LMFDB - Embedded newform 1050.2.i.n.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1050.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.i (of order $3$, degree $2$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			751.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.751
Dual form			1050.2.i.n.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{12} +5.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.50000 - 6.06218i) q^{19} +(2.50000 - 0.866025i) q^{21} +(3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{26} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +1.00000 q^{36} +(0.500000 - 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-2.50000 - 4.33013i) q^{39} +(0.500000 - 2.59808i) q^{42} +8.00000 q^{43} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(3.00000 + 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} -7.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} -8.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(6.50000 + 11.2583i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} +12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.50000 - 4.33013i) q^{73} +(-0.500000 - 0.866025i) q^{74} -7.00000 q^{76} -5.00000 q^{78} +(3.50000 - 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} -18.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{89} +(-2.50000 + 12.9904i) q^{91} -6.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} -7.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} - q^{12} + 10 q^{13} + 4 q^{14} - q^{16} + 6 q^{17} + q^{18} + 7 q^{19} + 5 q^{21} + 6 q^{23} + q^{24} + 5 q^{26} + 2 q^{27} + 5 q^{28} - 8 q^{31} + q^{32} + 12 q^{34} + 2 q^{36} + q^{37} - 7 q^{38} - 5 q^{39} + q^{42} + 16 q^{43} - 6 q^{46} - 6 q^{47} + 2 q^{48} - 13 q^{49} + 6 q^{51} - 5 q^{52} + 6 q^{53} + q^{54} + q^{56} - 14 q^{57} + 6 q^{59} + q^{61} - 16 q^{62} - 4 q^{63} + 2 q^{64} + 13 q^{67} + 6 q^{68} - 12 q^{69} + 24 q^{71} + q^{72} - 5 q^{73} - q^{74} - 14 q^{76} - 10 q^{78} + 7 q^{79} - q^{81} - 36 q^{83} - 4 q^{84} + 8 q^{86} + 6 q^{89} - 5 q^{91} - 12 q^{92} - 8 q^{93} + 6 q^{94} + q^{96} - 14 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9 - q^12 + 10 * q^13 + 4 * q^14 - q^16 + 6 * q^17 + q^18 + 7 * q^19 + 5 * q^21 + 6 * q^23 + q^24 + 5 * q^26 + 2 * q^27 + 5 * q^28 - 8 * q^31 + q^32 + 12 * q^34 + 2 * q^36 + q^37 - 7 * q^38 - 5 * q^39 + q^42 + 16 * q^43 - 6 * q^46 - 6 * q^47 + 2 * q^48 - 13 * q^49 + 6 * q^51 - 5 * q^52 + 6 * q^53 + q^54 + q^56 - 14 * q^57 + 6 * q^59 + q^61 - 16 * q^62 - 4 * q^63 + 2 * q^64 + 13 * q^67 + 6 * q^68 - 12 * q^69 + 24 * q^71 + q^72 - 5 * q^73 - q^74 - 14 * q^76 - 10 * q^78 + 7 * q^79 - q^81 - 36 * q^83 - 4 * q^84 + 8 * q^86 + 6 * q^89 - 5 * q^91 - 12 * q^92 - 8 * q^93 + 6 * q^94 + q^96 - 14 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$	2.50000	−	0.866025i	0.545545	−	0.188982i
$22$		0			0
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$	1.00000			0.192450
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	6.00000			1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−3.50000	−	6.06218i	−0.567775	−	0.983415i
$39$	−2.50000	−	4.33013i	−0.400320	−	0.693375i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.500000	−	2.59808i	0.0771517	−	0.400892i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	1.00000			0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$	−7.00000			−0.927173
$58$		0			0
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−8.00000			−1.01600
$63$	−2.00000	−	1.73205i	−0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	0.923408	+	0.383819i	$0.125391\pi$
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	−0.129307	+	0.991605i	$0.541275\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	−6.00000			−0.722315
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−2.50000	−	4.33013i	−0.292603	−	0.506803i	0.681822	−	0.731519i	$-0.261188\pi$
$73$	−2.50000	−	4.33013i	−0.292603	−	0.506803i	−0.974424	+	0.224716i	$0.927855\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	−7.00000			−0.802955
$77$		0			0
$78$	−5.00000			−0.566139
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	−0.599164	−	0.800626i	$-0.704500\pi$
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	0.992945	+	0.118578i	$0.0378336\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−18.0000			−1.97576			−0.987878	−	0.155230i	$-0.950388\pi$
$83$	−18.0000			−1.97576			−0.987878	+	0.155230i	$0.950388\pi$
$84$	−2.00000	−	1.73205i	−0.218218	−	0.188982i
$85$		0			0
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$		0			0
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	−2.50000	+	12.9904i	−0.262071	+	1.36176i
$92$	−6.00000			−0.625543
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$		0			0
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	6.00000			0.582772
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.00813215	−	0.999967i	$-0.497411\pi$
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.861931	−	0.507026i	$-0.169255\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$		0			0
$111$	−1.00000			−0.0949158
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−3.50000	+	6.06218i	−0.327805	+	0.567775i
$115$		0			0
$116$		0			0
$117$	−2.50000	+	4.33013i	−0.231125	+	0.400320i
$118$	6.00000			0.552345
$119$	−15.0000	+	5.19615i	−1.37505	+	0.476331i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−0.500000	−	0.866025i	−0.0452679	−	0.0784063i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$		0			0
$126$	−2.50000	+	0.866025i	−0.222718	+	0.0771517i
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$		0			0
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	14.0000	+	12.1244i	1.21395	+	1.05131i
$134$	13.0000			1.12303
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	11.0000			0.933008			0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000			0.933008			0.466504	+	0.884519i	$0.345513\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	−5.00000			−0.413803
$147$	1.00000	+	6.92820i	0.0824786	+	0.571429i
$148$	−1.00000			−0.0821995
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	−0.999953	−	0.00974235i	$-0.996899\pi$
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	0.508413	+	0.861113i	$0.330232\pi$
$150$		0			0
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	0.885653	−	0.464348i	$-0.153711\pi$
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	−0.844963	+	0.534824i	$0.820378\pi$
$152$	−3.50000	+	6.06218i	−0.283887	+	0.491708i
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$	−2.50000	+	4.33013i	−0.200160	+	0.346688i
$157$	0.500000	+	0.866025i	0.0399043	+	0.0691164i	0.885288	−	0.465044i	$-0.153961\pi$
$157$	0.500000	+	0.866025i	0.0399043	+	0.0691164i	−0.845383	+	0.534160i	$0.820628\pi$
$158$	−3.50000	−	6.06218i	−0.278445	−	0.482281i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$	12.0000	+	10.3923i	0.945732	+	0.819028i
$162$	−1.00000			−0.0785674
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$		0			0
$165$		0			0
$166$	−9.00000	+	15.5885i	−0.698535	+	1.20990i
$167$	−6.00000			−0.464294			−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000			−0.464294			−0.232147	+	0.972681i	$0.574575\pi$
$168$	−2.50000	+	0.866025i	−0.192879	+	0.0668153i
$169$	12.0000			0.923077
$170$		0			0
$171$	3.50000	+	6.06218i	0.267652	+	0.463586i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.00000	−	5.19615i	0.225494	−	0.390567i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	10.0000	+	8.66025i	0.741249	+	0.641941i
$183$	−1.00000			−0.0739221
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$		0			0
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$		0			0
$188$	6.00000			0.437595
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$		0			0
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	−0.992434	+	0.122782i	$0.960818\pi$
$200$		0			0
$201$	6.50000	−	11.2583i	0.458475	−	0.794101i
$202$		0			0
$203$		0			0
$204$	−6.00000			−0.420084
$205$		0			0
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$		0			0
$210$		0			0
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	−6.00000	−	10.3923i	−0.411113	−	0.712069i
$214$	−9.00000	−	15.5885i	−0.615227	−	1.06561i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	20.0000	−	6.92820i	1.35769	−	0.470317i
$218$	7.00000			0.474100
$219$	−2.50000	+	4.33013i	−0.168934	+	0.292603i
$220$		0			0
$221$	15.0000	+	25.9808i	1.00901	+	1.74766i
$222$	−0.500000	+	0.866025i	−0.0335578	+	0.0581238i
$223$	17.0000			1.13840			0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000			1.13840			0.569202	+	0.822198i	$0.307252\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$		0			0
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$	3.50000	+	6.06218i	0.231793	+	0.401478i
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	−0.936728	−	0.350058i	$-0.886162\pi$
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	0.771523	+	0.636201i	$0.219495\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	0.142166	+	0.989843i	$0.454593\pi$
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	−0.928312	+	0.371802i	$0.878740\pi$
$234$	2.50000	+	4.33013i	0.163430	+	0.283069i
$235$		0			0
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$	−7.00000			−0.454699
$238$	−3.00000	+	15.5885i	−0.194461	+	1.01045i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$	−5.50000	−	9.52628i	−0.353553	−	0.612372i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.00000			−0.0640184
$245$		0			0
$246$		0			0
$247$	17.5000	−	30.3109i	1.11350	−	1.92864i
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$	9.00000	+	15.5885i	0.570352	+	0.987878i
$250$		0			0
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$	−0.500000	+	2.59808i	−0.0314970	+	0.163663i
$253$		0			0
$254$	5.50000	−	9.52628i	0.345101	−	0.597732i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.0000	−	20.7846i	0.748539	−	1.29651i	−0.199983	−	0.979799i	$-0.564089\pi$
$257$	12.0000	−	20.7846i	0.748539	−	1.29651i	0.948523	−	0.316709i	$-0.102578\pi$
$258$	−8.00000			−0.498058
$259$	2.00000	+	1.73205i	0.124274	+	0.107624i
$260$		0			0
$261$		0			0
$262$	3.00000	+	5.19615i	0.185341	+	0.321019i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$		0			0
$266$	17.5000	−	6.06218i	1.07299	−	0.371696i
$267$	−6.00000			−0.367194
$268$	6.50000	−	11.2583i	0.397051	−	0.687712i
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$		0			0
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	0.384201	+	0.923249i	$0.374477\pi$
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	−0.991658	+	0.128897i	$0.958856\pi$
$272$	−6.00000			−0.363803
$273$	12.5000	−	4.33013i	0.756534	−	0.262071i
$274$	18.0000			1.08742
$275$		0			0
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$	5.50000	−	9.52628i	0.329868	−	0.571348i
$279$	8.00000			0.478947
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	0.782104	−	0.623148i	$-0.214146\pi$
$283$	−2.50000	−	4.33013i	−0.148610	−	0.257399i	−0.930714	+	0.365748i	$0.880813\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	3.50000	+	6.06218i	0.205174	+	0.355371i
$292$	−2.50000	+	4.33013i	−0.146301	+	0.253402i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$	6.50000	+	2.59808i	0.379088	+	0.151523i
$295$		0			0
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$		0			0
$298$	6.00000	+	10.3923i	0.347571	+	0.602010i
$299$	15.0000	−	25.9808i	0.867472	−	1.50251i
$300$		0			0
$301$	−4.00000	+	20.7846i	−0.230556	+	1.19800i
$302$	1.00000			0.0575435
$303$		0			0
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$		0			0
$306$	−3.00000	+	5.19615i	−0.171499	+	0.297044i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	−13.0000			−0.739544
$310$		0			0
$311$	−9.00000	−	15.5885i	−0.510343	−	0.883940i	−0.999928	−	0.0119847i	$-0.996185\pi$
$311$	−9.00000	−	15.5885i	−0.510343	−	0.883940i	0.489585	−	0.871956i	$-0.337148\pi$
$312$	2.50000	+	4.33013i	0.141535	+	0.245145i
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	1.00000			0.0564333
$315$		0			0
$316$	−7.00000			−0.393781
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$		0			0
$320$		0			0
$321$	−18.0000			−1.00466
$322$	15.0000	−	5.19615i	0.835917	−	0.289570i
$323$	42.0000			2.33694
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−0.500000	−	0.866025i	−0.0276924	−	0.0479647i
$327$	3.50000	−	6.06218i	0.193550	−	0.335239i
$328$		0			0
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$		0			0
$331$	9.50000	−	16.4545i	0.522167	−	0.904420i	−0.477500	−	0.878632i	$-0.658457\pi$
$331$	9.50000	−	16.4545i	0.522167	−	0.904420i	0.999667	−	0.0257885i	$-0.00820965\pi$
$332$	9.00000	+	15.5885i	0.493939	+	0.855528i
$333$	0.500000	+	0.866025i	0.0273998	+	0.0474579i
$334$	−3.00000	+	5.19615i	−0.164153	+	0.284321i
$335$		0			0
$336$	−0.500000	+	2.59808i	−0.0272772	+	0.141737i
$337$	−34.0000			−1.85210			−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−34.0000			−1.85210			−0.926049	+	0.377403i	$0.876817\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$		0			0
$342$	7.00000			0.378517
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−8.00000			−0.431331
$345$		0			0
$346$	9.00000	+	15.5885i	0.483843	+	0.838041i
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$		0			0
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$		0			0
$356$	−6.00000			−0.317999
$357$	12.0000	+	10.3923i	0.635107	+	0.550019i
$358$	−12.0000			−0.634220
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	0.133263	+	0.991081i	$0.457455\pi$
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	−0.924932	+	0.380131i	$0.875879\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$	−11.0000			−0.577350
$364$	12.5000	−	4.33013i	0.655178	−	0.226960i
$365$		0			0
$366$	−0.500000	+	0.866025i	−0.0261354	+	0.0452679i
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$		0			0
$371$	−15.0000	+	5.19615i	−0.778761	+	0.269771i
$372$	8.00000			0.414781
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$		0			0
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$		0			0
$378$	2.00000	+	1.73205i	0.102869	+	0.0890871i
$379$	11.0000			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$380$		0			0
$381$	−5.50000	−	9.52628i	−0.281774	−	0.488046i
$382$	12.0000	+	20.7846i	0.613973	+	1.06343i
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	10.0000			0.508987
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	3.50000	+	6.06218i	0.177686	+	0.307760i
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	0.977086	−	0.212847i	$-0.0682735\pi$
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	−0.672874	+	0.739758i	$0.734940\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$	6.00000			0.302660
$394$	−6.00000	+	10.3923i	−0.302276	+	0.523557i
$395$		0			0
$396$		0			0
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	−11.0000			−0.551380
$399$	3.50000	−	18.1865i	0.175219	−	0.910465i
$400$		0			0
$401$	18.0000	−	31.1769i	0.898877	−	1.55690i	0.0699455	−	0.997551i	$-0.477717\pi$
$401$	18.0000	−	31.1769i	0.898877	−	1.55690i	0.828932	−	0.559350i	$-0.188949\pi$
$402$	−6.50000	−	11.2583i	−0.324191	−	0.561514i
$403$	−20.0000	−	34.6410i	−0.996271	−	1.72559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$	−13.0000			−0.640464
$413$	−15.0000	+	5.19615i	−0.738102	+	0.255686i
$414$	6.00000			0.294884
$415$		0			0
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	−5.50000	−	9.52628i	−0.269336	−	0.466504i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	5.00000			0.243685			0.121843	−	0.992549i	$-0.461120\pi$
$421$	5.00000			0.243685			0.121843	+	0.992549i	$0.461120\pi$
$422$	−6.50000	+	11.2583i	−0.316415	+	0.548047i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$		0			0
$426$	−12.0000			−0.581402
$427$	2.00000	+	1.73205i	0.0967868	+	0.0838198i
$428$	−18.0000			−0.870063
$429$		0			0
$430$		0			0
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	4.00000	−	20.7846i	0.192006	−	0.997693i
$435$		0			0
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	−21.0000	−	36.3731i	−1.00457	−	1.73996i
$438$	2.50000	+	4.33013i	0.119455	+	0.206901i
$439$	−2.50000	+	4.33013i	−0.119318	+	0.206666i	−0.919498	−	0.393095i	$-0.871404\pi$
$439$	−2.50000	+	4.33013i	−0.119318	+	0.206666i	0.800179	+	0.599761i	$0.204738\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	30.0000			1.42695
$443$	21.0000	−	36.3731i	0.997740	−	1.72814i	0.440681	−	0.897664i	$-0.354737\pi$
$443$	21.0000	−	36.3731i	0.997740	−	1.72814i	0.557059	−	0.830473i	$-0.311930\pi$
$444$	0.500000	+	0.866025i	0.0237289	+	0.0410997i
$445$		0			0
$446$	8.50000	−	14.7224i	0.402487	−	0.697127i
$447$	12.0000			0.567581
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$		0			0
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	0.500000	−	0.866025i	0.0234920	−	0.0406894i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	7.00000			0.327805
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	0.297217	+	0.954810i	$0.403942\pi$
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	−0.975498	+	0.220008i	$0.929392\pi$
$458$	2.50000	+	4.33013i	0.116817	+	0.202334i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$		0			0
$465$		0			0
$466$	12.0000	+	20.7846i	0.555889	+	0.962828i
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	0.276360	+	0.961054i	$0.410872\pi$
$467$	−15.0000	+	25.9808i	−0.694117	+	1.20225i	−0.970477	+	0.241192i	$0.922462\pi$
$468$	5.00000			0.231125
$469$	−32.5000	+	11.2583i	−1.50071	+	0.519861i
$470$		0			0
$471$	0.500000	−	0.866025i	0.0230388	−	0.0399043i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$		0			0
$474$	−3.50000	+	6.06218i	−0.160760	+	0.278445i
$475$		0			0
$476$	12.0000	+	10.3923i	0.550019	+	0.476331i
$477$	−6.00000			−0.274721
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$	−5.00000			−0.227744
$483$	3.00000	−	15.5885i	0.136505	−	0.709299i
$484$	−11.0000			−0.500000
$485$		0			0
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.819181	+	0.573535i	$0.194428\pi$
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.0871056	+	0.996199i	$0.472238\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$	−1.00000			−0.0452216
$490$		0			0
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$		0			0
$493$		0			0
$494$	−17.5000	−	30.3109i	−0.787362	−	1.36375i
$495$		0			0
$496$	8.00000			0.359211
$497$	−6.00000	+	31.1769i	−0.269137	+	1.39848i
$498$	18.0000			0.806599
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$		0			0
$501$	3.00000	+	5.19615i	0.134030	+	0.232147i
$502$	−12.0000	+	20.7846i	−0.535586	+	0.927663i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	2.00000	+	1.73205i	0.0890871	+	0.0771517i
$505$		0			0
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$	−5.50000	−	9.52628i	−0.244023	−	0.422660i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	12.5000	−	4.33013i	0.552967	−	0.191554i
$512$	−1.00000			−0.0441942
$513$	3.50000	−	6.06218i	0.154529	−	0.267652i
$514$	−12.0000	−	20.7846i	−0.529297	−	0.916770i
$515$		0			0
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$		0			0
$518$	2.50000	−	0.866025i	0.109844	−	0.0380510i
$519$	18.0000			0.790112
$520$		0			0
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.799370	−	0.600839i	$-0.794833\pi$
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.120656	−	0.992694i	$-0.538500\pi$
$522$		0			0
$523$	−16.0000	+	27.7128i	−0.699631	+	1.21180i	0.268963	+	0.963150i	$0.413319\pi$
$523$	−16.0000	+	27.7128i	−0.699631	+	1.21180i	−0.968594	+	0.248646i	$0.920014\pi$
$524$	6.00000			0.262111
$525$		0			0
$526$		0			0
$527$	24.0000	−	41.5692i	1.04546	−	1.81078i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−6.00000			−0.260378
$532$	3.50000	−	18.1865i	0.151744	−	0.788486i
$533$		0			0
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$		0			0
$536$	−6.50000	−	11.2583i	−0.280757	−	0.486286i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	24.0000			1.03471
$539$		0			0
$540$		0			0
$541$	21.5000	−	37.2391i	0.924357	−	1.60103i	0.131765	−	0.991281i	$-0.457935\pi$
$541$	21.5000	−	37.2391i	0.924357	−	1.60103i	0.792592	−	0.609753i	$-0.208731\pi$
$542$	10.0000	+	17.3205i	0.429537	+	0.743980i
$543$	5.00000	+	8.66025i	0.214571	+	0.371647i
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$		0			0
$546$	2.50000	−	12.9904i	0.106990	−	0.555937i
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	9.00000	−	15.5885i	0.384461	−	0.665906i
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$		0			0
$552$	6.00000			0.255377
$553$	14.0000	+	12.1244i	0.595341	+	0.515580i
$554$	19.0000			0.807233
$555$		0			0
$556$	−5.50000	−	9.52628i	−0.233252	−	0.404004i
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$	4.00000	−	6.92820i	0.169334	−	0.293294i
$559$	40.0000			1.69182
$560$		0			0
$561$		0			0
$562$	−9.00000	+	15.5885i	−0.379642	+	0.657559i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$		0			0
$566$	−5.00000			−0.210166
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	−12.0000			−0.503509
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	−0.190974	−	0.981595i	$-0.561165\pi$
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	0.945573	−	0.325409i	$-0.105502\pi$
$570$		0			0
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866697\pi$
$572$		0			0
$573$	24.0000			1.00261
$574$		0			0
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	0.682730	−	0.730670i	$-0.260792\pi$
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	−0.974144	+	0.225927i	$0.927459\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	5.00000	−	8.66025i	0.207793	−	0.359908i
$580$		0			0
$581$	9.00000	−	46.7654i	0.373383	−	1.94015i
$582$	7.00000			0.290159
$583$		0			0
$584$	2.50000	+	4.33013i	0.103451	+	0.179182i
$585$		0			0
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$	−30.0000			−1.23823			−0.619116	−	0.785299i	$-0.712509\pi$
$587$	−30.0000			−1.23823			−0.619116	+	0.785299i	$0.712509\pi$
$588$	5.50000	−	4.33013i	0.226816	−	0.178571i
$589$	−56.0000			−2.30744
$590$		0			0
$591$	6.00000	+	10.3923i	0.246807	+	0.427482i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$	12.0000			0.491539
$597$	−5.50000	+	9.52628i	−0.225100	+	0.389885i
$598$	−15.0000	−	25.9808i	−0.613396	−	1.06243i
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	16.0000	+	13.8564i	0.652111	+	0.564745i
$603$	−13.0000			−0.529401
$604$	0.500000	−	0.866025i	0.0203447	−	0.0352381i
$605$		0			0
$606$		0			0
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	7.00000			0.283887
$609$		0			0
$610$		0			0
$611$	−15.0000	+	25.9808i	−0.606835	+	1.05107i
$612$	3.00000	+	5.19615i	0.121268	+	0.210042i
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	−0.938967	−	0.344008i	$-0.888215\pi$
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	0.171564	−	0.985173i	$-0.445118\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		0			0
$616$		0			0
$617$	48.0000			1.93241			0.966204	−	0.257780i	$-0.0829910\pi$
$617$	48.0000			1.93241			0.966204	+	0.257780i	$0.0829910\pi$
$618$	−6.50000	+	11.2583i	−0.261468	+	0.452876i
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$		0			0
$621$	3.00000	−	5.19615i	0.120386	−	0.208514i
$622$	−18.0000			−0.721734
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$	5.00000			0.200160
$625$		0			0
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$		0			0
$628$	0.500000	−	0.866025i	0.0199522	−	0.0345582i
$629$	6.00000			0.239236
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	−3.50000	+	6.06218i	−0.139223	+	0.241140i
$633$	6.50000	+	11.2583i	0.258352	+	0.447478i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−32.5000	−	12.9904i	−1.28770	−	0.514698i
$638$		0			0
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$		0			0
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$	−9.00000	+	15.5885i	−0.355202	+	0.615227i
$643$	11.0000			0.433798			0.216899	−	0.976194i	$-0.430406\pi$
$643$	11.0000			0.433798			0.216899	+	0.976194i	$0.430406\pi$
$644$	3.00000	−	15.5885i	0.118217	−	0.614271i
$645$		0			0
$646$	21.0000	−	36.3731i	0.826234	−	1.43108i
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	0.959529	−	0.281609i	$-0.0908680\pi$
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	−0.723645	+	0.690172i	$0.757535\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$		0			0
$650$		0			0
$651$	−16.0000	−	13.8564i	−0.627089	−	0.543075i
$652$	−1.00000			−0.0391630
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$	−3.50000	−	6.06218i	−0.136861	−	0.237050i
$655$		0			0
$656$		0			0
$657$	5.00000			0.195069
$658$	−15.0000	+	5.19615i	−0.584761	+	0.202567i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−17.5000	−	30.3109i	−0.680671	−	1.17896i	−0.974776	−	0.223184i	$-0.928355\pi$
$661$	−17.5000	−	30.3109i	−0.680671	−	1.17896i	0.294105	−	0.955773i	$-0.404978\pi$
$662$	−9.50000	−	16.4545i	−0.369228	−	0.639522i
$663$	15.0000	−	25.9808i	0.582552	−	1.00901i
$664$	18.0000			0.698535
$665$		0			0
$666$	1.00000			0.0387492
$667$		0			0
$668$	3.00000	+	5.19615i	0.116073	+	0.201045i
$669$	−8.50000	−	14.7224i	−0.328629	−	0.569202i
$670$		0			0
$671$		0			0
$672$	2.00000	+	1.73205i	0.0771517	+	0.0668153i
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$	−17.0000	+	29.4449i	−0.654816	+	1.13417i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$	6.00000			0.230429
$679$	3.50000	−	18.1865i	0.134318	−	0.697935i
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	0.539750	−	0.841825i	$-0.318519\pi$
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	−0.998917	+	0.0465244i	$0.985185\pi$
$684$	3.50000	−	6.06218i	0.133826	−	0.231793i
$685$		0			0
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	5.00000			0.190762
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	15.0000	+	25.9808i	0.571454	+	0.989788i
$690$		0			0
$691$	3.50000	−	6.06218i	0.133146	−	0.230616i	−0.791742	−	0.610856i	$-0.790825\pi$
$691$	3.50000	−	6.06218i	0.133146	−	0.230616i	0.924888	+	0.380240i	$0.124159\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	−18.0000			−0.683271
$695$		0			0
$696$		0			0
$697$		0			0
$698$	13.0000	−	22.5167i	0.492057	−	0.852268i
$699$	24.0000			0.907763
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	2.50000	−	4.33013i	0.0943564	−	0.163430i
$703$	−3.50000	−	6.06218i	−0.132005	−	0.228639i
$704$		0			0
$705$		0			0
$706$	24.0000			0.903252
$707$		0			0
$708$	−6.00000			−0.225494
$709$	3.50000	−	6.06218i	0.131445	−	0.227670i	−0.792789	−	0.609497i	$-0.791372\pi$
$709$	3.50000	−	6.06218i	0.131445	−	0.227670i	0.924234	+	0.381827i	$0.124705\pi$
$710$		0			0
$711$	3.50000	+	6.06218i	0.131260	+	0.227349i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	−48.0000			−1.79761
$714$	15.0000	−	5.19615i	0.561361	−	0.194461i
$715$		0			0
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	15.0000	+	25.9808i	0.559795	+	0.969593i
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	−0.306253	−	0.951950i	$-0.599075\pi$
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	0.977539	−	0.210752i	$-0.0675914\pi$
$720$		0			0
$721$	26.0000	+	22.5167i	0.968291	+	0.838564i
$722$	−30.0000			−1.11648
$723$	−2.50000	+	4.33013i	−0.0929760	+	0.161039i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$		0			0
$726$	−5.50000	+	9.52628i	−0.204124	+	0.353553i
$727$	−37.0000			−1.37225			−0.686127	−	0.727482i	$-0.740691\pi$
$727$	−37.0000			−1.37225			−0.686127	+	0.727482i	$0.740691\pi$
$728$	2.50000	−	12.9904i	0.0926562	−	0.481456i
$729$	1.00000			0.0370370
$730$		0			0
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$	0.500000	+	0.866025i	0.0184805	+	0.0320092i
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	0.187096	+	0.982342i	$0.440092\pi$
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	−0.944281	+	0.329141i	$0.893241\pi$
$734$	−8.00000			−0.295285
$735$		0			0
$736$	6.00000			0.221163
$737$		0			0
$738$		0			0
$739$	12.5000	+	21.6506i	0.459820	+	0.796431i	0.998951	−	0.0457903i	$-0.0145806\pi$
$739$	12.5000	+	21.6506i	0.459820	+	0.796431i	−0.539131	+	0.842222i	$0.681247\pi$
$740$		0			0
$741$	−35.0000			−1.28576
$742$	−3.00000	+	15.5885i	−0.110133	+	0.572270i
$743$	30.0000			1.10059			0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000			1.10059			0.550297	+	0.834969i	$0.314515\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$		0			0
$746$	−6.50000	−	11.2583i	−0.237982	−	0.412197i
$747$	9.00000	−	15.5885i	0.329293	−	0.570352i
$748$		0			0
$749$	36.0000	+	31.1769i	1.31541	+	1.13918i
$750$		0			0
$751$	12.5000	−	21.6506i	0.456131	−	0.790043i	−0.542621	−	0.839978i	$-0.682568\pi$
$751$	12.5000	−	21.6506i	0.456131	−	0.790043i	0.998752	+	0.0499348i	$0.0159013\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$	12.0000	+	20.7846i	0.437304	+	0.757433i
$754$		0			0
$755$		0			0
$756$	2.50000	−	0.866025i	0.0909241	−	0.0314970i
$757$	29.0000			1.05402			0.527011	−	0.849858i	$-0.323312\pi$
$757$	29.0000			1.05402			0.527011	+	0.849858i	$0.323312\pi$
$758$	5.50000	−	9.52628i	0.199769	−	0.346010i
$759$		0			0
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$	−11.0000			−0.398488
$763$	−17.5000	+	6.06218i	−0.633543	+	0.219466i
$764$	24.0000			0.868290
$765$		0			0
$766$	−3.00000	−	5.19615i	−0.108394	−	0.187745i
$767$	15.0000	+	25.9808i	0.541619	+	0.938111i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$	5.00000	−	8.66025i	0.179954	−	0.311689i
$773$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$773$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$		0			0
$776$	7.00000			0.251285
$777$	0.500000	−	2.59808i	0.0179374	−	0.0932055i
$778$	12.0000			0.430221
$779$		0			0
$780$		0			0
$781$		0			0
$782$	18.0000	−	31.1769i	0.643679	−	1.11488i
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$		0			0
$786$	3.00000	−	5.19615i	0.107006	−	0.185341i
$787$	−11.5000	−	19.9186i	−0.409931	−	0.710021i	0.584951	−	0.811069i	$-0.301114\pi$
$787$	−11.5000	−	19.9186i	−0.409931	−	0.710021i	−0.994882	+	0.101048i	$0.967780\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$		0			0
$790$		0			0
$791$	3.00000	−	15.5885i	0.106668	−	0.554262i
$792$		0			0
$793$	2.50000	−	4.33013i	0.0887776	−	0.153767i
$794$	7.00000	+	12.1244i	0.248421	+	0.430277i
$795$		0			0
$796$	−5.50000	+	9.52628i	−0.194942	+	0.337650i
$797$	54.0000			1.91278			0.956389	−	0.292096i	$-0.0943526\pi$
$797$	54.0000			1.91278			0.956389	+	0.292096i	$0.0943526\pi$
$798$	−14.0000	−	12.1244i	−0.495595	−	0.429198i
$799$	−36.0000			−1.27359
$800$		0			0
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	−18.0000	−	31.1769i	−0.635602	−	1.10090i
$803$		0			0
$804$	−13.0000			−0.458475
$805$		0			0
$806$	−40.0000			−1.40894
$807$	12.0000	−	20.7846i	0.422420	−	0.731653i
$808$		0			0
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$		0			0
$811$	11.0000			0.386262			0.193131	−	0.981173i	$-0.438136\pi$
$811$	11.0000			0.386262			0.193131	+	0.981173i	$0.438136\pi$
$812$		0			0
$813$	20.0000			0.701431
$814$		0			0
$815$		0			0
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	28.0000	−	48.4974i	0.979596	−	1.69671i
$818$	−5.00000			−0.174821
$819$	−10.0000	−	8.66025i	−0.349428	−	0.302614i
$820$		0			0
$821$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$821$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$822$	−9.00000	−	15.5885i	−0.313911	−	0.543710i
$823$	−2.50000	−	4.33013i	−0.0871445	−	0.150939i	0.819159	−	0.573567i	$-0.194441\pi$
$823$	−2.50000	−	4.33013i	−0.0871445	−	0.150939i	−0.906303	+	0.422628i	$0.861108\pi$
$824$	−6.50000	+	11.2583i	−0.226438	+	0.392203i
$825$		0			0
$826$	−3.00000	+	15.5885i	−0.104383	+	0.542392i
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$	3.00000	−	5.19615i	0.104257	−	0.180579i
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	0.920383	−	0.391018i	$-0.127877\pi$
$829$	3.50000	+	6.06218i	0.121560	+	0.210548i	−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$	9.50000	−	16.4545i	0.329551	−	0.570800i
$832$	5.00000			0.173344
$833$	−6.00000	−	41.5692i	−0.207888	−	1.44029i
$834$	−11.0000			−0.380899
$835$		0			0
$836$		0			0
$837$	−4.00000	−	6.92820i	−0.138260	−	0.239474i
$838$		0			0
$839$	−18.0000			−0.621429			−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000			−0.621429			−0.310715	+	0.950503i	$0.600568\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	2.50000	−	4.33013i	0.0861557	−	0.149226i
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$	6.50000	+	11.2583i	0.223739	+	0.387528i
$845$		0			0
$846$	−6.00000			−0.206284
$847$	22.0000	+	19.0526i	0.755929	+	0.654654i
$848$	−6.00000			−0.206041
$849$	−2.50000	+	4.33013i	−0.0857998	+	0.148610i
$850$		0			0
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$	2.50000	−	0.866025i	0.0855482	−	0.0296348i
$855$		0			0
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$		0			0
$861$		0			0
$862$	18.0000			0.613082
$863$	−15.0000	+	25.9808i	−0.510606	+	0.884395i	0.489319	+	0.872105i	$0.337246\pi$
$863$	−15.0000	+	25.9808i	−0.510606	+	0.884395i	−0.999924	+	0.0122903i	$0.996088\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−17.0000	+	29.4449i	−0.577684	+	1.00058i
$867$	19.0000			0.645274
$868$	−16.0000	−	13.8564i	−0.543075	−	0.470317i
$869$		0			0
$870$		0			0
$871$	32.5000	+	56.2917i	1.10122	+	1.90737i
$872$	−3.50000	−	6.06218i	−0.118525	−	0.205291i
$873$	3.50000	−	6.06218i	0.118457	−	0.205174i
$874$	−42.0000			−1.42067
$875$		0			0
$876$	5.00000			0.168934
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	0.130224	+	0.991485i	$0.458430\pi$
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	−0.923763	+	0.382965i	$0.874903\pi$
$878$	2.50000	+	4.33013i	0.0843709	+	0.146135i
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$		0			0
$881$	−12.0000			−0.404290			−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$	−1.00000	−	6.92820i	−0.0336718	−	0.233285i
$883$	−25.0000			−0.841317			−0.420658	−	0.907219i	$-0.638201\pi$
$883$	−25.0000			−0.841317			−0.420658	+	0.907219i	$0.638201\pi$
$884$	15.0000	−	25.9808i	0.504505	−	0.873828i
$885$		0			0
$886$	−21.0000	−	36.3731i	−0.705509	−	1.22198i
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	−0.811256	−	0.584692i	$-0.801215\pi$
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	0.911986	+	0.410222i	$0.134549\pi$
$888$	1.00000			0.0335578
$889$	−5.50000	+	28.5788i	−0.184464	+	0.958503i
$890$		0			0
$891$		0			0
$892$	−8.50000	−	14.7224i	−0.284601	−	0.492943i
$893$	21.0000	+	36.3731i	0.702738	+	1.21718i
$894$	6.00000	−	10.3923i	0.200670	−	0.347571i
$895$		0			0
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$	−30.0000			−1.00167
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$		0			0
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$	20.0000	−	6.92820i	0.665558	−	0.230556i
$904$	6.00000			0.199557
$905$		0			0
$906$	−0.500000	−	0.866025i	−0.0166114	−	0.0287718i
$907$	3.50000	+	6.06218i	0.116216	+	0.201291i	0.918265	−	0.395966i	$-0.129590\pi$
$907$	3.50000	+	6.06218i	0.116216	+	0.201291i	−0.802049	+	0.597258i	$0.796257\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$		0			0
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	3.50000	−	6.06218i	0.115897	−	0.200739i
$913$		0			0
$914$	14.5000	+	25.1147i	0.479617	+	0.830722i
$915$		0			0
$916$	5.00000			0.165205
$917$	−12.0000	−	10.3923i	−0.396275	−	0.343184i
$918$	6.00000			0.198030
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	3.00000	−	5.19615i	0.0987997	−	0.171126i
$923$	60.0000			1.97492
$924$		0			0
$925$		0			0
$926$	−15.5000	+	26.8468i	−0.509362	+	0.882240i
$927$	6.50000	+	11.2583i	0.213488	+	0.369772i
$928$		0			0
$929$	18.0000	−	31.1769i	0.590561	−	1.02288i	−0.403596	−	0.914937i	$-0.632240\pi$
$929$	18.0000	−	31.1769i	0.590561	−	1.02288i	0.994157	−	0.107944i	$-0.0344268\pi$
$930$		0			0
$931$	−38.5000	+	30.3109i	−1.26179	+	0.993399i
$932$	24.0000			0.786146
$933$	−9.00000	+	15.5885i	−0.294647	+	0.510343i
$934$	15.0000	+	25.9808i	0.490815	+	0.850117i
$935$		0			0
$936$	2.50000	−	4.33013i	0.0817151	−	0.141535i
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$	−6.50000	+	33.7750i	−0.212233	+	1.10279i
$939$	14.0000			0.456873
$940$		0			0
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	0.910773	−	0.412908i	$-0.135487\pi$
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	−0.812975	+	0.582298i	$0.802154\pi$
$942$	−0.500000	−	0.866025i	−0.0162909	−	0.0282166i
$943$		0			0
$944$	−6.00000			−0.195283
$945$		0			0
$946$		0			0
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	0.291835	+	0.956469i	$0.405734\pi$
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927599\pi$
$948$	3.50000	+	6.06218i	0.113675	+	0.196890i
$949$	−12.5000	−	21.6506i	−0.405767	−	0.702809i
$950$		0			0
$951$	−18.0000			−0.583690
$952$	15.0000	−	5.19615i	0.486153	−	0.168408i
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$		0			0
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$		0			0
$958$	−18.0000			−0.581554
$959$	−45.0000	+	15.5885i	−1.45313	+	0.503378i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−2.50000	−	4.33013i	−0.0806032	−	0.139609i
$963$	9.00000	+	15.5885i	0.290021	+	0.502331i
$964$	−2.50000	+	4.33013i	−0.0805196	+	0.139464i
$965$		0			0
$966$	−12.0000	−	10.3923i	−0.386094	−	0.334367i
$967$	41.0000			1.31847			0.659236	−	0.751936i	$-0.270880\pi$
$967$	41.0000			1.31847			0.659236	+	0.751936i	$0.270880\pi$
$968$	−5.50000	+	9.52628i	−0.176777	+	0.306186i
$969$	−21.0000	−	36.3731i	−0.674617	−	1.16847i
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$	1.00000			0.0320750
$973$	−5.50000	+	28.5788i	−0.176322	+	0.916195i
$974$	40.0000			1.28168
$975$		0			0
$976$	0.500000	+	0.866025i	0.0160046	+	0.0277208i
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$	−0.500000	+	0.866025i	−0.0159882	+	0.0276924i
$979$		0			0
$980$		0			0
$981$	−7.00000			−0.223493
$982$	−3.00000	+	5.19615i	−0.0957338	+	0.165816i
$983$	15.0000	+	25.9808i	0.478426	+	0.828658i	0.999694	−	0.0247352i	$-0.00787426\pi$
$983$	15.0000	+	25.9808i	0.478426	+	0.828658i	−0.521268	+	0.853393i	$0.674541\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.00000	+	15.5885i	−0.0954911	+	0.496186i
$988$	−35.0000			−1.11350
$989$	24.0000	−	41.5692i	0.763156	−	1.32182i
$990$		0			0
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	−0.999954	−	0.00956046i	$-0.996957\pi$
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	0.491698	−	0.870766i	$-0.336377\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	−19.0000			−0.602947
$994$	24.0000	+	20.7846i	0.761234	+	0.659248i
$995$		0			0
$996$	9.00000	−	15.5885i	0.285176	−	0.493939i
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	0.950405	−	0.311014i	$-0.100668\pi$
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	−0.744548	+	0.667568i	$0.767335\pi$
$998$	2.50000	+	4.33013i	0.0791361	+	0.137068i
$999$	0.500000	−	0.866025i	0.0158193	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.n.751.1	yes	2
5.2	odd	4		1050.2.o.d.499.2		4
5.3	odd	4		1050.2.o.d.499.1		4
5.4	even	2		1050.2.i.g.751.1	yes	2
7.2	even	3		7350.2.a.bf.1.1		1
7.4	even	3	inner	1050.2.i.n.151.1	yes	2
7.5	odd	6		7350.2.a.k.1.1		1
35.4	even	6		1050.2.i.g.151.1	✓	2
35.9	even	6		7350.2.a.bv.1.1		1
35.18	odd	12		1050.2.o.d.949.2		4
35.19	odd	6		7350.2.a.cv.1.1		1
35.32	odd	12		1050.2.o.d.949.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.g.151.1	✓	2	35.4	even	6
1050.2.i.g.751.1	yes	2	5.4	even	2
1050.2.i.n.151.1	yes	2	7.4	even	3	inner
1050.2.i.n.751.1	yes	2	1.1	even	1	trivial
1050.2.o.d.499.1		4	5.3	odd	4
1050.2.o.d.499.2		4	5.2	odd	4
1050.2.o.d.949.1		4	35.32	odd	12
1050.2.o.d.949.2		4	35.18	odd	12
7350.2.a.k.1.1		1	7.5	odd	6
7350.2.a.bf.1.1		1	7.2	even	3
7350.2.a.bv.1.1		1	35.9	even	6
7350.2.a.cv.1.1		1	35.19	odd	6

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{12} +5.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.50000 - 6.06218i) q^{19} +(2.50000 - 0.866025i) q^{21} +(3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{26} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +1.00000 q^{36} +(0.500000 - 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-2.50000 - 4.33013i) q^{39} +(0.500000 - 2.59808i) q^{42} +8.00000 q^{43} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(3.00000 + 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} -7.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} -8.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(6.50000 + 11.2583i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} +12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.50000 - 4.33013i) q^{73} +(-0.500000 - 0.866025i) q^{74} -7.00000 q^{76} -5.00000 q^{78} +(3.50000 - 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} -18.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{89} +(-2.50000 + 12.9904i) q^{91} -6.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} -7.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} - q^{12} + 10 q^{13} + 4 q^{14} - q^{16} + 6 q^{17} + q^{18} + 7 q^{19} + 5 q^{21} + 6 q^{23} + q^{24} + 5 q^{26} + 2 q^{27} + 5 q^{28} - 8 q^{31} + q^{32} + 12 q^{34} + 2 q^{36} + q^{37} - 7 q^{38} - 5 q^{39} + q^{42} + 16 q^{43} - 6 q^{46} - 6 q^{47} + 2 q^{48} - 13 q^{49} + 6 q^{51} - 5 q^{52} + 6 q^{53} + q^{54} + q^{56} - 14 q^{57} + 6 q^{59} + q^{61} - 16 q^{62} - 4 q^{63} + 2 q^{64} + 13 q^{67} + 6 q^{68} - 12 q^{69} + 24 q^{71} + q^{72} - 5 q^{73} - q^{74} - 14 q^{76} - 10 q^{78} + 7 q^{79} - q^{81} - 36 q^{83} - 4 q^{84} + 8 q^{86} + 6 q^{89} - 5 q^{91} - 12 q^{92} - 8 q^{93} + 6 q^{94} + q^{96} - 14 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 - q^7 - 2 * q^8 - q^9 - q^12 + 10 * q^13 + 4 * q^14 - q^16 + 6 * q^17 + q^18 + 7 * q^19 + 5 * q^21 + 6 * q^23 + q^24 + 5 * q^26 + 2 * q^27 + 5 * q^28 - 8 * q^31 + q^32 + 12 * q^34 + 2 * q^36 + q^37 - 7 * q^38 - 5 * q^39 + q^42 + 16 * q^43 - 6 * q^46 - 6 * q^47 + 2 * q^48 - 13 * q^49 + 6 * q^51 - 5 * q^52 + 6 * q^53 + q^54 + q^56 - 14 * q^57 + 6 * q^59 + q^61 - 16 * q^62 - 4 * q^63 + 2 * q^64 + 13 * q^67 + 6 * q^68 - 12 * q^69 + 24 * q^71 + q^72 - 5 * q^73 - q^74 - 14 * q^76 - 10 * q^78 + 7 * q^79 - q^81 - 36 * q^83 - 4 * q^84 + 8 * q^86 + 6 * q^89 - 5 * q^91 - 12 * q^92 - 8 * q^93 + 6 * q^94 + q^96 - 14 * q^97 - 11 * q^98

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