LMFDB - Embedded newform 1170.2.bs.d.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:	$4$
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			901.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.901
Dual form			1170.2.bs.d.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(3.23205 + 1.86603i) q^{11} +(-0.866025 - 3.50000i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-1.96410 + 1.13397i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.86603 + 3.23205i) q^{22} +(-1.73205 + 3.00000i) q^{23} -1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +(-2.59808 - 1.50000i) q^{28} +(-2.73205 + 4.73205i) q^{29} +8.92820i q^{31} +(-0.866025 + 0.500000i) q^{32} +4.00000i q^{34} +(-1.50000 - 2.59808i) q^{35} +(-6.86603 - 3.96410i) q^{37} -2.26795 q^{38} -1.00000 q^{40} +(-3.46410 - 2.00000i) q^{41} +(-3.00000 - 5.19615i) q^{43} +3.73205i q^{44} +(-3.00000 + 1.73205i) q^{46} +0.464102i q^{47} +(1.00000 - 1.73205i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(2.59808 - 2.50000i) q^{52} +3.73205 q^{53} +(-1.86603 + 3.23205i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(-4.73205 + 2.73205i) q^{58} +(-3.92820 + 2.26795i) q^{59} +(3.73205 + 6.46410i) q^{61} +(-4.46410 + 7.73205i) q^{62} -1.00000 q^{64} +(3.50000 - 0.866025i) q^{65} +(4.73205 + 2.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} -3.00000i q^{70} +(0.803848 - 0.464102i) q^{71} -6.92820i q^{73} +(-3.96410 - 6.86603i) q^{74} +(-1.96410 - 1.13397i) q^{76} -11.1962 q^{77} +16.9282 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-2.00000 - 3.46410i) q^{82} +2.53590i q^{83} +(-3.46410 + 2.00000i) q^{85} -6.00000i q^{86} +(-1.86603 + 3.23205i) q^{88} +(8.76795 + 5.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} -3.46410 q^{92} +(-0.232051 + 0.401924i) q^{94} +(-1.13397 - 1.96410i) q^{95} +(10.7321 - 6.19615i) q^{97} +(1.73205 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

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

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
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.902867	−	0.429919i	$-0.858542\pi$
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.0791130	+	0.996866i	$0.525209\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	3.23205	+	1.86603i	0.974500	+	0.562628i	0.900605	−	0.434638i	$-0.143124\pi$
$11$	3.23205	+	1.86603i	0.974500	+	0.562628i	0.0738948	+	0.997266i	$0.476457\pi$
$12$		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	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	−0.708082	−	0.706130i	$-0.750439\pi$
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	0.257486	+	0.966282i	$0.417106\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$		0			0
$22$	1.86603	+	3.23205i	0.397838	+	0.689076i
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	−0.988152	−	0.153481i	$-0.950952\pi$
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	0.626994	+	0.779024i	$0.284285\pi$
$24$		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
$29$	−2.73205	+	4.73205i	−0.507329	+	0.878720i	0.492635	+	0.870236i	$0.336034\pi$
$29$	−2.73205	+	4.73205i	−0.507329	+	0.878720i	−0.999964	+	0.00848369i	$0.997300\pi$
$30$		0			0
$31$			8.92820i			1.60355i	0.597624	+	0.801776i	$0.296111\pi$
$31$			8.92820i			1.60355i	−0.597624	+	0.801776i	$0.703889\pi$
$32$	−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
$37$	−6.86603	−	3.96410i	−1.12877	−	0.651694i	−0.185143	−	0.982712i	$-0.559275\pi$
$37$	−6.86603	−	3.96410i	−1.12877	−	0.651694i	−0.943625	+	0.331017i	$0.892608\pi$
$38$	−2.26795			−0.367910
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−3.46410	−	2.00000i	−0.541002	−	0.312348i	0.204483	−	0.978870i	$-0.434449\pi$
$41$	−3.46410	−	2.00000i	−0.541002	−	0.312348i	−0.745485	+	0.666523i	$0.767782\pi$
$42$		0			0
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$			3.73205i			0.562628i
$45$		0			0
$46$	−3.00000	+	1.73205i	−0.442326	+	0.255377i
$47$			0.464102i			0.0676962i	0.999427	+	0.0338481i	$0.0107762\pi$
$47$			0.464102i			0.0676962i	−0.999427	+	0.0338481i	$0.989224\pi$
$48$		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
$53$	3.73205			0.512637			0.256318	−	0.966592i	$-0.417490\pi$
$53$	3.73205			0.512637			0.256318	+	0.966592i	$0.417490\pi$
$54$		0			0
$55$	−1.86603	+	3.23205i	−0.251615	+	0.435810i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$		0			0
$58$	−4.73205	+	2.73205i	−0.621349	+	0.358736i
$59$	−3.92820	+	2.26795i	−0.511409	+	0.295262i	−0.733412	−	0.679784i	$-0.762074\pi$
$59$	−3.92820	+	2.26795i	−0.511409	+	0.295262i	0.222004	+	0.975046i	$0.428740\pi$
$60$		0			0
$61$	3.73205	+	6.46410i	0.477840	+	0.827643i	0.999677	−	0.0254017i	$-0.00808648\pi$
$61$	3.73205	+	6.46410i	0.477840	+	0.827643i	−0.521837	+	0.853045i	$0.674753\pi$
$62$	−4.46410	+	7.73205i	−0.566941	+	0.981971i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.50000	−	0.866025i	0.434122	−	0.107417i
$66$		0			0
$67$	4.73205	+	2.73205i	0.578112	+	0.333773i	0.760383	−	0.649475i	$-0.225011\pi$
$67$	4.73205	+	2.73205i	0.578112	+	0.333773i	−0.182271	+	0.983248i	$0.558345\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$		0			0
$70$		−	3.00000i		−	0.358569i
$71$	0.803848	−	0.464102i	0.0953992	−	0.0550787i	−0.451541	−	0.892250i	$-0.649126\pi$
$71$	0.803848	−	0.464102i	0.0953992	−	0.0550787i	0.546941	+	0.837171i	$0.315792\pi$
$72$		0			0
$73$		−	6.92820i		−	0.810885i	−0.914121	−	0.405442i	$-0.867117\pi$
$73$		−	6.92820i		−	0.810885i	0.914121	−	0.405442i	$-0.132883\pi$
$74$	−3.96410	−	6.86603i	−0.460817	−	0.798159i
$75$		0			0
$76$	−1.96410	−	1.13397i	−0.225298	−	0.130076i
$77$	−11.1962			−1.27592
$78$		0			0
$79$	16.9282			1.90457			0.952286	−	0.305208i	$-0.0987259\pi$
$79$	16.9282			1.90457			0.952286	+	0.305208i	$0.0987259\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$		0			0
$82$	−2.00000	−	3.46410i	−0.220863	−	0.382546i
$83$			2.53590i			0.278351i	0.990268	+	0.139176i	$0.0444452\pi$
$83$			2.53590i			0.278351i	−0.990268	+	0.139176i	$0.955555\pi$
$84$		0			0
$85$	−3.46410	+	2.00000i	−0.375735	+	0.216930i
$86$		−	6.00000i		−	0.646997i
$87$		0			0
$88$	−1.86603	+	3.23205i	−0.198919	+	0.344538i
$89$	8.76795	+	5.06218i	0.929401	+	0.536590i	0.886622	−	0.462495i	$-0.153046\pi$
$89$	8.76795	+	5.06218i	0.929401	+	0.536590i	0.0427788	+	0.999085i	$0.486379\pi$
$90$		0			0
$91$	7.50000	+	7.79423i	0.786214	+	0.817057i
$92$	−3.46410			−0.361158
$93$		0			0
$94$	−0.232051	+	0.401924i	−0.0239342	+	0.0414553i
$95$	−1.13397	−	1.96410i	−0.116343	−	0.201513i
$96$		0			0
$97$	10.7321	−	6.19615i	1.08967	−	0.629124i	0.156185	−	0.987728i	$-0.450080\pi$
$97$	10.7321	−	6.19615i	1.08967	−	0.629124i	0.933490	+	0.358604i	$0.116747\pi$
$98$	1.73205	−	1.00000i	0.174964	−	0.101015i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−4.19615	+	7.26795i	−0.417533	+	0.723188i	−0.995691	−	0.0927369i	$-0.970438\pi$
$101$	−4.19615	+	7.26795i	−0.417533	+	0.723188i	0.578158	+	0.815925i	$0.303772\pi$
$102$		0			0
$103$	19.5885			1.93011			0.965054	−	0.262051i	$-0.0843989\pi$
$103$	19.5885			1.93011			0.965054	+	0.262051i	$0.0843989\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$		0			0
$106$	3.23205	+	1.86603i	0.313925	+	0.181244i
$107$	0.464102	−	0.803848i	0.0448664	−	0.0777109i	−0.842720	−	0.538352i	$-0.819047\pi$
$107$	0.464102	−	0.803848i	0.0448664	−	0.0777109i	0.887587	+	0.460641i	$0.152380\pi$
$108$		0			0
$109$		−	10.3923i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$109$		−	10.3923i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$110$	−3.23205	+	1.86603i	−0.308164	+	0.177919i
$111$		0			0
$112$		−	3.00000i		−	0.283473i
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	−0.997102	−	0.0760733i	$-0.975762\pi$
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	0.432670	−	0.901553i	$-0.357572\pi$
$114$		0			0
$115$	−3.00000	−	1.73205i	−0.279751	−	0.161515i
$116$	−5.46410			−0.507329
$117$		0			0
$118$	−4.53590			−0.417563
$119$	−10.3923	−	6.00000i	−0.952661	−	0.550019i
$120$		0			0
$121$	1.46410	+	2.53590i	0.133100	+	0.230536i
$122$			7.46410i			0.675768i
$123$		0			0
$124$	−7.73205	+	4.46410i	−0.694359	+	0.400888i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−2.33013	+	4.03590i	−0.206765	+	0.358128i	−0.950694	−	0.310131i	$-0.899627\pi$
$127$	−2.33013	+	4.03590i	−0.206765	+	0.358128i	0.743928	+	0.668259i	$0.232960\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	3.46410	+	1.00000i	0.303822	+	0.0877058i
$131$	20.3205			1.77541			0.887706	−	0.460412i	$-0.152298\pi$
$131$	20.3205			1.77541			0.887706	+	0.460412i	$0.152298\pi$
$132$		0			0
$133$	3.40192	−	5.89230i	0.294984	−	0.510928i
$134$	2.73205	+	4.73205i	0.236013	+	0.408787i
$135$		0			0
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	5.66025	−	3.26795i	0.483588	−	0.279200i	−0.238322	−	0.971186i	$-0.576598\pi$
$137$	5.66025	−	3.26795i	0.483588	−	0.279200i	0.721911	+	0.691986i	$0.243264\pi$
$138$		0			0
$139$	−10.8923	−	18.8660i	−0.923873	−	1.60020i	−0.793363	−	0.608748i	$-0.791672\pi$
$139$	−10.8923	−	18.8660i	−0.923873	−	1.60020i	−0.130510	−	0.991447i	$-0.541661\pi$
$140$	1.50000	−	2.59808i	0.126773	−	0.219578i
$141$		0			0
$142$	0.928203			0.0778931
$143$	3.73205	−	12.9282i	0.312090	−	1.08111i
$144$		0			0
$145$	−4.73205	−	2.73205i	−0.392975	−	0.226884i
$146$	3.46410	−	6.00000i	0.286691	−	0.496564i
$147$		0			0
$148$		−	7.92820i		−	0.651694i
$149$	−19.7321	+	11.3923i	−1.61651	+	0.933294i	−0.628700	+	0.777648i	$0.716413\pi$
$149$	−19.7321	+	11.3923i	−1.61651	+	0.933294i	−0.987813	+	0.155646i	$0.950254\pi$
$150$		0			0
$151$			18.7846i			1.52867i	0.644819	+	0.764335i	$0.276933\pi$
$151$			18.7846i			1.52867i	−0.644819	+	0.764335i	$0.723067\pi$
$152$	−1.13397	−	1.96410i	−0.0919775	−	0.159310i
$153$		0			0
$154$	−9.69615	−	5.59808i	−0.781338	−	0.451106i
$155$	−8.92820			−0.717131
$156$		0			0
$157$	10.8038			0.862241			0.431120	−	0.902294i	$-0.358118\pi$
$157$	10.8038			0.862241			0.431120	+	0.902294i	$0.358118\pi$
$158$	14.6603	+	8.46410i	1.16631	+	0.673368i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		−	10.3923i		−	0.819028i
$162$		0			0
$163$	−9.46410	+	5.46410i	−0.741286	+	0.427981i	−0.822537	−	0.568712i	$-0.807442\pi$
$163$	−9.46410	+	5.46410i	−0.741286	+	0.427981i	0.0812509	+	0.996694i	$0.474108\pi$
$164$		−	4.00000i		−	0.312348i
$165$		0			0
$166$	−1.26795	+	2.19615i	−0.0984119	+	0.170454i
$167$	5.59808	+	3.23205i	0.433192	+	0.250104i	0.700706	−	0.713451i	$-0.252869\pi$
$167$	5.59808	+	3.23205i	0.433192	+	0.250104i	−0.267513	+	0.963554i	$0.586202\pi$
$168$		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
$173$	11.0622	+	19.1603i	0.841042	+	1.45673i	0.889015	+	0.457879i	$0.151391\pi$
$173$	11.0622	+	19.1603i	0.841042	+	1.45673i	−0.0479730	+	0.998849i	$0.515276\pi$
$174$		0			0
$175$	2.59808	−	1.50000i	0.196396	−	0.113389i
$176$	−3.23205	+	1.86603i	−0.243625	+	0.140657i
$177$		0			0
$178$	5.06218	+	8.76795i	0.379426	+	0.657186i
$179$	11.4641	−	19.8564i	0.856867	−	1.48414i	−0.0180347	−	0.999837i	$-0.505741\pi$
$179$	11.4641	−	19.8564i	0.856867	−	1.48414i	0.874902	−	0.484300i	$-0.160926\pi$
$180$		0			0
$181$	3.07180			0.228325			0.114162	−	0.993462i	$-0.463582\pi$
$181$	3.07180			0.228325			0.114162	+	0.993462i	$0.463582\pi$
$182$	2.59808	+	10.5000i	0.192582	+	0.778312i
$183$		0			0
$184$	−3.00000	−	1.73205i	−0.221163	−	0.127688i
$185$	3.96410	−	6.86603i	0.291447	−	0.504800i
$186$		0			0
$187$			14.9282i			1.09166i
$188$	−0.401924	+	0.232051i	−0.0293133	+	0.0169240i
$189$		0			0
$190$		−	2.26795i		−	0.164534i
$191$	8.66025	+	15.0000i	0.626634	+	1.08536i	0.988222	+	0.153024i	$0.0489012\pi$
$191$	8.66025	+	15.0000i	0.626634	+	1.08536i	−0.361588	+	0.932338i	$0.617765\pi$
$192$		0			0
$193$	−15.4641	−	8.92820i	−1.11313	−	0.642666i	−0.173492	−	0.984835i	$-0.555505\pi$
$193$	−15.4641	−	8.92820i	−1.11313	−	0.642666i	−0.939638	+	0.342169i	$0.888838\pi$
$194$	12.3923			0.889716
$195$		0			0
$196$	2.00000			0.142857
$197$	8.13397	+	4.69615i	0.579522	+	0.334587i	0.760943	−	0.648818i	$-0.224737\pi$
$197$	8.13397	+	4.69615i	0.579522	+	0.334587i	−0.181422	+	0.983405i	$0.558070\pi$
$198$		0			0
$199$	5.53590	+	9.58846i	0.392429	+	0.679708i	0.992769	−	0.120037i	$-0.0383014\pi$
$199$	5.53590	+	9.58846i	0.392429	+	0.679708i	−0.600340	+	0.799745i	$0.704968\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	−7.26795	+	4.19615i	−0.511371	+	0.295240i
$203$		−	16.3923i		−	1.15051i
$204$		0			0
$205$	2.00000	−	3.46410i	0.139686	−	0.241943i
$206$	16.9641	+	9.79423i	1.18194	+	0.682396i
$207$		0			0
$208$	3.46410	+	1.00000i	0.240192	+	0.0693375i
$209$	−8.46410			−0.585474
$210$		0			0
$211$	10.9641	−	18.9904i	0.754800	−	1.30735i	−0.190674	−	0.981653i	$-0.561067\pi$
$211$	10.9641	−	18.9904i	0.754800	−	1.30735i	0.945474	−	0.325698i	$-0.105599\pi$
$212$	1.86603	+	3.23205i	0.128159	+	0.221978i
$213$		0			0
$214$	0.803848	−	0.464102i	0.0549499	−	0.0317253i
$215$	5.19615	−	3.00000i	0.354375	−	0.204598i
$216$		0			0
$217$	−13.3923	−	23.1962i	−0.909129	−	1.57466i
$218$	5.19615	−	9.00000i	0.351928	−	0.609557i
$219$		0			0
$220$	−3.73205			−0.251615
$221$	10.3923	−	10.0000i	0.699062	−	0.672673i
$222$		0			0
$223$	−7.66987	−	4.42820i	−0.513613	−	0.296534i	0.220705	−	0.975341i	$-0.429164\pi$
$223$	−7.66987	−	4.42820i	−0.513613	−	0.296534i	−0.734317	+	0.678806i	$0.762498\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$		0			0
$226$		−	12.0000i		−	0.798228i
$227$	11.6603	−	6.73205i	0.773918	−	0.446822i	−0.0603523	−	0.998177i	$-0.519222\pi$
$227$	11.6603	−	6.73205i	0.773918	−	0.446822i	0.834271	+	0.551355i	$0.185889\pi$
$228$		0			0
$229$		−	11.4641i		−	0.757569i	−0.925485	−	0.378785i	$-0.876342\pi$
$229$		−	11.4641i		−	0.757569i	0.925485	−	0.378785i	$-0.123658\pi$
$230$	−1.73205	−	3.00000i	−0.114208	−	0.197814i
$231$		0			0
$232$	−4.73205	−	2.73205i	−0.310674	−	0.179368i
$233$	−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
$235$	−0.464102			−0.0302747
$236$	−3.92820	−	2.26795i	−0.255704	−	0.147631i
$237$		0			0
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$			3.46410i			0.224074i	0.993704	+	0.112037i	$0.0357375\pi$
$239$			3.46410i			0.224074i	−0.993704	+	0.112037i	$0.964262\pi$
$240$		0			0
$241$	12.8205	−	7.40192i	0.825842	−	0.476800i	−0.0265852	−	0.999647i	$-0.508463\pi$
$241$	12.8205	−	7.40192i	0.825842	−	0.476800i	0.852427	+	0.522847i	$0.175130\pi$
$242$			2.92820i			0.188232i
$243$		0			0
$244$	−3.73205	+	6.46410i	−0.238920	+	0.413822i
$245$	1.73205	+	1.00000i	0.110657	+	0.0638877i
$246$		0			0
$247$	5.66987	+	5.89230i	0.360765	+	0.374918i
$248$	−8.92820			−0.566941
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	13.2321	+	22.9186i	0.835200	+	1.44661i	0.893868	+	0.448331i	$0.147981\pi$
$251$	13.2321	+	22.9186i	0.835200	+	1.44661i	−0.0586681	+	0.998278i	$0.518685\pi$
$252$		0			0
$253$	−11.1962	+	6.46410i	−0.703896	+	0.406395i
$254$	−4.03590	+	2.33013i	−0.253235	+	0.146205i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.7321	−	18.5885i	0.669447	−	1.15952i	−0.308612	−	0.951188i	$-0.599864\pi$
$257$	10.7321	−	18.5885i	0.669447	−	1.15952i	0.978059	−	0.208328i	$-0.0668022\pi$
$258$		0			0
$259$	23.7846			1.47790
$260$	2.50000	+	2.59808i	0.155043	+	0.161126i
$261$		0			0
$262$	17.5981	+	10.1603i	1.08721	+	0.627703i
$263$	10.2583	−	17.7679i	0.632556	−	1.09562i	−0.354472	−	0.935067i	$-0.615339\pi$
$263$	10.2583	−	17.7679i	0.632556	−	1.09562i	0.987027	−	0.160552i	$-0.0513274\pi$
$264$		0			0
$265$			3.73205i			0.229258i
$266$	5.89230	−	3.40192i	0.361280	−	0.208585i
$267$		0			0
$268$			5.46410i			0.333773i
$269$	−15.4641	−	26.7846i	−0.942863	−	1.63309i	−0.759975	−	0.649953i	$-0.774789\pi$
$269$	−15.4641	−	26.7846i	−0.942863	−	1.63309i	−0.182888	−	0.983134i	$-0.558545\pi$
$270$		0			0
$271$	−3.12436	−	1.80385i	−0.189791	−	0.109576i	0.402094	−	0.915599i	$-0.368283\pi$
$271$	−3.12436	−	1.80385i	−0.189791	−	0.109576i	−0.591885	+	0.806023i	$0.701616\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	6.53590			0.394848
$275$	−3.23205	−	1.86603i	−0.194900	−	0.112526i
$276$		0			0
$277$	9.79423	+	16.9641i	0.588478	+	1.01927i	0.994432	+	0.105380i	$0.0336060\pi$
$277$	9.79423	+	16.9641i	0.588478	+	1.01927i	−0.405954	+	0.913894i	$0.633061\pi$
$278$		−	21.7846i		−	1.30655i
$279$		0			0
$280$	2.59808	−	1.50000i	0.155265	−	0.0896421i
$281$			6.92820i			0.413302i	0.978415	+	0.206651i	$0.0662565\pi$
$281$			6.92820i			0.413302i	−0.978415	+	0.206651i	$0.933744\pi$
$282$		0			0
$283$	−7.19615	+	12.4641i	−0.427767	+	0.740914i	−0.996674	−	0.0814876i	$-0.974033\pi$
$283$	−7.19615	+	12.4641i	−0.427767	+	0.740914i	0.568907	+	0.822402i	$0.307366\pi$
$284$	0.803848	+	0.464102i	0.0476996	+	0.0275394i
$285$		0			0
$286$	9.69615	−	9.33013i	0.573346	−	0.551702i
$287$	12.0000			0.708338
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−2.73205	−	4.73205i	−0.160432	−	0.277876i
$291$		0			0
$292$	6.00000	−	3.46410i	0.351123	−	0.202721i
$293$	−16.6699	+	9.62436i	−0.973864	+	0.562261i	−0.900412	−	0.435038i	$-0.856735\pi$
$293$	−16.6699	+	9.62436i	−0.973864	+	0.562261i	−0.0734522	+	0.997299i	$0.523402\pi$
$294$		0			0
$295$	−2.26795	−	3.92820i	−0.132045	−	0.228709i
$296$	3.96410	−	6.86603i	0.230409	−	0.399080i
$297$		0			0
$298$	−22.7846			−1.31988
$299$	12.0000	+	3.46410i	0.693978	+	0.200334i
$300$		0			0
$301$	15.5885	+	9.00000i	0.898504	+	0.518751i
$302$	−9.39230	+	16.2679i	−0.540466	+	0.936115i
$303$		0			0
$304$		−	2.26795i		−	0.130076i
$305$	−6.46410	+	3.73205i	−0.370133	+	0.213697i
$306$		0			0
$307$			20.2487i			1.15565i	0.816159	+	0.577827i	$0.196099\pi$
$307$			20.2487i			1.15565i	−0.816159	+	0.577827i	$0.803901\pi$
$308$	−5.59808	−	9.69615i	−0.318980	−	0.552490i
$309$		0			0
$310$	−7.73205	−	4.46410i	−0.439151	−	0.253544i
$311$	−5.07180			−0.287595			−0.143798	−	0.989607i	$-0.545931\pi$
$311$	−5.07180			−0.287595			−0.143798	+	0.989607i	$0.545931\pi$
$312$		0			0
$313$	1.32051			0.0746395			0.0373198	−	0.999303i	$-0.488118\pi$
$313$	1.32051			0.0746395			0.0373198	+	0.999303i	$0.488118\pi$
$314$	9.35641	+	5.40192i	0.528013	+	0.304848i
$315$		0			0
$316$	8.46410	+	14.6603i	0.476143	+	0.824704i
$317$		−	23.5359i		−	1.32191i	−0.750427	−	0.660954i	$-0.770152\pi$
$317$		−	23.5359i		−	1.32191i	0.750427	−	0.660954i	$-0.229848\pi$
$318$		0			0
$319$	−17.6603	+	10.1962i	−0.988784	+	0.570875i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	5.19615	−	9.00000i	0.289570	−	0.501550i
$323$	−7.85641	−	4.53590i	−0.437142	−	0.252384i
$324$		0			0
$325$	0.866025	+	3.50000i	0.0480384	+	0.194145i
$326$	−10.9282			−0.605257
$327$		0			0
$328$	2.00000	−	3.46410i	0.110432	−	0.191273i
$329$	−0.696152	−	1.20577i	−0.0383801	−	0.0664763i
$330$		0			0
$331$	5.53590	−	3.19615i	0.304280	−	0.175676i	−0.340084	−	0.940395i	$-0.610455\pi$
$331$	5.53590	−	3.19615i	0.304280	−	0.175676i	0.644364	+	0.764719i	$0.277122\pi$
$332$	−2.19615	+	1.26795i	−0.120530	+	0.0695878i
$333$		0			0
$334$	3.23205	+	5.59808i	0.176850	+	0.306313i
$335$	−2.73205	+	4.73205i	−0.149268	+	0.258540i
$336$		0			0
$337$	−5.60770			−0.305471			−0.152735	−	0.988267i	$-0.548808\pi$
$337$	−5.60770			−0.305471			−0.152735	+	0.988267i	$0.548808\pi$
$338$	−12.9904	−	0.500000i	−0.706584	−	0.0271964i
$339$		0			0
$340$	−3.46410	−	2.00000i	−0.187867	−	0.108465i
$341$	−16.6603	+	28.8564i	−0.902203	+	1.56266i
$342$		0			0
$343$		−	15.0000i		−	0.809924i
$344$	5.19615	−	3.00000i	0.280158	−	0.161749i
$345$		0			0
$346$			22.1244i			1.18941i
$347$	−8.19615	−	14.1962i	−0.439993	−	0.762089i	0.557696	−	0.830045i	$-0.311686\pi$
$347$	−8.19615	−	14.1962i	−0.439993	−	0.762089i	−0.997688	+	0.0679560i	$0.978352\pi$
$348$		0			0
$349$	15.1244	+	8.73205i	0.809588	+	0.467416i	0.846813	−	0.531891i	$-0.178518\pi$
$349$	15.1244	+	8.73205i	0.809588	+	0.467416i	−0.0372247	+	0.999307i	$0.511852\pi$
$350$	3.00000			0.160357
$351$		0			0
$352$	−3.73205			−0.198919
$353$	24.5885	+	14.1962i	1.30871	+	0.755585i	0.981881	−	0.189498i	$-0.0606861\pi$
$353$	24.5885	+	14.1962i	1.30871	+	0.755585i	0.326830	+	0.945083i	$0.394019\pi$
$354$		0			0
$355$	0.464102	+	0.803848i	0.0246320	+	0.0426638i
$356$			10.1244i			0.536590i
$357$		0			0
$358$	19.8564	−	11.4641i	1.04944	−	0.605897i
$359$			12.9282i			0.682324i	0.940004	+	0.341162i	$0.110821\pi$
$359$			12.9282i			0.682324i	−0.940004	+	0.341162i	$0.889179\pi$
$360$		0			0
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	2.66025	+	1.53590i	0.139820	+	0.0807250i
$363$		0			0
$364$	−3.00000	+	10.3923i	−0.157243	+	0.544705i
$365$	6.92820			0.362639
$366$		0			0
$367$	6.66025	−	11.5359i	0.347662	−	0.602169i	−0.638171	−	0.769894i	$-0.720309\pi$
$367$	6.66025	−	11.5359i	0.347662	−	0.602169i	0.985834	+	0.167725i	$0.0536422\pi$
$368$	−1.73205	−	3.00000i	−0.0902894	−	0.156386i
$369$		0			0
$370$	6.86603	−	3.96410i	0.356948	−	0.206084i
$371$	−9.69615	+	5.59808i	−0.503399	+	0.290638i
$372$		0			0
$373$	−11.4641	−	19.8564i	−0.593589	−	1.02813i	−0.993744	−	0.111679i	$-0.964377\pi$
$373$	−11.4641	−	19.8564i	−0.593589	−	1.02813i	0.400156	−	0.916447i	$-0.368956\pi$
$374$	−7.46410	+	12.9282i	−0.385960	+	0.668501i
$375$		0			0
$376$	−0.464102			−0.0239342
$377$	18.9282	+	5.46410i	0.974852	+	0.281416i
$378$		0			0
$379$	5.42820	+	3.13397i	0.278828	+	0.160981i	0.632893	−	0.774239i	$-0.281867\pi$
$379$	5.42820	+	3.13397i	0.278828	+	0.160981i	−0.354065	+	0.935221i	$0.615201\pi$
$380$	1.13397	−	1.96410i	0.0581717	−	0.100756i
$381$		0			0
$382$			17.3205i			0.886194i
$383$	−31.8564	+	18.3923i	−1.62779	+	0.939803i	−0.643035	+	0.765837i	$0.722325\pi$
$383$	−31.8564	+	18.3923i	−1.62779	+	0.939803i	−0.984752	+	0.173966i	$0.944342\pi$
$384$		0			0
$385$		−	11.1962i		−	0.570609i
$386$	−8.92820	−	15.4641i	−0.454434	−	0.787102i
$387$		0			0
$388$	10.7321	+	6.19615i	0.544837	+	0.314562i
$389$	9.85641			0.499740			0.249870	−	0.968279i	$-0.419612\pi$
$389$	9.85641			0.499740			0.249870	+	0.968279i	$0.419612\pi$
$390$		0			0
$391$	−13.8564			−0.700749
$392$	1.73205	+	1.00000i	0.0874818	+	0.0505076i
$393$		0			0
$394$	4.69615	+	8.13397i	0.236589	+	0.409784i
$395$			16.9282i			0.851750i
$396$		0			0
$397$	−6.86603	+	3.96410i	−0.344596	+	0.198953i	−0.662303	−	0.749237i	$-0.730421\pi$
$397$	−6.86603	+	3.96410i	−0.344596	+	0.198953i	0.317707	+	0.948189i	$0.397087\pi$
$398$			11.0718i			0.554979i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	1.83975	+	1.06218i	0.0918725	+	0.0530426i	0.545232	−	0.838285i	$-0.316441\pi$
$401$	1.83975	+	1.06218i	0.0918725	+	0.0530426i	−0.453360	+	0.891328i	$0.649775\pi$
$402$		0			0
$403$	31.2487	−	7.73205i	1.55661	−	0.385161i
$404$	−8.39230			−0.417533
$405$		0			0
$406$	8.19615	−	14.1962i	0.406768	−	0.704543i
$407$	−14.7942	−	25.6244i	−0.733323	−	1.27015i
$408$		0			0
$409$	0.820508	−	0.473721i	0.0405715	−	0.0234240i	−0.479577	−	0.877500i	$-0.659210\pi$
$409$	0.820508	−	0.473721i	0.0405715	−	0.0234240i	0.520149	+	0.854076i	$0.325877\pi$
$410$	3.46410	−	2.00000i	0.171080	−	0.0987730i
$411$		0			0
$412$	9.79423	+	16.9641i	0.482527	+	0.835761i
$413$	6.80385	−	11.7846i	0.334795	−	0.579883i
$414$		0			0
$415$	−2.53590			−0.124482
$416$	2.50000	+	2.59808i	0.122573	+	0.127381i
$417$		0			0
$418$	−7.33013	−	4.23205i	−0.358528	−	0.206996i
$419$	−8.92820	+	15.4641i	−0.436171	+	0.755471i	−0.997390	−	0.0721964i	$-0.976999\pi$
$419$	−8.92820	+	15.4641i	−0.436171	+	0.755471i	0.561219	+	0.827667i	$0.310332\pi$
$420$		0			0
$421$		−	5.85641i		−	0.285424i	−0.989764	−	0.142712i	$-0.954418\pi$
$421$		−	5.85641i		−	0.285424i	0.989764	−	0.142712i	$-0.0455822\pi$
$422$	18.9904	−	10.9641i	0.924437	−	0.533724i
$423$		0			0
$424$			3.73205i			0.181244i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$	−19.3923	−	11.1962i	−0.938459	−	0.541820i
$428$	0.928203			0.0448664
$429$		0			0
$430$	6.00000			0.289346
$431$	12.0000	+	6.92820i	0.578020	+	0.333720i	0.760346	−	0.649518i	$-0.225029\pi$
$431$	12.0000	+	6.92820i	0.578020	+	0.333720i	−0.182326	+	0.983238i	$0.558363\pi$
$432$		0			0
$433$	−16.3923	−	28.3923i	−0.787764	−	1.36445i	−0.927334	−	0.374235i	$-0.877905\pi$
$433$	−16.3923	−	28.3923i	−0.787764	−	1.36445i	0.139570	−	0.990212i	$-0.455428\pi$
$434$		−	26.7846i		−	1.28570i
$435$		0			0
$436$	9.00000	−	5.19615i	0.431022	−	0.248851i
$437$		−	7.85641i		−	0.375823i
$438$		0			0
$439$	−10.6603	+	18.4641i	−0.508786	+	0.881243i	0.491162	+	0.871068i	$0.336572\pi$
$439$	−10.6603	+	18.4641i	−0.508786	+	0.881243i	−0.999948	+	0.0101753i	$0.996761\pi$
$440$	−3.23205	−	1.86603i	−0.154082	−	0.0889593i
$441$		0			0
$442$	14.0000	−	3.46410i	0.665912	−	0.164771i
$443$	−7.85641			−0.373269			−0.186635	−	0.982429i	$-0.559758\pi$
$443$	−7.85641			−0.373269			−0.186635	+	0.982429i	$0.559758\pi$
$444$		0			0
$445$	−5.06218	+	8.76795i	−0.239970	+	0.415641i
$446$	−4.42820	−	7.66987i	−0.209682	−	0.363179i
$447$		0			0
$448$	2.59808	−	1.50000i	0.122748	−	0.0708683i
$449$	15.6962	−	9.06218i	0.740747	−	0.427671i	−0.0815937	−	0.996666i	$-0.526001\pi$
$449$	15.6962	−	9.06218i	0.740747	−	0.427671i	0.822341	+	0.568995i	$0.192668\pi$
$450$		0			0
$451$	−7.46410	−	12.9282i	−0.351471	−	0.608765i
$452$	6.00000	−	10.3923i	0.282216	−	0.488813i
$453$		0			0
$454$	13.4641			0.631902
$455$	−7.79423	+	7.50000i	−0.365399	+	0.351605i
$456$		0			0
$457$	0.464102	+	0.267949i	0.0217098	+	0.0125341i	0.510816	−	0.859690i	$-0.329343\pi$
$457$	0.464102	+	0.267949i	0.0217098	+	0.0125341i	−0.489106	+	0.872224i	$0.662677\pi$
$458$	5.73205	−	9.92820i	0.267841	−	0.463914i
$459$		0			0
$460$		−	3.46410i		−	0.161515i
$461$	−28.0526	+	16.1962i	−1.30654	+	0.754330i	−0.981517	−	0.191377i	$-0.938705\pi$
$461$	−28.0526	+	16.1962i	−1.30654	+	0.754330i	−0.325021	+	0.945707i	$0.605371\pi$
$462$		0			0
$463$			0.784610i			0.0364639i	0.999834	+	0.0182320i	$0.00580373\pi$
$463$			0.784610i			0.0364639i	−0.999834	+	0.0182320i	$0.994196\pi$
$464$	−2.73205	−	4.73205i	−0.126832	−	0.219680i
$465$		0			0
$466$	−15.5885	−	9.00000i	−0.722121	−	0.416917i
$467$	−3.60770			−0.166944			−0.0834721	−	0.996510i	$-0.526601\pi$
$467$	−3.60770			−0.166944			−0.0834721	+	0.996510i	$0.526601\pi$
$468$		0			0
$469$	−16.3923			−0.756926
$470$	−0.401924	−	0.232051i	−0.0185394	−	0.0107037i
$471$		0			0
$472$	−2.26795	−	3.92820i	−0.104391	−	0.180810i
$473$		−	22.3923i		−	1.02960i
$474$		0			0
$475$	1.96410	−	1.13397i	0.0901192	−	0.0520303i
$476$		−	12.0000i		−	0.550019i
$477$		0			0
$478$	−1.73205	+	3.00000i	−0.0792222	+	0.137217i
$479$	22.7321	+	13.1244i	1.03865	+	0.599667i	0.919452	−	0.393203i	$-0.128633\pi$
$479$	22.7321	+	13.1244i	1.03865	+	0.599667i	0.119202	+	0.992870i	$0.461966\pi$
$480$		0			0
$481$	−7.92820	+	27.4641i	−0.361495	+	1.25226i
$482$	14.8038			0.674297
$483$		0			0
$484$	−1.46410	+	2.53590i	−0.0665501	+	0.115268i
$485$	6.19615	+	10.7321i	0.281353	+	0.487317i
$486$		0			0
$487$	−18.1865	+	10.5000i	−0.824110	+	0.475800i	−0.851832	−	0.523815i	$-0.824508\pi$
$487$	−18.1865	+	10.5000i	−0.824110	+	0.475800i	0.0277214	+	0.999616i	$0.491175\pi$
$488$	−6.46410	+	3.73205i	−0.292616	+	0.168942i
$489$		0			0
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	−7.69615	+	13.3301i	−0.347322	+	0.601580i	−0.985773	−	0.168083i	$-0.946242\pi$
$491$	−7.69615	+	13.3301i	−0.347322	+	0.601580i	0.638450	+	0.769663i	$0.279576\pi$
$492$		0			0
$493$	−21.8564			−0.984363
$494$	1.96410	+	7.93782i	0.0883691	+	0.357140i
$495$		0			0
$496$	−7.73205	−	4.46410i	−0.347179	−	0.200444i
$497$	−1.39230	+	2.41154i	−0.0624534	+	0.108172i
$498$		0			0
$499$		−	1.32051i		−	0.0591141i	−0.999563	−	0.0295570i	$-0.990590\pi$
$499$		−	1.32051i		−	0.0591141i	0.999563	−	0.0295570i	$-0.00940967\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$		0			0
$502$			26.4641i			1.18115i
$503$	0.133975	+	0.232051i	0.00597363	+	0.0103466i	0.868997	−	0.494818i	$-0.164765\pi$
$503$	0.133975	+	0.232051i	0.00597363	+	0.0103466i	−0.863023	+	0.505164i	$0.831432\pi$
$504$		0			0
$505$	−7.26795	−	4.19615i	−0.323419	−	0.186726i
$506$	−12.9282			−0.574729
$507$		0			0
$508$	−4.66025			−0.206765
$509$	−4.60770	−	2.66025i	−0.204232	−	0.117914i	0.394396	−	0.918941i	$-0.370954\pi$
$509$	−4.60770	−	2.66025i	−0.204232	−	0.117914i	−0.598628	+	0.801027i	$0.704287\pi$
$510$		0			0
$511$	10.3923	+	18.0000i	0.459728	+	0.796273i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	18.5885	−	10.7321i	0.819902	−	0.473370i
$515$			19.5885i			0.863171i
$516$		0			0
$517$	−0.866025	+	1.50000i	−0.0380878	+	0.0659699i
$518$	20.5981	+	11.8923i	0.905028	+	0.522518i
$519$		0			0
$520$	0.866025	+	3.50000i	0.0379777	+	0.153485i
$521$	27.3923			1.20008			0.600039	−	0.799970i	$-0.295152\pi$
$521$	27.3923			1.20008			0.600039	+	0.799970i	$0.295152\pi$
$522$		0			0
$523$	−6.85641	+	11.8756i	−0.299810	+	0.519286i	−0.976092	−	0.217357i	$-0.930257\pi$
$523$	−6.85641	+	11.8756i	−0.299810	+	0.519286i	0.676283	+	0.736642i	$0.263590\pi$
$524$	10.1603	+	17.5981i	0.443853	+	0.768776i
$525$		0			0
$526$	17.7679	−	10.2583i	0.774719	−	0.447284i
$527$	−30.9282	+	17.8564i	−1.34725	+	0.777837i
$528$		0			0
$529$	5.50000	+	9.52628i	0.239130	+	0.414186i
$530$	−1.86603	+	3.23205i	−0.0810550	+	0.140391i
$531$		0			0
$532$	6.80385			0.294984
$533$	−4.00000	+	13.8564i	−0.173259	+	0.600188i
$534$		0			0
$535$	0.803848	+	0.464102i	0.0347534	+	0.0200649i
$536$	−2.73205	+	4.73205i	−0.118007	+	0.204393i
$537$		0			0
$538$		−	30.9282i		−	1.33341i
$539$	6.46410	−	3.73205i	0.278429	−	0.160751i
$540$		0			0
$541$		−	26.7846i		−	1.15156i	−0.817605	−	0.575780i	$-0.804698\pi$
$541$		−	26.7846i		−	1.15156i	0.817605	−	0.575780i	$-0.195302\pi$
$542$	−1.80385	−	3.12436i	−0.0774819	−	0.134203i
$543$		0			0
$544$	−3.46410	−	2.00000i	−0.148522	−	0.0857493i
$545$	10.3923			0.445157
$546$		0			0
$547$	29.3205			1.25365			0.626827	−	0.779158i	$-0.284353\pi$
$547$	29.3205			1.25365			0.626827	+	0.779158i	$0.284353\pi$
$548$	5.66025	+	3.26795i	0.241794	+	0.139600i
$549$		0			0
$550$	−1.86603	−	3.23205i	−0.0795676	−	0.137815i
$551$		−	12.3923i		−	0.527930i
$552$		0			0
$553$	−43.9808	+	25.3923i	−1.87025	+	1.07979i
$554$			19.5885i			0.832234i
$555$		0			0
$556$	10.8923	−	18.8660i	0.461937	−	0.800098i
$557$	−37.5788	−	21.6962i	−1.59227	−	0.919295i	−0.992917	−	0.118808i	$-0.962093\pi$
$557$	−37.5788	−	21.6962i	−1.59227	−	0.919295i	−0.599349	−	0.800488i	$-0.704574\pi$
$558$		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
$563$	9.66025	+	16.7321i	0.407131	+	0.705172i	0.994567	−	0.104099i	$-0.0331959\pi$
$563$	9.66025	+	16.7321i	0.407131	+	0.705172i	−0.587436	+	0.809271i	$0.699863\pi$
$564$		0			0
$565$	10.3923	−	6.00000i	0.437208	−	0.252422i
$566$	−12.4641	+	7.19615i	−0.523905	+	0.302477i
$567$		0			0
$568$	0.464102	+	0.803848i	0.0194733	+	0.0337287i
$569$	9.16025	−	15.8660i	0.384018	−	0.665138i	−0.607615	−	0.794232i	$-0.707873\pi$
$569$	9.16025	−	15.8660i	0.384018	−	0.665138i	0.991632	+	0.129094i	$0.0412068\pi$
$570$		0			0
$571$	−16.8564			−0.705419			−0.352709	−	0.935733i	$-0.614740\pi$
$571$	−16.8564			−0.705419			−0.352709	+	0.935733i	$0.614740\pi$
$572$	13.0622	−	3.23205i	0.546157	−	0.135139i
$573$		0			0
$574$	10.3923	+	6.00000i	0.433766	+	0.250435i
$575$	1.73205	−	3.00000i	0.0722315	−	0.125109i
$576$		0			0
$577$			25.3205i			1.05411i	0.849832	+	0.527053i	$0.176703\pi$
$577$			25.3205i			1.05411i	−0.849832	+	0.527053i	$0.823297\pi$
$578$	0.866025	−	0.500000i	0.0360219	−	0.0207973i
$579$		0			0
$580$		−	5.46410i		−	0.226884i
$581$	−3.80385	−	6.58846i	−0.157810	−	0.273335i
$582$		0			0
$583$	12.0622	+	6.96410i	0.499564	+	0.288424i
$584$	6.92820			0.286691
$585$		0			0
$586$	−19.2487			−0.795157
$587$	4.26795	+	2.46410i	0.176157	+	0.101704i	0.585486	−	0.810683i	$-0.300904\pi$
$587$	4.26795	+	2.46410i	0.176157	+	0.101704i	−0.409329	+	0.912387i	$0.634237\pi$
$588$		0			0
$589$	−10.1244	−	17.5359i	−0.417167	−	0.722554i
$590$		−	4.53590i		−	0.186740i
$591$		0			0
$592$	6.86603	−	3.96410i	0.282192	−	0.162924i
$593$			3.21539i			0.132040i	0.997818	+	0.0660201i	$0.0210302\pi$
$593$			3.21539i			0.132040i	−0.997818	+	0.0660201i	$0.978970\pi$
$594$		0			0
$595$	6.00000	−	10.3923i	0.245976	−	0.426043i
$596$	−19.7321	−	11.3923i	−0.808256	−	0.466647i
$597$		0			0
$598$	8.66025	+	9.00000i	0.354144	+	0.368037i
$599$	−15.0718			−0.615817			−0.307908	−	0.951416i	$-0.599629\pi$
$599$	−15.0718			−0.615817			−0.307908	+	0.951416i	$0.599629\pi$
$600$		0			0
$601$	12.3564	−	21.4019i	0.504028	−	0.873003i	−0.495961	−	0.868345i	$-0.665184\pi$
$601$	12.3564	−	21.4019i	0.504028	−	0.873003i	0.999989	−	0.00465778i	$-0.00148262\pi$
$602$	9.00000	+	15.5885i	0.366813	+	0.635338i
$603$		0			0
$604$	−16.2679	+	9.39230i	−0.661933	+	0.382167i
$605$	−2.53590	+	1.46410i	−0.103099	+	0.0595242i
$606$		0			0
$607$	−18.7224	−	32.4282i	−0.759920	−	1.31622i	−0.942891	−	0.333102i	$-0.891905\pi$
$607$	−18.7224	−	32.4282i	−0.759920	−	1.31622i	0.182971	−	0.983118i	$-0.441429\pi$
$608$	1.13397	−	1.96410i	0.0459887	−	0.0796548i
$609$		0			0
$610$	−7.46410			−0.302213
$611$	1.62436	−	0.401924i	0.0657144	−	0.0162601i
$612$		0			0
$613$	−38.9711	−	22.5000i	−1.57403	−	0.908766i	−0.995667	−	0.0929864i	$-0.970359\pi$
$613$	−38.9711	−	22.5000i	−1.57403	−	0.908766i	−0.578362	−	0.815780i	$-0.696308\pi$
$614$	−10.1244	+	17.5359i	−0.408586	+	0.707691i
$615$		0			0
$616$		−	11.1962i		−	0.451106i
$617$	−24.7128	+	14.2679i	−0.994900	+	0.574406i	−0.906735	−	0.421700i	$-0.861434\pi$
$617$	−24.7128	+	14.2679i	−0.994900	+	0.574406i	−0.0881649	+	0.996106i	$0.528100\pi$
$618$		0			0
$619$		−	42.5167i		−	1.70889i	−0.519543	−	0.854444i	$-0.673898\pi$
$619$		−	42.5167i		−	1.70889i	0.519543	−	0.854444i	$-0.326102\pi$
$620$	−4.46410	−	7.73205i	−0.179283	−	0.310527i
$621$		0			0
$622$	−4.39230	−	2.53590i	−0.176115	−	0.101680i
$623$	−30.3731			−1.21687
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.14359	+	0.660254i	0.0457072	+	0.0263891i
$627$		0			0
$628$	5.40192	+	9.35641i	0.215560	+	0.373361i
$629$		−	31.7128i		−	1.26447i
$630$		0			0
$631$	6.92820	−	4.00000i	0.275807	−	0.159237i	−0.355716	−	0.934594i	$-0.615763\pi$
$631$	6.92820	−	4.00000i	0.275807	−	0.159237i	0.631524	+	0.775356i	$0.282430\pi$
$632$			16.9282i			0.673368i
$633$		0			0
$634$	11.7679	−	20.3827i	0.467365	−	0.809500i
$635$	−4.03590	−	2.33013i	−0.160160	−	0.0924683i
$636$		0			0
$637$	−6.92820	−	2.00000i	−0.274505	−	0.0792429i
$638$	−20.3923			−0.807339
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	3.76795	+	6.52628i	0.148825	+	0.257773i	0.930793	−	0.365546i	$-0.119118\pi$
$641$	3.76795	+	6.52628i	0.148825	+	0.257773i	−0.781968	+	0.623318i	$0.785784\pi$
$642$		0			0
$643$	24.9282	−	14.3923i	0.983072	−	0.567577i	0.0798761	−	0.996805i	$-0.474548\pi$
$643$	24.9282	−	14.3923i	0.983072	−	0.567577i	0.903196	+	0.429228i	$0.141214\pi$
$644$	9.00000	−	5.19615i	0.354650	−	0.204757i
$645$		0			0
$646$	−4.53590	−	7.85641i	−0.178463	−	0.309106i
$647$	−16.1340	+	27.9449i	−0.634292	+	1.09863i	0.352373	+	0.935860i	$0.385375\pi$
$647$	−16.1340	+	27.9449i	−0.634292	+	1.09863i	−0.986665	+	0.162766i	$0.947958\pi$
$648$		0			0
$649$	−16.9282			−0.664490
$650$	−1.00000	+	3.46410i	−0.0392232	+	0.135873i
$651$		0			0
$652$	−9.46410	−	5.46410i	−0.370643	−	0.213991i
$653$	14.7942	−	25.6244i	0.578943	−	1.00276i	−0.416658	−	0.909063i	$-0.636799\pi$
$653$	14.7942	−	25.6244i	0.578943	−	1.00276i	0.995601	−	0.0936952i	$-0.0298679\pi$
$654$		0			0
$655$			20.3205i			0.793988i
$656$	3.46410	−	2.00000i	0.135250	−	0.0780869i
$657$		0			0
$658$		−	1.39230i		−	0.0542777i
$659$	7.85641	+	13.6077i	0.306042	+	0.530081i	0.977493	−	0.210969i	$-0.0676618\pi$
$659$	7.85641	+	13.6077i	0.306042	+	0.530081i	−0.671451	+	0.741049i	$0.734328\pi$
$660$		0			0
$661$	36.7128	+	21.1962i	1.42796	+	0.824435i	0.996960	−	0.0779157i	$-0.0248265\pi$
$661$	36.7128	+	21.1962i	1.42796	+	0.824435i	0.431003	+	0.902351i	$0.358160\pi$
$662$	6.39230			0.248444
$663$		0			0
$664$	−2.53590			−0.0984119
$665$	5.89230	+	3.40192i	0.228494	+	0.131921i
$666$		0			0
$667$	−9.46410	−	16.3923i	−0.366451	−	0.634713i
$668$			6.46410i			0.250104i
$669$		0			0
$670$	−4.73205	+	2.73205i	−0.182815	+	0.105548i
$671$			27.8564i			1.07538i
$672$		0			0
$673$	−12.3923	+	21.4641i	−0.477688	+	0.827380i	−0.999673	−	0.0255746i	$-0.991858\pi$
$673$	−12.3923	+	21.4641i	−0.477688	+	0.827380i	0.521985	+	0.852955i	$0.325192\pi$
$674$	−4.85641	−	2.80385i	−0.187062	−	0.108000i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	2.92820			0.112540			0.0562700	−	0.998416i	$-0.482079\pi$
$677$	2.92820			0.112540			0.0562700	+	0.998416i	$0.482079\pi$
$678$		0			0
$679$	−18.5885	+	32.1962i	−0.713360	+	1.23557i
$680$	−2.00000	−	3.46410i	−0.0766965	−	0.132842i
$681$		0			0
$682$	−28.8564	+	16.6603i	−1.10497	+	0.637954i
$683$	5.78461	−	3.33975i	0.221342	−	0.127792i	−0.385230	−	0.922821i	$-0.625878\pi$
$683$	5.78461	−	3.33975i	0.221342	−	0.127792i	0.606571	+	0.795029i	$0.292544\pi$
$684$		0			0
$685$	3.26795	+	5.66025i	0.124862	+	0.216267i
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$		0			0
$688$	6.00000			0.228748
$689$	−3.23205	−	13.0622i	−0.123131	−	0.497629i
$690$		0			0
$691$	19.9641	+	11.5263i	0.759470	+	0.438480i	0.829106	−	0.559092i	$-0.188850\pi$
$691$	19.9641	+	11.5263i	0.759470	+	0.438480i	−0.0696353	+	0.997573i	$0.522184\pi$
$692$	−11.0622	+	19.1603i	−0.420521	+	0.728364i
$693$		0			0
$694$		−	16.3923i		−	0.622243i
$695$	18.8660	−	10.8923i	0.715629	−	0.413169i
$696$		0			0
$697$		−	16.0000i		−	0.606043i
$698$	8.73205	+	15.1244i	0.330513	+	0.572465i
$699$		0			0
$700$	2.59808	+	1.50000i	0.0981981	+	0.0566947i
$701$	−16.3923			−0.619129			−0.309564	−	0.950878i	$-0.600183\pi$
$701$	−16.3923			−0.619129			−0.309564	+	0.950878i	$0.600183\pi$
$702$		0			0
$703$	17.9808			0.678157
$704$	−3.23205	−	1.86603i	−0.121812	−	0.0703285i
$705$		0			0
$706$	14.1962	+	24.5885i	0.534279	+	0.925399i
$707$		−	25.1769i		−	0.946875i
$708$		0			0
$709$	−6.33975	+	3.66025i	−0.238094	+	0.137464i	−0.614300	−	0.789072i	$-0.710562\pi$
$709$	−6.33975	+	3.66025i	−0.238094	+	0.137464i	0.376206	+	0.926536i	$0.377228\pi$
$710$			0.928203i			0.0348348i
$711$		0			0
$712$	−5.06218	+	8.76795i	−0.189713	+	0.328593i
$713$	−26.7846	−	15.4641i	−1.00309	−	0.579135i
$714$		0			0
$715$	12.9282	+	3.73205i	0.483487	+	0.139571i
$716$	22.9282			0.856867
$717$		0			0
$718$	−6.46410	+	11.1962i	−0.241238	+	0.417837i
$719$	8.00000	+	13.8564i	0.298350	+	0.516757i	0.975759	−	0.218850i	$-0.0702305\pi$
$719$	8.00000	+	13.8564i	0.298350	+	0.516757i	−0.677409	+	0.735607i	$0.736897\pi$
$720$		0			0
$721$	−50.8923	+	29.3827i	−1.89533	+	1.09427i
$722$	−12.0000	+	6.92820i	−0.446594	+	0.257841i
$723$		0			0
$724$	1.53590	+	2.66025i	0.0570812	+	0.0988676i
$725$	2.73205	−	4.73205i	0.101466	−	0.175744i
$726$		0			0
$727$	12.6603			0.469543			0.234771	−	0.972051i	$-0.424566\pi$
$727$	12.6603			0.469543			0.234771	+	0.972051i	$0.424566\pi$
$728$	−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
$733$		−	6.85641i		−	0.253247i	−0.991951	−	0.126624i	$-0.959586\pi$
$733$		−	6.85641i		−	0.253247i	0.991951	−	0.126624i	$-0.0404140\pi$
$734$	11.5359	−	6.66025i	0.425798	−	0.245834i
$735$		0			0
$736$		−	3.46410i		−	0.127688i
$737$	10.1962	+	17.6603i	0.375580	+	0.650524i
$738$		0			0
$739$	37.9641	+	21.9186i	1.39653	+	0.806288i	0.994028	−	0.109130i	$-0.0348064\pi$
$739$	37.9641	+	21.9186i	1.39653	+	0.806288i	0.402505	+	0.915418i	$0.368140\pi$
$740$	7.92820			0.291447
$741$		0			0
$742$	−11.1962			−0.411024
$743$	2.53590	+	1.46410i	0.0930331	+	0.0537127i	0.545795	−	0.837919i	$-0.316228\pi$
$743$	2.53590	+	1.46410i	0.0930331	+	0.0537127i	−0.452762	+	0.891632i	$0.649561\pi$
$744$		0			0
$745$	−11.3923	−	19.7321i	−0.417382	−	0.722926i
$746$		−	22.9282i		−	0.839461i
$747$		0			0
$748$	−12.9282	+	7.46410i	−0.472702	+	0.272915i
$749$			2.78461i			0.101747i
$750$		0			0
$751$	−20.5885	+	35.6603i	−0.751283	+	1.30126i	0.195917	+	0.980620i	$0.437232\pi$
$751$	−20.5885	+	35.6603i	−0.751283	+	1.30126i	−0.947201	+	0.320641i	$0.896102\pi$
$752$	−0.401924	−	0.232051i	−0.0146567	−	0.00846202i
$753$		0			0
$754$	13.6603	+	14.1962i	0.497477	+	0.516993i
$755$	−18.7846			−0.683642
$756$		0			0
$757$	−9.13397	+	15.8205i	−0.331980	+	0.575006i	−0.982900	−	0.184140i	$-0.941050\pi$
$757$	−9.13397	+	15.8205i	−0.331980	+	0.575006i	0.650920	+	0.759146i	$0.274383\pi$
$758$	3.13397	+	5.42820i	0.113831	+	0.197161i
$759$		0			0
$760$	1.96410	−	1.13397i	0.0712455	−	0.0411336i
$761$	−38.0885	+	21.9904i	−1.38071	+	0.797151i	−0.992243	−	0.124314i	$-0.960327\pi$
$761$	−38.0885	+	21.9904i	−1.38071	+	0.797151i	−0.388463	+	0.921465i	$0.626994\pi$
$762$		0			0
$763$	15.5885	+	27.0000i	0.564340	+	0.977466i
$764$	−8.66025	+	15.0000i	−0.313317	+	0.542681i
$765$		0			0
$766$	−36.7846			−1.32908
$767$	11.3397	+	11.7846i	0.409454	+	0.425518i
$768$		0			0
$769$	34.3923	+	19.8564i	1.24022	+	0.716040i	0.969139	−	0.246517i	$-0.0792860\pi$
$769$	34.3923	+	19.8564i	1.24022	+	0.716040i	0.271080	+	0.962557i	$0.412619\pi$
$770$	5.59808	−	9.69615i	0.201741	−	0.349425i
$771$		0			0
$772$		−	17.8564i		−	0.642666i
$773$	−46.2391	+	26.6962i	−1.66310	+	0.960194i	−0.691885	+	0.722008i	$0.743220\pi$
$773$	−46.2391	+	26.6962i	−1.66310	+	0.960194i	−0.971220	+	0.238186i	$0.923447\pi$
$774$		0			0
$775$		−	8.92820i		−	0.320711i
$776$	6.19615	+	10.7321i	0.222429	+	0.385258i
$777$		0			0
$778$	8.53590	+	4.92820i	0.306027	+	0.176685i
$779$	9.07180			0.325031
$780$		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
$785$			10.8038i			0.385606i
$786$		0			0
$787$	4.73205	−	2.73205i	0.168679	−	0.0973871i	−0.413284	−	0.910602i	$-0.635618\pi$
$787$	4.73205	−	2.73205i	0.168679	−	0.0973871i	0.581963	+	0.813215i	$0.302285\pi$
$788$			9.39230i			0.334587i
$789$		0			0
$790$	−8.46410	+	14.6603i	−0.301139	+	0.521588i
$791$	31.1769	+	18.0000i	1.10852	+	0.640006i
$792$		0			0
$793$	19.3923	−	18.6603i	0.688641	−	0.662645i
$794$	−7.92820			−0.281361
$795$		0			0
$796$	−5.53590	+	9.58846i	−0.196215	+	0.339854i
$797$	−18.9282	−	32.7846i	−0.670471	−	1.16129i	−0.977771	−	0.209678i	$-0.932759\pi$
$797$	−18.9282	−	32.7846i	−0.670471	−	1.16129i	0.307299	−	0.951613i	$-0.400575\pi$
$798$		0			0
$799$	−1.60770	+	0.928203i	−0.0568762	+	0.0328375i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$		0			0
$802$	1.06218	+	1.83975i	0.0375068	+	0.0649637i
$803$	12.9282	−	22.3923i	0.456226	−	0.790207i
$804$		0			0
$805$	10.3923			0.366281
$806$	30.9282	+	8.92820i	1.08940	+	0.314483i
$807$		0			0
$808$	−7.26795	−	4.19615i	−0.255686	−	0.147620i
$809$	17.3923	−	30.1244i	0.611481	−	1.05912i	−0.379510	−	0.925188i	$-0.623907\pi$
$809$	17.3923	−	30.1244i	0.611481	−	1.05912i	0.990991	−	0.133928i	$-0.0427592\pi$
$810$		0			0
$811$		−	7.58846i		−	0.266467i	−0.991085	−	0.133233i	$-0.957464\pi$
$811$		−	7.58846i		−	0.266467i	0.991085	−	0.133233i	$-0.0425360\pi$
$812$	14.1962	−	8.19615i	0.498187	−	0.287629i
$813$		0			0
$814$		−	29.5885i		−	1.03707i
$815$	−5.46410	−	9.46410i	−0.191399	−	0.331513i
$816$		0			0
$817$	11.7846	+	6.80385i	0.412291	+	0.238036i
$818$	0.947441			0.0331265
$819$		0			0
$820$	4.00000			0.139686
$821$	−42.7128	−	24.6603i	−1.49069	−	0.860649i	−0.490744	−	0.871304i	$-0.663275\pi$
$821$	−42.7128	−	24.6603i	−1.49069	−	0.860649i	−0.999943	+	0.0106549i	$0.996608\pi$
$822$		0			0
$823$	19.7942	+	34.2846i	0.689983	+	1.19509i	0.971843	+	0.235631i	$0.0757155\pi$
$823$	19.7942	+	34.2846i	0.689983	+	1.19509i	−0.281859	+	0.959456i	$0.590951\pi$
$824$			19.5885i			0.682396i
$825$		0			0
$826$	11.7846	−	6.80385i	0.410039	−	0.236736i
$827$			50.4974i			1.75597i	0.478690	+	0.877984i	$0.341112\pi$
$827$			50.4974i			1.75597i	−0.478690	+	0.877984i	$0.658888\pi$
$828$		0			0
$829$	19.6603	−	34.0526i	0.682829	−	1.18269i	−0.291285	−	0.956636i	$-0.594083\pi$
$829$	19.6603	−	34.0526i	0.682829	−	1.18269i	0.974114	−	0.226058i	$-0.0725839\pi$
$830$	−2.19615	−	1.26795i	−0.0762296	−	0.0440112i
$831$		0			0
$832$	0.866025	+	3.50000i	0.0300240	+	0.121341i
$833$	8.00000			0.277184
$834$		0			0
$835$	−3.23205	+	5.59808i	−0.111850	+	0.193729i
$836$	−4.23205	−	7.33013i	−0.146369	−	0.253518i
$837$		0			0
$838$	−15.4641	+	8.92820i	−0.534199	+	0.308420i
$839$	−37.3923	+	21.5885i	−1.29093	+	0.745316i	−0.978818	−	0.204731i	$-0.934368\pi$
$839$	−37.3923	+	21.5885i	−1.29093	+	0.745316i	−0.312107	+	0.950047i	$0.601035\pi$
$840$		0			0
$841$	−0.428203	−	0.741670i	−0.0147656	−	0.0255748i
$842$	2.92820	−	5.07180i	0.100913	−	0.174786i
$843$		0			0
$844$	21.9282			0.754800
$845$	−6.06218	−	11.5000i	−0.208545	−	0.395612i
$846$		0			0
$847$	−7.60770	−	4.39230i	−0.261403	−	0.150921i
$848$	−1.86603	+	3.23205i	−0.0640796	+	0.110989i
$849$		0			0
$850$		−	4.00000i		−	0.137199i
$851$	23.7846	−	13.7321i	0.815326	−	0.470729i
$852$		0			0
$853$			44.6410i			1.52848i	0.644932	+	0.764240i	$0.276886\pi$
$853$			44.6410i			1.52848i	−0.644932	+	0.764240i	$0.723114\pi$
$854$	−11.1962	−	19.3923i	−0.383124	−	0.663591i
$855$		0			0
$856$	0.803848	+	0.464102i	0.0274749	+	0.0158627i
$857$	15.0718			0.514843			0.257421	−	0.966299i	$-0.417127\pi$
$857$	15.0718			0.514843			0.257421	+	0.966299i	$0.417127\pi$
$858$		0			0
$859$	−19.9282			−0.679942			−0.339971	−	0.940436i	$-0.610417\pi$
$859$	−19.9282			−0.679942			−0.339971	+	0.940436i	$0.610417\pi$
$860$	5.19615	+	3.00000i	0.177187	+	0.102299i
$861$		0			0
$862$	6.92820	+	12.0000i	0.235976	+	0.408722i
$863$			10.9282i			0.372000i	0.982550	+	0.186000i	$0.0595525\pi$
$863$			10.9282i			0.372000i	−0.982550	+	0.186000i	$0.940447\pi$
$864$		0			0
$865$	−19.1603	+	11.0622i	−0.651468	+	0.376125i
$866$		−	32.7846i		−	1.11407i
$867$		0			0
$868$	13.3923	−	23.1962i	0.454564	−	0.787329i
$869$	54.7128	+	31.5885i	1.85601	+	1.07157i
$870$		0			0
$871$	5.46410	−	18.9282i	0.185144	−	0.641358i
$872$	10.3923			0.351928
$873$		0			0
$874$	3.92820	−	6.80385i	0.132873	−	0.230144i
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$		0			0
$877$	29.1962	−	16.8564i	0.985884	−	0.569200i	0.0818426	−	0.996645i	$-0.473920\pi$
$877$	29.1962	−	16.8564i	0.985884	−	0.569200i	0.904041	+	0.427445i	$0.140586\pi$
$878$	−18.4641	+	10.6603i	−0.623133	+	0.359766i
$879$		0			0
$880$	−1.86603	−	3.23205i	−0.0629037	−	0.108952i
$881$	−18.5526	+	32.1340i	−0.625052	+	1.08262i	0.363479	+	0.931602i	$0.381589\pi$
$881$	−18.5526	+	32.1340i	−0.625052	+	1.08262i	−0.988531	+	0.151019i	$0.951745\pi$
$882$		0			0
$883$	21.3205			0.717492			0.358746	−	0.933435i	$-0.383204\pi$
$883$	21.3205			0.717492			0.358746	+	0.933435i	$0.383204\pi$
$884$	13.8564	+	4.00000i	0.466041	+	0.134535i
$885$		0			0
$886$	−6.80385	−	3.92820i	−0.228580	−	0.131971i
$887$	26.1340	−	45.2654i	0.877493	−	1.51986i	0.0234098	−	0.999726i	$-0.492548\pi$
$887$	26.1340	−	45.2654i	0.877493	−	1.51986i	0.854083	−	0.520136i	$-0.174119\pi$
$888$		0			0
$889$		−	13.9808i		−	0.468900i
$890$	−8.76795	+	5.06218i	−0.293902	+	0.169685i
$891$		0			0
$892$		−	8.85641i		−	0.296534i
$893$	−0.526279	−	0.911543i	−0.0176113	−	0.0305036i
$894$		0			0
$895$	19.8564	+	11.4641i	0.663726	+	0.383203i
$896$	3.00000			0.100223
$897$		0			0
$898$	18.1244			0.604818
$899$	−42.2487	−	24.3923i	−1.40907	−	0.813529i
$900$		0			0
$901$	7.46410	+	12.9282i	0.248665	+	0.430701i
$902$		−	14.9282i		−	0.497055i
$903$		0			0
$904$	10.3923	−	6.00000i	0.345643	−	0.199557i
$905$			3.07180i			0.102110i
$906$		0			0
$907$	−3.53590	+	6.12436i	−0.117408	+	0.203356i	−0.918740	−	0.394864i	$-0.870792\pi$
$907$	−3.53590	+	6.12436i	−0.117408	+	0.203356i	0.801332	+	0.598220i	$0.204125\pi$
$908$	11.6603	+	6.73205i	0.386959	+	0.223411i
$909$		0			0
$910$	−10.5000	+	2.59808i	−0.348072	+	0.0861254i
$911$	28.7846			0.953677			0.476838	−	0.878991i	$-0.341783\pi$
$911$	28.7846			0.953677			0.476838	+	0.878991i	$0.341783\pi$
$912$		0			0
$913$	−4.73205	+	8.19615i	−0.156608	+	0.271253i
$914$	0.267949	+	0.464102i	0.00886297	+	0.0153511i
$915$		0			0
$916$	9.92820	−	5.73205i	0.328037	−	0.189392i
$917$	−52.7942	+	30.4808i	−1.74342	+	1.00656i
$918$		0			0
$919$	−27.9808	−	48.4641i	−0.923000	−	1.59868i	−0.794746	−	0.606942i	$-0.792396\pi$
$919$	−27.9808	−	48.4641i	−0.923000	−	1.59868i	−0.128254	−	0.991741i	$-0.540937\pi$
$920$	1.73205	−	3.00000i	0.0571040	−	0.0989071i
$921$		0			0
$922$	−32.3923			−1.06678
$923$	−2.32051	−	2.41154i	−0.0763805	−	0.0793769i
$924$		0			0
$925$	6.86603	+	3.96410i	0.225754	+	0.130339i
$926$	−0.392305	+	0.679492i	−0.0128919	+	0.0223295i
$927$		0			0
$928$		−	5.46410i		−	0.179368i
$929$	26.1051	−	15.0718i	0.856481	−	0.494490i	−0.00635120	−	0.999980i	$-0.502022\pi$
$929$	26.1051	−	15.0718i	0.856481	−	0.494490i	0.862832	+	0.505490i	$0.168688\pi$
$930$		0			0
$931$			4.53590i			0.148658i
$932$	−9.00000	−	15.5885i	−0.294805	−	0.510617i
$933$		0			0
$934$	−3.12436	−	1.80385i	−0.102232	−	0.0590237i
$935$	−14.9282			−0.488204
$936$		0			0
$937$	33.7128			1.10135			0.550675	−	0.834720i	$-0.314370\pi$
$937$	33.7128			1.10135			0.550675	+	0.834720i	$0.314370\pi$
$938$	−14.1962	−	8.19615i	−0.463521	−	0.267614i
$939$		0			0
$940$	−0.232051	−	0.401924i	−0.00756866	−	0.0131093i
$941$		−	36.4974i		−	1.18978i	−0.803806	−	0.594891i	$-0.797195\pi$
$941$		−	36.4974i		−	1.18978i	0.803806	−	0.594891i	$-0.202805\pi$
$942$		0			0
$943$	12.0000	−	6.92820i	0.390774	−	0.225613i
$944$		−	4.53590i		−	0.147631i
$945$		0			0
$946$	11.1962	−	19.3923i	0.364018	−	0.630498i
$947$	11.7846	+	6.80385i	0.382948	+	0.221095i	0.679100	−	0.734046i	$-0.262370\pi$
$947$	11.7846	+	6.80385i	0.382948	+	0.221095i	−0.296152	+	0.955141i	$0.595703\pi$
$948$		0			0
$949$	−24.2487	+	6.00000i	−0.787146	+	0.194768i
$950$	2.26795			0.0735820
$951$		0			0
$952$	6.00000	−	10.3923i	0.194461	−	0.336817i
$953$	−9.33975	−	16.1769i	−0.302544	−	0.524022i	0.674167	−	0.738579i	$-0.264503\pi$
$953$	−9.33975	−	16.1769i	−0.302544	−	0.524022i	−0.976711	+	0.214557i	$0.931169\pi$
$954$		0			0
$955$	−15.0000	+	8.66025i	−0.485389	+	0.280239i
$956$	−3.00000	+	1.73205i	−0.0970269	+	0.0560185i
$957$		0			0
$958$	13.1244	+	22.7321i	0.424029	+	0.734439i
$959$	−9.80385	+	16.9808i	−0.316583	+	0.548337i
$960$		0			0
$961$	−48.7128			−1.57138
$962$	−20.5981	+	19.8205i	−0.664109	+	0.639039i
$963$		0			0
$964$	12.8205	+	7.40192i	0.412921	+	0.238400i
$965$	8.92820	−	15.4641i	0.287409	−	0.497807i
$966$		0			0
$967$		−	28.8564i		−	0.927959i	−0.885846	−	0.463980i	$-0.846421\pi$
$967$		−	28.8564i		−	0.927959i	0.885846	−	0.463980i	$-0.153579\pi$
$968$	−2.53590	+	1.46410i	−0.0815069	+	0.0470580i
$969$		0			0
$970$			12.3923i			0.397893i
$971$	−10.3038	−	17.8468i	−0.330666	−	0.572731i	0.651976	−	0.758239i	$-0.273940\pi$
$971$	−10.3038	−	17.8468i	−0.330666	−	0.572731i	−0.982643	+	0.185509i	$0.940607\pi$
$972$		0			0
$973$	56.5981	+	32.6769i	1.81445	+	1.04757i
$974$	−21.0000			−0.672883
$975$		0			0
$976$	−7.46410			−0.238920
$977$	1.26795	+	0.732051i	0.0405653	+	0.0234204i	0.520145	−	0.854078i	$-0.325878\pi$
$977$	1.26795	+	0.732051i	0.0405653	+	0.0234204i	−0.479580	+	0.877498i	$0.659211\pi$
$978$		0			0
$979$	18.8923	+	32.7224i	0.603801	+	1.04581i
$980$			2.00000i			0.0638877i
$981$		0			0
$982$	−13.3301	+	7.69615i	−0.425381	+	0.245594i
$983$			16.1769i			0.515963i	0.966150	+	0.257982i	$0.0830574\pi$
$983$			16.1769i			0.515963i	−0.966150	+	0.257982i	$0.916943\pi$
$984$		0			0
$985$	−4.69615	+	8.13397i	−0.149632	+	0.259170i
$986$	−18.9282	−	10.9282i	−0.602797	−	0.348025i
$987$		0			0
$988$	−2.26795	+	7.85641i	−0.0721531	+	0.249946i
$989$	20.7846			0.660912
$990$		0			0
$991$	11.5885	−	20.0718i	0.368119	−	0.637602i	−0.621152	−	0.783690i	$-0.713335\pi$
$991$	11.5885	−	20.0718i	0.368119	−	0.637602i	0.989272	+	0.146088i	$0.0466684\pi$
$992$	−4.46410	−	7.73205i	−0.141735	−	0.245493i
$993$		0			0
$994$	−2.41154	+	1.39230i	−0.0764895	+	0.0441612i
$995$	−9.58846	+	5.53590i	−0.303975	+	0.175500i
$996$		0			0
$997$	−5.00962	−	8.67691i	−0.158656	−	0.274801i	0.775728	−	0.631067i	$-0.217383\pi$
$997$	−5.00962	−	8.67691i	−0.158656	−	0.274801i	−0.934384	+	0.356267i	$0.884049\pi$
$998$	0.660254	−	1.14359i	0.0209000	−	0.0361998i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.d.901.2		4
3.2	odd	2		390.2.bb.a.121.1	✓	4
13.10	even	6	inner	1170.2.bs.d.361.2		4
15.2	even	4		1950.2.y.e.199.1		4
15.8	even	4		1950.2.y.d.199.2		4
15.14	odd	2		1950.2.bc.a.901.2		4
39.17	odd	6		5070.2.b.p.1351.1		4
39.20	even	12		5070.2.a.ba.1.2		2
39.23	odd	6		390.2.bb.a.361.1	yes	4
39.32	even	12		5070.2.a.be.1.1		2
39.35	odd	6		5070.2.b.p.1351.4		4
195.23	even	12		1950.2.y.e.49.1		4
195.62	even	12		1950.2.y.d.49.2		4
195.179	odd	6		1950.2.bc.a.751.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.a.121.1	✓	4	3.2	odd	2
390.2.bb.a.361.1	yes	4	39.23	odd	6
1170.2.bs.d.361.2		4	13.10	even	6	inner
1170.2.bs.d.901.2		4	1.1	even	1	trivial
1950.2.y.d.49.2		4	195.62	even	12
1950.2.y.d.199.2		4	15.8	even	4
1950.2.y.e.49.1		4	195.23	even	12
1950.2.y.e.199.1		4	15.2	even	4
1950.2.bc.a.751.2		4	195.179	odd	6
1950.2.bc.a.901.2		4	15.14	odd	2
5070.2.a.ba.1.2		2	39.20	even	12
5070.2.a.be.1.1		2	39.32	even	12
5070.2.b.p.1351.1		4	39.17	odd	6
5070.2.b.p.1351.4		4	39.35	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.59808 + 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(3.23205 + 1.86603i) q^{11} +(-0.866025 - 3.50000i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-1.96410 + 1.13397i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.86603 + 3.23205i) q^{22} +(-1.73205 + 3.00000i) q^{23} -1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +(-2.59808 - 1.50000i) q^{28} +(-2.73205 + 4.73205i) q^{29} +8.92820i q^{31} +(-0.866025 + 0.500000i) q^{32} +4.00000i q^{34} +(-1.50000 - 2.59808i) q^{35} +(-6.86603 - 3.96410i) q^{37} -2.26795 q^{38} -1.00000 q^{40} +(-3.46410 - 2.00000i) q^{41} +(-3.00000 - 5.19615i) q^{43} +3.73205i q^{44} +(-3.00000 + 1.73205i) q^{46} +0.464102i q^{47} +(1.00000 - 1.73205i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(2.59808 - 2.50000i) q^{52} +3.73205 q^{53} +(-1.86603 + 3.23205i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(-4.73205 + 2.73205i) q^{58} +(-3.92820 + 2.26795i) q^{59} +(3.73205 + 6.46410i) q^{61} +(-4.46410 + 7.73205i) q^{62} -1.00000 q^{64} +(3.50000 - 0.866025i) q^{65} +(4.73205 + 2.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} -3.00000i q^{70} +(0.803848 - 0.464102i) q^{71} -6.92820i q^{73} +(-3.96410 - 6.86603i) q^{74} +(-1.96410 - 1.13397i) q^{76} -11.1962 q^{77} +16.9282 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-2.00000 - 3.46410i) q^{82} +2.53590i q^{83} +(-3.46410 + 2.00000i) q^{85} -6.00000i q^{86} +(-1.86603 + 3.23205i) q^{88} +(8.76795 + 5.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} -3.46410 q^{92} +(-0.232051 + 0.401924i) q^{94} +(-1.13397 - 1.96410i) q^{95} +(10.7321 - 6.19615i) q^{97} +(1.73205 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 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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