LMFDB - Embedded newform 1170.2.bs.d.361.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.d.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-0.232051 + 0.133975i) q^{11} +(0.866025 - 3.50000i) q^{13} -3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(4.96410 + 2.86603i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.133975 - 0.232051i) q^{22} +(1.73205 + 3.00000i) q^{23} -1.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +(2.59808 - 1.50000i) q^{28} +(0.732051 + 1.26795i) q^{29} -4.92820i q^{31} +(0.866025 + 0.500000i) q^{32} +4.00000i q^{34} +(-1.50000 + 2.59808i) q^{35} +(-5.13397 + 2.96410i) q^{37} -5.73205 q^{38} -1.00000 q^{40} +(3.46410 - 2.00000i) q^{41} +(-3.00000 + 5.19615i) q^{43} +0.267949i q^{44} +(-3.00000 - 1.73205i) q^{46} -6.46410i q^{47} +(1.00000 + 1.73205i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-2.59808 - 2.50000i) q^{52} +0.267949 q^{53} +(-0.133975 - 0.232051i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(-1.26795 - 0.732051i) q^{58} +(9.92820 + 5.73205i) q^{59} +(0.267949 - 0.464102i) q^{61} +(2.46410 + 4.26795i) q^{62} -1.00000 q^{64} +(3.50000 + 0.866025i) q^{65} +(1.26795 - 0.732051i) q^{67} +(-2.00000 - 3.46410i) q^{68} -3.00000i q^{70} +(11.1962 + 6.46410i) q^{71} +6.92820i q^{73} +(2.96410 - 5.13397i) q^{74} +(4.96410 - 2.86603i) q^{76} -0.803848 q^{77} +3.07180 q^{79} +(0.866025 - 0.500000i) q^{80} +(-2.00000 + 3.46410i) q^{82} +9.46410i q^{83} +(3.46410 + 2.00000i) q^{85} -6.00000i q^{86} +(-0.133975 - 0.232051i) q^{88} +(12.2321 - 7.06218i) q^{89} +(7.50000 - 7.79423i) q^{91} +3.46410 q^{92} +(3.23205 + 5.59808i) q^{94} +(-2.86603 + 4.96410i) q^{95} +(7.26795 + 4.19615i) q^{97} +(-1.73205 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} - 2 q^{10} + 6 q^{11} - 12 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 4 q^{22} - 4 q^{25} + 4 q^{26} - 4 q^{29} - 6 q^{35} - 24 q^{37} - 16 q^{38} - 4 q^{40} - 12 q^{43} - 12 q^{46} + 4 q^{49} + 8 q^{53} - 4 q^{55} - 6 q^{56} - 12 q^{58} + 12 q^{59} + 8 q^{61} - 4 q^{62} - 4 q^{64} + 14 q^{65} + 12 q^{67} - 8 q^{68} + 24 q^{71} - 2 q^{74} + 6 q^{76} - 24 q^{77} + 40 q^{79} - 8 q^{82} - 4 q^{88} + 42 q^{89} + 30 q^{91} + 6 q^{94} - 8 q^{95} + 36 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 + 6 * q^11 - 12 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 4 * q^22 - 4 * q^25 + 4 * q^26 - 4 * q^29 - 6 * q^35 - 24 * q^37 - 16 * q^38 - 4 * q^40 - 12 * q^43 - 12 * q^46 + 4 * q^49 + 8 * q^53 - 4 * q^55 - 6 * q^56 - 12 * q^58 + 12 * q^59 + 8 * q^61 - 4 * q^62 - 4 * q^64 + 14 * q^65 + 12 * q^67 - 8 * q^68 + 24 * q^71 - 2 * q^74 + 6 * q^76 - 24 * q^77 + 40 * q^79 - 8 * q^82 - 4 * q^88 + 42 * q^89 + 30 * q^91 + 6 * q^94 - 8 * q^95 + 36 * q^97

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
$7$	2.59808	+	1.50000i	0.981981	+	0.566947i	0.902867	−	0.429919i	$-0.141458\pi$
$7$	2.59808	+	1.50000i	0.981981	+	0.566947i	0.0791130	+	0.996866i	$0.474791\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.232051	+	0.133975i	−0.0699660	+	0.0403949i	−0.534575	−	0.845121i	$-0.679528\pi$
$11$	−0.232051	+	0.133975i	−0.0699660	+	0.0403949i	0.464609	+	0.885516i	$0.346195\pi$
$12$		0			0
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$14$	−3.00000			−0.801784
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	4.96410	+	2.86603i	1.13884	+	0.657511i	0.946144	−	0.323747i	$-0.104943\pi$
$19$	4.96410	+	2.86603i	1.13884	+	0.657511i	0.192699	+	0.981258i	$0.438276\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		0			0
$22$	0.133975	−	0.232051i	0.0285635	−	0.0494734i
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$		0			0
$28$	2.59808	−	1.50000i	0.490990	−	0.283473i
$29$	0.732051	+	1.26795i	0.135938	+	0.235452i	0.925956	−	0.377633i	$-0.123262\pi$
$29$	0.732051	+	1.26795i	0.135938	+	0.235452i	−0.790017	+	0.613085i	$0.789928\pi$
$30$		0			0
$31$		−	4.92820i		−	0.885131i	−0.896736	−	0.442566i	$-0.854068\pi$
$31$		−	4.92820i		−	0.885131i	0.896736	−	0.442566i	$-0.145932\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			4.00000i			0.685994i
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$		0			0
$37$	−5.13397	+	2.96410i	−0.844020	+	0.487295i	−0.858629	−	0.512598i	$-0.828683\pi$
$37$	−5.13397	+	2.96410i	−0.844020	+	0.487295i	0.0146085	+	0.999893i	$0.495350\pi$
$38$	−5.73205			−0.929861
$39$		0			0
$40$	−1.00000			−0.158114
$41$	3.46410	−	2.00000i	0.541002	−	0.312348i	−0.204483	−	0.978870i	$-0.565551\pi$
$41$	3.46410	−	2.00000i	0.541002	−	0.312348i	0.745485	+	0.666523i	$0.232218\pi$
$42$		0			0
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$			0.267949i			0.0403949i
$45$		0			0
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$		−	6.46410i		−	0.942886i	−0.881897	−	0.471443i	$-0.843733\pi$
$47$		−	6.46410i		−	0.942886i	0.881897	−	0.471443i	$-0.156267\pi$
$48$		0			0
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		0			0
$52$	−2.59808	−	2.50000i	−0.360288	−	0.346688i
$53$	0.267949			0.0368057			0.0184028	−	0.999831i	$-0.494142\pi$
$53$	0.267949			0.0368057			0.0184028	+	0.999831i	$0.494142\pi$
$54$		0			0
$55$	−0.133975	−	0.232051i	−0.0180651	−	0.0312897i
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$		0			0
$58$	−1.26795	−	0.732051i	−0.166490	−	0.0961230i
$59$	9.92820	+	5.73205i	1.29254	+	0.746249i	0.979104	−	0.203359i	$-0.0651859\pi$
$59$	9.92820	+	5.73205i	1.29254	+	0.746249i	0.313438	+	0.949609i	$0.398519\pi$
$60$		0			0
$61$	0.267949	−	0.464102i	0.0343074	−	0.0594221i	−0.848362	−	0.529417i	$-0.822411\pi$
$61$	0.267949	−	0.464102i	0.0343074	−	0.0594221i	0.882669	+	0.469995i	$0.155744\pi$
$62$	2.46410	+	4.26795i	0.312941	+	0.542030i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.50000	+	0.866025i	0.434122	+	0.107417i
$66$		0			0
$67$	1.26795	−	0.732051i	0.154905	−	0.0894342i	−0.420544	−	0.907272i	$-0.638161\pi$
$67$	1.26795	−	0.732051i	0.154905	−	0.0894342i	0.575449	+	0.817838i	$0.304827\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$		0			0
$70$		−	3.00000i		−	0.358569i
$71$	11.1962	+	6.46410i	1.32874	+	0.767148i	0.985105	−	0.171956i	$-0.0550086\pi$
$71$	11.1962	+	6.46410i	1.32874	+	0.767148i	0.343634	+	0.939104i	$0.388342\pi$
$72$		0			0
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	2.96410	−	5.13397i	0.344570	−	0.596812i
$75$		0			0
$76$	4.96410	−	2.86603i	0.569422	−	0.328756i
$77$	−0.803848			−0.0916069
$78$		0			0
$79$	3.07180			0.345604			0.172802	−	0.984957i	$-0.444718\pi$
$79$	3.07180			0.345604			0.172802	+	0.984957i	$0.444718\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$		0			0
$82$	−2.00000	+	3.46410i	−0.220863	+	0.382546i
$83$			9.46410i			1.03882i	0.854525	+	0.519410i	$0.173848\pi$
$83$			9.46410i			1.03882i	−0.854525	+	0.519410i	$0.826152\pi$
$84$		0			0
$85$	3.46410	+	2.00000i	0.375735	+	0.216930i
$86$		−	6.00000i		−	0.646997i
$87$		0			0
$88$	−0.133975	−	0.232051i	−0.0142817	−	0.0247367i
$89$	12.2321	−	7.06218i	1.29659	−	0.748589i	0.316780	−	0.948499i	$-0.397398\pi$
$89$	12.2321	−	7.06218i	1.29659	−	0.748589i	0.979814	+	0.199910i	$0.0640648\pi$
$90$		0			0
$91$	7.50000	−	7.79423i	0.786214	−	0.817057i
$92$	3.46410			0.361158
$93$		0			0
$94$	3.23205	+	5.59808i	0.333361	+	0.577397i
$95$	−2.86603	+	4.96410i	−0.294048	+	0.509306i
$96$		0			0
$97$	7.26795	+	4.19615i	0.737948	+	0.426055i	0.821323	−	0.570464i	$-0.193236\pi$
$97$	7.26795	+	4.19615i	0.737948	+	0.426055i	−0.0833745	+	0.996518i	$0.526570\pi$
$98$	−1.73205	−	1.00000i	−0.174964	−	0.101015i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.19615	+	10.7321i	0.616540	+	1.06788i	0.990112	+	0.140278i	$0.0447996\pi$
$101$	6.19615	+	10.7321i	0.616540	+	1.06788i	−0.373572	+	0.927601i	$0.621867\pi$
$102$		0			0
$103$	−11.5885			−1.14184			−0.570922	−	0.821004i	$-0.693414\pi$
$103$	−11.5885			−1.14184			−0.570922	+	0.821004i	$0.693414\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$		0			0
$106$	−0.232051	+	0.133975i	−0.0225388	+	0.0130128i
$107$	−6.46410	−	11.1962i	−0.624908	−	1.08237i	−0.988559	−	0.150837i	$-0.951803\pi$
$107$	−6.46410	−	11.1962i	−0.624908	−	1.08237i	0.363650	−	0.931536i	$-0.381530\pi$
$108$		0			0
$109$			10.3923i			0.995402i	0.867349	+	0.497701i	$0.165822\pi$
$109$			10.3923i			0.995402i	−0.867349	+	0.497701i	$0.834178\pi$
$110$	0.232051	+	0.133975i	0.0221252	+	0.0127740i
$111$		0			0
$112$		−	3.00000i		−	0.283473i
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	0.432670	+	0.901553i	$0.357572\pi$
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	−0.997102	+	0.0760733i	$0.975762\pi$
$114$		0			0
$115$	−3.00000	+	1.73205i	−0.279751	+	0.161515i
$116$	1.46410			0.135938
$117$		0			0
$118$	−11.4641			−1.05536
$119$	10.3923	−	6.00000i	0.952661	−	0.550019i
$120$		0			0
$121$	−5.46410	+	9.46410i	−0.496737	+	0.860373i
$122$			0.535898i			0.0485180i
$123$		0			0
$124$	−4.26795	−	2.46410i	−0.383273	−	0.221283i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	6.33013	+	10.9641i	0.561708	+	0.972907i	0.997348	+	0.0727855i	$0.0231889\pi$
$127$	6.33013	+	10.9641i	0.561708	+	0.972907i	−0.435640	+	0.900121i	$0.643478\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−3.46410	+	1.00000i	−0.303822	+	0.0877058i
$131$	−14.3205			−1.25119			−0.625594	−	0.780149i	$-0.715143\pi$
$131$	−14.3205			−1.25119			−0.625594	+	0.780149i	$0.715143\pi$
$132$		0			0
$133$	8.59808	+	14.8923i	0.745548	+	1.29133i
$134$	−0.732051	+	1.26795i	−0.0632396	+	0.109534i
$135$		0			0
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	−11.6603	−	6.73205i	−0.996203	−	0.575158i	−0.0890802	−	0.996024i	$-0.528393\pi$
$137$	−11.6603	−	6.73205i	−0.996203	−	0.575158i	−0.907123	+	0.420867i	$0.861726\pi$
$138$		0			0
$139$	9.89230	−	17.1340i	0.839054	−	1.45328i	−0.0516319	−	0.998666i	$-0.516442\pi$
$139$	9.89230	−	17.1340i	0.839054	−	1.45328i	0.890686	−	0.454619i	$-0.150224\pi$
$140$	1.50000	+	2.59808i	0.126773	+	0.219578i
$141$		0			0
$142$	−12.9282			−1.08491
$143$	0.267949	+	0.928203i	0.0224070	+	0.0776203i
$144$		0			0
$145$	−1.26795	+	0.732051i	−0.105297	+	0.0607935i
$146$	−3.46410	−	6.00000i	−0.286691	−	0.496564i
$147$		0			0
$148$			5.92820i			0.487295i
$149$	−16.2679	−	9.39230i	−1.33272	−	0.769448i	−0.347006	−	0.937863i	$-0.612802\pi$
$149$	−16.2679	−	9.39230i	−1.33272	−	0.769448i	−0.985716	+	0.168415i	$0.946135\pi$
$150$		0			0
$151$		−	22.7846i		−	1.85419i	−0.374832	−	0.927093i	$-0.622300\pi$
$151$		−	22.7846i		−	1.85419i	0.374832	−	0.927093i	$-0.377700\pi$
$152$	−2.86603	+	4.96410i	−0.232465	+	0.402642i
$153$		0			0
$154$	0.696152	−	0.401924i	0.0560976	−	0.0323879i
$155$	4.92820			0.395843
$156$		0			0
$157$	21.1962			1.69164			0.845819	−	0.533471i	$-0.179113\pi$
$157$	21.1962			1.69164			0.845819	+	0.533471i	$0.179113\pi$
$158$	−2.66025	+	1.53590i	−0.211638	+	0.122190i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$			10.3923i			0.819028i
$162$		0			0
$163$	−2.53590	−	1.46410i	−0.198627	−	0.114677i	0.397388	−	0.917651i	$-0.369917\pi$
$163$	−2.53590	−	1.46410i	−0.198627	−	0.114677i	−0.596015	+	0.802973i	$0.703250\pi$
$164$		−	4.00000i		−	0.312348i
$165$		0			0
$166$	−4.73205	−	8.19615i	−0.367278	−	0.636145i
$167$	0.401924	−	0.232051i	0.0311018	−	0.0179566i	−0.484368	−	0.874864i	$-0.660951\pi$
$167$	0.401924	−	0.232051i	0.0311018	−	0.0179566i	0.515470	+	0.856907i	$0.327617\pi$
$168$		0			0
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	−1.06218	+	1.83975i	−0.0807559	+	0.139873i	−0.903575	−	0.428430i	$-0.859067\pi$
$173$	−1.06218	+	1.83975i	−0.0807559	+	0.139873i	0.822819	+	0.568304i	$0.192400\pi$
$174$		0			0
$175$	−2.59808	−	1.50000i	−0.196396	−	0.113389i
$176$	0.232051	+	0.133975i	0.0174915	+	0.0100987i
$177$		0			0
$178$	−7.06218	+	12.2321i	−0.529333	+	0.916831i
$179$	4.53590	+	7.85641i	0.339029	+	0.587215i	0.984250	−	0.176780i	$-0.0565682\pi$
$179$	4.53590	+	7.85641i	0.339029	+	0.587215i	−0.645221	+	0.763996i	$0.723235\pi$
$180$		0			0
$181$	16.9282			1.25826			0.629132	−	0.777299i	$-0.283411\pi$
$181$	16.9282			1.25826			0.629132	+	0.777299i	$0.283411\pi$
$182$	−2.59808	+	10.5000i	−0.192582	+	0.778312i
$183$		0			0
$184$	−3.00000	+	1.73205i	−0.221163	+	0.127688i
$185$	−2.96410	−	5.13397i	−0.217925	−	0.377457i
$186$		0			0
$187$			1.07180i			0.0783775i
$188$	−5.59808	−	3.23205i	−0.408282	−	0.235722i
$189$		0			0
$190$		−	5.73205i		−	0.415847i
$191$	−8.66025	+	15.0000i	−0.626634	+	1.08536i	0.361588	+	0.932338i	$0.382235\pi$
$191$	−8.66025	+	15.0000i	−0.626634	+	1.08536i	−0.988222	+	0.153024i	$0.951099\pi$
$192$		0			0
$193$	−8.53590	+	4.92820i	−0.614427	+	0.354740i	−0.774696	−	0.632334i	$-0.782097\pi$
$193$	−8.53590	+	4.92820i	−0.614427	+	0.354740i	0.160269	+	0.987073i	$0.448764\pi$
$194$	−8.39230			−0.602532
$195$		0			0
$196$	2.00000			0.142857
$197$	9.86603	−	5.69615i	0.702925	−	0.405834i	−0.105511	−	0.994418i	$-0.533648\pi$
$197$	9.86603	−	5.69615i	0.702925	−	0.405834i	0.808436	+	0.588584i	$0.200314\pi$
$198$		0			0
$199$	12.4641	−	21.5885i	0.883557	−	1.53037i	0.0361978	−	0.999345i	$-0.488475\pi$
$199$	12.4641	−	21.5885i	0.883557	−	1.53037i	0.847359	−	0.531021i	$-0.178191\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	−10.7321	−	6.19615i	−0.755104	−	0.435960i
$203$			4.39230i			0.308279i
$204$		0			0
$205$	2.00000	+	3.46410i	0.139686	+	0.241943i
$206$	10.0359	−	5.79423i	0.699234	−	0.403703i
$207$		0			0
$208$	−3.46410	+	1.00000i	−0.240192	+	0.0693375i
$209$	−1.53590			−0.106240
$210$		0			0
$211$	4.03590	+	6.99038i	0.277843	+	0.481238i	0.970848	−	0.239694i	$-0.0770473\pi$
$211$	4.03590	+	6.99038i	0.277843	+	0.481238i	−0.693006	+	0.720932i	$0.743714\pi$
$212$	0.133975	−	0.232051i	0.00920141	−	0.0159373i
$213$		0			0
$214$	11.1962	+	6.46410i	0.765353	+	0.441877i
$215$	−5.19615	−	3.00000i	−0.354375	−	0.204598i
$216$		0			0
$217$	7.39230	−	12.8038i	0.501822	−	0.869182i
$218$	−5.19615	−	9.00000i	−0.351928	−	0.609557i
$219$		0			0
$220$	−0.267949			−0.0180651
$221$	−10.3923	−	10.0000i	−0.699062	−	0.672673i
$222$		0			0
$223$	−16.3301	+	9.42820i	−1.09355	+	0.631359i	−0.934518	−	0.355915i	$-0.884169\pi$
$223$	−16.3301	+	9.42820i	−1.09355	+	0.631359i	−0.159028	+	0.987274i	$0.550836\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$		0			0
$226$		−	12.0000i		−	0.798228i
$227$	−5.66025	−	3.26795i	−0.375684	−	0.216901i	0.300255	−	0.953859i	$-0.402928\pi$
$227$	−5.66025	−	3.26795i	−0.375684	−	0.216901i	−0.675939	+	0.736958i	$0.736262\pi$
$228$		0			0
$229$		−	4.53590i		−	0.299741i	−0.988706	−	0.149870i	$-0.952114\pi$
$229$		−	4.53590i		−	0.299741i	0.988706	−	0.149870i	$-0.0478856\pi$
$230$	1.73205	−	3.00000i	0.114208	−	0.197814i
$231$		0			0
$232$	−1.26795	+	0.732051i	−0.0832449	+	0.0480615i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	6.46410			0.421671
$236$	9.92820	−	5.73205i	0.646271	−	0.373125i
$237$		0			0
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$		−	3.46410i		−	0.224074i	−0.993704	−	0.112037i	$-0.964262\pi$
$239$		−	3.46410i		−	0.224074i	0.993704	−	0.112037i	$-0.0357375\pi$
$240$		0			0
$241$	−21.8205	−	12.5981i	−1.40558	−	0.811513i	−0.410624	−	0.911805i	$-0.634689\pi$
$241$	−21.8205	−	12.5981i	−1.40558	−	0.811513i	−0.994958	+	0.100291i	$0.968023\pi$
$242$		−	10.9282i		−	0.702492i
$243$		0			0
$244$	−0.267949	−	0.464102i	−0.0171537	−	0.0297111i
$245$	−1.73205	+	1.00000i	−0.110657	+	0.0638877i
$246$		0			0
$247$	14.3301	−	14.8923i	0.911804	−	0.947575i
$248$	4.92820			0.312941
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	9.76795	−	16.9186i	0.616547	−	1.06789i	−0.373563	−	0.927605i	$-0.621864\pi$
$251$	9.76795	−	16.9186i	0.616547	−	1.06789i	0.990111	−	0.140287i	$-0.0448025\pi$
$252$		0			0
$253$	−0.803848	−	0.464102i	−0.0505375	−	0.0291778i
$254$	−10.9641	−	6.33013i	−0.687949	−	0.397187i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.26795	+	12.5885i	0.453362	+	0.785246i	0.998592	−	0.0530400i	$-0.0168911\pi$
$257$	7.26795	+	12.5885i	0.453362	+	0.785246i	−0.545230	+	0.838286i	$0.683558\pi$
$258$		0			0
$259$	−17.7846			−1.10508
$260$	2.50000	−	2.59808i	0.155043	−	0.161126i
$261$		0			0
$262$	12.4019	−	7.16025i	0.766193	−	0.442362i
$263$	−12.2583	−	21.2321i	−0.755881	−	1.30922i	−0.944935	−	0.327258i	$-0.893875\pi$
$263$	−12.2583	−	21.2321i	−0.755881	−	1.30922i	0.189054	−	0.981967i	$-0.439458\pi$
$264$		0			0
$265$			0.267949i			0.0164600i
$266$	−14.8923	−	8.59808i	−0.913106	−	0.527182i
$267$		0			0
$268$		−	1.46410i		−	0.0894342i
$269$	−8.53590	+	14.7846i	−0.520443	+	0.901434i	0.479275	+	0.877665i	$0.340900\pi$
$269$	−8.53590	+	14.7846i	−0.520443	+	0.901434i	−0.999717	+	0.0237685i	$0.992434\pi$
$270$		0			0
$271$	21.1244	−	12.1962i	1.28321	−	0.740863i	0.305779	−	0.952103i	$-0.401083\pi$
$271$	21.1244	−	12.1962i	1.28321	−	0.740863i	0.977434	+	0.211239i	$0.0677499\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	13.4641			0.813396
$275$	0.232051	−	0.133975i	0.0139932	−	0.00807897i
$276$		0			0
$277$	−5.79423	+	10.0359i	−0.348141	+	0.602999i	−0.985919	−	0.167222i	$-0.946520\pi$
$277$	−5.79423	+	10.0359i	−0.348141	+	0.602999i	0.637778	+	0.770220i	$0.279854\pi$
$278$			19.7846i			1.18660i
$279$		0			0
$280$	−2.59808	−	1.50000i	−0.155265	−	0.0896421i
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$		0			0
$283$	3.19615	+	5.53590i	0.189992	+	0.329075i	0.945247	−	0.326355i	$-0.105821\pi$
$283$	3.19615	+	5.53590i	0.189992	+	0.329075i	−0.755256	+	0.655430i	$0.772487\pi$
$284$	11.1962	−	6.46410i	0.664369	−	0.383574i
$285$		0			0
$286$	−0.696152	−	0.669873i	−0.0411644	−	0.0396104i
$287$	12.0000			0.708338
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	0.732051	−	1.26795i	0.0429875	−	0.0744565i
$291$		0			0
$292$	6.00000	+	3.46410i	0.351123	+	0.202721i
$293$	−25.3301	−	14.6244i	−1.47980	−	0.854364i	−0.480063	−	0.877234i	$-0.659386\pi$
$293$	−25.3301	−	14.6244i	−1.47980	−	0.854364i	−0.999738	+	0.0228698i	$0.992720\pi$
$294$		0			0
$295$	−5.73205	+	9.92820i	−0.333733	+	0.578042i
$296$	−2.96410	−	5.13397i	−0.172285	−	0.298406i
$297$		0			0
$298$	18.7846			1.08816
$299$	12.0000	−	3.46410i	0.693978	−	0.200334i
$300$		0			0
$301$	−15.5885	+	9.00000i	−0.898504	+	0.518751i
$302$	11.3923	+	19.7321i	0.655553	+	1.13545i
$303$		0			0
$304$		−	5.73205i		−	0.328756i
$305$	0.464102	+	0.267949i	0.0265744	+	0.0153427i
$306$		0			0
$307$		−	28.2487i		−	1.61224i	−0.591753	−	0.806120i	$-0.701564\pi$
$307$		−	28.2487i		−	1.61224i	0.591753	−	0.806120i	$-0.298436\pi$
$308$	−0.401924	+	0.696152i	−0.0229017	+	0.0396670i
$309$		0			0
$310$	−4.26795	+	2.46410i	−0.242403	+	0.139952i
$311$	−18.9282			−1.07332			−0.536660	−	0.843799i	$-0.680314\pi$
$311$	−18.9282			−1.07332			−0.536660	+	0.843799i	$0.680314\pi$
$312$		0			0
$313$	−33.3205			−1.88339			−0.941693	−	0.336473i	$-0.890766\pi$
$313$	−33.3205			−1.88339			−0.941693	+	0.336473i	$0.890766\pi$
$314$	−18.3564	+	10.5981i	−1.03591	+	0.598084i
$315$		0			0
$316$	1.53590	−	2.66025i	0.0864010	−	0.149651i
$317$		−	30.4641i		−	1.71103i	−0.517774	−	0.855517i	$-0.673239\pi$
$317$		−	30.4641i		−	1.71103i	0.517774	−	0.855517i	$-0.326761\pi$
$318$		0			0
$319$	−0.339746	−	0.196152i	−0.0190221	−	0.0109824i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	−5.19615	−	9.00000i	−0.289570	−	0.501550i
$323$	19.8564	−	11.4641i	1.10484	−	0.637880i
$324$		0			0
$325$	−0.866025	+	3.50000i	−0.0480384	+	0.194145i
$326$	2.92820			0.162178
$327$		0			0
$328$	2.00000	+	3.46410i	0.110432	+	0.191273i
$329$	9.69615	−	16.7942i	0.534566	−	0.925896i
$330$		0			0
$331$	12.4641	+	7.19615i	0.685089	+	0.395536i	0.801770	−	0.597633i	$-0.203892\pi$
$331$	12.4641	+	7.19615i	0.685089	+	0.395536i	−0.116681	+	0.993169i	$0.537225\pi$
$332$	8.19615	+	4.73205i	0.449822	+	0.259705i
$333$		0			0
$334$	−0.232051	+	0.401924i	−0.0126973	+	0.0219923i
$335$	0.732051	+	1.26795i	0.0399962	+	0.0692755i
$336$		0			0
$337$	−26.3923			−1.43768			−0.718840	−	0.695175i	$-0.755327\pi$
$337$	−26.3923			−1.43768			−0.718840	+	0.695175i	$0.755327\pi$
$338$	12.9904	−	0.500000i	0.706584	−	0.0271964i
$339$		0			0
$340$	3.46410	−	2.00000i	0.187867	−	0.108465i
$341$	0.660254	+	1.14359i	0.0357548	+	0.0619291i
$342$		0			0
$343$		−	15.0000i		−	0.809924i
$344$	−5.19615	−	3.00000i	−0.280158	−	0.161749i
$345$		0			0
$346$		−	2.12436i		−	0.114206i
$347$	2.19615	−	3.80385i	0.117896	−	0.204201i	−0.801038	−	0.598614i	$-0.795719\pi$
$347$	2.19615	−	3.80385i	0.117896	−	0.204201i	0.918934	+	0.394412i	$0.129052\pi$
$348$		0			0
$349$	−9.12436	+	5.26795i	−0.488416	+	0.281987i	−0.723917	−	0.689887i	$-0.757660\pi$
$349$	−9.12436	+	5.26795i	−0.488416	+	0.281987i	0.235501	+	0.971874i	$0.424327\pi$
$350$	3.00000			0.160357
$351$		0			0
$352$	−0.267949			−0.0142817
$353$	−6.58846	+	3.80385i	−0.350668	+	0.202458i	−0.664980	−	0.746862i	$-0.731560\pi$
$353$	−6.58846	+	3.80385i	−0.350668	+	0.202458i	0.314311	+	0.949320i	$0.398226\pi$
$354$		0			0
$355$	−6.46410	+	11.1962i	−0.343079	+	0.594230i
$356$		−	14.1244i		−	0.748589i
$357$		0			0
$358$	−7.85641	−	4.53590i	−0.415224	−	0.239730i
$359$		−	0.928203i		−	0.0489887i	−0.999700	−	0.0244943i	$-0.992202\pi$
$359$		−	0.928203i		−	0.0489887i	0.999700	−	0.0244943i	$-0.00779757\pi$
$360$		0			0
$361$	6.92820	+	12.0000i	0.364642	+	0.631579i
$362$	−14.6603	+	8.46410i	−0.770526	+	0.444863i
$363$		0			0
$364$	−3.00000	−	10.3923i	−0.157243	−	0.544705i
$365$	−6.92820			−0.362639
$366$		0			0
$367$	−10.6603	−	18.4641i	−0.556461	−	0.963818i	−0.997788	−	0.0664722i	$-0.978826\pi$
$367$	−10.6603	−	18.4641i	−0.556461	−	0.963818i	0.441328	−	0.897346i	$-0.354508\pi$
$368$	1.73205	−	3.00000i	0.0902894	−	0.156386i
$369$		0			0
$370$	5.13397	+	2.96410i	0.266903	+	0.154096i
$371$	0.696152	+	0.401924i	0.0361424	+	0.0208668i
$372$		0			0
$373$	−4.53590	+	7.85641i	−0.234860	+	0.406789i	−0.959232	−	0.282620i	$-0.908796\pi$
$373$	−4.53590	+	7.85641i	−0.234860	+	0.406789i	0.724372	+	0.689409i	$0.242130\pi$
$374$	−0.535898	−	0.928203i	−0.0277106	−	0.0479962i
$375$		0			0
$376$	6.46410			0.333361
$377$	5.07180	−	1.46410i	0.261211	−	0.0754051i
$378$		0			0
$379$	−8.42820	+	4.86603i	−0.432928	+	0.249951i	−0.700593	−	0.713561i	$-0.747081\pi$
$379$	−8.42820	+	4.86603i	−0.432928	+	0.249951i	0.267665	+	0.963512i	$0.413748\pi$
$380$	2.86603	+	4.96410i	0.147024	+	0.254653i
$381$		0			0
$382$		−	17.3205i		−	0.886194i
$383$	−4.14359	−	2.39230i	−0.211728	−	0.122241i	0.390386	−	0.920651i	$-0.372341\pi$
$383$	−4.14359	−	2.39230i	−0.211728	−	0.122241i	−0.602114	+	0.798410i	$0.705675\pi$
$384$		0			0
$385$		−	0.803848i		−	0.0409679i
$386$	4.92820	−	8.53590i	0.250839	−	0.434466i
$387$		0			0
$388$	7.26795	−	4.19615i	0.368974	−	0.213027i
$389$	−17.8564			−0.905356			−0.452678	−	0.891674i	$-0.649531\pi$
$389$	−17.8564			−0.905356			−0.452678	+	0.891674i	$0.649531\pi$
$390$		0			0
$391$	13.8564			0.700749
$392$	−1.73205	+	1.00000i	−0.0874818	+	0.0505076i
$393$		0			0
$394$	−5.69615	+	9.86603i	−0.286968	+	0.497043i
$395$			3.07180i			0.154559i
$396$		0			0
$397$	−5.13397	−	2.96410i	−0.257667	−	0.148764i	0.365603	−	0.930771i	$-0.380863\pi$
$397$	−5.13397	−	2.96410i	−0.257667	−	0.148764i	−0.623270	+	0.782007i	$0.714196\pi$
$398$			24.9282i			1.24954i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	19.1603	−	11.0622i	0.956817	−	0.552419i	0.0616254	−	0.998099i	$-0.480372\pi$
$401$	19.1603	−	11.0622i	0.956817	−	0.552419i	0.895192	+	0.445681i	$0.147038\pi$
$402$		0			0
$403$	−17.2487	−	4.26795i	−0.859220	−	0.212602i
$404$	12.3923			0.616540
$405$		0			0
$406$	−2.19615	−	3.80385i	−0.108993	−	0.188782i
$407$	0.794229	−	1.37564i	0.0393685	−	0.0681882i
$408$		0			0
$409$	−33.8205	−	19.5263i	−1.67232	−	0.965512i	−0.966337	−	0.257280i	$-0.917174\pi$
$409$	−33.8205	−	19.5263i	−1.67232	−	0.965512i	−0.705980	−	0.708232i	$-0.749493\pi$
$410$	−3.46410	−	2.00000i	−0.171080	−	0.0987730i
$411$		0			0
$412$	−5.79423	+	10.0359i	−0.285461	+	0.494433i
$413$	17.1962	+	29.7846i	0.846167	+	1.46560i
$414$		0			0
$415$	−9.46410			−0.464574
$416$	2.50000	−	2.59808i	0.122573	−	0.127381i
$417$		0			0
$418$	1.33013	−	0.767949i	0.0650586	−	0.0375616i
$419$	4.92820	+	8.53590i	0.240758	+	0.417006i	0.960931	−	0.276790i	$-0.0892705\pi$
$419$	4.92820	+	8.53590i	0.240758	+	0.417006i	−0.720172	+	0.693795i	$0.755937\pi$
$420$		0			0
$421$			21.8564i			1.06522i	0.846362	+	0.532608i	$0.178788\pi$
$421$			21.8564i			1.06522i	−0.846362	+	0.532608i	$0.821212\pi$
$422$	−6.99038	−	4.03590i	−0.340286	−	0.196464i
$423$		0			0
$424$			0.267949i			0.0130128i
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$		0			0
$427$	1.39230	−	0.803848i	0.0673784	−	0.0389009i
$428$	−12.9282			−0.624908
$429$		0			0
$430$	6.00000			0.289346
$431$	12.0000	−	6.92820i	0.578020	−	0.333720i	−0.182326	−	0.983238i	$-0.558363\pi$
$431$	12.0000	−	6.92820i	0.578020	−	0.333720i	0.760346	+	0.649518i	$0.225029\pi$
$432$		0			0
$433$	4.39230	−	7.60770i	0.211081	−	0.365602i	−0.740972	−	0.671536i	$-0.765635\pi$
$433$	4.39230	−	7.60770i	0.211081	−	0.365602i	0.952053	+	0.305933i	$0.0989684\pi$
$434$			14.7846i			0.709684i
$435$		0			0
$436$	9.00000	+	5.19615i	0.431022	+	0.248851i
$437$			19.8564i			0.949861i
$438$		0			0
$439$	6.66025	+	11.5359i	0.317877	+	0.550578i	0.980045	−	0.198777i	$-0.0636969\pi$
$439$	6.66025	+	11.5359i	0.317877	+	0.550578i	−0.662168	+	0.749355i	$0.730364\pi$
$440$	0.232051	−	0.133975i	0.0110626	−	0.00638699i
$441$		0			0
$442$	14.0000	+	3.46410i	0.665912	+	0.164771i
$443$	19.8564			0.943406			0.471703	−	0.881757i	$-0.343639\pi$
$443$	19.8564			0.943406			0.471703	+	0.881757i	$0.343639\pi$
$444$		0			0
$445$	7.06218	+	12.2321i	0.334779	+	0.579855i
$446$	9.42820	−	16.3301i	0.446438	−	0.773254i
$447$		0			0
$448$	−2.59808	−	1.50000i	−0.122748	−	0.0708683i
$449$	5.30385	+	3.06218i	0.250304	+	0.144513i	0.619903	−	0.784678i	$-0.287172\pi$
$449$	5.30385	+	3.06218i	0.250304	+	0.144513i	−0.369599	+	0.929191i	$0.620505\pi$
$450$		0			0
$451$	−0.535898	+	0.928203i	−0.0252345	+	0.0437074i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$		0			0
$454$	6.53590			0.306745
$455$	7.79423	+	7.50000i	0.365399	+	0.351605i
$456$		0			0
$457$	−6.46410	+	3.73205i	−0.302378	+	0.174578i	−0.643511	−	0.765437i	$-0.722523\pi$
$457$	−6.46410	+	3.73205i	−0.302378	+	0.174578i	0.341133	+	0.940015i	$0.389189\pi$
$458$	2.26795	+	3.92820i	0.105974	+	0.183553i
$459$		0			0
$460$			3.46410i			0.161515i
$461$	10.0526	+	5.80385i	0.468194	+	0.270312i	0.715484	−	0.698630i	$-0.246206\pi$
$461$	10.0526	+	5.80385i	0.468194	+	0.270312i	−0.247289	+	0.968942i	$0.579540\pi$
$462$		0			0
$463$		−	40.7846i		−	1.89542i	−0.319131	−	0.947711i	$-0.603391\pi$
$463$		−	40.7846i		−	1.89542i	0.319131	−	0.947711i	$-0.396609\pi$
$464$	0.732051	−	1.26795i	0.0339846	−	0.0588631i
$465$		0			0
$466$	15.5885	−	9.00000i	0.722121	−	0.416917i
$467$	−24.3923			−1.12874			−0.564371	−	0.825522i	$-0.690881\pi$
$467$	−24.3923			−1.12874			−0.564371	+	0.825522i	$0.690881\pi$
$468$		0			0
$469$	4.39230			0.202818
$470$	−5.59808	+	3.23205i	−0.258220	+	0.149083i
$471$		0			0
$472$	−5.73205	+	9.92820i	−0.263839	+	0.456983i
$473$		−	1.60770i		−	0.0739219i
$474$		0			0
$475$	−4.96410	−	2.86603i	−0.227769	−	0.131502i
$476$		−	12.0000i		−	0.550019i
$477$		0			0
$478$	1.73205	+	3.00000i	0.0792222	+	0.137217i
$479$	19.2679	−	11.1244i	0.880375	−	0.508285i	0.00959301	−	0.999954i	$-0.496946\pi$
$479$	19.2679	−	11.1244i	0.880375	−	0.508285i	0.870782	+	0.491669i	$0.163613\pi$
$480$		0			0
$481$	5.92820	+	20.5359i	0.270303	+	0.936356i
$482$	25.1962			1.14765
$483$		0			0
$484$	5.46410	+	9.46410i	0.248368	+	0.430186i
$485$	−4.19615	+	7.26795i	−0.190537	+	0.330021i
$486$		0			0
$487$	18.1865	+	10.5000i	0.824110	+	0.475800i	0.851832	−	0.523815i	$-0.175492\pi$
$487$	18.1865	+	10.5000i	0.824110	+	0.475800i	−0.0277214	+	0.999616i	$0.508825\pi$
$488$	0.464102	+	0.267949i	0.0210089	+	0.0121295i
$489$		0			0
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	2.69615	+	4.66987i	0.121676	+	0.210748i	0.920429	−	0.390911i	$-0.127840\pi$
$491$	2.69615	+	4.66987i	0.121676	+	0.210748i	−0.798753	+	0.601659i	$0.794507\pi$
$492$		0			0
$493$	5.85641			0.263759
$494$	−4.96410	+	20.0622i	−0.223345	+	0.902640i
$495$		0			0
$496$	−4.26795	+	2.46410i	−0.191637	+	0.110641i
$497$	19.3923	+	33.5885i	0.869864	+	1.50665i
$498$		0			0
$499$			33.3205i			1.49163i	0.666153	+	0.745815i	$0.267940\pi$
$499$			33.3205i			1.49163i	−0.666153	+	0.745815i	$0.732060\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$		0			0
$502$			19.5359i			0.871930i
$503$	1.86603	−	3.23205i	0.0832020	−	0.144110i	−0.821422	−	0.570321i	$-0.806819\pi$
$503$	1.86603	−	3.23205i	0.0832020	−	0.144110i	0.904624	+	0.426211i	$0.140152\pi$
$504$		0			0
$505$	−10.7321	+	6.19615i	−0.477570	+	0.275725i
$506$	0.928203			0.0412637
$507$		0			0
$508$	12.6603			0.561708
$509$	−25.3923	+	14.6603i	−1.12549	+	0.649804i	−0.942798	−	0.333365i	$-0.891816\pi$
$509$	−25.3923	+	14.6603i	−1.12549	+	0.649804i	−0.182696	+	0.983169i	$0.558483\pi$
$510$		0			0
$511$	−10.3923	+	18.0000i	−0.459728	+	0.796273i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−12.5885	−	7.26795i	−0.555253	−	0.320575i
$515$		−	11.5885i		−	0.510648i
$516$		0			0
$517$	0.866025	+	1.50000i	0.0380878	+	0.0659699i
$518$	15.4019	−	8.89230i	0.676722	−	0.390705i
$519$		0			0
$520$	−0.866025	+	3.50000i	−0.0379777	+	0.153485i
$521$	6.60770			0.289488			0.144744	−	0.989469i	$-0.453764\pi$
$521$	6.60770			0.289488			0.144744	+	0.989469i	$0.453764\pi$
$522$		0			0
$523$	20.8564	+	36.1244i	0.911987	+	1.57961i	0.811254	+	0.584694i	$0.198786\pi$
$523$	20.8564	+	36.1244i	0.911987	+	1.57961i	0.100733	+	0.994913i	$0.467881\pi$
$524$	−7.16025	+	12.4019i	−0.312797	+	0.541781i
$525$		0			0
$526$	21.2321	+	12.2583i	0.925761	+	0.534489i
$527$	−17.0718	−	9.85641i	−0.743659	−	0.429352i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	−0.133975	−	0.232051i	−0.00581948	−	0.0100796i
$531$		0			0
$532$	17.1962			0.745548
$533$	−4.00000	−	13.8564i	−0.173259	−	0.600188i
$534$		0			0
$535$	11.1962	−	6.46410i	0.484052	−	0.279467i
$536$	0.732051	+	1.26795i	0.0316198	+	0.0547671i
$537$		0			0
$538$		−	17.0718i		−	0.736017i
$539$	−0.464102	−	0.267949i	−0.0199903	−	0.0115414i
$540$		0			0
$541$			14.7846i			0.635640i	0.948151	+	0.317820i	$0.102951\pi$
$541$			14.7846i			0.635640i	−0.948151	+	0.317820i	$0.897049\pi$
$542$	−12.1962	+	21.1244i	−0.523870	+	0.907369i
$543$		0			0
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$	−10.3923			−0.445157
$546$		0			0
$547$	−5.32051			−0.227488			−0.113744	−	0.993510i	$-0.536284\pi$
$547$	−5.32051			−0.227488			−0.113744	+	0.993510i	$0.536284\pi$
$548$	−11.6603	+	6.73205i	−0.498101	+	0.287579i
$549$		0			0
$550$	−0.133975	+	0.232051i	−0.00571270	+	0.00989468i
$551$			8.39230i			0.357524i
$552$		0			0
$553$	7.98076	+	4.60770i	0.339377	+	0.195939i
$554$		−	11.5885i		−	0.492346i
$555$		0			0
$556$	−9.89230	−	17.1340i	−0.419527	−	0.726642i
$557$	19.5788	−	11.3038i	0.829582	−	0.478959i	−0.0241275	−	0.999709i	$-0.507681\pi$
$557$	19.5788	−	11.3038i	0.829582	−	0.478959i	0.853710	+	0.520749i	$0.174347\pi$
$558$		0			0
$559$	15.5885	+	15.0000i	0.659321	+	0.634432i
$560$	3.00000			0.126773
$561$		0			0
$562$	3.46410	+	6.00000i	0.146124	+	0.253095i
$563$	−7.66025	+	13.2679i	−0.322841	+	0.559177i	−0.981073	−	0.193638i	$-0.937971\pi$
$563$	−7.66025	+	13.2679i	−0.322841	+	0.559177i	0.658232	+	0.752815i	$0.271305\pi$
$564$		0			0
$565$	−10.3923	−	6.00000i	−0.437208	−	0.252422i
$566$	−5.53590	−	3.19615i	−0.232691	−	0.134344i
$567$		0			0
$568$	−6.46410	+	11.1962i	−0.271228	+	0.469780i
$569$	−8.16025	−	14.1340i	−0.342096	−	0.592527i	0.642726	−	0.766096i	$-0.277803\pi$
$569$	−8.16025	−	14.1340i	−0.342096	−	0.592527i	−0.984822	+	0.173569i	$0.944470\pi$
$570$		0			0
$571$	10.8564			0.454326			0.227163	−	0.973857i	$-0.427055\pi$
$571$	10.8564			0.454326			0.227163	+	0.973857i	$0.427055\pi$
$572$	0.937822	+	0.232051i	0.0392123	+	0.00970253i
$573$		0			0
$574$	−10.3923	+	6.00000i	−0.433766	+	0.250435i
$575$	−1.73205	−	3.00000i	−0.0722315	−	0.125109i
$576$		0			0
$577$		−	9.32051i		−	0.388018i	−0.981000	−	0.194009i	$-0.937851\pi$
$577$		−	9.32051i		−	0.388018i	0.981000	−	0.194009i	$-0.0621491\pi$
$578$	−0.866025	−	0.500000i	−0.0360219	−	0.0207973i
$579$		0			0
$580$			1.46410i			0.0607935i
$581$	−14.1962	+	24.5885i	−0.588956	+	1.02010i
$582$		0			0
$583$	−0.0621778	+	0.0358984i	−0.00257514	+	0.00148676i
$584$	−6.92820			−0.286691
$585$		0			0
$586$	29.2487			1.20825
$587$	7.73205	−	4.46410i	0.319136	−	0.184253i	−0.331871	−	0.943325i	$-0.607680\pi$
$587$	7.73205	−	4.46410i	0.319136	−	0.184253i	0.651007	+	0.759071i	$0.274347\pi$
$588$		0			0
$589$	14.1244	−	24.4641i	0.581984	−	1.00803i
$590$		−	11.4641i		−	0.471970i
$591$		0			0
$592$	5.13397	+	2.96410i	0.211005	+	0.121824i
$593$			44.7846i			1.83908i	0.392992	+	0.919542i	$0.371440\pi$
$593$			44.7846i			1.83908i	−0.392992	+	0.919542i	$0.628560\pi$
$594$		0			0
$595$	6.00000	+	10.3923i	0.245976	+	0.426043i
$596$	−16.2679	+	9.39230i	−0.666361	+	0.384724i
$597$		0			0
$598$	−8.66025	+	9.00000i	−0.354144	+	0.368037i
$599$	−28.9282			−1.18197			−0.590987	−	0.806681i	$-0.701262\pi$
$599$	−28.9282			−1.18197			−0.590987	+	0.806681i	$0.701262\pi$
$600$		0			0
$601$	−15.3564	−	26.5981i	−0.626401	−	1.08496i	−0.988268	−	0.152729i	$-0.951194\pi$
$601$	−15.3564	−	26.5981i	−0.626401	−	1.08496i	0.361867	−	0.932230i	$-0.382139\pi$
$602$	9.00000	−	15.5885i	0.366813	−	0.635338i
$603$		0			0
$604$	−19.7321	−	11.3923i	−0.802886	−	0.463546i
$605$	−9.46410	−	5.46410i	−0.384770	−	0.222147i
$606$		0			0
$607$	10.7224	−	18.5718i	0.435210	−	0.753806i	−0.562103	−	0.827067i	$-0.690007\pi$
$607$	10.7224	−	18.5718i	0.435210	−	0.753806i	0.997313	+	0.0732615i	$0.0233408\pi$
$608$	2.86603	+	4.96410i	0.116233	+	0.201321i
$609$		0			0
$610$	−0.535898			−0.0216979
$611$	−22.6244	−	5.59808i	−0.915283	−	0.226474i
$612$		0			0
$613$	38.9711	−	22.5000i	1.57403	−	0.908766i	0.578362	−	0.815780i	$-0.303692\pi$
$613$	38.9711	−	22.5000i	1.57403	−	0.908766i	0.995667	−	0.0929864i	$-0.0296413\pi$
$614$	14.1244	+	24.4641i	0.570013	+	0.987291i
$615$		0			0
$616$		−	0.803848i		−	0.0323879i
$617$	30.7128	+	17.7321i	1.23645	+	0.713865i	0.968367	−	0.249530i	$-0.0802761\pi$
$617$	30.7128	+	17.7321i	1.23645	+	0.713865i	0.268084	+	0.963395i	$0.413609\pi$
$618$		0			0
$619$			2.51666i			0.101153i	0.998720	+	0.0505766i	$0.0161059\pi$
$619$			2.51666i			0.101153i	−0.998720	+	0.0505766i	$0.983894\pi$
$620$	2.46410	−	4.26795i	0.0989607	−	0.171405i
$621$		0			0
$622$	16.3923	−	9.46410i	0.657272	−	0.379476i
$623$	42.3731			1.69764
$624$		0			0
$625$	1.00000			0.0400000
$626$	28.8564	−	16.6603i	1.15333	−	0.665878i
$627$		0			0
$628$	10.5981	−	18.3564i	0.422909	−	0.732500i
$629$			23.7128i			0.945492i
$630$		0			0
$631$	−6.92820	−	4.00000i	−0.275807	−	0.159237i	0.355716	−	0.934594i	$-0.384237\pi$
$631$	−6.92820	−	4.00000i	−0.275807	−	0.159237i	−0.631524	+	0.775356i	$0.717570\pi$
$632$			3.07180i			0.122190i
$633$		0			0
$634$	15.2321	+	26.3827i	0.604942	+	1.04779i
$635$	−10.9641	+	6.33013i	−0.435097	+	0.251203i
$636$		0			0
$637$	6.92820	−	2.00000i	0.274505	−	0.0792429i
$638$	0.392305			0.0155315
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	7.23205	−	12.5263i	0.285649	−	0.494758i	−0.687117	−	0.726546i	$-0.741124\pi$
$641$	7.23205	−	12.5263i	0.285649	−	0.494758i	0.972766	+	0.231788i	$0.0744576\pi$
$642$		0			0
$643$	11.0718	+	6.39230i	0.436629	+	0.252088i	0.702167	−	0.712013i	$-0.252216\pi$
$643$	11.0718	+	6.39230i	0.436629	+	0.252088i	−0.265538	+	0.964100i	$0.585549\pi$
$644$	9.00000	+	5.19615i	0.354650	+	0.204757i
$645$		0			0
$646$	−11.4641	+	19.8564i	−0.451049	+	0.781240i
$647$	−17.8660	−	30.9449i	−0.702386	−	1.21657i	−0.967627	−	0.252386i	$-0.918785\pi$
$647$	−17.8660	−	30.9449i	−0.702386	−	1.21657i	0.265241	−	0.964182i	$-0.414549\pi$
$648$		0			0
$649$	−3.07180			−0.120579
$650$	−1.00000	−	3.46410i	−0.0392232	−	0.135873i
$651$		0			0
$652$	−2.53590	+	1.46410i	−0.0993134	+	0.0573386i
$653$	−0.794229	−	1.37564i	−0.0310806	−	0.0538331i	0.850067	−	0.526675i	$-0.176562\pi$
$653$	−0.794229	−	1.37564i	−0.0310806	−	0.0538331i	−0.881147	+	0.472842i	$0.843228\pi$
$654$		0			0
$655$		−	14.3205i		−	0.559549i
$656$	−3.46410	−	2.00000i	−0.135250	−	0.0780869i
$657$		0			0
$658$			19.3923i			0.755991i
$659$	−19.8564	+	34.3923i	−0.773496	+	1.33973i	0.162140	+	0.986768i	$0.448160\pi$
$659$	−19.8564	+	34.3923i	−0.773496	+	1.33973i	−0.935636	+	0.352966i	$0.885173\pi$
$660$		0			0
$661$	−18.7128	+	10.8038i	−0.727844	+	0.420221i	−0.817633	−	0.575740i	$-0.804714\pi$
$661$	−18.7128	+	10.8038i	−0.727844	+	0.420221i	0.0897889	+	0.995961i	$0.471381\pi$
$662$	−14.3923			−0.559373
$663$		0			0
$664$	−9.46410			−0.367278
$665$	−14.8923	+	8.59808i	−0.577499	+	0.333419i
$666$		0			0
$667$	−2.53590	+	4.39230i	−0.0981904	+	0.170071i
$668$		−	0.464102i		−	0.0179566i
$669$		0			0
$670$	−1.26795	−	0.732051i	−0.0489852	−	0.0282816i
$671$			0.143594i			0.00554337i
$672$		0			0
$673$	8.39230	+	14.5359i	0.323500	+	0.560318i	0.981208	−	0.192955i	$-0.0618072\pi$
$673$	8.39230	+	14.5359i	0.323500	+	0.560318i	−0.657708	+	0.753273i	$0.728474\pi$
$674$	22.8564	−	13.1962i	0.880396	−	0.508297i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	−10.9282			−0.420005			−0.210002	−	0.977701i	$-0.567347\pi$
$677$	−10.9282			−0.420005			−0.210002	+	0.977701i	$0.567347\pi$
$678$		0			0
$679$	12.5885	+	21.8038i	0.483101	+	0.836755i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$		0			0
$682$	−1.14359	−	0.660254i	−0.0437905	−	0.0252824i
$683$	−35.7846	−	20.6603i	−1.36926	−	0.790543i	−0.378427	−	0.925631i	$-0.623535\pi$
$683$	−35.7846	−	20.6603i	−1.36926	−	0.790543i	−0.990834	+	0.135089i	$0.956868\pi$
$684$		0			0
$685$	6.73205	−	11.6603i	0.257218	−	0.445515i
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$		0			0
$688$	6.00000			0.228748
$689$	0.232051	−	0.937822i	0.00884043	−	0.0357282i
$690$		0			0
$691$	13.0359	−	7.52628i	0.495909	−	0.286313i	−0.231114	−	0.972927i	$-0.574237\pi$
$691$	13.0359	−	7.52628i	0.495909	−	0.286313i	0.727023	+	0.686614i	$0.240904\pi$
$692$	1.06218	+	1.83975i	0.0403779	+	0.0699366i
$693$		0			0
$694$			4.39230i			0.166730i
$695$	17.1340	+	9.89230i	0.649929	+	0.375237i
$696$		0			0
$697$		−	16.0000i		−	0.606043i
$698$	5.26795	−	9.12436i	0.199395	−	0.345362i
$699$		0			0
$700$	−2.59808	+	1.50000i	−0.0981981	+	0.0566947i
$701$	4.39230			0.165895			0.0829475	−	0.996554i	$-0.473567\pi$
$701$	4.39230			0.165895			0.0829475	+	0.996554i	$0.473567\pi$
$702$		0			0
$703$	−33.9808			−1.28161
$704$	0.232051	−	0.133975i	0.00874574	−	0.00504936i
$705$		0			0
$706$	3.80385	−	6.58846i	0.143160	−	0.247960i
$707$			37.1769i			1.39818i
$708$		0			0
$709$	−23.6603	−	13.6603i	−0.888579	−	0.513022i	−0.0151019	−	0.999886i	$-0.504807\pi$
$709$	−23.6603	−	13.6603i	−0.888579	−	0.513022i	−0.873478	+	0.486864i	$0.838141\pi$
$710$		−	12.9282i		−	0.485187i
$711$		0			0
$712$	7.06218	+	12.2321i	0.264666	+	0.458415i
$713$	14.7846	−	8.53590i	0.553688	−	0.319672i
$714$		0			0
$715$	−0.928203	+	0.267949i	−0.0347128	+	0.0100207i
$716$	9.07180			0.339029
$717$		0			0
$718$	0.464102	+	0.803848i	0.0173201	+	0.0299993i
$719$	8.00000	−	13.8564i	0.298350	−	0.516757i	−0.677409	−	0.735607i	$-0.736897\pi$
$719$	8.00000	−	13.8564i	0.298350	−	0.516757i	0.975759	+	0.218850i	$0.0702305\pi$
$720$		0			0
$721$	−30.1077	−	17.3827i	−1.12127	−	0.647365i
$722$	−12.0000	−	6.92820i	−0.446594	−	0.257841i
$723$		0			0
$724$	8.46410	−	14.6603i	0.314566	−	0.544844i
$725$	−0.732051	−	1.26795i	−0.0271877	−	0.0470905i
$726$		0			0
$727$	−4.66025			−0.172839			−0.0864196	−	0.996259i	$-0.527543\pi$
$727$	−4.66025			−0.172839			−0.0864196	+	0.996259i	$0.527543\pi$
$728$	7.79423	+	7.50000i	0.288873	+	0.277968i
$729$		0			0
$730$	6.00000	−	3.46410i	0.222070	−	0.128212i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$			20.8564i			0.770349i	0.922844	+	0.385174i	$0.125859\pi$
$733$			20.8564i			0.770349i	−0.922844	+	0.385174i	$0.874141\pi$
$734$	18.4641	+	10.6603i	0.681522	+	0.393477i
$735$		0			0
$736$			3.46410i			0.127688i
$737$	−0.196152	+	0.339746i	−0.00722537	+	0.0125147i
$738$		0			0
$739$	31.0359	−	17.9186i	1.14167	−	0.659146i	0.194829	−	0.980837i	$-0.437585\pi$
$739$	31.0359	−	17.9186i	1.14167	−	0.659146i	0.946845	+	0.321691i	$0.104251\pi$
$740$	−5.92820			−0.217925
$741$		0			0
$742$	−0.803848			−0.0295102
$743$	9.46410	−	5.46410i	0.347204	−	0.200458i	−0.316249	−	0.948676i	$-0.602424\pi$
$743$	9.46410	−	5.46410i	0.347204	−	0.200458i	0.663453	+	0.748218i	$0.269090\pi$
$744$		0			0
$745$	9.39230	−	16.2679i	0.344107	−	0.596012i
$746$		−	9.07180i		−	0.332142i
$747$		0			0
$748$	0.928203	+	0.535898i	0.0339385	+	0.0195944i
$749$		−	38.7846i		−	1.41716i
$750$		0			0
$751$	10.5885	+	18.3397i	0.386378	+	0.669227i	0.991959	−	0.126557i	$-0.0403926\pi$
$751$	10.5885	+	18.3397i	0.386378	+	0.669227i	−0.605581	+	0.795784i	$0.707059\pi$
$752$	−5.59808	+	3.23205i	−0.204141	+	0.117861i
$753$		0			0
$754$	−3.66025	+	3.80385i	−0.133299	+	0.138528i
$755$	22.7846			0.829217
$756$		0			0
$757$	−10.8660	−	18.8205i	−0.394932	−	0.684043i	0.598160	−	0.801377i	$-0.295899\pi$
$757$	−10.8660	−	18.8205i	−0.394932	−	0.684043i	−0.993093	+	0.117334i	$0.962565\pi$
$758$	4.86603	−	8.42820i	0.176742	−	0.306126i
$759$		0			0
$760$	−4.96410	−	2.86603i	−0.180067	−	0.103962i
$761$	−6.91154	−	3.99038i	−0.250543	−	0.144651i	0.369470	−	0.929243i	$-0.379539\pi$
$761$	−6.91154	−	3.99038i	−0.250543	−	0.144651i	−0.620013	+	0.784592i	$0.712873\pi$
$762$		0			0
$763$	−15.5885	+	27.0000i	−0.564340	+	0.977466i
$764$	8.66025	+	15.0000i	0.313317	+	0.542681i
$765$		0			0
$766$	4.78461			0.172875
$767$	28.6603	−	29.7846i	1.03486	−	1.07546i
$768$		0			0
$769$	13.6077	−	7.85641i	0.490706	−	0.283309i	−0.234161	−	0.972198i	$-0.575234\pi$
$769$	13.6077	−	7.85641i	0.490706	−	0.283309i	0.724867	+	0.688889i	$0.241901\pi$
$770$	0.401924	+	0.696152i	0.0144843	+	0.0250876i
$771$		0			0
$772$			9.85641i			0.354740i
$773$	28.2391	+	16.3038i	1.01569	+	0.586409i	0.912852	−	0.408290i	$-0.133875\pi$
$773$	28.2391	+	16.3038i	1.01569	+	0.586409i	0.102837	+	0.994698i	$0.467208\pi$
$774$		0			0
$775$			4.92820i			0.177026i
$776$	−4.19615	+	7.26795i	−0.150633	+	0.260904i
$777$		0			0
$778$	15.4641	−	8.92820i	0.554415	−	0.320092i
$779$	22.9282			0.821488
$780$		0			0
$781$	−3.46410			−0.123955
$782$	−12.0000	+	6.92820i	−0.429119	+	0.247752i
$783$		0			0
$784$	1.00000	−	1.73205i	0.0357143	−	0.0618590i
$785$			21.1962i			0.756523i
$786$		0			0
$787$	1.26795	+	0.732051i	0.0451975	+	0.0260948i	0.522428	−	0.852683i	$-0.325026\pi$
$787$	1.26795	+	0.732051i	0.0451975	+	0.0260948i	−0.477231	+	0.878778i	$0.658359\pi$
$788$		−	11.3923i		−	0.405834i
$789$		0			0
$790$	−1.53590	−	2.66025i	−0.0546448	−	0.0946476i
$791$	−31.1769	+	18.0000i	−1.10852	+	0.640006i
$792$		0			0
$793$	−1.39230	−	1.33975i	−0.0494422	−	0.0475758i
$794$	5.92820			0.210384
$795$		0			0
$796$	−12.4641	−	21.5885i	−0.441778	−	0.765183i
$797$	−5.07180	+	8.78461i	−0.179652	+	0.311167i	−0.941761	−	0.336282i	$-0.890831\pi$
$797$	−5.07180	+	8.78461i	−0.179652	+	0.311167i	0.762109	+	0.647449i	$0.224164\pi$
$798$		0			0
$799$	−22.3923	−	12.9282i	−0.792183	−	0.457367i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		0			0
$802$	−11.0622	+	19.1603i	−0.390619	+	0.676572i
$803$	−0.928203	−	1.60770i	−0.0327556	−	0.0567343i
$804$		0			0
$805$	−10.3923			−0.366281
$806$	17.0718	−	4.92820i	0.601328	−	0.173589i
$807$		0			0
$808$	−10.7321	+	6.19615i	−0.377552	+	0.217980i
$809$	−3.39230	−	5.87564i	−0.119267	−	0.206577i	0.800210	−	0.599719i	$-0.204721\pi$
$809$	−3.39230	−	5.87564i	−0.119267	−	0.206577i	−0.919477	+	0.393143i	$0.871388\pi$
$810$		0			0
$811$			23.5885i			0.828303i	0.910208	+	0.414151i	$0.135922\pi$
$811$			23.5885i			0.828303i	−0.910208	+	0.414151i	$0.864078\pi$
$812$	3.80385	+	2.19615i	0.133489	+	0.0770698i
$813$		0			0
$814$			1.58846i			0.0556754i
$815$	1.46410	−	2.53590i	0.0512852	−	0.0888286i
$816$		0			0
$817$	−29.7846	+	17.1962i	−1.04203	+	0.601617i
$818$	39.0526			1.36544
$819$		0			0
$820$	4.00000			0.139686
$821$	12.7128	−	7.33975i	0.443680	−	0.256159i	−0.261477	−	0.965210i	$-0.584210\pi$
$821$	12.7128	−	7.33975i	0.443680	−	0.256159i	0.705157	+	0.709051i	$0.250876\pi$
$822$		0			0
$823$	4.20577	−	7.28461i	0.146604	−	0.253926i	−0.783366	−	0.621560i	$-0.786499\pi$
$823$	4.20577	−	7.28461i	0.146604	−	0.253926i	0.929970	+	0.367635i	$0.119832\pi$
$824$		−	11.5885i		−	0.403703i
$825$		0			0
$826$	−29.7846	−	17.1962i	−1.03634	−	0.598331i
$827$		−	46.4974i		−	1.61687i	−0.588583	−	0.808437i	$-0.700314\pi$
$827$		−	46.4974i		−	1.61687i	0.588583	−	0.808437i	$-0.299686\pi$
$828$		0			0
$829$	2.33975	+	4.05256i	0.0812627	+	0.140751i	0.903793	−	0.427971i	$-0.140771\pi$
$829$	2.33975	+	4.05256i	0.0812627	+	0.140751i	−0.822530	+	0.568722i	$0.807438\pi$
$830$	8.19615	−	4.73205i	0.284493	−	0.164252i
$831$		0			0
$832$	−0.866025	+	3.50000i	−0.0300240	+	0.121341i
$833$	8.00000			0.277184
$834$		0			0
$835$	0.232051	+	0.401924i	0.00803045	+	0.0139091i
$836$	−0.767949	+	1.33013i	−0.0265601	+	0.0460034i
$837$		0			0
$838$	−8.53590	−	4.92820i	−0.294868	−	0.170242i
$839$	−16.6077	−	9.58846i	−0.573361	−	0.331030i	0.185129	−	0.982714i	$-0.440730\pi$
$839$	−16.6077	−	9.58846i	−0.573361	−	0.331030i	−0.758491	+	0.651684i	$0.774063\pi$
$840$		0			0
$841$	13.4282	−	23.2583i	0.463041	−	0.802011i
$842$	−10.9282	−	18.9282i	−0.376611	−	0.652309i
$843$		0			0
$844$	8.07180			0.277843
$845$	6.06218	−	11.5000i	0.208545	−	0.395612i
$846$		0			0
$847$	−28.3923	+	16.3923i	−0.975571	+	0.563246i
$848$	−0.133975	−	0.232051i	−0.00460071	−	0.00796866i
$849$		0			0
$850$		−	4.00000i		−	0.137199i
$851$	−17.7846	−	10.2679i	−0.609649	−	0.351981i
$852$		0			0
$853$		−	24.6410i		−	0.843692i	−0.906667	−	0.421846i	$-0.861382\pi$
$853$		−	24.6410i		−	0.843692i	0.906667	−	0.421846i	$-0.138618\pi$
$854$	−0.803848	+	1.39230i	−0.0275071	+	0.0476437i
$855$		0			0
$856$	11.1962	−	6.46410i	0.382677	−	0.220938i
$857$	28.9282			0.988169			0.494084	−	0.869414i	$-0.335503\pi$
$857$	28.9282			0.988169			0.494084	+	0.869414i	$0.335503\pi$
$858$		0			0
$859$	−6.07180			−0.207167			−0.103584	−	0.994621i	$-0.533031\pi$
$859$	−6.07180			−0.207167			−0.103584	+	0.994621i	$0.533031\pi$
$860$	−5.19615	+	3.00000i	−0.177187	+	0.102299i
$861$		0			0
$862$	−6.92820	+	12.0000i	−0.235976	+	0.408722i
$863$		−	2.92820i		−	0.0996772i	−0.998757	−	0.0498386i	$-0.984129\pi$
$863$		−	2.92820i		−	0.0996772i	0.998757	−	0.0498386i	$-0.0158707\pi$
$864$		0			0
$865$	−1.83975	−	1.06218i	−0.0625532	−	0.0361151i
$866$			8.78461i			0.298513i
$867$		0			0
$868$	−7.39230	−	12.8038i	−0.250911	−	0.434591i
$869$	−0.712813	+	0.411543i	−0.0241805	+	0.0139606i
$870$		0			0
$871$	−1.46410	−	5.07180i	−0.0496092	−	0.171851i
$872$	−10.3923			−0.351928
$873$		0			0
$874$	−9.92820	−	17.1962i	−0.335826	−	0.581669i
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$		0			0
$877$	18.8038	+	10.8564i	0.634961	+	0.366595i	0.782671	−	0.622436i	$-0.213857\pi$
$877$	18.8038	+	10.8564i	0.634961	+	0.366595i	−0.147710	+	0.989031i	$0.547190\pi$
$878$	−11.5359	−	6.66025i	−0.389318	−	0.224773i
$879$		0			0
$880$	−0.133975	+	0.232051i	−0.00451628	+	0.00782243i
$881$	19.5526	+	33.8660i	0.658742	+	1.14098i	0.980941	+	0.194303i	$0.0622446\pi$
$881$	19.5526	+	33.8660i	0.658742	+	1.14098i	−0.322199	+	0.946672i	$0.604422\pi$
$882$		0			0
$883$	−13.3205			−0.448271			−0.224135	−	0.974558i	$-0.571956\pi$
$883$	−13.3205			−0.448271			−0.224135	+	0.974558i	$0.571956\pi$
$884$	−13.8564	+	4.00000i	−0.466041	+	0.134535i
$885$		0			0
$886$	−17.1962	+	9.92820i	−0.577716	+	0.333545i
$887$	27.8660	+	48.2654i	0.935650	+	1.62059i	0.773472	+	0.633831i	$0.218519\pi$
$887$	27.8660	+	48.2654i	0.935650	+	1.62059i	0.162178	+	0.986762i	$0.448148\pi$
$888$		0			0
$889$			37.9808i			1.27383i
$890$	−12.2321	−	7.06218i	−0.410019	−	0.236725i
$891$		0			0
$892$			18.8564i			0.631359i
$893$	18.5263	−	32.0885i	0.619958	−	1.07380i
$894$		0			0
$895$	−7.85641	+	4.53590i	−0.262611	+	0.151618i
$896$	3.00000			0.100223
$897$		0			0
$898$	−6.12436			−0.204372
$899$	6.24871	−	3.60770i	0.208406	−	0.120323i
$900$		0			0
$901$	0.535898	−	0.928203i	0.0178534	−	0.0309229i
$902$		−	1.07180i		−	0.0356869i
$903$		0			0
$904$	−10.3923	−	6.00000i	−0.345643	−	0.199557i
$905$			16.9282i			0.562713i
$906$		0			0
$907$	−10.4641	−	18.1244i	−0.347455	−	0.601809i	0.638342	−	0.769753i	$-0.279621\pi$
$907$	−10.4641	−	18.1244i	−0.347455	−	0.601809i	−0.985797	+	0.167944i	$0.946287\pi$
$908$	−5.66025	+	3.26795i	−0.187842	+	0.108451i
$909$		0			0
$910$	−10.5000	−	2.59808i	−0.348072	−	0.0861254i
$911$	−12.7846			−0.423573			−0.211787	−	0.977316i	$-0.567928\pi$
$911$	−12.7846			−0.423573			−0.211787	+	0.977316i	$0.567928\pi$
$912$		0			0
$913$	−1.26795	−	2.19615i	−0.0419630	−	0.0726820i
$914$	3.73205	−	6.46410i	0.123445	−	0.213813i
$915$		0			0
$916$	−3.92820	−	2.26795i	−0.129791	−	0.0749352i
$917$	−37.2058	−	21.4808i	−1.22864	−	0.709357i
$918$		0			0
$919$	23.9808	−	41.5359i	0.791052	−	1.37014i	−0.134264	−	0.990946i	$-0.542867\pi$
$919$	23.9808	−	41.5359i	0.791052	−	1.37014i	0.925316	−	0.379197i	$-0.123800\pi$
$920$	−1.73205	−	3.00000i	−0.0571040	−	0.0989071i
$921$		0			0
$922$	−11.6077			−0.382279
$923$	32.3205	−	33.5885i	1.06384	−	1.10558i
$924$		0			0
$925$	5.13397	−	2.96410i	0.168804	−	0.0974591i
$926$	20.3923	+	35.3205i	0.670133	+	1.16070i
$927$		0			0
$928$			1.46410i			0.0480615i
$929$	−50.1051	−	28.9282i	−1.64390	−	0.949104i	−0.979430	−	0.201785i	$-0.935326\pi$
$929$	−50.1051	−	28.9282i	−1.64390	−	0.949104i	−0.664466	−	0.747319i	$-0.731341\pi$
$930$		0			0
$931$			11.4641i			0.375721i
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$		0			0
$934$	21.1244	−	12.1962i	0.691210	−	0.399070i
$935$	−1.07180			−0.0350515
$936$		0			0
$937$	−21.7128			−0.709327			−0.354663	−	0.934994i	$-0.615405\pi$
$937$	−21.7128			−0.709327			−0.354663	+	0.934994i	$0.615405\pi$
$938$	−3.80385	+	2.19615i	−0.124200	+	0.0717069i
$939$		0			0
$940$	3.23205	−	5.59808i	0.105418	−	0.182589i
$941$			60.4974i			1.97216i	0.166273	+	0.986080i	$0.446827\pi$
$941$			60.4974i			1.97216i	−0.166273	+	0.986080i	$0.553173\pi$
$942$		0			0
$943$	12.0000	+	6.92820i	0.390774	+	0.225613i
$944$		−	11.4641i		−	0.373125i
$945$		0			0
$946$	0.803848	+	1.39230i	0.0261353	+	0.0452677i
$947$	−29.7846	+	17.1962i	−0.967870	+	0.558800i	−0.898586	−	0.438797i	$-0.855405\pi$
$947$	−29.7846	+	17.1962i	−0.967870	+	0.558800i	−0.0692836	+	0.997597i	$0.522071\pi$
$948$		0			0
$949$	24.2487	+	6.00000i	0.787146	+	0.194768i
$950$	5.73205			0.185972
$951$		0			0
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	−26.6603	+	46.1769i	−0.863610	+	1.49582i	0.00481009	+	0.999988i	$0.498469\pi$
$953$	−26.6603	+	46.1769i	−0.863610	+	1.49582i	−0.868420	+	0.495829i	$0.834864\pi$
$954$		0			0
$955$	−15.0000	−	8.66025i	−0.485389	−	0.280239i
$956$	−3.00000	−	1.73205i	−0.0970269	−	0.0560185i
$957$		0			0
$958$	−11.1244	+	19.2679i	−0.359412	+	0.622519i
$959$	−20.1962	−	34.9808i	−0.652168	−	1.12959i
$960$		0			0
$961$	6.71281			0.216542
$962$	−15.4019	−	14.8205i	−0.496578	−	0.477832i
$963$		0			0
$964$	−21.8205	+	12.5981i	−0.702791	+	0.405757i
$965$	−4.92820	−	8.53590i	−0.158644	−	0.274780i
$966$		0			0
$967$		−	1.14359i		−	0.0367755i	−0.999831	−	0.0183877i	$-0.994147\pi$
$967$		−	1.14359i		−	0.0367755i	0.999831	−	0.0183877i	$-0.00585333\pi$
$968$	−9.46410	−	5.46410i	−0.304188	−	0.175623i
$969$		0			0
$970$		−	8.39230i		−	0.269461i
$971$	−20.6962	+	35.8468i	−0.664171	+	1.15038i	0.315338	+	0.948979i	$0.397882\pi$
$971$	−20.6962	+	35.8468i	−0.664171	+	1.15038i	−0.979509	+	0.201399i	$0.935451\pi$
$972$		0			0
$973$	51.4019	−	29.6769i	1.64787	−	0.951398i
$974$	−21.0000			−0.672883
$975$		0			0
$976$	−0.535898			−0.0171537
$977$	4.73205	−	2.73205i	0.151392	−	0.0874060i	−0.422391	−	0.906414i	$-0.638809\pi$
$977$	4.73205	−	2.73205i	0.151392	−	0.0874060i	0.573782	+	0.819008i	$0.305476\pi$
$978$		0			0
$979$	−1.89230	+	3.27757i	−0.0604783	+	0.104752i
$980$			2.00000i			0.0638877i
$981$		0			0
$982$	−4.66987	−	2.69615i	−0.149022	−	0.0860377i
$983$		−	46.1769i		−	1.47281i	−0.676538	−	0.736407i	$-0.736521\pi$
$983$		−	46.1769i		−	1.47281i	0.676538	−	0.736407i	$-0.263479\pi$
$984$		0			0
$985$	5.69615	+	9.86603i	0.181495	+	0.314358i
$986$	−5.07180	+	2.92820i	−0.161519	+	0.0932530i
$987$		0			0
$988$	−5.73205	−	19.8564i	−0.182361	−	0.631716i
$989$	−20.7846			−0.660912
$990$		0			0
$991$	−19.5885	−	33.9282i	−0.622248	−	1.07776i	−0.989066	−	0.147472i	$-0.952886\pi$
$991$	−19.5885	−	33.9282i	−0.622248	−	1.07776i	0.366818	−	0.930293i	$-0.380447\pi$
$992$	2.46410	−	4.26795i	0.0782353	−	0.135508i
$993$		0			0
$994$	−33.5885	−	19.3923i	−1.06536	−	0.615087i
$995$	21.5885	+	12.4641i	0.684400	+	0.395139i
$996$		0			0
$997$	−30.9904	+	53.6769i	−0.981475	+	1.69996i	−0.324817	+	0.945777i	$0.605303\pi$
$997$	−30.9904	+	53.6769i	−0.981475	+	1.69996i	−0.656659	+	0.754188i	$0.728031\pi$
$998$	−16.6603	−	28.8564i	−0.527371	−	0.913434i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.d.361.1		4
3.2	odd	2		390.2.bb.a.361.2	yes	4
13.4	even	6	inner	1170.2.bs.d.901.1		4
15.2	even	4		1950.2.y.e.49.2		4
15.8	even	4		1950.2.y.d.49.1		4
15.14	odd	2		1950.2.bc.a.751.1		4
39.2	even	12		5070.2.a.be.1.2		2
39.11	even	12		5070.2.a.ba.1.1		2
39.17	odd	6		390.2.bb.a.121.2	✓	4
39.23	odd	6		5070.2.b.p.1351.2		4
39.29	odd	6		5070.2.b.p.1351.3		4
195.17	even	12		1950.2.y.d.199.1		4
195.134	odd	6		1950.2.bc.a.901.1		4
195.173	even	12		1950.2.y.e.199.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.a.121.2	✓	4	39.17	odd	6
390.2.bb.a.361.2	yes	4	3.2	odd	2
1170.2.bs.d.361.1		4	1.1	even	1	trivial
1170.2.bs.d.901.1		4	13.4	even	6	inner
1950.2.y.d.49.1		4	15.8	even	4
1950.2.y.d.199.1		4	195.17	even	12
1950.2.y.e.49.2		4	15.2	even	4
1950.2.y.e.199.2		4	195.173	even	12
1950.2.bc.a.751.1		4	15.14	odd	2
1950.2.bc.a.901.1		4	195.134	odd	6
5070.2.a.ba.1.1		2	39.11	even	12
5070.2.a.be.1.2		2	39.2	even	12
5070.2.b.p.1351.2		4	39.23	odd	6
5070.2.b.p.1351.3		4	39.29	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-0.232051 + 0.133975i) q^{11} +(0.866025 - 3.50000i) q^{13} -3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(4.96410 + 2.86603i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.133975 - 0.232051i) q^{22} +(1.73205 + 3.00000i) q^{23} -1.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +(2.59808 - 1.50000i) q^{28} +(0.732051 + 1.26795i) q^{29} -4.92820i q^{31} +(0.866025 + 0.500000i) q^{32} +4.00000i q^{34} +(-1.50000 + 2.59808i) q^{35} +(-5.13397 + 2.96410i) q^{37} -5.73205 q^{38} -1.00000 q^{40} +(3.46410 - 2.00000i) q^{41} +(-3.00000 + 5.19615i) q^{43} +0.267949i q^{44} +(-3.00000 - 1.73205i) q^{46} -6.46410i q^{47} +(1.00000 + 1.73205i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-2.59808 - 2.50000i) q^{52} +0.267949 q^{53} +(-0.133975 - 0.232051i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(-1.26795 - 0.732051i) q^{58} +(9.92820 + 5.73205i) q^{59} +(0.267949 - 0.464102i) q^{61} +(2.46410 + 4.26795i) q^{62} -1.00000 q^{64} +(3.50000 + 0.866025i) q^{65} +(1.26795 - 0.732051i) q^{67} +(-2.00000 - 3.46410i) q^{68} -3.00000i q^{70} +(11.1962 + 6.46410i) q^{71} +6.92820i q^{73} +(2.96410 - 5.13397i) q^{74} +(4.96410 - 2.86603i) q^{76} -0.803848 q^{77} +3.07180 q^{79} +(0.866025 - 0.500000i) q^{80} +(-2.00000 + 3.46410i) q^{82} +9.46410i q^{83} +(3.46410 + 2.00000i) q^{85} -6.00000i q^{86} +(-0.133975 - 0.232051i) q^{88} +(12.2321 - 7.06218i) q^{89} +(7.50000 - 7.79423i) q^{91} +3.46410 q^{92} +(3.23205 + 5.59808i) q^{94} +(-2.86603 + 4.96410i) q^{95} +(7.26795 + 4.19615i) q^{97} +(-1.73205 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} + 6 q^{11} - 12 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 4 q^{22} - 4 q^{25} + 4 q^{26} - 4 q^{29} - 6 q^{35} - 24 q^{37} - 16 q^{38} - 4 q^{40} - 12 q^{43} - 12 q^{46} + 4 q^{49} + 8 q^{53} - 4 q^{55} - 6 q^{56} - 12 q^{58} + 12 q^{59} + 8 q^{61} - 4 q^{62} - 4 q^{64} + 14 q^{65} + 12 q^{67} - 8 q^{68} + 24 q^{71} - 2 q^{74} + 6 q^{76} - 24 q^{77} + 40 q^{79} - 8 q^{82} - 4 q^{88} + 42 q^{89} + 30 q^{91} + 6 q^{94} - 8 q^{95} + 36 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 + 6 * q^11 - 12 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 4 * q^22 - 4 * q^25 + 4 * q^26 - 4 * q^29 - 6 * q^35 - 24 * q^37 - 16 * q^38 - 4 * q^40 - 12 * q^43 - 12 * q^46 + 4 * q^49 + 8 * q^53 - 4 * q^55 - 6 * q^56 - 12 * q^58 + 12 * q^59 + 8 * q^61 - 4 * q^62 - 4 * q^64 + 14 * q^65 + 12 * q^67 - 8 * q^68 + 24 * q^71 - 2 * q^74 + 6 * q^76 - 24 * q^77 + 40 * q^79 - 8 * q^82 - 4 * q^88 + 42 * q^89 + 30 * q^91 + 6 * q^94 - 8 * q^95 + 36 * q^97

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