LMFDB - Embedded newform 490.2.c.b.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(99,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.2.c.b.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -3.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +3.00000 q^{6} -1.00000i q^{8} -6.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -3.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +3.00000 q^{6} -1.00000i q^{8} -6.00000 q^{9} +(2.00000 - 1.00000i) q^{10} +3.00000i q^{12} -2.00000i q^{13} +(-6.00000 + 3.00000i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -6.00000i q^{18} -2.00000 q^{19} +(1.00000 + 2.00000i) q^{20} +1.00000i q^{23} -3.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +2.00000 q^{26} +9.00000i q^{27} +1.00000 q^{29} +(-3.00000 - 6.00000i) q^{30} -10.0000 q^{31} +1.00000i q^{32} -2.00000 q^{34} +6.00000 q^{36} -8.00000i q^{37} -2.00000i q^{38} -6.00000 q^{39} +(-2.00000 + 1.00000i) q^{40} +3.00000 q^{41} -5.00000i q^{43} +(6.00000 + 12.0000i) q^{45} -1.00000 q^{46} -8.00000i q^{47} -3.00000i q^{48} +(-4.00000 - 3.00000i) q^{50} +6.00000 q^{51} +2.00000i q^{52} +6.00000i q^{53} -9.00000 q^{54} +6.00000i q^{57} +1.00000i q^{58} +2.00000 q^{59} +(6.00000 - 3.00000i) q^{60} +9.00000 q^{61} -10.0000i q^{62} -1.00000 q^{64} +(-4.00000 + 2.00000i) q^{65} -7.00000i q^{67} -2.00000i q^{68} +3.00000 q^{69} +6.00000 q^{71} +6.00000i q^{72} -10.0000i q^{73} +8.00000 q^{74} +(12.0000 + 9.00000i) q^{75} +2.00000 q^{76} -6.00000i q^{78} +10.0000 q^{79} +(-1.00000 - 2.00000i) q^{80} +9.00000 q^{81} +3.00000i q^{82} -9.00000i q^{83} +(4.00000 - 2.00000i) q^{85} +5.00000 q^{86} -3.00000i q^{87} -7.00000 q^{89} +(-12.0000 + 6.00000i) q^{90} -1.00000i q^{92} +30.0000i q^{93} +8.00000 q^{94} +(2.00000 + 4.00000i) q^{95} +3.00000 q^{96} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{5} + 6 q^{6} - 12 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^5 + 6 * q^6 - 12 * q^9	$ 2 q - 2 q^{4} - 2 q^{5} + 6 q^{6} - 12 q^{9} + 4 q^{10} - 12 q^{15} + 2 q^{16} - 4 q^{19} + 2 q^{20} - 6 q^{24} - 6 q^{25} + 4 q^{26} + 2 q^{29} - 6 q^{30} - 20 q^{31} - 4 q^{34} + 12 q^{36} - 12 q^{39} - 4 q^{40} + 6 q^{41} + 12 q^{45} - 2 q^{46} - 8 q^{50} + 12 q^{51} - 18 q^{54} + 4 q^{59} + 12 q^{60} + 18 q^{61} - 2 q^{64} - 8 q^{65} + 6 q^{69} + 12 q^{71} + 16 q^{74} + 24 q^{75} + 4 q^{76} + 20 q^{79} - 2 q^{80} + 18 q^{81} + 8 q^{85} + 10 q^{86} - 14 q^{89} - 24 q^{90} + 16 q^{94} + 4 q^{95} + 6 q^{96}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^5 + 6 * q^6 - 12 * q^9 + 4 * q^10 - 12 * q^15 + 2 * q^16 - 4 * q^19 + 2 * q^20 - 6 * q^24 - 6 * q^25 + 4 * q^26 + 2 * q^29 - 6 * q^30 - 20 * q^31 - 4 * q^34 + 12 * q^36 - 12 * q^39 - 4 * q^40 + 6 * q^41 + 12 * q^45 - 2 * q^46 - 8 * q^50 + 12 * q^51 - 18 * q^54 + 4 * q^59 + 12 * q^60 + 18 * q^61 - 2 * q^64 - 8 * q^65 + 6 * q^69 + 12 * q^71 + 16 * q^74 + 24 * q^75 + 4 * q^76 + 20 * q^79 - 2 * q^80 + 18 * q^81 + 8 * q^85 + 10 * q^86 - 14 * q^89 - 24 * q^90 + 16 * q^94 + 4 * q^95 + 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	3.00000i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$		−	3.00000i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$4$	−1.00000			−0.500000
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$	3.00000			1.22474
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−6.00000			−2.00000
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$			3.00000i			0.866025i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		0			0
$15$	−6.00000	+	3.00000i	−1.54919	+	0.774597i
$16$	1.00000			0.250000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		−	6.00000i		−	1.41421i
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	1.00000	+	2.00000i	0.223607	+	0.447214i
$21$		0			0
$22$		0			0
$23$			1.00000i			0.208514i	0.994550	+	0.104257i	$0.0332465\pi$
$23$			1.00000i			0.208514i	−0.994550	+	0.104257i	$0.966753\pi$
$24$	−3.00000			−0.612372
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	2.00000			0.392232
$27$			9.00000i			1.73205i
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$	−3.00000	−	6.00000i	−0.547723	−	1.09545i
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	6.00000			1.00000
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$		−	2.00000i		−	0.324443i
$39$	−6.00000			−0.960769
$40$	−2.00000	+	1.00000i	−0.316228	+	0.158114i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$		−	5.00000i		−	0.762493i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$		−	5.00000i		−	0.762493i	0.924473	−	0.381246i	$-0.124505\pi$
$44$		0			0
$45$	6.00000	+	12.0000i	0.894427	+	1.78885i
$46$	−1.00000			−0.147442
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		−	3.00000i		−	0.433013i
$49$		0			0
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	6.00000			0.840168
$52$			2.00000i			0.277350i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	−9.00000			−1.22474
$55$		0			0
$56$		0			0
$57$			6.00000i			0.794719i
$58$			1.00000i			0.131306i
$59$	2.00000			0.260378			0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000			0.260378			0.130189	+	0.991489i	$0.458442\pi$
$60$	6.00000	−	3.00000i	0.774597	−	0.387298i
$61$	9.00000			1.15233			0.576166	−	0.817333i	$-0.304548\pi$
$61$	9.00000			1.15233			0.576166	+	0.817333i	$0.304548\pi$
$62$		−	10.0000i		−	1.27000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.00000	+	2.00000i	−0.496139	+	0.248069i
$66$		0			0
$67$		−	7.00000i		−	0.855186i	−0.903971	−	0.427593i	$-0.859362\pi$
$67$		−	7.00000i		−	0.855186i	0.903971	−	0.427593i	$-0.140638\pi$
$68$		−	2.00000i		−	0.242536i
$69$	3.00000			0.361158
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$			6.00000i			0.707107i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$	8.00000			0.929981
$75$	12.0000	+	9.00000i	1.38564	+	1.03923i
$76$	2.00000			0.229416
$77$		0			0
$78$		−	6.00000i		−	0.679366i
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$	9.00000			1.00000
$82$			3.00000i			0.331295i
$83$		−	9.00000i		−	0.987878i	−0.869496	−	0.493939i	$-0.835557\pi$
$83$		−	9.00000i		−	0.987878i	0.869496	−	0.493939i	$-0.164443\pi$
$84$		0			0
$85$	4.00000	−	2.00000i	0.433861	−	0.216930i
$86$	5.00000			0.539164
$87$		−	3.00000i		−	0.321634i
$88$		0			0
$89$	−7.00000			−0.741999			−0.370999	−	0.928633i	$-0.620985\pi$
$89$	−7.00000			−0.741999			−0.370999	+	0.928633i	$0.620985\pi$
$90$	−12.0000	+	6.00000i	−1.26491	+	0.632456i
$91$		0			0
$92$		−	1.00000i		−	0.104257i
$93$			30.0000i			3.11086i
$94$	8.00000			0.825137
$95$	2.00000	+	4.00000i	0.205196	+	0.410391i
$96$	3.00000			0.306186
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$		0			0
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	15.0000			1.49256			0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000			1.49256			0.746278	+	0.665635i	$0.231839\pi$
$102$			6.00000i			0.594089i
$103$		−	11.0000i		−	1.08386i	−0.840423	−	0.541931i	$-0.817693\pi$
$103$		−	11.0000i		−	1.08386i	0.840423	−	0.541931i	$-0.182307\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$		−	7.00000i		−	0.676716i	−0.941018	−	0.338358i	$-0.890129\pi$
$107$		−	7.00000i		−	0.676716i	0.941018	−	0.338358i	$-0.109871\pi$
$108$		−	9.00000i		−	0.866025i
$109$	−5.00000			−0.478913			−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000			−0.478913			−0.239457	+	0.970907i	$0.576969\pi$
$110$		0			0
$111$	−24.0000			−2.27798
$112$		0			0
$113$			10.0000i			0.940721i	0.882474	+	0.470360i	$0.155876\pi$
$113$			10.0000i			0.940721i	−0.882474	+	0.470360i	$0.844124\pi$
$114$	−6.00000			−0.561951
$115$	2.00000	−	1.00000i	0.186501	−	0.0932505i
$116$	−1.00000			−0.0928477
$117$			12.0000i			1.10940i
$118$			2.00000i			0.184115i
$119$		0			0
$120$	3.00000	+	6.00000i	0.273861	+	0.547723i
$121$	−11.0000			−1.00000
$122$			9.00000i			0.814822i
$123$		−	9.00000i		−	0.811503i
$124$	10.0000			0.898027
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−15.0000			−1.32068
$130$	−2.00000	−	4.00000i	−0.175412	−	0.350823i
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$		0			0
$133$		0			0
$134$	7.00000			0.604708
$135$	18.0000	−	9.00000i	1.54919	−	0.774597i
$136$	2.00000			0.171499
$137$			16.0000i			1.36697i	0.729964	+	0.683486i	$0.239537\pi$
$137$			16.0000i			1.36697i	−0.729964	+	0.683486i	$0.760463\pi$
$138$			3.00000i			0.255377i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−24.0000			−2.02116
$142$			6.00000i			0.503509i
$143$		0			0
$144$	−6.00000			−0.500000
$145$	−1.00000	−	2.00000i	−0.0830455	−	0.166091i
$146$	10.0000			0.827606
$147$		0			0
$148$			8.00000i			0.657596i
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$	−9.00000	+	12.0000i	−0.734847	+	0.979796i
$151$	6.00000			0.488273			0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000			0.488273			0.244137	+	0.969741i	$0.421495\pi$
$152$			2.00000i			0.162221i
$153$		−	12.0000i		−	0.970143i
$154$		0			0
$155$	10.0000	+	20.0000i	0.803219	+	1.60644i
$156$	6.00000			0.480384
$157$			12.0000i			0.957704i	0.877896	+	0.478852i	$0.158947\pi$
$157$			12.0000i			0.957704i	−0.877896	+	0.478852i	$0.841053\pi$
$158$			10.0000i			0.795557i
$159$	18.0000			1.42749
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$		0			0
$162$			9.00000i			0.707107i
$163$		−	12.0000i		−	0.939913i	−0.882690	−	0.469956i	$-0.844270\pi$
$163$		−	12.0000i		−	0.939913i	0.882690	−	0.469956i	$-0.155730\pi$
$164$	−3.00000			−0.234261
$165$		0			0
$166$	9.00000			0.698535
$167$			9.00000i			0.696441i	0.937413	+	0.348220i	$0.113214\pi$
$167$			9.00000i			0.696441i	−0.937413	+	0.348220i	$0.886786\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	2.00000	+	4.00000i	0.153393	+	0.306786i
$171$	12.0000			0.917663
$172$			5.00000i			0.381246i
$173$			12.0000i			0.912343i	0.889892	+	0.456172i	$0.150780\pi$
$173$			12.0000i			0.912343i	−0.889892	+	0.456172i	$0.849220\pi$
$174$	3.00000			0.227429
$175$		0			0
$176$		0			0
$177$		−	6.00000i		−	0.450988i
$178$		−	7.00000i		−	0.524672i
$179$	26.0000			1.94333			0.971666	−	0.236360i	$-0.0759544\pi$
$179$	26.0000			1.94333			0.971666	+	0.236360i	$0.0759544\pi$
$180$	−6.00000	−	12.0000i	−0.447214	−	0.894427i
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$		0			0
$183$		−	27.0000i		−	1.99590i
$184$	1.00000			0.0737210
$185$	−16.0000	+	8.00000i	−1.17634	+	0.588172i
$186$	−30.0000			−2.19971
$187$		0			0
$188$			8.00000i			0.583460i
$189$		0			0
$190$	−4.00000	+	2.00000i	−0.290191	+	0.145095i
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$			3.00000i			0.216506i
$193$		−	20.0000i		−	1.43963i	−0.694165	−	0.719816i	$-0.744226\pi$
$193$		−	20.0000i		−	1.43963i	0.694165	−	0.719816i	$-0.255774\pi$
$194$		0			0
$195$	6.00000	+	12.0000i	0.429669	+	0.859338i
$196$		0			0
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$		0			0
$199$	12.0000			0.850657			0.425329	−	0.905039i	$-0.360158\pi$
$199$	12.0000			0.850657			0.425329	+	0.905039i	$0.360158\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$	−21.0000			−1.48123
$202$			15.0000i			1.05540i
$203$		0			0
$204$	−6.00000			−0.420084
$205$	−3.00000	−	6.00000i	−0.209529	−	0.419058i
$206$	11.0000			0.766406
$207$		−	6.00000i		−	0.417029i
$208$		−	2.00000i		−	0.138675i
$209$		0			0
$210$		0			0
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$		−	6.00000i		−	0.412082i
$213$		−	18.0000i		−	1.23334i
$214$	7.00000			0.478510
$215$	−10.0000	+	5.00000i	−0.681994	+	0.340997i
$216$	9.00000			0.612372
$217$		0			0
$218$		−	5.00000i		−	0.338643i
$219$	−30.0000			−2.02721
$220$		0			0
$221$	4.00000			0.269069
$222$		−	24.0000i		−	1.61077i
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		0			0
$225$	18.0000	−	24.0000i	1.20000	−	1.60000i
$226$	−10.0000			−0.665190
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	6.00000i		−	0.397360i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	1.00000	+	2.00000i	0.0659380	+	0.131876i
$231$		0			0
$232$		−	1.00000i		−	0.0656532i
$233$			14.0000i			0.917170i	0.888650	+	0.458585i	$0.151644\pi$
$233$			14.0000i			0.917170i	−0.888650	+	0.458585i	$0.848356\pi$
$234$	−12.0000			−0.784465
$235$	−16.0000	+	8.00000i	−1.04372	+	0.521862i
$236$	−2.00000			−0.130189
$237$		−	30.0000i		−	1.94871i
$238$		0			0
$239$	10.0000			0.646846			0.323423	−	0.946254i	$-0.395166\pi$
$239$	10.0000			0.646846			0.323423	+	0.946254i	$0.395166\pi$
$240$	−6.00000	+	3.00000i	−0.387298	+	0.193649i
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		−	11.0000i		−	0.707107i
$243$		0			0
$244$	−9.00000			−0.576166
$245$		0			0
$246$	9.00000			0.573819
$247$			4.00000i			0.254514i
$248$			10.0000i			0.635001i
$249$	−27.0000			−1.71106
$250$	−2.00000	+	11.0000i	−0.126491	+	0.695701i
$251$	10.0000			0.631194			0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000			0.631194			0.315597	+	0.948893i	$0.397795\pi$
$252$		0			0
$253$		0			0
$254$	8.00000			0.501965
$255$	−6.00000	−	12.0000i	−0.375735	−	0.751469i
$256$	1.00000			0.0625000
$257$		−	12.0000i		−	0.748539i	−0.927320	−	0.374270i	$-0.877893\pi$
$257$		−	12.0000i		−	0.748539i	0.927320	−	0.374270i	$-0.122107\pi$
$258$		−	15.0000i		−	0.933859i
$259$		0			0
$260$	4.00000	−	2.00000i	0.248069	−	0.124035i
$261$	−6.00000			−0.371391
$262$		−	20.0000i		−	1.23560i
$263$		−	21.0000i		−	1.29492i	−0.762101	−	0.647458i	$-0.775832\pi$
$263$		−	21.0000i		−	1.29492i	0.762101	−	0.647458i	$-0.224168\pi$
$264$		0			0
$265$	12.0000	−	6.00000i	0.737154	−	0.368577i
$266$		0			0
$267$			21.0000i			1.28518i
$268$			7.00000i			0.427593i
$269$	5.00000			0.304855			0.152428	−	0.988315i	$-0.451291\pi$
$269$	5.00000			0.304855			0.152428	+	0.988315i	$0.451291\pi$
$270$	9.00000	+	18.0000i	0.547723	+	1.09545i
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	−16.0000			−0.966595
$275$		0			0
$276$	−3.00000			−0.180579
$277$		−	26.0000i		−	1.56219i	−0.624413	−	0.781094i	$-0.714662\pi$
$277$		−	26.0000i		−	1.56219i	0.624413	−	0.781094i	$-0.285338\pi$
$278$		−	8.00000i		−	0.479808i
$279$	60.0000			3.59211
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		−	24.0000i		−	1.42918i
$283$			8.00000i			0.475551i	0.971320	+	0.237775i	$0.0764182\pi$
$283$			8.00000i			0.475551i	−0.971320	+	0.237775i	$0.923582\pi$
$284$	−6.00000			−0.356034
$285$	12.0000	−	6.00000i	0.710819	−	0.355409i
$286$		0			0
$287$		0			0
$288$		−	6.00000i		−	0.353553i
$289$	13.0000			0.764706
$290$	2.00000	−	1.00000i	0.117444	−	0.0587220i
$291$		0			0
$292$			10.0000i			0.585206i
$293$			24.0000i			1.40209i	0.713115	+	0.701047i	$0.247284\pi$
$293$			24.0000i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$		0			0
$295$	−2.00000	−	4.00000i	−0.116445	−	0.232889i
$296$	−8.00000			−0.464991
$297$		0			0
$298$			15.0000i			0.868927i
$299$	2.00000			0.115663
$300$	−12.0000	−	9.00000i	−0.692820	−	0.519615i
$301$		0			0
$302$			6.00000i			0.345261i
$303$		−	45.0000i		−	2.58518i
$304$	−2.00000			−0.114708
$305$	−9.00000	−	18.0000i	−0.515339	−	1.03068i
$306$	12.0000			0.685994
$307$			19.0000i			1.08439i	0.840254	+	0.542194i	$0.182406\pi$
$307$			19.0000i			1.08439i	−0.840254	+	0.542194i	$0.817594\pi$
$308$		0			0
$309$	−33.0000			−1.87730
$310$	−20.0000	+	10.0000i	−1.13592	+	0.567962i
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$			6.00000i			0.339683i
$313$			8.00000i			0.452187i	0.974106	+	0.226093i	$0.0725954\pi$
$313$			8.00000i			0.452187i	−0.974106	+	0.226093i	$0.927405\pi$
$314$	−12.0000			−0.677199
$315$		0			0
$316$	−10.0000			−0.562544
$317$			22.0000i			1.23564i	0.786318	+	0.617822i	$0.211985\pi$
$317$			22.0000i			1.23564i	−0.786318	+	0.617822i	$0.788015\pi$
$318$			18.0000i			1.00939i
$319$		0			0
$320$	1.00000	+	2.00000i	0.0559017	+	0.111803i
$321$	−21.0000			−1.17211
$322$		0			0
$323$		−	4.00000i		−	0.222566i
$324$	−9.00000			−0.500000
$325$	8.00000	+	6.00000i	0.443760	+	0.332820i
$326$	12.0000			0.664619
$327$			15.0000i			0.829502i
$328$		−	3.00000i		−	0.165647i
$329$		0			0
$330$		0			0
$331$	14.0000			0.769510			0.384755	−	0.923019i	$-0.374286\pi$
$331$	14.0000			0.769510			0.384755	+	0.923019i	$0.374286\pi$
$332$			9.00000i			0.493939i
$333$			48.0000i			2.63038i
$334$	−9.00000			−0.492458
$335$	−14.0000	+	7.00000i	−0.764902	+	0.382451i
$336$		0			0
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$			9.00000i			0.489535i
$339$	30.0000			1.62938
$340$	−4.00000	+	2.00000i	−0.216930	+	0.108465i
$341$		0			0
$342$			12.0000i			0.648886i
$343$		0			0
$344$	−5.00000			−0.269582
$345$	−3.00000	−	6.00000i	−0.161515	−	0.323029i
$346$	−12.0000			−0.645124
$347$			21.0000i			1.12734i	0.826000	+	0.563670i	$0.190611\pi$
$347$			21.0000i			1.12734i	−0.826000	+	0.563670i	$0.809389\pi$
$348$			3.00000i			0.160817i
$349$	−9.00000			−0.481759			−0.240879	−	0.970555i	$-0.577436\pi$
$349$	−9.00000			−0.481759			−0.240879	+	0.970555i	$0.577436\pi$
$350$		0			0
$351$	18.0000			0.960769
$352$		0			0
$353$		−	6.00000i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$		−	6.00000i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$	6.00000			0.318896
$355$	−6.00000	−	12.0000i	−0.318447	−	0.636894i
$356$	7.00000			0.370999
$357$		0			0
$358$			26.0000i			1.37414i
$359$	14.0000			0.738892			0.369446	−	0.929252i	$-0.379548\pi$
$359$	14.0000			0.738892			0.369446	+	0.929252i	$0.379548\pi$
$360$	12.0000	−	6.00000i	0.632456	−	0.316228i
$361$	−15.0000			−0.789474
$362$		−	5.00000i		−	0.262794i
$363$			33.0000i			1.73205i
$364$		0			0
$365$	−20.0000	+	10.0000i	−1.04685	+	0.523424i
$366$	27.0000			1.41131
$367$			23.0000i			1.20059i	0.799779	+	0.600295i	$0.204950\pi$
$367$			23.0000i			1.20059i	−0.799779	+	0.600295i	$0.795050\pi$
$368$			1.00000i			0.0521286i
$369$	−18.0000			−0.937043
$370$	−8.00000	−	16.0000i	−0.415900	−	0.831800i
$371$		0			0
$372$		−	30.0000i		−	1.55543i
$373$		−	8.00000i		−	0.414224i	−0.978317	−	0.207112i	$-0.933593\pi$
$373$		−	8.00000i		−	0.414224i	0.978317	−	0.207112i	$-0.0664065\pi$
$374$		0			0
$375$	6.00000	−	33.0000i	0.309839	−	1.70411i
$376$	−8.00000			−0.412568
$377$		−	2.00000i		−	0.103005i
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	−2.00000	−	4.00000i	−0.102598	−	0.205196i
$381$	−24.0000			−1.22956
$382$		−	20.0000i		−	1.02329i
$383$		−	9.00000i		−	0.459879i	−0.973205	−	0.229939i	$-0.926147\pi$
$383$		−	9.00000i		−	0.459879i	0.973205	−	0.229939i	$-0.0738528\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	20.0000			1.01797
$387$			30.0000i			1.52499i
$388$		0			0
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$	−12.0000	+	6.00000i	−0.607644	+	0.303822i
$391$	−2.00000			−0.101144
$392$		0			0
$393$			60.0000i			3.02660i
$394$	8.00000			0.403034
$395$	−10.0000	−	20.0000i	−0.503155	−	1.00631i
$396$		0			0
$397$			32.0000i			1.60603i	0.595956	+	0.803017i	$0.296773\pi$
$397$			32.0000i			1.60603i	−0.595956	+	0.803017i	$0.703227\pi$
$398$			12.0000i			0.601506i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	3.00000			0.149813			0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000			0.149813			0.0749064	+	0.997191i	$0.476134\pi$
$402$		−	21.0000i		−	1.04738i
$403$			20.0000i			0.996271i
$404$	−15.0000			−0.746278
$405$	−9.00000	−	18.0000i	−0.447214	−	0.894427i
$406$		0			0
$407$		0			0
$408$		−	6.00000i		−	0.297044i
$409$	−17.0000			−0.840596			−0.420298	−	0.907386i	$-0.638074\pi$
$409$	−17.0000			−0.840596			−0.420298	+	0.907386i	$0.638074\pi$
$410$	6.00000	−	3.00000i	0.296319	−	0.148159i
$411$	48.0000			2.36767
$412$			11.0000i			0.541931i
$413$		0			0
$414$	6.00000			0.294884
$415$	−18.0000	+	9.00000i	−0.883585	+	0.441793i
$416$	2.00000			0.0980581
$417$			24.0000i			1.17529i
$418$		0			0
$419$	−40.0000			−1.95413			−0.977064	−	0.212946i	$-0.931694\pi$
$419$	−40.0000			−1.95413			−0.977064	+	0.212946i	$0.931694\pi$
$420$		0			0
$421$	31.0000			1.51085			0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000			1.51085			0.755424	+	0.655237i	$0.227431\pi$
$422$		−	18.0000i		−	0.876226i
$423$			48.0000i			2.33384i
$424$	6.00000			0.291386
$425$	−8.00000	−	6.00000i	−0.388057	−	0.291043i
$426$	18.0000			0.872103
$427$		0			0
$428$			7.00000i			0.338358i
$429$		0			0
$430$	−5.00000	−	10.0000i	−0.241121	−	0.482243i
$431$	32.0000			1.54139			0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000			1.54139			0.770693	+	0.637207i	$0.219910\pi$
$432$			9.00000i			0.433013i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$		0			0
$435$	−6.00000	+	3.00000i	−0.287678	+	0.143839i
$436$	5.00000			0.239457
$437$		−	2.00000i		−	0.0956730i
$438$		−	30.0000i		−	1.43346i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$		0			0
$442$			4.00000i			0.190261i
$443$			3.00000i			0.142534i	0.997457	+	0.0712672i	$0.0227043\pi$
$443$			3.00000i			0.142534i	−0.997457	+	0.0712672i	$0.977296\pi$
$444$	24.0000			1.13899
$445$	7.00000	+	14.0000i	0.331832	+	0.663664i
$446$	8.00000			0.378811
$447$		−	45.0000i		−	2.12843i
$448$		0			0
$449$	−23.0000			−1.08544			−0.542719	−	0.839915i	$-0.682605\pi$
$449$	−23.0000			−1.08544			−0.542719	+	0.839915i	$0.682605\pi$
$450$	24.0000	+	18.0000i	1.13137	+	0.848528i
$451$		0			0
$452$		−	10.0000i		−	0.470360i
$453$		−	18.0000i		−	0.845714i
$454$	12.0000			0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$			32.0000i			1.49690i	0.663193	+	0.748448i	$0.269201\pi$
$457$			32.0000i			1.49690i	−0.663193	+	0.748448i	$0.730799\pi$
$458$			10.0000i			0.467269i
$459$	−18.0000			−0.840168
$460$	−2.00000	+	1.00000i	−0.0932505	+	0.0466252i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$		−	25.0000i		−	1.16185i	−0.813958	−	0.580924i	$-0.802691\pi$
$463$		−	25.0000i		−	1.16185i	0.813958	−	0.580924i	$-0.197309\pi$
$464$	1.00000			0.0464238
$465$	60.0000	−	30.0000i	2.78243	−	1.39122i
$466$	−14.0000			−0.648537
$467$		−	1.00000i		−	0.0462745i	−0.999732	−	0.0231372i	$-0.992635\pi$
$467$		−	1.00000i		−	0.0462745i	0.999732	−	0.0231372i	$-0.00736547\pi$
$468$		−	12.0000i		−	0.554700i
$469$		0			0
$470$	−8.00000	−	16.0000i	−0.369012	−	0.738025i
$471$	36.0000			1.65879
$472$		−	2.00000i		−	0.0920575i
$473$		0			0
$474$	30.0000			1.37795
$475$	6.00000	−	8.00000i	0.275299	−	0.367065i
$476$		0			0
$477$		−	36.0000i		−	1.64833i
$478$			10.0000i			0.457389i
$479$	18.0000			0.822441			0.411220	−	0.911536i	$-0.365103\pi$
$479$	18.0000			0.822441			0.411220	+	0.911536i	$0.365103\pi$
$480$	−3.00000	−	6.00000i	−0.136931	−	0.273861i
$481$	−16.0000			−0.729537
$482$		−	18.0000i		−	0.819878i
$483$		0			0
$484$	11.0000			0.500000
$485$		0			0
$486$		0			0
$487$			4.00000i			0.181257i	0.995885	+	0.0906287i	$0.0288876\pi$
$487$			4.00000i			0.181257i	−0.995885	+	0.0906287i	$0.971112\pi$
$488$		−	9.00000i		−	0.407411i
$489$	−36.0000			−1.62798
$490$		0			0
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$			9.00000i			0.405751i
$493$			2.00000i			0.0900755i
$494$	−4.00000			−0.179969
$495$		0			0
$496$	−10.0000			−0.449013
$497$		0			0
$498$		−	27.0000i		−	1.20990i
$499$	−16.0000			−0.716258			−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000			−0.716258			−0.358129	+	0.933672i	$0.616585\pi$
$500$	−11.0000	−	2.00000i	−0.491935	−	0.0894427i
$501$	27.0000			1.20627
$502$			10.0000i			0.446322i
$503$		−	5.00000i		−	0.222939i	−0.993768	−	0.111469i	$-0.964444\pi$
$503$		−	5.00000i		−	0.222939i	0.993768	−	0.111469i	$-0.0355557\pi$
$504$		0			0
$505$	−15.0000	−	30.0000i	−0.667491	−	1.33498i
$506$		0			0
$507$		−	27.0000i		−	1.19911i
$508$			8.00000i			0.354943i
$509$	35.0000			1.55135			0.775674	−	0.631134i	$-0.217410\pi$
$509$	35.0000			1.55135			0.775674	+	0.631134i	$0.217410\pi$
$510$	12.0000	−	6.00000i	0.531369	−	0.265684i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		−	18.0000i		−	0.794719i
$514$	12.0000			0.529297
$515$	−22.0000	+	11.0000i	−0.969436	+	0.484718i
$516$	15.0000			0.660338
$517$		0			0
$518$		0			0
$519$	36.0000			1.58022
$520$	2.00000	+	4.00000i	0.0877058	+	0.175412i
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		−	6.00000i		−	0.262613i
$523$			4.00000i			0.174908i	0.996169	+	0.0874539i	$0.0278730\pi$
$523$			4.00000i			0.174908i	−0.996169	+	0.0874539i	$0.972127\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	21.0000			0.915644
$527$		−	20.0000i		−	0.871214i
$528$		0			0
$529$	22.0000			0.956522
$530$	6.00000	+	12.0000i	0.260623	+	0.521247i
$531$	−12.0000			−0.520756
$532$		0			0
$533$		−	6.00000i		−	0.259889i
$534$	−21.0000			−0.908759
$535$	−14.0000	+	7.00000i	−0.605273	+	0.302636i
$536$	−7.00000			−0.302354
$537$		−	78.0000i		−	3.36595i
$538$			5.00000i			0.215565i
$539$		0			0
$540$	−18.0000	+	9.00000i	−0.774597	+	0.387298i
$541$	5.00000			0.214967			0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000			0.214967			0.107483	+	0.994207i	$0.465721\pi$
$542$		−	6.00000i		−	0.257722i
$543$			15.0000i			0.643712i
$544$	−2.00000			−0.0857493
$545$	5.00000	+	10.0000i	0.214176	+	0.428353i
$546$		0			0
$547$			37.0000i			1.58201i	0.611812	+	0.791003i	$0.290441\pi$
$547$			37.0000i			1.58201i	−0.611812	+	0.791003i	$0.709559\pi$
$548$		−	16.0000i		−	0.683486i
$549$	−54.0000			−2.30466
$550$		0			0
$551$	−2.00000			−0.0852029
$552$		−	3.00000i		−	0.127688i
$553$		0			0
$554$	26.0000			1.10463
$555$	24.0000	+	48.0000i	1.01874	+	2.03749i
$556$	8.00000			0.339276
$557$		−	4.00000i		−	0.169485i	−0.996403	−	0.0847427i	$-0.972993\pi$
$557$		−	4.00000i		−	0.169485i	0.996403	−	0.0847427i	$-0.0270068\pi$
$558$			60.0000i			2.54000i
$559$	−10.0000			−0.422955
$560$		0			0
$561$		0			0
$562$			18.0000i			0.759284i
$563$			11.0000i			0.463595i	0.972764	+	0.231797i	$0.0744606\pi$
$563$			11.0000i			0.463595i	−0.972764	+	0.231797i	$0.925539\pi$
$564$	24.0000			1.01058
$565$	20.0000	−	10.0000i	0.841406	−	0.420703i
$566$	−8.00000			−0.336265
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$	6.00000	+	12.0000i	0.251312	+	0.502625i
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$		0			0
$573$			60.0000i			2.50654i
$574$		0			0
$575$	−4.00000	−	3.00000i	−0.166812	−	0.125109i
$576$	6.00000			0.250000
$577$			16.0000i			0.666089i	0.942911	+	0.333044i	$0.108076\pi$
$577$			16.0000i			0.666089i	−0.942911	+	0.333044i	$0.891924\pi$
$578$			13.0000i			0.540729i
$579$	−60.0000			−2.49351
$580$	1.00000	+	2.00000i	0.0415227	+	0.0830455i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−10.0000			−0.413803
$585$	24.0000	−	12.0000i	0.992278	−	0.496139i
$586$	−24.0000			−0.991431
$587$		−	28.0000i		−	1.15568i	−0.816149	−	0.577842i	$-0.803895\pi$
$587$		−	28.0000i		−	1.15568i	0.816149	−	0.577842i	$-0.196105\pi$
$588$		0			0
$589$	20.0000			0.824086
$590$	4.00000	−	2.00000i	0.164677	−	0.0823387i
$591$	−24.0000			−0.987228
$592$		−	8.00000i		−	0.328798i
$593$			42.0000i			1.72473i	0.506284	+	0.862367i	$0.331019\pi$
$593$			42.0000i			1.72473i	−0.506284	+	0.862367i	$0.668981\pi$
$594$		0			0
$595$		0			0
$596$	−15.0000			−0.614424
$597$		−	36.0000i		−	1.47338i
$598$			2.00000i			0.0817861i
$599$	−36.0000			−1.47092			−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000			−1.47092			−0.735460	+	0.677568i	$0.763034\pi$
$600$	9.00000	−	12.0000i	0.367423	−	0.489898i
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$			42.0000i			1.71037i
$604$	−6.00000			−0.244137
$605$	11.0000	+	22.0000i	0.447214	+	0.894427i
$606$	45.0000			1.82800
$607$		−	5.00000i		−	0.202944i	−0.994838	−	0.101472i	$-0.967645\pi$
$607$		−	5.00000i		−	0.202944i	0.994838	−	0.101472i	$-0.0323552\pi$
$608$		−	2.00000i		−	0.0811107i
$609$		0			0
$610$	18.0000	−	9.00000i	0.728799	−	0.364399i
$611$	−16.0000			−0.647291
$612$			12.0000i			0.485071i
$613$		−	18.0000i		−	0.727013i	−0.931592	−	0.363507i	$-0.881579\pi$
$613$		−	18.0000i		−	0.727013i	0.931592	−	0.363507i	$-0.118421\pi$
$614$	−19.0000			−0.766778
$615$	−18.0000	+	9.00000i	−0.725830	+	0.362915i
$616$		0			0
$617$			20.0000i			0.805170i	0.915383	+	0.402585i	$0.131888\pi$
$617$			20.0000i			0.805170i	−0.915383	+	0.402585i	$0.868112\pi$
$618$		−	33.0000i		−	1.32745i
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$	−10.0000	−	20.0000i	−0.401610	−	0.803219i
$621$	−9.00000			−0.361158
$622$		−	6.00000i		−	0.240578i
$623$		0			0
$624$	−6.00000			−0.240192
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−8.00000			−0.319744
$627$		0			0
$628$		−	12.0000i		−	0.478852i
$629$	16.0000			0.637962
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$		−	10.0000i		−	0.397779i
$633$			54.0000i			2.14631i
$634$	−22.0000			−0.873732
$635$	−16.0000	+	8.00000i	−0.634941	+	0.317470i
$636$	−18.0000			−0.713746
$637$		0			0
$638$		0			0
$639$	−36.0000			−1.42414
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$	−35.0000			−1.38242			−0.691208	−	0.722655i	$-0.742921\pi$
$641$	−35.0000			−1.38242			−0.691208	+	0.722655i	$0.742921\pi$
$642$		−	21.0000i		−	0.828804i
$643$		−	20.0000i		−	0.788723i	−0.918955	−	0.394362i	$-0.870966\pi$
$643$		−	20.0000i		−	0.788723i	0.918955	−	0.394362i	$-0.129034\pi$
$644$		0			0
$645$	15.0000	+	30.0000i	0.590624	+	1.18125i
$646$	4.00000			0.157378
$647$		−	21.0000i		−	0.825595i	−0.910823	−	0.412798i	$-0.864552\pi$
$647$		−	21.0000i		−	0.825595i	0.910823	−	0.412798i	$-0.135448\pi$
$648$		−	9.00000i		−	0.353553i
$649$		0			0
$650$	−6.00000	+	8.00000i	−0.235339	+	0.313786i
$651$		0			0
$652$			12.0000i			0.469956i
$653$		−	42.0000i		−	1.64359i	−0.569785	−	0.821794i	$-0.692974\pi$
$653$		−	42.0000i		−	1.64359i	0.569785	−	0.821794i	$-0.307026\pi$
$654$	−15.0000			−0.586546
$655$	20.0000	+	40.0000i	0.781465	+	1.56293i
$656$	3.00000			0.117130
$657$			60.0000i			2.34082i
$658$		0			0
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$	41.0000			1.59472			0.797358	−	0.603507i	$-0.206231\pi$
$661$	41.0000			1.59472			0.797358	+	0.603507i	$0.206231\pi$
$662$			14.0000i			0.544125i
$663$		−	12.0000i		−	0.466041i
$664$	−9.00000			−0.349268
$665$		0			0
$666$	−48.0000			−1.85996
$667$			1.00000i			0.0387202i
$668$		−	9.00000i		−	0.348220i
$669$	−24.0000			−0.927894
$670$	−7.00000	−	14.0000i	−0.270434	−	0.540867i
$671$		0			0
$672$		0			0
$673$		−	20.0000i		−	0.770943i	−0.922720	−	0.385472i	$-0.874039\pi$
$673$		−	20.0000i		−	0.770943i	0.922720	−	0.385472i	$-0.125961\pi$
$674$	2.00000			0.0770371
$675$	−36.0000	−	27.0000i	−1.38564	−	1.03923i
$676$	−9.00000			−0.346154
$677$			2.00000i			0.0768662i	0.999261	+	0.0384331i	$0.0122367\pi$
$677$			2.00000i			0.0768662i	−0.999261	+	0.0384331i	$0.987763\pi$
$678$			30.0000i			1.15214i
$679$		0			0
$680$	−2.00000	−	4.00000i	−0.0766965	−	0.153393i
$681$	−36.0000			−1.37952
$682$		0			0
$683$		−	25.0000i		−	0.956598i	−0.878197	−	0.478299i	$-0.841253\pi$
$683$		−	25.0000i		−	0.956598i	0.878197	−	0.478299i	$-0.158747\pi$
$684$	−12.0000			−0.458831
$685$	32.0000	−	16.0000i	1.22266	−	0.611329i
$686$		0			0
$687$		−	30.0000i		−	1.14457i
$688$		−	5.00000i		−	0.190623i
$689$	12.0000			0.457164
$690$	6.00000	−	3.00000i	0.228416	−	0.114208i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$		−	12.0000i		−	0.456172i
$693$		0			0
$694$	−21.0000			−0.797149
$695$	8.00000	+	16.0000i	0.303457	+	0.606915i
$696$	−3.00000			−0.113715
$697$			6.00000i			0.227266i
$698$		−	9.00000i		−	0.340655i
$699$	42.0000			1.58859
$700$		0			0
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$			18.0000i			0.679366i
$703$			16.0000i			0.603451i
$704$		0			0
$705$	24.0000	+	48.0000i	0.903892	+	1.80778i
$706$	6.00000			0.225813
$707$		0			0
$708$			6.00000i			0.225494i
$709$	9.00000			0.338002			0.169001	−	0.985616i	$-0.445946\pi$
$709$	9.00000			0.338002			0.169001	+	0.985616i	$0.445946\pi$
$710$	12.0000	−	6.00000i	0.450352	−	0.225176i
$711$	−60.0000			−2.25018
$712$			7.00000i			0.262336i
$713$		−	10.0000i		−	0.374503i
$714$		0			0
$715$		0			0
$716$	−26.0000			−0.971666
$717$		−	30.0000i		−	1.12037i
$718$			14.0000i			0.522475i
$719$	20.0000			0.745874			0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$	6.00000	+	12.0000i	0.223607	+	0.447214i
$721$		0			0
$722$		−	15.0000i		−	0.558242i
$723$			54.0000i			2.00828i
$724$	5.00000			0.185824
$725$	−3.00000	+	4.00000i	−0.111417	+	0.148556i
$726$	−33.0000			−1.22474
$727$			29.0000i			1.07555i	0.843088	+	0.537775i	$0.180735\pi$
$727$			29.0000i			1.07555i	−0.843088	+	0.537775i	$0.819265\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−10.0000	−	20.0000i	−0.370117	−	0.740233i
$731$	10.0000			0.369863
$732$			27.0000i			0.997949i
$733$		−	16.0000i		−	0.590973i	−0.955347	−	0.295487i	$-0.904518\pi$
$733$		−	16.0000i		−	0.590973i	0.955347	−	0.295487i	$-0.0954818\pi$
$734$	−23.0000			−0.848945
$735$		0			0
$736$	−1.00000			−0.0368605
$737$		0			0
$738$		−	18.0000i		−	0.662589i
$739$	32.0000			1.17714			0.588570	−	0.808447i	$-0.299691\pi$
$739$	32.0000			1.17714			0.588570	+	0.808447i	$0.299691\pi$
$740$	16.0000	−	8.00000i	0.588172	−	0.294086i
$741$	12.0000			0.440831
$742$		0			0
$743$			3.00000i			0.110059i	0.998485	+	0.0550297i	$0.0175253\pi$
$743$			3.00000i			0.110059i	−0.998485	+	0.0550297i	$0.982475\pi$
$744$	30.0000			1.09985
$745$	−15.0000	−	30.0000i	−0.549557	−	1.09911i
$746$	8.00000			0.292901
$747$			54.0000i			1.97576i
$748$		0			0
$749$		0			0
$750$	33.0000	+	6.00000i	1.20499	+	0.219089i
$751$	4.00000			0.145962			0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000			0.145962			0.0729810	+	0.997333i	$0.476749\pi$
$752$		−	8.00000i		−	0.291730i
$753$		−	30.0000i		−	1.09326i
$754$	2.00000			0.0728357
$755$	−6.00000	−	12.0000i	−0.218362	−	0.436725i
$756$		0			0
$757$		−	6.00000i		−	0.218074i	−0.994038	−	0.109037i	$-0.965223\pi$
$757$		−	6.00000i		−	0.218074i	0.994038	−	0.109037i	$-0.0347767\pi$
$758$			2.00000i			0.0726433i
$759$		0			0
$760$	4.00000	−	2.00000i	0.145095	−	0.0725476i
$761$	50.0000			1.81250			0.906249	−	0.422744i	$-0.138933\pi$
$761$	50.0000			1.81250			0.906249	+	0.422744i	$0.138933\pi$
$762$		−	24.0000i		−	0.869428i
$763$		0			0
$764$	20.0000			0.723575
$765$	−24.0000	+	12.0000i	−0.867722	+	0.433861i
$766$	9.00000			0.325183
$767$		−	4.00000i		−	0.144432i
$768$		−	3.00000i		−	0.108253i
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−36.0000			−1.29651
$772$			20.0000i			0.719816i
$773$		−	18.0000i		−	0.647415i	−0.946157	−	0.323708i	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$	−30.0000			−1.07833
$775$	30.0000	−	40.0000i	1.07763	−	1.43684i
$776$		0			0
$777$		0			0
$778$			18.0000i			0.645331i
$779$	−6.00000			−0.214972
$780$	−6.00000	−	12.0000i	−0.214834	−	0.429669i
$781$		0			0
$782$		−	2.00000i		−	0.0715199i
$783$			9.00000i			0.321634i
$784$		0			0
$785$	24.0000	−	12.0000i	0.856597	−	0.428298i
$786$	−60.0000			−2.14013
$787$		−	21.0000i		−	0.748569i	−0.927314	−	0.374285i	$-0.877888\pi$
$787$		−	21.0000i		−	0.748569i	0.927314	−	0.374285i	$-0.122112\pi$
$788$			8.00000i			0.284988i
$789$	−63.0000			−2.24286
$790$	20.0000	−	10.0000i	0.711568	−	0.355784i
$791$		0			0
$792$		0			0
$793$		−	18.0000i		−	0.639199i
$794$	−32.0000			−1.13564
$795$	−18.0000	−	36.0000i	−0.638394	−	1.27679i
$796$	−12.0000			−0.425329
$797$			8.00000i			0.283375i	0.989911	+	0.141687i	$0.0452527\pi$
$797$			8.00000i			0.283375i	−0.989911	+	0.141687i	$0.954747\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$	42.0000			1.48400
$802$			3.00000i			0.105934i
$803$		0			0
$804$	21.0000			0.740613
$805$		0			0
$806$	−20.0000			−0.704470
$807$		−	15.0000i		−	0.528025i
$808$		−	15.0000i		−	0.527698i
$809$	−25.0000			−0.878953			−0.439477	−	0.898254i	$-0.644836\pi$
$809$	−25.0000			−0.878953			−0.439477	+	0.898254i	$0.644836\pi$
$810$	18.0000	−	9.00000i	0.632456	−	0.316228i
$811$	−6.00000			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$812$		0			0
$813$			18.0000i			0.631288i
$814$		0			0
$815$	−24.0000	+	12.0000i	−0.840683	+	0.420342i
$816$	6.00000			0.210042
$817$			10.0000i			0.349856i
$818$		−	17.0000i		−	0.594391i
$819$		0			0
$820$	3.00000	+	6.00000i	0.104765	+	0.209529i
$821$	−42.0000			−1.46581			−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000			−1.46581			−0.732905	+	0.680331i	$0.761836\pi$
$822$			48.0000i			1.67419i
$823$			45.0000i			1.56860i	0.620381	+	0.784301i	$0.286978\pi$
$823$			45.0000i			1.56860i	−0.620381	+	0.784301i	$0.713022\pi$
$824$	−11.0000			−0.383203
$825$		0			0
$826$		0			0
$827$		−	37.0000i		−	1.28662i	−0.765607	−	0.643308i	$-0.777561\pi$
$827$		−	37.0000i		−	1.28662i	0.765607	−	0.643308i	$-0.222439\pi$
$828$			6.00000i			0.208514i
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	−9.00000	−	18.0000i	−0.312395	−	0.624789i
$831$	−78.0000			−2.70579
$832$			2.00000i			0.0693375i
$833$		0			0
$834$	−24.0000			−0.831052
$835$	18.0000	−	9.00000i	0.622916	−	0.311458i
$836$		0			0
$837$		−	90.0000i		−	3.11086i
$838$		−	40.0000i		−	1.38178i
$839$	32.0000			1.10476			0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000			1.10476			0.552381	+	0.833592i	$0.313719\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$			31.0000i			1.06833i
$843$		−	54.0000i		−	1.85986i
$844$	18.0000			0.619586
$845$	−9.00000	−	18.0000i	−0.309609	−	0.619219i
$846$	−48.0000			−1.65027
$847$		0			0
$848$			6.00000i			0.206041i
$849$	24.0000			0.823678
$850$	6.00000	−	8.00000i	0.205798	−	0.274398i
$851$	8.00000			0.274236
$852$			18.0000i			0.616670i
$853$		−	10.0000i		−	0.342393i	−0.985237	−	0.171197i	$-0.945237\pi$
$853$		−	10.0000i		−	0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$		0			0
$855$	−12.0000	−	24.0000i	−0.410391	−	0.820783i
$856$	−7.00000			−0.239255
$857$			4.00000i			0.136637i	0.997664	+	0.0683187i	$0.0217635\pi$
$857$			4.00000i			0.136637i	−0.997664	+	0.0683187i	$0.978237\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$	10.0000	−	5.00000i	0.340997	−	0.170499i
$861$		0			0
$862$			32.0000i			1.08992i
$863$			11.0000i			0.374444i	0.982318	+	0.187222i	$0.0599484\pi$
$863$			11.0000i			0.374444i	−0.982318	+	0.187222i	$0.940052\pi$
$864$	−9.00000			−0.306186
$865$	24.0000	−	12.0000i	0.816024	−	0.408012i
$866$	14.0000			0.475739
$867$		−	39.0000i		−	1.32451i
$868$		0			0
$869$		0			0
$870$	−3.00000	−	6.00000i	−0.101710	−	0.203419i
$871$	−14.0000			−0.474372
$872$			5.00000i			0.169321i
$873$		0			0
$874$	2.00000			0.0676510
$875$		0			0
$876$	30.0000			1.01361
$877$		−	14.0000i		−	0.472746i	−0.971662	−	0.236373i	$-0.924041\pi$
$877$		−	14.0000i		−	0.472746i	0.971662	−	0.236373i	$-0.0759588\pi$
$878$			8.00000i			0.269987i
$879$	72.0000			2.42850
$880$		0			0
$881$	3.00000			0.101073			0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000			0.101073			0.0505363	+	0.998722i	$0.483907\pi$
$882$		0			0
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$	−4.00000			−0.134535
$885$	−12.0000	+	6.00000i	−0.403376	+	0.201688i
$886$	−3.00000			−0.100787
$887$		−	9.00000i		−	0.302190i	−0.988519	−	0.151095i	$-0.951720\pi$
$887$		−	9.00000i		−	0.302190i	0.988519	−	0.151095i	$-0.0482800\pi$
$888$			24.0000i			0.805387i
$889$		0			0
$890$	−14.0000	+	7.00000i	−0.469281	+	0.234641i
$891$		0			0
$892$			8.00000i			0.267860i
$893$			16.0000i			0.535420i
$894$	45.0000			1.50503
$895$	−26.0000	−	52.0000i	−0.869084	−	1.73817i
$896$		0			0
$897$		−	6.00000i		−	0.200334i
$898$		−	23.0000i		−	0.767520i
$899$	−10.0000			−0.333519
$900$	−18.0000	+	24.0000i	−0.600000	+	0.800000i
$901$	−12.0000			−0.399778
$902$		0			0
$903$		0			0
$904$	10.0000			0.332595
$905$	5.00000	+	10.0000i	0.166206	+	0.332411i
$906$	18.0000			0.598010
$907$		−	25.0000i		−	0.830111i	−0.909796	−	0.415056i	$-0.863762\pi$
$907$		−	25.0000i		−	0.830111i	0.909796	−	0.415056i	$-0.136238\pi$
$908$			12.0000i			0.398234i
$909$	−90.0000			−2.98511
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$			6.00000i			0.198680i
$913$		0			0
$914$	−32.0000			−1.05847
$915$	−54.0000	+	27.0000i	−1.78518	+	0.892592i
$916$	−10.0000			−0.330409
$917$		0			0
$918$		−	18.0000i		−	0.594089i
$919$	−26.0000			−0.857661			−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000			−0.857661			−0.428830	+	0.903385i	$0.641074\pi$
$920$	−1.00000	−	2.00000i	−0.0329690	−	0.0659380i
$921$	57.0000			1.87821
$922$			14.0000i			0.461065i
$923$		−	12.0000i		−	0.394985i
$924$		0			0
$925$	32.0000	+	24.0000i	1.05215	+	0.789115i
$926$	25.0000			0.821551
$927$			66.0000i			2.16772i
$928$			1.00000i			0.0328266i
$929$	27.0000			0.885841			0.442921	−	0.896561i	$-0.353942\pi$
$929$	27.0000			0.885841			0.442921	+	0.896561i	$0.353942\pi$
$930$	30.0000	+	60.0000i	0.983739	+	1.96748i
$931$		0			0
$932$		−	14.0000i		−	0.458585i
$933$			18.0000i			0.589294i
$934$	1.00000			0.0327210
$935$		0			0
$936$	12.0000			0.392232
$937$			56.0000i			1.82944i	0.404088	+	0.914720i	$0.367589\pi$
$937$			56.0000i			1.82944i	−0.404088	+	0.914720i	$0.632411\pi$
$938$		0			0
$939$	24.0000			0.783210
$940$	16.0000	−	8.00000i	0.521862	−	0.260931i
$941$	−14.0000			−0.456387			−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000			−0.456387			−0.228193	+	0.973616i	$0.573282\pi$
$942$			36.0000i			1.17294i
$943$			3.00000i			0.0976934i
$944$	2.00000			0.0650945
$945$		0			0
$946$		0			0
$947$		−	3.00000i		−	0.0974869i	−0.998811	−	0.0487435i	$-0.984478\pi$
$947$		−	3.00000i		−	0.0974869i	0.998811	−	0.0487435i	$-0.0155217\pi$
$948$			30.0000i			0.974355i
$949$	−20.0000			−0.649227
$950$	8.00000	+	6.00000i	0.259554	+	0.194666i
$951$	66.0000			2.14020
$952$		0			0
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$	36.0000			1.16554
$955$	20.0000	+	40.0000i	0.647185	+	1.29437i
$956$	−10.0000			−0.323423
$957$		0			0
$958$			18.0000i			0.581554i
$959$		0			0
$960$	6.00000	−	3.00000i	0.193649	−	0.0968246i
$961$	69.0000			2.22581
$962$		−	16.0000i		−	0.515861i
$963$			42.0000i			1.35343i
$964$	18.0000			0.579741
$965$	−40.0000	+	20.0000i	−1.28765	+	0.643823i
$966$		0			0
$967$			17.0000i			0.546683i	0.961917	+	0.273342i	$0.0881289\pi$
$967$			17.0000i			0.546683i	−0.961917	+	0.273342i	$0.911871\pi$
$968$			11.0000i			0.353553i
$969$	−12.0000			−0.385496
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$		0			0
$974$	−4.00000			−0.128168
$975$	18.0000	−	24.0000i	0.576461	−	0.768615i
$976$	9.00000			0.288083
$977$			36.0000i			1.15174i	0.817541	+	0.575871i	$0.195337\pi$
$977$			36.0000i			1.15174i	−0.817541	+	0.575871i	$0.804663\pi$
$978$		−	36.0000i		−	1.15115i
$979$		0			0
$980$		0			0
$981$	30.0000			0.957826
$982$		−	18.0000i		−	0.574403i
$983$			25.0000i			0.797376i	0.917087	+	0.398688i	$0.130534\pi$
$983$			25.0000i			0.797376i	−0.917087	+	0.398688i	$0.869466\pi$
$984$	−9.00000			−0.286910
$985$	−16.0000	+	8.00000i	−0.509802	+	0.254901i
$986$	−2.00000			−0.0636930
$987$		0			0
$988$		−	4.00000i		−	0.127257i
$989$	5.00000			0.158991
$990$		0			0
$991$	−26.0000			−0.825917			−0.412959	−	0.910750i	$-0.635505\pi$
$991$	−26.0000			−0.825917			−0.412959	+	0.910750i	$0.635505\pi$
$992$		−	10.0000i		−	0.317500i
$993$		−	42.0000i		−	1.33283i
$994$		0			0
$995$	−12.0000	−	24.0000i	−0.380426	−	0.760851i
$996$	27.0000			0.855528
$997$		−	34.0000i		−	1.07679i	−0.842692	−	0.538395i	$-0.819031\pi$
$997$		−	34.0000i		−	1.07679i	0.842692	−	0.538395i	$-0.180969\pi$
$998$		−	16.0000i		−	0.506471i
$999$	72.0000			2.27798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.c.b.99.2		2
5.2	odd	4		2450.2.a.c.1.1		1
5.3	odd	4		2450.2.a.bh.1.1		1
5.4	even	2	inner	490.2.c.b.99.1		2
7.2	even	3		490.2.i.b.459.2		4
7.3	odd	6		70.2.i.a.9.1	✓	4
7.4	even	3		490.2.i.b.79.1		4
7.5	odd	6		70.2.i.a.39.2	yes	4
7.6	odd	2		490.2.c.c.99.2		2
21.5	even	6		630.2.u.b.109.1		4
21.17	even	6		630.2.u.b.289.2		4
28.3	even	6		560.2.bw.c.289.1		4
28.19	even	6		560.2.bw.c.529.2		4
35.3	even	12		350.2.e.f.51.1		2
35.4	even	6		490.2.i.b.79.2		4
35.9	even	6		490.2.i.b.459.1		4
35.12	even	12		350.2.e.g.151.1		2
35.13	even	4		2450.2.a.s.1.1		1
35.17	even	12		350.2.e.g.51.1		2
35.19	odd	6		70.2.i.a.39.1	yes	4
35.24	odd	6		70.2.i.a.9.2	yes	4
35.27	even	4		2450.2.a.r.1.1		1
35.33	even	12		350.2.e.f.151.1		2
35.34	odd	2		490.2.c.c.99.1		2
105.59	even	6		630.2.u.b.289.1		4
105.89	even	6		630.2.u.b.109.2		4
140.19	even	6		560.2.bw.c.529.1		4
140.59	even	6		560.2.bw.c.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.a.9.1	✓	4	7.3	odd	6
70.2.i.a.9.2	yes	4	35.24	odd	6
70.2.i.a.39.1	yes	4	35.19	odd	6
70.2.i.a.39.2	yes	4	7.5	odd	6
350.2.e.f.51.1		2	35.3	even	12
350.2.e.f.151.1		2	35.33	even	12
350.2.e.g.51.1		2	35.17	even	12
350.2.e.g.151.1		2	35.12	even	12
490.2.c.b.99.1		2	5.4	even	2	inner
490.2.c.b.99.2		2	1.1	even	1	trivial
490.2.c.c.99.1		2	35.34	odd	2
490.2.c.c.99.2		2	7.6	odd	2
490.2.i.b.79.1		4	7.4	even	3
490.2.i.b.79.2		4	35.4	even	6
490.2.i.b.459.1		4	35.9	even	6
490.2.i.b.459.2		4	7.2	even	3
560.2.bw.c.289.1		4	28.3	even	6
560.2.bw.c.289.2		4	140.59	even	6
560.2.bw.c.529.1		4	140.19	even	6
560.2.bw.c.529.2		4	28.19	even	6
630.2.u.b.109.1		4	21.5	even	6
630.2.u.b.109.2		4	105.89	even	6
630.2.u.b.289.1		4	105.59	even	6
630.2.u.b.289.2		4	21.17	even	6
2450.2.a.c.1.1		1	5.2	odd	4
2450.2.a.r.1.1		1	35.27	even	4
2450.2.a.s.1.1		1	35.13	even	4
2450.2.a.bh.1.1		1	5.3	odd	4

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +3.00000 q^{6} -1.00000i q^{8} -6.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -3.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +3.00000 q^{6} -1.00000i q^{8} -6.00000 q^{9} +(2.00000 - 1.00000i) q^{10} +3.00000i q^{12} -2.00000i q^{13} +(-6.00000 + 3.00000i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -6.00000i q^{18} -2.00000 q^{19} +(1.00000 + 2.00000i) q^{20} +1.00000i q^{23} -3.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +2.00000 q^{26} +9.00000i q^{27} +1.00000 q^{29} +(-3.00000 - 6.00000i) q^{30} -10.0000 q^{31} +1.00000i q^{32} -2.00000 q^{34} +6.00000 q^{36} -8.00000i q^{37} -2.00000i q^{38} -6.00000 q^{39} +(-2.00000 + 1.00000i) q^{40} +3.00000 q^{41} -5.00000i q^{43} +(6.00000 + 12.0000i) q^{45} -1.00000 q^{46} -8.00000i q^{47} -3.00000i q^{48} +(-4.00000 - 3.00000i) q^{50} +6.00000 q^{51} +2.00000i q^{52} +6.00000i q^{53} -9.00000 q^{54} +6.00000i q^{57} +1.00000i q^{58} +2.00000 q^{59} +(6.00000 - 3.00000i) q^{60} +9.00000 q^{61} -10.0000i q^{62} -1.00000 q^{64} +(-4.00000 + 2.00000i) q^{65} -7.00000i q^{67} -2.00000i q^{68} +3.00000 q^{69} +6.00000 q^{71} +6.00000i q^{72} -10.0000i q^{73} +8.00000 q^{74} +(12.0000 + 9.00000i) q^{75} +2.00000 q^{76} -6.00000i q^{78} +10.0000 q^{79} +(-1.00000 - 2.00000i) q^{80} +9.00000 q^{81} +3.00000i q^{82} -9.00000i q^{83} +(4.00000 - 2.00000i) q^{85} +5.00000 q^{86} -3.00000i q^{87} -7.00000 q^{89} +(-12.0000 + 6.00000i) q^{90} -1.00000i q^{92} +30.0000i q^{93} +8.00000 q^{94} +(2.00000 + 4.00000i) q^{95} +3.00000 q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{5} + 6 q^{6} - 12 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^5 + 6 * q^6 - 12 * q^9	\( 2 q - 2 q^{4} - 2 q^{5} + 6 q^{6} - 12 q^{9} + 4 q^{10} - 12 q^{15} + 2 q^{16} - 4 q^{19} + 2 q^{20} - 6 q^{24} - 6 q^{25} + 4 q^{26} + 2 q^{29} - 6 q^{30} - 20 q^{31} - 4 q^{34} + 12 q^{36} - 12 q^{39} - 4 q^{40} + 6 q^{41} + 12 q^{45} - 2 q^{46} - 8 q^{50} + 12 q^{51} - 18 q^{54} + 4 q^{59} + 12 q^{60} + 18 q^{61} - 2 q^{64} - 8 q^{65} + 6 q^{69} + 12 q^{71} + 16 q^{74} + 24 q^{75} + 4 q^{76} + 20 q^{79} - 2 q^{80} + 18 q^{81} + 8 q^{85} + 10 q^{86} - 14 q^{89} - 24 q^{90} + 16 q^{94} + 4 q^{95} + 6 q^{96}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^5 + 6 * q^6 - 12 * q^9 + 4 * q^10 - 12 * q^15 + 2 * q^16 - 4 * q^19 + 2 * q^20 - 6 * q^24 - 6 * q^25 + 4 * q^26 + 2 * q^29 - 6 * q^30 - 20 * q^31 - 4 * q^34 + 12 * q^36 - 12 * q^39 - 4 * q^40 + 6 * q^41 + 12 * q^45 - 2 * q^46 - 8 * q^50 + 12 * q^51 - 18 * q^54 + 4 * q^59 + 12 * q^60 + 18 * q^61 - 2 * q^64 - 8 * q^65 + 6 * q^69 + 12 * q^71 + 16 * q^74 + 24 * q^75 + 4 * q^76 + 20 * q^79 - 2 * q^80 + 18 * q^81 + 8 * q^85 + 10 * q^86 - 14 * q^89 - 24 * q^90 + 16 * q^94 + 4 * q^95 + 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more