LMFDB - Embedded newform 390.2.e.c.79.2

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			79.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	390.79
Dual form			390.2.e.c.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +2.00000 q^{11} +1.00000i q^{12} +1.00000i q^{13} -2.00000 q^{14} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -1.00000i q^{18} +4.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} +2.00000 q^{21} +2.00000i q^{22} -1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000 q^{26} +1.00000i q^{27} -2.00000i q^{28} -4.00000 q^{29} +(2.00000 + 1.00000i) q^{30} +8.00000 q^{31} +1.00000i q^{32} -2.00000i q^{33} -2.00000 q^{34} +(-2.00000 + 4.00000i) q^{35} +1.00000 q^{36} +6.00000i q^{37} +4.00000i q^{38} +1.00000 q^{39} +(1.00000 - 2.00000i) q^{40} -6.00000 q^{41} +2.00000i q^{42} -4.00000i q^{43} -2.00000 q^{44} +(-2.00000 - 1.00000i) q^{45} -8.00000i q^{47} -1.00000i q^{48} +3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +2.00000 q^{51} -1.00000i q^{52} -2.00000i q^{53} -1.00000 q^{54} +(4.00000 + 2.00000i) q^{55} +2.00000 q^{56} -4.00000i q^{57} -4.00000i q^{58} -10.0000 q^{59} +(-1.00000 + 2.00000i) q^{60} -14.0000 q^{61} +8.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(-1.00000 + 2.00000i) q^{65} +2.00000 q^{66} -16.0000i q^{67} -2.00000i q^{68} +(-4.00000 - 2.00000i) q^{70} -4.00000 q^{71} +1.00000i q^{72} -8.00000i q^{73} -6.00000 q^{74} +(4.00000 - 3.00000i) q^{75} -4.00000 q^{76} +4.00000i q^{77} +1.00000i q^{78} +8.00000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -6.00000i q^{82} -12.0000i q^{83} -2.00000 q^{84} +(-2.00000 + 4.00000i) q^{85} +4.00000 q^{86} +4.00000i q^{87} -2.00000i q^{88} -6.00000 q^{89} +(1.00000 - 2.00000i) q^{90} -2.00000 q^{91} -8.00000i q^{93} +8.00000 q^{94} +(8.00000 + 4.00000i) q^{95} +1.00000 q^{96} +12.0000i q^{97} +3.00000i q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{11} - 4 q^{14} + 2 q^{15} + 2 q^{16} + 8 q^{19} - 4 q^{20} + 4 q^{21} - 2 q^{24} + 6 q^{25} - 2 q^{26} - 8 q^{29} + 4 q^{30} + 16 q^{31} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 2 q^{39} + 2 q^{40} - 12 q^{41} - 4 q^{44} - 4 q^{45} + 6 q^{49} - 8 q^{50} + 4 q^{51} - 2 q^{54} + 8 q^{55} + 4 q^{56} - 20 q^{59} - 2 q^{60} - 28 q^{61} - 2 q^{64} - 2 q^{65} + 4 q^{66} - 8 q^{70} - 8 q^{71} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 16 q^{79} + 4 q^{80} + 2 q^{81} - 4 q^{84} - 4 q^{85} + 8 q^{86} - 12 q^{89} + 2 q^{90} - 4 q^{91} + 16 q^{94} + 16 q^{95} + 2 q^{96} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^14 + 2 * q^15 + 2 * q^16 + 8 * q^19 - 4 * q^20 + 4 * q^21 - 2 * q^24 + 6 * q^25 - 2 * q^26 - 8 * q^29 + 4 * q^30 + 16 * q^31 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 2 * q^39 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 4 * q^45 + 6 * q^49 - 8 * q^50 + 4 * q^51 - 2 * q^54 + 8 * q^55 + 4 * q^56 - 20 * q^59 - 2 * q^60 - 28 * q^61 - 2 * q^64 - 2 * q^65 + 4 * q^66 - 8 * q^70 - 8 * q^71 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 16 * q^79 + 4 * q^80 + 2 * q^81 - 4 * q^84 - 4 * q^85 + 8 * q^86 - 12 * q^89 + 2 * q^90 - 4 * q^91 + 16 * q^94 + 16 * q^95 + 2 * q^96 - 4 * 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
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$			1.00000i			0.288675i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−2.00000			−0.534522
$15$	1.00000	−	2.00000i	0.258199	−	0.516398i
$16$	1.00000			0.250000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	2.00000			0.436436
$22$			2.00000i			0.426401i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−1.00000			−0.204124
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	−1.00000			−0.196116
$27$			1.00000i			0.192450i
$28$		−	2.00000i		−	0.377964i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$	2.00000	+	1.00000i	0.365148	+	0.182574i
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$			1.00000i			0.176777i
$33$		−	2.00000i		−	0.348155i
$34$	−2.00000			−0.342997
$35$	−2.00000	+	4.00000i	−0.338062	+	0.676123i
$36$	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	$0.835828\pi$
$38$			4.00000i			0.648886i
$39$	1.00000			0.160128
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$			2.00000i			0.308607i
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	−2.00000			−0.301511
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$		0			0
$47$		−	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
$49$	3.00000			0.428571
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	2.00000			0.280056
$52$		−	1.00000i		−	0.138675i
$53$		−	2.00000i		−	0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	−1.00000			−0.136083
$55$	4.00000	+	2.00000i	0.539360	+	0.269680i
$56$	2.00000			0.267261
$57$		−	4.00000i		−	0.529813i
$58$		−	4.00000i		−	0.525226i
$59$	−10.0000			−1.30189			−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000			−1.30189			−0.650945	+	0.759125i	$0.725627\pi$
$60$	−1.00000	+	2.00000i	−0.129099	+	0.258199i
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$			8.00000i			1.01600i
$63$		−	2.00000i		−	0.251976i
$64$	−1.00000			−0.125000
$65$	−1.00000	+	2.00000i	−0.124035	+	0.248069i
$66$	2.00000			0.246183
$67$		−	16.0000i		−	1.95471i	−0.211604	−	0.977356i	$-0.567869\pi$
$67$		−	16.0000i		−	1.95471i	0.211604	−	0.977356i	$-0.432131\pi$
$68$		−	2.00000i		−	0.242536i
$69$		0			0
$70$	−4.00000	−	2.00000i	−0.478091	−	0.239046i
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$			1.00000i			0.117851i
$73$		−	8.00000i		−	0.936329i	−0.883641	−	0.468165i	$-0.844915\pi$
$73$		−	8.00000i		−	0.936329i	0.883641	−	0.468165i	$-0.155085\pi$
$74$	−6.00000			−0.697486
$75$	4.00000	−	3.00000i	0.461880	−	0.346410i
$76$	−4.00000			−0.458831
$77$			4.00000i			0.455842i
$78$			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
$82$		−	6.00000i		−	0.662589i
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	−2.00000			−0.218218
$85$	−2.00000	+	4.00000i	−0.216930	+	0.433861i
$86$	4.00000			0.431331
$87$			4.00000i			0.428845i
$88$		−	2.00000i		−	0.213201i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	−	2.00000i	0.105409	−	0.210819i
$91$	−2.00000			−0.209657
$92$		0			0
$93$		−	8.00000i		−	0.829561i
$94$	8.00000			0.825137
$95$	8.00000	+	4.00000i	0.820783	+	0.410391i
$96$	1.00000			0.102062
$97$			12.0000i			1.21842i	0.793011	+	0.609208i	$0.208512\pi$
$97$			12.0000i			1.21842i	−0.793011	+	0.609208i	$0.791488\pi$
$98$			3.00000i			0.303046i
$99$	−2.00000			−0.201008
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	4.00000			0.398015			0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000			0.398015			0.199007	+	0.979998i	$0.436228\pi$
$102$			2.00000i			0.198030i
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	1.00000			0.0980581
$105$	4.00000	+	2.00000i	0.390360	+	0.195180i
$106$	2.00000			0.194257
$107$		−	4.00000i		−	0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$		−	4.00000i		−	0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	18.0000			1.72409			0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000			1.72409			0.862044	+	0.506834i	$0.169184\pi$
$110$	−2.00000	+	4.00000i	−0.190693	+	0.381385i
$111$	6.00000			0.569495
$112$			2.00000i			0.188982i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	4.00000			0.374634
$115$		0			0
$116$	4.00000			0.371391
$117$		−	1.00000i		−	0.0924500i
$118$		−	10.0000i		−	0.920575i
$119$	−4.00000			−0.366679
$120$	−2.00000	−	1.00000i	−0.182574	−	0.0912871i
$121$	−7.00000			−0.636364
$122$		−	14.0000i		−	1.26750i
$123$			6.00000i			0.541002i
$124$	−8.00000			−0.718421
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	2.00000			0.178174
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.00000			−0.352180
$130$	−2.00000	−	1.00000i	−0.175412	−	0.0877058i
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$			2.00000i			0.174078i
$133$			8.00000i			0.693688i
$134$	16.0000			1.38219
$135$	−1.00000	+	2.00000i	−0.0860663	+	0.172133i
$136$	2.00000			0.171499
$137$		−	14.0000i		−	1.19610i	−0.801459	−	0.598050i	$-0.795942\pi$
$137$		−	14.0000i		−	1.19610i	0.801459	−	0.598050i	$-0.204058\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	2.00000	−	4.00000i	0.169031	−	0.338062i
$141$	−8.00000			−0.673722
$142$		−	4.00000i		−	0.335673i
$143$			2.00000i			0.167248i
$144$	−1.00000			−0.0833333
$145$	−8.00000	−	4.00000i	−0.664364	−	0.332182i
$146$	8.00000			0.662085
$147$		−	3.00000i		−	0.247436i
$148$		−	6.00000i		−	0.493197i
$149$	−12.0000			−0.983078			−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000			−0.983078			−0.491539	+	0.870855i	$0.663566\pi$
$150$	3.00000	+	4.00000i	0.244949	+	0.326599i
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		−	4.00000i		−	0.324443i
$153$		−	2.00000i		−	0.161690i
$154$	−4.00000			−0.322329
$155$	16.0000	+	8.00000i	1.28515	+	0.642575i
$156$	−1.00000			−0.0800641
$157$			10.0000i			0.798087i	0.916932	+	0.399043i	$0.130658\pi$
$157$			10.0000i			0.798087i	−0.916932	+	0.399043i	$0.869342\pi$
$158$			8.00000i			0.636446i
$159$	−2.00000			−0.158610
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$			8.00000i			0.626608i	0.949653	+	0.313304i	$0.101436\pi$
$163$			8.00000i			0.626608i	−0.949653	+	0.313304i	$0.898564\pi$
$164$	6.00000			0.468521
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$	12.0000			0.931381
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		−	2.00000i		−	0.154303i
$169$	−1.00000			−0.0769231
$170$	−4.00000	−	2.00000i	−0.306786	−	0.153393i
$171$	−4.00000			−0.305888
$172$			4.00000i			0.304997i
$173$		−	14.0000i		−	1.06440i	−0.846619	−	0.532200i	$-0.821365\pi$
$173$		−	14.0000i		−	1.06440i	0.846619	−	0.532200i	$-0.178635\pi$
$174$	−4.00000			−0.303239
$175$	−8.00000	+	6.00000i	−0.604743	+	0.453557i
$176$	2.00000			0.150756
$177$			10.0000i			0.751646i
$178$		−	6.00000i		−	0.449719i
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$	2.00000	+	1.00000i	0.149071	+	0.0745356i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		−	2.00000i		−	0.148250i
$183$			14.0000i			1.03491i
$184$		0			0
$185$	−6.00000	+	12.0000i	−0.441129	+	0.882258i
$186$	8.00000			0.586588
$187$			4.00000i			0.292509i
$188$			8.00000i			0.583460i
$189$	−2.00000			−0.145479
$190$	−4.00000	+	8.00000i	−0.290191	+	0.580381i
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$			1.00000i			0.0721688i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$	−12.0000			−0.861550
$195$	2.00000	+	1.00000i	0.143223	+	0.0716115i
$196$	−3.00000			−0.214286
$197$			10.0000i			0.712470i	0.934396	+	0.356235i	$0.115940\pi$
$197$			10.0000i			0.712470i	−0.934396	+	0.356235i	$0.884060\pi$
$198$		−	2.00000i		−	0.142134i
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$	−16.0000			−1.12855
$202$			4.00000i			0.281439i
$203$		−	8.00000i		−	0.561490i
$204$	−2.00000			−0.140028
$205$	−12.0000	−	6.00000i	−0.838116	−	0.419058i
$206$	6.00000			0.418040
$207$		0			0
$208$			1.00000i			0.0693375i
$209$	8.00000			0.553372
$210$	−2.00000	+	4.00000i	−0.138013	+	0.276026i
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$			2.00000i			0.137361i
$213$			4.00000i			0.274075i
$214$	4.00000			0.273434
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$	1.00000			0.0680414
$217$			16.0000i			1.08615i
$218$			18.0000i			1.21911i
$219$	−8.00000			−0.540590
$220$	−4.00000	−	2.00000i	−0.269680	−	0.134840i
$221$	−2.00000			−0.134535
$222$			6.00000i			0.402694i
$223$			14.0000i			0.937509i	0.883328	+	0.468755i	$0.155297\pi$
$223$			14.0000i			0.937509i	−0.883328	+	0.468755i	$0.844703\pi$
$224$	−2.00000			−0.133631
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	6.00000			0.399114
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$			4.00000i			0.264906i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	4.00000			0.263181
$232$			4.00000i			0.262613i
$233$			14.0000i			0.917170i	0.888650	+	0.458585i	$0.151644\pi$
$233$			14.0000i			0.917170i	−0.888650	+	0.458585i	$0.848356\pi$
$234$	1.00000			0.0653720
$235$	8.00000	−	16.0000i	0.521862	−	1.04372i
$236$	10.0000			0.650945
$237$		−	8.00000i		−	0.519656i
$238$		−	4.00000i		−	0.259281i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	1.00000	−	2.00000i	0.0645497	−	0.129099i
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		−	7.00000i		−	0.449977i
$243$		−	1.00000i		−	0.0641500i
$244$	14.0000			0.896258
$245$	6.00000	+	3.00000i	0.383326	+	0.191663i
$246$	−6.00000			−0.382546
$247$			4.00000i			0.254514i
$248$		−	8.00000i		−	0.508001i
$249$	−12.0000			−0.760469
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$			2.00000i			0.125988i
$253$		0			0
$254$	−6.00000			−0.376473
$255$	4.00000	+	2.00000i	0.250490	+	0.125245i
$256$	1.00000			0.0625000
$257$		−	18.0000i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$		−	18.0000i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$		−	4.00000i		−	0.249029i
$259$	−12.0000			−0.745644
$260$	1.00000	−	2.00000i	0.0620174	−	0.124035i
$261$	4.00000			0.247594
$262$		−	6.00000i		−	0.370681i
$263$			8.00000i			0.493301i	0.969104	+	0.246651i	$0.0793300\pi$
$263$			8.00000i			0.493301i	−0.969104	+	0.246651i	$0.920670\pi$
$264$	−2.00000			−0.123091
$265$	2.00000	−	4.00000i	0.122859	−	0.245718i
$266$	−8.00000			−0.490511
$267$			6.00000i			0.367194i
$268$			16.0000i			0.977356i
$269$	20.0000			1.21942			0.609711	−	0.792624i	$-0.291286\pi$
$269$	20.0000			1.21942			0.609711	+	0.792624i	$0.291286\pi$
$270$	−2.00000	−	1.00000i	−0.121716	−	0.0608581i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$			2.00000i			0.121268i
$273$			2.00000i			0.121046i
$274$	14.0000			0.845771
$275$	6.00000	+	8.00000i	0.361814	+	0.482418i
$276$		0			0
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$		−	4.00000i		−	0.239904i
$279$	−8.00000			−0.478947
$280$	4.00000	+	2.00000i	0.239046	+	0.119523i
$281$	−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
$283$		−	16.0000i		−	0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$		−	16.0000i		−	0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$	4.00000			0.237356
$285$	4.00000	−	8.00000i	0.236940	−	0.473879i
$286$	−2.00000			−0.118262
$287$		−	12.0000i		−	0.708338i
$288$		−	1.00000i		−	0.0589256i
$289$	13.0000			0.764706
$290$	4.00000	−	8.00000i	0.234888	−	0.469776i
$291$	12.0000			0.703452
$292$			8.00000i			0.468165i
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$	3.00000			0.174964
$295$	−20.0000	−	10.0000i	−1.16445	−	0.582223i
$296$	6.00000			0.348743
$297$			2.00000i			0.116052i
$298$		−	12.0000i		−	0.695141i
$299$		0			0
$300$	−4.00000	+	3.00000i	−0.230940	+	0.173205i
$301$	8.00000			0.461112
$302$		−	16.0000i		−	0.920697i
$303$		−	4.00000i		−	0.229794i
$304$	4.00000			0.229416
$305$	−28.0000	−	14.0000i	−1.60328	−	0.801638i
$306$	2.00000			0.114332
$307$		−	28.0000i		−	1.59804i	−0.601302	−	0.799022i	$-0.705351\pi$
$307$		−	28.0000i		−	1.59804i	0.601302	−	0.799022i	$-0.294649\pi$
$308$		−	4.00000i		−	0.227921i
$309$	−6.00000			−0.341328
$310$	−8.00000	+	16.0000i	−0.454369	+	0.908739i
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$		−	1.00000i		−	0.0566139i
$313$			20.0000i			1.13047i	0.824931	+	0.565233i	$0.191214\pi$
$313$			20.0000i			1.13047i	−0.824931	+	0.565233i	$0.808786\pi$
$314$	−10.0000			−0.564333
$315$	2.00000	−	4.00000i	0.112687	−	0.225374i
$316$	−8.00000			−0.450035
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$		−	2.00000i		−	0.112154i
$319$	−8.00000			−0.447914
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$	−4.00000			−0.223258
$322$		0			0
$323$			8.00000i			0.445132i
$324$	−1.00000			−0.0555556
$325$	−4.00000	+	3.00000i	−0.221880	+	0.166410i
$326$	−8.00000			−0.443079
$327$		−	18.0000i		−	0.995402i
$328$			6.00000i			0.331295i
$329$	16.0000			0.882109
$330$	4.00000	+	2.00000i	0.220193	+	0.110096i
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$			12.0000i			0.658586i
$333$		−	6.00000i		−	0.328798i
$334$	−12.0000			−0.656611
$335$	16.0000	−	32.0000i	0.874173	−	1.74835i
$336$	2.00000			0.109109
$337$			20.0000i			1.08947i	0.838608	+	0.544735i	$0.183370\pi$
$337$			20.0000i			1.08947i	−0.838608	+	0.544735i	$0.816630\pi$
$338$		−	1.00000i		−	0.0543928i
$339$	−6.00000			−0.325875
$340$	2.00000	−	4.00000i	0.108465	−	0.216930i
$341$	16.0000			0.866449
$342$		−	4.00000i		−	0.216295i
$343$			20.0000i			1.07990i
$344$	−4.00000			−0.215666
$345$		0			0
$346$	14.0000			0.752645
$347$			12.0000i			0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$			12.0000i			0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$		−	4.00000i		−	0.214423i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	−6.00000	−	8.00000i	−0.320713	−	0.427618i
$351$	−1.00000			−0.0533761
$352$			2.00000i			0.106600i
$353$			34.0000i			1.80964i	0.425797	+	0.904819i	$0.359994\pi$
$353$			34.0000i			1.80964i	−0.425797	+	0.904819i	$0.640006\pi$
$354$	−10.0000			−0.531494
$355$	−8.00000	−	4.00000i	−0.424596	−	0.212298i
$356$	6.00000			0.317999
$357$			4.00000i			0.211702i
$358$			18.0000i			0.951330i
$359$	−32.0000			−1.68890			−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000			−1.68890			−0.844448	+	0.535638i	$0.820071\pi$
$360$	−1.00000	+	2.00000i	−0.0527046	+	0.105409i
$361$	−3.00000			−0.157895
$362$		−	6.00000i		−	0.315353i
$363$			7.00000i			0.367405i
$364$	2.00000			0.104828
$365$	8.00000	−	16.0000i	0.418739	−	0.837478i
$366$	−14.0000			−0.731792
$367$		−	10.0000i		−	0.521996i	−0.965339	−	0.260998i	$-0.915948\pi$
$367$		−	10.0000i		−	0.521996i	0.965339	−	0.260998i	$-0.0840516\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$	−12.0000	−	6.00000i	−0.623850	−	0.311925i
$371$	4.00000			0.207670
$372$			8.00000i			0.414781i
$373$			22.0000i			1.13912i	0.821951	+	0.569558i	$0.192886\pi$
$373$			22.0000i			1.13912i	−0.821951	+	0.569558i	$0.807114\pi$
$374$	−4.00000			−0.206835
$375$	11.0000	−	2.00000i	0.568038	−	0.103280i
$376$	−8.00000			−0.412568
$377$		−	4.00000i		−	0.206010i
$378$		−	2.00000i		−	0.102869i
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$	−8.00000	−	4.00000i	−0.410391	−	0.205196i
$381$	6.00000			0.307389
$382$		−	12.0000i		−	0.613973i
$383$		−	24.0000i		−	1.22634i	−0.789950	−	0.613171i	$-0.789894\pi$
$383$		−	24.0000i		−	1.22634i	0.789950	−	0.613171i	$-0.210106\pi$
$384$	−1.00000			−0.0510310
$385$	−4.00000	+	8.00000i	−0.203859	+	0.407718i
$386$		0			0
$387$			4.00000i			0.203331i
$388$		−	12.0000i		−	0.609208i
$389$	−16.0000			−0.811232			−0.405616	−	0.914044i	$-0.632943\pi$
$389$	−16.0000			−0.811232			−0.405616	+	0.914044i	$0.632943\pi$
$390$	−1.00000	+	2.00000i	−0.0506370	+	0.101274i
$391$		0			0
$392$		−	3.00000i		−	0.151523i
$393$			6.00000i			0.302660i
$394$	−10.0000			−0.503793
$395$	16.0000	+	8.00000i	0.805047	+	0.402524i
$396$	2.00000			0.100504
$397$		−	18.0000i		−	0.903394i	−0.892171	−	0.451697i	$-0.850819\pi$
$397$		−	18.0000i		−	0.903394i	0.892171	−	0.451697i	$-0.149181\pi$
$398$			24.0000i			1.20301i
$399$	8.00000			0.400501
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		−	16.0000i		−	0.798007i
$403$			8.00000i			0.398508i
$404$	−4.00000			−0.199007
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$	8.00000			0.397033
$407$			12.0000i			0.594818i
$408$		−	2.00000i		−	0.0990148i
$409$	26.0000			1.28562			0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000			1.28562			0.642809	+	0.766027i	$0.277769\pi$
$410$	6.00000	−	12.0000i	0.296319	−	0.592638i
$411$	−14.0000			−0.690569
$412$			6.00000i			0.295599i
$413$		−	20.0000i		−	0.984136i
$414$		0			0
$415$	12.0000	−	24.0000i	0.589057	−	1.17811i
$416$	−1.00000			−0.0490290
$417$			4.00000i			0.195881i
$418$			8.00000i			0.391293i
$419$	14.0000			0.683945			0.341972	−	0.939710i	$-0.388905\pi$
$419$	14.0000			0.683945			0.341972	+	0.939710i	$0.388905\pi$
$420$	−4.00000	−	2.00000i	−0.195180	−	0.0975900i
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$		−	4.00000i		−	0.194717i
$423$			8.00000i			0.388973i
$424$	−2.00000			−0.0971286
$425$	−8.00000	+	6.00000i	−0.388057	+	0.291043i
$426$	−4.00000			−0.193801
$427$		−	28.0000i		−	1.35501i
$428$			4.00000i			0.193347i
$429$	2.00000			0.0965609
$430$	8.00000	+	4.00000i	0.385794	+	0.192897i
$431$	16.0000			0.770693			0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000			0.770693			0.385346	+	0.922772i	$0.374082\pi$
$432$			1.00000i			0.0481125i
$433$		−	12.0000i		−	0.576683i	−0.957528	−	0.288342i	$-0.906896\pi$
$433$		−	12.0000i		−	0.576683i	0.957528	−	0.288342i	$-0.0931039\pi$
$434$	−16.0000			−0.768025
$435$	−4.00000	+	8.00000i	−0.191785	+	0.383571i
$436$	−18.0000			−0.862044
$437$		0			0
$438$		−	8.00000i		−	0.382255i
$439$	−32.0000			−1.52728			−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000			−1.52728			−0.763638	+	0.645644i	$0.776589\pi$
$440$	2.00000	−	4.00000i	0.0953463	−	0.190693i
$441$	−3.00000			−0.142857
$442$		−	2.00000i		−	0.0951303i
$443$		−	4.00000i		−	0.190046i	−0.995475	−	0.0950229i	$-0.969708\pi$
$443$		−	4.00000i		−	0.190046i	0.995475	−	0.0950229i	$-0.0302924\pi$
$444$	−6.00000			−0.284747
$445$	−12.0000	−	6.00000i	−0.568855	−	0.284427i
$446$	−14.0000			−0.662919
$447$			12.0000i			0.567581i
$448$		−	2.00000i		−	0.0944911i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	−12.0000			−0.565058
$452$			6.00000i			0.282216i
$453$			16.0000i			0.751746i
$454$	−12.0000			−0.563188
$455$	−4.00000	−	2.00000i	−0.187523	−	0.0937614i
$456$	−4.00000			−0.187317
$457$		−	28.0000i		−	1.30978i	−0.755722	−	0.654892i	$-0.772714\pi$
$457$		−	28.0000i		−	1.30978i	0.755722	−	0.654892i	$-0.227286\pi$
$458$			22.0000i			1.02799i
$459$	−2.00000			−0.0933520
$460$		0			0
$461$	20.0000			0.931493			0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000			0.931493			0.465746	+	0.884918i	$0.345786\pi$
$462$			4.00000i			0.186097i
$463$		−	6.00000i		−	0.278844i	−0.990233	−	0.139422i	$-0.955476\pi$
$463$		−	6.00000i		−	0.278844i	0.990233	−	0.139422i	$-0.0445244\pi$
$464$	−4.00000			−0.185695
$465$	8.00000	−	16.0000i	0.370991	−	0.741982i
$466$	−14.0000			−0.648537
$467$			28.0000i			1.29569i	0.761774	+	0.647843i	$0.224329\pi$
$467$			28.0000i			1.29569i	−0.761774	+	0.647843i	$0.775671\pi$
$468$			1.00000i			0.0462250i
$469$	32.0000			1.47762
$470$	16.0000	+	8.00000i	0.738025	+	0.369012i
$471$	10.0000			0.460776
$472$			10.0000i			0.460287i
$473$		−	8.00000i		−	0.367840i
$474$	8.00000			0.367452
$475$	12.0000	+	16.0000i	0.550598	+	0.734130i
$476$	4.00000			0.183340
$477$			2.00000i			0.0915737i
$478$			12.0000i			0.548867i
$479$	−36.0000			−1.64488			−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000			−1.64488			−0.822441	+	0.568850i	$0.807388\pi$
$480$	2.00000	+	1.00000i	0.0912871	+	0.0456435i
$481$	−6.00000			−0.273576
$482$		−	18.0000i		−	0.819878i
$483$		0			0
$484$	7.00000			0.318182
$485$	−12.0000	+	24.0000i	−0.544892	+	1.08978i
$486$	1.00000			0.0453609
$487$		−	26.0000i		−	1.17817i	−0.808070	−	0.589086i	$-0.799488\pi$
$487$		−	26.0000i		−	1.17817i	0.808070	−	0.589086i	$-0.200512\pi$
$488$			14.0000i			0.633750i
$489$	8.00000			0.361773
$490$	−3.00000	+	6.00000i	−0.135526	+	0.271052i
$491$	−22.0000			−0.992846			−0.496423	−	0.868081i	$-0.665354\pi$
$491$	−22.0000			−0.992846			−0.496423	+	0.868081i	$0.665354\pi$
$492$		−	6.00000i		−	0.270501i
$493$		−	8.00000i		−	0.360302i
$494$	−4.00000			−0.179969
$495$	−4.00000	−	2.00000i	−0.179787	−	0.0898933i
$496$	8.00000			0.359211
$497$		−	8.00000i		−	0.358849i
$498$		−	12.0000i		−	0.537733i
$499$	−36.0000			−1.61158			−0.805791	−	0.592200i	$-0.798259\pi$
$499$	−36.0000			−1.61158			−0.805791	+	0.592200i	$0.798259\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	12.0000			0.536120
$502$			18.0000i			0.803379i
$503$			36.0000i			1.60516i	0.596544	+	0.802580i	$0.296540\pi$
$503$			36.0000i			1.60516i	−0.596544	+	0.802580i	$0.703460\pi$
$504$	−2.00000			−0.0890871
$505$	8.00000	+	4.00000i	0.355995	+	0.177998i
$506$		0			0
$507$			1.00000i			0.0444116i
$508$		−	6.00000i		−	0.266207i
$509$	40.0000			1.77297			0.886484	−	0.462758i	$-0.153140\pi$
$509$	40.0000			1.77297			0.886484	+	0.462758i	$0.153140\pi$
$510$	−2.00000	+	4.00000i	−0.0885615	+	0.177123i
$511$	16.0000			0.707798
$512$			1.00000i			0.0441942i
$513$			4.00000i			0.176604i
$514$	18.0000			0.793946
$515$	6.00000	−	12.0000i	0.264392	−	0.528783i
$516$	4.00000			0.176090
$517$		−	16.0000i		−	0.703679i
$518$		−	12.0000i		−	0.527250i
$519$	−14.0000			−0.614532
$520$	2.00000	+	1.00000i	0.0877058	+	0.0438529i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$			4.00000i			0.175075i
$523$		−	16.0000i		−	0.699631i	−0.936819	−	0.349816i	$-0.886244\pi$
$523$		−	16.0000i		−	0.699631i	0.936819	−	0.349816i	$-0.113756\pi$
$524$	6.00000			0.262111
$525$	6.00000	+	8.00000i	0.261861	+	0.349149i
$526$	−8.00000			−0.348817
$527$			16.0000i			0.696971i
$528$		−	2.00000i		−	0.0870388i
$529$	23.0000			1.00000
$530$	4.00000	+	2.00000i	0.173749	+	0.0868744i
$531$	10.0000			0.433963
$532$		−	8.00000i		−	0.346844i
$533$		−	6.00000i		−	0.259889i
$534$	−6.00000			−0.259645
$535$	4.00000	−	8.00000i	0.172935	−	0.345870i
$536$	−16.0000			−0.691095
$537$		−	18.0000i		−	0.776757i
$538$			20.0000i			0.862261i
$539$	6.00000			0.258438
$540$	1.00000	−	2.00000i	0.0430331	−	0.0860663i
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$			16.0000i			0.687259i
$543$			6.00000i			0.257485i
$544$	−2.00000			−0.0857493
$545$	36.0000	+	18.0000i	1.54207	+	0.771035i
$546$	−2.00000			−0.0855921
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$			14.0000i			0.598050i
$549$	14.0000			0.597505
$550$	−8.00000	+	6.00000i	−0.341121	+	0.255841i
$551$	−16.0000			−0.681623
$552$		0			0
$553$			16.0000i			0.680389i
$554$	2.00000			0.0849719
$555$	12.0000	+	6.00000i	0.509372	+	0.254686i
$556$	4.00000			0.169638
$557$		−	14.0000i		−	0.593199i	−0.955002	−	0.296600i	$-0.904147\pi$
$557$		−	14.0000i		−	0.593199i	0.955002	−	0.296600i	$-0.0958526\pi$
$558$		−	8.00000i		−	0.338667i
$559$	4.00000			0.169182
$560$	−2.00000	+	4.00000i	−0.0845154	+	0.169031i
$561$	4.00000			0.168880
$562$		−	18.0000i		−	0.759284i
$563$			44.0000i			1.85438i	0.374593	+	0.927189i	$0.377783\pi$
$563$			44.0000i			1.85438i	−0.374593	+	0.927189i	$0.622217\pi$
$564$	8.00000			0.336861
$565$	6.00000	−	12.0000i	0.252422	−	0.504844i
$566$	16.0000			0.672530
$567$			2.00000i			0.0839921i
$568$			4.00000i			0.167836i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	8.00000	+	4.00000i	0.335083	+	0.167542i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		−	2.00000i		−	0.0836242i
$573$			12.0000i			0.501307i
$574$	12.0000			0.500870
$575$		0			0
$576$	1.00000			0.0416667
$577$			28.0000i			1.16566i	0.812596	+	0.582828i	$0.198054\pi$
$577$			28.0000i			1.16566i	−0.812596	+	0.582828i	$0.801946\pi$
$578$			13.0000i			0.540729i
$579$		0			0
$580$	8.00000	+	4.00000i	0.332182	+	0.166091i
$581$	24.0000			0.995688
$582$			12.0000i			0.497416i
$583$		−	4.00000i		−	0.165663i
$584$	−8.00000			−0.331042
$585$	1.00000	−	2.00000i	0.0413449	−	0.0826898i
$586$	26.0000			1.07405
$587$			36.0000i			1.48588i	0.669359	+	0.742940i	$0.266569\pi$
$587$			36.0000i			1.48588i	−0.669359	+	0.742940i	$0.733431\pi$
$588$			3.00000i			0.123718i
$589$	32.0000			1.31854
$590$	10.0000	−	20.0000i	0.411693	−	0.823387i
$591$	10.0000			0.411345
$592$			6.00000i			0.246598i
$593$		−	34.0000i		−	1.39621i	−0.715994	−	0.698106i	$-0.754026\pi$
$593$		−	34.0000i		−	1.39621i	0.715994	−	0.698106i	$-0.245974\pi$
$594$	−2.00000			−0.0820610
$595$	−8.00000	−	4.00000i	−0.327968	−	0.163984i
$596$	12.0000			0.491539
$597$		−	24.0000i		−	0.982255i
$598$		0			0
$599$	−32.0000			−1.30748			−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000			−1.30748			−0.653742	+	0.756717i	$0.726802\pi$
$600$	−3.00000	−	4.00000i	−0.122474	−	0.163299i
$601$	−46.0000			−1.87638			−0.938190	−	0.346122i	$-0.887498\pi$
$601$	−46.0000			−1.87638			−0.938190	+	0.346122i	$0.887498\pi$
$602$			8.00000i			0.326056i
$603$			16.0000i			0.651570i
$604$	16.0000			0.651031
$605$	−14.0000	−	7.00000i	−0.569181	−	0.284590i
$606$	4.00000			0.162489
$607$			18.0000i			0.730597i	0.930890	+	0.365299i	$0.119033\pi$
$607$			18.0000i			0.730597i	−0.930890	+	0.365299i	$0.880967\pi$
$608$			4.00000i			0.162221i
$609$	−8.00000			−0.324176
$610$	14.0000	−	28.0000i	0.566843	−	1.13369i
$611$	8.00000			0.323645
$612$			2.00000i			0.0808452i
$613$			2.00000i			0.0807792i	0.999184	+	0.0403896i	$0.0128599\pi$
$613$			2.00000i			0.0807792i	−0.999184	+	0.0403896i	$0.987140\pi$
$614$	28.0000			1.12999
$615$	−6.00000	+	12.0000i	−0.241943	+	0.483887i
$616$	4.00000			0.161165
$617$			46.0000i			1.85189i	0.377658	+	0.925945i	$0.376729\pi$
$617$			46.0000i			1.85189i	−0.377658	+	0.925945i	$0.623271\pi$
$618$		−	6.00000i		−	0.241355i
$619$	24.0000			0.964641			0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000			0.964641			0.482321	+	0.875995i	$0.339794\pi$
$620$	−16.0000	−	8.00000i	−0.642575	−	0.321288i
$621$		0			0
$622$			20.0000i			0.801927i
$623$		−	12.0000i		−	0.480770i
$624$	1.00000			0.0400320
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−20.0000			−0.799361
$627$		−	8.00000i		−	0.319489i
$628$		−	10.0000i		−	0.399043i
$629$	−12.0000			−0.478471
$630$	4.00000	+	2.00000i	0.159364	+	0.0796819i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		−	8.00000i		−	0.318223i
$633$			4.00000i			0.158986i
$634$	18.0000			0.714871
$635$	−6.00000	+	12.0000i	−0.238103	+	0.476205i
$636$	2.00000			0.0793052
$637$			3.00000i			0.118864i
$638$		−	8.00000i		−	0.316723i
$639$	4.00000			0.158238
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$	−38.0000			−1.50091			−0.750455	−	0.660922i	$-0.770166\pi$
$641$	−38.0000			−1.50091			−0.750455	+	0.660922i	$0.770166\pi$
$642$		−	4.00000i		−	0.157867i
$643$		−	32.0000i		−	1.26196i	−0.775800	−	0.630978i	$-0.782654\pi$
$643$		−	32.0000i		−	1.26196i	0.775800	−	0.630978i	$-0.217346\pi$
$644$		0			0
$645$	−8.00000	−	4.00000i	−0.315000	−	0.157500i
$646$	−8.00000			−0.314756
$647$			36.0000i			1.41531i	0.706560	+	0.707653i	$0.250246\pi$
$647$			36.0000i			1.41531i	−0.706560	+	0.707653i	$0.749754\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−20.0000			−0.785069
$650$	−3.00000	−	4.00000i	−0.117670	−	0.156893i
$651$	16.0000			0.627089
$652$		−	8.00000i		−	0.313304i
$653$			34.0000i			1.33052i	0.746611	+	0.665261i	$0.231680\pi$
$653$			34.0000i			1.33052i	−0.746611	+	0.665261i	$0.768320\pi$
$654$	18.0000			0.703856
$655$	−12.0000	−	6.00000i	−0.468879	−	0.234439i
$656$	−6.00000			−0.234261
$657$			8.00000i			0.312110i
$658$			16.0000i			0.623745i
$659$	−10.0000			−0.389545			−0.194772	−	0.980848i	$-0.562397\pi$
$659$	−10.0000			−0.389545			−0.194772	+	0.980848i	$0.562397\pi$
$660$	−2.00000	+	4.00000i	−0.0778499	+	0.155700i
$661$	30.0000			1.16686			0.583432	−	0.812162i	$-0.301709\pi$
$661$	30.0000			1.16686			0.583432	+	0.812162i	$0.301709\pi$
$662$		−	12.0000i		−	0.466393i
$663$			2.00000i			0.0776736i
$664$	−12.0000			−0.465690
$665$	−8.00000	+	16.0000i	−0.310227	+	0.620453i
$666$	6.00000			0.232495
$667$		0			0
$668$		−	12.0000i		−	0.464294i
$669$	14.0000			0.541271
$670$	32.0000	+	16.0000i	1.23627	+	0.618134i
$671$	−28.0000			−1.08093
$672$			2.00000i			0.0771517i
$673$			36.0000i			1.38770i	0.720121	+	0.693849i	$0.244086\pi$
$673$			36.0000i			1.38770i	−0.720121	+	0.693849i	$0.755914\pi$
$674$	−20.0000			−0.770371
$675$	−4.00000	+	3.00000i	−0.153960	+	0.115470i
$676$	1.00000			0.0384615
$677$		−	10.0000i		−	0.384331i	−0.981363	−	0.192166i	$-0.938449\pi$
$677$		−	10.0000i		−	0.384331i	0.981363	−	0.192166i	$-0.0615511\pi$
$678$		−	6.00000i		−	0.230429i
$679$	−24.0000			−0.921035
$680$	4.00000	+	2.00000i	0.153393	+	0.0766965i
$681$	12.0000			0.459841
$682$			16.0000i			0.612672i
$683$		−	12.0000i		−	0.459167i	−0.973289	−	0.229584i	$-0.926264\pi$
$683$		−	12.0000i		−	0.459167i	0.973289	−	0.229584i	$-0.0737364\pi$
$684$	4.00000			0.152944
$685$	14.0000	−	28.0000i	0.534913	−	1.06983i
$686$	−20.0000			−0.763604
$687$		−	22.0000i		−	0.839352i
$688$		−	4.00000i		−	0.152499i
$689$	2.00000			0.0761939
$690$		0			0
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$			14.0000i			0.532200i
$693$		−	4.00000i		−	0.151947i
$694$	−12.0000			−0.455514
$695$	−8.00000	−	4.00000i	−0.303457	−	0.151729i
$696$	4.00000			0.151620
$697$		−	12.0000i		−	0.454532i
$698$		−	14.0000i		−	0.529908i
$699$	14.0000			0.529529
$700$	8.00000	−	6.00000i	0.302372	−	0.226779i
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		−	1.00000i		−	0.0377426i
$703$			24.0000i			0.905177i
$704$	−2.00000			−0.0753778
$705$	−16.0000	−	8.00000i	−0.602595	−	0.301297i
$706$	−34.0000			−1.27961
$707$			8.00000i			0.300871i
$708$		−	10.0000i		−	0.375823i
$709$	−34.0000			−1.27690			−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000			−1.27690			−0.638448	+	0.769665i	$0.720423\pi$
$710$	4.00000	−	8.00000i	0.150117	−	0.300235i
$711$	−8.00000			−0.300023
$712$			6.00000i			0.224860i
$713$		0			0
$714$	−4.00000			−0.149696
$715$	−2.00000	+	4.00000i	−0.0747958	+	0.149592i
$716$	−18.0000			−0.672692
$717$		−	12.0000i		−	0.448148i
$718$		−	32.0000i		−	1.19423i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$	−2.00000	−	1.00000i	−0.0745356	−	0.0372678i
$721$	12.0000			0.446903
$722$		−	3.00000i		−	0.111648i
$723$			18.0000i			0.669427i
$724$	6.00000			0.222988
$725$	−12.0000	−	16.0000i	−0.445669	−	0.594225i
$726$	−7.00000			−0.259794
$727$			34.0000i			1.26099i	0.776193	+	0.630495i	$0.217148\pi$
$727$			34.0000i			1.26099i	−0.776193	+	0.630495i	$0.782852\pi$
$728$			2.00000i			0.0741249i
$729$	−1.00000			−0.0370370
$730$	16.0000	+	8.00000i	0.592187	+	0.296093i
$731$	8.00000			0.295891
$732$		−	14.0000i		−	0.517455i
$733$		−	14.0000i		−	0.517102i	−0.965998	−	0.258551i	$-0.916755\pi$
$733$		−	14.0000i		−	0.517102i	0.965998	−	0.258551i	$-0.0832450\pi$
$734$	10.0000			0.369107
$735$	3.00000	−	6.00000i	0.110657	−	0.221313i
$736$		0			0
$737$		−	32.0000i		−	1.17874i
$738$			6.00000i			0.220863i
$739$	−28.0000			−1.03000			−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000			−1.03000			−0.514998	+	0.857191i	$0.672207\pi$
$740$	6.00000	−	12.0000i	0.220564	−	0.441129i
$741$	4.00000			0.146944
$742$			4.00000i			0.146845i
$743$		−	16.0000i		−	0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$		−	16.0000i		−	0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$	−8.00000			−0.293294
$745$	−24.0000	−	12.0000i	−0.879292	−	0.439646i
$746$	−22.0000			−0.805477
$747$			12.0000i			0.439057i
$748$		−	4.00000i		−	0.146254i
$749$	8.00000			0.292314
$750$	2.00000	+	11.0000i	0.0730297	+	0.401663i
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		−	8.00000i		−	0.291730i
$753$		−	18.0000i		−	0.655956i
$754$	4.00000			0.145671
$755$	−32.0000	−	16.0000i	−1.16460	−	0.582300i
$756$	2.00000			0.0727393
$757$		−	26.0000i		−	0.944986i	−0.881334	−	0.472493i	$-0.843354\pi$
$757$		−	26.0000i		−	0.944986i	0.881334	−	0.472493i	$-0.156646\pi$
$758$		−	8.00000i		−	0.290573i
$759$		0			0
$760$	4.00000	−	8.00000i	0.145095	−	0.290191i
$761$	38.0000			1.37750			0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000			1.37750			0.688749	+	0.724999i	$0.258160\pi$
$762$			6.00000i			0.217357i
$763$			36.0000i			1.30329i
$764$	12.0000			0.434145
$765$	2.00000	−	4.00000i	0.0723102	−	0.144620i
$766$	24.0000			0.867155
$767$		−	10.0000i		−	0.361079i
$768$		−	1.00000i		−	0.0360844i
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$	−8.00000	−	4.00000i	−0.288300	−	0.144150i
$771$	−18.0000			−0.648254
$772$		0			0
$773$		−	22.0000i		−	0.791285i	−0.918405	−	0.395643i	$-0.870522\pi$
$773$		−	22.0000i		−	0.791285i	0.918405	−	0.395643i	$-0.129478\pi$
$774$	−4.00000			−0.143777
$775$	24.0000	+	32.0000i	0.862105	+	1.14947i
$776$	12.0000			0.430775
$777$			12.0000i			0.430498i
$778$		−	16.0000i		−	0.573628i
$779$	−24.0000			−0.859889
$780$	−2.00000	−	1.00000i	−0.0716115	−	0.0358057i
$781$	−8.00000			−0.286263
$782$		0			0
$783$		−	4.00000i		−	0.142948i
$784$	3.00000			0.107143
$785$	−10.0000	+	20.0000i	−0.356915	+	0.713831i
$786$	−6.00000			−0.214013
$787$		−	8.00000i		−	0.285169i	−0.989783	−	0.142585i	$-0.954459\pi$
$787$		−	8.00000i		−	0.285169i	0.989783	−	0.142585i	$-0.0455413\pi$
$788$		−	10.0000i		−	0.356235i
$789$	8.00000			0.284808
$790$	−8.00000	+	16.0000i	−0.284627	+	0.569254i
$791$	12.0000			0.426671
$792$			2.00000i			0.0710669i
$793$		−	14.0000i		−	0.497155i
$794$	18.0000			0.638796
$795$	−4.00000	−	2.00000i	−0.141865	−	0.0709327i
$796$	−24.0000			−0.850657
$797$			14.0000i			0.495905i	0.968772	+	0.247953i	$0.0797578\pi$
$797$			14.0000i			0.495905i	−0.968772	+	0.247953i	$0.920242\pi$
$798$			8.00000i			0.283197i
$799$	16.0000			0.566039
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	6.00000			0.212000
$802$		−	18.0000i		−	0.635602i
$803$		−	16.0000i		−	0.564628i
$804$	16.0000			0.564276
$805$		0			0
$806$	−8.00000			−0.281788
$807$		−	20.0000i		−	0.704033i
$808$		−	4.00000i		−	0.140720i
$809$	22.0000			0.773479			0.386739	−	0.922189i	$-0.373601\pi$
$809$	22.0000			0.773479			0.386739	+	0.922189i	$0.373601\pi$
$810$	−1.00000	+	2.00000i	−0.0351364	+	0.0702728i
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$			8.00000i			0.280745i
$813$		−	16.0000i		−	0.561144i
$814$	−12.0000			−0.420600
$815$	−8.00000	+	16.0000i	−0.280228	+	0.560456i
$816$	2.00000			0.0700140
$817$		−	16.0000i		−	0.559769i
$818$			26.0000i			0.909069i
$819$	2.00000			0.0698857
$820$	12.0000	+	6.00000i	0.419058	+	0.209529i
$821$	24.0000			0.837606			0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000			0.837606			0.418803	+	0.908077i	$0.362450\pi$
$822$		−	14.0000i		−	0.488306i
$823$		−	34.0000i		−	1.18517i	−0.805510	−	0.592583i	$-0.798108\pi$
$823$		−	34.0000i		−	1.18517i	0.805510	−	0.592583i	$-0.201892\pi$
$824$	−6.00000			−0.209020
$825$	8.00000	−	6.00000i	0.278524	−	0.208893i
$826$	20.0000			0.695889
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$		0			0
$829$	−18.0000			−0.625166			−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000			−0.625166			−0.312583	+	0.949890i	$0.601194\pi$
$830$	24.0000	+	12.0000i	0.833052	+	0.416526i
$831$	−2.00000			−0.0693792
$832$		−	1.00000i		−	0.0346688i
$833$			6.00000i			0.207888i
$834$	−4.00000			−0.138509
$835$	−12.0000	+	24.0000i	−0.415277	+	0.830554i
$836$	−8.00000			−0.276686
$837$			8.00000i			0.276520i
$838$			14.0000i			0.483622i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$	2.00000	−	4.00000i	0.0690066	−	0.138013i
$841$	−13.0000			−0.448276
$842$			34.0000i			1.17172i
$843$			18.0000i			0.619953i
$844$	4.00000			0.137686
$845$	−2.00000	−	1.00000i	−0.0688021	−	0.0344010i
$846$	−8.00000			−0.275046
$847$		−	14.0000i		−	0.481046i
$848$		−	2.00000i		−	0.0686803i
$849$	−16.0000			−0.549119
$850$	−6.00000	−	8.00000i	−0.205798	−	0.274398i
$851$		0			0
$852$		−	4.00000i		−	0.137038i
$853$			18.0000i			0.616308i	0.951336	+	0.308154i	$0.0997113\pi$
$853$			18.0000i			0.616308i	−0.951336	+	0.308154i	$0.900289\pi$
$854$	28.0000			0.958140
$855$	−8.00000	−	4.00000i	−0.273594	−	0.136797i
$856$	−4.00000			−0.136717
$857$			34.0000i			1.16142i	0.814111	+	0.580709i	$0.197225\pi$
$857$			34.0000i			1.16142i	−0.814111	+	0.580709i	$0.802775\pi$
$858$			2.00000i			0.0682789i
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$	−12.0000			−0.408959
$862$			16.0000i			0.544962i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$	−1.00000			−0.0340207
$865$	14.0000	−	28.0000i	0.476014	−	0.952029i
$866$	12.0000			0.407777
$867$		−	13.0000i		−	0.441503i
$868$		−	16.0000i		−	0.543075i
$869$	16.0000			0.542763
$870$	−8.00000	−	4.00000i	−0.271225	−	0.135613i
$871$	16.0000			0.542139
$872$		−	18.0000i		−	0.609557i
$873$		−	12.0000i		−	0.406138i
$874$		0			0
$875$	−22.0000	+	4.00000i	−0.743736	+	0.135225i
$876$	8.00000			0.270295
$877$			42.0000i			1.41824i	0.705088	+	0.709120i	$0.250907\pi$
$877$			42.0000i			1.41824i	−0.705088	+	0.709120i	$0.749093\pi$
$878$		−	32.0000i		−	1.07995i
$879$	−26.0000			−0.876958
$880$	4.00000	+	2.00000i	0.134840	+	0.0674200i
$881$	−10.0000			−0.336909			−0.168454	−	0.985709i	$-0.553878\pi$
$881$	−10.0000			−0.336909			−0.168454	+	0.985709i	$0.553878\pi$
$882$		−	3.00000i		−	0.101015i
$883$		−	24.0000i		−	0.807664i	−0.914833	−	0.403832i	$-0.867678\pi$
$883$		−	24.0000i		−	0.807664i	0.914833	−	0.403832i	$-0.132322\pi$
$884$	2.00000			0.0672673
$885$	−10.0000	+	20.0000i	−0.336146	+	0.672293i
$886$	4.00000			0.134383
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$		−	6.00000i		−	0.201347i
$889$	−12.0000			−0.402467
$890$	6.00000	−	12.0000i	0.201120	−	0.402241i
$891$	2.00000			0.0670025
$892$		−	14.0000i		−	0.468755i
$893$		−	32.0000i		−	1.07084i
$894$	−12.0000			−0.401340
$895$	36.0000	+	18.0000i	1.20335	+	0.601674i
$896$	2.00000			0.0668153
$897$		0			0
$898$		−	30.0000i		−	1.00111i
$899$	−32.0000			−1.06726
$900$	3.00000	+	4.00000i	0.100000	+	0.133333i
$901$	4.00000			0.133259
$902$		−	12.0000i		−	0.399556i
$903$		−	8.00000i		−	0.266223i
$904$	−6.00000			−0.199557
$905$	−12.0000	−	6.00000i	−0.398893	−	0.199447i
$906$	−16.0000			−0.531564
$907$		−	28.0000i		−	0.929725i	−0.885383	−	0.464862i	$-0.846104\pi$
$907$		−	28.0000i		−	0.929725i	0.885383	−	0.464862i	$-0.153896\pi$
$908$		−	12.0000i		−	0.398234i
$909$	−4.00000			−0.132672
$910$	2.00000	−	4.00000i	0.0662994	−	0.132599i
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$		−	4.00000i		−	0.132453i
$913$		−	24.0000i		−	0.794284i
$914$	28.0000			0.926158
$915$	−14.0000	+	28.0000i	−0.462826	+	0.925651i
$916$	−22.0000			−0.726900
$917$		−	12.0000i		−	0.396275i
$918$		−	2.00000i		−	0.0660098i
$919$	48.0000			1.58337			0.791687	−	0.610927i	$-0.209203\pi$
$919$	48.0000			1.58337			0.791687	+	0.610927i	$0.209203\pi$
$920$		0			0
$921$	−28.0000			−0.922631
$922$			20.0000i			0.658665i
$923$		−	4.00000i		−	0.131662i
$924$	−4.00000			−0.131590
$925$	−24.0000	+	18.0000i	−0.789115	+	0.591836i
$926$	6.00000			0.197172
$927$			6.00000i			0.197066i
$928$		−	4.00000i		−	0.131306i
$929$	50.0000			1.64045			0.820223	−	0.572043i	$-0.193849\pi$
$929$	50.0000			1.64045			0.820223	+	0.572043i	$0.193849\pi$
$930$	16.0000	+	8.00000i	0.524661	+	0.262330i
$931$	12.0000			0.393284
$932$		−	14.0000i		−	0.458585i
$933$		−	20.0000i		−	0.654771i
$934$	−28.0000			−0.916188
$935$	−4.00000	+	8.00000i	−0.130814	+	0.261628i
$936$	−1.00000			−0.0326860
$937$			56.0000i			1.82944i	0.404088	+	0.914720i	$0.367589\pi$
$937$			56.0000i			1.82944i	−0.404088	+	0.914720i	$0.632411\pi$
$938$			32.0000i			1.04484i
$939$	20.0000			0.652675
$940$	−8.00000	+	16.0000i	−0.260931	+	0.521862i
$941$	−44.0000			−1.43436			−0.717180	−	0.696888i	$-0.754567\pi$
$941$	−44.0000			−1.43436			−0.717180	+	0.696888i	$0.754567\pi$
$942$			10.0000i			0.325818i
$943$		0			0
$944$	−10.0000			−0.325472
$945$	−4.00000	−	2.00000i	−0.130120	−	0.0650600i
$946$	8.00000			0.260102
$947$		−	36.0000i		−	1.16984i	−0.811090	−	0.584921i	$-0.801125\pi$
$947$		−	36.0000i		−	1.16984i	0.811090	−	0.584921i	$-0.198875\pi$
$948$			8.00000i			0.259828i
$949$	8.00000			0.259691
$950$	−16.0000	+	12.0000i	−0.519109	+	0.389331i
$951$	−18.0000			−0.583690
$952$			4.00000i			0.129641i
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$	−2.00000			−0.0647524
$955$	−24.0000	−	12.0000i	−0.776622	−	0.388311i
$956$	−12.0000			−0.388108
$957$			8.00000i			0.258603i
$958$		−	36.0000i		−	1.16311i
$959$	28.0000			0.904167
$960$	−1.00000	+	2.00000i	−0.0322749	+	0.0645497i
$961$	33.0000			1.06452
$962$		−	6.00000i		−	0.193448i
$963$			4.00000i			0.128898i
$964$	18.0000			0.579741
$965$		0			0
$966$		0			0
$967$			58.0000i			1.86515i	0.360971	+	0.932577i	$0.382445\pi$
$967$			58.0000i			1.86515i	−0.360971	+	0.932577i	$0.617555\pi$
$968$			7.00000i			0.224989i
$969$	8.00000			0.256997
$970$	−24.0000	−	12.0000i	−0.770594	−	0.385297i
$971$	50.0000			1.60458			0.802288	−	0.596937i	$-0.203616\pi$
$971$	50.0000			1.60458			0.802288	+	0.596937i	$0.203616\pi$
$972$			1.00000i			0.0320750i
$973$		−	8.00000i		−	0.256468i
$974$	26.0000			0.833094
$975$	3.00000	+	4.00000i	0.0960769	+	0.128103i
$976$	−14.0000			−0.448129
$977$		−	18.0000i		−	0.575871i	−0.957650	−	0.287936i	$-0.907031\pi$
$977$		−	18.0000i		−	0.575871i	0.957650	−	0.287936i	$-0.0929689\pi$
$978$			8.00000i			0.255812i
$979$	−12.0000			−0.383522
$980$	−6.00000	−	3.00000i	−0.191663	−	0.0958315i
$981$	−18.0000			−0.574696
$982$		−	22.0000i		−	0.702048i
$983$		−	56.0000i		−	1.78612i	−0.449935	−	0.893061i	$-0.648553\pi$
$983$		−	56.0000i		−	1.78612i	0.449935	−	0.893061i	$-0.351447\pi$
$984$	6.00000			0.191273
$985$	−10.0000	+	20.0000i	−0.318626	+	0.637253i
$986$	8.00000			0.254772
$987$		−	16.0000i		−	0.509286i
$988$		−	4.00000i		−	0.127257i
$989$		0			0
$990$	2.00000	−	4.00000i	0.0635642	−	0.127128i
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$			8.00000i			0.254000i
$993$			12.0000i			0.380808i
$994$	8.00000			0.253745
$995$	48.0000	+	24.0000i	1.52170	+	0.760851i
$996$	12.0000			0.380235
$997$		−	14.0000i		−	0.443384i	−0.975117	−	0.221692i	$-0.928842\pi$
$997$		−	14.0000i		−	0.443384i	0.975117	−	0.221692i	$-0.0711580\pi$
$998$		−	36.0000i		−	1.13956i
$999$	−6.00000			−0.189832

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.e.c.79.1	✓	2	5.4	even	2	inner
390.2.e.c.79.2	yes	2	1.1	even	1	trivial
1170.2.e.a.469.1		2	3.2	odd	2
1170.2.e.a.469.2		2	15.14	odd	2
1950.2.a.c.1.1		1	5.2	odd	4
1950.2.a.z.1.1		1	5.3	odd	4
3120.2.l.g.1249.1		2	20.19	odd	2
3120.2.l.g.1249.2		2	4.3	odd	2
5850.2.a.t.1.1		1	15.8	even	4
5850.2.a.bj.1.1		1	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +2.00000 q^{11} +1.00000i q^{12} +1.00000i q^{13} -2.00000 q^{14} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -1.00000i q^{18} +4.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} +2.00000 q^{21} +2.00000i q^{22} -1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000 q^{26} +1.00000i q^{27} -2.00000i q^{28} -4.00000 q^{29} +(2.00000 + 1.00000i) q^{30} +8.00000 q^{31} +1.00000i q^{32} -2.00000i q^{33} -2.00000 q^{34} +(-2.00000 + 4.00000i) q^{35} +1.00000 q^{36} +6.00000i q^{37} +4.00000i q^{38} +1.00000 q^{39} +(1.00000 - 2.00000i) q^{40} -6.00000 q^{41} +2.00000i q^{42} -4.00000i q^{43} -2.00000 q^{44} +(-2.00000 - 1.00000i) q^{45} -8.00000i q^{47} -1.00000i q^{48} +3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +2.00000 q^{51} -1.00000i q^{52} -2.00000i q^{53} -1.00000 q^{54} +(4.00000 + 2.00000i) q^{55} +2.00000 q^{56} -4.00000i q^{57} -4.00000i q^{58} -10.0000 q^{59} +(-1.00000 + 2.00000i) q^{60} -14.0000 q^{61} +8.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(-1.00000 + 2.00000i) q^{65} +2.00000 q^{66} -16.0000i q^{67} -2.00000i q^{68} +(-4.00000 - 2.00000i) q^{70} -4.00000 q^{71} +1.00000i q^{72} -8.00000i q^{73} -6.00000 q^{74} +(4.00000 - 3.00000i) q^{75} -4.00000 q^{76} +4.00000i q^{77} +1.00000i q^{78} +8.00000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -6.00000i q^{82} -12.0000i q^{83} -2.00000 q^{84} +(-2.00000 + 4.00000i) q^{85} +4.00000 q^{86} +4.00000i q^{87} -2.00000i q^{88} -6.00000 q^{89} +(1.00000 - 2.00000i) q^{90} -2.00000 q^{91} -8.00000i q^{93} +8.00000 q^{94} +(8.00000 + 4.00000i) q^{95} +1.00000 q^{96} +12.0000i q^{97} +3.00000i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{14} + 2 q^{15} + 2 q^{16} + 8 q^{19} - 4 q^{20} + 4 q^{21} - 2 q^{24} + 6 q^{25} - 2 q^{26} - 8 q^{29} + 4 q^{30} + 16 q^{31} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 2 q^{39} + 2 q^{40} - 12 q^{41} - 4 q^{44} - 4 q^{45} + 6 q^{49} - 8 q^{50} + 4 q^{51} - 2 q^{54} + 8 q^{55} + 4 q^{56} - 20 q^{59} - 2 q^{60} - 28 q^{61} - 2 q^{64} - 2 q^{65} + 4 q^{66} - 8 q^{70} - 8 q^{71} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 16 q^{79} + 4 q^{80} + 2 q^{81} - 4 q^{84} - 4 q^{85} + 8 q^{86} - 12 q^{89} + 2 q^{90} - 4 q^{91} + 16 q^{94} + 16 q^{95} + 2 q^{96} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^14 + 2 * q^15 + 2 * q^16 + 8 * q^19 - 4 * q^20 + 4 * q^21 - 2 * q^24 + 6 * q^25 - 2 * q^26 - 8 * q^29 + 4 * q^30 + 16 * q^31 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 2 * q^39 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 4 * q^45 + 6 * q^49 - 8 * q^50 + 4 * q^51 - 2 * q^54 + 8 * q^55 + 4 * q^56 - 20 * q^59 - 2 * q^60 - 28 * q^61 - 2 * q^64 - 2 * q^65 + 4 * q^66 - 8 * q^70 - 8 * q^71 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 16 * q^79 + 4 * q^80 + 2 * q^81 - 4 * q^84 - 4 * q^85 + 8 * q^86 - 12 * q^89 + 2 * q^90 - 4 * q^91 + 16 * q^94 + 16 * q^95 + 2 * q^96 - 4 * q^99

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