LMFDB - Embedded newform 1170.2.bs.f.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:	8.0.17284886784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 $ x^8 - 2x^7 + 2x^6 + 30x^5 + 185x^4 + 36x^3 + 8x^2 + 208*x + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$-1.80668 - 1.80668i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.f.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.14539 + 0.661290i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.14539 + 0.661290i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(3.99528 - 2.30668i) q^{11} +(3.20002 + 1.66129i) q^{13} +1.32258 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(1.98387 + 1.14539i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(2.30668 - 3.99528i) q^{22} +(-4.33399 - 7.50670i) q^{23} -1.00000 q^{25} +(3.60194 - 0.161290i) q^{26} +(1.14539 - 0.661290i) q^{28} +(-1.01141 - 1.75182i) q^{29} +10.1321i q^{31} +(-0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(0.661290 - 1.14539i) q^{35} +(5.89721 - 3.40475i) q^{37} +2.29078 q^{38} -1.00000 q^{40} +(4.02283 - 2.32258i) q^{41} +(4.30281 - 7.45269i) q^{43} -4.61335i q^{44} +(-7.50670 - 4.33399i) q^{46} -9.10926i q^{47} +(-2.62539 - 4.54731i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.03873 - 1.94065i) q^{52} -0.826674 q^{53} +(-2.30668 - 3.99528i) q^{55} +(0.661290 - 1.14539i) q^{56} +(-1.75182 - 1.01141i) q^{58} +(-2.72064 - 1.57076i) q^{59} +(-0.267949 + 0.464102i) q^{61} +(5.06604 + 8.77464i) q^{62} -1.00000 q^{64} +(1.66129 - 3.20002i) q^{65} +(-2.75488 + 1.59053i) q^{67} +(2.00000 + 3.46410i) q^{68} -1.32258i q^{70} +(9.81724 + 5.66799i) q^{71} +6.28304i q^{73} +(3.40475 - 5.89721i) q^{74} +(1.98387 - 1.14539i) q^{76} +6.10153 q^{77} +2.96774 q^{79} +(-0.866025 + 0.500000i) q^{80} +(2.32258 - 4.02283i) q^{82} +15.8719i q^{83} +(3.46410 + 2.00000i) q^{85} -8.60562i q^{86} +(-2.30668 - 3.99528i) q^{88} +(-10.2746 + 5.93207i) q^{89} +(2.56667 + 4.01896i) q^{91} -8.66799 q^{92} +(-4.55463 - 7.88885i) q^{94} +(1.14539 - 1.98387i) q^{95} +(-7.63743 - 4.40947i) q^{97} +(-4.54731 - 2.62539i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 4 q^{10} - 6 q^{11} - 12 q^{13} - 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} + 2 q^{22} - 4 q^{23} - 8 q^{25} + 12 q^{26} + 8 q^{29} - 2 q^{35} + 30 q^{37} - 8 q^{40} + 14 q^{43} - 6 q^{46} + 14 q^{49} - 6 q^{52} - 16 q^{53} - 2 q^{55} - 2 q^{56} - 6 q^{58} - 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} + 6 q^{65} + 24 q^{67} + 16 q^{68} + 12 q^{71} - 10 q^{74} - 6 q^{76} - 16 q^{77} - 20 q^{79} + 4 q^{82} - 2 q^{88} - 42 q^{89} - 10 q^{91} - 8 q^{92} - 8 q^{94} - 24 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^10 - 6 * q^11 - 12 * q^13 - 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 + 2 * q^22 - 4 * q^23 - 8 * q^25 + 12 * q^26 + 8 * q^29 - 2 * q^35 + 30 * q^37 - 8 * q^40 + 14 * q^43 - 6 * q^46 + 14 * q^49 - 6 * q^52 - 16 * q^53 - 2 * q^55 - 2 * q^56 - 6 * q^58 - 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 + 6 * q^65 + 24 * q^67 + 16 * q^68 + 12 * q^71 - 10 * q^74 - 6 * q^76 - 16 * q^77 - 20 * q^79 + 4 * q^82 - 2 * q^88 - 42 * q^89 - 10 * q^91 - 8 * q^92 - 8 * q^94 - 24 * 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
$7$	1.14539	+	0.661290i	0.432916	+	0.249944i	0.700588	−	0.713566i	$-0.252921\pi$
$7$	1.14539	+	0.661290i	0.432916	+	0.249944i	−0.267672	+	0.963510i	$0.586254\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	3.99528	−	2.30668i	1.20462	−	0.695489i	0.243043	−	0.970015i	$-0.421854\pi$
$11$	3.99528	−	2.30668i	1.20462	−	0.695489i	0.961580	+	0.274526i	$0.0885209\pi$
$12$		0			0
$13$	3.20002	+	1.66129i	0.887525	+	0.460759i
$13$	3.20002	+	1.66129i	0.887525	+	0.460759i
$14$	1.32258			0.353474
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	1.98387	+	1.14539i	0.455131	+	0.262770i	0.709995	−	0.704207i	$-0.248697\pi$
$19$	1.98387	+	1.14539i	0.455131	+	0.262770i	−0.254864	+	0.966977i	$0.582031\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$	2.30668	−	3.99528i	0.491785	−	0.851797i
$23$	−4.33399	−	7.50670i	−0.903700	−	1.56525i	−0.822653	−	0.568544i	$-0.807507\pi$
$23$	−4.33399	−	7.50670i	−0.903700	−	1.56525i	−0.0810471	−	0.996710i	$-0.525826\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	3.60194	−	0.161290i	0.706399	−	0.0316315i
$27$		0			0
$28$	1.14539	−	0.661290i	0.216458	−	0.124972i
$29$	−1.01141	−	1.75182i	−0.187815	−	0.325305i	0.756707	−	0.653755i	$-0.226807\pi$
$29$	−1.01141	−	1.75182i	−0.187815	−	0.325305i	−0.944521	+	0.328450i	$0.893474\pi$
$30$		0			0
$31$			10.1321i			1.81978i	0.414853	+	0.909888i	$0.363833\pi$
$31$			10.1321i			1.81978i	−0.414853	+	0.909888i	$0.636167\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			4.00000i			0.685994i
$35$	0.661290	−	1.14539i	0.111778	−	0.193606i
$36$		0			0
$37$	5.89721	−	3.40475i	0.969495	−	0.559738i	0.0704126	−	0.997518i	$-0.477568\pi$
$37$	5.89721	−	3.40475i	0.969495	−	0.559738i	0.899082	+	0.437780i	$0.144235\pi$
$38$	2.29078			0.371613
$39$		0			0
$40$	−1.00000			−0.158114
$41$	4.02283	−	2.32258i	0.628260	−	0.362726i	−0.151818	−	0.988408i	$-0.548513\pi$
$41$	4.02283	−	2.32258i	0.628260	−	0.362726i	0.780078	+	0.625682i	$0.215179\pi$
$42$		0			0
$43$	4.30281	−	7.45269i	0.656173	−	1.13652i	−0.325426	−	0.945568i	$-0.605508\pi$
$43$	4.30281	−	7.45269i	0.656173	−	1.13652i	0.981598	−	0.190957i	$-0.0611590\pi$
$44$		−	4.61335i		−	0.695489i
$45$		0			0
$46$	−7.50670	−	4.33399i	−1.10680	−	0.639012i
$47$		−	9.10926i		−	1.32872i	−0.747412	−	0.664361i	$-0.768704\pi$
$47$		−	9.10926i		−	1.32872i	0.747412	−	0.664361i	$-0.231296\pi$
$48$		0			0
$49$	−2.62539	−	4.54731i	−0.375056	−	0.649616i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	3.03873	−	1.94065i	0.421396	−	0.269120i
$53$	−0.826674			−0.113552			−0.0567762	−	0.998387i	$-0.518082\pi$
$53$	−0.826674			−0.113552			−0.0567762	+	0.998387i	$0.518082\pi$
$54$		0			0
$55$	−2.30668	−	3.99528i	−0.311032	−	0.538724i
$56$	0.661290	−	1.14539i	0.0883686	−	0.153059i
$57$		0			0
$58$	−1.75182	−	1.01141i	−0.230025	−	0.132805i
$59$	−2.72064	−	1.57076i	−0.354197	−	0.204496i	0.312335	−	0.949972i	$-0.398889\pi$
$59$	−2.72064	−	1.57076i	−0.354197	−	0.204496i	−0.666532	+	0.745476i	$0.732222\pi$
$60$		0			0
$61$	−0.267949	+	0.464102i	−0.0343074	+	0.0594221i	−0.882669	−	0.469995i	$-0.844256\pi$
$61$	−0.267949	+	0.464102i	−0.0343074	+	0.0594221i	0.848362	+	0.529417i	$0.177589\pi$
$62$	5.06604	+	8.77464i	0.643388	+	1.11438i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.66129	−	3.20002i	0.206058	−	0.396913i
$66$		0			0
$67$	−2.75488	+	1.59053i	−0.336562	+	0.194314i	−0.658751	−	0.752361i	$-0.728915\pi$
$67$	−2.75488	+	1.59053i	−0.336562	+	0.194314i	0.322189	+	0.946675i	$0.395581\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		0			0
$70$		−	1.32258i		−	0.158079i
$71$	9.81724	+	5.66799i	1.16509	+	0.672666i	0.952519	−	0.304479i	$-0.0984824\pi$
$71$	9.81724	+	5.66799i	1.16509	+	0.672666i	0.212573	+	0.977145i	$0.431816\pi$
$72$		0			0
$73$			6.28304i			0.735375i	0.929949	+	0.367687i	$0.119850\pi$
$73$			6.28304i			0.735375i	−0.929949	+	0.367687i	$0.880150\pi$
$74$	3.40475	−	5.89721i	0.395795	−	0.685536i
$75$		0			0
$76$	1.98387	−	1.14539i	0.227565	−	0.131385i
$77$	6.10153			0.695334
$78$		0			0
$79$	2.96774			0.333897			0.166948	−	0.985966i	$-0.446609\pi$
$79$	2.96774			0.333897			0.166948	+	0.985966i	$0.446609\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$		0			0
$82$	2.32258	−	4.02283i	0.256486	−	0.444247i
$83$			15.8719i			1.74216i	0.491138	+	0.871082i	$0.336581\pi$
$83$			15.8719i			1.74216i	−0.491138	+	0.871082i	$0.663419\pi$
$84$		0			0
$85$	3.46410	+	2.00000i	0.375735	+	0.216930i
$86$		−	8.60562i		−	0.927968i
$87$		0			0
$88$	−2.30668	−	3.99528i	−0.245893	−	0.425899i
$89$	−10.2746	+	5.93207i	−1.08911	+	0.628798i	−0.933339	−	0.358995i	$-0.883119\pi$
$89$	−10.2746	+	5.93207i	−1.08911	+	0.628798i	−0.155771	+	0.987793i	$0.549786\pi$
$90$		0			0
$91$	2.56667	+	4.01896i	0.269060	+	0.421302i
$92$	−8.66799			−0.903700
$93$		0			0
$94$	−4.55463	−	7.88885i	−0.469774	−	0.813673i
$95$	1.14539	−	1.98387i	0.117514	−	0.203541i
$96$		0			0
$97$	−7.63743	−	4.40947i	−0.775463	−	0.447714i	0.0593568	−	0.998237i	$-0.481095\pi$
$97$	−7.63743	−	4.40947i	−0.775463	−	0.447714i	−0.834820	+	0.550523i	$0.814428\pi$
$98$	−4.54731	−	2.62539i	−0.459348	−	0.265205i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	3.61335	+	6.25851i	0.359542	+	0.622745i	0.987884	−	0.155192i	$-0.0495995\pi$
$101$	3.61335	+	6.25851i	0.359542	+	0.622745i	−0.628342	+	0.777937i	$0.716266\pi$
$102$		0			0
$103$	−18.4000			−1.81301			−0.906505	−	0.422196i	$-0.861260\pi$
$103$	−18.4000			−1.81301			−0.906505	+	0.422196i	$0.861260\pi$
$104$	1.66129	−	3.20002i	0.162903	−	0.313788i
$105$		0			0
$106$	−0.715920	+	0.413337i	−0.0695363	+	0.0401468i
$107$	1.53590	+	2.66025i	0.148481	+	0.257176i	0.930666	−	0.365869i	$-0.119228\pi$
$107$	1.53590	+	2.66025i	0.148481	+	0.257176i	−0.782185	+	0.623046i	$0.785895\pi$
$108$		0			0
$109$		−	13.2267i		−	1.26689i	−0.773788	−	0.633445i	$-0.781640\pi$
$109$		−	13.2267i		−	1.26689i	0.773788	−	0.633445i	$-0.218360\pi$
$110$	−3.99528	−	2.30668i	−0.380935	−	0.219933i
$111$		0			0
$112$		−	1.32258i		−	0.124972i
$113$	−4.04322	+	7.00306i	−0.380354	+	0.658792i	−0.991113	−	0.133024i	$-0.957531\pi$
$113$	−4.04322	+	7.00306i	−0.380354	+	0.658792i	0.610759	+	0.791817i	$0.290864\pi$
$114$		0			0
$115$	−7.50670	+	4.33399i	−0.700003	+	0.404147i
$116$	−2.02283			−0.187815
$117$		0			0
$118$	−3.14152			−0.289201
$119$	−4.58155	+	2.64516i	−0.419990	+	0.242481i
$120$		0			0
$121$	5.14152	−	8.90538i	0.467411	−	0.809580i
$122$			0.535898i			0.0485180i
$123$		0			0
$124$	8.77464	+	5.06604i	0.787986	+	0.454944i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	5.73592	+	9.93490i	0.508980	+	0.881580i	0.999946	+	0.0104008i	$0.00331073\pi$
$127$	5.73592	+	9.93490i	0.508980	+	0.881580i	−0.490966	+	0.871179i	$0.663356\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.161290	−	3.60194i	−0.0141461	−	0.315911i
$131$	15.9906			1.39710			0.698551	−	0.715560i	$-0.253828\pi$
$131$	15.9906			1.39710			0.698551	+	0.715560i	$0.253828\pi$
$132$		0			0
$133$	1.51487	+	2.62383i	0.131356	+	0.227515i
$134$	−1.59053	+	2.75488i	−0.137401	+	0.237985i
$135$		0			0
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	−13.9168	−	8.03486i	−1.18899	−	0.686465i	−0.230914	−	0.972974i	$-0.574172\pi$
$137$	−13.9168	−	8.03486i	−1.18899	−	0.686465i	−0.958077	+	0.286509i	$0.907505\pi$
$138$		0			0
$139$	−4.66129	+	8.07359i	−0.395365	+	0.684793i	−0.993148	−	0.116865i	$-0.962715\pi$
$139$	−4.66129	+	8.07359i	−0.395365	+	0.684793i	0.597782	+	0.801658i	$0.296049\pi$
$140$	−0.661290	−	1.14539i	−0.0558892	−	0.0968029i
$141$		0			0
$142$	11.3360			0.951294
$143$	16.6170	−	0.744087i	1.38959	−	0.0622237i
$144$		0			0
$145$	−1.75182	+	1.01141i	−0.145481	+	0.0839933i
$146$	3.14152	+	5.44128i	0.259994	+	0.450323i
$147$		0			0
$148$		−	6.80951i		−	0.559738i
$149$	−3.53788	−	2.04259i	−0.289834	−	0.167336i	0.348033	−	0.937482i	$-0.386850\pi$
$149$	−3.53788	−	2.04259i	−0.289834	−	0.167336i	−0.637867	+	0.770146i	$0.720183\pi$
$150$		0			0
$151$			19.9811i			1.62604i	0.582235	+	0.813021i	$0.302178\pi$
$151$			19.9811i			1.62604i	−0.582235	+	0.813021i	$0.697822\pi$
$152$	1.14539	−	1.98387i	0.0929032	−	0.160913i
$153$		0			0
$154$	5.28408	−	3.05076i	0.425803	−	0.245838i
$155$	10.1321			0.813829
$156$		0			0
$157$	7.13379			0.569338			0.284669	−	0.958626i	$-0.408116\pi$
$157$	7.13379			0.569338			0.284669	+	0.958626i	$0.408116\pi$
$158$	2.57014	−	1.48387i	0.204469	−	0.118050i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		−	11.4641i		−	0.903498i
$162$		0			0
$163$	−8.56906	−	4.94735i	−0.671180	−	0.387506i	0.125343	−	0.992113i	$-0.459997\pi$
$163$	−8.56906	−	4.94735i	−0.671180	−	0.387506i	−0.796524	+	0.604607i	$0.793330\pi$
$164$		−	4.64516i		−	0.362726i
$165$		0			0
$166$	7.93593	+	13.7454i	0.615948	+	1.06685i
$167$	−20.8171	+	12.0187i	−1.61087	+	0.930037i	−0.621704	+	0.783253i	$0.713559\pi$
$167$	−20.8171	+	12.0187i	−1.61087	+	0.930037i	−0.989168	+	0.146785i	$0.953108\pi$
$168$		0			0
$169$	7.48023	+	10.6323i	0.575402	+	0.817870i
$170$	4.00000			0.306786
$171$		0			0
$172$	−4.30281	−	7.45269i	−0.328086	−	0.568262i
$173$	−1.26408	+	2.18946i	−0.0961065	+	0.166461i	−0.910070	−	0.414455i	$-0.863972\pi$
$173$	−1.26408	+	2.18946i	−0.0961065	+	0.166461i	0.813963	+	0.580916i	$0.197306\pi$
$174$		0			0
$175$	−1.14539	−	0.661290i	−0.0865832	−	0.0499888i
$176$	−3.99528	−	2.30668i	−0.301156	−	0.173872i
$177$		0			0
$178$	−5.93207	+	10.2746i	−0.444627	+	0.770117i
$179$	3.13784	+	5.43490i	0.234533	+	0.406223i	0.959137	−	0.282942i	$-0.0913105\pi$
$179$	3.13784	+	5.43490i	0.234533	+	0.406223i	−0.724604	+	0.689166i	$0.757977\pi$
$180$		0			0
$181$	−12.2830			−0.912991			−0.456496	−	0.889726i	$-0.650896\pi$
$181$	−12.2830			−0.912991			−0.456496	+	0.889726i	$0.650896\pi$
$182$	4.23228	+	2.19719i	0.313717	+	0.162866i
$183$		0			0
$184$	−7.50670	+	4.33399i	−0.553401	+	0.319506i
$185$	−3.40475	−	5.89721i	−0.250322	−	0.433571i
$186$		0			0
$187$			18.4534i			1.34945i
$188$	−7.88885	−	4.55463i	−0.575354	−	0.332181i
$189$		0			0
$190$		−	2.29078i		−	0.166190i
$191$	−4.87357	+	8.44128i	−0.352639	+	0.610789i	−0.986711	−	0.162485i	$-0.948049\pi$
$191$	−4.87357	+	8.44128i	−0.352639	+	0.610789i	0.634072	+	0.773274i	$0.281382\pi$
$192$		0			0
$193$	−11.9188	+	6.88130i	−0.857932	+	0.495327i	−0.863319	−	0.504658i	$-0.831618\pi$
$193$	−11.9188	+	6.88130i	−0.857932	+	0.495327i	0.00538741	+	0.999985i	$0.498285\pi$
$194$	−8.81894			−0.633163
$195$		0			0
$196$	−5.25078			−0.375056
$197$	8.78282	−	5.07076i	0.625750	−	0.361277i	−0.153354	−	0.988171i	$-0.549008\pi$
$197$	8.78282	−	5.07076i	0.625750	−	0.361277i	0.779104	+	0.626894i	$0.215674\pi$
$198$		0			0
$199$	4.78668	−	8.29078i	0.339319	−	0.587717i	−0.644986	−	0.764194i	$-0.723137\pi$
$199$	4.78668	−	8.29078i	0.339319	−	0.587717i	0.984305	+	0.176477i	$0.0564701\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	6.25851	+	3.61335i	0.440348	+	0.254235i
$203$		−	2.67535i		−	0.187773i
$204$		0			0
$205$	−2.32258	−	4.02283i	−0.162216	−	0.280966i
$206$	−15.9349	+	9.20002i	−1.11024	+	0.640996i
$207$		0			0
$208$	−0.161290	−	3.60194i	−0.0111834	−	0.249750i
$209$	10.5682			0.731015
$210$		0			0
$211$	0.542594	+	0.939800i	0.0373537	+	0.0646985i	0.884098	−	0.467302i	$-0.154774\pi$
$211$	0.542594	+	0.939800i	0.0373537	+	0.0646985i	−0.846744	+	0.532000i	$0.821441\pi$
$212$	−0.413337	+	0.715920i	−0.0283881	+	0.0491696i
$213$		0			0
$214$	2.66025	+	1.53590i	0.181851	+	0.104992i
$215$	−7.45269	−	4.30281i	−0.508269	−	0.293449i
$216$		0			0
$217$	−6.70025	+	11.6052i	−0.454842	+	0.787810i
$218$	−6.61335	−	11.4547i	−0.447913	−	0.775808i
$219$		0			0
$220$	−4.61335			−0.311032
$221$	−12.1549	+	7.76261i	−0.817628	+	0.522170i
$222$		0			0
$223$	21.6001	−	12.4708i	1.44645	−	0.835106i	0.448179	−	0.893944i	$-0.352073\pi$
$223$	21.6001	−	12.4708i	1.44645	−	0.835106i	0.998268	+	0.0588375i	$0.0187394\pi$
$224$	−0.661290	−	1.14539i	−0.0441843	−	0.0765294i
$225$		0			0
$226$			8.08643i			0.537902i
$227$	16.7321	+	9.66025i	1.11055	+	0.641174i	0.938971	−	0.343998i	$-0.111781\pi$
$227$	16.7321	+	9.66025i	1.11055	+	0.641174i	0.171575	+	0.985171i	$0.445115\pi$
$228$		0			0
$229$		−	4.15491i		−	0.274564i	−0.990532	−	0.137282i	$-0.956163\pi$
$229$		−	4.15491i		−	0.274564i	0.990532	−	0.137282i	$-0.0438367\pi$
$230$	−4.33399	+	7.50670i	−0.285775	+	0.494977i
$231$		0			0
$232$	−1.75182	+	1.01141i	−0.115013	+	0.0664025i
$233$	−16.9665			−1.11151			−0.555756	−	0.831346i	$-0.687571\pi$
$233$	−16.9665			−1.11151			−0.555756	+	0.831346i	$0.687571\pi$
$234$		0			0
$235$	−9.10926			−0.594223
$236$	−2.72064	+	1.57076i	−0.177098	+	0.102248i
$237$		0			0
$238$	−2.64516	+	4.58155i	−0.171460	+	0.296978i
$239$		−	6.34416i		−	0.410370i	−0.978723	−	0.205185i	$-0.934220\pi$
$239$		−	6.34416i		−	0.410370i	0.978723	−	0.205185i	$-0.0657795\pi$
$240$		0			0
$241$	20.9452	+	12.0927i	1.34920	+	0.778962i	0.988136	−	0.153579i	$-0.0490800\pi$
$241$	20.9452	+	12.0927i	1.34920	+	0.778962i	0.361065	+	0.932541i	$0.382413\pi$
$242$		−	10.2830i		−	0.661019i
$243$		0			0
$244$	0.267949	+	0.464102i	0.0171537	+	0.0297111i
$245$	−4.54731	+	2.62539i	−0.290517	+	0.167730i
$246$		0			0
$247$	4.44560	+	6.96104i	0.282867	+	0.442921i
$248$	10.1321			0.643388
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−4.41249	+	7.64265i	−0.278514	+	0.482400i	−0.971016	−	0.239016i	$-0.923175\pi$
$251$	−4.41249	+	7.64265i	−0.278514	+	0.482400i	0.692502	+	0.721416i	$0.256508\pi$
$252$		0			0
$253$	−34.6311	−	19.9942i	−2.17724	−	1.25703i
$254$	9.93490	+	5.73592i	0.623371	+	0.359903i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.19247	−	7.26157i	−0.261519	−	0.452964i	0.705127	−	0.709081i	$-0.250890\pi$
$257$	−4.19247	−	7.26157i	−0.261519	−	0.452964i	−0.966646	+	0.256117i	$0.917557\pi$
$258$		0			0
$259$	9.00612			0.559613
$260$	−1.94065	−	3.03873i	−0.120354	−	0.188454i
$261$		0			0
$262$	13.8482	−	7.99528i	0.855547	−	0.493950i
$263$	0.960648	+	1.66389i	0.0592361	+	0.102600i	0.894123	−	0.447822i	$-0.147800\pi$
$263$	0.960648	+	1.66389i	0.0592361	+	0.102600i	−0.834887	+	0.550422i	$0.814467\pi$
$264$		0			0
$265$			0.826674i			0.0507822i
$266$	2.62383	+	1.51487i	0.160877	+	0.0928824i
$267$		0			0
$268$			3.18106i			0.194314i
$269$	−16.1549	+	27.9811i	−0.984982	+	1.70604i	−0.342968	+	0.939347i	$0.611432\pi$
$269$	−16.1549	+	27.9811i	−0.984982	+	1.70604i	−0.642014	+	0.766693i	$0.721901\pi$
$270$		0			0
$271$	20.3105	−	11.7263i	1.23378	−	0.712322i	0.265962	−	0.963983i	$-0.414310\pi$
$271$	20.3105	−	11.7263i	1.23378	−	0.712322i	0.967815	+	0.251662i	$0.0809770\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−16.0697			−0.970808
$275$	−3.99528	+	2.30668i	−0.240925	+	0.139098i
$276$		0			0
$277$	−4.50283	+	7.79913i	−0.270549	+	0.468604i	−0.969002	−	0.247051i	$-0.920538\pi$
$277$	−4.50283	+	7.79913i	−0.270549	+	0.468604i	0.698454	+	0.715655i	$0.253872\pi$
$278$			9.32258i			0.559131i
$279$		0			0
$280$	−1.14539	−	0.661290i	−0.0684500	−	0.0395196i
$281$			1.71696i			0.102425i	0.998688	+	0.0512125i	$0.0163086\pi$
$281$			1.71696i			0.102425i	−0.998688	+	0.0512125i	$0.983691\pi$
$282$		0			0
$283$	−0.774645	−	1.34172i	−0.0460479	−	0.0797572i	0.842083	−	0.539348i	$-0.181329\pi$
$283$	−0.774645	−	1.34172i	−0.0460479	−	0.0797572i	−0.888131	+	0.459591i	$0.847996\pi$
$284$	9.81724	−	5.66799i	0.582546	−	0.336333i
$285$		0			0
$286$	14.0187	−	8.95292i	0.828945	−	0.529397i
$287$	6.14359			0.362645
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−1.01141	+	1.75182i	−0.0593922	+	0.102870i
$291$		0			0
$292$	5.44128	+	3.14152i	0.318427	+	0.183844i
$293$	−26.3321	−	15.2028i	−1.53834	−	0.888160i	−0.998936	−	0.0461113i	$-0.985317\pi$
$293$	−26.3321	−	15.2028i	−1.53834	−	0.888160i	−0.539402	−	0.842049i	$-0.681350\pi$
$294$		0			0
$295$	−1.57076	+	2.72064i	−0.0914532	+	0.158402i
$296$	−3.40475	−	5.89721i	−0.197897	−	0.342768i
$297$		0			0
$298$	−4.08519			−0.236649
$299$	−1.39806	−	31.2216i	−0.0808518	−	1.80559i
$300$		0			0
$301$	9.85677	−	5.69081i	0.568135	−	0.328013i
$302$	9.99057	+	17.3042i	0.574892	+	0.995743i
$303$		0			0
$304$		−	2.29078i		−	0.131385i
$305$	0.464102	+	0.267949i	0.0265744	+	0.0153427i
$306$		0			0
$307$		−	9.82622i		−	0.560812i	−0.959882	−	0.280406i	$-0.909531\pi$
$307$		−	9.82622i		−	0.560812i	0.959882	−	0.280406i	$-0.0904691\pi$
$308$	3.05076	−	5.28408i	0.173833	−	0.301088i
$309$		0			0
$310$	8.77464	−	5.06604i	0.498366	−	0.287732i
$311$	3.40049			0.192824			0.0964121	−	0.995342i	$-0.469263\pi$
$311$	3.40049			0.192824			0.0964121	+	0.995342i	$0.469263\pi$
$312$		0			0
$313$	−16.2340			−0.917599			−0.458800	−	0.888540i	$-0.651720\pi$
$313$	−16.2340			−0.917599			−0.458800	+	0.888540i	$0.651720\pi$
$314$	6.17804	−	3.56690i	0.348647	−	0.201292i
$315$		0			0
$316$	1.48387	−	2.57014i	0.0834742	−	0.144582i
$317$			23.5231i			1.32119i	0.750742	+	0.660596i	$0.229696\pi$
$317$			23.5231i			1.32119i	−0.750742	+	0.660596i	$0.770304\pi$
$318$		0			0
$319$	−8.08176	−	4.66601i	−0.452492	−	0.261246i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	−5.73205	−	9.92820i	−0.319435	−	0.553277i
$323$	−7.93548	+	4.58155i	−0.441542	+	0.254924i
$324$		0			0
$325$	−3.20002	−	1.66129i	−0.177505	−	0.0921518i
$326$	−9.89470			−0.548016
$327$		0			0
$328$	−2.32258	−	4.02283i	−0.128243	−	0.222123i
$329$	6.02386	−	10.4336i	0.332106	−	0.575225i
$330$		0			0
$331$	15.6667	+	9.04520i	0.861122	+	0.497169i	0.864388	−	0.502826i	$-0.167706\pi$
$331$	15.6667	+	9.04520i	0.861122	+	0.497169i	−0.00326597	+	0.999995i	$0.501040\pi$
$332$	13.7454	+	7.93593i	0.754379	+	0.435541i
$333$		0			0
$334$	−12.0187	+	20.8171i	−0.657636	+	1.13906i
$335$	1.59053	+	2.75488i	0.0868999	+	0.150515i
$336$		0			0
$337$	−5.69900			−0.310444			−0.155222	−	0.987880i	$-0.549609\pi$
$337$	−5.69900			−0.310444			−0.155222	+	0.987880i	$0.549609\pi$
$338$	11.7942	+	5.46774i	0.641521	+	0.297406i
$339$		0			0
$340$	3.46410	−	2.00000i	0.187867	−	0.108465i
$341$	23.3715	+	40.4806i	1.26564	+	2.19214i
$342$		0			0
$343$		−	16.2026i		−	0.874860i
$344$	−7.45269	−	4.30281i	−0.401822	−	0.231992i
$345$		0			0
$346$			2.52817i			0.135915i
$347$	−7.87357	+	13.6374i	−0.422676	+	0.732095i	−0.996200	−	0.0870928i	$-0.972242\pi$
$347$	−7.87357	+	13.6374i	−0.422676	+	0.732095i	0.573525	+	0.819188i	$0.305576\pi$
$348$		0			0
$349$	13.2679	−	7.66025i	0.710217	−	0.410044i	−0.100924	−	0.994894i	$-0.532180\pi$
$349$	13.2679	−	7.66025i	0.710217	−	0.410044i	0.811141	+	0.584850i	$0.198847\pi$
$350$	−1.32258			−0.0706949
$351$		0			0
$352$	−4.61335			−0.245893
$353$	−1.03917	+	0.599964i	−0.0553093	+	0.0319328i	−0.527400	−	0.849617i	$-0.676833\pi$
$353$	−1.03917	+	0.599964i	−0.0553093	+	0.0319328i	0.472090	+	0.881550i	$0.343500\pi$
$354$		0			0
$355$	5.66799	−	9.81724i	0.300825	−	0.521045i
$356$			11.8641i			0.628798i
$357$		0			0
$358$	5.43490	+	3.13784i	0.287243	+	0.165840i
$359$			16.2830i			0.859386i	0.902975	+	0.429693i	$0.141378\pi$
$359$			16.2830i			0.859386i	−0.902975	+	0.429693i	$0.858622\pi$
$360$		0			0
$361$	−6.87617	−	11.9099i	−0.361904	−	0.626836i
$362$	−10.6374	+	6.14152i	−0.559091	+	0.322791i
$363$		0			0
$364$	4.76386	−	0.213319i	0.249694	−	0.0111809i
$365$	6.28304			0.328870
$366$		0			0
$367$	9.81724	+	17.0040i	0.512456	+	0.887599i	0.999896	+	0.0144428i	$0.00459745\pi$
$367$	9.81724	+	17.0040i	0.512456	+	0.887599i	−0.487440	+	0.873156i	$0.662069\pi$
$368$	−4.33399	+	7.50670i	−0.225925	+	0.391314i
$369$		0			0
$370$	−5.89721	−	3.40475i	−0.306581	−	0.177005i
$371$	−0.946862	−	0.546671i	−0.0491586	−	0.0283817i
$372$		0			0
$373$	1.27874	−	2.21484i	0.0662106	−	0.114680i	−0.831020	−	0.556243i	$-0.812242\pi$
$373$	1.27874	−	2.21484i	0.0662106	−	0.114680i	0.897230	+	0.441563i	$0.145576\pi$
$374$	9.22671	+	15.9811i	0.477102	+	0.826365i
$375$		0			0
$376$	−9.10926			−0.469774
$377$	−0.326261	−	7.28610i	−0.0168033	−	0.375253i
$378$		0			0
$379$	−13.0846	+	7.55440i	−0.672111	+	0.388044i	−0.796876	−	0.604143i	$-0.793516\pi$
$379$	−13.0846	+	7.55440i	−0.672111	+	0.388044i	0.124765	+	0.992186i	$0.460182\pi$
$380$	−1.14539	−	1.98387i	−0.0587571	−	0.101770i
$381$		0			0
$382$			9.74715i			0.498707i
$383$	16.2210	+	9.36517i	0.828852	+	0.478538i	0.853459	−	0.521159i	$-0.174500\pi$
$383$	16.2210	+	9.36517i	0.828852	+	0.478538i	−0.0246073	+	0.999697i	$0.507834\pi$
$384$		0			0
$385$		−	6.10153i		−	0.310963i
$386$	−6.88130	+	11.9188i	−0.350249	+	0.606649i
$387$		0			0
$388$	−7.63743	+	4.40947i	−0.387732	+	0.223857i
$389$	−6.96899			−0.353342			−0.176671	−	0.984270i	$-0.556533\pi$
$389$	−6.96899			−0.353342			−0.176671	+	0.984270i	$0.556533\pi$
$390$		0			0
$391$	34.6719			1.75344
$392$	−4.54731	+	2.62539i	−0.229674	+	0.132602i
$393$		0			0
$394$	5.07076	−	8.78282i	0.255461	−	0.442472i
$395$		−	2.96774i		−	0.149323i
$396$		0			0
$397$	−16.0839	−	9.28606i	−0.807229	−	0.466054i	0.0387637	−	0.999248i	$-0.487658\pi$
$397$	−16.0839	−	9.28606i	−0.807229	−	0.466054i	−0.845993	+	0.533195i	$0.820991\pi$
$398$		−	9.57336i		−	0.479869i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	25.7126	−	14.8452i	1.28403	−	0.741333i	0.306444	−	0.951889i	$-0.400861\pi$
$401$	25.7126	−	14.8452i	1.28403	−	0.741333i	0.977582	+	0.210556i	$0.0675274\pi$
$402$		0			0
$403$	−16.8323	+	32.4229i	−0.838478	+	1.61510i
$404$	7.22671			0.359542
$405$		0			0
$406$	−1.33767	−	2.31692i	−0.0663877	−	0.114987i
$407$	15.7073	−	27.2059i	0.778584	−	1.34855i
$408$		0			0
$409$	−21.0752	−	12.1678i	−1.04210	−	0.601657i	−0.121673	−	0.992570i	$-0.538826\pi$
$409$	−21.0752	−	12.1678i	−1.04210	−	0.601657i	−0.920427	+	0.390913i	$0.872159\pi$
$410$	−4.02283	−	2.32258i	−0.198673	−	0.114704i
$411$		0			0
$412$	−9.20002	+	15.9349i	−0.453252	+	0.785056i
$413$	−2.07746	−	3.59826i	−0.102225	−	0.177059i
$414$		0			0
$415$	15.8719			0.779119
$416$	−1.94065	−	3.03873i	−0.0951483	−	0.148986i
$417$		0			0
$418$	9.15229	−	5.28408i	0.447653	−	0.258453i
$419$	−1.44128	−	2.49636i	−0.0704109	−	0.121955i	0.828671	−	0.559737i	$-0.189098\pi$
$419$	−1.44128	−	2.49636i	−0.0704109	−	0.121955i	−0.899081	+	0.437781i	$0.855764\pi$
$420$		0			0
$421$			4.94707i			0.241106i	0.992707	+	0.120553i	$0.0384667\pi$
$421$			4.94707i			0.241106i	−0.992707	+	0.120553i	$0.961533\pi$
$422$	0.939800	+	0.542594i	0.0457488	+	0.0264131i
$423$		0			0
$424$			0.826674i			0.0401468i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	−0.613811	+	0.354384i	−0.0297044	+	0.0171499i
$428$	3.07180			0.148481
$429$		0			0
$430$	−8.60562			−0.415000
$431$	15.3829	−	8.88130i	0.740967	−	0.427797i	−0.0814539	−	0.996677i	$-0.525956\pi$
$431$	15.3829	−	8.88130i	0.740967	−	0.427797i	0.822421	+	0.568880i	$0.192623\pi$
$432$		0			0
$433$	17.9188	−	31.0362i	0.861121	−	1.49151i	−0.00972676	−	0.999953i	$-0.503096\pi$
$433$	17.9188	−	31.0362i	0.861121	−	1.49151i	0.870848	−	0.491553i	$-0.163570\pi$
$434$			13.4005i			0.643244i
$435$		0			0
$436$	−11.4547	−	6.61335i	−0.548579	−	0.316722i
$437$		−	19.8564i		−	0.949861i
$438$		0			0
$439$	5.04520	+	8.73854i	0.240794	+	0.417068i	0.960941	−	0.276754i	$-0.0892588\pi$
$439$	5.04520	+	8.73854i	0.240794	+	0.417068i	−0.720147	+	0.693822i	$0.755925\pi$
$440$	−3.99528	+	2.30668i	−0.190468	+	0.109967i
$441$		0			0
$442$	−6.64516	+	12.8001i	−0.316078	+	0.608837i
$443$	−13.6981			−0.650816			−0.325408	−	0.945574i	$-0.605502\pi$
$443$	−13.6981			−0.650816			−0.325408	+	0.945574i	$0.605502\pi$
$444$		0			0
$445$	5.93207	+	10.2746i	0.281207	+	0.487065i
$446$	12.4708	−	21.6001i	0.590509	−	1.02279i
$447$		0			0
$448$	−1.14539	−	0.661290i	−0.0541145	−	0.0312430i
$449$	−13.2613	−	7.65639i	−0.625837	−	0.361327i	0.153301	−	0.988180i	$-0.451010\pi$
$449$	−13.2613	−	7.65639i	−0.625837	−	0.361327i	−0.779138	+	0.626852i	$0.784343\pi$
$450$		0			0
$451$	10.7149	−	18.5587i	0.504544	−	0.873896i
$452$	4.04322	+	7.00306i	0.190177	+	0.329396i
$453$		0			0
$454$	19.3205			0.906756
$455$	4.01896	−	2.56667i	0.188412	−	0.120327i
$456$		0			0
$457$	−13.4714	+	7.77770i	−0.630164	+	0.363826i	−0.780816	−	0.624761i	$-0.785196\pi$
$457$	−13.4714	+	7.77770i	−0.630164	+	0.363826i	0.150651	+	0.988587i	$0.451863\pi$
$458$	−2.07746	−	3.59826i	−0.0970732	−	0.168136i
$459$		0			0
$460$			8.66799i			0.404147i
$461$	−13.5473	−	7.82154i	−0.630961	−	0.364286i	0.150163	−	0.988661i	$-0.452020\pi$
$461$	−13.5473	−	7.82154i	−0.630961	−	0.364286i	−0.781124	+	0.624376i	$0.785353\pi$
$462$		0			0
$463$		−	13.7170i		−	0.637481i	−0.947842	−	0.318741i	$-0.896740\pi$
$463$		−	13.7170i		−	0.637481i	0.947842	−	0.318741i	$-0.103260\pi$
$464$	−1.01141	+	1.75182i	−0.0469537	+	0.0813261i
$465$		0			0
$466$	−14.6934	+	8.48325i	−0.680659	+	0.392979i
$467$	0.943666			0.0436677			0.0218338	−	0.999762i	$-0.493050\pi$
$467$	0.943666			0.0436677			0.0218338	+	0.999762i	$0.493050\pi$
$468$		0			0
$469$	−4.20720			−0.194271
$470$	−7.88885	+	4.55463i	−0.363886	+	0.210089i
$471$		0			0
$472$	−1.57076	+	2.72064i	−0.0723001	+	0.125228i
$473$		−	39.7008i		−	1.82544i
$474$		0			0
$475$	−1.98387	−	1.14539i	−0.0910262	−	0.0525540i
$476$			5.29032i			0.242481i
$477$		0			0
$478$	−3.17208	−	5.49420i	−0.145088	−	0.251299i
$479$	9.61460	−	5.55099i	0.439302	−	0.253631i	−0.263999	−	0.964523i	$-0.585042\pi$
$479$	9.61460	−	5.55099i	0.439302	−	0.253631i	0.703302	+	0.710892i	$0.251708\pi$
$480$		0			0
$481$	24.5275	−	1.09830i	1.11836	−	0.0500784i
$482$	24.1855			1.10162
$483$		0			0
$484$	−5.14152	−	8.90538i	−0.233706	−	0.404790i
$485$	−4.40947	+	7.63743i	−0.200224	+	0.346798i
$486$		0			0
$487$	−28.5283	−	16.4708i	−1.29274	−	0.746363i	−0.313600	−	0.949555i	$-0.601535\pi$
$487$	−28.5283	−	16.4708i	−1.29274	−	0.746363i	−0.979139	+	0.203192i	$0.934868\pi$
$488$	0.464102	+	0.267949i	0.0210089	+	0.0121295i
$489$		0			0
$490$	−2.62539	+	4.54731i	−0.118603	+	0.205427i
$491$	−14.2257	−	24.6396i	−0.641996	−	1.11197i	−0.984987	−	0.172630i	$-0.944773\pi$
$491$	−14.2257	−	24.6396i	−0.641996	−	1.11197i	0.342991	−	0.939339i	$-0.388560\pi$
$492$		0			0
$493$	8.09130			0.364414
$494$	7.33052	+	3.80564i	0.329816	+	0.171224i
$495$		0			0
$496$	8.77464	−	5.06604i	0.393993	−	0.227472i
$497$	7.49636	+	12.9841i	0.336258	+	0.582416i
$498$		0			0
$499$			4.10926i			0.183956i	0.995761	+	0.0919779i	$0.0293189\pi$
$499$			4.10926i			0.183956i	−0.995761	+	0.0919779i	$0.970681\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$		0			0
$502$			8.82497i			0.393878i
$503$	2.86800	−	4.96753i	0.127878	−	0.221491i	−0.794976	−	0.606641i	$-0.792517\pi$
$503$	2.86800	−	4.96753i	0.127878	−	0.221491i	0.922854	+	0.385149i	$0.125850\pi$
$504$		0			0
$505$	6.25851	−	3.61335i	0.278500	−	0.160792i
$506$	−39.9885			−1.77771
$507$		0			0
$508$	11.4718			0.508980
$509$	13.1129	−	7.57076i	0.581221	−	0.335568i	−0.180397	−	0.983594i	$-0.557738\pi$
$509$	13.1129	−	7.57076i	0.581221	−	0.335568i	0.761618	+	0.648026i	$0.224405\pi$
$510$		0			0
$511$	−4.15491	+	7.19652i	−0.183803	+	0.318355i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−7.26157	−	4.19247i	−0.320294	−	0.184922i
$515$			18.4000i			0.810802i
$516$		0			0
$517$	−21.0121	−	36.3941i	−0.924112	−	1.60061i
$518$	7.79953	−	4.50306i	0.342691	−	0.197853i
$519$		0			0
$520$	−3.20002	−	1.66129i	−0.140330	−	0.0728524i
$521$	−8.93027			−0.391242			−0.195621	−	0.980680i	$-0.562672\pi$
$521$	−8.93027			−0.391242			−0.195621	+	0.980680i	$0.562672\pi$
$522$		0			0
$523$	4.90844	+	8.50166i	0.214631	+	0.371752i	0.953158	−	0.302472i	$-0.0978118\pi$
$523$	4.90844	+	8.50166i	0.214631	+	0.371752i	−0.738527	+	0.674223i	$0.764478\pi$
$524$	7.99528	−	13.8482i	0.349276	−	0.604963i
$525$		0			0
$526$	1.66389	+	0.960648i	0.0725491	+	0.0418863i
$527$	−35.0986	−	20.2642i	−1.52892	−	0.882721i
$528$		0			0
$529$	−26.0670	+	45.1493i	−1.13335	+	1.96301i
$530$	0.413337	+	0.715920i	0.0179542	+	0.0310976i
$531$		0			0
$532$	3.02973			0.131356
$533$	16.7316	−	0.749217i	0.724726	−	0.0324522i
$534$		0			0
$535$	2.66025	−	1.53590i	0.115013	−	0.0664027i
$536$	1.59053	+	2.75488i	0.0687004	+	0.118993i
$537$		0			0
$538$			32.3098i			1.39298i
$539$	−20.9784	−	12.1119i	−0.903602	−	0.521695i
$540$		0			0
$541$		−	3.80826i		−	0.163730i	−0.996643	−	0.0818650i	$-0.973912\pi$
$541$		−	3.80826i		−	0.163730i	0.996643	−	0.0818650i	$-0.0260876\pi$
$542$	11.7263	−	20.3105i	0.503688	−	0.872413i
$543$		0			0
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$	−13.2267			−0.566570
$546$		0			0
$547$	45.5847			1.94906			0.974530	−	0.224257i	$-0.0719954\pi$
$547$	45.5847			1.94906			0.974530	+	0.224257i	$0.0719954\pi$
$548$	−13.9168	+	8.03486i	−0.594496	+	0.343232i
$549$		0			0
$550$	−2.30668	+	3.99528i	−0.0983571	+	0.170359i
$551$		−	4.63384i		−	0.197408i
$552$		0			0
$553$	3.39921	+	1.96254i	0.144549	+	0.0834555i
$554$			9.00566i			0.382614i
$555$		0			0
$556$	4.66129	+	8.07359i	0.197683	+	0.342397i
$557$	31.9209	−	18.4296i	1.35253	−	0.780885i	0.363929	−	0.931427i	$-0.381435\pi$
$557$	31.9209	−	18.4296i	1.35253	−	0.780885i	0.988604	+	0.150541i	$0.0481016\pi$
$558$		0			0
$559$	26.1502	−	16.7005i	1.10603	−	0.706357i
$560$	−1.32258			−0.0558892
$561$		0			0
$562$	0.858478	+	1.48693i	0.0362127	+	0.0627223i
$563$	−16.8870	+	29.2491i	−0.711701	+	1.23270i	0.252518	+	0.967592i	$0.418741\pi$
$563$	−16.8870	+	29.2491i	−0.711701	+	1.23270i	−0.964218	+	0.265109i	$0.914592\pi$
$564$		0			0
$565$	7.00306	+	4.04322i	0.294621	+	0.170099i
$566$	−1.34172	−	0.774645i	−0.0563969	−	0.0325607i
$567$		0			0
$568$	5.66799	−	9.81724i	0.237823	−	0.411922i
$569$	12.7159	+	22.0246i	0.533079	+	0.923320i	0.999254	+	0.0386274i	$0.0122985\pi$
$569$	12.7159	+	22.0246i	0.533079	+	0.923320i	−0.466175	+	0.884693i	$0.654368\pi$
$570$		0			0
$571$	13.3682			0.559443			0.279722	−	0.960081i	$-0.409758\pi$
$571$	13.3682			0.559443			0.279722	+	0.960081i	$0.409758\pi$
$572$	7.66412	−	14.7628i	0.320453	−	0.617264i
$573$		0			0
$574$	5.32051	−	3.07180i	0.222074	−	0.128214i
$575$	4.33399	+	7.50670i	0.180740	+	0.313051i
$576$		0			0
$577$			9.57428i			0.398582i	0.979940	+	0.199291i	$0.0638639\pi$
$577$			9.57428i			0.398582i	−0.979940	+	0.199291i	$0.936136\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$		0			0
$580$			2.02283i			0.0839933i
$581$	−10.4959	+	18.1794i	−0.435444	+	0.754210i
$582$		0			0
$583$	−3.30279	+	1.90687i	−0.136788	+	0.0789745i
$584$	6.28304			0.259994
$585$		0			0
$586$	−30.4057			−1.25605
$587$	−1.21286	+	0.700246i	−0.0500602	+	0.0289023i	−0.524821	−	0.851212i	$-0.675868\pi$
$587$	−1.21286	+	0.700246i	−0.0500602	+	0.0289023i	0.474761	+	0.880115i	$0.342534\pi$
$588$		0			0
$589$	−11.6052	+	20.1007i	−0.478183	+	0.828237i
$590$			3.14152i			0.129334i
$591$		0			0
$592$	−5.89721	−	3.40475i	−0.242374	−	0.139935i
$593$		−	10.7303i		−	0.440643i	−0.975427	−	0.220321i	$-0.929289\pi$
$593$		−	10.7303i		−	0.440643i	0.975427	−	0.220321i	$-0.0707106\pi$
$594$		0			0
$595$	2.64516	+	4.58155i	0.108441	+	0.187825i
$596$	−3.53788	+	2.04259i	−0.144917	+	0.0836679i
$597$		0			0
$598$	−16.8215	−	26.3397i	−0.687884	−	1.07711i
$599$	40.7967			1.66691			0.833453	−	0.552590i	$-0.186360\pi$
$599$	40.7967			1.66691			0.833453	+	0.552590i	$0.186360\pi$
$600$		0			0
$601$	−21.4416	−	37.1379i	−0.874621	−	1.51489i	−0.857166	−	0.515040i	$-0.827777\pi$
$601$	−21.4416	−	37.1379i	−0.874621	−	1.51489i	−0.0174548	−	0.999848i	$-0.505556\pi$
$602$	5.69081	−	9.85677i	0.231940	−	0.401732i
$603$		0			0
$604$	17.3042	+	9.99057i	0.704097	+	0.406510i
$605$	−8.90538	−	5.14152i	−0.362055	−	0.209033i
$606$		0			0
$607$	3.43616	−	5.95161i	0.139470	−	0.241568i	−0.787826	−	0.615897i	$-0.788794\pi$
$607$	3.43616	−	5.95161i	0.139470	−	0.241568i	0.927296	+	0.374329i	$0.122127\pi$
$608$	−1.14539	−	1.98387i	−0.0464516	−	0.0804565i
$609$		0			0
$610$	0.535898			0.0216979
$611$	15.1331	−	29.1498i	0.612221	−	1.17927i
$612$		0			0
$613$	−0.659358	+	0.380681i	−0.0266312	+	0.0153755i	−0.513257	−	0.858235i	$-0.671561\pi$
$613$	−0.659358	+	0.380681i	−0.0266312	+	0.0153755i	0.486625	+	0.873611i	$0.338228\pi$
$614$	−4.91311	−	8.50975i	−0.198277	−	0.343426i
$615$		0			0
$616$		−	6.10153i		−	0.245838i
$617$	−21.3061	−	12.3011i	−0.857753	−	0.495224i	0.00550613	−	0.999985i	$-0.498247\pi$
$617$	−21.3061	−	12.3011i	−0.857753	−	0.495224i	−0.863259	+	0.504761i	$0.831581\pi$
$618$		0			0
$619$		−	17.2035i		−	0.691468i	−0.938333	−	0.345734i	$-0.887630\pi$
$619$		−	17.2035i		−	0.691468i	0.938333	−	0.345734i	$-0.112370\pi$
$620$	5.06604	−	8.77464i	0.203457	−	0.352398i
$621$		0			0
$622$	2.94491	−	1.70025i	0.118080	−	0.0681737i
$623$	−15.6913			−0.628657
$624$		0			0
$625$	1.00000			0.0400000
$626$	−14.0590	+	8.11699i	−0.561912	+	0.324420i
$627$		0			0
$628$	3.56690	−	6.17804i	0.142335	−	0.246531i
$629$			27.2380i			1.08605i
$630$		0			0
$631$	2.08519	+	1.20388i	0.0830100	+	0.0479259i	0.540930	−	0.841067i	$-0.318072\pi$
$631$	2.08519	+	1.20388i	0.0830100	+	0.0479259i	−0.457920	+	0.888993i	$0.651406\pi$
$632$		−	2.96774i		−	0.118050i
$633$		0			0
$634$	11.7616	+	20.3716i	0.467112	+	0.809061i
$635$	9.93490	−	5.73592i	0.394254	−	0.227623i
$636$		0			0
$637$	−0.846898	−	18.9130i	−0.0335553	−	0.749361i
$638$	−9.33201			−0.369458
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	9.73875	−	16.8680i	0.384657	−	0.666246i	−0.607064	−	0.794653i	$-0.707653\pi$
$641$	9.73875	−	16.8680i	0.384657	−	0.666246i	0.991722	+	0.128407i	$0.0409863\pi$
$642$		0			0
$643$	−20.7451	−	11.9772i	−0.818106	−	0.472334i	0.0316570	−	0.999499i	$-0.489922\pi$
$643$	−20.7451	−	11.9772i	−0.818106	−	0.472334i	−0.849763	+	0.527165i	$0.823255\pi$
$644$	−9.92820	−	5.73205i	−0.391226	−	0.225874i
$645$		0			0
$646$	−4.58155	+	7.93548i	−0.180259	+	0.312217i
$647$	−9.10540	−	15.7710i	−0.357970	−	0.620022i	0.629652	−	0.776878i	$-0.283198\pi$
$647$	−9.10540	−	15.7710i	−0.357970	−	0.620022i	−0.987622	+	0.156855i	$0.949864\pi$
$648$		0			0
$649$	−14.4930			−0.568898
$650$	−3.60194	+	0.161290i	−0.141280	+	0.00632631i
$651$		0			0
$652$	−8.56906	+	4.94735i	−0.335590	+	0.193753i
$653$	−24.0793	−	41.7065i	−0.942294	−	1.63210i	−0.761081	−	0.648657i	$-0.775331\pi$
$653$	−24.0793	−	41.7065i	−0.942294	−	1.63210i	−0.181213	−	0.983444i	$-0.558002\pi$
$654$		0			0
$655$		−	15.9906i		−	0.624803i
$656$	−4.02283	−	2.32258i	−0.157065	−	0.0906815i
$657$		0			0
$658$		−	12.0477i		−	0.469669i
$659$	−18.4127	+	31.8917i	−0.717257	+	1.24233i	0.244826	+	0.969567i	$0.421269\pi$
$659$	−18.4127	+	31.8917i	−0.717257	+	1.24233i	−0.962083	+	0.272758i	$0.912064\pi$
$660$		0			0
$661$	−19.5131	+	11.2659i	−0.758971	+	0.438192i	−0.828926	−	0.559358i	$-0.811048\pi$
$661$	−19.5131	+	11.2659i	−0.758971	+	0.438192i	0.0699555	+	0.997550i	$0.477714\pi$
$662$	18.0904			0.703103
$663$		0			0
$664$	15.8719			0.615948
$665$	2.62383	−	1.51487i	0.101748	−	0.0587440i
$666$		0			0
$667$	−8.76691	+	15.1847i	−0.339456	+	0.587955i
$668$			24.0375i			0.930037i
$669$		0			0
$670$	2.75488	+	1.59053i	0.106430	+	0.0614475i
$671$			2.47229i			0.0954417i
$672$		0			0
$673$	11.8719	+	20.5627i	0.457627	+	0.792633i	0.998835	−	0.0482556i	$-0.0153662\pi$
$673$	11.8719	+	20.5627i	0.457627	+	0.792633i	−0.541208	+	0.840889i	$0.682033\pi$
$674$	−4.93548	+	2.84950i	−0.190108	+	0.109759i
$675$		0			0
$676$	12.9480	−	1.16191i	0.497999	−	0.0446890i
$677$	−1.16559			−0.0447975			−0.0223987	−	0.999749i	$-0.507130\pi$
$677$	−1.16559			−0.0447975			−0.0223987	+	0.999749i	$0.507130\pi$
$678$		0			0
$679$	−5.83188	−	10.1011i	−0.223807	−	0.387645i
$680$	2.00000	−	3.46410i	0.0766965	−	0.132842i
$681$		0			0
$682$	40.4806	+	23.3715i	1.55008	+	0.894939i
$683$	−12.0134	−	6.93593i	−0.459680	−	0.265396i	0.252230	−	0.967667i	$-0.418836\pi$
$683$	−12.0134	−	6.93593i	−0.459680	−	0.265396i	−0.711910	+	0.702271i	$0.752169\pi$
$684$		0			0
$685$	−8.03486	+	13.9168i	−0.306996	+	0.531733i
$686$	−8.10132	−	14.0319i	−0.309310	−	0.535740i
$687$		0			0
$688$	−8.60562			−0.328086
$689$	−2.64537	−	1.37334i	−0.100781	−	0.0523203i
$690$		0			0
$691$	−35.6967	+	20.6095i	−1.35797	+	0.784022i	−0.989349	−	0.145560i	$-0.953502\pi$
$691$	−35.6967	+	20.6095i	−1.35797	+	0.784022i	−0.368616	+	0.929582i	$0.620168\pi$
$692$	1.26408	+	2.18946i	0.0480532	+	0.0832307i
$693$		0			0
$694$			15.7471i			0.597753i
$695$	8.07359	+	4.66129i	0.306249	+	0.176813i
$696$		0			0
$697$			18.5806i			0.703792i
$698$	7.66025	−	13.2679i	0.289945	−	0.502199i
$699$		0			0
$700$	−1.14539	+	0.661290i	−0.0432916	+	0.0249944i
$701$	23.0112			0.869122			0.434561	−	0.900642i	$-0.356904\pi$
$701$	23.0112			0.869122			0.434561	+	0.900642i	$0.356904\pi$
$702$		0			0
$703$	15.5991			0.588329
$704$	−3.99528	+	2.30668i	−0.150578	+	0.0869362i
$705$		0			0
$706$	−0.599964	+	1.03917i	−0.0225799	+	0.0391096i
$707$			9.55790i			0.359462i
$708$		0			0
$709$	−14.7944	−	8.54156i	−0.555616	−	0.320785i	0.195768	−	0.980650i	$-0.437280\pi$
$709$	−14.7944	−	8.54156i	−0.555616	−	0.320785i	−0.751384	+	0.659865i	$0.770613\pi$
$710$		−	11.3360i		−	0.425431i
$711$		0			0
$712$	5.93207	+	10.2746i	0.222314	+	0.385059i
$713$	76.0585	−	43.9124i	2.84841	−	1.64453i
$714$		0			0
$715$	−0.744087	−	16.6170i	−0.0278273	−	0.621442i
$716$	6.27568			0.234533
$717$		0			0
$718$	8.14152	+	14.1015i	0.303839	+	0.526264i
$719$	21.8564	−	37.8564i	0.815106	−	1.41181i	−0.0941451	−	0.995558i	$-0.530012\pi$
$719$	21.8564	−	37.8564i	0.815106	−	1.41181i	0.909251	−	0.416247i	$-0.136655\pi$
$720$		0			0
$721$	−21.0752	−	12.1678i	−0.784880	−	0.453151i
$722$	−11.9099	−	6.87617i	−0.443240	−	0.255905i
$723$		0			0
$724$	−6.14152	+	10.6374i	−0.228248	+	0.395337i
$725$	1.01141	+	1.75182i	0.0375629	+	0.0650609i
$726$		0			0
$727$	31.8453			1.18108			0.590538	−	0.807010i	$-0.298916\pi$
$727$	31.8453			1.18108			0.590538	+	0.807010i	$0.298916\pi$
$728$	4.01896	−	2.56667i	0.148953	−	0.0951270i
$729$		0			0
$730$	5.44128	−	3.14152i	0.201391	−	0.116273i
$731$	17.2112	+	29.8108i	0.636581	+	1.10259i
$732$		0			0
$733$			5.96774i			0.220423i	0.993908	+	0.110212i	$0.0351529\pi$
$733$			5.96774i			0.220423i	−0.993908	+	0.110212i	$0.964847\pi$
$734$	17.0040	+	9.81724i	0.627627	+	0.362361i
$735$		0			0
$736$			8.66799i			0.319506i
$737$	−7.33767	+	12.7092i	−0.270287	+	0.468150i
$738$		0			0
$739$	9.37833	−	5.41458i	0.344988	−	0.199179i	−0.317488	−	0.948262i	$-0.602839\pi$
$739$	9.37833	−	5.41458i	0.344988	−	0.199179i	0.662475	+	0.749084i	$0.269506\pi$
$740$	−6.80951			−0.250322
$741$		0			0
$742$	−1.09334			−0.0401378
$743$	−17.1909	+	9.92515i	−0.630671	+	0.364118i	−0.781012	−	0.624516i	$-0.785296\pi$
$743$	−17.1909	+	9.92515i	−0.630671	+	0.364118i	0.150341	+	0.988634i	$0.451963\pi$
$744$		0			0
$745$	−2.04259	+	3.53788i	−0.0748349	+	0.129618i
$746$		−	2.55748i		−	0.0936359i
$747$		0			0
$748$	15.9811	+	9.22671i	0.584328	+	0.337362i
$749$			4.06270i			0.148448i
$750$		0			0
$751$	−7.66538	−	13.2768i	−0.279714	−	0.484479i	0.691600	−	0.722281i	$-0.256906\pi$
$751$	−7.66538	−	13.2768i	−0.279714	−	0.484479i	−0.971314	+	0.237802i	$0.923573\pi$
$752$	−7.88885	+	4.55463i	−0.287677	+	0.166090i
$753$		0			0
$754$	−3.92560	−	6.14682i	−0.142962	−	0.223854i
$755$	19.9811			0.727188
$756$		0			0
$757$	−22.5816	−	39.1125i	−0.820744	−	1.42157i	−0.905129	−	0.425137i	$-0.860226\pi$
$757$	−22.5816	−	39.1125i	−0.820744	−	1.42157i	0.0843855	−	0.996433i	$-0.473107\pi$
$758$	−7.55440	+	13.0846i	−0.274388	+	0.475254i
$759$		0			0
$760$	−1.98387	−	1.14539i	−0.0719625	−	0.0415476i
$761$	18.7978	+	10.8529i	0.681419	+	0.393418i	0.800390	−	0.599480i	$-0.204626\pi$
$761$	18.7978	+	10.8529i	0.681419	+	0.393418i	−0.118970	+	0.992898i	$0.537959\pi$
$762$		0			0
$763$	8.74669	−	15.1497i	0.316651	−	0.548456i
$764$	4.87357	+	8.44128i	0.176320	+	0.305395i
$765$		0			0
$766$	18.7303			0.676755
$767$	−6.09660	−	9.54623i	−0.220136	−	0.344694i
$768$		0			0
$769$	36.4711	−	21.0566i	1.31518	−	0.759321i	0.332233	−	0.943197i	$-0.392198\pi$
$769$	36.4711	−	21.0566i	1.31518	−	0.759321i	0.982949	+	0.183877i	$0.0588647\pi$
$770$	−3.05076	−	5.28408i	−0.109942	−	0.190425i
$771$		0			0
$772$			13.7626i			0.495327i
$773$	−25.7734	−	14.8803i	−0.927004	−	0.535206i	−0.0411413	−	0.999153i	$-0.513099\pi$
$773$	−25.7734	−	14.8803i	−0.927004	−	0.535206i	−0.885863	+	0.463947i	$0.846433\pi$
$774$		0			0
$775$		−	10.1321i		−	0.363955i
$776$	−4.40947	+	7.63743i	−0.158291	+	0.274168i
$777$		0			0
$778$	−6.03532	+	3.48449i	−0.216377	+	0.124925i
$779$	10.6410			0.381254
$780$		0			0
$781$	52.2969			1.87133
$782$	30.0268	−	17.3360i	1.07376	−	0.619933i
$783$		0			0
$784$	−2.62539	+	4.54731i	−0.0937640	+	0.162404i
$785$		−	7.13379i		−	0.254616i
$786$		0			0
$787$	−35.5459	−	20.5224i	−1.26707	−	0.731545i	−0.292640	−	0.956223i	$-0.594534\pi$
$787$	−35.5459	−	20.5224i	−1.26707	−	0.731545i	−0.974433	+	0.224678i	$0.927867\pi$
$788$		−	10.1415i		−	0.361277i
$789$		0			0
$790$	−1.48387	−	2.57014i	−0.0527937	−	0.0914414i
$791$	−9.26210	+	5.34748i	−0.329322	+	0.190134i
$792$		0			0
$793$	−1.62845	+	1.03999i	−0.0578279	+	0.0369312i
$794$	−18.5721			−0.659100
$795$		0			0
$796$	−4.78668	−	8.29078i	−0.169659	−	0.293859i
$797$	−22.6263	+	39.1899i	−0.801464	+	1.38818i	0.117188	+	0.993110i	$0.462612\pi$
$797$	−22.6263	+	39.1899i	−0.801464	+	1.38818i	−0.918652	+	0.395067i	$0.870721\pi$
$798$		0			0
$799$	31.5554	+	18.2185i	1.11635	+	0.644525i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	14.8452	−	25.7126i	0.524201	−	0.907944i
$803$	14.4930	+	25.1025i	0.511445	+	0.885849i
$804$		0			0
$805$	−11.4641			−0.404056
$806$	1.63420	+	36.4952i	0.0575623	+	1.28549i
$807$		0			0
$808$	6.25851	−	3.61335i	0.220174	−	0.127117i
$809$	−14.2267	−	24.6414i	−0.500184	−	0.866345i	−1.00000		0.000213036i	$-0.999932\pi$
$809$	−14.2267	−	24.6414i	−0.500184	−	0.866345i	0.499815	−	0.866132i	$-0.333401\pi$
$810$		0			0
$811$			44.4114i			1.55949i	0.626095	+	0.779747i	$0.284652\pi$
$811$			44.4114i			1.55949i	−0.626095	+	0.779747i	$0.715348\pi$
$812$	−2.31692	−	1.33767i	−0.0813079	−	0.0469432i
$813$		0			0
$814$		−	31.4147i		−	1.10108i
$815$	−4.94735	+	8.56906i	−0.173298	+	0.300161i
$816$		0			0
$817$	17.0724	−	9.85677i	0.597289	−	0.344845i
$818$	−24.3355			−0.850871
$819$		0			0
$820$	−4.64516			−0.162216
$821$	39.1169	−	22.5842i	1.36519	−	0.788192i	0.374880	−	0.927073i	$-0.377684\pi$
$821$	39.1169	−	22.5842i	1.36519	−	0.788192i	0.990309	+	0.138881i	$0.0443505\pi$
$822$		0			0
$823$	1.20900	−	2.09404i	0.0421430	−	0.0729938i	−0.844185	−	0.536053i	$-0.819915\pi$
$823$	1.20900	−	2.09404i	0.0421430	−	0.0729938i	0.886328	+	0.463059i	$0.153248\pi$
$824$			18.4000i			0.640996i
$825$		0			0
$826$	−3.59826	−	2.07746i	−0.125199	−	0.0722840i
$827$			4.26832i			0.148424i	0.997242	+	0.0742120i	$0.0236441\pi$
$827$			4.26832i			0.148424i	−0.997242	+	0.0742120i	$0.976356\pi$
$828$		0			0
$829$	−21.4926	−	37.2263i	−0.746468	−	1.29292i	−0.949506	−	0.313750i	$-0.898415\pi$
$829$	−21.4926	−	37.2263i	−0.746468	−	1.29292i	0.203037	−	0.979171i	$-0.434919\pi$
$830$	13.7454	−	7.93593i	0.477111	−	0.275460i
$831$		0			0
$832$	−3.20002	−	1.66129i	−0.110941	−	0.0575949i
$833$	21.0031			0.727715
$834$		0			0
$835$	12.0187	+	20.8171i	0.415925	+	0.720404i
$836$	5.28408	−	9.15229i	0.182754	−	0.316539i
$837$		0			0
$838$	−2.49636	−	1.44128i	−0.0862354	−	0.0497880i
$839$	20.1798	+	11.6508i	0.696684	+	0.402231i	0.806111	−	0.591764i	$-0.201568\pi$
$839$	20.1798	+	11.6508i	0.696684	+	0.402231i	−0.109427	+	0.993995i	$0.534902\pi$
$840$		0			0
$841$	12.4541	−	21.5711i	0.429451	−	0.743831i
$842$	2.47354	+	4.28429i	0.0852437	+	0.147646i
$843$		0			0
$844$	1.08519			0.0373537
$845$	10.6323	−	7.48023i	0.365763	−	0.257328i
$846$		0			0
$847$	11.7781	−	6.80007i	0.404699	−	0.233653i
$848$	0.413337	+	0.715920i	0.0141940	+	0.0245848i
$849$		0			0
$850$		−	4.00000i		−	0.137199i
$851$	−51.1169	−	29.5124i	−1.75226	−	1.01167i
$852$		0			0
$853$		−	20.8418i		−	0.713609i	−0.934179	−	0.356804i	$-0.883866\pi$
$853$		−	20.8418i		−	0.713609i	0.934179	−	0.356804i	$-0.116134\pi$
$854$	−0.354384	+	0.613811i	−0.0121268	+	0.0210042i
$855$		0			0
$856$	2.66025	−	1.53590i	0.0909256	−	0.0524959i
$857$	−36.7250			−1.25450			−0.627250	−	0.778818i	$-0.715820\pi$
$857$	−36.7250			−1.25450			−0.627250	+	0.778818i	$0.715820\pi$
$858$		0			0
$859$	0.914812			0.0312130			0.0156065	−	0.999878i	$-0.495032\pi$
$859$	0.914812			0.0312130			0.0156065	+	0.999878i	$0.495032\pi$
$860$	−7.45269	+	4.30281i	−0.254135	+	0.146725i
$861$		0			0
$862$	8.88130	−	15.3829i	0.302498	−	0.523943i
$863$			33.6104i			1.14411i	0.820215	+	0.572056i	$0.193854\pi$
$863$			33.6104i			1.14411i	−0.820215	+	0.572056i	$0.806146\pi$
$864$		0			0
$865$	2.18946	+	1.26408i	0.0744438	+	0.0429801i
$866$		−	35.8375i		−	1.21781i
$867$		0			0
$868$	6.70025	+	11.6052i	0.227421	+	0.393905i
$869$	11.8570	−	6.84562i	0.402220	−	0.232222i
$870$		0			0
$871$	−11.4580	+	0.513072i	−0.388239	+	0.0173848i
$872$	−13.2267			−0.447913
$873$		0			0
$874$	−9.92820	−	17.1962i	−0.335826	−	0.581669i
$875$	−0.661290	+	1.14539i	−0.0223557	+	0.0387212i
$876$		0			0
$877$	−21.0629	−	12.1607i	−0.711243	−	0.410637i	0.100278	−	0.994959i	$-0.468027\pi$
$877$	−21.0629	−	12.1607i	−0.711243	−	0.410637i	−0.811521	+	0.584323i	$0.801360\pi$
$878$	8.73854	+	5.04520i	0.294911	+	0.170267i
$879$		0			0
$880$	−2.30668	+	3.99528i	−0.0777581	+	0.134681i
$881$	4.95207	+	8.57723i	0.166839	+	0.288974i	0.937307	−	0.348505i	$-0.113311\pi$
$881$	4.95207	+	8.57723i	0.166839	+	0.288974i	−0.770468	+	0.637479i	$0.779977\pi$
$882$		0			0
$883$	−43.9718			−1.47977			−0.739884	−	0.672734i	$-0.765120\pi$
$883$	−43.9718			−1.47977			−0.739884	+	0.672734i	$0.765120\pi$
$884$	0.645159	+	14.4078i	0.0216991	+	0.484586i
$885$		0			0
$886$	−11.8629	+	6.84904i	−0.398542	+	0.230098i
$887$	25.2807	+	43.7875i	0.848843	+	1.47024i	0.882242	+	0.470797i	$0.156034\pi$
$887$	25.2807	+	43.7875i	0.848843	+	1.47024i	−0.0333988	+	0.999442i	$0.510633\pi$
$888$		0			0
$889$			15.1724i			0.508866i
$890$	10.2746	+	5.93207i	0.344407	+	0.198843i
$891$		0			0
$892$		−	24.9416i		−	0.835106i
$893$	10.4336	−	18.0716i	0.349148	−	0.604743i
$894$		0			0
$895$	5.43490	−	3.13784i	0.181669	−	0.104886i
$896$	−1.32258			−0.0441843
$897$		0			0
$898$	−15.3128			−0.510994
$899$	17.7496	−	10.2477i	0.591982	−	0.341781i
$900$		0			0
$901$	1.65335	−	2.86368i	0.0550810	−	0.0954031i
$902$		−	21.4298i		−	0.713533i
$903$		0			0
$904$	7.00306	+	4.04322i	0.232918	+	0.134475i
$905$			12.2830i			0.408302i
$906$		0			0
$907$	7.12175	+	12.3352i	0.236474	+	0.409585i	0.959700	−	0.281026i	$-0.0906749\pi$
$907$	7.12175	+	12.3352i	0.236474	+	0.409585i	−0.723226	+	0.690611i	$0.757342\pi$
$908$	16.7321	−	9.66025i	0.555273	−	0.320587i
$909$		0			0
$910$	2.19719	−	4.23228i	0.0728361	−	0.140299i
$911$	−21.8108			−0.722623			−0.361311	−	0.932445i	$-0.617671\pi$
$911$	−21.8108			−0.722623			−0.361311	+	0.932445i	$0.617671\pi$
$912$		0			0
$913$	36.6113	+	63.4126i	1.21166	+	2.09865i
$914$	−7.77770	+	13.4714i	−0.257264	+	0.445594i
$915$		0			0
$916$	−3.59826	−	2.07746i	−0.118890	−	0.0686411i
$917$	18.3154	+	10.5744i	0.604828	+	0.349197i
$918$		0			0
$919$	2.65289	−	4.59494i	0.0875108	−	0.151573i	−0.818948	−	0.573868i	$-0.805442\pi$
$919$	2.65289	−	4.59494i	0.0875108	−	0.151573i	0.906458	+	0.422295i	$0.138775\pi$
$920$	4.33399	+	7.50670i	0.142888	+	0.247488i
$921$		0			0
$922$	−15.6431			−0.515178
$923$	21.9992	+	34.4469i	0.724112	+	1.13383i
$924$		0			0
$925$	−5.89721	+	3.40475i	−0.193899	+	0.111948i
$926$	−6.85848	−	11.8792i	−0.225384	−	0.390376i
$927$		0			0
$928$			2.02283i			0.0664025i
$929$	38.4002	+	22.1704i	1.25987	+	0.727386i	0.973049	−	0.230598i	$-0.0740681\pi$
$929$	38.4002	+	22.1704i	1.25987	+	0.727386i	0.286821	+	0.957984i	$0.407401\pi$
$930$		0			0
$931$		−	12.0284i		−	0.394214i
$932$	−8.48325	+	14.6934i	−0.277878	+	0.481299i
$933$		0			0
$934$	0.817239	−	0.471833i	0.0267409	−	0.0154388i
$935$	18.4534			0.603491
$936$		0			0
$937$	38.5283			1.25867			0.629333	−	0.777136i	$-0.283328\pi$
$937$	38.5283			1.25867			0.629333	+	0.777136i	$0.283328\pi$
$938$	−3.64354	+	2.10360i	−0.118966	+	0.0686850i
$939$		0			0
$940$	−4.55463	+	7.88885i	−0.148556	+	0.257306i
$941$			28.8637i			0.940929i	0.882419	+	0.470465i	$0.155914\pi$
$941$			28.8637i			0.940929i	−0.882419	+	0.470465i	$0.844086\pi$
$942$		0			0
$943$	−34.8698	−	20.1321i	−1.13552	−	0.655591i
$944$			3.14152i			0.102248i
$945$		0			0
$946$	−19.8504	−	34.3819i	−0.645392	−	1.11785i
$947$	−42.6384	+	24.6173i	−1.38556	+	0.799955i	−0.992811	−	0.119689i	$-0.961810\pi$
$947$	−42.6384	+	24.6173i	−1.38556	+	0.799955i	−0.392752	+	0.919645i	$0.628477\pi$
$948$		0			0
$949$	−10.4380	+	20.1059i	−0.338830	+	0.652664i
$950$	−2.29078			−0.0743226
$951$		0			0
$952$	2.64516	+	4.58155i	0.0857301	+	0.148489i
$953$	13.2548	−	22.9580i	0.429366	−	0.743684i	−0.567451	−	0.823407i	$-0.692070\pi$
$953$	13.2548	−	22.9580i	0.429366	−	0.743684i	0.996817	+	0.0797233i	$0.0254037\pi$
$954$		0			0
$955$	8.44128	+	4.87357i	0.273153	+	0.157705i
$956$	−5.49420	−	3.17208i	−0.177695	−	0.102592i
$957$		0			0
$958$	5.55099	−	9.61460i	0.179344	−	0.310634i
$959$	−10.6267	−	18.4061i	−0.343156	−	0.594363i
$960$		0			0
$961$	−71.6592			−2.31159
$962$	20.6922	−	13.2149i	0.667145	−	0.426065i
$963$		0			0
$964$	20.9452	−	12.0927i	0.674600	−	0.389481i
$965$	6.88130	+	11.9188i	0.221517	+	0.383679i
$966$		0			0
$967$		−	52.3877i		−	1.68468i	−0.538950	−	0.842338i	$-0.681179\pi$
$967$		−	52.3877i		−	1.68468i	0.538950	−	0.842338i	$-0.318821\pi$
$968$	−8.90538	−	5.14152i	−0.286230	−	0.165255i
$969$		0			0
$970$			8.81894i			0.283159i
$971$	−14.3215	+	24.8056i	−0.459600	+	0.796051i	−0.998940	−	0.0460375i	$-0.985341\pi$
$971$	−14.3215	+	24.8056i	−0.459600	+	0.796051i	0.539339	+	0.842088i	$0.318674\pi$
$972$		0			0
$973$	−10.6780	+	6.16493i	−0.342320	+	0.197638i
$974$	−32.9416			−1.05552
$975$		0			0
$976$	0.535898			0.0171537
$977$	−35.1173	+	20.2750i	−1.12350	+	0.648654i	−0.942292	−	0.334791i	$-0.891334\pi$
$977$	−35.1173	+	20.2750i	−1.12350	+	0.648654i	−0.181209	+	0.983445i	$0.558001\pi$
$978$		0			0
$979$	−27.3667	+	47.4006i	−0.874645	+	1.51493i
$980$			5.25078i			0.167730i
$981$		0			0
$982$	−24.6396	−	14.2257i	−0.786281	−	0.453960i
$983$			22.4160i			0.714958i	0.933921	+	0.357479i	$0.116364\pi$
$983$			22.4160i			0.714958i	−0.933921	+	0.357479i	$0.883636\pi$
$984$		0			0
$985$	−5.07076	−	8.78282i	−0.161568	−	0.279844i
$986$	7.00727	−	4.04565i	0.223157	−	0.128840i
$987$		0			0
$988$	8.25124	−	0.369479i	0.262507	−	0.0117547i
$989$	−74.5934			−2.37193
$990$		0			0
$991$	14.2844	+	24.7413i	0.453759	+	0.785933i	0.998616	−	0.0525955i	$-0.0167494\pi$
$991$	14.2844	+	24.7413i	0.453759	+	0.785933i	−0.544857	+	0.838529i	$0.683416\pi$
$992$	5.06604	−	8.77464i	0.160847	−	0.278595i
$993$		0			0
$994$	12.9841	+	7.49636i	0.411830	+	0.237770i
$995$	−8.29078	−	4.78668i	−0.262835	−	0.151748i
$996$		0			0
$997$	17.2000	−	29.7913i	0.544730	−	0.943500i	−0.453894	−	0.891056i	$-0.649965\pi$
$997$	17.2000	−	29.7913i	0.544730	−	0.943500i	0.998624	−	0.0524443i	$-0.0167012\pi$
$998$	2.05463	+	3.55872i	0.0650382	+	0.112649i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.f.361.4		8
3.2	odd	2		390.2.bb.c.361.2	yes	8
13.4	even	6	inner	1170.2.bs.f.901.4		8
15.2	even	4		1950.2.y.j.49.1		8
15.8	even	4		1950.2.y.k.49.4		8
15.14	odd	2		1950.2.bc.g.751.3		8
39.2	even	12		5070.2.a.bz.1.3		4
39.11	even	12		5070.2.a.ca.1.2		4
39.17	odd	6		390.2.bb.c.121.2	✓	8
39.23	odd	6		5070.2.b.ba.1351.7		8
39.29	odd	6		5070.2.b.ba.1351.2		8
195.17	even	12		1950.2.y.k.199.4		8
195.134	odd	6		1950.2.bc.g.901.3		8
195.173	even	12		1950.2.y.j.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.2	✓	8	39.17	odd	6
390.2.bb.c.361.2	yes	8	3.2	odd	2
1170.2.bs.f.361.4		8	1.1	even	1	trivial
1170.2.bs.f.901.4		8	13.4	even	6	inner
1950.2.y.j.49.1		8	15.2	even	4
1950.2.y.j.199.1		8	195.173	even	12
1950.2.y.k.49.4		8	15.8	even	4
1950.2.y.k.199.4		8	195.17	even	12
1950.2.bc.g.751.3		8	15.14	odd	2
1950.2.bc.g.901.3		8	195.134	odd	6
5070.2.a.bz.1.3		4	39.2	even	12
5070.2.a.ca.1.2		4	39.11	even	12
5070.2.b.ba.1351.2		8	39.29	odd	6
5070.2.b.ba.1351.7		8	39.23	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.14539 + 0.661290i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.14539 + 0.661290i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(3.99528 - 2.30668i) q^{11} +(3.20002 + 1.66129i) q^{13} +1.32258 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(1.98387 + 1.14539i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(2.30668 - 3.99528i) q^{22} +(-4.33399 - 7.50670i) q^{23} -1.00000 q^{25} +(3.60194 - 0.161290i) q^{26} +(1.14539 - 0.661290i) q^{28} +(-1.01141 - 1.75182i) q^{29} +10.1321i q^{31} +(-0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(0.661290 - 1.14539i) q^{35} +(5.89721 - 3.40475i) q^{37} +2.29078 q^{38} -1.00000 q^{40} +(4.02283 - 2.32258i) q^{41} +(4.30281 - 7.45269i) q^{43} -4.61335i q^{44} +(-7.50670 - 4.33399i) q^{46} -9.10926i q^{47} +(-2.62539 - 4.54731i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.03873 - 1.94065i) q^{52} -0.826674 q^{53} +(-2.30668 - 3.99528i) q^{55} +(0.661290 - 1.14539i) q^{56} +(-1.75182 - 1.01141i) q^{58} +(-2.72064 - 1.57076i) q^{59} +(-0.267949 + 0.464102i) q^{61} +(5.06604 + 8.77464i) q^{62} -1.00000 q^{64} +(1.66129 - 3.20002i) q^{65} +(-2.75488 + 1.59053i) q^{67} +(2.00000 + 3.46410i) q^{68} -1.32258i q^{70} +(9.81724 + 5.66799i) q^{71} +6.28304i q^{73} +(3.40475 - 5.89721i) q^{74} +(1.98387 - 1.14539i) q^{76} +6.10153 q^{77} +2.96774 q^{79} +(-0.866025 + 0.500000i) q^{80} +(2.32258 - 4.02283i) q^{82} +15.8719i q^{83} +(3.46410 + 2.00000i) q^{85} -8.60562i q^{86} +(-2.30668 - 3.99528i) q^{88} +(-10.2746 + 5.93207i) q^{89} +(2.56667 + 4.01896i) q^{91} -8.66799 q^{92} +(-4.55463 - 7.88885i) q^{94} +(1.14539 - 1.98387i) q^{95} +(-7.63743 - 4.40947i) q^{97} +(-4.54731 - 2.62539i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 4 q^{10} - 6 q^{11} - 12 q^{13} - 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} + 2 q^{22} - 4 q^{23} - 8 q^{25} + 12 q^{26} + 8 q^{29} - 2 q^{35} + 30 q^{37} - 8 q^{40} + 14 q^{43} - 6 q^{46} + 14 q^{49} - 6 q^{52} - 16 q^{53} - 2 q^{55} - 2 q^{56} - 6 q^{58} - 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} + 6 q^{65} + 24 q^{67} + 16 q^{68} + 12 q^{71} - 10 q^{74} - 6 q^{76} - 16 q^{77} - 20 q^{79} + 4 q^{82} - 2 q^{88} - 42 q^{89} - 10 q^{91} - 8 q^{92} - 8 q^{94} - 24 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^10 - 6 * q^11 - 12 * q^13 - 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 + 2 * q^22 - 4 * q^23 - 8 * q^25 + 12 * q^26 + 8 * q^29 - 2 * q^35 + 30 * q^37 - 8 * q^40 + 14 * q^43 - 6 * q^46 + 14 * q^49 - 6 * q^52 - 16 * q^53 - 2 * q^55 - 2 * q^56 - 6 * q^58 - 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 + 6 * q^65 + 24 * q^67 + 16 * q^68 + 12 * q^71 - 10 * q^74 - 6 * q^76 - 16 * q^77 - 20 * q^79 + 4 * q^82 - 2 * q^88 - 42 * q^89 - 10 * q^91 - 8 * q^92 - 8 * q^94 - 24 * q^97 - 48 * q^98

Introduction

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