LMFDB - Embedded newform 600.2.d.a.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(349,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
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 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	600.349
Dual form			600.2.d.a.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} +(1.00000 + 1.00000i) q^{6} -2.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} +(1.00000 + 1.00000i) q^{6} -2.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000 q^{9} +4.00000i q^{11} -2.00000i q^{12} +(-2.00000 + 2.00000i) q^{14} -4.00000 q^{16} +6.00000i q^{17} +(-1.00000 - 1.00000i) q^{18} -4.00000i q^{19} +2.00000i q^{21} +(4.00000 - 4.00000i) q^{22} -4.00000i q^{23} +(-2.00000 + 2.00000i) q^{24} -1.00000 q^{27} +4.00000 q^{28} +6.00000i q^{29} +10.0000 q^{31} +(4.00000 + 4.00000i) q^{32} -4.00000i q^{33} +(6.00000 - 6.00000i) q^{34} +2.00000i q^{36} +4.00000 q^{37} +(-4.00000 + 4.00000i) q^{38} +10.0000 q^{41} +(2.00000 - 2.00000i) q^{42} +4.00000 q^{43} -8.00000 q^{44} +(-4.00000 + 4.00000i) q^{46} +4.00000i q^{47} +4.00000 q^{48} +3.00000 q^{49} -6.00000i q^{51} +10.0000 q^{53} +(1.00000 + 1.00000i) q^{54} +(-4.00000 - 4.00000i) q^{56} +4.00000i q^{57} +(6.00000 - 6.00000i) q^{58} -8.00000i q^{59} -8.00000i q^{61} +(-10.0000 - 10.0000i) q^{62} -2.00000i q^{63} -8.00000i q^{64} +(-4.00000 + 4.00000i) q^{66} -12.0000 q^{67} -12.0000 q^{68} +4.00000i q^{69} -4.00000 q^{71} +(2.00000 - 2.00000i) q^{72} +10.0000i q^{73} +(-4.00000 - 4.00000i) q^{74} +8.00000 q^{76} +8.00000 q^{77} +14.0000 q^{79} +1.00000 q^{81} +(-10.0000 - 10.0000i) q^{82} -4.00000 q^{84} +(-4.00000 - 4.00000i) q^{86} -6.00000i q^{87} +(8.00000 + 8.00000i) q^{88} -14.0000 q^{89} +8.00000 q^{92} -10.0000 q^{93} +(4.00000 - 4.00000i) q^{94} +(-4.00000 - 4.00000i) q^{96} +10.0000i q^{97} +(-3.00000 - 3.00000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^6 + 4 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{6} + 4 q^{8} + 2 q^{9} - 4 q^{14} - 8 q^{16} - 2 q^{18} + 8 q^{22} - 4 q^{24} - 2 q^{27} + 8 q^{28} + 20 q^{31} + 8 q^{32} + 12 q^{34} + 8 q^{37} - 8 q^{38} + 20 q^{41} + 4 q^{42} + 8 q^{43} - 16 q^{44} - 8 q^{46} + 8 q^{48} + 6 q^{49} + 20 q^{53} + 2 q^{54} - 8 q^{56} + 12 q^{58} - 20 q^{62} - 8 q^{66} - 24 q^{67} - 24 q^{68} - 8 q^{71} + 4 q^{72} - 8 q^{74} + 16 q^{76} + 16 q^{77} + 28 q^{79} + 2 q^{81} - 20 q^{82} - 8 q^{84} - 8 q^{86} + 16 q^{88} - 28 q^{89} + 16 q^{92} - 20 q^{93} + 8 q^{94} - 8 q^{96} - 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^6 + 4 * q^8 + 2 * q^9 - 4 * q^14 - 8 * q^16 - 2 * q^18 + 8 * q^22 - 4 * q^24 - 2 * q^27 + 8 * q^28 + 20 * q^31 + 8 * q^32 + 12 * q^34 + 8 * q^37 - 8 * q^38 + 20 * q^41 + 4 * q^42 + 8 * q^43 - 16 * q^44 - 8 * q^46 + 8 * q^48 + 6 * q^49 + 20 * q^53 + 2 * q^54 - 8 * q^56 + 12 * q^58 - 20 * q^62 - 8 * q^66 - 24 * q^67 - 24 * q^68 - 8 * q^71 + 4 * q^72 - 8 * q^74 + 16 * q^76 + 16 * q^77 + 28 * q^79 + 2 * q^81 - 20 * q^82 - 8 * q^84 - 8 * q^86 + 16 * q^88 - 28 * q^89 + 16 * q^92 - 20 * q^93 + 8 * q^94 - 8 * q^96 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$			2.00000i			1.00000i
$5$		0			0
$5$		0			0
$6$	1.00000	+	1.00000i	0.408248	+	0.408248i
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	1.00000			0.333333
$10$		0			0
$11$			4.00000i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$11$			4.00000i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$12$		−	2.00000i		−	0.577350i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.00000	+	2.00000i	−0.534522	+	0.534522i
$15$		0			0
$16$	−4.00000			−1.00000
$17$			6.00000i			1.45521i	0.685994	+	0.727607i	$0.259367\pi$
$17$			6.00000i			1.45521i	−0.685994	+	0.727607i	$0.740633\pi$
$18$	−1.00000	−	1.00000i	−0.235702	−	0.235702i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$			2.00000i			0.436436i
$22$	4.00000	−	4.00000i	0.852803	−	0.852803i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−2.00000	+	2.00000i	−0.408248	+	0.408248i
$25$		0			0
$26$		0			0
$27$	−1.00000			−0.192450
$28$	4.00000			0.755929
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$		0			0
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$		−	4.00000i		−	0.696311i
$34$	6.00000	−	6.00000i	1.02899	−	1.02899i
$35$		0			0
$36$			2.00000i			0.333333i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	−4.00000	+	4.00000i	−0.648886	+	0.648886i
$39$		0			0
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$	2.00000	−	2.00000i	0.308607	−	0.308607i
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−8.00000			−1.20605
$45$		0			0
$46$	−4.00000	+	4.00000i	−0.589768	+	0.589768i
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$	4.00000			0.577350
$49$	3.00000			0.428571
$50$		0			0
$51$		−	6.00000i		−	0.840168i
$52$		0			0
$53$	10.0000			1.37361			0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000			1.37361			0.686803	+	0.726844i	$0.259014\pi$
$54$	1.00000	+	1.00000i	0.136083	+	0.136083i
$55$		0			0
$56$	−4.00000	−	4.00000i	−0.534522	−	0.534522i
$57$			4.00000i			0.529813i
$58$	6.00000	−	6.00000i	0.787839	−	0.787839i
$59$		−	8.00000i		−	1.04151i	−0.853706	−	0.520756i	$-0.825650\pi$
$59$		−	8.00000i		−	1.04151i	0.853706	−	0.520756i	$-0.174350\pi$
$60$		0			0
$61$		−	8.00000i		−	1.02430i	−0.858898	−	0.512148i	$-0.828850\pi$
$61$		−	8.00000i		−	1.02430i	0.858898	−	0.512148i	$-0.171150\pi$
$62$	−10.0000	−	10.0000i	−1.27000	−	1.27000i
$63$		−	2.00000i		−	0.251976i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−4.00000	+	4.00000i	−0.492366	+	0.492366i
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−12.0000			−1.45521
$69$			4.00000i			0.481543i
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$	2.00000	−	2.00000i	0.235702	−	0.235702i
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$	−4.00000	−	4.00000i	−0.464991	−	0.464991i
$75$		0			0
$76$	8.00000			0.917663
$77$	8.00000			0.911685
$78$		0			0
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−10.0000	−	10.0000i	−1.10432	−	1.10432i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−4.00000			−0.436436
$85$		0			0
$86$	−4.00000	−	4.00000i	−0.431331	−	0.431331i
$87$		−	6.00000i		−	0.643268i
$88$	8.00000	+	8.00000i	0.852803	+	0.852803i
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$		0			0
$91$		0			0
$92$	8.00000			0.834058
$93$	−10.0000			−1.03695
$94$	4.00000	−	4.00000i	0.412568	−	0.412568i
$95$		0			0
$96$	−4.00000	−	4.00000i	−0.408248	−	0.408248i
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$	−3.00000	−	3.00000i	−0.303046	−	0.303046i
$99$			4.00000i			0.402015i
$100$		0			0
$101$			14.0000i			1.39305i	0.717532	+	0.696526i	$0.245272\pi$
$101$			14.0000i			1.39305i	−0.717532	+	0.696526i	$0.754728\pi$
$102$	−6.00000	+	6.00000i	−0.594089	+	0.594089i
$103$		−	2.00000i		−	0.197066i	−0.995134	−	0.0985329i	$-0.968585\pi$
$103$		−	2.00000i		−	0.197066i	0.995134	−	0.0985329i	$-0.0314150\pi$
$104$		0			0
$105$		0			0
$106$	−10.0000	−	10.0000i	−0.971286	−	0.971286i
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$		−	2.00000i		−	0.192450i
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$			8.00000i			0.755929i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	4.00000	−	4.00000i	0.374634	−	0.374634i
$115$		0			0
$116$	−12.0000			−1.11417
$117$		0			0
$118$	−8.00000	+	8.00000i	−0.736460	+	0.736460i
$119$	12.0000			1.10004
$120$		0			0
$121$	−5.00000			−0.454545
$122$	−8.00000	+	8.00000i	−0.724286	+	0.724286i
$123$	−10.0000			−0.901670
$124$			20.0000i			1.79605i
$125$		0			0
$126$	−2.00000	+	2.00000i	−0.178174	+	0.178174i
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	−4.00000			−0.352180
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	8.00000			0.696311
$133$	−8.00000			−0.693688
$134$	12.0000	+	12.0000i	1.03664	+	1.03664i
$135$		0			0
$136$	12.0000	+	12.0000i	1.02899	+	1.02899i
$137$			2.00000i			0.170872i	0.996344	+	0.0854358i	$0.0272282\pi$
$137$			2.00000i			0.170872i	−0.996344	+	0.0854358i	$0.972772\pi$
$138$	4.00000	−	4.00000i	0.340503	−	0.340503i
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$		0			0
$141$		−	4.00000i		−	0.336861i
$142$	4.00000	+	4.00000i	0.335673	+	0.335673i
$143$		0			0
$144$	−4.00000			−0.333333
$145$		0			0
$146$	10.0000	−	10.0000i	0.827606	−	0.827606i
$147$	−3.00000			−0.247436
$148$			8.00000i			0.657596i
$149$			6.00000i			0.491539i	0.969328	+	0.245770i	$0.0790407\pi$
$149$			6.00000i			0.491539i	−0.969328	+	0.245770i	$0.920959\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	−8.00000	−	8.00000i	−0.648886	−	0.648886i
$153$			6.00000i			0.485071i
$154$	−8.00000	−	8.00000i	−0.644658	−	0.644658i
$155$		0			0
$156$		0			0
$157$	20.0000			1.59617			0.798087	−	0.602542i	$-0.205846\pi$
$157$	20.0000			1.59617			0.798087	+	0.602542i	$0.205846\pi$
$158$	−14.0000	−	14.0000i	−1.11378	−	1.11378i
$159$	−10.0000			−0.793052
$160$		0			0
$161$	−8.00000			−0.630488
$162$	−1.00000	−	1.00000i	−0.0785674	−	0.0785674i
$163$	−20.0000			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$164$			20.0000i			1.56174i
$165$		0			0
$166$		0			0
$167$		−	24.0000i		−	1.85718i	−0.371113	−	0.928588i	$-0.621024\pi$
$167$		−	24.0000i		−	1.85718i	0.371113	−	0.928588i	$-0.378976\pi$
$168$	4.00000	+	4.00000i	0.308607	+	0.308607i
$169$	−13.0000			−1.00000
$170$		0			0
$171$		−	4.00000i		−	0.305888i
$172$			8.00000i			0.609994i
$173$	10.0000			0.760286			0.380143	−	0.924928i	$-0.375875\pi$
$173$	10.0000			0.760286			0.380143	+	0.924928i	$0.375875\pi$
$174$	−6.00000	+	6.00000i	−0.454859	+	0.454859i
$175$		0			0
$176$		−	16.0000i		−	1.20605i
$177$			8.00000i			0.601317i
$178$	14.0000	+	14.0000i	1.04934	+	1.04934i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$		0			0
$183$			8.00000i			0.591377i
$184$	−8.00000	−	8.00000i	−0.589768	−	0.589768i
$185$		0			0
$186$	10.0000	+	10.0000i	0.733236	+	0.733236i
$187$	−24.0000			−1.75505
$188$	−8.00000			−0.583460
$189$			2.00000i			0.145479i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$			8.00000i			0.577350i
$193$		−	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	−	10.0000i	0.717958	−	0.717958i
$195$		0			0
$196$			6.00000i			0.428571i
$197$	−10.0000			−0.712470			−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000			−0.712470			−0.356235	+	0.934396i	$0.615940\pi$
$198$	4.00000	−	4.00000i	0.284268	−	0.284268i
$199$	6.00000			0.425329			0.212664	−	0.977125i	$-0.431786\pi$
$199$	6.00000			0.425329			0.212664	+	0.977125i	$0.431786\pi$
$200$		0			0
$201$	12.0000			0.846415
$202$	14.0000	−	14.0000i	0.985037	−	0.985037i
$203$	12.0000			0.842235
$204$	12.0000			0.840168
$205$		0			0
$206$	−2.00000	+	2.00000i	−0.139347	+	0.139347i
$207$		−	4.00000i		−	0.278019i
$208$		0			0
$209$	16.0000			1.10674
$210$		0			0
$211$			12.0000i			0.826114i	0.910705	+	0.413057i	$0.135539\pi$
$211$			12.0000i			0.826114i	−0.910705	+	0.413057i	$0.864461\pi$
$212$			20.0000i			1.37361i
$213$	4.00000			0.274075
$214$	−4.00000	−	4.00000i	−0.273434	−	0.273434i
$215$		0			0
$216$	−2.00000	+	2.00000i	−0.136083	+	0.136083i
$217$		−	20.0000i		−	1.35769i
$218$	−4.00000	+	4.00000i	−0.270914	+	0.270914i
$219$		−	10.0000i		−	0.675737i
$220$		0			0
$221$		0			0
$222$	4.00000	+	4.00000i	0.268462	+	0.268462i
$223$			10.0000i			0.669650i	0.942280	+	0.334825i	$0.108677\pi$
$223$			10.0000i			0.669650i	−0.942280	+	0.334825i	$0.891323\pi$
$224$	8.00000	−	8.00000i	0.534522	−	0.534522i
$225$		0			0
$226$	6.00000	−	6.00000i	0.399114	−	0.399114i
$227$		0			0			−	1.00000i	$-0.5\pi$
$227$		0			0				1.00000i	$0.5\pi$
$228$	−8.00000			−0.529813
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$		0			0
$231$	−8.00000			−0.526361
$232$	12.0000	+	12.0000i	0.787839	+	0.787839i
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$		0			0
$235$		0			0
$236$	16.0000			1.04151
$237$	−14.0000			−0.909398
$238$	−12.0000	−	12.0000i	−0.777844	−	0.777844i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−30.0000			−1.93247			−0.966235	−	0.257663i	$-0.917048\pi$
$241$	−30.0000			−1.93247			−0.966235	+	0.257663i	$0.917048\pi$
$242$	5.00000	+	5.00000i	0.321412	+	0.321412i
$243$	−1.00000			−0.0641500
$244$	16.0000			1.02430
$245$		0			0
$246$	10.0000	+	10.0000i	0.637577	+	0.637577i
$247$		0			0
$248$	20.0000	−	20.0000i	1.27000	−	1.27000i
$249$		0			0
$250$		0			0
$251$			12.0000i			0.757433i	0.925513	+	0.378717i	$0.123635\pi$
$251$			12.0000i			0.757433i	−0.925513	+	0.378717i	$0.876365\pi$
$252$	4.00000			0.251976
$253$	16.0000			1.00591
$254$	6.00000	−	6.00000i	0.376473	−	0.376473i
$255$		0			0
$256$	16.0000			1.00000
$257$			2.00000i			0.124757i	0.998053	+	0.0623783i	$0.0198685\pi$
$257$			2.00000i			0.124757i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$	4.00000	+	4.00000i	0.249029	+	0.249029i
$259$		−	8.00000i		−	0.497096i
$260$		0			0
$261$			6.00000i			0.371391i
$262$		0			0
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	−8.00000	−	8.00000i	−0.492366	−	0.492366i
$265$		0			0
$266$	8.00000	+	8.00000i	0.490511	+	0.490511i
$267$	14.0000			0.856786
$268$		−	24.0000i		−	1.46603i
$269$		−	10.0000i		−	0.609711i	−0.952399	−	0.304855i	$-0.901392\pi$
$269$		−	10.0000i		−	0.609711i	0.952399	−	0.304855i	$-0.0986081\pi$
$270$		0			0
$271$	−2.00000			−0.121491			−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000			−0.121491			−0.0607457	+	0.998153i	$0.519348\pi$
$272$		−	24.0000i		−	1.45521i
$273$		0			0
$274$	2.00000	−	2.00000i	0.120824	−	0.120824i
$275$		0			0
$276$	−8.00000			−0.481543
$277$	−16.0000			−0.961347			−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000			−0.961347			−0.480673	+	0.876900i	$0.659608\pi$
$278$	4.00000	−	4.00000i	0.239904	−	0.239904i
$279$	10.0000			0.598684
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	−4.00000	+	4.00000i	−0.238197	+	0.238197i
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$		−	8.00000i		−	0.474713i
$285$		0			0
$286$		0			0
$287$		−	20.0000i		−	1.18056i
$288$	4.00000	+	4.00000i	0.235702	+	0.235702i
$289$	−19.0000			−1.11765
$290$		0			0
$291$		−	10.0000i		−	0.586210i
$292$	−20.0000			−1.17041
$293$	2.00000			0.116841			0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000			0.116841			0.0584206	+	0.998292i	$0.481394\pi$
$294$	3.00000	+	3.00000i	0.174964	+	0.174964i
$295$		0			0
$296$	8.00000	−	8.00000i	0.464991	−	0.464991i
$297$		−	4.00000i		−	0.232104i
$298$	6.00000	−	6.00000i	0.347571	−	0.347571i
$299$		0			0
$300$		0			0
$301$		−	8.00000i		−	0.461112i
$302$	2.00000	+	2.00000i	0.115087	+	0.115087i
$303$		−	14.0000i		−	0.804279i
$304$			16.0000i			0.917663i
$305$		0			0
$306$	6.00000	−	6.00000i	0.342997	−	0.342997i
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$			16.0000i			0.911685i
$309$			2.00000i			0.113776i
$310$		0			0
$311$	8.00000			0.453638			0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000			0.453638			0.226819	+	0.973937i	$0.427167\pi$
$312$		0			0
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$	−20.0000	−	20.0000i	−1.12867	−	1.12867i
$315$		0			0
$316$			28.0000i			1.57512i
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$	10.0000	+	10.0000i	0.560772	+	0.560772i
$319$	−24.0000			−1.34374
$320$		0			0
$321$	−4.00000			−0.223258
$322$	8.00000	+	8.00000i	0.445823	+	0.445823i
$323$	24.0000			1.33540
$324$			2.00000i			0.111111i
$325$		0			0
$326$	20.0000	+	20.0000i	1.10770	+	1.10770i
$327$			4.00000i			0.221201i
$328$	20.0000	−	20.0000i	1.10432	−	1.10432i
$329$	8.00000			0.441054
$330$		0			0
$331$			4.00000i			0.219860i	0.993939	+	0.109930i	$0.0350627\pi$
$331$			4.00000i			0.219860i	−0.993939	+	0.109930i	$0.964937\pi$
$332$		0			0
$333$	4.00000			0.219199
$334$	−24.0000	+	24.0000i	−1.31322	+	1.31322i
$335$		0			0
$336$		−	8.00000i		−	0.436436i
$337$		−	30.0000i		−	1.63420i	−0.576493	−	0.817102i	$-0.695579\pi$
$337$		−	30.0000i		−	1.63420i	0.576493	−	0.817102i	$-0.304421\pi$
$338$	13.0000	+	13.0000i	0.707107	+	0.707107i
$339$		−	6.00000i		−	0.325875i
$340$		0			0
$341$			40.0000i			2.16612i
$342$	−4.00000	+	4.00000i	−0.216295	+	0.216295i
$343$		−	20.0000i		−	1.07990i
$344$	8.00000	−	8.00000i	0.431331	−	0.431331i
$345$		0			0
$346$	−10.0000	−	10.0000i	−0.537603	−	0.537603i
$347$	16.0000			0.858925			0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000			0.858925			0.429463	+	0.903085i	$0.358703\pi$
$348$	12.0000			0.643268
$349$		−	8.00000i		−	0.428230i	−0.976808	−	0.214115i	$-0.931313\pi$
$349$		−	8.00000i		−	0.428230i	0.976808	−	0.214115i	$-0.0686868\pi$
$350$		0			0
$351$		0			0
$352$	−16.0000	+	16.0000i	−0.852803	+	0.852803i
$353$		−	18.0000i		−	0.958043i	−0.877803	−	0.479022i	$-0.840992\pi$
$353$		−	18.0000i		−	0.958043i	0.877803	−	0.479022i	$-0.159008\pi$
$354$	8.00000	−	8.00000i	0.425195	−	0.425195i
$355$		0			0
$356$		−	28.0000i		−	1.48400i
$357$	−12.0000			−0.635107
$358$		0			0
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−20.0000	+	20.0000i	−1.05118	+	1.05118i
$363$	5.00000			0.262432
$364$		0			0
$365$		0			0
$366$	8.00000	−	8.00000i	0.418167	−	0.418167i
$367$			18.0000i			0.939592i	0.882775	+	0.469796i	$0.155673\pi$
$367$			18.0000i			0.939592i	−0.882775	+	0.469796i	$0.844327\pi$
$368$			16.0000i			0.834058i
$369$	10.0000			0.520579
$370$		0			0
$371$		−	20.0000i		−	1.03835i
$372$		−	20.0000i		−	1.03695i
$373$	−20.0000			−1.03556			−0.517780	−	0.855514i	$-0.673242\pi$
$373$	−20.0000			−1.03556			−0.517780	+	0.855514i	$0.673242\pi$
$374$	24.0000	+	24.0000i	1.24101	+	1.24101i
$375$		0			0
$376$	8.00000	+	8.00000i	0.412568	+	0.412568i
$377$		0			0
$378$	2.00000	−	2.00000i	0.102869	−	0.102869i
$379$			36.0000i			1.84920i	0.380945	+	0.924598i	$0.375599\pi$
$379$			36.0000i			1.84920i	−0.380945	+	0.924598i	$0.624401\pi$
$380$		0			0
$381$		−	6.00000i		−	0.307389i
$382$	8.00000	+	8.00000i	0.409316	+	0.409316i
$383$			24.0000i			1.22634i	0.789950	+	0.613171i	$0.210106\pi$
$383$			24.0000i			1.22634i	−0.789950	+	0.613171i	$0.789894\pi$
$384$	8.00000	−	8.00000i	0.408248	−	0.408248i
$385$		0			0
$386$	−14.0000	+	14.0000i	−0.712581	+	0.712581i
$387$	4.00000			0.203331
$388$	−20.0000			−1.01535
$389$		−	10.0000i		−	0.507020i	−0.967333	−	0.253510i	$-0.918415\pi$
$389$		−	10.0000i		−	0.507020i	0.967333	−	0.253510i	$-0.0815851\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$	6.00000	−	6.00000i	0.303046	−	0.303046i
$393$		0			0
$394$	10.0000	+	10.0000i	0.503793	+	0.503793i
$395$		0			0
$396$	−8.00000			−0.402015
$397$	20.0000			1.00377			0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000			1.00377			0.501886	+	0.864934i	$0.332640\pi$
$398$	−6.00000	−	6.00000i	−0.300753	−	0.300753i
$399$	8.00000			0.400501
$400$		0			0
$401$	30.0000			1.49813			0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000			1.49813			0.749064	+	0.662497i	$0.230503\pi$
$402$	−12.0000	−	12.0000i	−0.598506	−	0.598506i
$403$		0			0
$404$	−28.0000			−1.39305
$405$		0			0
$406$	−12.0000	−	12.0000i	−0.595550	−	0.595550i
$407$			16.0000i			0.793091i
$408$	−12.0000	−	12.0000i	−0.594089	−	0.594089i
$409$	6.00000			0.296681			0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000			0.296681			0.148340	+	0.988936i	$0.452607\pi$
$410$		0			0
$411$		−	2.00000i		−	0.0986527i
$412$	4.00000			0.197066
$413$	−16.0000			−0.787309
$414$	−4.00000	+	4.00000i	−0.196589	+	0.196589i
$415$		0			0
$416$		0			0
$417$		−	4.00000i		−	0.195881i
$418$	−16.0000	−	16.0000i	−0.782586	−	0.782586i
$419$			4.00000i			0.195413i	0.995215	+	0.0977064i	$0.0311506\pi$
$419$			4.00000i			0.195413i	−0.995215	+	0.0977064i	$0.968849\pi$
$420$		0			0
$421$			20.0000i			0.974740i	0.873195	+	0.487370i	$0.162044\pi$
$421$			20.0000i			0.974740i	−0.873195	+	0.487370i	$0.837956\pi$
$422$	12.0000	−	12.0000i	0.584151	−	0.584151i
$423$			4.00000i			0.194487i
$424$	20.0000	−	20.0000i	0.971286	−	0.971286i
$425$		0			0
$426$	−4.00000	−	4.00000i	−0.193801	−	0.193801i
$427$	−16.0000			−0.774294
$428$			8.00000i			0.386695i
$429$		0			0
$430$		0			0
$431$	−36.0000			−1.73406			−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000			−1.73406			−0.867029	+	0.498257i	$0.833974\pi$
$432$	4.00000			0.192450
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	−20.0000	+	20.0000i	−0.960031	+	0.960031i
$435$		0			0
$436$	8.00000			0.383131
$437$	−16.0000			−0.765384
$438$	−10.0000	+	10.0000i	−0.477818	+	0.477818i
$439$	−2.00000			−0.0954548			−0.0477274	−	0.998860i	$-0.515198\pi$
$439$	−2.00000			−0.0954548			−0.0477274	+	0.998860i	$0.515198\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$		0			0
$443$	−16.0000			−0.760183			−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000			−0.760183			−0.380091	+	0.924949i	$0.624107\pi$
$444$		−	8.00000i		−	0.379663i
$445$		0			0
$446$	10.0000	−	10.0000i	0.473514	−	0.473514i
$447$		−	6.00000i		−	0.283790i
$448$	−16.0000			−0.755929
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$			40.0000i			1.88353i
$452$	−12.0000			−0.564433
$453$	2.00000			0.0939682
$454$		0			0
$455$		0			0
$456$	8.00000	+	8.00000i	0.374634	+	0.374634i
$457$		−	18.0000i		−	0.842004i	−0.907060	−	0.421002i	$-0.861678\pi$
$457$		−	18.0000i		−	0.842004i	0.907060	−	0.421002i	$-0.138322\pi$
$458$	4.00000	−	4.00000i	0.186908	−	0.186908i
$459$		−	6.00000i		−	0.280056i
$460$		0			0
$461$		−	34.0000i		−	1.58354i	−0.610821	−	0.791769i	$-0.709160\pi$
$461$		−	34.0000i		−	1.58354i	0.610821	−	0.791769i	$-0.290840\pi$
$462$	8.00000	+	8.00000i	0.372194	+	0.372194i
$463$		−	22.0000i		−	1.02243i	−0.859454	−	0.511213i	$-0.829196\pi$
$463$		−	22.0000i		−	1.02243i	0.859454	−	0.511213i	$-0.170804\pi$
$464$		−	24.0000i		−	1.11417i
$465$		0			0
$466$	−6.00000	+	6.00000i	−0.277945	+	0.277945i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$			24.0000i			1.10822i
$470$		0			0
$471$	−20.0000			−0.921551
$472$	−16.0000	−	16.0000i	−0.736460	−	0.736460i
$473$			16.0000i			0.735681i
$474$	14.0000	+	14.0000i	0.643041	+	0.643041i
$475$		0			0
$476$			24.0000i			1.10004i
$477$	10.0000			0.457869
$478$	16.0000	+	16.0000i	0.731823	+	0.731823i
$479$	−4.00000			−0.182765			−0.0913823	−	0.995816i	$-0.529129\pi$
$479$	−4.00000			−0.182765			−0.0913823	+	0.995816i	$0.529129\pi$
$480$		0			0
$481$		0			0
$482$	30.0000	+	30.0000i	1.36646	+	1.36646i
$483$	8.00000			0.364013
$484$		−	10.0000i		−	0.454545i
$485$		0			0
$486$	1.00000	+	1.00000i	0.0453609	+	0.0453609i
$487$			30.0000i			1.35943i	0.733476	+	0.679715i	$0.237896\pi$
$487$			30.0000i			1.35943i	−0.733476	+	0.679715i	$0.762104\pi$
$488$	−16.0000	−	16.0000i	−0.724286	−	0.724286i
$489$	20.0000			0.904431
$490$		0			0
$491$		−	40.0000i		−	1.80517i	−0.430507	−	0.902587i	$-0.641665\pi$
$491$		−	40.0000i		−	1.80517i	0.430507	−	0.902587i	$-0.358335\pi$
$492$		−	20.0000i		−	0.901670i
$493$	−36.0000			−1.62136
$494$		0			0
$495$		0			0
$496$	−40.0000			−1.79605
$497$			8.00000i			0.358849i
$498$		0			0
$499$			20.0000i			0.895323i	0.894203	+	0.447661i	$0.147743\pi$
$499$			20.0000i			0.895323i	−0.894203	+	0.447661i	$0.852257\pi$
$500$		0			0
$501$			24.0000i			1.07224i
$502$	12.0000	−	12.0000i	0.535586	−	0.535586i
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$	−4.00000	−	4.00000i	−0.178174	−	0.178174i
$505$		0			0
$506$	−16.0000	−	16.0000i	−0.711287	−	0.711287i
$507$	13.0000			0.577350
$508$	−12.0000			−0.532414
$509$		−	18.0000i		−	0.797836i	−0.916987	−	0.398918i	$-0.869386\pi$
$509$		−	18.0000i		−	0.797836i	0.916987	−	0.398918i	$-0.130614\pi$
$510$		0			0
$511$	20.0000			0.884748
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$			4.00000i			0.176604i
$514$	2.00000	−	2.00000i	0.0882162	−	0.0882162i
$515$		0			0
$516$		−	8.00000i		−	0.352180i
$517$	−16.0000			−0.703679
$518$	−8.00000	+	8.00000i	−0.351500	+	0.351500i
$519$	−10.0000			−0.438951
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	6.00000	−	6.00000i	0.262613	−	0.262613i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			60.0000i			2.61364i
$528$			16.0000i			0.696311i
$529$	7.00000			0.304348
$530$		0			0
$531$		−	8.00000i		−	0.347170i
$532$		−	16.0000i		−	0.693688i
$533$		0			0
$534$	−14.0000	−	14.0000i	−0.605839	−	0.605839i
$535$		0			0
$536$	−24.0000	+	24.0000i	−1.03664	+	1.03664i
$537$		0			0
$538$	−10.0000	+	10.0000i	−0.431131	+	0.431131i
$539$			12.0000i			0.516877i
$540$		0			0
$541$		−	44.0000i		−	1.89171i	−0.324593	−	0.945854i	$-0.605227\pi$
$541$		−	44.0000i		−	1.89171i	0.324593	−	0.945854i	$-0.394773\pi$
$542$	2.00000	+	2.00000i	0.0859074	+	0.0859074i
$543$			20.0000i			0.858282i
$544$	−24.0000	+	24.0000i	−1.02899	+	1.02899i
$545$		0			0
$546$		0			0
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−4.00000			−0.170872
$549$		−	8.00000i		−	0.341432i
$550$		0			0
$551$	24.0000			1.02243
$552$	8.00000	+	8.00000i	0.340503	+	0.340503i
$553$		−	28.0000i		−	1.19068i
$554$	16.0000	+	16.0000i	0.679775	+	0.679775i
$555$		0			0
$556$	−8.00000			−0.339276
$557$	−42.0000			−1.77960			−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000			−1.77960			−0.889799	+	0.456354i	$0.849155\pi$
$558$	−10.0000	−	10.0000i	−0.423334	−	0.423334i
$559$		0			0
$560$		0			0
$561$	24.0000			1.01328
$562$	10.0000	+	10.0000i	0.421825	+	0.421825i
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$	8.00000			0.336861
$565$		0			0
$566$	−4.00000	−	4.00000i	−0.168133	−	0.168133i
$567$		−	2.00000i		−	0.0839921i
$568$	−8.00000	+	8.00000i	−0.335673	+	0.335673i
$569$	−2.00000			−0.0838444			−0.0419222	−	0.999121i	$-0.513348\pi$
$569$	−2.00000			−0.0838444			−0.0419222	+	0.999121i	$0.513348\pi$
$570$		0			0
$571$		−	20.0000i		−	0.836974i	−0.908223	−	0.418487i	$-0.862561\pi$
$571$		−	20.0000i		−	0.836974i	0.908223	−	0.418487i	$-0.137439\pi$
$572$		0			0
$573$	8.00000			0.334205
$574$	−20.0000	+	20.0000i	−0.834784	+	0.834784i
$575$		0			0
$576$		−	8.00000i		−	0.333333i
$577$			2.00000i			0.0832611i	0.999133	+	0.0416305i	$0.0132552\pi$
$577$			2.00000i			0.0832611i	−0.999133	+	0.0416305i	$0.986745\pi$
$578$	19.0000	+	19.0000i	0.790296	+	0.790296i
$579$			14.0000i			0.581820i
$580$		0			0
$581$		0			0
$582$	−10.0000	+	10.0000i	−0.414513	+	0.414513i
$583$			40.0000i			1.65663i
$584$	20.0000	+	20.0000i	0.827606	+	0.827606i
$585$		0			0
$586$	−2.00000	−	2.00000i	−0.0826192	−	0.0826192i
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		−	6.00000i		−	0.247436i
$589$		−	40.0000i		−	1.64817i
$590$		0			0
$591$	10.0000			0.411345
$592$	−16.0000			−0.657596
$593$			22.0000i			0.903432i	0.892162	+	0.451716i	$0.149188\pi$
$593$			22.0000i			0.903432i	−0.892162	+	0.451716i	$0.850812\pi$
$594$	−4.00000	+	4.00000i	−0.164122	+	0.164122i
$595$		0			0
$596$	−12.0000			−0.491539
$597$	−6.00000			−0.245564
$598$		0			0
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		0			0
$601$	−14.0000			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$602$	−8.00000	+	8.00000i	−0.326056	+	0.326056i
$603$	−12.0000			−0.488678
$604$		−	4.00000i		−	0.162758i
$605$		0			0
$606$	−14.0000	+	14.0000i	−0.568711	+	0.568711i
$607$		−	2.00000i		−	0.0811775i	−0.999176	−	0.0405887i	$-0.987077\pi$
$607$		−	2.00000i		−	0.0811775i	0.999176	−	0.0405887i	$-0.0129233\pi$
$608$	16.0000	−	16.0000i	0.648886	−	0.648886i
$609$	−12.0000			−0.486265
$610$		0			0
$611$		0			0
$612$	−12.0000			−0.485071
$613$	20.0000			0.807792			0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000			0.807792			0.403896	+	0.914805i	$0.367656\pi$
$614$	−28.0000	−	28.0000i	−1.12999	−	1.12999i
$615$		0			0
$616$	16.0000	−	16.0000i	0.644658	−	0.644658i
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$	2.00000	−	2.00000i	0.0804518	−	0.0804518i
$619$		−	20.0000i		−	0.803868i	−0.915669	−	0.401934i	$-0.868338\pi$
$619$		−	20.0000i		−	0.803868i	0.915669	−	0.401934i	$-0.131662\pi$
$620$		0			0
$621$			4.00000i			0.160514i
$622$	−8.00000	−	8.00000i	−0.320771	−	0.320771i
$623$			28.0000i			1.12180i
$624$		0			0
$625$		0			0
$626$	6.00000	−	6.00000i	0.239808	−	0.239808i
$627$	−16.0000			−0.638978
$628$			40.0000i			1.59617i
$629$			24.0000i			0.956943i
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	28.0000	−	28.0000i	1.11378	−	1.11378i
$633$		−	12.0000i		−	0.476957i
$634$	−18.0000	−	18.0000i	−0.714871	−	0.714871i
$635$		0			0
$636$		−	20.0000i		−	0.793052i
$637$		0			0
$638$	24.0000	+	24.0000i	0.950169	+	0.950169i
$639$	−4.00000			−0.158238
$640$		0			0
$641$	14.0000			0.552967			0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000			0.552967			0.276483	+	0.961019i	$0.410831\pi$
$642$	4.00000	+	4.00000i	0.157867	+	0.157867i
$643$	12.0000			0.473234			0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000			0.473234			0.236617	+	0.971603i	$0.423961\pi$
$644$		−	16.0000i		−	0.630488i
$645$		0			0
$646$	−24.0000	−	24.0000i	−0.944267	−	0.944267i
$647$		−	12.0000i		−	0.471769i	−0.971781	−	0.235884i	$-0.924201\pi$
$647$		−	12.0000i		−	0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$	2.00000	−	2.00000i	0.0785674	−	0.0785674i
$649$	32.0000			1.25611
$650$		0			0
$651$			20.0000i			0.783862i
$652$		−	40.0000i		−	1.56652i
$653$	−30.0000			−1.17399			−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000			−1.17399			−0.586995	+	0.809590i	$0.699689\pi$
$654$	4.00000	−	4.00000i	0.156412	−	0.156412i
$655$		0			0
$656$	−40.0000			−1.56174
$657$			10.0000i			0.390137i
$658$	−8.00000	−	8.00000i	−0.311872	−	0.311872i
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$			32.0000i			1.24466i	0.782757	+	0.622328i	$0.213813\pi$
$661$			32.0000i			1.24466i	−0.782757	+	0.622328i	$0.786187\pi$
$662$	4.00000	−	4.00000i	0.155464	−	0.155464i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−4.00000	−	4.00000i	−0.154997	−	0.154997i
$667$	24.0000			0.929284
$668$	48.0000			1.85718
$669$		−	10.0000i		−	0.386622i
$670$		0			0
$671$	32.0000			1.23535
$672$	−8.00000	+	8.00000i	−0.308607	+	0.308607i
$673$		−	2.00000i		−	0.0770943i	−0.999257	−	0.0385472i	$-0.987727\pi$
$673$		−	2.00000i		−	0.0770943i	0.999257	−	0.0385472i	$-0.0122730\pi$
$674$	−30.0000	+	30.0000i	−1.15556	+	1.15556i
$675$		0			0
$676$		−	26.0000i		−	1.00000i
$677$	−38.0000			−1.46046			−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000			−1.46046			−0.730229	+	0.683202i	$0.760587\pi$
$678$	−6.00000	+	6.00000i	−0.230429	+	0.230429i
$679$	20.0000			0.767530
$680$		0			0
$681$		0			0
$682$	40.0000	−	40.0000i	1.53168	−	1.53168i
$683$	−48.0000			−1.83667			−0.918334	−	0.395805i	$-0.870466\pi$
$683$	−48.0000			−1.83667			−0.918334	+	0.395805i	$0.870466\pi$
$684$	8.00000			0.305888
$685$		0			0
$686$	−20.0000	+	20.0000i	−0.763604	+	0.763604i
$687$		−	4.00000i		−	0.152610i
$688$	−16.0000			−0.609994
$689$		0			0
$690$		0			0
$691$			12.0000i			0.456502i	0.973602	+	0.228251i	$0.0733006\pi$
$691$			12.0000i			0.456502i	−0.973602	+	0.228251i	$0.926699\pi$
$692$			20.0000i			0.760286i
$693$	8.00000			0.303895
$694$	−16.0000	−	16.0000i	−0.607352	−	0.607352i
$695$		0			0
$696$	−12.0000	−	12.0000i	−0.454859	−	0.454859i
$697$			60.0000i			2.27266i
$698$	−8.00000	+	8.00000i	−0.302804	+	0.302804i
$699$			6.00000i			0.226941i
$700$		0			0
$701$		−	22.0000i		−	0.830929i	−0.909610	−	0.415464i	$-0.863619\pi$
$701$		−	22.0000i		−	0.830929i	0.909610	−	0.415464i	$-0.136381\pi$
$702$		0			0
$703$		−	16.0000i		−	0.603451i
$704$	32.0000			1.20605
$705$		0			0
$706$	−18.0000	+	18.0000i	−0.677439	+	0.677439i
$707$	28.0000			1.05305
$708$	−16.0000			−0.601317
$709$		−	44.0000i		−	1.65245i	−0.563337	−	0.826227i	$-0.690483\pi$
$709$		−	44.0000i		−	1.65245i	0.563337	−	0.826227i	$-0.309517\pi$
$710$		0			0
$711$	14.0000			0.525041
$712$	−28.0000	+	28.0000i	−1.04934	+	1.04934i
$713$		−	40.0000i		−	1.49801i
$714$	12.0000	+	12.0000i	0.449089	+	0.449089i
$715$		0			0
$716$		0			0
$717$	16.0000			0.597531
$718$	12.0000	+	12.0000i	0.447836	+	0.447836i
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$	−4.00000			−0.148968
$722$	−3.00000	−	3.00000i	−0.111648	−	0.111648i
$723$	30.0000			1.11571
$724$	40.0000			1.48659
$725$		0			0
$726$	−5.00000	−	5.00000i	−0.185567	−	0.185567i
$727$			14.0000i			0.519231i	0.965712	+	0.259616i	$0.0835959\pi$
$727$			14.0000i			0.519231i	−0.965712	+	0.259616i	$0.916404\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$			24.0000i			0.887672i
$732$	−16.0000			−0.591377
$733$	24.0000			0.886460			0.443230	−	0.896408i	$-0.353832\pi$
$733$	24.0000			0.886460			0.443230	+	0.896408i	$0.353832\pi$
$734$	18.0000	−	18.0000i	0.664392	−	0.664392i
$735$		0			0
$736$	16.0000	−	16.0000i	0.589768	−	0.589768i
$737$		−	48.0000i		−	1.76810i
$738$	−10.0000	−	10.0000i	−0.368105	−	0.368105i
$739$		−	12.0000i		−	0.441427i	−0.975339	−	0.220714i	$-0.929161\pi$
$739$		−	12.0000i		−	0.441427i	0.975339	−	0.220714i	$-0.0708386\pi$
$740$		0			0
$741$		0			0
$742$	−20.0000	+	20.0000i	−0.734223	+	0.734223i
$743$		−	48.0000i		−	1.76095i	−0.474093	−	0.880475i	$-0.657224\pi$
$743$		−	48.0000i		−	1.76095i	0.474093	−	0.880475i	$-0.342776\pi$
$744$	−20.0000	+	20.0000i	−0.733236	+	0.733236i
$745$		0			0
$746$	20.0000	+	20.0000i	0.732252	+	0.732252i
$747$		0			0
$748$		−	48.0000i		−	1.75505i
$749$		−	8.00000i		−	0.292314i
$750$		0			0
$751$	26.0000			0.948753			0.474377	−	0.880322i	$-0.342673\pi$
$751$	26.0000			0.948753			0.474377	+	0.880322i	$0.342673\pi$
$752$		−	16.0000i		−	0.583460i
$753$		−	12.0000i		−	0.437304i
$754$		0			0
$755$		0			0
$756$	−4.00000			−0.145479
$757$	−8.00000			−0.290765			−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000			−0.290765			−0.145382	+	0.989376i	$0.546441\pi$
$758$	36.0000	−	36.0000i	1.30758	−	1.30758i
$759$	−16.0000			−0.580763
$760$		0			0
$761$	10.0000			0.362500			0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000			0.362500			0.181250	+	0.983437i	$0.441986\pi$
$762$	−6.00000	+	6.00000i	−0.217357	+	0.217357i
$763$	−8.00000			−0.289619
$764$		−	16.0000i		−	0.578860i
$765$		0			0
$766$	24.0000	−	24.0000i	0.867155	−	0.867155i
$767$		0			0
$768$	−16.0000			−0.577350
$769$	6.00000			0.216366			0.108183	−	0.994131i	$-0.465497\pi$
$769$	6.00000			0.216366			0.108183	+	0.994131i	$0.465497\pi$
$770$		0			0
$771$		−	2.00000i		−	0.0720282i
$772$	28.0000			1.00774
$773$	−6.00000			−0.215805			−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000			−0.215805			−0.107903	+	0.994161i	$0.534413\pi$
$774$	−4.00000	−	4.00000i	−0.143777	−	0.143777i
$775$		0			0
$776$	20.0000	+	20.0000i	0.717958	+	0.717958i
$777$			8.00000i			0.286998i
$778$	−10.0000	+	10.0000i	−0.358517	+	0.358517i
$779$		−	40.0000i		−	1.43315i
$780$		0			0
$781$		−	16.0000i		−	0.572525i
$782$	−24.0000	−	24.0000i	−0.858238	−	0.858238i
$783$		−	6.00000i		−	0.214423i
$784$	−12.0000			−0.428571
$785$		0			0
$786$		0			0
$787$	28.0000			0.998092			0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000			0.998092			0.499046	+	0.866575i	$0.333684\pi$
$788$		−	20.0000i		−	0.712470i
$789$		0			0
$790$		0			0
$791$	12.0000			0.426671
$792$	8.00000	+	8.00000i	0.284268	+	0.284268i
$793$		0			0
$794$	−20.0000	−	20.0000i	−0.709773	−	0.709773i
$795$		0			0
$796$			12.0000i			0.425329i
$797$	30.0000			1.06265			0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000			1.06265			0.531327	+	0.847167i	$0.321693\pi$
$798$	−8.00000	−	8.00000i	−0.283197	−	0.283197i
$799$	−24.0000			−0.849059
$800$		0			0
$801$	−14.0000			−0.494666
$802$	−30.0000	−	30.0000i	−1.05934	−	1.05934i
$803$	−40.0000			−1.41157
$804$			24.0000i			0.846415i
$805$		0			0
$806$		0			0
$807$			10.0000i			0.352017i
$808$	28.0000	+	28.0000i	0.985037	+	0.985037i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$		0			0
$811$		−	4.00000i		−	0.140459i	−0.997531	−	0.0702295i	$-0.977627\pi$
$811$		−	4.00000i		−	0.140459i	0.997531	−	0.0702295i	$-0.0223732\pi$
$812$			24.0000i			0.842235i
$813$	2.00000			0.0701431
$814$	16.0000	−	16.0000i	0.560800	−	0.560800i
$815$		0			0
$816$			24.0000i			0.840168i
$817$		−	16.0000i		−	0.559769i
$818$	−6.00000	−	6.00000i	−0.209785	−	0.209785i
$819$		0			0
$820$		0			0
$821$		−	10.0000i		−	0.349002i	−0.984657	−	0.174501i	$-0.944169\pi$
$821$		−	10.0000i		−	0.349002i	0.984657	−	0.174501i	$-0.0558313\pi$
$822$	−2.00000	+	2.00000i	−0.0697580	+	0.0697580i
$823$			42.0000i			1.46403i	0.681290	+	0.732014i	$0.261419\pi$
$823$			42.0000i			1.46403i	−0.681290	+	0.732014i	$0.738581\pi$
$824$	−4.00000	−	4.00000i	−0.139347	−	0.139347i
$825$		0			0
$826$	16.0000	+	16.0000i	0.556711	+	0.556711i
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$	8.00000			0.278019
$829$			44.0000i			1.52818i	0.645108	+	0.764092i	$0.276812\pi$
$829$			44.0000i			1.52818i	−0.645108	+	0.764092i	$0.723188\pi$
$830$		0			0
$831$	16.0000			0.555034
$832$		0			0
$833$			18.0000i			0.623663i
$834$	−4.00000	+	4.00000i	−0.138509	+	0.138509i
$835$		0			0
$836$			32.0000i			1.10674i
$837$	−10.0000			−0.345651
$838$	4.00000	−	4.00000i	0.138178	−	0.138178i
$839$	−4.00000			−0.138095			−0.0690477	−	0.997613i	$-0.521996\pi$
$839$	−4.00000			−0.138095			−0.0690477	+	0.997613i	$0.521996\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	20.0000	−	20.0000i	0.689246	−	0.689246i
$843$	10.0000			0.344418
$844$	−24.0000			−0.826114
$845$		0			0
$846$	4.00000	−	4.00000i	0.137523	−	0.137523i
$847$			10.0000i			0.343604i
$848$	−40.0000			−1.37361
$849$	−4.00000			−0.137280
$850$		0			0
$851$		−	16.0000i		−	0.548473i
$852$			8.00000i			0.274075i
$853$	44.0000			1.50653			0.753266	−	0.657716i	$-0.228477\pi$
$853$	44.0000			1.50653			0.753266	+	0.657716i	$0.228477\pi$
$854$	16.0000	+	16.0000i	0.547509	+	0.547509i
$855$		0			0
$856$	8.00000	−	8.00000i	0.273434	−	0.273434i
$857$		−	6.00000i		−	0.204956i	−0.994735	−	0.102478i	$-0.967323\pi$
$857$		−	6.00000i		−	0.204956i	0.994735	−	0.102478i	$-0.0326771\pi$
$858$		0			0
$859$			44.0000i			1.50126i	0.660722	+	0.750630i	$0.270250\pi$
$859$			44.0000i			1.50126i	−0.660722	+	0.750630i	$0.729750\pi$
$860$		0			0
$861$			20.0000i			0.681598i
$862$	36.0000	+	36.0000i	1.22616	+	1.22616i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	−4.00000	−	4.00000i	−0.136083	−	0.136083i
$865$		0			0
$866$	14.0000	−	14.0000i	0.475739	−	0.475739i
$867$	19.0000			0.645274
$868$	40.0000			1.35769
$869$			56.0000i			1.89967i
$870$		0			0
$871$		0			0
$872$	−8.00000	−	8.00000i	−0.270914	−	0.270914i
$873$			10.0000i			0.338449i
$874$	16.0000	+	16.0000i	0.541208	+	0.541208i
$875$		0			0
$876$	20.0000			0.675737
$877$	44.0000			1.48577			0.742887	−	0.669417i	$-0.233456\pi$
$877$	44.0000			1.48577			0.742887	+	0.669417i	$0.233456\pi$
$878$	2.00000	+	2.00000i	0.0674967	+	0.0674967i
$879$	−2.00000			−0.0674583
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$	−3.00000	−	3.00000i	−0.101015	−	0.101015i
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$		0			0
$885$		0			0
$886$	16.0000	+	16.0000i	0.537531	+	0.537531i
$887$		−	16.0000i		−	0.537227i	−0.963248	−	0.268614i	$-0.913434\pi$
$887$		−	16.0000i		−	0.537227i	0.963248	−	0.268614i	$-0.0865655\pi$
$888$	−8.00000	+	8.00000i	−0.268462	+	0.268462i
$889$	12.0000			0.402467
$890$		0			0
$891$			4.00000i			0.134005i
$892$	−20.0000			−0.669650
$893$	16.0000			0.535420
$894$	−6.00000	+	6.00000i	−0.200670	+	0.200670i
$895$		0			0
$896$	16.0000	+	16.0000i	0.534522	+	0.534522i
$897$		0			0
$898$	−18.0000	−	18.0000i	−0.600668	−	0.600668i
$899$			60.0000i			2.00111i
$900$		0			0
$901$			60.0000i			1.99889i
$902$	40.0000	−	40.0000i	1.33185	−	1.33185i
$903$			8.00000i			0.266223i
$904$	12.0000	+	12.0000i	0.399114	+	0.399114i
$905$		0			0
$906$	−2.00000	−	2.00000i	−0.0664455	−	0.0664455i
$907$	−52.0000			−1.72663			−0.863316	−	0.504664i	$-0.831616\pi$
$907$	−52.0000			−1.72663			−0.863316	+	0.504664i	$0.831616\pi$
$908$		0			0
$909$			14.0000i			0.464351i
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		−	16.0000i		−	0.529813i
$913$		0			0
$914$	−18.0000	+	18.0000i	−0.595387	+	0.595387i
$915$		0			0
$916$	−8.00000			−0.264327
$917$		0			0
$918$	−6.00000	+	6.00000i	−0.198030	+	0.198030i
$919$	26.0000			0.857661			0.428830	−	0.903385i	$-0.358926\pi$
$919$	26.0000			0.857661			0.428830	+	0.903385i	$0.358926\pi$
$920$		0			0
$921$	−28.0000			−0.922631
$922$	−34.0000	+	34.0000i	−1.11973	+	1.11973i
$923$		0			0
$924$		−	16.0000i		−	0.526361i
$925$		0			0
$926$	−22.0000	+	22.0000i	−0.722965	+	0.722965i
$927$		−	2.00000i		−	0.0656886i
$928$	−24.0000	+	24.0000i	−0.787839	+	0.787839i
$929$	−46.0000			−1.50921			−0.754606	−	0.656179i	$-0.772172\pi$
$929$	−46.0000			−1.50921			−0.754606	+	0.656179i	$0.772172\pi$
$930$		0			0
$931$		−	12.0000i		−	0.393284i
$932$	12.0000			0.393073
$933$	−8.00000			−0.261908
$934$	8.00000	+	8.00000i	0.261768	+	0.261768i
$935$		0			0
$936$		0			0
$937$		−	22.0000i		−	0.718709i	−0.933201	−	0.359354i	$-0.882997\pi$
$937$		−	22.0000i		−	0.718709i	0.933201	−	0.359354i	$-0.117003\pi$
$938$	24.0000	−	24.0000i	0.783628	−	0.783628i
$939$		−	6.00000i		−	0.195803i
$940$		0			0
$941$		−	26.0000i		−	0.847576i	−0.905761	−	0.423788i	$-0.860700\pi$
$941$		−	26.0000i		−	0.847576i	0.905761	−	0.423788i	$-0.139300\pi$
$942$	20.0000	+	20.0000i	0.651635	+	0.651635i
$943$		−	40.0000i		−	1.30258i
$944$			32.0000i			1.04151i
$945$		0			0
$946$	16.0000	−	16.0000i	0.520205	−	0.520205i
$947$	−36.0000			−1.16984			−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000			−1.16984			−0.584921	+	0.811090i	$0.698875\pi$
$948$		−	28.0000i		−	0.909398i
$949$		0			0
$950$		0			0
$951$	−18.0000			−0.583690
$952$	24.0000	−	24.0000i	0.777844	−	0.777844i
$953$		−	26.0000i		−	0.842223i	−0.907009	−	0.421111i	$-0.861640\pi$
$953$		−	26.0000i		−	0.842223i	0.907009	−	0.421111i	$-0.138360\pi$
$954$	−10.0000	−	10.0000i	−0.323762	−	0.323762i
$955$		0			0
$956$		−	32.0000i		−	1.03495i
$957$	24.0000			0.775810
$958$	4.00000	+	4.00000i	0.129234	+	0.129234i
$959$	4.00000			0.129167
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$	4.00000			0.128898
$964$		−	60.0000i		−	1.93247i
$965$		0			0
$966$	−8.00000	−	8.00000i	−0.257396	−	0.257396i
$967$		−	46.0000i		−	1.47926i	−0.673014	−	0.739630i	$-0.735000\pi$
$967$		−	46.0000i		−	1.47926i	0.673014	−	0.739630i	$-0.265000\pi$
$968$	−10.0000	+	10.0000i	−0.321412	+	0.321412i
$969$	−24.0000			−0.770991
$970$		0			0
$971$			12.0000i			0.385098i	0.981287	+	0.192549i	$0.0616755\pi$
$971$			12.0000i			0.385098i	−0.981287	+	0.192549i	$0.938325\pi$
$972$		−	2.00000i		−	0.0641500i
$973$	8.00000			0.256468
$974$	30.0000	−	30.0000i	0.961262	−	0.961262i
$975$		0			0
$976$			32.0000i			1.02430i
$977$			22.0000i			0.703842i	0.936030	+	0.351921i	$0.114471\pi$
$977$			22.0000i			0.703842i	−0.936030	+	0.351921i	$0.885529\pi$
$978$	−20.0000	−	20.0000i	−0.639529	−	0.639529i
$979$		−	56.0000i		−	1.78977i
$980$		0			0
$981$		−	4.00000i		−	0.127710i
$982$	−40.0000	+	40.0000i	−1.27645	+	1.27645i
$983$		−	32.0000i		−	1.02064i	−0.859984	−	0.510321i	$-0.829527\pi$
$983$		−	32.0000i		−	1.02064i	0.859984	−	0.510321i	$-0.170473\pi$
$984$	−20.0000	+	20.0000i	−0.637577	+	0.637577i
$985$		0			0
$986$	36.0000	+	36.0000i	1.14647	+	1.14647i
$987$	−8.00000			−0.254643
$988$		0			0
$989$		−	16.0000i		−	0.508770i
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	40.0000	+	40.0000i	1.27000	+	1.27000i
$993$		−	4.00000i		−	0.126936i
$994$	8.00000	−	8.00000i	0.253745	−	0.253745i
$995$		0			0
$996$		0			0
$997$	−28.0000			−0.886769			−0.443384	−	0.896332i	$-0.646222\pi$
$997$	−28.0000			−0.886769			−0.443384	+	0.896332i	$0.646222\pi$
$998$	20.0000	−	20.0000i	0.633089	−	0.633089i
$999$	−4.00000			−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.d.a.349.1		2
3.2	odd	2		1800.2.d.h.1549.2		2
4.3	odd	2		2400.2.d.d.49.2		2
5.2	odd	4		120.2.k.a.61.1	✓	2
5.3	odd	4		600.2.k.a.301.2		2
5.4	even	2		600.2.d.d.349.2		2
8.3	odd	2		2400.2.d.a.49.2		2
8.5	even	2		600.2.d.d.349.1		2
12.11	even	2		7200.2.d.f.2449.2		2
15.2	even	4		360.2.k.b.181.2		2
15.8	even	4		1800.2.k.g.901.1		2
15.14	odd	2		1800.2.d.c.1549.1		2
20.3	even	4		2400.2.k.b.1201.2		2
20.7	even	4		480.2.k.a.241.1		2
20.19	odd	2		2400.2.d.a.49.1		2
24.5	odd	2		1800.2.d.c.1549.2		2
24.11	even	2		7200.2.d.e.2449.2		2
40.3	even	4		2400.2.k.b.1201.1		2
40.13	odd	4		600.2.k.a.301.1		2
40.19	odd	2		2400.2.d.d.49.1		2
40.27	even	4		480.2.k.a.241.2		2
40.29	even	2	inner	600.2.d.a.349.2		2
40.37	odd	4		120.2.k.a.61.2	yes	2
60.23	odd	4		7200.2.k.f.3601.2		2
60.47	odd	4		1440.2.k.a.721.2		2
60.59	even	2		7200.2.d.e.2449.1		2
80.27	even	4		3840.2.a.m.1.1		1
80.37	odd	4		3840.2.a.w.1.1		1
80.67	even	4		3840.2.a.r.1.1		1
80.77	odd	4		3840.2.a.d.1.1		1
120.29	odd	2		1800.2.d.h.1549.1		2
120.53	even	4		1800.2.k.g.901.2		2
120.59	even	2		7200.2.d.f.2449.1		2
120.77	even	4		360.2.k.b.181.1		2
120.83	odd	4		7200.2.k.f.3601.1		2
120.107	odd	4		1440.2.k.a.721.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.k.a.61.1	✓	2	5.2	odd	4
120.2.k.a.61.2	yes	2	40.37	odd	4
360.2.k.b.181.1		2	120.77	even	4
360.2.k.b.181.2		2	15.2	even	4
480.2.k.a.241.1		2	20.7	even	4
480.2.k.a.241.2		2	40.27	even	4
600.2.d.a.349.1		2	1.1	even	1	trivial
600.2.d.a.349.2		2	40.29	even	2	inner
600.2.d.d.349.1		2	8.5	even	2
600.2.d.d.349.2		2	5.4	even	2
600.2.k.a.301.1		2	40.13	odd	4
600.2.k.a.301.2		2	5.3	odd	4
1440.2.k.a.721.1		2	120.107	odd	4
1440.2.k.a.721.2		2	60.47	odd	4
1800.2.d.c.1549.1		2	15.14	odd	2
1800.2.d.c.1549.2		2	24.5	odd	2
1800.2.d.h.1549.1		2	120.29	odd	2
1800.2.d.h.1549.2		2	3.2	odd	2
1800.2.k.g.901.1		2	15.8	even	4
1800.2.k.g.901.2		2	120.53	even	4
2400.2.d.a.49.1		2	20.19	odd	2
2400.2.d.a.49.2		2	8.3	odd	2
2400.2.d.d.49.1		2	40.19	odd	2
2400.2.d.d.49.2		2	4.3	odd	2
2400.2.k.b.1201.1		2	40.3	even	4
2400.2.k.b.1201.2		2	20.3	even	4
3840.2.a.d.1.1		1	80.77	odd	4
3840.2.a.m.1.1		1	80.27	even	4
3840.2.a.r.1.1		1	80.67	even	4
3840.2.a.w.1.1		1	80.37	odd	4
7200.2.d.e.2449.1		2	60.59	even	2
7200.2.d.e.2449.2		2	24.11	even	2
7200.2.d.f.2449.1		2	120.59	even	2
7200.2.d.f.2449.2		2	12.11	even	2
7200.2.k.f.3601.1		2	120.83	odd	4
7200.2.k.f.3601.2		2	60.23	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} +(1.00000 + 1.00000i) q^{6} -2.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} +(1.00000 + 1.00000i) q^{6} -2.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +1.00000 q^{9} +4.00000i q^{11} -2.00000i q^{12} +(-2.00000 + 2.00000i) q^{14} -4.00000 q^{16} +6.00000i q^{17} +(-1.00000 - 1.00000i) q^{18} -4.00000i q^{19} +2.00000i q^{21} +(4.00000 - 4.00000i) q^{22} -4.00000i q^{23} +(-2.00000 + 2.00000i) q^{24} -1.00000 q^{27} +4.00000 q^{28} +6.00000i q^{29} +10.0000 q^{31} +(4.00000 + 4.00000i) q^{32} -4.00000i q^{33} +(6.00000 - 6.00000i) q^{34} +2.00000i q^{36} +4.00000 q^{37} +(-4.00000 + 4.00000i) q^{38} +10.0000 q^{41} +(2.00000 - 2.00000i) q^{42} +4.00000 q^{43} -8.00000 q^{44} +(-4.00000 + 4.00000i) q^{46} +4.00000i q^{47} +4.00000 q^{48} +3.00000 q^{49} -6.00000i q^{51} +10.0000 q^{53} +(1.00000 + 1.00000i) q^{54} +(-4.00000 - 4.00000i) q^{56} +4.00000i q^{57} +(6.00000 - 6.00000i) q^{58} -8.00000i q^{59} -8.00000i q^{61} +(-10.0000 - 10.0000i) q^{62} -2.00000i q^{63} -8.00000i q^{64} +(-4.00000 + 4.00000i) q^{66} -12.0000 q^{67} -12.0000 q^{68} +4.00000i q^{69} -4.00000 q^{71} +(2.00000 - 2.00000i) q^{72} +10.0000i q^{73} +(-4.00000 - 4.00000i) q^{74} +8.00000 q^{76} +8.00000 q^{77} +14.0000 q^{79} +1.00000 q^{81} +(-10.0000 - 10.0000i) q^{82} -4.00000 q^{84} +(-4.00000 - 4.00000i) q^{86} -6.00000i q^{87} +(8.00000 + 8.00000i) q^{88} -14.0000 q^{89} +8.00000 q^{92} -10.0000 q^{93} +(4.00000 - 4.00000i) q^{94} +(-4.00000 - 4.00000i) q^{96} +10.0000i q^{97} +(-3.00000 - 3.00000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^6 + 4 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{6} + 4 q^{8} + 2 q^{9} - 4 q^{14} - 8 q^{16} - 2 q^{18} + 8 q^{22} - 4 q^{24} - 2 q^{27} + 8 q^{28} + 20 q^{31} + 8 q^{32} + 12 q^{34} + 8 q^{37} - 8 q^{38} + 20 q^{41} + 4 q^{42} + 8 q^{43} - 16 q^{44} - 8 q^{46} + 8 q^{48} + 6 q^{49} + 20 q^{53} + 2 q^{54} - 8 q^{56} + 12 q^{58} - 20 q^{62} - 8 q^{66} - 24 q^{67} - 24 q^{68} - 8 q^{71} + 4 q^{72} - 8 q^{74} + 16 q^{76} + 16 q^{77} + 28 q^{79} + 2 q^{81} - 20 q^{82} - 8 q^{84} - 8 q^{86} + 16 q^{88} - 28 q^{89} + 16 q^{92} - 20 q^{93} + 8 q^{94} - 8 q^{96} - 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^6 + 4 * q^8 + 2 * q^9 - 4 * q^14 - 8 * q^16 - 2 * q^18 + 8 * q^22 - 4 * q^24 - 2 * q^27 + 8 * q^28 + 20 * q^31 + 8 * q^32 + 12 * q^34 + 8 * q^37 - 8 * q^38 + 20 * q^41 + 4 * q^42 + 8 * q^43 - 16 * q^44 - 8 * q^46 + 8 * q^48 + 6 * q^49 + 20 * q^53 + 2 * q^54 - 8 * q^56 + 12 * q^58 - 20 * q^62 - 8 * q^66 - 24 * q^67 - 24 * q^68 - 8 * q^71 + 4 * q^72 - 8 * q^74 + 16 * q^76 + 16 * q^77 + 28 * q^79 + 2 * q^81 - 20 * q^82 - 8 * q^84 - 8 * q^86 + 16 * q^88 - 28 * q^89 + 16 * q^92 - 20 * q^93 + 8 * q^94 - 8 * q^96 - 6 * q^98

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