LMFDB - Embedded newform 570.2.d.a.229.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(229,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.d (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:	$4.55147291521$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	570.229
Dual form			570.2.d.a.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(2.00000 - 1.00000i) q^{10} -4.00000 q^{11} -1.00000i q^{12} -2.00000i q^{13} +(2.00000 - 1.00000i) q^{15} +1.00000 q^{16} -6.00000i q^{17} -1.00000i q^{18} +1.00000 q^{19} +(1.00000 + 2.00000i) q^{20} -4.00000i q^{22} -6.00000i q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} +2.00000 q^{29} +(1.00000 + 2.00000i) q^{30} -6.00000 q^{31} +1.00000i q^{32} -4.00000i q^{33} +6.00000 q^{34} +1.00000 q^{36} -10.0000i q^{37} +1.00000i q^{38} +2.00000 q^{39} +(-2.00000 + 1.00000i) q^{40} +6.00000i q^{43} +4.00000 q^{44} +(1.00000 + 2.00000i) q^{45} +6.00000 q^{46} +6.00000i q^{47} +1.00000i q^{48} +7.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +6.00000 q^{51} +2.00000i q^{52} -10.0000i q^{53} +1.00000 q^{54} +(4.00000 + 8.00000i) q^{55} +1.00000i q^{57} +2.00000i q^{58} -2.00000 q^{59} +(-2.00000 + 1.00000i) q^{60} -6.00000 q^{61} -6.00000i q^{62} -1.00000 q^{64} +(-4.00000 + 2.00000i) q^{65} +4.00000 q^{66} +8.00000i q^{67} +6.00000i q^{68} +6.00000 q^{69} -12.0000 q^{71} +1.00000i q^{72} +16.0000i q^{73} +10.0000 q^{74} +(-4.00000 - 3.00000i) q^{75} -1.00000 q^{76} +2.00000i q^{78} +14.0000 q^{79} +(-1.00000 - 2.00000i) q^{80} +1.00000 q^{81} -12.0000i q^{83} +(-12.0000 + 6.00000i) q^{85} -6.00000 q^{86} +2.00000i q^{87} +4.00000i q^{88} -4.00000 q^{89} +(-2.00000 + 1.00000i) q^{90} +6.00000i q^{92} -6.00000i q^{93} -6.00000 q^{94} +(-1.00000 - 2.00000i) q^{95} -1.00000 q^{96} -10.0000i q^{97} +7.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9} + 4 q^{10} - 8 q^{11} + 4 q^{15} + 2 q^{16} + 2 q^{19} + 2 q^{20} + 2 q^{24} - 6 q^{25} + 4 q^{26} + 4 q^{29} + 2 q^{30} - 12 q^{31} + 12 q^{34} + 2 q^{36} + 4 q^{39} - 4 q^{40} + 8 q^{44} + 2 q^{45} + 12 q^{46} + 14 q^{49} - 8 q^{50} + 12 q^{51} + 2 q^{54} + 8 q^{55} - 4 q^{59} - 4 q^{60} - 12 q^{61} - 2 q^{64} - 8 q^{65} + 8 q^{66} + 12 q^{69} - 24 q^{71} + 20 q^{74} - 8 q^{75} - 2 q^{76} + 28 q^{79} - 2 q^{80} + 2 q^{81} - 24 q^{85} - 12 q^{86} - 8 q^{89} - 4 q^{90} - 12 q^{94} - 2 q^{95} - 2 q^{96} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^9 + 4 * q^10 - 8 * q^11 + 4 * q^15 + 2 * q^16 + 2 * q^19 + 2 * q^20 + 2 * q^24 - 6 * q^25 + 4 * q^26 + 4 * q^29 + 2 * q^30 - 12 * q^31 + 12 * q^34 + 2 * q^36 + 4 * q^39 - 4 * q^40 + 8 * q^44 + 2 * q^45 + 12 * q^46 + 14 * q^49 - 8 * q^50 + 12 * q^51 + 2 * q^54 + 8 * q^55 - 4 * q^59 - 4 * q^60 - 12 * q^61 - 2 * q^64 - 8 * q^65 + 8 * q^66 + 12 * q^69 - 24 * q^71 + 20 * q^74 - 8 * q^75 - 2 * q^76 + 28 * q^79 - 2 * q^80 + 2 * q^81 - 24 * q^85 - 12 * q^86 - 8 * q^89 - 4 * q^90 - 12 * q^94 - 2 * q^95 - 2 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$1$	$-1$

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
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$	−1.00000			−0.408248
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$	−4.00000			−1.20605			−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000			−1.20605			−0.603023	+	0.797724i	$0.706037\pi$
$12$		−	1.00000i		−	0.288675i
$13$		−	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
$15$	2.00000	−	1.00000i	0.516398	−	0.258199i
$16$	1.00000			0.250000
$17$		−	6.00000i		−	1.45521i	−0.685994	−	0.727607i	$-0.740633\pi$
$17$		−	6.00000i		−	1.45521i	0.685994	−	0.727607i	$-0.259367\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	1.00000	+	2.00000i	0.223607	+	0.447214i
$21$		0			0
$22$		−	4.00000i		−	0.852803i
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$	1.00000			0.204124
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	2.00000			0.392232
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	1.00000	+	2.00000i	0.182574	+	0.365148i
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$			1.00000i			0.176777i
$33$		−	4.00000i		−	0.696311i
$34$	6.00000			1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$		−	10.0000i		−	1.64399i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$		−	10.0000i		−	1.64399i	0.569495	−	0.821995i	$-0.307139\pi$
$38$			1.00000i			0.162221i
$39$	2.00000			0.320256
$40$	−2.00000	+	1.00000i	−0.316228	+	0.158114i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	4.00000			0.603023
$45$	1.00000	+	2.00000i	0.149071	+	0.298142i
$46$	6.00000			0.884652
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$			1.00000i			0.144338i
$49$	7.00000			1.00000
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	6.00000			0.840168
$52$			2.00000i			0.277350i
$53$		−	10.0000i		−	1.37361i	−0.726844	−	0.686803i	$-0.759014\pi$
$53$		−	10.0000i		−	1.37361i	0.726844	−	0.686803i	$-0.240986\pi$
$54$	1.00000			0.136083
$55$	4.00000	+	8.00000i	0.539360	+	1.07872i
$56$		0			0
$57$			1.00000i			0.132453i
$58$			2.00000i			0.262613i
$59$	−2.00000			−0.260378			−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000			−0.260378			−0.130189	+	0.991489i	$0.541558\pi$
$60$	−2.00000	+	1.00000i	−0.258199	+	0.129099i
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$		−	6.00000i		−	0.762001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.00000	+	2.00000i	−0.496139	+	0.248069i
$66$	4.00000			0.492366
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$			6.00000i			0.727607i
$69$	6.00000			0.722315
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$			1.00000i			0.117851i
$73$			16.0000i			1.87266i	0.351123	+	0.936329i	$0.385800\pi$
$73$			16.0000i			1.87266i	−0.351123	+	0.936329i	$0.614200\pi$
$74$	10.0000			1.16248
$75$	−4.00000	−	3.00000i	−0.461880	−	0.346410i
$76$	−1.00000			−0.114708
$77$		0			0
$78$			2.00000i			0.226455i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$	1.00000			0.111111
$82$		0			0
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$		0			0
$85$	−12.0000	+	6.00000i	−1.30158	+	0.650791i
$86$	−6.00000			−0.646997
$87$			2.00000i			0.214423i
$88$			4.00000i			0.426401i
$89$	−4.00000			−0.423999			−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000			−0.423999			−0.212000	+	0.977270i	$0.567998\pi$
$90$	−2.00000	+	1.00000i	−0.210819	+	0.105409i
$91$		0			0
$92$			6.00000i			0.625543i
$93$		−	6.00000i		−	0.622171i
$94$	−6.00000			−0.618853
$95$	−1.00000	−	2.00000i	−0.102598	−	0.205196i
$96$	−1.00000			−0.102062
$97$		−	10.0000i		−	1.01535i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$		−	10.0000i		−	1.01535i	0.861550	−	0.507673i	$-0.169494\pi$
$98$			7.00000i			0.707107i
$99$	4.00000			0.402015
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$			6.00000i			0.594089i
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	10.0000			0.971286
$107$		−	4.00000i		−	0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$		−	4.00000i		−	0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$			1.00000i			0.0962250i
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	−8.00000	+	4.00000i	−0.762770	+	0.381385i
$111$	10.0000			0.949158
$112$		0			0
$113$		−	2.00000i		−	0.188144i	−0.995565	−	0.0940721i	$-0.970012\pi$
$113$		−	2.00000i		−	0.188144i	0.995565	−	0.0940721i	$-0.0299884\pi$
$114$	−1.00000			−0.0936586
$115$	−12.0000	+	6.00000i	−1.11901	+	0.559503i
$116$	−2.00000			−0.185695
$117$			2.00000i			0.184900i
$118$		−	2.00000i		−	0.184115i
$119$		0			0
$120$	−1.00000	−	2.00000i	−0.0912871	−	0.182574i
$121$	5.00000			0.454545
$122$		−	6.00000i		−	0.543214i
$123$		0			0
$124$	6.00000			0.538816
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.00000			−0.528271
$130$	−2.00000	−	4.00000i	−0.175412	−	0.350823i
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$			4.00000i			0.348155i
$133$		0			0
$134$	−8.00000			−0.691095
$135$	−2.00000	+	1.00000i	−0.172133	+	0.0860663i
$136$	−6.00000			−0.514496
$137$			6.00000i			0.512615i	0.966595	+	0.256307i	$0.0825059\pi$
$137$			6.00000i			0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$			6.00000i			0.510754i
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		−	12.0000i		−	1.00702i
$143$			8.00000i			0.668994i
$144$	−1.00000			−0.0833333
$145$	−2.00000	−	4.00000i	−0.166091	−	0.332182i
$146$	−16.0000			−1.32417
$147$			7.00000i			0.577350i
$148$			10.0000i			0.821995i
$149$	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
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		−	1.00000i		−	0.0811107i
$153$			6.00000i			0.485071i
$154$		0			0
$155$	6.00000	+	12.0000i	0.481932	+	0.963863i
$156$	−2.00000			−0.160128
$157$		−	18.0000i		−	1.43656i	−0.695756	−	0.718278i	$-0.744931\pi$
$157$		−	18.0000i		−	1.43656i	0.695756	−	0.718278i	$-0.255069\pi$
$158$			14.0000i			1.11378i
$159$	10.0000			0.793052
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$			10.0000i			0.783260i	0.920123	+	0.391630i	$0.128089\pi$
$163$			10.0000i			0.783260i	−0.920123	+	0.391630i	$0.871911\pi$
$164$		0			0
$165$	−8.00000	+	4.00000i	−0.622799	+	0.311400i
$166$	12.0000			0.931381
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−6.00000	−	12.0000i	−0.460179	−	0.920358i
$171$	−1.00000			−0.0764719
$172$		−	6.00000i		−	0.457496i
$173$			14.0000i			1.06440i	0.846619	+	0.532200i	$0.178635\pi$
$173$			14.0000i			1.06440i	−0.846619	+	0.532200i	$0.821365\pi$
$174$	−2.00000			−0.151620
$175$		0			0
$176$	−4.00000			−0.301511
$177$		−	2.00000i		−	0.150329i
$178$		−	4.00000i		−	0.299813i
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$	−1.00000	−	2.00000i	−0.0745356	−	0.149071i
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$		0			0
$183$		−	6.00000i		−	0.443533i
$184$	−6.00000			−0.442326
$185$	−20.0000	+	10.0000i	−1.47043	+	0.735215i
$186$	6.00000			0.439941
$187$			24.0000i			1.75505i
$188$		−	6.00000i		−	0.437595i
$189$		0			0
$190$	2.00000	−	1.00000i	0.145095	−	0.0725476i
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	14.0000i		−	1.00774i	−0.863779	−	0.503871i	$-0.831909\pi$
$193$		−	14.0000i		−	1.00774i	0.863779	−	0.503871i	$-0.168091\pi$
$194$	10.0000			0.717958
$195$	−2.00000	−	4.00000i	−0.143223	−	0.286446i
$196$	−7.00000			−0.500000
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$			4.00000i			0.284268i
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$	−8.00000			−0.564276
$202$		−	18.0000i		−	1.26648i
$203$		0			0
$204$	−6.00000			−0.420084
$205$		0			0
$206$	8.00000			0.557386
$207$			6.00000i			0.417029i
$208$		−	2.00000i		−	0.138675i
$209$	−4.00000			−0.276686
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$			10.0000i			0.686803i
$213$		−	12.0000i		−	0.822226i
$214$	4.00000			0.273434
$215$	12.0000	−	6.00000i	0.818393	−	0.409197i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$		−	4.00000i		−	0.270914i
$219$	−16.0000			−1.08118
$220$	−4.00000	−	8.00000i	−0.269680	−	0.539360i
$221$	−12.0000			−0.807207
$222$			10.0000i			0.671156i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$	2.00000			0.133038
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	1.00000i		−	0.0662266i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	−6.00000	−	12.0000i	−0.395628	−	0.791257i
$231$		0			0
$232$		−	2.00000i		−	0.131306i
$233$		−	14.0000i		−	0.917170i	−0.888650	−	0.458585i	$-0.848356\pi$
$233$		−	14.0000i		−	0.917170i	0.888650	−	0.458585i	$-0.151644\pi$
$234$	−2.00000			−0.130744
$235$	12.0000	−	6.00000i	0.782794	−	0.391397i
$236$	2.00000			0.130189
$237$			14.0000i			0.909398i
$238$		0			0
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$	2.00000	−	1.00000i	0.129099	−	0.0645497i
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$			5.00000i			0.321412i
$243$			1.00000i			0.0641500i
$244$	6.00000			0.384111
$245$	−7.00000	−	14.0000i	−0.447214	−	0.894427i
$246$		0			0
$247$		−	2.00000i		−	0.127257i
$248$			6.00000i			0.381000i
$249$	12.0000			0.760469
$250$	−2.00000	+	11.0000i	−0.126491	+	0.695701i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$			24.0000i			1.50887i
$254$	−8.00000			−0.501965
$255$	−6.00000	−	12.0000i	−0.375735	−	0.751469i
$256$	1.00000			0.0625000
$257$			22.0000i			1.37232i	0.727450	+	0.686161i	$0.240706\pi$
$257$			22.0000i			1.37232i	−0.727450	+	0.686161i	$0.759294\pi$
$258$		−	6.00000i		−	0.373544i
$259$		0			0
$260$	4.00000	−	2.00000i	0.248069	−	0.124035i
$261$	−2.00000			−0.123797
$262$		−	8.00000i		−	0.494242i
$263$			2.00000i			0.123325i	0.998097	+	0.0616626i	$0.0196403\pi$
$263$			2.00000i			0.123325i	−0.998097	+	0.0616626i	$0.980360\pi$
$264$	−4.00000			−0.246183
$265$	−20.0000	+	10.0000i	−1.22859	+	0.614295i
$266$		0			0
$267$		−	4.00000i		−	0.244796i
$268$		−	8.00000i		−	0.488678i
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$	−1.00000	−	2.00000i	−0.0608581	−	0.121716i
$271$	32.0000			1.94386			0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000			1.94386			0.971931	+	0.235267i	$0.0755965\pi$
$272$		−	6.00000i		−	0.363803i
$273$		0			0
$274$	−6.00000			−0.362473
$275$	12.0000	−	16.0000i	0.723627	−	0.964836i
$276$	−6.00000			−0.361158
$277$		−	26.0000i		−	1.56219i	−0.624413	−	0.781094i	$-0.714662\pi$
$277$		−	26.0000i		−	1.56219i	0.624413	−	0.781094i	$-0.285338\pi$
$278$		−	12.0000i		−	0.719712i
$279$	6.00000			0.359211
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		−	6.00000i		−	0.357295i
$283$		−	22.0000i		−	1.30776i	−0.756596	−	0.653882i	$-0.773139\pi$
$283$		−	22.0000i		−	1.30776i	0.756596	−	0.653882i	$-0.226861\pi$
$284$	12.0000			0.712069
$285$	2.00000	−	1.00000i	0.118470	−	0.0592349i
$286$	−8.00000			−0.473050
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−19.0000			−1.11765
$290$	4.00000	−	2.00000i	0.234888	−	0.117444i
$291$	10.0000			0.586210
$292$		−	16.0000i		−	0.936329i
$293$		−	2.00000i		−	0.116841i	−0.998292	−	0.0584206i	$-0.981394\pi$
$293$		−	2.00000i		−	0.116841i	0.998292	−	0.0584206i	$-0.0186065\pi$
$294$	−7.00000			−0.408248
$295$	2.00000	+	4.00000i	0.116445	+	0.232889i
$296$	−10.0000			−0.581238
$297$			4.00000i			0.232104i
$298$			6.00000i			0.347571i
$299$	−12.0000			−0.693978
$300$	4.00000	+	3.00000i	0.230940	+	0.173205i
$301$		0			0
$302$			10.0000i			0.575435i
$303$		−	18.0000i		−	1.03407i
$304$	1.00000			0.0573539
$305$	6.00000	+	12.0000i	0.343559	+	0.687118i
$306$	−6.00000			−0.342997
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$	−12.0000	+	6.00000i	−0.681554	+	0.340777i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		−	2.00000i		−	0.113228i
$313$		−	28.0000i		−	1.58265i	−0.611393	−	0.791327i	$-0.709391\pi$
$313$		−	28.0000i		−	1.58265i	0.611393	−	0.791327i	$-0.290609\pi$
$314$	18.0000			1.01580
$315$		0			0
$316$	−14.0000			−0.787562
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$			10.0000i			0.560772i
$319$	−8.00000			−0.447914
$320$	1.00000	+	2.00000i	0.0559017	+	0.111803i
$321$	4.00000			0.223258
$322$		0			0
$323$		−	6.00000i		−	0.333849i
$324$	−1.00000			−0.0555556
$325$	8.00000	+	6.00000i	0.443760	+	0.332820i
$326$	−10.0000			−0.553849
$327$		−	4.00000i		−	0.221201i
$328$		0			0
$329$		0			0
$330$	−4.00000	−	8.00000i	−0.220193	−	0.440386i
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$			12.0000i			0.658586i
$333$			10.0000i			0.547997i
$334$		0			0
$335$	16.0000	−	8.00000i	0.874173	−	0.437087i
$336$		0			0
$337$			6.00000i			0.326841i	0.986557	+	0.163420i	$0.0522527\pi$
$337$			6.00000i			0.326841i	−0.986557	+	0.163420i	$0.947747\pi$
$338$			9.00000i			0.489535i
$339$	2.00000			0.108625
$340$	12.0000	−	6.00000i	0.650791	−	0.325396i
$341$	24.0000			1.29967
$342$		−	1.00000i		−	0.0540738i
$343$		0			0
$344$	6.00000			0.323498
$345$	−6.00000	−	12.0000i	−0.323029	−	0.646058i
$346$	−14.0000			−0.752645
$347$			20.0000i			1.07366i	0.843692	+	0.536828i	$0.180378\pi$
$347$			20.0000i			1.07366i	−0.843692	+	0.536828i	$0.819622\pi$
$348$		−	2.00000i		−	0.107211i
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		−	4.00000i		−	0.213201i
$353$			2.00000i			0.106449i	0.998583	+	0.0532246i	$0.0169499\pi$
$353$			2.00000i			0.106449i	−0.998583	+	0.0532246i	$0.983050\pi$
$354$	2.00000			0.106299
$355$	12.0000	+	24.0000i	0.636894	+	1.27379i
$356$	4.00000			0.212000
$357$		0			0
$358$			18.0000i			0.951330i
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$	2.00000	−	1.00000i	0.105409	−	0.0527046i
$361$	1.00000			0.0526316
$362$		−	4.00000i		−	0.210235i
$363$			5.00000i			0.262432i
$364$		0			0
$365$	32.0000	−	16.0000i	1.67496	−	0.837478i
$366$	6.00000			0.313625
$367$			12.0000i			0.626395i	0.949688	+	0.313197i	$0.101400\pi$
$367$			12.0000i			0.626395i	−0.949688	+	0.313197i	$0.898600\pi$
$368$		−	6.00000i		−	0.312772i
$369$		0			0
$370$	−10.0000	−	20.0000i	−0.519875	−	1.03975i
$371$		0			0
$372$			6.00000i			0.311086i
$373$		−	6.00000i		−	0.310668i	−0.987862	−	0.155334i	$-0.950355\pi$
$373$		−	6.00000i		−	0.310668i	0.987862	−	0.155334i	$-0.0496454\pi$
$374$	−24.0000			−1.24101
$375$	−2.00000	+	11.0000i	−0.103280	+	0.568038i
$376$	6.00000			0.309426
$377$		−	4.00000i		−	0.206010i
$378$		0			0
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$	1.00000	+	2.00000i	0.0512989	+	0.102598i
$381$	−8.00000			−0.409852
$382$			24.0000i			1.22795i
$383$		−	36.0000i		−	1.83951i	−0.392488	−	0.919757i	$-0.628386\pi$
$383$		−	36.0000i		−	1.83951i	0.392488	−	0.919757i	$-0.371614\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	14.0000			0.712581
$387$		−	6.00000i		−	0.304997i
$388$			10.0000i			0.507673i
$389$	−38.0000			−1.92668			−0.963338	−	0.268290i	$-0.913542\pi$
$389$	−38.0000			−1.92668			−0.963338	+	0.268290i	$0.913542\pi$
$390$	4.00000	−	2.00000i	0.202548	−	0.101274i
$391$	−36.0000			−1.82060
$392$		−	7.00000i		−	0.353553i
$393$		−	8.00000i		−	0.403547i
$394$	−8.00000			−0.403034
$395$	−14.0000	−	28.0000i	−0.704416	−	1.40883i
$396$	−4.00000			−0.201008
$397$		−	30.0000i		−	1.50566i	−0.658217	−	0.752828i	$-0.728689\pi$
$397$		−	30.0000i		−	1.50566i	0.658217	−	0.752828i	$-0.271311\pi$
$398$			16.0000i			0.802008i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	16.0000			0.799002			0.399501	−	0.916733i	$-0.369183\pi$
$401$	16.0000			0.799002			0.399501	+	0.916733i	$0.369183\pi$
$402$		−	8.00000i		−	0.399004i
$403$			12.0000i			0.597763i
$404$	18.0000			0.895533
$405$	−1.00000	−	2.00000i	−0.0496904	−	0.0993808i
$406$		0			0
$407$			40.0000i			1.98273i
$408$		−	6.00000i		−	0.297044i
$409$	−26.0000			−1.28562			−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000			−1.28562			−0.642809	+	0.766027i	$0.722231\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$			8.00000i			0.394132i
$413$		0			0
$414$	−6.00000			−0.294884
$415$	−24.0000	+	12.0000i	−1.17811	+	0.589057i
$416$	2.00000			0.0980581
$417$		−	12.0000i		−	0.587643i
$418$		−	4.00000i		−	0.195646i
$419$	−8.00000			−0.390826			−0.195413	−	0.980721i	$-0.562605\pi$
$419$	−8.00000			−0.390826			−0.195413	+	0.980721i	$0.562605\pi$
$420$		0			0
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$		−	8.00000i		−	0.389434i
$423$		−	6.00000i		−	0.291730i
$424$	−10.0000			−0.485643
$425$	24.0000	+	18.0000i	1.16417	+	0.873128i
$426$	12.0000			0.581402
$427$		0			0
$428$			4.00000i			0.193347i
$429$	−8.00000			−0.386244
$430$	6.00000	+	12.0000i	0.289346	+	0.578691i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	6.00000i		−	0.288342i	−0.989553	−	0.144171i	$-0.953949\pi$
$433$		−	6.00000i		−	0.288342i	0.989553	−	0.144171i	$-0.0460515\pi$
$434$		0			0
$435$	4.00000	−	2.00000i	0.191785	−	0.0958927i
$436$	4.00000			0.191565
$437$		−	6.00000i		−	0.287019i
$438$		−	16.0000i		−	0.764510i
$439$	14.0000			0.668184			0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000			0.668184			0.334092	+	0.942541i	$0.391570\pi$
$440$	8.00000	−	4.00000i	0.381385	−	0.190693i
$441$	−7.00000			−0.333333
$442$		−	12.0000i		−	0.570782i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−10.0000			−0.474579
$445$	4.00000	+	8.00000i	0.189618	+	0.379236i
$446$	−8.00000			−0.378811
$447$			6.00000i			0.283790i
$448$		0			0
$449$	−4.00000			−0.188772			−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000			−0.188772			−0.0943858	+	0.995536i	$0.530089\pi$
$450$	4.00000	+	3.00000i	0.188562	+	0.141421i
$451$		0			0
$452$			2.00000i			0.0940721i
$453$			10.0000i			0.469841i
$454$	12.0000			0.563188
$455$		0			0
$456$	1.00000			0.0468293
$457$			16.0000i			0.748448i	0.927338	+	0.374224i	$0.122091\pi$
$457$			16.0000i			0.748448i	−0.927338	+	0.374224i	$0.877909\pi$
$458$			10.0000i			0.467269i
$459$	−6.00000			−0.280056
$460$	12.0000	−	6.00000i	0.559503	−	0.279751i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$			8.00000i			0.371792i	0.982569	+	0.185896i	$0.0595187\pi$
$463$			8.00000i			0.371792i	−0.982569	+	0.185896i	$0.940481\pi$
$464$	2.00000			0.0928477
$465$	−12.0000	+	6.00000i	−0.556487	+	0.278243i
$466$	14.0000			0.648537
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		−	2.00000i		−	0.0924500i
$469$		0			0
$470$	6.00000	+	12.0000i	0.276759	+	0.553519i
$471$	18.0000			0.829396
$472$			2.00000i			0.0920575i
$473$		−	24.0000i		−	1.10352i
$474$	−14.0000			−0.643041
$475$	−3.00000	+	4.00000i	−0.137649	+	0.183533i
$476$		0			0
$477$			10.0000i			0.457869i
$478$			8.00000i			0.365911i
$479$	16.0000			0.731059			0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000			0.731059			0.365529	+	0.930800i	$0.380888\pi$
$480$	1.00000	+	2.00000i	0.0456435	+	0.0912871i
$481$	−20.0000			−0.911922
$482$		−	10.0000i		−	0.455488i
$483$		0			0
$484$	−5.00000			−0.227273
$485$	−20.0000	+	10.0000i	−0.908153	+	0.454077i
$486$	−1.00000			−0.0453609
$487$			24.0000i			1.08754i	0.839233	+	0.543772i	$0.183004\pi$
$487$			24.0000i			1.08754i	−0.839233	+	0.543772i	$0.816996\pi$
$488$			6.00000i			0.271607i
$489$	−10.0000			−0.452216
$490$	14.0000	−	7.00000i	0.632456	−	0.316228i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$		−	12.0000i		−	0.540453i
$494$	2.00000			0.0899843
$495$	−4.00000	−	8.00000i	−0.179787	−	0.359573i
$496$	−6.00000			−0.269408
$497$		0			0
$498$			12.0000i			0.537733i
$499$	−20.0000			−0.895323			−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000			−0.895323			−0.447661	+	0.894203i	$0.647743\pi$
$500$	−11.0000	−	2.00000i	−0.491935	−	0.0894427i
$501$		0			0
$502$			12.0000i			0.535586i
$503$			14.0000i			0.624229i	0.950044	+	0.312115i	$0.101037\pi$
$503$			14.0000i			0.624229i	−0.950044	+	0.312115i	$0.898963\pi$
$504$		0			0
$505$	18.0000	+	36.0000i	0.800989	+	1.60198i
$506$	−24.0000			−1.06693
$507$			9.00000i			0.399704i
$508$		−	8.00000i		−	0.354943i
$509$	−6.00000			−0.265945			−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000			−0.265945			−0.132973	+	0.991120i	$0.542452\pi$
$510$	12.0000	−	6.00000i	0.531369	−	0.265684i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		−	1.00000i		−	0.0441511i
$514$	−22.0000			−0.970378
$515$	−16.0000	+	8.00000i	−0.705044	+	0.352522i
$516$	6.00000			0.264135
$517$		−	24.0000i		−	1.05552i
$518$		0			0
$519$	−14.0000			−0.614532
$520$	2.00000	+	4.00000i	0.0877058	+	0.175412i
$521$	−24.0000			−1.05146			−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000			−1.05146			−0.525730	+	0.850652i	$0.676208\pi$
$522$		−	2.00000i		−	0.0875376i
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$	8.00000			0.349482
$525$		0			0
$526$	−2.00000			−0.0872041
$527$			36.0000i			1.56818i
$528$		−	4.00000i		−	0.174078i
$529$	−13.0000			−0.565217
$530$	−10.0000	−	20.0000i	−0.434372	−	0.868744i
$531$	2.00000			0.0867926
$532$		0			0
$533$		0			0
$534$	4.00000			0.173097
$535$	−8.00000	+	4.00000i	−0.345870	+	0.172935i
$536$	8.00000			0.345547
$537$			18.0000i			0.776757i
$538$			14.0000i			0.603583i
$539$	−28.0000			−1.20605
$540$	2.00000	−	1.00000i	0.0860663	−	0.0430331i
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$			32.0000i			1.37452i
$543$		−	4.00000i		−	0.171656i
$544$	6.00000			0.257248
$545$	4.00000	+	8.00000i	0.171341	+	0.342682i
$546$		0			0
$547$		−	36.0000i		−	1.53925i	−0.638497	−	0.769624i	$-0.720443\pi$
$547$		−	36.0000i		−	1.53925i	0.638497	−	0.769624i	$-0.279557\pi$
$548$		−	6.00000i		−	0.256307i
$549$	6.00000			0.256074
$550$	16.0000	+	12.0000i	0.682242	+	0.511682i
$551$	2.00000			0.0852029
$552$		−	6.00000i		−	0.255377i
$553$		0			0
$554$	26.0000			1.10463
$555$	−10.0000	−	20.0000i	−0.424476	−	0.848953i
$556$	12.0000			0.508913
$557$			24.0000i			1.01691i	0.861088	+	0.508456i	$0.169784\pi$
$557$			24.0000i			1.01691i	−0.861088	+	0.508456i	$0.830216\pi$
$558$			6.00000i			0.254000i
$559$	12.0000			0.507546
$560$		0			0
$561$	−24.0000			−1.01328
$562$		0			0
$563$			12.0000i			0.505740i	0.967500	+	0.252870i	$0.0813744\pi$
$563$			12.0000i			0.505740i	−0.967500	+	0.252870i	$0.918626\pi$
$564$	6.00000			0.252646
$565$	−4.00000	+	2.00000i	−0.168281	+	0.0841406i
$566$	22.0000			0.924729
$567$		0			0
$568$			12.0000i			0.503509i
$569$	28.0000			1.17382			0.586911	−	0.809652i	$-0.300344\pi$
$569$	28.0000			1.17382			0.586911	+	0.809652i	$0.300344\pi$
$570$	1.00000	+	2.00000i	0.0418854	+	0.0837708i
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$		−	8.00000i		−	0.334497i
$573$			24.0000i			1.00261i
$574$		0			0
$575$	24.0000	+	18.0000i	1.00087	+	0.750652i
$576$	1.00000			0.0416667
$577$		−	8.00000i		−	0.333044i	−0.986038	−	0.166522i	$-0.946746\pi$
$577$		−	8.00000i		−	0.333044i	0.986038	−	0.166522i	$-0.0532537\pi$
$578$		−	19.0000i		−	0.790296i
$579$	14.0000			0.581820
$580$	2.00000	+	4.00000i	0.0830455	+	0.166091i
$581$		0			0
$582$			10.0000i			0.414513i
$583$			40.0000i			1.65663i
$584$	16.0000			0.662085
$585$	4.00000	−	2.00000i	0.165380	−	0.0826898i
$586$	2.00000			0.0826192
$587$		−	28.0000i		−	1.15568i	−0.816149	−	0.577842i	$-0.803895\pi$
$587$		−	28.0000i		−	1.15568i	0.816149	−	0.577842i	$-0.196105\pi$
$588$		−	7.00000i		−	0.288675i
$589$	−6.00000			−0.247226
$590$	−4.00000	+	2.00000i	−0.164677	+	0.0823387i
$591$	−8.00000			−0.329076
$592$		−	10.0000i		−	0.410997i
$593$			46.0000i			1.88899i	0.328521	+	0.944497i	$0.393450\pi$
$593$			46.0000i			1.88899i	−0.328521	+	0.944497i	$0.606550\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−6.00000			−0.245770
$597$			16.0000i			0.654836i
$598$		−	12.0000i		−	0.490716i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−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
$603$		−	8.00000i		−	0.325785i
$604$	−10.0000			−0.406894
$605$	−5.00000	−	10.0000i	−0.203279	−	0.406558i
$606$	18.0000			0.731200
$607$		−	24.0000i		−	0.974130i	−0.873366	−	0.487065i	$-0.838067\pi$
$607$		−	24.0000i		−	0.974130i	0.873366	−	0.487065i	$-0.161933\pi$
$608$			1.00000i			0.0405554i
$609$		0			0
$610$	−12.0000	+	6.00000i	−0.485866	+	0.242933i
$611$	12.0000			0.485468
$612$		−	6.00000i		−	0.242536i
$613$			22.0000i			0.888572i	0.895885	+	0.444286i	$0.146543\pi$
$613$			22.0000i			0.888572i	−0.895885	+	0.444286i	$0.853457\pi$
$614$	12.0000			0.484281
$615$		0			0
$616$		0			0
$617$		−	18.0000i		−	0.724653i	−0.932051	−	0.362326i	$-0.881983\pi$
$617$		−	18.0000i		−	0.724653i	0.932051	−	0.362326i	$-0.118017\pi$
$618$			8.00000i			0.321807i
$619$	−44.0000			−1.76851			−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000			−1.76851			−0.884255	+	0.467005i	$0.845333\pi$
$620$	−6.00000	−	12.0000i	−0.240966	−	0.481932i
$621$	−6.00000			−0.240772
$622$			24.0000i			0.962312i
$623$		0			0
$624$	2.00000			0.0800641
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	28.0000			1.11911
$627$		−	4.00000i		−	0.159745i
$628$			18.0000i			0.718278i
$629$	−60.0000			−2.39236
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$		−	14.0000i		−	0.556890i
$633$		−	8.00000i		−	0.317971i
$634$	−6.00000			−0.238290
$635$	16.0000	−	8.00000i	0.634941	−	0.317470i
$636$	−10.0000			−0.396526
$637$		−	14.0000i		−	0.554700i
$638$		−	8.00000i		−	0.316723i
$639$	12.0000			0.474713
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$	48.0000			1.89589			0.947943	−	0.318440i	$-0.103159\pi$
$641$	48.0000			1.89589			0.947943	+	0.318440i	$0.103159\pi$
$642$			4.00000i			0.157867i
$643$			26.0000i			1.02534i	0.858586	+	0.512670i	$0.171344\pi$
$643$			26.0000i			1.02534i	−0.858586	+	0.512670i	$0.828656\pi$
$644$		0			0
$645$	6.00000	+	12.0000i	0.236250	+	0.472500i
$646$	6.00000			0.236067
$647$			6.00000i			0.235884i	0.993020	+	0.117942i	$0.0376297\pi$
$647$			6.00000i			0.235884i	−0.993020	+	0.117942i	$0.962370\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	8.00000			0.314027
$650$	−6.00000	+	8.00000i	−0.235339	+	0.313786i
$651$		0			0
$652$		−	10.0000i		−	0.391630i
$653$		−	48.0000i		−	1.87839i	−0.343391	−	0.939193i	$-0.611576\pi$
$653$		−	48.0000i		−	1.87839i	0.343391	−	0.939193i	$-0.388424\pi$
$654$	4.00000			0.156412
$655$	8.00000	+	16.0000i	0.312586	+	0.625172i
$656$		0			0
$657$		−	16.0000i		−	0.624219i
$658$		0			0
$659$	−46.0000			−1.79191			−0.895953	−	0.444149i	$-0.853506\pi$
$659$	−46.0000			−1.79191			−0.895953	+	0.444149i	$0.853506\pi$
$660$	8.00000	−	4.00000i	0.311400	−	0.155700i
$661$	−8.00000			−0.311164			−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000			−0.311164			−0.155582	+	0.987823i	$0.549725\pi$
$662$		−	4.00000i		−	0.155464i
$663$		−	12.0000i		−	0.466041i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−10.0000			−0.387492
$667$		−	12.0000i		−	0.464642i
$668$		0			0
$669$	−8.00000			−0.309298
$670$	8.00000	+	16.0000i	0.309067	+	0.618134i
$671$	24.0000			0.926510
$672$		0			0
$673$		−	26.0000i		−	1.00223i	−0.865382	−	0.501113i	$-0.832924\pi$
$673$		−	26.0000i		−	1.00223i	0.865382	−	0.501113i	$-0.167076\pi$
$674$	−6.00000			−0.231111
$675$	4.00000	+	3.00000i	0.153960	+	0.115470i
$676$	−9.00000			−0.346154
$677$		−	6.00000i		−	0.230599i	−0.993331	−	0.115299i	$-0.963217\pi$
$677$		−	6.00000i		−	0.230599i	0.993331	−	0.115299i	$-0.0367827\pi$
$678$			2.00000i			0.0768095i
$679$		0			0
$680$	6.00000	+	12.0000i	0.230089	+	0.460179i
$681$	12.0000			0.459841
$682$			24.0000i			0.919007i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	1.00000			0.0382360
$685$	12.0000	−	6.00000i	0.458496	−	0.229248i
$686$		0			0
$687$			10.0000i			0.381524i
$688$			6.00000i			0.228748i
$689$	−20.0000			−0.761939
$690$	12.0000	−	6.00000i	0.456832	−	0.228416i
$691$	44.0000			1.67384			0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000			1.67384			0.836919	+	0.547326i	$0.184354\pi$
$692$		−	14.0000i		−	0.532200i
$693$		0			0
$694$	−20.0000			−0.759190
$695$	12.0000	+	24.0000i	0.455186	+	0.910372i
$696$	2.00000			0.0758098
$697$		0			0
$698$			26.0000i			0.984115i
$699$	14.0000			0.529529
$700$		0			0
$701$	−22.0000			−0.830929			−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000			−0.830929			−0.415464	+	0.909610i	$0.636381\pi$
$702$		−	2.00000i		−	0.0754851i
$703$		−	10.0000i		−	0.377157i
$704$	4.00000			0.150756
$705$	6.00000	+	12.0000i	0.225973	+	0.451946i
$706$	−2.00000			−0.0752710
$707$		0			0
$708$			2.00000i			0.0751646i
$709$	2.00000			0.0751116			0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000			0.0751116			0.0375558	+	0.999295i	$0.488043\pi$
$710$	−24.0000	+	12.0000i	−0.900704	+	0.450352i
$711$	−14.0000			−0.525041
$712$			4.00000i			0.149906i
$713$			36.0000i			1.34821i
$714$		0			0
$715$	16.0000	−	8.00000i	0.598366	−	0.299183i
$716$	−18.0000			−0.672692
$717$			8.00000i			0.298765i
$718$			8.00000i			0.298557i
$719$	−48.0000			−1.79010			−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000			−1.79010			−0.895049	+	0.445968i	$0.852860\pi$
$720$	1.00000	+	2.00000i	0.0372678	+	0.0745356i
$721$		0			0
$722$			1.00000i			0.0372161i
$723$		−	10.0000i		−	0.371904i
$724$	4.00000			0.148659
$725$	−6.00000	+	8.00000i	−0.222834	+	0.297113i
$726$	−5.00000			−0.185567
$727$		−	28.0000i		−	1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$727$		−	28.0000i		−	1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	16.0000	+	32.0000i	0.592187	+	1.18437i
$731$	36.0000			1.33151
$732$			6.00000i			0.221766i
$733$		−	46.0000i		−	1.69905i	−0.527549	−	0.849524i	$-0.676889\pi$
$733$		−	46.0000i		−	1.69905i	0.527549	−	0.849524i	$-0.323111\pi$
$734$	−12.0000			−0.442928
$735$	14.0000	−	7.00000i	0.516398	−	0.258199i
$736$	6.00000			0.221163
$737$		−	32.0000i		−	1.17874i
$738$		0			0
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$	20.0000	−	10.0000i	0.735215	−	0.367607i
$741$	2.00000			0.0734718
$742$		0			0
$743$			8.00000i			0.293492i	0.989174	+	0.146746i	$0.0468799\pi$
$743$			8.00000i			0.293492i	−0.989174	+	0.146746i	$0.953120\pi$
$744$	−6.00000			−0.219971
$745$	−6.00000	−	12.0000i	−0.219823	−	0.439646i
$746$	6.00000			0.219676
$747$			12.0000i			0.439057i
$748$		−	24.0000i		−	0.877527i
$749$		0			0
$750$	−11.0000	−	2.00000i	−0.401663	−	0.0730297i
$751$	−26.0000			−0.948753			−0.474377	−	0.880322i	$-0.657327\pi$
$751$	−26.0000			−0.948753			−0.474377	+	0.880322i	$0.657327\pi$
$752$			6.00000i			0.218797i
$753$			12.0000i			0.437304i
$754$	4.00000			0.145671
$755$	−10.0000	−	20.0000i	−0.363937	−	0.727875i
$756$		0			0
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$		−	24.0000i		−	0.871719i
$759$	−24.0000			−0.871145
$760$	−2.00000	+	1.00000i	−0.0725476	+	0.0362738i
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$		−	8.00000i		−	0.289809i
$763$		0			0
$764$	−24.0000			−0.868290
$765$	12.0000	−	6.00000i	0.433861	−	0.216930i
$766$	36.0000			1.30073
$767$			4.00000i			0.144432i
$768$			1.00000i			0.0360844i
$769$	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
$771$	−22.0000			−0.792311
$772$			14.0000i			0.503871i
$773$			50.0000i			1.79838i	0.437564	+	0.899188i	$0.355842\pi$
$773$			50.0000i			1.79838i	−0.437564	+	0.899188i	$0.644158\pi$
$774$	6.00000			0.215666
$775$	18.0000	−	24.0000i	0.646579	−	0.862105i
$776$	−10.0000			−0.358979
$777$		0			0
$778$		−	38.0000i		−	1.36237i
$779$		0			0
$780$	2.00000	+	4.00000i	0.0716115	+	0.143223i
$781$	48.0000			1.71758
$782$		−	36.0000i		−	1.28736i
$783$		−	2.00000i		−	0.0714742i
$784$	7.00000			0.250000
$785$	−36.0000	+	18.0000i	−1.28490	+	0.642448i
$786$	8.00000			0.285351
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$		−	8.00000i		−	0.284988i
$789$	−2.00000			−0.0712019
$790$	28.0000	−	14.0000i	0.996195	−	0.498098i
$791$		0			0
$792$		−	4.00000i		−	0.142134i
$793$			12.0000i			0.426132i
$794$	30.0000			1.06466
$795$	−10.0000	−	20.0000i	−0.354663	−	0.709327i
$796$	−16.0000			−0.567105
$797$		−	54.0000i		−	1.91278i	−0.292096	−	0.956389i	$-0.594353\pi$
$797$		−	54.0000i		−	1.91278i	0.292096	−	0.956389i	$-0.405647\pi$
$798$		0			0
$799$	36.0000			1.27359
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$	4.00000			0.141333
$802$			16.0000i			0.564980i
$803$		−	64.0000i		−	2.25851i
$804$	8.00000			0.282138
$805$		0			0
$806$	−12.0000			−0.422682
$807$			14.0000i			0.492823i
$808$			18.0000i			0.633238i
$809$	10.0000			0.351581			0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000			0.351581			0.175791	+	0.984428i	$0.443752\pi$
$810$	2.00000	−	1.00000i	0.0702728	−	0.0351364i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$		0			0
$813$			32.0000i			1.12229i
$814$	−40.0000			−1.40200
$815$	20.0000	−	10.0000i	0.700569	−	0.350285i
$816$	6.00000			0.210042
$817$			6.00000i			0.209913i
$818$		−	26.0000i		−	0.909069i
$819$		0			0
$820$		0			0
$821$	50.0000			1.74501			0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000			1.74501			0.872506	+	0.488603i	$0.162493\pi$
$822$		−	6.00000i		−	0.209274i
$823$			12.0000i			0.418294i	0.977884	+	0.209147i	$0.0670687\pi$
$823$			12.0000i			0.418294i	−0.977884	+	0.209147i	$0.932931\pi$
$824$	−8.00000			−0.278693
$825$	16.0000	+	12.0000i	0.557048	+	0.417786i
$826$		0			0
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$		−	6.00000i		−	0.208514i
$829$	28.0000			0.972480			0.486240	−	0.873825i	$-0.338368\pi$
$829$	28.0000			0.972480			0.486240	+	0.873825i	$0.338368\pi$
$830$	−12.0000	−	24.0000i	−0.416526	−	0.833052i
$831$	26.0000			0.901930
$832$			2.00000i			0.0693375i
$833$		−	42.0000i		−	1.45521i
$834$	12.0000			0.415526
$835$		0			0
$836$	4.00000			0.138343
$837$			6.00000i			0.207390i
$838$		−	8.00000i		−	0.276355i
$839$	−44.0000			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$			16.0000i			0.551396i
$843$		0			0
$844$	8.00000			0.275371
$845$	−9.00000	−	18.0000i	−0.309609	−	0.619219i
$846$	6.00000			0.206284
$847$		0			0
$848$		−	10.0000i		−	0.343401i
$849$	22.0000			0.755038
$850$	−18.0000	+	24.0000i	−0.617395	+	0.823193i
$851$	−60.0000			−2.05677
$852$			12.0000i			0.411113i
$853$			14.0000i			0.479351i	0.970853	+	0.239675i	$0.0770410\pi$
$853$			14.0000i			0.479351i	−0.970853	+	0.239675i	$0.922959\pi$
$854$		0			0
$855$	1.00000	+	2.00000i	0.0341993	+	0.0683986i
$856$	−4.00000			−0.136717
$857$		−	18.0000i		−	0.614868i	−0.951569	−	0.307434i	$-0.900530\pi$
$857$		−	18.0000i		−	0.614868i	0.951569	−	0.307434i	$-0.0994704\pi$
$858$		−	8.00000i		−	0.273115i
$859$	28.0000			0.955348			0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000			0.955348			0.477674	+	0.878537i	$0.341480\pi$
$860$	−12.0000	+	6.00000i	−0.409197	+	0.204598i
$861$		0			0
$862$		−	24.0000i		−	0.817443i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$	1.00000			0.0340207
$865$	28.0000	−	14.0000i	0.952029	−	0.476014i
$866$	6.00000			0.203888
$867$		−	19.0000i		−	0.645274i
$868$		0			0
$869$	−56.0000			−1.89967
$870$	2.00000	+	4.00000i	0.0678064	+	0.135613i
$871$	16.0000			0.542139
$872$			4.00000i			0.135457i
$873$			10.0000i			0.338449i
$874$	6.00000			0.202953
$875$		0			0
$876$	16.0000			0.540590
$877$		−	46.0000i		−	1.55331i	−0.629926	−	0.776655i	$-0.716915\pi$
$877$		−	46.0000i		−	1.55331i	0.629926	−	0.776655i	$-0.283085\pi$
$878$			14.0000i			0.472477i
$879$	2.00000			0.0674583
$880$	4.00000	+	8.00000i	0.134840	+	0.269680i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		−	7.00000i		−	0.235702i
$883$		−	10.0000i		−	0.336527i	−0.985742	−	0.168263i	$-0.946184\pi$
$883$		−	10.0000i		−	0.336527i	0.985742	−	0.168263i	$-0.0538159\pi$
$884$	12.0000			0.403604
$885$	−4.00000	+	2.00000i	−0.134459	+	0.0672293i
$886$		0			0
$887$		−	12.0000i		−	0.402921i	−0.979497	−	0.201460i	$-0.935431\pi$
$887$		−	12.0000i		−	0.402921i	0.979497	−	0.201460i	$-0.0645687\pi$
$888$		−	10.0000i		−	0.335578i
$889$		0			0
$890$	−8.00000	+	4.00000i	−0.268161	+	0.134080i
$891$	−4.00000			−0.134005
$892$		−	8.00000i		−	0.267860i
$893$			6.00000i			0.200782i
$894$	−6.00000			−0.200670
$895$	−18.0000	−	36.0000i	−0.601674	−	1.20335i
$896$		0			0
$897$		−	12.0000i		−	0.400668i
$898$		−	4.00000i		−	0.133482i
$899$	−12.0000			−0.400222
$900$	−3.00000	+	4.00000i	−0.100000	+	0.133333i
$901$	−60.0000			−1.99889
$902$		0			0
$903$		0			0
$904$	−2.00000			−0.0665190
$905$	4.00000	+	8.00000i	0.132964	+	0.265929i
$906$	−10.0000			−0.332228
$907$			24.0000i			0.796907i	0.917189	+	0.398453i	$0.130453\pi$
$907$			24.0000i			0.796907i	−0.917189	+	0.398453i	$0.869547\pi$
$908$			12.0000i			0.398234i
$909$	18.0000			0.597022
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$			1.00000i			0.0331133i
$913$			48.0000i			1.58857i
$914$	−16.0000			−0.529233
$915$	−12.0000	+	6.00000i	−0.396708	+	0.198354i
$916$	−10.0000			−0.330409
$917$		0			0
$918$		−	6.00000i		−	0.198030i
$919$	−28.0000			−0.923635			−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000			−0.923635			−0.461817	+	0.886975i	$0.652802\pi$
$920$	6.00000	+	12.0000i	0.197814	+	0.395628i
$921$	12.0000			0.395413
$922$		−	18.0000i		−	0.592798i
$923$			24.0000i			0.789970i
$924$		0			0
$925$	40.0000	+	30.0000i	1.31519	+	0.986394i
$926$	−8.00000			−0.262896
$927$			8.00000i			0.262754i
$928$			2.00000i			0.0656532i
$929$	−18.0000			−0.590561			−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000			−0.590561			−0.295280	+	0.955411i	$0.595413\pi$
$930$	−6.00000	−	12.0000i	−0.196748	−	0.393496i
$931$	7.00000			0.229416
$932$			14.0000i			0.458585i
$933$			24.0000i			0.785725i
$934$		0			0
$935$	48.0000	−	24.0000i	1.56977	−	0.784884i
$936$	2.00000			0.0653720
$937$		−	44.0000i		−	1.43742i	−0.695311	−	0.718709i	$-0.744734\pi$
$937$		−	44.0000i		−	1.43742i	0.695311	−	0.718709i	$-0.255266\pi$
$938$		0			0
$939$	28.0000			0.913745
$940$	−12.0000	+	6.00000i	−0.391397	+	0.195698i
$941$	22.0000			0.717180			0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000			0.717180			0.358590	+	0.933495i	$0.383258\pi$
$942$			18.0000i			0.586472i
$943$		0			0
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	24.0000			0.780307
$947$		−	8.00000i		−	0.259965i	−0.991516	−	0.129983i	$-0.958508\pi$
$947$		−	8.00000i		−	0.259965i	0.991516	−	0.129983i	$-0.0414921\pi$
$948$		−	14.0000i		−	0.454699i
$949$	32.0000			1.03876
$950$	−4.00000	−	3.00000i	−0.129777	−	0.0973329i
$951$	−6.00000			−0.194563
$952$		0			0
$953$			42.0000i			1.36051i	0.732974	+	0.680257i	$0.238132\pi$
$953$			42.0000i			1.36051i	−0.732974	+	0.680257i	$0.761868\pi$
$954$	−10.0000			−0.323762
$955$	−24.0000	−	48.0000i	−0.776622	−	1.55324i
$956$	−8.00000			−0.258738
$957$		−	8.00000i		−	0.258603i
$958$			16.0000i			0.516937i
$959$		0			0
$960$	−2.00000	+	1.00000i	−0.0645497	+	0.0322749i
$961$	5.00000			0.161290
$962$		−	20.0000i		−	0.644826i
$963$			4.00000i			0.128898i
$964$	10.0000			0.322078
$965$	−28.0000	+	14.0000i	−0.901352	+	0.450676i
$966$		0			0
$967$			28.0000i			0.900419i	0.892923	+	0.450210i	$0.148651\pi$
$967$			28.0000i			0.900419i	−0.892923	+	0.450210i	$0.851349\pi$
$968$		−	5.00000i		−	0.160706i
$969$	6.00000			0.192748
$970$	−10.0000	−	20.0000i	−0.321081	−	0.642161i
$971$	−58.0000			−1.86131			−0.930654	−	0.365900i	$-0.880761\pi$
$971$	−58.0000			−1.86131			−0.930654	+	0.365900i	$0.880761\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	−24.0000			−0.769010
$975$	−6.00000	+	8.00000i	−0.192154	+	0.256205i
$976$	−6.00000			−0.192055
$977$		−	26.0000i		−	0.831814i	−0.909407	−	0.415907i	$-0.863464\pi$
$977$		−	26.0000i		−	0.831814i	0.909407	−	0.415907i	$-0.136536\pi$
$978$		−	10.0000i		−	0.319765i
$979$	16.0000			0.511362
$980$	7.00000	+	14.0000i	0.223607	+	0.447214i
$981$	4.00000			0.127710
$982$		0			0
$983$		−	56.0000i		−	1.78612i	−0.449935	−	0.893061i	$-0.648553\pi$
$983$		−	56.0000i		−	1.78612i	0.449935	−	0.893061i	$-0.351447\pi$
$984$		0			0
$985$	16.0000	−	8.00000i	0.509802	−	0.254901i
$986$	12.0000			0.382158
$987$		0			0
$988$			2.00000i			0.0636285i
$989$	36.0000			1.14473
$990$	8.00000	−	4.00000i	0.254257	−	0.127128i
$991$	−6.00000			−0.190596			−0.0952981	−	0.995449i	$-0.530380\pi$
$991$	−6.00000			−0.190596			−0.0952981	+	0.995449i	$0.530380\pi$
$992$		−	6.00000i		−	0.190500i
$993$		−	4.00000i		−	0.126936i
$994$		0			0
$995$	−16.0000	−	32.0000i	−0.507234	−	1.01447i
$996$	−12.0000			−0.380235
$997$		−	2.00000i		−	0.0633406i	−0.999498	−	0.0316703i	$-0.989917\pi$
$997$		−	2.00000i		−	0.0633406i	0.999498	−	0.0316703i	$-0.0100827\pi$
$998$		−	20.0000i		−	0.633089i
$999$	−10.0000			−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.d.a.229.2	yes	2
3.2	odd	2		1710.2.d.b.1369.1		2
5.2	odd	4		2850.2.a.i.1.1		1
5.3	odd	4		2850.2.a.t.1.1		1
5.4	even	2	inner	570.2.d.a.229.1	✓	2
15.2	even	4		8550.2.a.bb.1.1		1
15.8	even	4		8550.2.a.k.1.1		1
15.14	odd	2		1710.2.d.b.1369.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.a.229.1	✓	2	5.4	even	2	inner
570.2.d.a.229.2	yes	2	1.1	even	1	trivial
1710.2.d.b.1369.1		2	3.2	odd	2
1710.2.d.b.1369.2		2	15.14	odd	2
2850.2.a.i.1.1		1	5.2	odd	4
2850.2.a.t.1.1		1	5.3	odd	4
8550.2.a.k.1.1		1	15.8	even	4
8550.2.a.bb.1.1		1	15.2	even	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(2.00000 - 1.00000i) q^{10} -4.00000 q^{11} -1.00000i q^{12} -2.00000i q^{13} +(2.00000 - 1.00000i) q^{15} +1.00000 q^{16} -6.00000i q^{17} -1.00000i q^{18} +1.00000 q^{19} +(1.00000 + 2.00000i) q^{20} -4.00000i q^{22} -6.00000i q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} +2.00000 q^{26} -1.00000i q^{27} +2.00000 q^{29} +(1.00000 + 2.00000i) q^{30} -6.00000 q^{31} +1.00000i q^{32} -4.00000i q^{33} +6.00000 q^{34} +1.00000 q^{36} -10.0000i q^{37} +1.00000i q^{38} +2.00000 q^{39} +(-2.00000 + 1.00000i) q^{40} +6.00000i q^{43} +4.00000 q^{44} +(1.00000 + 2.00000i) q^{45} +6.00000 q^{46} +6.00000i q^{47} +1.00000i q^{48} +7.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +6.00000 q^{51} +2.00000i q^{52} -10.0000i q^{53} +1.00000 q^{54} +(4.00000 + 8.00000i) q^{55} +1.00000i q^{57} +2.00000i q^{58} -2.00000 q^{59} +(-2.00000 + 1.00000i) q^{60} -6.00000 q^{61} -6.00000i q^{62} -1.00000 q^{64} +(-4.00000 + 2.00000i) q^{65} +4.00000 q^{66} +8.00000i q^{67} +6.00000i q^{68} +6.00000 q^{69} -12.0000 q^{71} +1.00000i q^{72} +16.0000i q^{73} +10.0000 q^{74} +(-4.00000 - 3.00000i) q^{75} -1.00000 q^{76} +2.00000i q^{78} +14.0000 q^{79} +(-1.00000 - 2.00000i) q^{80} +1.00000 q^{81} -12.0000i q^{83} +(-12.0000 + 6.00000i) q^{85} -6.00000 q^{86} +2.00000i q^{87} +4.00000i q^{88} -4.00000 q^{89} +(-2.00000 + 1.00000i) q^{90} +6.00000i q^{92} -6.00000i q^{93} -6.00000 q^{94} +(-1.00000 - 2.00000i) q^{95} -1.00000 q^{96} -10.0000i q^{97} +7.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{9} + 4 q^{10} - 8 q^{11} + 4 q^{15} + 2 q^{16} + 2 q^{19} + 2 q^{20} + 2 q^{24} - 6 q^{25} + 4 q^{26} + 4 q^{29} + 2 q^{30} - 12 q^{31} + 12 q^{34} + 2 q^{36} + 4 q^{39} - 4 q^{40} + 8 q^{44} + 2 q^{45} + 12 q^{46} + 14 q^{49} - 8 q^{50} + 12 q^{51} + 2 q^{54} + 8 q^{55} - 4 q^{59} - 4 q^{60} - 12 q^{61} - 2 q^{64} - 8 q^{65} + 8 q^{66} + 12 q^{69} - 24 q^{71} + 20 q^{74} - 8 q^{75} - 2 q^{76} + 28 q^{79} - 2 q^{80} + 2 q^{81} - 24 q^{85} - 12 q^{86} - 8 q^{89} - 4 q^{90} - 12 q^{94} - 2 q^{95} - 2 q^{96} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^9 + 4 * q^10 - 8 * q^11 + 4 * q^15 + 2 * q^16 + 2 * q^19 + 2 * q^20 + 2 * q^24 - 6 * q^25 + 4 * q^26 + 4 * q^29 + 2 * q^30 - 12 * q^31 + 12 * q^34 + 2 * q^36 + 4 * q^39 - 4 * q^40 + 8 * q^44 + 2 * q^45 + 12 * q^46 + 14 * q^49 - 8 * q^50 + 12 * q^51 + 2 * q^54 + 8 * q^55 - 4 * q^59 - 4 * q^60 - 12 * q^61 - 2 * q^64 - 8 * q^65 + 8 * q^66 + 12 * q^69 - 24 * q^71 + 20 * q^74 - 8 * q^75 - 2 * q^76 + 28 * q^79 - 2 * q^80 + 2 * q^81 - 24 * q^85 - 12 * q^86 - 8 * q^89 - 4 * q^90 - 12 * q^94 - 2 * q^95 - 2 * q^96 + 8 * q^99

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