LMFDB - Embedded newform 1170.2.bs.c.361.2

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 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.c.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(3.50000 + 0.866025i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.09808 - 7.09808i) q^{17} +(-0.401924 - 0.232051i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(4.73205 + 8.19615i) q^{23} -1.00000 q^{25} +(3.46410 - 1.00000i) q^{26} +(2.59808 - 1.50000i) q^{28} +(-1.26795 - 2.19615i) q^{29} -4.73205i q^{31} +(-0.866025 - 0.500000i) q^{32} -8.19615i q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.696152 + 0.401924i) q^{37} -0.464102 q^{38} -1.00000 q^{40} +(9.00000 - 5.19615i) q^{41} +(-1.00000 + 1.73205i) q^{43} +3.00000i q^{44} +(8.19615 + 4.73205i) q^{46} +3.00000i q^{47} +(1.00000 + 1.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(2.50000 - 2.59808i) q^{52} -0.464102 q^{53} +(1.50000 + 2.59808i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-2.19615 - 1.26795i) q^{58} +(-9.00000 - 5.19615i) q^{59} +(-3.09808 + 5.36603i) q^{61} +(-2.36603 - 4.09808i) q^{62} -1.00000 q^{64} +(0.866025 - 3.50000i) q^{65} +(-4.09808 - 7.09808i) q^{68} -3.00000i q^{70} +(5.19615 + 3.00000i) q^{71} -11.6603i q^{73} +(-0.401924 + 0.696152i) q^{74} +(-0.401924 + 0.232051i) q^{76} -9.00000 q^{77} -4.19615 q^{79} +(-0.866025 + 0.500000i) q^{80} +(5.19615 - 9.00000i) q^{82} -8.19615i q^{83} +(-7.09808 - 4.09808i) q^{85} +2.00000i q^{86} +(1.50000 + 2.59808i) q^{88} +(-5.89230 + 3.40192i) q^{89} +(7.79423 + 7.50000i) q^{91} +9.46410 q^{92} +(1.50000 + 2.59808i) q^{94} +(-0.232051 + 0.401924i) q^{95} +(7.90192 + 4.56218i) q^{97} +(1.73205 + 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} - 2 q^{10} + 14 q^{13} + 12 q^{14} - 2 q^{16} + 6 q^{17} - 12 q^{19} - 6 q^{22} + 12 q^{23} - 4 q^{25} - 12 q^{29} + 6 q^{35} + 18 q^{37} + 12 q^{38} - 4 q^{40} + 36 q^{41} - 4 q^{43} + 12 q^{46} + 4 q^{49} + 10 q^{52} + 12 q^{53} + 6 q^{55} + 6 q^{56} + 12 q^{58} - 36 q^{59} - 2 q^{61} - 6 q^{62} - 4 q^{64} - 6 q^{68} - 12 q^{74} - 12 q^{76} - 36 q^{77} + 4 q^{79} - 18 q^{85} + 6 q^{88} + 18 q^{89} + 24 q^{92} + 6 q^{94} + 6 q^{95} + 42 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 + 14 * q^13 + 12 * q^14 - 2 * q^16 + 6 * q^17 - 12 * q^19 - 6 * q^22 + 12 * q^23 - 4 * q^25 - 12 * q^29 + 6 * q^35 + 18 * q^37 + 12 * q^38 - 4 * q^40 + 36 * q^41 - 4 * q^43 + 12 * q^46 + 4 * q^49 + 10 * q^52 + 12 * q^53 + 6 * q^55 + 6 * q^56 + 12 * q^58 - 36 * q^59 - 2 * q^61 - 6 * q^62 - 4 * q^64 - 6 * q^68 - 12 * q^74 - 12 * q^76 - 36 * q^77 + 4 * q^79 - 18 * q^85 + 6 * q^88 + 18 * q^89 + 24 * q^92 + 6 * q^94 + 6 * q^95 + 42 * 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
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.09808	−	7.09808i	0.993929	−	1.72154i	0.401685	−	0.915778i	$-0.368425\pi$
$17$	4.09808	−	7.09808i	0.993929	−	1.72154i	0.592244	−	0.805759i	$-0.298242\pi$
$18$		0			0
$19$	−0.401924	−	0.232051i	−0.0922076	−	0.0532361i	0.453187	−	0.891415i	$-0.350287\pi$
$19$	−0.401924	−	0.232051i	−0.0922076	−	0.0532361i	−0.545395	+	0.838179i	$0.683620\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	4.73205	+	8.19615i	0.986701	+	1.70902i	0.634120	+	0.773234i	$0.281362\pi$
$23$	4.73205	+	8.19615i	0.986701	+	1.70902i	0.352581	+	0.935781i	$0.385304\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	3.46410	−	1.00000i	0.679366	−	0.196116i
$27$		0			0
$28$	2.59808	−	1.50000i	0.490990	−	0.283473i
$29$	−1.26795	−	2.19615i	−0.235452	−	0.407815i	0.723952	−	0.689851i	$-0.242324\pi$
$29$	−1.26795	−	2.19615i	−0.235452	−	0.407815i	−0.959404	+	0.282035i	$0.908990\pi$
$30$		0			0
$31$		−	4.73205i		−	0.849901i	−0.905216	−	0.424951i	$-0.860291\pi$
$31$		−	4.73205i		−	0.849901i	0.905216	−	0.424951i	$-0.139709\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	8.19615i		−	1.40563i
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$		0			0
$37$	−0.696152	+	0.401924i	−0.114447	+	0.0660759i	−0.556131	−	0.831095i	$-0.687715\pi$
$37$	−0.696152	+	0.401924i	−0.114447	+	0.0660759i	0.441684	+	0.897171i	$0.354381\pi$
$38$	−0.464102			−0.0752872
$39$		0			0
$40$	−1.00000			−0.158114
$41$	9.00000	−	5.19615i	1.40556	−	0.811503i	0.410608	−	0.911812i	$-0.365317\pi$
$41$	9.00000	−	5.19615i	1.40556	−	0.811503i	0.994956	+	0.100309i	$0.0319833\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	8.19615	+	4.73205i	1.20846	+	0.697703i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$		0			0
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$	−0.464102			−0.0637493			−0.0318746	−	0.999492i	$-0.510148\pi$
$53$	−0.464102			−0.0637493			−0.0318746	+	0.999492i	$0.510148\pi$
$54$		0			0
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		0			0
$58$	−2.19615	−	1.26795i	−0.288369	−	0.166490i
$59$	−9.00000	−	5.19615i	−1.17170	−	0.676481i	−0.217620	−	0.976034i	$-0.569829\pi$
$59$	−9.00000	−	5.19615i	−1.17170	−	0.676481i	−0.954080	+	0.299552i	$0.903163\pi$
$60$		0			0
$61$	−3.09808	+	5.36603i	−0.396668	+	0.687049i	−0.993313	−	0.115456i	$-0.963167\pi$
$61$	−3.09808	+	5.36603i	−0.396668	+	0.687049i	0.596645	+	0.802506i	$0.296500\pi$
$62$	−2.36603	−	4.09808i	−0.300486	−	0.520456i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.866025	−	3.50000i	0.107417	−	0.434122i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−4.09808	−	7.09808i	−0.496965	−	0.860768i
$69$		0			0
$70$		−	3.00000i		−	0.358569i
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$		0			0
$73$		−	11.6603i		−	1.36473i	−0.731012	−	0.682365i	$-0.760952\pi$
$73$		−	11.6603i		−	1.36473i	0.731012	−	0.682365i	$-0.239048\pi$
$74$	−0.401924	+	0.696152i	−0.0467227	+	0.0809261i
$75$		0			0
$76$	−0.401924	+	0.232051i	−0.0461038	+	0.0266181i
$77$	−9.00000			−1.02565
$78$		0			0
$79$	−4.19615			−0.472104			−0.236052	−	0.971740i	$-0.575854\pi$
$79$	−4.19615			−0.472104			−0.236052	+	0.971740i	$0.575854\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$		0			0
$82$	5.19615	−	9.00000i	0.573819	−	0.993884i
$83$		−	8.19615i		−	0.899645i	−0.893118	−	0.449822i	$-0.851487\pi$
$83$		−	8.19615i		−	0.899645i	0.893118	−	0.449822i	$-0.148513\pi$
$84$		0			0
$85$	−7.09808	−	4.09808i	−0.769894	−	0.444499i
$86$			2.00000i			0.215666i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−5.89230	+	3.40192i	−0.624583	+	0.360603i	−0.778651	−	0.627457i	$-0.784096\pi$
$89$	−5.89230	+	3.40192i	−0.624583	+	0.360603i	0.154068	+	0.988060i	$0.450762\pi$
$90$		0			0
$91$	7.79423	+	7.50000i	0.817057	+	0.786214i
$92$	9.46410			0.986701
$93$		0			0
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	−0.232051	+	0.401924i	−0.0238079	+	0.0412365i
$96$		0			0
$97$	7.90192	+	4.56218i	0.802319	+	0.463219i	0.844281	−	0.535900i	$-0.180028\pi$
$97$	7.90192	+	4.56218i	0.802319	+	0.463219i	−0.0419625	+	0.999119i	$0.513361\pi$
$98$	1.73205	+	1.00000i	0.174964	+	0.101015i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	5.36603	+	9.29423i	0.533939	+	0.924810i	0.999214	+	0.0396438i	$0.0126223\pi$
$101$	5.36603	+	9.29423i	0.533939	+	0.924810i	−0.465274	+	0.885167i	$0.654044\pi$
$102$		0			0
$103$	−9.19615			−0.906124			−0.453062	−	0.891479i	$-0.649668\pi$
$103$	−9.19615			−0.906124			−0.453062	+	0.891479i	$0.649668\pi$
$104$	0.866025	−	3.50000i	0.0849208	−	0.343203i
$105$		0			0
$106$	−0.401924	+	0.232051i	−0.0390383	+	0.0225388i
$107$	8.83013	+	15.2942i	0.853641	+	1.47855i	0.877900	+	0.478843i	$0.158944\pi$
$107$	8.83013	+	15.2942i	0.853641	+	1.47855i	−0.0242598	+	0.999706i	$0.507723\pi$
$108$		0			0
$109$			8.53590i			0.817591i	0.912626	+	0.408795i	$0.134051\pi$
$109$			8.53590i			0.817591i	−0.912626	+	0.408795i	$0.865949\pi$
$110$	2.59808	+	1.50000i	0.247717	+	0.143019i
$111$		0			0
$112$		−	3.00000i		−	0.283473i
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	−0.655814	−	0.754923i	$-0.727674\pi$
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	0.981689	+	0.190490i	$0.0610077\pi$
$114$		0			0
$115$	8.19615	−	4.73205i	0.764295	−	0.441266i
$116$	−2.53590			−0.235452
$117$		0			0
$118$	−10.3923			−0.956689
$119$	21.2942	−	12.2942i	1.95204	−	1.12701i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$			6.19615i			0.560973i
$123$		0			0
$124$	−4.09808	−	2.36603i	−0.368018	−	0.212475i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−5.40192	−	9.35641i	−0.479343	−	0.830247i	0.520376	−	0.853937i	$-0.325792\pi$
$127$	−5.40192	−	9.35641i	−0.479343	−	0.830247i	−0.999719	+	0.0236904i	$0.992458\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.00000	−	3.46410i	−0.0877058	−	0.303822i
$131$	−6.12436			−0.535087			−0.267544	−	0.963546i	$-0.586212\pi$
$131$	−6.12436			−0.535087			−0.267544	+	0.963546i	$0.586212\pi$
$132$		0			0
$133$	−0.696152	−	1.20577i	−0.0603641	−	0.104554i
$134$		0			0
$135$		0			0
$136$	−7.09808	−	4.09808i	−0.608655	−	0.351407i
$137$	−1.90192	−	1.09808i	−0.162492	−	0.0938150i	0.416549	−	0.909113i	$-0.363240\pi$
$137$	−1.90192	−	1.09808i	−0.162492	−	0.0938150i	−0.579041	+	0.815298i	$0.696573\pi$
$138$		0			0
$139$	−0.598076	+	1.03590i	−0.0507282	+	0.0878638i	−0.890274	−	0.455424i	$-0.849488\pi$
$139$	−0.598076	+	1.03590i	−0.0507282	+	0.0878638i	0.839546	+	0.543288i	$0.182821\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$		0			0
$142$	6.00000			0.503509
$143$	−10.3923	+	3.00000i	−0.869048	+	0.250873i
$144$		0			0
$145$	−2.19615	+	1.26795i	−0.182381	+	0.105297i
$146$	−5.83013	−	10.0981i	−0.482505	−	0.835723i
$147$		0			0
$148$			0.803848i			0.0660759i
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	0.271821	−	0.962348i	$-0.412374\pi$
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	−0.697507	+	0.716578i	$0.745707\pi$
$150$		0			0
$151$			23.6603i			1.92544i	0.270492	+	0.962722i	$0.412813\pi$
$151$			23.6603i			1.92544i	−0.270492	+	0.962722i	$0.587187\pi$
$152$	−0.232051	+	0.401924i	−0.0188218	+	0.0326003i
$153$		0			0
$154$	−7.79423	+	4.50000i	−0.628077	+	0.362620i
$155$	−4.73205			−0.380087
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	−3.63397	+	2.09808i	−0.289103	+	0.166914i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$			28.3923i			2.23763i
$162$		0			0
$163$	−9.29423	−	5.36603i	−0.727980	−	0.420300i	0.0897026	−	0.995969i	$-0.471408\pi$
$163$	−9.29423	−	5.36603i	−0.727980	−	0.420300i	−0.817683	+	0.575669i	$0.804742\pi$
$164$		−	10.3923i		−	0.811503i
$165$		0			0
$166$	−4.09808	−	7.09808i	−0.318072	−	0.550918i
$167$	−2.59808	+	1.50000i	−0.201045	+	0.116073i	−0.597143	−	0.802135i	$-0.703697\pi$
$167$	−2.59808	+	1.50000i	−0.201045	+	0.116073i	0.396098	+	0.918208i	$0.370364\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	−8.19615			−0.628616
$171$		0			0
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	0.426329	+	0.904568i	$0.359807\pi$
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	−0.996544	+	0.0830722i	$0.973527\pi$
$174$		0			0
$175$	−2.59808	−	1.50000i	−0.196396	−	0.113389i
$176$	2.59808	+	1.50000i	0.195837	+	0.113067i
$177$		0			0
$178$	−3.40192	+	5.89230i	−0.254985	+	0.441647i
$179$	−4.73205	−	8.19615i	−0.353690	−	0.612609i	0.633203	−	0.773986i	$-0.281740\pi$
$179$	−4.73205	−	8.19615i	−0.353690	−	0.612609i	−0.986893	+	0.161377i	$0.948407\pi$
$180$		0			0
$181$	14.5885			1.08435			0.542176	−	0.840265i	$-0.317601\pi$
$181$	14.5885			1.08435			0.542176	+	0.840265i	$0.317601\pi$
$182$	10.5000	+	2.59808i	0.778312	+	0.192582i
$183$		0			0
$184$	8.19615	−	4.73205i	0.604228	−	0.348851i
$185$	0.401924	+	0.696152i	0.0295500	+	0.0511821i
$186$		0			0
$187$			24.5885i			1.79809i
$188$	2.59808	+	1.50000i	0.189484	+	0.109399i
$189$		0			0
$190$			0.464102i			0.0336695i
$191$	−11.3660	+	19.6865i	−0.822417	+	1.42447i	0.0814609	+	0.996677i	$0.474041\pi$
$191$	−11.3660	+	19.6865i	−0.822417	+	1.42447i	−0.903878	+	0.427791i	$0.859292\pi$
$192$		0			0
$193$	−14.1962	+	8.19615i	−1.02186	+	0.589972i	−0.914643	−	0.404263i	$-0.867528\pi$
$193$	−14.1962	+	8.19615i	−1.02186	+	0.589972i	−0.107219	+	0.994235i	$0.534195\pi$
$194$	9.12436			0.655091
$195$		0			0
$196$	2.00000			0.142857
$197$	−18.6962	+	10.7942i	−1.33205	+	0.769057i	−0.985613	−	0.169018i	$-0.945940\pi$
$197$	−18.6962	+	10.7942i	−1.33205	+	0.769057i	−0.346433	+	0.938075i	$0.612607\pi$
$198$		0			0
$199$	3.19615	−	5.53590i	0.226569	−	0.392429i	−0.730220	−	0.683212i	$-0.760582\pi$
$199$	3.19615	−	5.53590i	0.226569	−	0.392429i	0.956789	+	0.290783i	$0.0939157\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	9.29423	+	5.36603i	0.653940	+	0.377552i
$203$		−	7.60770i		−	0.533956i
$204$		0			0
$205$	−5.19615	−	9.00000i	−0.362915	−	0.628587i
$206$	−7.96410	+	4.59808i	−0.554885	+	0.320363i
$207$		0			0
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	1.39230			0.0963077
$210$		0			0
$211$	8.79423	+	15.2321i	0.605420	+	1.04862i	0.991985	+	0.126356i	$0.0403280\pi$
$211$	8.79423	+	15.2321i	0.605420	+	1.04862i	−0.386565	+	0.922262i	$0.626339\pi$
$212$	−0.232051	+	0.401924i	−0.0159373	+	0.0276042i
$213$		0			0
$214$	15.2942	+	8.83013i	1.04549	+	0.603615i
$215$	1.73205	+	1.00000i	0.118125	+	0.0681994i
$216$		0			0
$217$	7.09808	−	12.2942i	0.481849	−	0.834587i
$218$	4.26795	+	7.39230i	0.289062	+	0.500670i
$219$		0			0
$220$	3.00000			0.202260
$221$	20.4904	−	21.2942i	1.37833	−	1.43240i
$222$		0			0
$223$	−5.59808	+	3.23205i	−0.374875	+	0.216434i	−0.675586	−	0.737281i	$-0.736109\pi$
$223$	−5.59808	+	3.23205i	−0.374875	+	0.216434i	0.300711	+	0.953715i	$0.402776\pi$
$224$	−1.50000	−	2.59808i	−0.100223	−	0.173591i
$225$		0			0
$226$		−	6.92820i		−	0.460857i
$227$	−14.1962	−	8.19615i	−0.942232	−	0.543998i	−0.0515725	−	0.998669i	$-0.516423\pi$
$227$	−14.1962	−	8.19615i	−0.942232	−	0.543998i	−0.890659	+	0.454672i	$0.849757\pi$
$228$		0			0
$229$			1.26795i			0.0837884i	0.999122	+	0.0418942i	$0.0133392\pi$
$229$			1.26795i			0.0837884i	−0.999122	+	0.0418942i	$0.986661\pi$
$230$	4.73205	−	8.19615i	0.312022	−	0.540438i
$231$		0			0
$232$	−2.19615	+	1.26795i	−0.144184	+	0.0832449i
$233$	−4.73205			−0.310007			−0.155003	−	0.987914i	$-0.549539\pi$
$233$	−4.73205			−0.310007			−0.155003	+	0.987914i	$0.549539\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	−9.00000	+	5.19615i	−0.585850	+	0.338241i
$237$		0			0
$238$	12.2942	−	21.2942i	0.796916	−	1.38030i
$239$			2.19615i			0.142057i	0.997474	+	0.0710286i	$0.0226282\pi$
$239$			2.19615i			0.142057i	−0.997474	+	0.0710286i	$0.977372\pi$
$240$		0			0
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	0.238597	−	0.971119i	$-0.423312\pi$
$241$	−7.50000	−	4.33013i	−0.483117	−	0.278928i	−0.721715	+	0.692191i	$0.756646\pi$
$242$			2.00000i			0.128565i
$243$		0			0
$244$	3.09808	+	5.36603i	0.198334	+	0.343525i
$245$	1.73205	−	1.00000i	0.110657	−	0.0638877i
$246$		0			0
$247$	−1.20577	−	1.16025i	−0.0767214	−	0.0738252i
$248$	−4.73205			−0.300486
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	8.59808	−	14.8923i	0.542706	−	0.939994i	−0.456042	−	0.889958i	$-0.650733\pi$
$251$	8.59808	−	14.8923i	0.542706	−	0.939994i	0.998747	−	0.0500355i	$-0.0159335\pi$
$252$		0			0
$253$	−24.5885	−	14.1962i	−1.54586	−	0.892504i
$254$	−9.35641	−	5.40192i	−0.587073	−	0.338947i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.92820	−	12.0000i	−0.432169	−	0.748539i	0.564890	−	0.825166i	$-0.308918\pi$
$257$	−6.92820	−	12.0000i	−0.432169	−	0.748539i	−0.997060	+	0.0766265i	$0.975585\pi$
$258$		0			0
$259$	−2.41154			−0.149846
$260$	−2.59808	−	2.50000i	−0.161126	−	0.155043i
$261$		0			0
$262$	−5.30385	+	3.06218i	−0.327673	+	0.189182i
$263$	1.79423	+	3.10770i	0.110637	+	0.191629i	0.916027	−	0.401116i	$-0.131378\pi$
$263$	1.79423	+	3.10770i	0.110637	+	0.191629i	−0.805390	+	0.592745i	$0.798044\pi$
$264$		0			0
$265$			0.464102i			0.0285095i
$266$	−1.20577	−	0.696152i	−0.0739306	−	0.0426838i
$267$		0			0
$268$		0			0
$269$	−13.5622	+	23.4904i	−0.826901	+	1.43223i	0.0735575	+	0.997291i	$0.476565\pi$
$269$	−13.5622	+	23.4904i	−0.826901	+	1.43223i	−0.900458	+	0.434943i	$0.856769\pi$
$270$		0			0
$271$	8.19615	−	4.73205i	0.497881	−	0.287452i	−0.229957	−	0.973201i	$-0.573859\pi$
$271$	8.19615	−	4.73205i	0.497881	−	0.287452i	0.727838	+	0.685749i	$0.240525\pi$
$272$	−8.19615			−0.496965
$273$		0			0
$274$	−2.19615			−0.132674
$275$	2.59808	−	1.50000i	0.156670	−	0.0904534i
$276$		0			0
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$			1.19615i			0.0717405i
$279$		0			0
$280$	−2.59808	−	1.50000i	−0.155265	−	0.0896421i
$281$		−	10.3923i		−	0.619953i	−0.950744	−	0.309976i	$-0.899679\pi$
$281$		−	10.3923i		−	0.619953i	0.950744	−	0.309976i	$-0.100321\pi$
$282$		0			0
$283$	4.80385	+	8.32051i	0.285559	+	0.494603i	0.972745	−	0.231879i	$-0.0744874\pi$
$283$	4.80385	+	8.32051i	0.285559	+	0.494603i	−0.687186	+	0.726482i	$0.741154\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$		0			0
$286$	−7.50000	+	7.79423i	−0.443484	+	0.460882i
$287$	31.1769			1.84032
$288$		0			0
$289$	−25.0885	−	43.4545i	−1.47579	−	2.55615i
$290$	−1.26795	+	2.19615i	−0.0744565	+	0.128963i
$291$		0			0
$292$	−10.0981	−	5.83013i	−0.590945	−	0.341182i
$293$	−9.69615	−	5.59808i	−0.566455	−	0.327043i	0.189277	−	0.981924i	$-0.439386\pi$
$293$	−9.69615	−	5.59808i	−0.566455	−	0.327043i	−0.755732	+	0.654881i	$0.772719\pi$
$294$		0			0
$295$	−5.19615	+	9.00000i	−0.302532	+	0.524000i
$296$	0.401924	+	0.696152i	0.0233613	+	0.0404630i
$297$		0			0
$298$	−6.00000			−0.347571
$299$	9.46410	+	32.7846i	0.547323	+	1.89598i
$300$		0			0
$301$	−5.19615	+	3.00000i	−0.299501	+	0.172917i
$302$	11.8301	+	20.4904i	0.680747	+	1.17909i
$303$		0			0
$304$			0.464102i			0.0266181i
$305$	5.36603	+	3.09808i	0.307258	+	0.177395i
$306$		0			0
$307$			27.4641i			1.56746i	0.621102	+	0.783730i	$0.286685\pi$
$307$			27.4641i			1.56746i	−0.621102	+	0.783730i	$0.713315\pi$
$308$	−4.50000	+	7.79423i	−0.256411	+	0.444117i
$309$		0			0
$310$	−4.09808	+	2.36603i	−0.232755	+	0.134381i
$311$	9.12436			0.517395			0.258697	−	0.965958i	$-0.416707\pi$
$311$	9.12436			0.517395			0.258697	+	0.965958i	$0.416707\pi$
$312$		0			0
$313$	26.3923			1.49178			0.745891	−	0.666068i	$-0.232024\pi$
$313$	26.3923			1.49178			0.745891	+	0.666068i	$0.232024\pi$
$314$	−11.2583	+	6.50000i	−0.635344	+	0.366816i
$315$		0			0
$316$	−2.09808	+	3.63397i	−0.118026	+	0.204427i
$317$		−	23.1962i		−	1.30283i	−0.758723	−	0.651413i	$-0.774177\pi$
$317$		−	23.1962i		−	1.30283i	0.758723	−	0.651413i	$-0.225823\pi$
$318$		0			0
$319$	6.58846	+	3.80385i	0.368883	+	0.212975i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	14.1962	+	24.5885i	0.791121	+	1.37026i
$323$	−3.29423	+	1.90192i	−0.183296	+	0.105826i
$324$		0			0
$325$	−3.50000	−	0.866025i	−0.194145	−	0.0480384i
$326$	−10.7321			−0.594393
$327$		0			0
$328$	−5.19615	−	9.00000i	−0.286910	−	0.496942i
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	11.1962	+	6.46410i	0.615396	+	0.355299i	0.775074	−	0.631870i	$-0.217712\pi$
$331$	11.1962	+	6.46410i	0.615396	+	0.355299i	−0.159678	+	0.987169i	$0.551046\pi$
$332$	−7.09808	−	4.09808i	−0.389558	−	0.224911i
$333$		0			0
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$		0			0
$336$		0			0
$337$	6.19615			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$337$	6.19615			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$338$	12.9904	−	0.500000i	0.706584	−	0.0271964i
$339$		0			0
$340$	−7.09808	+	4.09808i	−0.384947	+	0.222249i
$341$	7.09808	+	12.2942i	0.384382	+	0.665770i
$342$		0			0
$343$		−	15.0000i		−	0.809924i
$344$	1.73205	+	1.00000i	0.0933859	+	0.0539164i
$345$		0			0
$346$			15.0000i			0.806405i
$347$	−14.3660	+	24.8827i	−0.771209	+	1.33577i	0.165692	+	0.986178i	$0.447014\pi$
$347$	−14.3660	+	24.8827i	−0.771209	+	1.33577i	−0.936901	+	0.349595i	$0.886319\pi$
$348$		0			0
$349$	−3.50962	+	2.02628i	−0.187866	+	0.108464i	−0.590983	−	0.806684i	$-0.701260\pi$
$349$	−3.50962	+	2.02628i	−0.187866	+	0.108464i	0.403117	+	0.915148i	$0.367927\pi$
$350$	−3.00000			−0.160357
$351$		0			0
$352$	3.00000			0.159901
$353$	−8.49038	+	4.90192i	−0.451897	+	0.260903i	−0.708631	−	0.705579i	$-0.750687\pi$
$353$	−8.49038	+	4.90192i	−0.451897	+	0.260903i	0.256734	+	0.966482i	$0.417354\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$			6.80385i			0.360603i
$357$		0			0
$358$	−8.19615	−	4.73205i	−0.433180	−	0.250097i
$359$			1.60770i			0.0848509i	0.999100	+	0.0424255i	$0.0135085\pi$
$359$			1.60770i			0.0848509i	−0.999100	+	0.0424255i	$0.986492\pi$
$360$		0			0
$361$	−9.39230	−	16.2679i	−0.494332	−	0.856208i
$362$	12.6340	−	7.29423i	0.664027	−	0.383376i
$363$		0			0
$364$	10.3923	−	3.00000i	0.544705	−	0.157243i
$365$	−11.6603			−0.610326
$366$		0			0
$367$	2.80385	+	4.85641i	0.146360	+	0.253502i	0.929879	−	0.367865i	$-0.119911\pi$
$367$	2.80385	+	4.85641i	0.146360	+	0.253502i	−0.783520	+	0.621367i	$0.786578\pi$
$368$	4.73205	−	8.19615i	0.246675	−	0.427254i
$369$		0			0
$370$	0.696152	+	0.401924i	0.0361912	+	0.0208950i
$371$	−1.20577	−	0.696152i	−0.0626005	−	0.0361424i
$372$		0			0
$373$	0.196152	−	0.339746i	0.0101564	−	0.0175914i	−0.860903	−	0.508770i	$-0.830100\pi$
$373$	0.196152	−	0.339746i	0.0101564	−	0.0175914i	0.871059	+	0.491179i	$0.163434\pi$
$374$	12.2942	+	21.2942i	0.635719	+	1.10110i
$375$		0			0
$376$	3.00000			0.154713
$377$	−2.53590	−	8.78461i	−0.130605	−	0.452430i
$378$		0			0
$379$	25.7942	−	14.8923i	1.32496	−	0.764966i	0.340445	−	0.940264i	$-0.389422\pi$
$379$	25.7942	−	14.8923i	1.32496	−	0.764966i	0.984515	+	0.175298i	$0.0560889\pi$
$380$	0.232051	+	0.401924i	0.0119040	+	0.0206183i
$381$		0			0
$382$			22.7321i			1.16307i
$383$	−19.3923	−	11.1962i	−0.990900	−	0.572097i	−0.0853571	−	0.996350i	$-0.527203\pi$
$383$	−19.3923	−	11.1962i	−0.990900	−	0.572097i	−0.905543	+	0.424254i	$0.860536\pi$
$384$		0			0
$385$			9.00000i			0.458682i
$386$	−8.19615	+	14.1962i	−0.417173	+	0.722565i
$387$		0			0
$388$	7.90192	−	4.56218i	0.401159	−	0.231609i
$389$	−22.7321			−1.15256			−0.576280	−	0.817252i	$-0.695496\pi$
$389$	−22.7321			−1.15256			−0.576280	+	0.817252i	$0.695496\pi$
$390$		0			0
$391$	77.5692			3.92284
$392$	1.73205	−	1.00000i	0.0874818	−	0.0505076i
$393$		0			0
$394$	−10.7942	+	18.6962i	−0.543805	+	0.941899i
$395$			4.19615i			0.211131i
$396$		0			0
$397$	−9.69615	−	5.59808i	−0.486636	−	0.280959i	0.236542	−	0.971621i	$-0.423986\pi$
$397$	−9.69615	−	5.59808i	−0.486636	−	0.280959i	−0.723178	+	0.690662i	$0.757319\pi$
$398$		−	6.39230i		−	0.320417i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	4.50000	−	2.59808i	0.224719	−	0.129742i	−0.383414	−	0.923576i	$-0.625252\pi$
$401$	4.50000	−	2.59808i	0.224719	−	0.129742i	0.608134	+	0.793835i	$0.291919\pi$
$402$		0			0
$403$	4.09808	−	16.5622i	0.204140	−	0.825021i
$404$	10.7321			0.533939
$405$		0			0
$406$	−3.80385	−	6.58846i	−0.188782	−	0.326980i
$407$	1.20577	−	2.08846i	0.0597679	−	0.103521i
$408$		0			0
$409$	−14.0885	−	8.13397i	−0.696629	−	0.402199i	0.109461	−	0.993991i	$-0.465087\pi$
$409$	−14.0885	−	8.13397i	−0.696629	−	0.402199i	−0.806091	+	0.591792i	$0.798421\pi$
$410$	−9.00000	−	5.19615i	−0.444478	−	0.256620i
$411$		0			0
$412$	−4.59808	+	7.96410i	−0.226531	+	0.392363i
$413$	−15.5885	−	27.0000i	−0.767058	−	1.32858i
$414$		0			0
$415$	−8.19615			−0.402333
$416$	−2.59808	−	2.50000i	−0.127381	−	0.122573i
$417$		0			0
$418$	1.20577	−	0.696152i	0.0589762	−	0.0340499i
$419$	−8.66025	−	15.0000i	−0.423081	−	0.732798i	0.573158	−	0.819445i	$-0.305718\pi$
$419$	−8.66025	−	15.0000i	−0.423081	−	0.732798i	−0.996239	+	0.0866469i	$0.972385\pi$
$420$		0			0
$421$		−	2.87564i		−	0.140150i	−0.997542	−	0.0700752i	$-0.977676\pi$
$421$		−	2.87564i		−	0.140150i	0.997542	−	0.0700752i	$-0.0223239\pi$
$422$	15.2321	+	8.79423i	0.741485	+	0.428096i
$423$		0			0
$424$			0.464102i			0.0225388i
$425$	−4.09808	+	7.09808i	−0.198786	+	0.344307i
$426$		0			0
$427$	−16.0981	+	9.29423i	−0.779041	+	0.449779i
$428$	17.6603			0.853641
$429$		0			0
$430$	2.00000			0.0964486
$431$	7.09808	−	4.09808i	0.341902	−	0.197397i	−0.319211	−	0.947684i	$-0.603418\pi$
$431$	7.09808	−	4.09808i	0.341902	−	0.197397i	0.661113	+	0.750286i	$0.270084\pi$
$432$		0			0
$433$	−4.19615	+	7.26795i	−0.201654	+	0.349275i	−0.949062	−	0.315091i	$-0.897965\pi$
$433$	−4.19615	+	7.26795i	−0.201654	+	0.349275i	0.747407	+	0.664366i	$0.231298\pi$
$434$		−	14.1962i		−	0.681437i
$435$		0			0
$436$	7.39230	+	4.26795i	0.354027	+	0.204398i
$437$		−	4.39230i		−	0.210112i
$438$		0			0
$439$	1.70577	+	2.95448i	0.0814120	+	0.141010i	0.903857	−	0.427835i	$-0.140724\pi$
$439$	1.70577	+	2.95448i	0.0814120	+	0.141010i	−0.822445	+	0.568845i	$0.807390\pi$
$440$	2.59808	−	1.50000i	0.123858	−	0.0715097i
$441$		0			0
$442$	7.09808	−	28.6865i	0.337621	−	1.36448i
$443$	22.3923			1.06389			0.531945	−	0.846779i	$-0.321461\pi$
$443$	22.3923			1.06389			0.531945	+	0.846779i	$0.321461\pi$
$444$		0			0
$445$	3.40192	+	5.89230i	0.161267	+	0.279322i
$446$	−3.23205	+	5.59808i	−0.153042	+	0.265077i
$447$		0			0
$448$	−2.59808	−	1.50000i	−0.122748	−	0.0708683i
$449$	−13.5000	−	7.79423i	−0.637104	−	0.367832i	0.146394	−	0.989226i	$-0.453233\pi$
$449$	−13.5000	−	7.79423i	−0.637104	−	0.367832i	−0.783498	+	0.621394i	$0.786567\pi$
$450$		0			0
$451$	−15.5885	+	27.0000i	−0.734032	+	1.27138i
$452$	−3.46410	−	6.00000i	−0.162938	−	0.282216i
$453$		0			0
$454$	−16.3923			−0.769329
$455$	7.50000	−	7.79423i	0.351605	−	0.365399i
$456$		0			0
$457$	15.8827	−	9.16987i	0.742961	−	0.428949i	−0.0801841	−	0.996780i	$-0.525551\pi$
$457$	15.8827	−	9.16987i	0.742961	−	0.428949i	0.823145	+	0.567832i	$0.192217\pi$
$458$	0.633975	+	1.09808i	0.0296237	+	0.0513097i
$459$		0			0
$460$		−	9.46410i		−	0.441266i
$461$	26.4904	+	15.2942i	1.23378	+	0.712323i	0.967816	−	0.251660i	$-0.0809764\pi$
$461$	26.4904	+	15.2942i	1.23378	+	0.712323i	0.265964	+	0.963983i	$0.414310\pi$
$462$		0			0
$463$		−	12.9282i		−	0.600825i	−0.953809	−	0.300412i	$-0.902876\pi$
$463$		−	12.9282i		−	0.600825i	0.953809	−	0.300412i	$-0.0971243\pi$
$464$	−1.26795	+	2.19615i	−0.0588631	+	0.101954i
$465$		0			0
$466$	−4.09808	+	2.36603i	−0.189840	+	0.109604i
$467$	37.8564			1.75179			0.875893	−	0.482506i	$-0.160273\pi$
$467$	37.8564			1.75179			0.875893	+	0.482506i	$0.160273\pi$
$468$		0			0
$469$		0			0
$470$	2.59808	−	1.50000i	0.119840	−	0.0691898i
$471$		0			0
$472$	−5.19615	+	9.00000i	−0.239172	+	0.414259i
$473$		−	6.00000i		−	0.275880i
$474$		0			0
$475$	0.401924	+	0.232051i	0.0184415	+	0.0106472i
$476$		−	24.5885i		−	1.12701i
$477$		0			0
$478$	1.09808	+	1.90192i	0.0502248	+	0.0869920i
$479$	35.4904	−	20.4904i	1.62160	−	0.936229i	0.635104	−	0.772427i	$-0.280957\pi$
$479$	35.4904	−	20.4904i	1.62160	−	0.936229i	0.986493	−	0.163803i	$-0.0523760\pi$
$480$		0			0
$481$	−2.78461	+	0.803848i	−0.126967	+	0.0366523i
$482$	−8.66025			−0.394464
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	4.56218	−	7.90192i	0.207158	−	0.358808i
$486$		0			0
$487$	−13.2058	−	7.62436i	−0.598411	−	0.345493i	0.170005	−	0.985443i	$-0.445621\pi$
$487$	−13.2058	−	7.62436i	−0.598411	−	0.345493i	−0.768416	+	0.639951i	$0.778955\pi$
$488$	5.36603	+	3.09808i	0.242909	+	0.140243i
$489$		0			0
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	10.3301	+	17.8923i	0.466192	+	0.807468i	0.999254	−	0.0386076i	$-0.0122922\pi$
$491$	10.3301	+	17.8923i	0.466192	+	0.807468i	−0.533062	+	0.846076i	$0.678959\pi$
$492$		0			0
$493$	−20.7846			−0.936092
$494$	−1.62436	−	0.401924i	−0.0730832	−	0.0180834i
$495$		0			0
$496$	−4.09808	+	2.36603i	−0.184009	+	0.106238i
$497$	9.00000	+	15.5885i	0.403705	+	0.699238i
$498$		0			0
$499$		−	25.8564i		−	1.15749i	−0.815508	−	0.578746i	$-0.803542\pi$
$499$		−	25.8564i		−	1.15749i	0.815508	−	0.578746i	$-0.196458\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$		0			0
$502$		−	17.1962i		−	0.767502i
$503$	−13.3301	+	23.0885i	−0.594361	+	1.02946i	0.399276	+	0.916831i	$0.369262\pi$
$503$	−13.3301	+	23.0885i	−0.594361	+	1.02946i	−0.993637	+	0.112633i	$0.964072\pi$
$504$		0			0
$505$	9.29423	−	5.36603i	0.413588	−	0.238785i
$506$	−28.3923			−1.26219
$507$		0			0
$508$	−10.8038			−0.479343
$509$	19.3923	−	11.1962i	0.859549	−	0.496261i	−0.00431237	−	0.999991i	$-0.501373\pi$
$509$	19.3923	−	11.1962i	0.859549	−	0.496261i	0.863861	+	0.503730i	$0.168039\pi$
$510$		0			0
$511$	17.4904	−	30.2942i	0.773729	−	1.34014i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.0000	−	6.92820i	−0.529297	−	0.305590i
$515$			9.19615i			0.405231i
$516$		0			0
$517$	−4.50000	−	7.79423i	−0.197910	−	0.342790i
$518$	−2.08846	+	1.20577i	−0.0917615	+	0.0529786i
$519$		0			0
$520$	−3.50000	−	0.866025i	−0.153485	−	0.0379777i
$521$	−6.46410			−0.283197			−0.141599	−	0.989924i	$-0.545224\pi$
$521$	−6.46410			−0.283197			−0.141599	+	0.989924i	$0.545224\pi$
$522$		0			0
$523$	1.19615	+	2.07180i	0.0523041	+	0.0905933i	0.890992	−	0.454019i	$-0.150010\pi$
$523$	1.19615	+	2.07180i	0.0523041	+	0.0905933i	−0.838688	+	0.544612i	$0.816677\pi$
$524$	−3.06218	+	5.30385i	−0.133772	+	0.231700i
$525$		0			0
$526$	3.10770	+	1.79423i	0.135502	+	0.0782321i
$527$	−33.5885	−	19.3923i	−1.46314	−	0.844742i
$528$		0			0
$529$	−33.2846	+	57.6506i	−1.44716	+	2.50655i
$530$	0.232051	+	0.401924i	0.0100796	+	0.0174585i
$531$		0			0
$532$	−1.39230			−0.0603641
$533$	36.0000	−	10.3923i	1.55933	−	0.450141i
$534$		0			0
$535$	15.2942	−	8.83013i	0.661227	−	0.381760i
$536$		0			0
$537$		0			0
$538$			27.1244i			1.16941i
$539$	−5.19615	−	3.00000i	−0.223814	−	0.129219i
$540$		0			0
$541$		−	22.0526i		−	0.948114i	−0.880494	−	0.474057i	$-0.842789\pi$
$541$		−	22.0526i		−	0.948114i	0.880494	−	0.474057i	$-0.157211\pi$
$542$	4.73205	−	8.19615i	0.203259	−	0.352055i
$543$		0			0
$544$	−7.09808	+	4.09808i	−0.304328	+	0.175704i
$545$	8.53590			0.365638
$546$		0			0
$547$	−6.78461			−0.290089			−0.145044	−	0.989425i	$-0.546333\pi$
$547$	−6.78461			−0.290089			−0.145044	+	0.989425i	$0.546333\pi$
$548$	−1.90192	+	1.09808i	−0.0812462	+	0.0469075i
$549$		0			0
$550$	1.50000	−	2.59808i	0.0639602	−	0.110782i
$551$			1.17691i			0.0501382i
$552$		0			0
$553$	−10.9019	−	6.29423i	−0.463597	−	0.267658i
$554$		−	1.00000i		−	0.0424859i
$555$		0			0
$556$	0.598076	+	1.03590i	0.0253641	+	0.0439319i
$557$	5.89230	−	3.40192i	0.249665	−	0.144144i	−0.369946	−	0.929053i	$-0.620624\pi$
$557$	5.89230	−	3.40192i	0.249665	−	0.144144i	0.619611	+	0.784909i	$0.287290\pi$
$558$		0			0
$559$	−5.00000	+	5.19615i	−0.211477	+	0.219774i
$560$	−3.00000			−0.126773
$561$		0			0
$562$	−5.19615	−	9.00000i	−0.219186	−	0.379642i
$563$	7.26795	−	12.5885i	0.306308	−	0.530540i	−0.671244	−	0.741236i	$-0.734240\pi$
$563$	7.26795	−	12.5885i	0.306308	−	0.530540i	0.977552	+	0.210696i	$0.0675731\pi$
$564$		0			0
$565$	−6.00000	−	3.46410i	−0.252422	−	0.145736i
$566$	8.32051	+	4.80385i	0.349737	+	0.201921i
$567$		0			0
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	−13.6244	−	23.5981i	−0.571163	−	0.989283i	−0.996447	−	0.0842230i	$-0.973159\pi$
$569$	−13.6244	−	23.5981i	−0.571163	−	0.989283i	0.425284	−	0.905060i	$-0.360174\pi$
$570$		0			0
$571$	−38.3731			−1.60586			−0.802931	−	0.596071i	$-0.796728\pi$
$571$	−38.3731			−1.60586			−0.802931	+	0.596071i	$0.796728\pi$
$572$	−2.59808	+	10.5000i	−0.108631	+	0.439027i
$573$		0			0
$574$	27.0000	−	15.5885i	1.12696	−	0.650650i
$575$	−4.73205	−	8.19615i	−0.197340	−	0.341803i
$576$		0			0
$577$			26.4449i			1.10091i	0.834863	+	0.550457i	$0.185547\pi$
$577$			26.4449i			1.10091i	−0.834863	+	0.550457i	$0.814453\pi$
$578$	−43.4545	−	25.0885i	−1.80747	−	1.04354i
$579$		0			0
$580$			2.53590i			0.105297i
$581$	12.2942	−	21.2942i	0.510051	−	0.883433i
$582$		0			0
$583$	1.20577	−	0.696152i	0.0499379	−	0.0288317i
$584$	−11.6603			−0.482505
$585$		0			0
$586$	−11.1962			−0.462509
$587$	−25.9808	+	15.0000i	−1.07234	+	0.619116i	−0.928820	−	0.370531i	$-0.879176\pi$
$587$	−25.9808	+	15.0000i	−1.07234	+	0.619116i	−0.143521	+	0.989647i	$0.545842\pi$
$588$		0			0
$589$	−1.09808	+	1.90192i	−0.0452454	+	0.0783674i
$590$			10.3923i			0.427844i
$591$		0			0
$592$	0.696152	+	0.401924i	0.0286117	+	0.0165190i
$593$		−	20.7846i		−	0.853522i	−0.904365	−	0.426761i	$-0.859655\pi$
$593$		−	20.7846i		−	0.853522i	0.904365	−	0.426761i	$-0.140345\pi$
$594$		0			0
$595$	−12.2942	−	21.2942i	−0.504014	−	0.872978i
$596$	−5.19615	+	3.00000i	−0.212843	+	0.122885i
$597$		0			0
$598$	24.5885	+	23.6603i	1.00550	+	0.967540i
$599$	19.8564			0.811311			0.405655	−	0.914026i	$-0.367043\pi$
$599$	19.8564			0.811311			0.405655	+	0.914026i	$0.367043\pi$
$600$		0			0
$601$	18.8923	+	32.7224i	0.770633	+	1.33478i	0.937216	+	0.348748i	$0.113393\pi$
$601$	18.8923	+	32.7224i	0.770633	+	1.33478i	−0.166583	+	0.986027i	$0.553273\pi$
$602$	−3.00000	+	5.19615i	−0.122271	+	0.211779i
$603$		0			0
$604$	20.4904	+	11.8301i	0.833742	+	0.481361i
$605$	1.73205	+	1.00000i	0.0704179	+	0.0406558i
$606$		0			0
$607$	18.7942	−	32.5526i	0.762834	−	1.32127i	−0.178550	−	0.983931i	$-0.557141\pi$
$607$	18.7942	−	32.5526i	0.762834	−	1.32127i	0.941384	−	0.337337i	$-0.109526\pi$
$608$	0.232051	+	0.401924i	0.00941090	+	0.0163002i
$609$		0			0
$610$	6.19615			0.250875
$611$	−2.59808	+	10.5000i	−0.105107	+	0.424785i
$612$		0			0
$613$	33.6962	−	19.4545i	1.36097	−	0.785759i	0.371221	−	0.928545i	$-0.378939\pi$
$613$	33.6962	−	19.4545i	1.36097	−	0.785759i	0.989754	+	0.142785i	$0.0456059\pi$
$614$	13.7321	+	23.7846i	0.554180	+	0.959869i
$615$		0			0
$616$			9.00000i			0.362620i
$617$	−15.5885	−	9.00000i	−0.627568	−	0.362326i	0.152242	−	0.988343i	$-0.451351\pi$
$617$	−15.5885	−	9.00000i	−0.627568	−	0.362326i	−0.779809	+	0.626017i	$0.784684\pi$
$618$		0			0
$619$			31.3923i			1.26176i	0.775879	+	0.630882i	$0.217307\pi$
$619$			31.3923i			1.26176i	−0.775879	+	0.630882i	$0.782693\pi$
$620$	−2.36603	+	4.09808i	−0.0950219	+	0.164583i
$621$		0			0
$622$	7.90192	−	4.56218i	0.316838	−	0.182927i
$623$	−20.4115			−0.817771
$624$		0			0
$625$	1.00000			0.0400000
$626$	22.8564	−	13.1962i	0.913526	−	0.527424i
$627$		0			0
$628$	−6.50000	+	11.2583i	−0.259378	+	0.449256i
$629$			6.58846i			0.262699i
$630$		0			0
$631$	−18.0000	−	10.3923i	−0.716569	−	0.413711i	0.0969198	−	0.995292i	$-0.469101\pi$
$631$	−18.0000	−	10.3923i	−0.716569	−	0.413711i	−0.813488	+	0.581581i	$0.802434\pi$
$632$			4.19615i			0.166914i
$633$		0			0
$634$	−11.5981	−	20.0885i	−0.460618	−	0.797815i
$635$	−9.35641	+	5.40192i	−0.371298	+	0.214369i
$636$		0			0
$637$	2.00000	+	6.92820i	0.0792429	+	0.274505i
$638$	7.60770			0.301192
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	16.0359	−	27.7750i	0.633380	−	1.09705i	−0.353476	−	0.935444i	$-0.615000\pi$
$641$	16.0359	−	27.7750i	0.633380	−	1.09705i	0.986856	−	0.161603i	$-0.0516663\pi$
$642$		0			0
$643$	−9.29423	−	5.36603i	−0.366529	−	0.211615i	0.305412	−	0.952220i	$-0.401206\pi$
$643$	−9.29423	−	5.36603i	−0.366529	−	0.211615i	−0.671941	+	0.740605i	$0.734539\pi$
$644$	24.5885	+	14.1962i	0.968921	+	0.559407i
$645$		0			0
$646$	−1.90192	+	3.29423i	−0.0748302	+	0.129610i
$647$	−0.401924	−	0.696152i	−0.0158013	−	0.0273686i	0.858017	−	0.513622i	$-0.171697\pi$
$647$	−0.401924	−	0.696152i	−0.0158013	−	0.0273686i	−0.873818	+	0.486253i	$0.838363\pi$
$648$		0			0
$649$	31.1769			1.22380
$650$	−3.46410	+	1.00000i	−0.135873	+	0.0392232i
$651$		0			0
$652$	−9.29423	+	5.36603i	−0.363990	+	0.210150i
$653$	0.696152	+	1.20577i	0.0272425	+	0.0471855i	0.879325	−	0.476222i	$-0.157994\pi$
$653$	0.696152	+	1.20577i	0.0272425	+	0.0471855i	−0.852083	+	0.523407i	$0.824661\pi$
$654$		0			0
$655$			6.12436i			0.239298i
$656$	−9.00000	−	5.19615i	−0.351391	−	0.202876i
$657$		0			0
$658$			9.00000i			0.350857i
$659$	−2.66025	+	4.60770i	−0.103629	+	0.179490i	−0.913177	−	0.407563i	$-0.866379\pi$
$659$	−2.66025	+	4.60770i	−0.103629	+	0.179490i	0.809548	+	0.587053i	$0.199712\pi$
$660$		0			0
$661$	31.0981	−	17.9545i	1.20957	−	0.698348i	0.246909	−	0.969039i	$-0.420585\pi$
$661$	31.0981	−	17.9545i	1.20957	−	0.698348i	0.962666	+	0.270690i	$0.0872520\pi$
$662$	12.9282			0.502469
$663$		0			0
$664$	−8.19615			−0.318072
$665$	−1.20577	+	0.696152i	−0.0467578	+	0.0269956i
$666$		0			0
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$			3.00000i			0.116073i
$669$		0			0
$670$		0			0
$671$		−	18.5885i		−	0.717599i
$672$		0			0
$673$	−12.1962	−	21.1244i	−0.470127	−	0.814284i	0.529289	−	0.848441i	$-0.322459\pi$
$673$	−12.1962	−	21.1244i	−0.470127	−	0.814284i	−0.999416	+	0.0341573i	$0.989125\pi$
$674$	5.36603	−	3.09808i	0.206692	−	0.119333i
$675$		0			0
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$	25.8564			0.993742			0.496871	−	0.867824i	$-0.334482\pi$
$677$	25.8564			0.993742			0.496871	+	0.867824i	$0.334482\pi$
$678$		0			0
$679$	13.6865	+	23.7058i	0.525241	+	0.909744i
$680$	−4.09808	+	7.09808i	−0.157154	+	0.272199i
$681$		0			0
$682$	12.2942	+	7.09808i	0.470770	+	0.271799i
$683$	−27.0000	−	15.5885i	−1.03313	−	0.596476i	−0.115248	−	0.993337i	$-0.536766\pi$
$683$	−27.0000	−	15.5885i	−1.03313	−	0.596476i	−0.917879	+	0.396861i	$0.870099\pi$
$684$		0			0
$685$	−1.09808	+	1.90192i	−0.0419553	+	0.0726688i
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$		0			0
$688$	2.00000			0.0762493
$689$	−1.62436	−	0.401924i	−0.0618830	−	0.0153121i
$690$		0			0
$691$	−31.7942	+	18.3564i	−1.20951	+	0.698311i	−0.962652	−	0.270741i	$-0.912731\pi$
$691$	−31.7942	+	18.3564i	−1.20951	+	0.698311i	−0.246857	+	0.969052i	$0.579398\pi$
$692$	7.50000	+	12.9904i	0.285107	+	0.493820i
$693$		0			0
$694$			28.7321i			1.09065i
$695$	1.03590	+	0.598076i	0.0392939	+	0.0226863i
$696$		0			0
$697$		−	85.1769i		−	3.22631i
$698$	−2.02628	+	3.50962i	−0.0766958	+	0.132841i
$699$		0			0
$700$	−2.59808	+	1.50000i	−0.0981981	+	0.0566947i
$701$	−35.9090			−1.35626			−0.678131	−	0.734941i	$-0.737210\pi$
$701$	−35.9090			−1.35626			−0.678131	+	0.734941i	$0.737210\pi$
$702$		0			0
$703$	0.373067			0.0140705
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$		0			0
$706$	−4.90192	+	8.49038i	−0.184486	+	0.319540i
$707$			32.1962i			1.21086i
$708$		0			0
$709$	9.50962	+	5.49038i	0.357141	+	0.206196i	0.667826	−	0.744317i	$-0.267225\pi$
$709$	9.50962	+	5.49038i	0.357141	+	0.206196i	−0.310685	+	0.950513i	$0.600558\pi$
$710$		−	6.00000i		−	0.225176i
$711$		0			0
$712$	3.40192	+	5.89230i	0.127492	+	0.220823i
$713$	38.7846	−	22.3923i	1.45250	−	0.838598i
$714$		0			0
$715$	3.00000	+	10.3923i	0.112194	+	0.388650i
$716$	−9.46410			−0.353690
$717$		0			0
$718$	0.803848	+	1.39230i	0.0299993	+	0.0519604i
$719$	12.9282	−	22.3923i	0.482141	−	0.835092i	−0.517649	−	0.855593i	$-0.673193\pi$
$719$	12.9282	−	22.3923i	0.482141	−	0.835092i	0.999790	+	0.0205009i	$0.00652609\pi$
$720$		0			0
$721$	−23.8923	−	13.7942i	−0.889796	−	0.513724i
$722$	−16.2679	−	9.39230i	−0.605430	−	0.349545i
$723$		0			0
$724$	7.29423	−	12.6340i	0.271088	−	0.469538i
$725$	1.26795	+	2.19615i	0.0470905	+	0.0815631i
$726$		0			0
$727$	34.3731			1.27483			0.637413	−	0.770522i	$-0.280004\pi$
$727$	34.3731			1.27483			0.637413	+	0.770522i	$0.280004\pi$
$728$	7.50000	−	7.79423i	0.277968	−	0.288873i
$729$		0			0
$730$	−10.0981	+	5.83013i	−0.373747	+	0.215783i
$731$	8.19615	+	14.1962i	0.303146	+	0.525064i
$732$		0			0
$733$		−	14.9090i		−	0.550675i	−0.961348	−	0.275338i	$-0.911210\pi$
$733$		−	14.9090i		−	0.550675i	0.961348	−	0.275338i	$-0.0887896\pi$
$734$	4.85641	+	2.80385i	0.179253	+	0.103492i
$735$		0			0
$736$		−	9.46410i		−	0.348851i
$737$		0			0
$738$		0			0
$739$	28.2058	−	16.2846i	1.03757	−	0.599039i	0.118423	−	0.992963i	$-0.462216\pi$
$739$	28.2058	−	16.2846i	1.03757	−	0.599039i	0.919143	+	0.393924i	$0.128883\pi$
$740$	0.803848			0.0295500
$741$		0			0
$742$	−1.39230			−0.0511131
$743$	11.7846	−	6.80385i	0.432335	−	0.249609i	−0.268006	−	0.963417i	$-0.586365\pi$
$743$	11.7846	−	6.80385i	0.432335	−	0.249609i	0.700341	+	0.713808i	$0.253031\pi$
$744$		0			0
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$		−	0.392305i		−	0.0143633i
$747$		0			0
$748$	21.2942	+	12.2942i	0.778594	+	0.449522i
$749$			52.9808i			1.93587i
$750$		0			0
$751$	10.1962	+	17.6603i	0.372063	+	0.644432i	0.989883	−	0.141888i	$-0.0453172\pi$
$751$	10.1962	+	17.6603i	0.372063	+	0.644432i	−0.617820	+	0.786320i	$0.711984\pi$
$752$	2.59808	−	1.50000i	0.0947421	−	0.0546994i
$753$		0			0
$754$	−6.58846	−	6.33975i	−0.239937	−	0.230880i
$755$	23.6603			0.861085
$756$		0			0
$757$	18.8923	+	32.7224i	0.686652	+	1.18932i	0.972914	+	0.231166i	$0.0742539\pi$
$757$	18.8923	+	32.7224i	0.686652	+	1.18932i	−0.286262	+	0.958151i	$0.592413\pi$
$758$	14.8923	−	25.7942i	0.540913	−	0.936889i
$759$		0			0
$760$	0.401924	+	0.232051i	0.0145793	+	0.00841737i
$761$	−16.2846	−	9.40192i	−0.590317	−	0.340819i	0.174906	−	0.984585i	$-0.444038\pi$
$761$	−16.2846	−	9.40192i	−0.590317	−	0.340819i	−0.765223	+	0.643766i	$0.777371\pi$
$762$		0			0
$763$	−12.8038	+	22.1769i	−0.463530	+	0.802858i
$764$	11.3660	+	19.6865i	0.411208	+	0.712234i
$765$		0			0
$766$	−22.3923			−0.809067
$767$	−27.0000	−	25.9808i	−0.974913	−	0.938111i
$768$		0			0
$769$	−33.0000	+	19.0526i	−1.19001	+	0.687053i	−0.958309	−	0.285734i	$-0.907763\pi$
$769$	−33.0000	+	19.0526i	−1.19001	+	0.687053i	−0.231701	+	0.972787i	$0.574429\pi$
$770$	4.50000	+	7.79423i	0.162169	+	0.280885i
$771$		0			0
$772$			16.3923i			0.589972i
$773$	−2.08846	−	1.20577i	−0.0751166	−	0.0433686i	0.461971	−	0.886895i	$-0.347142\pi$
$773$	−2.08846	−	1.20577i	−0.0751166	−	0.0433686i	−0.537088	+	0.843526i	$0.680476\pi$
$774$		0			0
$775$			4.73205i			0.169980i
$776$	4.56218	−	7.90192i	0.163773	−	0.283663i
$777$		0			0
$778$	−19.6865	+	11.3660i	−0.705796	+	0.407492i
$779$	−4.82309			−0.172805
$780$		0			0
$781$	−18.0000			−0.644091
$782$	67.1769	−	38.7846i	2.40224	−	1.38693i
$783$		0			0
$784$	1.00000	−	1.73205i	0.0357143	−	0.0618590i
$785$			13.0000i			0.463990i
$786$		0			0
$787$	−37.0981	−	21.4186i	−1.32240	−	0.763490i	−0.338292	−	0.941041i	$-0.609849\pi$
$787$	−37.0981	−	21.4186i	−1.32240	−	0.763490i	−0.984112	+	0.177551i	$0.943182\pi$
$788$			21.5885i			0.769057i
$789$		0			0
$790$	2.09808	+	3.63397i	0.0746462	+	0.129291i
$791$	18.0000	−	10.3923i	0.640006	−	0.369508i
$792$		0			0
$793$	−15.4904	+	16.0981i	−0.550080	+	0.571659i
$794$	−11.1962			−0.397337
$795$		0			0
$796$	−3.19615	−	5.53590i	−0.113285	−	0.196215i
$797$	−6.46410	+	11.1962i	−0.228970	+	0.396588i	−0.957503	−	0.288423i	$-0.906869\pi$
$797$	−6.46410	+	11.1962i	−0.228970	+	0.396588i	0.728533	+	0.685011i	$0.240203\pi$
$798$		0			0
$799$	21.2942	+	12.2942i	0.753336	+	0.434939i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	2.59808	−	4.50000i	0.0917413	−	0.158901i
$803$	17.4904	+	30.2942i	0.617222	+	1.06906i
$804$		0			0
$805$	28.3923			1.00070
$806$	−4.73205	−	16.3923i	−0.166679	−	0.577394i
$807$		0			0
$808$	9.29423	−	5.36603i	0.326970	−	0.188776i
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	0.996125	−	0.0879478i	$-0.0280309\pi$
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	−0.574228	+	0.818696i	$0.694698\pi$
$810$		0			0
$811$		−	43.3923i		−	1.52371i	−0.647748	−	0.761855i	$-0.724289\pi$
$811$		−	43.3923i		−	1.52371i	0.647748	−	0.761855i	$-0.275711\pi$
$812$	−6.58846	−	3.80385i	−0.231210	−	0.133489i
$813$		0			0
$814$		−	2.41154i		−	0.0845245i
$815$	−5.36603	+	9.29423i	−0.187964	+	0.325563i
$816$		0			0
$817$	0.803848	−	0.464102i	0.0281231	−	0.0162369i
$818$	−16.2679			−0.568796
$819$		0			0
$820$	−10.3923			−0.362915
$821$	−17.4904	+	10.0981i	−0.610419	+	0.352425i	−0.773129	−	0.634249i	$-0.781310\pi$
$821$	−17.4904	+	10.0981i	−0.610419	+	0.352425i	0.162711	+	0.986674i	$0.447976\pi$
$822$		0			0
$823$	13.5981	−	23.5526i	0.473999	−	0.820991i	−0.525558	−	0.850758i	$-0.676143\pi$
$823$	13.5981	−	23.5526i	0.473999	−	0.820991i	0.999557	+	0.0297674i	$0.00947664\pi$
$824$			9.19615i			0.320363i
$825$		0			0
$826$	−27.0000	−	15.5885i	−0.939450	−	0.542392i
$827$		−	42.5885i		−	1.48095i	−0.672086	−	0.740473i	$-0.734602\pi$
$827$		−	42.5885i		−	1.48095i	0.672086	−	0.740473i	$-0.265398\pi$
$828$		0			0
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	0.985771	−	0.168091i	$-0.0537604\pi$
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	−0.638457	+	0.769657i	$0.720427\pi$
$830$	−7.09808	+	4.09808i	−0.246378	+	0.142246i
$831$		0			0
$832$	−3.50000	−	0.866025i	−0.121341	−	0.0300240i
$833$	16.3923			0.567960
$834$		0			0
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$	0.696152	−	1.20577i	0.0240769	−	0.0417025i
$837$		0			0
$838$	−15.0000	−	8.66025i	−0.518166	−	0.299164i
$839$	−18.8827	−	10.9019i	−0.651903	−	0.376376i	0.137282	−	0.990532i	$-0.456163\pi$
$839$	−18.8827	−	10.9019i	−0.651903	−	0.376376i	−0.789185	+	0.614156i	$0.789497\pi$
$840$		0			0
$841$	11.2846	−	19.5455i	0.389124	−	0.673983i
$842$	−1.43782	−	2.49038i	−0.0495506	−	0.0858242i
$843$		0			0
$844$	17.5885			0.605420
$845$	6.06218	−	11.5000i	0.208545	−	0.395612i
$846$		0			0
$847$	−5.19615	+	3.00000i	−0.178542	+	0.103081i
$848$	0.232051	+	0.401924i	0.00796866	+	0.0138021i
$849$		0			0
$850$			8.19615i			0.281126i
$851$	−6.58846	−	3.80385i	−0.225849	−	0.130394i
$852$		0			0
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$	−9.29423	+	16.0981i	−0.318042	+	0.550865i
$855$		0			0
$856$	15.2942	−	8.83013i	0.522746	−	0.301808i
$857$	16.7321			0.571556			0.285778	−	0.958296i	$-0.407748\pi$
$857$	16.7321			0.571556			0.285778	+	0.958296i	$0.407748\pi$
$858$		0			0
$859$	−20.3731			−0.695120			−0.347560	−	0.937658i	$-0.612990\pi$
$859$	−20.3731			−0.695120			−0.347560	+	0.937658i	$0.612990\pi$
$860$	1.73205	−	1.00000i	0.0590624	−	0.0340997i
$861$		0			0
$862$	4.09808	−	7.09808i	0.139581	−	0.241761i
$863$			43.1769i			1.46976i	0.678198	+	0.734880i	$0.262761\pi$
$863$			43.1769i			1.46976i	−0.678198	+	0.734880i	$0.737239\pi$
$864$		0			0
$865$	12.9904	+	7.50000i	0.441686	+	0.255008i
$866$			8.39230i			0.285182i
$867$		0			0
$868$	−7.09808	−	12.2942i	−0.240924	−	0.417293i
$869$	10.9019	−	6.29423i	0.369822	−	0.213517i
$870$		0			0
$871$		0			0
$872$	8.53590			0.289062
$873$		0			0
$874$	−2.19615	−	3.80385i	−0.0742860	−	0.128667i
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		0			0
$877$	−23.7846	−	13.7321i	−0.803149	−	0.463698i	0.0414220	−	0.999142i	$-0.486811\pi$
$877$	−23.7846	−	13.7321i	−0.803149	−	0.463698i	−0.844571	+	0.535443i	$0.820145\pi$
$878$	2.95448	+	1.70577i	0.0997090	+	0.0575670i
$879$		0			0
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	13.1603	+	22.7942i	0.443380	+	0.767957i	0.997938	−	0.0641883i	$-0.0204458\pi$
$881$	13.1603	+	22.7942i	0.443380	+	0.767957i	−0.554558	+	0.832145i	$0.687112\pi$
$882$		0			0
$883$	4.58846			0.154414			0.0772069	−	0.997015i	$-0.475400\pi$
$883$	4.58846			0.154414			0.0772069	+	0.997015i	$0.475400\pi$
$884$	−8.19615	−	28.3923i	−0.275666	−	0.954937i
$885$		0			0
$886$	19.3923	−	11.1962i	0.651497	−	0.376142i
$887$	−20.3827	−	35.3038i	−0.684384	−	1.18539i	−0.973630	−	0.228133i	$-0.926738\pi$
$887$	−20.3827	−	35.3038i	−0.684384	−	1.18539i	0.289246	−	0.957255i	$-0.406595\pi$
$888$		0			0
$889$		−	32.4115i		−	1.08705i
$890$	5.89230	+	3.40192i	0.197511	+	0.114033i
$891$		0			0
$892$			6.46410i			0.216434i
$893$	0.696152	−	1.20577i	0.0232959	−	0.0403496i
$894$		0			0
$895$	−8.19615	+	4.73205i	−0.273967	+	0.158175i
$896$	−3.00000			−0.100223
$897$		0			0
$898$	−15.5885			−0.520194
$899$	−10.3923	+	6.00000i	−0.346603	+	0.200111i
$900$		0			0
$901$	−1.90192	+	3.29423i	−0.0633623	+	0.109747i
$902$			31.1769i			1.03808i
$903$		0			0
$904$	−6.00000	−	3.46410i	−0.199557	−	0.115214i
$905$		−	14.5885i		−	0.484937i
$906$		0			0
$907$	−2.29423	−	3.97372i	−0.0761786	−	0.131945i	0.825420	−	0.564520i	$-0.190939\pi$
$907$	−2.29423	−	3.97372i	−0.0761786	−	0.131945i	−0.901598	+	0.432574i	$0.857605\pi$
$908$	−14.1962	+	8.19615i	−0.471116	+	0.271999i
$909$		0			0
$910$	2.59808	−	10.5000i	0.0861254	−	0.348072i
$911$	21.4641			0.711137			0.355569	−	0.934650i	$-0.384287\pi$
$911$	21.4641			0.711137			0.355569	+	0.934650i	$0.384287\pi$
$912$		0			0
$913$	12.2942	+	21.2942i	0.406880	+	0.704736i
$914$	9.16987	−	15.8827i	0.303312	−	0.525353i
$915$		0			0
$916$	1.09808	+	0.633975i	0.0362815	+	0.0209471i
$917$	−15.9115	−	9.18653i	−0.525445	−	0.303366i
$918$		0			0
$919$	−15.3923	+	26.6603i	−0.507745	+	0.879441i	0.492215	+	0.870474i	$0.336188\pi$
$919$	−15.3923	+	26.6603i	−0.507745	+	0.879441i	−0.999960	+	0.00896670i	$0.997146\pi$
$920$	−4.73205	−	8.19615i	−0.156011	−	0.270219i
$921$		0			0
$922$	30.5885			1.00738
$923$	15.5885	+	15.0000i	0.513100	+	0.493731i
$924$		0			0
$925$	0.696152	−	0.401924i	0.0228894	−	0.0132152i
$926$	−6.46410	−	11.1962i	−0.212424	−	0.367928i
$927$		0			0
$928$			2.53590i			0.0832449i
$929$	2.78461	+	1.60770i	0.0913601	+	0.0527468i	0.544984	−	0.838446i	$-0.316536\pi$
$929$	2.78461	+	1.60770i	0.0913601	+	0.0527468i	−0.453624	+	0.891193i	$0.649869\pi$
$930$		0			0
$931$		−	0.928203i		−	0.0304206i
$932$	−2.36603	+	4.09808i	−0.0775017	+	0.134237i
$933$		0			0
$934$	32.7846	−	18.9282i	1.07275	−	0.619350i
$935$	24.5885			0.804129
$936$		0			0
$937$	−9.60770			−0.313870			−0.156935	−	0.987609i	$-0.550161\pi$
$937$	−9.60770			−0.313870			−0.156935	+	0.987609i	$0.550161\pi$
$938$		0			0
$939$		0			0
$940$	1.50000	−	2.59808i	0.0489246	−	0.0847399i
$941$			3.21539i			0.104819i	0.998626	+	0.0524094i	$0.0166901\pi$
$941$			3.21539i			0.104819i	−0.998626	+	0.0524094i	$0.983310\pi$
$942$		0			0
$943$	85.1769	+	49.1769i	2.77374	+	1.60142i
$944$			10.3923i			0.338241i
$945$		0			0
$946$	−3.00000	−	5.19615i	−0.0975384	−	0.168941i
$947$	−13.3135	+	7.68653i	−0.432630	+	0.249779i	−0.700466	−	0.713686i	$-0.747025\pi$
$947$	−13.3135	+	7.68653i	−0.432630	+	0.249779i	0.267837	+	0.963464i	$0.413691\pi$
$948$		0			0
$949$	10.0981	−	40.8109i	0.327797	−	1.32478i
$950$	0.464102			0.0150574
$951$		0			0
$952$	−12.2942	−	21.2942i	−0.398458	−	0.690150i
$953$	−3.29423	+	5.70577i	−0.106711	+	0.184828i	−0.914436	−	0.404731i	$-0.867365\pi$
$953$	−3.29423	+	5.70577i	−0.106711	+	0.184828i	0.807725	+	0.589559i	$0.200698\pi$
$954$		0			0
$955$	19.6865	+	11.3660i	0.637041	+	0.367796i
$956$	1.90192	+	1.09808i	0.0615126	+	0.0355143i
$957$		0			0
$958$	20.4904	−	35.4904i	0.662014	−	1.14664i
$959$	−3.29423	−	5.70577i	−0.106376	−	0.184249i
$960$		0			0
$961$	8.60770			0.277668
$962$	−2.00962	+	2.08846i	−0.0647927	+	0.0673346i
$963$		0			0
$964$	−7.50000	+	4.33013i	−0.241559	+	0.139464i
$965$	8.19615	+	14.1962i	0.263843	+	0.456990i
$966$		0			0
$967$			44.5692i			1.43325i	0.697459	+	0.716625i	$0.254314\pi$
$967$			44.5692i			1.43325i	−0.697459	+	0.716625i	$0.745686\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$		0			0
$970$		−	9.12436i		−	0.292965i
$971$	23.3827	−	40.5000i	0.750386	−	1.29971i	−0.197250	−	0.980353i	$-0.563201\pi$
$971$	23.3827	−	40.5000i	0.750386	−	1.29971i	0.947636	−	0.319354i	$-0.103466\pi$
$972$		0			0
$973$	−3.10770	+	1.79423i	−0.0996281	+	0.0575203i
$974$	−15.2487			−0.488600
$975$		0			0
$976$	6.19615			0.198334
$977$	−14.1962	+	8.19615i	−0.454175	+	0.262218i	−0.709592	−	0.704613i	$-0.751121\pi$
$977$	−14.1962	+	8.19615i	−0.454175	+	0.262218i	0.255417	+	0.966831i	$0.417787\pi$
$978$		0			0
$979$	10.2058	−	17.6769i	0.326178	−	0.564957i
$980$		−	2.00000i		−	0.0638877i
$981$		0			0
$982$	17.8923	+	10.3301i	0.570966	+	0.329648i
$983$			44.5692i			1.42154i	0.703426	+	0.710769i	$0.251653\pi$
$983$			44.5692i			1.42154i	−0.703426	+	0.710769i	$0.748347\pi$
$984$		0			0
$985$	10.7942	+	18.6962i	0.343933	+	0.595709i
$986$	−18.0000	+	10.3923i	−0.573237	+	0.330958i
$987$		0			0
$988$	−1.60770	+	0.464102i	−0.0511476	+	0.0147650i
$989$	−18.9282			−0.601882
$990$		0			0
$991$	5.58846	+	9.67949i	0.177523	+	0.307479i	0.941032	−	0.338319i	$-0.109858\pi$
$991$	5.58846	+	9.67949i	0.177523	+	0.307479i	−0.763508	+	0.645798i	$0.776525\pi$
$992$	−2.36603	+	4.09808i	−0.0751214	+	0.130114i
$993$		0			0
$994$	15.5885	+	9.00000i	0.494436	+	0.285463i
$995$	−5.53590	−	3.19615i	−0.175500	−	0.101325i
$996$		0			0
$997$	−20.2846	+	35.1340i	−0.642420	+	1.11270i	0.342471	+	0.939528i	$0.388736\pi$
$997$	−20.2846	+	35.1340i	−0.642420	+	1.11270i	−0.984891	+	0.173176i	$0.944597\pi$
$998$	−12.9282	−	22.3923i	−0.409235	−	0.708816i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.c.361.2		4
3.2	odd	2		130.2.l.a.101.1	✓	4
12.11	even	2		1040.2.da.a.881.2		4
13.4	even	6	inner	1170.2.bs.c.901.2		4
15.2	even	4		650.2.n.a.49.2		4
15.8	even	4		650.2.n.b.49.1		4
15.14	odd	2		650.2.m.a.101.2		4
39.2	even	12		1690.2.a.j.1.2		2
39.5	even	4		1690.2.e.n.991.1		4
39.8	even	4		1690.2.e.l.991.1		4
39.11	even	12		1690.2.a.m.1.2		2
39.17	odd	6		130.2.l.a.121.1	yes	4
39.20	even	12		1690.2.e.l.191.1		4
39.23	odd	6		1690.2.d.f.1351.4		4
39.29	odd	6		1690.2.d.f.1351.2		4
39.32	even	12		1690.2.e.n.191.1		4
39.35	odd	6		1690.2.l.g.1161.2		4
39.38	odd	2		1690.2.l.g.361.2		4
156.95	even	6		1040.2.da.a.641.2		4
195.17	even	12		650.2.n.b.199.1		4
195.89	even	12		8450.2.a.bf.1.1		2
195.119	even	12		8450.2.a.bm.1.1		2
195.134	odd	6		650.2.m.a.251.2		4
195.173	even	12		650.2.n.a.199.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.a.101.1	✓	4	3.2	odd	2
130.2.l.a.121.1	yes	4	39.17	odd	6
650.2.m.a.101.2		4	15.14	odd	2
650.2.m.a.251.2		4	195.134	odd	6
650.2.n.a.49.2		4	15.2	even	4
650.2.n.a.199.2		4	195.173	even	12
650.2.n.b.49.1		4	15.8	even	4
650.2.n.b.199.1		4	195.17	even	12
1040.2.da.a.641.2		4	156.95	even	6
1040.2.da.a.881.2		4	12.11	even	2
1170.2.bs.c.361.2		4	1.1	even	1	trivial
1170.2.bs.c.901.2		4	13.4	even	6	inner
1690.2.a.j.1.2		2	39.2	even	12
1690.2.a.m.1.2		2	39.11	even	12
1690.2.d.f.1351.2		4	39.29	odd	6
1690.2.d.f.1351.4		4	39.23	odd	6
1690.2.e.l.191.1		4	39.20	even	12
1690.2.e.l.991.1		4	39.8	even	4
1690.2.e.n.191.1		4	39.32	even	12
1690.2.e.n.991.1		4	39.5	even	4
1690.2.l.g.361.2		4	39.38	odd	2
1690.2.l.g.1161.2		4	39.35	odd	6
8450.2.a.bf.1.1		2	195.89	even	12
8450.2.a.bm.1.1		2	195.119	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-2.59808 + 1.50000i) q^{11} +(3.50000 + 0.866025i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.09808 - 7.09808i) q^{17} +(-0.401924 - 0.232051i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(4.73205 + 8.19615i) q^{23} -1.00000 q^{25} +(3.46410 - 1.00000i) q^{26} +(2.59808 - 1.50000i) q^{28} +(-1.26795 - 2.19615i) q^{29} -4.73205i q^{31} +(-0.866025 - 0.500000i) q^{32} -8.19615i q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.696152 + 0.401924i) q^{37} -0.464102 q^{38} -1.00000 q^{40} +(9.00000 - 5.19615i) q^{41} +(-1.00000 + 1.73205i) q^{43} +3.00000i q^{44} +(8.19615 + 4.73205i) q^{46} +3.00000i q^{47} +(1.00000 + 1.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(2.50000 - 2.59808i) q^{52} -0.464102 q^{53} +(1.50000 + 2.59808i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-2.19615 - 1.26795i) q^{58} +(-9.00000 - 5.19615i) q^{59} +(-3.09808 + 5.36603i) q^{61} +(-2.36603 - 4.09808i) q^{62} -1.00000 q^{64} +(0.866025 - 3.50000i) q^{65} +(-4.09808 - 7.09808i) q^{68} -3.00000i q^{70} +(5.19615 + 3.00000i) q^{71} -11.6603i q^{73} +(-0.401924 + 0.696152i) q^{74} +(-0.401924 + 0.232051i) q^{76} -9.00000 q^{77} -4.19615 q^{79} +(-0.866025 + 0.500000i) q^{80} +(5.19615 - 9.00000i) q^{82} -8.19615i q^{83} +(-7.09808 - 4.09808i) q^{85} +2.00000i q^{86} +(1.50000 + 2.59808i) q^{88} +(-5.89230 + 3.40192i) q^{89} +(7.79423 + 7.50000i) q^{91} +9.46410 q^{92} +(1.50000 + 2.59808i) q^{94} +(-0.232051 + 0.401924i) q^{95} +(7.90192 + 4.56218i) q^{97} +(1.73205 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} + 14 q^{13} + 12 q^{14} - 2 q^{16} + 6 q^{17} - 12 q^{19} - 6 q^{22} + 12 q^{23} - 4 q^{25} - 12 q^{29} + 6 q^{35} + 18 q^{37} + 12 q^{38} - 4 q^{40} + 36 q^{41} - 4 q^{43} + 12 q^{46} + 4 q^{49} + 10 q^{52} + 12 q^{53} + 6 q^{55} + 6 q^{56} + 12 q^{58} - 36 q^{59} - 2 q^{61} - 6 q^{62} - 4 q^{64} - 6 q^{68} - 12 q^{74} - 12 q^{76} - 36 q^{77} + 4 q^{79} - 18 q^{85} + 6 q^{88} + 18 q^{89} + 24 q^{92} + 6 q^{94} + 6 q^{95} + 42 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 + 14 * q^13 + 12 * q^14 - 2 * q^16 + 6 * q^17 - 12 * q^19 - 6 * q^22 + 12 * q^23 - 4 * q^25 - 12 * q^29 + 6 * q^35 + 18 * q^37 + 12 * q^38 - 4 * q^40 + 36 * q^41 - 4 * q^43 + 12 * q^46 + 4 * q^49 + 10 * q^52 + 12 * q^53 + 6 * q^55 + 6 * q^56 + 12 * q^58 - 36 * q^59 - 2 * q^61 - 6 * q^62 - 4 * q^64 - 6 * q^68 - 12 * q^74 - 12 * q^76 - 36 * q^77 + 4 * q^79 - 18 * q^85 + 6 * q^88 + 18 * q^89 + 24 * q^92 + 6 * q^94 + 6 * q^95 + 42 * q^97

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