LMFDB - Embedded newform 450.2.j.f.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(49,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, 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("450.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.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:	$3.59326809096$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	450.49
Dual form			450.2.j.f.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.41421 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.724745 - 1.57313i) q^{6} +(0.389270 - 0.224745i) q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.41421 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.724745 - 1.57313i) q^{6} +(0.389270 - 0.224745i) q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(2.44949 + 4.24264i) q^{11} +(-0.158919 - 1.72474i) q^{12} +(0.389270 + 0.224745i) q^{13} +(0.224745 - 0.389270i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.89898i q^{17} +(-0.548188 - 2.94949i) q^{18} -7.44949 q^{19} +(0.325765 - 0.707107i) q^{21} +(4.24264 + 2.44949i) q^{22} +(2.12132 + 1.22474i) q^{23} +(-1.00000 - 1.41421i) q^{24} +0.449490 q^{26} +(-1.41421 - 5.00000i) q^{27} -0.449490i q^{28} +(-1.22474 - 2.12132i) q^{29} +(-2.22474 + 3.85337i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(7.70674 + 3.55051i) q^{33} +(-2.44949 - 4.24264i) q^{34} +(-1.94949 - 2.28024i) q^{36} +11.3485i q^{37} +(-6.45145 + 3.72474i) q^{38} +(0.775255 - 0.0714323i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(-0.0714323 - 0.775255i) q^{42} +(2.20881 - 1.27526i) q^{43} +4.89898 q^{44} +2.44949 q^{46} +(9.43879 - 5.44949i) q^{47} +(-1.57313 - 0.724745i) q^{48} +(-3.39898 + 5.88721i) q^{49} +(-4.89898 - 6.92820i) q^{51} +(0.389270 - 0.224745i) q^{52} -3.55051i q^{53} +(-3.72474 - 3.62302i) q^{54} +(-0.224745 - 0.389270i) q^{56} +(-10.5352 + 7.44949i) q^{57} +(-2.12132 - 1.22474i) q^{58} +(-2.72474 + 4.71940i) q^{59} +(-4.00000 - 6.92820i) q^{61} +4.44949i q^{62} +(-0.246405 - 1.32577i) q^{63} -1.00000 q^{64} +(8.44949 - 0.778539i) q^{66} +(0.301783 + 0.174235i) q^{67} +(-4.24264 - 2.44949i) q^{68} +(4.22474 - 0.389270i) q^{69} +13.3485 q^{71} +(-2.82843 - 1.00000i) q^{72} -1.00000i q^{73} +(5.67423 + 9.82806i) q^{74} +(-3.72474 + 6.45145i) q^{76} +(1.90702 + 1.10102i) q^{77} +(0.635674 - 0.449490i) q^{78} +(8.34847 + 14.4600i) q^{79} +(-7.00000 - 5.65685i) q^{81} +9.00000i q^{82} +(-4.71940 + 2.72474i) q^{83} +(-0.449490 - 0.635674i) q^{84} +(1.27526 - 2.20881i) q^{86} +(-3.85337 - 1.77526i) q^{87} +(4.24264 - 2.44949i) q^{88} +9.00000 q^{89} +0.202041 q^{91} +(2.12132 - 1.22474i) q^{92} +(0.707107 + 7.67423i) q^{93} +(5.44949 - 9.43879i) q^{94} +(-1.72474 + 0.158919i) q^{96} +(-7.61926 + 4.39898i) q^{97} +6.79796i q^{98} +(14.4495 - 2.68556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^6 + 8 * q^9	$ 8 q + 4 q^{4} - 4 q^{6} + 8 q^{9} - 8 q^{14} - 4 q^{16} - 40 q^{19} + 32 q^{21} - 8 q^{24} - 16 q^{26} - 8 q^{31} + 4 q^{36} + 16 q^{39} - 36 q^{41} + 12 q^{49} - 20 q^{54} + 8 q^{56} - 12 q^{59} - 32 q^{61} - 8 q^{64} + 48 q^{66} + 24 q^{69} + 48 q^{71} + 16 q^{74} - 20 q^{76} + 8 q^{79} - 56 q^{81} + 16 q^{84} + 20 q^{86} + 72 q^{89} + 80 q^{91} + 24 q^{94} - 4 q^{96} + 96 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^6 + 8 * q^9 - 8 * q^14 - 4 * q^16 - 40 * q^19 + 32 * q^21 - 8 * q^24 - 16 * q^26 - 8 * q^31 + 4 * q^36 + 16 * q^39 - 36 * q^41 + 12 * q^49 - 20 * q^54 + 8 * q^56 - 12 * q^59 - 32 * q^61 - 8 * q^64 + 48 * q^66 + 24 * q^69 + 48 * q^71 + 16 * q^74 - 20 * q^76 + 8 * q^79 - 56 * q^81 + 16 * q^84 + 20 * q^86 + 72 * q^89 + 80 * q^91 + 24 * q^94 - 4 * q^96 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	1.41421	−	1.00000i	0.816497	−	0.577350i
$3$	1.41421	−	1.00000i	0.816497	−	0.577350i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.724745	−	1.57313i	0.295876	−	0.642229i
$7$	0.389270	−	0.224745i	0.147130	−	0.0849456i	−0.424628	−	0.905368i	$-0.639595\pi$
$7$	0.389270	−	0.224745i	0.147130	−	0.0849456i	0.571758	+	0.820422i	$0.306262\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000	−	2.82843i	0.333333	−	0.942809i
$10$		0			0
$11$	2.44949	+	4.24264i	0.738549	+	1.27920i	0.953149	+	0.302502i	$0.0978220\pi$
$11$	2.44949	+	4.24264i	0.738549	+	1.27920i	−0.214600	+	0.976702i	$0.568845\pi$
$12$	−0.158919	−	1.72474i	−0.0458759	−	0.497891i
$13$	0.389270	+	0.224745i	0.107964	+	0.0623330i	0.553010	−	0.833175i	$-0.313479\pi$
$13$	0.389270	+	0.224745i	0.107964	+	0.0623330i	−0.445046	+	0.895508i	$0.646813\pi$
$14$	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	$-0.202487\pi$
$18$	−0.548188	−	2.94949i	−0.129209	−	0.695201i
$19$	−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
$21$	0.325765	−	0.707107i	0.0710878	−	0.154303i
$22$	4.24264	+	2.44949i	0.904534	+	0.522233i
$23$	2.12132	+	1.22474i	0.442326	+	0.255377i	0.704584	−	0.709621i	$-0.251134\pi$
$23$	2.12132	+	1.22474i	0.442326	+	0.255377i	−0.262258	+	0.964998i	$0.584467\pi$
$24$	−1.00000	−	1.41421i	−0.204124	−	0.288675i
$25$		0			0
$26$	0.449490			0.0881522
$27$	−1.41421	−	5.00000i	−0.272166	−	0.962250i
$28$		−	0.449490i		−	0.0849456i
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	0.729616	−	0.683857i	$-0.239699\pi$
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	−0.957046	+	0.289938i	$0.906365\pi$
$30$		0			0
$31$	−2.22474	+	3.85337i	−0.399576	+	0.692086i	−0.993674	−	0.112307i	$-0.964176\pi$
$31$	−2.22474	+	3.85337i	−0.399576	+	0.692086i	0.594098	+	0.804393i	$0.297509\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	7.70674	+	3.55051i	1.34157	+	0.618065i
$34$	−2.44949	−	4.24264i	−0.420084	−	0.727607i
$35$		0			0
$36$	−1.94949	−	2.28024i	−0.324915	−	0.380040i
$37$			11.3485i			1.86568i	0.360295	+	0.932838i	$0.382676\pi$
$37$			11.3485i			1.86568i	−0.360295	+	0.932838i	$0.617324\pi$
$38$	−6.45145	+	3.72474i	−1.04656	+	0.604233i
$39$	0.775255	−	0.0714323i	0.124140	−	0.0114383i
$40$		0			0
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$	−0.0714323	−	0.775255i	−0.0110222	−	0.119624i
$43$	2.20881	−	1.27526i	0.336840	−	0.194475i	−0.322034	−	0.946728i	$-0.604366\pi$
$43$	2.20881	−	1.27526i	0.336840	−	0.194475i	0.658874	+	0.752254i	$0.271033\pi$
$44$	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	$-0.374195\pi$
$47$	9.43879	−	5.44949i	1.37679	−	0.794890i	0.991772	+	0.128019i	$0.0408620\pi$
$48$	−1.57313	−	0.724745i	−0.227062	−	0.104608i
$49$	−3.39898	+	5.88721i	−0.485568	+	0.841029i
$50$		0			0
$51$	−4.89898	−	6.92820i	−0.685994	−	0.970143i
$52$	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	$-0.0784105\pi$
$54$	−3.72474	−	3.62302i	−0.506874	−	0.493031i
$55$		0			0
$56$	−0.224745	−	0.389270i	−0.0300328	−	0.0520183i
$57$	−10.5352	+	7.44949i	−1.39542	+	0.986709i
$58$	−2.12132	−	1.22474i	−0.278543	−	0.160817i
$59$	−2.72474	+	4.71940i	−0.354732	+	0.614413i	−0.987072	−	0.160278i	$-0.948761\pi$
$59$	−2.72474	+	4.71940i	−0.354732	+	0.614413i	0.632340	+	0.774691i	$0.282094\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$			4.44949i			0.565086i
$63$	−0.246405	−	1.32577i	−0.0310441	−	0.167031i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	8.44949	−	0.778539i	1.04006	−	0.0958315i
$67$	0.301783	+	0.174235i	0.0368687	+	0.0212861i	0.518321	−	0.855186i	$-0.326557\pi$
$67$	0.301783	+	0.174235i	0.0368687	+	0.0212861i	−0.481452	+	0.876472i	$0.659891\pi$
$68$	−4.24264	−	2.44949i	−0.514496	−	0.297044i
$69$	4.22474	−	0.389270i	0.508600	−	0.0468625i
$70$		0			0
$71$	13.3485			1.58417			0.792086	−	0.610410i	$-0.208995\pi$
$71$	13.3485			1.58417			0.792086	+	0.610410i	$0.208995\pi$
$72$	−2.82843	−	1.00000i	−0.333333	−	0.117851i
$73$		−	1.00000i		−	0.117041i	−0.998286	−	0.0585206i	$-0.981362\pi$
$73$		−	1.00000i		−	0.117041i	0.998286	−	0.0585206i	$-0.0186383\pi$
$74$	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
$78$	0.635674	−	0.449490i	0.0719760	−	0.0508947i
$79$	8.34847	+	14.4600i	0.939276	+	1.62687i	0.766825	+	0.641856i	$0.221835\pi$
$79$	8.34847	+	14.4600i	0.939276	+	1.62687i	0.172451	+	0.985018i	$0.444831\pi$
$80$		0			0
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$			9.00000i			0.993884i
$83$	−4.71940	+	2.72474i	−0.518021	+	0.299080i	−0.736125	−	0.676846i	$-0.763346\pi$
$83$	−4.71940	+	2.72474i	−0.518021	+	0.299080i	0.218104	+	0.975926i	$0.430013\pi$
$84$	−0.449490	−	0.635674i	−0.0490434	−	0.0693578i
$85$		0			0
$86$	1.27526	−	2.20881i	0.137514	−	0.238182i
$87$	−3.85337	−	1.77526i	−0.413125	−	0.190327i
$88$	4.24264	−	2.44949i	0.452267	−	0.261116i
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$	0.202041			0.0211797
$92$	2.12132	−	1.22474i	0.221163	−	0.127688i
$93$	0.707107	+	7.67423i	0.0733236	+	0.795781i
$94$	5.44949	−	9.43879i	0.562072	−	0.973537i
$95$		0			0
$96$	−1.72474	+	0.158919i	−0.176031	+	0.0162196i
$97$	−7.61926	+	4.39898i	−0.773618	+	0.446649i	−0.834164	−	0.551517i	$-0.814049\pi$
$97$	−7.61926	+	4.39898i	−0.773618	+	0.446649i	0.0605456	+	0.998165i	$0.480716\pi$
$98$			6.79796i			0.686698i
$99$	14.4495	−	2.68556i	1.45223	−	0.269909i
$100$		0			0
$101$	−4.22474	−	7.31747i	−0.420378	−	0.728116i	0.575599	−	0.817732i	$-0.304769\pi$
$101$	−4.22474	−	7.31747i	−0.420378	−	0.728116i	−0.995976	+	0.0896167i	$0.971436\pi$
$102$	−7.70674	−	3.55051i	−0.763081	−	0.351553i
$103$	−14.4600	−	8.34847i	−1.42478	−	0.822599i	−0.428081	−	0.903740i	$-0.640810\pi$
$103$	−14.4600	−	8.34847i	−1.42478	−	0.822599i	−0.996703	+	0.0811413i	$0.974143\pi$
$104$	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	$-0.147505\pi$
$108$	−5.03723	−	1.27526i	−0.484708	−	0.122711i
$109$	−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
$111$	11.3485	+	16.0492i	1.07715	+	1.52332i
$112$	−0.389270	−	0.224745i	−0.0367825	−	0.0212364i
$113$	3.55159	+	2.05051i	0.334105	+	0.192896i	0.657662	−	0.753313i	$-0.271545\pi$
$113$	3.55159	+	2.05051i	0.334105	+	0.192896i	−0.323557	+	0.946209i	$0.604879\pi$
$114$	−5.39898	+	11.7190i	−0.505661	+	1.09759i
$115$		0			0
$116$	−2.44949			−0.227429
$117$	1.02494	−	0.876276i	0.0947561	−	0.0810117i
$118$			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
$123$	1.43027	+	15.5227i	0.128963	+	1.39964i
$124$	2.22474	+	3.85337i	0.199788	+	0.346043i
$125$		0			0
$126$	−0.876276	−	1.02494i	−0.0780648	−	0.0913093i
$127$		−	3.34847i		−	0.297129i	−0.988903	−	0.148564i	$-0.952535\pi$
$127$		−	3.34847i		−	0.297129i	0.988903	−	0.148564i	$-0.0474652\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	1.84847	−	4.01229i	0.162749	−	0.353262i
$130$		0			0
$131$	1.89898	−	3.28913i	0.165915	−	0.287373i	−0.771065	−	0.636756i	$-0.780276\pi$
$131$	1.89898	−	3.28913i	0.165915	−	0.287373i	0.936980	+	0.349384i	$0.113609\pi$
$132$	6.92820	−	4.89898i	0.603023	−	0.426401i
$133$	−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	$-0.707572\pi$
$137$	−2.59808	+	1.50000i	−0.221969	+	0.128154i	0.384893	+	0.922961i	$0.374238\pi$
$138$	3.46410	−	2.44949i	0.294884	−	0.208514i
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	7.89898	−	17.1455i	0.665214	−	1.44391i
$142$	11.5601	−	6.67423i	0.970103	−	0.560089i
$143$			2.20204i			0.184144i
$144$	−2.94949	+	0.548188i	−0.245791	+	0.0456823i
$145$		0			0
$146$	−0.500000	−	0.866025i	−0.0413803	−	0.0716728i
$147$	1.08032	+	11.7247i	0.0891035	+	0.967041i
$148$	9.82806	+	5.67423i	0.807862	+	0.466419i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	−0.910195	−	0.414181i	$-0.864068\pi$
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	0.0964061	−	0.995342i	$-0.469265\pi$
$152$			7.44949i			0.604233i
$153$	−13.8564	−	4.89898i	−1.12022	−	0.396059i
$154$	2.20204			0.177446
$155$		0			0
$156$	0.325765	−	0.707107i	0.0260821	−	0.0566139i
$157$	−17.1455	−	9.89898i	−1.36836	−	0.790025i	−0.377644	−	0.925951i	$-0.623266\pi$
$157$	−17.1455	−	9.89898i	−1.36836	−	0.790025i	−0.990719	+	0.135926i	$0.956599\pi$
$158$	14.4600	+	8.34847i	1.15037	+	0.664169i
$159$	−3.55051	−	5.02118i	−0.281574	−	0.398205i
$160$		0			0
$161$	1.10102			0.0867726
$162$	−8.89060	−	1.39898i	−0.698512	−	0.109914i
$163$			7.44949i			0.583489i	0.956496	+	0.291745i	$0.0942357\pi$
$163$			7.44949i			0.583489i	−0.956496	+	0.291745i	$0.905764\pi$
$164$	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	$-0.0594178\pi$
$167$	16.9706	+	9.79796i	1.31322	+	0.758189i	0.330593	+	0.943773i	$0.392751\pi$
$168$	−0.707107	−	0.325765i	−0.0545545	−	0.0251333i
$169$	−6.39898	−	11.0834i	−0.492229	−	0.852566i
$170$		0			0
$171$	−7.44949	+	21.0703i	−0.569677	+	1.61129i
$172$		−	2.55051i		−	0.194475i
$173$	8.48528	−	4.89898i	0.645124	−	0.372463i	−0.141462	−	0.989944i	$-0.545180\pi$
$173$	8.48528	−	4.89898i	0.645124	−	0.372463i	0.786586	+	0.617481i	$0.211847\pi$
$174$	−4.22474	+	0.389270i	−0.320277	+	0.0295104i
$175$		0			0
$176$	2.44949	−	4.24264i	0.184637	−	0.319801i
$177$	0.866025	+	9.39898i	0.0650945	+	0.706471i
$178$	7.79423	−	4.50000i	0.584202	−	0.337289i
$179$	−9.24745			−0.691187			−0.345593	−	0.938384i	$-0.612322\pi$
$179$	−9.24745			−0.691187			−0.345593	+	0.938384i	$0.612322\pi$
$180$		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
$183$	−12.5851	−	5.79796i	−0.930314	−	0.428597i
$184$	1.22474	−	2.12132i	0.0902894	−	0.156386i
$185$		0			0
$186$	4.44949	+	6.29253i	0.326252	+	0.461391i
$187$	20.7846	−	12.0000i	1.51992	−	0.877527i
$188$		−	10.8990i		−	0.794890i
$189$	−1.67423	−	1.62851i	−0.121783	−	0.118457i
$190$		0			0
$191$	0.550510	+	0.953512i	0.0398335	+	0.0689937i	0.885255	−	0.465106i	$-0.153984\pi$
$191$	0.550510	+	0.953512i	0.0398335	+	0.0689937i	−0.845421	+	0.534100i	$0.820651\pi$
$192$	−1.41421	+	1.00000i	−0.102062	+	0.0721688i
$193$	−17.3205	−	10.0000i	−1.24676	−	0.719816i	−0.276296	−	0.961073i	$-0.589107\pi$
$193$	−17.3205	−	10.0000i	−1.24676	−	0.719816i	−0.970461	+	0.241257i	$0.922440\pi$
$194$	−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	$0.997194\pi$
$198$	11.1708	−	9.55051i	0.793877	−	0.678725i
$199$	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
$201$	0.601021	−	0.0553782i	0.0423927	−	0.00390608i
$202$	−7.31747	−	4.22474i	−0.514856	−	0.297252i
$203$	−0.953512	−	0.550510i	−0.0669234	−	0.0386382i
$204$	−8.44949	+	0.778539i	−0.591583	+	0.0545086i
$205$		0			0
$206$	−16.6969			−1.16333
$207$	5.58542	−	4.77526i	0.388214	−	0.331903i
$208$		−	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	−0.800531	−	0.599292i	$-0.795449\pi$
$211$	1.72474	−	2.98735i	0.118736	−	0.205657i	0.919267	+	0.393634i	$0.128782\pi$
$212$	−3.07483	−	1.77526i	−0.211180	−	0.121925i
$213$	18.8776	−	13.3485i	1.29347	−	0.914622i
$214$	−4.62372	−	8.00853i	−0.316071	−	0.547452i
$215$		0			0
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$			2.00000i			0.135769i
$218$	−4.80688	+	2.77526i	−0.325563	+	0.187964i
$219$	−1.00000	−	1.41421i	−0.0675737	−	0.0955637i
$220$		0			0
$221$	1.10102	−	1.90702i	0.0740627	−	0.128280i
$222$	17.8526	+	8.22474i	1.19819	+	0.552009i
$223$	15.4135	−	8.89898i	1.03216	−	0.595920i	0.114560	−	0.993416i	$-0.463454\pi$
$223$	15.4135	−	8.89898i	1.03216	−	0.595920i	0.917604	+	0.397497i	$0.130121\pi$
$224$	−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	$-0.816328\pi$
$227$	−11.8226	+	6.82577i	−0.784692	+	0.453042i	0.0533987	+	0.998573i	$0.482995\pi$
$228$	1.18386	+	12.8485i	0.0784032	+	0.850911i
$229$	6.57321	−	11.3851i	0.434370	−	0.752351i	−0.562874	−	0.826543i	$-0.690304\pi$
$229$	6.57321	−	11.3851i	0.434370	−	0.752351i	0.997244	+	0.0741916i	$0.0236376\pi$
$230$		0			0
$231$	3.79796	−	0.349945i	0.249887	−	0.0230247i
$232$	−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	$-0.282865\pi$
$234$	0.449490	−	1.27135i	0.0293841	−	0.0831107i
$235$		0			0
$236$	2.72474	+	4.71940i	0.177366	+	0.307207i
$237$	26.2665	+	12.1010i	1.70619	+	0.786046i
$238$	−1.90702	−	1.10102i	−0.123614	−	0.0713686i
$239$	7.22474	−	12.5136i	0.467330	−	0.809439i	−0.531973	−	0.846761i	$-0.678549\pi$
$239$	7.22474	−	12.5136i	0.467330	−	0.809439i	0.999303	+	0.0373219i	$0.0118827\pi$
$240$		0			0
$241$	1.60102	+	2.77305i	0.103131	+	0.178628i	0.912973	−	0.408020i	$-0.133781\pi$
$241$	1.60102	+	2.77305i	0.103131	+	0.178628i	−0.809842	+	0.586648i	$0.800447\pi$
$242$			13.0000i			0.835672i
$243$	−15.5563	−	1.00000i	−0.997940	−	0.0641500i
$244$	−8.00000			−0.512148
$245$		0			0
$246$	9.00000	+	12.7279i	0.573819	+	0.811503i
$247$	−2.89986	−	1.67423i	−0.184514	−	0.106529i
$248$	3.85337	+	2.22474i	0.244689	+	0.141271i
$249$	−3.94949	+	8.57277i	−0.250289	+	0.543277i
$250$		0			0
$251$	−0.550510			−0.0347479			−0.0173739	−	0.999849i	$-0.505531\pi$
$251$	−0.550510			−0.0347479			−0.0173739	+	0.999849i	$0.505531\pi$
$252$	−1.27135	−	0.449490i	−0.0800875	−	0.0283152i
$253$			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	$-0.464031\pi$
$257$	−11.0834	−	6.39898i	−0.691361	−	0.399157i	−0.804122	+	0.594465i	$0.797364\pi$
$258$	−0.405324	−	4.39898i	−0.0252343	−	0.273869i
$259$	2.55051	+	4.41761i	0.158481	+	0.274497i
$260$		0			0
$261$	−7.22474	+	1.34278i	−0.447200	+	0.0831161i
$262$		−	3.79796i		−	0.234639i
$263$	17.7098	−	10.2247i	1.09203	−	0.630485i	0.157915	−	0.987453i	$-0.449523\pi$
$263$	17.7098	−	10.2247i	1.09203	−	0.630485i	0.934117	+	0.356968i	$0.116189\pi$
$264$	3.55051	−	7.70674i	0.218519	−	0.474317i
$265$		0			0
$266$	−1.67423	+	2.89986i	−0.102654	+	0.177802i
$267$	12.7279	−	9.00000i	0.778936	−	0.550791i
$268$	0.301783	−	0.174235i	0.0184343	−	0.0106431i
$269$	−14.4495			−0.881001			−0.440500	−	0.897752i	$-0.645199\pi$
$269$	−14.4495			−0.881001			−0.440500	+	0.897752i	$0.645199\pi$
$270$		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
$273$	0.285729	−	0.202041i	0.0172931	−	0.0122281i
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$		0			0
$276$	1.77526	−	3.85337i	0.106858	−	0.231946i
$277$	1.34278	−	0.775255i	0.0806799	−	0.0465806i	−0.459117	−	0.888376i	$-0.651834\pi$
$277$	1.34278	−	0.775255i	0.0806799	−	0.0465806i	0.539797	+	0.841795i	$0.318501\pi$
$278$			4.00000i			0.239904i
$279$	8.67423	+	10.1459i	0.519313	+	0.607419i
$280$		0			0
$281$	−9.55051	−	16.5420i	−0.569736	−	0.986811i	−0.996592	−	0.0824916i	$-0.973712\pi$
$281$	−9.55051	−	16.5420i	−0.569736	−	0.986811i	0.426856	−	0.904320i	$-0.359621\pi$
$282$	−1.73205	−	18.7980i	−0.103142	−	1.11940i
$283$	11.4726	+	6.62372i	0.681977	+	0.393740i	0.800599	−	0.599200i	$-0.204515\pi$
$283$	11.4726	+	6.62372i	0.681977	+	0.393740i	−0.118623	+	0.992939i	$0.537848\pi$
$284$	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
$288$	−2.28024	+	1.94949i	−0.134364	+	0.114875i
$289$	−7.00000			−0.411765
$290$		0			0
$291$	−6.37628	+	13.8404i	−0.373784	+	0.811336i
$292$	−0.866025	−	0.500000i	−0.0506803	−	0.0292603i
$293$	−13.8957	−	8.02270i	−0.811797	−	0.468691i	0.0357824	−	0.999360i	$-0.488608\pi$
$293$	−13.8957	−	8.02270i	−0.811797	−	0.468691i	−0.847580	+	0.530668i	$0.821941\pi$
$294$	6.79796	+	9.61377i	0.396465	+	0.560686i
$295$		0			0
$296$	11.3485			0.659616
$297$	17.7491	−	18.2474i	1.02991	−	1.05882i
$298$			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
$303$	−13.2922	−	6.12372i	−0.763615	−	0.351799i
$304$	3.72474	+	6.45145i	0.213629	+	0.370016i
$305$		0			0
$306$	−14.4495	+	2.68556i	−0.826022	+	0.153523i
$307$		−	22.6969i		−	1.29538i	−0.761903	−	0.647691i	$-0.775735\pi$
$307$		−	22.6969i		−	1.29538i	0.761903	−	0.647691i	$-0.224265\pi$
$308$	1.90702	−	1.10102i	0.108663	−	0.0627365i
$309$	−28.7980	+	2.65345i	−1.63826	+	0.150950i
$310$		0			0
$311$	0.550510	−	0.953512i	0.0312166	−	0.0540687i	−0.849995	−	0.526791i	$-0.823395\pi$
$311$	0.550510	−	0.953512i	0.0312166	−	0.0540687i	0.881212	+	0.472722i	$0.156729\pi$
$312$	−0.0714323	−	0.775255i	−0.00404406	−	0.0438902i
$313$	−5.10867	+	2.94949i	−0.288759	+	0.166715i	−0.637382	−	0.770548i	$-0.719983\pi$
$313$	−5.10867	+	2.94949i	−0.288759	+	0.166715i	0.348623	+	0.937263i	$0.386649\pi$
$314$	−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	$-0.826582\pi$
$317$	−14.8492	+	8.57321i	−0.834017	+	0.481520i	0.0212094	+	0.999775i	$0.493248\pi$
$318$	−5.58542	−	2.57321i	−0.313215	−	0.144299i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	−9.24745	−	13.0779i	−0.516142	−	0.729935i
$322$	0.953512	−	0.550510i	0.0531371	−	0.0306787i
$323$			36.4949i			2.03063i
$324$	−8.39898	+	3.23375i	−0.466610	+	0.179653i
$325$		0			0
$326$	3.72474	+	6.45145i	0.206295	+	0.357313i
$327$	−7.84961	+	5.55051i	−0.434084	+	0.306944i
$328$	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	0.765507	−	0.643428i	$-0.222488\pi$
$331$	−3.17423	−	5.49794i	−0.174472	−	0.302194i	−0.939978	+	0.341234i	$0.889155\pi$
$332$			5.44949i			0.299080i
$333$	32.0983	+	11.3485i	1.75898	+	0.621892i
$334$	19.5959			1.07224
$335$		0			0
$336$	−0.775255	+	0.0714323i	−0.0422936	+	0.00389695i
$337$	−18.0990	−	10.4495i	−0.985918	−	0.569220i	−0.0818663	−	0.996643i	$-0.526088\pi$
$337$	−18.0990	−	10.4495i	−0.985918	−	0.569220i	−0.904052	+	0.427423i	$0.859421\pi$
$338$	−11.0834	−	6.39898i	−0.602855	−	0.348059i
$339$	7.07321	−	0.651729i	0.384164	−	0.0353970i
$340$		0			0
$341$	−21.7980			−1.18043
$342$	4.08372	+	21.9722i	0.220822	+	1.18812i
$343$			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	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$	−3.46410	+	2.44949i	−0.185695	+	0.131306i
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	0.990282	−	0.139072i	$-0.0444119\pi$
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	−0.615581	+	0.788074i	$0.711079\pi$
$350$		0			0
$351$	0.573214	−	2.26418i	0.0305959	−	0.120853i
$352$		−	4.89898i		−	0.261116i
$353$	−7.79423	+	4.50000i	−0.414845	+	0.239511i	−0.692869	−	0.721063i	$-0.743654\pi$
$353$	−7.79423	+	4.50000i	−0.414845	+	0.239511i	0.278024	+	0.960574i	$0.410320\pi$
$354$	5.44949	+	7.70674i	0.289637	+	0.409609i
$355$		0			0
$356$	4.50000	−	7.79423i	0.238500	−	0.413093i
$357$	−3.46410	−	1.59592i	−0.183340	−	0.0844649i
$358$	−8.00853	+	4.62372i	−0.423264	+	0.244371i
$359$	14.2020			0.749555			0.374778	−	0.927115i	$-0.377719\pi$
$359$	14.2020			0.749555			0.374778	+	0.927115i	$0.377719\pi$
$360$		0			0
$361$	36.4949			1.92078
$362$	15.4135	−	8.89898i	0.810115	−	0.467720i
$363$	2.06594	+	22.4217i	0.108434	+	1.17683i
$364$	0.101021	−	0.174973i	0.00529491	−	0.00917106i
$365$		0			0
$366$	−13.7980	+	1.27135i	−0.721231	+	0.0664545i
$367$	10.9959	−	6.34847i	0.573980	−	0.331387i	−0.184757	−	0.982784i	$-0.559150\pi$
$367$	10.9959	−	6.34847i	0.573980	−	0.331387i	0.758737	+	0.651397i	$0.225817\pi$
$368$		−	2.44949i		−	0.127688i
$369$	17.5454	+	20.5222i	0.913377	+	1.06834i
$370$		0			0
$371$	−0.797959	−	1.38211i	−0.0414280	−	0.0717553i
$372$	6.99964	+	3.22474i	0.362914	+	0.167195i
$373$	20.4347	+	11.7980i	1.05807	+	0.610875i	0.924897	−	0.380218i	$-0.124151\pi$
$373$	20.4347	+	11.7980i	1.05807	+	0.610875i	0.133170	+	0.991093i	$0.457484\pi$
$374$	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
$378$	−2.26418	−	0.573214i	−0.116457	−	0.0294830i
$379$	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
$381$	−3.34847	−	4.73545i	−0.171547	−	0.242604i
$382$	0.953512	+	0.550510i	0.0487859	+	0.0281666i
$383$	−18.6633	−	10.7753i	−0.953650	−	0.550590i	−0.0594368	−	0.998232i	$-0.518930\pi$
$383$	−18.6633	−	10.7753i	−0.953650	−	0.550590i	−0.894213	+	0.447642i	$0.852264\pi$
$384$	−0.724745	+	1.57313i	−0.0369845	+	0.0802786i
$385$		0			0
$386$	−20.0000			−1.01797
$387$	−1.39816	−	7.52270i	−0.0710724	−	0.382401i
$388$			8.79796i			0.446649i
$389$	12.7980	+	22.1667i	0.648882	+	1.12390i	0.983390	+	0.181504i	$0.0580966\pi$
$389$	12.7980	+	22.1667i	0.648882	+	1.12390i	−0.334508	+	0.942393i	$0.608570\pi$
$390$		0			0
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	5.88721	+	3.39898i	0.297349	+	0.171674i
$393$	−0.603566	−	6.55051i	−0.0304459	−	0.330430i
$394$	0.123724	+	0.214297i	0.00623314	+	0.0107961i
$395$		0			0
$396$	4.89898	−	13.8564i	0.246183	−	0.696311i
$397$			17.5959i			0.883114i	0.897233	+	0.441557i	$0.145574\pi$
$397$			17.5959i			0.883114i	−0.897233	+	0.441557i	$0.854426\pi$
$398$	11.9494	−	6.89898i	0.598968	−	0.345815i
$399$	−2.42679	+	5.26758i	−0.121491	+	0.263709i
$400$		0			0
$401$	−19.3485	+	33.5125i	−0.966216	+	1.67354i	−0.259906	+	0.965634i	$0.583692\pi$
$401$	−19.3485	+	33.5125i	−0.966216	+	1.67354i	−0.706311	+	0.707902i	$0.749642\pi$
$402$	0.492810	−	0.348469i	0.0245791	−	0.0173801i
$403$	−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
$408$	−6.92820	+	4.89898i	−0.342997	+	0.242536i
$409$	0.0505103	−	0.0874863i	0.00249757	−	0.00432592i	−0.864774	−	0.502161i	$-0.832538\pi$
$409$	0.0505103	−	0.0874863i	0.00249757	−	0.00432592i	0.867271	+	0.497835i	$0.165872\pi$
$410$		0			0
$411$	−2.17423	+	4.71940i	−0.107247	+	0.232791i
$412$	−14.4600	+	8.34847i	−0.712392	+	0.411300i
$413$			2.44949i			0.120532i
$414$	2.44949	−	6.92820i	0.120386	−	0.340503i
$415$		0			0
$416$	−0.224745	−	0.389270i	−0.0110190	−	0.0190855i
$417$	0.635674	+	6.89898i	0.0311291	+	0.337844i
$418$	−31.6055	−	18.2474i	−1.54588	−	0.892512i
$419$	−13.0732	+	22.6435i	−0.638668	+	1.10621i	0.347057	+	0.937844i	$0.387181\pi$
$419$	−13.0732	+	22.6435i	−0.638668	+	1.10621i	−0.985725	+	0.168362i	$0.946152\pi$
$420$		0			0
$421$	13.0227	+	22.5560i	0.634688	+	1.09931i	0.986581	+	0.163271i	$0.0522046\pi$
$421$	13.0227	+	22.5560i	0.634688	+	1.09931i	−0.351893	+	0.936040i	$0.614462\pi$
$422$		−	3.44949i		−	0.167919i
$423$	−5.97469	−	32.1464i	−0.290499	−	1.56301i
$424$	−3.55051			−0.172428
$425$		0			0
$426$	9.67423	−	20.9989i	0.468718	−	1.01740i
$427$	−3.11416	−	1.79796i	−0.150705	−	0.0870093i
$428$	−8.00853	−	4.62372i	−0.387107	−	0.223496i
$429$	2.20204	+	3.11416i	0.106316	+	0.150353i
$430$		0			0
$431$	25.3485			1.22099			0.610496	−	0.792019i	$-0.290970\pi$
$431$	25.3485			1.22099			0.610496	+	0.792019i	$0.290970\pi$
$432$	−3.62302	+	3.72474i	−0.174313	+	0.179207i
$433$			9.59592i			0.461150i	0.973055	+	0.230575i	$0.0740608\pi$
$433$			9.59592i			0.461150i	−0.973055	+	0.230575i	$0.925939\pi$
$434$	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
$438$	−1.57313	−	0.724745i	−0.0751672	−	0.0346296i
$439$	1.67423	+	2.89986i	0.0799069	+	0.138403i	0.903210	−	0.429200i	$-0.141204\pi$
$439$	1.67423	+	2.89986i	0.0799069	+	0.138403i	−0.823303	+	0.567603i	$0.807871\pi$
$440$		0			0
$441$	13.2526	+	15.5010i	0.631074	+	0.738141i
$442$		−	2.20204i		−	0.104740i
$443$	7.10318	−	4.10102i	0.337482	−	0.194845i	−0.321676	−	0.946850i	$-0.604246\pi$
$443$	7.10318	−	4.10102i	0.337482	−	0.194845i	0.659158	+	0.752004i	$0.270913\pi$
$444$	19.5732	−	1.80348i	0.928904	−	0.0855895i
$445$		0			0
$446$	8.89898	−	15.4135i	0.421379	−	0.729850i
$447$	0.953512	+	10.3485i	0.0450996	+	0.489466i
$448$	−0.389270	+	0.224745i	−0.0183913	+	0.0106182i
$449$	28.5959			1.34952			0.674762	−	0.738035i	$-0.264246\pi$
$449$	28.5959			1.34952			0.674762	+	0.738035i	$0.264246\pi$
$450$		0			0
$451$	−44.0908			−2.07616
$452$	3.55159	−	2.05051i	0.167053	−	0.0964479i
$453$	−31.4626	−	14.4949i	−1.47824	−	0.681030i
$454$	−6.82577	+	11.8226i	−0.320349	+	0.554861i
$455$		0			0
$456$	7.44949	+	10.5352i	0.348854	+	0.493355i
$457$	−11.8619	+	6.84847i	−0.554876	+	0.320358i	−0.751086	−	0.660204i	$-0.770470\pi$
$457$	−11.8619	+	6.84847i	−0.554876	+	0.320358i	0.196210	+	0.980562i	$0.437136\pi$
$458$		−	13.1464i		−	0.614292i
$459$	−24.4949	+	6.92820i	−1.14332	+	0.323381i
$460$		0			0
$461$	−2.32577	−	4.02834i	−0.108322	−	0.187619i	0.806769	−	0.590867i	$-0.201214\pi$
$461$	−2.32577	−	4.02834i	−0.108322	−	0.187619i	−0.915090	+	0.403249i	$0.867881\pi$
$462$	3.11416	−	2.20204i	0.144884	−	0.102448i
$463$	4.63191	+	2.67423i	0.215263	+	0.124282i	0.603755	−	0.797170i	$-0.293671\pi$
$463$	4.63191	+	2.67423i	0.215263	+	0.124282i	−0.388492	+	0.921452i	$0.627004\pi$
$464$	−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	$0.923038\pi$
$468$	−0.246405	−	1.32577i	−0.0113901	−	0.0612835i
$469$	0.156633			0.00723266
$470$		0			0
$471$	−34.1464	+	3.14626i	−1.57338	+	0.144972i
$472$	4.71940	+	2.72474i	0.217228	+	0.125417i
$473$	10.8209	+	6.24745i	0.497545	+	0.287258i
$474$	28.7980	−	2.65345i	1.32273	−	0.121877i
$475$		0			0
$476$	−2.20204			−0.100930
$477$	−10.0424	−	3.55051i	−0.459808	−	0.162567i
$478$		−	14.4495i		−	0.660904i
$479$	0.123724	+	0.214297i	0.00565311	+	0.00979147i	0.868838	−	0.495096i	$-0.164867\pi$
$479$	0.123724	+	0.214297i	0.00565311	+	0.00979147i	−0.863185	+	0.504888i	$0.831534\pi$
$480$		0			0
$481$	−2.55051	+	4.41761i	−0.116293	+	0.201426i
$482$	2.77305	+	1.60102i	0.126309	+	0.0729245i
$483$	1.55708	−	1.10102i	0.0708495	−	0.0500982i
$484$	6.50000	+	11.2583i	0.295455	+	0.511742i
$485$		0			0
$486$	−13.9722	+	6.91215i	−0.633792	+	0.313541i
$487$			24.4495i			1.10791i	0.832546	+	0.553956i	$0.186882\pi$
$487$			24.4495i			1.10791i	−0.832546	+	0.553956i	$0.813118\pi$
$488$	−6.92820	+	4.00000i	−0.313625	+	0.181071i
$489$	7.44949	+	10.5352i	0.336878	+	0.476417i
$490$		0			0
$491$	13.6237	−	23.5970i	0.614830	−	1.06492i	−0.375584	−	0.926788i	$-0.622558\pi$
$491$	13.6237	−	23.5970i	0.614830	−	1.06492i	0.990414	−	0.138129i	$-0.0441087\pi$
$492$	14.1582	+	6.52270i	0.638300	+	0.294066i
$493$	−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
$498$	0.866025	+	9.39898i	0.0388075	+	0.421178i
$499$	−4.17423	+	7.22999i	−0.186864	+	0.323659i	−0.944203	−	0.329364i	$-0.893166\pi$
$499$	−4.17423	+	7.22999i	−0.186864	+	0.323659i	0.757339	+	0.653022i	$0.226499\pi$
$500$		0			0
$501$	33.7980	−	3.11416i	1.50998	−	0.139130i
$502$	−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	$0.840475\pi$
$504$	−1.32577	+	0.246405i	−0.0590543	+	0.0109757i
$505$		0			0
$506$	6.00000	+	10.3923i	0.266733	+	0.461994i
$507$	−20.1329	−	9.27526i	−0.894133	−	0.411929i
$508$	−2.89986	−	1.67423i	−0.128660	−	0.0742821i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	−0.224745	−	0.389270i	−0.00994213	−	0.0172203i
$512$			1.00000i			0.0441942i
$513$	10.5352	+	37.2474i	0.465139	+	1.64452i
$514$	−12.7980			−0.564494
$515$		0			0
$516$	−2.55051	−	3.60697i	−0.112280	−	0.158788i
$517$	46.2405	+	26.6969i	2.03365	+	1.17413i
$518$	4.41761	+	2.55051i	0.194099	+	0.112063i
$519$	7.10102	−	15.4135i	0.311700	−	0.676577i
$520$		0			0
$521$	−29.3939			−1.28777			−0.643885	−	0.765123i	$-0.722678\pi$
$521$	−29.3939			−1.28777			−0.643885	+	0.765123i	$0.722678\pi$
$522$	−5.58542	+	4.77526i	−0.244467	+	0.209007i
$523$		−	20.3485i		−	0.889776i	−0.895586	−	0.444888i	$-0.853243\pi$
$523$		−	20.3485i		−	0.889776i	0.895586	−	0.444888i	$-0.146757\pi$
$524$	−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
$528$	−0.778539	−	8.44949i	−0.0338816	−	0.367717i
$529$	−8.50000	−	14.7224i	−0.369565	−	0.640106i
$530$		0			0
$531$	10.6237	+	12.4261i	0.461030	+	0.539248i
$532$			3.34847i			0.145175i
$533$	−3.50343	+	2.02270i	−0.151750	+	0.0876130i
$534$	6.52270	−	14.1582i	0.282265	−	0.612685i
$535$		0			0
$536$	0.174235	−	0.301783i	0.00752579	−	0.0130350i
$537$	−13.0779	+	9.24745i	−0.564352	+	0.399057i
$538$	−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
$543$	25.1701	−	17.7980i	1.08015	−	0.763784i
$544$	−2.44949	+	4.24264i	−0.105021	+	0.181902i
$545$		0			0
$546$	0.146428	−	0.317837i	0.00626655	−	0.0136022i
$547$	−13.5546	+	7.82577i	−0.579554	+	0.334606i	−0.760956	−	0.648803i	$-0.775270\pi$
$547$	−13.5546	+	7.82577i	−0.579554	+	0.334606i	0.181402	+	0.983409i	$0.441936\pi$
$548$			3.00000i			0.128154i
$549$	−23.5959	+	4.38551i	−1.00705	+	0.187169i
$550$		0			0
$551$	9.12372	+	15.8028i	0.388684	+	0.673220i
$552$	−0.389270	−	4.22474i	−0.0165684	−	0.179817i
$553$	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	$-0.340430\pi$
$558$	12.5851	+	4.44949i	0.532768	+	0.188362i
$559$	1.14643			0.0484887
$560$		0			0
$561$	17.3939	−	37.7552i	0.734370	−	1.59402i
$562$	−16.5420	−	9.55051i	−0.697781	−	0.402864i
$563$	20.7364	+	11.9722i	0.873937	+	0.504568i	0.868655	−	0.495418i	$-0.164985\pi$
$563$	20.7364	+	11.9722i	0.873937	+	0.504568i	0.00528250	+	0.999986i	$0.498319\pi$
$564$	−10.8990	−	15.4135i	−0.458930	−	0.649025i
$565$		0			0
$566$	13.2474			0.556832
$567$	−3.99624	−	0.628827i	−0.167826	−	0.0264082i
$568$		−	13.3485i		−	0.560089i
$569$	16.8990	+	29.2699i	0.708442	+	1.22706i	0.965435	+	0.260644i	$0.0839350\pi$
$569$	16.8990	+	29.2699i	0.708442	+	1.22706i	−0.256993	+	0.966413i	$0.582732\pi$
$570$		0			0
$571$	−12.9722	+	22.4685i	−0.542869	+	0.940277i	0.455868	+	0.890047i	$0.349329\pi$
$571$	−12.9722	+	22.4685i	−0.542869	+	0.940277i	−0.998738	+	0.0502301i	$0.984005\pi$
$572$	1.90702	+	1.10102i	0.0797367	+	0.0460360i
$573$	1.73205	+	0.797959i	0.0723575	+	0.0333352i
$574$	2.02270	+	3.50343i	0.0844260	+	0.146230i
$575$		0			0
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$		−	40.3939i		−	1.68162i	−0.541331	−	0.840810i	$-0.682079\pi$
$577$		−	40.3939i		−	1.68162i	0.541331	−	0.840810i	$-0.317921\pi$
$578$	−6.06218	+	3.50000i	−0.252153	+	0.145581i
$579$	−34.4949	+	3.17837i	−1.43356	+	0.132089i
$580$		0			0
$581$	−1.22474	+	2.12132i	−0.0508110	+	0.0880072i
$582$	1.39816	+	15.1742i	0.0579556	+	0.628992i
$583$	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	$-0.480932\pi$
$587$	23.1202	−	13.3485i	0.954274	−	0.550950i	0.894406	+	0.447256i	$0.147599\pi$
$588$	10.6941	+	4.92679i	0.441017	+	0.203177i
$589$	16.5732	−	28.7056i	0.682887	−	1.18280i
$590$		0			0
$591$	0.247449	+	0.349945i	0.0101787	+	0.0143948i
$592$	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	$-0.0518545\pi$
$594$	6.24745	−	24.6773i	0.256336	−	1.01252i
$595$		0			0
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	19.5133	−	13.7980i	0.798625	−	0.564713i
$598$	0.953512	+	0.550510i	0.0389920	+	0.0225120i
$599$	−11.3258	+	19.6168i	−0.462758	+	0.801521i	−0.999097	−	0.0424819i	$-0.986474\pi$
$599$	−11.3258	+	19.6168i	−0.462758	+	0.801521i	0.536339	+	0.844003i	$0.319807\pi$
$600$		0			0
$601$	8.24745	+	14.2850i	0.336420	+	0.582697i	0.983757	−	0.179507i	$-0.0574503\pi$
$601$	8.24745	+	14.2850i	0.336420	+	0.582697i	−0.647336	+	0.762205i	$0.724117\pi$
$602$		−	1.14643i		−	0.0467249i
$603$	0.794593	−	0.679337i	0.0323583	−	0.0276647i
$604$	−20.0000			−0.813788
$605$		0			0
$606$	−14.5732	+	1.34278i	−0.591996	+	0.0545468i
$607$	2.89986	+	1.67423i	0.117702	+	0.0679551i	0.557695	−	0.830046i	$-0.311686\pi$
$607$	2.89986	+	1.67423i	0.117702	+	0.0679551i	−0.439993	+	0.898001i	$0.645019\pi$
$608$	6.45145	+	3.72474i	0.261641	+	0.151058i
$609$	−1.89898	+	0.174973i	−0.0769505	+	0.00709025i
$610$		0			0
$611$	4.89898			0.198191
$612$	−11.1708	+	9.55051i	−0.451555	+	0.386056i
$613$			12.0454i			0.486509i	0.969962	+	0.243255i	$0.0782151\pi$
$613$			12.0454i			0.486509i	−0.969962	+	0.243255i	$0.921785\pi$
$614$	−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	0.998310	+	0.0581058i	$0.0185061\pi$
$617$	38.4462	+	22.1969i	1.54779	+	0.893615i	0.549476	+	0.835509i	$0.314827\pi$
$618$	−23.6130	+	16.6969i	−0.949856	+	0.671649i
$619$	−15.8712	−	27.4897i	−0.637916	−	1.10490i	−0.985889	−	0.167399i	$-0.946463\pi$
$619$	−15.8712	−	27.4897i	−0.637916	−	1.10490i	0.347973	−	0.937505i	$-0.386870\pi$
$620$		0			0
$621$	3.12372	−	12.3387i	0.125351	−	0.495133i
$622$		−	1.10102i		−	0.0441469i
$623$	3.50343	−	2.02270i	0.140362	−	0.0810379i
$624$	−0.449490	−	0.635674i	−0.0179940	−	0.0254473i
$625$		0			0
$626$	−2.94949	+	5.10867i	−0.117885	+	0.204183i
$627$	−57.4113	−	26.4495i	−2.29279	−	1.05629i
$628$	−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
$633$	−0.548188	−	5.94949i	−0.0217885	−	0.236471i
$634$	−8.57321	+	14.8492i	−0.340486	+	0.589739i
$635$		0			0
$636$	−6.12372	+	0.564242i	−0.242821	+	0.0223737i
$637$	−2.64624	+	1.52781i	−0.104848	+	0.0605339i
$638$		−	12.0000i		−	0.475085i
$639$	13.3485	−	37.7552i	0.528057	−	1.49357i
$640$		0			0
$641$	7.19694	+	12.4655i	0.284262	+	0.492356i	0.972430	−	0.233195i	$-0.0749181\pi$
$641$	7.19694	+	12.4655i	0.284262	+	0.492356i	−0.688168	+	0.725551i	$0.741585\pi$
$642$	−14.5475	−	6.70204i	−0.574142	−	0.264508i
$643$	15.2867	+	8.82577i	0.602848	+	0.348054i	0.770161	−	0.637850i	$-0.220176\pi$
$643$	15.2867	+	8.82577i	0.602848	+	0.348054i	−0.167313	+	0.985904i	$0.553509\pi$
$644$	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	$-0.158143\pi$
$648$	−5.65685	+	7.00000i	−0.222222	+	0.274986i
$649$	−26.6969			−1.04795
$650$		0			0
$651$	2.00000	+	2.82843i	0.0783862	+	0.110855i
$652$	6.45145	+	3.72474i	0.252658	+	0.145872i
$653$	−15.8028	−	9.12372i	−0.618410	−	0.357039i	0.157840	−	0.987465i	$-0.449547\pi$
$653$	−15.8028	−	9.12372i	−0.618410	−	0.357039i	−0.776250	+	0.630426i	$0.782880\pi$
$654$	−4.02270	+	8.73169i	−0.157300	+	0.341436i
$655$		0			0
$656$	9.00000			0.351391
$657$	−2.82843	−	1.00000i	−0.110347	−	0.0390137i
$658$		−	4.89898i		−	0.190982i
$659$	4.92679	+	8.53344i	0.191920	+	0.332416i	0.945887	−	0.324497i	$-0.105195\pi$
$659$	4.92679	+	8.53344i	0.191920	+	0.332416i	−0.753966	+	0.656913i	$0.771862\pi$
$660$		0			0
$661$	−3.69694	+	6.40329i	−0.143794	+	0.249059i	−0.928922	−	0.370274i	$-0.879264\pi$
$661$	−3.69694	+	6.40329i	−0.143794	+	0.249059i	0.785128	+	0.619333i	$0.212597\pi$
$662$	−5.49794	−	3.17423i	−0.213683	−	0.123370i
$663$	−0.349945	−	3.79796i	−0.0135908	−	0.147501i
$664$	2.72474	+	4.71940i	0.105741	+	0.183148i
$665$		0			0
$666$	33.4722	−	6.22110i	1.29702	−	0.241063i
$667$		−	6.00000i		−	0.232321i
$668$	16.9706	−	9.79796i	0.656611	−	0.379094i
$669$	12.8990	−	27.9985i	0.498703	−	1.08249i
$670$		0			0
$671$	19.5959	−	33.9411i	0.756492	−	1.31028i
$672$	−0.635674	+	0.449490i	−0.0245217	+	0.0173394i
$673$	19.6561	−	11.3485i	0.757688	−	0.437451i	−0.0707771	−	0.997492i	$-0.522548\pi$
$673$	19.6561	−	11.3485i	0.757688	−	0.437451i	0.828465	+	0.560041i	$0.189215\pi$
$674$	−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	$-0.501241\pi$
$677$	22.3810	−	12.9217i	0.860172	−	0.496621i	0.864070	+	0.503372i	$0.167907\pi$
$678$	5.79972	−	4.10102i	0.222737	−	0.157499i
$679$	−1.97730	+	3.42478i	−0.0758817	+	0.131431i
$680$		0			0
$681$	−9.89388	+	21.4757i	−0.379134	+	0.822949i
$682$	−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	$0.703514\pi$
$684$	14.5227	+	16.9866i	0.555289	+	0.649500i
$685$		0			0
$686$	3.10102	+	5.37113i	0.118398	+	0.205071i
$687$	−2.08921	−	22.6742i	−0.0797084	−	0.865076i
$688$	−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	−0.951271	−	0.308355i	$-0.900222\pi$
$691$	−19.5227	−	33.8143i	−0.742679	−	1.28636i	0.208593	−	0.978003i	$-0.433112\pi$
$692$		−	9.79796i		−	0.372463i
$693$	5.02118	−	4.29286i	0.190739	−	0.163072i
$694$	12.0000			0.455514
$695$		0			0
$696$	−1.77526	+	3.85337i	−0.0672909	+	0.146062i
$697$	38.1838	+	22.0454i	1.44631	+	0.835029i
$698$	12.1244	+	7.00000i	0.458914	+	0.264954i
$699$	−23.6969	−	33.5125i	−0.896301	−	1.26756i
$700$		0			0
$701$	33.7980			1.27653			0.638266	−	0.769816i	$-0.279652\pi$
$701$	33.7980			1.27653			0.638266	+	0.769816i	$0.279652\pi$
$702$	−0.635674	−	2.24745i	−0.0239920	−	0.0848245i
$703$		−	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
$708$	8.57277	+	3.94949i	0.322184	+	0.148431i
$709$	2.22474	+	3.85337i	0.0835520	+	0.144716i	0.904773	−	0.425894i	$-0.140040\pi$
$709$	2.22474	+	3.85337i	0.0835520	+	0.144716i	−0.821221	+	0.570610i	$0.806707\pi$
$710$		0			0
$711$	49.2474	−	9.15306i	1.84692	−	0.343267i
$712$		−	9.00000i		−	0.337289i
$713$	−9.43879	+	5.44949i	−0.353486	+	0.204085i
$714$	−3.79796	+	0.349945i	−0.142135	+	0.0130964i
$715$		0			0
$716$	−4.62372	+	8.00853i	−0.172797	+	0.299293i
$717$	−2.29629	−	24.9217i	−0.0857566	−	0.930717i
$718$	12.2993	−	7.10102i	0.459007	−	0.265008i
$719$	−7.95459			−0.296656			−0.148328	−	0.988938i	$-0.547389\pi$
$719$	−7.95459			−0.296656			−0.148328	+	0.988938i	$0.547389\pi$
$720$		0			0
$721$	−7.50510			−0.279505
$722$	31.6055	−	18.2474i	1.17624	−	0.679100i
$723$	5.03723	+	2.32066i	0.187337	+	0.0863064i
$724$	8.89898	−	15.4135i	0.330728	−	0.572838i
$725$		0			0
$726$	13.0000	+	18.3848i	0.482475	+	0.682323i
$727$	13.8564	−	8.00000i	0.513906	−	0.296704i	−0.220532	−	0.975380i	$-0.570779\pi$
$727$	13.8564	−	8.00000i	0.513906	−	0.296704i	0.734438	+	0.678676i	$0.237446\pi$
$728$		−	0.202041i		−	0.00748814i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$		0			0
$731$	−6.24745	−	10.8209i	−0.231070	−	0.400225i
$732$	−11.3137	+	8.00000i	−0.418167	+	0.295689i
$733$	−22.5167	−	13.0000i	−0.831672	−	0.480166i	0.0227529	−	0.999741i	$-0.492757\pi$
$733$	−22.5167	−	13.0000i	−0.831672	−	0.480166i	−0.854425	+	0.519575i	$0.826090\pi$
$734$	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
$738$	25.4558	+	9.00000i	0.937043	+	0.331295i
$739$	−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
$741$	−5.77526	+	0.532134i	−0.212159	+	0.0195484i
$742$	−1.38211	−	0.797959i	−0.0507387	−	0.0292940i
$743$	−42.7370	−	24.6742i	−1.56787	−	0.905210i	−0.996417	−	0.0845746i	$-0.973047\pi$
$743$	−42.7370	−	24.6742i	−1.56787	−	0.905210i	−0.571452	−	0.820635i	$-0.693620\pi$
$744$	7.67423	−	0.707107i	0.281351	−	0.0259238i
$745$		0			0
$746$	23.5959			0.863908
$747$	2.98735	+	16.0732i	0.109301	+	0.588088i
$748$		−	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	−0.806578	−	0.591128i	$-0.798683\pi$
$751$	2.97730	−	5.15683i	0.108643	−	0.188175i	0.915221	+	0.402953i	$0.132016\pi$
$752$	−9.43879	−	5.44949i	−0.344197	−	0.198722i
$753$	−0.778539	+	0.550510i	−0.0283715	+	0.0200617i
$754$	−0.550510	−	0.953512i	−0.0200484	−	0.0347248i
$755$		0			0
$756$	−2.24745	+	0.635674i	−0.0817389	+	0.0231193i
$757$			38.0454i			1.38278i	0.722480	+	0.691392i	$0.243002\pi$
$757$			38.0454i			1.38278i	−0.722480	+	0.691392i	$0.756998\pi$
$758$	7.70674	−	4.44949i	0.279921	−	0.161613i
$759$	12.0000	+	16.9706i	0.435572	+	0.615992i
$760$		0			0
$761$	−6.94949	+	12.0369i	−0.251919	+	0.436336i	−0.964054	−	0.265706i	$-0.914395\pi$
$761$	−6.94949	+	12.0369i	−0.251919	+	0.436336i	0.712135	+	0.702042i	$0.247728\pi$
$762$	−5.26758	−	2.42679i	−0.190824	−	0.0879132i
$763$	−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
$768$	0.158919	+	1.72474i	0.00573448	+	0.0622364i
$769$	−14.0959	+	24.4148i	−0.508312	+	0.880422i	0.491642	+	0.870797i	$0.336397\pi$
$769$	−14.0959	+	24.4148i	−0.508312	+	0.880422i	−0.999954	+	0.00962438i	$0.996936\pi$
$770$		0			0
$771$	−22.0732	+	2.03383i	−0.794947	+	0.0732467i
$772$	−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	$-0.0599103\pi$
$774$	−4.97219	−	5.81577i	−0.178722	−	0.209044i
$775$		0			0
$776$	4.39898	+	7.61926i	0.157914	+	0.273515i
$777$	8.02458	+	3.69694i	0.287880	+	0.132627i
$778$	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
$783$	−8.87455	+	9.12372i	−0.317151	+	0.326055i
$784$	6.79796			0.242784
$785$		0			0
$786$	−3.79796	−	5.37113i	−0.135469	−	0.191582i
$787$	30.0484	+	17.3485i	1.07111	+	0.618406i	0.928485	−	0.371370i	$-0.121112\pi$
$787$	30.0484	+	17.3485i	1.07111	+	0.618406i	0.142626	+	0.989777i	$0.454445\pi$
$788$	0.214297	+	0.123724i	0.00763401	+	0.00440750i
$789$	14.8207	−	32.1698i	0.527630	−	1.14527i
$790$		0			0
$791$	1.84337			0.0655426
$792$	−2.68556	−	14.4495i	−0.0954273	−	0.513440i
$793$		−	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	$-0.513289\pi$
$797$	−26.1951	−	15.1237i	−0.927877	−	0.535710i	−0.886139	+	0.463419i	$0.846623\pi$
$798$	0.532134	+	5.77526i	0.0188373	+	0.204442i
$799$	−26.6969	−	46.2405i	−0.944470	−	1.63587i
$800$		0			0
$801$	9.00000	−	25.4558i	0.317999	−	0.899438i
$802$			38.6969i			1.36644i
$803$	4.24264	−	2.44949i	0.149720	−	0.0864406i
$804$	0.252551	−	0.548188i	0.00890680	−	0.0193331i
$805$		0			0
$806$	−1.00000	+	1.73205i	−0.0352235	+	0.0610089i
$807$	−20.4347	+	14.4495i	−0.719334	+	0.508646i
$808$	−7.31747	+	4.22474i	−0.257428	+	0.148626i
$809$	6.30306			0.221604			0.110802	−	0.993843i	$-0.464658\pi$
$809$	6.30306			0.221604			0.110802	+	0.993843i	$0.464658\pi$
$810$		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
$813$	21.7060	−	15.3485i	0.761263	−	0.538294i
$814$	−27.7980	+	48.1475i	−0.974318	+	1.68757i
$815$		0			0
$816$	−3.55051	+	7.70674i	−0.124293	+	0.269790i
$817$	−16.4545	+	9.50000i	−0.575669	+	0.332363i
$818$		−	0.101021i		−	0.00353210i
$819$	0.202041	−	0.571458i	0.00705988	−	0.0199684i
$820$		0			0
$821$	−13.5959	−	23.5488i	−0.474501	−	0.821860i	0.525073	−	0.851057i	$-0.324038\pi$
$821$	−13.5959	−	23.5488i	−0.474501	−	0.821860i	−0.999574	+	0.0291978i	$0.990705\pi$
$822$	0.476756	+	5.17423i	0.0166288	+	0.180472i
$823$	14.8099	+	8.55051i	0.516241	+	0.298052i	0.735395	−	0.677638i	$-0.236996\pi$
$823$	14.8099	+	8.55051i	0.516241	+	0.298052i	−0.219154	+	0.975690i	$0.570330\pi$
$824$	−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	$0.785118\pi$
$828$	−1.34278	−	7.22474i	−0.0466649	−	0.251077i
$829$	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
$831$	1.12372	−	2.43916i	0.0389816	−	0.0846134i
$832$	−0.389270	−	0.224745i	−0.0134955	−	0.00779163i
$833$	28.8413	+	16.6515i	0.999292	+	0.576941i
$834$	4.00000	+	5.65685i	0.138509	+	0.195881i
$835$		0			0
$836$	−36.4949			−1.26220
$837$	22.4131	+	5.67423i	0.774711	+	0.196130i
$838$			26.1464i			0.903213i
$839$	18.6742	+	32.3447i	0.644706	+	1.11666i	0.984369	+	0.176117i	$0.0563536\pi$
$839$	18.6742	+	32.3447i	0.644706	+	1.11666i	−0.339663	+	0.940547i	$0.610313\pi$
$840$		0			0
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$	22.5560	+	13.0227i	0.777331	+	0.448792i
$843$	−30.0484	−	13.8434i	−1.03492	−	0.476791i
$844$	−1.72474	−	2.98735i	−0.0593682	−	0.102829i
$845$		0			0
$846$	−21.2474	−	24.8523i	−0.730502	−	0.854439i
$847$			5.84337i			0.200780i
$848$	−3.07483	+	1.77526i	−0.105590	+	0.0609625i
$849$	22.8485	−	2.10527i	0.784157	−	0.0722526i
$850$		0			0
$851$	−13.8990	+	24.0737i	−0.476451	+	0.825237i
$852$	−2.12132	−	23.0227i	−0.0726752	−	0.788745i
$853$	−39.8372	+	23.0000i	−1.36400	+	0.787505i	−0.990153	−	0.139986i	$-0.955294\pi$
$853$	−39.8372	+	23.0000i	−1.36400	+	0.787505i	−0.373845	+	0.927491i	$0.621961\pi$
$854$	−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	$-0.341899\pi$
$857$	43.2138	−	24.9495i	1.47615	−	0.852258i	0.999638	+	0.0269070i	$0.00856581\pi$
$858$	3.46410	+	1.59592i	0.118262	+	0.0544837i
$859$	−10.1742	+	17.6223i	−0.347140	+	0.601265i	−0.985740	−	0.168274i	$-0.946181\pi$
$859$	−10.1742	+	17.6223i	−0.347140	+	0.601265i	0.638600	+	0.769539i	$0.279514\pi$
$860$		0			0
$861$	4.04541	+	5.72107i	0.137867	+	0.194974i
$862$	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	$-0.268135\pi$
$864$	−1.27526	+	5.03723i	−0.0433851	+	0.171370i
$865$		0			0
$866$	4.79796	+	8.31031i	0.163041	+	0.282396i
$867$	−9.89949	+	7.00000i	−0.336204	+	0.237732i
$868$	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
$873$	4.82294	+	25.9495i	0.163232	+	0.878257i
$874$	−18.2474			−0.617229
$875$		0			0
$876$	−1.72474	+	0.158919i	−0.0582737	+	0.00536936i
$877$	−27.5378	−	15.8990i	−0.929887	−	0.536870i	−0.0431110	−	0.999070i	$-0.513727\pi$
$877$	−27.5378	−	15.8990i	−0.929887	−	0.536870i	−0.886776	+	0.462200i	$0.847060\pi$
$878$	2.89986	+	1.67423i	0.0978655	+	0.0565027i
$879$	−27.6742	+	2.54991i	−0.933429	+	0.0860065i
$880$		0			0
$881$	38.6969			1.30373			0.651866	−	0.758334i	$-0.273986\pi$
$881$	38.6969			1.30373			0.651866	+	0.758334i	$0.273986\pi$
$882$	19.2275	+	6.79796i	0.647425	+	0.228899i
$883$			47.7980i			1.60853i	0.594271	+	0.804265i	$0.297441\pi$
$883$			47.7980i			1.60853i	−0.594271	+	0.804265i	$0.702559\pi$
$884$	−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	$-0.303873\pi$
$887$	4.76756	+	2.75255i	0.160079	+	0.0924216i	−0.417821	+	0.908530i	$0.637206\pi$
$888$	16.0492	−	11.3485i	0.538575	−	0.380830i
$889$	−0.752551	−	1.30346i	−0.0252398	−	0.0437165i
$890$		0			0
$891$	6.85357	−	43.5549i	0.229603	−	1.45914i
$892$		−	17.7980i		−	0.595920i
$893$	−70.3142	+	40.5959i	−2.35297	+	1.35849i
$894$	6.00000	+	8.48528i	0.200670	+	0.283790i
$895$		0			0
$896$	−0.224745	+	0.389270i	−0.00750820	+	0.0130046i
$897$	1.73205	+	0.797959i	0.0578315	+	0.0266431i
$898$	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
$903$	−0.182189	−	1.97730i	−0.00606286	−	0.0658003i
$904$	2.05051	−	3.55159i	0.0681990	−	0.118124i
$905$		0			0
$906$	−34.4949	+	3.17837i	−1.14602	+	0.105594i
$907$	−31.4787	+	18.1742i	−1.04523	+	0.603466i	−0.921311	−	0.388826i	$-0.872881\pi$
$907$	−31.4787	+	18.1742i	−1.04523	+	0.603466i	−0.123922	+	0.992292i	$0.539547\pi$
$908$			13.6515i			0.453042i
$909$	−24.9217	+	4.63191i	−0.826600	+	0.153631i
$910$		0			0
$911$	3.67423	+	6.36396i	0.121733	+	0.210847i	0.920451	−	0.390858i	$-0.127822\pi$
$911$	3.67423	+	6.36396i	0.121733	+	0.210847i	−0.798718	+	0.601705i	$0.794488\pi$
$912$	11.7190	+	5.39898i	0.388056	+	0.178778i
$913$	−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
$918$	−17.7491	+	18.2474i	−0.585808	+	0.602256i
$919$	−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
$921$	−22.6969	−	32.0983i	−0.747890	−	1.05768i
$922$	−4.02834	−	2.32577i	−0.132666	−	0.0765950i
$923$	5.19615	+	3.00000i	0.171033	+	0.0987462i
$924$	1.59592	−	3.46410i	0.0525018	−	0.113961i
$925$		0			0
$926$	5.34847			0.175762
$927$	−38.0730	+	32.5505i	−1.25048	+	1.06910i
$928$			2.44949i			0.0804084i
$929$	−25.5959	−	44.3334i	−0.839775	−	1.45453i	−0.890083	−	0.455799i	$-0.849354\pi$
$929$	−25.5959	−	44.3334i	−0.839775	−	1.45453i	0.0503079	−	0.998734i	$-0.483980\pi$
$930$		0			0
$931$	25.3207	−	43.8567i	0.829851	−	1.43734i
$932$	−20.5222	−	11.8485i	−0.672225	−	0.388110i
$933$	−0.174973	−	1.89898i	−0.00572835	−	0.0621698i
$934$	5.17423	+	8.96204i	0.169306	+	0.293247i
$935$		0			0
$936$	−0.876276	−	1.02494i	−0.0286420	−	0.0335013i
$937$		−	7.20204i		−	0.235280i	−0.993056	−	0.117640i	$-0.962467\pi$
$937$		−	7.20204i		−	0.235280i	0.993056	−	0.117640i	$-0.0375330\pi$
$938$	0.135648	−	0.0783167i	0.00442908	−	0.00255713i
$939$	−4.27526	+	9.27987i	−0.139518	+	0.302837i
$940$		0			0
$941$	−26.8207	+	46.4548i	−0.874329	+	1.51438i	−0.0168524	+	0.999858i	$0.505365\pi$
$941$	−26.8207	+	46.4548i	−0.874329	+	1.51438i	−0.857476	+	0.514524i	$0.827969\pi$
$942$	−27.9985	+	19.7980i	−0.912242	+	0.645052i
$943$	−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	$-0.806330\pi$
$947$	−22.6435	+	13.0732i	−0.735814	+	0.424822i	0.0847314	+	0.996404i	$0.472997\pi$
$948$	23.6130	−	16.6969i	0.766916	−	0.542291i
$949$	0.224745	−	0.389270i	0.00729553	−	0.0126362i
$950$		0			0
$951$	−12.4268	+	26.9736i	−0.402966	+	0.874679i
$952$	−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	$0.988645\pi$
$954$	−10.4722	+	1.94635i	−0.339050	+	0.0630153i
$955$		0			0
$956$	−7.22474	−	12.5136i	−0.233665	−	0.404720i
$957$	−1.90702	−	20.6969i	−0.0616453	−	0.669037i
$958$	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
$963$	−26.1557	−	9.24745i	−0.842857	−	0.297995i
$964$	3.20204			0.103131
$965$		0			0
$966$	0.797959	−	1.73205i	0.0256739	−	0.0557278i
$967$	27.7128	+	16.0000i	0.891184	+	0.514525i	0.874330	−	0.485333i	$-0.161301\pi$
$967$	27.7128	+	16.0000i	0.891184	+	0.514525i	0.0168544	+	0.999858i	$0.494635\pi$
$968$	11.2583	+	6.50000i	0.361856	+	0.208918i
$969$	36.4949	+	51.6116i	1.17239	+	1.65800i
$970$		0			0
$971$	−40.8434			−1.31073			−0.655363	−	0.755314i	$-0.727484\pi$
$971$	−40.8434			−1.31073			−0.655363	+	0.755314i	$0.727484\pi$
$972$	−8.64420	+	12.9722i	−0.277263	+	0.416083i
$973$			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	$-0.379319\pi$
$977$	−7.79423	−	4.50000i	−0.249359	−	0.143968i	−0.619471	+	0.785020i	$0.712653\pi$
$978$	11.7190	+	5.39898i	0.374733	+	0.172640i
$979$	22.0454	+	38.1838i	0.704574	+	1.22036i
$980$		0			0
$981$	−5.55051	+	15.6992i	−0.177214	+	0.501237i
$982$		−	27.2474i		−	0.869501i
$983$	−11.3458	+	6.55051i	−0.361875	+	0.208929i	−0.669903	−	0.742449i	$-0.733664\pi$
$983$	−11.3458	+	6.55051i	−0.361875	+	0.208929i	0.308028	+	0.951377i	$0.400331\pi$
$984$	15.5227	−	1.43027i	0.494846	−	0.0455953i
$985$		0			0
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$	−0.778539	−	8.44949i	−0.0247812	−	0.268950i
$988$	−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
$993$	−9.98698	−	4.60102i	−0.316927	−	0.146009i
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$	5.44949	+	7.70674i	0.172674	+	0.244197i
$997$	6.96753	−	4.02270i	0.220664	−	0.127400i	−0.385594	−	0.922669i	$-0.626003\pi$
$997$	6.96753	−	4.02270i	0.220664	−	0.127400i	0.606258	+	0.795268i	$0.292670\pi$
$998$			8.34847i			0.264266i
$999$	56.7423	−	16.0492i	1.79525	−	0.507773i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.41421 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.724745 - 1.57313i) q^{6} +(0.389270 - 0.224745i) q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.41421 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.724745 - 1.57313i) q^{6} +(0.389270 - 0.224745i) q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(2.44949 + 4.24264i) q^{11} +(-0.158919 - 1.72474i) q^{12} +(0.389270 + 0.224745i) q^{13} +(0.224745 - 0.389270i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.89898i q^{17} +(-0.548188 - 2.94949i) q^{18} -7.44949 q^{19} +(0.325765 - 0.707107i) q^{21} +(4.24264 + 2.44949i) q^{22} +(2.12132 + 1.22474i) q^{23} +(-1.00000 - 1.41421i) q^{24} +0.449490 q^{26} +(-1.41421 - 5.00000i) q^{27} -0.449490i q^{28} +(-1.22474 - 2.12132i) q^{29} +(-2.22474 + 3.85337i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(7.70674 + 3.55051i) q^{33} +(-2.44949 - 4.24264i) q^{34} +(-1.94949 - 2.28024i) q^{36} +11.3485i q^{37} +(-6.45145 + 3.72474i) q^{38} +(0.775255 - 0.0714323i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(-0.0714323 - 0.775255i) q^{42} +(2.20881 - 1.27526i) q^{43} +4.89898 q^{44} +2.44949 q^{46} +(9.43879 - 5.44949i) q^{47} +(-1.57313 - 0.724745i) q^{48} +(-3.39898 + 5.88721i) q^{49} +(-4.89898 - 6.92820i) q^{51} +(0.389270 - 0.224745i) q^{52} -3.55051i q^{53} +(-3.72474 - 3.62302i) q^{54} +(-0.224745 - 0.389270i) q^{56} +(-10.5352 + 7.44949i) q^{57} +(-2.12132 - 1.22474i) q^{58} +(-2.72474 + 4.71940i) q^{59} +(-4.00000 - 6.92820i) q^{61} +4.44949i q^{62} +(-0.246405 - 1.32577i) q^{63} -1.00000 q^{64} +(8.44949 - 0.778539i) q^{66} +(0.301783 + 0.174235i) q^{67} +(-4.24264 - 2.44949i) q^{68} +(4.22474 - 0.389270i) q^{69} +13.3485 q^{71} +(-2.82843 - 1.00000i) q^{72} -1.00000i q^{73} +(5.67423 + 9.82806i) q^{74} +(-3.72474 + 6.45145i) q^{76} +(1.90702 + 1.10102i) q^{77} +(0.635674 - 0.449490i) q^{78} +(8.34847 + 14.4600i) q^{79} +(-7.00000 - 5.65685i) q^{81} +9.00000i q^{82} +(-4.71940 + 2.72474i) q^{83} +(-0.449490 - 0.635674i) q^{84} +(1.27526 - 2.20881i) q^{86} +(-3.85337 - 1.77526i) q^{87} +(4.24264 - 2.44949i) q^{88} +9.00000 q^{89} +0.202041 q^{91} +(2.12132 - 1.22474i) q^{92} +(0.707107 + 7.67423i) q^{93} +(5.44949 - 9.43879i) q^{94} +(-1.72474 + 0.158919i) q^{96} +(-7.61926 + 4.39898i) q^{97} +6.79796i q^{98} +(14.4495 - 2.68556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^6 + 8 * q^9	\( 8 q + 4 q^{4} - 4 q^{6} + 8 q^{9} - 8 q^{14} - 4 q^{16} - 40 q^{19} + 32 q^{21} - 8 q^{24} - 16 q^{26} - 8 q^{31} + 4 q^{36} + 16 q^{39} - 36 q^{41} + 12 q^{49} - 20 q^{54} + 8 q^{56} - 12 q^{59} - 32 q^{61} - 8 q^{64} + 48 q^{66} + 24 q^{69} + 48 q^{71} + 16 q^{74} - 20 q^{76} + 8 q^{79} - 56 q^{81} + 16 q^{84} + 20 q^{86} + 72 q^{89} + 80 q^{91} + 24 q^{94} - 4 q^{96} + 96 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^6 + 8 * q^9 - 8 * q^14 - 4 * q^16 - 40 * q^19 + 32 * q^21 - 8 * q^24 - 16 * q^26 - 8 * q^31 + 4 * q^36 + 16 * q^39 - 36 * q^41 + 12 * q^49 - 20 * q^54 + 8 * q^56 - 12 * q^59 - 32 * q^61 - 8 * q^64 + 48 * q^66 + 24 * q^69 + 48 * q^71 + 16 * q^74 - 20 * q^76 + 8 * q^79 - 56 * q^81 + 16 * q^84 + 20 * q^86 + 72 * q^89 + 80 * q^91 + 24 * q^94 - 4 * q^96 + 96 * q^99

Introduction

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