LMFDB - Embedded newform 1890.2.t.a.1601.1

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			1601.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1890.1601
Dual form			1890.2.t.a.1151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} -1.26795i q^{11} +(3.00000 - 1.73205i) q^{13} +(-1.73205 - 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.09808 + 2.36603i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.633975 + 1.09808i) q^{22} -9.46410i q^{23} +1.00000 q^{25} +(-1.73205 + 3.00000i) q^{26} +(2.50000 + 0.866025i) q^{28} +(0.401924 + 0.232051i) q^{29} +(-1.90192 - 1.09808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.500000 + 2.59808i) q^{35} +(2.09808 - 3.63397i) q^{37} -4.73205 q^{38} +1.00000i q^{40} +(4.50000 + 7.79423i) q^{41} +(3.59808 - 6.23205i) q^{43} +(-1.09808 - 0.633975i) q^{44} +(4.73205 + 8.19615i) q^{46} +(4.50000 + 7.79423i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-0.866025 + 0.500000i) q^{50} -3.46410i q^{52} +(-9.29423 + 5.36603i) q^{53} -1.26795i q^{55} +(-2.59808 + 0.500000i) q^{56} -0.464102 q^{58} +(4.09808 - 7.09808i) q^{59} +(0.803848 - 0.464102i) q^{61} +2.19615 q^{62} -1.00000 q^{64} +(3.00000 - 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.73205 - 2.00000i) q^{70} +1.26795i q^{71} +(6.00000 - 3.46410i) q^{73} +4.19615i q^{74} +(4.09808 - 2.36603i) q^{76} +(3.29423 - 0.633975i) q^{77} +(8.29423 + 14.3660i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-7.79423 - 4.50000i) q^{82} +(-0.401924 + 0.696152i) q^{83} +7.19615i q^{86} +1.26795 q^{88} +(-8.19615 + 14.1962i) q^{89} +(6.00000 + 6.92820i) q^{91} +(-8.19615 - 4.73205i) q^{92} +(-7.79423 - 4.50000i) q^{94} +(4.09808 + 2.36603i) q^{95} +(-13.3923 - 7.73205i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.00000			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
$11$		−	1.26795i		−	0.382301i	−0.981561	−	0.191151i	$-0.938778\pi$
$11$		−	1.26795i		−	0.382301i	0.981561	−	0.191151i	$-0.0612219\pi$
$12$		0			0
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	−0.0225039	−	0.999747i	$-0.507164\pi$
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	0.854554	+	0.519362i	$0.173830\pi$
$14$	−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	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	4.09808	+	2.36603i	0.940163	+	0.542803i	0.890011	−	0.455938i	$-0.150696\pi$
$19$	4.09808	+	2.36603i	0.940163	+	0.542803i	0.0501517	+	0.998742i	$0.484030\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	0.633975	+	1.09808i	0.135164	+	0.234111i
$23$		−	9.46410i		−	1.97340i	−0.162547	−	0.986701i	$-0.551971\pi$
$23$		−	9.46410i		−	1.97340i	0.162547	−	0.986701i	$-0.448029\pi$
$24$		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
$29$	0.401924	+	0.232051i	0.0746354	+	0.0430908i	0.536853	−	0.843676i	$-0.319613\pi$
$29$	0.401924	+	0.232051i	0.0746354	+	0.0430908i	−0.462218	+	0.886766i	$0.652946\pi$
$30$		0			0
$31$	−1.90192	−	1.09808i	−0.341596	−	0.197220i	0.319382	−	0.947626i	$-0.396525\pi$
$31$	−1.90192	−	1.09808i	−0.341596	−	0.197220i	−0.660977	+	0.750406i	$0.729858\pi$
$32$	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
$37$	2.09808	−	3.63397i	0.344922	−	0.597422i	−0.640418	−	0.768027i	$-0.721239\pi$
$37$	2.09808	−	3.63397i	0.344922	−	0.597422i	0.985340	+	0.170605i	$0.0545722\pi$
$38$	−4.73205			−0.767640
$39$		0			0
$40$			1.00000i			0.158114i
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	3.59808	−	6.23205i	0.548701	−	0.950379i	−0.449662	−	0.893199i	$-0.648456\pi$
$43$	3.59808	−	6.23205i	0.548701	−	0.950379i	0.998364	−	0.0571802i	$-0.0182110\pi$
$44$	−1.09808	−	0.633975i	−0.165541	−	0.0955753i
$45$		0			0
$46$	4.73205	+	8.19615i	0.697703	+	1.20846i
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$		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
$53$	−9.29423	+	5.36603i	−1.27666	+	0.737080i	−0.976233	−	0.216724i	$-0.930463\pi$
$53$	−9.29423	+	5.36603i	−1.27666	+	0.737080i	−0.300428	+	0.953805i	$0.597129\pi$
$54$		0			0
$55$		−	1.26795i		−	0.170970i
$56$	−2.59808	+	0.500000i	−0.347183	+	0.0668153i
$57$		0			0
$58$	−0.464102			−0.0609395
$59$	4.09808	−	7.09808i	0.533524	−	0.924091i	−0.465709	−	0.884938i	$-0.654201\pi$
$59$	4.09808	−	7.09808i	0.533524	−	0.924091i	0.999233	−	0.0391530i	$-0.0124660\pi$
$60$		0			0
$61$	0.803848	−	0.464102i	0.102922	−	0.0594221i	−0.447655	−	0.894206i	$-0.647741\pi$
$61$	0.803848	−	0.464102i	0.102922	−	0.0594221i	0.550578	+	0.834784i	$0.314408\pi$
$62$	2.19615			0.278912
$63$		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	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$		0			0
$69$		0			0
$70$	−1.73205	−	2.00000i	−0.207020	−	0.239046i
$71$			1.26795i			0.150478i	0.997166	+	0.0752389i	$0.0239720\pi$
$71$			1.26795i			0.150478i	−0.997166	+	0.0752389i	$0.976028\pi$
$72$		0			0
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	−0.105937	−	0.994373i	$-0.533784\pi$
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	0.808184	+	0.588930i	$0.200451\pi$
$74$			4.19615i			0.487793i
$75$		0			0
$76$	4.09808	−	2.36603i	0.470082	−	0.271402i
$77$	3.29423	−	0.633975i	0.375412	−	0.0722481i
$78$		0			0
$79$	8.29423	+	14.3660i	0.933174	+	1.61630i	0.777859	+	0.628439i	$0.216306\pi$
$79$	8.29423	+	14.3660i	0.933174	+	1.61630i	0.155315	+	0.987865i	$0.450361\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	−7.79423	−	4.50000i	−0.860729	−	0.496942i
$83$	−0.401924	+	0.696152i	−0.0441169	+	0.0764127i	−0.887241	−	0.461307i	$-0.847381\pi$
$83$	−0.401924	+	0.696152i	−0.0441169	+	0.0764127i	0.843124	+	0.537720i	$0.180714\pi$
$84$		0			0
$85$		0			0
$86$			7.19615i			0.775981i
$87$		0			0
$88$	1.26795			0.135164
$89$	−8.19615	+	14.1962i	−0.868790	+	1.50479i	−0.00555677	+	0.999985i	$0.501769\pi$
$89$	−8.19615	+	14.1962i	−0.868790	+	1.50479i	−0.863234	+	0.504805i	$0.831565\pi$
$90$		0			0
$91$	6.00000	+	6.92820i	0.628971	+	0.726273i
$92$	−8.19615	−	4.73205i	−0.854508	−	0.493350i
$93$		0			0
$94$	−7.79423	−	4.50000i	−0.803913	−	0.464140i
$95$	4.09808	+	2.36603i	0.420454	+	0.242749i
$96$		0			0
$97$	−13.3923	−	7.73205i	−1.35978	−	0.785071i	−0.370188	−	0.928957i	$-0.620707\pi$
$97$	−13.3923	−	7.73205i	−1.35978	−	0.785071i	−0.989594	+	0.143886i	$0.954040\pi$
$98$	4.33013	−	5.50000i	0.437409	−	0.555584i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	0.803848			0.0799858			0.0399929	−	0.999200i	$-0.487266\pi$
$101$	0.803848			0.0799858			0.0399929	+	0.999200i	$0.487266\pi$
$102$		0			0
$103$		−	12.1244i		−	1.19465i	−0.802000	−	0.597324i	$-0.796231\pi$
$103$		−	12.1244i		−	1.19465i	0.802000	−	0.597324i	$-0.203769\pi$
$104$	1.73205	+	3.00000i	0.169842	+	0.294174i
$105$		0			0
$106$	5.36603	−	9.29423i	0.521194	−	0.902735i
$107$	1.79423	+	1.03590i	0.173455	+	0.100144i	0.584214	−	0.811600i	$-0.301403\pi$
$107$	1.79423	+	1.03590i	0.173455	+	0.100144i	−0.410759	+	0.911744i	$0.634736\pi$
$108$		0			0
$109$	−1.59808	−	2.76795i	−0.153068	−	0.265121i	0.779286	−	0.626669i	$-0.215582\pi$
$109$	−1.59808	−	2.76795i	−0.153068	−	0.265121i	−0.932354	+	0.361547i	$0.882249\pi$
$110$	0.633975	+	1.09808i	0.0604471	+	0.104697i
$111$		0			0
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	16.0981	−	9.29423i	1.51438	−	0.874327i	0.514522	−	0.857477i	$-0.327970\pi$
$113$	16.0981	−	9.29423i	1.51438	−	0.874327i	0.999858	−	0.0168501i	$-0.00536380\pi$
$114$		0			0
$115$		−	9.46410i		−	0.882532i
$116$	0.401924	−	0.232051i	0.0373177	−	0.0215454i
$117$		0			0
$118$			8.19615i			0.754517i
$119$		0			0
$120$		0			0
$121$	9.39230			0.853846
$122$	−0.464102	+	0.803848i	−0.0420178	+	0.0727769i
$123$		0			0
$124$	−1.90192	+	1.09808i	−0.170798	+	0.0986102i
$125$	1.00000			0.0894427
$126$		0			0
$127$	9.39230			0.833432			0.416716	−	0.909037i	$-0.363181\pi$
$127$	9.39230			0.833432			0.416716	+	0.909037i	$0.363181\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.73205	+	3.00000i	−0.151911	+	0.263117i
$131$	16.3923			1.43220			0.716101	−	0.697997i	$-0.245925\pi$
$131$	16.3923			1.43220			0.716101	+	0.697997i	$0.245925\pi$
$132$		0			0
$133$	−4.09808	+	11.8301i	−0.355348	+	1.02580i
$134$			4.00000i			0.345547i
$135$		0			0
$136$		0			0
$137$			10.7321i			0.916901i	0.888720	+	0.458450i	$0.151595\pi$
$137$			10.7321i			0.916901i	−0.888720	+	0.458450i	$0.848405\pi$
$138$		0			0
$139$	13.9019	−	8.02628i	1.17915	−	0.680780i	0.223329	−	0.974743i	$-0.428308\pi$
$139$	13.9019	−	8.02628i	1.17915	−	0.680780i	0.955817	+	0.293963i	$0.0949742\pi$
$140$	2.50000	+	0.866025i	0.211289	+	0.0731925i
$141$		0			0
$142$	−0.633975	−	1.09808i	−0.0532020	−	0.0921485i
$143$	−2.19615	−	3.80385i	−0.183651	−	0.318094i
$144$		0			0
$145$	0.401924	+	0.232051i	0.0333780	+	0.0192708i
$146$	−3.46410	+	6.00000i	−0.286691	+	0.496564i
$147$		0			0
$148$	−2.09808	−	3.63397i	−0.172461	−	0.298711i
$149$		−	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
$151$	6.19615			0.504236			0.252118	−	0.967697i	$-0.418873\pi$
$151$	6.19615			0.504236			0.252118	+	0.967697i	$0.418873\pi$
$152$	−2.36603	+	4.09808i	−0.191910	+	0.332398i
$153$		0			0
$154$	−2.53590	+	2.19615i	−0.204349	+	0.176971i
$155$	−1.90192	−	1.09808i	−0.152766	−	0.0881996i
$156$		0			0
$157$	0.294229	+	0.169873i	0.0234820	+	0.0135573i	0.511695	−	0.859167i	$-0.329018\pi$
$157$	0.294229	+	0.169873i	0.0234820	+	0.0135573i	−0.488213	+	0.872724i	$0.662351\pi$
$158$	−14.3660	−	8.29423i	−1.14290	−	0.659853i
$159$		0			0
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	24.5885	−	4.73205i	1.93784	−	0.372938i
$162$		0			0
$163$	−6.19615	+	10.7321i	−0.485320	+	0.840599i	−0.999858	−	0.0168687i	$-0.994630\pi$
$163$	−6.19615	+	10.7321i	−0.485320	+	0.840599i	0.514538	+	0.857468i	$0.327964\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$		−	0.803848i		−	0.0623907i
$167$	5.19615	+	9.00000i	0.402090	+	0.696441i	0.993978	−	0.109580i	$-0.0349504\pi$
$167$	5.19615	+	9.00000i	0.402090	+	0.696441i	−0.591888	+	0.806020i	$0.701617\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$		0			0
$172$	−3.59808	−	6.23205i	−0.274351	−	0.475189i
$173$	1.09808	+	1.90192i	0.0834852	+	0.144601i	0.904745	−	0.425954i	$-0.140062\pi$
$173$	1.09808	+	1.90192i	0.0834852	+	0.144601i	−0.821260	+	0.570555i	$0.806728\pi$
$174$		0			0
$175$	0.500000	+	2.59808i	0.0377964	+	0.196396i
$176$	−1.09808	+	0.633975i	−0.0827706	+	0.0477876i
$177$		0			0
$178$		−	16.3923i		−	1.22866i
$179$	−5.70577	+	3.29423i	−0.426469	+	0.246222i	−0.697841	−	0.716252i	$-0.745856\pi$
$179$	−5.70577	+	3.29423i	−0.426469	+	0.246222i	0.271372	+	0.962475i	$0.412523\pi$
$180$		0			0
$181$			7.39230i			0.549466i	0.961521	+	0.274733i	$0.0885894\pi$
$181$			7.39230i			0.549466i	−0.961521	+	0.274733i	$0.911411\pi$
$182$	−8.66025	−	3.00000i	−0.641941	−	0.222375i
$183$		0			0
$184$	9.46410			0.697703
$185$	2.09808	−	3.63397i	0.154254	−	0.267175i
$186$		0			0
$187$		0			0
$188$	9.00000			0.656392
$189$		0			0
$190$	−4.73205			−0.343299
$191$	−3.00000	+	1.73205i	−0.217072	+	0.125327i	−0.604594	−	0.796534i	$-0.706665\pi$
$191$	−3.00000	+	1.73205i	−0.217072	+	0.125327i	0.387522	+	0.921861i	$0.373331\pi$
$192$		0			0
$193$	−12.0981	+	20.9545i	−0.870839	+	1.50834i	−0.00970797	+	0.999953i	$0.503090\pi$
$193$	−12.0981	+	20.9545i	−0.870839	+	1.50834i	−0.861131	+	0.508384i	$0.830243\pi$
$194$	15.4641			1.11026
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			6.33975i			0.451688i	0.974163	+	0.225844i	$0.0725140\pi$
$197$			6.33975i			0.451688i	−0.974163	+	0.225844i	$0.927486\pi$
$198$		0			0
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	−0.272026	−	0.962290i	$-0.587694\pi$
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	0.697355	+	0.716726i	$0.254360\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−0.696152	+	0.401924i	−0.0489811	+	0.0282793i
$203$	−0.401924	+	1.16025i	−0.0282095	+	0.0814339i
$204$		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
$211$	−5.29423	−	9.16987i	−0.364470	−	0.631280i	0.624221	−	0.781248i	$-0.285416\pi$
$211$	−5.29423	−	9.16987i	−0.364470	−	0.631280i	−0.988691	+	0.149968i	$0.952083\pi$
$212$			10.7321i			0.737080i
$213$		0			0
$214$	−2.07180			−0.141625
$215$	3.59808	−	6.23205i	0.245387	−	0.425022i
$216$		0			0
$217$	1.90192	−	5.49038i	0.129111	−	0.372711i
$218$	2.76795	+	1.59808i	0.187469	+	0.108235i
$219$		0			0
$220$	−1.09808	−	0.633975i	−0.0740323	−	0.0427426i
$221$		0			0
$222$		0			0
$223$	−8.89230	−	5.13397i	−0.595473	−	0.343796i	0.171786	−	0.985134i	$-0.445046\pi$
$223$	−8.89230	−	5.13397i	−0.595473	−	0.343796i	−0.767259	+	0.641338i	$0.778380\pi$
$224$	−0.866025	+	2.50000i	−0.0578638	+	0.167038i
$225$		0			0
$226$	−9.29423	+	16.0981i	−0.618243	+	1.07083i
$227$	−4.39230			−0.291528			−0.145764	−	0.989319i	$-0.546564\pi$
$227$	−4.39230			−0.291528			−0.145764	+	0.989319i	$0.546564\pi$
$228$		0			0
$229$			27.9282i			1.84555i	0.385342	+	0.922774i	$0.374083\pi$
$229$			27.9282i			1.84555i	−0.385342	+	0.922774i	$0.625917\pi$
$230$	4.73205	+	8.19615i	0.312022	+	0.540438i
$231$		0			0
$232$	−0.232051	+	0.401924i	−0.0152349	+	0.0263876i
$233$	4.09808	+	2.36603i	0.268474	+	0.155003i	0.628194	−	0.778057i	$-0.283794\pi$
$233$	4.09808	+	2.36603i	0.268474	+	0.155003i	−0.359720	+	0.933060i	$0.617128\pi$
$234$		0			0
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$	−4.09808	−	7.09808i	−0.266762	−	0.462045i
$237$		0			0
$238$		0			0
$239$	−18.2942	+	10.5622i	−1.18336	+	0.683210i	−0.956788	−	0.290785i	$-0.906084\pi$
$239$	−18.2942	+	10.5622i	−1.18336	+	0.683210i	−0.226567	+	0.973996i	$0.572750\pi$
$240$		0			0
$241$			20.6603i			1.33084i	0.746467	+	0.665422i	$0.231748\pi$
$241$			20.6603i			1.33084i	−0.746467	+	0.665422i	$0.768252\pi$
$242$	−8.13397	+	4.69615i	−0.522872	+	0.301880i
$243$		0			0
$244$		−	0.928203i		−	0.0594221i
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$		0			0
$247$	16.3923			1.04302
$248$	1.09808	−	1.90192i	0.0697279	−	0.120772i
$249$		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
$254$	−8.13397	+	4.69615i	−0.510371	+	0.294663i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.60770			−0.474555			−0.237277	−	0.971442i	$-0.576255\pi$
$257$	−7.60770			−0.474555			−0.237277	+	0.971442i	$0.576255\pi$
$258$		0			0
$259$	10.4904	+	3.63397i	0.651841	+	0.225804i
$260$		−	3.46410i		−	0.214834i
$261$		0			0
$262$	−14.1962	+	8.19615i	−0.877041	+	0.506360i
$263$		−	10.2679i		−	0.633149i	−0.948568	−	0.316574i	$-0.897467\pi$
$263$		−	10.2679i		−	0.633149i	0.948568	−	0.316574i	$-0.102533\pi$
$264$		0			0
$265$	−9.29423	+	5.36603i	−0.570940	+	0.329632i
$266$	−2.36603	−	12.2942i	−0.145070	−	0.753808i
$267$		0			0
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	21.2942	+	12.2942i	1.29353	+	0.746821i	0.979279	−	0.202518i	$-0.0649124\pi$
$271$	21.2942	+	12.2942i	1.29353	+	0.746821i	0.314254	+	0.949339i	$0.398246\pi$
$272$		0			0
$273$		0			0
$274$	−5.36603	−	9.29423i	−0.324173	−	0.561485i
$275$		−	1.26795i		−	0.0764602i
$276$		0			0
$277$	−13.8038			−0.829393			−0.414696	−	0.909960i	$-0.636112\pi$
$277$	−13.8038			−0.829393			−0.414696	+	0.909960i	$0.636112\pi$
$278$	−8.02628	+	13.9019i	−0.481384	+	0.833782i
$279$		0			0
$280$	−2.59808	+	0.500000i	−0.155265	+	0.0298807i
$281$	−2.30385	−	1.33013i	−0.137436	−	0.0793487i	0.429705	−	0.902969i	$-0.358617\pi$
$281$	−2.30385	−	1.33013i	−0.137436	−	0.0793487i	−0.567141	+	0.823620i	$0.691951\pi$
$282$		0			0
$283$	−9.40192	−	5.42820i	−0.558886	−	0.322673i	0.193812	−	0.981039i	$-0.437915\pi$
$283$	−9.40192	−	5.42820i	−0.558886	−	0.322673i	−0.752698	+	0.658365i	$0.771248\pi$
$284$	1.09808	+	0.633975i	0.0651588	+	0.0376195i
$285$		0			0
$286$	3.80385	+	2.19615i	0.224926	+	0.129861i
$287$	−18.0000	+	15.5885i	−1.06251	+	0.920158i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−0.464102			−0.0272530
$291$		0			0
$292$		−	6.92820i		−	0.405442i
$293$	−2.19615	−	3.80385i	−0.128301	−	0.222223i	0.794718	−	0.606979i	$-0.207619\pi$
$293$	−2.19615	−	3.80385i	−0.128301	−	0.222223i	−0.923018	+	0.384756i	$0.874286\pi$
$294$		0			0
$295$	4.09808	−	7.09808i	0.238599	−	0.413266i
$296$	3.63397	+	2.09808i	0.211220	+	0.121948i
$297$		0			0
$298$	6.00000	+	10.3923i	0.347571	+	0.602010i
$299$	−16.3923	−	28.3923i	−0.947991	−	1.64197i
$300$		0			0
$301$	17.9904	+	6.23205i	1.03695	+	0.359209i
$302$	−5.36603	+	3.09808i	−0.308780	+	0.178274i
$303$		0			0
$304$		−	4.73205i		−	0.271402i
$305$	0.803848	−	0.464102i	0.0460282	−	0.0265744i
$306$		0			0
$307$		−	17.7846i		−	1.01502i	−0.861645	−	0.507511i	$-0.830566\pi$
$307$		−	17.7846i		−	1.01502i	0.861645	−	0.507511i	$-0.169434\pi$
$308$	1.09808	−	3.16987i	0.0625687	−	0.180620i
$309$		0			0
$310$	2.19615			0.124733
$311$	13.0981	−	22.6865i	0.742724	−	1.28644i	−0.208527	−	0.978017i	$-0.566867\pi$
$311$	13.0981	−	22.6865i	0.742724	−	1.28644i	0.951251	−	0.308419i	$-0.0997998\pi$
$312$		0			0
$313$	8.49038	−	4.90192i	0.479905	−	0.277073i	−0.240472	−	0.970656i	$-0.577302\pi$
$313$	8.49038	−	4.90192i	0.479905	−	0.277073i	0.720377	+	0.693583i	$0.243969\pi$
$314$	−0.339746			−0.0191730
$315$		0			0
$316$	16.5885			0.933174
$317$	23.7846	−	13.7321i	1.33588	−	0.771269i	0.349684	−	0.936868i	$-0.386289\pi$
$317$	23.7846	−	13.7321i	1.33588	−	0.771269i	0.986193	+	0.165599i	$0.0529558\pi$
$318$		0			0
$319$	0.294229	−	0.509619i	0.0164736	−	0.0285332i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−18.9282	+	16.3923i	−1.05483	+	0.913507i
$323$		0			0
$324$		0			0
$325$	3.00000	−	1.73205i	0.166410	−	0.0960769i
$326$		−	12.3923i		−	0.686346i
$327$		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	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	0.401924	+	0.696152i	0.0220584	+	0.0382063i
$333$		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	0.697100	−	0.716974i	$-0.254473\pi$
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	−0.969468	+	0.245220i	$0.921140\pi$
$338$		−	1.00000i		−	0.0543928i
$339$		0			0
$340$		0			0
$341$	−1.39230	+	2.41154i	−0.0753975	+	0.130592i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	6.23205	+	3.59808i	0.336010	+	0.193995i
$345$		0			0
$346$	−1.90192	−	1.09808i	−0.102248	−	0.0590329i
$347$	−23.5981	−	13.6244i	−1.26681	−	0.731394i	−0.292428	−	0.956288i	$-0.594463\pi$
$347$	−23.5981	−	13.6244i	−1.26681	−	0.731394i	−0.974383	+	0.224894i	$0.927796\pi$
$348$		0			0
$349$	3.80385	+	2.19615i	0.203615	+	0.117557i	0.598341	−	0.801242i	$-0.295827\pi$
$349$	3.80385	+	2.19615i	0.203615	+	0.117557i	−0.394725	+	0.918799i	$0.629160\pi$
$350$	−1.73205	−	2.00000i	−0.0925820	−	0.106904i
$351$		0			0
$352$	0.633975	−	1.09808i	0.0337910	−	0.0585277i
$353$	−30.5885			−1.62806			−0.814030	−	0.580823i	$-0.802731\pi$
$353$	−30.5885			−1.62806			−0.814030	+	0.580823i	$0.802731\pi$
$354$		0			0
$355$			1.26795i			0.0672958i
$356$	8.19615	+	14.1962i	0.434395	+	0.752395i
$357$		0			0
$358$	3.29423	−	5.70577i	0.174105	−	0.301559i
$359$	−22.6865	−	13.0981i	−1.19735	−	0.691290i	−0.237386	−	0.971415i	$-0.576291\pi$
$359$	−22.6865	−	13.0981i	−1.19735	−	0.691290i	−0.959963	+	0.280125i	$0.909624\pi$
$360$		0			0
$361$	1.69615	+	2.93782i	0.0892712	+	0.154622i
$362$	−3.69615	−	6.40192i	−0.194265	−	0.336478i
$363$		0			0
$364$	9.00000	−	1.73205i	0.471728	−	0.0907841i
$365$	6.00000	−	3.46410i	0.314054	−	0.181319i
$366$		0			0
$367$		−	18.8038i		−	0.981553i	−0.871286	−	0.490776i	$-0.836713\pi$
$367$		−	18.8038i		−	0.981553i	0.871286	−	0.490776i	$-0.163287\pi$
$368$	−8.19615	+	4.73205i	−0.427254	+	0.246675i
$369$		0			0
$370$			4.19615i			0.218148i
$371$	−18.5885	−	21.4641i	−0.965065	−	1.11436i
$372$		0			0
$373$	−0.196152			−0.0101564			−0.00507819	−	0.999987i	$-0.501616\pi$
$373$	−0.196152			−0.0101564			−0.00507819	+	0.999987i	$0.501616\pi$
$374$		0			0
$375$		0			0
$376$	−7.79423	+	4.50000i	−0.401957	+	0.232070i
$377$	1.60770			0.0828005
$378$		0			0
$379$	−30.3923			−1.56115			−0.780574	−	0.625063i	$-0.785073\pi$
$379$	−30.3923			−1.56115			−0.780574	+	0.625063i	$0.785073\pi$
$380$	4.09808	−	2.36603i	0.210227	−	0.121375i
$381$		0			0
$382$	1.73205	−	3.00000i	0.0886194	−	0.153493i
$383$	1.39230			0.0711435			0.0355717	−	0.999367i	$-0.488675\pi$
$383$	1.39230			0.0711435			0.0355717	+	0.999367i	$0.488675\pi$
$384$		0			0
$385$	3.29423	−	0.633975i	0.167889	−	0.0323103i
$386$		−	24.1962i		−	1.23155i
$387$		0			0
$388$	−13.3923	+	7.73205i	−0.679891	+	0.392535i
$389$		−	30.7128i		−	1.55720i	−0.627520	−	0.778601i	$-0.715930\pi$
$389$		−	30.7128i		−	1.55720i	0.627520	−	0.778601i	$-0.284070\pi$
$390$		0			0
$391$		0			0
$392$	−2.59808	−	6.50000i	−0.131223	−	0.328300i
$393$		0			0
$394$	−3.16987	−	5.49038i	−0.159696	−	0.276601i
$395$	8.29423	+	14.3660i	0.417328	+	0.722833i
$396$		0			0
$397$	−0.509619	−	0.294229i	−0.0255770	−	0.0147669i	0.487157	−	0.873314i	$-0.338034\pi$
$397$	−0.509619	−	0.294229i	−0.0255770	−	0.0147669i	−0.512734	+	0.858548i	$0.671367\pi$
$398$	−3.46410	+	6.00000i	−0.173640	+	0.300753i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$			27.5885i			1.37770i	0.724903	+	0.688851i	$0.241885\pi$
$401$			27.5885i			1.37770i	−0.724903	+	0.688851i	$0.758115\pi$
$402$		0			0
$403$	−7.60770			−0.378966
$404$	0.401924	−	0.696152i	0.0199965	−	0.0346349i
$405$		0			0
$406$	−0.232051	−	1.20577i	−0.0115165	−	0.0598414i
$407$	−4.60770	−	2.66025i	−0.228395	−	0.131864i
$408$		0			0
$409$	−29.8923	−	17.2583i	−1.47808	−	0.853370i	−0.478386	−	0.878149i	$-0.658778\pi$
$409$	−29.8923	−	17.2583i	−1.47808	−	0.853370i	−0.999693	+	0.0247799i	$0.992111\pi$
$410$	−7.79423	−	4.50000i	−0.384930	−	0.222239i
$411$		0			0
$412$	−10.5000	−	6.06218i	−0.517298	−	0.298662i
$413$	20.4904	+	7.09808i	1.00827	+	0.349273i
$414$		0			0
$415$	−0.401924	+	0.696152i	−0.0197297	+	0.0341728i
$416$	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	$-0.0849701\pi$
$419$	5.19615	+	9.00000i	0.253849	+	0.439679i	−0.710734	+	0.703461i	$0.751637\pi$
$420$		0			0
$421$	−10.9904	+	19.0359i	−0.535638	+	0.927753i	0.463494	+	0.886100i	$0.346596\pi$
$421$	−10.9904	+	19.0359i	−0.535638	+	0.927753i	−0.999132	+	0.0416527i	$0.986738\pi$
$422$	9.16987	+	5.29423i	0.446382	+	0.257719i
$423$		0			0
$424$	−5.36603	−	9.29423i	−0.260597	−	0.451368i
$425$		0			0
$426$		0			0
$427$	1.60770	+	1.85641i	0.0778018	+	0.0898378i
$428$	1.79423	−	1.03590i	0.0867273	−	0.0500720i
$429$		0			0
$430$			7.19615i			0.347029i
$431$	2.41154	−	1.39230i	0.116160	−	0.0670650i	−0.440794	−	0.897608i	$-0.645303\pi$
$431$	2.41154	−	1.39230i	0.116160	−	0.0670650i	0.556954	+	0.830543i	$0.311970\pi$
$432$		0			0
$433$		−	18.0000i		−	0.865025i	−0.901628	−	0.432512i	$-0.857627\pi$
$433$		−	18.0000i		−	0.865025i	0.901628	−	0.432512i	$-0.142373\pi$
$434$	1.09808	+	5.70577i	0.0527093	+	0.273886i
$435$		0			0
$436$	−3.19615			−0.153068
$437$	22.3923	−	38.7846i	1.07117	−	1.85532i
$438$		0			0
$439$	−10.6865	+	6.16987i	−0.510040	+	0.294472i	−0.732850	−	0.680390i	$-0.761810\pi$
$439$	−10.6865	+	6.16987i	−0.510040	+	0.294472i	0.222810	+	0.974862i	$0.428477\pi$
$440$	1.26795			0.0604471
$441$		0			0
$442$		0			0
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$		0			0
$445$	−8.19615	+	14.1962i	−0.388535	+	0.672962i
$446$	10.2679			0.486201
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$			21.5885i			1.01882i	0.860523	+	0.509411i	$0.170137\pi$
$449$			21.5885i			1.01882i	−0.860523	+	0.509411i	$0.829863\pi$
$450$		0			0
$451$	9.88269	−	5.70577i	0.465358	−	0.268674i
$452$		−	18.5885i		−	0.874327i
$453$		0			0
$454$	3.80385	−	2.19615i	0.178523	−	0.103071i
$455$	6.00000	+	6.92820i	0.281284	+	0.324799i
$456$		0			0
$457$	9.19615	+	15.9282i	0.430178	+	0.745090i	0.996888	−	0.0788271i	$-0.0251175\pi$
$457$	9.19615	+	15.9282i	0.430178	+	0.745090i	−0.566710	+	0.823917i	$0.691784\pi$
$458$	−13.9641	−	24.1865i	−0.652500	−	1.13016i
$459$		0			0
$460$	−8.19615	−	4.73205i	−0.382148	−	0.220633i
$461$	−2.59808	+	4.50000i	−0.121004	+	0.209586i	−0.920164	−	0.391533i	$-0.871945\pi$
$461$	−2.59808	+	4.50000i	−0.121004	+	0.209586i	0.799160	+	0.601119i	$0.205278\pi$
$462$		0			0
$463$	11.6962	+	20.2583i	0.543566	+	0.941484i	0.998696	+	0.0510591i	$0.0162597\pi$
$463$	11.6962	+	20.2583i	0.543566	+	0.941484i	−0.455129	+	0.890425i	$0.650407\pi$
$464$		−	0.464102i		−	0.0215454i
$465$		0			0
$466$	−4.73205			−0.219208
$467$	−8.59808	+	14.8923i	−0.397872	+	0.689134i	−0.993463	−	0.114154i	$-0.963584\pi$
$467$	−8.59808	+	14.8923i	−0.397872	+	0.689134i	0.595592	+	0.803287i	$0.296918\pi$
$468$		0			0
$469$	10.0000	+	3.46410i	0.461757	+	0.159957i
$470$	−7.79423	−	4.50000i	−0.359521	−	0.207570i
$471$		0			0
$472$	7.09808	+	4.09808i	0.326715	+	0.188629i
$473$	−7.90192	−	4.56218i	−0.363331	−	0.209769i
$474$		0			0
$475$	4.09808	+	2.36603i	0.188033	+	0.108561i
$476$		0			0
$477$		0			0
$478$	10.5622	−	18.2942i	0.483103	−	0.836759i
$479$	−10.3923			−0.474837			−0.237418	−	0.971408i	$-0.576301\pi$
$479$	−10.3923			−0.474837			−0.237418	+	0.971408i	$0.576301\pi$
$480$		0			0
$481$		−	14.5359i		−	0.662780i
$482$	−10.3301	−	17.8923i	−0.470524	−	0.814972i
$483$		0			0
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	−13.3923	−	7.73205i	−0.608113	−	0.351094i
$486$		0			0
$487$	−17.0000	−	29.4449i	−0.770344	−	1.33427i	−0.937375	−	0.348323i	$-0.886751\pi$
$487$	−17.0000	−	29.4449i	−0.770344	−	1.33427i	0.167031	−	0.985952i	$-0.446582\pi$
$488$	0.464102	+	0.803848i	0.0210089	+	0.0363885i
$489$		0			0
$490$	4.33013	−	5.50000i	0.195615	−	0.248465i
$491$	−2.49038	+	1.43782i	−0.112389	+	0.0648880i	−0.555141	−	0.831756i	$-0.687336\pi$
$491$	−2.49038	+	1.43782i	−0.112389	+	0.0648880i	0.442752	+	0.896644i	$0.354002\pi$
$492$		0			0
$493$		0			0
$494$	−14.1962	+	8.19615i	−0.638715	+	0.368762i
$495$		0			0
$496$			2.19615i			0.0986102i
$497$	−3.29423	+	0.633975i	−0.147766	+	0.0284376i
$498$		0			0
$499$	−5.80385			−0.259816			−0.129908	−	0.991526i	$-0.541468\pi$
$499$	−5.80385			−0.259816			−0.129908	+	0.991526i	$0.541468\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−15.5885	+	9.00000i	−0.695747	+	0.401690i
$503$	−13.3923			−0.597133			−0.298567	−	0.954389i	$-0.596509\pi$
$503$	−13.3923			−0.597133			−0.298567	+	0.954389i	$0.596509\pi$
$504$		0			0
$505$	0.803848			0.0357707
$506$	10.3923	−	6.00000i	0.461994	−	0.266733i
$507$		0			0
$508$	4.69615	−	8.13397i	0.208358	−	0.360887i
$509$	21.5885			0.956892			0.478446	−	0.878117i	$-0.341200\pi$
$509$	21.5885			0.956892			0.478446	+	0.878117i	$0.341200\pi$
$510$		0			0
$511$	12.0000	+	13.8564i	0.530849	+	0.612971i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	6.58846	−	3.80385i	0.290604	−	0.167781i
$515$		−	12.1244i		−	0.534263i
$516$		0			0
$517$	9.88269	−	5.70577i	0.434640	−	0.250940i
$518$	−10.9019	+	2.09808i	−0.479003	+	0.0921842i
$519$		0			0
$520$	1.73205	+	3.00000i	0.0759555	+	0.131559i
$521$	−10.5000	−	18.1865i	−0.460013	−	0.796766i	0.538948	−	0.842339i	$-0.318822\pi$
$521$	−10.5000	−	18.1865i	−0.460013	−	0.796766i	−0.998961	+	0.0455727i	$0.985489\pi$
$522$		0			0
$523$	−28.5788	−	16.5000i	−1.24967	−	0.721495i	−0.278623	−	0.960401i	$-0.589878\pi$
$523$	−28.5788	−	16.5000i	−1.24967	−	0.721495i	−0.971043	+	0.238906i	$0.923211\pi$
$524$	8.19615	−	14.1962i	0.358051	−	0.620162i
$525$		0			0
$526$	5.13397	+	8.89230i	0.223852	+	0.387723i
$527$		0			0
$528$		0			0
$529$	−66.5692			−2.89431
$530$	5.36603	−	9.29423i	0.233085	−	0.403715i
$531$		0			0
$532$	8.19615	+	9.46410i	0.355348	+	0.410321i
$533$	27.0000	+	15.5885i	1.16950	+	0.675211i
$534$		0			0
$535$	1.79423	+	1.03590i	0.0775713	+	0.0447858i
$536$	3.46410	+	2.00000i	0.149626	+	0.0863868i
$537$		0			0
$538$	15.5885	+	9.00000i	0.672066	+	0.388018i
$539$	3.29423	+	8.24167i	0.141892	+	0.354994i
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	−24.5885			−1.05616
$543$		0			0
$544$		0			0
$545$	−1.59808	−	2.76795i	−0.0684541	−	0.118566i
$546$		0			0
$547$	12.7942	−	22.1603i	0.547042	−	0.947504i	−0.451434	−	0.892305i	$-0.649087\pi$
$547$	12.7942	−	22.1603i	0.547042	−	0.947504i	0.998475	−	0.0551993i	$-0.0175794\pi$
$548$	9.29423	+	5.36603i	0.397030	+	0.229225i
$549$		0			0
$550$	0.633975	+	1.09808i	0.0270328	+	0.0468221i
$551$	1.09808	+	1.90192i	0.0467796	+	0.0810247i
$552$		0			0
$553$	−33.1769	+	28.7321i	−1.41083	+	1.22181i
$554$	11.9545	−	6.90192i	0.507897	−	0.293235i
$555$		0			0
$556$		−	16.0526i		−	0.680780i
$557$	−7.60770	+	4.39230i	−0.322348	+	0.186108i	−0.652439	−	0.757841i	$-0.726254\pi$
$557$	−7.60770	+	4.39230i	−0.322348	+	0.186108i	0.330090	+	0.943949i	$0.392921\pi$
$558$		0			0
$559$		−	24.9282i		−	1.05435i
$560$	2.00000	−	1.73205i	0.0845154	−	0.0731925i
$561$		0			0
$562$	2.66025			0.112216
$563$	17.1962	−	29.7846i	0.724731	−	1.25527i	−0.234353	−	0.972152i	$-0.575297\pi$
$563$	17.1962	−	29.7846i	0.724731	−	1.25527i	0.959084	−	0.283120i	$-0.0913695\pi$
$564$		0			0
$565$	16.0981	−	9.29423i	0.677251	−	0.391011i
$566$	10.8564			0.456329
$567$		0			0
$568$	−1.26795			−0.0532020
$569$	−5.19615	+	3.00000i	−0.217834	+	0.125767i	−0.604947	−	0.796266i	$-0.706806\pi$
$569$	−5.19615	+	3.00000i	−0.217834	+	0.125767i	0.387113	+	0.922032i	$0.373472\pi$
$570$		0			0
$571$	−21.1962	+	36.7128i	−0.887031	+	1.53638i	−0.0436638	+	0.999046i	$0.513903\pi$
$571$	−21.1962	+	36.7128i	−0.887031	+	1.53638i	−0.843368	+	0.537337i	$0.819430\pi$
$572$	−4.39230			−0.183651
$573$		0			0
$574$	7.79423	−	22.5000i	0.325325	−	0.939132i
$575$		−	9.46410i		−	0.394680i
$576$		0			0
$577$	−20.7846	+	12.0000i	−0.865275	+	0.499567i	−0.865775	−	0.500433i	$-0.833174\pi$
$577$	−20.7846	+	12.0000i	−0.865275	+	0.499567i	0.000500448		1.00000i	$0.499841\pi$
$578$			17.0000i			0.707107i
$579$		0			0
$580$	0.401924	−	0.232051i	0.0166890	−	0.00963539i
$581$	−2.00962	−	0.696152i	−0.0833730	−	0.0288813i
$582$		0			0
$583$	6.80385	+	11.7846i	0.281787	+	0.488069i
$584$	3.46410	+	6.00000i	0.143346	+	0.248282i
$585$		0			0
$586$	3.80385	+	2.19615i	0.157135	+	0.0907222i
$587$	−20.5981	+	35.6769i	−0.850174	+	1.47254i	0.0308777	+	0.999523i	$0.490170\pi$
$587$	−20.5981	+	35.6769i	−0.850174	+	1.47254i	−0.881051	+	0.473021i	$0.843164\pi$
$588$		0			0
$589$	−5.19615	−	9.00000i	−0.214104	−	0.370839i
$590$			8.19615i			0.337430i
$591$		0			0
$592$	−4.19615			−0.172461
$593$	−7.39230	+	12.8038i	−0.303566	+	0.525791i	−0.976941	−	0.213510i	$-0.931510\pi$
$593$	−7.39230	+	12.8038i	−0.303566	+	0.525791i	0.673375	+	0.739301i	$0.264844\pi$
$594$		0			0
$595$		0			0
$596$	−10.3923	−	6.00000i	−0.425685	−	0.245770i
$597$		0			0
$598$	28.3923	+	16.3923i	1.16105	+	0.670331i
$599$	−14.1962	−	8.19615i	−0.580039	−	0.334886i	0.181110	−	0.983463i	$-0.442031\pi$
$599$	−14.1962	−	8.19615i	−0.580039	−	0.334886i	−0.761149	+	0.648577i	$0.775364\pi$
$600$		0			0
$601$	−3.58846	−	2.07180i	−0.146376	−	0.0845104i	0.425023	−	0.905182i	$-0.360266\pi$
$601$	−3.58846	−	2.07180i	−0.146376	−	0.0845104i	−0.571399	+	0.820672i	$0.693599\pi$
$602$	−18.6962	+	3.59808i	−0.761998	+	0.146647i
$603$		0			0
$604$	3.09808	−	5.36603i	0.126059	−	0.218340i
$605$	9.39230			0.381851
$606$		0			0
$607$		−	18.1244i		−	0.735645i	−0.929896	−	0.367822i	$-0.880103\pi$
$607$		−	18.1244i		−	0.735645i	0.929896	−	0.367822i	$-0.119897\pi$
$608$	2.36603	+	4.09808i	0.0959550	+	0.166199i
$609$		0			0
$610$	−0.464102	+	0.803848i	−0.0187909	+	0.0325468i
$611$	27.0000	+	15.5885i	1.09230	+	0.630641i
$612$		0			0
$613$	−17.3923	−	30.1244i	−0.702469	−	1.21671i	−0.967597	−	0.252498i	$-0.918748\pi$
$613$	−17.3923	−	30.1244i	−0.702469	−	1.21671i	0.265129	−	0.964213i	$-0.414586\pi$
$614$	8.89230	+	15.4019i	0.358864	+	0.621571i
$615$		0			0
$616$	0.633975	+	3.29423i	0.0255436	+	0.132728i
$617$	−26.1962	+	15.1244i	−1.05462	+	0.608884i	−0.923938	−	0.382541i	$-0.875049\pi$
$617$	−26.1962	+	15.1244i	−1.05462	+	0.608884i	−0.130679	+	0.991425i	$0.541716\pi$
$618$		0			0
$619$		−	4.39230i		−	0.176542i	−0.996097	−	0.0882708i	$-0.971866\pi$
$619$		−	4.39230i		−	0.176542i	0.996097	−	0.0882708i	$-0.0281341\pi$
$620$	−1.90192	+	1.09808i	−0.0763831	+	0.0440998i
$621$		0			0
$622$			26.1962i			1.05037i
$623$	−40.9808	−	14.1962i	−1.64186	−	0.568757i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−4.90192	+	8.49038i	−0.195920	+	0.339344i
$627$		0			0
$628$	0.294229	−	0.169873i	0.0117410	−	0.00677867i
$629$		0			0
$630$		0			0
$631$	−8.39230			−0.334092			−0.167046	−	0.985949i	$-0.553423\pi$
$631$	−8.39230			−0.334092			−0.167046	+	0.985949i	$0.553423\pi$
$632$	−14.3660	+	8.29423i	−0.571450	+	0.329927i
$633$		0			0
$634$	−13.7321	+	23.7846i	−0.545369	+	0.944608i
$635$	9.39230			0.372722
$636$		0			0
$637$	−15.0000	+	19.0526i	−0.594322	+	0.754890i
$638$			0.588457i			0.0232972i
$639$		0			0
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$			44.7846i			1.76889i	0.466648	+	0.884443i	$0.345461\pi$
$641$			44.7846i			1.76889i	−0.466648	+	0.884443i	$0.654539\pi$
$642$		0			0
$643$	31.7942	−	18.3564i	1.25384	−	0.723906i	0.281972	−	0.959423i	$-0.409012\pi$
$643$	31.7942	−	18.3564i	1.25384	−	0.723906i	0.971870	+	0.235517i	$0.0756782\pi$
$644$	8.19615	−	23.6603i	0.322974	−	0.932345i
$645$		0			0
$646$		0			0
$647$	−12.6962	−	21.9904i	−0.499137	−	0.864531i	0.500862	−	0.865527i	$-0.333016\pi$
$647$	−12.6962	−	21.9904i	−0.499137	−	0.864531i	−1.00000		0.000995924i	$0.999683\pi$
$648$		0			0
$649$	−9.00000	−	5.19615i	−0.353281	−	0.203967i
$650$	−1.73205	+	3.00000i	−0.0679366	+	0.117670i
$651$		0			0
$652$	6.19615	+	10.7321i	0.242660	+	0.420300i
$653$			22.1436i			0.866546i	0.901263	+	0.433273i	$0.142641\pi$
$653$			22.1436i			0.866546i	−0.901263	+	0.433273i	$0.857359\pi$
$654$		0			0
$655$	16.3923			0.640500
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$		0			0
$658$	7.79423	−	22.5000i	0.303851	−	0.877141i
$659$	17.7058	+	10.2224i	0.689719	+	0.398209i	0.803507	−	0.595296i	$-0.202965\pi$
$659$	17.7058	+	10.2224i	0.689719	+	0.398209i	−0.113788	+	0.993505i	$0.536298\pi$
$660$		0			0
$661$	−35.3827	−	20.4282i	−1.37623	−	0.794565i	−0.384524	−	0.923115i	$-0.625634\pi$
$661$	−35.3827	−	20.4282i	−1.37623	−	0.794565i	−0.991703	+	0.128550i	$0.958968\pi$
$662$	−6.92820	−	4.00000i	−0.269272	−	0.155464i
$663$		0			0
$664$	−0.696152	−	0.401924i	−0.0270160	−	0.0155977i
$665$	−4.09808	+	11.8301i	−0.158917	+	0.458753i
$666$		0			0
$667$	2.19615	−	3.80385i	0.0850354	−	0.147286i
$668$	10.3923			0.402090
$669$		0			0
$670$			4.00000i			0.154533i
$671$	−0.588457	−	1.01924i	−0.0227171	−	0.0393472i
$672$		0			0
$673$	−13.4904	+	23.3660i	−0.520016	+	0.900694i	0.479713	+	0.877425i	$0.340741\pi$
$673$	−13.4904	+	23.3660i	−0.520016	+	0.900694i	−0.999729	+	0.0232688i	$0.992593\pi$
$674$	8.66025	+	5.00000i	0.333581	+	0.192593i
$675$		0			0
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	14.4904	+	25.0981i	0.556911	+	0.964597i	0.997752	+	0.0670125i	$0.0213467\pi$
$677$	14.4904	+	25.0981i	0.556911	+	0.964597i	−0.440842	+	0.897585i	$0.645320\pi$
$678$		0			0
$679$	13.3923	−	38.6603i	0.513949	−	1.48364i
$680$		0			0
$681$		0			0
$682$		−	2.78461i		−	0.106628i
$683$	36.7750	−	21.2321i	1.40716	−	0.812422i	0.412043	−	0.911164i	$-0.364815\pi$
$683$	36.7750	−	21.2321i	1.40716	−	0.812422i	0.995113	+	0.0987426i	$0.0314820\pi$
$684$		0			0
$685$			10.7321i			0.410051i
$686$	16.4545	+	8.50000i	0.628235	+	0.324532i
$687$		0			0
$688$	−7.19615			−0.274351
$689$	−18.5885	+	32.1962i	−0.708164	+	1.22658i
$690$		0			0
$691$	16.3923	−	9.46410i	0.623593	−	0.360031i	−0.154674	−	0.987966i	$-0.549433\pi$
$691$	16.3923	−	9.46410i	0.623593	−	0.360031i	0.778266	+	0.627934i	$0.216099\pi$
$692$	2.19615			0.0834852
$693$		0			0
$694$	27.2487			1.03435
$695$	13.9019	−	8.02628i	0.527330	−	0.304454i
$696$		0			0
$697$		0			0
$698$	−4.39230			−0.166251
$699$		0			0
$700$	2.50000	+	0.866025i	0.0944911	+	0.0327327i
$701$		−	9.67949i		−	0.365589i	−0.983151	−	0.182795i	$-0.941486\pi$
$701$		−	9.67949i		−	0.365589i	0.983151	−	0.182795i	$-0.0585144\pi$
$702$		0			0
$703$	17.1962	−	9.92820i	0.648565	−	0.374449i
$704$			1.26795i			0.0477876i
$705$		0			0
$706$	26.4904	−	15.2942i	0.996979	−	0.575606i
$707$	0.401924	+	2.08846i	0.0151159	+	0.0785445i
$708$		0			0
$709$	2.60770	+	4.51666i	0.0979340	+	0.169627i	0.910829	−	0.412783i	$-0.135443\pi$
$709$	2.60770	+	4.51666i	0.0979340	+	0.169627i	−0.812895	+	0.582410i	$0.802110\pi$
$710$	−0.633975	−	1.09808i	−0.0237926	−	0.0412101i
$711$		0			0
$712$	−14.1962	−	8.19615i	−0.532023	−	0.307164i
$713$	−10.3923	+	18.0000i	−0.389195	+	0.674105i
$714$		0			0
$715$	−2.19615	−	3.80385i	−0.0821314	−	0.142256i
$716$			6.58846i			0.246222i
$717$		0			0
$718$	26.1962			0.977632
$719$	20.7846	−	36.0000i	0.775135	−	1.34257i	−0.159583	−	0.987184i	$-0.551015\pi$
$719$	20.7846	−	36.0000i	0.775135	−	1.34257i	0.934718	−	0.355389i	$-0.115652\pi$
$720$		0			0
$721$	31.5000	−	6.06218i	1.17312	−	0.225767i
$722$	−2.93782	−	1.69615i	−0.109334	−	0.0631243i
$723$		0			0
$724$	6.40192	+	3.69615i	0.237926	+	0.137366i
$725$	0.401924	+	0.232051i	0.0149271	+	0.00861815i
$726$		0			0
$727$	−0.215390	−	0.124356i	−0.00798838	−	0.00461210i	0.496000	−	0.868322i	$-0.334801\pi$
$727$	−0.215390	−	0.124356i	−0.00798838	−	0.00461210i	−0.503989	+	0.863710i	$0.668135\pi$
$728$	−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
$733$		−	4.05256i		−	0.149685i	−0.997195	−	0.0748423i	$-0.976155\pi$
$733$		−	4.05256i		−	0.149685i	0.997195	−	0.0748423i	$-0.0238454\pi$
$734$	9.40192	+	16.2846i	0.347031	+	0.601076i
$735$		0			0
$736$	4.73205	−	8.19615i	0.174426	−	0.302114i
$737$	−4.39230	−	2.53590i	−0.161793	−	0.0934110i
$738$		0			0
$739$	14.5885	+	25.2679i	0.536645	+	0.929497i	0.999082	+	0.0428442i	$0.0136419\pi$
$739$	14.5885	+	25.2679i	0.536645	+	0.929497i	−0.462437	+	0.886652i	$0.653025\pi$
$740$	−2.09808	−	3.63397i	−0.0771268	−	0.133588i
$741$		0			0
$742$	26.8301	+	9.29423i	0.984965	+	0.341202i
$743$	−38.6769	+	22.3301i	−1.41892	+	0.819213i	−0.996204	−	0.0870500i	$-0.972256\pi$
$743$	−38.6769	+	22.3301i	−1.41892	+	0.819213i	−0.422714	+	0.906263i	$0.638923\pi$
$744$		0			0
$745$		−	12.0000i		−	0.439646i
$746$	0.169873	−	0.0980762i	0.00621949	−	0.00359083i
$747$		0			0
$748$		0			0
$749$	−1.79423	+	5.17949i	−0.0655597	+	0.189255i
$750$		0			0
$751$	−42.3923			−1.54692			−0.773459	−	0.633847i	$-0.781475\pi$
$751$	−42.3923			−1.54692			−0.773459	+	0.633847i	$0.781475\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$		0			0
$754$	−1.39230	+	0.803848i	−0.0507048	+	0.0292744i
$755$	6.19615			0.225501
$756$		0			0
$757$	22.5885			0.820991			0.410496	−	0.911863i	$-0.365356\pi$
$757$	22.5885			0.820991			0.410496	+	0.911863i	$0.365356\pi$
$758$	26.3205	−	15.1962i	0.956004	−	0.551949i
$759$		0			0
$760$	−2.36603	+	4.09808i	−0.0858248	+	0.148653i
$761$	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
$763$	6.39230	−	5.53590i	0.231417	−	0.200413i
$764$			3.46410i			0.125327i
$765$		0			0
$766$	−1.20577	+	0.696152i	−0.0435663	+	0.0251530i
$767$		−	28.3923i		−	1.02519i
$768$		0			0
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	−0.236433	−	0.971648i	$-0.575978\pi$
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	0.723255	+	0.690581i	$0.242645\pi$
$770$	−2.53590	+	2.19615i	−0.0913874	+	0.0791438i
$771$		0			0
$772$	12.0981	+	20.9545i	0.435419	+	0.754168i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$		0			0
$775$	−1.90192	−	1.09808i	−0.0683191	−	0.0394441i
$776$	7.73205	−	13.3923i	0.277564	−	0.480756i
$777$		0			0
$778$	15.3564	+	26.5981i	0.550554	+	0.953587i
$779$			42.5885i			1.52589i
$780$		0			0
$781$	1.60770			0.0575279
$782$		0			0
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	0.294229	+	0.169873i	0.0105015	+	0.00606303i
$786$		0			0
$787$	−33.9904	−	19.6244i	−1.21163	−	0.699533i	−0.248513	−	0.968629i	$-0.579942\pi$
$787$	−33.9904	−	19.6244i	−1.21163	−	0.699533i	−0.963113	+	0.269096i	$0.913275\pi$
$788$	5.49038	+	3.16987i	0.195587	+	0.112922i
$789$		0			0
$790$	−14.3660	−	8.29423i	−0.511120	−	0.295095i
$791$	32.1962	+	37.1769i	1.14476	+	1.32186i
$792$		0			0
$793$	1.60770	−	2.78461i	0.0570909	−	0.0988844i
$794$	0.588457			0.0208836
$795$		0			0
$796$		−	6.92820i		−	0.245564i
$797$	−21.5885	−	37.3923i	−0.764702	−	1.32450i	−0.940404	−	0.340060i	$-0.889553\pi$
$797$	−21.5885	−	37.3923i	−0.764702	−	1.32450i	0.175701	−	0.984444i	$-0.443781\pi$
$798$		0			0
$799$		0			0
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	−13.7942	−	23.8923i	−0.487091	−	0.843667i
$803$	−4.39230	−	7.60770i	−0.155001	−	0.268470i
$804$		0			0
$805$	24.5885	−	4.73205i	0.866629	−	0.166783i
$806$	6.58846	−	3.80385i	0.232069	−	0.133985i
$807$		0			0
$808$			0.803848i			0.0282793i
$809$	6.48076	−	3.74167i	0.227851	−	0.131550i	−0.381729	−	0.924274i	$-0.624671\pi$
$809$	6.48076	−	3.74167i	0.227851	−	0.131550i	0.609580	+	0.792724i	$0.291338\pi$
$810$		0			0
$811$			51.4641i			1.80715i	0.428431	+	0.903575i	$0.359067\pi$
$811$			51.4641i			1.80715i	−0.428431	+	0.903575i	$0.640933\pi$
$812$	0.803848	+	0.928203i	0.0282095	+	0.0325735i
$813$		0			0
$814$	5.32051			0.186484
$815$	−6.19615	+	10.7321i	−0.217042	+	0.375927i
$816$		0			0
$817$	29.4904	−	17.0263i	1.03174	−	0.595674i
$818$	34.5167			1.20685
$819$		0			0
$820$	9.00000			0.314294
$821$	−16.2058	+	9.35641i	−0.565585	+	0.326541i	−0.755384	−	0.655282i	$-0.772550\pi$
$821$	−16.2058	+	9.35641i	−0.565585	+	0.326541i	0.189799	+	0.981823i	$0.439216\pi$
$822$		0			0
$823$	−25.6962	+	44.5070i	−0.895712	+	1.55142i	−0.0627901	+	0.998027i	$0.520000\pi$
$823$	−25.6962	+	44.5070i	−0.895712	+	1.55142i	−0.832921	+	0.553391i	$0.813333\pi$
$824$	12.1244			0.422372
$825$		0			0
$826$	−21.2942	+	4.09808i	−0.740921	+	0.142590i
$827$		−	37.6410i		−	1.30891i	−0.756103	−	0.654453i	$-0.772899\pi$
$827$		−	37.6410i		−	1.30891i	0.756103	−	0.654453i	$-0.227101\pi$
$828$		0			0
$829$	−6.18653	+	3.57180i	−0.214867	+	0.124054i	−0.603571	−	0.797309i	$-0.706256\pi$
$829$	−6.18653	+	3.57180i	−0.214867	+	0.124054i	0.388704	+	0.921363i	$0.372923\pi$
$830$		−	0.803848i		−	0.0279020i
$831$		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
$839$	−7.09808	+	12.2942i	−0.245053	+	0.424444i	−0.962146	−	0.272533i	$-0.912139\pi$
$839$	−7.09808	+	12.2942i	−0.245053	+	0.424444i	0.717094	+	0.696977i	$0.245472\pi$
$840$		0			0
$841$	−14.3923	−	24.9282i	−0.496286	−	0.859593i
$842$		−	21.9808i		−	0.757507i
$843$		0			0
$844$	−10.5885			−0.364470
$845$	−0.500000	+	0.866025i	−0.0172005	+	0.0297922i
$846$		0			0
$847$	4.69615	+	24.4019i	0.161362	+	0.838460i
$848$	9.29423	+	5.36603i	0.319165	+	0.184270i
$849$		0			0
$850$		0			0
$851$	−34.3923	−	19.8564i	−1.17895	−	0.680669i
$852$		0			0
$853$	38.7846	+	22.3923i	1.32796	+	0.766698i	0.984984	−	0.172646i	$-0.0552318\pi$
$853$	38.7846	+	22.3923i	1.32796	+	0.766698i	0.342976	+	0.939344i	$0.388565\pi$
$854$	−2.32051	−	0.803848i	−0.0794062	−	0.0275071i
$855$		0			0
$856$	−1.03590	+	1.79423i	−0.0354063	+	0.0613255i
$857$	48.5885			1.65975			0.829875	−	0.557949i	$-0.188412\pi$
$857$	48.5885			1.65975			0.829875	+	0.557949i	$0.188412\pi$
$858$		0			0
$859$			26.1962i			0.893801i	0.894584	+	0.446901i	$0.147472\pi$
$859$			26.1962i			0.893801i	−0.894584	+	0.446901i	$0.852528\pi$
$860$	−3.59808	−	6.23205i	−0.122693	−	0.212511i
$861$		0			0
$862$	−1.39230	+	2.41154i	−0.0474221	+	0.0821375i
$863$	−4.60770	−	2.66025i	−0.156848	−	0.0905561i	0.419522	−	0.907745i	$-0.362198\pi$
$863$	−4.60770	−	2.66025i	−0.156848	−	0.0905561i	−0.576370	+	0.817189i	$0.695531\pi$
$864$		0			0
$865$	1.09808	+	1.90192i	0.0373357	+	0.0646673i
$866$	9.00000	+	15.5885i	0.305832	+	0.529717i
$867$		0			0
$868$	−3.80385	−	4.39230i	−0.129111	−	0.149085i
$869$	18.2154	−	10.5167i	0.617915	−	0.356753i
$870$		0			0
$871$		−	13.8564i		−	0.469506i
$872$	2.76795	−	1.59808i	0.0937346	−	0.0541177i
$873$		0			0
$874$			44.7846i			1.51486i
$875$	0.500000	+	2.59808i	0.0169031	+	0.0878310i
$876$		0			0
$877$	−41.7654			−1.41032			−0.705158	−	0.709050i	$-0.749124\pi$
$877$	−41.7654			−1.41032			−0.705158	+	0.709050i	$0.749124\pi$
$878$	6.16987	−	10.6865i	0.208223	−	0.360653i
$879$		0			0
$880$	−1.09808	+	0.633975i	−0.0370161	+	0.0213713i
$881$	−4.39230			−0.147981			−0.0739903	−	0.997259i	$-0.523573\pi$
$881$	−4.39230			−0.147981			−0.0739903	+	0.997259i	$0.523573\pi$
$882$		0			0
$883$	−44.3731			−1.49327			−0.746636	−	0.665232i	$-0.768332\pi$
$883$	−44.3731			−1.49327			−0.746636	+	0.665232i	$0.768332\pi$
$884$		0			0
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	28.6077			0.960552			0.480276	−	0.877117i	$-0.340536\pi$
$887$	28.6077			0.960552			0.480276	+	0.877117i	$0.340536\pi$
$888$		0			0
$889$	4.69615	+	24.4019i	0.157504	+	0.818414i
$890$		−	16.3923i		−	0.549471i
$891$		0			0
$892$	−8.89230	+	5.13397i	−0.297736	+	0.171898i
$893$			42.5885i			1.42517i
$894$		0			0
$895$	−5.70577	+	3.29423i	−0.190723	+	0.110114i
$896$	1.73205	+	2.00000i	0.0578638	+	0.0668153i
$897$		0			0
$898$	−10.7942	−	18.6962i	−0.360208	−	0.623899i
$899$	−0.509619	−	0.882686i	−0.0169967	−	0.0294392i
$900$		0			0
$901$		0			0
$902$	−5.70577	+	9.88269i	−0.189981	+	0.329057i
$903$		0			0
$904$	9.29423	+	16.0981i	0.309121	+	0.535414i
$905$			7.39230i			0.245729i
$906$		0			0
$907$	33.1962			1.10226			0.551130	−	0.834419i	$-0.314197\pi$
$907$	33.1962			1.10226			0.551130	+	0.834419i	$0.314197\pi$
$908$	−2.19615	+	3.80385i	−0.0728819	+	0.126235i
$909$		0			0
$910$	−8.66025	−	3.00000i	−0.287085	−	0.0994490i
$911$	−4.90192	−	2.83013i	−0.162408	−	0.0937663i	0.416593	−	0.909093i	$-0.363224\pi$
$911$	−4.90192	−	2.83013i	−0.162408	−	0.0937663i	−0.579001	+	0.815327i	$0.696557\pi$
$912$		0			0
$913$	0.882686	+	0.509619i	0.0292126	+	0.0168659i
$914$	−15.9282	−	9.19615i	−0.526858	−	0.304182i
$915$		0			0
$916$	24.1865	+	13.9641i	0.799146	+	0.461387i
$917$	8.19615	+	42.5885i	0.270661	+	1.40639i
$918$		0			0
$919$	13.2942	−	23.0263i	0.438536	−	0.759567i	−0.559041	−	0.829140i	$-0.688830\pi$
$919$	13.2942	−	23.0263i	0.438536	−	0.759567i	0.997577	+	0.0695733i	$0.0221638\pi$
$920$	9.46410			0.312022
$921$		0			0
$922$		−	5.19615i		−	0.171126i
$923$	2.19615	+	3.80385i	0.0722872	+	0.125205i
$924$		0			0
$925$	2.09808	−	3.63397i	0.0689843	−	0.119484i
$926$	−20.2583	−	11.6962i	−0.665730	−	0.384359i
$927$		0			0
$928$	0.232051	+	0.401924i	0.00761744	+	0.0131938i
$929$	−16.2846	−	28.2058i	−0.534281	−	0.925401i	−0.999198	−	0.0400471i	$-0.987249\pi$
$929$	−16.2846	−	28.2058i	−0.534281	−	0.925401i	0.464917	−	0.885354i	$-0.346084\pi$
$930$		0			0
$931$	−32.7846	−	4.73205i	−1.07447	−	0.155087i
$932$	4.09808	−	2.36603i	0.134237	−	0.0775017i
$933$		0			0
$934$		−	17.1962i		−	0.562675i
$935$		0			0
$936$		0			0
$937$		−	11.4115i		−	0.372799i	−0.982474	−	0.186399i	$-0.940318\pi$
$937$		−	11.4115i		−	0.372799i	0.982474	−	0.186399i	$-0.0596818\pi$
$938$	−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	$-0.972523\pi$
$941$	−12.9904	+	22.5000i	−0.423474	+	0.733479i	0.572802	+	0.819694i	$0.305856\pi$
$942$		0			0
$943$	73.7654	−	42.5885i	2.40213	−	1.38687i
$944$	−8.19615			−0.266762
$945$		0			0
$946$	9.12436			0.296658
$947$	51.5885	−	29.7846i	1.67640	−	0.967870i	0.712474	−	0.701699i	$-0.247575\pi$
$947$	51.5885	−	29.7846i	1.67640	−	0.967870i	0.963926	−	0.266171i	$-0.0857586\pi$
$948$		0			0
$949$	12.0000	−	20.7846i	0.389536	−	0.674697i
$950$	−4.73205			−0.153528
$951$		0			0
$952$		0			0
$953$			4.73205i			0.153286i	0.997059	+	0.0766431i	$0.0244202\pi$
$953$			4.73205i			0.153286i	−0.997059	+	0.0766431i	$0.975580\pi$
$954$		0			0
$955$	−3.00000	+	1.73205i	−0.0970777	+	0.0560478i
$956$			21.1244i			0.683210i
$957$		0			0
$958$	9.00000	−	5.19615i	0.290777	−	0.167880i
$959$	−27.8827	+	5.36603i	−0.900379	+	0.173278i
$960$		0			0
$961$	−13.0885	−	22.6699i	−0.422208	−	0.731286i
$962$	7.26795	+	12.5885i	0.234328	+	0.405868i
$963$		0			0
$964$	17.8923	+	10.3301i	0.576272	+	0.332711i
$965$	−12.0981	+	20.9545i	−0.389451	+	0.674549i
$966$		0			0
$967$	8.00000	+	13.8564i	0.257263	+	0.445592i	0.965508	−	0.260375i	$-0.0838461\pi$
$967$	8.00000	+	13.8564i	0.257263	+	0.445592i	−0.708245	+	0.705967i	$0.750513\pi$
$968$			9.39230i			0.301880i
$969$		0			0
$970$	15.4641			0.496522
$971$	13.3923	−	23.1962i	0.429780	−	0.744400i	−0.567074	−	0.823667i	$-0.691925\pi$
$971$	13.3923	−	23.1962i	0.429780	−	0.744400i	0.996853	+	0.0792670i	$0.0252580\pi$
$972$		0			0
$973$	27.8038	+	32.1051i	0.891350	+	1.02924i
$974$	29.4449	+	17.0000i	0.943474	+	0.544715i
$975$		0			0
$976$	−0.803848	−	0.464102i	−0.0257305	−	0.0148555i
$977$	16.3923	+	9.46410i	0.524436	+	0.302783i	0.738748	−	0.673982i	$-0.235417\pi$
$977$	16.3923	+	9.46410i	0.524436	+	0.302783i	−0.214312	+	0.976765i	$0.568751\pi$
$978$		0			0
$979$	18.0000	+	10.3923i	0.575282	+	0.332140i
$980$	−1.00000	+	6.92820i	−0.0319438	+	0.221313i
$981$		0			0
$982$	1.43782	−	2.49038i	0.0458827	−	0.0794713i
$983$	10.6077			0.338333			0.169166	−	0.985587i	$-0.445892\pi$
$983$	10.6077			0.338333			0.169166	+	0.985587i	$0.445892\pi$
$984$		0			0
$985$			6.33975i			0.202001i
$986$		0			0
$987$		0			0
$988$	8.19615	−	14.1962i	0.260754	−	0.451640i
$989$	−58.9808	−	34.0526i	−1.87548	−	1.08281i
$990$		0			0
$991$	22.2942	+	38.6147i	0.708200	+	1.22664i	0.965524	+	0.260313i	$0.0838256\pi$
$991$	22.2942	+	38.6147i	0.708200	+	1.22664i	−0.257325	+	0.966325i	$0.582841\pi$
$992$	−1.09808	−	1.90192i	−0.0348640	−	0.0603861i
$993$		0			0
$994$	2.53590	−	2.19615i	0.0804338	−	0.0696577i
$995$	6.00000	−	3.46410i	0.190213	−	0.109819i
$996$		0			0
$997$			13.5167i			0.428077i	0.976825	+	0.214038i	$0.0686618\pi$
$997$			13.5167i			0.428077i	−0.976825	+	0.214038i	$0.931338\pi$
$998$	5.02628	−	2.90192i	0.159104	−	0.0918588i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.a.1601.1		4
3.2	odd	2		630.2.t.a.551.2	yes	4
7.3	odd	6		1890.2.bk.a.521.1		4
9.4	even	3		630.2.bk.a.131.1	yes	4
9.5	odd	6		1890.2.bk.a.341.2		4
21.17	even	6		630.2.bk.a.101.2	yes	4
63.31	odd	6		630.2.t.a.311.2	✓	4
63.59	even	6	inner	1890.2.t.a.1151.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.a.311.2	✓	4	63.31	odd	6
630.2.t.a.551.2	yes	4	3.2	odd	2
630.2.bk.a.101.2	yes	4	21.17	even	6
630.2.bk.a.131.1	yes	4	9.4	even	3
1890.2.t.a.1151.1		4	63.59	even	6	inner
1890.2.t.a.1601.1		4	1.1	even	1	trivial
1890.2.bk.a.341.2		4	9.5	odd	6
1890.2.bk.a.521.1		4	7.3	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} -1.26795i q^{11} +(3.00000 - 1.73205i) q^{13} +(-1.73205 - 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.09808 + 2.36603i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.633975 + 1.09808i) q^{22} -9.46410i q^{23} +1.00000 q^{25} +(-1.73205 + 3.00000i) q^{26} +(2.50000 + 0.866025i) q^{28} +(0.401924 + 0.232051i) q^{29} +(-1.90192 - 1.09808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.500000 + 2.59808i) q^{35} +(2.09808 - 3.63397i) q^{37} -4.73205 q^{38} +1.00000i q^{40} +(4.50000 + 7.79423i) q^{41} +(3.59808 - 6.23205i) q^{43} +(-1.09808 - 0.633975i) q^{44} +(4.73205 + 8.19615i) q^{46} +(4.50000 + 7.79423i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-0.866025 + 0.500000i) q^{50} -3.46410i q^{52} +(-9.29423 + 5.36603i) q^{53} -1.26795i q^{55} +(-2.59808 + 0.500000i) q^{56} -0.464102 q^{58} +(4.09808 - 7.09808i) q^{59} +(0.803848 - 0.464102i) q^{61} +2.19615 q^{62} -1.00000 q^{64} +(3.00000 - 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.73205 - 2.00000i) q^{70} +1.26795i q^{71} +(6.00000 - 3.46410i) q^{73} +4.19615i q^{74} +(4.09808 - 2.36603i) q^{76} +(3.29423 - 0.633975i) q^{77} +(8.29423 + 14.3660i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-7.79423 - 4.50000i) q^{82} +(-0.401924 + 0.696152i) q^{83} +7.19615i q^{86} +1.26795 q^{88} +(-8.19615 + 14.1962i) q^{89} +(6.00000 + 6.92820i) q^{91} +(-8.19615 - 4.73205i) q^{92} +(-7.79423 - 4.50000i) q^{94} +(4.09808 + 2.36603i) q^{95} +(-13.3923 - 7.73205i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} + 2 q^{7}+O(q^{10}) \) 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

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Database

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