LMFDB - Embedded newform 1170.2.bj.e.829.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1170.199");

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.bj (of order $6$, degree $2$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 12 x^{13} + 13 x^{12} + 24 x^{11} - 26 x^{10} - 12 x^{9} - 686 x^{8} - 60 x^{7} + \cdots + 390625 $ x^16 + x^14 - 12x^13 + 13x^12 + 24x^11 - 26x^10 - 12x^9 - 686x^8 - 60x^7 - 650x^6 + 3000x^5 + 8125x^4 - 37500x^3 + 15625x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.3
Root			$-2.19357 + 0.433866i$ of defining polynomial
Character	$\chi$	$=$	1170.829
Dual form			1170.2.bj.e.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.721047 - 2.11662i) q^{5} +(0.889112 - 1.53999i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.721047 - 2.11662i) q^{5} +(0.889112 - 1.53999i) q^{7} +1.00000 q^{8} +(-1.47253 + 1.68276i) q^{10} +(-2.73365 + 1.57828i) q^{11} +(-3.27303 + 1.51238i) q^{13} -1.77822 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.96018 - 2.86376i) q^{17} +(4.65809 + 2.68935i) q^{19} +(2.19357 + 0.433866i) q^{20} +(2.73365 + 1.57828i) q^{22} +(-1.19791 + 0.691615i) q^{23} +(-3.96018 + 3.05237i) q^{25} +(2.94627 + 2.07833i) q^{26} +(0.889112 + 1.53999i) q^{28} +(-1.16805 - 2.02312i) q^{29} +9.60853i q^{31} +(-0.500000 + 0.866025i) q^{32} +5.72753i q^{34} +(-3.90066 - 0.771512i) q^{35} +(-3.99285 - 6.91582i) q^{37} -5.37870i q^{38} +(-0.721047 - 2.11662i) q^{40} +(7.38001 - 4.26085i) q^{41} +(-3.55196 - 2.05073i) q^{43} -3.15655i q^{44} +(1.19791 + 0.691615i) q^{46} -4.44209 q^{47} +(1.91896 + 3.32373i) q^{49} +(4.62352 + 1.90343i) q^{50} +(0.326754 - 3.59071i) q^{52} +11.1062i q^{53} +(5.31171 + 4.64810i) q^{55} +(0.889112 - 1.53999i) q^{56} +(-1.16805 + 2.02312i) q^{58} +(-5.17272 - 2.98647i) q^{59} +(-1.72105 + 2.98094i) q^{61} +(8.32123 - 4.80427i) q^{62} +1.00000 q^{64} +(5.56114 + 5.83727i) q^{65} +(2.40690 + 4.16887i) q^{67} +(4.96018 - 2.86376i) q^{68} +(1.28218 + 3.76383i) q^{70} +(8.95295 + 5.16899i) q^{71} -1.21138 q^{73} +(-3.99285 + 6.91582i) q^{74} +(-4.65809 + 2.68935i) q^{76} +5.61306i q^{77} -11.7583 q^{79} +(-1.47253 + 1.68276i) q^{80} +(-7.38001 - 4.26085i) q^{82} -11.3625 q^{83} +(-2.48498 + 12.5637i) q^{85} +4.10145i q^{86} +(-2.73365 + 1.57828i) q^{88} +(-13.4852 + 7.78567i) q^{89} +(-0.581042 + 6.38510i) q^{91} -1.38323i q^{92} +(2.22105 + 3.84697i) q^{94} +(2.33364 - 11.7986i) q^{95} +(-4.34259 + 7.52159i) q^{97} +(1.91896 - 3.32373i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{4} + 16 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^8	$ 16 q - 8 q^{2} - 8 q^{4} + 16 q^{8} - 8 q^{16} - 12 q^{17} - 18 q^{19} + 6 q^{23} + 4 q^{25} - 8 q^{32} + 24 q^{35} - 6 q^{46} - 48 q^{47} - 6 q^{49} - 2 q^{50} + 14 q^{55} - 16 q^{61} + 6 q^{62} + 16 q^{64} + 6 q^{65} + 12 q^{68} + 18 q^{76} + 20 q^{79} - 24 q^{83} - 18 q^{85} - 46 q^{91} + 24 q^{94} + 30 q^{95} - 6 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^8 - 8 * q^16 - 12 * q^17 - 18 * q^19 + 6 * q^23 + 4 * q^25 - 8 * q^32 + 24 * q^35 - 6 * q^46 - 48 * q^47 - 6 * q^49 - 2 * q^50 + 14 * q^55 - 16 * q^61 + 6 * q^62 + 16 * q^64 + 6 * q^65 + 12 * q^68 + 18 * q^76 + 20 * q^79 - 24 * q^83 - 18 * q^85 - 46 * q^91 + 24 * q^94 + 30 * q^95 - 6 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.721047	−	2.11662i	−0.322462	−	0.946582i
$5$	−0.721047	−	2.11662i	−0.322462	−	0.946582i
$6$		0			0
$7$	0.889112	−	1.53999i	0.336053	−	0.582061i	−0.647634	−	0.761952i	$-0.724241\pi$
$7$	0.889112	−	1.53999i	0.336053	−	0.582061i	0.983687	+	0.179891i	$0.0575746\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.47253	+	1.68276i	−0.465653	+	0.532134i
$11$	−2.73365	+	1.57828i	−0.824228	+	0.475868i	−0.851872	−	0.523750i	$-0.824533\pi$
$11$	−2.73365	+	1.57828i	−0.824228	+	0.475868i	0.0276444	+	0.999618i	$0.491199\pi$
$12$		0			0
$13$	−3.27303	+	1.51238i	−0.907774	+	0.419459i
$13$	−3.27303	+	1.51238i	−0.907774	+	0.419459i
$14$	−1.77822			−0.475251
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.96018	−	2.86376i	−1.20302	−	0.694565i	−0.241795	−	0.970327i	$-0.577736\pi$
$17$	−4.96018	−	2.86376i	−1.20302	−	0.694565i	−0.961226	+	0.275763i	$0.911070\pi$
$18$		0			0
$19$	4.65809	+	2.68935i	1.06864	+	0.616980i	0.927810	−	0.373054i	$-0.121689\pi$
$19$	4.65809	+	2.68935i	1.06864	+	0.616980i	0.140831	+	0.990034i	$0.455023\pi$
$20$	2.19357	+	0.433866i	0.490498	+	0.0970155i
$21$		0			0
$22$	2.73365	+	1.57828i	0.582817	+	0.336490i
$23$	−1.19791	+	0.691615i	−0.249782	+	0.144212i	−0.619664	−	0.784867i	$-0.712731\pi$
$23$	−1.19791	+	0.691615i	−0.249782	+	0.144212i	0.369883	+	0.929079i	$0.379398\pi$
$24$		0			0
$25$	−3.96018	+	3.05237i	−0.792037	+	0.610474i
$26$	2.94627	+	2.07833i	0.577812	+	0.407595i
$27$		0			0
$28$	0.889112	+	1.53999i	0.168026	+	0.291030i
$29$	−1.16805	−	2.02312i	−0.216901	−	0.375684i	0.736958	−	0.675939i	$-0.236262\pi$
$29$	−1.16805	−	2.02312i	−0.216901	−	0.375684i	−0.953859	+	0.300255i	$0.902928\pi$
$30$		0			0
$31$			9.60853i			1.72574i	0.505423	+	0.862872i	$0.331337\pi$
$31$			9.60853i			1.72574i	−0.505423	+	0.862872i	$0.668663\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$			5.72753i			0.982263i
$35$	−3.90066	−	0.771512i	−0.659333	−	0.130409i
$36$		0			0
$37$	−3.99285	−	6.91582i	−0.656421	−	1.13695i	−0.981536	−	0.191280i	$-0.938736\pi$
$37$	−3.99285	−	6.91582i	−0.656421	−	1.13695i	0.325115	−	0.945675i	$-0.394597\pi$
$38$		−	5.37870i		−	0.872541i
$39$		0			0
$40$	−0.721047	−	2.11662i	−0.114008	−	0.334667i
$41$	7.38001	−	4.26085i	1.15256	−	0.665433i	0.203054	−	0.979168i	$-0.434913\pi$
$41$	7.38001	−	4.26085i	1.15256	−	0.665433i	0.949511	+	0.313734i	$0.101580\pi$
$42$		0			0
$43$	−3.55196	−	2.05073i	−0.541669	−	0.312733i	0.204086	−	0.978953i	$-0.434578\pi$
$43$	−3.55196	−	2.05073i	−0.541669	−	0.312733i	−0.745755	+	0.666220i	$0.767911\pi$
$44$		−	3.15655i		−	0.475868i
$45$		0			0
$46$	1.19791	+	0.691615i	0.176622	+	0.101973i
$47$	−4.44209			−0.647946			−0.323973	−	0.946066i	$-0.605019\pi$
$47$	−4.44209			−0.647946			−0.323973	+	0.946066i	$0.605019\pi$
$48$		0			0
$49$	1.91896	+	3.32373i	0.274137	+	0.474819i
$50$	4.62352	+	1.90343i	0.653864	+	0.269186i
$51$		0			0
$52$	0.326754	−	3.59071i	0.0453126	−	0.497943i
$53$			11.1062i			1.52556i	0.646659	+	0.762779i	$0.276166\pi$
$53$			11.1062i			1.52556i	−0.646659	+	0.762779i	$0.723834\pi$
$54$		0			0
$55$	5.31171	+	4.64810i	0.716231	+	0.626750i
$56$	0.889112	−	1.53999i	0.118813	−	0.205790i
$57$		0			0
$58$	−1.16805	+	2.02312i	−0.153372	+	0.265649i
$59$	−5.17272	−	2.98647i	−0.673431	−	0.388806i	0.123944	−	0.992289i	$-0.460446\pi$
$59$	−5.17272	−	2.98647i	−0.673431	−	0.388806i	−0.797375	+	0.603484i	$0.793779\pi$
$60$		0			0
$61$	−1.72105	+	2.98094i	−0.220357	+	0.381670i	−0.954917	−	0.296874i	$-0.904056\pi$
$61$	−1.72105	+	2.98094i	−0.220357	+	0.381670i	0.734559	+	0.678545i	$0.237389\pi$
$62$	8.32123	−	4.80427i	1.05680	−	0.610143i
$63$		0			0
$64$	1.00000			0.125000
$65$	5.56114	+	5.83727i	0.689775	+	0.724024i
$66$		0			0
$67$	2.40690	+	4.16887i	0.294050	+	0.509309i	0.974763	−	0.223241i	$-0.0716635\pi$
$67$	2.40690	+	4.16887i	0.294050	+	0.509309i	−0.680714	+	0.732550i	$0.738330\pi$
$68$	4.96018	−	2.86376i	0.601511	−	0.347282i
$69$		0			0
$70$	1.28218	+	3.76383i	0.153250	+	0.449864i
$71$	8.95295	+	5.16899i	1.06252	+	0.613446i	0.926128	−	0.377209i	$-0.123116\pi$
$71$	8.95295	+	5.16899i	1.06252	+	0.613446i	0.136392	+	0.990655i	$0.456449\pi$
$72$		0			0
$73$	−1.21138			−0.141781			−0.0708906	−	0.997484i	$-0.522584\pi$
$73$	−1.21138			−0.141781			−0.0708906	+	0.997484i	$0.522584\pi$
$74$	−3.99285	+	6.91582i	−0.464160	+	0.803948i
$75$		0			0
$76$	−4.65809	+	2.68935i	−0.534320	+	0.308490i
$77$			5.61306i			0.639667i
$78$		0			0
$79$	−11.7583			−1.32291			−0.661455	−	0.749985i	$-0.730061\pi$
$79$	−11.7583			−1.32291			−0.661455	+	0.749985i	$0.730061\pi$
$80$	−1.47253	+	1.68276i	−0.164633	+	0.188138i
$81$		0			0
$82$	−7.38001	−	4.26085i	−0.814986	−	0.470532i
$83$	−11.3625			−1.24719			−0.623596	−	0.781747i	$-0.714329\pi$
$83$	−11.3625			−1.24719			−0.623596	+	0.781747i	$0.714329\pi$
$84$		0			0
$85$	−2.48498	+	12.5637i	−0.269534	+	1.36273i
$86$			4.10145i			0.442271i
$87$		0			0
$88$	−2.73365	+	1.57828i	−0.291409	+	0.168245i
$89$	−13.4852	+	7.78567i	−1.42943	+	0.825280i	−0.997075	−	0.0764259i	$-0.975649\pi$
$89$	−13.4852	+	7.78567i	−1.42943	+	0.825280i	−0.432351	+	0.901705i	$0.642316\pi$
$90$		0			0
$91$	−0.581042	+	6.38510i	−0.0609097	+	0.669340i
$92$		−	1.38323i		−	0.144212i
$93$		0			0
$94$	2.22105	+	3.84697i	0.229083	+	0.396784i
$95$	2.33364	−	11.7986i	0.239426	−	1.21051i
$96$		0			0
$97$	−4.34259	+	7.52159i	−0.440923	+	0.763702i	−0.997758	−	0.0669215i	$-0.978682\pi$
$97$	−4.34259	+	7.52159i	−0.440923	+	0.763702i	0.556835	+	0.830623i	$0.312016\pi$
$98$	1.91896	−	3.32373i	0.193844	−	0.335748i
$99$		0			0
$100$	−0.663337	−	4.95580i	−0.0663337	−	0.495580i
$101$	−0.763156	−	1.32182i	−0.0759369	−	0.131526i	0.825556	−	0.564320i	$-0.190861\pi$
$101$	−0.763156	−	1.32182i	−0.0759369	−	0.131526i	−0.901493	+	0.432793i	$0.857528\pi$
$102$		0			0
$103$		−	3.07998i		−	0.303479i	−0.988421	−	0.151740i	$-0.951513\pi$
$103$		−	3.07998i		−	0.303479i	0.988421	−	0.151740i	$-0.0484875\pi$
$104$	−3.27303	+	1.51238i	−0.320947	+	0.148301i
$105$		0			0
$106$	9.61828	−	5.55312i	0.934210	−	0.539366i
$107$	10.1233	−	5.84470i	0.978659	−	0.565029i	0.0767937	−	0.997047i	$-0.475532\pi$
$107$	10.1233	−	5.84470i	0.978659	−	0.565029i	0.901865	+	0.432018i	$0.142198\pi$
$108$		0			0
$109$			1.53146i			0.146687i	0.997307	+	0.0733435i	$0.0233669\pi$
$109$			1.53146i			0.146687i	−0.997307	+	0.0733435i	$0.976633\pi$
$110$	1.36952	−	6.92413i	0.130579	−	0.660189i
$111$		0			0
$112$	−1.77822			−0.168026
$113$	−0.965229	−	0.557275i	−0.0908011	−	0.0524240i	0.453912	−	0.891047i	$-0.350028\pi$
$113$	−0.965229	−	0.557275i	−0.0908011	−	0.0524240i	−0.544713	+	0.838623i	$0.683361\pi$
$114$		0			0
$115$	2.32764	+	2.03684i	0.217053	+	0.189936i
$116$	2.33610			0.216901
$117$		0			0
$118$			5.97294i			0.549854i
$119$	−8.82032	+	5.09241i	−0.808557	+	0.466821i
$120$		0			0
$121$	−0.518089	+	0.897357i	−0.0470990	+	0.0815779i
$122$	3.44209			0.311633
$123$		0			0
$124$	−8.32123	−	4.80427i	−0.747269	−	0.431436i
$125$	9.31619	+	6.18131i	0.833265	+	0.552873i
$126$		0			0
$127$	17.0876	−	9.86553i	1.51628	−	0.875424i	0.516462	−	0.856310i	$-0.327249\pi$
$127$	17.0876	−	9.86553i	1.51628	−	0.875424i	0.999817	−	0.0191142i	$-0.00608461\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	2.27465	−	7.73473i	0.199500	−	0.678380i
$131$	−8.03168			−0.701731			−0.350865	−	0.936426i	$-0.614113\pi$
$131$	−8.03168			−0.701731			−0.350865	+	0.936426i	$0.614113\pi$
$132$		0			0
$133$	8.28314	−	4.78227i	0.718239	−	0.414676i
$134$	2.40690	−	4.16887i	0.207925	−	0.360136i
$135$		0			0
$136$	−4.96018	−	2.86376i	−0.425332	−	0.245566i
$137$	−10.2814	+	17.8079i	−0.878401	+	1.52143i	−0.0253055	+	0.999680i	$0.508056\pi$
$137$	−10.2814	+	17.8079i	−0.878401	+	1.52143i	−0.853095	+	0.521755i	$0.825277\pi$
$138$		0			0
$139$	0.976865	−	1.69198i	0.0828566	−	0.143512i	−0.821619	−	0.570037i	$-0.806929\pi$
$139$	0.976865	−	1.69198i	0.0828566	−	0.143512i	0.904476	+	0.426525i	$0.140262\pi$
$140$	2.61848	−	2.99232i	0.221302	−	0.252897i
$141$		0			0
$142$		−	10.3380i		−	0.867544i
$143$	6.56037	−	9.30007i	0.548606	−	0.777711i
$144$		0			0
$145$	−3.43996	+	3.93108i	−0.285673	+	0.326459i
$146$	0.605690	+	1.04909i	0.0501272	+	0.0868229i
$147$		0			0
$148$	7.98570			0.656421
$149$	−16.1710	−	9.33634i	−1.32478	−	0.764863i	−0.340294	−	0.940319i	$-0.610527\pi$
$149$	−16.1710	−	9.33634i	−1.32478	−	0.764863i	−0.984487	+	0.175456i	$0.943860\pi$
$150$		0			0
$151$		−	16.2163i		−	1.31966i	−0.751415	−	0.659830i	$-0.770628\pi$
$151$		−	16.2163i		−	1.31966i	0.751415	−	0.659830i	$-0.229372\pi$
$152$	4.65809	+	2.68935i	0.377821	+	0.218135i
$153$		0			0
$154$	4.86105	−	2.80653i	0.391715	−	0.226157i
$155$	20.3376	−	6.92820i	1.63356	−	0.556487i
$156$		0			0
$157$		−	17.7278i		−	1.41483i	−0.706798	−	0.707415i	$-0.749861\pi$
$157$		−	17.7278i		−	1.41483i	0.706798	−	0.707415i	$-0.250139\pi$
$158$	5.87914	+	10.1830i	0.467719	+	0.810114i
$159$		0			0
$160$	2.19357	+	0.433866i	0.173417	+	0.0343002i
$161$			2.45969i			0.193851i
$162$		0			0
$163$	−11.6085	+	20.1065i	−0.909246	+	1.57486i	−0.0941309	+	0.995560i	$0.530007\pi$
$163$	−11.6085	+	20.1065i	−0.909246	+	1.57486i	−0.815115	+	0.579300i	$0.803326\pi$
$164$			8.52171i			0.665433i
$165$		0			0
$166$	5.68123	+	9.84018i	0.440949	+	0.763746i
$167$	3.57600	+	6.19381i	0.276719	+	0.479291i	0.970567	−	0.240830i	$-0.0774196\pi$
$167$	3.57600	+	6.19381i	0.276719	+	0.479291i	−0.693848	+	0.720121i	$0.744086\pi$
$168$		0			0
$169$	8.42541	−	9.90012i	0.648109	−	0.761548i
$170$	12.1230	−	4.12981i	0.929793	−	0.316742i
$171$		0			0
$172$	3.55196	−	2.05073i	0.270835	−	0.156366i
$173$	1.86105	+	1.07448i	0.141493	+	0.0816911i	0.569075	−	0.822285i	$-0.307301\pi$
$173$	1.86105	+	1.07448i	0.141493	+	0.0816911i	−0.427582	+	0.903976i	$0.640635\pi$
$174$		0			0
$175$	1.17956	+	8.81253i	0.0891665	+	0.666165i
$176$	2.73365	+	1.57828i	0.206057	+	0.118967i
$177$		0			0
$178$	13.4852	+	7.78567i	1.01076	+	0.583561i
$179$	−9.01927	−	15.6218i	−0.674132	−	1.16763i	−0.976722	−	0.214510i	$-0.931185\pi$
$179$	−9.01927	−	15.6218i	−0.674132	−	1.16763i	0.302590	−	0.953121i	$-0.402149\pi$
$180$		0			0
$181$	14.3986			1.07024			0.535121	−	0.844775i	$-0.320266\pi$
$181$	14.3986			1.07024			0.535121	+	0.844775i	$0.320266\pi$
$182$	5.82018	−	2.68935i	0.431420	−	0.199348i
$183$		0			0
$184$	−1.19791	+	0.691615i	−0.0883112	+	0.0509865i
$185$	−11.7592	+	13.4380i	−0.864550	+	0.987981i
$186$		0			0
$187$	18.0792			1.32208
$188$	2.22105	−	3.84697i	0.161986	−	0.280569i
$189$		0			0
$190$	−11.3847	+	3.87830i	−0.825932	+	0.281361i
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	−6.72651	−	11.6507i	−0.484185	−	0.838632i	0.515650	−	0.856799i	$-0.327550\pi$
$193$	−6.72651	−	11.6507i	−0.484185	−	0.838632i	−0.999835	+	0.0181669i	$0.994217\pi$
$194$	8.68518			0.623560
$195$		0			0
$196$	−3.83792			−0.274137
$197$	1.02314	+	1.77212i	0.0728954	+	0.126258i	0.900169	−	0.435541i	$-0.143443\pi$
$197$	1.02314	+	1.77212i	0.0728954	+	0.126258i	−0.827274	+	0.561799i	$0.810109\pi$
$198$		0			0
$199$	3.12332	−	5.40975i	0.221407	−	0.383487i	−0.733829	−	0.679334i	$-0.762269\pi$
$199$	3.12332	−	5.40975i	0.221407	−	0.383487i	0.955235	+	0.295847i	$0.0956019\pi$
$200$	−3.96018	+	3.05237i	−0.280027	+	0.215835i
$201$		0			0
$202$	−0.763156	+	1.32182i	−0.0536955	+	0.0930033i
$203$	−4.15411			−0.291561
$204$		0			0
$205$	−14.3400	−	12.5484i	−1.00155	−	0.876420i
$206$	−2.66734	+	1.53999i	−0.185842	+	0.107296i
$207$		0			0
$208$	2.94627	+	2.07833i	0.204287	+	0.144107i
$209$	−16.9782			−1.17440
$210$		0			0
$211$	−11.4551	−	19.8409i	−0.788604	−	1.36590i	−0.926822	−	0.375501i	$-0.877471\pi$
$211$	−11.4551	−	19.8409i	−0.788604	−	1.36590i	0.138218	−	0.990402i	$-0.455863\pi$
$212$	−9.61828	−	5.55312i	−0.660586	−	0.381390i
$213$		0			0
$214$	−10.1233	−	5.84470i	−0.692016	−	0.399536i
$215$	−1.77948	+	8.99684i	−0.121360	+	0.613579i
$216$		0			0
$217$	14.7970	+	8.54307i	1.00449	+	0.579941i
$218$	1.32628	−	0.765729i	0.0898271	−	0.0518617i
$219$		0			0
$220$	−6.68123	+	2.27602i	−0.450448	+	0.153449i
$221$	20.5659	+	1.87149i	1.38341	+	0.125890i
$222$		0			0
$223$	−10.9668	−	18.9950i	−0.734390	−	1.27200i	−0.954990	−	0.296637i	$-0.904135\pi$
$223$	−10.9668	−	18.9950i	−0.734390	−	1.27200i	0.220600	−	0.975364i	$-0.429198\pi$
$224$	0.889112	+	1.53999i	0.0594063	+	0.102895i
$225$		0			0
$226$			1.11455i			0.0741388i
$227$	−0.318770	+	0.552126i	−0.0211575	+	0.0366459i	−0.876410	−	0.481565i	$-0.840068\pi$
$227$	−0.318770	+	0.552126i	−0.0211575	+	0.0366459i	0.855253	+	0.518211i	$0.173402\pi$
$228$		0			0
$229$		−	15.7530i		−	1.04099i	−0.853866	−	0.520493i	$-0.825748\pi$
$229$		−	15.7530i		−	1.04099i	0.853866	−	0.520493i	$-0.174252\pi$
$230$	0.600137	−	3.03421i	0.0395718	−	0.200070i
$231$		0			0
$232$	−1.16805	−	2.02312i	−0.0766861	−	0.132824i
$233$			5.08169i			0.332912i	0.986049	+	0.166456i	$0.0532324\pi$
$233$			5.08169i			0.332912i	−0.986049	+	0.166456i	$0.946768\pi$
$234$		0			0
$235$	3.20296	+	9.40224i	0.208938	+	0.613334i
$236$	5.17272	−	2.98647i	0.336716	−	0.194403i
$237$		0			0
$238$	8.82032	+	5.09241i	0.571736	+	0.330092i
$239$			21.3319i			1.37984i	0.723884	+	0.689922i	$0.242355\pi$
$239$			21.3319i			1.37984i	−0.723884	+	0.689922i	$0.757645\pi$
$240$		0			0
$241$	−16.4688	−	9.50824i	−1.06085	−	0.612479i	−0.135179	−	0.990821i	$-0.543161\pi$
$241$	−16.4688	−	9.50824i	−1.06085	−	0.612479i	−0.925666	+	0.378342i	$0.876494\pi$
$242$	1.03618			0.0666081
$243$		0			0
$244$	−1.72105	−	2.98094i	−0.110179	−	0.190835i
$245$	5.65143	−	6.45828i	0.361057	−	0.412604i
$246$		0			0
$247$	−19.3134	−	1.75751i	−1.22888	−	0.111828i
$248$			9.60853i			0.610143i
$249$		0			0
$250$	0.695079	−	11.1587i	0.0439607	−	0.705739i
$251$	11.1198	−	19.2600i	0.701873	−	1.21568i	−0.265935	−	0.963991i	$-0.585681\pi$
$251$	11.1198	−	19.2600i	0.701873	−	1.21568i	0.967808	−	0.251689i	$-0.0809861\pi$
$252$		0			0
$253$	2.18312	−	3.78127i	0.137251	−	0.237726i
$254$	−17.0876	−	9.86553i	−1.07217	−	0.619018i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.96523	−	2.28933i	0.247344	−	0.142804i	−0.371203	−	0.928552i	$-0.621055\pi$
$257$	3.96523	−	2.28933i	0.247344	−	0.142804i	0.618548	+	0.785747i	$0.287721\pi$
$258$		0			0
$259$	−14.2004			−0.882368
$260$	−7.83579	+	1.89746i	−0.485955	+	0.117675i
$261$		0			0
$262$	4.01584	+	6.95563i	0.248099	+	0.429721i
$263$	3.05896	−	1.76609i	0.188624	−	0.108902i	−0.402714	−	0.915326i	$-0.631933\pi$
$263$	3.05896	−	1.76609i	0.188624	−	0.108902i	0.591338	+	0.806424i	$0.298600\pi$
$264$		0			0
$265$	23.5077	−	8.00811i	1.44407	−	0.491934i
$266$	−8.28314	−	4.78227i	−0.507872	−	0.293220i
$267$		0			0
$268$	−4.81380			−0.294050
$269$	−4.76783	+	8.25812i	−0.290700	+	0.503507i	−0.973975	−	0.226654i	$-0.927221\pi$
$269$	−4.76783	+	8.25812i	−0.290700	+	0.503507i	0.683276	+	0.730160i	$0.260555\pi$
$270$		0			0
$271$	21.6475	−	12.4982i	1.31499	−	0.759212i	0.332074	−	0.943253i	$-0.392251\pi$
$271$	21.6475	−	12.4982i	1.31499	−	0.759212i	0.982918	+	0.184042i	$0.0589181\pi$
$272$			5.72753i			0.347282i
$273$		0			0
$274$	20.5628			1.24225
$275$	6.00829	−	14.5944i	0.362314	−	0.880074i
$276$		0			0
$277$	−8.15315	−	4.70722i	−0.489875	−	0.282829i	0.234648	−	0.972081i	$-0.424606\pi$
$277$	−8.15315	−	4.70722i	−0.489875	−	0.282829i	−0.724523	+	0.689251i	$0.757940\pi$
$278$	−1.95373			−0.117177
$279$		0			0
$280$	−3.90066	−	0.771512i	−0.233109	−	0.0461067i
$281$			0.208368i			0.0124302i	0.999981	+	0.00621510i	$0.00197834\pi$
$281$			0.208368i			0.0124302i	−0.999981	+	0.00621510i	$0.998022\pi$
$282$		0			0
$283$	−1.78271	+	1.02925i	−0.105971	+	0.0611825i	−0.552049	−	0.833812i	$-0.686154\pi$
$283$	−1.78271	+	1.02925i	−0.105971	+	0.0611825i	0.446078	+	0.894994i	$0.352820\pi$
$284$	−8.95295	+	5.16899i	−0.531260	+	0.306723i
$285$		0			0
$286$	−11.3343	−	1.03142i	−0.670210	−	0.0609889i
$287$		−	15.1535i		−	0.894483i
$288$		0			0
$289$	7.90228	+	13.6871i	0.464840	+	0.805126i
$290$	5.12440	+	1.01355i	0.300915	+	0.0595179i
$291$		0			0
$292$	0.605690	−	1.04909i	0.0354453	−	0.0613931i
$293$	−2.58210	+	4.47233i	−0.150848	+	0.261276i	−0.931539	−	0.363640i	$-0.881534\pi$
$293$	−2.58210	+	4.47233i	−0.150848	+	0.261276i	0.780692	+	0.624917i	$0.214867\pi$
$294$		0			0
$295$	−2.59146	+	13.1021i	−0.150881	+	0.762833i
$296$	−3.99285	−	6.91582i	−0.232080	−	0.401974i
$297$		0			0
$298$			18.6727i			1.08168i
$299$	2.87481	−	4.07537i	0.166255	−	0.235685i
$300$		0			0
$301$	−6.31619	+	3.64665i	−0.364059	+	0.210190i
$302$	−14.0437	+	8.10813i	−0.808124	+	0.466570i
$303$		0			0
$304$		−	5.37870i		−	0.308490i
$305$	7.55048	+	1.49341i	0.432339	+	0.0855123i
$306$		0			0
$307$	−9.00012			−0.513664			−0.256832	−	0.966456i	$-0.582679\pi$
$307$	−9.00012			−0.513664			−0.256832	+	0.966456i	$0.582679\pi$
$308$	−4.86105	−	2.80653i	−0.276984	−	0.159917i
$309$		0			0
$310$	−16.1688	−	14.1488i	−0.918327	−	0.803599i
$311$	1.43068			0.0811262			0.0405631	−	0.999177i	$-0.487085\pi$
$311$	1.43068			0.0811262			0.0405631	+	0.999177i	$0.487085\pi$
$312$		0			0
$313$		−	14.2524i		−	0.805595i	−0.915289	−	0.402797i	$-0.868038\pi$
$313$		−	14.2524i		−	0.805595i	0.915289	−	0.402797i	$-0.131962\pi$
$314$	−15.3527	+	8.86389i	−0.866403	+	0.500218i
$315$		0			0
$316$	5.87914	−	10.1830i	0.330728	−	0.572837i
$317$	−0.372552			−0.0209246			−0.0104623	−	0.999945i	$-0.503330\pi$
$317$	−0.372552			−0.0209246			−0.0104623	+	0.999945i	$0.503330\pi$
$318$		0			0
$319$	6.38608	+	3.68701i	0.357552	+	0.206433i
$320$	−0.721047	−	2.11662i	−0.0403077	−	0.118323i
$321$		0			0
$322$	2.13016	−	1.22985i	0.118709	−	0.0685366i
$323$	−15.4033	−	26.6794i	−0.857064	−	1.48448i
$324$		0			0
$325$	8.34544	−	15.9798i	0.462922	−	0.886399i
$326$	23.2169			1.28587
$327$		0			0
$328$	7.38001	−	4.26085i	0.407493	−	0.235266i
$329$	−3.94952	+	6.84077i	−0.217744	+	0.377144i
$330$		0			0
$331$	−13.3263	−	7.69393i	−0.732479	−	0.422897i	0.0868496	−	0.996221i	$-0.472320\pi$
$331$	−13.3263	−	7.69393i	−0.732479	−	0.422897i	−0.819328	+	0.573325i	$0.805653\pi$
$332$	5.68123	−	9.84018i	0.311798	−	0.540050i
$333$		0			0
$334$	3.57600	−	6.19381i	0.195670	−	0.338910i
$335$	7.08845	−	8.10045i	0.387283	−	0.442575i
$336$		0			0
$337$			16.5715i			0.902705i	0.892346	+	0.451352i	$0.149058\pi$
$337$			16.5715i			0.902705i	−0.892346	+	0.451352i	$0.850942\pi$
$338$	−12.7865	−	2.34656i	−0.695492	−	0.127636i
$339$		0			0
$340$	−9.63803	−	8.43393i	−0.522696	−	0.457394i
$341$	−15.1649	−	26.2664i	−0.821226	−	1.42241i
$342$		0			0
$343$	19.2723			1.04060
$344$	−3.55196	−	2.05073i	−0.191509	−	0.110568i
$345$		0			0
$346$		−	2.14896i		−	0.115529i
$347$	−31.4395	−	18.1516i	−1.68776	−	0.974430i	−0.956227	−	0.292625i	$-0.905471\pi$
$347$	−31.4395	−	18.1516i	−1.68776	−	0.974430i	−0.731534	−	0.681805i	$-0.761195\pi$
$348$		0			0
$349$	−4.67372	+	2.69837i	−0.250178	+	0.144441i	−0.619846	−	0.784724i	$-0.712805\pi$
$349$	−4.67372	+	2.69837i	−0.250178	+	0.144441i	0.369668	+	0.929164i	$0.379472\pi$
$350$	7.04210	−	5.42780i	0.376416	−	0.290128i
$351$		0			0
$352$		−	3.15655i		−	0.168245i
$353$	9.40228	+	16.2852i	0.500433	+	0.866775i	1.00000		0.000499698i	$0.000159059\pi$
$353$	9.40228	+	16.2852i	0.500433	+	0.866775i	−0.499567	+	0.866275i	$0.666508\pi$
$354$		0			0
$355$	4.48530	−	22.6771i	0.238055	−	1.20358i
$356$		−	15.5713i		−	0.825280i
$357$		0			0
$358$	−9.01927	+	15.6218i	−0.476683	+	0.825640i
$359$			6.28869i			0.331905i	0.986134	+	0.165952i	$0.0530698\pi$
$359$			6.28869i			0.331905i	−0.986134	+	0.165952i	$0.946930\pi$
$360$		0			0
$361$	4.96523	+	8.60003i	0.261328	+	0.452633i
$362$	−7.19932	−	12.4696i	−0.378388	−	0.655387i
$363$		0			0
$364$	−5.23914	−	3.69575i	−0.274605	−	0.193710i
$365$	0.873461	+	2.56403i	0.0457191	+	0.134208i
$366$		0			0
$367$	20.1106	−	11.6108i	1.04976	−	0.606081i	0.127180	−	0.991880i	$-0.459407\pi$
$367$	20.1106	−	11.6108i	1.04976	−	0.606081i	0.922583	+	0.385799i	$0.126074\pi$
$368$	1.19791	+	0.691615i	0.0624455	+	0.0360529i
$369$		0			0
$370$	17.5172	+	3.46473i	0.910677	+	0.180123i
$371$	17.1035	+	9.87469i	0.887967	+	0.512668i
$372$		0			0
$373$	18.4924	+	10.6766i	0.957502	+	0.552814i	0.895403	−	0.445256i	$-0.146887\pi$
$373$	18.4924	+	10.6766i	0.957502	+	0.552814i	0.0620989	+	0.998070i	$0.480221\pi$
$374$	−9.03962	−	15.6571i	−0.467427	−	0.809608i
$375$		0			0
$376$	−4.44209			−0.229083
$377$	6.88278	+	4.85519i	0.354481	+	0.250055i
$378$		0			0
$379$	0.940686	−	0.543105i	0.0483198	−	0.0278974i	−0.475645	−	0.879637i	$-0.657785\pi$
$379$	0.940686	−	0.543105i	0.0483198	−	0.0278974i	0.523965	+	0.851740i	$0.324452\pi$
$380$	9.05105	+	7.92028i	0.464309	+	0.406302i
$381$		0			0
$382$		0			0
$383$	14.3212	−	24.8051i	0.731781	−	1.26748i	−0.224340	−	0.974511i	$-0.572023\pi$
$383$	14.3212	−	24.8051i	0.731781	−	1.26748i	0.956121	−	0.292971i	$-0.0946439\pi$
$384$		0			0
$385$	11.8807	−	4.04728i	0.605498	−	0.206268i
$386$	−6.72651	+	11.6507i	−0.342370	+	0.593002i
$387$		0			0
$388$	−4.34259	−	7.52159i	−0.220462	−	0.381851i
$389$	−32.3420			−1.63981			−0.819903	−	0.572502i	$-0.805973\pi$
$389$	−32.3420			−1.63981			−0.819903	+	0.572502i	$0.805973\pi$
$390$		0			0
$391$	7.92248			0.400657
$392$	1.91896	+	3.32373i	0.0969220	+	0.167874i
$393$		0			0
$394$	1.02314	−	1.77212i	0.0515448	−	0.0892782i
$395$	8.47827	+	24.8878i	0.426588	+	1.25224i
$396$		0			0
$397$	−17.1946	+	29.7819i	−0.862973	+	1.49471i	0.00607355	+	0.999982i	$0.498067\pi$
$397$	−17.1946	+	29.7819i	−0.862973	+	1.49471i	−0.869046	+	0.494731i	$0.835267\pi$
$398$	−6.24665			−0.313116
$399$		0			0
$400$	4.62352	+	1.90343i	0.231176	+	0.0951717i
$401$	−33.6647	+	19.4363i	−1.68113	+	0.970604i	−0.720226	+	0.693740i	$0.755962\pi$
$401$	−33.6647	+	19.4363i	−1.68113	+	0.970604i	−0.960909	+	0.276864i	$0.910705\pi$
$402$		0			0
$403$	−14.5318	−	31.4490i	−0.723878	−	1.56659i
$404$	1.52631			0.0759369
$405$		0			0
$406$	2.07705	+	3.59756i	0.103082	+	0.178544i
$407$	21.8302	+	12.6036i	1.08208	+	0.624739i
$408$		0			0
$409$	−16.1374	−	9.31695i	−0.797944	−	0.460693i	0.0448076	−	0.998996i	$-0.485733\pi$
$409$	−16.1374	−	9.31695i	−0.797944	−	0.460693i	−0.842752	+	0.538302i	$0.819066\pi$
$410$	−3.69728	+	18.6930i	−0.182596	+	0.923180i
$411$		0			0
$412$	2.66734	+	1.53999i	0.131410	+	0.0758698i
$413$	−9.19826	+	5.31062i	−0.452617	+	0.261318i
$414$		0			0
$415$	8.19287	+	24.0500i	0.402172	+	1.18057i
$416$	0.326754	−	3.59071i	0.0160204	−	0.176049i
$417$		0			0
$418$	8.48908	+	14.7035i	0.415214	+	0.719173i
$419$	−5.46731	−	9.46966i	−0.267096	−	0.462623i	0.701015	−	0.713147i	$-0.252731\pi$
$419$	−5.46731	−	9.46966i	−0.267096	−	0.462623i	−0.968111	+	0.250524i	$0.919397\pi$
$420$		0			0
$421$		−	1.33143i		−	0.0648897i	−0.999474	−	0.0324449i	$-0.989671\pi$
$421$		−	1.33143i		−	0.0648897i	0.999474	−	0.0324449i	$-0.0103293\pi$
$422$	−11.4551	+	19.8409i	−0.557627	+	0.965839i
$423$		0			0
$424$			11.1062i			0.539366i
$425$	28.3845	−	3.79928i	1.37685	−	0.184292i
$426$		0			0
$427$	3.06041	+	5.30078i	0.148104	+	0.256523i
$428$			11.6894i			0.565029i
$429$		0			0
$430$	8.68123	−	2.95734i	0.418646	−	0.142616i
$431$	12.1945	−	7.04048i	0.587387	−	0.339128i	−0.176677	−	0.984269i	$-0.556535\pi$
$431$	12.1945	−	7.04048i	0.587387	−	0.339128i	0.764064	+	0.645141i	$0.223201\pi$
$432$		0			0
$433$	−34.5786	−	19.9640i	−1.66174	−	0.959408i	−0.971883	−	0.235466i	$-0.924338\pi$
$433$	−34.5786	−	19.9640i	−1.66174	−	0.959408i	−0.689861	−	0.723942i	$-0.742328\pi$
$434$		−	17.0861i		−	0.820161i
$435$		0			0
$436$	−1.32628	−	0.765729i	−0.0635173	−	0.0366718i
$437$	−7.43998			−0.355902
$438$		0			0
$439$	−0.192865	−	0.334053i	−0.00920496	−	0.0159435i	0.861386	−	0.507951i	$-0.169597\pi$
$439$	−0.192865	−	0.334053i	−0.00920496	−	0.0159435i	−0.870591	+	0.492007i	$0.836263\pi$
$440$	5.31171	+	4.64810i	0.253226	+	0.221590i
$441$		0			0
$442$	−8.66220	−	18.7463i	−0.412019	−	0.891673i
$443$		−	9.52241i		−	0.452423i	−0.974078	−	0.226212i	$-0.927366\pi$
$443$		−	9.52241i		−	0.452423i	0.974078	−	0.226212i	$-0.0726341\pi$
$444$		0			0
$445$	26.2028	+	22.9292i	1.24213	+	1.08695i
$446$	−10.9668	+	18.9950i	−0.519292	+	0.899441i
$447$		0			0
$448$	0.889112	−	1.53999i	0.0420066	−	0.0727576i
$449$	24.5524	+	14.1754i	1.15870	+	0.668976i	0.950992	−	0.309215i	$-0.100066\pi$
$449$	24.5524	+	14.1754i	1.15870	+	0.668976i	0.207709	+	0.978191i	$0.433399\pi$
$450$		0			0
$451$	−13.4496	+	23.2954i	−0.633317	+	1.09694i
$452$	0.965229	−	0.557275i	0.0454006	−	0.0262120i
$453$		0			0
$454$	0.637540			0.0299213
$455$	13.9338	−	3.37411i	0.653227	−	0.158181i
$456$		0			0
$457$	9.07158	+	15.7124i	0.424350	+	0.734997i	0.996360	−	0.0852508i	$-0.0271691\pi$
$457$	9.07158	+	15.7124i	0.424350	+	0.734997i	−0.572009	+	0.820247i	$0.693836\pi$
$458$	−13.6425	+	7.87648i	−0.637471	+	0.368044i
$459$		0			0
$460$	−2.92777	+	0.997373i	−0.136508	+	0.0465028i
$461$	−0.358264	−	0.206844i	−0.0166860	−	0.00963366i	0.491634	−	0.870802i	$-0.336400\pi$
$461$	−0.358264	−	0.206844i	−0.0166860	−	0.00963366i	−0.508320	+	0.861168i	$0.669733\pi$
$462$		0			0
$463$	−12.7299			−0.591608			−0.295804	−	0.955249i	$-0.595588\pi$
$463$	−12.7299			−0.591608			−0.295804	+	0.955249i	$0.595588\pi$
$464$	−1.16805	+	2.02312i	−0.0542253	+	0.0939210i
$465$		0			0
$466$	4.40087	−	2.54084i	0.203866	−	0.117702i
$467$		−	18.2851i		−	0.846132i	−0.906099	−	0.423066i	$-0.860954\pi$
$467$		−	18.2851i		−	0.846132i	0.906099	−	0.423066i	$-0.139046\pi$
$468$		0			0
$469$	8.56002			0.395265
$470$	6.54110	−	7.47496i	0.301718	−	0.344794i
$471$		0			0
$472$	−5.17272	−	2.98647i	−0.238094	−	0.137464i
$473$	12.9465			0.595279
$474$		0			0
$475$	−26.6558	+	3.56789i	−1.22305	+	0.163706i
$476$		−	10.1848i		−	0.466821i
$477$		0			0
$478$	18.4739	−	10.6659i	0.844978	−	0.487849i
$479$	−13.0595	+	7.53990i	−0.596703	+	0.344507i	−0.767744	−	0.640757i	$-0.778621\pi$
$479$	−13.0595	+	7.53990i	−0.596703	+	0.344507i	0.171040	+	0.985264i	$0.445287\pi$
$480$		0			0
$481$	23.5281	+	16.5970i	1.07279	+	0.756756i
$482$			19.0165i			0.866177i
$483$		0			0
$484$	−0.518089	−	0.897357i	−0.0235495	−	0.0407890i
$485$	19.0516	+	3.76821i	0.865088	+	0.171106i
$486$		0			0
$487$	−6.68602	+	11.5805i	−0.302973	+	0.524764i	−0.976808	−	0.214118i	$-0.931312\pi$
$487$	−6.68602	+	11.5805i	−0.302973	+	0.524764i	0.673835	+	0.738882i	$0.264646\pi$
$488$	−1.72105	+	2.98094i	−0.0779081	+	0.134941i
$489$		0			0
$490$	−8.41875	−	1.66514i	−0.380320	−	0.0752235i
$491$	9.52832	+	16.5035i	0.430007	+	0.744794i	0.996873	−	0.0790155i	$-0.0251777\pi$
$491$	9.52832	+	16.5035i	0.430007	+	0.744794i	−0.566866	+	0.823810i	$0.691844\pi$
$492$		0			0
$493$			13.3801i			0.602607i
$494$	8.13465	+	17.6046i	0.365995	+	0.792070i
$495$		0			0
$496$	8.32123	−	4.80427i	0.373634	−	0.215718i
$497$	15.9204	−	9.19163i	0.714126	−	0.412301i
$498$		0			0
$499$		−	5.39675i		−	0.241592i	−0.992677	−	0.120796i	$-0.961455\pi$
$499$		−	5.39675i		−	0.241592i	0.992677	−	0.120796i	$-0.0385446\pi$
$500$	−10.0113	+	4.97740i	−0.447718	+	0.222596i
$501$		0			0
$502$	−22.2395			−0.992599
$503$	27.9047	+	16.1108i	1.24421	+	0.718346i	0.969949	−	0.243309i	$-0.0782331\pi$
$503$	27.9047	+	16.1108i	1.24421	+	0.718346i	0.274262	+	0.961655i	$0.411566\pi$
$504$		0			0
$505$	−2.24753	+	2.56841i	−0.100014	+	0.114293i
$506$	−4.36623			−0.194103
$507$		0			0
$508$			19.7311i			0.875424i
$509$	21.9992	−	12.7013i	0.975099	−	0.562973i	0.0743118	−	0.997235i	$-0.476324\pi$
$509$	21.9992	−	12.7013i	0.975099	−	0.562973i	0.900787	+	0.434262i	$0.142991\pi$
$510$		0			0
$511$	−1.07705	+	1.86551i	−0.0476460	+	0.0825253i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.96523	−	2.28933i	−0.174899	−	0.100978i
$515$	−6.51915	+	2.22081i	−0.287268	+	0.0978604i
$516$		0			0
$517$	12.1431	−	7.01085i	0.534055	−	0.308337i
$518$	7.10019	+	12.2979i	0.311964	+	0.540338i
$519$		0			0
$520$	5.56114	+	5.83727i	0.243872	+	0.255981i
$521$	24.2786			1.06367			0.531833	−	0.846849i	$-0.321503\pi$
$521$	24.2786			1.06367			0.531833	+	0.846849i	$0.321503\pi$
$522$		0			0
$523$	−7.28174	+	4.20411i	−0.318408	+	0.183833i	−0.650683	−	0.759350i	$-0.725517\pi$
$523$	−7.28174	+	4.20411i	−0.318408	+	0.183833i	0.332275	+	0.943183i	$0.392184\pi$
$524$	4.01584	−	6.95563i	0.175433	−	0.303858i
$525$		0			0
$526$	−3.05896	−	1.76609i	−0.133377	−	0.0770053i
$527$	27.5166	−	47.6601i	1.19864	−	2.07611i
$528$		0			0
$529$	−10.5433	+	18.2616i	−0.458406	+	0.793983i
$530$	−18.6891	−	16.3542i	−0.811802	−	0.710381i
$531$		0			0
$532$			9.56455i			0.414676i
$533$	−17.7110	+	25.1073i	−0.767147	+	1.08752i
$534$		0			0
$535$	−19.6704	−	17.2130i	−0.850427	−	0.744181i
$536$	2.40690	+	4.16887i	0.103962	+	0.180068i
$537$		0			0
$538$	9.53566			0.411111
$539$	−10.4915	−	6.05729i	−0.451903	−	0.260906i
$540$		0			0
$541$			29.4093i			1.26441i	0.774803	+	0.632203i	$0.217849\pi$
$541$			29.4093i			1.26441i	−0.774803	+	0.632203i	$0.782151\pi$
$542$	−21.6475	−	12.4982i	−0.929840	−	0.536844i
$543$		0			0
$544$	4.96018	−	2.86376i	0.212666	−	0.122783i
$545$	3.24152	−	1.10425i	0.138851	−	0.0473010i
$546$		0			0
$547$			7.65743i			0.327408i	0.986510	+	0.163704i	$0.0523442\pi$
$547$			7.65743i			0.327408i	−0.986510	+	0.163704i	$0.947656\pi$
$548$	−10.2814	−	17.8079i	−0.439200	−	0.760717i
$549$		0			0
$550$	−15.6433	+	2.09386i	−0.667030	+	0.0892824i
$551$		−	12.5652i		−	0.535294i
$552$		0			0
$553$	−10.4544	+	18.1076i	−0.444568	+	0.770014i
$554$			9.41444i			0.399981i
$555$		0			0
$556$	0.976865	+	1.69198i	0.0414283	+	0.0717559i
$557$	18.6183	+	32.2478i	0.788882	+	1.36638i	0.926652	+	0.375919i	$0.122673\pi$
$557$	18.6183	+	32.2478i	0.788882	+	1.36638i	−0.137771	+	0.990464i	$0.543994\pi$
$558$		0			0
$559$	14.7271	+	1.34017i	0.622892	+	0.0566830i
$560$	1.28218	+	3.76383i	0.0541821	+	0.159051i
$561$		0			0
$562$	0.180452	−	0.104184i	0.00761191	−	0.00439474i
$563$	−7.06954	−	4.08160i	−0.297946	−	0.172019i	0.343574	−	0.939126i	$-0.388362\pi$
$563$	−7.06954	−	4.08160i	−0.297946	−	0.172019i	−0.641520	+	0.767107i	$0.721696\pi$
$564$		0			0
$565$	−0.483566	+	2.44485i	−0.0203438	+	0.102855i
$566$	1.78271	+	1.02925i	0.0749329	+	0.0432626i
$567$		0			0
$568$	8.95295	+	5.16899i	0.375658	+	0.216886i
$569$	−3.94952	−	6.84077i	−0.165573	−	0.286780i	0.771286	−	0.636489i	$-0.219614\pi$
$569$	−3.94952	−	6.84077i	−0.165573	−	0.286780i	−0.936858	+	0.349709i	$0.886281\pi$
$570$		0			0
$571$	−23.1771			−0.969932			−0.484966	−	0.874533i	$-0.661168\pi$
$571$	−23.1771			−0.969932			−0.484966	+	0.874533i	$0.661168\pi$
$572$	4.77391	+	10.3315i	0.199607	+	0.431981i
$573$		0			0
$574$	−13.1233	+	7.57675i	−0.547757	+	0.316248i
$575$	2.63289	−	6.39539i	0.109799	−	0.266706i
$576$		0			0
$577$	−12.3666			−0.514829			−0.257414	−	0.966301i	$-0.582871\pi$
$577$	−12.3666			−0.514829			−0.257414	+	0.966301i	$0.582871\pi$
$578$	7.90228	−	13.6871i	0.328691	−	0.569310i
$579$		0			0
$580$	−1.68444	−	4.94464i	−0.0699424	−	0.205315i
$581$	−10.1025	+	17.4980i	−0.419122	+	0.725941i
$582$		0			0
$583$	−17.5287	−	30.3606i	−0.725964	−	1.25741i
$584$	−1.21138			−0.0501272
$585$		0			0
$586$	5.16420			0.213331
$587$	6.83792	+	11.8436i	0.282231	+	0.488838i	0.971934	−	0.235254i	$-0.0755922\pi$
$587$	6.83792	+	11.8436i	0.282231	+	0.488838i	−0.689703	+	0.724092i	$0.742259\pi$
$588$		0			0
$589$	−25.8407	+	44.7575i	−1.06475	+	1.84420i
$590$	12.6425	−	4.30677i	0.520482	−	0.177307i
$591$		0			0
$592$	−3.99285	+	6.91582i	−0.164105	+	0.284239i
$593$	43.3545			1.78036			0.890178	−	0.455614i	$-0.150580\pi$
$593$	43.3545			1.78036			0.890178	+	0.455614i	$0.150580\pi$
$594$		0			0
$595$	17.1386	+	14.9974i	0.702613	+	0.614834i
$596$	16.1710	−	9.33634i	0.662391	−	0.382431i
$597$		0			0
$598$	−4.96678	−	0.451975i	−0.203107	−	0.0184826i
$599$	−14.1785			−0.579318			−0.289659	−	0.957130i	$-0.593542\pi$
$599$	−14.1785			−0.579318			−0.289659	+	0.957130i	$0.593542\pi$
$600$		0			0
$601$	4.30455	+	7.45570i	0.175586	+	0.304125i	0.940364	−	0.340170i	$-0.110485\pi$
$601$	4.30455	+	7.45570i	0.175586	+	0.304125i	−0.764778	+	0.644294i	$0.777151\pi$
$602$	6.31619	+	3.64665i	0.257429	+	0.148626i
$603$		0			0
$604$	14.0437	+	8.10813i	0.571430	+	0.329915i
$605$	2.27293	+	0.449563i	0.0924079	+	0.0182773i
$606$		0			0
$607$	35.6144	+	20.5620i	1.44554	+	0.834585i	0.998211	−	0.0597825i	$-0.0190407\pi$
$607$	35.6144	+	20.5620i	1.44554	+	0.834585i	0.447333	+	0.894368i	$0.352374\pi$
$608$	−4.65809	+	2.68935i	−0.188911	+	0.109068i
$609$		0			0
$610$	−2.48191	−	7.28561i	−0.100490	−	0.294986i
$611$	14.5391	−	6.71813i	0.588189	−	0.271787i
$612$		0			0
$613$	−16.1885	−	28.0393i	−0.653848	−	1.13250i	−0.982181	−	0.187936i	$-0.939820\pi$
$613$	−16.1885	−	28.0393i	−0.653848	−	1.13250i	0.328333	−	0.944562i	$-0.393513\pi$
$614$	4.50006	+	7.79433i	0.181608	+	0.314553i
$615$		0			0
$616$			5.61306i			0.226157i
$617$	−10.0810	+	17.4609i	−0.405847	+	0.702948i	−0.994420	−	0.105496i	$-0.966357\pi$
$617$	−10.0810	+	17.4609i	−0.405847	+	0.702948i	0.588572	+	0.808445i	$0.299690\pi$
$618$		0			0
$619$			14.1414i			0.568390i	0.958767	+	0.284195i	$0.0917262\pi$
$619$			14.1414i			0.568390i	−0.958767	+	0.284195i	$0.908274\pi$
$620$	−4.16882	+	21.0770i	−0.167424	+	0.846473i
$621$		0			0
$622$	−0.715338	−	1.23900i	−0.0286824	−	0.0496795i
$623$			27.6893i			1.10935i
$624$		0			0
$625$	6.36610	−	24.1759i	0.254644	−	0.967035i
$626$	−12.3430	+	7.12621i	−0.493324	+	0.284821i
$627$		0			0
$628$	15.3527	+	8.86389i	0.612640	+	0.353708i
$629$			45.7383i			1.82371i
$630$		0			0
$631$	25.9899	+	15.0053i	1.03464	+	0.597351i	0.918311	−	0.395860i	$-0.129553\pi$
$631$	25.9899	+	15.0053i	1.03464	+	0.597351i	0.116331	+	0.993211i	$0.462887\pi$
$632$	−11.7583			−0.467719
$633$		0			0
$634$	0.186276	+	0.322639i	0.00739796	+	0.0128136i
$635$	−33.2026	−	29.0545i	−1.31760	−	1.15299i
$636$		0			0
$637$	−11.3076	−	7.97647i	−0.448021	−	0.316039i
$638$		−	7.37401i		−	0.291940i
$639$		0			0
$640$	−1.47253	+	1.68276i	−0.0582067	+	0.0665168i
$641$	−11.9110	+	20.6305i	−0.470458	+	0.814857i	−0.999429	−	0.0337824i	$-0.989245\pi$
$641$	−11.9110	+	20.6305i	−0.470458	+	0.814857i	0.528971	+	0.848640i	$0.322578\pi$
$642$		0			0
$643$	−2.11680	+	3.66641i	−0.0834784	+	0.144589i	−0.904742	−	0.425960i	$-0.859936\pi$
$643$	−2.11680	+	3.66641i	−0.0834784	+	0.144589i	0.821263	+	0.570549i	$0.193270\pi$
$644$	−2.13016	−	1.22985i	−0.0839399	−	0.0484627i
$645$		0			0
$646$	−15.4033	+	26.6794i	−0.606036	+	1.04969i
$647$	−7.30596	+	4.21810i	−0.287227	+	0.165831i	−0.636691	−	0.771119i	$-0.719697\pi$
$647$	−7.30596	+	4.21810i	−0.287227	+	0.165831i	0.349464	+	0.936950i	$0.386364\pi$
$648$		0			0
$649$	18.8539			0.740081
$650$	−18.0116	+	0.762526i	−0.706474	+	0.0299087i
$651$		0			0
$652$	−11.6085	−	20.1065i	−0.454623	−	0.787430i
$653$	18.7915	−	10.8493i	0.735369	−	0.424565i	−0.0850144	−	0.996380i	$-0.527094\pi$
$653$	18.7915	−	10.8493i	0.735369	−	0.424565i	0.820383	+	0.571814i	$0.193760\pi$
$654$		0			0
$655$	5.79121	+	17.0000i	0.226281	+	0.664246i
$656$	−7.38001	−	4.26085i	−0.288141	−	0.166358i
$657$		0			0
$658$	7.89904			0.307937
$659$	−0.161953	+	0.280510i	−0.00630878	+	0.0109271i	−0.869163	−	0.494526i	$-0.835341\pi$
$659$	−0.161953	+	0.280510i	−0.00630878	+	0.0109271i	0.862854	+	0.505454i	$0.168675\pi$
$660$		0			0
$661$	21.8369	−	12.6075i	0.849355	−	0.490376i	−0.0110779	−	0.999939i	$-0.503526\pi$
$661$	21.8369	−	12.6075i	0.849355	−	0.490376i	0.860433	+	0.509563i	$0.170193\pi$
$662$			15.3879i			0.598066i
$663$		0			0
$664$	−11.3625			−0.440949
$665$	−16.0948	−	14.0840i	−0.624129	−	0.546156i
$666$		0			0
$667$	2.79844	+	1.61568i	0.108356	+	0.0625593i
$668$	−7.15199			−0.276719
$669$		0			0
$670$	−10.5594	−	2.08855i	−0.407946	−	0.0806876i
$671$		−	10.8651i		−	0.419444i
$672$		0			0
$673$	20.0839	−	11.5954i	0.774177	−	0.446971i	−0.0601858	−	0.998187i	$-0.519169\pi$
$673$	20.0839	−	11.5954i	0.774177	−	0.446971i	0.834363	+	0.551216i	$0.185836\pi$
$674$	14.3513	−	8.28573i	0.552792	−	0.319154i
$675$		0			0
$676$	4.36105	+	12.2467i	0.167733	+	0.471026i
$677$		−	30.3070i		−	1.16479i	−0.812905	−	0.582397i	$-0.802115\pi$
$677$		−	30.3070i		−	1.16479i	0.812905	−	0.582397i	$-0.197885\pi$
$678$		0			0
$679$	7.72210	+	13.3751i	0.296347	+	0.513288i
$680$	−2.48498	+	12.5637i	−0.0952947	+	0.481798i
$681$		0			0
$682$	−15.1649	+	26.2664i	−0.580695	+	1.00579i
$683$	11.3625	−	19.6804i	0.434772	−	0.753048i	−0.562505	−	0.826794i	$-0.690162\pi$
$683$	11.3625	−	19.6804i	0.434772	−	0.753048i	0.997277	+	0.0737462i	$0.0234955\pi$
$684$		0			0
$685$	45.1061	+	8.92152i	1.72341	+	0.340874i
$686$	−9.63613	−	16.6903i	−0.367909	−	0.637237i
$687$		0			0
$688$			4.10145i			0.156366i
$689$	−16.7968	−	36.3510i	−0.639909	−	1.38486i
$690$		0			0
$691$	−3.33181	+	1.92362i	−0.126748	+	0.0731781i	−0.562034	−	0.827114i	$-0.689981\pi$
$691$	−3.33181	+	1.92362i	−0.126748	+	0.0731781i	0.435285	+	0.900293i	$0.356647\pi$
$692$	−1.86105	+	1.07448i	−0.0707466	+	0.0408456i
$693$		0			0
$694$			36.3032i			1.37805i
$695$	−4.28565	−	0.847658i	−0.162564	−	0.0321535i
$696$		0			0
$697$	−48.8083			−1.84875
$698$	4.67372	+	2.69837i	0.176903	+	0.102135i
$699$		0			0
$700$	−8.22166	−	3.38474i	−0.310749	−	0.127931i
$701$	−4.73083			−0.178681			−0.0893405	−	0.996001i	$-0.528476\pi$
$701$	−4.73083			−0.178681			−0.0893405	+	0.996001i	$0.528476\pi$
$702$		0			0
$703$		−	42.9527i		−	1.61999i
$704$	−2.73365	+	1.57828i	−0.103028	+	0.0594835i
$705$		0			0
$706$	9.40228	−	16.2852i	0.353859	−	0.612902i
$707$	−2.71413			−0.102075
$708$		0			0
$709$	−40.5768	−	23.4270i	−1.52389	−	0.879820i	−0.999600	−	0.0282830i	$-0.990996\pi$
$709$	−40.5768	−	23.4270i	−1.52389	−	0.879820i	−0.524294	−	0.851537i	$-0.675671\pi$
$710$	−21.8816	+	7.45417i	−0.821202	+	0.279750i
$711$		0			0
$712$	−13.4852	+	7.78567i	−0.505378	+	0.291780i
$713$	−6.64540	−	11.5102i	−0.248872	−	0.431059i
$714$		0			0
$715$	−24.4151	−	7.18005i	−0.913072	−	0.268519i
$716$	18.0385			0.674132
$717$		0			0
$718$	5.44617	−	3.14435i	0.203249	−	0.117346i
$719$	−3.37415	+	5.84420i	−0.125835	+	0.217952i	−0.922059	−	0.387050i	$-0.873494\pi$
$719$	−3.37415	+	5.84420i	−0.125835	+	0.217952i	0.796224	+	0.605002i	$0.206828\pi$
$720$		0			0
$721$	−4.74313	−	2.73844i	−0.176643	−	0.101985i
$722$	4.96523	−	8.60003i	0.184787	−	0.320060i
$723$		0			0
$724$	−7.19932	+	12.4696i	−0.267561	+	0.463429i
$725$	10.8010	+	4.44661i	0.401139	+	0.165143i
$726$		0			0
$727$			34.5290i			1.28061i	0.768121	+	0.640304i	$0.221192\pi$
$727$			34.5290i			1.28061i	−0.768121	+	0.640304i	$0.778808\pi$
$728$	−0.581042	+	6.38510i	−0.0215348	+	0.236647i
$729$		0			0
$730$	1.78379	−	2.03846i	0.0660209	−	0.0754467i
$731$	11.7456	+	20.3440i	0.434426	+	0.752449i
$732$		0			0
$733$	24.1370			0.891522			0.445761	−	0.895152i	$-0.352933\pi$
$733$	24.1370			0.891522			0.445761	+	0.895152i	$0.352933\pi$
$734$	−20.1106	−	11.6108i	−0.742294	−	0.428564i
$735$		0			0
$736$		−	1.38323i		−	0.0509865i
$737$	−13.1593	−	7.59751i	−0.484728	−	0.279858i
$738$		0			0
$739$	1.71188	−	0.988352i	0.0629724	−	0.0363571i	−0.468183	−	0.883631i	$-0.655091\pi$
$739$	1.71188	−	0.988352i	0.0629724	−	0.0363571i	0.531156	+	0.847274i	$0.321758\pi$
$740$	−5.75807	−	16.9027i	−0.211671	−	0.621356i
$741$		0			0
$742$		−	19.7494i		−	0.725022i
$743$	−13.9153	−	24.1020i	−0.510504	−	0.884218i	−0.999926	−	0.0121712i	$-0.996126\pi$
$743$	−13.9153	−	24.1020i	−0.510504	−	0.884218i	0.489422	−	0.872047i	$-0.337208\pi$
$744$		0			0
$745$	−8.10145	+	40.9599i	−0.296814	+	1.50065i
$746$		−	21.3532i		−	0.781797i
$747$		0			0
$748$	−9.03962	+	15.6571i	−0.330521	+	0.572479i
$749$		−	20.7864i		−	0.759518i
$750$		0			0
$751$	−5.28036	−	9.14585i	−0.192683	−	0.333737i	0.753455	−	0.657499i	$-0.228386\pi$
$751$	−5.28036	−	9.14585i	−0.192683	−	0.333737i	−0.946139	+	0.323762i	$0.895052\pi$
$752$	2.22105	+	3.84697i	0.0809932	+	0.140284i
$753$		0			0
$754$	0.763329	−	8.38826i	0.0277988	−	0.305482i
$755$	−34.3237	+	11.6927i	−1.24917	+	0.425540i
$756$		0			0
$757$	−31.4867	+	18.1789i	−1.14440	+	0.660722i	−0.947517	−	0.319704i	$-0.896417\pi$
$757$	−31.4867	+	18.1789i	−1.14440	+	0.660722i	−0.196887	+	0.980426i	$0.563083\pi$
$758$	−0.940686	−	0.543105i	−0.0341673	−	0.0197265i
$759$		0			0
$760$	2.33364	−	11.7986i	0.0846500	−	0.427979i
$761$	15.4457	+	8.91758i	0.559906	+	0.323262i	0.753108	−	0.657897i	$-0.228554\pi$
$761$	15.4457	+	8.91758i	0.559906	+	0.323262i	−0.193202	+	0.981159i	$0.561887\pi$
$762$		0			0
$763$	2.35843	+	1.36164i	0.0853807	+	0.0492946i
$764$		0			0
$765$		0			0
$766$	−28.6425			−1.03489
$767$	21.4471	+	1.95168i	0.774411	+	0.0704712i
$768$		0			0
$769$	38.0823	−	21.9868i	1.37328	−	0.792866i	0.381944	−	0.924185i	$-0.375255\pi$
$769$	38.0823	−	21.9868i	1.37328	−	0.792866i	0.991340	+	0.131320i	$0.0419214\pi$
$770$	−9.44541	−	8.26537i	−0.340389	−	0.297863i
$771$		0			0
$772$	13.4530			0.484185
$773$	−17.9818	+	31.1454i	−0.646760	+	1.12022i	0.337132	+	0.941457i	$0.390543\pi$
$773$	−17.9818	+	31.1454i	−0.646760	+	1.12022i	−0.983892	+	0.178764i	$0.942790\pi$
$774$		0			0
$775$	−29.3288	−	38.0516i	−1.05352	−	1.36685i
$776$	−4.34259	+	7.52159i	−0.155890	+	0.270009i
$777$		0			0
$778$	16.1710	+	28.0090i	0.579759	+	1.00417i
$779$	45.8357			1.64224
$780$		0			0
$781$	−32.6324			−1.16768
$782$	−3.96124	−	6.86107i	−0.141654	−	0.245351i
$783$		0			0
$784$	1.91896	−	3.32373i	0.0685342	−	0.118705i
$785$	−37.5230	+	12.7826i	−1.33925	+	0.456229i
$786$		0			0
$787$	−26.7441	+	46.3221i	−0.953323	+	1.65120i	−0.215164	+	0.976578i	$0.569029\pi$
$787$	−26.7441	+	46.3221i	−0.953323	+	1.65120i	−0.738160	+	0.674626i	$0.764305\pi$
$788$	−2.04627			−0.0728954
$789$		0			0
$790$	17.3144	−	19.7863i	0.616018	−	0.703966i
$791$	−1.71639	+	0.990961i	−0.0610280	+	0.0352345i
$792$		0			0
$793$	1.12472	−	12.3596i	0.0399399	−	0.438901i
$794$	34.3892			1.22043
$795$		0			0
$796$	3.12332	+	5.40975i	0.110703	+	0.191744i
$797$	17.9103	+	10.3405i	0.634414	+	0.366279i	0.782460	−	0.622701i	$-0.213965\pi$
$797$	17.9103	+	10.3405i	0.634414	+	0.366279i	−0.148045	+	0.988981i	$0.547298\pi$
$798$		0			0
$799$	22.0336	+	12.7211i	0.779493	+	0.450040i
$800$	−0.663337	−	4.95580i	−0.0234525	−	0.175214i
$801$		0			0
$802$	33.6647	+	19.4363i	1.18874	+	0.686320i
$803$	3.31149	−	1.91189i	0.116860	−	0.0674692i
$804$		0			0
$805$	5.20624	−	1.77355i	0.183496	−	0.0625095i
$806$	−19.9697	+	28.3094i	−0.703404	+	0.997155i
$807$		0			0
$808$	−0.763156	−	1.32182i	−0.0268477	−	0.0465016i
$809$	−9.14927	−	15.8470i	−0.321671	−	0.557151i	0.659162	−	0.752001i	$-0.270911\pi$
$809$	−9.14927	−	15.8470i	−0.321671	−	0.557151i	−0.980833	+	0.194850i	$0.937578\pi$
$810$		0			0
$811$			33.5187i			1.17700i	0.808497	+	0.588501i	$0.200282\pi$
$811$			33.5187i			1.17700i	−0.808497	+	0.588501i	$0.799718\pi$
$812$	2.07705	−	3.59756i	0.0728903	−	0.126250i
$813$		0			0
$814$		−	25.2073i		−	0.883515i
$815$	50.9280	+	10.0731i	1.78393	+	0.352844i
$816$		0			0
$817$	−11.0303	−	19.1050i	−0.385900	−	0.668398i
$818$			18.6339i			0.651519i
$819$		0			0
$820$	18.0372	−	6.14455i	0.629888	−	0.214577i
$821$	3.75909	−	2.17031i	0.131193	−	0.0757445i	−0.432967	−	0.901410i	$-0.642533\pi$
$821$	3.75909	−	2.17031i	0.131193	−	0.0757445i	0.564160	+	0.825665i	$0.309200\pi$
$822$		0			0
$823$	8.37877	+	4.83749i	0.292066	+	0.168624i	0.638873	−	0.769312i	$-0.279401\pi$
$823$	8.37877	+	4.83749i	0.292066	+	0.168624i	−0.346807	+	0.937936i	$0.612734\pi$
$824$		−	3.07998i		−	0.107296i
$825$		0			0
$826$	9.19826	+	5.31062i	0.320048	+	0.184780i
$827$	−53.1924			−1.84968			−0.924840	−	0.380355i	$-0.875802\pi$
$827$	−53.1924			−1.84968			−0.924840	+	0.380355i	$0.875802\pi$
$828$		0			0
$829$	8.08351	+	14.0010i	0.280752	+	0.486276i	0.971570	−	0.236752i	$-0.0760829\pi$
$829$	8.08351	+	14.0010i	0.280752	+	0.486276i	−0.690818	+	0.723028i	$0.742750\pi$
$830$	16.7315	−	19.1202i	0.580759	−	0.663674i
$831$		0			0
$832$	−3.27303	+	1.51238i	−0.113472	+	0.0524324i
$833$		−	21.9818i		−	0.761623i
$834$		0			0
$835$	10.5315	−	12.0351i	0.364457	−	0.416490i
$836$	8.48908	−	14.7035i	0.293601	−	0.508532i
$837$		0			0
$838$	−5.46731	+	9.46966i	−0.188865	+	0.327124i
$839$	16.2693	+	9.39308i	0.561678	+	0.324285i	0.753819	−	0.657082i	$-0.228210\pi$
$839$	16.2693	+	9.39308i	0.561678	+	0.324285i	−0.192141	+	0.981367i	$0.561543\pi$
$840$		0			0
$841$	11.7713	−	20.3885i	0.405908	−	0.703053i
$842$	−1.15305	+	0.665713i	−0.0397367	+	0.0229420i
$843$		0			0
$844$	22.9103			0.788604
$845$	−27.0299	−	10.6950i	−0.929858	−	0.367918i
$846$		0			0
$847$	0.921279	+	1.59570i	0.0316555	+	0.0548290i
$848$	9.61828	−	5.55312i	0.330293	−	0.190695i
$849$		0			0
$850$	−17.4825	−	22.6821i	−0.599645	−	0.777988i
$851$	9.56617	+	5.52303i	0.327924	+	0.189327i
$852$		0			0
$853$	−44.7749			−1.53306			−0.766532	−	0.642206i	$-0.778019\pi$
$853$	−44.7749			−1.53306			−0.766532	+	0.642206i	$0.778019\pi$
$854$	3.06041	−	5.30078i	0.104725	−	0.181389i
$855$		0			0
$856$	10.1233	−	5.84470i	0.346008	−	0.199768i
$857$			40.7162i			1.39084i	0.718605	+	0.695419i	$0.244781\pi$
$857$			40.7162i			1.39084i	−0.718605	+	0.695419i	$0.755219\pi$
$858$		0			0
$859$	27.1771			0.927271			0.463635	−	0.886026i	$-0.346545\pi$
$859$	27.1771			0.927271			0.463635	+	0.886026i	$0.346545\pi$
$860$	−6.90175	−	6.03950i	−0.235348	−	0.205945i
$861$		0			0
$862$	−12.1945	−	7.04048i	−0.415345	−	0.239800i
$863$	−18.4884			−0.629351			−0.314676	−	0.949199i	$-0.601896\pi$
$863$	−18.4884			−0.629351			−0.314676	+	0.949199i	$0.601896\pi$
$864$		0			0
$865$	0.932361	−	4.71389i	0.0317012	−	0.160277i
$866$			39.9280i			1.35681i
$867$		0			0
$868$	−14.7970	+	8.54307i	−0.502244	+	0.289971i
$869$	32.1431	−	18.5578i	1.09038	−	0.629531i
$870$		0			0
$871$	−14.1828	−	10.0047i	−0.480565	−	0.338996i
$872$			1.53146i			0.0518617i
$873$		0			0
$874$	3.71999	+	6.44321i	0.125831	+	0.217945i
$875$	17.8023	−	8.85094i	0.601827	−	0.299216i
$876$		0			0
$877$	7.76007	−	13.4408i	0.262039	−	0.453865i	−0.704745	−	0.709461i	$-0.748938\pi$
$877$	7.76007	−	13.4408i	0.262039	−	0.453865i	0.966784	+	0.255596i	$0.0822717\pi$
$878$	−0.192865	+	0.334053i	−0.00650889	+	0.0112737i
$879$		0			0
$880$	1.36952	−	6.92413i	0.0461666	−	0.233412i
$881$	−16.4359	−	28.4679i	−0.553741	−	0.959107i	−0.998000	−	0.0632091i	$-0.979866\pi$
$881$	−16.4359	−	28.4679i	−0.553741	−	0.959107i	0.444259	−	0.895898i	$-0.353467\pi$
$882$		0			0
$883$			8.95371i			0.301316i	0.988586	+	0.150658i	$0.0481393\pi$
$883$			8.95371i			0.301316i	−0.988586	+	0.150658i	$0.951861\pi$
$884$	−11.9037	+	16.8749i	−0.400365	+	0.567563i
$885$		0			0
$886$	−8.24665	+	4.76120i	−0.277052	+	0.159956i
$887$	4.47028	−	2.58091i	0.150097	−	0.0866586i	−0.423070	−	0.906097i	$-0.639048\pi$
$887$	4.47028	−	2.58091i	0.150097	−	0.0866586i	0.573168	+	0.819438i	$0.305714\pi$
$888$		0			0
$889$		−	35.0863i		−	1.17676i
$890$	6.75588	−	34.1569i	0.226458	−	1.14494i
$891$		0			0
$892$	21.9336			0.734390
$893$	−20.6917	−	11.9464i	−0.692421	−	0.399769i
$894$		0			0
$895$	−26.5622	+	30.3545i	−0.887877	+	1.01464i
$896$	−1.77822			−0.0594063
$897$		0			0
$898$		−	28.3507i		−	0.946075i
$899$	19.4392	−	11.2232i	0.648334	−	0.374316i
$900$		0			0
$901$	31.8056	−	55.0889i	1.05960	−	1.83528i
$902$	26.8992			0.895646
$903$		0			0
$904$	−0.965229	−	0.557275i	−0.0321030	−	0.0185347i
$905$	−10.3821	−	30.4765i	−0.345112	−	1.01307i
$906$		0			0
$907$	48.6354	−	28.0796i	1.61491	−	0.932369i	0.626701	−	0.779259i	$-0.284405\pi$
$907$	48.6354	−	28.0796i	1.61491	−	0.932369i	0.988209	−	0.153110i	$-0.0489288\pi$
$908$	−0.318770	−	0.552126i	−0.0105788	−	0.0183230i
$909$		0			0
$910$	−9.88896	−	10.3800i	−0.327816	−	0.344093i
$911$	−48.6654			−1.61236			−0.806178	−	0.591673i	$-0.798468\pi$
$911$	−48.6654			−1.61236			−0.806178	+	0.591673i	$0.798468\pi$
$912$		0			0
$913$	31.0610	−	17.9331i	1.02797	−	0.593499i
$914$	9.07158	−	15.7124i	0.300061	−	0.519721i
$915$		0			0
$916$	13.6425	+	7.87648i	0.450760	+	0.260246i
$917$	−7.14106	+	12.3687i	−0.235819	+	0.408450i
$918$		0			0
$919$	−9.76837	+	16.9193i	−0.322229	+	0.558117i	−0.980948	−	0.194272i	$-0.937765\pi$
$919$	−9.76837	+	16.9193i	−0.322229	+	0.558117i	0.658719	+	0.752389i	$0.271099\pi$
$920$	2.32764	+	2.03684i	0.0767399	+	0.0671526i
$921$		0			0
$922$			0.413687i			0.0136241i
$923$	−37.1207	−	3.37797i	−1.22184	−	0.111187i
$924$		0			0
$925$	36.9221	+	15.2003i	1.21399	+	0.499782i
$926$	6.36494	+	11.0244i	0.209165	+	0.362285i
$927$		0			0
$928$	2.33610			0.0766861
$929$	43.0592	+	24.8602i	1.41273	+	0.815638i	0.995645	−	0.0932309i	$-0.0297195\pi$
$929$	43.0592	+	24.8602i	1.41273	+	0.815638i	0.417082	+	0.908869i	$0.363053\pi$
$930$		0			0
$931$			20.6430i			0.676548i
$932$	−4.40087	−	2.54084i	−0.144155	−	0.0832281i
$933$		0			0
$934$	−15.8353	+	9.14254i	−0.518148	+	0.299153i
$935$	−13.0360	−	38.2669i	−0.426322	−	1.25146i
$936$		0			0
$937$			2.42946i			0.0793671i	0.999212	+	0.0396835i	$0.0126350\pi$
$937$			2.42946i			0.0793671i	−0.999212	+	0.0396835i	$0.987365\pi$
$938$	−4.28001	−	7.41320i	−0.139747	−	0.242049i
$939$		0			0
$940$	−9.74405	−	1.92728i	−0.317816	−	0.0628608i
$941$			42.2897i			1.37861i	0.724473	+	0.689303i	$0.242083\pi$
$941$			42.2897i			1.37861i	−0.724473	+	0.689303i	$0.757917\pi$
$942$		0			0
$943$	−5.89374	+	10.2082i	−0.191926	+	0.332426i
$944$			5.97294i			0.194403i
$945$		0			0
$946$	−6.47323	−	11.2120i	−0.210463	−	0.364532i
$947$	−13.1207	−	22.7258i	−0.426367	−	0.738489i	0.570180	−	0.821520i	$-0.306873\pi$
$947$	−13.1207	−	22.7258i	−0.426367	−	0.738489i	−0.996547	+	0.0830307i	$0.973540\pi$
$948$		0			0
$949$	3.96488	−	1.83207i	0.128705	−	0.0594714i
$950$	16.4178	+	21.3007i	0.532663	+	0.691084i
$951$		0			0
$952$	−8.82032	+	5.09241i	−0.285868	+	0.165046i
$953$	−28.6858	−	16.5618i	−0.929224	−	0.536488i	−0.0426583	−	0.999090i	$-0.513583\pi$
$953$	−28.6858	−	16.5618i	−0.929224	−	0.536488i	−0.886566	+	0.462602i	$0.846916\pi$
$954$		0			0
$955$		0			0
$956$	−18.4739	−	10.6659i	−0.597490	−	0.344961i
$957$		0			0
$958$	13.0595	+	7.53990i	0.421933	+	0.243603i
$959$	18.2827	+	31.6665i	0.590378	+	1.02257i
$960$		0			0
$961$	−61.3239			−1.97819
$962$	2.60936	−	28.6744i	0.0841291	−	0.924499i
$963$		0			0
$964$	16.4688	−	9.50824i	0.530423	−	0.306240i
$965$	−19.8099	+	22.6381i	−0.637703	+	0.728748i
$966$		0			0
$967$	18.2355			0.586415			0.293207	−	0.956049i	$-0.405277\pi$
$967$	18.2355			0.586415			0.293207	+	0.956049i	$0.405277\pi$
$968$	−0.518089	+	0.897357i	−0.0166520	+	0.0288421i
$969$		0			0
$970$	−6.26242	−	18.3833i	−0.201074	−	0.590251i
$971$	12.4471	−	21.5591i	0.399447	−	0.691863i	−0.594211	−	0.804310i	$-0.702535\pi$
$971$	12.4471	−	21.5591i	0.399447	−	0.691863i	0.993658	+	0.112447i	$0.0358687\pi$
$972$		0			0
$973$	−1.73708	−	3.00872i	−0.0556884	−	0.0964551i
$974$	13.3720			0.428468
$975$		0			0
$976$	3.44209			0.110179
$977$	11.4073	+	19.7581i	0.364953	+	0.632116i	0.988769	−	0.149455i	$-0.0477519\pi$
$977$	11.4073	+	19.7581i	0.364953	+	0.632116i	−0.623816	+	0.781571i	$0.714419\pi$
$978$		0			0
$979$	24.5759	−	42.5667i	0.785448	−	1.36044i
$980$	2.76732	+	8.12342i	0.0883987	+	0.259493i
$981$		0			0
$982$	9.52832	−	16.5035i	0.304061	−	0.526649i
$983$	32.8278			1.04704			0.523522	−	0.852012i	$-0.324618\pi$
$983$	32.8278			1.04704			0.523522	+	0.852012i	$0.324618\pi$
$984$		0			0
$985$	3.01319	−	3.44337i	0.0960081	−	0.109715i
$986$	11.5875	−	6.69003i	0.369020	−	0.213054i
$987$		0			0
$988$	11.1787	−	15.8471i	0.355643	−	0.504164i
$989$	5.67325			0.180399
$990$		0			0
$991$	−18.5242	−	32.0848i	−0.588440	−	1.01921i	−0.994437	−	0.105334i	$-0.966409\pi$
$991$	−18.5242	−	32.0848i	−0.588440	−	1.01921i	0.405997	−	0.913875i	$-0.366924\pi$
$992$	−8.32123	−	4.80427i	−0.264199	−	0.152536i
$993$		0			0
$994$	−15.9204	−	9.19163i	−0.504963	−	0.291541i
$995$	−13.7025	−	2.71021i	−0.434398	−	0.0859195i
$996$		0			0
$997$	1.20589	+	0.696221i	0.0381909	+	0.0220495i	0.518974	−	0.854790i	$-0.326314\pi$
$997$	1.20589	+	0.696221i	0.0381909	+	0.0220495i	−0.480783	+	0.876840i	$0.659648\pi$
$998$	−4.67372	+	2.69837i	−0.147944	+	0.0854155i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.e.829.3	yes	16
3.2	odd	2		1170.2.bj.f.829.6	yes	16
5.4	even	2		1170.2.bj.f.829.5	yes	16
13.4	even	6		1170.2.bj.f.199.6	yes	16
15.14	odd	2	inner	1170.2.bj.e.829.4	yes	16
39.17	odd	6	inner	1170.2.bj.e.199.3	✓	16
65.4	even	6	inner	1170.2.bj.e.199.4	yes	16
195.134	odd	6		1170.2.bj.f.199.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.bj.e.199.3	✓	16	39.17	odd	6	inner
1170.2.bj.e.199.4	yes	16	65.4	even	6	inner
1170.2.bj.e.829.3	yes	16	1.1	even	1	trivial
1170.2.bj.e.829.4	yes	16	15.14	odd	2	inner
1170.2.bj.f.199.5	yes	16	195.134	odd	6
1170.2.bj.f.199.6	yes	16	13.4	even	6
1170.2.bj.f.829.5	yes	16	5.4	even	2
1170.2.bj.f.829.6	yes	16	3.2	odd	2

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.721047 - 2.11662i) q^{5} +(0.889112 - 1.53999i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.721047 - 2.11662i) q^{5} +(0.889112 - 1.53999i) q^{7} +1.00000 q^{8} +(-1.47253 + 1.68276i) q^{10} +(-2.73365 + 1.57828i) q^{11} +(-3.27303 + 1.51238i) q^{13} -1.77822 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.96018 - 2.86376i) q^{17} +(4.65809 + 2.68935i) q^{19} +(2.19357 + 0.433866i) q^{20} +(2.73365 + 1.57828i) q^{22} +(-1.19791 + 0.691615i) q^{23} +(-3.96018 + 3.05237i) q^{25} +(2.94627 + 2.07833i) q^{26} +(0.889112 + 1.53999i) q^{28} +(-1.16805 - 2.02312i) q^{29} +9.60853i q^{31} +(-0.500000 + 0.866025i) q^{32} +5.72753i q^{34} +(-3.90066 - 0.771512i) q^{35} +(-3.99285 - 6.91582i) q^{37} -5.37870i q^{38} +(-0.721047 - 2.11662i) q^{40} +(7.38001 - 4.26085i) q^{41} +(-3.55196 - 2.05073i) q^{43} -3.15655i q^{44} +(1.19791 + 0.691615i) q^{46} -4.44209 q^{47} +(1.91896 + 3.32373i) q^{49} +(4.62352 + 1.90343i) q^{50} +(0.326754 - 3.59071i) q^{52} +11.1062i q^{53} +(5.31171 + 4.64810i) q^{55} +(0.889112 - 1.53999i) q^{56} +(-1.16805 + 2.02312i) q^{58} +(-5.17272 - 2.98647i) q^{59} +(-1.72105 + 2.98094i) q^{61} +(8.32123 - 4.80427i) q^{62} +1.00000 q^{64} +(5.56114 + 5.83727i) q^{65} +(2.40690 + 4.16887i) q^{67} +(4.96018 - 2.86376i) q^{68} +(1.28218 + 3.76383i) q^{70} +(8.95295 + 5.16899i) q^{71} -1.21138 q^{73} +(-3.99285 + 6.91582i) q^{74} +(-4.65809 + 2.68935i) q^{76} +5.61306i q^{77} -11.7583 q^{79} +(-1.47253 + 1.68276i) q^{80} +(-7.38001 - 4.26085i) q^{82} -11.3625 q^{83} +(-2.48498 + 12.5637i) q^{85} +4.10145i q^{86} +(-2.73365 + 1.57828i) q^{88} +(-13.4852 + 7.78567i) q^{89} +(-0.581042 + 6.38510i) q^{91} -1.38323i q^{92} +(2.22105 + 3.84697i) q^{94} +(2.33364 - 11.7986i) q^{95} +(-4.34259 + 7.52159i) q^{97} +(1.91896 - 3.32373i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{4} + 16 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^8	\( 16 q - 8 q^{2} - 8 q^{4} + 16 q^{8} - 8 q^{16} - 12 q^{17} - 18 q^{19} + 6 q^{23} + 4 q^{25} - 8 q^{32} + 24 q^{35} - 6 q^{46} - 48 q^{47} - 6 q^{49} - 2 q^{50} + 14 q^{55} - 16 q^{61} + 6 q^{62} + 16 q^{64} + 6 q^{65} + 12 q^{68} + 18 q^{76} + 20 q^{79} - 24 q^{83} - 18 q^{85} - 46 q^{91} + 24 q^{94} + 30 q^{95} - 6 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^8 - 8 * q^16 - 12 * q^17 - 18 * q^19 + 6 * q^23 + 4 * q^25 - 8 * q^32 + 24 * q^35 - 6 * q^46 - 48 * q^47 - 6 * q^49 - 2 * q^50 + 14 * q^55 - 16 * q^61 + 6 * q^62 + 16 * q^64 + 6 * q^65 + 12 * q^68 + 18 * q^76 + 20 * q^79 - 24 * q^83 - 18 * q^85 - 46 * q^91 + 24 * q^94 + 30 * q^95 - 6 * q^98

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