LMFDB - Embedded newform 930.2.n.d.481.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 13 x^{10} - 9 x^{9} + 60 x^{8} + x^{7} + 263 x^{6} + 823 x^{5} + 1931 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 13x^10 - 9x^9 + 60x^8 + x^7 + 263x^6 + 823x^5 + 1931x^4 + 1170x^3 + 1340x^2 + 1000x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			481.3
Root			$1.01072 - 3.11068i$ of defining polynomial
Character	$\chi$	$=$	930.481
Dual form			930.2.n.d.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.624660 - 1.92251i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.624660 - 1.92251i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.809017 - 0.587785i) q^{10} +(1.08411 - 3.33653i) q^{11} +(0.809017 - 0.587785i) q^{12} +(4.70338 + 3.41721i) q^{13} +(0.624660 + 1.92251i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.32044 - 4.06390i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-6.20740 + 4.50994i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(1.63538 - 1.18817i) q^{21} +(1.08411 + 3.33653i) q^{22} +(-2.75050 - 8.46516i) q^{23} +(-0.309017 + 0.951057i) q^{24} +1.00000 q^{25} -5.81370 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.63538 - 1.18817i) q^{28} +(5.98249 - 4.34653i) q^{29} +1.00000 q^{30} +(5.18787 - 2.02138i) q^{31} +1.00000 q^{32} +(2.83822 - 2.06209i) q^{33} +(3.45696 + 2.51163i) q^{34} +(-0.624660 + 1.92251i) q^{35} +1.00000 q^{36} -0.145898 q^{37} +(2.37101 - 7.29723i) q^{38} +(1.79653 + 5.52915i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(6.14962 - 4.46796i) q^{41} +(-0.624660 + 1.92251i) q^{42} +(5.10420 - 3.70842i) q^{43} +(-2.83822 - 2.06209i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(7.20090 + 5.23176i) q^{46} +(-0.715329 - 0.519717i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(2.35729 + 1.71267i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(1.32044 - 4.06390i) q^{51} +(4.70338 - 3.41721i) q^{52} +(0.994498 + 3.06075i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-1.08411 + 3.33653i) q^{55} +2.02144 q^{56} -7.67276 q^{57} +(-2.28511 + 7.03283i) q^{58} +(1.97317 + 1.43359i) q^{59} +(-0.809017 + 0.587785i) q^{60} -0.0928597 q^{61} +(-3.00894 + 4.68468i) q^{62} +2.02144 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-4.70338 - 3.41721i) q^{65} +(-1.08411 + 3.33653i) q^{66} +0.403254 q^{67} -4.27304 q^{68} +(2.75050 - 8.46516i) q^{69} +(-0.624660 - 1.92251i) q^{70} +(4.39294 + 13.5201i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(2.11437 - 6.50737i) q^{73} +(0.118034 - 0.0857567i) q^{74} +(0.809017 + 0.587785i) q^{75} +(2.37101 + 7.29723i) q^{76} +(-5.73731 - 4.16840i) q^{77} +(-4.70338 - 3.41721i) q^{78} +(-2.51888 - 7.75232i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-2.34895 + 7.22931i) q^{82} +(-11.2813 + 8.19631i) q^{83} +(-0.624660 - 1.92251i) q^{84} +(1.32044 + 4.06390i) q^{85} +(-1.94963 + 6.00035i) q^{86} +7.39476 q^{87} +3.50824 q^{88} +(3.54332 - 10.9052i) q^{89} +(0.809017 + 0.587785i) q^{90} +(9.50761 - 6.90768i) q^{91} -8.90080 q^{92} +(5.38521 + 1.41403i) q^{93} +0.884195 q^{94} +(6.20740 - 4.50994i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-1.14565 + 3.52596i) q^{97} -2.91377 q^{98} +3.50824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000			−0.408248
$7$	0.624660	−	1.92251i	0.236099	−	0.726639i	−0.760874	−	0.648899i	$-0.775230\pi$
$7$	0.624660	−	1.92251i	0.236099	−	0.726639i	0.996974	−	0.0777398i	$-0.0247703\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	0.809017	−	0.587785i	0.255834	−	0.185874i
$11$	1.08411	−	3.33653i	0.326870	−	1.00600i	−0.643719	−	0.765262i	$-0.722610\pi$
$11$	1.08411	−	3.33653i	0.326870	−	1.00600i	0.970589	−	0.240741i	$-0.0773904\pi$
$12$	0.809017	−	0.587785i	0.233543	−	0.169679i
$13$	4.70338	+	3.41721i	1.30448	+	0.947762i	0.999989	−	0.00475212i	$-0.00151265\pi$
$13$	4.70338	+	3.41721i	1.30448	+	0.947762i	0.304494	+	0.952514i	$0.401513\pi$
$14$	0.624660	+	1.92251i	0.166947	+	0.513811i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.32044	−	4.06390i	−0.320254	−	0.985641i	−0.973537	−	0.228528i	$-0.926609\pi$
$17$	−1.32044	−	4.06390i	−0.320254	−	0.985641i	0.653283	−	0.757114i	$-0.273391\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	−6.20740	+	4.50994i	−1.42407	+	1.03465i	−0.432993	+	0.901397i	$0.642542\pi$
$19$	−6.20740	+	4.50994i	−1.42407	+	1.03465i	−0.991082	+	0.133253i	$0.957458\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	1.63538	−	1.18817i	0.356870	−	0.259281i
$22$	1.08411	+	3.33653i	0.231132	+	0.711351i
$23$	−2.75050	−	8.46516i	−0.573518	−	1.76511i	−0.641170	−	0.767399i	$-0.721551\pi$
$23$	−2.75050	−	8.46516i	−0.573518	−	1.76511i	0.0676514	−	0.997709i	$-0.478449\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	1.00000			0.200000
$26$	−5.81370			−1.14016
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−1.63538	−	1.18817i	−0.309058	−	0.224544i
$29$	5.98249	−	4.34653i	1.11092	−	0.807130i	0.128111	−	0.991760i	$-0.459108\pi$
$29$	5.98249	−	4.34653i	1.11092	−	0.807130i	0.982808	+	0.184629i	$0.0591085\pi$
$30$	1.00000			0.182574
$31$	5.18787	−	2.02138i	0.931770	−	0.363050i
$31$	5.18787	−	2.02138i	0.931770	−	0.363050i
$32$	1.00000			0.176777
$33$	2.83822	−	2.06209i	0.494071	−	0.358964i
$34$	3.45696	+	2.51163i	0.592864	+	0.430741i
$35$	−0.624660	+	1.92251i	−0.105587	+	0.324963i
$36$	1.00000			0.166667
$37$	−0.145898			−0.0239855			−0.0119927	−	0.999928i	$-0.503818\pi$
$37$	−0.145898			−0.0239855			−0.0119927	+	0.999928i	$0.503818\pi$
$38$	2.37101	−	7.29723i	0.384629	−	1.18377i
$39$	1.79653	+	5.52915i	0.287675	+	0.885373i
$40$	−0.309017	−	0.951057i	−0.0488599	−	0.150375i
$41$	6.14962	−	4.46796i	0.960409	−	0.697778i	0.00716348	−	0.999974i	$-0.497720\pi$
$41$	6.14962	−	4.46796i	0.960409	−	0.697778i	0.953246	+	0.302196i	$0.0977198\pi$
$42$	−0.624660	+	1.92251i	−0.0963872	+	0.296649i
$43$	5.10420	−	3.70842i	0.778384	−	0.565529i	−0.126110	−	0.992016i	$-0.540249\pi$
$43$	5.10420	−	3.70842i	0.778384	−	0.565529i	0.904493	+	0.426487i	$0.140249\pi$
$44$	−2.83822	−	2.06209i	−0.427878	−	0.310872i
$45$	−0.309017	−	0.951057i	−0.0460655	−	0.141775i
$46$	7.20090	+	5.23176i	1.06171	+	0.771381i
$47$	−0.715329	−	0.519717i	−0.104341	−	0.0758085i	0.534391	−	0.845237i	$-0.320541\pi$
$47$	−0.715329	−	0.519717i	−0.104341	−	0.0758085i	−0.638733	+	0.769429i	$0.720541\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	2.35729	+	1.71267i	0.336756	+	0.244667i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	1.32044	−	4.06390i	0.184899	−	0.569060i
$52$	4.70338	−	3.41721i	0.652241	−	0.473881i
$53$	0.994498	+	3.06075i	0.136605	+	0.420426i	0.995836	−	0.0911609i	$-0.0290577\pi$
$53$	0.994498	+	3.06075i	0.136605	+	0.420426i	−0.859231	+	0.511587i	$0.829058\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−1.08411	+	3.33653i	−0.146181	+	0.449898i
$56$	2.02144			0.270127
$57$	−7.67276			−1.01628
$58$	−2.28511	+	7.03283i	−0.300049	+	0.923456i
$59$	1.97317	+	1.43359i	0.256885	+	0.186638i	0.708773	−	0.705437i	$-0.249249\pi$
$59$	1.97317	+	1.43359i	0.256885	+	0.186638i	−0.451888	+	0.892075i	$0.649249\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−0.0928597			−0.0118895			−0.00594474	−	0.999982i	$-0.501892\pi$
$61$	−0.0928597			−0.0118895			−0.00594474	+	0.999982i	$0.501892\pi$
$62$	−3.00894	+	4.68468i	−0.382136	+	0.594956i
$63$	2.02144			0.254678
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−4.70338	−	3.41721i	−0.583382	−	0.423852i
$66$	−1.08411	+	3.33653i	−0.133444	+	0.410699i
$67$	0.403254			0.0492654			0.0246327	−	0.999697i	$-0.492158\pi$
$67$	0.403254			0.0492654			0.0246327	+	0.999697i	$0.492158\pi$
$68$	−4.27304			−0.518182
$69$	2.75050	−	8.46516i	0.331121	−	1.01909i
$70$	−0.624660	−	1.92251i	−0.0746612	−	0.229783i
$71$	4.39294	+	13.5201i	0.521346	+	1.60454i	0.771430	+	0.636314i	$0.219542\pi$
$71$	4.39294	+	13.5201i	0.521346	+	1.60454i	−0.250084	+	0.968224i	$0.580458\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	2.11437	−	6.50737i	0.247469	−	0.761630i	−0.747752	−	0.663978i	$-0.768867\pi$
$73$	2.11437	−	6.50737i	0.247469	−	0.761630i	0.995221	−	0.0976521i	$-0.0311333\pi$
$74$	0.118034	−	0.0857567i	0.0137212	−	0.00996902i
$75$	0.809017	+	0.587785i	0.0934172	+	0.0678716i
$76$	2.37101	+	7.29723i	0.271974	+	0.837050i
$77$	−5.73731	−	4.16840i	−0.653827	−	0.475033i
$78$	−4.70338	−	3.41721i	−0.532553	−	0.386922i
$79$	−2.51888	−	7.75232i	−0.283396	−	0.872204i	−0.986875	−	0.161488i	$-0.948371\pi$
$79$	−2.51888	−	7.75232i	−0.283396	−	0.872204i	0.703478	−	0.710717i	$-0.251629\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−2.34895	+	7.22931i	−0.259398	+	0.798344i
$83$	−11.2813	+	8.19631i	−1.23828	+	0.899662i	−0.997482	−	0.0709137i	$-0.977409\pi$
$83$	−11.2813	+	8.19631i	−1.23828	+	0.899662i	−0.240796	+	0.970576i	$0.577409\pi$
$84$	−0.624660	−	1.92251i	−0.0681560	−	0.209763i
$85$	1.32044	+	4.06390i	0.143222	+	0.440792i
$86$	−1.94963	+	6.00035i	−0.210234	+	0.647034i
$87$	7.39476			0.792801
$88$	3.50824			0.373979
$89$	3.54332	−	10.9052i	0.375591	−	1.15595i	−0.567488	−	0.823382i	$-0.692085\pi$
$89$	3.54332	−	10.9052i	0.375591	−	1.15595i	0.943079	−	0.332569i	$-0.107915\pi$
$90$	0.809017	+	0.587785i	0.0852779	+	0.0619580i
$91$	9.50761	−	6.90768i	0.996669	−	0.724122i
$92$	−8.90080			−0.927972
$93$	5.38521	+	1.41403i	0.558421	+	0.146628i
$94$	0.884195			0.0911977
$95$	6.20740	−	4.50994i	0.636866	−	0.462710i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−1.14565	+	3.52596i	−0.116323	+	0.358007i	−0.992221	−	0.124491i	$-0.960270\pi$
$97$	−1.14565	+	3.52596i	−0.116323	+	0.358007i	0.875897	+	0.482498i	$0.160270\pi$
$98$	−2.91377			−0.294335
$99$	3.50824			0.352591
$100$	0.309017	−	0.951057i	0.0309017	−	0.0951057i
$101$	4.76095	+	14.6527i	0.473732	+	1.45800i	0.847660	+	0.530540i	$0.178011\pi$
$101$	4.76095	+	14.6527i	0.473732	+	1.45800i	−0.373928	+	0.927458i	$0.621989\pi$
$102$	1.32044	+	4.06390i	0.130743	+	0.402386i
$103$	3.11826	−	2.26555i	0.307251	−	0.223231i	−0.423465	−	0.905913i	$-0.639186\pi$
$103$	3.11826	−	2.26555i	0.307251	−	0.223231i	0.730716	+	0.682681i	$0.239186\pi$
$104$	−1.79653	+	5.52915i	−0.176164	+	0.542178i
$105$	−1.63538	+	1.18817i	−0.159597	+	0.115954i
$106$	−2.60363	−	1.89165i	−0.252887	−	0.183733i
$107$	−0.227946	−	0.701545i	−0.0220364	−	0.0678209i	0.939434	−	0.342731i	$-0.111352\pi$
$107$	−0.227946	−	0.701545i	−0.0220364	−	0.0678209i	−0.961470	+	0.274910i	$0.911352\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	3.87416	+	2.81474i	0.371077	+	0.269603i	0.757657	−	0.652652i	$-0.226344\pi$
$109$	3.87416	+	2.81474i	0.371077	+	0.269603i	−0.386580	+	0.922256i	$0.626344\pi$
$110$	−1.08411	−	3.33653i	−0.103365	−	0.318126i
$111$	−0.118034	−	0.0857567i	−0.0112033	−	0.00813967i
$112$	−1.63538	+	1.18817i	−0.154529	+	0.112272i
$113$	2.09182	−	6.43797i	0.196782	−	0.605633i	−0.803169	−	0.595751i	$-0.796854\pi$
$113$	2.09182	−	6.43797i	0.196782	−	0.605633i	0.999951	−	0.00988180i	$-0.00314553\pi$
$114$	6.20740	−	4.50994i	0.581376	−	0.422394i
$115$	2.75050	+	8.46516i	0.256485	+	0.789380i
$116$	−2.28511	−	7.03283i	−0.212167	−	0.652982i
$117$	−1.79653	+	5.52915i	−0.166089	+	0.511170i
$118$	−2.43897			−0.224526
$119$	−8.63771			−0.791817
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	−1.05798	−	0.768667i	−0.0961800	−	0.0698788i
$122$	0.0751251	−	0.0545816i	0.00680151	−	0.00494158i
$123$	7.60135			0.685390
$124$	−0.319304	−	5.55860i	−0.0286743	−	0.499177i
$125$	−1.00000			−0.0894427
$126$	−1.63538	+	1.18817i	−0.145691	+	0.105851i
$127$	−12.2786	−	8.92093i	−1.08955	−	0.791604i	−0.110227	−	0.993906i	$-0.535158\pi$
$127$	−12.2786	−	8.92093i	−1.08955	−	0.791604i	−0.979323	+	0.202302i	$0.935158\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	6.30914			0.555489
$130$	5.81370			0.509895
$131$	−0.608270	+	1.87206i	−0.0531448	+	0.163563i	−0.974106	−	0.226091i	$-0.927405\pi$
$131$	−0.608270	+	1.87206i	−0.0531448	+	0.163563i	0.920961	+	0.389654i	$0.127405\pi$
$132$	−1.08411	−	3.33653i	−0.0943592	−	0.290408i
$133$	4.79287	+	14.7509i	0.415595	+	1.27907i
$134$	−0.326240	+	0.237027i	−0.0281828	+	0.0204760i
$135$	0.309017	−	0.951057i	0.0265959	−	0.0818539i
$136$	3.45696	−	2.51163i	0.296432	−	0.215370i
$137$	−4.09593	−	2.97586i	−0.349939	−	0.254245i	0.398905	−	0.916992i	$-0.369390\pi$
$137$	−4.09593	−	2.97586i	−0.349939	−	0.254245i	−0.748843	+	0.662747i	$0.769390\pi$
$138$	2.75050	+	8.46516i	0.234138	+	0.720602i
$139$	13.2361	+	9.61661i	1.12267	+	0.815670i	0.984612	−	0.174753i	$-0.0559128\pi$
$139$	13.2361	+	9.61661i	1.12267	+	0.815670i	0.138061	+	0.990424i	$0.455913\pi$
$140$	1.63538	+	1.18817i	0.138215	+	0.100419i
$141$	−0.273231	−	0.840919i	−0.0230102	−	0.0708182i
$142$	−11.5009	−	8.35587i	−0.965131	−	0.701209i
$143$	16.5006	−	11.9884i	1.37985	−	1.00252i
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$	−5.98249	+	4.34653i	−0.496818	+	0.360960i
$146$	2.11437	+	6.50737i	0.174987	+	0.538554i
$147$	0.900404	+	2.77116i	0.0742641	+	0.228561i
$148$	−0.0450850	+	0.138757i	−0.00370596	+	0.0114058i
$149$	−17.4579			−1.43021			−0.715105	−	0.699017i	$-0.753621\pi$
$149$	−17.4579			−1.43021			−0.715105	+	0.699017i	$0.753621\pi$
$150$	−1.00000			−0.0816497
$151$	3.07424	−	9.46153i	0.250178	−	0.769969i	−0.744564	−	0.667552i	$-0.767342\pi$
$151$	3.07424	−	9.46153i	0.250178	−	0.769969i	0.994742	−	0.102417i	$-0.0326576\pi$
$152$	−6.20740	−	4.50994i	−0.503486	−	0.365804i
$153$	3.45696	−	2.51163i	0.279479	−	0.203053i
$154$	7.09170			0.571466
$155$	−5.18787	+	2.02138i	−0.416700	+	0.162361i
$156$	5.81370			0.465468
$157$	−17.9063	+	13.0097i	−1.42908	+	1.03829i	−0.438889	+	0.898541i	$0.644628\pi$
$157$	−17.9063	+	13.0097i	−1.42908	+	1.03829i	−0.990188	+	0.139744i	$0.955372\pi$
$158$	6.59452	+	4.79120i	0.524632	+	0.381167i
$159$	−0.994498	+	3.06075i	−0.0788688	+	0.242733i
$160$	−1.00000			−0.0790569
$161$	−17.9925			−1.41800
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	−3.96793	−	12.2120i	−0.310792	−	0.956520i	−0.977452	−	0.211158i	$-0.932277\pi$
$163$	−3.96793	−	12.2120i	−0.310792	−	0.956520i	0.666660	−	0.745362i	$-0.267723\pi$
$164$	−2.34895	−	7.22931i	−0.183422	−	0.564514i
$165$	−2.83822	+	2.06209i	−0.220955	+	0.160534i
$166$	4.30906	−	13.2619i	0.334448	−	1.02932i
$167$	−11.1771	+	8.12065i	−0.864911	+	0.628394i	−0.929216	−	0.369536i	$-0.879517\pi$
$167$	−11.1771	+	8.12065i	−0.864911	+	0.628394i	0.0643058	+	0.997930i	$0.479517\pi$
$168$	1.63538	+	1.18817i	0.126172	+	0.0916696i
$169$	6.42726	+	19.7811i	0.494405	+	1.52162i
$170$	−3.45696	−	2.51163i	−0.265137	−	0.192633i
$171$	−6.20740	−	4.50994i	−0.474692	−	0.344884i
$172$	−1.94963	−	6.00035i	−0.148658	−	0.457522i
$173$	−2.48081	−	1.80241i	−0.188613	−	0.137035i	0.489472	−	0.872019i	$-0.337190\pi$
$173$	−2.48081	−	1.80241i	−0.188613	−	0.137035i	−0.678084	+	0.734984i	$0.737190\pi$
$174$	−5.98249	+	4.34653i	−0.453531	+	0.329510i
$175$	0.624660	−	1.92251i	0.0472199	−	0.145328i
$176$	−2.83822	+	2.06209i	−0.213939	+	0.155436i
$177$	0.753684	+	2.31960i	0.0566504	+	0.174352i
$178$	3.54332	+	10.9052i	0.265583	+	0.817381i
$179$	3.76059	−	11.5739i	0.281080	−	0.865075i	−0.706466	−	0.707747i	$-0.749712\pi$
$179$	3.76059	−	11.5739i	0.281080	−	0.865075i	0.987546	−	0.157328i	$-0.0502881\pi$
$180$	−1.00000			−0.0745356
$181$	10.6347			0.790472			0.395236	−	0.918580i	$-0.370663\pi$
$181$	10.6347			0.790472			0.395236	+	0.918580i	$0.370663\pi$
$182$	−3.63158	+	11.1769i	−0.269191	+	0.828485i
$183$	−0.0751251	−	0.0545816i	−0.00555341	−	0.00403479i
$184$	7.20090	−	5.23176i	0.530857	−	0.385690i
$185$	0.145898			0.0107266
$186$	−5.18787	+	2.02138i	−0.380393	+	0.148215i
$187$	−14.9908			−1.09624
$188$	−0.715329	+	0.519717i	−0.0521707	+	0.0379042i
$189$	1.63538	+	1.18817i	0.118957	+	0.0864270i
$190$	−2.37101	+	7.29723i	−0.172011	+	0.529397i
$191$	9.21926			0.667082			0.333541	−	0.942736i	$-0.391756\pi$
$191$	9.21926			0.667082			0.333541	+	0.942736i	$0.391756\pi$
$192$	−1.00000			−0.0721688
$193$	1.95257	−	6.00938i	0.140549	−	0.432564i	−0.855863	−	0.517203i	$-0.826973\pi$
$193$	1.95257	−	6.00938i	0.140549	−	0.432564i	0.996412	+	0.0846380i	$0.0269734\pi$
$194$	−1.14565	−	3.52596i	−0.0822531	−	0.253149i
$195$	−1.79653	−	5.52915i	−0.128652	−	0.395951i
$196$	2.35729	−	1.71267i	0.168378	−	0.122334i
$197$	4.82206	−	14.8408i	0.343558	−	1.05736i	−0.618794	−	0.785554i	$-0.712378\pi$
$197$	4.82206	−	14.8408i	0.343558	−	1.05736i	0.962351	−	0.271809i	$-0.0876217\pi$
$198$	−2.83822	+	2.06209i	−0.201704	+	0.146546i
$199$	−19.6984	−	14.3117i	−1.39638	−	1.01453i	−0.995131	−	0.0985602i	$-0.968576\pi$
$199$	−19.6984	−	14.3117i	−1.39638	−	1.01453i	−0.401249	−	0.915969i	$-0.631424\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	0.326240	+	0.237027i	0.0230112	+	0.0167186i
$202$	−12.4643	−	9.05587i	−0.876987	−	0.637168i
$203$	−4.61921	−	14.2165i	−0.324205	−	0.997801i
$204$	−3.45696	−	2.51163i	−0.242036	−	0.175849i
$205$	−6.14962	+	4.46796i	−0.429508	+	0.312056i
$206$	−1.19107	+	3.66574i	−0.0829857	+	0.255404i
$207$	7.20090	−	5.23176i	0.500497	−	0.363632i
$208$	−1.79653	−	5.52915i	−0.124567	−	0.383378i
$209$	8.31808	+	25.6004i	0.575374	+	1.77082i
$210$	0.624660	−	1.92251i	0.0431056	−	0.132666i
$211$	5.35935			0.368953			0.184476	−	0.982837i	$-0.440941\pi$
$211$	5.35935			0.368953			0.184476	+	0.982837i	$0.440941\pi$
$212$	3.21826			0.221031
$213$	−4.39294	+	13.5201i	−0.300999	+	0.926381i
$214$	0.596770	+	0.433579i	0.0407944	+	0.0296388i
$215$	−5.10420	+	3.70842i	−0.348104	+	0.252912i
$216$	−1.00000			−0.0680414
$217$	−0.645454	−	11.2364i	−0.0438163	−	0.762776i
$218$	−4.78872			−0.324333
$219$	5.53550	−	4.02178i	0.374055	−	0.271767i
$220$	2.83822	+	2.06209i	0.191353	+	0.139026i
$221$	7.67665	−	23.6263i	0.516387	−	1.58928i
$222$	0.145898			0.00979203
$223$	−5.43761			−0.364129			−0.182065	−	0.983287i	$-0.558278\pi$
$223$	−5.43761			−0.364129			−0.182065	+	0.983287i	$0.558278\pi$
$224$	0.624660	−	1.92251i	0.0417369	−	0.128453i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	2.09182	+	6.43797i	0.139146	+	0.428247i
$227$	−9.60298	+	6.97698i	−0.637372	+	0.463078i	−0.858946	−	0.512065i	$-0.828881\pi$
$227$	−9.60298	+	6.97698i	−0.637372	+	0.463078i	0.221574	+	0.975144i	$0.428881\pi$
$228$	−2.37101	+	7.29723i	−0.157024	+	0.483271i
$229$	5.56558	−	4.04363i	0.367784	−	0.267211i	−0.388507	−	0.921446i	$-0.627009\pi$
$229$	5.56558	−	4.04363i	0.367784	−	0.267211i	0.756291	+	0.654235i	$0.227009\pi$
$230$	−7.20090	−	5.23176i	−0.474813	−	0.344972i
$231$	−2.19146	−	6.74461i	−0.144187	−	0.443763i
$232$	5.98249	+	4.34653i	0.392769	+	0.285364i
$233$	0.274963	+	0.199772i	0.0180134	+	0.0130875i	0.596756	−	0.802423i	$-0.296456\pi$
$233$	0.274963	+	0.199772i	0.0180134	+	0.0130875i	−0.578742	+	0.815511i	$0.696456\pi$
$234$	−1.79653	−	5.52915i	−0.117443	−	0.361452i
$235$	0.715329	+	0.519717i	0.0466629	+	0.0339026i
$236$	1.97317	−	1.43359i	0.128442	−	0.0933189i
$237$	2.51888	−	7.75232i	0.163619	−	0.503567i
$238$	6.98805	−	5.07712i	0.452968	−	0.329101i
$239$	8.28620	+	25.5023i	0.535990	+	1.64961i	0.741500	+	0.670953i	$0.234115\pi$
$239$	8.28620	+	25.5023i	0.535990	+	1.64961i	−0.205510	+	0.978655i	$0.565885\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	−7.45067	+	22.9308i	−0.479940	+	1.47710i	0.359238	+	0.933246i	$0.383037\pi$
$241$	−7.45067	+	22.9308i	−0.479940	+	1.47710i	−0.839178	+	0.543857i	$0.816963\pi$
$242$	1.30773			0.0840644
$243$	−1.00000			−0.0641500
$244$	−0.0286952	+	0.0883149i	−0.00183702	+	0.00565378i
$245$	−2.35729	−	1.71267i	−0.150602	−	0.109419i
$246$	−6.14962	+	4.46796i	−0.392085	+	0.284867i
$247$	−44.6071			−2.83828
$248$	3.52559	+	4.30932i	0.223875	+	0.273642i
$249$	−13.9444			−0.883690
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−14.4997	−	10.5347i	−0.915215	−	0.664942i	0.0271136	−	0.999632i	$-0.491368\pi$
$251$	−14.4997	−	10.5347i	−0.915215	−	0.664942i	−0.942328	+	0.334690i	$0.891368\pi$
$252$	0.624660	−	1.92251i	0.0393499	−	0.121107i
$253$	−31.2261			−1.96317
$254$	15.1772			0.952301
$255$	−1.32044	+	4.06390i	−0.0826893	+	0.254491i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	7.25010	+	22.3135i	0.452249	+	1.39188i	0.874335	+	0.485323i	$0.161298\pi$
$257$	7.25010	+	22.3135i	0.452249	+	1.39188i	−0.422086	+	0.906556i	$0.638702\pi$
$258$	−5.10420	+	3.70842i	−0.317774	+	0.230876i
$259$	−0.0911367	+	0.280490i	−0.00566296	+	0.0174288i
$260$	−4.70338	+	3.41721i	−0.291691	+	0.211926i
$261$	5.98249	+	4.34653i	0.370307	+	0.269043i
$262$	−0.608270	−	1.87206i	−0.0375791	−	0.115656i
$263$	−21.8210	−	15.8539i	−1.34554	−	0.977591i	−0.999221	−	0.0394742i	$-0.987432\pi$
$263$	−21.8210	−	15.8539i	−1.34554	−	0.977591i	−0.346318	−	0.938117i	$-0.612568\pi$
$264$	2.83822	+	2.06209i	0.174681	+	0.126913i
$265$	−0.994498	−	3.06075i	−0.0610915	−	0.188020i
$266$	−12.5479	−	9.11658i	−0.769361	−	0.558973i
$267$	9.27653	−	6.73980i	0.567715	−	0.412469i
$268$	0.124612	−	0.383518i	0.00761192	−	0.0234271i
$269$	−21.5191	+	15.6346i	−1.31204	+	0.953256i	−0.312050	+	0.950066i	$0.601016\pi$
$269$	−21.5191	+	15.6346i	−1.31204	+	0.953256i	−0.999995	+	0.00319080i	$0.998984\pi$
$270$	0.309017	+	0.951057i	0.0188062	+	0.0578795i
$271$	5.79493	+	17.8350i	0.352017	+	1.08340i	0.957719	+	0.287706i	$0.0928925\pi$
$271$	5.79493	+	17.8350i	0.352017	+	1.08340i	−0.605702	+	0.795692i	$0.707108\pi$
$272$	−1.32044	+	4.06390i	−0.0800636	+	0.246410i
$273$	11.7521			0.711267
$274$	5.06284			0.305858
$275$	1.08411	−	3.33653i	0.0653740	−	0.201200i
$276$	−7.20090	−	5.23176i	−0.433443	−	0.314915i
$277$	−10.4771	+	7.61203i	−0.629505	+	0.457362i	−0.856229	−	0.516597i	$-0.827199\pi$
$277$	−10.4771	+	7.61203i	−0.629505	+	0.457362i	0.226723	+	0.973959i	$0.427199\pi$
$278$	−16.3608			−0.981253
$279$	3.52559	+	4.30932i	0.211071	+	0.257992i
$280$	−2.02144			−0.120804
$281$	−12.0933	+	8.78629i	−0.721425	+	0.524146i	−0.886839	−	0.462078i	$-0.847104\pi$
$281$	−12.0933	+	8.78629i	−0.721425	+	0.524146i	0.165414	+	0.986224i	$0.447104\pi$
$282$	0.715329	+	0.519717i	0.0425972	+	0.0309487i
$283$	−4.34891	+	13.3846i	−0.258516	+	0.795631i	0.734600	+	0.678500i	$0.237370\pi$
$283$	−4.34891	+	13.3846i	−0.258516	+	0.795631i	−0.993117	+	0.117131i	$0.962630\pi$
$284$	14.2159			0.843556
$285$	7.67276			0.454495
$286$	−6.30266	+	19.3976i	−0.372684	+	1.14700i
$287$	−4.74826	−	14.6136i	−0.280281	−	0.862616i
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	−1.01845	+	0.739945i	−0.0599086	+	0.0435262i
$290$	2.28511	−	7.03283i	0.134186	−	0.412982i
$291$	−2.99936	+	2.17916i	−0.175826	+	0.127745i
$292$	−5.53550	−	4.02178i	−0.323941	−	0.235357i
$293$	3.93551	+	12.1123i	0.229915	+	0.707605i	0.997755	+	0.0669643i	$0.0213314\pi$
$293$	3.93551	+	12.1123i	0.229915	+	0.707605i	−0.767840	+	0.640641i	$0.778669\pi$
$294$	−2.35729	−	1.71267i	−0.137480	−	0.0998850i
$295$	−1.97317	−	1.43359i	−0.114882	−	0.0834670i
$296$	−0.0450850	−	0.138757i	−0.00262051	−	0.00806510i
$297$	2.83822	+	2.06209i	0.164690	+	0.119655i
$298$	14.1238	−	10.2615i	0.818168	−	0.594434i
$299$	15.9906	−	49.2139i	0.924758	−	2.84611i
$300$	0.809017	−	0.587785i	0.0467086	−	0.0339358i
$301$	−3.94107	−	12.1294i	−0.227159	−	0.699125i
$302$	3.07424	+	9.46153i	0.176903	+	0.544450i
$303$	−4.76095	+	14.6527i	−0.273509	+	0.841776i
$304$	7.67276			0.440063
$305$	0.0928597			0.00531713
$306$	−1.32044	+	4.06390i	−0.0754846	+	0.232318i
$307$	2.99998	+	2.17961i	0.171218	+	0.124397i	0.670094	−	0.742276i	$-0.266254\pi$
$307$	2.99998	+	2.17961i	0.171218	+	0.124397i	−0.498876	+	0.866673i	$0.666254\pi$
$308$	−5.73731	+	4.16840i	−0.326913	+	0.237517i
$309$	3.85438			0.219268
$310$	3.00894	−	4.68468i	0.170896	−	0.266072i
$311$	−21.4168			−1.21443			−0.607217	−	0.794536i	$-0.707714\pi$
$311$	−21.4168			−1.21443			−0.607217	+	0.794536i	$0.707714\pi$
$312$	−4.70338	+	3.41721i	−0.266276	+	0.193461i
$313$	26.4825	+	19.2407i	1.49688	+	1.08755i	0.971603	+	0.236618i	$0.0760391\pi$
$313$	26.4825	+	19.2407i	1.49688	+	1.08755i	0.525279	+	0.850930i	$0.323961\pi$
$314$	6.83959	−	21.0501i	0.385980	−	1.18793i
$315$	−2.02144			−0.113895
$316$	−8.15127			−0.458545
$317$	−7.54980	+	23.2359i	−0.424039	+	1.30506i	0.479872	+	0.877339i	$0.340683\pi$
$317$	−7.54980	+	23.2359i	−0.424039	+	1.30506i	−0.903911	+	0.427720i	$0.859317\pi$
$318$	−0.994498	−	3.06075i	−0.0557687	−	0.171638i
$319$	−8.01670	−	24.6729i	−0.448849	−	1.38141i
$320$	0.809017	−	0.587785i	0.0452254	−	0.0328582i
$321$	0.227946	−	0.701545i	0.0127227	−	0.0391564i
$322$	14.5562	−	10.5757i	0.811185	−	0.589361i
$323$	26.5245	+	19.2711i	1.47586	+	1.07228i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	4.70338	+	3.41721i	0.260897	+	0.189552i
$326$	10.3882	+	7.54745i	0.575348	+	0.418014i
$327$	1.47980	+	4.55435i	0.0818330	+	0.251856i
$328$	6.14962	+	4.46796i	0.339556	+	0.246702i
$329$	−1.44600	+	1.05058i	−0.0797203	+	0.0579202i
$330$	1.08411	−	3.33653i	0.0596780	−	0.183670i
$331$	5.41171	−	3.93184i	0.297455	−	0.216113i	−0.429040	−	0.903285i	$-0.641148\pi$
$331$	5.41171	−	3.93184i	0.297455	−	0.216113i	0.726495	+	0.687172i	$0.241148\pi$
$332$	4.30906	+	13.2619i	0.236490	+	0.727842i
$333$	−0.0450850	−	0.138757i	−0.00247064	−	0.00760385i
$334$	4.26928	−	13.1395i	0.233604	−	0.718960i
$335$	−0.403254			−0.0220321
$336$	−2.02144			−0.110279
$337$	3.57401	−	10.9997i	0.194689	−	0.599190i	−0.805291	−	0.592879i	$-0.797991\pi$
$337$	3.57401	−	10.9997i	0.194689	−	0.599190i	0.999980	−	0.00631094i	$-0.00200885\pi$
$338$	−16.8268	−	12.2254i	−0.915257	−	0.664973i
$339$	5.47646	−	3.97888i	0.297441	−	0.216103i
$340$	4.27304			0.231738
$341$	−1.12019	−	19.5009i	−0.0606619	−	1.05603i
$342$	7.67276			0.414896
$343$	16.2128	−	11.7793i	0.875409	−	0.636022i
$344$	5.10420	+	3.70842i	0.275200	+	0.199945i
$345$	−2.75050	+	8.46516i	−0.148082	+	0.455749i
$346$	3.06645			0.164853
$347$	−16.2474			−0.872207			−0.436104	−	0.899896i	$-0.643642\pi$
$347$	−16.2474			−0.872207			−0.436104	+	0.899896i	$0.643642\pi$
$348$	2.28511	−	7.03283i	0.122495	−	0.376999i
$349$	−5.90133	−	18.1624i	−0.315891	−	0.972213i	−0.975386	−	0.220504i	$-0.929230\pi$
$349$	−5.90133	−	18.1624i	−0.315891	−	0.972213i	0.659495	−	0.751709i	$-0.270770\pi$
$350$	0.624660	+	1.92251i	0.0333895	+	0.102762i
$351$	−4.70338	+	3.41721i	−0.251048	+	0.182397i
$352$	1.08411	−	3.33653i	0.0577830	−	0.177838i
$353$	12.6457	−	9.18764i	0.673063	−	0.489009i	−0.197986	−	0.980205i	$-0.563440\pi$
$353$	12.6457	−	9.18764i	0.673063	−	0.489009i	0.871049	+	0.491196i	$0.163440\pi$
$354$	−1.97317	−	1.43359i	−0.104873	−	0.0761946i
$355$	−4.39294	−	13.5201i	−0.233153	−	0.717571i
$356$	−9.27653	−	6.73980i	−0.491655	−	0.357208i
$357$	−6.98805	−	5.07712i	−0.369847	−	0.268709i
$358$	3.76059	+	11.5739i	0.198753	+	0.611700i
$359$	7.52317	+	5.46590i	0.397057	+	0.288479i	0.768341	−	0.640040i	$-0.221082\pi$
$359$	7.52317	+	5.46590i	0.397057	+	0.288479i	−0.371284	+	0.928519i	$0.621082\pi$
$360$	0.809017	−	0.587785i	0.0426389	−	0.0309790i
$361$	12.3209	−	37.9199i	0.648469	−	1.99578i
$362$	−8.60366	+	6.25093i	−0.452199	+	0.328541i
$363$	−0.404112	−	1.24373i	−0.0212104	−	0.0652789i
$364$	−3.63158	−	11.1769i	−0.190347	−	0.585827i
$365$	−2.11437	+	6.50737i	−0.110671	+	0.340611i
$366$	0.0928597			0.00485386
$367$	−19.7865			−1.03285			−0.516424	−	0.856333i	$-0.672737\pi$
$367$	−19.7865			−1.03285			−0.516424	+	0.856333i	$0.672737\pi$
$368$	−2.75050	+	8.46516i	−0.143380	+	0.441277i
$369$	6.14962	+	4.46796i	0.320136	+	0.232593i
$370$	−0.118034	+	0.0857567i	−0.00613629	+	0.00445828i
$371$	6.50553			0.337750
$372$	3.00894	−	4.68468i	0.156006	−	0.242890i
$373$	−11.6581			−0.603634			−0.301817	−	0.953366i	$-0.597593\pi$
$373$	−11.6581			−0.603634			−0.301817	+	0.953366i	$0.597593\pi$
$374$	12.1278	−	8.81140i	0.627116	−	0.455626i
$375$	−0.809017	−	0.587785i	−0.0417775	−	0.0303531i
$376$	0.273231	−	0.840919i	0.0140908	−	0.0433671i
$377$	42.9909			2.21414
$378$	−2.02144			−0.103972
$379$	−5.78761	+	17.8124i	−0.297289	+	0.914963i	0.685153	+	0.728399i	$0.259735\pi$
$379$	−5.78761	+	17.8124i	−0.297289	+	0.914963i	−0.982443	+	0.186564i	$0.940265\pi$
$380$	−2.37101	−	7.29723i	−0.121630	−	0.374340i
$381$	−4.69001	−	14.4344i	−0.240276	−	0.739495i
$382$	−7.45854	+	5.41894i	−0.381612	+	0.277257i
$383$	−8.41161	+	25.8883i	−0.429813	+	1.32283i	0.468496	+	0.883466i	$0.344796\pi$
$383$	−8.41161	+	25.8883i	−0.429813	+	1.32283i	−0.898309	+	0.439364i	$0.855204\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	5.73731	+	4.16840i	0.292400	+	0.212441i
$386$	1.95257	+	6.00938i	0.0993830	+	0.305869i
$387$	5.10420	+	3.70842i	0.259461	+	0.188510i
$388$	2.99936	+	2.17916i	0.152269	+	0.110630i
$389$	9.90338	+	30.4795i	0.502121	+	1.54537i	0.805557	+	0.592518i	$0.201866\pi$
$389$	9.90338	+	30.4795i	0.502121	+	1.54537i	−0.303436	+	0.952852i	$0.598134\pi$
$390$	4.70338	+	3.41721i	0.238165	+	0.173037i
$391$	−30.7697	+	22.3555i	−1.55609	+	1.13057i
$392$	−0.900404	+	2.77116i	−0.0454773	+	0.139965i
$393$	−1.59247	+	1.15700i	−0.0803296	+	0.0583629i
$394$	4.82206	+	14.8408i	0.242932	+	0.747668i
$395$	2.51888	+	7.75232i	0.126739	+	0.390062i
$396$	1.08411	−	3.33653i	0.0544783	−	0.167667i
$397$	29.1658			1.46379			0.731894	−	0.681418i	$-0.238637\pi$
$397$	29.1658			1.46379			0.731894	+	0.681418i	$0.238637\pi$
$398$	24.3485			1.22048
$399$	−4.79287	+	14.7509i	−0.239944	+	0.738471i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	4.15851	−	3.02134i	0.207666	−	0.150878i	−0.479091	−	0.877765i	$-0.659034\pi$
$401$	4.15851	−	3.02134i	0.207666	−	0.150878i	0.686757	+	0.726887i	$0.259034\pi$
$402$	−0.403254			−0.0201125
$403$	31.3080	+	8.22072i	1.55956	+	0.409503i
$404$	15.4068			0.766515
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	12.0933	+	8.78626i	0.600178	+	0.436055i
$407$	−0.158169	+	0.486794i	−0.00784014	+	0.0241295i
$408$	4.27304			0.211547
$409$	24.8045			1.22651			0.613253	−	0.789887i	$-0.289861\pi$
$409$	24.8045			1.22651			0.613253	+	0.789887i	$0.289861\pi$
$410$	2.34895	−	7.22931i	0.116006	−	0.357030i
$411$	−1.56450	−	4.81505i	−0.0771713	−	0.237509i
$412$	−1.19107	−	3.66574i	−0.0586798	−	0.180598i
$413$	3.98865	−	2.89793i	0.196269	−	0.142598i
$414$	−2.75050	+	8.46516i	−0.135180	+	0.416040i
$415$	11.2813	−	8.19631i	0.553775	−	0.402341i
$416$	4.70338	+	3.41721i	0.230602	+	0.167542i
$417$	5.05575	+	15.5600i	0.247581	+	0.761977i
$418$	−21.7770	−	15.8219i	−1.06515	−	0.773876i
$419$	4.87788	+	3.54399i	0.238300	+	0.173135i	0.700526	−	0.713627i	$-0.252949\pi$
$419$	4.87788	+	3.54399i	0.238300	+	0.173135i	−0.462226	+	0.886762i	$0.652949\pi$
$420$	0.624660	+	1.92251i	0.0304803	+	0.0938087i
$421$	17.5021	+	12.7160i	0.852998	+	0.619739i	0.925971	−	0.377595i	$-0.123249\pi$
$421$	17.5021	+	12.7160i	0.852998	+	0.619739i	−0.0729731	+	0.997334i	$0.523249\pi$
$422$	−4.33580	+	3.15015i	−0.211064	+	0.153347i
$423$	0.273231	−	0.840919i	0.0132850	−	0.0408869i
$424$	−2.60363	+	1.89165i	−0.126443	+	0.0918665i
$425$	−1.32044	−	4.06390i	−0.0640508	−	0.197128i
$426$	−4.39294	−	13.5201i	−0.212839	−	0.655050i
$427$	−0.0580058	+	0.178523i	−0.00280710	+	0.00863936i
$428$	−0.737648			−0.0356556
$429$	20.3958			0.984720
$430$	1.94963	−	6.00035i	0.0940196	−	0.289363i
$431$	17.3268	+	12.5887i	0.834603	+	0.606375i	0.920858	−	0.389898i	$-0.127490\pi$
$431$	17.3268	+	12.5887i	0.834603	+	0.606375i	−0.0862545	+	0.996273i	$0.527490\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	−9.57229			−0.460015			−0.230007	−	0.973189i	$-0.573875\pi$
$433$	−9.57229			−0.460015			−0.230007	+	0.973189i	$0.573875\pi$
$434$	7.12677	+	8.71105i	0.342096	+	0.418144i
$435$	−7.39476			−0.354552
$436$	3.87416	−	2.81474i	0.185539	−	0.134802i
$437$	55.2508	+	40.1420i	2.64300	+	1.92025i
$438$	−2.11437	+	6.50737i	−0.101029	+	0.310934i
$439$	−25.5389			−1.21890			−0.609452	−	0.792823i	$-0.708610\pi$
$439$	−25.5389			−1.21890			−0.609452	+	0.792823i	$0.708610\pi$
$440$	−3.50824			−0.167249
$441$	−0.900404	+	2.77116i	−0.0428764	+	0.131960i
$442$	7.67665	+	23.6263i	0.365141	+	1.12379i
$443$	−2.69600	−	8.29742i	−0.128091	−	0.394222i	0.866361	−	0.499419i	$-0.166453\pi$
$443$	−2.69600	−	8.29742i	−0.128091	−	0.394222i	−0.994451	+	0.105196i	$0.966453\pi$
$444$	−0.118034	+	0.0857567i	−0.00560165	+	0.00406983i
$445$	−3.54332	+	10.9052i	−0.167969	+	0.516957i
$446$	4.39912	−	3.19615i	0.208304	−	0.151342i
$447$	−14.1238	−	10.2615i	−0.668031	−	0.485353i
$448$	0.624660	+	1.92251i	0.0295124	+	0.0908299i
$449$	−0.720914	−	0.523775i	−0.0340220	−	0.0247185i	0.570644	−	0.821197i	$-0.306694\pi$
$449$	−0.720914	−	0.523775i	−0.0340220	−	0.0247185i	−0.604666	+	0.796479i	$0.706694\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	−8.24066	−	25.3621i	−0.388038	−	1.19426i
$452$	−5.47646	−	3.97888i	−0.257591	−	0.187151i
$453$	8.04846	−	5.84755i	0.378150	−	0.274742i
$454$	3.66801	−	11.2890i	0.172148	−	0.529818i
$455$	−9.50761	+	6.90768i	−0.445724	+	0.323837i
$456$	−2.37101	−	7.29723i	−0.111033	−	0.341724i
$457$	6.04218	+	18.5959i	0.282641	+	0.869881i	0.987096	+	0.160131i	$0.0511918\pi$
$457$	6.04218	+	18.5959i	0.282641	+	0.869881i	−0.704454	+	0.709749i	$0.748808\pi$
$458$	−2.12586	+	6.54273i	−0.0993351	+	0.305722i
$459$	4.27304			0.199448
$460$	8.90080			0.415002
$461$	6.68503	−	20.5744i	0.311353	−	0.958245i	−0.665877	−	0.746061i	$-0.731942\pi$
$461$	6.68503	−	20.5744i	0.311353	−	0.958245i	0.977230	−	0.212184i	$-0.0680575\pi$
$462$	5.73731	+	4.16840i	0.266924	+	0.193931i
$463$	20.3500	−	14.7851i	0.945743	−	0.687122i	−0.00405341	−	0.999992i	$-0.501290\pi$
$463$	20.3500	−	14.7851i	0.945743	−	0.687122i	0.949796	+	0.312869i	$0.101290\pi$
$464$	−7.39476			−0.343293
$465$	−5.38521	−	1.41403i	−0.249733	−	0.0655739i
$466$	−0.339873			−0.0157443
$467$	26.3853	−	19.1701i	1.22097	−	0.887085i	0.224787	−	0.974408i	$-0.427831\pi$
$467$	26.3853	−	19.1701i	1.22097	−	0.887085i	0.996180	+	0.0873233i	$0.0278313\pi$
$468$	4.70338	+	3.41721i	0.217414	+	0.157960i
$469$	0.251897	−	0.775259i	0.0116315	−	0.0357981i
$470$	−0.884195			−0.0407849
$471$	−22.1334			−1.01985
$472$	−0.753684	+	2.31960i	−0.0346911	+	0.106768i
$473$	−6.83977	−	21.0507i	−0.314493	−	0.967910i
$474$	2.51888	+	7.75232i	0.115696	+	0.356076i
$475$	−6.20740	+	4.50994i	−0.284815	+	0.206930i
$476$	−2.66920	+	8.21495i	−0.122342	+	0.376531i
$477$	−2.60363	+	1.89165i	−0.119212	+	0.0866126i
$478$	−21.6936	−	15.7613i	−0.992241	−	0.720905i
$479$	4.69358	+	14.4454i	0.214455	+	0.660026i	0.999192	+	0.0401961i	$0.0127983\pi$
$479$	4.69358	+	14.4454i	0.214455	+	0.660026i	−0.784736	+	0.619830i	$0.787202\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	−0.686214	−	0.498563i	−0.0312887	−	0.0227325i
$482$	−7.45067	−	22.9308i	−0.339369	−	1.04447i
$483$	−14.5562	−	10.5757i	−0.662330	−	0.481211i
$484$	−1.05798	+	0.768667i	−0.0480900	+	0.0349394i
$485$	1.14565	−	3.52596i	0.0520214	−	0.160105i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−3.57015	−	10.9878i	−0.161779	−	0.497904i	0.837006	−	0.547194i	$-0.184304\pi$
$487$	−3.57015	−	10.9878i	−0.161779	−	0.497904i	−0.998785	+	0.0492900i	$0.984304\pi$
$488$	−0.0286952	−	0.0883149i	−0.00129897	−	0.00399783i
$489$	3.96793	−	12.2120i	0.179436	−	0.552247i
$490$	2.91377			0.131631
$491$	36.1683			1.63225			0.816126	−	0.577874i	$-0.196118\pi$
$491$	36.1683			1.63225			0.816126	+	0.577874i	$0.196118\pi$
$492$	2.34895	−	7.22931i	0.105899	−	0.325923i
$493$	−25.5634	−	18.5729i	−1.15132	−	0.836481i
$494$	36.0879	−	26.2194i	1.62367	−	1.17967i
$495$	−3.50824			−0.157684
$496$	−5.38521	−	1.41403i	−0.241803	−	0.0634917i
$497$	28.7365			1.28901
$498$	11.2813	−	8.19631i	0.505525	−	0.367285i
$499$	−18.3543	−	13.3352i	−0.821651	−	0.596965i	0.0955336	−	0.995426i	$-0.469544\pi$
$499$	−18.3543	−	13.3352i	−0.821651	−	0.596965i	−0.917185	+	0.398461i	$0.869544\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−13.8157			−0.617239
$502$	17.9226			0.799927
$503$	3.11477	−	9.58626i	0.138881	−	0.427430i	−0.857293	−	0.514829i	$-0.827855\pi$
$503$	3.11477	−	9.58626i	0.138881	−	0.427430i	0.996173	+	0.0873986i	$0.0278554\pi$
$504$	0.624660	+	1.92251i	0.0278246	+	0.0856352i
$505$	−4.76095	−	14.6527i	−0.211860	−	0.652037i
$506$	25.2625	−	18.3543i	1.12305	−	0.815946i
$507$	−6.42726	+	19.7811i	−0.285445	+	0.878509i
$508$	−12.2786	+	8.92093i	−0.544775	+	0.395802i
$509$	−23.3018	−	16.9297i	−1.03283	−	0.750397i	−0.0639589	−	0.997953i	$-0.520373\pi$
$509$	−23.3018	−	16.9297i	−1.03283	−	0.750397i	−0.968874	+	0.247556i	$0.920373\pi$
$510$	−1.32044	−	4.06390i	−0.0584702	−	0.179953i
$511$	−11.1897	−	8.12979i	−0.495003	−	0.359641i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−2.37101	−	7.29723i	−0.104683	−	0.322181i
$514$	−18.9810	−	13.7905i	−0.837217	−	0.608273i
$515$	−3.11826	+	2.26555i	−0.137407	+	0.0998320i
$516$	1.94963	−	6.00035i	0.0858278	−	0.264151i
$517$	−2.50954	+	1.82329i	−0.110370	+	0.0801882i
$518$	−0.0911367	−	0.280490i	−0.00400432	−	0.0123240i
$519$	−0.947585	−	2.91637i	−0.0415944	−	0.128014i
$520$	1.79653	−	5.52915i	0.0787831	−	0.242469i
$521$	−11.7630			−0.515345			−0.257672	−	0.966232i	$-0.582956\pi$
$521$	−11.7630			−0.515345			−0.257672	+	0.966232i	$0.582956\pi$
$522$	−7.39476			−0.323660
$523$	4.44657	−	13.6851i	0.194435	−	0.598409i	−0.805548	−	0.592531i	$-0.798129\pi$
$523$	4.44657	−	13.6851i	0.194435	−	0.598409i	0.999983	−	0.00587853i	$-0.00187120\pi$
$524$	1.59247	+	1.15700i	0.0695675	+	0.0505437i
$525$	1.63538	−	1.18817i	0.0713739	−	0.0518562i
$526$	26.9722			1.17604
$527$	−15.0650	−	18.4139i	−0.656240	−	0.802122i
$528$	−3.50824			−0.152676
$529$	−45.4863	+	33.0477i	−1.97767	+	1.43686i
$530$	2.60363	+	1.89165i	0.113094	+	0.0821679i
$531$	−0.753684	+	2.31960i	−0.0327071	+	0.100662i
$532$	15.5101			0.672446
$533$	44.1919			1.91416
$534$	−3.54332	+	10.9052i	−0.153334	+	0.471915i
$535$	0.227946	+	0.701545i	0.00985496	+	0.0303305i
$536$	0.124612	+	0.383518i	0.00538244	+	0.0165654i
$537$	9.84536	−	7.15307i	0.424859	−	0.308678i
$538$	8.21958	−	25.2973i	0.354371	−	1.09064i
$539$	8.26993	−	6.00846i	0.356211	−	0.258803i
$540$	−0.809017	−	0.587785i	−0.0348145	−	0.0252942i
$541$	13.5745	+	41.7779i	0.583612	+	1.79617i	0.604774	+	0.796397i	$0.293264\pi$
$541$	13.5745	+	41.7779i	0.583612	+	1.79617i	−0.0211615	+	0.999776i	$0.506736\pi$
$542$	−15.1713	−	11.0226i	−0.651665	−	0.473462i
$543$	8.60366	+	6.25093i	0.369219	+	0.268253i
$544$	−1.32044	−	4.06390i	−0.0566135	−	0.174238i
$545$	−3.87416	−	2.81474i	−0.165951	−	0.120570i
$546$	−9.50761	+	6.90768i	−0.406888	+	0.295622i
$547$	6.30882	−	19.4165i	0.269746	−	0.830191i	−0.720816	−	0.693126i	$-0.756233\pi$
$547$	6.30882	−	19.4165i	0.269746	−	0.830191i	0.990562	−	0.137065i	$-0.0437671\pi$
$548$	−4.09593	+	2.97586i	−0.174969	+	0.127123i
$549$	−0.0286952	−	0.0883149i	−0.00122468	−	0.00376919i
$550$	1.08411	+	3.33653i	0.0462264	+	0.142270i
$551$	−17.5331	+	53.9613i	−0.746934	+	2.29883i
$552$	8.90080			0.378843
$553$	−16.4773			−0.700688
$554$	4.00188	−	12.3165i	0.170024	−	0.523279i
$555$	0.118034	+	0.0857567i	0.00501026	+	0.00364017i
$556$	13.2361	−	9.61661i	0.561337	−	0.407835i
$557$	25.1150			1.06416			0.532078	−	0.846695i	$-0.321411\pi$
$557$	25.1150			1.06416			0.532078	+	0.846695i	$0.321411\pi$
$558$	−5.38521	−	1.41403i	−0.227974	−	0.0598605i
$559$	36.6794			1.55137
$560$	1.63538	−	1.18817i	0.0691075	−	0.0502095i
$561$	−12.1278	−	8.81140i	−0.512038	−	0.372017i
$562$	4.61923	−	14.2165i	0.194850	−	0.599688i
$563$	−6.96390			−0.293493			−0.146747	−	0.989174i	$-0.546880\pi$
$563$	−6.96390			−0.293493			−0.146747	+	0.989174i	$0.546880\pi$
$564$	−0.884195			−0.0372313
$565$	−2.09182	+	6.43797i	−0.0880036	+	0.270847i
$566$	−4.34891	−	13.3846i	−0.182798	−	0.562596i
$567$	0.624660	+	1.92251i	0.0262333	+	0.0807377i
$568$	−11.5009	+	8.35587i	−0.482566	+	0.350604i
$569$	−1.90685	+	5.86868i	−0.0799393	+	0.246028i	−0.983037	−	0.183407i	$-0.941287\pi$
$569$	−1.90685	+	5.86868i	−0.0799393	+	0.246028i	0.903098	+	0.429435i	$0.141287\pi$
$570$	−6.20740	+	4.50994i	−0.259999	+	0.188901i
$571$	26.9536	+	19.5830i	1.12797	+	0.819522i	0.985399	−	0.170262i	$-0.0544615\pi$
$571$	26.9536	+	19.5830i	1.12797	+	0.819522i	0.142576	+	0.989784i	$0.454461\pi$
$572$	−6.30266	−	19.3976i	−0.263527	−	0.811054i
$573$	7.45854	+	5.41894i	0.311585	+	0.226380i
$574$	12.4311	+	9.03173i	0.518864	+	0.376977i
$575$	−2.75050	−	8.46516i	−0.114704	−	0.353022i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−17.6872	+	12.8505i	−0.736328	+	0.534974i	−0.891559	−	0.452905i	$-0.850388\pi$
$577$	−17.6872	+	12.8505i	−0.736328	+	0.534974i	0.155231	+	0.987878i	$0.450388\pi$
$578$	0.389012	−	1.19726i	0.0161808	−	0.0497993i
$579$	5.11188	−	3.71400i	0.212443	−	0.154349i
$580$	2.28511	+	7.03283i	0.0948839	+	0.292023i
$581$	8.71051	+	26.8082i	0.361373	+	1.11219i
$582$	1.14565	−	3.52596i	0.0474888	−	0.146156i
$583$	11.2904			0.467602
$584$	6.84226			0.283135
$585$	1.79653	−	5.52915i	0.0742774	−	0.228602i
$586$	−10.3033	−	7.48579i	−0.425625	−	0.309235i
$587$	15.0543	−	10.9376i	0.621356	−	0.451442i	−0.232039	−	0.972707i	$-0.574540\pi$
$587$	15.0543	−	10.9376i	0.621356	−	0.451442i	0.853395	+	0.521265i	$0.174540\pi$
$588$	2.91377			0.120162
$589$	−23.0869	+	35.9445i	−0.951279	+	1.48107i
$590$	2.43897			0.100411
$591$	12.6243	−	9.17211i	0.519295	−	0.377290i
$592$	0.118034	+	0.0857567i	0.00485117	+	0.00352458i
$593$	1.01565	−	3.12585i	0.0417078	−	0.128363i	−0.928035	−	0.372494i	$-0.878503\pi$
$593$	1.01565	−	3.12585i	0.0417078	−	0.128363i	0.969742	+	0.244131i	$0.0785026\pi$
$594$	−3.50824			−0.143945
$595$	8.63771			0.354111
$596$	−5.39480	+	16.6035i	−0.220979	+	0.680105i
$597$	−7.52410	−	23.1568i	−0.307941	−	0.947745i
$598$	15.9906	+	49.2139i	0.653903	+	2.01251i
$599$	−31.1730	+	22.6485i	−1.27370	+	0.925394i	−0.999343	−	0.0362348i	$-0.988464\pi$
$599$	−31.1730	+	22.6485i	−1.27370	+	0.925394i	−0.274353	+	0.961629i	$0.588464\pi$
$600$	−0.309017	+	0.951057i	−0.0126156	+	0.0388267i
$601$	−4.84337	+	3.51892i	−0.197565	+	0.143540i	−0.682170	−	0.731194i	$-0.738964\pi$
$601$	−4.84337	+	3.51892i	−0.197565	+	0.143540i	0.484604	+	0.874733i	$0.338964\pi$
$602$	10.3179	+	7.49636i	0.420524	+	0.305529i
$603$	0.124612	+	0.383518i	0.00507461	+	0.0156180i
$604$	−8.04846	−	5.84755i	−0.327487	−	0.237933i
$605$	1.05798	+	0.768667i	0.0430130	+	0.0312508i
$606$	−4.76095	−	14.6527i	−0.193400	−	0.595225i
$607$	6.94556	+	5.04625i	0.281912	+	0.204821i	0.719751	−	0.694233i	$-0.244256\pi$
$607$	6.94556	+	5.04625i	0.281912	+	0.204821i	−0.437839	+	0.899053i	$0.644256\pi$
$608$	−6.20740	+	4.50994i	−0.251743	+	0.182902i
$609$	4.61921	−	14.2165i	0.187180	−	0.576080i
$610$	−0.0751251	+	0.0545816i	−0.00304173	+	0.00220994i
$611$	−1.58848	−	4.88885i	−0.0642632	−	0.197782i
$612$	−1.32044	−	4.06390i	−0.0533757	−	0.164274i
$613$	−10.2532	+	31.5561i	−0.414123	+	1.27454i	0.498910	+	0.866654i	$0.333734\pi$
$613$	−10.2532	+	31.5561i	−0.414123	+	1.27454i	−0.913033	+	0.407886i	$0.866266\pi$
$614$	−3.70818			−0.149650
$615$	−7.60135			−0.306516
$616$	2.19146	−	6.74461i	0.0882963	−	0.271748i
$617$	−12.3695	−	8.98695i	−0.497977	−	0.361801i	0.310267	−	0.950649i	$-0.399582\pi$
$617$	−12.3695	−	8.98695i	−0.497977	−	0.361801i	−0.808244	+	0.588848i	$0.799582\pi$
$618$	−3.11826	+	2.26555i	−0.125435	+	0.0911337i
$619$	26.9722			1.08410			0.542052	−	0.840345i	$-0.317648\pi$
$619$	26.9722			1.08410			0.542052	+	0.840345i	$0.317648\pi$
$620$	0.319304	+	5.55860i	0.0128235	+	0.223239i
$621$	8.90080			0.357177
$622$	17.3265	−	12.5885i	0.694730	−	0.504751i
$623$	−18.7520	−	13.6241i	−0.751282	−	0.545839i
$624$	1.79653	−	5.52915i	0.0719188	−	0.221343i
$625$	1.00000			0.0400000
$626$	−32.7342			−1.30832
$627$	−8.31808	+	25.6004i	−0.332192	+	1.02238i
$628$	6.83959	+	21.0501i	0.272929	+	0.839990i
$629$	0.192650	+	0.592915i	0.00768145	+	0.0236411i
$630$	1.63538	−	1.18817i	0.0651552	−	0.0473380i
$631$	−3.67758	+	11.3184i	−0.146402	+	0.450579i	−0.997189	−	0.0749320i	$-0.976126\pi$
$631$	−3.67758	+	11.3184i	−0.146402	+	0.450579i	0.850787	+	0.525511i	$0.176126\pi$
$632$	6.59452	−	4.79120i	0.262316	−	0.190584i
$633$	4.33580	+	3.15015i	0.172333	+	0.125207i
$634$	−7.54980	−	23.2359i	−0.299841	−	0.922816i
$635$	12.2786	+	8.92093i	0.487261	+	0.354016i
$636$	2.60363	+	1.89165i	0.103241	+	0.0750087i
$637$	5.23468	+	16.1107i	0.207405	+	0.638328i
$638$	20.9880	+	15.2487i	0.830922	+	0.603700i
$639$	−11.5009	+	8.35587i	−0.454967	+	0.330553i
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	7.34738	−	5.33818i	0.290204	−	0.210846i	−0.433152	−	0.901321i	$-0.642599\pi$
$641$	7.34738	−	5.33818i	0.290204	−	0.210846i	0.723356	+	0.690475i	$0.242599\pi$
$642$	0.227946	+	0.701545i	0.00899631	+	0.0276878i
$643$	−12.5966	−	38.7684i	−0.496763	−	1.52888i	−0.814192	−	0.580596i	$-0.802819\pi$
$643$	−12.5966	−	38.7684i	−0.496763	−	1.52888i	0.317429	−	0.948282i	$-0.397181\pi$
$644$	−5.55997	+	17.1118i	−0.219094	+	0.674301i
$645$	−6.30914			−0.248422
$646$	−32.7860			−1.28995
$647$	−8.62743	+	26.5525i	−0.339179	+	1.04389i	0.625447	+	0.780267i	$0.284917\pi$
$647$	−8.62743	+	26.5525i	−0.339179	+	1.04389i	−0.964627	+	0.263620i	$0.915083\pi$
$648$	−0.809017	−	0.587785i	−0.0317812	−	0.0230904i
$649$	6.92235	−	5.02938i	0.271726	−	0.197421i
$650$	−5.81370			−0.228032
$651$	6.08240	−	9.46982i	0.238388	−	0.371152i
$652$	−12.8405			−0.502872
$653$	−12.8568	+	9.34098i	−0.503124	+	0.365541i	−0.810209	−	0.586141i	$-0.800646\pi$
$653$	−12.8568	+	9.34098i	−0.503124	+	0.365541i	0.307085	+	0.951682i	$0.400646\pi$
$654$	−3.87416	−	2.81474i	−0.151492	−	0.110065i
$655$	0.608270	−	1.87206i	0.0237671	−	0.0731476i
$656$	−7.60135			−0.296783
$657$	6.84226			0.266942
$658$	0.552321	−	1.69987i	0.0215317	−	0.0662678i
$659$	−5.90127	−	18.1623i	−0.229881	−	0.707501i	−0.997759	−	0.0669053i	$-0.978687\pi$
$659$	−5.90127	−	18.1623i	−0.229881	−	0.707501i	0.767878	−	0.640596i	$-0.221313\pi$
$660$	1.08411	+	3.33653i	0.0421987	+	0.129874i
$661$	−4.80380	+	3.49016i	−0.186846	+	0.135752i	−0.677276	−	0.735729i	$-0.736840\pi$
$661$	−4.80380	+	3.49016i	−0.186846	+	0.135752i	0.490430	+	0.871481i	$0.336840\pi$
$662$	−2.06709	+	6.36185i	−0.0803397	+	0.247260i
$663$	20.0977	−	14.6019i	0.780531	−	0.567089i
$664$	−11.2813	−	8.19631i	−0.437798	−	0.318079i
$665$	−4.79287	−	14.7509i	−0.185860	−	0.572017i
$666$	0.118034	+	0.0857567i	0.00457372	+	0.00332301i
$667$	−53.2489	−	38.6876i	−2.06181	−	1.49799i
$668$	4.26928	+	13.1395i	0.165183	+	0.508382i
$669$	−4.39912	−	3.19615i	−0.170080	−	0.123570i
$670$	0.326240	−	0.237027i	0.0126037	−	0.00915715i
$671$	−0.100670	+	0.309830i	−0.00388631	+	0.0119608i
$672$	1.63538	−	1.18817i	0.0630862	−	0.0458348i
$673$	−3.98911	−	12.2772i	−0.153769	−	0.473252i	0.844265	−	0.535926i	$-0.180037\pi$
$673$	−3.98911	−	12.2772i	−0.153769	−	0.473252i	−0.998034	+	0.0626735i	$0.980037\pi$
$674$	3.57401	+	10.9997i	0.137666	+	0.423691i
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$	20.7991			0.799964
$677$	−5.71307			−0.219571			−0.109786	−	0.993955i	$-0.535016\pi$
$677$	−5.71307			−0.219571			−0.109786	+	0.993955i	$0.535016\pi$
$678$	−2.09182	+	6.43797i	−0.0803359	+	0.247249i
$679$	6.06303	+	4.40505i	0.232678	+	0.169050i
$680$	−3.45696	+	2.51163i	−0.132568	+	0.0963166i
$681$	−11.8699			−0.454857
$682$	12.3686	+	15.1181i	0.473618	+	0.578903i
$683$	21.7834			0.833519			0.416759	−	0.909017i	$-0.363166\pi$
$683$	21.7834			0.833519			0.416759	+	0.909017i	$0.363166\pi$
$684$	−6.20740	+	4.50994i	−0.237346	+	0.172442i
$685$	4.09593	+	2.97586i	0.156497	+	0.113702i
$686$	−6.19274	+	19.0593i	−0.236440	+	0.727687i
$687$	6.87944			0.262467
$688$	−6.30914			−0.240534
$689$	−5.78171	+	17.7943i	−0.220266	+	0.677908i
$690$	−2.75050	−	8.46516i	−0.104710	−	0.322263i
$691$	11.7805	+	36.2567i	0.448152	+	1.37927i	0.878990	+	0.476841i	$0.158218\pi$
$691$	11.7805	+	36.2567i	0.448152	+	1.37927i	−0.430838	+	0.902429i	$0.641782\pi$
$692$	−2.48081	+	1.80241i	−0.0943063	+	0.0685175i
$693$	2.19146	−	6.74461i	0.0832466	−	0.256207i
$694$	13.1444	−	9.55000i	0.498956	−	0.362513i
$695$	−13.2361	−	9.61661i	−0.502075	−	0.364779i
$696$	2.28511	+	7.03283i	0.0866167	+	0.266579i
$697$	−26.2776	−	19.0918i	−0.995334	−	0.723152i
$698$	15.4499	+	11.2250i	0.584787	+	0.424872i
$699$	0.105027	+	0.323239i	0.00397247	+	0.0122260i
$700$	−1.63538	−	1.18817i	−0.0618116	−	0.0449088i
$701$	−9.83429	+	7.14503i	−0.371436	+	0.269864i	−0.757806	−	0.652480i	$-0.773729\pi$
$701$	−9.83429	+	7.14503i	−0.371436	+	0.269864i	0.386370	+	0.922344i	$0.373729\pi$
$702$	1.79653	−	5.52915i	0.0678057	−	0.208684i
$703$	0.905647	−	0.657991i	0.0341571	−	0.0248166i
$704$	1.08411	+	3.33653i	0.0408588	+	0.125750i
$705$	0.273231	+	0.840919i	0.0102905	+	0.0316709i
$706$	−4.83023	+	14.8659i	−0.181788	+	0.559486i
$707$	31.1439			1.17129
$708$	2.43897			0.0916622
$709$	−9.40355	+	28.9411i	−0.353158	+	1.08691i	0.603913	+	0.797051i	$0.293608\pi$
$709$	−9.40355	+	28.9411i	−0.353158	+	1.08691i	−0.957070	+	0.289857i	$0.906392\pi$
$710$	11.5009	+	8.35587i	0.431620	+	0.313590i
$711$	6.59452	−	4.79120i	0.247314	−	0.179684i
$712$	11.4664			0.429722
$713$	−31.3805	−	38.3564i	−1.17521	−	1.43646i
$714$	8.63771			0.323258
$715$	−16.5006	+	11.9884i	−0.617086	+	0.448340i
$716$	−9.84536	−	7.15307i	−0.367938	−	0.267323i
$717$	−8.28620	+	25.5023i	−0.309454	+	0.952401i
$718$	−9.29914			−0.347041
$719$	35.4954			1.32376			0.661878	−	0.749612i	$-0.269760\pi$
$719$	35.4954			1.32376			0.661878	+	0.749612i	$0.269760\pi$
$720$	−0.309017	+	0.951057i	−0.0115164	+	0.0354438i
$721$	−2.40768	−	7.41007i	−0.0896667	−	0.275966i
$722$	12.3209	+	37.9199i	0.458537	+	1.41123i
$723$	−19.5061	+	14.1720i	−0.725440	+	0.527063i
$724$	3.28631	−	10.1142i	0.122135	−	0.375892i
$725$	5.98249	−	4.34653i	0.222184	−	0.161426i
$726$	1.05798	+	0.768667i	0.0392653	+	0.0285279i
$727$	−10.6944	−	32.9140i	−0.396634	−	1.22071i	−0.927682	−	0.373372i	$-0.878201\pi$
$727$	−10.6944	−	32.9140i	−0.396634	−	1.22071i	0.531048	−	0.847342i	$-0.321799\pi$
$728$	9.50761	+	6.90768i	0.352376	+	0.256016i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−2.11437	−	6.50737i	−0.0782565	−	0.240849i
$731$	−21.8105	−	15.8462i	−0.806689	−	0.586094i
$732$	−0.0751251	+	0.0545816i	−0.00277670	+	0.00201739i
$733$	−4.01280	+	12.3501i	−0.148216	+	0.456162i	−0.997411	−	0.0719179i	$-0.977088\pi$
$733$	−4.01280	+	12.3501i	−0.148216	+	0.456162i	0.849194	+	0.528080i	$0.177088\pi$
$734$	16.0076	−	11.6302i	0.590853	−	0.429280i
$735$	−0.900404	−	2.77116i	−0.0332119	−	0.102216i
$736$	−2.75050	−	8.46516i	−0.101385	−	0.312030i
$737$	0.437170	−	1.34547i	0.0161034	−	0.0495611i
$738$	−7.60135			−0.279809
$739$	−40.4669			−1.48860			−0.744300	−	0.667845i	$-0.767217\pi$
$739$	−40.4669			−1.48860			−0.744300	+	0.667845i	$0.767217\pi$
$740$	0.0450850	−	0.138757i	0.00165736	−	0.00510082i
$741$	−36.0879	−	26.2194i	−1.32572	−	0.963194i
$742$	−5.26309	+	3.82386i	−0.193214	+	0.140378i
$743$	23.2603			0.853339			0.426669	−	0.904408i	$-0.359687\pi$
$743$	23.2603			0.853339			0.426669	+	0.904408i	$0.359687\pi$
$744$	0.319304	+	5.55860i	0.0117062	+	0.203788i
$745$	17.4579			0.639609
$746$	9.43161	−	6.85246i	0.345316	−	0.250886i
$747$	−11.2813	−	8.19631i	−0.412760	−	0.299887i
$748$	−4.63242	+	14.2571i	−0.169378	+	0.521293i
$749$	−1.49111			−0.0544841
$750$	1.00000			0.0365148
$751$	8.50237	−	26.1676i	0.310256	−	0.954870i	−0.667407	−	0.744693i	$-0.732596\pi$
$751$	8.50237	−	26.1676i	0.310256	−	0.954870i	0.977663	−	0.210177i	$-0.0674040\pi$
$752$	0.273231	+	0.840919i	0.00996372	+	0.0306652i
$753$	−5.53840	−	17.0455i	−0.201831	−	0.621171i
$754$	−34.7804	+	25.2694i	−1.26663	+	0.920257i
$755$	−3.07424	+	9.46153i	−0.111883	+	0.344340i
$756$	1.63538	−	1.18817i	0.0594783	−	0.0432135i
$757$	−17.3899	−	12.6345i	−0.632048	−	0.459210i	0.225061	−	0.974345i	$-0.427742\pi$
$757$	−17.3899	−	12.6345i	−0.632048	−	0.459210i	−0.857109	+	0.515135i	$0.827742\pi$
$758$	−5.78761	−	17.8124i	−0.210215	−	0.646976i
$759$	−25.2625	−	18.3543i	−0.916969	−	0.666217i
$760$	6.20740	+	4.50994i	0.225166	+	0.163593i
$761$	6.87355	+	21.1546i	0.249166	+	0.766854i	0.994923	+	0.100636i	$0.0320879\pi$
$761$	6.87355	+	21.1546i	0.249166	+	0.766854i	−0.745757	+	0.666218i	$0.767912\pi$
$762$	12.2786	+	8.92093i	0.444807	+	0.323171i
$763$	7.83139	−	5.68984i	0.283515	−	0.205986i
$764$	2.84891	−	8.76803i	0.103070	−	0.317216i
$765$	−3.45696	+	2.51163i	−0.124987	+	0.0908082i
$766$	−8.41161	−	25.8883i	−0.303924	−	0.935382i
$767$	4.38169	+	13.4855i	0.158214	+	0.486932i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	46.5515			1.67869			0.839344	−	0.543600i	$-0.182939\pi$
$769$	46.5515			1.67869			0.839344	+	0.543600i	$0.182939\pi$
$770$	−7.09170			−0.255567
$771$	−7.25010	+	22.3135i	−0.261106	+	0.803602i
$772$	−5.11188	−	3.71400i	−0.183981	−	0.133670i
$773$	14.8247	−	10.7707i	0.533206	−	0.387397i	−0.288350	−	0.957525i	$-0.593107\pi$
$773$	14.8247	−	10.7707i	0.533206	−	0.387397i	0.821556	+	0.570128i	$0.193107\pi$
$774$	−6.30914			−0.226777
$775$	5.18787	−	2.02138i	0.186354	−	0.0726100i
$776$	−3.70741			−0.133088
$777$	−0.238599	+	0.173352i	−0.00855969	+	0.00621898i
$778$	−25.9274	−	18.8373i	−0.929542	−	0.675352i
$779$	−18.0229	+	55.4688i	−0.645738	+	1.98738i
$780$	−5.81370			−0.208164
$781$	49.8726			1.78458
$782$	11.7530	−	36.1720i	0.420286	−	1.29351i
$783$	2.28511	+	7.03283i	0.0816630	+	0.251333i
$784$	−0.900404	−	2.77116i	−0.0321573	−	0.0989700i
$785$	17.9063	−	13.0097i	0.639103	−	0.464335i
$786$	0.608270	−	1.87206i	0.0216963	−	0.0667743i
$787$	25.4816	−	18.5134i	0.908319	−	0.659933i	−0.0322698	−	0.999479i	$-0.510274\pi$
$787$	25.4816	−	18.5134i	0.908319	−	0.659933i	0.940589	+	0.339546i	$0.110274\pi$
$788$	−12.6243	−	9.17211i	−0.449723	−	0.326743i
$789$	−8.33487	−	25.6521i	−0.296729	−	0.913239i
$790$	−6.59452	−	4.79120i	−0.234622	−	0.170463i
$791$	−11.0704	−	8.04308i	−0.393616	−	0.285979i
$792$	1.08411	+	3.33653i	0.0385220	+	0.118559i
$793$	−0.436755	−	0.317321i	−0.0155096	−	0.0112684i
$794$	−23.5956	+	17.1432i	−0.837377	+	0.608390i
$795$	0.994498	−	3.06075i	0.0352712	−	0.108554i
$796$	−19.6984	+	14.3117i	−0.698190	+	0.507265i
$797$	4.37189	+	13.4553i	0.154860	+	0.476610i	0.998147	−	0.0608537i	$-0.0193823\pi$
$797$	4.37189	+	13.4553i	0.154860	+	0.476610i	−0.843287	+	0.537464i	$0.819382\pi$
$798$	−4.79287	−	14.7509i	−0.169666	−	0.522178i
$799$	−1.16753	+	3.59328i	−0.0413042	+	0.127121i
$800$	1.00000			0.0353553
$801$	11.4664			0.405146
$802$	−1.58841	+	4.88862i	−0.0560887	+	0.172623i
$803$	−19.4199	−	14.1094i	−0.685312	−	0.497908i
$804$	0.326240	−	0.237027i	0.0115056	−	0.00835930i
$805$	17.9925			0.634151
$806$	−30.1607	+	11.7517i	−1.06237	+	0.413935i
$807$	−26.5991			−0.936333
$808$	−12.4643	+	9.05587i	−0.438494	+	0.318584i
$809$	19.5729	+	14.2205i	0.688146	+	0.499967i	0.876050	−	0.482220i	$-0.160169\pi$
$809$	19.5729	+	14.2205i	0.688146	+	0.499967i	−0.187904	+	0.982187i	$0.560169\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	36.1618			1.26981			0.634907	−	0.772589i	$-0.281039\pi$
$811$	36.1618			1.26981			0.634907	+	0.772589i	$0.281039\pi$
$812$	−14.9481			−0.524575
$813$	−5.79493	+	17.8350i	−0.203237	+	0.625500i
$814$	−0.158169	−	0.486794i	−0.00554381	−	0.0170621i
$815$	3.96793	+	12.2120i	0.138990	+	0.427769i
$816$	−3.45696	+	2.51163i	−0.121018	+	0.0879246i
$817$	−14.9591	+	46.0393i	−0.523352	+	1.61071i
$818$	−20.0673	+	14.5797i	−0.701636	+	0.509769i
$819$	9.50761	+	6.90768i	0.332223	+	0.241374i
$820$	2.34895	+	7.22931i	0.0820287	+	0.252459i
$821$	−36.3404	−	26.4029i	−1.26829	−	0.921466i	−0.269157	−	0.963096i	$-0.586745\pi$
$821$	−36.3404	−	26.4029i	−1.26829	−	0.921466i	−0.999133	+	0.0416300i	$0.986745\pi$
$822$	4.09593	+	2.97586i	0.142862	+	0.103795i
$823$	−4.25998	−	13.1109i	−0.148493	−	0.457016i	0.848950	−	0.528473i	$-0.177235\pi$
$823$	−4.25998	−	13.1109i	−0.148493	−	0.457016i	−0.997444	+	0.0714570i	$0.977235\pi$
$824$	3.11826	+	2.26555i	0.108630	+	0.0789241i
$825$	2.83822	−	2.06209i	0.0988143	−	0.0717928i
$826$	−1.52353	+	4.68894i	−0.0530104	+	0.163149i
$827$	28.4141	−	20.6440i	0.988054	−	0.717863i	0.0285595	−	0.999592i	$-0.490908\pi$
$827$	28.4141	−	20.6440i	0.988054	−	0.717863i	0.959494	+	0.281729i	$0.0909080\pi$
$828$	−2.75050	−	8.46516i	−0.0955864	−	0.294185i
$829$	−17.1407	−	52.7536i	−0.595320	−	1.83221i	−0.553127	−	0.833097i	$-0.686566\pi$
$829$	−17.1407	−	52.7536i	−0.595320	−	1.83221i	−0.0421932	−	0.999109i	$-0.513434\pi$
$830$	−4.30906	+	13.2619i	−0.149570	+	0.460328i
$831$	−12.9504			−0.449243
$832$	−5.81370			−0.201554
$833$	3.84746	−	11.8413i	0.133307	−	0.410276i
$834$	−13.2361	−	9.61661i	−0.458330	−	0.332996i
$835$	11.1771	−	8.12065i	0.386800	−	0.281027i
$836$	26.9179			0.930975
$837$	0.319304	+	5.55860i	0.0110367	+	0.192133i
$838$	−6.02939			−0.208282
$839$	−37.9881	+	27.6000i	−1.31150	+	0.952858i	−0.311500	+	0.950246i	$0.600831\pi$
$839$	−37.9881	+	27.6000i	−1.31150	+	0.952858i	−0.999997	+	0.00261167i	$0.999169\pi$
$840$	−1.63538	−	1.18817i	−0.0564260	−	0.0409959i
$841$	7.93631	−	24.4255i	0.273666	−	0.842257i
$842$	−21.6337			−0.745548
$843$	−14.9481			−0.514841
$844$	1.65613	−	5.09704i	0.0570063	−	0.175447i
$845$	−6.42726	−	19.7811i	−0.221105	−	0.680490i
$846$	0.273231	+	0.840919i	0.00939388	+	0.0289114i
$847$	−2.13865	+	1.55382i	−0.0734847	+	0.0533898i
$848$	0.994498	−	3.06075i	0.0341512	−	0.105107i
$849$	−11.3856	+	8.27212i	−0.390753	+	0.283899i
$850$	3.45696	+	2.51163i	0.118573	+	0.0861482i
$851$	0.401292	+	1.23505i	0.0137561	+	0.0423370i
$852$	11.5009	+	8.35587i	0.394013	+	0.286267i
$853$	27.4793	+	19.9649i	0.940874	+	0.683585i	0.948631	−	0.316385i	$-0.102469\pi$
$853$	27.4793	+	19.9649i	0.940874	+	0.683585i	−0.00775651	+	0.999970i	$0.502469\pi$
$854$	−0.0580058	−	0.178523i	−0.00198492	−	0.00610895i
$855$	6.20740	+	4.50994i	0.212289	+	0.154237i
$856$	0.596770	−	0.433579i	0.0203972	−	0.0148194i
$857$	−1.68697	+	5.19197i	−0.0576259	+	0.177354i	−0.975726	−	0.218994i	$-0.929723\pi$
$857$	−1.68697	+	5.19197i	−0.0576259	+	0.177354i	0.918100	+	0.396348i	$0.129723\pi$
$858$	−16.5006	+	11.9884i	−0.563320	+	0.409276i
$859$	7.28779	+	22.4295i	0.248656	+	0.765285i	0.995014	+	0.0997397i	$0.0318010\pi$
$859$	7.28779	+	22.4295i	0.248656	+	0.765285i	−0.746357	+	0.665545i	$0.768199\pi$
$860$	1.94963	+	6.00035i	0.0664819	+	0.204610i
$861$	4.74826	−	14.6136i	0.161820	−	0.498031i
$862$	−21.4171			−0.729470
$863$	−31.7061			−1.07929			−0.539644	−	0.841893i	$-0.681441\pi$
$863$	−31.7061			−1.07929			−0.539644	+	0.841893i	$0.681441\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	2.48081	+	1.80241i	0.0843501	+	0.0612839i
$866$	7.74414	−	5.62645i	0.263157	−	0.191195i
$867$	−1.25887			−0.0427534
$868$	−10.8859	−	2.85837i	−0.369492	−	0.0970195i
$869$	−28.5966			−0.970074
$870$	5.98249	−	4.34653i	0.202825	−	0.147361i
$871$	1.89666	+	1.37800i	0.0642658	+	0.0466918i
$872$	−1.47980	+	4.55435i	−0.0501123	+	0.154230i
$873$	−3.70741			−0.125477
$874$	−68.2937			−2.31007
$875$	−0.624660	+	1.92251i	−0.0211174	+	0.0649926i
$876$	−2.11437	−	6.50737i	−0.0714381	−	0.219864i
$877$	9.97614	+	30.7034i	0.336870	+	1.03678i	0.965793	+	0.259313i	$0.0834960\pi$
$877$	9.97614	+	30.7034i	0.336870	+	1.03678i	−0.628923	+	0.777467i	$0.716504\pi$
$878$	20.6614	−	15.0114i	0.697288	−	0.506609i
$879$	−3.93551	+	12.1123i	−0.132741	+	0.408536i
$880$	2.83822	−	2.06209i	0.0956765	−	0.0695131i
$881$	−32.4063	−	23.5445i	−1.09179	−	0.793235i	−0.112093	−	0.993698i	$-0.535756\pi$
$881$	−32.4063	−	23.5445i	−1.09179	−	0.793235i	−0.979701	+	0.200462i	$0.935756\pi$
$882$	−0.900404	−	2.77116i	−0.0303182	−	0.0933098i
$883$	9.13498	+	6.63695i	0.307417	+	0.223351i	0.730787	−	0.682605i	$-0.239153\pi$
$883$	9.13498	+	6.63695i	0.307417	+	0.223351i	−0.423371	+	0.905957i	$0.639153\pi$
$884$	−20.0977	−	14.6019i	−0.675960	−	0.491113i
$885$	−0.753684	−	2.31960i	−0.0253348	−	0.0779726i
$886$	7.05821	+	5.12809i	0.237125	+	0.172282i
$887$	46.5074	−	33.7896i	1.56157	−	1.13454i	0.626856	−	0.779135i	$-0.284341\pi$
$887$	46.5074	−	33.7896i	1.56157	−	1.13454i	0.934711	−	0.355410i	$-0.115659\pi$
$888$	0.0450850	−	0.138757i	0.00151295	−	0.00465639i
$889$	−24.8205	+	18.0331i	−0.832453	+	0.604812i
$890$	−3.54332	−	10.9052i	−0.118772	−	0.365544i
$891$	1.08411	+	3.33653i	0.0363189	+	0.111778i
$892$	−1.68031	+	5.17147i	−0.0562611	+	0.173154i
$893$	6.78422			0.227025
$894$	17.4579			0.583881
$895$	−3.76059	+	11.5739i	−0.125703	+	0.386873i
$896$	−1.63538	−	1.18817i	−0.0546343	−	0.0396941i
$897$	41.8638	−	30.4158i	1.39779	−	1.01556i
$898$	0.891099			0.0297364
$899$	22.2504	−	34.6421i	0.742092	−	1.15538i
$900$	1.00000			0.0333333
$901$	11.1254	−	8.08308i	0.370641	−	0.269287i
$902$	21.5743	+	15.6747i	0.718347	+	0.521909i
$903$	3.94107	−	12.1294i	0.131151	−	0.403640i
$904$	6.76928			0.225143
$905$	−10.6347			−0.353510
$906$	−3.07424	+	9.46153i	−0.102135	+	0.314338i
$907$	3.77463	+	11.6171i	0.125335	+	0.385740i	0.993962	−	0.109726i	$-0.0349973\pi$
$907$	3.77463	+	11.6171i	0.125335	+	0.385740i	−0.868627	+	0.495466i	$0.834997\pi$
$908$	3.66801	+	11.2890i	0.121727	+	0.374638i
$909$	−12.4643	+	9.05587i	−0.413416	+	0.300364i
$910$	3.63158	−	11.1769i	0.120386	−	0.370510i
$911$	7.81943	−	5.68115i	0.259069	−	0.188225i	−0.450667	−	0.892692i	$-0.648814\pi$
$911$	7.81943	−	5.68115i	0.259069	−	0.188225i	0.709737	+	0.704467i	$0.248814\pi$
$912$	6.20740	+	4.50994i	0.205547	+	0.149339i
$913$	15.1172	+	46.5259i	0.500306	+	1.53978i
$914$	−15.8186	−	11.4929i	−0.523234	−	0.380152i
$915$	0.0751251	+	0.0545816i	0.00248356	+	0.00180441i
$916$	−2.12586	−	6.54273i	−0.0702405	−	0.216178i
$917$	3.21909	+	2.33881i	0.106304	+	0.0772342i
$918$	−3.45696	+	2.51163i	−0.114097	+	0.0828961i
$919$	5.17560	−	15.9289i	0.170727	−	0.525445i	−0.828685	−	0.559715i	$-0.810911\pi$
$919$	5.17560	−	15.9289i	0.170727	−	0.525445i	0.999413	+	0.0342703i	$0.0109107\pi$
$920$	−7.20090	+	5.23176i	−0.237407	+	0.172486i
$921$	1.14589	+	3.52668i	0.0377583	+	0.116208i
$922$	6.68503	+	20.5744i	0.220160	+	0.677582i
$923$	−25.5392	+	78.6016i	−0.840634	+	2.58720i
$924$	−7.09170			−0.233300
$925$	−0.145898			−0.00479710
$926$	−7.77299	+	23.9228i	−0.255436	+	0.786152i
$927$	3.11826	+	2.26555i	0.102417	+	0.0744104i
$928$	5.98249	−	4.34653i	0.196385	−	0.142682i
$929$	−26.7225			−0.876737			−0.438368	−	0.898795i	$-0.644443\pi$
$929$	−26.7225			−0.876737			−0.438368	+	0.898795i	$0.644443\pi$
$930$	5.18787	−	2.02138i	0.170117	−	0.0662836i
$931$	−22.3567			−0.732710
$932$	0.274963	−	0.199772i	0.00900672	−	0.00654377i
$933$	−17.3265	−	12.5885i	−0.567245	−	0.412128i
$934$	−10.0783	+	31.0178i	−0.329772	+	1.01493i
$935$	14.9908			0.490253
$936$	−5.81370			−0.190027
$937$	6.47494	−	19.9278i	0.211527	−	0.651014i	−0.787855	−	0.615861i	$-0.788808\pi$
$937$	6.47494	−	19.9278i	0.211527	−	0.651014i	0.999382	−	0.0351525i	$-0.0111917\pi$
$938$	0.251897	+	0.775259i	0.00822473	+	0.0253131i
$939$	10.1154	+	31.1321i	0.330105	+	1.01596i
$940$	0.715329	−	0.519717i	0.0233315	−	0.0169513i
$941$	7.02736	−	21.6280i	0.229085	−	0.705052i	−0.768766	−	0.639530i	$-0.779129\pi$
$941$	7.02736	−	21.6280i	0.229085	−	0.705052i	0.997851	−	0.0655216i	$-0.0208711\pi$
$942$	17.9063	−	13.0097i	0.583418	−	0.423878i
$943$	−54.7365	−	39.7684i	−1.78247	−	1.29504i
$944$	−0.753684	−	2.31960i	−0.0245303	−	0.0754966i
$945$	−1.63538	−	1.18817i	−0.0531990	−	0.0386513i
$946$	17.9068	+	13.0100i	0.582199	+	0.422992i
$947$	−5.81217	−	17.8880i	−0.188870	−	0.581283i	0.811123	−	0.584875i	$-0.198856\pi$
$947$	−5.81217	−	17.8880i	−0.188870	−	0.581283i	−0.999994	+	0.00359249i	$0.998856\pi$
$948$	−6.59452	−	4.79120i	−0.214180	−	0.155611i
$949$	32.1817	−	23.3814i	1.04466	−	0.758992i
$950$	2.37101	−	7.29723i	0.0769259	−	0.236754i
$951$	−19.7656	+	14.3606i	−0.640945	+	0.465674i
$952$	−2.66920	−	8.21495i	−0.0865092	−	0.266248i
$953$	−9.50112	−	29.2414i	−0.307772	−	0.947223i	−0.978628	−	0.205637i	$-0.934074\pi$
$953$	−9.50112	−	29.2414i	−0.307772	−	0.947223i	0.670857	−	0.741587i	$-0.265926\pi$
$954$	0.994498	−	3.06075i	0.0321981	−	0.0990954i
$955$	−9.21926			−0.298328
$956$	26.8147			0.867250
$957$	8.01670	−	24.6729i	0.259143	−	0.797560i
$958$	−12.2880	−	8.92773i	−0.397006	−	0.288442i
$959$	−8.27968	+	6.01554i	−0.267365	+	0.194252i
$960$	1.00000			0.0322749
$961$	22.8281	−	20.9733i	0.736389	−	0.676558i
$962$	0.848207			0.0273473
$963$	0.596770	−	0.433579i	0.0192306	−	0.0139719i
$964$	19.5061	+	14.1720i	0.628249	+	0.456450i
$965$	−1.95257	+	6.00938i	−0.0628553	+	0.193449i
$966$	17.9925			0.578898
$967$	48.3123			1.55362			0.776810	−	0.629735i	$-0.216836\pi$
$967$	48.3123			1.55362			0.776810	+	0.629735i	$0.216836\pi$
$968$	0.404112	−	1.24373i	0.0129887	−	0.0399750i
$969$	10.1314	+	31.1814i	0.325469	+	1.00169i
$970$	1.14565	+	3.52596i	0.0367847	+	0.113212i
$971$	−8.85523	+	6.43370i	−0.284178	+	0.206467i	−0.720738	−	0.693208i	$-0.756197\pi$
$971$	−8.85523	+	6.43370i	−0.284178	+	0.206467i	0.436560	+	0.899675i	$0.356197\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	26.7561	−	19.4394i	0.857760	−	0.623199i
$974$	9.34678	+	6.79083i	0.299490	+	0.217592i
$975$	1.79653	+	5.52915i	0.0575350	+	0.177075i
$976$	0.0751251	+	0.0545816i	0.00240470	+	0.00174711i
$977$	44.7762	+	32.5318i	1.43252	+	1.04078i	0.989541	+	0.144250i	$0.0460769\pi$
$977$	44.7762	+	32.5318i	1.43252	+	1.04078i	0.442975	+	0.896534i	$0.353923\pi$
$978$	3.96793	+	12.2120i	0.126880	+	0.390498i
$979$	−32.5443	−	23.6448i	−1.04012	−	0.755691i
$980$	−2.35729	+	1.71267i	−0.0753008	+	0.0547093i
$981$	−1.47980	+	4.55435i	−0.0472463	+	0.145409i
$982$	−29.2608	+	21.2592i	−0.933748	+	0.678408i
$983$	1.71227	+	5.26982i	0.0546129	+	0.168081i	0.974643	−	0.223768i	$-0.0718356\pi$
$983$	1.71227	+	5.26982i	0.0546129	+	0.168081i	−0.920030	+	0.391849i	$0.871836\pi$
$984$	2.34895	+	7.22931i	0.0748817	+	0.230462i
$985$	−4.82206	+	14.8408i	−0.153644	+	0.472867i
$986$	31.5981			1.00629
$987$	−1.78735			−0.0568920
$988$	−13.7844	+	42.4239i	−0.438539	+	1.34968i
$989$	−45.4315	−	33.0079i	−1.44464	−	1.04959i
$990$	2.83822	−	2.06209i	0.0902047	−	0.0655375i
$991$	−15.8018			−0.501961			−0.250981	−	0.967992i	$-0.580753\pi$
$991$	−15.8018			−0.501961			−0.250981	+	0.967992i	$0.580753\pi$
$992$	5.18787	−	2.02138i	0.164715	−	0.0641788i
$993$	6.68924			0.212277
$994$	−23.2483	+	16.8909i	−0.737393	+	0.535747i
$995$	19.6984	+	14.3117i	0.624480	+	0.453711i
$996$	−4.30906	+	13.2619i	−0.136538	+	0.420220i
$997$	37.1625			1.17695			0.588474	−	0.808516i	$-0.299729\pi$
$997$	37.1625			1.17695			0.588474	+	0.808516i	$0.299729\pi$
$998$	22.6872			0.718150
$999$	0.0450850	−	0.138757i	0.00142643	−	0.00439009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.d.481.3	✓	12
31.2	even	5	inner	930.2.n.d.901.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.d.481.3	✓	12	1.1	even	1	trivial
930.2.n.d.901.3	yes	12	31.2	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.624660 - 1.92251i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.624660 - 1.92251i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.809017 - 0.587785i) q^{10} +(1.08411 - 3.33653i) q^{11} +(0.809017 - 0.587785i) q^{12} +(4.70338 + 3.41721i) q^{13} +(0.624660 + 1.92251i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.32044 - 4.06390i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-6.20740 + 4.50994i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(1.63538 - 1.18817i) q^{21} +(1.08411 + 3.33653i) q^{22} +(-2.75050 - 8.46516i) q^{23} +(-0.309017 + 0.951057i) q^{24} +1.00000 q^{25} -5.81370 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.63538 - 1.18817i) q^{28} +(5.98249 - 4.34653i) q^{29} +1.00000 q^{30} +(5.18787 - 2.02138i) q^{31} +1.00000 q^{32} +(2.83822 - 2.06209i) q^{33} +(3.45696 + 2.51163i) q^{34} +(-0.624660 + 1.92251i) q^{35} +1.00000 q^{36} -0.145898 q^{37} +(2.37101 - 7.29723i) q^{38} +(1.79653 + 5.52915i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(6.14962 - 4.46796i) q^{41} +(-0.624660 + 1.92251i) q^{42} +(5.10420 - 3.70842i) q^{43} +(-2.83822 - 2.06209i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(7.20090 + 5.23176i) q^{46} +(-0.715329 - 0.519717i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(2.35729 + 1.71267i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(1.32044 - 4.06390i) q^{51} +(4.70338 - 3.41721i) q^{52} +(0.994498 + 3.06075i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-1.08411 + 3.33653i) q^{55} +2.02144 q^{56} -7.67276 q^{57} +(-2.28511 + 7.03283i) q^{58} +(1.97317 + 1.43359i) q^{59} +(-0.809017 + 0.587785i) q^{60} -0.0928597 q^{61} +(-3.00894 + 4.68468i) q^{62} +2.02144 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-4.70338 - 3.41721i) q^{65} +(-1.08411 + 3.33653i) q^{66} +0.403254 q^{67} -4.27304 q^{68} +(2.75050 - 8.46516i) q^{69} +(-0.624660 - 1.92251i) q^{70} +(4.39294 + 13.5201i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(2.11437 - 6.50737i) q^{73} +(0.118034 - 0.0857567i) q^{74} +(0.809017 + 0.587785i) q^{75} +(2.37101 + 7.29723i) q^{76} +(-5.73731 - 4.16840i) q^{77} +(-4.70338 - 3.41721i) q^{78} +(-2.51888 - 7.75232i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-2.34895 + 7.22931i) q^{82} +(-11.2813 + 8.19631i) q^{83} +(-0.624660 - 1.92251i) q^{84} +(1.32044 + 4.06390i) q^{85} +(-1.94963 + 6.00035i) q^{86} +7.39476 q^{87} +3.50824 q^{88} +(3.54332 - 10.9052i) q^{89} +(0.809017 + 0.587785i) q^{90} +(9.50761 - 6.90768i) q^{91} -8.90080 q^{92} +(5.38521 + 1.41403i) q^{93} +0.884195 q^{94} +(6.20740 - 4.50994i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-1.14565 + 3.52596i) q^{97} -2.91377 q^{98} +3.50824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

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