LMFDB - Embedded newform 961.2.g.w.547.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] 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("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [128,16,0,-16,64,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			547.8
Character	$\chi$	$=$	961.547
Dual form			961.2.g.w.448.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.406689 - 1.25166i) q^{2} +(0.826019 + 0.917387i) q^{3} +(0.216779 - 0.157499i) q^{4} +(-0.00363912 - 0.00630315i) q^{5} +(0.812323 - 1.40699i) q^{6} +(0.0830915 + 0.790563i) q^{7} +(-2.41475 - 1.75442i) q^{8} +(0.154294 - 1.46801i) q^{9} +(-0.00640940 + 0.00711836i) q^{10} +(-3.63377 - 1.61786i) q^{11} +(0.323551 + 0.0687729i) q^{12} +(-6.17185 + 1.31187i) q^{13} +(0.955723 - 0.425515i) q^{14} +(0.00277644 - 0.00854501i) q^{15} +(-1.04828 + 3.22626i) q^{16} +(-5.73784 + 2.55465i) q^{17} +(-1.90020 + 0.403899i) q^{18} +(-3.65299 - 0.776467i) q^{19} +(-0.00178162 - 0.000793230i) q^{20} +(-0.656617 + 0.729247i) q^{21} +(-0.547194 + 5.20620i) q^{22} +(0.391299 + 0.284295i) q^{23} +(-0.385148 - 3.66444i) q^{24} +(2.49997 - 4.33008i) q^{25} +(4.15203 + 7.19153i) q^{26} +(4.47029 - 3.24786i) q^{27} +(0.142525 + 0.158290i) q^{28} +(0.500767 + 1.54120i) q^{29} -0.0118246 q^{30} -1.50508 q^{32} +(-1.51736 - 4.66995i) q^{33} +(5.53107 + 6.14288i) q^{34} +(0.00468065 - 0.00340069i) q^{35} +(-0.197762 - 0.342534i) q^{36} +(3.74519 - 6.48685i) q^{37} +(0.513758 + 4.88808i) q^{38} +(-6.30155 - 4.57835i) q^{39} +(-0.00227078 + 0.0216050i) q^{40} +(-2.69583 + 2.99403i) q^{41} +(1.17981 + 0.525284i) q^{42} +(0.686175 + 0.145851i) q^{43} +(-1.04253 + 0.221598i) q^{44} +(-0.00981457 + 0.00436973i) q^{45} +(0.196704 - 0.605393i) q^{46} +(1.33042 - 4.09460i) q^{47} +(-3.82563 + 1.70328i) q^{48} +(6.22895 - 1.32400i) q^{49} +(-6.43650 - 1.36812i) q^{50} +(-7.08317 - 3.15363i) q^{51} +(-1.13131 + 1.25644i) q^{52} +(-0.426443 + 4.05734i) q^{53} +(-5.88323 - 4.27442i) q^{54} +(0.00302614 + 0.0287918i) q^{55} +(1.18633 - 2.05479i) q^{56} +(-2.30512 - 3.99258i) q^{57} +(1.72540 - 1.25358i) q^{58} +(-9.16950 - 10.1838i) q^{59} +(-0.000743956 - 0.00228966i) q^{60} +5.02369 q^{61} +1.17337 q^{63} +(2.70865 + 8.33637i) q^{64} +(0.0307290 + 0.0341280i) q^{65} +(-5.22809 + 3.79843i) q^{66} +(7.26276 + 12.5795i) q^{67} +(-0.841487 + 1.45750i) q^{68} +(0.0624115 + 0.593806i) q^{69} +(-0.00616008 - 0.00447556i) q^{70} +(0.983952 - 9.36168i) q^{71} +(-2.94808 + 3.27417i) q^{72} +(-4.04078 - 1.79907i) q^{73} +(-9.64245 - 2.04957i) q^{74} +(6.03738 - 1.28329i) q^{75} +(-0.914183 + 0.407021i) q^{76} +(0.977083 - 3.00715i) q^{77} +(-3.16776 + 9.74936i) q^{78} +(9.55464 - 4.25400i) q^{79} +(0.0241504 - 0.00513333i) q^{80} +(2.34057 + 0.497504i) q^{81} +(4.84387 + 2.15663i) q^{82} +(1.34369 - 1.49232i) q^{83} +(-0.0274849 + 0.261502i) q^{84} +(0.0369831 + 0.0268698i) q^{85} +(-0.0965039 - 0.918173i) q^{86} +(-1.00024 + 1.73246i) q^{87} +(5.93623 + 10.2819i) q^{88} +(-0.908022 + 0.659717i) q^{89} +(0.00946088 + 0.0105074i) q^{90} +(-1.54994 - 4.77023i) q^{91} +0.129602 q^{92} -5.66611 q^{94} +(0.00839950 + 0.0258510i) q^{95} +(-1.24322 - 1.38074i) q^{96} +(-5.88584 + 4.27631i) q^{97} +(-4.19044 - 7.25806i) q^{98} +(-2.93570 + 5.08477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} - 16 q^{4} + 64 q^{5} - 16 q^{7} + 8 q^{10} - 8 q^{14} + 16 q^{16} - 24 q^{18} - 32 q^{19} - 24 q^{20} - 8 q^{28} - 64 q^{32} + 64 q^{33} + 32 q^{35} + 160 q^{36} - 24 q^{38} + 64 q^{39}+ \cdots - 64 q^{98}+O(q^{100}) $ 128 * q + 16 * q^2 - 16 * q^4 + 64 * q^5 - 16 * q^7 + 8 * q^10 - 8 * q^14 + 16 * q^16 - 24 * q^18 - 32 * q^19 - 24 * q^20 - 8 * q^28 - 64 * q^32 + 64 * q^33 + 32 * q^35 + 160 * q^36 - 24 * q^38 + 64 * q^39 - 32 * q^41 - 16 * q^45 + 64 * q^47 - 16 * q^49 - 32 * q^50 - 32 * q^51 + 192 * q^56 - 64 * q^59 - 128 * q^63 + 32 * q^64 - 64 * q^67 - 32 * q^69 - 176 * q^70 - 48 * q^71 + 48 * q^72 + 40 * q^76 - 64 * q^78 - 40 * q^80 - 16 * q^81 + 88 * q^82 + 128 * q^87 + 40 * q^90 - 256 * q^94 + 96 * q^95 - 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.406689	−	1.25166i	−0.287572	−	0.885057i	−0.985616	−	0.169001i	$-0.945946\pi$
$2$	−0.406689	−	1.25166i	−0.287572	−	0.885057i	0.698043	−	0.716055i	$-0.254054\pi$
$3$	0.826019	+	0.917387i	0.476902	+	0.529654i	0.932808	−	0.360375i	$-0.117351\pi$
$3$	0.826019	+	0.917387i	0.476902	+	0.529654i	−0.455905	+	0.890028i	$0.650684\pi$
$4$	0.216779	−	0.157499i	0.108389	−	0.0787495i
$5$	−0.00363912	−	0.00630315i	−0.00162747	−	0.00281885i	0.865211	−	0.501409i	$-0.167185\pi$
$5$	−0.00363912	−	0.00630315i	−0.00162747	−	0.00281885i	−0.866838	+	0.498590i	$0.833851\pi$
$6$	0.812323	−	1.40699i	0.331630	−	0.574399i
$7$	0.0830915	+	0.790563i	0.0314056	+	0.298805i	0.998939	+	0.0460601i	$0.0146666\pi$
$7$	0.0830915	+	0.790563i	0.0314056	+	0.298805i	−0.967533	+	0.252745i	$0.918667\pi$
$8$	−2.41475	−	1.75442i	−0.853742	−	0.620280i
$9$	0.154294	−	1.46801i	0.0514313	−	0.489336i
$10$	−0.00640940	+	0.00711836i	−0.00202683	+	0.00225102i
$11$	−3.63377	−	1.61786i	−1.09562	−	0.487802i	−0.222316	−	0.974975i	$-0.571362\pi$
$11$	−3.63377	−	1.61786i	−1.09562	−	0.487802i	−0.873306	+	0.487172i	$0.838028\pi$
$12$	0.323551	+	0.0687729i	0.0934011	+	0.0198530i
$13$	−6.17185	+	1.31187i	−1.71176	+	0.363846i	−0.956535	−	0.291616i	$-0.905807\pi$
$13$	−6.17185	+	1.31187i	−1.71176	+	0.363846i	−0.755227	+	0.655463i	$0.772474\pi$
$14$	0.955723	−	0.425515i	0.255428	−	0.113724i
$15$	0.00277644	−	0.00854501i	0.000716874	−	0.00220631i
$16$	−1.04828	+	3.22626i	−0.262069	+	0.806566i
$17$	−5.73784	+	2.55465i	−1.39163	+	0.619594i	−0.959369	−	0.282154i	$-0.908951\pi$
$17$	−5.73784	+	2.55465i	−1.39163	+	0.619594i	−0.432262	+	0.901748i	$0.642284\pi$
$18$	−1.90020	+	0.403899i	−0.447880	+	0.0951999i
$19$	−3.65299	−	0.776467i	−0.838053	−	0.178134i	−0.231159	−	0.972916i	$-0.574252\pi$
$19$	−3.65299	−	0.776467i	−0.838053	−	0.178134i	−0.606894	+	0.794782i	$0.707585\pi$
$20$	−0.00178162		0.000793230i	−0.000398383		0.000177372i
$21$	−0.656617	+	0.729247i	−0.143286	+	0.159135i
$22$	−0.547194	+	5.20620i	−0.116662	+	1.10997i
$23$	0.391299	+	0.284295i	0.0815915	+	0.0592797i	0.627833	−	0.778348i	$-0.283942\pi$
$23$	0.391299	+	0.284295i	0.0815915	+	0.0592797i	−0.546242	+	0.837628i	$0.683942\pi$
$24$	−0.385148	−	3.66444i	−0.0786180	−	0.748000i
$25$	2.49997	−	4.33008i	0.499995	−	0.866016i
$26$	4.15203	+	7.19153i	0.814280	+	1.41038i
$27$	4.47029	−	3.24786i	0.860308	−	0.625050i
$28$	0.142525	+	0.158290i	0.0269348	+	0.0299141i
$29$	0.500767	+	1.54120i	0.0929901	+	0.286194i	0.986725	−	0.162402i	$-0.0519241\pi$
$29$	0.500767	+	1.54120i	0.0929901	+	0.286194i	−0.893735	+	0.448596i	$0.851924\pi$
$30$	−0.0118246			−0.00215886
$31$		0			0
$31$		0			0
$32$	−1.50508			−0.266062
$33$	−1.51736	−	4.66995i	−0.264138	−	0.812934i
$34$	5.53107	+	6.14288i	0.948571	+	1.05349i
$35$	0.00468065	−	0.00340069i	0.000791175	−	0.000574822i
$36$	−0.197762	−	0.342534i	−0.0329604	−	0.0570890i
$37$	3.74519	−	6.48685i	0.615705	−	1.06643i	−0.374556	−	0.927204i	$-0.622205\pi$
$37$	3.74519	−	6.48685i	0.615705	−	1.06643i	0.990260	−	0.139228i	$-0.0444620\pi$
$38$	0.513758	+	4.88808i	0.0833425	+	0.792951i
$39$	−6.30155	−	4.57835i	−1.00906	−	0.733122i
$40$	−0.00227078	+	0.0216050i	−0.000359042	+	0.00341606i
$41$	−2.69583	+	2.99403i	−0.421019	+	0.467589i	−0.915920	−	0.401361i	$-0.868537\pi$
$41$	−2.69583	+	2.99403i	−0.421019	+	0.467589i	0.494902	+	0.868949i	$0.335204\pi$
$42$	1.17981	+	0.525284i	0.182048	+	0.0810531i
$43$	0.686175	+	0.145851i	0.104641	+	0.0222421i	0.259934	−	0.965626i	$-0.416299\pi$
$43$	0.686175	+	0.145851i	0.104641	+	0.0222421i	−0.155294	+	0.987868i	$0.549632\pi$
$44$	−1.04253	+	0.221598i	−0.157168	+	0.0334071i
$45$	−0.00981457	+	0.00436973i	−0.00146307	+	0.000651400i
$46$	0.196704	−	0.605393i	0.0290024	−	0.0892603i
$47$	1.33042	−	4.09460i	0.194061	−	0.597259i	−0.805925	−	0.592017i	$-0.798332\pi$
$47$	1.33042	−	4.09460i	0.194061	−	0.597259i	0.999986	−	0.00524124i	$-0.00166835\pi$
$48$	−3.82563	+	1.70328i	−0.552182	+	0.245847i
$49$	6.22895	−	1.32400i	0.889850	−	0.189143i
$50$	−6.43650	−	1.36812i	−0.910258	−	0.193481i
$51$	−7.08317	−	3.15363i	−0.991842	−	0.441597i
$52$	−1.13131	+	1.25644i	−0.156884	+	0.174238i
$53$	−0.426443	+	4.05734i	−0.0585765	+	0.557318i	0.925396	+	0.379001i	$0.123732\pi$
$53$	−0.426443	+	4.05734i	−0.0585765	+	0.557318i	−0.983973	+	0.178318i	$0.942935\pi$
$54$	−5.88323	−	4.27442i	−0.800606	−	0.581674i
$55$	0.00302614	+	0.0287918i	0.000408044	+	0.00388228i
$56$	1.18633	−	2.05479i	0.158530	−	0.274582i
$57$	−2.30512	−	3.99258i	−0.305320	−	0.528830i
$58$	1.72540	−	1.25358i	0.226557	−	0.164603i
$59$	−9.16950	−	10.1838i	−1.19377	−	1.32581i	−0.932770	−	0.360473i	$-0.882615\pi$
$59$	−9.16950	−	10.1838i	−1.19377	−	1.32581i	−0.260997	−	0.965340i	$-0.584051\pi$
$60$	−0.000743956	−	0.00228966i	−9.60444e−5	−	0.000295594i
$61$	5.02369			0.643218			0.321609	−	0.946873i	$-0.395776\pi$
$61$	5.02369			0.643218			0.321609	+	0.946873i	$0.395776\pi$
$62$		0			0
$63$	1.17337			0.147831
$64$	2.70865	+	8.33637i	0.338581	+	1.04205i
$65$	0.0307290	+	0.0341280i	0.00381147	+	0.00423306i
$66$	−5.22809	+	3.79843i	−0.643534	+	0.467555i
$67$	7.26276	+	12.5795i	0.887287	+	1.53683i	0.843069	+	0.537805i	$0.180746\pi$
$67$	7.26276	+	12.5795i	0.887287	+	1.53683i	0.0442180	+	0.999022i	$0.485920\pi$
$68$	−0.841487	+	1.45750i	−0.102045	+	0.176748i
$69$	0.0624115	+	0.593806i	0.00751346	+	0.0714858i
$70$	−0.00616008	−	0.00447556i	−0.000736270	−	0.000534932i
$71$	0.983952	−	9.36168i	0.116774	−	1.11103i	−0.766524	−	0.642215i	$-0.778016\pi$
$71$	0.983952	−	9.36168i	0.116774	−	1.11103i	0.883298	−	0.468812i	$-0.155318\pi$
$72$	−2.94808	+	3.27417i	−0.347434	+	0.385865i
$73$	−4.04078	−	1.79907i	−0.472937	−	0.210565i	0.156406	−	0.987693i	$-0.450009\pi$
$73$	−4.04078	−	1.79907i	−0.472937	−	0.210565i	−0.629343	+	0.777128i	$0.716676\pi$
$74$	−9.64245	−	2.04957i	−1.12091	−	0.238257i
$75$	6.03738	−	1.28329i	0.697137	−	0.148181i
$76$	−0.914183	+	0.407021i	−0.104864	+	0.0466885i
$77$	0.977083	−	3.00715i	0.111349	−	0.342697i
$78$	−3.16776	+	9.74936i	−0.358678	+	1.10390i
$79$	9.55464	−	4.25400i	1.07498	−	0.478612i	0.208602	−	0.978001i	$-0.433109\pi$
$79$	9.55464	−	4.25400i	1.07498	−	0.478612i	0.866378	+	0.499388i	$0.166442\pi$
$80$	0.0241504	−	0.00513333i	0.00270010	−	0.000573924i
$81$	2.34057	+	0.497504i	0.260064	+	0.0552783i
$82$	4.84387	+	2.15663i	0.534916	+	0.238160i
$83$	1.34369	−	1.49232i	0.147490	−	0.163804i	−0.664873	−	0.746956i	$-0.731514\pi$
$83$	1.34369	−	1.49232i	0.147490	−	0.163804i	0.812363	+	0.583153i	$0.198181\pi$
$84$	−0.0274849	+	0.261502i	−0.00299885	+	0.0285322i
$85$	0.0369831	+	0.0268698i	0.00401138	+	0.00291444i
$86$	−0.0965039	−	0.918173i	−0.0104063	−	0.0990091i
$87$	−1.00024	+	1.73246i	−0.107237	+	0.185739i
$88$	5.93623	+	10.2819i	0.632804	+	1.09605i
$89$	−0.908022	+	0.659717i	−0.0962502	+	0.0699298i	−0.634869	−	0.772619i	$-0.718946\pi$
$89$	−0.908022	+	0.659717i	−0.0962502	+	0.0699298i	0.538619	+	0.842549i	$0.318946\pi$
$90$	0.00946088	+	0.0105074i	0.000997265	+	0.00110757i
$91$	−1.54994	−	4.77023i	−0.162478	−	0.500056i
$92$	0.129602			0.0135119
$93$		0			0
$94$	−5.66611			−0.584414
$95$	0.00839950	+	0.0258510i	0.000861770	+	0.00265226i
$96$	−1.24322	−	1.38074i	−0.126886	−	0.140921i
$97$	−5.88584	+	4.27631i	−0.597616	+	0.434194i	−0.845032	−	0.534716i	$-0.820419\pi$
$97$	−5.88584	+	4.27631i	−0.597616	+	0.434194i	0.247416	+	0.968909i	$0.420419\pi$
$98$	−4.19044	−	7.25806i	−0.423299	−	0.733175i
$99$	−2.93570	+	5.08477i	−0.295048	+	0.511039i
$100$	−0.140042	−	1.33241i	−0.0140042	−	0.133241i
$101$	5.20394	+	3.78088i	0.517811	+	0.376212i	0.815779	−	0.578364i	$-0.196309\pi$
$101$	5.20394	+	3.78088i	0.517811	+	0.376212i	−0.297967	+	0.954576i	$0.596309\pi$
$102$	−1.06663	+	10.1483i	−0.105612	+	1.00483i
$103$	−5.71132	+	6.34306i	−0.562753	+	0.625000i	−0.955623	−	0.294594i	$-0.904816\pi$
$103$	−5.71132	+	6.34306i	−0.562753	+	0.625000i	0.392870	+	0.919594i	$0.371482\pi$
$104$	17.2050	+	7.66016i	1.68709	+	0.751141i
$105$	0.00698606	+	0.00148493i	0.000681770	+	0.000144915i
$106$	5.25184	−	1.11631i	0.510103	−	0.108426i
$107$	−12.3463	+	5.49694i	−1.19356	+	0.531409i	−0.904736	−	0.425972i	$-0.859932\pi$
$107$	−12.3463	+	5.49694i	−1.19356	+	0.531409i	−0.288828	+	0.957381i	$0.593266\pi$
$108$	0.457530	−	1.40813i	0.0440259	−	0.135498i
$109$	3.16153	−	9.73018i	0.302819	−	0.931982i	−0.677662	−	0.735373i	$-0.737007\pi$
$109$	3.16153	−	9.73018i	0.302819	−	0.931982i	0.980482	−	0.196609i	$-0.0629930\pi$
$110$	0.0348068	−	0.0154970i	0.00331870	−	0.00147758i
$111$	9.04455	−	1.92248i	0.858471	−	0.182474i
$112$	−2.63767	−	0.560653i	−0.249236	−	0.0529768i
$113$	−7.60469	−	3.38583i	−0.715389	−	0.318512i	0.0165676	−	0.999863i	$-0.494726\pi$
$113$	−7.60469	−	3.38583i	−0.715389	−	0.318512i	−0.731957	+	0.681351i	$0.761393\pi$
$114$	−4.05988	+	4.50896i	−0.380243	+	0.422303i
$115$	0.000367970	−	0.00350100i	3.43134e−5	−	0.000326470i
$116$	0.351294	+	0.255230i	0.0326168	+	0.0236975i
$117$	0.973553	+	9.26274i	0.0900050	+	0.856340i
$118$	−9.01747	+	15.6187i	−0.830125	+	1.43782i
$119$	−2.49638	−	4.32385i	−0.228843	−	0.396367i
$120$	−0.0216959	+	0.0157630i	−0.00198056	+	0.00143896i
$121$	3.22636	+	3.58324i	0.293306	+	0.325749i
$122$	−2.04308	−	6.28795i	−0.184972	−	0.569284i
$123$	−4.97349			−0.448445
$124$		0			0
$125$	−0.0727821			−0.00650983
$126$	−0.477198	−	1.46866i	−0.0425121	−	0.130839i
$127$	−7.52528	−	8.35767i	−0.667761	−	0.741623i	0.310141	−	0.950691i	$-0.399624\pi$
$127$	−7.52528	−	8.35767i	−0.667761	−	0.741623i	−0.977901	+	0.209067i	$0.932957\pi$
$128$	6.89745	−	5.01129i	0.609654	−	0.442940i
$129$	0.432991	+	0.749963i	0.0381228	+	0.0660306i
$130$	0.0302195	−	0.0523418i	0.00265043	−	0.00459068i
$131$	−0.0674812	−	0.642041i	−0.00589586	−	0.0560954i	0.991178	−	0.132535i	$-0.0423116\pi$
$131$	−0.0674812	−	0.642041i	−0.00589586	−	0.0560954i	−0.997074	+	0.0764392i	$0.975645\pi$
$132$	−1.06444	−	0.773364i	−0.0926479	−	0.0673127i
$133$	0.310313	−	2.95243i	0.0269076	−	0.256009i
$134$	12.7915	−	14.2064i	1.10502	−	1.22725i
$135$	−0.0367397	−	0.0163576i	−0.00316205	−	0.00140783i
$136$	18.3374	+	3.89773i	1.57242	+	0.334227i
$137$	2.82093	−	0.599608i	0.241009	−	0.0512280i	−0.0858236	−	0.996310i	$-0.527352\pi$
$137$	2.82093	−	0.599608i	0.241009	−	0.0512280i	0.326832	+	0.945082i	$0.394019\pi$
$138$	0.717861	−	0.319612i	0.0611084	−	0.0272072i
$139$	−1.04412	+	3.21346i	−0.0885609	+	0.272562i	−0.985522	−	0.169547i	$-0.945770\pi$
$139$	−1.04412	+	3.21346i	−0.0885609	+	0.272562i	0.896961	+	0.442109i	$0.145770\pi$
$140$	0.000479061	−	0.00147440i	4.04880e−5	−	0.000124609i
$141$	4.85528	−	2.16171i	0.408888	−	0.182049i
$142$	−12.1178	+	2.57572i	−1.01690	+	0.216149i
$143$	24.5495	+	5.21815i	2.05293	+	0.436364i
$144$	4.57444	+	2.03667i	0.381203	+	0.169723i
$145$	0.00789208	−	0.00876504i	0.000655401	−	0.000727897i
$146$	−0.608484	+	5.78934i	−0.0503585	+	0.479129i
$147$	6.35985	+	4.62070i	0.524552	+	0.381109i
$148$	−0.209796	−	1.99607i	−0.0172451	−	0.164076i
$149$	5.88496	−	10.1931i	0.482115	−	0.835047i	−0.517674	−	0.855578i	$-0.673202\pi$
$149$	5.88496	−	10.1931i	0.482115	−	0.835047i	0.999789	+	0.0205303i	$0.00653545\pi$
$150$	−4.06157	−	7.03485i	−0.331626	−	0.574393i
$151$	−14.4560	+	10.5029i	−1.17641	+	0.854711i	−0.991762	−	0.128094i	$-0.959114\pi$
$151$	−14.4560	+	10.5029i	−1.17641	+	0.854711i	−0.184647	+	0.982805i	$0.559114\pi$
$152$	7.45880	+	8.28383i	0.604988	+	0.671907i
$153$	2.86494	+	8.81737i	0.231616	+	0.712842i
$154$	−4.16130			−0.335327
$155$		0			0
$156$	−2.08713			−0.167104
$157$	0.822280	+	2.53072i	0.0656251	+	0.201973i	0.978492	−	0.206283i	$-0.0661369\pi$
$157$	0.822280	+	2.53072i	0.0656251	+	0.201973i	−0.912867	+	0.408257i	$0.866137\pi$
$158$	−9.21032	−	10.2291i	−0.732734	−	0.813783i
$159$	−4.07440	+	2.96022i	−0.323121	+	0.234761i
$160$	0.00547716	+	0.00948672i	0.000433008	+	0.000749991i
$161$	−0.192240	+	0.332969i	−0.0151506	+	0.0262416i
$162$	−0.329179	−	3.13193i	−0.0258628	−	0.246068i
$163$	13.6764	+	9.93647i	1.07122	+	0.778284i	0.976130	−	0.217185i	$-0.0696875\pi$
$163$	13.6764	+	9.93647i	1.07122	+	0.778284i	0.0950856	+	0.995469i	$0.469688\pi$
$164$	−0.112843	+	1.07363i	−0.00881159	+	0.0838366i
$165$	−0.0239135	+	0.0265587i	−0.00186167	+	0.00206759i
$166$	−2.41435	−	1.07494i	−0.187390	−	0.0834312i
$167$	−15.1442	−	3.21901i	−1.17190	−	0.249094i	−0.419469	−	0.907770i	$-0.637784\pi$
$167$	−15.1442	−	3.21901i	−1.17190	−	0.249094i	−0.752427	+	0.658675i	$0.771117\pi$
$168$	2.86497	−	0.608967i	0.221037	−	0.0469828i
$169$	24.4946	−	10.9057i	1.88420	−	0.838901i
$170$	0.0185912	−	0.0572179i	0.00142588	−	0.00438841i
$171$	−1.70349	+	5.24281i	−0.130269	+	0.400928i
$172$	0.171719	−	0.0764544i	0.0130935	−	0.00582960i
$173$	−6.75963	+	1.43680i	−0.513925	+	0.109238i	−0.457572	−	0.889173i	$-0.651281\pi$
$173$	−6.75963	+	1.43680i	−0.513925	+	0.109238i	−0.0563533	+	0.998411i	$0.517947\pi$
$174$	2.57523	+	0.547383i	0.195228	+	0.0414970i
$175$	3.63093	+	1.61659i	0.274472	+	0.122203i
$176$	9.02883	−	10.0275i	0.680573	−	0.755853i
$177$	1.76827	−	16.8240i	0.132911	−	1.26457i
$178$	1.19502	+	0.868235i	0.0895708	+	0.0650770i
$179$	1.51369	+	14.4018i	0.113138	+	1.07644i	0.892867	+	0.450321i	$0.148690\pi$
$179$	1.51369	+	14.4018i	0.113138	+	1.07644i	−0.779729	+	0.626117i	$0.784643\pi$
$180$	−0.00143936	+	0.00249305i	−0.000107284	+	0.000185821i
$181$	−8.67667	−	15.0284i	−0.644932	−	1.11706i	−0.984317	−	0.176408i	$-0.943552\pi$
$181$	−8.67667	−	15.0284i	−0.644932	−	1.11706i	0.339385	−	0.940647i	$-0.389781\pi$
$182$	−5.34036	+	3.88000i	−0.395854	+	0.287605i
$183$	4.14967	+	4.60867i	0.306752	+	0.340683i
$184$	−0.446116	−	1.37300i	−0.0328881	−	0.101219i
$185$	−0.0545168			−0.00400815
$186$		0			0
$187$	24.9830			1.82694
$188$	−0.356489	−	1.09716i	−0.0259997	−	0.0800187i
$189$	2.93908	+	3.26418i	0.213787	+	0.237434i
$190$	0.0289407	−	0.0210266i	0.00209958	−	0.00152543i
$191$	−7.45255	−	12.9082i	−0.539248	−	0.934005i	−0.998945	−	0.0459289i	$-0.985375\pi$
$191$	−7.45255	−	12.9082i	−0.539248	−	0.934005i	0.459697	−	0.888076i	$-0.347958\pi$
$192$	−5.41028	+	9.37088i	−0.390453	+	0.676285i
$193$	−1.07408	−	10.2192i	−0.0773142	−	0.735595i	−0.962669	−	0.270680i	$-0.912751\pi$
$193$	−1.07408	−	10.2192i	−0.0773142	−	0.735595i	0.885355	−	0.464915i	$-0.153915\pi$
$194$	7.74619	+	5.62793i	0.556144	+	0.404062i
$195$	−0.00592586	+	0.0563808i	−0.000424360	+	0.00403751i
$196$	1.14177	−	1.26807i	0.0815553	−	0.0905764i
$197$	−13.3425	−	5.94047i	−0.950615	−	0.423241i	−0.127958	−	0.991780i	$-0.540842\pi$
$197$	−13.3425	−	5.94047i	−0.950615	−	0.423241i	−0.822657	+	0.568538i	$0.807509\pi$
$198$	7.55832	+	1.60657i	0.537146	+	0.114174i
$199$	−10.3603	+	2.20215i	−0.734423	+	0.156107i	−0.559916	−	0.828549i	$-0.689167\pi$
$199$	−10.3603	+	2.20215i	−0.734423	+	0.156107i	−0.174507	+	0.984656i	$0.555833\pi$
$200$	−13.6336	+	6.07005i	−0.964039	+	0.429218i
$201$	−5.54106	+	17.0536i	−0.390836	+	1.20287i
$202$	2.61599	−	8.05120i	0.184061	−	0.566481i
$203$	−1.17681	+	0.523949i	−0.0825957	+	0.0367740i
$204$	−2.03217	+	0.431952i	−0.142281	+	0.0302427i
$205$	0.0286823	+	0.00609661i	0.00200326	+	0.000425806i
$206$	10.2621	+	4.56897i	0.714993	+	0.318335i
$207$	0.477723	−	0.530565i	0.0332040	−	0.0368768i
$208$	2.23738	−	21.2872i	0.155134	−	1.47600i
$209$	12.0179	+	8.73151i	0.831295	+	0.603971i
$210$	−0.000982522	−	0.00934807i	−6.78005e−5	−	0.000645078i
$211$	−8.28017	+	14.3417i	−0.570030	+	0.987322i	0.426532	+	0.904473i	$0.359735\pi$
$211$	−8.28017	+	14.3417i	−0.570030	+	0.987322i	−0.996562	+	0.0828491i	$0.973598\pi$
$212$	0.546583	+	0.946709i	0.0375395	+	0.0650203i
$213$	9.40105	−	6.83026i	0.644149	−	0.468002i
$214$	11.9014	+	13.2179i	0.813563	+	0.903554i
$215$	−0.00157776	−	0.00485583i	−0.000107602	−	0.000331165i
$216$	−16.4927			−1.12219
$217$		0			0
$218$	−13.4646			−0.911940
$219$	−1.68732	−	5.19302i	−0.114018	−	0.350912i
$220$	0.00519067	+	0.00576483i	0.000349955	+	0.000388665i
$221$	32.0617	−	23.2942i	2.15671	−	1.56694i
$222$	−6.08460	−	10.5388i	−0.408372	−	0.707321i
$223$	−0.402597	+	0.697318i	−0.0269599	+	0.0466959i	−0.879191	−	0.476470i	$-0.841916\pi$
$223$	−0.402597	+	0.697318i	−0.0269599	+	0.0466959i	0.852231	+	0.523166i	$0.175249\pi$
$224$	−0.125059	−	1.18986i	−0.00835586	−	0.0795007i
$225$	−5.97086	−	4.33809i	−0.398058	−	0.289206i
$226$	−1.14516	+	10.8955i	−0.0761749	+	0.724755i
$227$	9.01627	−	10.0136i	0.598431	−	0.664625i	−0.365489	−	0.930815i	$-0.619098\pi$
$227$	9.01627	−	10.0136i	0.598431	−	0.664625i	0.963920	+	0.266191i	$0.0857650\pi$
$228$	−1.12853	−	0.502453i	−0.0747386	−	0.0332758i
$229$	12.6665	+	2.69236i	0.837028	+	0.177916i	0.606434	−	0.795134i	$-0.292600\pi$
$229$	12.6665	+	2.69236i	0.837028	+	0.177916i	0.230595	+	0.973050i	$0.425933\pi$
$230$	−0.00453171		0.000963245i	−0.000298812		6.35145e-5i
$231$	3.56581	−	1.58760i	0.234613	−	0.104456i
$232$	1.49469	−	4.60017i	0.0981309	−	0.302016i
$233$	3.81820	−	11.7512i	0.250138	−	0.769847i	−0.744610	−	0.667499i	$-0.767365\pi$
$233$	3.81820	−	11.7512i	0.250138	−	0.769847i	0.994749	−	0.102347i	$-0.0326353\pi$
$234$	11.1979	−	4.98561i	0.732027	−	0.325919i
$235$	−0.0306504	+	0.00651495i	−0.00199941	+	0.000424988i
$236$	−3.59168	−	0.763436i	−0.233799	−	0.0496955i
$237$	11.7949	+	5.25141i	0.766159	+	0.341116i
$238$	−4.39674	+	4.88308i	−0.284999	+	0.316523i
$239$	1.66547	−	15.8458i	0.107730	−	1.02498i	−0.798442	−	0.602072i	$-0.794342\pi$
$239$	1.66547	−	15.8458i	0.107730	−	1.02498i	0.906172	−	0.422910i	$-0.138991\pi$
$240$	0.0246580	+	0.0179151i	0.00159166	+	0.00115641i
$241$	−2.14511	−	20.4093i	−0.138178	−	1.31468i	−0.815399	−	0.578900i	$-0.803482\pi$
$241$	−2.14511	−	20.4093i	−0.138178	−	1.31468i	0.677220	−	0.735780i	$-0.263184\pi$
$242$	3.17287	−	5.49557i	0.203960	−	0.353269i
$243$	−6.81142	−	11.7977i	−0.436953	−	0.756825i
$244$	1.08903	−	0.791227i	0.0697180	−	0.0506531i
$245$	−0.0310133	−	0.0344438i	−0.00198137	−	0.00220053i
$246$	2.02266	+	6.22512i	0.128960	+	0.396899i
$247$	23.5643			1.49936
$248$		0			0
$249$	2.47896			0.157097
$250$	0.0295997	+	0.0910984i	0.00187205	+	0.00576157i
$251$	2.83005	+	3.14309i	0.178631	+	0.198390i	0.825810	−	0.563948i	$-0.190718\pi$
$251$	2.83005	+	3.14309i	0.178631	+	0.198390i	−0.647179	+	0.762338i	$0.724052\pi$
$252$	0.254362	−	0.184805i	0.0160233	−	0.0116416i
$253$	−0.961940	−	1.66613i	−0.0604767	−	0.104749i
$254$	−7.40051	+	12.8181i	−0.464349	+	0.804276i
$255$	0.00589874	+	0.0561227i	0.000369393	+	0.00351454i
$256$	5.10513	+	3.70910i	0.319071	+	0.231819i
$257$	−1.93876	+	18.4461i	−0.120937	+	1.15063i	0.750756	+	0.660580i	$0.229690\pi$
$257$	−1.93876	+	18.4461i	−0.120937	+	1.15063i	−0.871692	+	0.490054i	$0.836977\pi$
$258$	0.762606	−	0.846959i	0.0474778	−	0.0527294i
$259$	5.43946	+	2.42180i	0.337991	+	0.150483i
$260$	0.0120365	+	0.00255844i	0.000746474	+	0.000158668i
$261$	2.33976	−	0.497332i	0.144828	−	0.0307841i
$262$	−0.776173	+	0.345574i	−0.0479521	+	0.0213497i
$263$	4.47659	−	13.7775i	0.276038	−	0.849558i	−0.712905	−	0.701261i	$-0.752621\pi$
$263$	4.47659	−	13.7775i	0.276038	−	0.849558i	0.988943	−	0.148297i	$-0.0473792\pi$
$264$	−4.52900	+	13.9388i	−0.278741	+	0.857875i
$265$	0.0271259	−	0.0120772i	0.00166633	−	0.000741898i
$266$	−3.82164	+	0.812315i	−0.234320	+	0.0498062i
$267$	−1.35526	−	0.288069i	−0.0829405	−	0.0176295i
$268$	3.55567	+	1.58308i	0.217197	+	0.0967023i
$269$	10.0645	−	11.1778i	0.613645	−	0.681521i	−0.353591	−	0.935400i	$-0.615040\pi$
$269$	10.0645	−	11.1778i	0.613645	−	0.681521i	0.967236	+	0.253878i	$0.0817063\pi$
$270$	−0.00553248	+	0.0526380i	−0.000336696	+	0.00320345i
$271$	−18.5387	−	13.4691i	−1.12614	−	0.818192i	−0.141016	−	0.990007i	$-0.545037\pi$
$271$	−18.5387	−	13.4691i	−1.12614	−	0.818192i	−0.985129	+	0.171815i	$0.945037\pi$
$272$	−2.22714	−	21.1898i	−0.135040	−	1.28482i
$273$	3.09586	−	5.36219i	0.187370	−	0.324535i
$274$	−1.89775	−	3.28699i	−0.114647	−	0.198575i
$275$	−16.0898	+	11.6899i	−0.970250	+	0.704928i
$276$	0.107053	+	0.118895i	0.00644385	+	0.00715662i
$277$	4.46549	+	13.7434i	0.268306	+	0.825759i	0.990913	+	0.134501i	$0.0429432\pi$
$277$	4.46549	+	13.7434i	0.268306	+	0.825759i	−0.722608	+	0.691258i	$0.757057\pi$
$278$	4.44679			0.266701
$279$		0			0
$280$	−0.0172688			−0.00103201
$281$	−1.79775	−	5.53291i	−0.107245	−	0.330066i	0.883006	−	0.469362i	$-0.155516\pi$
$281$	−1.79775	−	5.53291i	−0.107245	−	0.330066i	−0.990251	+	0.139296i	$0.955516\pi$
$282$	−4.68031	−	5.19801i	−0.278709	−	0.309537i
$283$	−2.08970	+	1.51826i	−0.124220	+	0.0902511i	−0.648160	−	0.761504i	$-0.724461\pi$
$283$	−2.08970	+	1.51826i	−0.124220	+	0.0902511i	0.523941	+	0.851755i	$0.324461\pi$
$284$	−1.26116	−	2.18439i	−0.0748358	−	0.129619i
$285$	−0.0167772	+	0.0290590i	−0.000993797	+	0.00172131i
$286$	−3.45265	−	32.8497i	−0.204159	−	1.94245i
$287$	−2.59097	−	1.88245i	−0.152940	−	0.111117i
$288$	−0.232224	+	2.20946i	−0.0136839	+	0.130194i
$289$	15.0214	−	16.6829i	0.883610	−	0.981348i
$290$	−0.0141805	−	0.00631355i	−0.000832705	−	0.000370744i
$291$	−8.78484	−	1.86728i	−0.514977	−	0.109462i
$292$	−1.15931	+	0.246418i	−0.0678433	+	0.0144205i
$293$	16.8552	−	7.50442i	0.984692	−	0.438413i	0.149734	−	0.988726i	$-0.452158\pi$
$293$	16.8552	−	7.50442i	0.984692	−	0.438413i	0.834958	+	0.550313i	$0.185492\pi$
$294$	3.19707	−	9.83956i	0.186457	−	0.573855i
$295$	−0.0308208	+	0.0948567i	−0.00179446	+	0.00552277i
$296$	−20.4243	+	9.09349i	−1.18714	+	0.528548i
$297$	−21.4986	+	4.56966i	−1.24747	+	0.265159i
$298$	−15.1516	−	3.22057i	−0.877707	−	0.186562i
$299$	−2.78800	−	1.24130i	−0.161234	−	0.0717860i
$300$	1.10666	−	1.22907i	0.0638931	−	0.0709605i
$301$	−0.0582890	+	0.554583i	−0.00335972	+	0.0319656i
$302$	19.0251	+	13.8225i	1.09477	+	0.795397i
$303$	0.830019	+	7.89711i	0.0476834	+	0.453677i
$304$	6.33443	−	10.9716i	0.363304	−	0.629262i
$305$	−0.0182818	−	0.0316651i	−0.00104682	−	0.00181314i
$306$	9.87120	−	7.17185i	0.564299	−	0.409987i
$307$	1.10122	+	1.22303i	0.0628498	+	0.0698018i	0.773750	−	0.633491i	$-0.218379\pi$
$307$	1.10122	+	1.22303i	0.0628498	+	0.0698018i	−0.710900	+	0.703293i	$0.751712\pi$
$308$	−0.261812	−	0.805776i	−0.0149182	−	0.0459133i
$309$	−10.5367			−0.599412
$310$		0			0
$311$	−19.2427			−1.09115			−0.545576	−	0.838061i	$-0.683689\pi$
$311$	−19.2427			−1.09115			−0.545576	+	0.838061i	$0.683689\pi$
$312$	7.18433	+	22.1111i	0.406733	+	1.25179i
$313$	10.3066	+	11.4467i	0.582565	+	0.647004i	0.960320	−	0.278902i	$-0.0899704\pi$
$313$	10.3066	+	11.4467i	0.582565	+	0.647004i	−0.377755	+	0.925906i	$0.623304\pi$
$314$	2.83318	−	2.05843i	0.159886	−	0.116164i
$315$	−0.00427005	−	0.00739594i	−0.000240590	−	0.000416714i
$316$	1.40124	−	2.42702i	0.0788260	−	0.136531i
$317$	3.02357	+	28.7674i	0.169821	+	1.61574i	0.664929	+	0.746906i	$0.268462\pi$
$317$	3.02357	+	28.7674i	0.169821	+	1.61574i	−0.495108	+	0.868831i	$0.664872\pi$
$318$	5.36221	+	3.89587i	0.300698	+	0.218470i
$319$	0.673775	−	6.41054i	0.0377242	−	0.358921i
$320$	0.0426883	−	0.0474101i	0.00238635	−	0.00265031i
$321$	−15.2411	−	6.78578i	−0.850676	−	0.378745i
$322$	0.494945	+	0.105204i	0.0275822	+	0.00586278i
$323$	22.9439	−	4.87687i	1.27663	−	0.271356i
$324$	0.585743	−	0.260790i	0.0325413	−	0.0144883i
$325$	−9.74897	+	30.0042i	−0.540775	+	1.66434i
$326$	6.87504	−	21.1592i	0.380773	−	1.17190i
$327$	11.5378	−	5.13697i	0.638043	−	0.284075i
$328$	11.7625	−	2.50020i	0.649477	−	0.138051i
$329$	3.34758	+	0.711551i	0.184558	+	0.0392291i
$330$	0.0429678	+	0.0191305i	0.00236530	+	0.00105310i
$331$	−1.23596	+	1.37267i	−0.0679343	+	0.0754487i	−0.776154	−	0.630544i	$-0.782832\pi$
$331$	−1.23596	+	1.37267i	−0.0679343	+	0.0754487i	0.708220	+	0.705992i	$0.249499\pi$
$332$	0.0562449	−	0.535135i	0.00308684	−	0.0293693i
$333$	−8.94489	−	6.49884i	−0.490177	−	0.356134i
$334$	2.12989	+	20.2646i	0.116542	+	1.10883i
$335$	0.0528602	−	0.0915565i	0.00288806	−	0.00500227i
$336$	−1.66443	−	2.88287i	−0.0908019	−	0.157274i
$337$	14.9454	−	10.8585i	0.814127	−	0.591498i	−0.100897	−	0.994897i	$-0.532171\pi$
$337$	14.9454	−	10.8585i	0.814127	−	0.591498i	0.915024	+	0.403399i	$0.132171\pi$
$338$	−23.6119	−	26.2237i	−1.28432	−	1.42638i
$339$	−3.17551	−	9.77320i	−0.172470	−	0.530807i
$340$	0.0122491			0.000664301
$341$		0			0
$342$	7.25501			0.392306
$343$	3.28378	+	10.1064i	0.177308	+	0.545697i
$344$	−1.40105	−	1.55603i	−0.0755398	−	0.0838955i
$345$	0.00351572	−	0.00255432i	0.000189280	−	0.000137520i
$346$	4.54745	+	7.87642i	0.244473	+	0.423439i
$347$	6.06471	−	10.5044i	0.325571	−	0.563905i	−0.656057	−	0.754712i	$-0.727777\pi$
$347$	6.06471	−	10.5044i	0.325571	−	0.563905i	0.981628	+	0.190806i	$0.0611102\pi$
$348$	0.0560307	+	0.533097i	0.00300356	+	0.0285770i
$349$	−0.874345	−	0.635249i	−0.0468026	−	0.0340041i	0.564138	−	0.825681i	$-0.309209\pi$
$349$	−0.874345	−	0.635249i	−0.0468026	−	0.0340041i	−0.610941	+	0.791676i	$0.709209\pi$
$350$	0.546766	−	5.20213i	0.0292259	−	0.278066i
$351$	−23.3292	+	25.9097i	−1.24522	+	1.38296i
$352$	5.46910	+	2.43500i	0.291504	+	0.129786i
$353$	−17.9720	−	3.82008i	−0.956556	−	0.203322i	−0.296916	−	0.954904i	$-0.595958\pi$
$353$	−17.9720	−	3.82008i	−0.956556	−	0.203322i	−0.659640	+	0.751582i	$0.729291\pi$
$354$	−21.7770	+	4.62884i	−1.15743	+	0.246020i
$355$	−0.0625888	+	0.0278663i	−0.00332187	+	0.00147899i
$356$	−0.0929352	+	0.286025i	−0.00492556	+	0.0151593i
$357$	1.90459	−	5.86173i	0.100802	−	0.310236i
$358$	17.4105	−	7.75165i	0.920173	−	0.409688i
$359$	27.0886	−	5.75785i	1.42968	−	0.303888i	0.572923	−	0.819609i	$-0.305809\pi$
$359$	27.0886	−	5.75785i	1.42968	−	0.303888i	0.856756	+	0.515721i	$0.172476\pi$
$360$	0.0313660	+	0.00666705i	0.00165313	+	0.000351384i
$361$	−4.61594	−	2.05515i	−0.242944	−	0.108166i
$362$	−15.2818	+	16.9721i	−0.803192	+	0.892036i
$363$	−0.622180	+	5.91964i	−0.0326560	+	0.310701i
$364$	−1.08730	−	0.789970i	−0.0569900	−	0.0414057i
$365$	0.00336509	+	0.0320167i	0.000176137	+	0.00167583i
$366$	4.08086	−	7.06826i	0.213310	−	0.369464i
$367$	2.76280	+	4.78532i	0.144217	+	0.249791i	0.929081	−	0.369877i	$-0.120600\pi$
$367$	2.76280	+	4.78532i	0.144217	+	0.249791i	−0.784863	+	0.619669i	$0.787267\pi$
$368$	−1.32740	+	0.964414i	−0.0691956	+	0.0502735i
$369$	3.97931	+	4.41947i	0.207154	+	0.230068i
$370$	0.0221714	+	0.0682365i	0.00115263	+	0.00354744i
$371$	−3.24301			−0.168369
$372$		0			0
$373$	5.64476			0.292274			0.146137	−	0.989264i	$-0.453316\pi$
$373$	5.64476			0.292274			0.146137	+	0.989264i	$0.453316\pi$
$374$	−10.1603	−	31.2703i	−0.525378	−	1.61695i
$375$	−0.0601194	−	0.0667694i	−0.00310455	−	0.00344795i
$376$	−10.3962	+	7.55332i	−0.536146	+	0.389533i
$377$	−5.11251	−	8.85513i	−0.263308	−	0.456062i
$378$	2.89035	−	5.00623i	0.148663	−	0.257493i
$379$	1.16785	+	11.1113i	0.0599883	+	0.570751i	0.982693	+	0.185243i	$0.0593072\pi$
$379$	1.16785	+	11.1113i	0.0599883	+	0.570751i	−0.922704	+	0.385508i	$0.874026\pi$
$380$	0.00589234	+	0.00428103i	0.000302271	+	0.000219612i
$381$	1.45119	−	13.8072i	0.0743469	−	0.707364i
$382$	−13.1258	+	14.5777i	−0.671574	+	0.745859i
$383$	16.9193	+	7.53297i	0.864537	+	0.384917i	0.790590	−	0.612345i	$-0.209774\pi$
$383$	16.9193	+	7.53297i	0.864537	+	0.384917i	0.0739468	+	0.997262i	$0.476440\pi$
$384$	10.2947	+	2.18821i	0.525350	+	0.111667i
$385$	−0.0225102	+	0.00478470i	−0.00114723	+	0.000243851i
$386$	−12.3542	+	5.50043i	−0.628810	+	0.279964i
$387$	0.319983	−	0.984806i	0.0162656	−	0.0500605i
$388$	−0.602410	+	1.85403i	−0.0305827	+	0.0941239i
$389$	−21.5468	+	9.59325i	−1.09247	+	0.486397i	−0.872253	−	0.489055i	$-0.837342\pi$
$389$	−21.5468	+	9.59325i	−1.09247	+	0.486397i	−0.220212	+	0.975452i	$0.570675\pi$
$390$	0.0729795	−	0.0155123i	0.00369546	−	0.000785495i
$391$	−2.97149	−	0.631609i	−0.150275	−	0.0319419i
$392$	−17.3642	−	7.73103i	−0.877024	−	0.390476i
$393$	0.533259	−	0.592244i	0.0268994	−	0.0298748i
$394$	−2.00919	+	19.1162i	−0.101222	+	0.963061i
$395$	−0.0615841	−	0.0447435i	−0.00309863	−	0.00225129i
$396$	0.164450	+	1.56464i	0.00826394	+	0.0786261i
$397$	−5.45457	+	9.44759i	−0.273757	+	0.474161i	−0.969821	−	0.243819i	$-0.921600\pi$
$397$	−5.45457	+	9.44759i	−0.273757	+	0.474161i	0.696064	+	0.717980i	$0.254933\pi$
$398$	6.96977	+	12.0720i	0.349363	+	0.605114i
$399$	2.96485	−	2.15409i	0.148428	−	0.107839i
$400$	11.3493	+	12.6047i	0.567466	+	0.630235i
$401$	−3.29749	−	10.1486i	−0.164669	−	0.506798i	0.834343	−	0.551246i	$-0.185847\pi$
$401$	−3.29749	−	10.1486i	−0.164669	−	0.506798i	−0.999012	+	0.0444473i	$0.985847\pi$
$402$	23.5988			1.17700
$403$		0			0
$404$	1.72359			0.0857517
$405$	−0.00538180	−	0.0165635i	−0.000267424	−	0.000823045i
$406$	1.13440	+	1.25988i	0.0562993	+	0.0625267i
$407$	−24.1039	+	17.5125i	−1.19479	+	0.868064i
$408$	11.5713	+	20.0420i	0.572864	+	0.992229i
$409$	4.71296	−	8.16309i	0.233041	−	0.403639i	−0.725661	−	0.688053i	$-0.758466\pi$
$409$	4.71296	−	8.16309i	0.233041	−	0.403639i	0.958702	+	0.284414i	$0.0917991\pi$
$410$	−0.00403389	−	0.0383799i	−0.000199219	−	0.00189545i
$411$	2.88022	+	2.09260i	0.142071	+	0.103220i
$412$	−0.239067	+	2.27457i	−0.0117780	+	0.112060i
$413$	7.28899	−	8.09525i	0.358668	−	0.398341i
$414$	−0.858371	−	0.382171i	−0.0421866	−	0.0187827i
$415$	−0.0142962	−	0.00303875i	−0.000701773	−	0.000149167i
$416$	9.28910	−	1.97446i	0.455436	−	0.0968059i
$417$	−3.81045	+	1.69652i	−0.186599	+	0.0830790i
$418$	6.04134	−	18.5933i	0.295491	−	0.909429i
$419$	−9.02532	+	27.7771i	−0.440916	+	1.35700i	0.445986	+	0.895040i	$0.352853\pi$
$419$	−9.02532	+	27.7771i	−0.440916	+	1.35700i	−0.886902	+	0.461958i	$0.847147\pi$
$420$	0.00174831		0.000778396i	8.53086e−5		3.79818e-5i
$421$	−0.583617	+	0.124052i	−0.0284438	+	0.00604591i	−0.222112	−	0.975021i	$-0.571295\pi$
$421$	−0.583617	+	0.124052i	−0.0284438	+	0.00604591i	0.193668	+	0.981067i	$0.437962\pi$
$422$	21.3183	+	4.53135i	1.03776	+	0.220583i
$423$	−5.80563	−	2.58483i	−0.282279	−	0.125679i
$424$	8.14801	−	9.04929i	0.395702	−	0.439472i
$425$	−3.28260	+	31.2319i	−0.159230	+	1.51497i
$426$	−12.3725	−	8.98912i	−0.599448	−	0.435524i
$427$	0.417426	+	3.97154i	0.0202007	+	0.192197i
$428$	−1.81066	+	3.13615i	−0.0875215	+	0.151592i
$429$	15.4913	+	26.8317i	0.747925	+	1.29544i
$430$	−0.00543619	+	0.00394962i	−0.000262156	+	0.000190468i
$431$	−16.0621	−	17.8388i	−0.773684	−	0.859264i	0.219525	−	0.975607i	$-0.429549\pi$
$431$	−16.0621	−	17.8388i	−0.773684	−	0.859264i	−0.993209	+	0.116343i	$0.962883\pi$
$432$	5.79234	+	17.8270i	0.278684	+	0.857702i
$433$	−12.5443			−0.602840			−0.301420	−	0.953492i	$-0.597461\pi$
$433$	−12.5443			−0.602840			−0.301420	+	0.953492i	$0.597461\pi$
$434$		0			0
$435$	0.0145599			0.000698096
$436$	−0.847142	−	2.60723i	−0.0405707	−	0.124864i
$437$	−1.20866	−	1.34236i	−0.0578183	−	0.0642137i
$438$	−5.81369	+	4.22389i	−0.277789	+	0.201825i
$439$	19.5586	+	33.8765i	0.933482	+	1.61684i	0.777319	+	0.629106i	$0.216579\pi$
$439$	19.5586	+	33.8765i	0.933482	+	1.61684i	0.156163	+	0.987731i	$0.450088\pi$
$440$	0.0432054	−	0.0748339i	0.00205974	−	0.00356757i
$441$	−0.982560	−	9.34843i	−0.0467886	−	0.445163i
$442$	−42.1956	−	30.6569i	−2.00704	−	1.45820i
$443$	0.783135	−	7.45103i	0.0372078	−	0.354009i	−0.960040	−	0.279864i	$-0.909711\pi$
$443$	0.783135	−	7.45103i	0.0372078	−	0.354009i	0.997247	−	0.0741449i	$-0.0236227\pi$
$444$	1.65788	−	1.84126i	0.0786794	−	0.0873823i
$445$	0.00746270	+	0.00332261i	0.000353766	+	0.000157507i
$446$	1.03654	+	0.220323i	0.0490814	+	0.0104326i
$447$	14.2121	−	3.02087i	0.672207	−	0.142882i
$448$	−6.36536	+	2.83404i	−0.300735	+	0.133896i
$449$	5.41215	−	16.6569i	0.255415	−	0.786088i	−0.738332	−	0.674437i	$-0.764386\pi$
$449$	5.41215	−	16.6569i	0.255415	−	0.786088i	0.993748	−	0.111650i	$-0.0356137\pi$
$450$	−3.00152	+	9.23774i	−0.141493	+	0.435471i
$451$	14.6399	−	6.51812i	0.689368	−	0.306926i
$452$	−2.18180	+	0.463756i	−0.102623	+	0.0218132i
$453$	−21.5761	−	4.58614i	−1.01373	−	0.215476i
$454$	−16.2004	−	7.21289i	−0.760323	−	0.338518i
$455$	−0.0244270	+	0.0271290i	−0.00114516	+	0.00127183i
$456$	−1.43837	+	13.6852i	−0.0673580	+	0.640868i
$457$	3.95938	+	2.87665i	0.185212	+	0.134564i	0.676528	−	0.736417i	$-0.263484\pi$
$457$	3.95938	+	2.87665i	0.185212	+	0.134564i	−0.491316	+	0.870981i	$0.663484\pi$
$458$	−1.78143	−	16.9491i	−0.0832406	−	0.791981i
$459$	−17.3527	+	30.0557i	−0.809954	+	1.40288i
$460$	−0.000471636	0	0.000816898i	−2.19902e−5	0	3.80881e-5i
$461$	−16.4046	+	11.9187i	−0.764040	+	0.555108i	−0.900147	−	0.435586i	$-0.856541\pi$
$461$	−16.4046	+	11.9187i	−0.764040	+	0.555108i	0.136107	+	0.990694i	$0.456541\pi$
$462$	−3.43731	−	3.81752i	−0.159918	−	0.177607i
$463$	−7.09373	−	21.8323i	−0.329674	−	1.01463i	−0.969287	−	0.245934i	$-0.920905\pi$
$463$	−7.09373	−	21.8323i	−0.329674	−	1.01463i	0.639613	−	0.768697i	$-0.279095\pi$
$464$	−5.49727			−0.255204
$465$		0			0
$466$	−16.2613			−0.753291
$467$	8.43227	+	25.9519i	0.390199	+	1.20091i	0.932638	+	0.360814i	$0.117501\pi$
$467$	8.43227	+	25.9519i	0.390199	+	1.20091i	−0.542439	+	0.840095i	$0.682499\pi$
$468$	1.66992	+	1.85463i	0.0771919	+	0.0857303i
$469$	−9.34139	+	6.78691i	−0.431345	+	0.313391i
$470$	0.0206197	+	0.0357143i	0.000951115	+	0.00164738i
$471$	−1.64243	+	2.84477i	−0.0756791	+	0.131080i
$472$	4.27546	+	40.6783i	0.196794	+	1.87237i
$473$	−2.25743	−	1.64012i	−0.103797	−	0.0754128i
$474$	1.77614	−	16.8989i	0.0815808	−	0.776190i
$475$	−12.4945	+	13.8766i	−0.573289	+	0.636702i
$476$	−1.22216	−	0.544143i	−0.0560178	−	0.0249407i
$477$	5.89041	+	1.25204i	0.269703	+	0.0573272i
$478$	−20.5109	+	4.35973i	−0.938148	+	0.199409i
$479$	−31.4188	+	13.9885i	−1.43556	+	0.639153i	−0.969386	−	0.245540i	$-0.921035\pi$
$479$	−31.4188	+	13.9885i	−1.43556	+	0.639153i	−0.466174	+	0.884693i	$0.654368\pi$
$480$	−0.00417876	+	0.0128609i	−0.000190733	+	0.000587016i
$481$	−14.6048	+	44.9491i	−0.665923	+	2.04950i
$482$	−24.6731	+	10.9852i	−1.12383	+	0.500361i
$483$	−0.464255	+	0.0986804i	−0.0211243	+	0.00449012i
$484$	1.26376	+	0.268621i	0.0574438	+	0.0122101i
$485$	0.0483735	+	0.0215373i	0.00219653	+	0.000977957i
$486$	−11.9966	+	13.3236i	−0.544177	+	0.604370i
$487$	−2.85444	+	27.1582i	−0.129347	+	1.23066i	0.716636	+	0.697447i	$0.245681\pi$
$487$	−2.85444	+	27.1582i	−0.129347	+	1.23066i	−0.845984	+	0.533209i	$0.820986\pi$
$488$	−12.1309	−	8.81365i	−0.549142	−	0.398975i
$489$	2.18136	+	20.7542i	0.0986444	+	0.938539i
$490$	−0.0304991	+	0.0528260i	−0.00137781	+	0.00238644i
$491$	17.7513	+	30.7461i	0.801103	+	1.38755i	0.918891	+	0.394512i	$0.129087\pi$
$491$	17.7513	+	30.7461i	0.801103	+	1.38755i	−0.117787	+	0.993039i	$0.537580\pi$
$492$	−1.07815	+	0.783320i	−0.0486066	+	0.0353148i
$493$	−6.81056	−	7.56389i	−0.306732	−	0.340661i
$494$	−9.58334	−	29.4945i	−0.431175	−	1.32702i
$495$	0.0427334			0.00192073
$496$		0			0
$497$	7.48275			0.335647
$498$	−1.00816	−	3.10281i	−0.0451769	−	0.139040i
$499$	−7.49946	−	8.32899i	−0.335722	−	0.372857i	0.551520	−	0.834162i	$-0.314048\pi$
$499$	−7.49946	−	8.32899i	−0.335722	−	0.372857i	−0.887242	+	0.461305i	$0.847381\pi$
$500$	−0.0157776	+	0.0114631i	−0.000705596	+	0.000512646i
$501$	−9.55635	−	16.5521i	−0.426946	−	0.739493i
$502$	2.78312	−	4.82051i	0.124217	−	0.215150i
$503$	0.177630	+	1.69004i	0.00792013	+	0.0753550i	0.997768	−	0.0667759i	$-0.0212713\pi$
$503$	0.177630	+	1.69004i	0.00792013	+	0.0753550i	−0.989848	+	0.142131i	$0.954605\pi$
$504$	−2.83340	−	2.05858i	−0.126210	−	0.0916966i
$505$	0.00489369	−	0.0465603i	0.000217766	−	0.00207191i
$506$	−1.69422	+	1.88162i	−0.0753171	+	0.0836481i
$507$	30.2378	+	13.4627i	1.34291	+	0.597901i
$508$	−2.94765	−	0.626541i	−0.130781	−	0.0277983i
$509$	−40.6010	+	8.63000i	−1.79961	+	0.382518i	−0.981334	−	0.192313i	$-0.938401\pi$
$509$	−40.6010	+	8.63000i	−1.79961	+	0.382518i	−0.818272	+	0.574831i	$0.805068\pi$
$510$	0.0678476	−	0.0302077i	0.00300434	−	0.00133762i
$511$	1.08652	−	3.34398i	0.0480650	−	0.147929i
$512$	7.83551	−	24.1152i	0.346284	−	1.06575i
$513$	−18.8518	+	8.39335i	−0.832326	+	0.370576i
$514$	23.8767	−	5.07514i	1.05315	−	0.223855i
$515$	0.0607654	+	0.0129161i	0.00267765	+	0.000569151i
$516$	0.211982	+	0.0943804i	0.00933198	+	0.00415486i
$517$	−11.4589	+	12.7264i	−0.503962	+	0.559706i
$518$	0.819105	−	7.79327i	0.0359894	−	0.342417i
$519$	−6.90168	−	5.01437i	−0.302950	−	0.220106i
$520$	−0.0143280	−	0.136322i	−0.000628325	−	0.00597812i
$521$	16.2836	−	28.2041i	0.713399	−	1.23564i	−0.250175	−	0.968201i	$-0.580488\pi$
$521$	16.2836	−	28.2041i	0.713399	−	1.23564i	0.963574	−	0.267443i	$-0.0861787\pi$
$522$	−1.57405	−	2.72633i	−0.0688941	−	0.119328i
$523$	11.7584	−	8.54294i	0.514157	−	0.373557i	−0.300241	−	0.953863i	$-0.597067\pi$
$523$	11.7584	−	8.54294i	0.514157	−	0.373557i	0.814398	+	0.580306i	$0.197067\pi$
$524$	−0.115749	−	0.128553i	−0.00505653	−	0.00561585i
$525$	1.51617	+	4.66630i	0.0661712	+	0.203654i
$526$	−19.0653			−0.831288
$527$		0			0
$528$	16.6571			0.724907
$529$	−7.03510	−	21.6518i	−0.305874	−	0.941383i
$530$	−0.0261484	−	0.0290407i	−0.00113581	−	0.00126145i
$531$	−16.3646	+	11.8896i	−0.710165	+	0.515965i
$532$	−0.397736	−	0.688899i	−0.0172440	−	0.0298676i
$533$	12.7105	−	22.0153i	0.550554	−	0.953587i
$534$	0.190604	+	1.81348i	0.00824825	+	0.0784768i
$535$	0.0795778	+	0.0578167i	0.00344045	+	0.00249963i
$536$	4.53190	−	43.1181i	0.195748	−	1.86242i
$537$	−11.9617	+	13.2848i	−0.516183	+	0.573280i
$538$	−18.0839	−	8.05147i	−0.779652	−	0.347124i
$539$	−24.7766	−	5.26643i	−1.06720	−	0.226841i
$540$	−0.0105407	+	0.00224049i	−0.000453599	+	9.64154e-5i
$541$	−7.67210	+	3.41584i	−0.329849	+	0.146858i	−0.564978	−	0.825106i	$-0.691115\pi$
$541$	−7.67210	+	3.41584i	−0.329849	+	0.146858i	0.235129	+	0.971964i	$0.424449\pi$
$542$	−9.31930	+	28.6819i	−0.400298	+	1.23199i
$543$	6.61980	−	20.3736i	0.284083	−	0.874317i
$544$	8.63589	−	3.84495i	0.370261	−	0.164851i
$545$	−0.0728360	+	0.0154818i	−0.00311995	+	0.000663166i
$546$	−7.97069	−	1.69422i	−0.341114	−	0.0725061i
$547$	11.4127	+	5.08125i	0.487971	+	0.217259i	0.635948	−	0.771732i	$-0.280609\pi$
$547$	11.4127	+	5.08125i	0.487971	+	0.217259i	−0.147977	+	0.988991i	$0.547276\pi$
$548$	0.517081	−	0.574276i	0.0220886	−	0.0245319i
$549$	0.775125	−	7.37482i	0.0330815	−	0.314750i
$550$	21.1753	+	15.3848i	0.902918	+	0.656008i
$551$	−0.632604	−	6.01883i	−0.0269498	−	0.256411i
$552$	0.891075	−	1.54339i	0.0379267	−	0.0656909i
$553$	4.15696	+	7.20007i	0.176772	+	0.306178i
$554$	15.3860	−	11.1786i	0.653687	−	0.474931i
$555$	−0.0450319	−	0.0500130i	−0.00191150	−	0.00212293i
$556$	0.279775	+	0.861058i	0.0118651	+	0.0365170i
$557$	16.8308			0.713144			0.356572	−	0.934268i	$-0.383946\pi$
$557$	16.8308			0.713144			0.356572	+	0.934268i	$0.383946\pi$
$558$		0			0
$559$	−4.42630			−0.187213
$560$	0.00606492	+	0.0186659i	0.000256290	+	0.000788778i
$561$	20.6365	+	22.9191i	0.871272	+	0.967646i
$562$	−6.19419	+	4.50034i	−0.261286	+	0.189835i
$563$	8.36744	+	14.4928i	0.352645	+	0.610800i	0.986712	−	0.162479i	$-0.0519488\pi$
$563$	8.36744	+	14.4928i	0.352645	+	0.610800i	−0.634067	+	0.773278i	$0.718616\pi$
$564$	0.712055	−	1.23331i	0.0299829	−	0.0519319i
$565$	0.00633305	+	0.0602550i	0.000266433	+	0.00253495i
$566$	2.75020	+	1.99814i	0.115600	+	0.0839880i
$567$	−0.198827	+	1.89171i	−0.00834993	+	0.0794443i
$568$	−18.8003	+	20.8798i	−0.788842	+	0.876098i
$569$	−4.87676	−	2.17127i	−0.204444	−	0.0910245i	0.301960	−	0.953321i	$-0.402359\pi$
$569$	−4.87676	−	2.17127i	−0.204444	−	0.0910245i	−0.506404	+	0.862296i	$0.669026\pi$
$570$	0.0431951	+	0.00918139i	0.00180924	+	0.000384566i
$571$	35.2139	−	7.48495i	1.47366	−	0.313235i	0.600087	−	0.799934i	$-0.295132\pi$
$571$	35.2139	−	7.48495i	1.47366	−	0.313235i	0.873570	+	0.486699i	$0.161799\pi$
$572$	6.14366	−	2.73533i	0.256879	−	0.114370i
$573$	5.68587	−	17.4993i	0.237530	−	0.731044i
$574$	−1.30247	+	4.00858i	−0.0543639	+	0.167315i
$575$	2.20926	−	0.983626i	0.0921325	−	0.0410200i
$576$	12.6558	−	2.69007i	0.527324	−	0.112086i
$577$	−2.23923	−	0.475963i	−0.0932203	−	0.0198146i	0.161065	−	0.986944i	$-0.448507\pi$
$577$	−2.23923	−	0.475963i	−0.0932203	−	0.0198146i	−0.254286	+	0.967129i	$0.581840\pi$
$578$	−26.9904	−	12.0169i	−1.12265	−	0.499836i
$579$	8.48776	−	9.42662i	0.352739	−	0.391757i
$580$	0.000330350	−	0.00314307i	1.37170e−5	−	0.000130509i
$581$	1.29143	+	0.938275i	0.0535773	+	0.0389262i
$582$	1.23550	+	11.7550i	0.0512133	+	0.487262i
$583$	8.11379	−	14.0535i	0.336039	−	0.582036i
$584$	6.60114	+	11.4335i	0.273157	+	0.473122i
$585$	0.0548415	−	0.0398447i	0.00226742	−	0.00164738i
$586$	−16.2478	−	18.0450i	−0.671191	−	0.745433i
$587$	−0.648214	−	1.99500i	−0.0267547	−	0.0823424i	0.936788	−	0.349899i	$-0.113784\pi$
$587$	−0.648214	−	1.99500i	−0.0267547	−	0.0823424i	−0.963542	+	0.267556i	$0.913784\pi$
$588$	2.10644			0.0868680
$589$		0			0
$590$	0.131263			0.00540400
$591$	−5.57146	−	17.1472i	−0.229179	−	0.705341i
$592$	17.0023	+	18.8830i	0.698791	+	0.776085i
$593$	5.37256	−	3.90340i	0.220625	−	0.160293i	−0.471983	−	0.881608i	$-0.656462\pi$
$593$	5.37256	−	3.90340i	0.220625	−	0.160293i	0.692608	+	0.721314i	$0.256462\pi$
$594$	14.4629	+	25.0505i	0.593419	+	1.02783i
$595$	−0.0181693	+	0.0314701i	−0.000744867	+	0.00129015i
$596$	−0.329661	−	3.13651i	−0.0135034	−	0.128477i
$597$	−10.5780	−	7.68540i	−0.432930	−	0.314542i
$598$	−0.419833	+	3.99444i	−0.0171682	+	0.163345i
$599$	20.5576	−	22.8315i	0.839960	−	0.932870i	−0.158555	−	0.987350i	$-0.550683\pi$
$599$	20.5576	−	22.8315i	0.839960	−	0.932870i	0.998515	+	0.0544800i	$0.0173501\pi$
$600$	−16.8302	−	7.49328i	−0.687089	−	0.305912i
$601$	16.5897	+	3.52624i	0.676707	+	0.143839i	0.533430	−	0.845844i	$-0.320903\pi$
$601$	16.5897	+	3.52624i	0.676707	+	0.143839i	0.143277	+	0.989683i	$0.454236\pi$
$602$	0.717855	−	0.152585i	0.0292576	−	0.00621889i
$603$	19.5874	−	8.72085i	0.797659	−	0.355141i
$604$	−1.47955	+	4.55360i	−0.0602022	+	0.185283i
$605$	0.0108446	−	0.0333761i	0.000440894	−	0.00135693i
$606$	9.54693	−	4.25057i	0.387817	−	0.172667i
$607$	−17.5251	+	3.72507i	−0.711321	+	0.151196i	−0.549341	−	0.835598i	$-0.685121\pi$
$607$	−17.5251	+	3.72507i	−0.711321	+	0.151196i	−0.161980	+	0.986794i	$0.551788\pi$
$608$	5.49803	+	1.16864i	0.222974	+	0.0473947i
$609$	−1.45273	−	0.646797i	−0.0588676	−	0.0262095i
$610$	−0.0321989	+	0.0357605i	−0.00130369	+	0.00144790i
$611$	−2.83956	+	27.0166i	−0.114876	+	1.09297i
$612$	2.00978	+	1.46019i	0.0812407	+	0.0590248i
$613$	−1.84539	−	17.5577i	−0.0745348	−	0.709151i	−0.966434	−	0.256916i	$-0.917294\pi$
$613$	−1.84539	−	17.5577i	−0.0745348	−	0.709151i	0.891899	−	0.452235i	$-0.149373\pi$
$614$	1.08296	−	1.87574i	0.0437047	−	0.0756987i
$615$	0.0180992	+	0.0313487i	0.000729828	+	0.00126410i
$616$	−7.63520	+	5.54730i	−0.307631	+	0.223507i
$617$	13.6116	+	15.1173i	0.547984	+	0.608598i	0.951979	−	0.306164i	$-0.0990454\pi$
$617$	13.6116	+	15.1173i	0.547984	+	0.608598i	−0.403995	+	0.914761i	$0.632379\pi$
$618$	4.28516	+	13.1884i	0.172374	+	0.530513i
$619$	−16.4294			−0.660354			−0.330177	−	0.943919i	$-0.607108\pi$
$619$	−16.4294			−0.660354			−0.330177	+	0.943919i	$0.607108\pi$
$620$		0			0
$621$	2.67257			0.107247
$622$	7.82578	+	24.0853i	0.313785	+	0.965731i
$623$	−0.596996	−	0.663032i	−0.0239182	−	0.0265638i
$624$	21.3767	−	15.5311i	0.855754	−	0.621742i
$625$	−12.4996	−	21.6499i	−0.499984	−	0.865998i
$626$	10.1357	−	17.5556i	0.405106	−	0.701664i
$627$	1.91683	+	18.2375i	0.0765510	+	0.728334i
$628$	0.576838	+	0.419098i	0.0230184	+	0.0167238i
$629$	−4.91764	+	46.7882i	−0.196079	+	1.86557i
$630$	−0.00752062	+	0.00835250i	−0.000299629	+	0.000332771i
$631$	−9.51541	−	4.23653i	−0.378803	−	0.168654i	0.208498	−	0.978023i	$-0.433143\pi$
$631$	−9.51541	−	4.23653i	−0.378803	−	0.168654i	−0.587300	+	0.809369i	$0.699809\pi$
$632$	−30.5353	−	6.49048i	−1.21463	−	0.258177i
$633$	−19.9964	+	4.25038i	−0.794787	+	0.168937i
$634$	34.7773	−	15.4839i	1.38118	−	0.614943i
$635$	−0.0252942	+	0.0778476i	−0.00100377	+	0.00308929i
$636$	−0.417011	+	1.28343i	−0.0165356	+	0.0508912i
$637$	−36.7072	+	16.3431i	−1.45439	+	0.647537i
$638$	−8.29783	+	1.76376i	−0.328514	+	0.0698279i
$639$	−13.5912	−	2.88890i	−0.537660	−	0.114283i
$640$	−0.0566876	−	0.0252390i	−0.00224077	−	0.000997657i
$641$	15.2653	−	16.9539i	0.602945	−	0.669638i	−0.361974	−	0.932188i	$-0.617897\pi$
$641$	15.2653	−	16.9539i	0.602945	−	0.669638i	0.964918	+	0.262551i	$0.0845636\pi$
$642$	−2.29510	+	21.8364i	−0.0905802	+	0.861814i
$643$	−19.4065	−	14.0996i	−0.765316	−	0.556034i	0.135220	−	0.990816i	$-0.456826\pi$
$643$	−19.4065	−	14.0996i	−0.765316	−	0.556034i	−0.900536	+	0.434781i	$0.856826\pi$
$644$	0.0107688	+	0.102458i	0.000424350	+	0.00403742i
$645$	0.00315142	−	0.00545842i	0.000124087	−	0.000214925i
$646$	−15.4352	−	26.7345i	−0.607290	−	1.05186i
$647$	15.9324	−	11.5756i	0.626367	−	0.455082i	−0.228773	−	0.973480i	$-0.573471\pi$
$647$	15.9324	−	11.5756i	0.626367	−	0.455082i	0.855140	+	0.518398i	$0.173471\pi$
$648$	−4.77906	−	5.30769i	−0.187739	−	0.208506i
$649$	16.8439	+	51.8403i	0.661183	+	2.03491i
$650$	41.5199			1.62854
$651$		0			0
$652$	4.52973			0.177398
$653$	−1.53522	−	4.72491i	−0.0600776	−	0.184900i	0.916514	−	0.400003i	$-0.130991\pi$
$653$	−1.53522	−	4.72491i	−0.0600776	−	0.184900i	−0.976591	+	0.215104i	$0.930991\pi$
$654$	−11.1220	−	12.3523i	−0.434906	−	0.483012i
$655$	−0.00380131	+	0.00276181i	−0.000148529	+	0.000107913i
$656$	−6.83354	−	11.8360i	−0.266805	−	0.462120i
$657$	−3.26452	+	5.65431i	−0.127361	+	0.220596i
$658$	−0.470805	−	4.47941i	−0.0183539	−	0.174626i
$659$	−1.24888	−	0.907368i	−0.0486496	−	0.0353460i	0.563195	−	0.826324i	$-0.309572\pi$
$659$	−1.24888	−	0.907368i	−0.0486496	−	0.0353460i	−0.611844	+	0.790978i	$0.709572\pi$
$660$	−0.00100098	+	0.00952371i	−3.89632e−5	+	0.000370710i
$661$	10.7306	−	11.9176i	0.417373	−	0.463540i	−0.497392	−	0.867526i	$-0.665709\pi$
$661$	10.7306	−	11.9176i	0.417373	−	0.463540i	0.914765	+	0.403986i	$0.132376\pi$
$662$	2.22076	+	0.988747i	0.0863124	+	0.0384288i
$663$	47.8534	+	10.1716i	1.85847	+	0.395030i
$664$	−5.86284	+	1.24618i	−0.227522	+	0.0483613i
$665$	−0.0197389	+	0.00878833i	−0.000765442	+	0.000340797i
$666$	−4.49655	+	13.8390i	−0.174238	+	0.536249i
$667$	−0.242207	+	0.745437i	−0.00937830	+	0.0288634i
$668$	−3.78994	+	1.68739i	−0.146637	+	0.0652871i
$669$	−0.972263	+	0.206661i	−0.0375898	+	0.00798997i
$670$	−0.136095	−	0.0289279i	−0.00525782	−	0.00111758i
$671$	−18.2549	−	8.12762i	−0.704724	−	0.313763i
$672$	0.988258	−	1.09757i	0.0381229	−	0.0423398i
$673$	4.18877	−	39.8535i	0.161465	−	1.53624i	−0.550984	−	0.834516i	$-0.685747\pi$
$673$	4.18877	−	39.8535i	0.161465	−	1.53624i	0.712449	−	0.701724i	$-0.247586\pi$
$674$	−19.6692	−	14.2905i	−0.757630	−	0.550450i
$675$	−2.88787	−	27.4763i	−0.111154	−	1.05756i
$676$	3.59228	−	6.22201i	0.138164	−	0.239308i
$677$	−18.2734	−	31.6504i	−0.702303	−	1.21642i	−0.967656	−	0.252273i	$-0.918822\pi$
$677$	−18.2734	−	31.6504i	−0.702303	−	1.21642i	0.265354	−	0.964151i	$-0.414511\pi$
$678$	−10.9413	+	7.94930i	−0.420197	+	0.305291i
$679$	−3.86975	−	4.29780i	−0.148508	−	0.164934i
$680$	−0.0421640	−	0.129767i	−0.00161692	−	0.00497635i
$681$	16.6339			0.637414
$682$		0			0
$683$	−37.5447			−1.43661			−0.718303	−	0.695730i	$-0.755081\pi$
$683$	−37.5447			−1.43661			−0.718303	+	0.695730i	$0.755081\pi$
$684$	0.456457	+	1.40483i	0.0174531	+	0.0537150i
$685$	−0.0140451	−	0.0155987i	−0.000536637	−	0.000595996i
$686$	11.3143	−	8.22035i	0.431984	−	0.313854i
$687$	7.99287	+	13.8441i	0.304947	+	0.528183i
$688$	−1.18985	+	2.06089i	−0.0453628	+	0.0785706i
$689$	−2.69074	−	25.6007i	−0.102509	−	0.975310i
$690$	−0.00462695	−	0.00336167i	−0.000176145	−	0.000127977i
$691$	−0.194346	+	1.84907i	−0.00739325	+	0.0703421i	−0.997596	−	0.0692920i	$-0.977926\pi$
$691$	−0.194346	+	1.84907i	−0.00739325	+	0.0703421i	0.990203	+	0.139634i	$0.0445926\pi$
$692$	−1.23905	+	1.37610i	−0.0471016	+	0.0523116i
$693$	−4.26376	−	1.89835i	−0.161967	−	0.0721123i
$694$	−15.6144	−	3.31894i	−0.592713	−	0.125985i
$695$	0.0240546	−	0.00511297i	0.000912444	−	0.000193946i
$696$	5.45477	−	2.42862i	0.206763	−	0.0920566i
$697$	7.81958	−	24.0662i	0.296188	−	0.911572i
$698$	−0.439529	+	1.35273i	−0.0166364	+	0.0512016i
$699$	13.9343	−	6.20395i	0.527044	−	0.234655i
$700$	1.04172	−	0.221424i	0.0393733	−	0.00836905i
$701$	−42.2482	−	8.98013i	−1.59569	−	0.339175i	−0.677565	−	0.735463i	$-0.736965\pi$
$701$	−42.2482	−	8.98013i	−1.59569	−	0.339175i	−0.918126	+	0.396288i	$0.870298\pi$
$702$	41.9179	+	18.6630i	1.58209	+	0.704391i
$703$	−18.7179	+	20.7884i	−0.705961	+	0.784049i
$704$	3.64445	−	34.6746i	0.137355	−	1.30685i
$705$	−0.0312946	−	0.0227368i	−0.00117862	−	0.000856318i
$706$	2.52760	+	24.0485i	0.0951273	+	0.905076i
$707$	−2.55662	+	4.42820i	−0.0961517	+	0.166540i
$708$	−2.26643	−	3.92558i	−0.0851778	−	0.147532i
$709$	39.2460	−	28.5139i	1.47392	−	1.07086i	0.494460	−	0.869200i	$-0.335366\pi$
$709$	39.2460	−	28.5139i	1.47392	−	1.07086i	0.979455	−	0.201662i	$-0.0646342\pi$
$710$	0.0603333	+	0.0670069i	0.00226427	+	0.00251473i
$711$	−4.77068	−	14.6826i	−0.178915	−	0.550642i
$712$	3.35006			0.125549
$713$		0			0
$714$	−8.11147			−0.303564
$715$	−0.0564478	−	0.173728i	−0.00211103	−	0.00649708i
$716$	2.59640	+	2.88359i	0.0970319	+	0.107765i
$717$	15.9125	−	11.5611i	0.594262	−	0.431757i
$718$	−18.2235	−	31.5640i	−0.680094	−	1.17796i
$719$	−13.3329	+	23.0932i	−0.497233	+	0.861233i	−0.999995	−	0.00319224i	$-0.998984\pi$
$719$	−13.3329	+	23.0932i	−0.497233	+	0.861233i	0.502762	+	0.864425i	$0.332317\pi$
$720$	−0.00380951	−	0.0362451i	−0.000141972	−	0.00135077i
$721$	−5.48915	−	3.98810i	−0.204427	−	0.148525i
$722$	−0.695095	+	6.61339i	−0.0258688	+	0.246125i
$723$	16.9513	−	18.8264i	0.630427	−	0.700160i
$724$	−4.24788	−	1.89128i	−0.157871	−	0.0702888i
$725$	7.92544	+	1.68460i	0.294343	+	0.0625646i
$726$	7.66241	−	1.62870i	0.284379	−	0.0604466i
$727$	−33.5884	+	14.9545i	−1.24572	+	0.554632i	−0.920403	−	0.390972i	$-0.872139\pi$
$727$	−33.5884	+	14.9545i	−1.24572	+	0.554632i	−0.325321	+	0.945604i	$0.605472\pi$
$728$	−4.62625	+	14.2381i	−0.171460	+	0.527700i
$729$	7.41503	−	22.8211i	0.274631	−	0.845226i
$730$	0.0387054	−	0.0172328i	0.00143255	−	0.000637813i
$731$	−4.30976	+	0.916068i	−0.159402	+	0.0338820i
$732$	1.62542	+	0.345494i	0.0600773	+	0.0127698i
$733$	45.3017	+	20.1696i	1.67326	+	0.744981i	0.999984	+	0.00558543i	$0.00177791\pi$
$733$	45.3017	+	20.1696i	1.67326	+	0.744981i	0.673271	+	0.739396i	$0.264889\pi$
$734$	4.86598	−	5.40422i	0.179607	−	0.199473i
$735$	0.00598068	−	0.0569024i	0.000220601	−	0.00209888i
$736$	−0.588935	−	0.427886i	−0.0217084	−	0.0157721i
$737$	−6.03939	−	57.4610i	−0.222464	−	2.11660i
$738$	3.91333	−	6.77808i	0.144052	−	0.249505i
$739$	15.4840	+	26.8190i	0.569587	+	0.986554i	0.996607	+	0.0823114i	$0.0262302\pi$
$739$	15.4840	+	26.8190i	0.569587	+	0.986554i	−0.427020	+	0.904242i	$0.640436\pi$
$740$	−0.0118181	+	0.00858634i	−0.000434441	+	0.000315640i
$741$	19.4646	+	21.6176i	0.715049	+	0.794142i
$742$	1.31890	+	4.05915i	0.0484183	+	0.149016i
$743$	−45.6267			−1.67388			−0.836940	−	0.547294i	$-0.815658\pi$
$743$	−45.6267			−1.67388			−0.836940	+	0.547294i	$0.815658\pi$
$744$		0			0
$745$	−0.0856644			−0.00313850
$746$	−2.29566	−	7.06531i	−0.0840501	−	0.258679i
$747$	−1.98342	−	2.20281i	−0.0725695	−	0.0805966i
$748$	5.41579	−	3.93480i	0.198021	−	0.143871i
$749$	−5.37155	−	9.30380i	−0.196272	−	0.339953i
$750$	−0.0591226	+	0.102403i	−0.00215885	+	0.00373924i
$751$	−2.98841	−	28.4328i	−0.109049	−	1.03753i	−0.903028	−	0.429582i	$-0.858661\pi$
$751$	−2.98841	−	28.4328i	−0.109049	−	1.03753i	0.793979	−	0.607945i	$-0.208006\pi$
$752$	11.8156	+	8.58455i	0.430871	+	0.313046i
$753$	−0.545753	+	5.19250i	−0.0198884	+	0.189225i
$754$	−9.00441	+	10.0004i	−0.327921	+	0.364193i
$755$	0.118808	+	0.0528968i	0.00432387	+	0.00192511i
$756$	1.15123	+	0.244702i	0.0418700	+	0.00889974i
$757$	−7.74122	+	1.64545i	−0.281360	+	0.0598048i	−0.346430	−	0.938076i	$-0.612606\pi$
$757$	−7.74122	+	1.64545i	−0.281360	+	0.0598048i	0.0650704	+	0.997881i	$0.479273\pi$
$758$	13.4327	−	5.98060i	0.487896	−	0.217225i
$759$	0.733904	−	2.25873i	0.0266390	−	0.0819865i
$760$	0.0250707	−	0.0771598i	0.000909411	−	0.00279888i
$761$	20.8933	−	9.30229i	0.757381	−	0.337208i	0.00854512	−	0.999963i	$-0.497280\pi$
$761$	20.8933	−	9.30229i	0.757381	−	0.337208i	0.748835	+	0.662756i	$0.230613\pi$
$762$	−17.8721	+	3.79883i	−0.647437	+	0.137617i
$763$	7.95502	+	1.69089i	0.287991	+	0.0612144i
$764$	−3.64858	−	1.62445i	−0.132001	−	0.0587707i
$765$	0.0451513	−	0.0501456i	0.00163245	−	0.00181302i
$766$	2.54781	−	24.2408i	0.0920562	−	0.875856i
$767$	69.9525	+	50.8235i	2.52584	+	1.83513i
$768$	0.814260	+	7.74717i	0.0293821	+	0.279552i
$769$	11.6069	−	20.1037i	0.418555	−	0.724959i	−0.577239	−	0.816575i	$-0.695870\pi$
$769$	11.6069	−	20.1037i	0.418555	−	0.724959i	0.995794	+	0.0916164i	$0.0292034\pi$
$770$	0.0151435	+	0.0262293i	0.000545733	+	0.000945237i
$771$	−18.5236	+	13.4582i	−0.667112	+	0.484685i
$772$	−1.84236	−	2.04614i	−0.0663078	−	0.0736423i
$773$	−6.91253	−	21.2746i	−0.248626	−	0.765193i	−0.995019	−	0.0996871i	$-0.968216\pi$
$773$	−6.91253	−	21.2746i	−0.248626	−	0.765193i	0.746393	−	0.665506i	$-0.231784\pi$
$774$	−1.36277			−0.0489839
$775$		0			0
$776$	21.7152			0.779531
$777$	2.27136	+	6.99054i	0.0814848	+	0.250784i
$778$	20.7703	+	23.0678i	0.744652	+	0.827019i
$779$	12.1726	−	8.84392i	0.436129	−	0.316866i
$780$	0.00759532	+	0.0131555i	0.000271956	+	0.000471042i
$781$	−18.7213	+	32.4263i	−0.669901	+	1.16030i
$782$	0.417911	+	3.97616i	0.0149445	+	0.142187i
$783$	7.24418	+	5.26321i	0.258886	+	0.188092i
$784$	−2.25808	+	21.4842i	−0.0806455	+	0.767291i
$785$	0.0129591	−	0.0143926i	0.000462531	−	0.000513692i
$786$	−0.958159	−	0.426600i	−0.0341764	−	0.0152163i
$787$	−11.2127	−	2.38333i	−0.399689	−	0.0849565i	0.00368164	−	0.999993i	$-0.498828\pi$
$787$	−11.2127	−	2.38333i	−0.399689	−	0.0849565i	−0.403371	+	0.915037i	$0.632161\pi$
$788$	−3.82799	+	0.813665i	−0.136367	+	0.0289856i
$789$	16.3371	−	7.27373i	0.581615	−	0.258952i
$790$	−0.0309580	+	0.0952790i	−0.00110144	+	0.00338987i
$791$	2.04482	−	6.29332i	0.0727056	−	0.223765i
$792$	16.0098	−	7.12801i	0.568882	−	0.253283i
$793$	−31.0055	+	6.59042i	−1.10104	+	0.234033i
$794$	14.0435	+	2.98503i	0.498384	+	0.105935i
$795$	0.0334860	+	0.0149089i	0.00118763	+	0.000528765i
$796$	−1.89906	+	2.10912i	−0.0673104	+	0.0747558i
$797$	3.69929	−	35.1964i	0.131036	−	1.24672i	−0.709399	−	0.704807i	$-0.751033\pi$
$797$	3.69929	−	35.1964i	0.131036	−	1.24672i	0.840434	−	0.541913i	$-0.182300\pi$
$798$	−3.90196	−	2.83494i	−0.138128	−	0.100356i
$799$	2.82656	+	26.8929i	0.0999965	+	0.951403i
$800$	−3.76265	+	6.51710i	−0.133030	+	0.230414i
$801$	0.828367	+	1.43477i	0.0292689	+	0.0506953i
$802$	−11.3616	+	8.25467i	−0.401191	+	0.291482i
$803$	11.7726	+	13.0748i	0.415446	+	0.461400i
$804$	1.48475	+	4.56958i	0.0523630	+	0.161157i
$805$	0.00279834			9.86284e−5
$806$		0			0
$807$	18.5678			0.653619
$808$	−5.93295	−	18.2597i	−0.208721	−	0.642376i
$809$	7.26680	+	8.07060i	0.255487	+	0.283747i	0.857220	−	0.514950i	$-0.172190\pi$
$809$	7.26680	+	8.07060i	0.255487	+	0.283747i	−0.601733	+	0.798697i	$0.705523\pi$
$810$	−0.0185431	+	0.0134724i	−0.000651538	+	0.000473370i
$811$	−20.6303	−	35.7328i	−0.724429	−	1.25475i	−0.959209	−	0.282699i	$-0.908770\pi$
$811$	−20.6303	−	35.7328i	−0.724429	−	1.25475i	0.234779	−	0.972049i	$-0.424563\pi$
$812$	−0.172586	+	0.298927i	−0.00605657	+	0.0104903i
$813$	−2.95689	−	28.1329i	−0.103703	−	0.986664i
$814$	31.7225	+	23.0478i	1.11187	+	0.807824i
$815$	0.0128610	−	0.122364i	0.000450501	−	0.00428623i
$816$	17.5996	−	19.5463i	0.616108	−	0.684257i
$817$	−2.39334	−	1.06558i	−0.0837324	−	0.0372800i
$818$	−12.1341	−	2.57918i	−0.424259	−	0.0901791i
$819$	−7.24188	+	1.53931i	−0.253052	+	0.0537878i
$820$	0.00717792	−	0.00319582i	0.000250664	−	0.000111603i
$821$	−1.82635	+	5.62093i	−0.0637401	+	0.196172i	−0.977855	−	0.209283i	$-0.932887\pi$
$821$	−1.82635	+	5.62093i	−0.0637401	+	0.196172i	0.914115	+	0.405455i	$0.132887\pi$
$822$	1.44787	−	4.45609i	0.0505003	−	0.155424i
$823$	−10.1476	+	4.51800i	−0.353723	+	0.157488i	−0.575903	−	0.817518i	$-0.695349\pi$
$823$	−10.1476	+	4.51800i	−0.353723	+	0.157488i	0.222180	+	0.975006i	$0.428683\pi$
$824$	24.9197	−	5.29686i	0.868121	−	0.184525i
$825$	−24.0146	−	5.10447i	−0.836082	−	0.177715i
$826$	−13.0968	−	5.83109i	−0.455697	−	0.202890i
$827$	3.67006	−	4.07601i	0.127620	−	0.141737i	−0.675948	−	0.736950i	$-0.736266\pi$
$827$	3.67006	−	4.07601i	0.127620	−	0.141737i	0.803568	+	0.595213i	$0.202932\pi$
$828$	0.0199967	−	0.190256i	0.000694934	−	0.00661186i
$829$	−30.0479	−	21.8310i	−1.04360	−	0.758223i	−0.0726190	−	0.997360i	$-0.523136\pi$
$829$	−30.0479	−	21.8310i	−1.04360	−	0.758223i	−0.970986	+	0.239136i	$0.923136\pi$
$830$	0.00201062	+	0.0191298i	6.97898e−5	+	0.000664005i
$831$	−8.91941	+	15.4489i	−0.309411	+	0.535915i
$832$	−27.6536	−	47.8974i	−0.958716	−	1.66054i
$833$	−32.3584	+	23.5097i	−1.12115	+	0.814564i
$834$	3.67313	+	4.07943i	0.127190	+	0.141259i
$835$	0.0348219	+	0.107171i	0.00120506	+	0.00370880i
$836$	3.98043			0.137666
$837$		0			0
$838$	38.4379			1.32782
$839$	11.1865	+	34.4285i	0.386201	+	1.18860i	0.935606	+	0.353047i	$0.114854\pi$
$839$	11.1865	+	34.4285i	0.386201	+	1.18860i	−0.549405	+	0.835556i	$0.685146\pi$
$840$	−0.0142644	−	0.0158422i	−0.000492168	−	0.000546608i
$841$	21.3370	−	15.5022i	0.735757	−	0.534559i
$842$	0.392621	+	0.680040i	0.0135306	+	0.0234357i
$843$	3.59084	−	6.21952i	0.123675	−	0.214212i
$844$	0.463834	+	4.41309i	0.0159658	+	0.151905i
$845$	−0.157879	−	0.114706i	−0.00543121	−	0.00394601i
$846$	−0.874246	+	8.31789i	−0.0300572	+	0.285975i
$847$	−2.56469	+	2.84838i	−0.0881238	+	0.0978714i
$848$	−12.6430	−	5.62903i	−0.434163	−	0.193302i
$849$	−3.11896	−	0.662956i	−0.107043	−	0.0227526i
$850$	40.4267	−	8.59296i	1.38662	−	0.294736i
$851$	3.30967	−	1.47356i	0.113454	−	0.0505130i
$852$	0.962188	−	2.96131i	0.0329640	−	0.101453i
$853$	−3.45298	+	10.6272i	−0.118228	+	0.363867i	−0.992607	−	0.121377i	$-0.961269\pi$
$853$	−3.45298	+	10.6272i	−0.118228	+	0.363867i	0.874379	+	0.485244i	$0.161269\pi$
$854$	4.80126	−	2.13766i	0.164296	−	0.0731492i
$855$	0.0392454	−	0.00834188i	0.00134217	−	0.000285286i
$856$	39.4572	+	8.38688i	1.34862	+	0.286658i
$857$	50.1227	+	22.3160i	1.71216	+	0.762302i	0.998060	+	0.0622553i	$0.0198293\pi$
$857$	50.1227	+	22.3160i	1.71216	+	0.762302i	0.714097	+	0.700046i	$0.246837\pi$
$858$	27.2840	−	30.3019i	0.931459	−	1.03449i
$859$	2.08125	−	19.8018i	0.0710115	−	0.675629i	−0.899885	−	0.436128i	$-0.856350\pi$
$859$	2.08125	−	19.8018i	0.0710115	−	0.675629i	0.970896	−	0.239501i	$-0.0769838\pi$
$860$	−0.00110681		0.000804146i	−3.77420e−5		2.74212e-5i
$861$	−0.413255	−	3.93186i	−0.0140837	−	0.133997i
$862$	−15.7958	+	27.3591i	−0.538007	+	0.931855i
$863$	−5.58861	−	9.67975i	−0.190238	−	0.329503i	0.755091	−	0.655620i	$-0.227593\pi$
$863$	−5.58861	−	9.67975i	−0.190238	−	0.329503i	−0.945329	+	0.326118i	$0.894259\pi$
$864$	−6.72813	+	4.88827i	−0.228896	+	0.166302i
$865$	0.0336555	+	0.0373782i	0.00114432	+	0.00127090i
$866$	5.10162	+	15.7012i	0.173360	+	0.533547i
$867$	27.7126			0.941170
$868$		0			0
$869$	−41.6017			−1.41124
$870$	−0.00592136	−	0.0182241i	−0.000200753	−	0.000617854i
$871$	−61.3272	−	68.1108i	−2.07799	−	2.30785i
$872$	−24.7051	+	17.9493i	−0.836619	+	0.607840i
$873$	5.36951	+	9.30026i	0.181730	+	0.314766i
$874$	−1.18862	+	2.05876i	−0.0402058	+	0.0696386i
$875$	−0.00604757	−	0.0575388i	−0.000204445	−	0.00194517i
$876$	−1.18367	−	0.859987i	−0.0399925	−	0.0290563i
$877$	2.87961	−	27.3976i	0.0972374	−	0.925152i	−0.831777	−	0.555109i	$-0.812676\pi$
$877$	2.87961	−	27.3976i	0.0972374	−	0.925152i	0.929015	−	0.370043i	$-0.120657\pi$
$878$	34.4476	−	38.2579i	1.16255	−	1.29114i
$879$	20.8072	+	9.26395i	0.701809	+	0.312465i
$880$	−0.0960620	−	0.0204186i	−0.00323825	−	0.000688311i
$881$	−13.9508	+	2.96533i	−0.470014	+	0.0999045i	−0.436829	−	0.899545i	$-0.643898\pi$
$881$	−13.9508	+	2.96533i	−0.470014	+	0.0999045i	−0.0331850	+	0.999449i	$0.510565\pi$
$882$	−11.3015	+	5.03173i	−0.380540	+	0.169427i
$883$	−5.77085	+	17.7608i	−0.194205	+	0.597700i	0.805780	+	0.592214i	$0.201746\pi$
$883$	−5.77085	+	17.7608i	−0.194205	+	0.597700i	−0.999985	+	0.00548562i	$0.998254\pi$
$884$	3.28149	−	10.0994i	0.110368	−	0.339679i
$885$	−0.112479	+	0.0500788i	−0.00378094	+	0.00168338i
$886$	−9.64464	+	2.05003i	−0.324018	+	0.0688722i
$887$	33.9794	+	7.22254i	1.14092	+	0.242509i	0.739350	−	0.673321i	$-0.235133\pi$
$887$	33.9794	+	7.22254i	1.14092	+	0.242509i	0.401565	+	0.915830i	$0.368466\pi$
$888$	−25.2131	−	11.2256i	−0.846097	−	0.376707i
$889$	5.98198	−	6.64366i	0.200629	−	0.222821i
$890$	0.00112378	−	0.0106920i	3.76691e−5	−	0.000358397i
$891$	−7.70021	−	5.59453i	−0.257967	−	0.187424i
$892$	0.0225525	+	0.214572i	0.000755112	+	0.00718441i
$893$	−8.03931	+	13.9245i	−0.269025	+	0.465966i
$894$	−9.56098	−	16.5601i	−0.319767	−	0.553853i
$895$	0.0852679	−	0.0619508i	0.00285019	−	0.00207079i
$896$	4.53486	+	5.03647i	0.151499	+	0.168257i
$897$	−1.16419	−	3.58300i	−0.0388711	−	0.119633i
$898$	−23.0498			−0.769183
$899$		0			0
$900$	−1.97760			−0.0659200
$901$	−7.91822	−	24.3698i	−0.263794	−	0.811875i
$902$	−14.1124	−	15.6734i	−0.469890	−	0.521866i
$903$	−0.556915	+	0.404623i	−0.0185330	+	0.0134650i
$904$	12.4233	+	21.5177i	0.413191	+	0.715668i
$905$	−0.0631510	+	0.109381i	−0.00209921	+	0.00363594i
$906$	3.03447	+	28.8710i	0.100813	+	0.959176i
$907$	5.15331	+	3.74410i	0.171113	+	0.124321i	0.670046	−	0.742320i	$-0.266275\pi$
$907$	5.15331	+	3.74410i	0.171113	+	0.124321i	−0.498933	+	0.866641i	$0.666275\pi$
$908$	0.377407	−	3.59079i	0.0125247	−	0.119164i
$909$	6.35330	−	7.05606i	0.210726	−	0.234035i
$910$	0.0438904	+	0.0195413i	0.00145495	+	0.000647787i
$911$	53.1544	+	11.2983i	1.76108	+	0.374330i	0.971077	−	0.238767i	$-0.0767431\pi$
$911$	53.1544	+	11.2983i	1.76108	+	0.374330i	0.790008	+	0.613097i	$0.210076\pi$
$912$	15.2975	−	3.25159i	0.506551	−	0.107671i
$913$	−7.29704	+	3.24885i	−0.241497	+	0.107521i
$914$	1.99036	−	6.12569i	0.0658352	−	0.202620i
$915$	0.0139480	−	0.0429275i	0.000461106	−	0.00141914i
$916$	3.16988	−	1.41132i	0.104736	−	0.0466314i
$917$	0.501967	−	0.106696i	0.0165764	−	0.00352342i
$918$	44.6767	+	9.49632i	1.47455	+	0.313425i
$919$	−40.8325	−	18.1798i	−1.34694	−	0.599696i	−0.398650	−	0.917103i	$-0.630521\pi$
$919$	−40.8325	−	18.1798i	−1.34694	−	0.599696i	−0.948289	+	0.317407i	$0.897188\pi$
$920$	−0.00703077	+	0.00780846i	−0.000231798	+	0.000257437i
$921$	−0.212362	+	2.02049i	−0.00699755	+	0.0665773i
$922$	21.5897	+	15.6858i	0.711019	+	0.516585i
$923$	6.20847	+	59.0697i	0.204354	+	1.94430i
$924$	0.522946	−	0.905770i	0.0172037	−	0.0297976i
$925$	−18.7257	−	32.4339i	−0.615698	−	1.06642i
$926$	−24.4416	+	17.7579i	−0.803201	+	0.583560i
$927$	8.43044	+	9.36295i	0.276892	+	0.307520i
$928$	−0.753693	−	2.31963i	−0.0247412	−	0.0761455i
$929$	−15.4573			−0.507139			−0.253569	−	0.967317i	$-0.581605\pi$
$929$	−15.4573			−0.507139			−0.253569	+	0.967317i	$0.581605\pi$
$930$		0			0
$931$	−23.7823			−0.779434
$932$	−1.02310	−	3.14877i	−0.0335127	−	0.103141i
$933$	−15.8948	−	17.6530i	−0.520373	−	0.577932i
$934$	29.0536	−	21.1087i	0.950662	−	0.690697i
$935$	−0.0909164	−	0.157472i	−0.00297328	−	0.00514988i
$936$	13.8998	−	24.0752i	0.454329	−	0.786922i
$937$	0.555874	+	5.28879i	0.0181596	+	0.172777i	0.999843	−	0.0177447i	$-0.00564861\pi$
$937$	0.555874	+	5.28879i	0.0181596	+	0.172777i	−0.981683	+	0.190522i	$0.938982\pi$
$938$	12.2939	+	8.93207i	0.401411	+	0.291642i
$939$	−1.98756	+	18.9103i	−0.0648614	+	0.617115i
$940$	−0.00561826	+	0.00623971i	−0.000183248	+	0.000203517i
$941$	−12.2222	−	5.44166i	−0.398431	−	0.177393i	0.197732	−	0.980256i	$-0.436642\pi$
$941$	−12.2222	−	5.44166i	−0.398431	−	0.177393i	−0.596164	+	0.802863i	$0.703309\pi$
$942$	4.22864	+	0.898825i	0.137777	+	0.0292853i
$943$	−1.90607	+	0.405147i	−0.0620700	+	0.0131934i
$944$	42.4677	−	18.9078i	1.38220	−	0.615397i
$945$	0.00987892	−	0.0304042i	0.000321361	−	0.000989049i
$946$	−1.13480	+	3.49256i	−0.0368955	+	0.113553i
$947$	6.13691	−	2.73233i	0.199423	−	0.0887887i	−0.304595	−	0.952482i	$-0.598521\pi$
$947$	6.13691	−	2.73233i	0.199423	−	0.0887887i	0.504018	+	0.863693i	$0.331855\pi$
$948$	3.38397	−	0.719285i	0.109906	−	0.0233613i
$949$	27.2992	+	5.80263i	0.886170	+	0.188361i
$950$	22.4502	+	9.99545i	0.728379	+	0.324295i
$951$	−23.8933	+	26.5362i	−0.774793	+	0.860495i
$952$	−1.55772	+	14.8207i	−0.0504859	+	0.480342i
$953$	16.6753	+	12.1153i	0.540166	+	0.392453i	0.824147	−	0.566377i	$-0.191655\pi$
$953$	16.6753	+	12.1153i	0.540166	+	0.392453i	−0.283981	+	0.958830i	$0.591655\pi$
$954$	−0.828429	−	7.88198i	−0.0268214	−	0.255188i
$955$	−0.0542416	+	0.0939491i	−0.00175522	+	0.00304012i
$956$	−2.13467	−	3.69735i	−0.0690401	−	0.119581i
$957$	6.43750	−	4.67712i	0.208095	−	0.151190i
$958$	30.2865	+	33.6366i	0.978514	+	1.08675i
$959$	0.708423	+	2.18030i	0.0228762	+	0.0704056i
$960$	0.0787547			0.00254180
$961$		0			0
$962$	62.2005			2.00543
$963$	6.16459	+	18.9726i	0.198651	+	0.611385i
$964$	−3.67946	−	4.08645i	−0.118507	−	0.131616i
$965$	−0.0605045	+	0.0439591i	−0.00194771	+	0.00141509i
$966$	0.312322	+	0.540957i	0.0100488	+	0.0174050i
$967$	−29.5645	+	51.2072i	−0.950731	+	1.64671i	−0.206881	+	0.978366i	$0.566331\pi$
$967$	−29.5645	+	51.2072i	−0.950731	+	1.64671i	−0.743849	+	0.668348i	$0.767002\pi$
$968$	−1.50436	−	14.3130i	−0.0483518	−	0.460037i
$969$	23.4261	+	17.0200i	0.752553	+	0.546762i
$970$	0.00728437	−	0.0693061i	0.000233887	−	0.00222529i
$971$	−30.6339	+	34.0224i	−0.983090	+	1.09183i	0.0126775	+	0.999920i	$0.495965\pi$
$971$	−30.6339	+	34.0224i	−0.983090	+	1.09183i	−0.995767	+	0.0919120i	$0.970702\pi$
$972$	−3.33470	−	1.48471i	−0.106961	−	0.0476219i
$973$	−2.62720	−	0.558429i	−0.0842242	−	0.0179024i
$974$	35.1537	−	7.47215i	1.12640	−	0.239423i
$975$	−35.5783	+	15.8405i	−1.13942	+	0.507302i
$976$	−5.26622	+	16.2078i	−0.168568	+	0.518798i
$977$	2.29811	−	7.07286i	0.0735231	−	0.226281i	−0.907541	−	0.419963i	$-0.862043\pi$
$977$	2.29811	−	7.07286i	0.0735231	−	0.226281i	0.981064	+	0.193682i	$0.0620431\pi$
$978$	25.0901	−	11.1708i	0.802293	−	0.357204i
$979$	4.36687	−	0.928207i	0.139566	−	0.0296656i
$980$	−0.0121479	−	0.00258211i	−0.000388050	−	8.24826e-5i
$981$	−13.7962	−	6.14245i	−0.440478	−	0.196113i
$982$	31.2644	−	34.7226i	0.997687	−	1.10804i
$983$	−2.84423	+	27.0610i	−0.0907169	+	0.863113i	0.850651	+	0.525731i	$0.176208\pi$
$983$	−2.84423	+	27.0610i	−0.0907169	+	0.863113i	−0.941368	+	0.337382i	$0.890459\pi$
$984$	12.0097	+	8.72557i	0.382856	+	0.278161i
$985$	0.0111114	+	0.105718i	0.000354039	+	0.00336846i
$986$	−6.69764	+	11.6007i	−0.213296	+	0.369440i
$987$	2.11240	+	3.65878i	0.0672384	+	0.116460i
$988$	5.10824	−	3.71136i	0.162515	−	0.118074i
$989$	0.227035	+	0.252148i	0.00721928	+	0.00801783i
$990$	−0.0173792	−	0.0534877i	−0.000552348	−	0.00169995i
$991$	−17.2059			−0.546563			−0.273282	−	0.961934i	$-0.588109\pi$
$991$	−17.2059			−0.546563			−0.273282	+	0.961934i	$0.588109\pi$
$992$		0			0
$993$	−2.28019			−0.0723597
$994$	−3.04315	−	9.36586i	−0.0965229	−	0.297067i
$995$	0.0515830	+	0.0572887i	0.00163529	+	0.00181617i
$996$	0.537385	−	0.390433i	0.0170277	−	0.0123713i
$997$	−14.7528	−	25.5527i	−0.467227	−	0.809261i	0.532072	−	0.846699i	$-0.321414\pi$
$997$	−14.7528	−	25.5527i	−0.467227	−	0.809261i	−0.999299	+	0.0374383i	$0.988080\pi$
$998$	−7.37511	+	12.7741i	−0.233455	+	0.404356i
$999$	−4.32630	−	41.1620i	−0.136878	−	1.30231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.w.547.8		128
31.2	even	5	inner	961.2.g.w.235.10		128
31.3	odd	30		961.2.c.l.521.8		32
31.4	even	5	inner	961.2.g.w.816.9		128
31.5	even	3		961.2.d.s.531.8		64
31.6	odd	6	inner	961.2.g.w.844.8		128
31.7	even	15	inner	961.2.g.w.732.10		128
31.8	even	5	inner	961.2.g.w.846.7		128
31.9	even	15		961.2.d.s.628.8		64
31.10	even	15		961.2.d.s.388.9		64
31.11	odd	30		961.2.d.s.374.10		64
31.12	odd	30	inner	961.2.g.w.338.10		128
31.13	odd	30		961.2.a.l.1.7	✓	16
31.14	even	15	inner	961.2.g.w.448.8		128
31.15	odd	10		961.2.c.l.439.8		32
31.16	even	5		961.2.c.l.439.7		32
31.17	odd	30	inner	961.2.g.w.448.7		128
31.18	even	15		961.2.a.l.1.8	yes	16
31.19	even	15	inner	961.2.g.w.338.9		128
31.20	even	15		961.2.d.s.374.9		64
31.21	odd	30		961.2.d.s.388.10		64
31.22	odd	30		961.2.d.s.628.7		64
31.23	odd	10	inner	961.2.g.w.846.8		128
31.24	odd	30	inner	961.2.g.w.732.9		128
31.25	even	3	inner	961.2.g.w.844.7		128
31.26	odd	6		961.2.d.s.531.7		64
31.27	odd	10	inner	961.2.g.w.816.10		128
31.28	even	15		961.2.c.l.521.7		32
31.29	odd	10	inner	961.2.g.w.235.9		128
31.30	odd	2	inner	961.2.g.w.547.7		128
93.44	even	30		8649.2.a.bs.1.9		16
93.80	odd	30		8649.2.a.bs.1.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.7	✓	16	31.13	odd	30
961.2.a.l.1.8	yes	16	31.18	even	15
961.2.c.l.439.7		32	31.16	even	5
961.2.c.l.439.8		32	31.15	odd	10
961.2.c.l.521.7		32	31.28	even	15
961.2.c.l.521.8		32	31.3	odd	30
961.2.d.s.374.9		64	31.20	even	15
961.2.d.s.374.10		64	31.11	odd	30
961.2.d.s.388.9		64	31.10	even	15
961.2.d.s.388.10		64	31.21	odd	30
961.2.d.s.531.7		64	31.26	odd	6
961.2.d.s.531.8		64	31.5	even	3
961.2.d.s.628.7		64	31.22	odd	30
961.2.d.s.628.8		64	31.9	even	15
961.2.g.w.235.9		128	31.29	odd	10	inner
961.2.g.w.235.10		128	31.2	even	5	inner
961.2.g.w.338.9		128	31.19	even	15	inner
961.2.g.w.338.10		128	31.12	odd	30	inner
961.2.g.w.448.7		128	31.17	odd	30	inner
961.2.g.w.448.8		128	31.14	even	15	inner
961.2.g.w.547.7		128	31.30	odd	2	inner
961.2.g.w.547.8		128	1.1	even	1	trivial
961.2.g.w.732.9		128	31.24	odd	30	inner
961.2.g.w.732.10		128	31.7	even	15	inner
961.2.g.w.816.9		128	31.4	even	5	inner
961.2.g.w.816.10		128	31.27	odd	10	inner
961.2.g.w.844.7		128	31.25	even	3	inner
961.2.g.w.844.8		128	31.6	odd	6	inner
961.2.g.w.846.7		128	31.8	even	5	inner
961.2.g.w.846.8		128	31.23	odd	10	inner
8649.2.a.bs.1.9		16	93.44	even	30
8649.2.a.bs.1.10		16	93.80	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.406689 - 1.25166i) q^{2} +(0.826019 + 0.917387i) q^{3} +(0.216779 - 0.157499i) q^{4} +(-0.00363912 - 0.00630315i) q^{5} +(0.812323 - 1.40699i) q^{6} +(0.0830915 + 0.790563i) q^{7} +(-2.41475 - 1.75442i) q^{8} +(0.154294 - 1.46801i) q^{9} +(-0.00640940 + 0.00711836i) q^{10} +(-3.63377 - 1.61786i) q^{11} +(0.323551 + 0.0687729i) q^{12} +(-6.17185 + 1.31187i) q^{13} +(0.955723 - 0.425515i) q^{14} +(0.00277644 - 0.00854501i) q^{15} +(-1.04828 + 3.22626i) q^{16} +(-5.73784 + 2.55465i) q^{17} +(-1.90020 + 0.403899i) q^{18} +(-3.65299 - 0.776467i) q^{19} +(-0.00178162 - 0.000793230i) q^{20} +(-0.656617 + 0.729247i) q^{21} +(-0.547194 + 5.20620i) q^{22} +(0.391299 + 0.284295i) q^{23} +(-0.385148 - 3.66444i) q^{24} +(2.49997 - 4.33008i) q^{25} +(4.15203 + 7.19153i) q^{26} +(4.47029 - 3.24786i) q^{27} +(0.142525 + 0.158290i) q^{28} +(0.500767 + 1.54120i) q^{29} -0.0118246 q^{30} -1.50508 q^{32} +(-1.51736 - 4.66995i) q^{33} +(5.53107 + 6.14288i) q^{34} +(0.00468065 - 0.00340069i) q^{35} +(-0.197762 - 0.342534i) q^{36} +(3.74519 - 6.48685i) q^{37} +(0.513758 + 4.88808i) q^{38} +(-6.30155 - 4.57835i) q^{39} +(-0.00227078 + 0.0216050i) q^{40} +(-2.69583 + 2.99403i) q^{41} +(1.17981 + 0.525284i) q^{42} +(0.686175 + 0.145851i) q^{43} +(-1.04253 + 0.221598i) q^{44} +(-0.00981457 + 0.00436973i) q^{45} +(0.196704 - 0.605393i) q^{46} +(1.33042 - 4.09460i) q^{47} +(-3.82563 + 1.70328i) q^{48} +(6.22895 - 1.32400i) q^{49} +(-6.43650 - 1.36812i) q^{50} +(-7.08317 - 3.15363i) q^{51} +(-1.13131 + 1.25644i) q^{52} +(-0.426443 + 4.05734i) q^{53} +(-5.88323 - 4.27442i) q^{54} +(0.00302614 + 0.0287918i) q^{55} +(1.18633 - 2.05479i) q^{56} +(-2.30512 - 3.99258i) q^{57} +(1.72540 - 1.25358i) q^{58} +(-9.16950 - 10.1838i) q^{59} +(-0.000743956 - 0.00228966i) q^{60} +5.02369 q^{61} +1.17337 q^{63} +(2.70865 + 8.33637i) q^{64} +(0.0307290 + 0.0341280i) q^{65} +(-5.22809 + 3.79843i) q^{66} +(7.26276 + 12.5795i) q^{67} +(-0.841487 + 1.45750i) q^{68} +(0.0624115 + 0.593806i) q^{69} +(-0.00616008 - 0.00447556i) q^{70} +(0.983952 - 9.36168i) q^{71} +(-2.94808 + 3.27417i) q^{72} +(-4.04078 - 1.79907i) q^{73} +(-9.64245 - 2.04957i) q^{74} +(6.03738 - 1.28329i) q^{75} +(-0.914183 + 0.407021i) q^{76} +(0.977083 - 3.00715i) q^{77} +(-3.16776 + 9.74936i) q^{78} +(9.55464 - 4.25400i) q^{79} +(0.0241504 - 0.00513333i) q^{80} +(2.34057 + 0.497504i) q^{81} +(4.84387 + 2.15663i) q^{82} +(1.34369 - 1.49232i) q^{83} +(-0.0274849 + 0.261502i) q^{84} +(0.0369831 + 0.0268698i) q^{85} +(-0.0965039 - 0.918173i) q^{86} +(-1.00024 + 1.73246i) q^{87} +(5.93623 + 10.2819i) q^{88} +(-0.908022 + 0.659717i) q^{89} +(0.00946088 + 0.0105074i) q^{90} +(-1.54994 - 4.77023i) q^{91} +0.129602 q^{92} -5.66611 q^{94} +(0.00839950 + 0.0258510i) q^{95} +(-1.24322 - 1.38074i) q^{96} +(-5.88584 + 4.27631i) q^{97} +(-4.19044 - 7.25806i) q^{98} +(-2.93570 + 5.08477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} - 16 q^{4} + 64 q^{5} - 16 q^{7} + 8 q^{10} - 8 q^{14} + 16 q^{16} - 24 q^{18} - 32 q^{19} - 24 q^{20} - 8 q^{28} - 64 q^{32} + 64 q^{33} + 32 q^{35} + 160 q^{36} - 24 q^{38} + 64 q^{39}+ \cdots - 64 q^{98}+O(q^{100}) \) 128 * q + 16 * q^2 - 16 * q^4 + 64 * q^5 - 16 * q^7 + 8 * q^10 - 8 * q^14 + 16 * q^16 - 24 * q^18 - 32 * q^19 - 24 * q^20 - 8 * q^28 - 64 * q^32 + 64 * q^33 + 32 * q^35 + 160 * q^36 - 24 * q^38 + 64 * q^39 - 32 * q^41 - 16 * q^45 + 64 * q^47 - 16 * q^49 - 32 * q^50 - 32 * q^51 + 192 * q^56 - 64 * q^59 - 128 * q^63 + 32 * q^64 - 64 * q^67 - 32 * q^69 - 176 * q^70 - 48 * q^71 + 48 * q^72 + 40 * q^76 - 64 * q^78 - 40 * q^80 - 16 * q^81 + 88 * q^82 + 128 * q^87 + 40 * q^90 - 256 * q^94 + 96 * q^95 - 64 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more