LMFDB - Embedded newform 1890.2.t.a.1151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.a.1601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -4.73205i q^{11} +(3.00000 + 1.73205i) q^{13} +(1.73205 - 2.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.09808 + 0.633975i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.36603 - 4.09808i) q^{22} -2.53590i q^{23} +1.00000 q^{25} +(1.73205 + 3.00000i) q^{26} +(2.50000 - 0.866025i) q^{28} +(5.59808 - 3.23205i) q^{29} +(-7.09808 + 4.09808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.500000 - 2.59808i) q^{35} +(-3.09808 - 5.36603i) q^{37} -1.26795 q^{38} +1.00000i q^{40} +(4.50000 - 7.79423i) q^{41} +(-1.59808 - 2.76795i) q^{43} +(4.09808 - 2.36603i) q^{44} +(1.26795 - 2.19615i) q^{46} +(4.50000 - 7.79423i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(0.866025 + 0.500000i) q^{50} +3.46410i q^{52} +(6.29423 + 3.63397i) q^{53} -4.73205i q^{55} +(2.59808 + 0.500000i) q^{56} +6.46410 q^{58} +(-1.09808 - 1.90192i) q^{59} +(11.1962 + 6.46410i) q^{61} -8.19615 q^{62} -1.00000 q^{64} +(3.00000 + 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.73205 - 2.00000i) q^{70} +4.73205i q^{71} +(6.00000 + 3.46410i) q^{73} -6.19615i q^{74} +(-1.09808 - 0.633975i) q^{76} +(-12.2942 - 2.36603i) q^{77} +(-7.29423 + 12.6340i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(7.79423 - 4.50000i) q^{82} +(-5.59808 - 9.69615i) q^{83} -3.19615i q^{86} +4.73205 q^{88} +(2.19615 + 3.80385i) q^{89} +(6.00000 - 6.92820i) q^{91} +(2.19615 - 1.26795i) q^{92} +(7.79423 - 4.50000i) q^{94} +(-1.09808 + 0.633975i) q^{95} +(7.39230 - 4.26795i) q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^7	$ 4 q + 2 q^{4} + 4 q^{5} + 2 q^{7} + 12 q^{13} - 2 q^{16} + 6 q^{19} + 2 q^{20} + 6 q^{22} + 4 q^{25} + 10 q^{28} + 12 q^{29} - 18 q^{31} + 2 q^{35} - 2 q^{37} - 12 q^{38} + 18 q^{41} + 4 q^{43} + 6 q^{44} + 12 q^{46} + 18 q^{47} - 26 q^{49} - 6 q^{53} + 12 q^{58} + 6 q^{59} + 24 q^{61} - 12 q^{62} - 4 q^{64} + 12 q^{65} + 8 q^{67} + 24 q^{73} + 6 q^{76} - 18 q^{77} + 2 q^{79} - 2 q^{80} - 12 q^{83} + 12 q^{88} - 12 q^{89} + 24 q^{91} - 12 q^{92} + 6 q^{95} - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^7 + 12 * q^13 - 2 * q^16 + 6 * q^19 + 2 * q^20 + 6 * q^22 + 4 * q^25 + 10 * q^28 + 12 * q^29 - 18 * q^31 + 2 * q^35 - 2 * q^37 - 12 * q^38 + 18 * q^41 + 4 * q^43 + 6 * q^44 + 12 * q^46 + 18 * q^47 - 26 * q^49 - 6 * q^53 + 12 * q^58 + 6 * q^59 + 24 * q^61 - 12 * q^62 - 4 * q^64 + 12 * q^65 + 8 * q^67 + 24 * q^73 + 6 * q^76 - 18 * q^77 + 2 * q^79 - 2 * q^80 - 12 * q^83 + 12 * q^88 - 12 * q^89 + 24 * q^91 - 12 * q^92 + 6 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	4.73205i		−	1.42677i	−0.700774	−	0.713384i	$-0.747162\pi$
$11$		−	4.73205i		−	1.42677i	0.700774	−	0.713384i	$-0.252838\pi$
$12$		0			0
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$	1.73205	−	2.00000i	0.462910	−	0.534522i
$15$		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
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	−0.620641	−	0.784095i	$-0.713128\pi$
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	0.368725	+	0.929538i	$0.379794\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	2.36603	−	4.09808i	0.504438	−	0.873713i
$23$		−	2.53590i		−	0.528771i	−0.964417	−	0.264386i	$-0.914831\pi$
$23$		−	2.53590i		−	0.528771i	0.964417	−	0.264386i	$-0.0851692\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.73205	+	3.00000i	0.339683	+	0.588348i
$27$		0			0
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	5.59808	−	3.23205i	1.03954	−	0.600177i	0.119835	−	0.992794i	$-0.461764\pi$
$29$	5.59808	−	3.23205i	1.03954	−	0.600177i	0.919702	+	0.392617i	$0.128430\pi$
$30$		0			0
$31$	−7.09808	+	4.09808i	−1.27485	+	0.736036i	−0.975897	−	0.218231i	$-0.929971\pi$
$31$	−7.09808	+	4.09808i	−1.27485	+	0.736036i	−0.298955	+	0.954267i	$0.596638\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$		0			0
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$		0			0
$37$	−3.09808	−	5.36603i	−0.509321	−	0.882169i	−0.999942	−	0.0107961i	$-0.996563\pi$
$37$	−3.09808	−	5.36603i	−0.509321	−	0.882169i	0.490621	−	0.871373i	$-0.336770\pi$
$38$	−1.26795			−0.205689
$39$		0			0
$40$			1.00000i			0.158114i
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	−1.59808	−	2.76795i	−0.243704	−	0.422108i	0.718062	−	0.695979i	$-0.245029\pi$
$43$	−1.59808	−	2.76795i	−0.243704	−	0.422108i	−0.961767	+	0.273871i	$0.911696\pi$
$44$	4.09808	−	2.36603i	0.617808	−	0.356692i
$45$		0			0
$46$	1.26795	−	2.19615i	0.186949	−	0.323805i
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	−0.325150	−	0.945662i	$-0.605415\pi$
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	0.981543	−	0.191243i	$-0.0612518\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$			3.46410i			0.480384i
$53$	6.29423	+	3.63397i	0.864579	+	0.499165i	0.865543	−	0.500835i	$-0.166974\pi$
$53$	6.29423	+	3.63397i	0.864579	+	0.499165i	−0.000964138		1.00000i	$0.500307\pi$
$54$		0			0
$55$		−	4.73205i		−	0.638070i
$56$	2.59808	+	0.500000i	0.347183	+	0.0668153i
$57$		0			0
$58$	6.46410			0.848778
$59$	−1.09808	−	1.90192i	−0.142957	−	0.247609i	0.785652	−	0.618669i	$-0.212328\pi$
$59$	−1.09808	−	1.90192i	−0.142957	−	0.247609i	−0.928609	+	0.371060i	$0.878995\pi$
$60$		0			0
$61$	11.1962	+	6.46410i	1.43352	+	0.827643i	0.997387	−	0.0722388i	$-0.0230144\pi$
$61$	11.1962	+	6.46410i	1.43352	+	0.827643i	0.436133	+	0.899882i	$0.356348\pi$
$62$	−8.19615			−1.04091
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.00000	+	1.73205i	0.372104	+	0.214834i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$		0			0
$70$	1.73205	−	2.00000i	0.207020	−	0.239046i
$71$			4.73205i			0.561591i	0.959768	+	0.280796i	$0.0905983\pi$
$71$			4.73205i			0.561591i	−0.959768	+	0.280796i	$0.909402\pi$
$72$		0			0
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	0.808184	−	0.588930i	$-0.200451\pi$
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	−0.105937	+	0.994373i	$0.533784\pi$
$74$		−	6.19615i		−	0.720288i
$75$		0			0
$76$	−1.09808	−	0.633975i	−0.125958	−	0.0727219i
$77$	−12.2942	−	2.36603i	−1.40106	−	0.269634i
$78$		0			0
$79$	−7.29423	+	12.6340i	−0.820665	+	1.42143i	0.0845230	+	0.996422i	$0.473063\pi$
$79$	−7.29423	+	12.6340i	−0.820665	+	1.42143i	−0.905188	+	0.425012i	$0.860270\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	7.79423	−	4.50000i	0.860729	−	0.496942i
$83$	−5.59808	−	9.69615i	−0.614469	−	1.06429i	−0.990477	−	0.137675i	$-0.956037\pi$
$83$	−5.59808	−	9.69615i	−0.614469	−	1.06429i	0.376009	−	0.926616i	$-0.377296\pi$
$84$		0			0
$85$		0			0
$86$		−	3.19615i		−	0.344650i
$87$		0			0
$88$	4.73205			0.504438
$89$	2.19615	+	3.80385i	0.232792	+	0.403207i	0.958629	−	0.284660i	$-0.0918806\pi$
$89$	2.19615	+	3.80385i	0.232792	+	0.403207i	−0.725837	+	0.687867i	$0.758547\pi$
$90$		0			0
$91$	6.00000	−	6.92820i	0.628971	−	0.726273i
$92$	2.19615	−	1.26795i	0.228965	−	0.132193i
$93$		0			0
$94$	7.79423	−	4.50000i	0.803913	−	0.464140i
$95$	−1.09808	+	0.633975i	−0.112660	+	0.0650444i
$96$		0			0
$97$	7.39230	−	4.26795i	0.750575	−	0.433345i	−0.0753267	−	0.997159i	$-0.524000\pi$
$97$	7.39230	−	4.26795i	0.750575	−	0.433345i	0.825902	+	0.563814i	$0.190667\pi$
$98$	−4.33013	−	5.50000i	−0.437409	−	0.555584i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	11.1962			1.11406			0.557029	−	0.830493i	$-0.311941\pi$
$101$	11.1962			1.11406			0.557029	+	0.830493i	$0.311941\pi$
$102$		0			0
$103$			12.1244i			1.19465i	0.802000	+	0.597324i	$0.203769\pi$
$103$			12.1244i			1.19465i	−0.802000	+	0.597324i	$0.796231\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$		0			0
$106$	3.63397	+	6.29423i	0.352963	+	0.611350i
$107$	−13.7942	+	7.96410i	−1.33354	+	0.769919i	−0.985840	−	0.167688i	$-0.946370\pi$
$107$	−13.7942	+	7.96410i	−1.33354	+	0.769919i	−0.347698	+	0.937606i	$0.613037\pi$
$108$		0			0
$109$	3.59808	−	6.23205i	0.344633	−	0.596922i	−0.640654	−	0.767830i	$-0.721337\pi$
$109$	3.59808	−	6.23205i	0.344633	−	0.596922i	0.985287	+	0.170908i	$0.0546700\pi$
$110$	2.36603	−	4.09808i	0.225592	−	0.390736i
$111$		0			0
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	10.9019	+	6.29423i	1.02557	+	0.592111i	0.915711	−	0.401836i	$-0.131628\pi$
$113$	10.9019	+	6.29423i	1.02557	+	0.592111i	0.109855	+	0.993948i	$0.464961\pi$
$114$		0			0
$115$		−	2.53590i		−	0.236474i
$116$	5.59808	+	3.23205i	0.519768	+	0.300088i
$117$		0			0
$118$		−	2.19615i		−	0.202172i
$119$		0			0
$120$		0			0
$121$	−11.3923			−1.03566
$122$	6.46410	+	11.1962i	0.585232	+	1.01365i
$123$		0			0
$124$	−7.09808	−	4.09808i	−0.637426	−	0.368018i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−11.3923			−1.01090			−0.505452	−	0.862855i	$-0.668674\pi$
$127$	−11.3923			−1.01090			−0.505452	+	0.862855i	$0.668674\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	1.73205	+	3.00000i	0.151911	+	0.263117i
$131$	−4.39230			−0.383757			−0.191879	−	0.981419i	$-0.561458\pi$
$131$	−4.39230			−0.383757			−0.191879	+	0.981419i	$0.561458\pi$
$132$		0			0
$133$	1.09808	+	3.16987i	0.0952153	+	0.274863i
$134$			4.00000i			0.345547i
$135$		0			0
$136$		0			0
$137$			7.26795i			0.620943i	0.950583	+	0.310471i	$0.100487\pi$
$137$			7.26795i			0.620943i	−0.950583	+	0.310471i	$0.899513\pi$
$138$		0			0
$139$	19.0981	+	11.0263i	1.61988	+	0.935237i	0.986950	+	0.161026i	$0.0514802\pi$
$139$	19.0981	+	11.0263i	1.61988	+	0.935237i	0.632927	+	0.774211i	$0.281853\pi$
$140$	2.50000	−	0.866025i	0.211289	−	0.0731925i
$141$		0			0
$142$	−2.36603	+	4.09808i	−0.198552	+	0.343903i
$143$	8.19615	−	14.1962i	0.685397	−	1.18714i
$144$		0			0
$145$	5.59808	−	3.23205i	0.464895	−	0.268407i
$146$	3.46410	+	6.00000i	0.286691	+	0.496564i
$147$		0			0
$148$	3.09808	−	5.36603i	0.254660	−	0.441085i
$149$		−	12.0000i		−	0.983078i	−0.870855	−	0.491539i	$-0.836434\pi$
$149$		−	12.0000i		−	0.983078i	0.870855	−	0.491539i	$-0.163566\pi$
$150$		0			0
$151$	−4.19615			−0.341478			−0.170739	−	0.985316i	$-0.554616\pi$
$151$	−4.19615			−0.341478			−0.170739	+	0.985316i	$0.554616\pi$
$152$	−0.633975	−	1.09808i	−0.0514221	−	0.0890657i
$153$		0			0
$154$	−9.46410	−	8.19615i	−0.762639	−	0.660465i
$155$	−7.09808	+	4.09808i	−0.570131	+	0.329165i
$156$		0			0
$157$	−15.2942	+	8.83013i	−1.22061	+	0.704721i	−0.965049	−	0.262071i	$-0.915594\pi$
$157$	−15.2942	+	8.83013i	−1.22061	+	0.704721i	−0.255564	+	0.966792i	$0.582261\pi$
$158$	−12.6340	+	7.29423i	−1.00511	+	0.580298i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−6.58846	−	1.26795i	−0.519243	−	0.0999284i
$162$		0			0
$163$	4.19615	+	7.26795i	0.328668	+	0.569270i	0.982248	−	0.187588i	$-0.0600669\pi$
$163$	4.19615	+	7.26795i	0.328668	+	0.569270i	−0.653580	+	0.756858i	$0.726734\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$		−	11.1962i		−	0.868990i
$167$	−5.19615	+	9.00000i	−0.402090	+	0.696441i	−0.993978	−	0.109580i	$-0.965050\pi$
$167$	−5.19615	+	9.00000i	−0.402090	+	0.696441i	0.591888	+	0.806020i	$0.298383\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$		0			0
$172$	1.59808	−	2.76795i	0.121852	−	0.211054i
$173$	−4.09808	+	7.09808i	−0.311571	+	0.539657i	−0.978703	−	0.205283i	$-0.934188\pi$
$173$	−4.09808	+	7.09808i	−0.311571	+	0.539657i	0.667132	+	0.744940i	$0.267522\pi$
$174$		0			0
$175$	0.500000	−	2.59808i	0.0377964	−	0.196396i
$176$	4.09808	+	2.36603i	0.308904	+	0.178346i
$177$		0			0
$178$			4.39230i			0.329217i
$179$	−21.2942	−	12.2942i	−1.59161	−	0.918914i	−0.993032	−	0.117846i	$-0.962401\pi$
$179$	−21.2942	−	12.2942i	−1.59161	−	0.918914i	−0.598573	−	0.801068i	$-0.704266\pi$
$180$		0			0
$181$		−	13.3923i		−	0.995442i	−0.867337	−	0.497721i	$-0.834170\pi$
$181$		−	13.3923i		−	0.995442i	0.867337	−	0.497721i	$-0.165830\pi$
$182$	8.66025	−	3.00000i	0.641941	−	0.222375i
$183$		0			0
$184$	2.53590			0.186949
$185$	−3.09808	−	5.36603i	−0.227775	−	0.394518i
$186$		0			0
$187$		0			0
$188$	9.00000			0.656392
$189$		0			0
$190$	−1.26795			−0.0919867
$191$	−3.00000	−	1.73205i	−0.217072	−	0.125327i	0.387522	−	0.921861i	$-0.373331\pi$
$191$	−3.00000	−	1.73205i	−0.217072	−	0.125327i	−0.604594	+	0.796534i	$0.706665\pi$
$192$		0			0
$193$	−6.90192	−	11.9545i	−0.496811	−	0.860502i	0.503182	−	0.864181i	$-0.332163\pi$
$193$	−6.90192	−	11.9545i	−0.496811	−	0.860502i	−0.999993	+	0.00367804i	$0.998829\pi$
$194$	8.53590			0.612842
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$			23.6603i			1.68572i	0.538130	+	0.842862i	$0.319131\pi$
$197$			23.6603i			1.68572i	−0.538130	+	0.842862i	$0.680869\pi$
$198$		0			0
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	0.697355	−	0.716726i	$-0.254360\pi$
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	−0.272026	+	0.962290i	$0.587694\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	9.69615	+	5.59808i	0.682219	+	0.393879i
$203$	−5.59808	−	16.1603i	−0.392908	−	1.13423i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	−6.06218	+	10.5000i	−0.422372	+	0.731570i
$207$		0			0
$208$	−3.00000	+	1.73205i	−0.208013	+	0.120096i
$209$	3.00000	+	5.19615i	0.207514	+	0.359425i
$210$		0			0
$211$	10.2942	−	17.8301i	0.708684	−	1.22748i	−0.256662	−	0.966501i	$-0.582623\pi$
$211$	10.2942	−	17.8301i	0.708684	−	1.22748i	0.965345	−	0.260975i	$-0.0840441\pi$
$212$			7.26795i			0.499165i
$213$		0			0
$214$	−15.9282			−1.08883
$215$	−1.59808	−	2.76795i	−0.108988	−	0.188773i
$216$		0			0
$217$	7.09808	+	20.4904i	0.481849	+	1.39098i
$218$	6.23205	−	3.59808i	0.422088	−	0.243692i
$219$		0			0
$220$	4.09808	−	2.36603i	0.276292	−	0.159517i
$221$		0			0
$222$		0			0
$223$	11.8923	−	6.86603i	0.796368	−	0.459783i	−0.0458318	−	0.998949i	$-0.514594\pi$
$223$	11.8923	−	6.86603i	0.796368	−	0.459783i	0.842199	+	0.539166i	$0.181260\pi$
$224$	0.866025	+	2.50000i	0.0578638	+	0.167038i
$225$		0			0
$226$	6.29423	+	10.9019i	0.418686	+	0.725185i
$227$	16.3923			1.08800			0.543998	−	0.839087i	$-0.316910\pi$
$227$	16.3923			1.08800			0.543998	+	0.839087i	$0.316910\pi$
$228$		0			0
$229$			14.0718i			0.929891i	0.885339	+	0.464945i	$0.153926\pi$
$229$			14.0718i			0.929891i	−0.885339	+	0.464945i	$0.846074\pi$
$230$	1.26795	−	2.19615i	0.0836061	−	0.144810i
$231$		0			0
$232$	3.23205	+	5.59808i	0.212195	+	0.367532i
$233$	−1.09808	+	0.633975i	−0.0719374	+	0.0415331i	−0.535537	−	0.844512i	$-0.679891\pi$
$233$	−1.09808	+	0.633975i	−0.0719374	+	0.0415331i	0.463600	+	0.886045i	$0.346558\pi$
$234$		0			0
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	1.09808	−	1.90192i	0.0714787	−	0.123805i
$237$		0			0
$238$		0			0
$239$	−2.70577	−	1.56218i	−0.175022	−	0.101049i	0.409930	−	0.912117i	$-0.365553\pi$
$239$	−2.70577	−	1.56218i	−0.175022	−	0.101049i	−0.584952	+	0.811068i	$0.698887\pi$
$240$		0			0
$241$			3.33975i			0.215132i	0.994198	+	0.107566i	$0.0343057\pi$
$241$			3.33975i			0.215132i	−0.994198	+	0.107566i	$0.965694\pi$
$242$	−9.86603	−	5.69615i	−0.634212	−	0.366163i
$243$		0			0
$244$			12.9282i			0.827643i
$245$	−6.50000	−	2.59808i	−0.415270	−	0.165985i
$246$		0			0
$247$	−4.39230			−0.279476
$248$	−4.09808	−	7.09808i	−0.260228	−	0.450728i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	−9.86603	−	5.69615i	−0.619049	−	0.357408i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−28.3923			−1.77106			−0.885532	−	0.464579i	$-0.846206\pi$
$257$	−28.3923			−1.77106			−0.885532	+	0.464579i	$0.846206\pi$
$258$		0			0
$259$	−15.4904	+	5.36603i	−0.962525	+	0.333429i
$260$			3.46410i			0.214834i
$261$		0			0
$262$	−3.80385	−	2.19615i	−0.235002	−	0.135679i
$263$		−	13.7321i		−	0.846755i	−0.905953	−	0.423377i	$-0.860844\pi$
$263$		−	13.7321i		−	0.846755i	0.905953	−	0.423377i	$-0.139156\pi$
$264$		0			0
$265$	6.29423	+	3.63397i	0.386651	+	0.223233i
$266$	−0.633975	+	3.29423i	−0.0388715	+	0.201982i
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$		0			0
$271$	5.70577	−	3.29423i	0.346601	−	0.200110i	−0.316586	−	0.948564i	$-0.602537\pi$
$271$	5.70577	−	3.29423i	0.346601	−	0.200110i	0.663187	+	0.748454i	$0.269203\pi$
$272$		0			0
$273$		0			0
$274$	−3.63397	+	6.29423i	−0.219536	+	0.380248i
$275$		−	4.73205i		−	0.285353i
$276$		0			0
$277$	−24.1962			−1.45381			−0.726903	−	0.686740i	$-0.759041\pi$
$277$	−24.1962			−1.45381			−0.726903	+	0.686740i	$0.759041\pi$
$278$	11.0263	+	19.0981i	0.661312	+	1.14543i
$279$		0			0
$280$	2.59808	+	0.500000i	0.155265	+	0.0298807i
$281$	−12.6962	+	7.33013i	−0.757389	+	0.437279i	−0.828357	−	0.560200i	$-0.810724\pi$
$281$	−12.6962	+	7.33013i	−0.757389	+	0.437279i	0.0709685	+	0.997479i	$0.477391\pi$
$282$		0			0
$283$	−14.5981	+	8.42820i	−0.867766	+	0.501005i	−0.866605	−	0.498995i	$-0.833703\pi$
$283$	−14.5981	+	8.42820i	−0.867766	+	0.501005i	−0.00116049	+	0.999999i	$0.500369\pi$
$284$	−4.09808	+	2.36603i	−0.243176	+	0.140398i
$285$		0			0
$286$	14.1962	−	8.19615i	0.839436	−	0.484649i
$287$	−18.0000	−	15.5885i	−1.06251	−	0.920158i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	6.46410			0.379585
$291$		0			0
$292$			6.92820i			0.405442i
$293$	8.19615	−	14.1962i	0.478824	−	0.829348i	−0.520881	−	0.853629i	$-0.674396\pi$
$293$	8.19615	−	14.1962i	0.478824	−	0.829348i	0.999705	+	0.0242813i	$0.00772975\pi$
$294$		0			0
$295$	−1.09808	−	1.90192i	−0.0639325	−	0.110734i
$296$	5.36603	−	3.09808i	0.311894	−	0.180072i
$297$		0			0
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$	4.39230	−	7.60770i	0.254014	−	0.439964i
$300$		0			0
$301$	−7.99038	+	2.76795i	−0.460558	+	0.159542i
$302$	−3.63397	−	2.09808i	−0.209112	−	0.120731i
$303$		0			0
$304$		−	1.26795i		−	0.0727219i
$305$	11.1962	+	6.46410i	0.641090	+	0.370133i
$306$		0			0
$307$			23.7846i			1.35746i	0.734388	+	0.678730i	$0.237469\pi$
$307$			23.7846i			1.35746i	−0.734388	+	0.678730i	$0.762531\pi$
$308$	−4.09808	−	11.8301i	−0.233510	−	0.674084i
$309$		0			0
$310$	−8.19615			−0.465510
$311$	7.90192	+	13.6865i	0.448077	+	0.776092i	0.998261	−	0.0589514i	$-0.0187757\pi$
$311$	7.90192	+	13.6865i	0.448077	+	0.776092i	−0.550184	+	0.835044i	$0.685442\pi$
$312$		0			0
$313$	−17.4904	−	10.0981i	−0.988615	−	0.570777i	−0.0837548	−	0.996486i	$-0.526691\pi$
$313$	−17.4904	−	10.0981i	−0.988615	−	0.570777i	−0.904860	+	0.425709i	$0.860025\pi$
$314$	−17.6603			−0.996626
$315$		0			0
$316$	−14.5885			−0.820665
$317$	−17.7846	−	10.2679i	−0.998883	−	0.576705i	−0.0909655	−	0.995854i	$-0.528995\pi$
$317$	−17.7846	−	10.2679i	−0.998883	−	0.576705i	−0.907918	+	0.419149i	$0.862329\pi$
$318$		0			0
$319$	−15.2942	−	26.4904i	−0.856312	−	1.48318i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−5.07180	−	4.39230i	−0.282640	−	0.244774i
$323$		0			0
$324$		0			0
$325$	3.00000	+	1.73205i	0.166410	+	0.0960769i
$326$			8.39230i			0.464807i
$327$		0			0
$328$	7.79423	+	4.50000i	0.430364	+	0.248471i
$329$	−18.0000	−	15.5885i	−0.992372	−	0.859419i
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	5.59808	−	9.69615i	0.307234	−	0.532145i
$333$		0			0
$334$	−9.00000	+	5.19615i	−0.492458	+	0.284321i
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$		0			0
$337$	−5.00000	+	8.66025i	−0.272367	+	0.471754i	−0.969468	−	0.245220i	$-0.921140\pi$
$337$	−5.00000	+	8.66025i	−0.272367	+	0.471754i	0.697100	+	0.716974i	$0.254473\pi$
$338$		−	1.00000i		−	0.0543928i
$339$		0			0
$340$		0			0
$341$	19.3923	+	33.5885i	1.05015	+	1.81892i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	2.76795	−	1.59808i	0.149238	−	0.0861625i
$345$		0			0
$346$	−7.09808	+	4.09808i	−0.381595	+	0.220314i
$347$	−18.4019	+	10.6244i	−0.987867	+	0.570345i	−0.904636	−	0.426185i	$-0.859857\pi$
$347$	−18.4019	+	10.6244i	−0.987867	+	0.570345i	−0.0832310	+	0.996530i	$0.526524\pi$
$348$		0			0
$349$	14.1962	−	8.19615i	0.759903	−	0.438730i	−0.0693582	−	0.997592i	$-0.522095\pi$
$349$	14.1962	−	8.19615i	0.759903	−	0.438730i	0.829261	+	0.558862i	$0.188762\pi$
$350$	1.73205	−	2.00000i	0.0925820	−	0.106904i
$351$		0			0
$352$	2.36603	+	4.09808i	0.126110	+	0.218428i
$353$	0.588457			0.0313204			0.0156602	−	0.999877i	$-0.495015\pi$
$353$	0.588457			0.0313204			0.0156602	+	0.999877i	$0.495015\pi$
$354$		0			0
$355$			4.73205i			0.251151i
$356$	−2.19615	+	3.80385i	−0.116396	+	0.201604i
$357$		0			0
$358$	−12.2942	−	21.2942i	−0.649770	−	1.12543i
$359$	13.6865	−	7.90192i	0.722348	−	0.417048i	−0.0932685	−	0.995641i	$-0.529732\pi$
$359$	13.6865	−	7.90192i	0.722348	−	0.417048i	0.815616	+	0.578593i	$0.196398\pi$
$360$		0			0
$361$	−8.69615	+	15.0622i	−0.457692	+	0.792746i
$362$	6.69615	−	11.5981i	0.351942	−	0.609581i
$363$		0			0
$364$	9.00000	+	1.73205i	0.471728	+	0.0907841i
$365$	6.00000	+	3.46410i	0.314054	+	0.181319i
$366$		0			0
$367$		−	29.1962i		−	1.52403i	−0.647561	−	0.762013i	$-0.724211\pi$
$367$		−	29.1962i		−	1.52403i	0.647561	−	0.762013i	$-0.275789\pi$
$368$	2.19615	+	1.26795i	0.114482	+	0.0660964i
$369$		0			0
$370$		−	6.19615i		−	0.322123i
$371$	12.5885	−	14.5359i	0.653560	−	0.754666i
$372$		0			0
$373$	10.1962			0.527937			0.263968	−	0.964531i	$-0.414969\pi$
$373$	10.1962			0.527937			0.263968	+	0.964531i	$0.414969\pi$
$374$		0			0
$375$		0			0
$376$	7.79423	+	4.50000i	0.401957	+	0.232070i
$377$	22.3923			1.15326
$378$		0			0
$379$	−9.60770			−0.493514			−0.246757	−	0.969077i	$-0.579365\pi$
$379$	−9.60770			−0.493514			−0.246757	+	0.969077i	$0.579365\pi$
$380$	−1.09808	−	0.633975i	−0.0563301	−	0.0325222i
$381$		0			0
$382$	−1.73205	−	3.00000i	−0.0886194	−	0.153493i
$383$	−19.3923			−0.990900			−0.495450	−	0.868636i	$-0.664997\pi$
$383$	−19.3923			−0.990900			−0.495450	+	0.868636i	$0.664997\pi$
$384$		0			0
$385$	−12.2942	−	2.36603i	−0.626572	−	0.120584i
$386$		−	13.8038i		−	0.702597i
$387$		0			0
$388$	7.39230	+	4.26795i	0.375287	+	0.216672i
$389$			24.7128i			1.25299i	0.779426	+	0.626495i	$0.215511\pi$
$389$			24.7128i			1.25299i	−0.779426	+	0.626495i	$0.784489\pi$
$390$		0			0
$391$		0			0
$392$	2.59808	−	6.50000i	0.131223	−	0.328300i
$393$		0			0
$394$	−11.8301	+	20.4904i	−0.595993	+	1.03229i
$395$	−7.29423	+	12.6340i	−0.367012	+	0.635684i
$396$		0			0
$397$	−26.4904	+	15.2942i	−1.32951	+	0.767595i	−0.985224	−	0.171268i	$-0.945214\pi$
$397$	−26.4904	+	15.2942i	−1.32951	+	0.767595i	−0.344290	+	0.938863i	$0.611880\pi$
$398$	3.46410	+	6.00000i	0.173640	+	0.300753i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	3.58846i		−	0.179199i	−0.995978	−	0.0895995i	$-0.971441\pi$
$401$		−	3.58846i		−	0.179199i	0.995978	−	0.0895995i	$-0.0285587\pi$
$402$		0			0
$403$	−28.3923			−1.41432
$404$	5.59808	+	9.69615i	0.278515	+	0.482402i
$405$		0			0
$406$	3.23205	−	16.7942i	0.160404	−	0.833484i
$407$	−25.3923	+	14.6603i	−1.25865	+	0.726682i
$408$		0			0
$409$	−9.10770	+	5.25833i	−0.450347	+	0.260008i	−0.707977	−	0.706236i	$-0.750392\pi$
$409$	−9.10770	+	5.25833i	−0.450347	+	0.260008i	0.257630	+	0.966244i	$0.417058\pi$
$410$	7.79423	−	4.50000i	0.384930	−	0.222239i
$411$		0			0
$412$	−10.5000	+	6.06218i	−0.517298	+	0.298662i
$413$	−5.49038	+	1.90192i	−0.270164	+	0.0935876i
$414$		0			0
$415$	−5.59808	−	9.69615i	−0.274799	−	0.475965i
$416$	−3.46410			−0.169842
$417$		0			0
$418$			6.00000i			0.293470i
$419$	−5.19615	+	9.00000i	−0.253849	+	0.439679i	−0.964582	−	0.263783i	$-0.915030\pi$
$419$	−5.19615	+	9.00000i	−0.253849	+	0.439679i	0.710734	+	0.703461i	$0.248363\pi$
$420$		0			0
$421$	14.9904	+	25.9641i	0.730586	+	1.26541i	0.956633	+	0.291296i	$0.0940866\pi$
$421$	14.9904	+	25.9641i	0.730586	+	1.26541i	−0.226046	+	0.974117i	$0.572580\pi$
$422$	17.8301	−	10.2942i	0.867957	−	0.501115i
$423$		0			0
$424$	−3.63397	+	6.29423i	−0.176481	+	0.305675i
$425$		0			0
$426$		0			0
$427$	22.3923	−	25.8564i	1.08364	−	1.25128i
$428$	−13.7942	−	7.96410i	−0.666769	−	0.384959i
$429$		0			0
$430$		−	3.19615i		−	0.154132i
$431$	33.5885	+	19.3923i	1.61790	+	0.934094i	0.987463	+	0.157854i	$0.0504574\pi$
$431$	33.5885	+	19.3923i	1.61790	+	0.934094i	0.630437	+	0.776241i	$0.282876\pi$
$432$		0			0
$433$		−	18.0000i		−	0.865025i	−0.901628	−	0.432512i	$-0.857627\pi$
$433$		−	18.0000i		−	0.865025i	0.901628	−	0.432512i	$-0.142373\pi$
$434$	−4.09808	+	21.2942i	−0.196714	+	1.02216i
$435$		0			0
$436$	7.19615			0.344633
$437$	1.60770	+	2.78461i	0.0769065	+	0.133206i
$438$		0			0
$439$	25.6865	+	14.8301i	1.22595	+	0.707803i	0.966180	−	0.257867i	$-0.0830196\pi$
$439$	25.6865	+	14.8301i	1.22595	+	0.707803i	0.259771	+	0.965670i	$0.416353\pi$
$440$	4.73205			0.225592
$441$		0			0
$442$		0			0
$443$	−7.79423	−	4.50000i	−0.370315	−	0.213801i	0.303281	−	0.952901i	$-0.401918\pi$
$443$	−7.79423	−	4.50000i	−0.370315	−	0.213801i	−0.673596	+	0.739100i	$0.735251\pi$
$444$		0			0
$445$	2.19615	+	3.80385i	0.104108	+	0.180320i
$446$	13.7321			0.650231
$447$		0			0
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$		−	9.58846i		−	0.452507i	−0.974068	−	0.226254i	$-0.927352\pi$
$449$		−	9.58846i		−	0.452507i	0.974068	−	0.226254i	$-0.0726478\pi$
$450$		0			0
$451$	−36.8827	−	21.2942i	−1.73674	−	1.00271i
$452$			12.5885i			0.592111i
$453$		0			0
$454$	14.1962	+	8.19615i	0.666258	+	0.384664i
$455$	6.00000	−	6.92820i	0.281284	−	0.324799i
$456$		0			0
$457$	−1.19615	+	2.07180i	−0.0559537	+	0.0969146i	−0.892645	−	0.450759i	$-0.851153\pi$
$457$	−1.19615	+	2.07180i	−0.0559537	+	0.0969146i	0.836692	+	0.547674i	$0.184487\pi$
$458$	−7.03590	+	12.1865i	−0.328766	+	0.569439i
$459$		0			0
$460$	2.19615	−	1.26795i	0.102396	−	0.0591184i
$461$	2.59808	+	4.50000i	0.121004	+	0.209586i	0.920164	−	0.391533i	$-0.128055\pi$
$461$	2.59808	+	4.50000i	0.121004	+	0.209586i	−0.799160	+	0.601119i	$0.794722\pi$
$462$		0			0
$463$	1.30385	−	2.25833i	0.0605949	−	0.104954i	−0.834137	−	0.551558i	$-0.814034\pi$
$463$	1.30385	−	2.25833i	0.0605949	−	0.104954i	0.894731	+	0.446604i	$0.147367\pi$
$464$			6.46410i			0.300088i
$465$		0			0
$466$	−1.26795			−0.0587366
$467$	−3.40192	−	5.89230i	−0.157422	−	0.272663i	0.776516	−	0.630097i	$-0.216985\pi$
$467$	−3.40192	−	5.89230i	−0.157422	−	0.272663i	−0.933938	+	0.357434i	$0.883652\pi$
$468$		0			0
$469$	10.0000	−	3.46410i	0.461757	−	0.159957i
$470$	7.79423	−	4.50000i	0.359521	−	0.207570i
$471$		0			0
$472$	1.90192	−	1.09808i	0.0875431	−	0.0505431i
$473$	−13.0981	+	7.56218i	−0.602250	+	0.347709i
$474$		0			0
$475$	−1.09808	+	0.633975i	−0.0503832	+	0.0290887i
$476$		0			0
$477$		0			0
$478$	−1.56218	−	2.70577i	−0.0714524	−	0.123759i
$479$	10.3923			0.474837			0.237418	−	0.971408i	$-0.423699\pi$
$479$	10.3923			0.474837			0.237418	+	0.971408i	$0.423699\pi$
$480$		0			0
$481$		−	21.4641i		−	0.978679i
$482$	−1.66987	+	2.89230i	−0.0760606	+	0.131741i
$483$		0			0
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	7.39230	−	4.26795i	0.335667	−	0.193798i
$486$		0			0
$487$	−17.0000	+	29.4449i	−0.770344	+	1.33427i	0.167031	+	0.985952i	$0.446582\pi$
$487$	−17.0000	+	29.4449i	−0.770344	+	1.33427i	−0.937375	+	0.348323i	$0.886751\pi$
$488$	−6.46410	+	11.1962i	−0.292616	+	0.506826i
$489$		0			0
$490$	−4.33013	−	5.50000i	−0.195615	−	0.248465i
$491$	23.4904	+	13.5622i	1.06011	+	0.612053i	0.925462	−	0.378841i	$-0.123677\pi$
$491$	23.4904	+	13.5622i	1.06011	+	0.612053i	0.134644	+	0.990894i	$0.457011\pi$
$492$		0			0
$493$		0			0
$494$	−3.80385	−	2.19615i	−0.171143	−	0.0988096i
$495$		0			0
$496$		−	8.19615i		−	0.368018i
$497$	12.2942	+	2.36603i	0.551472	+	0.106131i
$498$		0			0
$499$	−16.1962			−0.725039			−0.362520	−	0.931976i	$-0.618083\pi$
$499$	−16.1962			−0.725039			−0.362520	+	0.931976i	$0.618083\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	15.5885	+	9.00000i	0.695747	+	0.401690i
$503$	7.39230			0.329607			0.164803	−	0.986326i	$-0.447301\pi$
$503$	7.39230			0.329607			0.164803	+	0.986326i	$0.447301\pi$
$504$		0			0
$505$	11.1962			0.498222
$506$	−10.3923	−	6.00000i	−0.461994	−	0.266733i
$507$		0			0
$508$	−5.69615	−	9.86603i	−0.252726	−	0.437734i
$509$	−9.58846			−0.425001			−0.212500	−	0.977161i	$-0.568161\pi$
$509$	−9.58846			−0.425001			−0.212500	+	0.977161i	$0.568161\pi$
$510$		0			0
$511$	12.0000	−	13.8564i	0.530849	−	0.612971i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−24.5885	−	14.1962i	−1.08455	−	0.626165i
$515$			12.1244i			0.534263i
$516$		0			0
$517$	−36.8827	−	21.2942i	−1.62210	−	0.936519i
$518$	−16.0981	−	3.09808i	−0.707309	−	0.136122i
$519$		0			0
$520$	−1.73205	+	3.00000i	−0.0759555	+	0.131559i
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	−0.998961	−	0.0455727i	$-0.985489\pi$
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	0.538948	+	0.842339i	$0.318822\pi$
$522$		0			0
$523$	28.5788	−	16.5000i	1.24967	−	0.721495i	0.278623	−	0.960401i	$-0.410122\pi$
$523$	28.5788	−	16.5000i	1.24967	−	0.721495i	0.971043	+	0.238906i	$0.0767888\pi$
$524$	−2.19615	−	3.80385i	−0.0959394	−	0.166172i
$525$		0			0
$526$	6.86603	−	11.8923i	0.299373	−	0.518529i
$527$		0			0
$528$		0			0
$529$	16.5692			0.720401
$530$	3.63397	+	6.29423i	0.157850	+	0.273404i
$531$		0			0
$532$	−2.19615	+	2.53590i	−0.0952153	+	0.109945i
$533$	27.0000	−	15.5885i	1.16950	−	0.675211i
$534$		0			0
$535$	−13.7942	+	7.96410i	−0.596377	+	0.344318i
$536$	−3.46410	+	2.00000i	−0.149626	+	0.0863868i
$537$		0			0
$538$	−15.5885	+	9.00000i	−0.672066	+	0.388018i
$539$	−12.2942	+	30.7583i	−0.529550	+	1.32486i
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	6.58846			0.282998
$543$		0			0
$544$		0			0
$545$	3.59808	−	6.23205i	0.154125	−	0.266952i
$546$		0			0
$547$	−2.79423	−	4.83975i	−0.119473	−	0.206933i	0.800086	−	0.599885i	$-0.204787\pi$
$547$	−2.79423	−	4.83975i	−0.119473	−	0.206933i	−0.919559	+	0.392952i	$0.871454\pi$
$548$	−6.29423	+	3.63397i	−0.268876	+	0.155236i
$549$		0			0
$550$	2.36603	−	4.09808i	0.100888	−	0.174743i
$551$	−4.09808	+	7.09808i	−0.174584	+	0.302388i
$552$		0			0
$553$	29.1769	+	25.2679i	1.24073	+	1.07450i
$554$	−20.9545	−	12.0981i	−0.890271	−	0.513998i
$555$		0			0
$556$			22.0526i			0.935237i
$557$	−28.3923	−	16.3923i	−1.20302	−	0.694564i	−0.241795	−	0.970327i	$-0.577736\pi$
$557$	−28.3923	−	16.3923i	−1.20302	−	0.694564i	−0.961226	+	0.275763i	$0.911069\pi$
$558$		0			0
$559$		−	11.0718i		−	0.468287i
$560$	2.00000	+	1.73205i	0.0845154	+	0.0731925i
$561$		0			0
$562$	−14.6603			−0.618405
$563$	6.80385	+	11.7846i	0.286748	+	0.496662i	0.973032	−	0.230672i	$-0.0740924\pi$
$563$	6.80385	+	11.7846i	0.286748	+	0.496662i	−0.686284	+	0.727334i	$0.740759\pi$
$564$		0			0
$565$	10.9019	+	6.29423i	0.458647	+	0.264800i
$566$	−16.8564			−0.708528
$567$		0			0
$568$	−4.73205			−0.198552
$569$	5.19615	+	3.00000i	0.217834	+	0.125767i	0.604947	−	0.796266i	$-0.293194\pi$
$569$	5.19615	+	3.00000i	0.217834	+	0.125767i	−0.387113	+	0.922032i	$0.626528\pi$
$570$		0			0
$571$	−10.8038	−	18.7128i	−0.452127	−	0.783107i	0.546391	−	0.837530i	$-0.316001\pi$
$571$	−10.8038	−	18.7128i	−0.452127	−	0.783107i	−0.998518	+	0.0544234i	$0.982668\pi$
$572$	16.3923			0.685397
$573$		0			0
$574$	−7.79423	−	22.5000i	−0.325325	−	0.939132i
$575$		−	2.53590i		−	0.105754i
$576$		0			0
$577$	20.7846	+	12.0000i	0.865275	+	0.499567i	0.865775	−	0.500433i	$-0.166826\pi$
$577$	20.7846	+	12.0000i	0.865275	+	0.499567i	−0.000500448		1.00000i	$0.500159\pi$
$578$			17.0000i			0.707107i
$579$		0			0
$580$	5.59808	+	3.23205i	0.232447	+	0.134204i
$581$	−27.9904	+	9.69615i	−1.16124	+	0.402264i
$582$		0			0
$583$	17.1962	−	29.7846i	0.712192	−	1.23355i
$584$	−3.46410	+	6.00000i	−0.143346	+	0.248282i
$585$		0			0
$586$	14.1962	−	8.19615i	0.586438	−	0.338580i
$587$	−15.4019	−	26.6769i	−0.635705	−	1.10107i	−0.986365	−	0.164571i	$-0.947376\pi$
$587$	−15.4019	−	26.6769i	−0.635705	−	1.10107i	0.350660	−	0.936503i	$-0.385957\pi$
$588$		0			0
$589$	5.19615	−	9.00000i	0.214104	−	0.370839i
$590$		−	2.19615i		−	0.0904142i
$591$		0			0
$592$	6.19615			0.254660
$593$	13.3923	+	23.1962i	0.549956	+	0.952552i	0.998277	+	0.0586791i	$0.0186889\pi$
$593$	13.3923	+	23.1962i	0.549956	+	0.952552i	−0.448321	+	0.893873i	$0.647978\pi$
$594$		0			0
$595$		0			0
$596$	10.3923	−	6.00000i	0.425685	−	0.245770i
$597$		0			0
$598$	7.60770	−	4.39230i	0.311102	−	0.179615i
$599$	−3.80385	+	2.19615i	−0.155421	+	0.0897324i	−0.575693	−	0.817666i	$-0.695268\pi$
$599$	−3.80385	+	2.19615i	−0.155421	+	0.0897324i	0.420272	+	0.907398i	$0.361934\pi$
$600$		0			0
$601$	27.5885	−	15.9282i	1.12536	−	0.649725i	0.182594	−	0.983188i	$-0.441551\pi$
$601$	27.5885	−	15.9282i	1.12536	−	0.649725i	0.942763	+	0.333464i	$0.108217\pi$
$602$	−8.30385	−	1.59808i	−0.338440	−	0.0651327i
$603$		0			0
$604$	−2.09808	−	3.63397i	−0.0853695	−	0.147864i
$605$	−11.3923			−0.463163
$606$		0			0
$607$			6.12436i			0.248580i	0.992246	+	0.124290i	$0.0396653\pi$
$607$			6.12436i			0.248580i	−0.992246	+	0.124290i	$0.960335\pi$
$608$	0.633975	−	1.09808i	0.0257111	−	0.0445329i
$609$		0			0
$610$	6.46410	+	11.1962i	0.261724	+	0.453319i
$611$	27.0000	−	15.5885i	1.09230	−	0.630641i
$612$		0			0
$613$	3.39230	−	5.87564i	0.137014	−	0.237315i	−0.789351	−	0.613942i	$-0.789583\pi$
$613$	3.39230	−	5.87564i	0.137014	−	0.237315i	0.926365	+	0.376627i	$0.122916\pi$
$614$	−11.8923	+	20.5981i	−0.479934	+	0.831271i
$615$		0			0
$616$	2.36603	−	12.2942i	0.0953299	−	0.495349i
$617$	−15.8038	−	9.12436i	−0.636239	−	0.367333i	0.146925	−	0.989148i	$-0.453062\pi$
$617$	−15.8038	−	9.12436i	−0.636239	−	0.367333i	−0.783164	+	0.621815i	$0.786396\pi$
$618$		0			0
$619$			16.3923i			0.658862i	0.944180	+	0.329431i	$0.106857\pi$
$619$			16.3923i			0.658862i	−0.944180	+	0.329431i	$0.893143\pi$
$620$	−7.09808	−	4.09808i	−0.285066	−	0.164583i
$621$		0			0
$622$			15.8038i			0.633677i
$623$	10.9808	−	3.80385i	0.439935	−	0.152398i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−10.0981	−	17.4904i	−0.403600	−	0.699056i
$627$		0			0
$628$	−15.2942	−	8.83013i	−0.610306	−	0.352360i
$629$		0			0
$630$		0			0
$631$	12.3923			0.493330			0.246665	−	0.969101i	$-0.420665\pi$
$631$	12.3923			0.493330			0.246665	+	0.969101i	$0.420665\pi$
$632$	−12.6340	−	7.29423i	−0.502553	−	0.290149i
$633$		0			0
$634$	−10.2679	−	17.7846i	−0.407792	−	0.706317i
$635$	−11.3923			−0.452090
$636$		0			0
$637$	−15.0000	−	19.0526i	−0.594322	−	0.754890i
$638$		−	30.5885i		−	1.21101i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			3.21539i			0.127000i	0.997982	+	0.0635001i	$0.0202263\pi$
$641$			3.21539i			0.127000i	−0.997982	+	0.0635001i	$0.979774\pi$
$642$		0			0
$643$	16.2058	+	9.35641i	0.639093	+	0.368981i	0.784265	−	0.620426i	$-0.213040\pi$
$643$	16.2058	+	9.35641i	0.639093	+	0.368981i	−0.145172	+	0.989406i	$0.546374\pi$
$644$	−2.19615	−	6.33975i	−0.0865405	−	0.249821i
$645$		0			0
$646$		0			0
$647$	−2.30385	+	3.99038i	−0.0905736	+	0.156878i	−0.907753	−	0.419506i	$-0.862203\pi$
$647$	−2.30385	+	3.99038i	−0.0905736	+	0.156878i	0.817179	+	0.576384i	$0.195537\pi$
$648$		0			0
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$	1.73205	+	3.00000i	0.0679366	+	0.117670i
$651$		0			0
$652$	−4.19615	+	7.26795i	−0.164334	+	0.284635i
$653$			49.8564i			1.95103i	0.219929	+	0.975516i	$0.429418\pi$
$653$			49.8564i			1.95103i	−0.219929	+	0.975516i	$0.570582\pi$
$654$		0			0
$655$	−4.39230			−0.171622
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		0			0
$658$	−7.79423	−	22.5000i	−0.303851	−	0.877141i
$659$	33.2942	−	19.2224i	1.29696	−	0.748800i	0.317081	−	0.948398i	$-0.397297\pi$
$659$	33.2942	−	19.2224i	1.29696	−	0.748800i	0.979878	+	0.199599i	$0.0639639\pi$
$660$		0			0
$661$	11.3827	−	6.57180i	0.442735	−	0.255613i	−0.262022	−	0.965062i	$-0.584389\pi$
$661$	11.3827	−	6.57180i	0.442735	−	0.255613i	0.704757	+	0.709449i	$0.251056\pi$
$662$	6.92820	−	4.00000i	0.269272	−	0.155464i
$663$		0			0
$664$	9.69615	−	5.59808i	0.376284	−	0.217247i
$665$	1.09808	+	3.16987i	0.0425816	+	0.122922i
$666$		0			0
$667$	−8.19615	−	14.1962i	−0.317356	−	0.549677i
$668$	−10.3923			−0.402090
$669$		0			0
$670$			4.00000i			0.154533i
$671$	30.5885	−	52.9808i	1.18085	−	2.04530i
$672$		0			0
$673$	12.4904	+	21.6340i	0.481469	+	0.833928i	0.999774	−	0.0212674i	$-0.00677013\pi$
$673$	12.4904	+	21.6340i	0.481469	+	0.833928i	−0.518305	+	0.855196i	$0.673437\pi$
$674$	−8.66025	+	5.00000i	−0.333581	+	0.192593i
$675$		0			0
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	−11.4904	+	19.9019i	−0.441611	+	0.764893i	−0.997809	−	0.0661567i	$-0.978926\pi$
$677$	−11.4904	+	19.9019i	−0.441611	+	0.764893i	0.556198	+	0.831050i	$0.312260\pi$
$678$		0			0
$679$	−7.39230	−	21.3397i	−0.283691	−	0.818944i
$680$		0			0
$681$		0			0
$682$			38.7846i			1.48514i
$683$	−30.7750	−	17.7679i	−1.17757	−	0.679872i	−0.222121	−	0.975019i	$-0.571298\pi$
$683$	−30.7750	−	17.7679i	−1.17757	−	0.679872i	−0.955452	+	0.295148i	$0.904631\pi$
$684$		0			0
$685$			7.26795i			0.277694i
$686$	−16.4545	+	8.50000i	−0.628235	+	0.324532i
$687$		0			0
$688$	3.19615			0.121852
$689$	12.5885	+	21.8038i	0.479582	+	0.830660i
$690$		0			0
$691$	−4.39230	−	2.53590i	−0.167091	−	0.0964701i	0.414122	−	0.910221i	$-0.364089\pi$
$691$	−4.39230	−	2.53590i	−0.167091	−	0.0964701i	−0.581214	+	0.813751i	$0.697422\pi$
$692$	−8.19615			−0.311571
$693$		0			0
$694$	−21.2487			−0.806590
$695$	19.0981	+	11.0263i	0.724431	+	0.418251i
$696$		0			0
$697$		0			0
$698$	16.3923			0.620458
$699$		0			0
$700$	2.50000	−	0.866025i	0.0944911	−	0.0327327i
$701$		−	44.3205i		−	1.67396i	−0.547232	−	0.836981i	$-0.684318\pi$
$701$		−	44.3205i		−	1.67396i	0.547232	−	0.836981i	$-0.315682\pi$
$702$		0			0
$703$	6.80385	+	3.92820i	0.256612	+	0.148155i
$704$			4.73205i			0.178346i
$705$		0			0
$706$	0.509619	+	0.294229i	0.0191798	+	0.0110734i
$707$	5.59808	−	29.0885i	0.210537	−	1.09398i
$708$		0			0
$709$	23.3923	−	40.5167i	0.878516	−	1.52164i	0.0255474	−	0.999674i	$-0.491867\pi$
$709$	23.3923	−	40.5167i	0.878516	−	1.52164i	0.852969	−	0.521962i	$-0.174800\pi$
$710$	−2.36603	+	4.09808i	−0.0887954	+	0.153798i
$711$		0			0
$712$	−3.80385	+	2.19615i	−0.142555	+	0.0823043i
$713$	10.3923	+	18.0000i	0.389195	+	0.674105i
$714$		0			0
$715$	8.19615	−	14.1962i	0.306519	−	0.530906i
$716$		−	24.5885i		−	0.918914i
$717$		0			0
$718$	15.8038			0.589794
$719$	−20.7846	−	36.0000i	−0.775135	−	1.34257i	−0.934718	−	0.355389i	$-0.884348\pi$
$719$	−20.7846	−	36.0000i	−0.775135	−	1.34257i	0.159583	−	0.987184i	$-0.448985\pi$
$720$		0			0
$721$	31.5000	+	6.06218i	1.17312	+	0.225767i
$722$	−15.0622	+	8.69615i	−0.560556	+	0.323637i
$723$		0			0
$724$	11.5981	−	6.69615i	0.431039	−	0.248861i
$725$	5.59808	−	3.23205i	0.207907	−	0.120035i
$726$		0			0
$727$	−41.7846	+	24.1244i	−1.54971	+	0.894723i	−0.551542	+	0.834147i	$0.685960\pi$
$727$	−41.7846	+	24.1244i	−1.54971	+	0.894723i	−0.998164	+	0.0605756i	$0.980706\pi$
$728$	6.92820	+	6.00000i	0.256776	+	0.222375i
$729$		0			0
$730$	3.46410	+	6.00000i	0.128212	+	0.222070i
$731$		0			0
$732$		0			0
$733$			34.0526i			1.25776i	0.777502	+	0.628880i	$0.216486\pi$
$733$			34.0526i			1.25776i	−0.777502	+	0.628880i	$0.783514\pi$
$734$	14.5981	−	25.2846i	0.538825	−	0.933272i
$735$		0			0
$736$	1.26795	+	2.19615i	0.0467372	+	0.0809513i
$737$	16.3923	−	9.46410i	0.603818	−	0.348615i
$738$		0			0
$739$	−16.5885	+	28.7321i	−0.610216	+	1.05693i	0.380987	+	0.924580i	$0.375584\pi$
$739$	−16.5885	+	28.7321i	−0.610216	+	1.05693i	−0.991204	+	0.132345i	$0.957749\pi$
$740$	3.09808	−	5.36603i	0.113888	−	0.197259i
$741$		0			0
$742$	18.1699	−	6.29423i	0.667037	−	0.231068i
$743$	23.6769	+	13.6699i	0.868622	+	0.501499i	0.866890	−	0.498499i	$-0.166115\pi$
$743$	23.6769	+	13.6699i	0.868622	+	0.501499i	0.00173176	+	0.999999i	$0.499449\pi$
$744$		0			0
$745$		−	12.0000i		−	0.439646i
$746$	8.83013	+	5.09808i	0.323294	+	0.186654i
$747$		0			0
$748$		0			0
$749$	13.7942	+	39.8205i	0.504030	+	1.45501i
$750$		0			0
$751$	−21.6077			−0.788476			−0.394238	−	0.919008i	$-0.628991\pi$
$751$	−21.6077			−0.788476			−0.394238	+	0.919008i	$0.628991\pi$
$752$	4.50000	+	7.79423i	0.164098	+	0.284226i
$753$		0			0
$754$	19.3923	+	11.1962i	0.706226	+	0.407740i
$755$	−4.19615			−0.152714
$756$		0			0
$757$	−8.58846			−0.312153			−0.156076	−	0.987745i	$-0.549885\pi$
$757$	−8.58846			−0.312153			−0.156076	+	0.987745i	$0.549885\pi$
$758$	−8.32051	−	4.80385i	−0.302214	−	0.174484i
$759$		0			0
$760$	−0.633975	−	1.09808i	−0.0229967	−	0.0398314i
$761$	33.0000			1.19625			0.598125	−	0.801403i	$-0.295913\pi$
$761$	33.0000			1.19625			0.598125	+	0.801403i	$0.295913\pi$
$762$		0			0
$763$	−14.3923	−	12.4641i	−0.521036	−	0.451231i
$764$		−	3.46410i		−	0.125327i
$765$		0			0
$766$	−16.7942	−	9.69615i	−0.606800	−	0.350336i
$767$		−	7.60770i		−	0.274698i
$768$		0			0
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	0.723255	−	0.690581i	$-0.242645\pi$
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	−0.236433	+	0.971648i	$0.575978\pi$
$770$	−9.46410	−	8.19615i	−0.341063	−	0.295369i
$771$		0			0
$772$	6.90192	−	11.9545i	0.248406	−	0.430251i
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		0			0
$775$	−7.09808	+	4.09808i	−0.254970	+	0.147207i
$776$	4.26795	+	7.39230i	0.153210	+	0.265368i
$777$		0			0
$778$	−12.3564	+	21.4019i	−0.442999	+	0.767296i
$779$			11.4115i			0.408861i
$780$		0			0
$781$	22.3923			0.801260
$782$		0			0
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−15.2942	+	8.83013i	−0.545874	+	0.315161i
$786$		0			0
$787$	−8.00962	+	4.62436i	−0.285512	+	0.164840i	−0.635916	−	0.771758i	$-0.719378\pi$
$787$	−8.00962	+	4.62436i	−0.285512	+	0.164840i	0.350404	+	0.936599i	$0.386044\pi$
$788$	−20.4904	+	11.8301i	−0.729940	+	0.421431i
$789$		0			0
$790$	−12.6340	+	7.29423i	−0.449497	+	0.259517i
$791$	21.8038	−	25.1769i	0.775256	−	0.895188i
$792$		0			0
$793$	22.3923	+	38.7846i	0.795174	+	1.37728i
$794$	−30.5885			−1.08554
$795$		0			0
$796$			6.92820i			0.245564i
$797$	9.58846	−	16.6077i	0.339641	−	0.588275i	−0.644724	−	0.764415i	$-0.723028\pi$
$797$	9.58846	−	16.6077i	0.339641	−	0.588275i	0.984365	+	0.176140i	$0.0563612\pi$
$798$		0			0
$799$		0			0
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	1.79423	−	3.10770i	0.0633564	−	0.109737i
$803$	16.3923	−	28.3923i	0.578472	−	1.00194i
$804$		0			0
$805$	−6.58846	−	1.26795i	−0.232213	−	0.0446893i
$806$	−24.5885	−	14.1962i	−0.866091	−	0.500038i
$807$		0			0
$808$			11.1962i			0.393879i
$809$	−45.4808	−	26.2583i	−1.59902	−	0.923194i	−0.991677	−	0.128753i	$-0.958903\pi$
$809$	−45.4808	−	26.2583i	−1.59902	−	0.923194i	−0.607342	−	0.794441i	$-0.707764\pi$
$810$		0			0
$811$			44.5359i			1.56387i	0.623362	+	0.781933i	$0.285766\pi$
$811$			44.5359i			1.56387i	−0.623362	+	0.781933i	$0.714234\pi$
$812$	11.1962	−	12.9282i	0.392908	−	0.453691i
$813$		0			0
$814$	−29.3205			−1.02768
$815$	4.19615	+	7.26795i	0.146985	+	0.254585i
$816$		0			0
$817$	3.50962	+	2.02628i	0.122786	+	0.0708905i
$818$	−10.5167			−0.367706
$819$		0			0
$820$	9.00000			0.314294
$821$	−31.7942	−	18.3564i	−1.10963	−	0.640643i	−0.170894	−	0.985289i	$-0.554665\pi$
$821$	−31.7942	−	18.3564i	−1.10963	−	0.640643i	−0.938733	+	0.344646i	$0.887999\pi$
$822$		0			0
$823$	−15.3038	−	26.5070i	−0.533459	−	0.923977i	−0.999236	−	0.0390756i	$-0.987559\pi$
$823$	−15.3038	−	26.5070i	−0.533459	−	0.923977i	0.465778	−	0.884902i	$-0.345775\pi$
$824$	−12.1244			−0.422372
$825$		0			0
$826$	−5.70577	−	1.09808i	−0.198529	−	0.0382070i
$827$			31.6410i			1.10027i	0.835077	+	0.550133i	$0.185423\pi$
$827$			31.6410i			1.10027i	−0.835077	+	0.550133i	$0.814577\pi$
$828$		0			0
$829$	30.1865	+	17.4282i	1.04842	+	0.605307i	0.922207	−	0.386696i	$-0.126384\pi$
$829$	30.1865	+	17.4282i	1.04842	+	0.605307i	0.126215	+	0.992003i	$0.459717\pi$
$830$		−	11.1962i		−	0.388624i
$831$		0			0
$832$	−3.00000	−	1.73205i	−0.104006	−	0.0600481i
$833$		0			0
$834$		0			0
$835$	−5.19615	+	9.00000i	−0.179820	+	0.311458i
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$		0			0
$838$	−9.00000	+	5.19615i	−0.310900	+	0.179498i
$839$	−1.90192	−	3.29423i	−0.0656617	−	0.113729i	0.831326	−	0.555786i	$-0.187582\pi$
$839$	−1.90192	−	3.29423i	−0.0656617	−	0.113729i	−0.896987	+	0.442056i	$0.854249\pi$
$840$		0			0
$841$	6.39230	−	11.0718i	0.220424	−	0.381786i
$842$			29.9808i			1.03321i
$843$		0			0
$844$	20.5885			0.708684
$845$	−0.500000	−	0.866025i	−0.0172005	−	0.0297922i
$846$		0			0
$847$	−5.69615	+	29.5981i	−0.195722	+	1.01700i
$848$	−6.29423	+	3.63397i	−0.216145	+	0.124791i
$849$		0			0
$850$		0			0
$851$	−13.6077	+	7.85641i	−0.466466	+	0.269314i
$852$		0			0
$853$	−2.78461	+	1.60770i	−0.0953432	+	0.0550464i	−0.546914	−	0.837189i	$-0.684197\pi$
$853$	−2.78461	+	1.60770i	−0.0953432	+	0.0550464i	0.451570	+	0.892236i	$0.350864\pi$
$854$	32.3205	−	11.1962i	1.10599	−	0.383124i
$855$		0			0
$856$	−7.96410	−	13.7942i	−0.272207	−	0.471477i
$857$	17.4115			0.594767			0.297383	−	0.954758i	$-0.403886\pi$
$857$	17.4115			0.594767			0.297383	+	0.954758i	$0.403886\pi$
$858$		0			0
$859$			15.8038i			0.539220i	0.962970	+	0.269610i	$0.0868948\pi$
$859$			15.8038i			0.539220i	−0.962970	+	0.269610i	$0.913105\pi$
$860$	1.59808	−	2.76795i	0.0544939	−	0.0943863i
$861$		0			0
$862$	19.3923	+	33.5885i	0.660505	+	1.14403i
$863$	−25.3923	+	14.6603i	−0.864364	+	0.499041i	−0.865471	−	0.500959i	$-0.832981\pi$
$863$	−25.3923	+	14.6603i	−0.864364	+	0.499041i	0.00110718	+	0.999999i	$0.499648\pi$
$864$		0			0
$865$	−4.09808	+	7.09808i	−0.139339	+	0.241342i
$866$	9.00000	−	15.5885i	0.305832	−	0.529717i
$867$		0			0
$868$	−14.1962	+	16.3923i	−0.481849	+	0.556391i
$869$	59.7846	+	34.5167i	2.02805	+	1.17090i
$870$		0			0
$871$			13.8564i			0.469506i
$872$	6.23205	+	3.59808i	0.211044	+	0.121846i
$873$		0			0
$874$			3.21539i			0.108762i
$875$	0.500000	−	2.59808i	0.0169031	−	0.0878310i
$876$		0			0
$877$	51.7654			1.74799			0.873996	−	0.485933i	$-0.161520\pi$
$877$	51.7654			1.74799			0.873996	+	0.485933i	$0.161520\pi$
$878$	14.8301	+	25.6865i	0.500493	+	0.866879i
$879$		0			0
$880$	4.09808	+	2.36603i	0.138146	+	0.0797587i
$881$	16.3923			0.552271			0.276135	−	0.961119i	$-0.410946\pi$
$881$	16.3923			0.552271			0.276135	+	0.961119i	$0.410946\pi$
$882$		0			0
$883$	28.3731			0.954830			0.477415	−	0.878678i	$-0.341574\pi$
$883$	28.3731			0.954830			0.477415	+	0.878678i	$0.341574\pi$
$884$		0			0
$885$		0			0
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$	49.3923			1.65843			0.829216	−	0.558929i	$-0.188788\pi$
$887$	49.3923			1.65843			0.829216	+	0.558929i	$0.188788\pi$
$888$		0			0
$889$	−5.69615	+	29.5981i	−0.191043	+	0.992688i
$890$			4.39230i			0.147230i
$891$		0			0
$892$	11.8923	+	6.86603i	0.398184	+	0.229892i
$893$			11.4115i			0.381873i
$894$		0			0
$895$	−21.2942	−	12.2942i	−0.711788	−	0.410951i
$896$	−1.73205	+	2.00000i	−0.0578638	+	0.0668153i
$897$		0			0
$898$	4.79423	−	8.30385i	0.159985	−	0.277103i
$899$	−26.4904	+	45.8827i	−0.883504	+	1.53027i
$900$		0			0
$901$		0			0
$902$	−21.2942	−	36.8827i	−0.709020	−	1.22806i
$903$		0			0
$904$	−6.29423	+	10.9019i	−0.209343	+	0.362593i
$905$		−	13.3923i		−	0.445175i
$906$		0			0
$907$	22.8038			0.757189			0.378595	−	0.925563i	$-0.376407\pi$
$907$	22.8038			0.757189			0.378595	+	0.925563i	$0.376407\pi$
$908$	8.19615	+	14.1962i	0.271999	+	0.471116i
$909$		0			0
$910$	8.66025	−	3.00000i	0.287085	−	0.0994490i
$911$	−10.0981	+	5.83013i	−0.334564	+	0.193161i	−0.657866	−	0.753135i	$-0.728541\pi$
$911$	−10.0981	+	5.83013i	−0.334564	+	0.193161i	0.323301	+	0.946296i	$0.395207\pi$
$912$		0			0
$913$	−45.8827	+	26.4904i	−1.51850	+	0.876704i
$914$	−2.07180	+	1.19615i	−0.0685289	+	0.0395652i
$915$		0			0
$916$	−12.1865	+	7.03590i	−0.402654	+	0.232473i
$917$	−2.19615	+	11.4115i	−0.0725233	+	0.376842i
$918$		0			0
$919$	−2.29423	−	3.97372i	−0.0756796	−	0.131081i	0.825702	−	0.564107i	$-0.190779\pi$
$919$	−2.29423	−	3.97372i	−0.0756796	−	0.131081i	−0.901382	+	0.433026i	$0.857446\pi$
$920$	2.53590			0.0836061
$921$		0			0
$922$			5.19615i			0.171126i
$923$	−8.19615	+	14.1962i	−0.269780	+	0.467272i
$924$		0			0
$925$	−3.09808	−	5.36603i	−0.101864	−	0.176434i
$926$	2.25833	−	1.30385i	0.0742133	−	0.0428471i
$927$		0			0
$928$	−3.23205	+	5.59808i	−0.106097	+	0.183766i
$929$	25.2846	−	43.7942i	0.829561	−	1.43684i	−0.0688218	−	0.997629i	$-0.521924\pi$
$929$	25.2846	−	43.7942i	0.829561	−	1.43684i	0.898383	−	0.439213i	$-0.144743\pi$
$930$		0			0
$931$	8.78461	−	1.26795i	0.287904	−	0.0415554i
$932$	−1.09808	−	0.633975i	−0.0359687	−	0.0207665i
$933$		0			0
$934$		−	6.80385i		−	0.222629i
$935$		0			0
$936$		0			0
$937$		−	42.5885i		−	1.39130i	−0.718379	−	0.695652i	$-0.755116\pi$
$937$		−	42.5885i		−	1.39130i	0.718379	−	0.695652i	$-0.244884\pi$
$938$	10.3923	+	2.00000i	0.339321	+	0.0653023i
$939$		0			0
$940$	9.00000			0.293548
$941$	12.9904	+	22.5000i	0.423474	+	0.733479i	0.996277	−	0.0862145i	$-0.0274771\pi$
$941$	12.9904	+	22.5000i	0.423474	+	0.733479i	−0.572802	+	0.819694i	$0.694144\pi$
$942$		0			0
$943$	−19.7654	−	11.4115i	−0.643649	−	0.371611i
$944$	2.19615			0.0714787
$945$		0			0
$946$	−15.1244			−0.491735
$947$	20.4115	+	11.7846i	0.663286	+	0.382948i	0.793528	−	0.608534i	$-0.208242\pi$
$947$	20.4115	+	11.7846i	0.663286	+	0.382948i	−0.130242	+	0.991482i	$0.541575\pi$
$948$		0			0
$949$	12.0000	+	20.7846i	0.389536	+	0.674697i
$950$	−1.26795			−0.0411377
$951$		0			0
$952$		0			0
$953$			1.26795i			0.0410729i	0.999789	+	0.0205365i	$0.00653742\pi$
$953$			1.26795i			0.0410729i	−0.999789	+	0.0205365i	$0.993463\pi$
$954$		0			0
$955$	−3.00000	−	1.73205i	−0.0970777	−	0.0560478i
$956$		−	3.12436i		−	0.101049i
$957$		0			0
$958$	9.00000	+	5.19615i	0.290777	+	0.167880i
$959$	18.8827	+	3.63397i	0.609754	+	0.117347i
$960$		0			0
$961$	18.0885	−	31.3301i	0.583499	−	1.01065i
$962$	10.7321	−	18.5885i	0.346015	−	0.599316i
$963$		0			0
$964$	−2.89230	+	1.66987i	−0.0931549	+	0.0537830i
$965$	−6.90192	−	11.9545i	−0.222181	−	0.384828i
$966$		0			0
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$		−	11.3923i		−	0.366163i
$969$		0			0
$970$	8.53590			0.274071
$971$	−7.39230	−	12.8038i	−0.237230	−	0.410895i	0.722688	−	0.691174i	$-0.242906\pi$
$971$	−7.39230	−	12.8038i	−0.237230	−	0.410895i	−0.959919	+	0.280279i	$0.909573\pi$
$972$		0			0
$973$	38.1962	−	44.1051i	1.22451	−	1.41395i
$974$	−29.4449	+	17.0000i	−0.943474	+	0.544715i
$975$		0			0
$976$	−11.1962	+	6.46410i	−0.358380	+	0.206911i
$977$	−4.39230	+	2.53590i	−0.140522	+	0.0811306i	−0.568613	−	0.822605i	$-0.692520\pi$
$977$	−4.39230	+	2.53590i	−0.140522	+	0.0811306i	0.428091	+	0.903736i	$0.359186\pi$
$978$		0			0
$979$	18.0000	−	10.3923i	0.575282	−	0.332140i
$980$	−1.00000	−	6.92820i	−0.0319438	−	0.221313i
$981$		0			0
$982$	13.5622	+	23.4904i	0.432786	+	0.749608i
$983$	31.3923			1.00126			0.500630	−	0.865662i	$-0.333102\pi$
$983$	31.3923			1.00126			0.500630	+	0.865662i	$0.333102\pi$
$984$		0			0
$985$			23.6603i			0.753878i
$986$		0			0
$987$		0			0
$988$	−2.19615	−	3.80385i	−0.0698689	−	0.121017i
$989$	−7.01924	+	4.05256i	−0.223199	+	0.128864i
$990$		0			0
$991$	6.70577	−	11.6147i	0.213016	−	0.368954i	−0.739641	−	0.673002i	$-0.765005\pi$
$991$	6.70577	−	11.6147i	0.213016	−	0.368954i	0.952657	+	0.304047i	$0.0983381\pi$
$992$	4.09808	−	7.09808i	0.130114	−	0.225364i
$993$		0			0
$994$	9.46410	+	8.19615i	0.300183	+	0.259966i
$995$	6.00000	+	3.46410i	0.190213	+	0.109819i
$996$		0			0
$997$		−	31.5167i		−	0.998143i	−0.866561	−	0.499071i	$-0.833675\pi$
$997$		−	31.5167i		−	0.998143i	0.866561	−	0.499071i	$-0.166325\pi$
$998$	−14.0263	−	8.09808i	−0.443994	−	0.256340i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.a.1151.2		4
3.2	odd	2		630.2.t.a.311.1	✓	4
7.5	odd	6		1890.2.bk.a.341.1		4
9.2	odd	6		1890.2.bk.a.521.2		4
9.7	even	3		630.2.bk.a.101.1	yes	4
21.5	even	6		630.2.bk.a.131.2	yes	4
63.47	even	6	inner	1890.2.t.a.1601.2		4
63.61	odd	6		630.2.t.a.551.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.a.311.1	✓	4	3.2	odd	2
630.2.t.a.551.1	yes	4	63.61	odd	6
630.2.bk.a.101.1	yes	4	9.7	even	3
630.2.bk.a.131.2	yes	4	21.5	even	6
1890.2.t.a.1151.2		4	1.1	even	1	trivial
1890.2.t.a.1601.2		4	63.47	even	6	inner
1890.2.bk.a.341.1		4	7.5	odd	6
1890.2.bk.a.521.2		4	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} -4.73205i q^{11} +(3.00000 + 1.73205i) q^{13} +(1.73205 - 2.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.09808 + 0.633975i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.36603 - 4.09808i) q^{22} -2.53590i q^{23} +1.00000 q^{25} +(1.73205 + 3.00000i) q^{26} +(2.50000 - 0.866025i) q^{28} +(5.59808 - 3.23205i) q^{29} +(-7.09808 + 4.09808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.500000 - 2.59808i) q^{35} +(-3.09808 - 5.36603i) q^{37} -1.26795 q^{38} +1.00000i q^{40} +(4.50000 - 7.79423i) q^{41} +(-1.59808 - 2.76795i) q^{43} +(4.09808 - 2.36603i) q^{44} +(1.26795 - 2.19615i) q^{46} +(4.50000 - 7.79423i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(0.866025 + 0.500000i) q^{50} +3.46410i q^{52} +(6.29423 + 3.63397i) q^{53} -4.73205i q^{55} +(2.59808 + 0.500000i) q^{56} +6.46410 q^{58} +(-1.09808 - 1.90192i) q^{59} +(11.1962 + 6.46410i) q^{61} -8.19615 q^{62} -1.00000 q^{64} +(3.00000 + 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.73205 - 2.00000i) q^{70} +4.73205i q^{71} +(6.00000 + 3.46410i) q^{73} -6.19615i q^{74} +(-1.09808 - 0.633975i) q^{76} +(-12.2942 - 2.36603i) q^{77} +(-7.29423 + 12.6340i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(7.79423 - 4.50000i) q^{82} +(-5.59808 - 9.69615i) q^{83} -3.19615i q^{86} +4.73205 q^{88} +(2.19615 + 3.80385i) q^{89} +(6.00000 - 6.92820i) q^{91} +(2.19615 - 1.26795i) q^{92} +(7.79423 - 4.50000i) q^{94} +(-1.09808 + 0.633975i) q^{95} +(7.39230 - 4.26795i) q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^7	\( 4 q + 2 q^{4} + 4 q^{5} + 2 q^{7} + 12 q^{13} - 2 q^{16} + 6 q^{19} + 2 q^{20} + 6 q^{22} + 4 q^{25} + 10 q^{28} + 12 q^{29} - 18 q^{31} + 2 q^{35} - 2 q^{37} - 12 q^{38} + 18 q^{41} + 4 q^{43} + 6 q^{44} + 12 q^{46} + 18 q^{47} - 26 q^{49} - 6 q^{53} + 12 q^{58} + 6 q^{59} + 24 q^{61} - 12 q^{62} - 4 q^{64} + 12 q^{65} + 8 q^{67} + 24 q^{73} + 6 q^{76} - 18 q^{77} + 2 q^{79} - 2 q^{80} - 12 q^{83} + 12 q^{88} - 12 q^{89} + 24 q^{91} - 12 q^{92} + 6 q^{95} - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 + 2 * q^7 + 12 * q^13 - 2 * q^16 + 6 * q^19 + 2 * q^20 + 6 * q^22 + 4 * q^25 + 10 * q^28 + 12 * q^29 - 18 * q^31 + 2 * q^35 - 2 * q^37 - 12 * q^38 + 18 * q^41 + 4 * q^43 + 6 * q^44 + 12 * q^46 + 18 * q^47 - 26 * q^49 - 6 * q^53 + 12 * q^58 + 6 * q^59 + 24 * q^61 - 12 * q^62 - 4 * q^64 + 12 * q^65 + 8 * q^67 + 24 * q^73 + 6 * q^76 - 18 * q^77 + 2 * q^79 - 2 * q^80 - 12 * q^83 + 12 * q^88 - 12 * q^89 + 24 * q^91 - 12 * q^92 + 6 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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