LMFDB - Embedded newform 390.2.e.d.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(79,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, 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("390.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
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			79.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	390.79
Dual form			390.2.e.d.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} +1.00000i q^{13} +4.00000 q^{14} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +4.00000i q^{17} +1.00000i q^{18} -2.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{21} +6.00000i q^{22} -6.00000i q^{23} -1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +1.00000 q^{26} -1.00000i q^{27} -4.00000i q^{28} +10.0000 q^{29} +(2.00000 + 1.00000i) q^{30} +4.00000 q^{31} -1.00000i q^{32} -6.00000i q^{33} +4.00000 q^{34} +(-4.00000 + 8.00000i) q^{35} +1.00000 q^{36} +6.00000i q^{37} +2.00000i q^{38} -1.00000 q^{39} +(-1.00000 + 2.00000i) q^{40} +10.0000 q^{41} +4.00000i q^{42} +6.00000 q^{44} +(-2.00000 - 1.00000i) q^{45} -6.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} -9.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -4.00000 q^{51} -1.00000i q^{52} -6.00000i q^{53} -1.00000 q^{54} +(-12.0000 - 6.00000i) q^{55} -4.00000 q^{56} -2.00000i q^{57} -10.0000i q^{58} +6.00000 q^{59} +(1.00000 - 2.00000i) q^{60} -6.00000 q^{61} -4.00000i q^{62} -4.00000i q^{63} -1.00000 q^{64} +(-1.00000 + 2.00000i) q^{65} -6.00000 q^{66} +12.0000i q^{67} -4.00000i q^{68} +6.00000 q^{69} +(8.00000 + 4.00000i) q^{70} -1.00000i q^{72} +2.00000i q^{73} +6.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} +2.00000 q^{76} -24.0000i q^{77} +1.00000i q^{78} +8.00000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -10.0000i q^{82} -4.00000i q^{83} +4.00000 q^{84} +(-4.00000 + 8.00000i) q^{85} +10.0000i q^{87} -6.00000i q^{88} -14.0000 q^{89} +(-1.00000 + 2.00000i) q^{90} -4.00000 q^{91} +6.00000i q^{92} +4.00000i q^{93} -8.00000 q^{94} +(-4.00000 - 2.00000i) q^{95} +1.00000 q^{96} -14.0000i q^{97} +9.00000i q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 2 q^{15} + 2 q^{16} - 4 q^{19} - 4 q^{20} - 8 q^{21} - 2 q^{24} + 6 q^{25} + 2 q^{26} + 20 q^{29} + 4 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 2 q^{36} - 2 q^{39} - 2 q^{40} + 20 q^{41} + 12 q^{44} - 4 q^{45} - 12 q^{46} - 18 q^{49} + 8 q^{50} - 8 q^{51} - 2 q^{54} - 24 q^{55} - 8 q^{56} + 12 q^{59} + 2 q^{60} - 12 q^{61} - 2 q^{64} - 2 q^{65} - 12 q^{66} + 12 q^{69} + 16 q^{70} + 12 q^{74} - 8 q^{75} + 4 q^{76} + 16 q^{79} + 4 q^{80} + 2 q^{81} + 8 q^{84} - 8 q^{85} - 28 q^{89} - 2 q^{90} - 8 q^{91} - 16 q^{94} - 8 q^{95} + 2 q^{96} + 12 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 2 * q^15 + 2 * q^16 - 4 * q^19 - 4 * q^20 - 8 * q^21 - 2 * q^24 + 6 * q^25 + 2 * q^26 + 20 * q^29 + 4 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 2 * q^36 - 2 * q^39 - 2 * q^40 + 20 * q^41 + 12 * q^44 - 4 * q^45 - 12 * q^46 - 18 * q^49 + 8 * q^50 - 8 * q^51 - 2 * q^54 - 24 * q^55 - 8 * q^56 + 12 * q^59 + 2 * q^60 - 12 * q^61 - 2 * q^64 - 2 * q^65 - 12 * q^66 + 12 * q^69 + 16 * q^70 + 12 * q^74 - 8 * q^75 + 4 * q^76 + 16 * q^79 + 4 * q^80 + 2 * q^81 + 8 * q^84 - 8 * q^85 - 28 * q^89 - 2 * q^90 - 8 * q^91 - 16 * q^94 - 8 * q^95 + 2 * q^96 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	1.00000			0.408248
$7$			4.00000i			1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$			4.00000i			1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$	−6.00000			−1.80907			−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000			−1.80907			−0.904534	+	0.426401i	$0.859781\pi$
$12$		−	1.00000i		−	0.288675i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	4.00000			1.06904
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$	1.00000			0.250000
$17$			4.00000i			0.970143i	0.874475	+	0.485071i	$0.161206\pi$
$17$			4.00000i			0.970143i	−0.874475	+	0.485071i	$0.838794\pi$
$18$			1.00000i			0.235702i
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	−4.00000			−0.872872
$22$			6.00000i			1.27920i
$23$		−	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
$26$	1.00000			0.196116
$27$		−	1.00000i		−	0.192450i
$28$		−	4.00000i		−	0.755929i
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$	2.00000	+	1.00000i	0.365148	+	0.182574i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	6.00000i		−	1.04447i
$34$	4.00000			0.685994
$35$	−4.00000	+	8.00000i	−0.676123	+	1.35225i
$36$	1.00000			0.166667
$37$			6.00000i			0.986394i	0.869918	+	0.493197i	$0.164172\pi$
$37$			6.00000i			0.986394i	−0.869918	+	0.493197i	$0.835828\pi$
$38$			2.00000i			0.324443i
$39$	−1.00000			−0.160128
$40$	−1.00000	+	2.00000i	−0.158114	+	0.316228i
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$			4.00000i			0.617213i
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	6.00000			0.904534
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$	−6.00000			−0.884652
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$			1.00000i			0.144338i
$49$	−9.00000			−1.28571
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	−4.00000			−0.560112
$52$		−	1.00000i		−	0.138675i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	−1.00000			−0.136083
$55$	−12.0000	−	6.00000i	−1.61808	−	0.809040i
$56$	−4.00000			−0.534522
$57$		−	2.00000i		−	0.264906i
$58$		−	10.0000i		−	1.31306i
$59$	6.00000			0.781133			0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000			0.781133			0.390567	+	0.920575i	$0.372279\pi$
$60$	1.00000	−	2.00000i	0.129099	−	0.258199i
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$		−	4.00000i		−	0.508001i
$63$		−	4.00000i		−	0.503953i
$64$	−1.00000			−0.125000
$65$	−1.00000	+	2.00000i	−0.124035	+	0.248069i
$66$	−6.00000			−0.738549
$67$			12.0000i			1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$			12.0000i			1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$		−	4.00000i		−	0.485071i
$69$	6.00000			0.722315
$70$	8.00000	+	4.00000i	0.956183	+	0.478091i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		−	1.00000i		−	0.117851i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	6.00000			0.697486
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$	2.00000			0.229416
$77$		−	24.0000i		−	2.73505i
$78$			1.00000i			0.113228i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	1.00000			0.111111
$82$		−	10.0000i		−	1.10432i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$	4.00000			0.436436
$85$	−4.00000	+	8.00000i	−0.433861	+	0.867722i
$86$		0			0
$87$			10.0000i			1.07211i
$88$		−	6.00000i		−	0.639602i
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$	−1.00000	+	2.00000i	−0.105409	+	0.210819i
$91$	−4.00000			−0.419314
$92$			6.00000i			0.625543i
$93$			4.00000i			0.414781i
$94$	−8.00000			−0.825137
$95$	−4.00000	−	2.00000i	−0.410391	−	0.205196i
$96$	1.00000			0.102062
$97$		−	14.0000i		−	1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$		−	14.0000i		−	1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$			9.00000i			0.909137i
$99$	6.00000			0.603023
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$			4.00000i			0.396059i
$103$		−	2.00000i		−	0.197066i	−0.995134	−	0.0985329i	$-0.968585\pi$
$103$		−	2.00000i		−	0.197066i	0.995134	−	0.0985329i	$-0.0314150\pi$
$104$	−1.00000			−0.0980581
$105$	−8.00000	−	4.00000i	−0.780720	−	0.390360i
$106$	−6.00000			−0.582772
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$			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	$0.561356\pi$
$110$	−6.00000	+	12.0000i	−0.572078	+	1.14416i
$111$	−6.00000			−0.569495
$112$			4.00000i			0.377964i
$113$		−	4.00000i		−	0.376288i	−0.982141	−	0.188144i	$-0.939753\pi$
$113$		−	4.00000i		−	0.376288i	0.982141	−	0.188144i	$-0.0602472\pi$
$114$	−2.00000			−0.187317
$115$	6.00000	−	12.0000i	0.559503	−	1.11901i
$116$	−10.0000			−0.928477
$117$		−	1.00000i		−	0.0924500i
$118$		−	6.00000i		−	0.552345i
$119$	−16.0000			−1.46672
$120$	−2.00000	−	1.00000i	−0.182574	−	0.0912871i
$121$	25.0000			2.27273
$122$			6.00000i			0.543214i
$123$			10.0000i			0.901670i
$124$	−4.00000			−0.359211
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−4.00000			−0.356348
$127$			10.0000i			0.887357i	0.896186	+	0.443678i	$0.146327\pi$
$127$			10.0000i			0.887357i	−0.896186	+	0.443678i	$0.853673\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	2.00000	+	1.00000i	0.175412	+	0.0877058i
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$			6.00000i			0.522233i
$133$		−	8.00000i		−	0.693688i
$134$	12.0000			1.03664
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	−4.00000			−0.342997
$137$			14.0000i			1.19610i	0.801459	+	0.598050i	$0.204058\pi$
$137$			14.0000i			1.19610i	−0.801459	+	0.598050i	$0.795942\pi$
$138$		−	6.00000i		−	0.510754i
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$	4.00000	−	8.00000i	0.338062	−	0.676123i
$141$	8.00000			0.673722
$142$		0			0
$143$		−	6.00000i		−	0.501745i
$144$	−1.00000			−0.0833333
$145$	20.0000	+	10.0000i	1.66091	+	0.830455i
$146$	2.00000			0.165521
$147$		−	9.00000i		−	0.742307i
$148$		−	6.00000i		−	0.493197i
$149$	−16.0000			−1.31077			−0.655386	−	0.755295i	$-0.727494\pi$
$149$	−16.0000			−1.31077			−0.655386	+	0.755295i	$0.727494\pi$
$150$	3.00000	+	4.00000i	0.244949	+	0.326599i
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		−	2.00000i		−	0.162221i
$153$		−	4.00000i		−	0.323381i
$154$	−24.0000			−1.93398
$155$	8.00000	+	4.00000i	0.642575	+	0.321288i
$156$	1.00000			0.0800641
$157$		−	6.00000i		−	0.478852i	−0.970915	−	0.239426i	$-0.923041\pi$
$157$		−	6.00000i		−	0.478852i	0.970915	−	0.239426i	$-0.0769593\pi$
$158$		−	8.00000i		−	0.636446i
$159$	6.00000			0.475831
$160$	1.00000	−	2.00000i	0.0790569	−	0.158114i
$161$	24.0000			1.89146
$162$		−	1.00000i		−	0.0785674i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−10.0000			−0.780869
$165$	6.00000	−	12.0000i	0.467099	−	0.934199i
$166$	−4.00000			−0.310460
$167$			16.0000i			1.23812i	0.785345	+	0.619059i	$0.212486\pi$
$167$			16.0000i			1.23812i	−0.785345	+	0.619059i	$0.787514\pi$
$168$		−	4.00000i		−	0.308607i
$169$	−1.00000			−0.0769231
$170$	8.00000	+	4.00000i	0.613572	+	0.306786i
$171$	2.00000			0.152944
$172$		0			0
$173$		−	22.0000i		−	1.67263i	−0.548250	−	0.836315i	$-0.684706\pi$
$173$		−	22.0000i		−	1.67263i	0.548250	−	0.836315i	$-0.315294\pi$
$174$	10.0000			0.758098
$175$	−16.0000	+	12.0000i	−1.20949	+	0.907115i
$176$	−6.00000			−0.452267
$177$			6.00000i			0.450988i
$178$			14.0000i			1.04934i
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$	2.00000	+	1.00000i	0.149071	+	0.0745356i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$			4.00000i			0.296500i
$183$		−	6.00000i		−	0.443533i
$184$	6.00000			0.442326
$185$	−6.00000	+	12.0000i	−0.441129	+	0.882258i
$186$	4.00000			0.293294
$187$		−	24.0000i		−	1.75505i
$188$			8.00000i			0.583460i
$189$	4.00000			0.290957
$190$	−2.00000	+	4.00000i	−0.145095	+	0.290191i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	2.00000i		−	0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$		−	2.00000i		−	0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$	−14.0000			−1.00514
$195$	−2.00000	−	1.00000i	−0.143223	−	0.0716115i
$196$	9.00000			0.642857
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		−	6.00000i		−	0.426401i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$	−12.0000			−0.846415
$202$		−	10.0000i		−	0.703598i
$203$			40.0000i			2.80745i
$204$	4.00000			0.280056
$205$	20.0000	+	10.0000i	1.39686	+	0.698430i
$206$	−2.00000			−0.139347
$207$			6.00000i			0.417029i
$208$			1.00000i			0.0693375i
$209$	12.0000			0.830057
$210$	−4.00000	+	8.00000i	−0.276026	+	0.552052i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$			6.00000i			0.412082i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	1.00000			0.0680414
$217$			16.0000i			1.08615i
$218$			4.00000i			0.270914i
$219$	−2.00000			−0.135147
$220$	12.0000	+	6.00000i	0.809040	+	0.404520i
$221$	−4.00000			−0.269069
$222$			6.00000i			0.402694i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	4.00000			0.267261
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	−4.00000			−0.266076
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$			2.00000i			0.132453i
$229$	−8.00000			−0.528655			−0.264327	−	0.964433i	$-0.585150\pi$
$229$	−8.00000			−0.528655			−0.264327	+	0.964433i	$0.585150\pi$
$230$	−12.0000	−	6.00000i	−0.791257	−	0.395628i
$231$	24.0000			1.57908
$232$			10.0000i			0.656532i
$233$		−	12.0000i		−	0.786146i	−0.919507	−	0.393073i	$-0.871412\pi$
$233$		−	12.0000i		−	0.786146i	0.919507	−	0.393073i	$-0.128588\pi$
$234$	−1.00000			−0.0653720
$235$	8.00000	−	16.0000i	0.521862	−	1.04372i
$236$	−6.00000			−0.390567
$237$			8.00000i			0.519656i
$238$			16.0000i			1.03713i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	−1.00000	+	2.00000i	−0.0645497	+	0.129099i
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$		−	25.0000i		−	1.60706i
$243$			1.00000i			0.0641500i
$244$	6.00000			0.384111
$245$	−18.0000	−	9.00000i	−1.14998	−	0.574989i
$246$	10.0000			0.637577
$247$		−	2.00000i		−	0.127257i
$248$			4.00000i			0.254000i
$249$	4.00000			0.253490
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$	−20.0000			−1.26239			−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$			4.00000i			0.251976i
$253$			36.0000i			2.26330i
$254$	10.0000			0.627456
$255$	−8.00000	−	4.00000i	−0.500979	−	0.250490i
$256$	1.00000			0.0625000
$257$		−	28.0000i		−	1.74659i	−0.487190	−	0.873296i	$-0.661978\pi$
$257$		−	28.0000i		−	1.74659i	0.487190	−	0.873296i	$-0.338022\pi$
$258$		0			0
$259$	−24.0000			−1.49129
$260$	1.00000	−	2.00000i	0.0620174	−	0.124035i
$261$	−10.0000			−0.618984
$262$			8.00000i			0.494242i
$263$		−	10.0000i		−	0.616626i	−0.951285	−	0.308313i	$-0.900236\pi$
$263$		−	10.0000i		−	0.616626i	0.951285	−	0.308313i	$-0.0997645\pi$
$264$	6.00000			0.369274
$265$	6.00000	−	12.0000i	0.368577	−	0.737154i
$266$	−8.00000			−0.490511
$267$		−	14.0000i		−	0.856786i
$268$		−	12.0000i		−	0.733017i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$	−2.00000	−	1.00000i	−0.121716	−	0.0608581i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$			4.00000i			0.242536i
$273$		−	4.00000i		−	0.242091i
$274$	14.0000			0.845771
$275$	−18.0000	−	24.0000i	−1.08544	−	1.44725i
$276$	−6.00000			−0.361158
$277$			14.0000i			0.841178i	0.907251	+	0.420589i	$0.138177\pi$
$277$			14.0000i			0.841178i	−0.907251	+	0.420589i	$0.861823\pi$
$278$			16.0000i			0.959616i
$279$	−4.00000			−0.239474
$280$	−8.00000	−	4.00000i	−0.478091	−	0.239046i
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		−	8.00000i		−	0.476393i
$283$		−	12.0000i		−	0.713326i	−0.934233	−	0.356663i	$-0.883914\pi$
$283$		−	12.0000i		−	0.713326i	0.934233	−	0.356663i	$-0.116086\pi$
$284$		0			0
$285$	2.00000	−	4.00000i	0.118470	−	0.236940i
$286$	−6.00000			−0.354787
$287$			40.0000i			2.36113i
$288$			1.00000i			0.0589256i
$289$	1.00000			0.0588235
$290$	10.0000	−	20.0000i	0.587220	−	1.17444i
$291$	14.0000			0.820695
$292$		−	2.00000i		−	0.117041i
$293$			18.0000i			1.05157i	0.850617	+	0.525786i	$0.176229\pi$
$293$			18.0000i			1.05157i	−0.850617	+	0.525786i	$0.823771\pi$
$294$	−9.00000			−0.524891
$295$	12.0000	+	6.00000i	0.698667	+	0.349334i
$296$	−6.00000			−0.348743
$297$			6.00000i			0.348155i
$298$			16.0000i			0.926855i
$299$	6.00000			0.346989
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$		0			0
$302$		−	16.0000i		−	0.920697i
$303$			10.0000i			0.574485i
$304$	−2.00000			−0.114708
$305$	−12.0000	−	6.00000i	−0.687118	−	0.343559i
$306$	−4.00000			−0.228665
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$			24.0000i			1.36753i
$309$	2.00000			0.113776
$310$	4.00000	−	8.00000i	0.227185	−	0.454369i
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$		−	1.00000i		−	0.0566139i
$313$		−	8.00000i		−	0.452187i	−0.974106	−	0.226093i	$-0.927405\pi$
$313$		−	8.00000i		−	0.452187i	0.974106	−	0.226093i	$-0.0725954\pi$
$314$	−6.00000			−0.338600
$315$	4.00000	−	8.00000i	0.225374	−	0.450749i
$316$	−8.00000			−0.450035
$317$		−	2.00000i		−	0.112331i	−0.998421	−	0.0561656i	$-0.982113\pi$
$317$		−	2.00000i		−	0.112331i	0.998421	−	0.0561656i	$-0.0178875\pi$
$318$		−	6.00000i		−	0.336463i
$319$	−60.0000			−3.35936
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$		0			0
$322$		−	24.0000i		−	1.33747i
$323$		−	8.00000i		−	0.445132i
$324$	−1.00000			−0.0555556
$325$	−4.00000	+	3.00000i	−0.221880	+	0.166410i
$326$	−4.00000			−0.221540
$327$		−	4.00000i		−	0.221201i
$328$			10.0000i			0.552158i
$329$	32.0000			1.76422
$330$	−12.0000	−	6.00000i	−0.660578	−	0.330289i
$331$	2.00000			0.109930			0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000			0.109930			0.0549650	+	0.998488i	$0.482495\pi$
$332$			4.00000i			0.219529i
$333$		−	6.00000i		−	0.328798i
$334$	16.0000			0.875481
$335$	−12.0000	+	24.0000i	−0.655630	+	1.31126i
$336$	−4.00000			−0.218218
$337$		−	16.0000i		−	0.871576i	−0.900049	−	0.435788i	$-0.856470\pi$
$337$		−	16.0000i		−	0.871576i	0.900049	−	0.435788i	$-0.143530\pi$
$338$			1.00000i			0.0543928i
$339$	4.00000			0.217250
$340$	4.00000	−	8.00000i	0.216930	−	0.433861i
$341$	−24.0000			−1.29967
$342$		−	2.00000i		−	0.108148i
$343$		−	8.00000i		−	0.431959i
$344$		0			0
$345$	12.0000	+	6.00000i	0.646058	+	0.323029i
$346$	−22.0000			−1.18273
$347$		−	16.0000i		−	0.858925i	−0.903085	−	0.429463i	$-0.858703\pi$
$347$		−	16.0000i		−	0.858925i	0.903085	−	0.429463i	$-0.141297\pi$
$348$		−	10.0000i		−	0.536056i
$349$	4.00000			0.214115			0.107058	−	0.994253i	$-0.465857\pi$
$349$	4.00000			0.214115			0.107058	+	0.994253i	$0.465857\pi$
$350$	12.0000	+	16.0000i	0.641427	+	0.855236i
$351$	1.00000			0.0533761
$352$			6.00000i			0.319801i
$353$		−	26.0000i		−	1.38384i	−0.721974	−	0.691920i	$-0.756765\pi$
$353$		−	26.0000i		−	1.38384i	0.721974	−	0.691920i	$-0.243235\pi$
$354$	6.00000			0.318896
$355$		0			0
$356$	14.0000			0.741999
$357$		−	16.0000i		−	0.846810i
$358$		−	24.0000i		−	1.26844i
$359$	20.0000			1.05556			0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000			1.05556			0.527780	+	0.849381i	$0.323025\pi$
$360$	1.00000	−	2.00000i	0.0527046	−	0.105409i
$361$	−15.0000			−0.789474
$362$		−	6.00000i		−	0.315353i
$363$			25.0000i			1.31216i
$364$	4.00000			0.209657
$365$	−2.00000	+	4.00000i	−0.104685	+	0.209370i
$366$	−6.00000			−0.313625
$367$			18.0000i			0.939592i	0.882775	+	0.469796i	$0.155673\pi$
$367$			18.0000i			0.939592i	−0.882775	+	0.469796i	$0.844327\pi$
$368$		−	6.00000i		−	0.312772i
$369$	−10.0000			−0.520579
$370$	12.0000	+	6.00000i	0.623850	+	0.311925i
$371$	24.0000			1.24602
$372$		−	4.00000i		−	0.207390i
$373$		−	18.0000i		−	0.932005i	−0.884783	−	0.466002i	$-0.845694\pi$
$373$		−	18.0000i		−	0.932005i	0.884783	−	0.466002i	$-0.154306\pi$
$374$	−24.0000			−1.24101
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$	8.00000			0.412568
$377$			10.0000i			0.515026i
$378$		−	4.00000i		−	0.205738i
$379$	−10.0000			−0.513665			−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000			−0.513665			−0.256833	+	0.966456i	$0.582679\pi$
$380$	4.00000	+	2.00000i	0.205196	+	0.102598i
$381$	−10.0000			−0.512316
$382$		0			0
$383$			20.0000i			1.02195i	0.859595	+	0.510976i	$0.170716\pi$
$383$			20.0000i			1.02195i	−0.859595	+	0.510976i	$0.829284\pi$
$384$	−1.00000			−0.0510310
$385$	24.0000	−	48.0000i	1.22315	−	2.44631i
$386$	−2.00000			−0.101797
$387$		0			0
$388$			14.0000i			0.710742i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$	−1.00000	+	2.00000i	−0.0506370	+	0.101274i
$391$	24.0000			1.21373
$392$		−	9.00000i		−	0.454569i
$393$		−	8.00000i		−	0.403547i
$394$	6.00000			0.302276
$395$	16.0000	+	8.00000i	0.805047	+	0.402524i
$396$	−6.00000			−0.301511
$397$			10.0000i			0.501886i	0.968002	+	0.250943i	$0.0807406\pi$
$397$			10.0000i			0.501886i	−0.968002	+	0.250943i	$0.919259\pi$
$398$		−	8.00000i		−	0.401004i
$399$	8.00000			0.400501
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	30.0000			1.49813			0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000			1.49813			0.749064	+	0.662497i	$0.230503\pi$
$402$			12.0000i			0.598506i
$403$			4.00000i			0.199254i
$404$	−10.0000			−0.497519
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$	40.0000			1.98517
$407$		−	36.0000i		−	1.78445i
$408$		−	4.00000i		−	0.198030i
$409$	34.0000			1.68119			0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000			1.68119			0.840596	+	0.541663i	$0.182205\pi$
$410$	10.0000	−	20.0000i	0.493865	−	0.987730i
$411$	−14.0000			−0.690569
$412$			2.00000i			0.0985329i
$413$			24.0000i			1.18096i
$414$	6.00000			0.294884
$415$	4.00000	−	8.00000i	0.196352	−	0.392705i
$416$	1.00000			0.0490290
$417$		−	16.0000i		−	0.783523i
$418$		−	12.0000i		−	0.586939i
$419$	−8.00000			−0.390826			−0.195413	−	0.980721i	$-0.562605\pi$
$419$	−8.00000			−0.390826			−0.195413	+	0.980721i	$0.562605\pi$
$420$	8.00000	+	4.00000i	0.390360	+	0.195180i
$421$	4.00000			0.194948			0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000			0.194948			0.0974740	+	0.995238i	$0.468924\pi$
$422$		−	4.00000i		−	0.194717i
$423$			8.00000i			0.388973i
$424$	6.00000			0.291386
$425$	−16.0000	+	12.0000i	−0.776114	+	0.582086i
$426$		0			0
$427$		−	24.0000i		−	1.16144i
$428$		0			0
$429$	6.00000			0.289683
$430$		0			0
$431$	−16.0000			−0.770693			−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000			−0.770693			−0.385346	+	0.922772i	$0.625918\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$	16.0000			0.768025
$435$	−10.0000	+	20.0000i	−0.479463	+	0.958927i
$436$	4.00000			0.191565
$437$			12.0000i			0.574038i
$438$			2.00000i			0.0955637i
$439$	32.0000			1.52728			0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000			1.52728			0.763638	+	0.645644i	$0.223411\pi$
$440$	6.00000	−	12.0000i	0.286039	−	0.572078i
$441$	9.00000			0.428571
$442$			4.00000i			0.190261i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	6.00000			0.284747
$445$	−28.0000	−	14.0000i	−1.32733	−	0.663664i
$446$	8.00000			0.378811
$447$		−	16.0000i		−	0.756774i
$448$		−	4.00000i		−	0.188982i
$449$	−38.0000			−1.79333			−0.896665	−	0.442709i	$-0.854018\pi$
$449$	−38.0000			−1.79333			−0.896665	+	0.442709i	$0.854018\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	−60.0000			−2.82529
$452$			4.00000i			0.188144i
$453$			16.0000i			0.751746i
$454$	4.00000			0.187729
$455$	−8.00000	−	4.00000i	−0.375046	−	0.187523i
$456$	2.00000			0.0936586
$457$		−	14.0000i		−	0.654892i	−0.944870	−	0.327446i	$-0.893812\pi$
$457$		−	14.0000i		−	0.654892i	0.944870	−	0.327446i	$-0.106188\pi$
$458$			8.00000i			0.373815i
$459$	4.00000			0.186704
$460$	−6.00000	+	12.0000i	−0.279751	+	0.559503i
$461$	−4.00000			−0.186299			−0.0931493	−	0.995652i	$-0.529693\pi$
$461$	−4.00000			−0.186299			−0.0931493	+	0.995652i	$0.529693\pi$
$462$		−	24.0000i		−	1.11658i
$463$			4.00000i			0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$			4.00000i			0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$	10.0000			0.464238
$465$	−4.00000	+	8.00000i	−0.185496	+	0.370991i
$466$	−12.0000			−0.555889
$467$		−	8.00000i		−	0.370196i	−0.982720	−	0.185098i	$-0.940740\pi$
$467$		−	8.00000i		−	0.370196i	0.982720	−	0.185098i	$-0.0592602\pi$
$468$			1.00000i			0.0462250i
$469$	−48.0000			−2.21643
$470$	−16.0000	−	8.00000i	−0.738025	−	0.369012i
$471$	6.00000			0.276465
$472$			6.00000i			0.276172i
$473$		0			0
$474$	8.00000			0.367452
$475$	−6.00000	−	8.00000i	−0.275299	−	0.367065i
$476$	16.0000			0.733359
$477$			6.00000i			0.274721i
$478$		−	4.00000i		−	0.182956i
$479$	20.0000			0.913823			0.456912	−	0.889512i	$-0.348956\pi$
$479$	20.0000			0.913823			0.456912	+	0.889512i	$0.348956\pi$
$480$	2.00000	+	1.00000i	0.0912871	+	0.0456435i
$481$	−6.00000			−0.273576
$482$		−	18.0000i		−	0.819878i
$483$			24.0000i			1.09204i
$484$	−25.0000			−1.13636
$485$	14.0000	−	28.0000i	0.635707	−	1.27141i
$486$	1.00000			0.0453609
$487$		−	32.0000i		−	1.45006i	−0.688718	−	0.725029i	$-0.741826\pi$
$487$		−	32.0000i		−	1.45006i	0.688718	−	0.725029i	$-0.258174\pi$
$488$		−	6.00000i		−	0.271607i
$489$	4.00000			0.180886
$490$	−9.00000	+	18.0000i	−0.406579	+	0.813157i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		−	10.0000i		−	0.450835i
$493$			40.0000i			1.80151i
$494$	−2.00000			−0.0899843
$495$	12.0000	+	6.00000i	0.539360	+	0.269680i
$496$	4.00000			0.179605
$497$		0			0
$498$		−	4.00000i		−	0.179244i
$499$	18.0000			0.805791			0.402895	−	0.915246i	$-0.368004\pi$
$499$	18.0000			0.805791			0.402895	+	0.915246i	$0.368004\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	−16.0000			−0.714827
$502$			20.0000i			0.892644i
$503$		−	14.0000i		−	0.624229i	−0.950044	−	0.312115i	$-0.898963\pi$
$503$		−	14.0000i		−	0.624229i	0.950044	−	0.312115i	$-0.101037\pi$
$504$	4.00000			0.178174
$505$	20.0000	+	10.0000i	0.889988	+	0.444994i
$506$	36.0000			1.60040
$507$		−	1.00000i		−	0.0444116i
$508$		−	10.0000i		−	0.443678i
$509$	−16.0000			−0.709188			−0.354594	−	0.935020i	$-0.615381\pi$
$509$	−16.0000			−0.709188			−0.354594	+	0.935020i	$0.615381\pi$
$510$	−4.00000	+	8.00000i	−0.177123	+	0.354246i
$511$	−8.00000			−0.353899
$512$		−	1.00000i		−	0.0441942i
$513$			2.00000i			0.0883022i
$514$	−28.0000			−1.23503
$515$	2.00000	−	4.00000i	0.0881305	−	0.176261i
$516$		0			0
$517$			48.0000i			2.11104i
$518$			24.0000i			1.05450i
$519$	22.0000			0.965693
$520$	−2.00000	−	1.00000i	−0.0877058	−	0.0438529i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$			10.0000i			0.437688i
$523$			16.0000i			0.699631i	0.936819	+	0.349816i	$0.113756\pi$
$523$			16.0000i			0.699631i	−0.936819	+	0.349816i	$0.886244\pi$
$524$	8.00000			0.349482
$525$	−12.0000	−	16.0000i	−0.523723	−	0.698297i
$526$	−10.0000			−0.436021
$527$			16.0000i			0.696971i
$528$		−	6.00000i		−	0.261116i
$529$	−13.0000			−0.565217
$530$	−12.0000	−	6.00000i	−0.521247	−	0.260623i
$531$	−6.00000			−0.260378
$532$			8.00000i			0.346844i
$533$			10.0000i			0.433148i
$534$	−14.0000			−0.605839
$535$		0			0
$536$	−12.0000			−0.518321
$537$			24.0000i			1.03568i
$538$			10.0000i			0.431131i
$539$	54.0000			2.32594
$540$	−1.00000	+	2.00000i	−0.0430331	+	0.0860663i
$541$	−32.0000			−1.37579			−0.687894	−	0.725811i	$-0.741464\pi$
$541$	−32.0000			−1.37579			−0.687894	+	0.725811i	$0.741464\pi$
$542$			8.00000i			0.343629i
$543$			6.00000i			0.257485i
$544$	4.00000			0.171499
$545$	−8.00000	−	4.00000i	−0.342682	−	0.171341i
$546$	−4.00000			−0.171184
$547$		−	36.0000i		−	1.53925i	−0.638497	−	0.769624i	$-0.720443\pi$
$547$		−	36.0000i		−	1.53925i	0.638497	−	0.769624i	$-0.279557\pi$
$548$		−	14.0000i		−	0.598050i
$549$	6.00000			0.256074
$550$	−24.0000	+	18.0000i	−1.02336	+	0.767523i
$551$	−20.0000			−0.852029
$552$			6.00000i			0.255377i
$553$			32.0000i			1.36078i
$554$	14.0000			0.594803
$555$	−12.0000	−	6.00000i	−0.509372	−	0.254686i
$556$	16.0000			0.678551
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$			4.00000i			0.169334i
$559$		0			0
$560$	−4.00000	+	8.00000i	−0.169031	+	0.338062i
$561$	24.0000			1.01328
$562$			18.0000i			0.759284i
$563$			24.0000i			1.01148i	0.862686	+	0.505740i	$0.168780\pi$
$563$			24.0000i			1.01148i	−0.862686	+	0.505740i	$0.831220\pi$
$564$	−8.00000			−0.336861
$565$	4.00000	−	8.00000i	0.168281	−	0.336563i
$566$	−12.0000			−0.504398
$567$			4.00000i			0.167984i
$568$		0			0
$569$	42.0000			1.76073			0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000			1.76073			0.880366	+	0.474295i	$0.157297\pi$
$570$	−4.00000	−	2.00000i	−0.167542	−	0.0837708i
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$			6.00000i			0.250873i
$573$		0			0
$574$	40.0000			1.66957
$575$	24.0000	−	18.0000i	1.00087	−	0.750652i
$576$	1.00000			0.0416667
$577$		−	2.00000i		−	0.0832611i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$		−	2.00000i		−	0.0832611i	0.999133	−	0.0416305i	$-0.0132552\pi$
$578$		−	1.00000i		−	0.0415945i
$579$	2.00000			0.0831172
$580$	−20.0000	−	10.0000i	−0.830455	−	0.415227i
$581$	16.0000			0.663792
$582$		−	14.0000i		−	0.580319i
$583$			36.0000i			1.49097i
$584$	−2.00000			−0.0827606
$585$	1.00000	−	2.00000i	0.0413449	−	0.0826898i
$586$	18.0000			0.743573
$587$			28.0000i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$587$			28.0000i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$588$			9.00000i			0.371154i
$589$	−8.00000			−0.329634
$590$	6.00000	−	12.0000i	0.247016	−	0.494032i
$591$	−6.00000			−0.246807
$592$			6.00000i			0.246598i
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$	6.00000			0.246183
$595$	−32.0000	−	16.0000i	−1.31187	−	0.655936i
$596$	16.0000			0.655386
$597$			8.00000i			0.327418i
$598$		−	6.00000i		−	0.245358i
$599$	32.0000			1.30748			0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000			1.30748			0.653742	+	0.756717i	$0.273198\pi$
$600$	−3.00000	−	4.00000i	−0.122474	−	0.163299i
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$	−16.0000			−0.651031
$605$	50.0000	+	25.0000i	2.03279	+	1.01639i
$606$	10.0000			0.406222
$607$		−	42.0000i		−	1.70473i	−0.522949	−	0.852364i	$-0.675168\pi$
$607$		−	42.0000i		−	1.70473i	0.522949	−	0.852364i	$-0.324832\pi$
$608$			2.00000i			0.0811107i
$609$	−40.0000			−1.62088
$610$	−6.00000	+	12.0000i	−0.242933	+	0.485866i
$611$	8.00000			0.323645
$612$			4.00000i			0.161690i
$613$		−	38.0000i		−	1.53481i	−0.641165	−	0.767403i	$-0.721549\pi$
$613$		−	38.0000i		−	1.53481i	0.641165	−	0.767403i	$-0.278451\pi$
$614$	4.00000			0.161427
$615$	−10.0000	+	20.0000i	−0.403239	+	0.806478i
$616$	24.0000			0.966988
$617$			18.0000i			0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$			18.0000i			0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$		−	2.00000i		−	0.0804518i
$619$	22.0000			0.884255			0.442127	−	0.896952i	$-0.354224\pi$
$619$	22.0000			0.884255			0.442127	+	0.896952i	$0.354224\pi$
$620$	−8.00000	−	4.00000i	−0.321288	−	0.160644i
$621$	−6.00000			−0.240772
$622$			8.00000i			0.320771i
$623$		−	56.0000i		−	2.24359i
$624$	−1.00000			−0.0400320
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−8.00000			−0.319744
$627$			12.0000i			0.479234i
$628$			6.00000i			0.239426i
$629$	−24.0000			−0.956943
$630$	−8.00000	−	4.00000i	−0.318728	−	0.159364i
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$			8.00000i			0.318223i
$633$			4.00000i			0.158986i
$634$	−2.00000			−0.0794301
$635$	−10.0000	+	20.0000i	−0.396838	+	0.793676i
$636$	−6.00000			−0.237915
$637$		−	9.00000i		−	0.356593i
$638$			60.0000i			2.37542i
$639$		0			0
$640$	−1.00000	+	2.00000i	−0.0395285	+	0.0790569i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$		0			0
$643$		−	20.0000i		−	0.788723i	−0.918955	−	0.394362i	$-0.870966\pi$
$643$		−	20.0000i		−	0.788723i	0.918955	−	0.394362i	$-0.129034\pi$
$644$	−24.0000			−0.945732
$645$		0			0
$646$	−8.00000			−0.314756
$647$			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
$649$	−36.0000			−1.41312
$650$	3.00000	+	4.00000i	0.117670	+	0.156893i
$651$	−16.0000			−0.627089
$652$			4.00000i			0.156652i
$653$		−	10.0000i		−	0.391330i	−0.980671	−	0.195665i	$-0.937313\pi$
$653$		−	10.0000i		−	0.391330i	0.980671	−	0.195665i	$-0.0626866\pi$
$654$	−4.00000			−0.156412
$655$	−16.0000	−	8.00000i	−0.625172	−	0.312586i
$656$	10.0000			0.390434
$657$		−	2.00000i		−	0.0780274i
$658$		−	32.0000i		−	1.24749i
$659$	32.0000			1.24654			0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000			1.24654			0.623272	+	0.782006i	$0.285803\pi$
$660$	−6.00000	+	12.0000i	−0.233550	+	0.467099i
$661$	−32.0000			−1.24466			−0.622328	−	0.782757i	$-0.713813\pi$
$661$	−32.0000			−1.24466			−0.622328	+	0.782757i	$0.713813\pi$
$662$		−	2.00000i		−	0.0777322i
$663$		−	4.00000i		−	0.155347i
$664$	4.00000			0.155230
$665$	8.00000	−	16.0000i	0.310227	−	0.620453i
$666$	−6.00000			−0.232495
$667$		−	60.0000i		−	2.32321i
$668$		−	16.0000i		−	0.619059i
$669$	−8.00000			−0.309298
$670$	24.0000	+	12.0000i	0.927201	+	0.463600i
$671$	36.0000			1.38976
$672$			4.00000i			0.154303i
$673$			44.0000i			1.69608i	0.529936	+	0.848038i	$0.322216\pi$
$673$			44.0000i			1.69608i	−0.529936	+	0.848038i	$0.677784\pi$
$674$	−16.0000			−0.616297
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	1.00000			0.0384615
$677$		−	6.00000i		−	0.230599i	−0.993331	−	0.115299i	$-0.963217\pi$
$677$		−	6.00000i		−	0.230599i	0.993331	−	0.115299i	$-0.0367827\pi$
$678$		−	4.00000i		−	0.153619i
$679$	56.0000			2.14908
$680$	−8.00000	−	4.00000i	−0.306786	−	0.153393i
$681$	−4.00000			−0.153280
$682$			24.0000i			0.919007i
$683$		−	20.0000i		−	0.765279i	−0.923898	−	0.382639i	$-0.875015\pi$
$683$		−	20.0000i		−	0.765279i	0.923898	−	0.382639i	$-0.124985\pi$
$684$	−2.00000			−0.0764719
$685$	−14.0000	+	28.0000i	−0.534913	+	1.06983i
$686$	−8.00000			−0.305441
$687$		−	8.00000i		−	0.305219i
$688$		0			0
$689$	6.00000			0.228582
$690$	6.00000	−	12.0000i	0.228416	−	0.456832i
$691$	18.0000			0.684752			0.342376	−	0.939563i	$-0.388768\pi$
$691$	18.0000			0.684752			0.342376	+	0.939563i	$0.388768\pi$
$692$			22.0000i			0.836315i
$693$			24.0000i			0.911685i
$694$	−16.0000			−0.607352
$695$	−32.0000	−	16.0000i	−1.21383	−	0.606915i
$696$	−10.0000			−0.379049
$697$			40.0000i			1.51511i
$698$		−	4.00000i		−	0.151402i
$699$	12.0000			0.453882
$700$	16.0000	−	12.0000i	0.604743	−	0.453557i
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		−	1.00000i		−	0.0377426i
$703$		−	12.0000i		−	0.452589i
$704$	6.00000			0.226134
$705$	16.0000	+	8.00000i	0.602595	+	0.301297i
$706$	−26.0000			−0.978523
$707$			40.0000i			1.50435i
$708$		−	6.00000i		−	0.225494i
$709$	8.00000			0.300446			0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000			0.300446			0.150223	+	0.988652i	$0.452001\pi$
$710$		0			0
$711$	−8.00000			−0.300023
$712$		−	14.0000i		−	0.524672i
$713$		−	24.0000i		−	0.898807i
$714$	−16.0000			−0.598785
$715$	6.00000	−	12.0000i	0.224387	−	0.448775i
$716$	−24.0000			−0.896922
$717$			4.00000i			0.149383i
$718$		−	20.0000i		−	0.746393i
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$	−2.00000	−	1.00000i	−0.0745356	−	0.0372678i
$721$	8.00000			0.297936
$722$			15.0000i			0.558242i
$723$			18.0000i			0.669427i
$724$	−6.00000			−0.222988
$725$	30.0000	+	40.0000i	1.11417	+	1.48556i
$726$	25.0000			0.927837
$727$		−	38.0000i		−	1.40934i	−0.709534	−	0.704671i	$-0.751095\pi$
$727$		−	38.0000i		−	1.40934i	0.709534	−	0.704671i	$-0.248905\pi$
$728$		−	4.00000i		−	0.148250i
$729$	−1.00000			−0.0370370
$730$	4.00000	+	2.00000i	0.148047	+	0.0740233i
$731$		0			0
$732$			6.00000i			0.221766i
$733$		−	18.0000i		−	0.664845i	−0.943131	−	0.332423i	$-0.892134\pi$
$733$		−	18.0000i		−	0.664845i	0.943131	−	0.332423i	$-0.107866\pi$
$734$	18.0000			0.664392
$735$	9.00000	−	18.0000i	0.331970	−	0.663940i
$736$	−6.00000			−0.221163
$737$		−	72.0000i		−	2.65215i
$738$			10.0000i			0.368105i
$739$	2.00000			0.0735712			0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000			0.0735712			0.0367856	+	0.999323i	$0.488288\pi$
$740$	6.00000	−	12.0000i	0.220564	−	0.441129i
$741$	2.00000			0.0734718
$742$		−	24.0000i		−	0.881068i
$743$		−	36.0000i		−	1.32071i	−0.750953	−	0.660356i	$-0.770405\pi$
$743$		−	36.0000i		−	1.32071i	0.750953	−	0.660356i	$-0.229595\pi$
$744$	−4.00000			−0.146647
$745$	−32.0000	−	16.0000i	−1.17239	−	0.586195i
$746$	−18.0000			−0.659027
$747$			4.00000i			0.146352i
$748$			24.0000i			0.877527i
$749$		0			0
$750$	2.00000	+	11.0000i	0.0730297	+	0.401663i
$751$	−48.0000			−1.75154			−0.875772	−	0.482724i	$-0.839647\pi$
$751$	−48.0000			−1.75154			−0.875772	+	0.482724i	$0.839647\pi$
$752$		−	8.00000i		−	0.291730i
$753$		−	20.0000i		−	0.728841i
$754$	10.0000			0.364179
$755$	32.0000	+	16.0000i	1.16460	+	0.582300i
$756$	−4.00000			−0.145479
$757$			22.0000i			0.799604i	0.916602	+	0.399802i	$0.130921\pi$
$757$			22.0000i			0.799604i	−0.916602	+	0.399802i	$0.869079\pi$
$758$			10.0000i			0.363216i
$759$	−36.0000			−1.30672
$760$	2.00000	−	4.00000i	0.0725476	−	0.145095i
$761$	30.0000			1.08750			0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000			1.08750			0.543750	+	0.839248i	$0.317004\pi$
$762$			10.0000i			0.362262i
$763$		−	16.0000i		−	0.579239i
$764$		0			0
$765$	4.00000	−	8.00000i	0.144620	−	0.289241i
$766$	20.0000			0.722629
$767$			6.00000i			0.216647i
$768$			1.00000i			0.0360844i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$	−48.0000	−	24.0000i	−1.72980	−	0.864900i
$771$	28.0000			1.00840
$772$			2.00000i			0.0719816i
$773$		−	18.0000i		−	0.647415i	−0.946157	−	0.323708i	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$		0			0
$775$	12.0000	+	16.0000i	0.431053	+	0.574737i
$776$	14.0000			0.502571
$777$		−	24.0000i		−	0.860995i
$778$			30.0000i			1.07555i
$779$	−20.0000			−0.716574
$780$	2.00000	+	1.00000i	0.0716115	+	0.0358057i
$781$		0			0
$782$		−	24.0000i		−	0.858238i
$783$		−	10.0000i		−	0.357371i
$784$	−9.00000			−0.321429
$785$	6.00000	−	12.0000i	0.214149	−	0.428298i
$786$	−8.00000			−0.285351
$787$			12.0000i			0.427754i	0.976861	+	0.213877i	$0.0686091\pi$
$787$			12.0000i			0.427754i	−0.976861	+	0.213877i	$0.931391\pi$
$788$		−	6.00000i		−	0.213741i
$789$	10.0000			0.356009
$790$	8.00000	−	16.0000i	0.284627	−	0.569254i
$791$	16.0000			0.568895
$792$			6.00000i			0.213201i
$793$		−	6.00000i		−	0.213066i
$794$	10.0000			0.354887
$795$	12.0000	+	6.00000i	0.425596	+	0.212798i
$796$	−8.00000			−0.283552
$797$			30.0000i			1.06265i	0.847167	+	0.531327i	$0.178307\pi$
$797$			30.0000i			1.06265i	−0.847167	+	0.531327i	$0.821693\pi$
$798$		−	8.00000i		−	0.283197i
$799$	32.0000			1.13208
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$	14.0000			0.494666
$802$		−	30.0000i		−	1.05934i
$803$		−	12.0000i		−	0.423471i
$804$	12.0000			0.423207
$805$	48.0000	+	24.0000i	1.69178	+	0.845889i
$806$	4.00000			0.140894
$807$		−	10.0000i		−	0.352017i
$808$			10.0000i			0.351799i
$809$	2.00000			0.0703163			0.0351581	−	0.999382i	$-0.488807\pi$
$809$	2.00000			0.0703163			0.0351581	+	0.999382i	$0.488807\pi$
$810$	1.00000	−	2.00000i	0.0351364	−	0.0702728i
$811$	−50.0000			−1.75574			−0.877869	−	0.478901i	$-0.841035\pi$
$811$	−50.0000			−1.75574			−0.877869	+	0.478901i	$0.841035\pi$
$812$		−	40.0000i		−	1.40372i
$813$		−	8.00000i		−	0.280572i
$814$	−36.0000			−1.26180
$815$	4.00000	−	8.00000i	0.140114	−	0.280228i
$816$	−4.00000			−0.140028
$817$		0			0
$818$		−	34.0000i		−	1.18878i
$819$	4.00000			0.139771
$820$	−20.0000	−	10.0000i	−0.698430	−	0.349215i
$821$	−28.0000			−0.977207			−0.488603	−	0.872506i	$-0.662493\pi$
$821$	−28.0000			−0.977207			−0.488603	+	0.872506i	$0.662493\pi$
$822$			14.0000i			0.488306i
$823$		−	14.0000i		−	0.488009i	−0.969774	−	0.244005i	$-0.921539\pi$
$823$		−	14.0000i		−	0.488009i	0.969774	−	0.244005i	$-0.0784612\pi$
$824$	2.00000			0.0696733
$825$	24.0000	−	18.0000i	0.835573	−	0.626680i
$826$	24.0000			0.835067
$827$			44.0000i			1.53003i	0.644013	+	0.765015i	$0.277268\pi$
$827$			44.0000i			1.53003i	−0.644013	+	0.765015i	$0.722732\pi$
$828$		−	6.00000i		−	0.208514i
$829$	−26.0000			−0.903017			−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000			−0.903017			−0.451509	+	0.892267i	$0.649114\pi$
$830$	−8.00000	−	4.00000i	−0.277684	−	0.138842i
$831$	−14.0000			−0.485655
$832$		−	1.00000i		−	0.0346688i
$833$		−	36.0000i		−	1.24733i
$834$	−16.0000			−0.554035
$835$	−16.0000	+	32.0000i	−0.553703	+	1.10741i
$836$	−12.0000			−0.415029
$837$		−	4.00000i		−	0.138260i
$838$			8.00000i			0.276355i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$	4.00000	−	8.00000i	0.138013	−	0.276026i
$841$	71.0000			2.44828
$842$		−	4.00000i		−	0.137849i
$843$		−	18.0000i		−	0.619953i
$844$	−4.00000			−0.137686
$845$	−2.00000	−	1.00000i	−0.0688021	−	0.0344010i
$846$	8.00000			0.275046
$847$			100.000i			3.43604i
$848$		−	6.00000i		−	0.206041i
$849$	12.0000			0.411839
$850$	12.0000	+	16.0000i	0.411597	+	0.548795i
$851$	36.0000			1.23406
$852$		0			0
$853$		−	26.0000i		−	0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$		−	26.0000i		−	0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$	−24.0000			−0.821263
$855$	4.00000	+	2.00000i	0.136797	+	0.0683986i
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		−	6.00000i		−	0.204837i
$859$	−28.0000			−0.955348			−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000			−0.955348			−0.477674	+	0.878537i	$0.658520\pi$
$860$		0			0
$861$	−40.0000			−1.36320
$862$			16.0000i			0.544962i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	−1.00000			−0.0340207
$865$	22.0000	−	44.0000i	0.748022	−	1.49604i
$866$	16.0000			0.543702
$867$			1.00000i			0.0339618i
$868$		−	16.0000i		−	0.543075i
$869$	−48.0000			−1.62829
$870$	20.0000	+	10.0000i	0.678064	+	0.339032i
$871$	−12.0000			−0.406604
$872$		−	4.00000i		−	0.135457i
$873$			14.0000i			0.473828i
$874$	12.0000			0.405906
$875$	−44.0000	+	8.00000i	−1.48747	+	0.270449i
$876$	2.00000			0.0675737
$877$		−	18.0000i		−	0.607817i	−0.952701	−	0.303908i	$-0.901708\pi$
$877$		−	18.0000i		−	0.607817i	0.952701	−	0.303908i	$-0.0982917\pi$
$878$		−	32.0000i		−	1.07995i
$879$	−18.0000			−0.607125
$880$	−12.0000	−	6.00000i	−0.404520	−	0.202260i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		−	9.00000i		−	0.303046i
$883$			40.0000i			1.34611i	0.739594	+	0.673054i	$0.235018\pi$
$883$			40.0000i			1.34611i	−0.739594	+	0.673054i	$0.764982\pi$
$884$	4.00000			0.134535
$885$	−6.00000	+	12.0000i	−0.201688	+	0.403376i
$886$		0			0
$887$			6.00000i			0.201460i	0.994914	+	0.100730i	$0.0321179\pi$
$887$			6.00000i			0.201460i	−0.994914	+	0.100730i	$0.967882\pi$
$888$		−	6.00000i		−	0.201347i
$889$	−40.0000			−1.34156
$890$	−14.0000	+	28.0000i	−0.469281	+	0.938562i
$891$	−6.00000			−0.201008
$892$		−	8.00000i		−	0.267860i
$893$			16.0000i			0.535420i
$894$	−16.0000			−0.535120
$895$	48.0000	+	24.0000i	1.60446	+	0.802232i
$896$	−4.00000			−0.133631
$897$			6.00000i			0.200334i
$898$			38.0000i			1.26808i
$899$	40.0000			1.33407
$900$	3.00000	+	4.00000i	0.100000	+	0.133333i
$901$	24.0000			0.799556
$902$			60.0000i			1.99778i
$903$		0			0
$904$	4.00000			0.133038
$905$	12.0000	+	6.00000i	0.398893	+	0.199447i
$906$	16.0000			0.531564
$907$		−	40.0000i		−	1.32818i	−0.747653	−	0.664089i	$-0.768820\pi$
$907$		−	40.0000i		−	1.32818i	0.747653	−	0.664089i	$-0.231180\pi$
$908$		−	4.00000i		−	0.132745i
$909$	−10.0000			−0.331679
$910$	−4.00000	+	8.00000i	−0.132599	+	0.265197i
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		−	2.00000i		−	0.0662266i
$913$			24.0000i			0.794284i
$914$	−14.0000			−0.463079
$915$	6.00000	−	12.0000i	0.198354	−	0.396708i
$916$	8.00000			0.264327
$917$		−	32.0000i		−	1.05673i
$918$		−	4.00000i		−	0.132020i
$919$	56.0000			1.84727			0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000			1.84727			0.923635	+	0.383274i	$0.125203\pi$
$920$	12.0000	+	6.00000i	0.395628	+	0.197814i
$921$	−4.00000			−0.131804
$922$			4.00000i			0.131733i
$923$		0			0
$924$	−24.0000			−0.789542
$925$	−24.0000	+	18.0000i	−0.789115	+	0.591836i
$926$	4.00000			0.131448
$927$			2.00000i			0.0656886i
$928$		−	10.0000i		−	0.328266i
$929$	−46.0000			−1.50921			−0.754606	−	0.656179i	$-0.772172\pi$
$929$	−46.0000			−1.50921			−0.754606	+	0.656179i	$0.772172\pi$
$930$	8.00000	+	4.00000i	0.262330	+	0.131165i
$931$	18.0000			0.589926
$932$			12.0000i			0.393073i
$933$		−	8.00000i		−	0.261908i
$934$	−8.00000			−0.261768
$935$	24.0000	−	48.0000i	0.784884	−	1.56977i
$936$	1.00000			0.0326860
$937$		−	48.0000i		−	1.56809i	−0.620703	−	0.784046i	$-0.713153\pi$
$937$		−	48.0000i		−	1.56809i	0.620703	−	0.784046i	$-0.286847\pi$
$938$			48.0000i			1.56726i
$939$	8.00000			0.261070
$940$	−8.00000	+	16.0000i	−0.260931	+	0.521862i
$941$	−8.00000			−0.260793			−0.130396	−	0.991462i	$-0.541625\pi$
$941$	−8.00000			−0.260793			−0.130396	+	0.991462i	$0.541625\pi$
$942$		−	6.00000i		−	0.195491i
$943$		−	60.0000i		−	1.95387i
$944$	6.00000			0.195283
$945$	8.00000	+	4.00000i	0.260240	+	0.130120i
$946$		0			0
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$		−	8.00000i		−	0.259828i
$949$	−2.00000			−0.0649227
$950$	−8.00000	+	6.00000i	−0.259554	+	0.194666i
$951$	2.00000			0.0648544
$952$		−	16.0000i		−	0.518563i
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$	6.00000			0.194257
$955$		0			0
$956$	−4.00000			−0.129369
$957$		−	60.0000i		−	1.93952i
$958$		−	20.0000i		−	0.646171i
$959$	−56.0000			−1.80833
$960$	1.00000	−	2.00000i	0.0322749	−	0.0645497i
$961$	−15.0000			−0.483871
$962$			6.00000i			0.193448i
$963$		0			0
$964$	−18.0000			−0.579741
$965$	2.00000	−	4.00000i	0.0643823	−	0.128765i
$966$	24.0000			0.772187
$967$			4.00000i			0.128631i	0.997930	+	0.0643157i	$0.0204865\pi$
$967$			4.00000i			0.128631i	−0.997930	+	0.0643157i	$0.979514\pi$
$968$			25.0000i			0.803530i
$969$	8.00000			0.256997
$970$	−28.0000	−	14.0000i	−0.899026	−	0.449513i
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	64.0000i		−	2.05175i
$974$	−32.0000			−1.02535
$975$	−3.00000	−	4.00000i	−0.0960769	−	0.128103i
$976$	−6.00000			−0.192055
$977$		−	58.0000i		−	1.85558i	−0.373097	−	0.927792i	$-0.621704\pi$
$977$		−	58.0000i		−	1.85558i	0.373097	−	0.927792i	$-0.378296\pi$
$978$		−	4.00000i		−	0.127906i
$979$	84.0000			2.68465
$980$	18.0000	+	9.00000i	0.574989	+	0.287494i
$981$	4.00000			0.127710
$982$		0			0
$983$		−	28.0000i		−	0.893061i	−0.894768	−	0.446531i	$-0.852659\pi$
$983$		−	28.0000i		−	0.893061i	0.894768	−	0.446531i	$-0.147341\pi$
$984$	−10.0000			−0.318788
$985$	−6.00000	+	12.0000i	−0.191176	+	0.382352i
$986$	40.0000			1.27386
$987$			32.0000i			1.01857i
$988$			2.00000i			0.0636285i
$989$		0			0
$990$	6.00000	−	12.0000i	0.190693	−	0.381385i
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$		−	4.00000i		−	0.127000i
$993$			2.00000i			0.0634681i
$994$		0			0
$995$	16.0000	+	8.00000i	0.507234	+	0.253617i
$996$	−4.00000			−0.126745
$997$			10.0000i			0.316703i	0.987383	+	0.158352i	$0.0506179\pi$
$997$			10.0000i			0.316703i	−0.987383	+	0.158352i	$0.949382\pi$
$998$		−	18.0000i		−	0.569780i
$999$	6.00000			0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.e.d.79.1	✓	2
3.2	odd	2		1170.2.e.c.469.2		2
4.3	odd	2		3120.2.l.i.1249.1		2
5.2	odd	4		1950.2.a.v.1.1		1
5.3	odd	4		1950.2.a.d.1.1		1
5.4	even	2	inner	390.2.e.d.79.2	yes	2
15.2	even	4		5850.2.a.e.1.1		1
15.8	even	4		5850.2.a.cc.1.1		1
15.14	odd	2		1170.2.e.c.469.1		2
20.19	odd	2		3120.2.l.i.1249.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.e.d.79.1	✓	2	1.1	even	1	trivial
390.2.e.d.79.2	yes	2	5.4	even	2	inner
1170.2.e.c.469.1		2	15.14	odd	2
1170.2.e.c.469.2		2	3.2	odd	2
1950.2.a.d.1.1		1	5.3	odd	4
1950.2.a.v.1.1		1	5.2	odd	4
3120.2.l.i.1249.1		2	4.3	odd	2
3120.2.l.i.1249.2		2	20.19	odd	2
5850.2.a.e.1.1		1	15.2	even	4
5850.2.a.cc.1.1		1	15.8	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} +1.00000i q^{13} +4.00000 q^{14} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +4.00000i q^{17} +1.00000i q^{18} -2.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{21} +6.00000i q^{22} -6.00000i q^{23} -1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +1.00000 q^{26} -1.00000i q^{27} -4.00000i q^{28} +10.0000 q^{29} +(2.00000 + 1.00000i) q^{30} +4.00000 q^{31} -1.00000i q^{32} -6.00000i q^{33} +4.00000 q^{34} +(-4.00000 + 8.00000i) q^{35} +1.00000 q^{36} +6.00000i q^{37} +2.00000i q^{38} -1.00000 q^{39} +(-1.00000 + 2.00000i) q^{40} +10.0000 q^{41} +4.00000i q^{42} +6.00000 q^{44} +(-2.00000 - 1.00000i) q^{45} -6.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} -9.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -4.00000 q^{51} -1.00000i q^{52} -6.00000i q^{53} -1.00000 q^{54} +(-12.0000 - 6.00000i) q^{55} -4.00000 q^{56} -2.00000i q^{57} -10.0000i q^{58} +6.00000 q^{59} +(1.00000 - 2.00000i) q^{60} -6.00000 q^{61} -4.00000i q^{62} -4.00000i q^{63} -1.00000 q^{64} +(-1.00000 + 2.00000i) q^{65} -6.00000 q^{66} +12.0000i q^{67} -4.00000i q^{68} +6.00000 q^{69} +(8.00000 + 4.00000i) q^{70} -1.00000i q^{72} +2.00000i q^{73} +6.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} +2.00000 q^{76} -24.0000i q^{77} +1.00000i q^{78} +8.00000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -10.0000i q^{82} -4.00000i q^{83} +4.00000 q^{84} +(-4.00000 + 8.00000i) q^{85} +10.0000i q^{87} -6.00000i q^{88} -14.0000 q^{89} +(-1.00000 + 2.00000i) q^{90} -4.00000 q^{91} +6.00000i q^{92} +4.00000i q^{93} -8.00000 q^{94} +(-4.00000 - 2.00000i) q^{95} +1.00000 q^{96} -14.0000i q^{97} +9.00000i q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 2 q^{15} + 2 q^{16} - 4 q^{19} - 4 q^{20} - 8 q^{21} - 2 q^{24} + 6 q^{25} + 2 q^{26} + 20 q^{29} + 4 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 2 q^{36} - 2 q^{39} - 2 q^{40} + 20 q^{41} + 12 q^{44} - 4 q^{45} - 12 q^{46} - 18 q^{49} + 8 q^{50} - 8 q^{51} - 2 q^{54} - 24 q^{55} - 8 q^{56} + 12 q^{59} + 2 q^{60} - 12 q^{61} - 2 q^{64} - 2 q^{65} - 12 q^{66} + 12 q^{69} + 16 q^{70} + 12 q^{74} - 8 q^{75} + 4 q^{76} + 16 q^{79} + 4 q^{80} + 2 q^{81} + 8 q^{84} - 8 q^{85} - 28 q^{89} - 2 q^{90} - 8 q^{91} - 16 q^{94} - 8 q^{95} + 2 q^{96} + 12 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 2 * q^15 + 2 * q^16 - 4 * q^19 - 4 * q^20 - 8 * q^21 - 2 * q^24 + 6 * q^25 + 2 * q^26 + 20 * q^29 + 4 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 2 * q^36 - 2 * q^39 - 2 * q^40 + 20 * q^41 + 12 * q^44 - 4 * q^45 - 12 * q^46 - 18 * q^49 + 8 * q^50 - 8 * q^51 - 2 * q^54 - 24 * q^55 - 8 * q^56 + 12 * q^59 + 2 * q^60 - 12 * q^61 - 2 * q^64 - 2 * q^65 - 12 * q^66 + 12 * q^69 + 16 * q^70 + 12 * q^74 - 8 * q^75 + 4 * q^76 + 16 * q^79 + 4 * q^80 + 2 * q^81 + 8 * q^84 - 8 * q^85 - 28 * q^89 - 2 * q^90 - 8 * q^91 - 16 * q^94 - 8 * q^95 + 2 * q^96 + 12 * q^99

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