LMFDB - Embedded newform 312.2.bt.d.19.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	312.19
Dual form			312.2.bt.d.115.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.21599 - 0.722056i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.957270 - 1.75603i) q^{4} +(-0.403590 - 0.403590i) q^{5} +(-0.0173234 - 1.41411i) q^{6} +(4.65174 + 1.24643i) q^{7} +(-0.103920 - 2.82652i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.782176 - 0.199347i) q^{10} +(-5.72510 + 1.53404i) q^{11} +(-1.04213 - 1.70703i) q^{12} +(-0.849788 + 3.50398i) q^{13} +(6.55647 - 1.84317i) q^{14} +(-0.551314 + 0.147724i) q^{15} +(-2.16727 - 3.36198i) q^{16} +(-0.917794 + 0.529889i) q^{17} +(-1.23331 - 0.692051i) q^{18} +(0.617530 + 0.165467i) q^{19} +(-1.09506 + 0.322371i) q^{20} +(3.40531 - 3.40531i) q^{21} +(-5.85401 + 5.99922i) q^{22} +(1.02761 - 1.77988i) q^{23} +(-2.49980 - 1.32326i) q^{24} -4.67423i q^{25} +(1.49673 + 4.87440i) q^{26} -1.00000 q^{27} +(6.64174 - 6.97542i) q^{28} +(4.86733 + 2.81016i) q^{29} +(-0.563728 + 0.577711i) q^{30} +(-2.54931 - 2.54931i) q^{31} +(-5.06292 - 2.52325i) q^{32} +(-1.53404 + 5.72510i) q^{33} +(-0.733420 + 1.30704i) q^{34} +(-1.37435 - 2.38044i) q^{35} +(-1.99940 + 0.0489943i) q^{36} +(1.83349 + 6.84268i) q^{37} +(0.870387 - 0.244685i) q^{38} +(2.60964 + 2.48793i) q^{39} +(-1.09881 + 1.18269i) q^{40} +(1.37457 + 5.12996i) q^{41} +(1.68200 - 6.59966i) q^{42} +(-8.58213 + 4.95490i) q^{43} +(-2.78665 + 11.5219i) q^{44} +(-0.147724 + 0.551314i) q^{45} +(-0.0356035 - 2.90631i) q^{46} +(-5.92269 + 5.92269i) q^{47} +(-3.99520 + 0.195919i) q^{48} +(14.0230 + 8.09616i) q^{49} +(-3.37506 - 5.68382i) q^{50} +1.05978i q^{51} +(5.33961 + 4.84650i) q^{52} +1.19577i q^{53} +(-1.21599 + 0.722056i) q^{54} +(2.92971 + 1.69147i) q^{55} +(3.03965 - 13.2778i) q^{56} +(0.452063 - 0.452063i) q^{57} +(7.94772 - 0.0973630i) q^{58} +(2.11560 - 7.89551i) q^{59} +(-0.268348 + 1.10953i) q^{60} +(5.30143 - 3.06078i) q^{61} +(-4.94068 - 1.25919i) q^{62} +(-1.24643 - 4.65174i) q^{63} +(-7.97840 + 0.587462i) q^{64} +(1.75714 - 1.07120i) q^{65} +(2.26847 + 8.06933i) q^{66} +(-2.06834 - 7.71916i) q^{67} +(0.0519231 + 2.11892i) q^{68} +(-1.02761 - 1.77988i) q^{69} +(-3.39001 - 1.90224i) q^{70} +(0.113135 - 0.422224i) q^{71} +(-2.39588 + 1.50326i) q^{72} +(7.34514 + 7.34514i) q^{73} +(7.17031 + 6.99675i) q^{74} +(-4.04800 - 2.33712i) q^{75} +(0.881707 - 0.926004i) q^{76} -28.5438 q^{77} +(4.96972 + 1.14099i) q^{78} -7.20853i q^{79} +(-0.482175 + 2.23155i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.37559 + 5.24547i) q^{82} +(7.79731 - 7.79731i) q^{83} +(-2.72002 - 9.23963i) q^{84} +(0.584270 + 0.156555i) q^{85} +(-6.85808 + 12.2219i) q^{86} +(4.86733 - 2.81016i) q^{87} +(4.93093 + 16.0227i) q^{88} +(-0.708365 + 0.189806i) q^{89} +(0.218448 + 0.777058i) q^{90} +(-8.32047 + 15.2404i) q^{91} +(-2.14181 - 3.50834i) q^{92} +(-3.48242 + 0.933112i) q^{93} +(-2.92542 + 11.4784i) q^{94} +(-0.182448 - 0.316009i) q^{95} +(-4.71666 + 3.12299i) q^{96} +(-4.48735 - 1.20238i) q^{97} +(22.8977 - 0.280506i) q^{98} +(4.19106 + 4.19106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100}) $ 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.21599	−	0.722056i	0.859836	−	0.510571i
$2$	1.21599	−	0.722056i	0.859836	−	0.510571i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.957270	−	1.75603i	0.478635	−	0.878014i
$5$	−0.403590	−	0.403590i	−0.180491	−	0.180491i	0.611079	−	0.791570i	$-0.290736\pi$
$5$	−0.403590	−	0.403590i	−0.180491	−	0.180491i	−0.791570	+	0.611079i	$0.790736\pi$
$6$	−0.0173234	−	1.41411i	−0.00707225	−	0.577307i
$7$	4.65174	+	1.24643i	1.75819	+	0.471107i	0.986344	−	0.164698i	$-0.0526649\pi$
$7$	4.65174	+	1.24643i	1.75819	+	0.471107i	0.771850	+	0.635805i	$0.219332\pi$
$8$	−0.103920	−	2.82652i	−0.0367412	−	0.999325i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.782176	−	0.199347i	−0.247346	−	0.0630391i
$11$	−5.72510	+	1.53404i	−1.72618	+	0.462529i	−0.979298	−	0.202424i	$-0.935118\pi$
$11$	−5.72510	+	1.53404i	−1.72618	+	0.462529i	−0.746885	+	0.664953i	$0.768451\pi$
$12$	−1.04213	−	1.70703i	−0.300837	−	0.492778i
$13$	−0.849788	+	3.50398i	−0.235689	+	0.971829i
$13$	−0.849788	+	3.50398i	−0.235689	+	0.971829i
$14$	6.55647	−	1.84317i	1.75229	−	0.492608i
$15$	−0.551314	+	0.147724i	−0.142349	+	0.0381422i
$16$	−2.16727	−	3.36198i	−0.541818	−	0.840496i
$17$	−0.917794	+	0.529889i	−0.222598	+	0.128517i	−0.607153	−	0.794585i	$-0.707688\pi$
$17$	−0.917794	+	0.529889i	−0.222598	+	0.128517i	0.384555	+	0.923102i	$0.374355\pi$
$18$	−1.23331	−	0.692051i	−0.290695	−	0.163118i
$19$	0.617530	+	0.165467i	0.141671	+	0.0379606i	0.328958	−	0.944345i	$-0.393303\pi$
$19$	0.617530	+	0.165467i	0.141671	+	0.0379606i	−0.187287	+	0.982305i	$0.559969\pi$
$20$	−1.09506	+	0.322371i	−0.244863	+	0.0720843i
$21$	3.40531	−	3.40531i	0.743100	−	0.743100i
$22$	−5.85401	+	5.99922i	−1.24808	+	1.27904i
$23$	1.02761	−	1.77988i	0.214272	−	0.371130i	−0.738775	−	0.673952i	$-0.764595\pi$
$23$	1.02761	−	1.77988i	0.214272	−	0.371130i	0.953047	+	0.302822i	$0.0979288\pi$
$24$	−2.49980	−	1.32326i	−0.510269	−	0.270110i
$25$		−	4.67423i		−	0.934846i
$26$	1.49673	+	4.87440i	0.293534	+	0.955949i
$27$	−1.00000			−0.192450
$28$	6.64174	−	6.97542i	1.25517	−	1.31823i
$29$	4.86733	+	2.81016i	0.903841	+	0.521833i	0.878444	−	0.477845i	$-0.158582\pi$
$29$	4.86733	+	2.81016i	0.903841	+	0.521833i	0.0253965	+	0.999677i	$0.491915\pi$
$30$	−0.563728	+	0.577711i	−0.102922	+	0.105475i
$31$	−2.54931	−	2.54931i	−0.457869	−	0.457869i	0.440086	−	0.897956i	$-0.354948\pi$
$31$	−2.54931	−	2.54931i	−0.457869	−	0.457869i	−0.897956	+	0.440086i	$0.854948\pi$
$32$	−5.06292	−	2.52325i	−0.895007	−	0.446052i
$33$	−1.53404	+	5.72510i	−0.267041	+	0.996612i
$34$	−0.733420	+	1.30704i	−0.125781	+	0.224155i
$35$	−1.37435	−	2.38044i	−0.232308	−	0.402368i
$36$	−1.99940	+	0.0489943i	−0.333233	+	0.00816572i
$37$	1.83349	+	6.84268i	0.301424	+	1.12493i	0.935980	+	0.352053i	$0.114516\pi$
$37$	1.83349	+	6.84268i	0.301424	+	1.12493i	−0.634556	+	0.772877i	$0.718817\pi$
$38$	0.870387	−	0.244685i	0.141195	−	0.0396932i
$39$	2.60964	+	2.48793i	0.417877	+	0.398387i
$40$	−1.09881	+	1.18269i	−0.173738	+	0.187000i
$41$	1.37457	+	5.12996i	0.214672	+	0.801166i	0.986282	+	0.165070i	$0.0527850\pi$
$41$	1.37457	+	5.12996i	0.214672	+	0.801166i	−0.771610	+	0.636096i	$0.780548\pi$
$42$	1.68200	−	6.59966i	0.259539	−	1.01835i
$43$	−8.58213	+	4.95490i	−1.30876	+	0.755615i	−0.981890	−	0.189454i	$-0.939328\pi$
$43$	−8.58213	+	4.95490i	−1.30876	+	0.755615i	−0.326873	+	0.945068i	$0.605995\pi$
$44$	−2.78665	+	11.5219i	−0.420104	+	1.73700i
$45$	−0.147724	+	0.551314i	−0.0220214	+	0.0821850i
$46$	−0.0356035	−	2.90631i	−0.00524945	−	0.428512i
$47$	−5.92269	+	5.92269i	−0.863912	+	0.863912i	−0.991790	−	0.127878i	$-0.959184\pi$
$47$	−5.92269	+	5.92269i	−0.863912	+	0.863912i	0.127878	+	0.991790i	$0.459184\pi$
$48$	−3.99520	+	0.195919i	−0.576657	+	0.0282784i
$49$	14.0230	+	8.09616i	2.00328	+	1.15659i
$50$	−3.37506	−	5.68382i	−0.477305	−	0.803814i
$51$			1.05978i			0.148399i
$52$	5.33961	+	4.84650i	0.740470	+	0.672089i
$53$			1.19577i			0.164251i	0.996622	+	0.0821255i	$0.0261708\pi$
$53$			1.19577i			0.164251i	−0.996622	+	0.0821255i	$0.973829\pi$
$54$	−1.21599	+	0.722056i	−0.165475	+	0.0982594i
$55$	2.92971	+	1.69147i	0.395043	+	0.228078i
$56$	3.03965	−	13.2778i	0.406191	−	1.77432i
$57$	0.452063	−	0.452063i	0.0598772	−	0.0598772i
$58$	7.94772	−	0.0973630i	1.04359	−	0.0127844i
$59$	2.11560	−	7.89551i	0.275427	−	1.02791i	−0.680127	−	0.733094i	$-0.738076\pi$
$59$	2.11560	−	7.89551i	0.275427	−	1.02791i	0.955555	−	0.294814i	$-0.0952578\pi$
$60$	−0.268348	+	1.10953i	−0.0346436	+	0.143240i
$61$	5.30143	−	3.06078i	0.678778	−	0.391893i	−0.120616	−	0.992699i	$-0.538487\pi$
$61$	5.30143	−	3.06078i	0.678778	−	0.391893i	0.799395	+	0.600806i	$0.205154\pi$
$62$	−4.94068	−	1.25919i	−0.627467	−	0.159918i
$63$	−1.24643	−	4.65174i	−0.157036	−	0.586065i
$64$	−7.97840	+	0.587462i	−0.997300	+	0.0734327i
$65$	1.75714	−	1.07120i	0.217946	−	0.132866i
$66$	2.26847	+	8.06933i	0.279229	+	0.993266i
$67$	−2.06834	−	7.71916i	−0.252688	−	0.943045i	−0.969362	−	0.245637i	$-0.921003\pi$
$67$	−2.06834	−	7.71916i	−0.252688	−	0.943045i	0.716674	−	0.697409i	$-0.245664\pi$
$68$	0.0519231	+	2.11892i	0.00629660	+	0.256957i
$69$	−1.02761	−	1.77988i	−0.123710	−	0.214272i
$70$	−3.39001	−	1.90224i	−0.405184	−	0.227361i
$71$	0.113135	−	0.422224i	0.0134266	−	0.0501087i	−0.958888	−	0.283786i	$-0.908409\pi$
$71$	0.113135	−	0.422224i	0.0134266	−	0.0501087i	0.972314	+	0.233678i	$0.0750760\pi$
$72$	−2.39588	+	1.50326i	−0.282357	+	0.177160i
$73$	7.34514	+	7.34514i	0.859684	+	0.859684i	0.991301	−	0.131617i	$-0.0420169\pi$
$73$	7.34514	+	7.34514i	0.859684	+	0.859684i	−0.131617	+	0.991301i	$0.542017\pi$
$74$	7.17031	+	6.99675i	0.833531	+	0.813356i
$75$	−4.04800	−	2.33712i	−0.467423	−	0.269867i
$76$	0.881707	−	0.926004i	0.101139	−	0.106220i
$77$	−28.5438			−3.25287
$78$	4.96972	+	1.14099i	0.562710	+	0.129192i
$79$		−	7.20853i		−	0.811023i	−0.914090	−	0.405511i	$-0.867093\pi$
$79$		−	7.20853i		−	0.811023i	0.914090	−	0.405511i	$-0.132907\pi$
$80$	−0.482175	+	2.23155i	−0.0539088	+	0.249495i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.37559	+	5.24547i	0.593634	+	0.579266i
$83$	7.79731	−	7.79731i	0.855866	−	0.855866i	−0.134982	−	0.990848i	$-0.543098\pi$
$83$	7.79731	−	7.79731i	0.855866	−	0.855866i	0.990848	+	0.134982i	$0.0430977\pi$
$84$	−2.72002	−	9.23963i	−0.296779	−	1.00813i
$85$	0.584270	+	0.156555i	0.0633730	+	0.0169807i
$86$	−6.85808	+	12.2219i	−0.739526	+	1.31792i
$87$	4.86733	−	2.81016i	0.521833	−	0.301280i
$88$	4.93093	+	16.0227i	0.525639	+	1.70802i
$89$	−0.708365	+	0.189806i	−0.0750865	+	0.0201194i	−0.296167	−	0.955136i	$-0.595708\pi$
$89$	−0.708365	+	0.189806i	−0.0750865	+	0.0201194i	0.221080	+	0.975256i	$0.429042\pi$
$90$	0.218448	+	0.777058i	0.0230265	+	0.0819091i
$91$	−8.32047	+	15.2404i	−0.872222	+	1.59763i
$92$	−2.14181	−	3.50834i	−0.223299	−	0.365770i
$93$	−3.48242	+	0.933112i	−0.361110	+	0.0967592i
$94$	−2.92542	+	11.4784i	−0.301734	+	1.18391i
$95$	−0.182448	−	0.316009i	−0.0187188	−	0.0324219i
$96$	−4.71666	+	3.12299i	−0.481392	+	0.318739i
$97$	−4.48735	−	1.20238i	−0.455621	−	0.122083i	0.0237071	−	0.999719i	$-0.492453\pi$
$97$	−4.48735	−	1.20238i	−0.455621	−	0.122083i	−0.479329	+	0.877636i	$0.659120\pi$
$98$	22.8977	−	0.280506i	2.31301	−	0.0283354i
$99$	4.19106	+	4.19106i	0.421218	+	0.421218i
$100$	−8.20808	−	4.47450i	−0.820808	−	0.447450i
$101$	2.03641	−	3.52717i	0.202631	−	0.350966i	−0.746745	−	0.665111i	$-0.768384\pi$
$101$	2.03641	−	3.52717i	0.202631	−	0.350966i	0.949375	+	0.314144i	$0.101718\pi$
$102$	0.765219	+	1.28868i	0.0757680	+	0.127598i
$103$	−0.447521			−0.0440955			−0.0220478	−	0.999757i	$-0.507019\pi$
$103$	−0.447521			−0.0440955			−0.0220478	+	0.999757i	$0.507019\pi$
$104$	9.99236	+	2.03781i	0.979832	+	0.199824i
$105$	−2.74870			−0.268246
$106$	0.863410	+	1.45404i	0.0838618	+	0.141229i
$107$	3.67665	−	6.36815i	0.355436	−	0.615632i	−0.631757	−	0.775167i	$-0.717666\pi$
$107$	3.67665	−	6.36815i	0.355436	−	0.615632i	0.987192	+	0.159534i	$0.0509992\pi$
$108$	−0.957270	+	1.75603i	−0.0921133	+	0.168974i
$109$	−1.83648	−	1.83648i	−0.175903	−	0.175903i	0.613664	−	0.789567i	$-0.289695\pi$
$109$	−1.83648	−	1.83648i	−0.175903	−	0.175903i	−0.789567	+	0.613664i	$0.789695\pi$
$110$	4.78384	−	0.0586041i	0.456122	−	0.00558768i
$111$	6.84268	+	1.83349i	0.649478	+	0.174027i
$112$	−5.89110	−	18.3404i	−0.556657	−	1.73301i
$113$	−9.71582	−	16.8283i	−0.913987	−	1.58307i	−0.808378	−	0.588664i	$-0.799654\pi$
$113$	−9.71582	−	16.8283i	−0.913987	−	1.58307i	−0.105609	−	0.994408i	$-0.533679\pi$
$114$	0.223290	−	0.876120i	0.0209130	−	0.0820562i
$115$	−1.13307	+	0.303606i	−0.105660	+	0.0283114i
$116$	9.59406	−	5.85710i	0.890786	−	0.543818i
$117$	3.45943	−	1.01605i	0.319824	−	0.0939339i
$118$	−3.12846	−	11.1285i	−0.287998	−	1.02446i
$119$	−4.92981	+	1.32094i	−0.451915	+	0.121090i
$120$	0.474837	+	1.54295i	0.0433465	+	0.140851i
$121$	20.8972	−	12.0650i	1.89975	−	1.09682i
$122$	4.23644	−	7.54981i	0.383549	−	0.683528i
$123$	5.12996	+	1.37457i	0.462553	+	0.123941i
$124$	−6.91703	+	2.03628i	−0.621168	+	0.182864i
$125$	−3.90442	+	3.90442i	−0.349222	+	0.349222i
$126$	−4.87447	−	4.75649i	−0.434252	−	0.423742i
$127$	−6.86367	+	11.8882i	−0.609053	+	1.05491i	0.382344	+	0.924020i	$0.375117\pi$
$127$	−6.86367	+	11.8882i	−0.609053	+	1.05491i	−0.991397	+	0.130890i	$0.958217\pi$
$128$	−9.27749	+	6.47520i	−0.820022	+	0.572332i
$129$			9.90979i			0.872509i
$130$	1.36319	−	2.57133i	0.119560	−	0.225520i
$131$	−5.90363			−0.515802			−0.257901	−	0.966171i	$-0.583031\pi$
$131$	−5.90363			−0.515802			−0.257901	+	0.966171i	$0.583031\pi$
$132$	8.58495	+	8.17428i	0.747224	+	0.711479i
$133$	2.66635	+	1.53942i	0.231202	+	0.133484i
$134$	−8.08875	−	7.89297i	−0.698762	−	0.681849i
$135$	0.403590	+	0.403590i	0.0347355	+	0.0347355i
$136$	1.59312	+	2.53909i	0.136609	+	0.217726i
$137$	−4.50130	+	16.7991i	−0.384572	+	1.43524i	0.454268	+	0.890865i	$0.349901\pi$
$137$	−4.50130	+	16.7991i	−0.384572	+	1.43524i	−0.838840	+	0.544378i	$0.816766\pi$
$138$	−2.53474	−	1.42232i	−0.215771	−	0.121076i
$139$	−7.04702	−	12.2058i	−0.597721	−	1.03528i	−0.993157	−	0.116789i	$-0.962740\pi$
$139$	−7.04702	−	12.2058i	−0.597721	−	1.03528i	0.395436	−	0.918494i	$-0.370594\pi$
$140$	−5.49575	+	0.134671i	−0.464476	+	0.0113818i
$141$	2.16785	+	8.09054i	0.182566	+	0.681346i
$142$	−0.167299	−	0.595110i	−0.0140394	−	0.0499405i
$143$	−0.510104	−	21.3642i	−0.0426570	−	1.78657i
$144$	−1.82793	+	3.55790i	−0.152327	+	0.296492i
$145$	−0.830256	−	3.09856i	−0.0689490	−	0.257321i
$146$	14.2352	+	3.62802i	1.17812	+	0.300257i
$147$	14.0230	−	8.09616i	1.15659	−	0.667760i
$148$	13.7711	+	3.33063i	1.13198	+	0.273776i
$149$	2.88789	−	10.7777i	0.236585	−	0.882947i	−0.740843	−	0.671678i	$-0.765574\pi$
$149$	2.88789	−	10.7777i	0.236585	−	0.882947i	0.977428	−	0.211269i	$-0.0677596\pi$
$150$	−6.60986	+	0.0809736i	−0.539693	+	0.00661147i
$151$	−8.18475	+	8.18475i	−0.666066	+	0.666066i	−0.956803	−	0.290737i	$-0.906099\pi$
$151$	−8.18475	+	8.18475i	−0.666066	+	0.666066i	0.290737	+	0.956803i	$0.406099\pi$
$152$	0.403521	−	1.76265i	0.0327299	−	0.142970i
$153$	0.917794	+	0.529889i	0.0741993	+	0.0428390i
$154$	−34.7090	+	20.6102i	−2.79693	+	1.66082i
$155$			2.05775i			0.165283i
$156$	6.86700	−	2.20098i	0.549800	−	0.176220i
$157$		−	19.5674i		−	1.56165i	−0.624750	−	0.780825i	$-0.714799\pi$
$157$		−	19.5674i		−	1.56165i	0.624750	−	0.780825i	$-0.285201\pi$
$158$	−5.20496	−	8.76551i	−0.414085	−	0.697346i
$159$	1.03556	+	0.597883i	0.0821255	+	0.0474152i
$160$	1.02499	+	3.06170i	0.0810322	+	0.242049i
$161$	6.99869	−	6.99869i	0.551574	−	0.551574i
$162$	0.0173234	+	1.41411i	0.00136106	+	0.111103i
$163$	−1.63834	+	6.11436i	−0.128325	+	0.478914i	−0.999936	−	0.0112829i	$-0.996408\pi$
$163$	−1.63834	+	6.11436i	−0.128325	+	0.478914i	0.871612	+	0.490197i	$0.163075\pi$
$164$	10.3242	+	2.49697i	0.806184	+	0.194981i
$165$	2.92971	−	1.69147i	0.228078	−	0.131681i
$166$	3.85136	−	15.1116i	0.298924	−	1.17288i
$167$	1.29517	+	4.83364i	0.100223	+	0.374039i	0.997760	−	0.0669022i	$-0.0213115\pi$
$167$	1.29517	+	4.83364i	0.100223	+	0.374039i	−0.897536	+	0.440941i	$0.854645\pi$
$168$	−9.97906	−	9.27130i	−0.769901	−	0.715296i
$169$	−11.5557	−	5.95528i	−0.888901	−	0.458098i
$170$	0.823509	−	0.231507i	0.0631602	−	0.0177558i
$171$	−0.165467	−	0.617530i	−0.0126535	−	0.0472237i
$172$	0.485524	+	19.8136i	0.0370208	+	1.51078i
$173$	6.02967	+	10.4437i	0.458427	+	0.794019i	0.998878	−	0.0473563i	$-0.0150796\pi$
$173$	6.02967	+	10.4437i	0.458427	+	0.794019i	−0.540451	+	0.841376i	$0.681746\pi$
$174$	3.88954	−	6.93161i	0.294865	−	0.525484i
$175$	5.82611	−	21.7433i	0.440412	−	1.64364i
$176$	17.5652	+	15.9230i	1.32403	+	1.20024i
$177$	−5.77992	−	5.77992i	−0.434445	−	0.434445i
$178$	−0.724315	+	0.742281i	−0.0542897	+	0.0556363i
$179$	−15.2086	−	8.78071i	−1.13675	−	0.656301i	−0.191123	−	0.981566i	$-0.561213\pi$
$179$	−15.2086	−	8.78071i	−1.13675	−	0.656301i	−0.945623	+	0.325265i	$0.894546\pi$
$180$	0.826711	+	0.787164i	0.0616194	+	0.0586717i
$181$	7.03736			0.523083			0.261541	−	0.965192i	$-0.415769\pi$
$181$	7.03736			0.523083			0.261541	+	0.965192i	$0.415769\pi$
$182$	0.886817	+	24.5400i	0.0657352	+	1.81903i
$183$		−	6.12156i		−	0.452519i
$184$	−5.13764	−	2.71960i	−0.378752	−	0.200492i
$185$	2.02166	−	3.50161i	0.148635	−	0.257444i
$186$	−3.56083	+	3.64916i	−0.261093	+	0.267569i
$187$	4.44160	−	4.44160i	0.324802	−	0.324802i
$188$	4.73080	+	16.0700i	0.345029	+	1.17203i
$189$	−4.65174	−	1.24643i	−0.338365	−	0.0906645i
$190$	−0.450032	−	0.252527i	−0.0326488	−	0.0183202i
$191$	−17.8511	+	10.3063i	−1.29166	+	0.745740i	−0.978948	−	0.204108i	$-0.934571\pi$
$191$	−17.8511	+	10.3063i	−1.29166	+	0.745740i	−0.312711	+	0.949848i	$0.601237\pi$
$192$	−3.48044	+	7.20323i	−0.251179	+	0.519848i
$193$	−4.18310	+	1.12086i	−0.301106	+	0.0806812i	−0.406209	−	0.913780i	$-0.633150\pi$
$193$	−4.18310	+	1.12086i	−0.301106	+	0.0806812i	0.105103	+	0.994461i	$0.466483\pi$
$194$	−6.32477	+	1.77803i	−0.454092	+	0.127655i
$195$	−0.0491218	−	2.05733i	−0.00351769	−	0.147328i
$196$	27.6408	−	16.8745i	1.97435	−	1.20532i
$197$	10.2512	−	2.74681i	0.730370	−	0.195702i	0.125576	−	0.992084i	$-0.459922\pi$
$197$	10.2512	−	2.74681i	0.730370	−	0.195702i	0.604794	+	0.796382i	$0.293255\pi$
$198$	8.12248	+	2.07011i	0.577240	+	0.147117i
$199$	−12.0604	−	20.8892i	−0.854937	−	1.48079i	−0.876703	−	0.481031i	$-0.840262\pi$
$199$	−12.0604	−	20.8892i	−0.854937	−	1.48079i	0.0217665	−	0.999763i	$-0.493071\pi$
$200$	−13.2118	+	0.485745i	−0.934215	+	0.0343473i
$201$	−7.71916	−	2.06834i	−0.544467	−	0.145890i
$202$	−0.0705552	−	5.75941i	−0.00496425	−	0.405231i
$203$	19.1389	+	19.1389i	1.34329	+	1.34329i
$204$	1.86100	+	1.01449i	0.130296	+	0.0710287i
$205$	1.51564	−	2.62516i	0.105857	−	0.183349i
$206$	−0.544182	+	0.323135i	−0.0379149	+	0.0225139i
$207$	−2.05523			−0.142848
$208$	13.6220	−	4.73709i	0.944519	−	0.328458i
$209$	−3.78925			−0.262108
$210$	−3.34240	+	1.98472i	−0.230647	+	0.136958i
$211$	−7.25156	+	12.5601i	−0.499218	+	0.864671i	−1.00000		0.000902928i	$-0.999713\pi$
$211$	−7.25156	+	12.5601i	−0.499218	+	0.864671i	0.500782	+	0.865574i	$0.333046\pi$
$212$	2.09980	+	1.14467i	0.144215	+	0.0786162i
$213$	−0.309089	−	0.309089i	−0.0211784	−	0.0211784i
$214$	−0.127384	−	10.3984i	−0.00870782	−	0.710818i
$215$	5.46341	+	1.46392i	0.372601	+	0.0998382i
$216$	0.103920	+	2.82652i	0.00707084	+	0.192320i
$217$	−8.68120	−	15.0363i	−0.589318	−	1.02073i
$218$	−3.55919	−	0.907102i	−0.241059	−	0.0614367i
$219$	10.0336	−	2.68851i	0.678011	−	0.181673i
$220$	5.77480	−	3.52547i	0.389337	−	0.237687i
$221$	−1.07679	−	3.66622i	−0.0724325	−	0.246617i
$222$	9.64452	−	2.71129i	0.647298	−	0.181970i
$223$	23.4642	−	6.28722i	1.57128	−	0.421024i	0.635068	−	0.772456i	$-0.280972\pi$
$223$	23.4642	−	6.28722i	1.57128	−	0.421024i	0.936213	+	0.351432i	$0.114305\pi$
$224$	−20.4064	−	18.0481i	−1.36346	−	1.20589i
$225$	−4.04800	+	2.33712i	−0.269867	+	0.155808i
$226$	−23.9653	−	13.4477i	−1.59415	−	0.894527i
$227$	19.5131	+	5.22852i	1.29513	+	0.347029i	0.839607	−	0.543195i	$-0.182785\pi$
$227$	19.5131	+	5.22852i	1.29513	+	0.347029i	0.455524	+	0.890224i	$0.349452\pi$
$228$	−0.361089	−	1.22658i	−0.0239137	−	0.0812324i
$229$	0.537694	−	0.537694i	0.0355318	−	0.0355318i	−0.689118	−	0.724649i	$-0.742002\pi$
$229$	0.537694	−	0.537694i	0.0355318	−	0.0355318i	0.724649	+	0.689118i	$0.242002\pi$
$230$	−1.15859	+	1.18733i	−0.0763950	+	0.0782900i
$231$	−14.2719	+	24.7196i	−0.939021	+	1.62643i
$232$	7.43714	−	14.0496i	0.488272	−	0.922403i
$233$			5.06336i			0.331712i	0.986150	+	0.165856i	$0.0530387\pi$
$233$			5.06336i			0.331712i	−0.986150	+	0.165856i	$0.946961\pi$
$234$	3.47299	−	3.73341i	0.227036	−	0.244061i
$235$	4.78067			0.311857
$236$	−11.8395	−	11.2732i	−0.770689	−	0.733822i
$237$	−6.24277	−	3.60426i	−0.405511	−	0.234122i
$238$	−5.04082	+	5.16585i	−0.326748	+	0.334853i
$239$	20.1780	+	20.1780i	1.30521	+	1.30521i	0.924832	+	0.380376i	$0.124205\pi$
$239$	20.1780	+	20.1780i	1.30521	+	1.30521i	0.380376	+	0.924832i	$0.375795\pi$
$240$	1.69149	+	1.53335i	0.109185	+	0.0989774i
$241$	3.50678	−	13.0875i	0.225891	−	0.843038i	−0.756154	−	0.654394i	$-0.772924\pi$
$241$	3.50678	−	13.0875i	0.225891	−	0.843038i	0.982045	−	0.188645i	$-0.0604094\pi$
$242$	16.6992	−	29.7599i	1.07347	−	1.91304i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.299922	−	12.2395i	−0.0192005	−	0.783551i
$245$	−2.39200	−	8.92705i	−0.152819	−	0.570328i
$246$	7.23051	−	2.03266i	0.461000	−	0.129597i
$247$	−1.10456	+	2.02320i	−0.0702815	+	0.128733i
$248$	−6.94074	+	7.47059i	−0.440738	+	0.474383i
$249$	−2.85401	−	10.6513i	−0.180866	−	0.675000i
$250$	−1.92853	+	7.56695i	−0.121971	+	0.478576i
$251$	14.5185	−	8.38225i	0.916398	−	0.529083i	0.0339142	−	0.999425i	$-0.489203\pi$
$251$	14.5185	−	8.38225i	0.916398	−	0.529083i	0.882484	+	0.470342i	$0.155869\pi$
$252$	−9.36177	−	2.26421i	−0.589736	−	0.142632i
$253$	−3.15279	+	11.7664i	−0.198214	+	0.739745i
$254$	0.237805	+	19.4119i	0.0149212	+	1.21801i
$255$	0.427715	−	0.427715i	0.0267846	−	0.0267846i
$256$	−6.60588	+	14.5727i	−0.412868	+	0.910791i
$257$	−7.66304	−	4.42426i	−0.478007	−	0.275978i	0.241578	−	0.970381i	$-0.422335\pi$
$257$	−7.66304	−	4.42426i	−0.478007	−	0.275978i	−0.719586	+	0.694404i	$0.755668\pi$
$258$	7.15543	+	12.0502i	0.445477	+	0.750214i
$259$			34.1157i			2.11985i
$260$	−0.199012	−	4.11101i	−0.0123422	−	0.254954i
$261$		−	5.62031i		−	0.347889i
$262$	−7.17876	+	4.26275i	−0.443505	+	0.263354i
$263$	−5.49660	−	3.17346i	−0.338935	−	0.195684i	0.320866	−	0.947125i	$-0.396026\pi$
$263$	−5.49660	−	3.17346i	−0.338935	−	0.195684i	−0.659801	+	0.751440i	$0.729359\pi$
$264$	16.3415	+	3.74103i	1.00575	+	0.230244i
$265$	0.482599	−	0.482599i	0.0296458	−	0.0296458i
$266$	4.35380	−	0.0533359i	0.266949	−	0.00327024i
$267$	−0.189806	+	0.708365i	−0.0116159	+	0.0433512i
$268$	−15.5350	−	3.75725i	−0.948952	−	0.229510i
$269$	−5.51917	+	3.18649i	−0.336509	+	0.194284i	−0.658727	−	0.752382i	$-0.728905\pi$
$269$	−5.51917	+	3.18649i	−0.336509	+	0.194284i	0.322218	+	0.946666i	$0.395572\pi$
$270$	0.782176	+	0.199347i	0.0476017	+	0.0121319i
$271$	2.27246	+	8.48094i	0.138042	+	0.515181i	0.999967	+	0.00814415i	$0.00259239\pi$
$271$	2.27246	+	8.48094i	0.138042	+	0.515181i	−0.861925	+	0.507036i	$0.830741\pi$
$272$	3.77058	+	1.93720i	0.228625	+	0.117460i
$273$	9.03835	+	14.8259i	0.547026	+	0.897307i
$274$	6.65634	+	23.6777i	0.402124	+	1.43042i
$275$	7.17044	+	26.7604i	0.432394	+	1.61372i
$276$	−4.10922	+	0.100694i	−0.247346	+	0.00606109i
$277$	3.44140	+	5.96068i	0.206774	+	0.358143i	0.950696	−	0.310123i	$-0.100370\pi$
$277$	3.44140	+	5.96068i	0.206774	+	0.358143i	−0.743923	+	0.668266i	$0.767037\pi$
$278$	−17.3824	−	9.75380i	−1.04253	−	0.584994i
$279$	−0.933112	+	3.48242i	−0.0558639	+	0.208487i
$280$	−6.58554	+	4.13200i	−0.393562	+	0.246934i
$281$	1.24628	+	1.24628i	0.0743466	+	0.0743466i	0.743302	−	0.668956i	$-0.233258\pi$
$281$	1.24628	+	1.24628i	0.0743466	+	0.0743466i	−0.668956	+	0.743302i	$0.733258\pi$
$282$	8.47791	+	8.27271i	0.504852	+	0.492633i
$283$	11.6080	+	6.70190i	0.690025	+	0.398386i	0.803622	−	0.595141i	$-0.202904\pi$
$283$	11.6080	+	6.70190i	0.690025	+	0.398386i	−0.113596	+	0.993527i	$0.536237\pi$
$284$	−0.633137	−	0.602849i	−0.0375697	−	0.0357725i
$285$	−0.364896			−0.0216146
$286$	−16.0465	−	25.6104i	−0.948847	−	1.51437i
$287$			25.5766i			1.50974i
$288$	0.346260	+	5.64625i	0.0204036	+	0.332708i
$289$	−7.93844	+	13.7498i	−0.466967	+	0.808810i
$290$	−3.24692	−	3.16833i	−0.190665	−	0.186051i
$291$	−3.28497	+	3.28497i	−0.192568	+	0.192568i
$292$	19.9296	−	5.86700i	1.16629	−	0.343340i
$293$	22.6215	+	6.06142i	1.32156	+	0.354112i	0.849563	−	0.527486i	$-0.176865\pi$
$293$	22.6215	+	6.06142i	1.32156	+	0.354112i	0.472000	+	0.881598i	$0.343532\pi$
$294$	11.2059	−	19.9702i	0.653542	−	1.16469i
$295$	−4.04038	+	2.33272i	−0.235240	+	0.135816i
$296$	19.1504	−	5.89348i	1.11310	−	0.342552i
$297$	5.72510	−	1.53404i	0.332204	−	0.0890138i
$298$	−4.27049	−	15.1909i	−0.247383	−	0.879983i
$299$	5.36340	+	5.11325i	0.310173	+	0.295707i
$300$	−7.97907	+	4.87116i	−0.460672	+	0.281236i
$301$	−46.0978	+	12.3519i	−2.65703	+	0.711950i
$302$	−4.04274	+	15.8624i	−0.232633	+	0.912781i
$303$	−2.03641	−	3.52717i	−0.116989	−	0.202631i
$304$	−0.782058	−	2.43474i	−0.0448541	−	0.139642i
$305$	−3.37490	−	0.904303i	−0.193246	−	0.0517802i
$306$	1.49864	−	0.0183590i	0.0856715	−	0.00104951i
$307$	−21.1986	−	21.1986i	−1.20987	−	1.20987i	−0.971069	−	0.238798i	$-0.923247\pi$
$307$	−21.1986	−	21.1986i	−1.20987	−	1.20987i	−0.238798	−	0.971069i	$-0.576753\pi$
$308$	−27.3241	+	50.1237i	−1.55693	+	2.85606i
$309$	−0.223760	+	0.387565i	−0.0127293	+	0.0220478i
$310$	1.48581	+	2.50221i	0.0843884	+	0.142116i
$311$	23.6077			1.33867			0.669335	−	0.742961i	$-0.266579\pi$
$311$	23.6077			1.33867			0.669335	+	0.742961i	$0.266579\pi$
$312$	6.76098	−	7.63474i	0.382765	−	0.432232i
$313$	−1.67315			−0.0945720			−0.0472860	−	0.998881i	$-0.515057\pi$
$313$	−1.67315			−0.0945720			−0.0472860	+	0.998881i	$0.515057\pi$
$314$	−14.1288	−	23.7938i	−0.797333	−	1.34276i
$315$	−1.37435	+	2.38044i	−0.0774359	+	0.134123i
$316$	−12.6584	−	6.90050i	−0.712089	−	0.388184i
$317$	−1.99292	−	1.99292i	−0.111933	−	0.111933i	0.648922	−	0.760855i	$-0.275220\pi$
$317$	−1.99292	−	1.99292i	−0.111933	−	0.111933i	−0.760855	+	0.648922i	$0.775220\pi$
$318$	1.69094	−	0.0207147i	0.0948233	−	0.00116163i
$319$	−32.1768	−	8.62176i	−1.80156	−	0.482726i
$320$	3.45710	+	2.98291i	0.193258	+	0.166750i
$321$	−3.67665	−	6.36815i	−0.205211	−	0.355436i
$322$	3.45690	−	13.5638i	0.192645	−	0.755880i
$323$	−0.654444	+	0.175358i	−0.0364142	+	0.00975717i
$324$	1.04213	+	1.70703i	0.0578961	+	0.0948352i
$325$	16.3784	+	3.97211i	0.908510	+	0.220333i
$326$	2.42271	+	8.61799i	0.134181	+	0.477306i
$327$	−2.50868	+	0.672199i	−0.138730	+	0.0371727i
$328$	14.3571	−	4.41835i	0.792737	−	0.243962i
$329$	−34.9330	+	20.1686i	−1.92592	+	1.11193i
$330$	2.34117	−	4.17223i	0.128877	−	0.229674i
$331$	−5.44493	−	1.45897i	−0.299281	−	0.0801920i	0.106054	−	0.994360i	$-0.466178\pi$
$331$	−5.44493	−	1.45897i	−0.299281	−	0.0801920i	−0.405335	+	0.914168i	$0.632845\pi$
$332$	−6.22817	−	21.1564i	−0.341815	−	1.16111i
$333$	5.00919	−	5.00919i	0.274502	−	0.274502i
$334$	5.06508	+	4.94248i	0.277149	+	0.270441i
$335$	−2.28061	+	3.95014i	−0.124603	+	0.215819i
$336$	−18.8288	−	4.06838i	−1.02720	−	0.221948i
$337$		−	9.98987i		−	0.544183i	−0.962271	−	0.272091i	$-0.912285\pi$
$337$		−	9.98987i		−	0.544183i	0.962271	−	0.272091i	$-0.0877153\pi$
$338$	−18.3517	+	1.10231i	−0.998201	+	0.0599578i
$339$	−19.4316			−1.05538
$340$	0.834218	−	0.876130i	0.0452418	−	0.0475148i
$341$	18.5058	+	10.6843i	1.00214	+	0.578588i
$342$	−0.647097	−	0.631435i	−0.0349910	−	0.0341441i
$343$	31.3027	+	31.3027i	1.69019	+	1.69019i
$344$	14.8970	+	23.7426i	0.803190	+	1.28012i
$345$	−0.303606	+	1.13307i	−0.0163456	+	0.0610027i
$346$	14.8730	+	8.34568i	0.799575	+	0.448666i
$347$	−11.8582	−	20.5391i	−0.636584	−	1.10260i	−0.986177	−	0.165694i	$-0.947014\pi$
$347$	−11.8582	−	20.5391i	−0.636584	−	1.10260i	0.349594	−	0.936901i	$-0.386320\pi$
$348$	−0.275363	−	11.2372i	−0.0147610	−	0.602380i
$349$	5.11905	+	19.1046i	0.274017	+	1.02264i	0.956498	+	0.291740i	$0.0942343\pi$
$349$	5.11905	+	19.1046i	0.274017	+	1.02264i	−0.682481	+	0.730903i	$0.739099\pi$
$350$	−8.61541	−	30.6465i	−0.460513	−	1.63812i
$351$	0.849788	−	3.50398i	0.0453584	−	0.187028i
$352$	32.8565	+	6.67917i	1.75126	+	0.356001i
$353$	2.87468	+	10.7284i	0.153004	+	0.571017i	0.999268	+	0.0382541i	$0.0121796\pi$
$353$	2.87468	+	10.7284i	0.153004	+	0.571017i	−0.846264	+	0.532763i	$0.821154\pi$
$354$	−11.2018	−	2.85490i	−0.595367	−	0.151736i
$355$	−0.216065	+	0.124745i	−0.0114675	+	0.00662079i
$356$	−0.344792	+	1.42560i	−0.0182739	+	0.0755569i
$357$	−1.32094	+	4.92981i	−0.0699115	+	0.260913i
$358$	−24.8337	+	0.304224i	−1.31250	+	0.0160787i
$359$	10.0901	−	10.0901i	0.532537	−	0.532537i	−0.388790	−	0.921327i	$-0.627107\pi$
$359$	10.0901	−	10.0901i	0.532537	−	0.532537i	0.921327	+	0.388790i	$0.127107\pi$
$360$	1.57365	+	0.360253i	0.0829386	+	0.0189870i
$361$	−16.1005	−	9.29564i	−0.847396	−	0.489244i
$362$	8.55736	−	5.08137i	0.449765	−	0.267071i
$363$		−	24.1300i		−	1.26650i
$364$	18.7977	+	29.2001i	0.985265	+	1.53050i
$365$		−	5.92885i		−	0.310330i
$366$	−4.42011	−	7.44377i	−0.231043	−	0.389092i
$367$	−5.69564	−	3.28838i	−0.297310	−	0.171652i	0.343924	−	0.938997i	$-0.388244\pi$
$367$	−5.69564	−	3.28838i	−0.297310	−	0.171652i	−0.641234	+	0.767346i	$0.721577\pi$
$368$	−8.21103	+	0.402657i	−0.428030	+	0.0209899i
$369$	3.75539	−	3.75539i	0.195498	−	0.195498i
$370$	−0.0700440	−	5.71768i	−0.00364142	−	0.297248i
$371$	−1.49044	+	5.56240i	−0.0773798	+	0.288785i
$372$	−1.69504	+	7.00847i	−0.0878840	+	0.363372i
$373$	7.36621	−	4.25288i	0.381408	−	0.220206i	−0.297023	−	0.954870i	$-0.595994\pi$
$373$	7.36621	−	4.25288i	0.381408	−	0.220206i	0.678431	+	0.734665i	$0.262660\pi$
$374$	2.19386	−	8.60802i	0.113442	−	0.445110i
$375$	1.42912	+	5.33354i	0.0737993	+	0.275423i
$376$	17.3561	+	16.1251i	0.895070	+	0.831588i
$377$	−13.9829	+	14.6670i	−0.720157	+	0.755388i
$378$	−6.55647	+	1.84317i	−0.337229	+	0.0948025i
$379$	4.52705	+	16.8952i	0.232539	+	0.867847i	0.979243	+	0.202690i	$0.0649685\pi$
$379$	4.52705	+	16.8952i	0.232539	+	0.867847i	−0.746704	+	0.665156i	$0.768365\pi$
$380$	−0.729574	+	0.0178779i	−0.0374263	+	0.000917115i
$381$	6.86367	+	11.8882i	0.351637	+	0.609053i
$382$	−14.2650	+	25.4219i	−0.729862	+	1.30070i
$383$	2.58315	−	9.64043i	0.131993	−	0.492603i	−0.868000	−	0.496565i	$-0.834594\pi$
$383$	2.58315	−	9.64043i	0.131993	−	0.492603i	0.999992	+	0.00396183i	$0.00126109\pi$
$384$	0.968947	+	11.2721i	0.0494464	+	0.575229i
$385$	11.5200	+	11.5200i	0.587113	+	0.587113i
$386$	−4.27729	+	4.38339i	−0.217709	+	0.223109i
$387$	8.58213	+	4.95490i	0.436254	+	0.251872i
$388$	−6.40702	+	6.72891i	−0.325267	+	0.341609i
$389$	0.803809			0.0407547			0.0203774	−	0.999792i	$-0.493513\pi$
$389$	0.803809			0.0407547			0.0203774	+	0.999792i	$0.493513\pi$
$390$	−1.54524	−	2.46622i	−0.0782461	−	0.124882i
$391$			2.17808i			0.110150i
$392$	21.4267	−	40.4775i	1.08221	−	2.04442i
$393$	−2.95181	+	5.11269i	−0.148899	+	0.257901i
$394$	10.4821	−	10.7421i	0.528079	−	0.541177i
$395$	−2.90929	+	2.90929i	−0.146382	+	0.146382i
$396$	11.3716	−	3.34765i	0.571445	−	0.168226i
$397$	1.17900	+	0.315913i	0.0591725	+	0.0158552i	0.288284	−	0.957545i	$-0.406915\pi$
$397$	1.17900	+	0.315913i	0.0591725	+	0.0158552i	−0.229111	+	0.973400i	$0.573582\pi$
$398$	−29.7485	−	16.6928i	−1.49116	−	0.836734i
$399$	2.66635	−	1.53942i	0.133484	−	0.0770672i
$400$	−15.7147	+	10.1303i	−0.785735	+	0.506516i
$401$	−4.73196	+	1.26792i	−0.236303	+	0.0633171i	−0.375027	−	0.927014i	$-0.622367\pi$
$401$	−4.73196	+	1.26792i	−0.236303	+	0.0633171i	0.138724	+	0.990331i	$0.455700\pi$
$402$	−10.8799	+	3.05858i	−0.542640	+	0.152548i
$403$	11.0991	−	6.76635i	0.552885	−	0.337056i
$404$	−4.24441	−	6.95245i	−0.211167	−	0.345897i
$405$	0.551314	−	0.147724i	0.0273950	−	0.00734047i
$406$	37.0921	+	9.45338i	1.84085	+	0.469164i
$407$	−20.9938	−	36.3624i	−1.04063	−	1.80242i
$408$	2.99548	−	0.110132i	0.148298	−	0.00545233i
$409$	13.7141	+	3.67467i	0.678117	+	0.181701i	0.581408	−	0.813612i	$-0.302502\pi$
$409$	13.7141	+	3.67467i	0.678117	+	0.181701i	0.0967086	+	0.995313i	$0.469169\pi$
$410$	−0.0525121	−	4.28655i	−0.00259339	−	0.211698i
$411$	12.2978	+	12.2978i	0.606605	+	0.606605i
$412$	−0.428398	+	0.785859i	−0.0211057	+	0.0387165i
$413$	19.6824	−	34.0910i	0.968509	−	1.67751i
$414$	−2.49914	+	1.48399i	−0.122826	+	0.0729340i
$415$	−6.29383			−0.308952
$416$	13.1438	−	15.5961i	0.644430	−	0.764664i
$417$	−14.0940			−0.690189
$418$	−4.60770	+	2.73605i	−0.225370	+	0.133825i
$419$	−2.36107	+	4.08949i	−0.115346	+	0.199785i	−0.917918	−	0.396770i	$-0.870131\pi$
$419$	−2.36107	+	4.08949i	−0.115346	+	0.199785i	0.802572	+	0.596555i	$0.203464\pi$
$420$	−2.63125	+	4.82679i	−0.128392	+	0.235523i
$421$	4.38018	+	4.38018i	0.213477	+	0.213477i	0.805743	−	0.592266i	$-0.201766\pi$
$421$	4.38018	+	4.38018i	0.213477	+	0.213477i	−0.592266	+	0.805743i	$0.701766\pi$
$422$	0.251244	+	20.5090i	0.0122303	+	0.998361i
$423$	8.09054	+	2.16785i	0.393375	+	0.105405i
$424$	3.37985	−	0.124264i	0.164140	−	0.00603477i
$425$	2.47682	+	4.28998i	0.120143	+	0.208095i
$426$	−0.599030	−	0.152670i	−0.0290231	−	0.00739689i
$427$	28.4759	−	7.63011i	1.37805	−	0.369247i
$428$	−7.66310	−	12.5523i	−0.370410	−	0.606740i
$429$	−18.7570	−	10.2404i	−0.905597	−	0.494409i
$430$	7.70049	−	2.16478i	0.371350	−	0.104395i
$431$	2.21278	−	0.592912i	0.106586	−	0.0285596i	−0.205132	−	0.978734i	$-0.565762\pi$
$431$	2.21278	−	0.592912i	0.106586	−	0.0285596i	0.311718	+	0.950175i	$0.399096\pi$
$432$	2.16727	+	3.36198i	0.104273	+	0.161754i
$433$	13.9535	−	8.05603i	0.670560	−	0.387148i	−0.125729	−	0.992065i	$-0.540127\pi$
$433$	13.9535	−	8.05603i	0.670560	−	0.387148i	0.796289	+	0.604917i	$0.206794\pi$
$434$	−21.4133	−	12.0157i	−1.02787	−	0.576770i
$435$	−3.09856	−	0.830256i	−0.148564	−	0.0398077i
$436$	−4.98292	+	1.46690i	−0.238639	+	0.0702520i
$437$	0.929092	−	0.929092i	0.0444445	−	0.0444445i
$438$	10.2596	−	10.5141i	0.490222	−	0.502381i
$439$	−10.1992	+	17.6656i	−0.486783	+	0.843133i	−0.999885	−	0.0151950i	$-0.995163\pi$
$439$	−10.1992	+	17.6656i	−0.486783	+	0.843133i	0.513102	+	0.858328i	$0.328496\pi$
$440$	4.47652	−	8.45667i	0.213410	−	0.403156i
$441$		−	16.1923i		−	0.771063i
$442$	−3.95658	−	3.68059i	−0.188195	−	0.175068i
$443$	4.48358			0.213021			0.106511	−	0.994312i	$-0.466032\pi$
$443$	4.48358			0.213021			0.106511	+	0.994312i	$0.466032\pi$
$444$	9.76995	−	10.2608i	0.463661	−	0.486956i
$445$	0.362493	+	0.209285i	0.0171838	+	0.00992107i
$446$	23.9926	−	24.5877i	1.13608	−	1.16426i
$447$	−7.88986	−	7.88986i	−0.373177	−	0.373177i
$448$	−37.8457	−	7.21181i	−1.78804	−	0.340726i
$449$	3.28057	−	12.2433i	0.154820	−	0.577795i	−0.844301	−	0.535869i	$-0.819984\pi$
$449$	3.28057	−	12.2433i	0.154820	−	0.577795i	0.999121	−	0.0419259i	$-0.0133493\pi$
$450$	−3.23481	+	5.76480i	−0.152490	+	0.271755i
$451$	−15.7391	−	27.2609i	−0.741125	−	1.28367i
$452$	−38.8516	+	0.952040i	−1.82743	+	0.0447802i
$453$	2.99583	+	11.1806i	0.140756	+	0.525309i
$454$	27.5031	−	7.73172i	1.29078	−	0.362868i
$455$	9.50893	−	2.79282i	0.445786	−	0.130929i
$456$	−1.32474	−	1.23079i	−0.0620368	−	0.0576369i
$457$	6.68865	+	24.9624i	0.312882	+	1.16769i	0.925946	+	0.377657i	$0.123270\pi$
$457$	6.68865	+	24.9624i	0.312882	+	1.16769i	−0.613064	+	0.790033i	$0.710063\pi$
$458$	0.265586	−	1.04208i	0.0124100	−	0.0486930i
$459$	0.917794	−	0.529889i	0.0428390	−	0.0247331i
$460$	−0.551516	+	2.28034i	−0.0257146	+	0.106322i
$461$	−4.57308	+	17.0670i	−0.212990	+	0.794888i	0.773875	+	0.633338i	$0.218316\pi$
$461$	−4.57308	+	17.0670i	−0.212990	+	0.794888i	−0.986865	+	0.161550i	$0.948351\pi$
$462$	0.494476	+	40.3640i	0.0230051	+	1.87790i
$463$	−0.916082	+	0.916082i	−0.0425740	+	0.0425740i	−0.728073	−	0.685499i	$-0.759584\pi$
$463$	−0.916082	+	0.916082i	−0.0425740	+	0.0425740i	0.685499	+	0.728073i	$0.259584\pi$
$464$	−1.10112	−	22.4543i	−0.0511184	−	1.04241i
$465$	1.78206	+	1.02888i	0.0826413	+	0.0477130i
$466$	3.65603	+	6.15700i	0.169362	+	0.285218i
$467$			1.02377i			0.0473745i	0.999719	+	0.0236872i	$0.00754059\pi$
$467$			1.02377i			0.0473745i	−0.999719	+	0.0236872i	$0.992459\pi$
$468$	1.52739	−	7.04749i	0.0706037	−	0.325770i
$469$		−	38.4856i		−	1.77710i
$470$	5.81326	−	3.45191i	0.268145	−	0.159225i
$471$	−16.9459	−	9.78370i	−0.780825	−	0.450809i
$472$	−22.5367	−	5.15927i	−1.03733	−	0.237475i
$473$	41.5326	−	41.5326i	1.90967	−	1.90967i
$474$	−10.1936	+	0.124876i	−0.468209	+	0.00573576i
$475$	0.773429	−	2.88648i	0.0354874	−	0.132441i
$476$	−2.39955	+	9.92139i	−0.109983	+	0.454746i
$477$	1.03556	−	0.597883i	0.0474152	−	0.0273752i
$478$	39.1060	+	9.96663i	1.78867	+	0.455863i
$479$	−0.0511532	−	0.190906i	−0.00233725	−	0.00872273i	0.964747	−	0.263178i	$-0.0847706\pi$
$479$	−0.0511532	−	0.190906i	−0.00233725	−	0.00872273i	−0.967085	+	0.254455i	$0.918104\pi$
$480$	3.16401	+	0.643189i	0.144416	+	0.0293574i
$481$	−25.5347	+	0.609680i	−1.16428	+	0.0277990i
$482$	−5.18568	−	18.4463i	−0.236201	−	0.840208i
$483$	−2.56170	−	9.56038i	−0.116561	−	0.435012i
$484$	−1.18224	−	48.2456i	−0.0537380	−	2.19298i
$485$	1.32578	+	2.29632i	0.0602006	+	0.104270i
$486$	1.23331	+	0.692051i	0.0559443	+	0.0313921i
$487$	2.09884	−	7.83299i	0.0951077	−	0.354947i	−0.901928	−	0.431886i	$-0.857848\pi$
$487$	2.09884	−	7.83299i	0.0951077	−	0.354947i	0.997036	+	0.0769395i	$0.0245148\pi$
$488$	−9.20228	−	14.6665i	−0.416567	−	0.663922i
$489$	4.47602	+	4.47602i	0.202413	+	0.202413i
$490$	−9.35448	−	9.12806i	−0.422592	−	0.412364i
$491$	13.2895	+	7.67272i	0.599748	+	0.346265i	0.768943	−	0.639318i	$-0.220783\pi$
$491$	13.2895	+	7.67272i	0.599748	+	0.346265i	−0.169194	+	0.985583i	$0.554116\pi$
$492$	7.32454	−	7.69253i	0.330216	−	0.346806i
$493$	−5.95628			−0.268257
$494$	0.117727	+	3.25775i	0.00529679	+	0.146573i
$495$		−	3.38294i		−	0.152052i
$496$	−3.04570	+	14.0958i	−0.136756	+	0.632919i
$497$	1.05255	−	1.82306i	0.0472131	−	0.0817755i
$498$	−11.1613	−	10.8912i	−0.500150	−	0.488044i
$499$	10.5996	−	10.5996i	0.474502	−	0.474502i	−0.428866	−	0.903368i	$-0.641087\pi$
$499$	10.5996	−	10.5996i	0.474502	−	0.474502i	0.903368	+	0.428866i	$0.141087\pi$
$500$	3.11869	+	10.5939i	0.139472	+	0.473772i
$501$	4.83364	+	1.29517i	0.215951	+	0.0578640i
$502$	11.6019	−	20.6759i	0.517818	−	0.922811i
$503$	32.2230	−	18.6039i	1.43675	−	0.829508i	0.439128	−	0.898424i	$-0.355287\pi$
$503$	32.2230	−	18.6039i	1.43675	−	0.829508i	0.997622	+	0.0689162i	$0.0219541\pi$
$504$	−13.0187	+	4.00647i	−0.579899	+	0.178462i
$505$	−2.24541	+	0.601655i	−0.0999192	+	0.0267733i
$506$	4.66222	+	16.5843i	0.207261	+	0.737262i
$507$	−10.9353	+	7.02991i	−0.485653	+	0.312209i
$508$	14.3057	+	23.4330i	0.634712	+	1.03967i
$509$	−39.9366	+	10.7010i	−1.77016	+	0.474312i	−0.988733	−	0.149687i	$-0.952173\pi$
$509$	−39.9366	+	10.7010i	−1.77016	+	0.474312i	−0.781425	+	0.624000i	$0.785507\pi$
$510$	0.211264	−	0.828933i	0.00935491	−	0.0367058i
$511$	25.0125	+	43.3229i	1.10649	+	1.91649i
$512$	2.48958	+	22.4900i	0.110025	+	0.993929i
$513$	−0.617530	−	0.165467i	−0.0272646	−	0.00730553i
$514$	−12.5127	+	0.153286i	−0.551914	+	0.00676118i
$515$	0.180615	+	0.180615i	0.00795884	+	0.00795884i
$516$	17.4019	+	9.48634i	0.766075	+	0.417613i
$517$	24.8224	−	42.9936i	1.09169	−	1.89086i
$518$	24.6335	+	41.4844i	1.08233	+	1.82272i
$519$	12.0593			0.529346
$520$	−3.21038	−	4.85526i	−0.140784	−	0.212917i
$521$	35.6854			1.56341			0.781703	−	0.623650i	$-0.214351\pi$
$521$	35.6854			1.56341			0.781703	+	0.623650i	$0.214351\pi$
$522$	−4.05818	−	6.83425i	−0.177622	−	0.299127i
$523$	2.52621	−	4.37553i	0.110464	−	0.191328i	−0.805494	−	0.592604i	$-0.798100\pi$
$523$	2.52621	−	4.37553i	0.110464	−	0.191328i	0.915957	+	0.401276i	$0.131433\pi$
$524$	−5.65136	+	10.3669i	−0.246881	+	0.452882i
$525$	−15.9172	−	15.9172i	−0.694684	−	0.694684i
$526$	−8.97524	+	0.109950i	−0.391339	+	0.00479407i
$527$	3.69059	+	0.988891i	0.160765	+	0.0430768i
$528$	22.5724	−	7.25043i	0.982336	−	0.315535i
$529$	9.38802	+	16.2605i	0.408175	+	0.706980i
$530$	0.238372	−	0.935299i	0.0103542	−	0.0406268i
$531$	−7.89551	+	2.11560i	−0.342636	+	0.0918091i
$532$	5.25567	−	3.20855i	0.227862	−	0.139108i
$533$	−19.1434	+	0.457077i	−0.829191	+	0.0197982i
$534$	0.280677	+	0.998416i	0.0121461	+	0.0432057i
$535$	−4.05398	+	1.08626i	−0.175269	+	0.0469632i
$536$	−21.6034	+	6.64838i	−0.933125	+	0.287166i
$537$	−15.2086	+	8.78071i	−0.656301	+	0.378915i
$538$	−4.41043	+	7.85989i	−0.190147	+	0.338864i
$539$	−92.7027	−	24.8396i	−3.99299	−	1.06992i
$540$	1.09506	−	0.322371i	0.0471239	−	0.0138726i
$541$	−16.2450	+	16.2450i	−0.698429	+	0.698429i	−0.964072	−	0.265643i	$-0.914416\pi$
$541$	−16.2450	+	16.2450i	−0.698429	+	0.698429i	0.265643	+	0.964072i	$0.414416\pi$
$542$	8.88701	+	8.67191i	0.381730	+	0.372490i
$543$	3.51868	−	6.09453i	0.151001	−	0.261541i
$544$	5.98376	−	0.366959i	0.256552	−	0.0157332i
$545$			1.48237i			0.0634978i
$546$	21.6957	+	11.5020i	0.928491	+	0.492241i
$547$	−6.47392			−0.276805			−0.138402	−	0.990376i	$-0.544197\pi$
$547$	−6.47392			−0.276805			−0.138402	+	0.990376i	$0.544197\pi$
$548$	25.1907	+	23.9857i	1.07609	+	1.02462i
$549$	−5.30143	−	3.06078i	−0.226259	−	0.130631i
$550$	28.0417	+	27.3630i	1.19570	+	1.16676i
$551$	2.54074	+	2.54074i	0.108239	+	0.108239i
$552$	−4.92406	+	3.08953i	−0.209582	+	0.131499i
$553$	8.98493	−	33.5322i	0.382078	−	1.42594i
$554$	8.48866	+	4.76325i	0.360649	+	0.202371i
$555$	−2.02166	−	3.50161i	−0.0858146	−	0.148635i
$556$	−28.1796	+	0.690529i	−1.19508	+	0.0292849i
$557$	4.79101	+	17.8803i	0.203002	+	0.757612i	0.990049	+	0.140720i	$0.0449418\pi$
$557$	4.79101	+	17.8803i	0.203002	+	0.757612i	−0.787048	+	0.616892i	$0.788392\pi$
$558$	1.37985	+	4.90835i	0.0584136	+	0.207787i
$559$	−10.0688	−	34.2822i	−0.425867	−	1.44998i
$560$	−5.02443	+	9.77961i	−0.212321	+	0.413264i
$561$	−1.62574	−	6.06733i	−0.0686387	−	0.256163i
$562$	2.41534	+	0.615579i	0.101885	+	0.0259666i
$563$	11.7692	−	6.79494i	0.496012	−	0.286373i	−0.231053	−	0.972941i	$-0.574217\pi$
$563$	11.7692	−	6.79494i	0.496012	−	0.286373i	0.727065	+	0.686568i	$0.240884\pi$
$564$	16.2824	+	3.93801i	0.685614	+	0.165820i
$565$	−2.87052	+	10.7129i	−0.120764	+	0.450696i
$566$	18.9544	−	0.232199i	0.796713	−	0.00976007i
$567$	−3.40531	+	3.40531i	−0.143010	+	0.143010i
$568$	−1.20518	−	0.275899i	−0.0505682	−	0.0115765i
$569$	5.17128	+	2.98564i	0.216791	+	0.125164i	0.604464	−	0.796633i	$-0.293387\pi$
$569$	5.17128	+	2.98564i	0.216791	+	0.125164i	−0.387672	+	0.921797i	$0.626721\pi$
$570$	−0.443711	+	0.263476i	−0.0185850	+	0.0110358i
$571$		−	7.35140i		−	0.307647i	−0.988098	−	0.153823i	$-0.950841\pi$
$571$		−	7.35140i		−	0.307647i	0.988098	−	0.153823i	$-0.0491587\pi$
$572$	−38.0045	−	19.5556i	−1.58905	−	0.817660i
$573$			20.6127i			0.861106i
$574$	18.4677	+	31.1009i	0.770828	+	1.29813i
$575$	−8.31956	−	4.80330i	−0.346949	−	0.200311i
$576$	4.49796	+	6.61577i	0.187415	+	0.275657i
$577$	8.59954	−	8.59954i	0.358004	−	0.358004i	−0.505073	−	0.863077i	$-0.668534\pi$
$577$	8.59954	−	8.59954i	0.358004	−	0.358004i	0.863077	+	0.505073i	$0.168534\pi$
$578$	0.275042	+	22.4516i	0.0114402	+	0.933864i
$579$	−1.12086	+	4.18310i	−0.0465813	+	0.173844i
$580$	−6.23593	−	1.50820i	−0.258933	−	0.0626247i
$581$	45.9899	−	26.5523i	1.90798	−	1.10157i
$582$	−1.62256	+	6.36643i	−0.0672573	+	0.263897i
$583$	−1.83435	−	6.84588i	−0.0759709	−	0.283527i
$584$	19.9979	−	21.5245i	0.827518	−	0.890689i
$585$	−1.80626	−	0.986122i	−0.0746796	−	0.0407711i
$586$	31.8843	−	8.96338i	1.31713	−	0.370274i
$587$	5.77087	+	21.5372i	0.238189	+	0.888934i	0.976685	+	0.214676i	$0.0688697\pi$
$587$	5.77087	+	21.5372i	0.238189	+	0.888934i	−0.738496	+	0.674258i	$0.764464\pi$
$588$	−0.793332	−	32.3749i	−0.0327165	−	1.33512i
$589$	−1.15245	−	1.99610i	−0.0474858	−	0.0822479i
$590$	−3.22872	+	5.75395i	−0.132924	+	0.236886i
$591$	2.74681	−	10.2512i	0.112989	−	0.421679i
$592$	19.0313	−	20.9941i	0.782182	−	0.862852i
$593$	24.9155	+	24.9155i	1.02316	+	1.02316i	0.999725	+	0.0234302i	$0.00745874\pi$
$593$	24.9155	+	24.9155i	1.02316	+	1.02316i	0.0234302	+	0.999725i	$0.492541\pi$
$594$	5.85401	−	5.99922i	0.240193	−	0.246151i
$595$	2.52274	+	1.45650i	0.103422	+	0.0597109i
$596$	−16.1615	−	15.3884i	−0.662002	−	0.630334i
$597$	−24.1207			−0.987196
$598$	10.2139	+	2.34499i	0.417677	+	0.0958939i
$599$		−	32.0155i		−	1.30812i	−0.756444	−	0.654059i	$-0.773065\pi$
$599$		−	32.0155i		−	1.30812i	0.756444	−	0.654059i	$-0.226935\pi$
$600$	−6.18523	+	11.6846i	−0.252511	+	0.477023i
$601$	−6.17445	+	10.6945i	−0.251861	+	0.436236i	−0.964038	−	0.265764i	$-0.914376\pi$
$601$	−6.17445	+	10.6945i	−0.251861	+	0.436236i	0.712177	+	0.702000i	$0.247709\pi$
$602$	−47.1358	+	48.3050i	−1.92111	+	1.96876i
$603$	−5.65082	+	5.65082i	−0.230119	+	0.230119i
$604$	6.53764	+	22.2077i	0.266013	+	0.903617i
$605$	−13.3032	−	3.56459i	−0.540853	−	0.144921i
$606$	−5.02307	−	2.81860i	−0.204048	−	0.114498i
$607$	−23.6311	+	13.6435i	−0.959159	+	0.553771i	−0.895914	−	0.444227i	$-0.853478\pi$
$607$	−23.6311	+	13.6435i	−0.959159	+	0.553771i	−0.0632447	+	0.997998i	$0.520145\pi$
$608$	−2.70899	−	2.39593i	−0.109864	−	0.0971678i
$609$	26.1443	−	7.00533i	1.05942	−	0.283870i
$610$	−4.75681	+	1.33725i	−0.192598	+	0.0541435i
$611$	−15.7199	−	25.7860i	−0.635960	−	1.04319i
$612$	1.80908	−	1.10443i	0.0731276	−	0.0446438i
$613$	1.68752	−	0.452170i	0.0681583	−	0.0182630i	−0.224579	−	0.974456i	$-0.572101\pi$
$613$	1.68752	−	0.452170i	0.0681583	−	0.0182630i	0.292737	+	0.956193i	$0.405434\pi$
$614$	−41.0839	−	10.4707i	−1.65801	−	0.422564i
$615$	−1.51564	−	2.62516i	−0.0611165	−	0.105857i
$616$	2.96626	+	80.6795i	0.119514	+	3.25067i
$617$	−21.8225	−	5.84731i	−0.878539	−	0.235404i	−0.208762	−	0.977966i	$-0.566943\pi$
$617$	−21.8225	−	5.84731i	−0.878539	−	0.235404i	−0.669777	+	0.742563i	$0.733610\pi$
$618$	0.00775259	+	0.632843i	0.000311855	+	0.0254567i
$619$	−16.8078	−	16.8078i	−0.675564	−	0.675564i	0.283429	−	0.958993i	$-0.408528\pi$
$619$	−16.8078	−	16.8078i	−0.675564	−	0.675564i	−0.958993	+	0.283429i	$0.908528\pi$
$620$	3.61347	+	1.96982i	0.145120	+	0.0791100i
$621$	−1.02761	+	1.77988i	−0.0412367	+	0.0714240i
$622$	28.7068	−	17.0461i	1.15104	−	0.683486i
$623$	−3.53171			−0.141495
$624$	2.70858	−	14.1656i	0.108430	−	0.567077i
$625$	−20.2196			−0.808783
$626$	−2.03454	+	1.20811i	−0.0813164	+	0.0482857i
$627$	−1.89463	+	3.28159i	−0.0756641	+	0.131054i
$628$	−34.3609	−	18.7313i	−1.37115	−	0.747460i
$629$	−5.30862	−	5.30862i	−0.211669	−	0.211669i
$630$	0.0476169	+	3.88696i	0.00189710	+	0.154860i
$631$	−28.5528	−	7.65071i	−1.13667	−	0.304570i	−0.359059	−	0.933315i	$-0.616902\pi$
$631$	−28.5528	−	7.65071i	−1.13667	−	0.304570i	−0.777612	+	0.628745i	$0.783569\pi$
$632$	−20.3750	+	0.749108i	−0.810475	+	0.0297979i
$633$	7.25156	+	12.5601i	0.288224	+	0.499218i
$634$	−3.86237	−	0.984372i	−0.153394	−	0.0390944i
$635$	7.56808	−	2.02786i	0.300330	−	0.0804732i
$636$	2.04121	−	1.24614i	0.0809393	−	0.0494128i
$637$	−40.2853	+	42.2561i	−1.59616	+	1.67425i
$638$	−45.3522	+	12.7495i	−1.79551	+	0.504758i
$639$	−0.422224	+	0.113135i	−0.0167029	+	0.00447553i
$640$	6.35763	+	1.13097i	0.251307	+	0.0447056i
$641$	16.7228	−	9.65492i	0.660511	−	0.381346i	−0.131961	−	0.991255i	$-0.542127\pi$
$641$	16.7228	−	9.65492i	0.660511	−	0.381346i	0.792472	+	0.609909i	$0.208794\pi$
$642$	−9.06894	−	5.08887i	−0.357923	−	0.200841i
$643$	20.6865	+	5.54294i	0.815797	+	0.218592i	0.642508	−	0.766279i	$-0.277894\pi$
$643$	20.6865	+	5.54294i	0.815797	+	0.218592i	0.173289	+	0.984871i	$0.444561\pi$
$644$	−5.59026	−	18.9895i	−0.220287	−	0.748292i
$645$	3.99949	−	3.99949i	0.157480	−	0.157480i
$646$	−0.669180	+	0.685779i	−0.0263285	+	0.0269816i
$647$	−13.1707	+	22.8124i	−0.517794	+	0.896846i	0.481992	+	0.876176i	$0.339913\pi$
$647$	−13.1707	+	22.8124i	−0.517794	+	0.896846i	−0.999786	+	0.0206706i	$0.993420\pi$
$648$	2.49980	+	1.32326i	0.0982013	+	0.0519826i
$649$			48.4480i			1.90175i
$650$	22.7841	−	6.99608i	0.893665	−	0.274409i
$651$	−17.3624			−0.680486
$652$	9.16866	+	8.73006i	0.359073	+	0.341896i
$653$	4.85800	+	2.80477i	0.190108	+	0.109759i	0.592033	−	0.805914i	$-0.298325\pi$
$653$	4.85800	+	2.80477i	0.190108	+	0.109759i	−0.401925	+	0.915673i	$0.631659\pi$
$654$	−2.56517	+	2.62880i	−0.100306	+	0.102794i
$655$	2.38264	+	2.38264i	0.0930976	+	0.0930976i
$656$	14.2678	−	15.7393i	0.557064	−	0.614516i
$657$	2.68851	−	10.0336i	0.104889	−	0.391450i
$658$	−27.9154	+	49.7485i	−1.08826	+	1.93940i
$659$	18.1430	+	31.4246i	0.706751	+	1.22413i	0.966056	+	0.258333i	$0.0831732\pi$
$659$	18.1430	+	31.4246i	0.706751	+	1.22413i	−0.259305	+	0.965795i	$0.583493\pi$
$660$	−0.165745	−	6.76385i	−0.00645162	−	0.263283i
$661$	3.16335	+	11.8058i	0.123040	+	0.459192i	0.999762	−	0.0218054i	$-0.00694141\pi$
$661$	3.16335	+	11.8058i	0.123040	+	0.459192i	−0.876722	+	0.480997i	$0.840275\pi$
$662$	−7.67444	+	2.15746i	−0.298276	+	0.0838520i
$663$	−3.71344	−	0.900586i	−0.144218	−	0.0349759i
$664$	−22.8495	−	21.2289i	−0.886734	−	0.823842i
$665$	−0.454818	−	1.69740i	−0.0176371	−	0.0658225i
$666$	2.47421	−	9.70805i	0.0958738	−	0.376179i
$667$	10.0035	−	5.77550i	0.387336	−	0.223628i
$668$	9.72784	+	2.35274i	0.376382	+	0.0910304i
$669$	6.28722	−	23.4642i	0.243078	−	0.907180i
$670$	0.0790160	+	6.45006i	0.00305265	+	0.249188i
$671$	−25.6559	+	25.6559i	−0.990434	+	0.990434i
$672$	−25.8333	+	8.64837i	−0.996542	+	0.333618i
$673$	21.4840	+	12.4038i	0.828146	+	0.478130i	0.853217	−	0.521556i	$-0.174648\pi$
$673$	21.4840	+	12.4038i	0.828146	+	0.478130i	−0.0250717	+	0.999686i	$0.507981\pi$
$674$	−7.21325	−	12.1476i	−0.277844	−	0.467908i
$675$			4.67423i			0.179911i
$676$	−21.5196	+	14.5914i	−0.827676	+	0.561206i
$677$			41.5137i			1.59550i	0.602988	+	0.797750i	$0.293977\pi$
$677$			41.5137i			1.59550i	−0.602988	+	0.797750i	$0.706023\pi$
$678$	−23.6287	+	14.0307i	−0.907455	+	0.538847i
$679$	−19.3753	−	11.1863i	−0.743557	−	0.429293i
$680$	0.381787	−	1.66772i	0.0146409	−	0.0639541i
$681$	14.2846	−	14.2846i	0.547387	−	0.547387i
$682$	30.2176	−	0.370178i	1.15709	−	0.0141748i
$683$	−9.94935	+	37.1315i	−0.380701	+	1.42080i	0.464132	+	0.885766i	$0.346366\pi$
$683$	−9.94935	+	37.1315i	−0.380701	+	1.42080i	−0.844833	+	0.535030i	$0.820300\pi$
$684$	−1.24280	−	0.300578i	−0.0475195	−	0.0114929i
$685$	8.59662	−	4.96326i	0.328460	−	0.189636i
$686$	60.6662	+	15.4615i	2.31625	+	0.590323i
$687$	−0.196809	−	0.734503i	−0.00750875	−	0.0280230i
$688$	35.2581	+	18.1144i	1.34420	+	0.690605i
$689$	−4.18994	−	1.01615i	−0.159624	−	0.0387121i
$690$	0.448961	+	1.59703i	0.0170916	+	0.0607979i
$691$	−0.476425	−	1.77804i	−0.0181241	−	0.0676399i	0.956272	−	0.292480i	$-0.0944806\pi$
$691$	−0.476425	−	1.77804i	−0.0181241	−	0.0676399i	−0.974396	+	0.224840i	$0.927814\pi$
$692$	24.1114	−	0.590839i	0.916579	−	0.0224603i
$693$	14.2719	+	24.7196i	0.542144	+	0.939021i
$694$	−29.2499	−	16.4130i	−1.11031	−	0.623030i
$695$	−2.08203	+	7.77025i	−0.0789760	+	0.294742i
$696$	−8.44877	−	13.4656i	−0.320250	−	0.510411i
$697$	−3.97988	−	3.97988i	−0.150749	−	0.150749i
$698$	20.0193	+	19.5347i	0.757741	+	0.739401i
$699$	4.38500	+	2.53168i	0.165856	+	0.0957569i
$700$	−32.6047	−	31.0450i	−1.23234	−	1.17339i
$701$	−30.7524			−1.16150			−0.580752	−	0.814081i	$-0.697241\pi$
$701$	−30.7524			−1.16150			−0.580752	+	0.814081i	$0.697241\pi$
$702$	−1.49673	−	4.87440i	−0.0564906	−	0.183972i
$703$			4.52894i			0.170812i
$704$	44.7760	−	15.6024i	1.68756	−	0.588039i
$705$	2.39034	−	4.14018i	0.0900253	−	0.155928i
$706$	11.2421	+	10.9700i	0.423103	+	0.412862i
$707$	13.8692	−	13.8692i	0.521607	−	0.521607i
$708$	−15.6826	+	4.61676i	−0.589390	+	0.173508i
$709$	6.75910	+	1.81110i	0.253844	+	0.0680172i	0.383497	−	0.923542i	$-0.374720\pi$
$709$	6.75910	+	1.81110i	0.253844	+	0.0680172i	−0.129653	+	0.991559i	$0.541386\pi$
$710$	−0.172660	+	0.307700i	−0.00647982	+	0.0115478i
$711$	−6.24277	+	3.60426i	−0.234122	+	0.135170i
$712$	0.610102	+	1.98248i	0.0228646	+	0.0742966i
$713$	−7.15716	+	1.91775i	−0.268038	+	0.0718205i
$714$	1.95335	+	6.94840i	0.0731023	+	0.260037i
$715$	−8.41652	+	8.82826i	−0.314760	+	0.330158i
$716$	−29.9779	+	18.3013i	−1.12033	+	0.683951i
$717$	27.5637	−	7.38567i	1.02938	−	0.275823i
$718$	4.98387	−	19.5552i	0.185996	−	0.729792i
$719$	10.9833	+	19.0236i	0.409608	+	0.709461i	0.994846	−	0.101400i	$-0.0323323\pi$
$719$	10.9833	+	19.0236i	0.409608	+	0.709461i	−0.585238	+	0.810862i	$0.698999\pi$
$720$	2.17367	−	0.698200i	0.0810078	−	0.0260204i
$721$	−2.08175	−	0.557804i	−0.0775285	−	0.0207737i
$722$	−26.2901	+	0.322064i	−0.978415	+	0.0119860i
$723$	−9.58070	−	9.58070i	−0.356310	−	0.356310i
$724$	6.73665	−	12.3578i	0.250365	−	0.459274i
$725$	13.1353	−	22.7510i	0.487833	−	0.844952i
$726$	−17.4233	−	29.3419i	−0.646637	−	1.08898i
$727$	32.3235			1.19881			0.599407	−	0.800445i	$-0.295403\pi$
$727$	32.3235			1.19881			0.599407	+	0.800445i	$0.295403\pi$
$728$	43.9419	+	21.9342i	1.62860	+	0.812934i
$729$	1.00000			0.0370370
$730$	−4.28096	−	7.20943i	−0.158446	−	0.266833i
$731$	5.25109	−	9.09515i	0.194218	−	0.336396i
$732$	−10.7496	−	5.85999i	−0.397318	−	0.216591i
$733$	−27.9317	−	27.9317i	−1.03168	−	1.03168i	−0.999482	−	0.0321977i	$-0.989749\pi$
$733$	−27.9317	−	27.9317i	−1.03168	−	1.03168i	−0.0321977	−	0.999482i	$-0.510251\pi$
$734$	−9.30024	+	0.113932i	−0.343278	+	0.00420530i
$735$	−8.92705	−	2.39200i	−0.329279	−	0.0882301i
$736$	−9.69380	+	6.41846i	−0.357318	+	0.236587i
$737$	23.6829	+	41.0200i	0.872372	+	1.51099i
$738$	1.85492	−	7.27813i	0.0682806	−	0.267912i
$739$	33.0386	−	8.85267i	1.21534	−	0.325651i	0.406488	−	0.913656i	$-0.366753\pi$
$739$	33.0386	−	8.85267i	1.21534	−	0.325651i	0.808857	+	0.588005i	$0.200087\pi$
$740$	−4.21366	−	6.90208i	−0.154897	−	0.253725i
$741$	1.19986	+	1.96818i	0.0440780	+	0.0723028i
$742$	2.20400	+	7.84001i	0.0809114	+	0.287816i
$743$	−48.6992	+	13.0489i	−1.78660	+	0.478718i	−0.991761	−	0.128102i	$-0.959112\pi$
$743$	−48.6992	+	13.0489i	−1.78660	+	0.478718i	−0.794839	+	0.606820i	$0.792445\pi$
$744$	2.99935	+	9.74616i	0.109961	+	0.357311i
$745$	−5.51531	+	3.18427i	−0.202065	+	0.116662i
$746$	5.88642	−	10.4903i	0.215517	−	0.384077i
$747$	−10.6513	−	2.85401i	−0.389712	−	0.104423i
$748$	−3.54776	−	12.0514i	−0.129719	−	0.440642i
$749$	25.0403	−	25.0403i	0.914953	−	0.914953i
$750$	5.58891	+	5.45363i	0.204078	+	0.199139i
$751$	24.4568	−	42.3605i	0.892443	−	1.54576i	0.0555049	−	0.998458i	$-0.482323\pi$
$751$	24.4568	−	42.3605i	0.892443	−	1.54576i	0.836938	−	0.547298i	$-0.184343\pi$
$752$	32.7480	+	7.07592i	1.19420	+	0.258032i
$753$		−	16.7645i		−	0.610932i
$754$	−6.41273	+	27.9314i	−0.233538	+	1.01720i
$755$	6.60657			0.240438
$756$	−6.64174	+	6.97542i	−0.241558	+	0.253694i
$757$	1.35085	+	0.779913i	0.0490974	+	0.0283464i	0.524348	−	0.851504i	$-0.324309\pi$
$757$	1.35085	+	0.779913i	0.0490974	+	0.0283464i	−0.475250	+	0.879851i	$0.657643\pi$
$758$	17.7041	+	17.2756i	0.643042	+	0.627478i
$759$	8.61358	+	8.61358i	0.312653	+	0.312653i
$760$	−0.874246	+	0.548532i	−0.0317122	+	0.0198974i
$761$	−2.75025	+	10.2641i	−0.0996966	+	0.372073i	−0.997690	−	0.0679370i	$-0.978358\pi$
$761$	−2.75025	+	10.2641i	−0.0996966	+	0.372073i	0.897993	+	0.440010i	$0.145025\pi$
$762$	16.9301	+	9.50003i	0.613314	+	0.344150i
$763$	−6.25379	−	10.8319i	−0.226402	−	0.392141i
$764$	1.00990	+	41.2130i	0.0365370	+	1.49103i
$765$	−0.156555	−	0.584270i	−0.00566025	−	0.0211243i
$766$	−3.81985	−	13.5879i	−0.138017	−	0.490949i
$767$	25.8679	+	14.1225i	0.934036	+	0.509935i
$768$	9.31735	+	13.0072i	0.336211	+	0.469357i
$769$	−11.1442	−	41.5908i	−0.401871	−	1.49980i	−0.809755	−	0.586768i	$-0.800400\pi$
$769$	−11.1442	−	41.5908i	−0.401871	−	1.49980i	0.407885	−	0.913033i	$-0.366267\pi$
$770$	22.3263	+	5.69012i	0.804583	+	0.205058i
$771$	−7.66304	+	4.42426i	−0.275978	+	0.159336i
$772$	−2.03610	+	8.41861i	−0.0732808	+	0.302993i
$773$	4.01263	−	14.9753i	0.144324	−	0.538626i	−0.855460	−	0.517869i	$-0.826726\pi$
$773$	4.01263	−	14.9753i	0.144324	−	0.538626i	0.999785	−	0.0207572i	$-0.00660770\pi$
$774$	14.0135	−	0.171671i	0.503705	−	0.00617060i
$775$	−11.9161	+	11.9161i	−0.428037	+	0.428037i
$776$	−2.93223	+	12.8085i	−0.105261	+	0.459799i
$777$	29.5451	+	17.0579i	1.05992	+	0.611947i
$778$	0.977425	−	0.580395i	0.0350424	−	0.0208082i
$779$			3.39535i			0.121651i
$780$	−3.65975	−	1.88316i	−0.131040	−	0.0674278i
$781$			2.59083i			0.0927070i
$782$	1.57270	+	2.64853i	0.0562395	+	0.0947111i
$783$	−4.86733	−	2.81016i	−0.173944	−	0.100427i
$784$	−3.17238	−	64.6915i	−0.113299	−	2.31041i
$785$	−7.89721	+	7.89721i	−0.281863	+	0.281863i
$786$	0.102271	+	8.34836i	0.00364788	+	0.297776i
$787$	9.97812	−	37.2389i	0.355682	−	1.32742i	−0.523943	−	0.851753i	$-0.675539\pi$
$787$	9.97812	−	37.2389i	0.355682	−	1.32742i	0.879624	−	0.475669i	$-0.157794\pi$
$788$	4.98972	−	20.6309i	0.177751	−	0.734945i
$789$	−5.49660	+	3.17346i	−0.195684	+	0.112978i
$790$	−1.43700	+	5.63834i	−0.0511262	+	0.200603i
$791$	−24.2202	−	90.3910i	−0.861171	−	3.21393i
$792$	11.4106	−	12.2817i	0.405457	−	0.436409i
$793$	6.21982	+	21.1771i	0.220872	+	0.752021i
$794$	1.66176	−	0.467159i	0.0589738	−	0.0165789i
$795$	−0.176643	−	0.659242i	−0.00626490	−	0.0233809i
$796$	−48.2270	+	1.18178i	−1.70936	+	0.0418871i
$797$	2.47797	+	4.29197i	0.0877742	+	0.152029i	0.906570	−	0.422055i	$-0.138691\pi$
$797$	2.47797	+	4.29197i	0.0877742	+	0.152029i	−0.818796	+	0.574085i	$0.805358\pi$
$798$	2.13071	−	3.79717i	0.0754263	−	0.134418i
$799$	2.29744	−	8.57417i	0.0812776	−	0.303332i
$800$	−11.7943	+	23.6653i	−0.416990	+	0.836694i
$801$	0.518559	+	0.518559i	0.0183224	+	0.0183224i
$802$	−4.83851	+	4.95852i	−0.170854	+	0.175092i
$803$	−53.3194	−	30.7840i	−1.88160	−	1.08634i
$804$	−11.0214	+	11.5751i	−0.388694	+	0.408222i
$805$	−5.64920			−0.199108
$806$	8.61072	−	16.2420i	0.303300	−	0.572100i
$807$			6.37298i			0.224340i
$808$	−10.1812	−	5.38941i	−0.358174	−	0.189599i
$809$	24.9370	−	43.1921i	0.876738	−	1.51855i	0.0218374	−	0.999762i	$-0.493048\pi$
$809$	24.9370	−	43.1921i	0.876738	−	1.51855i	0.854900	−	0.518793i	$-0.173618\pi$
$810$	0.563728	−	0.577711i	0.0198074	−	0.0202987i
$811$	−25.0953	+	25.0953i	−0.881216	+	0.881216i	−0.993658	−	0.112442i	$-0.964133\pi$
$811$	−25.0953	+	25.0953i	−0.881216	+	0.881216i	0.112442	+	0.993658i	$0.464133\pi$
$812$	51.9296	−	15.2874i	1.82237	−	0.536482i
$813$	8.48094	+	2.27246i	0.297440	+	0.0796987i
$814$	−51.7840	−	29.0576i	−1.81503	−	1.01847i
$815$	3.12891	−	1.80648i	0.109601	−	0.0632782i
$816$	3.56295	−	2.29682i	0.124728	−	0.0804049i
$817$	−6.11959	+	1.63974i	−0.214097	+	0.0573672i
$818$	19.3295	−	5.43396i	0.675840	−	0.189994i
$819$	17.3588	−	0.414468i	0.606566	−	0.0144827i
$820$	−3.15899	−	5.17449i	−0.110317	−	0.180701i
$821$	−41.6756	+	11.1669i	−1.45449	+	0.389729i	−0.897582	−	0.440847i	$-0.854678\pi$
$821$	−41.6756	+	11.1669i	−1.45449	+	0.389729i	−0.556906	+	0.830576i	$0.688012\pi$
$822$	23.8337	+	6.07431i	0.831295	+	0.211866i
$823$	6.03038	+	10.4449i	0.210206	+	0.364087i	0.951779	−	0.306785i	$-0.0992532\pi$
$823$	6.03038	+	10.4449i	0.210206	+	0.364087i	−0.741573	+	0.670872i	$0.765920\pi$
$824$	0.0465062	+	1.26493i	0.00162012	+	0.0440658i
$825$	26.7604	+	7.17044i	0.931679	+	0.249643i
$826$	−0.681934	−	55.6661i	−0.0237275	−	1.93687i
$827$	−13.3380	−	13.3380i	−0.463809	−	0.463809i	0.436093	−	0.899902i	$-0.356362\pi$
$827$	−13.3380	−	13.3380i	−0.463809	−	0.463809i	−0.899902	+	0.436093i	$0.856362\pi$
$828$	−1.96740	+	3.60903i	−0.0683720	+	0.125423i
$829$	−19.5075	+	33.7880i	−0.677524	+	1.17351i	0.298201	+	0.954503i	$0.403613\pi$
$829$	−19.5075	+	33.7880i	−0.677524	+	1.17351i	−0.975724	+	0.219002i	$0.929720\pi$
$830$	−7.65324	+	4.54450i	−0.265648	+	0.157742i
$831$	6.88280			0.238762
$832$	4.72150	−	28.4554i	0.163689	−	0.986512i
$833$	−17.1603			−0.594567
$834$	−17.1382	+	10.1767i	−0.593449	+	0.352390i
$835$	1.42809	−	2.47353i	0.0494212	−	0.0856000i
$836$	−3.62734	+	6.65403i	−0.125454	+	0.230135i
$837$	2.54931	+	2.54931i	0.0881170	+	0.0881170i
$838$	0.0818036	+	6.67762i	0.00282586	+	0.230674i
$839$	35.6287	+	9.54667i	1.23004	+	0.329588i	0.814594	−	0.580031i	$-0.196960\pi$
$839$	35.6287	+	9.54667i	1.23004	+	0.329588i	0.415444	+	0.909619i	$0.363626\pi$
$840$	0.285644	+	7.76925i	0.00985566	+	0.268065i
$841$	1.29395	+	2.24118i	0.0446189	+	0.0772822i
$842$	8.48899	+	2.16352i	0.292550	+	0.0745599i
$843$	1.70244	−	0.456169i	0.0586353	−	0.0157113i
$844$	15.1141	+	24.7573i	0.520250	+	0.852182i
$845$	2.26028	+	7.06726i	0.0777560	+	0.243121i
$846$	11.4033	−	3.20573i	0.392055	−	0.110215i
$847$	112.247	−	30.0764i	3.85685	−	1.03344i
$848$	4.02014	−	2.59155i	0.138052	−	0.0889941i
$849$	11.6080	−	6.70190i	0.398386	−	0.230008i
$850$	6.10940	+	3.42817i	0.209551	+	0.117585i
$851$	14.0632	+	3.76824i	0.482082	+	0.129173i
$852$	−0.838651	+	0.246888i	−0.0287317	+	0.00845823i
$853$	30.9178	−	30.9178i	1.05861	−	1.05861i	0.0604339	−	0.998172i	$-0.480752\pi$
$853$	30.9178	−	30.9178i	1.05861	−	1.05861i	0.998172	−	0.0604339i	$-0.0192484\pi$
$854$	29.1171	−	29.8394i	0.996368	−	1.02108i
$855$	−0.182448	+	0.316009i	−0.00623960	+	0.0108073i
$856$	−18.3818	−	9.73035i	−0.628276	−	0.332576i
$857$			3.63834i			0.124283i	0.998067	+	0.0621417i	$0.0197931\pi$
$857$			3.63834i			0.124283i	−0.998067	+	0.0621417i	$0.980207\pi$
$858$	−30.2025	+	1.09144i	−1.03110	+	0.0372613i
$859$	−10.4247			−0.355686			−0.177843	−	0.984059i	$-0.556912\pi$
$859$	−10.4247			−0.355686			−0.177843	+	0.984059i	$0.556912\pi$
$860$	7.80063	−	8.19254i	0.265999	−	0.279363i
$861$	22.1500	+	12.7883i	0.754869	+	0.435824i
$862$	2.26260	−	2.31873i	0.0770646	−	0.0789762i
$863$	23.3831	+	23.3831i	0.795970	+	0.795970i	0.982457	−	0.186488i	$-0.0597104\pi$
$863$	23.3831	+	23.3831i	0.795970	+	0.795970i	−0.186488	+	0.982457i	$0.559710\pi$
$864$	5.06292	+	2.52325i	0.172244	+	0.0858428i
$865$	1.78146	−	6.64848i	0.0605713	−	0.226055i
$866$	11.1504	−	19.8712i	0.378905	−	0.675252i
$867$	7.93844	+	13.7498i	0.269603	+	0.466967i
$868$	−34.7144	+	0.850659i	−1.17828	+	0.0288732i
$869$	11.0581	+	41.2695i	0.375122	+	1.39997i
$870$	−4.36731	+	1.22775i	−0.148066	+	0.0416246i
$871$	28.8054	−	0.687774i	0.976034	−	0.0233043i
$872$	−5.00000	+	5.38169i	−0.169321	+	0.182247i
$873$	1.20238	+	4.48735i	0.0406945	+	0.151874i
$874$	0.458911	−	1.80062i	0.0155229	−	0.0609070i
$875$	−23.0290	+	13.2958i	−0.778521	+	0.449479i
$876$	4.88381	−	20.1930i	0.165009	−	0.682258i
$877$	1.72948	−	6.45450i	0.0584004	−	0.217953i	−0.930559	−	0.366143i	$-0.880678\pi$
$877$	1.72948	−	6.45450i	0.0584004	−	0.217953i	0.988959	+	0.148190i	$0.0473447\pi$
$878$	0.353371	+	28.8456i	0.0119257	+	0.973493i
$879$	16.5601	−	16.5601i	0.558559	−	0.558559i
$880$	−0.662781	−	13.5155i	−0.0223424	−	0.455608i
$881$	−5.79984	−	3.34854i	−0.195401	−	0.112815i	0.399107	−	0.916904i	$-0.369320\pi$
$881$	−5.79984	−	3.34854i	−0.195401	−	0.112815i	−0.594509	+	0.804089i	$0.702653\pi$
$882$	−11.6918	−	19.6897i	−0.393682	−	0.662987i
$883$			6.47692i			0.217966i	0.994044	+	0.108983i	$0.0347594\pi$
$883$			6.47692i			0.217966i	−0.994044	+	0.108983i	$0.965241\pi$
$884$	−7.46877	−	1.61870i	−0.251202	−	0.0544426i
$885$			4.66543i			0.156827i
$886$	5.45199	−	3.23740i	0.183163	−	0.108762i
$887$	−24.2718	−	14.0133i	−0.814967	−	0.470521i	0.0337108	−	0.999432i	$-0.489267\pi$
$887$	−24.2718	−	14.0133i	−0.814967	−	0.470521i	−0.848678	+	0.528910i	$0.822601\pi$
$888$	4.47130	−	19.5315i	0.150047	−	0.655434i
$889$	−46.7459	+	46.7459i	−1.56781	+	1.56781i
$890$	0.591904	−	0.00725107i	0.0198407	−	0.000243056i
$891$	1.53404	−	5.72510i	0.0513921	−	0.191798i
$892$	11.4211	−	47.2224i	0.382405	−	1.58112i
$893$	−4.63744	+	2.67743i	−0.155186	+	0.0895967i
$894$	−15.2909	−	3.89708i	−0.511405	−	0.130338i
$895$	2.59424	+	9.68185i	0.0867160	+	0.323629i
$896$	−51.2274	+	18.5572i	−1.71139	+	0.619954i
$897$	7.10990	−	2.08821i	0.237393	−	0.0697234i
$898$	−4.85118	−	17.2565i	−0.161886	−	0.575855i
$899$	−5.24438	−	19.5723i	−0.174910	−	0.652772i
$900$	0.229011	+	9.34566i	0.00763369	+	0.311522i
$901$	−0.633623	−	1.09747i	−0.0211090	−	0.0365619i
$902$	−38.8225	−	21.7845i	−1.29265	−	0.725345i
$903$	−12.3519	+	46.0978i	−0.411045	+	1.53404i
$904$	−46.5558	+	29.2107i	−1.54842	+	0.971534i
$905$	−2.84021	−	2.84021i	−0.0944116	−	0.0944116i
$906$	11.7159	+	11.4323i	0.389235	+	0.379814i
$907$	12.9360	+	7.46860i	0.429533	+	0.247991i	0.699148	−	0.714977i	$-0.253563\pi$
$907$	12.9360	+	7.46860i	0.429533	+	0.247991i	−0.269615	+	0.962968i	$0.586896\pi$
$908$	27.8607	−	29.2605i	0.924591	−	0.971043i
$909$	−4.07282			−0.135087
$910$	9.54620	−	10.2620i	0.316454	−	0.340183i
$911$			47.5530i			1.57550i	0.615995	+	0.787750i	$0.288754\pi$
$911$			47.5530i			1.57550i	−0.615995	+	0.787750i	$0.711246\pi$
$912$	−2.49957	−	0.540087i	−0.0827691	−	0.0178841i
$913$	−32.6790	+	56.6017i	−1.08152	+	1.87324i
$914$	26.1576	+	25.5244i	0.865215	+	0.844273i
$915$	−2.47060	+	2.47060i	−0.0816756	+	0.0816756i
$916$	−0.429487	−	1.45892i	−0.0141907	−	0.0482042i
$917$	−27.4622	−	7.35846i	−0.906880	−	0.242998i
$918$	0.733420	−	1.30704i	0.0242065	−	0.0431387i
$919$	−23.4113	+	13.5165i	−0.772268	+	0.445869i	−0.833683	−	0.552243i	$-0.813772\pi$
$919$	−23.4113	+	13.5165i	−0.772268	+	0.445869i	0.0614148	+	0.998112i	$0.480439\pi$
$920$	0.975897	+	3.17110i	0.0321744	+	0.104548i
$921$	−28.9578	+	7.75922i	−0.954192	+	0.255675i
$922$	6.76248	+	24.0553i	0.222711	+	0.792219i
$923$	1.38332	+	0.755222i	0.0455326	+	0.0248584i
$924$	29.7463	+	48.7252i	0.978583	+	1.60294i
$925$	31.9843	−	8.57016i	1.05164	−	0.281785i
$926$	−0.452485	+	1.77541i	−0.0148696	+	0.0583436i
$927$	0.223760	+	0.387565i	0.00734926	+	0.0127293i
$928$	−17.5522	−	26.5091i	−0.576179	−	0.870204i
$929$	−8.36041	−	2.24016i	−0.274296	−	0.0734974i	0.119049	−	0.992888i	$-0.462016\pi$
$929$	−8.36041	−	2.24016i	−0.274296	−	0.0734974i	−0.393345	+	0.919391i	$0.628682\pi$
$930$	2.90988	−	0.0356473i	0.0954187	−	0.00116892i
$931$	7.31995	+	7.31995i	0.239902	+	0.239902i
$932$	8.89140	+	4.84700i	0.291248	+	0.158769i
$933$	11.8038	−	20.4449i	0.386441	−	0.669335i
$934$	0.739220	+	1.24490i	0.0241880	+	0.0407343i
$935$	−3.58517			−0.117247
$936$	−3.23139	−	9.67255i	−0.105621	−	0.316157i
$937$	−24.9116			−0.813826			−0.406913	−	0.913467i	$-0.633395\pi$
$937$	−24.9116			−0.813826			−0.406913	+	0.913467i	$0.633395\pi$
$938$	−27.7888	−	46.7982i	−0.907335	−	1.52801i
$939$	−0.836575	+	1.44899i	−0.0273006	+	0.0472860i
$940$	4.57639	−	8.39499i	0.149265	−	0.273815i
$941$	1.97405	+	1.97405i	0.0643522	+	0.0643522i	0.738550	−	0.674198i	$-0.235511\pi$
$941$	1.97405	+	1.97405i	0.0643522	+	0.0643522i	−0.674198	+	0.738550i	$0.735511\pi$
$942$	−27.6704	+	0.338974i	−0.901551	+	0.0110444i
$943$	10.5432	+	2.82505i	0.343335	+	0.0919963i
$944$	−31.1297	+	9.99911i	−1.01318	+	0.325443i
$945$	1.37435	+	2.38044i	0.0447076	+	0.0774359i
$946$	20.5144	−	80.4921i	0.666981	−	2.61702i
$947$	−31.0163	+	8.31080i	−1.00790	+	0.270065i	−0.724750	−	0.689012i	$-0.758045\pi$
$947$	−31.0163	+	8.31080i	−1.00790	+	0.270065i	−0.283146	+	0.959077i	$0.591378\pi$
$948$	−12.3052	+	7.51222i	−0.399654	+	0.243986i
$949$	−31.9790	+	19.4954i	−1.03808	+	0.632847i
$950$	−1.14372	−	4.06839i	−0.0371070	−	0.131996i
$951$	−2.72238	+	0.729459i	−0.0882791	+	0.0236543i
$952$	4.24596	+	13.7969i	0.137612	+	0.447161i
$953$	12.1425	−	7.01048i	0.393334	−	0.227092i	−0.290269	−	0.956945i	$-0.593745\pi$
$953$	12.1425	−	7.01048i	0.393334	−	0.227092i	0.683604	+	0.729853i	$0.260412\pi$
$954$	0.827531	−	1.47476i	0.0267923	−	0.0477470i
$955$	11.3640	+	3.04499i	0.367732	+	0.0985335i
$956$	54.7490	−	16.1174i	1.77071	−	0.521273i
$957$	−23.5551	+	23.5551i	−0.761428	+	0.761428i
$958$	−0.200047	−	0.195205i	−0.00646322	−	0.00630678i
$959$	−41.8778	+	72.5345i	−1.35230	+	2.34226i
$960$	4.31182	−	1.50248i	0.139163	−	0.0484923i
$961$		−	18.0020i		−	0.580711i
$962$	−30.6097	+	19.1788i	−0.986897	+	0.618350i
$963$	−7.35331			−0.236957
$964$	−19.6250	−	18.6862i	−0.632080	−	0.601843i
$965$	2.14063	+	1.23589i	0.0689092	+	0.0397847i
$966$	−10.0181	−	9.77565i	−0.322328	−	0.314526i
$967$	5.06111	+	5.06111i	0.162754	+	0.162754i	0.783786	−	0.621031i	$-0.213286\pi$
$967$	5.06111	+	5.06111i	0.162754	+	0.162754i	−0.621031	+	0.783786i	$0.713286\pi$
$968$	−36.2736	−	57.8126i	−1.16588	−	1.85817i
$969$	−0.175358	+	0.654444i	−0.00563330	+	0.0210238i
$970$	3.27021	+	1.83502i	0.105000	+	0.0589188i
$971$	1.08352	+	1.87671i	0.0347718	+	0.0602264i	0.882888	−	0.469584i	$-0.155596\pi$
$971$	1.08352	+	1.87671i	0.0347718	+	0.0602264i	−0.848116	+	0.529811i	$0.822263\pi$
$972$	1.99940	−	0.0489943i	0.0641308	−	0.00157149i
$973$	−17.5673	−	65.5619i	−0.563181	−	2.10182i
$974$	−3.10368	−	11.0403i	−0.0994485	−	0.353755i
$975$	11.6291	−	12.1981i	0.372431	−	0.390650i
$976$	−21.7799	−	11.1898i	−0.697159	−	0.358176i
$977$	4.67577	+	17.4502i	0.149591	+	0.558282i	0.999508	+	0.0313649i	$0.00998538\pi$
$977$	4.67577	+	17.4502i	0.149591	+	0.558282i	−0.849917	+	0.526917i	$0.823348\pi$
$978$	8.67475	+	2.21087i	0.277388	+	0.0706957i
$979$	3.76429	−	2.17331i	0.120307	−	0.0694594i
$980$	−17.9659	−	4.34518i	−0.573901	−	0.138802i
$981$	−0.672199	+	2.50868i	−0.0214616	+	0.0800960i
$982$	21.7001	−	0.265835i	0.692478	−	0.00848315i
$983$	4.75595	−	4.75595i	0.151691	−	0.151691i	−0.627182	−	0.778873i	$-0.715792\pi$
$983$	4.75595	−	4.75595i	0.151691	−	0.151691i	0.778873	+	0.627182i	$0.215792\pi$
$984$	3.35214	−	14.6428i	0.106862	−	0.466795i
$985$	−5.24588	−	3.02871i	−0.167148	−	0.0965027i
$986$	−7.24278	+	4.30077i	−0.230657	+	0.136964i
$987$			40.3372i			1.28395i
$988$	2.49543	+	3.87639i	0.0793903	+	0.123324i
$989$			20.3669i			0.647628i
$990$	−2.44267	−	4.11363i	−0.0776333	−	0.130740i
$991$	−13.6470	−	7.87912i	−0.433512	−	0.250288i	0.267330	−	0.963605i	$-0.413859\pi$
$991$	−13.6470	−	7.87912i	−0.433512	−	0.250288i	−0.700842	+	0.713317i	$0.747192\pi$
$992$	6.47440	+	19.3395i	0.205563	+	0.614030i
$993$	−3.98597	+	3.98597i	−0.126491	+	0.126491i
$994$	−0.0364674	−	2.97683i	−0.00115667	−	0.0944192i
$995$	−3.56322	+	13.2981i	−0.112962	+	0.421578i
$996$	−21.4361	−	5.18446i	−0.679228	−	0.164276i
$997$	43.1151	−	24.8925i	1.36547	−	0.788354i	0.375123	−	0.926975i	$-0.377600\pi$
$997$	43.1151	−	24.8925i	1.36547	−	0.788354i	0.990345	+	0.138621i	$0.0442671\pi$
$998$	5.23550	−	20.5425i	0.165727	−	0.650261i
$999$	−1.83349	−	6.84268i	−0.0580091	−	0.216493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.d.19.12	yes	56
3.2	odd	2		936.2.ed.e.19.3		56
8.3	odd	2	inner	312.2.bt.d.19.1	✓	56
13.11	odd	12	inner	312.2.bt.d.115.1	yes	56
24.11	even	2		936.2.ed.e.19.14		56
39.11	even	12		936.2.ed.e.739.14		56
104.11	even	12	inner	312.2.bt.d.115.12	yes	56
312.11	odd	12		936.2.ed.e.739.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.1	✓	56	8.3	odd	2	inner
312.2.bt.d.19.12	yes	56	1.1	even	1	trivial
312.2.bt.d.115.1	yes	56	13.11	odd	12	inner
312.2.bt.d.115.12	yes	56	104.11	even	12	inner
936.2.ed.e.19.3		56	3.2	odd	2
936.2.ed.e.19.14		56	24.11	even	2
936.2.ed.e.739.3		56	312.11	odd	12
936.2.ed.e.739.14		56	39.11	even	12

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21599 - 0.722056i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.957270 - 1.75603i) q^{4} +(-0.403590 - 0.403590i) q^{5} +(-0.0173234 - 1.41411i) q^{6} +(4.65174 + 1.24643i) q^{7} +(-0.103920 - 2.82652i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.782176 - 0.199347i) q^{10} +(-5.72510 + 1.53404i) q^{11} +(-1.04213 - 1.70703i) q^{12} +(-0.849788 + 3.50398i) q^{13} +(6.55647 - 1.84317i) q^{14} +(-0.551314 + 0.147724i) q^{15} +(-2.16727 - 3.36198i) q^{16} +(-0.917794 + 0.529889i) q^{17} +(-1.23331 - 0.692051i) q^{18} +(0.617530 + 0.165467i) q^{19} +(-1.09506 + 0.322371i) q^{20} +(3.40531 - 3.40531i) q^{21} +(-5.85401 + 5.99922i) q^{22} +(1.02761 - 1.77988i) q^{23} +(-2.49980 - 1.32326i) q^{24} -4.67423i q^{25} +(1.49673 + 4.87440i) q^{26} -1.00000 q^{27} +(6.64174 - 6.97542i) q^{28} +(4.86733 + 2.81016i) q^{29} +(-0.563728 + 0.577711i) q^{30} +(-2.54931 - 2.54931i) q^{31} +(-5.06292 - 2.52325i) q^{32} +(-1.53404 + 5.72510i) q^{33} +(-0.733420 + 1.30704i) q^{34} +(-1.37435 - 2.38044i) q^{35} +(-1.99940 + 0.0489943i) q^{36} +(1.83349 + 6.84268i) q^{37} +(0.870387 - 0.244685i) q^{38} +(2.60964 + 2.48793i) q^{39} +(-1.09881 + 1.18269i) q^{40} +(1.37457 + 5.12996i) q^{41} +(1.68200 - 6.59966i) q^{42} +(-8.58213 + 4.95490i) q^{43} +(-2.78665 + 11.5219i) q^{44} +(-0.147724 + 0.551314i) q^{45} +(-0.0356035 - 2.90631i) q^{46} +(-5.92269 + 5.92269i) q^{47} +(-3.99520 + 0.195919i) q^{48} +(14.0230 + 8.09616i) q^{49} +(-3.37506 - 5.68382i) q^{50} +1.05978i q^{51} +(5.33961 + 4.84650i) q^{52} +1.19577i q^{53} +(-1.21599 + 0.722056i) q^{54} +(2.92971 + 1.69147i) q^{55} +(3.03965 - 13.2778i) q^{56} +(0.452063 - 0.452063i) q^{57} +(7.94772 - 0.0973630i) q^{58} +(2.11560 - 7.89551i) q^{59} +(-0.268348 + 1.10953i) q^{60} +(5.30143 - 3.06078i) q^{61} +(-4.94068 - 1.25919i) q^{62} +(-1.24643 - 4.65174i) q^{63} +(-7.97840 + 0.587462i) q^{64} +(1.75714 - 1.07120i) q^{65} +(2.26847 + 8.06933i) q^{66} +(-2.06834 - 7.71916i) q^{67} +(0.0519231 + 2.11892i) q^{68} +(-1.02761 - 1.77988i) q^{69} +(-3.39001 - 1.90224i) q^{70} +(0.113135 - 0.422224i) q^{71} +(-2.39588 + 1.50326i) q^{72} +(7.34514 + 7.34514i) q^{73} +(7.17031 + 6.99675i) q^{74} +(-4.04800 - 2.33712i) q^{75} +(0.881707 - 0.926004i) q^{76} -28.5438 q^{77} +(4.96972 + 1.14099i) q^{78} -7.20853i q^{79} +(-0.482175 + 2.23155i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.37559 + 5.24547i) q^{82} +(7.79731 - 7.79731i) q^{83} +(-2.72002 - 9.23963i) q^{84} +(0.584270 + 0.156555i) q^{85} +(-6.85808 + 12.2219i) q^{86} +(4.86733 - 2.81016i) q^{87} +(4.93093 + 16.0227i) q^{88} +(-0.708365 + 0.189806i) q^{89} +(0.218448 + 0.777058i) q^{90} +(-8.32047 + 15.2404i) q^{91} +(-2.14181 - 3.50834i) q^{92} +(-3.48242 + 0.933112i) q^{93} +(-2.92542 + 11.4784i) q^{94} +(-0.182448 - 0.316009i) q^{95} +(-4.71666 + 3.12299i) q^{96} +(-4.48735 - 1.20238i) q^{97} +(22.8977 - 0.280506i) q^{98} +(4.19106 + 4.19106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100}) \) 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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