0.808219i
$623$	−32.9130	−	19.7715i	−1.31863	−	0.792127i
$624$	0.247414	+	4.05995i	0.00990448	+	0.162528i
$625$	−7.35265	−	23.8943i	−0.294106	−	0.955773i
$626$	2.12261	−	1.22549i	0.0848366	−	0.0489804i
$627$	−1.18243	−	1.04659i	−0.0472218	−	0.0417969i
$628$	−1.72196	+	0.461398i	−0.0687137	+	0.0184118i
$629$	15.1812			0.605316
$630$	−5.41273	−	16.9027i	−0.215648	−	0.673421i
$631$	−21.7142			−0.864428			−0.432214	−	0.901771i	$-0.642268\pi$
$631$	−21.7142			−0.864428			−0.432214	+	0.901771i	$0.642268\pi$
$632$	−8.37523	+	2.24414i	−0.333149	+	0.0892670i
$633$	−6.59436	+	32.3756i	−0.262102	+	1.28681i
$634$	−14.2461	+	8.22496i	−0.565783	+	0.326655i
$635$	25.4610	+	8.38297i	1.01039	+	0.332668i
$636$	−11.2007	−	5.58758i	−0.444138	−	0.221562i
$637$	4.80290	−	15.7212i	0.190298	−	0.622898i
$638$	0.0702251	−	0.0702251i	0.00278024	−	0.00278024i
$639$	22.7657	−	17.1394i	0.900598	−	0.678024i
$640$	1.48971	+	1.66756i	0.0588861	+	0.0659161i
$641$	−13.1468			−0.519266			−0.259633	−	0.965707i	$-0.583602\pi$
$641$	−13.1468			−0.519266			−0.259633	+	0.965707i	$0.583602\pi$
$642$	−5.79515	−	17.3326i	−0.228716	−	0.684065i
$643$	−13.9541	+	3.73898i	−0.550295	+	0.147451i	−0.523244	−	0.852183i	$-0.675278\pi$
$643$	−13.9541	+	3.73898i	−0.550295	+	0.147451i	−0.0270510	+	0.999634i	$0.508612\pi$
$644$	1.09950	+	4.40791i	0.0433264	+	0.173696i
$645$	−31.5625	+	18.4165i	−1.24277	+	0.725150i
$646$	−10.7990	+	18.7045i	−0.424882	+	0.735917i
$647$	−3.61315	−	13.4845i	−0.142047	−	0.530128i	−0.999869	−	0.0161809i	$-0.994849\pi$
$647$	−3.61315	−	13.4845i	−0.142047	−	0.530128i	0.857822	−	0.513948i	$-0.171817\pi$
$648$	4.35631	+	7.87544i	0.171132	+	0.309377i
$649$	−0.0879135	−	0.152271i	−0.00345091	−	0.00597714i
$650$	−1.31863	+	11.6675i	−0.0517208	+	0.457638i
$651$	4.26181	−	19.2131i	0.167033	−	0.753019i
$652$	1.42458	−	0.381715i	0.0557908	−	0.0149491i
$653$	20.8507	−	20.8507i	0.815952	−	0.815952i	−0.169567	−	0.985519i	$-0.554237\pi$
$653$	20.8507	−	20.8507i	0.815952	−	0.815952i	0.985519	+	0.169567i	$0.0542368\pi$
$654$	−33.8224	+	2.06114i	−1.32256	+	0.0805971i
$655$	3.69718	+	7.32679i	0.144461	+	0.286281i
$656$	9.70992	−	5.60603i	0.379109	−	0.218879i
$657$	11.1508	−	14.2594i	0.435036	−	0.556312i
$658$	1.77482	+	1.06617i	0.0691896	+	0.0415636i
$659$	9.00663	−	5.19998i	0.350849	−	0.202563i	−0.314210	−	0.949353i	$-0.601740\pi$
$659$	9.00663	−	5.19998i	0.350849	−	0.202563i	0.665059	+	0.746791i	$0.268406\pi$
$660$	0.164512	−	0.625451i	0.00640363	−	0.0243456i
$661$	36.6278	−	21.1471i	1.42466	−	0.822525i	0.427963	−	0.903796i	$-0.359231\pi$
$661$	36.6278	−	21.1471i	1.42466	−	0.822525i	0.996692	+	0.0812711i	$0.0258980\pi$
$662$	1.80796	−	6.74742i	0.0702686	−	0.262246i
$663$	−12.0487	−	10.6646i	−0.467933	−	0.414177i
$664$	−3.28966	−	5.69786i	−0.127664	−	0.221120i
$665$	32.2127	+	2.37576i	1.24915	+	0.0921282i
$666$	6.92455	+	9.19767i	0.268321	+	0.356403i
$667$	0.264314	−	0.986434i	0.0102343	−	0.0381949i
$668$	5.10941	+	5.10941i	0.197689	+	0.197689i
$669$	−0.693929	−	11.3871i	−0.0268288	−	0.440249i
$670$	12.6967	+	25.1614i	0.490516	+	0.972070i
$671$	−0.811597	−	0.468576i	−0.0313314	−	0.0180892i
$672$	2.46176	+	3.86520i	0.0949645	+	0.149103i
$673$	20.5230	+	5.49912i	0.791104	+	0.211976i	0.631674	−	0.775234i	$-0.282368\pi$
$673$	20.5230	+	5.49912i	0.791104	+	0.211976i	0.159429	+	0.987209i	$0.449035\pi$
$674$	21.3745	−	12.3406i	0.823316	−	0.475342i
$675$	8.46445	+	24.5632i	0.325797	+	0.945440i
$676$	−3.74260	+	6.48237i	−0.143946	+	0.249322i
$677$	6.71406	+	25.0572i	0.258042	+	0.963027i	0.966373	+	0.257146i	$0.0827821\pi$
$677$	6.71406	+	25.0572i	0.258042	+	0.963027i	−0.708330	+	0.705881i	$0.750551\pi$
$678$	−5.39789	−	4.77778i	−0.207305	−	0.183489i
$679$	36.8172	−	9.18362i	1.41292	−	0.352435i
$680$	−8.83164	−	0.497478i	−0.338678	−	0.0190774i
$681$	−15.1036	+	30.2764i	−0.578772	+	1.16019i
$682$	0.507079	−	0.507079i	0.0194170	−	0.0194170i
$683$	6.58171	+	24.5633i	0.251842	+	0.939887i	0.969820	+	0.243822i	$0.0784011\pi$
$683$	6.58171	+	24.5633i	0.251842	+	0.939887i	−0.717978	+	0.696066i	$0.754932\pi$
$684$	−16.2580	+	1.98891i	−0.621639	+	0.0760479i
$685$	−43.6853	−	14.3833i	−1.66913	−	0.549557i
$686$	−3.85622	−	18.1143i	−0.147231	−	0.691609i
$687$	29.7825	−	9.95775i	1.13627	−	0.379912i
$688$	6.67174	−	6.67174i	0.254358	−	0.254358i
$689$	8.48550	+	14.6973i	0.323272	+	0.559923i
$690$	−1.75070	−	6.41565i	−0.0666482	−	0.244240i
$691$	4.93331	+	2.84825i	0.187672	+	0.108352i	0.590892	−	0.806751i	$-0.298776\pi$
$691$	4.93331	+	2.84825i	0.187672	+	0.108352i	−0.403220	+	0.915103i	$0.632109\pi$
$692$	−10.4006	+	10.4006i	−0.395370	+	0.395370i
$693$	0.539496	−	1.21062i	0.0204938	−	0.0459877i
$694$		−	21.3228i		−	0.809401i
$695$	−2.18578	+	38.8037i	−0.0829112	+	1.47191i
$696$	−0.0626603	−	1.02823i	−0.00237513	−	0.0389749i
$697$	−11.4796	+	42.8423i	−0.434819	+	1.62277i
$698$	−16.0405	−	16.0405i	−0.607143	−	0.607143i
$699$	21.3398	−	1.30045i	0.807145	−	0.0491875i
$700$	5.07478	+	12.2167i	0.191809	+	0.461746i
$701$	−5.56170			−0.210063			−0.105031	−	0.994469i	$-0.533494\pi$
$701$	−5.56170			−0.210063			−0.105031	+	0.994469i	$0.533494\pi$
$702$	0.965482	−	12.1642i	0.0364398	−	0.459108i
$703$	−20.2385	+	5.42288i	−0.763308	+	0.204528i
$704$			0.166984i			0.00629343i
$705$	−2.63169	−	1.50333i	−0.0991152	−	0.0566185i
$706$	−21.9042	−	12.6464i	−0.824376	−	0.475954i
$707$	1.21340	+	2.18849i	0.0456345	+	0.0823066i
$708$	−1.78709	−	0.363999i	−0.0671628	−	0.0136799i
$709$	10.0452	+	5.79957i	0.377254	+	0.217807i	0.676623	−	0.736330i	$-0.263443\pi$
$709$	10.0452	+	5.79957i	0.377254	+	0.217807i	−0.299369	+	0.954137i	$0.596776\pi$
$710$	−15.8397	+	14.1504i	−0.594455	+	0.531056i
$711$	25.8195	−	3.15862i	0.968309	−	0.118458i
$712$	−14.0175	−	3.75597i	−0.525326	−	0.140761i
$713$	1.90855	−	7.12281i	0.0714758	−	0.266751i
$714$	−17.6980	−	3.92574i	−0.662330	−	0.146917i
$715$	−0.653913	+	0.584173i	−0.0244550	+	0.0218468i
$716$	8.24082			0.307974
$717$	28.1017	+	5.72384i	1.04948	+	0.213761i
$718$	16.0409	−	16.0409i	0.598643	−	0.598643i
$719$	−19.2115	−	33.2753i	−0.716469	−	1.24096i	−0.962390	−	0.271671i	$-0.912424\pi$
$719$	−19.2115	−	33.2753i	−0.716469	−	1.24096i	0.245921	−	0.969290i	$-0.420909\pi$
$720$	−3.72694	−	5.57763i	−0.138895	−	0.207866i
$721$	37.6853	+	10.8018i	1.40347	+	0.402282i
$722$	2.79746	−	10.4403i	0.104111	−	0.388547i
$723$	3.36611	+	10.0677i	0.125187	+	0.374421i
$724$	4.35183	+	7.53759i	0.161734	+	0.280132i
$725$	0.333957	−	2.95493i	0.0124029	−	0.109743i
$726$	−15.8497	+	10.4856i	−0.588238	+	0.389159i
$727$	25.4538	+	6.82031i	0.944027	+	0.252951i	0.697826	−	0.716267i	$-0.254151\pi$
$727$	25.4538	+	6.82031i	0.944027	+	0.252951i	0.246201	+	0.969219i	$0.420818\pi$
$728$	0.107790	−	6.21225i	0.00399497	−	0.230241i
$729$	−9.64240	−	25.2195i	−0.357126	−	0.934056i
$730$	−7.39257	+	11.2867i	−0.273611	+	0.417739i
$731$			37.3248i			1.38051i
$732$	−9.21904	+	3.08237i	−0.340745	+	0.113928i
$733$	−22.9377	−	22.9377i	−0.847224	−	0.847224i	0.142562	−	0.989786i	$-0.454466\pi$
$733$	−22.9377	−	22.9377i	−0.847224	−	0.847224i	−0.989786	+	0.142562i	$0.954466\pi$
$734$	−3.39972	+	5.88848i	−0.125486	+	0.217348i
$735$	6.22542	+	26.3864i	0.229628	+	0.973278i
$736$	0.858541	+	1.48704i	0.0316462	+	0.0548129i
$737$	−0.544726	+	2.03294i	−0.0200652	+	0.0748845i
$738$	−31.1925	+	12.5865i	−1.14821	+	0.463315i
$739$	−22.9824	−	13.2689i	−0.845422	−	0.488104i	0.0136817	−	0.999906i	$-0.495645\pi$
$739$	−22.9824	−	13.2689i	−0.845422	−	0.488104i	−0.859103	+	0.511802i	$0.828978\pi$
$740$	−5.71697	−	6.39948i	−0.210160	−	0.235249i
$741$	19.8719	+	9.91326i	0.730012	+	0.364173i
$742$	16.3902	+	9.84591i	0.601703	+	0.361455i
$743$	11.5457	+	43.0891i	0.423570	+	1.58078i	0.767026	+	0.641615i	$0.221735\pi$
$743$	11.5457	+	43.0891i	0.423570	+	1.58078i	−0.343457	+	0.939169i	$0.611598\pi$
$744$	−0.452455	−	7.42459i	−0.0165878	−	0.272199i
$745$	−19.9511	−	39.5375i	−0.730950	−	1.44854i
$746$	−15.0065	+	25.9920i	−0.549427	+	0.951635i
$747$	7.38585	+	18.3040i	0.270234	+	0.669708i
$748$	−0.467092	−	0.467092i	−0.0170786	−	0.0170786i
$749$	6.75648	+	27.0868i	0.246876	+	0.989729i
$750$	−7.81934	−	17.7160i	−0.285522	−	0.646898i
$751$	18.1818			0.663465			0.331732	−	0.943374i	$-0.392367\pi$
$751$	18.1818			0.663465			0.331732	+	0.943374i	$0.392367\pi$
$752$	0.755886	+	0.202539i	0.0275643	+	0.00738584i
$753$	−7.59301	−	22.7099i	−0.276705	−	0.827593i
$754$	−0.698342	+	1.20956i	−0.0254321	+	0.0440497i
$755$	33.5895	−	16.9496i	1.22245	−	0.616860i
$756$	−5.69407	−	12.5131i	−0.207091	−	0.455097i
$757$	−19.1776	−	19.1776i	−0.697020	−	0.697020i	0.266747	−	0.963767i	$-0.414051\pi$
$757$	−19.1776	−	19.1776i	−0.697020	−	0.697020i	−0.963767	+	0.266747i	$0.914051\pi$
$758$	−1.28913	−	4.81110i	−0.0468233	−	0.174747i
$759$	0.221690	−	0.444394i	0.00804683	−	0.0161305i
$760$	11.9514	−	2.49154i	0.433521	−	0.0903777i
$761$			46.7616i			1.69511i	0.530710	+	0.847553i	$0.321925\pi$
$761$			46.7616i			1.69511i	−0.530710	+	0.847553i	$0.678075\pi$
$762$	20.3457	+	4.14408i	0.737047	+	0.150124i
$763$	51.7527	+	0.897973i	1.87357	+	0.0325088i
$764$		−	1.49000i		−	0.0539062i
$765$	26.0271	+	5.17683i	0.941010	+	0.187169i
$766$	8.93779	+	5.16024i	0.322936	+	0.186447i
$767$	1.74848	+	1.74848i	0.0631341	+	0.0631341i
$768$	1.29697	+	1.14798i	0.0468006	+	0.0414241i
$769$	−17.6862	+	30.6333i	−0.637780	+	1.10467i	0.348139	+	0.937443i	$0.386814\pi$
$769$	−17.6862	+	30.6333i	−0.637780	+	1.10467i	−0.985919	+	0.167224i	$0.946520\pi$
$770$	−0.325178	+	0.932836i	−0.0117186	+	0.0336171i
$771$	11.5793	−	23.2115i	0.417017	−	0.835943i
$772$	18.7608	−	5.02694i	0.675216	−	0.180923i
$773$	−23.1635	+	6.20664i	−0.833133	+	0.223237i	−0.650080	−	0.759866i	$-0.725265\pi$
$773$	−23.1635	+	6.20664i	−0.833133	+	0.223237i	−0.183053	+	0.983103i	$0.558598\pi$
$774$	−22.6135	+	17.0248i	−0.812827	+	0.611944i
$775$	2.41143	−	21.3369i	0.0866210	−	0.766443i
$776$	12.4205	−	7.17099i	0.445871	−	0.257424i
$777$	−9.44733	−	14.8332i	−0.338921	−	0.532138i
$778$	−2.27075	−	8.47457i	−0.0814105	−	0.303828i
$779$		−	61.2147i		−	2.19324i
$780$	0.0417938	+	9.09507i	0.00149646	+	0.325656i
$781$	−1.58614			−0.0567564
$782$	−6.56113	−	1.75805i	−0.234626	−	0.0628677i
$783$	−0.244519	+	3.08072i	−0.00873840	+	0.110096i
$784$	−3.28758	−	6.17995i	−0.117414	−	0.220713i
$785$	−3.90235	+	0.813537i	−0.139281	+	0.0290364i
$786$	3.50745	+	5.30173i	0.125107	+	0.189107i
$787$	34.4800	+	9.23890i	1.22908	+	0.329331i	0.814221	−	0.580554i	$-0.197164\pi$
$787$	34.4800	+	9.23890i	1.22908	+	0.329331i	0.414859	+	0.909886i	$0.363831\pi$
$788$	10.4288	+	2.79438i	0.371509	+	0.0995456i
$789$	7.36948	−	14.7727i	0.262361	−	0.525922i
$790$	−18.9802	+	3.95686i	−0.675284	+	0.140779i
$791$	7.64996	+	7.92012i	0.272001	+	0.281607i
$792$	0.0699388	−	0.496045i	0.00248517	−	0.0176262i
$793$	12.7305	+	3.41112i	0.452073	+	0.121133i
$794$	−6.29162			−0.223281
$795$	−24.3033	−	13.8830i	−0.861948	−	0.492379i
$796$			11.7280i			0.415688i
$797$	−6.46506	−	24.1279i	−0.229004	−	0.854655i	−0.980761	−	0.195214i	$-0.937460\pi$
$797$	−6.46506	−	24.1279i	−0.229004	−	0.854655i	0.751757	−	0.659441i	$-0.229207\pi$
$798$	24.9959	−	1.08839i	0.884846	−	0.0385287i
$799$	−2.68094	+	1.54784i	−0.0948448	+	0.0547587i
$800$	3.11612	+	3.91022i	0.110172	+	0.138247i
$801$	40.0674	+	17.0286i	1.41571	+	0.601675i
$802$	8.65366	−	2.31874i	0.305571	−	0.0818776i
$803$	−0.973230	+	0.260776i	−0.0343445	+	0.00920259i
$804$	12.0452	+	18.2070i	0.424800	+	0.642112i
$805$	1.90035	+	9.97906i	0.0669784	+	0.351715i
$806$	−5.04256	+	8.73398i	−0.177617	+	0.307641i
$807$	−3.60702	+	17.7090i	−0.126973	+	0.623386i
$808$	0.668784	+	0.668784i	0.0235277	+	0.0235277i
$809$	45.2547	+	26.1278i	1.59107	+	0.918604i	0.993124	+	0.117067i	$0.0373492\pi$
$809$	45.2547	+	26.1278i	1.59107	+	0.918604i	0.597945	+	0.801537i	$0.295984\pi$
$810$	8.73519	+	18.1300i	0.306923	+	0.637023i
$811$			3.77916i			0.132704i	0.997796	+	0.0663521i	$0.0211361\pi$
$811$			3.77916i			0.132704i	−0.997796	+	0.0663521i	$0.978864\pi$
$812$	−0.0272991	+	1.57332i	−0.000958009	+	0.0552127i
$813$	−1.30714	+	1.47680i	−0.0458435	+	0.0517936i
$814$		−	0.640821i		−	0.0224608i
$815$	3.22842	−	0.673040i	0.113087	−	0.0235755i
$816$	−6.83911	+	0.416776i	−0.239417	+	0.0145901i
$817$	−13.3328	−	49.7586i	−0.466455	−	1.74083i
$818$	−0.546022	−	0.546022i	−0.0190912	−	0.0190912i
$819$	−2.92212	+	18.4091i	−0.102107	+	0.643265i
$820$	22.3827	−	11.2945i	0.781637	−	0.394422i
$821$	−6.26216	+	10.8464i	−0.218551	+	0.378541i	−0.954365	−	0.298642i	$-0.903466\pi$
$821$	−6.26216	+	10.8464i	−0.218551	+	0.378541i	0.735814	+	0.677183i	$0.236800\pi$
$822$	−34.9086	−	7.11030i	−1.21758	−	0.248000i
$823$	42.6435	+	11.4263i	1.48646	+	0.398296i	0.908540	−	0.417798i	$-0.137198\pi$
$823$	42.6435	+	11.4263i	1.48646	+	0.398296i	0.577920	+	0.816093i	$0.303865\pi$
$824$	14.8173			0.516184
$825$	0.445933	−	1.37565i	0.0155254	−	0.0478939i
$826$	2.67803	+	0.767612i	0.0931806	+	0.0267086i
$827$	5.40704	+	5.40704i	0.188021	+	0.188021i	0.794840	−	0.606819i	$-0.207555\pi$
$827$	5.40704	+	5.40704i	0.188021	+	0.188021i	−0.606819	+	0.794840i	$0.707555\pi$
$828$	−1.92757	−	4.77700i	−0.0669878	−	0.166012i
$829$	15.3365	−	26.5637i	0.532660	−	0.922594i	−0.466613	−	0.884462i	$-0.654526\pi$
$829$	15.3365	−	26.5637i	0.532660	−	0.922594i	0.999273	−	0.0381321i	$-0.0121408\pi$
$830$	−6.62772	−	13.1343i	−0.230051	−	0.455899i
$831$	26.7837	+	13.3613i	0.929116	+	0.463497i
$832$	−0.607801	−	2.26834i	−0.0210717	−	0.0786406i
$833$	26.4829	+	8.09063i	0.917579	+	0.280324i
$834$	1.83119	+	30.0491i	0.0634091	+	1.04051i
$835$	10.7644	+	12.0495i	0.372516	+	0.416989i
$836$	0.789541	+	0.455842i	0.0273069	+	0.0157656i
$837$	−1.76561	+	22.2451i	−0.0610285	+	0.768904i
$838$	−4.97918	+	18.5825i	−0.172003	+	0.641923i
$839$	−14.9676	−	25.9246i	−0.516739	−	0.895017i	−0.999811	−	0.0194370i	$-0.993813\pi$
$839$	−14.9676	−	25.9246i	−0.516739	−	0.895017i	0.483073	−	0.875580i	$-0.339521\pi$
$840$	5.00988	+	8.93874i	0.172857	+	0.308416i
$841$	−14.3231	+	24.8084i	−0.493901	+	0.855462i
$842$	16.0281	+	16.0281i	0.552364	+	0.552364i
$843$	−10.3296	−	9.14290i	−0.355769	−	0.314898i
$844$		−	19.0758i		−	0.656618i
$845$	−9.17066	+	14.0014i	−0.315480	+	0.481664i
$846$	−2.16062	−	0.918258i	−0.0742836	−	0.0315704i
$847$	25.3883	−	14.0764i	0.872352	−	0.483671i
$848$	6.98049	+	1.87042i	0.239711	+	0.0642304i
$849$	0.484921	+	7.95733i	0.0166424	+	0.273095i
$850$	−19.6543	−	2.22127i	−0.674138	−	0.0761889i
$851$	−3.29476	−	5.70669i	−0.112943	−	0.195623i
$852$	−10.9044	+	12.3196i	−0.373578	+	0.422064i
$853$	14.9862	−	55.9292i	0.513117	−	1.91498i	0.129175	−	0.991622i	$-0.458767\pi$
$853$	14.9862	−	55.9292i	0.513117	−	1.91498i	0.383942	−	0.923357i	$-0.374566\pi$
$854$	14.4071	−	3.59369i	0.493002	−	0.122974i
$855$	−36.5465	+	2.39576i	−1.24986	+	0.0819332i
$856$	5.27577	+	9.13789i	0.180322	+	0.312327i
$857$	−24.2185	+	24.2185i	−0.827288	+	0.827288i	−0.987141	−	0.159853i	$-0.948898\pi$
$857$	−24.2185	+	24.2185i	−0.827288	+	0.827288i	0.159853	+	0.987141i	$0.448898\pi$
$858$	−0.450166	+	0.508593i	−0.0153684	+	0.0173631i
$859$	−0.797571			−0.0272128			−0.0136064	−	0.999907i	$-0.504331\pi$
$859$	−0.797571			−0.0272128			−0.0136064	+	0.999907i	$0.504331\pi$
$860$	15.7339	−	14.0558i	0.536520	−	0.479300i
$861$	49.0039	−	15.4445i	1.67005	−	0.526348i
$862$	6.47151	−	24.1520i	0.220421	−	0.822621i
$863$	−35.8728	−	9.61208i	−1.22112	−	0.327199i	−0.410006	−	0.912083i	$-0.634474\pi$
$863$	−35.8728	−	9.61208i	−1.22112	−	0.327199i	−0.811117	+	0.584883i	$0.801140\pi$
$864$	−3.37200	−	3.95343i	−0.114718	−	0.134498i
$865$	−24.5275	+	21.9116i	−0.833960	+	0.745017i
$866$	28.8625	+	16.6638i	0.980788	+	0.566258i
$867$	−1.55086	+	1.75214i	−0.0526699	+	0.0595059i
$868$	−0.197120	+	11.3606i	−0.00669069	+	0.385603i
$869$	−1.25388	−	0.723930i	−0.0425351	−	0.0245577i
$870$	−0.0105847	−	2.30343i	−0.000358856	−	0.0780935i
$871$		−	29.5987i		−	1.00291i
$872$	18.8970	−	5.06344i	0.639933	−	0.171470i
$873$	−39.9001	+	16.1001i	−1.35041	+	0.544906i
$874$	9.37479			0.317107
$875$	9.79326	+	27.9122i	0.331073	+	0.943605i
$876$	−4.66529	+	9.35194i	−0.157626	+	0.315973i
$877$	15.8847	+	15.8847i	0.536389	+	0.536389i	0.922466	−	0.386078i	$-0.126170\pi$
$877$	15.8847	+	15.8847i	0.536389	+	0.536389i	−0.386078	+	0.922466i	$0.626170\pi$
$878$	10.0954	−	37.6767i	0.340704	−	1.27153i
$879$	9.84814	−	6.51520i	0.332169	−	0.219752i
$880$	−0.0209993	+	0.372796i	−0.000707885	+	0.0125669i
$881$		−	39.0129i		−	1.31438i	−0.753726	−	0.657189i	$-0.771745\pi$
$881$		−	39.0129i		−	1.31438i	0.753726	−	0.657189i	$-0.228255\pi$
$882$	7.17777	+	19.7352i	0.241688	+	0.664520i
$883$	−23.4714	+	23.4714i	−0.789874	+	0.789874i	−0.981473	−	0.191599i	$-0.938633\pi$
$883$	−23.4714	+	23.4714i	−0.789874	+	0.789874i	0.191599	+	0.981473i	$0.438633\pi$
$884$	8.04525	+	4.64493i	0.270591	+	0.156226i
$885$	−3.94395	−	1.03738i	−0.132574	−	0.0348710i
$886$	12.2766	+	21.2636i	0.412440	+	0.714366i
$887$	25.0422	−	25.0422i	0.840834	−	0.840834i	−0.148133	−	0.988967i	$-0.547326\pi$
$887$	25.0422	−	25.0422i	0.840834	−	0.840834i	0.988967	+	0.148133i	$0.0473265\pi$
$888$	−4.97731	−	4.40552i	−0.167028	−	0.147840i
$889$	−30.4890	−	8.73914i	−1.02257	−	0.293101i
$890$	−30.8220	−	10.1481i	−1.03316	−	0.340165i
$891$	−0.415523	+	1.44427i	−0.0139205	+	0.0483847i
$892$	1.70472	+	6.36209i	0.0570781	+	0.213018i
$893$	3.02112	−	3.02112i	0.101098	−	0.101098i
$894$	−18.9272	−	28.6097i	−0.633022	−	0.956852i
$895$	18.3979	+	1.03634i	0.614973	+	0.0346409i
$896$	−1.83809	−	1.90300i	−0.0614063	−	0.0635749i
$897$	−1.39394	+	6.84368i	−0.0465424	+	0.228504i
$898$	−2.61149	−	9.74622i	−0.0871466	−	0.325235i
$899$	1.27709	−	2.21198i	0.0425932	−	0.0737736i
$900$	−7.61907	−	12.9209i	−0.253969	−	0.430697i
$901$	−24.7581	+	14.2941i	−0.824811	+	0.476205i
$902$	1.80843	+	0.484568i	0.0602143	+	0.0161344i
$903$	36.4691	−	23.2273i	1.21362	−	0.772958i
$904$	3.60431	+	2.08095i	0.119878	+	0.0692114i
$905$	8.76769	+	17.3752i	0.291448	+	0.577570i
$906$	24.3057	−	16.0798i	0.807503	−	0.534217i
$907$	−2.46661	−	2.46661i	−0.0819024	−	0.0819024i	0.664969	−	0.746871i	$-0.268445\pi$
$907$	−2.46661	−	2.46661i	−0.0819024	−	0.0819024i	−0.746871	+	0.664969i	$0.768445\pi$
$908$	5.05588	−	18.8688i	0.167785	−	0.626183i
$909$	−1.70659	−	2.26681i	−0.0566041	−	0.0751855i
$910$	1.02187	−	13.8555i	0.0338748	−	0.459304i
$911$	−5.27969	−	9.14468i	−0.174924	−	0.302977i	0.765211	−	0.643779i	$-0.222635\pi$
$911$	−5.27969	−	9.14468i	−0.174924	−	0.302977i	−0.940135	+	0.340803i	$0.889301\pi$
$912$	8.96850	−	2.99861i	0.296977	−	0.0992939i
$913$	0.284348	−	1.06120i	0.00941056	−	0.0351207i
$914$	5.10397	−	2.94678i	0.168824	−	0.0974707i
$915$	−20.9694	+	5.72214i	−0.693227	+	0.189168i
$916$	−15.7016	+	9.06530i	−0.518794	+	0.299526i
$917$	−4.70857	−	8.49240i	−0.155491	−	0.280444i
$918$	20.4910	+	1.62638i	0.676302	+	0.0536787i
$919$	−52.4185	+	30.2638i	−1.72913	+	0.998312i	−0.835524	+	0.549454i	$0.814836\pi$
$919$	−52.4185	+	30.2638i	−1.72913	+	0.998312i	−0.893603	+	0.448858i	$0.851831\pi$
$920$	1.72971	+	3.42782i	0.0570269	+	0.113012i
$921$	−14.4695	+	29.0053i	−0.476787	+	0.955756i
$922$	−22.7118	+	22.7118i	−0.747973	+	0.747973i
$923$	21.5464	−	5.77335i	0.709209	−	0.190032i
$924$	−0.165711	+	0.747057i	−0.00545149	+	0.0245764i
$925$	−11.9585	−	15.0060i	−0.393194	−	0.493393i
$926$	1.19441	+	2.06877i	0.0392507	+	0.0679841i
$927$	−44.0165	−	6.20601i	−1.44569	−	0.203832i
$928$	0.153932	+	0.574483i	0.00505307	+	0.0188583i
$929$	−16.3032	+	28.2379i	−0.534890	+	0.926456i	0.464279	+	0.885689i	$0.346314\pi$
$929$	−16.3032	+	28.2379i	−0.534890	+	0.926456i	−0.999169	+	0.0407672i	$0.987020\pi$
$930$	−0.0764299	−	16.6325i	−0.00250624	−	0.545401i
$931$	−38.1951	−	1.32586i	−1.25179	−	0.0434534i
$932$	−11.9228	+	3.19471i	−0.390544	+	0.104646i
$933$	32.7245	−	36.9718i	1.07135	−	1.21040i
$934$	21.8066			0.713533
$935$	−0.984057	−	1.10154i	−0.0321821	−	0.0360241i
$936$	0.855480	+	6.99295i	0.0279622	+	0.228572i
$937$	17.5113	−	17.5113i	0.572068	−	0.572068i	−0.360638	−	0.932706i	$-0.617441\pi$
$937$	17.5113	−	17.5113i	0.572068	−	0.572068i	0.932706	+	0.360638i	$0.117441\pi$
$938$	−16.1700	−	29.1643i	−0.527969	−	0.952247i
$939$	3.54055	−	2.34231i	0.115541	−	0.0764384i
$940$	1.66207	+	0.547232i	0.0542106	+	0.0178487i
$941$	31.3245	−	18.0852i	1.02115	−	0.589560i	0.106712	−	0.994290i	$-0.465968\pi$
$941$	31.3245	−	18.0852i	1.02115	−	0.589560i	0.914436	+	0.404730i	$0.132634\pi$
$942$	−2.92839	+	0.979104i	−0.0954121	+	0.0319009i
$943$	18.5960	−	4.98278i	0.605569	−	0.162262i
$944$	1.05296			0.0342709
$945$	−11.1386	−	28.6519i	−0.362338	−	0.932047i
$946$	1.57553			0.0512250
$947$	5.72168	−	1.53312i	0.185929	−	0.0498197i	−0.164653	−	0.986352i	$-0.552650\pi$
$947$	5.72168	−	1.53312i	0.185929	−	0.0498197i	0.350582	+	0.936532i	$0.385984\pi$
$948$	−14.2430	+	4.76214i	−0.462592	+	0.154667i
$949$	12.2714	−	7.08488i	0.398346	−	0.229985i
$950$	26.9951	−	4.05948i	0.875836	−	0.131707i
$951$	−23.7626	+	15.7206i	−0.770557	+	0.509775i
$952$	10.4647	+	0.181576i	0.339164	+	0.00588491i
$953$	−35.5250	+	35.5250i	−1.15077	+	1.15077i	−0.164370	+	0.986399i	$0.552559\pi$
$953$	−35.5250	+	35.5250i	−1.15077	+	1.15077i	−0.986399	+	0.164370i	$0.947441\pi$
$954$	−19.9530	−	8.47998i	−0.646002	−	0.274550i
$955$	0.187377	−	3.32646i	0.00606337	−	0.107642i
$956$	−16.5576			−0.535513
$957$	0.114010	−	0.128807i	0.00368540	−	0.00416373i
$958$	−37.9221	+	10.1612i	−1.22521	+	0.328293i
$959$	52.3121	+	14.9944i	1.68925	+	0.484194i
$960$	2.75117	+	2.72600i	0.0887936	+	0.0879813i
$961$	−6.27847	+	10.8746i	−0.202531	+	0.350794i
$962$	2.33251	+	8.70506i	0.0752033	+	0.280662i
$963$	−11.8450	−	29.3549i	−0.381700	−	0.945948i
$964$	−3.06443	−	5.30774i	−0.0986986	−	0.170951i
$965$	42.5162	−	8.86349i	1.36864	−	0.285326i
$966$	2.36527	+	7.50475i	0.0761012	+	0.241461i
$967$	−3.58824	+	0.961467i	−0.115390	+	0.0309187i	−0.316052	−	0.948742i	$-0.602357\pi$
$967$	−3.58824	+	0.961467i	−0.115390	+	0.0309187i	0.200662	+	0.979661i	$0.435691\pi$
$968$	7.75846	−	7.75846i	0.249366	−	0.249366i
$969$	−16.6992	+	33.4748i	−0.536456	+	1.07537i
$970$	28.6310	−	14.4475i	0.919285	−	0.463881i
$971$	−16.6527	+	9.61441i	−0.534409	+	0.308541i	−0.742810	−	0.669502i	$-0.766507\pi$
$971$	−16.6527	+	9.61441i	−0.534409	+	0.308541i	0.208401	+	0.978043i	$0.433174\pi$
$972$	8.36110	+	13.1564i	0.268182	+	0.421993i
$973$	0.797792	−	45.9790i	0.0255760	−	1.47402i
$974$	−22.2991	+	12.8744i	−0.714508	+	0.412521i
$975$	−1.05046	+	20.3103i	−0.0336416	+	0.650449i
$976$	4.86034	−	2.80612i	0.155576	−	0.0898217i
$977$	−1.21813	+	4.54614i	−0.0389716	+	0.145444i	−0.982670	−	0.185363i	$-0.940654\pi$
$977$	−1.21813	+	4.54614i	−0.0389716	+	0.145444i	0.943699	+	0.330806i	$0.107321\pi$
$978$	2.42266	−	0.810013i	0.0774681	−	0.0259014i
$979$	−1.21163	−	2.09860i	−0.0387238	−	0.0670716i
$980$	−6.56246	−	14.2104i	−0.209630	−	0.453933i
$981$	−58.2565	+	7.12679i	−1.85999	+	0.227541i
$982$	−9.19233	+	34.3062i	−0.293339	+	1.09476i
$983$	−10.3857	−	10.3857i	−0.331251	−	0.331251i	0.521811	−	0.853061i	$-0.325257\pi$
$983$	−10.3857	−	10.3857i	−0.331251	−	0.331251i	−0.853061	+	0.521811i	$0.825257\pi$
$984$	16.1963	−	10.7149i	0.516319	−	0.341580i
$985$	22.9311	+	7.55002i	0.730646	+	0.240564i
$986$	−2.03755	−	1.17638i	−0.0648888	−	0.0374636i
$987$	3.18071	+	1.65625i	0.101243	+	0.0527190i
$988$	−12.3845	−	3.31842i	−0.394004	−	0.105573i
$989$	14.0306	−	8.10055i	0.446146	−	0.257583i
$990$	0.218521	−	1.09864i	0.00694506	−	0.0349170i
$991$	4.01128	−	6.94775i	0.127423	−	0.220703i	−0.795255	−	0.606276i	$-0.792663\pi$
$991$	4.01128	−	6.94775i	0.127423	−	0.220703i	0.922677	+	0.385573i	$0.125996\pi$
$992$	1.11151	+	4.14821i	0.0352904	+	0.131706i
$993$	2.41481	−	11.8557i	0.0766316	−	0.376230i
$994$	18.0762	−	17.4596i	0.573341	−	0.553784i
$995$	−1.47487	+	26.1831i	−0.0467566	+	0.830060i
$996$	−6.28761	−	9.50412i	−0.199231	−	0.301149i
$997$	−3.37633	+	3.37633i	−0.106929	+	0.106929i	−0.758547	−	0.651618i	$-0.774091\pi$
$997$	−3.37633	+	3.37633i	−0.106929	+	0.106929i	0.651618	+	0.758547i	$0.274091\pi$
$998$	−2.65708	−	9.91635i	−0.0841084	−	0.313897i
$999$	12.9405	+	15.1718i	0.409419	+	0.480014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cg.a.157.3	yes	192
5.3	odd	4	inner	630.2.cg.a.283.35	yes	192
7.5	odd	6		630.2.bw.a.607.34	yes	192
9.7	even	3		630.2.bw.a.367.25	yes	192
35.33	even	12		630.2.bw.a.103.25	✓	192
45.43	odd	12		630.2.bw.a.493.34	yes	192
63.61	odd	6	inner	630.2.cg.a.187.35	yes	192
315.313	even	12	inner	630.2.cg.a.313.3	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.25	✓	192	35.33	even	12
630.2.bw.a.367.25	yes	192	9.7	even	3
630.2.bw.a.493.34	yes	192	45.43	odd	12
630.2.bw.a.607.34	yes	192	7.5	odd	6
630.2.cg.a.157.3	yes	192	1.1	even	1	trivial
630.2.cg.a.187.35	yes	192	63.61	odd	6	inner
630.2.cg.a.283.35	yes	192	5.3	odd	4	inner
630.2.cg.a.313.3	yes	192	315.313	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.64267 + 0.549224i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.99630 - 1.00736i) q^{5} +(1.44454 - 0.955663i) q^{6} +(-2.31389 + 1.28293i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.39671 - 1.80438i) q^{9} +(-1.66756 + 1.48971i) q^{10} -0.166984 q^{11} +(-1.14798 + 1.29697i) q^{12} +(2.26834 - 0.607801i) q^{13} +(1.90300 - 1.83809i) q^{14} +(-2.72600 + 2.75117i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.02386 + 3.82109i) q^{17} +(-1.84803 + 2.36321i) q^{18} +(-2.72986 - 4.72826i) q^{19} +(1.22517 - 1.87055i) q^{20} +(3.09634 - 3.37826i) q^{21} +(0.161294 - 0.0432185i) q^{22} +(1.21416 - 1.21416i) q^{23} +(0.773181 - 1.54990i) q^{24} +(2.97047 - 4.02198i) q^{25} +(-2.03374 + 1.17418i) q^{26} +(-2.94598 + 4.28033i) q^{27} +(-1.36243 + 2.26799i) q^{28} +(0.515067 - 0.297374i) q^{29} +(1.92106 - 3.36297i) q^{30} +(3.71918 - 2.14727i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.274298 - 0.0917113i) q^{33} +(-1.97794 - 3.42590i) q^{34} +(-3.32687 + 4.89203i) q^{35} +(1.17342 - 2.76099i) q^{36} +(0.993252 - 3.70687i) q^{37} +(3.86061 + 3.86061i) q^{38} +(-3.39231 + 2.24424i) q^{39} +(-0.699292 + 2.12391i) q^{40} +(9.70992 + 5.60603i) q^{41} +(-2.11648 + 4.06454i) q^{42} +(9.11376 + 2.44202i) q^{43} +(-0.144612 + 0.0834918i) q^{44} +(2.96690 - 6.01644i) q^{45} +(-0.858541 + 1.48704i) q^{46} +(0.202539 + 0.755886i) q^{47} +(-0.345692 + 1.69720i) q^{48} +(3.70820 - 5.93711i) q^{49} +(-1.82829 + 4.65375i) q^{50} +(-3.78050 - 5.71446i) q^{51} +(1.66054 - 1.66054i) q^{52} +(1.87042 + 6.98049i) q^{53} +(1.73777 - 4.89695i) q^{54} +(-0.333350 + 0.168212i) q^{55} +(0.729004 - 2.54334i) q^{56} +(7.08112 + 6.26765i) q^{57} +(-0.420551 + 0.420551i) q^{58} +(0.526480 + 0.911890i) q^{59} +(-0.985201 + 3.74558i) q^{60} +(4.86034 + 2.80612i) q^{61} +(-3.03670 + 3.03670i) q^{62} +(-3.23083 + 7.24995i) q^{63} -1.00000i q^{64} +(3.91603 - 3.49838i) q^{65} +(-0.241215 + 0.159580i) q^{66} +(3.26215 - 12.1745i) q^{67} +(2.79724 + 2.79724i) q^{68} +(-1.32761 + 2.66130i) q^{69} +(1.94736 - 5.58639i) q^{70} +9.49875 q^{71} +(-0.418836 + 2.97062i) q^{72} +(5.82830 - 1.56169i) q^{73} +3.83763i q^{74} +(-2.67052 + 8.23822i) q^{75} +(-4.72826 - 2.72986i) q^{76} +(0.386382 - 0.214228i) q^{77} +(2.69587 - 3.04577i) q^{78} +(7.50903 + 4.33534i) q^{79} +(0.125756 - 2.23253i) q^{80} +(2.48841 - 8.64915i) q^{81} +(-10.8300 - 2.90189i) q^{82} +(-1.70285 + 6.35513i) q^{83} +(0.992378 - 4.47383i) q^{84} +(5.89314 + 6.59668i) q^{85} -9.43526 q^{86} +(-0.682759 + 0.771374i) q^{87} +(0.118075 - 0.118075i) q^{88} +(7.25597 + 12.5677i) q^{89} +(-1.30864 + 6.57932i) q^{90} +(-4.46894 + 4.31650i) q^{91} +(0.444413 - 1.65857i) q^{92} +(-4.93004 + 5.56991i) q^{93} +(-0.391275 - 0.677709i) q^{94} +(-10.2127 - 6.68910i) q^{95} +(-0.105356 - 1.72884i) q^{96} +(-13.8533 - 3.71198i) q^{97} +(-2.04521 + 6.69456i) q^{98} +(-0.400211 + 0.301302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{11} - 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 12 q^{30} - 60 q^{33} + 48 q^{35} - 16 q^{36} + 12 q^{41} + 4 q^{42} - 36 q^{45} + 12 q^{46} - 16 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 192 * q - 16 * q^11 - 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 + 12 * q^21 - 16 * q^23 - 36 * q^27 + 12 * q^30 - 60 * q^33 + 48 * q^35 - 16 * q^36 + 12 * q^41 + 4 * q^42 - 36 * q^45 + 12 * q^46 - 16 * q^50 + 24 * q^51 - 40 * q^53 + 8 * q^56 - 32 * q^57 + 24 * q^58 + 8 * q^60 + 36 * q^61 - 108 * q^63 - 8 * q^65 + 16 * q^71 - 8 * q^72 + 80 * q^77 - 16 * q^78 + 4 * q^81 - 168 * q^83 - 16 * q^86 + 36 * q^90 + 8 * q^92 - 60 * q^93 + 64 * q^95 - 12 * q^96 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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