LMFDB - Embedded newform 450.2.e.l.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(151,450)]

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([4, 0]))

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

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

chi := DirichletCharacter("450.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.e (of order $3$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.151
Dual form			450.2.e.l.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.00000 + 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.72474 + 0.158919i) q^{6} +(2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 + 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.72474 + 0.158919i) q^{6} +(2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +(-2.44949 + 4.24264i) q^{11} +(0.724745 - 1.57313i) q^{12} +(2.22474 + 3.85337i) q^{13} +(2.22474 + 3.85337i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.89898 q^{17} +(-1.94949 - 2.28024i) q^{18} +2.55051 q^{19} +(7.67423 - 0.707107i) q^{21} +(-2.44949 - 4.24264i) q^{22} +(1.22474 + 2.12132i) q^{23} +(1.00000 + 1.41421i) q^{24} -4.44949 q^{26} +(-5.00000 + 1.41421i) q^{27} -4.44949 q^{28} +(-1.22474 + 2.12132i) q^{29} +(0.224745 + 0.389270i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-8.44949 + 0.778539i) q^{33} +(-2.44949 + 4.24264i) q^{34} +(2.94949 - 0.548188i) q^{36} -3.34847 q^{37} +(-1.27526 + 2.20881i) q^{38} +(-3.22474 + 6.99964i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(-3.22474 + 6.99964i) q^{42} +(3.72474 - 6.45145i) q^{43} +4.89898 q^{44} -2.44949 q^{46} +(-0.550510 + 0.953512i) q^{47} +(-1.72474 + 0.158919i) q^{48} +(-6.39898 - 11.0834i) q^{49} +(4.89898 + 6.92820i) q^{51} +(2.22474 - 3.85337i) q^{52} +8.44949 q^{53} +(1.27526 - 5.03723i) q^{54} +(2.22474 - 3.85337i) q^{56} +(2.55051 + 3.60697i) q^{57} +(-1.22474 - 2.12132i) q^{58} +(0.275255 + 0.476756i) q^{59} +(-4.00000 + 6.92820i) q^{61} -0.449490 q^{62} +(8.67423 + 10.1459i) q^{63} +1.00000 q^{64} +(3.55051 - 7.70674i) q^{66} +(-7.17423 - 12.4261i) q^{67} +(-2.44949 - 4.24264i) q^{68} +(-1.77526 + 3.85337i) q^{69} -1.34847 q^{71} +(-1.00000 + 2.82843i) q^{72} +1.00000 q^{73} +(1.67423 - 2.89986i) q^{74} +(-1.27526 - 2.20881i) q^{76} +(10.8990 + 18.8776i) q^{77} +(-4.44949 - 6.29253i) q^{78} +(6.34847 - 10.9959i) q^{79} +(-7.00000 - 5.65685i) q^{81} +9.00000 q^{82} +(-0.275255 + 0.476756i) q^{83} +(-4.44949 - 6.29253i) q^{84} +(3.72474 + 6.45145i) q^{86} +(-4.22474 + 0.389270i) q^{87} +(-2.44949 + 4.24264i) q^{88} -9.00000 q^{89} +19.7980 q^{91} +(1.22474 - 2.12132i) q^{92} +(-0.325765 + 0.707107i) q^{93} +(-0.550510 - 0.953512i) q^{94} +(0.724745 - 1.57313i) q^{96} +(-5.39898 + 9.35131i) q^{97} +12.7980 q^{98} +(-9.55051 - 11.1708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{8} - 4 q^{9} - 2 q^{12} + 4 q^{13} + 4 q^{14} - 2 q^{16} + 2 q^{18} + 20 q^{19} + 16 q^{21} + 4 q^{24} - 8 q^{26} - 20 q^{27} - 8 q^{28} - 4 q^{31} - 2 q^{32} - 24 q^{33} + 2 q^{36} + 16 q^{37} - 10 q^{38} - 8 q^{39} - 18 q^{41} - 8 q^{42} + 10 q^{43} - 12 q^{47} - 2 q^{48} - 6 q^{49} + 4 q^{52} + 24 q^{53} + 10 q^{54} + 4 q^{56} + 20 q^{57} + 6 q^{59} - 16 q^{61} + 8 q^{62} + 20 q^{63} + 4 q^{64} + 24 q^{66} - 14 q^{67} - 12 q^{69} + 24 q^{71} - 4 q^{72} + 4 q^{73} - 8 q^{74} - 10 q^{76} + 24 q^{77} - 8 q^{78} - 4 q^{79} - 28 q^{81} + 36 q^{82} - 6 q^{83} - 8 q^{84} + 10 q^{86} - 12 q^{87} - 36 q^{89} + 40 q^{91} - 16 q^{93} - 12 q^{94} - 2 q^{96} - 2 q^{97} + 12 q^{98} - 48 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^8 - 4 * q^9 - 2 * q^12 + 4 * q^13 + 4 * q^14 - 2 * q^16 + 2 * q^18 + 20 * q^19 + 16 * q^21 + 4 * q^24 - 8 * q^26 - 20 * q^27 - 8 * q^28 - 4 * q^31 - 2 * q^32 - 24 * q^33 + 2 * q^36 + 16 * q^37 - 10 * q^38 - 8 * q^39 - 18 * q^41 - 8 * q^42 + 10 * q^43 - 12 * q^47 - 2 * q^48 - 6 * q^49 + 4 * q^52 + 24 * q^53 + 10 * q^54 + 4 * q^56 + 20 * q^57 + 6 * q^59 - 16 * q^61 + 8 * q^62 + 20 * q^63 + 4 * q^64 + 24 * q^66 - 14 * q^67 - 12 * q^69 + 24 * q^71 - 4 * q^72 + 4 * q^73 - 8 * q^74 - 10 * q^76 + 24 * q^77 - 8 * q^78 - 4 * q^79 - 28 * q^81 + 36 * q^82 - 6 * q^83 - 8 * q^84 + 10 * q^86 - 12 * q^87 - 36 * q^89 + 40 * q^91 - 16 * q^93 - 12 * q^94 - 2 * q^96 - 2 * q^97 + 12 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.72474	+	0.158919i	−0.704124	+	0.0648783i
$7$	2.22474	−	3.85337i	0.840875	−	1.45644i	−0.0482818	−	0.998834i	$-0.515375\pi$
$7$	2.22474	−	3.85337i	0.840875	−	1.45644i	0.889156	−	0.457604i	$-0.151292\pi$
$8$	1.00000			0.353553
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$		0			0
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	0.214600	+	0.976702i	$0.431155\pi$
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	−0.953149	+	0.302502i	$0.902178\pi$
$12$	0.724745	−	1.57313i	0.209216	−	0.454124i
$13$	2.22474	+	3.85337i	0.617033	+	1.06873i	0.990024	+	0.140898i	$0.0449989\pi$
$13$	2.22474	+	3.85337i	0.617033	+	1.06873i	−0.372991	+	0.927835i	$0.621668\pi$
$14$	2.22474	+	3.85337i	0.594588	+	1.02986i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.89898			1.18818			0.594089	−	0.804400i	$-0.297513\pi$
$17$	4.89898			1.18818			0.594089	+	0.804400i	$0.297513\pi$
$18$	−1.94949	−	2.28024i	−0.459499	−	0.537457i
$19$	2.55051			0.585127			0.292564	−	0.956246i	$-0.405492\pi$
$19$	2.55051			0.585127			0.292564	+	0.956246i	$0.405492\pi$
$20$		0			0
$21$	7.67423	−	0.707107i	1.67466	−	0.154303i
$22$	−2.44949	−	4.24264i	−0.522233	−	0.904534i
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	0.964998	−	0.262258i	$-0.0844671\pi$
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	−0.709621	+	0.704584i	$0.751134\pi$
$24$	1.00000	+	1.41421i	0.204124	+	0.288675i
$25$		0			0
$26$	−4.44949			−0.872617
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$	−4.44949			−0.840875
$29$	−1.22474	+	2.12132i	−0.227429	+	0.393919i	−0.957046	−	0.289938i	$-0.906365\pi$
$29$	−1.22474	+	2.12132i	−0.227429	+	0.393919i	0.729616	+	0.683857i	$0.239699\pi$
$30$		0			0
$31$	0.224745	+	0.389270i	0.0403654	+	0.0699149i	0.885502	−	0.464635i	$-0.153814\pi$
$31$	0.224745	+	0.389270i	0.0403654	+	0.0699149i	−0.845137	+	0.534550i	$0.820481\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−8.44949	+	0.778539i	−1.47087	+	0.135526i
$34$	−2.44949	+	4.24264i	−0.420084	+	0.727607i
$35$		0			0
$36$	2.94949	−	0.548188i	0.491582	−	0.0913647i
$37$	−3.34847			−0.550485			−0.275242	−	0.961375i	$-0.588758\pi$
$37$	−3.34847			−0.550485			−0.275242	+	0.961375i	$0.588758\pi$
$38$	−1.27526	+	2.20881i	−0.206874	+	0.358316i
$39$	−3.22474	+	6.99964i	−0.516372	+	1.12084i
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	−3.22474	+	6.99964i	−0.497589	+	1.08007i
$43$	3.72474	−	6.45145i	0.568018	−	0.983836i	−0.428744	−	0.903426i	$-0.641044\pi$
$43$	3.72474	−	6.45145i	0.568018	−	0.983836i	0.996762	−	0.0804103i	$-0.0256230\pi$
$44$	4.89898			0.738549
$45$		0			0
$46$	−2.44949			−0.361158
$47$	−0.550510	+	0.953512i	−0.0803002	+	0.139084i	−0.903379	−	0.428843i	$-0.858921\pi$
$47$	−0.550510	+	0.953512i	−0.0803002	+	0.139084i	0.823079	+	0.567927i	$0.192255\pi$
$48$	−1.72474	+	0.158919i	−0.248945	+	0.0229379i
$49$	−6.39898	−	11.0834i	−0.914140	−	1.58334i
$50$		0			0
$51$	4.89898	+	6.92820i	0.685994	+	0.970143i
$52$	2.22474	−	3.85337i	0.308517	−	0.534366i
$53$	8.44949			1.16063			0.580313	−	0.814393i	$-0.302930\pi$
$53$	8.44949			1.16063			0.580313	+	0.814393i	$0.302930\pi$
$54$	1.27526	−	5.03723i	0.173540	−	0.685481i
$55$		0			0
$56$	2.22474	−	3.85337i	0.297294	−	0.514928i
$57$	2.55051	+	3.60697i	0.337823	+	0.477754i
$58$	−1.22474	−	2.12132i	−0.160817	−	0.278543i
$59$	0.275255	+	0.476756i	0.0358352	+	0.0620683i	0.883387	−	0.468645i	$-0.155258\pi$
$59$	0.275255	+	0.476756i	0.0358352	+	0.0620683i	−0.847552	+	0.530713i	$0.821924\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−0.449490			−0.0570853
$63$	8.67423	+	10.1459i	1.09285	+	1.27826i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.55051	−	7.70674i	0.437038	−	0.948634i
$67$	−7.17423	−	12.4261i	−0.876472	−	1.51809i	−0.855186	−	0.518321i	$-0.826557\pi$
$67$	−7.17423	−	12.4261i	−0.876472	−	1.51809i	−0.0212861	−	0.999773i	$-0.506776\pi$
$68$	−2.44949	−	4.24264i	−0.297044	−	0.514496i
$69$	−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	$0.525497\pi$
$72$	−1.00000	+	2.82843i	−0.117851	+	0.333333i
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$	1.67423	−	2.89986i	0.194626	−	0.337102i
$75$		0			0
$76$	−1.27526	−	2.20881i	−0.146282	−	0.253368i
$77$	10.8990	+	18.8776i	1.24205	+	2.15130i
$78$	−4.44949	−	6.29253i	−0.503806	−	0.712489i
$79$	6.34847	−	10.9959i	0.714259	−	1.23713i	−0.248986	−	0.968507i	$-0.580097\pi$
$79$	6.34847	−	10.9959i	0.714259	−	1.23713i	0.963245	−	0.268625i	$-0.0865693\pi$
$80$		0			0
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	9.00000			0.993884
$83$	−0.275255	+	0.476756i	−0.0302132	+	0.0523308i	−0.880737	−	0.473606i	$-0.842952\pi$
$83$	−0.275255	+	0.476756i	−0.0302132	+	0.0523308i	0.850523	+	0.525937i	$0.176285\pi$
$84$	−4.44949	−	6.29253i	−0.485479	−	0.686571i
$85$		0			0
$86$	3.72474	+	6.45145i	0.401650	+	0.695677i
$87$	−4.22474	+	0.389270i	−0.452940	+	0.0417341i
$88$	−2.44949	+	4.24264i	−0.261116	+	0.452267i
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$		0			0
$91$	19.7980			2.07539
$92$	1.22474	−	2.12132i	0.127688	−	0.221163i
$93$	−0.325765	+	0.707107i	−0.0337803	+	0.0733236i
$94$	−0.550510	−	0.953512i	−0.0567808	−	0.0983472i
$95$		0			0
$96$	0.724745	−	1.57313i	0.0739690	−	0.160557i
$97$	−5.39898	+	9.35131i	−0.548183	+	0.949481i	0.450216	+	0.892920i	$0.351347\pi$
$97$	−5.39898	+	9.35131i	−0.548183	+	0.949481i	−0.998399	+	0.0565616i	$0.981986\pi$
$98$	12.7980			1.29279
$99$	−9.55051	−	11.1708i	−0.959862	−	1.12271i
$100$		0			0
$101$	−1.77526	+	3.07483i	−0.176644	+	0.305957i	−0.940729	−	0.339159i	$-0.889858\pi$
$101$	−1.77526	+	3.07483i	−0.176644	+	0.305957i	0.764085	+	0.645116i	$0.223191\pi$
$102$	−8.44949	+	0.778539i	−0.836624	+	0.0770869i
$103$	−6.34847	−	10.9959i	−0.625533	−	1.08346i	−0.988437	−	0.151629i	$-0.951548\pi$
$103$	−6.34847	−	10.9959i	−0.625533	−	1.08346i	0.362904	−	0.931826i	$-0.381785\pi$
$104$	2.22474	+	3.85337i	0.218154	+	0.377854i
$105$		0			0
$106$	−4.22474	+	7.31747i	−0.410343	+	0.710736i
$107$	15.2474			1.47403			0.737013	−	0.675878i	$-0.236236\pi$
$107$	15.2474			1.47403			0.737013	+	0.675878i	$0.236236\pi$
$108$	3.72474	+	3.62302i	0.358414	+	0.348625i
$109$	10.4495			1.00088			0.500440	−	0.865771i	$-0.333172\pi$
$109$	10.4495			1.00088			0.500440	+	0.865771i	$0.333172\pi$
$110$		0			0
$111$	−3.34847	−	4.73545i	−0.317823	−	0.449469i
$112$	2.22474	+	3.85337i	0.210219	+	0.364109i
$113$	−6.94949	−	12.0369i	−0.653753	−	1.13233i	−0.982205	−	0.187813i	$-0.939860\pi$
$113$	−6.94949	−	12.0369i	−0.653753	−	1.13233i	0.328452	−	0.944521i	$-0.393473\pi$
$114$	−4.39898	+	0.405324i	−0.412002	+	0.0379620i
$115$		0			0
$116$	2.44949			0.227429
$117$	−13.1237	+	2.43916i	−1.21329	+	0.225500i
$118$	−0.550510			−0.0506786
$119$	10.8990	−	18.8776i	0.999108	−	1.73051i
$120$		0			0
$121$	−6.50000	−	11.2583i	−0.590909	−	1.02348i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$	6.52270	−	14.1582i	0.588132	−	1.27660i
$124$	0.224745	−	0.389270i	0.0201827	−	0.0349574i
$125$		0			0
$126$	−13.1237	+	2.43916i	−1.16915	+	0.217297i
$127$	11.3485			1.00701			0.503507	−	0.863991i	$-0.332043\pi$
$127$	11.3485			1.00701			0.503507	+	0.863991i	$0.332043\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	12.8485	−	1.18386i	1.13124	−	0.104233i
$130$		0			0
$131$	−7.89898	−	13.6814i	−0.690137	−	1.19535i	−0.971793	−	0.235837i	$-0.924217\pi$
$131$	−7.89898	−	13.6814i	−0.690137	−	1.19535i	0.281656	−	0.959516i	$-0.409116\pi$
$132$	4.89898	+	6.92820i	0.426401	+	0.603023i
$133$	5.67423	−	9.82806i	0.492019	−	0.852201i
$134$	14.3485			1.23952
$135$		0			0
$136$	4.89898			0.420084
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$	−2.44949	−	3.46410i	−0.208514	−	0.294884i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		0			0
$141$	−1.89898	+	0.174973i	−0.159923	+	0.0147354i
$142$	0.674235	−	1.16781i	0.0565805	−	0.0980003i
$143$	−21.7980			−1.82284
$144$	−1.94949	−	2.28024i	−0.162457	−	0.190020i
$145$		0			0
$146$	−0.500000	+	0.866025i	−0.0413803	+	0.0716728i
$147$	9.27526	−	20.1329i	0.765010	−	1.66053i
$148$	1.67423	+	2.89986i	0.137621	+	0.238367i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$	2.55051			0.206874
$153$	−4.89898	+	13.8564i	−0.396059	+	1.12022i
$154$	−21.7980			−1.75653
$155$		0			0
$156$	7.67423	−	0.707107i	0.614431	−	0.0566139i
$157$	−0.101021	−	0.174973i	−0.00806231	−	0.0139643i	0.861966	−	0.506966i	$-0.169233\pi$
$157$	−0.101021	−	0.174973i	−0.00806231	−	0.0139643i	−0.870028	+	0.493002i	$0.835900\pi$
$158$	6.34847	+	10.9959i	0.505057	+	0.874785i
$159$	8.44949	+	11.9494i	0.670088	+	0.947648i
$160$		0			0
$161$	10.8990			0.858960
$162$	8.39898	−	3.23375i	0.659886	−	0.254067i
$163$	−2.55051			−0.199771			−0.0998857	−	0.994999i	$-0.531848\pi$
$163$	−2.55051			−0.199771			−0.0998857	+	0.994999i	$0.531848\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$	−0.275255	−	0.476756i	−0.0213639	−	0.0370034i
$167$	−9.79796	−	16.9706i	−0.758189	−	1.31322i	−0.943773	−	0.330593i	$-0.892751\pi$
$167$	−9.79796	−	16.9706i	−0.758189	−	1.31322i	0.185584	−	0.982628i	$-0.440582\pi$
$168$	7.67423	−	0.707107i	0.592080	−	0.0545545i
$169$	−3.39898	+	5.88721i	−0.261460	+	0.452862i
$170$		0			0
$171$	−2.55051	+	7.21393i	−0.195042	+	0.551663i
$172$	−7.44949			−0.568018
$173$	−4.89898	+	8.48528i	−0.372463	+	0.645124i	−0.989944	−	0.141462i	$-0.954820\pi$
$173$	−4.89898	+	8.48528i	−0.372463	+	0.645124i	0.617481	+	0.786586i	$0.288153\pi$
$174$	1.77526	−	3.85337i	0.134582	−	0.292123i
$175$		0			0
$176$	−2.44949	−	4.24264i	−0.184637	−	0.319801i
$177$	−0.398979	+	0.866025i	−0.0299891	+	0.0650945i
$178$	4.50000	−	7.79423i	0.337289	−	0.584202i
$179$	−15.2474			−1.13965			−0.569824	−	0.821767i	$-0.692989\pi$
$179$	−15.2474			−1.13965			−0.569824	+	0.821767i	$0.692989\pi$
$180$		0			0
$181$	−1.79796			−0.133641			−0.0668206	−	0.997765i	$-0.521286\pi$
$181$	−1.79796			−0.133641			−0.0668206	+	0.997765i	$0.521286\pi$
$182$	−9.89898	+	17.1455i	−0.733761	+	1.27091i
$183$	−13.7980	+	1.27135i	−1.01997	+	0.0939808i
$184$	1.22474	+	2.12132i	0.0902894	+	0.156386i
$185$		0			0
$186$	−0.449490	−	0.635674i	−0.0329582	−	0.0466099i
$187$	−12.0000	+	20.7846i	−0.877527	+	1.51992i
$188$	1.10102			0.0803002
$189$	−5.67423	+	22.4131i	−0.412740	+	1.63031i
$190$		0			0
$191$	5.44949	−	9.43879i	0.394311	−	0.682967i	−0.598702	−	0.800972i	$-0.704317\pi$
$191$	5.44949	−	9.43879i	0.394311	−	0.682967i	0.993013	+	0.118005i	$0.0376499\pi$
$192$	1.00000	+	1.41421i	0.0721688	+	0.102062i
$193$	10.0000	+	17.3205i	0.719816	+	1.24676i	0.961073	+	0.276296i	$0.0891071\pi$
$193$	10.0000	+	17.3205i	0.719816	+	1.24676i	−0.241257	+	0.970461i	$0.577560\pi$
$194$	−5.39898	−	9.35131i	−0.387624	−	0.671385i
$195$		0			0
$196$	−6.39898	+	11.0834i	−0.457070	+	0.791668i
$197$	−24.2474			−1.72756			−0.863780	−	0.503870i	$-0.831909\pi$
$197$	−24.2474			−1.72756			−0.863780	+	0.503870i	$0.831909\pi$
$198$	14.4495	−	2.68556i	1.02688	−	0.190855i
$199$	5.79796			0.411006			0.205503	−	0.978656i	$-0.434117\pi$
$199$	5.79796			0.411006			0.205503	+	0.978656i	$0.434117\pi$
$200$		0			0
$201$	10.3990	−	22.5720i	0.733487	−	1.59211i
$202$	−1.77526	−	3.07483i	−0.124907	−	0.216344i
$203$	5.44949	+	9.43879i	0.382479	+	0.662473i
$204$	3.55051	−	7.70674i	0.248585	−	0.539580i
$205$		0			0
$206$	12.6969			0.884638
$207$	−7.22474	+	1.34278i	−0.502154	+	0.0933298i
$208$	−4.44949			−0.308517
$209$	−6.24745	+	10.8209i	−0.432145	+	0.748497i
$210$		0			0
$211$	−0.724745	−	1.25529i	−0.0498935	−	0.0864181i	0.840000	−	0.542586i	$-0.182555\pi$
$211$	−0.724745	−	1.25529i	−0.0498935	−	0.0864181i	−0.889894	+	0.456168i	$0.849222\pi$
$212$	−4.22474	−	7.31747i	−0.290157	−	0.502566i
$213$	−1.34847	−	1.90702i	−0.0923956	−	0.130667i
$214$	−7.62372	+	13.2047i	−0.521147	+	0.902653i
$215$		0			0
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$	2.00000			0.135769
$218$	−5.22474	+	9.04952i	−0.353864	+	0.612911i
$219$	1.00000	+	1.41421i	0.0675737	+	0.0955637i
$220$		0			0
$221$	10.8990	+	18.8776i	0.733145	+	1.26984i
$222$	5.77526	−	0.532134i	0.387610	−	0.0357145i
$223$	−0.898979	+	1.55708i	−0.0602001	+	0.104270i	−0.894555	−	0.446958i	$-0.852507\pi$
$223$	−0.898979	+	1.55708i	−0.0602001	+	0.104270i	0.834355	+	0.551228i	$0.185841\pi$
$224$	−4.44949			−0.297294
$225$		0			0
$226$	13.8990			0.924546
$227$	14.1742	−	24.5505i	0.940777	−	1.62947i	0.176783	−	0.984250i	$-0.443431\pi$
$227$	14.1742	−	24.5505i	0.940777	−	1.62947i	0.763994	−	0.645224i	$-0.223236\pi$
$228$	1.84847	−	4.01229i	0.122418	−	0.265720i
$229$	10.5732	+	18.3133i	0.698698	+	1.21018i	0.968918	+	0.247381i	$0.0795701\pi$
$229$	10.5732	+	18.3133i	0.698698	+	1.21018i	−0.270221	+	0.962798i	$0.587097\pi$
$230$		0			0
$231$	−15.7980	+	34.2911i	−1.03943	+	2.25619i
$232$	−1.22474	+	2.12132i	−0.0804084	+	0.139272i
$233$	−5.69694			−0.373219			−0.186609	−	0.982434i	$-0.559750\pi$
$233$	−5.69694			−0.373219			−0.186609	+	0.982434i	$0.559750\pi$
$234$	4.44949	−	12.5851i	0.290872	−	0.822711i
$235$		0			0
$236$	0.275255	−	0.476756i	0.0179176	−	0.0310342i
$237$	21.8990	−	2.01778i	1.42249	−	0.131069i
$238$	10.8990	+	18.8776i	0.706476	+	1.22365i
$239$	−4.77526	−	8.27098i	−0.308886	−	0.535006i	0.669233	−	0.743052i	$-0.266623\pi$
$239$	−4.77526	−	8.27098i	−0.308886	−	0.535006i	−0.978119	+	0.208047i	$0.933289\pi$
$240$		0			0
$241$	11.3990	−	19.7436i	0.734273	−	1.27180i	−0.220769	−	0.975326i	$-0.570857\pi$
$241$	11.3990	−	19.7436i	0.734273	−	1.27180i	0.955042	−	0.296472i	$-0.0958100\pi$
$242$	13.0000			0.835672
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$	8.00000			0.512148
$245$		0			0
$246$	9.00000	+	12.7279i	0.573819	+	0.811503i
$247$	5.67423	+	9.82806i	0.361043	+	0.625345i
$248$	0.224745	+	0.389270i	0.0142713	+	0.0247186i
$249$	−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	$0.555018\pi$
$252$	4.44949	−	12.5851i	0.280292	−	0.792784i
$253$	−12.0000			−0.754434
$254$	−5.67423	+	9.82806i	−0.356033	+	0.616667i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.39898	+	5.88721i	0.212023	+	0.367234i	0.952347	−	0.305016i	$-0.0986616\pi$
$257$	3.39898	+	5.88721i	0.212023	+	0.367234i	−0.740325	+	0.672249i	$0.765328\pi$
$258$	−5.39898	+	11.7190i	−0.336126	+	0.729595i
$259$	−7.44949	+	12.9029i	−0.462889	+	0.801747i
$260$		0			0
$261$	−4.77526	−	5.58542i	−0.295581	−	0.345729i
$262$	15.7980			0.976001
$263$	7.77526	−	13.4671i	0.479443	−	0.830419i	−0.520279	−	0.853996i	$-0.674172\pi$
$263$	7.77526	−	13.4671i	0.479443	−	0.830419i	0.999722	+	0.0235770i	$0.00750547\pi$
$264$	−8.44949	+	0.778539i	−0.520030	+	0.0479158i
$265$		0			0
$266$	5.67423	+	9.82806i	0.347910	+	0.602597i
$267$	−9.00000	−	12.7279i	−0.550791	−	0.778936i
$268$	−7.17423	+	12.4261i	−0.438236	+	0.759047i
$269$	9.55051			0.582305			0.291152	−	0.956677i	$-0.405961\pi$
$269$	9.55051			0.582305			0.291152	+	0.956677i	$0.405961\pi$
$270$		0			0
$271$	0.651531			0.0395777			0.0197888	−	0.999804i	$-0.493701\pi$
$271$	0.651531			0.0395777			0.0197888	+	0.999804i	$0.493701\pi$
$272$	−2.44949	+	4.24264i	−0.148522	+	0.257248i
$273$	19.7980	+	27.9985i	1.19823	+	1.69455i
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$		0			0
$276$	4.22474	−	0.389270i	0.254300	−	0.0234313i
$277$	−3.22474	+	5.58542i	−0.193756	+	0.335595i	−0.946492	−	0.322727i	$-0.895400\pi$
$277$	−3.22474	+	5.58542i	−0.193756	+	0.335595i	0.752736	+	0.658323i	$0.228734\pi$
$278$	−4.00000			−0.239904
$279$	−1.32577	+	0.246405i	−0.0793715	+	0.0147519i
$280$		0			0
$281$	−14.4495	+	25.0273i	−0.861984	+	1.49300i	0.00802643	+	0.999968i	$0.497445\pi$
$281$	−14.4495	+	25.0273i	−0.861984	+	1.49300i	−0.870011	+	0.493033i	$0.835888\pi$
$282$	0.797959	−	1.73205i	0.0475178	−	0.103142i
$283$	5.62372	+	9.74058i	0.334296	+	0.579017i	0.983349	−	0.181726i	$-0.0581682\pi$
$283$	5.62372	+	9.74058i	0.334296	+	0.579017i	−0.649054	+	0.760743i	$0.724835\pi$
$284$	0.674235	+	1.16781i	0.0400085	+	0.0692967i
$285$		0			0
$286$	10.8990	−	18.8776i	0.644470	−	1.11626i
$287$	−40.0454			−2.36381
$288$	2.94949	−	0.548188i	0.173800	−	0.0323023i
$289$	7.00000			0.411765
$290$		0			0
$291$	−18.6237	+	1.71600i	−1.09174	+	0.100594i
$292$	−0.500000	−	0.866025i	−0.0292603	−	0.0506803i
$293$	−14.0227	−	24.2880i	−0.819215	−	1.41892i	−0.906261	−	0.422718i	$-0.861076\pi$
$293$	−14.0227	−	24.2880i	−0.819215	−	1.41892i	0.0870462	−	0.996204i	$-0.472257\pi$
$294$	12.7980	+	18.0990i	0.746392	+	1.05556i
$295$		0			0
$296$	−3.34847			−0.194626
$297$	6.24745	−	24.6773i	0.362514	−	1.43192i
$298$	−6.00000			−0.347571
$299$	−5.44949	+	9.43879i	−0.315152	+	0.545859i
$300$		0			0
$301$	−16.5732	−	28.7056i	−0.955264	−	1.65457i
$302$	−10.0000	−	17.3205i	−0.575435	−	0.996683i
$303$	−6.12372	+	0.564242i	−0.351799	+	0.0324149i
$304$	−1.27526	+	2.20881i	−0.0731409	+	0.126684i
$305$		0			0
$306$	−9.55051	−	11.1708i	−0.545966	−	0.638595i
$307$	6.69694			0.382214			0.191107	−	0.981569i	$-0.438792\pi$
$307$	6.69694			0.382214			0.191107	+	0.981569i	$0.438792\pi$
$308$	10.8990	−	18.8776i	0.621027	−	1.07565i
$309$	9.20204	−	19.9740i	0.523486	−	1.13628i
$310$		0			0
$311$	5.44949	+	9.43879i	0.309012	+	0.535225i	0.978147	−	0.207917i	$-0.0666683\pi$
$311$	5.44949	+	9.43879i	0.309012	+	0.535225i	−0.669134	+	0.743141i	$0.733335\pi$
$312$	−3.22474	+	6.99964i	−0.182565	+	0.396276i
$313$	1.94949	−	3.37662i	0.110192	−	0.190858i	−0.805656	−	0.592384i	$-0.798187\pi$
$313$	1.94949	−	3.37662i	0.110192	−	0.190858i	0.915847	+	0.401526i	$0.131520\pi$
$314$	0.202041			0.0114018
$315$		0			0
$316$	−12.6969			−0.714259
$317$	−8.57321	+	14.8492i	−0.481520	+	0.834017i	−0.999775	−	0.0212094i	$-0.993248\pi$
$317$	−8.57321	+	14.8492i	−0.481520	+	0.834017i	0.518255	+	0.855226i	$0.326582\pi$
$318$	−14.5732	+	1.34278i	−0.817225	+	0.0752994i
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$		0			0
$321$	15.2474	+	21.5631i	0.851030	+	1.20354i
$322$	−5.44949	+	9.43879i	−0.303688	+	0.526003i
$323$	12.4949			0.695235
$324$	−1.39898	+	8.89060i	−0.0777211	+	0.493922i
$325$		0			0
$326$	1.27526	−	2.20881i	0.0706298	−	0.122334i
$327$	10.4495	+	14.7778i	0.577858	+	0.817215i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	2.44949	+	4.24264i	0.135045	+	0.233904i
$330$		0			0
$331$	4.17423	−	7.22999i	0.229437	−	0.397396i	−0.728205	−	0.685360i	$-0.759645\pi$
$331$	4.17423	−	7.22999i	0.229437	−	0.397396i	0.957641	+	0.287964i	$0.0929783\pi$
$332$	0.550510			0.0302132
$333$	3.34847	−	9.47090i	0.183495	−	0.519002i
$334$	19.5959			1.07224
$335$		0			0
$336$	−3.22474	+	6.99964i	−0.175924	+	0.381861i
$337$	−5.55051	−	9.61377i	−0.302356	−	0.523695i	0.674313	−	0.738445i	$-0.264440\pi$
$337$	−5.55051	−	9.61377i	−0.302356	−	0.523695i	−0.976669	+	0.214750i	$0.931106\pi$
$338$	−3.39898	−	5.88721i	−0.184880	−	0.320222i
$339$	10.0732	−	21.8649i	0.547102	−	1.18754i
$340$		0			0
$341$	−2.20204			−0.119247
$342$	−4.97219	−	5.81577i	−0.268865	−	0.314481i
$343$	−25.7980			−1.39296
$344$	3.72474	−	6.45145i	0.200825	−	0.347839i
$345$		0			0
$346$	−4.89898	−	8.48528i	−0.263371	−	0.456172i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	2.44949	+	3.46410i	0.131306	+	0.185695i
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$	−16.5732	−	16.1206i	−0.884613	−	0.860454i
$352$	4.89898			0.261116
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	−0.960574	−	0.278024i	$-0.910320\pi$
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	0.721063	+	0.692869i	$0.243654\pi$
$354$	−0.550510	−	0.778539i	−0.0292593	−	0.0413789i
$355$		0			0
$356$	4.50000	+	7.79423i	0.238500	+	0.413093i
$357$	37.5959	−	3.46410i	1.98979	−	0.183340i
$358$	7.62372	−	13.2047i	0.402926	−	0.697889i
$359$	−33.7980			−1.78379			−0.891894	−	0.452244i	$-0.850623\pi$
$359$	−33.7980			−1.78379			−0.891894	+	0.452244i	$0.850623\pi$
$360$		0			0
$361$	−12.4949			−0.657626
$362$	0.898979	−	1.55708i	0.0472493	−	0.0818382i
$363$	9.42168	−	20.4507i	0.494510	−	1.07338i
$364$	−9.89898	−	17.1455i	−0.518848	−	0.898670i
$365$		0			0
$366$	5.79796	−	12.5851i	0.303064	−	0.657831i
$367$	8.34847	−	14.4600i	0.435787	−	0.754804i	−0.561573	−	0.827427i	$-0.689804\pi$
$367$	8.34847	−	14.4600i	0.435787	−	0.754804i	0.997359	+	0.0726228i	$0.0231369\pi$
$368$	−2.44949			−0.127688
$369$	26.5454	−	4.93369i	1.38190	−	0.256838i
$370$		0			0
$371$	18.7980	−	32.5590i	0.975941	−	1.69038i
$372$	0.775255	−	0.0714323i	0.0401951	−	0.00370359i
$373$	7.79796	+	13.5065i	0.403763	+	0.699338i	0.994177	−	0.107763i	$-0.0343687\pi$
$373$	7.79796	+	13.5065i	0.403763	+	0.699338i	−0.590414	+	0.807101i	$0.701035\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$		0			0
$376$	−0.550510	+	0.953512i	−0.0283904	+	0.0491736i
$377$	−10.8990			−0.561326
$378$	−16.5732	−	16.1206i	−0.852434	−	0.829154i
$379$	0.898979			0.0461775			0.0230887	−	0.999733i	$-0.492650\pi$
$379$	0.898979			0.0461775			0.0230887	+	0.999733i	$0.492650\pi$
$380$		0			0
$381$	11.3485	+	16.0492i	0.581400	+	0.822223i
$382$	5.44949	+	9.43879i	0.278820	+	0.482931i
$383$	13.2247	+	22.9059i	0.675753	+	1.17044i	0.976248	+	0.216655i	$0.0695147\pi$
$383$	13.2247	+	22.9059i	0.675753	+	1.17044i	−0.300495	+	0.953783i	$0.597152\pi$
$384$	−1.72474	+	0.158919i	−0.0880155	+	0.00810978i
$385$		0			0
$386$	−20.0000			−1.01797
$387$	14.5227	+	16.9866i	0.738231	+	0.863478i
$388$	10.7980			0.548183
$389$	6.79796	−	11.7744i	0.344670	−	0.596986i	−0.640624	−	0.767855i	$-0.721324\pi$
$389$	6.79796	−	11.7744i	0.344670	−	0.596986i	0.985294	+	0.170869i	$0.0546574\pi$
$390$		0			0
$391$	6.00000	+	10.3923i	0.303433	+	0.525561i
$392$	−6.39898	−	11.0834i	−0.323197	−	0.559794i
$393$	11.4495	−	24.8523i	0.577550	−	1.25363i
$394$	12.1237	−	20.9989i	0.610784	−	1.05791i
$395$		0			0
$396$	−4.89898	+	13.8564i	−0.246183	+	0.696311i
$397$	−21.5959			−1.08387			−0.541934	−	0.840421i	$-0.682308\pi$
$397$	−21.5959			−1.08387			−0.541934	+	0.840421i	$0.682308\pi$
$398$	−2.89898	+	5.02118i	−0.145313	+	0.251689i
$399$	19.5732	−	1.80348i	0.979886	−	0.0902871i
$400$		0			0
$401$	−4.65153	−	8.05669i	−0.232286	−	0.402332i	0.726194	−	0.687490i	$-0.241287\pi$
$401$	−4.65153	−	8.05669i	−0.232286	−	0.402332i	−0.958481	+	0.285158i	$0.907954\pi$
$402$	14.3485	+	20.2918i	0.715637	+	1.01206i
$403$	−1.00000	+	1.73205i	−0.0498135	+	0.0862796i
$404$	3.55051			0.176644
$405$		0			0
$406$	−10.8990			−0.540907
$407$	8.20204	−	14.2064i	0.406560	−	0.704183i
$408$	4.89898	+	6.92820i	0.242536	+	0.342997i
$409$	−4.94949	−	8.57277i	−0.244737	−	0.423896i	0.717321	−	0.696743i	$-0.245368\pi$
$409$	−4.94949	−	8.57277i	−0.244737	−	0.423896i	−0.962058	+	0.272847i	$0.912035\pi$
$410$		0			0
$411$	5.17423	−	0.476756i	0.255226	−	0.0235166i
$412$	−6.34847	+	10.9959i	−0.312767	+	0.541728i
$413$	2.44949			0.120532
$414$	2.44949	−	6.92820i	0.120386	−	0.340503i
$415$		0			0
$416$	2.22474	−	3.85337i	0.109077	−	0.188927i
$417$	−2.89898	+	6.29253i	−0.141964	+	0.308146i
$418$	−6.24745	−	10.8209i	−0.305573	−	0.529267i
$419$	−4.07321	−	7.05501i	−0.198990	−	0.344660i	0.749212	−	0.662331i	$-0.230433\pi$
$419$	−4.07321	−	7.05501i	−0.198990	−	0.344660i	−0.948201	+	0.317671i	$0.897099\pi$
$420$		0			0
$421$	−9.02270	+	15.6278i	−0.439740	+	0.761651i	−0.997669	−	0.0682369i	$-0.978263\pi$
$421$	−9.02270	+	15.6278i	−0.439740	+	0.761651i	0.557929	+	0.829888i	$0.311596\pi$
$422$	1.44949			0.0705601
$423$	−2.14643	−	2.51059i	−0.104363	−	0.122069i
$424$	8.44949			0.410343
$425$		0			0
$426$	2.32577	−	0.214297i	0.112684	−	0.0103827i
$427$	17.7980	+	30.8270i	0.861304	+	1.49182i
$428$	−7.62372	−	13.2047i	−0.368507	−	0.638272i
$429$	−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	$0.417420\pi$
$432$	1.27526	−	5.03723i	0.0613557	−	0.242354i
$433$	29.5959			1.42229			0.711145	−	0.703046i	$-0.248177\pi$
$433$	29.5959			1.42229			0.711145	+	0.703046i	$0.248177\pi$
$434$	−1.00000	+	1.73205i	−0.0480015	+	0.0831411i
$435$		0			0
$436$	−5.22474	−	9.04952i	−0.250220	−	0.433394i
$437$	3.12372	+	5.41045i	0.149428	+	0.258817i
$438$	−1.72474	+	0.158919i	−0.0824115	+	0.00759343i
$439$	5.67423	−	9.82806i	0.270816	−	0.469068i	−0.698255	−	0.715849i	$-0.746040\pi$
$439$	5.67423	−	9.82806i	0.270816	−	0.469068i	0.969071	+	0.246782i	$0.0793730\pi$
$440$		0			0
$441$	37.7474	−	7.01569i	1.79750	−	0.334080i
$442$	−21.7980			−1.03682
$443$	13.8990	−	24.0737i	0.660360	−	1.14378i	−0.320161	−	0.947363i	$-0.603737\pi$
$443$	13.8990	−	24.0737i	0.660360	−	1.14378i	0.980521	−	0.196415i	$-0.0629298\pi$
$444$	−2.42679	+	5.26758i	−0.115170	+	0.249989i
$445$		0			0
$446$	−0.898979	−	1.55708i	−0.0425679	−	0.0737298i
$447$	−4.34847	+	9.43879i	−0.205676	+	0.446440i
$448$	2.22474	−	3.85337i	0.105109	−	0.182055i
$449$	10.5959			0.500052			0.250026	−	0.968239i	$-0.419561\pi$
$449$	10.5959			0.500052			0.250026	+	0.968239i	$0.419561\pi$
$450$		0			0
$451$	44.0908			2.07616
$452$	−6.94949	+	12.0369i	−0.326877	+	0.566167i
$453$	−34.4949	+	3.17837i	−1.62071	+	0.149333i
$454$	14.1742	+	24.5505i	0.665230	+	1.15221i
$455$		0			0
$456$	2.55051	+	3.60697i	0.119439	+	0.168912i
$457$	−7.84847	+	13.5939i	−0.367136	+	0.635898i	−0.989116	−	0.147135i	$-0.952995\pi$
$457$	−7.84847	+	13.5939i	−0.367136	+	0.635898i	0.621981	+	0.783033i	$0.286328\pi$
$458$	−21.1464			−0.988108
$459$	−24.4949	+	6.92820i	−1.14332	+	0.323381i
$460$		0			0
$461$	−9.67423	+	16.7563i	−0.450574	+	0.780417i	−0.998422	−	0.0561610i	$-0.982114\pi$
$461$	−9.67423	+	16.7563i	−0.450574	+	0.780417i	0.547848	+	0.836578i	$0.315447\pi$
$462$	−21.7980	−	30.8270i	−1.01413	−	1.43420i
$463$	4.67423	+	8.09601i	0.217230	+	0.376254i	0.953960	−	0.299933i	$-0.0969645\pi$
$463$	4.67423	+	8.09601i	0.217230	+	0.376254i	−0.736730	+	0.676187i	$0.763631\pi$
$464$	−1.22474	−	2.12132i	−0.0568574	−	0.0984798i
$465$		0			0
$466$	2.84847	−	4.93369i	0.131953	−	0.228549i
$467$	−4.34847			−0.201223			−0.100612	−	0.994926i	$-0.532080\pi$
$467$	−4.34847			−0.201223			−0.100612	+	0.994926i	$0.532080\pi$
$468$	8.67423	+	10.1459i	0.400967	+	0.468994i
$469$	−63.8434			−2.94801
$470$		0			0
$471$	0.146428	−	0.317837i	0.00674706	−	0.0146452i
$472$	0.275255	+	0.476756i	0.0126696	+	0.0219445i
$473$	18.2474	+	31.6055i	0.839019	+	1.45322i
$474$	−9.20204	+	19.9740i	−0.422664	+	0.917434i
$475$		0			0
$476$	−21.7980			−0.999108
$477$	−8.44949	+	23.8988i	−0.386876	+	1.09425i
$478$	9.55051			0.436830
$479$	12.1237	−	20.9989i	0.553947	−	0.959465i	−0.444038	−	0.896008i	$-0.646454\pi$
$479$	12.1237	−	20.9989i	0.553947	−	0.959465i	0.997985	−	0.0634563i	$-0.0202124\pi$
$480$		0			0
$481$	−7.44949	−	12.9029i	−0.339667	−	0.588321i
$482$	11.3990	+	19.7436i	0.519209	+	0.899297i
$483$	10.8990	+	15.4135i	0.495921	+	0.701338i
$484$	−6.50000	+	11.2583i	−0.295455	+	0.511742i
$485$		0			0
$486$	12.9722	+	8.64420i	0.588431	+	0.392109i
$487$	19.5505			0.885918			0.442959	−	0.896542i	$-0.353929\pi$
$487$	19.5505			0.885918			0.442959	+	0.896542i	$0.353929\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	−2.55051	−	3.60697i	−0.115338	−	0.163113i
$490$		0			0
$491$	1.37628	+	2.38378i	0.0621105	+	0.107578i	0.895409	−	0.445245i	$-0.146884\pi$
$491$	1.37628	+	2.38378i	0.0621105	+	0.107578i	−0.833298	+	0.552824i	$0.813550\pi$
$492$	−15.5227	+	1.43027i	−0.699818	+	0.0644814i
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$	−11.3485			−0.510592
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$	0.398979	−	0.866025i	0.0178787	−	0.0388075i
$499$	−3.17423	−	5.49794i	−0.142098	−	0.246121i	0.786188	−	0.617987i	$-0.212052\pi$
$499$	−3.17423	−	5.49794i	−0.142098	−	0.246121i	−0.928287	+	0.371866i	$0.878718\pi$
$500$		0			0
$501$	14.2020	−	30.8270i	0.634500	−	1.37725i
$502$	2.72474	−	4.71940i	0.121611	−	0.210637i
$503$	−26.4495			−1.17932			−0.589662	−	0.807650i	$-0.700739\pi$
$503$	−26.4495			−1.17932			−0.589662	+	0.807650i	$0.700739\pi$
$504$	8.67423	+	10.1459i	0.386381	+	0.451934i
$505$		0			0
$506$	6.00000	−	10.3923i	0.266733	−	0.461994i
$507$	−11.7247	+	1.08032i	−0.520714	+	0.0479788i
$508$	−5.67423	−	9.82806i	−0.251753	−	0.436050i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	2.22474	−	3.85337i	0.0984169	−	0.170463i
$512$	1.00000			0.0441942
$513$	−12.7526	+	3.60697i	−0.563039	+	0.159251i
$514$	−6.79796			−0.299845
$515$		0			0
$516$	−7.44949	−	10.5352i	−0.327945	−	0.463785i
$517$	−2.69694	−	4.67123i	−0.118611	−	0.205441i
$518$	−7.44949	−	12.9029i	−0.327312	−	0.566921i
$519$	−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	$0.277322\pi$
$522$	7.22474	−	1.34278i	0.316218	−	0.0587719i
$523$	5.65153			0.247124			0.123562	−	0.992337i	$-0.460568\pi$
$523$	5.65153			0.247124			0.123562	+	0.992337i	$0.460568\pi$
$524$	−7.89898	+	13.6814i	−0.345069	+	0.597676i
$525$		0			0
$526$	7.77526	+	13.4671i	0.339017	+	0.587195i
$527$	1.10102	+	1.90702i	0.0479612	+	0.0830712i
$528$	3.55051	−	7.70674i	0.154516	−	0.335393i
$529$	8.50000	−	14.7224i	0.369565	−	0.640106i
$530$		0			0
$531$	−1.62372	+	0.301783i	−0.0704636	+	0.0130963i
$532$	−11.3485			−0.492019
$533$	20.0227	−	34.6803i	0.867280	−	1.50217i
$534$	15.5227	−	1.43027i	0.671733	−	0.0618937i
$535$		0			0
$536$	−7.17423	−	12.4261i	−0.309880	−	0.536727i
$537$	−15.2474	−	21.5631i	−0.657976	−	0.930519i
$538$	−4.77526	+	8.27098i	−0.205876	+	0.356587i
$539$	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	$0.627969\pi$
$542$	−0.325765	+	0.564242i	−0.0139928	+	0.0242363i
$543$	−1.79796	−	2.54270i	−0.0771578	−	0.109118i
$544$	−2.44949	−	4.24264i	−0.105021	−	0.181902i
$545$		0			0
$546$	−34.1464	+	3.14626i	−1.46133	+	0.134648i
$547$	15.1742	−	26.2825i	0.648803	−	1.12376i	−0.334606	−	0.942358i	$-0.608603\pi$
$547$	15.1742	−	26.2825i	0.648803	−	1.12376i	0.983409	−	0.181402i	$-0.0580636\pi$
$548$	−3.00000			−0.128154
$549$	−15.5959	−	18.2419i	−0.665618	−	0.778546i
$550$		0			0
$551$	−3.12372	+	5.41045i	−0.133075	+	0.230493i
$552$	−1.77526	+	3.85337i	−0.0755599	+	0.164010i
$553$	−28.2474	−	48.9260i	−1.20120	−	2.08055i
$554$	−3.22474	−	5.58542i	−0.137006	−	0.237302i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	17.3939			0.737002			0.368501	−	0.929627i	$-0.379871\pi$
$557$	17.3939			0.737002			0.368501	+	0.929627i	$0.379871\pi$
$558$	0.449490	−	1.27135i	0.0190284	−	0.0538205i
$559$	33.1464			1.40194
$560$		0			0
$561$	−41.3939	+	3.81405i	−1.74765	+	0.161029i
$562$	−14.4495	−	25.0273i	−0.609515	−	1.05571i
$563$	14.9722	+	25.9326i	0.631003	+	1.09293i	0.987347	+	0.158574i	$0.0506897\pi$
$563$	14.9722	+	25.9326i	0.631003	+	1.09293i	−0.356344	+	0.934355i	$0.615977\pi$
$564$	1.10102	+	1.55708i	0.0463613	+	0.0655648i
$565$		0			0
$566$	−11.2474			−0.472766
$567$	−37.3712	+	14.3885i	−1.56944	+	0.604262i
$568$	−1.34847			−0.0565805
$569$	−7.10102	+	12.2993i	−0.297690	+	0.515615i	−0.975607	−	0.219524i	$-0.929550\pi$
$569$	−7.10102	+	12.2993i	−0.297690	+	0.515615i	0.677917	+	0.735139i	$0.262883\pi$
$570$		0			0
$571$	13.9722	+	24.2005i	0.584718	+	1.01276i	0.994911	+	0.100762i	$0.0321282\pi$
$571$	13.9722	+	24.2005i	0.584718	+	1.01276i	−0.410192	+	0.911999i	$0.634538\pi$
$572$	10.8990	+	18.8776i	0.455709	+	0.789312i
$573$	18.7980	−	1.73205i	0.785296	−	0.0723575i
$574$	20.0227	−	34.6803i	0.835732	−	1.44753i
$575$		0			0
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$	18.3939			0.765747			0.382874	−	0.923801i	$-0.374934\pi$
$577$	18.3939			0.765747			0.382874	+	0.923801i	$0.374934\pi$
$578$	−3.50000	+	6.06218i	−0.145581	+	0.252153i
$579$	−14.4949	+	31.4626i	−0.602387	+	1.30754i
$580$		0			0
$581$	1.22474	+	2.12132i	0.0508110	+	0.0880072i
$582$	7.82577	−	16.9866i	0.324388	−	0.704118i
$583$	−20.6969	+	35.8481i	−0.857180	+	1.48468i
$584$	1.00000			0.0413803
$585$		0			0
$586$	28.0454			1.15855
$587$	1.34847	−	2.33562i	0.0556573	−	0.0964012i	−0.836854	−	0.547426i	$-0.815608\pi$
$587$	1.34847	−	2.33562i	0.0556573	−	0.0964012i	0.892512	+	0.451024i	$0.148941\pi$
$588$	−22.0732	+	2.03383i	−0.910284	+	0.0838739i
$589$	0.573214	+	0.992836i	0.0236189	+	0.0409091i
$590$		0			0
$591$	−24.2474	−	34.2911i	−0.997407	−	1.41055i
$592$	1.67423	−	2.89986i	0.0688106	−	0.119183i
$593$	−1.89898			−0.0779817			−0.0389909	−	0.999240i	$-0.512414\pi$
$593$	−1.89898			−0.0779817			−0.0389909	+	0.999240i	$0.512414\pi$
$594$	18.2474	+	17.7491i	0.748702	+	0.728254i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	5.79796	+	8.19955i	0.237295	+	0.335585i
$598$	−5.44949	−	9.43879i	−0.222846	−	0.385981i
$599$	18.6742	+	32.3447i	0.763009	+	1.32157i	0.941293	+	0.337591i	$0.109612\pi$
$599$	18.6742	+	32.3447i	0.763009	+	1.32157i	−0.178285	+	0.983979i	$0.557055\pi$
$600$		0			0
$601$	−16.2474	+	28.1414i	−0.662747	+	1.14791i	0.317144	+	0.948378i	$0.397276\pi$
$601$	−16.2474	+	28.1414i	−0.662747	+	1.14791i	−0.979891	+	0.199534i	$0.936057\pi$
$602$	33.1464			1.35095
$603$	42.3207	−	7.86566i	1.72343	−	0.320314i
$604$	20.0000			0.813788
$605$		0			0
$606$	2.57321	−	5.58542i	0.104530	−	0.226892i
$607$	−5.67423	−	9.82806i	−0.230310	−	0.398909i	0.727589	−	0.686013i	$-0.240641\pi$
$607$	−5.67423	−	9.82806i	−0.230310	−	0.398909i	−0.957899	+	0.287104i	$0.907307\pi$
$608$	−1.27526	−	2.20881i	−0.0517184	−	0.0895789i
$609$	−7.89898	+	17.1455i	−0.320083	+	0.694772i
$610$		0			0
$611$	−4.89898			−0.198191
$612$	14.4495	−	2.68556i	0.584086	−	0.108557i
$613$	32.0454			1.29430			0.647151	−	0.762362i	$-0.275960\pi$
$613$	32.0454			1.29430			0.647151	+	0.762362i	$0.275960\pi$
$614$	−3.34847	+	5.79972i	−0.135133	+	0.234058i
$615$		0			0
$616$	10.8990	+	18.8776i	0.439132	+	0.760600i
$617$	−7.19694	−	12.4655i	−0.289738	−	0.501841i	0.684009	−	0.729473i	$-0.260235\pi$
$617$	−7.19694	−	12.4655i	−0.289738	−	0.501841i	−0.973747	+	0.227633i	$0.926901\pi$
$618$	12.6969	+	17.9562i	0.510746	+	0.722304i
$619$	−20.8712	+	36.1499i	−0.838883	+	1.45299i	0.0519458	+	0.998650i	$0.483458\pi$
$619$	−20.8712	+	36.1499i	−0.838883	+	1.45299i	−0.890829	+	0.454339i	$0.849876\pi$
$620$		0			0
$621$	−9.12372	−	8.87455i	−0.366122	−	0.356123i
$622$	−10.8990			−0.437009
$623$	−20.0227	+	34.6803i	−0.802193	+	1.38944i
$624$	−4.44949	−	6.29253i	−0.178122	−	0.251903i
$625$		0			0
$626$	1.94949	+	3.37662i	0.0779173	+	0.134957i
$627$	−21.5505	+	1.98567i	−0.860644	+	0.0793001i
$628$	−0.101021	+	0.174973i	−0.00403116	+	0.00698217i
$629$	−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	$0.671651\pi$
$632$	6.34847	−	10.9959i	0.252529	−	0.437392i
$633$	1.05051	−	2.28024i	0.0417540	−	0.0906314i
$634$	−8.57321	−	14.8492i	−0.340486	−	0.589739i
$635$		0			0
$636$	6.12372	−	13.2922i	0.242821	−	0.527069i
$637$	28.4722	−	49.3153i	1.12811	−	1.95394i
$638$	12.0000			0.475085
$639$	1.34847	−	3.81405i	0.0533446	−	0.150881i
$640$		0			0
$641$	−22.1969	+	38.4462i	−0.876726	+	1.51853i	−0.0218141	+	0.999762i	$0.506944\pi$
$641$	−22.1969	+	38.4462i	−0.876726	+	1.51853i	−0.854912	+	0.518773i	$0.826389\pi$
$642$	−26.2980	+	2.42310i	−1.03790	+	0.0956323i
$643$	−16.1742	−	28.0146i	−0.637850	−	1.10479i	−0.985904	−	0.167313i	$-0.946491\pi$
$643$	−16.1742	−	28.0146i	−0.637850	−	1.10479i	0.348054	−	0.937474i	$-0.386843\pi$
$644$	−5.44949	−	9.43879i	−0.214740	−	0.371941i
$645$		0			0
$646$	−6.24745	+	10.8209i	−0.245803	+	0.425743i
$647$	0.247449			0.00972821			0.00486411	−	0.999988i	$-0.498452\pi$
$647$	0.247449			0.00972821			0.00486411	+	0.999988i	$0.498452\pi$
$648$	−7.00000	−	5.65685i	−0.274986	−	0.222222i
$649$	−2.69694			−0.105864
$650$		0			0
$651$	2.00000	+	2.82843i	0.0783862	+	0.110855i
$652$	1.27526	+	2.20881i	0.0499428	+	0.0865035i
$653$	−3.12372	−	5.41045i	−0.122241	−	0.211727i	0.798410	−	0.602114i	$-0.205675\pi$
$653$	−3.12372	−	5.41045i	−0.122241	−	0.211727i	−0.920651	+	0.390387i	$0.872341\pi$
$654$	−18.0227	+	1.66062i	−0.704743	+	0.0649353i
$655$		0			0
$656$	9.00000			0.351391
$657$	−1.00000	+	2.82843i	−0.0390137	+	0.110347i
$658$	−4.89898			−0.190982
$659$	−22.0732	+	38.2319i	−0.859850	+	1.48930i	0.0122208	+	0.999925i	$0.496110\pi$
$659$	−22.0732	+	38.2319i	−0.859850	+	1.48930i	−0.872071	+	0.489379i	$0.837223\pi$
$660$		0			0
$661$	25.6969	+	44.5084i	0.999495	+	1.73118i	0.527265	+	0.849701i	$0.323218\pi$
$661$	25.6969	+	44.5084i	0.999495	+	1.73118i	0.472230	+	0.881475i	$0.343449\pi$
$662$	4.17423	+	7.22999i	0.162236	+	0.281001i
$663$	−15.7980	+	34.2911i	−0.613542	+	1.33175i
$664$	−0.275255	+	0.476756i	−0.0106820	+	0.0185017i
$665$		0			0
$666$	6.52781	+	7.63531i	0.252947	+	0.295862i
$667$	−6.00000			−0.232321
$668$	−9.79796	+	16.9706i	−0.379094	+	0.656611i
$669$	−3.10102	+	0.285729i	−0.119892	+	0.0110469i
$670$		0			0
$671$	−19.5959	−	33.9411i	−0.756492	−	1.31028i
$672$	−4.44949	−	6.29253i	−0.171643	−	0.242740i
$673$	−3.34847	+	5.79972i	−0.129074	+	0.223563i	−0.923318	−	0.384036i	$-0.874534\pi$
$673$	−3.34847	+	5.79972i	−0.129074	+	0.223563i	0.794244	+	0.607599i	$0.207867\pi$
$674$	11.1010			0.427595
$675$		0			0
$676$	6.79796			0.261460
$677$	18.9217	−	32.7733i	0.727219	−	1.25958i	−0.230835	−	0.972993i	$-0.574146\pi$
$677$	18.9217	−	32.7733i	0.727219	−	1.25958i	0.958054	−	0.286588i	$-0.0925210\pi$
$678$	13.8990	+	19.6561i	0.533787	+	0.754889i
$679$	24.0227	+	41.6085i	0.921907	+	1.59679i
$680$		0			0
$681$	48.8939	−	4.50510i	1.87362	−	0.172636i
$682$	1.10102	−	1.90702i	0.0421603	−	0.0730237i
$683$	11.9444			0.457039			0.228520	−	0.973539i	$-0.426611\pi$
$683$	11.9444			0.457039			0.228520	+	0.973539i	$0.426611\pi$
$684$	7.52270	−	1.39816i	0.287638	−	0.0534600i
$685$		0			0
$686$	12.8990	−	22.3417i	0.492485	−	0.853010i
$687$	−15.3258	+	33.2661i	−0.584714	+	1.26918i
$688$	3.72474	+	6.45145i	0.142005	+	0.245959i
$689$	18.7980	+	32.5590i	0.716145	+	1.24040i
$690$		0			0
$691$	2.52270	−	4.36945i	0.0959682	−	0.166222i	−0.814044	−	0.580803i	$-0.802739\pi$
$691$	2.52270	−	4.36945i	0.0959682	−	0.166222i	0.910012	+	0.414581i	$0.136072\pi$
$692$	9.79796			0.372463
$693$	−64.2929	+	11.9494i	−2.44228	+	0.453920i
$694$	−12.0000			−0.455514
$695$		0			0
$696$	−4.22474	+	0.389270i	−0.160139	+	0.0147552i
$697$	−22.0454	−	38.1838i	−0.835029	−	1.44631i
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$	−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	$0.413571\pi$
$702$	22.2474	−	6.29253i	0.839676	−	0.237496i
$703$	−8.54031			−0.322104
$704$	−2.44949	+	4.24264i	−0.0923186	+	0.159901i
$705$		0			0
$706$	−4.50000	−	7.79423i	−0.169360	−	0.293340i
$707$	7.89898	+	13.6814i	0.297072	+	0.514543i
$708$	0.949490	−	0.0874863i	0.0356840	−	0.00328794i
$709$	0.224745	−	0.389270i	0.00844047	−	0.0146193i	−0.861774	−	0.507292i	$-0.830647\pi$
$709$	0.224745	−	0.389270i	0.00844047	−	0.0146193i	0.870215	+	0.492673i	$0.163980\pi$
$710$		0			0
$711$	24.7526	+	28.9521i	0.928293	+	1.08579i
$712$	−9.00000			−0.337289
$713$	−0.550510	+	0.953512i	−0.0206168	+	0.0357093i
$714$	−15.7980	+	34.2911i	−0.591224	+	1.28331i
$715$		0			0
$716$	7.62372	+	13.2047i	0.284912	+	0.493482i
$717$	6.92168	−	15.0242i	0.258495	−	0.561090i
$718$	16.8990	−	29.2699i	0.630664	−	1.09234i
$719$	52.0454			1.94097			0.970483	−	0.241169i	$-0.0775309\pi$
$719$	52.0454			1.94097			0.970483	+	0.241169i	$0.0775309\pi$
$720$		0			0
$721$	−56.4949			−2.10398
$722$	6.24745	−	10.8209i	0.232506	−	0.402712i
$723$	39.3207	−	3.62302i	1.46235	−	0.134742i
$724$	0.898979	+	1.55708i	0.0334103	+	0.0578684i
$725$		0			0
$726$	13.0000	+	18.3848i	0.482475	+	0.682323i
$727$	−8.00000	+	13.8564i	−0.296704	+	0.513906i	−0.975380	−	0.220532i	$-0.929221\pi$
$727$	−8.00000	+	13.8564i	−0.296704	+	0.513906i	0.678676	+	0.734438i	$0.262554\pi$
$728$	19.7980			0.733761
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		0			0
$731$	18.2474	−	31.6055i	0.674906	−	1.16897i
$732$	8.00000	+	11.3137i	0.295689	+	0.418167i
$733$	13.0000	+	22.5167i	0.480166	+	0.831672i	0.999741	−	0.0227529i	$-0.00724310\pi$
$733$	13.0000	+	22.5167i	0.480166	+	0.831672i	−0.519575	+	0.854425i	$0.673910\pi$
$734$	8.34847	+	14.4600i	0.308148	+	0.533727i
$735$		0			0
$736$	1.22474	−	2.12132i	0.0451447	−	0.0781929i
$737$	70.2929			2.58927
$738$	−9.00000	+	25.4558i	−0.331295	+	0.937043i
$739$	−41.0454			−1.50988			−0.754940	−	0.655794i	$-0.772334\pi$
$739$	−41.0454			−1.50988			−0.754940	+	0.655794i	$0.772334\pi$
$740$		0			0
$741$	−8.22474	+	17.8526i	−0.302144	+	0.655833i
$742$	18.7980	+	32.5590i	0.690095	+	1.19528i
$743$	17.3258	+	30.0091i	0.635621	+	1.10093i	0.986383	+	0.164463i	$0.0525891\pi$
$743$	17.3258	+	30.0091i	0.635621	+	1.10093i	−0.350763	+	0.936464i	$0.614078\pi$
$744$	−0.325765	+	0.707107i	−0.0119431	+	0.0259238i
$745$		0			0
$746$	−15.5959			−0.571007
$747$	−1.07321	−	1.25529i	−0.0392669	−	0.0459288i
$748$	24.0000			0.877527
$749$	33.9217	−	58.7541i	1.23947	−	2.14683i
$750$		0			0
$751$	25.0227	+	43.3406i	0.913091	+	1.58152i	0.809672	+	0.586883i	$0.199645\pi$
$751$	25.0227	+	43.3406i	0.913091	+	1.58152i	0.103420	+	0.994638i	$0.467022\pi$
$752$	−0.550510	−	0.953512i	−0.0200750	−	0.0347710i
$753$	−5.44949	−	7.70674i	−0.198590	−	0.280849i
$754$	5.44949	−	9.43879i	0.198459	−	0.343741i
$755$		0			0
$756$	22.2474	−	6.29253i	0.809132	−	0.228857i
$757$	−6.04541			−0.219724			−0.109862	−	0.993947i	$-0.535041\pi$
$757$	−6.04541			−0.219724			−0.109862	+	0.993947i	$0.535041\pi$
$758$	−0.449490	+	0.778539i	−0.0163262	+	0.0282778i
$759$	−12.0000	−	16.9706i	−0.435572	−	0.615992i
$760$		0			0
$761$	−2.05051	−	3.55159i	−0.0743309	−	0.128745i	0.826464	−	0.562989i	$-0.190349\pi$
$761$	−2.05051	−	3.55159i	−0.0743309	−	0.128745i	−0.900795	+	0.434244i	$0.857015\pi$
$762$	−19.5732	+	1.80348i	−0.709063	+	0.0653333i
$763$	23.2474	−	40.2658i	0.841614	−	1.45772i
$764$	−10.8990			−0.394311
$765$		0			0
$766$	−26.4495			−0.955659
$767$	−1.22474	+	2.12132i	−0.0442230	+	0.0765964i
$768$	0.724745	−	1.57313i	0.0261520	−	0.0567655i
$769$	−25.0959	−	43.4674i	−0.904982	−	1.56747i	−0.820941	−	0.571012i	$-0.806551\pi$
$769$	−25.0959	−	43.4674i	−0.904982	−	1.56747i	−0.0840405	−	0.996462i	$-0.526783\pi$
$770$		0			0
$771$	−4.92679	+	10.6941i	−0.177434	+	0.385138i
$772$	10.0000	−	17.3205i	0.359908	−	0.623379i
$773$	49.5959			1.78384			0.891921	−	0.452192i	$-0.149358\pi$
$773$	49.5959			1.78384			0.891921	+	0.452192i	$0.149358\pi$
$774$	−21.9722	+	4.08372i	−0.789774	+	0.146786i
$775$		0			0
$776$	−5.39898	+	9.35131i	−0.193812	+	0.335692i
$777$	−25.6969	+	2.36773i	−0.921873	+	0.0849417i
$778$	6.79796	+	11.7744i	0.243719	+	0.422133i
$779$	−11.4773	−	19.8793i	−0.411217	−	0.712248i
$780$		0			0
$781$	3.30306	−	5.72107i	0.118193	−	0.204716i
$782$	−12.0000			−0.429119
$783$	3.12372	−	12.3387i	0.111633	−	0.440947i
$784$	12.7980			0.457070
$785$		0			0
$786$	15.7980	+	22.3417i	0.563495	+	0.796902i
$787$	2.65153	+	4.59259i	0.0945169	+	0.163708i	0.909407	−	0.415908i	$-0.136536\pi$
$787$	2.65153	+	4.59259i	0.0945169	+	0.163708i	−0.814890	+	0.579616i	$0.803203\pi$
$788$	12.1237	+	20.9989i	0.431890	+	0.748055i
$789$	26.8207	−	2.47127i	0.954841	−	0.0879794i
$790$		0			0
$791$	−61.8434			−2.19890
$792$	−9.55051	−	11.1708i	−0.339363	−	0.396939i
$793$	−35.5959			−1.26405
$794$	10.7980	−	18.7026i	0.383205	−	0.663731i
$795$		0			0
$796$	−2.89898	−	5.02118i	−0.102752	−	0.177971i
$797$	−2.87628	−	4.98186i	−0.101883	−	0.176466i	0.810577	−	0.585631i	$-0.199153\pi$
$797$	−2.87628	−	4.98186i	−0.101883	−	0.176466i	−0.912460	+	0.409165i	$0.865820\pi$
$798$	−8.22474	+	17.8526i	−0.291153	+	0.631977i
$799$	−2.69694	+	4.67123i	−0.0954108	+	0.165256i
$800$		0			0
$801$	9.00000	−	25.4558i	0.317999	−	0.899438i
$802$	9.30306			0.328503
$803$	−2.44949	+	4.24264i	−0.0864406	+	0.149720i
$804$	−24.7474	+	2.28024i	−0.872775	+	0.0804178i
$805$		0			0
$806$	−1.00000	−	1.73205i	−0.0352235	−	0.0610089i
$807$	9.55051	+	13.5065i	0.336194	+	0.475450i
$808$	−1.77526	+	3.07483i	−0.0624533	+	0.108172i
$809$	−35.6969			−1.25504			−0.627519	−	0.778601i	$-0.715929\pi$
$809$	−35.6969			−1.25504			−0.627519	+	0.778601i	$0.715929\pi$
$810$		0			0
$811$	−33.4495			−1.17457			−0.587285	−	0.809380i	$-0.699803\pi$
$811$	−33.4495			−1.17457			−0.587285	+	0.809380i	$0.699803\pi$
$812$	5.44949	−	9.43879i	0.191240	−	0.331237i
$813$	0.651531	+	0.921404i	0.0228502	+	0.0323150i
$814$	8.20204	+	14.2064i	0.287481	+	0.497932i
$815$		0			0
$816$	−8.44949	+	0.778539i	−0.295791	+	0.0272543i
$817$	9.50000	−	16.4545i	0.332363	−	0.575669i
$818$	9.89898			0.346110
$819$	−19.7980	+	55.9971i	−0.691797	+	1.95670i
$820$		0			0
$821$	25.5959	−	44.3334i	0.893304	−	1.54725i	0.0574136	−	0.998350i	$-0.481715\pi$
$821$	25.5959	−	44.3334i	0.893304	−	1.54725i	0.835890	−	0.548897i	$-0.184952\pi$
$822$	−2.17423	+	4.71940i	−0.0758351	+	0.164608i
$823$	−13.4495	−	23.2952i	−0.468820	−	0.812020i	0.530545	−	0.847657i	$-0.321987\pi$
$823$	−13.4495	−	23.2952i	−0.468820	−	0.812020i	−0.999365	+	0.0356371i	$0.988654\pi$
$824$	−6.34847	−	10.9959i	−0.221159	−	0.383059i
$825$		0			0
$826$	−1.22474	+	2.12132i	−0.0426143	+	0.0738102i
$827$	−17.9444			−0.623987			−0.311994	−	0.950084i	$-0.600997\pi$
$827$	−17.9444			−0.623987			−0.311994	+	0.950084i	$0.600997\pi$
$828$	4.77526	+	5.58542i	0.165952	+	0.194107i
$829$	26.7423			0.928800			0.464400	−	0.885626i	$-0.346270\pi$
$829$	26.7423			0.928800			0.464400	+	0.885626i	$0.346270\pi$
$830$		0			0
$831$	−11.1237	+	1.02494i	−0.385878	+	0.0355549i
$832$	2.22474	+	3.85337i	0.0771292	+	0.133592i
$833$	−31.3485	−	54.2971i	−1.08616	−	1.88128i
$834$	−4.00000	−	5.65685i	−0.138509	−	0.195881i
$835$		0			0
$836$	12.4949			0.432145
$837$	−1.67423	−	1.62851i	−0.0578700	−	0.0562896i
$838$	8.14643			0.281414
$839$	−11.3258	+	19.6168i	−0.391009	+	0.677247i	−0.992583	−	0.121570i	$-0.961207\pi$
$839$	−11.3258	+	19.6168i	−0.391009	+	0.677247i	0.601574	+	0.798817i	$0.294540\pi$
$840$		0			0
$841$	11.5000	+	19.9186i	0.396552	+	0.686848i
$842$	−9.02270	−	15.6278i	−0.310943	−	0.538569i
$843$	−49.8434	+	4.59259i	−1.71670	+	0.158177i
$844$	−0.724745	+	1.25529i	−0.0249467	+	0.0432090i
$845$		0			0
$846$	3.24745	−	0.603566i	0.111650	−	0.0207510i
$847$	−57.8434			−1.98752
$848$	−4.22474	+	7.31747i	−0.145078	+	0.251283i
$849$	−8.15153	+	17.6937i	−0.279760	+	0.607247i
$850$		0			0
$851$	−4.10102	−	7.10318i	−0.140581	−	0.243494i
$852$	−0.977296	+	2.12132i	−0.0334816	+	0.0726752i
$853$	−23.0000	+	39.8372i	−0.787505	+	1.36400i	0.139986	+	0.990153i	$0.455294\pi$
$853$	−23.0000	+	39.8372i	−0.787505	+	1.36400i	−0.927491	+	0.373845i	$0.878039\pi$
$854$	−35.5959			−1.21807
$855$		0			0
$856$	15.2474			0.521147
$857$	−20.0505	+	34.7285i	−0.684912	+	1.18630i	0.288552	+	0.957464i	$0.406826\pi$
$857$	−20.0505	+	34.7285i	−0.684912	+	1.18630i	−0.973464	+	0.228839i	$0.926507\pi$
$858$	37.5959	−	3.46410i	1.28350	−	0.118262i
$859$	2.82577	+	4.89437i	0.0964139	+	0.166994i	0.910198	−	0.414174i	$-0.135929\pi$
$859$	2.82577	+	4.89437i	0.0964139	+	0.166994i	−0.813784	+	0.581168i	$0.802596\pi$
$860$		0			0
$861$	−40.0454	−	56.6328i	−1.36474	−	1.93004i
$862$	−5.32577	+	9.22450i	−0.181396	+	0.314188i
$863$	−19.8434			−0.675476			−0.337738	−	0.941240i	$-0.609662\pi$
$863$	−19.8434			−0.675476			−0.337738	+	0.941240i	$0.609662\pi$
$864$	3.72474	+	3.62302i	0.126718	+	0.123258i
$865$		0			0
$866$	−14.7980	+	25.6308i	−0.502855	+	0.870971i
$867$	7.00000	+	9.89949i	0.237732	+	0.336204i
$868$	−1.00000	−	1.73205i	−0.0339422	−	0.0587896i
$869$	31.1010	+	53.8685i	1.05503	+	1.82737i
$870$		0			0
$871$	31.9217	−	55.2900i	1.08162	−	1.87343i
$872$	10.4495			0.353864
$873$	−21.0505	−	24.6219i	−0.712452	−	0.833326i
$874$	−6.24745			−0.211323
$875$		0			0
$876$	0.724745	−	1.57313i	0.0244869	−	0.0531512i
$877$	−6.10102	−	10.5673i	−0.206017	−	0.356832i	0.744439	−	0.667690i	$-0.232717\pi$
$877$	−6.10102	−	10.5673i	−0.206017	−	0.356832i	−0.950456	+	0.310858i	$0.899383\pi$
$878$	5.67423	+	9.82806i	0.191496	+	0.331681i
$879$	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	$0.449910\pi$
$882$	−12.7980	+	36.1981i	−0.430930	+	1.21885i
$883$	−28.2020			−0.949074			−0.474537	−	0.880235i	$-0.657385\pi$
$883$	−28.2020			−0.949074			−0.474537	+	0.880235i	$0.657385\pi$
$884$	10.8990	−	18.8776i	0.366572	−	0.634922i
$885$		0			0
$886$	13.8990	+	24.0737i	0.466945	+	0.808773i
$887$	27.2474	+	47.1940i	0.914880	+	1.58462i	0.807077	+	0.590446i	$0.201048\pi$
$887$	27.2474	+	47.1940i	0.914880	+	1.58462i	0.107803	+	0.994172i	$0.465619\pi$
$888$	−3.34847	−	4.73545i	−0.112367	−	0.158911i
$889$	25.2474	−	43.7299i	0.846772	−	1.46665i
$890$		0			0
$891$	41.1464	−	15.8421i	1.37846	−	0.530730i
$892$	1.79796			0.0602001
$893$	−1.40408	+	2.43194i	−0.0469858	+	0.0813818i
$894$	−6.00000	−	8.48528i	−0.200670	−	0.283790i
$895$		0			0
$896$	2.22474	+	3.85337i	0.0743235	+	0.128732i
$897$	−18.7980	+	1.73205i	−0.627646	+	0.0578315i
$898$	−5.29796	+	9.17633i	−0.176795	+	0.306218i
$899$	−1.10102			−0.0367211
$900$		0			0
$901$	41.3939			1.37903
$902$	−22.0454	+	38.1838i	−0.734032	+	1.27138i
$903$	24.0227	−	52.1437i	0.799426	−	1.73523i
$904$	−6.94949	−	12.0369i	−0.231137	−	0.400340i
$905$		0			0
$906$	14.4949	−	31.4626i	0.481561	−	1.04528i
$907$	10.8258	−	18.7508i	0.359464	−	0.622609i	−0.628408	−	0.777884i	$-0.716293\pi$
$907$	10.8258	−	18.7508i	0.359464	−	0.622609i	0.987871	+	0.155275i	$0.0496263\pi$
$908$	−28.3485			−0.940777
$909$	−6.92168	−	8.09601i	−0.229578	−	0.268528i
$910$		0			0
$911$	−3.67423	+	6.36396i	−0.121733	+	0.210847i	−0.920451	−	0.390858i	$-0.872178\pi$
$911$	−3.67423	+	6.36396i	−0.121733	+	0.210847i	0.798718	+	0.601705i	$0.205512\pi$
$912$	−4.39898	+	0.405324i	−0.145665	+	0.0134216i
$913$	−1.34847	−	2.33562i	−0.0446278	−	0.0772976i
$914$	−7.84847	−	13.5939i	−0.259604	−	0.449648i
$915$		0			0
$916$	10.5732	−	18.3133i	0.349349	−	0.605090i
$917$	−70.2929			−2.32127
$918$	6.24745	−	24.6773i	0.206197	−	0.814472i
$919$	−11.3485			−0.374351			−0.187176	−	0.982326i	$-0.559933\pi$
$919$	−11.3485			−0.374351			−0.187176	+	0.982326i	$0.559933\pi$
$920$		0			0
$921$	6.69694	+	9.47090i	0.220672	+	0.312077i
$922$	−9.67423	−	16.7563i	−0.318604	−	0.551838i
$923$	−3.00000	−	5.19615i	−0.0987462	−	0.171033i
$924$	37.5959	−	3.46410i	1.23681	−	0.113961i
$925$		0			0
$926$	−9.34847			−0.307210
$927$	37.4495	−	6.96031i	1.23000	−	0.228607i
$928$	2.44949			0.0804084
$929$	−13.5959	+	23.5488i	−0.446068	+	0.772612i	−0.998126	−	0.0611938i	$-0.980509\pi$
$929$	−13.5959	+	23.5488i	−0.446068	+	0.772612i	0.552058	+	0.833806i	$0.313843\pi$
$930$		0			0
$931$	−16.3207	−	28.2682i	−0.534888	−	0.926453i
$932$	2.84847	+	4.93369i	0.0933047	+	0.161609i
$933$	−7.89898	+	17.1455i	−0.258601	+	0.561320i
$934$	2.17423	−	3.76588i	0.0711431	−	0.123224i
$935$		0			0
$936$	−13.1237	+	2.43916i	−0.428962	+	0.0797264i
$937$	−26.7980			−0.875451			−0.437726	−	0.899109i	$-0.644216\pi$
$937$	−26.7980			−0.875451			−0.437726	+	0.899109i	$0.644216\pi$
$938$	31.9217	−	55.2900i	1.04228	−	1.80528i
$939$	6.72474	−	0.619620i	0.219454	−	0.0202205i
$940$		0			0
$941$	14.8207	+	25.6701i	0.483140	+	0.836823i	0.999813	−	0.0193603i	$-0.00616295\pi$
$941$	14.8207	+	25.6701i	0.483140	+	0.836823i	−0.516673	+	0.856183i	$0.672830\pi$
$942$	0.202041	+	0.285729i	0.00658285	+	0.00930956i
$943$	11.0227	−	19.0919i	0.358949	−	0.621717i
$944$	−0.550510			−0.0179176
$945$		0			0
$946$	−36.4949			−1.18655
$947$	−4.07321	+	7.05501i	−0.132362	+	0.229257i	−0.924587	−	0.380972i	$-0.875589\pi$
$947$	−4.07321	+	7.05501i	−0.132362	+	0.229257i	0.792225	+	0.610229i	$0.208923\pi$
$948$	−12.6969	−	17.9562i	−0.412377	−	0.583190i
$949$	2.22474	+	3.85337i	0.0722183	+	0.125086i
$950$		0			0
$951$	−29.5732	+	2.72489i	−0.958977	+	0.0883605i
$952$	10.8990	−	18.8776i	0.353238	−	0.611826i
$953$	−21.7980			−0.706105			−0.353053	−	0.935603i	$-0.614856\pi$
$953$	−21.7980			−0.706105			−0.353053	+	0.935603i	$0.614856\pi$
$954$	−16.4722	−	19.2669i	−0.533307	−	0.623787i
$955$		0			0
$956$	−4.77526	+	8.27098i	−0.154443	+	0.267503i
$957$	8.69694	−	18.8776i	0.281132	−	0.610226i
$958$	12.1237	+	20.9989i	0.391700	+	0.678444i
$959$	−6.67423	−	11.5601i	−0.215522	−	0.373296i
$960$		0			0
$961$	15.3990	−	26.6718i	0.496741	−	0.860381i
$962$	14.8990			0.480362
$963$	−15.2474	+	43.1263i	−0.491342	+	1.38973i
$964$	−22.7980			−0.734273
$965$		0			0
$966$	−18.7980	+	1.73205i	−0.604814	+	0.0557278i
$967$	16.0000	+	27.7128i	0.514525	+	0.891184i	0.999858	+	0.0168544i	$0.00536518\pi$
$967$	16.0000	+	27.7128i	0.514525	+	0.891184i	−0.485333	+	0.874330i	$0.661301\pi$
$968$	−6.50000	−	11.2583i	−0.208918	−	0.361856i
$969$	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	$0.380543\pi$
$972$	−13.9722	+	6.91215i	−0.448158	+	0.221707i
$973$	17.7980			0.570576
$974$	−9.77526	+	16.9312i	−0.313219	+	0.542512i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	0.785020	−	0.619471i	$-0.212653\pi$
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	−0.928987	+	0.370111i	$0.879319\pi$
$978$	4.39898	−	0.405324i	0.140664	−	0.0129608i
$979$	22.0454	−	38.1838i	0.704574	−	1.22036i
$980$		0			0
$981$	−10.4495	+	29.5556i	−0.333627	+	0.943638i
$982$	−2.75255			−0.0878374
$983$	−11.4495	+	19.8311i	−0.365182	+	0.632514i	−0.988805	−	0.149211i	$-0.952327\pi$
$983$	−11.4495	+	19.8311i	−0.365182	+	0.632514i	0.623623	+	0.781725i	$0.285660\pi$
$984$	6.52270	−	14.1582i	0.207936	−	0.451347i
$985$		0			0
$986$	−6.00000	−	10.3923i	−0.191079	−	0.330958i
$987$	−3.55051	+	7.70674i	−0.113014	+	0.245308i
$988$	5.67423	−	9.82806i	0.180521	−	0.312672i
$989$	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	$0.581789\pi$
$992$	0.224745	−	0.389270i	0.00713566	−	0.0123593i
$993$	14.3990	−	1.32673i	0.456938	−	0.0421024i
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		0			0
$996$	0.550510	+	0.778539i	0.0174436	+	0.0246690i
$997$	18.0227	−	31.2162i	0.570785	−	0.988628i	−0.425701	−	0.904864i	$-0.639972\pi$
$997$	18.0227	−	31.2162i	0.570785	−	0.988628i	0.996486	−	0.0837642i	$-0.0266943\pi$
$998$	6.34847			0.200957
$999$	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.e.l.151.2	✓	4
3.2	odd	2		1350.2.e.n.451.2		4
5.2	odd	4		450.2.j.f.349.2		8
5.3	odd	4		450.2.j.f.349.3		8
5.4	even	2		450.2.e.m.151.1	yes	4
9.2	odd	6		4050.2.a.bl.1.1		2
9.4	even	3	inner	450.2.e.l.301.1	yes	4
9.5	odd	6		1350.2.e.n.901.2		4
9.7	even	3		4050.2.a.bu.1.1		2
15.2	even	4		1350.2.j.g.1099.4		8
15.8	even	4		1350.2.j.g.1099.1		8
15.14	odd	2		1350.2.e.k.451.1		4
45.2	even	12		4050.2.c.w.649.1		4
45.4	even	6		450.2.e.m.301.2	yes	4
45.7	odd	12		4050.2.c.y.649.3		4
45.13	odd	12		450.2.j.f.49.2		8
45.14	odd	6		1350.2.e.k.901.1		4
45.22	odd	12		450.2.j.f.49.3		8
45.23	even	12		1350.2.j.g.199.4		8
45.29	odd	6		4050.2.a.by.1.2		2
45.32	even	12		1350.2.j.g.199.1		8
45.34	even	6		4050.2.a.br.1.2		2
45.38	even	12		4050.2.c.w.649.4		4
45.43	odd	12		4050.2.c.y.649.2		4

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

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 + 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.72474 + 0.158919i) q^{6} +(2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 + 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.72474 + 0.158919i) q^{6} +(2.22474 - 3.85337i) q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +(-2.44949 + 4.24264i) q^{11} +(0.724745 - 1.57313i) q^{12} +(2.22474 + 3.85337i) q^{13} +(2.22474 + 3.85337i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.89898 q^{17} +(-1.94949 - 2.28024i) q^{18} +2.55051 q^{19} +(7.67423 - 0.707107i) q^{21} +(-2.44949 - 4.24264i) q^{22} +(1.22474 + 2.12132i) q^{23} +(1.00000 + 1.41421i) q^{24} -4.44949 q^{26} +(-5.00000 + 1.41421i) q^{27} -4.44949 q^{28} +(-1.22474 + 2.12132i) q^{29} +(0.224745 + 0.389270i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-8.44949 + 0.778539i) q^{33} +(-2.44949 + 4.24264i) q^{34} +(2.94949 - 0.548188i) q^{36} -3.34847 q^{37} +(-1.27526 + 2.20881i) q^{38} +(-3.22474 + 6.99964i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(-3.22474 + 6.99964i) q^{42} +(3.72474 - 6.45145i) q^{43} +4.89898 q^{44} -2.44949 q^{46} +(-0.550510 + 0.953512i) q^{47} +(-1.72474 + 0.158919i) q^{48} +(-6.39898 - 11.0834i) q^{49} +(4.89898 + 6.92820i) q^{51} +(2.22474 - 3.85337i) q^{52} +8.44949 q^{53} +(1.27526 - 5.03723i) q^{54} +(2.22474 - 3.85337i) q^{56} +(2.55051 + 3.60697i) q^{57} +(-1.22474 - 2.12132i) q^{58} +(0.275255 + 0.476756i) q^{59} +(-4.00000 + 6.92820i) q^{61} -0.449490 q^{62} +(8.67423 + 10.1459i) q^{63} +1.00000 q^{64} +(3.55051 - 7.70674i) q^{66} +(-7.17423 - 12.4261i) q^{67} +(-2.44949 - 4.24264i) q^{68} +(-1.77526 + 3.85337i) q^{69} -1.34847 q^{71} +(-1.00000 + 2.82843i) q^{72} +1.00000 q^{73} +(1.67423 - 2.89986i) q^{74} +(-1.27526 - 2.20881i) q^{76} +(10.8990 + 18.8776i) q^{77} +(-4.44949 - 6.29253i) q^{78} +(6.34847 - 10.9959i) q^{79} +(-7.00000 - 5.65685i) q^{81} +9.00000 q^{82} +(-0.275255 + 0.476756i) q^{83} +(-4.44949 - 6.29253i) q^{84} +(3.72474 + 6.45145i) q^{86} +(-4.22474 + 0.389270i) q^{87} +(-2.44949 + 4.24264i) q^{88} -9.00000 q^{89} +19.7980 q^{91} +(1.22474 - 2.12132i) q^{92} +(-0.325765 + 0.707107i) q^{93} +(-0.550510 - 0.953512i) q^{94} +(0.724745 - 1.57313i) q^{96} +(-5.39898 + 9.35131i) q^{97} +12.7980 q^{98} +(-9.55051 - 11.1708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{8} - 4 q^{9} - 2 q^{12} + 4 q^{13} + 4 q^{14} - 2 q^{16} + 2 q^{18} + 20 q^{19} + 16 q^{21} + 4 q^{24} - 8 q^{26} - 20 q^{27} - 8 q^{28} - 4 q^{31} - 2 q^{32} - 24 q^{33} + 2 q^{36} + 16 q^{37} - 10 q^{38} - 8 q^{39} - 18 q^{41} - 8 q^{42} + 10 q^{43} - 12 q^{47} - 2 q^{48} - 6 q^{49} + 4 q^{52} + 24 q^{53} + 10 q^{54} + 4 q^{56} + 20 q^{57} + 6 q^{59} - 16 q^{61} + 8 q^{62} + 20 q^{63} + 4 q^{64} + 24 q^{66} - 14 q^{67} - 12 q^{69} + 24 q^{71} - 4 q^{72} + 4 q^{73} - 8 q^{74} - 10 q^{76} + 24 q^{77} - 8 q^{78} - 4 q^{79} - 28 q^{81} + 36 q^{82} - 6 q^{83} - 8 q^{84} + 10 q^{86} - 12 q^{87} - 36 q^{89} + 40 q^{91} - 16 q^{93} - 12 q^{94} - 2 q^{96} - 2 q^{97} + 12 q^{98} - 48 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^8 - 4 * q^9 - 2 * q^12 + 4 * q^13 + 4 * q^14 - 2 * q^16 + 2 * q^18 + 20 * q^19 + 16 * q^21 + 4 * q^24 - 8 * q^26 - 20 * q^27 - 8 * q^28 - 4 * q^31 - 2 * q^32 - 24 * q^33 + 2 * q^36 + 16 * q^37 - 10 * q^38 - 8 * q^39 - 18 * q^41 - 8 * q^42 + 10 * q^43 - 12 * q^47 - 2 * q^48 - 6 * q^49 + 4 * q^52 + 24 * q^53 + 10 * q^54 + 4 * q^56 + 20 * q^57 + 6 * q^59 - 16 * q^61 + 8 * q^62 + 20 * q^63 + 4 * q^64 + 24 * q^66 - 14 * q^67 - 12 * q^69 + 24 * q^71 - 4 * q^72 + 4 * q^73 - 8 * q^74 - 10 * q^76 + 24 * q^77 - 8 * q^78 - 4 * q^79 - 28 * q^81 + 36 * q^82 - 6 * q^83 - 8 * q^84 + 10 * q^86 - 12 * q^87 - 36 * q^89 + 40 * q^91 - 16 * q^93 - 12 * q^94 - 2 * q^96 - 2 * q^97 + 12 * q^98 - 48 * q^99

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