LMFDB - Embedded newform 1040.2.df.b.49.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(49,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	1040.49
Dual form			1040.2.df.b.849.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{3} +(2.18890 + 0.456850i) q^{5} +(-0.866025 + 1.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(2.29129 - 1.32288i) q^{11} +(-3.46410 + 1.00000i) q^{13} +(2.12407 - 0.698807i) q^{15} +(3.96863 + 2.29129i) q^{17} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(3.96863 - 2.29129i) q^{23} +(4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +(2.29129 + 3.96863i) q^{29} +6.20520i q^{31} +(1.32288 - 2.29129i) q^{33} +(-2.58092 + 2.88771i) q^{35} +(-3.96863 - 6.87386i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(2.29129 - 1.32288i) q^{41} +(-9.16478 - 5.29129i) q^{43} +(-2.98019 + 3.33444i) q^{45} +1.82740 q^{47} +(2.00000 + 3.46410i) q^{49} +4.58258 q^{51} -7.58258i q^{53} +(5.61976 - 1.84887i) q^{55} +1.73205 q^{57} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(-1.73205 - 3.00000i) q^{63} +(-8.03943 + 0.606325i) q^{65} +(-0.504525 - 0.873864i) q^{67} +(2.29129 - 3.96863i) q^{69} +(-6.08258 - 3.51178i) q^{71} +(4.96863 - 0.559237i) q^{75} +4.58258i q^{77} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} -6.01450 q^{83} +(7.64016 + 6.82847i) q^{85} +(3.96863 + 2.29129i) q^{87} +(8.29129 - 4.78698i) q^{89} +(1.50000 - 6.06218i) q^{91} +(3.10260 + 5.37386i) q^{93} +(2.88771 + 2.58092i) q^{95} +(5.70068 - 9.87386i) q^{97} +5.29150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{9} + 6 q^{15} + 12 q^{19} - 6 q^{35} - 20 q^{39} + 12 q^{45} + 16 q^{49} + 14 q^{55} + 60 q^{59} + 24 q^{61} - 24 q^{65} - 12 q^{71} + 8 q^{75} - 48 q^{79} - 4 q^{81} + 42 q^{85} + 48 q^{89}+ \cdots + 6 q^{95}+O(q^{100}) $ 8 * q - 8 * q^9 + 6 * q^15 + 12 * q^19 - 6 * q^35 - 20 * q^39 + 12 * q^45 + 16 * q^49 + 14 * q^55 + 60 * q^59 + 24 * q^61 - 24 * q^65 - 12 * q^71 + 8 * q^75 - 48 * q^79 - 4 * q^81 + 42 * q^85 + 48 * q^89 + 12 * q^91 + 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i	−0.228714	−	0.973494i	$-0.573452\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i	0.728714	+	0.684819i	$0.240119\pi$
$4$		0			0
$5$	2.18890	+	0.456850i	0.978906	+	0.204310i
$5$	2.18890	+	0.456850i	0.978906	+	0.204310i
$6$		0			0
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	0.654654	+	0.755929i	$0.272814\pi$
$8$		0			0
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	−0.113081	−	0.993586i	$-0.536072\pi$
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	0.803930	+	0.594724i	$0.202739\pi$
$12$		0			0
$13$	−3.46410	+	1.00000i	−0.960769	+	0.277350i
$13$	−3.46410	+	1.00000i	−0.960769	+	0.277350i
$14$		0			0
$15$	2.12407	−	0.698807i	0.548432	−	0.180431i
$16$		0			0
$17$	3.96863	+	2.29129i	0.962533	+	0.555719i	0.896952	−	0.442128i	$-0.145776\pi$
$17$	3.96863	+	2.29129i	0.962533	+	0.555719i	0.0655816	+	0.997847i	$0.479110\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$			1.73205i			0.377964i
$22$		0			0
$23$	3.96863	−	2.29129i	0.827516	−	0.477767i	−0.0254855	−	0.999675i	$-0.508113\pi$
$23$	3.96863	−	2.29129i	0.827516	−	0.477767i	0.853001	+	0.521909i	$0.174780\pi$
$24$		0			0
$25$	4.58258	+	2.00000i	0.916515	+	0.400000i
$26$		0			0
$27$			5.00000i			0.962250i
$28$		0			0
$29$	2.29129	+	3.96863i	0.425481	+	0.736956i	0.996465	−	0.0840058i	$-0.0267714\pi$
$29$	2.29129	+	3.96863i	0.425481	+	0.736956i	−0.570984	+	0.820961i	$0.693438\pi$
$30$		0			0
$31$			6.20520i			1.11449i	0.830349	+	0.557244i	$0.188141\pi$
$31$			6.20520i			1.11449i	−0.830349	+	0.557244i	$0.811859\pi$
$32$		0			0
$33$	1.32288	−	2.29129i	0.230283	−	0.398862i
$34$		0			0
$35$	−2.58092	+	2.88771i	−0.436255	+	0.488112i
$36$		0			0
$37$	−3.96863	−	6.87386i	−0.652438	−	1.13006i	−0.982529	−	0.186107i	$-0.940413\pi$
$37$	−3.96863	−	6.87386i	−0.652438	−	1.13006i	0.330091	−	0.943949i	$-0.392920\pi$
$38$		0			0
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	2.29129	−	1.32288i	0.357839	−	0.206598i	−0.310293	−	0.950641i	$-0.600427\pi$
$41$	2.29129	−	1.32288i	0.357839	−	0.206598i	0.668132	+	0.744042i	$0.267094\pi$
$42$		0			0
$43$	−9.16478	−	5.29129i	−1.39762	−	0.806914i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$	−9.16478	−	5.29129i	−1.39762	−	0.806914i	−0.994142	+	0.108078i	$0.965531\pi$
$44$		0			0
$45$	−2.98019	+	3.33444i	−0.444260	+	0.497069i
$46$		0			0
$47$	1.82740			0.266554			0.133277	−	0.991079i	$-0.457450\pi$
$47$	1.82740			0.266554			0.133277	+	0.991079i	$0.457450\pi$
$48$		0			0
$49$	2.00000	+	3.46410i	0.285714	+	0.494872i
$50$		0			0
$51$	4.58258			0.641689
$52$		0			0
$53$		−	7.58258i		−	1.04155i	−0.853695	−	0.520773i	$-0.825644\pi$
$53$		−	7.58258i		−	1.04155i	0.853695	−	0.520773i	$-0.174356\pi$
$54$		0			0
$55$	5.61976	−	1.84887i	0.757768	−	0.249301i
$56$		0			0
$57$	1.73205			0.229416
$58$		0			0
$59$	12.0826	+	6.97588i	1.57302	+	0.908182i	0.995796	+	0.0915940i	$0.0291962\pi$
$59$	12.0826	+	6.97588i	1.57302	+	0.908182i	0.577221	+	0.816588i	$0.304137\pi$
$60$		0			0
$61$	0.708712	−	1.22753i	0.0907413	−	0.157169i	−0.817082	−	0.576522i	$-0.804410\pi$
$61$	0.708712	−	1.22753i	0.0907413	−	0.157169i	0.907823	+	0.419353i	$0.137743\pi$
$62$		0			0
$63$	−1.73205	−	3.00000i	−0.218218	−	0.377964i
$64$		0			0
$65$	−8.03943	+	0.606325i	−0.997168	+	0.0752054i
$66$		0			0
$67$	−0.504525	−	0.873864i	−0.0616376	−	0.106759i	0.833560	−	0.552429i	$-0.186299\pi$
$67$	−0.504525	−	0.873864i	−0.0616376	−	0.106759i	−0.895198	+	0.445670i	$0.852966\pi$
$68$		0			0
$69$	2.29129	−	3.96863i	0.275839	−	0.477767i
$70$		0			0
$71$	−6.08258	−	3.51178i	−0.721869	−	0.416771i	0.0935712	−	0.995613i	$-0.470172\pi$
$71$	−6.08258	−	3.51178i	−0.721869	−	0.416771i	−0.815440	+	0.578841i	$0.803505\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$		0			0
$75$	4.96863	−	0.559237i	0.573728	−	0.0645751i
$76$		0			0
$77$			4.58258i			0.522233i
$78$		0			0
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−6.01450			−0.660177			−0.330089	−	0.943950i	$-0.607079\pi$
$83$	−6.01450			−0.660177			−0.330089	+	0.943950i	$0.607079\pi$
$84$		0			0
$85$	7.64016	+	6.82847i	0.828691	+	0.740652i
$86$		0			0
$87$	3.96863	+	2.29129i	0.425481	+	0.245652i
$88$		0			0
$89$	8.29129	−	4.78698i	0.878875	−	0.507419i	0.00858752	−	0.999963i	$-0.497266\pi$
$89$	8.29129	−	4.78698i	0.878875	−	0.507419i	0.870287	+	0.492545i	$0.163933\pi$
$90$		0			0
$91$	1.50000	−	6.06218i	0.157243	−	0.635489i
$92$		0			0
$93$	3.10260	+	5.37386i	0.321725	+	0.557244i
$94$		0			0
$95$	2.88771	+	2.58092i	0.296273	+	0.264797i
$96$		0			0
$97$	5.70068	−	9.87386i	0.578816	−	1.00254i	−0.416799	−	0.908999i	$-0.636848\pi$
$97$	5.70068	−	9.87386i	0.578816	−	1.00254i	0.995615	−	0.0935404i	$-0.0298184\pi$
$98$		0			0
$99$			5.29150i			0.531816i
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$			3.16515i			0.311872i	0.987767	+	0.155936i	$0.0498393\pi$
$103$			3.16515i			0.311872i	−0.987767	+	0.155936i	$0.950161\pi$
$104$		0			0
$105$	−0.791288	+	3.79129i	−0.0772218	+	0.369992i
$106$		0			0
$107$	9.16478	−	5.29129i	0.885993	−	0.511528i	0.0133631	−	0.999911i	$-0.495746\pi$
$107$	9.16478	−	5.29129i	0.885993	−	0.511528i	0.872630	+	0.488383i	$0.162413\pi$
$108$		0			0
$109$			13.1334i			1.25795i	0.777425	+	0.628976i	$0.216526\pi$
$109$			13.1334i			1.25795i	−0.777425	+	0.628976i	$0.783474\pi$
$110$		0			0
$111$	−6.87386	−	3.96863i	−0.652438	−	0.376685i
$112$		0			0
$113$	−6.42368	−	3.70871i	−0.604289	−	0.348886i	0.166438	−	0.986052i	$-0.446773\pi$
$113$	−6.42368	−	3.70871i	−0.604289	−	0.348886i	−0.770727	+	0.637166i	$0.780107\pi$
$114$		0			0
$115$	9.73371	−	3.20233i	0.907673	−	0.298619i
$116$		0			0
$117$	1.73205	−	7.00000i	0.160128	−	0.647150i
$118$		0			0
$119$	−6.87386	+	3.96863i	−0.630126	+	0.363803i
$120$		0			0
$121$	−2.00000	+	3.46410i	−0.181818	+	0.314918i
$122$		0			0
$123$	1.32288	−	2.29129i	0.119280	−	0.206598i
$124$		0			0
$125$	9.11710	+	6.47135i	0.815459	+	0.578815i
$126$		0			0
$127$	−15.3700	+	8.87386i	−1.36387	+	0.787428i	−0.990136	−	0.140110i	$-0.955254\pi$
$127$	−15.3700	+	8.87386i	−1.36387	+	0.787428i	−0.373729	+	0.927538i	$0.621921\pi$
$128$		0			0
$129$	−10.5826			−0.931744
$130$		0			0
$131$	7.58258			0.662493			0.331246	−	0.943544i	$-0.392531\pi$
$131$	7.58258			0.662493			0.331246	+	0.943544i	$0.392531\pi$
$132$		0			0
$133$	−2.59808	+	1.50000i	−0.225282	+	0.130066i
$134$		0			0
$135$	−2.28425	+	10.9445i	−0.196597	+	0.941953i
$136$		0			0
$137$	−5.24383	+	9.08258i	−0.448010	+	0.775977i	−0.998256	−	0.0590258i	$-0.981201\pi$
$137$	−5.24383	+	9.08258i	−0.448010	+	0.775977i	0.550246	+	0.835003i	$0.314534\pi$
$138$		0			0
$139$	10.8739	−	18.8341i	0.922309	−	1.59749i	0.126476	−	0.991970i	$-0.459633\pi$
$139$	10.8739	−	18.8341i	0.922309	−	1.59749i	0.795833	−	0.605517i	$-0.207033\pi$
$140$		0			0
$141$	1.58258	−	0.913701i	0.133277	−	0.0769475i
$142$		0			0
$143$	−6.61438	+	6.87386i	−0.553122	+	0.574821i
$144$		0			0
$145$	3.20233	+	9.73371i	0.265939	+	0.808340i
$146$		0			0
$147$	3.46410	+	2.00000i	0.285714	+	0.164957i
$148$		0			0
$149$	−14.4564	−	8.34643i	−1.18432	−	0.683766i	−0.227308	−	0.973823i	$-0.572992\pi$
$149$	−14.4564	−	8.34643i	−1.18432	−	0.683766i	−0.957009	+	0.290057i	$0.906326\pi$
$150$		0			0
$151$		−	9.66930i		−	0.786877i	−0.919351	−	0.393438i	$-0.871285\pi$
$151$		−	9.66930i		−	0.786877i	0.919351	−	0.393438i	$-0.128715\pi$
$152$		0			0
$153$	−7.93725	+	4.58258i	−0.641689	+	0.370479i
$154$		0			0
$155$	−2.83485	+	13.5826i	−0.227701	+	1.09098i
$156$		0			0
$157$			9.16515i			0.731459i	0.930721	+	0.365729i	$0.119180\pi$
$157$			9.16515i			0.731459i	−0.930721	+	0.365729i	$0.880820\pi$
$158$		0			0
$159$	−3.79129	−	6.56670i	−0.300669	−	0.520773i
$160$		0			0
$161$			7.93725i			0.625543i
$162$		0			0
$163$	10.5353	−	18.2477i	0.825191	−	1.42927i	−0.0765827	−	0.997063i	$-0.524401\pi$
$163$	10.5353	−	18.2477i	0.825191	−	1.42927i	0.901773	−	0.432209i	$-0.142266\pi$
$164$		0			0
$165$	3.94242	−	4.41105i	0.306917	−	0.343399i
$166$		0			0
$167$	−4.78698	−	8.29129i	−0.370427	−	0.641599i	0.619204	−	0.785230i	$-0.287455\pi$
$167$	−4.78698	−	8.29129i	−0.370427	−	0.641599i	−0.989631	+	0.143631i	$0.954122\pi$
$168$		0			0
$169$	11.0000	−	6.92820i	0.846154	−	0.532939i
$170$		0			0
$171$	−3.00000	+	1.73205i	−0.229416	+	0.132453i
$172$		0			0
$173$	−14.3609	−	8.29129i	−1.09184	−	0.630375i	−0.157775	−	0.987475i	$-0.550432\pi$
$173$	−14.3609	−	8.29129i	−1.09184	−	0.630375i	−0.934066	+	0.357100i	$0.883766\pi$
$174$		0			0
$175$	−6.96863	+	5.14181i	−0.526779	+	0.388685i
$176$		0			0
$177$	13.9518			1.04868
$178$		0			0
$179$	−9.08258	−	15.7315i	−0.678864	−	1.17583i	−0.975323	−	0.220781i	$-0.929139\pi$
$179$	−9.08258	−	15.7315i	−0.678864	−	1.17583i	0.296460	−	0.955045i	$-0.404194\pi$
$180$		0			0
$181$	8.74773			0.650213			0.325107	−	0.945677i	$-0.394600\pi$
$181$	8.74773			0.650213			0.325107	+	0.945677i	$0.394600\pi$
$182$		0			0
$183$		−	1.41742i		−	0.104779i
$184$		0			0
$185$	−5.54661	−	16.8593i	−0.407795	−	1.23952i
$186$		0			0
$187$	12.1244			0.886621
$188$		0			0
$189$	−7.50000	−	4.33013i	−0.545545	−	0.314970i
$190$		0			0
$191$	−8.29129	+	14.3609i	−0.599937	+	1.03912i	0.392893	+	0.919584i	$0.371474\pi$
$191$	−8.29129	+	14.3609i	−0.599937	+	1.03912i	−0.992830	+	0.119536i	$0.961859\pi$
$192$		0			0
$193$	−7.43273	−	12.8739i	−0.535020	−	0.926681i	−0.999162	−	0.0409206i	$-0.986971\pi$
$193$	−7.43273	−	12.8739i	−0.535020	−	0.926681i	0.464143	−	0.885760i	$-0.346362\pi$
$194$		0			0
$195$	−6.65918	+	4.54481i	−0.476874	+	0.325460i
$196$		0			0
$197$	7.33738	+	12.7087i	0.522767	+	0.905458i	0.999649	+	0.0264912i	$0.00843339\pi$
$197$	7.33738	+	12.7087i	0.522767	+	0.905458i	−0.476882	+	0.878967i	$0.658233\pi$
$198$		0			0
$199$	−5.29129	+	9.16478i	−0.375089	+	0.649674i	−0.990340	−	0.138657i	$-0.955721\pi$
$199$	−5.29129	+	9.16478i	−0.375089	+	0.649674i	0.615251	+	0.788331i	$0.289055\pi$
$200$		0			0
$201$	−0.873864	−	0.504525i	−0.0616376	−	0.0355865i
$202$		0			0
$203$	−7.93725			−0.557086
$204$		0			0
$205$	5.61976	−	1.84887i	0.392501	−	0.129131i
$206$		0			0
$207$			9.16515i			0.637022i
$208$		0			0
$209$	4.58258			0.316983
$210$		0			0
$211$	−0.0825757	−	0.143025i	−0.00568475	−	0.00984627i	0.863169	−	0.504915i	$-0.168476\pi$
$211$	−0.0825757	−	0.143025i	−0.00568475	−	0.00984627i	−0.868854	+	0.495069i	$0.835143\pi$
$212$		0			0
$213$	−7.02355			−0.481246
$214$		0			0
$215$	−17.6435	−	15.7690i	−1.20327	−	1.07544i
$216$		0			0
$217$	−9.30780	−	5.37386i	−0.631855	−	0.364802i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−16.0390	−	3.96863i	−1.07890	−	0.266959i
$222$		0			0
$223$	−4.33013	−	7.50000i	−0.289967	−	0.502237i	0.683835	−	0.729637i	$-0.260311\pi$
$223$	−4.33013	−	7.50000i	−0.289967	−	0.502237i	−0.973801	+	0.227400i	$0.926978\pi$
$224$		0			0
$225$	−8.04668	+	5.93725i	−0.536445	+	0.395817i
$226$		0			0
$227$	0.409175	−	0.708712i	0.0271579	−	0.0470389i	−0.852127	−	0.523335i	$-0.824688\pi$
$227$	0.409175	−	0.708712i	0.0271579	−	0.0470389i	0.879285	+	0.476296i	$0.158021\pi$
$228$		0			0
$229$		−	26.2668i		−	1.73576i	−0.496774	−	0.867880i	$-0.665482\pi$
$229$		−	26.2668i		−	1.73576i	0.496774	−	0.867880i	$-0.334518\pi$
$230$		0			0
$231$	2.29129	+	3.96863i	0.150756	+	0.261116i
$232$		0			0
$233$		−	2.83485i		−	0.185717i	−0.995679	−	0.0928586i	$-0.970400\pi$
$233$		−	2.83485i		−	0.185717i	0.995679	−	0.0928586i	$-0.0296004\pi$
$234$		0			0
$235$	4.00000	+	0.834849i	0.260931	+	0.0544595i
$236$		0			0
$237$	−5.19615	+	3.00000i	−0.337526	+	0.194871i
$238$		0			0
$239$			0.190700i			0.0123354i	0.999981	+	0.00616769i	$0.00196325\pi$
$239$			0.190700i			0.0123354i	−0.999981	+	0.00616769i	$0.998037\pi$
$240$		0			0
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$		0			0
$243$	−13.8564	−	8.00000i	−0.888889	−	0.513200i
$244$		0			0
$245$	2.79523	+	8.49628i	0.178580	+	0.542807i
$246$		0			0
$247$	−6.06218	−	1.50000i	−0.385727	−	0.0954427i
$248$		0			0
$249$	−5.20871	+	3.00725i	−0.330089	+	0.190577i
$250$		0			0
$251$	−0.0825757	+	0.143025i	−0.00521213	+	0.00902768i	−0.868620	−	0.495479i	$-0.834992\pi$
$251$	−0.0825757	+	0.143025i	−0.00521213	+	0.00902768i	0.863408	+	0.504507i	$0.168326\pi$
$252$		0			0
$253$	6.06218	−	10.5000i	0.381126	−	0.660129i
$254$		0			0
$255$	10.0308	+	2.09355i	0.628153	+	0.131103i
$256$		0			0
$257$	−15.7315	+	9.08258i	−0.981303	+	0.566556i	−0.902663	−	0.430348i	$-0.858391\pi$
$257$	−15.7315	+	9.08258i	−0.981303	+	0.566556i	−0.0786397	+	0.996903i	$0.525058\pi$
$258$		0			0
$259$	13.7477			0.854242
$260$		0			0
$261$	−9.16515			−0.567309
$262$		0			0
$263$	7.79423	−	4.50000i	0.480613	−	0.277482i	−0.240059	−	0.970758i	$-0.577167\pi$
$263$	7.79423	−	4.50000i	0.480613	−	0.277482i	0.720672	+	0.693276i	$0.243833\pi$
$264$		0			0
$265$	3.46410	−	16.5975i	0.212798	−	1.01958i
$266$		0			0
$267$	4.78698	−	8.29129i	0.292958	−	0.507419i
$268$		0			0
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	−0.998816	−	0.0486418i	$-0.984511\pi$
$269$	−7.50000	+	12.9904i	−0.457283	+	0.792038i	0.541533	+	0.840679i	$0.317844\pi$
$270$		0			0
$271$	−7.50000	+	4.33013i	−0.455593	+	0.263036i	−0.710189	−	0.704011i	$-0.751391\pi$
$271$	−7.50000	+	4.33013i	−0.455593	+	0.263036i	0.254597	+	0.967047i	$0.418057\pi$
$272$		0			0
$273$	−1.73205	−	6.00000i	−0.104828	−	0.363137i
$274$		0			0
$275$	13.1458	−	1.47960i	0.792719	−	0.0892234i
$276$		0			0
$277$	6.42368	+	3.70871i	0.385961	+	0.222835i	0.680409	−	0.732833i	$-0.261802\pi$
$277$	6.42368	+	3.70871i	0.385961	+	0.222835i	−0.294447	+	0.955668i	$0.595136\pi$
$278$		0			0
$279$	−10.7477	−	6.20520i	−0.643450	−	0.371496i
$280$		0			0
$281$		−	3.65480i		−	0.218027i	−0.994040	−	0.109014i	$-0.965231\pi$
$281$		−	3.65480i		−	0.218027i	0.994040	−	0.109014i	$-0.0347692\pi$
$282$		0			0
$283$	−24.0302	+	13.8739i	−1.42845	+	0.824716i	−0.996998	−	0.0774209i	$-0.975331\pi$
$283$	−24.0302	+	13.8739i	−1.42845	+	0.824716i	−0.431451	+	0.902136i	$0.641998\pi$
$284$		0			0
$285$	3.79129	+	0.791288i	0.224577	+	0.0468718i
$286$		0			0
$287$			4.58258i			0.270501i
$288$		0			0
$289$	2.00000	+	3.46410i	0.117647	+	0.203771i
$290$		0			0
$291$		−	11.4014i		−	0.668359i
$292$		0			0
$293$	9.06943	−	15.7087i	0.529842	−	0.917713i	−0.469552	−	0.882905i	$-0.655585\pi$
$293$	9.06943	−	15.7087i	0.529842	−	0.917713i	0.999394	−	0.0348081i	$-0.0110820\pi$
$294$		0			0
$295$	23.2606	+	20.7894i	1.35429	+	1.21041i
$296$		0			0
$297$	6.61438	+	11.4564i	0.383805	+	0.664770i
$298$		0			0
$299$	−11.4564	+	11.9059i	−0.662543	+	0.688535i
$300$		0			0
$301$	15.8739	−	9.16478i	0.914954	−	0.528249i
$302$		0			0
$303$	−7.79423	−	4.50000i	−0.447767	−	0.258518i
$304$		0			0
$305$	2.11210	−	2.36316i	0.120938	−	0.135314i
$306$		0			0
$307$	24.2487			1.38395			0.691974	−	0.721923i	$-0.256741\pi$
$307$	24.2487			1.38395			0.691974	+	0.721923i	$0.256741\pi$
$308$		0			0
$309$	1.58258	+	2.74110i	0.0900296	+	0.155936i
$310$		0			0
$311$	−7.58258			−0.429968			−0.214984	−	0.976618i	$-0.568970\pi$
$311$	−7.58258			−0.429968			−0.214984	+	0.976618i	$0.568970\pi$
$312$		0			0
$313$			3.25227i			0.183829i	0.995767	+	0.0919147i	$0.0292987\pi$
$313$			3.25227i			0.183829i	−0.995767	+	0.0919147i	$0.970701\pi$
$314$		0			0
$315$	−2.42074	−	7.35799i	−0.136393	−	0.414576i
$316$		0			0
$317$	0.190700			0.0107108			0.00535540	−	0.999986i	$-0.498295\pi$
$317$	0.190700			0.0107108			0.00535540	+	0.999986i	$0.498295\pi$
$318$		0			0
$319$	10.5000	+	6.06218i	0.587887	+	0.339417i
$320$		0			0
$321$	5.29129	−	9.16478i	0.295331	−	0.511528i
$322$		0			0
$323$	3.96863	+	6.87386i	0.220820	+	0.382472i
$324$		0			0
$325$	−17.8745	−	2.34563i	−0.991499	−	0.130112i
$326$		0			0
$327$	6.56670	+	11.3739i	0.363140	+	0.628976i
$328$		0			0
$329$	−1.58258	+	2.74110i	−0.0872502	+	0.151122i
$330$		0			0
$331$	3.87386	+	2.23658i	0.212927	+	0.122933i	0.602671	−	0.797990i	$-0.294103\pi$
$331$	3.87386	+	2.23658i	0.212927	+	0.122933i	−0.389744	+	0.920923i	$0.627437\pi$
$332$		0			0
$333$	15.8745			0.869918
$334$		0			0
$335$	−0.705131	−	2.14329i	−0.0385254	−	0.117101i
$336$		0			0
$337$			30.7477i			1.67494i	0.546487	+	0.837468i	$0.315965\pi$
$337$			30.7477i			1.67494i	−0.546487	+	0.837468i	$0.684035\pi$
$338$		0			0
$339$	−7.41742			−0.402859
$340$		0			0
$341$	8.20871	+	14.2179i	0.444527	+	0.769943i
$342$		0			0
$343$	−19.0526			−1.02874
$344$		0			0
$345$	6.82847	−	7.64016i	0.367633	−	0.411332i
$346$		0			0
$347$	−18.4726	−	10.6652i	−0.991660	−	0.572535i	−0.0858901	−	0.996305i	$-0.527373\pi$
$347$	−18.4726	−	10.6652i	−0.991660	−	0.572535i	−0.905770	+	0.423769i	$0.860707\pi$
$348$		0			0
$349$	2.12614	−	1.22753i	0.113809	−	0.0657079i	−0.442015	−	0.897008i	$-0.645736\pi$
$349$	2.12614	−	1.22753i	0.113809	−	0.0657079i	0.555824	+	0.831300i	$0.312403\pi$
$350$		0			0
$351$	−5.00000	−	17.3205i	−0.266880	−	0.924500i
$352$		0			0
$353$	−3.41643	−	5.91742i	−0.181838	−	0.314953i	0.760668	−	0.649141i	$-0.224871\pi$
$353$	−3.41643	−	5.91742i	−0.181838	−	0.314953i	−0.942506	+	0.334188i	$0.891538\pi$
$354$		0			0
$355$	−11.7098	−	10.4658i	−0.621492	−	0.555465i
$356$		0			0
$357$	−3.96863	+	6.87386i	−0.210042	+	0.363803i
$358$		0			0
$359$		−	19.5293i		−	1.03072i	−0.856975	−	0.515359i	$-0.827659\pi$
$359$		−	19.5293i		−	1.03072i	0.856975	−	0.515359i	$-0.172341\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$		0			0
$363$			4.00000i			0.209946i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.51358	−	0.873864i	0.0790080	−	0.0456153i	−0.459976	−	0.887932i	$-0.652142\pi$
$367$	1.51358	−	0.873864i	0.0790080	−	0.0456153i	0.538984	+	0.842316i	$0.318808\pi$
$368$		0			0
$369$			5.29150i			0.275465i
$370$		0			0
$371$	11.3739	+	6.56670i	0.590502	+	0.340926i
$372$		0			0
$373$	−11.2583	−	6.50000i	−0.582934	−	0.336557i	0.179364	−	0.983783i	$-0.442596\pi$
$373$	−11.2583	−	6.50000i	−0.582934	−	0.336557i	−0.762299	+	0.647225i	$0.775929\pi$
$374$		0			0
$375$	11.1313	+	1.04580i	0.574819	+	0.0540051i
$376$		0			0
$377$	−11.9059	−	11.4564i	−0.613184	−	0.590037i
$378$		0			0
$379$	9.24773	−	5.33918i	0.475024	−	0.274255i	−0.243317	−	0.969947i	$-0.578235\pi$
$379$	9.24773	−	5.33918i	0.475024	−	0.274255i	0.718340	+	0.695692i	$0.244902\pi$
$380$		0			0
$381$	−8.87386	+	15.3700i	−0.454622	+	0.787428i
$382$		0			0
$383$	11.8105	−	20.4564i	0.603490	−	1.04528i	−0.388798	−	0.921323i	$-0.627110\pi$
$383$	11.8105	−	20.4564i	0.603490	−	1.04528i	0.992288	−	0.123952i	$-0.0395570\pi$
$384$		0			0
$385$	−2.09355	+	10.0308i	−0.106697	+	0.511217i
$386$		0			0
$387$	18.3296	−	10.5826i	0.931744	−	0.537943i
$388$		0			0
$389$	3.16515			0.160480			0.0802398	−	0.996776i	$-0.474431\pi$
$389$	3.16515			0.160480			0.0802398	+	0.996776i	$0.474431\pi$
$390$		0			0
$391$	21.0000			1.06202
$392$		0			0
$393$	6.56670	−	3.79129i	0.331246	−	0.191245i
$394$		0			0
$395$	−13.1334	−	2.74110i	−0.660813	−	0.137920i
$396$		0			0
$397$	10.1738	−	17.6216i	0.510610	−	0.884402i	−0.489315	−	0.872107i	$-0.662753\pi$
$397$	10.1738	−	17.6216i	0.510610	−	0.884402i	0.999924	−	0.0122949i	$-0.00391368\pi$
$398$		0			0
$399$	−1.50000	+	2.59808i	−0.0750939	+	0.130066i
$400$		0			0
$401$	−25.8303	+	14.9131i	−1.28990	+	0.744726i	−0.978637	−	0.205596i	$-0.934087\pi$
$401$	−25.8303	+	14.9131i	−1.28990	+	0.744726i	−0.311267	+	0.950323i	$0.600753\pi$
$402$		0			0
$403$	−6.20520	−	21.4955i	−0.309103	−	1.07076i
$404$		0			0
$405$	−0.698807	−	2.12407i	−0.0347240	−	0.105546i
$406$		0			0
$407$	−18.1865	−	10.5000i	−0.901473	−	0.520466i
$408$		0			0
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	0.673830	−	0.738886i	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$		0			0
$411$			10.4877i			0.517318i
$412$		0			0
$413$	−20.9276	+	12.0826i	−1.02978	+	0.594545i
$414$		0			0
$415$	−13.1652	−	2.74773i	−0.646252	−	0.134881i
$416$		0			0
$417$		−	21.7477i		−	1.06499i
$418$		0			0
$419$	2.91742	+	5.05313i	0.142526	+	0.246861i	0.928447	−	0.371465i	$-0.121144\pi$
$419$	2.91742	+	5.05313i	0.142526	+	0.246861i	−0.785922	+	0.618326i	$0.787811\pi$
$420$		0			0
$421$		−	5.48220i		−	0.267186i	−0.991036	−	0.133593i	$-0.957348\pi$
$421$		−	5.48220i		−	0.267186i	0.991036	−	0.133593i	$-0.0426515\pi$
$422$		0			0
$423$	−1.82740	+	3.16515i	−0.0888513	+	0.153895i
$424$		0			0
$425$	13.6040	+	18.4373i	0.659889	+	0.894338i
$426$		0			0
$427$	1.22753	+	2.12614i	0.0594041	+	0.102891i
$428$		0			0
$429$	−2.29129	+	9.26013i	−0.110624	+	0.447083i
$430$		0			0
$431$	−7.33485	+	4.23478i	−0.353307	+	0.203982i	−0.666141	−	0.745826i	$-0.732055\pi$
$431$	−7.33485	+	4.23478i	−0.353307	+	0.203982i	0.312834	+	0.949808i	$0.398722\pi$
$432$		0			0
$433$	8.44178	+	4.87386i	0.405686	+	0.234223i	0.688934	−	0.724824i	$-0.258079\pi$
$433$	8.44178	+	4.87386i	0.405686	+	0.234223i	−0.283248	+	0.959047i	$0.591412\pi$
$434$		0			0
$435$	7.64016	+	6.82847i	0.366317	+	0.327400i
$436$		0			0
$437$	7.93725			0.379690
$438$		0			0
$439$	7.24773	+	12.5534i	0.345915	+	0.599143i	0.985520	−	0.169562i	$-0.0542352\pi$
$439$	7.24773	+	12.5534i	0.345915	+	0.599143i	−0.639604	+	0.768704i	$0.720902\pi$
$440$		0			0
$441$	−8.00000			−0.380952
$442$		0			0
$443$			19.9129i			0.946089i	0.881038	+	0.473045i	$0.156845\pi$
$443$			19.9129i			0.946089i	−0.881038	+	0.473045i	$0.843155\pi$
$444$		0			0
$445$	20.3357	−	6.69034i	0.964007	−	0.317153i
$446$		0			0
$447$	−16.6929			−0.789545
$448$		0			0
$449$	9.54356	+	5.50998i	0.450388	+	0.260032i	0.707994	−	0.706218i	$-0.249600\pi$
$449$	9.54356	+	5.50998i	0.450388	+	0.260032i	−0.257606	+	0.966250i	$0.582934\pi$
$450$		0			0
$451$	3.50000	−	6.06218i	0.164809	−	0.285457i
$452$		0			0
$453$	−4.83465	−	8.37386i	−0.227152	−	0.393438i
$454$		0			0
$455$	6.05286	−	12.5842i	0.283762	−	0.589958i
$456$		0			0
$457$	−0.866025	−	1.50000i	−0.0405110	−	0.0701670i	0.845059	−	0.534673i	$-0.179565\pi$
$457$	−0.866025	−	1.50000i	−0.0405110	−	0.0701670i	−0.885570	+	0.464506i	$0.846232\pi$
$458$		0			0
$459$	−11.4564	+	19.8431i	−0.534741	+	0.926198i
$460$		0			0
$461$	31.0390	+	17.9204i	1.44563	+	0.834635i	0.998217	−	0.0596914i	$-0.0190117\pi$
$461$	31.0390	+	17.9204i	1.44563	+	0.834635i	0.447414	+	0.894327i	$0.352345\pi$
$462$		0			0
$463$	39.4002			1.83108			0.915542	−	0.402223i	$-0.131762\pi$
$463$	39.4002			1.83108			0.915542	+	0.402223i	$0.131762\pi$
$464$		0			0
$465$	4.33624	+	13.1803i	0.201088	+	0.611221i
$466$		0			0
$467$			24.3303i			1.12587i	0.826500	+	0.562936i	$0.190328\pi$
$467$			24.3303i			1.12587i	−0.826500	+	0.562936i	$0.809672\pi$
$468$		0			0
$469$	1.74773			0.0807025
$470$		0			0
$471$	4.58258	+	7.93725i	0.211154	+	0.365729i
$472$		0			0
$473$	−27.9989			−1.28739
$474$		0			0
$475$	5.14181	+	6.96863i	0.235923	+	0.319743i
$476$		0			0
$477$	13.1334	+	7.58258i	0.601337	+	0.347182i
$478$		0			0
$479$	−4.03901	+	2.33193i	−0.184547	+	0.106548i	−0.589427	−	0.807821i	$-0.700647\pi$
$479$	−4.03901	+	2.33193i	−0.184547	+	0.106548i	0.404880	+	0.914370i	$0.367313\pi$
$480$		0			0
$481$	20.6216	+	19.8431i	0.940264	+	0.904769i
$482$		0			0
$483$	3.96863	+	6.87386i	0.180579	+	0.312772i
$484$		0			0
$485$	16.9891	−	19.0086i	0.771435	−	0.863134i
$486$		0			0
$487$	5.33918	−	9.24773i	0.241941	−	0.419055i	−0.719326	−	0.694673i	$-0.755549\pi$
$487$	5.33918	−	9.24773i	0.241941	−	0.419055i	0.961267	+	0.275618i	$0.0888825\pi$
$488$		0			0
$489$		−	21.0707i		−	0.952848i
$490$		0			0
$491$	9.70871	+	16.8160i	0.438148	+	0.758895i	0.997547	−	0.0700041i	$-0.0223012\pi$
$491$	9.70871	+	16.8160i	0.438148	+	0.758895i	−0.559399	+	0.828899i	$0.688968\pi$
$492$		0			0
$493$			21.0000i			0.945792i
$494$		0			0
$495$	−2.41742	+	11.5826i	−0.108655	+	0.520598i
$496$		0			0
$497$	10.5353	−	6.08258i	0.472574	−	0.272841i
$498$		0			0
$499$			0.723000i			0.0323659i	0.999869	+	0.0161830i	$0.00515142\pi$
$499$			0.723000i			0.0323659i	−0.999869	+	0.0161830i	$0.994849\pi$
$500$		0			0
$501$	−8.29129	−	4.78698i	−0.370427	−	0.213866i
$502$		0			0
$503$	−0.143025	−	0.0825757i	−0.00637718	−	0.00368187i	0.496808	−	0.867860i	$-0.334505\pi$
$503$	−0.143025	−	0.0825757i	−0.00637718	−	0.00368187i	−0.503185	+	0.864179i	$0.667839\pi$
$504$		0			0
$505$	−6.28926	−	19.1166i	−0.279868	−	0.850678i
$506$		0			0
$507$	6.06218	−	11.5000i	0.269231	−	0.510733i
$508$		0			0
$509$	−7.33485	+	4.23478i	−0.325111	+	0.187703i	−0.653669	−	0.756781i	$-0.726771\pi$
$509$	−7.33485	+	4.23478i	−0.325111	+	0.187703i	0.328557	+	0.944484i	$0.393438\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−4.33013	+	7.50000i	−0.191180	+	0.331133i
$514$		0			0
$515$	−1.44600	+	6.92820i	−0.0637184	+	0.305293i
$516$		0			0
$517$	4.18710	−	2.41742i	0.184149	−	0.106318i
$518$		0			0
$519$	−16.5826			−0.727894
$520$		0			0
$521$	27.4955			1.20460			0.602299	−	0.798271i	$-0.294252\pi$
$521$	27.4955			1.20460			0.602299	+	0.798271i	$0.294252\pi$
$522$		0			0
$523$	0.143025	−	0.0825757i	0.00625406	−	0.00361078i	−0.496870	−	0.867825i	$-0.665517\pi$
$523$	0.143025	−	0.0825757i	0.00625406	−	0.00361078i	0.503124	+	0.864214i	$0.332184\pi$
$524$		0			0
$525$	−3.46410	+	7.93725i	−0.151186	+	0.346410i
$526$		0			0
$527$	−14.2179	+	24.6261i	−0.619342	+	1.07273i
$528$		0			0
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$		0			0
$531$	−24.1652	+	13.9518i	−1.04868	+	0.605455i
$532$		0			0
$533$	−6.61438	+	6.87386i	−0.286501	+	0.297740i
$534$		0			0
$535$	22.4781	−	7.39517i	0.971814	−	0.319721i
$536$		0			0
$537$	−15.7315	−	9.08258i	−0.678864	−	0.391942i
$538$		0			0
$539$	9.16515	+	5.29150i	0.394771	+	0.227921i
$540$		0			0
$541$			10.3923i			0.446800i	0.974727	+	0.223400i	$0.0717156\pi$
$541$			10.3923i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$542$		0			0
$543$	7.57575	−	4.37386i	0.325107	−	0.187700i
$544$		0			0
$545$	−6.00000	+	28.7477i	−0.257012	+	1.23142i
$546$		0			0
$547$		−	28.7477i		−	1.22916i	−0.788853	−	0.614582i	$-0.789325\pi$
$547$		−	28.7477i		−	1.22916i	0.788853	−	0.614582i	$-0.210675\pi$
$548$		0			0
$549$	1.41742	+	2.45505i	0.0604942	+	0.104779i
$550$		0			0
$551$			7.93725i			0.338138i
$552$		0			0
$553$	5.19615	−	9.00000i	0.220963	−	0.382719i
$554$		0			0
$555$	−13.2331	−	11.8273i	−0.561715	−	0.502039i
$556$		0			0
$557$	−3.87328	−	6.70871i	−0.164116	−	0.284257i	0.772225	−	0.635349i	$-0.219144\pi$
$557$	−3.87328	−	6.70871i	−0.164116	−	0.284257i	−0.936341	+	0.351092i	$0.885810\pi$
$558$		0			0
$559$	37.0390	+	9.16478i	1.56658	+	0.387629i
$560$		0			0
$561$	10.5000	−	6.06218i	0.443310	−	0.255945i
$562$		0			0
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	0.655169	−	0.755482i	$-0.272597\pi$
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	−0.326682	+	0.945134i	$0.605931\pi$
$564$		0			0
$565$	−12.3665	−	11.0527i	−0.520261	−	0.464989i
$566$		0			0
$567$	1.73205			0.0727393
$568$		0			0
$569$	3.87386	+	6.70973i	0.162401	+	0.281286i	0.935729	−	0.352719i	$-0.114743\pi$
$569$	3.87386	+	6.70973i	0.162401	+	0.281286i	−0.773328	+	0.634006i	$0.781410\pi$
$570$		0			0
$571$	35.0780			1.46797			0.733985	−	0.679166i	$-0.237658\pi$
$571$	35.0780			1.46797			0.733985	+	0.679166i	$0.237658\pi$
$572$		0			0
$573$			16.5826i			0.692747i
$574$		0			0
$575$	22.7691	−	2.56275i	0.949537	−	0.106874i
$576$		0			0
$577$	6.92820			0.288425			0.144212	−	0.989547i	$-0.453935\pi$
$577$	6.92820			0.288425			0.144212	+	0.989547i	$0.453935\pi$
$578$		0			0
$579$	−12.8739	−	7.43273i	−0.535020	−	0.308894i
$580$		0			0
$581$	5.20871	−	9.02175i	0.216094	−	0.374285i
$582$		0			0
$583$	−10.0308	−	17.3739i	−0.415433	−	0.719552i
$584$		0			0
$585$	6.98924	−	14.5310i	0.288969	−	0.600784i
$586$		0			0
$587$	19.7478	+	34.2042i	0.815078	+	1.41176i	0.909272	+	0.416203i	$0.136639\pi$
$587$	19.7478	+	34.2042i	0.815078	+	1.41176i	−0.0941934	+	0.995554i	$0.530027\pi$
$588$		0			0
$589$	−5.37386	+	9.30780i	−0.221426	+	0.383521i
$590$		0			0
$591$	12.7087	+	7.33738i	0.522767	+	0.301819i
$592$		0			0
$593$	21.1660			0.869184			0.434592	−	0.900627i	$-0.356893\pi$
$593$	21.1660			0.869184			0.434592	+	0.900627i	$0.356893\pi$
$594$		0			0
$595$	−16.8593	+	5.54661i	−0.691163	+	0.227389i
$596$		0			0
$597$			10.5826i			0.433116i
$598$		0			0
$599$	15.4955			0.633127			0.316564	−	0.948571i	$-0.397471\pi$
$599$	15.4955			0.633127			0.316564	+	0.948571i	$0.397471\pi$
$600$		0			0
$601$	−8.45644	−	14.6470i	−0.344945	−	0.597463i	0.640398	−	0.768043i	$-0.278769\pi$
$601$	−8.45644	−	14.6470i	−0.344945	−	0.597463i	−0.985344	+	0.170580i	$0.945436\pi$
$602$		0			0
$603$	2.01810			0.0821834
$604$		0			0
$605$	−5.96038	+	6.66888i	−0.242324	+	0.271128i
$606$		0			0
$607$	6.70973	+	3.87386i	0.272339	+	0.157235i	0.629950	−	0.776635i	$-0.283075\pi$
$607$	6.70973	+	3.87386i	0.272339	+	0.157235i	−0.357611	+	0.933871i	$0.616409\pi$
$608$		0			0
$609$	−6.87386	+	3.96863i	−0.278543	+	0.160817i
$610$		0			0
$611$	−6.33030	+	1.82740i	−0.256097	+	0.0739287i
$612$		0			0
$613$	2.95958	+	5.12614i	0.119536	+	0.207043i	0.919584	−	0.392894i	$-0.128526\pi$
$613$	2.95958	+	5.12614i	0.119536	+	0.207043i	−0.800048	+	0.599936i	$0.795193\pi$
$614$		0			0
$615$	3.94242	−	4.41105i	0.158974	−	0.177871i
$616$		0			0
$617$	6.97588	−	12.0826i	0.280838	−	0.486426i	−0.690753	−	0.723091i	$-0.742721\pi$
$617$	6.97588	−	12.0826i	0.280838	−	0.486426i	0.971591	+	0.236664i	$0.0760542\pi$
$618$		0			0
$619$		−	29.7309i		−	1.19499i	−0.801874	−	0.597493i	$-0.796164\pi$
$619$		−	29.7309i		−	1.19499i	0.801874	−	0.597493i	$-0.203836\pi$
$620$		0			0
$621$	11.4564	+	19.8431i	0.459731	+	0.796278i
$622$		0			0
$623$			16.5826i			0.664367i
$624$		0			0
$625$	17.0000	+	18.3303i	0.680000	+	0.733212i
$626$		0			0
$627$	3.96863	−	2.29129i	0.158492	−	0.0915052i
$628$		0			0
$629$		−	36.3731i		−	1.45029i
$630$		0			0
$631$	5.12614	+	2.95958i	0.204068	+	0.117819i	0.598552	−	0.801084i	$-0.295743\pi$
$631$	5.12614	+	2.95958i	0.204068	+	0.117819i	−0.394483	+	0.918903i	$0.629076\pi$
$632$		0			0
$633$	−0.143025	−	0.0825757i	−0.00568475	−	0.00328209i
$634$		0			0
$635$	−37.6974	+	12.4022i	−1.49598	+	0.492167i
$636$		0			0
$637$	−10.3923	−	10.0000i	−0.411758	−	0.396214i
$638$		0			0
$639$	12.1652	−	7.02355i	0.481246	−	0.277847i
$640$		0			0
$641$	−9.08258	+	15.7315i	−0.358740	+	0.621356i	−0.987751	−	0.156041i	$-0.950127\pi$
$641$	−9.08258	+	15.7315i	−0.358740	+	0.621356i	0.629010	+	0.777397i	$0.283460\pi$
$642$		0			0
$643$	−10.8968	+	18.8739i	−0.429729	+	0.744313i	−0.996849	−	0.0793227i	$-0.974724\pi$
$643$	−10.8968	+	18.8739i	−0.429729	+	0.744313i	0.567120	+	0.823635i	$0.308058\pi$
$644$		0			0
$645$	−23.1642	−	4.83465i	−0.912090	−	0.190364i
$646$		0			0
$647$	−23.3827	+	13.5000i	−0.919268	+	0.530740i	−0.883402	−	0.468617i	$-0.844753\pi$
$647$	−23.3827	+	13.5000i	−0.919268	+	0.530740i	−0.0358667	+	0.999357i	$0.511419\pi$
$648$		0			0
$649$	36.9129			1.44896
$650$		0			0
$651$	−10.7477			−0.421237
$652$		0			0
$653$	37.0882	−	21.4129i	1.45137	−	0.837951i	0.452814	−	0.891605i	$-0.350420\pi$
$653$	37.0882	−	21.4129i	1.45137	−	0.837951i	0.998560	+	0.0536545i	$0.0170870\pi$
$654$		0			0
$655$	16.5975	+	3.46410i	0.648518	+	0.135354i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−15.2477	+	26.4098i	−0.593967	+	1.02878i	0.399725	+	0.916635i	$0.369106\pi$
$659$	−15.2477	+	26.4098i	−0.593967	+	1.02878i	−0.993692	+	0.112146i	$0.964228\pi$
$660$		0			0
$661$	15.8739	−	9.16478i	0.617422	−	0.356469i	−0.158443	−	0.987368i	$-0.550647\pi$
$661$	15.8739	−	9.16478i	0.617422	−	0.356469i	0.775865	+	0.630900i	$0.217314\pi$
$662$		0			0
$663$	−15.8745	+	4.58258i	−0.616515	+	0.177972i
$664$		0			0
$665$	−6.37221	+	2.09642i	−0.247104	+	0.0812957i
$666$		0			0
$667$	18.1865	+	10.5000i	0.704185	+	0.406562i
$668$		0			0
$669$	−7.50000	−	4.33013i	−0.289967	−	0.167412i
$670$		0			0
$671$		−	3.75015i		−	0.144773i
$672$		0			0
$673$	20.9276	−	12.0826i	0.806701	−	0.465749i	−0.0391079	−	0.999235i	$-0.512452\pi$
$673$	20.9276	−	12.0826i	0.806701	−	0.465749i	0.845809	+	0.533486i	$0.179118\pi$
$674$		0			0
$675$	−10.0000	+	22.9129i	−0.384900	+	0.881917i
$676$		0			0
$677$		−	2.83485i		−	0.108952i	−0.998515	−	0.0544760i	$-0.982651\pi$
$677$		−	2.83485i		−	0.108952i	0.998515	−	0.0544760i	$-0.0173489\pi$
$678$		0			0
$679$	9.87386	+	17.1020i	0.378924	+	0.656316i
$680$		0			0
$681$		−	0.818350i		−	0.0313593i
$682$		0			0
$683$	16.5498	−	28.6652i	0.633262	−	1.09684i	−0.353619	−	0.935390i	$-0.615049\pi$
$683$	16.5498	−	28.6652i	0.633262	−	1.09684i	0.986881	−	0.161452i	$-0.0516177\pi$
$684$		0			0
$685$	−15.6276	+	17.4852i	−0.597100	+	0.668076i
$686$		0			0
$687$	−13.1334	−	22.7477i	−0.501071	−	0.867880i
$688$		0			0
$689$	7.58258	+	26.2668i	0.288873	+	1.00069i
$690$		0			0
$691$	−17.1261	+	9.88778i	−0.651509	+	0.376149i	−0.789034	−	0.614349i	$-0.789419\pi$
$691$	−17.1261	+	9.88778i	−0.651509	+	0.376149i	0.137525	+	0.990498i	$0.456085\pi$
$692$		0			0
$693$	−7.93725	−	4.58258i	−0.301511	−	0.174078i
$694$		0			0
$695$	32.4062	−	36.2582i	1.22924	−	1.37535i
$696$		0			0
$697$	12.1244			0.459243
$698$		0			0
$699$	−1.41742	−	2.45505i	−0.0536119	−	0.0928586i
$700$		0			0
$701$	−21.1652			−0.799397			−0.399698	−	0.916647i	$-0.630885\pi$
$701$	−21.1652			−0.799397			−0.399698	+	0.916647i	$0.630885\pi$
$702$		0			0
$703$		−	13.7477i		−	0.518505i
$704$		0			0
$705$	3.88153	−	1.27700i	0.146187	−	0.0480946i
$706$		0			0
$707$	15.5885			0.586264
$708$		0			0
$709$	31.5000	+	18.1865i	1.18301	+	0.683010i	0.956708	−	0.291048i	$-0.0940040\pi$
$709$	31.5000	+	18.1865i	1.18301	+	0.683010i	0.226299	+	0.974058i	$0.427337\pi$
$710$		0			0
$711$	6.00000	−	10.3923i	0.225018	−	0.389742i
$712$		0			0
$713$	14.2179	+	24.6261i	0.532465	+	0.922256i
$714$		0			0
$715$	−17.6185	+	12.0244i	−0.658896	+	0.449688i
$716$		0			0
$717$	0.0953502	+	0.165151i	0.00356092	+	0.00616769i
$718$		0			0
$719$	12.2477	−	21.2137i	0.456763	−	0.791137i	−0.542025	−	0.840363i	$-0.682342\pi$
$719$	12.2477	−	21.2137i	0.456763	−	0.791137i	0.998788	+	0.0492257i	$0.0156754\pi$
$720$		0			0
$721$	−4.74773	−	2.74110i	−0.176815	−	0.102084i
$722$		0			0
$723$	−1.73205			−0.0644157
$724$		0			0
$725$	2.56275	+	22.7691i	0.0951780	+	0.845623i
$726$		0			0
$727$			15.2523i			0.565675i	0.959168	+	0.282838i	$0.0912758\pi$
$727$			15.2523i			0.565675i	−0.959168	+	0.282838i	$0.908724\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−24.2477	−	41.9983i	−0.896835	−	1.55336i
$732$		0			0
$733$	−22.8027			−0.842237			−0.421119	−	0.907006i	$-0.638362\pi$
$733$	−22.8027			−0.842237			−0.421119	+	0.907006i	$0.638362\pi$
$734$		0			0
$735$	6.66888	+	5.96038i	0.245985	+	0.219852i
$736$		0			0
$737$	−2.31203	−	1.33485i	−0.0851646	−	0.0491698i
$738$		0			0
$739$	14.7523	−	8.51723i	0.542671	−	0.313311i	−0.203490	−	0.979077i	$-0.565228\pi$
$739$	14.7523	−	8.51723i	0.542671	−	0.313311i	0.746161	+	0.665766i	$0.231895\pi$
$740$		0			0
$741$	−6.00000	+	1.73205i	−0.220416	+	0.0636285i
$742$		0			0
$743$	2.86423	+	4.96099i	0.105078	+	0.182001i	0.913770	−	0.406232i	$-0.133157\pi$
$743$	2.86423	+	4.96099i	0.105078	+	0.182001i	−0.808692	+	0.588232i	$0.799824\pi$
$744$		0			0
$745$	−27.8306	−	24.8739i	−1.01964	−	0.911310i
$746$		0			0
$747$	6.01450	−	10.4174i	0.220059	−	0.381154i
$748$		0			0
$749$			18.3296i			0.669748i
$750$		0			0
$751$	5.87386	+	10.1738i	0.214340	+	0.371248i	0.953068	−	0.302755i	$-0.0979065\pi$
$751$	5.87386	+	10.1738i	0.214340	+	0.371248i	−0.738728	+	0.674004i	$0.764573\pi$
$752$		0			0
$753$			0.165151i			0.00601845i
$754$		0			0
$755$	4.41742	−	21.1652i	0.160767	−	0.770279i
$756$		0			0
$757$	8.44178	−	4.87386i	0.306822	−	0.177144i	−0.338682	−	0.940901i	$-0.609981\pi$
$757$	8.44178	−	4.87386i	0.306822	−	0.177144i	0.645503	+	0.763757i	$0.276648\pi$
$758$		0			0
$759$		−	12.1244i		−	0.440086i
$760$		0			0
$761$	−30.7087	−	17.7297i	−1.11319	−	0.642701i	−0.173536	−	0.984827i	$-0.555519\pi$
$761$	−30.7087	−	17.7297i	−1.11319	−	0.642701i	−0.939654	+	0.342127i	$0.888853\pi$
$762$		0			0
$763$	−19.7001	−	11.3739i	−0.713192	−	0.411762i
$764$		0			0
$765$	−19.4674	+	6.40467i	−0.703846	+	0.231561i
$766$		0			0
$767$	−48.8311	−	12.0826i	−1.76319	−	0.436277i
$768$		0			0
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	−0.723255	−	0.690581i	$-0.757355\pi$
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	0.236433	+	0.971648i	$0.424022\pi$
$770$		0			0
$771$	−9.08258	+	15.7315i	−0.327101	+	0.566556i
$772$		0			0
$773$	12.0767	−	20.9174i	0.434368	−	0.752347i	−0.562876	−	0.826541i	$-0.690305\pi$
$773$	12.0767	−	20.9174i	0.434368	−	0.752347i	0.997244	+	0.0741940i	$0.0236384\pi$
$774$		0			0
$775$	−12.4104	+	28.4358i	−0.445795	+	1.02144i
$776$		0			0
$777$	11.9059	−	6.87386i	0.427121	−	0.246598i
$778$		0			0
$779$	4.58258			0.164188
$780$		0			0
$781$	−18.5826			−0.664937
$782$		0			0
$783$	−19.8431	+	11.4564i	−0.709136	+	0.409420i
$784$		0			0
$785$	−4.18710	+	20.0616i	−0.149444	+	0.716030i
$786$		0			0
$787$	8.15573	−	14.1261i	0.290720	−	0.503542i	−0.683260	−	0.730175i	$-0.739438\pi$
$787$	8.15573	−	14.1261i	0.290720	−	0.503542i	0.973980	+	0.226633i	$0.0727717\pi$
$788$		0			0
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$		0			0
$791$	11.1261	−	6.42368i	0.395600	−	0.228400i
$792$		0			0
$793$	−1.22753	+	4.96099i	−0.0435907	+	0.176170i
$794$		0			0
$795$	−5.29875	−	16.1059i	−0.187927	−	0.571218i
$796$		0			0
$797$	−38.1727	−	22.0390i	−1.35215	−	0.780662i	−0.363596	−	0.931557i	$-0.618451\pi$
$797$	−38.1727	−	22.0390i	−1.35215	−	0.780662i	−0.988550	+	0.150895i	$0.951785\pi$
$798$		0			0
$799$	7.25227	+	4.18710i	0.256567	+	0.148129i
$800$		0			0
$801$			19.1479i			0.676558i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−3.62614	+	17.3739i	−0.127805	+	0.612348i
$806$		0			0
$807$			15.0000i			0.528025i
$808$		0			0
$809$	−27.4129	−	47.4805i	−0.963785	−	1.66933i	−0.712843	−	0.701323i	$-0.752593\pi$
$809$	−27.4129	−	47.4805i	−0.963785	−	1.66933i	−0.250942	−	0.968002i	$-0.580740\pi$
$810$		0			0
$811$		−	50.5155i		−	1.77384i	−0.461923	−	0.886920i	$-0.652840\pi$
$811$		−	50.5155i		−	1.77384i	0.461923	−	0.886920i	$-0.347160\pi$
$812$		0			0
$813$	−4.33013	+	7.50000i	−0.151864	+	0.263036i
$814$		0			0
$815$	31.3973	−	35.1294i	1.09980	−	1.23053i
$816$		0			0
$817$	−9.16478	−	15.8739i	−0.320635	−	0.555356i
$818$		0			0
$819$	9.00000	+	8.66025i	0.314485	+	0.302614i
$820$		0			0
$821$	15.7087	−	9.06943i	0.548238	−	0.316525i	−0.200173	−	0.979761i	$-0.564150\pi$
$821$	15.7087	−	9.06943i	0.548238	−	0.316525i	0.748411	+	0.663235i	$0.230817\pi$
$822$		0			0
$823$	27.2083	+	15.7087i	0.948421	+	0.547571i	0.892590	−	0.450869i	$-0.148886\pi$
$823$	27.2083	+	15.7087i	0.948421	+	0.547571i	0.0558311	+	0.998440i	$0.482219\pi$
$824$		0			0
$825$	10.6448	−	7.85425i	0.370603	−	0.273450i
$826$		0			0
$827$	10.7737			0.374638			0.187319	−	0.982299i	$-0.440020\pi$
$827$	10.7737			0.374638			0.187319	+	0.982299i	$0.440020\pi$
$828$		0			0
$829$	−16.6652	−	28.8649i	−0.578805	−	1.00252i	−0.995617	−	0.0935264i	$-0.970186\pi$
$829$	−16.6652	−	28.8649i	−0.578805	−	1.00252i	0.416812	−	0.908993i	$-0.363147\pi$
$830$		0			0
$831$	7.41742			0.257308
$832$		0			0
$833$			18.3303i			0.635107i
$834$		0			0
$835$	−6.69034	−	20.3357i	−0.231529	−	0.703747i
$836$		0			0
$837$	−31.0260			−1.07242
$838$		0			0
$839$	−37.8303	−	21.8413i	−1.30605	−	0.754047i	−0.324613	−	0.945847i	$-0.605234\pi$
$839$	−37.8303	−	21.8413i	−1.30605	−	0.754047i	−0.981434	+	0.191800i	$0.938567\pi$
$840$		0			0
$841$	4.00000	−	6.92820i	0.137931	−	0.238904i
$842$		0			0
$843$	−1.82740	−	3.16515i	−0.0629390	−	0.109014i
$844$		0			0
$845$	27.2431	−	10.1398i	0.937190	−	0.348820i
$846$		0			0
$847$	−3.46410	−	6.00000i	−0.119028	−	0.206162i
$848$		0			0
$849$	−13.8739	+	24.0302i	−0.476150	+	0.824716i
$850$		0			0
$851$	−31.5000	−	18.1865i	−1.07981	−	0.623426i
$852$		0			0
$853$	5.63310			0.192874			0.0964369	−	0.995339i	$-0.469255\pi$
$853$	5.63310			0.192874			0.0964369	+	0.995339i	$0.469255\pi$
$854$		0			0
$855$	−7.35799	+	2.42074i	−0.251638	+	0.0827875i
$856$		0			0
$857$		−	4.74773i		−	0.162179i	−0.996707	−	0.0810896i	$-0.974160\pi$
$857$		−	4.74773i		−	0.162179i	0.996707	−	0.0810896i	$-0.0258400\pi$
$858$		0			0
$859$	−44.2432			−1.50956			−0.754779	−	0.655979i	$-0.772256\pi$
$859$	−44.2432			−1.50956			−0.754779	+	0.655979i	$0.772256\pi$
$860$		0			0
$861$	2.29129	+	3.96863i	0.0780869	+	0.135250i
$862$		0			0
$863$	13.6657			0.465186			0.232593	−	0.972574i	$-0.425279\pi$
$863$	13.6657			0.465186			0.232593	+	0.972574i	$0.425279\pi$
$864$		0			0
$865$	−27.6468	−	24.7096i	−0.940019	−	0.840152i
$866$		0			0
$867$	3.46410	+	2.00000i	0.117647	+	0.0679236i
$868$		0			0
$869$	−13.7477	+	7.93725i	−0.466360	+	0.269253i
$870$		0			0
$871$	2.62159	+	2.52263i	0.0888292	+	0.0854759i
$872$		0			0
$873$	11.4014	+	19.7477i	0.385877	+	0.668359i
$874$		0			0
$875$	−17.6027	+	8.07130i	−0.595079	+	0.272860i
$876$		0			0
$877$	3.96863	−	6.87386i	0.134011	−	0.232114i	−0.791208	−	0.611547i	$-0.790548\pi$
$877$	3.96863	−	6.87386i	0.134011	−	0.232114i	0.925219	+	0.379433i	$0.123881\pi$
$878$		0			0
$879$		−	18.1389i		−	0.611809i
$880$		0			0
$881$	−18.2477	−	31.6060i	−0.614782	−	1.06483i	−0.990423	−	0.138068i	$-0.955911\pi$
$881$	−18.2477	−	31.6060i	−0.614782	−	1.06483i	0.375641	−	0.926765i	$-0.377422\pi$
$882$		0			0
$883$			36.2432i			1.21968i	0.792524	+	0.609840i	$0.208766\pi$
$883$			36.2432i			1.21968i	−0.792524	+	0.609840i	$0.791234\pi$
$884$		0			0
$885$	30.5390	+	6.37386i	1.02656	+	0.214255i
$886$		0			0
$887$	−47.1944	+	27.2477i	−1.58463	+	0.914889i	−0.590465	+	0.807064i	$0.701055\pi$
$887$	−47.1944	+	27.2477i	−1.58463	+	0.914889i	−0.994170	+	0.107826i	$0.965611\pi$
$888$		0			0
$889$		−	30.7400i		−	1.03099i
$890$		0			0
$891$	−2.29129	−	1.32288i	−0.0767610	−	0.0443180i
$892$		0			0
$893$	2.74110	+	1.58258i	0.0917275	+	0.0529589i
$894$		0			0
$895$	−12.6939	−	38.5840i	−0.424311	−	1.28972i
$896$		0			0
$897$	−3.96863	+	16.0390i	−0.132509	+	0.535527i
$898$		0			0
$899$	−24.6261	+	14.2179i	−0.821328	+	0.474194i
$900$		0			0
$901$	17.3739	−	30.0924i	0.578807	−	1.00252i
$902$		0			0
$903$	9.16478	−	15.8739i	0.304985	−	0.528249i
$904$		0			0
$905$	19.1479	+	3.99640i	0.636498	+	0.132845i
$906$		0			0
$907$	5.41463	−	3.12614i	0.179790	−	0.103802i	−0.407404	−	0.913248i	$-0.633566\pi$
$907$	5.41463	−	3.12614i	0.179790	−	0.103802i	0.587194	+	0.809446i	$0.300233\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	7.91288			0.262165			0.131083	−	0.991371i	$-0.458155\pi$
$911$	7.91288			0.262165			0.131083	+	0.991371i	$0.458155\pi$
$912$		0			0
$913$	−13.7810	+	7.95644i	−0.456083	+	0.263320i
$914$		0			0
$915$	0.647551	−	3.10260i	0.0214074	−	0.102569i
$916$		0			0
$917$	−6.56670	+	11.3739i	−0.216852	+	0.375598i
$918$		0			0
$919$	−27.0826	+	46.9084i	−0.893372	+	1.54737i	−0.0575648	+	0.998342i	$0.518334\pi$
$919$	−27.0826	+	46.9084i	−0.893372	+	1.54737i	−0.835807	+	0.549023i	$0.815000\pi$
$920$		0			0
$921$	21.0000	−	12.1244i	0.691974	−	0.399511i
$922$		0			0
$923$	24.5824	+	6.08258i	0.809141	+	0.200210i
$924$		0			0
$925$	−4.43881	−	39.4373i	−0.145947	−	1.29669i
$926$		0			0
$927$	−5.48220	−	3.16515i	−0.180059	−	0.103957i
$928$		0			0
$929$	22.8303	+	13.1811i	0.749038	+	0.432457i	0.825346	−	0.564627i	$-0.190980\pi$
$929$	22.8303	+	13.1811i	0.749038	+	0.432457i	−0.0763082	+	0.997084i	$0.524313\pi$
$930$		0			0
$931$			6.92820i			0.227063i
$932$		0			0
$933$	−6.56670	+	3.79129i	−0.214984	+	0.124121i
$934$		0			0
$935$	26.5390	+	5.53901i	0.867919	+	0.181145i
$936$		0			0
$937$			31.4955i			1.02891i	0.857517	+	0.514456i	$0.172006\pi$
$937$			31.4955i			1.02891i	−0.857517	+	0.514456i	$0.827994\pi$
$938$		0			0
$939$	1.62614	+	2.81655i	0.0530670	+	0.0919147i
$940$		0			0
$941$			26.4575i			0.862490i	0.902235	+	0.431245i	$0.141926\pi$
$941$			26.4575i			0.862490i	−0.902235	+	0.431245i	$0.858074\pi$
$942$		0			0
$943$	6.06218	−	10.5000i	0.197412	−	0.341927i
$944$		0			0
$945$	−14.4385	−	12.9046i	−0.469686	−	0.419787i
$946$		0			0
$947$	7.16658	+	12.4129i	0.232883	+	0.403364i	0.958655	−	0.284570i	$-0.0918509\pi$
$947$	7.16658	+	12.4129i	0.232883	+	0.403364i	−0.725773	+	0.687935i	$0.758518\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	0.165151	−	0.0953502i	0.00535540	−	0.00309194i
$952$		0			0
$953$	−6.99578	−	4.03901i	−0.226616	−	0.130837i	0.382394	−	0.923999i	$-0.375100\pi$
$953$	−6.99578	−	4.03901i	−0.226616	−	0.130837i	−0.609010	+	0.793163i	$0.708433\pi$
$954$		0			0
$955$	−24.7096	+	27.6468i	−0.799584	+	0.894629i
$956$		0			0
$957$	12.1244			0.391925
$958$		0			0
$959$	−9.08258	−	15.7315i	−0.293292	−	0.507996i
$960$		0			0
$961$	−7.50455			−0.242082
$962$		0			0
$963$			21.1652i			0.682037i
$964$		0			0
$965$	−10.3881	−	31.5753i	−0.334404	−	1.01644i
$966$		0			0
$967$	−37.3821			−1.20213			−0.601064	−	0.799201i	$-0.705256\pi$
$967$	−37.3821			−1.20213			−0.601064	+	0.799201i	$0.705256\pi$
$968$		0			0
$969$	6.87386	+	3.96863i	0.220820	+	0.127491i
$970$		0			0
$971$	−9.24773	+	16.0175i	−0.296774	+	0.514027i	−0.975396	−	0.220460i	$-0.929244\pi$
$971$	−9.24773	+	16.0175i	−0.296774	+	0.514027i	0.678622	+	0.734487i	$0.262577\pi$
$972$		0			0
$973$	18.8341	+	32.6216i	0.603793	+	1.04580i
$974$		0			0
$975$	−16.6526	+	6.90588i	−0.533310	+	0.221165i
$976$		0			0
$977$	17.6542	+	30.5780i	0.564809	+	0.978278i	0.997067	+	0.0765281i	$0.0243835\pi$
$977$	17.6542	+	30.5780i	0.564809	+	0.978278i	−0.432258	+	0.901750i	$0.642283\pi$
$978$		0			0
$979$	12.6652	−	21.9367i	0.404780	−	0.701100i
$980$		0			0
$981$	−22.7477	−	13.1334i	−0.726279	−	0.419317i
$982$		0			0
$983$	55.0840			1.75691			0.878454	−	0.477827i	$-0.158576\pi$
$983$	55.0840			1.75691			0.878454	+	0.477827i	$0.158576\pi$
$984$		0			0
$985$	10.2548	+	31.1702i	0.326746	+	0.993165i
$986$		0			0
$987$			3.16515i			0.100748i
$988$		0			0
$989$	−48.4955			−1.54207
$990$		0			0
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	0.744124	−	0.668042i	$-0.232867\pi$
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	−0.950603	+	0.310409i	$0.899534\pi$
$992$		0			0
$993$	4.47315			0.141951
$994$		0			0
$995$	−15.7690	+	17.6435i	−0.499912	+	0.559336i
$996$		0			0
$997$	−0.143025	−	0.0825757i	−0.00452966	−	0.00261520i	0.497733	−	0.867330i	$-0.334166\pi$
$997$	−0.143025	−	0.0825757i	−0.00452966	−	0.00261520i	−0.502263	+	0.864715i	$0.667499\pi$
$998$		0			0
$999$	34.3693	−	19.8431i	1.08740	−	0.627809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.df.b.49.4		8
4.3	odd	2		65.2.l.a.49.2	yes	8
5.4	even	2	inner	1040.2.df.b.49.1		8
12.11	even	2		585.2.bf.a.244.3		8
13.4	even	6	inner	1040.2.df.b.849.1		8
20.3	even	4		325.2.n.c.101.1		4
20.7	even	4		325.2.n.b.101.2		4
20.19	odd	2		65.2.l.a.49.3	yes	8
52.3	odd	6		845.2.d.c.844.5		8
52.7	even	12		845.2.n.d.529.2		8
52.11	even	12		845.2.b.f.339.5		8
52.15	even	12		845.2.b.f.339.3		8
52.19	even	12		845.2.n.c.529.4		8
52.23	odd	6		845.2.d.c.844.3		8
52.31	even	4		845.2.n.d.484.1		8
52.35	odd	6		845.2.l.c.654.2		8
52.43	odd	6		65.2.l.a.4.3	yes	8
52.47	even	4		845.2.n.c.484.3		8
52.51	odd	2		845.2.l.c.699.3		8
60.59	even	2		585.2.bf.a.244.2		8
65.4	even	6	inner	1040.2.df.b.849.4		8
156.95	even	6		585.2.bf.a.199.2		8
260.19	even	12		845.2.n.d.529.1		8
260.43	even	12		325.2.n.c.251.1		4
260.59	even	12		845.2.n.c.529.3		8
260.63	odd	12		4225.2.a.bk.1.3		4
260.67	odd	12		4225.2.a.bj.1.3		4
260.99	even	4		845.2.n.d.484.2		8
260.119	even	12		845.2.b.f.339.6		8
260.139	odd	6		845.2.l.c.654.3		8
260.147	even	12		325.2.n.b.251.2		4
260.159	odd	6		845.2.d.c.844.4		8
260.167	odd	12		4225.2.a.bj.1.2		4
260.179	odd	6		845.2.d.c.844.6		8
260.199	odd	6		65.2.l.a.4.2	✓	8
260.219	even	12		845.2.b.f.339.4		8
260.223	odd	12		4225.2.a.bk.1.2		4
260.239	even	4		845.2.n.c.484.4		8
260.259	odd	2		845.2.l.c.699.2		8
780.719	even	6		585.2.bf.a.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	260.199	odd	6
65.2.l.a.4.3	yes	8	52.43	odd	6
65.2.l.a.49.2	yes	8	4.3	odd	2
65.2.l.a.49.3	yes	8	20.19	odd	2
325.2.n.b.101.2		4	20.7	even	4
325.2.n.b.251.2		4	260.147	even	12
325.2.n.c.101.1		4	20.3	even	4
325.2.n.c.251.1		4	260.43	even	12
585.2.bf.a.199.2		8	156.95	even	6
585.2.bf.a.199.3		8	780.719	even	6
585.2.bf.a.244.2		8	60.59	even	2
585.2.bf.a.244.3		8	12.11	even	2
845.2.b.f.339.3		8	52.15	even	12
845.2.b.f.339.4		8	260.219	even	12
845.2.b.f.339.5		8	52.11	even	12
845.2.b.f.339.6		8	260.119	even	12
845.2.d.c.844.3		8	52.23	odd	6
845.2.d.c.844.4		8	260.159	odd	6
845.2.d.c.844.5		8	52.3	odd	6
845.2.d.c.844.6		8	260.179	odd	6
845.2.l.c.654.2		8	52.35	odd	6
845.2.l.c.654.3		8	260.139	odd	6
845.2.l.c.699.2		8	260.259	odd	2
845.2.l.c.699.3		8	52.51	odd	2
845.2.n.c.484.3		8	52.47	even	4
845.2.n.c.484.4		8	260.239	even	4
845.2.n.c.529.3		8	260.59	even	12
845.2.n.c.529.4		8	52.19	even	12
845.2.n.d.484.1		8	52.31	even	4
845.2.n.d.484.2		8	260.99	even	4
845.2.n.d.529.1		8	260.19	even	12
845.2.n.d.529.2		8	52.7	even	12
1040.2.df.b.49.1		8	5.4	even	2	inner
1040.2.df.b.49.4		8	1.1	even	1	trivial
1040.2.df.b.849.1		8	13.4	even	6	inner
1040.2.df.b.849.4		8	65.4	even	6	inner
4225.2.a.bj.1.2		4	260.167	odd	12
4225.2.a.bj.1.3		4	260.67	odd	12
4225.2.a.bk.1.2		4	260.223	odd	12
4225.2.a.bk.1.3		4	260.63	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(2.18890 + 0.456850i) q^{5} +(-0.866025 + 1.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(2.29129 - 1.32288i) q^{11} +(-3.46410 + 1.00000i) q^{13} +(2.12407 - 0.698807i) q^{15} +(3.96863 + 2.29129i) q^{17} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(3.96863 - 2.29129i) q^{23} +(4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +(2.29129 + 3.96863i) q^{29} +6.20520i q^{31} +(1.32288 - 2.29129i) q^{33} +(-2.58092 + 2.88771i) q^{35} +(-3.96863 - 6.87386i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(2.29129 - 1.32288i) q^{41} +(-9.16478 - 5.29129i) q^{43} +(-2.98019 + 3.33444i) q^{45} +1.82740 q^{47} +(2.00000 + 3.46410i) q^{49} +4.58258 q^{51} -7.58258i q^{53} +(5.61976 - 1.84887i) q^{55} +1.73205 q^{57} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(-1.73205 - 3.00000i) q^{63} +(-8.03943 + 0.606325i) q^{65} +(-0.504525 - 0.873864i) q^{67} +(2.29129 - 3.96863i) q^{69} +(-6.08258 - 3.51178i) q^{71} +(4.96863 - 0.559237i) q^{75} +4.58258i q^{77} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} -6.01450 q^{83} +(7.64016 + 6.82847i) q^{85} +(3.96863 + 2.29129i) q^{87} +(8.29129 - 4.78698i) q^{89} +(1.50000 - 6.06218i) q^{91} +(3.10260 + 5.37386i) q^{93} +(2.88771 + 2.58092i) q^{95} +(5.70068 - 9.87386i) q^{97} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9} + 6 q^{15} + 12 q^{19} - 6 q^{35} - 20 q^{39} + 12 q^{45} + 16 q^{49} + 14 q^{55} + 60 q^{59} + 24 q^{61} - 24 q^{65} - 12 q^{71} + 8 q^{75} - 48 q^{79} - 4 q^{81} + 42 q^{85} + 48 q^{89}+ \cdots + 6 q^{95}+O(q^{100}) \) 8 * q - 8 * q^9 + 6 * q^15 + 12 * q^19 - 6 * q^35 - 20 * q^39 + 12 * q^45 + 16 * q^49 + 14 * q^55 + 60 * q^59 + 24 * q^61 - 24 * q^65 - 12 * q^71 + 8 * q^75 - 48 * q^79 - 4 * q^81 + 42 * q^85 + 48 * q^89 + 12 * q^91 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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