LMFDB - Embedded newform 783.2.be.a.665.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(8,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.be (of order $84$, degree $24$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	no (minimal twist has level 261)
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			665.21
Character	$\chi$	$=$	783.665
Dual form			783.2.be.a.710.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.571642 + 1.31022i) q^{2} +(-0.0295503 + 0.0318477i) q^{4} +(-2.61481 + 0.394119i) q^{5} +(-1.32416 + 1.22864i) q^{7} +(2.63993 + 0.923750i) q^{8} +(-2.01111 - 3.20067i) q^{10} +(0.291375 + 0.250749i) q^{11} +(1.83426 + 2.69036i) q^{13} +(-2.36673 - 1.03259i) q^{14} +(0.305273 + 4.07358i) q^{16} +(-0.359515 + 0.359515i) q^{17} +(-6.57779 + 4.13310i) q^{19} +(0.0647166 - 0.0949219i) q^{20} +(-0.161973 + 0.525104i) q^{22} +(-0.0597689 + 0.0234575i) q^{23} +(1.90402 - 0.587312i) q^{25} +(-2.47642 + 3.94120i) q^{26} -0.0784782i q^{28} +(-2.80031 + 4.59981i) q^{29} +(-7.73493 - 5.70864i) q^{31} +(-0.217246 + 0.114818i) q^{32} +(-0.676557 - 0.265529i) q^{34} +(2.97819 - 3.73453i) q^{35} +(-1.91078 + 5.46069i) q^{37} +(-9.17541 - 6.25569i) q^{38} +(-7.26696 - 1.37498i) q^{40} +(1.60421 - 0.429846i) q^{41} +(1.21456 + 1.64567i) q^{43} +(-0.0165960 + 0.00186992i) q^{44} +(-0.0649009 - 0.0649009i) q^{46} +(0.331957 - 0.385741i) q^{47} +(-0.279270 + 3.72659i) q^{49} +(1.85792 + 2.15895i) q^{50} +(-0.139885 - 0.0210842i) q^{52} +(-1.68105 + 1.34059i) q^{53} +(-0.860715 - 0.540823i) q^{55} +(-4.63064 + 2.02033i) q^{56} +(-7.62753 - 1.03957i) q^{58} +(-3.87386 - 2.23658i) q^{59} +(9.16119 + 0.342788i) q^{61} +(3.05795 - 13.3977i) q^{62} +(6.11295 + 4.87491i) q^{64} +(-5.85654 - 6.31185i) q^{65} +(13.5780 + 1.01753i) q^{67} +(-0.000825933 - 0.0220735i) q^{68} +(6.59551 + 1.76726i) q^{70} +(14.0494 + 6.76584i) q^{71} +(-0.264280 - 2.34555i) q^{73} +(-8.24697 + 0.618025i) q^{74} +(0.0627463 - 0.331622i) q^{76} +(-0.693908 + 0.0259642i) q^{77} +(1.45117 + 7.66960i) q^{79} +(-2.40370 - 10.5313i) q^{80} +(1.48022 + 1.85614i) q^{82} +(-0.0736019 - 0.238612i) q^{83} +(0.798370 - 1.08175i) q^{85} +(-1.46189 + 2.53208i) q^{86} +(0.537580 + 0.931116i) q^{88} +(-8.94513 - 1.00787i) q^{89} +(-5.73433 - 1.30882i) q^{91} +(0.00101912 - 0.00259668i) q^{92} +(0.695166 + 0.214430i) q^{94} +(15.5707 - 13.3997i) q^{95} +(5.87063 - 11.1078i) q^{97} +(-5.04229 + 1.76437i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 36 q^{2} - 14 q^{4} + 42 q^{5} - 10 q^{7} - 56 q^{10} + 48 q^{11} - 14 q^{13} + 24 q^{14} - 54 q^{16} - 48 q^{19} + 30 q^{20} - 14 q^{22} + 30 q^{23} + 30 q^{25} - 12 q^{31} - 24 q^{32} - 14 q^{34}+ \cdots - 36 q^{97}+O(q^{100}) $ 672 * q + 36 * q^2 - 14 * q^4 + 42 * q^5 - 10 * q^7 - 56 * q^10 + 48 * q^11 - 14 * q^13 + 24 * q^14 - 54 * q^16 - 48 * q^19 + 30 * q^20 - 14 * q^22 + 30 * q^23 + 30 * q^25 - 12 * q^31 - 24 * q^32 - 14 * q^34 - 48 * q^37 + 42 * q^38 - 2 * q^40 + 24 * q^41 - 12 * q^43 - 64 * q^46 + 42 * q^47 + 22 * q^49 + 66 * q^50 + 22 * q^52 + 76 * q^55 + 42 * q^56 - 42 * q^58 + 132 * q^59 - 308 * q^64 + 66 * q^65 - 14 * q^67 - 60 * q^68 - 14 * q^70 - 48 * q^73 - 66 * q^74 - 28 * q^76 - 30 * q^77 - 12 * q^79 - 136 * q^82 - 246 * q^83 + 34 * q^85 + 8 * q^88 - 56 * q^91 - 462 * q^92 + 26 * q^94 + 246 * q^95 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.571642	+	1.31022i	0.404212	+	0.926464i	0.992993	+	0.118171i	$0.0377032\pi$
$2$	0.571642	+	1.31022i	0.404212	+	0.926464i	−0.588781	+	0.808292i	$0.700392\pi$
$3$		0			0
$3$		0			0
$4$	−0.0295503	+	0.0318477i	−0.0147752	+	0.0159238i
$5$	−2.61481	+	0.394119i	−1.16938	+	0.176255i	−0.704885	−	0.709322i	$-0.749001\pi$
$5$	−2.61481	+	0.394119i	−1.16938	+	0.176255i	−0.464492	+	0.885577i	$0.653763\pi$
$6$		0			0
$7$	−1.32416	+	1.22864i	−0.500485	+	0.464383i	−0.889557	−	0.456825i	$-0.848987\pi$
$7$	−1.32416	+	1.22864i	−0.500485	+	0.464383i	0.389071	+	0.921208i	$0.372796\pi$
$8$	2.63993	+	0.923750i	0.933355	+	0.326595i
$9$		0			0
$10$	−2.01111	−	3.20067i	−0.635970	−	1.01214i
$11$	0.291375	+	0.250749i	0.0878530	+	0.0756036i	0.695118	−	0.718896i	$-0.255352\pi$
$11$	0.291375	+	0.250749i	0.0878530	+	0.0756036i	−0.607265	+	0.794500i	$0.707733\pi$
$12$		0			0
$13$	1.83426	+	2.69036i	0.508731	+	0.746171i	0.991575	−	0.129535i	$-0.0413485\pi$
$13$	1.83426	+	2.69036i	0.508731	+	0.746171i	−0.482844	+	0.875706i	$0.660396\pi$
$14$	−2.36673	−	1.03259i	−0.632536	−	0.275973i
$15$		0			0
$16$	0.305273	+	4.07358i	0.0763182	+	1.01840i
$17$	−0.359515	+	0.359515i	−0.0871952	+	0.0871952i	−0.749359	−	0.662164i	$-0.769638\pi$
$17$	−0.359515	+	0.359515i	−0.0871952	+	0.0871952i	0.662164	+	0.749359i	$0.269638\pi$
$18$		0			0
$19$	−6.57779	+	4.13310i	−1.50905	+	0.948198i	−0.513095	+	0.858332i	$0.671501\pi$
$19$	−6.57779	+	4.13310i	−1.50905	+	0.948198i	−0.995954	+	0.0898667i	$0.971356\pi$
$20$	0.0647166	−	0.0949219i	0.0144711	−	0.0212252i
$21$		0			0
$22$	−0.161973	+	0.525104i	−0.0345328	+	0.111953i
$23$	−0.0597689	+	0.0234575i	−0.0124627	+	0.00489124i	−0.371564	−	0.928407i	$-0.621178\pi$
$23$	−0.0597689	+	0.0234575i	−0.0124627	+	0.00489124i	0.359102	+	0.933299i	$0.383083\pi$
$24$		0			0
$25$	1.90402	−	0.587312i	0.380804	−	0.117462i
$26$	−2.47642	+	3.94120i	−0.485666	+	0.772932i
$27$		0			0
$28$		−	0.0784782i		−	0.0148310i
$29$	−2.80031	+	4.59981i	−0.520004	+	0.854164i
$29$	−2.80031	+	4.59981i	−0.520004	+	0.854164i
$30$		0			0
$31$	−7.73493	−	5.70864i	−1.38924	−	1.02530i	−0.994303	−	0.106592i	$-0.966006\pi$
$31$	−7.73493	−	5.70864i	−1.38924	−	1.02530i	−0.394933	−	0.918710i	$-0.629232\pi$
$32$	−0.217246	+	0.114818i	−0.0384040	+	0.0202971i
$33$		0			0
$34$	−0.676557	−	0.265529i	−0.116029	−	0.0455378i
$35$	2.97819	−	3.73453i	0.503406	−	0.631251i
$36$		0			0
$37$	−1.91078	+	5.46069i	−0.314130	+	0.897732i	0.673257	+	0.739408i	$0.264895\pi$
$37$	−1.91078	+	5.46069i	−0.314130	+	0.897732i	−0.987387	+	0.158324i	$0.949391\pi$
$38$	−9.17541	−	6.25569i	−1.48845	−	1.01481i
$39$		0			0
$40$	−7.26696	−	1.37498i	−1.14901	−	0.217404i
$41$	1.60421	−	0.429846i	0.250535	−	0.0671306i	−0.131366	−	0.991334i	$-0.541936\pi$
$41$	1.60421	−	0.429846i	0.250535	−	0.0671306i	0.381901	+	0.924203i	$0.375270\pi$
$42$		0			0
$43$	1.21456	+	1.64567i	0.185219	+	0.250963i	0.887362	−	0.461073i	$-0.152535\pi$
$43$	1.21456	+	1.64567i	0.185219	+	0.250963i	−0.702143	+	0.712036i	$0.747773\pi$
$44$	−0.0165960	+	0.00186992i	−0.00250194	+	0.000281901i
$45$		0			0
$46$	−0.0649009	−	0.0649009i	−0.00956911	−	0.00956911i
$47$	0.331957	−	0.385741i	0.0484209	−	0.0562661i	−0.733239	−	0.679971i	$-0.761992\pi$
$47$	0.331957	−	0.385741i	0.0484209	−	0.0562661i	0.781660	+	0.623705i	$0.214373\pi$
$48$		0			0
$49$	−0.279270	+	3.72659i	−0.0398957	+	0.532370i
$50$	1.85792	+	2.15895i	0.262750	+	0.305321i
$51$		0			0
$52$	−0.139885	−	0.0210842i	−0.0193985	−	0.00292385i
$53$	−1.68105	+	1.34059i	−0.230910	+	0.184144i	−0.732109	−	0.681188i	$-0.761464\pi$
$53$	−1.68105	+	1.34059i	−0.230910	+	0.184144i	0.501199	+	0.865332i	$0.332892\pi$
$54$		0			0
$55$	−0.860715	−	0.540823i	−0.116059	−	0.0729246i
$56$	−4.63064	+	2.02033i	−0.618796	+	0.269978i
$57$		0			0
$58$	−7.62753	−	1.03957i	−1.00154	−	0.136502i
$59$	−3.87386	−	2.23658i	−0.504334	−	0.291177i	0.226167	−	0.974088i	$-0.427380\pi$
$59$	−3.87386	−	2.23658i	−0.504334	−	0.291177i	−0.730502	+	0.682911i	$0.760714\pi$
$60$		0			0
$61$	9.16119	+	0.342788i	1.17297	+	0.0438895i	0.616759	−	0.787152i	$-0.288445\pi$
$61$	9.16119	+	0.342788i	1.17297	+	0.0438895i	0.556211	+	0.831041i	$0.312255\pi$
$62$	3.05795	−	13.3977i	0.388360	−	1.70152i
$63$		0			0
$64$	6.11295	+	4.87491i	0.764118	+	0.609364i
$65$	−5.85654	−	6.31185i	−0.726415	−	0.782889i
$66$		0			0
$67$	13.5780	+	1.01753i	1.65881	+	0.124311i	0.870895	−	0.491469i	$-0.163540\pi$
$67$	13.5780	+	1.01753i	1.65881	+	0.124311i	0.787918	+	0.615780i	$0.211159\pi$
$68$	−0.000825933	−	0.0220735i	−0.000100159	−	0.00267681i
$69$		0			0
$70$	6.59551	+	1.76726i	0.788314	+	0.211228i
$71$	14.0494	+	6.76584i	1.66736	+	0.802957i	0.998209	+	0.0598288i	$0.0190555\pi$
$71$	14.0494	+	6.76584i	1.66736	+	0.802957i	0.669149	+	0.743128i	$0.266659\pi$
$72$		0			0
$73$	−0.264280	−	2.34555i	−0.0309317	−	0.274526i	−0.999652	−	0.0263719i	$-0.991605\pi$
$73$	−0.264280	−	2.34555i	−0.0309317	−	0.274526i	0.968721	−	0.248154i	$-0.0798240\pi$
$74$	−8.24697	+	0.618025i	−0.958691	+	0.0718440i
$75$		0			0
$76$	0.0627463	−	0.331622i	0.00719749	−	0.0380397i
$77$	−0.693908	+	0.0259642i	−0.0790781	+	0.00295890i
$78$		0			0
$79$	1.45117	+	7.66960i	0.163269	+	0.862897i	0.964408	+	0.264419i	$0.0851801\pi$
$79$	1.45117	+	7.66960i	0.163269	+	0.862897i	−0.801139	+	0.598478i	$0.795772\pi$
$80$	−2.40370	−	10.5313i	−0.268742	−	1.17744i
$81$		0			0
$82$	1.48022	+	1.85614i	0.163463	+	0.204977i
$83$	−0.0736019	−	0.238612i	−0.00807886	−	0.0261910i	0.951444	−	0.307823i	$-0.0996005\pi$
$83$	−0.0736019	−	0.238612i	−0.00807886	−	0.0261910i	−0.959523	+	0.281632i	$0.909124\pi$
$84$		0			0
$85$	0.798370	−	1.08175i	0.0865954	−	0.117333i
$86$	−1.46189	+	2.53208i	−0.157640	+	0.273041i
$87$		0			0
$88$	0.537580	+	0.931116i	0.0573063	+	0.0992574i
$89$	−8.94513	−	1.00787i	−0.948182	−	0.106834i	−0.375691	−	0.926745i	$-0.622594\pi$
$89$	−8.94513	−	1.00787i	−0.948182	−	0.106834i	−0.572492	+	0.819911i	$0.694023\pi$
$90$		0			0
$91$	−5.73433	−	1.30882i	−0.601121	−	0.137202i
$92$	0.00101912	−	0.00259668i	0.000106251	−	0.000270722i
$93$		0			0
$94$	0.695166	+	0.214430i	0.0717009	+	0.0221168i
$95$	15.5707	−	13.3997i	1.59752	−	1.37478i
$96$		0			0
$97$	5.87063	−	11.1078i	0.596072	−	1.12782i	−0.382892	−	0.923793i	$-0.625072\pi$
$97$	5.87063	−	11.1078i	0.596072	−	1.12782i	0.978964	−	0.204031i	$-0.0654042\pi$
$98$	−5.04229	+	1.76437i	−0.509348	+	0.178229i
$99$		0			0
$100$	−0.0375599	+	0.0779939i	−0.00375599	+	0.00779939i
$101$	14.5170	−	10.7141i	1.44450	−	1.06609i	0.460550	−	0.887634i	$-0.347652\pi$
$101$	14.5170	−	10.7141i	1.44450	−	1.06609i	0.983948	−	0.178455i	$-0.0571098\pi$
$102$		0			0
$103$	9.92230	−	6.76491i	0.977673	−	0.666566i	0.0346869	−	0.999398i	$-0.488957\pi$
$103$	9.92230	−	6.76491i	0.977673	−	0.666566i	0.942986	+	0.332832i	$0.108004\pi$
$104$	2.35708	+	8.79674i	0.231131	+	0.862592i
$105$		0			0
$106$	−2.71742	−	1.43620i	−0.263939	−	0.139496i
$107$	−3.27119	−	6.79269i	−0.316238	−	0.656674i	0.680892	−	0.732384i	$-0.261592\pi$
$107$	−3.27119	−	6.79269i	−0.316238	−	0.656674i	−0.997130	+	0.0757093i	$0.975878\pi$
$108$		0			0
$109$	−12.2777	+	2.80231i	−1.17599	+	0.268412i	−0.765490	−	0.643448i	$-0.777503\pi$
$109$	−12.2777	+	2.80231i	−1.17599	+	0.268412i	−0.410501	+	0.911860i	$0.634646\pi$
$110$	0.216575	−	1.43688i	0.0206496	−	0.137001i
$111$		0			0
$112$	−5.40920	−	5.01900i	−0.511121	−	0.474251i
$113$	2.55738	+	4.83879i	0.240578	+	0.455195i	0.974607	−	0.223923i	$-0.0718863\pi$
$113$	2.55738	+	4.83879i	0.240578	+	0.455195i	−0.734029	+	0.679118i	$0.762363\pi$
$114$		0			0
$115$	0.147039	−	0.0848930i	0.0137114	−	0.00791631i
$116$	−0.0637434	−	0.225109i	−0.00591842	−	0.0209009i
$117$		0			0
$118$	0.715938	−	6.35413i	0.0659074	−	0.584945i
$119$	0.0343405	−	0.917770i	0.00314799	−	0.0841318i
$120$		0			0
$121$	−1.61744	−	10.7310i	−0.147040	−	0.975547i
$122$	4.78780	+	12.1991i	0.433467	+	1.10446i
$123$		0			0
$124$	0.410377	−	0.0776475i	0.0368529	−	0.00697295i
$125$	7.16518	−	3.45057i	0.640873	−	0.308628i
$126$		0			0
$127$	−0.888975	−	2.54054i	−0.0788838	−	0.225437i	0.897687	−	0.440634i	$-0.145246\pi$
$127$	−0.888975	−	2.54054i	−0.0788838	−	0.225437i	−0.976571	+	0.215197i	$0.930961\pi$
$128$	−3.01997	+	11.2707i	−0.266930	+	0.996198i
$129$		0			0
$130$	4.92206	−	11.2815i	0.431693	−	0.989450i
$131$	−2.57590	+	5.90403i	−0.225058	+	0.515837i	−0.992054	−	0.125814i	$-0.959846\pi$
$131$	−2.57590	+	5.90403i	−0.225058	+	0.515837i	0.766996	+	0.641652i	$0.221750\pi$
$132$		0			0
$133$	3.63195	−	13.5546i	0.314930	−	1.17534i
$134$	6.42856	+	18.3718i	0.555343	+	1.58708i
$135$		0			0
$136$	−1.28120	+	0.616991i	−0.109862	+	0.0529065i
$137$	−2.20230	+	0.416697i	−0.188155	+	0.0356008i	−0.279135	−	0.960252i	$-0.590048\pi$
$137$	−2.20230	+	0.416697i	−0.188155	+	0.0356008i	0.0909800	+	0.995853i	$0.471000\pi$
$138$		0			0
$139$	−4.99129	−	12.7176i	−0.423356	−	1.07869i	−0.970381	−	0.241578i	$-0.922335\pi$
$139$	−4.99129	−	12.7176i	−0.423356	−	1.07869i	0.547025	−	0.837116i	$-0.315760\pi$
$140$	0.0309297	+	0.205205i	0.00261404	+	0.0173430i
$141$		0			0
$142$	−0.833487	+	22.2754i	−0.0699447	+	1.86931i
$143$	−0.140147	+	1.24384i	−0.0117197	+	0.104015i
$144$		0			0
$145$	5.50939	−	13.1313i	0.457530	−	1.09049i
$146$	2.92211	−	1.68708i	0.241836	−	0.139624i
$147$		0			0
$148$	−0.117446	−	0.222219i	−0.00965402	−	0.0182663i
$149$	11.0712	+	10.2726i	0.906991	+	0.841565i	0.987890	−	0.155158i	$-0.0495886\pi$
$149$	11.0712	+	10.2726i	0.906991	+	0.841565i	−0.0808987	+	0.996722i	$0.525779\pi$
$150$		0			0
$151$	0.331182	−	2.19725i	0.0269512	−	0.178809i	−0.971305	−	0.237836i	$-0.923562\pi$
$151$	0.331182	−	2.19725i	0.0269512	−	0.178809i	0.998256	+	0.0590272i	$0.0187999\pi$
$152$	−21.1828	+	4.83485i	−1.71816	+	0.392158i
$153$		0			0
$154$	−0.430686	−	0.894328i	−0.0347056	−	0.0720670i
$155$	22.4752	+	11.8785i	1.80525	+	0.954105i
$156$		0			0
$157$	4.12541	+	15.3963i	0.329244	+	1.22876i	0.909976	+	0.414660i	$0.136100\pi$
$157$	4.12541	+	15.3963i	0.329244	+	1.22876i	−0.580732	+	0.814095i	$0.697234\pi$
$158$	−9.21929	+	6.28561i	−0.733448	+	0.500056i
$159$		0			0
$160$	0.522803	−	0.385846i	0.0413312	−	0.0305038i
$161$	0.0503226	−	0.104496i	0.00396598	−	0.00823544i
$162$		0			0
$163$	−12.1571	+	4.25394i	−0.952215	+	0.333194i	−0.761291	−	0.648411i	$-0.775434\pi$
$163$	−12.1571	+	4.25394i	−0.952215	+	0.333194i	−0.190924	+	0.981605i	$0.561148\pi$
$164$	−0.0337153	+	0.0637924i	−0.00263272	+	0.00498135i
$165$		0			0
$166$	0.270559	−	0.232835i	0.0209995	−	0.0180715i
$167$	−23.7126	−	7.31438i	−1.83494	−	0.566004i	−0.999874	−	0.0158514i	$-0.994954\pi$
$167$	−23.7126	−	7.31438i	−1.83494	−	0.566004i	−0.835064	−	0.550152i	$-0.814570\pi$
$168$		0			0
$169$	0.875895	−	2.23174i	0.0673766	−	0.171673i
$170$	1.87371	+	0.427663i	0.143707	+	0.0328003i
$171$		0			0
$172$	−0.0883016	−	0.00994920i	−0.00673293	−	0.000758619i
$173$	8.04318	+	13.9312i	0.611511	+	1.05917i	0.990986	+	0.133967i	$0.0427715\pi$
$173$	8.04318	+	13.9312i	0.611511	+	1.05917i	−0.379474	+	0.925202i	$0.623895\pi$
$174$		0			0
$175$	−1.79963	+	3.11705i	−0.136039	+	0.235627i
$176$	−0.932497	+	1.26349i	−0.0702896	+	0.0952390i
$177$		0			0
$178$	−3.79288	−	12.2962i	−0.284288	−	0.921640i
$179$	−0.841890	−	1.05570i	−0.0629258	−	0.0789065i	0.749372	−	0.662149i	$-0.230355\pi$
$179$	−0.841890	−	1.05570i	−0.0629258	−	0.0789065i	−0.812298	+	0.583242i	$0.801784\pi$
$180$		0			0
$181$	1.98920	+	8.71524i	0.147856	+	0.647799i	0.993479	+	0.114018i	$0.0363722\pi$
$181$	1.98920	+	8.71524i	0.147856	+	0.647799i	−0.845623	+	0.533781i	$0.820771\pi$
$182$	−1.56314	−	8.26140i	−0.115868	−	0.612376i
$183$		0			0
$184$	−0.179454	+	0.00671471i	−0.0132295	+	0.000495015i
$185$	2.84416	−	15.0317i	0.209106	−	1.10515i
$186$		0			0
$187$	−0.194902	+	0.0146059i	−0.0142526	+	0.00106809i
$188$	0.00247552	+	0.0219709i	0.000180546	+	0.00160239i
$189$		0			0
$190$	26.4574	+	12.7412i	1.91942	+	0.924344i
$191$	25.7956	+	6.91191i	1.86650	+	0.500128i	1.00000		0.000956810i	$0.000304562\pi$
$191$	25.7956	+	6.91191i	1.86650	+	0.500128i	0.866503	+	0.499171i	$0.166362\pi$
$192$		0			0
$193$	−0.278862	−	7.45275i	−0.0200729	−	0.536461i	−0.972665	−	0.232211i	$-0.925404\pi$
$193$	−0.278862	−	7.45275i	−0.0200729	−	0.536461i	0.952592	−	0.304249i	$-0.0984056\pi$
$194$	17.9095	+	1.34213i	1.28583	+	0.0963594i
$195$		0			0
$196$	−0.110431	−	0.119016i	−0.00788792	−	0.00850116i
$197$	−6.58790	−	5.25367i	−0.469368	−	0.374309i	0.360053	−	0.932932i	$-0.382758\pi$
$197$	−6.58790	−	5.25367i	−0.469368	−	0.374309i	−0.829422	+	0.558623i	$0.811330\pi$
$198$		0			0
$199$	−3.65786	+	16.0262i	−0.259299	+	1.13606i	0.662704	+	0.748881i	$0.269409\pi$
$199$	−3.65786	+	16.0262i	−0.259299	+	1.13606i	−0.922003	+	0.387182i	$0.873448\pi$
$200$	5.56900	+	0.208377i	0.393788	+	0.0147345i
$201$		0			0
$202$	22.3363	+	12.8959i	1.57158	+	0.907350i
$203$	−1.94346	−	9.53146i	−0.136404	−	0.668977i
$204$		0			0
$205$	−4.02528	+	1.75621i	−0.281138	+	0.122659i
$206$	14.5355	+	9.13326i	1.01274	+	0.636345i
$207$		0			0
$208$	−10.3994	+	8.29328i	−0.721072	+	0.575036i
$209$	−2.95298	−	0.445090i	−0.204262	−	0.0307875i
$210$		0			0
$211$	−2.48569	−	2.88842i	−0.171122	−	0.198847i	0.665862	−	0.746075i	$-0.268064\pi$
$211$	−2.48569	−	2.88842i	−0.171122	−	0.198847i	−0.836984	+	0.547228i	$0.815683\pi$
$212$	0.00698081	−	0.0931524i	0.000479444	−	0.00639773i
$213$		0			0
$214$	7.02996	−	8.16896i	0.480558	−	0.558418i
$215$	−3.82443	−	3.82443i	−0.260824	−	0.260824i
$216$		0			0
$217$	17.2562	−	1.94430i	1.17142	−	0.131988i
$218$	−10.6901	−	14.4846i	−0.724024	−	0.981018i
$219$		0			0
$220$	0.0426584	−	0.0114303i	0.00287603	−	0.000770629i
$221$	−1.62667	−	0.307782i	−0.109421	−	0.0207037i
$222$		0			0
$223$	−7.25621	−	4.94720i	−0.485912	−	0.331289i	0.295460	−	0.955355i	$-0.404527\pi$
$223$	−7.25621	−	4.94720i	−0.485912	−	0.331289i	−0.781371	+	0.624066i	$0.785480\pi$
$224$	0.146598	−	0.418954i	0.00979501	−	0.0279925i
$225$		0			0
$226$	−4.87797	+	6.11678i	−0.324477	+	0.406882i
$227$	12.3848	+	4.86069i	0.822011	+	0.322615i	0.738807	−	0.673917i	$-0.235390\pi$
$227$	12.3848	+	4.86069i	0.822011	+	0.322615i	0.0832038	+	0.996533i	$0.473485\pi$
$228$		0			0
$229$	21.6411	−	11.4377i	1.43009	−	0.755823i	0.440229	−	0.897885i	$-0.354897\pi$
$229$	21.6411	−	11.4377i	1.43009	−	0.755823i	0.989858	+	0.142062i	$0.0453734\pi$
$230$	0.195282	+	0.144125i	0.0128765	+	0.00950330i
$231$		0			0
$232$	−11.6417	+	9.55638i	−0.764314	+	0.627407i
$233$			11.6588i			0.763791i	0.924206	+	0.381895i	$0.124729\pi$
$233$			11.6588i			0.763791i	−0.924206	+	0.381895i	$0.875271\pi$
$234$		0			0
$235$	−0.715976	+	1.13947i	−0.0467051	+	0.0743308i
$236$	0.185704	−	0.0572820i	0.0120883	−	0.00372874i
$237$		0			0
$238$	1.22211	−	0.479642i	0.0792176	−	0.0310906i
$239$	4.69767	−	15.2295i	0.303867	−	0.985113i	−0.666912	−	0.745137i	$-0.732384\pi$
$239$	4.69767	−	15.2295i	0.303867	−	0.985113i	0.970779	−	0.239976i	$-0.0771396\pi$
$240$		0			0
$241$	−8.84502	+	12.9733i	−0.569758	+	0.835681i	−0.997676	−	0.0681362i	$-0.978295\pi$
$241$	−8.84502	+	12.9733i	−0.569758	+	0.835681i	0.427918	+	0.903817i	$0.359247\pi$
$242$	13.1354	−	8.25350i	0.844374	−	0.530555i
$243$		0			0
$244$	−0.281633	+	0.281633i	−0.0180297	+	0.0180297i
$245$	−0.738484	−	9.85438i	−0.0471800	−	0.629574i
$246$		0			0
$247$	−23.1849	−	10.1155i	−1.47522	−	0.643631i
$248$	−15.1463	−	22.2155i	−0.961791	−	1.41069i
$249$		0			0
$250$	8.61691	+	7.41545i	0.544981	+	0.468994i
$251$	13.6271	+	21.6874i	0.860136	+	1.36890i	0.928537	+	0.371241i	$0.121067\pi$
$251$	13.6271	+	21.6874i	0.860136	+	1.36890i	−0.0684008	+	0.997658i	$0.521790\pi$
$252$		0			0
$253$	−0.0232971	−	0.00815202i	−0.00146468	−	0.000512513i
$254$	2.82049	−	2.61703i	0.176973	−	0.164207i
$255$		0			0
$256$	−1.03056	+	0.155332i	−0.0644100	+	0.00970824i
$257$	−19.2515	+	20.7482i	−1.20088	+	1.29424i	−0.256049	+	0.966664i	$0.582421\pi$
$257$	−19.2515	+	20.7482i	−1.20088	+	1.29424i	−0.944826	+	0.327572i	$0.893770\pi$
$258$		0			0
$259$	−4.17905	−	9.57849i	−0.259674	−	0.595178i
$260$	0.374081			0.0231995
$261$		0			0
$262$	−9.20806			−0.568876
$263$	−0.647554	−	1.48421i	−0.0399299	−	0.0915203i	0.895454	−	0.445153i	$-0.146851\pi$
$263$	−0.647554	−	1.48421i	−0.0399299	−	0.0915203i	−0.935384	+	0.353633i	$0.884946\pi$
$264$		0			0
$265$	3.86726	−	4.16792i	0.237564	−	0.256033i
$266$	19.8357	−	2.98975i	1.21620	−	0.183313i
$267$		0			0
$268$	−0.433640	+	0.402359i	−0.0264888	+	0.0245780i
$269$	−10.4695	−	3.66344i	−0.638337	−	0.223364i	−0.00834497	−	0.999965i	$-0.502656\pi$
$269$	−10.4695	−	3.66344i	−0.638337	−	0.223364i	−0.629992	+	0.776601i	$0.716942\pi$
$270$		0			0
$271$	−5.46346	−	8.69504i	−0.331881	−	0.528186i	0.638545	−	0.769585i	$-0.279537\pi$
$271$	−5.46346	−	8.69504i	−0.331881	−	0.528186i	−0.970426	+	0.241399i	$0.922394\pi$
$272$	−1.57426	−	1.35476i	−0.0954537	−	0.0821446i
$273$		0			0
$274$	−1.80489	−	2.64729i	−0.109037	−	0.159928i
$275$	0.702052	+	0.306302i	0.0423353	+	0.0184707i
$276$		0			0
$277$	0.745645	+	9.94995i	0.0448015	+	0.597834i	0.973749	+	0.227623i	$0.0730955\pi$
$277$	0.745645	+	9.94995i	0.0448015	+	0.597834i	−0.928948	+	0.370211i	$0.879285\pi$
$278$	13.8096	−	13.8096i	0.828245	−	0.828245i
$279$		0			0
$280$	11.3120	−	7.10779i	0.676020	−	0.424772i
$281$	−10.5753	+	15.5111i	−0.630868	+	0.925314i	−0.999992	−	0.00406632i	$-0.998706\pi$
$281$	−10.5753	+	15.5111i	−0.630868	+	0.925314i	0.369123	+	0.929380i	$0.379658\pi$
$282$		0			0
$283$	2.37356	−	7.69490i	0.141094	−	0.457414i	−0.857253	−	0.514896i	$-0.827831\pi$
$283$	2.37356	−	7.69490i	0.141094	−	0.457414i	0.998347	+	0.0574811i	$0.0183069\pi$
$284$	−0.630641	+	0.247508i	−0.0374217	+	0.0146869i
$285$		0			0
$286$	−1.70982	+	0.527409i	−0.101104	+	0.0311863i
$287$	−1.59610	+	2.54018i	−0.0942148	+	0.149942i
$288$		0			0
$289$			16.7415i			0.984794i
$290$	20.3542	−	0.287889i	1.19524	−	0.0169054i
$291$		0			0
$292$	0.0825100	+	0.0608952i	0.00482853	+	0.00356362i
$293$	−7.58785	+	4.01030i	−0.443287	+	0.234284i	−0.673990	−	0.738740i	$-0.735421\pi$
$293$	−7.58785	+	4.01030i	−0.443287	+	0.234284i	0.230703	+	0.973024i	$0.425897\pi$
$294$		0			0
$295$	11.0109	+	4.32145i	0.641078	+	0.251605i
$296$	−10.0886	+	12.6507i	−0.586390	+	0.735309i
$297$		0			0
$298$	−7.13057	+	20.3780i	−0.413063	+	1.18046i
$299$	−0.172741	−	0.117773i	−0.00998985	−	0.00681096i
$300$		0			0
$301$	−3.63021	−	0.686873i	−0.209242	−	0.0395907i
$302$	3.06819	−	0.822118i	0.176554	−	0.0473076i
$303$		0			0
$304$	−18.8445	−	25.5334i	−1.08081	−	1.46444i
$305$	−24.0898	+	2.71427i	−1.37938	+	0.155419i
$306$		0			0
$307$	−10.0713	−	10.0713i	−0.574798	−	0.574798i	0.358668	−	0.933465i	$-0.383231\pi$
$307$	−10.0713	−	10.0713i	−0.574798	−	0.574798i	−0.933465	+	0.358668i	$0.883231\pi$
$308$	0.0196783	−	0.0228666i	0.00112128	−	0.00130295i
$309$		0			0
$310$	−2.71564	+	36.2377i	−0.154238	+	2.05816i
$311$	5.43852	+	6.31968i	0.308390	+	0.358356i	0.890684	−	0.454622i	$-0.150226\pi$
$311$	5.43852	+	6.31968i	0.308390	+	0.358356i	−0.582294	+	0.812978i	$0.697845\pi$
$312$		0			0
$313$	−1.63694	−	0.246730i	−0.0925255	−	0.0139460i	0.102616	−	0.994721i	$-0.467279\pi$
$313$	−1.63694	−	0.246730i	−0.0925255	−	0.0139460i	−0.195142	+	0.980775i	$0.562517\pi$
$314$	−17.8142	+	14.2063i	−1.00531	+	0.801710i
$315$		0			0
$316$	−0.287141	−	0.180423i	−0.0161530	−	0.0101496i
$317$	6.44315	−	2.81112i	0.361884	−	0.157888i	−0.211080	−	0.977469i	$-0.567698\pi$
$317$	6.44315	−	2.81112i	0.361884	−	0.157888i	0.572964	+	0.819580i	$0.305793\pi$
$318$		0			0
$319$	−1.96934	+	0.638099i	−0.110262	+	0.0357267i
$320$	−17.9055	−	10.3377i	−1.00095	−	0.577896i
$321$		0			0
$322$	0.165679	+	0.00619927i	0.00923293	+	0.000345472i
$323$	0.878903	−	3.85073i	0.0489035	−	0.214260i
$324$		0			0
$325$	5.07254	+	4.04521i	0.281374	+	0.224388i
$326$	−12.5231	−	13.4967i	−0.693589	−	0.747511i
$327$		0			0
$328$	4.63206	+	0.347125i	0.255763	+	0.0191668i
$329$	0.0343731	+	0.918639i	0.00189505	+	0.0506462i
$330$		0			0
$331$	29.1989	+	7.82382i	1.60492	+	0.430036i	0.946522	−	0.322638i	$-0.104570\pi$
$331$	29.1989	+	7.82382i	1.60492	+	0.430036i	0.658393	+	0.752674i	$0.271236\pi$
$332$	0.00977419	+	0.00470700i	0.000536429	+	0.000258330i
$333$		0			0
$334$	−3.97171	−	35.2499i	−0.217322	−	1.92879i
$335$	−35.9048	+	2.69069i	−1.96169	+	0.147008i
$336$		0			0
$337$	−3.68473	+	19.4743i	−0.200720	+	1.06083i	0.726741	+	0.686911i	$0.241034\pi$
$337$	−3.68473	+	19.4743i	−0.200720	+	1.06083i	−0.927461	+	0.373919i	$0.878014\pi$
$338$	3.42477	−	0.128146i	0.186283	−	0.00697022i
$339$		0			0
$340$	0.0108592	+	0.0573924i	0.000588925	+	0.00311254i
$341$	−0.822335	−	3.60288i	−0.0445319	−	0.195107i
$342$		0			0
$343$	−12.0926	−	15.1636i	−0.652939	−	0.818760i
$344$	1.68616	+	5.46640i	0.0909118	+	0.294729i
$345$		0			0
$346$	−13.6551	+	18.5020i	−0.734101	+	0.994672i
$347$	14.9881	−	25.9602i	0.804604	−	1.39361i	−0.111955	−	0.993713i	$-0.535711\pi$
$347$	14.9881	−	25.9602i	0.804604	−	1.39361i	0.916558	−	0.399901i	$-0.130955\pi$
$348$		0			0
$349$	9.77235	+	16.9262i	0.523102	+	0.906039i	0.999639	+	0.0268847i	$0.00855871\pi$
$349$	9.77235	+	16.9262i	0.523102	+	0.906039i	−0.476536	+	0.879155i	$0.658108\pi$
$350$	−5.11276	−	0.576069i	−0.273288	−	0.0307922i
$351$		0			0
$352$	−0.0920904	−	0.0210190i	−0.00490843	−	0.00112032i
$353$	5.27594	−	13.4429i	0.280810	−	0.715492i	−0.718981	−	0.695030i	$-0.755391\pi$
$353$	5.27594	−	13.4429i	0.280810	−	0.715492i	0.999791	−	0.0204619i	$-0.00651368\pi$
$354$		0			0
$355$	−39.4030	−	12.1542i	−2.09129	−	0.645079i
$356$	0.296430	−	0.255099i	0.0157108	−	0.0135202i
$357$		0			0
$358$	0.901933	−	1.70654i	0.0476686	−	0.0901935i
$359$	6.39826	−	2.23885i	0.337687	−	0.118162i	−0.156108	−	0.987740i	$-0.549895\pi$
$359$	6.39826	−	2.23885i	0.337687	−	0.118162i	0.493795	+	0.869578i	$0.335609\pi$
$360$		0			0
$361$	17.9410	−	37.2549i	0.944265	−	1.96079i
$362$	−10.2818	+	7.58828i	−0.540397	+	0.398831i
$363$		0			0
$364$	0.211135	−	0.143949i	0.0110665	−	0.00754498i
$365$	1.61547	+	6.02901i	0.0845575	+	0.315573i
$366$		0			0
$367$	−8.73503	−	4.61660i	−0.455965	−	0.240984i	0.223484	−	0.974708i	$-0.428257\pi$
$367$	−8.73503	−	4.61660i	−0.455965	−	0.240984i	−0.679448	+	0.733723i	$0.737781\pi$
$368$	−0.113802	−	0.236312i	−0.00593234	−	0.0123186i
$369$		0			0
$370$	21.3207	−	4.86630i	1.10841	−	0.252987i
$371$	0.578871	−	3.84056i	0.0300535	−	0.199392i
$372$		0			0
$373$	1.71082	+	1.58741i	0.0885830	+	0.0821930i	0.723222	−	0.690616i	$-0.242661\pi$
$373$	1.71082	+	1.58741i	0.0885830	+	0.0821930i	−0.634639	+	0.772809i	$0.718851\pi$
$374$	−0.130551	−	0.247014i	−0.00675063	−	0.0127728i
$375$		0			0
$376$	1.23267	−	0.711683i	0.0635702	−	0.0367022i
$377$	−17.5116	+	0.903401i	−0.901895	+	0.0465275i
$378$		0			0
$379$	2.66109	−	23.6178i	0.136691	−	1.21317i	−0.718751	−	0.695267i	$-0.755286\pi$
$379$	2.66109	−	23.6178i	0.136691	−	1.21317i	0.855442	−	0.517898i	$-0.173285\pi$
$380$	−0.0333709	+	0.891857i	−0.00171189	+	0.0457513i
$381$		0			0
$382$	5.68974	+	37.7490i	0.291113	+	1.93141i
$383$	−8.68644	−	22.1327i	−0.443856	−	1.13093i	−0.961372	−	0.275254i	$-0.911238\pi$
$383$	−8.68644	−	22.1327i	−0.443856	−	1.13093i	0.517515	−	0.855674i	$-0.326857\pi$
$384$		0			0
$385$	1.80420	−	0.341373i	0.0919506	−	0.0173980i
$386$	9.60531	−	4.62567i	0.488898	−	0.235441i
$387$		0			0
$388$	0.180278	+	0.515205i	0.00915222	+	0.0261555i
$389$	−1.58423	+	5.91242i	−0.0803236	+	0.299772i	−0.994388	−	0.105798i	$-0.966260\pi$
$389$	−1.58423	+	5.91242i	−0.0803236	+	0.299772i	0.914064	+	0.405570i	$0.132927\pi$
$390$		0			0
$391$	0.0130545	−	0.0299211i	0.000660192	−	0.00151318i
$392$	−4.17969	+	9.57996i	−0.211106	+	0.483861i
$393$		0			0
$394$	3.11754	−	11.6348i	0.157059	−	0.586153i
$395$	−6.81725	−	19.4826i	−0.343013	−	0.980275i
$396$		0			0
$397$	0.105265	−	0.0506928i	0.00528308	−	0.00254420i	−0.431240	−	0.902237i	$-0.641924\pi$
$397$	0.105265	−	0.0506928i	0.00528308	−	0.00254420i	0.436523	+	0.899693i	$0.356210\pi$
$398$	−23.0887	+	4.36862i	−1.15733	+	0.218979i
$399$		0			0
$400$	2.97371	+	7.57688i	0.148685	+	0.378844i
$401$	3.35978	+	22.2907i	0.167780	+	1.11315i	0.901211	+	0.433381i	$0.142680\pi$
$401$	3.35978	+	22.2907i	0.167780	+	1.11315i	−0.733431	+	0.679764i	$0.762082\pi$
$402$		0			0
$403$	1.17045	−	31.2809i	0.0583041	−	1.55821i
$404$	−0.0877652	+	0.778938i	−0.00436648	+	0.0387536i
$405$		0			0
$406$	11.3773	−	7.99494i	0.564647	−	0.396782i
$407$	−1.92602	+	1.11199i	−0.0954690	+	0.0551191i
$408$		0			0
$409$	−11.5388	−	21.8325i	−0.570557	−	1.07955i	−0.985496	−	0.169698i	$-0.945721\pi$
$409$	−11.5388	−	21.8325i	−0.570557	−	1.07955i	0.414939	−	0.909849i	$-0.363803\pi$
$410$	−4.60204	−	4.27007i	−0.227279	−	0.210884i
$411$		0			0
$412$	−0.0777606	+	0.515908i	−0.00383099	+	0.0254169i
$413$	7.87756	−	1.79800i	0.387630	−	0.0884739i
$414$		0			0
$415$	0.286496	+	0.594915i	0.0140635	+	0.0292032i
$416$	−0.707385	−	0.373864i	−0.0346824	−	0.0183302i
$417$		0			0
$418$	−1.10488	−	4.12348i	−0.0540415	−	0.201686i
$419$	−8.83796	+	6.02562i	−0.431763	+	0.294371i	−0.759633	−	0.650352i	$-0.774621\pi$
$419$	−8.83796	+	6.02562i	−0.431763	+	0.294371i	0.327870	+	0.944723i	$0.393669\pi$
$420$		0			0
$421$	−18.3893	+	13.5719i	−0.896240	+	0.661455i	−0.941315	−	0.337529i	$-0.890409\pi$
$421$	−18.3893	+	13.5719i	−0.896240	+	0.661455i	0.0450756	+	0.998984i	$0.485647\pi$
$422$	2.36354	−	4.90794i	0.115055	−	0.238915i
$423$		0			0
$424$	−5.67621	+	1.98619i	−0.275661	+	0.0964580i
$425$	−0.473376	+	0.895671i	−0.0229621	+	0.0434464i
$426$		0			0
$427$	−12.5520	+	10.8019i	−0.607436	+	0.522741i
$428$	0.312996	+	0.0965466i	0.0151292	+	0.00466675i
$429$		0			0
$430$	2.82463	−	7.19705i	0.136216	−	0.347072i
$431$	−8.06014	−	1.83967i	−0.388243	−	0.0886140i	0.0239437	−	0.999713i	$-0.492378\pi$
$431$	−8.06014	−	1.83967i	−0.388243	−	0.0886140i	−0.412187	+	0.911099i	$0.635235\pi$
$432$		0			0
$433$	16.7797	+	1.89062i	0.806380	+	0.0908572i	0.505524	−	0.862812i	$-0.331299\pi$
$433$	16.7797	+	1.89062i	0.806380	+	0.0908572i	0.300856	+	0.953670i	$0.402728\pi$
$434$	12.4118	+	21.4979i	0.595786	+	1.03193i
$435$		0			0
$436$	0.273563	−	0.473826i	0.0131013	−	0.0226921i
$437$	0.296195	−	0.401330i	0.0141689	−	0.0191982i
$438$		0			0
$439$	2.85228	+	9.24685i	0.136132	+	0.441328i	0.997811	−	0.0661244i	$-0.0210634\pi$
$439$	2.85228	+	9.24685i	0.136132	+	0.441328i	−0.861680	+	0.507453i	$0.830587\pi$
$440$	−1.77264	−	2.22282i	−0.0845072	−	0.105969i
$441$		0			0
$442$	−0.526610	−	2.30723i	−0.0250483	−	0.109744i
$443$	−5.82951	−	30.8097i	−0.276969	−	1.46381i	−0.794037	−	0.607870i	$-0.792024\pi$
$443$	−5.82951	−	30.8097i	−0.276969	−	1.46381i	0.517068	−	0.855944i	$-0.327023\pi$
$444$		0			0
$445$	23.7870	−	0.890047i	1.12761	−	0.0421923i
$446$	2.33395	−	12.3352i	0.110516	−	0.584090i
$447$		0			0
$448$	−14.0840	+	1.05545i	−0.665408	+	0.0498654i
$449$	−3.24721	−	28.8197i	−0.153245	−	1.36009i	−0.801194	−	0.598404i	$-0.795802\pi$
$449$	−3.24721	−	28.8197i	−0.153245	−	1.36009i	0.647949	−	0.761684i	$-0.275627\pi$
$450$		0			0
$451$	0.575210	+	0.277006i	0.0270856	+	0.0130437i
$452$	−0.229676	−	0.0615414i	−0.0108030	−	0.00289466i
$453$		0			0
$454$	0.711133	+	19.0054i	0.0333751	+	0.891968i
$455$	15.5100	+	1.16231i	0.727120	+	0.0544901i
$456$		0			0
$457$	9.78392	+	10.5446i	0.457672	+	0.493253i	0.919155	−	0.393896i	$-0.128873\pi$
$457$	9.78392	+	10.5446i	0.457672	+	0.493253i	−0.461483	+	0.887149i	$0.652682\pi$
$458$	27.3568	+	21.8163i	1.27830	+	1.01941i
$459$		0			0
$460$	−0.00164141	+	0.00719147i	−7.65309e−5	+	0.000335304i
$461$	−18.3098	−	0.685104i	−0.852772	−	0.0319085i	−0.392569	−	0.919722i	$-0.628414\pi$
$461$	−18.3098	−	0.685104i	−0.852772	−	0.0319085i	−0.460203	+	0.887814i	$0.652223\pi$
$462$		0			0
$463$	33.6155	+	19.4079i	1.56224	+	0.901961i	0.997030	+	0.0770159i	$0.0245392\pi$
$463$	33.6155	+	19.4079i	1.56224	+	0.901961i	0.565213	+	0.824945i	$0.308794\pi$
$464$	−19.5926	−	10.0031i	−0.909562	−	0.464381i
$465$		0			0
$466$	−15.2755	+	6.66464i	−0.707624	+	0.308733i
$467$	−1.23733	−	0.777467i	−0.0572569	−	0.0359769i	0.503099	−	0.864229i	$-0.332193\pi$
$467$	−1.23733	−	0.777467i	−0.0572569	−	0.0359769i	−0.560356	+	0.828252i	$0.689336\pi$
$468$		0			0
$469$	−19.2296	+	15.3351i	−0.887939	+	0.708108i
$470$	−1.90223	−	0.286716i	−0.0877435	−	0.0132252i
$471$		0			0
$472$	−8.16068	−	9.48288i	−0.375626	−	0.436485i
$473$	−0.0587570	+	0.784058i	−0.00270165	+	0.0360510i
$474$		0			0
$475$	−10.0968	+	11.7327i	−0.463274	+	0.538334i
$476$	0.0282141	+	0.0282141i	0.00129319	+	0.00129319i
$477$		0			0
$478$	22.6393	−	2.55084i	1.03550	−	0.116673i
$479$	6.51383	+	8.82593i	0.297625	+	0.403267i	0.927736	−	0.373238i	$-0.121753\pi$
$479$	6.51383	+	8.82593i	0.297625	+	0.403267i	−0.630111	+	0.776505i	$0.716991\pi$
$480$		0			0
$481$	−18.1961	+	4.87562i	−0.829670	+	0.222309i
$482$	−22.0540	−	4.17284i	−1.00453	−	0.190068i
$483$		0			0
$484$	0.389554	+	0.265593i	0.0177070	+	0.0120724i
$485$	−10.9728	+	31.3584i	−0.498248	+	1.42391i
$486$		0			0
$487$	−26.6681	+	33.4407i	−1.20845	+	1.51534i	−0.411367	+	0.911470i	$0.634948\pi$
$487$	−26.6681	+	33.4407i	−1.20845	+	1.51534i	−0.797080	+	0.603874i	$0.793623\pi$
$488$	23.8682	+	9.36759i	1.08046	+	0.424051i
$489$		0			0
$490$	12.4892	−	6.60076i	0.564206	−	0.298192i
$491$	−17.4189	−	12.8557i	−0.786102	−	0.580170i	0.125093	−	0.992145i	$-0.460077\pi$
$491$	−17.4189	−	12.8557i	−0.786102	−	0.580170i	−0.911195	+	0.411975i	$0.864839\pi$
$492$		0			0
$493$	−0.646949	−	2.66045i	−0.0291371	−	0.119821i
$494$		−	36.1597i		−	1.62690i
$495$		0			0
$496$	20.8933	−	33.2516i	0.938139	−	1.49304i
$497$	−26.9164	+	8.30262i	−1.20737	+	0.372424i
$498$		0			0
$499$	−15.5114	+	6.08776i	−0.694384	+	0.272526i	−0.686170	−	0.727441i	$-0.740710\pi$
$499$	−15.5114	+	6.08776i	−0.694384	+	0.272526i	−0.00821319	+	0.999966i	$0.502614\pi$
$500$	−0.101841	+	0.330160i	−0.00455446	+	0.0147652i
$501$		0			0
$502$	−20.6254	+	30.2519i	−0.920558	+	1.35021i
$503$	−15.0260	+	9.44146i	−0.669976	+	0.420974i	−0.823612	−	0.567154i	$-0.808045\pi$
$503$	−15.0260	+	9.44146i	−0.669976	+	0.420974i	0.153636	+	0.988128i	$0.450902\pi$
$504$		0			0
$505$	−33.7366	+	33.7366i	−1.50126	+	1.50126i
$506$	−0.00263670	−	0.0351843i	−0.000117216	−	0.00156413i
$507$		0			0
$508$	0.107180	+	0.0467622i	0.00475534	+	0.00207473i
$509$	24.8956	+	36.5152i	1.10348	+	1.61851i	0.718410	+	0.695620i	$0.244870\pi$
$509$	24.8956	+	36.5152i	1.10348	+	1.61851i	0.385070	+	0.922887i	$0.374177\pi$
$510$		0			0
$511$	3.23179	+	2.78118i	0.142966	+	0.123032i
$512$	11.6232	+	18.4982i	0.513676	+	0.817511i
$513$		0			0
$514$	−38.1896	−	13.3631i	−1.68447	−	0.589422i
$515$	−23.2787	+	21.5995i	−1.02578	+	0.951787i
$516$		0			0
$517$	0.193448	−	0.0291576i	0.00850785	−	0.00128235i
$518$	10.1610	−	10.9509i	0.446448	−	0.481156i
$519$		0			0
$520$	−9.63027	−	22.0728i	−0.422315	−	0.967957i
$521$	36.5638			1.60189			0.800944	−	0.598740i	$-0.204332\pi$
$521$	36.5638			1.60189			0.800944	+	0.598740i	$0.204332\pi$
$522$		0			0
$523$	9.42150			0.411974			0.205987	−	0.978555i	$-0.433960\pi$
$523$	9.42150			0.411974			0.205987	+	0.978555i	$0.433960\pi$
$524$	−0.111911	−	0.256503i	−0.00488885	−	0.0112054i
$525$		0			0
$526$	1.57447	−	1.69687i	0.0686501	−	0.0739872i
$527$	4.83317	−	0.728483i	0.210536	−	0.0317332i
$528$		0			0
$529$	−16.8572	+	15.6412i	−0.732920	+	0.680051i
$530$	7.67157	+	2.68440i	0.333232	+	0.116603i
$531$		0			0
$532$	0.324358	+	0.516213i	0.0140627	+	0.0223807i
$533$	4.09897	+	3.52744i	0.177546	+	0.152791i
$534$		0			0
$535$	11.2307	+	16.4723i	0.485543	+	0.712161i
$536$	34.9049	+	15.2289i	1.50766	+	0.657786i
$537$		0			0
$538$	−1.18491	−	15.8115i	−0.0510851	−	0.681683i
$539$	−1.01581	+	1.01581i	−0.0437541	+	0.0437541i
$540$		0			0
$541$	22.6807	−	14.2512i	0.975120	−	0.612708i	0.0525827	−	0.998617i	$-0.483255\pi$
$541$	22.6807	−	14.2512i	0.975120	−	0.612708i	0.922537	+	0.385908i	$0.126112\pi$
$542$	8.26926	−	12.1288i	0.355195	−	0.520975i
$543$		0			0
$544$	0.0368244	−	0.119382i	0.00157883	−	0.00511845i
$545$	30.9994	−	12.1664i	1.32787	−	0.521150i
$546$		0			0
$547$	30.1316	−	9.29437i	1.28833	−	0.397399i	0.426454	−	0.904509i	$-0.359763\pi$
$547$	30.1316	−	9.29437i	1.28833	−	0.397399i	0.861881	+	0.507111i	$0.169287\pi$
$548$	0.0518078	−	0.0824516i	0.00221312	−	0.00352216i
$549$		0			0
$550$			1.09494i			0.0466882i
$551$	−0.591649	−	41.8306i	−0.0252051	−	1.78204i
$552$		0			0
$553$	−11.3448	−	8.37281i	−0.482428	−	0.356048i
$554$	−12.6104	+	6.66477i	−0.535763	+	0.283159i
$555$		0			0
$556$	0.552521	+	0.216849i	0.0234321	+	0.00919643i
$557$	22.5590	−	28.2880i	0.955854	−	1.19860i	−0.0241667	−	0.999708i	$-0.507693\pi$
$557$	22.5590	−	28.2880i	0.955854	−	1.19860i	0.980021	−	0.198895i	$-0.0637353\pi$
$558$		0			0
$559$	−2.19963	+	6.28619i	−0.0930346	+	0.265877i
$560$	16.1221	+	10.9919i	0.681282	+	0.464490i
$561$		0			0
$562$	−26.3682	−	4.98913i	−1.11227	−	0.210454i
$563$	−30.5864	+	8.19561i	−1.28906	+	0.345404i	−0.837305	−	0.546736i	$-0.815870\pi$
$563$	−30.5864	+	8.19561i	−1.28906	+	0.345404i	−0.451759	+	0.892140i	$0.649203\pi$
$564$		0			0
$565$	−8.59410	−	11.6446i	−0.361557	−	0.489892i
$566$	11.4388	−	1.28885i	0.480810	−	0.0541742i
$567$		0			0
$568$	30.8395	+	30.8395i	1.29399	+	1.29399i
$569$	−5.39437	+	6.26838i	−0.226144	+	0.262784i	−0.859569	−	0.511020i	$-0.829268\pi$
$569$	−5.39437	+	6.26838i	−0.226144	+	0.262784i	0.633425	+	0.773804i	$0.281649\pi$
$570$		0			0
$571$	0.481270	−	6.42210i	0.0201405	−	0.268756i	−0.978038	−	0.208427i	$-0.933166\pi$
$571$	0.481270	−	6.42210i	0.0201405	−	0.268756i	0.998179	−	0.0603297i	$-0.0192152\pi$
$572$	−0.0354721	−	0.0412193i	−0.00148316	−	0.00172347i
$573$		0			0
$574$	−4.24058	−	0.639165i	−0.176999	−	0.0266782i
$575$	−0.100024	+	0.0797666i	−0.00417129	+	0.00332650i
$576$		0			0
$577$	20.7599	+	13.0443i	0.864246	+	0.543042i	0.889654	−	0.456635i	$-0.150946\pi$
$577$	20.7599	+	13.0443i	0.864246	+	0.543042i	−0.0254077	+	0.999677i	$0.508088\pi$
$578$	−21.9350	+	9.57015i	−0.912376	+	0.398066i
$579$		0			0
$580$	0.255396	+	0.563495i	0.0106048	+	0.0233979i
$581$	0.390629	+	0.225530i	0.0162060	+	0.00935654i
$582$		0			0
$583$	−0.825967	−	0.0309055i	−0.0342081	−	0.00127998i
$584$	1.46902	−	6.43622i	0.0607887	−	0.266333i
$585$		0			0
$586$	−9.59190	−	7.64928i	−0.396238	−	0.315989i
$587$	−20.4785	−	22.0706i	−0.845240	−	0.910952i	0.151755	−	0.988418i	$-0.451507\pi$
$587$	−20.4785	−	22.0706i	−0.845240	−	0.910952i	−0.996995	+	0.0774662i	$0.975317\pi$
$588$		0			0
$589$	74.4732	+	5.58099i	3.06861	+	0.229961i
$590$	0.632240	+	16.8970i	0.0260289	+	0.695637i
$591$		0			0
$592$	−22.8279	−	6.11671i	−0.938220	−	0.251395i
$593$	−10.3675	−	4.99273i	−0.425742	−	0.205027i	0.208728	−	0.977974i	$-0.433068\pi$
$593$	−10.3675	−	4.99273i	−0.425742	−	0.205027i	−0.634471	+	0.772947i	$0.718782\pi$
$594$		0			0
$595$	0.271916	+	2.41332i	0.0111475	+	0.0989367i
$596$	−0.654318	+	0.0490343i	−0.0268019	+	0.00200852i
$597$		0			0
$598$	0.0555619	−	0.293652i	0.00227209	−	0.0120083i
$599$	9.04081	−	0.338283i	0.369397	−	0.0138219i	0.147952	−	0.988995i	$-0.452732\pi$
$599$	9.04081	−	0.338283i	0.369397	−	0.0138219i	0.221446	+	0.975173i	$0.428922\pi$
$600$		0			0
$601$	0.533841	+	2.82142i	0.0217758	+	0.115088i	0.991768	−	0.128049i	$-0.0408713\pi$
$601$	0.533841	+	2.82142i	0.0217758	+	0.115088i	−0.969992	+	0.243137i	$0.921824\pi$
$602$	−1.17523	−	5.14902i	−0.0478988	−	0.209858i
$603$		0			0
$604$	0.0601907	+	0.0754767i	0.00244912	+	0.00307110i
$605$	8.45859	+	27.4221i	0.343890	+	1.11487i
$606$		0			0
$607$	−3.88614	+	5.26554i	−0.157734	+	0.213722i	−0.876337	−	0.481699i	$-0.840020\pi$
$607$	−3.88614	+	5.26554i	−0.157734	+	0.213722i	0.718603	+	0.695420i	$0.244782\pi$
$608$	0.954443	−	1.65314i	0.0387078	−	0.0670439i
$609$		0			0
$610$	−17.3271	−	30.0113i	−0.701552	−	1.21512i
$611$	1.64668	+	0.185536i	0.0666174	+	0.00750598i
$612$		0			0
$613$	29.6777	+	6.77374i	1.19867	+	0.273589i	0.774843	−	0.632154i	$-0.217829\pi$
$613$	29.6777	+	6.77374i	1.19867	+	0.273589i	0.423828	+	0.905743i	$0.360686\pi$
$614$	7.43839	−	18.9527i	0.300189	−	0.764869i
$615$		0			0
$616$	−1.85585	−	0.572454i	−0.0747743	−	0.0230648i
$617$	−12.8443	+	11.0534i	−0.517092	+	0.444994i	−0.871713	−	0.490016i	$-0.836991\pi$
$617$	−12.8443	+	11.0534i	−0.517092	+	0.444994i	0.354621	+	0.935010i	$0.384610\pi$
$618$		0			0
$619$	−19.8590	+	37.5750i	−0.798199	+	1.51027i	0.0607199	+	0.998155i	$0.480660\pi$
$619$	−19.8590	+	37.5750i	−0.798199	+	1.51027i	−0.858919	+	0.512112i	$0.828863\pi$
$620$	−1.04245	+	0.364770i	−0.0418660	+	0.0146495i
$621$		0			0
$622$	−5.17126	+	10.7382i	−0.207349	+	0.430564i
$623$	13.0831	−	9.65577i	0.524163	−	0.386850i
$624$		0			0
$625$	−25.6072	+	17.4587i	−1.02429	+	0.698348i
$626$	−0.612477	−	2.28579i	−0.0244795	−	0.0913587i
$627$		0			0
$628$	−0.612243	−	0.323580i	−0.0244311	−	0.0129122i
$629$	−1.27625	−	2.65015i	−0.0508873	−	0.105669i
$630$		0			0
$631$	−2.84923	+	0.650318i	−0.113426	+	0.0258888i	−0.278857	−	0.960333i	$-0.589956\pi$
$631$	−2.84923	+	0.650318i	−0.113426	+	0.0258888i	0.165431	+	0.986221i	$0.447098\pi$
$632$	−3.25382	+	21.5877i	−0.129430	+	0.858712i
$633$		0			0
$634$	7.36636	+	6.83498i	0.292555	+	0.271452i
$635$	3.32577	+	6.29267i	0.131979	+	0.249717i
$636$		0			0
$637$	−10.5381	+	6.08419i	−0.417536	+	0.241064i
$638$	−1.96180	−	2.21550i	−0.0776686	−	0.0877124i
$639$		0			0
$640$	3.45465	−	30.6609i	0.136557	−	1.21198i
$641$	0.609023	−	16.2765i	0.0240550	−	0.642882i	−0.934164	−	0.356845i	$-0.883852\pi$
$641$	0.609023	−	16.2765i	0.0240550	−	0.642882i	0.958219	−	0.286037i	$-0.0923381\pi$
$642$		0			0
$643$	−3.72753	−	24.7305i	−0.146999	−	0.975278i	−0.933729	−	0.357980i	$-0.883466\pi$
$643$	−3.72753	−	24.7305i	−0.146999	−	0.975278i	0.786730	−	0.617298i	$-0.211773\pi$
$644$	0.00184091	+	0.00469055i	7.25418e−5	+	0.000184834i
$645$		0			0
$646$	5.54771	−	1.04968i	0.218272	−	0.0412992i
$647$	−0.000657666	0	0.000316715i	−2.58555e−5	0	1.24514e-5i	−0.433897	−	0.900963i	$-0.642862\pi$
$647$	−0.000657666	0	0.000316715i	−2.58555e−5	0	1.24514e-5i	0.433871	+	0.900975i	$0.357147\pi$
$648$		0			0
$649$	−0.567930	−	1.62305i	−0.0222932	−	0.0637103i
$650$	−2.40043	+	8.95854i	−0.0941528	+	0.351383i
$651$		0			0
$652$	0.223767	−	0.512880i	0.00876340	−	0.0200859i
$653$	6.93910	−	15.9046i	0.271548	−	0.622395i	−0.726341	−	0.687334i	$-0.758781\pi$
$653$	6.93910	−	15.9046i	0.271548	−	0.622395i	0.997889	+	0.0649397i	$0.0206855\pi$
$654$		0			0
$655$	4.40860	−	16.4531i	0.172258	−	0.642876i
$656$	2.24073	+	6.40365i	0.0874859	+	0.250020i
$657$		0			0
$658$	−1.18397	+	0.570169i	−0.0461559	+	0.0222275i
$659$	−33.6993	+	6.37624i	−1.31274	+	0.248383i	−0.794714	−	0.606984i	$-0.792379\pi$
$659$	−33.6993	+	6.37624i	−1.31274	+	0.248383i	−0.518023	+	0.855367i	$0.673332\pi$
$660$		0			0
$661$	14.4271	+	36.7596i	0.561149	+	1.42978i	0.876775	+	0.480901i	$0.159690\pi$
$661$	14.4271	+	36.7596i	0.561149	+	1.42978i	−0.315626	+	0.948884i	$0.602214\pi$
$662$	6.44041	+	42.7293i	0.250314	+	1.66072i
$663$		0			0
$664$	0.0261138	−	0.697907i	0.00101341	−	0.0270840i
$665$	−4.15472	+	36.8742i	−0.161113	+	1.42992i
$666$		0			0
$667$	0.0594708	−	0.340614i	0.00230272	−	0.0131886i
$668$	0.933663	−	0.539050i	0.0361245	−	0.0208565i
$669$		0			0
$670$	−24.0501	−	45.5050i	−0.929136	−	1.75801i
$671$	2.58339	+	2.39704i	0.0997308	+	0.0925366i
$672$		0			0
$673$	0.650382	−	4.31500i	0.0250704	−	0.166331i	−0.972792	−	0.231680i	$-0.925578\pi$
$673$	0.650382	−	4.31500i	0.0250704	−	0.166331i	0.997862	+	0.0653487i	$0.0208160\pi$
$674$	−27.6219	+	6.30451i	−1.06395	+	0.242841i
$675$		0			0
$676$	0.0451929	+	0.0938441i	0.00173819	+	0.00360939i
$677$	−1.66140	−	0.878074i	−0.0638527	−	0.0337471i	0.435038	−	0.900412i	$-0.356735\pi$
$677$	−1.66140	−	0.878074i	−0.0638527	−	0.0337471i	−0.498890	+	0.866665i	$0.666259\pi$
$678$		0			0
$679$	5.87381	+	21.9214i	0.225416	+	0.841265i
$680$	3.10691	−	2.11825i	0.119145	−	0.0812314i
$681$		0			0
$682$	4.25048	−	3.13700i	0.162759	−	0.120122i
$683$	18.9004	−	39.2471i	0.723205	−	1.50175i	−0.136325	−	0.990664i	$-0.543529\pi$
$683$	18.9004	−	39.2471i	0.723205	−	1.50175i	0.859529	−	0.511086i	$-0.170757\pi$
$684$		0			0
$685$	5.59435	−	1.95755i	0.213749	−	0.0747941i
$686$	12.9550	−	24.5121i	0.494625	−	0.935877i
$687$		0			0
$688$	−6.33301	+	5.44999i	−0.241444	+	0.207779i
$689$	−6.69014	−	2.06364i	−0.254874	−	0.0786182i
$690$		0			0
$691$	1.03107	−	2.62712i	0.0392236	−	0.0999402i	−0.909920	−	0.414784i	$-0.863857\pi$
$691$	1.03107	−	2.62712i	0.0392236	−	0.0999402i	0.949143	+	0.314844i	$0.101952\pi$
$692$	−0.681355	−	0.155515i	−0.0259012	−	0.00591179i
$693$		0			0
$694$	42.5813	+	4.79776i	1.61636	+	0.182120i
$695$	18.0635	+	31.2869i	0.685188	+	1.18678i
$696$		0			0
$697$	−0.422200	+	0.731272i	−0.0159920	+	0.0276989i
$698$	−16.5907	+	22.4797i	−0.627969	+	0.850867i
$699$		0			0
$700$	−0.0460912	−	0.149424i	−0.00174208	−	0.00564769i
$701$	30.7014	+	38.4983i	1.15957	+	1.45406i	0.867341	+	0.497714i	$0.165827\pi$
$701$	30.7014	+	38.4983i	1.15957	+	1.45406i	0.292233	+	0.956347i	$0.405602\pi$
$702$		0			0
$703$	−10.0009	−	43.8167i	−0.377190	−	1.65258i
$704$	0.558784	+	2.95324i	0.0210600	+	0.111305i
$705$		0			0
$706$	20.6290	−	0.771884i	0.776384	−	0.0290502i
$707$	−6.05914	+	32.0233i	−0.227877	+	1.20436i
$708$		0			0
$709$	6.56663	−	0.492101i	0.246615	−	0.0184812i	0.0491510	−	0.998791i	$-0.484348\pi$
$709$	6.56663	−	0.492101i	0.246615	−	0.0184812i	0.197464	+	0.980310i	$0.436729\pi$
$710$	−6.59975	−	58.5744i	−0.247684	−	2.19826i
$711$		0			0
$712$	−22.6835	−	10.9238i	−0.850099	−	0.409386i
$713$	0.596219	+	0.159756i	0.0223286	+	0.00598292i
$714$		0			0
$715$	−0.123763	−	3.30764i	−0.00462848	−	0.123699i
$716$	0.0584997	+	0.00438394i	0.00218623	+	0.000163836i
$717$		0			0
$718$	6.59089	+	7.10329i	0.245970	+	0.265092i
$719$	9.87142	+	7.87220i	0.368142	+	0.293583i	0.790034	−	0.613062i	$-0.210063\pi$
$719$	9.87142	+	7.87220i	0.368142	+	0.293583i	−0.421892	+	0.906646i	$0.638634\pi$
$720$		0			0
$721$	−4.82707	+	21.1488i	−0.179769	+	0.787621i
$722$	59.0680	+	2.21017i	2.19828	+	0.0822539i
$723$		0			0
$724$	−0.336342	−	0.194187i	−0.0125000	−	0.00721690i
$725$	−2.63031	+	10.4028i	−0.0976873	+	0.386350i
$726$		0			0
$727$	−5.91730	+	2.58169i	−0.219460	+	0.0957496i	−0.506746	−	0.862095i	$-0.669152\pi$
$727$	−5.91730	+	2.58169i	−0.219460	+	0.0957496i	0.287286	+	0.957845i	$0.407247\pi$
$728$	−13.9292	−	8.75229i	−0.516250	−	0.324381i
$729$		0			0
$730$	−6.97584	+	5.56305i	−0.258188	+	0.205898i
$731$	−1.02830	−	0.154991i	−0.0380329	−	0.00573254i
$732$		0			0
$733$	1.34347	+	1.56114i	0.0496221	+	0.0576619i	0.782234	−	0.622984i	$-0.214080\pi$
$733$	1.34347	+	1.56114i	0.0496221	+	0.0576619i	−0.732612	+	0.680646i	$0.761699\pi$
$734$	1.05544	−	14.0838i	0.0389569	−	0.519844i
$735$		0			0
$736$	0.0102912	−	0.0119586i	0.000379338	−	0.000440799i
$737$	3.70114	+	3.70114i	0.136333	+	0.136333i
$738$		0			0
$739$	34.8879	−	3.93092i	1.28337	−	0.144601i	0.556196	−	0.831051i	$-0.312261\pi$
$739$	34.8879	−	3.93092i	1.28337	−	0.144601i	0.727177	+	0.686450i	$0.240832\pi$
$740$	0.394680	+	0.534772i	0.0145087	+	0.0196586i
$741$		0			0
$742$	5.36288	−	1.43698i	0.196877	−	0.0527531i
$743$	−24.4829	−	4.63242i	−0.898191	−	0.169947i	−0.283739	−	0.958901i	$-0.591575\pi$
$743$	−24.4829	−	4.63242i	−0.898191	−	0.169947i	−0.614452	+	0.788955i	$0.710623\pi$
$744$		0			0
$745$	−32.9978	−	22.4975i	−1.20894	−	0.824244i
$746$	−1.10188	+	3.14898i	−0.0403425	+	0.115292i
$747$		0			0
$748$	0.00529425	−	0.00663878i	0.000193577	−	0.000242738i
$749$	12.6774	+	4.97550i	0.463220	+	0.181801i
$750$		0			0
$751$	25.4167	−	13.4331i	0.927469	−	0.490182i	0.0659022	−	0.997826i	$-0.479007\pi$
$751$	25.4167	−	13.4331i	0.927469	−	0.490182i	0.861567	+	0.507645i	$0.169484\pi$
$752$	1.67269	+	1.23450i	0.0609966	+	0.0450175i
$753$		0			0
$754$	−11.1940	−	22.4276i	−0.407663	−	0.816766i
$755$			5.87590i			0.213846i
$756$		0			0
$757$	−9.12064	+	14.5154i	−0.331495	+	0.527572i	−0.970334	−	0.241769i	$-0.922272\pi$
$757$	−9.12064	+	14.5154i	−0.331495	+	0.527572i	0.638838	+	0.769341i	$0.279415\pi$
$758$	32.4657	−	10.0143i	1.17921	−	0.363737i
$759$		0			0
$760$	53.4835	−	20.9907i	1.94005	−	0.761414i
$761$	−0.283559	+	0.919276i	−0.0102790	+	0.0333237i	−0.960567	−	0.278049i	$-0.910312\pi$
$761$	−0.283559	+	0.919276i	−0.0102790	+	0.0333237i	0.950288	+	0.311372i	$0.100789\pi$
$762$		0			0
$763$	12.8146	−	18.7956i	0.463920	−	0.680446i
$764$	−0.982397	+	0.617281i	−0.0355419	+	0.0223324i
$765$		0			0
$766$	24.0331	−	24.0331i	0.868352	−	0.868352i
$767$	−1.08846	−	14.5245i	−0.0393021	−	0.524451i
$768$		0			0
$769$	−24.5823	−	10.7251i	−0.886461	−	0.386759i	−0.0932045	−	0.995647i	$-0.529711\pi$
$769$	−24.5823	−	10.7251i	−0.886461	−	0.386759i	−0.793256	+	0.608888i	$0.791616\pi$
$770$	1.47863	+	2.16875i	0.0532862	+	0.0781565i
$771$		0			0
$772$	0.245593	+	0.211350i	0.00883910	+	0.00760666i
$773$	18.5005	+	29.4435i	0.665418	+	1.05901i	0.993442	+	0.114338i	$0.0364746\pi$
$773$	18.5005	+	29.4435i	0.665418	+	1.05901i	−0.328023	+	0.944670i	$0.606382\pi$
$774$		0			0
$775$	−18.0802	−	6.32654i	−0.649460	−	0.227256i
$776$	25.7588	−	23.9007i	0.924689	−	0.857986i
$777$		0			0
$778$	−8.65217	+	1.30411i	−0.310195	+	0.0467544i
$779$	−8.77554	+	9.45778i	−0.314416	+	0.338860i
$780$		0			0
$781$	2.39713	+	5.49427i	0.0857759	+	0.196600i
$782$	0.0466657			0.00166876
$783$		0			0
$784$	−15.2658			−0.545208
$785$	−16.8551	−	38.6323i	−0.601585	−	1.37885i
$786$		0			0
$787$	30.9115	−	33.3146i	1.10187	−	1.18754i	0.121050	−	0.992646i	$-0.461374\pi$
$787$	30.9115	−	33.3146i	1.10187	−	1.18754i	0.980825	−	0.194892i	$-0.0624355\pi$
$788$	0.361992	−	0.0545615i	0.0128954	−	0.00194367i
$789$		0			0
$790$	21.6294	−	20.0691i	0.769539	−	0.714028i
$791$	−9.33151	−	3.26524i	−0.331790	−	0.116098i
$792$		0			0
$793$	15.8817	+	25.2757i	0.563977	+	0.897565i
$794$	0.126592	+	0.108942i	0.00449260	+	0.00386619i
$795$		0			0
$796$	−0.402305	−	0.590073i	−0.0142593	−	0.0209146i
$797$	38.8974	+	16.9708i	1.37782	+	0.601135i	0.952675	−	0.303992i	$-0.0983197\pi$
$797$	38.8974	+	16.9708i	1.37782	+	0.601135i	0.425141	+	0.905127i	$0.360224\pi$
$798$		0			0
$799$	0.0193362	+	0.258023i	0.000684065	+	0.00912821i
$800$	−0.346206	+	0.346206i	−0.0122402	+	0.0122402i
$801$		0			0
$802$	−27.2851	+	17.1444i	−0.963470	+	0.605388i
$803$	0.511140	−	0.749704i	0.0180377	−	0.0264565i
$804$		0			0
$805$	−0.0904001	+	0.293070i	−0.00318618	+	0.0103294i
$806$	41.6538	−	16.3479i	1.46719	−	0.575831i
$807$		0			0
$808$	48.2210	−	14.8742i	1.69641	−	0.523273i
$809$	−0.151577	+	0.241234i	−0.00532917	+	0.00848133i	−0.849378	−	0.527785i	$-0.823023\pi$
$809$	−0.151577	+	0.241234i	−0.00532917	+	0.00848133i	0.844049	+	0.536266i	$0.180166\pi$
$810$		0			0
$811$		−	34.1033i		−	1.19753i	−0.800925	−	0.598765i	$-0.795658\pi$
$811$		−	34.1033i		−	1.19753i	0.800925	−	0.598765i	$-0.204342\pi$
$812$	0.360985	+	0.219763i	0.0126681	+	0.00771217i
$813$		0			0
$814$	−2.55793	−	1.88784i	−0.0896556	−	0.0661688i
$815$	30.1118	−	15.9146i	1.05477	−	0.557463i
$816$		0			0
$817$	−14.7909	−	5.80498i	−0.517467	−	0.203091i
$818$	22.0092	−	27.5987i	0.769535	−	0.964967i
$819$		0			0
$820$	0.0630171	−	0.180093i	0.00220065	−	0.00628910i
$821$	−2.75820	−	1.88051i	−0.0962618	−	0.0656302i	0.514233	−	0.857651i	$-0.328077\pi$
$821$	−2.75820	−	1.88051i	−0.0962618	−	0.0656302i	−0.610494	+	0.792021i	$0.709029\pi$
$822$		0			0
$823$	−16.2913	−	3.08248i	−0.567879	−	0.107449i	−0.105960	−	0.994370i	$-0.533791\pi$
$823$	−16.2913	−	3.08248i	−0.567879	−	0.107449i	−0.461919	+	0.886922i	$0.652839\pi$
$824$	32.4432	−	8.69313i	1.13021	−	0.302840i
$825$		0			0
$826$	6.85892	+	9.29351i	0.238652	+	0.323363i
$827$	−32.7221	+	3.68690i	−1.13786	+	0.128206i	−0.660728	−	0.750625i	$-0.729752\pi$
$827$	−32.7221	+	3.68690i	−1.13786	+	0.128206i	−0.477132	+	0.878831i	$0.658324\pi$
$828$		0			0
$829$	26.7657	+	26.7657i	0.929611	+	0.929611i	0.997681	−	0.0680695i	$-0.0216840\pi$
$829$	26.7657	+	26.7657i	0.929611	+	0.929611i	−0.0680695	+	0.997681i	$0.521684\pi$
$830$	−0.615695	+	0.715451i	−0.0213711	+	0.0248337i
$831$		0			0
$832$	−1.90256	+	25.3879i	−0.0659593	+	0.880165i
$833$	−1.23936	−	1.44017i	−0.0429414	−	0.0498988i
$834$		0			0
$835$	64.8867	+	9.78009i	2.24550	+	0.338454i
$836$	0.101437	−	0.0808930i	0.00350826	−	0.00279774i
$837$		0			0
$838$	−12.9470	−	8.13516i	−0.447248	−	0.281024i
$839$	−11.1500	+	4.86470i	−0.384941	+	0.167948i	−0.583446	−	0.812152i	$-0.698296\pi$
$839$	−11.1500	+	4.86470i	−0.384941	+	0.167948i	0.198505	+	0.980100i	$0.436391\pi$
$840$		0			0
$841$	−13.3166	−	25.7618i	−0.459192	−	0.888337i
$842$	−28.2943	−	16.3357i	−0.975085	−	0.562966i
$843$		0			0
$844$	0.165443	+	0.00619043i	0.00569477	+	0.000213083i
$845$	−1.41072	+	6.18079i	−0.0485304	+	0.212626i
$846$		0			0
$847$	15.3263	+	12.2223i	0.526618	+	0.419964i
$848$	−5.97418	−	6.43864i	−0.205154	−	0.221104i
$849$		0			0
$850$	−1.44412	−	0.108222i	−0.0495331	−	0.00371199i
$851$	−0.0138894	−	0.371201i	−0.000476122	−	0.0127246i
$852$		0			0
$853$	−55.2666	−	14.8086i	−1.89229	−	0.507038i	−0.998256	−	0.0590413i	$-0.981196\pi$
$853$	−55.2666	−	14.8086i	−1.89229	−	0.507038i	−0.894035	−	0.447997i	$-0.852138\pi$
$854$	−21.3281	−	10.2711i	−0.729834	−	0.351469i
$855$		0			0
$856$	−2.36095	−	20.9540i	−0.0806954	−	0.716192i
$857$	43.2322	−	3.23980i	1.47678	−	0.110670i	0.688165	−	0.725554i	$-0.258416\pi$
$857$	43.2322	−	3.23980i	1.47678	−	0.110670i	0.788617	+	0.614884i	$0.210797\pi$
$858$		0			0
$859$	−4.96865	+	26.2599i	−0.169528	+	0.895978i	0.789732	+	0.613452i	$0.210220\pi$
$859$	−4.96865	+	26.2599i	−0.169528	+	0.895978i	−0.959260	+	0.282525i	$0.908828\pi$
$860$	0.234813	−	0.00878607i	0.00800704	−	0.000299602i
$861$		0			0
$862$	−2.19714	−	11.6122i	−0.0748349	−	0.395512i
$863$	6.11960	+	26.8117i	0.208314	+	0.912682i	0.965689	+	0.259702i	$0.0836243\pi$
$863$	6.11960	+	26.8117i	0.208314	+	0.912682i	−0.757375	+	0.652980i	$0.773519\pi$
$864$		0			0
$865$	−26.5219	−	33.2574i	−0.901771	−	1.13079i
$866$	7.11485	+	23.0658i	0.241773	+	0.783808i
$867$		0			0
$868$	−0.448004	+	0.607024i	−0.0152062	+	0.0206037i
$869$	−1.50031	+	2.59861i	−0.0508945	+	0.0881518i
$870$		0			0
$871$	22.1680	+	38.3960i	0.751133	+	1.30100i
$872$	−35.0009	−	3.94365i	−1.18528	−	0.133549i
$873$		0			0
$874$	0.695146	+	0.158663i	0.0235137	+	0.00536684i
$875$	−5.24833	+	13.3725i	−0.177426	+	0.452074i
$876$		0			0
$877$	−30.2023	−	9.31619i	−1.01986	−	0.314585i	−0.260652	−	0.965433i	$-0.583937\pi$
$877$	−30.2023	−	9.31619i	−1.01986	−	0.314585i	−0.759208	+	0.650848i	$0.774414\pi$
$878$	−10.4849	+	9.02300i	−0.353849	+	0.304511i
$879$		0			0
$880$	1.94033	−	3.67129i	0.0654086	−	0.123759i
$881$	−45.8134	+	16.0308i	−1.54349	+	0.540092i	−0.961903	−	0.273390i	$-0.911855\pi$
$881$	−45.8134	+	16.0308i	−1.54349	+	0.540092i	−0.581590	+	0.813482i	$0.697569\pi$
$882$		0			0
$883$	−4.39277	+	9.12168i	−0.147828	+	0.306969i	−0.961713	−	0.274057i	$-0.911634\pi$
$883$	−4.39277	+	9.12168i	−0.147828	+	0.306969i	0.813885	+	0.581026i	$0.197349\pi$
$884$	0.0578707	−	0.0427105i	0.00194640	−	0.00143651i
$885$		0			0
$886$	37.0350	−	25.2501i	1.24422	−	0.848293i
$887$	−9.16695	−	34.2115i	−0.307796	−	1.14871i	−0.930512	−	0.366262i	$-0.880637\pi$
$887$	−9.16695	−	34.2115i	−0.307796	−	1.14871i	0.622716	−	0.782448i	$-0.286029\pi$
$888$		0			0
$889$	4.29856	+	2.27186i	0.144169	+	0.0761956i
$890$	14.7638	+	30.6574i	0.494884	+	1.02764i
$891$		0			0
$892$	0.371980	−	0.0849021i	0.0124548	−	0.00284273i
$893$	−0.589238	+	3.90934i	−0.0197181	+	0.130821i
$894$		0			0
$895$	2.61745	+	2.42864i	0.0874917	+	0.0811804i
$896$	−9.84870	−	18.6347i	−0.329022	−	0.622540i
$897$		0			0
$898$	35.9039	−	20.7291i	1.19813	−	0.691740i
$899$	47.9189	−	19.5933i	1.59818	−	0.653473i
$900$		0			0
$901$	0.122399	−	1.08632i	0.00407771	−	0.0361907i
$902$	−0.0341246	+	0.911999i	−0.00113622	+	0.0303662i
$903$		0			0
$904$	2.28145	+	15.1364i	0.0758799	+	0.503430i
$905$	−8.63621	−	22.0047i	−0.287077	−	0.731461i
$906$		0			0
$907$	31.1760	−	5.89881i	1.03518	−	0.195867i	0.359565	−	0.933120i	$-0.382925\pi$
$907$	31.1760	−	5.89881i	1.03518	−	0.195867i	0.675617	+	0.737253i	$0.263878\pi$
$908$	−0.520778	+	0.250794i	−0.0172826	+	0.00832288i
$909$		0			0
$910$	7.34329	+	20.9859i	0.243428	+	0.695676i
$911$	9.98200	−	37.2533i	0.330719	−	1.23426i	−0.577718	−	0.816236i	$-0.696057\pi$
$911$	9.98200	−	37.2533i	0.330719	−	1.23426i	0.908437	−	0.418022i	$-0.137277\pi$
$912$		0			0
$913$	0.0383858	−	0.0879812i	0.00127038	−	0.00291175i
$914$	−8.22276	+	18.8468i	−0.271985	+	0.623396i
$915$		0			0
$916$	−0.275239	+	1.02721i	−0.00909417	+	0.0339399i
$917$	−3.84302	−	10.9827i	−0.126908	−	0.362682i
$918$		0			0
$919$	36.0572	−	17.3642i	1.18942	−	0.572793i	0.268776	−	0.963203i	$-0.413381\pi$
$919$	36.0572	−	17.3642i	1.18942	−	0.572793i	0.920641	+	0.390409i	$0.127666\pi$
$920$	0.466592	−	0.0882839i	0.0153831	−	0.00291064i
$921$		0			0
$922$	−9.56901	−	24.3814i	−0.315139	−	0.802960i
$923$	7.56767	+	50.2082i	0.249093	+	1.65262i
$924$		0			0
$925$	−0.431028	+	11.5195i	−0.0141721	+	0.378758i
$926$	−6.21255	+	55.1379i	−0.204157	+	1.81194i
$927$		0			0
$928$	0.0802148	−	1.32081i	0.00263318	−	0.0433578i
$929$	−7.27103	+	4.19793i	−0.238555	+	0.137730i	−0.614512	−	0.788907i	$-0.710647\pi$
$929$	−7.27103	+	4.19793i	−0.238555	+	0.137730i	0.375958	+	0.926637i	$0.377314\pi$
$930$		0			0
$931$	−13.5654	−	25.6670i	−0.444588	−	0.841202i
$932$	−0.371305	−	0.344520i	−0.0121625	−	0.0112851i
$933$		0			0
$934$	0.311340	−	2.06561i	0.0101874	−	0.0675887i
$935$	0.503874	−	0.115006i	0.0164784	−	0.00376110i
$936$		0			0
$937$	−4.48545	−	9.31413i	−0.146533	−	0.304279i	0.814764	−	0.579793i	$-0.196866\pi$
$937$	−4.48545	−	9.31413i	−0.146533	−	0.304279i	−0.961297	+	0.275513i	$0.911152\pi$
$938$	−31.0847	−	16.4288i	−1.01495	−	0.536418i
$939$		0			0
$940$	−0.0151321	−	0.0564739i	−0.000493556	−	0.00184197i
$941$	−14.3238	+	9.76582i	−0.466943	+	0.318357i	−0.773834	−	0.633388i	$-0.781664\pi$
$941$	−14.3238	+	9.76582i	−0.466943	+	0.318357i	0.306891	+	0.951745i	$0.400711\pi$
$942$		0			0
$943$	−0.0857985	+	0.0633221i	−0.00279398	+	0.00206205i
$944$	7.92829	−	16.4633i	0.258044	−	0.535834i
$945$		0			0
$946$	−1.06087	+	0.371216i	−0.0344920	+	0.0120693i
$947$	−22.6435	+	42.8437i	−0.735816	+	1.39223i	0.177145	+	0.984185i	$0.443314\pi$
$947$	−22.6435	+	42.8437i	−0.735816	+	1.39223i	−0.912961	+	0.408047i	$0.866210\pi$
$948$		0			0
$949$	5.82562	−	5.01335i	0.189108	−	0.162740i
$950$	−21.1442	−	6.52212i	−0.686008	−	0.211605i
$951$		0			0
$952$	0.938447	−	2.39112i	0.0304152	−	0.0774967i
$953$	−13.7708	−	3.14309i	−0.446079	−	0.101815i	−0.00642014	−	0.999979i	$-0.502044\pi$
$953$	−13.7708	−	3.14309i	−0.446079	−	0.101815i	−0.439659	+	0.898165i	$0.644901\pi$
$954$		0			0
$955$	−70.1746	−	7.90677i	−2.27080	−	0.255857i
$956$	0.346206	+	0.599646i	0.0111971	+	0.0193939i
$957$		0			0
$958$	−7.84031	+	13.5798i	−0.253309	+	0.438744i
$959$	2.40422	−	3.25761i	0.0776364	−	0.105194i
$960$		0			0
$961$	18.1032	+	58.6892i	0.583975	+	1.89320i
$962$	−16.7898	−	21.0537i	−0.541324	−	0.678799i
$963$		0			0
$964$	−0.151795	−	0.665058i	−0.00488899	−	0.0214201i
$965$	3.66644	+	19.3776i	0.118027	+	0.623787i
$966$		0			0
$967$	−11.6409	+	0.435571i	−0.374345	+	0.0140070i	−0.223902	−	0.974612i	$-0.571880\pi$
$967$	−11.6409	+	0.435571i	−0.374345	+	0.0140070i	−0.150443	+	0.988619i	$0.548070\pi$
$968$	5.64285	−	29.8232i	0.181368	−	0.958554i
$969$		0			0
$970$	−47.3588	+	3.54905i	−1.52060	+	0.113953i
$971$	−1.95962	−	17.3921i	−0.0628873	−	0.558140i	−0.985165	−	0.171612i	$-0.945103\pi$
$971$	−1.95962	−	17.3921i	−0.0628873	−	0.558140i	0.922277	−	0.386529i	$-0.126326\pi$
$972$		0			0
$973$	22.2346	+	10.7076i	0.712810	+	0.343271i
$974$	−59.0592	−	15.8249i	−1.89238	−	0.507062i
$975$		0			0
$976$	1.40029	+	37.4235i	0.0448221	+	1.19790i
$977$	−15.1895	−	1.13829i	−0.485954	−	0.0364172i	−0.170499	−	0.985358i	$-0.554538\pi$
$977$	−15.1895	−	1.13829i	−0.485954	−	0.0364172i	−0.315455	+	0.948941i	$0.602157\pi$
$978$		0			0
$979$	−2.35367	−	2.53665i	−0.0752236	−	0.0810717i
$980$	0.335662	+	0.267681i	0.0107223	+	0.00855077i
$981$		0			0
$982$	6.88642	−	30.1714i	0.219754	−	0.962807i
$983$	49.2137	+	1.84145i	1.56967	+	0.0587331i	0.807982	−	0.589207i	$-0.200560\pi$
$983$	49.2137	+	1.84145i	1.56967	+	0.0587331i	0.761692	+	0.647940i	$0.224369\pi$
$984$		0			0
$985$	19.2966	+	11.1409i	0.614842	+	0.354979i
$986$	3.11595	−	2.36847i	0.0992321	−	0.0754275i
$987$		0			0
$988$	1.00728	−	0.439470i	0.0320457	−	0.0139814i
$989$	−0.111196	−	0.0698693i	−0.00353584	−	0.00222171i
$990$		0			0
$991$	3.45860	−	2.75814i	0.109866	−	0.0876153i	−0.567016	−	0.823707i	$-0.691902\pi$
$991$	3.45860	−	2.75814i	0.109866	−	0.0876153i	0.676882	+	0.736092i	$0.263331\pi$
$992$	2.33583	+	0.352070i	0.0741628	+	0.0111782i
$993$		0			0
$994$	−26.2648	−	30.5203i	−0.833069	−	0.968044i
$995$	3.24840	−	43.3469i	0.102981	−	1.37419i
$996$		0			0
$997$	−4.36849	+	5.07627i	−0.138351	+	0.160767i	−0.822873	−	0.568225i	$-0.807630\pi$
$997$	−4.36849	+	5.07627i	−0.138351	+	0.160767i	0.684522	+	0.728993i	$0.260011\pi$
$998$	−16.8432	−	16.8432i	−0.533163	−	0.533163i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.be.a.665.21		672
3.2	odd	2		261.2.x.a.230.8	yes	672
9.2	odd	6	inner	783.2.be.a.143.8		672
9.7	even	3		261.2.x.a.56.21	yes	672
29.14	odd	28	inner	783.2.be.a.449.8		672
87.14	even	28		261.2.x.a.14.21	✓	672
261.43	odd	84		261.2.x.a.101.8	yes	672
261.101	even	84	inner	783.2.be.a.710.21		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.21	✓	672	87.14	even	28
261.2.x.a.56.21	yes	672	9.7	even	3
261.2.x.a.101.8	yes	672	261.43	odd	84
261.2.x.a.230.8	yes	672	3.2	odd	2
783.2.be.a.143.8		672	9.2	odd	6	inner
783.2.be.a.449.8		672	29.14	odd	28	inner
783.2.be.a.665.21		672	1.1	even	1	trivial
783.2.be.a.710.21		672	261.101	even	84	inner

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:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.be (of order \(84\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.571642 + 1.31022i) q^{2} +(-0.0295503 + 0.0318477i) q^{4} +(-2.61481 + 0.394119i) q^{5} +(-1.32416 + 1.22864i) q^{7} +(2.63993 + 0.923750i) q^{8} +(-2.01111 - 3.20067i) q^{10} +(0.291375 + 0.250749i) q^{11} +(1.83426 + 2.69036i) q^{13} +(-2.36673 - 1.03259i) q^{14} +(0.305273 + 4.07358i) q^{16} +(-0.359515 + 0.359515i) q^{17} +(-6.57779 + 4.13310i) q^{19} +(0.0647166 - 0.0949219i) q^{20} +(-0.161973 + 0.525104i) q^{22} +(-0.0597689 + 0.0234575i) q^{23} +(1.90402 - 0.587312i) q^{25} +(-2.47642 + 3.94120i) q^{26} -0.0784782i q^{28} +(-2.80031 + 4.59981i) q^{29} +(-7.73493 - 5.70864i) q^{31} +(-0.217246 + 0.114818i) q^{32} +(-0.676557 - 0.265529i) q^{34} +(2.97819 - 3.73453i) q^{35} +(-1.91078 + 5.46069i) q^{37} +(-9.17541 - 6.25569i) q^{38} +(-7.26696 - 1.37498i) q^{40} +(1.60421 - 0.429846i) q^{41} +(1.21456 + 1.64567i) q^{43} +(-0.0165960 + 0.00186992i) q^{44} +(-0.0649009 - 0.0649009i) q^{46} +(0.331957 - 0.385741i) q^{47} +(-0.279270 + 3.72659i) q^{49} +(1.85792 + 2.15895i) q^{50} +(-0.139885 - 0.0210842i) q^{52} +(-1.68105 + 1.34059i) q^{53} +(-0.860715 - 0.540823i) q^{55} +(-4.63064 + 2.02033i) q^{56} +(-7.62753 - 1.03957i) q^{58} +(-3.87386 - 2.23658i) q^{59} +(9.16119 + 0.342788i) q^{61} +(3.05795 - 13.3977i) q^{62} +(6.11295 + 4.87491i) q^{64} +(-5.85654 - 6.31185i) q^{65} +(13.5780 + 1.01753i) q^{67} +(-0.000825933 - 0.0220735i) q^{68} +(6.59551 + 1.76726i) q^{70} +(14.0494 + 6.76584i) q^{71} +(-0.264280 - 2.34555i) q^{73} +(-8.24697 + 0.618025i) q^{74} +(0.0627463 - 0.331622i) q^{76} +(-0.693908 + 0.0259642i) q^{77} +(1.45117 + 7.66960i) q^{79} +(-2.40370 - 10.5313i) q^{80} +(1.48022 + 1.85614i) q^{82} +(-0.0736019 - 0.238612i) q^{83} +(0.798370 - 1.08175i) q^{85} +(-1.46189 + 2.53208i) q^{86} +(0.537580 + 0.931116i) q^{88} +(-8.94513 - 1.00787i) q^{89} +(-5.73433 - 1.30882i) q^{91} +(0.00101912 - 0.00259668i) q^{92} +(0.695166 + 0.214430i) q^{94} +(15.5707 - 13.3997i) q^{95} +(5.87063 - 11.1078i) q^{97} +(-5.04229 + 1.76437i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 36 q^{2} - 14 q^{4} + 42 q^{5} - 10 q^{7} - 56 q^{10} + 48 q^{11} - 14 q^{13} + 24 q^{14} - 54 q^{16} - 48 q^{19} + 30 q^{20} - 14 q^{22} + 30 q^{23} + 30 q^{25} - 12 q^{31} - 24 q^{32} - 14 q^{34}+ \cdots - 36 q^{97}+O(q^{100}) \) 672 * q + 36 * q^2 - 14 * q^4 + 42 * q^5 - 10 * q^7 - 56 * q^10 + 48 * q^11 - 14 * q^13 + 24 * q^14 - 54 * q^16 - 48 * q^19 + 30 * q^20 - 14 * q^22 + 30 * q^23 + 30 * q^25 - 12 * q^31 - 24 * q^32 - 14 * q^34 - 48 * q^37 + 42 * q^38 - 2 * q^40 + 24 * q^41 - 12 * q^43 - 64 * q^46 + 42 * q^47 + 22 * q^49 + 66 * q^50 + 22 * q^52 + 76 * q^55 + 42 * q^56 - 42 * q^58 + 132 * q^59 - 308 * q^64 + 66 * q^65 - 14 * q^67 - 60 * q^68 - 14 * q^70 - 48 * q^73 - 66 * q^74 - 28 * q^76 - 30 * q^77 - 12 * q^79 - 136 * q^82 - 246 * q^83 + 34 * q^85 + 8 * q^88 - 56 * q^91 - 462 * q^92 + 26 * q^94 + 246 * q^95 - 36 * q^97

Introduction

L-functions

Modular forms

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Database

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