LMFDB - Embedded newform 450.2.e.m.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.m.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.724745 + 1.57313i) q^{6} +(0.224745 - 0.389270i) q^{7} -1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.724745 + 1.57313i) q^{6} +(0.224745 - 0.389270i) q^{7} -1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +(2.44949 - 4.24264i) q^{11} +(1.72474 + 0.158919i) q^{12} +(0.224745 + 0.389270i) q^{13} +(-0.224745 - 0.389270i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.89898 q^{17} +(-2.94949 - 0.548188i) q^{18} +7.44949 q^{19} +(0.325765 + 0.707107i) q^{21} +(-2.44949 - 4.24264i) q^{22} +(1.22474 + 2.12132i) q^{23} +(1.00000 - 1.41421i) q^{24} +0.449490 q^{26} +(5.00000 + 1.41421i) q^{27} -0.449490 q^{28} +(1.22474 - 2.12132i) q^{29} +(-2.22474 - 3.85337i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.55051 + 7.70674i) q^{33} +(2.44949 - 4.24264i) q^{34} +(-1.94949 + 2.28024i) q^{36} -11.3485 q^{37} +(3.72474 - 6.45145i) q^{38} +(-0.775255 - 0.0714323i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(0.775255 + 0.0714323i) q^{42} +(-1.27526 + 2.20881i) q^{43} -4.89898 q^{44} +2.44949 q^{46} +(5.44949 - 9.43879i) q^{47} +(-0.724745 - 1.57313i) q^{48} +(3.39898 + 5.88721i) q^{49} +(-4.89898 + 6.92820i) q^{51} +(0.224745 - 0.389270i) q^{52} -3.55051 q^{53} +(3.72474 - 3.62302i) q^{54} +(-0.224745 + 0.389270i) q^{56} +(-7.44949 + 10.5352i) q^{57} +(-1.22474 - 2.12132i) q^{58} +(2.72474 + 4.71940i) q^{59} +(-4.00000 + 6.92820i) q^{61} -4.44949 q^{62} +(-1.32577 - 0.246405i) q^{63} +1.00000 q^{64} +(8.44949 + 0.778539i) q^{66} +(-0.174235 - 0.301783i) q^{67} +(-2.44949 - 4.24264i) q^{68} +(-4.22474 - 0.389270i) q^{69} +13.3485 q^{71} +(1.00000 + 2.82843i) q^{72} -1.00000 q^{73} +(-5.67423 + 9.82806i) q^{74} +(-3.72474 - 6.45145i) q^{76} +(-1.10102 - 1.90702i) q^{77} +(-0.449490 + 0.635674i) q^{78} +(-8.34847 + 14.4600i) q^{79} +(-7.00000 + 5.65685i) q^{81} -9.00000 q^{82} +(2.72474 - 4.71940i) q^{83} +(0.449490 - 0.635674i) q^{84} +(1.27526 + 2.20881i) q^{86} +(1.77526 + 3.85337i) q^{87} +(-2.44949 + 4.24264i) q^{88} -9.00000 q^{89} +0.202041 q^{91} +(1.22474 - 2.12132i) q^{92} +(7.67423 + 0.707107i) q^{93} +(-5.44949 - 9.43879i) q^{94} +(-1.72474 - 0.158919i) q^{96} +(-4.39898 + 7.61926i) q^{97} +6.79796 q^{98} +(-14.4495 - 2.68556i) 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
$6$	0.724745	+	1.57313i	0.295876	+	0.642229i
$7$	0.224745	−	0.389270i	0.0849456	−	0.147130i	−0.820422	−	0.571758i	$-0.806262\pi$
$7$	0.224745	−	0.389270i	0.0849456	−	0.147130i	0.905368	+	0.424628i	$0.139595\pi$
$8$	−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	$-0.568845\pi$
$11$	2.44949	−	4.24264i	0.738549	−	1.27920i	0.953149	−	0.302502i	$-0.0978220\pi$
$12$	1.72474	+	0.158919i	0.497891	+	0.0458759i
$13$	0.224745	+	0.389270i	0.0623330	+	0.107964i	0.895508	−	0.445046i	$-0.146813\pi$
$13$	0.224745	+	0.389270i	0.0623330	+	0.107964i	−0.833175	+	0.553010i	$0.813479\pi$
$14$	−0.224745	−	0.389270i	−0.0600656	−	0.104037i
$15$		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	$0.297513\pi$
$18$	−2.94949	−	0.548188i	−0.695201	−	0.129209i
$19$	7.44949			1.70903			0.854515	−	0.519427i	$-0.173854\pi$
$19$	7.44949			1.70903			0.854515	+	0.519427i	$0.173854\pi$
$20$		0			0
$21$	0.325765	+	0.707107i	0.0710878	+	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
$26$	0.449490			0.0881522
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	−0.449490			−0.0849456
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	−0.729616	−	0.683857i	$-0.760301\pi$
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	0.957046	+	0.289938i	$0.0936346\pi$
$30$		0			0
$31$	−2.22474	−	3.85337i	−0.399576	−	0.692086i	0.594098	−	0.804393i	$-0.297509\pi$
$31$	−2.22474	−	3.85337i	−0.399576	−	0.692086i	−0.993674	+	0.112307i	$0.964176\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.55051	+	7.70674i	0.618065	+	1.34157i
$34$	2.44949	−	4.24264i	0.420084	−	0.727607i
$35$		0			0
$36$	−1.94949	+	2.28024i	−0.324915	+	0.380040i
$37$	−11.3485			−1.86568			−0.932838	−	0.360295i	$-0.882676\pi$
$37$	−11.3485			−1.86568			−0.932838	+	0.360295i	$0.882676\pi$
$38$	3.72474	−	6.45145i	0.604233	−	1.04656i
$39$	−0.775255	−	0.0714323i	−0.124140	−	0.0114383i
$40$		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	$-0.414726\pi$
$42$	0.775255	+	0.0714323i	0.119624	+	0.0110222i
$43$	−1.27526	+	2.20881i	−0.194475	+	0.336840i	−0.946728	−	0.322034i	$-0.895634\pi$
$43$	−1.27526	+	2.20881i	−0.194475	+	0.336840i	0.752254	+	0.658874i	$0.228967\pi$
$44$	−4.89898			−0.738549
$45$		0			0
$46$	2.44949			0.361158
$47$	5.44949	−	9.43879i	0.794890	−	1.37679i	−0.128019	−	0.991772i	$-0.540862\pi$
$47$	5.44949	−	9.43879i	0.794890	−	1.37679i	0.922909	−	0.385018i	$-0.125805\pi$
$48$	−0.724745	−	1.57313i	−0.104608	−	0.227062i
$49$	3.39898	+	5.88721i	0.485568	+	0.841029i
$50$		0			0
$51$	−4.89898	+	6.92820i	−0.685994	+	0.970143i
$52$	0.224745	−	0.389270i	0.0311665	−	0.0539820i
$53$	−3.55051			−0.487700			−0.243850	−	0.969813i	$-0.578410\pi$
$53$	−3.55051			−0.487700			−0.243850	+	0.969813i	$0.578410\pi$
$54$	3.72474	−	3.62302i	0.506874	−	0.493031i
$55$		0			0
$56$	−0.224745	+	0.389270i	−0.0300328	+	0.0520183i
$57$	−7.44949	+	10.5352i	−0.986709	+	1.39542i
$58$	−1.22474	−	2.12132i	−0.160817	−	0.278543i
$59$	2.72474	+	4.71940i	0.354732	+	0.614413i	0.987072	−	0.160278i	$-0.0512389\pi$
$59$	2.72474	+	4.71940i	0.354732	+	0.614413i	−0.632340	+	0.774691i	$0.717906\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−4.44949			−0.565086
$63$	−1.32577	−	0.246405i	−0.167031	−	0.0310441i
$64$	1.00000			0.125000
$65$		0			0
$66$	8.44949	+	0.778539i	1.04006	+	0.0958315i
$67$	−0.174235	−	0.301783i	−0.0212861	−	0.0368687i	0.855186	−	0.518321i	$-0.173443\pi$
$67$	−0.174235	−	0.301783i	−0.0212861	−	0.0368687i	−0.876472	+	0.481452i	$0.840109\pi$
$68$	−2.44949	−	4.24264i	−0.297044	−	0.514496i
$69$	−4.22474	−	0.389270i	−0.508600	−	0.0468625i
$70$		0			0
$71$	13.3485			1.58417			0.792086	−	0.610410i	$-0.208995\pi$
$71$	13.3485			1.58417			0.792086	+	0.610410i	$0.208995\pi$
$72$	1.00000	+	2.82843i	0.117851	+	0.333333i
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	−5.67423	+	9.82806i	−0.659616	+	1.14249i
$75$		0			0
$76$	−3.72474	−	6.45145i	−0.427258	−	0.740032i
$77$	−1.10102	−	1.90702i	−0.125473	−	0.217325i
$78$	−0.449490	+	0.635674i	−0.0508947	+	0.0719760i
$79$	−8.34847	+	14.4600i	−0.939276	+	1.62687i	−0.172451	+	0.985018i	$0.555169\pi$
$79$	−8.34847	+	14.4600i	−0.939276	+	1.62687i	−0.766825	+	0.641856i	$0.778165\pi$
$80$		0			0
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	−9.00000			−0.993884
$83$	2.72474	−	4.71940i	0.299080	−	0.518021i	−0.676846	−	0.736125i	$-0.736654\pi$
$83$	2.72474	−	4.71940i	0.299080	−	0.518021i	0.975926	+	0.218104i	$0.0699871\pi$
$84$	0.449490	−	0.635674i	0.0490434	−	0.0693578i
$85$		0			0
$86$	1.27526	+	2.20881i	0.137514	+	0.238182i
$87$	1.77526	+	3.85337i	0.190327	+	0.413125i
$88$	−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
$91$	0.202041			0.0211797
$92$	1.22474	−	2.12132i	0.127688	−	0.221163i
$93$	7.67423	+	0.707107i	0.795781	+	0.0733236i
$94$	−5.44949	−	9.43879i	−0.562072	−	0.973537i
$95$		0			0
$96$	−1.72474	−	0.158919i	−0.176031	−	0.0162196i
$97$	−4.39898	+	7.61926i	−0.446649	+	0.773618i	−0.998165	−	0.0605456i	$-0.980716\pi$
$97$	−4.39898	+	7.61926i	−0.446649	+	0.773618i	0.551517	+	0.834164i	$0.314049\pi$
$98$	6.79796			0.686698
$99$	−14.4495	−	2.68556i	−1.45223	−	0.269909i
$100$		0			0
$101$	−4.22474	+	7.31747i	−0.420378	+	0.728116i	−0.995976	−	0.0896167i	$-0.971436\pi$
$101$	−4.22474	+	7.31747i	−0.420378	+	0.728116i	0.575599	+	0.817732i	$0.304769\pi$
$102$	3.55051	+	7.70674i	0.351553	+	0.763081i
$103$	−8.34847	−	14.4600i	−0.822599	−	1.42478i	−0.903740	−	0.428081i	$-0.859190\pi$
$103$	−8.34847	−	14.4600i	−0.822599	−	1.42478i	0.0811413	−	0.996703i	$-0.474143\pi$
$104$	−0.224745	−	0.389270i	−0.0220380	−	0.0381710i
$105$		0			0
$106$	−1.77526	+	3.07483i	−0.172428	+	0.298654i
$107$	9.24745			0.893985			0.446992	−	0.894538i	$-0.352495\pi$
$107$	9.24745			0.893985			0.446992	+	0.894538i	$0.352495\pi$
$108$	−1.27526	−	5.03723i	−0.122711	−	0.484708i
$109$	5.55051			0.531642			0.265821	−	0.964022i	$-0.414357\pi$
$109$	5.55051			0.531642			0.265821	+	0.964022i	$0.414357\pi$
$110$		0			0
$111$	11.3485	−	16.0492i	1.07715	−	1.52332i
$112$	0.224745	+	0.389270i	0.0212364	+	0.0367825i
$113$	2.05051	+	3.55159i	0.192896	+	0.334105i	0.946209	−	0.323557i	$-0.104879\pi$
$113$	2.05051	+	3.55159i	0.192896	+	0.334105i	−0.753313	+	0.657662i	$0.771545\pi$
$114$	5.39898	+	11.7190i	0.505661	+	1.09759i
$115$		0			0
$116$	−2.44949			−0.227429
$117$	0.876276	−	1.02494i	0.0810117	−	0.0947561i
$118$	5.44949			0.501666
$119$	1.10102	−	1.90702i	0.100930	−	0.174817i
$120$		0			0
$121$	−6.50000	−	11.2583i	−0.590909	−	1.02348i
$122$	4.00000	+	6.92820i	0.362143	+	0.627250i
$123$	15.5227	+	1.43027i	1.39964	+	0.128963i
$124$	−2.22474	+	3.85337i	−0.199788	+	0.346043i
$125$		0			0
$126$	−0.876276	+	1.02494i	−0.0780648	+	0.0913093i
$127$	3.34847			0.297129			0.148564	−	0.988903i	$-0.452535\pi$
$127$	3.34847			0.297129			0.148564	+	0.988903i	$0.452535\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.84847	−	4.01229i	−0.162749	−	0.353262i
$130$		0			0
$131$	1.89898	+	3.28913i	0.165915	+	0.287373i	0.936980	−	0.349384i	$-0.113609\pi$
$131$	1.89898	+	3.28913i	0.165915	+	0.287373i	−0.771065	+	0.636756i	$0.780276\pi$
$132$	4.89898	−	6.92820i	0.426401	−	0.603023i
$133$	1.67423	−	2.89986i	0.145175	−	0.251450i
$134$	−0.348469			−0.0301032
$135$		0			0
$136$	−4.89898			−0.420084
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$	−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
$141$	7.89898	+	17.1455i	0.665214	+	1.44391i
$142$	6.67423	−	11.5601i	0.560089	−	0.970103i
$143$	2.20204			0.184144
$144$	2.94949	+	0.548188i	0.245791	+	0.0456823i
$145$		0			0
$146$	−0.500000	+	0.866025i	−0.0413803	+	0.0716728i
$147$	−11.7247	−	1.08032i	−0.967041	−	0.0891035i
$148$	5.67423	+	9.82806i	0.466419	+	0.807862i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$	−7.44949			−0.604233
$153$	−4.89898	−	13.8564i	−0.396059	−	1.12022i
$154$	−2.20204			−0.177446
$155$		0			0
$156$	0.325765	+	0.707107i	0.0260821	+	0.0566139i
$157$	9.89898	+	17.1455i	0.790025	+	1.36836i	0.925951	+	0.377644i	$0.123266\pi$
$157$	9.89898	+	17.1455i	0.790025	+	1.36836i	−0.135926	+	0.990719i	$0.543401\pi$
$158$	8.34847	+	14.4600i	0.664169	+	1.15037i
$159$	3.55051	−	5.02118i	0.281574	−	0.398205i
$160$		0			0
$161$	1.10102			0.0867726
$162$	1.39898	+	8.89060i	0.109914	+	0.698512i
$163$	7.44949			0.583489			0.291745	−	0.956496i	$-0.405764\pi$
$163$	7.44949			0.583489			0.291745	+	0.956496i	$0.405764\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$	−2.72474	−	4.71940i	−0.211481	−	0.366296i
$167$	−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	$-0.440582\pi$
$168$	−0.325765	−	0.707107i	−0.0251333	−	0.0545545i
$169$	6.39898	−	11.0834i	0.492229	−	0.852566i
$170$		0			0
$171$	−7.44949	−	21.0703i	−0.569677	−	1.61129i
$172$	2.55051			0.194475
$173$	−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	$0.288153\pi$
$174$	4.22474	+	0.389270i	0.320277	+	0.0295104i
$175$		0			0
$176$	2.44949	+	4.24264i	0.184637	+	0.319801i
$177$	−9.39898	−	0.866025i	−0.706471	−	0.0650945i
$178$	−4.50000	+	7.79423i	−0.337289	+	0.584202i
$179$	9.24745			0.691187			0.345593	−	0.938384i	$-0.387678\pi$
$179$	9.24745			0.691187			0.345593	+	0.938384i	$0.387678\pi$
$180$		0			0
$181$	17.7980			1.32291			0.661456	−	0.749984i	$-0.269939\pi$
$181$	17.7980			1.32291			0.661456	+	0.749984i	$0.269939\pi$
$182$	0.101021	−	0.174973i	0.00748814	−	0.0129698i
$183$	−5.79796	−	12.5851i	−0.428597	−	0.930314i
$184$	−1.22474	−	2.12132i	−0.0902894	−	0.156386i
$185$		0			0
$186$	4.44949	−	6.29253i	0.326252	−	0.461391i
$187$	12.0000	−	20.7846i	0.877527	−	1.51992i
$188$	−10.8990			−0.794890
$189$	1.67423	−	1.62851i	0.121783	−	0.118457i
$190$		0			0
$191$	0.550510	−	0.953512i	0.0398335	−	0.0689937i	−0.845421	−	0.534100i	$-0.820651\pi$
$191$	0.550510	−	0.953512i	0.0398335	−	0.0689937i	0.885255	+	0.465106i	$0.153984\pi$
$192$	−1.00000	+	1.41421i	−0.0721688	+	0.102062i
$193$	−10.0000	−	17.3205i	−0.719816	−	1.24676i	−0.961073	−	0.276296i	$-0.910893\pi$
$193$	−10.0000	−	17.3205i	−0.719816	−	1.24676i	0.241257	−	0.970461i	$-0.422440\pi$
$194$	4.39898	+	7.61926i	0.315828	+	0.547031i
$195$		0			0
$196$	3.39898	−	5.88721i	0.242784	−	0.420515i
$197$	−0.247449			−0.0176300			−0.00881500	−	0.999961i	$-0.502806\pi$
$197$	−0.247449			−0.0176300			−0.00881500	+	0.999961i	$0.502806\pi$
$198$	−9.55051	+	11.1708i	−0.678725	+	0.793877i
$199$	−13.7980			−0.978111			−0.489056	−	0.872253i	$-0.662659\pi$
$199$	−13.7980			−0.978111			−0.489056	+	0.872253i	$0.662659\pi$
$200$		0			0
$201$	0.601021	+	0.0553782i	0.0423927	+	0.00390608i
$202$	4.22474	+	7.31747i	0.297252	+	0.514856i
$203$	−0.550510	−	0.953512i	−0.0386382	−	0.0669234i
$204$	8.44949	+	0.778539i	0.591583	+	0.0545086i
$205$		0			0
$206$	−16.6969			−1.16333
$207$	4.77526	−	5.58542i	0.331903	−	0.388214i
$208$	−0.449490			−0.0311665
$209$	18.2474	−	31.6055i	1.26220	−	2.18620i
$210$		0			0
$211$	1.72474	+	2.98735i	0.118736	+	0.205657i	0.919267	−	0.393634i	$-0.128782\pi$
$211$	1.72474	+	2.98735i	0.118736	+	0.205657i	−0.800531	+	0.599292i	$0.795449\pi$
$212$	1.77526	+	3.07483i	0.121925	+	0.211180i
$213$	−13.3485	+	18.8776i	−0.914622	+	1.29347i
$214$	4.62372	−	8.00853i	0.316071	−	0.547452i
$215$		0			0
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$	−2.00000			−0.135769
$218$	2.77526	−	4.80688i	0.187964	−	0.325563i
$219$	1.00000	−	1.41421i	0.0675737	−	0.0955637i
$220$		0			0
$221$	1.10102	+	1.90702i	0.0740627	+	0.128280i
$222$	−8.22474	−	17.8526i	−0.552009	−	1.19819i
$223$	−8.89898	+	15.4135i	−0.595920	+	1.03216i	0.397497	+	0.917604i	$0.369879\pi$
$223$	−8.89898	+	15.4135i	−0.595920	+	1.03216i	−0.993416	+	0.114560i	$0.963454\pi$
$224$	0.449490			0.0300328
$225$		0			0
$226$	4.10102			0.272796
$227$	−6.82577	+	11.8226i	−0.453042	+	0.784692i	−0.998573	−	0.0533987i	$-0.982995\pi$
$227$	−6.82577	+	11.8226i	−0.453042	+	0.784692i	0.545531	+	0.838090i	$0.316328\pi$
$228$	12.8485	+	1.18386i	0.850911	+	0.0784032i
$229$	−6.57321	−	11.3851i	−0.434370	−	0.752351i	0.562874	−	0.826543i	$-0.309696\pi$
$229$	−6.57321	−	11.3851i	−0.434370	−	0.752351i	−0.997244	+	0.0741916i	$0.976362\pi$
$230$		0			0
$231$	3.79796	+	0.349945i	0.249887	+	0.0230247i
$232$	−1.22474	+	2.12132i	−0.0804084	+	0.139272i
$233$	−23.6969			−1.55244			−0.776219	−	0.630463i	$-0.782865\pi$
$233$	−23.6969			−1.55244			−0.776219	+	0.630463i	$0.782865\pi$
$234$	−0.449490	−	1.27135i	−0.0293841	−	0.0831107i
$235$		0			0
$236$	2.72474	−	4.71940i	0.177366	−	0.307207i
$237$	−12.1010	−	26.2665i	−0.786046	−	1.70619i
$238$	−1.10102	−	1.90702i	−0.0713686	−	0.123614i
$239$	−7.22474	−	12.5136i	−0.467330	−	0.809439i	0.531973	−	0.846761i	$-0.321451\pi$
$239$	−7.22474	−	12.5136i	−0.467330	−	0.809439i	−0.999303	+	0.0373219i	$0.988117\pi$
$240$		0			0
$241$	1.60102	−	2.77305i	0.103131	−	0.178628i	−0.809842	−	0.586648i	$-0.800447\pi$
$241$	1.60102	−	2.77305i	0.103131	−	0.178628i	0.912973	+	0.408020i	$0.133781\pi$
$242$	−13.0000			−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
$247$	1.67423	+	2.89986i	0.106529	+	0.184514i
$248$	2.22474	+	3.85337i	0.141271	+	0.244689i
$249$	3.94949	+	8.57277i	0.250289	+	0.543277i
$250$		0			0
$251$	−0.550510			−0.0347479			−0.0173739	−	0.999849i	$-0.505531\pi$
$251$	−0.550510			−0.0347479			−0.0173739	+	0.999849i	$0.505531\pi$
$252$	0.449490	+	1.27135i	0.0283152	+	0.0800875i
$253$	12.0000			0.754434
$254$	1.67423	−	2.89986i	0.105051	−	0.181953i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.39898	+	11.0834i	0.399157	+	0.691361i	0.993622	−	0.112761i	$-0.0359694\pi$
$257$	6.39898	+	11.0834i	0.399157	+	0.691361i	−0.594465	+	0.804122i	$0.702636\pi$
$258$	−4.39898	−	0.405324i	−0.273869	−	0.0252343i
$259$	−2.55051	+	4.41761i	−0.158481	+	0.274497i
$260$		0			0
$261$	−7.22474	−	1.34278i	−0.447200	−	0.0831161i
$262$	3.79796			0.234639
$263$	−10.2247	+	17.7098i	−0.630485	+	1.09203i	0.356968	+	0.934117i	$0.383811\pi$
$263$	−10.2247	+	17.7098i	−0.630485	+	1.09203i	−0.987453	+	0.157915i	$0.949523\pi$
$264$	−3.55051	−	7.70674i	−0.218519	−	0.474317i
$265$		0			0
$266$	−1.67423	−	2.89986i	−0.102654	−	0.177802i
$267$	9.00000	−	12.7279i	0.550791	−	0.778936i
$268$	−0.174235	+	0.301783i	−0.0106431	+	0.0184343i
$269$	14.4495			0.881001			0.440500	−	0.897752i	$-0.354801\pi$
$269$	14.4495			0.881001			0.440500	+	0.897752i	$0.354801\pi$
$270$		0			0
$271$	15.3485			0.932353			0.466177	−	0.884692i	$-0.345631\pi$
$271$	15.3485			0.932353			0.466177	+	0.884692i	$0.345631\pi$
$272$	−2.44949	+	4.24264i	−0.148522	+	0.257248i
$273$	−0.202041	+	0.285729i	−0.0122281	+	0.0172931i
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$		0			0
$276$	1.77526	+	3.85337i	0.106858	+	0.231946i
$277$	0.775255	−	1.34278i	0.0465806	−	0.0806799i	−0.841795	−	0.539797i	$-0.818501\pi$
$277$	0.775255	−	1.34278i	0.0465806	−	0.0806799i	0.888376	+	0.459117i	$0.151834\pi$
$278$	4.00000			0.239904
$279$	−8.67423	+	10.1459i	−0.519313	+	0.607419i
$280$		0			0
$281$	−9.55051	+	16.5420i	−0.569736	+	0.986811i	0.426856	+	0.904320i	$0.359621\pi$
$281$	−9.55051	+	16.5420i	−0.569736	+	0.986811i	−0.996592	+	0.0824916i	$0.973712\pi$
$282$	18.7980	+	1.73205i	1.11940	+	0.103142i
$283$	6.62372	+	11.4726i	0.393740	+	0.681977i	0.992939	−	0.118623i	$-0.0378479\pi$
$283$	6.62372	+	11.4726i	0.393740	+	0.681977i	−0.599200	+	0.800599i	$0.704515\pi$
$284$	−6.67423	−	11.5601i	−0.396043	−	0.685967i
$285$		0			0
$286$	1.10102	−	1.90702i	0.0651047	−	0.112765i
$287$	−4.04541			−0.238793
$288$	1.94949	−	2.28024i	0.114875	−	0.134364i
$289$	7.00000			0.411765
$290$		0			0
$291$	−6.37628	−	13.8404i	−0.373784	−	0.811336i
$292$	0.500000	+	0.866025i	0.0292603	+	0.0506803i
$293$	−8.02270	−	13.8957i	−0.468691	−	0.811797i	0.530668	−	0.847580i	$-0.321941\pi$
$293$	−8.02270	−	13.8957i	−0.468691	−	0.811797i	−0.999360	+	0.0357824i	$0.988608\pi$
$294$	−6.79796	+	9.61377i	−0.396465	+	0.560686i
$295$		0			0
$296$	11.3485			0.659616
$297$	18.2474	−	17.7491i	1.05882	−	1.02991i
$298$	6.00000			0.347571
$299$	−0.550510	+	0.953512i	−0.0318368	+	0.0551430i
$300$		0			0
$301$	0.573214	+	0.992836i	0.0330395	+	0.0572261i
$302$	10.0000	+	17.3205i	0.575435	+	0.996683i
$303$	−6.12372	−	13.2922i	−0.351799	−	0.763615i
$304$	−3.72474	+	6.45145i	−0.213629	+	0.370016i
$305$		0			0
$306$	−14.4495	−	2.68556i	−0.826022	−	0.153523i
$307$	22.6969			1.29538			0.647691	−	0.761903i	$-0.275735\pi$
$307$	22.6969			1.29538			0.647691	+	0.761903i	$0.275735\pi$
$308$	−1.10102	+	1.90702i	−0.0627365	+	0.108663i
$309$	28.7980	+	2.65345i	1.63826	+	0.150950i
$310$		0			0
$311$	0.550510	+	0.953512i	0.0312166	+	0.0540687i	0.881212	−	0.472722i	$-0.156729\pi$
$311$	0.550510	+	0.953512i	0.0312166	+	0.0540687i	−0.849995	+	0.526791i	$0.823395\pi$
$312$	0.775255	+	0.0714323i	0.0438902	+	0.00404406i
$313$	2.94949	−	5.10867i	0.166715	−	0.288759i	−0.770548	−	0.637382i	$-0.780017\pi$
$313$	2.94949	−	5.10867i	0.166715	−	0.288759i	0.937263	+	0.348623i	$0.113351\pi$
$314$	19.7980			1.11726
$315$		0			0
$316$	16.6969			0.939276
$317$	−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	$0.326582\pi$
$318$	−2.57321	−	5.58542i	−0.144299	−	0.313215i
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$		0			0
$321$	−9.24745	+	13.0779i	−0.516142	+	0.729935i
$322$	0.550510	−	0.953512i	0.0306787	−	0.0531371i
$323$	36.4949			2.03063
$324$	8.39898	+	3.23375i	0.466610	+	0.179653i
$325$		0			0
$326$	3.72474	−	6.45145i	0.206295	−	0.357313i
$327$	−5.55051	+	7.84961i	−0.306944	+	0.434084i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	−2.44949	−	4.24264i	−0.135045	−	0.233904i
$330$		0			0
$331$	−3.17423	+	5.49794i	−0.174472	+	0.302194i	−0.939978	−	0.341234i	$-0.889155\pi$
$331$	−3.17423	+	5.49794i	−0.174472	+	0.302194i	0.765507	+	0.643428i	$0.222488\pi$
$332$	−5.44949			−0.299080
$333$	11.3485	+	32.0983i	0.621892	+	1.75898i
$334$	−19.5959			−1.07224
$335$		0			0
$336$	−0.775255	−	0.0714323i	−0.0422936	−	0.00389695i
$337$	10.4495	+	18.0990i	0.569220	+	0.985918i	0.996643	+	0.0818663i	$0.0260881\pi$
$337$	10.4495	+	18.0990i	0.569220	+	0.985918i	−0.427423	+	0.904052i	$0.640579\pi$
$338$	−6.39898	−	11.0834i	−0.348059	−	0.602855i
$339$	−7.07321	−	0.651729i	−0.384164	−	0.0353970i
$340$		0			0
$341$	−21.7980			−1.18043
$342$	−21.9722	−	4.08372i	−1.18812	−	0.220822i
$343$	6.20204			0.334879
$344$	1.27526	−	2.20881i	0.0687571	−	0.119091i
$345$		0			0
$346$	4.89898	+	8.48528i	0.263371	+	0.456172i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	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
$351$	0.573214	+	2.26418i	0.0305959	+	0.120853i
$352$	4.89898			0.261116
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	−0.721063	−	0.692869i	$-0.756346\pi$
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	0.960574	+	0.278024i	$0.0896796\pi$
$354$	−5.44949	+	7.70674i	−0.289637	+	0.409609i
$355$		0			0
$356$	4.50000	+	7.79423i	0.238500	+	0.413093i
$357$	1.59592	+	3.46410i	0.0844649	+	0.183340i
$358$	4.62372	−	8.00853i	0.244371	−	0.423264i
$359$	−14.2020			−0.749555			−0.374778	−	0.927115i	$-0.622281\pi$
$359$	−14.2020			−0.749555			−0.374778	+	0.927115i	$0.622281\pi$
$360$		0			0
$361$	36.4949			1.92078
$362$	8.89898	−	15.4135i	0.467720	−	0.810115i
$363$	22.4217	+	2.06594i	1.17683	+	0.108434i
$364$	−0.101021	−	0.174973i	−0.00529491	−	0.00917106i
$365$		0			0
$366$	−13.7980	−	1.27135i	−0.721231	−	0.0664545i
$367$	6.34847	−	10.9959i	0.331387	−	0.573980i	−0.651397	−	0.758737i	$-0.725817\pi$
$367$	6.34847	−	10.9959i	0.331387	−	0.573980i	0.982784	+	0.184757i	$0.0591500\pi$
$368$	−2.44949			−0.127688
$369$	−17.5454	+	20.5222i	−0.913377	+	1.06834i
$370$		0			0
$371$	−0.797959	+	1.38211i	−0.0414280	+	0.0717553i
$372$	−3.22474	−	6.99964i	−0.167195	−	0.362914i
$373$	11.7980	+	20.4347i	0.610875	+	1.05807i	0.991093	+	0.133170i	$0.0425156\pi$
$373$	11.7980	+	20.4347i	0.610875	+	1.05807i	−0.380218	+	0.924897i	$0.624151\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$		0			0
$376$	−5.44949	+	9.43879i	−0.281036	+	0.486769i
$377$	1.10102			0.0567054
$378$	−0.573214	−	2.26418i	−0.0294830	−	0.116457i
$379$	−8.89898			−0.457110			−0.228555	−	0.973531i	$-0.573400\pi$
$379$	−8.89898			−0.457110			−0.228555	+	0.973531i	$0.573400\pi$
$380$		0			0
$381$	−3.34847	+	4.73545i	−0.171547	+	0.242604i
$382$	−0.550510	−	0.953512i	−0.0281666	−	0.0487859i
$383$	−10.7753	−	18.6633i	−0.550590	−	0.953650i	−0.998232	−	0.0594368i	$-0.981070\pi$
$383$	−10.7753	−	18.6633i	−0.550590	−	0.953650i	0.447642	−	0.894213i	$-0.352264\pi$
$384$	0.724745	+	1.57313i	0.0369845	+	0.0802786i
$385$		0			0
$386$	−20.0000			−1.01797
$387$	7.52270	+	1.39816i	0.382401	+	0.0710724i
$388$	8.79796			0.446649
$389$	−12.7980	+	22.1667i	−0.648882	+	1.12390i	0.334508	+	0.942393i	$0.391430\pi$
$389$	−12.7980	+	22.1667i	−0.648882	+	1.12390i	−0.983390	+	0.181504i	$0.941903\pi$
$390$		0			0
$391$	6.00000	+	10.3923i	0.303433	+	0.525561i
$392$	−3.39898	−	5.88721i	−0.171674	−	0.297349i
$393$	−6.55051	−	0.603566i	−0.330430	−	0.0304459i
$394$	−0.123724	+	0.214297i	−0.00623314	+	0.0107961i
$395$		0			0
$396$	4.89898	+	13.8564i	0.246183	+	0.696311i
$397$	−17.5959			−0.883114			−0.441557	−	0.897233i	$-0.645574\pi$
$397$	−17.5959			−0.883114			−0.441557	+	0.897233i	$0.645574\pi$
$398$	−6.89898	+	11.9494i	−0.345815	+	0.598968i
$399$	2.42679	+	5.26758i	0.121491	+	0.263709i
$400$		0			0
$401$	−19.3485	−	33.5125i	−0.966216	−	1.67354i	−0.706311	−	0.707902i	$-0.749642\pi$
$401$	−19.3485	−	33.5125i	−0.966216	−	1.67354i	−0.259906	−	0.965634i	$-0.583692\pi$
$402$	0.348469	−	0.492810i	0.0173801	−	0.0245791i
$403$	1.00000	−	1.73205i	0.0498135	−	0.0862796i
$404$	8.44949			0.420378
$405$		0			0
$406$	−1.10102			−0.0546427
$407$	−27.7980	+	48.1475i	−1.37789	+	2.38658i
$408$	4.89898	−	6.92820i	0.242536	−	0.342997i
$409$	−0.0505103	−	0.0874863i	−0.00249757	−	0.00432592i	0.864774	−	0.502161i	$-0.167462\pi$
$409$	−0.0505103	−	0.0874863i	−0.00249757	−	0.00432592i	−0.867271	+	0.497835i	$0.834128\pi$
$410$		0			0
$411$	−2.17423	−	4.71940i	−0.107247	−	0.232791i
$412$	−8.34847	+	14.4600i	−0.411300	+	0.712392i
$413$	2.44949			0.120532
$414$	−2.44949	−	6.92820i	−0.120386	−	0.340503i
$415$		0			0
$416$	−0.224745	+	0.389270i	−0.0110190	+	0.0190855i
$417$	−6.89898	−	0.635674i	−0.337844	−	0.0311291i
$418$	−18.2474	−	31.6055i	−0.892512	−	1.54588i
$419$	13.0732	+	22.6435i	0.638668	+	1.10621i	0.985725	+	0.168362i	$0.0538477\pi$
$419$	13.0732	+	22.6435i	0.638668	+	1.10621i	−0.347057	+	0.937844i	$0.612819\pi$
$420$		0			0
$421$	13.0227	−	22.5560i	0.634688	−	1.09931i	−0.351893	−	0.936040i	$-0.614462\pi$
$421$	13.0227	−	22.5560i	0.634688	−	1.09931i	0.986581	−	0.163271i	$-0.0522046\pi$
$422$	3.44949			0.167919
$423$	−32.1464	−	5.97469i	−1.56301	−	0.290499i
$424$	3.55051			0.172428
$425$		0			0
$426$	9.67423	+	20.9989i	0.468718	+	1.01740i
$427$	1.79796	+	3.11416i	0.0870093	+	0.150705i
$428$	−4.62372	−	8.00853i	−0.223496	−	0.387107i
$429$	−2.20204	+	3.11416i	−0.106316	+	0.150353i
$430$		0			0
$431$	25.3485			1.22099			0.610496	−	0.792019i	$-0.290970\pi$
$431$	25.3485			1.22099			0.610496	+	0.792019i	$0.290970\pi$
$432$	−3.72474	+	3.62302i	−0.179207	+	0.174313i
$433$	9.59592			0.461150			0.230575	−	0.973055i	$-0.425939\pi$
$433$	9.59592			0.461150			0.230575	+	0.973055i	$0.425939\pi$
$434$	−1.00000	+	1.73205i	−0.0480015	+	0.0831411i
$435$		0			0
$436$	−2.77526	−	4.80688i	−0.132911	−	0.230208i
$437$	9.12372	+	15.8028i	0.436447	+	0.755948i
$438$	−0.724745	−	1.57313i	−0.0346296	−	0.0751672i
$439$	−1.67423	+	2.89986i	−0.0799069	+	0.138403i	−0.903210	−	0.429200i	$-0.858796\pi$
$439$	−1.67423	+	2.89986i	−0.0799069	+	0.138403i	0.823303	+	0.567603i	$0.192129\pi$
$440$		0			0
$441$	13.2526	−	15.5010i	0.631074	−	0.738141i
$442$	2.20204			0.104740
$443$	−4.10102	+	7.10318i	−0.194845	+	0.337482i	−0.946850	−	0.321676i	$-0.895754\pi$
$443$	−4.10102	+	7.10318i	−0.194845	+	0.337482i	0.752004	+	0.659158i	$0.229087\pi$
$444$	−19.5732	−	1.80348i	−0.928904	−	0.0855895i
$445$		0			0
$446$	8.89898	+	15.4135i	0.421379	+	0.729850i
$447$	−10.3485	−	0.953512i	−0.489466	−	0.0450996i
$448$	0.224745	−	0.389270i	0.0106182	−	0.0183913i
$449$	−28.5959			−1.34952			−0.674762	−	0.738035i	$-0.735754\pi$
$449$	−28.5959			−1.34952			−0.674762	+	0.738035i	$0.735754\pi$
$450$		0			0
$451$	−44.0908			−2.07616
$452$	2.05051	−	3.55159i	0.0964479	−	0.167053i
$453$	−14.4949	−	31.4626i	−0.681030	−	1.47824i
$454$	6.82577	+	11.8226i	0.320349	+	0.554861i
$455$		0			0
$456$	7.44949	−	10.5352i	0.348854	−	0.493355i
$457$	−6.84847	+	11.8619i	−0.320358	+	0.554876i	−0.980562	−	0.196210i	$-0.937136\pi$
$457$	−6.84847	+	11.8619i	−0.320358	+	0.554876i	0.660204	+	0.751086i	$0.270470\pi$
$458$	−13.1464			−0.614292
$459$	24.4949	+	6.92820i	1.14332	+	0.323381i
$460$		0			0
$461$	−2.32577	+	4.02834i	−0.108322	+	0.187619i	−0.915090	−	0.403249i	$-0.867881\pi$
$461$	−2.32577	+	4.02834i	−0.108322	+	0.187619i	0.806769	+	0.590867i	$0.201214\pi$
$462$	2.20204	−	3.11416i	0.102448	−	0.144884i
$463$	2.67423	+	4.63191i	0.124282	+	0.215263i	0.921452	−	0.388492i	$-0.127004\pi$
$463$	2.67423	+	4.63191i	0.124282	+	0.215263i	−0.797170	+	0.603755i	$0.793671\pi$
$464$	1.22474	+	2.12132i	0.0568574	+	0.0984798i
$465$		0			0
$466$	−11.8485	+	20.5222i	−0.548870	+	0.950670i
$467$	−10.3485			−0.478870			−0.239435	−	0.970912i	$-0.576962\pi$
$467$	−10.3485			−0.478870			−0.239435	+	0.970912i	$0.576962\pi$
$468$	−1.32577	−	0.246405i	−0.0612835	−	0.0113901i
$469$	−0.156633			−0.00723266
$470$		0			0
$471$	−34.1464	−	3.14626i	−1.57338	−	0.144972i
$472$	−2.72474	−	4.71940i	−0.125417	−	0.217228i
$473$	6.24745	+	10.8209i	0.287258	+	0.497545i
$474$	−28.7980	−	2.65345i	−1.32273	−	0.121877i
$475$		0			0
$476$	−2.20204			−0.100930
$477$	3.55051	+	10.0424i	0.162567	+	0.459808i
$478$	−14.4495			−0.660904
$479$	−0.123724	+	0.214297i	−0.00565311	+	0.00979147i	−0.868838	−	0.495096i	$-0.835133\pi$
$479$	−0.123724	+	0.214297i	−0.00565311	+	0.00979147i	0.863185	+	0.504888i	$0.168466\pi$
$480$		0			0
$481$	−2.55051	−	4.41761i	−0.116293	−	0.201426i
$482$	−1.60102	−	2.77305i	−0.0729245	−	0.126309i
$483$	−1.10102	+	1.55708i	−0.0500982	+	0.0708495i
$484$	−6.50000	+	11.2583i	−0.295455	+	0.511742i
$485$		0			0
$486$	−13.9722	−	6.91215i	−0.633792	−	0.313541i
$487$	−24.4495			−1.10791			−0.553956	−	0.832546i	$-0.686882\pi$
$487$	−24.4495			−1.10791			−0.553956	+	0.832546i	$0.686882\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$	−7.44949	+	10.5352i	−0.336878	+	0.476417i
$490$		0			0
$491$	13.6237	+	23.5970i	0.614830	+	1.06492i	0.990414	+	0.138129i	$0.0441087\pi$
$491$	13.6237	+	23.5970i	0.614830	+	1.06492i	−0.375584	+	0.926788i	$0.622558\pi$
$492$	−6.52270	−	14.1582i	−0.294066	−	0.638300i
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$	3.34847			0.150655
$495$		0			0
$496$	4.44949			0.199788
$497$	3.00000	−	5.19615i	0.134568	−	0.233079i
$498$	9.39898	+	0.866025i	0.421178	+	0.0388075i
$499$	4.17423	+	7.22999i	0.186864	+	0.323659i	0.944203	−	0.329364i	$-0.106834\pi$
$499$	4.17423	+	7.22999i	0.186864	+	0.323659i	−0.757339	+	0.653022i	$0.773501\pi$
$500$		0			0
$501$	33.7980	+	3.11416i	1.50998	+	0.139130i
$502$	−0.275255	+	0.476756i	−0.0122852	+	0.0212787i
$503$	21.5505			0.960890			0.480445	−	0.877025i	$-0.340475\pi$
$503$	21.5505			0.960890			0.480445	+	0.877025i	$0.340475\pi$
$504$	1.32577	+	0.246405i	0.0590543	+	0.0109757i
$505$		0			0
$506$	6.00000	−	10.3923i	0.266733	−	0.461994i
$507$	9.27526	+	20.1329i	0.411929	+	0.894133i
$508$	−1.67423	−	2.89986i	−0.0742821	−	0.128660i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	−0.224745	+	0.389270i	−0.00994213	+	0.0172203i
$512$	−1.00000			−0.0441942
$513$	37.2474	+	10.5352i	1.64452	+	0.465139i
$514$	12.7980			0.564494
$515$		0			0
$516$	−2.55051	+	3.60697i	−0.112280	+	0.158788i
$517$	−26.6969	−	46.2405i	−1.17413	−	2.03365i
$518$	2.55051	+	4.41761i	0.112063	+	0.194099i
$519$	−7.10102	−	15.4135i	−0.311700	−	0.676577i
$520$		0			0
$521$	−29.3939			−1.28777			−0.643885	−	0.765123i	$-0.722678\pi$
$521$	−29.3939			−1.28777			−0.643885	+	0.765123i	$0.722678\pi$
$522$	−4.77526	+	5.58542i	−0.209007	+	0.244467i
$523$	−20.3485			−0.889776			−0.444888	−	0.895586i	$-0.646757\pi$
$523$	−20.3485			−0.889776			−0.444888	+	0.895586i	$0.646757\pi$
$524$	1.89898	−	3.28913i	0.0829573	−	0.143686i
$525$		0			0
$526$	10.2247	+	17.7098i	0.445820	+	0.772183i
$527$	−10.8990	−	18.8776i	−0.474767	−	0.822321i
$528$	−8.44949	−	0.778539i	−0.367717	−	0.0338816i
$529$	8.50000	−	14.7224i	0.369565	−	0.640106i
$530$		0			0
$531$	10.6237	−	12.4261i	0.461030	−	0.539248i
$532$	−3.34847			−0.145175
$533$	2.02270	−	3.50343i	0.0876130	−	0.151750i
$534$	−6.52270	−	14.1582i	−0.282265	−	0.612685i
$535$		0			0
$536$	0.174235	+	0.301783i	0.00752579	+	0.0130350i
$537$	−9.24745	+	13.0779i	−0.399057	+	0.564352i
$538$	7.22474	−	12.5136i	0.311481	−	0.539501i
$539$	33.3031			1.43446
$540$		0			0
$541$	−37.7980			−1.62506			−0.812531	−	0.582919i	$-0.801911\pi$
$541$	−37.7980			−1.62506			−0.812531	+	0.582919i	$0.801911\pi$
$542$	7.67423	−	13.2922i	0.329637	−	0.570947i
$543$	−17.7980	+	25.1701i	−0.763784	+	1.08015i
$544$	2.44949	+	4.24264i	0.105021	+	0.181902i
$545$		0			0
$546$	0.146428	+	0.317837i	0.00626655	+	0.0136022i
$547$	−7.82577	+	13.5546i	−0.334606	+	0.579554i	−0.983409	−	0.181402i	$-0.941936\pi$
$547$	−7.82577	+	13.5546i	−0.334606	+	0.579554i	0.648803	+	0.760956i	$0.275270\pi$
$548$	3.00000			0.128154
$549$	23.5959	+	4.38551i	1.00705	+	0.187169i
$550$		0			0
$551$	9.12372	−	15.8028i	0.388684	−	0.673220i
$552$	4.22474	+	0.389270i	0.179817	+	0.0165684i
$553$	3.75255	+	6.49961i	0.159575	+	0.276392i
$554$	−0.775255	−	1.34278i	−0.0329374	−	0.0570493i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	41.3939			1.75391			0.876957	−	0.480568i	$-0.159570\pi$
$557$	41.3939			1.75391			0.876957	+	0.480568i	$0.159570\pi$
$558$	4.44949	+	12.5851i	0.188362	+	0.532768i
$559$	−1.14643			−0.0484887
$560$		0			0
$561$	17.3939	+	37.7552i	0.734370	+	1.59402i
$562$	9.55051	+	16.5420i	0.402864	+	0.697781i
$563$	11.9722	+	20.7364i	0.504568	+	0.873937i	0.999986	+	0.00528250i	$0.00168148\pi$
$563$	11.9722	+	20.7364i	0.504568	+	0.873937i	−0.495418	+	0.868655i	$0.664985\pi$
$564$	10.8990	−	15.4135i	0.458930	−	0.649025i
$565$		0			0
$566$	13.2474			0.556832
$567$	0.628827	+	3.99624i	0.0264082	+	0.167826i
$568$	−13.3485			−0.560089
$569$	−16.8990	+	29.2699i	−0.708442	+	1.22706i	0.256993	+	0.966413i	$0.417268\pi$
$569$	−16.8990	+	29.2699i	−0.708442	+	1.22706i	−0.965435	+	0.260644i	$0.916065\pi$
$570$		0			0
$571$	−12.9722	−	22.4685i	−0.542869	−	0.940277i	−0.998738	−	0.0502301i	$-0.984005\pi$
$571$	−12.9722	−	22.4685i	−0.542869	−	0.940277i	0.455868	−	0.890047i	$-0.349329\pi$
$572$	−1.10102	−	1.90702i	−0.0460360	−	0.0797367i
$573$	0.797959	+	1.73205i	0.0333352	+	0.0723575i
$574$	−2.02270	+	3.50343i	−0.0844260	+	0.146230i
$575$		0			0
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$	40.3939			1.68162			0.840810	−	0.541331i	$-0.182079\pi$
$577$	40.3939			1.68162			0.840810	+	0.541331i	$0.182079\pi$
$578$	3.50000	−	6.06218i	0.145581	−	0.252153i
$579$	34.4949	+	3.17837i	1.43356	+	0.132089i
$580$		0			0
$581$	−1.22474	−	2.12132i	−0.0508110	−	0.0880072i
$582$	−15.1742	−	1.39816i	−0.628992	−	0.0579556i
$583$	−8.69694	+	15.0635i	−0.360190	+	0.623868i
$584$	1.00000			0.0413803
$585$		0			0
$586$	−16.0454			−0.662830
$587$	13.3485	−	23.1202i	0.550950	−	0.954274i	−0.447256	−	0.894406i	$-0.647599\pi$
$587$	13.3485	−	23.1202i	0.550950	−	0.954274i	0.998206	−	0.0598679i	$-0.0190680\pi$
$588$	4.92679	+	10.6941i	0.203177	+	0.441017i
$589$	−16.5732	−	28.7056i	−0.682887	−	1.18280i
$590$		0			0
$591$	0.247449	−	0.349945i	0.0101787	−	0.0143948i
$592$	5.67423	−	9.82806i	0.233210	−	0.403931i
$593$	−7.89898			−0.324372			−0.162186	−	0.986760i	$-0.551854\pi$
$593$	−7.89898			−0.324372			−0.162186	+	0.986760i	$0.551854\pi$
$594$	−6.24745	−	24.6773i	−0.256336	−	1.01252i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	13.7980	−	19.5133i	0.564713	−	0.798625i
$598$	0.550510	+	0.953512i	0.0225120	+	0.0389920i
$599$	11.3258	+	19.6168i	0.462758	+	0.801521i	0.999097	−	0.0424819i	$-0.0135265\pi$
$599$	11.3258	+	19.6168i	0.462758	+	0.801521i	−0.536339	+	0.844003i	$0.680193\pi$
$600$		0			0
$601$	8.24745	−	14.2850i	0.336420	−	0.582697i	−0.647336	−	0.762205i	$-0.724117\pi$
$601$	8.24745	−	14.2850i	0.336420	−	0.582697i	0.983757	+	0.179507i	$0.0574503\pi$
$602$	1.14643			0.0467249
$603$	−0.679337	+	0.794593i	−0.0276647	+	0.0323583i
$604$	20.0000			0.813788
$605$		0			0
$606$	−14.5732	−	1.34278i	−0.591996	−	0.0545468i
$607$	−1.67423	−	2.89986i	−0.0679551	−	0.117702i	0.830046	−	0.557695i	$-0.188314\pi$
$607$	−1.67423	−	2.89986i	−0.0679551	−	0.117702i	−0.898001	+	0.439993i	$0.854981\pi$
$608$	3.72474	+	6.45145i	0.151058	+	0.261641i
$609$	1.89898	+	0.174973i	0.0769505	+	0.00709025i
$610$		0			0
$611$	4.89898			0.198191
$612$	−9.55051	+	11.1708i	−0.386056	+	0.451555i
$613$	12.0454			0.486509			0.243255	−	0.969962i	$-0.421785\pi$
$613$	12.0454			0.486509			0.243255	+	0.969962i	$0.421785\pi$
$614$	11.3485	−	19.6561i	0.457987	−	0.793257i
$615$		0			0
$616$	1.10102	+	1.90702i	0.0443614	+	0.0768362i
$617$	−22.1969	−	38.4462i	−0.893615	−	1.54779i	−0.835509	−	0.549476i	$-0.814827\pi$
$617$	−22.1969	−	38.4462i	−0.893615	−	1.54779i	−0.0581058	−	0.998310i	$-0.518506\pi$
$618$	16.6969	−	23.6130i	0.671649	−	0.949856i
$619$	15.8712	−	27.4897i	0.637916	−	1.10490i	−0.347973	−	0.937505i	$-0.613130\pi$
$619$	15.8712	−	27.4897i	0.637916	−	1.10490i	0.985889	−	0.167399i	$-0.0535368\pi$
$620$		0			0
$621$	3.12372	+	12.3387i	0.125351	+	0.495133i
$622$	1.10102			0.0441469
$623$	−2.02270	+	3.50343i	−0.0810379	+	0.140362i
$624$	0.449490	−	0.635674i	0.0179940	−	0.0254473i
$625$		0			0
$626$	−2.94949	−	5.10867i	−0.117885	−	0.204183i
$627$	26.4495	+	57.4113i	1.05629	+	2.29279i
$628$	9.89898	−	17.1455i	0.395012	−	0.684181i
$629$	−55.5959			−2.21675
$630$		0			0
$631$	−6.20204			−0.246899			−0.123450	−	0.992351i	$-0.539396\pi$
$631$	−6.20204			−0.246899			−0.123450	+	0.992351i	$0.539396\pi$
$632$	8.34847	−	14.4600i	0.332084	−	0.575187i
$633$	−5.94949	−	0.548188i	−0.236471	−	0.0217885i
$634$	8.57321	+	14.8492i	0.340486	+	0.589739i
$635$		0			0
$636$	−6.12372	−	0.564242i	−0.242821	−	0.0223737i
$637$	−1.52781	+	2.64624i	−0.0605339	+	0.104848i
$638$	−12.0000			−0.475085
$639$	−13.3485	−	37.7552i	−0.528057	−	1.49357i
$640$		0			0
$641$	7.19694	−	12.4655i	0.284262	−	0.492356i	−0.688168	−	0.725551i	$-0.741585\pi$
$641$	7.19694	−	12.4655i	0.284262	−	0.492356i	0.972430	+	0.233195i	$0.0749181\pi$
$642$	6.70204	+	14.5475i	0.264508	+	0.574142i
$643$	8.82577	+	15.2867i	0.348054	+	0.602848i	0.985904	−	0.167313i	$-0.0535092\pi$
$643$	8.82577	+	15.2867i	0.348054	+	0.602848i	−0.637850	+	0.770161i	$0.720176\pi$
$644$	−0.550510	−	0.953512i	−0.0216931	−	0.0375736i
$645$		0			0
$646$	18.2474	−	31.6055i	0.717936	−	1.24350i
$647$	24.2474			0.953266			0.476633	−	0.879102i	$-0.341857\pi$
$647$	24.2474			0.953266			0.476633	+	0.879102i	$0.341857\pi$
$648$	7.00000	−	5.65685i	0.274986	−	0.222222i
$649$	26.6969			1.04795
$650$		0			0
$651$	2.00000	−	2.82843i	0.0783862	−	0.110855i
$652$	−3.72474	−	6.45145i	−0.145872	−	0.252658i
$653$	−9.12372	−	15.8028i	−0.357039	−	0.618410i	0.630426	−	0.776250i	$-0.282880\pi$
$653$	−9.12372	−	15.8028i	−0.357039	−	0.618410i	−0.987465	+	0.157840i	$0.949547\pi$
$654$	4.02270	+	8.73169i	0.157300	+	0.341436i
$655$		0			0
$656$	9.00000			0.351391
$657$	1.00000	+	2.82843i	0.0390137	+	0.110347i
$658$	−4.89898			−0.190982
$659$	−4.92679	+	8.53344i	−0.191920	+	0.332416i	−0.945887	−	0.324497i	$-0.894805\pi$
$659$	−4.92679	+	8.53344i	−0.191920	+	0.332416i	0.753966	+	0.656913i	$0.228138\pi$
$660$		0			0
$661$	−3.69694	−	6.40329i	−0.143794	−	0.249059i	0.785128	−	0.619333i	$-0.212597\pi$
$661$	−3.69694	−	6.40329i	−0.143794	−	0.249059i	−0.928922	+	0.370274i	$0.879264\pi$
$662$	3.17423	+	5.49794i	0.123370	+	0.213683i
$663$	−3.79796	−	0.349945i	−0.147501	−	0.0135908i
$664$	−2.72474	+	4.71940i	−0.105741	+	0.183148i
$665$		0			0
$666$	33.4722	+	6.22110i	1.29702	+	0.241063i
$667$	6.00000			0.232321
$668$	−9.79796	+	16.9706i	−0.379094	+	0.656611i
$669$	−12.8990	−	27.9985i	−0.498703	−	1.08249i
$670$		0			0
$671$	19.5959	+	33.9411i	0.756492	+	1.31028i
$672$	−0.449490	+	0.635674i	−0.0173394	+	0.0245217i
$673$	−11.3485	+	19.6561i	−0.437451	+	0.757688i	−0.997492	−	0.0707771i	$-0.977452\pi$
$673$	−11.3485	+	19.6561i	−0.437451	+	0.757688i	0.560041	+	0.828465i	$0.310785\pi$
$674$	20.8990			0.804999
$675$		0			0
$676$	−12.7980			−0.492229
$677$	12.9217	−	22.3810i	0.496621	−	0.860172i	−0.503372	−	0.864070i	$-0.667907\pi$
$677$	12.9217	−	22.3810i	0.496621	−	0.860172i	0.999992	+	0.00389777i	$0.00124070\pi$
$678$	−4.10102	+	5.79972i	−0.157499	+	0.222737i
$679$	1.97730	+	3.42478i	0.0758817	+	0.131431i
$680$		0			0
$681$	−9.89388	−	21.4757i	−0.379134	−	0.822949i
$682$	−10.8990	+	18.8776i	−0.417343	+	0.722860i
$683$	41.9444			1.60496			0.802479	−	0.596681i	$-0.203514\pi$
$683$	41.9444			1.60496			0.802479	+	0.596681i	$0.203514\pi$
$684$	−14.5227	+	16.9866i	−0.555289	+	0.649500i
$685$		0			0
$686$	3.10102	−	5.37113i	0.118398	−	0.205071i
$687$	22.6742	+	2.08921i	0.865076	+	0.0797084i
$688$	−1.27526	−	2.20881i	−0.0486186	−	0.0842100i
$689$	−0.797959	−	1.38211i	−0.0303998	−	0.0526540i
$690$		0			0
$691$	−19.5227	+	33.8143i	−0.742679	+	1.28636i	0.208593	+	0.978003i	$0.433112\pi$
$691$	−19.5227	+	33.8143i	−0.742679	+	1.28636i	−0.951271	+	0.308355i	$0.900222\pi$
$692$	9.79796			0.372463
$693$	−4.29286	+	5.02118i	−0.163072	+	0.190739i
$694$	−12.0000			−0.455514
$695$		0			0
$696$	−1.77526	−	3.85337i	−0.0672909	−	0.146062i
$697$	−22.0454	−	38.1838i	−0.835029	−	1.44631i
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$	23.6969	−	33.5125i	0.896301	−	1.26756i
$700$		0			0
$701$	33.7980			1.27653			0.638266	−	0.769816i	$-0.279652\pi$
$701$	33.7980			1.27653			0.638266	+	0.769816i	$0.279652\pi$
$702$	2.24745	+	0.635674i	0.0848245	+	0.0239920i
$703$	−84.5403			−3.18850
$704$	2.44949	−	4.24264i	0.0923186	−	0.159901i
$705$		0			0
$706$	−4.50000	−	7.79423i	−0.169360	−	0.293340i
$707$	1.89898	+	3.28913i	0.0714185	+	0.123700i
$708$	3.94949	+	8.57277i	0.148431	+	0.322184i
$709$	−2.22474	+	3.85337i	−0.0835520	+	0.144716i	−0.904773	−	0.425894i	$-0.859960\pi$
$709$	−2.22474	+	3.85337i	−0.0835520	+	0.144716i	0.821221	+	0.570610i	$0.193293\pi$
$710$		0			0
$711$	49.2474	+	9.15306i	1.84692	+	0.343267i
$712$	9.00000			0.337289
$713$	5.44949	−	9.43879i	0.204085	−	0.353486i
$714$	3.79796	+	0.349945i	0.142135	+	0.0130964i
$715$		0			0
$716$	−4.62372	−	8.00853i	−0.172797	−	0.299293i
$717$	24.9217	+	2.29629i	0.930717	+	0.0857566i
$718$	−7.10102	+	12.2993i	−0.265008	+	0.459007i
$719$	7.95459			0.296656			0.148328	−	0.988938i	$-0.452611\pi$
$719$	7.95459			0.296656			0.148328	+	0.988938i	$0.452611\pi$
$720$		0			0
$721$	−7.50510			−0.279505
$722$	18.2474	−	31.6055i	0.679100	−	1.17624i
$723$	2.32066	+	5.03723i	0.0863064	+	0.187337i
$724$	−8.89898	−	15.4135i	−0.330728	−	0.572838i
$725$		0			0
$726$	13.0000	−	18.3848i	0.482475	−	0.682323i
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	−0.678676	−	0.734438i	$-0.737446\pi$
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	0.975380	+	0.220532i	$0.0707793\pi$
$728$	−0.202041			−0.00748814
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$	−6.24745	+	10.8209i	−0.231070	+	0.400225i
$732$	−8.00000	+	11.3137i	−0.295689	+	0.418167i
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	0.519575	−	0.854425i	$-0.326090\pi$
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	−0.999741	+	0.0227529i	$0.992757\pi$
$734$	−6.34847	−	10.9959i	−0.234326	−	0.405865i
$735$		0			0
$736$	−1.22474	+	2.12132i	−0.0451447	+	0.0781929i
$737$	−1.70714			−0.0628834
$738$	9.00000	+	25.4558i	0.331295	+	0.937043i
$739$	3.04541			0.112027			0.0560136	−	0.998430i	$-0.482161\pi$
$739$	3.04541			0.112027			0.0560136	+	0.998430i	$0.482161\pi$
$740$		0			0
$741$	−5.77526	−	0.532134i	−0.212159	−	0.0195484i
$742$	0.797959	+	1.38211i	0.0292940	+	0.0507387i
$743$	−24.6742	−	42.7370i	−0.905210	−	1.56787i	−0.820635	−	0.571452i	$-0.806380\pi$
$743$	−24.6742	−	42.7370i	−0.905210	−	1.56787i	−0.0845746	−	0.996417i	$-0.526953\pi$
$744$	−7.67423	−	0.707107i	−0.281351	−	0.0259238i
$745$		0			0
$746$	23.5959			0.863908
$747$	−16.0732	−	2.98735i	−0.588088	−	0.109301i
$748$	−24.0000			−0.877527
$749$	2.07832	−	3.59975i	0.0759400	−	0.131532i
$750$		0			0
$751$	2.97730	+	5.15683i	0.108643	+	0.188175i	0.915221	−	0.402953i	$-0.132016\pi$
$751$	2.97730	+	5.15683i	0.108643	+	0.188175i	−0.806578	+	0.591128i	$0.798683\pi$
$752$	5.44949	+	9.43879i	0.198722	+	0.344197i
$753$	0.550510	−	0.778539i	0.0200617	−	0.0283715i
$754$	0.550510	−	0.953512i	0.0200484	−	0.0347248i
$755$		0			0
$756$	−2.24745	−	0.635674i	−0.0817389	−	0.0231193i
$757$	−38.0454			−1.38278			−0.691392	−	0.722480i	$-0.743002\pi$
$757$	−38.0454			−1.38278			−0.691392	+	0.722480i	$0.743002\pi$
$758$	−4.44949	+	7.70674i	−0.161613	+	0.279921i
$759$	−12.0000	+	16.9706i	−0.435572	+	0.615992i
$760$		0			0
$761$	−6.94949	−	12.0369i	−0.251919	−	0.436336i	0.712135	−	0.702042i	$-0.247728\pi$
$761$	−6.94949	−	12.0369i	−0.251919	−	0.436336i	−0.964054	+	0.265706i	$0.914395\pi$
$762$	2.42679	+	5.26758i	0.0879132	+	0.190824i
$763$	1.24745	−	2.16064i	0.0451607	−	0.0782206i
$764$	−1.10102			−0.0398335
$765$		0			0
$766$	−21.5505			−0.778652
$767$	−1.22474	+	2.12132i	−0.0442230	+	0.0765964i
$768$	1.72474	+	0.158919i	0.0622364	+	0.00573448i
$769$	14.0959	+	24.4148i	0.508312	+	0.880422i	0.999954	+	0.00962438i	$0.00306358\pi$
$769$	14.0959	+	24.4148i	0.508312	+	0.880422i	−0.491642	+	0.870797i	$0.663603\pi$
$770$		0			0
$771$	−22.0732	−	2.03383i	−0.794947	−	0.0732467i
$772$	−10.0000	+	17.3205i	−0.359908	+	0.623379i
$773$	−10.4041			−0.374209			−0.187104	−	0.982340i	$-0.559910\pi$
$773$	−10.4041			−0.374209			−0.187104	+	0.982340i	$0.559910\pi$
$774$	4.97219	−	5.81577i	0.178722	−	0.209044i
$775$		0			0
$776$	4.39898	−	7.61926i	0.157914	−	0.273515i
$777$	−3.69694	−	8.02458i	−0.132627	−	0.287880i
$778$	12.7980	+	22.1667i	0.458829	+	0.794715i
$779$	−33.5227	−	58.0630i	−1.20108	−	2.08032i
$780$		0			0
$781$	32.6969	−	56.6328i	1.16999	−	2.02648i
$782$	12.0000			0.429119
$783$	9.12372	−	8.87455i	0.326055	−	0.317151i
$784$	−6.79796			−0.242784
$785$		0			0
$786$	−3.79796	+	5.37113i	−0.135469	+	0.191582i
$787$	−17.3485	−	30.0484i	−0.618406	−	1.07111i	−0.989777	−	0.142626i	$-0.954445\pi$
$787$	−17.3485	−	30.0484i	−0.618406	−	1.07111i	0.371370	−	0.928485i	$-0.378888\pi$
$788$	0.123724	+	0.214297i	0.00440750	+	0.00763401i
$789$	−14.8207	−	32.1698i	−0.527630	−	1.14527i
$790$		0			0
$791$	1.84337			0.0655426
$792$	14.4495	+	2.68556i	0.513440	+	0.0954273i
$793$	−3.59592			−0.127695
$794$	−8.79796	+	15.2385i	−0.312228	+	0.540795i
$795$		0			0
$796$	6.89898	+	11.9494i	0.244528	+	0.423535i
$797$	15.1237	+	26.1951i	0.535710	+	0.927877i	0.999129	+	0.0417372i	$0.0132892\pi$
$797$	15.1237	+	26.1951i	0.535710	+	0.927877i	−0.463419	+	0.886139i	$0.653377\pi$
$798$	5.77526	+	0.532134i	0.204442	+	0.0188373i
$799$	26.6969	−	46.2405i	0.944470	−	1.63587i
$800$		0			0
$801$	9.00000	+	25.4558i	0.317999	+	0.899438i
$802$	−38.6969			−1.36644
$803$	−2.44949	+	4.24264i	−0.0864406	+	0.149720i
$804$	−0.252551	−	0.548188i	−0.00890680	−	0.0193331i
$805$		0			0
$806$	−1.00000	−	1.73205i	−0.0352235	−	0.0610089i
$807$	−14.4495	+	20.4347i	−0.508646	+	0.719334i
$808$	4.22474	−	7.31747i	0.148626	−	0.257428i
$809$	−6.30306			−0.221604			−0.110802	−	0.993843i	$-0.535342\pi$
$809$	−6.30306			−0.221604			−0.110802	+	0.993843i	$0.535342\pi$
$810$		0			0
$811$	−28.5505			−1.00254			−0.501272	−	0.865290i	$-0.667134\pi$
$811$	−28.5505			−1.00254			−0.501272	+	0.865290i	$0.667134\pi$
$812$	−0.550510	+	0.953512i	−0.0193191	+	0.0334617i
$813$	−15.3485	+	21.7060i	−0.538294	+	0.761263i
$814$	27.7980	+	48.1475i	0.974318	+	1.68757i
$815$		0			0
$816$	−3.55051	−	7.70674i	−0.124293	−	0.269790i
$817$	−9.50000	+	16.4545i	−0.332363	+	0.575669i
$818$	−0.101021			−0.00353210
$819$	−0.202041	−	0.571458i	−0.00705988	−	0.0199684i
$820$		0			0
$821$	−13.5959	+	23.5488i	−0.474501	+	0.821860i	−0.999574	−	0.0291978i	$-0.990705\pi$
$821$	−13.5959	+	23.5488i	−0.474501	+	0.821860i	0.525073	+	0.851057i	$0.324038\pi$
$822$	−5.17423	−	0.476756i	−0.180472	−	0.0166288i
$823$	8.55051	+	14.8099i	0.298052	+	0.516241i	0.975690	−	0.219154i	$-0.0703298\pi$
$823$	8.55051	+	14.8099i	0.298052	+	0.516241i	−0.677638	+	0.735395i	$0.736996\pi$
$824$	8.34847	+	14.4600i	0.290833	+	0.503737i
$825$		0			0
$826$	1.22474	−	2.12132i	0.0426143	−	0.0738102i
$827$	−35.9444			−1.24991			−0.624954	−	0.780661i	$-0.714882\pi$
$827$	−35.9444			−1.24991			−0.624954	+	0.780661i	$0.714882\pi$
$828$	−7.22474	−	1.34278i	−0.251077	−	0.0466649i
$829$	−46.7423			−1.62343			−0.811714	−	0.584055i	$-0.801465\pi$
$829$	−46.7423			−1.62343			−0.811714	+	0.584055i	$0.801465\pi$
$830$		0			0
$831$	1.12372	+	2.43916i	0.0389816	+	0.0846134i
$832$	0.224745	+	0.389270i	0.00779163	+	0.0134955i
$833$	16.6515	+	28.8413i	0.576941	+	0.999292i
$834$	−4.00000	+	5.65685i	−0.138509	+	0.195881i
$835$		0			0
$836$	−36.4949			−1.26220
$837$	−5.67423	−	22.4131i	−0.196130	−	0.774711i
$838$	26.1464			0.903213
$839$	−18.6742	+	32.3447i	−0.644706	+	1.11666i	0.339663	+	0.940547i	$0.389687\pi$
$839$	−18.6742	+	32.3447i	−0.644706	+	1.11666i	−0.984369	+	0.176117i	$0.943646\pi$
$840$		0			0
$841$	11.5000	+	19.9186i	0.396552	+	0.686848i
$842$	−13.0227	−	22.5560i	−0.448792	−	0.777331i
$843$	−13.8434	−	30.0484i	−0.476791	−	1.03492i
$844$	1.72474	−	2.98735i	0.0593682	−	0.102829i
$845$		0			0
$846$	−21.2474	+	24.8523i	−0.730502	+	0.854439i
$847$	−5.84337			−0.200780
$848$	1.77526	−	3.07483i	0.0609625	−	0.105590i
$849$	−22.8485	−	2.10527i	−0.784157	−	0.0722526i
$850$		0			0
$851$	−13.8990	−	24.0737i	−0.476451	−	0.825237i
$852$	23.0227	+	2.12132i	0.788745	+	0.0726752i
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	0.927491	−	0.373845i	$-0.121961\pi$
$854$	3.59592			0.123050
$855$		0			0
$856$	−9.24745			−0.316071
$857$	24.9495	−	43.2138i	0.852258	−	1.47615i	−0.0269070	−	0.999638i	$-0.508566\pi$
$857$	24.9495	−	43.2138i	0.852258	−	1.47615i	0.879165	−	0.476517i	$-0.158101\pi$
$858$	1.59592	+	3.46410i	0.0544837	+	0.118262i
$859$	10.1742	+	17.6223i	0.347140	+	0.601265i	0.985740	−	0.168274i	$-0.0538194\pi$
$859$	10.1742	+	17.6223i	0.347140	+	0.601265i	−0.638600	+	0.769539i	$0.720486\pi$
$860$		0			0
$861$	4.04541	−	5.72107i	0.137867	−	0.194974i
$862$	12.6742	−	21.9524i	0.431686	−	0.747702i
$863$	−43.8434			−1.49245			−0.746223	−	0.665696i	$-0.768135\pi$
$863$	−43.8434			−1.49245			−0.746223	+	0.665696i	$0.768135\pi$
$864$	1.27526	+	5.03723i	0.0433851	+	0.171370i
$865$		0			0
$866$	4.79796	−	8.31031i	0.163041	−	0.282396i
$867$	−7.00000	+	9.89949i	−0.237732	+	0.336204i
$868$	1.00000	+	1.73205i	0.0339422	+	0.0587896i
$869$	40.8990	+	70.8391i	1.38740	+	2.40305i
$870$		0			0
$871$	0.0783167	−	0.135648i	0.00265366	−	0.00459627i
$872$	−5.55051			−0.187964
$873$	25.9495	+	4.82294i	0.878257	+	0.163232i
$874$	18.2474			0.617229
$875$		0			0
$876$	−1.72474	−	0.158919i	−0.0582737	−	0.00536936i
$877$	15.8990	+	27.5378i	0.536870	+	0.929887i	0.999070	+	0.0431110i	$0.0137269\pi$
$877$	15.8990	+	27.5378i	0.536870	+	0.929887i	−0.462200	+	0.886776i	$0.652940\pi$
$878$	1.67423	+	2.89986i	0.0565027	+	0.0978655i
$879$	27.6742	+	2.54991i	0.933429	+	0.0860065i
$880$		0			0
$881$	38.6969			1.30373			0.651866	−	0.758334i	$-0.273986\pi$
$881$	38.6969			1.30373			0.651866	+	0.758334i	$0.273986\pi$
$882$	−6.79796	−	19.2275i	−0.228899	−	0.647425i
$883$	47.7980			1.60853			0.804265	−	0.594271i	$-0.202559\pi$
$883$	47.7980			1.60853			0.804265	+	0.594271i	$0.202559\pi$
$884$	1.10102	−	1.90702i	0.0370313	−	0.0641401i
$885$		0			0
$886$	4.10102	+	7.10318i	0.137776	+	0.238636i
$887$	−2.75255	−	4.76756i	−0.0924216	−	0.160079i	0.816108	−	0.577899i	$-0.196127\pi$
$887$	−2.75255	−	4.76756i	−0.0924216	−	0.160079i	−0.908530	+	0.417821i	$0.862794\pi$
$888$	−11.3485	+	16.0492i	−0.380830	+	0.538575i
$889$	0.752551	−	1.30346i	0.0252398	−	0.0437165i
$890$		0			0
$891$	6.85357	+	43.5549i	0.229603	+	1.45914i
$892$	17.7980			0.595920
$893$	40.5959	−	70.3142i	1.35849	−	2.35297i
$894$	−6.00000	+	8.48528i	−0.200670	+	0.283790i
$895$		0			0
$896$	−0.224745	−	0.389270i	−0.00750820	−	0.0130046i
$897$	−0.797959	−	1.73205i	−0.0266431	−	0.0578315i
$898$	−14.2980	+	24.7648i	−0.477129	+	0.826412i
$899$	−10.8990			−0.363501
$900$		0			0
$901$	−17.3939			−0.579474
$902$	−22.0454	+	38.1838i	−0.734032	+	1.27138i
$903$	−1.97730	−	0.182189i	−0.0658003	−	0.00606286i
$904$	−2.05051	−	3.55159i	−0.0681990	−	0.118124i
$905$		0			0
$906$	−34.4949	−	3.17837i	−1.14602	−	0.105594i
$907$	−18.1742	+	31.4787i	−0.603466	+	1.04523i	0.388826	+	0.921311i	$0.372881\pi$
$907$	−18.1742	+	31.4787i	−0.603466	+	1.04523i	−0.992292	+	0.123922i	$0.960453\pi$
$908$	13.6515			0.453042
$909$	24.9217	+	4.63191i	0.826600	+	0.153631i
$910$		0			0
$911$	3.67423	−	6.36396i	0.121733	−	0.210847i	−0.798718	−	0.601705i	$-0.794488\pi$
$911$	3.67423	−	6.36396i	0.121733	−	0.210847i	0.920451	+	0.390858i	$0.127822\pi$
$912$	−5.39898	−	11.7190i	−0.178778	−	0.388056i
$913$	−13.3485	−	23.1202i	−0.441770	−	0.765168i
$914$	6.84847	+	11.8619i	0.226527	+	0.392357i
$915$		0			0
$916$	−6.57321	+	11.3851i	−0.217185	+	0.376176i
$917$	1.70714			0.0563748
$918$	18.2474	−	17.7491i	0.602256	−	0.585808i
$919$	3.34847			0.110456			0.0552279	−	0.998474i	$-0.482411\pi$
$919$	3.34847			0.110456			0.0552279	+	0.998474i	$0.482411\pi$
$920$		0			0
$921$	−22.6969	+	32.0983i	−0.747890	+	1.05768i
$922$	2.32577	+	4.02834i	0.0765950	+	0.132666i
$923$	3.00000	+	5.19615i	0.0987462	+	0.171033i
$924$	−1.59592	−	3.46410i	−0.0525018	−	0.113961i
$925$		0			0
$926$	5.34847			0.175762
$927$	−32.5505	+	38.0730i	−1.06910	+	1.25048i
$928$	2.44949			0.0804084
$929$	25.5959	−	44.3334i	0.839775	−	1.45453i	−0.0503079	−	0.998734i	$-0.516020\pi$
$929$	25.5959	−	44.3334i	0.839775	−	1.45453i	0.890083	−	0.455799i	$-0.150646\pi$
$930$		0			0
$931$	25.3207	+	43.8567i	0.829851	+	1.43734i
$932$	11.8485	+	20.5222i	0.388110	+	0.672225i
$933$	−1.89898	−	0.174973i	−0.0621698	−	0.00572835i
$934$	−5.17423	+	8.96204i	−0.169306	+	0.293247i
$935$		0			0
$936$	−0.876276	+	1.02494i	−0.0286420	+	0.0335013i
$937$	7.20204			0.235280			0.117640	−	0.993056i	$-0.462467\pi$
$937$	7.20204			0.235280			0.117640	+	0.993056i	$0.462467\pi$
$938$	−0.0783167	+	0.135648i	−0.00255713	+	0.00442908i
$939$	4.27526	+	9.27987i	0.139518	+	0.302837i
$940$		0			0
$941$	−26.8207	−	46.4548i	−0.874329	−	1.51438i	−0.857476	−	0.514524i	$-0.827969\pi$
$941$	−26.8207	−	46.4548i	−0.874329	−	1.51438i	−0.0168524	−	0.999858i	$-0.505365\pi$
$942$	−19.7980	+	27.9985i	−0.645052	+	0.912242i
$943$	11.0227	−	19.0919i	0.358949	−	0.621717i
$944$	−5.44949			−0.177366
$945$		0			0
$946$	12.4949			0.406244
$947$	−13.0732	+	22.6435i	−0.424822	+	0.735814i	−0.996404	−	0.0847314i	$-0.972997\pi$
$947$	−13.0732	+	22.6435i	−0.424822	+	0.735814i	0.571581	+	0.820545i	$0.306330\pi$
$948$	−16.6969	+	23.6130i	−0.542291	+	0.766916i
$949$	−0.224745	−	0.389270i	−0.00729553	−	0.0126362i
$950$		0			0
$951$	−12.4268	−	26.9736i	−0.402966	−	0.874679i
$952$	−1.10102	+	1.90702i	−0.0356843	+	0.0618070i
$953$	2.20204			0.0713311			0.0356656	−	0.999364i	$-0.488645\pi$
$953$	2.20204			0.0713311			0.0356656	+	0.999364i	$0.488645\pi$
$954$	10.4722	+	1.94635i	0.339050	+	0.0630153i
$955$		0			0
$956$	−7.22474	+	12.5136i	−0.233665	+	0.404720i
$957$	20.6969	+	1.90702i	0.669037	+	0.0616453i
$958$	0.123724	+	0.214297i	0.00399735	+	0.00692362i
$959$	0.674235	+	1.16781i	0.0217722	+	0.0377105i
$960$		0			0
$961$	5.60102	−	9.70125i	0.180678	−	0.312944i
$962$	−5.10102			−0.164464
$963$	−9.24745	−	26.1557i	−0.297995	−	0.842857i
$964$	−3.20204			−0.103131
$965$		0			0
$966$	0.797959	+	1.73205i	0.0256739	+	0.0557278i
$967$	−16.0000	−	27.7128i	−0.514525	−	0.891184i	−0.999858	−	0.0168544i	$-0.994635\pi$
$967$	−16.0000	−	27.7128i	−0.514525	−	0.891184i	0.485333	−	0.874330i	$-0.338699\pi$
$968$	6.50000	+	11.2583i	0.208918	+	0.361856i
$969$	−36.4949	+	51.6116i	−1.17239	+	1.65800i
$970$		0			0
$971$	−40.8434			−1.31073			−0.655363	−	0.755314i	$-0.727484\pi$
$971$	−40.8434			−1.31073			−0.655363	+	0.755314i	$0.727484\pi$
$972$	−12.9722	+	8.64420i	−0.416083	+	0.277263i
$973$	1.79796			0.0576399
$974$	−12.2247	+	21.1739i	−0.391706	+	0.678455i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	4.50000	+	7.79423i	0.143968	+	0.249359i	0.928987	−	0.370111i	$-0.120681\pi$
$977$	4.50000	+	7.79423i	0.143968	+	0.249359i	−0.785020	+	0.619471i	$0.787347\pi$
$978$	5.39898	+	11.7190i	0.172640	+	0.374733i
$979$	−22.0454	+	38.1838i	−0.704574	+	1.22036i
$980$		0			0
$981$	−5.55051	−	15.6992i	−0.177214	−	0.501237i
$982$	27.2474			0.869501
$983$	6.55051	−	11.3458i	0.208929	−	0.361875i	−0.742449	−	0.669903i	$-0.766336\pi$
$983$	6.55051	−	11.3458i	0.208929	−	0.361875i	0.951377	+	0.308028i	$0.0996690\pi$
$984$	−15.5227	−	1.43027i	−0.494846	−	0.0455953i
$985$		0			0
$986$	−6.00000	−	10.3923i	−0.191079	−	0.330958i
$987$	8.44949	+	0.778539i	0.268950	+	0.0247812i
$988$	1.67423	−	2.89986i	0.0532645	−	0.0922568i
$989$	−6.24745			−0.198657
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	2.22474	−	3.85337i	0.0706357	−	0.122345i
$993$	−4.60102	−	9.98698i	−0.146009	−	0.316927i
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		0			0
$996$	5.44949	−	7.70674i	0.172674	−	0.244197i
$997$	4.02270	−	6.96753i	0.127400	−	0.220664i	−0.795268	−	0.606258i	$-0.792670\pi$
$997$	4.02270	−	6.96753i	0.127400	−	0.220664i	0.922669	+	0.385594i	$0.126003\pi$
$998$	8.34847			0.264266
$999$	−56.7423	−	16.0492i	−1.79525	−	0.507773i

Twists

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

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

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