LMFDB - Embedded newform 1350.2.e.k.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(451,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([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("1350.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			901.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1350.901
Dual form			1350.2.e.k.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.224745 + 0.389270i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.224745 + 0.389270i) q^{7} +1.00000 q^{8} +(-2.44949 - 4.24264i) q^{11} +(0.224745 - 0.389270i) q^{13} +(0.224745 - 0.389270i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.89898 q^{17} +7.44949 q^{19} +(-2.44949 + 4.24264i) q^{22} +(-1.22474 + 2.12132i) q^{23} -0.449490 q^{26} -0.449490 q^{28} +(-1.22474 - 2.12132i) q^{29} +(-2.22474 + 3.85337i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.44949 + 4.24264i) q^{34} -11.3485 q^{37} +(-3.72474 - 6.45145i) q^{38} +(4.50000 - 7.79423i) q^{41} +(-1.27526 - 2.20881i) q^{43} +4.89898 q^{44} +2.44949 q^{46} +(-5.44949 - 9.43879i) q^{47} +(3.39898 - 5.88721i) q^{49} +(0.224745 + 0.389270i) q^{52} +3.55051 q^{53} +(0.224745 + 0.389270i) q^{56} +(-1.22474 + 2.12132i) q^{58} +(-2.72474 + 4.71940i) q^{59} +(-4.00000 - 6.92820i) q^{61} +4.44949 q^{62} +1.00000 q^{64} +(-0.174235 + 0.301783i) q^{67} +(2.44949 - 4.24264i) q^{68} -13.3485 q^{71} -1.00000 q^{73} +(5.67423 + 9.82806i) q^{74} +(-3.72474 + 6.45145i) q^{76} +(1.10102 - 1.90702i) q^{77} +(-8.34847 - 14.4600i) q^{79} -9.00000 q^{82} +(-2.72474 - 4.71940i) q^{83} +(-1.27526 + 2.20881i) q^{86} +(-2.44949 - 4.24264i) q^{88} +9.00000 q^{89} +0.202041 q^{91} +(-1.22474 - 2.12132i) q^{92} +(-5.44949 + 9.43879i) q^{94} +(-4.39898 - 7.61926i) q^{97} -6.79796 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} - 4 q^{13} - 4 q^{14} - 2 q^{16} + 20 q^{19} + 8 q^{26} + 8 q^{28} - 4 q^{31} - 2 q^{32} - 16 q^{37} - 10 q^{38} + 18 q^{41} - 10 q^{43} - 12 q^{47} - 6 q^{49} - 4 q^{52} + 24 q^{53} - 4 q^{56} - 6 q^{59} - 16 q^{61} + 8 q^{62} + 4 q^{64} + 14 q^{67} - 24 q^{71} - 4 q^{73} + 8 q^{74} - 10 q^{76} + 24 q^{77} - 4 q^{79} - 36 q^{82} - 6 q^{83} - 10 q^{86} + 36 q^{89} + 40 q^{91} - 12 q^{94} + 2 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 - 4 * q^13 - 4 * q^14 - 2 * q^16 + 20 * q^19 + 8 * q^26 + 8 * q^28 - 4 * q^31 - 2 * q^32 - 16 * q^37 - 10 * q^38 + 18 * q^41 - 10 * q^43 - 12 * q^47 - 6 * q^49 - 4 * q^52 + 24 * q^53 - 4 * q^56 - 6 * q^59 - 16 * q^61 + 8 * q^62 + 4 * q^64 + 14 * q^67 - 24 * q^71 - 4 * q^73 + 8 * q^74 - 10 * q^76 + 24 * q^77 - 4 * q^79 - 36 * q^82 - 6 * q^83 - 10 * q^86 + 36 * q^89 + 40 * q^91 - 12 * q^94 + 2 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.224745	+	0.389270i	0.0849456	+	0.147130i	0.905368	−	0.424628i	$-0.139595\pi$
$7$	0.224745	+	0.389270i	0.0849456	+	0.147130i	−0.820422	+	0.571758i	$0.806262\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	−2.44949	−	4.24264i	−0.738549	−	1.27920i	−0.953149	−	0.302502i	$-0.902178\pi$
$11$	−2.44949	−	4.24264i	−0.738549	−	1.27920i	0.214600	−	0.976702i	$-0.431155\pi$
$12$		0			0
$13$	0.224745	−	0.389270i	0.0623330	−	0.107964i	−0.833175	−	0.553010i	$-0.813479\pi$
$13$	0.224745	−	0.389270i	0.0623330	−	0.107964i	0.895508	+	0.445046i	$0.146813\pi$
$14$	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	$-0.702487\pi$
$17$	−4.89898			−1.18818			−0.594089	+	0.804400i	$0.702487\pi$
$18$		0			0
$19$	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			0
$22$	−2.44949	+	4.24264i	−0.522233	+	0.904534i
$23$	−1.22474	+	2.12132i	−0.255377	+	0.442326i	−0.964998	−	0.262258i	$-0.915533\pi$
$23$	−1.22474	+	2.12132i	−0.255377	+	0.442326i	0.709621	+	0.704584i	$0.248866\pi$
$24$		0			0
$25$		0			0
$26$	−0.449490			−0.0881522
$27$		0			0
$28$	−0.449490			−0.0849456
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	0.729616	−	0.683857i	$-0.239699\pi$
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	−0.957046	+	0.289938i	$0.906365\pi$
$30$		0			0
$31$	−2.22474	+	3.85337i	−0.399576	+	0.692086i	−0.993674	−	0.112307i	$-0.964176\pi$
$31$	−2.22474	+	3.85337i	−0.399576	+	0.692086i	0.594098	+	0.804393i	$0.297509\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	2.44949	+	4.24264i	0.420084	+	0.727607i
$35$		0			0
$36$		0			0
$37$	−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			0
$40$		0			0
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	−1.27526	−	2.20881i	−0.194475	−	0.336840i	0.752254	−	0.658874i	$-0.228967\pi$
$43$	−1.27526	−	2.20881i	−0.194475	−	0.336840i	−0.946728	+	0.322034i	$0.895634\pi$
$44$	4.89898			0.738549
$45$		0			0
$46$	2.44949			0.361158
$47$	−5.44949	−	9.43879i	−0.794890	−	1.37679i	−0.922909	−	0.385018i	$-0.874195\pi$
$47$	−5.44949	−	9.43879i	−0.794890	−	1.37679i	0.128019	−	0.991772i	$-0.459138\pi$
$48$		0			0
$49$	3.39898	−	5.88721i	0.485568	−	0.841029i
$50$		0			0
$51$		0			0
$52$	0.224745	+	0.389270i	0.0311665	+	0.0539820i
$53$	3.55051			0.487700			0.243850	−	0.969813i	$-0.421590\pi$
$53$	3.55051			0.487700			0.243850	+	0.969813i	$0.421590\pi$
$54$		0			0
$55$		0			0
$56$	0.224745	+	0.389270i	0.0300328	+	0.0520183i
$57$		0			0
$58$	−1.22474	+	2.12132i	−0.160817	+	0.278543i
$59$	−2.72474	+	4.71940i	−0.354732	+	0.614413i	−0.987072	−	0.160278i	$-0.948761\pi$
$59$	−2.72474	+	4.71940i	−0.354732	+	0.614413i	0.632340	+	0.774691i	$0.282094\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	4.44949			0.565086
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−0.174235	+	0.301783i	−0.0212861	+	0.0368687i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−0.174235	+	0.301783i	−0.0212861	+	0.0368687i	0.855186	+	0.518321i	$0.173443\pi$
$68$	2.44949	−	4.24264i	0.297044	−	0.514496i
$69$		0			0
$70$		0			0
$71$	−13.3485			−1.58417			−0.792086	−	0.610410i	$-0.791005\pi$
$71$	−13.3485			−1.58417			−0.792086	+	0.610410i	$0.791005\pi$
$72$		0			0
$73$	−1.00000			−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			0
$79$	−8.34847	−	14.4600i	−0.939276	−	1.62687i	−0.766825	−	0.641856i	$-0.778165\pi$
$79$	−8.34847	−	14.4600i	−0.939276	−	1.62687i	−0.172451	−	0.985018i	$-0.555169\pi$
$80$		0			0
$81$		0			0
$82$	−9.00000			−0.993884
$83$	−2.72474	−	4.71940i	−0.299080	−	0.518021i	0.676846	−	0.736125i	$-0.263346\pi$
$83$	−2.72474	−	4.71940i	−0.299080	−	0.518021i	−0.975926	+	0.218104i	$0.930013\pi$
$84$		0			0
$85$		0			0
$86$	−1.27526	+	2.20881i	−0.137514	+	0.238182i
$87$		0			0
$88$	−2.44949	−	4.24264i	−0.261116	−	0.452267i
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$	0.202041			0.0211797
$92$	−1.22474	−	2.12132i	−0.127688	−	0.221163i
$93$		0			0
$94$	−5.44949	+	9.43879i	−0.562072	+	0.973537i
$95$		0			0
$96$		0			0
$97$	−4.39898	−	7.61926i	−0.446649	−	0.773618i	0.551517	−	0.834164i	$-0.314049\pi$
$97$	−4.39898	−	7.61926i	−0.446649	−	0.773618i	−0.998165	+	0.0605456i	$0.980716\pi$
$98$	−6.79796			−0.686698
$99$		0			0
$100$		0			0
$101$	4.22474	+	7.31747i	0.420378	+	0.728116i	0.995976	−	0.0896167i	$-0.0285642\pi$
$101$	4.22474	+	7.31747i	0.420378	+	0.728116i	−0.575599	+	0.817732i	$0.695231\pi$
$102$		0			0
$103$	−8.34847	+	14.4600i	−0.822599	+	1.42478i	0.0811413	+	0.996703i	$0.474143\pi$
$103$	−8.34847	+	14.4600i	−0.822599	+	1.42478i	−0.903740	+	0.428081i	$0.859190\pi$
$104$	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	$-0.647505\pi$
$107$	−9.24745			−0.893985			−0.446992	+	0.894538i	$0.647505\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	0.224745	−	0.389270i	0.0212364	−	0.0367825i
$113$	−2.05051	+	3.55159i	−0.192896	+	0.334105i	−0.946209	−	0.323557i	$-0.895121\pi$
$113$	−2.05051	+	3.55159i	−0.192896	+	0.334105i	0.753313	+	0.657662i	$0.228455\pi$
$114$		0			0
$115$		0			0
$116$	2.44949			0.227429
$117$		0			0
$118$	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
$123$		0			0
$124$	−2.22474	−	3.85337i	−0.199788	−	0.346043i
$125$		0			0
$126$		0			0
$127$	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
$129$		0			0
$130$		0			0
$131$	−1.89898	+	3.28913i	−0.165915	+	0.287373i	−0.936980	−	0.349384i	$-0.886391\pi$
$131$	−1.89898	+	3.28913i	−0.165915	+	0.287373i	0.771065	+	0.636756i	$0.219724\pi$
$132$		0			0
$133$	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	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$		0			0
$142$	6.67423	+	11.5601i	0.560089	+	0.970103i
$143$	−2.20204			−0.184144
$144$		0			0
$145$		0			0
$146$	0.500000	+	0.866025i	0.0413803	+	0.0716728i
$147$		0			0
$148$	5.67423	−	9.82806i	0.466419	−	0.807862i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	−0.910195	−	0.414181i	$-0.864068\pi$
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	0.0964061	−	0.995342i	$-0.469265\pi$
$152$	7.44949			0.604233
$153$		0			0
$154$	−2.20204			−0.177446
$155$		0			0
$156$		0			0
$157$	9.89898	−	17.1455i	0.790025	−	1.36836i	−0.135926	−	0.990719i	$-0.543401\pi$
$157$	9.89898	−	17.1455i	0.790025	−	1.36836i	0.925951	−	0.377644i	$-0.123266\pi$
$158$	−8.34847	+	14.4600i	−0.664169	+	1.15037i
$159$		0			0
$160$		0			0
$161$	−1.10102			−0.0867726
$162$		0			0
$163$	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	−0.185584	−	0.982628i	$-0.559418\pi$
$167$	9.79796	−	16.9706i	0.758189	−	1.31322i	0.943773	−	0.330593i	$-0.107249\pi$
$168$		0			0
$169$	6.39898	+	11.0834i	0.492229	+	0.852566i
$170$		0			0
$171$		0			0
$172$	2.55051			0.194475
$173$	4.89898	+	8.48528i	0.372463	+	0.645124i	0.989944	−	0.141462i	$-0.0451802\pi$
$173$	4.89898	+	8.48528i	0.372463	+	0.645124i	−0.617481	+	0.786586i	$0.711847\pi$
$174$		0			0
$175$		0			0
$176$	−2.44949	+	4.24264i	−0.184637	+	0.319801i
$177$		0			0
$178$	−4.50000	−	7.79423i	−0.337289	−	0.584202i
$179$	−9.24745			−0.691187			−0.345593	−	0.938384i	$-0.612322\pi$
$179$	−9.24745			−0.691187			−0.345593	+	0.938384i	$0.612322\pi$
$180$		0			0
$181$	17.7980			1.32291			0.661456	−	0.749984i	$-0.269939\pi$
$181$	17.7980			1.32291			0.661456	+	0.749984i	$0.269939\pi$
$182$	−0.101021	−	0.174973i	−0.00748814	−	0.0129698i
$183$		0			0
$184$	−1.22474	+	2.12132i	−0.0902894	+	0.156386i
$185$		0			0
$186$		0			0
$187$	12.0000	+	20.7846i	0.877527	+	1.51992i
$188$	10.8990			0.794890
$189$		0			0
$190$		0			0
$191$	−0.550510	−	0.953512i	−0.0398335	−	0.0689937i	0.845421	−	0.534100i	$-0.179349\pi$
$191$	−0.550510	−	0.953512i	−0.0398335	−	0.0689937i	−0.885255	+	0.465106i	$0.846016\pi$
$192$		0			0
$193$	−10.0000	+	17.3205i	−0.719816	+	1.24676i	0.241257	+	0.970461i	$0.422440\pi$
$193$	−10.0000	+	17.3205i	−0.719816	+	1.24676i	−0.961073	+	0.276296i	$0.910893\pi$
$194$	−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	$-0.497194\pi$
$197$	0.247449			0.0176300			0.00881500	+	0.999961i	$0.497194\pi$
$198$		0			0
$199$	−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			0
$202$	4.22474	−	7.31747i	0.297252	−	0.514856i
$203$	0.550510	−	0.953512i	0.0386382	−	0.0669234i
$204$		0			0
$205$		0			0
$206$	16.6969			1.16333
$207$		0			0
$208$	−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	−0.800531	−	0.599292i	$-0.795449\pi$
$211$	1.72474	−	2.98735i	0.118736	−	0.205657i	0.919267	+	0.393634i	$0.128782\pi$
$212$	−1.77526	+	3.07483i	−0.121925	+	0.211180i
$213$		0			0
$214$	4.62372	+	8.00853i	0.316071	+	0.547452i
$215$		0			0
$216$		0			0
$217$	−2.00000			−0.135769
$218$	−2.77526	−	4.80688i	−0.187964	−	0.325563i
$219$		0			0
$220$		0			0
$221$	−1.10102	+	1.90702i	−0.0740627	+	0.128280i
$222$		0			0
$223$	−8.89898	−	15.4135i	−0.595920	−	1.03216i	−0.993416	−	0.114560i	$-0.963454\pi$
$223$	−8.89898	−	15.4135i	−0.595920	−	1.03216i	0.397497	−	0.917604i	$-0.369879\pi$
$224$	−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	$-0.0170054\pi$
$227$	6.82577	+	11.8226i	0.453042	+	0.784692i	−0.545531	+	0.838090i	$0.683672\pi$
$228$		0			0
$229$	−6.57321	+	11.3851i	−0.434370	+	0.752351i	−0.997244	−	0.0741916i	$-0.976362\pi$
$229$	−6.57321	+	11.3851i	−0.434370	+	0.752351i	0.562874	+	0.826543i	$0.309696\pi$
$230$		0			0
$231$		0			0
$232$	−1.22474	−	2.12132i	−0.0804084	−	0.139272i
$233$	23.6969			1.55244			0.776219	−	0.630463i	$-0.217135\pi$
$233$	23.6969			1.55244			0.776219	+	0.630463i	$0.217135\pi$
$234$		0			0
$235$		0			0
$236$	−2.72474	−	4.71940i	−0.177366	−	0.307207i
$237$		0			0
$238$	−1.10102	+	1.90702i	−0.0713686	+	0.123614i
$239$	7.22474	−	12.5136i	0.467330	−	0.809439i	−0.531973	−	0.846761i	$-0.678549\pi$
$239$	7.22474	−	12.5136i	0.467330	−	0.809439i	0.999303	+	0.0373219i	$0.0118827\pi$
$240$		0			0
$241$	1.60102	+	2.77305i	0.103131	+	0.178628i	0.912973	−	0.408020i	$-0.133781\pi$
$241$	1.60102	+	2.77305i	0.103131	+	0.178628i	−0.809842	+	0.586648i	$0.800447\pi$
$242$	13.0000			0.835672
$243$		0			0
$244$	8.00000			0.512148
$245$		0			0
$246$		0			0
$247$	1.67423	−	2.89986i	0.106529	−	0.184514i
$248$	−2.22474	+	3.85337i	−0.141271	+	0.244689i
$249$		0			0
$250$		0			0
$251$	0.550510			0.0347479			0.0173739	−	0.999849i	$-0.494469\pi$
$251$	0.550510			0.0347479			0.0173739	+	0.999849i	$0.494469\pi$
$252$		0			0
$253$	12.0000			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	$-0.964031\pi$
$257$	−6.39898	+	11.0834i	−0.399157	+	0.691361i	0.594465	+	0.804122i	$0.297364\pi$
$258$		0			0
$259$	−2.55051	−	4.41761i	−0.158481	−	0.274497i
$260$		0			0
$261$		0			0
$262$	3.79796			0.234639
$263$	10.2247	+	17.7098i	0.630485	+	1.09203i	0.987453	+	0.157915i	$0.0504772\pi$
$263$	10.2247	+	17.7098i	0.630485	+	1.09203i	−0.356968	+	0.934117i	$0.616189\pi$
$264$		0			0
$265$		0			0
$266$	1.67423	−	2.89986i	0.102654	−	0.177802i
$267$		0			0
$268$	−0.174235	−	0.301783i	−0.0106431	−	0.0184343i
$269$	−14.4495			−0.881001			−0.440500	−	0.897752i	$-0.645199\pi$
$269$	−14.4495			−0.881001			−0.440500	+	0.897752i	$0.645199\pi$
$270$		0			0
$271$	15.3485			0.932353			0.466177	−	0.884692i	$-0.345631\pi$
$271$	15.3485			0.932353			0.466177	+	0.884692i	$0.345631\pi$
$272$	2.44949	+	4.24264i	0.148522	+	0.257248i
$273$		0			0
$274$	1.50000	−	2.59808i	0.0906183	−	0.156956i
$275$		0			0
$276$		0			0
$277$	0.775255	+	1.34278i	0.0465806	+	0.0806799i	0.888376	−	0.459117i	$-0.151834\pi$
$277$	0.775255	+	1.34278i	0.0465806	+	0.0806799i	−0.841795	+	0.539797i	$0.818501\pi$
$278$	−4.00000			−0.239904
$279$		0			0
$280$		0			0
$281$	9.55051	+	16.5420i	0.569736	+	0.986811i	0.996592	+	0.0824916i	$0.0262878\pi$
$281$	9.55051	+	16.5420i	0.569736	+	0.986811i	−0.426856	+	0.904320i	$0.640379\pi$
$282$		0			0
$283$	6.62372	−	11.4726i	0.393740	−	0.681977i	−0.599200	−	0.800599i	$-0.704515\pi$
$283$	6.62372	−	11.4726i	0.393740	−	0.681977i	0.992939	+	0.118623i	$0.0378479\pi$
$284$	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
$288$		0			0
$289$	7.00000			0.411765
$290$		0			0
$291$		0			0
$292$	0.500000	−	0.866025i	0.0292603	−	0.0506803i
$293$	8.02270	−	13.8957i	0.468691	−	0.811797i	−0.530668	−	0.847580i	$-0.678059\pi$
$293$	8.02270	−	13.8957i	0.468691	−	0.811797i	0.999360	+	0.0357824i	$0.0113923\pi$
$294$		0			0
$295$		0			0
$296$	−11.3485			−0.659616
$297$		0			0
$298$	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
$303$		0			0
$304$	−3.72474	−	6.45145i	−0.213629	−	0.370016i
$305$		0			0
$306$		0			0
$307$	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
$309$		0			0
$310$		0			0
$311$	−0.550510	+	0.953512i	−0.0312166	+	0.0540687i	−0.881212	−	0.472722i	$-0.843271\pi$
$311$	−0.550510	+	0.953512i	−0.0312166	+	0.0540687i	0.849995	+	0.526791i	$0.176605\pi$
$312$		0			0
$313$	2.94949	+	5.10867i	0.166715	+	0.288759i	0.937263	−	0.348623i	$-0.113351\pi$
$313$	2.94949	+	5.10867i	0.166715	+	0.288759i	−0.770548	+	0.637382i	$0.780017\pi$
$314$	−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	$-0.00675166\pi$
$317$	8.57321	+	14.8492i	0.481520	+	0.834017i	−0.518255	+	0.855226i	$0.673418\pi$
$318$		0			0
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$		0			0
$321$		0			0
$322$	0.550510	+	0.953512i	0.0306787	+	0.0531371i
$323$	−36.4949			−2.03063
$324$		0			0
$325$		0			0
$326$	−3.72474	−	6.45145i	−0.206295	−	0.357313i
$327$		0			0
$328$	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	0.765507	−	0.643428i	$-0.222488\pi$
$331$	−3.17423	−	5.49794i	−0.174472	−	0.302194i	−0.939978	+	0.341234i	$0.889155\pi$
$332$	5.44949			0.299080
$333$		0			0
$334$	−19.5959			−1.07224
$335$		0			0
$336$		0			0
$337$	10.4495	−	18.0990i	0.569220	−	0.985918i	−0.427423	−	0.904052i	$-0.640579\pi$
$337$	10.4495	−	18.0990i	0.569220	−	0.985918i	0.996643	−	0.0818663i	$-0.0260881\pi$
$338$	6.39898	−	11.0834i	0.348059	−	0.602855i
$339$		0			0
$340$		0			0
$341$	21.7980			1.18043
$342$		0			0
$343$	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	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$		0			0
$352$	4.89898			0.261116
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		0			0
$355$		0			0
$356$	−4.50000	+	7.79423i	−0.238500	+	0.413093i
$357$		0			0
$358$	4.62372	+	8.00853i	0.244371	+	0.423264i
$359$	14.2020			0.749555			0.374778	−	0.927115i	$-0.377719\pi$
$359$	14.2020			0.749555			0.374778	+	0.927115i	$0.377719\pi$
$360$		0			0
$361$	36.4949			1.92078
$362$	−8.89898	−	15.4135i	−0.467720	−	0.810115i
$363$		0			0
$364$	−0.101021	+	0.174973i	−0.00529491	+	0.00917106i
$365$		0			0
$366$		0			0
$367$	6.34847	+	10.9959i	0.331387	+	0.573980i	0.982784	−	0.184757i	$-0.0591500\pi$
$367$	6.34847	+	10.9959i	0.331387	+	0.573980i	−0.651397	+	0.758737i	$0.725817\pi$
$368$	2.44949			0.127688
$369$		0			0
$370$		0			0
$371$	0.797959	+	1.38211i	0.0414280	+	0.0717553i
$372$		0			0
$373$	11.7980	−	20.4347i	0.610875	−	1.05807i	−0.380218	−	0.924897i	$-0.624151\pi$
$373$	11.7980	−	20.4347i	0.610875	−	1.05807i	0.991093	−	0.133170i	$-0.0425156\pi$
$374$	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			0
$379$	−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
$381$		0			0
$382$	−0.550510	+	0.953512i	−0.0281666	+	0.0487859i
$383$	10.7753	−	18.6633i	0.550590	−	0.953650i	−0.447642	−	0.894213i	$-0.647736\pi$
$383$	10.7753	−	18.6633i	0.550590	−	0.953650i	0.998232	−	0.0594368i	$-0.0189305\pi$
$384$		0			0
$385$		0			0
$386$	20.0000			1.01797
$387$		0			0
$388$	8.79796			0.446649
$389$	12.7980	+	22.1667i	0.648882	+	1.12390i	0.983390	+	0.181504i	$0.0580966\pi$
$389$	12.7980	+	22.1667i	0.648882	+	1.12390i	−0.334508	+	0.942393i	$0.608570\pi$
$390$		0			0
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	3.39898	−	5.88721i	0.171674	−	0.297349i
$393$		0			0
$394$	−0.123724	−	0.214297i	−0.00623314	−	0.0107961i
$395$		0			0
$396$		0			0
$397$	−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
$399$		0			0
$400$		0			0
$401$	19.3485	−	33.5125i	0.966216	−	1.67354i	0.259906	−	0.965634i	$-0.416308\pi$
$401$	19.3485	−	33.5125i	0.966216	−	1.67354i	0.706311	−	0.707902i	$-0.250358\pi$
$402$		0			0
$403$	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
$408$		0			0
$409$	−0.0505103	+	0.0874863i	−0.00249757	+	0.00432592i	−0.867271	−	0.497835i	$-0.834128\pi$
$409$	−0.0505103	+	0.0874863i	−0.00249757	+	0.00432592i	0.864774	+	0.502161i	$0.167462\pi$
$410$		0			0
$411$		0			0
$412$	−8.34847	−	14.4600i	−0.411300	−	0.712392i
$413$	−2.44949			−0.120532
$414$		0			0
$415$		0			0
$416$	0.224745	+	0.389270i	0.0110190	+	0.0190855i
$417$		0			0
$418$	−18.2474	+	31.6055i	−0.892512	+	1.54588i
$419$	−13.0732	+	22.6435i	−0.638668	+	1.10621i	0.347057	+	0.937844i	$0.387181\pi$
$419$	−13.0732	+	22.6435i	−0.638668	+	1.10621i	−0.985725	+	0.168362i	$0.946152\pi$
$420$		0			0
$421$	13.0227	+	22.5560i	0.634688	+	1.09931i	0.986581	+	0.163271i	$0.0522046\pi$
$421$	13.0227	+	22.5560i	0.634688	+	1.09931i	−0.351893	+	0.936040i	$0.614462\pi$
$422$	−3.44949			−0.167919
$423$		0			0
$424$	3.55051			0.172428
$425$		0			0
$426$		0			0
$427$	1.79796	−	3.11416i	0.0870093	−	0.150705i
$428$	4.62372	−	8.00853i	0.223496	−	0.387107i
$429$		0			0
$430$		0			0
$431$	−25.3485			−1.22099			−0.610496	−	0.792019i	$-0.709030\pi$
$431$	−25.3485			−1.22099			−0.610496	+	0.792019i	$0.709030\pi$
$432$		0			0
$433$	9.59592			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			0
$439$	−1.67423	−	2.89986i	−0.0799069	−	0.138403i	0.823303	−	0.567603i	$-0.192129\pi$
$439$	−1.67423	−	2.89986i	−0.0799069	−	0.138403i	−0.903210	+	0.429200i	$0.858796\pi$
$440$		0			0
$441$		0			0
$442$	2.20204			0.104740
$443$	4.10102	+	7.10318i	0.194845	+	0.337482i	0.946850	−	0.321676i	$-0.104246\pi$
$443$	4.10102	+	7.10318i	0.194845	+	0.337482i	−0.752004	+	0.659158i	$0.770913\pi$
$444$		0			0
$445$		0			0
$446$	−8.89898	+	15.4135i	−0.421379	+	0.729850i
$447$		0			0
$448$	0.224745	+	0.389270i	0.0106182	+	0.0183913i
$449$	28.5959			1.34952			0.674762	−	0.738035i	$-0.264246\pi$
$449$	28.5959			1.34952			0.674762	+	0.738035i	$0.264246\pi$
$450$		0			0
$451$	−44.0908			−2.07616
$452$	−2.05051	−	3.55159i	−0.0964479	−	0.167053i
$453$		0			0
$454$	6.82577	−	11.8226i	0.320349	−	0.554861i
$455$		0			0
$456$		0			0
$457$	−6.84847	−	11.8619i	−0.320358	−	0.554876i	0.660204	−	0.751086i	$-0.270470\pi$
$457$	−6.84847	−	11.8619i	−0.320358	−	0.554876i	−0.980562	+	0.196210i	$0.937136\pi$
$458$	13.1464			0.614292
$459$		0			0
$460$		0			0
$461$	2.32577	+	4.02834i	0.108322	+	0.187619i	0.915090	−	0.403249i	$-0.132119\pi$
$461$	2.32577	+	4.02834i	0.108322	+	0.187619i	−0.806769	+	0.590867i	$0.798786\pi$
$462$		0			0
$463$	2.67423	−	4.63191i	0.124282	−	0.215263i	−0.797170	−	0.603755i	$-0.793671\pi$
$463$	2.67423	−	4.63191i	0.124282	−	0.215263i	0.921452	+	0.388492i	$0.127004\pi$
$464$	−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	$-0.423038\pi$
$467$	10.3485			0.478870			0.239435	+	0.970912i	$0.423038\pi$
$468$		0			0
$469$	−0.156633			−0.00723266
$470$		0			0
$471$		0			0
$472$	−2.72474	+	4.71940i	−0.125417	+	0.217228i
$473$	−6.24745	+	10.8209i	−0.287258	+	0.497545i
$474$		0			0
$475$		0			0
$476$	2.20204			0.100930
$477$		0			0
$478$	−14.4495			−0.660904
$479$	0.123724	+	0.214297i	0.00565311	+	0.00979147i	0.868838	−	0.495096i	$-0.164867\pi$
$479$	0.123724	+	0.214297i	0.00565311	+	0.00979147i	−0.863185	+	0.504888i	$0.831534\pi$
$480$		0			0
$481$	−2.55051	+	4.41761i	−0.116293	+	0.201426i
$482$	1.60102	−	2.77305i	0.0729245	−	0.126309i
$483$		0			0
$484$	−6.50000	−	11.2583i	−0.295455	−	0.511742i
$485$		0			0
$486$		0			0
$487$	−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
$489$		0			0
$490$		0			0
$491$	−13.6237	+	23.5970i	−0.614830	+	1.06492i	0.375584	+	0.926788i	$0.377442\pi$
$491$	−13.6237	+	23.5970i	−0.614830	+	1.06492i	−0.990414	+	0.138129i	$0.955891\pi$
$492$		0			0
$493$	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
$498$		0			0
$499$	4.17423	−	7.22999i	0.186864	−	0.323659i	−0.757339	−	0.653022i	$-0.773501\pi$
$499$	4.17423	−	7.22999i	0.186864	−	0.323659i	0.944203	+	0.329364i	$0.106834\pi$
$500$		0			0
$501$		0			0
$502$	−0.275255	−	0.476756i	−0.0122852	−	0.0212787i
$503$	−21.5505			−0.960890			−0.480445	−	0.877025i	$-0.659525\pi$
$503$	−21.5505			−0.960890			−0.480445	+	0.877025i	$0.659525\pi$
$504$		0			0
$505$		0			0
$506$	−6.00000	−	10.3923i	−0.266733	−	0.461994i
$507$		0			0
$508$	−1.67423	+	2.89986i	−0.0742821	+	0.128660i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	−0.224745	−	0.389270i	−0.00994213	−	0.0172203i
$512$	1.00000			0.0441942
$513$		0			0
$514$	12.7980			0.564494
$515$		0			0
$516$		0			0
$517$	−26.6969	+	46.2405i	−1.17413	+	2.03365i
$518$	−2.55051	+	4.41761i	−0.112063	+	0.194099i
$519$		0			0
$520$		0			0
$521$	29.3939			1.28777			0.643885	−	0.765123i	$-0.277322\pi$
$521$	29.3939			1.28777			0.643885	+	0.765123i	$0.277322\pi$
$522$		0			0
$523$	−20.3485			−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
$528$		0			0
$529$	8.50000	+	14.7224i	0.369565	+	0.640106i
$530$		0			0
$531$		0			0
$532$	−3.34847			−0.145175
$533$	−2.02270	−	3.50343i	−0.0876130	−	0.151750i
$534$		0			0
$535$		0			0
$536$	−0.174235	+	0.301783i	−0.00752579	+	0.0130350i
$537$		0			0
$538$	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
$543$		0			0
$544$	2.44949	−	4.24264i	0.105021	−	0.181902i
$545$		0			0
$546$		0			0
$547$	−7.82577	−	13.5546i	−0.334606	−	0.579554i	0.648803	−	0.760956i	$-0.275270\pi$
$547$	−7.82577	−	13.5546i	−0.334606	−	0.579554i	−0.983409	+	0.181402i	$0.941936\pi$
$548$	−3.00000			−0.128154
$549$		0			0
$550$		0			0
$551$	−9.12372	−	15.8028i	−0.388684	−	0.673220i
$552$		0			0
$553$	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	$-0.840430\pi$
$557$	−41.3939			−1.75391			−0.876957	+	0.480568i	$0.840430\pi$
$558$		0			0
$559$	−1.14643			−0.0484887
$560$		0			0
$561$		0			0
$562$	9.55051	−	16.5420i	0.402864	−	0.697781i
$563$	−11.9722	+	20.7364i	−0.504568	+	0.873937i	0.495418	+	0.868655i	$0.335015\pi$
$563$	−11.9722	+	20.7364i	−0.504568	+	0.873937i	−0.999986	+	0.00528250i	$0.998319\pi$
$564$		0			0
$565$		0			0
$566$	−13.2474			−0.556832
$567$		0			0
$568$	−13.3485			−0.560089
$569$	16.8990	+	29.2699i	0.708442	+	1.22706i	0.965435	+	0.260644i	$0.0839350\pi$
$569$	16.8990	+	29.2699i	0.708442	+	1.22706i	−0.256993	+	0.966413i	$0.582732\pi$
$570$		0			0
$571$	−12.9722	+	22.4685i	−0.542869	+	0.940277i	0.455868	+	0.890047i	$0.349329\pi$
$571$	−12.9722	+	22.4685i	−0.542869	+	0.940277i	−0.998738	+	0.0502301i	$0.984005\pi$
$572$	1.10102	−	1.90702i	0.0460360	−	0.0797367i
$573$		0			0
$574$	−2.02270	−	3.50343i	−0.0844260	−	0.146230i
$575$		0			0
$576$		0			0
$577$	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
$579$		0			0
$580$		0			0
$581$	1.22474	−	2.12132i	0.0508110	−	0.0880072i
$582$		0			0
$583$	−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	−0.998206	−	0.0598679i	$-0.980932\pi$
$587$	−13.3485	−	23.1202i	−0.550950	−	0.954274i	0.447256	−	0.894406i	$-0.352401\pi$
$588$		0			0
$589$	−16.5732	+	28.7056i	−0.682887	+	1.18280i
$590$		0			0
$591$		0			0
$592$	5.67423	+	9.82806i	0.233210	+	0.403931i
$593$	7.89898			0.324372			0.162186	−	0.986760i	$-0.448146\pi$
$593$	7.89898			0.324372			0.162186	+	0.986760i	$0.448146\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	0.550510	−	0.953512i	0.0225120	−	0.0389920i
$599$	−11.3258	+	19.6168i	−0.462758	+	0.801521i	−0.999097	−	0.0424819i	$-0.986474\pi$
$599$	−11.3258	+	19.6168i	−0.462758	+	0.801521i	0.536339	+	0.844003i	$0.319807\pi$
$600$		0			0
$601$	8.24745	+	14.2850i	0.336420	+	0.582697i	0.983757	−	0.179507i	$-0.0574503\pi$
$601$	8.24745	+	14.2850i	0.336420	+	0.582697i	−0.647336	+	0.762205i	$0.724117\pi$
$602$	−1.14643			−0.0467249
$603$		0			0
$604$	20.0000			0.813788
$605$		0			0
$606$		0			0
$607$	−1.67423	+	2.89986i	−0.0679551	+	0.117702i	−0.898001	−	0.439993i	$-0.854981\pi$
$607$	−1.67423	+	2.89986i	−0.0679551	+	0.117702i	0.830046	+	0.557695i	$0.188314\pi$
$608$	−3.72474	+	6.45145i	−0.151058	+	0.261641i
$609$		0			0
$610$		0			0
$611$	−4.89898			−0.198191
$612$		0			0
$613$	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	0.0581058	−	0.998310i	$-0.481494\pi$
$617$	22.1969	−	38.4462i	0.893615	−	1.54779i	0.835509	−	0.549476i	$-0.185173\pi$
$618$		0			0
$619$	15.8712	+	27.4897i	0.637916	+	1.10490i	0.985889	+	0.167399i	$0.0535368\pi$
$619$	15.8712	+	27.4897i	0.637916	+	1.10490i	−0.347973	+	0.937505i	$0.613130\pi$
$620$		0			0
$621$		0			0
$622$	1.10102			0.0441469
$623$	2.02270	+	3.50343i	0.0810379	+	0.140362i
$624$		0			0
$625$		0			0
$626$	2.94949	−	5.10867i	0.117885	−	0.204183i
$627$		0			0
$628$	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
$633$		0			0
$634$	8.57321	−	14.8492i	0.340486	−	0.589739i
$635$		0			0
$636$		0			0
$637$	−1.52781	−	2.64624i	−0.0605339	−	0.104848i
$638$	12.0000			0.475085
$639$		0			0
$640$		0			0
$641$	−7.19694	−	12.4655i	−0.284262	−	0.492356i	0.688168	−	0.725551i	$-0.258415\pi$
$641$	−7.19694	−	12.4655i	−0.284262	−	0.492356i	−0.972430	+	0.233195i	$0.925082\pi$
$642$		0			0
$643$	8.82577	−	15.2867i	0.348054	−	0.602848i	−0.637850	−	0.770161i	$-0.720176\pi$
$643$	8.82577	−	15.2867i	0.348054	−	0.602848i	0.985904	+	0.167313i	$0.0535092\pi$
$644$	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	$-0.658143\pi$
$647$	−24.2474			−0.953266			−0.476633	+	0.879102i	$0.658143\pi$
$648$		0			0
$649$	26.6969			1.04795
$650$		0			0
$651$		0			0
$652$	−3.72474	+	6.45145i	−0.145872	+	0.252658i
$653$	9.12372	−	15.8028i	0.357039	−	0.618410i	−0.630426	−	0.776250i	$-0.717120\pi$
$653$	9.12372	−	15.8028i	0.357039	−	0.618410i	0.987465	+	0.157840i	$0.0504530\pi$
$654$		0			0
$655$		0			0
$656$	−9.00000			−0.351391
$657$		0			0
$658$	−4.89898			−0.190982
$659$	4.92679	+	8.53344i	0.191920	+	0.332416i	0.945887	−	0.324497i	$-0.105195\pi$
$659$	4.92679	+	8.53344i	0.191920	+	0.332416i	−0.753966	+	0.656913i	$0.771862\pi$
$660$		0			0
$661$	−3.69694	+	6.40329i	−0.143794	+	0.249059i	−0.928922	−	0.370274i	$-0.879264\pi$
$661$	−3.69694	+	6.40329i	−0.143794	+	0.249059i	0.785128	+	0.619333i	$0.212597\pi$
$662$	−3.17423	+	5.49794i	−0.123370	+	0.213683i
$663$		0			0
$664$	−2.72474	−	4.71940i	−0.105741	−	0.183148i
$665$		0			0
$666$		0			0
$667$	6.00000			0.232321
$668$	9.79796	+	16.9706i	0.379094	+	0.656611i
$669$		0			0
$670$		0			0
$671$	−19.5959	+	33.9411i	−0.756492	+	1.31028i
$672$		0			0
$673$	−11.3485	−	19.6561i	−0.437451	−	0.757688i	0.560041	−	0.828465i	$-0.310785\pi$
$673$	−11.3485	−	19.6561i	−0.437451	−	0.757688i	−0.997492	+	0.0707771i	$0.977452\pi$
$674$	−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	$-0.332093\pi$
$677$	−12.9217	−	22.3810i	−0.496621	−	0.860172i	−0.999992	+	0.00389777i	$0.998759\pi$
$678$		0			0
$679$	1.97730	−	3.42478i	0.0758817	−	0.131431i
$680$		0			0
$681$		0			0
$682$	−10.8990	−	18.8776i	−0.417343	−	0.722860i
$683$	−41.9444			−1.60496			−0.802479	−	0.596681i	$-0.796486\pi$
$683$	−41.9444			−1.60496			−0.802479	+	0.596681i	$0.796486\pi$
$684$		0			0
$685$		0			0
$686$	−3.10102	−	5.37113i	−0.118398	−	0.205071i
$687$		0			0
$688$	−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	−0.951271	−	0.308355i	$-0.900222\pi$
$691$	−19.5227	−	33.8143i	−0.742679	−	1.28636i	0.208593	−	0.978003i	$-0.433112\pi$
$692$	−9.79796			−0.372463
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$		0			0
$697$	−22.0454	+	38.1838i	−0.835029	+	1.44631i
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$		0			0
$700$		0			0
$701$	−33.7980			−1.27653			−0.638266	−	0.769816i	$-0.720348\pi$
$701$	−33.7980			−1.27653			−0.638266	+	0.769816i	$0.720348\pi$
$702$		0			0
$703$	−84.5403			−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
$708$		0			0
$709$	−2.22474	−	3.85337i	−0.0835520	−	0.144716i	0.821221	−	0.570610i	$-0.193293\pi$
$709$	−2.22474	−	3.85337i	−0.0835520	−	0.144716i	−0.904773	+	0.425894i	$0.859960\pi$
$710$		0			0
$711$		0			0
$712$	9.00000			0.337289
$713$	−5.44949	−	9.43879i	−0.204085	−	0.353486i
$714$		0			0
$715$		0			0
$716$	4.62372	−	8.00853i	0.172797	−	0.299293i
$717$		0			0
$718$	−7.10102	−	12.2993i	−0.265008	−	0.459007i
$719$	−7.95459			−0.296656			−0.148328	−	0.988938i	$-0.547389\pi$
$719$	−7.95459			−0.296656			−0.148328	+	0.988938i	$0.547389\pi$
$720$		0			0
$721$	−7.50510			−0.279505
$722$	−18.2474	−	31.6055i	−0.679100	−	1.17624i
$723$		0			0
$724$	−8.89898	+	15.4135i	−0.330728	+	0.572838i
$725$		0			0
$726$		0			0
$727$	8.00000	+	13.8564i	0.296704	+	0.513906i	0.975380	−	0.220532i	$-0.0707793\pi$
$727$	8.00000	+	13.8564i	0.296704	+	0.513906i	−0.678676	+	0.734438i	$0.737446\pi$
$728$	0.202041			0.00748814
$729$		0			0
$730$		0			0
$731$	6.24745	+	10.8209i	0.231070	+	0.400225i
$732$		0			0
$733$	−13.0000	+	22.5167i	−0.480166	+	0.831672i	−0.999741	−	0.0227529i	$-0.992757\pi$
$733$	−13.0000	+	22.5167i	−0.480166	+	0.831672i	0.519575	+	0.854425i	$0.326090\pi$
$734$	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
$738$		0			0
$739$	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
$741$		0			0
$742$	0.797959	−	1.38211i	0.0292940	−	0.0507387i
$743$	24.6742	−	42.7370i	0.905210	−	1.56787i	0.0845746	−	0.996417i	$-0.473047\pi$
$743$	24.6742	−	42.7370i	0.905210	−	1.56787i	0.820635	−	0.571452i	$-0.193620\pi$
$744$		0			0
$745$		0			0
$746$	−23.5959			−0.863908
$747$		0			0
$748$	−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	−0.806578	−	0.591128i	$-0.798683\pi$
$751$	2.97730	−	5.15683i	0.108643	−	0.188175i	0.915221	+	0.402953i	$0.132016\pi$
$752$	−5.44949	+	9.43879i	−0.198722	+	0.344197i
$753$		0			0
$754$	0.550510	+	0.953512i	0.0200484	+	0.0347248i
$755$		0			0
$756$		0			0
$757$	−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
$759$		0			0
$760$		0			0
$761$	6.94949	−	12.0369i	0.251919	−	0.436336i	−0.712135	−	0.702042i	$-0.752272\pi$
$761$	6.94949	−	12.0369i	0.251919	−	0.436336i	0.964054	+	0.265706i	$0.0856051\pi$
$762$		0			0
$763$	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
$768$		0			0
$769$	14.0959	−	24.4148i	0.508312	−	0.880422i	−0.491642	−	0.870797i	$-0.663603\pi$
$769$	14.0959	−	24.4148i	0.508312	−	0.880422i	0.999954	−	0.00962438i	$-0.00306358\pi$
$770$		0			0
$771$		0			0
$772$	−10.0000	−	17.3205i	−0.359908	−	0.623379i
$773$	10.4041			0.374209			0.187104	−	0.982340i	$-0.440090\pi$
$773$	10.4041			0.374209			0.187104	+	0.982340i	$0.440090\pi$
$774$		0			0
$775$		0			0
$776$	−4.39898	−	7.61926i	−0.157914	−	0.273515i
$777$		0			0
$778$	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
$783$		0			0
$784$	−6.79796			−0.242784
$785$		0			0
$786$		0			0
$787$	−17.3485	+	30.0484i	−0.618406	+	1.07111i	0.371370	+	0.928485i	$0.378888\pi$
$787$	−17.3485	+	30.0484i	−0.618406	+	1.07111i	−0.989777	+	0.142626i	$0.954445\pi$
$788$	−0.123724	+	0.214297i	−0.00440750	+	0.00763401i
$789$		0			0
$790$		0			0
$791$	−1.84337			−0.0655426
$792$		0			0
$793$	−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	0.463419	+	0.886139i	$0.346623\pi$
$797$	−15.1237	+	26.1951i	−0.535710	+	0.927877i	−0.999129	+	0.0417372i	$0.986711\pi$
$798$		0			0
$799$	26.6969	+	46.2405i	0.944470	+	1.63587i
$800$		0			0
$801$		0			0
$802$	−38.6969			−1.36644
$803$	2.44949	+	4.24264i	0.0864406	+	0.149720i
$804$		0			0
$805$		0			0
$806$	1.00000	−	1.73205i	0.0352235	−	0.0610089i
$807$		0			0
$808$	4.22474	+	7.31747i	0.148626	+	0.257428i
$809$	6.30306			0.221604			0.110802	−	0.993843i	$-0.464658\pi$
$809$	6.30306			0.221604			0.110802	+	0.993843i	$0.464658\pi$
$810$		0			0
$811$	−28.5505			−1.00254			−0.501272	−	0.865290i	$-0.667134\pi$
$811$	−28.5505			−1.00254			−0.501272	+	0.865290i	$0.667134\pi$
$812$	0.550510	+	0.953512i	0.0193191	+	0.0334617i
$813$		0			0
$814$	27.7980	−	48.1475i	0.974318	−	1.68757i
$815$		0			0
$816$		0			0
$817$	−9.50000	−	16.4545i	−0.332363	−	0.575669i
$818$	0.101021			0.00353210
$819$		0			0
$820$		0			0
$821$	13.5959	+	23.5488i	0.474501	+	0.821860i	0.999574	−	0.0291978i	$-0.00929526\pi$
$821$	13.5959	+	23.5488i	0.474501	+	0.821860i	−0.525073	+	0.851057i	$0.675962\pi$
$822$		0			0
$823$	8.55051	−	14.8099i	0.298052	−	0.516241i	−0.677638	−	0.735395i	$-0.736996\pi$
$823$	8.55051	−	14.8099i	0.298052	−	0.516241i	0.975690	+	0.219154i	$0.0703298\pi$
$824$	−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	$-0.285118\pi$
$827$	35.9444			1.24991			0.624954	+	0.780661i	$0.285118\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	0.224745	−	0.389270i	0.00779163	−	0.0134955i
$833$	−16.6515	+	28.8413i	−0.576941	+	0.999292i
$834$		0			0
$835$		0			0
$836$	36.4949			1.26220
$837$		0			0
$838$	26.1464			0.903213
$839$	18.6742	+	32.3447i	0.644706	+	1.11666i	0.984369	+	0.176117i	$0.0563536\pi$
$839$	18.6742	+	32.3447i	0.644706	+	1.11666i	−0.339663	+	0.940547i	$0.610313\pi$
$840$		0			0
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$	13.0227	−	22.5560i	0.448792	−	0.777331i
$843$		0			0
$844$	1.72474	+	2.98735i	0.0593682	+	0.102829i
$845$		0			0
$846$		0			0
$847$	−5.84337			−0.200780
$848$	−1.77526	−	3.07483i	−0.0609625	−	0.105590i
$849$		0			0
$850$		0			0
$851$	13.8990	−	24.0737i	0.476451	−	0.825237i
$852$		0			0
$853$	23.0000	+	39.8372i	0.787505	+	1.36400i	0.927491	+	0.373845i	$0.121961\pi$
$853$	23.0000	+	39.8372i	0.787505	+	1.36400i	−0.139986	+	0.990153i	$0.544706\pi$
$854$	−3.59592			−0.123050
$855$		0			0
$856$	−9.24745			−0.316071
$857$	−24.9495	−	43.2138i	−0.852258	−	1.47615i	−0.879165	−	0.476517i	$-0.841899\pi$
$857$	−24.9495	−	43.2138i	−0.852258	−	1.47615i	0.0269070	−	0.999638i	$-0.491434\pi$
$858$		0			0
$859$	10.1742	−	17.6223i	0.347140	−	0.601265i	−0.638600	−	0.769539i	$-0.720486\pi$
$859$	10.1742	−	17.6223i	0.347140	−	0.601265i	0.985740	+	0.168274i	$0.0538194\pi$
$860$		0			0
$861$		0			0
$862$	12.6742	+	21.9524i	0.431686	+	0.747702i
$863$	43.8434			1.49245			0.746223	−	0.665696i	$-0.231865\pi$
$863$	43.8434			1.49245			0.746223	+	0.665696i	$0.231865\pi$
$864$		0			0
$865$		0			0
$866$	−4.79796	−	8.31031i	−0.163041	−	0.282396i
$867$		0			0
$868$	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
$873$		0			0
$874$	18.2474			0.617229
$875$		0			0
$876$		0			0
$877$	15.8990	−	27.5378i	0.536870	−	0.929887i	−0.462200	−	0.886776i	$-0.652940\pi$
$877$	15.8990	−	27.5378i	0.536870	−	0.929887i	0.999070	−	0.0431110i	$-0.0137269\pi$
$878$	−1.67423	+	2.89986i	−0.0565027	+	0.0978655i
$879$		0			0
$880$		0			0
$881$	−38.6969			−1.30373			−0.651866	−	0.758334i	$-0.726014\pi$
$881$	−38.6969			−1.30373			−0.651866	+	0.758334i	$0.726014\pi$
$882$		0			0
$883$	47.7980			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	$-0.803873\pi$
$887$	2.75255	−	4.76756i	0.0924216	−	0.160079i	0.908530	+	0.417821i	$0.137206\pi$
$888$		0			0
$889$	0.752551	+	1.30346i	0.0252398	+	0.0437165i
$890$		0			0
$891$		0			0
$892$	17.7980			0.595920
$893$	−40.5959	−	70.3142i	−1.35849	−	2.35297i
$894$		0			0
$895$		0			0
$896$	0.224745	−	0.389270i	0.00750820	−	0.0130046i
$897$		0			0
$898$	−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
$903$		0			0
$904$	−2.05051	+	3.55159i	−0.0681990	+	0.118124i
$905$		0			0
$906$		0			0
$907$	−18.1742	−	31.4787i	−0.603466	−	1.04523i	−0.992292	−	0.123922i	$-0.960453\pi$
$907$	−18.1742	−	31.4787i	−0.603466	−	1.04523i	0.388826	−	0.921311i	$-0.372881\pi$
$908$	−13.6515			−0.453042
$909$		0			0
$910$		0			0
$911$	−3.67423	−	6.36396i	−0.121733	−	0.210847i	0.798718	−	0.601705i	$-0.205512\pi$
$911$	−3.67423	−	6.36396i	−0.121733	−	0.210847i	−0.920451	+	0.390858i	$0.872178\pi$
$912$		0			0
$913$	−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
$918$		0			0
$919$	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
$921$		0			0
$922$	2.32577	−	4.02834i	0.0765950	−	0.132666i
$923$	−3.00000	+	5.19615i	−0.0987462	+	0.171033i
$924$		0			0
$925$		0			0
$926$	−5.34847			−0.175762
$927$		0			0
$928$	2.44949			0.0804084
$929$	−25.5959	−	44.3334i	−0.839775	−	1.45453i	−0.890083	−	0.455799i	$-0.849354\pi$
$929$	−25.5959	−	44.3334i	−0.839775	−	1.45453i	0.0503079	−	0.998734i	$-0.483980\pi$
$930$		0			0
$931$	25.3207	−	43.8567i	0.829851	−	1.43734i
$932$	−11.8485	+	20.5222i	−0.388110	+	0.672225i
$933$		0			0
$934$	−5.17423	−	8.96204i	−0.169306	−	0.293247i
$935$		0			0
$936$		0			0
$937$	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
$939$		0			0
$940$		0			0
$941$	26.8207	−	46.4548i	0.874329	−	1.51438i	0.0168524	−	0.999858i	$-0.494635\pi$
$941$	26.8207	−	46.4548i	0.874329	−	1.51438i	0.857476	−	0.514524i	$-0.172031\pi$
$942$		0			0
$943$	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	$-0.0270032\pi$
$947$	13.0732	+	22.6435i	0.424822	+	0.735814i	−0.571581	+	0.820545i	$0.693670\pi$
$948$		0			0
$949$	−0.224745	+	0.389270i	−0.00729553	+	0.0126362i
$950$		0			0
$951$		0			0
$952$	−1.10102	−	1.90702i	−0.0356843	−	0.0618070i
$953$	−2.20204			−0.0713311			−0.0356656	−	0.999364i	$-0.511355\pi$
$953$	−2.20204			−0.0713311			−0.0356656	+	0.999364i	$0.511355\pi$
$954$		0			0
$955$		0			0
$956$	7.22474	+	12.5136i	0.233665	+	0.404720i
$957$		0			0
$958$	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
$963$		0			0
$964$	−3.20204			−0.103131
$965$		0			0
$966$		0			0
$967$	−16.0000	+	27.7128i	−0.514525	+	0.891184i	0.485333	+	0.874330i	$0.338699\pi$
$967$	−16.0000	+	27.7128i	−0.514525	+	0.891184i	−0.999858	+	0.0168544i	$0.994635\pi$
$968$	−6.50000	+	11.2583i	−0.208918	+	0.361856i
$969$		0			0
$970$		0			0
$971$	40.8434			1.31073			0.655363	−	0.755314i	$-0.272516\pi$
$971$	40.8434			1.31073			0.655363	+	0.755314i	$0.272516\pi$
$972$		0			0
$973$	1.79796			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	$-0.879319\pi$
$977$	−4.50000	+	7.79423i	−0.143968	+	0.249359i	0.785020	+	0.619471i	$0.212653\pi$
$978$		0			0
$979$	−22.0454	−	38.1838i	−0.704574	−	1.22036i
$980$		0			0
$981$		0			0
$982$	27.2474			0.869501
$983$	−6.55051	−	11.3458i	−0.208929	−	0.361875i	0.742449	−	0.669903i	$-0.233664\pi$
$983$	−6.55051	−	11.3458i	−0.208929	−	0.361875i	−0.951377	+	0.308028i	$0.900331\pi$
$984$		0			0
$985$		0			0
$986$	6.00000	−	10.3923i	0.191079	−	0.330958i
$987$		0			0
$988$	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
$993$		0			0
$994$	−3.00000	+	5.19615i	−0.0951542	+	0.164812i
$995$		0			0
$996$		0			0
$997$	4.02270	+	6.96753i	0.127400	+	0.220664i	0.922669	−	0.385594i	$-0.126003\pi$
$997$	4.02270	+	6.96753i	0.127400	+	0.220664i	−0.795268	+	0.606258i	$0.792670\pi$
$998$	−8.34847			−0.264266
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.224745 + 0.389270i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.224745 + 0.389270i) q^{7} +1.00000 q^{8} +(-2.44949 - 4.24264i) q^{11} +(0.224745 - 0.389270i) q^{13} +(0.224745 - 0.389270i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.89898 q^{17} +7.44949 q^{19} +(-2.44949 + 4.24264i) q^{22} +(-1.22474 + 2.12132i) q^{23} -0.449490 q^{26} -0.449490 q^{28} +(-1.22474 - 2.12132i) q^{29} +(-2.22474 + 3.85337i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.44949 + 4.24264i) q^{34} -11.3485 q^{37} +(-3.72474 - 6.45145i) q^{38} +(4.50000 - 7.79423i) q^{41} +(-1.27526 - 2.20881i) q^{43} +4.89898 q^{44} +2.44949 q^{46} +(-5.44949 - 9.43879i) q^{47} +(3.39898 - 5.88721i) q^{49} +(0.224745 + 0.389270i) q^{52} +3.55051 q^{53} +(0.224745 + 0.389270i) q^{56} +(-1.22474 + 2.12132i) q^{58} +(-2.72474 + 4.71940i) q^{59} +(-4.00000 - 6.92820i) q^{61} +4.44949 q^{62} +1.00000 q^{64} +(-0.174235 + 0.301783i) q^{67} +(2.44949 - 4.24264i) q^{68} -13.3485 q^{71} -1.00000 q^{73} +(5.67423 + 9.82806i) q^{74} +(-3.72474 + 6.45145i) q^{76} +(1.10102 - 1.90702i) q^{77} +(-8.34847 - 14.4600i) q^{79} -9.00000 q^{82} +(-2.72474 - 4.71940i) q^{83} +(-1.27526 + 2.20881i) q^{86} +(-2.44949 - 4.24264i) q^{88} +9.00000 q^{89} +0.202041 q^{91} +(-1.22474 - 2.12132i) q^{92} +(-5.44949 + 9.43879i) q^{94} +(-4.39898 - 7.61926i) q^{97} -6.79796 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} - 4 q^{13} - 4 q^{14} - 2 q^{16} + 20 q^{19} + 8 q^{26} + 8 q^{28} - 4 q^{31} - 2 q^{32} - 16 q^{37} - 10 q^{38} + 18 q^{41} - 10 q^{43} - 12 q^{47} - 6 q^{49} - 4 q^{52} + 24 q^{53} - 4 q^{56} - 6 q^{59} - 16 q^{61} + 8 q^{62} + 4 q^{64} + 14 q^{67} - 24 q^{71} - 4 q^{73} + 8 q^{74} - 10 q^{76} + 24 q^{77} - 4 q^{79} - 36 q^{82} - 6 q^{83} - 10 q^{86} + 36 q^{89} + 40 q^{91} - 12 q^{94} + 2 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 - 4 * q^13 - 4 * q^14 - 2 * q^16 + 20 * q^19 + 8 * q^26 + 8 * q^28 - 4 * q^31 - 2 * q^32 - 16 * q^37 - 10 * q^38 + 18 * q^41 - 10 * q^43 - 12 * q^47 - 6 * q^49 - 4 * q^52 + 24 * q^53 - 4 * q^56 - 6 * q^59 - 16 * q^61 + 8 * q^62 + 4 * q^64 + 14 * q^67 - 24 * q^71 - 4 * q^73 + 8 * q^74 - 10 * q^76 + 24 * q^77 - 4 * q^79 - 36 * q^82 - 6 * q^83 - 10 * q^86 + 36 * q^89 + 40 * q^91 - 12 * q^94 + 2 * q^97 + 12 * q^98

Introduction

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