LMFDB - Embedded newform 1110.2.d.a.889.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(889,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, 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("1110.889");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
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			889.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1110.889
Dual form			1110.2.d.a.889.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} +1.00000i q^{12} -2.00000i q^{13} -2.00000 q^{14} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -1.00000i q^{18} +2.00000 q^{19} +(2.00000 + 1.00000i) q^{20} +2.00000 q^{21} +4.00000i q^{23} -1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{27} -2.00000i q^{28} +(-2.00000 - 1.00000i) q^{30} +8.00000 q^{31} +1.00000i q^{32} -2.00000 q^{34} +(2.00000 - 4.00000i) q^{35} +1.00000 q^{36} -1.00000i q^{37} +2.00000i q^{38} -2.00000 q^{39} +(-1.00000 + 2.00000i) q^{40} +6.00000 q^{41} +2.00000i q^{42} +4.00000i q^{43} +(2.00000 + 1.00000i) q^{45} -4.00000 q^{46} +10.0000i q^{47} -1.00000i q^{48} +3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +2.00000 q^{51} +2.00000i q^{52} -2.00000i q^{53} -1.00000 q^{54} +2.00000 q^{56} -2.00000i q^{57} -6.00000 q^{59} +(1.00000 - 2.00000i) q^{60} +8.00000 q^{61} +8.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(-2.00000 + 4.00000i) q^{65} +4.00000i q^{67} -2.00000i q^{68} +4.00000 q^{69} +(4.00000 + 2.00000i) q^{70} +8.00000 q^{71} +1.00000i q^{72} +8.00000i q^{73} +1.00000 q^{74} +(4.00000 - 3.00000i) q^{75} -2.00000 q^{76} -2.00000i q^{78} +16.0000 q^{79} +(-2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +6.00000i q^{82} -2.00000 q^{84} +(2.00000 - 4.00000i) q^{85} -4.00000 q^{86} -6.00000 q^{89} +(-1.00000 + 2.00000i) q^{90} +4.00000 q^{91} -4.00000i q^{92} -8.00000i q^{93} -10.0000 q^{94} +(-4.00000 - 2.00000i) q^{95} +1.00000 q^{96} +14.0000i q^{97} +3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{14} - 2 q^{15} + 2 q^{16} + 4 q^{19} + 4 q^{20} + 4 q^{21} - 2 q^{24} + 6 q^{25} + 4 q^{26} - 4 q^{30} + 16 q^{31} - 4 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{39} - 2 q^{40} + 12 q^{41} + 4 q^{45} - 8 q^{46} + 6 q^{49} - 8 q^{50} + 4 q^{51} - 2 q^{54} + 4 q^{56} - 12 q^{59} + 2 q^{60} + 16 q^{61} - 2 q^{64} - 4 q^{65} + 8 q^{69} + 8 q^{70} + 16 q^{71} + 2 q^{74} + 8 q^{75} - 4 q^{76} + 32 q^{79} - 4 q^{80} + 2 q^{81} - 4 q^{84} + 4 q^{85} - 8 q^{86} - 12 q^{89} - 2 q^{90} + 8 q^{91} - 20 q^{94} - 8 q^{95} + 2 q^{96}+O(q^{100}) $ 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^9 + 2 * q^10 - 4 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^19 + 4 * q^20 + 4 * q^21 - 2 * q^24 + 6 * q^25 + 4 * q^26 - 4 * q^30 + 16 * q^31 - 4 * q^34 + 4 * q^35 + 2 * q^36 - 4 * q^39 - 2 * q^40 + 12 * q^41 + 4 * q^45 - 8 * q^46 + 6 * q^49 - 8 * q^50 + 4 * q^51 - 2 * q^54 + 4 * q^56 - 12 * q^59 + 2 * q^60 + 16 * q^61 - 2 * q^64 - 4 * q^65 + 8 * q^69 + 8 * q^70 + 16 * q^71 + 2 * q^74 + 8 * q^75 - 4 * q^76 + 32 * q^79 - 4 * q^80 + 2 * q^81 - 4 * q^84 + 4 * q^85 - 8 * q^86 - 12 * q^89 - 2 * q^90 + 8 * q^91 - 20 * q^94 - 8 * q^95 + 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$			1.00000i			0.288675i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−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
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$	2.00000			0.436436
$22$		0			0
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	−1.00000			−0.204124
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	2.00000			0.392232
$27$			1.00000i			0.192450i
$28$		−	2.00000i		−	0.377964i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−2.00000	−	1.00000i	−0.365148	−	0.182574i
$31$	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
$33$		0			0
$34$	−2.00000			−0.342997
$35$	2.00000	−	4.00000i	0.338062	−	0.676123i
$36$	1.00000			0.166667
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$			2.00000i			0.324443i
$39$	−2.00000			−0.320256
$40$	−1.00000	+	2.00000i	−0.158114	+	0.316228i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$			2.00000i			0.308607i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$		0			0
$45$	2.00000	+	1.00000i	0.298142	+	0.149071i
$46$	−4.00000			−0.589768
$47$			10.0000i			1.45865i	0.684167	+	0.729325i	$0.260166\pi$
$47$			10.0000i			1.45865i	−0.684167	+	0.729325i	$0.739834\pi$
$48$		−	1.00000i		−	0.144338i
$49$	3.00000			0.428571
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	2.00000			0.280056
$52$			2.00000i			0.277350i
$53$		−	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
$55$		0			0
$56$	2.00000			0.267261
$57$		−	2.00000i		−	0.264906i
$58$		0			0
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$	1.00000	−	2.00000i	0.129099	−	0.258199i
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$			8.00000i			1.01600i
$63$		−	2.00000i		−	0.251976i
$64$	−1.00000			−0.125000
$65$	−2.00000	+	4.00000i	−0.248069	+	0.496139i
$66$		0			0
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$		−	2.00000i		−	0.242536i
$69$	4.00000			0.481543
$70$	4.00000	+	2.00000i	0.478091	+	0.239046i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$			1.00000i			0.117851i
$73$			8.00000i			0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$73$			8.00000i			0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$74$	1.00000			0.116248
$75$	4.00000	−	3.00000i	0.461880	−	0.346410i
$76$	−2.00000			−0.229416
$77$		0			0
$78$		−	2.00000i		−	0.226455i
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$	1.00000			0.111111
$82$			6.00000i			0.662589i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	−2.00000			−0.218218
$85$	2.00000	−	4.00000i	0.216930	−	0.433861i
$86$	−4.00000			−0.431331
$87$		0			0
$88$		0			0
$89$	−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
$91$	4.00000			0.419314
$92$		−	4.00000i		−	0.417029i
$93$		−	8.00000i		−	0.829561i
$94$	−10.0000			−1.03142
$95$	−4.00000	−	2.00000i	−0.410391	−	0.205196i
$96$	1.00000			0.102062
$97$			14.0000i			1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$			14.0000i			1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$			3.00000i			0.303046i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$			2.00000i			0.198030i
$103$			8.00000i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$			8.00000i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$	−2.00000			−0.196116
$105$	−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
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$		0			0
$111$	−1.00000			−0.0949158
$112$			2.00000i			0.188982i
$113$		−	10.0000i		−	0.940721i	−0.882474	−	0.470360i	$-0.844124\pi$
$113$		−	10.0000i		−	0.940721i	0.882474	−	0.470360i	$-0.155876\pi$
$114$	2.00000			0.187317
$115$	4.00000	−	8.00000i	0.373002	−	0.746004i
$116$		0			0
$117$			2.00000i			0.184900i
$118$		−	6.00000i		−	0.552345i
$119$	−4.00000			−0.366679
$120$	2.00000	+	1.00000i	0.182574	+	0.0912871i
$121$	−11.0000			−1.00000
$122$			8.00000i			0.724286i
$123$		−	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	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.00000			0.352180
$130$	−4.00000	−	2.00000i	−0.350823	−	0.175412i
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$		0			0
$133$			4.00000i			0.346844i
$134$	−4.00000			−0.345547
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	2.00000			0.171499
$137$		−	8.00000i		−	0.683486i	−0.939793	−	0.341743i	$-0.888983\pi$
$137$		−	8.00000i		−	0.683486i	0.939793	−	0.341743i	$-0.111017\pi$
$138$			4.00000i			0.340503i
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$	−2.00000	+	4.00000i	−0.169031	+	0.338062i
$141$	10.0000			0.842152
$142$			8.00000i			0.671345i
$143$		0			0
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−8.00000			−0.662085
$147$		−	3.00000i		−	0.247436i
$148$			1.00000i			0.0821995i
$149$	−14.0000			−1.14692			−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000			−1.14692			−0.573462	+	0.819232i	$0.694400\pi$
$150$	3.00000	+	4.00000i	0.244949	+	0.326599i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		−	2.00000i		−	0.162221i
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	−16.0000	−	8.00000i	−1.28515	−	0.642575i
$156$	2.00000			0.160128
$157$			6.00000i			0.478852i	0.970915	+	0.239426i	$0.0769593\pi$
$157$			6.00000i			0.478852i	−0.970915	+	0.239426i	$0.923041\pi$
$158$			16.0000i			1.27289i
$159$	−2.00000			−0.158610
$160$	1.00000	−	2.00000i	0.0790569	−	0.158114i
$161$	−8.00000			−0.630488
$162$			1.00000i			0.0785674i
$163$		−	20.0000i		−	1.56652i	−0.621694	−	0.783260i	$-0.713555\pi$
$163$		−	20.0000i		−	1.56652i	0.621694	−	0.783260i	$-0.286445\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$		0			0
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		−	2.00000i		−	0.154303i
$169$	9.00000			0.692308
$170$	4.00000	+	2.00000i	0.306786	+	0.153393i
$171$	−2.00000			−0.152944
$172$		−	4.00000i		−	0.304997i
$173$			14.0000i			1.06440i	0.846619	+	0.532200i	$0.178635\pi$
$173$			14.0000i			1.06440i	−0.846619	+	0.532200i	$0.821365\pi$
$174$		0			0
$175$	−8.00000	+	6.00000i	−0.604743	+	0.453557i
$176$		0			0
$177$			6.00000i			0.450988i
$178$		−	6.00000i		−	0.449719i
$179$	−6.00000			−0.448461			−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000			−0.448461			−0.224231	+	0.974536i	$0.571987\pi$
$180$	−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	$0.571581\pi$
$182$			4.00000i			0.296500i
$183$		−	8.00000i		−	0.591377i
$184$	4.00000			0.294884
$185$	−1.00000	+	2.00000i	−0.0735215	+	0.147043i
$186$	8.00000			0.586588
$187$		0			0
$188$		−	10.0000i		−	0.729325i
$189$	−2.00000			−0.145479
$190$	2.00000	−	4.00000i	0.145095	−	0.290191i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$			1.00000i			0.0721688i
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	−14.0000			−1.00514
$195$	4.00000	+	2.00000i	0.286446	+	0.143223i
$196$	−3.00000			−0.214286
$197$		−	10.0000i		−	0.712470i	−0.934396	−	0.356235i	$-0.884060\pi$
$197$		−	10.0000i		−	0.712470i	0.934396	−	0.356235i	$-0.115940\pi$
$198$		0			0
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$	4.00000			0.282138
$202$		−	10.0000i		−	0.703598i
$203$		0			0
$204$	−2.00000			−0.140028
$205$	−12.0000	−	6.00000i	−0.838116	−	0.419058i
$206$	−8.00000			−0.557386
$207$		−	4.00000i		−	0.278019i
$208$		−	2.00000i		−	0.138675i
$209$		0			0
$210$	2.00000	−	4.00000i	0.138013	−	0.276026i
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$			2.00000i			0.137361i
$213$		−	8.00000i		−	0.548151i
$214$	4.00000			0.273434
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$	1.00000			0.0680414
$217$			16.0000i			1.08615i
$218$			12.0000i			0.812743i
$219$	8.00000			0.540590
$220$		0			0
$221$	4.00000			0.269069
$222$		−	1.00000i		−	0.0671156i
$223$		−	26.0000i		−	1.74109i	−0.492090	−	0.870544i	$-0.663767\pi$
$223$		−	26.0000i		−	1.74109i	0.492090	−	0.870544i	$-0.336233\pi$
$224$	−2.00000			−0.133631
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	10.0000			0.665190
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$			2.00000i			0.132453i
$229$	−2.00000			−0.132164			−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000			−0.132164			−0.0660819	+	0.997814i	$0.521050\pi$
$230$	8.00000	+	4.00000i	0.527504	+	0.263752i
$231$		0			0
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$	−2.00000			−0.130744
$235$	10.0000	−	20.0000i	0.652328	−	1.30466i
$236$	6.00000			0.390567
$237$		−	16.0000i		−	1.03931i
$238$		−	4.00000i		−	0.259281i
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$	−1.00000	+	2.00000i	−0.0645497	+	0.129099i
$241$	−22.0000			−1.41714			−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000			−1.41714			−0.708572	+	0.705638i	$0.750660\pi$
$242$		−	11.0000i		−	0.707107i
$243$		−	1.00000i		−	0.0641500i
$244$	−8.00000			−0.512148
$245$	−6.00000	−	3.00000i	−0.383326	−	0.191663i
$246$	6.00000			0.382546
$247$		−	4.00000i		−	0.254514i
$248$		−	8.00000i		−	0.508001i
$249$		0			0
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$	30.0000			1.89358			0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$			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
$257$			26.0000i			1.62184i	0.585160	+	0.810918i	$0.301032\pi$
$257$			26.0000i			1.62184i	−0.585160	+	0.810918i	$0.698968\pi$
$258$			4.00000i			0.249029i
$259$	2.00000			0.124274
$260$	2.00000	−	4.00000i	0.124035	−	0.248069i
$261$		0			0
$262$		−	6.00000i		−	0.370681i
$263$			6.00000i			0.369976i	0.982741	+	0.184988i	$0.0592246\pi$
$263$			6.00000i			0.369976i	−0.982741	+	0.184988i	$0.940775\pi$
$264$		0			0
$265$	−2.00000	+	4.00000i	−0.122859	+	0.245718i
$266$	−4.00000			−0.245256
$267$			6.00000i			0.367194i
$268$		−	4.00000i		−	0.244339i
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$	2.00000	+	1.00000i	0.121716	+	0.0608581i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$			2.00000i			0.121268i
$273$		−	4.00000i		−	0.242091i
$274$	8.00000			0.483298
$275$		0			0
$276$	−4.00000			−0.240772
$277$			14.0000i			0.841178i	0.907251	+	0.420589i	$0.138177\pi$
$277$			14.0000i			0.841178i	−0.907251	+	0.420589i	$0.861823\pi$
$278$		−	12.0000i		−	0.719712i
$279$	−8.00000			−0.478947
$280$	−4.00000	−	2.00000i	−0.239046	−	0.119523i
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$			10.0000i			0.595491i
$283$		−	12.0000i		−	0.713326i	−0.934233	−	0.356663i	$-0.883914\pi$
$283$		−	12.0000i		−	0.713326i	0.934233	−	0.356663i	$-0.116086\pi$
$284$	−8.00000			−0.474713
$285$	−2.00000	+	4.00000i	−0.118470	+	0.236940i
$286$		0			0
$287$			12.0000i			0.708338i
$288$		−	1.00000i		−	0.0589256i
$289$	13.0000			0.764706
$290$		0			0
$291$	14.0000			0.820695
$292$		−	8.00000i		−	0.468165i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	3.00000			0.174964
$295$	12.0000	+	6.00000i	0.698667	+	0.349334i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$		−	14.0000i		−	0.810998i
$299$	8.00000			0.462652
$300$	−4.00000	+	3.00000i	−0.230940	+	0.173205i
$301$	−8.00000			−0.461112
$302$		0			0
$303$			10.0000i			0.574485i
$304$	2.00000			0.114708
$305$	−16.0000	−	8.00000i	−0.916157	−	0.458079i
$306$	2.00000			0.114332
$307$		−	16.0000i		−	0.913168i	−0.889680	−	0.456584i	$-0.849073\pi$
$307$		−	16.0000i		−	0.913168i	0.889680	−	0.456584i	$-0.150927\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$	8.00000	−	16.0000i	0.454369	−	0.908739i
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$			2.00000i			0.113228i
$313$		−	10.0000i		−	0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$		−	10.0000i		−	0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$	−6.00000			−0.338600
$315$	−2.00000	+	4.00000i	−0.112687	+	0.225374i
$316$	−16.0000			−0.900070
$317$			26.0000i			1.46031i	0.683284	+	0.730153i	$0.260551\pi$
$317$			26.0000i			1.46031i	−0.683284	+	0.730153i	$0.739449\pi$
$318$		−	2.00000i		−	0.112154i
$319$		0			0
$320$	2.00000	+	1.00000i	0.111803	+	0.0559017i
$321$	−4.00000			−0.223258
$322$		−	8.00000i		−	0.445823i
$323$			4.00000i			0.222566i
$324$	−1.00000			−0.0555556
$325$	8.00000	−	6.00000i	0.443760	−	0.332820i
$326$	20.0000			1.10770
$327$		−	12.0000i		−	0.663602i
$328$		−	6.00000i		−	0.331295i
$329$	−20.0000			−1.10264
$330$		0			0
$331$	10.0000			0.549650			0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000			0.549650			0.274825	+	0.961494i	$0.411380\pi$
$332$		0			0
$333$			1.00000i			0.0547997i
$334$		0			0
$335$	4.00000	−	8.00000i	0.218543	−	0.437087i
$336$	2.00000			0.109109
$337$		−	8.00000i		−	0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$		−	8.00000i		−	0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$			9.00000i			0.489535i
$339$	−10.0000			−0.543125
$340$	−2.00000	+	4.00000i	−0.108465	+	0.216930i
$341$		0			0
$342$		−	2.00000i		−	0.108148i
$343$			20.0000i			1.07990i
$344$	4.00000			0.215666
$345$	−8.00000	−	4.00000i	−0.430706	−	0.215353i
$346$	−14.0000			−0.752645
$347$		−	28.0000i		−	1.50312i	−0.659665	−	0.751559i	$-0.729302\pi$
$347$		−	28.0000i		−	1.50312i	0.659665	−	0.751559i	$-0.270698\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	−6.00000	−	8.00000i	−0.320713	−	0.427618i
$351$	2.00000			0.106752
$352$		0			0
$353$			2.00000i			0.106449i	0.998583	+	0.0532246i	$0.0169499\pi$
$353$			2.00000i			0.106449i	−0.998583	+	0.0532246i	$0.983050\pi$
$354$	−6.00000			−0.318896
$355$	−16.0000	−	8.00000i	−0.849192	−	0.424596i
$356$	6.00000			0.317999
$357$			4.00000i			0.211702i
$358$		−	6.00000i		−	0.317110i
$359$	16.0000			0.844448			0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000			0.844448			0.422224	+	0.906492i	$0.361250\pi$
$360$	1.00000	−	2.00000i	0.0527046	−	0.105409i
$361$	−15.0000			−0.789474
$362$		−	6.00000i		−	0.315353i
$363$			11.0000i			0.577350i
$364$	−4.00000			−0.209657
$365$	8.00000	−	16.0000i	0.418739	−	0.837478i
$366$	8.00000			0.418167
$367$		−	22.0000i		−	1.14839i	−0.818718	−	0.574195i	$-0.805315\pi$
$367$		−	22.0000i		−	1.14839i	0.818718	−	0.574195i	$-0.194685\pi$
$368$			4.00000i			0.208514i
$369$	−6.00000			−0.312348
$370$	−2.00000	−	1.00000i	−0.103975	−	0.0519875i
$371$	4.00000			0.207670
$372$			8.00000i			0.414781i
$373$			2.00000i			0.103556i	0.998659	+	0.0517780i	$0.0164888\pi$
$373$			2.00000i			0.103556i	−0.998659	+	0.0517780i	$0.983511\pi$
$374$		0			0
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$	10.0000			0.515711
$377$		0			0
$378$		−	2.00000i		−	0.102869i
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$	4.00000	+	2.00000i	0.205196	+	0.102598i
$381$	−6.00000			−0.307389
$382$			8.00000i			0.409316i
$383$			4.00000i			0.204390i	0.994764	+	0.102195i	$0.0325866\pi$
$383$			4.00000i			0.204390i	−0.994764	+	0.102195i	$0.967413\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−14.0000			−0.712581
$387$		−	4.00000i		−	0.203331i
$388$		−	14.0000i		−	0.710742i
$389$	16.0000			0.811232			0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000			0.811232			0.405616	+	0.914044i	$0.367057\pi$
$390$	−2.00000	+	4.00000i	−0.101274	+	0.202548i
$391$	−8.00000			−0.404577
$392$		−	3.00000i		−	0.151523i
$393$			6.00000i			0.302660i
$394$	10.0000			0.503793
$395$	−32.0000	−	16.0000i	−1.61009	−	0.805047i
$396$		0			0
$397$			34.0000i			1.70641i	0.521575	+	0.853206i	$0.325345\pi$
$397$			34.0000i			1.70641i	−0.521575	+	0.853206i	$0.674655\pi$
$398$			16.0000i			0.802008i
$399$	4.00000			0.200250
$400$	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	$0.648376\pi$
$402$			4.00000i			0.199502i
$403$		−	16.0000i		−	0.797017i
$404$	10.0000			0.497519
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$		0			0
$407$		0			0
$408$		−	2.00000i		−	0.0990148i
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$	6.00000	−	12.0000i	0.296319	−	0.592638i
$411$	−8.00000			−0.394611
$412$		−	8.00000i		−	0.394132i
$413$		−	12.0000i		−	0.590481i
$414$	4.00000			0.196589
$415$		0			0
$416$	2.00000			0.0980581
$417$			12.0000i			0.587643i
$418$		0			0
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$	4.00000	+	2.00000i	0.195180	+	0.0975900i
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$		−	8.00000i		−	0.389434i
$423$		−	10.0000i		−	0.486217i
$424$	−2.00000			−0.0971286
$425$	−8.00000	+	6.00000i	−0.388057	+	0.291043i
$426$	8.00000			0.387601
$427$			16.0000i			0.774294i
$428$			4.00000i			0.193347i
$429$		0			0
$430$	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
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	−16.0000			−0.768025
$435$		0			0
$436$	−12.0000			−0.574696
$437$			8.00000i			0.382692i
$438$			8.00000i			0.382255i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$			4.00000i			0.190261i
$443$			12.0000i			0.570137i	0.958507	+	0.285069i	$0.0920164\pi$
$443$			12.0000i			0.570137i	−0.958507	+	0.285069i	$0.907984\pi$
$444$	1.00000			0.0474579
$445$	12.0000	+	6.00000i	0.568855	+	0.284427i
$446$	26.0000			1.23114
$447$			14.0000i			0.662177i
$448$		−	2.00000i		−	0.0944911i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$		0			0
$452$			10.0000i			0.470360i
$453$		0			0
$454$	−12.0000			−0.563188
$455$	−8.00000	−	4.00000i	−0.375046	−	0.187523i
$456$	−2.00000			−0.0936586
$457$			14.0000i			0.654892i	0.944870	+	0.327446i	$0.106188\pi$
$457$			14.0000i			0.654892i	−0.944870	+	0.327446i	$0.893812\pi$
$458$		−	2.00000i		−	0.0934539i
$459$	−2.00000			−0.0933520
$460$	−4.00000	+	8.00000i	−0.186501	+	0.373002i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$			4.00000i			0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$			4.00000i			0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$		0			0
$465$	−8.00000	+	16.0000i	−0.370991	+	0.741982i
$466$		0			0
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$		−	2.00000i		−	0.0924500i
$469$	−8.00000			−0.369406
$470$	20.0000	+	10.0000i	0.922531	+	0.461266i
$471$	6.00000			0.276465
$472$			6.00000i			0.276172i
$473$		0			0
$474$	16.0000			0.734904
$475$	6.00000	+	8.00000i	0.275299	+	0.367065i
$476$	4.00000			0.183340
$477$			2.00000i			0.0915737i
$478$			8.00000i			0.365911i
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$	−2.00000	−	1.00000i	−0.0912871	−	0.0456435i
$481$	−2.00000			−0.0911922
$482$		−	22.0000i		−	1.00207i
$483$			8.00000i			0.364013i
$484$	11.0000			0.500000
$485$	14.0000	−	28.0000i	0.635707	−	1.27141i
$486$	1.00000			0.0453609
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		−	8.00000i		−	0.362143i
$489$	−20.0000			−0.904431
$490$	3.00000	−	6.00000i	0.135526	−	0.271052i
$491$	8.00000			0.361035			0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000			0.361035			0.180517	+	0.983572i	$0.442223\pi$
$492$			6.00000i			0.270501i
$493$		0			0
$494$	4.00000			0.179969
$495$		0			0
$496$	8.00000			0.359211
$497$			16.0000i			0.717698i
$498$		0			0
$499$	6.00000			0.268597			0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000			0.268597			0.134298	+	0.990941i	$0.457122\pi$
$500$	2.00000	+	11.0000i	0.0894427	+	0.491935i
$501$		0			0
$502$			30.0000i			1.33897i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$	−2.00000			−0.0890871
$505$	20.0000	+	10.0000i	0.889988	+	0.444994i
$506$		0			0
$507$		−	9.00000i		−	0.399704i
$508$			6.00000i			0.266207i
$509$	10.0000			0.443242			0.221621	−	0.975133i	$-0.428865\pi$
$509$	10.0000			0.443242			0.221621	+	0.975133i	$0.428865\pi$
$510$	2.00000	−	4.00000i	0.0885615	−	0.177123i
$511$	−16.0000			−0.707798
$512$			1.00000i			0.0441942i
$513$			2.00000i			0.0883022i
$514$	−26.0000			−1.14681
$515$	8.00000	−	16.0000i	0.352522	−	0.705044i
$516$	−4.00000			−0.176090
$517$		0			0
$518$			2.00000i			0.0878750i
$519$	14.0000			0.614532
$520$	4.00000	+	2.00000i	0.175412	+	0.0877058i
$521$	−22.0000			−0.963837			−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000			−0.963837			−0.481919	+	0.876216i	$0.660060\pi$
$522$		0			0
$523$			36.0000i			1.57417i	0.616844	+	0.787085i	$0.288411\pi$
$523$			36.0000i			1.57417i	−0.616844	+	0.787085i	$0.711589\pi$
$524$	6.00000			0.262111
$525$	6.00000	+	8.00000i	0.261861	+	0.349149i
$526$	−6.00000			−0.261612
$527$			16.0000i			0.696971i
$528$		0			0
$529$	7.00000			0.304348
$530$	−4.00000	−	2.00000i	−0.173749	−	0.0868744i
$531$	6.00000			0.260378
$532$		−	4.00000i		−	0.173422i
$533$		−	12.0000i		−	0.519778i
$534$	−6.00000			−0.259645
$535$	−4.00000	+	8.00000i	−0.172935	+	0.345870i
$536$	4.00000			0.172774
$537$			6.00000i			0.258919i
$538$		−	6.00000i		−	0.258678i
$539$		0			0
$540$	−1.00000	+	2.00000i	−0.0430331	+	0.0860663i
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$		0			0
$543$			6.00000i			0.257485i
$544$	−2.00000			−0.0857493
$545$	−24.0000	−	12.0000i	−1.02805	−	0.514024i
$546$	4.00000			0.171184
$547$			12.0000i			0.513083i	0.966533	+	0.256541i	$0.0825830\pi$
$547$			12.0000i			0.513083i	−0.966533	+	0.256541i	$0.917417\pi$
$548$			8.00000i			0.341743i
$549$	−8.00000			−0.341432
$550$		0			0
$551$		0			0
$552$		−	4.00000i		−	0.170251i
$553$			32.0000i			1.36078i
$554$	−14.0000			−0.594803
$555$	2.00000	+	1.00000i	0.0848953	+	0.0424476i
$556$	12.0000			0.508913
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$		−	8.00000i		−	0.338667i
$559$	8.00000			0.338364
$560$	2.00000	−	4.00000i	0.0845154	−	0.169031i
$561$		0			0
$562$		−	10.0000i		−	0.421825i
$563$			12.0000i			0.505740i	0.967500	+	0.252870i	$0.0813744\pi$
$563$			12.0000i			0.505740i	−0.967500	+	0.252870i	$0.918626\pi$
$564$	−10.0000			−0.421076
$565$	−10.0000	+	20.0000i	−0.420703	+	0.841406i
$566$	12.0000			0.504398
$567$			2.00000i			0.0839921i
$568$		−	8.00000i		−	0.335673i
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$	−4.00000	−	2.00000i	−0.167542	−	0.0837708i
$571$	−28.0000			−1.17176			−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000			−1.17176			−0.585882	+	0.810397i	$0.699252\pi$
$572$		0			0
$573$		−	8.00000i		−	0.334205i
$574$	−12.0000			−0.500870
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$	1.00000			0.0416667
$577$			10.0000i			0.416305i	0.978096	+	0.208153i	$0.0667451\pi$
$577$			10.0000i			0.416305i	−0.978096	+	0.208153i	$0.933255\pi$
$578$			13.0000i			0.540729i
$579$	14.0000			0.581820
$580$		0			0
$581$		0			0
$582$			14.0000i			0.580319i
$583$		0			0
$584$	8.00000			0.331042
$585$	2.00000	−	4.00000i	0.0826898	−	0.165380i
$586$	6.00000			0.247858
$587$		−	4.00000i		−	0.165098i	−0.996587	−	0.0825488i	$-0.973694\pi$
$587$		−	4.00000i		−	0.165098i	0.996587	−	0.0825488i	$-0.0263060\pi$
$588$			3.00000i			0.123718i
$589$	16.0000			0.659269
$590$	−6.00000	+	12.0000i	−0.247016	+	0.494032i
$591$	−10.0000			−0.411345
$592$		−	1.00000i		−	0.0410997i
$593$			16.0000i			0.657041i	0.944497	+	0.328521i	$0.106550\pi$
$593$			16.0000i			0.657041i	−0.944497	+	0.328521i	$0.893450\pi$
$594$		0			0
$595$	8.00000	+	4.00000i	0.327968	+	0.163984i
$596$	14.0000			0.573462
$597$		−	16.0000i		−	0.654836i
$598$			8.00000i			0.327144i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$	−3.00000	−	4.00000i	−0.122474	−	0.163299i
$601$	−42.0000			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$602$		−	8.00000i		−	0.326056i
$603$		−	4.00000i		−	0.162893i
$604$		0			0
$605$	22.0000	+	11.0000i	0.894427	+	0.447214i
$606$	−10.0000			−0.406222
$607$			44.0000i			1.78590i	0.450151	+	0.892952i	$0.351370\pi$
$607$			44.0000i			1.78590i	−0.450151	+	0.892952i	$0.648630\pi$
$608$			2.00000i			0.0811107i
$609$		0			0
$610$	8.00000	−	16.0000i	0.323911	−	0.647821i
$611$	20.0000			0.809113
$612$			2.00000i			0.0808452i
$613$		−	2.00000i		−	0.0807792i	−0.999184	−	0.0403896i	$-0.987140\pi$
$613$		−	2.00000i		−	0.0807792i	0.999184	−	0.0403896i	$-0.0128599\pi$
$614$	16.0000			0.645707
$615$	−6.00000	+	12.0000i	−0.241943	+	0.483887i
$616$		0			0
$617$			4.00000i			0.161034i	0.996753	+	0.0805170i	$0.0256571\pi$
$617$			4.00000i			0.161034i	−0.996753	+	0.0805170i	$0.974343\pi$
$618$			8.00000i			0.321807i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$	16.0000	+	8.00000i	0.642575	+	0.321288i
$621$	−4.00000			−0.160514
$622$		−	4.00000i		−	0.160385i
$623$		−	12.0000i		−	0.480770i
$624$	−2.00000			−0.0800641
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	10.0000			0.399680
$627$		0			0
$628$		−	6.00000i		−	0.239426i
$629$	2.00000			0.0797452
$630$	−4.00000	−	2.00000i	−0.159364	−	0.0796819i
$631$	−12.0000			−0.477712			−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000			−0.477712			−0.238856	+	0.971055i	$0.576772\pi$
$632$		−	16.0000i		−	0.636446i
$633$			8.00000i			0.317971i
$634$	−26.0000			−1.03259
$635$	−6.00000	+	12.0000i	−0.238103	+	0.476205i
$636$	2.00000			0.0793052
$637$		−	6.00000i		−	0.237729i
$638$		0			0
$639$	−8.00000			−0.316475
$640$	−1.00000	+	2.00000i	−0.0395285	+	0.0790569i
$641$	−34.0000			−1.34292			−0.671460	−	0.741041i	$-0.734332\pi$
$641$	−34.0000			−1.34292			−0.671460	+	0.741041i	$0.734332\pi$
$642$		−	4.00000i		−	0.157867i
$643$		−	28.0000i		−	1.10421i	−0.833774	−	0.552106i	$-0.813824\pi$
$643$		−	28.0000i		−	1.10421i	0.833774	−	0.552106i	$-0.186176\pi$
$644$	8.00000			0.315244
$645$	−8.00000	−	4.00000i	−0.315000	−	0.157500i
$646$	−4.00000			−0.157378
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		−	1.00000i		−	0.0392837i
$649$		0			0
$650$	6.00000	+	8.00000i	0.235339	+	0.313786i
$651$	16.0000			0.627089
$652$			20.0000i			0.783260i
$653$		−	14.0000i		−	0.547862i	−0.961749	−	0.273931i	$-0.911676\pi$
$653$		−	14.0000i		−	0.547862i	0.961749	−	0.273931i	$-0.0883240\pi$
$654$	12.0000			0.469237
$655$	12.0000	+	6.00000i	0.468879	+	0.234439i
$656$	6.00000			0.234261
$657$		−	8.00000i		−	0.312110i
$658$		−	20.0000i		−	0.779681i
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$		0			0
$661$	−4.00000			−0.155582			−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000			−0.155582			−0.0777910	+	0.996970i	$0.524787\pi$
$662$			10.0000i			0.388661i
$663$		−	4.00000i		−	0.155347i
$664$		0			0
$665$	4.00000	−	8.00000i	0.155113	−	0.310227i
$666$	−1.00000			−0.0387492
$667$		0			0
$668$		0			0
$669$	−26.0000			−1.00522
$670$	8.00000	+	4.00000i	0.309067	+	0.154533i
$671$		0			0
$672$			2.00000i			0.0771517i
$673$		−	28.0000i		−	1.07932i	−0.841883	−	0.539660i	$-0.818553\pi$
$673$		−	28.0000i		−	1.07932i	0.841883	−	0.539660i	$-0.181447\pi$
$674$	8.00000			0.308148
$675$	−4.00000	+	3.00000i	−0.153960	+	0.115470i
$676$	−9.00000			−0.346154
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$		−	10.0000i		−	0.384048i
$679$	−28.0000			−1.07454
$680$	−4.00000	−	2.00000i	−0.153393	−	0.0766965i
$681$	12.0000			0.459841
$682$		0			0
$683$		−	12.0000i		−	0.459167i	−0.973289	−	0.229584i	$-0.926264\pi$
$683$		−	12.0000i		−	0.459167i	0.973289	−	0.229584i	$-0.0737364\pi$
$684$	2.00000			0.0764719
$685$	−8.00000	+	16.0000i	−0.305664	+	0.611329i
$686$	−20.0000			−0.763604
$687$			2.00000i			0.0763048i
$688$			4.00000i			0.152499i
$689$	−4.00000			−0.152388
$690$	4.00000	−	8.00000i	0.152277	−	0.304555i
$691$	4.00000			0.152167			0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000			0.152167			0.0760836	+	0.997101i	$0.475758\pi$
$692$		−	14.0000i		−	0.532200i
$693$		0			0
$694$	28.0000			1.06287
$695$	24.0000	+	12.0000i	0.910372	+	0.455186i
$696$		0			0
$697$			12.0000i			0.454532i
$698$			26.0000i			0.984115i
$699$		0			0
$700$	8.00000	−	6.00000i	0.302372	−	0.226779i
$701$	−4.00000			−0.151078			−0.0755390	−	0.997143i	$-0.524068\pi$
$701$	−4.00000			−0.151078			−0.0755390	+	0.997143i	$0.524068\pi$
$702$			2.00000i			0.0754851i
$703$		−	2.00000i		−	0.0754314i
$704$		0			0
$705$	−20.0000	−	10.0000i	−0.753244	−	0.376622i
$706$	−2.00000			−0.0752710
$707$		−	20.0000i		−	0.752177i
$708$		−	6.00000i		−	0.225494i
$709$	32.0000			1.20179			0.600893	−	0.799330i	$-0.294812\pi$
$709$	32.0000			1.20179			0.600893	+	0.799330i	$0.294812\pi$
$710$	8.00000	−	16.0000i	0.300235	−	0.600469i
$711$	−16.0000			−0.600047
$712$			6.00000i			0.224860i
$713$			32.0000i			1.19841i
$714$	−4.00000			−0.149696
$715$		0			0
$716$	6.00000			0.224231
$717$		−	8.00000i		−	0.298765i
$718$			16.0000i			0.597115i
$719$	16.0000			0.596699			0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000			0.596699			0.298350	+	0.954457i	$0.403564\pi$
$720$	2.00000	+	1.00000i	0.0745356	+	0.0372678i
$721$	−16.0000			−0.595871
$722$		−	15.0000i		−	0.558242i
$723$			22.0000i			0.818189i
$724$	6.00000			0.222988
$725$		0			0
$726$	−11.0000			−0.408248
$727$		−	52.0000i		−	1.92857i	−0.264861	−	0.964287i	$-0.585326\pi$
$727$		−	52.0000i		−	1.92857i	0.264861	−	0.964287i	$-0.414674\pi$
$728$		−	4.00000i		−	0.148250i
$729$	−1.00000			−0.0370370
$730$	16.0000	+	8.00000i	0.592187	+	0.296093i
$731$	−8.00000			−0.295891
$732$			8.00000i			0.295689i
$733$			22.0000i			0.812589i	0.913742	+	0.406294i	$0.133179\pi$
$733$			22.0000i			0.812589i	−0.913742	+	0.406294i	$0.866821\pi$
$734$	22.0000			0.812035
$735$	−3.00000	+	6.00000i	−0.110657	+	0.221313i
$736$	−4.00000			−0.147442
$737$		0			0
$738$		−	6.00000i		−	0.220863i
$739$	52.0000			1.91285			0.956425	−	0.291977i	$-0.0943129\pi$
$739$	52.0000			1.91285			0.956425	+	0.291977i	$0.0943129\pi$
$740$	1.00000	−	2.00000i	0.0367607	−	0.0735215i
$741$	−4.00000			−0.146944
$742$			4.00000i			0.146845i
$743$		−	38.0000i		−	1.39408i	−0.717030	−	0.697042i	$-0.754499\pi$
$743$		−	38.0000i		−	1.39408i	0.717030	−	0.697042i	$-0.245501\pi$
$744$	−8.00000			−0.293294
$745$	28.0000	+	14.0000i	1.02584	+	0.512920i
$746$	−2.00000			−0.0732252
$747$		0			0
$748$		0			0
$749$	8.00000			0.292314
$750$	−2.00000	−	11.0000i	−0.0730297	−	0.401663i
$751$	−40.0000			−1.45962			−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000			−1.45962			−0.729810	+	0.683650i	$0.760392\pi$
$752$			10.0000i			0.364662i
$753$		−	30.0000i		−	1.09326i
$754$		0			0
$755$		0			0
$756$	2.00000			0.0727393
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$			4.00000i			0.145287i
$759$		0			0
$760$	−2.00000	+	4.00000i	−0.0725476	+	0.145095i
$761$	18.0000			0.652499			0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000			0.652499			0.326250	+	0.945284i	$0.394215\pi$
$762$		−	6.00000i		−	0.217357i
$763$			24.0000i			0.868858i
$764$	−8.00000			−0.289430
$765$	−2.00000	+	4.00000i	−0.0723102	+	0.144620i
$766$	−4.00000			−0.144526
$767$			12.0000i			0.433295i
$768$		−	1.00000i		−	0.0360844i
$769$	38.0000			1.37032			0.685158	−	0.728395i	$-0.259733\pi$
$769$	38.0000			1.37032			0.685158	+	0.728395i	$0.259733\pi$
$770$		0			0
$771$	26.0000			0.936367
$772$		−	14.0000i		−	0.503871i
$773$		−	42.0000i		−	1.51064i	−0.655359	−	0.755318i	$-0.727483\pi$
$773$		−	42.0000i		−	1.51064i	0.655359	−	0.755318i	$-0.272517\pi$
$774$	4.00000			0.143777
$775$	24.0000	+	32.0000i	0.862105	+	1.14947i
$776$	14.0000			0.502571
$777$		−	2.00000i		−	0.0717496i
$778$			16.0000i			0.573628i
$779$	12.0000			0.429945
$780$	−4.00000	−	2.00000i	−0.143223	−	0.0716115i
$781$		0			0
$782$		−	8.00000i		−	0.286079i
$783$		0			0
$784$	3.00000			0.107143
$785$	6.00000	−	12.0000i	0.214149	−	0.428298i
$786$	−6.00000			−0.214013
$787$		−	36.0000i		−	1.28326i	−0.767014	−	0.641631i	$-0.778258\pi$
$787$		−	36.0000i		−	1.28326i	0.767014	−	0.641631i	$-0.221742\pi$
$788$			10.0000i			0.356235i
$789$	6.00000			0.213606
$790$	16.0000	−	32.0000i	0.569254	−	1.13851i
$791$	20.0000			0.711118
$792$		0			0
$793$		−	16.0000i		−	0.568177i
$794$	−34.0000			−1.20661
$795$	4.00000	+	2.00000i	0.141865	+	0.0709327i
$796$	−16.0000			−0.567105
$797$		−	42.0000i		−	1.48772i	−0.668338	−	0.743858i	$-0.732994\pi$
$797$		−	42.0000i		−	1.48772i	0.668338	−	0.743858i	$-0.267006\pi$
$798$			4.00000i			0.141598i
$799$	−20.0000			−0.707549
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	6.00000			0.212000
$802$		−	18.0000i		−	0.635602i
$803$		0			0
$804$	−4.00000			−0.141069
$805$	16.0000	+	8.00000i	0.563926	+	0.281963i
$806$	16.0000			0.563576
$807$			6.00000i			0.211210i
$808$			10.0000i			0.351799i
$809$	54.0000			1.89854			0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000			1.89854			0.949269	+	0.314464i	$0.101825\pi$
$810$	1.00000	−	2.00000i	0.0351364	−	0.0702728i
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−20.0000	+	40.0000i	−0.700569	+	1.40114i
$816$	2.00000			0.0700140
$817$			8.00000i			0.279885i
$818$		−	14.0000i		−	0.489499i
$819$	−4.00000			−0.139771
$820$	12.0000	+	6.00000i	0.419058	+	0.209529i
$821$	54.0000			1.88461			0.942306	−	0.334751i	$-0.108652\pi$
$821$	54.0000			1.88461			0.942306	+	0.334751i	$0.108652\pi$
$822$		−	8.00000i		−	0.279032i
$823$		−	2.00000i		−	0.0697156i	−0.999392	−	0.0348578i	$-0.988902\pi$
$823$		−	2.00000i		−	0.0697156i	0.999392	−	0.0348578i	$-0.0110978\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$	12.0000			0.417533
$827$			44.0000i			1.53003i	0.644013	+	0.765015i	$0.277268\pi$
$827$			44.0000i			1.53003i	−0.644013	+	0.765015i	$0.722732\pi$
$828$			4.00000i			0.139010i
$829$	−4.00000			−0.138926			−0.0694629	−	0.997585i	$-0.522129\pi$
$829$	−4.00000			−0.138926			−0.0694629	+	0.997585i	$0.522129\pi$
$830$		0			0
$831$	14.0000			0.485655
$832$			2.00000i			0.0693375i
$833$			6.00000i			0.207888i
$834$	−12.0000			−0.415526
$835$		0			0
$836$		0			0
$837$			8.00000i			0.276520i
$838$			20.0000i			0.690889i
$839$	−48.0000			−1.65714			−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000			−1.65714			−0.828572	+	0.559883i	$0.810846\pi$
$840$	−2.00000	+	4.00000i	−0.0690066	+	0.138013i
$841$	−29.0000			−1.00000
$842$		−	20.0000i		−	0.689246i
$843$			10.0000i			0.344418i
$844$	8.00000			0.275371
$845$	−18.0000	−	9.00000i	−0.619219	−	0.309609i
$846$	10.0000			0.343807
$847$		−	22.0000i		−	0.755929i
$848$		−	2.00000i		−	0.0686803i
$849$	−12.0000			−0.411839
$850$	−6.00000	−	8.00000i	−0.205798	−	0.274398i
$851$	4.00000			0.137118
$852$			8.00000i			0.274075i
$853$		−	14.0000i		−	0.479351i	−0.970853	−	0.239675i	$-0.922959\pi$
$853$		−	14.0000i		−	0.479351i	0.970853	−	0.239675i	$-0.0770410\pi$
$854$	−16.0000			−0.547509
$855$	4.00000	+	2.00000i	0.136797	+	0.0683986i
$856$	−4.00000			−0.136717
$857$		−	34.0000i		−	1.16142i	−0.814111	−	0.580709i	$-0.802775\pi$
$857$		−	34.0000i		−	1.16142i	0.814111	−	0.580709i	$-0.197225\pi$
$858$		0			0
$859$	−14.0000			−0.477674			−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000			−0.477674			−0.238837	+	0.971060i	$0.576766\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$	12.0000			0.408959
$862$			16.0000i			0.544962i
$863$		−	46.0000i		−	1.56586i	−0.622111	−	0.782929i	$-0.713725\pi$
$863$		−	46.0000i		−	1.56586i	0.622111	−	0.782929i	$-0.286275\pi$
$864$	−1.00000			−0.0340207
$865$	14.0000	−	28.0000i	0.476014	−	0.952029i
$866$	16.0000			0.543702
$867$		−	13.0000i		−	0.441503i
$868$		−	16.0000i		−	0.543075i
$869$		0			0
$870$		0			0
$871$	8.00000			0.271070
$872$		−	12.0000i		−	0.406371i
$873$		−	14.0000i		−	0.473828i
$874$	−8.00000			−0.270604
$875$	22.0000	−	4.00000i	0.743736	−	0.135225i
$876$	−8.00000			−0.270295
$877$		−	2.00000i		−	0.0675352i	−0.999430	−	0.0337676i	$-0.989249\pi$
$877$		−	2.00000i		−	0.0675352i	0.999430	−	0.0337676i	$-0.0107506\pi$
$878$			8.00000i			0.269987i
$879$	−6.00000			−0.202375
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		−	3.00000i		−	0.101015i
$883$			36.0000i			1.21150i	0.795656	+	0.605748i	$0.207126\pi$
$883$			36.0000i			1.21150i	−0.795656	+	0.605748i	$0.792874\pi$
$884$	−4.00000			−0.134535
$885$	6.00000	−	12.0000i	0.201688	−	0.403376i
$886$	−12.0000			−0.403148
$887$		−	30.0000i		−	1.00730i	−0.863907	−	0.503651i	$-0.831990\pi$
$887$		−	30.0000i		−	1.00730i	0.863907	−	0.503651i	$-0.168010\pi$
$888$			1.00000i			0.0335578i
$889$	12.0000			0.402467
$890$	−6.00000	+	12.0000i	−0.201120	+	0.402241i
$891$		0			0
$892$			26.0000i			0.870544i
$893$			20.0000i			0.669274i
$894$	−14.0000			−0.468230
$895$	12.0000	+	6.00000i	0.401116	+	0.200558i
$896$	2.00000			0.0668153
$897$		−	8.00000i		−	0.267112i
$898$			2.00000i			0.0667409i
$899$		0			0
$900$	3.00000	+	4.00000i	0.100000	+	0.133333i
$901$	4.00000			0.133259
$902$		0			0
$903$			8.00000i			0.266223i
$904$	−10.0000			−0.332595
$905$	12.0000	+	6.00000i	0.398893	+	0.199447i
$906$		0			0
$907$		−	44.0000i		−	1.46100i	−0.682915	−	0.730498i	$-0.739288\pi$
$907$		−	44.0000i		−	1.46100i	0.682915	−	0.730498i	$-0.260712\pi$
$908$		−	12.0000i		−	0.398234i
$909$	10.0000			0.331679
$910$	4.00000	−	8.00000i	0.132599	−	0.265197i
$911$	20.0000			0.662630			0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000			0.662630			0.331315	+	0.943520i	$0.392508\pi$
$912$		−	2.00000i		−	0.0662266i
$913$		0			0
$914$	−14.0000			−0.463079
$915$	−8.00000	+	16.0000i	−0.264472	+	0.528944i
$916$	2.00000			0.0660819
$917$		−	12.0000i		−	0.396275i
$918$		−	2.00000i		−	0.0660098i
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$	−8.00000	−	4.00000i	−0.263752	−	0.131876i
$921$	−16.0000			−0.527218
$922$		0			0
$923$		−	16.0000i		−	0.526646i
$924$		0			0
$925$	4.00000	−	3.00000i	0.131519	−	0.0986394i
$926$	−4.00000			−0.131448
$927$		−	8.00000i		−	0.262754i
$928$		0			0
$929$	−14.0000			−0.459325			−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000			−0.459325			−0.229663	+	0.973270i	$0.573762\pi$
$930$	−16.0000	−	8.00000i	−0.524661	−	0.262330i
$931$	6.00000			0.196642
$932$		0			0
$933$			4.00000i			0.130954i
$934$	−12.0000			−0.392652
$935$		0			0
$936$	2.00000			0.0653720
$937$		−	12.0000i		−	0.392023i	−0.980602	−	0.196011i	$-0.937201\pi$
$937$		−	12.0000i		−	0.392023i	0.980602	−	0.196011i	$-0.0627990\pi$
$938$		−	8.00000i		−	0.261209i
$939$	−10.0000			−0.326338
$940$	−10.0000	+	20.0000i	−0.326164	+	0.652328i
$941$	26.0000			0.847576			0.423788	−	0.905761i	$-0.360700\pi$
$941$	26.0000			0.847576			0.423788	+	0.905761i	$0.360700\pi$
$942$			6.00000i			0.195491i
$943$			24.0000i			0.781548i
$944$	−6.00000			−0.195283
$945$	4.00000	+	2.00000i	0.130120	+	0.0650600i
$946$		0			0
$947$		−	4.00000i		−	0.129983i	−0.997886	−	0.0649913i	$-0.979298\pi$
$947$		−	4.00000i		−	0.129983i	0.997886	−	0.0649913i	$-0.0207020\pi$
$948$			16.0000i			0.519656i
$949$	16.0000			0.519382
$950$	−8.00000	+	6.00000i	−0.259554	+	0.194666i
$951$	26.0000			0.843108
$952$			4.00000i			0.129641i
$953$			16.0000i			0.518291i	0.965838	+	0.259145i	$0.0834409\pi$
$953$			16.0000i			0.518291i	−0.965838	+	0.259145i	$0.916559\pi$
$954$	−2.00000			−0.0647524
$955$	−16.0000	−	8.00000i	−0.517748	−	0.258874i
$956$	−8.00000			−0.258738
$957$		0			0
$958$			24.0000i			0.775405i
$959$	16.0000			0.516667
$960$	1.00000	−	2.00000i	0.0322749	−	0.0645497i
$961$	33.0000			1.06452
$962$		−	2.00000i		−	0.0644826i
$963$			4.00000i			0.128898i
$964$	22.0000			0.708572
$965$	14.0000	−	28.0000i	0.450676	−	0.901352i
$966$	−8.00000			−0.257396
$967$			4.00000i			0.128631i	0.997930	+	0.0643157i	$0.0204865\pi$
$967$			4.00000i			0.128631i	−0.997930	+	0.0643157i	$0.979514\pi$
$968$			11.0000i			0.353553i
$969$	4.00000			0.128499
$970$	28.0000	+	14.0000i	0.899026	+	0.449513i
$971$	−32.0000			−1.02693			−0.513464	−	0.858111i	$-0.671638\pi$
$971$	−32.0000			−1.02693			−0.513464	+	0.858111i	$0.671638\pi$
$972$			1.00000i			0.0320750i
$973$		−	24.0000i		−	0.769405i
$974$		0			0
$975$	−6.00000	−	8.00000i	−0.192154	−	0.256205i
$976$	8.00000			0.256074
$977$		−	30.0000i		−	0.959785i	−0.877327	−	0.479893i	$-0.840676\pi$
$977$		−	30.0000i		−	0.959785i	0.877327	−	0.479893i	$-0.159324\pi$
$978$		−	20.0000i		−	0.639529i
$979$		0			0
$980$	6.00000	+	3.00000i	0.191663	+	0.0958315i
$981$	−12.0000			−0.383131
$982$			8.00000i			0.255290i
$983$			10.0000i			0.318950i	0.987202	+	0.159475i	$0.0509802\pi$
$983$			10.0000i			0.318950i	−0.987202	+	0.159475i	$0.949020\pi$
$984$	−6.00000			−0.191273
$985$	−10.0000	+	20.0000i	−0.318626	+	0.637253i
$986$		0			0
$987$			20.0000i			0.636607i
$988$			4.00000i			0.127257i
$989$	−16.0000			−0.508770
$990$		0			0
$991$	44.0000			1.39771			0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000			1.39771			0.698853	+	0.715265i	$0.253694\pi$
$992$			8.00000i			0.254000i
$993$		−	10.0000i		−	0.317340i
$994$	−16.0000			−0.507489
$995$	−32.0000	−	16.0000i	−1.01447	−	0.507234i
$996$		0			0
$997$		−	26.0000i		−	0.823428i	−0.911313	−	0.411714i	$-0.864930\pi$
$997$		−	26.0000i		−	0.823428i	0.911313	−	0.411714i	$-0.135070\pi$
$998$			6.00000i			0.189927i
$999$	1.00000			0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.d.a.889.2	yes	2
3.2	odd	2		3330.2.d.g.1999.1		2
5.2	odd	4		5550.2.a.c.1.1		1
5.3	odd	4		5550.2.a.bp.1.1		1
5.4	even	2	inner	1110.2.d.a.889.1	✓	2
15.14	odd	2		3330.2.d.g.1999.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.d.a.889.1	✓	2	5.4	even	2	inner
1110.2.d.a.889.2	yes	2	1.1	even	1	trivial
3330.2.d.g.1999.1		2	3.2	odd	2
3330.2.d.g.1999.2		2	15.14	odd	2
5550.2.a.c.1.1		1	5.2	odd	4
5550.2.a.bp.1.1		1	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} +1.00000i q^{12} -2.00000i q^{13} -2.00000 q^{14} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -1.00000i q^{18} +2.00000 q^{19} +(2.00000 + 1.00000i) q^{20} +2.00000 q^{21} +4.00000i q^{23} -1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{27} -2.00000i q^{28} +(-2.00000 - 1.00000i) q^{30} +8.00000 q^{31} +1.00000i q^{32} -2.00000 q^{34} +(2.00000 - 4.00000i) q^{35} +1.00000 q^{36} -1.00000i q^{37} +2.00000i q^{38} -2.00000 q^{39} +(-1.00000 + 2.00000i) q^{40} +6.00000 q^{41} +2.00000i q^{42} +4.00000i q^{43} +(2.00000 + 1.00000i) q^{45} -4.00000 q^{46} +10.0000i q^{47} -1.00000i q^{48} +3.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +2.00000 q^{51} +2.00000i q^{52} -2.00000i q^{53} -1.00000 q^{54} +2.00000 q^{56} -2.00000i q^{57} -6.00000 q^{59} +(1.00000 - 2.00000i) q^{60} +8.00000 q^{61} +8.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(-2.00000 + 4.00000i) q^{65} +4.00000i q^{67} -2.00000i q^{68} +4.00000 q^{69} +(4.00000 + 2.00000i) q^{70} +8.00000 q^{71} +1.00000i q^{72} +8.00000i q^{73} +1.00000 q^{74} +(4.00000 - 3.00000i) q^{75} -2.00000 q^{76} -2.00000i q^{78} +16.0000 q^{79} +(-2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +6.00000i q^{82} -2.00000 q^{84} +(2.00000 - 4.00000i) q^{85} -4.00000 q^{86} -6.00000 q^{89} +(-1.00000 + 2.00000i) q^{90} +4.00000 q^{91} -4.00000i q^{92} -8.00000i q^{93} -10.0000 q^{94} +(-4.00000 - 2.00000i) q^{95} +1.00000 q^{96} +14.0000i q^{97} +3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} - 4 q^{5} + 2 q^{6} - 2 q^{9} + 2 q^{10} - 4 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{19} + 4 q^{20} + 4 q^{21} - 2 q^{24} + 6 q^{25} + 4 q^{26} - 4 q^{30} + 16 q^{31} - 4 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{39} - 2 q^{40} + 12 q^{41} + 4 q^{45} - 8 q^{46} + 6 q^{49} - 8 q^{50} + 4 q^{51} - 2 q^{54} + 4 q^{56} - 12 q^{59} + 2 q^{60} + 16 q^{61} - 2 q^{64} - 4 q^{65} + 8 q^{69} + 8 q^{70} + 16 q^{71} + 2 q^{74} + 8 q^{75} - 4 q^{76} + 32 q^{79} - 4 q^{80} + 2 q^{81} - 4 q^{84} + 4 q^{85} - 8 q^{86} - 12 q^{89} - 2 q^{90} + 8 q^{91} - 20 q^{94} - 8 q^{95} + 2 q^{96}+O(q^{100}) \) 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^6 - 2 * q^9 + 2 * q^10 - 4 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^19 + 4 * q^20 + 4 * q^21 - 2 * q^24 + 6 * q^25 + 4 * q^26 - 4 * q^30 + 16 * q^31 - 4 * q^34 + 4 * q^35 + 2 * q^36 - 4 * q^39 - 2 * q^40 + 12 * q^41 + 4 * q^45 - 8 * q^46 + 6 * q^49 - 8 * q^50 + 4 * q^51 - 2 * q^54 + 4 * q^56 - 12 * q^59 + 2 * q^60 + 16 * q^61 - 2 * q^64 - 4 * q^65 + 8 * q^69 + 8 * q^70 + 16 * q^71 + 2 * q^74 + 8 * q^75 - 4 * q^76 + 32 * q^79 - 4 * q^80 + 2 * q^81 - 4 * q^84 + 4 * q^85 - 8 * q^86 - 12 * q^89 - 2 * q^90 + 8 * q^91 - 20 * q^94 - 8 * q^95 + 2 * q^96

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