LMFDB - Embedded newform 1170.2.bs.g.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

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, 0, 5]))

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

//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: 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:	$8$
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			361.4
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.g.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(3.45632 + 1.99551i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(3.45632 + 1.99551i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(4.24026 - 2.44811i) q^{11} +(-2.87423 + 2.17688i) q^{13} +3.99102 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.31414 + 5.74026i) q^{17} +(1.81414 + 1.04739i) q^{19} +(0.866025 + 0.500000i) q^{20} +(2.44811 - 4.24026i) q^{22} +(0.495508 + 0.858244i) q^{23} -1.00000 q^{25} +(-1.40072 + 3.32235i) q^{26} +(3.45632 - 1.99551i) q^{28} +(2.92163 + 5.06040i) q^{29} -10.8179i q^{31} +(-0.866025 - 0.500000i) q^{32} +6.62828i q^{34} +(-1.99551 + 3.45632i) q^{35} +(-2.85782 + 1.64996i) q^{37} +2.09479 q^{38} +1.00000 q^{40} +(4.48652 - 2.59030i) q^{41} +(0.567874 - 0.983586i) q^{43} -4.89623i q^{44} +(0.858244 + 0.495508i) q^{46} -1.61186i q^{47} +(4.46410 + 7.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(0.448114 + 3.57760i) q^{52} +0.549905 q^{53} +(2.44811 + 4.24026i) q^{55} +(1.99551 - 3.45632i) q^{56} +(5.06040 + 2.92163i) q^{58} +(3.00000 + 1.73205i) q^{59} +(0.685861 - 1.18795i) q^{61} +(-5.40893 - 9.36854i) q^{62} -1.00000 q^{64} +(-2.17688 - 2.87423i) q^{65} +(3.13575 - 1.81042i) q^{67} +(3.31414 + 5.74026i) q^{68} +3.99102i q^{70} +(5.19615 + 3.00000i) q^{71} +8.94462i q^{73} +(-1.64996 + 2.85782i) q^{74} +(1.81414 - 1.04739i) q^{76} +19.5409 q^{77} +2.55231 q^{79} +(0.866025 - 0.500000i) q^{80} +(2.59030 - 4.48652i) q^{82} -16.4207i q^{83} +(-5.74026 - 3.31414i) q^{85} -1.13575i q^{86} +(-2.44811 - 4.24026i) q^{88} +(-2.98652 + 1.72427i) q^{89} +(-14.2782 + 1.78843i) q^{91} +0.991015 q^{92} +(-0.805932 - 1.39592i) q^{94} +(-1.04739 + 1.81414i) q^{95} +(-10.0910 - 5.82606i) q^{97} +(7.73205 + 4.46410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 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}+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

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 $

$2$	0.866025	−	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	0.981488	−	0.191525i	$-0.0613432\pi$
$7$	3.45632	+	1.99551i	1.30637	+	0.754231i	0.324879	+	0.945756i	$0.394677\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	4.24026	−	2.44811i	1.27849	−	0.738134i	0.301916	−	0.953335i	$-0.402374\pi$
$11$	4.24026	−	2.44811i	1.27849	−	0.738134i	0.976570	+	0.215200i	$0.0690405\pi$
$12$		0			0
$13$	−2.87423	+	2.17688i	−0.797169	+	0.603757i
$13$	−2.87423	+	2.17688i	−0.797169	+	0.603757i
$14$	3.99102			1.06664
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.31414	+	5.74026i	−0.803797	+	1.39222i	0.113303	+	0.993560i	$0.463857\pi$
$17$	−3.31414	+	5.74026i	−0.803797	+	1.39222i	−0.917100	+	0.398657i	$0.869477\pi$
$18$		0			0
$19$	1.81414	+	1.04739i	0.416192	+	0.240289i	0.693447	−	0.720508i	$-0.256091\pi$
$19$	1.81414	+	1.04739i	0.416192	+	0.240289i	−0.277255	+	0.960796i	$0.589425\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		0			0
$22$	2.44811	−	4.24026i	0.521940	−	0.904026i
$23$	0.495508	+	0.858244i	0.103320	+	0.178956i	0.913051	−	0.407846i	$-0.133720\pi$
$23$	0.495508	+	0.858244i	0.103320	+	0.178956i	−0.809730	+	0.586802i	$0.800387\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−1.40072	+	3.32235i	−0.274704	+	0.651566i
$27$		0			0
$28$	3.45632	−	1.99551i	0.653183	−	0.377115i
$29$	2.92163	+	5.06040i	0.542532	+	0.939694i	0.998758	+	0.0498293i	$0.0158677\pi$
$29$	2.92163	+	5.06040i	0.542532	+	0.939694i	−0.456225	+	0.889864i	$0.650799\pi$
$30$		0			0
$31$		−	10.8179i		−	1.94294i	−0.237155	−	0.971472i	$-0.576215\pi$
$31$		−	10.8179i		−	1.94294i	0.237155	−	0.971472i	$-0.423785\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			6.62828i			1.13674i
$35$	−1.99551	+	3.45632i	−0.337302	+	0.584225i
$36$		0			0
$37$	−2.85782	+	1.64996i	−0.469822	+	0.271252i	−0.716165	−	0.697931i	$-0.754104\pi$
$37$	−2.85782	+	1.64996i	−0.469822	+	0.271252i	0.246343	+	0.969183i	$0.420771\pi$
$38$	2.09479			0.339819
$39$		0			0
$40$	1.00000			0.158114
$41$	4.48652	−	2.59030i	0.700677	−	0.404536i	−0.106922	−	0.994267i	$-0.534100\pi$
$41$	4.48652	−	2.59030i	0.700677	−	0.404536i	0.807600	+	0.589731i	$0.200766\pi$
$42$		0			0
$43$	0.567874	−	0.983586i	0.0866000	−	0.149996i	−0.819472	−	0.573119i	$-0.805733\pi$
$43$	0.567874	−	0.983586i	0.0866000	−	0.149996i	0.906072	+	0.423124i	$0.139066\pi$
$44$		−	4.89623i		−	0.738134i
$45$		0			0
$46$	0.858244	+	0.495508i	0.126541	+	0.0730586i
$47$		−	1.61186i		−	0.235115i	−0.993066	−	0.117557i	$-0.962494\pi$
$47$		−	1.61186i		−	0.235115i	0.993066	−	0.117557i	$-0.0375064\pi$
$48$		0			0
$49$	4.46410	+	7.73205i	0.637729	+	1.10458i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	0.448114	+	3.57760i	0.0621422	+	0.496123i
$53$	0.549905			0.0755352			0.0377676	−	0.999287i	$-0.487975\pi$
$53$	0.549905			0.0755352			0.0377676	+	0.999287i	$0.487975\pi$
$54$		0			0
$55$	2.44811	+	4.24026i	0.330104	+	0.571756i
$56$	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
$61$	0.685861	−	1.18795i	0.0878155	−	0.152101i	−0.818772	−	0.574119i	$-0.805345\pi$
$61$	0.685861	−	1.18795i	0.0878155	−	0.152101i	0.906587	+	0.422018i	$0.138678\pi$
$62$	−5.40893	−	9.36854i	−0.686934	−	1.18981i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.17688	−	2.87423i	−0.270008	−	0.356505i
$66$		0			0
$67$	3.13575	−	1.81042i	0.383093	−	0.221179i	−0.296070	−	0.955166i	$-0.595676\pi$
$67$	3.13575	−	1.81042i	0.383093	−	0.221179i	0.679163	+	0.733988i	$0.262343\pi$
$68$	3.31414	+	5.74026i	0.401898	+	0.696108i
$69$		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
$73$			8.94462i			1.04689i	0.852060	+	0.523444i	$0.175353\pi$
$73$			8.94462i			1.04689i	−0.852060	+	0.523444i	$0.824647\pi$
$74$	−1.64996	+	2.85782i	−0.191804	+	0.332215i
$75$		0			0
$76$	1.81414	−	1.04739i	0.208096	−	0.120144i
$77$	19.5409			2.22689
$78$		0			0
$79$	2.55231			0.287158			0.143579	−	0.989639i	$-0.454139\pi$
$79$	2.55231			0.287158			0.143579	+	0.989639i	$0.454139\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$		0			0
$82$	2.59030	−	4.48652i	0.286050	−	0.495454i
$83$		−	16.4207i		−	1.80241i	−0.433393	−	0.901205i	$-0.642684\pi$
$83$		−	16.4207i		−	1.80241i	0.433393	−	0.901205i	$-0.357316\pi$
$84$		0			0
$85$	−5.74026	−	3.31414i	−0.622618	−	0.359469i
$86$		−	1.13575i		−	0.122471i
$87$		0			0
$88$	−2.44811	−	4.24026i	−0.260970	−	0.452013i
$89$	−2.98652	+	1.72427i	−0.316571	+	0.182772i	−0.649863	−	0.760051i	$-0.725174\pi$
$89$	−2.98652	+	1.72427i	−0.316571	+	0.182772i	0.333292	+	0.942824i	$0.391840\pi$
$90$		0			0
$91$	−14.2782	+	1.78843i	−1.49677	+	0.187478i
$92$	0.991015			0.103320
$93$		0			0
$94$	−0.805932	−	1.39592i	−0.0831256	−	0.143978i
$95$	−1.04739	+	1.81414i	−0.107460	+	0.186127i
$96$		0			0
$97$	−10.0910	−	5.82606i	−1.02459	−	0.591547i	−0.109159	−	0.994024i	$-0.534816\pi$
$97$	−10.0910	−	5.82606i	−1.02459	−	0.591547i	−0.915430	+	0.402477i	$0.868149\pi$
$98$	7.73205	+	4.46410i	0.781055	+	0.450942i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−1.03961	−	1.80066i	−0.103445	−	0.179173i	0.809657	−	0.586904i	$-0.199653\pi$
$101$	−1.03961	−	1.80066i	−0.103445	−	0.179173i	−0.913102	+	0.407731i	$0.866320\pi$
$102$		0			0
$103$	−2.26795			−0.223468			−0.111734	−	0.993738i	$-0.535640\pi$
$103$	−2.26795			−0.223468			−0.111734	+	0.993738i	$0.535640\pi$
$104$	2.17688	+	2.87423i	0.213460	+	0.281842i
$105$		0			0
$106$	0.476231	−	0.274952i	0.0462557	−	0.0267057i
$107$	−1.25076	−	2.16638i	−0.120915	−	0.209431i	0.799214	−	0.601047i	$-0.205250\pi$
$107$	−1.25076	−	2.16638i	−0.120915	−	0.209431i	−0.920129	+	0.391616i	$0.871916\pi$
$108$		0			0
$109$		−	15.6357i		−	1.49763i	−0.662780	−	0.748815i	$-0.730623\pi$
$109$		−	15.6357i		−	1.49763i	0.662780	−	0.748815i	$-0.269377\pi$
$110$	4.24026	+	2.44811i	0.404293	+	0.233418i
$111$		0			0
$112$		−	3.99102i		−	0.377115i
$113$	8.55889	−	14.8244i	0.805153	−	1.39457i	−0.111035	−	0.993816i	$-0.535417\pi$
$113$	8.55889	−	14.8244i	0.805153	−	1.39457i	0.916188	−	0.400749i	$-0.131250\pi$
$114$		0			0
$115$	−0.858244	+	0.495508i	−0.0800317	+	0.0462063i
$116$	5.84325			0.542532
$117$		0			0
$118$	3.46410			0.318896
$119$	−22.9095	+	13.2268i	−2.10011	+	1.21250i
$120$		0			0
$121$	6.48652	−	11.2350i	0.589684	−	1.02136i
$122$		−	1.37172i		−	0.124190i
$123$		0			0
$124$	−9.36854	−	5.40893i	−0.841319	−	0.485736i
$125$		−	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
$130$	−3.32235	−	1.40072i	−0.291389	−	0.122851i
$131$	−14.1773			−1.23868			−0.619340	−	0.785123i	$-0.712600\pi$
$131$	−14.1773			−1.23868			−0.619340	+	0.785123i	$0.712600\pi$
$132$		0			0
$133$	4.18016	+	7.24026i	0.362466	+	0.627810i
$134$	1.81042	−	3.13575i	0.156397	−	0.270887i
$135$		0			0
$136$	5.74026	+	3.31414i	0.492223	+	0.284185i
$137$	−12.1386	−	7.00821i	−1.03707	−	0.598752i	−0.118067	−	0.993006i	$-0.537670\pi$
$137$	−12.1386	−	7.00821i	−1.03707	−	0.598752i	−0.919001	+	0.394254i	$0.871003\pi$
$138$		0			0
$139$	−7.99473	+	13.8473i	−0.678104	+	1.17451i	0.297447	+	0.954738i	$0.403865\pi$
$139$	−7.99473	+	13.8473i	−0.678104	+	1.17451i	−0.975551	+	0.219772i	$0.929469\pi$
$140$	1.99551	+	3.45632i	0.168651	+	0.292112i
$141$		0			0
$142$	6.00000			0.503509
$143$	−6.85824	+	16.2670i	−0.573515	+	1.36031i
$144$		0			0
$145$	−5.06040	+	2.92163i	−0.420244	+	0.242628i
$146$	4.47231	+	7.74627i	0.370131	+	0.641085i
$147$		0			0
$148$			3.29992i			0.271252i
$149$	−6.49253	−	3.74846i	−0.531889	−	0.307086i	0.209896	−	0.977724i	$-0.432687\pi$
$149$	−6.49253	−	3.74846i	−0.531889	−	0.307086i	−0.741785	+	0.670637i	$0.766021\pi$
$150$		0			0
$151$			4.24913i			0.345789i	0.984940	+	0.172895i	$0.0553120\pi$
$151$			4.24913i			0.345789i	−0.984940	+	0.172895i	$0.944688\pi$
$152$	1.04739	−	1.81414i	0.0849549	−	0.147146i
$153$		0			0
$154$	16.9229	−	9.77046i	1.36369	−	0.787326i
$155$	10.8179			0.868911
$156$		0			0
$157$	−22.7526			−1.81586			−0.907929	−	0.419124i	$-0.862337\pi$
$157$	−22.7526			−1.81586			−0.907929	+	0.419124i	$0.862337\pi$
$158$	2.21037	−	1.27616i	0.175847	−	0.101526i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			3.95516i			0.311710i
$162$		0			0
$163$	4.51630	+	2.60749i	0.353744	+	0.204234i	0.666333	−	0.745654i	$-0.267863\pi$
$163$	4.51630	+	2.60749i	0.353744	+	0.204234i	−0.312589	+	0.949888i	$0.601196\pi$
$164$		−	5.18059i		−	0.404536i
$165$		0			0
$166$	−8.21037	−	14.2208i	−0.637248	−	1.10375i
$167$	5.80624	−	3.35224i	0.449301	−	0.259404i	−0.258234	−	0.966082i	$-0.583141\pi$
$167$	5.80624	−	3.35224i	0.449301	−	0.259404i	0.707535	+	0.706679i	$0.249807\pi$
$168$		0			0
$169$	3.52242	−	12.5137i	0.270955	−	0.962592i
$170$	−6.62828			−0.508366
$171$		0			0
$172$	−0.567874	−	0.983586i	−0.0433000	−	0.0749978i
$173$	−9.77046	+	16.9229i	−0.742834	+	1.28663i	0.208365	+	0.978051i	$0.433186\pi$
$173$	−9.77046	+	16.9229i	−0.742834	+	1.28663i	−0.951200	+	0.308576i	$0.900148\pi$
$174$		0			0
$175$	−3.45632	−	1.99551i	−0.261273	−	0.150846i
$176$	−4.24026	−	2.44811i	−0.319621	−	0.184534i
$177$		0			0
$178$	−1.72427	+	2.98652i	−0.129239	+	0.223849i
$179$	−4.48950	−	7.77604i	−0.335561	−	0.581209i	0.648031	−	0.761614i	$-0.275593\pi$
$179$	−4.48950	−	7.77604i	−0.335561	−	0.581209i	−0.983592	+	0.180405i	$0.942259\pi$
$180$		0			0
$181$	−5.55648			−0.413010			−0.206505	−	0.978446i	$-0.566209\pi$
$181$	−5.55648			−0.413010			−0.206505	+	0.978446i	$0.566209\pi$
$182$	−11.4711	+	8.68795i	−0.850295	+	0.643993i
$183$		0			0
$184$	0.858244	−	0.495508i	0.0632706	−	0.0365293i
$185$	−1.64996	−	2.85782i	−0.121308	−	0.210111i
$186$		0			0
$187$			32.4536i			2.37324i
$188$	−1.39592	−	0.805932i	−0.101808	−	0.0587787i
$189$		0			0
$190$			2.09479i			0.151972i
$191$	5.09316	−	8.82161i	0.368528	−	0.638309i	−0.620808	−	0.783963i	$-0.713195\pi$
$191$	5.09316	−	8.82161i	0.368528	−	0.638309i	0.989336	+	0.145654i	$0.0465285\pi$
$192$		0			0
$193$	7.04839	−	4.06939i	0.507354	−	0.292921i	−0.224391	−	0.974499i	$-0.572039\pi$
$193$	7.04839	−	4.06939i	0.507354	−	0.292921i	0.731745	+	0.681578i	$0.238706\pi$
$194$	−11.6521			−0.836574
$195$		0			0
$196$	8.92820			0.637729
$197$	−12.5405	+	7.24026i	−0.893473	+	0.515847i	−0.875077	−	0.483984i	$-0.839189\pi$
$197$	−12.5405	+	7.24026i	−0.893473	+	0.515847i	−0.0183962	+	0.999831i	$0.505856\pi$
$198$		0			0
$199$	−5.62828	+	9.74846i	−0.398978	+	0.691050i	−0.993600	−	0.112955i	$-0.963968\pi$
$199$	−5.62828	+	9.74846i	−0.398978	+	0.691050i	0.594622	+	0.804005i	$0.297302\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−1.80066	−	1.03961i	−0.126694	−	0.0731469i
$203$			23.3205i			1.63678i
$204$		0			0
$205$	2.59030	+	4.48652i	0.180914	+	0.313352i
$206$	−1.96410	+	1.13397i	−0.136845	+	0.0790078i
$207$		0			0
$208$	3.32235	+	1.40072i	0.230363	+	0.0971225i
$209$	10.2566			0.709461
$210$		0			0
$211$	−4.79257	−	8.30097i	−0.329934	−	0.571463i	0.652564	−	0.757733i	$-0.273693\pi$
$211$	−4.79257	−	8.30097i	−0.329934	−	0.571463i	−0.982498	+	0.186271i	$0.940360\pi$
$212$	0.274952	−	0.476231i	0.0188838	−	0.0327077i
$213$		0			0
$214$	−2.16638	−	1.25076i	−0.148090	−	0.0855000i
$215$	0.983586	+	0.567874i	0.0670800	+	0.0387287i
$216$		0			0
$217$	21.5871	−	37.3900i	1.46543	−	2.53820i
$218$	−7.81785	−	13.5409i	−0.529492	−	0.917107i
$219$		0			0
$220$	4.89623			0.330104
$221$	−2.97022	−	23.7133i	−0.199799	−	1.59513i
$222$		0			0
$223$	−23.5660	+	13.6058i	−1.57809	+	0.911113i	−0.582968	+	0.812495i	$0.698109\pi$
$223$	−23.5660	+	13.6058i	−1.57809	+	0.911113i	−0.995125	+	0.0986181i	$0.968558\pi$
$224$	−1.99551	−	3.45632i	−0.133330	−	0.230935i
$225$		0			0
$226$		−	17.1178i		−	1.13866i
$227$	−5.48052	−	3.16418i	−0.363755	−	0.210014i	0.306972	−	0.951719i	$-0.400684\pi$
$227$	−5.48052	−	3.16418i	−0.363755	−	0.210014i	−0.670726	+	0.741705i	$0.734018\pi$
$228$		0			0
$229$			2.50152i			0.165305i	0.996578	+	0.0826524i	$0.0263391\pi$
$229$			2.50152i			0.165305i	−0.996578	+	0.0826524i	$0.973661\pi$
$230$	−0.495508	+	0.858244i	−0.0326728	+	0.0565910i
$231$		0			0
$232$	5.06040	−	2.92163i	0.332232	−	0.191814i
$233$	−9.17903			−0.601339			−0.300669	−	0.953728i	$-0.597210\pi$
$233$	−9.17903			−0.601339			−0.300669	+	0.953728i	$0.597210\pi$
$234$		0			0
$235$	1.61186			0.105146
$236$	3.00000	−	1.73205i	0.195283	−	0.112747i
$237$		0			0
$238$	−13.2268	+	22.9095i	−0.857365	+	1.48500i
$239$		−	6.54030i		−	0.423057i	−0.977372	−	0.211528i	$-0.932156\pi$
$239$		−	6.54030i		−	0.423057i	0.977372	−	0.211528i	$-0.0678441\pi$
$240$		0			0
$241$	7.86571	+	4.54127i	0.506675	+	0.292529i	0.731466	−	0.681878i	$-0.238837\pi$
$241$	7.86571	+	4.54127i	0.506675	+	0.292529i	−0.224791	+	0.974407i	$0.572170\pi$
$242$		−	12.9730i		−	0.833939i
$243$		0			0
$244$	−0.685861	−	1.18795i	−0.0439077	−	0.0760504i
$245$	−7.73205	+	4.46410i	−0.493983	+	0.285201i
$246$		0			0
$247$	−7.49430	+	0.938703i	−0.476851	+	0.0597283i
$248$	−10.8179			−0.686934
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	4.81414	−	8.33833i	0.303866	−	0.526311i	−0.673142	−	0.739513i	$-0.735056\pi$
$251$	4.81414	−	8.33833i	0.303866	−	0.526311i	0.977008	+	0.213202i	$0.0683892\pi$
$252$		0			0
$253$	4.20216	+	2.42612i	0.264188	+	0.152529i
$254$	7.03590	+	4.06218i	0.441472	+	0.254884i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.41113	+	12.8364i	0.462293	+	0.800716i	0.999075	−	0.0430058i	$-0.0136934\pi$
$257$	7.41113	+	12.8364i	0.462293	+	0.800716i	−0.536781	+	0.843721i	$0.680360\pi$
$258$		0			0
$259$	−13.1700			−0.818347
$260$	−3.57760	+	0.448114i	−0.221873	+	0.0277908i
$261$		0			0
$262$	−12.2779	+	7.08867i	−0.758533	+	0.437939i
$263$	5.51673	+	9.55525i	0.340176	+	0.589202i	0.984465	−	0.175580i	$-0.0561801\pi$
$263$	5.51673	+	9.55525i	0.340176	+	0.589202i	−0.644289	+	0.764782i	$0.722847\pi$
$264$		0			0
$265$			0.549905i			0.0337804i
$266$	7.24026	+	4.18016i	0.443929	+	0.256302i
$267$		0			0
$268$		−	3.62085i		−	0.221179i
$269$	−1.30515	+	2.26059i	−0.0795767	+	0.137831i	−0.903067	−	0.429499i	$-0.858690\pi$
$269$	−1.30515	+	2.26059i	−0.0795767	+	0.137831i	0.823491	+	0.567330i	$0.192024\pi$
$270$		0			0
$271$	24.8459	−	14.3448i	1.50928	−	0.871383i	0.509337	−	0.860567i	$-0.329891\pi$
$271$	24.8459	−	14.3448i	1.50928	−	0.871383i	0.999942	−	0.0108156i	$-0.00344279\pi$
$272$	6.62828			0.401898
$273$		0			0
$274$	−14.0164			−0.846763
$275$	−4.24026	+	2.44811i	−0.255697	+	0.147627i
$276$		0			0
$277$	2.35035	−	4.07092i	0.141219	−	0.244598i	−0.786737	−	0.617288i	$-0.788231\pi$
$277$	2.35035	−	4.07092i	0.141219	−	0.244598i	0.927956	+	0.372690i	$0.121565\pi$
$278$			15.9895i			0.958984i
$279$		0			0
$280$	3.45632	+	1.99551i	0.206555	+	0.119254i
$281$		−	3.32418i		−	0.198304i	−0.995072	−	0.0991521i	$-0.968387\pi$
$281$		−	3.32418i		−	0.198304i	0.995072	−	0.0991521i	$-0.0316130\pi$
$282$		0			0
$283$	12.9886	+	22.4969i	0.772093	+	1.33730i	0.936414	+	0.350897i	$0.114123\pi$
$283$	12.9886	+	22.4969i	0.772093	+	1.33730i	−0.164322	+	0.986407i	$0.552543\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$		0			0
$286$	2.19407	+	17.5167i	0.129738	+	1.03579i
$287$	20.6758			1.22045
$288$		0			0
$289$	−13.4670	−	23.3256i	−0.792179	−	1.37209i
$290$	−2.92163	+	5.06040i	−0.171564	+	0.297157i
$291$		0			0
$292$	7.74627	+	4.47231i	0.453316	+	0.261722i
$293$	−0.824857	−	0.476231i	−0.0481886	−	0.0278217i	0.475712	−	0.879601i	$-0.342190\pi$
$293$	−0.824857	−	0.476231i	−0.0481886	−	0.0278217i	−0.523901	+	0.851779i	$0.675524\pi$
$294$		0			0
$295$	−1.73205	+	3.00000i	−0.100844	+	0.174667i
$296$	1.64996	+	2.85782i	0.0959021	+	0.166107i
$297$		0			0
$298$	−7.49693			−0.434285
$299$	−3.29250	−	1.38814i	−0.190410	−	0.0802779i
$300$		0			0
$301$	3.92551	−	2.26639i	0.226263	−	0.130633i
$302$	2.12456	+	3.67985i	0.122255	+	0.211752i
$303$		0			0
$304$		−	2.09479i		−	0.120144i
$305$	1.18795	+	0.685861i	0.0680216	+	0.0392723i
$306$		0			0
$307$		−	32.5819i		−	1.85955i	−0.368133	−	0.929773i	$-0.620003\pi$
$307$		−	32.5819i		−	1.85955i	0.368133	−	0.929773i	$-0.379997\pi$
$308$	9.77046	−	16.9229i	0.556724	−	0.964274i
$309$		0			0
$310$	9.36854	−	5.40893i	0.532097	−	0.307206i
$311$	−18.2831			−1.03674			−0.518370	−	0.855157i	$-0.673461\pi$
$311$	−18.2831			−1.03674			−0.518370	+	0.855157i	$0.673461\pi$
$312$		0			0
$313$	−16.0968			−0.909844			−0.454922	−	0.890531i	$-0.650333\pi$
$313$	−16.0968			−0.909844			−0.454922	+	0.890531i	$0.650333\pi$
$314$	−19.7044	+	11.3763i	−1.11198	+	0.642003i
$315$		0			0
$316$	1.27616	−	2.21037i	0.0717894	−	0.124343i
$317$			7.38961i			0.415042i	0.978231	+	0.207521i	$0.0665395\pi$
$317$			7.38961i			0.415042i	−0.978231	+	0.207521i	$0.933460\pi$
$318$		0			0
$319$	24.7769	+	14.3049i	1.38724	+	0.800923i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	1.97758	+	3.42527i	0.110206	+	0.190883i
$323$	−12.0246	+	6.94242i	−0.669068	+	0.386286i
$324$		0			0
$325$	2.87423	−	2.17688i	0.159434	−	0.120751i
$326$	5.21497			0.288831
$327$		0			0
$328$	−2.59030	−	4.48652i	−0.143025	−	0.247727i
$329$	3.21649	−	5.57112i	0.177331	−	0.307146i
$330$		0			0
$331$	−16.8848	−	9.74846i	−0.928074	−	0.535824i	−0.0418724	−	0.999123i	$-0.513332\pi$
$331$	−16.8848	−	9.74846i	−0.928074	−	0.535824i	−0.886202	+	0.463299i	$0.846666\pi$
$332$	−14.2208	−	8.21037i	−0.780466	−	0.450602i
$333$		0			0
$334$	3.35224	−	5.80624i	0.183426	−	0.317704i
$335$	1.81042	+	3.13575i	0.0989141	+	0.171324i
$336$		0			0
$337$	27.8865			1.51908			0.759538	−	0.650463i	$-0.225425\pi$
$337$	27.8865			1.51908			0.759538	+	0.650463i	$0.225425\pi$
$338$	−3.20634	−	12.5984i	−0.174402	−	0.685262i
$339$		0			0
$340$	−5.74026	+	3.31414i	−0.311309	+	0.179734i
$341$	−26.4833	−	45.8705i	−1.43415	−	2.48403i
$342$		0			0
$343$			7.69549i			0.415517i
$344$	−0.983586	−	0.567874i	−0.0530314	−	0.0306177i
$345$		0			0
$346$			19.5409i			1.05053i
$347$	10.0940	−	17.4833i	0.541875	−	0.938555i	−0.456922	−	0.889507i	$-0.651048\pi$
$347$	10.0940	−	17.4833i	0.541875	−	0.938555i	0.998796	−	0.0490478i	$-0.0156187\pi$
$348$		0			0
$349$	−30.8885	+	17.8335i	−1.65342	+	0.954605i	−0.677774	+	0.735270i	$0.737055\pi$
$349$	−30.8885	+	17.8335i	−1.65342	+	0.954605i	−0.975650	+	0.219335i	$0.929611\pi$
$350$	−3.99102			−0.213329
$351$		0			0
$352$	−4.89623			−0.260970
$353$	22.1506	−	12.7886i	1.17896	−	0.680671i	0.223184	−	0.974776i	$-0.428355\pi$
$353$	22.1506	−	12.7886i	1.17896	−	0.680671i	0.955773	+	0.294105i	$0.0950217\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$			3.44854i			0.182772i
$357$		0			0
$358$	−7.77604	−	4.48950i	−0.410977	−	0.237277i
$359$			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
$361$	−7.30593	−	12.6542i	−0.384523	−	0.666013i
$362$	−4.81205	+	2.77824i	−0.252916	+	0.146021i
$363$		0			0
$364$	−5.59030	+	13.2595i	−0.293011	+	0.694988i
$365$	−8.94462			−0.468183
$366$		0			0
$367$	−1.47966	−	2.56285i	−0.0772378	−	0.133780i	0.824819	−	0.565396i	$-0.191277\pi$
$367$	−1.47966	−	2.56285i	−0.0772378	−	0.133780i	−0.902057	+	0.431616i	$0.857943\pi$
$368$	0.495508	−	0.858244i	0.0258301	−	0.0447391i
$369$		0			0
$370$	−2.85782	−	1.64996i	−0.148571	−	0.0857775i
$371$	1.90065	+	1.09734i	0.0986766	+	0.0569710i
$372$		0			0
$373$	2.91179	−	5.04337i	0.150767	−	0.261136i	−0.780743	−	0.624853i	$-0.785159\pi$
$373$	2.91179	−	5.04337i	0.150767	−	0.261136i	0.931510	+	0.363717i	$0.118492\pi$
$374$	16.2268	+	28.1056i	0.839067	+	1.45331i
$375$		0			0
$376$	−1.61186			−0.0831256
$377$	−19.4133	−	8.18476i	−0.999836	−	0.421537i
$378$		0			0
$379$	−0.503185	+	0.290514i	−0.0258469	+	0.0149227i	−0.512868	−	0.858468i	$-0.671417\pi$
$379$	−0.503185	+	0.290514i	−0.0258469	+	0.0149227i	0.487021	+	0.873390i	$0.338084\pi$
$380$	1.04739	+	1.81414i	0.0537302	+	0.0930634i
$381$		0			0
$382$		−	10.1863i		−	0.521177i
$383$	13.2514	+	7.65070i	0.677115	+	0.390933i	0.798767	−	0.601640i	$-0.205486\pi$
$383$	13.2514	+	7.65070i	0.677115	+	0.390933i	−0.121652	+	0.992573i	$0.538819\pi$
$384$		0			0
$385$			19.5409i			0.995897i
$386$	4.06939	−	7.04839i	0.207126	−	0.358754i
$387$		0			0
$388$	−10.0910	+	5.82606i	−0.512295	+	0.295773i
$389$	19.7281			1.00025			0.500127	−	0.865952i	$-0.333287\pi$
$389$	19.7281			1.00025			0.500127	+	0.865952i	$0.333287\pi$
$390$		0			0
$391$	−6.56873			−0.332195
$392$	7.73205	−	4.46410i	0.390528	−	0.225471i
$393$		0			0
$394$	−7.24026	+	12.5405i	−0.364759	+	0.631781i
$395$			2.55231i			0.128421i
$396$		0			0
$397$	−0.716063	−	0.413419i	−0.0359382	−	0.0207489i	0.481923	−	0.876213i	$-0.339938\pi$
$397$	−0.716063	−	0.413419i	−0.0359382	−	0.0207489i	−0.517861	+	0.855465i	$0.673272\pi$
$398$			11.2566i			0.564240i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−27.3668	+	15.8002i	−1.36663	+	0.789026i	−0.990496	−	0.137538i	$-0.956081\pi$
$401$	−27.3668	+	15.8002i	−1.36663	+	0.789026i	−0.376137	+	0.926564i	$0.622748\pi$
$402$		0			0
$403$	23.5491	+	31.0930i	1.17307	+	1.54885i
$404$	−2.07923			−0.103445
$405$		0			0
$406$	11.6603	+	20.1962i	0.578689	+	1.00232i
$407$	−8.07859	+	13.9925i	−0.400441	+	0.693584i
$408$		0			0
$409$	18.9951	+	10.9668i	0.939247	+	0.542274i	0.889724	−	0.456499i	$-0.150897\pi$
$409$	18.9951	+	10.9668i	0.939247	+	0.542274i	0.0495227	+	0.998773i	$0.484230\pi$
$410$	4.48652	+	2.59030i	0.221574	+	0.127926i
$411$		0			0
$412$	−1.13397	+	1.96410i	−0.0558669	+	0.0967643i
$413$	6.91264	+	11.9730i	0.340149	+	0.589155i
$414$		0			0
$415$	16.4207			0.806062
$416$	3.57760	−	0.448114i	0.175406	−	0.0219706i
$417$		0			0
$418$	8.88244	−	5.12828i	0.434454	−	0.250832i
$419$	−15.2814	−	26.4681i	−0.746545	−	1.29305i	−0.949470	−	0.313859i	$-0.898378\pi$
$419$	−15.2814	−	26.4681i	−0.746545	−	1.29305i	0.202925	−	0.979194i	$-0.434955\pi$
$420$		0			0
$421$		−	21.4565i		−	1.04573i	−0.852417	−	0.522863i	$-0.824864\pi$
$421$		−	21.4565i		−	1.04573i	0.852417	−	0.522863i	$-0.175136\pi$
$422$	−8.30097	−	4.79257i	−0.404085	−	0.233299i
$423$		0			0
$424$		−	0.549905i		−	0.0267057i
$425$	3.31414	−	5.74026i	0.160759	−	0.278443i
$426$		0			0
$427$	4.74111	−	2.73728i	0.229438	−	0.132466i
$428$	−2.50152			−0.120915
$429$		0			0
$430$	1.13575			0.0547706
$431$	7.93641	−	4.58209i	0.382283	−	0.220711i	−0.296528	−	0.955024i	$-0.595829\pi$
$431$	7.93641	−	4.58209i	0.382283	−	0.220711i	0.678811	+	0.734313i	$0.262495\pi$
$432$		0			0
$433$	5.04839	−	8.74407i	0.242610	−	0.420213i	−0.718847	−	0.695168i	$-0.755330\pi$
$433$	5.04839	−	8.74407i	0.242610	−	0.420213i	0.961457	+	0.274955i	$0.0886631\pi$
$434$		−	43.1742i		−	2.07243i
$435$		0			0
$436$	−13.5409	−	7.81785i	−0.648492	−	0.374407i
$437$			2.07597i			0.0993069i
$438$		0			0
$439$	13.2648	+	22.9752i	0.633093	+	1.09655i	0.986916	+	0.161236i	$0.0515481\pi$
$439$	13.2648	+	22.9752i	0.633093	+	1.09655i	−0.353823	+	0.935312i	$0.615119\pi$
$440$	4.24026	−	2.44811i	0.202146	−	0.116709i
$441$		0			0
$442$	−14.4289	−	19.0512i	−0.686315	−	0.906174i
$443$	−12.9851			−0.616939			−0.308469	−	0.951234i	$-0.599817\pi$
$443$	−12.9851			−0.616939			−0.308469	+	0.951234i	$0.599817\pi$
$444$		0			0
$445$	−1.72427	−	2.98652i	−0.0817382	−	0.141575i
$446$	−13.6058	+	23.5660i	−0.644254	+	1.11588i
$447$		0			0
$448$	−3.45632	−	1.99551i	−0.163296	−	0.0942789i
$449$	27.5283	+	15.8935i	1.29914	+	0.750059i	0.980256	−	0.197734i	$-0.0633583\pi$
$449$	27.5283	+	15.8935i	1.29914	+	0.750059i	0.318885	+	0.947793i	$0.396692\pi$
$450$		0			0
$451$	12.6827	−	21.9670i	0.597204	−	1.03439i
$452$	−8.55889	−	14.8244i	−0.402576	−	0.697283i
$453$		0			0
$454$	−6.32835			−0.297004
$455$	−1.78843	−	14.2782i	−0.0838429	−	0.669374i
$456$		0			0
$457$	−6.42293	+	3.70828i	−0.300452	+	0.173466i	−0.642646	−	0.766163i	$-0.722163\pi$
$457$	−6.42293	+	3.70828i	−0.300452	+	0.173466i	0.342194	+	0.939629i	$0.388830\pi$
$458$	1.25076	+	2.16638i	0.0584441	+	0.101228i
$459$		0			0
$460$			0.991015i			0.0462063i
$461$	34.6924	+	20.0296i	1.61578	+	0.932873i	0.987994	+	0.154491i	$0.0493736\pi$
$461$	34.6924	+	20.0296i	1.61578	+	0.932873i	0.627790	+	0.778383i	$0.283960\pi$
$462$		0			0
$463$		−	22.6119i		−	1.05086i	−0.850836	−	0.525431i	$-0.823904\pi$
$463$		−	22.6119i		−	1.05086i	0.850836	−	0.525431i	$-0.176096\pi$
$464$	2.92163	−	5.06040i	0.135633	−	0.234923i
$465$		0			0
$466$	−7.94928	+	4.58952i	−0.368243	+	0.212605i
$467$	7.72244			0.357352			0.178676	−	0.983908i	$-0.442819\pi$
$467$	7.72244			0.357352			0.178676	+	0.983908i	$0.442819\pi$
$468$		0			0
$469$	14.4509			0.667279
$470$	1.39592	−	0.805932i	0.0643888	−	0.0371749i
$471$		0			0
$472$	1.73205	−	3.00000i	0.0797241	−	0.138086i
$473$		−	5.56088i		−	0.255690i
$474$		0			0
$475$	−1.81414	−	1.04739i	−0.0832384	−	0.0480577i
$476$			26.4536i			1.21250i
$477$		0			0
$478$	−3.27015	−	5.66406i	−0.149573	−	0.259068i
$479$	−4.32100	+	2.49473i	−0.197431	+	0.113987i	−0.595457	−	0.803387i	$-0.703029\pi$
$479$	−4.32100	+	2.49473i	−0.197431	+	0.113987i	0.398025	+	0.917374i	$0.369696\pi$
$480$		0			0
$481$	4.62227	−	10.9635i	0.210757	−	0.499892i
$482$	9.08254			0.413699
$483$		0			0
$484$	−6.48652	−	11.2350i	−0.294842	−	0.510681i
$485$	5.82606	−	10.0910i	0.264548	−	0.458210i
$486$		0			0
$487$	22.3741	+	12.9177i	1.01387	+	0.585357i	0.912322	−	0.409474i	$-0.134288\pi$
$487$	22.3741	+	12.9177i	1.01387	+	0.585357i	0.101546	+	0.994831i	$0.467621\pi$
$488$	−1.18795	−	0.685861i	−0.0537758	−	0.0310475i
$489$		0			0
$490$	−4.46410	+	7.73205i	−0.201668	+	0.349298i
$491$	−8.75076	−	15.1568i	−0.394916	−	0.684015i	0.598174	−	0.801366i	$-0.295893\pi$
$491$	−8.75076	−	15.1568i	−0.394916	−	0.684015i	−0.993090	+	0.117351i	$0.962560\pi$
$492$		0			0
$493$	−38.7307			−1.74434
$494$	−6.02091	+	4.56009i	−0.270893	+	0.205168i
$495$		0			0
$496$	−9.36854	+	5.40893i	−0.420660	+	0.242868i
$497$	11.9730	+	20.7379i	0.537065	+	0.930223i
$498$		0			0
$499$		−	19.0519i		−	0.852878i	−0.904516	−	0.426439i	$-0.859768\pi$
$499$		−	19.0519i		−	0.852878i	0.904516	−	0.426439i	$-0.140232\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$		0			0
$502$		−	9.62828i		−	0.429731i
$503$	−1.96384	+	3.40148i	−0.0875635	+	0.151664i	−0.906481	−	0.422247i	$-0.861241\pi$
$503$	−1.96384	+	3.40148i	−0.0875635	+	0.151664i	0.818917	+	0.573912i	$0.194575\pi$
$504$		0			0
$505$	1.80066	−	1.03961i	0.0801284	−	0.0462622i
$506$	4.85224			0.215708
$507$		0			0
$508$	8.12436			0.360460
$509$	36.9221	−	21.3170i	1.63654	−	0.944858i	0.654530	−	0.756036i	$-0.272866\pi$
$509$	36.9221	−	21.3170i	1.63654	−	0.944858i	0.982011	−	0.188822i	$-0.0604669\pi$
$510$		0			0
$511$	−17.8491	+	30.9155i	−0.789596	+	1.36762i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	12.8364	+	7.41113i	0.566191	+	0.326891i
$515$		−	2.26795i		−	0.0999378i
$516$		0			0
$517$	−3.94603	−	6.83472i	−0.173546	−	0.300591i
$518$	−11.4056	+	6.58502i	−0.501133	+	0.289329i
$519$		0			0
$520$	−2.87423	+	2.17688i	−0.126043	+	0.0954623i
$521$	−32.4921			−1.42351			−0.711753	−	0.702430i	$-0.752098\pi$
$521$	−32.4921			−1.42351			−0.711753	+	0.702430i	$0.752098\pi$
$522$		0			0
$523$	−5.31194	−	9.20055i	−0.232275	−	0.402312i	0.726202	−	0.687481i	$-0.241284\pi$
$523$	−5.31194	−	9.20055i	−0.232275	−	0.402312i	−0.958477	+	0.285169i	$0.907950\pi$
$524$	−7.08867	+	12.2779i	−0.309670	+	0.536364i
$525$		0			0
$526$	9.55525	+	5.51673i	0.416629	+	0.240541i
$527$	62.0973	+	35.8519i	2.70500	+	1.56173i
$528$		0			0
$529$	11.0089	−	19.0681i	0.478650	−	0.829046i
$530$	0.274952	+	0.476231i	0.0119432	+	0.0206862i
$531$		0			0
$532$	8.36033			0.362466
$533$	−7.25656	+	17.2117i	−0.314316	+	0.745522i
$534$		0			0
$535$	2.16638	−	1.25076i	0.0936606	−	0.0540750i
$536$	−1.81042	−	3.13575i	−0.0781984	−	0.135444i
$537$		0			0
$538$			2.61031i			0.112538i
$539$	37.8579	+	21.8573i	1.63065	+	0.941459i
$540$		0			0
$541$		−	36.2860i		−	1.56006i	−0.625743	−	0.780029i	$-0.715204\pi$
$541$		−	36.2860i		−	1.56006i	0.625743	−	0.780029i	$-0.284796\pi$
$542$	14.3448	−	24.8459i	0.616161	−	1.06722i
$543$		0			0
$544$	5.74026	−	3.31414i	0.246112	−	0.142093i
$545$	15.6357			0.669760
$546$		0			0
$547$	−21.3774			−0.914030			−0.457015	−	0.889459i	$-0.651081\pi$
$547$	−21.3774			−0.914030			−0.457015	+	0.889459i	$0.651081\pi$
$548$	−12.1386	+	7.00821i	−0.518534	+	0.299376i
$549$		0			0
$550$	−2.44811	+	4.24026i	−0.104388	+	0.180805i
$551$			12.2404i			0.521457i
$552$		0			0
$553$	8.82161	+	5.09316i	0.375133	+	0.216583i
$554$		−	4.70070i		−	0.199714i
$555$		0			0
$556$	7.99473	+	13.8473i	0.339052	+	0.587255i
$557$	−25.0600	+	14.4684i	−1.06183	+	0.613045i	−0.925937	−	0.377679i	$-0.876722\pi$
$557$	−25.0600	+	14.4684i	−1.06183	+	0.613045i	−0.135889	+	0.990724i	$0.543389\pi$
$558$		0			0
$559$	0.508944	+	4.06325i	0.0215261	+	0.171857i
$560$	3.99102			0.168651
$561$		0			0
$562$	−1.66209	−	2.87883i	−0.0701111	−	0.121436i
$563$	9.18717	−	15.9126i	0.387193	−	0.670638i	−0.604878	−	0.796318i	$-0.706778\pi$
$563$	9.18717	−	15.9126i	0.387193	−	0.670638i	0.992071	+	0.125680i	$0.0401114\pi$
$564$		0			0
$565$	14.8244	+	8.55889i	0.623668	+	0.360075i
$566$	22.4969	+	12.9886i	0.945616	+	0.545952i
$567$		0			0
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	1.40280	+	2.42973i	0.0588086	+	0.101860i	0.893931	−	0.448205i	$-0.147936\pi$
$569$	1.40280	+	2.42973i	0.0588086	+	0.101860i	−0.835122	+	0.550064i	$0.814603\pi$
$570$		0			0
$571$	−0.119334			−0.00499398			−0.00249699	−	0.999997i	$-0.500795\pi$
$571$	−0.119334			−0.00499398			−0.00249699	+	0.999997i	$0.500795\pi$
$572$	10.6585	+	14.0729i	0.445653	+	0.588417i
$573$		0			0
$574$	17.9058	−	10.3379i	0.747373	−	0.431496i
$575$	−0.495508	−	0.858244i	−0.0206641	−	0.0357913i
$576$		0			0
$577$			27.6701i			1.15192i	0.817478	+	0.575960i	$0.195372\pi$
$577$			27.6701i			1.15192i	−0.817478	+	0.575960i	$0.804628\pi$
$578$	−23.3256	−	13.4670i	−0.970217	−	0.560155i
$579$		0			0
$580$			5.84325i			0.242628i
$581$	32.7677	−	56.7553i	1.35943	−	2.35461i
$582$		0			0
$583$	2.33174	−	1.34623i	0.0965707	−	0.0557551i
$584$	8.94462			0.370131
$585$		0			0
$586$	−0.952463			−0.0393459
$587$	−15.5195	+	8.96018i	−0.640558	+	0.369826i	−0.784829	−	0.619712i	$-0.787249\pi$
$587$	−15.5195	+	8.96018i	−0.640558	+	0.369826i	0.144272	+	0.989538i	$0.453916\pi$
$588$		0			0
$589$	11.3306	−	19.6251i	0.466867	−	0.808638i
$590$			3.46410i			0.142615i
$591$		0			0
$592$	2.85782	+	1.64996i	0.117456	+	0.0678130i
$593$		−	22.0640i		−	0.906058i	−0.891496	−	0.453029i	$-0.850343\pi$
$593$		−	22.0640i		−	0.906058i	0.891496	−	0.453029i	$-0.149657\pi$
$594$		0			0
$595$	−13.2268	−	22.9095i	−0.542245	−	0.939196i
$596$	−6.49253	+	3.74846i	−0.265944	+	0.153543i
$597$		0			0
$598$	−3.54545	+	0.444088i	−0.144984	+	0.0181601i
$599$	−47.3354			−1.93407			−0.967035	−	0.254642i	$-0.918042\pi$
$599$	−47.3354			−1.93407			−0.967035	+	0.254642i	$0.918042\pi$
$600$		0			0
$601$	13.4610	+	23.3152i	0.549087	+	0.951046i	0.998337	+	0.0576406i	$0.0183577\pi$
$601$	13.4610	+	23.3152i	0.549087	+	0.951046i	−0.449251	+	0.893406i	$0.648309\pi$
$602$	2.26639	−	3.92551i	0.0923713	−	0.159992i
$603$		0			0
$604$	3.67985	+	2.12456i	0.149731	+	0.0864473i
$605$	11.2350	+	6.48652i	0.456767	+	0.263715i
$606$		0			0
$607$	−9.85548	+	17.0702i	−0.400022	+	0.692858i	−0.993728	−	0.111824i	$-0.964331\pi$
$607$	−9.85548	+	17.0702i	−0.400022	+	0.692858i	0.593706	+	0.804682i	$0.297664\pi$
$608$	−1.04739	−	1.81414i	−0.0424774	−	0.0735731i
$609$		0			0
$610$	1.37172			0.0555394
$611$	3.50883	+	4.63287i	0.141952	+	0.187426i
$612$		0			0
$613$	12.6840	−	7.32308i	0.512300	−	0.295777i	−0.221479	−	0.975165i	$-0.571088\pi$
$613$	12.6840	−	7.32308i	0.512300	−	0.295777i	0.733779	+	0.679389i	$0.237755\pi$
$614$	−16.2909	−	28.2167i	−0.657449	−	1.13873i
$615$		0			0
$616$		−	19.5409i		−	0.787326i
$617$	4.08821	+	2.36033i	0.164585	+	0.0950233i	0.580030	−	0.814595i	$-0.303041\pi$
$617$	4.08821	+	2.36033i	0.164585	+	0.0950233i	−0.415445	+	0.909618i	$0.636374\pi$
$618$		0			0
$619$		−	25.6874i		−	1.03246i	−0.856449	−	0.516231i	$-0.827335\pi$
$619$		−	25.6874i		−	1.03246i	0.856449	−	0.516231i	$-0.172665\pi$
$620$	5.40893	−	9.36854i	0.217228	−	0.376249i
$621$		0			0
$622$	−15.8336	+	9.14155i	−0.634870	+	0.366543i
$623$	−13.7632			−0.551410
$624$		0			0
$625$	1.00000			0.0400000
$626$	−13.9402	+	8.04839i	−0.557163	+	0.321678i
$627$		0			0
$628$	−11.3763	+	19.7044i	−0.453964	+	0.786290i
$629$		−	21.8728i		−	0.872126i
$630$		0			0
$631$	24.3662	+	14.0678i	0.970003	+	0.560032i	0.899237	−	0.437461i	$-0.144122\pi$
$631$	24.3662	+	14.0678i	0.970003	+	0.560032i	0.0707660	+	0.997493i	$0.477456\pi$
$632$		−	2.55231i		−	0.101526i
$633$		0			0
$634$	3.69481	+	6.39959i	0.146739	+	0.254160i
$635$	−7.03590	+	4.06218i	−0.279211	+	0.161203i
$636$		0			0
$637$	−29.6626	−	12.5059i	−1.17527	−	0.495502i
$638$	28.6099			1.13268
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−6.86874	+	11.8970i	−0.271299	+	0.469904i	−0.969195	−	0.246296i	$-0.920787\pi$
$641$	−6.86874	+	11.8970i	−0.271299	+	0.469904i	0.697896	+	0.716199i	$0.254120\pi$
$642$		0			0
$643$	10.0859	+	5.82308i	0.397748	+	0.229640i	0.685512	−	0.728061i	$-0.259578\pi$
$643$	10.0859	+	5.82308i	0.397748	+	0.229640i	−0.287764	+	0.957701i	$0.592912\pi$
$644$	3.42527	+	1.97758i	0.134974	+	0.0779275i
$645$		0			0
$646$	−6.94242	+	12.0246i	−0.273146	+	0.473102i
$647$	−17.2324	−	29.8473i	−0.677474	−	1.17342i	−0.975739	−	0.218936i	$-0.929741\pi$
$647$	−17.2324	−	29.8473i	−0.677474	−	1.17342i	0.298265	−	0.954483i	$-0.403592\pi$
$648$		0			0
$649$	16.9610			0.665779
$650$	1.40072	−	3.32235i	0.0549408	−	0.130313i
$651$		0			0
$652$	4.51630	−	2.60749i	0.176872	−	0.102117i
$653$	−2.43255	−	4.21330i	−0.0951931	−	0.164879i	0.814496	−	0.580169i	$-0.197014\pi$
$653$	−2.43255	−	4.21330i	−0.0951931	−	0.164879i	−0.909689	+	0.415290i	$0.863680\pi$
$654$		0			0
$655$		−	14.1773i		−	0.553954i
$656$	−4.48652	−	2.59030i	−0.175169	−	0.101134i
$657$		0			0
$658$		−	6.43298i		−	0.250784i
$659$	−8.82145	+	15.2792i	−0.343635	+	0.595193i	−0.985105	−	0.171955i	$-0.944992\pi$
$659$	−8.82145	+	15.2792i	−0.343635	+	0.595193i	0.641470	+	0.767148i	$0.278325\pi$
$660$		0			0
$661$	3.16552	−	1.82762i	0.123125	−	0.0710860i	−0.437173	−	0.899378i	$-0.644020\pi$
$661$	3.16552	−	1.82762i	0.123125	−	0.0710860i	0.560297	+	0.828292i	$0.310687\pi$
$662$	−19.4969			−0.757770
$663$		0			0
$664$	−16.4207			−0.637248
$665$	−7.24026	+	4.18016i	−0.280765	+	0.162100i
$666$		0			0
$667$	−2.89538	+	5.01494i	−0.112109	+	0.194179i
$668$		−	6.70447i		−	0.259404i
$669$		0			0
$670$	3.13575	+	1.81042i	0.121145	+	0.0699428i
$671$		−	6.71626i		−	0.259278i
$672$		0			0
$673$	15.4685	+	26.7922i	0.596267	+	1.03276i	0.993367	+	0.114989i	$0.0366833\pi$
$673$	15.4685	+	26.7922i	0.596267	+	1.03276i	−0.397100	+	0.917775i	$0.629983\pi$
$674$	24.1505	−	13.9433i	0.930241	−	0.537075i
$675$		0			0
$676$	−9.07597	−	9.30735i	−0.349076	−	0.357975i
$677$	25.6685			0.986522			0.493261	−	0.869881i	$-0.335805\pi$
$677$	25.6685			0.986522			0.493261	+	0.869881i	$0.335805\pi$
$678$		0			0
$679$	−23.2519	−	40.2735i	−0.892326	−	1.54555i
$680$	−3.31414	+	5.74026i	−0.127091	+	0.220129i
$681$		0			0
$682$	−45.8705	−	26.4833i	−1.75647	−	1.01410i
$683$	26.3774	+	15.2290i	1.00930	+	0.582721i	0.910987	−	0.412435i	$-0.135321\pi$
$683$	26.3774	+	15.2290i	1.00930	+	0.582721i	0.0983147	+	0.995155i	$0.468655\pi$
$684$		0			0
$685$	7.00821	−	12.1386i	0.267770	−	0.463791i
$686$	3.84774	+	6.66449i	0.146908	+	0.254451i
$687$		0			0
$688$	−1.13575			−0.0433000
$689$	−1.58055	+	1.19707i	−0.0602143	+	0.0456049i
$690$		0			0
$691$	−5.41546	+	3.12662i	−0.206014	+	0.118942i	−0.599458	−	0.800407i	$-0.704617\pi$
$691$	−5.41546	+	3.12662i	−0.206014	+	0.118942i	0.393444	+	0.919349i	$0.371284\pi$
$692$	9.77046	+	16.9229i	0.371417	+	0.643313i
$693$		0			0
$694$		−	20.1880i		−	0.766327i
$695$	−13.8473	−	7.99473i	−0.525257	−	0.303257i
$696$		0			0
$697$			34.3384i			1.30066i
$698$	−17.8335	+	30.8885i	−0.675008	+	1.16915i
$699$		0			0
$700$	−3.45632	+	1.99551i	−0.130637	+	0.0754231i
$701$	−9.17903			−0.346687			−0.173344	−	0.984861i	$-0.555457\pi$
$701$	−9.17903			−0.346687			−0.173344	+	0.984861i	$0.555457\pi$
$702$		0			0
$703$	−6.91264			−0.260715
$704$	−4.24026	+	2.44811i	−0.159811	+	0.0922668i
$705$		0			0
$706$	12.7886	−	22.1506i	0.481307	−	0.833648i
$707$		−	8.29822i		−	0.312087i
$708$		0			0
$709$	30.0521	+	17.3506i	1.12863	+	0.651614i	0.943590	−	0.331117i	$-0.107425\pi$
$709$	30.0521	+	17.3506i	1.12863	+	0.651614i	0.185039	+	0.982731i	$0.440759\pi$
$710$			6.00000i			0.225176i
$711$		0			0
$712$	1.72427	+	2.98652i	0.0646197	+	0.111925i
$713$	9.28436	−	5.36033i	0.347702	−	0.200746i
$714$		0			0
$715$	−16.2670	−	6.85824i	−0.608350	−	0.256484i
$716$	−8.97900			−0.335561
$717$		0			0
$718$	12.1244	+	21.0000i	0.452477	+	0.783713i
$719$	−9.12761	+	15.8095i	−0.340403	+	0.589595i	−0.984507	−	0.175343i	$-0.943897\pi$
$719$	−9.12761	+	15.8095i	−0.340403	+	0.589595i	0.644105	+	0.764937i	$0.277230\pi$
$720$		0			0
$721$	−7.83876	−	4.52571i	−0.291931	−	0.168546i
$722$	−12.6542	−	7.30593i	−0.470942	−	0.271899i
$723$		0			0
$724$	−2.77824	+	4.81205i	−0.103253	+	0.178839i
$725$	−2.92163	−	5.06040i	−0.108506	−	0.187939i
$726$		0			0
$727$	4.76025			0.176548			0.0882740	−	0.996096i	$-0.471865\pi$
$727$	4.76025			0.176548			0.0882740	+	0.996096i	$0.471865\pi$
$728$	1.78843	+	14.2782i	0.0662836	+	0.529187i
$729$		0			0
$730$	−7.74627	+	4.47231i	−0.286702	+	0.165528i
$731$	3.76403	+	6.51948i	0.139218	+	0.241132i
$732$		0			0
$733$			1.44352i			0.0533176i	0.999645	+	0.0266588i	$0.00848676\pi$
$733$			1.44352i			0.0533176i	−0.999645	+	0.0266588i	$0.991513\pi$
$734$	−2.56285	−	1.47966i	−0.0945966	−	0.0546154i
$735$		0			0
$736$		−	0.991015i		−	0.0365293i
$737$	8.86425	−	15.3533i	0.326519	−	0.565547i
$738$		0			0
$739$	−27.0111	+	15.5949i	−0.993621	+	0.573667i	−0.906355	−	0.422518i	$-0.861146\pi$
$739$	−27.0111	+	15.5949i	−0.993621	+	0.573667i	−0.0872663	+	0.996185i	$0.527813\pi$
$740$	−3.29992			−0.121308
$741$		0			0
$742$	2.19468			0.0805691
$743$	20.8591	−	12.0430i	0.765246	−	0.441815i	−0.0659301	−	0.997824i	$-0.521001\pi$
$743$	20.8591	−	12.0430i	0.765246	−	0.441815i	0.831176	+	0.556009i	$0.187668\pi$
$744$		0			0
$745$	3.74846	−	6.49253i	0.137333	−	0.237868i
$746$		−	5.82358i		−	0.213216i
$747$		0			0
$748$	28.1056	+	16.2268i	1.02764	+	0.593310i
$749$		−	9.98359i		−	0.364792i
$750$		0			0
$751$	−0.944617	−	1.63612i	−0.0344696	−	0.0597030i	0.848276	−	0.529554i	$-0.177641\pi$
$751$	−0.944617	−	1.63612i	−0.0344696	−	0.0597030i	−0.882746	+	0.469851i	$0.844308\pi$
$752$	−1.39592	+	0.805932i	−0.0509038	+	0.0293893i
$753$		0			0
$754$	−20.9048	+	2.61844i	−0.761308	+	0.0953580i
$755$	−4.24913			−0.154642
$756$		0			0
$757$	11.7385	+	20.3317i	0.426642	+	0.738966i	0.996572	−	0.0827270i	$-0.0263629\pi$
$757$	11.7385	+	20.3317i	0.426642	+	0.738966i	−0.569930	+	0.821693i	$0.693030\pi$
$758$	−0.290514	+	0.503185i	−0.0105520	+	0.0182765i
$759$		0			0
$760$	1.81414	+	1.04739i	0.0658057	+	0.0379930i
$761$	20.4760	+	11.8218i	0.742253	+	0.428540i	0.822888	−	0.568204i	$-0.192361\pi$
$761$	20.4760	+	11.8218i	0.742253	+	0.428540i	−0.0806347	+	0.996744i	$0.525695\pi$
$762$		0			0
$763$	31.2012	−	54.0420i	1.12956	−	1.95645i
$764$	−5.09316	−	8.82161i	−0.184264	−	0.319155i
$765$		0			0
$766$	15.3014			0.552862
$767$	−12.3932	+	1.55231i	−0.447491	+	0.0560507i
$768$		0			0
$769$	33.5563	−	19.3738i	1.21007	−	0.698636i	0.247298	−	0.968940i	$-0.420457\pi$
$769$	33.5563	−	19.3738i	1.21007	−	0.698636i	0.962775	+	0.270304i	$0.0871241\pi$
$770$	9.77046	+	16.9229i	0.352103	+	0.609860i
$771$		0			0
$772$		−	8.13878i		−	0.292921i
$773$	6.16020	+	3.55660i	0.221567	+	0.127922i	0.606676	−	0.794949i	$-0.292503\pi$
$773$	6.16020	+	3.55660i	0.221567	+	0.127922i	−0.385109	+	0.922871i	$0.625836\pi$
$774$		0			0
$775$			10.8179i			0.388589i
$776$	−5.82606	+	10.0910i	−0.209143	+	0.362247i
$777$		0			0
$778$	17.0850	−	9.86404i	0.612528	−	0.353643i
$779$	10.8522			0.388822
$780$		0			0
$781$	29.3774			1.05120
$782$	−5.68868	+	3.28436i	−0.203427	+	0.117449i
$783$		0			0
$784$	4.46410	−	7.73205i	0.159432	−	0.276145i
$785$		−	22.7526i		−	0.812076i
$786$		0			0
$787$	2.28033	+	1.31655i	0.0812848	+	0.0469298i	0.540092	−	0.841606i	$-0.318390\pi$
$787$	2.28033	+	1.31655i	0.0812848	+	0.0469298i	−0.458807	+	0.888536i	$0.651723\pi$
$788$			14.4805i			0.515847i
$789$		0			0
$790$	1.27616	+	2.21037i	0.0454036	+	0.0786413i
$791$	59.1645	−	34.1587i	2.10365	−	1.21454i
$792$		0			0
$793$	0.614687	+	4.90747i	0.0218282	+	0.174269i
$794$	−0.826838			−0.0293434
$795$		0			0
$796$	5.62828	+	9.74846i	0.199489	+	0.345525i
$797$	1.25953	−	2.18158i	0.0446150	−	0.0772754i	−0.842856	−	0.538140i	$-0.819127\pi$
$797$	1.25953	−	2.18158i	0.0446150	−	0.0772754i	0.887471	+	0.460864i	$0.152461\pi$
$798$		0			0
$799$	9.25252	+	5.34194i	0.327331	+	0.188984i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	−15.8002	+	27.3668i	−0.557926	+	0.966356i
$803$	21.8974	+	37.9275i	0.772744	+	1.33843i
$804$		0			0
$805$	−3.95516			−0.139401
$806$	35.9407	+	15.1528i	1.26596	+	0.533734i
$807$		0			0
$808$	−1.80066	+	1.03961i	−0.0633471	+	0.0365735i
$809$	4.35078	+	7.53576i	0.152965	+	0.264943i	0.932316	−	0.361644i	$-0.117784\pi$
$809$	4.35078	+	7.53576i	0.152965	+	0.264943i	−0.779351	+	0.626587i	$0.784451\pi$
$810$		0			0
$811$			40.3063i			1.41535i	0.706540	+	0.707673i	$0.250255\pi$
$811$			40.3063i			1.41535i	−0.706540	+	0.707673i	$0.749745\pi$
$812$	20.1962	+	11.6603i	0.708746	+	0.409195i
$813$		0			0
$814$			16.1572i			0.566309i
$815$	−2.60749	+	4.51630i	−0.0913363	+	0.158199i
$816$		0			0
$817$	2.06040	−	1.18958i	0.0720844	−	0.0416180i
$818$	21.9336			0.766892
$819$		0			0
$820$	5.18059			0.180914
$821$	−29.2880	+	16.9095i	−1.02216	+	0.590144i	−0.914729	−	0.404068i	$-0.867596\pi$
$821$	−29.2880	+	16.9095i	−1.02216	+	0.590144i	−0.107431	+	0.994213i	$0.534262\pi$
$822$		0			0
$823$	−24.1874	+	41.8938i	−0.843119	+	1.46033i	0.0441253	+	0.999026i	$0.485950\pi$
$823$	−24.1874	+	41.8938i	−0.843119	+	1.46033i	−0.887245	+	0.461299i	$0.847383\pi$
$824$			2.26795i			0.0790078i
$825$		0			0
$826$	11.9730	+	6.91264i	0.416596	+	0.240522i
$827$			15.1331i			0.526228i	0.964765	+	0.263114i	$0.0847495\pi$
$827$			15.1331i			0.526228i	−0.964765	+	0.263114i	$0.915250\pi$
$828$		0			0
$829$	−4.22458	−	7.31719i	−0.146726	−	0.254137i	0.783290	−	0.621657i	$-0.213540\pi$
$829$	−4.22458	−	7.31719i	−0.146726	−	0.254137i	−0.930015	+	0.367520i	$0.880207\pi$
$830$	14.2208	−	8.21037i	0.493610	−	0.284986i
$831$		0			0
$832$	2.87423	−	2.17688i	0.0996461	−	0.0754696i
$833$	−59.1786			−2.05042
$834$		0			0
$835$	3.35224	+	5.80624i	0.116009	+	0.200933i
$836$	5.12828	−	8.88244i	0.177365	−	0.307206i
$837$		0			0
$838$	−26.4681	−	15.2814i	−0.914327	−	0.527887i
$839$	15.7792	+	9.11014i	0.544759	+	0.314517i	0.747006	−	0.664818i	$-0.231491\pi$
$839$	15.7792	+	9.11014i	0.544759	+	0.314517i	−0.202246	+	0.979335i	$0.564824\pi$
$840$		0			0
$841$	−2.57180	+	4.45448i	−0.0886826	+	0.153603i
$842$	−10.7282	−	18.5819i	−0.369720	−	0.640373i
$843$		0			0
$844$	−9.58514			−0.329934
$845$	12.5137	+	3.52242i	0.430484	+	0.121175i
$846$		0			0
$847$	44.8390	−	25.8878i	1.54069	−	0.889516i
$848$	−0.274952	−	0.476231i	−0.00944190	−	0.0163538i
$849$		0			0
$850$		−	6.62828i		−	0.227348i
$851$	−2.83214	−	1.63514i	−0.0970846	−	0.0560518i
$852$		0			0
$853$			37.4425i			1.28201i	0.767539	+	0.641003i	$0.221481\pi$
$853$			37.4425i			1.28201i	−0.767539	+	0.641003i	$0.778519\pi$
$854$	2.73728	−	4.74111i	0.0936678	−	0.162237i
$855$		0			0
$856$	−2.16638	+	1.25076i	−0.0740452	+	0.0427500i
$857$	28.6086			0.977251			0.488626	−	0.872494i	$-0.337498\pi$
$857$	28.6086			0.977251			0.488626	+	0.872494i	$0.337498\pi$
$858$		0			0
$859$	−22.4266			−0.765186			−0.382593	−	0.923917i	$-0.624969\pi$
$859$	−22.4266			−0.765186			−0.382593	+	0.923917i	$0.624969\pi$
$860$	0.983586	−	0.567874i	0.0335400	−	0.0193643i
$861$		0			0
$862$	4.58209	−	7.93641i	0.156067	−	0.270315i
$863$			3.08381i			0.104974i	0.998622	+	0.0524871i	$0.0167148\pi$
$863$			3.08381i			0.104974i	−0.998622	+	0.0524871i	$0.983285\pi$
$864$		0			0
$865$	−16.9229	−	9.77046i	−0.575397	−	0.332206i
$866$		−	10.0968i		−	0.343102i
$867$		0			0
$868$	−21.5871	−	37.3900i	−0.732714	−	1.26910i
$869$	10.8225	−	6.24835i	0.367127	−	0.211961i
$870$		0			0
$871$	−5.07180	+	12.0297i	−0.171851	+	0.407611i
$872$	−15.6357			−0.529492
$873$		0			0
$874$	1.03798	+	1.79784i	0.0351103	+	0.0608128i
$875$	1.99551	−	3.45632i	0.0674605	−	0.116845i
$876$		0			0
$877$	33.0587	+	19.0864i	1.11631	+	0.644503i	0.940457	−	0.339913i	$-0.110398\pi$
$877$	33.0587	+	19.0864i	1.11631	+	0.644503i	0.175855	+	0.984416i	$0.443731\pi$
$878$	22.9752	+	13.2648i	0.775377	+	0.447664i
$879$		0			0
$880$	2.44811	−	4.24026i	0.0825259	−	0.142939i
$881$	11.9835	+	20.7561i	0.403736	+	0.699291i	0.994173	−	0.107792i	$-0.0343781\pi$
$881$	11.9835	+	20.7561i	0.403736	+	0.699291i	−0.590438	+	0.807083i	$0.701045\pi$
$882$		0			0
$883$	19.7537			0.664765			0.332383	−	0.943145i	$-0.392147\pi$
$883$	19.7537			0.664765			0.332383	+	0.943145i	$0.392147\pi$
$884$	−22.0214	−	9.28436i	−0.740661	−	0.312267i
$885$		0			0
$886$	−11.2454	+	6.49253i	−0.377796	+	0.218121i
$887$	10.0846	+	17.4670i	0.338608	+	0.586486i	0.984171	−	0.177221i	$-0.0567107\pi$
$887$	10.0846	+	17.4670i	0.338608	+	0.586486i	−0.645563	+	0.763707i	$0.723377\pi$
$888$		0			0
$889$			32.4244i			1.08748i
$890$	−2.98652	−	1.72427i	−0.100108	−	0.0577977i
$891$		0			0
$892$			27.2116i			0.911113i
$893$	1.68826	−	2.92415i	0.0564954	−	0.0978529i
$894$		0			0
$895$	7.77604	−	4.48950i	0.259924	−	0.150067i
$896$	−3.99102			−0.133330
$897$		0			0
$898$	31.7869			1.06074
$899$	54.7427	−	31.6057i	1.82577	−	1.05411i
$900$		0			0
$901$	−1.82246	+	3.15659i	−0.0607150	+	0.105161i
$902$		−	25.3654i		−	0.844574i
$903$		0			0
$904$	−14.8244	−	8.55889i	−0.493053	−	0.284664i
$905$		−	5.55648i		−	0.184704i
$906$		0			0
$907$	−11.9528	−	20.7029i	−0.396887	−	0.687428i	0.596453	−	0.802648i	$-0.296576\pi$
$907$	−11.9528	−	20.7029i	−0.396887	−	0.687428i	−0.993340	+	0.115220i	$0.963243\pi$
$908$	−5.48052	+	3.16418i	−0.181877	+	0.105007i
$909$		0			0
$910$	−8.68795	−	11.4711i	−0.288003	−	0.380263i
$911$	26.3025			0.871439			0.435720	−	0.900082i	$-0.356494\pi$
$911$	26.3025			0.871439			0.435720	+	0.900082i	$0.356494\pi$
$912$		0			0
$913$	−40.1998	−	69.6281i	−1.33042	−	2.30436i
$914$	−3.70828	+	6.42293i	−0.122659	+	0.212452i
$915$		0			0
$916$	2.16638	+	1.25076i	0.0715791	+	0.0413262i
$917$	−49.0014	−	28.2910i	−1.61817	−	0.934250i
$918$		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	$0.306074\pi$
$920$	0.495508	+	0.858244i	0.0163364	+	0.0282955i
$921$		0			0
$922$	40.0593			1.31928
$923$	−21.4656	+	2.68868i	−0.706548	+	0.0884991i
$924$		0			0
$925$	2.85782	−	1.64996i	0.0939645	−	0.0542504i
$926$	−11.3059	−	19.5824i	−0.371536	−	0.643519i
$927$		0			0
$928$		−	5.84325i		−	0.191814i
$929$	−22.9610	−	13.2566i	−0.753327	−	0.434934i	0.0735678	−	0.997290i	$-0.476561\pi$
$929$	−22.9610	−	13.2566i	−0.753327	−	0.434934i	−0.826895	+	0.562357i	$0.809895\pi$
$930$		0			0
$931$			18.7027i			0.612956i
$932$	−4.58952	+	7.94928i	−0.150335	+	0.260387i
$933$		0			0
$934$	6.68783	−	3.86122i	0.218833	−	0.126343i
$935$	−32.4536			−1.06134
$936$		0			0
$937$	24.3940			0.796918			0.398459	−	0.917186i	$-0.369545\pi$
$937$	24.3940			0.796918			0.398459	+	0.917186i	$0.369545\pi$
$938$	12.5148	−	7.22543i	0.408623	−	0.235919i
$939$		0			0
$940$	0.805932	−	1.39592i	0.0262866	−	0.0455298i
$941$		−	3.13575i		−	0.102222i	−0.998693	−	0.0511112i	$-0.983724\pi$
$941$		−	3.13575i		−	0.102222i	0.998693	−	0.0511112i	$-0.0162763\pi$
$942$		0			0
$943$	4.44621	+	2.56702i	0.144789	+	0.0835937i
$944$		−	3.46410i		−	0.112747i
$945$		0			0
$946$	−2.78044	−	4.81586i	−0.0903999	−	0.156577i
$947$	−16.2718	+	9.39450i	−0.528761	+	0.305280i	−0.740512	−	0.672043i	$-0.765417\pi$
$947$	−16.2718	+	9.39450i	−0.528761	+	0.305280i	0.211751	+	0.977324i	$0.432084\pi$
$948$		0			0
$949$	−19.4713	−	25.7089i	−0.632066	−	0.834546i
$950$	−2.09479			−0.0679639
$951$		0			0
$952$	13.2268	+	22.9095i	0.428682	+	0.742500i
$953$	3.80667	−	6.59335i	0.123310	−	0.213579i	−0.797761	−	0.602974i	$-0.793982\pi$
$953$	3.80667	−	6.59335i	0.123310	−	0.213579i	0.921071	+	0.389394i	$0.127316\pi$
$954$		0			0
$955$	8.82161	+	5.09316i	0.285461	+	0.164811i
$956$	−5.66406	−	3.27015i	−0.183189	−	0.105764i
$957$		0			0
$958$	−2.49473	+	4.32100i	−0.0806011	+	0.139605i
$959$	−27.9699	−	48.4452i	−0.903194	−	1.56438i
$960$		0			0
$961$	−86.0260			−2.77503
$962$	−1.47874	−	11.8058i	−0.0476766	−	0.380634i
$963$		0			0
$964$	7.86571	−	4.54127i	0.253338	−	0.146265i
$965$	4.06939	+	7.04839i	0.130998	+	0.226896i
$966$		0			0
$967$			22.5849i			0.726282i	0.931734	+	0.363141i	$0.118296\pi$
$967$			22.5849i			0.726282i	−0.931734	+	0.363141i	$0.881704\pi$
$968$	−11.2350	−	6.48652i	−0.361106	−	0.208485i
$969$		0			0
$970$		−	11.6521i		−	0.374127i
$971$	−16.3491	+	28.3174i	−0.524666	+	0.908748i	0.474921	+	0.880028i	$0.342476\pi$
$971$	−16.3491	+	28.3174i	−0.524666	+	0.908748i	−0.999587	+	0.0287200i	$0.990857\pi$
$972$		0			0
$973$	−55.2647	+	31.9071i	−1.77170	+	1.02289i
$974$	25.8354			0.827820
$975$		0			0
$976$	−1.37172			−0.0439077
$977$	−42.3066	+	24.4258i	−1.35351	+	0.781449i	−0.988739	−	0.149648i	$-0.952186\pi$
$977$	−42.3066	+	24.4258i	−1.35351	+	0.781449i	−0.364770	+	0.931098i	$0.618853\pi$
$978$		0			0
$979$	−8.44242	+	14.6227i	−0.269821	+	0.467343i
$980$			8.92820i			0.285201i
$981$		0			0
$982$	−15.1568	−	8.75076i	−0.483672	−	0.279248i
$983$		−	16.3881i		−	0.522700i	−0.965244	−	0.261350i	$-0.915832\pi$
$983$		−	16.3881i		−	0.522700i	0.965244	−	0.261350i	$-0.0841677\pi$
$984$		0			0
$985$	−7.24026	−	12.5405i	−0.230694	−	0.399573i
$986$	−33.5418	+	19.3654i	−1.06819	+	0.616718i
$987$		0			0
$988$	−2.93421	+	6.95961i	−0.0933497	+	0.221415i
$989$	1.12554			0.0357902
$990$		0			0
$991$	21.8977	+	37.9279i	0.695603	+	1.20482i	0.969977	+	0.243197i	$0.0781962\pi$
$991$	21.8977	+	37.9279i	0.695603	+	1.20482i	−0.274373	+	0.961623i	$0.588470\pi$
$992$	−5.40893	+	9.36854i	−0.171734	+	0.297451i
$993$		0			0
$994$	20.7379	+	11.9730i	0.657767	+	0.379762i
$995$	−9.74846	−	5.62828i	−0.309047	−	0.178428i
$996$		0			0
$997$	22.5569	−	39.0697i	0.714384	−	1.23735i	−0.248812	−	0.968552i	$-0.580040\pi$
$997$	22.5569	−	39.0697i	0.714384	−	1.23735i	0.963196	−	0.268798i	$-0.0866265\pi$
$998$	−9.52593	−	16.4994i	−0.301538	−	0.522279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.g.361.4		8
3.2	odd	2		130.2.l.b.101.2	✓	8
12.11	even	2		1040.2.da.d.881.1		8
13.4	even	6	inner	1170.2.bs.g.901.4		8
15.2	even	4		650.2.n.d.49.3		8
15.8	even	4		650.2.n.e.49.2		8
15.14	odd	2		650.2.m.c.101.3		8
39.2	even	12		1690.2.a.t.1.1		4
39.5	even	4		1690.2.e.t.991.4		8
39.8	even	4		1690.2.e.s.991.4		8
39.11	even	12		1690.2.a.u.1.1		4
39.17	odd	6		130.2.l.b.121.2	yes	8
39.20	even	12		1690.2.e.s.191.4		8
39.23	odd	6		1690.2.d.k.1351.5		8
39.29	odd	6		1690.2.d.k.1351.1		8
39.32	even	12		1690.2.e.t.191.4		8
39.35	odd	6		1690.2.l.j.1161.4		8
39.38	odd	2		1690.2.l.j.361.4		8
156.95	even	6		1040.2.da.d.641.1		8
195.17	even	12		650.2.n.e.199.2		8
195.89	even	12		8450.2.a.ci.1.4		4
195.119	even	12		8450.2.a.cm.1.4		4
195.134	odd	6		650.2.m.c.251.3		8
195.173	even	12		650.2.n.d.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.2	✓	8	3.2	odd	2
130.2.l.b.121.2	yes	8	39.17	odd	6
650.2.m.c.101.3		8	15.14	odd	2
650.2.m.c.251.3		8	195.134	odd	6
650.2.n.d.49.3		8	15.2	even	4
650.2.n.d.199.3		8	195.173	even	12
650.2.n.e.49.2		8	15.8	even	4
650.2.n.e.199.2		8	195.17	even	12
1040.2.da.d.641.1		8	156.95	even	6
1040.2.da.d.881.1		8	12.11	even	2
1170.2.bs.g.361.4		8	1.1	even	1	trivial
1170.2.bs.g.901.4		8	13.4	even	6	inner
1690.2.a.t.1.1		4	39.2	even	12
1690.2.a.u.1.1		4	39.11	even	12
1690.2.d.k.1351.1		8	39.29	odd	6
1690.2.d.k.1351.5		8	39.23	odd	6
1690.2.e.s.191.4		8	39.20	even	12
1690.2.e.s.991.4		8	39.8	even	4
1690.2.e.t.191.4		8	39.32	even	12
1690.2.e.t.991.4		8	39.5	even	4
1690.2.l.j.361.4		8	39.38	odd	2
1690.2.l.j.1161.4		8	39.35	odd	6
8450.2.a.ci.1.4		4	195.89	even	12
8450.2.a.cm.1.4		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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(3.45632 + 1.99551i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(3.45632 + 1.99551i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(4.24026 - 2.44811i) q^{11} +(-2.87423 + 2.17688i) q^{13} +3.99102 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.31414 + 5.74026i) q^{17} +(1.81414 + 1.04739i) q^{19} +(0.866025 + 0.500000i) q^{20} +(2.44811 - 4.24026i) q^{22} +(0.495508 + 0.858244i) q^{23} -1.00000 q^{25} +(-1.40072 + 3.32235i) q^{26} +(3.45632 - 1.99551i) q^{28} +(2.92163 + 5.06040i) q^{29} -10.8179i q^{31} +(-0.866025 - 0.500000i) q^{32} +6.62828i q^{34} +(-1.99551 + 3.45632i) q^{35} +(-2.85782 + 1.64996i) q^{37} +2.09479 q^{38} +1.00000 q^{40} +(4.48652 - 2.59030i) q^{41} +(0.567874 - 0.983586i) q^{43} -4.89623i q^{44} +(0.858244 + 0.495508i) q^{46} -1.61186i q^{47} +(4.46410 + 7.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(0.448114 + 3.57760i) q^{52} +0.549905 q^{53} +(2.44811 + 4.24026i) q^{55} +(1.99551 - 3.45632i) q^{56} +(5.06040 + 2.92163i) q^{58} +(3.00000 + 1.73205i) q^{59} +(0.685861 - 1.18795i) q^{61} +(-5.40893 - 9.36854i) q^{62} -1.00000 q^{64} +(-2.17688 - 2.87423i) q^{65} +(3.13575 - 1.81042i) q^{67} +(3.31414 + 5.74026i) q^{68} +3.99102i q^{70} +(5.19615 + 3.00000i) q^{71} +8.94462i q^{73} +(-1.64996 + 2.85782i) q^{74} +(1.81414 - 1.04739i) q^{76} +19.5409 q^{77} +2.55231 q^{79} +(0.866025 - 0.500000i) q^{80} +(2.59030 - 4.48652i) q^{82} -16.4207i q^{83} +(-5.74026 - 3.31414i) q^{85} -1.13575i q^{86} +(-2.44811 - 4.24026i) q^{88} +(-2.98652 + 1.72427i) q^{89} +(-14.2782 + 1.78843i) q^{91} +0.991015 q^{92} +(-0.805932 - 1.39592i) q^{94} +(-1.04739 + 1.81414i) q^{95} +(-10.0910 - 5.82606i) q^{97} +(7.73205 + 4.46410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 4 q^{10} + 6 q^{11} - 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} + 6 q^{22} - 12 q^{23} - 8 q^{25} - 30 q^{37} + 12 q^{38} + 8 q^{40} - 12 q^{41} + 4 q^{43} + 8 q^{49} - 10 q^{52} - 60 q^{53} + 6 q^{55} + 24 q^{59} + 26 q^{61} - 18 q^{62} - 8 q^{64} - 6 q^{65} + 24 q^{67} + 6 q^{68} - 6 q^{74} - 6 q^{76} + 60 q^{77} + 20 q^{79} - 18 q^{85} - 6 q^{88} + 24 q^{89} - 66 q^{91} - 24 q^{92} - 6 q^{95} - 6 q^{97} + 48 q^{98}+O(q^{100}) \) 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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