LMFDB - Embedded newform 1350.2.e.n.901.1

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			901.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1350.901
Dual form			1350.2.e.n.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.224745 - 0.389270i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.224745 - 0.389270i) q^{7} -1.00000 q^{8} +(-2.44949 - 4.24264i) q^{11} +(-0.224745 + 0.389270i) q^{13} +(0.224745 - 0.389270i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.89898 q^{17} +7.44949 q^{19} +(2.44949 - 4.24264i) q^{22} +(1.22474 - 2.12132i) q^{23} -0.449490 q^{26} +0.449490 q^{28} +(-1.22474 - 2.12132i) q^{29} +(-2.22474 + 3.85337i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.44949 + 4.24264i) q^{34} +11.3485 q^{37} +(3.72474 + 6.45145i) q^{38} +(4.50000 - 7.79423i) q^{41} +(1.27526 + 2.20881i) q^{43} +4.89898 q^{44} +2.44949 q^{46} +(5.44949 + 9.43879i) q^{47} +(3.39898 - 5.88721i) q^{49} +(-0.224745 - 0.389270i) q^{52} -3.55051 q^{53} +(0.224745 + 0.389270i) q^{56} +(1.22474 - 2.12132i) q^{58} +(-2.72474 + 4.71940i) q^{59} +(-4.00000 - 6.92820i) q^{61} -4.44949 q^{62} +1.00000 q^{64} +(0.174235 - 0.301783i) q^{67} +(-2.44949 + 4.24264i) q^{68} -13.3485 q^{71} +1.00000 q^{73} +(5.67423 + 9.82806i) q^{74} +(-3.72474 + 6.45145i) q^{76} +(-1.10102 + 1.90702i) q^{77} +(-8.34847 - 14.4600i) q^{79} +9.00000 q^{82} +(2.72474 + 4.71940i) q^{83} +(-1.27526 + 2.20881i) q^{86} +(2.44949 + 4.24264i) q^{88} +9.00000 q^{89} +0.202041 q^{91} +(1.22474 + 2.12132i) q^{92} +(-5.44949 + 9.43879i) q^{94} +(4.39898 + 7.61926i) q^{97} +6.79796 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.820422	−	0.571758i	$-0.193738\pi$
$7$	−0.224745	−	0.389270i	−0.0849456	−	0.147130i	−0.905368	+	0.424628i	$0.860405\pi$
$8$	−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	−0.895508	−	0.445046i	$-0.853187\pi$
$13$	−0.224745	+	0.389270i	−0.0623330	+	0.107964i	0.833175	+	0.553010i	$0.186521\pi$
$14$	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	$0.297513\pi$
$18$		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	−0.709621	−	0.704584i	$-0.751134\pi$
$23$	1.22474	−	2.12132i	0.255377	−	0.442326i	0.964998	+	0.262258i	$0.0844671\pi$
$24$		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	$-0.117324\pi$
$37$	11.3485			1.86568			0.932838	+	0.360295i	$0.117324\pi$
$38$	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	0.946728	−	0.322034i	$-0.104366\pi$
$43$	1.27526	+	2.20881i	0.194475	+	0.336840i	−0.752254	+	0.658874i	$0.771033\pi$
$44$	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	$0.125805\pi$
$47$	5.44949	+	9.43879i	0.794890	+	1.37679i	−0.128019	+	0.991772i	$0.540862\pi$
$48$		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	$-0.578410\pi$
$53$	−3.55051			−0.487700			−0.243850	+	0.969813i	$0.578410\pi$
$54$		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	−0.855186	−	0.518321i	$-0.826557\pi$
$67$	0.174235	−	0.301783i	0.0212861	−	0.0368687i	0.876472	+	0.481452i	$0.159891\pi$
$68$	−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	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$	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	0.975926	−	0.218104i	$-0.0699871\pi$
$83$	2.72474	+	4.71940i	0.299080	+	0.518021i	−0.676846	+	0.736125i	$0.736654\pi$
$84$		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	0.998165	−	0.0605456i	$-0.0192841\pi$
$97$	4.39898	+	7.61926i	0.446649	+	0.773618i	−0.551517	+	0.834164i	$0.685951\pi$
$98$	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	$-0.525857\pi$
$103$	8.34847	−	14.4600i	0.822599	−	1.42478i	0.903740	−	0.428081i	$-0.140810\pi$
$104$	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	$0.352495\pi$
$108$		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	−0.753313	−	0.657662i	$-0.771545\pi$
$113$	2.05051	−	3.55159i	0.192896	−	0.334105i	0.946209	+	0.323557i	$0.104879\pi$
$114$		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	$-0.547465\pi$
$127$	−3.34847			−0.297129			−0.148564	+	0.988903i	$0.547465\pi$
$128$	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	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		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	$0.456599\pi$
$157$	−9.89898	+	17.1455i	−0.790025	+	1.36836i	−0.925951	+	0.377644i	$0.876734\pi$
$158$	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	$-0.594236\pi$
$163$	−7.44949			−0.583489			−0.291745	+	0.956496i	$0.594236\pi$
$164$	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	$0.440582\pi$
$167$	−9.79796	+	16.9706i	−0.758189	+	1.31322i	−0.943773	+	0.330593i	$0.892751\pi$
$168$		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	0.617481	−	0.786586i	$-0.288153\pi$
$173$	−4.89898	−	8.48528i	−0.372463	−	0.645124i	−0.989944	+	0.141462i	$0.954820\pi$
$174$		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	$-0.577560\pi$
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	0.961073	−	0.276296i	$-0.0891071\pi$
$194$	−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	$0.502806\pi$
$198$		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	$0.0365457\pi$
$223$	8.89898	+	15.4135i	0.595920	+	1.03216i	−0.397497	+	0.917604i	$0.630121\pi$
$224$	−0.449490			−0.0300328
$225$		0			0
$226$	4.10102			0.272796
$227$	−6.82577	−	11.8226i	−0.453042	−	0.784692i	0.545531	−	0.838090i	$-0.316328\pi$
$227$	−6.82577	−	11.8226i	−0.453042	−	0.784692i	−0.998573	+	0.0533987i	$0.982995\pi$
$228$		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	$-0.782865\pi$
$233$	−23.6969			−1.55244			−0.776219	+	0.630463i	$0.782865\pi$
$234$		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	−0.594465	−	0.804122i	$-0.702636\pi$
$257$	6.39898	−	11.0834i	0.399157	−	0.691361i	0.993622	+	0.112761i	$0.0359694\pi$
$258$		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	$-0.949523\pi$
$263$	−10.2247	−	17.7098i	−0.630485	−	1.09203i	0.356968	−	0.934117i	$-0.383811\pi$
$264$		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	0.841795	−	0.539797i	$-0.181499\pi$
$277$	−0.775255	−	1.34278i	−0.0465806	−	0.0806799i	−0.888376	+	0.459117i	$0.848166\pi$
$278$	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	−0.992939	−	0.118623i	$-0.962152\pi$
$283$	−6.62372	+	11.4726i	−0.393740	+	0.681977i	0.599200	+	0.800599i	$0.295485\pi$
$284$	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	−0.999360	−	0.0357824i	$-0.988608\pi$
$293$	−8.02270	+	13.8957i	−0.468691	+	0.811797i	0.530668	+	0.847580i	$0.321941\pi$
$294$		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	$-0.724265\pi$
$307$	−22.6969			−1.29538			−0.647691	+	0.761903i	$0.724265\pi$
$308$	−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	0.770548	−	0.637382i	$-0.219983\pi$
$313$	−2.94949	−	5.10867i	−0.166715	−	0.288759i	−0.937263	+	0.348623i	$0.886649\pi$
$314$	−19.7980			−1.11726
$315$		0			0
$316$	16.6969			0.939276
$317$	−8.57321	−	14.8492i	−0.481520	−	0.834017i	0.518255	−	0.855226i	$-0.326582\pi$
$317$	−8.57321	−	14.8492i	−0.481520	−	0.834017i	−0.999775	+	0.0212094i	$0.993248\pi$
$318$		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	$0.359421\pi$
$337$	−10.4495	+	18.0990i	−0.569220	+	0.985918i	−0.996643	+	0.0818663i	$0.973912\pi$
$338$	−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	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		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	0.960574	−	0.278024i	$-0.0896796\pi$
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	−0.721063	+	0.692869i	$0.756346\pi$
$354$		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	0.651397	−	0.758737i	$-0.274183\pi$
$367$	−6.34847	−	10.9959i	−0.331387	−	0.573980i	−0.982784	+	0.184757i	$0.940850\pi$
$368$	−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	$0.375849\pi$
$373$	−11.7980	+	20.4347i	−0.610875	+	1.05807i	−0.991093	+	0.133170i	$0.957484\pi$
$374$	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	$0.352264\pi$
$383$	−10.7753	+	18.6633i	−0.550590	+	0.953650i	−0.998232	+	0.0594368i	$0.981070\pi$
$384$		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	$-0.354426\pi$
$397$	17.5959			0.883114			0.441557	+	0.897233i	$0.354426\pi$
$398$	−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	$-0.574061\pi$
$433$	−9.59592			−0.461150			−0.230575	+	0.973055i	$0.574061\pi$
$434$	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	0.752004	−	0.659158i	$-0.229087\pi$
$443$	−4.10102	−	7.10318i	−0.194845	−	0.337482i	−0.946850	+	0.321676i	$0.895754\pi$
$444$		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	0.980562	−	0.196210i	$-0.0628635\pi$
$457$	6.84847	+	11.8619i	0.320358	+	0.554876i	−0.660204	+	0.751086i	$0.729530\pi$
$458$	−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	−0.921452	−	0.388492i	$-0.872996\pi$
$463$	−2.67423	+	4.63191i	−0.124282	+	0.215263i	0.797170	+	0.603755i	$0.206329\pi$
$464$	−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	$0.576962\pi$
$468$		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	$-0.313118\pi$
$487$	24.4495			1.10791			0.553956	+	0.832546i	$0.313118\pi$
$488$	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	$-0.340475\pi$
$503$	21.5505			0.960890			0.480445	+	0.877025i	$0.340475\pi$
$504$		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	$-0.353243\pi$
$523$	20.3485			0.889776			0.444888	+	0.895586i	$0.353243\pi$
$524$	−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	0.983409	−	0.181402i	$-0.0580636\pi$
$547$	7.82577	+	13.5546i	0.334606	+	0.579554i	−0.648803	+	0.760956i	$0.724730\pi$
$548$	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	$-0.159570\pi$
$557$	41.3939			1.75391			0.876957	+	0.480568i	$0.159570\pi$
$558$		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	$-0.664985\pi$
$563$	11.9722	−	20.7364i	0.504568	−	0.873937i	0.999986	−	0.00528250i	$-0.00168148\pi$
$564$		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	$-0.817921\pi$
$577$	−40.3939			−1.68162			−0.840810	+	0.541331i	$0.817921\pi$
$578$	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	$0.0190680\pi$
$587$	13.3485	+	23.1202i	0.550950	+	0.954274i	−0.447256	+	0.894406i	$0.647599\pi$
$588$		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	$-0.551854\pi$
$593$	−7.89898			−0.324372			−0.162186	+	0.986760i	$0.551854\pi$
$594$		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	−0.830046	−	0.557695i	$-0.811686\pi$
$607$	1.67423	−	2.89986i	0.0679551	−	0.117702i	0.898001	+	0.439993i	$0.145019\pi$
$608$	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	$-0.578215\pi$
$613$	−12.0454			−0.486509			−0.243255	+	0.969962i	$0.578215\pi$
$614$	−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	$0.518506\pi$
$617$	−22.1969	+	38.4462i	−0.893615	+	1.54779i	−0.835509	+	0.549476i	$0.814827\pi$
$618$		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	−0.985904	−	0.167313i	$-0.946491\pi$
$643$	−8.82577	+	15.2867i	−0.348054	+	0.602848i	0.637850	+	0.770161i	$0.279824\pi$
$644$	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	$0.341857\pi$
$648$		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	−0.987465	−	0.157840i	$-0.949547\pi$
$653$	−9.12372	+	15.8028i	−0.357039	+	0.618410i	0.630426	+	0.776250i	$0.282880\pi$
$654$		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	0.997492	−	0.0707771i	$-0.0225479\pi$
$673$	11.3485	+	19.6561i	0.437451	+	0.757688i	−0.560041	+	0.828465i	$0.689215\pi$
$674$	−20.8990			−0.804999
$675$		0			0
$676$	−12.7980			−0.492229
$677$	12.9217	+	22.3810i	0.496621	+	0.860172i	0.999992	−	0.00389777i	$-0.00124070\pi$
$677$	12.9217	+	22.3810i	0.496621	+	0.860172i	−0.503372	+	0.864070i	$0.667907\pi$
$678$		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	$-0.203514\pi$
$683$	41.9444			1.60496			0.802479	+	0.596681i	$0.203514\pi$
$684$		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	0.678676	−	0.734438i	$-0.262554\pi$
$727$	−8.00000	−	13.8564i	−0.296704	−	0.513906i	−0.975380	+	0.220532i	$0.929221\pi$
$728$	−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	−0.519575	−	0.854425i	$-0.673910\pi$
$733$	13.0000	−	22.5167i	0.480166	−	0.831672i	0.999741	+	0.0227529i	$0.00724310\pi$
$734$	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	$0.526953\pi$
$743$	−24.6742	+	42.7370i	−0.905210	+	1.56787i	−0.820635	+	0.571452i	$0.806380\pi$
$744$		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	$-0.256998\pi$
$757$	38.0454			1.38278			0.691392	+	0.722480i	$0.256998\pi$
$758$	−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	$-0.559910\pi$
$773$	−10.4041			−0.374209			−0.187104	+	0.982340i	$0.559910\pi$
$774$		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	$-0.621112\pi$
$787$	17.3485	−	30.0484i	0.618406	−	1.07111i	0.989777	−	0.142626i	$-0.0455546\pi$
$788$	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	$-0.653377\pi$
$797$	15.1237	−	26.1951i	0.535710	−	0.927877i	0.999129	−	0.0417372i	$-0.0132892\pi$
$798$		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	−0.975690	−	0.219154i	$-0.929670\pi$
$823$	−8.55051	+	14.8099i	−0.298052	+	0.516241i	0.677638	+	0.735395i	$0.263004\pi$
$824$	−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	$0.714882\pi$
$828$		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	$-0.878039\pi$
$853$	−23.0000	−	39.8372i	−0.787505	−	1.36400i	0.139986	−	0.990153i	$-0.455294\pi$
$854$	−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	$0.158101\pi$
$857$	24.9495	+	43.2138i	0.852258	+	1.47615i	−0.0269070	+	0.999638i	$0.508566\pi$
$858$		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	$-0.768135\pi$
$863$	−43.8434			−1.49245			−0.746223	+	0.665696i	$0.768135\pi$
$864$		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	$0.347060\pi$
$877$	−15.8990	+	27.5378i	−0.536870	+	0.929887i	−0.999070	+	0.0431110i	$0.986273\pi$
$878$	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	$-0.797441\pi$
$883$	−47.7980			−1.60853			−0.804265	+	0.594271i	$0.797441\pi$
$884$	−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	−0.908530	−	0.417821i	$-0.862794\pi$
$887$	−2.75255	+	4.76756i	−0.0924216	+	0.160079i	0.816108	+	0.577899i	$0.196127\pi$
$888$		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	$0.0395473\pi$
$907$	18.1742	+	31.4787i	0.603466	+	1.04523i	−0.388826	+	0.921311i	$0.627119\pi$
$908$	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	$-0.537533\pi$
$937$	−7.20204			−0.235280			−0.117640	+	0.993056i	$0.537533\pi$
$938$	−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	0.571581	−	0.820545i	$-0.306330\pi$
$947$	−13.0732	−	22.6435i	−0.424822	−	0.735814i	−0.996404	+	0.0847314i	$0.972997\pi$
$948$		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	$-0.488645\pi$
$953$	2.20204			0.0713311			0.0356656	+	0.999364i	$0.488645\pi$
$954$		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	$-0.661301\pi$
$967$	16.0000	−	27.7128i	0.514525	−	0.891184i	0.999858	−	0.0168544i	$-0.00536518\pi$
$968$	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	−0.785020	−	0.619471i	$-0.787347\pi$
$977$	4.50000	−	7.79423i	0.143968	−	0.249359i	0.928987	+	0.370111i	$0.120681\pi$
$978$		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	0.951377	−	0.308028i	$-0.0996690\pi$
$983$	6.55051	+	11.3458i	0.208929	+	0.361875i	−0.742449	+	0.669903i	$0.766336\pi$
$984$		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	0.795268	−	0.606258i	$-0.207330\pi$
$997$	−4.02270	−	6.96753i	−0.127400	−	0.220664i	−0.922669	+	0.385594i	$0.873997\pi$
$998$	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.n.901.1		4
3.2	odd	2		450.2.e.l.301.2	yes	4
5.2	odd	4		1350.2.j.g.199.2		8
5.3	odd	4		1350.2.j.g.199.3		8
5.4	even	2		1350.2.e.k.901.2		4
9.2	odd	6		450.2.e.l.151.1	✓	4
9.4	even	3		4050.2.a.bl.1.2		2
9.5	odd	6		4050.2.a.bu.1.2		2
9.7	even	3	inner	1350.2.e.n.451.1		4
15.2	even	4		450.2.j.f.49.4		8
15.8	even	4		450.2.j.f.49.1		8
15.14	odd	2		450.2.e.m.301.1	yes	4
45.2	even	12		450.2.j.f.349.1		8
45.4	even	6		4050.2.a.by.1.1		2
45.7	odd	12		1350.2.j.g.1099.3		8
45.13	odd	12		4050.2.c.w.649.3		4
45.14	odd	6		4050.2.a.br.1.1		2
45.22	odd	12		4050.2.c.w.649.2		4
45.23	even	12		4050.2.c.y.649.1		4
45.29	odd	6		450.2.e.m.151.2	yes	4
45.32	even	12		4050.2.c.y.649.4		4
45.34	even	6		1350.2.e.k.451.2		4
45.38	even	12		450.2.j.f.349.4		8
45.43	odd	12		1350.2.j.g.1099.2		8

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more