LMFDB - Embedded newform 450.2.j.f.49.3

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			49.3
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	450.49
Dual form			450.2.j.f.349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.41421 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.72474 - 0.158919i) q^{6} +(-3.85337 + 2.22474i) q^{7} -1.00000i q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.41421 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.72474 - 0.158919i) q^{6} +(-3.85337 + 2.22474i) q^{7} -1.00000i q^{8} +(1.00000 + 2.82843i) q^{9} +(-2.44949 - 4.24264i) q^{11} +(-1.57313 + 0.724745i) q^{12} +(-3.85337 - 2.22474i) q^{13} +(-2.22474 + 3.85337i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.89898i q^{17} +(2.28024 + 1.94949i) q^{18} -2.55051 q^{19} +(7.67423 + 0.707107i) q^{21} +(-4.24264 - 2.44949i) q^{22} +(-2.12132 - 1.22474i) q^{23} +(-1.00000 + 1.41421i) q^{24} -4.44949 q^{26} +(1.41421 - 5.00000i) q^{27} +4.44949i q^{28} +(1.22474 + 2.12132i) q^{29} +(0.224745 - 0.389270i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.778539 + 8.44949i) q^{33} +(2.44949 + 4.24264i) q^{34} +(2.94949 + 0.548188i) q^{36} -3.34847i q^{37} +(-2.20881 + 1.27526i) q^{38} +(3.22474 + 6.99964i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(6.99964 - 3.22474i) q^{42} +(6.45145 - 3.72474i) q^{43} -4.89898 q^{44} -2.44949 q^{46} +(0.953512 - 0.550510i) q^{47} +(-0.158919 + 1.72474i) q^{48} +(6.39898 - 11.0834i) q^{49} +(4.89898 - 6.92820i) q^{51} +(-3.85337 + 2.22474i) q^{52} -8.44949i q^{53} +(-1.27526 - 5.03723i) q^{54} +(2.22474 + 3.85337i) q^{56} +(3.60697 + 2.55051i) q^{57} +(2.12132 + 1.22474i) q^{58} +(-0.275255 + 0.476756i) q^{59} +(-4.00000 - 6.92820i) q^{61} -0.449490i q^{62} +(-10.1459 - 8.67423i) q^{63} -1.00000 q^{64} +(3.55051 + 7.70674i) q^{66} +(-12.4261 - 7.17423i) q^{67} +(4.24264 + 2.44949i) q^{68} +(1.77526 + 3.85337i) q^{69} -1.34847 q^{71} +(2.82843 - 1.00000i) q^{72} -1.00000i q^{73} +(-1.67423 - 2.89986i) q^{74} +(-1.27526 + 2.20881i) q^{76} +(18.8776 + 10.8990i) q^{77} +(6.29253 + 4.44949i) q^{78} +(-6.34847 - 10.9959i) q^{79} +(-7.00000 + 5.65685i) q^{81} +9.00000i q^{82} +(-0.476756 + 0.275255i) q^{83} +(4.44949 - 6.29253i) q^{84} +(3.72474 - 6.45145i) q^{86} +(0.389270 - 4.22474i) q^{87} +(-4.24264 + 2.44949i) q^{88} +9.00000 q^{89} +19.7980 q^{91} +(-2.12132 + 1.22474i) q^{92} +(-0.707107 + 0.325765i) q^{93} +(0.550510 - 0.953512i) q^{94} +(0.724745 + 1.57313i) q^{96} +(9.35131 - 5.39898i) q^{97} -12.7980i q^{98} +(9.55051 - 11.1708i) 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
$6$	−1.72474	−	0.158919i	−0.704124	−	0.0648783i
$7$	−3.85337	+	2.22474i	−1.45644	+	0.840875i	−0.998834	−	0.0482818i	$-0.984625\pi$
$7$	−3.85337	+	2.22474i	−1.45644	+	0.840875i	−0.457604	+	0.889156i	$0.651292\pi$
$8$		−	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	$-0.902178\pi$
$11$	−2.44949	−	4.24264i	−0.738549	−	1.27920i	0.214600	−	0.976702i	$-0.431155\pi$
$12$	−1.57313	+	0.724745i	−0.454124	+	0.209216i
$13$	−3.85337	−	2.22474i	−1.06873	−	0.617033i	−0.140898	−	0.990024i	$-0.544999\pi$
$13$	−3.85337	−	2.22474i	−1.06873	−	0.617033i	−0.927835	+	0.372991i	$0.878332\pi$
$14$	−2.22474	+	3.85337i	−0.594588	+	1.02986i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			4.89898i			1.18818i	0.804400	+	0.594089i	$0.202487\pi$
$17$			4.89898i			1.18818i	−0.804400	+	0.594089i	$0.797513\pi$
$18$	2.28024	+	1.94949i	0.537457	+	0.459499i
$19$	−2.55051			−0.585127			−0.292564	−	0.956246i	$-0.594508\pi$
$19$	−2.55051			−0.585127			−0.292564	+	0.956246i	$0.594508\pi$
$20$		0			0
$21$	7.67423	+	0.707107i	1.67466	+	0.154303i
$22$	−4.24264	−	2.44949i	−0.904534	−	0.522233i
$23$	−2.12132	−	1.22474i	−0.442326	−	0.255377i	0.262258	−	0.964998i	$-0.415533\pi$
$23$	−2.12132	−	1.22474i	−0.442326	−	0.255377i	−0.704584	+	0.709621i	$0.748866\pi$
$24$	−1.00000	+	1.41421i	−0.204124	+	0.288675i
$25$		0			0
$26$	−4.44949			−0.872617
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$			4.44949i			0.840875i
$29$	1.22474	+	2.12132i	0.227429	+	0.393919i	0.957046	−	0.289938i	$-0.0936346\pi$
$29$	1.22474	+	2.12132i	0.227429	+	0.393919i	−0.729616	+	0.683857i	$0.760301\pi$
$30$		0			0
$31$	0.224745	−	0.389270i	0.0403654	−	0.0699149i	−0.845137	−	0.534550i	$-0.820481\pi$
$31$	0.224745	−	0.389270i	0.0403654	−	0.0699149i	0.885502	+	0.464635i	$0.153814\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.778539	+	8.44949i	−0.135526	+	1.47087i
$34$	2.44949	+	4.24264i	0.420084	+	0.727607i
$35$		0			0
$36$	2.94949	+	0.548188i	0.491582	+	0.0913647i
$37$		−	3.34847i		−	0.550485i	−0.961375	−	0.275242i	$-0.911242\pi$
$37$		−	3.34847i		−	0.550485i	0.961375	−	0.275242i	$-0.0887581\pi$
$38$	−2.20881	+	1.27526i	−0.358316	+	0.206874i
$39$	3.22474	+	6.99964i	0.516372	+	1.12084i
$40$		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	$0.918608\pi$
$42$	6.99964	−	3.22474i	1.08007	−	0.497589i
$43$	6.45145	−	3.72474i	0.983836	−	0.568018i	0.0804103	−	0.996762i	$-0.474377\pi$
$43$	6.45145	−	3.72474i	0.983836	−	0.568018i	0.903426	+	0.428744i	$0.141044\pi$
$44$	−4.89898			−0.738549
$45$		0			0
$46$	−2.44949			−0.361158
$47$	0.953512	−	0.550510i	0.139084	−	0.0803002i	−0.428843	−	0.903379i	$-0.641079\pi$
$47$	0.953512	−	0.550510i	0.139084	−	0.0803002i	0.567927	+	0.823079i	$0.307745\pi$
$48$	−0.158919	+	1.72474i	−0.0229379	+	0.248945i
$49$	6.39898	−	11.0834i	0.914140	−	1.58334i
$50$		0			0
$51$	4.89898	−	6.92820i	0.685994	−	0.970143i
$52$	−3.85337	+	2.22474i	−0.534366	+	0.308517i
$53$		−	8.44949i		−	1.16063i	−0.814393	−	0.580313i	$-0.802930\pi$
$53$		−	8.44949i		−	1.16063i	0.814393	−	0.580313i	$-0.197070\pi$
$54$	−1.27526	−	5.03723i	−0.173540	−	0.685481i
$55$		0			0
$56$	2.22474	+	3.85337i	0.297294	+	0.514928i
$57$	3.60697	+	2.55051i	0.477754	+	0.337823i
$58$	2.12132	+	1.22474i	0.278543	+	0.160817i
$59$	−0.275255	+	0.476756i	−0.0358352	+	0.0620683i	−0.883387	−	0.468645i	$-0.844742\pi$
$59$	−0.275255	+	0.476756i	−0.0358352	+	0.0620683i	0.847552	+	0.530713i	$0.178076\pi$
$60$		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	$-0.337817\pi$
$62$		−	0.449490i		−	0.0570853i
$63$	−10.1459	−	8.67423i	−1.27826	−	1.09285i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.55051	+	7.70674i	0.437038	+	0.948634i
$67$	−12.4261	−	7.17423i	−1.51809	−	0.876472i	−0.999773	−	0.0212861i	$-0.993224\pi$
$67$	−12.4261	−	7.17423i	−1.51809	−	0.876472i	−0.518321	−	0.855186i	$-0.673443\pi$
$68$	4.24264	+	2.44949i	0.514496	+	0.297044i
$69$	1.77526	+	3.85337i	0.213716	+	0.463891i
$70$		0			0
$71$	−1.34847			−0.160034			−0.0800169	−	0.996794i	$-0.525497\pi$
$71$	−1.34847			−0.160034			−0.0800169	+	0.996794i	$0.525497\pi$
$72$	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	$-0.0186383\pi$
$74$	−1.67423	−	2.89986i	−0.194626	−	0.337102i
$75$		0			0
$76$	−1.27526	+	2.20881i	−0.146282	+	0.253368i
$77$	18.8776	+	10.8990i	2.15130	+	1.24205i
$78$	6.29253	+	4.44949i	0.712489	+	0.503806i
$79$	−6.34847	−	10.9959i	−0.714259	−	1.23713i	−0.963245	−	0.268625i	$-0.913431\pi$
$79$	−6.34847	−	10.9959i	−0.714259	−	1.23713i	0.248986	−	0.968507i	$-0.419903\pi$
$80$		0			0
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$			9.00000i			0.993884i
$83$	−0.476756	+	0.275255i	−0.0523308	+	0.0302132i	−0.525937	−	0.850523i	$-0.676285\pi$
$83$	−0.476756	+	0.275255i	−0.0523308	+	0.0302132i	0.473606	+	0.880737i	$0.342952\pi$
$84$	4.44949	−	6.29253i	0.485479	−	0.686571i
$85$		0			0
$86$	3.72474	−	6.45145i	0.401650	−	0.695677i
$87$	0.389270	−	4.22474i	0.0417341	−	0.452940i
$88$	−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
$91$	19.7980			2.07539
$92$	−2.12132	+	1.22474i	−0.221163	+	0.127688i
$93$	−0.707107	+	0.325765i	−0.0733236	+	0.0337803i
$94$	0.550510	−	0.953512i	0.0567808	−	0.0983472i
$95$		0			0
$96$	0.724745	+	1.57313i	0.0739690	+	0.160557i
$97$	9.35131	−	5.39898i	0.949481	−	0.548183i	0.0565616	−	0.998399i	$-0.481986\pi$
$97$	9.35131	−	5.39898i	0.949481	−	0.548183i	0.892920	+	0.450216i	$0.148653\pi$
$98$		−	12.7980i		−	1.29279i
$99$	9.55051	−	11.1708i	0.959862	−	1.12271i
$100$		0			0
$101$	−1.77526	−	3.07483i	−0.176644	−	0.305957i	0.764085	−	0.645116i	$-0.223191\pi$
$101$	−1.77526	−	3.07483i	−0.176644	−	0.305957i	−0.940729	+	0.339159i	$0.889858\pi$
$102$	0.778539	−	8.44949i	0.0770869	−	0.836624i
$103$	10.9959	+	6.34847i	1.08346	+	0.625533i	0.931826	−	0.362904i	$-0.118215\pi$
$103$	10.9959	+	6.34847i	1.08346	+	0.625533i	0.151629	+	0.988437i	$0.451548\pi$
$104$	−2.22474	+	3.85337i	−0.218154	+	0.377854i
$105$		0			0
$106$	−4.22474	−	7.31747i	−0.410343	−	0.710736i
$107$			15.2474i			1.47403i	0.675878	+	0.737013i	$0.263764\pi$
$107$			15.2474i			1.47403i	−0.675878	+	0.737013i	$0.736236\pi$
$108$	−3.62302	−	3.72474i	−0.348625	−	0.358414i
$109$	−10.4495			−1.00088			−0.500440	−	0.865771i	$-0.666828\pi$
$109$	−10.4495			−1.00088			−0.500440	+	0.865771i	$0.666828\pi$
$110$		0			0
$111$	−3.34847	+	4.73545i	−0.317823	+	0.449469i
$112$	3.85337	+	2.22474i	0.364109	+	0.210219i
$113$	12.0369	+	6.94949i	1.13233	+	0.653753i	0.944521	−	0.328452i	$-0.106527\pi$
$113$	12.0369	+	6.94949i	1.13233	+	0.653753i	0.187813	+	0.982205i	$0.439860\pi$
$114$	4.39898	+	0.405324i	0.412002	+	0.0379620i
$115$		0			0
$116$	2.44949			0.227429
$117$	2.43916	−	13.1237i	0.225500	−	1.21329i
$118$			0.550510i			0.0506786i
$119$	−10.8990	−	18.8776i	−0.999108	−	1.73051i
$120$		0			0
$121$	−6.50000	+	11.2583i	−0.590909	+	1.02348i
$122$	−6.92820	−	4.00000i	−0.627250	−	0.362143i
$123$	14.1582	−	6.52270i	1.27660	−	0.588132i
$124$	−0.224745	−	0.389270i	−0.0201827	−	0.0349574i
$125$		0			0
$126$	−13.1237	−	2.43916i	−1.16915	−	0.217297i
$127$			11.3485i			1.00701i	0.863991	+	0.503507i	$0.167957\pi$
$127$			11.3485i			1.00701i	−0.863991	+	0.503507i	$0.832043\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−12.8485	−	1.18386i	−1.13124	−	0.104233i
$130$		0			0
$131$	−7.89898	+	13.6814i	−0.690137	+	1.19535i	0.281656	+	0.959516i	$0.409116\pi$
$131$	−7.89898	+	13.6814i	−0.690137	+	1.19535i	−0.971793	+	0.235837i	$0.924217\pi$
$132$	6.92820	+	4.89898i	0.603023	+	0.426401i
$133$	9.82806	−	5.67423i	0.852201	−	0.492019i
$134$	−14.3485			−1.23952
$135$		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
$141$	−1.89898	−	0.174973i	−0.159923	−	0.0147354i
$142$	−1.16781	+	0.674235i	−0.0980003	+	0.0565805i
$143$			21.7980i			1.82284i
$144$	1.94949	−	2.28024i	0.162457	−	0.190020i
$145$		0			0
$146$	−0.500000	−	0.866025i	−0.0413803	−	0.0716728i
$147$	−20.1329	+	9.27526i	−1.66053	+	0.765010i
$148$	−2.89986	−	1.67423i	−0.238367	−	0.137621i
$149$	−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	$-0.469265\pi$
$152$			2.55051i			0.206874i
$153$	−13.8564	+	4.89898i	−1.12022	+	0.396059i
$154$	21.7980			1.75653
$155$		0			0
$156$	7.67423	+	0.707107i	0.614431	+	0.0566139i
$157$	−0.174973	−	0.101021i	−0.0139643	−	0.00806231i	0.493002	−	0.870028i	$-0.335900\pi$
$157$	−0.174973	−	0.101021i	−0.0139643	−	0.00806231i	−0.506966	+	0.861966i	$0.669233\pi$
$158$	−10.9959	−	6.34847i	−0.874785	−	0.505057i
$159$	−8.44949	+	11.9494i	−0.670088	+	0.947648i
$160$		0			0
$161$	10.8990			0.858960
$162$	−3.23375	+	8.39898i	−0.254067	+	0.659886i
$163$			2.55051i			0.199771i	0.994999	+	0.0998857i	$0.0318477\pi$
$163$			2.55051i			0.199771i	−0.994999	+	0.0998857i	$0.968152\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$		0			0
$166$	−0.275255	+	0.476756i	−0.0213639	+	0.0370034i
$167$	−16.9706	−	9.79796i	−1.31322	−	0.758189i	−0.330593	−	0.943773i	$-0.607249\pi$
$167$	−16.9706	−	9.79796i	−1.31322	−	0.758189i	−0.982628	+	0.185584i	$0.940582\pi$
$168$	0.707107	−	7.67423i	0.0545545	−	0.592080i
$169$	3.39898	+	5.88721i	0.261460	+	0.452862i
$170$		0			0
$171$	−2.55051	−	7.21393i	−0.195042	−	0.551663i
$172$		−	7.44949i		−	0.568018i
$173$	−8.48528	+	4.89898i	−0.645124	+	0.372463i	−0.786586	−	0.617481i	$-0.788153\pi$
$173$	−8.48528	+	4.89898i	−0.645124	+	0.372463i	0.141462	+	0.989944i	$0.454820\pi$
$174$	−1.77526	−	3.85337i	−0.134582	−	0.292123i
$175$		0			0
$176$	−2.44949	+	4.24264i	−0.184637	+	0.319801i
$177$	0.866025	−	0.398979i	0.0650945	−	0.0299891i
$178$	7.79423	−	4.50000i	0.584202	−	0.337289i
$179$	15.2474			1.13965			0.569824	−	0.821767i	$-0.307011\pi$
$179$	15.2474			1.13965			0.569824	+	0.821767i	$0.307011\pi$
$180$		0			0
$181$	−1.79796			−0.133641			−0.0668206	−	0.997765i	$-0.521286\pi$
$181$	−1.79796			−0.133641			−0.0668206	+	0.997765i	$0.521286\pi$
$182$	17.1455	−	9.89898i	1.27091	−	0.733761i
$183$	−1.27135	+	13.7980i	−0.0939808	+	1.01997i
$184$	−1.22474	+	2.12132i	−0.0902894	+	0.156386i
$185$		0			0
$186$	−0.449490	+	0.635674i	−0.0329582	+	0.0466099i
$187$	20.7846	−	12.0000i	1.51992	−	0.877527i
$188$		−	1.10102i		−	0.0803002i
$189$	5.67423	+	22.4131i	0.412740	+	1.63031i
$190$		0			0
$191$	5.44949	+	9.43879i	0.394311	+	0.682967i	0.993013	−	0.118005i	$-0.0376499\pi$
$191$	5.44949	+	9.43879i	0.394311	+	0.682967i	−0.598702	+	0.800972i	$0.704317\pi$
$192$	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	$0.922440\pi$
$194$	5.39898	−	9.35131i	0.387624	−	0.671385i
$195$		0			0
$196$	−6.39898	−	11.0834i	−0.457070	−	0.791668i
$197$		−	24.2474i		−	1.72756i	−0.503870	−	0.863780i	$-0.668091\pi$
$197$		−	24.2474i		−	1.72756i	0.503870	−	0.863780i	$-0.331909\pi$
$198$	2.68556	−	14.4495i	0.190855	−	1.02688i
$199$	−5.79796			−0.411006			−0.205503	−	0.978656i	$-0.565883\pi$
$199$	−5.79796			−0.411006			−0.205503	+	0.978656i	$0.565883\pi$
$200$		0			0
$201$	10.3990	+	22.5720i	0.733487	+	1.59211i
$202$	−3.07483	−	1.77526i	−0.216344	−	0.124907i
$203$	−9.43879	−	5.44949i	−0.662473	−	0.382479i
$204$	−3.55051	−	7.70674i	−0.248585	−	0.539580i
$205$		0			0
$206$	12.6969			0.884638
$207$	1.34278	−	7.22474i	0.0933298	−	0.502154i
$208$			4.44949i			0.308517i
$209$	6.24745	+	10.8209i	0.432145	+	0.748497i
$210$		0			0
$211$	−0.724745	+	1.25529i	−0.0498935	+	0.0864181i	−0.889894	−	0.456168i	$-0.849222\pi$
$211$	−0.724745	+	1.25529i	−0.0498935	+	0.0864181i	0.840000	+	0.542586i	$0.182555\pi$
$212$	−7.31747	−	4.22474i	−0.502566	−	0.290157i
$213$	1.90702	+	1.34847i	0.130667	+	0.0923956i
$214$	7.62372	+	13.2047i	0.521147	+	0.902653i
$215$		0			0
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$			2.00000i			0.135769i
$218$	−9.04952	+	5.22474i	−0.612911	+	0.353864i
$219$	−1.00000	+	1.41421i	−0.0675737	+	0.0955637i
$220$		0			0
$221$	10.8990	−	18.8776i	0.733145	−	1.26984i
$222$	−0.532134	+	5.77526i	−0.0357145	+	0.387610i
$223$	−1.55708	+	0.898979i	−0.104270	+	0.0602001i	−0.551228	−	0.834355i	$-0.685841\pi$
$223$	−1.55708	+	0.898979i	−0.104270	+	0.0602001i	0.446958	+	0.894555i	$0.352507\pi$
$224$	4.44949			0.297294
$225$		0			0
$226$	13.8990			0.924546
$227$	−24.5505	+	14.1742i	−1.62947	+	0.940777i	−0.645224	+	0.763994i	$0.723236\pi$
$227$	−24.5505	+	14.1742i	−1.62947	+	0.940777i	−0.984250	+	0.176783i	$0.943431\pi$
$228$	4.01229	−	1.84847i	0.265720	−	0.122418i
$229$	−10.5732	+	18.3133i	−0.698698	+	1.21018i	0.270221	+	0.962798i	$0.412903\pi$
$229$	−10.5732	+	18.3133i	−0.698698	+	1.21018i	−0.968918	+	0.247381i	$0.920430\pi$
$230$		0			0
$231$	−15.7980	−	34.2911i	−1.03943	−	2.25619i
$232$	2.12132	−	1.22474i	0.139272	−	0.0804084i
$233$			5.69694i			0.373219i	0.982434	+	0.186609i	$0.0597499\pi$
$233$			5.69694i			0.373219i	−0.982434	+	0.186609i	$0.940250\pi$
$234$	−4.44949	−	12.5851i	−0.290872	−	0.822711i
$235$		0			0
$236$	0.275255	+	0.476756i	0.0179176	+	0.0310342i
$237$	−2.01778	+	21.8990i	−0.131069	+	1.42249i
$238$	−18.8776	−	10.8990i	−1.22365	−	0.706476i
$239$	4.77526	−	8.27098i	0.308886	−	0.535006i	−0.669233	−	0.743052i	$-0.733377\pi$
$239$	4.77526	−	8.27098i	0.308886	−	0.535006i	0.978119	+	0.208047i	$0.0667107\pi$
$240$		0			0
$241$	11.3990	+	19.7436i	0.734273	+	1.27180i	0.955042	+	0.296472i	$0.0958100\pi$
$241$	11.3990	+	19.7436i	0.734273	+	1.27180i	−0.220769	+	0.975326i	$0.570857\pi$
$242$			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
$247$	9.82806	+	5.67423i	0.625345	+	0.361043i
$248$	−0.389270	−	0.224745i	−0.0247186	−	0.0142713i
$249$	0.949490	+	0.0874863i	0.0601715	+	0.00554422i
$250$		0			0
$251$	−5.44949			−0.343969			−0.171984	−	0.985100i	$-0.555018\pi$
$251$	−5.44949			−0.343969			−0.171984	+	0.985100i	$0.555018\pi$
$252$	−12.5851	+	4.44949i	−0.792784	+	0.280292i
$253$			12.0000i			0.754434i
$254$	5.67423	+	9.82806i	0.356033	+	0.616667i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.88721	+	3.39898i	0.367234	+	0.212023i	0.672249	−	0.740325i	$-0.265328\pi$
$257$	5.88721	+	3.39898i	0.367234	+	0.212023i	−0.305016	+	0.952347i	$0.598662\pi$
$258$	−11.7190	+	5.39898i	−0.729595	+	0.336126i
$259$	7.44949	+	12.9029i	0.462889	+	0.801747i
$260$		0			0
$261$	−4.77526	+	5.58542i	−0.295581	+	0.345729i
$262$			15.7980i			0.976001i
$263$	13.4671	−	7.77526i	0.830419	−	0.479443i	−0.0235770	−	0.999722i	$-0.507505\pi$
$263$	13.4671	−	7.77526i	0.830419	−	0.479443i	0.853996	+	0.520279i	$0.174172\pi$
$264$	8.44949	+	0.778539i	0.520030	+	0.0479158i
$265$		0			0
$266$	5.67423	−	9.82806i	0.347910	−	0.602597i
$267$	−12.7279	−	9.00000i	−0.778936	−	0.550791i
$268$	−12.4261	+	7.17423i	−0.759047	+	0.438236i
$269$	−9.55051			−0.582305			−0.291152	−	0.956677i	$-0.594039\pi$
$269$	−9.55051			−0.582305			−0.291152	+	0.956677i	$0.594039\pi$
$270$		0			0
$271$	0.651531			0.0395777			0.0197888	−	0.999804i	$-0.493701\pi$
$271$	0.651531			0.0395777			0.0197888	+	0.999804i	$0.493701\pi$
$272$	4.24264	−	2.44949i	0.257248	−	0.148522i
$273$	−27.9985	−	19.7980i	−1.69455	−	1.19823i
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$		0			0
$276$	4.22474	+	0.389270i	0.254300	+	0.0234313i
$277$	5.58542	−	3.22474i	0.335595	−	0.193756i	−0.322727	−	0.946492i	$-0.604600\pi$
$277$	5.58542	−	3.22474i	0.335595	−	0.193756i	0.658323	+	0.752736i	$0.271266\pi$
$278$			4.00000i			0.239904i
$279$	1.32577	+	0.246405i	0.0793715	+	0.0147519i
$280$		0			0
$281$	−14.4495	−	25.0273i	−0.861984	−	1.49300i	−0.870011	−	0.493033i	$-0.835888\pi$
$281$	−14.4495	−	25.0273i	−0.861984	−	1.49300i	0.00802643	−	0.999968i	$-0.497445\pi$
$282$	−1.73205	+	0.797959i	−0.103142	+	0.0475178i
$283$	−9.74058	−	5.62372i	−0.579017	−	0.334296i	0.181726	−	0.983349i	$-0.441832\pi$
$283$	−9.74058	−	5.62372i	−0.579017	−	0.334296i	−0.760743	+	0.649054i	$0.775165\pi$
$284$	−0.674235	+	1.16781i	−0.0400085	+	0.0692967i
$285$		0			0
$286$	10.8990	+	18.8776i	0.644470	+	1.11626i
$287$		−	40.0454i		−	2.36381i
$288$	0.548188	−	2.94949i	0.0323023	−	0.173800i
$289$	−7.00000			−0.411765
$290$		0			0
$291$	−18.6237	−	1.71600i	−1.09174	−	0.100594i
$292$	−0.866025	−	0.500000i	−0.0506803	−	0.0292603i
$293$	24.2880	+	14.0227i	1.41892	+	0.819215i	0.996204	−	0.0870462i	$-0.0277428\pi$
$293$	24.2880	+	14.0227i	1.41892	+	0.819215i	0.422718	+	0.906261i	$0.361076\pi$
$294$	−12.7980	+	18.0990i	−0.746392	+	1.05556i
$295$		0			0
$296$	−3.34847			−0.194626
$297$	−24.6773	+	6.24745i	−1.43192	+	0.362514i
$298$			6.00000i			0.347571i
$299$	5.44949	+	9.43879i	0.315152	+	0.545859i
$300$		0			0
$301$	−16.5732	+	28.7056i	−0.955264	+	1.65457i
$302$	−17.3205	−	10.0000i	−0.996683	−	0.575435i
$303$	−0.564242	+	6.12372i	−0.0324149	+	0.351799i
$304$	1.27526	+	2.20881i	0.0731409	+	0.126684i
$305$		0			0
$306$	−9.55051	+	11.1708i	−0.545966	+	0.638595i
$307$			6.69694i			0.382214i	0.981569	+	0.191107i	$0.0612078\pi$
$307$			6.69694i			0.382214i	−0.981569	+	0.191107i	$0.938792\pi$
$308$	18.8776	−	10.8990i	1.07565	−	0.621027i
$309$	−9.20204	−	19.9740i	−0.523486	−	1.13628i
$310$		0			0
$311$	5.44949	−	9.43879i	0.309012	−	0.535225i	−0.669134	−	0.743141i	$-0.733335\pi$
$311$	5.44949	−	9.43879i	0.309012	−	0.535225i	0.978147	+	0.207917i	$0.0666683\pi$
$312$	6.99964	−	3.22474i	0.396276	−	0.182565i
$313$	3.37662	−	1.94949i	0.190858	−	0.110192i	−0.401526	−	0.915847i	$-0.631520\pi$
$313$	3.37662	−	1.94949i	0.190858	−	0.110192i	0.592384	+	0.805656i	$0.298187\pi$
$314$	−0.202041			−0.0114018
$315$		0			0
$316$	−12.6969			−0.714259
$317$	14.8492	−	8.57321i	0.834017	−	0.481520i	−0.0212094	−	0.999775i	$-0.506752\pi$
$317$	14.8492	−	8.57321i	0.834017	−	0.481520i	0.855226	+	0.518255i	$0.173418\pi$
$318$	−1.34278	+	14.5732i	−0.0752994	+	0.817225i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	15.2474	−	21.5631i	0.851030	−	1.20354i
$322$	9.43879	−	5.44949i	0.526003	−	0.303688i
$323$		−	12.4949i		−	0.695235i
$324$	1.39898	+	8.89060i	0.0777211	+	0.493922i
$325$		0			0
$326$	1.27526	+	2.20881i	0.0706298	+	0.122334i
$327$	14.7778	+	10.4495i	0.817215	+	0.577858i
$328$	7.79423	+	4.50000i	0.430364	+	0.248471i
$329$	−2.44949	+	4.24264i	−0.135045	+	0.233904i
$330$		0			0
$331$	4.17423	+	7.22999i	0.229437	+	0.397396i	0.957641	−	0.287964i	$-0.0929783\pi$
$331$	4.17423	+	7.22999i	0.229437	+	0.397396i	−0.728205	+	0.685360i	$0.759645\pi$
$332$			0.550510i			0.0302132i
$333$	9.47090	−	3.34847i	0.519002	−	0.183495i
$334$	−19.5959			−1.07224
$335$		0			0
$336$	−3.22474	−	6.99964i	−0.175924	−	0.381861i
$337$	−9.61377	−	5.55051i	−0.523695	−	0.302356i	0.214750	−	0.976669i	$-0.431106\pi$
$337$	−9.61377	−	5.55051i	−0.523695	−	0.302356i	−0.738445	+	0.674313i	$0.764440\pi$
$338$	5.88721	+	3.39898i	0.320222	+	0.184880i
$339$	−10.0732	−	21.8649i	−0.547102	−	1.18754i
$340$		0			0
$341$	−2.20204			−0.119247
$342$	−5.81577	−	4.97219i	−0.314481	−	0.268865i
$343$			25.7980i			1.39296i
$344$	−3.72474	−	6.45145i	−0.200825	−	0.347839i
$345$		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
$351$	−16.5732	+	16.1206i	−0.884613	+	0.860454i
$352$			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	$0.410320\pi$
$354$	0.550510	−	0.778539i	0.0292593	−	0.0413789i
$355$		0			0
$356$	4.50000	−	7.79423i	0.238500	−	0.413093i
$357$	−3.46410	+	37.5959i	−0.183340	+	1.98979i
$358$	13.2047	−	7.62372i	0.697889	−	0.402926i
$359$	33.7980			1.78379			0.891894	−	0.452244i	$-0.149377\pi$
$359$	33.7980			1.78379			0.891894	+	0.452244i	$0.149377\pi$
$360$		0			0
$361$	−12.4949			−0.657626
$362$	−1.55708	+	0.898979i	−0.0818382	+	0.0472493i
$363$	20.4507	−	9.42168i	1.07338	−	0.494510i
$364$	9.89898	−	17.1455i	0.518848	−	0.898670i
$365$		0			0
$366$	5.79796	+	12.5851i	0.303064	+	0.657831i
$367$	−14.4600	+	8.34847i	−0.754804	+	0.435787i	−0.827427	−	0.561573i	$-0.810196\pi$
$367$	−14.4600	+	8.34847i	−0.754804	+	0.435787i	0.0726228	+	0.997359i	$0.476863\pi$
$368$			2.44949i			0.127688i
$369$	−26.5454	−	4.93369i	−1.38190	−	0.256838i
$370$		0			0
$371$	18.7980	+	32.5590i	0.975941	+	1.69038i
$372$	−0.0714323	+	0.775255i	−0.00370359	+	0.0401951i
$373$	−13.5065	−	7.79796i	−0.699338	−	0.403763i	0.107763	−	0.994177i	$-0.465631\pi$
$373$	−13.5065	−	7.79796i	−0.699338	−	0.403763i	−0.807101	+	0.590414i	$0.798965\pi$
$374$	12.0000	−	20.7846i	0.620505	−	1.07475i
$375$		0			0
$376$	−0.550510	−	0.953512i	−0.0283904	−	0.0491736i
$377$		−	10.8990i		−	0.561326i
$378$	16.1206	+	16.5732i	0.829154	+	0.852434i
$379$	−0.898979			−0.0461775			−0.0230887	−	0.999733i	$-0.507350\pi$
$379$	−0.898979			−0.0461775			−0.0230887	+	0.999733i	$0.507350\pi$
$380$		0			0
$381$	11.3485	−	16.0492i	0.581400	−	0.822223i
$382$	9.43879	+	5.44949i	0.482931	+	0.278820i
$383$	−22.9059	−	13.2247i	−1.17044	−	0.675753i	−0.216655	−	0.976248i	$-0.569515\pi$
$383$	−22.9059	−	13.2247i	−1.17044	−	0.675753i	−0.953783	+	0.300495i	$0.902848\pi$
$384$	1.72474	+	0.158919i	0.0880155	+	0.00810978i
$385$		0			0
$386$	−20.0000			−1.01797
$387$	16.9866	+	14.5227i	0.863478	+	0.738231i
$388$		−	10.7980i		−	0.548183i
$389$	−6.79796	−	11.7744i	−0.344670	−	0.596986i	0.640624	−	0.767855i	$-0.278676\pi$
$389$	−6.79796	−	11.7744i	−0.344670	−	0.596986i	−0.985294	+	0.170869i	$0.945343\pi$
$390$		0			0
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	−11.0834	−	6.39898i	−0.559794	−	0.323197i
$393$	24.8523	−	11.4495i	1.25363	−	0.577550i
$394$	−12.1237	−	20.9989i	−0.610784	−	1.05791i
$395$		0			0
$396$	−4.89898	−	13.8564i	−0.246183	−	0.696311i
$397$		−	21.5959i		−	1.08387i	−0.840421	−	0.541934i	$-0.817692\pi$
$397$		−	21.5959i		−	1.08387i	0.840421	−	0.541934i	$-0.182308\pi$
$398$	−5.02118	+	2.89898i	−0.251689	+	0.145313i
$399$	−19.5732	−	1.80348i	−0.979886	−	0.0902871i
$400$		0			0
$401$	−4.65153	+	8.05669i	−0.232286	+	0.402332i	−0.958481	−	0.285158i	$-0.907954\pi$
$401$	−4.65153	+	8.05669i	−0.232286	+	0.402332i	0.726194	+	0.687490i	$0.241287\pi$
$402$	20.2918	+	14.3485i	1.01206	+	0.715637i
$403$	−1.73205	+	1.00000i	−0.0862796	+	0.0498135i
$404$	−3.55051			−0.176644
$405$		0			0
$406$	−10.8990			−0.540907
$407$	−14.2064	+	8.20204i	−0.704183	+	0.406560i
$408$	−6.92820	−	4.89898i	−0.342997	−	0.242536i
$409$	4.94949	−	8.57277i	0.244737	−	0.423896i	−0.717321	−	0.696743i	$-0.754632\pi$
$409$	4.94949	−	8.57277i	0.244737	−	0.423896i	0.962058	+	0.272847i	$0.0879652\pi$
$410$		0			0
$411$	5.17423	+	0.476756i	0.255226	+	0.0235166i
$412$	10.9959	−	6.34847i	0.541728	−	0.312767i
$413$		−	2.44949i		−	0.120532i
$414$	−2.44949	−	6.92820i	−0.120386	−	0.340503i
$415$		0			0
$416$	2.22474	+	3.85337i	0.109077	+	0.188927i
$417$	6.29253	−	2.89898i	0.308146	−	0.141964i
$418$	10.8209	+	6.24745i	0.529267	+	0.305573i
$419$	4.07321	−	7.05501i	0.198990	−	0.344660i	−0.749212	−	0.662331i	$-0.769567\pi$
$419$	4.07321	−	7.05501i	0.198990	−	0.344660i	0.948201	+	0.317671i	$0.102901\pi$
$420$		0			0
$421$	−9.02270	−	15.6278i	−0.439740	−	0.761651i	0.557929	−	0.829888i	$-0.311596\pi$
$421$	−9.02270	−	15.6278i	−0.439740	−	0.761651i	−0.997669	+	0.0682369i	$0.978263\pi$
$422$			1.44949i			0.0705601i
$423$	2.51059	+	2.14643i	0.122069	+	0.104363i
$424$	−8.44949			−0.410343
$425$		0			0
$426$	2.32577	+	0.214297i	0.112684	+	0.0103827i
$427$	30.8270	+	17.7980i	1.49182	+	0.861304i
$428$	13.2047	+	7.62372i	0.638272	+	0.368507i
$429$	21.7980	−	30.8270i	1.05242	−	1.48834i
$430$		0			0
$431$	10.6515			0.513066			0.256533	−	0.966535i	$-0.417420\pi$
$431$	10.6515			0.513066			0.256533	+	0.966535i	$0.417420\pi$
$432$	−5.03723	+	1.27526i	−0.242354	+	0.0613557i
$433$		−	29.5959i		−	1.42229i	−0.703046	−	0.711145i	$-0.748177\pi$
$433$		−	29.5959i		−	1.42229i	0.703046	−	0.711145i	$-0.251823\pi$
$434$	1.00000	+	1.73205i	0.0480015	+	0.0831411i
$435$		0			0
$436$	−5.22474	+	9.04952i	−0.250220	+	0.433394i
$437$	5.41045	+	3.12372i	0.258817	+	0.149428i
$438$	−0.158919	+	1.72474i	−0.00759343	+	0.0824115i
$439$	−5.67423	−	9.82806i	−0.270816	−	0.469068i	0.698255	−	0.715849i	$-0.253960\pi$
$439$	−5.67423	−	9.82806i	−0.270816	−	0.469068i	−0.969071	+	0.246782i	$0.920627\pi$
$440$		0			0
$441$	37.7474	+	7.01569i	1.79750	+	0.334080i
$442$		−	21.7980i		−	1.03682i
$443$	24.0737	−	13.8990i	1.14378	−	0.660360i	0.196415	−	0.980521i	$-0.437070\pi$
$443$	24.0737	−	13.8990i	1.14378	−	0.660360i	0.947363	+	0.320161i	$0.103737\pi$
$444$	2.42679	+	5.26758i	0.115170	+	0.249989i
$445$		0			0
$446$	−0.898979	+	1.55708i	−0.0425679	+	0.0737298i
$447$	9.43879	−	4.34847i	0.446440	−	0.205676i
$448$	3.85337	−	2.22474i	0.182055	−	0.105109i
$449$	−10.5959			−0.500052			−0.250026	−	0.968239i	$-0.580439\pi$
$449$	−10.5959			−0.500052			−0.250026	+	0.968239i	$0.580439\pi$
$450$		0			0
$451$	44.0908			2.07616
$452$	12.0369	−	6.94949i	0.566167	−	0.326877i
$453$	−3.17837	+	34.4949i	−0.149333	+	1.62071i
$454$	−14.1742	+	24.5505i	−0.665230	+	1.15221i
$455$		0			0
$456$	2.55051	−	3.60697i	0.119439	−	0.168912i
$457$	13.5939	−	7.84847i	0.635898	−	0.367136i	−0.147135	−	0.989116i	$-0.547005\pi$
$457$	13.5939	−	7.84847i	0.635898	−	0.367136i	0.783033	+	0.621981i	$0.213672\pi$
$458$			21.1464i			0.988108i
$459$	24.4949	+	6.92820i	1.14332	+	0.323381i
$460$		0			0
$461$	−9.67423	−	16.7563i	−0.450574	−	0.780417i	0.547848	−	0.836578i	$-0.315447\pi$
$461$	−9.67423	−	16.7563i	−0.450574	−	0.780417i	−0.998422	+	0.0561610i	$0.982114\pi$
$462$	−30.8270	−	21.7980i	−1.43420	−	1.01413i
$463$	−8.09601	−	4.67423i	−0.376254	−	0.217230i	0.299933	−	0.953960i	$-0.403036\pi$
$463$	−8.09601	−	4.67423i	−0.376254	−	0.217230i	−0.676187	+	0.736730i	$0.736369\pi$
$464$	1.22474	−	2.12132i	0.0568574	−	0.0984798i
$465$		0			0
$466$	2.84847	+	4.93369i	0.131953	+	0.228549i
$467$		−	4.34847i		−	0.201223i	−0.994926	−	0.100612i	$-0.967920\pi$
$467$		−	4.34847i		−	0.201223i	0.994926	−	0.100612i	$-0.0320799\pi$
$468$	−10.1459	−	8.67423i	−0.468994	−	0.400967i
$469$	63.8434			2.94801
$470$		0			0
$471$	0.146428	+	0.317837i	0.00674706	+	0.0146452i
$472$	0.476756	+	0.275255i	0.0219445	+	0.0126696i
$473$	−31.6055	−	18.2474i	−1.45322	−	0.839019i
$474$	9.20204	+	19.9740i	0.422664	+	0.917434i
$475$		0			0
$476$	−21.7980			−0.999108
$477$	23.8988	−	8.44949i	1.09425	−	0.386876i
$478$		−	9.55051i		−	0.436830i
$479$	−12.1237	−	20.9989i	−0.553947	−	0.959465i	−0.997985	−	0.0634563i	$-0.979788\pi$
$479$	−12.1237	−	20.9989i	−0.553947	−	0.959465i	0.444038	−	0.896008i	$-0.353546\pi$
$480$		0			0
$481$	−7.44949	+	12.9029i	−0.339667	+	0.588321i
$482$	19.7436	+	11.3990i	0.899297	+	0.519209i
$483$	−15.4135	−	10.8990i	−0.701338	−	0.495921i
$484$	6.50000	+	11.2583i	0.295455	+	0.511742i
$485$		0			0
$486$	12.9722	−	8.64420i	0.588431	−	0.392109i
$487$			19.5505i			0.885918i	0.896542	+	0.442959i	$0.146071\pi$
$487$			19.5505i			0.885918i	−0.896542	+	0.442959i	$0.853929\pi$
$488$	−6.92820	+	4.00000i	−0.313625	+	0.181071i
$489$	2.55051	−	3.60697i	0.115338	−	0.163113i
$490$		0			0
$491$	1.37628	−	2.38378i	0.0621105	−	0.107578i	−0.833298	−	0.552824i	$-0.813550\pi$
$491$	1.37628	−	2.38378i	0.0621105	−	0.107578i	0.895409	+	0.445245i	$0.146884\pi$
$492$	1.43027	−	15.5227i	0.0644814	−	0.699818i
$493$	−10.3923	+	6.00000i	−0.468046	+	0.270226i
$494$	11.3485			0.510592
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	5.19615	−	3.00000i	0.233079	−	0.134568i
$498$	0.866025	−	0.398979i	0.0388075	−	0.0178787i
$499$	3.17423	−	5.49794i	0.142098	−	0.246121i	−0.786188	−	0.617987i	$-0.787948\pi$
$499$	3.17423	−	5.49794i	0.142098	−	0.246121i	0.928287	+	0.371866i	$0.121282\pi$
$500$		0			0
$501$	14.2020	+	30.8270i	0.634500	+	1.37725i
$502$	−4.71940	+	2.72474i	−0.210637	+	0.121611i
$503$			26.4495i			1.17932i	0.807650	+	0.589662i	$0.200739\pi$
$503$			26.4495i			1.17932i	−0.807650	+	0.589662i	$0.799261\pi$
$504$	−8.67423	+	10.1459i	−0.386381	+	0.451934i
$505$		0			0
$506$	6.00000	+	10.3923i	0.266733	+	0.461994i
$507$	1.08032	−	11.7247i	0.0479788	−	0.520714i
$508$	9.82806	+	5.67423i	0.436050	+	0.251753i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	2.22474	+	3.85337i	0.0984169	+	0.170463i
$512$			1.00000i			0.0441942i
$513$	−3.60697	+	12.7526i	−0.159251	+	0.563039i
$514$	6.79796			0.299845
$515$		0			0
$516$	−7.44949	+	10.5352i	−0.327945	+	0.463785i
$517$	−4.67123	−	2.69694i	−0.205441	−	0.118611i
$518$	12.9029	+	7.44949i	0.566921	+	0.327312i
$519$	16.8990	+	1.55708i	0.741783	+	0.0683481i
$520$		0			0
$521$	29.3939			1.28777			0.643885	−	0.765123i	$-0.277322\pi$
$521$	29.3939			1.28777			0.643885	+	0.765123i	$0.277322\pi$
$522$	−1.34278	+	7.22474i	−0.0587719	+	0.316218i
$523$		−	5.65153i		−	0.247124i	−0.992337	−	0.123562i	$-0.960568\pi$
$523$		−	5.65153i		−	0.247124i	0.992337	−	0.123562i	$-0.0394318\pi$
$524$	7.89898	+	13.6814i	0.345069	+	0.597676i
$525$		0			0
$526$	7.77526	−	13.4671i	0.339017	−	0.587195i
$527$	1.90702	+	1.10102i	0.0830712	+	0.0479612i
$528$	7.70674	−	3.55051i	0.335393	−	0.154516i
$529$	−8.50000	−	14.7224i	−0.369565	−	0.640106i
$530$		0			0
$531$	−1.62372	−	0.301783i	−0.0704636	−	0.0130963i
$532$		−	11.3485i		−	0.492019i
$533$	34.6803	−	20.0227i	1.50217	−	0.867280i
$534$	−15.5227	−	1.43027i	−0.671733	−	0.0618937i
$535$		0			0
$536$	−7.17423	+	12.4261i	−0.309880	+	0.536727i
$537$	−21.5631	−	15.2474i	−0.930519	−	0.657976i
$538$	−8.27098	+	4.77526i	−0.356587	+	0.205876i
$539$	−62.6969			−2.70055
$540$		0			0
$541$	−18.2020			−0.782567			−0.391283	−	0.920270i	$-0.627969\pi$
$541$	−18.2020			−0.782567			−0.391283	+	0.920270i	$0.627969\pi$
$542$	0.564242	−	0.325765i	0.0242363	−	0.0139928i
$543$	2.54270	+	1.79796i	0.109118	+	0.0771578i
$544$	2.44949	−	4.24264i	0.105021	−	0.181902i
$545$		0			0
$546$	−34.1464	−	3.14626i	−1.46133	−	0.134648i
$547$	−26.2825	+	15.1742i	−1.12376	+	0.648803i	−0.942358	−	0.334606i	$-0.891397\pi$
$547$	−26.2825	+	15.1742i	−1.12376	+	0.648803i	−0.181402	+	0.983409i	$0.558064\pi$
$548$			3.00000i			0.128154i
$549$	15.5959	−	18.2419i	0.665618	−	0.778546i
$550$		0			0
$551$	−3.12372	−	5.41045i	−0.133075	−	0.230493i
$552$	3.85337	−	1.77526i	0.164010	−	0.0755599i
$553$	48.9260	+	28.2474i	2.08055	+	1.20120i
$554$	3.22474	−	5.58542i	0.137006	−	0.237302i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$			17.3939i			0.737002i	0.929627	+	0.368501i	$0.120129\pi$
$557$			17.3939i			0.737002i	−0.929627	+	0.368501i	$0.879871\pi$
$558$	1.27135	−	0.449490i	0.0538205	−	0.0190284i
$559$	−33.1464			−1.40194
$560$		0			0
$561$	−41.3939	−	3.81405i	−1.74765	−	0.161029i
$562$	−25.0273	−	14.4495i	−1.05571	−	0.609515i
$563$	−25.9326	−	14.9722i	−1.09293	−	0.631003i	−0.158574	−	0.987347i	$-0.550690\pi$
$563$	−25.9326	−	14.9722i	−1.09293	−	0.631003i	−0.934355	+	0.356344i	$0.884023\pi$
$564$	−1.10102	+	1.55708i	−0.0463613	+	0.0655648i
$565$		0			0
$566$	−11.2474			−0.472766
$567$	14.3885	−	37.3712i	0.604262	−	1.56944i
$568$			1.34847i			0.0565805i
$569$	7.10102	+	12.2993i	0.297690	+	0.515615i	0.975607	−	0.219524i	$-0.0704504\pi$
$569$	7.10102	+	12.2993i	0.297690	+	0.515615i	−0.677917	+	0.735139i	$0.737117\pi$
$570$		0			0
$571$	13.9722	−	24.2005i	0.584718	−	1.01276i	−0.410192	−	0.911999i	$-0.634538\pi$
$571$	13.9722	−	24.2005i	0.584718	−	1.01276i	0.994911	−	0.100762i	$-0.0321282\pi$
$572$	18.8776	+	10.8990i	0.789312	+	0.455709i
$573$	1.73205	−	18.7980i	0.0723575	−	0.785296i
$574$	−20.0227	−	34.6803i	−0.835732	−	1.44753i
$575$		0			0
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$			18.3939i			0.765747i	0.923801	+	0.382874i	$0.125066\pi$
$577$			18.3939i			0.765747i	−0.923801	+	0.382874i	$0.874934\pi$
$578$	−6.06218	+	3.50000i	−0.252153	+	0.145581i
$579$	14.4949	+	31.4626i	0.602387	+	1.30754i
$580$		0			0
$581$	1.22474	−	2.12132i	0.0508110	−	0.0880072i
$582$	−16.9866	+	7.82577i	−0.704118	+	0.324388i
$583$	−35.8481	+	20.6969i	−1.48468	+	0.857180i
$584$	−1.00000			−0.0413803
$585$		0			0
$586$	28.0454			1.15855
$587$	−2.33562	+	1.34847i	−0.0964012	+	0.0556573i	−0.547426	−	0.836854i	$-0.684392\pi$
$587$	−2.33562	+	1.34847i	−0.0964012	+	0.0556573i	0.451024	+	0.892512i	$0.351059\pi$
$588$	−2.03383	+	22.0732i	−0.0838739	+	0.910284i
$589$	−0.573214	+	0.992836i	−0.0236189	+	0.0409091i
$590$		0			0
$591$	−24.2474	+	34.2911i	−0.997407	+	1.41055i
$592$	−2.89986	+	1.67423i	−0.119183	+	0.0688106i
$593$			1.89898i			0.0779817i	0.999240	+	0.0389909i	$0.0124143\pi$
$593$			1.89898i			0.0779817i	−0.999240	+	0.0389909i	$0.987586\pi$
$594$	−18.2474	+	17.7491i	−0.748702	+	0.728254i
$595$		0			0
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	8.19955	+	5.79796i	0.335585	+	0.237295i
$598$	9.43879	+	5.44949i	0.385981	+	0.222846i
$599$	−18.6742	+	32.3447i	−0.763009	+	1.32157i	0.178285	+	0.983979i	$0.442945\pi$
$599$	−18.6742	+	32.3447i	−0.763009	+	1.32157i	−0.941293	+	0.337591i	$0.890388\pi$
$600$		0			0
$601$	−16.2474	−	28.1414i	−0.662747	−	1.14791i	−0.979891	−	0.199534i	$-0.936057\pi$
$601$	−16.2474	−	28.1414i	−0.662747	−	1.14791i	0.317144	−	0.948378i	$-0.397276\pi$
$602$			33.1464i			1.35095i
$603$	7.86566	−	42.3207i	0.320314	−	1.72343i
$604$	−20.0000			−0.813788
$605$		0			0
$606$	2.57321	+	5.58542i	0.104530	+	0.226892i
$607$	−9.82806	−	5.67423i	−0.398909	−	0.230310i	0.287104	−	0.957899i	$-0.407307\pi$
$607$	−9.82806	−	5.67423i	−0.398909	−	0.230310i	−0.686013	+	0.727589i	$0.740641\pi$
$608$	2.20881	+	1.27526i	0.0895789	+	0.0517184i
$609$	7.89898	+	17.1455i	0.320083	+	0.694772i
$610$		0			0
$611$	−4.89898			−0.198191
$612$	−2.68556	+	14.4495i	−0.108557	+	0.584086i
$613$		−	32.0454i		−	1.29430i	−0.762362	−	0.647151i	$-0.775960\pi$
$613$		−	32.0454i		−	1.29430i	0.762362	−	0.647151i	$-0.224040\pi$
$614$	3.34847	+	5.79972i	0.135133	+	0.234058i
$615$		0			0
$616$	10.8990	−	18.8776i	0.439132	−	0.760600i
$617$	−12.4655	−	7.19694i	−0.501841	−	0.289738i	0.227633	−	0.973747i	$-0.426901\pi$
$617$	−12.4655	−	7.19694i	−0.501841	−	0.289738i	−0.729473	+	0.684009i	$0.760235\pi$
$618$	−17.9562	−	12.6969i	−0.722304	−	0.510746i
$619$	20.8712	+	36.1499i	0.838883	+	1.45299i	0.890829	+	0.454339i	$0.150124\pi$
$619$	20.8712	+	36.1499i	0.838883	+	1.45299i	−0.0519458	+	0.998650i	$0.516542\pi$
$620$		0			0
$621$	−9.12372	+	8.87455i	−0.366122	+	0.356123i
$622$		−	10.8990i		−	0.437009i
$623$	−34.6803	+	20.0227i	−1.38944	+	0.802193i
$624$	4.44949	−	6.29253i	0.178122	−	0.251903i
$625$		0			0
$626$	1.94949	−	3.37662i	0.0779173	−	0.134957i
$627$	1.98567	−	21.5505i	0.0793001	−	0.860644i
$628$	−0.174973	+	0.101021i	−0.00698217	+	0.00403116i
$629$	16.4041			0.654074
$630$		0			0
$631$	−25.7980			−1.02700			−0.513500	−	0.858089i	$-0.671651\pi$
$631$	−25.7980			−1.02700			−0.513500	+	0.858089i	$0.671651\pi$
$632$	−10.9959	+	6.34847i	−0.437392	+	0.252529i
$633$	2.28024	−	1.05051i	0.0906314	−	0.0417540i
$634$	8.57321	−	14.8492i	0.340486	−	0.589739i
$635$		0			0
$636$	6.12372	+	13.2922i	0.242821	+	0.527069i
$637$	−49.3153	+	28.4722i	−1.95394	+	1.12811i
$638$		−	12.0000i		−	0.475085i
$639$	−1.34847	−	3.81405i	−0.0533446	−	0.150881i
$640$		0			0
$641$	−22.1969	−	38.4462i	−0.876726	−	1.51853i	−0.854912	−	0.518773i	$-0.826389\pi$
$641$	−22.1969	−	38.4462i	−0.876726	−	1.51853i	−0.0218141	−	0.999762i	$-0.506944\pi$
$642$	2.42310	−	26.2980i	0.0956323	−	1.03790i
$643$	28.0146	+	16.1742i	1.10479	+	0.637850i	0.937474	−	0.348054i	$-0.113157\pi$
$643$	28.0146	+	16.1742i	1.10479	+	0.637850i	0.167313	+	0.985904i	$0.446491\pi$
$644$	5.44949	−	9.43879i	0.214740	−	0.371941i
$645$		0			0
$646$	−6.24745	−	10.8209i	−0.245803	−	0.425743i
$647$			0.247449i			0.00972821i	0.999988	+	0.00486411i	$0.00154830\pi$
$647$			0.247449i			0.00972821i	−0.999988	+	0.00486411i	$0.998452\pi$
$648$	5.65685	+	7.00000i	0.222222	+	0.274986i
$649$	2.69694			0.105864
$650$		0			0
$651$	2.00000	−	2.82843i	0.0783862	−	0.110855i
$652$	2.20881	+	1.27526i	0.0865035	+	0.0499428i
$653$	5.41045	+	3.12372i	0.211727	+	0.122241i	0.602114	−	0.798410i	$-0.294325\pi$
$653$	5.41045	+	3.12372i	0.211727	+	0.122241i	−0.390387	+	0.920651i	$0.627659\pi$
$654$	18.0227	+	1.66062i	0.704743	+	0.0649353i
$655$		0			0
$656$	9.00000			0.351391
$657$	2.82843	−	1.00000i	0.110347	−	0.0390137i
$658$			4.89898i			0.190982i
$659$	22.0732	+	38.2319i	0.859850	+	1.48930i	0.872071	+	0.489379i	$0.162777\pi$
$659$	22.0732	+	38.2319i	0.859850	+	1.48930i	−0.0122208	+	0.999925i	$0.503890\pi$
$660$		0			0
$661$	25.6969	−	44.5084i	0.999495	−	1.73118i	0.472230	−	0.881475i	$-0.343449\pi$
$661$	25.6969	−	44.5084i	0.999495	−	1.73118i	0.527265	−	0.849701i	$-0.323218\pi$
$662$	7.22999	+	4.17423i	0.281001	+	0.162236i
$663$	−34.2911	+	15.7980i	−1.33175	+	0.613542i
$664$	0.275255	+	0.476756i	0.0106820	+	0.0185017i
$665$		0			0
$666$	6.52781	−	7.63531i	0.252947	−	0.295862i
$667$		−	6.00000i		−	0.232321i
$668$	−16.9706	+	9.79796i	−0.656611	+	0.379094i
$669$	3.10102	+	0.285729i	0.119892	+	0.0110469i
$670$		0			0
$671$	−19.5959	+	33.9411i	−0.756492	+	1.31028i
$672$	−6.29253	−	4.44949i	−0.242740	−	0.171643i
$673$	−5.79972	+	3.34847i	−0.223563	+	0.129074i	−0.607599	−	0.794244i	$-0.707867\pi$
$673$	−5.79972	+	3.34847i	−0.223563	+	0.129074i	0.384036	+	0.923318i	$0.374534\pi$
$674$	−11.1010			−0.427595
$675$		0			0
$676$	6.79796			0.261460
$677$	−32.7733	+	18.9217i	−1.25958	+	0.727219i	−0.972993	−	0.230835i	$-0.925854\pi$
$677$	−32.7733	+	18.9217i	−1.25958	+	0.727219i	−0.286588	+	0.958054i	$0.592521\pi$
$678$	−19.6561	−	13.8990i	−0.754889	−	0.533787i
$679$	−24.0227	+	41.6085i	−0.921907	+	1.59679i
$680$		0			0
$681$	48.8939	+	4.50510i	1.87362	+	0.172636i
$682$	−1.90702	+	1.10102i	−0.0730237	+	0.0421603i
$683$		−	11.9444i		−	0.457039i	−0.973539	−	0.228520i	$-0.926611\pi$
$683$		−	11.9444i		−	0.457039i	0.973539	−	0.228520i	$-0.0733885\pi$
$684$	−7.52270	−	1.39816i	−0.287638	−	0.0534600i
$685$		0			0
$686$	12.8990	+	22.3417i	0.492485	+	0.853010i
$687$	33.2661	−	15.3258i	1.26918	−	0.584714i
$688$	−6.45145	−	3.72474i	−0.245959	−	0.142005i
$689$	−18.7980	+	32.5590i	−0.716145	+	1.24040i
$690$		0			0
$691$	2.52270	+	4.36945i	0.0959682	+	0.166222i	0.910012	−	0.414581i	$-0.136072\pi$
$691$	2.52270	+	4.36945i	0.0959682	+	0.166222i	−0.814044	+	0.580803i	$0.802739\pi$
$692$			9.79796i			0.372463i
$693$	−11.9494	+	64.2929i	−0.453920	+	2.44228i
$694$	12.0000			0.455514
$695$		0			0
$696$	−4.22474	−	0.389270i	−0.160139	−	0.0147552i
$697$	−38.1838	−	22.0454i	−1.44631	−	0.835029i
$698$	12.1244	+	7.00000i	0.458914	+	0.264954i
$699$	5.69694	−	8.05669i	0.215478	−	0.304732i
$700$		0			0
$701$	14.2020			0.536404			0.268202	−	0.963363i	$-0.413571\pi$
$701$	14.2020			0.536404			0.268202	+	0.963363i	$0.413571\pi$
$702$	−6.29253	+	22.2474i	−0.237496	+	0.839676i
$703$			8.54031i			0.322104i
$704$	2.44949	+	4.24264i	0.0923186	+	0.159901i
$705$		0			0
$706$	−4.50000	+	7.79423i	−0.169360	+	0.293340i
$707$	13.6814	+	7.89898i	0.514543	+	0.297072i
$708$	0.0874863	−	0.949490i	0.00328794	−	0.0356840i
$709$	−0.224745	−	0.389270i	−0.00844047	−	0.0146193i	0.861774	−	0.507292i	$-0.169353\pi$
$709$	−0.224745	−	0.389270i	−0.00844047	−	0.0146193i	−0.870215	+	0.492673i	$0.836020\pi$
$710$		0			0
$711$	24.7526	−	28.9521i	0.928293	−	1.08579i
$712$		−	9.00000i		−	0.337289i
$713$	−0.953512	+	0.550510i	−0.0357093	+	0.0206168i
$714$	15.7980	+	34.2911i	0.591224	+	1.28331i
$715$		0			0
$716$	7.62372	−	13.2047i	0.284912	−	0.493482i
$717$	−15.0242	+	6.92168i	−0.561090	+	0.258495i
$718$	29.2699	−	16.8990i	1.09234	−	0.630664i
$719$	−52.0454			−1.94097			−0.970483	−	0.241169i	$-0.922469\pi$
$719$	−52.0454			−1.94097			−0.970483	+	0.241169i	$0.922469\pi$
$720$		0			0
$721$	−56.4949			−2.10398
$722$	−10.8209	+	6.24745i	−0.402712	+	0.232506i
$723$	3.62302	−	39.3207i	0.134742	−	1.46235i
$724$	−0.898979	+	1.55708i	−0.0334103	+	0.0578684i
$725$		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	$0.237446\pi$
$728$		−	19.7980i		−	0.733761i
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$		0			0
$731$	18.2474	+	31.6055i	0.674906	+	1.16897i
$732$	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	$0.826090\pi$
$734$	−8.34847	+	14.4600i	−0.308148	+	0.533727i
$735$		0			0
$736$	1.22474	+	2.12132i	0.0451447	+	0.0781929i
$737$			70.2929i			2.58927i
$738$	−25.4558	+	9.00000i	−0.937043	+	0.331295i
$739$	41.0454			1.50988			0.754940	−	0.655794i	$-0.227666\pi$
$739$	41.0454			1.50988			0.754940	+	0.655794i	$0.227666\pi$
$740$		0			0
$741$	−8.22474	−	17.8526i	−0.302144	−	0.655833i
$742$	32.5590	+	18.7980i	1.19528	+	0.690095i
$743$	−30.0091	−	17.3258i	−1.10093	−	0.635621i	−0.164463	−	0.986383i	$-0.552589\pi$
$743$	−30.0091	−	17.3258i	−1.10093	−	0.635621i	−0.936464	+	0.350763i	$0.885922\pi$
$744$	0.325765	+	0.707107i	0.0119431	+	0.0259238i
$745$		0			0
$746$	−15.5959			−0.571007
$747$	−1.25529	−	1.07321i	−0.0459288	−	0.0392669i
$748$		−	24.0000i		−	0.877527i
$749$	−33.9217	−	58.7541i	−1.23947	−	2.14683i
$750$		0			0
$751$	25.0227	−	43.3406i	0.913091	−	1.58152i	0.103420	−	0.994638i	$-0.467022\pi$
$751$	25.0227	−	43.3406i	0.913091	−	1.58152i	0.809672	−	0.586883i	$-0.199645\pi$
$752$	−0.953512	−	0.550510i	−0.0347710	−	0.0200750i
$753$	7.70674	+	5.44949i	0.280849	+	0.198590i
$754$	−5.44949	−	9.43879i	−0.198459	−	0.343741i
$755$		0			0
$756$	22.2474	+	6.29253i	0.809132	+	0.228857i
$757$		−	6.04541i		−	0.219724i	−0.993947	−	0.109862i	$-0.964959\pi$
$757$		−	6.04541i		−	0.219724i	0.993947	−	0.109862i	$-0.0350409\pi$
$758$	−0.778539	+	0.449490i	−0.0282778	+	0.0163262i
$759$	12.0000	−	16.9706i	0.435572	−	0.615992i
$760$		0			0
$761$	−2.05051	+	3.55159i	−0.0743309	+	0.128745i	−0.900795	−	0.434244i	$-0.857015\pi$
$761$	−2.05051	+	3.55159i	−0.0743309	+	0.128745i	0.826464	+	0.562989i	$0.190349\pi$
$762$	1.80348	−	19.5732i	0.0653333	−	0.709063i
$763$	40.2658	−	23.2474i	1.45772	−	0.841614i
$764$	10.8990			0.394311
$765$		0			0
$766$	−26.4495			−0.955659
$767$	2.12132	−	1.22474i	0.0765964	−	0.0442230i
$768$	1.57313	−	0.724745i	0.0567655	−	0.0261520i
$769$	25.0959	−	43.4674i	0.904982	−	1.56747i	0.0840405	−	0.996462i	$-0.473217\pi$
$769$	25.0959	−	43.4674i	0.904982	−	1.56747i	0.820941	−	0.571012i	$-0.193449\pi$
$770$		0			0
$771$	−4.92679	−	10.6941i	−0.177434	−	0.385138i
$772$	−17.3205	+	10.0000i	−0.623379	+	0.359908i
$773$		−	49.5959i		−	1.78384i	−0.452192	−	0.891921i	$-0.649358\pi$
$773$		−	49.5959i		−	1.78384i	0.452192	−	0.891921i	$-0.350642\pi$
$774$	21.9722	+	4.08372i	0.789774	+	0.146786i
$775$		0			0
$776$	−5.39898	−	9.35131i	−0.193812	−	0.335692i
$777$	2.36773	−	25.6969i	0.0849417	−	0.921873i
$778$	−11.7744	−	6.79796i	−0.422133	−	0.243719i
$779$	11.4773	−	19.8793i	0.411217	−	0.712248i
$780$		0			0
$781$	3.30306	+	5.72107i	0.118193	+	0.204716i
$782$		−	12.0000i		−	0.429119i
$783$	12.3387	−	3.12372i	0.440947	−	0.111633i
$784$	−12.7980			−0.457070
$785$		0			0
$786$	15.7980	−	22.3417i	0.563495	−	0.796902i
$787$	4.59259	+	2.65153i	0.163708	+	0.0945169i	0.579616	−	0.814890i	$-0.303203\pi$
$787$	4.59259	+	2.65153i	0.163708	+	0.0945169i	−0.415908	+	0.909407i	$0.636536\pi$
$788$	−20.9989	−	12.1237i	−0.748055	−	0.431890i
$789$	−26.8207	−	2.47127i	−0.954841	−	0.0879794i
$790$		0			0
$791$	−61.8434			−2.19890
$792$	−11.1708	−	9.55051i	−0.396939	−	0.339363i
$793$			35.5959i			1.26405i
$794$	−10.7980	−	18.7026i	−0.383205	−	0.663731i
$795$		0			0
$796$	−2.89898	+	5.02118i	−0.102752	+	0.177971i
$797$	−4.98186	−	2.87628i	−0.176466	−	0.101883i	0.409165	−	0.912460i	$-0.365820\pi$
$797$	−4.98186	−	2.87628i	−0.176466	−	0.101883i	−0.585631	+	0.810577i	$0.699153\pi$
$798$	−17.8526	+	8.22474i	−0.631977	+	0.291153i
$799$	2.69694	+	4.67123i	0.0954108	+	0.165256i
$800$		0			0
$801$	9.00000	+	25.4558i	0.317999	+	0.899438i
$802$			9.30306i			0.328503i
$803$	−4.24264	+	2.44949i	−0.149720	+	0.0864406i
$804$	24.7474	+	2.28024i	0.872775	+	0.0804178i
$805$		0			0
$806$	−1.00000	+	1.73205i	−0.0352235	+	0.0610089i
$807$	13.5065	+	9.55051i	0.475450	+	0.336194i
$808$	−3.07483	+	1.77526i	−0.108172	+	0.0624533i
$809$	35.6969			1.25504			0.627519	−	0.778601i	$-0.284071\pi$
$809$	35.6969			1.25504			0.627519	+	0.778601i	$0.284071\pi$
$810$		0			0
$811$	−33.4495			−1.17457			−0.587285	−	0.809380i	$-0.699803\pi$
$811$	−33.4495			−1.17457			−0.587285	+	0.809380i	$0.699803\pi$
$812$	−9.43879	+	5.44949i	−0.331237	+	0.191240i
$813$	−0.921404	−	0.651531i	−0.0323150	−	0.0228502i
$814$	−8.20204	+	14.2064i	−0.287481	+	0.497932i
$815$		0			0
$816$	−8.44949	−	0.778539i	−0.295791	−	0.0272543i
$817$	−16.4545	+	9.50000i	−0.575669	+	0.332363i
$818$		−	9.89898i		−	0.346110i
$819$	19.7980	+	55.9971i	0.691797	+	1.95670i
$820$		0			0
$821$	25.5959	+	44.3334i	0.893304	+	1.54725i	0.835890	+	0.548897i	$0.184952\pi$
$821$	25.5959	+	44.3334i	0.893304	+	1.54725i	0.0574136	+	0.998350i	$0.481715\pi$
$822$	4.71940	−	2.17423i	0.164608	−	0.0758351i
$823$	23.2952	+	13.4495i	0.812020	+	0.468820i	0.847657	−	0.530545i	$-0.178013\pi$
$823$	23.2952	+	13.4495i	0.812020	+	0.468820i	−0.0356371	+	0.999365i	$0.511346\pi$
$824$	6.34847	−	10.9959i	0.221159	−	0.383059i
$825$		0			0
$826$	−1.22474	−	2.12132i	−0.0426143	−	0.0738102i
$827$		−	17.9444i		−	0.623987i	−0.950084	−	0.311994i	$-0.899003\pi$
$827$		−	17.9444i		−	0.623987i	0.950084	−	0.311994i	$-0.100997\pi$
$828$	−5.58542	−	4.77526i	−0.194107	−	0.165952i
$829$	−26.7423			−0.928800			−0.464400	−	0.885626i	$-0.653730\pi$
$829$	−26.7423			−0.928800			−0.464400	+	0.885626i	$0.653730\pi$
$830$		0			0
$831$	−11.1237	−	1.02494i	−0.385878	−	0.0355549i
$832$	3.85337	+	2.22474i	0.133592	+	0.0771292i
$833$	54.2971	+	31.3485i	1.88128	+	1.08616i
$834$	4.00000	−	5.65685i	0.138509	−	0.195881i
$835$		0			0
$836$	12.4949			0.432145
$837$	−1.62851	−	1.67423i	−0.0562896	−	0.0578700i
$838$		−	8.14643i		−	0.281414i
$839$	11.3258	+	19.6168i	0.391009	+	0.677247i	0.992583	−	0.121570i	$-0.0387928\pi$
$839$	11.3258	+	19.6168i	0.391009	+	0.677247i	−0.601574	+	0.798817i	$0.705460\pi$
$840$		0			0
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$	−15.6278	−	9.02270i	−0.538569	−	0.310943i
$843$	−4.59259	+	49.8434i	−0.158177	+	1.71670i
$844$	0.724745	+	1.25529i	0.0249467	+	0.0432090i
$845$		0			0
$846$	3.24745	+	0.603566i	0.111650	+	0.0207510i
$847$		−	57.8434i		−	1.98752i
$848$	−7.31747	+	4.22474i	−0.251283	+	0.145078i
$849$	8.15153	+	17.6937i	0.279760	+	0.607247i
$850$		0			0
$851$	−4.10102	+	7.10318i	−0.140581	+	0.243494i
$852$	2.12132	−	0.977296i	0.0726752	−	0.0334816i
$853$	−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	$0.621961\pi$
$854$	35.5959			1.21807
$855$		0			0
$856$	15.2474			0.521147
$857$	34.7285	−	20.0505i	1.18630	−	0.684912i	0.228839	−	0.973464i	$-0.426507\pi$
$857$	34.7285	−	20.0505i	1.18630	−	0.684912i	0.957464	+	0.288552i	$0.0931738\pi$
$858$	3.46410	−	37.5959i	0.118262	−	1.28350i
$859$	−2.82577	+	4.89437i	−0.0964139	+	0.166994i	−0.910198	−	0.414174i	$-0.864071\pi$
$859$	−2.82577	+	4.89437i	−0.0964139	+	0.166994i	0.813784	+	0.581168i	$0.197404\pi$
$860$		0			0
$861$	−40.0454	+	56.6328i	−1.36474	+	1.93004i
$862$	9.22450	−	5.32577i	0.314188	−	0.181396i
$863$			19.8434i			0.675476i	0.941240	+	0.337738i	$0.109662\pi$
$863$			19.8434i			0.675476i	−0.941240	+	0.337738i	$0.890338\pi$
$864$	−3.72474	+	3.62302i	−0.126718	+	0.123258i
$865$		0			0
$866$	−14.7980	−	25.6308i	−0.502855	−	0.870971i
$867$	9.89949	+	7.00000i	0.336204	+	0.237732i
$868$	1.73205	+	1.00000i	0.0587896	+	0.0339422i
$869$	−31.1010	+	53.8685i	−1.05503	+	1.82737i
$870$		0			0
$871$	31.9217	+	55.2900i	1.08162	+	1.87343i
$872$			10.4495i			0.353864i
$873$	24.6219	+	21.0505i	0.833326	+	0.712452i
$874$	6.24745			0.211323
$875$		0			0
$876$	0.724745	+	1.57313i	0.0244869	+	0.0531512i
$877$	−10.5673	−	6.10102i	−0.356832	−	0.206017i	0.310858	−	0.950456i	$-0.399383\pi$
$877$	−10.5673	−	6.10102i	−0.356832	−	0.206017i	−0.667690	+	0.744439i	$0.732717\pi$
$878$	−9.82806	−	5.67423i	−0.331681	−	0.191496i
$879$	−20.3258	−	44.1191i	−0.685571	−	1.48810i
$880$		0			0
$881$	9.30306			0.313428			0.156714	−	0.987644i	$-0.449910\pi$
$881$	9.30306			0.313428			0.156714	+	0.987644i	$0.449910\pi$
$882$	36.1981	−	12.7980i	1.21885	−	0.430930i
$883$			28.2020i			0.949074i	0.880235	+	0.474537i	$0.157385\pi$
$883$			28.2020i			0.949074i	−0.880235	+	0.474537i	$0.842615\pi$
$884$	−10.8990	−	18.8776i	−0.366572	−	0.634922i
$885$		0			0
$886$	13.8990	−	24.0737i	0.466945	−	0.808773i
$887$	47.1940	+	27.2474i	1.58462	+	0.914880i	0.994172	+	0.107803i	$0.0343815\pi$
$887$	47.1940	+	27.2474i	1.58462	+	0.914880i	0.590446	+	0.807077i	$0.298952\pi$
$888$	4.73545	+	3.34847i	0.158911	+	0.112367i
$889$	−25.2474	−	43.7299i	−0.846772	−	1.46665i
$890$		0			0
$891$	41.1464	+	15.8421i	1.37846	+	0.530730i
$892$			1.79796i			0.0602001i
$893$	−2.43194	+	1.40408i	−0.0813818	+	0.0469858i
$894$	6.00000	−	8.48528i	0.200670	−	0.283790i
$895$		0			0
$896$	2.22474	−	3.85337i	0.0743235	−	0.128732i
$897$	1.73205	−	18.7980i	0.0578315	−	0.627646i
$898$	−9.17633	+	5.29796i	−0.306218	+	0.176795i
$899$	1.10102			0.0367211
$900$		0			0
$901$	41.3939			1.37903
$902$	38.1838	−	22.0454i	1.27138	−	0.734032i
$903$	52.1437	−	24.0227i	1.73523	−	0.799426i
$904$	6.94949	−	12.0369i	0.231137	−	0.400340i
$905$		0			0
$906$	14.4949	+	31.4626i	0.481561	+	1.04528i
$907$	−18.7508	+	10.8258i	−0.622609	+	0.359464i	−0.777884	−	0.628408i	$-0.783707\pi$
$907$	−18.7508	+	10.8258i	−0.622609	+	0.359464i	0.155275	+	0.987871i	$0.450374\pi$
$908$			28.3485i			0.940777i
$909$	6.92168	−	8.09601i	0.229578	−	0.268528i
$910$		0			0
$911$	−3.67423	−	6.36396i	−0.121733	−	0.210847i	0.798718	−	0.601705i	$-0.205512\pi$
$911$	−3.67423	−	6.36396i	−0.121733	−	0.210847i	−0.920451	+	0.390858i	$0.872178\pi$
$912$	0.405324	−	4.39898i	0.0134216	−	0.145665i
$913$	2.33562	+	1.34847i	0.0772976	+	0.0446278i
$914$	7.84847	−	13.5939i	0.259604	−	0.449648i
$915$		0			0
$916$	10.5732	+	18.3133i	0.349349	+	0.605090i
$917$		−	70.2929i		−	2.32127i
$918$	24.6773	−	6.24745i	0.814472	−	0.206197i
$919$	11.3485			0.374351			0.187176	−	0.982326i	$-0.440067\pi$
$919$	11.3485			0.374351			0.187176	+	0.982326i	$0.440067\pi$
$920$		0			0
$921$	6.69694	−	9.47090i	0.220672	−	0.312077i
$922$	−16.7563	−	9.67423i	−0.551838	−	0.318604i
$923$	5.19615	+	3.00000i	0.171033	+	0.0987462i
$924$	−37.5959	−	3.46410i	−1.23681	−	0.113961i
$925$		0			0
$926$	−9.34847			−0.307210
$927$	−6.96031	+	37.4495i	−0.228607	+	1.23000i
$928$		−	2.44949i		−	0.0804084i
$929$	13.5959	+	23.5488i	0.446068	+	0.772612i	0.998126	−	0.0611938i	$-0.0194908\pi$
$929$	13.5959	+	23.5488i	0.446068	+	0.772612i	−0.552058	+	0.833806i	$0.686157\pi$
$930$		0			0
$931$	−16.3207	+	28.2682i	−0.534888	+	0.926453i
$932$	4.93369	+	2.84847i	0.161609	+	0.0933047i
$933$	−17.1455	+	7.89898i	−0.561320	+	0.258601i
$934$	−2.17423	−	3.76588i	−0.0711431	−	0.123224i
$935$		0			0
$936$	−13.1237	−	2.43916i	−0.428962	−	0.0797264i
$937$		−	26.7980i		−	0.875451i	−0.899109	−	0.437726i	$-0.855784\pi$
$937$		−	26.7980i		−	0.875451i	0.899109	−	0.437726i	$-0.144216\pi$
$938$	55.2900	−	31.9217i	1.80528	−	1.04228i
$939$	−6.72474	−	0.619620i	−0.219454	−	0.0202205i
$940$		0			0
$941$	14.8207	−	25.6701i	0.483140	−	0.836823i	−0.516673	−	0.856183i	$-0.672830\pi$
$941$	14.8207	−	25.6701i	0.483140	−	0.836823i	0.999813	+	0.0193603i	$0.00616295\pi$
$942$	0.285729	+	0.202041i	0.00930956	+	0.00658285i
$943$	19.0919	−	11.0227i	0.621717	−	0.358949i
$944$	0.550510			0.0179176
$945$		0			0
$946$	−36.4949			−1.18655
$947$	7.05501	−	4.07321i	0.229257	−	0.132362i	−0.380972	−	0.924587i	$-0.624411\pi$
$947$	7.05501	−	4.07321i	0.229257	−	0.132362i	0.610229	+	0.792225i	$0.291077\pi$
$948$	17.9562	+	12.6969i	0.583190	+	0.412377i
$949$	−2.22474	+	3.85337i	−0.0722183	+	0.125086i
$950$		0			0
$951$	−29.5732	−	2.72489i	−0.958977	−	0.0883605i
$952$	−18.8776	+	10.8990i	−0.611826	+	0.353238i
$953$			21.7980i			0.706105i	0.935603	+	0.353053i	$0.114856\pi$
$953$			21.7980i			0.706105i	−0.935603	+	0.353053i	$0.885144\pi$
$954$	16.4722	−	19.2669i	0.533307	−	0.623787i
$955$		0			0
$956$	−4.77526	−	8.27098i	−0.154443	−	0.267503i
$957$	−18.8776	+	8.69694i	−0.610226	+	0.281132i
$958$	−20.9989	−	12.1237i	−0.678444	−	0.391700i
$959$	6.67423	−	11.5601i	0.215522	−	0.373296i
$960$		0			0
$961$	15.3990	+	26.6718i	0.496741	+	0.860381i
$962$			14.8990i			0.480362i
$963$	−43.1263	+	15.2474i	−1.38973	+	0.491342i
$964$	22.7980			0.734273
$965$		0			0
$966$	−18.7980	−	1.73205i	−0.604814	−	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
$969$	−12.4949	+	17.6705i	−0.401394	+	0.567657i
$970$		0			0
$971$	22.8434			0.733079			0.366539	−	0.930403i	$-0.380543\pi$
$971$	22.8434			0.733079			0.366539	+	0.930403i	$0.380543\pi$
$972$	6.91215	−	13.9722i	0.221707	−	0.448158i
$973$		−	17.7980i		−	0.570576i
$974$	9.77526	+	16.9312i	0.313219	+	0.542512i
$975$		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	$0.712653\pi$
$978$	0.405324	−	4.39898i	0.0129608	−	0.140664i
$979$	−22.0454	−	38.1838i	−0.704574	−	1.22036i
$980$		0			0
$981$	−10.4495	−	29.5556i	−0.333627	−	0.943638i
$982$		−	2.75255i		−	0.0878374i
$983$	−19.8311	+	11.4495i	−0.632514	+	0.365182i	−0.781725	−	0.623623i	$-0.785660\pi$
$983$	−19.8311	+	11.4495i	−0.632514	+	0.365182i	0.149211	+	0.988805i	$0.452327\pi$
$984$	−6.52270	−	14.1582i	−0.207936	−	0.451347i
$985$		0			0
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$	7.70674	−	3.55051i	0.245308	−	0.113014i
$988$	9.82806	−	5.67423i	0.312672	−	0.180521i
$989$	−18.2474			−0.580235
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−0.389270	+	0.224745i	−0.0123593	+	0.00713566i
$993$	1.32673	−	14.3990i	0.0421024	−	0.456938i
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$	0.550510	−	0.778539i	0.0174436	−	0.0246690i
$997$	−31.2162	+	18.0227i	−0.988628	+	0.570785i	−0.904864	−	0.425701i	$-0.860028\pi$
$997$	−31.2162	+	18.0227i	−0.988628	+	0.570785i	−0.0837642	+	0.996486i	$0.526694\pi$
$998$		−	6.34847i		−	0.200957i
$999$	−16.7423	−	4.73545i	−0.529704	−	0.149823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.j.f.49.3		8
3.2	odd	2		1350.2.j.g.199.1		8
5.2	odd	4		450.2.e.m.301.2	yes	4
5.3	odd	4		450.2.e.l.301.1	yes	4
5.4	even	2	inner	450.2.j.f.49.2		8
9.2	odd	6		1350.2.j.g.1099.4		8
9.4	even	3		4050.2.c.y.649.3		4
9.5	odd	6		4050.2.c.w.649.1		4
9.7	even	3	inner	450.2.j.f.349.2		8
15.2	even	4		1350.2.e.k.901.1		4
15.8	even	4		1350.2.e.n.901.2		4
15.14	odd	2		1350.2.j.g.199.4		8
45.2	even	12		1350.2.e.k.451.1		4
45.4	even	6		4050.2.c.y.649.2		4
45.7	odd	12		450.2.e.m.151.1	yes	4
45.13	odd	12		4050.2.a.bu.1.1		2
45.14	odd	6		4050.2.c.w.649.4		4
45.22	odd	12		4050.2.a.br.1.2		2
45.23	even	12		4050.2.a.bl.1.1		2
45.29	odd	6		1350.2.j.g.1099.1		8
45.32	even	12		4050.2.a.by.1.2		2
45.34	even	6	inner	450.2.j.f.349.3		8
45.38	even	12		1350.2.e.n.451.2		4
45.43	odd	12		450.2.e.l.151.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.e.l.151.2	✓	4	45.43	odd	12
450.2.e.l.301.1	yes	4	5.3	odd	4
450.2.e.m.151.1	yes	4	45.7	odd	12
450.2.e.m.301.2	yes	4	5.2	odd	4
450.2.j.f.49.2		8	5.4	even	2	inner
450.2.j.f.49.3		8	1.1	even	1	trivial
450.2.j.f.349.2		8	9.7	even	3	inner
450.2.j.f.349.3		8	45.34	even	6	inner
1350.2.e.k.451.1		4	45.2	even	12
1350.2.e.k.901.1		4	15.2	even	4
1350.2.e.n.451.2		4	45.38	even	12
1350.2.e.n.901.2		4	15.8	even	4
1350.2.j.g.199.1		8	3.2	odd	2
1350.2.j.g.199.4		8	15.14	odd	2
1350.2.j.g.1099.1		8	45.29	odd	6
1350.2.j.g.1099.4		8	9.2	odd	6
4050.2.a.bl.1.1		2	45.23	even	12
4050.2.a.br.1.2		2	45.22	odd	12
4050.2.a.bu.1.1		2	45.13	odd	12
4050.2.a.by.1.2		2	45.32	even	12
4050.2.c.w.649.1		4	9.5	odd	6
4050.2.c.w.649.4		4	45.14	odd	6
4050.2.c.y.649.2		4	45.4	even	6
4050.2.c.y.649.3		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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.41421 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.72474 - 0.158919i) q^{6} +(-3.85337 + 2.22474i) q^{7} -1.00000i q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.41421 - 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.72474 - 0.158919i) q^{6} +(-3.85337 + 2.22474i) q^{7} -1.00000i q^{8} +(1.00000 + 2.82843i) q^{9} +(-2.44949 - 4.24264i) q^{11} +(-1.57313 + 0.724745i) q^{12} +(-3.85337 - 2.22474i) q^{13} +(-2.22474 + 3.85337i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.89898i q^{17} +(2.28024 + 1.94949i) q^{18} -2.55051 q^{19} +(7.67423 + 0.707107i) q^{21} +(-4.24264 - 2.44949i) q^{22} +(-2.12132 - 1.22474i) q^{23} +(-1.00000 + 1.41421i) q^{24} -4.44949 q^{26} +(1.41421 - 5.00000i) q^{27} +4.44949i q^{28} +(1.22474 + 2.12132i) q^{29} +(0.224745 - 0.389270i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.778539 + 8.44949i) q^{33} +(2.44949 + 4.24264i) q^{34} +(2.94949 + 0.548188i) q^{36} -3.34847i q^{37} +(-2.20881 + 1.27526i) q^{38} +(3.22474 + 6.99964i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(6.99964 - 3.22474i) q^{42} +(6.45145 - 3.72474i) q^{43} -4.89898 q^{44} -2.44949 q^{46} +(0.953512 - 0.550510i) q^{47} +(-0.158919 + 1.72474i) q^{48} +(6.39898 - 11.0834i) q^{49} +(4.89898 - 6.92820i) q^{51} +(-3.85337 + 2.22474i) q^{52} -8.44949i q^{53} +(-1.27526 - 5.03723i) q^{54} +(2.22474 + 3.85337i) q^{56} +(3.60697 + 2.55051i) q^{57} +(2.12132 + 1.22474i) q^{58} +(-0.275255 + 0.476756i) q^{59} +(-4.00000 - 6.92820i) q^{61} -0.449490i q^{62} +(-10.1459 - 8.67423i) q^{63} -1.00000 q^{64} +(3.55051 + 7.70674i) q^{66} +(-12.4261 - 7.17423i) q^{67} +(4.24264 + 2.44949i) q^{68} +(1.77526 + 3.85337i) q^{69} -1.34847 q^{71} +(2.82843 - 1.00000i) q^{72} -1.00000i q^{73} +(-1.67423 - 2.89986i) q^{74} +(-1.27526 + 2.20881i) q^{76} +(18.8776 + 10.8990i) q^{77} +(6.29253 + 4.44949i) q^{78} +(-6.34847 - 10.9959i) q^{79} +(-7.00000 + 5.65685i) q^{81} +9.00000i q^{82} +(-0.476756 + 0.275255i) q^{83} +(4.44949 - 6.29253i) q^{84} +(3.72474 - 6.45145i) q^{86} +(0.389270 - 4.22474i) q^{87} +(-4.24264 + 2.44949i) q^{88} +9.00000 q^{89} +19.7980 q^{91} +(-2.12132 + 1.22474i) q^{92} +(-0.707107 + 0.325765i) q^{93} +(0.550510 - 0.953512i) q^{94} +(0.724745 + 1.57313i) q^{96} +(9.35131 - 5.39898i) q^{97} -12.7980i q^{98} +(9.55051 - 11.1708i) 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

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