LMFDB - Embedded newform 1170.2.bs.f.901.2

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			901.2
Root			$-1.70006 - 1.70006i$ of defining polynomial
Character	$\chi$	$=$	1170.901
Dual form			1170.2.bs.f.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(4.02239 - 2.32233i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(4.02239 - 2.32233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(-3.81062 - 2.20006i) q^{11} +(-3.35432 - 1.32233i) q^{13} -4.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-6.96699 + 4.02239i) q^{19} +(0.866025 - 0.500000i) q^{20} +(2.20006 + 3.81062i) q^{22} +(0.488292 - 0.845746i) q^{23} -1.00000 q^{25} +(2.24376 + 2.82233i) q^{26} +(4.02239 + 2.32233i) q^{28} +(-2.15637 + 3.73494i) q^{29} -6.44069i q^{31} +(0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(-2.32233 - 4.02239i) q^{35} +(3.28745 + 1.89801i) q^{37} +8.04479 q^{38} -1.00000 q^{40} +(6.31274 + 3.64466i) q^{41} +(0.358228 + 0.620469i) q^{43} -4.40013i q^{44} +(-0.845746 + 0.488292i) q^{46} +9.75342i q^{47} +(7.28643 - 12.6205i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-0.531987 - 3.56609i) q^{52} -13.5089 q^{53} +(-2.20006 + 3.81062i) q^{55} +(-2.32233 - 4.02239i) q^{56} +(3.73494 - 2.15637i) q^{58} +(1.88842 - 1.09028i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(-3.22034 + 5.57780i) q^{62} -1.00000 q^{64} +(-1.32233 + 3.35432i) q^{65} +(-1.58068 - 0.912609i) q^{67} +(2.00000 - 3.46410i) q^{68} +4.64466i q^{70} +(6.88764 - 3.97658i) q^{71} +4.36112i q^{73} +(-1.89801 - 3.28745i) q^{74} +(-6.96699 - 4.02239i) q^{76} -20.4371 q^{77} -14.9340 q^{79} +(0.866025 + 0.500000i) q^{80} +(-3.64466 - 6.31274i) q^{82} +3.51093i q^{83} +(-3.46410 + 2.00000i) q^{85} -0.716456i q^{86} +(-2.20006 + 3.81062i) q^{88} +(-7.07780 - 4.08637i) q^{89} +(-16.5633 + 2.47090i) q^{91} +0.976584 q^{92} +(4.87671 - 8.44671i) q^{94} +(4.02239 + 6.96699i) q^{95} +(11.9730 - 6.91261i) q^{97} +(-12.6205 + 7.28643i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

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

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
$7$	4.02239	−	2.32233i	1.52032	−	0.877758i	0.520609	−	0.853795i	$-0.325705\pi$
$7$	4.02239	−	2.32233i	1.52032	−	0.877758i	0.999713	−	0.0239629i	$-0.00762835\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−3.81062	−	2.20006i	−1.14895	−	0.663344i	−0.200316	−	0.979731i	$-0.564197\pi$
$11$	−3.81062	−	2.20006i	−1.14895	−	0.663344i	−0.948630	+	0.316387i	$0.897530\pi$
$12$		0			0
$13$	−3.35432	−	1.32233i	−0.930320	−	0.366748i
$13$	−3.35432	−	1.32233i	−0.930320	−	0.366748i
$14$	−4.64466			−1.24134
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$		0			0
$19$	−6.96699	+	4.02239i	−1.59834	+	0.922800i	−0.606529	+	0.795061i	$0.707439\pi$
$19$	−6.96699	+	4.02239i	−1.59834	+	0.922800i	−0.991808	+	0.127739i	$0.959228\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		0			0
$22$	2.20006	+	3.81062i	0.469055	+	0.812427i
$23$	0.488292	−	0.845746i	0.101816	−	0.176350i	−0.810617	−	0.585577i	$-0.800868\pi$
$23$	0.488292	−	0.845746i	0.101816	−	0.176350i	0.912433	+	0.409226i	$0.134201\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.24376	+	2.82233i	0.440037	+	0.553504i
$27$		0			0
$28$	4.02239	+	2.32233i	0.760161	+	0.438879i
$29$	−2.15637	+	3.73494i	−0.400427	+	0.693561i	−0.993777	−	0.111384i	$-0.964472\pi$
$29$	−2.15637	+	3.73494i	−0.400427	+	0.693561i	0.593350	+	0.804945i	$0.297805\pi$
$30$		0			0
$31$		−	6.44069i		−	1.15678i	−0.815760	−	0.578391i	$-0.803681\pi$
$31$		−	6.44069i		−	1.15678i	0.815760	−	0.578391i	$-0.196319\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			4.00000i			0.685994i
$35$	−2.32233	−	4.02239i	−0.392545	−	0.679909i
$36$		0			0
$37$	3.28745	+	1.89801i	0.540454	+	0.312031i	0.745263	−	0.666771i	$-0.232324\pi$
$37$	3.28745	+	1.89801i	0.540454	+	0.312031i	−0.204809	+	0.978802i	$0.565657\pi$
$38$	8.04479			1.30504
$39$		0			0
$40$	−1.00000			−0.158114
$41$	6.31274	+	3.64466i	0.985884	+	0.569200i	0.904041	−	0.427445i	$-0.140586\pi$
$41$	6.31274	+	3.64466i	0.985884	+	0.569200i	0.0818424	+	0.996645i	$0.473920\pi$
$42$		0			0
$43$	0.358228	+	0.620469i	0.0546293	+	0.0946207i	0.892047	−	0.451943i	$-0.149269\pi$
$43$	0.358228	+	0.620469i	0.0546293	+	0.0946207i	−0.837418	+	0.546564i	$0.815936\pi$
$44$		−	4.40013i		−	0.663344i
$45$		0			0
$46$	−0.845746	+	0.488292i	−0.124698	+	0.0719947i
$47$			9.75342i			1.42268i	0.702847	+	0.711341i	$0.251912\pi$
$47$			9.75342i			1.42268i	−0.702847	+	0.711341i	$0.748088\pi$
$48$		0			0
$49$	7.28643	−	12.6205i	1.04092	−	1.80292i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$	−0.531987	−	3.56609i	−0.0737734	−	0.494528i
$53$	−13.5089			−1.85559			−0.927794	−	0.373092i	$-0.878297\pi$
$53$	−13.5089			−1.85559			−0.927794	+	0.373092i	$0.878297\pi$
$54$		0			0
$55$	−2.20006	+	3.81062i	−0.296656	+	0.513824i
$56$	−2.32233	−	4.02239i	−0.310334	−	0.537515i
$57$		0			0
$58$	3.73494	−	2.15637i	0.490421	−	0.283145i
$59$	1.88842	−	1.09028i	0.245851	−	0.141942i	−0.372012	−	0.928228i	$-0.621332\pi$
$59$	1.88842	−	1.09028i	0.245851	−	0.141942i	0.617863	+	0.786286i	$0.287999\pi$
$60$		0			0
$61$	−3.73205	−	6.46410i	−0.477840	−	0.827643i	0.521837	−	0.853045i	$-0.325247\pi$
$61$	−3.73205	−	6.46410i	−0.477840	−	0.827643i	−0.999677	+	0.0254017i	$0.991914\pi$
$62$	−3.22034	+	5.57780i	−0.408984	+	0.708381i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.32233	+	3.35432i	−0.164015	+	0.416052i
$66$		0			0
$67$	−1.58068	−	0.912609i	−0.193111	−	0.111493i	0.400327	−	0.916372i	$-0.368897\pi$
$67$	−1.58068	−	0.912609i	−0.193111	−	0.111493i	−0.593438	+	0.804879i	$0.702230\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		0			0
$70$			4.64466i			0.555143i
$71$	6.88764	−	3.97658i	0.817413	−	0.471934i	−0.0321105	−	0.999484i	$-0.510223\pi$
$71$	6.88764	−	3.97658i	0.817413	−	0.471934i	0.849524	+	0.527551i	$0.176890\pi$
$72$		0			0
$73$			4.36112i			0.510430i	0.966884	+	0.255215i	$0.0821463\pi$
$73$			4.36112i			0.510430i	−0.966884	+	0.255215i	$0.917854\pi$
$74$	−1.89801	−	3.28745i	−0.220640	−	0.382159i
$75$		0			0
$76$	−6.96699	−	4.02239i	−0.799168	−	0.461400i
$77$	−20.4371			−2.32902
$78$		0			0
$79$	−14.9340			−1.68020			−0.840102	−	0.542429i	$-0.817505\pi$
$79$	−14.9340			−1.68020			−0.840102	+	0.542429i	$0.817505\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$		0			0
$82$	−3.64466	−	6.31274i	−0.402485	−	0.697125i
$83$			3.51093i			0.385375i	0.981260	+	0.192688i	$0.0617204\pi$
$83$			3.51093i			0.385375i	−0.981260	+	0.192688i	$0.938280\pi$
$84$		0			0
$85$	−3.46410	+	2.00000i	−0.375735	+	0.216930i
$86$		−	0.716456i		−	0.0772575i
$87$		0			0
$88$	−2.20006	+	3.81062i	−0.234528	+	0.406214i
$89$	−7.07780	−	4.08637i	−0.750245	−	0.433154i	0.0755374	−	0.997143i	$-0.475933\pi$
$89$	−7.07780	−	4.08637i	−0.750245	−	0.433154i	−0.825782	+	0.563989i	$0.809266\pi$
$90$		0			0
$91$	−16.5633	+	2.47090i	−1.73630	+	0.259021i
$92$	0.976584			0.101816
$93$		0			0
$94$	4.87671	−	8.44671i	0.502994	−	0.871212i
$95$	4.02239	+	6.96699i	0.412689	+	0.714798i
$96$		0			0
$97$	11.9730	−	6.91261i	1.21567	−	0.701869i	0.251683	−	0.967810i	$-0.419016\pi$
$97$	11.9730	−	6.91261i	1.21567	−	0.701869i	0.963989	+	0.265941i	$0.0856825\pi$
$98$	−12.6205	+	7.28643i	−1.27486	+	0.736041i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.40013	−	5.88919i	0.338325	−	0.585997i	−0.645793	−	0.763513i	$-0.723473\pi$
$101$	3.40013	−	5.88919i	0.338325	−	0.585997i	0.984118	+	0.177516i	$0.0568063\pi$
$102$		0			0
$103$	−5.29137			−0.521374			−0.260687	−	0.965423i	$-0.583949\pi$
$103$	−5.29137			−0.521374			−0.260687	+	0.965423i	$0.583949\pi$
$104$	−1.32233	+	3.35432i	−0.129665	+	0.328918i
$105$		0			0
$106$	11.6990	+	6.75444i	1.13631	+	0.656050i
$107$	8.46410	−	14.6603i	0.818256	−	1.41726i	−0.0887109	−	0.996057i	$-0.528275\pi$
$107$	8.46410	−	14.6603i	0.818256	−	1.41726i	0.906966	−	0.421203i	$-0.138392\pi$
$108$		0			0
$109$		−	12.8003i		−	1.22604i	−0.790067	−	0.613021i	$-0.789954\pi$
$109$		−	12.8003i		−	1.22604i	0.790067	−	0.613021i	$-0.210046\pi$
$110$	3.81062	−	2.20006i	0.363329	−	0.209768i
$111$		0			0
$112$			4.64466i			0.438879i
$113$	6.53308	+	11.3156i	0.614580	+	1.06448i	0.990458	+	0.137815i	$0.0440079\pi$
$113$	6.53308	+	11.3156i	0.614580	+	1.06448i	−0.375878	+	0.926669i	$0.622659\pi$
$114$		0			0
$115$	−0.845746	−	0.488292i	−0.0788662	−	0.0455334i
$116$	−4.31274			−0.400427
$117$		0			0
$118$	−2.18056			−0.200737
$119$	−16.0896	−	9.28932i	−1.47493	−	0.851550i
$120$		0			0
$121$	4.18056	+	7.24094i	0.380051	+	0.658267i
$122$			7.46410i			0.675768i
$123$		0			0
$124$	5.57780	−	3.22034i	0.500901	−	0.289195i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	6.10978	−	10.5825i	0.542156	−	0.939041i	−0.456624	−	0.889660i	$-0.650942\pi$
$127$	6.10978	−	10.5825i	0.542156	−	0.939041i	0.998780	−	0.0493816i	$-0.0157250\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	2.82233	−	2.24376i	0.247535	−	0.196791i
$131$	0.378757			0.0330921			0.0165461	−	0.999863i	$-0.494733\pi$
$131$	0.378757			0.0330921			0.0165461	+	0.999863i	$0.494733\pi$
$132$		0			0
$133$	−18.6826	+	32.3593i	−1.61999	+	2.80591i
$134$	0.912609	+	1.58068i	0.0788374	+	0.136550i
$135$		0			0
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	1.08457	−	0.626177i	0.0926612	−	0.0534979i	−0.452953	−	0.891534i	$-0.649630\pi$
$137$	1.08457	−	0.626177i	0.0926612	−	0.0534979i	0.545615	+	0.838036i	$0.316296\pi$
$138$		0			0
$139$	−1.67767	−	2.90581i	−0.142298	−	0.246468i	0.786064	−	0.618146i	$-0.212116\pi$
$139$	−1.67767	−	2.90581i	−0.142298	−	0.246468i	−0.928362	+	0.371678i	$0.878783\pi$
$140$	2.32233	−	4.02239i	0.196273	−	0.339954i
$141$		0			0
$142$	−7.95317			−0.667415
$143$	9.87282	+	12.4186i	0.825607	+	1.03850i
$144$		0			0
$145$	3.73494	+	2.15637i	0.310170	+	0.179077i
$146$	2.18056	−	3.77684i	0.180464	−	0.312573i
$147$		0			0
$148$			3.79603i			0.312031i
$149$	4.00077	−	2.30985i	0.327756	−	0.189230i	−0.327088	−	0.944994i	$-0.606067\pi$
$149$	4.00077	−	2.30985i	0.327756	−	0.189230i	0.654844	+	0.755764i	$0.272734\pi$
$150$		0			0
$151$		−	11.2425i		−	0.914901i	−0.889235	−	0.457450i	$-0.848763\pi$
$151$		−	11.2425i		−	0.914901i	0.889235	−	0.457450i	$-0.151237\pi$
$152$	4.02239	+	6.96699i	0.326259	+	0.565097i
$153$		0			0
$154$	17.6990	+	10.2185i	1.42623	+	0.823434i
$155$	−6.44069			−0.517328
$156$		0			0
$157$	−1.50311			−0.119961			−0.0599807	−	0.998200i	$-0.519104\pi$
$157$	−1.50311			−0.119961			−0.0599807	+	0.998200i	$0.519104\pi$
$158$	12.9332	+	7.46699i	1.02891	+	0.594042i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		−	4.53590i		−	0.357479i
$162$		0			0
$163$	−0.152706	+	0.0881650i	−0.0119609	+	0.00690561i	−0.505969	−	0.862552i	$-0.668865\pi$
$163$	−0.152706	+	0.0881650i	−0.0119609	+	0.00690561i	0.494008	+	0.869458i	$0.335531\pi$
$164$			7.28932i			0.569200i
$165$		0			0
$166$	1.75547	−	3.04056i	0.136251	−	0.235993i
$167$	−7.51851	−	4.34081i	−0.581800	−	0.335902i	0.180049	−	0.983658i	$-0.442374\pi$
$167$	−7.51851	−	4.34081i	−0.581800	−	0.335902i	−0.761848	+	0.647756i	$0.775708\pi$
$168$		0			0
$169$	9.50289	+	8.87103i	0.730991	+	0.682387i
$170$	4.00000			0.306786
$171$		0			0
$172$	−0.358228	+	0.620469i	−0.0273146	+	0.0473103i
$173$	−0.890216	−	1.54190i	−0.0676818	−	0.117228i	0.830199	−	0.557468i	$-0.188227\pi$
$173$	−0.890216	−	1.54190i	−0.0676818	−	0.117228i	−0.897880	+	0.440239i	$0.854894\pi$
$174$		0			0
$175$	−4.02239	+	2.32233i	−0.304064	+	0.175552i
$176$	3.81062	−	2.20006i	0.287236	−	0.165836i
$177$		0			0
$178$	4.08637	+	7.07780i	0.306286	+	0.530503i
$179$	8.70786	−	15.0825i	0.650856	−	1.12732i	−0.332059	−	0.943258i	$-0.607743\pi$
$179$	8.70786	−	15.0825i	0.650856	−	1.12732i	0.982916	−	0.184057i	$-0.0589232\pi$
$180$		0			0
$181$	−10.3611			−0.770136			−0.385068	−	0.922888i	$-0.625822\pi$
$181$	−10.3611			−0.770136			−0.385068	+	0.922888i	$0.625822\pi$
$182$	15.5797	+	6.14177i	1.15484	+	0.455258i
$183$		0			0
$184$	−0.845746	−	0.488292i	−0.0623492	−	0.0359973i
$185$	1.89801	−	3.28745i	0.139545	−	0.241698i
$186$		0			0
$187$			17.6005i			1.28708i
$188$	−8.44671	+	4.87671i	−0.616040	+	0.355671i
$189$		0			0
$190$		−	8.04479i		−	0.583630i
$191$	−0.448507	−	0.776837i	−0.0324528	−	0.0562100i	0.849343	−	0.527842i	$-0.176999\pi$
$191$	−0.448507	−	0.776837i	−0.0324528	−	0.0562100i	−0.881796	+	0.471632i	$0.843665\pi$
$192$		0			0
$193$	17.5494	+	10.1322i	1.26324	+	0.729330i	0.973699	−	0.227837i	$-0.0731652\pi$
$193$	17.5494	+	10.1322i	1.26324	+	0.729330i	0.289537	+	0.957167i	$0.406499\pi$
$194$	−13.8252			−0.992593
$195$		0			0
$196$	14.5729			1.04092
$197$	−7.95060	−	4.59028i	−0.566457	−	0.327044i	0.189276	−	0.981924i	$-0.439386\pi$
$197$	−7.95060	−	4.59028i	−0.566457	−	0.327044i	−0.755733	+	0.654880i	$0.772719\pi$
$198$		0			0
$199$	−8.10876	−	14.0448i	−0.574815	−	0.995609i	−0.996062	−	0.0886625i	$-0.971741\pi$
$199$	−8.10876	−	14.0448i	−0.574815	−	0.995609i	0.421247	−	0.906946i	$-0.361593\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−5.88919	+	3.40013i	−0.414362	+	0.239232i
$203$			20.0312i			1.40591i
$204$		0			0
$205$	3.64466	−	6.31274i	0.254554	−	0.440901i
$206$	4.58246	+	2.64568i	0.319275	+	0.184333i
$207$		0			0
$208$	2.82233	−	2.24376i	0.195693	−	0.155577i
$209$	35.3981			2.44854
$210$		0			0
$211$	0.809848	−	1.40270i	0.0557522	−	0.0965657i	−0.836802	−	0.547505i	$-0.815578\pi$
$211$	0.809848	−	1.40270i	0.0557522	−	0.0965657i	0.892555	+	0.450939i	$0.148911\pi$
$212$	−6.75444	−	11.6990i	−0.463897	−	0.803493i
$213$		0			0
$214$	−14.6603	+	8.46410i	−1.00215	+	0.578594i
$215$	0.620469	−	0.358228i	0.0423157	−	0.0244310i
$216$		0			0
$217$	−14.9574	−	25.9070i	−1.01537	−	1.75868i
$218$	−6.40013	+	11.0853i	−0.433471	+	0.750794i
$219$		0			0
$220$	−4.40013			−0.296656
$221$	2.12795	+	14.2644i	0.143141	+	0.959524i
$222$		0			0
$223$	1.93705	+	1.11836i	0.129714	+	0.0748906i	0.563453	−	0.826148i	$-0.309473\pi$
$223$	1.93705	+	1.11836i	0.129714	+	0.0748906i	−0.433739	+	0.901039i	$0.642806\pi$
$224$	2.32233	−	4.02239i	0.155167	−	0.268757i
$225$		0			0
$226$		−	13.0662i		−	0.869148i
$227$	13.2679	−	7.66025i	0.880625	−	0.508429i	0.00976038	−	0.999952i	$-0.496893\pi$
$227$	13.2679	−	7.66025i	0.880625	−	0.508429i	0.870864	+	0.491523i	$0.163560\pi$
$228$		0			0
$229$			10.1279i			0.669274i	0.942347	+	0.334637i	$0.108614\pi$
$229$			10.1279i			0.669274i	−0.942347	+	0.334637i	$0.891386\pi$
$230$	0.488292	+	0.845746i	0.0321970	+	0.0557669i
$231$		0			0
$232$	3.73494	+	2.15637i	0.245211	+	0.141572i
$233$	−20.7519			−1.35950			−0.679750	−	0.733444i	$-0.737912\pi$
$233$	−20.7519			−1.35950			−0.679750	+	0.733444i	$0.737912\pi$
$234$		0			0
$235$	9.75342			0.636243
$236$	1.88842	+	1.09028i	0.122926	+	0.0709711i
$237$		0			0
$238$	9.28932	+	16.0896i	0.602137	+	1.04293i
$239$		−	24.3539i		−	1.57532i	−0.616107	−	0.787662i	$-0.711291\pi$
$239$		−	24.3539i		−	1.57532i	0.616107	−	0.787662i	$-0.288709\pi$
$240$		0			0
$241$	−17.2066	+	9.93423i	−1.10837	+	0.639920i	−0.938408	−	0.345530i	$-0.887699\pi$
$241$	−17.2066	+	9.93423i	−1.10837	+	0.639920i	−0.169966	+	0.985450i	$0.554366\pi$
$242$		−	8.36112i		−	0.537473i
$243$		0			0
$244$	3.73205	−	6.46410i	0.238920	−	0.413822i
$245$	−12.6205	−	7.28643i	−0.806292	−	0.465513i
$246$		0			0
$247$	28.6884	−	4.27973i	1.82540	−	0.272312i
$248$	−6.44069			−0.408984
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−6.78566	−	11.7531i	−0.428307	−	0.741849i	0.568416	−	0.822741i	$-0.307556\pi$
$251$	−6.78566	−	11.7531i	−0.428307	−	0.741849i	−0.996723	+	0.0808920i	$0.974223\pi$
$252$		0			0
$253$	−3.72139	+	2.14855i	−0.233962	+	0.135078i
$254$	−10.5825	+	6.10978i	−0.664002	+	0.383362i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.331150	+	0.573569i	−0.0206566	+	0.0357783i	−0.876169	−	0.482004i	$-0.839909\pi$
$257$	−0.331150	+	0.573569i	−0.0206566	+	0.0357783i	0.855512	+	0.517782i	$0.173242\pi$
$258$		0			0
$259$	17.6312			1.09555
$260$	−3.56609	+	0.531987i	−0.221159	+	0.0329925i
$261$		0			0
$262$	−0.328013	−	0.189378i	−0.0202647	−	0.0116998i
$263$	15.3749	−	26.6301i	0.948058	−	1.64208i	0.198548	−	0.980091i	$-0.436377\pi$
$263$	15.3749	−	26.6301i	0.948058	−	1.64208i	0.749510	−	0.661993i	$-0.230289\pi$
$264$		0			0
$265$			13.5089i			0.829844i
$266$	32.3593	−	18.6826i	1.98408	−	1.14551i
$267$		0			0
$268$		−	1.82522i		−	0.111493i
$269$	−1.87205	−	3.24249i	−0.114141	−	0.197698i	0.803295	−	0.595581i	$-0.203078\pi$
$269$	−1.87205	−	3.24249i	−0.114141	−	0.197698i	−0.917436	+	0.397883i	$0.869745\pi$
$270$		0			0
$271$	24.0419	+	13.8806i	1.46044	+	0.843186i	0.999031	−	0.0440009i	$-0.0140104\pi$
$271$	24.0419	+	13.8806i	1.46044	+	0.843186i	0.461410	+	0.887187i	$0.347344\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−1.25235			−0.0756575
$275$	3.81062	+	2.20006i	0.229789	+	0.132669i
$276$		0			0
$277$	5.99609	+	10.3855i	0.360270	+	0.624006i	0.988005	−	0.154421i	$-0.0493512\pi$
$277$	5.99609	+	10.3855i	0.360270	+	0.624006i	−0.627735	+	0.778427i	$0.716018\pi$
$278$			3.35534i			0.201240i
$279$		0			0
$280$	−4.02239	+	2.32233i	−0.240384	+	0.138786i
$281$			3.63888i			0.217078i	0.994092	+	0.108539i	$0.0346172\pi$
$281$			3.63888i			0.217078i	−0.994092	+	0.108539i	$0.965383\pi$
$282$		0			0
$283$	2.42220	−	4.19538i	0.143985	−	0.249389i	−0.785009	−	0.619485i	$-0.787342\pi$
$283$	2.42220	−	4.19538i	0.143985	−	0.249389i	0.928994	+	0.370095i	$0.120675\pi$
$284$	6.88764	+	3.97658i	0.408707	+	0.235967i
$285$		0			0
$286$	−2.34081	−	15.6912i	−0.138415	−	0.927843i
$287$	33.8564			1.99848
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−2.15637	−	3.73494i	−0.126626	−	0.219323i
$291$		0			0
$292$	−3.77684	+	2.18056i	−0.221023	+	0.127608i
$293$	−3.20500	+	1.85041i	−0.187238	+	0.108102i	−0.590689	−	0.806899i	$-0.701144\pi$
$293$	−3.20500	+	1.85041i	−0.187238	+	0.108102i	0.403451	+	0.915001i	$0.367811\pi$
$294$		0			0
$295$	−1.09028	−	1.88842i	−0.0634785	−	0.109948i
$296$	1.89801	−	3.28745i	0.110320	−	0.191079i
$297$		0			0
$298$	−4.61970			−0.267612
$299$	−2.75624	+	2.19122i	−0.159398	+	0.126721i
$300$		0			0
$301$	2.88187	+	1.66385i	0.166108	+	0.0959026i
$302$	−5.62124	+	9.73628i	−0.323466	+	0.560260i
$303$		0			0
$304$		−	8.04479i		−	0.461400i
$305$	−6.46410	+	3.73205i	−0.370133	+	0.213697i
$306$		0			0
$307$			7.11454i			0.406048i	0.979174	+	0.203024i	$0.0650770\pi$
$307$			7.11454i			0.406048i	−0.979174	+	0.203024i	$0.934923\pi$
$308$	−10.2185	−	17.6990i	−0.582256	−	1.00850i
$309$		0			0
$310$	5.57780	+	3.22034i	0.316798	+	0.182903i
$311$	19.9148			1.12926			0.564632	−	0.825343i	$-0.309018\pi$
$311$	19.9148			1.12926			0.564632	+	0.825343i	$0.309018\pi$
$312$		0			0
$313$	6.13950			0.347025			0.173513	−	0.984832i	$-0.444488\pi$
$313$	6.13950			0.347025			0.173513	+	0.984832i	$0.444488\pi$
$314$	1.30173	+	0.751556i	0.0734611	+	0.0424128i
$315$		0			0
$316$	−7.46699	−	12.9332i	−0.420051	−	0.727550i
$317$			7.85286i			0.441061i	0.975380	+	0.220530i	$0.0707788\pi$
$317$			7.85286i			0.441061i	−0.975380	+	0.220530i	$0.929221\pi$
$318$		0			0
$319$	16.4342	−	9.48829i	0.920139	−	0.531242i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	−2.26795	+	3.92820i	−0.126388	+	0.218910i
$323$	27.8680	+	16.0896i	1.55061	+	0.895248i
$324$		0			0
$325$	3.35432	+	1.32233i	0.186064	+	0.0733497i
$326$	0.176330			0.00976601
$327$		0			0
$328$	3.64466	−	6.31274i	0.201243	−	0.348563i
$329$	22.6507	+	39.2321i	1.24877	+	2.16294i
$330$		0			0
$331$	27.7093	−	15.9980i	1.52304	−	0.879327i	0.523410	−	0.852081i	$-0.324659\pi$
$331$	27.7093	−	15.9980i	1.52304	−	0.879327i	0.999629	−	0.0272463i	$-0.00867385\pi$
$332$	−3.04056	+	1.75547i	−0.166872	+	0.0963438i
$333$		0			0
$334$	4.34081	+	7.51851i	0.237519	+	0.411394i
$335$	−0.912609	+	1.58068i	−0.0498611	+	0.0863620i
$336$		0			0
$337$	−35.6432			−1.94161			−0.970806	−	0.239867i	$-0.922896\pi$
$337$	−35.6432			−1.94161			−0.970806	+	0.239867i	$0.922896\pi$
$338$	−3.79423	−	12.4340i	−0.206379	−	0.676319i
$339$		0			0
$340$	−3.46410	−	2.00000i	−0.187867	−	0.108465i
$341$	−14.1699	+	24.5430i	−0.767344	+	1.32908i
$342$		0			0
$343$		−	35.1734i		−	1.89918i
$344$	0.620469	−	0.358228i	0.0334535	−	0.0193144i
$345$		0			0
$346$			1.78043i			0.0957166i
$347$	−3.44851	−	5.97299i	−0.185126	−	0.320647i	0.758493	−	0.651681i	$-0.225936\pi$
$347$	−3.44851	−	5.97299i	−0.185126	−	0.320647i	−0.943619	+	0.331034i	$0.892603\pi$
$348$		0			0
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.875785	−	0.482701i	$-0.160344\pi$
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.0198610	+	0.999803i	$0.493678\pi$
$350$	4.64466			0.248267
$351$		0			0
$352$	−4.40013			−0.234528
$353$	23.7441	+	13.7086i	1.26377	+	0.729637i	0.973802	−	0.227400i	$-0.0730224\pi$
$353$	23.7441	+	13.7086i	1.26377	+	0.729637i	0.289967	+	0.957037i	$0.406356\pi$
$354$		0			0
$355$	−3.97658	−	6.88764i	−0.211055	−	0.365558i
$356$		−	8.17274i		−	0.433154i
$357$		0			0
$358$	−15.0825	+	8.70786i	−0.797133	+	0.460225i
$359$			14.3611i			0.757951i	0.925407	+	0.378975i	$0.123723\pi$
$359$			14.3611i			0.757951i	−0.925407	+	0.378975i	$0.876277\pi$
$360$		0			0
$361$	22.8593	−	39.5935i	1.20312	−	2.08387i
$362$	8.97299	+	5.18056i	0.471610	+	0.272284i
$363$		0			0
$364$	−10.4215	−	13.1088i	−0.546235	−	0.687086i
$365$	4.36112			0.228271
$366$		0			0
$367$	6.88764	−	11.9298i	0.359532	−	0.622728i	−0.628351	−	0.777930i	$-0.716270\pi$
$367$	6.88764	−	11.9298i	0.359532	−	0.622728i	0.987883	+	0.155202i	$0.0496030\pi$
$368$	0.488292	+	0.845746i	0.0254540	+	0.0440876i
$369$		0			0
$370$	−3.28745	+	1.89801i	−0.170907	+	0.0986730i
$371$	−54.3381	+	31.3721i	−2.82109	+	1.62876i
$372$		0			0
$373$	16.7313	+	28.9795i	0.866316	+	1.50050i	0.865734	+	0.500504i	$0.166852\pi$
$373$	16.7313	+	28.9795i	0.866316	+	1.50050i	0.000581860		1.00000i	$0.499815\pi$
$374$	8.80025	−	15.2425i	0.455050	−	0.788170i
$375$		0			0
$376$	9.75342			0.502994
$377$	12.1720	−	9.67674i	0.626888	−	0.498377i
$378$		0			0
$379$	−28.9052	−	16.6884i	−1.48476	−	0.857227i	−0.484910	−	0.874564i	$-0.661148\pi$
$379$	−28.9052	−	16.6884i	−1.48476	−	0.857227i	−0.999850	+	0.0173371i	$0.994481\pi$
$380$	−4.02239	+	6.96699i	−0.206344	+	0.357399i
$381$		0			0
$382$			0.897014i			0.0458952i
$383$	−6.34829	+	3.66519i	−0.324383	+	0.187282i	−0.653344	−	0.757061i	$-0.726635\pi$
$383$	−6.34829	+	3.66519i	−0.324383	+	0.187282i	0.328962	+	0.944343i	$0.393301\pi$
$384$		0			0
$385$			20.4371i			1.04157i
$386$	−10.1322	−	17.5494i	−0.515714	−	0.893243i
$387$		0			0
$388$	11.9730	+	6.91261i	0.607836	+	0.350935i
$389$	32.6198			1.65389			0.826946	−	0.562282i	$-0.190076\pi$
$389$	32.6198			1.65389			0.826946	+	0.562282i	$0.190076\pi$
$390$		0			0
$391$	−3.90633			−0.197552
$392$	−12.6205	−	7.28643i	−0.637430	−	0.368020i
$393$		0			0
$394$	4.59028	+	7.95060i	0.231255	+	0.400545i
$395$			14.9340i			0.751410i
$396$		0			0
$397$	12.5299	−	7.23416i	0.628860	−	0.363072i	−0.151451	−	0.988465i	$-0.548394\pi$
$397$	12.5299	−	7.23416i	0.628860	−	0.363072i	0.780310	+	0.625392i	$0.215061\pi$
$398$			16.2175i			0.812911i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	6.31096	+	3.64364i	0.315154	+	0.181955i	0.649231	−	0.760592i	$-0.275091\pi$
$401$	6.31096	+	3.64364i	0.315154	+	0.181955i	−0.334076	+	0.942546i	$0.608424\pi$
$402$		0			0
$403$	−8.51671	+	21.6041i	−0.424248	+	1.07618i
$404$	6.80025			0.338325
$405$		0			0
$406$	10.0156	−	17.3475i	0.497066	−	0.860943i
$407$	−8.35150	−	14.4652i	−0.413968	−	0.717014i
$408$		0			0
$409$	−21.2840	+	12.2883i	−1.05242	+	0.607617i	−0.923327	−	0.384015i	$-0.874541\pi$
$409$	−21.2840	+	12.2883i	−1.05242	+	0.607617i	−0.129097	+	0.991632i	$0.541208\pi$
$410$	−6.31274	+	3.64466i	−0.311764	+	0.179997i
$411$		0			0
$412$	−2.64568	−	4.58246i	−0.130343	−	0.225761i
$413$	5.06397	−	8.77106i	0.249182	−	0.431596i
$414$		0			0
$415$	3.51093			0.172345
$416$	−3.56609	+	0.531987i	−0.174842	+	0.0260828i
$417$		0			0
$418$	−30.6556	−	17.6990i	−1.49942	−	0.865688i
$419$	7.77684	−	13.4699i	0.379923	−	0.658047i	−0.611127	−	0.791532i	$-0.709284\pi$
$419$	7.77684	−	13.4699i	0.379923	−	0.658047i	0.991051	+	0.133486i	$0.0426170\pi$
$420$		0			0
$421$			22.3143i			1.08753i	0.839237	+	0.543766i	$0.183002\pi$
$421$			22.3143i			1.08753i	−0.839237	+	0.543766i	$0.816998\pi$
$422$	−1.40270	+	0.809848i	−0.0682822	+	0.0394228i
$423$		0			0
$424$			13.5089i			0.656050i
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$		0			0
$427$	−30.0236	−	17.3341i	−1.45294	−	0.838856i
$428$	16.9282			0.818256
$429$		0			0
$430$	−0.716456			−0.0345506
$431$	−21.0135	−	12.1322i	−1.01219	−	0.584386i	−0.100356	−	0.994952i	$-0.531998\pi$
$431$	−21.0135	−	12.1322i	−1.01219	−	0.584386i	−0.911831	+	0.410565i	$0.865331\pi$
$432$		0			0
$433$	−11.5494	−	20.0042i	−0.555031	−	0.961342i	−0.997901	−	0.0647561i	$-0.979373\pi$
$433$	−11.5494	−	20.0042i	−0.555031	−	0.961342i	0.442870	−	0.896586i	$-0.353960\pi$
$434$			29.9148i			1.43596i
$435$		0			0
$436$	11.0853	−	6.40013i	0.530892	−	0.306510i
$437$			7.85641i			0.375823i
$438$		0			0
$439$	−19.9980	+	34.6375i	−0.954450	+	1.65316i	−0.218829	+	0.975763i	$0.570224\pi$
$439$	−19.9980	+	34.6375i	−0.954450	+	1.65316i	−0.735621	+	0.677393i	$0.763110\pi$
$440$	3.81062	+	2.20006i	0.181664	+	0.104884i
$441$		0			0
$442$	5.28932	−	13.4173i	0.251587	−	0.638194i
$443$	15.6036			0.741350			0.370675	−	0.928763i	$-0.379126\pi$
$443$	15.6036			0.741350			0.370675	+	0.928763i	$0.379126\pi$
$444$		0			0
$445$	−4.08637	+	7.07780i	−0.193712	+	0.335520i
$446$	−1.11836	−	1.93705i	−0.0529557	−	0.0917219i
$447$		0			0
$448$	−4.02239	+	2.32233i	−0.190040	+	0.109720i
$449$	−23.3863	+	13.5021i	−1.10367	+	0.637203i	−0.937182	−	0.348841i	$-0.886575\pi$
$449$	−23.3863	+	13.5021i	−1.10367	+	0.637203i	−0.166486	+	0.986044i	$0.553242\pi$
$450$		0			0
$451$	−16.0370	−	27.7768i	−0.755151	−	1.30796i
$452$	−6.53308	+	11.3156i	−0.307290	+	0.532242i
$453$		0			0
$454$	−15.3205			−0.719027
$455$	2.47090	+	16.5633i	0.115838	+	0.776498i
$456$		0			0
$457$	15.4039	+	8.89342i	0.720562	+	0.416017i	0.814959	−	0.579518i	$-0.196759\pi$
$457$	15.4039	+	8.89342i	0.720562	+	0.416017i	−0.0943975	+	0.995535i	$0.530092\pi$
$458$	5.06397	−	8.77106i	0.236624	−	0.409845i
$459$		0			0
$460$		−	0.976584i		−	0.0455334i
$461$	−21.6205	+	12.4826i	−1.00697	+	0.581372i	−0.910302	−	0.413945i	$-0.864151\pi$
$461$	−21.6205	+	12.4826i	−1.00697	+	0.581372i	−0.0966638	+	0.995317i	$0.530817\pi$
$462$		0			0
$463$		−	15.6389i		−	0.726801i	−0.931633	−	0.363400i	$-0.881616\pi$
$463$		−	15.6389i		−	0.726801i	0.931633	−	0.363400i	$-0.118384\pi$
$464$	−2.15637	−	3.73494i	−0.100107	−	0.173390i
$465$		0			0
$466$	17.9716	+	10.3759i	0.832521	+	0.480656i
$467$	2.43914			0.112870			0.0564349	−	0.998406i	$-0.482027\pi$
$467$	2.43914			0.112870			0.0564349	+	0.998406i	$0.482027\pi$
$468$		0			0
$469$	−8.47751			−0.391455
$470$	−8.44671	−	4.87671i	−0.389618	−	0.224946i
$471$		0			0
$472$	−1.09028	−	1.88842i	−0.0501842	−	0.0869215i
$473$		−	3.15250i		−	0.144952i
$474$		0			0
$475$	6.96699	−	4.02239i	0.319667	−	0.184560i
$476$		−	18.5786i		−	0.851550i
$477$		0			0
$478$	−12.1770	+	21.0911i	−0.556961	+	0.964685i
$479$	−12.2857	−	7.09317i	−0.561349	−	0.324095i	0.192338	−	0.981329i	$-0.438393\pi$
$479$	−12.2857	−	7.09317i	−0.561349	−	0.324095i	−0.753687	+	0.657234i	$0.771726\pi$
$480$		0			0
$481$	−8.51737	−	10.7136i	−0.388358	−	0.488500i
$482$	19.8685			0.904983
$483$		0			0
$484$	−4.18056	+	7.24094i	−0.190025	+	0.329134i
$485$	−6.91261	−	11.9730i	−0.313885	−	0.543665i
$486$		0			0
$487$	4.99115	−	2.88164i	0.226171	−	0.130580i	−0.382633	−	0.923900i	$-0.624983\pi$
$487$	4.99115	−	2.88164i	0.226171	−	0.130580i	0.608804	+	0.793320i	$0.291649\pi$
$488$	−6.46410	+	3.73205i	−0.292616	+	0.168942i
$489$		0			0
$490$	7.28643	+	12.6205i	0.329167	+	0.570135i
$491$	0.537671	−	0.931273i	0.0242647	−	0.0420278i	−0.853638	−	0.520867i	$-0.825609\pi$
$491$	0.537671	−	0.931273i	0.0242647	−	0.0420278i	0.877903	+	0.478839i	$0.158942\pi$
$492$		0			0
$493$	17.2509			0.776943
$494$	−26.9848	−	10.6379i	−1.21410	−	0.478620i
$495$		0			0
$496$	5.57780	+	3.22034i	0.250450	+	0.144598i
$497$	18.4699	−	31.9908i	0.828487	−	1.43498i
$498$		0			0
$499$		−	14.7534i		−	0.660454i	−0.943902	−	0.330227i	$-0.892875\pi$
$499$		−	14.7534i		−	0.660454i	0.943902	−	0.330227i	$-0.107125\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$		0			0
$502$			13.5713i			0.605717i
$503$	−13.3309	−	23.0898i	−0.594395	−	1.02952i	−0.993632	−	0.112675i	$-0.964058\pi$
$503$	−13.3309	−	23.0898i	−0.594395	−	1.02952i	0.399236	−	0.916848i	$-0.369275\pi$
$504$		0			0
$505$	−5.88919	−	3.40013i	−0.262066	−	0.151304i
$506$	4.29709			0.191029
$507$		0			0
$508$	12.2196			0.542156
$509$	−12.2807	−	7.09028i	−0.544333	−	0.314271i	0.202500	−	0.979282i	$-0.435093\pi$
$509$	−12.2807	−	7.09028i	−0.544333	−	0.314271i	−0.746833	+	0.665011i	$0.768427\pi$
$510$		0			0
$511$	10.1279	+	17.5421i	0.448034	+	0.776018i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	0.573569	−	0.331150i	0.0252990	−	0.0146064i
$515$			5.29137i			0.233165i
$516$		0			0
$517$	21.4581	−	37.1666i	0.943728	−	1.63459i
$518$	−15.2691	−	8.81562i	−0.670886	−	0.387336i
$519$		0			0
$520$	3.35432	+	1.32233i	0.147097	+	0.0579880i
$521$	−23.7476			−1.04040			−0.520202	−	0.854043i	$-0.674143\pi$
$521$	−23.7476			−1.04040			−0.520202	+	0.854043i	$0.674143\pi$
$522$		0			0
$523$	−6.92532	+	11.9950i	−0.302823	+	0.524505i	−0.976774	−	0.214271i	$-0.931262\pi$
$523$	−6.92532	+	11.9950i	−0.302823	+	0.524505i	0.673951	+	0.738776i	$0.264596\pi$
$524$	0.189378	+	0.328013i	0.00827303	+	0.0143293i
$525$		0			0
$526$	−26.6301	+	15.3749i	−1.16113	+	0.670378i
$527$	−22.3112	+	12.8814i	−0.971891	+	0.561121i
$528$		0			0
$529$	11.0231	+	19.0926i	0.479267	+	0.830115i
$530$	6.75444	−	11.6990i	0.293394	−	0.508174i
$531$		0			0
$532$	−37.3653			−1.61999
$533$	−16.3555	−	20.5729i	−0.708434	−	0.891110i
$534$		0			0
$535$	−14.6603	−	8.46410i	−0.633818	−	0.365935i
$536$	−0.912609	+	1.58068i	−0.0394187	+	0.0682752i
$537$		0			0
$538$			3.74410i			0.161420i
$539$	−55.5317	+	32.0612i	−2.39192	+	1.38097i
$540$		0			0
$541$		−	14.8898i		−	0.640164i	−0.947390	−	0.320082i	$-0.896290\pi$
$541$		−	14.8898i		−	0.640164i	0.947390	−	0.320082i	$-0.103710\pi$
$542$	−13.8806	−	24.0419i	−0.596223	−	1.03269i
$543$		0			0
$544$	−3.46410	−	2.00000i	−0.148522	−	0.0857493i
$545$	−12.8003			−0.548303
$546$		0			0
$547$	−22.2019			−0.949284			−0.474642	−	0.880179i	$-0.657422\pi$
$547$	−22.2019			−0.949284			−0.474642	+	0.880179i	$0.657422\pi$
$548$	1.08457	+	0.626177i	0.0463306	+	0.0267490i
$549$		0			0
$550$	−2.20006	−	3.81062i	−0.0938110	−	0.162485i
$551$		−	34.6950i		−	1.47806i
$552$		0			0
$553$	−60.0703	+	34.6816i	−2.55445	+	1.47481i
$554$		−	11.9922i		−	0.509499i
$555$		0			0
$556$	1.67767	−	2.90581i	0.0711491	−	0.123234i
$557$	−1.64518	−	0.949847i	−0.0697087	−	0.0402463i	0.464741	−	0.885447i	$-0.346148\pi$
$557$	−1.64518	−	0.949847i	−0.0697087	−	0.0402463i	−0.534449	+	0.845201i	$0.679481\pi$
$558$		0			0
$559$	−0.381146	−	2.55495i	−0.0161207	−	0.108063i
$560$	4.64466			0.196273
$561$		0			0
$562$	1.81944	−	3.15137i	0.0767485	−	0.132932i
$563$	0.860000	+	1.48956i	0.0362447	+	0.0627777i	0.883579	−	0.468283i	$-0.155127\pi$
$563$	0.860000	+	1.48956i	0.0362447	+	0.0627777i	−0.847334	+	0.531060i	$0.821794\pi$
$564$		0			0
$565$	11.3156	−	6.53308i	0.476052	−	0.274849i
$566$	−4.19538	+	2.42220i	−0.176345	+	0.101813i
$567$		0			0
$568$	−3.97658	−	6.88764i	−0.166854	−	0.288999i
$569$	0.300960	−	0.521278i	0.0126169	−	0.0218531i	−0.859648	−	0.510887i	$-0.829317\pi$
$569$	0.300960	−	0.521278i	0.0126169	−	0.0218531i	0.872265	+	0.489034i	$0.162650\pi$
$570$		0			0
$571$	11.9808			0.501381			0.250691	−	0.968067i	$-0.419342\pi$
$571$	11.9808			0.501381			0.250691	+	0.968067i	$0.419342\pi$
$572$	−5.81842	+	14.7594i	−0.243280	+	0.617122i
$573$		0			0
$574$	−29.3205	−	16.9282i	−1.22381	−	0.706570i
$575$	−0.488292	+	0.845746i	−0.0203632	+	0.0352701i
$576$		0			0
$577$			43.0293i			1.79133i	0.444725	+	0.895667i	$0.353301\pi$
$577$			43.0293i			1.79133i	−0.444725	+	0.895667i	$0.646699\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$		0			0
$580$			4.31274i			0.179077i
$581$	8.15355	+	14.1224i	0.338266	+	0.585894i
$582$		0			0
$583$	51.4773	+	29.7204i	2.13197	+	1.23089i
$584$	4.36112			0.180464
$585$		0			0
$586$	3.70081			0.152879
$587$	15.5147	+	8.95740i	0.640359	+	0.369711i	0.784753	−	0.619809i	$-0.212790\pi$
$587$	15.5147	+	8.95740i	0.640359	+	0.369711i	−0.144394	+	0.989520i	$0.546123\pi$
$588$		0			0
$589$	25.9070	+	44.8722i	1.06748	+	1.84893i
$590$			2.18056i			0.0897722i
$591$		0			0
$592$	−3.28745	+	1.89801i	−0.135114	+	0.0780078i
$593$			0.669624i			0.0274981i	0.999905	+	0.0137491i	$0.00437660\pi$
$593$			0.669624i			0.0274981i	−0.999905	+	0.0137491i	$0.995623\pi$
$594$		0			0
$595$	−9.28932	+	16.0896i	−0.380825	+	0.659608i
$596$	4.00077	+	2.30985i	0.163878	+	0.0946151i
$597$		0			0
$598$	3.48258	−	0.519530i	0.142413	−	0.0212452i
$599$	−1.29241			−0.0528066			−0.0264033	−	0.999651i	$-0.508405\pi$
$599$	−1.29241			−0.0528066			−0.0264033	+	0.999651i	$0.508405\pi$
$600$		0			0
$601$	5.73671	−	9.93627i	0.234005	−	0.405309i	−0.724978	−	0.688772i	$-0.758150\pi$
$601$	5.73671	−	9.93627i	0.234005	−	0.405309i	0.958983	+	0.283463i	$0.0914834\pi$
$602$	−1.66385	−	2.88187i	−0.0678134	−	0.117456i
$603$		0			0
$604$	9.73628	−	5.62124i	0.396164	−	0.228725i
$605$	7.24094	−	4.18056i	0.294386	−	0.169964i
$606$		0			0
$607$	12.0672	+	20.9010i	0.489792	+	0.848344i	0.999931	−	0.0117477i	$-0.00373949\pi$
$607$	12.0672	+	20.9010i	0.489792	+	0.848344i	−0.510139	+	0.860092i	$0.670406\pi$
$608$	−4.02239	+	6.96699i	−0.163130	+	0.282549i
$609$		0			0
$610$	7.46410			0.302213
$611$	12.8972	−	32.7161i	0.521766	−	1.32355i
$612$		0			0
$613$	25.0716	+	14.4751i	1.01263	+	0.584644i	0.911961	−	0.410276i	$-0.134568\pi$
$613$	25.0716	+	14.4751i	1.01263	+	0.584644i	0.100671	+	0.994920i	$0.467901\pi$
$614$	3.55727	−	6.16137i	0.143560	−	0.248653i
$615$		0			0
$616$			20.4371i			0.823434i
$617$	0.728597	−	0.420655i	0.0293322	−	0.0169349i	−0.485262	−	0.874369i	$-0.661276\pi$
$617$	0.728597	−	0.420655i	0.0293322	−	0.0169349i	0.514594	+	0.857434i	$0.327943\pi$
$618$		0			0
$619$			6.25076i			0.251239i	0.992078	+	0.125620i	$0.0400919\pi$
$619$			6.25076i			0.251239i	−0.992078	+	0.125620i	$0.959908\pi$
$620$	−3.22034	−	5.57780i	−0.129332	−	0.224010i
$621$		0			0
$622$	−17.2467	−	9.95740i	−0.691530	−	0.399255i
$623$	−37.9596			−1.52082
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.31696	−	3.06975i	−0.212509	−	0.122692i
$627$		0			0
$628$	−0.751556	−	1.30173i	−0.0299904	−	0.0519448i
$629$		−	15.1841i		−	0.605430i
$630$		0			0
$631$	2.61970	−	1.51248i	0.104288	−	0.0602110i	−0.446949	−	0.894560i	$-0.647489\pi$
$631$	2.61970	−	1.51248i	0.104288	−	0.0602110i	0.551237	+	0.834349i	$0.314156\pi$
$632$			14.9340i			0.594042i
$633$		0			0
$634$	3.92643	−	6.80078i	0.155938	−	0.270093i
$635$	−10.5825	−	6.10978i	−0.419952	−	0.242459i
$636$		0			0
$637$	−41.1294	+	32.6980i	−1.62961	+	1.29554i
$638$	−18.9766			−0.751290
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−0.386305	−	0.669099i	−0.0152581	−	0.0264278i	0.858296	−	0.513156i	$-0.171524\pi$
$641$	−0.386305	−	0.669099i	−0.0152581	−	0.0264278i	−0.873554	+	0.486728i	$0.838190\pi$
$642$		0			0
$643$	16.7788	−	9.68726i	0.661693	−	0.382028i	−0.131229	−	0.991352i	$-0.541892\pi$
$643$	16.7788	−	9.68726i	0.661693	−	0.382028i	0.792922	+	0.609324i	$0.208559\pi$
$644$	3.92820	−	2.26795i	0.154793	−	0.0893697i
$645$		0			0
$646$	−16.0896	−	27.8680i	−0.633036	−	1.09645i
$647$	13.5953	−	23.5477i	0.534485	−	0.925755i	−0.464703	−	0.885466i	$-0.653839\pi$
$647$	13.5953	−	23.5477i	0.534485	−	0.925755i	0.999188	−	0.0402882i	$-0.0128276\pi$
$648$		0			0
$649$	−9.59473			−0.376626
$650$	−2.24376	−	2.82233i	−0.0880075	−	0.110701i
$651$		0			0
$652$	−0.152706	−	0.0881650i	−0.00598044	−	0.00345281i
$653$	7.89799	−	13.6797i	0.309072	−	0.535329i	−0.669088	−	0.743184i	$-0.733315\pi$
$653$	7.89799	−	13.6797i	0.309072	−	0.535329i	0.978160	+	0.207855i	$0.0666482\pi$
$654$		0			0
$655$		−	0.378757i		−	0.0147993i
$656$	−6.31274	+	3.64466i	−0.246471	+	0.142300i
$657$		0			0
$658$		−	45.3013i		−	1.76603i
$659$	15.2381	+	26.3932i	0.593593	+	1.02813i	0.993744	+	0.111684i	$0.0356243\pi$
$659$	15.2381	+	26.3932i	0.593593	+	1.02813i	−0.400151	+	0.916449i	$0.631042\pi$
$660$		0			0
$661$	−24.1514	−	13.9438i	−0.939379	−	0.542351i	−0.0496136	−	0.998768i	$-0.515799\pi$
$661$	−24.1514	−	13.9438i	−0.939379	−	0.542351i	−0.889766	+	0.456418i	$0.849132\pi$
$662$	−31.9959			−1.24356
$663$		0			0
$664$	3.51093			0.136251
$665$	32.3593	+	18.6826i	1.25484	+	0.724482i
$666$		0			0
$667$	2.10587	+	3.64748i	0.0815397	+	0.141231i
$668$		−	8.68162i		−	0.335902i
$669$		0			0
$670$	1.58068	−	0.912609i	0.0610672	−	0.0352572i
$671$			32.8430i			1.26789i
$672$		0			0
$673$	−0.489066	+	0.847086i	−0.0188521	+	0.0326528i	−0.875298	−	0.483585i	$-0.839334\pi$
$673$	−0.489066	+	0.847086i	−0.0188521	+	0.0326528i	0.856445	+	0.516238i	$0.172668\pi$
$674$	30.8680	+	17.8216i	1.18899	+	0.686463i
$675$		0			0
$676$	−2.93109	+	12.6653i	−0.112734	+	0.487125i
$677$	19.1926			0.737630			0.368815	−	0.929503i	$-0.379764\pi$
$677$	19.1926			0.737630			0.368815	+	0.929503i	$0.379764\pi$
$678$		0			0
$679$	32.1067	−	55.6105i	1.23214	−	2.13413i
$680$	2.00000	+	3.46410i	0.0766965	+	0.132842i
$681$		0			0
$682$	24.5430	−	14.1699i	0.939801	−	0.542594i
$683$	1.30851	−	0.755467i	0.0500687	−	0.0289071i	−0.474757	−	0.880117i	$-0.657464\pi$
$683$	1.30851	−	0.755467i	0.0500687	−	0.0289071i	0.524825	+	0.851210i	$0.324131\pi$
$684$		0			0
$685$	−0.626177	−	1.08457i	−0.0239250	−	0.0414393i
$686$	−17.5867	+	30.4610i	−0.671463	+	1.16301i
$687$		0			0
$688$	−0.716456			−0.0273146
$689$	45.3131	+	17.8632i	1.72629	+	0.680534i
$690$		0			0
$691$	28.6798	+	16.5583i	1.09103	+	0.629907i	0.933851	−	0.357663i	$-0.116426\pi$
$691$	28.6798	+	16.5583i	1.09103	+	0.629907i	0.157180	+	0.987570i	$0.449760\pi$
$692$	0.890216	−	1.54190i	0.0338409	−	0.0586142i
$693$		0			0
$694$			6.89701i			0.261807i
$695$	−2.90581	+	1.67767i	−0.110224	+	0.0636377i
$696$		0			0
$697$		−	29.1573i		−	1.10441i
$698$	−9.66025	−	16.7321i	−0.365646	−	0.633317i
$699$		0			0
$700$	−4.02239	−	2.32233i	−0.152032	−	0.0877758i
$701$	−27.8695			−1.05262			−0.526308	−	0.850294i	$-0.676424\pi$
$701$	−27.8695			−1.05262			−0.526308	+	0.850294i	$0.676424\pi$
$702$		0			0
$703$	−30.5382			−1.15177
$704$	3.81062	+	2.20006i	0.143618	+	0.0829180i
$705$		0			0
$706$	−13.7086	−	23.7441i	−0.515931	−	0.893619i
$707$		−	31.5849i		−	1.18787i
$708$		0			0
$709$	−9.57491	+	5.52808i	−0.359593	+	0.207611i	−0.668902	−	0.743350i	$-0.733236\pi$
$709$	−9.57491	+	5.52808i	−0.359593	+	0.207611i	0.309309	+	0.950962i	$0.399902\pi$
$710$			7.95317i			0.298477i
$711$		0			0
$712$	−4.08637	+	7.07780i	−0.153143	+	0.265252i
$713$	−5.44719	−	3.14493i	−0.203999	−	0.117779i
$714$		0			0
$715$	12.4186	−	9.87282i	0.464430	−	0.369223i
$716$	17.4157			0.650856
$717$		0			0
$718$	7.18056	−	12.4371i	0.267976	−	0.464148i
$719$	−5.85641	−	10.1436i	−0.218407	−	0.378292i	0.735914	−	0.677075i	$-0.236753\pi$
$719$	−5.85641	−	10.1436i	−0.218407	−	0.378292i	−0.954321	+	0.298783i	$0.903419\pi$
$720$		0			0
$721$	−21.2840	+	12.2883i	−0.792656	+	0.457640i
$722$	−39.5935	+	22.8593i	−1.47352	+	0.850735i
$723$		0			0
$724$	−5.18056	−	8.97299i	−0.192534	−	0.333479i
$725$	2.15637	−	3.73494i	0.0800855	−	0.138712i
$726$		0			0
$727$	−19.4152			−0.720071			−0.360035	−	0.932939i	$-0.617235\pi$
$727$	−19.4152			−0.720071			−0.360035	+	0.932939i	$0.617235\pi$
$728$	2.47090	+	16.5633i	0.0915777	+	0.613876i
$729$		0			0
$730$	−3.77684	−	2.18056i	−0.139787	−	0.0807061i
$731$	1.43291	−	2.48188i	0.0529982	−	0.0917956i
$732$		0			0
$733$		−	11.9340i		−	0.440792i	−0.975411	−	0.220396i	$-0.929265\pi$
$733$		−	11.9340i		−	0.440792i	0.975411	−	0.220396i	$-0.0707349\pi$
$734$	−11.9298	+	6.88764i	−0.440335	+	0.254228i
$735$		0			0
$736$		−	0.976584i		−	0.0359973i
$737$	4.01559	+	6.95521i	0.147916	+	0.256199i
$738$		0			0
$739$	17.2017	+	9.93141i	0.632775	+	0.365333i	0.781826	−	0.623497i	$-0.214289\pi$
$739$	17.2017	+	9.93141i	0.632775	+	0.365333i	−0.149051	+	0.988830i	$0.547622\pi$
$740$	3.79603			0.139545
$741$		0			0
$742$	62.7442			2.30341
$743$	−14.2787	−	8.24383i	−0.523836	−	0.302437i	0.214667	−	0.976687i	$-0.431133\pi$
$743$	−14.2787	−	8.24383i	−0.523836	−	0.302437i	−0.738503	+	0.674251i	$0.764467\pi$
$744$		0			0
$745$	−2.30985	−	4.00077i	−0.0846263	−	0.146577i
$746$		−	33.4627i		−	1.22516i
$747$		0			0
$748$	−15.2425	+	8.80025i	−0.557320	+	0.321769i
$749$		−	78.6257i		−	2.87292i
$750$		0			0
$751$	−23.3312	+	40.4109i	−0.851368	+	1.47461i	0.0286056	+	0.999591i	$0.490893\pi$
$751$	−23.3312	+	40.4109i	−0.851368	+	1.47461i	−0.879974	+	0.475022i	$0.842440\pi$
$752$	−8.44671	−	4.87671i	−0.308020	−	0.177835i
$753$		0			0
$754$	−15.3796	+	2.29432i	−0.560092	+	0.0835542i
$755$	−11.2425			−0.409156
$756$		0			0
$757$	−1.31799	+	2.28282i	−0.0479030	+	0.0829705i	−0.888983	−	0.457941i	$-0.848587\pi$
$757$	−1.31799	+	2.28282i	−0.0479030	+	0.0829705i	0.841080	+	0.540911i	$0.181921\pi$
$758$	16.6884	+	28.9052i	0.606151	+	1.04988i
$759$		0			0
$760$	6.96699	−	4.02239i	0.252719	−	0.145908i
$761$	−0.0693410	+	0.0400340i	−0.00251361	+	0.00145123i	−0.501256	−	0.865299i	$-0.667129\pi$
$761$	−0.0693410	+	0.0400340i	−0.00251361	+	0.00145123i	0.498743	+	0.866750i	$0.333795\pi$
$762$		0			0
$763$	−29.7264	−	51.4877i	−1.07617	−	1.86398i
$764$	0.448507	−	0.776837i	0.0162264	−	0.0281050i
$765$		0			0
$766$	7.33038			0.264857
$767$	−7.77606	+	1.16003i	−0.280777	+	0.0418862i
$768$		0			0
$769$	4.92177	+	2.84159i	0.177484	+	0.102470i	0.586110	−	0.810232i	$-0.300659\pi$
$769$	4.92177	+	2.84159i	0.177484	+	0.102470i	−0.408626	+	0.912702i	$0.633992\pi$
$770$	10.2185	−	17.6990i	0.368251	−	0.637829i
$771$		0			0
$772$			20.2644i			0.729330i
$773$	6.57184	−	3.79425i	0.236373	−	0.136470i	−0.377136	−	0.926158i	$-0.623091\pi$
$773$	6.57184	−	3.79425i	0.236373	−	0.136470i	0.613508	+	0.789688i	$0.289758\pi$
$774$		0			0
$775$			6.44069i			0.231356i
$776$	−6.91261	−	11.9730i	−0.248148	−	0.429805i
$777$		0			0
$778$	−28.2496	−	16.3099i	−1.01280	−	0.584739i
$779$	−58.6410			−2.10103
$780$		0			0
$781$	−34.9949			−1.25222
$782$	3.38298	+	1.95317i	0.120975	+	0.0698451i
$783$		0			0
$784$	7.28643	+	12.6205i	0.260230	+	0.450731i
$785$			1.50311i			0.0536484i
$786$		0			0
$787$	−4.10169	+	2.36811i	−0.146210	+	0.0844142i	−0.571320	−	0.820727i	$-0.693569\pi$
$787$	−4.10169	+	2.36811i	−0.146210	+	0.0844142i	0.425111	+	0.905141i	$0.360235\pi$
$788$		−	9.18056i		−	0.327044i
$789$		0			0
$790$	7.46699	−	12.9332i	0.265664	−	0.460143i
$791$	52.5572	+	30.3439i	1.86872	+	1.07891i
$792$		0			0
$793$	3.97081	+	26.6176i	0.141008	+	0.945220i
$794$	−14.4683			−0.513462
$795$		0			0
$796$	8.10876	−	14.0448i	0.287407	−	0.497804i
$797$	20.5318	+	35.5621i	0.727274	+	1.25968i	0.958031	+	0.286664i	$0.0925463\pi$
$797$	20.5318	+	35.5621i	0.727274	+	1.25968i	−0.230757	+	0.973011i	$0.574120\pi$
$798$		0			0
$799$	33.7868	−	19.5068i	1.19529	−	0.690102i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−3.64364	−	6.31096i	−0.128661	−	0.222848i
$803$	9.59473	−	16.6186i	0.338591	−	0.586456i
$804$		0			0
$805$	−4.53590			−0.159869
$806$	18.1777	−	14.4513i	0.640284	−	0.509027i
$807$		0			0
$808$	−5.88919	−	3.40013i	−0.207181	−	0.119616i
$809$	−13.8003	+	23.9027i	−0.485191	+	0.840376i	−0.999855	−	0.0170163i	$-0.994583\pi$
$809$	−13.8003	+	23.9027i	−0.485191	+	0.840376i	0.514664	+	0.857392i	$0.327917\pi$
$810$		0			0
$811$		−	10.6930i		−	0.375482i	−0.982219	−	0.187741i	$-0.939883\pi$
$811$		−	10.6930i		−	0.375482i	0.982219	−	0.187741i	$-0.0601165\pi$
$812$	−17.3475	+	10.0156i	−0.608779	+	0.351478i
$813$		0			0
$814$			16.7030i			0.585440i
$815$	0.0881650	+	0.152706i	0.00308828	+	0.00534907i
$816$		0			0
$817$	−4.99154	−	2.88187i	−0.174632	−	0.100824i
$818$	24.5766			0.859300
$819$		0			0
$820$	7.28932			0.254554
$821$	−15.2105	−	8.78177i	−0.530849	−	0.306486i	0.210513	−	0.977591i	$-0.432487\pi$
$821$	−15.2105	−	8.78177i	−0.530849	−	0.306486i	−0.741362	+	0.671105i	$0.765820\pi$
$822$		0			0
$823$	−19.3565	−	33.5264i	−0.674725	−	1.16866i	−0.976549	−	0.215295i	$-0.930929\pi$
$823$	−19.3565	−	33.5264i	−0.674725	−	1.16866i	0.301824	−	0.953364i	$-0.402404\pi$
$824$			5.29137i			0.184333i
$825$		0			0
$826$	−8.77106	+	5.06397i	−0.305184	+	0.176198i
$827$			28.4703i			0.990010i	0.868890	+	0.495005i	$0.164834\pi$
$827$			28.4703i			0.990010i	−0.868890	+	0.495005i	$0.835166\pi$
$828$		0			0
$829$	4.14354	−	7.17683i	0.143911	−	0.249262i	−0.785055	−	0.619426i	$-0.787365\pi$
$829$	4.14354	−	7.17683i	0.143911	−	0.249262i	0.928966	+	0.370165i	$0.120699\pi$
$830$	−3.04056	−	1.75547i	−0.105539	−	0.0609332i
$831$		0			0
$832$	3.35432	+	1.32233i	0.116290	+	0.0458435i
$833$	−58.2915			−2.01968
$834$		0			0
$835$	−4.34081	+	7.51851i	−0.150220	+	0.260189i
$836$	17.6990	+	30.6556i	0.612134	+	1.06025i
$837$		0			0
$838$	−13.4699	+	7.77684i	−0.465309	+	0.268646i
$839$	36.8606	−	21.2815i	1.27257	−	0.734719i	0.297099	−	0.954847i	$-0.403981\pi$
$839$	36.8606	−	21.2815i	1.27257	−	0.734719i	0.975471	+	0.220128i	$0.0706474\pi$
$840$		0			0
$841$	5.20016	+	9.00693i	0.179316	+	0.310584i
$842$	11.1571	−	19.3247i	0.384500	−	0.665974i
$843$		0			0
$844$	1.61970			0.0557522
$845$	8.87103	−	9.50289i	0.305173	−	0.326909i
$846$		0			0
$847$	33.6317	+	19.4173i	1.15560	+	0.667185i
$848$	6.75444	−	11.6990i	0.231949	−	0.401747i
$849$		0			0
$850$		−	4.00000i		−	0.137199i
$851$	3.21047	−	1.85357i	0.110054	−	0.0635395i
$852$		0			0
$853$		−	28.1380i		−	0.963425i	−0.876329	−	0.481713i	$-0.840015\pi$
$853$		−	28.1380i		−	0.963425i	0.876329	−	0.481713i	$-0.159985\pi$
$854$	17.3341	+	30.0236i	0.593161	+	1.02738i
$855$		0			0
$856$	−14.6603	−	8.46410i	−0.501077	−	0.289297i
$857$	10.3355			0.353053			0.176526	−	0.984296i	$-0.443514\pi$
$857$	10.3355			0.353053			0.176526	+	0.984296i	$0.443514\pi$
$858$		0			0
$859$	0.380304			0.0129758			0.00648791	−	0.999979i	$-0.497935\pi$
$859$	0.380304			0.0129758			0.00648791	+	0.999979i	$0.497935\pi$
$860$	0.620469	+	0.358228i	0.0211578	+	0.0122155i
$861$		0			0
$862$	12.1322	+	21.0135i	0.413224	+	0.715724i
$863$			47.1484i			1.60495i	0.596685	+	0.802475i	$0.296484\pi$
$863$			47.1484i			1.60495i	−0.596685	+	0.802475i	$0.703516\pi$
$864$		0			0
$865$	−1.54190	+	0.890216i	−0.0524261	+	0.0302682i
$866$			23.0989i			0.784932i
$867$		0			0
$868$	14.9574	−	25.9070i	0.507687	−	0.879340i
$869$	56.9077	+	32.8557i	1.93046	+	1.11455i
$870$		0			0
$871$	4.09535	+	5.15137i	0.138766	+	0.174547i
$872$	−12.8003			−0.433471
$873$		0			0
$874$	3.92820	−	6.80385i	0.132873	−	0.230144i
$875$	2.32233	+	4.02239i	0.0785091	+	0.135982i
$876$		0			0
$877$	34.6767	−	20.0206i	1.17095	−	0.676047i	0.217045	−	0.976162i	$-0.430358\pi$
$877$	34.6767	−	20.0206i	1.17095	−	0.676047i	0.953903	+	0.300114i	$0.0970247\pi$
$878$	34.6375	−	19.9980i	1.16896	−	0.674898i
$879$		0			0
$880$	−2.20006	−	3.81062i	−0.0741641	−	0.128456i
$881$	7.72246	−	13.3757i	0.260176	−	0.450638i	−0.706112	−	0.708100i	$-0.749553\pi$
$881$	7.72246	−	13.3757i	0.260176	−	0.450638i	0.966289	+	0.257461i	$0.0828860\pi$
$882$		0			0
$883$	−6.02142			−0.202637			−0.101318	−	0.994854i	$-0.532306\pi$
$883$	−6.02142			−0.202637			−0.101318	+	0.994854i	$0.532306\pi$
$884$	−11.2893	+	8.97504i	−0.379701	+	0.301863i
$885$		0			0
$886$	−13.5131	−	7.80180i	−0.453982	−	0.262107i
$887$	−24.5690	+	42.5548i	−0.824947	+	1.42885i	0.0770129	+	0.997030i	$0.475462\pi$
$887$	−24.5690	+	42.5548i	−0.824947	+	1.42885i	−0.901960	+	0.431820i	$0.857872\pi$
$888$		0			0
$889$		−	56.7557i		−	1.90353i
$890$	7.07780	−	4.08637i	0.237248	−	0.136975i
$891$		0			0
$892$			2.23671i			0.0748906i
$893$	−39.2321	−	67.9520i	−1.31285	−	2.27393i
$894$		0			0
$895$	−15.0825	−	8.70786i	−0.504151	−	0.291072i
$896$	4.64466			0.155167
$897$		0			0
$898$	27.0042			0.901141
$899$	24.0556	+	13.8885i	0.802298	+	0.463207i
$900$		0			0
$901$	27.0178	+	46.7962i	0.900093	+	1.55901i
$902$			32.0739i			1.06795i
$903$		0			0
$904$	11.3156	−	6.53308i	0.376352	−	0.217287i
$905$			10.3611i			0.344415i
$906$		0			0
$907$	8.18345	−	14.1741i	0.271727	−	0.470645i	−0.697577	−	0.716510i	$-0.745739\pi$
$907$	8.18345	−	14.1741i	0.271727	−	0.470645i	0.969304	+	0.245865i	$0.0790719\pi$
$908$	13.2679	+	7.66025i	0.440312	+	0.254214i
$909$		0			0
$910$	6.14177	−	15.5797i	0.203598	−	0.516461i
$911$	10.4819			0.347280			0.173640	−	0.984809i	$-0.444447\pi$
$911$	10.4819			0.347280			0.173640	+	0.984809i	$0.444447\pi$
$912$		0			0
$913$	7.72428	−	13.3788i	0.255636	−	0.442775i
$914$	−8.89342	−	15.4039i	−0.294168	−	0.509514i
$915$		0			0
$916$	−8.77106	+	5.06397i	−0.289804	+	0.167318i
$917$	1.52351	−	0.879598i	0.0503107	−	0.0290469i
$918$		0			0
$919$	−1.60565	−	2.78107i	−0.0529655	−	0.0917389i	0.838327	−	0.545168i	$-0.183534\pi$
$919$	−1.60565	−	2.78107i	−0.0529655	−	0.0917389i	−0.891293	+	0.453429i	$0.850201\pi$
$920$	−0.488292	+	0.845746i	−0.0160985	+	0.0278834i
$921$		0			0
$922$	24.9652			0.822184
$923$	−28.3617	+	4.23098i	−0.933537	+	0.139265i
$924$		0			0
$925$	−3.28745	−	1.89801i	−0.108091	−	0.0624063i
$926$	−7.81944	+	13.5437i	−0.256963	+	0.445073i
$927$		0			0
$928$			4.31274i			0.141572i
$929$	−40.2518	+	23.2394i	−1.32062	+	0.762460i	−0.983827	−	0.179120i	$-0.942675\pi$
$929$	−40.2518	+	23.2394i	−1.32062	+	0.762460i	−0.336792	+	0.941579i	$0.609342\pi$
$930$		0			0
$931$			117.236i			3.84224i
$932$	−10.3759	−	17.9716i	−0.339875	−	0.588681i
$933$		0			0
$934$	−2.11236	−	1.21957i	−0.0691184	−	0.0399055i
$935$	17.6005			0.575598
$936$		0			0
$937$	−27.7627			−0.906969			−0.453485	−	0.891264i	$-0.649819\pi$
$937$	−27.7627			−0.906969			−0.453485	+	0.891264i	$0.649819\pi$
$938$	7.34174	+	4.23876i	0.239716	+	0.138400i
$939$		0			0
$940$	4.87671	+	8.44671i	0.159061	+	0.275501i
$941$		−	20.7962i		−	0.677935i	−0.940798	−	0.338968i	$-0.889922\pi$
$941$		−	20.7962i		−	0.677935i	0.940798	−	0.338968i	$-0.110078\pi$
$942$		0			0
$943$	6.16491	−	3.55931i	0.200757	−	0.115907i
$944$			2.18056i			0.0709711i
$945$		0			0
$946$	−1.57625	+	2.73014i	−0.0512483	+	0.0887646i
$947$	−7.84554	−	4.52962i	−0.254946	−	0.147193i	0.367081	−	0.930189i	$-0.380357\pi$
$947$	−7.84554	−	4.52962i	−0.254946	−	0.147193i	−0.622027	+	0.782996i	$0.713691\pi$
$948$		0			0
$949$	5.76683	−	14.6286i	0.187199	−	0.474863i
$950$	−8.04479			−0.261007
$951$		0			0
$952$	−9.28932	+	16.0896i	−0.301069	+	0.521466i
$953$	7.63811	+	13.2296i	0.247423	+	0.428549i	0.962810	−	0.270180i	$-0.0870831\pi$
$953$	7.63811	+	13.2296i	0.247423	+	0.428549i	−0.715387	+	0.698728i	$0.753750\pi$
$954$		0			0
$955$	−0.776837	+	0.448507i	−0.0251379	+	0.0145134i
$956$	21.0911	−	12.1770i	0.682136	−	0.393831i
$957$		0			0
$958$	7.09317	+	12.2857i	0.229170	+	0.396934i
$959$	2.90838	−	5.03746i	0.0939165	−	0.162668i
$960$		0			0
$961$	−10.4824			−0.338143
$962$	2.01944	+	13.5370i	0.0651093	+	0.436449i
$963$		0			0
$964$	−17.2066	−	9.93423i	−0.554187	−	0.319960i
$965$	10.1322	−	17.5494i	0.326166	−	0.564937i
$966$		0			0
$967$		−	46.3036i		−	1.48902i	−0.667610	−	0.744511i	$-0.732683\pi$
$967$		−	46.3036i		−	1.48902i	0.667610	−	0.744511i	$-0.267317\pi$
$968$	7.24094	−	4.18056i	0.232733	−	0.134368i
$969$		0			0
$970$			13.8252i			0.443901i
$971$	5.98258	+	10.3621i	0.191990	+	0.332537i	0.945910	−	0.324430i	$-0.105172\pi$
$971$	5.98258	+	10.3621i	0.191990	+	0.332537i	−0.753919	+	0.656967i	$0.771839\pi$
$972$		0			0
$973$	−13.4965	−	7.79221i	−0.432678	−	0.249807i
$974$	−5.76329			−0.184668
$975$		0			0
$976$	7.46410			0.238920
$977$	−1.52780	−	0.882077i	−0.0488787	−	0.0282201i	0.475362	−	0.879791i	$-0.342317\pi$
$977$	−1.52780	−	0.882077i	−0.0488787	−	0.0282201i	−0.524240	+	0.851570i	$0.675651\pi$
$978$		0			0
$979$	17.9805	+	31.1432i	0.574660	+	0.995341i
$980$		−	14.5729i		−	0.465513i
$981$		0			0
$982$	−0.931273	+	0.537671i	−0.0297181	+	0.0171578i
$983$			54.2821i			1.73133i	0.500623	+	0.865666i	$0.333104\pi$
$983$			54.2821i			1.73133i	−0.500623	+	0.865666i	$0.666896\pi$
$984$		0			0
$985$	−4.59028	+	7.95060i	−0.146258	+	0.253327i
$986$	−14.9398	−	8.62547i	−0.475779	−	0.274691i
$987$		0			0
$988$	18.0506	+	22.7050i	0.574265	+	0.722344i
$989$	0.699680			0.0222485
$990$		0			0
$991$	8.73917	−	15.1367i	0.277609	−	0.480833i	−0.693181	−	0.720763i	$-0.743791\pi$
$991$	8.73917	−	15.1367i	0.277609	−	0.480833i	0.970790	+	0.239931i	$0.0771248\pi$
$992$	−3.22034	−	5.57780i	−0.102246	−	0.177095i
$993$		0			0
$994$	−31.9908	+	18.4699i	−1.01469	+	0.585829i
$995$	−14.0448	+	8.10876i	−0.445250	+	0.257065i
$996$		0			0
$997$	10.6457	+	18.4389i	0.337152	+	0.583965i	0.983896	−	0.178743i	$-0.0572030\pi$
$997$	10.6457	+	18.4389i	0.337152	+	0.583965i	−0.646744	+	0.762707i	$0.723870\pi$
$998$	−7.37671	+	12.7768i	−0.233506	+	0.404444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.f.901.2		8
3.2	odd	2		390.2.bb.c.121.4	✓	8
13.10	even	6	inner	1170.2.bs.f.361.2		8
15.2	even	4		1950.2.y.j.199.4		8
15.8	even	4		1950.2.y.k.199.1		8
15.14	odd	2		1950.2.bc.g.901.1		8
39.17	odd	6		5070.2.b.ba.1351.5		8
39.20	even	12		5070.2.a.ca.1.4		4
39.23	odd	6		390.2.bb.c.361.4	yes	8
39.32	even	12		5070.2.a.bz.1.1		4
39.35	odd	6		5070.2.b.ba.1351.4		8
195.23	even	12		1950.2.y.j.49.4		8
195.62	even	12		1950.2.y.k.49.1		8
195.179	odd	6		1950.2.bc.g.751.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.4	✓	8	3.2	odd	2
390.2.bb.c.361.4	yes	8	39.23	odd	6
1170.2.bs.f.361.2		8	13.10	even	6	inner
1170.2.bs.f.901.2		8	1.1	even	1	trivial
1950.2.y.j.49.4		8	195.23	even	12
1950.2.y.j.199.4		8	15.2	even	4
1950.2.y.k.49.1		8	195.62	even	12
1950.2.y.k.199.1		8	15.8	even	4
1950.2.bc.g.751.1		8	195.179	odd	6
1950.2.bc.g.901.1		8	15.14	odd	2
5070.2.a.bz.1.1		4	39.32	even	12
5070.2.a.ca.1.4		4	39.20	even	12
5070.2.b.ba.1351.4		8	39.35	odd	6
5070.2.b.ba.1351.5		8	39.17	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(4.02239 - 2.32233i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(4.02239 - 2.32233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(-3.81062 - 2.20006i) q^{11} +(-3.35432 - 1.32233i) q^{13} -4.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-6.96699 + 4.02239i) q^{19} +(0.866025 - 0.500000i) q^{20} +(2.20006 + 3.81062i) q^{22} +(0.488292 - 0.845746i) q^{23} -1.00000 q^{25} +(2.24376 + 2.82233i) q^{26} +(4.02239 + 2.32233i) q^{28} +(-2.15637 + 3.73494i) q^{29} -6.44069i q^{31} +(0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(-2.32233 - 4.02239i) q^{35} +(3.28745 + 1.89801i) q^{37} +8.04479 q^{38} -1.00000 q^{40} +(6.31274 + 3.64466i) q^{41} +(0.358228 + 0.620469i) q^{43} -4.40013i q^{44} +(-0.845746 + 0.488292i) q^{46} +9.75342i q^{47} +(7.28643 - 12.6205i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-0.531987 - 3.56609i) q^{52} -13.5089 q^{53} +(-2.20006 + 3.81062i) q^{55} +(-2.32233 - 4.02239i) q^{56} +(3.73494 - 2.15637i) q^{58} +(1.88842 - 1.09028i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(-3.22034 + 5.57780i) q^{62} -1.00000 q^{64} +(-1.32233 + 3.35432i) q^{65} +(-1.58068 - 0.912609i) q^{67} +(2.00000 - 3.46410i) q^{68} +4.64466i q^{70} +(6.88764 - 3.97658i) q^{71} +4.36112i q^{73} +(-1.89801 - 3.28745i) q^{74} +(-6.96699 - 4.02239i) q^{76} -20.4371 q^{77} -14.9340 q^{79} +(0.866025 + 0.500000i) q^{80} +(-3.64466 - 6.31274i) q^{82} +3.51093i q^{83} +(-3.46410 + 2.00000i) q^{85} -0.716456i q^{86} +(-2.20006 + 3.81062i) q^{88} +(-7.07780 - 4.08637i) q^{89} +(-16.5633 + 2.47090i) q^{91} +0.976584 q^{92} +(4.87671 - 8.44671i) q^{94} +(4.02239 + 6.96699i) q^{95} +(11.9730 - 6.91261i) q^{97} +(-12.6205 + 7.28643i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 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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