LMFDB - Embedded newform 961.2.g.k.338.1

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)

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")

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);

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 = [16,-6,3,-14,-3,11,-13] 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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			338.1
Root			$-1.42343i$ of defining polynomial
Character	$\chi$	$=$	961.338
Dual form			961.2.g.k.816.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.86683 + 1.35633i) q^{2} +(0.265787 - 2.52879i) q^{3} +(1.02738 - 3.16196i) q^{4} +(1.24923 - 2.16373i) q^{5} +(2.93370 + 5.08132i) q^{6} +(-1.56687 + 0.333049i) q^{7} +(0.944583 + 2.90713i) q^{8} +(-3.38972 - 0.720507i) q^{9} +(0.602634 + 5.73368i) q^{10} +(0.490912 + 0.545213i) q^{11} +(-7.72288 - 3.43845i) q^{12} +(-1.73206 + 0.771163i) q^{13} +(2.47336 - 2.74694i) q^{14} +(-5.13960 - 3.73414i) q^{15} +(-0.326952 - 0.237545i) q^{16} +(-2.93028 + 3.25441i) q^{17} +(7.30526 - 3.25251i) q^{18} +(-4.23705 - 1.88646i) q^{19} +(-5.55818 - 6.17299i) q^{20} +(0.425758 + 4.05082i) q^{21} +(-1.65594 - 0.351980i) q^{22} +(-2.19973 - 6.77006i) q^{23} +(7.60258 - 1.61598i) q^{24} +(-0.621150 - 1.07586i) q^{25} +(2.18751 - 3.78887i) q^{26} +(-0.365721 + 1.12557i) q^{27} +(-0.556691 + 5.29656i) q^{28} +(0.104314 - 0.0757884i) q^{29} +14.6595 q^{30} -5.18091 q^{32} +(1.50921 - 1.09651i) q^{33} +(1.05628 - 10.0499i) q^{34} +(-1.23676 + 3.80635i) q^{35} +(-5.76075 + 9.97791i) q^{36} +(-4.21474 - 7.30014i) q^{37} +(10.4685 - 2.22515i) q^{38} +(1.48975 + 4.58499i) q^{39} +(7.47024 + 1.58785i) q^{40} +(0.770791 + 7.33358i) q^{41} +(-6.28907 - 6.98472i) q^{42} +(0.210565 + 0.0937494i) q^{43} +(2.22830 - 0.992101i) q^{44} +(-5.79352 + 6.43435i) q^{45} +(13.2889 + 9.65498i) q^{46} +(6.50168 + 4.72375i) q^{47} +(-0.687602 + 0.763659i) q^{48} +(-4.05065 + 1.80346i) q^{49} +(2.61881 + 1.16597i) q^{50} +(7.45090 + 8.27507i) q^{51} +(0.658896 + 6.26898i) q^{52} +(-5.60893 - 1.19222i) q^{53} +(-0.843912 - 2.59729i) q^{54} +(1.79296 - 0.381105i) q^{55} +(-2.44826 - 4.24051i) q^{56} +(-5.89661 + 10.2132i) q^{57} +(-0.0919419 + 0.282968i) q^{58} +(-0.993409 + 9.45166i) q^{59} +(-17.0875 + 12.4148i) q^{60} -7.84044 q^{61} +5.55122 q^{63} +(10.3258 - 7.50212i) q^{64} +(-0.495153 + 4.71107i) q^{65} +(-1.33021 + 4.09397i) q^{66} +(-2.41329 + 4.17994i) q^{67} +(7.27978 + 12.6090i) q^{68} +(-17.7047 + 3.76326i) q^{69} +(-2.85385 - 8.78324i) q^{70} +(3.33061 + 0.707943i) q^{71} +(-1.10726 - 10.5349i) q^{72} +(1.80133 + 2.00058i) q^{73} +(17.7696 + 7.91153i) q^{74} +(-2.88573 + 1.28481i) q^{75} +(-10.3180 + 11.4593i) q^{76} +(-0.950780 - 0.690782i) q^{77} +(-8.99987 - 6.53879i) q^{78} +(3.02979 - 3.36492i) q^{79} +(-0.922421 + 0.410688i) q^{80} +(-6.74838 - 3.00457i) q^{81} +(-11.3857 - 12.6451i) q^{82} +(-0.279128 - 2.65572i) q^{83} +(13.2459 + 2.81551i) q^{84} +(3.38106 + 10.4058i) q^{85} +(-0.520243 + 0.110581i) q^{86} +(-0.163928 - 0.283932i) q^{87} +(-1.12130 + 1.94214i) q^{88} +(-0.681255 + 2.09669i) q^{89} +(2.08840 - 19.8698i) q^{90} +(2.45708 - 1.78518i) q^{91} -23.6666 q^{92} -18.5445 q^{94} +(-9.37482 + 6.81121i) q^{95} +(-1.37702 + 13.1015i) q^{96} +(3.79778 - 11.6884i) q^{97} +(5.11577 - 8.86077i) q^{98} +(-1.27122 - 2.20182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−1.86683	+	1.35633i	−1.32005	+	0.959070i	−0.320115	+	0.947379i	$0.603722\pi$
$2$	−1.86683	+	1.35633i	−1.32005	+	0.959070i	−0.999932	+	0.0116917i	$0.996278\pi$
$3$	0.265787	−	2.52879i	0.153452	−	1.46000i	−0.598680	−	0.800988i	$-0.704308\pi$
$3$	0.265787	−	2.52879i	0.153452	−	1.46000i	0.752132	−	0.659012i	$-0.229025\pi$
$4$	1.02738	−	3.16196i	0.513691	−	1.58098i
$5$	1.24923	−	2.16373i	0.558673	−	0.967649i	−0.438935	−	0.898519i	$-0.644644\pi$
$5$	1.24923	−	2.16373i	0.558673	−	0.967649i	0.997608	−	0.0691304i	$-0.0220225\pi$
$6$	2.93370	+	5.08132i	1.19768	+	2.07444i
$7$	−1.56687	+	0.333049i	−0.592223	+	0.125881i	−0.494267	−	0.869310i	$-0.664564\pi$
$7$	−1.56687	+	0.333049i	−0.592223	+	0.125881i	−0.0979553	+	0.995191i	$0.531230\pi$
$8$	0.944583	+	2.90713i	0.333960	+	1.02782i
$9$	−3.38972	−	0.720507i	−1.12991	−	0.240169i
$10$	0.602634	+	5.73368i	0.190570	+	1.81315i
$11$	0.490912	+	0.545213i	0.148016	+	0.164388i	0.812593	−	0.582831i	$-0.198055\pi$
$11$	0.490912	+	0.545213i	0.148016	+	0.164388i	−0.664578	+	0.747219i	$0.731388\pi$
$12$	−7.72288	−	3.43845i	−2.22940	−	0.992594i
$13$	−1.73206	+	0.771163i	−0.480387	+	0.213882i	−0.632620	−	0.774463i	$-0.718020\pi$
$13$	−1.73206	+	0.771163i	−0.480387	+	0.213882i	0.152233	+	0.988345i	$0.451354\pi$
$14$	2.47336	−	2.74694i	0.661033	−	0.734152i
$15$	−5.13960	−	3.73414i	−1.32704	−	0.964150i
$16$	−0.326952	−	0.237545i	−0.0817381	−	0.0593862i
$17$	−2.93028	+	3.25441i	−0.710698	+	0.789310i	−0.985041	−	0.172322i	$-0.944873\pi$
$17$	−2.93028	+	3.25441i	−0.710698	+	0.789310i	0.274343	+	0.961632i	$0.411540\pi$
$18$	7.30526	−	3.25251i	1.72187	−	0.766625i
$19$	−4.23705	−	1.88646i	−0.972045	−	0.432783i	−0.141625	−	0.989920i	$-0.545233\pi$
$19$	−4.23705	−	1.88646i	−0.972045	−	0.432783i	−0.830420	+	0.557138i	$0.811900\pi$
$20$	−5.55818	−	6.17299i	−1.24285	−	1.38032i
$21$	0.425758	+	4.05082i	0.0929081	+	0.883962i
$22$	−1.65594	−	0.351980i	−0.353047	−	0.0750425i
$23$	−2.19973	−	6.77006i	−0.458675	−	1.41166i	−0.866766	−	0.498714i	$-0.833806\pi$
$23$	−2.19973	−	6.77006i	−0.458675	−	1.41166i	0.408092	−	0.912941i	$-0.366194\pi$
$24$	7.60258	−	1.61598i	1.55187	−	0.329860i
$25$	−0.621150	−	1.07586i	−0.124230	−	0.215173i
$26$	2.18751	−	3.78887i	0.429005	−	0.743059i
$27$	−0.365721	+	1.12557i	−0.0703831	+	0.216617i
$28$	−0.556691	+	5.29656i	−0.105205	+	1.00096i
$29$	0.104314	−	0.0757884i	0.0193706	−	0.0140736i	−0.578058	−	0.815996i	$-0.696189\pi$
$29$	0.104314	−	0.0757884i	0.0193706	−	0.0140736i	0.597428	+	0.801922i	$0.296189\pi$
$30$	14.6595			2.67644
$31$		0			0
$31$		0			0
$32$	−5.18091			−0.915865
$33$	1.50921	−	1.09651i	0.262720	−	0.190877i
$34$	1.05628	−	10.0499i	0.181151	−	1.72354i
$35$	−1.23676	+	3.80635i	−0.209050	+	0.643390i
$36$	−5.76075	+	9.97791i	−0.960125	+	1.66298i
$37$	−4.21474	−	7.30014i	−0.692899	−	1.20014i	−0.970884	−	0.239550i	$-0.923000\pi$
$37$	−4.21474	−	7.30014i	−0.692899	−	1.20014i	0.277985	−	0.960585i	$-0.410333\pi$
$38$	10.4685	−	2.22515i	1.69821	−	0.360967i
$39$	1.48975	+	4.58499i	0.238551	+	0.734186i
$40$	7.47024	+	1.58785i	1.18115	+	0.251061i
$41$	0.770791	+	7.33358i	0.120377	+	1.14531i	0.873293	+	0.487196i	$0.161980\pi$
$41$	0.770791	+	7.33358i	0.120377	+	1.14531i	−0.752915	+	0.658117i	$0.771353\pi$
$42$	−6.28907	−	6.98472i	−0.970424	−	1.07777i
$43$	0.210565	+	0.0937494i	0.0321108	+	0.0142967i	0.422729	−	0.906256i	$-0.361072\pi$
$43$	0.210565	+	0.0937494i	0.0321108	+	0.0142967i	−0.390618	+	0.920553i	$0.627739\pi$
$44$	2.22830	−	0.992101i	0.335928	−	0.149565i
$45$	−5.79352	+	6.43435i	−0.863646	+	0.959177i
$46$	13.2889	+	9.65498i	1.95935	+	1.42355i
$47$	6.50168	+	4.72375i	0.948368	+	0.689030i	0.950420	−	0.310968i	$-0.100653\pi$
$47$	6.50168	+	4.72375i	0.948368	+	0.689030i	−0.00205222	+	0.999998i	$0.500653\pi$
$48$	−0.687602	+	0.763659i	−0.0992468	+	0.110225i
$49$	−4.05065	+	1.80346i	−0.578664	+	0.257638i
$50$	2.61881	+	1.16597i	0.370355	+	0.164893i
$51$	7.45090	+	8.27507i	1.04333	+	1.15874i
$52$	0.658896	+	6.26898i	0.0913725	+	0.869351i
$53$	−5.60893	−	1.19222i	−0.770446	−	0.163763i	−0.194114	−	0.980979i	$-0.562183\pi$
$53$	−5.60893	−	1.19222i	−0.770446	−	0.163763i	−0.576332	+	0.817216i	$0.695517\pi$
$54$	−0.843912	−	2.59729i	−0.114842	−	0.353447i
$55$	1.79296	−	0.381105i	0.241762	−	0.0513881i
$56$	−2.44826	−	4.24051i	−0.327162	−	0.566662i
$57$	−5.89661	+	10.2132i	−0.781025	+	1.35278i
$58$	−0.0919419	+	0.282968i	−0.0120726	+	0.0371555i
$59$	−0.993409	+	9.45166i	−0.129331	+	1.23050i	0.716706	+	0.697376i	$0.245649\pi$
$59$	−0.993409	+	9.45166i	−0.129331	+	1.23050i	−0.846037	+	0.533125i	$0.821018\pi$
$60$	−17.0875	+	12.4148i	−2.20599	+	1.60274i
$61$	−7.84044			−1.00387			−0.501933	−	0.864907i	$-0.667377\pi$
$61$	−7.84044			−1.00387			−0.501933	+	0.864907i	$0.667377\pi$
$62$		0			0
$63$	5.55122			0.699388
$64$	10.3258	−	7.50212i	1.29072	−	0.937765i
$65$	−0.495153	+	4.71107i	−0.0614162	+	0.584336i
$66$	−1.33021	+	4.09397i	−0.163738	+	0.503933i
$67$	−2.41329	+	4.17994i	−0.294830	+	0.510661i	−0.974945	−	0.222444i	$-0.928596\pi$
$67$	−2.41329	+	4.17994i	−0.294830	+	0.510661i	0.680115	+	0.733105i	$0.261930\pi$
$68$	7.27978	+	12.6090i	0.882804	+	1.52906i
$69$	−17.7047	+	3.76326i	−2.13140	+	0.453043i
$70$	−2.85385	−	8.78324i	−0.341100	−	1.04980i
$71$	3.33061	+	0.707943i	0.395271	+	0.0840174i	0.401259	−	0.915965i	$-0.368573\pi$
$71$	3.33061	+	0.707943i	0.395271	+	0.0840174i	−0.00598824	+	0.999982i	$0.501906\pi$
$72$	−1.10726	−	10.5349i	−0.130492	−	1.24155i
$73$	1.80133	+	2.00058i	0.210830	+	0.234150i	0.839280	−	0.543700i	$-0.182977\pi$
$73$	1.80133	+	2.00058i	0.210830	+	0.234150i	−0.628450	+	0.777850i	$0.716310\pi$
$74$	17.7696	+	7.91153i	2.06567	+	0.919697i
$75$	−2.88573	+	1.28481i	−0.333215	+	0.148357i
$76$	−10.3180	+	11.4593i	−1.18355	+	1.31447i
$77$	−0.950780	−	0.690782i	−0.108351	−	0.0787219i
$78$	−8.99987	−	6.53879i	−1.01903	−	0.740372i
$79$	3.02979	−	3.36492i	0.340878	−	0.378583i	−0.548194	−	0.836351i	$-0.684684\pi$
$79$	3.02979	−	3.36492i	0.340878	−	0.378583i	0.889072	+	0.457768i	$0.151351\pi$
$80$	−0.922421	+	0.410688i	−0.103130	+	0.0459164i
$81$	−6.74838	−	3.00457i	−0.749820	−	0.333841i
$82$	−11.3857	−	12.6451i	−1.25734	−	1.39642i
$83$	−0.279128	−	2.65572i	−0.0306382	−	0.291503i	−0.999103	−	0.0423518i	$-0.986515\pi$
$83$	−0.279128	−	2.65572i	−0.0306382	−	0.291503i	0.968465	−	0.249151i	$-0.0801517\pi$
$84$	13.2459	+	2.81551i	1.44525	+	0.307198i
$85$	3.38106	+	10.4058i	0.366728	+	1.12867i
$86$	−0.520243	+	0.110581i	−0.0560993	+	0.0119243i
$87$	−0.163928	−	0.283932i	−0.0175749	−	0.0304407i
$88$	−1.12130	+	1.94214i	−0.119531	+	0.207033i
$89$	−0.681255	+	2.09669i	−0.0722129	+	0.222248i	−0.980649	−	0.195776i	$-0.937277\pi$
$89$	−0.681255	+	2.09669i	−0.0722129	+	0.222248i	0.908436	+	0.418025i	$0.137277\pi$
$90$	2.08840	−	19.8698i	0.220136	−	2.09446i
$91$	2.45708	−	1.78518i	0.257572	−	0.187137i
$92$	−23.6666			−2.46741
$93$		0			0
$94$	−18.5445			−1.91272
$95$	−9.37482	+	6.81121i	−0.961837	+	0.698815i
$96$	−1.37702	+	13.1015i	−0.140541	+	1.33716i
$97$	3.79778	−	11.6884i	0.385606	−	1.18677i	−0.550434	−	0.834879i	$-0.685538\pi$
$97$	3.79778	−	11.6884i	0.385606	−	1.18677i	0.936040	−	0.351894i	$-0.114462\pi$
$98$	5.11577	−	8.86077i	0.516771	−	0.895073i
$99$	−1.27122	−	2.20182i	−0.127763	−	0.221292i
$100$	−4.03999	+	0.858727i	−0.403999	+	0.0858727i
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	0.998207	+	0.0598605i	$0.0190656\pi$
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	−0.772381	+	0.635159i	$0.780934\pi$
$102$	−25.1333	−	5.34224i	−2.48857	−	0.528961i
$103$	−0.584184	−	5.55814i	−0.0575613	−	0.547659i	−0.984862	−	0.173342i	$-0.944544\pi$
$103$	−0.584184	−	5.55814i	−0.0575613	−	0.547659i	0.927300	−	0.374318i	$-0.122123\pi$
$104$	−3.87794	−	4.30689i	−0.380263	−	0.422325i
$105$	9.29675	+	4.13918i	0.907270	+	0.403943i
$106$	12.0880	−	5.38190i	1.17409	−	0.522737i
$107$	1.22060	−	1.35562i	0.118000	−	0.131052i	−0.681250	−	0.732051i	$-0.738563\pi$
$107$	1.22060	−	1.35562i	0.118000	−	0.131052i	0.799250	+	0.600998i	$0.205230\pi$
$108$	3.18328	+	2.31279i	0.306312	+	0.222548i
$109$	−9.51832	−	6.91546i	−0.911689	−	0.662381i	0.0297521	−	0.999557i	$-0.490528\pi$
$109$	−9.51832	−	6.91546i	−0.911689	−	0.662381i	−0.941442	+	0.337176i	$0.890528\pi$
$110$	−2.83024	+	3.14330i	−0.269853	+	0.299702i
$111$	−19.5808	+	8.71793i	−1.85853	+	0.827469i
$112$	0.591407	+	0.263311i	0.0558827	+	0.0248806i
$113$	7.39693	+	8.21512i	0.695844	+	0.772813i	0.982709	−	0.185158i	$-0.0592796\pi$
$113$	7.39693	+	8.21512i	0.695844	+	0.772813i	−0.286864	+	0.957971i	$0.592613\pi$
$114$	−2.84455	−	27.0641i	−0.266417	−	2.53478i
$115$	−17.3965	−	3.69775i	−1.62224	−	0.344817i
$116$	−0.132470	−	0.407700i	−0.0122995	−	0.0378540i
$117$	6.42682	−	1.36606i	0.594160	−	0.126293i
$118$	−10.9650	−	18.9920i	−1.00941	−	1.74836i
$119$	3.50750	−	6.07518i	0.321532	−	0.556911i
$120$	6.00083	−	18.4687i	0.547799	−	1.68595i
$121$	1.09355	−	10.4044i	0.0994137	−	0.945858i
$122$	14.6368	−	10.6342i	1.32515	−	0.962777i
$123$	18.7500			1.69063
$124$		0			0
$125$	9.38846			0.839730
$126$	−10.3632	+	7.52929i	−0.923225	+	0.670762i
$127$	0.134532	−	1.27998i	0.0119377	−	0.113580i	−0.986930	−	0.161148i	$-0.948480\pi$
$127$	0.134532	−	1.27998i	0.0119377	−	0.113580i	0.998868	+	0.0475679i	$0.0151470\pi$
$128$	−5.89913	+	18.1557i	−0.521414	+	1.60475i
$129$	0.293038	−	0.507557i	0.0258006	−	0.0446879i
$130$	−5.46540	−	9.46635i	−0.479347	−	0.830254i
$131$	7.84509	−	1.66753i	0.685429	−	0.145692i	0.147982	−	0.988990i	$-0.452722\pi$
$131$	7.84509	−	1.66753i	0.685429	−	0.145692i	0.537447	+	0.843298i	$0.319389\pi$
$132$	−1.91657	−	5.89859i	−0.166816	−	0.513406i
$133$	7.26720	+	1.54469i	0.630146	+	0.133942i
$134$	−1.16418	−	11.0764i	−0.100570	−	0.956859i
$135$	1.97857	+	2.19742i	0.170288	+	0.189124i
$136$	−12.2289	−	5.44465i	−1.04862	−	0.466875i
$137$	−15.0523	+	6.70170i	−1.28600	+	0.572565i	−0.931925	−	0.362651i	$-0.881872\pi$
$137$	−15.0523	+	6.70170i	−1.28600	+	0.572565i	−0.354077	+	0.935216i	$0.615205\pi$
$138$	27.9475	−	31.0388i	2.37905	−	2.64220i
$139$	−5.93804	−	4.31424i	−0.503658	−	0.365929i	0.306755	−	0.951789i	$-0.400757\pi$
$139$	−5.93804	−	4.31424i	−0.503658	−	0.365929i	−0.810412	+	0.585860i	$0.800757\pi$
$140$	10.7649	+	7.82114i	0.909799	+	0.661007i
$141$	13.6735	−	15.1859i	1.15151	−	1.27888i
$142$	−7.17788	+	3.19580i	−0.602354	+	0.268185i
$143$	−1.27074	−	0.565769i	−0.106264	−	0.0473120i
$144$	0.937123	+	1.04078i	0.0780936	+	0.0867317i
$145$	−0.0336737	−	0.320384i	−0.00279645	−	0.0266064i
$146$	−6.07622	−	1.29154i	−0.502872	−	0.106889i
$147$	3.48398	+	10.7226i	0.287354	+	0.884385i
$148$	−27.4129	+	5.82679i	−2.25333	+	0.478959i
$149$	3.18096	+	5.50959i	0.260595	+	0.451363i	0.966400	−	0.257043i	$-0.0827480\pi$
$149$	3.18096	+	5.50959i	0.260595	+	0.451363i	−0.705805	+	0.708406i	$0.749415\pi$
$150$	3.64454	−	6.31252i	0.297575	−	0.515415i
$151$	−1.70724	+	5.25433i	−0.138933	+	0.427592i	−0.996181	−	0.0873120i	$-0.972172\pi$
$151$	−1.70724	+	5.25433i	−0.138933	+	0.427592i	0.857248	+	0.514904i	$0.172172\pi$
$152$	1.48192	−	14.0995i	0.120200	−	1.14362i
$153$	12.2777	−	8.92024i	0.992590	−	0.721159i
$154$	2.71187			0.218529
$155$		0			0
$156$	16.0281			1.28327
$157$	−6.46767	+	4.69903i	−0.516176	+	0.375024i	−0.815161	−	0.579234i	$-0.803352\pi$
$157$	−6.46767	+	4.69903i	−0.516176	+	0.375024i	0.298985	+	0.954258i	$0.403352\pi$
$158$	−1.09215	+	10.3911i	−0.0868868	+	0.826673i
$159$	−4.50565	+	13.8670i	−0.357321	+	1.09972i
$160$	−6.47215	+	11.2101i	−0.511669	+	0.886236i
$161$	5.70146	+	9.87521i	0.449338	+	0.778276i
$162$	16.6733	−	3.54401i	1.30998	−	0.278444i
$163$	−5.27350	−	16.2302i	−0.413052	−	1.27124i	−0.913981	−	0.405756i	$-0.867008\pi$
$163$	−5.27350	−	16.2302i	−0.413052	−	1.27124i	0.500929	−	0.865488i	$-0.332992\pi$
$164$	23.9804	+	5.09719i	1.87255	+	0.398024i
$165$	−0.487191	−	4.63531i	−0.0379277	−	0.360858i
$166$	4.12312	+	4.57919i	0.320016	+	0.355414i
$167$	−22.2651	−	9.91307i	−1.72293	−	0.767096i	−0.996835	−	0.0794987i	$-0.974668\pi$
$167$	−22.2651	−	9.91307i	−1.72293	−	0.767096i	−0.726092	−	0.687598i	$-0.758665\pi$
$168$	−11.3741	+	5.06407i	−0.877530	+	0.390701i
$169$	−6.29336	+	6.98948i	−0.484104	+	0.537652i
$170$	−20.4256	−	14.8401i	−1.56657	−	1.13818i
$171$	13.0032	+	9.44737i	0.994379	+	0.722458i
$172$	0.512762	−	0.569480i	0.0390978	−	0.0434225i
$173$	8.19779	−	3.64989i	0.623267	−	0.277496i	−0.0707063	−	0.997497i	$-0.522525\pi$
$173$	8.19779	−	3.64989i	0.623267	−	0.277496i	0.693973	+	0.720001i	$0.255859\pi$
$174$	0.691131	+	0.307711i	0.0523945	+	0.0233275i
$175$	1.33158	+	1.47887i	0.100658	+	0.111792i
$176$	−0.0309923	−	0.294872i	−0.00233614	−	0.0222268i
$177$	23.6373	+	5.02425i	1.77669	+	0.377646i
$178$	−1.57201	−	4.83816i	−0.117827	−	0.362635i
$179$	11.0438	−	2.34743i	0.825452	−	0.175455i	0.224229	−	0.974537i	$-0.428014\pi$
$179$	11.0438	−	2.34743i	0.825452	−	0.175455i	0.601223	+	0.799081i	$0.294680\pi$
$180$	14.3930	+	24.9294i	1.07279	+	1.85813i
$181$	7.47052	−	12.9393i	0.555279	−	0.961772i	−0.442602	−	0.896718i	$-0.645945\pi$
$181$	7.47052	−	12.9393i	0.555279	−	0.961772i	0.997882	−	0.0650542i	$-0.0207220\pi$
$182$	−2.16567	+	6.66523i	−0.160530	+	0.494060i
$183$	−2.08389	+	19.8269i	−0.154045	+	1.46564i
$184$	17.6036	−	12.7898i	1.29775	−	0.942874i
$185$	−21.0607			−1.54841
$186$		0			0
$187$	−3.21286			−0.234947
$188$	21.6160	−	15.7050i	1.57651	−	1.14540i
$189$	0.198167	−	1.88544i	0.0144146	−	0.137145i
$190$	8.26294	−	25.4307i	0.599457	−	1.84494i
$191$	−1.13046	+	1.95802i	−0.0817975	+	0.141677i	−0.904022	−	0.427486i	$-0.859399\pi$
$191$	−1.13046	+	1.95802i	−0.0817975	+	0.141677i	0.822225	+	0.569163i	$0.192733\pi$
$192$	−16.2269	−	28.1057i	−1.17107	−	2.02836i
$193$	−25.1034	+	5.33590i	−1.80698	+	0.384086i	−0.983158	−	0.182756i	$-0.941498\pi$
$193$	−25.1034	+	5.33590i	−1.80698	+	0.384086i	−0.823826	+	0.566843i	$0.808165\pi$
$194$	8.76347	+	26.9712i	0.629181	+	1.93642i
$195$	11.7817	+	2.50428i	0.843706	+	0.179335i
$196$	1.54091	+	14.6608i	0.110065	+	1.04720i
$197$	−4.14574	−	4.60431i	−0.295372	−	0.328044i	0.577132	−	0.816651i	$-0.304172\pi$
$197$	−4.14574	−	4.60431i	−0.295372	−	0.328044i	−0.872504	+	0.488607i	$0.837505\pi$
$198$	5.35956	+	2.38623i	0.380887	+	0.169582i
$199$	−4.17429	+	1.85851i	−0.295908	+	0.131747i	−0.549321	−	0.835612i	$-0.685113\pi$
$199$	−4.17429	+	1.85851i	−0.295908	+	0.131747i	0.253413	+	0.967358i	$0.418447\pi$
$200$	2.54094	−	2.82200i	0.179672	−	0.199546i
$201$	9.92879	+	7.21369i	0.700323	+	0.508814i
$202$	−13.7106	−	9.96132i	−0.964673	−	0.700876i
$203$	−0.138205	+	0.153493i	−0.00970011	+	0.0107731i
$204$	33.8203	−	15.0578i	2.36790	−	1.05426i
$205$	16.8308	+	7.49355i	1.17551	+	0.523372i
$206$	8.62924	+	9.58374i	0.601227	+	0.667731i
$207$	2.57858	+	24.5335i	0.179223	+	1.70520i
$208$	0.749487	+	0.159308i	0.0519676	+	0.0110460i
$209$	−1.05150	−	3.23618i	−0.0727336	−	0.223851i
$210$	−22.9695	+	4.88233i	−1.58505	+	0.336912i
$211$	9.30839	+	16.1226i	0.640816	+	1.10993i	0.985251	+	0.171115i	$0.0547371\pi$
$211$	9.30839	+	16.1226i	0.640816	+	1.10993i	−0.344435	+	0.938810i	$0.611930\pi$
$212$	−9.53225	+	16.5103i	−0.654678	+	1.13394i
$213$	2.67547	−	8.23426i	0.183321	−	0.564203i
$214$	−0.439991	+	4.18624i	−0.0300772	+	0.286165i
$215$	0.465892	−	0.338490i	0.0317736	−	0.0230849i
$216$	−3.61764			−0.246149
$217$		0			0
$218$	27.1487			1.83874
$219$	5.53783	−	4.02347i	0.374212	−	0.271881i
$220$	0.637015	−	6.06079i	0.0429475	−	0.408618i
$221$	2.56575	−	7.89656i	0.172591	−	0.531180i
$222$	24.7296	−	42.8329i	1.65974	−	2.87475i
$223$	−3.10748	−	5.38231i	−0.208092	−	0.360426i	0.743021	−	0.669268i	$-0.233392\pi$
$223$	−3.10748	−	5.38231i	−0.208092	−	0.360426i	−0.951113	+	0.308842i	$0.900059\pi$
$224$	8.11784	−	1.72550i	0.542396	−	0.115290i
$225$	1.33036	+	4.09441i	0.0886904	+	0.272961i
$226$	−24.9512	−	5.30354i	−1.65973	−	0.352786i
$227$	1.36387	+	12.9763i	0.0905230	+	0.861269i	0.941714	+	0.336413i	$0.109214\pi$
$227$	1.36387	+	12.9763i	0.0905230	+	0.861269i	−0.851191	+	0.524855i	$0.824119\pi$
$228$	26.2357	+	29.1377i	1.73750	+	1.92969i
$229$	13.9571	+	6.21410i	0.922310	+	0.410639i	0.812266	−	0.583288i	$-0.198234\pi$
$229$	13.9571	+	6.21410i	0.922310	+	0.410639i	0.110045	+	0.993927i	$0.464901\pi$
$230$	37.4917	−	16.6924i	2.47213	−	1.10066i
$231$	−1.99955	+	2.22073i	−0.131561	+	0.146113i
$232$	0.318860	+	0.231665i	0.0209342	+	0.0152096i
$233$	−10.5668	−	7.67721i	−0.692253	−	0.502951i	0.185147	−	0.982711i	$-0.440724\pi$
$233$	−10.5668	−	7.67721i	−0.692253	−	0.502951i	−0.877400	+	0.479760i	$0.840724\pi$
$234$	−10.1449	+	11.2671i	−0.663195	+	0.736553i
$235$	18.3430	−	8.16684i	1.19657	−	0.532746i
$236$	28.8651	+	12.8516i	1.87896	+	0.836567i
$237$	−7.70391	−	8.55606i	−0.500423	−	0.555776i
$238$	1.69204	+	16.0986i	0.109678	+	1.04352i
$239$	22.9300	+	4.87391i	1.48322	+	0.315267i	0.877177	−	0.480168i	$-0.159424\pi$
$239$	22.9300	+	4.87391i	1.48322	+	0.315267i	0.606039	+	0.795435i	$0.292758\pi$
$240$	0.793379	+	2.44177i	0.0512124	+	0.157616i
$241$	−24.1721	+	5.13793i	−1.55706	+	0.330963i	−0.904399	−	0.426687i	$-0.859681\pi$
$241$	−24.1721	+	5.13793i	−1.55706	+	0.330963i	−0.652660	+	0.757651i	$0.726347\pi$
$242$	12.0704	+	20.9065i	0.775914	+	1.34392i
$243$	−11.1668	+	19.3415i	−0.716353	+	1.24076i
$244$	−8.05513	+	24.7911i	−0.515677	+	1.58709i
$245$	−1.15798	+	11.0174i	−0.0739806	+	0.703879i
$246$	−35.0030	+	25.4312i	−2.23171	+	1.62143i
$247$	8.79358			0.559522
$248$		0			0
$249$	−6.78996			−0.430296
$250$	−17.5266	+	12.7339i	−1.10848	+	0.805360i
$251$	2.42445	−	23.0671i	0.153030	−	1.45598i	−0.601057	−	0.799206i	$-0.705253\pi$
$251$	2.42445	−	23.0671i	0.153030	−	1.45598i	0.754087	−	0.656775i	$-0.228080\pi$
$252$	5.70323	−	17.5527i	0.359270	−	1.10572i
$253$	2.61125	−	4.52282i	0.164168	−	0.284348i
$254$	1.48493	+	2.57198i	0.0931729	+	0.161380i
$255$	27.2129	−	5.78428i	1.70414	−	0.362226i
$256$	−5.72420	−	17.6173i	−0.357763	−	1.10108i
$257$	−15.0108	−	3.19064i	−0.936345	−	0.199026i	−0.285623	−	0.958342i	$-0.592201\pi$
$257$	−15.0108	−	3.19064i	−0.936345	−	0.199026i	−0.650722	+	0.759316i	$0.725534\pi$
$258$	0.141363	+	1.34498i	0.00880088	+	0.0837348i
$259$	9.03527	+	10.0347i	0.561424	+	0.623525i
$260$	14.3875	+	6.40572i	0.892274	+	0.397266i
$261$	−0.408200	+	0.181743i	−0.0252670	+	0.0112496i
$262$	−12.3837	+	13.7535i	−0.765069	+	0.849695i
$263$	5.50607	+	4.00039i	0.339519	+	0.246675i	0.744459	−	0.667668i	$-0.232708\pi$
$263$	5.50607	+	4.00039i	0.339519	+	0.246675i	−0.404940	+	0.914343i	$0.632708\pi$
$264$	4.61325	+	3.35173i	0.283926	+	0.206284i
$265$	−9.58648	+	10.6469i	−0.588893	+	0.654031i
$266$	−15.6617	+	6.97305i	−0.960282	+	0.427545i
$267$	5.12102	+	2.28003i	0.313401	+	0.139535i
$268$	10.7374	+	11.9251i	0.655893	+	0.728442i
$269$	−1.09960	−	10.4620i	−0.0670439	−	0.637881i	−0.975515	−	0.219933i	$-0.929416\pi$
$269$	−1.09960	−	10.4620i	−0.0670439	−	0.637881i	0.908471	−	0.417948i	$-0.137250\pi$
$270$	−6.67408	−	1.41862i	−0.406172	−	0.0863344i
$271$	−0.487363	−	1.49995i	−0.0296052	−	0.0911154i	0.935162	−	0.354220i	$-0.115254\pi$
$271$	−0.487363	−	1.49995i	−0.0296052	−	0.0911154i	−0.964767	+	0.263105i	$0.915254\pi$
$272$	1.73113	−	0.367963i	0.104965	−	0.0223111i
$273$	−3.86128	−	6.68794i	−0.233695	−	0.404772i
$274$	19.0103	−	32.9268i	1.14845	−	1.98918i
$275$	0.281645	−	0.866813i	0.0169838	−	0.0522708i
$276$	−6.29028	+	59.8480i	−0.378630	+	3.60243i
$277$	−9.79020	+	7.11300i	−0.588236	+	0.427379i	−0.841684	−	0.539970i	$-0.818435\pi$
$277$	−9.79020	+	7.11300i	−0.588236	+	0.427379i	0.253448	+	0.967349i	$0.418435\pi$
$278$	16.9368			1.01580
$279$		0			0
$280$	−12.2337			−0.731106
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.0667525	−	0.997770i	$-0.478736\pi$
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.969563	+	0.244842i	$0.0787362\pi$
$282$	−4.92889	+	46.8952i	−0.293511	+	2.79257i
$283$	−0.212853	+	0.655094i	−0.0126528	+	0.0389413i	−0.957184	−	0.289482i	$-0.906517\pi$
$283$	−0.212853	+	0.655094i	−0.0126528	+	0.0389413i	0.944531	+	0.328423i	$0.106517\pi$
$284$	5.66030	−	9.80392i	0.335877	−	0.581756i
$285$	14.7324	+	25.5173i	0.872675	+	1.51152i
$286$	3.13962	−	0.667346i	0.185649	−	0.0394610i
$287$	−3.65018	−	11.2341i	−0.215463	−	0.663127i
$288$	17.5618	+	3.73288i	1.03484	+	0.219962i
$289$	−0.227636	−	2.16581i	−0.0133904	−	0.127401i
$290$	0.497410	+	0.552429i	0.0292089	+	0.0324398i
$291$	−28.5481	−	12.7104i	−1.67352	−	0.745098i
$292$	8.17641	−	3.64037i	0.478488	−	0.213037i
$293$	6.03012	−	6.69713i	0.352284	−	0.391251i	−0.540793	−	0.841156i	$-0.681876\pi$
$293$	6.03012	−	6.69713i	0.352284	−	0.391251i	0.893076	+	0.449905i	$0.148542\pi$
$294$	−21.0474	−	15.2918i	−1.22751	−	0.891837i
$295$	19.2098	+	13.9568i	1.11844	+	0.812594i
$296$	17.2413	−	19.1484i	1.00213	−	1.11298i
$297$	−0.793215	+	0.353162i	−0.0460270	+	0.0204925i
$298$	−13.4111	−	5.97102i	−0.776886	−	0.345892i
$299$	9.03087	+	10.0298i	0.522269	+	0.580038i
$300$	1.09777	+	10.4445i	0.0633796	+	0.603016i
$301$	−0.361151	−	0.0767651i	−0.0208164	−	0.00442467i
$302$	−3.93949	−	12.1245i	−0.226692	−	0.697688i
$303$	18.2665	−	3.88266i	1.04938	−	0.223053i
$304$	0.937195	+	1.62327i	0.0537518	+	0.0931009i
$305$	−9.79451	+	16.9646i	−0.560832	+	0.971389i
$306$	−10.8215	+	33.3051i	−0.618623	+	1.90393i
$307$	3.27515	−	31.1610i	0.186923	−	1.77845i	−0.351904	−	0.936036i	$-0.614466\pi$
$307$	3.27515	−	31.1610i	0.186923	−	1.77845i	0.538827	−	0.842416i	$-0.318868\pi$
$308$	−3.16104	+	2.29663i	−0.180117	+	0.130863i
$309$	−14.2107			−0.808416
$310$		0			0
$311$	−17.7139			−1.00447			−0.502233	−	0.864732i	$-0.667488\pi$
$311$	−17.7139			−1.00447			−0.502233	+	0.864732i	$0.667488\pi$
$312$	−11.9219	+	8.66180i	−0.674947	+	0.490378i
$313$	2.26500	−	21.5500i	0.128025	−	1.21808i	−0.722210	−	0.691674i	$-0.756873\pi$
$313$	2.26500	−	21.5500i	0.128025	−	1.21808i	0.850235	−	0.526404i	$-0.176460\pi$
$314$	5.70058	−	17.5446i	0.321702	−	0.990098i
$315$	6.93475	−	12.0113i	0.390729	−	0.676762i
$316$	−7.52698	−	13.0371i	−0.423426	−	0.733395i
$317$	−0.993843	+	0.211248i	−0.0558198	+	0.0118649i	−0.235737	−	0.971817i	$-0.575750\pi$
$317$	−0.993843	+	0.211248i	−0.0558198	+	0.0118649i	0.179917	+	0.983682i	$0.442417\pi$
$318$	−10.3969	−	31.9984i	−0.583030	−	1.79438i
$319$	0.0925298	+	0.0196678i	0.00518067	+	0.00110119i
$320$	−3.33328	−	31.7141i	−0.186336	−	1.77287i
$321$	−3.10365	−	3.44696i	−0.173229	−	0.192390i
$322$	−24.0377	−	10.7023i	−1.33957	−	0.596414i
$323$	18.5550	−	8.26124i	1.03243	−	0.459668i
$324$	−16.4335	+	18.2513i	−0.912973	+	1.01396i
$325$	1.90553	+	1.38445i	0.105700	+	0.0767955i
$326$	31.8582	+	23.1463i	1.76446	+	1.28196i
$327$	−20.0176	+	22.2318i	−1.10698	+	1.22942i
$328$	−20.5916	+	9.16796i	−1.13698	+	0.506216i
$329$	−11.7606	−	5.23614i	−0.648381	−	0.288678i
$330$	7.19651	+	7.99254i	0.396155	+	0.439975i
$331$	−2.78981	−	26.5432i	−0.153342	−	1.45895i	−0.752645	−	0.658426i	$-0.771222\pi$
$331$	−2.78981	−	26.5432i	−0.153342	−	1.45895i	0.599304	−	0.800522i	$-0.295444\pi$
$332$	−8.68405	−	1.84585i	−0.476599	−	0.101304i
$333$	9.02697	+	27.7822i	0.494675	+	1.52245i
$334$	55.0106	−	11.6929i	3.01004	−	0.639805i
$335$	6.02951	+	10.4434i	0.329427	+	0.570584i
$336$	0.823049	−	1.42556i	0.0449010	−	0.0777708i
$337$	9.87048	−	30.3782i	0.537679	−	1.65481i	−0.200108	−	0.979774i	$-0.564129\pi$
$337$	9.87048	−	30.3782i	0.537679	−	1.65481i	0.737788	−	0.675033i	$-0.235871\pi$
$338$	2.26857	−	21.5840i	0.123394	−	1.17402i
$339$	22.7404	−	16.5218i	1.23509	−	0.897343i
$340$	36.3765			1.97279
$341$		0			0
$342$	−37.0885			−2.00552
$343$	14.8178	−	10.7658i	0.800088	−	0.581298i
$344$	−0.0736457	+	0.700692i	−0.00397071	+	0.0377788i
$345$	−13.9746	+	43.0095i	−0.752368	+	2.31555i
$346$	−10.3534	+	17.9326i	−0.556603	+	0.964065i
$347$	−1.56066	−	2.70314i	−0.0837804	−	0.145112i	0.821090	−	0.570798i	$-0.193366\pi$
$347$	−1.56066	−	2.70314i	−0.0837804	−	0.145112i	−0.904871	+	0.425686i	$0.860033\pi$
$348$	−1.06620	+	0.226627i	−0.0571542	+	0.0121485i
$349$	−6.80655	−	20.9484i	−0.364346	−	1.12134i	−0.950389	−	0.311063i	$-0.899315\pi$
$349$	−6.80655	−	20.9484i	−0.364346	−	1.12134i	0.586043	−	0.810280i	$-0.300685\pi$
$350$	−4.49166	−	0.954732i	−0.240089	−	0.0510326i
$351$	−0.234550	−	2.23159i	−0.0125193	−	0.119114i
$352$	−2.54337	−	2.82470i	−0.135562	−	0.150557i
$353$	4.50596	+	2.00618i	0.239828	+	0.106778i	0.523132	−	0.852252i	$-0.324764\pi$
$353$	4.50596	+	2.00618i	0.239828	+	0.106778i	−0.283303	+	0.959030i	$0.591430\pi$
$354$	−50.9413	+	22.6805i	−2.70750	+	1.20546i
$355$	5.69249	−	6.32215i	0.302126	−	0.335545i
$356$	5.92973	+	4.30820i	0.314275	+	0.228334i
$357$	−14.4306	−	10.4845i	−0.763750	−	0.554897i
$358$	−17.4330	+	19.3613i	−0.921361	+	1.02328i
$359$	−0.329662	+	0.146775i	−0.0173989	+	0.00774648i	−0.415418	−	0.909631i	$-0.636365\pi$
$359$	−0.329662	+	0.146775i	−0.0173989	+	0.00774648i	0.398019	+	0.917377i	$0.369698\pi$
$360$	−24.1779	−	10.7647i	−1.27429	−	0.567350i
$361$	1.68038	+	1.86625i	0.0884410	+	0.0982237i
$362$	3.60381	+	34.2880i	0.189412	+	1.80214i
$363$	−26.0200	−	5.53073i	−1.36570	−	0.290288i
$364$	−3.12029	−	9.60325i	−0.163547	−	0.503347i
$365$	6.57899	−	1.39841i	0.344360	−	0.0731960i
$366$	−23.0015	−	39.8398i	−1.20231	−	2.08246i
$367$	14.6935	−	25.4498i	0.766992	−	1.32847i	−0.172195	−	0.985063i	$-0.555086\pi$
$367$	14.6935	−	25.4498i	0.766992	−	1.32847i	0.939187	−	0.343406i	$-0.111581\pi$
$368$	−0.888987	+	2.73602i	−0.0463416	+	0.142625i
$369$	2.67113	−	25.4141i	0.139054	−	1.32301i
$370$	39.3167	−	28.5653i	2.04398	−	1.48504i
$371$	9.18555			0.476890
$372$		0			0
$373$	17.7284			0.917941			0.458971	−	0.888451i	$-0.348218\pi$
$373$	17.7284			0.917941			0.458971	+	0.888451i	$0.348218\pi$
$374$	5.99786	−	4.35770i	0.310142	−	0.225331i
$375$	2.49533	−	23.7415i	0.128858	−	1.22601i
$376$	−7.59116	+	23.3632i	−0.391484	+	1.20486i
$377$	−0.122233	+	0.211713i	−0.00629530	+	0.0109038i
$378$	2.18733	+	3.78857i	0.112504	+	0.194863i
$379$	2.40665	−	0.511550i	0.123622	−	0.0262766i	−0.145685	−	0.989331i	$-0.546539\pi$
$379$	2.40665	−	0.511550i	0.123622	−	0.0262766i	0.269307	+	0.963054i	$0.413205\pi$
$380$	11.9052	+	36.6405i	0.610725	+	1.87962i
$381$	−3.20106	−	0.680405i	−0.163995	−	0.0348582i
$382$	−0.545341	−	5.18857i	−0.0279021	−	0.265470i
$383$	−12.7924	−	14.2074i	−0.653660	−	0.725963i	0.321636	−	0.946863i	$-0.395767\pi$
$383$	−12.7924	−	14.2074i	−0.653660	−	0.725963i	−0.975296	+	0.220900i	$0.929101\pi$
$384$	44.3440	+	19.7432i	2.26292	+	1.00752i
$385$	−2.68241	+	1.19429i	−0.136708	+	0.0608664i
$386$	39.6265	−	44.0097i	2.01694	−	2.24004i
$387$	−0.646208	−	0.469497i	−0.0328486	−	0.0238659i
$388$	−33.0563	−	24.0168i	−1.67818	−	1.21927i
$389$	3.52703	−	3.91716i	0.178827	−	0.198608i	−0.647066	−	0.762434i	$-0.724004\pi$
$389$	3.52703	−	3.91716i	0.178827	−	0.198608i	0.825894	+	0.563826i	$0.190671\pi$
$390$	−25.3911	+	11.3048i	−1.28573	+	0.572443i
$391$	28.4784	+	12.6794i	1.44021	+	0.641224i
$392$	−9.06907	−	10.0722i	−0.458057	−	0.508724i
$393$	−2.13171	−	20.2818i	−0.107530	−	1.02308i
$394$	13.9843	+	2.97247i	0.704521	+	0.149751i
$395$	−3.49587	−	10.7592i	−0.175897	−	0.541354i
$396$	−8.26811	+	1.75744i	−0.415488	+	0.0883147i
$397$	−8.46275	−	14.6579i	−0.424733	−	0.735660i	0.571662	−	0.820489i	$-0.306299\pi$
$397$	−8.46275	−	14.6579i	−0.424733	−	0.735660i	−0.996395	+	0.0848295i	$0.972965\pi$
$398$	5.27193	−	9.13124i	0.264258	−	0.457708i
$399$	5.83773	−	17.9667i	0.292252	−	0.899460i
$400$	−0.0524793	+	0.499307i	−0.00262396	+	0.0249653i
$401$	−30.7747	+	22.3591i	−1.53682	+	1.11656i	−0.584524	+	0.811377i	$0.698719\pi$
$401$	−30.7747	+	22.3591i	−1.53682	+	1.11656i	−0.952293	+	0.305186i	$0.901281\pi$
$402$	−28.3195			−1.41245
$403$		0			0
$404$	24.4175			1.21482
$405$	−14.9314	+	10.8483i	−0.741945	+	0.539055i
$406$	0.0498190	−	0.473996i	0.00247248	−	0.0235240i
$407$	1.91107	−	5.88166i	0.0947281	−	0.291543i
$408$	−17.0187	+	29.4772i	−0.842550	+	1.45934i
$409$	−0.249342	−	0.431873i	−0.0123292	−	0.0213547i	0.859795	−	0.510639i	$-0.170591\pi$
$409$	−0.249342	−	0.431873i	−0.0123292	−	0.0213547i	−0.872124	+	0.489285i	$0.837258\pi$
$410$	−41.5839	+	8.83893i	−2.05368	+	0.436524i
$411$	12.9465	+	39.8453i	0.638605	+	1.96542i
$412$	−18.1748	−	3.86317i	−0.895407	−	0.190325i
$413$	−1.59132	−	15.1404i	−0.0783038	−	0.745010i
$414$	−38.0893	−	42.3024i	−1.87199	−	2.07905i
$415$	−6.09496	−	2.71365i	−0.299190	−	0.133208i
$416$	8.97365	−	3.99533i	0.439970	−	0.195887i
$417$	−12.4881	+	13.8694i	−0.611544	+	0.679188i
$418$	6.35229	+	4.61521i	0.310701	+	0.225737i
$419$	−10.9298	−	7.94098i	−0.533957	−	0.387942i	0.287879	−	0.957667i	$-0.407050\pi$
$419$	−10.9298	−	7.94098i	−0.533957	−	0.387942i	−0.821836	+	0.569725i	$0.807050\pi$
$420$	22.6392	−	25.1434i	1.10468	−	1.22687i
$421$	−28.2424	+	12.5743i	−1.37645	+	0.612834i	−0.955700	−	0.294343i	$-0.904899\pi$
$421$	−28.2424	+	12.5743i	−1.37645	+	0.612834i	−0.420749	+	0.907177i	$0.638233\pi$
$422$	−39.2447	−	17.4729i	−1.91040	−	0.850566i
$423$	−18.6354	−	20.6967i	−0.906083	−	1.00631i
$424$	−1.83218	−	17.4320i	−0.0889785	−	0.846574i
$425$	5.32144	+	1.13111i	0.258128	+	0.0548668i
$426$	6.17373	+	19.0008i	0.299118	+	0.920591i
$427$	12.2850	−	2.61125i	0.594512	−	0.126367i
$428$	−3.03237	−	5.25223i	−0.146575	−	0.253876i
$429$	−1.76846	+	3.06306i	−0.0853820	+	0.147886i
$430$	−0.410636	+	1.26381i	−0.0198026	+	0.0609462i
$431$	1.26007	−	11.9888i	0.0606954	−	0.577478i	−0.921337	−	0.388765i	$-0.872902\pi$
$431$	1.26007	−	11.9888i	0.0606954	−	0.577478i	0.982032	−	0.188713i	$-0.0604316\pi$
$432$	0.386948	−	0.281134i	0.0186170	−	0.0135261i
$433$	−32.3919			−1.55665			−0.778327	−	0.627860i	$-0.783931\pi$
$433$	−32.3919			−1.55665			−0.778327	+	0.627860i	$0.783931\pi$
$434$		0			0
$435$	−0.819136			−0.0392745
$436$	−31.6454	+	22.9917i	−1.51554	+	1.10110i
$437$	−3.45107	+	32.8348i	−0.165087	+	1.57070i
$438$	−4.88102	+	15.0222i	−0.233224	+	0.717790i
$439$	−6.18408	+	10.7111i	−0.295150	+	0.511215i	−0.975020	−	0.222118i	$-0.928703\pi$
$439$	−6.18408	+	10.7111i	−0.295150	+	0.511215i	0.679870	+	0.733333i	$0.262036\pi$
$440$	2.80151	+	4.85236i	0.133557	+	0.231327i
$441$	15.0300	−	3.19472i	0.715712	−	0.152129i
$442$	5.92053	+	18.2215i	0.281611	+	0.866709i
$443$	4.62019	+	0.982051i	0.219512	+	0.0466587i	0.316355	−	0.948641i	$-0.397541\pi$
$443$	4.62019	+	0.982051i	0.219512	+	0.0466587i	−0.0968428	+	0.995300i	$0.530874\pi$
$444$	7.44876	+	70.8703i	0.353503	+	3.36335i
$445$	3.68562	+	4.09329i	0.174715	+	0.194041i
$446$	13.1013	+	5.83308i	0.620365	+	0.276204i
$447$	14.7781	−	6.57963i	0.698979	−	0.311206i
$448$	−13.6806	+	15.1939i	−0.646348	+	0.717843i
$449$	12.9315	+	9.39528i	0.610275	+	0.443390i	0.849511	−	0.527571i	$-0.176897\pi$
$449$	12.9315	+	9.39528i	0.610275	+	0.443390i	−0.239236	+	0.970961i	$0.576897\pi$
$450$	−8.03692	−	5.83917i	−0.378864	−	0.275261i
$451$	−3.61998	+	4.02039i	−0.170458	+	0.189313i
$452$	33.5753	−	14.9487i	1.57925	−	0.703128i
$453$	12.8334	+	5.71379i	0.602964	+	0.268457i
$454$	−20.1463	−	22.3747i	−0.945512	−	1.05010i
$455$	−0.793175	−	7.54656i	−0.0371846	−	0.353788i
$456$	−35.2610	−	7.49495i	−1.65125	−	0.350983i
$457$	1.40842	+	4.33468i	0.0658832	+	0.202768i	0.978579	−	0.205872i	$-0.0660032\pi$
$457$	1.40842	+	4.33468i	0.0658832	+	0.202768i	−0.912696	+	0.408640i	$0.866003\pi$
$458$	−34.4839	+	7.32977i	−1.61132	+	0.342498i
$459$	−2.59141	−	4.48846i	−0.120957	−	0.209503i
$460$	−29.5650	+	51.2081i	−1.37848	+	2.38759i
$461$	−5.25050	+	16.1594i	−0.244540	+	0.752618i	0.751171	+	0.660107i	$0.229489\pi$
$461$	−5.25050	+	16.1594i	−0.244540	+	0.752618i	−0.995712	+	0.0925105i	$0.970511\pi$
$462$	0.720780	−	6.85777i	0.0335337	−	0.319052i
$463$	−22.1896	+	16.1217i	−1.03124	+	0.749239i	−0.968556	−	0.248795i	$-0.919965\pi$
$463$	−22.1896	+	16.1217i	−1.03124	+	0.749239i	−0.0626822	+	0.998034i	$0.519965\pi$
$464$	−0.0521088			−0.00241909
$465$		0			0
$466$	30.1392			1.39617
$467$	18.5350	−	13.4665i	0.857697	−	0.623153i	−0.0695608	−	0.997578i	$-0.522160\pi$
$467$	18.5350	−	13.4665i	0.857697	−	0.623153i	0.927257	+	0.374425i	$0.122160\pi$
$468$	2.28337	−	21.7248i	0.105549	−	1.00423i
$469$	2.38919	−	7.35318i	0.110323	−	0.339538i
$470$	−23.1663	+	40.1253i	−1.06858	+	1.85084i
$471$	10.1639	+	17.6043i	0.468327	+	0.811165i
$472$	−28.4155	+	6.03990i	−1.30793	+	0.278009i
$473$	0.0522553	+	0.160825i	0.00240270	+	0.00739476i
$474$	25.9867	+	5.52365i	1.19361	+	0.253710i
$475$	0.602274	+	5.73025i	0.0276342	+	0.262922i
$476$	−15.6059	−	17.3321i	−0.715295	−	0.794416i
$477$	18.1537	+	8.08255i	0.831201	+	0.370074i
$478$	−49.4169	+	22.0018i	−2.26028	+	1.00634i
$479$	6.05366	−	6.72327i	0.276599	−	0.307194i	−0.588799	−	0.808279i	$-0.700399\pi$
$479$	6.05366	−	6.72327i	0.276599	−	0.307194i	0.865398	+	0.501085i	$0.167066\pi$
$480$	26.6278	+	19.3462i	1.21539	+	0.883031i
$481$	12.9298	+	9.39403i	0.589547	+	0.428331i
$482$	38.1564	−	42.3769i	1.73797	−	1.93022i
$483$	26.4878	−	11.7931i	1.20523	−	0.536605i
$484$	−31.7749	−	14.1471i	−1.44431	−	0.643050i
$485$	−20.5461	−	22.8188i	−0.932952	−	1.03615i
$486$	−5.38693	−	51.2532i	−0.244356	−	2.32489i
$487$	23.1065	+	4.91143i	1.04705	+	0.222558i	0.699152	−	0.714973i	$-0.253561\pi$
$487$	23.1065	+	4.91143i	1.04705	+	0.222558i	0.347901	+	0.937531i	$0.386894\pi$
$488$	−7.40594	−	22.7931i	−0.335251	−	1.03180i
$489$	−42.4444	+	9.02183i	−1.91940	+	0.407981i
$490$	−12.7815	−	22.1383i	−0.577411	−	1.00011i
$491$	−4.61346	+	7.99074i	−0.208202	+	0.360617i	−0.951148	−	0.308734i	$-0.900095\pi$
$491$	−4.61346	+	7.99074i	−0.208202	+	0.360617i	0.742946	+	0.669351i	$0.233428\pi$
$492$	19.2634	−	59.2867i	0.868462	−	2.67285i
$493$	−0.0590225	+	0.561562i	−0.00265824	+	0.0252915i
$494$	−16.4161	+	11.9270i	−0.738596	+	0.536621i
$495$	−6.35220			−0.285510
$496$		0			0
$497$	−5.45442			−0.244664
$498$	12.6757	−	9.20943i	0.568011	−	0.412684i
$499$	−2.97007	+	28.2583i	−0.132958	+	1.26501i	0.700989	+	0.713172i	$0.252742\pi$
$499$	−2.97007	+	28.2583i	−0.132958	+	1.26501i	−0.833948	+	0.551843i	$0.813925\pi$
$500$	9.64554	−	29.6859i	0.431362	−	1.32759i
$501$	−30.9859	+	53.6692i	−1.38435	+	2.39776i
$502$	26.7606	+	46.3506i	1.19438	+	2.06873i
$503$	−17.8786	+	3.80022i	−0.797170	+	0.169444i	−0.588452	−	0.808532i	$-0.700262\pi$
$503$	−17.8786	+	3.80022i	−0.797170	+	0.169444i	−0.208718	+	0.977976i	$0.566929\pi$
$504$	5.24359	+	16.1381i	0.233568	+	0.718848i
$505$	17.9485	+	3.81507i	0.798698	+	0.169768i
$506$	1.25968	+	11.9851i	0.0559996	+	0.532801i
$507$	16.0023	+	17.7723i	0.710686	+	0.789297i
$508$	−3.90903	−	1.74041i	−0.173435	−	0.0772184i
$509$	9.48841	−	4.22451i	0.420566	−	0.187248i	−0.185532	−	0.982638i	$-0.559401\pi$
$509$	9.48841	−	4.22451i	0.420566	−	0.187248i	0.606098	+	0.795390i	$0.292734\pi$
$510$	−42.9564	+	47.7079i	−1.90214	+	2.11254i
$511$	−3.48875	−	2.53472i	−0.154333	−	0.112130i
$512$	3.69272	+	2.68292i	0.163197	+	0.118569i
$513$	3.67293	−	4.07920i	0.162164	−	0.180101i
$514$	32.3501	−	14.4032i	1.42690	−	0.635297i
$515$	−12.7561	−	5.67937i	−0.562100	−	0.250263i
$516$	−1.30381	−	1.44803i	−0.0573972	−	0.0637460i
$517$	0.616305	+	5.86375i	0.0271051	+	0.257887i
$518$	−30.4776	−	6.47822i	−1.33911	−	0.284637i
$519$	−7.05096	−	21.7006i	−0.309503	−	0.952552i
$520$	−14.1634	+	3.01052i	−0.621105	+	0.132020i
$521$	−4.62522	−	8.01111i	−0.202635	−	0.350973i	0.746742	−	0.665114i	$-0.231617\pi$
$521$	−4.62522	−	8.01111i	−0.202635	−	0.350973i	−0.949376	+	0.314141i	$0.898284\pi$
$522$	0.515537	−	0.892937i	0.0225645	−	0.0390828i
$523$	−2.03184	+	6.25335i	−0.0888461	+	0.273440i	−0.985601	−	0.169087i	$-0.945918\pi$
$523$	−2.03184	+	6.25335i	−0.0888461	+	0.273440i	0.896755	+	0.442527i	$0.145918\pi$
$524$	2.78726	−	26.5190i	0.121762	−	1.15849i
$525$	4.09367	−	2.97422i	0.178662	−	0.129806i
$526$	−15.7047			−0.684759
$527$		0			0
$528$	−0.753909			−0.0328097
$529$	−22.3875	+	16.2655i	−0.973371	+	0.707195i
$530$	3.45565	−	32.8783i	0.150104	−	1.42814i
$531$	10.1774	−	31.3227i	0.441660	−	1.35929i
$532$	12.3504	−	21.3916i	0.535460	−	0.927443i
$533$	−6.99044	−	12.1078i	−0.302790	−	0.524447i
$534$	−12.6525	+	2.68938i	−0.547529	+	0.116381i
$535$	−1.40837	−	4.33453i	−0.0608893	−	0.187398i
$536$	−14.4312	−	3.06744i	−0.623331	−	0.132493i
$537$	−3.00087	−	28.5514i	−0.129497	−	1.23208i
$538$	16.2427	+	18.0394i	0.700273	+	0.777732i
$539$	−2.97178	−	1.32312i	−0.128004	−	0.0569910i
$540$	8.98091	−	3.99856i	0.386477	−	0.172071i
$541$	−1.47428	+	1.63735i	−0.0633842	+	0.0703953i	−0.774003	−	0.633182i	$-0.781748\pi$
$541$	−1.47428	+	1.63735i	−0.0633842	+	0.0703953i	0.710619	+	0.703577i	$0.248415\pi$
$542$	2.94425	+	2.13912i	0.126466	+	0.0918831i
$543$	−30.7353	−	22.3305i	−1.31898	−	0.958294i
$544$	15.1815	−	16.8608i	0.650903	−	0.722902i
$545$	−26.8538	+	11.9561i	−1.15029	+	0.512141i
$546$	16.2794	+	7.24806i	0.696694	+	0.310188i
$547$	−3.25428	−	3.61424i	−0.139143	−	0.154534i	0.669546	−	0.742771i	$-0.266489\pi$
$547$	−3.25428	−	3.61424i	−0.139143	−	0.154534i	−0.808689	+	0.588237i	$0.799822\pi$
$548$	5.72606	+	54.4798i	0.244605	+	2.32726i
$549$	26.5769	+	5.64909i	1.13427	+	0.241097i
$550$	0.649903	+	2.00019i	0.0277119	+	0.0852886i
$551$	−0.584954	+	0.124336i	−0.0249199	+	0.00529689i
$552$	−27.6639	−	47.9152i	−1.17745	−	2.03941i
$553$	−3.62661	+	6.28147i	−0.154219	+	0.267115i
$554$	8.62905	−	26.5575i	0.366613	−	1.12832i
$555$	−5.59766	+	53.2582i	−0.237608	+	2.26068i
$556$	−19.7421	+	14.3435i	−0.837251	+	0.608298i
$557$	11.0363			0.467623			0.233811	−	0.972282i	$-0.424880\pi$
$557$	11.0363			0.467623			0.233811	+	0.972282i	$0.424880\pi$
$558$		0			0
$559$	−0.437007			−0.0184834
$560$	1.30854	−	0.950708i	0.0552958	−	0.0401748i
$561$	−0.853936	+	8.12466i	−0.0360532	+	0.343023i
$562$	−15.3115	+	47.1238i	−0.645875	+	1.98780i
$563$	5.59621	−	9.69292i	0.235852	−	0.408508i	−0.723668	−	0.690148i	$-0.757545\pi$
$563$	5.59621	−	9.69292i	0.235852	−	0.408508i	0.959520	+	0.281641i	$0.0908786\pi$
$564$	−33.9694	−	58.8366i	−1.43037	−	2.47747i
$565$	27.0158	−	5.74238i	1.13656	−	0.241584i
$566$	−0.491164	−	1.51165i	−0.0206452	−	0.0635393i
$567$	11.5745	+	2.46024i	0.486085	+	0.103320i
$568$	1.08796	+	10.3512i	0.0456496	+	0.434327i
$569$	−31.3969	−	34.8698i	−1.31623	−	1.46182i	−0.792410	−	0.609989i	$-0.791174\pi$
$569$	−31.3969	−	34.8698i	−1.31623	−	1.46182i	−0.523818	−	0.851830i	$-0.675493\pi$
$570$	−62.1129	−	27.6544i	−2.60162	−	1.15832i
$571$	−18.6908	+	8.32170i	−0.782187	+	0.348252i	−0.758673	−	0.651471i	$-0.774152\pi$
$571$	−18.6908	+	8.32170i	−0.782187	+	0.348252i	−0.0235138	+	0.999724i	$0.507485\pi$
$572$	−3.09447	+	3.43676i	−0.129386	+	0.143698i
$573$	4.65097	+	3.37913i	0.194297	+	0.141165i
$574$	22.0514	+	16.0213i	0.920407	+	0.668715i
$575$	−5.91730	+	6.57182i	−0.246768	+	0.274064i
$576$	−40.4068	+	17.9903i	−1.68362	+	0.749595i
$577$	3.33293	+	1.48392i	0.138752	+	0.0617762i	0.474938	−	0.880019i	$-0.342470\pi$
$577$	3.33293	+	1.48392i	0.138752	+	0.0617762i	−0.336186	+	0.941796i	$0.609137\pi$
$578$	3.36251	+	3.73445i	0.139862	+	0.155333i
$579$	6.82123	+	64.8996i	0.283480	+	2.69714i
$580$	−1.04764	−	0.222682i	−0.0435008	−	0.00924637i
$581$	1.32184	+	4.06822i	0.0548393	+	0.168778i
$582$	70.5338	−	14.9924i	2.92372	−	0.621456i
$583$	−2.10348	−	3.64334i	−0.0871173	−	0.150892i
$584$	−4.11443	+	7.12641i	−0.170256	+	0.294893i
$585$	5.07279	−	15.6124i	0.209734	−	0.645494i
$586$	−2.17369	+	20.6812i	−0.0897941	+	0.854334i
$587$	18.5043	−	13.4442i	0.763755	−	0.554901i	−0.136305	−	0.990667i	$-0.543523\pi$
$587$	18.5043	−	13.4442i	0.763755	−	0.554901i	0.900060	+	0.435766i	$0.143523\pi$
$588$	37.4838			1.54580
$589$		0			0
$590$	−54.7914			−2.25573
$591$	−12.7452	+	9.25996i	−0.524269	+	0.380904i
$592$	−0.356092	+	3.38799i	−0.0146353	+	0.139245i
$593$	−6.01340	+	18.5073i	−0.246941	+	0.760005i	0.748371	+	0.663281i	$0.230837\pi$
$593$	−6.01340	+	18.5073i	−0.246941	+	0.760005i	−0.995311	+	0.0967243i	$0.969163\pi$
$594$	1.00179	−	1.73515i	0.0411040	−	0.0711943i
$595$	−8.76336	−	15.1786i	−0.359263	−	0.622261i
$596$	20.6892	−	4.39762i	0.847461	−	0.180133i
$597$	3.59033	+	11.0499i	0.146942	+	0.452242i
$598$	−30.4628	−	6.47507i	−1.24572	−	0.264785i
$599$	−3.67646	−	34.9792i	−0.150216	−	1.42921i	−0.766782	−	0.641907i	$-0.778143\pi$
$599$	−3.67646	−	34.9792i	−0.150216	−	1.42921i	0.616566	−	0.787303i	$-0.288523\pi$
$600$	−6.46091	−	7.17557i	−0.263766	−	0.292942i
$601$	5.37901	+	2.39489i	0.219414	+	0.0976895i	0.513500	−	0.858089i	$-0.328349\pi$
$601$	5.37901	+	2.39489i	0.219414	+	0.0976895i	−0.294086	+	0.955779i	$0.595015\pi$
$602$	0.778326	−	0.346533i	0.0317222	−	0.0141236i
$603$	11.1920	−	12.4300i	0.455775	−	0.506190i
$604$	14.8600	+	10.7964i	0.604645	+	0.439300i
$605$	−21.1463	−	15.3637i	−0.859719	−	0.624622i
$606$	−28.8342	+	32.0237i	−1.17131	+	1.30087i
$607$	35.5231	−	15.8159i	1.44184	−	0.641947i	0.471097	−	0.882081i	$-0.343858\pi$
$607$	35.5231	−	15.8159i	1.44184	−	0.641947i	0.970740	+	0.240134i	$0.0771915\pi$
$608$	21.9518	+	9.77356i	0.890262	+	0.396370i
$609$	0.351418	+	0.390289i	0.0142402	+	0.0158153i
$610$	−4.72491	−	44.9546i	−0.191306	−	1.82016i
$611$	−14.9041	−	3.16796i	−0.602955	−	0.128162i
$612$	−15.5916	−	47.9859i	−0.630252	−	1.93972i
$613$	44.6059	−	9.48127i	1.80161	−	0.382945i	0.819779	−	0.572681i	$-0.194096\pi$
$613$	44.6059	−	9.48127i	1.80161	−	0.382945i	0.981835	+	0.189736i	$0.0607632\pi$
$614$	36.1505	+	62.6144i	1.45891	+	2.52691i
$615$	23.4231	−	40.5699i	0.944509	−	1.63594i
$616$	1.11010	−	3.41654i	0.0447272	−	0.137656i
$617$	0.692656	−	6.59018i	0.0278853	−	0.265311i	−0.971692	−	0.236250i	$-0.924082\pi$
$617$	0.692656	−	6.59018i	0.0278853	−	0.265311i	0.999578	−	0.0290609i	$-0.00925166\pi$
$618$	26.5288	−	19.2743i	1.06715	−	0.775328i
$619$	41.5360			1.66947			0.834736	−	0.550650i	$-0.185620\pi$
$619$	41.5360			1.66947			0.834736	+	0.550650i	$0.185620\pi$
$620$		0			0
$621$	8.42469			0.338071
$622$	33.0689	−	24.0260i	1.32594	−	0.963353i
$623$	0.369140	−	3.51213i	0.0147893	−	0.140711i
$624$	0.602062	−	1.85296i	0.0241018	−	0.0741776i
$625$	14.8341	−	25.6934i	0.593364	−	1.02774i
$626$	25.0006	+	43.3022i	0.999223	+	1.73071i
$627$	−8.46310	+	1.79889i	−0.337984	+	0.0718407i
$628$	8.21338	+	25.2782i	0.327750	+	1.00871i
$629$	36.1080	+	7.67500i	1.43972	+	0.306022i
$630$	3.34535	+	31.8289i	0.133282	+	1.26809i
$631$	7.45727	+	8.28213i	0.296869	+	0.329707i	0.873064	−	0.487606i	$-0.162130\pi$
$631$	7.45727	+	8.28213i	0.296869	+	0.329707i	−0.576195	+	0.817312i	$0.695463\pi$
$632$	12.6441	+	5.62953i	0.502956	+	0.223931i
$633$	43.2448	−	19.2538i	1.71883	−	0.765271i
$634$	1.56881	−	1.74234i	0.0623055	−	0.0691973i
$635$	−2.60147	−	1.89008i	−0.103236	−	0.0750056i
$636$	39.2177	+	28.4934i	1.55508	+	1.12983i
$637$	5.62520	−	6.24742i	0.222879	−	0.247532i
$638$	−0.199413	+	0.0887845i	−0.00789485	+	0.00351501i
$639$	−10.7797	−	4.79945i	−0.426440	−	0.189863i
$640$	31.9146	+	35.4447i	1.26153	+	1.40107i
$641$	−1.83482	−	17.4571i	−0.0724710	−	0.689516i	−0.969089	−	0.246711i	$-0.920650\pi$
$641$	−1.83482	−	17.4571i	−0.0724710	−	0.689516i	0.896618	−	0.442805i	$-0.146017\pi$
$642$	10.4692	+	2.22530i	0.413186	+	0.0878254i
$643$	−0.678617	−	2.08857i	−0.0267621	−	0.0823651i	0.936783	−	0.349910i	$-0.113788\pi$
$643$	−0.678617	−	2.08857i	−0.0267621	−	0.0823651i	−0.963545	+	0.267545i	$0.913788\pi$
$644$	37.0826	−	7.88214i	1.46126	−	0.310600i
$645$	−0.732145	−	1.26811i	−0.0288282	−	0.0499318i
$646$	−23.4341	+	40.5891i	−0.922003	+	1.59696i
$647$	−10.0259	+	30.8566i	−0.394160	+	1.21310i	0.535454	+	0.844564i	$0.320140\pi$
$647$	−10.0259	+	30.8566i	−0.394160	+	1.21310i	−0.929614	+	0.368535i	$0.879860\pi$
$648$	2.36027	−	22.4565i	0.0927202	−	0.882173i
$649$	−5.64084	+	4.09831i	−0.221422	+	0.160873i
$650$	−5.43508			−0.213181
$651$		0			0
$652$	−56.7370			−2.22199
$653$	−13.3407	+	9.69256i	−0.522061	+	0.379299i	−0.817380	−	0.576099i	$-0.804574\pi$
$653$	−13.3407	+	9.69256i	−0.522061	+	0.379299i	0.295319	+	0.955399i	$0.404574\pi$
$654$	7.21578	−	68.6535i	0.282159	−	2.68457i
$655$	6.19225	−	19.0578i	0.241951	−	0.744649i
$656$	1.49004	−	2.58083i	0.0581764	−	0.100764i
$657$	−4.66457	−	8.07927i	−0.181982	−	0.315202i
$658$	29.0569	−	6.17623i	1.13275	−	0.240774i
$659$	−6.10043	−	18.7752i	−0.237639	−	0.731377i	−0.996760	−	0.0804282i	$-0.974371\pi$
$659$	−6.10043	−	18.7752i	−0.237639	−	0.731377i	0.759122	−	0.650949i	$-0.225629\pi$
$660$	−15.1572	−	3.22176i	−0.589993	−	0.125407i
$661$	−1.23143	−	11.7163i	−0.0478971	−	0.455710i	−0.992017	−	0.126107i	$-0.959752\pi$
$661$	−1.23143	−	11.7163i	−0.0478971	−	0.455710i	0.944120	−	0.329603i	$-0.106915\pi$
$662$	41.2095	+	45.7678i	1.60165	+	1.77881i
$663$	−19.2868	−	8.58705i	−0.749038	−	0.333493i
$664$	7.45686	−	3.32001i	0.289382	−	0.128841i
$665$	12.4207	−	13.7946i	0.481654	−	0.534931i
$666$	−54.5336	−	39.6210i	−2.11313	−	1.53528i
$667$	−0.742554	−	0.539497i	−0.0287518	−	0.0208894i
$668$	−54.2195	+	60.2169i	−2.09782	+	2.32986i
$669$	−14.4367	+	6.42762i	−0.558154	+	0.248506i
$670$	−25.4208	−	11.3181i	−0.982090	−	0.437255i
$671$	−3.84897	−	4.27471i	−0.148588	−	0.165023i
$672$	−2.20582	−	20.9870i	−0.0850913	−	0.809590i
$673$	−49.2811	−	10.4750i	−1.89965	−	0.403783i	−0.900154	−	0.435572i	$-0.856546\pi$
$673$	−49.2811	−	10.4750i	−1.89965	−	0.403783i	−0.999495	+	0.0317890i	$0.989880\pi$
$674$	22.7764	+	70.0985i	0.877314	+	2.70009i
$675$	1.43813	−	0.305684i	0.0553537	−	0.0117658i
$676$	15.6348	+	27.0802i	0.601337	+	1.04155i
$677$	1.98998	−	3.44674i	0.0764810	−	0.132469i	−0.825248	−	0.564770i	$-0.808965\pi$
$677$	1.98998	−	3.44674i	0.0764810	−	0.132469i	0.901729	+	0.432301i	$0.142298\pi$
$678$	−20.0433	+	61.6869i	−0.769758	+	2.36907i
$679$	−2.05784	+	19.5790i	−0.0789726	+	0.751374i
$680$	−27.0574	+	19.6584i	−1.03760	+	0.753864i
$681$	33.1770			1.27134
$682$		0			0
$683$	5.23244			0.200214			0.100107	−	0.994977i	$-0.468082\pi$
$683$	5.23244			0.200214			0.100107	+	0.994977i	$0.468082\pi$
$684$	43.2314	−	31.4095i	1.65300	−	1.20097i
$685$	−4.30307	+	40.9410i	−0.164412	+	1.56427i
$686$	−13.0604	+	40.1958i	−0.498648	+	1.53468i
$687$	19.4238	−	33.6430i	0.741064	−	1.28356i
$688$	−0.0465749	−	0.0806701i	−0.00177565	−	0.00307552i
$689$	10.6344	−	2.26041i	0.405138	−	0.0861148i
$690$	−32.2468	−	99.2455i	−1.22762	−	3.77821i
$691$	−8.99459	−	1.91186i	−0.342170	−	0.0727305i	0.0336216	−	0.999435i	$-0.489296\pi$
$691$	−8.99459	−	1.91186i	−0.342170	−	0.0727305i	−0.375792	+	0.926704i	$0.622629\pi$
$692$	−3.11854	−	29.6709i	−0.118549	−	1.12792i
$693$	2.72516	+	3.02660i	0.103520	+	0.114971i
$694$	6.57982	+	2.92952i	0.249767	+	0.111203i
$695$	−16.7528	+	7.45883i	−0.635471	+	0.282930i
$696$	0.670582	−	0.744757i	0.0254184	−	0.0282299i
$697$	−26.1251	−	18.9810i	−0.989560	−	0.718957i
$698$	41.1196	+	29.8751i	1.55640	+	1.13079i
$699$	−22.2226	+	24.6807i	−0.840536	+	0.933510i
$700$	6.04416	−	2.69103i	0.228448	−	0.101711i
$701$	−37.0482	−	16.4949i	−1.39929	−	0.623005i	−0.438110	−	0.898921i	$-0.644352\pi$
$701$	−37.0482	−	16.4949i	−1.39929	−	0.623005i	−0.961182	+	0.275917i	$0.911019\pi$
$702$	3.46464	+	3.84787i	0.130764	+	0.145229i
$703$	4.08666	+	38.8820i	0.154131	+	1.46646i
$704$	9.15931	+	1.94687i	0.345204	+	0.0733754i
$705$	−15.7769	−	48.5564i	−0.594193	−	1.82874i
$706$	−11.1329	+	2.36637i	−0.418993	+	0.0890596i
$707$	−5.88235	−	10.1885i	−0.221229	−	0.383179i
$708$	40.1710	−	69.5782i	1.50972	−	2.61491i
$709$	−11.5220	+	35.4612i	−0.432719	+	1.33177i	0.462687	+	0.886521i	$0.346885\pi$
$709$	−11.5220	+	35.4612i	−0.432719	+	1.33177i	−0.895406	+	0.445250i	$0.853115\pi$
$710$	−2.05198	+	19.5233i	−0.0770094	+	0.732695i
$711$	−12.6946	+	9.22314i	−0.476083	+	0.345895i
$712$	−6.73883			−0.252548
$713$		0			0
$714$	41.1599			1.54037
$715$	−2.81161	+	2.04276i	−0.105148	+	0.0763948i
$716$	3.92372	−	37.3317i	0.146636	−	1.39515i
$717$	18.4196	−	56.6897i	0.687893	−	2.11712i
$718$	0.416347	−	0.721134i	0.0155379	−	0.0269125i
$719$	9.28994	+	16.0906i	0.346456	+	0.600080i	0.985617	−	0.168993i	$-0.0540516\pi$
$719$	9.28994	+	16.0906i	0.346456	+	0.600080i	−0.639161	+	0.769073i	$0.720718\pi$
$720$	3.42265	−	0.727507i	0.127555	−	0.0271126i
$721$	2.76647	+	8.51433i	0.103029	+	0.317090i
$722$	−5.66823	−	1.20482i	−0.210950	−	0.0448387i
$723$	6.56815	+	62.4918i	0.244272	+	2.32409i
$724$	−33.2385	−	36.9151i	−1.23530	−	1.37194i
$725$	−0.146332	−	0.0651514i	−0.00543465	−	0.00241966i
$726$	56.0764	−	24.9668i	2.08119	−	0.926606i
$727$	10.9585	−	12.1706i	0.406427	−	0.451383i	−0.504831	−	0.863218i	$-0.668445\pi$
$727$	10.9585	−	12.1706i	0.406427	−	0.451383i	0.911258	+	0.411835i	$0.135112\pi$
$728$	7.51065	+	5.45681i	0.278363	+	0.202243i
$729$	28.0140	+	20.3534i	1.03756	+	0.753829i
$730$	−10.3851	+	11.5339i	−0.384371	+	0.426888i
$731$	−0.922113	+	0.410551i	−0.0341056	+	0.0151848i
$732$	60.5507	+	26.9589i	2.23802	+	0.996431i
$733$	−0.770396	−	0.855611i	−0.0284552	−	0.0316027i	0.728749	−	0.684781i	$-0.240102\pi$
$733$	−0.770396	−	0.855611i	−0.0284552	−	0.0316027i	−0.757204	+	0.653178i	$0.773435\pi$
$734$	7.08819	+	67.4396i	0.261630	+	2.48924i
$735$	27.5531	+	5.85659i	1.01631	+	0.216024i
$736$	11.3966	+	35.0751i	0.420084	+	1.29289i
$737$	−3.46367	+	0.736226i	−0.127586	+	0.0271192i
$738$	29.4834	+	51.0668i	1.08530	+	1.87979i
$739$	10.3579	−	17.9404i	0.381022	−	0.659949i	−0.610187	−	0.792257i	$-0.708906\pi$
$739$	10.3579	−	17.9404i	0.381022	−	0.659949i	0.991209	+	0.132309i	$0.0422390\pi$
$740$	−21.6374	+	66.5931i	−0.795407	+	2.44801i
$741$	2.33722	−	22.2372i	0.0858600	−	0.816903i
$742$	−17.1479	+	12.4586i	−0.629517	+	0.457371i
$743$	−35.2367			−1.29271			−0.646354	−	0.763038i	$-0.723707\pi$
$743$	−35.2367			−1.29271			−0.646354	+	0.763038i	$0.723707\pi$
$744$		0			0
$745$	15.8950			0.582348
$746$	−33.0959	+	24.0456i	−1.21173	+	0.880370i
$747$	−0.967301	+	9.20326i	−0.0353917	+	0.336730i
$748$	−3.30083	+	10.1589i	−0.120690	+	0.371447i
$749$	−1.46104	+	2.53060i	−0.0533853	+	0.0924660i
$750$	27.5429	+	47.7058i	1.00573	+	1.74197i
$751$	42.2030	−	8.97053i	1.54001	−	0.327339i	0.641788	−	0.766882i	$-0.278193\pi$
$751$	42.2030	−	8.97053i	1.54001	−	0.327339i	0.898222	+	0.439543i	$0.144859\pi$
$752$	−1.00364	−	3.08888i	−0.0365989	−	0.112640i
$753$	−57.6875	−	12.2619i	−2.10225	−	0.446847i
$754$	−0.0589655	−	0.561020i	−0.00214740	−	0.0204311i
$755$	9.23623	+	10.2579i	0.336141	+	0.373322i
$756$	−5.75808	−	2.56366i	−0.209419	−	0.0932395i
$757$	−24.9750	+	11.1196i	−0.907733	+	0.404149i	−0.806855	−	0.590750i	$-0.798832\pi$
$757$	−24.9750	+	11.1196i	−0.907733	+	0.404149i	−0.100878	+	0.994899i	$0.532165\pi$
$758$	−3.79898	+	4.21919i	−0.137985	+	0.153248i
$759$	−10.7433	−	7.80543i	−0.389955	−	0.283319i
$760$	−28.6563	−	20.8201i	−1.03947	−	0.755223i
$761$	11.5037	−	12.7761i	0.417008	−	0.463134i	−0.497641	−	0.867383i	$-0.665800\pi$
$761$	11.5037	−	12.7761i	0.417008	−	0.463134i	0.914649	+	0.404249i	$0.132467\pi$
$762$	6.89867	−	3.07149i	0.249913	−	0.111268i
$763$	17.2172	+	7.66559i	0.623304	+	0.277513i
$764$	5.02976	+	5.58612i	0.181970	+	0.202099i
$765$	−3.96337	−	37.7089i	−0.143296	−	1.36337i
$766$	43.1511	+	9.17204i	1.55911	+	0.331399i
$767$	−5.56812	−	17.1369i	−0.201053	−	0.618778i
$768$	−46.0719	+	9.79289i	−1.66248	+	0.353371i
$769$	−7.02837	−	12.1735i	−0.253450	−	0.438987i	0.711024	−	0.703168i	$-0.248232\pi$
$769$	−7.02837	−	12.1735i	−0.253450	−	0.438987i	−0.964473	+	0.264181i	$0.914899\pi$
$770$	3.38775	−	5.86776i	0.122086	−	0.211459i
$771$	−12.0581	+	37.1111i	−0.434263	+	1.33652i
$772$	−8.91893	+	84.8580i	−0.320999	+	3.05411i
$773$	17.9900	−	13.0705i	0.647054	−	0.470112i	−0.215212	−	0.976567i	$-0.569044\pi$
$773$	17.9900	−	13.0705i	0.647054	−	0.470112i	0.862266	+	0.506455i	$0.169044\pi$
$774$	1.84315			0.0662507
$775$		0			0
$776$	37.5668			1.34857
$777$	27.7771	−	20.1813i	0.996498	−	0.723998i
$778$	−1.27139	+	12.0965i	−0.0455816	+	0.433680i
$779$	10.5686	−	32.5268i	0.378659	−	1.16539i
$780$	20.0228	−	34.6804i	0.716930	−	1.24176i
$781$	1.24906	+	2.16343i	0.0446948	+	0.0774136i
$782$	−70.3617	+	14.9558i	−2.51613	+	0.534819i
$783$	0.0471557	+	0.145130i	0.00168521	+	0.00518654i
$784$	1.75277	+	0.372563i	0.0625990	+	0.0133058i
$785$	2.08784	+	19.8645i	0.0745181	+	0.708993i
$786$	31.4884	+	34.9714i	1.12315	+	1.24739i
$787$	29.2643	+	13.0293i	1.04316	+	0.464445i	0.855508	−	0.517790i	$-0.173245\pi$
$787$	29.2643	+	13.0293i	1.04316	+	0.464445i	0.187654	+	0.982235i	$0.439912\pi$
$788$	−18.8179	+	8.37827i	−0.670360	+	0.298463i
$789$	11.5796	−	12.8605i	0.412245	−	0.457845i
$790$	21.1192	+	15.3440i	0.751388	+	0.545915i
$791$	−14.3261	−	10.4085i	−0.509377	−	0.370084i
$792$	5.20020	−	5.77541i	0.184781	−	0.205220i
$793$	13.5801	−	6.04625i	0.482244	−	0.214709i
$794$	35.6795	+	15.8855i	1.26622	+	0.563756i
$795$	24.3758	+	27.0720i	0.864519	+	0.960146i
$796$	1.58795	+	15.1083i	0.0562834	+	0.535501i
$797$	−25.4800	−	5.41595i	−0.902549	−	0.191843i	−0.266812	−	0.963749i	$-0.585970\pi$
$797$	−25.4800	−	5.41595i	−0.902549	−	0.191843i	−0.635737	+	0.771906i	$0.719304\pi$
$798$	13.4707	+	41.4586i	0.476859	+	1.46762i
$799$	−34.4248	+	7.31722i	−1.21786	+	0.258864i
$800$	3.21812	+	5.57395i	0.113778	+	0.197069i
$801$	3.81994	−	6.61633i	0.134971	−	0.233776i
$802$	27.1247	−	83.4814i	0.957808	−	2.94783i
$803$	−0.206448	+	1.96422i	−0.00728538	+	0.0693157i
$804$	33.0100	−	23.9832i	1.16417	−	0.845822i
$805$	28.4897			1.00413
$806$		0			0
$807$	−26.7486			−0.941594
$808$	−18.1621	+	13.1956i	−0.638942	+	0.464218i
$809$	0.912472	−	8.68159i	0.0320808	−	0.305229i	−0.966702	−	0.255905i	$-0.917627\pi$
$809$	0.912472	−	8.68159i	0.0320808	−	0.305229i	0.998783	−	0.0493239i	$-0.0157067\pi$
$810$	13.1605	−	40.5037i	0.462411	−	1.42316i
$811$	25.0392	−	43.3692i	0.879245	−	1.52290i	0.0270750	−	0.999633i	$-0.491381\pi$
$811$	25.0392	−	43.3692i	0.879245	−	1.52290i	0.852170	−	0.523264i	$-0.175286\pi$
$812$	0.343347	+	0.594695i	0.0120491	+	0.0208697i
$813$	−3.92260	+	0.833774i	−0.137571	+	0.0292417i
$814$	4.40984	+	13.5721i	0.154565	+	0.475701i
$815$	−41.7055	−	8.86477i	−1.46088	−	0.310520i
$816$	−0.470391	−	4.47547i	−0.0164670	−	0.156673i
$817$	−0.715318	−	0.794442i	−0.0250258	−	0.0277940i
$818$	1.05124	+	0.468042i	0.0367558	+	0.0163647i
$819$	−9.61505	+	4.28090i	−0.335977	+	0.149587i
$820$	40.9859	−	45.5195i	1.43129	−	1.58961i
$821$	41.0844	+	29.8495i	1.43385	+	1.04176i	0.989283	+	0.146013i	$0.0466441\pi$
$821$	41.0844	+	29.8495i	1.43385	+	1.04176i	0.444572	+	0.895743i	$0.353356\pi$
$822$	−78.2123	−	56.8246i	−2.72797	−	1.98199i
$823$	−4.23506	+	4.70351i	−0.147625	+	0.163954i	−0.812422	−	0.583070i	$-0.801851\pi$
$823$	−4.23506	+	4.70351i	−0.147625	+	0.163954i	0.664797	+	0.747024i	$0.268518\pi$
$824$	15.6064	−	6.94841i	0.543674	−	0.242059i
$825$	−2.11713	−	0.942609i	−0.0737092	−	0.0328174i
$826$	23.5061	+	26.1062i	0.817882	+	0.908350i
$827$	−0.386489	−	3.67720i	−0.0134395	−	0.127869i	0.985745	−	0.168247i	$-0.0538105\pi$
$827$	−0.386489	−	3.67720i	−0.0134395	−	0.127869i	−0.999184	+	0.0403779i	$0.987144\pi$
$828$	80.2231	+	17.0519i	2.78795	+	0.592596i
$829$	8.04729	+	24.7670i	0.279494	+	0.860193i	0.987995	+	0.154484i	$0.0493715\pi$
$829$	8.04729	+	24.7670i	0.279494	+	0.860193i	−0.708501	+	0.705709i	$0.750628\pi$
$830$	15.0588	−	3.20086i	0.522700	−	0.111103i
$831$	15.3852	+	26.6479i	0.533707	+	0.924407i
$832$	−12.0995	+	20.9570i	−0.419475	+	0.726553i
$833$	6.00033	−	18.4671i	0.207899	−	0.639848i
$834$	4.50159	−	42.8298i	0.155877	−	1.48307i
$835$	−49.2635	+	35.7920i	−1.70483	+	1.23863i
$836$	−11.3130			−0.391267
$837$		0			0
$838$	31.1747			1.07691
$839$	−6.06196	+	4.40427i	−0.209282	+	0.152052i	−0.687489	−	0.726195i	$-0.741287\pi$
$839$	−6.06196	+	4.40427i	−0.209282	+	0.152052i	0.478207	+	0.878247i	$0.341287\pi$
$840$	−3.25157	+	30.9366i	−0.112190	+	1.06742i
$841$	−8.95636	+	27.5648i	−0.308840	+	0.950511i
$842$	35.6687	−	61.7800i	1.22923	−	2.12908i
$843$	−27.2996	−	47.2843i	−0.940249	−	1.62856i
$844$	60.5423	−	12.8687i	2.08395	−	0.442957i
$845$	7.26150	+	22.3486i	0.249803	+	0.768815i
$846$	62.8606	+	13.3614i	2.16119	+	0.459375i
$847$	1.75173	+	16.6666i	0.0601903	+	0.572673i
$848$	1.55065	+	1.72217i	0.0532495	+	0.0591396i
$849$	1.60002	+	0.712377i	0.0549127	+	0.0244487i
$850$	−11.4684	+	5.10605i	−0.393362	+	0.175136i
$851$	−40.1511	+	44.5923i	−1.37636	+	1.52861i
$852$	−23.2877	−	16.9195i	−0.797822	−	0.579652i
$853$	35.2626	+	25.6198i	1.20737	+	0.877204i	0.994989	−	0.0999836i	$-0.0318790\pi$
$853$	35.2626	+	25.6198i	1.20737	+	0.877204i	0.212378	+	0.977187i	$0.431879\pi$
$854$	−19.3922	+	21.5372i	−0.663588	+	0.736989i
$855$	36.6855	−	16.3334i	1.25462	−	0.558592i
$856$	5.09390	+	2.26795i	0.174106	+	0.0775170i
$857$	26.2452	+	29.1482i	0.896518	+	0.995684i	0.999999	+	0.00105245i	$0.000335004\pi$
$857$	26.2452	+	29.1482i	0.896518	+	0.995684i	−0.103482	+	0.994631i	$0.532998\pi$
$858$	−0.853112	−	8.11682i	−0.0291248	−	0.277104i
$859$	17.8036	+	3.78426i	0.607449	+	0.129117i	0.501359	−	0.865239i	$-0.332833\pi$
$859$	17.8036	+	3.78426i	0.607449	+	0.129117i	0.106090	+	0.994357i	$0.466167\pi$
$860$	−0.591643	−	1.82089i	−0.0201749	−	0.0620918i
$861$	−29.3789	+	6.24467i	−1.00123	+	0.212818i
$862$	13.9084	+	24.0900i	0.473721	+	0.820509i
$863$	−22.4738	+	38.9258i	−0.765018	+	1.32505i	0.175219	+	0.984530i	$0.443937\pi$
$863$	−22.4738	+	38.9258i	−0.765018	+	1.32505i	−0.940237	+	0.340521i	$0.889397\pi$
$864$	1.89477	−	5.83151i	0.0644614	−	0.198392i
$865$	2.34355	−	22.2974i	0.0796830	−	0.758133i
$866$	60.4700	−	43.9340i	2.05486	−	1.49294i
$867$	−5.53740			−0.188060
$868$		0			0
$869$	3.32196			0.112690
$870$	1.52919	−	1.11102i	0.0518442	−	0.0376670i
$871$	0.956548	−	9.10095i	0.0324114	−	0.308374i
$872$	11.1133	−	34.2032i	0.376343	−	1.15827i
$873$	−21.2949	+	36.8839i	−0.720724	+	1.24833i
$874$	−38.0922	−	65.9776i	−1.28849	−	2.23173i
$875$	−14.7105	+	3.12682i	−0.497307	+	0.105706i
$876$	−7.03257	−	21.6440i	−0.237608	−	0.731283i
$877$	41.7190	+	8.86765i	1.40875	+	0.299439i	0.848637	−	0.528976i	$-0.177424\pi$
$877$	41.7190	+	8.86765i	1.40875	+	0.299439i	0.560114	+	0.828415i	$0.310757\pi$
$878$	−2.98323	−	28.3835i	−0.100679	−	0.957897i
$879$	−15.3329	−	17.0290i	−0.517167	−	0.574372i
$880$	−0.676740	−	0.301304i	−0.0228129	−	0.0101570i
$881$	−8.14565	+	3.62668i	−0.274434	+	0.122186i	−0.539339	−	0.842089i	$-0.681326\pi$
$881$	−8.14565	+	3.62668i	−0.274434	+	0.122186i	0.264905	+	0.964274i	$0.414659\pi$
$882$	−23.7253	+	26.3496i	−0.798871	+	0.887236i
$883$	−38.0791	−	27.6661i	−1.28146	−	0.931038i	−0.281867	−	0.959453i	$-0.590954\pi$
$883$	−38.0791	−	27.6661i	−1.28146	−	0.931038i	−0.999596	+	0.0284158i	$0.990954\pi$
$884$	−22.3326	−	16.2256i	−0.751126	−	0.545725i
$885$	40.3995	−	44.8682i	1.35801	−	1.50823i
$886$	−9.95708	+	4.43318i	−0.334515	+	0.148936i
$887$	2.88367	+	1.28389i	0.0968241	+	0.0431089i	0.454577	−	0.890707i	$-0.349790\pi$
$887$	2.88367	+	1.28389i	0.0968241	+	0.0431089i	−0.357753	+	0.933816i	$0.616457\pi$
$888$	−43.8398	−	48.6890i	−1.47117	−	1.63390i
$889$	0.215503	+	2.05038i	0.00722774	+	0.0687674i
$890$	−12.4323	−	2.64256i	−0.416731	−	0.0885789i
$891$	−1.67473	−	5.15429i	−0.0561056	−	0.172675i
$892$	−20.2112	+	4.29602i	−0.676721	+	0.143841i
$893$	−18.6368	−	32.2799i	−0.623657	−	1.08021i
$894$	−18.6640	+	32.3270i	−0.624217	+	1.08118i
$895$	8.71703	−	26.8283i	0.291378	−	0.896770i
$896$	3.19646	−	30.4123i	0.106786	−	1.01600i
$897$	27.7636	−	20.1714i	0.927000	−	0.673505i
$898$	−36.8840			−1.23083
$899$		0			0
$900$	14.3131			0.477105
$901$	20.3157	−	14.7602i	0.676815	−	0.491735i
$902$	1.30490	−	12.4153i	0.0434483	−	0.413383i
$903$	−0.290113	+	0.892875i	−0.00965434	+	0.0297130i
$904$	−16.8954	+	29.2637i	−0.561932	+	0.973295i
$905$	−18.6648	−	32.3284i	−0.620439	−	1.07463i
$906$	−31.7075	+	6.73963i	−1.05341	+	0.223909i
$907$	8.33208	+	25.6435i	0.276662	+	0.851478i	0.988775	+	0.149413i	$0.0477384\pi$
$907$	8.33208	+	25.6435i	0.276662	+	0.851478i	−0.712113	+	0.702065i	$0.752262\pi$
$908$	42.4318	+	9.01916i	1.40815	+	0.299311i
$909$	−2.66039	−	25.3119i	−0.0882395	−	0.839543i
$910$	11.7163	+	13.0123i	0.388393	+	0.431354i
$911$	4.63900	+	2.06542i	0.153697	+	0.0684303i	0.482143	−	0.876092i	$-0.339858\pi$
$911$	4.63900	+	2.06542i	0.153697	+	0.0684303i	−0.328446	+	0.944523i	$0.606525\pi$
$912$	4.35401	−	1.93853i	0.144176	−	0.0641911i
$913$	1.31091	−	1.45591i	0.0433847	−	0.0481836i
$914$	−8.50854	−	6.18181i	−0.281437	−	0.204476i
$915$	40.2967	+	29.2773i	1.33217	+	0.967876i
$916$	33.9880	−	37.7475i	1.12299	−	1.24721i
$917$	−11.7369	+	5.22560i	−0.387586	+	0.172565i
$918$	10.9256	+	4.86437i	0.360597	+	0.160548i
$919$	−32.9727	−	36.6199i	−1.08767	−	1.20798i	−0.976802	−	0.214145i	$-0.931304\pi$
$919$	−32.9727	−	36.6199i	−1.08767	−	1.20798i	−0.110868	−	0.993835i	$-0.535363\pi$
$920$	−5.68265	−	54.0668i	−0.187351	−	1.78253i
$921$	−77.9293	−	16.5644i	−2.56786	−	0.545815i
$922$	−12.1157	−	37.2882i	−0.399009	−	1.22802i
$923$	−6.31475	+	1.34224i	−0.207853	+	0.0441804i
$924$	4.96754	+	8.60403i	0.163420	+	0.283052i
$925$	−5.23597	+	9.06896i	−0.172158	+	0.298186i
$926$	19.5578	−	60.1929i	0.642711	−	1.97806i
$927$	−2.02446	+	19.2614i	−0.0664919	+	0.632628i
$928$	−0.540441	+	0.392653i	−0.0177408	+	0.0128895i
$929$	−39.9606			−1.31107			−0.655533	−	0.755167i	$-0.727556\pi$
$929$	−39.9606			−1.31107			−0.655533	+	0.755167i	$0.727556\pi$
$930$		0			0
$931$	20.5649			0.673989
$932$	−35.1311	+	25.5243i	−1.15076	+	0.836075i
$933$	−4.70814	+	44.7949i	−0.154137	+	1.46652i
$934$	−16.3367	+	50.2791i	−0.534552	+	1.64518i
$935$	−4.01360	+	6.95176i	−0.131259	+	0.227347i
$936$	10.0420	+	17.3932i	0.328232	+	0.568515i
$937$	−44.1040	+	9.37459i	−1.44081	+	0.306255i	−0.861046	−	0.508527i	$-0.830190\pi$
$937$	−44.1040	+	9.37459i	−1.44081	+	0.306255i	−0.579768	+	0.814781i	$0.696857\pi$
$938$	5.51313	+	16.9677i	0.180010	+	0.554014i
$939$	−53.8935	−	11.4554i	−1.75875	−	0.373834i
$940$	−6.97790	−	66.3903i	−0.227594	−	2.16541i
$941$	33.5852	+	37.3002i	1.09485	+	1.21595i	0.974776	+	0.223185i	$0.0716455\pi$
$941$	33.5852	+	37.3002i	1.09485	+	1.21595i	0.120071	+	0.992765i	$0.461688\pi$
$942$	−42.8515	−	19.0787i	−1.39618	−	0.621618i
$943$	47.9533	−	21.3502i	1.56157	−	0.695257i
$944$	2.56999	−	2.85426i	0.0836460	−	0.0928983i
$945$	−3.83202	−	2.78412i	−0.124656	−	0.0905675i
$946$	−0.315684	−	0.229358i	−0.0102638	−	0.00745707i
$947$	20.2920	−	22.5366i	0.659402	−	0.732340i	−0.316970	−	0.948435i	$-0.602666\pi$
$947$	20.2920	−	22.5366i	0.659402	−	0.732340i	0.976372	+	0.216095i	$0.0693322\pi$
$948$	−34.9688	+	15.5691i	−1.13573	+	0.505661i
$949$	−4.66278	−	2.07601i	−0.151360	−	0.0673900i
$950$	−8.89646	−	9.88052i	−0.288639	−	0.320566i
$951$	0.270052	+	2.56937i	0.00875703	+	0.0833176i
$952$	20.9744	+	4.45825i	0.679785	+	0.144493i
$953$	−10.9631	−	33.7411i	−0.355131	−	1.09298i	−0.955934	−	0.293583i	$-0.905152\pi$
$953$	−10.9631	−	33.7411i	−0.355131	−	1.09298i	0.600803	−	0.799397i	$-0.294848\pi$
$954$	−44.8524	+	9.53368i	−1.45215	+	0.308664i
$955$	2.82442	+	4.89204i	0.0913961	+	0.158303i
$956$	38.9689	−	67.4962i	1.26035	−	2.18298i
$957$	0.0743291	−	0.228761i	0.00240272	−	0.00739481i
$958$	−2.18217	+	20.7620i	−0.0705027	+	0.670788i
$959$	21.3530	−	15.5139i	0.689524	−	0.500969i
$960$	−81.0843			−2.61698
$961$		0			0
$962$	−36.8791			−1.18903
$963$	−5.11422	+	3.71570i	−0.164804	+	0.119737i
$964$	−8.58803	+	81.7097i	−0.276602	+	2.63169i
$965$	−19.8145	+	60.9828i	−0.637852	+	1.96311i
$966$	−33.4527	+	57.9418i	−1.07632	+	1.86425i
$967$	17.7222	+	30.6957i	0.569906	+	0.987107i	0.996575	+	0.0826987i	$0.0263539\pi$
$967$	17.7222	+	30.6957i	0.569906	+	0.987107i	−0.426668	+	0.904408i	$0.640313\pi$
$968$	31.2800	−	6.64876i	1.00538	−	0.213699i
$969$	−15.9593	−	49.1176i	−0.512686	−	1.57789i
$970$	69.3060	+	14.7314i	2.22528	+	0.472998i
$971$	4.19130	+	39.8776i	0.134505	+	1.27973i	0.828597	+	0.559846i	$0.189140\pi$
$971$	4.19130	+	39.8776i	0.134505	+	1.27973i	−0.694092	+	0.719887i	$0.744194\pi$
$972$	49.6845	+	55.1802i	1.59363	+	1.76991i
$973$	10.7410	+	4.78221i	0.344341	+	0.153310i
$974$	−49.7973	+	22.1712i	−1.59561	+	0.710411i
$975$	4.00746	−	4.45073i	0.128341	−	0.142538i
$976$	2.56345	+	1.86246i	0.0820540	+	0.0596157i
$977$	31.2854	+	22.7302i	1.00091	+	0.727202i	0.962283	−	0.272052i	$-0.0877022\pi$
$977$	31.2854	+	22.7302i	1.00091	+	0.727202i	0.0386252	+	0.999254i	$0.487702\pi$
$978$	66.9998	−	74.4108i	2.14242	−	2.37939i
$979$	−1.47758	+	0.657860i	−0.0472236	+	0.0210253i
$980$	33.6470	+	14.9806i	1.07481	+	0.478538i
$981$	27.2818	+	30.2995i	0.871040	+	0.967388i
$982$	−2.22555	−	21.1747i	−0.0710202	−	0.675712i
$983$	21.1080	+	4.48665i	0.673242	+	0.143102i	0.531833	−	0.846849i	$-0.321503\pi$
$983$	21.1080	+	4.48665i	0.673242	+	0.143102i	0.141409	+	0.989951i	$0.454837\pi$
$984$	17.7109	+	54.5086i	0.564604	+	1.73767i
$985$	−15.1415	+	3.21842i	−0.482447	+	0.102547i
$986$	−0.651478	−	1.12839i	−0.0207473	−	0.0359354i
$987$	−16.3669	+	28.3483i	−0.520965	+	0.902338i
$988$	9.03438	−	27.8049i	0.287422	−	0.884593i
$989$	0.171505	−	1.63176i	0.00545353	−	0.0518869i
$990$	11.8585	−	8.61568i	0.376887	−	0.273824i
$991$	46.8764			1.48908			0.744538	−	0.667580i	$-0.232670\pi$
$991$	46.8764			1.48908			0.744538	+	0.667580i	$0.232670\pi$
$992$		0			0
$993$	−67.8639			−2.15360
$994$	10.1825	−	7.39800i	0.322968	−	0.234650i
$995$	−1.19333	+	11.3537i	−0.0378310	+	0.359938i
$996$	−6.97589	+	21.4696i	−0.221039	+	0.680290i
$997$	−22.2695	+	38.5718i	−0.705281	+	1.22158i	0.261309	+	0.965255i	$0.415846\pi$
$997$	−22.2695	+	38.5718i	−0.705281	+	1.22158i	−0.966590	+	0.256327i	$0.917488\pi$
$998$	−32.7830	−	56.7818i	−1.03773	−	1.79740i
$999$	9.75827	−	2.07419i	0.308738	−	0.0656243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.k.338.1		16
31.2	even	5		31.2.g.a.19.1	yes	16
31.3	odd	30		961.2.d.q.531.4		16
31.4	even	5		961.2.g.t.448.2		16
31.5	even	3		31.2.g.a.18.1	✓	16
31.6	odd	6		961.2.d.n.388.1		16
31.7	even	15		961.2.d.p.628.4		16
31.8	even	5		961.2.c.j.521.8		16
31.9	even	15		961.2.c.j.439.8		16
31.10	even	15	inner	961.2.g.k.816.1		16
31.11	odd	30		961.2.g.m.846.2		16
31.12	odd	30		961.2.d.n.374.1		16
31.13	odd	30		961.2.g.n.547.2		16
31.14	even	15		961.2.a.i.1.8		8
31.15	odd	10		961.2.g.m.844.2		16
31.16	even	5		961.2.g.s.844.2		16
31.17	odd	30		961.2.a.j.1.8		8
31.18	even	15		961.2.g.t.547.2		16
31.19	even	15		961.2.d.o.374.1		16
31.20	even	15		961.2.g.s.846.2		16
31.21	odd	30		961.2.g.j.816.1		16
31.22	odd	30		961.2.c.i.439.8		16
31.23	odd	10		961.2.c.i.521.8		16
31.24	odd	30		961.2.d.q.628.4		16
31.25	even	3		961.2.d.o.388.1		16
31.26	odd	6		961.2.g.l.235.1		16
31.27	odd	10		961.2.g.n.448.2		16
31.28	even	15		961.2.d.p.531.4		16
31.29	odd	10		961.2.g.l.732.1		16
31.30	odd	2		961.2.g.j.338.1		16
93.2	odd	10		279.2.y.c.19.2		16
93.5	odd	6		279.2.y.c.235.2		16
93.14	odd	30		8649.2.a.bf.1.1		8
93.17	even	30		8649.2.a.be.1.1		8
124.67	odd	6		496.2.bg.c.49.2		16
124.95	odd	10		496.2.bg.c.81.2		16
155.2	odd	20		775.2.ck.a.174.4		32
155.33	odd	20		775.2.ck.a.174.1		32
155.64	even	10		775.2.bl.a.701.2		16
155.67	odd	12		775.2.ck.a.49.1		32
155.98	odd	12		775.2.ck.a.49.4		32
155.129	even	6		775.2.bl.a.576.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.1	✓	16	31.5	even	3
31.2.g.a.19.1	yes	16	31.2	even	5
279.2.y.c.19.2		16	93.2	odd	10
279.2.y.c.235.2		16	93.5	odd	6
496.2.bg.c.49.2		16	124.67	odd	6
496.2.bg.c.81.2		16	124.95	odd	10
775.2.bl.a.576.2		16	155.129	even	6
775.2.bl.a.701.2		16	155.64	even	10
775.2.ck.a.49.1		32	155.67	odd	12
775.2.ck.a.49.4		32	155.98	odd	12
775.2.ck.a.174.1		32	155.33	odd	20
775.2.ck.a.174.4		32	155.2	odd	20
961.2.a.i.1.8		8	31.14	even	15
961.2.a.j.1.8		8	31.17	odd	30
961.2.c.i.439.8		16	31.22	odd	30
961.2.c.i.521.8		16	31.23	odd	10
961.2.c.j.439.8		16	31.9	even	15
961.2.c.j.521.8		16	31.8	even	5
961.2.d.n.374.1		16	31.12	odd	30
961.2.d.n.388.1		16	31.6	odd	6
961.2.d.o.374.1		16	31.19	even	15
961.2.d.o.388.1		16	31.25	even	3
961.2.d.p.531.4		16	31.28	even	15
961.2.d.p.628.4		16	31.7	even	15
961.2.d.q.531.4		16	31.3	odd	30
961.2.d.q.628.4		16	31.24	odd	30
961.2.g.j.338.1		16	31.30	odd	2
961.2.g.j.816.1		16	31.21	odd	30
961.2.g.k.338.1		16	1.1	even	1	trivial
961.2.g.k.816.1		16	31.10	even	15	inner
961.2.g.l.235.1		16	31.26	odd	6
961.2.g.l.732.1		16	31.29	odd	10
961.2.g.m.844.2		16	31.15	odd	10
961.2.g.m.846.2		16	31.11	odd	30
961.2.g.n.448.2		16	31.27	odd	10
961.2.g.n.547.2		16	31.13	odd	30
961.2.g.s.844.2		16	31.16	even	5
961.2.g.s.846.2		16	31.20	even	15
961.2.g.t.448.2		16	31.4	even	5
961.2.g.t.547.2		16	31.18	even	15
8649.2.a.be.1.1		8	93.17	even	30
8649.2.a.bf.1.1		8	93.14	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+(-1.86683 + 1.35633i) q^{2} +(0.265787 - 2.52879i) q^{3} +(1.02738 - 3.16196i) q^{4} +(1.24923 - 2.16373i) q^{5} +(2.93370 + 5.08132i) q^{6} +(-1.56687 + 0.333049i) q^{7} +(0.944583 + 2.90713i) q^{8} +(-3.38972 - 0.720507i) q^{9} +(0.602634 + 5.73368i) q^{10} +(0.490912 + 0.545213i) q^{11} +(-7.72288 - 3.43845i) q^{12} +(-1.73206 + 0.771163i) q^{13} +(2.47336 - 2.74694i) q^{14} +(-5.13960 - 3.73414i) q^{15} +(-0.326952 - 0.237545i) q^{16} +(-2.93028 + 3.25441i) q^{17} +(7.30526 - 3.25251i) q^{18} +(-4.23705 - 1.88646i) q^{19} +(-5.55818 - 6.17299i) q^{20} +(0.425758 + 4.05082i) q^{21} +(-1.65594 - 0.351980i) q^{22} +(-2.19973 - 6.77006i) q^{23} +(7.60258 - 1.61598i) q^{24} +(-0.621150 - 1.07586i) q^{25} +(2.18751 - 3.78887i) q^{26} +(-0.365721 + 1.12557i) q^{27} +(-0.556691 + 5.29656i) q^{28} +(0.104314 - 0.0757884i) q^{29} +14.6595 q^{30} -5.18091 q^{32} +(1.50921 - 1.09651i) q^{33} +(1.05628 - 10.0499i) q^{34} +(-1.23676 + 3.80635i) q^{35} +(-5.76075 + 9.97791i) q^{36} +(-4.21474 - 7.30014i) q^{37} +(10.4685 - 2.22515i) q^{38} +(1.48975 + 4.58499i) q^{39} +(7.47024 + 1.58785i) q^{40} +(0.770791 + 7.33358i) q^{41} +(-6.28907 - 6.98472i) q^{42} +(0.210565 + 0.0937494i) q^{43} +(2.22830 - 0.992101i) q^{44} +(-5.79352 + 6.43435i) q^{45} +(13.2889 + 9.65498i) q^{46} +(6.50168 + 4.72375i) q^{47} +(-0.687602 + 0.763659i) q^{48} +(-4.05065 + 1.80346i) q^{49} +(2.61881 + 1.16597i) q^{50} +(7.45090 + 8.27507i) q^{51} +(0.658896 + 6.26898i) q^{52} +(-5.60893 - 1.19222i) q^{53} +(-0.843912 - 2.59729i) q^{54} +(1.79296 - 0.381105i) q^{55} +(-2.44826 - 4.24051i) q^{56} +(-5.89661 + 10.2132i) q^{57} +(-0.0919419 + 0.282968i) q^{58} +(-0.993409 + 9.45166i) q^{59} +(-17.0875 + 12.4148i) q^{60} -7.84044 q^{61} +5.55122 q^{63} +(10.3258 - 7.50212i) q^{64} +(-0.495153 + 4.71107i) q^{65} +(-1.33021 + 4.09397i) q^{66} +(-2.41329 + 4.17994i) q^{67} +(7.27978 + 12.6090i) q^{68} +(-17.7047 + 3.76326i) q^{69} +(-2.85385 - 8.78324i) q^{70} +(3.33061 + 0.707943i) q^{71} +(-1.10726 - 10.5349i) q^{72} +(1.80133 + 2.00058i) q^{73} +(17.7696 + 7.91153i) q^{74} +(-2.88573 + 1.28481i) q^{75} +(-10.3180 + 11.4593i) q^{76} +(-0.950780 - 0.690782i) q^{77} +(-8.99987 - 6.53879i) q^{78} +(3.02979 - 3.36492i) q^{79} +(-0.922421 + 0.410688i) q^{80} +(-6.74838 - 3.00457i) q^{81} +(-11.3857 - 12.6451i) q^{82} +(-0.279128 - 2.65572i) q^{83} +(13.2459 + 2.81551i) q^{84} +(3.38106 + 10.4058i) q^{85} +(-0.520243 + 0.110581i) q^{86} +(-0.163928 - 0.283932i) q^{87} +(-1.12130 + 1.94214i) q^{88} +(-0.681255 + 2.09669i) q^{89} +(2.08840 - 19.8698i) q^{90} +(2.45708 - 1.78518i) q^{91} -23.6666 q^{92} -18.5445 q^{94} +(-9.37482 + 6.81121i) q^{95} +(-1.37702 + 13.1015i) q^{96} +(3.79778 - 11.6884i) q^{97} +(5.11577 - 8.86077i) q^{98} +(-1.27122 - 2.20182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

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