LMFDB - Embedded newform 1170.2.bs.g.361.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(361,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4,0,0,0,0,0,4,6,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$1.20036 + 0.747754i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.g.901.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-3.45632 - 1.99551i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.142181 + 0.0820885i) q^{11} +(1.50821 - 3.27495i) q^{13} -3.99102 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.783937 + 1.35782i) q^{17} +(-0.716063 - 0.413419i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.0820885 + 0.142181i) q^{22} +(-3.49551 - 6.05440i) q^{23} -1.00000 q^{25} +(-0.331331 - 3.59030i) q^{26} +(-3.45632 + 1.99551i) q^{28} +(-2.92163 - 5.06040i) q^{29} +0.0858029i q^{31} +(-0.866025 - 0.500000i) q^{32} +1.56787i q^{34} +(1.99551 - 3.45632i) q^{35} +(-7.24026 + 4.18016i) q^{37} -0.826838 q^{38} +1.00000 q^{40} +(-7.48652 + 4.32235i) q^{41} +(5.62828 - 9.74846i) q^{43} +0.164177i q^{44} +(-6.05440 - 3.49551i) q^{46} -5.31634i q^{47} +(4.46410 + 7.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-2.08209 - 2.94362i) q^{52} -10.3538 q^{53} +(-0.0820885 - 0.142181i) q^{55} +(-1.99551 + 3.45632i) q^{56} +(-5.06040 - 2.92163i) q^{58} +(3.00000 + 1.73205i) q^{59} +(3.21606 - 5.57038i) q^{61} +(0.0429015 + 0.0743075i) q^{62} -1.00000 q^{64} +(3.27495 + 1.50821i) q^{65} +(13.2566 - 7.65368i) q^{67} +(0.783937 + 1.35782i) q^{68} -3.99102i q^{70} +(5.19615 + 3.00000i) q^{71} +0.179739i q^{73} +(-4.18016 + 7.24026i) q^{74} +(-0.716063 + 0.413419i) q^{76} +0.655233 q^{77} -6.21257 q^{79} +(0.866025 - 0.500000i) q^{80} +(-4.32235 + 7.48652i) q^{82} -1.23952i q^{83} +(-1.35782 - 0.783937i) q^{85} -11.2566i q^{86} +(0.0820885 + 0.142181i) q^{88} +(8.98652 - 5.18837i) q^{89} +(-11.7480 + 8.30965i) q^{91} -6.99102 q^{92} +(-2.65817 - 4.60408i) q^{94} +(0.413419 - 0.716063i) q^{95} +(16.3853 + 9.46004i) q^{97} +(7.73205 + 4.46410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{10} + 6 q^{11} - 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} + 6 q^{22} - 12 q^{23} - 8 q^{25} - 30 q^{37} + 12 q^{38} + 8 q^{40} - 12 q^{41} + 4 q^{43} + 8 q^{49} - 10 q^{52} - 60 q^{53}+ \cdots + 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^10 + 6 * q^11 - 2 * q^13 - 4 * q^16 - 6 * q^17 - 6 * q^19 + 6 * q^22 - 12 * q^23 - 8 * q^25 - 30 * q^37 + 12 * q^38 + 8 * q^40 - 12 * q^41 + 4 * q^43 + 8 * q^49 - 10 * q^52 - 60 * q^53 + 6 * q^55 + 24 * q^59 + 26 * q^61 - 18 * q^62 - 8 * q^64 - 6 * q^65 + 24 * q^67 + 6 * q^68 - 6 * q^74 - 6 * q^76 + 60 * q^77 + 20 * q^79 - 18 * q^85 - 6 * q^88 + 24 * q^89 - 66 * q^91 - 24 * q^92 - 6 * q^95 - 6 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−3.45632	−	1.99551i	−1.30637	−	0.754231i	−0.324879	−	0.945756i	$-0.605323\pi$
$7$	−3.45632	−	1.99551i	−1.30637	−	0.754231i	−0.981488	+	0.191525i	$0.938657\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.142181	+	0.0820885i	−0.0428693	+	0.0247506i	−0.521281	−	0.853385i	$-0.674546\pi$
$11$	−0.142181	+	0.0820885i	−0.0428693	+	0.0247506i	0.478412	+	0.878135i	$0.341212\pi$
$12$		0			0
$13$	1.50821	−	3.27495i	0.418301	−	0.908308i
$13$	1.50821	−	3.27495i	0.418301	−	0.908308i
$14$	−3.99102			−1.06664
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.783937	+	1.35782i	−0.190133	+	0.329319i	−0.945294	−	0.326220i	$-0.894225\pi$
$17$	−0.783937	+	1.35782i	−0.190133	+	0.329319i	0.755161	+	0.655539i	$0.227558\pi$
$18$		0			0
$19$	−0.716063	−	0.413419i	−0.164276	−	0.0948449i	0.415608	−	0.909544i	$-0.363569\pi$
$19$	−0.716063	−	0.413419i	−0.164276	−	0.0948449i	−0.579884	+	0.814699i	$0.696902\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		0			0
$22$	−0.0820885	+	0.142181i	−0.0175013	+	0.0303132i
$23$	−3.49551	−	6.05440i	−0.728864	−	1.26243i	−0.957364	−	0.288885i	$-0.906715\pi$
$23$	−3.49551	−	6.05440i	−0.728864	−	1.26243i	0.228500	−	0.973544i	$-0.426618\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.331331	−	3.59030i	−0.0649793	−	0.704115i
$27$		0			0
$28$	−3.45632	+	1.99551i	−0.653183	+	0.377115i
$29$	−2.92163	−	5.06040i	−0.542532	−	0.939694i	−0.998758	−	0.0498293i	$-0.984132\pi$
$29$	−2.92163	−	5.06040i	−0.542532	−	0.939694i	0.456225	−	0.889864i	$-0.349201\pi$
$30$		0			0
$31$			0.0858029i			0.0154107i	0.999970	+	0.00770533i	$0.00245271\pi$
$31$			0.0858029i			0.0154107i	−0.999970	+	0.00770533i	$0.997547\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			1.56787i			0.268888i
$35$	1.99551	−	3.45632i	0.337302	−	0.584225i
$36$		0			0
$37$	−7.24026	+	4.18016i	−1.19029	+	0.687215i	−0.958373	−	0.285520i	$-0.907834\pi$
$37$	−7.24026	+	4.18016i	−1.19029	+	0.687215i	−0.231918	+	0.972735i	$0.574500\pi$
$38$	−0.826838			−0.134131
$39$		0			0
$40$	1.00000			0.158114
$41$	−7.48652	+	4.32235i	−1.16920	+	0.675037i	−0.953491	−	0.301421i	$-0.902539\pi$
$41$	−7.48652	+	4.32235i	−1.16920	+	0.675037i	−0.215707	+	0.976458i	$0.569206\pi$
$42$		0			0
$43$	5.62828	−	9.74846i	0.858304	−	1.48663i	−0.0152408	−	0.999884i	$-0.504851\pi$
$43$	5.62828	−	9.74846i	0.858304	−	1.48663i	0.873545	−	0.486743i	$-0.161815\pi$
$44$			0.164177i			0.0247506i
$45$		0			0
$46$	−6.05440	−	3.49551i	−0.892672	−	0.515384i
$47$		−	5.31634i		−	0.775468i	−0.921771	−	0.387734i	$-0.873258\pi$
$47$		−	5.31634i		−	0.775468i	0.921771	−	0.387734i	$-0.126742\pi$
$48$		0			0
$49$	4.46410	+	7.73205i	0.637729	+	1.10458i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	−2.08209	−	2.94362i	−0.288734	−	0.408207i
$53$	−10.3538			−1.42220			−0.711099	−	0.703092i	$-0.751802\pi$
$53$	−10.3538			−1.42220			−0.711099	+	0.703092i	$0.751802\pi$
$54$		0			0
$55$	−0.0820885	−	0.142181i	−0.0110688	−	0.0191717i
$56$	−1.99551	+	3.45632i	−0.266661	+	0.461870i
$57$		0			0
$58$	−5.06040	−	2.92163i	−0.664464	−	0.383628i
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	0.682406	−	0.730974i	$-0.260934\pi$
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	−0.291839	+	0.956467i	$0.594267\pi$
$60$		0			0
$61$	3.21606	−	5.57038i	0.411775	−	0.713215i	−0.583309	−	0.812250i	$-0.698242\pi$
$61$	3.21606	−	5.57038i	0.411775	−	0.713215i	0.995084	+	0.0990355i	$0.0315757\pi$
$62$	0.0429015	+	0.0743075i	0.00544849	+	0.00943706i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.27495	+	1.50821i	0.406208	+	0.187070i
$66$		0			0
$67$	13.2566	−	7.65368i	1.61955	−	0.935045i	0.632509	−	0.774553i	$-0.282025\pi$
$67$	13.2566	−	7.65368i	1.61955	−	0.935045i	0.987037	−	0.160493i	$-0.0513083\pi$
$68$	0.783937	+	1.35782i	0.0950663	+	0.164660i
$69$		0			0
$70$		−	3.99102i		−	0.477018i
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$		0			0
$73$			0.179739i			0.0210368i	0.999945	+	0.0105184i	$0.00334818\pi$
$73$			0.179739i			0.0210368i	−0.999945	+	0.0105184i	$0.996652\pi$
$74$	−4.18016	+	7.24026i	−0.485934	+	0.841663i
$75$		0			0
$76$	−0.716063	+	0.413419i	−0.0821381	+	0.0474224i
$77$	0.655233			0.0746707
$78$		0			0
$79$	−6.21257			−0.698968			−0.349484	−	0.936942i	$-0.613643\pi$
$79$	−6.21257			−0.698968			−0.349484	+	0.936942i	$0.613643\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$		0			0
$82$	−4.32235	+	7.48652i	−0.477323	+	0.826748i
$83$		−	1.23952i		−	0.136055i	−0.997683	−	0.0680275i	$-0.978329\pi$
$83$		−	1.23952i		−	0.136055i	0.997683	−	0.0680275i	$-0.0216706\pi$
$84$		0			0
$85$	−1.35782	−	0.783937i	−0.147276	−	0.0850299i
$86$		−	11.2566i		−	1.21383i
$87$		0			0
$88$	0.0820885	+	0.142181i	0.00875066	+	0.0151566i
$89$	8.98652	−	5.18837i	0.952570	−	0.549966i	0.0586913	−	0.998276i	$-0.481307\pi$
$89$	8.98652	−	5.18837i	0.952570	−	0.549966i	0.893878	+	0.448310i	$0.147974\pi$
$90$		0			0
$91$	−11.7480	+	8.30965i	−1.23153	+	0.871088i
$92$	−6.99102			−0.728864
$93$		0			0
$94$	−2.65817	−	4.60408i	−0.274169	−	0.474875i
$95$	0.413419	−	0.716063i	0.0424159	−	0.0734665i
$96$		0			0
$97$	16.3853	+	9.46004i	1.66367	+	0.960521i	0.970939	+	0.239326i	$0.0769264\pi$
$97$	16.3853	+	9.46004i	1.66367	+	0.960521i	0.692732	+	0.721195i	$0.256407\pi$
$98$	7.73205	+	4.46410i	0.781055	+	0.450942i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	7.33384	+	12.7026i	0.729745	+	1.26395i	0.956991	+	0.290117i	$0.0936943\pi$
$101$	7.33384	+	12.7026i	0.729745	+	1.26395i	−0.227247	+	0.973837i	$0.572972\pi$
$102$		0			0
$103$	−2.26795			−0.223468			−0.111734	−	0.993738i	$-0.535640\pi$
$103$	−2.26795			−0.223468			−0.111734	+	0.993738i	$0.535640\pi$
$104$	−3.27495	−	1.50821i	−0.321135	−	0.147892i
$105$		0			0
$106$	−8.96661	+	5.17688i	−0.870914	+	0.502823i
$107$	2.34883	+	4.06830i	0.227070	+	0.393297i	0.956939	−	0.290290i	$-0.0937519\pi$
$107$	2.34883	+	4.06830i	0.227070	+	0.393297i	−0.729868	+	0.683588i	$0.760419\pi$
$108$		0			0
$109$			6.17161i			0.591133i	0.955322	+	0.295566i	$0.0955083\pi$
$109$			6.17161i			0.591133i	−0.955322	+	0.295566i	$0.904492\pi$
$110$	−0.142181	−	0.0820885i	−0.0135565	−	0.00782683i
$111$		0			0
$112$			3.99102i			0.377115i
$113$	5.63726	−	9.76403i	0.530309	−	0.918522i	−0.469066	−	0.883163i	$-0.655409\pi$
$113$	5.63726	−	9.76403i	0.530309	−	0.918522i	0.999375	−	0.0353590i	$-0.0112575\pi$
$114$		0			0
$115$	6.05440	−	3.49551i	0.564575	−	0.325958i
$116$	−5.84325			−0.542532
$117$		0			0
$118$	3.46410			0.318896
$119$	5.41907	−	3.12870i	0.496766	−	0.286808i
$120$		0			0
$121$	−5.48652	+	9.50294i	−0.498775	+	0.863903i
$122$		−	6.43213i		−	0.582337i
$123$		0			0
$124$	0.0743075	+	0.0429015i	0.00667301	+	0.00385266i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	4.06218	+	7.03590i	0.360460	+	0.624335i	0.988037	−	0.154220i	$-0.0492864\pi$
$127$	4.06218	+	7.03590i	0.360460	+	0.624335i	−0.627577	+	0.778555i	$0.715953\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	3.59030	−	0.331331i	0.314890	−	0.0290596i
$131$	−20.8034			−1.81760			−0.908802	−	0.417227i	$-0.863002\pi$
$131$	−20.8034			−1.81760			−0.908802	+	0.417227i	$0.863002\pi$
$132$		0			0
$133$	1.64996	+	2.85782i	0.143070	+	0.247804i
$134$	7.65368	−	13.2566i	0.661177	−	1.14519i
$135$		0			0
$136$	1.35782	+	0.783937i	0.116432	+	0.0672220i
$137$	−4.54796	−	2.62577i	−0.388559	−	0.224334i	0.292977	−	0.956120i	$-0.405354\pi$
$137$	−4.54796	−	2.62577i	−0.388559	−	0.224334i	−0.681535	+	0.731785i	$0.738687\pi$
$138$		0			0
$139$	8.36076	−	14.4813i	0.709150	−	1.22828i	−0.256023	−	0.966671i	$-0.582412\pi$
$139$	8.36076	−	14.4813i	0.709150	−	1.22828i	0.965173	−	0.261613i	$-0.0842544\pi$
$140$	−1.99551	−	3.45632i	−0.168651	−	0.292112i
$141$		0			0
$142$	6.00000			0.503509
$143$	0.0543969	+	0.589444i	0.00454889	+	0.0492918i
$144$		0			0
$145$	5.06040	−	2.92163i	0.420244	−	0.242628i
$146$	0.0898694	+	0.155658i	0.00743765	+	0.0128824i
$147$		0			0
$148$			8.36033i			0.687215i
$149$	8.68868	+	5.01641i	0.711805	+	0.410961i	0.811729	−	0.584034i	$-0.198527\pi$
$149$	8.68868	+	5.01641i	0.711805	+	0.410961i	−0.0999242	+	0.994995i	$0.531860\pi$
$150$		0			0
$151$			10.8752i			0.885013i	0.896765	+	0.442507i	$0.145911\pi$
$151$			10.8752i			0.885013i	−0.896765	+	0.442507i	$0.854089\pi$
$152$	−0.413419	+	0.716063i	−0.0335327	+	0.0580804i
$153$		0			0
$154$	0.567448	−	0.327616i	0.0457263	−	0.0264001i
$155$	−0.0858029			−0.00689185
$156$		0			0
$157$	−17.6922			−1.41199			−0.705997	−	0.708215i	$-0.749501\pi$
$157$	−17.6922			−1.41199			−0.705997	+	0.708215i	$0.749501\pi$
$158$	−5.38024	+	3.10628i	−0.428029	+	0.247123i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			27.9012i			2.19893i
$162$		0			0
$163$	−1.22207	−	0.705563i	−0.0957200	−	0.0552640i	0.451376	−	0.892334i	$-0.350933\pi$
$163$	−1.22207	−	0.705563i	−0.0957200	−	0.0552640i	−0.547096	+	0.837070i	$0.684267\pi$
$164$			8.64469i			0.675037i
$165$		0			0
$166$	−0.619760	−	1.07346i	−0.0481027	−	0.0833163i
$167$	−0.610092	+	0.352237i	−0.0472103	+	0.0272569i	−0.523419	−	0.852075i	$-0.675344\pi$
$167$	−0.610092	+	0.352237i	−0.0472103	+	0.0272569i	0.476209	+	0.879332i	$0.342011\pi$
$168$		0			0
$169$	−8.45062	−	9.87861i	−0.650048	−	0.759893i
$170$	−1.56787			−0.120250
$171$		0			0
$172$	−5.62828	−	9.74846i	−0.429152	−	0.743313i
$173$	−0.327616	+	0.567448i	−0.0249082	+	0.0431423i	−0.878211	−	0.478274i	$-0.841263\pi$
$173$	−0.327616	+	0.567448i	−0.0249082	+	0.0431423i	0.853303	+	0.521416i	$0.174596\pi$
$174$		0			0
$175$	3.45632	+	1.99551i	0.261273	+	0.150846i
$176$	0.142181	+	0.0820885i	0.0107173	+	0.00618765i
$177$		0			0
$178$	5.18837	−	8.98652i	0.388885	−	0.673568i
$179$	−3.70665	−	6.42011i	−0.277048	−	0.479862i	0.693602	−	0.720359i	$-0.256023\pi$
$179$	−3.70665	−	6.42011i	−0.277048	−	0.479862i	−0.970650	+	0.240497i	$0.922690\pi$
$180$		0			0
$181$	−0.496077			−0.0368731			−0.0184366	−	0.999830i	$-0.505869\pi$
$181$	−0.496077			−0.0368731			−0.0184366	+	0.999830i	$0.505869\pi$
$182$	−6.01928	+	13.0704i	−0.446178	+	0.968841i
$183$		0			0
$184$	−6.05440	+	3.49551i	−0.446336	+	0.257692i
$185$	−4.18016	−	7.24026i	−0.307332	−	0.532314i
$186$		0			0
$187$		−	0.257409i		−	0.0188236i
$188$	−4.60408	−	2.65817i	−0.335787	−	0.193867i
$189$		0			0
$190$		−	0.826838i		−	0.0599852i
$191$	12.3972	−	21.4726i	0.897032	−	1.55370i	0.0657616	−	0.997835i	$-0.479052\pi$
$191$	12.3972	−	21.4726i	0.897032	−	1.55370i	0.831270	−	0.555869i	$-0.187614\pi$
$192$		0			0
$193$	3.34392	−	1.93061i	0.240700	−	0.138968i	−0.374798	−	0.927106i	$-0.622288\pi$
$193$	3.34392	−	1.93061i	0.240700	−	0.138968i	0.615499	+	0.788138i	$0.288955\pi$
$194$	18.9201			1.35838
$195$		0			0
$196$	8.92820			0.637729
$197$	−4.94989	+	2.85782i	−0.352665	+	0.203611i	−0.665858	−	0.746078i	$-0.731934\pi$
$197$	−4.94989	+	2.85782i	−0.352665	+	0.203611i	0.313193	+	0.949689i	$0.398601\pi$
$198$		0			0
$199$	−0.567874	+	0.983586i	−0.0402555	+	0.0697246i	−0.885451	−	0.464732i	$-0.846151\pi$
$199$	−0.567874	+	0.983586i	−0.0402555	+	0.0697246i	0.845196	+	0.534457i	$0.179484\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	12.7026	+	7.33384i	0.893751	+	0.516007i
$203$			23.3205i			1.63678i
$204$		0			0
$205$	−4.32235	−	7.48652i	−0.301886	−	0.522881i
$206$	−1.96410	+	1.13397i	−0.136845	+	0.0790078i
$207$		0			0
$208$	−3.59030	+	0.331331i	−0.248942	+	0.0229737i
$209$	0.135748			0.00938987
$210$		0			0
$211$	8.35475	+	14.4708i	0.575165	+	0.996214i	0.996024	+	0.0890882i	$0.0283953\pi$
$211$	8.35475	+	14.4708i	0.575165	+	0.996214i	−0.420859	+	0.907126i	$0.638271\pi$
$212$	−5.17688	+	8.96661i	−0.355549	+	0.615829i
$213$		0			0
$214$	4.06830	+	2.34883i	0.278103	+	0.160563i
$215$	9.74846	+	5.62828i	0.664840	+	0.383845i
$216$		0			0
$217$	0.171220	−	0.296562i	0.0116232	−	0.0201320i
$218$	3.08580	+	5.34477i	0.208997	+	0.361993i
$219$		0			0
$220$	−0.164177			−0.0110688
$221$	3.26445	+	4.61523i	0.219591	+	0.310454i
$222$		0			0
$223$	19.7621	−	11.4097i	1.32337	−	0.764048i	0.339105	−	0.940749i	$-0.389876\pi$
$223$	19.7621	−	11.4097i	1.32337	−	0.764048i	0.984265	+	0.176701i	$0.0565426\pi$
$224$	1.99551	+	3.45632i	0.133330	+	0.230935i
$225$		0			0
$226$		−	11.2745i		−	0.749970i
$227$	3.28436	+	1.89623i	0.217991	+	0.125857i	0.605020	−	0.796211i	$-0.293165\pi$
$227$	3.28436	+	1.89623i	0.217991	+	0.125857i	−0.387029	+	0.922068i	$0.626499\pi$
$228$		0			0
$229$		−	4.69767i		−	0.310431i	−0.987881	−	0.155215i	$-0.950393\pi$
$229$		−	4.69767i		−	0.310431i	0.987881	−	0.155215i	$-0.0496071\pi$
$230$	3.49551	−	6.05440i	0.230487	−	0.399215i
$231$		0			0
$232$	−5.06040	+	2.92163i	−0.332232	+	0.191814i
$233$	29.3752			1.92443			0.962216	−	0.272286i	$-0.0877798\pi$
$233$	29.3752			1.92443			0.962216	+	0.272286i	$0.0877798\pi$
$234$		0			0
$235$	5.31634			0.346800
$236$	3.00000	−	1.73205i	0.195283	−	0.112747i
$237$		0			0
$238$	3.12870	−	5.41907i	0.202804	−	0.351266i
$239$		−	4.19175i		−	0.271142i	−0.990768	−	0.135571i	$-0.956713\pi$
$239$		−	4.19175i		−	0.271142i	0.990768	−	0.135571i	$-0.0432869\pi$
$240$		0			0
$241$	16.1343	+	9.31513i	1.03930	+	0.600041i	0.919635	−	0.392774i	$-0.128484\pi$
$241$	16.1343	+	9.31513i	1.03930	+	0.600041i	0.119666	+	0.992814i	$0.461818\pi$
$242$			10.9730i			0.705374i
$243$		0			0
$244$	−3.21606	−	5.57038i	−0.205887	−	0.356607i
$245$	−7.73205	+	4.46410i	−0.493983	+	0.285201i
$246$		0			0
$247$	−2.43390	+	1.72155i	−0.154865	+	0.109540i
$248$	0.0858029			0.00544849
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	2.28394	−	3.95589i	0.144161	−	0.249694i	−0.784899	−	0.619624i	$-0.787285\pi$
$251$	2.28394	−	3.95589i	0.144161	−	0.249694i	0.929060	+	0.369930i	$0.120618\pi$
$252$		0			0
$253$	0.993992	+	0.573882i	0.0624918	+	0.0360796i
$254$	7.03590	+	4.06218i	0.441472	+	0.254884i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.785027	+	1.35971i	0.0489686	+	0.0848161i	0.889471	−	0.456992i	$-0.151073\pi$
$257$	0.785027	+	1.35971i	0.0489686	+	0.0848161i	−0.840502	+	0.541808i	$0.817740\pi$
$258$		0			0
$259$	33.3662			2.07327
$260$	2.94362	−	2.08209i	0.182556	−	0.129126i
$261$		0			0
$262$	−18.0163	+	10.4017i	−1.11305	+	0.642620i
$263$	−11.5167	−	19.9476i	−0.710152	−	1.23002i	−0.964800	−	0.262985i	$-0.915293\pi$
$263$	−11.5167	−	19.9476i	−0.710152	−	1.23002i	0.254648	−	0.967034i	$-0.418040\pi$
$264$		0			0
$265$		−	10.3538i		−	0.636026i
$266$	2.85782	+	1.64996i	0.175224	+	0.101166i
$267$		0			0
$268$		−	15.3074i		−	0.935045i
$269$	9.20708	−	15.9471i	0.561365	−	0.972314i	−0.436012	−	0.899941i	$-0.643610\pi$
$269$	9.20708	−	15.9471i	0.561365	−	0.972314i	0.997378	−	0.0723728i	$-0.0230571\pi$
$270$		0			0
$271$	−7.86510	+	4.54092i	−0.477771	+	0.275841i	−0.719487	−	0.694506i	$-0.755623\pi$
$271$	−7.86510	+	4.54092i	−0.477771	+	0.275841i	0.241716	+	0.970347i	$0.422290\pi$
$272$	1.56787			0.0950663
$273$		0			0
$274$	−5.25154			−0.317257
$275$	0.142181	−	0.0820885i	0.00857386	−	0.00495012i
$276$		0			0
$277$	−8.44843	+	14.6331i	−0.507617	+	0.879218i	0.492344	+	0.870400i	$0.336140\pi$
$277$	−8.44843	+	14.6331i	−0.507617	+	0.879218i	−0.999961	+	0.00881745i	$0.997193\pi$
$278$		−	16.7215i		−	1.00289i
$279$		0			0
$280$	−3.45632	−	1.99551i	−0.206555	−	0.119254i
$281$			10.5011i			0.626443i	0.949680	+	0.313222i	$0.101408\pi$
$281$			10.5011i			0.626443i	−0.949680	+	0.313222i	$0.898592\pi$
$282$		0			0
$283$	2.86780	+	4.96717i	0.170473	+	0.295268i	0.938585	−	0.345047i	$-0.112137\pi$
$283$	2.86780	+	4.96717i	0.170473	+	0.295268i	−0.768112	+	0.640315i	$0.778804\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$		0			0
$286$	0.341831	+	0.483275i	0.0202129	+	0.0285766i
$287$	34.5011			2.03654
$288$		0			0
$289$	7.27089	+	12.5935i	0.427699	+	0.740797i
$290$	2.92163	−	5.06040i	0.171564	−	0.297157i
$291$		0			0
$292$	0.155658	+	0.0898694i	0.00910922	+	0.00525921i
$293$	15.5306	+	8.96661i	0.907309	+	0.523835i	0.879564	−	0.475780i	$-0.157834\pi$
$293$	15.5306	+	8.96661i	0.907309	+	0.523835i	0.0277446	+	0.999615i	$0.491167\pi$
$294$		0			0
$295$	−1.73205	+	3.00000i	−0.100844	+	0.174667i
$296$	4.18016	+	7.24026i	0.242967	+	0.420831i
$297$		0			0
$298$	10.0328			0.581186
$299$	−25.0998	+	2.31634i	−1.45156	+	0.133957i
$300$		0			0
$301$	−38.9063	+	22.4625i	−2.24252	+	1.29472i
$302$	5.43761	+	9.41822i	0.312900	+	0.541958i
$303$		0			0
$304$			0.826838i			0.0474224i
$305$	5.57038	+	3.21606i	0.318959	+	0.184151i
$306$		0			0
$307$		−	26.7386i		−	1.52605i	−0.646367	−	0.763027i	$-0.723712\pi$
$307$		−	26.7386i		−	1.52605i	0.646367	−	0.763027i	$-0.276288\pi$
$308$	0.327616	−	0.567448i	0.0186677	−	0.0323334i
$309$		0			0
$310$	−0.0743075	+	0.0429015i	−0.00422038	+	0.00243664i
$311$	−25.4823			−1.44497			−0.722484	−	0.691388i	$-0.757000\pi$
$311$	−25.4823			−1.44497			−0.722484	+	0.691388i	$0.757000\pi$
$312$		0			0
$313$	−8.68783			−0.491065			−0.245533	−	0.969388i	$-0.578963\pi$
$313$	−8.68783			−0.491065			−0.245533	+	0.969388i	$0.578963\pi$
$314$	−15.3219	+	8.84611i	−0.864666	+	0.499215i
$315$		0			0
$316$	−3.10628	+	5.38024i	−0.174742	+	0.302662i
$317$		−	35.4422i		−	1.99063i	−0.0966826	−	0.995315i	$-0.530823\pi$
$317$		−	35.4422i		−	1.99063i	0.0966826	−	0.995315i	$-0.469177\pi$
$318$		0			0
$319$	0.830802	+	0.479664i	0.0465160	+	0.0268560i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	13.9506	+	24.1632i	0.777438	+	1.34656i
$323$	1.12270	−	0.648189i	0.0624685	−	0.0360662i
$324$		0			0
$325$	−1.50821	+	3.27495i	−0.0836603	+	0.181662i
$326$	−1.41113			−0.0781550
$327$		0			0
$328$	4.32235	+	7.48652i	0.238662	+	0.413374i
$329$	−10.6088	+	18.3750i	−0.584882	+	1.01304i
$330$		0			0
$331$	−1.70362	−	0.983586i	−0.0936395	−	0.0540628i	0.452449	−	0.891790i	$-0.350550\pi$
$331$	−1.70362	−	0.983586i	−0.0936395	−	0.0540628i	−0.546089	+	0.837727i	$0.683884\pi$
$332$	−1.07346	−	0.619760i	−0.0589135	−	0.0340138i
$333$		0			0
$334$	−0.352237	+	0.610092i	−0.0192735	+	0.0333827i
$335$	7.65368	+	13.2566i	0.418165	+	0.724283i
$336$		0			0
$337$	−32.4750			−1.76903			−0.884513	−	0.466516i	$-0.845509\pi$
$337$	−32.4750			−1.76903			−0.884513	+	0.466516i	$0.845509\pi$
$338$	−12.2578	−	4.32982i	−0.666734	−	0.235511i
$339$		0			0
$340$	−1.35782	+	0.783937i	−0.0736381	+	0.0425150i
$341$	−0.00704343	−	0.0121996i	−0.000381423	−	0.000660644i
$342$		0			0
$343$		−	7.69549i		−	0.415517i
$344$	−9.74846	−	5.62828i	−0.525602	−	0.303456i
$345$		0			0
$346$			0.655233i			0.0352255i
$347$	−5.19209	+	8.99296i	−0.278726	+	0.482767i	−0.971068	−	0.238802i	$-0.923245\pi$
$347$	−5.19209	+	8.99296i	−0.278726	+	0.482767i	0.692343	+	0.721569i	$0.256579\pi$
$348$		0			0
$349$	24.5943	−	14.1995i	1.31650	−	0.760083i	0.333338	−	0.942808i	$-0.391825\pi$
$349$	24.5943	−	14.1995i	1.31650	−	0.760083i	0.983164	+	0.182725i	$0.0584918\pi$
$350$	3.99102			0.213329
$351$		0			0
$352$	0.164177			0.00875066
$353$	8.14364	−	4.70173i	0.433442	−	0.250248i	−0.267370	−	0.963594i	$-0.586154\pi$
$353$	8.14364	−	4.70173i	0.433442	−	0.250248i	0.700812	+	0.713346i	$0.252821\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$		−	10.3767i		−	0.549966i
$357$		0			0
$358$	−6.42011	−	3.70665i	−0.339313	−	0.195903i
$359$			24.2487i			1.27980i	0.768459	+	0.639899i	$0.221024\pi$
$359$			24.2487i			1.27980i	−0.768459	+	0.639899i	$0.778976\pi$
$360$		0			0
$361$	−9.15817	−	15.8624i	−0.482009	−	0.834864i
$362$	−0.429615	+	0.248039i	−0.0225801	+	0.0130366i
$363$		0			0
$364$	1.32235	+	14.3289i	0.0693098	+	0.751040i
$365$	−0.179739			−0.00940796
$366$		0			0
$367$	−15.3049	−	26.5089i	−0.798912	−	1.38376i	−0.920325	−	0.391154i	$-0.872076\pi$
$367$	−15.3049	−	26.5089i	−0.798912	−	1.38376i	0.121414	−	0.992602i	$-0.461257\pi$
$368$	−3.49551	+	6.05440i	−0.182216	+	0.315607i
$369$		0			0
$370$	−7.24026	−	4.18016i	−0.376403	−	0.217316i
$371$	35.7859	+	20.6610i	1.85791	+	1.07267i
$372$		0			0
$373$	11.6767	−	20.2246i	0.604595	−	1.04719i	−0.387520	−	0.921861i	$-0.626668\pi$
$373$	11.6767	−	20.2246i	0.604595	−	1.04719i	0.992115	−	0.125328i	$-0.0399983\pi$
$374$	−0.128704	−	0.222922i	−0.00665514	−	0.0115270i
$375$		0			0
$376$	−5.31634			−0.274169
$377$	−20.9790	+	1.93605i	−1.08047	+	0.0997116i
$378$		0			0
$379$	−15.0064	+	8.66397i	−0.770829	+	0.445038i	−0.833170	−	0.553017i	$-0.813477\pi$
$379$	−15.0064	+	8.66397i	−0.770829	+	0.445038i	0.0623414	+	0.998055i	$0.480143\pi$
$380$	−0.413419	−	0.716063i	−0.0212080	−	0.0367333i
$381$		0			0
$382$		−	24.7944i		−	1.26859i
$383$	−16.2514	−	9.38275i	−0.830408	−	0.479436i	0.0235845	−	0.999722i	$-0.492492\pi$
$383$	−16.2514	−	9.38275i	−0.830408	−	0.479436i	−0.853992	+	0.520286i	$0.825825\pi$
$384$		0			0
$385$			0.655233i			0.0333937i
$386$	1.93061	−	3.34392i	0.0982655	−	0.170201i
$387$		0			0
$388$	16.3853	−	9.46004i	0.831836	−	0.480261i
$389$	−7.13963			−0.361994			−0.180997	−	0.983484i	$-0.557932\pi$
$389$	−7.13963			−0.361994			−0.180997	+	0.983484i	$0.557932\pi$
$390$		0			0
$391$	10.9610			0.554323
$392$	7.73205	−	4.46410i	0.390528	−	0.225471i
$393$		0			0
$394$	−2.85782	+	4.94989i	−0.143975	+	0.249372i
$395$		−	6.21257i		−	0.312588i
$396$		0			0
$397$	1.81414	+	1.04739i	0.0910490	+	0.0525672i	0.544833	−	0.838544i	$-0.316593\pi$
$397$	1.81414	+	1.04739i	0.0910490	+	0.0525672i	−0.453784	+	0.891112i	$0.649926\pi$
$398$			1.13575i			0.0569299i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−21.8101	+	12.5921i	−1.08914	+	0.628818i	−0.933349	−	0.358971i	$-0.883128\pi$
$401$	−21.8101	+	12.5921i	−1.08914	+	0.628818i	−0.155796	+	0.987789i	$0.549794\pi$
$402$		0			0
$403$	0.281000	+	0.129409i	0.0139976	+	0.00644630i
$404$	14.6677			0.729745
$405$		0			0
$406$	11.6603	+	20.1962i	0.578689	+	1.00232i
$407$	0.686287	−	1.18868i	0.0340180	−	0.0589208i
$408$		0			0
$409$	8.37798	+	4.83703i	0.414264	+	0.239176i	0.692620	−	0.721302i	$-0.256456\pi$
$409$	8.37798	+	4.83703i	0.414264	+	0.239176i	−0.278356	+	0.960478i	$0.589790\pi$
$410$	−7.48652	−	4.32235i	−0.369733	−	0.213465i
$411$		0			0
$412$	−1.13397	+	1.96410i	−0.0558669	+	0.0967643i
$413$	−6.91264	−	11.9730i	−0.340149	−	0.589155i
$414$		0			0
$415$	1.23952			0.0608456
$416$	−2.94362	+	2.08209i	−0.144323	+	0.102083i
$417$		0			0
$418$	0.117561	−	0.0678739i	0.00575010	−	0.00331982i
$419$	4.67369	+	8.09507i	0.228325	+	0.395470i	0.957312	−	0.289057i	$-0.0933419\pi$
$419$	4.67369	+	8.09507i	0.228325	+	0.395470i	−0.728987	+	0.684528i	$0.760009\pi$
$420$		0			0
$421$		−	25.5243i		−	1.24398i	−0.783026	−	0.621989i	$-0.786325\pi$
$421$		−	25.5243i		−	1.24398i	0.783026	−	0.621989i	$-0.213675\pi$
$422$	14.4708	+	8.35475i	0.704430	+	0.406703i
$423$		0			0
$424$			10.3538i			0.502823i
$425$	0.783937	−	1.35782i	0.0380265	−	0.0658639i
$426$		0			0
$427$	−22.2315	+	12.8354i	−1.07586	+	0.621146i
$428$	4.69767			0.227070
$429$		0			0
$430$	11.2566			0.542839
$431$	3.55397	−	2.05189i	0.171189	−	0.0988359i	−0.411957	−	0.911203i	$-0.635155\pi$
$431$	3.55397	−	2.05189i	0.171189	−	0.0988359i	0.583146	+	0.812367i	$0.301821\pi$
$432$		0			0
$433$	1.34392	−	2.32773i	0.0645845	−	0.111864i	−0.831925	−	0.554888i	$-0.812761\pi$
$433$	1.34392	−	2.32773i	0.0645845	−	0.111864i	0.896510	+	0.443024i	$0.146094\pi$
$434$		−	0.342441i		−	0.0164377i
$435$		0			0
$436$	5.34477	+	3.08580i	0.255968	+	0.147783i
$437$			5.78044i			0.276516i
$438$		0			0
$439$	−1.23848	−	2.14512i	−0.0591096	−	0.102381i	0.834956	−	0.550316i	$-0.185493\pi$
$439$	−1.23848	−	2.14512i	−0.0591096	−	0.102381i	−0.894066	+	0.447935i	$0.852159\pi$
$440$	−0.142181	+	0.0820885i	−0.00677823	+	0.00391341i
$441$		0			0
$442$	5.13471	+	2.36468i	0.244233	+	0.112476i
$443$	17.3774			0.825624			0.412812	−	0.910816i	$-0.364547\pi$
$443$	17.3774			0.825624			0.412812	+	0.910816i	$0.364547\pi$
$444$		0			0
$445$	5.18837	+	8.98652i	0.245952	+	0.426002i
$446$	11.4097	−	19.7621i	0.540263	−	0.935763i
$447$		0			0
$448$	3.45632	+	1.99551i	0.163296	+	0.0942789i
$449$	−25.9206	−	14.9653i	−1.22327	−	0.706255i	−0.257655	−	0.966237i	$-0.582950\pi$
$449$	−25.9206	−	14.9653i	−1.22327	−	0.706255i	−0.965613	+	0.259982i	$0.916283\pi$
$450$		0			0
$451$	0.709629	−	1.22911i	0.0334151	−	0.0578767i
$452$	−5.63726	−	9.76403i	−0.265155	−	0.459261i
$453$		0			0
$454$	3.79246			0.177989
$455$	−8.30965	−	11.7480i	−0.389562	−	0.550757i
$456$		0			0
$457$	9.93255	−	5.73456i	0.464625	−	0.268251i	−0.249362	−	0.968410i	$-0.580221\pi$
$457$	9.93255	−	5.73456i	0.464625	−	0.268251i	0.713987	+	0.700159i	$0.246888\pi$
$458$	−2.34883	−	4.06830i	−0.109754	−	0.190099i
$459$		0			0
$460$		−	6.99102i		−	0.325958i
$461$	−20.7904	−	12.0034i	−0.968307	−	0.559052i	−0.0695873	−	0.997576i	$-0.522168\pi$
$461$	−20.7904	−	12.0034i	−0.968307	−	0.559052i	−0.898720	+	0.438524i	$0.855502\pi$
$462$		0			0
$463$		−	26.3163i		−	1.22302i	−0.791235	−	0.611512i	$-0.790562\pi$
$463$		−	26.3163i		−	1.22302i	0.791235	−	0.611512i	$-0.209438\pi$
$464$	−2.92163	+	5.06040i	−0.135633	+	0.234923i
$465$		0			0
$466$	25.4397	−	14.6876i	1.17847	−	0.680390i
$467$	16.2776			0.753236			0.376618	−	0.926369i	$-0.377087\pi$
$467$	16.2776			0.753236			0.376618	+	0.926369i	$0.377087\pi$
$468$		0			0
$469$	−61.0919			−2.82096
$470$	4.60408	−	2.65817i	0.212371	−	0.122612i
$471$		0			0
$472$	1.73205	−	3.00000i	0.0797241	−	0.138086i
$473$			1.84807i			0.0849742i
$474$		0			0
$475$	0.716063	+	0.413419i	0.0328552	+	0.0189690i
$476$		−	6.25741i		−	0.286808i
$477$		0			0
$478$	−2.09588	−	3.63017i	−0.0958632	−	0.166040i
$479$	24.0075	−	13.8608i	1.09693	−	0.633314i	0.161519	−	0.986870i	$-0.448361\pi$
$479$	24.0075	−	13.8608i	1.09693	−	0.633314i	0.935414	+	0.353556i	$0.115027\pi$
$480$		0			0
$481$	2.77003	+	30.0161i	0.126303	+	1.36861i
$482$	18.6303			0.848586
$483$		0			0
$484$	5.48652	+	9.50294i	0.249387	+	0.431952i
$485$	−9.46004	+	16.3853i	−0.429558	+	0.744016i
$486$		0			0
$487$	21.0182	+	12.1349i	0.952425	+	0.549883i	0.893833	−	0.448399i	$-0.148006\pi$
$487$	21.0182	+	12.1349i	0.952425	+	0.549883i	0.0585916	+	0.998282i	$0.481339\pi$
$488$	−5.57038	−	3.21606i	−0.252159	−	0.145584i
$489$		0			0
$490$	−4.46410	+	7.73205i	−0.201668	+	0.349298i
$491$	−5.15117	−	8.92208i	−0.232469	−	0.402648i	0.726065	−	0.687626i	$-0.241347\pi$
$491$	−5.15117	−	8.92208i	−0.232469	−	0.402648i	−0.958534	+	0.284978i	$0.908014\pi$
$492$		0			0
$493$	9.16148			0.412612
$494$	−1.24704	+	2.70786i	−0.0561071	+	0.121832i
$495$		0			0
$496$	0.0743075	−	0.0429015i	0.00333650	−	0.00192633i
$497$	−11.9730	−	20.7379i	−0.537065	−	0.930223i
$498$		0			0
$499$			28.2672i			1.26542i	0.774391	+	0.632708i	$0.218057\pi$
$499$			28.2672i			1.26542i	−0.774391	+	0.632708i	$0.781943\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$		0			0
$502$		−	4.56787i		−	0.203874i
$503$	15.3561	−	26.5976i	0.684697	−	1.18593i	−0.288835	−	0.957379i	$-0.593268\pi$
$503$	15.3561	−	26.5976i	0.684697	−	1.18593i	0.973532	−	0.228551i	$-0.0733987\pi$
$504$		0			0
$505$	−12.7026	+	7.33384i	−0.565258	+	0.326352i
$506$	1.14776			0.0510243
$507$		0			0
$508$	8.12436			0.360460
$509$	1.86255	−	1.07534i	0.0825560	−	0.0476637i	−0.458154	−	0.888873i	$-0.651489\pi$
$509$	1.86255	−	1.07534i	0.0825560	−	0.0476637i	0.540710	+	0.841209i	$0.318156\pi$
$510$		0			0
$511$	0.358670	−	0.621235i	0.0158666	−	0.0274818i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	1.35971	+	0.785027i	0.0599741	+	0.0346260i
$515$		−	2.26795i		−	0.0999378i
$516$		0			0
$517$	0.436410	+	0.755884i	0.0191933	+	0.0332438i
$518$	28.8960	−	16.6831i	1.26962	−	0.733013i
$519$		0			0
$520$	1.50821	−	3.27495i	0.0661392	−	0.143616i
$521$	−10.6848			−0.468110			−0.234055	−	0.972223i	$-0.575200\pi$
$521$	−10.6848			−0.468110			−0.234055	+	0.972223i	$0.575200\pi$
$522$		0			0
$523$	−3.95601	−	6.85201i	−0.172984	−	0.299617i	0.766478	−	0.642271i	$-0.222008\pi$
$523$	−3.95601	−	6.85201i	−0.172984	−	0.299617i	−0.939462	+	0.342654i	$0.888674\pi$
$524$	−10.4017	+	18.0163i	−0.454401	+	0.787046i
$525$		0			0
$526$	−19.9476	−	11.5167i	−0.869755	−	0.502153i
$527$	−0.116505	−	0.0672641i	−0.00507503	−	0.00293007i
$528$		0			0
$529$	−12.9371	+	22.4078i	−0.562485	+	0.974252i
$530$	−5.17688	−	8.96661i	−0.224869	−	0.389485i
$531$		0			0
$532$	3.29992			0.143070
$533$	2.86425	+	31.0370i	0.124065	+	1.34436i
$534$		0			0
$535$	−4.06830	+	2.34883i	−0.175888	+	0.101549i
$536$	−7.65368	−	13.2566i	−0.330588	−	0.572596i
$537$		0			0
$538$		−	18.4142i		−	0.793891i
$539$	−1.26942	−	0.732902i	−0.0546780	−	0.0315683i
$540$		0			0
$541$			34.7694i			1.49485i	0.664345	+	0.747426i	$0.268711\pi$
$541$			34.7694i			1.49485i	−0.664345	+	0.747426i	$0.731289\pi$
$542$	−4.54092	+	7.86510i	−0.195049	+	0.337835i
$543$		0			0
$544$	1.35782	−	0.783937i	0.0582160	−	0.0336110i
$545$	−6.17161			−0.264363
$546$		0			0
$547$	8.98506			0.384173			0.192087	−	0.981378i	$-0.438475\pi$
$547$	8.98506			0.384173			0.192087	+	0.981378i	$0.438475\pi$
$548$	−4.54796	+	2.62577i	−0.194279	+	0.112167i
$549$		0			0
$550$	0.0820885	−	0.142181i	0.00350026	−	0.00606263i
$551$			4.83143i			0.205826i
$552$		0			0
$553$	21.4726	+	12.3972i	0.913109	+	0.527184i
$554$			16.8969i			0.717878i
$555$		0			0
$556$	−8.36076	−	14.4813i	−0.354575	−	0.614142i
$557$	−26.2342	+	15.1464i	−1.11158	+	0.641771i	−0.939238	−	0.343266i	$-0.888467\pi$
$557$	−26.2342	+	15.1464i	−1.11158	+	0.641771i	−0.172342	+	0.985037i	$0.555134\pi$
$558$		0			0
$559$	−23.4371	−	33.1350i	−0.991286	−	1.40146i
$560$	−3.99102			−0.168651
$561$		0			0
$562$	5.25055	+	9.09422i	0.221481	+	0.383616i
$563$	1.20514	−	2.08736i	0.0507905	−	0.0879717i	−0.839512	−	0.543341i	$-0.817159\pi$
$563$	1.20514	−	2.08736i	0.0507905	−	0.0879717i	0.890303	+	0.455369i	$0.150493\pi$
$564$		0			0
$565$	9.76403	+	5.63726i	0.410776	+	0.237161i
$566$	4.96717	+	2.86780i	0.208786	+	0.120543i
$567$		0			0
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	2.18565	+	3.78566i	0.0916273	+	0.158703i	0.908196	−	0.418545i	$-0.137460\pi$
$569$	2.18565	+	3.78566i	0.0916273	+	0.158703i	−0.816569	+	0.577248i	$0.804126\pi$
$570$		0			0
$571$	−19.0050			−0.795335			−0.397668	−	0.917530i	$-0.630180\pi$
$571$	−19.0050			−0.795335			−0.397668	+	0.917530i	$0.630180\pi$
$572$	0.537672	+	0.247613i	0.0224812	+	0.0103532i
$573$		0			0
$574$	29.8788	−	17.2505i	1.24712	−	0.720024i
$575$	3.49551	+	6.05440i	0.145773	+	0.252486i
$576$		0			0
$577$			13.0620i			0.543777i	0.962329	+	0.271888i	$0.0876481\pi$
$577$			13.0620i			0.543777i	−0.962329	+	0.271888i	$0.912352\pi$
$578$	12.5935	+	7.27089i	0.523822	+	0.302429i
$579$		0			0
$580$		−	5.84325i		−	0.242628i
$581$	−2.47347	+	4.28418i	−0.102617	+	0.177738i
$582$		0			0
$583$	1.47211	−	0.849924i	0.0609686	−	0.0352002i
$584$	0.179739			0.00743765
$585$		0			0
$586$	17.9332			0.740815
$587$	−24.2844	+	14.0206i	−1.00232	+	0.578691i	−0.908935	−	0.416938i	$-0.863103\pi$
$587$	−24.2844	+	14.0206i	−1.00232	+	0.578691i	−0.0933882	+	0.995630i	$0.529770\pi$
$588$		0			0
$589$	0.0354726	−	0.0614403i	0.00146162	−	0.00253160i
$590$			3.46410i			0.142615i
$591$		0			0
$592$	7.24026	+	4.18016i	0.297573	+	0.171804i
$593$		−	32.1848i		−	1.32167i	−0.750531	−	0.660835i	$-0.770202\pi$
$593$		−	32.1848i		−	1.32167i	0.750531	−	0.660835i	$-0.229798\pi$
$594$		0			0
$595$	3.12870	+	5.41907i	0.128264	+	0.222160i
$596$	8.68868	−	5.01641i	0.355902	−	0.205480i
$597$		0			0
$598$	−20.5789	+	14.5559i	−0.841534	+	0.595236i
$599$	−13.8415			−0.565550			−0.282775	−	0.959186i	$-0.591255\pi$
$599$	−13.8415			−0.565550			−0.282775	+	0.959186i	$0.591255\pi$
$600$		0			0
$601$	−4.06873	−	7.04724i	−0.165967	−	0.287463i	0.771031	−	0.636797i	$-0.219741\pi$
$601$	−4.06873	−	7.04724i	−0.165967	−	0.287463i	−0.936998	+	0.349334i	$0.886408\pi$
$602$	−22.4625	+	38.9063i	−0.915505	+	1.58570i
$603$		0			0
$604$	9.41822	+	5.43761i	0.383222	+	0.221253i
$605$	−9.50294	−	5.48652i	−0.386349	−	0.223059i
$606$		0			0
$607$	22.8555	−	39.5869i	0.927676	−	1.60678i	0.140475	−	0.990084i	$-0.455137\pi$
$607$	22.8555	−	39.5869i	0.927676	−	1.60678i	0.787201	−	0.616697i	$-0.211530\pi$
$608$	0.413419	+	0.716063i	0.0167664	+	0.0290402i
$609$		0			0
$610$	6.43213			0.260429
$611$	−17.4108	−	8.01814i	−0.704364	−	0.324379i
$612$		0			0
$613$	−33.1743	+	19.1532i	−1.33990	+	0.773591i	−0.986792	−	0.161992i	$-0.948208\pi$
$613$	−33.1743	+	19.1532i	−1.33990	+	0.773591i	−0.353107	+	0.935583i	$0.614875\pi$
$614$	−13.3693	−	23.1563i	−0.539542	−	0.934513i
$615$		0			0
$616$		−	0.655233i		−	0.0264001i
$617$	−4.67667	−	2.70008i	−0.188276	−	0.108701i	0.402899	−	0.915244i	$-0.368002\pi$
$617$	−4.67667	−	2.70008i	−0.188276	−	0.108701i	−0.591175	+	0.806543i	$0.701336\pi$
$618$		0			0
$619$			20.2758i			0.814954i	0.913216	+	0.407477i	$0.133591\pi$
$619$			20.2758i			0.814954i	−0.913216	+	0.407477i	$0.866409\pi$
$620$	−0.0429015	+	0.0743075i	−0.00172296	+	0.00298426i
$621$		0			0
$622$	−22.0683	+	12.7411i	−0.884858	+	0.510873i
$623$	−41.4137			−1.65921
$624$		0			0
$625$	1.00000			0.0400000
$626$	−7.52388	+	4.34392i	−0.300715	+	0.173618i
$627$		0			0
$628$	−8.84611	+	15.3219i	−0.352998	+	0.611411i
$629$		−	13.1079i		−	0.522648i
$630$		0			0
$631$	−22.1700	−	12.7999i	−0.882576	−	0.509555i	−0.0110689	−	0.999939i	$-0.503523\pi$
$631$	−22.1700	−	12.7999i	−0.882576	−	0.509555i	−0.871507	+	0.490383i	$0.836857\pi$
$632$			6.21257i			0.247123i
$633$		0			0
$634$	−17.7211	−	30.6938i	−0.703794	−	1.21901i
$635$	−7.03590	+	4.06218i	−0.279211	+	0.161203i
$636$		0			0
$637$	32.0549	−	2.95819i	1.27006	−	0.117208i
$638$	0.959327			0.0379801
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−0.738951	+	1.27990i	−0.0291868	+	0.0505530i	−0.880250	−	0.474510i	$-0.842625\pi$
$641$	−0.738951	+	1.27990i	−0.0291868	+	0.0505530i	0.851063	+	0.525063i	$0.175958\pi$
$642$		0			0
$643$	−35.7724	−	20.6532i	−1.41073	−	0.814483i	−0.415269	−	0.909698i	$-0.636313\pi$
$643$	−35.7724	−	20.6532i	−1.41073	−	0.814483i	−0.995457	+	0.0952153i	$0.969646\pi$
$644$	24.1632	+	13.9506i	0.952163	+	0.549732i
$645$		0			0
$646$	0.648189	−	1.12270i	0.0255027	−	0.0441719i
$647$	−8.96379	−	15.5257i	−0.352403	−	0.610380i	0.634267	−	0.773114i	$-0.281302\pi$
$647$	−8.96379	−	15.5257i	−0.352403	−	0.610380i	−0.986670	+	0.162734i	$0.947969\pi$
$648$		0			0
$649$	−0.568726			−0.0223244
$650$	0.331331	+	3.59030i	0.0129959	+	0.140823i
$651$		0			0
$652$	−1.22207	+	0.705563i	−0.0478600	+	0.0276320i
$653$	13.9229	+	24.1152i	0.544846	+	0.943702i	0.998617	+	0.0525830i	$0.0167454\pi$
$653$	13.9229	+	24.1152i	0.544846	+	0.943702i	−0.453770	+	0.891119i	$0.649921\pi$
$654$		0			0
$655$		−	20.8034i		−	0.812857i
$656$	7.48652	+	4.32235i	0.292300	+	0.168759i
$657$		0			0
$658$			21.2176i			0.827148i
$659$	7.42915	−	12.8677i	0.289399	−	0.501253i	−0.684268	−	0.729231i	$-0.739878\pi$
$659$	7.42915	−	12.8677i	0.289399	−	0.501253i	0.973666	+	0.227978i	$0.0732114\pi$
$660$		0			0
$661$	19.5210	−	11.2705i	0.759279	−	0.438370i	−0.0697577	−	0.997564i	$-0.522223\pi$
$661$	19.5210	−	11.2705i	0.759279	−	0.438370i	0.829037	+	0.559194i	$0.188889\pi$
$662$	−1.96717			−0.0764563
$663$		0			0
$664$	−1.23952			−0.0481027
$665$	−2.85782	+	1.64996i	−0.110821	+	0.0639828i
$666$		0			0
$667$	−20.4251	+	35.3774i	−0.790864	+	1.36982i
$668$			0.704473i			0.0272569i
$669$		0			0
$670$	13.2566	+	7.65368i	0.512145	+	0.295687i
$671$			1.05601i			0.0407667i
$672$		0			0
$673$	13.1200	+	22.7244i	0.505737	+	0.875963i	0.999978	+	0.00663747i	$0.00211279\pi$
$673$	13.1200	+	22.7244i	0.505737	+	0.875963i	−0.494241	+	0.869325i	$0.664554\pi$
$674$	−28.1242	+	16.2375i	−1.08330	+	0.625445i
$675$		0			0
$676$	−12.7804	+	2.37915i	−0.491555	+	0.0915058i
$677$	−13.6685			−0.525324			−0.262662	−	0.964888i	$-0.584600\pi$
$677$	−13.6685			−0.525324			−0.262662	+	0.964888i	$0.584600\pi$
$678$		0			0
$679$	−37.7551	−	65.3938i	−1.44891	−	2.50958i
$680$	−0.783937	+	1.35782i	−0.0300626	+	0.0520700i
$681$		0			0
$682$	−0.0121996	−	0.00704343i	−0.000467146	−	0.000269707i
$683$	−3.98506	−	2.30078i	−0.152484	−	0.0880368i	0.421817	−	0.906681i	$-0.361393\pi$
$683$	−3.98506	−	2.30078i	−0.152484	−	0.0880368i	−0.574301	+	0.818644i	$0.694726\pi$
$684$		0			0
$685$	2.62577	−	4.54796i	0.100325	−	0.173769i
$686$	−3.84774	−	6.66449i	−0.146908	−	0.254451i
$687$		0			0
$688$	−11.2566			−0.429152
$689$	−15.6156	+	33.9080i	−0.594907	+	1.29179i
$690$		0			0
$691$	26.1212	−	15.0811i	0.993699	−	0.573712i	0.0873208	−	0.996180i	$-0.472169\pi$
$691$	26.1212	−	15.0811i	0.993699	−	0.573712i	0.906378	+	0.422468i	$0.138836\pi$
$692$	0.327616	+	0.567448i	0.0124541	+	0.0215711i
$693$		0			0
$694$			10.3842i			0.394178i
$695$	14.4813	+	8.36076i	0.549305	+	0.317142i
$696$		0			0
$697$		−	13.5538i		−	0.513386i
$698$	14.1995	−	24.5943i	0.537460	−	0.930907i
$699$		0			0
$700$	3.45632	−	1.99551i	0.130637	−	0.0754231i
$701$	29.3752			1.10949			0.554743	−	0.832022i	$-0.312817\pi$
$701$	29.3752			1.10949			0.554743	+	0.832022i	$0.312817\pi$
$702$		0			0
$703$	6.91264			0.260715
$704$	0.142181	−	0.0820885i	0.00535866	−	0.00309383i
$705$		0			0
$706$	4.70173	−	8.14364i	0.176952	−	0.306490i
$707$		−	58.5389i		−	2.20158i
$708$		0			0
$709$	−13.9540	−	8.05634i	−0.524053	−	0.302562i	0.214538	−	0.976716i	$-0.431175\pi$
$709$	−13.9540	−	8.05634i	−0.524053	−	0.302562i	−0.738591	+	0.674153i	$0.764509\pi$
$710$			6.00000i			0.225176i
$711$		0			0
$712$	−5.18837	−	8.98652i	−0.194442	−	0.336784i
$713$	0.519485	−	0.299925i	0.0194549	−	0.0112323i
$714$		0			0
$715$	−0.589444	+	0.0543969i	−0.0220439	+	0.00203433i
$716$	−7.41331			−0.277048
$717$		0			0
$718$	12.1244	+	21.0000i	0.452477	+	0.783713i
$719$	11.3238	−	19.6133i	0.422305	−	0.731454i	−0.573859	−	0.818954i	$-0.694554\pi$
$719$	11.3238	−	19.6133i	0.422305	−	0.731454i	0.996165	+	0.0874998i	$0.0278877\pi$
$720$		0			0
$721$	7.83876	+	4.52571i	0.291931	+	0.168546i
$722$	−15.8624	−	9.15817i	−0.590338	−	0.340832i
$723$		0			0
$724$	−0.248039	+	0.429615i	−0.00921828	+	0.0159665i
$725$	2.92163	+	5.06040i	0.108506	+	0.187939i
$726$		0			0
$727$	−4.36795			−0.161998			−0.0809991	−	0.996714i	$-0.525811\pi$
$727$	−4.36795			−0.161998			−0.0809991	+	0.996714i	$0.525811\pi$
$728$	8.30965	+	11.7480i	0.307976	+	0.435411i
$729$		0			0
$730$	−0.155658	+	0.0898694i	−0.00576118	+	0.00332622i
$731$	8.82443	+	15.2844i	0.326383	+	0.565313i
$732$		0			0
$733$			6.50392i			0.240228i	0.992760	+	0.120114i	$0.0383260\pi$
$733$			6.50392i			0.240228i	−0.992760	+	0.120114i	$0.961674\pi$
$734$	−26.5089	−	15.3049i	−0.978463	−	0.564916i
$735$		0			0
$736$			6.99102i			0.257692i
$737$	−1.25656	+	2.17642i	−0.0462859	+	0.0801695i
$738$		0			0
$739$	−1.89078	+	1.09164i	−0.0695535	+	0.0401567i	−0.534373	−	0.845249i	$-0.679452\pi$
$739$	−1.89078	+	1.09164i	−0.0695535	+	0.0401567i	0.464820	+	0.885405i	$0.346119\pi$
$740$	−8.36033			−0.307332
$741$		0			0
$742$	41.3220			1.51698
$743$	−8.64371	+	4.99045i	−0.317107	+	0.183082i	−0.650102	−	0.759847i	$-0.725274\pi$
$743$	−8.64371	+	4.99045i	−0.317107	+	0.183082i	0.332995	+	0.942928i	$0.391941\pi$
$744$		0			0
$745$	−5.01641	+	8.68868i	−0.183787	+	0.318329i
$746$		−	23.3533i		−	0.855026i
$747$		0			0
$748$	−0.222922	−	0.128704i	−0.00815085	−	0.00470590i
$749$		−	18.7485i		−	0.685054i
$750$		0			0
$751$	7.82026	+	13.5451i	0.285365	+	0.494267i	0.972698	−	0.232076i	$-0.0745517\pi$
$751$	7.82026	+	13.5451i	0.285365	+	0.494267i	−0.687332	+	0.726343i	$0.741218\pi$
$752$	−4.60408	+	2.65817i	−0.167894	+	0.0969335i
$753$		0			0
$754$	−17.2003	+	12.1662i	−0.626399	+	0.443066i
$755$	−10.8752			−0.395790
$756$		0			0
$757$	−2.76476	−	4.78871i	−0.100487	−	0.174049i	0.811398	−	0.584494i	$-0.198707\pi$
$757$	−2.76476	−	4.78871i	−0.100487	−	0.174049i	−0.911885	+	0.410445i	$0.865373\pi$
$758$	−8.66397	+	15.0064i	−0.314690	+	0.545058i
$759$		0			0
$760$	−0.716063	−	0.413419i	−0.0259743	−	0.0149963i
$761$	33.3086	+	19.2308i	1.20744	+	0.697114i	0.962199	−	0.272349i	$-0.0878004\pi$
$761$	33.3086	+	19.2308i	1.20744	+	0.697114i	0.245239	+	0.969463i	$0.421134\pi$
$762$		0			0
$763$	12.3155	−	21.3310i	0.445851	−	0.772236i
$764$	−12.3972	−	21.4726i	−0.448516	−	0.776852i
$765$		0			0
$766$	−18.7655			−0.678025
$767$	10.1970	−	7.21257i	0.368192	−	0.260431i
$768$		0			0
$769$	−9.77174	+	5.64172i	−0.352378	+	0.203445i	−0.665732	−	0.746191i	$-0.731881\pi$
$769$	−9.77174	+	5.64172i	−0.352378	+	0.203445i	0.313354	+	0.949636i	$0.398547\pi$
$770$	0.327616	+	0.567448i	0.0118065	+	0.0204494i
$771$		0			0
$772$		−	3.86122i		−	0.138968i
$773$	−7.84674	−	4.53032i	−0.282228	−	0.162944i	0.352204	−	0.935923i	$-0.385432\pi$
$773$	−7.84674	−	4.53032i	−0.282228	−	0.162944i	−0.634431	+	0.772979i	$0.718766\pi$
$774$		0			0
$775$		−	0.0858029i		−	0.00308213i
$776$	9.46004	−	16.3853i	0.339595	−	0.588197i
$777$		0			0
$778$	−6.18310	+	3.56982i	−0.221675	+	0.127984i
$779$	7.14776			0.256095
$780$		0			0
$781$	−0.985062			−0.0352483
$782$	9.49253	−	5.48052i	0.339452	−	0.195983i
$783$		0			0
$784$	4.46410	−	7.73205i	0.159432	−	0.276145i
$785$		−	17.6922i		−	0.631463i
$786$		0			0
$787$	1.60236	+	0.925123i	0.0571180	+	0.0329771i	0.528287	−	0.849066i	$-0.322835\pi$
$787$	1.60236	+	0.925123i	0.0571180	+	0.0329771i	−0.471169	+	0.882043i	$0.656168\pi$
$788$			5.71564i			0.203611i
$789$		0			0
$790$	−3.10628	−	5.38024i	−0.110517	−	0.191420i
$791$	−38.9684	+	22.4984i	−1.38556	+	0.799951i
$792$		0			0
$793$	−13.3923	−	18.9337i	−0.475573	−	0.672357i
$794$	2.09479			0.0743412
$795$		0			0
$796$	0.567874	+	0.983586i	0.0201278	+	0.0348623i
$797$	2.32892	−	4.03381i	0.0824947	−	0.142885i	−0.821826	−	0.569738i	$-0.807045\pi$
$797$	2.32892	−	4.03381i	0.0824947	−	0.142885i	0.904321	+	0.426853i	$0.140378\pi$
$798$		0			0
$799$	7.21862	+	4.16767i	0.255377	+	0.147442i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	−12.5921	+	21.8101i	−0.444641	+	0.770141i
$803$	−0.0147545	−	0.0255555i	−0.000520674	−	0.000901835i
$804$		0			0
$805$	−27.9012			−0.983390
$806$	0.308058	−	0.0284291i	0.0108509	−	0.00100137i
$807$		0			0
$808$	12.7026	−	7.33384i	0.446875	−	0.258004i
$809$	−17.7431	−	30.7319i	−0.623813	−	1.08048i	−0.988769	−	0.149452i	$-0.952249\pi$
$809$	−17.7431	−	30.7319i	−0.623813	−	1.08048i	0.364956	−	0.931025i	$-0.381084\pi$
$810$		0			0
$811$			38.5309i			1.35300i	0.736442	+	0.676501i	$0.236504\pi$
$811$			38.5309i			1.35300i	−0.736442	+	0.676501i	$0.763496\pi$
$812$	20.1962	+	11.6603i	0.708746	+	0.409195i
$813$		0			0
$814$		−	1.37257i		−	0.0481087i
$815$	0.705563	−	1.22207i	0.0247148	−	0.0428073i
$816$		0			0
$817$	−8.06040	+	4.65368i	−0.281998	+	0.162812i
$818$	9.67405			0.338245
$819$		0			0
$820$	−8.64469			−0.301886
$821$	19.7784	−	11.4191i	0.690272	−	0.398528i	−0.113442	−	0.993545i	$-0.536188\pi$
$821$	19.7784	−	11.4191i	0.690272	−	0.398528i	0.803714	+	0.595016i	$0.202854\pi$
$822$		0			0
$823$	−1.59722	+	2.76647i	−0.0556757	+	0.0964332i	−0.892520	−	0.451008i	$-0.851065\pi$
$823$	−1.59722	+	2.76647i	−0.0556757	+	0.0964332i	0.836844	+	0.547441i	$0.184398\pi$
$824$			2.26795i			0.0790078i
$825$		0			0
$826$	−11.9730	−	6.91264i	−0.416596	−	0.240522i
$827$		−	17.5779i		−	0.611244i	−0.952153	−	0.305622i	$-0.901136\pi$
$827$		−	17.5779i		−	0.611244i	0.952153	−	0.305622i	$-0.0988644\pi$
$828$		0			0
$829$	10.9566	+	18.9774i	0.380540	+	0.659114i	0.991139	−	0.132825i	$-0.0424050\pi$
$829$	10.9566	+	18.9774i	0.380540	+	0.659114i	−0.610600	+	0.791939i	$0.709072\pi$
$830$	1.07346	−	0.619760i	0.0372602	−	0.0215122i
$831$		0			0
$832$	−1.50821	+	3.27495i	−0.0522877	+	0.113539i
$833$	−13.9983			−0.485012
$834$		0			0
$835$	−0.352237	−	0.610092i	−0.0121897	−	0.0211131i
$836$	0.0678739	−	0.117561i	0.00234747	−	0.00406593i
$837$		0			0
$838$	8.09507	+	4.67369i	0.279640	+	0.161450i
$839$	28.9265	+	16.7007i	0.998655	+	0.576574i	0.907850	−	0.419295i	$-0.137723\pi$
$839$	28.9265	+	16.7007i	0.998655	+	0.576574i	0.0908051	+	0.995869i	$0.471056\pi$
$840$		0			0
$841$	−2.57180	+	4.45448i	−0.0886826	+	0.153603i
$842$	−12.7621	−	22.1047i	−0.439812	−	0.761777i
$843$		0			0
$844$	16.7095			0.575165
$845$	9.87861	−	8.45062i	0.339835	−	0.290710i
$846$		0			0
$847$	37.9264	−	21.8968i	1.30317	−	0.752383i
$848$	5.17688	+	8.96661i	0.177775	+	0.307915i
$849$		0			0
$850$		−	1.56787i		−	0.0537776i
$851$	50.6168	+	29.2236i	1.73512	+	1.00177i
$852$		0			0
$853$			35.3037i			1.20877i	0.796691	+	0.604387i	$0.206582\pi$
$853$			35.3037i			1.20877i	−0.796691	+	0.604387i	$0.793418\pi$
$854$	−12.8354	+	22.2315i	−0.439217	+	0.760746i
$855$		0			0
$856$	4.06830	−	2.34883i	0.139052	−	0.0802815i
$857$	52.7645			1.80240			0.901200	−	0.433404i	$-0.142688\pi$
$857$	52.7645			1.80240			0.901200	+	0.433404i	$0.142688\pi$
$858$		0			0
$859$	34.2305			1.16793			0.583964	−	0.811780i	$-0.301501\pi$
$859$	34.2305			1.16793			0.583964	+	0.811780i	$0.301501\pi$
$860$	9.74846	−	5.62828i	0.332420	−	0.191923i
$861$		0			0
$862$	2.05189	−	3.55397i	0.0698875	−	0.121049i
$863$		−	3.33252i		−	0.113440i	−0.998390	−	0.0567202i	$-0.981936\pi$
$863$		−	3.33252i		−	0.113440i	0.998390	−	0.0567202i	$-0.0180643\pi$
$864$		0			0
$865$	−0.567448	−	0.327616i	−0.0192938	−	0.0111393i
$866$		−	2.68783i		−	0.0913362i
$867$		0			0
$868$	−0.171220	−	0.296562i	−0.00581160	−	0.0100660i
$869$	0.883311	−	0.509980i	0.0299643	−	0.0172999i
$870$		0			0
$871$	−5.07180	−	54.9579i	−0.171851	−	1.86218i
$872$	6.17161			0.208997
$873$		0			0
$874$	2.89022	+	5.00601i	0.0977631	+	0.169331i
$875$	−1.99551	+	3.45632i	−0.0674605	+	0.116845i
$876$		0			0
$877$	−14.4702	−	8.35438i	−0.488624	−	0.282107i	0.235379	−	0.971904i	$-0.424367\pi$
$877$	−14.4702	−	8.35438i	−0.488624	−	0.282107i	−0.724003	+	0.689796i	$0.757700\pi$
$878$	−2.14512	−	1.23848i	−0.0723942	−	0.0417968i
$879$		0			0
$880$	−0.0820885	+	0.142181i	−0.00276720	+	0.00479293i
$881$	−11.1797	−	19.3638i	−0.376654	−	0.652383i	0.613919	−	0.789369i	$-0.289592\pi$
$881$	−11.1797	−	19.3638i	−0.376654	−	0.652383i	−0.990573	+	0.136985i	$0.956259\pi$
$882$		0			0
$883$	−13.9499			−0.469450			−0.234725	−	0.972062i	$-0.575419\pi$
$883$	−13.9499			−0.469450			−0.234725	+	0.972062i	$0.575419\pi$
$884$	5.62913	−	0.519485i	0.189328	−	0.0174722i
$885$		0			0
$886$	15.0492	−	8.68868i	0.505589	−	0.291902i
$887$	−1.88845	−	3.27089i	−0.0634078	−	0.109826i	0.832579	−	0.553907i	$-0.186864\pi$
$887$	−1.88845	−	3.27089i	−0.0634078	−	0.109826i	−0.895987	+	0.444081i	$0.853530\pi$
$888$		0			0
$889$		−	32.4244i		−	1.08748i
$890$	8.98652	+	5.18837i	0.301229	+	0.173915i
$891$		0			0
$892$		−	22.8193i		−	0.764048i
$893$	−2.19788	+	3.80683i	−0.0735491	+	0.127391i
$894$		0			0
$895$	6.42011	−	3.70665i	0.214601	−	0.123900i
$896$	3.99102			0.133330
$897$		0			0
$898$	−29.9305			−0.998795
$899$	0.434197	−	0.250684i	0.0144813	−	0.00836078i
$900$		0			0
$901$	8.11669	−	14.0585i	0.270406	−	0.468357i
$902$		−	1.41926i		−	0.0472562i
$903$		0			0
$904$	−9.76403	−	5.63726i	−0.324747	−	0.187493i
$905$		−	0.496077i		−	0.0164902i
$906$		0			0
$907$	1.19449	+	2.06892i	0.0396625	+	0.0686975i	0.885175	−	0.465258i	$-0.154038\pi$
$907$	1.19449	+	2.06892i	0.0396625	+	0.0686975i	−0.845513	+	0.533955i	$0.820705\pi$
$908$	3.28436	−	1.89623i	0.108995	−	0.0629285i
$909$		0			0
$910$	−13.0704	−	6.01928i	−0.433279	−	0.199537i
$911$	−53.5178			−1.77313			−0.886563	−	0.462608i	$-0.846914\pi$
$911$	−53.5178			−1.77313			−0.886563	+	0.462608i	$0.846914\pi$
$912$		0			0
$913$	0.101750	+	0.176237i	0.00336744	+	0.00583258i
$914$	5.73456	−	9.93255i	0.189682	−	0.328540i
$915$		0			0
$916$	−4.06830	−	2.34883i	−0.134420	−	0.0776077i
$917$	71.9033	+	41.5134i	2.37446	+	1.37089i
$918$		0			0
$919$	−12.8564	+	22.2679i	−0.424094	+	0.734552i	−0.996335	−	0.0855332i	$-0.972741\pi$
$919$	−12.8564	+	22.2679i	−0.424094	+	0.734552i	0.572242	+	0.820085i	$0.306074\pi$
$920$	−3.49551	−	6.05440i	−0.115243	−	0.199608i
$921$		0			0
$922$	−24.0067			−0.790619
$923$	17.6617	−	12.4925i	0.581343	−	0.411197i
$924$		0			0
$925$	7.24026	−	4.18016i	0.238058	−	0.137443i
$926$	−13.1582	−	22.7906i	−0.432404	−	0.748946i
$927$		0			0
$928$			5.84325i			0.191814i
$929$	−5.43127	−	3.13575i	−0.178194	−	0.102881i	0.408250	−	0.912870i	$-0.366139\pi$
$929$	−5.43127	−	3.13575i	−0.178194	−	0.102881i	−0.586444	+	0.809990i	$0.699473\pi$
$930$		0			0
$931$		−	7.38218i		−	0.241941i
$932$	14.6876	−	25.4397i	0.481108	−	0.833304i
$933$		0			0
$934$	14.0968	−	8.13878i	0.461261	−	0.266309i
$935$	0.257409			0.00841816
$936$		0			0
$937$	−20.7863			−0.679059			−0.339530	−	0.940595i	$-0.610268\pi$
$937$	−20.7863			−0.679059			−0.339530	+	0.940595i	$0.610268\pi$
$938$	−52.9071	+	30.5459i	−1.72748	+	0.997360i
$939$		0			0
$940$	2.65817	−	4.60408i	0.0866999	−	0.150169i
$941$		−	13.2566i		−	0.432151i	−0.976377	−	0.216076i	$-0.930674\pi$
$941$		−	13.2566i		−	0.432151i	0.976377	−	0.216076i	$-0.0693258\pi$
$942$		0			0
$943$	52.3384	+	30.2176i	1.70437	+	0.984020i
$944$		−	3.46410i		−	0.112747i
$945$		0			0
$946$	0.924033	+	1.60047i	0.0300429	+	0.0520359i
$947$	−14.2379	+	8.22023i	−0.462668	+	0.267122i	−0.713166	−	0.700996i	$-0.752739\pi$
$947$	−14.2379	+	8.22023i	−0.462668	+	0.267122i	0.250497	+	0.968117i	$0.419406\pi$
$948$		0			0
$949$	0.588636	+	0.271083i	0.0191079	+	0.00879974i
$950$	0.826838			0.0268262
$951$		0			0
$952$	−3.12870	−	5.41907i	−0.101402	−	0.175633i
$953$	−13.9047	+	24.0837i	−0.450419	+	0.780148i	−0.998412	−	0.0563345i	$-0.982059\pi$
$953$	−13.9047	+	24.0837i	−0.450419	+	0.780148i	0.547993	+	0.836483i	$0.315392\pi$
$954$		0			0
$955$	21.4726	+	12.3972i	0.694838	+	0.401165i
$956$	−3.63017	−	2.09588i	−0.117408	−	0.0677855i
$957$		0			0
$958$	13.8608	−	24.0075i	0.447821	−	0.775648i
$959$	10.4795	+	18.1510i	0.338400	+	0.586126i
$960$		0			0
$961$	30.9926			0.999763
$962$	17.4069	+	24.6096i	0.561222	+	0.793447i
$963$		0			0
$964$	16.1343	−	9.31513i	0.519650	−	0.300020i
$965$	1.93061	+	3.34392i	0.0621486	+	0.107644i
$966$		0			0
$967$			2.34329i			0.0753552i	0.999290	+	0.0376776i	$0.0119960\pi$
$967$			2.34329i			0.0753552i	−0.999290	+	0.0376776i	$0.988004\pi$
$968$	9.50294	+	5.48652i	0.305436	+	0.176344i
$969$		0			0
$970$			18.9201i			0.607487i
$971$	1.85867	−	3.21931i	0.0596476	−	0.103313i	−0.834660	−	0.550766i	$-0.814336\pi$
$971$	1.85867	−	3.21931i	0.0596476	−	0.103313i	0.894307	+	0.447453i	$0.147669\pi$
$972$		0			0
$973$	−57.7949	+	33.3679i	−1.85282	+	1.06973i
$974$	24.2697			0.777652
$975$		0			0
$976$	−6.43213			−0.205887
$977$	16.6990	−	9.64115i	0.534247	−	0.308448i	−0.208497	−	0.978023i	$-0.566857\pi$
$977$	16.6990	−	9.64115i	0.534247	−	0.308448i	0.742744	+	0.669575i	$0.233524\pi$
$978$		0			0
$979$	−0.851811	+	1.47538i	−0.0272240	+	0.0471533i
$980$			8.92820i			0.285201i
$981$		0			0
$982$	−8.92208	−	5.15117i	−0.284715	−	0.164380i
$983$		−	12.6837i		−	0.404546i	−0.979329	−	0.202273i	$-0.935167\pi$
$983$		−	12.6837i		−	0.404546i	0.979329	−	0.202273i	$-0.0648328\pi$
$984$		0			0
$985$	−2.85782	−	4.94989i	−0.0910577	−	0.157717i
$986$	7.93408	−	4.58074i	0.252672	−	0.145881i
$987$		0			0
$988$	0.273957	+	2.96859i	0.00871573	+	0.0944436i
$989$	−78.6948			−2.50235
$990$		0			0
$991$	−22.2900	−	38.6074i	−0.708065	−	1.22641i	−0.965574	−	0.260129i	$-0.916235\pi$
$991$	−22.2900	−	38.6074i	−0.708065	−	1.22641i	0.257508	−	0.966276i	$-0.417099\pi$
$992$	0.0429015	−	0.0743075i	0.00136212	−	0.00235927i
$993$		0			0
$994$	−20.7379	−	11.9730i	−0.657767	−	0.379762i
$995$	−0.983586	−	0.567874i	−0.0311818	−	0.0180028i
$996$		0			0
$997$	6.20142	−	10.7412i	0.196401	−	0.340177i	−0.750958	−	0.660350i	$-0.770408\pi$
$997$	6.20142	−	10.7412i	0.196401	−	0.340177i	0.947359	+	0.320174i	$0.103741\pi$
$998$	14.1336	+	24.4802i	0.447392	+	0.774906i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.g.361.3		8
3.2	odd	2		130.2.l.b.101.1	✓	8
12.11	even	2		1040.2.da.d.881.3		8
13.4	even	6	inner	1170.2.bs.g.901.3		8
15.2	even	4		650.2.n.d.49.1		8
15.8	even	4		650.2.n.e.49.4		8
15.14	odd	2		650.2.m.c.101.4		8
39.2	even	12		1690.2.a.t.1.3		4
39.5	even	4		1690.2.e.t.991.2		8
39.8	even	4		1690.2.e.s.991.2		8
39.11	even	12		1690.2.a.u.1.3		4
39.17	odd	6		130.2.l.b.121.1	yes	8
39.20	even	12		1690.2.e.s.191.2		8
39.23	odd	6		1690.2.d.k.1351.7		8
39.29	odd	6		1690.2.d.k.1351.3		8
39.32	even	12		1690.2.e.t.191.2		8
39.35	odd	6		1690.2.l.j.1161.3		8
39.38	odd	2		1690.2.l.j.361.3		8
156.95	even	6		1040.2.da.d.641.3		8
195.17	even	12		650.2.n.e.199.4		8
195.89	even	12		8450.2.a.ci.1.2		4
195.119	even	12		8450.2.a.cm.1.2		4
195.134	odd	6		650.2.m.c.251.4		8
195.173	even	12		650.2.n.d.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.1	✓	8	3.2	odd	2
130.2.l.b.121.1	yes	8	39.17	odd	6
650.2.m.c.101.4		8	15.14	odd	2
650.2.m.c.251.4		8	195.134	odd	6
650.2.n.d.49.1		8	15.2	even	4
650.2.n.d.199.1		8	195.173	even	12
650.2.n.e.49.4		8	15.8	even	4
650.2.n.e.199.4		8	195.17	even	12
1040.2.da.d.641.3		8	156.95	even	6
1040.2.da.d.881.3		8	12.11	even	2
1170.2.bs.g.361.3		8	1.1	even	1	trivial
1170.2.bs.g.901.3		8	13.4	even	6	inner
1690.2.a.t.1.3		4	39.2	even	12
1690.2.a.u.1.3		4	39.11	even	12
1690.2.d.k.1351.3		8	39.29	odd	6
1690.2.d.k.1351.7		8	39.23	odd	6
1690.2.e.s.191.2		8	39.20	even	12
1690.2.e.s.991.2		8	39.8	even	4
1690.2.e.t.191.2		8	39.32	even	12
1690.2.e.t.991.2		8	39.5	even	4
1690.2.l.j.361.3		8	39.38	odd	2
1690.2.l.j.1161.3		8	39.35	odd	6
8450.2.a.ci.1.2		4	195.89	even	12
8450.2.a.cm.1.2		4	195.119	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-3.45632 - 1.99551i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.142181 + 0.0820885i) q^{11} +(1.50821 - 3.27495i) q^{13} -3.99102 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.783937 + 1.35782i) q^{17} +(-0.716063 - 0.413419i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.0820885 + 0.142181i) q^{22} +(-3.49551 - 6.05440i) q^{23} -1.00000 q^{25} +(-0.331331 - 3.59030i) q^{26} +(-3.45632 + 1.99551i) q^{28} +(-2.92163 - 5.06040i) q^{29} +0.0858029i q^{31} +(-0.866025 - 0.500000i) q^{32} +1.56787i q^{34} +(1.99551 - 3.45632i) q^{35} +(-7.24026 + 4.18016i) q^{37} -0.826838 q^{38} +1.00000 q^{40} +(-7.48652 + 4.32235i) q^{41} +(5.62828 - 9.74846i) q^{43} +0.164177i q^{44} +(-6.05440 - 3.49551i) q^{46} -5.31634i q^{47} +(4.46410 + 7.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-2.08209 - 2.94362i) q^{52} -10.3538 q^{53} +(-0.0820885 - 0.142181i) q^{55} +(-1.99551 + 3.45632i) q^{56} +(-5.06040 - 2.92163i) q^{58} +(3.00000 + 1.73205i) q^{59} +(3.21606 - 5.57038i) q^{61} +(0.0429015 + 0.0743075i) q^{62} -1.00000 q^{64} +(3.27495 + 1.50821i) q^{65} +(13.2566 - 7.65368i) q^{67} +(0.783937 + 1.35782i) q^{68} -3.99102i q^{70} +(5.19615 + 3.00000i) q^{71} +0.179739i q^{73} +(-4.18016 + 7.24026i) q^{74} +(-0.716063 + 0.413419i) q^{76} +0.655233 q^{77} -6.21257 q^{79} +(0.866025 - 0.500000i) q^{80} +(-4.32235 + 7.48652i) q^{82} -1.23952i q^{83} +(-1.35782 - 0.783937i) q^{85} -11.2566i q^{86} +(0.0820885 + 0.142181i) q^{88} +(8.98652 - 5.18837i) q^{89} +(-11.7480 + 8.30965i) q^{91} -6.99102 q^{92} +(-2.65817 - 4.60408i) q^{94} +(0.413419 - 0.716063i) q^{95} +(16.3853 + 9.46004i) q^{97} +(7.73205 + 4.46410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{10} + 6 q^{11} - 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} + 6 q^{22} - 12 q^{23} - 8 q^{25} - 30 q^{37} + 12 q^{38} + 8 q^{40} - 12 q^{41} + 4 q^{43} + 8 q^{49} - 10 q^{52} - 60 q^{53}+ \cdots + 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^10 + 6 * q^11 - 2 * q^13 - 4 * q^16 - 6 * q^17 - 6 * q^19 + 6 * q^22 - 12 * q^23 - 8 * q^25 - 30 * q^37 + 12 * q^38 + 8 * q^40 - 12 * q^41 + 4 * q^43 + 8 * q^49 - 10 * q^52 - 60 * q^53 + 6 * q^55 + 24 * q^59 + 26 * q^61 - 18 * q^62 - 8 * q^64 - 6 * q^65 + 24 * q^67 + 6 * q^68 - 6 * q^74 - 6 * q^76 + 60 * q^77 + 20 * q^79 - 18 * q^85 - 6 * q^88 + 24 * q^89 - 66 * q^91 - 24 * q^92 - 6 * q^95 - 6 * q^97 + 48 * q^98

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