LMFDB - Embedded newform 1350.2.j.g.1099.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(199,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1350.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.j (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:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1099.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.1099
Dual form			1350.2.j.g.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.389270 + 0.224745i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.389270 + 0.224745i) q^{7} -1.00000i q^{8} +(-2.44949 + 4.24264i) q^{11} +(0.389270 - 0.224745i) q^{13} +(-0.224745 - 0.389270i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.89898i q^{17} -7.44949 q^{19} +(4.24264 - 2.44949i) q^{22} +(-2.12132 + 1.22474i) q^{23} -0.449490 q^{26} +0.449490i q^{28} +(1.22474 - 2.12132i) q^{29} +(-2.22474 - 3.85337i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.44949 + 4.24264i) q^{34} -11.3485i q^{37} +(6.45145 + 3.72474i) q^{38} +(4.50000 + 7.79423i) q^{41} +(2.20881 + 1.27526i) q^{43} -4.89898 q^{44} +2.44949 q^{46} +(-9.43879 - 5.44949i) q^{47} +(-3.39898 - 5.88721i) q^{49} +(0.389270 + 0.224745i) q^{52} -3.55051i q^{53} +(0.224745 - 0.389270i) q^{56} +(-2.12132 + 1.22474i) q^{58} +(2.72474 + 4.71940i) q^{59} +(-4.00000 + 6.92820i) q^{61} +4.44949i q^{62} -1.00000 q^{64} +(0.301783 - 0.174235i) q^{67} +(4.24264 - 2.44949i) q^{68} -13.3485 q^{71} +1.00000i q^{73} +(-5.67423 + 9.82806i) q^{74} +(-3.72474 - 6.45145i) q^{76} +(-1.90702 + 1.10102i) q^{77} +(8.34847 - 14.4600i) q^{79} -9.00000i q^{82} +(4.71940 + 2.72474i) q^{83} +(-1.27526 - 2.20881i) q^{86} +(4.24264 + 2.44949i) q^{88} -9.00000 q^{89} +0.202041 q^{91} +(-2.12132 - 1.22474i) q^{92} +(5.44949 + 9.43879i) q^{94} +(-7.61926 - 4.39898i) q^{97} +6.79796i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 8 q^{14} - 4 q^{16} - 40 q^{19} + 16 q^{26} - 8 q^{31} + 36 q^{41} + 12 q^{49} - 8 q^{56} + 12 q^{59} - 32 q^{61} - 8 q^{64} - 48 q^{71} - 16 q^{74} - 20 q^{76} + 8 q^{79} - 20 q^{86} - 72 q^{89} + 80 q^{91} + 24 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 + 8 * q^14 - 4 * q^16 - 40 * q^19 + 16 * q^26 - 8 * q^31 + 36 * q^41 + 12 * q^49 - 8 * q^56 + 12 * q^59 - 32 * q^61 - 8 * q^64 - 48 * q^71 - 16 * q^74 - 20 * q^76 + 8 * q^79 - 20 * q^86 - 72 * q^89 + 80 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.389270	+	0.224745i	0.147130	+	0.0849456i	0.571758	−	0.820422i	$-0.306262\pi$
$7$	0.389270	+	0.224745i	0.147130	+	0.0849456i	−0.424628	+	0.905368i	$0.639595\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	0.214600	+	0.976702i	$0.431155\pi$
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	−0.953149	+	0.302502i	$0.902178\pi$
$12$		0			0
$13$	0.389270	−	0.224745i	0.107964	−	0.0623330i	−0.445046	−	0.895508i	$-0.646813\pi$
$13$	0.389270	−	0.224745i	0.107964	−	0.0623330i	0.553010	+	0.833175i	$0.313479\pi$
$14$	−0.224745	−	0.389270i	−0.0600656	−	0.104037i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	4.89898i		−	1.18818i	−0.804400	−	0.594089i	$-0.797513\pi$
$17$		−	4.89898i		−	1.18818i	0.804400	−	0.594089i	$-0.202487\pi$
$18$		0			0
$19$	−7.44949			−1.70903			−0.854515	−	0.519427i	$-0.826146\pi$
$19$	−7.44949			−1.70903			−0.854515	+	0.519427i	$0.826146\pi$
$20$		0			0
$21$		0			0
$22$	4.24264	−	2.44949i	0.904534	−	0.522233i
$23$	−2.12132	+	1.22474i	−0.442326	+	0.255377i	−0.704584	−	0.709621i	$-0.748866\pi$
$23$	−2.12132	+	1.22474i	−0.442326	+	0.255377i	0.262258	+	0.964998i	$0.415533\pi$
$24$		0			0
$25$		0			0
$26$	−0.449490			−0.0881522
$27$		0			0
$28$			0.449490i			0.0849456i
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	−0.729616	−	0.683857i	$-0.760301\pi$
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	0.957046	+	0.289938i	$0.0936346\pi$
$30$		0			0
$31$	−2.22474	−	3.85337i	−0.399576	−	0.692086i	0.594098	−	0.804393i	$-0.297509\pi$
$31$	−2.22474	−	3.85337i	−0.399576	−	0.692086i	−0.993674	+	0.112307i	$0.964176\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−2.44949	+	4.24264i	−0.420084	+	0.727607i
$35$		0			0
$36$		0			0
$37$		−	11.3485i		−	1.86568i	−0.360295	−	0.932838i	$-0.617324\pi$
$37$		−	11.3485i		−	1.86568i	0.360295	−	0.932838i	$-0.382676\pi$
$38$	6.45145	+	3.72474i	1.04656	+	0.604233i
$39$		0			0
$40$		0			0
$41$	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
$43$	2.20881	+	1.27526i	0.336840	+	0.194475i	0.658874	−	0.752254i	$-0.271033\pi$
$43$	2.20881	+	1.27526i	0.336840	+	0.194475i	−0.322034	+	0.946728i	$0.604366\pi$
$44$	−4.89898			−0.738549
$45$		0			0
$46$	2.44949			0.361158
$47$	−9.43879	−	5.44949i	−1.37679	−	0.794890i	−0.385018	−	0.922909i	$-0.625805\pi$
$47$	−9.43879	−	5.44949i	−1.37679	−	0.794890i	−0.991772	+	0.128019i	$0.959138\pi$
$48$		0			0
$49$	−3.39898	−	5.88721i	−0.485568	−	0.841029i
$50$		0			0
$51$		0			0
$52$	0.389270	+	0.224745i	0.0539820	+	0.0311665i
$53$		−	3.55051i		−	0.487700i	−0.969813	−	0.243850i	$-0.921590\pi$
$53$		−	3.55051i		−	0.487700i	0.969813	−	0.243850i	$-0.0784105\pi$
$54$		0			0
$55$		0			0
$56$	0.224745	−	0.389270i	0.0300328	−	0.0520183i
$57$		0			0
$58$	−2.12132	+	1.22474i	−0.278543	+	0.160817i
$59$	2.72474	+	4.71940i	0.354732	+	0.614413i	0.987072	−	0.160278i	$-0.0512389\pi$
$59$	2.72474	+	4.71940i	0.354732	+	0.614413i	−0.632340	+	0.774691i	$0.717906\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$			4.44949i			0.565086i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	0.301783	−	0.174235i	0.0368687	−	0.0212861i	−0.481452	−	0.876472i	$-0.659891\pi$
$67$	0.301783	−	0.174235i	0.0368687	−	0.0212861i	0.518321	+	0.855186i	$0.326557\pi$
$68$	4.24264	−	2.44949i	0.514496	−	0.297044i
$69$		0			0
$70$		0			0
$71$	−13.3485			−1.58417			−0.792086	−	0.610410i	$-0.791005\pi$
$71$	−13.3485			−1.58417			−0.792086	+	0.610410i	$0.791005\pi$
$72$		0			0
$73$			1.00000i			0.117041i	0.998286	+	0.0585206i	$0.0186383\pi$
$73$			1.00000i			0.117041i	−0.998286	+	0.0585206i	$0.981362\pi$
$74$	−5.67423	+	9.82806i	−0.659616	+	1.14249i
$75$		0			0
$76$	−3.72474	−	6.45145i	−0.427258	−	0.740032i
$77$	−1.90702	+	1.10102i	−0.217325	+	0.125473i
$78$		0			0
$79$	8.34847	−	14.4600i	0.939276	−	1.62687i	0.172451	−	0.985018i	$-0.444831\pi$
$79$	8.34847	−	14.4600i	0.939276	−	1.62687i	0.766825	−	0.641856i	$-0.221835\pi$
$80$		0			0
$81$		0			0
$82$		−	9.00000i		−	0.993884i
$83$	4.71940	+	2.72474i	0.518021	+	0.299080i	0.736125	−	0.676846i	$-0.236654\pi$
$83$	4.71940	+	2.72474i	0.518021	+	0.299080i	−0.218104	+	0.975926i	$0.569987\pi$
$84$		0			0
$85$		0			0
$86$	−1.27526	−	2.20881i	−0.137514	−	0.238182i
$87$		0			0
$88$	4.24264	+	2.44949i	0.452267	+	0.261116i
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$		0			0
$91$	0.202041			0.0211797
$92$	−2.12132	−	1.22474i	−0.221163	−	0.127688i
$93$		0			0
$94$	5.44949	+	9.43879i	0.562072	+	0.973537i
$95$		0			0
$96$		0			0
$97$	−7.61926	−	4.39898i	−0.773618	−	0.446649i	0.0605456	−	0.998165i	$-0.480716\pi$
$97$	−7.61926	−	4.39898i	−0.773618	−	0.446649i	−0.834164	+	0.551517i	$0.814049\pi$
$98$			6.79796i			0.686698i
$99$		0			0
$100$		0			0
$101$	4.22474	−	7.31747i	0.420378	−	0.728116i	−0.575599	−	0.817732i	$-0.695231\pi$
$101$	4.22474	−	7.31747i	0.420378	−	0.728116i	0.995976	+	0.0896167i	$0.0285642\pi$
$102$		0			0
$103$	−14.4600	+	8.34847i	−1.42478	+	0.822599i	−0.996703	−	0.0811413i	$-0.974143\pi$
$103$	−14.4600	+	8.34847i	−1.42478	+	0.822599i	−0.428081	+	0.903740i	$0.640810\pi$
$104$	−0.224745	−	0.389270i	−0.0220380	−	0.0381710i
$105$		0			0
$106$	−1.77526	+	3.07483i	−0.172428	+	0.298654i
$107$		−	9.24745i		−	0.893985i	−0.894538	−	0.446992i	$-0.852495\pi$
$107$		−	9.24745i		−	0.893985i	0.894538	−	0.446992i	$-0.147505\pi$
$108$		0			0
$109$	−5.55051			−0.531642			−0.265821	−	0.964022i	$-0.585643\pi$
$109$	−5.55051			−0.531642			−0.265821	+	0.964022i	$0.585643\pi$
$110$		0			0
$111$		0			0
$112$	−0.389270	+	0.224745i	−0.0367825	+	0.0212364i
$113$	−3.55159	+	2.05051i	−0.334105	+	0.192896i	−0.657662	−	0.753313i	$-0.728455\pi$
$113$	−3.55159	+	2.05051i	−0.334105	+	0.192896i	0.323557	+	0.946209i	$0.395121\pi$
$114$		0			0
$115$		0			0
$116$	2.44949			0.227429
$117$		0			0
$118$		−	5.44949i		−	0.501666i
$119$	1.10102	−	1.90702i	0.100930	−	0.174817i
$120$		0			0
$121$	−6.50000	−	11.2583i	−0.590909	−	1.02348i
$122$	6.92820	−	4.00000i	0.627250	−	0.362143i
$123$		0			0
$124$	2.22474	−	3.85337i	0.199788	−	0.346043i
$125$		0			0
$126$		0			0
$127$			3.34847i			0.297129i	0.988903	+	0.148564i	$0.0474652\pi$
$127$			3.34847i			0.297129i	−0.988903	+	0.148564i	$0.952535\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	−1.89898	−	3.28913i	−0.165915	−	0.287373i	0.771065	−	0.636756i	$-0.219724\pi$
$131$	−1.89898	−	3.28913i	−0.165915	−	0.287373i	−0.936980	+	0.349384i	$0.886391\pi$
$132$		0			0
$133$	−2.89986	−	1.67423i	−0.251450	−	0.145175i
$134$	−0.348469			−0.0301032
$135$		0			0
$136$	−4.89898			−0.420084
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	0.606861	−	0.794808i	$-0.292428\pi$
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	−0.384893	+	0.922961i	$0.625762\pi$
$138$		0			0
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$		0			0
$141$		0			0
$142$	11.5601	+	6.67423i	0.970103	+	0.560089i
$143$			2.20204i			0.184144i
$144$		0			0
$145$		0			0
$146$	0.500000	−	0.866025i	0.0413803	−	0.0716728i
$147$		0			0
$148$	9.82806	−	5.67423i	0.807862	−	0.466419i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$			7.44949i			0.604233i
$153$		0			0
$154$	2.20204			0.177446
$155$		0			0
$156$		0			0
$157$	−17.1455	+	9.89898i	−1.36836	+	0.790025i	−0.990719	−	0.135926i	$-0.956599\pi$
$157$	−17.1455	+	9.89898i	−1.36836	+	0.790025i	−0.377644	+	0.925951i	$0.623266\pi$
$158$	−14.4600	+	8.34847i	−1.15037	+	0.664169i
$159$		0			0
$160$		0			0
$161$	−1.10102			−0.0867726
$162$		0			0
$163$		−	7.44949i		−	0.583489i	−0.956496	−	0.291745i	$-0.905764\pi$
$163$		−	7.44949i		−	0.583489i	0.956496	−	0.291745i	$-0.0942357\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$	−2.72474	−	4.71940i	−0.211481	−	0.366296i
$167$	−16.9706	+	9.79796i	−1.31322	+	0.758189i	−0.982628	−	0.185584i	$-0.940582\pi$
$167$	−16.9706	+	9.79796i	−1.31322	+	0.758189i	−0.330593	+	0.943773i	$0.607249\pi$
$168$		0			0
$169$	−6.39898	+	11.0834i	−0.492229	+	0.852566i
$170$		0			0
$171$		0			0
$172$			2.55051i			0.194475i
$173$	−8.48528	−	4.89898i	−0.645124	−	0.372463i	0.141462	−	0.989944i	$-0.454820\pi$
$173$	−8.48528	−	4.89898i	−0.645124	−	0.372463i	−0.786586	+	0.617481i	$0.788153\pi$
$174$		0			0
$175$		0			0
$176$	−2.44949	−	4.24264i	−0.184637	−	0.319801i
$177$		0			0
$178$	7.79423	+	4.50000i	0.584202	+	0.337289i
$179$	9.24745			0.691187			0.345593	−	0.938384i	$-0.387678\pi$
$179$	9.24745			0.691187			0.345593	+	0.938384i	$0.387678\pi$
$180$		0			0
$181$	17.7980			1.32291			0.661456	−	0.749984i	$-0.269939\pi$
$181$	17.7980			1.32291			0.661456	+	0.749984i	$0.269939\pi$
$182$	−0.174973	−	0.101021i	−0.0129698	−	0.00748814i
$183$		0			0
$184$	1.22474	+	2.12132i	0.0902894	+	0.156386i
$185$		0			0
$186$		0			0
$187$	20.7846	+	12.0000i	1.51992	+	0.877527i
$188$		−	10.8990i		−	0.794890i
$189$		0			0
$190$		0			0
$191$	−0.550510	+	0.953512i	−0.0398335	+	0.0689937i	−0.885255	−	0.465106i	$-0.846016\pi$
$191$	−0.550510	+	0.953512i	−0.0398335	+	0.0689937i	0.845421	+	0.534100i	$0.179349\pi$
$192$		0			0
$193$	−17.3205	+	10.0000i	−1.24676	+	0.719816i	−0.970461	−	0.241257i	$-0.922440\pi$
$193$	−17.3205	+	10.0000i	−1.24676	+	0.719816i	−0.276296	+	0.961073i	$0.589107\pi$
$194$	4.39898	+	7.61926i	0.315828	+	0.547031i
$195$		0			0
$196$	3.39898	−	5.88721i	0.242784	−	0.420515i
$197$			0.247449i			0.0176300i	0.999961	+	0.00881500i	$0.00280594\pi$
$197$			0.247449i			0.0176300i	−0.999961	+	0.00881500i	$0.997194\pi$
$198$		0			0
$199$	13.7980			0.978111			0.489056	−	0.872253i	$-0.337341\pi$
$199$	13.7980			0.978111			0.489056	+	0.872253i	$0.337341\pi$
$200$		0			0
$201$		0			0
$202$	−7.31747	+	4.22474i	−0.514856	+	0.297252i
$203$	0.953512	−	0.550510i	0.0669234	−	0.0386382i
$204$		0			0
$205$		0			0
$206$	16.6969			1.16333
$207$		0			0
$208$			0.449490i			0.0311665i
$209$	18.2474	−	31.6055i	1.26220	−	2.18620i
$210$		0			0
$211$	1.72474	+	2.98735i	0.118736	+	0.205657i	0.919267	−	0.393634i	$-0.128782\pi$
$211$	1.72474	+	2.98735i	0.118736	+	0.205657i	−0.800531	+	0.599292i	$0.795449\pi$
$212$	3.07483	−	1.77526i	0.211180	−	0.121925i
$213$		0			0
$214$	−4.62372	+	8.00853i	−0.316071	+	0.547452i
$215$		0			0
$216$		0			0
$217$		−	2.00000i		−	0.135769i
$218$	4.80688	+	2.77526i	0.325563	+	0.187964i
$219$		0			0
$220$		0			0
$221$	−1.10102	−	1.90702i	−0.0740627	−	0.128280i
$222$		0			0
$223$	15.4135	+	8.89898i	1.03216	+	0.595920i	0.917604	−	0.397497i	$-0.130121\pi$
$223$	15.4135	+	8.89898i	1.03216	+	0.595920i	0.114560	+	0.993416i	$0.463454\pi$
$224$	0.449490			0.0300328
$225$		0			0
$226$	4.10102			0.272796
$227$	11.8226	+	6.82577i	0.784692	+	0.453042i	0.838090	−	0.545531i	$-0.183672\pi$
$227$	11.8226	+	6.82577i	0.784692	+	0.453042i	−0.0533987	+	0.998573i	$0.517005\pi$
$228$		0			0
$229$	6.57321	+	11.3851i	0.434370	+	0.752351i	0.997244	−	0.0741916i	$-0.0236376\pi$
$229$	6.57321	+	11.3851i	0.434370	+	0.752351i	−0.562874	+	0.826543i	$0.690304\pi$
$230$		0			0
$231$		0			0
$232$	−2.12132	−	1.22474i	−0.139272	−	0.0804084i
$233$		−	23.6969i		−	1.55244i	−0.630463	−	0.776219i	$-0.717135\pi$
$233$		−	23.6969i		−	1.55244i	0.630463	−	0.776219i	$-0.282865\pi$
$234$		0			0
$235$		0			0
$236$	−2.72474	+	4.71940i	−0.177366	+	0.307207i
$237$		0			0
$238$	−1.90702	+	1.10102i	−0.123614	+	0.0713686i
$239$	−7.22474	−	12.5136i	−0.467330	−	0.809439i	0.531973	−	0.846761i	$-0.321451\pi$
$239$	−7.22474	−	12.5136i	−0.467330	−	0.809439i	−0.999303	+	0.0373219i	$0.988117\pi$
$240$		0			0
$241$	1.60102	−	2.77305i	0.103131	−	0.178628i	−0.809842	−	0.586648i	$-0.800447\pi$
$241$	1.60102	−	2.77305i	0.103131	−	0.178628i	0.912973	+	0.408020i	$0.133781\pi$
$242$			13.0000i			0.835672i
$243$		0			0
$244$	−8.00000			−0.512148
$245$		0			0
$246$		0			0
$247$	−2.89986	+	1.67423i	−0.184514	+	0.106529i
$248$	−3.85337	+	2.22474i	−0.244689	+	0.141271i
$249$		0			0
$250$		0			0
$251$	0.550510			0.0347479			0.0173739	−	0.999849i	$-0.494469\pi$
$251$	0.550510			0.0347479			0.0173739	+	0.999849i	$0.494469\pi$
$252$		0			0
$253$		−	12.0000i		−	0.754434i
$254$	1.67423	−	2.89986i	0.105051	−	0.181953i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.0834	−	6.39898i	0.691361	−	0.399157i	−0.112761	−	0.993622i	$-0.535969\pi$
$257$	11.0834	−	6.39898i	0.691361	−	0.399157i	0.804122	+	0.594465i	$0.202636\pi$
$258$		0			0
$259$	2.55051	−	4.41761i	0.158481	−	0.274497i
$260$		0			0
$261$		0			0
$262$			3.79796i			0.234639i
$263$	−17.7098	−	10.2247i	−1.09203	−	0.630485i	−0.157915	−	0.987453i	$-0.550477\pi$
$263$	−17.7098	−	10.2247i	−1.09203	−	0.630485i	−0.934117	+	0.356968i	$0.883811\pi$
$264$		0			0
$265$		0			0
$266$	1.67423	+	2.89986i	0.102654	+	0.177802i
$267$		0			0
$268$	0.301783	+	0.174235i	0.0184343	+	0.0106431i
$269$	14.4495			0.881001			0.440500	−	0.897752i	$-0.354801\pi$
$269$	14.4495			0.881001			0.440500	+	0.897752i	$0.354801\pi$
$270$		0			0
$271$	15.3485			0.932353			0.466177	−	0.884692i	$-0.345631\pi$
$271$	15.3485			0.932353			0.466177	+	0.884692i	$0.345631\pi$
$272$	4.24264	+	2.44949i	0.257248	+	0.148522i
$273$		0			0
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$		0			0
$276$		0			0
$277$	1.34278	+	0.775255i	0.0806799	+	0.0465806i	0.539797	−	0.841795i	$-0.318501\pi$
$277$	1.34278	+	0.775255i	0.0806799	+	0.0465806i	−0.459117	+	0.888376i	$0.651834\pi$
$278$			4.00000i			0.239904i
$279$		0			0
$280$		0			0
$281$	9.55051	−	16.5420i	0.569736	−	0.986811i	−0.426856	−	0.904320i	$-0.640379\pi$
$281$	9.55051	−	16.5420i	0.569736	−	0.986811i	0.996592	−	0.0824916i	$-0.0262878\pi$
$282$		0			0
$283$	11.4726	−	6.62372i	0.681977	−	0.393740i	−0.118623	−	0.992939i	$-0.537848\pi$
$283$	11.4726	−	6.62372i	0.681977	−	0.393740i	0.800599	+	0.599200i	$0.204515\pi$
$284$	−6.67423	−	11.5601i	−0.396043	−	0.685967i
$285$		0			0
$286$	1.10102	−	1.90702i	0.0651047	−	0.112765i
$287$			4.04541i			0.238793i
$288$		0			0
$289$	−7.00000			−0.411765
$290$		0			0
$291$		0			0
$292$	−0.866025	+	0.500000i	−0.0506803	+	0.0292603i
$293$	13.8957	−	8.02270i	0.811797	−	0.468691i	−0.0357824	−	0.999360i	$-0.511392\pi$
$293$	13.8957	−	8.02270i	0.811797	−	0.468691i	0.847580	+	0.530668i	$0.178059\pi$
$294$		0			0
$295$		0			0
$296$	−11.3485			−0.659616
$297$		0			0
$298$		−	6.00000i		−	0.347571i
$299$	−0.550510	+	0.953512i	−0.0318368	+	0.0551430i
$300$		0			0
$301$	0.573214	+	0.992836i	0.0330395	+	0.0572261i
$302$	17.3205	−	10.0000i	0.996683	−	0.575435i
$303$		0			0
$304$	3.72474	−	6.45145i	0.213629	−	0.370016i
$305$		0			0
$306$		0			0
$307$			22.6969i			1.29538i	0.761903	+	0.647691i	$0.224265\pi$
$307$			22.6969i			1.29538i	−0.761903	+	0.647691i	$0.775735\pi$
$308$	−1.90702	−	1.10102i	−0.108663	−	0.0627365i
$309$		0			0
$310$		0			0
$311$	−0.550510	−	0.953512i	−0.0312166	−	0.0540687i	0.849995	−	0.526791i	$-0.176605\pi$
$311$	−0.550510	−	0.953512i	−0.0312166	−	0.0540687i	−0.881212	+	0.472722i	$0.843271\pi$
$312$		0			0
$313$	−5.10867	−	2.94949i	−0.288759	−	0.166715i	0.348623	−	0.937263i	$-0.386649\pi$
$313$	−5.10867	−	2.94949i	−0.288759	−	0.166715i	−0.637382	+	0.770548i	$0.719983\pi$
$314$	19.7980			1.11726
$315$		0			0
$316$	16.6969			0.939276
$317$	14.8492	+	8.57321i	0.834017	+	0.481520i	0.855226	−	0.518255i	$-0.173418\pi$
$317$	14.8492	+	8.57321i	0.834017	+	0.481520i	−0.0212094	+	0.999775i	$0.506752\pi$
$318$		0			0
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$		0			0
$321$		0			0
$322$	0.953512	+	0.550510i	0.0531371	+	0.0306787i
$323$			36.4949i			2.03063i
$324$		0			0
$325$		0			0
$326$	−3.72474	+	6.45145i	−0.206295	+	0.357313i
$327$		0			0
$328$	7.79423	−	4.50000i	0.430364	−	0.248471i
$329$	−2.44949	−	4.24264i	−0.135045	−	0.233904i
$330$		0			0
$331$	−3.17423	+	5.49794i	−0.174472	+	0.302194i	−0.939978	−	0.341234i	$-0.889155\pi$
$331$	−3.17423	+	5.49794i	−0.174472	+	0.302194i	0.765507	+	0.643428i	$0.222488\pi$
$332$			5.44949i			0.299080i
$333$		0			0
$334$	19.5959			1.07224
$335$		0			0
$336$		0			0
$337$	−18.0990	+	10.4495i	−0.985918	+	0.569220i	−0.904052	−	0.427423i	$-0.859421\pi$
$337$	−18.0990	+	10.4495i	−0.985918	+	0.569220i	−0.0818663	+	0.996643i	$0.526088\pi$
$338$	11.0834	−	6.39898i	0.602855	−	0.348059i
$339$		0			0
$340$		0			0
$341$	21.7980			1.18043
$342$		0			0
$343$		−	6.20204i		−	0.334879i
$344$	1.27526	−	2.20881i	0.0687571	−	0.119091i
$345$		0			0
$346$	4.89898	+	8.48528i	0.263371	+	0.456172i
$347$	−10.3923	+	6.00000i	−0.557888	+	0.322097i	−0.752297	−	0.658824i	$-0.771054\pi$
$347$	−10.3923	+	6.00000i	−0.557888	+	0.322097i	0.194409	+	0.980921i	$0.437721\pi$
$348$		0			0
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	−0.615581	−	0.788074i	$-0.711079\pi$
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	0.990282	+	0.139072i	$0.0444119\pi$
$350$		0			0
$351$		0			0
$352$			4.89898i			0.261116i
$353$	7.79423	+	4.50000i	0.414845	+	0.239511i	0.692869	−	0.721063i	$-0.256346\pi$
$353$	7.79423	+	4.50000i	0.414845	+	0.239511i	−0.278024	+	0.960574i	$0.589680\pi$
$354$		0			0
$355$		0			0
$356$	−4.50000	−	7.79423i	−0.238500	−	0.413093i
$357$		0			0
$358$	−8.00853	−	4.62372i	−0.423264	−	0.244371i
$359$	−14.2020			−0.749555			−0.374778	−	0.927115i	$-0.622281\pi$
$359$	−14.2020			−0.749555			−0.374778	+	0.927115i	$0.622281\pi$
$360$		0			0
$361$	36.4949			1.92078
$362$	−15.4135	−	8.89898i	−0.810115	−	0.467720i
$363$		0			0
$364$	0.101021	+	0.174973i	0.00529491	+	0.00917106i
$365$		0			0
$366$		0			0
$367$	10.9959	+	6.34847i	0.573980	+	0.331387i	0.758737	−	0.651397i	$-0.225817\pi$
$367$	10.9959	+	6.34847i	0.573980	+	0.331387i	−0.184757	+	0.982784i	$0.559150\pi$
$368$		−	2.44949i		−	0.127688i
$369$		0			0
$370$		0			0
$371$	0.797959	−	1.38211i	0.0414280	−	0.0717553i
$372$		0			0
$373$	20.4347	−	11.7980i	1.05807	−	0.610875i	0.133170	−	0.991093i	$-0.457484\pi$
$373$	20.4347	−	11.7980i	1.05807	−	0.610875i	0.924897	+	0.380218i	$0.124151\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$		0			0
$376$	−5.44949	+	9.43879i	−0.281036	+	0.486769i
$377$		−	1.10102i		−	0.0567054i
$378$		0			0
$379$	8.89898			0.457110			0.228555	−	0.973531i	$-0.426600\pi$
$379$	8.89898			0.457110			0.228555	+	0.973531i	$0.426600\pi$
$380$		0			0
$381$		0			0
$382$	0.953512	−	0.550510i	0.0487859	−	0.0281666i
$383$	18.6633	−	10.7753i	0.953650	−	0.550590i	0.0594368	−	0.998232i	$-0.481070\pi$
$383$	18.6633	−	10.7753i	0.953650	−	0.550590i	0.894213	+	0.447642i	$0.147736\pi$
$384$		0			0
$385$		0			0
$386$	20.0000			1.01797
$387$		0			0
$388$		−	8.79796i		−	0.446649i
$389$	−12.7980	+	22.1667i	−0.648882	+	1.12390i	0.334508	+	0.942393i	$0.391430\pi$
$389$	−12.7980	+	22.1667i	−0.648882	+	1.12390i	−0.983390	+	0.181504i	$0.941903\pi$
$390$		0			0
$391$	6.00000	+	10.3923i	0.303433	+	0.525561i
$392$	−5.88721	+	3.39898i	−0.297349	+	0.171674i
$393$		0			0
$394$	0.123724	−	0.214297i	0.00623314	−	0.0107961i
$395$		0			0
$396$		0			0
$397$		−	17.5959i		−	0.883114i	−0.897233	−	0.441557i	$-0.854426\pi$
$397$		−	17.5959i		−	0.883114i	0.897233	−	0.441557i	$-0.145574\pi$
$398$	−11.9494	−	6.89898i	−0.598968	−	0.345815i
$399$		0			0
$400$		0			0
$401$	19.3485	+	33.5125i	0.966216	+	1.67354i	0.706311	+	0.707902i	$0.250358\pi$
$401$	19.3485	+	33.5125i	0.966216	+	1.67354i	0.259906	+	0.965634i	$0.416308\pi$
$402$		0			0
$403$	−1.73205	−	1.00000i	−0.0862796	−	0.0498135i
$404$	8.44949			0.420378
$405$		0			0
$406$	−1.10102			−0.0546427
$407$	48.1475	+	27.7980i	2.38658	+	1.37789i
$408$		0			0
$409$	0.0505103	+	0.0874863i	0.00249757	+	0.00432592i	0.867271	−	0.497835i	$-0.165872\pi$
$409$	0.0505103	+	0.0874863i	0.00249757	+	0.00432592i	−0.864774	+	0.502161i	$0.832538\pi$
$410$		0			0
$411$		0			0
$412$	−14.4600	−	8.34847i	−0.712392	−	0.411300i
$413$			2.44949i			0.120532i
$414$		0			0
$415$		0			0
$416$	0.224745	−	0.389270i	0.0110190	−	0.0190855i
$417$		0			0
$418$	−31.6055	+	18.2474i	−1.54588	+	0.892512i
$419$	13.0732	+	22.6435i	0.638668	+	1.10621i	0.985725	+	0.168362i	$0.0538477\pi$
$419$	13.0732	+	22.6435i	0.638668	+	1.10621i	−0.347057	+	0.937844i	$0.612819\pi$
$420$		0			0
$421$	13.0227	−	22.5560i	0.634688	−	1.09931i	−0.351893	−	0.936040i	$-0.614462\pi$
$421$	13.0227	−	22.5560i	0.634688	−	1.09931i	0.986581	−	0.163271i	$-0.0522046\pi$
$422$		−	3.44949i		−	0.167919i
$423$		0			0
$424$	−3.55051			−0.172428
$425$		0			0
$426$		0			0
$427$	−3.11416	+	1.79796i	−0.150705	+	0.0870093i
$428$	8.00853	−	4.62372i	0.387107	−	0.223496i
$429$		0			0
$430$		0			0
$431$	−25.3485			−1.22099			−0.610496	−	0.792019i	$-0.709030\pi$
$431$	−25.3485			−1.22099			−0.610496	+	0.792019i	$0.709030\pi$
$432$		0			0
$433$		−	9.59592i		−	0.461150i	−0.973055	−	0.230575i	$-0.925939\pi$
$433$		−	9.59592i		−	0.461150i	0.973055	−	0.230575i	$-0.0740608\pi$
$434$	−1.00000	+	1.73205i	−0.0480015	+	0.0831411i
$435$		0			0
$436$	−2.77526	−	4.80688i	−0.132911	−	0.230208i
$437$	15.8028	−	9.12372i	0.755948	−	0.436447i
$438$		0			0
$439$	1.67423	−	2.89986i	0.0799069	−	0.138403i	−0.823303	−	0.567603i	$-0.807871\pi$
$439$	1.67423	−	2.89986i	0.0799069	−	0.138403i	0.903210	+	0.429200i	$0.141204\pi$
$440$		0			0
$441$		0			0
$442$			2.20204i			0.104740i
$443$	−7.10318	−	4.10102i	−0.337482	−	0.194845i	0.321676	−	0.946850i	$-0.395754\pi$
$443$	−7.10318	−	4.10102i	−0.337482	−	0.194845i	−0.659158	+	0.752004i	$0.729087\pi$
$444$		0			0
$445$		0			0
$446$	−8.89898	−	15.4135i	−0.421379	−	0.729850i
$447$		0			0
$448$	−0.389270	−	0.224745i	−0.0183913	−	0.0106182i
$449$	−28.5959			−1.34952			−0.674762	−	0.738035i	$-0.735754\pi$
$449$	−28.5959			−1.34952			−0.674762	+	0.738035i	$0.735754\pi$
$450$		0			0
$451$	−44.0908			−2.07616
$452$	−3.55159	−	2.05051i	−0.167053	−	0.0964479i
$453$		0			0
$454$	−6.82577	−	11.8226i	−0.320349	−	0.554861i
$455$		0			0
$456$		0			0
$457$	−11.8619	−	6.84847i	−0.554876	−	0.320358i	0.196210	−	0.980562i	$-0.437136\pi$
$457$	−11.8619	−	6.84847i	−0.554876	−	0.320358i	−0.751086	+	0.660204i	$0.770470\pi$
$458$		−	13.1464i		−	0.614292i
$459$		0			0
$460$		0			0
$461$	2.32577	−	4.02834i	0.108322	−	0.187619i	−0.806769	−	0.590867i	$-0.798786\pi$
$461$	2.32577	−	4.02834i	0.108322	−	0.187619i	0.915090	+	0.403249i	$0.132119\pi$
$462$		0			0
$463$	4.63191	−	2.67423i	0.215263	−	0.124282i	−0.388492	−	0.921452i	$-0.627004\pi$
$463$	4.63191	−	2.67423i	0.215263	−	0.124282i	0.603755	+	0.797170i	$0.293671\pi$
$464$	1.22474	+	2.12132i	0.0568574	+	0.0984798i
$465$		0			0
$466$	−11.8485	+	20.5222i	−0.548870	+	0.950670i
$467$			10.3485i			0.478870i	0.970912	+	0.239435i	$0.0769622\pi$
$467$			10.3485i			0.478870i	−0.970912	+	0.239435i	$0.923038\pi$
$468$		0			0
$469$	0.156633			0.00723266
$470$		0			0
$471$		0			0
$472$	4.71940	−	2.72474i	0.217228	−	0.125417i
$473$	−10.8209	+	6.24745i	−0.497545	+	0.287258i
$474$		0			0
$475$		0			0
$476$	2.20204			0.100930
$477$		0			0
$478$			14.4495i			0.660904i
$479$	−0.123724	+	0.214297i	−0.00565311	+	0.00979147i	−0.868838	−	0.495096i	$-0.835133\pi$
$479$	−0.123724	+	0.214297i	−0.00565311	+	0.00979147i	0.863185	+	0.504888i	$0.168466\pi$
$480$		0			0
$481$	−2.55051	−	4.41761i	−0.116293	−	0.201426i
$482$	−2.77305	+	1.60102i	−0.126309	+	0.0729245i
$483$		0			0
$484$	6.50000	−	11.2583i	0.295455	−	0.511742i
$485$		0			0
$486$		0			0
$487$		−	24.4495i		−	1.10791i	−0.832546	−	0.553956i	$-0.813118\pi$
$487$		−	24.4495i		−	1.10791i	0.832546	−	0.553956i	$-0.186882\pi$
$488$	6.92820	+	4.00000i	0.313625	+	0.181071i
$489$		0			0
$490$		0			0
$491$	−13.6237	−	23.5970i	−0.614830	−	1.06492i	−0.990414	−	0.138129i	$-0.955891\pi$
$491$	−13.6237	−	23.5970i	−0.614830	−	1.06492i	0.375584	−	0.926788i	$-0.377442\pi$
$492$		0			0
$493$	−10.3923	−	6.00000i	−0.468046	−	0.270226i
$494$	3.34847			0.150655
$495$		0			0
$496$	4.44949			0.199788
$497$	−5.19615	−	3.00000i	−0.233079	−	0.134568i
$498$		0			0
$499$	−4.17423	−	7.22999i	−0.186864	−	0.323659i	0.757339	−	0.653022i	$-0.226499\pi$
$499$	−4.17423	−	7.22999i	−0.186864	−	0.323659i	−0.944203	+	0.329364i	$0.893166\pi$
$500$		0			0
$501$		0			0
$502$	−0.476756	−	0.275255i	−0.0212787	−	0.0122852i
$503$			21.5505i			0.960890i	0.877025	+	0.480445i	$0.159525\pi$
$503$			21.5505i			0.960890i	−0.877025	+	0.480445i	$0.840475\pi$
$504$		0			0
$505$		0			0
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$		0			0
$508$	−2.89986	+	1.67423i	−0.128660	+	0.0742821i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	−0.224745	+	0.389270i	−0.00994213	+	0.0172203i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.7980			−0.564494
$515$		0			0
$516$		0			0
$517$	46.2405	−	26.6969i	2.03365	−	1.17413i
$518$	−4.41761	+	2.55051i	−0.194099	+	0.112063i
$519$		0			0
$520$		0			0
$521$	29.3939			1.28777			0.643885	−	0.765123i	$-0.277322\pi$
$521$	29.3939			1.28777			0.643885	+	0.765123i	$0.277322\pi$
$522$		0			0
$523$			20.3485i			0.889776i	0.895586	+	0.444888i	$0.146757\pi$
$523$			20.3485i			0.889776i	−0.895586	+	0.444888i	$0.853243\pi$
$524$	1.89898	−	3.28913i	0.0829573	−	0.143686i
$525$		0			0
$526$	10.2247	+	17.7098i	0.445820	+	0.772183i
$527$	−18.8776	+	10.8990i	−0.822321	+	0.474767i
$528$		0			0
$529$	−8.50000	+	14.7224i	−0.369565	+	0.640106i
$530$		0			0
$531$		0			0
$532$		−	3.34847i		−	0.145175i
$533$	3.50343	+	2.02270i	0.151750	+	0.0876130i
$534$		0			0
$535$		0			0
$536$	−0.174235	−	0.301783i	−0.00752579	−	0.0130350i
$537$		0			0
$538$	−12.5136	−	7.22474i	−0.539501	−	0.311481i
$539$	33.3031			1.43446
$540$		0			0
$541$	−37.7980			−1.62506			−0.812531	−	0.582919i	$-0.801911\pi$
$541$	−37.7980			−1.62506			−0.812531	+	0.582919i	$0.801911\pi$
$542$	−13.2922	−	7.67423i	−0.570947	−	0.329637i
$543$		0			0
$544$	−2.44949	−	4.24264i	−0.105021	−	0.181902i
$545$		0			0
$546$		0			0
$547$	−13.5546	−	7.82577i	−0.579554	−	0.334606i	0.181402	−	0.983409i	$-0.441936\pi$
$547$	−13.5546	−	7.82577i	−0.579554	−	0.334606i	−0.760956	+	0.648803i	$0.775270\pi$
$548$			3.00000i			0.128154i
$549$		0			0
$550$		0			0
$551$	−9.12372	+	15.8028i	−0.388684	+	0.673220i
$552$		0			0
$553$	6.49961	−	3.75255i	0.276392	−	0.159575i
$554$	−0.775255	−	1.34278i	−0.0329374	−	0.0570493i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$		−	41.3939i		−	1.75391i	−0.480568	−	0.876957i	$-0.659570\pi$
$557$		−	41.3939i		−	1.75391i	0.480568	−	0.876957i	$-0.340430\pi$
$558$		0			0
$559$	1.14643			0.0484887
$560$		0			0
$561$		0			0
$562$	−16.5420	+	9.55051i	−0.697781	+	0.402864i
$563$	−20.7364	+	11.9722i	−0.873937	+	0.504568i	−0.868655	−	0.495418i	$-0.835015\pi$
$563$	−20.7364	+	11.9722i	−0.873937	+	0.504568i	−0.00528250	+	0.999986i	$0.501681\pi$
$564$		0			0
$565$		0			0
$566$	−13.2474			−0.556832
$567$		0			0
$568$			13.3485i			0.560089i
$569$	−16.8990	+	29.2699i	−0.708442	+	1.22706i	0.256993	+	0.966413i	$0.417268\pi$
$569$	−16.8990	+	29.2699i	−0.708442	+	1.22706i	−0.965435	+	0.260644i	$0.916065\pi$
$570$		0			0
$571$	−12.9722	−	22.4685i	−0.542869	−	0.940277i	−0.998738	−	0.0502301i	$-0.984005\pi$
$571$	−12.9722	−	22.4685i	−0.542869	−	0.940277i	0.455868	−	0.890047i	$-0.349329\pi$
$572$	−1.90702	+	1.10102i	−0.0797367	+	0.0460360i
$573$		0			0
$574$	2.02270	−	3.50343i	0.0844260	−	0.146230i
$575$		0			0
$576$		0			0
$577$			40.3939i			1.68162i	0.541331	+	0.840810i	$0.317921\pi$
$577$			40.3939i			1.68162i	−0.541331	+	0.840810i	$0.682079\pi$
$578$	6.06218	+	3.50000i	0.252153	+	0.145581i
$579$		0			0
$580$		0			0
$581$	1.22474	+	2.12132i	0.0508110	+	0.0880072i
$582$		0			0
$583$	15.0635	+	8.69694i	0.623868	+	0.360190i
$584$	1.00000			0.0413803
$585$		0			0
$586$	−16.0454			−0.662830
$587$	−23.1202	−	13.3485i	−0.954274	−	0.550950i	−0.0598679	−	0.998206i	$-0.519068\pi$
$587$	−23.1202	−	13.3485i	−0.954274	−	0.550950i	−0.894406	+	0.447256i	$0.852401\pi$
$588$		0			0
$589$	16.5732	+	28.7056i	0.682887	+	1.18280i
$590$		0			0
$591$		0			0
$592$	9.82806	+	5.67423i	0.403931	+	0.233210i
$593$		−	7.89898i		−	0.324372i	−0.986760	−	0.162186i	$-0.948146\pi$
$593$		−	7.89898i		−	0.324372i	0.986760	−	0.162186i	$-0.0518545\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$	0.953512	−	0.550510i	0.0389920	−	0.0225120i
$599$	11.3258	+	19.6168i	0.462758	+	0.801521i	0.999097	−	0.0424819i	$-0.0135265\pi$
$599$	11.3258	+	19.6168i	0.462758	+	0.801521i	−0.536339	+	0.844003i	$0.680193\pi$
$600$		0			0
$601$	8.24745	−	14.2850i	0.336420	−	0.582697i	−0.647336	−	0.762205i	$-0.724117\pi$
$601$	8.24745	−	14.2850i	0.336420	−	0.582697i	0.983757	+	0.179507i	$0.0574503\pi$
$602$		−	1.14643i		−	0.0467249i
$603$		0			0
$604$	−20.0000			−0.813788
$605$		0			0
$606$		0			0
$607$	2.89986	−	1.67423i	0.117702	−	0.0679551i	−0.439993	−	0.898001i	$-0.645019\pi$
$607$	2.89986	−	1.67423i	0.117702	−	0.0679551i	0.557695	+	0.830046i	$0.311686\pi$
$608$	−6.45145	+	3.72474i	−0.261641	+	0.151058i
$609$		0			0
$610$		0			0
$611$	−4.89898			−0.198191
$612$		0			0
$613$		−	12.0454i		−	0.486509i	−0.969962	−	0.243255i	$-0.921785\pi$
$613$		−	12.0454i		−	0.486509i	0.969962	−	0.243255i	$-0.0782151\pi$
$614$	11.3485	−	19.6561i	0.457987	−	0.793257i
$615$		0			0
$616$	1.10102	+	1.90702i	0.0443614	+	0.0768362i
$617$	−38.4462	+	22.1969i	−1.54779	+	0.893615i	−0.549476	+	0.835509i	$0.685173\pi$
$617$	−38.4462	+	22.1969i	−1.54779	+	0.893615i	−0.998310	+	0.0581058i	$0.981494\pi$
$618$		0			0
$619$	−15.8712	+	27.4897i	−0.637916	+	1.10490i	0.347973	+	0.937505i	$0.386870\pi$
$619$	−15.8712	+	27.4897i	−0.637916	+	1.10490i	−0.985889	+	0.167399i	$0.946463\pi$
$620$		0			0
$621$		0			0
$622$			1.10102i			0.0441469i
$623$	−3.50343	−	2.02270i	−0.140362	−	0.0810379i
$624$		0			0
$625$		0			0
$626$	2.94949	+	5.10867i	0.117885	+	0.204183i
$627$		0			0
$628$	−17.1455	−	9.89898i	−0.684181	−	0.395012i
$629$	−55.5959			−2.21675
$630$		0			0
$631$	−6.20204			−0.246899			−0.123450	−	0.992351i	$-0.539396\pi$
$631$	−6.20204			−0.246899			−0.123450	+	0.992351i	$0.539396\pi$
$632$	−14.4600	−	8.34847i	−0.575187	−	0.332084i
$633$		0			0
$634$	−8.57321	−	14.8492i	−0.340486	−	0.589739i
$635$		0			0
$636$		0			0
$637$	−2.64624	−	1.52781i	−0.104848	−	0.0605339i
$638$		−	12.0000i		−	0.475085i
$639$		0			0
$640$		0			0
$641$	−7.19694	+	12.4655i	−0.284262	+	0.492356i	−0.972430	−	0.233195i	$-0.925082\pi$
$641$	−7.19694	+	12.4655i	−0.284262	+	0.492356i	0.688168	+	0.725551i	$0.258415\pi$
$642$		0			0
$643$	15.2867	−	8.82577i	0.602848	−	0.348054i	−0.167313	−	0.985904i	$-0.553509\pi$
$643$	15.2867	−	8.82577i	0.602848	−	0.348054i	0.770161	+	0.637850i	$0.220176\pi$
$644$	−0.550510	−	0.953512i	−0.0216931	−	0.0375736i
$645$		0			0
$646$	18.2474	−	31.6055i	0.717936	−	1.24350i
$647$		−	24.2474i		−	0.953266i	−0.879102	−	0.476633i	$-0.841857\pi$
$647$		−	24.2474i		−	0.953266i	0.879102	−	0.476633i	$-0.158143\pi$
$648$		0			0
$649$	−26.6969			−1.04795
$650$		0			0
$651$		0			0
$652$	6.45145	−	3.72474i	0.252658	−	0.145872i
$653$	15.8028	−	9.12372i	0.618410	−	0.357039i	−0.157840	−	0.987465i	$-0.550453\pi$
$653$	15.8028	−	9.12372i	0.618410	−	0.357039i	0.776250	+	0.630426i	$0.217120\pi$
$654$		0			0
$655$		0			0
$656$	−9.00000			−0.351391
$657$		0			0
$658$			4.89898i			0.190982i
$659$	−4.92679	+	8.53344i	−0.191920	+	0.332416i	−0.945887	−	0.324497i	$-0.894805\pi$
$659$	−4.92679	+	8.53344i	−0.191920	+	0.332416i	0.753966	+	0.656913i	$0.228138\pi$
$660$		0			0
$661$	−3.69694	−	6.40329i	−0.143794	−	0.249059i	0.785128	−	0.619333i	$-0.212597\pi$
$661$	−3.69694	−	6.40329i	−0.143794	−	0.249059i	−0.928922	+	0.370274i	$0.879264\pi$
$662$	5.49794	−	3.17423i	0.213683	−	0.123370i
$663$		0			0
$664$	2.72474	−	4.71940i	0.105741	−	0.183148i
$665$		0			0
$666$		0			0
$667$			6.00000i			0.232321i
$668$	−16.9706	−	9.79796i	−0.656611	−	0.379094i
$669$		0			0
$670$		0			0
$671$	−19.5959	−	33.9411i	−0.756492	−	1.31028i
$672$		0			0
$673$	19.6561	+	11.3485i	0.757688	+	0.437451i	0.828465	−	0.560041i	$-0.189215\pi$
$673$	19.6561	+	11.3485i	0.757688	+	0.437451i	−0.0707771	+	0.997492i	$0.522548\pi$
$674$	20.8990			0.804999
$675$		0			0
$676$	−12.7980			−0.492229
$677$	−22.3810	−	12.9217i	−0.860172	−	0.496621i	0.00389777	−	0.999992i	$-0.498759\pi$
$677$	−22.3810	−	12.9217i	−0.860172	−	0.496621i	−0.864070	+	0.503372i	$0.832093\pi$
$678$		0			0
$679$	−1.97730	−	3.42478i	−0.0758817	−	0.131431i
$680$		0			0
$681$		0			0
$682$	−18.8776	−	10.8990i	−0.722860	−	0.417343i
$683$			41.9444i			1.60496i	0.596681	+	0.802479i	$0.296486\pi$
$683$			41.9444i			1.60496i	−0.596681	+	0.802479i	$0.703514\pi$
$684$		0			0
$685$		0			0
$686$	−3.10102	+	5.37113i	−0.118398	+	0.205071i
$687$		0			0
$688$	−2.20881	+	1.27526i	−0.0842100	+	0.0486186i
$689$	−0.797959	−	1.38211i	−0.0303998	−	0.0526540i
$690$		0			0
$691$	−19.5227	+	33.8143i	−0.742679	+	1.28636i	0.208593	+	0.978003i	$0.433112\pi$
$691$	−19.5227	+	33.8143i	−0.742679	+	1.28636i	−0.951271	+	0.308355i	$0.900222\pi$
$692$		−	9.79796i		−	0.372463i
$693$		0			0
$694$	12.0000			0.455514
$695$		0			0
$696$		0			0
$697$	38.1838	−	22.0454i	1.44631	−	0.835029i
$698$	−12.1244	+	7.00000i	−0.458914	+	0.264954i
$699$		0			0
$700$		0			0
$701$	−33.7980			−1.27653			−0.638266	−	0.769816i	$-0.720348\pi$
$701$	−33.7980			−1.27653			−0.638266	+	0.769816i	$0.720348\pi$
$702$		0			0
$703$			84.5403i			3.18850i
$704$	2.44949	−	4.24264i	0.0923186	−	0.159901i
$705$		0			0
$706$	−4.50000	−	7.79423i	−0.169360	−	0.293340i
$707$	3.28913	−	1.89898i	0.123700	−	0.0714185i
$708$		0			0
$709$	2.22474	−	3.85337i	0.0835520	−	0.144716i	−0.821221	−	0.570610i	$-0.806707\pi$
$709$	2.22474	−	3.85337i	0.0835520	−	0.144716i	0.904773	+	0.425894i	$0.140040\pi$
$710$		0			0
$711$		0			0
$712$			9.00000i			0.337289i
$713$	9.43879	+	5.44949i	0.353486	+	0.204085i
$714$		0			0
$715$		0			0
$716$	4.62372	+	8.00853i	0.172797	+	0.299293i
$717$		0			0
$718$	12.2993	+	7.10102i	0.459007	+	0.265008i
$719$	7.95459			0.296656			0.148328	−	0.988938i	$-0.452611\pi$
$719$	7.95459			0.296656			0.148328	+	0.988938i	$0.452611\pi$
$720$		0			0
$721$	−7.50510			−0.279505
$722$	−31.6055	−	18.2474i	−1.17624	−	0.679100i
$723$		0			0
$724$	8.89898	+	15.4135i	0.330728	+	0.572838i
$725$		0			0
$726$		0			0
$727$	13.8564	+	8.00000i	0.513906	+	0.296704i	0.734438	−	0.678676i	$-0.237446\pi$
$727$	13.8564	+	8.00000i	0.513906	+	0.296704i	−0.220532	+	0.975380i	$0.570779\pi$
$728$		−	0.202041i		−	0.00748814i
$729$		0			0
$730$		0			0
$731$	6.24745	−	10.8209i	0.231070	−	0.400225i
$732$		0			0
$733$	−22.5167	+	13.0000i	−0.831672	+	0.480166i	−0.854425	−	0.519575i	$-0.826090\pi$
$733$	−22.5167	+	13.0000i	−0.831672	+	0.480166i	0.0227529	+	0.999741i	$0.492757\pi$
$734$	−6.34847	−	10.9959i	−0.234326	−	0.405865i
$735$		0			0
$736$	−1.22474	+	2.12132i	−0.0451447	+	0.0781929i
$737$			1.70714i			0.0628834i
$738$		0			0
$739$	−3.04541			−0.112027			−0.0560136	−	0.998430i	$-0.517839\pi$
$739$	−3.04541			−0.112027			−0.0560136	+	0.998430i	$0.517839\pi$
$740$		0			0
$741$		0			0
$742$	−1.38211	+	0.797959i	−0.0507387	+	0.0292940i
$743$	42.7370	−	24.6742i	1.56787	−	0.905210i	0.571452	−	0.820635i	$-0.306380\pi$
$743$	42.7370	−	24.6742i	1.56787	−	0.905210i	0.996417	−	0.0845746i	$-0.0269531\pi$
$744$		0			0
$745$		0			0
$746$	−23.5959			−0.863908
$747$		0			0
$748$			24.0000i			0.877527i
$749$	2.07832	−	3.59975i	0.0759400	−	0.131532i
$750$		0			0
$751$	2.97730	+	5.15683i	0.108643	+	0.188175i	0.915221	−	0.402953i	$-0.132016\pi$
$751$	2.97730	+	5.15683i	0.108643	+	0.188175i	−0.806578	+	0.591128i	$0.798683\pi$
$752$	9.43879	−	5.44949i	0.344197	−	0.198722i
$753$		0			0
$754$	−0.550510	+	0.953512i	−0.0200484	+	0.0347248i
$755$		0			0
$756$		0			0
$757$		−	38.0454i		−	1.38278i	−0.722480	−	0.691392i	$-0.756998\pi$
$757$		−	38.0454i		−	1.38278i	0.722480	−	0.691392i	$-0.243002\pi$
$758$	−7.70674	−	4.44949i	−0.279921	−	0.161613i
$759$		0			0
$760$		0			0
$761$	6.94949	+	12.0369i	0.251919	+	0.436336i	0.964054	−	0.265706i	$-0.0856051\pi$
$761$	6.94949	+	12.0369i	0.251919	+	0.436336i	−0.712135	+	0.702042i	$0.752272\pi$
$762$		0			0
$763$	−2.16064	−	1.24745i	−0.0782206	−	0.0451607i
$764$	−1.10102			−0.0398335
$765$		0			0
$766$	−21.5505			−0.778652
$767$	2.12132	+	1.22474i	0.0765964	+	0.0442230i
$768$		0			0
$769$	−14.0959	−	24.4148i	−0.508312	−	0.880422i	−0.999954	−	0.00962438i	$-0.996936\pi$
$769$	−14.0959	−	24.4148i	−0.508312	−	0.880422i	0.491642	−	0.870797i	$-0.336397\pi$
$770$		0			0
$771$		0			0
$772$	−17.3205	−	10.0000i	−0.623379	−	0.359908i
$773$		−	10.4041i		−	0.374209i	−0.982340	−	0.187104i	$-0.940090\pi$
$773$		−	10.4041i		−	0.374209i	0.982340	−	0.187104i	$-0.0599103\pi$
$774$		0			0
$775$		0			0
$776$	−4.39898	+	7.61926i	−0.157914	+	0.273515i
$777$		0			0
$778$	22.1667	−	12.7980i	0.794715	−	0.458829i
$779$	−33.5227	−	58.0630i	−1.20108	−	2.08032i
$780$		0			0
$781$	32.6969	−	56.6328i	1.16999	−	2.02648i
$782$		−	12.0000i		−	0.429119i
$783$		0			0
$784$	6.79796			0.242784
$785$		0			0
$786$		0			0
$787$	30.0484	−	17.3485i	1.07111	−	0.618406i	0.142626	−	0.989777i	$-0.454445\pi$
$787$	30.0484	−	17.3485i	1.07111	−	0.618406i	0.928485	+	0.371370i	$0.121112\pi$
$788$	−0.214297	+	0.123724i	−0.00763401	+	0.00440750i
$789$		0			0
$790$		0			0
$791$	−1.84337			−0.0655426
$792$		0			0
$793$			3.59592i			0.127695i
$794$	−8.79796	+	15.2385i	−0.312228	+	0.540795i
$795$		0			0
$796$	6.89898	+	11.9494i	0.244528	+	0.423535i
$797$	26.1951	−	15.1237i	0.927877	−	0.535710i	0.0417372	−	0.999129i	$-0.486711\pi$
$797$	26.1951	−	15.1237i	0.927877	−	0.535710i	0.886139	+	0.463419i	$0.153377\pi$
$798$		0			0
$799$	−26.6969	+	46.2405i	−0.944470	+	1.63587i
$800$		0			0
$801$		0			0
$802$		−	38.6969i		−	1.36644i
$803$	−4.24264	−	2.44949i	−0.149720	−	0.0864406i
$804$		0			0
$805$		0			0
$806$	1.00000	+	1.73205i	0.0352235	+	0.0610089i
$807$		0			0
$808$	−7.31747	−	4.22474i	−0.257428	−	0.148626i
$809$	−6.30306			−0.221604			−0.110802	−	0.993843i	$-0.535342\pi$
$809$	−6.30306			−0.221604			−0.110802	+	0.993843i	$0.535342\pi$
$810$		0			0
$811$	−28.5505			−1.00254			−0.501272	−	0.865290i	$-0.667134\pi$
$811$	−28.5505			−1.00254			−0.501272	+	0.865290i	$0.667134\pi$
$812$	0.953512	+	0.550510i	0.0334617	+	0.0193191i
$813$		0			0
$814$	−27.7980	−	48.1475i	−0.974318	−	1.68757i
$815$		0			0
$816$		0			0
$817$	−16.4545	−	9.50000i	−0.575669	−	0.332363i
$818$		−	0.101021i		−	0.00353210i
$819$		0			0
$820$		0			0
$821$	13.5959	−	23.5488i	0.474501	−	0.821860i	−0.525073	−	0.851057i	$-0.675962\pi$
$821$	13.5959	−	23.5488i	0.474501	−	0.821860i	0.999574	+	0.0291978i	$0.00929526\pi$
$822$		0			0
$823$	14.8099	−	8.55051i	0.516241	−	0.298052i	−0.219154	−	0.975690i	$-0.570330\pi$
$823$	14.8099	−	8.55051i	0.516241	−	0.298052i	0.735395	+	0.677638i	$0.236996\pi$
$824$	8.34847	+	14.4600i	0.290833	+	0.503737i
$825$		0			0
$826$	1.22474	−	2.12132i	0.0426143	−	0.0738102i
$827$			35.9444i			1.24991i	0.780661	+	0.624954i	$0.214882\pi$
$827$			35.9444i			1.24991i	−0.780661	+	0.624954i	$0.785118\pi$
$828$		0			0
$829$	46.7423			1.62343			0.811714	−	0.584055i	$-0.198535\pi$
$829$	46.7423			1.62343			0.811714	+	0.584055i	$0.198535\pi$
$830$		0			0
$831$		0			0
$832$	−0.389270	+	0.224745i	−0.0134955	+	0.00779163i
$833$	−28.8413	+	16.6515i	−0.999292	+	0.576941i
$834$		0			0
$835$		0			0
$836$	36.4949			1.26220
$837$		0			0
$838$		−	26.1464i		−	0.903213i
$839$	−18.6742	+	32.3447i	−0.644706	+	1.11666i	0.339663	+	0.940547i	$0.389687\pi$
$839$	−18.6742	+	32.3447i	−0.644706	+	1.11666i	−0.984369	+	0.176117i	$0.943646\pi$
$840$		0			0
$841$	11.5000	+	19.9186i	0.396552	+	0.686848i
$842$	−22.5560	+	13.0227i	−0.777331	+	0.448792i
$843$		0			0
$844$	−1.72474	+	2.98735i	−0.0593682	+	0.102829i
$845$		0			0
$846$		0			0
$847$		−	5.84337i		−	0.200780i
$848$	3.07483	+	1.77526i	0.105590	+	0.0609625i
$849$		0			0
$850$		0			0
$851$	13.8990	+	24.0737i	0.476451	+	0.825237i
$852$		0			0
$853$	−39.8372	−	23.0000i	−1.36400	−	0.787505i	−0.373845	−	0.927491i	$-0.621961\pi$
$853$	−39.8372	−	23.0000i	−1.36400	−	0.787505i	−0.990153	+	0.139986i	$0.955294\pi$
$854$	3.59592			0.123050
$855$		0			0
$856$	−9.24745			−0.316071
$857$	−43.2138	−	24.9495i	−1.47615	−	0.852258i	−0.476517	−	0.879165i	$-0.658101\pi$
$857$	−43.2138	−	24.9495i	−1.47615	−	0.852258i	−0.999638	+	0.0269070i	$0.991434\pi$
$858$		0			0
$859$	−10.1742	−	17.6223i	−0.347140	−	0.601265i	0.638600	−	0.769539i	$-0.279514\pi$
$859$	−10.1742	−	17.6223i	−0.347140	−	0.601265i	−0.985740	+	0.168274i	$0.946181\pi$
$860$		0			0
$861$		0			0
$862$	21.9524	+	12.6742i	0.747702	+	0.431686i
$863$		−	43.8434i		−	1.49245i	−0.665696	−	0.746223i	$-0.731865\pi$
$863$		−	43.8434i		−	1.49245i	0.665696	−	0.746223i	$-0.268135\pi$
$864$		0			0
$865$		0			0
$866$	−4.79796	+	8.31031i	−0.163041	+	0.282396i
$867$		0			0
$868$	1.73205	−	1.00000i	0.0587896	−	0.0339422i
$869$	40.8990	+	70.8391i	1.38740	+	2.40305i
$870$		0			0
$871$	0.0783167	−	0.135648i	0.00265366	−	0.00459627i
$872$			5.55051i			0.187964i
$873$		0			0
$874$	−18.2474			−0.617229
$875$		0			0
$876$		0			0
$877$	−27.5378	+	15.8990i	−0.929887	+	0.536870i	−0.886776	−	0.462200i	$-0.847060\pi$
$877$	−27.5378	+	15.8990i	−0.929887	+	0.536870i	−0.0431110	+	0.999070i	$0.513727\pi$
$878$	−2.89986	+	1.67423i	−0.0978655	+	0.0565027i
$879$		0			0
$880$		0			0
$881$	−38.6969			−1.30373			−0.651866	−	0.758334i	$-0.726014\pi$
$881$	−38.6969			−1.30373			−0.651866	+	0.758334i	$0.726014\pi$
$882$		0			0
$883$		−	47.7980i		−	1.60853i	−0.594271	−	0.804265i	$-0.702559\pi$
$883$		−	47.7980i		−	1.60853i	0.594271	−	0.804265i	$-0.297441\pi$
$884$	1.10102	−	1.90702i	0.0370313	−	0.0641401i
$885$		0			0
$886$	4.10102	+	7.10318i	0.137776	+	0.238636i
$887$	−4.76756	+	2.75255i	−0.160079	+	0.0924216i	−0.577899	−	0.816108i	$-0.696127\pi$
$887$	−4.76756	+	2.75255i	−0.160079	+	0.0924216i	0.417821	+	0.908530i	$0.362794\pi$
$888$		0			0
$889$	−0.752551	+	1.30346i	−0.0252398	+	0.0437165i
$890$		0			0
$891$		0			0
$892$			17.7980i			0.595920i
$893$	70.3142	+	40.5959i	2.35297	+	1.35849i
$894$		0			0
$895$		0			0
$896$	0.224745	+	0.389270i	0.00750820	+	0.0130046i
$897$		0			0
$898$	24.7648	+	14.2980i	0.826412	+	0.477129i
$899$	−10.8990			−0.363501
$900$		0			0
$901$	−17.3939			−0.579474
$902$	38.1838	+	22.0454i	1.27138	+	0.734032i
$903$		0			0
$904$	2.05051	+	3.55159i	0.0681990	+	0.118124i
$905$		0			0
$906$		0			0
$907$	−31.4787	−	18.1742i	−1.04523	−	0.603466i	−0.123922	−	0.992292i	$-0.539547\pi$
$907$	−31.4787	−	18.1742i	−1.04523	−	0.603466i	−0.921311	+	0.388826i	$0.872881\pi$
$908$			13.6515i			0.453042i
$909$		0			0
$910$		0			0
$911$	−3.67423	+	6.36396i	−0.121733	+	0.210847i	−0.920451	−	0.390858i	$-0.872178\pi$
$911$	−3.67423	+	6.36396i	−0.121733	+	0.210847i	0.798718	+	0.601705i	$0.205512\pi$
$912$		0			0
$913$	−23.1202	+	13.3485i	−0.765168	+	0.441770i
$914$	6.84847	+	11.8619i	0.226527	+	0.392357i
$915$		0			0
$916$	−6.57321	+	11.3851i	−0.217185	+	0.376176i
$917$		−	1.70714i		−	0.0563748i
$918$		0			0
$919$	−3.34847			−0.110456			−0.0552279	−	0.998474i	$-0.517589\pi$
$919$	−3.34847			−0.110456			−0.0552279	+	0.998474i	$0.517589\pi$
$920$		0			0
$921$		0			0
$922$	−4.02834	+	2.32577i	−0.132666	+	0.0765950i
$923$	−5.19615	+	3.00000i	−0.171033	+	0.0987462i
$924$		0			0
$925$		0			0
$926$	−5.34847			−0.175762
$927$		0			0
$928$		−	2.44949i		−	0.0804084i
$929$	25.5959	−	44.3334i	0.839775	−	1.45453i	−0.0503079	−	0.998734i	$-0.516020\pi$
$929$	25.5959	−	44.3334i	0.839775	−	1.45453i	0.890083	−	0.455799i	$-0.150646\pi$
$930$		0			0
$931$	25.3207	+	43.8567i	0.829851	+	1.43734i
$932$	20.5222	−	11.8485i	0.672225	−	0.388110i
$933$		0			0
$934$	5.17423	−	8.96204i	0.169306	−	0.293247i
$935$		0			0
$936$		0			0
$937$			7.20204i			0.235280i	0.993056	+	0.117640i	$0.0375330\pi$
$937$			7.20204i			0.235280i	−0.993056	+	0.117640i	$0.962467\pi$
$938$	−0.135648	−	0.0783167i	−0.00442908	−	0.00255713i
$939$		0			0
$940$		0			0
$941$	26.8207	+	46.4548i	0.874329	+	1.51438i	0.857476	+	0.514524i	$0.172031\pi$
$941$	26.8207	+	46.4548i	0.874329	+	1.51438i	0.0168524	+	0.999858i	$0.494635\pi$
$942$		0			0
$943$	−19.0919	−	11.0227i	−0.621717	−	0.358949i
$944$	−5.44949			−0.177366
$945$		0			0
$946$	12.4949			0.406244
$947$	22.6435	+	13.0732i	0.735814	+	0.424822i	0.820545	−	0.571581i	$-0.193670\pi$
$947$	22.6435	+	13.0732i	0.735814	+	0.424822i	−0.0847314	+	0.996404i	$0.527003\pi$
$948$		0			0
$949$	0.224745	+	0.389270i	0.00729553	+	0.0126362i
$950$		0			0
$951$		0			0
$952$	−1.90702	−	1.10102i	−0.0618070	−	0.0356843i
$953$			2.20204i			0.0713311i	0.999364	+	0.0356656i	$0.0113551\pi$
$953$			2.20204i			0.0713311i	−0.999364	+	0.0356656i	$0.988645\pi$
$954$		0			0
$955$		0			0
$956$	7.22474	−	12.5136i	0.233665	−	0.404720i
$957$		0			0
$958$	0.214297	−	0.123724i	0.00692362	−	0.00399735i
$959$	0.674235	+	1.16781i	0.0217722	+	0.0377105i
$960$		0			0
$961$	5.60102	−	9.70125i	0.180678	−	0.312944i
$962$			5.10102i			0.164464i
$963$		0			0
$964$	3.20204			0.103131
$965$		0			0
$966$		0			0
$967$	27.7128	−	16.0000i	0.891184	−	0.514525i	0.0168544	−	0.999858i	$-0.494635\pi$
$967$	27.7128	−	16.0000i	0.891184	−	0.514525i	0.874330	+	0.485333i	$0.161301\pi$
$968$	−11.2583	+	6.50000i	−0.361856	+	0.208918i
$969$		0			0
$970$		0			0
$971$	40.8434			1.31073			0.655363	−	0.755314i	$-0.272516\pi$
$971$	40.8434			1.31073			0.655363	+	0.755314i	$0.272516\pi$
$972$		0			0
$973$		−	1.79796i		−	0.0576399i
$974$	−12.2247	+	21.1739i	−0.391706	+	0.678455i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	7.79423	−	4.50000i	0.249359	−	0.143968i	−0.370111	−	0.928987i	$-0.620681\pi$
$977$	7.79423	−	4.50000i	0.249359	−	0.143968i	0.619471	+	0.785020i	$0.287347\pi$
$978$		0			0
$979$	22.0454	−	38.1838i	0.704574	−	1.22036i
$980$		0			0
$981$		0			0
$982$			27.2474i			0.869501i
$983$	11.3458	+	6.55051i	0.361875	+	0.208929i	0.669903	−	0.742449i	$-0.266336\pi$
$983$	11.3458	+	6.55051i	0.361875	+	0.208929i	−0.308028	+	0.951377i	$0.599669\pi$
$984$		0			0
$985$		0			0
$986$	6.00000	+	10.3923i	0.191079	+	0.330958i
$987$		0			0
$988$	−2.89986	−	1.67423i	−0.0922568	−	0.0532645i
$989$	−6.24745			−0.198657
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−3.85337	−	2.22474i	−0.122345	−	0.0706357i
$993$		0			0
$994$	3.00000	+	5.19615i	0.0951542	+	0.164812i
$995$		0			0
$996$		0			0
$997$	6.96753	+	4.02270i	0.220664	+	0.127400i	0.606258	−	0.795268i	$-0.292670\pi$
$997$	6.96753	+	4.02270i	0.220664	+	0.127400i	−0.385594	+	0.922669i	$0.626003\pi$
$998$			8.34847i			0.264266i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.j.g.1099.2		8
3.2	odd	2		450.2.j.f.349.4		8
5.2	odd	4		1350.2.e.n.451.1		4
5.3	odd	4		1350.2.e.k.451.2		4
5.4	even	2	inner	1350.2.j.g.1099.3		8
9.2	odd	6		4050.2.c.y.649.1		4
9.4	even	3	inner	1350.2.j.g.199.3		8
9.5	odd	6		450.2.j.f.49.1		8
9.7	even	3		4050.2.c.w.649.3		4
15.2	even	4		450.2.e.l.151.1	✓	4
15.8	even	4		450.2.e.m.151.2	yes	4
15.14	odd	2		450.2.j.f.349.1		8
45.2	even	12		4050.2.a.bu.1.2		2
45.4	even	6	inner	1350.2.j.g.199.2		8
45.7	odd	12		4050.2.a.bl.1.2		2
45.13	odd	12		1350.2.e.k.901.2		4
45.14	odd	6		450.2.j.f.49.4		8
45.22	odd	12		1350.2.e.n.901.1		4
45.23	even	12		450.2.e.m.301.1	yes	4
45.29	odd	6		4050.2.c.y.649.4		4
45.32	even	12		450.2.e.l.301.2	yes	4
45.34	even	6		4050.2.c.w.649.2		4
45.38	even	12		4050.2.a.br.1.1		2
45.43	odd	12		4050.2.a.by.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.e.l.151.1	✓	4	15.2	even	4
450.2.e.l.301.2	yes	4	45.32	even	12
450.2.e.m.151.2	yes	4	15.8	even	4
450.2.e.m.301.1	yes	4	45.23	even	12
450.2.j.f.49.1		8	9.5	odd	6
450.2.j.f.49.4		8	45.14	odd	6
450.2.j.f.349.1		8	15.14	odd	2
450.2.j.f.349.4		8	3.2	odd	2
1350.2.e.k.451.2		4	5.3	odd	4
1350.2.e.k.901.2		4	45.13	odd	12
1350.2.e.n.451.1		4	5.2	odd	4
1350.2.e.n.901.1		4	45.22	odd	12
1350.2.j.g.199.2		8	45.4	even	6	inner
1350.2.j.g.199.3		8	9.4	even	3	inner
1350.2.j.g.1099.2		8	1.1	even	1	trivial
1350.2.j.g.1099.3		8	5.4	even	2	inner
4050.2.a.bl.1.2		2	45.7	odd	12
4050.2.a.br.1.1		2	45.38	even	12
4050.2.a.bu.1.2		2	45.2	even	12
4050.2.a.by.1.1		2	45.43	odd	12
4050.2.c.w.649.2		4	45.34	even	6
4050.2.c.w.649.3		4	9.7	even	3
4050.2.c.y.649.1		4	9.2	odd	6
4050.2.c.y.649.4		4	45.29	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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.389270 + 0.224745i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.389270 + 0.224745i) q^{7} -1.00000i q^{8} +(-2.44949 + 4.24264i) q^{11} +(0.389270 - 0.224745i) q^{13} +(-0.224745 - 0.389270i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.89898i q^{17} -7.44949 q^{19} +(4.24264 - 2.44949i) q^{22} +(-2.12132 + 1.22474i) q^{23} -0.449490 q^{26} +0.449490i q^{28} +(1.22474 - 2.12132i) q^{29} +(-2.22474 - 3.85337i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.44949 + 4.24264i) q^{34} -11.3485i q^{37} +(6.45145 + 3.72474i) q^{38} +(4.50000 + 7.79423i) q^{41} +(2.20881 + 1.27526i) q^{43} -4.89898 q^{44} +2.44949 q^{46} +(-9.43879 - 5.44949i) q^{47} +(-3.39898 - 5.88721i) q^{49} +(0.389270 + 0.224745i) q^{52} -3.55051i q^{53} +(0.224745 - 0.389270i) q^{56} +(-2.12132 + 1.22474i) q^{58} +(2.72474 + 4.71940i) q^{59} +(-4.00000 + 6.92820i) q^{61} +4.44949i q^{62} -1.00000 q^{64} +(0.301783 - 0.174235i) q^{67} +(4.24264 - 2.44949i) q^{68} -13.3485 q^{71} +1.00000i q^{73} +(-5.67423 + 9.82806i) q^{74} +(-3.72474 - 6.45145i) q^{76} +(-1.90702 + 1.10102i) q^{77} +(8.34847 - 14.4600i) q^{79} -9.00000i q^{82} +(4.71940 + 2.72474i) q^{83} +(-1.27526 - 2.20881i) q^{86} +(4.24264 + 2.44949i) q^{88} -9.00000 q^{89} +0.202041 q^{91} +(-2.12132 - 1.22474i) q^{92} +(5.44949 + 9.43879i) q^{94} +(-7.61926 - 4.39898i) q^{97} +6.79796i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 8 q^{14} - 4 q^{16} - 40 q^{19} + 16 q^{26} - 8 q^{31} + 36 q^{41} + 12 q^{49} - 8 q^{56} + 12 q^{59} - 32 q^{61} - 8 q^{64} - 48 q^{71} - 16 q^{74} - 20 q^{76} + 8 q^{79} - 20 q^{86} - 72 q^{89} + 80 q^{91} + 24 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 + 8 * q^14 - 4 * q^16 - 40 * q^19 + 16 * q^26 - 8 * q^31 + 36 * q^41 + 12 * q^49 - 8 * q^56 + 12 * q^59 - 32 * q^61 - 8 * q^64 - 48 * q^71 - 16 * q^74 - 20 * q^76 + 8 * q^79 - 20 * q^86 - 72 * q^89 + 80 * q^91 + 24 * q^94

Introduction

L-functions

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