LMFDB - Embedded newform 1470.2.g.a.589.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(589,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1470.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.g (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:	$11.7380090971$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1470.589
Dual form			1470.2.g.a.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} -5.00000 q^{11} +1.00000i q^{12} -1.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} -2.00000i q^{17} -1.00000i q^{18} +7.00000 q^{19} +(2.00000 - 1.00000i) q^{20} -5.00000i q^{22} +3.00000i q^{23} -1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +1.00000 q^{26} +1.00000i q^{27} +(-2.00000 + 1.00000i) q^{30} +6.00000 q^{31} +1.00000i q^{32} +5.00000i q^{33} +2.00000 q^{34} +1.00000 q^{36} +5.00000i q^{37} +7.00000i q^{38} -1.00000 q^{39} +(1.00000 + 2.00000i) q^{40} +9.00000 q^{41} +10.0000i q^{43} +5.00000 q^{44} +(2.00000 - 1.00000i) q^{45} -3.00000 q^{46} -13.0000i q^{47} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} -2.00000 q^{51} +1.00000i q^{52} -1.00000i q^{53} -1.00000 q^{54} +(10.0000 - 5.00000i) q^{55} -7.00000i q^{57} +4.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} +2.00000 q^{61} +6.00000i q^{62} -1.00000 q^{64} +(1.00000 + 2.00000i) q^{65} -5.00000 q^{66} -6.00000i q^{67} +2.00000i q^{68} +3.00000 q^{69} -2.00000 q^{71} +1.00000i q^{72} -4.00000i q^{73} -5.00000 q^{74} +(-4.00000 - 3.00000i) q^{75} -7.00000 q^{76} -1.00000i q^{78} +14.0000 q^{79} +(-2.00000 + 1.00000i) q^{80} +1.00000 q^{81} +9.00000i q^{82} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} -10.0000 q^{86} +5.00000i q^{88} +10.0000 q^{89} +(1.00000 + 2.00000i) q^{90} -3.00000i q^{92} -6.00000i q^{93} +13.0000 q^{94} +(-14.0000 + 7.00000i) q^{95} +1.00000 q^{96} +8.00000i q^{97} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{9} - 2 q^{10} - 10 q^{11} + 2 q^{15} + 2 q^{16} + 14 q^{19} + 4 q^{20} - 2 q^{24} + 6 q^{25} + 2 q^{26} - 4 q^{30} + 12 q^{31} + 4 q^{34} + 2 q^{36} - 2 q^{39} + 2 q^{40}+ \cdots + 10 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^9 - 2 * q^10 - 10 * q^11 + 2 * q^15 + 2 * q^16 + 14 * q^19 + 4 * q^20 - 2 * q^24 + 6 * q^25 + 2 * q^26 - 4 * q^30 + 12 * q^31 + 4 * q^34 + 2 * q^36 - 2 * q^39 + 2 * q^40 + 18 * q^41 + 10 * q^44 + 4 * q^45 - 6 * q^46 + 8 * q^50 - 4 * q^51 - 2 * q^54 + 20 * q^55 + 8 * q^59 - 2 * q^60 + 4 * q^61 - 2 * q^64 + 2 * q^65 - 10 * q^66 + 6 * q^69 - 4 * q^71 - 10 * q^74 - 8 * q^75 - 14 * q^76 + 28 * q^79 - 4 * q^80 + 2 * q^81 + 4 * q^85 - 20 * q^86 + 20 * q^89 + 2 * q^90 + 26 * q^94 - 28 * q^95 + 2 * q^96 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$1$	$-1$

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
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$			1.00000i			0.288675i
$13$		−	1.00000i		−	0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$		−	1.00000i		−	0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$		0			0
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$	1.00000			0.250000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		−	1.00000i		−	0.235702i
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	2.00000	−	1.00000i	0.447214	−	0.223607i
$21$		0			0
$22$		−	5.00000i		−	1.06600i
$23$			3.00000i			0.625543i	0.949828	+	0.312772i	$0.101257\pi$
$23$			3.00000i			0.625543i	−0.949828	+	0.312772i	$0.898743\pi$
$24$	−1.00000			−0.204124
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	1.00000			0.196116
$27$			1.00000i			0.192450i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−2.00000	+	1.00000i	−0.365148	+	0.182574i
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$			1.00000i			0.176777i
$33$			5.00000i			0.870388i
$34$	2.00000			0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$			5.00000i			0.821995i	0.911636	+	0.410997i	$0.134819\pi$
$37$			5.00000i			0.821995i	−0.911636	+	0.410997i	$0.865181\pi$
$38$			7.00000i			1.13555i
$39$	−1.00000			−0.160128
$40$	1.00000	+	2.00000i	0.158114	+	0.316228i
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$		0			0
$43$			10.0000i			1.52499i	0.646997	+	0.762493i	$0.276025\pi$
$43$			10.0000i			1.52499i	−0.646997	+	0.762493i	$0.723975\pi$
$44$	5.00000			0.753778
$45$	2.00000	−	1.00000i	0.298142	−	0.149071i
$46$	−3.00000			−0.442326
$47$		−	13.0000i		−	1.89624i	−0.317905	−	0.948122i	$-0.602979\pi$
$47$		−	13.0000i		−	1.89624i	0.317905	−	0.948122i	$-0.397021\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$	−2.00000			−0.280056
$52$			1.00000i			0.138675i
$53$		−	1.00000i		−	0.137361i	−0.997639	−	0.0686803i	$-0.978121\pi$
$53$		−	1.00000i		−	0.137361i	0.997639	−	0.0686803i	$-0.0218788\pi$
$54$	−1.00000			−0.136083
$55$	10.0000	−	5.00000i	1.34840	−	0.674200i
$56$		0			0
$57$		−	7.00000i		−	0.927173i
$58$		0			0
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$	−1.00000	−	2.00000i	−0.129099	−	0.258199i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$			6.00000i			0.762001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.00000	+	2.00000i	0.124035	+	0.248069i
$66$	−5.00000			−0.615457
$67$		−	6.00000i		−	0.733017i	−0.930415	−	0.366508i	$-0.880553\pi$
$67$		−	6.00000i		−	0.733017i	0.930415	−	0.366508i	$-0.119447\pi$
$68$			2.00000i			0.242536i
$69$	3.00000			0.361158
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$			1.00000i			0.117851i
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$	−5.00000			−0.581238
$75$	−4.00000	−	3.00000i	−0.461880	−	0.346410i
$76$	−7.00000			−0.802955
$77$		0			0
$78$		−	1.00000i		−	0.113228i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	−2.00000	+	1.00000i	−0.223607	+	0.111803i
$81$	1.00000			0.111111
$82$			9.00000i			0.993884i
$83$			10.0000i			1.09764i	0.835940	+	0.548821i	$0.184923\pi$
$83$			10.0000i			1.09764i	−0.835940	+	0.548821i	$0.815077\pi$
$84$		0			0
$85$	2.00000	+	4.00000i	0.216930	+	0.433861i
$86$	−10.0000			−1.07833
$87$		0			0
$88$			5.00000i			0.533002i
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	1.00000	+	2.00000i	0.105409	+	0.210819i
$91$		0			0
$92$		−	3.00000i		−	0.312772i
$93$		−	6.00000i		−	0.622171i
$94$	13.0000			1.34085
$95$	−14.0000	+	7.00000i	−1.43637	+	0.718185i
$96$	1.00000			0.102062
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$		0			0
$99$	5.00000			0.502519
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−8.00000			−0.796030			−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000			−0.796030			−0.398015	+	0.917379i	$0.630301\pi$
$102$		−	2.00000i		−	0.198030i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	1.00000			0.0971286
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	18.0000			1.72409			0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000			1.72409			0.862044	+	0.506834i	$0.169184\pi$
$110$	5.00000	+	10.0000i	0.476731	+	0.953463i
$111$	5.00000			0.474579
$112$		0			0
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	7.00000			0.655610
$115$	−3.00000	−	6.00000i	−0.279751	−	0.559503i
$116$		0			0
$117$			1.00000i			0.0924500i
$118$			4.00000i			0.368230i
$119$		0			0
$120$	2.00000	−	1.00000i	0.182574	−	0.0912871i
$121$	14.0000			1.27273
$122$			2.00000i			0.181071i
$123$		−	9.00000i		−	0.811503i
$124$	−6.00000			−0.538816
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$		−	9.00000i		−	0.798621i	−0.916816	−	0.399310i	$-0.869250\pi$
$127$		−	9.00000i		−	0.798621i	0.916816	−	0.399310i	$-0.130750\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	10.0000			0.880451
$130$	−2.00000	+	1.00000i	−0.175412	+	0.0877058i
$131$	17.0000			1.48530			0.742648	−	0.669681i	$-0.233569\pi$
$131$	17.0000			1.48530			0.742648	+	0.669681i	$0.233569\pi$
$132$		−	5.00000i		−	0.435194i
$133$		0			0
$134$	6.00000			0.518321
$135$	−1.00000	−	2.00000i	−0.0860663	−	0.172133i
$136$	−2.00000			−0.171499
$137$			4.00000i			0.341743i	0.985293	+	0.170872i	$0.0546583\pi$
$137$			4.00000i			0.341743i	−0.985293	+	0.170872i	$0.945342\pi$
$138$			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
$141$	−13.0000			−1.09480
$142$		−	2.00000i		−	0.167836i
$143$			5.00000i			0.418121i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	4.00000			0.331042
$147$		0			0
$148$		−	5.00000i		−	0.410997i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	3.00000	−	4.00000i	0.244949	−	0.326599i
$151$	−22.0000			−1.79033			−0.895167	−	0.445730i	$-0.852944\pi$
$151$	−22.0000			−1.79033			−0.895167	+	0.445730i	$0.852944\pi$
$152$		−	7.00000i		−	0.567775i
$153$			2.00000i			0.161690i
$154$		0			0
$155$	−12.0000	+	6.00000i	−0.963863	+	0.481932i
$156$	1.00000			0.0800641
$157$			13.0000i			1.03751i	0.854922	+	0.518756i	$0.173605\pi$
$157$			13.0000i			1.03751i	−0.854922	+	0.518756i	$0.826395\pi$
$158$			14.0000i			1.11378i
$159$	−1.00000			−0.0793052
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$		−	12.0000i		−	0.939913i	−0.882690	−	0.469956i	$-0.844270\pi$
$163$		−	12.0000i		−	0.939913i	0.882690	−	0.469956i	$-0.155730\pi$
$164$	−9.00000			−0.702782
$165$	−5.00000	−	10.0000i	−0.389249	−	0.778499i
$166$	−10.0000			−0.776151
$167$		−	19.0000i		−	1.47026i	−0.677924	−	0.735132i	$-0.737120\pi$
$167$		−	19.0000i		−	1.47026i	0.677924	−	0.735132i	$-0.262880\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	−4.00000	+	2.00000i	−0.306786	+	0.153393i
$171$	−7.00000			−0.535303
$172$		−	10.0000i		−	0.762493i
$173$		−	7.00000i		−	0.532200i	−0.963945	−	0.266100i	$-0.914265\pi$
$173$		−	7.00000i		−	0.532200i	0.963945	−	0.266100i	$-0.0857352\pi$
$174$		0			0
$175$		0			0
$176$	−5.00000			−0.376889
$177$		−	4.00000i		−	0.300658i
$178$			10.0000i			0.749532i
$179$	11.0000			0.822179			0.411089	−	0.911595i	$-0.365148\pi$
$179$	11.0000			0.822179			0.411089	+	0.911595i	$0.365148\pi$
$180$	−2.00000	+	1.00000i	−0.149071	+	0.0745356i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		−	2.00000i		−	0.147844i
$184$	3.00000			0.221163
$185$	−5.00000	−	10.0000i	−0.367607	−	0.735215i
$186$	6.00000			0.439941
$187$			10.0000i			0.731272i
$188$			13.0000i			0.948122i
$189$		0			0
$190$	−7.00000	−	14.0000i	−0.507833	−	1.01567i
$191$	−16.0000			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$192$			1.00000i			0.0721688i
$193$		−	18.0000i		−	1.29567i	−0.761781	−	0.647834i	$-0.775675\pi$
$193$		−	18.0000i		−	1.29567i	0.761781	−	0.647834i	$-0.224325\pi$
$194$	−8.00000			−0.574367
$195$	2.00000	−	1.00000i	0.143223	−	0.0716115i
$196$		0			0
$197$			27.0000i			1.92367i	0.273629	+	0.961835i	$0.411776\pi$
$197$			27.0000i			1.92367i	−0.273629	+	0.961835i	$0.588224\pi$
$198$			5.00000i			0.355335i
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$	−6.00000			−0.423207
$202$		−	8.00000i		−	0.562878i
$203$		0			0
$204$	2.00000			0.140028
$205$	−18.0000	+	9.00000i	−1.25717	+	0.628587i
$206$		0			0
$207$		−	3.00000i		−	0.208514i
$208$		−	1.00000i		−	0.0693375i
$209$	−35.0000			−2.42100
$210$		0			0
$211$	19.0000			1.30801			0.654007	−	0.756489i	$-0.273087\pi$
$211$	19.0000			1.30801			0.654007	+	0.756489i	$0.273087\pi$
$212$			1.00000i			0.0686803i
$213$			2.00000i			0.137038i
$214$	12.0000			0.820303
$215$	−10.0000	−	20.0000i	−0.681994	−	1.36399i
$216$	1.00000			0.0680414
$217$		0			0
$218$			18.0000i			1.21911i
$219$	−4.00000			−0.270295
$220$	−10.0000	+	5.00000i	−0.674200	+	0.337100i
$221$	−2.00000			−0.134535
$222$			5.00000i			0.335578i
$223$		−	16.0000i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$		−	16.0000i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$		0			0
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$	−6.00000			−0.399114
$227$			14.0000i			0.929213i	0.885517	+	0.464606i	$0.153804\pi$
$227$			14.0000i			0.929213i	−0.885517	+	0.464606i	$0.846196\pi$
$228$			7.00000i			0.463586i
$229$	−4.00000			−0.264327			−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000			−0.264327			−0.132164	+	0.991228i	$0.542192\pi$
$230$	6.00000	−	3.00000i	0.395628	−	0.197814i
$231$		0			0
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$	−1.00000			−0.0653720
$235$	13.0000	+	26.0000i	0.848026	+	1.69605i
$236$	−4.00000			−0.260378
$237$		−	14.0000i		−	0.909398i
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$	1.00000	+	2.00000i	0.0645497	+	0.129099i
$241$	1.00000			0.0644157			0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000			0.0644157			0.0322078	+	0.999481i	$0.489746\pi$
$242$			14.0000i			0.899954i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	9.00000			0.573819
$247$		−	7.00000i		−	0.445399i
$248$		−	6.00000i		−	0.381000i
$249$	10.0000			0.633724
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$		−	15.0000i		−	0.943042i
$254$	9.00000			0.564710
$255$	4.00000	−	2.00000i	0.250490	−	0.125245i
$256$	1.00000			0.0625000
$257$		−	10.0000i		−	0.623783i	−0.950118	−	0.311891i	$-0.899037\pi$
$257$		−	10.0000i		−	0.623783i	0.950118	−	0.311891i	$-0.100963\pi$
$258$			10.0000i			0.622573i
$259$		0			0
$260$	−1.00000	−	2.00000i	−0.0620174	−	0.124035i
$261$		0			0
$262$			17.0000i			1.05026i
$263$			24.0000i			1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$			24.0000i			1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$	5.00000			0.307729
$265$	1.00000	+	2.00000i	0.0614295	+	0.122859i
$266$		0			0
$267$		−	10.0000i		−	0.611990i
$268$			6.00000i			0.366508i
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$	2.00000	−	1.00000i	0.121716	−	0.0608581i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$	−4.00000			−0.241649
$275$	−15.0000	+	20.0000i	−0.904534	+	1.20605i
$276$	−3.00000			−0.180579
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$		−	8.00000i		−	0.479808i
$279$	−6.00000			−0.359211
$280$		0			0
$281$	−11.0000			−0.656205			−0.328102	−	0.944642i	$-0.606409\pi$
$281$	−11.0000			−0.656205			−0.328102	+	0.944642i	$0.606409\pi$
$282$		−	13.0000i		−	0.774139i
$283$		−	26.0000i		−	1.54554i	−0.634686	−	0.772770i	$-0.718871\pi$
$283$		−	26.0000i		−	1.54554i	0.634686	−	0.772770i	$-0.281129\pi$
$284$	2.00000			0.118678
$285$	7.00000	+	14.0000i	0.414644	+	0.829288i
$286$	−5.00000			−0.295656
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	13.0000			0.764706
$290$		0			0
$291$	8.00000			0.468968
$292$			4.00000i			0.234082i
$293$		−	1.00000i		−	0.0584206i	−0.999573	−	0.0292103i	$-0.990701\pi$
$293$		−	1.00000i		−	0.0584206i	0.999573	−	0.0292103i	$-0.00929925\pi$
$294$		0			0
$295$	−8.00000	+	4.00000i	−0.465778	+	0.232889i
$296$	5.00000			0.290619
$297$		−	5.00000i		−	0.290129i
$298$			6.00000i			0.347571i
$299$	3.00000			0.173494
$300$	4.00000	+	3.00000i	0.230940	+	0.173205i
$301$		0			0
$302$		−	22.0000i		−	1.26596i
$303$			8.00000i			0.459588i
$304$	7.00000			0.401478
$305$	−4.00000	+	2.00000i	−0.229039	+	0.114520i
$306$	−2.00000			−0.114332
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$		0			0
$309$		0			0
$310$	−6.00000	−	12.0000i	−0.340777	−	0.681554i
$311$	26.0000			1.47432			0.737162	−	0.675716i	$-0.236165\pi$
$311$	26.0000			1.47432			0.737162	+	0.675716i	$0.236165\pi$
$312$			1.00000i			0.0566139i
$313$			10.0000i			0.565233i	0.959233	+	0.282617i	$0.0912024\pi$
$313$			10.0000i			0.565233i	−0.959233	+	0.282617i	$0.908798\pi$
$314$	−13.0000			−0.733632
$315$		0			0
$316$	−14.0000			−0.787562
$317$		−	2.00000i		−	0.112331i	−0.998421	−	0.0561656i	$-0.982113\pi$
$317$		−	2.00000i		−	0.112331i	0.998421	−	0.0561656i	$-0.0178875\pi$
$318$		−	1.00000i		−	0.0560772i
$319$		0			0
$320$	2.00000	−	1.00000i	0.111803	−	0.0559017i
$321$	−12.0000			−0.669775
$322$		0			0
$323$		−	14.0000i		−	0.778981i
$324$	−1.00000			−0.0555556
$325$	−4.00000	−	3.00000i	−0.221880	−	0.166410i
$326$	12.0000			0.664619
$327$		−	18.0000i		−	0.995402i
$328$		−	9.00000i		−	0.496942i
$329$		0			0
$330$	10.0000	−	5.00000i	0.550482	−	0.275241i
$331$	−15.0000			−0.824475			−0.412237	−	0.911077i	$-0.635253\pi$
$331$	−15.0000			−0.824475			−0.412237	+	0.911077i	$0.635253\pi$
$332$		−	10.0000i		−	0.548821i
$333$		−	5.00000i		−	0.273998i
$334$	19.0000			1.03963
$335$	6.00000	+	12.0000i	0.327815	+	0.655630i
$336$		0			0
$337$			14.0000i			0.762629i	0.924445	+	0.381314i	$0.124528\pi$
$337$			14.0000i			0.762629i	−0.924445	+	0.381314i	$0.875472\pi$
$338$			12.0000i			0.652714i
$339$	6.00000			0.325875
$340$	−2.00000	−	4.00000i	−0.108465	−	0.216930i
$341$	−30.0000			−1.62459
$342$		−	7.00000i		−	0.378517i
$343$		0			0
$344$	10.0000			0.539164
$345$	−6.00000	+	3.00000i	−0.323029	+	0.161515i
$346$	7.00000			0.376322
$347$			16.0000i			0.858925i	0.903085	+	0.429463i	$0.141297\pi$
$347$			16.0000i			0.858925i	−0.903085	+	0.429463i	$0.858703\pi$
$348$		0			0
$349$	−24.0000			−1.28469			−0.642345	−	0.766415i	$-0.722038\pi$
$349$	−24.0000			−1.28469			−0.642345	+	0.766415i	$0.722038\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$		−	5.00000i		−	0.266501i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	4.00000			0.212598
$355$	4.00000	−	2.00000i	0.212298	−	0.106149i
$356$	−10.0000			−0.529999
$357$		0			0
$358$			11.0000i			0.581368i
$359$	28.0000			1.47778			0.738892	−	0.673824i	$-0.235349\pi$
$359$	28.0000			1.47778			0.738892	+	0.673824i	$0.235349\pi$
$360$	−1.00000	−	2.00000i	−0.0527046	−	0.105409i
$361$	30.0000			1.57895
$362$			2.00000i			0.105118i
$363$		−	14.0000i		−	0.734809i
$364$		0			0
$365$	4.00000	+	8.00000i	0.209370	+	0.418739i
$366$	2.00000			0.104542
$367$		−	37.0000i		−	1.93138i	−0.259690	−	0.965692i	$-0.583620\pi$
$367$		−	37.0000i		−	1.93138i	0.259690	−	0.965692i	$-0.416380\pi$
$368$			3.00000i			0.156386i
$369$	−9.00000			−0.468521
$370$	10.0000	−	5.00000i	0.519875	−	0.259938i
$371$		0			0
$372$			6.00000i			0.311086i
$373$			6.00000i			0.310668i	0.987862	+	0.155334i	$0.0496454\pi$
$373$			6.00000i			0.310668i	−0.987862	+	0.155334i	$0.950355\pi$
$374$	−10.0000			−0.517088
$375$	11.0000	+	2.00000i	0.568038	+	0.103280i
$376$	−13.0000			−0.670424
$377$		0			0
$378$		0			0
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$	14.0000	−	7.00000i	0.718185	−	0.359092i
$381$	−9.00000			−0.461084
$382$		−	16.0000i		−	0.818631i
$383$			9.00000i			0.459879i	0.973205	+	0.229939i	$0.0738528\pi$
$383$			9.00000i			0.459879i	−0.973205	+	0.229939i	$0.926147\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	18.0000			0.916176
$387$		−	10.0000i		−	0.508329i
$388$		−	8.00000i		−	0.406138i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$	1.00000	+	2.00000i	0.0506370	+	0.101274i
$391$	6.00000			0.303433
$392$		0			0
$393$		−	17.0000i		−	0.857537i
$394$	−27.0000			−1.36024
$395$	−28.0000	+	14.0000i	−1.40883	+	0.704416i
$396$	−5.00000			−0.251259
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$		−	14.0000i		−	0.701757i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−27.0000			−1.34832			−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000			−1.34832			−0.674158	+	0.738587i	$0.735493\pi$
$402$		−	6.00000i		−	0.299253i
$403$		−	6.00000i		−	0.298881i
$404$	8.00000			0.398015
$405$	−2.00000	+	1.00000i	−0.0993808	+	0.0496904i
$406$		0			0
$407$		−	25.0000i		−	1.23920i
$408$			2.00000i			0.0990148i
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$	−9.00000	−	18.0000i	−0.444478	−	0.888957i
$411$	4.00000			0.197305
$412$		0			0
$413$		0			0
$414$	3.00000			0.147442
$415$	−10.0000	−	20.0000i	−0.490881	−	0.981761i
$416$	1.00000			0.0490290
$417$			8.00000i			0.391762i
$418$		−	35.0000i		−	1.71191i
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$			19.0000i			0.924906i
$423$			13.0000i			0.632082i
$424$	−1.00000			−0.0485643
$425$	−8.00000	−	6.00000i	−0.388057	−	0.291043i
$426$	−2.00000			−0.0969003
$427$		0			0
$428$			12.0000i			0.580042i
$429$	5.00000			0.241402
$430$	20.0000	−	10.0000i	0.964486	−	0.482243i
$431$	18.0000			0.867029			0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000			0.867029			0.433515	+	0.901146i	$0.357273\pi$
$432$			1.00000i			0.0481125i
$433$		−	4.00000i		−	0.192228i	−0.995370	−	0.0961139i	$-0.969359\pi$
$433$		−	4.00000i		−	0.192228i	0.995370	−	0.0961139i	$-0.0306413\pi$
$434$		0			0
$435$		0			0
$436$	−18.0000			−0.862044
$437$			21.0000i			1.00457i
$438$		−	4.00000i		−	0.191127i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	−5.00000	−	10.0000i	−0.238366	−	0.476731i
$441$		0			0
$442$		−	2.00000i		−	0.0951303i
$443$		−	6.00000i		−	0.285069i	−0.989790	−	0.142534i	$-0.954475\pi$
$443$		−	6.00000i		−	0.285069i	0.989790	−	0.142534i	$-0.0455251\pi$
$444$	−5.00000			−0.237289
$445$	−20.0000	+	10.0000i	−0.948091	+	0.474045i
$446$	16.0000			0.757622
$447$		−	6.00000i		−	0.283790i
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$	−45.0000			−2.11897
$452$		−	6.00000i		−	0.282216i
$453$			22.0000i			1.03365i
$454$	−14.0000			−0.657053
$455$		0			0
$456$	−7.00000			−0.327805
$457$			38.0000i			1.77757i	0.458329	+	0.888783i	$0.348448\pi$
$457$			38.0000i			1.77757i	−0.458329	+	0.888783i	$0.651552\pi$
$458$		−	4.00000i		−	0.186908i
$459$	2.00000			0.0933520
$460$	3.00000	+	6.00000i	0.139876	+	0.279751i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$		−	15.0000i		−	0.697109i	−0.937288	−	0.348555i	$-0.886673\pi$
$463$		−	15.0000i		−	0.697109i	0.937288	−	0.348555i	$-0.113327\pi$
$464$		0			0
$465$	6.00000	+	12.0000i	0.278243	+	0.556487i
$466$		0			0
$467$			2.00000i			0.0925490i	0.998929	+	0.0462745i	$0.0147349\pi$
$467$			2.00000i			0.0925490i	−0.998929	+	0.0462745i	$0.985265\pi$
$468$		−	1.00000i		−	0.0462250i
$469$		0			0
$470$	−26.0000	+	13.0000i	−1.19929	+	0.599645i
$471$	13.0000			0.599008
$472$		−	4.00000i		−	0.184115i
$473$		−	50.0000i		−	2.29900i
$474$	14.0000			0.643041
$475$	21.0000	−	28.0000i	0.963546	−	1.28473i
$476$		0			0
$477$			1.00000i			0.0457869i
$478$		−	20.0000i		−	0.914779i
$479$	8.00000			0.365529			0.182765	−	0.983157i	$-0.441495\pi$
$479$	8.00000			0.365529			0.182765	+	0.983157i	$0.441495\pi$
$480$	−2.00000	+	1.00000i	−0.0912871	+	0.0456435i
$481$	5.00000			0.227980
$482$			1.00000i			0.0455488i
$483$		0			0
$484$	−14.0000			−0.636364
$485$	−8.00000	−	16.0000i	−0.363261	−	0.726523i
$486$	1.00000			0.0453609
$487$		−	24.0000i		−	1.08754i	−0.839233	−	0.543772i	$-0.816996\pi$
$487$		−	24.0000i		−	1.08754i	0.839233	−	0.543772i	$-0.183004\pi$
$488$		−	2.00000i		−	0.0905357i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$			9.00000i			0.405751i
$493$		0			0
$494$	7.00000			0.314945
$495$	−10.0000	+	5.00000i	−0.449467	+	0.224733i
$496$	6.00000			0.269408
$497$		0			0
$498$			10.0000i			0.448111i
$499$	28.0000			1.25345			0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000			1.25345			0.626726	+	0.779240i	$0.284395\pi$
$500$	2.00000	−	11.0000i	0.0894427	−	0.491935i
$501$	−19.0000			−0.848857
$502$			3.00000i			0.133897i
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$		0			0
$505$	16.0000	−	8.00000i	0.711991	−	0.355995i
$506$	15.0000			0.666831
$507$		−	12.0000i		−	0.532939i
$508$			9.00000i			0.399310i
$509$	14.0000			0.620539			0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000			0.620539			0.310270	+	0.950649i	$0.399581\pi$
$510$	2.00000	+	4.00000i	0.0885615	+	0.177123i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			7.00000i			0.309058i
$514$	10.0000			0.441081
$515$		0			0
$516$	−10.0000			−0.440225
$517$			65.0000i			2.85870i
$518$		0			0
$519$	−7.00000			−0.307266
$520$	2.00000	−	1.00000i	0.0877058	−	0.0438529i
$521$	15.0000			0.657162			0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$		0			0
$523$		−	12.0000i		−	0.524723i	−0.964970	−	0.262362i	$-0.915499\pi$
$523$		−	12.0000i		−	0.524723i	0.964970	−	0.262362i	$-0.0845013\pi$
$524$	−17.0000			−0.742648
$525$		0			0
$526$	−24.0000			−1.04645
$527$		−	12.0000i		−	0.522728i
$528$			5.00000i			0.217597i
$529$	14.0000			0.608696
$530$	−2.00000	+	1.00000i	−0.0868744	+	0.0434372i
$531$	−4.00000			−0.173585
$532$		0			0
$533$		−	9.00000i		−	0.389833i
$534$	10.0000			0.432742
$535$	12.0000	+	24.0000i	0.518805	+	1.03761i
$536$	−6.00000			−0.259161
$537$		−	11.0000i		−	0.474685i
$538$			14.0000i			0.603583i
$539$		0			0
$540$	1.00000	+	2.00000i	0.0430331	+	0.0860663i
$541$	4.00000			0.171973			0.0859867	−	0.996296i	$-0.472596\pi$
$541$	4.00000			0.171973			0.0859867	+	0.996296i	$0.472596\pi$
$542$		−	8.00000i		−	0.343629i
$543$		−	2.00000i		−	0.0858282i
$544$	2.00000			0.0857493
$545$	−36.0000	+	18.0000i	−1.54207	+	0.771035i
$546$		0			0
$547$			14.0000i			0.598597i	0.954160	+	0.299298i	$0.0967526\pi$
$547$			14.0000i			0.598597i	−0.954160	+	0.299298i	$0.903247\pi$
$548$		−	4.00000i		−	0.170872i
$549$	−2.00000			−0.0853579
$550$	−20.0000	−	15.0000i	−0.852803	−	0.639602i
$551$		0			0
$552$		−	3.00000i		−	0.127688i
$553$		0			0
$554$	2.00000			0.0849719
$555$	−10.0000	+	5.00000i	−0.424476	+	0.212238i
$556$	8.00000			0.339276
$557$			39.0000i			1.65248i	0.563316	+	0.826242i	$0.309525\pi$
$557$			39.0000i			1.65248i	−0.563316	+	0.826242i	$0.690475\pi$
$558$		−	6.00000i		−	0.254000i
$559$	10.0000			0.422955
$560$		0			0
$561$	10.0000			0.422200
$562$		−	11.0000i		−	0.464007i
$563$		−	30.0000i		−	1.26435i	−0.774826	−	0.632175i	$-0.782163\pi$
$563$		−	30.0000i		−	1.26435i	0.774826	−	0.632175i	$-0.217837\pi$
$564$	13.0000			0.547399
$565$	−6.00000	−	12.0000i	−0.252422	−	0.504844i
$566$	26.0000			1.09286
$567$		0			0
$568$			2.00000i			0.0839181i
$569$	3.00000			0.125767			0.0628833	−	0.998021i	$-0.479970\pi$
$569$	3.00000			0.125767			0.0628833	+	0.998021i	$0.479970\pi$
$570$	−14.0000	+	7.00000i	−0.586395	+	0.293198i
$571$	−8.00000			−0.334790			−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000			−0.334790			−0.167395	+	0.985890i	$0.553535\pi$
$572$		−	5.00000i		−	0.209061i
$573$			16.0000i			0.668410i
$574$		0			0
$575$	12.0000	+	9.00000i	0.500435	+	0.375326i
$576$	1.00000			0.0416667
$577$			24.0000i			0.999133i	0.866276	+	0.499567i	$0.166507\pi$
$577$			24.0000i			0.999133i	−0.866276	+	0.499567i	$0.833493\pi$
$578$			13.0000i			0.540729i
$579$	−18.0000			−0.748054
$580$		0			0
$581$		0			0
$582$			8.00000i			0.331611i
$583$			5.00000i			0.207079i
$584$	−4.00000			−0.165521
$585$	−1.00000	−	2.00000i	−0.0413449	−	0.0826898i
$586$	1.00000			0.0413096
$587$			2.00000i			0.0825488i	0.999148	+	0.0412744i	$0.0131418\pi$
$587$			2.00000i			0.0825488i	−0.999148	+	0.0412744i	$0.986858\pi$
$588$		0			0
$589$	42.0000			1.73058
$590$	−4.00000	−	8.00000i	−0.164677	−	0.329355i
$591$	27.0000			1.11063
$592$			5.00000i			0.205499i
$593$			34.0000i			1.39621i	0.715994	+	0.698106i	$0.245974\pi$
$593$			34.0000i			1.39621i	−0.715994	+	0.698106i	$0.754026\pi$
$594$	5.00000			0.205152
$595$		0			0
$596$	−6.00000			−0.245770
$597$			14.0000i			0.572982i
$598$			3.00000i			0.122679i
$599$	28.0000			1.14405			0.572024	−	0.820237i	$-0.306158\pi$
$599$	28.0000			1.14405			0.572024	+	0.820237i	$0.306158\pi$
$600$	−3.00000	+	4.00000i	−0.122474	+	0.163299i
$601$	30.0000			1.22373			0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000			1.22373			0.611863	+	0.790964i	$0.290420\pi$
$602$		0			0
$603$			6.00000i			0.244339i
$604$	22.0000			0.895167
$605$	−28.0000	+	14.0000i	−1.13836	+	0.569181i
$606$	−8.00000			−0.324978
$607$			13.0000i			0.527654i	0.964570	+	0.263827i	$0.0849848\pi$
$607$			13.0000i			0.527654i	−0.964570	+	0.263827i	$0.915015\pi$
$608$			7.00000i			0.283887i
$609$		0			0
$610$	−2.00000	−	4.00000i	−0.0809776	−	0.161955i
$611$	−13.0000			−0.525924
$612$		−	2.00000i		−	0.0808452i
$613$			19.0000i			0.767403i	0.923457	+	0.383701i	$0.125351\pi$
$613$			19.0000i			0.767403i	−0.923457	+	0.383701i	$0.874649\pi$
$614$	−2.00000			−0.0807134
$615$	9.00000	+	18.0000i	0.362915	+	0.725830i
$616$		0			0
$617$		−	30.0000i		−	1.20775i	−0.797077	−	0.603877i	$-0.793622\pi$
$617$		−	30.0000i		−	1.20775i	0.797077	−	0.603877i	$-0.206378\pi$
$618$		0			0
$619$	15.0000			0.602901			0.301450	−	0.953482i	$-0.402529\pi$
$619$	15.0000			0.602901			0.301450	+	0.953482i	$0.402529\pi$
$620$	12.0000	−	6.00000i	0.481932	−	0.240966i
$621$	−3.00000			−0.120386
$622$			26.0000i			1.04251i
$623$		0			0
$624$	−1.00000			−0.0400320
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−10.0000			−0.399680
$627$			35.0000i			1.39777i
$628$		−	13.0000i		−	0.518756i
$629$	10.0000			0.398726
$630$		0			0
$631$	18.0000			0.716569			0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000			0.716569			0.358284	+	0.933613i	$0.383362\pi$
$632$		−	14.0000i		−	0.556890i
$633$		−	19.0000i		−	0.755182i
$634$	2.00000			0.0794301
$635$	9.00000	+	18.0000i	0.357154	+	0.714308i
$636$	1.00000			0.0396526
$637$		0			0
$638$		0			0
$639$	2.00000			0.0791188
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	−33.0000			−1.30342			−0.651711	−	0.758468i	$-0.725948\pi$
$641$	−33.0000			−1.30342			−0.651711	+	0.758468i	$0.725948\pi$
$642$		−	12.0000i		−	0.473602i
$643$		−	38.0000i		−	1.49857i	−0.662246	−	0.749287i	$-0.730396\pi$
$643$		−	38.0000i		−	1.49857i	0.662246	−	0.749287i	$-0.269604\pi$
$644$		0			0
$645$	−20.0000	+	10.0000i	−0.787499	+	0.393750i
$646$	14.0000			0.550823
$647$		−	1.00000i		−	0.0393141i	−0.999807	−	0.0196570i	$-0.993743\pi$
$647$		−	1.00000i		−	0.0393141i	0.999807	−	0.0196570i	$-0.00625743\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−20.0000			−0.785069
$650$	3.00000	−	4.00000i	0.117670	−	0.156893i
$651$		0			0
$652$			12.0000i			0.469956i
$653$			5.00000i			0.195665i	0.995203	+	0.0978326i	$0.0311910\pi$
$653$			5.00000i			0.195665i	−0.995203	+	0.0978326i	$0.968809\pi$
$654$	18.0000			0.703856
$655$	−34.0000	+	17.0000i	−1.32849	+	0.664245i
$656$	9.00000			0.351391
$657$			4.00000i			0.156055i
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	5.00000	+	10.0000i	0.194625	+	0.389249i
$661$	−40.0000			−1.55582			−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000			−1.55582			−0.777910	+	0.628376i	$0.783720\pi$
$662$		−	15.0000i		−	0.582992i
$663$			2.00000i			0.0776736i
$664$	10.0000			0.388075
$665$		0			0
$666$	5.00000			0.193746
$667$		0			0
$668$			19.0000i			0.735132i
$669$	−16.0000			−0.618596
$670$	−12.0000	+	6.00000i	−0.463600	+	0.231800i
$671$	−10.0000			−0.386046
$672$		0			0
$673$			36.0000i			1.38770i	0.720121	+	0.693849i	$0.244086\pi$
$673$			36.0000i			1.38770i	−0.720121	+	0.693849i	$0.755914\pi$
$674$	−14.0000			−0.539260
$675$	4.00000	+	3.00000i	0.153960	+	0.115470i
$676$	−12.0000			−0.461538
$677$			33.0000i			1.26829i	0.773213	+	0.634147i	$0.218648\pi$
$677$			33.0000i			1.26829i	−0.773213	+	0.634147i	$0.781352\pi$
$678$			6.00000i			0.230429i
$679$		0			0
$680$	4.00000	−	2.00000i	0.153393	−	0.0766965i
$681$	14.0000			0.536481
$682$		−	30.0000i		−	1.14876i
$683$		−	4.00000i		−	0.153056i	−0.997067	−	0.0765279i	$-0.975617\pi$
$683$		−	4.00000i		−	0.153056i	0.997067	−	0.0765279i	$-0.0243834\pi$
$684$	7.00000			0.267652
$685$	−4.00000	−	8.00000i	−0.152832	−	0.305664i
$686$		0			0
$687$			4.00000i			0.152610i
$688$			10.0000i			0.381246i
$689$	−1.00000			−0.0380970
$690$	−3.00000	−	6.00000i	−0.114208	−	0.228416i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$			7.00000i			0.266100i
$693$		0			0
$694$	−16.0000			−0.607352
$695$	16.0000	−	8.00000i	0.606915	−	0.303457i
$696$		0			0
$697$		−	18.0000i		−	0.681799i
$698$		−	24.0000i		−	0.908413i
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$			1.00000i			0.0377426i
$703$			35.0000i			1.32005i
$704$	5.00000			0.188445
$705$	26.0000	−	13.0000i	0.979217	−	0.489608i
$706$		0			0
$707$		0			0
$708$			4.00000i			0.150329i
$709$	−16.0000			−0.600893			−0.300446	−	0.953799i	$-0.597136\pi$
$709$	−16.0000			−0.600893			−0.300446	+	0.953799i	$0.597136\pi$
$710$	2.00000	+	4.00000i	0.0750587	+	0.150117i
$711$	−14.0000			−0.525041
$712$		−	10.0000i		−	0.374766i
$713$			18.0000i			0.674105i
$714$		0			0
$715$	−5.00000	−	10.0000i	−0.186989	−	0.373979i
$716$	−11.0000			−0.411089
$717$			20.0000i			0.746914i
$718$			28.0000i			1.04495i
$719$	−2.00000			−0.0745874			−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000			−0.0745874			−0.0372937	+	0.999304i	$0.511874\pi$
$720$	2.00000	−	1.00000i	0.0745356	−	0.0372678i
$721$		0			0
$722$			30.0000i			1.11648i
$723$		−	1.00000i		−	0.0371904i
$724$	−2.00000			−0.0743294
$725$		0			0
$726$	14.0000			0.519589
$727$			53.0000i			1.96566i	0.184510	+	0.982831i	$0.440930\pi$
$727$			53.0000i			1.96566i	−0.184510	+	0.982831i	$0.559070\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−8.00000	+	4.00000i	−0.296093	+	0.148047i
$731$	20.0000			0.739727
$732$			2.00000i			0.0739221i
$733$			21.0000i			0.775653i	0.921732	+	0.387826i	$0.126774\pi$
$733$			21.0000i			0.775653i	−0.921732	+	0.387826i	$0.873226\pi$
$734$	37.0000			1.36569
$735$		0			0
$736$	−3.00000			−0.110581
$737$			30.0000i			1.10506i
$738$		−	9.00000i		−	0.331295i
$739$	−47.0000			−1.72892			−0.864461	−	0.502699i	$-0.832340\pi$
$739$	−47.0000			−1.72892			−0.864461	+	0.502699i	$0.832340\pi$
$740$	5.00000	+	10.0000i	0.183804	+	0.367607i
$741$	−7.00000			−0.257151
$742$		0			0
$743$		−	31.0000i		−	1.13728i	−0.822587	−	0.568640i	$-0.807470\pi$
$743$		−	31.0000i		−	1.13728i	0.822587	−	0.568640i	$-0.192530\pi$
$744$	−6.00000			−0.219971
$745$	−12.0000	+	6.00000i	−0.439646	+	0.219823i
$746$	−6.00000			−0.219676
$747$		−	10.0000i		−	0.365881i
$748$		−	10.0000i		−	0.365636i
$749$		0			0
$750$	−2.00000	+	11.0000i	−0.0730297	+	0.401663i
$751$	4.00000			0.145962			0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000			0.145962			0.0729810	+	0.997333i	$0.476749\pi$
$752$		−	13.0000i		−	0.474061i
$753$		−	3.00000i		−	0.109326i
$754$		0			0
$755$	44.0000	−	22.0000i	1.60132	−	0.800662i
$756$		0			0
$757$			26.0000i			0.944986i	0.881334	+	0.472493i	$0.156646\pi$
$757$			26.0000i			0.944986i	−0.881334	+	0.472493i	$0.843354\pi$
$758$			1.00000i			0.0363216i
$759$	−15.0000			−0.544466
$760$	7.00000	+	14.0000i	0.253917	+	0.507833i
$761$	3.00000			0.108750			0.0543750	−	0.998521i	$-0.482683\pi$
$761$	3.00000			0.108750			0.0543750	+	0.998521i	$0.482683\pi$
$762$		−	9.00000i		−	0.326036i
$763$		0			0
$764$	16.0000			0.578860
$765$	−2.00000	−	4.00000i	−0.0723102	−	0.144620i
$766$	−9.00000			−0.325183
$767$		−	4.00000i		−	0.144432i
$768$		−	1.00000i		−	0.0360844i
$769$	51.0000			1.83911			0.919554	−	0.392965i	$-0.128551\pi$
$769$	51.0000			1.83911			0.919554	+	0.392965i	$0.128551\pi$
$770$		0			0
$771$	−10.0000			−0.360141
$772$			18.0000i			0.647834i
$773$			37.0000i			1.33080i	0.746488	+	0.665399i	$0.231738\pi$
$773$			37.0000i			1.33080i	−0.746488	+	0.665399i	$0.768262\pi$
$774$	10.0000			0.359443
$775$	18.0000	−	24.0000i	0.646579	−	0.862105i
$776$	8.00000			0.287183
$777$		0			0
$778$		−	6.00000i		−	0.215110i
$779$	63.0000			2.25721
$780$	−2.00000	+	1.00000i	−0.0716115	+	0.0358057i
$781$	10.0000			0.357828
$782$			6.00000i			0.214560i
$783$		0			0
$784$		0			0
$785$	−13.0000	−	26.0000i	−0.463990	−	0.927980i
$786$	17.0000			0.606370
$787$			38.0000i			1.35455i	0.735728	+	0.677277i	$0.236840\pi$
$787$			38.0000i			1.35455i	−0.735728	+	0.677277i	$0.763160\pi$
$788$		−	27.0000i		−	0.961835i
$789$	24.0000			0.854423
$790$	−14.0000	−	28.0000i	−0.498098	−	0.996195i
$791$		0			0
$792$		−	5.00000i		−	0.177667i
$793$		−	2.00000i		−	0.0710221i
$794$	2.00000			0.0709773
$795$	2.00000	−	1.00000i	0.0709327	−	0.0354663i
$796$	14.0000			0.496217
$797$		−	30.0000i		−	1.06265i	−0.847167	−	0.531327i	$-0.821693\pi$
$797$		−	30.0000i		−	1.06265i	0.847167	−	0.531327i	$-0.178307\pi$
$798$		0			0
$799$	−26.0000			−0.919814
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$	−10.0000			−0.353333
$802$		−	27.0000i		−	0.953403i
$803$			20.0000i			0.705785i
$804$	6.00000			0.211604
$805$		0			0
$806$	6.00000			0.211341
$807$		−	14.0000i		−	0.492823i
$808$			8.00000i			0.281439i
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$	−1.00000	−	2.00000i	−0.0351364	−	0.0702728i
$811$	−11.0000			−0.386262			−0.193131	−	0.981173i	$-0.561864\pi$
$811$	−11.0000			−0.386262			−0.193131	+	0.981173i	$0.561864\pi$
$812$		0			0
$813$			8.00000i			0.280572i
$814$	25.0000			0.876250
$815$	12.0000	+	24.0000i	0.420342	+	0.840683i
$816$	−2.00000			−0.0700140
$817$			70.0000i			2.44899i
$818$			10.0000i			0.349642i
$819$		0			0
$820$	18.0000	−	9.00000i	0.628587	−	0.314294i
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$			4.00000i			0.139516i
$823$		−	8.00000i		−	0.278862i	−0.990232	−	0.139431i	$-0.955473\pi$
$823$		−	8.00000i		−	0.278862i	0.990232	−	0.139431i	$-0.0445274\pi$
$824$		0			0
$825$	20.0000	+	15.0000i	0.696311	+	0.522233i
$826$		0			0
$827$			42.0000i			1.46048i	0.683189	+	0.730242i	$0.260592\pi$
$827$			42.0000i			1.46048i	−0.683189	+	0.730242i	$0.739408\pi$
$828$			3.00000i			0.104257i
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$	20.0000	−	10.0000i	0.694210	−	0.347105i
$831$	−2.00000			−0.0693792
$832$			1.00000i			0.0346688i
$833$		0			0
$834$	−8.00000			−0.277017
$835$	19.0000	+	38.0000i	0.657522	+	1.31504i
$836$	35.0000			1.21050
$837$			6.00000i			0.207390i
$838$			3.00000i			0.103633i
$839$	2.00000			0.0690477			0.0345238	−	0.999404i	$-0.489009\pi$
$839$	2.00000			0.0690477			0.0345238	+	0.999404i	$0.489009\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		−	20.0000i		−	0.689246i
$843$			11.0000i			0.378860i
$844$	−19.0000			−0.654007
$845$	−24.0000	+	12.0000i	−0.825625	+	0.412813i
$846$	−13.0000			−0.446949
$847$		0			0
$848$		−	1.00000i		−	0.0343401i
$849$	−26.0000			−0.892318
$850$	6.00000	−	8.00000i	0.205798	−	0.274398i
$851$	−15.0000			−0.514193
$852$		−	2.00000i		−	0.0685189i
$853$			49.0000i			1.67773i	0.544341	+	0.838864i	$0.316780\pi$
$853$			49.0000i			1.67773i	−0.544341	+	0.838864i	$0.683220\pi$
$854$		0			0
$855$	14.0000	−	7.00000i	0.478790	−	0.239395i
$856$	−12.0000			−0.410152
$857$		−	56.0000i		−	1.91292i	−0.291858	−	0.956462i	$-0.594273\pi$
$857$		−	56.0000i		−	1.91292i	0.291858	−	0.956462i	$-0.405727\pi$
$858$			5.00000i			0.170697i
$859$	36.0000			1.22830			0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000			1.22830			0.614152	+	0.789188i	$0.289498\pi$
$860$	10.0000	+	20.0000i	0.340997	+	0.681994i
$861$		0			0
$862$			18.0000i			0.613082i
$863$			15.0000i			0.510606i	0.966861	+	0.255303i	$0.0821752\pi$
$863$			15.0000i			0.510606i	−0.966861	+	0.255303i	$0.917825\pi$
$864$	−1.00000			−0.0340207
$865$	7.00000	+	14.0000i	0.238007	+	0.476014i
$866$	4.00000			0.135926
$867$		−	13.0000i		−	0.441503i
$868$		0			0
$869$	−70.0000			−2.37459
$870$		0			0
$871$	−6.00000			−0.203302
$872$		−	18.0000i		−	0.609557i
$873$		−	8.00000i		−	0.270759i
$874$	−21.0000			−0.710336
$875$		0			0
$876$	4.00000			0.135147
$877$			27.0000i			0.911725i	0.890050	+	0.455863i	$0.150669\pi$
$877$			27.0000i			0.911725i	−0.890050	+	0.455863i	$0.849331\pi$
$878$		0			0
$879$	−1.00000			−0.0337292
$880$	10.0000	−	5.00000i	0.337100	−	0.168550i
$881$	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
$883$		−	52.0000i		−	1.74994i	−0.484178	−	0.874970i	$-0.660881\pi$
$883$		−	52.0000i		−	1.74994i	0.484178	−	0.874970i	$-0.339119\pi$
$884$	2.00000			0.0672673
$885$	4.00000	+	8.00000i	0.134459	+	0.268917i
$886$	6.00000			0.201574
$887$		−	12.0000i		−	0.402921i	−0.979497	−	0.201460i	$-0.935431\pi$
$887$		−	12.0000i		−	0.402921i	0.979497	−	0.201460i	$-0.0645687\pi$
$888$		−	5.00000i		−	0.167789i
$889$		0			0
$890$	−10.0000	−	20.0000i	−0.335201	−	0.670402i
$891$	−5.00000			−0.167506
$892$			16.0000i			0.535720i
$893$		−	91.0000i		−	3.04520i
$894$	6.00000			0.200670
$895$	−22.0000	+	11.0000i	−0.735379	+	0.367689i
$896$		0			0
$897$		−	3.00000i		−	0.100167i
$898$		−	9.00000i		−	0.300334i
$899$		0			0
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$	−2.00000			−0.0666297
$902$		−	45.0000i		−	1.49834i
$903$		0			0
$904$	6.00000			0.199557
$905$	−4.00000	+	2.00000i	−0.132964	+	0.0664822i
$906$	−22.0000			−0.730901
$907$			16.0000i			0.531271i	0.964073	+	0.265636i	$0.0855818\pi$
$907$			16.0000i			0.531271i	−0.964073	+	0.265636i	$0.914418\pi$
$908$		−	14.0000i		−	0.464606i
$909$	8.00000			0.265343
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		−	7.00000i		−	0.231793i
$913$		−	50.0000i		−	1.65476i
$914$	−38.0000			−1.25693
$915$	2.00000	+	4.00000i	0.0661180	+	0.132236i
$916$	4.00000			0.132164
$917$		0			0
$918$			2.00000i			0.0660098i
$919$	−56.0000			−1.84727			−0.923635	−	0.383274i	$-0.874797\pi$
$919$	−56.0000			−1.84727			−0.923635	+	0.383274i	$0.874797\pi$
$920$	−6.00000	+	3.00000i	−0.197814	+	0.0989071i
$921$	2.00000			0.0659022
$922$			12.0000i			0.395199i
$923$			2.00000i			0.0658308i
$924$		0			0
$925$	20.0000	+	15.0000i	0.657596	+	0.493197i
$926$	15.0000			0.492931
$927$		0			0
$928$		0			0
$929$	33.0000			1.08269			0.541347	−	0.840799i	$-0.317914\pi$
$929$	33.0000			1.08269			0.541347	+	0.840799i	$0.317914\pi$
$930$	−12.0000	+	6.00000i	−0.393496	+	0.196748i
$931$		0			0
$932$		0			0
$933$		−	26.0000i		−	0.851202i
$934$	−2.00000			−0.0654420
$935$	−10.0000	−	20.0000i	−0.327035	−	0.654070i
$936$	1.00000			0.0326860
$937$		−	34.0000i		−	1.11073i	−0.831606	−	0.555366i	$-0.812578\pi$
$937$		−	34.0000i		−	1.11073i	0.831606	−	0.555366i	$-0.187422\pi$
$938$		0			0
$939$	10.0000			0.326338
$940$	−13.0000	−	26.0000i	−0.424013	−	0.848026i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$			13.0000i			0.423563i
$943$			27.0000i			0.879241i
$944$	4.00000			0.130189
$945$		0			0
$946$	50.0000			1.62564
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$			14.0000i			0.454699i
$949$	−4.00000			−0.129845
$950$	28.0000	+	21.0000i	0.908440	+	0.681330i
$951$	−2.00000			−0.0648544
$952$		0			0
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$	−1.00000			−0.0323762
$955$	32.0000	−	16.0000i	1.03550	−	0.517748i
$956$	20.0000			0.646846
$957$		0			0
$958$			8.00000i			0.258468i
$959$		0			0
$960$	−1.00000	−	2.00000i	−0.0322749	−	0.0645497i
$961$	5.00000			0.161290
$962$			5.00000i			0.161206i
$963$			12.0000i			0.386695i
$964$	−1.00000			−0.0322078
$965$	18.0000	+	36.0000i	0.579441	+	1.15888i
$966$		0			0
$967$			24.0000i			0.771788i	0.922543	+	0.385894i	$0.126107\pi$
$967$			24.0000i			0.771788i	−0.922543	+	0.385894i	$0.873893\pi$
$968$		−	14.0000i		−	0.449977i
$969$	−14.0000			−0.449745
$970$	16.0000	−	8.00000i	0.513729	−	0.256865i
$971$	−39.0000			−1.25157			−0.625785	−	0.779996i	$-0.715221\pi$
$971$	−39.0000			−1.25157			−0.625785	+	0.779996i	$0.715221\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	24.0000			0.769010
$975$	−3.00000	+	4.00000i	−0.0960769	+	0.128103i
$976$	2.00000			0.0640184
$977$		−	42.0000i		−	1.34370i	−0.740688	−	0.671850i	$-0.765500\pi$
$977$		−	42.0000i		−	1.34370i	0.740688	−	0.671850i	$-0.234500\pi$
$978$		−	12.0000i		−	0.383718i
$979$	−50.0000			−1.59801
$980$		0			0
$981$	−18.0000			−0.574696
$982$			24.0000i			0.765871i
$983$		−	33.0000i		−	1.05254i	−0.850319	−	0.526268i	$-0.823591\pi$
$983$		−	33.0000i		−	1.05254i	0.850319	−	0.526268i	$-0.176409\pi$
$984$	−9.00000			−0.286910
$985$	−27.0000	−	54.0000i	−0.860292	−	1.72058i
$986$		0			0
$987$		0			0
$988$			7.00000i			0.222700i
$989$	−30.0000			−0.953945
$990$	−5.00000	−	10.0000i	−0.158910	−	0.317821i
$991$	−36.0000			−1.14358			−0.571789	−	0.820401i	$-0.693750\pi$
$991$	−36.0000			−1.14358			−0.571789	+	0.820401i	$0.693750\pi$
$992$			6.00000i			0.190500i
$993$			15.0000i			0.476011i
$994$		0			0
$995$	28.0000	−	14.0000i	0.887660	−	0.443830i
$996$	−10.0000			−0.316862
$997$		−	10.0000i		−	0.316703i	−0.987383	−	0.158352i	$-0.949382\pi$
$997$		−	10.0000i		−	0.316703i	0.987383	−	0.158352i	$-0.0506179\pi$
$998$			28.0000i			0.886325i
$999$	−5.00000			−0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.g.a.589.2		2
5.2	odd	4		7350.2.a.b.1.1		1
5.3	odd	4		7350.2.a.ch.1.1		1
5.4	even	2	inner	1470.2.g.a.589.1		2
7.2	even	3		1470.2.n.i.949.2		4
7.3	odd	6		210.2.n.a.79.1	✓	4
7.4	even	3		1470.2.n.i.79.1		4
7.5	odd	6		210.2.n.a.109.2	yes	4
7.6	odd	2		1470.2.g.f.589.2		2
21.5	even	6		630.2.u.c.109.1		4
21.17	even	6		630.2.u.c.289.2		4
28.3	even	6		1680.2.di.a.289.1		4
28.19	even	6		1680.2.di.a.529.2		4
35.3	even	12		1050.2.i.f.751.1		2
35.4	even	6		1470.2.n.i.79.2		4
35.9	even	6		1470.2.n.i.949.1		4
35.12	even	12		1050.2.i.o.151.1		2
35.13	even	4		7350.2.a.bn.1.1		1
35.17	even	12		1050.2.i.o.751.1		2
35.19	odd	6		210.2.n.a.109.1	yes	4
35.24	odd	6		210.2.n.a.79.2	yes	4
35.27	even	4		7350.2.a.t.1.1		1
35.33	even	12		1050.2.i.f.151.1		2
35.34	odd	2		1470.2.g.f.589.1		2
105.59	even	6		630.2.u.c.289.1		4
105.89	even	6		630.2.u.c.109.2		4
140.19	even	6		1680.2.di.a.529.1		4
140.59	even	6		1680.2.di.a.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.a.79.1	✓	4	7.3	odd	6
210.2.n.a.79.2	yes	4	35.24	odd	6
210.2.n.a.109.1	yes	4	35.19	odd	6
210.2.n.a.109.2	yes	4	7.5	odd	6
630.2.u.c.109.1		4	21.5	even	6
630.2.u.c.109.2		4	105.89	even	6
630.2.u.c.289.1		4	105.59	even	6
630.2.u.c.289.2		4	21.17	even	6
1050.2.i.f.151.1		2	35.33	even	12
1050.2.i.f.751.1		2	35.3	even	12
1050.2.i.o.151.1		2	35.12	even	12
1050.2.i.o.751.1		2	35.17	even	12
1470.2.g.a.589.1		2	5.4	even	2	inner
1470.2.g.a.589.2		2	1.1	even	1	trivial
1470.2.g.f.589.1		2	35.34	odd	2
1470.2.g.f.589.2		2	7.6	odd	2
1470.2.n.i.79.1		4	7.4	even	3
1470.2.n.i.79.2		4	35.4	even	6
1470.2.n.i.949.1		4	35.9	even	6
1470.2.n.i.949.2		4	7.2	even	3
1680.2.di.a.289.1		4	28.3	even	6
1680.2.di.a.289.2		4	140.59	even	6
1680.2.di.a.529.1		4	140.19	even	6
1680.2.di.a.529.2		4	28.19	even	6
7350.2.a.b.1.1		1	5.2	odd	4
7350.2.a.t.1.1		1	35.27	even	4
7350.2.a.bn.1.1		1	35.13	even	4
7350.2.a.ch.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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} -5.00000 q^{11} +1.00000i q^{12} -1.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} -2.00000i q^{17} -1.00000i q^{18} +7.00000 q^{19} +(2.00000 - 1.00000i) q^{20} -5.00000i q^{22} +3.00000i q^{23} -1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +1.00000 q^{26} +1.00000i q^{27} +(-2.00000 + 1.00000i) q^{30} +6.00000 q^{31} +1.00000i q^{32} +5.00000i q^{33} +2.00000 q^{34} +1.00000 q^{36} +5.00000i q^{37} +7.00000i q^{38} -1.00000 q^{39} +(1.00000 + 2.00000i) q^{40} +9.00000 q^{41} +10.0000i q^{43} +5.00000 q^{44} +(2.00000 - 1.00000i) q^{45} -3.00000 q^{46} -13.0000i q^{47} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} -2.00000 q^{51} +1.00000i q^{52} -1.00000i q^{53} -1.00000 q^{54} +(10.0000 - 5.00000i) q^{55} -7.00000i q^{57} +4.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} +2.00000 q^{61} +6.00000i q^{62} -1.00000 q^{64} +(1.00000 + 2.00000i) q^{65} -5.00000 q^{66} -6.00000i q^{67} +2.00000i q^{68} +3.00000 q^{69} -2.00000 q^{71} +1.00000i q^{72} -4.00000i q^{73} -5.00000 q^{74} +(-4.00000 - 3.00000i) q^{75} -7.00000 q^{76} -1.00000i q^{78} +14.0000 q^{79} +(-2.00000 + 1.00000i) q^{80} +1.00000 q^{81} +9.00000i q^{82} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} -10.0000 q^{86} +5.00000i q^{88} +10.0000 q^{89} +(1.00000 + 2.00000i) q^{90} -3.00000i q^{92} -6.00000i q^{93} +13.0000 q^{94} +(-14.0000 + 7.00000i) q^{95} +1.00000 q^{96} +8.00000i q^{97} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{9} - 2 q^{10} - 10 q^{11} + 2 q^{15} + 2 q^{16} + 14 q^{19} + 4 q^{20} - 2 q^{24} + 6 q^{25} + 2 q^{26} - 4 q^{30} + 12 q^{31} + 4 q^{34} + 2 q^{36} - 2 q^{39} + 2 q^{40}+ \cdots + 10 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^9 - 2 * q^10 - 10 * q^11 + 2 * q^15 + 2 * q^16 + 14 * q^19 + 4 * q^20 - 2 * q^24 + 6 * q^25 + 2 * q^26 - 4 * q^30 + 12 * q^31 + 4 * q^34 + 2 * q^36 - 2 * q^39 + 2 * q^40 + 18 * q^41 + 10 * q^44 + 4 * q^45 - 6 * q^46 + 8 * q^50 - 4 * q^51 - 2 * q^54 + 20 * q^55 + 8 * q^59 - 2 * q^60 + 4 * q^61 - 2 * q^64 + 2 * q^65 - 10 * q^66 + 6 * q^69 - 4 * q^71 - 10 * q^74 - 8 * q^75 - 14 * q^76 + 28 * q^79 - 4 * q^80 + 2 * q^81 + 4 * q^85 - 20 * q^86 + 20 * q^89 + 2 * q^90 + 26 * q^94 - 28 * q^95 + 2 * q^96 + 10 * q^99

Introduction

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