LMFDB - Embedded newform 1890.2.i.a.1171.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(991,1890)] 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("1890.991"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1890, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,2,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1890.1171
Dual form			1890.2.i.a.991.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(2.00000 - 3.46410i) q^{13} +(2.00000 - 1.73205i) q^{14} +1.00000 q^{16} +(-1.00000 + 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +2.00000 q^{31} -1.00000 q^{32} +(2.50000 + 0.866025i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(1.50000 + 2.59808i) q^{46} -3.00000 q^{47} +(1.00000 - 6.92820i) q^{49} +(0.500000 - 0.866025i) q^{50} +(2.00000 - 3.46410i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.00000 - 1.73205i) q^{56} +(-3.00000 - 5.19615i) q^{58} -12.0000 q^{59} -7.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -7.00000 q^{67} +(-2.50000 - 0.866025i) q^{70} +(-1.00000 - 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{76} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.00000 - 5.19615i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(5.50000 + 9.52628i) q^{86} +(-7.50000 + 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} +(-1.50000 - 2.59808i) q^{92} +3.00000 q^{94} +2.00000 q^{95} +(5.00000 + 8.66025i) q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - q^{5} - 4 q^{7} - 2 q^{8} + q^{10} + 4 q^{13} + 4 q^{14} + 2 q^{16} - 2 q^{19} - q^{20} - 3 q^{23} - q^{25} - 4 q^{26} - 4 q^{28} + 6 q^{29} + 4 q^{31} - 2 q^{32} + 5 q^{35}+ \cdots - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - q^5 - 4 * q^7 - 2 * q^8 + q^10 + 4 * q^13 + 4 * q^14 + 2 * q^16 - 2 * q^19 - q^20 - 3 * q^23 - q^25 - 4 * q^26 - 4 * q^28 + 6 * q^29 + 4 * q^31 - 2 * q^32 + 5 * q^35 - 2 * q^37 + 2 * q^38 + q^40 - 6 * q^41 - 11 * q^43 + 3 * q^46 - 6 * q^47 + 2 * q^49 + q^50 + 4 * q^52 + 6 * q^53 + 4 * q^56 - 6 * q^58 - 24 * q^59 - 14 * q^61 - 4 * q^62 + 2 * q^64 - 8 * q^65 - 14 * q^67 - 5 * q^70 - 2 * q^73 + 2 * q^74 - 2 * q^76 - 8 * q^79 - q^80 + 6 * q^82 - 12 * q^83 + 11 * q^86 - 15 * q^89 + 4 * q^91 - 3 * q^92 + 6 * q^94 + 4 * q^95 + 10 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$		0			0
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$		0			0
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		0			0
$35$	2.50000	+	0.866025i	0.422577	+	0.146385i
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$		0			0
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$		0			0
$56$	2.00000	−	1.73205i	0.267261	−	0.231455i
$57$		0			0
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$		0			0
$61$	−7.00000			−0.896258			−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000			−0.896258			−0.448129	+	0.893969i	$0.647910\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.00000			−0.496139
$66$		0			0
$67$	−7.00000			−0.855186			−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000			−0.855186			−0.427593	+	0.903971i	$0.640638\pi$
$68$		0			0
$69$		0			0
$70$	−2.50000	−	0.866025i	−0.298807	−	0.103510i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$		0			0
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$		0			0
$86$	5.50000	+	9.52628i	0.593080	+	1.02725i
$87$		0			0
$88$		0			0
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	0.127842	+	0.991795i	$0.459195\pi$
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	−0.922840	+	0.385183i	$0.874138\pi$
$90$		0			0
$91$	2.00000	+	10.3923i	0.209657	+	1.08941i
$92$	−1.50000	−	2.59808i	−0.156386	−	0.270868i
$93$		0			0
$94$	3.00000			0.309426
$95$	2.00000			0.205196
$96$		0			0
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	−8.50000	−	14.7224i	−0.837530	−	1.45064i	−0.891954	−	0.452126i	$-0.850666\pi$
$103$	−8.50000	−	14.7224i	−0.837530	−	1.45064i	0.0544240	−	0.998518i	$-0.482668\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$		0			0
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	7.00000			0.633750
$123$		0			0
$124$	2.00000			0.179605
$125$	1.00000			0.0894427
$126$		0			0
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	4.00000			0.350823
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	−1.00000	−	5.19615i	−0.0867110	−	0.450564i
$134$	7.00000			0.604708
$135$		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
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	2.50000	+	0.866025i	0.211289	+	0.0731925i
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$		0			0
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$		0			0
$154$		0			0
$155$	−1.00000	−	1.73205i	−0.0803219	−	0.139122i
$156$		0			0
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	4.00000			0.318223
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	7.50000	+	2.59808i	0.591083	+	0.204757i
$162$		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	$0.880222\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$		0			0
$172$	−5.50000	−	9.52628i	−0.419371	−	0.726372i
$173$	−24.0000			−1.82469			−0.912343	−	0.409426i	$-0.865729\pi$
$173$	−24.0000			−1.82469			−0.912343	+	0.409426i	$0.865729\pi$
$174$		0			0
$175$	−0.500000	−	2.59808i	−0.0377964	−	0.196396i
$176$		0			0
$177$		0			0
$178$	7.50000	−	12.9904i	0.562149	−	0.973670i
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	0.304446	−	0.952529i	$-0.401529\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.00000	−	10.3923i	−0.148250	−	0.770329i
$183$		0			0
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$	2.00000			0.147043
$186$		0			0
$187$		0			0
$188$	−3.00000			−0.218797
$189$		0			0
$190$	−2.00000			−0.145095
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		0			0
$193$	−22.0000			−1.58359			−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000			−1.58359			−0.791797	+	0.610784i	$0.790854\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−1.50000	+	2.59808i	−0.105540	+	0.182800i
$203$	−15.0000	−	5.19615i	−1.05279	−	0.364698i
$204$		0			0
$205$	6.00000			0.419058
$206$	8.50000	+	14.7224i	0.592223	+	1.02576i
$207$		0			0
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$		0			0
$210$		0			0
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$		0			0
$215$	−5.50000	+	9.52628i	−0.375097	+	0.649687i
$216$		0			0
$217$	−4.00000	+	3.46410i	−0.271538	+	0.235159i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$	2.00000	−	1.73205i	0.133631	−	0.115728i
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	−0.125435	−	0.992102i	$-0.540033\pi$
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	0.921903	−	0.387421i	$-0.126634\pi$
$228$		0			0
$229$	−14.5000	−	25.1147i	−0.958187	−	1.65963i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−14.5000	−	25.1147i	−0.958187	−	1.65963i	−0.231287	−	0.972886i	$-0.574293\pi$
$230$	1.50000	−	2.59808i	0.0989071	−	0.171312i
$231$		0			0
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$		0			0
$235$	1.50000	+	2.59808i	0.0978492	+	0.169480i
$236$	−12.0000			−0.781133
$237$		0			0
$238$		0			0
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$		0			0
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	−0.378963	−	0.925412i	$-0.623719\pi$
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	0.990912	−	0.134515i	$-0.0429475\pi$
$242$	−5.50000	−	9.52628i	−0.353553	−	0.612372i
$243$		0			0
$244$	−7.00000			−0.448129
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$		0			0
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$	−2.00000			−0.127000
$249$		0			0
$250$	−1.00000			−0.0632456
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		0			0
$254$	13.0000			0.815693
$255$		0			0
$256$	1.00000			0.0625000
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	−1.00000	−	5.19615i	−0.0621370	−	0.322873i
$260$	−4.00000			−0.248069
$261$		0			0
$262$		0			0
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$	1.00000	+	5.19615i	0.0613139	+	0.318597i
$267$		0			0
$268$	−7.00000			−0.427593
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	−0.985389	−	0.170321i	$-0.945520\pi$
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	0.345192	−	0.938532i	$-0.387814\pi$
$270$		0			0
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	0.384201	+	0.923249i	$0.374477\pi$
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	−0.991658	+	0.128897i	$0.958856\pi$
$272$		0			0
$273$		0			0
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$		0			0
$277$	−16.0000	+	27.7128i	−0.961347	+	1.66510i	−0.242222	+	0.970221i	$0.577876\pi$
$277$	−16.0000	+	27.7128i	−0.961347	+	1.66510i	−0.719125	+	0.694881i	$0.755457\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$		0			0
$280$	−2.50000	−	0.866025i	−0.149404	−	0.0517549i
$281$	10.5000	+	18.1865i	0.626377	+	1.08492i	0.988273	+	0.152699i	$0.0487965\pi$
$281$	10.5000	+	18.1865i	0.626377	+	1.08492i	−0.361895	+	0.932219i	$0.617870\pi$
$282$		0			0
$283$	11.0000			0.653882			0.326941	−	0.945045i	$-0.393982\pi$
$283$	11.0000			0.653882			0.326941	+	0.945045i	$0.393982\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.00000	−	15.5885i	−0.177084	−	0.920158i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−3.00000	+	5.19615i	−0.176166	+	0.305129i
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−15.0000	+	25.9808i	−0.876309	+	1.51781i	−0.0209480	+	0.999781i	$0.506668\pi$
$293$	−15.0000	+	25.9808i	−0.876309	+	1.51781i	−0.855361	+	0.518032i	$0.826665\pi$
$294$		0			0
$295$	6.00000	+	10.3923i	0.349334	+	0.605063i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$		0			0
$298$	−7.50000	−	12.9904i	−0.434463	−	0.752513i
$299$	−12.0000			−0.693978
$300$		0			0
$301$	27.5000	+	9.52628i	1.58507	+	0.549086i
$302$	1.00000	−	1.73205i	0.0575435	−	0.0996683i
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	3.50000	+	6.06218i	0.200409	+	0.347119i
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$		0			0
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	26.0000			1.46961			0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000			1.46961			0.734803	+	0.678280i	$0.237274\pi$
$314$	22.0000			1.24153
$315$		0			0
$316$	−4.00000			−0.225018
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$		0			0
$319$		0			0
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	−7.50000	−	2.59808i	−0.417959	−	0.144785i
$323$		0			0
$324$		0			0
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$	10.0000	−	17.3205i	0.553849	−	0.959294i
$327$		0			0
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	6.00000	−	5.19615i	0.330791	−	0.286473i
$330$		0			0
$331$	26.0000			1.42909			0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000			1.42909			0.714545	+	0.699590i	$0.246634\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$		0			0
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$	3.50000	+	6.06218i	0.191225	+	0.331212i
$336$		0			0
$337$	−16.0000	+	27.7128i	−0.871576	+	1.50961i	−0.0112091	+	0.999937i	$0.503568\pi$
$337$	−16.0000	+	27.7128i	−0.871576	+	1.50961i	−0.860366	+	0.509676i	$0.829765\pi$
$338$	1.50000	+	2.59808i	0.0815892	+	0.141317i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	5.50000	+	9.52628i	0.296540	+	0.513623i
$345$		0			0
$346$	24.0000			1.29025
$347$	−27.0000			−1.44944			−0.724718	−	0.689046i	$-0.758030\pi$
$347$	−27.0000			−1.44944			−0.724718	+	0.689046i	$0.758030\pi$
$348$		0			0
$349$	3.50000	+	6.06218i	0.187351	+	0.324501i	0.944366	−	0.328896i	$-0.106677\pi$
$349$	3.50000	+	6.06218i	0.187351	+	0.324501i	−0.757015	+	0.653397i	$0.773343\pi$
$350$	0.500000	+	2.59808i	0.0267261	+	0.138873i
$351$		0			0
$352$		0			0
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$		0			0
$356$	−7.50000	+	12.9904i	−0.397499	+	0.688489i
$357$		0			0
$358$	9.00000	+	15.5885i	0.475665	+	0.823876i
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−2.00000			−0.105118
$363$		0			0
$364$	2.00000	+	10.3923i	0.104828	+	0.544705i
$365$	−1.00000	+	1.73205i	−0.0523424	+	0.0906597i
$366$		0			0
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$	−2.00000			−0.103975
$371$	−15.0000	−	5.19615i	−0.778761	−	0.269771i
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$		0			0
$376$	3.00000			0.154713
$377$	24.0000			1.23606
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	2.00000			0.102598
$381$		0			0
$382$	18.0000			0.920960
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$		0			0
$385$		0			0
$386$	22.0000			1.11977
$387$		0			0
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	13.5000	−	23.3827i	0.684477	−	1.18555i	−0.289124	−	0.957292i	$-0.593364\pi$
$389$	13.5000	−	23.3827i	0.684477	−	1.18555i	0.973601	−	0.228257i	$-0.0733028\pi$
$390$		0			0
$391$		0			0
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$		0			0
$394$	−12.0000			−0.604551
$395$	2.00000	+	3.46410i	0.100631	+	0.174298i
$396$		0			0
$397$	14.0000	−	24.2487i	0.702640	−	1.21701i	−0.264897	−	0.964277i	$-0.585338\pi$
$397$	14.0000	−	24.2487i	0.702640	−	1.21701i	0.967537	−	0.252731i	$-0.0813288\pi$
$398$	−2.00000	−	3.46410i	−0.100251	−	0.173640i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	1.50000	−	2.59808i	0.0746278	−	0.129259i
$405$		0			0
$406$	15.0000	+	5.19615i	0.744438	+	0.257881i
$407$		0			0
$408$		0			0
$409$	−1.00000			−0.0494468			−0.0247234	−	0.999694i	$-0.507871\pi$
$409$	−1.00000			−0.0494468			−0.0247234	+	0.999694i	$0.507871\pi$
$410$	−6.00000			−0.296319
$411$		0			0
$412$	−8.50000	−	14.7224i	−0.418765	−	0.725322i
$413$	24.0000	−	20.7846i	1.18096	−	1.02274i
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$		0			0
$418$		0			0
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$		0			0
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	0.581086	−	0.813842i	$-0.302628\pi$
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	−0.995351	+	0.0963145i	$0.969295\pi$
$422$	4.00000	−	6.92820i	0.194717	−	0.337260i
$423$		0			0
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$		0			0
$426$		0			0
$427$	14.0000	−	12.1244i	0.677507	−	0.586739i
$428$		0			0
$429$		0			0
$430$	5.50000	−	9.52628i	0.265234	−	0.459398i
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$		0			0
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$	4.00000	−	3.46410i	0.192006	−	0.166282i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	6.00000			0.287019
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	15.0000			0.711068
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$		0			0
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	−15.0000			−0.707894			−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$		0			0
$451$		0			0
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$		0			0
$454$	−12.0000	+	20.7846i	−0.563188	+	0.975470i
$455$	8.00000	−	6.92820i	0.375046	−	0.324799i
$456$		0			0
$457$	26.0000			1.21623			0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000			1.21623			0.608114	+	0.793849i	$0.291926\pi$
$458$	14.5000	+	25.1147i	0.677541	+	1.17353i
$459$		0			0
$460$	−1.50000	+	2.59808i	−0.0699379	+	0.121136i
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	0.987801	+	0.155719i	$0.0497696\pi$
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	−0.359044	+	0.933321i	$0.616897\pi$
$462$		0			0
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	−0.918253	−	0.395995i	$-0.870400\pi$
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	0.802068	+	0.597233i	$0.203733\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	7.50000	−	12.9904i	0.347059	−	0.601123i	−0.638667	−	0.769483i	$-0.720514\pi$
$467$	7.50000	−	12.9904i	0.347059	−	0.601123i	0.985726	+	0.168360i	$0.0538472\pi$
$468$		0			0
$469$	14.0000	−	12.1244i	0.646460	−	0.559851i
$470$	−1.50000	−	2.59808i	−0.0691898	−	0.119840i
$471$		0			0
$472$	12.0000			0.552345
$473$		0			0
$474$		0			0
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$		0			0
$477$		0			0
$478$	12.0000	−	20.7846i	0.548867	−	0.950666i
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$	−9.50000	+	16.4545i	−0.432713	+	0.749481i
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	5.00000	−	8.66025i	0.227038	−	0.393242i
$486$		0			0
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	0.545436	−	0.838152i	$-0.316364\pi$
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	−0.998579	+	0.0532853i	$0.983031\pi$
$488$	7.00000			0.316875
$489$		0			0
$490$	6.50000	−	2.59808i	0.293640	−	0.117369i
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$		0			0
$493$		0			0
$494$	−4.00000	−	6.92820i	−0.179969	−	0.311715i
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$		0			0
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	0.988204	+	0.153141i	$0.0489388\pi$
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	−0.361478	+	0.932381i	$0.617728\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$	−12.0000			−0.535586
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$		0			0
$507$		0			0
$508$	−13.0000			−0.576782
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$		0			0
$511$	5.00000	+	1.73205i	0.221187	+	0.0766214i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	9.00000	+	15.5885i	0.396973	+	0.687577i
$515$	−8.50000	+	14.7224i	−0.374555	+	0.648748i
$516$		0			0
$517$		0			0
$518$	1.00000	+	5.19615i	0.0439375	+	0.228306i
$519$		0			0
$520$	4.00000			0.175412
$521$	13.5000	+	23.3827i	0.591446	+	1.02441i	0.994038	+	0.109035i	$0.0347759\pi$
$521$	13.5000	+	23.3827i	0.591446	+	1.02441i	−0.402592	+	0.915379i	$0.631891\pi$
$522$		0			0
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$		0			0
$525$		0			0
$526$	−4.50000	+	7.79423i	−0.196209	+	0.339845i
$527$		0			0
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$		0			0
$532$	−1.00000	−	5.19615i	−0.0433555	−	0.225282i
$533$	12.0000	+	20.7846i	0.519778	+	0.900281i
$534$		0			0
$535$		0			0
$536$	7.00000			0.302354
$537$		0			0
$538$	10.5000	+	18.1865i	0.452687	+	0.784077i
$539$		0			0
$540$		0			0
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$	10.0000	−	17.3205i	0.429537	−	0.743980i
$543$		0			0
$544$		0			0
$545$	−1.00000	+	1.73205i	−0.0428353	+	0.0741929i
$546$		0			0
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$		0			0
$550$		0			0
$551$	−12.0000			−0.511217
$552$		0			0
$553$	8.00000	−	6.92820i	0.340195	−	0.294617i
$554$	16.0000	−	27.7128i	0.679775	−	1.17740i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	3.00000	+	5.19615i	0.127114	+	0.220168i	0.922557	−	0.385860i	$-0.126095\pi$
$557$	3.00000	+	5.19615i	0.127114	+	0.220168i	−0.795443	+	0.606028i	$0.792762\pi$
$558$		0			0
$559$	−44.0000			−1.86100
$560$	2.50000	+	0.866025i	0.105644	+	0.0365963i
$561$		0			0
$562$	−10.5000	−	18.1865i	−0.442916	−	0.767153i
$563$	9.00000			0.379305			0.189652	−	0.981851i	$-0.439264\pi$
$563$	9.00000			0.379305			0.189652	+	0.981851i	$0.439264\pi$
$564$		0			0
$565$	6.00000			0.252422
$566$	−11.0000			−0.462364
$567$		0			0
$568$		0			0
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$		0			0
$574$	3.00000	+	15.5885i	0.125218	+	0.650650i
$575$	3.00000			0.125109
$576$		0			0
$577$	−10.0000	−	17.3205i	−0.416305	−	0.721062i	0.579259	−	0.815144i	$-0.303342\pi$
$577$	−10.0000	−	17.3205i	−0.416305	−	0.721062i	−0.995565	+	0.0940813i	$0.970009\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$		0			0
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$	30.0000	+	10.3923i	1.24461	+	0.431145i
$582$		0			0
$583$		0			0
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$		0			0
$586$	15.0000	−	25.9808i	0.619644	−	1.07326i
$587$	22.5000	+	38.9711i	0.928674	+	1.60851i	0.785543	+	0.618808i	$0.212384\pi$
$587$	22.5000	+	38.9711i	0.928674	+	1.60851i	0.143132	+	0.989704i	$0.454283\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$	−6.00000	−	10.3923i	−0.247016	−	0.427844i
$591$		0			0
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$		0			0
$595$		0			0
$596$	7.50000	+	12.9904i	0.307212	+	0.532107i
$597$		0			0
$598$	12.0000			0.490716
$599$	−6.00000			−0.245153			−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000			−0.245153			−0.122577	+	0.992459i	$0.539116\pi$
$600$		0			0
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	0.949799	−	0.312861i	$-0.101287\pi$
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	−0.745845	+	0.666120i	$0.767954\pi$
$602$	−27.5000	−	9.52628i	−1.12082	−	0.388262i
$603$		0			0
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$	5.50000	−	9.52628i	0.223607	−	0.387298i
$606$		0			0
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$		0			0
$610$	−3.50000	−	6.06218i	−0.141711	−	0.245450i
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$		0			0
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	−0.938967	−	0.344008i	$-0.888215\pi$
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	0.171564	−	0.985173i	$-0.445118\pi$
$614$	−20.0000			−0.807134
$615$		0			0
$616$		0			0
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$		0			0
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$	−1.00000	−	1.73205i	−0.0401610	−	0.0695608i
$621$		0			0
$622$		0			0
$623$	−7.50000	−	38.9711i	−0.300481	−	1.56135i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−26.0000			−1.03917
$627$		0			0
$628$	−22.0000			−0.877896
$629$		0			0
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	4.00000			0.159111
$633$		0			0
$634$	−18.0000			−0.714871
$635$	6.50000	+	11.2583i	0.257945	+	0.446773i
$636$		0			0
$637$	−22.0000	−	17.3205i	−0.871672	−	0.686264i
$638$		0			0
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−7.50000	+	12.9904i	−0.296232	+	0.513089i	−0.975271	−	0.221013i	$-0.929064\pi$
$641$	−7.50000	+	12.9904i	−0.296232	+	0.513089i	0.679039	+	0.734103i	$0.262397\pi$
$642$		0			0
$643$	21.5000	−	37.2391i	0.847877	−	1.46857i	−0.0352216	−	0.999380i	$-0.511214\pi$
$643$	21.5000	−	37.2391i	0.847877	−	1.46857i	0.883099	−	0.469187i	$-0.155453\pi$
$644$	7.50000	+	2.59808i	0.295541	+	0.102379i
$645$		0			0
$646$		0			0
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$		0			0
$649$		0			0
$650$	−2.00000	−	3.46410i	−0.0784465	−	0.135873i
$651$		0			0
$652$	−10.0000	+	17.3205i	−0.391630	+	0.678323i
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	0.994623	+	0.103558i	$0.0330227\pi$
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	−0.407628	+	0.913148i	$0.633644\pi$
$654$		0			0
$655$		0			0
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$		0			0
$658$	−6.00000	+	5.19615i	−0.233904	+	0.202567i
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	0.999309	−	0.0371821i	$-0.0118382\pi$
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	−0.531855	+	0.846836i	$0.678505\pi$
$660$		0			0
$661$	5.00000			0.194477			0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000			0.194477			0.0972387	+	0.995261i	$0.468999\pi$
$662$	−26.0000			−1.01052
$663$		0			0
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$	−4.00000	+	3.46410i	−0.155113	+	0.134332i
$666$		0			0
$667$	9.00000	−	15.5885i	0.348481	−	0.603587i
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$		0			0
$670$	−3.50000	−	6.06218i	−0.135217	−	0.234202i
$671$		0			0
$672$		0			0
$673$	14.0000	+	24.2487i	0.539660	+	0.934719i	0.998922	+	0.0464181i	$0.0147807\pi$
$673$	14.0000	+	24.2487i	0.539660	+	0.934719i	−0.459262	+	0.888301i	$0.651886\pi$
$674$	16.0000	−	27.7128i	0.616297	−	1.06746i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$		0			0
$679$	−25.0000	−	8.66025i	−0.959412	−	0.332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	25.5000	+	44.1673i	0.975730	+	1.69001i	0.677503	+	0.735520i	$0.263062\pi$
$683$	25.5000	+	44.1673i	0.975730	+	1.69001i	0.298227	+	0.954495i	$0.403605\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$	−10.0000	−	15.5885i	−0.381802	−	0.595170i
$687$		0			0
$688$	−5.50000	−	9.52628i	−0.209686	−	0.363186i
$689$	24.0000			0.914327
$690$		0			0
$691$	−46.0000			−1.74992			−0.874961	−	0.484193i	$-0.839113\pi$
$691$	−46.0000			−1.74992			−0.874961	+	0.484193i	$0.839113\pi$
$692$	−24.0000			−0.912343
$693$		0			0
$694$	27.0000			1.02491
$695$	−4.00000			−0.151729
$696$		0			0
$697$		0			0
$698$	−3.50000	−	6.06218i	−0.132477	−	0.229457i
$699$		0			0
$700$	−0.500000	−	2.59808i	−0.0188982	−	0.0981981i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	−2.00000	−	3.46410i	−0.0754314	−	0.130651i
$704$		0			0
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	1.50000	+	7.79423i	0.0564133	+	0.293132i
$708$		0			0
$709$	−19.0000			−0.713560			−0.356780	−	0.934188i	$-0.616125\pi$
$709$	−19.0000			−0.713560			−0.356780	+	0.934188i	$0.616125\pi$
$710$		0			0
$711$		0			0
$712$	7.50000	−	12.9904i	0.281074	−	0.486835i
$713$	−3.00000	−	5.19615i	−0.112351	−	0.194597i
$714$		0			0
$715$		0			0
$716$	−9.00000	−	15.5885i	−0.336346	−	0.582568i
$717$		0			0
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	0.438141	+	0.898906i	$0.355637\pi$
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	−0.997546	+	0.0700124i	$0.977696\pi$
$720$		0			0
$721$	42.5000	+	14.7224i	1.58278	+	0.548292i
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$		0			0
$724$	2.00000			0.0743294
$725$	−6.00000			−0.222834
$726$		0			0
$727$	3.50000	+	6.06218i	0.129808	+	0.224834i	0.923602	−	0.383353i	$-0.125231\pi$
$727$	3.50000	+	6.06218i	0.129808	+	0.224834i	−0.793794	+	0.608186i	$0.791897\pi$
$728$	−2.00000	−	10.3923i	−0.0741249	−	0.385164i
$729$		0			0
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$		0			0
$732$		0			0
$733$	−4.00000	−	6.92820i	−0.147743	−	0.255899i	0.782650	−	0.622462i	$-0.213868\pi$
$733$	−4.00000	−	6.92820i	−0.147743	−	0.255899i	−0.930393	+	0.366563i	$0.880534\pi$
$734$	8.50000	−	14.7224i	0.313741	−	0.543415i
$735$		0			0
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$		0			0
$738$		0			0
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	−0.994420	−	0.105493i	$-0.966358\pi$
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	0.405851	−	0.913939i	$-0.366975\pi$
$740$	2.00000			0.0735215
$741$		0			0
$742$	15.0000	+	5.19615i	0.550667	+	0.190757i
$743$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$743$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$744$		0			0
$745$	7.50000	−	12.9904i	0.274779	−	0.475931i
$746$	7.00000	+	12.1244i	0.256288	+	0.443904i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	0.993895	−	0.110333i	$-0.0351919\pi$
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	−0.592499	+	0.805571i	$0.701859\pi$
$752$	−3.00000			−0.109399
$753$		0			0
$754$	−24.0000			−0.874028
$755$	2.00000			0.0727875
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	4.00000			0.145287
$759$		0			0
$760$	−2.00000			−0.0725476
$761$	7.50000	+	12.9904i	0.271875	+	0.470901i	0.969342	−	0.245716i	$-0.0790230\pi$
$761$	7.50000	+	12.9904i	0.271875	+	0.470901i	−0.697467	+	0.716617i	$0.745690\pi$
$762$		0			0
$763$	5.00000	+	1.73205i	0.181012	+	0.0627044i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	10.5000	+	18.1865i	0.379380	+	0.657106i
$767$	−24.0000	+	41.5692i	−0.866590	+	1.50098i
$768$		0			0
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$		0			0
$771$		0			0
$772$	−22.0000			−0.791797
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$		0			0
$775$	−1.00000	+	1.73205i	−0.0359211	+	0.0622171i
$776$	−5.00000	−	8.66025i	−0.179490	−	0.310885i
$777$		0			0
$778$	−13.5000	+	23.3827i	−0.483998	+	0.838310i
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	11.0000	+	19.0526i	0.392607	+	0.680015i
$786$		0			0
$787$	−1.00000			−0.0356462			−0.0178231	−	0.999841i	$-0.505674\pi$
$787$	−1.00000			−0.0356462			−0.0178231	+	0.999841i	$0.505674\pi$
$788$	12.0000			0.427482
$789$		0			0
$790$	−2.00000	−	3.46410i	−0.0711568	−	0.123247i
$791$	−3.00000	−	15.5885i	−0.106668	−	0.554262i
$792$		0			0
$793$	−14.0000	+	24.2487i	−0.497155	+	0.861097i
$794$	−14.0000	+	24.2487i	−0.496841	+	0.860555i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	−0.661441	−	0.749997i	$-0.730055\pi$
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	0.980237	+	0.197826i	$0.0633881\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	−7.50000	−	12.9904i	−0.264834	−	0.458706i
$803$		0			0
$804$		0			0
$805$	−1.50000	−	7.79423i	−0.0528681	−	0.274710i
$806$	−4.00000	+	6.92820i	−0.140894	+	0.244036i
$807$		0			0
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	−0.973253	−	0.229736i	$-0.926214\pi$
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	0.287670	−	0.957730i	$-0.407120\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	−15.0000	−	5.19615i	−0.526397	−	0.182349i
$813$		0			0
$814$		0			0
$815$	20.0000			0.700569
$816$		0			0
$817$	22.0000			0.769683
$818$	1.00000			0.0349642
$819$		0			0
$820$	6.00000			0.209529
$821$	3.00000			0.104701			0.0523504	−	0.998629i	$-0.483329\pi$
$821$	3.00000			0.104701			0.0523504	+	0.998629i	$0.483329\pi$
$822$		0			0
$823$	8.00000			0.278862			0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000			0.278862			0.139431	+	0.990232i	$0.455473\pi$
$824$	8.50000	+	14.7224i	0.296112	+	0.512880i
$825$		0			0
$826$	−24.0000	+	20.7846i	−0.835067	+	0.723189i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		0			0
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$		0			0
$834$		0			0
$835$	3.00000			0.103819
$836$		0			0
$837$		0			0
$838$	−18.0000	+	31.1769i	−0.621800	+	1.07699i
$839$	−9.00000	−	15.5885i	−0.310715	−	0.538173i	0.667803	−	0.744338i	$-0.267235\pi$
$839$	−9.00000	−	15.5885i	−0.310715	−	0.538173i	−0.978517	+	0.206165i	$0.933902\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	8.50000	+	14.7224i	0.292929	+	0.507369i
$843$		0			0
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	−1.50000	+	2.59808i	−0.0516016	+	0.0893765i
$846$		0			0
$847$	−27.5000	−	9.52628i	−0.944911	−	0.327327i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$		0			0
$850$		0			0
$851$	6.00000			0.205677
$852$		0			0
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	0.789386	−	0.613897i	$-0.210399\pi$
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	−0.926343	+	0.376680i	$0.877066\pi$
$854$	−14.0000	+	12.1244i	−0.479070	+	0.414887i
$855$		0			0
$856$		0			0
$857$	15.0000	−	25.9808i	0.512390	−	0.887486i	−0.487507	−	0.873119i	$-0.662093\pi$
$857$	15.0000	−	25.9808i	0.512390	−	0.887486i	0.999897	−	0.0143666i	$-0.00457319\pi$
$858$		0			0
$859$	−13.0000	−	22.5167i	−0.443554	−	0.768259i	0.554396	−	0.832253i	$-0.312949\pi$
$859$	−13.0000	−	22.5167i	−0.443554	−	0.768259i	−0.997950	+	0.0639945i	$0.979616\pi$
$860$	−5.50000	+	9.52628i	−0.187548	+	0.324843i
$861$		0			0
$862$	−15.0000	−	25.9808i	−0.510902	−	0.884908i
$863$	−10.5000	+	18.1865i	−0.357424	+	0.619077i	−0.987530	−	0.157433i	$-0.949678\pi$
$863$	−10.5000	+	18.1865i	−0.357424	+	0.619077i	0.630106	+	0.776509i	$0.283012\pi$
$864$		0			0
$865$	12.0000	+	20.7846i	0.408012	+	0.706698i
$866$	4.00000			0.135926
$867$		0			0
$868$	−4.00000	+	3.46410i	−0.135769	+	0.117579i
$869$		0			0
$870$		0			0
$871$	−14.0000	+	24.2487i	−0.474372	+	0.821636i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$		0			0
$874$	−6.00000			−0.202953
$875$	−2.00000	+	1.73205i	−0.0676123	+	0.0585540i
$876$		0			0
$877$	17.0000	+	29.4449i	0.574049	+	0.994282i	0.996144	+	0.0877308i	$0.0279615\pi$
$877$	17.0000	+	29.4449i	0.574049	+	0.994282i	−0.422095	+	0.906552i	$0.638705\pi$
$878$	−8.00000			−0.269987
$879$		0			0
$880$		0			0
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	−43.0000			−1.44707			−0.723533	−	0.690290i	$-0.757483\pi$
$883$	−43.0000			−1.44707			−0.723533	+	0.690290i	$0.757483\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	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
$889$	26.0000	−	22.5167i	0.872012	−	0.755185i
$890$	−15.0000			−0.502801
$891$		0			0
$892$	9.50000	+	16.4545i	0.318084	+	0.550937i
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$		0			0
$895$	−9.00000	+	15.5885i	−0.300837	+	0.521065i
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$		0			0
$898$	15.0000			0.500556
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$	3.00000	−	5.19615i	0.0997785	−	0.172821i
$905$	−1.00000	−	1.73205i	−0.0332411	−	0.0575753i
$906$		0			0
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	−0.830909	−	0.556408i	$-0.812179\pi$
$907$	2.00000	−	3.46410i	0.0664089	−	0.115024i	0.897318	+	0.441384i	$0.145512\pi$
$908$	12.0000	−	20.7846i	0.398234	−	0.689761i
$909$		0			0
$910$	−8.00000	+	6.92820i	−0.265197	+	0.229668i
$911$	−21.0000	−	36.3731i	−0.695761	−	1.20509i	−0.969923	−	0.243410i	$-0.921734\pi$
$911$	−21.0000	−	36.3731i	−0.695761	−	1.20509i	0.274162	−	0.961683i	$-0.411599\pi$
$912$		0			0
$913$		0			0
$914$	−26.0000			−0.860004
$915$		0			0
$916$	−14.5000	−	25.1147i	−0.479093	−	0.829814i
$917$		0			0
$918$		0			0
$919$	−28.0000	+	48.4974i	−0.923635	+	1.59978i	−0.129893	+	0.991528i	$0.541463\pi$
$919$	−28.0000	+	48.4974i	−0.923635	+	1.59978i	−0.793742	+	0.608254i	$0.791870\pi$
$920$	1.50000	−	2.59808i	0.0494535	−	0.0856560i
$921$		0			0
$922$	−13.5000	−	23.3827i	−0.444599	−	0.770068i
$923$		0			0
$924$		0			0
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$	2.50000	−	4.33013i	0.0821551	−	0.142297i
$927$		0			0
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	−15.0000			−0.492134			−0.246067	−	0.969253i	$-0.579138\pi$
$929$	−15.0000			−0.492134			−0.246067	+	0.969253i	$0.579138\pi$
$930$		0			0
$931$	11.0000	+	8.66025i	0.360510	+	0.283828i
$932$	9.00000	−	15.5885i	0.294805	−	0.510617i
$933$		0			0
$934$	−7.50000	+	12.9904i	−0.245407	+	0.425058i
$935$		0			0
$936$		0			0
$937$	44.0000			1.43742			0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000			1.43742			0.718709	+	0.695311i	$0.244734\pi$
$938$	−14.0000	+	12.1244i	−0.457116	+	0.395874i
$939$		0			0
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$	−15.0000			−0.488986			−0.244493	−	0.969651i	$-0.578622\pi$
$941$	−15.0000			−0.488986			−0.244493	+	0.969651i	$0.578622\pi$
$942$		0			0
$943$	18.0000			0.586161
$944$	−12.0000			−0.390567
$945$		0			0
$946$		0			0
$947$	−45.0000			−1.46230			−0.731152	−	0.682215i	$-0.761017\pi$
$947$	−45.0000			−1.46230			−0.731152	+	0.682215i	$0.761017\pi$
$948$		0			0
$949$	−8.00000			−0.259691
$950$	1.00000	+	1.73205i	0.0324443	+	0.0561951i
$951$		0			0
$952$		0			0
$953$	−18.0000			−0.583077			−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000			−0.583077			−0.291539	+	0.956559i	$0.594167\pi$
$954$		0			0
$955$	9.00000	+	15.5885i	0.291233	+	0.504431i
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	−9.00000	+	15.5885i	−0.290777	+	0.503640i
$959$	6.00000	+	31.1769i	0.193750	+	1.00676i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	−4.00000	−	6.92820i	−0.128965	−	0.223374i
$963$		0			0
$964$	9.50000	−	16.4545i	0.305974	−	0.529963i
$965$	11.0000	+	19.0526i	0.354103	+	0.613324i
$966$		0			0
$967$	0.500000	−	0.866025i	0.0160789	−	0.0278495i	−0.857874	−	0.513860i	$-0.828215\pi$
$967$	0.500000	−	0.866025i	0.0160789	−	0.0278495i	0.873953	+	0.486011i	$0.161548\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$		0			0
$970$	−5.00000	+	8.66025i	−0.160540	+	0.278064i
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	2.00000	+	10.3923i	0.0641171	+	0.333162i
$974$	10.0000	+	17.3205i	0.320421	+	0.554985i
$975$		0			0
$976$	−7.00000			−0.224065
$977$	−36.0000			−1.15174			−0.575871	−	0.817541i	$-0.695337\pi$
$977$	−36.0000			−1.15174			−0.575871	+	0.817541i	$0.695337\pi$
$978$		0			0
$979$		0			0
$980$	−6.50000	+	2.59808i	−0.207635	+	0.0829925i
$981$		0			0
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$		0			0
$988$	4.00000	+	6.92820i	0.127257	+	0.220416i
$989$	−16.5000	+	28.5788i	−0.524669	+	0.908754i
$990$		0			0
$991$	−28.0000	−	48.4974i	−0.889449	−	1.54057i	−0.840528	−	0.541769i	$-0.817755\pi$
$991$	−28.0000	−	48.4974i	−0.889449	−	1.54057i	−0.0489218	−	0.998803i	$-0.515578\pi$
$992$	−2.00000			−0.0635001
$993$		0			0
$994$		0			0
$995$	2.00000	−	3.46410i	0.0634043	−	0.109819i
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	−14.0000	−	24.2487i	−0.443162	−	0.767580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.i.a.1171.1		2
3.2	odd	2		630.2.i.d.121.1	✓	2
7.4	even	3		1890.2.l.d.361.1		2
9.2	odd	6		630.2.l.b.331.1	yes	2
9.7	even	3		1890.2.l.d.1801.1		2
21.11	odd	6		630.2.l.b.571.1	yes	2
63.11	odd	6		630.2.i.d.151.1	yes	2
63.25	even	3	inner	1890.2.i.a.991.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.d.121.1	✓	2	3.2	odd	2
630.2.i.d.151.1	yes	2	63.11	odd	6
630.2.l.b.331.1	yes	2	9.2	odd	6
630.2.l.b.571.1	yes	2	21.11	odd	6
1890.2.i.a.991.1		2	63.25	even	3	inner
1890.2.i.a.1171.1		2	1.1	even	1	trivial
1890.2.l.d.361.1		2	7.4	even	3
1890.2.l.d.1801.1		2	9.7	even	3

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(2.00000 - 3.46410i) q^{13} +(2.00000 - 1.73205i) q^{14} +1.00000 q^{16} +(-1.00000 + 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +2.00000 q^{31} -1.00000 q^{32} +(2.50000 + 0.866025i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(1.50000 + 2.59808i) q^{46} -3.00000 q^{47} +(1.00000 - 6.92820i) q^{49} +(0.500000 - 0.866025i) q^{50} +(2.00000 - 3.46410i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.00000 - 1.73205i) q^{56} +(-3.00000 - 5.19615i) q^{58} -12.0000 q^{59} -7.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -7.00000 q^{67} +(-2.50000 - 0.866025i) q^{70} +(-1.00000 - 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{76} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.00000 - 5.19615i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(5.50000 + 9.52628i) q^{86} +(-7.50000 + 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} +(-1.50000 - 2.59808i) q^{92} +3.00000 q^{94} +2.00000 q^{95} +(5.00000 + 8.66025i) q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - q^{5} - 4 q^{7} - 2 q^{8} + q^{10} + 4 q^{13} + 4 q^{14} + 2 q^{16} - 2 q^{19} - q^{20} - 3 q^{23} - q^{25} - 4 q^{26} - 4 q^{28} + 6 q^{29} + 4 q^{31} - 2 q^{32} + 5 q^{35}+ \cdots - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - q^5 - 4 * q^7 - 2 * q^8 + q^10 + 4 * q^13 + 4 * q^14 + 2 * q^16 - 2 * q^19 - q^20 - 3 * q^23 - q^25 - 4 * q^26 - 4 * q^28 + 6 * q^29 + 4 * q^31 - 2 * q^32 + 5 * q^35 - 2 * q^37 + 2 * q^38 + q^40 - 6 * q^41 - 11 * q^43 + 3 * q^46 - 6 * q^47 + 2 * q^49 + q^50 + 4 * q^52 + 6 * q^53 + 4 * q^56 - 6 * q^58 - 24 * q^59 - 14 * q^61 - 4 * q^62 + 2 * q^64 - 8 * q^65 - 14 * q^67 - 5 * q^70 - 2 * q^73 + 2 * q^74 - 2 * q^76 - 8 * q^79 - q^80 + 6 * q^82 - 12 * q^83 + 11 * q^86 - 15 * q^89 + 4 * q^91 - 3 * q^92 + 6 * q^94 + 4 * q^95 + 10 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

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Database

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