LMFDB - Embedded newform 483.2.h.a.160.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(160,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("483.160");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.2
Root			$-1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	483.160
Dual form			483.2.h.a.160.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.69614 q^{5} +1.00000i q^{6} +(2.17238 - 1.51022i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.69614 q^{5} +1.00000i q^{6} +(2.17238 - 1.51022i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +1.69614 q^{10} +1.32431i q^{11} +1.00000i q^{12} -5.12311i q^{13} +(-2.17238 + 1.51022i) q^{14} +1.69614i q^{15} -1.00000 q^{16} +1.69614 q^{17} +1.00000 q^{18} -7.73704 q^{19} +1.69614 q^{20} +(-1.51022 - 2.17238i) q^{21} -1.32431i q^{22} +(-2.56155 + 4.05444i) q^{23} -3.00000i q^{24} -2.12311 q^{25} +5.12311i q^{26} +1.00000i q^{27} +(-2.17238 + 1.51022i) q^{28} -8.24621 q^{29} -1.69614i q^{30} -6.24621i q^{31} -5.00000 q^{32} +1.32431 q^{33} -1.69614 q^{34} +(-3.68466 + 2.56155i) q^{35} +1.00000 q^{36} +6.04090i q^{37} +7.73704 q^{38} -5.12311 q^{39} -5.08842 q^{40} -2.87689i q^{41} +(1.51022 + 2.17238i) q^{42} +3.02045i q^{43} -1.32431i q^{44} +1.69614 q^{45} +(2.56155 - 4.05444i) q^{46} +1.12311i q^{47} +1.00000i q^{48} +(2.43845 - 6.56155i) q^{49} +2.12311 q^{50} -1.69614i q^{51} +5.12311i q^{52} +5.08842i q^{53} -1.00000i q^{54} -2.24621i q^{55} +(6.51713 - 4.53067i) q^{56} +7.73704i q^{57} +8.24621 q^{58} -1.12311i q^{59} -1.69614i q^{60} -6.04090 q^{61} +6.24621i q^{62} +(-2.17238 + 1.51022i) q^{63} +7.00000 q^{64} +8.68951i q^{65} -1.32431 q^{66} -15.1022i q^{67} -1.69614 q^{68} +(4.05444 + 2.56155i) q^{69} +(3.68466 - 2.56155i) q^{70} -2.87689 q^{71} -3.00000 q^{72} -10.2462i q^{73} -6.04090i q^{74} +2.12311i q^{75} +7.73704 q^{76} +(2.00000 + 2.87689i) q^{77} +5.12311 q^{78} -2.27678i q^{79} +1.69614 q^{80} +1.00000 q^{81} +2.87689i q^{82} -5.29723 q^{83} +(1.51022 + 2.17238i) q^{84} -2.87689 q^{85} -3.02045i q^{86} +8.24621i q^{87} +3.97292i q^{88} -5.08842 q^{89} -1.69614 q^{90} +(-7.73704 - 11.1293i) q^{91} +(2.56155 - 4.05444i) q^{92} -6.24621 q^{93} -1.12311i q^{94} +13.1231 q^{95} +5.00000i q^{96} +6.04090 q^{97} +(-2.43845 + 6.56155i) q^{98} -1.32431i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^4 + 24 * q^8 - 8 * q^9	$ 8 q - 8 q^{2} - 8 q^{4} + 24 q^{8} - 8 q^{9} - 8 q^{16} + 8 q^{18} - 4 q^{23} + 16 q^{25} - 40 q^{32} + 20 q^{35} + 8 q^{36} - 8 q^{39} + 4 q^{46} + 36 q^{49} - 16 q^{50} + 56 q^{64} - 20 q^{70} - 56 q^{71} - 24 q^{72} + 16 q^{77} + 8 q^{78} + 8 q^{81} - 56 q^{85} + 4 q^{92} + 16 q^{93} + 72 q^{95} - 36 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^4 + 24 * q^8 - 8 * q^9 - 8 * q^16 + 8 * q^18 - 4 * q^23 + 16 * q^25 - 40 * q^32 + 20 * q^35 + 8 * q^36 - 8 * q^39 + 4 * q^46 + 36 * q^49 - 16 * q^50 + 56 * q^64 - 20 * q^70 - 56 * q^71 - 24 * q^72 + 16 * q^77 + 8 * q^78 + 8 * q^81 - 56 * q^85 + 4 * q^92 + 16 * q^93 + 72 * q^95 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	−1.69614			−0.758537			−0.379269	−	0.925287i	$-0.623824\pi$
$5$	−1.69614			−0.758537			−0.379269	+	0.925287i	$0.623824\pi$
$6$			1.00000i			0.408248i
$7$	2.17238	−	1.51022i	0.821081	−	0.570811i
$7$	2.17238	−	1.51022i	0.821081	−	0.570811i
$8$	3.00000			1.06066
$9$	−1.00000			−0.333333
$10$	1.69614			0.536367
$11$			1.32431i			0.399294i	0.979868	+	0.199647i	$0.0639795\pi$
$11$			1.32431i			0.399294i	−0.979868	+	0.199647i	$0.936021\pi$
$12$			1.00000i			0.288675i
$13$		−	5.12311i		−	1.42089i	−0.703751	−	0.710447i	$-0.748493\pi$
$13$		−	5.12311i		−	1.42089i	0.703751	−	0.710447i	$-0.251507\pi$
$14$	−2.17238	+	1.51022i	−0.580592	+	0.403624i
$15$			1.69614i			0.437942i
$16$	−1.00000			−0.250000
$17$	1.69614			0.411375			0.205687	−	0.978618i	$-0.434057\pi$
$17$	1.69614			0.411375			0.205687	+	0.978618i	$0.434057\pi$
$18$	1.00000			0.235702
$19$	−7.73704			−1.77500			−0.887499	−	0.460810i	$-0.847559\pi$
$19$	−7.73704			−1.77500			−0.887499	+	0.460810i	$0.847559\pi$
$20$	1.69614			0.379269
$21$	−1.51022	−	2.17238i	−0.329558	−	0.474052i
$22$		−	1.32431i		−	0.282343i
$23$	−2.56155	+	4.05444i	−0.534121	+	0.845408i
$23$	−2.56155	+	4.05444i	−0.534121	+	0.845408i
$24$		−	3.00000i		−	0.612372i
$25$	−2.12311			−0.424621
$26$			5.12311i			1.00472i
$27$			1.00000i			0.192450i
$28$	−2.17238	+	1.51022i	−0.410541	+	0.285406i
$29$	−8.24621			−1.53128			−0.765641	−	0.643268i	$-0.777578\pi$
$29$	−8.24621			−1.53128			−0.765641	+	0.643268i	$0.777578\pi$
$30$		−	1.69614i		−	0.309672i
$31$		−	6.24621i		−	1.12185i	−0.827866	−	0.560926i	$-0.810445\pi$
$31$		−	6.24621i		−	1.12185i	0.827866	−	0.560926i	$-0.189555\pi$
$32$	−5.00000			−0.883883
$33$	1.32431			0.230532
$34$	−1.69614			−0.290886
$35$	−3.68466	+	2.56155i	−0.622821	+	0.432981i
$36$	1.00000			0.166667
$37$			6.04090i			0.993117i	0.868003	+	0.496559i	$0.165403\pi$
$37$			6.04090i			0.993117i	−0.868003	+	0.496559i	$0.834597\pi$
$38$	7.73704			1.25511
$39$	−5.12311			−0.820353
$40$	−5.08842			−0.804550
$41$		−	2.87689i		−	0.449295i	−0.974440	−	0.224648i	$-0.927877\pi$
$41$		−	2.87689i		−	0.449295i	0.974440	−	0.224648i	$-0.0721231\pi$
$42$	1.51022	+	2.17238i	0.233033	+	0.335205i
$43$			3.02045i			0.460614i	0.973118	+	0.230307i	$0.0739730\pi$
$43$			3.02045i			0.460614i	−0.973118	+	0.230307i	$0.926027\pi$
$44$		−	1.32431i		−	0.199647i
$45$	1.69614			0.252846
$46$	2.56155	−	4.05444i	0.377680	−	0.597794i
$47$			1.12311i			0.163822i	0.996640	+	0.0819109i	$0.0261023\pi$
$47$			1.12311i			0.163822i	−0.996640	+	0.0819109i	$0.973898\pi$
$48$			1.00000i			0.144338i
$49$	2.43845	−	6.56155i	0.348350	−	0.937365i
$50$	2.12311			0.300252
$51$		−	1.69614i		−	0.237507i
$52$			5.12311i			0.710447i
$53$			5.08842i			0.698949i	0.936946	+	0.349474i	$0.113640\pi$
$53$			5.08842i			0.698949i	−0.936946	+	0.349474i	$0.886360\pi$
$54$		−	1.00000i		−	0.136083i
$55$		−	2.24621i		−	0.302879i
$56$	6.51713	−	4.53067i	0.870888	−	0.605436i
$57$			7.73704i			1.02480i
$58$	8.24621			1.08278
$59$		−	1.12311i		−	0.146216i	−0.997324	−	0.0731079i	$-0.976708\pi$
$59$		−	1.12311i		−	0.146216i	0.997324	−	0.0731079i	$-0.0232918\pi$
$60$		−	1.69614i		−	0.218971i
$61$	−6.04090			−0.773457			−0.386729	−	0.922194i	$-0.626395\pi$
$61$	−6.04090			−0.773457			−0.386729	+	0.922194i	$0.626395\pi$
$62$			6.24621i			0.793270i
$63$	−2.17238	+	1.51022i	−0.273694	+	0.190270i
$64$	7.00000			0.875000
$65$			8.68951i			1.07780i
$66$	−1.32431			−0.163011
$67$		−	15.1022i		−	1.84503i	−0.385959	−	0.922516i	$-0.626129\pi$
$67$		−	15.1022i		−	1.84503i	0.385959	−	0.922516i	$-0.373871\pi$
$68$	−1.69614			−0.205687
$69$	4.05444	+	2.56155i	0.488097	+	0.308375i
$70$	3.68466	−	2.56155i	0.440401	−	0.306164i
$71$	−2.87689			−0.341425			−0.170712	−	0.985321i	$-0.554607\pi$
$71$	−2.87689			−0.341425			−0.170712	+	0.985321i	$0.554607\pi$
$72$	−3.00000			−0.353553
$73$		−	10.2462i		−	1.19923i	−0.800289	−	0.599614i	$-0.795321\pi$
$73$		−	10.2462i		−	1.19923i	0.800289	−	0.599614i	$-0.204679\pi$
$74$		−	6.04090i		−	0.702240i
$75$			2.12311i			0.245155i
$76$	7.73704			0.887499
$77$	2.00000	+	2.87689i	0.227921	+	0.327853i
$78$	5.12311			0.580077
$79$		−	2.27678i		−	0.256158i	−0.991764	−	0.128079i	$-0.959119\pi$
$79$		−	2.27678i		−	0.256158i	0.991764	−	0.128079i	$-0.0408811\pi$
$80$	1.69614			0.189634
$81$	1.00000			0.111111
$82$			2.87689i			0.317700i
$83$	−5.29723			−0.581446			−0.290723	−	0.956807i	$-0.593896\pi$
$83$	−5.29723			−0.581446			−0.290723	+	0.956807i	$0.593896\pi$
$84$	1.51022	+	2.17238i	0.164779	+	0.237026i
$85$	−2.87689			−0.312043
$86$		−	3.02045i		−	0.325703i
$87$			8.24621i			0.884087i
$88$			3.97292i			0.423515i
$89$	−5.08842			−0.539372			−0.269686	−	0.962948i	$-0.586920\pi$
$89$	−5.08842			−0.539372			−0.269686	+	0.962948i	$0.586920\pi$
$90$	−1.69614			−0.178789
$91$	−7.73704	−	11.1293i	−0.811062	−	1.16667i
$92$	2.56155	−	4.05444i	0.267060	−	0.422704i
$93$	−6.24621			−0.647702
$94$		−	1.12311i		−	0.115840i
$95$	13.1231			1.34640
$96$			5.00000i			0.510310i
$97$	6.04090			0.613360			0.306680	−	0.951813i	$-0.400782\pi$
$97$	6.04090			0.613360			0.306680	+	0.951813i	$0.400782\pi$
$98$	−2.43845	+	6.56155i	−0.246320	+	0.662817i
$99$		−	1.32431i		−	0.133098i
$100$	2.12311			0.212311
$101$			5.12311i			0.509768i	0.966972	+	0.254884i	$0.0820373\pi$
$101$			5.12311i			0.509768i	−0.966972	+	0.254884i	$0.917963\pi$
$102$			1.69614i			0.167943i
$103$	−4.34475			−0.428101			−0.214051	−	0.976823i	$-0.568666\pi$
$103$	−4.34475			−0.428101			−0.214051	+	0.976823i	$0.568666\pi$
$104$		−	15.3693i		−	1.50709i
$105$	2.56155	+	3.68466i	0.249982	+	0.359586i
$106$		−	5.08842i		−	0.494231i
$107$		−	8.10887i		−	0.783914i	−0.919984	−	0.391957i	$-0.871798\pi$
$107$		−	8.10887i		−	0.783914i	0.919984	−	0.391957i	$-0.128202\pi$
$108$		−	1.00000i		−	0.0962250i
$109$			14.7304i			1.41092i	0.708751	+	0.705458i	$0.249259\pi$
$109$			14.7304i			1.41092i	−0.708751	+	0.705458i	$0.750741\pi$
$110$			2.24621i			0.214168i
$111$	6.04090			0.573376
$112$	−2.17238	+	1.51022i	−0.205270	+	0.142703i
$113$		−	16.4265i		−	1.54528i	−0.634845	−	0.772640i	$-0.718936\pi$
$113$		−	16.4265i		−	1.54528i	0.634845	−	0.772640i	$-0.281064\pi$
$114$		−	7.73704i		−	0.724640i
$115$	4.34475	−	6.87689i	0.405150	−	0.641274i
$116$	8.24621			0.765641
$117$			5.12311i			0.473631i
$118$			1.12311i			0.103390i
$119$	3.68466	−	2.56155i	0.337772	−	0.234817i
$120$			5.08842i			0.464507i
$121$	9.24621			0.840565
$122$	6.04090			0.546917
$123$	−2.87689			−0.259401
$124$			6.24621i			0.560926i
$125$	12.0818			1.08063
$126$	2.17238	−	1.51022i	0.193531	−	0.134541i
$127$	10.2462			0.909204			0.454602	−	0.890695i	$-0.349781\pi$
$127$	10.2462			0.909204			0.454602	+	0.890695i	$0.349781\pi$
$128$	3.00000			0.265165
$129$	3.02045			0.265936
$130$		−	8.68951i		−	0.762120i
$131$			12.0000i			1.04844i	0.851581	+	0.524222i	$0.175644\pi$
$131$			12.0000i			1.04844i	−0.851581	+	0.524222i	$0.824356\pi$
$132$	−1.32431			−0.115266
$133$	−16.8078	+	11.6847i	−1.45742	+	1.01319i
$134$			15.1022i			1.30463i
$135$		−	1.69614i		−	0.145981i
$136$	5.08842			0.436329
$137$			14.5216i			1.24066i	0.784339	+	0.620332i	$0.213002\pi$
$137$			14.5216i			1.24066i	−0.784339	+	0.620332i	$0.786998\pi$
$138$	−4.05444	−	2.56155i	−0.345136	−	0.218054i
$139$			12.0000i			1.01783i	0.860818	+	0.508913i	$0.169953\pi$
$139$			12.0000i			1.01783i	−0.860818	+	0.508913i	$0.830047\pi$
$140$	3.68466	−	2.56155i	0.311410	−	0.216491i
$141$	1.12311			0.0945826
$142$	2.87689			0.241424
$143$	6.78456			0.567354
$144$	1.00000			0.0833333
$145$	13.9867			1.16154
$146$			10.2462i			0.847982i
$147$	−6.56155	−	2.43845i	−0.541188	−	0.201120i
$148$		−	6.04090i		−	0.496559i
$149$		−	13.7779i		−	1.12873i	−0.825525	−	0.564366i	$-0.809121\pi$
$149$		−	13.7779i		−	1.12873i	0.825525	−	0.564366i	$-0.190879\pi$
$150$		−	2.12311i		−	0.173351i
$151$	12.4924			1.01662			0.508309	−	0.861174i	$-0.330271\pi$
$151$	12.4924			1.01662			0.508309	+	0.861174i	$0.330271\pi$
$152$	−23.2111			−1.88267
$153$	−1.69614			−0.137125
$154$	−2.00000	−	2.87689i	−0.161165	−	0.231827i
$155$			10.5945i			0.850967i
$156$	5.12311			0.410177
$157$	0.743668			0.0593512			0.0296756	−	0.999560i	$-0.490553\pi$
$157$	0.743668			0.0593512			0.0296756	+	0.999560i	$0.490553\pi$
$158$			2.27678i			0.181131i
$159$	5.08842			0.403538
$160$	8.48071			0.670459
$161$	0.558446	+	12.6763i	0.0440117	+	0.999031i
$162$	−1.00000			−0.0785674
$163$	12.0000			0.939913			0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000			0.939913			0.469956	+	0.882690i	$0.344270\pi$
$164$			2.87689i			0.224648i
$165$	−2.24621			−0.174867
$166$	5.29723			0.411145
$167$		−	22.2462i		−	1.72146i	−0.509059	−	0.860732i	$-0.670006\pi$
$167$		−	22.2462i		−	1.72146i	0.509059	−	0.860732i	$-0.329994\pi$
$168$	−4.53067	−	6.51713i	−0.349549	−	0.502808i
$169$	−13.2462			−1.01894
$170$	2.87689			0.220648
$171$	7.73704			0.591666
$172$		−	3.02045i		−	0.230307i
$173$		−	5.12311i		−	0.389503i	−0.980853	−	0.194751i	$-0.937610\pi$
$173$		−	5.12311i		−	0.389503i	0.980853	−	0.194751i	$-0.0623900\pi$
$174$		−	8.24621i		−	0.625144i
$175$	−4.61219	+	3.20636i	−0.348649	+	0.242378i
$176$		−	1.32431i		−	0.0998234i
$177$	−1.12311			−0.0844178
$178$	5.08842			0.381393
$179$	−4.00000			−0.298974			−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000			−0.298974			−0.149487	+	0.988764i	$0.547762\pi$
$180$	−1.69614			−0.126423
$181$	−14.7304			−1.09490			−0.547451	−	0.836838i	$-0.684402\pi$
$181$	−14.7304			−1.09490			−0.547451	+	0.836838i	$0.684402\pi$
$182$	7.73704	+	11.1293i	0.573507	+	0.824960i
$183$			6.04090i			0.446556i
$184$	−7.68466	+	12.1633i	−0.566521	+	0.896691i
$185$		−	10.2462i		−	0.753316i
$186$	6.24621			0.457994
$187$			2.24621i			0.164259i
$188$		−	1.12311i		−	0.0819109i
$189$	1.51022	+	2.17238i	0.109853	+	0.158017i
$190$	−13.1231			−0.952050
$191$		−	26.2316i		−	1.89805i	−0.315202	−	0.949024i	$-0.602072\pi$
$191$		−	26.2316i		−	1.89805i	0.315202	−	0.949024i	$-0.397928\pi$
$192$		−	7.00000i		−	0.505181i
$193$	−15.6155			−1.12403			−0.562015	−	0.827127i	$-0.689974\pi$
$193$	−15.6155			−1.12403			−0.562015	+	0.827127i	$0.689974\pi$
$194$	−6.04090			−0.433711
$195$	8.68951			0.622269
$196$	−2.43845	+	6.56155i	−0.174175	+	0.468682i
$197$	−14.4924			−1.03254			−0.516271	−	0.856425i	$-0.672680\pi$
$197$	−14.4924			−1.03254			−0.516271	+	0.856425i	$0.672680\pi$
$198$			1.32431i			0.0941144i
$199$	−4.34475			−0.307992			−0.153996	−	0.988072i	$-0.549214\pi$
$199$	−4.34475			−0.307992			−0.153996	+	0.988072i	$0.549214\pi$
$200$	−6.36932			−0.450379
$201$	−15.1022			−1.06523
$202$		−	5.12311i		−	0.360460i
$203$	−17.9139	+	12.4536i	−1.25731	+	0.874073i
$204$			1.69614i			0.118754i
$205$			4.87962i			0.340807i
$206$	4.34475			0.302713
$207$	2.56155	−	4.05444i	0.178040	−	0.281803i
$208$			5.12311i			0.355223i
$209$		−	10.2462i		−	0.708745i
$210$	−2.56155	−	3.68466i	−0.176764	−	0.254266i
$211$	6.24621			0.430007			0.215003	−	0.976613i	$-0.431024\pi$
$211$	6.24621			0.430007			0.215003	+	0.976613i	$0.431024\pi$
$212$		−	5.08842i		−	0.349474i
$213$			2.87689i			0.197122i
$214$			8.10887i			0.554311i
$215$		−	5.12311i		−	0.349393i
$216$			3.00000i			0.204124i
$217$	−9.43318	−	13.5691i	−0.640366	−	0.921132i
$218$		−	14.7304i		−	0.997669i
$219$	−10.2462			−0.692375
$220$			2.24621i			0.151440i
$221$		−	8.68951i		−	0.584520i
$222$	−6.04090			−0.405438
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	−10.8619	+	7.55112i	−0.725740	+	0.504530i
$225$	2.12311			0.141540
$226$			16.4265i			1.09268i
$227$	3.39228			0.225154			0.112577	−	0.993643i	$-0.464090\pi$
$227$	3.39228			0.225154			0.112577	+	0.993643i	$0.464090\pi$
$228$		−	7.73704i		−	0.512398i
$229$	−14.7304			−0.973413			−0.486706	−	0.873566i	$-0.661802\pi$
$229$	−14.7304			−0.973413			−0.486706	+	0.873566i	$0.661802\pi$
$230$	−4.34475	+	6.87689i	−0.286485	+	0.453449i
$231$	2.87689	−	2.00000i	0.189286	−	0.131590i
$232$	−24.7386			−1.62417
$233$	−20.2462			−1.32637			−0.663187	−	0.748454i	$-0.730796\pi$
$233$	−20.2462			−1.32637			−0.663187	+	0.748454i	$0.730796\pi$
$234$		−	5.12311i		−	0.334908i
$235$		−	1.90495i		−	0.124265i
$236$			1.12311i			0.0731079i
$237$	−2.27678			−0.147893
$238$	−3.68466	+	2.56155i	−0.238841	+	0.166041i
$239$	23.3693			1.51164			0.755818	−	0.654782i	$-0.227240\pi$
$239$	23.3693			1.51164			0.755818	+	0.654782i	$0.227240\pi$
$240$		−	1.69614i		−	0.109485i
$241$	12.8255			0.826161			0.413080	−	0.910695i	$-0.364453\pi$
$241$	12.8255			0.826161			0.413080	+	0.910695i	$0.364453\pi$
$242$	−9.24621			−0.594369
$243$		−	1.00000i		−	0.0641500i
$244$	6.04090			0.386729
$245$	−4.13595	+	11.1293i	−0.264236	+	0.711026i
$246$	2.87689			0.183424
$247$			39.6377i			2.52208i
$248$		−	18.7386i		−	1.18990i
$249$			5.29723i			0.335698i
$250$	−12.0818			−0.764120
$251$	27.5559			1.73931			0.869655	−	0.493659i	$-0.164341\pi$
$251$	27.5559			1.73931			0.869655	+	0.493659i	$0.164341\pi$
$252$	2.17238	−	1.51022i	0.136847	−	0.0951352i
$253$	−5.36932	−	3.39228i	−0.337566	−	0.213271i
$254$	−10.2462			−0.642904
$255$			2.87689i			0.180158i
$256$	−17.0000			−1.06250
$257$		−	7.36932i		−	0.459685i	−0.973228	−	0.229843i	$-0.926179\pi$
$257$		−	7.36932i		−	0.459685i	0.973228	−	0.229843i	$-0.0738212\pi$
$258$	−3.02045			−0.188045
$259$	9.12311	+	13.1231i	0.566882	+	0.815430i
$260$		−	8.68951i		−	0.538901i
$261$	8.24621			0.510428
$262$		−	12.0000i		−	0.741362i
$263$			20.9343i			1.29087i	0.763817	+	0.645433i	$0.223323\pi$
$263$			20.9343i			1.29087i	−0.763817	+	0.645433i	$0.776677\pi$
$264$	3.97292			0.244516
$265$		−	8.63068i		−	0.530179i
$266$	16.8078	−	11.6847i	1.03055	−	0.716432i
$267$			5.08842i			0.311406i
$268$			15.1022i			0.922516i
$269$		−	31.3693i		−	1.91262i	−0.292353	−	0.956311i	$-0.594438\pi$
$269$		−	31.3693i		−	1.91262i	0.292353	−	0.956311i	$-0.405562\pi$
$270$			1.69614i			0.103224i
$271$		−	16.4924i		−	1.00184i	−0.865493	−	0.500922i	$-0.832994\pi$
$271$		−	16.4924i		−	1.00184i	0.865493	−	0.500922i	$-0.167006\pi$
$272$	−1.69614			−0.102844
$273$	−11.1293	+	7.73704i	−0.673577	+	0.468267i
$274$		−	14.5216i		−	0.877282i
$275$		−	2.81164i		−	0.169548i
$276$	−4.05444	−	2.56155i	−0.244048	−	0.154187i
$277$	−0.246211			−0.0147934			−0.00739670	−	0.999973i	$-0.502354\pi$
$277$	−0.246211			−0.0147934			−0.00739670	+	0.999973i	$0.502354\pi$
$278$		−	12.0000i		−	0.719712i
$279$			6.24621i			0.373951i
$280$	−11.0540	+	7.68466i	−0.660601	+	0.459246i
$281$		−	9.64198i		−	0.575192i	−0.957752	−	0.287596i	$-0.907144\pi$
$281$		−	9.64198i		−	0.575192i	0.957752	−	0.287596i	$-0.0928561\pi$
$282$	−1.12311			−0.0668800
$283$	25.1161			1.49299			0.746497	−	0.665388i	$-0.231734\pi$
$283$	25.1161			1.49299			0.746497	+	0.665388i	$0.231734\pi$
$284$	2.87689			0.170712
$285$		−	13.1231i		−	0.777346i
$286$	−6.78456			−0.401180
$287$	−4.34475	−	6.24970i	−0.256463	−	0.368908i
$288$	5.00000			0.294628
$289$	−14.1231			−0.830771
$290$	−13.9867			−0.821329
$291$		−	6.04090i		−	0.354124i
$292$			10.2462i			0.599614i
$293$	−32.6443			−1.90710			−0.953550	−	0.301235i	$-0.902601\pi$
$293$	−32.6443			−1.90710			−0.953550	+	0.301235i	$0.902601\pi$
$294$	6.56155	+	2.43845i	0.382678	+	0.142213i
$295$			1.90495i			0.110910i
$296$			18.1227i			1.05336i
$297$	−1.32431			−0.0768441
$298$			13.7779i			0.798134i
$299$	20.7713	+	13.1231i	1.20124	+	0.758929i
$300$		−	2.12311i		−	0.122578i
$301$	4.56155	+	6.56155i	0.262924	+	0.378202i
$302$	−12.4924			−0.718858
$303$	5.12311			0.294315
$304$	7.73704			0.443749
$305$	10.2462			0.586696
$306$	1.69614			0.0969619
$307$		−	14.2462i		−	0.813074i	−0.913634	−	0.406537i	$-0.866736\pi$
$307$		−	14.2462i		−	0.813074i	0.913634	−	0.406537i	$-0.133264\pi$
$308$	−2.00000	−	2.87689i	−0.113961	−	0.163926i
$309$			4.34475i			0.247164i
$310$		−	10.5945i		−	0.601725i
$311$			27.3693i			1.55197i	0.630750	+	0.775986i	$0.282747\pi$
$311$			27.3693i			1.55197i	−0.630750	+	0.775986i	$0.717253\pi$
$312$	−15.3693			−0.870116
$313$	28.2995			1.59958			0.799792	−	0.600277i	$-0.204943\pi$
$313$	28.2995			1.59958			0.799792	+	0.600277i	$0.204943\pi$
$314$	−0.743668			−0.0419676
$315$	3.68466	−	2.56155i	0.207607	−	0.144327i
$316$			2.27678i			0.128079i
$317$	−14.0000			−0.786318			−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000			−0.786318			−0.393159	+	0.919470i	$0.628618\pi$
$318$	−5.08842			−0.285345
$319$		−	10.9205i		−	0.611431i
$320$	−11.8730			−0.663720
$321$	−8.10887			−0.452593
$322$	−0.558446	−	12.6763i	−0.0311210	−	0.706422i
$323$	−13.1231			−0.730189
$324$	−1.00000			−0.0555556
$325$			10.8769i			0.603342i
$326$	−12.0000			−0.664619
$327$	14.7304			0.814593
$328$		−	8.63068i		−	0.476550i
$329$	1.69614	+	2.43981i	0.0935113	+	0.134511i
$330$	2.24621			0.123650
$331$	16.4924			0.906506			0.453253	−	0.891382i	$-0.350263\pi$
$331$	16.4924			0.906506			0.453253	+	0.891382i	$0.350263\pi$
$332$	5.29723			0.290723
$333$		−	6.04090i		−	0.331039i
$334$			22.2462i			1.21726i
$335$			25.6155i			1.39953i
$336$	1.51022	+	2.17238i	0.0823895	+	0.118513i
$337$		−	3.39228i		−	0.184789i	−0.995722	−	0.0923947i	$-0.970548\pi$
$337$		−	3.39228i		−	0.184789i	0.995722	−	0.0923947i	$-0.0294521\pi$
$338$	13.2462			0.720499
$339$	−16.4265			−0.892168
$340$	2.87689			0.156022
$341$	8.27190			0.447949
$342$	−7.73704			−0.418371
$343$	−4.61219	−	17.9368i	−0.249035	−	0.968495i
$344$			9.06134i			0.488555i
$345$	−6.87689	−	4.34475i	−0.370240	−	0.233914i
$346$			5.12311i			0.275420i
$347$	16.4924			0.885360			0.442680	−	0.896680i	$-0.354028\pi$
$347$	16.4924			0.885360			0.442680	+	0.896680i	$0.354028\pi$
$348$		−	8.24621i		−	0.442043i
$349$			15.3693i			0.822701i	0.911477	+	0.411350i	$0.134943\pi$
$349$			15.3693i			0.822701i	−0.911477	+	0.411350i	$0.865057\pi$
$350$	4.61219	−	3.20636i	0.246532	−	0.171387i
$351$	5.12311			0.273451
$352$		−	6.62153i		−	0.352929i
$353$			7.36932i			0.392229i	0.980581	+	0.196115i	$0.0628325\pi$
$353$			7.36932i			0.392229i	−0.980581	+	0.196115i	$0.937168\pi$
$354$	1.12311			0.0596924
$355$	4.87962			0.258983
$356$	5.08842			0.269686
$357$	−2.56155	−	3.68466i	−0.135572	−	0.195013i
$358$	4.00000			0.211407
$359$		−	30.3675i		−	1.60274i	−0.598172	−	0.801368i	$-0.704106\pi$
$359$		−	30.3675i		−	1.60274i	0.598172	−	0.801368i	$-0.295894\pi$
$360$	5.08842			0.268183
$361$	40.8617			2.15062
$362$	14.7304			0.774213
$363$		−	9.24621i		−	0.485300i
$364$	7.73704	+	11.1293i	0.405531	+	0.583335i
$365$			17.3790i			0.909659i
$366$		−	6.04090i		−	0.315763i
$367$	−28.5083			−1.48812			−0.744062	−	0.668111i	$-0.767103\pi$
$367$	−28.5083			−1.48812			−0.744062	+	0.668111i	$0.767103\pi$
$368$	2.56155	−	4.05444i	0.133530	−	0.211352i
$369$			2.87689i			0.149765i
$370$			10.2462i			0.532675i
$371$	7.68466	+	11.0540i	0.398968	+	0.573894i
$372$	6.24621			0.323851
$373$		−	0.743668i		−	0.0385057i	−0.999815	−	0.0192528i	$-0.993871\pi$
$373$		−	0.743668i		−	0.0385057i	0.999815	−	0.0192528i	$-0.00612875\pi$
$374$		−	2.24621i		−	0.116149i
$375$		−	12.0818i		−	0.623901i
$376$			3.36932i			0.173759i
$377$			42.2462i			2.17579i
$378$	−1.51022	−	2.17238i	−0.0776775	−	0.111735i
$379$		−	20.3995i		−	1.04785i	−0.851764	−	0.523925i	$-0.824467\pi$
$379$		−	20.3995i		−	1.04785i	0.851764	−	0.523925i	$-0.175533\pi$
$380$	−13.1231			−0.673201
$381$		−	10.2462i		−	0.524929i
$382$			26.2316i			1.34212i
$383$	22.2586			1.13736			0.568682	−	0.822558i	$-0.307454\pi$
$383$	22.2586			1.13736			0.568682	+	0.822558i	$0.307454\pi$
$384$		−	3.00000i		−	0.153093i
$385$	−3.39228	−	4.87962i	−0.172887	−	0.248688i
$386$	15.6155			0.794809
$387$		−	3.02045i		−	0.153538i
$388$	−6.04090			−0.306680
$389$		−	34.5492i		−	1.75172i	−0.482569	−	0.875858i	$-0.660296\pi$
$389$		−	34.5492i		−	1.75172i	0.482569	−	0.875858i	$-0.339704\pi$
$390$	−8.68951			−0.440010
$391$	−4.34475	+	6.87689i	−0.219724	+	0.347779i
$392$	7.31534	−	19.6847i	0.369481	−	0.994225i
$393$	12.0000			0.605320
$394$	14.4924			0.730118
$395$			3.86174i			0.194305i
$396$			1.32431i			0.0665489i
$397$		−	12.4924i		−	0.626977i	−0.949592	−	0.313488i	$-0.898502\pi$
$397$		−	12.4924i		−	0.626977i	0.949592	−	0.313488i	$-0.101498\pi$
$398$	4.34475			0.217783
$399$	11.6847	+	16.8078i	0.584965	+	0.841441i
$400$	2.12311			0.106155
$401$			0.952473i			0.0475642i	0.999717	+	0.0237821i	$0.00757079\pi$
$401$			0.952473i			0.0475642i	−0.999717	+	0.0237821i	$0.992429\pi$
$402$	15.1022			0.753231
$403$	−32.0000			−1.59403
$404$		−	5.12311i		−	0.254884i
$405$	−1.69614			−0.0842819
$406$	17.9139	−	12.4536i	0.889051	−	0.618063i
$407$	−8.00000			−0.396545
$408$		−	5.08842i		−	0.251914i
$409$			23.3693i			1.15554i	0.816200	+	0.577769i	$0.196077\pi$
$409$			23.3693i			1.15554i	−0.816200	+	0.577769i	$0.803923\pi$
$410$		−	4.87962i		−	0.240987i
$411$	14.5216			0.716298
$412$	4.34475			0.214051
$413$	−1.69614	−	2.43981i	−0.0834616	−	0.120055i
$414$	−2.56155	+	4.05444i	−0.125893	+	0.199265i
$415$	8.98485			0.441049
$416$			25.6155i			1.25590i
$417$	12.0000			0.587643
$418$			10.2462i			0.501159i
$419$	−18.8664			−0.921682			−0.460841	−	0.887483i	$-0.652452\pi$
$419$	−18.8664			−0.921682			−0.460841	+	0.887483i	$0.652452\pi$
$420$	−2.56155	−	3.68466i	−0.124991	−	0.179793i
$421$		−	7.94584i		−	0.387257i	−0.981075	−	0.193628i	$-0.937974\pi$
$421$		−	7.94584i		−	0.387257i	0.981075	−	0.193628i	$-0.0620256\pi$
$422$	−6.24621			−0.304061
$423$		−	1.12311i		−	0.0546073i
$424$			15.2653i			0.741347i
$425$	−3.60109			−0.174678
$426$		−	2.87689i		−	0.139386i
$427$	−13.1231	+	9.12311i	−0.635072	+	0.441498i
$428$			8.10887i			0.391957i
$429$		−	6.78456i		−	0.327562i
$430$			5.12311i			0.247058i
$431$			30.7851i			1.48287i	0.671026	+	0.741433i	$0.265854\pi$
$431$			30.7851i			1.48287i	−0.671026	+	0.741433i	$0.734146\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−16.2177			−0.779375			−0.389687	−	0.920947i	$-0.627417\pi$
$433$	−16.2177			−0.779375			−0.389687	+	0.920947i	$0.627417\pi$
$434$	9.43318	+	13.5691i	0.452807	+	0.651339i
$435$		−	13.9867i		−	0.670613i
$436$		−	14.7304i		−	0.705458i
$437$	19.8188	−	31.3693i	0.948063	−	1.50060i
$438$	10.2462			0.489583
$439$		−	38.2462i		−	1.82539i	−0.408639	−	0.912696i	$-0.633997\pi$
$439$		−	38.2462i		−	1.82539i	0.408639	−	0.912696i	$-0.366003\pi$
$440$		−	6.73863i		−	0.321252i
$441$	−2.43845	+	6.56155i	−0.116117	+	0.312455i
$442$			8.68951i			0.413318i
$443$	4.63068			0.220010			0.110005	−	0.993931i	$-0.464913\pi$
$443$	4.63068			0.220010			0.110005	+	0.993931i	$0.464913\pi$
$444$	−6.04090			−0.286688
$445$	8.63068			0.409134
$446$		−	4.00000i		−	0.189405i
$447$	−13.7779			−0.651674
$448$	15.2066	−	10.5716i	0.718446	−	0.499460i
$449$	34.4924			1.62780			0.813899	−	0.581006i	$-0.197341\pi$
$449$	34.4924			1.62780			0.813899	+	0.581006i	$0.197341\pi$
$450$	−2.12311			−0.100084
$451$	3.80989			0.179401
$452$			16.4265i			0.772640i
$453$		−	12.4924i		−	0.586945i
$454$	−3.39228			−0.159208
$455$	13.1231	+	18.8769i	0.615221	+	0.884962i
$456$			23.2111i			1.08696i
$457$			29.0432i			1.35858i	0.733868	+	0.679292i	$0.237713\pi$
$457$			29.0432i			1.35858i	−0.733868	+	0.679292i	$0.762287\pi$
$458$	14.7304			0.688307
$459$			1.69614i			0.0791691i
$460$	−4.34475	+	6.87689i	−0.202575	+	0.320637i
$461$			15.3693i			0.715820i	0.933756	+	0.357910i	$0.116511\pi$
$461$			15.3693i			0.715820i	−0.933756	+	0.357910i	$0.883489\pi$
$462$	−2.87689	+	2.00000i	−0.133845	+	0.0930484i
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	8.24621			0.382821
$465$	10.5945			0.491306
$466$	20.2462			0.937888
$467$	3.39228			0.156976			0.0784880	−	0.996915i	$-0.474991\pi$
$467$	3.39228			0.156976			0.0784880	+	0.996915i	$0.474991\pi$
$468$		−	5.12311i		−	0.236816i
$469$	−22.8078	−	32.8078i	−1.05316	−	1.51492i
$470$			1.90495i			0.0878686i
$471$		−	0.743668i		−	0.0342664i
$472$		−	3.36932i		−	0.155085i
$473$	−4.00000			−0.183920
$474$	2.27678			0.104576
$475$	16.4265			0.753702
$476$	−3.68466	+	2.56155i	−0.168886	+	0.117409i
$477$		−	5.08842i		−	0.232983i
$478$	−23.3693			−1.06889
$479$	−30.9481			−1.41406			−0.707028	−	0.707185i	$-0.749965\pi$
$479$	−30.9481			−1.41406			−0.707028	+	0.707185i	$0.749965\pi$
$480$		−	8.48071i		−	0.387089i
$481$	30.9481			1.41111
$482$	−12.8255			−0.584184
$483$	12.6763	−	0.558446i	0.576791	−	0.0254102i
$484$	−9.24621			−0.420282
$485$	−10.2462			−0.465256
$486$			1.00000i			0.0453609i
$487$	2.24621			0.101786			0.0508928	−	0.998704i	$-0.483793\pi$
$487$	2.24621			0.101786			0.0508928	+	0.998704i	$0.483793\pi$
$488$	−18.1227			−0.820376
$489$		−	12.0000i		−	0.542659i
$490$	4.13595	−	11.1293i	0.186843	−	0.502771i
$491$	0.492423			0.0222227			0.0111114	−	0.999938i	$-0.496463\pi$
$491$	0.492423			0.0222227			0.0111114	+	0.999938i	$0.496463\pi$
$492$	2.87689			0.129700
$493$	−13.9867			−0.629931
$494$		−	39.6377i		−	1.78338i
$495$			2.24621i			0.100960i
$496$			6.24621i			0.280463i
$497$	−6.24970	+	4.34475i	−0.280337	+	0.194889i
$498$		−	5.29723i		−	0.237374i
$499$	22.2462			0.995877			0.497939	−	0.867212i	$-0.334090\pi$
$499$	22.2462			0.995877			0.497939	+	0.867212i	$0.334090\pi$
$500$	−12.0818			−0.540314
$501$	−22.2462			−0.993887
$502$	−27.5559			−1.22988
$503$	10.5945			0.472383			0.236192	−	0.971706i	$-0.424101\pi$
$503$	10.5945			0.472383			0.236192	+	0.971706i	$0.424101\pi$
$504$	−6.51713	+	4.53067i	−0.290296	+	0.201812i
$505$		−	8.68951i		−	0.386678i
$506$	5.36932	+	3.39228i	0.238695	+	0.150805i
$507$			13.2462i			0.588285i
$508$	−10.2462			−0.454602
$509$		−	25.6155i		−	1.13539i	−0.823240	−	0.567694i	$-0.807836\pi$
$509$		−	25.6155i		−	1.13539i	0.823240	−	0.567694i	$-0.192164\pi$
$510$		−	2.87689i		−	0.127391i
$511$	−15.4741	−	22.2586i	−0.684533	−	0.984664i
$512$	11.0000			0.486136
$513$		−	7.73704i		−	0.341599i
$514$			7.36932i			0.325047i
$515$	7.36932			0.324731
$516$	−3.02045			−0.132968
$517$	−1.48734			−0.0654130
$518$	−9.12311	−	13.1231i	−0.400846	−	0.576596i
$519$	−5.12311			−0.224879
$520$			26.0685i			1.14318i
$521$	1.69614			0.0743093			0.0371546	−	0.999310i	$-0.488171\pi$
$521$	1.69614			0.0743093			0.0371546	+	0.999310i	$0.488171\pi$
$522$	−8.24621			−0.360927
$523$	−0.952473			−0.0416487			−0.0208244	−	0.999783i	$-0.506629\pi$
$523$	−0.952473			−0.0416487			−0.0208244	+	0.999783i	$0.506629\pi$
$524$		−	12.0000i		−	0.524222i
$525$	3.20636	+	4.61219i	0.139937	+	0.201292i
$526$		−	20.9343i		−	0.912780i
$527$		−	10.5945i		−	0.461502i
$528$	−1.32431			−0.0576331
$529$	−9.87689	−	20.7713i	−0.429430	−	0.903100i
$530$			8.63068i			0.374893i
$531$			1.12311i			0.0487386i
$532$	16.8078	−	11.6847i	0.728709	−	0.506594i
$533$	−14.7386			−0.638401
$534$		−	5.08842i		−	0.220198i
$535$			13.7538i			0.594628i
$536$		−	45.3067i		−	1.95695i
$537$			4.00000i			0.172613i
$538$			31.3693i			1.35243i
$539$	8.68951	+	3.22925i	0.374284	+	0.139094i
$540$			1.69614i			0.0729903i
$541$	31.1231			1.33809			0.669043	−	0.743223i	$-0.266704\pi$
$541$	31.1231			1.33809			0.669043	+	0.743223i	$0.266704\pi$
$542$			16.4924i			0.708410i
$543$			14.7304i			0.632142i
$544$	−8.48071			−0.363607
$545$		−	24.9848i		−	1.07023i
$546$	11.1293	−	7.73704i	0.476291	−	0.331115i
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$		−	14.5216i		−	0.620332i
$549$	6.04090			0.257819
$550$			2.81164i			0.119889i
$551$	63.8012			2.71802
$552$	12.1633	+	7.68466i	0.517705	+	0.327081i
$553$	−3.43845	−	4.94602i	−0.146218	−	0.210326i
$554$	0.246211			0.0104605
$555$	−10.2462			−0.434927
$556$		−	12.0000i		−	0.508913i
$557$			36.0366i			1.52692i	0.645856	+	0.763459i	$0.276501\pi$
$557$			36.0366i			1.52692i	−0.645856	+	0.763459i	$0.723499\pi$
$558$		−	6.24621i		−	0.264423i
$559$	15.4741			0.654484
$560$	3.68466	−	2.56155i	0.155705	−	0.108245i
$561$	2.24621			0.0948351
$562$			9.64198i			0.406722i
$563$	−27.5559			−1.16134			−0.580671	−	0.814139i	$-0.697210\pi$
$563$	−27.5559			−1.16134			−0.580671	+	0.814139i	$0.697210\pi$
$564$	−1.12311			−0.0472913
$565$			27.8617i			1.17215i
$566$	−25.1161			−1.05571
$567$	2.17238	−	1.51022i	0.0912313	−	0.0634234i
$568$	−8.63068			−0.362135
$569$			35.2929i			1.47956i	0.672851	+	0.739778i	$0.265069\pi$
$569$			35.2929i			1.47956i	−0.672851	+	0.739778i	$0.734931\pi$
$570$			13.1231i			0.549666i
$571$			4.92539i			0.206121i	0.994675	+	0.103061i	$0.0328636\pi$
$571$			4.92539i			0.206121i	−0.994675	+	0.103061i	$0.967136\pi$
$572$	−6.78456			−0.283677
$573$	−26.2316			−1.09584
$574$	4.34475	+	6.24970i	0.181347	+	0.260857i
$575$	5.43845	−	8.60799i	0.226799	−	0.358978i
$576$	−7.00000			−0.291667
$577$			18.8769i			0.785855i	0.919569	+	0.392928i	$0.128538\pi$
$577$			18.8769i			0.785855i	−0.919569	+	0.392928i	$0.871462\pi$
$578$	14.1231			0.587444
$579$			15.6155i			0.648959i
$580$	−13.9867			−0.580768
$581$	−11.5076	+	8.00000i	−0.477415	+	0.331896i
$582$			6.04090i			0.250403i
$583$	−6.73863			−0.279086
$584$		−	30.7386i		−	1.27197i
$585$		−	8.68951i		−	0.359267i
$586$	32.6443			1.34852
$587$			0.492423i			0.0203245i	0.999948	+	0.0101622i	$0.00323479\pi$
$587$			0.492423i			0.0203245i	−0.999948	+	0.0101622i	$0.996765\pi$
$588$	6.56155	+	2.43845i	0.270594	+	0.100560i
$589$			48.3272i			1.99129i
$590$		−	1.90495i		−	0.0784254i
$591$			14.4924i			0.596139i
$592$		−	6.04090i		−	0.248279i
$593$			7.36932i			0.302622i	0.988486	+	0.151311i	$0.0483494\pi$
$593$			7.36932i			0.302622i	−0.988486	+	0.151311i	$0.951651\pi$
$594$	1.32431			0.0543370
$595$	−6.24970	+	4.34475i	−0.256213	+	0.178118i
$596$			13.7779i			0.564366i
$597$			4.34475i			0.177819i
$598$	−20.7713	−	13.1231i	−0.849402	−	0.536644i
$599$	−39.3693			−1.60859			−0.804293	−	0.594232i	$-0.797456\pi$
$599$	−39.3693			−1.60859			−0.804293	+	0.594232i	$0.797456\pi$
$600$			6.36932i			0.260026i
$601$			8.63068i			0.352053i	0.984385	+	0.176026i	$0.0563244\pi$
$601$			8.63068i			0.352053i	−0.984385	+	0.176026i	$0.943676\pi$
$602$	−4.56155	−	6.56155i	−0.185915	−	0.267429i
$603$			15.1022i			0.615011i
$604$	−12.4924			−0.508309
$605$	−15.6829			−0.637600
$606$	−5.12311			−0.208112
$607$		−	26.7386i		−	1.08529i	−0.839963	−	0.542644i	$-0.817423\pi$
$607$		−	26.7386i		−	1.08529i	0.839963	−	0.542644i	$-0.182577\pi$
$608$	38.6852			1.56889
$609$	12.4536	+	17.9139i	0.504646	+	0.725907i
$610$	−10.2462			−0.414857
$611$	5.75379			0.232773
$612$	1.69614			0.0685624
$613$			14.3128i			0.578088i	0.957316	+	0.289044i	$0.0933375\pi$
$613$			14.3128i			0.578088i	−0.957316	+	0.289044i	$0.906663\pi$
$614$			14.2462i			0.574930i
$615$	4.87962			0.196765
$616$	6.00000	+	8.63068i	0.241747	+	0.347740i
$617$		−	26.6034i		−	1.07101i	−0.844531	−	0.535506i	$-0.820121\pi$
$617$		−	26.6034i		−	1.07101i	0.844531	−	0.535506i	$-0.179879\pi$
$618$		−	4.34475i		−	0.174772i
$619$	33.8056			1.35876			0.679380	−	0.733786i	$-0.262249\pi$
$619$	33.8056			1.35876			0.679380	+	0.733786i	$0.262249\pi$
$620$		−	10.5945i		−	0.425484i
$621$	−4.05444	−	2.56155i	−0.162699	−	0.102792i
$622$		−	27.3693i		−	1.09741i
$623$	−11.0540	+	7.68466i	−0.442868	+	0.307879i
$624$	5.12311			0.205088
$625$	−9.87689			−0.395076
$626$	−28.2995			−1.13108
$627$	−10.2462			−0.409194
$628$	−0.743668			−0.0296756
$629$			10.2462i			0.408543i
$630$	−3.68466	+	2.56155i	−0.146800	+	0.102055i
$631$		−	5.66906i		−	0.225682i	−0.993613	−	0.112841i	$-0.964005\pi$
$631$		−	5.66906i		−	0.225682i	0.993613	−	0.112841i	$-0.0359950\pi$
$632$		−	6.83034i		−	0.271696i
$633$		−	6.24621i		−	0.248265i
$634$	14.0000			0.556011
$635$	−17.3790			−0.689665
$636$	−5.08842			−0.201769
$637$	−33.6155	−	12.4924i	−1.33190	−	0.494968i
$638$			10.9205i			0.432347i
$639$	2.87689			0.113808
$640$	−5.08842			−0.201138
$641$			11.5469i			0.456076i	0.973652	+	0.228038i	$0.0732311\pi$
$641$			11.5469i			0.456076i	−0.973652	+	0.228038i	$0.926769\pi$
$642$	8.10887			0.320032
$643$	−2.85742			−0.112686			−0.0563428	−	0.998411i	$-0.517944\pi$
$643$	−2.85742			−0.112686			−0.0563428	+	0.998411i	$0.517944\pi$
$644$	−0.558446	−	12.6763i	−0.0220059	−	0.499516i
$645$	−5.12311			−0.201722
$646$	13.1231			0.516322
$647$			5.61553i			0.220769i	0.993889	+	0.110385i	$0.0352083\pi$
$647$			5.61553i			0.220769i	−0.993889	+	0.110385i	$0.964792\pi$
$648$	3.00000			0.117851
$649$	1.48734			0.0583831
$650$		−	10.8769i		−	0.426627i
$651$	−13.5691	+	9.43318i	−0.531816	+	0.369715i
$652$	−12.0000			−0.469956
$653$	14.0000			0.547862			0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000			0.547862			0.273931	+	0.961749i	$0.411676\pi$
$654$	−14.7304			−0.576004
$655$		−	20.3537i		−	0.795285i
$656$			2.87689i			0.112324i
$657$			10.2462i			0.399743i
$658$	−1.69614	−	2.43981i	−0.0661225	−	0.0951137i
$659$			8.85254i			0.344846i	0.985023	+	0.172423i	$0.0551596\pi$
$659$			8.85254i			0.344846i	−0.985023	+	0.172423i	$0.944840\pi$
$660$	2.24621			0.0874337
$661$	−26.3946			−1.02663			−0.513315	−	0.858200i	$-0.671583\pi$
$661$	−26.3946			−1.02663			−0.513315	+	0.858200i	$0.671583\pi$
$662$	−16.4924			−0.640996
$663$	−8.68951			−0.337473
$664$	−15.8917			−0.616717
$665$	28.5083	−	19.8188i	1.10551	−	0.768541i
$666$			6.04090i			0.234080i
$667$	21.1231	−	33.4337i	0.817890	−	1.29456i
$668$			22.2462i			0.860732i
$669$	4.00000			0.154649
$670$		−	25.6155i		−	0.989614i
$671$		−	8.00000i		−	0.308837i
$672$	7.55112	+	10.8619i	0.291291	+	0.419006i
$673$	−4.87689			−0.187990			−0.0939952	−	0.995573i	$-0.529964\pi$
$673$	−4.87689			−0.187990			−0.0939952	+	0.995573i	$0.529964\pi$
$674$			3.39228i			0.130666i
$675$		−	2.12311i		−	0.0817184i
$676$	13.2462			0.509470
$677$	−32.6443			−1.25462			−0.627311	−	0.778769i	$-0.715844\pi$
$677$	−32.6443			−1.25462			−0.627311	+	0.778769i	$0.715844\pi$
$678$	16.4265			0.630858
$679$	13.1231	−	9.12311i	0.503619	−	0.350113i
$680$	−8.63068			−0.330972
$681$		−	3.39228i		−	0.129993i
$682$	−8.27190			−0.316747
$683$	−1.12311			−0.0429744			−0.0214872	−	0.999769i	$-0.506840\pi$
$683$	−1.12311			−0.0429744			−0.0214872	+	0.999769i	$0.506840\pi$
$684$	−7.73704			−0.295833
$685$		−	24.6307i		−	0.941090i
$686$	4.61219	+	17.9368i	0.176094	+	0.684829i
$687$			14.7304i			0.562000i
$688$		−	3.02045i		−	0.115153i
$689$	26.0685			0.993132
$690$	6.87689	+	4.34475i	0.261799	+	0.165402i
$691$		−	14.2462i		−	0.541951i	−0.962586	−	0.270976i	$-0.912654\pi$
$691$		−	14.2462i		−	0.541951i	0.962586	−	0.270976i	$-0.0873463\pi$
$692$			5.12311i			0.194751i
$693$	−2.00000	−	2.87689i	−0.0759737	−	0.109284i
$694$	−16.4924			−0.626044
$695$		−	20.3537i		−	0.772060i
$696$			24.7386i			0.937715i
$697$		−	4.87962i		−	0.184829i
$698$		−	15.3693i		−	0.581737i
$699$			20.2462i			0.765782i
$700$	4.61219	−	3.20636i	0.174324	−	0.121189i
$701$			6.99337i			0.264136i	0.991241	+	0.132068i	$0.0421617\pi$
$701$			6.99337i			0.264136i	−0.991241	+	0.132068i	$0.957838\pi$
$702$	−5.12311			−0.193359
$703$		−	46.7386i		−	1.76278i
$704$			9.27015i			0.349382i
$705$	−1.90495			−0.0717444
$706$		−	7.36932i		−	0.277348i
$707$	7.73704	+	11.1293i	0.290981	+	0.418561i
$708$	1.12311			0.0422089
$709$			35.0841i			1.31761i	0.752313	+	0.658805i	$0.228938\pi$
$709$			35.0841i			1.31761i	−0.752313	+	0.658805i	$0.771062\pi$
$710$	−4.87962			−0.183129
$711$			2.27678i			0.0853859i
$712$	−15.2653			−0.572090
$713$	25.3249	+	16.0000i	0.948423	+	0.599205i
$714$	2.56155	+	3.68466i	0.0958637	+	0.137895i
$715$	−11.5076			−0.430359
$716$	4.00000			0.149487
$717$		−	23.3693i		−	0.872743i
$718$			30.3675i			1.13331i
$719$			27.3693i			1.02070i	0.859966	+	0.510352i	$0.170485\pi$
$719$			27.3693i			1.02070i	−0.859966	+	0.510352i	$0.829515\pi$
$720$	−1.69614			−0.0632114
$721$	−9.43845	+	6.56155i	−0.351506	+	0.244365i
$722$	−40.8617			−1.52072
$723$		−	12.8255i		−	0.476984i
$724$	14.7304			0.547451
$725$	17.5076			0.650215
$726$			9.24621i			0.343159i
$727$	8.15465			0.302439			0.151220	−	0.988500i	$-0.451680\pi$
$727$	8.15465			0.302439			0.151220	+	0.988500i	$0.451680\pi$
$728$	−23.2111	−	33.3880i	−0.860261	−	1.23744i
$729$	−1.00000			−0.0370370
$730$		−	17.3790i		−	0.643226i
$731$			5.12311i			0.189485i
$732$		−	6.04090i		−	0.223278i
$733$	2.64861			0.0978288			0.0489144	−	0.998803i	$-0.484424\pi$
$733$	2.64861			0.0978288			0.0489144	+	0.998803i	$0.484424\pi$
$734$	28.5083			1.05226
$735$	11.1293	+	4.13595i	0.410511	+	0.152557i
$736$	12.8078	−	20.2722i	0.472100	−	0.747242i
$737$	20.0000			0.736709
$738$		−	2.87689i		−	0.105900i
$739$	−34.7386			−1.27788			−0.638941	−	0.769256i	$-0.720627\pi$
$739$	−34.7386			−1.27788			−0.638941	+	0.769256i	$0.720627\pi$
$740$			10.2462i			0.376658i
$741$	39.6377			1.45613
$742$	−7.68466	−	11.0540i	−0.282113	−	0.405804i
$743$			14.1498i			0.519105i	0.965729	+	0.259552i	$0.0835750\pi$
$743$			14.1498i			0.519105i	−0.965729	+	0.259552i	$0.916425\pi$
$744$	−18.7386			−0.686992
$745$			23.3693i			0.856186i
$746$			0.743668i			0.0272276i
$747$	5.29723			0.193815
$748$		−	2.24621i		−	0.0821296i
$749$	−12.2462	−	17.6155i	−0.447467	−	0.643657i
$750$			12.0818i			0.441165i
$751$		−	40.0095i		−	1.45997i	−0.683465	−	0.729984i	$-0.739528\pi$
$751$		−	40.0095i		−	1.45997i	0.683465	−	0.729984i	$-0.260472\pi$
$752$		−	1.12311i		−	0.0409554i
$753$		−	27.5559i		−	1.00419i
$754$		−	42.2462i		−	1.53852i
$755$	−21.1889			−0.771143
$756$	−1.51022	−	2.17238i	−0.0549263	−	0.0790086i
$757$		−	14.7304i		−	0.535386i	−0.963504	−	0.267693i	$-0.913739\pi$
$757$		−	14.7304i		−	0.535386i	0.963504	−	0.267693i	$-0.0862612\pi$
$758$			20.3995i			0.740942i
$759$	−3.39228	+	5.36932i	−0.123132	+	0.194894i
$760$	39.3693			1.42808
$761$		−	29.1231i		−	1.05571i	−0.849334	−	0.527856i	$-0.822996\pi$
$761$		−	29.1231i		−	1.05571i	0.849334	−	0.527856i	$-0.177004\pi$
$762$			10.2462i			0.371181i
$763$	22.2462	+	32.0000i	0.805367	+	1.15848i
$764$			26.2316i			0.949024i
$765$	2.87689			0.104014
$766$	−22.2586			−0.804237
$767$	−5.75379			−0.207757
$768$			17.0000i			0.613435i
$769$	−53.9505			−1.94550			−0.972752	−	0.231850i	$-0.925522\pi$
$769$	−53.9505			−1.94550			−0.972752	+	0.231850i	$0.925522\pi$
$770$	3.39228	+	4.87962i	0.122249	+	0.175849i
$771$	−7.36932			−0.265399
$772$	15.6155			0.562015
$773$	−34.5492			−1.24265			−0.621325	−	0.783553i	$-0.713405\pi$
$773$	−34.5492			−1.24265			−0.621325	+	0.783553i	$0.713405\pi$
$774$			3.02045i			0.108568i
$775$			13.2614i			0.476362i
$776$	18.1227			0.650567
$777$	13.1231	−	9.12311i	0.470789	−	0.327290i
$778$			34.5492i			1.23865i
$779$			22.2586i			0.797498i
$780$	−8.68951			−0.311134
$781$		−	3.80989i		−	0.136329i
$782$	4.34475	−	6.87689i	0.155368	−	0.245917i
$783$		−	8.24621i		−	0.294696i
$784$	−2.43845	+	6.56155i	−0.0870874	+	0.234341i
$785$	−1.26137			−0.0450201
$786$	−12.0000			−0.428026
$787$	−33.8056			−1.20504			−0.602519	−	0.798104i	$-0.705836\pi$
$787$	−33.8056			−1.20504			−0.602519	+	0.798104i	$0.705836\pi$
$788$	14.4924			0.516271
$789$	20.9343			0.745282
$790$		−	3.86174i		−	0.137395i
$791$	−24.8078	−	35.6847i	−0.882063	−	1.26880i
$792$		−	3.97292i		−	0.141172i
$793$			30.9481i			1.09900i
$794$			12.4924i			0.443339i
$795$	−8.63068			−0.306099
$796$	4.34475			0.153996
$797$	−19.0752			−0.675677			−0.337838	−	0.941204i	$-0.609696\pi$
$797$	−19.0752			−0.675677			−0.337838	+	0.941204i	$0.609696\pi$
$798$	−11.6847	−	16.8078i	−0.413632	−	0.594988i
$799$			1.90495i			0.0673921i
$800$	10.6155			0.375316
$801$	5.08842			0.179791
$802$		−	0.952473i		−	0.0336330i
$803$	13.5691			0.478844
$804$	15.1022			0.532615
$805$	−0.947203	−	21.5008i	−0.0333845	−	0.757802i
$806$	32.0000			1.12715
$807$	−31.3693			−1.10425
$808$			15.3693i			0.540691i
$809$	−0.246211			−0.00865633			−0.00432816	−	0.999991i	$-0.501378\pi$
$809$	−0.246211			−0.00865633			−0.00432816	+	0.999991i	$0.501378\pi$
$810$	1.69614			0.0595963
$811$		−	30.2462i		−	1.06209i	−0.847344	−	0.531044i	$-0.821800\pi$
$811$		−	30.2462i		−	1.06209i	0.847344	−	0.531044i	$-0.178200\pi$
$812$	17.9139	−	12.4536i	0.628654	−	0.437037i
$813$	−16.4924			−0.578415
$814$	8.00000			0.280400
$815$	−20.3537			−0.712959
$816$			1.69614i			0.0593768i
$817$		−	23.3693i		−	0.817589i
$818$		−	23.3693i		−	0.817089i
$819$	7.73704	+	11.1293i	0.270354	+	0.388890i
$820$		−	4.87962i		−	0.170404i
$821$	−20.7386			−0.723783			−0.361892	−	0.932220i	$-0.617869\pi$
$821$	−20.7386			−0.723783			−0.361892	+	0.932220i	$0.617869\pi$
$822$	−14.5216			−0.506499
$823$	26.2462			0.914885			0.457443	−	0.889239i	$-0.348765\pi$
$823$	26.2462			0.914885			0.457443	+	0.889239i	$0.348765\pi$
$824$	−13.0343			−0.454070
$825$	−2.81164			−0.0978889
$826$	1.69614	+	2.43981i	0.0590163	+	0.0848918i
$827$			7.36520i			0.256113i	0.991767	+	0.128057i	$0.0408739\pi$
$827$			7.36520i			0.256113i	−0.991767	+	0.128057i	$0.959126\pi$
$828$	−2.56155	+	4.05444i	−0.0890201	+	0.140901i
$829$			21.1231i			0.733636i	0.930293	+	0.366818i	$0.119553\pi$
$829$			21.1231i			0.733636i	−0.930293	+	0.366818i	$0.880447\pi$
$830$	−8.98485			−0.311869
$831$			0.246211i			0.00854097i
$832$		−	35.8617i		−	1.24328i
$833$	4.13595	−	11.1293i	0.143302	−	0.385608i
$834$	−12.0000			−0.415526
$835$			37.7327i			1.30579i
$836$			10.2462i			0.354373i
$837$	6.24621			0.215901
$838$	18.8664			0.651727
$839$	−19.2840			−0.665756			−0.332878	−	0.942970i	$-0.608020\pi$
$839$	−19.2840			−0.665756			−0.332878	+	0.942970i	$0.608020\pi$
$840$	7.68466	+	11.0540i	0.265146	+	0.381398i
$841$	39.0000			1.34483
$842$			7.94584i			0.273832i
$843$	−9.64198			−0.332088
$844$	−6.24621			−0.215003
$845$	22.4674			0.772904
$846$			1.12311i			0.0386132i
$847$	20.0863	−	13.9638i	0.690172	−	0.479804i
$848$		−	5.08842i		−	0.174737i
$849$		−	25.1161i		−	0.861981i
$850$	3.60109			0.123516
$851$	−24.4924	−	15.4741i	−0.839589	−	0.530444i
$852$		−	2.87689i		−	0.0985608i
$853$		−	8.00000i		−	0.273915i	−0.990577	−	0.136957i	$-0.956268\pi$
$853$		−	8.00000i		−	0.273915i	0.990577	−	0.136957i	$-0.0437323\pi$
$854$	13.1231	−	9.12311i	0.449063	−	0.312186i
$855$	−13.1231			−0.448801
$856$		−	24.3266i		−	0.831467i
$857$			8.63068i			0.294819i	0.989076	+	0.147409i	$0.0470934\pi$
$857$			8.63068i			0.294819i	−0.989076	+	0.147409i	$0.952907\pi$
$858$			6.78456i			0.231621i
$859$			12.0000i			0.409435i	0.978821	+	0.204717i	$0.0656275\pi$
$859$			12.0000i			0.409435i	−0.978821	+	0.204717i	$0.934372\pi$
$860$			5.12311i			0.174696i
$861$	−6.24970	+	4.34475i	−0.212989	+	0.148069i
$862$		−	30.7851i		−	1.04855i
$863$	−56.0000			−1.90626			−0.953131	−	0.302558i	$-0.902160\pi$
$863$	−56.0000			−1.90626			−0.953131	+	0.302558i	$0.902160\pi$
$864$		−	5.00000i		−	0.170103i
$865$			8.68951i			0.295452i
$866$	16.2177			0.551101
$867$			14.1231i			0.479646i
$868$	9.43318	+	13.5691i	0.320183	+	0.460566i
$869$	3.01515			0.102282
$870$			13.9867i			0.474195i
$871$	−77.3704			−2.62159
$872$			44.1912i			1.49650i
$873$	−6.04090			−0.204453
$874$	−19.8188	+	31.3693i	−0.670382	+	1.06108i
$875$	26.2462	−	18.2462i	0.887284	−	0.616835i
$876$	10.2462			0.346187
$877$	−24.2462			−0.818736			−0.409368	−	0.912369i	$-0.634251\pi$
$877$	−24.2462			−0.818736			−0.409368	+	0.912369i	$0.634251\pi$
$878$			38.2462i			1.29075i
$879$			32.6443i			1.10106i
$880$			2.24621i			0.0757198i
$881$	−29.2520			−0.985525			−0.492763	−	0.870164i	$-0.664013\pi$
$881$	−29.2520			−0.985525			−0.492763	+	0.870164i	$0.664013\pi$
$882$	2.43845	−	6.56155i	0.0821068	−	0.220939i
$883$	−8.49242			−0.285793			−0.142896	−	0.989738i	$-0.545642\pi$
$883$	−8.49242			−0.285793			−0.142896	+	0.989738i	$0.545642\pi$
$884$			8.68951i			0.292260i
$885$	1.90495			0.0640340
$886$	−4.63068			−0.155571
$887$		−	7.86174i		−	0.263971i	−0.991252	−	0.131986i	$-0.957865\pi$
$887$		−	7.86174i		−	0.263971i	0.991252	−	0.131986i	$-0.0421353\pi$
$888$	18.1227			0.608158
$889$	22.2586	−	15.4741i	0.746531	−	0.518984i
$890$	−8.63068			−0.289301
$891$			1.32431i			0.0443660i
$892$		−	4.00000i		−	0.133930i
$893$		−	8.68951i		−	0.290783i
$894$	13.7779			0.460803
$895$	6.78456			0.226783
$896$	6.51713	−	4.53067i	0.217722	−	0.151359i
$897$	13.1231	−	20.7713i	0.438168	−	0.693534i
$898$	−34.4924			−1.15103
$899$			51.5076i			1.71787i
$900$	−2.12311			−0.0707702
$901$			8.63068i			0.287530i
$902$	−3.80989			−0.126855
$903$	6.56155	−	4.56155i	0.218355	−	0.151799i
$904$		−	49.2796i		−	1.63902i
$905$	24.9848			0.830524
$906$			12.4924i			0.415033i
$907$		−	1.85917i		−	0.0617327i	−0.999524	−	0.0308664i	$-0.990173\pi$
$907$		−	1.85917i		−	0.0617327i	0.999524	−	0.0308664i	$-0.00982663\pi$
$908$	−3.39228			−0.112577
$909$		−	5.12311i		−	0.169923i
$910$	−13.1231	−	18.8769i	−0.435027	−	0.625763i
$911$		−	37.5697i		−	1.24474i	−0.782724	−	0.622370i	$-0.786170\pi$
$911$		−	37.5697i		−	1.24474i	0.782724	−	0.622370i	$-0.213830\pi$
$912$		−	7.73704i		−	0.256199i
$913$		−	7.01515i		−	0.232168i
$914$		−	29.0432i		−	0.960664i
$915$		−	10.2462i		−	0.338729i
$916$	14.7304			0.486706
$917$	18.1227	+	26.0685i	0.598464	+	0.860859i
$918$		−	1.69614i		−	0.0559810i
$919$			3.02045i			0.0996354i	0.998758	+	0.0498177i	$0.0158640\pi$
$919$			3.02045i			0.0996354i	−0.998758	+	0.0498177i	$0.984136\pi$
$920$	13.0343	−	20.6307i	0.429727	−	0.680173i
$921$	−14.2462			−0.469429
$922$		−	15.3693i		−	0.506161i
$923$			14.7386i			0.485128i
$924$	−2.87689	+	2.00000i	−0.0946429	+	0.0657952i
$925$		−	12.8255i		−	0.421699i
$926$	−8.00000			−0.262896
$927$	4.34475			0.142700
$928$	41.2311			1.35348
$929$		−	18.8769i		−	0.619331i	−0.950846	−	0.309665i	$-0.899783\pi$
$929$		−	18.8769i		−	0.619331i	0.950846	−	0.309665i	$-0.100217\pi$
$930$	−10.5945			−0.347406
$931$	−18.8664	+	50.7670i	−0.618320	+	1.66382i
$932$	20.2462			0.663187
$933$	27.3693			0.896031
$934$	−3.39228			−0.110999
$935$		−	3.80989i		−	0.124597i
$936$			15.3693i			0.502362i
$937$	10.9205			0.356758			0.178379	−	0.983962i	$-0.442915\pi$
$937$	10.9205			0.356758			0.178379	+	0.983962i	$0.442915\pi$
$938$	22.8078	+	32.8078i	0.744700	+	1.07121i
$939$		−	28.2995i		−	0.923520i
$940$			1.90495i			0.0621325i
$941$	−6.57576			−0.214364			−0.107182	−	0.994239i	$-0.534183\pi$
$941$	−6.57576			−0.214364			−0.107182	+	0.994239i	$0.534183\pi$
$942$			0.743668i			0.0242300i
$943$	11.6642	+	7.36932i	0.379838	+	0.239978i
$944$			1.12311i			0.0365540i
$945$	−2.56155	−	3.68466i	−0.0833273	−	0.119862i
$946$	4.00000			0.130051
$947$	−0.492423			−0.0160016			−0.00800079	−	0.999968i	$-0.502547\pi$
$947$	−0.492423			−0.0160016			−0.00800079	+	0.999968i	$0.502547\pi$
$948$	2.27678			0.0739464
$949$	−52.4924			−1.70398
$950$	−16.4265			−0.532948
$951$			14.0000i			0.453981i
$952$	11.0540	−	7.68466i	0.358261	−	0.249061i
$953$			54.1593i			1.75439i	0.480134	+	0.877195i	$0.340588\pi$
$953$			54.1593i			1.75439i	−0.480134	+	0.877195i	$0.659412\pi$
$954$			5.08842i			0.164744i
$955$			44.4924i			1.43974i
$956$	−23.3693			−0.755818
$957$	−10.9205			−0.353010
$958$	30.9481			0.999889
$959$	21.9309	+	31.5464i	0.708185	+	1.01869i
$960$			11.8730i			0.383199i
$961$	−8.01515			−0.258553
$962$	−30.9481			−0.997808
$963$			8.10887i			0.261305i
$964$	−12.8255			−0.413080
$965$	26.4861			0.852619
$966$	−12.6763	+	0.558446i	−0.407853	+	0.0179677i
$967$	24.0000			0.771788			0.385894	−	0.922543i	$-0.373893\pi$
$967$	24.0000			0.771788			0.385894	+	0.922543i	$0.373893\pi$
$968$	27.7386			0.891553
$969$			13.1231i			0.421575i
$970$	10.2462			0.328986
$971$	−3.39228			−0.108864			−0.0544318	−	0.998517i	$-0.517335\pi$
$971$	−3.39228			−0.108864			−0.0544318	+	0.998517i	$0.517335\pi$
$972$			1.00000i			0.0320750i
$973$	18.1227	+	26.0685i	0.580987	+	0.835719i
$974$	−2.24621			−0.0719733
$975$	10.8769			0.348339
$976$	6.04090			0.193364
$977$		−	48.8620i		−	1.56323i	−0.623758	−	0.781617i	$-0.714395\pi$
$977$		−	48.8620i		−	1.56323i	0.623758	−	0.781617i	$-0.285605\pi$
$978$			12.0000i			0.383718i
$979$		−	6.73863i		−	0.215368i
$980$	4.13595	−	11.1293i	0.132118	−	0.355513i
$981$		−	14.7304i		−	0.470306i
$982$	−0.492423			−0.0157138
$983$	58.9216			1.87931			0.939654	−	0.342126i	$-0.111147\pi$
$983$	58.9216			1.87931			0.939654	+	0.342126i	$0.111147\pi$
$984$	−8.63068			−0.275136
$985$	24.5812			0.783222
$986$	13.9867			0.445428
$987$	2.43981	−	1.69614i	0.0776600	−	0.0539888i
$988$		−	39.6377i		−	1.26104i
$989$	−12.2462	−	7.73704i	−0.389407	−	0.246023i
$990$		−	2.24621i		−	0.0713893i
$991$	−3.50758			−0.111422			−0.0557109	−	0.998447i	$-0.517743\pi$
$991$	−3.50758			−0.111422			−0.0557109	+	0.998447i	$0.517743\pi$
$992$			31.2311i			0.991587i
$993$		−	16.4924i		−	0.523371i
$994$	6.24970	−	4.34475i	0.198228	−	0.137807i
$995$	7.36932			0.233623
$996$		−	5.29723i		−	0.167849i
$997$		−	53.1231i		−	1.68243i	−0.540704	−	0.841213i	$-0.681842\pi$
$997$		−	53.1231i		−	1.68243i	0.540704	−	0.841213i	$-0.318158\pi$
$998$	−22.2462			−0.704192
$999$	−6.04090			−0.191125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.h.a.160.2	✓	8
3.2	odd	2		1449.2.h.d.1126.5		8
7.6	odd	2	inner	483.2.h.a.160.7	yes	8
21.20	even	2		1449.2.h.d.1126.3		8
23.22	odd	2	inner	483.2.h.a.160.3	yes	8
69.68	even	2		1449.2.h.d.1126.4		8
161.160	even	2	inner	483.2.h.a.160.6	yes	8
483.482	odd	2		1449.2.h.d.1126.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.a.160.2	✓	8	1.1	even	1	trivial
483.2.h.a.160.3	yes	8	23.22	odd	2	inner
483.2.h.a.160.6	yes	8	161.160	even	2	inner
483.2.h.a.160.7	yes	8	7.6	odd	2	inner
1449.2.h.d.1126.3		8	21.20	even	2
1449.2.h.d.1126.4		8	69.68	even	2
1449.2.h.d.1126.5		8	3.2	odd	2
1449.2.h.d.1126.6		8	483.482	odd	2

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.69614 q^{5} +1.00000i q^{6} +(2.17238 - 1.51022i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.69614 q^{5} +1.00000i q^{6} +(2.17238 - 1.51022i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +1.69614 q^{10} +1.32431i q^{11} +1.00000i q^{12} -5.12311i q^{13} +(-2.17238 + 1.51022i) q^{14} +1.69614i q^{15} -1.00000 q^{16} +1.69614 q^{17} +1.00000 q^{18} -7.73704 q^{19} +1.69614 q^{20} +(-1.51022 - 2.17238i) q^{21} -1.32431i q^{22} +(-2.56155 + 4.05444i) q^{23} -3.00000i q^{24} -2.12311 q^{25} +5.12311i q^{26} +1.00000i q^{27} +(-2.17238 + 1.51022i) q^{28} -8.24621 q^{29} -1.69614i q^{30} -6.24621i q^{31} -5.00000 q^{32} +1.32431 q^{33} -1.69614 q^{34} +(-3.68466 + 2.56155i) q^{35} +1.00000 q^{36} +6.04090i q^{37} +7.73704 q^{38} -5.12311 q^{39} -5.08842 q^{40} -2.87689i q^{41} +(1.51022 + 2.17238i) q^{42} +3.02045i q^{43} -1.32431i q^{44} +1.69614 q^{45} +(2.56155 - 4.05444i) q^{46} +1.12311i q^{47} +1.00000i q^{48} +(2.43845 - 6.56155i) q^{49} +2.12311 q^{50} -1.69614i q^{51} +5.12311i q^{52} +5.08842i q^{53} -1.00000i q^{54} -2.24621i q^{55} +(6.51713 - 4.53067i) q^{56} +7.73704i q^{57} +8.24621 q^{58} -1.12311i q^{59} -1.69614i q^{60} -6.04090 q^{61} +6.24621i q^{62} +(-2.17238 + 1.51022i) q^{63} +7.00000 q^{64} +8.68951i q^{65} -1.32431 q^{66} -15.1022i q^{67} -1.69614 q^{68} +(4.05444 + 2.56155i) q^{69} +(3.68466 - 2.56155i) q^{70} -2.87689 q^{71} -3.00000 q^{72} -10.2462i q^{73} -6.04090i q^{74} +2.12311i q^{75} +7.73704 q^{76} +(2.00000 + 2.87689i) q^{77} +5.12311 q^{78} -2.27678i q^{79} +1.69614 q^{80} +1.00000 q^{81} +2.87689i q^{82} -5.29723 q^{83} +(1.51022 + 2.17238i) q^{84} -2.87689 q^{85} -3.02045i q^{86} +8.24621i q^{87} +3.97292i q^{88} -5.08842 q^{89} -1.69614 q^{90} +(-7.73704 - 11.1293i) q^{91} +(2.56155 - 4.05444i) q^{92} -6.24621 q^{93} -1.12311i q^{94} +13.1231 q^{95} +5.00000i q^{96} +6.04090 q^{97} +(-2.43845 + 6.56155i) q^{98} -1.32431i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^4 + 24 * q^8 - 8 * q^9	\( 8 q - 8 q^{2} - 8 q^{4} + 24 q^{8} - 8 q^{9} - 8 q^{16} + 8 q^{18} - 4 q^{23} + 16 q^{25} - 40 q^{32} + 20 q^{35} + 8 q^{36} - 8 q^{39} + 4 q^{46} + 36 q^{49} - 16 q^{50} + 56 q^{64} - 20 q^{70} - 56 q^{71} - 24 q^{72} + 16 q^{77} + 8 q^{78} + 8 q^{81} - 56 q^{85} + 4 q^{92} + 16 q^{93} + 72 q^{95} - 36 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^4 + 24 * q^8 - 8 * q^9 - 8 * q^16 + 8 * q^18 - 4 * q^23 + 16 * q^25 - 40 * q^32 + 20 * q^35 + 8 * q^36 - 8 * q^39 + 4 * q^46 + 36 * q^49 - 16 * q^50 + 56 * q^64 - 20 * q^70 - 56 * q^71 - 24 * q^72 + 16 * q^77 + 8 * q^78 + 8 * q^81 - 56 * q^85 + 4 * q^92 + 16 * q^93 + 72 * q^95 - 36 * q^98

Introduction

L-functions

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