LMFDB - Embedded newform 1110.2.d.e.889.1

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			889.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1110.889
Dual form			1110.2.d.e.889.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} -2.00000 q^{11} -1.00000i q^{12} -6.00000i q^{13} +2.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} -6.00000i q^{17} +1.00000i q^{18} +4.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} -2.00000 q^{21} +2.00000i q^{22} +4.00000i q^{23} -1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} -6.00000 q^{26} -1.00000i q^{27} -2.00000i q^{28} +8.00000 q^{29} +(2.00000 - 1.00000i) q^{30} -1.00000i q^{32} -2.00000i q^{33} -6.00000 q^{34} +(2.00000 + 4.00000i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -4.00000i q^{38} +6.00000 q^{39} +(1.00000 + 2.00000i) q^{40} +10.0000 q^{41} +2.00000i q^{42} -12.0000i q^{43} +2.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} +4.00000 q^{46} +12.0000i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +6.00000 q^{51} +6.00000i q^{52} +2.00000i q^{53} -1.00000 q^{54} +(-4.00000 + 2.00000i) q^{55} -2.00000 q^{56} +4.00000i q^{57} -8.00000i q^{58} -2.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} +6.00000 q^{61} -2.00000i q^{63} -1.00000 q^{64} +(-6.00000 - 12.0000i) q^{65} -2.00000 q^{66} +8.00000i q^{67} +6.00000i q^{68} -4.00000 q^{69} +(4.00000 - 2.00000i) q^{70} -12.0000 q^{71} -1.00000i q^{72} -4.00000i q^{73} -1.00000 q^{74} +(4.00000 + 3.00000i) q^{75} -4.00000 q^{76} -4.00000i q^{77} -6.00000i q^{78} +8.00000 q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -10.0000i q^{82} -4.00000i q^{83} +2.00000 q^{84} +(-6.00000 - 12.0000i) q^{85} -12.0000 q^{86} +8.00000i q^{87} -2.00000i q^{88} -14.0000 q^{89} +(1.00000 + 2.00000i) q^{90} +12.0000 q^{91} -4.00000i q^{92} +12.0000 q^{94} +(8.00000 - 4.00000i) q^{95} +1.00000 q^{96} +12.0000i q^{97} -3.00000i q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 12 q^{26} + 16 q^{29} + 4 q^{30} - 12 q^{34} + 4 q^{35} + 2 q^{36} + 12 q^{39} + 2 q^{40} + 20 q^{41} + 4 q^{44} - 4 q^{45} + 8 q^{46} + 6 q^{49} - 8 q^{50} + 12 q^{51} - 2 q^{54} - 8 q^{55} - 4 q^{56} - 4 q^{59} - 2 q^{60} + 12 q^{61} - 2 q^{64} - 12 q^{65} - 4 q^{66} - 8 q^{69} + 8 q^{70} - 24 q^{71} - 2 q^{74} + 8 q^{75} - 8 q^{76} + 16 q^{79} + 4 q^{80} + 2 q^{81} + 4 q^{84} - 12 q^{85} - 24 q^{86} - 28 q^{89} + 2 q^{90} + 24 q^{91} + 24 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 - 12 * q^26 + 16 * q^29 + 4 * q^30 - 12 * q^34 + 4 * q^35 + 2 * q^36 + 12 * q^39 + 2 * q^40 + 20 * q^41 + 4 * q^44 - 4 * q^45 + 8 * q^46 + 6 * q^49 - 8 * q^50 + 12 * q^51 - 2 * q^54 - 8 * q^55 - 4 * q^56 - 4 * q^59 - 2 * q^60 + 12 * q^61 - 2 * q^64 - 12 * q^65 - 4 * q^66 - 8 * q^69 + 8 * q^70 - 24 * q^71 - 2 * q^74 + 8 * q^75 - 8 * q^76 + 16 * q^79 + 4 * q^80 + 2 * q^81 + 4 * q^84 - 12 * q^85 - 24 * q^86 - 28 * q^89 + 2 * q^90 + 24 * q^91 + 24 * 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		−	1.00000i		−	0.288675i
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	2.00000			0.534522
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$	1.00000			0.250000
$17$		−	6.00000i		−	1.45521i	−0.685994	−	0.727607i	$-0.740633\pi$
$17$		−	6.00000i		−	1.45521i	0.685994	−	0.727607i	$-0.259367\pi$
$18$			1.00000i			0.235702i
$19$	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
$23$			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
$26$	−6.00000			−1.17670
$27$		−	1.00000i		−	0.192450i
$28$		−	2.00000i		−	0.377964i
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$	2.00000	−	1.00000i	0.365148	−	0.182574i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	2.00000i		−	0.348155i
$34$	−6.00000			−1.02899
$35$	2.00000	+	4.00000i	0.338062	+	0.676123i
$36$	1.00000			0.166667
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	4.00000i		−	0.648886i
$39$	6.00000			0.960769
$40$	1.00000	+	2.00000i	0.158114	+	0.316228i
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$			2.00000i			0.308607i
$43$		−	12.0000i		−	1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$		−	12.0000i		−	1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$	2.00000			0.301511
$45$	−2.00000	+	1.00000i	−0.298142	+	0.149071i
$46$	4.00000			0.589768
$47$			12.0000i			1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$47$			12.0000i			1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$48$			1.00000i			0.144338i
$49$	3.00000			0.428571
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	6.00000			0.840168
$52$			6.00000i			0.832050i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−1.00000			−0.136083
$55$	−4.00000	+	2.00000i	−0.539360	+	0.269680i
$56$	−2.00000			−0.267261
$57$			4.00000i			0.529813i
$58$		−	8.00000i		−	1.05045i
$59$	−2.00000			−0.260378			−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000			−0.260378			−0.130189	+	0.991489i	$0.541558\pi$
$60$	−1.00000	−	2.00000i	−0.129099	−	0.258199i
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$		0			0
$63$		−	2.00000i		−	0.251976i
$64$	−1.00000			−0.125000
$65$	−6.00000	−	12.0000i	−0.744208	−	1.48842i
$66$	−2.00000			−0.246183
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$			6.00000i			0.727607i
$69$	−4.00000			−0.481543
$70$	4.00000	−	2.00000i	0.478091	−	0.239046i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		−	1.00000i		−	0.117851i
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$	−1.00000			−0.116248
$75$	4.00000	+	3.00000i	0.461880	+	0.346410i
$76$	−4.00000			−0.458831
$77$		−	4.00000i		−	0.455842i
$78$		−	6.00000i		−	0.679366i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$	1.00000			0.111111
$82$		−	10.0000i		−	1.10432i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$	2.00000			0.218218
$85$	−6.00000	−	12.0000i	−0.650791	−	1.30158i
$86$	−12.0000			−1.29399
$87$			8.00000i			0.857690i
$88$		−	2.00000i		−	0.213201i
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$	1.00000	+	2.00000i	0.105409	+	0.210819i
$91$	12.0000			1.25794
$92$		−	4.00000i		−	0.417029i
$93$		0			0
$94$	12.0000			1.23771
$95$	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
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$		−	6.00000i		−	0.594089i
$103$		−	14.0000i		−	1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$		−	14.0000i		−	1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$	6.00000			0.588348
$105$	−4.00000	+	2.00000i	−0.390360	+	0.195180i
$106$	2.00000			0.194257
$107$		−	20.0000i		−	1.93347i	−0.255774	−	0.966736i	$-0.582330\pi$
$107$		−	20.0000i		−	1.93347i	0.255774	−	0.966736i	$-0.417670\pi$
$108$			1.00000i			0.0962250i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	2.00000	+	4.00000i	0.190693	+	0.381385i
$111$	1.00000			0.0949158
$112$			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
$115$	4.00000	+	8.00000i	0.373002	+	0.746004i
$116$	−8.00000			−0.742781
$117$			6.00000i			0.554700i
$118$			2.00000i			0.184115i
$119$	12.0000			1.10004
$120$	−2.00000	+	1.00000i	−0.182574	+	0.0912871i
$121$	−7.00000			−0.636364
$122$		−	6.00000i		−	0.543214i
$123$			10.0000i			0.901670i
$124$		0			0
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	−2.00000			−0.178174
$127$		−	14.0000i		−	1.24230i	−0.783692	−	0.621150i	$-0.786666\pi$
$127$		−	14.0000i		−	1.24230i	0.783692	−	0.621150i	$-0.213334\pi$
$128$			1.00000i			0.0883883i
$129$	12.0000			1.05654
$130$	−12.0000	+	6.00000i	−1.05247	+	0.526235i
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$			2.00000i			0.174078i
$133$			8.00000i			0.693688i
$134$	8.00000			0.691095
$135$	−1.00000	−	2.00000i	−0.0860663	−	0.172133i
$136$	6.00000			0.514496
$137$			18.0000i			1.53784i	0.639343	+	0.768922i	$0.279207\pi$
$137$			18.0000i			1.53784i	−0.639343	+	0.768922i	$0.720793\pi$
$138$			4.00000i			0.340503i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	−2.00000	−	4.00000i	−0.169031	−	0.338062i
$141$	−12.0000			−1.01058
$142$			12.0000i			1.00702i
$143$			12.0000i			1.00349i
$144$	−1.00000			−0.0833333
$145$	16.0000	−	8.00000i	1.32873	−	0.664364i
$146$	−4.00000			−0.331042
$147$			3.00000i			0.247436i
$148$			1.00000i			0.0821995i
$149$	−16.0000			−1.31077			−0.655386	−	0.755295i	$-0.727494\pi$
$149$	−16.0000			−1.31077			−0.655386	+	0.755295i	$0.727494\pi$
$150$	3.00000	−	4.00000i	0.244949	−	0.326599i
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$			4.00000i			0.324443i
$153$			6.00000i			0.485071i
$154$	−4.00000			−0.322329
$155$		0			0
$156$	−6.00000			−0.480384
$157$			14.0000i			1.11732i	0.829396	+	0.558661i	$0.188685\pi$
$157$			14.0000i			1.11732i	−0.829396	+	0.558661i	$0.811315\pi$
$158$		−	8.00000i		−	0.636446i
$159$	−2.00000			−0.158610
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$	−8.00000			−0.630488
$162$		−	1.00000i		−	0.0785674i
$163$			8.00000i			0.626608i	0.949653	+	0.313304i	$0.101436\pi$
$163$			8.00000i			0.626608i	−0.949653	+	0.313304i	$0.898564\pi$
$164$	−10.0000			−0.780869
$165$	−2.00000	−	4.00000i	−0.155700	−	0.311400i
$166$	−4.00000			−0.310460
$167$			20.0000i			1.54765i	0.633402	+	0.773823i	$0.281658\pi$
$167$			20.0000i			1.54765i	−0.633402	+	0.773823i	$0.718342\pi$
$168$		−	2.00000i		−	0.154303i
$169$	−23.0000			−1.76923
$170$	−12.0000	+	6.00000i	−0.920358	+	0.460179i
$171$	−4.00000			−0.305888
$172$			12.0000i			0.914991i
$173$		−	18.0000i		−	1.36851i	−0.729241	−	0.684257i	$-0.760127\pi$
$173$		−	18.0000i		−	1.36851i	0.729241	−	0.684257i	$-0.239873\pi$
$174$	8.00000			0.606478
$175$	8.00000	+	6.00000i	0.604743	+	0.453557i
$176$	−2.00000			−0.150756
$177$		−	2.00000i		−	0.150329i
$178$			14.0000i			1.04934i
$179$	−18.0000			−1.34538			−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000			−1.34538			−0.672692	+	0.739923i	$0.734862\pi$
$180$	2.00000	−	1.00000i	0.149071	−	0.0745356i
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$		−	12.0000i		−	0.889499i
$183$			6.00000i			0.443533i
$184$	−4.00000			−0.294884
$185$	−1.00000	−	2.00000i	−0.0735215	−	0.147043i
$186$		0			0
$187$			12.0000i			0.877527i
$188$		−	12.0000i		−	0.875190i
$189$	2.00000			0.145479
$190$	−4.00000	−	8.00000i	−0.290191	−	0.580381i
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			16.0000i			1.15171i	0.817554	+	0.575853i	$0.195330\pi$
$193$			16.0000i			1.15171i	−0.817554	+	0.575853i	$0.804670\pi$
$194$	12.0000			0.861550
$195$	12.0000	−	6.00000i	0.859338	−	0.429669i
$196$	−3.00000			−0.214286
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		−	2.00000i		−	0.142134i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$	−8.00000			−0.564276
$202$			12.0000i			0.844317i
$203$			16.0000i			1.12298i
$204$	−6.00000			−0.420084
$205$	20.0000	−	10.0000i	1.39686	−	0.698430i
$206$	−14.0000			−0.975426
$207$		−	4.00000i		−	0.278019i
$208$		−	6.00000i		−	0.416025i
$209$	−8.00000			−0.553372
$210$	2.00000	+	4.00000i	0.138013	+	0.276026i
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$		−	2.00000i		−	0.137361i
$213$		−	12.0000i		−	0.822226i
$214$	−20.0000			−1.36717
$215$	−12.0000	−	24.0000i	−0.818393	−	1.63679i
$216$	1.00000			0.0680414
$217$		0			0
$218$		−	10.0000i		−	0.677285i
$219$	4.00000			0.270295
$220$	4.00000	−	2.00000i	0.269680	−	0.134840i
$221$	−36.0000			−2.42162
$222$		−	1.00000i		−	0.0671156i
$223$			22.0000i			1.47323i	0.676313	+	0.736614i	$0.263577\pi$
$223$			22.0000i			1.47323i	−0.676313	+	0.736614i	$0.736423\pi$
$224$	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
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$	8.00000	−	4.00000i	0.527504	−	0.263752i
$231$	4.00000			0.263181
$232$			8.00000i			0.525226i
$233$			18.0000i			1.17922i	0.807688	+	0.589610i	$0.200718\pi$
$233$			18.0000i			1.17922i	−0.807688	+	0.589610i	$0.799282\pi$
$234$	6.00000			0.392232
$235$	12.0000	+	24.0000i	0.782794	+	1.56559i
$236$	2.00000			0.130189
$237$			8.00000i			0.519656i
$238$		−	12.0000i		−	0.777844i
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$	1.00000	+	2.00000i	0.0645497	+	0.129099i
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$			7.00000i			0.449977i
$243$			1.00000i			0.0641500i
$244$	−6.00000			−0.384111
$245$	6.00000	−	3.00000i	0.383326	−	0.191663i
$246$	10.0000			0.637577
$247$		−	24.0000i		−	1.52708i
$248$		0			0
$249$	4.00000			0.253490
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$			2.00000i			0.125988i
$253$		−	8.00000i		−	0.502956i
$254$	−14.0000			−0.878438
$255$	12.0000	−	6.00000i	0.751469	−	0.375735i
$256$	1.00000			0.0625000
$257$			14.0000i			0.873296i	0.899632	+	0.436648i	$0.143834\pi$
$257$			14.0000i			0.873296i	−0.899632	+	0.436648i	$0.856166\pi$
$258$		−	12.0000i		−	0.747087i
$259$	2.00000			0.124274
$260$	6.00000	+	12.0000i	0.372104	+	0.744208i
$261$	−8.00000			−0.495188
$262$		−	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
$267$		−	14.0000i		−	0.856786i
$268$		−	8.00000i		−	0.488678i
$269$	4.00000			0.243884			0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000			0.243884			0.121942	+	0.992537i	$0.461088\pi$
$270$	−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	$0.338468\pi$
$272$		−	6.00000i		−	0.363803i
$273$			12.0000i			0.726273i
$274$	18.0000			1.08742
$275$	−6.00000	+	8.00000i	−0.361814	+	0.482418i
$276$	4.00000			0.240772
$277$		−	14.0000i		−	0.841178i	−0.907251	−	0.420589i	$-0.861823\pi$
$277$		−	14.0000i		−	0.841178i	0.907251	−	0.420589i	$-0.138177\pi$
$278$		−	4.00000i		−	0.239904i
$279$		0			0
$280$	−4.00000	+	2.00000i	−0.239046	+	0.119523i
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$			12.0000i			0.714590i
$283$		−	8.00000i		−	0.475551i	−0.971320	−	0.237775i	$-0.923582\pi$
$283$		−	8.00000i		−	0.475551i	0.971320	−	0.237775i	$-0.0764182\pi$
$284$	12.0000			0.712069
$285$	4.00000	+	8.00000i	0.236940	+	0.473879i
$286$	12.0000			0.709575
$287$			20.0000i			1.18056i
$288$			1.00000i			0.0589256i
$289$	−19.0000			−1.11765
$290$	−8.00000	−	16.0000i	−0.469776	−	0.939552i
$291$	−12.0000			−0.703452
$292$			4.00000i			0.234082i
$293$			26.0000i			1.51894i	0.650545	+	0.759468i	$0.274541\pi$
$293$			26.0000i			1.51894i	−0.650545	+	0.759468i	$0.725459\pi$
$294$	3.00000			0.174964
$295$	−4.00000	+	2.00000i	−0.232889	+	0.116445i
$296$	1.00000			0.0581238
$297$			2.00000i			0.116052i
$298$			16.0000i			0.926855i
$299$	24.0000			1.38796
$300$	−4.00000	−	3.00000i	−0.230940	−	0.173205i
$301$	24.0000			1.38334
$302$			16.0000i			0.920697i
$303$		−	12.0000i		−	0.689382i
$304$	4.00000			0.229416
$305$	12.0000	−	6.00000i	0.687118	−	0.343559i
$306$	6.00000			0.342997
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$			4.00000i			0.227921i
$309$	14.0000			0.796432
$310$		0			0
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$			6.00000i			0.339683i
$313$		−	16.0000i		−	0.904373i	−0.891923	−	0.452187i	$-0.850644\pi$
$313$		−	16.0000i		−	0.904373i	0.891923	−	0.452187i	$-0.149356\pi$
$314$	14.0000			0.790066
$315$	−2.00000	−	4.00000i	−0.112687	−	0.225374i
$316$	−8.00000			−0.450035
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$			2.00000i			0.112154i
$319$	−16.0000			−0.895828
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$	20.0000			1.11629
$322$			8.00000i			0.445823i
$323$		−	24.0000i		−	1.33540i
$324$	−1.00000			−0.0555556
$325$	−24.0000	−	18.0000i	−1.33128	−	0.998460i
$326$	8.00000			0.443079
$327$			10.0000i			0.553001i
$328$			10.0000i			0.552158i
$329$	−24.0000			−1.32316
$330$	−4.00000	+	2.00000i	−0.220193	+	0.110096i
$331$	28.0000			1.53902			0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000			1.53902			0.769510	+	0.638635i	$0.220501\pi$
$332$			4.00000i			0.219529i
$333$			1.00000i			0.0547997i
$334$	20.0000			1.09435
$335$	8.00000	+	16.0000i	0.437087	+	0.874173i
$336$	−2.00000			−0.109109
$337$		−	4.00000i		−	0.217894i	−0.994048	−	0.108947i	$-0.965252\pi$
$337$		−	4.00000i		−	0.217894i	0.994048	−	0.108947i	$-0.0347479\pi$
$338$			23.0000i			1.25104i
$339$	6.00000			0.325875
$340$	6.00000	+	12.0000i	0.325396	+	0.650791i
$341$		0			0
$342$			4.00000i			0.216295i
$343$			20.0000i			1.07990i
$344$	12.0000			0.646997
$345$	−8.00000	+	4.00000i	−0.430706	+	0.215353i
$346$	−18.0000			−0.967686
$347$			4.00000i			0.214731i	0.994220	+	0.107366i	$0.0342415\pi$
$347$			4.00000i			0.214731i	−0.994220	+	0.107366i	$0.965758\pi$
$348$		−	8.00000i		−	0.428845i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$	6.00000	−	8.00000i	0.320713	−	0.427618i
$351$	−6.00000			−0.320256
$352$			2.00000i			0.106600i
$353$			14.0000i			0.745145i	0.928003	+	0.372572i	$0.121524\pi$
$353$			14.0000i			0.745145i	−0.928003	+	0.372572i	$0.878476\pi$
$354$	−2.00000			−0.106299
$355$	−24.0000	+	12.0000i	−1.27379	+	0.636894i
$356$	14.0000			0.741999
$357$			12.0000i			0.635107i
$358$			18.0000i			0.951330i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	−1.00000	−	2.00000i	−0.0527046	−	0.105409i
$361$	−3.00000			−0.157895
$362$		−	18.0000i		−	0.946059i
$363$		−	7.00000i		−	0.367405i
$364$	−12.0000			−0.628971
$365$	−4.00000	−	8.00000i	−0.209370	−	0.418739i
$366$	6.00000			0.313625
$367$			2.00000i			0.104399i	0.998637	+	0.0521996i	$0.0166232\pi$
$367$			2.00000i			0.104399i	−0.998637	+	0.0521996i	$0.983377\pi$
$368$			4.00000i			0.208514i
$369$	−10.0000			−0.520579
$370$	−2.00000	+	1.00000i	−0.103975	+	0.0519875i
$371$	−4.00000			−0.207670
$372$		0			0
$373$		−	22.0000i		−	1.13912i	−0.821951	−	0.569558i	$-0.807114\pi$
$373$		−	22.0000i		−	1.13912i	0.821951	−	0.569558i	$-0.192886\pi$
$374$	12.0000			0.620505
$375$	11.0000	+	2.00000i	0.568038	+	0.103280i
$376$	−12.0000			−0.618853
$377$		−	48.0000i		−	2.47213i
$378$		−	2.00000i		−	0.102869i
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	−8.00000	+	4.00000i	−0.410391	+	0.205196i
$381$	14.0000			0.717242
$382$		−	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
$386$	16.0000			0.814379
$387$			12.0000i			0.609994i
$388$		−	12.0000i		−	0.609208i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$	−6.00000	−	12.0000i	−0.303822	−	0.607644i
$391$	24.0000			1.21373
$392$			3.00000i			0.151523i
$393$			6.00000i			0.302660i
$394$	6.00000			0.302276
$395$	16.0000	−	8.00000i	0.805047	−	0.402524i
$396$	−2.00000			−0.100504
$397$			18.0000i			0.903394i	0.892171	+	0.451697i	$0.149181\pi$
$397$			18.0000i			0.903394i	−0.892171	+	0.451697i	$0.850819\pi$
$398$		−	8.00000i		−	0.401004i
$399$	−8.00000			−0.400501
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−10.0000			−0.499376			−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000			−0.499376			−0.249688	+	0.968326i	$0.580328\pi$
$402$			8.00000i			0.399004i
$403$		0			0
$404$	12.0000			0.597022
$405$	2.00000	−	1.00000i	0.0993808	−	0.0496904i
$406$	16.0000			0.794067
$407$			2.00000i			0.0991363i
$408$			6.00000i			0.297044i
$409$	−38.0000			−1.87898			−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−38.0000			−1.87898			−0.939490	+	0.342578i	$0.888700\pi$
$410$	−10.0000	−	20.0000i	−0.493865	−	0.987730i
$411$	−18.0000			−0.887875
$412$			14.0000i			0.689730i
$413$		−	4.00000i		−	0.196827i
$414$	−4.00000			−0.196589
$415$	−4.00000	−	8.00000i	−0.196352	−	0.392705i
$416$	−6.00000			−0.294174
$417$			4.00000i			0.195881i
$418$			8.00000i			0.391293i
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$	4.00000	−	2.00000i	0.195180	−	0.0975900i
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$			12.0000i			0.584151i
$423$		−	12.0000i		−	0.583460i
$424$	−2.00000			−0.0971286
$425$	−24.0000	−	18.0000i	−1.16417	−	0.873128i
$426$	−12.0000			−0.581402
$427$			12.0000i			0.580721i
$428$			20.0000i			0.966736i
$429$	−12.0000			−0.579365
$430$	−24.0000	+	12.0000i	−1.15738	+	0.578691i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	4.00000i		−	0.192228i	−0.995370	−	0.0961139i	$-0.969359\pi$
$433$		−	4.00000i		−	0.192228i	0.995370	−	0.0961139i	$-0.0306413\pi$
$434$		0			0
$435$	8.00000	+	16.0000i	0.383571	+	0.767141i
$436$	−10.0000			−0.478913
$437$			16.0000i			0.765384i
$438$		−	4.00000i		−	0.191127i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	−2.00000	−	4.00000i	−0.0953463	−	0.190693i
$441$	−3.00000			−0.142857
$442$			36.0000i			1.71235i
$443$		−	20.0000i		−	0.950229i	−0.879924	−	0.475114i	$-0.842407\pi$
$443$		−	20.0000i		−	0.950229i	0.879924	−	0.475114i	$-0.157593\pi$
$444$	−1.00000			−0.0474579
$445$	−28.0000	+	14.0000i	−1.32733	+	0.663664i
$446$	22.0000			1.04173
$447$		−	16.0000i		−	0.756774i
$448$		−	2.00000i		−	0.0944911i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	4.00000	+	3.00000i	0.188562	+	0.141421i
$451$	−20.0000			−0.941763
$452$			6.00000i			0.282216i
$453$		−	16.0000i		−	0.751746i
$454$	12.0000			0.563188
$455$	24.0000	−	12.0000i	1.12514	−	0.562569i
$456$	−4.00000			−0.187317
$457$			4.00000i			0.187112i	0.995614	+	0.0935561i	$0.0298234\pi$
$457$			4.00000i			0.187112i	−0.995614	+	0.0935561i	$0.970177\pi$
$458$			14.0000i			0.654177i
$459$	−6.00000			−0.280056
$460$	−4.00000	−	8.00000i	−0.186501	−	0.373002i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		−	4.00000i		−	0.186097i
$463$		−	34.0000i		−	1.58011i	−0.613033	−	0.790057i	$-0.710051\pi$
$463$		−	34.0000i		−	1.58011i	0.613033	−	0.790057i	$-0.289949\pi$
$464$	8.00000			0.371391
$465$		0			0
$466$	18.0000			0.833834
$467$			20.0000i			0.925490i	0.886492	+	0.462745i	$0.153135\pi$
$467$			20.0000i			0.925490i	−0.886492	+	0.462745i	$0.846865\pi$
$468$		−	6.00000i		−	0.277350i
$469$	−16.0000			−0.738811
$470$	24.0000	−	12.0000i	1.10704	−	0.553519i
$471$	−14.0000			−0.645086
$472$		−	2.00000i		−	0.0920575i
$473$			24.0000i			1.10352i
$474$	8.00000			0.367452
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$	−12.0000			−0.550019
$477$		−	2.00000i		−	0.0915737i
$478$			20.0000i			0.914779i
$479$	−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
$482$		−	14.0000i		−	0.637683i
$483$		−	8.00000i		−	0.364013i
$484$	7.00000			0.318182
$485$	12.0000	+	24.0000i	0.544892	+	1.08978i
$486$	1.00000			0.0453609
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$			6.00000i			0.271607i
$489$	−8.00000			−0.361773
$490$	−3.00000	−	6.00000i	−0.135526	−	0.271052i
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$		−	10.0000i		−	0.450835i
$493$		−	48.0000i		−	2.16181i
$494$	−24.0000			−1.07981
$495$	4.00000	−	2.00000i	0.179787	−	0.0898933i
$496$		0			0
$497$		−	24.0000i		−	1.07655i
$498$		−	4.00000i		−	0.179244i
$499$	12.0000			0.537194			0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000			0.537194			0.268597	+	0.963253i	$0.413440\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$	−20.0000			−0.893534
$502$			18.0000i			0.803379i
$503$			8.00000i			0.356702i	0.983967	+	0.178351i	$0.0570763\pi$
$503$			8.00000i			0.356702i	−0.983967	+	0.178351i	$0.942924\pi$
$504$	2.00000			0.0890871
$505$	−24.0000	+	12.0000i	−1.06799	+	0.533993i
$506$	−8.00000			−0.355643
$507$		−	23.0000i		−	1.02147i
$508$			14.0000i			0.621150i
$509$	−12.0000			−0.531891			−0.265945	−	0.963988i	$-0.585684\pi$
$509$	−12.0000			−0.531891			−0.265945	+	0.963988i	$0.585684\pi$
$510$	−6.00000	−	12.0000i	−0.265684	−	0.531369i
$511$	8.00000			0.353899
$512$		−	1.00000i		−	0.0441942i
$513$		−	4.00000i		−	0.176604i
$514$	14.0000			0.617514
$515$	−14.0000	−	28.0000i	−0.616914	−	1.23383i
$516$	−12.0000			−0.528271
$517$		−	24.0000i		−	1.05552i
$518$		−	2.00000i		−	0.0878750i
$519$	18.0000			0.790112
$520$	12.0000	−	6.00000i	0.526235	−	0.263117i
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$			8.00000i			0.350150i
$523$			8.00000i			0.349816i	0.984585	+	0.174908i	$0.0559627\pi$
$523$			8.00000i			0.349816i	−0.984585	+	0.174908i	$0.944037\pi$
$524$	−6.00000			−0.262111
$525$	−6.00000	+	8.00000i	−0.261861	+	0.349149i
$526$	8.00000			0.348817
$527$		0			0
$528$		−	2.00000i		−	0.0870388i
$529$	7.00000			0.304348
$530$	4.00000	−	2.00000i	0.173749	−	0.0868744i
$531$	2.00000			0.0867926
$532$		−	8.00000i		−	0.346844i
$533$		−	60.0000i		−	2.59889i
$534$	−14.0000			−0.605839
$535$	−20.0000	−	40.0000i	−0.864675	−	1.72935i
$536$	−8.00000			−0.345547
$537$		−	18.0000i		−	0.776757i
$538$		−	4.00000i		−	0.172452i
$539$	−6.00000			−0.258438
$540$	1.00000	+	2.00000i	0.0430331	+	0.0860663i
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$		−	16.0000i		−	0.687259i
$543$			18.0000i			0.772454i
$544$	−6.00000			−0.257248
$545$	20.0000	−	10.0000i	0.856706	−	0.428353i
$546$	12.0000			0.513553
$547$			20.0000i			0.855138i	0.903983	+	0.427569i	$0.140630\pi$
$547$			20.0000i			0.855138i	−0.903983	+	0.427569i	$0.859370\pi$
$548$		−	18.0000i		−	0.768922i
$549$	−6.00000			−0.256074
$550$	8.00000	+	6.00000i	0.341121	+	0.255841i
$551$	32.0000			1.36325
$552$		−	4.00000i		−	0.170251i
$553$			16.0000i			0.680389i
$554$	−14.0000			−0.594803
$555$	2.00000	−	1.00000i	0.0848953	−	0.0424476i
$556$	−4.00000			−0.169638
$557$			46.0000i			1.94908i	0.224208	+	0.974541i	$0.428020\pi$
$557$			46.0000i			1.94908i	−0.224208	+	0.974541i	$0.571980\pi$
$558$		0			0
$559$	−72.0000			−3.04528
$560$	2.00000	+	4.00000i	0.0845154	+	0.169031i
$561$	−12.0000			−0.506640
$562$		−	30.0000i		−	1.26547i
$563$			28.0000i			1.18006i	0.807382	+	0.590030i	$0.200884\pi$
$563$			28.0000i			1.18006i	−0.807382	+	0.590030i	$0.799116\pi$
$564$	12.0000			0.505291
$565$	−6.00000	−	12.0000i	−0.252422	−	0.504844i
$566$	−8.00000			−0.336265
$567$			2.00000i			0.0839921i
$568$		−	12.0000i		−	0.503509i
$569$	10.0000			0.419222			0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000			0.419222			0.209611	+	0.977785i	$0.432780\pi$
$570$	8.00000	−	4.00000i	0.335083	−	0.167542i
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$		−	12.0000i		−	0.501745i
$573$			12.0000i			0.501307i
$574$	20.0000			0.834784
$575$	16.0000	+	12.0000i	0.667246	+	0.500435i
$576$	1.00000			0.0416667
$577$		−	20.0000i		−	0.832611i	−0.909225	−	0.416305i	$-0.863325\pi$
$577$		−	20.0000i		−	0.832611i	0.909225	−	0.416305i	$-0.136675\pi$
$578$			19.0000i			0.790296i
$579$	−16.0000			−0.664937
$580$	−16.0000	+	8.00000i	−0.664364	+	0.332182i
$581$	8.00000			0.331896
$582$			12.0000i			0.497416i
$583$		−	4.00000i		−	0.165663i
$584$	4.00000			0.165521
$585$	6.00000	+	12.0000i	0.248069	+	0.496139i
$586$	26.0000			1.07405
$587$		−	36.0000i		−	1.48588i	−0.669359	−	0.742940i	$-0.733431\pi$
$587$		−	36.0000i		−	1.48588i	0.669359	−	0.742940i	$-0.266569\pi$
$588$		−	3.00000i		−	0.123718i
$589$		0			0
$590$	2.00000	+	4.00000i	0.0823387	+	0.164677i
$591$	−6.00000			−0.246807
$592$		−	1.00000i		−	0.0410997i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$	2.00000			0.0820610
$595$	24.0000	−	12.0000i	0.983904	−	0.491952i
$596$	16.0000			0.655386
$597$			8.00000i			0.327418i
$598$		−	24.0000i		−	0.981433i
$599$	16.0000			0.653742			0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000			0.653742			0.326871	+	0.945069i	$0.394006\pi$
$600$	−3.00000	+	4.00000i	−0.122474	+	0.163299i
$601$	34.0000			1.38689			0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000			1.38689			0.693444	+	0.720510i	$0.256092\pi$
$602$		−	24.0000i		−	0.978167i
$603$		−	8.00000i		−	0.325785i
$604$	16.0000			0.651031
$605$	−14.0000	+	7.00000i	−0.569181	+	0.284590i
$606$	−12.0000			−0.487467
$607$		−	14.0000i		−	0.568242i	−0.958788	−	0.284121i	$-0.908298\pi$
$607$		−	14.0000i		−	0.568242i	0.958788	−	0.284121i	$-0.0917018\pi$
$608$		−	4.00000i		−	0.162221i
$609$	−16.0000			−0.648353
$610$	−6.00000	−	12.0000i	−0.242933	−	0.485866i
$611$	72.0000			2.91281
$612$		−	6.00000i		−	0.242536i
$613$			6.00000i			0.242338i	0.992632	+	0.121169i	$0.0386643\pi$
$613$			6.00000i			0.242338i	−0.992632	+	0.121169i	$0.961336\pi$
$614$	−4.00000			−0.161427
$615$	10.0000	+	20.0000i	0.403239	+	0.806478i
$616$	4.00000			0.161165
$617$			22.0000i			0.885687i	0.896599	+	0.442843i	$0.146030\pi$
$617$			22.0000i			0.885687i	−0.896599	+	0.442843i	$0.853970\pi$
$618$		−	14.0000i		−	0.563163i
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$	4.00000			0.160514
$622$			4.00000i			0.160385i
$623$		−	28.0000i		−	1.12180i
$624$	6.00000			0.240192
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−16.0000			−0.639489
$627$		−	8.00000i		−	0.319489i
$628$		−	14.0000i		−	0.558661i
$629$	−6.00000			−0.239236
$630$	−4.00000	+	2.00000i	−0.159364	+	0.0796819i
$631$	48.0000			1.91085			0.955425	−	0.295234i	$-0.0953977\pi$
$631$	48.0000			1.91085			0.955425	+	0.295234i	$0.0953977\pi$
$632$			8.00000i			0.318223i
$633$		−	12.0000i		−	0.476957i
$634$	2.00000			0.0794301
$635$	−14.0000	−	28.0000i	−0.555573	−	1.11115i
$636$	2.00000			0.0793052
$637$		−	18.0000i		−	0.713186i
$638$			16.0000i			0.633446i
$639$	12.0000			0.474713
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	10.0000			0.394976			0.197488	−	0.980305i	$-0.436722\pi$
$641$	10.0000			0.394976			0.197488	+	0.980305i	$0.436722\pi$
$642$		−	20.0000i		−	0.789337i
$643$			16.0000i			0.630978i	0.948929	+	0.315489i	$0.102169\pi$
$643$			16.0000i			0.630978i	−0.948929	+	0.315489i	$0.897831\pi$
$644$	8.00000			0.315244
$645$	24.0000	−	12.0000i	0.944999	−	0.472500i
$646$	−24.0000			−0.944267
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$			1.00000i			0.0392837i
$649$	4.00000			0.157014
$650$	−18.0000	+	24.0000i	−0.706018	+	0.941357i
$651$		0			0
$652$		−	8.00000i		−	0.313304i
$653$			6.00000i			0.234798i	0.993085	+	0.117399i	$0.0374557\pi$
$653$			6.00000i			0.234798i	−0.993085	+	0.117399i	$0.962544\pi$
$654$	10.0000			0.391031
$655$	12.0000	−	6.00000i	0.468879	−	0.234439i
$656$	10.0000			0.390434
$657$			4.00000i			0.156055i
$658$			24.0000i			0.935617i
$659$	−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
$661$	−2.00000			−0.0777910			−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000			−0.0777910			−0.0388955	+	0.999243i	$0.512384\pi$
$662$		−	28.0000i		−	1.08825i
$663$		−	36.0000i		−	1.39812i
$664$	4.00000			0.155230
$665$	8.00000	+	16.0000i	0.310227	+	0.620453i
$666$	1.00000			0.0387492
$667$			32.0000i			1.23904i
$668$		−	20.0000i		−	0.773823i
$669$	−22.0000			−0.850569
$670$	16.0000	−	8.00000i	0.618134	−	0.309067i
$671$	−12.0000			−0.463255
$672$			2.00000i			0.0771517i
$673$		−	4.00000i		−	0.154189i	−0.997024	−	0.0770943i	$-0.975436\pi$
$673$		−	4.00000i		−	0.154189i	0.997024	−	0.0770943i	$-0.0245643\pi$
$674$	−4.00000			−0.154074
$675$	−4.00000	−	3.00000i	−0.153960	−	0.115470i
$676$	23.0000			0.884615
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$		−	6.00000i		−	0.230429i
$679$	−24.0000			−0.921035
$680$	12.0000	−	6.00000i	0.460179	−	0.230089i
$681$	−12.0000			−0.459841
$682$		0			0
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$	4.00000			0.152944
$685$	18.0000	+	36.0000i	0.687745	+	1.37549i
$686$	20.0000			0.763604
$687$		−	14.0000i		−	0.534133i
$688$		−	12.0000i		−	0.457496i
$689$	12.0000			0.457164
$690$	4.00000	+	8.00000i	0.152277	+	0.304555i
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$			18.0000i			0.684257i
$693$			4.00000i			0.151947i
$694$	4.00000			0.151838
$695$	8.00000	−	4.00000i	0.303457	−	0.151729i
$696$	−8.00000			−0.303239
$697$		−	60.0000i		−	2.27266i
$698$			2.00000i			0.0757011i
$699$	−18.0000			−0.680823
$700$	−8.00000	−	6.00000i	−0.302372	−	0.226779i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$			6.00000i			0.226455i
$703$		−	4.00000i		−	0.150863i
$704$	2.00000			0.0753778
$705$	−24.0000	+	12.0000i	−0.903892	+	0.451946i
$706$	14.0000			0.526897
$707$		−	24.0000i		−	0.902613i
$708$			2.00000i			0.0751646i
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$	12.0000	+	24.0000i	0.450352	+	0.900704i
$711$	−8.00000			−0.300023
$712$		−	14.0000i		−	0.524672i
$713$		0			0
$714$	12.0000			0.449089
$715$	12.0000	+	24.0000i	0.448775	+	0.897549i
$716$	18.0000			0.672692
$717$		−	20.0000i		−	0.746914i
$718$		0			0
$719$	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
$721$	28.0000			1.04277
$722$			3.00000i			0.111648i
$723$			14.0000i			0.520666i
$724$	−18.0000			−0.668965
$725$	24.0000	−	32.0000i	0.891338	−	1.18845i
$726$	−7.00000			−0.259794
$727$			26.0000i			0.964287i	0.876092	+	0.482143i	$0.160142\pi$
$727$			26.0000i			0.964287i	−0.876092	+	0.482143i	$0.839858\pi$
$728$			12.0000i			0.444750i
$729$	−1.00000			−0.0370370
$730$	−8.00000	+	4.00000i	−0.296093	+	0.148047i
$731$	−72.0000			−2.66302
$732$		−	6.00000i		−	0.221766i
$733$			14.0000i			0.517102i	0.965998	+	0.258551i	$0.0832450\pi$
$733$			14.0000i			0.517102i	−0.965998	+	0.258551i	$0.916755\pi$
$734$	2.00000			0.0738213
$735$	3.00000	+	6.00000i	0.110657	+	0.221313i
$736$	4.00000			0.147442
$737$		−	16.0000i		−	0.589368i
$738$			10.0000i			0.368105i
$739$	−32.0000			−1.17714			−0.588570	−	0.808447i	$-0.700309\pi$
$739$	−32.0000			−1.17714			−0.588570	+	0.808447i	$0.700309\pi$
$740$	1.00000	+	2.00000i	0.0367607	+	0.0735215i
$741$	24.0000			0.881662
$742$			4.00000i			0.146845i
$743$		−	4.00000i		−	0.146746i	−0.997305	−	0.0733729i	$-0.976624\pi$
$743$		−	4.00000i		−	0.146746i	0.997305	−	0.0733729i	$-0.0233763\pi$
$744$		0			0
$745$	−32.0000	+	16.0000i	−1.17239	+	0.586195i
$746$	−22.0000			−0.805477
$747$			4.00000i			0.146352i
$748$		−	12.0000i		−	0.438763i
$749$	40.0000			1.46157
$750$	2.00000	−	11.0000i	0.0730297	−	0.401663i
$751$	−8.00000			−0.291924			−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000			−0.291924			−0.145962	+	0.989290i	$0.546628\pi$
$752$			12.0000i			0.437595i
$753$		−	18.0000i		−	0.655956i
$754$	−48.0000			−1.74806
$755$	−32.0000	+	16.0000i	−1.16460	+	0.582300i
$756$	−2.00000			−0.0727393
$757$			50.0000i			1.81728i	0.417579	+	0.908640i	$0.362879\pi$
$757$			50.0000i			1.81728i	−0.417579	+	0.908640i	$0.637121\pi$
$758$			4.00000i			0.145287i
$759$	8.00000			0.290382
$760$	4.00000	+	8.00000i	0.145095	+	0.290191i
$761$	−10.0000			−0.362500			−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000			−0.362500			−0.181250	+	0.983437i	$0.558014\pi$
$762$		−	14.0000i		−	0.507166i
$763$			20.0000i			0.724049i
$764$	−12.0000			−0.434145
$765$	6.00000	+	12.0000i	0.216930	+	0.433861i
$766$	−24.0000			−0.867155
$767$			12.0000i			0.433295i
$768$			1.00000i			0.0360844i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$	−8.00000	+	4.00000i	−0.288300	+	0.144150i
$771$	−14.0000			−0.504198
$772$		−	16.0000i		−	0.575853i
$773$			38.0000i			1.36677i	0.730061	+	0.683383i	$0.239492\pi$
$773$			38.0000i			1.36677i	−0.730061	+	0.683383i	$0.760508\pi$
$774$	12.0000			0.431331
$775$		0			0
$776$	−12.0000			−0.430775
$777$			2.00000i			0.0717496i
$778$		−	12.0000i		−	0.430221i
$779$	40.0000			1.43315
$780$	−12.0000	+	6.00000i	−0.429669	+	0.214834i
$781$	24.0000			0.858788
$782$		−	24.0000i		−	0.858238i
$783$		−	8.00000i		−	0.285897i
$784$	3.00000			0.107143
$785$	14.0000	+	28.0000i	0.499681	+	0.999363i
$786$	6.00000			0.214013
$787$			16.0000i			0.570338i	0.958477	+	0.285169i	$0.0920498\pi$
$787$			16.0000i			0.570338i	−0.958477	+	0.285169i	$0.907950\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−8.00000			−0.284808
$790$	−8.00000	−	16.0000i	−0.284627	−	0.569254i
$791$	12.0000			0.426671
$792$			2.00000i			0.0710669i
$793$		−	36.0000i		−	1.27840i
$794$	18.0000			0.638796
$795$	−4.00000	+	2.00000i	−0.141865	+	0.0709327i
$796$	−8.00000			−0.283552
$797$		−	30.0000i		−	1.06265i	−0.847167	−	0.531327i	$-0.821693\pi$
$797$		−	30.0000i		−	1.06265i	0.847167	−	0.531327i	$-0.178307\pi$
$798$			8.00000i			0.283197i
$799$	72.0000			2.54718
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$	14.0000			0.494666
$802$			10.0000i			0.353112i
$803$			8.00000i			0.282314i
$804$	8.00000			0.282138
$805$	−16.0000	+	8.00000i	−0.563926	+	0.281963i
$806$		0			0
$807$			4.00000i			0.140807i
$808$		−	12.0000i		−	0.422159i
$809$	6.00000			0.210949			0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000			0.210949			0.105474	+	0.994422i	$0.466364\pi$
$810$	−1.00000	−	2.00000i	−0.0351364	−	0.0702728i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$		−	16.0000i		−	0.561490i
$813$			16.0000i			0.561144i
$814$	2.00000			0.0701000
$815$	8.00000	+	16.0000i	0.280228	+	0.560456i
$816$	6.00000			0.210042
$817$		−	48.0000i		−	1.67931i
$818$			38.0000i			1.32864i
$819$	−12.0000			−0.419314
$820$	−20.0000	+	10.0000i	−0.698430	+	0.349215i
$821$	−12.0000			−0.418803			−0.209401	−	0.977830i	$-0.567152\pi$
$821$	−12.0000			−0.418803			−0.209401	+	0.977830i	$0.567152\pi$
$822$			18.0000i			0.627822i
$823$			18.0000i			0.627441i	0.949515	+	0.313720i	$0.101575\pi$
$823$			18.0000i			0.627441i	−0.949515	+	0.313720i	$0.898425\pi$
$824$	14.0000			0.487713
$825$	−8.00000	−	6.00000i	−0.278524	−	0.208893i
$826$	−4.00000			−0.139178
$827$		−	20.0000i		−	0.695468i	−0.937593	−	0.347734i	$-0.886951\pi$
$827$		−	20.0000i		−	0.695468i	0.937593	−	0.347734i	$-0.113049\pi$
$828$			4.00000i			0.139010i
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	−8.00000	+	4.00000i	−0.277684	+	0.138842i
$831$	14.0000			0.485655
$832$			6.00000i			0.208013i
$833$		−	18.0000i		−	0.623663i
$834$	4.00000			0.138509
$835$	20.0000	+	40.0000i	0.692129	+	1.38426i
$836$	8.00000			0.276686
$837$		0			0
$838$		−	30.0000i		−	1.03633i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$	−2.00000	−	4.00000i	−0.0690066	−	0.138013i
$841$	35.0000			1.20690
$842$		−	10.0000i		−	0.344623i
$843$			30.0000i			1.03325i
$844$	12.0000			0.413057
$845$	−46.0000	+	23.0000i	−1.58245	+	0.791224i
$846$	−12.0000			−0.412568
$847$		−	14.0000i		−	0.481046i
$848$			2.00000i			0.0686803i
$849$	8.00000			0.274559
$850$	−18.0000	+	24.0000i	−0.617395	+	0.823193i
$851$	4.00000			0.137118
$852$			12.0000i			0.411113i
$853$		−	18.0000i		−	0.616308i	−0.951336	−	0.308154i	$-0.900289\pi$
$853$		−	18.0000i		−	0.616308i	0.951336	−	0.308154i	$-0.0997113\pi$
$854$	12.0000			0.410632
$855$	−8.00000	+	4.00000i	−0.273594	+	0.136797i
$856$	20.0000			0.683586
$857$			42.0000i			1.43469i	0.696717	+	0.717346i	$0.254643\pi$
$857$			42.0000i			1.43469i	−0.696717	+	0.717346i	$0.745357\pi$
$858$			12.0000i			0.409673i
$859$	−24.0000			−0.818869			−0.409435	−	0.912339i	$-0.634274\pi$
$859$	−24.0000			−0.818869			−0.409435	+	0.912339i	$0.634274\pi$
$860$	12.0000	+	24.0000i	0.409197	+	0.818393i
$861$	−20.0000			−0.681598
$862$		0			0
$863$		−	40.0000i		−	1.36162i	−0.732462	−	0.680808i	$-0.761629\pi$
$863$		−	40.0000i		−	1.36162i	0.732462	−	0.680808i	$-0.238371\pi$
$864$	−1.00000			−0.0340207
$865$	−18.0000	−	36.0000i	−0.612018	−	1.22404i
$866$	−4.00000			−0.135926
$867$		−	19.0000i		−	0.645274i
$868$		0			0
$869$	−16.0000			−0.542763
$870$	16.0000	−	8.00000i	0.542451	−	0.271225i
$871$	48.0000			1.62642
$872$			10.0000i			0.338643i
$873$		−	12.0000i		−	0.406138i
$874$	16.0000			0.541208
$875$	22.0000	+	4.00000i	0.743736	+	0.135225i
$876$	−4.00000			−0.135147
$877$			22.0000i			0.742887i	0.928456	+	0.371444i	$0.121137\pi$
$877$			22.0000i			0.742887i	−0.928456	+	0.371444i	$0.878863\pi$
$878$		−	8.00000i		−	0.269987i
$879$	−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
$883$			16.0000i			0.538443i	0.963078	+	0.269221i	$0.0867663\pi$
$883$			16.0000i			0.538443i	−0.963078	+	0.269221i	$0.913234\pi$
$884$	36.0000			1.21081
$885$	−2.00000	−	4.00000i	−0.0672293	−	0.134459i
$886$	−20.0000			−0.671913
$887$			24.0000i			0.805841i	0.915235	+	0.402921i	$0.132005\pi$
$887$			24.0000i			0.805841i	−0.915235	+	0.402921i	$0.867995\pi$
$888$			1.00000i			0.0335578i
$889$	28.0000			0.939090
$890$	14.0000	+	28.0000i	0.469281	+	0.938562i
$891$	−2.00000			−0.0670025
$892$		−	22.0000i		−	0.736614i
$893$			48.0000i			1.60626i
$894$	−16.0000			−0.535120
$895$	−36.0000	+	18.0000i	−1.20335	+	0.601674i
$896$	−2.00000			−0.0668153
$897$			24.0000i			0.801337i
$898$			6.00000i			0.200223i
$899$		0			0
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$	12.0000			0.399778
$902$			20.0000i			0.665927i
$903$			24.0000i			0.798670i
$904$	6.00000			0.199557
$905$	36.0000	−	18.0000i	1.19668	−	0.598340i
$906$	−16.0000			−0.531564
$907$		−	4.00000i		−	0.132818i	−0.997792	−	0.0664089i	$-0.978846\pi$
$907$		−	4.00000i		−	0.132818i	0.997792	−	0.0664089i	$-0.0211542\pi$
$908$		−	12.0000i		−	0.398234i
$909$	12.0000			0.398015
$910$	−12.0000	−	24.0000i	−0.397796	−	0.795592i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$			4.00000i			0.132453i
$913$			8.00000i			0.264761i
$914$	4.00000			0.132308
$915$	6.00000	+	12.0000i	0.198354	+	0.396708i
$916$	14.0000			0.462573
$917$			12.0000i			0.396275i
$918$			6.00000i			0.198030i
$919$	32.0000			1.05558			0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000			1.05558			0.527791	+	0.849374i	$0.323020\pi$
$920$	−8.00000	+	4.00000i	−0.263752	+	0.131876i
$921$	4.00000			0.131804
$922$		−	12.0000i		−	0.395199i
$923$			72.0000i			2.36991i
$924$	−4.00000			−0.131590
$925$	−4.00000	−	3.00000i	−0.131519	−	0.0986394i
$926$	−34.0000			−1.11731
$927$			14.0000i			0.459820i
$928$		−	8.00000i		−	0.262613i
$929$	−46.0000			−1.50921			−0.754606	−	0.656179i	$-0.772172\pi$
$929$	−46.0000			−1.50921			−0.754606	+	0.656179i	$0.772172\pi$
$930$		0			0
$931$	12.0000			0.393284
$932$		−	18.0000i		−	0.589610i
$933$		−	4.00000i		−	0.130954i
$934$	20.0000			0.654420
$935$	12.0000	+	24.0000i	0.392442	+	0.784884i
$936$	−6.00000			−0.196116
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$			16.0000i			0.522419i
$939$	16.0000			0.522140
$940$	−12.0000	−	24.0000i	−0.391397	−	0.782794i
$941$	−48.0000			−1.56476			−0.782378	−	0.622804i	$-0.785993\pi$
$941$	−48.0000			−1.56476			−0.782378	+	0.622804i	$0.785993\pi$
$942$			14.0000i			0.456145i
$943$			40.0000i			1.30258i
$944$	−2.00000			−0.0650945
$945$	4.00000	−	2.00000i	0.130120	−	0.0650600i
$946$	24.0000			0.780307
$947$			12.0000i			0.389948i	0.980808	+	0.194974i	$0.0624622\pi$
$947$			12.0000i			0.389948i	−0.980808	+	0.194974i	$0.937538\pi$
$948$		−	8.00000i		−	0.259828i
$949$	−24.0000			−0.779073
$950$	−16.0000	−	12.0000i	−0.519109	−	0.389331i
$951$	−2.00000			−0.0648544
$952$			12.0000i			0.388922i
$953$		−	2.00000i		−	0.0647864i	−0.999475	−	0.0323932i	$-0.989687\pi$
$953$		−	2.00000i		−	0.0647864i	0.999475	−	0.0323932i	$-0.0103129\pi$
$954$	−2.00000			−0.0647524
$955$	24.0000	−	12.0000i	0.776622	−	0.388311i
$956$	20.0000			0.646846
$957$		−	16.0000i		−	0.517207i
$958$			36.0000i			1.16311i
$959$	−36.0000			−1.16250
$960$	−1.00000	−	2.00000i	−0.0322749	−	0.0645497i
$961$	−31.0000			−1.00000
$962$			6.00000i			0.193448i
$963$			20.0000i			0.644491i
$964$	−14.0000			−0.450910
$965$	16.0000	+	32.0000i	0.515058	+	1.03012i
$966$	−8.00000			−0.257396
$967$		−	34.0000i		−	1.09337i	−0.837340	−	0.546683i	$-0.815890\pi$
$967$		−	34.0000i		−	1.09337i	0.837340	−	0.546683i	$-0.184110\pi$
$968$		−	7.00000i		−	0.224989i
$969$	24.0000			0.770991
$970$	24.0000	−	12.0000i	0.770594	−	0.385297i
$971$	−14.0000			−0.449281			−0.224641	−	0.974442i	$-0.572121\pi$
$971$	−14.0000			−0.449281			−0.224641	+	0.974442i	$0.572121\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			8.00000i			0.256468i
$974$	2.00000			0.0640841
$975$	18.0000	−	24.0000i	0.576461	−	0.768615i
$976$	6.00000			0.192055
$977$			2.00000i			0.0639857i	0.999488	+	0.0319928i	$0.0101854\pi$
$977$			2.00000i			0.0639857i	−0.999488	+	0.0319928i	$0.989815\pi$
$978$			8.00000i			0.255812i
$979$	28.0000			0.894884
$980$	−6.00000	+	3.00000i	−0.191663	+	0.0958315i
$981$	−10.0000			−0.319275
$982$		−	2.00000i		−	0.0638226i
$983$		−	12.0000i		−	0.382741i	−0.981518	−	0.191370i	$-0.938707\pi$
$983$		−	12.0000i		−	0.382741i	0.981518	−	0.191370i	$-0.0612931\pi$
$984$	−10.0000			−0.318788
$985$	6.00000	+	12.0000i	0.191176	+	0.382352i
$986$	−48.0000			−1.52863
$987$		−	24.0000i		−	0.763928i
$988$			24.0000i			0.763542i
$989$	48.0000			1.52631
$990$	−2.00000	−	4.00000i	−0.0635642	−	0.127128i
$991$	−56.0000			−1.77890			−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000			−1.77890			−0.889449	+	0.457034i	$0.848912\pi$
$992$		0			0
$993$			28.0000i			0.888553i
$994$	−24.0000			−0.761234
$995$	16.0000	−	8.00000i	0.507234	−	0.253617i
$996$	−4.00000			−0.126745
$997$		−	42.0000i		−	1.33015i	−0.746775	−	0.665077i	$-0.768399\pi$
$997$		−	42.0000i		−	1.33015i	0.746775	−	0.665077i	$-0.231601\pi$
$998$		−	12.0000i		−	0.379853i
$999$	−1.00000			−0.0316386

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} -2.00000 q^{11} -1.00000i q^{12} -6.00000i q^{13} +2.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} -6.00000i q^{17} +1.00000i q^{18} +4.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} -2.00000 q^{21} +2.00000i q^{22} +4.00000i q^{23} -1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} -6.00000 q^{26} -1.00000i q^{27} -2.00000i q^{28} +8.00000 q^{29} +(2.00000 - 1.00000i) q^{30} -1.00000i q^{32} -2.00000i q^{33} -6.00000 q^{34} +(2.00000 + 4.00000i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -4.00000i q^{38} +6.00000 q^{39} +(1.00000 + 2.00000i) q^{40} +10.0000 q^{41} +2.00000i q^{42} -12.0000i q^{43} +2.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} +4.00000 q^{46} +12.0000i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +6.00000 q^{51} +6.00000i q^{52} +2.00000i q^{53} -1.00000 q^{54} +(-4.00000 + 2.00000i) q^{55} -2.00000 q^{56} +4.00000i q^{57} -8.00000i q^{58} -2.00000 q^{59} +(-1.00000 - 2.00000i) q^{60} +6.00000 q^{61} -2.00000i q^{63} -1.00000 q^{64} +(-6.00000 - 12.0000i) q^{65} -2.00000 q^{66} +8.00000i q^{67} +6.00000i q^{68} -4.00000 q^{69} +(4.00000 - 2.00000i) q^{70} -12.0000 q^{71} -1.00000i q^{72} -4.00000i q^{73} -1.00000 q^{74} +(4.00000 + 3.00000i) q^{75} -4.00000 q^{76} -4.00000i q^{77} -6.00000i q^{78} +8.00000 q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -10.0000i q^{82} -4.00000i q^{83} +2.00000 q^{84} +(-6.00000 - 12.0000i) q^{85} -12.0000 q^{86} +8.00000i q^{87} -2.00000i q^{88} -14.0000 q^{89} +(1.00000 + 2.00000i) q^{90} +12.0000 q^{91} -4.00000i q^{92} +12.0000 q^{94} +(8.00000 - 4.00000i) q^{95} +1.00000 q^{96} +12.0000i q^{97} -3.00000i q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{9} - 2 q^{10} - 4 q^{11} + 4 q^{14} + 2 q^{15} + 2 q^{16} + 8 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{24} + 6 q^{25} - 12 q^{26} + 16 q^{29} + 4 q^{30} - 12 q^{34} + 4 q^{35} + 2 q^{36} + 12 q^{39} + 2 q^{40} + 20 q^{41} + 4 q^{44} - 4 q^{45} + 8 q^{46} + 6 q^{49} - 8 q^{50} + 12 q^{51} - 2 q^{54} - 8 q^{55} - 4 q^{56} - 4 q^{59} - 2 q^{60} + 12 q^{61} - 2 q^{64} - 12 q^{65} - 4 q^{66} - 8 q^{69} + 8 q^{70} - 24 q^{71} - 2 q^{74} + 8 q^{75} - 8 q^{76} + 16 q^{79} + 4 q^{80} + 2 q^{81} + 4 q^{84} - 12 q^{85} - 24 q^{86} - 28 q^{89} + 2 q^{90} + 24 q^{91} + 24 q^{94} + 16 q^{95} + 2 q^{96} + 4 q^{99}+O(q^{100}) \) 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 - 12 * q^26 + 16 * q^29 + 4 * q^30 - 12 * q^34 + 4 * q^35 + 2 * q^36 + 12 * q^39 + 2 * q^40 + 20 * q^41 + 4 * q^44 - 4 * q^45 + 8 * q^46 + 6 * q^49 - 8 * q^50 + 12 * q^51 - 2 * q^54 - 8 * q^55 - 4 * q^56 - 4 * q^59 - 2 * q^60 + 12 * q^61 - 2 * q^64 - 12 * q^65 - 4 * q^66 - 8 * q^69 + 8 * q^70 - 24 * q^71 - 2 * q^74 + 8 * q^75 - 8 * q^76 + 16 * q^79 + 4 * q^80 + 2 * q^81 + 4 * q^84 - 12 * q^85 - 24 * q^86 - 28 * q^89 + 2 * q^90 + 24 * q^91 + 24 * q^94 + 16 * q^95 + 2 * q^96 + 4 * q^99

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