LMFDB - Embedded newform 1170.2.i.c.991.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(451,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [2,-1,0,-1,2,0,-3,2,0,-1,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1170.991
Dual form			1170.2.i.c.451.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-2.50000 - 2.59808i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{23} +1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +(-1.50000 - 2.59808i) q^{28} +(-2.00000 - 3.46410i) q^{29} +6.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{35} +(-4.50000 - 7.79423i) q^{37} +3.00000 q^{38} +1.00000 q^{40} +(-5.00000 - 8.66025i) q^{41} +(5.00000 - 8.66025i) q^{43} +3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} +3.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(3.50000 - 0.866025i) q^{52} -9.00000 q^{53} +(-1.50000 - 2.59808i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(-2.00000 + 3.46410i) q^{58} +(6.00000 - 10.3923i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-3.00000 - 5.19615i) q^{62} +1.00000 q^{64} +(-2.50000 - 2.59808i) q^{65} +(4.00000 + 6.92820i) q^{67} +3.00000 q^{70} +(-7.00000 + 12.1244i) q^{71} -8.00000 q^{73} +(-4.50000 + 7.79423i) q^{74} +(-1.50000 - 2.59808i) q^{76} +9.00000 q^{77} +6.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-5.00000 + 8.66025i) q^{82} -16.0000 q^{83} -10.0000 q^{86} +(-1.50000 - 2.59808i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(10.5000 - 2.59808i) q^{91} +4.00000 q^{92} +(-1.50000 - 2.59808i) q^{94} +(-1.50000 + 2.59808i) q^{95} +(-4.00000 + 6.92820i) q^{97} +(-1.00000 + 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} - q^{10} - 3 q^{11} - 5 q^{13} + 6 q^{14} - q^{16} - 3 q^{19} - q^{20} - 3 q^{22} - 4 q^{23} + 2 q^{25} - 2 q^{26} - 3 q^{28} - 4 q^{29} + 12 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8 - q^10 - 3 * q^11 - 5 * q^13 + 6 * q^14 - q^16 - 3 * q^19 - q^20 - 3 * q^22 - 4 * q^23 + 2 * q^25 - 2 * q^26 - 3 * q^28 - 4 * q^29 + 12 * q^31 - q^32 - 3 * q^35 - 9 * q^37 + 6 * q^38 + 2 * q^40 - 10 * q^41 + 10 * q^43 + 6 * q^44 - 4 * q^46 + 6 * q^47 - 2 * q^49 - q^50 + 7 * q^52 - 18 * q^53 - 3 * q^55 - 3 * q^56 - 4 * q^58 + 12 * q^59 + 6 * q^61 - 6 * q^62 + 2 * q^64 - 5 * q^65 + 8 * q^67 + 6 * q^70 - 14 * q^71 - 16 * q^73 - 9 * q^74 - 3 * q^76 + 18 * q^77 + 12 * q^79 - q^80 - 10 * q^82 - 32 * q^83 - 20 * q^86 - 3 * q^88 - 3 * q^89 + 21 * q^91 + 8 * q^92 - 3 * q^94 - 3 * q^95 - 8 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$		0			0
$28$	−1.50000	−	2.59808i	−0.283473	−	0.490990i
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$		0			0
$37$	−4.50000	−	7.79423i	−0.739795	−	1.28136i	−0.952587	−	0.304266i	$-0.901589\pi$
$37$	−4.50000	−	7.79423i	−0.739795	−	1.28136i	0.212792	−	0.977098i	$-0.431744\pi$
$38$	3.00000			0.486664
$39$		0			0
$40$	1.00000			0.158114
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	−0.931436	−	0.363905i	$-0.881443\pi$
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	0.150567	−	0.988600i	$-0.451890\pi$
$42$		0			0
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$		0			0
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$		0			0
$58$	−2.00000	+	3.46410i	−0.262613	+	0.454859i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$	−3.00000	−	5.19615i	−0.381000	−	0.659912i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.50000	−	2.59808i	−0.310087	−	0.322252i
$66$		0			0
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	0.999915	−	0.0130248i	$-0.00414604\pi$
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	−0.511237	+	0.859440i	$0.670813\pi$
$68$		0			0
$69$		0			0
$70$	3.00000			0.358569
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	0.0666994	+	0.997773i	$0.478753\pi$
$71$	−7.00000	+	12.1244i	−0.830747	+	1.43890i	−0.897447	+	0.441123i	$0.854580\pi$
$72$		0			0
$73$	−8.00000			−0.936329			−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000			−0.936329			−0.468165	+	0.883641i	$0.655085\pi$
$74$	−4.50000	+	7.79423i	−0.523114	+	0.906061i
$75$		0			0
$76$	−1.50000	−	2.59808i	−0.172062	−	0.298020i
$77$	9.00000			1.02565
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	−5.00000	+	8.66025i	−0.552158	+	0.956365i
$83$	−16.0000			−1.75623			−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000			−1.75623			−0.878114	+	0.478451i	$0.841198\pi$
$84$		0			0
$85$		0			0
$86$	−10.0000			−1.07833
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$		0			0
$91$	10.5000	−	2.59808i	1.10070	−	0.272352i
$92$	4.00000			0.417029
$93$		0			0
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$	−1.50000	+	2.59808i	−0.153897	+	0.266557i
$96$		0			0
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	−0.994453	−	0.105180i	$-0.966458\pi$
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	0.588315	+	0.808632i	$0.299792\pi$
$98$	−1.00000	+	1.73205i	−0.101015	+	0.174964i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−15.0000			−1.47799			−0.738997	−	0.673709i	$-0.764700\pi$
$103$	−15.0000			−1.47799			−0.738997	+	0.673709i	$0.764700\pi$
$104$	−2.50000	−	2.59808i	−0.245145	−	0.254762i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$		0			0
$112$	3.00000			0.283473
$113$	−4.00000	+	6.92820i	−0.376288	+	0.651751i	−0.990519	−	0.137376i	$-0.956133\pi$
$113$	−4.00000	+	6.92820i	−0.376288	+	0.651751i	0.614231	+	0.789127i	$0.289466\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	4.00000			0.371391
$117$		0			0
$118$	−12.0000			−1.10469
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−6.00000			−0.543214
$123$		0			0
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−1.50000	−	2.59808i	−0.133103	−	0.230542i	0.791768	−	0.610822i	$-0.209161\pi$
$127$	−1.50000	−	2.59808i	−0.133103	−	0.230542i	−0.924871	+	0.380280i	$0.875828\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.00000	+	3.46410i	−0.0877058	+	0.303822i
$131$	3.00000			0.262111			0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000			0.262111			0.131056	+	0.991375i	$0.458163\pi$
$132$		0			0
$133$	−4.50000	−	7.79423i	−0.390199	−	0.675845i
$134$	4.00000	−	6.92820i	0.345547	−	0.598506i
$135$		0			0
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	8.50000	−	14.7224i	0.720961	−	1.24874i	−0.239655	−	0.970858i	$-0.577034\pi$
$139$	8.50000	−	14.7224i	0.720961	−	1.24874i	0.960615	−	0.277882i	$-0.0896325\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$		0			0
$142$	14.0000			1.17485
$143$	−3.00000	+	10.3923i	−0.250873	+	0.869048i
$144$		0			0
$145$	−2.00000	−	3.46410i	−0.166091	−	0.287678i
$146$	4.00000	+	6.92820i	0.331042	+	0.573382i
$147$		0			0
$148$	9.00000			0.739795
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	−0.904076	−	0.427372i	$-0.859440\pi$
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	0.822153	+	0.569267i	$0.192773\pi$
$150$		0			0
$151$	14.0000			1.13930			0.569652	−	0.821886i	$-0.307078\pi$
$151$	14.0000			1.13930			0.569652	+	0.821886i	$0.307078\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$		0			0
$154$	−4.50000	−	7.79423i	−0.362620	−	0.628077i
$155$	6.00000			0.481932
$156$		0			0
$157$	−17.0000			−1.35675			−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000			−1.35675			−0.678374	+	0.734717i	$0.737315\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	12.0000			0.945732
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	10.0000			0.780869
$165$		0			0
$166$	8.00000	+	13.8564i	0.620920	+	1.07547i
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	0.985933	−	0.167139i	$-0.0534527\pi$
$167$	4.50000	+	7.79423i	0.348220	+	0.603136i	−0.637713	+	0.770274i	$0.720119\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$		0			0
$172$	5.00000	+	8.66025i	0.381246	+	0.660338i
$173$	6.50000	−	11.2583i	0.494186	−	0.855955i	−0.505792	−	0.862656i	$-0.668800\pi$
$173$	6.50000	−	11.2583i	0.494186	−	0.855955i	0.999978	+	0.00670064i	$0.00213290\pi$
$174$		0			0
$175$	−1.50000	+	2.59808i	−0.113389	+	0.196396i
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$		0			0
$178$	−1.50000	+	2.59808i	−0.112430	+	0.194734i
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−7.50000	−	7.79423i	−0.555937	−	0.577747i
$183$		0			0
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$	−4.50000	−	7.79423i	−0.330847	−	0.573043i
$186$		0			0
$187$		0			0
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$		0			0
$190$	3.00000			0.217643
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	0.685388	−	0.728178i	$-0.259632\pi$
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	−0.973315	+	0.229475i	$0.926299\pi$
$194$	8.00000			0.574367
$195$		0			0
$196$	2.00000			0.142857
$197$	5.50000	+	9.52628i	0.391859	+	0.678719i	0.992695	−	0.120653i	$-0.0384988\pi$
$197$	5.50000	+	9.52628i	0.391859	+	0.678719i	−0.600836	+	0.799372i	$0.705166\pi$
$198$		0			0
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$	1.00000			0.0707107
$201$		0			0
$202$		0			0
$203$	12.0000			0.842235
$204$		0			0
$205$	−5.00000	−	8.66025i	−0.349215	−	0.604858i
$206$	7.50000	+	12.9904i	0.522550	+	0.905083i
$207$		0			0
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$	9.00000			0.622543
$210$		0			0
$211$	−4.50000	−	7.79423i	−0.309793	−	0.536577i	0.668524	−	0.743690i	$-0.266926\pi$
$211$	−4.50000	−	7.79423i	−0.309793	−	0.536577i	−0.978317	+	0.207114i	$0.933593\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$		0			0
$214$	1.00000	−	1.73205i	0.0683586	−	0.118401i
$215$	5.00000	−	8.66025i	0.340997	−	0.590624i
$216$		0			0
$217$	−9.00000	+	15.5885i	−0.610960	+	1.05821i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$		0			0
$220$	3.00000			0.202260
$221$		0			0
$222$		0			0
$223$	5.50000	+	9.52628i	0.368307	+	0.637927i	0.989301	−	0.145889i	$-0.0466041\pi$
$223$	5.50000	+	9.52628i	0.368307	+	0.637927i	−0.620994	+	0.783815i	$0.713271\pi$
$224$	−1.50000	−	2.59808i	−0.100223	−	0.173591i
$225$		0			0
$226$	8.00000			0.532152
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	0.468368	+	0.883534i	$0.344842\pi$
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	−0.999346	+	0.0361484i	$0.988491\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$		0			0
$232$	−2.00000	−	3.46410i	−0.131306	−	0.227429i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$		0			0
$238$		0			0
$239$	26.0000			1.68180			0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000			1.68180			0.840900	+	0.541190i	$0.182026\pi$
$240$		0			0
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	−0.956456	−	0.291877i	$-0.905720\pi$
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	0.731001	+	0.682376i	$0.239053\pi$
$242$	−2.00000			−0.128565
$243$		0			0
$244$	3.00000	+	5.19615i	0.192055	+	0.332650i
$245$	−1.00000	−	1.73205i	−0.0638877	−	0.110657i
$246$		0			0
$247$	10.5000	−	2.59808i	0.668099	−	0.165312i
$248$	6.00000			0.381000
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−0.500000	+	0.866025i	−0.0315597	+	0.0546630i	−0.881374	−	0.472419i	$-0.843381\pi$
$251$	−0.500000	+	0.866025i	−0.0315597	+	0.0546630i	0.849814	+	0.527082i	$0.176714\pi$
$252$		0			0
$253$	−6.00000	+	10.3923i	−0.377217	+	0.653359i
$254$	−1.50000	+	2.59808i	−0.0941184	+	0.163018i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	0.990217	−	0.139533i	$-0.0445601\pi$
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	−0.615948	+	0.787787i	$0.711227\pi$
$258$		0			0
$259$	27.0000			1.67770
$260$	3.50000	−	0.866025i	0.217061	−	0.0537086i
$261$		0			0
$262$	−1.50000	−	2.59808i	−0.0926703	−	0.160510i
$263$	−15.5000	−	26.8468i	−0.955771	−	1.65544i	−0.732594	−	0.680666i	$-0.761691\pi$
$263$	−15.5000	−	26.8468i	−0.955771	−	1.65544i	−0.223177	−	0.974778i	$-0.571643\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$	−4.50000	+	7.79423i	−0.275913	+	0.477895i
$267$		0			0
$268$	−8.00000			−0.488678
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$		0			0
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	0.988692	−	0.149963i	$-0.0479155\pi$
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	−0.624218	+	0.781251i	$0.714582\pi$
$272$		0			0
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−1.50000	−	2.59808i	−0.0904534	−	0.156670i
$276$		0			0
$277$	15.5000	−	26.8468i	0.931305	−	1.61307i	0.150210	−	0.988654i	$-0.452005\pi$
$277$	15.5000	−	26.8468i	0.931305	−	1.61307i	0.781094	−	0.624413i	$-0.214662\pi$
$278$	−17.0000			−1.01959
$279$		0			0
$280$	−1.50000	+	2.59808i	−0.0896421	+	0.155265i
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	−3.00000	−	5.19615i	−0.178331	−	0.308879i	0.762978	−	0.646425i	$-0.223737\pi$
$283$	−3.00000	−	5.19615i	−0.178331	−	0.308879i	−0.941309	+	0.337546i	$0.890403\pi$
$284$	−7.00000	−	12.1244i	−0.415374	−	0.719448i
$285$		0			0
$286$	10.5000	−	2.59808i	0.620878	−	0.153627i
$287$	30.0000			1.77084
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−2.00000	+	3.46410i	−0.117444	+	0.203419i
$291$		0			0
$292$	4.00000	−	6.92820i	0.234082	−	0.405442i
$293$	−0.500000	+	0.866025i	−0.0292103	+	0.0505937i	−0.880261	−	0.474490i	$-0.842633\pi$
$293$	−0.500000	+	0.866025i	−0.0292103	+	0.0505937i	0.851051	+	0.525084i	$0.175966\pi$
$294$		0			0
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	−4.50000	−	7.79423i	−0.261557	−	0.453030i
$297$		0			0
$298$	2.00000			0.115857
$299$	−4.00000	+	13.8564i	−0.231326	+	0.801337i
$300$		0			0
$301$	15.0000	+	25.9808i	0.864586	+	1.49751i
$302$	−7.00000	−	12.1244i	−0.402805	−	0.697678i
$303$		0			0
$304$	3.00000			0.172062
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$		0			0
$307$	26.0000			1.48390			0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000			1.48390			0.741949	+	0.670456i	$0.233902\pi$
$308$	−4.50000	+	7.79423i	−0.256411	+	0.444117i
$309$		0			0
$310$	−3.00000	−	5.19615i	−0.170389	−	0.295122i
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		0			0
$313$	26.0000			1.46961			0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000			1.46961			0.734803	+	0.678280i	$0.237274\pi$
$314$	8.50000	+	14.7224i	0.479683	+	0.830835i
$315$		0			0
$316$	−3.00000	+	5.19615i	−0.168763	+	0.292306i
$317$	−17.0000			−0.954815			−0.477408	−	0.878682i	$-0.658423\pi$
$317$	−17.0000			−0.954815			−0.477408	+	0.878682i	$0.658423\pi$
$318$		0			0
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	1.00000			0.0559017
$321$		0			0
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$		0			0
$324$		0			0
$325$	−2.50000	−	2.59808i	−0.138675	−	0.144115i
$326$	20.0000			1.10770
$327$		0			0
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	8.00000	−	13.8564i	0.439057	−	0.760469i
$333$		0			0
$334$	4.50000	−	7.79423i	0.246229	−	0.426481i
$335$	4.00000	+	6.92820i	0.218543	+	0.378528i
$336$		0			0
$337$	6.00000			0.326841			0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000			0.326841			0.163420	+	0.986557i	$0.447747\pi$
$338$	11.5000	−	6.06218i	0.625518	−	0.329739i
$339$		0			0
$340$		0			0
$341$	−9.00000	−	15.5885i	−0.487377	−	0.844162i
$342$		0			0
$343$	−15.0000			−0.809924
$344$	5.00000	−	8.66025i	0.269582	−	0.466930i
$345$		0			0
$346$	−13.0000			−0.698884
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	0.340293	+	0.940319i	$0.389474\pi$
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	−0.984487	+	0.175457i	$0.943860\pi$
$348$		0			0
$349$	−8.00000	−	13.8564i	−0.428230	−	0.741716i	0.568486	−	0.822693i	$-0.307529\pi$
$349$	−8.00000	−	13.8564i	−0.428230	−	0.741716i	−0.996716	+	0.0809766i	$0.974196\pi$
$350$	3.00000			0.160357
$351$		0			0
$352$	3.00000			0.159901
$353$	−4.00000	−	6.92820i	−0.212899	−	0.368751i	0.739722	−	0.672913i	$-0.234957\pi$
$353$	−4.00000	−	6.92820i	−0.212899	−	0.368751i	−0.952620	+	0.304162i	$0.901624\pi$
$354$		0			0
$355$	−7.00000	+	12.1244i	−0.371521	+	0.643494i
$356$	3.00000			0.159000
$357$		0			0
$358$	2.00000	−	3.46410i	0.105703	−	0.183083i
$359$	−30.0000			−1.58334			−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000			−1.58334			−0.791670	+	0.610949i	$0.790788\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$		0			0
$364$	−3.00000	+	10.3923i	−0.157243	+	0.544705i
$365$	−8.00000			−0.418739
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$		0			0
$370$	−4.50000	+	7.79423i	−0.233944	+	0.405203i
$371$	13.5000	−	23.3827i	0.700885	−	1.21397i
$372$		0			0
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$		0			0
$375$		0			0
$376$	3.00000			0.154713
$377$	−4.00000	+	13.8564i	−0.206010	+	0.713641i
$378$		0			0
$379$	16.5000	+	28.5788i	0.847548	+	1.46800i	0.883390	+	0.468639i	$0.155255\pi$
$379$	16.5000	+	28.5788i	0.847548	+	1.46800i	−0.0358418	+	0.999357i	$0.511411\pi$
$380$	−1.50000	−	2.59808i	−0.0769484	−	0.133278i
$381$		0			0
$382$	6.00000			0.306987
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	−0.810394	−	0.585886i	$-0.800747\pi$
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	0.912589	+	0.408879i	$0.134080\pi$
$384$		0			0
$385$	9.00000			0.458682
$386$	−4.00000	+	6.92820i	−0.203595	+	0.352636i
$387$		0			0
$388$	−4.00000	−	6.92820i	−0.203069	−	0.351726i
$389$	−24.0000			−1.21685			−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000			−1.21685			−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$		0			0
$392$	−1.00000	−	1.73205i	−0.0505076	−	0.0874818i
$393$		0			0
$394$	5.50000	−	9.52628i	0.277086	−	0.479927i
$395$	6.00000			0.301893
$396$		0			0
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	−0.418634	−	0.908155i	$-0.637491\pi$
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	0.995802	−	0.0915300i	$-0.0291757\pi$
$398$	−10.0000			−0.501255
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	−0.976714	−	0.214544i	$-0.931173\pi$
$401$	−13.5000	−	23.3827i	−0.674158	−	1.16768i	0.302556	−	0.953131i	$-0.402160\pi$
$402$		0			0
$403$	−15.0000	−	15.5885i	−0.747203	−	0.776516i
$404$		0			0
$405$		0			0
$406$	−6.00000	−	10.3923i	−0.297775	−	0.515761i
$407$	−13.5000	+	23.3827i	−0.669170	+	1.15904i
$408$		0			0
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	0.939490	+	0.342578i	$0.111300\pi$
$410$	−5.00000	+	8.66025i	−0.246932	+	0.427699i
$411$		0			0
$412$	7.50000	−	12.9904i	0.369498	−	0.639990i
$413$	18.0000	+	31.1769i	0.885722	+	1.53412i
$414$		0			0
$415$	−16.0000			−0.785409
$416$	3.50000	−	0.866025i	0.171602	−	0.0424604i
$417$		0			0
$418$	−4.50000	−	7.79423i	−0.220102	−	0.381228i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$	−4.50000	+	7.79423i	−0.219057	+	0.379417i
$423$		0			0
$424$	−9.00000			−0.437079
$425$		0			0
$426$		0			0
$427$	9.00000	+	15.5885i	0.435541	+	0.754378i
$428$	−2.00000			−0.0966736
$429$		0			0
$430$	−10.0000			−0.482243
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		0			0
$433$	8.00000	−	13.8564i	0.384455	−	0.665896i	−0.607238	−	0.794520i	$-0.707723\pi$
$433$	8.00000	−	13.8564i	0.384455	−	0.665896i	0.991693	+	0.128624i	$0.0410559\pi$
$434$	18.0000			0.864028
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	12.0000			0.574038
$438$		0			0
$439$	15.0000	+	25.9808i	0.715911	+	1.23999i	0.962607	+	0.270901i	$0.0873217\pi$
$439$	15.0000	+	25.9808i	0.715911	+	1.23999i	−0.246696	+	0.969093i	$0.579345\pi$
$440$	−1.50000	−	2.59808i	−0.0715097	−	0.123858i
$441$		0			0
$442$		0			0
$443$	10.0000			0.475114			0.237557	−	0.971374i	$-0.423653\pi$
$443$	10.0000			0.475114			0.237557	+	0.971374i	$0.423653\pi$
$444$		0			0
$445$	−1.50000	−	2.59808i	−0.0711068	−	0.123161i
$446$	5.50000	−	9.52628i	0.260433	−	0.451082i
$447$		0			0
$448$	−1.50000	+	2.59808i	−0.0708683	+	0.122748i
$449$	−17.5000	+	30.3109i	−0.825876	+	1.43046i	0.0753719	+	0.997155i	$0.475986\pi$
$449$	−17.5000	+	30.3109i	−0.825876	+	1.43046i	−0.901248	+	0.433304i	$0.857348\pi$
$450$		0			0
$451$	−15.0000	+	25.9808i	−0.706322	+	1.22339i
$452$	−4.00000	−	6.92820i	−0.188144	−	0.325875i
$453$		0			0
$454$	16.0000			0.750917
$455$	10.5000	−	2.59808i	0.492248	−	0.121800i
$456$		0			0
$457$	21.0000	+	36.3731i	0.982339	+	1.70146i	0.653213	+	0.757174i	$0.273421\pi$
$457$	21.0000	+	36.3731i	0.982339	+	1.70146i	0.329125	+	0.944286i	$0.393246\pi$
$458$	5.00000	+	8.66025i	0.233635	+	0.404667i
$459$		0			0
$460$	4.00000			0.186501
$461$	−16.0000	+	27.7128i	−0.745194	+	1.29071i	0.204910	+	0.978781i	$0.434310\pi$
$461$	−16.0000	+	27.7128i	−0.745194	+	1.29071i	−0.950104	+	0.311933i	$0.899023\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$	−24.0000			−1.10822
$470$	−1.50000	−	2.59808i	−0.0691898	−	0.119840i
$471$		0			0
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$	−30.0000			−1.37940
$474$		0			0
$475$	−1.50000	+	2.59808i	−0.0688247	+	0.119208i
$476$		0			0
$477$		0			0
$478$	−13.0000	−	22.5167i	−0.594606	−	1.02989i
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	−9.00000	+	31.1769i	−0.410365	+	1.42154i
$482$	7.00000			0.318841
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−4.00000	+	6.92820i	−0.181631	+	0.314594i
$486$		0			0
$487$	−14.5000	+	25.1147i	−0.657058	+	1.13806i	0.324316	+	0.945949i	$0.394866\pi$
$487$	−14.5000	+	25.1147i	−0.657058	+	1.13806i	−0.981374	+	0.192109i	$0.938467\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$		0			0
$490$	−1.00000	+	1.73205i	−0.0451754	+	0.0782461i
$491$	2.50000	+	4.33013i	0.112823	+	0.195416i	0.916908	−	0.399100i	$-0.130677\pi$
$491$	2.50000	+	4.33013i	0.112823	+	0.195416i	−0.804084	+	0.594515i	$0.797344\pi$
$492$		0			0
$493$		0			0
$494$	−7.50000	−	7.79423i	−0.337441	−	0.350679i
$495$		0			0
$496$	−3.00000	−	5.19615i	−0.134704	−	0.233314i
$497$	−21.0000	−	36.3731i	−0.941979	−	1.63156i
$498$		0			0
$499$	20.0000			0.895323			0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000			0.895323			0.447661	+	0.894203i	$0.352257\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	1.00000			0.0446322
$503$	10.5000	−	18.1865i	0.468172	−	0.810897i	−0.531167	−	0.847267i	$-0.678246\pi$
$503$	10.5000	−	18.1865i	0.468172	−	0.810897i	0.999338	+	0.0363700i	$0.0115795\pi$
$504$		0			0
$505$		0			0
$506$	12.0000			0.533465
$507$		0			0
$508$	3.00000			0.133103
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	0.955300	−	0.295637i	$-0.0955319\pi$
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	−0.733679	+	0.679496i	$0.762199\pi$
$510$		0			0
$511$	12.0000	−	20.7846i	0.530849	−	0.919457i
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.00000	−	10.3923i	0.264649	−	0.458385i
$515$	−15.0000			−0.660979
$516$		0			0
$517$	−4.50000	−	7.79423i	−0.197910	−	0.342790i
$518$	−13.5000	−	23.3827i	−0.593156	−	1.02738i
$519$		0			0
$520$	−2.50000	−	2.59808i	−0.109632	−	0.113933i
$521$	35.0000			1.53338			0.766689	−	0.642019i	$-0.221903\pi$
$521$	35.0000			1.53338			0.766689	+	0.642019i	$0.221903\pi$
$522$		0			0
$523$	−11.0000	−	19.0526i	−0.480996	−	0.833110i	0.518766	−	0.854916i	$-0.326392\pi$
$523$	−11.0000	−	19.0526i	−0.480996	−	0.833110i	−0.999762	+	0.0218062i	$0.993058\pi$
$524$	−1.50000	+	2.59808i	−0.0655278	+	0.113497i
$525$		0			0
$526$	−15.5000	+	26.8468i	−0.675832	+	1.17058i
$527$		0			0
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$		0			0
$532$	9.00000			0.390199
$533$	−10.0000	+	34.6410i	−0.433148	+	1.50047i
$534$		0			0
$535$	1.00000	+	1.73205i	0.0432338	+	0.0748831i
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$		0			0
$538$	4.00000			0.172452
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$		0			0
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$	6.00000	−	10.3923i	0.257722	−	0.446388i
$543$		0			0
$544$		0			0
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$		0			0
$550$	−1.50000	+	2.59808i	−0.0639602	+	0.110782i
$551$	12.0000			0.511217
$552$		0			0
$553$	−9.00000	+	15.5885i	−0.382719	+	0.662889i
$554$	−31.0000			−1.31706
$555$		0			0
$556$	8.50000	+	14.7224i	0.360480	+	0.624370i
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$		0			0
$559$	−35.0000	+	8.66025i	−1.48034	+	0.366290i
$560$	3.00000			0.126773
$561$		0			0
$562$	−15.0000	−	25.9808i	−0.632737	−	1.09593i
$563$	10.0000	−	17.3205i	0.421450	−	0.729972i	−0.574632	−	0.818412i	$-0.694855\pi$
$563$	10.0000	−	17.3205i	0.421450	−	0.729972i	0.996082	+	0.0884397i	$0.0281881\pi$
$564$		0			0
$565$	−4.00000	+	6.92820i	−0.168281	+	0.291472i
$566$	−3.00000	+	5.19615i	−0.126099	+	0.218411i
$567$		0			0
$568$	−7.00000	+	12.1244i	−0.293713	+	0.508727i
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$		0			0
$571$	23.0000			0.962520			0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000			0.962520			0.481260	+	0.876578i	$0.340179\pi$
$572$	−7.50000	−	7.79423i	−0.313591	−	0.325893i
$573$		0			0
$574$	−15.0000	−	25.9808i	−0.626088	−	1.08442i
$575$	−2.00000	−	3.46410i	−0.0834058	−	0.144463i
$576$		0			0
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$		0			0
$580$	4.00000			0.166091
$581$	24.0000	−	41.5692i	0.995688	−	1.72458i
$582$		0			0
$583$	13.5000	+	23.3827i	0.559113	+	0.968412i
$584$	−8.00000			−0.331042
$585$		0			0
$586$	1.00000			0.0413096
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	0.989792	−	0.142520i	$-0.0455206\pi$
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	−0.618322	+	0.785925i	$0.712187\pi$
$588$		0			0
$589$	−9.00000	+	15.5885i	−0.370839	+	0.642311i
$590$	−12.0000			−0.494032
$591$		0			0
$592$	−4.50000	+	7.79423i	−0.184949	+	0.320341i
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$		0			0
$595$		0			0
$596$	−1.00000	−	1.73205i	−0.0409616	−	0.0709476i
$597$		0			0
$598$	14.0000	−	3.46410i	0.572503	−	0.141658i
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	−10.5000	−	18.1865i	−0.428304	−	0.741844i	0.568419	−	0.822739i	$-0.307555\pi$
$601$	−10.5000	−	18.1865i	−0.428304	−	0.741844i	−0.996723	+	0.0808953i	$0.974222\pi$
$602$	15.0000	−	25.9808i	0.611354	−	1.05890i
$603$		0			0
$604$	−7.00000	+	12.1244i	−0.284826	+	0.493333i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	0.450467	+	0.892793i	$0.351258\pi$
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	−0.998415	+	0.0562808i	$0.982076\pi$
$608$	−1.50000	−	2.59808i	−0.0608330	−	0.105366i
$609$		0			0
$610$	−6.00000			−0.242933
$611$	−7.50000	−	7.79423i	−0.303418	−	0.315321i
$612$		0			0
$613$	3.50000	+	6.06218i	0.141364	+	0.244849i	0.928010	−	0.372554i	$-0.121518\pi$
$613$	3.50000	+	6.06218i	0.141364	+	0.244849i	−0.786647	+	0.617403i	$0.788185\pi$
$614$	−13.0000	−	22.5167i	−0.524637	−	0.908698i
$615$		0			0
$616$	9.00000			0.362620
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	0.388351	+	0.921512i	$0.373045\pi$
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	−0.992228	+	0.124434i	$0.960288\pi$
$618$		0			0
$619$	−23.0000			−0.924448			−0.462224	−	0.886763i	$-0.652948\pi$
$619$	−23.0000			−0.924448			−0.462224	+	0.886763i	$0.652948\pi$
$620$	−3.00000	+	5.19615i	−0.120483	+	0.208683i
$621$		0			0
$622$	−2.00000	−	3.46410i	−0.0801927	−	0.138898i
$623$	9.00000			0.360577
$624$		0			0
$625$	1.00000			0.0400000
$626$	−13.0000	−	22.5167i	−0.519584	−	0.899947i
$627$		0			0
$628$	8.50000	−	14.7224i	0.339187	−	0.587489i
$629$		0			0
$630$		0			0
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	−0.960386	−	0.278672i	$-0.910106\pi$
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	0.721530	+	0.692383i	$0.243439\pi$
$632$	6.00000			0.238667
$633$		0			0
$634$	8.50000	+	14.7224i	0.337578	+	0.584702i
$635$	−1.50000	−	2.59808i	−0.0595257	−	0.103102i
$636$		0			0
$637$	−2.00000	+	6.92820i	−0.0792429	+	0.274505i
$638$	12.0000			0.475085
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	17.5000	−	30.3109i	0.691208	−	1.19721i	−0.280234	−	0.959932i	$-0.590412\pi$
$641$	17.5000	−	30.3109i	0.691208	−	1.19721i	0.971442	−	0.237276i	$-0.0762547\pi$
$642$		0			0
$643$	−14.0000	+	24.2487i	−0.552106	+	0.956276i	0.446016	+	0.895025i	$0.352842\pi$
$643$	−14.0000	+	24.2487i	−0.552106	+	0.956276i	−0.998122	+	0.0612510i	$0.980491\pi$
$644$	−6.00000	+	10.3923i	−0.236433	+	0.409514i
$645$		0			0
$646$		0			0
$647$	−22.5000	−	38.9711i	−0.884566	−	1.53211i	−0.846210	−	0.532850i	$-0.821121\pi$
$647$	−22.5000	−	38.9711i	−0.884566	−	1.53211i	−0.0383563	−	0.999264i	$-0.512212\pi$
$648$		0			0
$649$	−36.0000			−1.41312
$650$	−1.00000	+	3.46410i	−0.0392232	+	0.135873i
$651$		0			0
$652$	−10.0000	−	17.3205i	−0.391630	−	0.678323i
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	0.893882	−	0.448303i	$-0.147971\pi$
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	−0.835182	+	0.549973i	$0.814638\pi$
$654$		0			0
$655$	3.00000			0.117220
$656$	−5.00000	+	8.66025i	−0.195217	+	0.338126i
$657$		0			0
$658$	9.00000			0.350857
$659$	2.00000	−	3.46410i	0.0779089	−	0.134942i	−0.824439	−	0.565951i	$-0.808509\pi$
$659$	2.00000	−	3.46410i	0.0779089	−	0.134942i	0.902348	+	0.431009i	$0.141842\pi$
$660$		0			0
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	−0.995069	−	0.0991864i	$-0.968376\pi$
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	0.411636	−	0.911348i	$-0.364957\pi$
$662$	−28.0000			−1.08825
$663$		0			0
$664$	−16.0000			−0.620920
$665$	−4.50000	−	7.79423i	−0.174503	−	0.302247i
$666$		0			0
$667$	−8.00000	+	13.8564i	−0.309761	+	0.536522i
$668$	−9.00000			−0.348220
$669$		0			0
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	−18.0000			−0.694882
$672$		0			0
$673$	−24.0000	−	41.5692i	−0.925132	−	1.60238i	−0.791349	−	0.611365i	$-0.790621\pi$
$673$	−24.0000	−	41.5692i	−0.925132	−	1.60238i	−0.133783	−	0.991011i	$-0.542713\pi$
$674$	−3.00000	−	5.19615i	−0.115556	−	0.200148i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$		0			0
$681$		0			0
$682$	−9.00000	+	15.5885i	−0.344628	+	0.596913i
$683$	15.0000	−	25.9808i	0.573959	−	0.994126i	−0.422195	−	0.906505i	$-0.638740\pi$
$683$	15.0000	−	25.9808i	0.573959	−	0.994126i	0.996154	−	0.0876211i	$-0.0279265\pi$
$684$		0			0
$685$	6.00000	−	10.3923i	0.229248	−	0.397070i
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$		0			0
$688$	−10.0000			−0.381246
$689$	22.5000	+	23.3827i	0.857182	+	0.890809i
$690$		0			0
$691$	3.50000	+	6.06218i	0.133146	+	0.230616i	0.924888	−	0.380240i	$-0.124159\pi$
$691$	3.50000	+	6.06218i	0.133146	+	0.230616i	−0.791742	+	0.610856i	$0.790825\pi$
$692$	6.50000	+	11.2583i	0.247093	+	0.427977i
$693$		0			0
$694$	24.0000			0.911028
$695$	8.50000	−	14.7224i	0.322423	−	0.558454i
$696$		0			0
$697$		0			0
$698$	−8.00000	+	13.8564i	−0.302804	+	0.524473i
$699$		0			0
$700$	−1.50000	−	2.59808i	−0.0566947	−	0.0981981i
$701$	−24.0000			−0.906467			−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000			−0.906467			−0.453234	+	0.891392i	$0.649730\pi$
$702$		0			0
$703$	27.0000			1.01832
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	−4.00000	+	6.92820i	−0.150542	+	0.260746i
$707$		0			0
$708$		0			0
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	−0.196167	−	0.980571i	$-0.562849\pi$
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	0.947282	−	0.320400i	$-0.103817\pi$
$710$	14.0000			0.525411
$711$		0			0
$712$	−1.50000	−	2.59808i	−0.0562149	−	0.0973670i
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$		0			0
$715$	−3.00000	+	10.3923i	−0.112194	+	0.388650i
$716$	−4.00000			−0.149487
$717$		0			0
$718$	15.0000	+	25.9808i	0.559795	+	0.969593i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$	22.5000	−	38.9711i	0.837944	−	1.45136i
$722$	5.00000	−	8.66025i	0.186081	−	0.322301i
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$		0			0
$727$	−3.00000			−0.111264			−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000			−0.111264			−0.0556319	+	0.998451i	$0.517717\pi$
$728$	10.5000	−	2.59808i	0.389156	−	0.0962911i
$729$		0			0
$730$	4.00000	+	6.92820i	0.148047	+	0.256424i
$731$		0			0
$732$		0			0
$733$	53.0000			1.95760			0.978800	−	0.204819i	$-0.0656606\pi$
$733$	53.0000			1.95760			0.978800	+	0.204819i	$0.0656606\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$		0			0
$736$	4.00000			0.147442
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$		0			0
$739$	−5.50000	−	9.52628i	−0.202321	−	0.350430i	0.746955	−	0.664875i	$-0.231515\pi$
$739$	−5.50000	−	9.52628i	−0.202321	−	0.350430i	−0.949276	+	0.314445i	$0.898182\pi$
$740$	9.00000			0.330847
$741$		0			0
$742$	−27.0000			−0.991201
$743$	24.0000	+	41.5692i	0.880475	+	1.52503i	0.850814	+	0.525467i	$0.176109\pi$
$743$	24.0000	+	41.5692i	0.880475	+	1.52503i	0.0296605	+	0.999560i	$0.490557\pi$
$744$		0			0
$745$	−1.00000	+	1.73205i	−0.0366372	+	0.0634574i
$746$	−26.0000			−0.951928
$747$		0			0
$748$		0			0
$749$	−6.00000			−0.219235
$750$		0			0
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	0.997526	−	0.0702946i	$-0.0223939\pi$
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	−0.559640	+	0.828736i	$0.689061\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$		0			0
$754$	14.0000	−	3.46410i	0.509850	−	0.126155i
$755$	14.0000			0.509512
$756$		0			0
$757$	−8.50000	−	14.7224i	−0.308938	−	0.535096i	0.669193	−	0.743089i	$-0.266640\pi$
$757$	−8.50000	−	14.7224i	−0.308938	−	0.535096i	−0.978130	+	0.207993i	$0.933307\pi$
$758$	16.5000	−	28.5788i	0.599307	−	1.03803i
$759$		0			0
$760$	−1.50000	+	2.59808i	−0.0544107	+	0.0942421i
$761$	−15.5000	+	26.8468i	−0.561875	+	0.973195i	0.435458	+	0.900209i	$0.356586\pi$
$761$	−15.5000	+	26.8468i	−0.561875	+	0.973195i	−0.997333	+	0.0729864i	$0.976747\pi$
$762$		0			0
$763$	3.00000	−	5.19615i	0.108607	−	0.188113i
$764$	−3.00000	−	5.19615i	−0.108536	−	0.187990i
$765$		0			0
$766$	−4.00000			−0.144526
$767$	−42.0000	+	10.3923i	−1.51653	+	0.375244i
$768$		0			0
$769$	−23.0000	−	39.8372i	−0.829401	−	1.43657i	−0.898509	−	0.438956i	$-0.855348\pi$
$769$	−23.0000	−	39.8372i	−0.829401	−	1.43657i	0.0691074	−	0.997609i	$-0.477985\pi$
$770$	−4.50000	−	7.79423i	−0.162169	−	0.280885i
$771$		0			0
$772$	8.00000			0.287926
$773$	−3.50000	+	6.06218i	−0.125886	+	0.218041i	−0.922079	−	0.387002i	$-0.873511\pi$
$773$	−3.50000	+	6.06218i	−0.125886	+	0.218041i	0.796193	+	0.605043i	$0.206844\pi$
$774$		0			0
$775$	6.00000			0.215526
$776$	−4.00000	+	6.92820i	−0.143592	+	0.248708i
$777$		0			0
$778$	12.0000	+	20.7846i	0.430221	+	0.745164i
$779$	30.0000			1.07486
$780$		0			0
$781$	42.0000			1.50288
$782$		0			0
$783$		0			0
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	−17.0000			−0.606756
$786$		0			0
$787$	18.0000	−	31.1769i	0.641631	−	1.11134i	−0.343438	−	0.939175i	$-0.611592\pi$
$787$	18.0000	−	31.1769i	0.641631	−	1.11134i	0.985069	−	0.172162i	$-0.0550751\pi$
$788$	−11.0000			−0.391859
$789$		0			0
$790$	−3.00000	−	5.19615i	−0.106735	−	0.184871i
$791$	−12.0000	−	20.7846i	−0.426671	−	0.739016i
$792$		0			0
$793$	−21.0000	+	5.19615i	−0.745732	+	0.184521i
$794$	−23.0000			−0.816239
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	0.206868	+	0.978369i	$0.433673\pi$
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	−0.950726	+	0.310031i	$0.899660\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	−13.5000	+	23.3827i	−0.476702	+	0.825671i
$803$	12.0000	+	20.7846i	0.423471	+	0.733473i
$804$		0			0
$805$	12.0000			0.422944
$806$	−6.00000	+	20.7846i	−0.211341	+	0.732107i
$807$		0			0
$808$		0			0
$809$	−5.00000	−	8.66025i	−0.175791	−	0.304478i	0.764644	−	0.644453i	$-0.222915\pi$
$809$	−5.00000	−	8.66025i	−0.175791	−	0.304478i	−0.940435	+	0.339975i	$0.889582\pi$
$810$		0			0
$811$	−31.0000			−1.08856			−0.544279	−	0.838905i	$-0.683197\pi$
$811$	−31.0000			−1.08856			−0.544279	+	0.838905i	$0.683197\pi$
$812$	−6.00000	+	10.3923i	−0.210559	+	0.364698i
$813$		0			0
$814$	27.0000			0.946350
$815$	−10.0000	+	17.3205i	−0.350285	+	0.606711i
$816$		0			0
$817$	15.0000	+	25.9808i	0.524784	+	0.908952i
$818$	−7.00000			−0.244749
$819$		0			0
$820$	10.0000			0.349215
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.859396	+	0.511311i	$0.170840\pi$
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.0131101	+	0.999914i	$0.495827\pi$
$822$		0			0
$823$	5.50000	−	9.52628i	0.191718	−	0.332065i	−0.754102	−	0.656758i	$-0.771927\pi$
$823$	5.50000	−	9.52628i	0.191718	−	0.332065i	0.945820	+	0.324692i	$0.105261\pi$
$824$	−15.0000			−0.522550
$825$		0			0
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$		0			0
$829$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$829$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$830$	8.00000	+	13.8564i	0.277684	+	0.480963i
$831$		0			0
$832$	−2.50000	−	2.59808i	−0.0866719	−	0.0900721i
$833$		0			0
$834$		0			0
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	−4.50000	+	7.79423i	−0.155636	+	0.269569i
$837$		0			0
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	−3.00000	+	5.19615i	−0.103572	+	0.179391i	−0.913154	−	0.407615i	$-0.866360\pi$
$839$	−3.00000	+	5.19615i	−0.103572	+	0.179391i	0.809582	+	0.587007i	$0.199694\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	14.0000	+	24.2487i	0.482472	+	0.835666i
$843$		0			0
$844$	9.00000			0.309793
$845$	−0.500000	+	12.9904i	−0.0172005	+	0.446883i
$846$		0			0
$847$	3.00000	+	5.19615i	0.103081	+	0.178542i
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$		0			0
$850$		0			0
$851$	−18.0000	+	31.1769i	−0.617032	+	1.06873i
$852$		0			0
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$	9.00000	−	15.5885i	0.307974	−	0.533426i
$855$		0			0
$856$	1.00000	+	1.73205i	0.0341793	+	0.0592003i
$857$	50.0000			1.70797			0.853984	−	0.520300i	$-0.174180\pi$
$857$	50.0000			1.70797			0.853984	+	0.520300i	$0.174180\pi$
$858$		0			0
$859$	−5.00000			−0.170598			−0.0852989	−	0.996355i	$-0.527185\pi$
$859$	−5.00000			−0.170598			−0.0852989	+	0.996355i	$0.527185\pi$
$860$	5.00000	+	8.66025i	0.170499	+	0.295312i
$861$		0			0
$862$	−6.00000	+	10.3923i	−0.204361	+	0.353963i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	6.50000	−	11.2583i	0.221007	−	0.382795i
$866$	−16.0000			−0.543702
$867$		0			0
$868$	−9.00000	−	15.5885i	−0.305480	−	0.529107i
$869$	−9.00000	−	15.5885i	−0.305304	−	0.528802i
$870$		0			0
$871$	8.00000	−	27.7128i	0.271070	−	0.939013i
$872$	−2.00000			−0.0677285
$873$		0			0
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		0			0
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	−0.343495	−	0.939155i	$-0.611611\pi$
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	0.985079	−	0.172102i	$-0.0550559\pi$
$878$	15.0000	−	25.9808i	0.506225	−	0.876808i
$879$		0			0
$880$	−1.50000	+	2.59808i	−0.0505650	+	0.0875811i
$881$	−11.5000	−	19.9186i	−0.387445	−	0.671074i	0.604660	−	0.796484i	$-0.293309\pi$
$881$	−11.5000	−	19.9186i	−0.387445	−	0.671074i	−0.992105	+	0.125409i	$0.959976\pi$
$882$		0			0
$883$	22.0000			0.740359			0.370179	−	0.928960i	$-0.379296\pi$
$883$	22.0000			0.740359			0.370179	+	0.928960i	$0.379296\pi$
$884$		0			0
$885$		0			0
$886$	−5.00000	−	8.66025i	−0.167978	−	0.290947i
$887$	4.50000	+	7.79423i	0.151095	+	0.261705i	0.931630	−	0.363407i	$-0.118387\pi$
$887$	4.50000	+	7.79423i	0.151095	+	0.261705i	−0.780535	+	0.625112i	$0.785053\pi$
$888$		0			0
$889$	9.00000			0.301850
$890$	−1.50000	+	2.59808i	−0.0502801	+	0.0870877i
$891$		0			0
$892$	−11.0000			−0.368307
$893$	−4.50000	+	7.79423i	−0.150587	+	0.260824i
$894$		0			0
$895$	2.00000	+	3.46410i	0.0668526	+	0.115792i
$896$	3.00000			0.100223
$897$		0			0
$898$	35.0000			1.16797
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$		0			0
$901$		0			0
$902$	30.0000			0.998891
$903$		0			0
$904$	−4.00000	+	6.92820i	−0.133038	+	0.230429i
$905$	−10.0000			−0.332411
$906$		0			0
$907$	7.00000	+	12.1244i	0.232431	+	0.402583i	0.958523	−	0.285015i	$-0.0919986\pi$
$907$	7.00000	+	12.1244i	0.232431	+	0.402583i	−0.726092	+	0.687598i	$0.758665\pi$
$908$	−8.00000	−	13.8564i	−0.265489	−	0.459841i
$909$		0			0
$910$	−7.50000	−	7.79423i	−0.248623	−	0.258376i
$911$	−28.0000			−0.927681			−0.463841	−	0.885919i	$-0.653529\pi$
$911$	−28.0000			−0.927681			−0.463841	+	0.885919i	$0.653529\pi$
$912$		0			0
$913$	24.0000	+	41.5692i	0.794284	+	1.37574i
$914$	21.0000	−	36.3731i	0.694618	−	1.20311i
$915$		0			0
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$	−4.50000	+	7.79423i	−0.148603	+	0.257388i
$918$		0			0
$919$	−7.00000	+	12.1244i	−0.230909	+	0.399946i	−0.958076	−	0.286515i	$-0.907503\pi$
$919$	−7.00000	+	12.1244i	−0.230909	+	0.399946i	0.727167	+	0.686461i	$0.240837\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$		0			0
$922$	32.0000			1.05386
$923$	49.0000	−	12.1244i	1.61285	−	0.399078i
$924$		0			0
$925$	−4.50000	−	7.79423i	−0.147959	−	0.256273i
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$		0			0
$928$	4.00000			0.131306
$929$	1.00000	−	1.73205i	0.0328089	−	0.0568267i	−0.849155	−	0.528144i	$-0.822888\pi$
$929$	1.00000	−	1.73205i	0.0328089	−	0.0568267i	0.881964	+	0.471317i	$0.156221\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$		0			0
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$		0			0
$936$		0			0
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$	12.0000	+	20.7846i	0.391814	+	0.678642i
$939$		0			0
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$	32.0000			1.04317			0.521585	−	0.853199i	$-0.325341\pi$
$941$	32.0000			1.04317			0.521585	+	0.853199i	$0.325341\pi$
$942$		0			0
$943$	−20.0000	+	34.6410i	−0.651290	+	1.12807i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	15.0000	+	25.9808i	0.487692	+	0.844707i
$947$	9.00000	+	15.5885i	0.292461	+	0.506557i	0.974391	−	0.224860i	$-0.0721926\pi$
$947$	9.00000	+	15.5885i	0.292461	+	0.506557i	−0.681930	+	0.731417i	$0.738859\pi$
$948$		0			0
$949$	20.0000	+	20.7846i	0.649227	+	0.674697i
$950$	3.00000			0.0973329
$951$		0			0
$952$		0			0
$953$	17.0000	−	29.4449i	0.550684	−	0.953813i	−0.447541	−	0.894263i	$-0.647700\pi$
$953$	17.0000	−	29.4449i	0.550684	−	0.953813i	0.998225	−	0.0595495i	$-0.0189664\pi$
$954$		0			0
$955$	−3.00000	+	5.19615i	−0.0970777	+	0.168144i
$956$	−13.0000	+	22.5167i	−0.420450	+	0.728241i
$957$		0			0
$958$	6.00000	−	10.3923i	0.193851	−	0.335760i
$959$	18.0000	+	31.1769i	0.581250	+	1.00676i
$960$		0			0
$961$	5.00000			0.161290
$962$	31.5000	−	7.79423i	1.01560	−	0.251296i
$963$		0			0
$964$	−3.50000	−	6.06218i	−0.112727	−	0.195250i
$965$	−4.00000	−	6.92820i	−0.128765	−	0.223027i
$966$		0			0
$967$	25.0000			0.803946			0.401973	−	0.915652i	$-0.368325\pi$
$967$	25.0000			0.803946			0.401973	+	0.915652i	$0.368325\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$	8.00000			0.256865
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$		0			0
$973$	25.5000	+	44.1673i	0.817492	+	1.41594i
$974$	29.0000			0.929220
$975$		0			0
$976$	−6.00000			−0.192055
$977$	−22.0000	−	38.1051i	−0.703842	−	1.21909i	−0.967108	−	0.254367i	$-0.918133\pi$
$977$	−22.0000	−	38.1051i	−0.703842	−	1.21909i	0.263265	−	0.964723i	$-0.415201\pi$
$978$		0			0
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$	2.00000			0.0638877
$981$		0			0
$982$	2.50000	−	4.33013i	0.0797782	−	0.138180i
$983$	−55.0000			−1.75423			−0.877114	−	0.480283i	$-0.840534\pi$
$983$	−55.0000			−1.75423			−0.877114	+	0.480283i	$0.840534\pi$
$984$		0			0
$985$	5.50000	+	9.52628i	0.175245	+	0.303533i
$986$		0			0
$987$		0			0
$988$	−3.00000	+	10.3923i	−0.0954427	+	0.330623i
$989$	−40.0000			−1.27193
$990$		0			0
$991$	−29.0000	−	50.2295i	−0.921215	−	1.59559i	−0.797537	−	0.603269i	$-0.793864\pi$
$991$	−29.0000	−	50.2295i	−0.921215	−	1.59559i	−0.123678	−	0.992322i	$-0.539469\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$		0			0
$994$	−21.0000	+	36.3731i	−0.666080	+	1.15368i
$995$	5.00000	−	8.66025i	0.158511	−	0.274549i
$996$		0			0
$997$	−23.5000	+	40.7032i	−0.744252	+	1.28908i	0.206291	+	0.978491i	$0.433861\pi$
$997$	−23.5000	+	40.7032i	−0.744252	+	1.28908i	−0.950543	+	0.310592i	$0.899473\pi$
$998$	−10.0000	−	17.3205i	−0.316544	−	0.548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.i.c.991.1		2
3.2	odd	2		390.2.i.e.211.1	yes	2
13.9	even	3	inner	1170.2.i.c.451.1		2
15.2	even	4		1950.2.z.d.1849.1		4
15.8	even	4		1950.2.z.d.1849.2		4
15.14	odd	2		1950.2.i.f.601.1		2
39.2	even	12		5070.2.b.b.1351.2		2
39.11	even	12		5070.2.b.b.1351.1		2
39.23	odd	6		5070.2.a.r.1.1		1
39.29	odd	6		5070.2.a.b.1.1		1
39.35	odd	6		390.2.i.e.61.1	✓	2
195.74	odd	6		1950.2.i.f.451.1		2
195.113	even	12		1950.2.z.d.1699.1		4
195.152	even	12		1950.2.z.d.1699.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.e.61.1	✓	2	39.35	odd	6
390.2.i.e.211.1	yes	2	3.2	odd	2
1170.2.i.c.451.1		2	13.9	even	3	inner
1170.2.i.c.991.1		2	1.1	even	1	trivial
1950.2.i.f.451.1		2	195.74	odd	6
1950.2.i.f.601.1		2	15.14	odd	2
1950.2.z.d.1699.1		4	195.113	even	12
1950.2.z.d.1699.2		4	195.152	even	12
1950.2.z.d.1849.1		4	15.2	even	4
1950.2.z.d.1849.2		4	15.8	even	4
5070.2.a.b.1.1		1	39.29	odd	6
5070.2.a.r.1.1		1	39.23	odd	6
5070.2.b.b.1351.1		2	39.11	even	12
5070.2.b.b.1351.2		2	39.2	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-2.50000 - 2.59808i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{23} +1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +(-1.50000 - 2.59808i) q^{28} +(-2.00000 - 3.46410i) q^{29} +6.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{35} +(-4.50000 - 7.79423i) q^{37} +3.00000 q^{38} +1.00000 q^{40} +(-5.00000 - 8.66025i) q^{41} +(5.00000 - 8.66025i) q^{43} +3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} +3.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(3.50000 - 0.866025i) q^{52} -9.00000 q^{53} +(-1.50000 - 2.59808i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(-2.00000 + 3.46410i) q^{58} +(6.00000 - 10.3923i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-3.00000 - 5.19615i) q^{62} +1.00000 q^{64} +(-2.50000 - 2.59808i) q^{65} +(4.00000 + 6.92820i) q^{67} +3.00000 q^{70} +(-7.00000 + 12.1244i) q^{71} -8.00000 q^{73} +(-4.50000 + 7.79423i) q^{74} +(-1.50000 - 2.59808i) q^{76} +9.00000 q^{77} +6.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-5.00000 + 8.66025i) q^{82} -16.0000 q^{83} -10.0000 q^{86} +(-1.50000 - 2.59808i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(10.5000 - 2.59808i) q^{91} +4.00000 q^{92} +(-1.50000 - 2.59808i) q^{94} +(-1.50000 + 2.59808i) q^{95} +(-4.00000 + 6.92820i) q^{97} +(-1.00000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} - q^{10} - 3 q^{11} - 5 q^{13} + 6 q^{14} - q^{16} - 3 q^{19} - q^{20} - 3 q^{22} - 4 q^{23} + 2 q^{25} - 2 q^{26} - 3 q^{28} - 4 q^{29} + 12 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8 - q^10 - 3 * q^11 - 5 * q^13 + 6 * q^14 - q^16 - 3 * q^19 - q^20 - 3 * q^22 - 4 * q^23 + 2 * q^25 - 2 * q^26 - 3 * q^28 - 4 * q^29 + 12 * q^31 - q^32 - 3 * q^35 - 9 * q^37 + 6 * q^38 + 2 * q^40 - 10 * q^41 + 10 * q^43 + 6 * q^44 - 4 * q^46 + 6 * q^47 - 2 * q^49 - q^50 + 7 * q^52 - 18 * q^53 - 3 * q^55 - 3 * q^56 - 4 * q^58 + 12 * q^59 + 6 * q^61 - 6 * q^62 + 2 * q^64 - 5 * q^65 + 8 * q^67 + 6 * q^70 - 14 * q^71 - 16 * q^73 - 9 * q^74 - 3 * q^76 + 18 * q^77 + 12 * q^79 - q^80 - 10 * q^82 - 32 * q^83 - 20 * q^86 - 3 * q^88 - 3 * q^89 + 21 * q^91 + 8 * q^92 - 3 * q^94 - 3 * q^95 - 8 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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