LMFDB - Embedded newform 961.2.g.n.844.1

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 = [16,4,-3,6,-3,-11,12] 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			844.1
Root			$-2.52368i$ of defining polynomial
Character	$\chi$	$=$	961.844
Dual form			961.2.g.n.846.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.108599 + 0.334232i) q^{2} +(-2.83007 + 0.601549i) q^{3} +(1.51812 - 1.10298i) q^{4} +(-1.48661 + 2.57489i) q^{5} +(-0.508398 - 0.880572i) q^{6} +(-0.988571 - 0.440140i) q^{7} +(1.10215 + 0.800755i) q^{8} +(4.90678 - 2.18464i) q^{9} +(-1.02206 - 0.217245i) q^{10} +(-0.254147 - 2.41805i) q^{11} +(-3.63288 + 4.03472i) q^{12} +(-1.92285 - 2.13554i) q^{13} +(0.0397516 - 0.378211i) q^{14} +(2.65829 - 8.18139i) q^{15} +(1.01179 - 3.11397i) q^{16} +(-0.190740 + 1.81477i) q^{17} +(1.26305 + 1.40275i) q^{18} +(1.41740 - 1.57418i) q^{19} +(0.583191 + 5.54869i) q^{20} +(3.06249 + 0.650952i) q^{21} +(0.780590 - 0.347541i) q^{22} +(-0.357760 - 0.259928i) q^{23} +(-3.60084 - 1.60320i) q^{24} +(-1.92005 - 3.32562i) q^{25} +(0.504947 - 0.874594i) q^{26} +(-5.55018 + 4.03244i) q^{27} +(-1.98623 + 0.422186i) q^{28} +(0.976227 + 3.00452i) q^{29} +3.02317 q^{30} +3.87532 q^{32} +(2.17383 + 6.69036i) q^{33} +(-0.627268 + 0.133330i) q^{34} +(2.60294 - 1.89115i) q^{35} +(5.03946 - 8.72860i) q^{36} +(1.57338 + 2.72517i) q^{37} +(0.680071 + 0.302787i) q^{38} +(6.72642 + 4.88703i) q^{39} +(-3.70032 + 1.64749i) q^{40} +(6.79444 + 1.44420i) q^{41} +(0.115013 + 1.09427i) q^{42} +(5.62898 - 6.25162i) q^{43} +(-3.05288 - 3.39056i) q^{44} +(-1.66928 + 15.8821i) q^{45} +(0.0480240 - 0.147803i) q^{46} +(-2.46041 + 7.57236i) q^{47} +(-0.990228 + 9.42139i) q^{48} +(-3.90036 - 4.33179i) q^{49} +(0.903015 - 1.00290i) q^{50} +(-0.551866 - 5.25066i) q^{51} +(-5.27456 - 1.12114i) q^{52} +(4.54671 - 2.02433i) q^{53} +(-1.95051 - 1.41713i) q^{54} +(6.60404 + 2.94031i) q^{55} +(-0.737104 - 1.27670i) q^{56} +(-3.06439 + 5.30768i) q^{57} +(-0.898189 + 0.652573i) q^{58} +(11.7514 - 2.49784i) q^{59} +(-4.98828 - 15.3523i) q^{60} +14.4351 q^{61} -5.81225 q^{63} +(-1.60273 - 4.93269i) q^{64} +(8.35732 - 1.77640i) q^{65} +(-2.00006 + 1.45313i) q^{66} +(3.21879 - 5.57511i) q^{67} +(1.71208 + 2.96541i) q^{68} +(1.16884 + 0.520403i) q^{69} +(0.914757 + 0.664610i) q^{70} +(1.53281 - 0.682453i) q^{71} +(7.15734 + 1.52134i) q^{72} +(1.50105 + 14.2815i) q^{73} +(-0.739972 + 0.821822i) q^{74} +(7.43439 + 8.25672i) q^{75} +(0.415493 - 3.95316i) q^{76} +(-0.813039 + 2.50228i) q^{77} +(-0.902923 + 2.77891i) q^{78} +(-0.360377 + 3.42876i) q^{79} +(6.51400 + 7.23453i) q^{80} +(2.49968 - 2.77618i) q^{81} +(0.255168 + 2.42776i) q^{82} +(12.5727 + 2.67242i) q^{83} +(5.36720 - 2.38963i) q^{84} +(-4.38928 - 3.18900i) q^{85} +(2.70079 + 1.20247i) q^{86} +(-4.57015 - 7.91573i) q^{87} +(1.65616 - 2.86855i) q^{88} +(1.82788 - 1.32803i) q^{89} +(-5.48961 + 1.16685i) q^{90} +(0.960936 + 2.95746i) q^{91} -0.829816 q^{92} -2.79812 q^{94} +(1.94622 + 5.98986i) q^{95} +(-10.9674 + 2.33120i) q^{96} +(-2.76106 + 2.00603i) q^{97} +(1.02425 - 1.77405i) q^{98} +(-6.52961 - 11.3096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} + 2 q^{11} - 25 q^{12} - 18 q^{13} + 24 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 + 12 * q^7 - 8 * q^8 + 5 * q^9 - 12 * q^10 + 2 * q^11 - 25 * q^12 - 18 * q^13 + 24 * q^14 - 4 * q^15 - 2 * q^16 + q^17 - 8 * q^18 + 11 * q^19 - 18 * q^20 + 31 * q^21 - 4 * q^22 - 21 * q^23 - 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 + 3 * q^38 + 2 * q^39 + 29 * q^40 - 3 * q^41 - 39 * q^42 - 8 * q^43 + 41 * q^44 - 20 * q^45 + 16 * q^46 + 4 * q^47 - 49 * q^48 + 12 * q^49 + 48 * q^50 - 2 * q^51 + 6 * q^52 + 69 * q^53 - 39 * q^54 - 23 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 54 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 + 27 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 27 * q^69 + 27 * q^70 + 6 * q^71 + 2 * q^72 + 18 * q^73 + 92 * q^74 - 13 * q^75 - 27 * q^76 + 42 * q^77 + 15 * q^78 + 22 * q^79 + 21 * q^80 - 22 * q^81 - 61 * q^82 + 71 * q^83 + 12 * q^84 + 63 * q^85 + 11 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 - 33 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 58 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	0.108599	+	0.334232i	0.0767908	+	0.236338i	0.982082	−	0.188453i	$-0.0603475\pi$
$2$	0.108599	+	0.334232i	0.0767908	+	0.236338i	−0.905291	+	0.424791i	$0.860347\pi$
$3$	−2.83007	+	0.601549i	−1.63394	+	0.347305i	−0.931303	−	0.364245i	$-0.881327\pi$
$3$	−2.83007	+	0.601549i	−1.63394	+	0.347305i	−0.702636	+	0.711549i	$0.747994\pi$
$4$	1.51812	−	1.10298i	0.759058	−	0.551488i
$5$	−1.48661	+	2.57489i	−0.664834	+	1.15153i	0.314496	+	0.949259i	$0.398165\pi$
$5$	−1.48661	+	2.57489i	−0.664834	+	1.15153i	−0.979330	+	0.202268i	$0.935169\pi$
$6$	−0.508398	−	0.880572i	−0.207553	−	0.359492i
$7$	−0.988571	−	0.440140i	−0.373645	−	0.166357i	0.211318	−	0.977417i	$-0.432224\pi$
$7$	−0.988571	−	0.440140i	−0.373645	−	0.166357i	−0.584963	+	0.811060i	$0.698891\pi$
$8$	1.10215	+	0.800755i	0.389667	+	0.283110i
$9$	4.90678	−	2.18464i	1.63559	−	0.728213i
$10$	−1.02206	−	0.217245i	−0.323203	−	0.0686988i
$11$	−0.254147	−	2.41805i	−0.0766283	−	0.729070i	−0.963618	−	0.267282i	$-0.913875\pi$
$11$	−0.254147	−	2.41805i	−0.0766283	−	0.729070i	0.886990	−	0.461788i	$-0.152792\pi$
$12$	−3.63288	+	4.03472i	−1.04872	+	1.16472i
$13$	−1.92285	−	2.13554i	−0.533302	−	0.592292i	0.414937	−	0.909850i	$-0.363804\pi$
$13$	−1.92285	−	2.13554i	−0.533302	−	0.592292i	−0.948239	+	0.317558i	$0.897137\pi$
$14$	0.0397516	−	0.378211i	0.0106241	−	0.101081i
$15$	2.65829	−	8.18139i	0.686369	−	2.11243i
$16$	1.01179	−	3.11397i	0.252948	−	0.778493i
$17$	−0.190740	+	1.81477i	−0.0462612	+	0.440146i	0.946736	+	0.322010i	$0.104359\pi$
$17$	−0.190740	+	1.81477i	−0.0462612	+	0.440146i	−0.992997	+	0.118136i	$0.962308\pi$
$18$	1.26305	+	1.40275i	0.297703	+	0.330632i
$19$	1.41740	−	1.57418i	0.325174	−	0.361143i	−0.558286	−	0.829648i	$-0.688541\pi$
$19$	1.41740	−	1.57418i	0.325174	−	0.361143i	0.883460	+	0.468506i	$0.155208\pi$
$20$	0.583191	+	5.54869i	0.130405	+	1.24072i
$21$	3.06249	+	0.650952i	0.668290	+	0.142049i
$22$	0.780590	−	0.347541i	0.166422	−	0.0740960i
$23$	−0.357760	−	0.259928i	−0.0745981	−	0.0541987i	0.549861	−	0.835256i	$-0.314681\pi$
$23$	−0.357760	−	0.259928i	−0.0745981	−	0.0541987i	−0.624459	+	0.781057i	$0.714681\pi$
$24$	−3.60084	−	1.60320i	−0.735018	−	0.327251i
$25$	−1.92005	−	3.32562i	−0.384010	−	0.665124i
$26$	0.504947	−	0.874594i	0.0990283	−	0.171522i
$27$	−5.55018	+	4.03244i	−1.06813	+	0.776043i
$28$	−1.98623	+	0.422186i	−0.375362	+	0.0797857i
$29$	0.976227	+	3.00452i	0.181281	+	0.557925i	0.999864	−	0.0164625i	$-0.00524041\pi$
$29$	0.976227	+	3.00452i	0.181281	+	0.557925i	−0.818584	+	0.574387i	$0.805240\pi$
$30$	3.02317			0.551953
$31$		0			0
$31$		0			0
$32$	3.87532			0.685067
$33$	2.17383	+	6.69036i	0.378415	+	1.16464i
$34$	−0.627268	+	0.133330i	−0.107576	+	0.0228659i
$35$	2.60294	−	1.89115i	0.439977	−	0.319662i
$36$	5.03946	−	8.72860i	0.839910	−	1.45477i
$37$	1.57338	+	2.72517i	0.258661	+	0.448015i	0.965884	−	0.258977i	$-0.0833853\pi$
$37$	1.57338	+	2.72517i	0.258661	+	0.448015i	−0.707222	+	0.706991i	$0.750052\pi$
$38$	0.680071	+	0.302787i	0.110322	+	0.0491185i
$39$	6.72642	+	4.88703i	1.07709	+	0.782551i
$40$	−3.70032	+	1.64749i	−0.585073	+	0.260491i
$41$	6.79444	+	1.44420i	1.06111	+	0.225547i	0.705227	−	0.708982i	$-0.250845\pi$
$41$	6.79444	+	1.44420i	1.06111	+	0.225547i	0.355887	+	0.934529i	$0.384179\pi$
$42$	0.115013	+	1.09427i	0.0177469	+	0.168850i
$43$	5.62898	−	6.25162i	0.858411	−	0.953362i	−0.140916	−	0.990022i	$-0.545005\pi$
$43$	5.62898	−	6.25162i	0.858411	−	0.953362i	0.999328	+	0.0366590i	$0.0116715\pi$
$44$	−3.05288	−	3.39056i	−0.460239	−	0.511147i
$45$	−1.66928	+	15.8821i	−0.248842	+	2.36757i
$46$	0.0480240	−	0.147803i	0.00708075	−	0.0217923i
$47$	−2.46041	+	7.57236i	−0.358888	+	1.10454i	0.594833	+	0.803849i	$0.297218\pi$
$47$	−2.46041	+	7.57236i	−0.358888	+	1.10454i	−0.953721	+	0.300693i	$0.902782\pi$
$48$	−0.990228	+	9.42139i	−0.142927	+	1.35986i
$49$	−3.90036	−	4.33179i	−0.557195	−	0.618828i
$50$	0.903015	−	1.00290i	0.127706	−	0.141831i
$51$	−0.551866	−	5.25066i	−0.0772767	−	0.735239i
$52$	−5.27456	−	1.12114i	−0.731450	−	0.155474i
$53$	4.54671	−	2.02433i	0.624539	−	0.278063i	−0.0699672	−	0.997549i	$-0.522289\pi$
$53$	4.54671	−	2.02433i	0.624539	−	0.278063i	0.694506	+	0.719487i	$0.255623\pi$
$54$	−1.95051	−	1.41713i	−0.265431	−	0.192847i
$55$	6.60404	+	2.94031i	0.890489	+	0.396471i
$56$	−0.737104	−	1.27670i	−0.0984997	−	0.170606i
$57$	−3.06439	+	5.30768i	−0.405889	+	0.703020i
$58$	−0.898189	+	0.652573i	−0.117938	+	0.0856870i
$59$	11.7514	−	2.49784i	1.52990	−	0.325191i	0.635375	−	0.772204i	$-0.280846\pi$
$59$	11.7514	−	2.49784i	1.52990	−	0.325191i	0.894527	+	0.447013i	$0.147512\pi$
$60$	−4.98828	−	15.3523i	−0.643984	−	1.98198i
$61$	14.4351			1.84823			0.924115	−	0.382115i	$-0.124804\pi$
$61$	14.4351			1.84823			0.924115	+	0.382115i	$0.124804\pi$
$62$		0			0
$63$	−5.81225			−0.732274
$64$	−1.60273	−	4.93269i	−0.200341	−	0.616586i
$65$	8.35732	−	1.77640i	1.03660	−	0.220336i
$66$	−2.00006	+	1.45313i	−0.246190	+	0.178868i
$67$	3.21879	−	5.57511i	0.393238	−	0.681108i	−0.599636	−	0.800273i	$-0.704688\pi$
$67$	3.21879	−	5.57511i	0.393238	−	0.681108i	0.992875	+	0.119164i	$0.0380215\pi$
$68$	1.71208	+	2.96541i	0.207620	+	0.359609i
$69$	1.16884	+	0.520403i	0.140712	+	0.0626491i
$70$	0.914757	+	0.664610i	0.109334	+	0.0794361i
$71$	1.53281	−	0.682453i	0.181912	−	0.0809923i	−0.313760	−	0.949502i	$-0.601589\pi$
$71$	1.53281	−	0.682453i	0.181912	−	0.0809923i	0.495671	+	0.868510i	$0.334922\pi$
$72$	7.15734	+	1.52134i	0.843501	+	0.179292i
$73$	1.50105	+	14.2815i	0.175684	+	1.67152i	0.626894	+	0.779105i	$0.284326\pi$
$73$	1.50105	+	14.2815i	0.175684	+	1.67152i	−0.451209	+	0.892418i	$0.649007\pi$
$74$	−0.739972	+	0.821822i	−0.0860200	+	0.0955349i
$75$	7.43439	+	8.25672i	0.858449	+	0.953404i
$76$	0.415493	−	3.95316i	0.0476604	−	0.453458i
$77$	−0.813039	+	2.50228i	−0.0926544	+	0.285161i
$78$	−0.902923	+	2.77891i	−0.102236	+	0.314650i
$79$	−0.360377	+	3.42876i	−0.0405456	+	0.385765i	0.955366	+	0.295426i	$0.0954617\pi$
$79$	−0.360377	+	3.42876i	−0.0405456	+	0.385765i	−0.995911	+	0.0903390i	$0.971205\pi$
$80$	6.51400	+	7.23453i	0.728288	+	0.808845i
$81$	2.49968	−	2.77618i	0.277742	−	0.308464i
$82$	0.255168	+	2.42776i	0.0281786	+	0.268101i
$83$	12.5727	+	2.67242i	1.38004	+	0.293336i	0.837381	−	0.546620i	$-0.184086\pi$
$83$	12.5727	+	2.67242i	1.38004	+	0.293336i	0.542655	+	0.839955i	$0.317419\pi$
$84$	5.36720	−	2.38963i	0.585609	−	0.260730i
$85$	−4.38928	−	3.18900i	−0.476084	−	0.345895i
$86$	2.70079	+	1.20247i	0.291234	+	0.129666i
$87$	−4.57015	−	7.91573i	−0.489972	−	0.848656i
$88$	1.65616	−	2.86855i	0.176547	−	0.305789i
$89$	1.82788	−	1.32803i	0.193755	−	0.140771i	−0.486678	−	0.873581i	$-0.661792\pi$
$89$	1.82788	−	1.32803i	0.193755	−	0.140771i	0.680433	+	0.732810i	$0.261792\pi$
$90$	−5.48961	+	1.16685i	−0.578655	+	0.122997i
$91$	0.960936	+	2.95746i	0.100733	+	0.310026i
$92$	−0.829816			−0.0865143
$93$		0			0
$94$	−2.79812			−0.288604
$95$	1.94622	+	5.98986i	0.199678	+	0.614547i
$96$	−10.9674	+	2.33120i	−1.11936	+	0.237927i
$97$	−2.76106	+	2.00603i	−0.280343	+	0.203681i	−0.719067	−	0.694941i	$-0.755431\pi$
$97$	−2.76106	+	2.00603i	−0.280343	+	0.203681i	0.438724	+	0.898622i	$0.355431\pi$
$98$	1.02425	−	1.77405i	0.103465	−	0.179207i
$99$	−6.52961	−	11.3096i	−0.656251	−	1.13666i
$100$	−6.58294	−	2.93091i	−0.658294	−	0.293091i
$101$	−14.3336	−	10.4140i	−1.42625	−	1.03623i	−0.990700	−	0.136062i	$-0.956555\pi$
$101$	−14.3336	−	10.4140i	−1.42625	−	1.03623i	−0.435546	−	0.900167i	$-0.643445\pi$
$102$	1.69501	−	0.754665i	0.167831	−	0.0747230i
$103$	−7.89741	−	1.67865i	−0.778155	−	0.165402i	−0.198322	−	0.980137i	$-0.563549\pi$
$103$	−7.89741	−	1.67865i	−0.778155	−	0.165402i	−0.579834	+	0.814735i	$0.696882\pi$
$104$	−0.409213	−	3.89341i	−0.0401267	−	0.381780i
$105$	−6.22887	+	6.91786i	−0.607876	+	0.675114i
$106$	1.17036	+	1.29982i	0.113676	+	0.126250i
$107$	1.27015	−	12.0846i	0.122790	−	1.16827i	−0.743505	−	0.668731i	$-0.766838\pi$
$107$	1.27015	−	12.0846i	0.122790	−	1.16827i	0.866294	−	0.499534i	$-0.166495\pi$
$108$	−3.97813	+	12.2434i	−0.382796	+	1.17812i
$109$	−0.195330	+	0.601165i	−0.0187093	+	0.0575812i	−0.959975	−	0.280085i	$-0.909637\pi$
$109$	−0.195330	+	0.601165i	−0.0187093	+	0.0575812i	0.941266	+	0.337666i	$0.109637\pi$
$110$	−0.265556	+	2.52660i	−0.0253198	+	0.240901i
$111$	−6.09208	−	6.76594i	−0.578235	−	0.642195i
$112$	−2.37081	+	2.63305i	−0.224021	+	0.248800i
$113$	1.18121	+	11.2384i	0.111119	+	1.05722i	0.897963	+	0.440071i	$0.145047\pi$
$113$	1.18121	+	11.2384i	0.111119	+	1.05722i	−0.786844	+	0.617152i	$0.788286\pi$
$114$	−2.10679	−	0.447811i	−0.197319	−	0.0419414i
$115$	1.20114	−	0.534781i	0.112007	−	0.0498686i
$116$	4.79594	+	3.48445i	0.445291	+	0.323523i
$117$	−14.1004	−	6.27789i	−1.30358	−	0.580391i
$118$	2.11104	+	3.65643i	0.194337	+	0.336602i
$119$	0.987313	−	1.71008i	0.0905068	−	0.156762i
$120$	9.48112	−	6.88844i	0.865504	−	0.628825i
$121$	4.97724	−	1.05795i	0.452477	−	0.0961769i
$122$	1.56764	+	4.82469i	0.141927	+	0.436806i
$123$	−20.0975			−1.81213
$124$		0			0
$125$	−3.44866			−0.308458
$126$	−0.631202	−	1.94264i	−0.0562319	−	0.173064i
$127$	0.115232	−	0.0244933i	0.0102252	−	0.00217343i	−0.202796	−	0.979221i	$-0.565003\pi$
$127$	0.115232	−	0.0244933i	0.0102252	−	0.00217343i	0.213021	+	0.977048i	$0.431670\pi$
$128$	7.74501	−	5.62708i	0.684569	−	0.497368i
$129$	−12.1697	+	21.0786i	−1.07149	+	1.85587i
$130$	1.50132	+	2.60037i	0.131675	+	0.228068i
$131$	5.28390	+	2.35255i	0.461657	+	0.205543i	0.624367	−	0.781131i	$-0.285357\pi$
$131$	5.28390	+	2.35255i	0.461657	+	0.205543i	−0.162710	+	0.986674i	$0.552024\pi$
$132$	10.6794	+	7.75907i	0.929526	+	0.675340i
$133$	−2.09406	+	0.932337i	−0.181578	+	0.0808439i
$134$	2.21294	+	0.470375i	0.191169	+	0.0406342i
$135$	−2.13212	−	20.2858i	−0.183504	−	1.74592i
$136$	−1.66341	+	1.84740i	−0.142636	+	0.158413i
$137$	−7.89937	−	8.77314i	−0.674889	−	0.749540i	0.304281	−	0.952582i	$-0.401584\pi$
$137$	−7.89937	−	8.77314i	−0.674889	−	0.749540i	−0.979170	+	0.203042i	$0.934917\pi$
$138$	−0.0470005	+	0.447180i	−0.00400095	+	0.0380665i
$139$	4.76566	−	14.6672i	0.404218	−	1.24406i	−0.517328	−	0.855787i	$-0.673073\pi$
$139$	4.76566	−	14.6672i	0.404218	−	1.24406i	0.921546	−	0.388268i	$-0.126927\pi$
$140$	1.86568	−	5.74196i	0.157678	−	0.485284i
$141$	2.40797	−	22.9103i	0.202788	−	1.92940i
$142$	0.394559	+	0.438203i	0.0331107	+	0.0367731i
$143$	−4.67516	+	5.19229i	−0.390956	+	0.434201i
$144$	−1.83827	−	17.4900i	−0.153189	−	1.45750i
$145$	−9.18758	−	1.95288i	−0.762987	−	0.162178i
$146$	−4.61032	+	2.05265i	−0.381553	+	0.169878i
$147$	13.6441	+	9.91300i	1.12534	+	0.817611i
$148$	5.39436	+	2.40172i	0.443414	+	0.197421i
$149$	5.97511	+	10.3492i	0.489500	+	0.847840i	0.999927	−	0.0120817i	$-0.00384583\pi$
$149$	5.97511	+	10.3492i	0.489500	+	0.847840i	−0.510427	+	0.859921i	$0.670512\pi$
$150$	−1.95230	+	3.38148i	−0.159404	+	0.276097i
$151$	−3.49668	+	2.54048i	−0.284556	+	0.206742i	−0.720902	−	0.693037i	$-0.756272\pi$
$151$	−3.49668	+	2.54048i	−0.284556	+	0.206742i	0.436346	+	0.899779i	$0.356272\pi$
$152$	2.82272	−	0.599987i	0.228953	−	0.0486654i
$153$	3.02870	+	9.32137i	0.244856	+	0.753588i
$154$	−0.924636			−0.0745093
$155$		0			0
$156$	15.6018			1.24914
$157$	−2.68982	−	8.27841i	−0.214671	−	0.660689i	−0.999177	−	0.0405678i	$-0.987083\pi$
$157$	−2.68982	−	8.27841i	−0.214671	−	0.660689i	0.784506	−	0.620121i	$-0.212917\pi$
$158$	−1.18514	+	0.251909i	−0.0942845	+	0.0200408i
$159$	−11.6498	+	8.46405i	−0.923887	+	0.671243i
$160$	−5.76111	+	9.97854i	−0.455456	+	0.788873i
$161$	0.239267	+	0.414422i	0.0188568	+	0.0326610i
$162$	1.19935	+	0.533985i	0.0942297	+	0.0419538i
$163$	−2.53053	−	1.83853i	−0.198206	−	0.144005i	0.484255	−	0.874927i	$-0.339091\pi$
$163$	−2.53053	−	1.83853i	−0.198206	−	0.144005i	−0.682462	+	0.730922i	$0.739091\pi$
$164$	11.9077	−	5.30164i	0.929834	−	0.413989i
$165$	−20.4586	−	4.34861i	−1.59270	−	0.338539i
$166$	0.472174	+	4.49243i	0.0366478	+	0.348680i
$167$	8.93619	−	9.92465i	0.691503	−	0.767992i	−0.290496	−	0.956876i	$-0.593820\pi$
$167$	8.93619	−	9.92465i	0.691503	−	0.767992i	0.981999	+	0.188884i	$0.0604870\pi$
$168$	2.85405	+	3.16975i	0.220195	+	0.244551i
$169$	0.495687	−	4.71614i	0.0381298	−	0.362780i
$170$	0.589196	−	1.81336i	0.0451893	−	0.139078i
$171$	3.51585	−	10.8207i	0.268864	−	0.827478i
$172$	1.65006	−	15.6993i	0.125816	−	1.19706i
$173$	12.7434	+	14.1530i	0.968864	+	1.07603i	0.997075	+	0.0764306i	$0.0243524\pi$
$173$	12.7434	+	14.1530i	0.968864	+	1.07603i	−0.0282108	+	0.999602i	$0.508981\pi$
$174$	2.14938	−	2.38713i	0.162944	−	0.180968i
$175$	0.434365	+	4.13270i	0.0328349	+	0.312403i
$176$	−7.78689	−	1.65515i	−0.586959	−	0.124762i
$177$	−31.7547	+	14.1381i	−2.38683	+	1.06268i
$178$	0.642377	+	0.466714i	0.0481482	+	0.0349817i
$179$	0.0724715	+	0.0322664i	0.00541678	+	0.00241170i	0.409443	−	0.912336i	$-0.365723\pi$
$179$	0.0724715	+	0.0322664i	0.00541678	+	0.00241170i	−0.404026	+	0.914747i	$0.632390\pi$
$180$	14.9835	+	25.9521i	1.11680	+	1.93436i
$181$	1.08143	−	1.87308i	0.0803817	−	0.139225i	−0.823032	−	0.567995i	$-0.807719\pi$
$181$	1.08143	−	1.87308i	0.0803817	−	0.139225i	0.903414	+	0.428769i	$0.141053\pi$
$182$	−0.884121	+	0.642351i	−0.0655354	+	0.0476142i
$183$	−40.8524	+	8.68344i	−3.01990	+	0.641899i
$184$	−0.186165	−	0.572956i	−0.0137243	−	0.0422389i
$185$	−9.35601			−0.687868
$186$		0			0
$187$	4.43668			0.324442
$188$	4.61695	+	14.2095i	0.336725	+	1.03633i
$189$	7.26158	−	1.54350i	0.528202	−	0.112273i
$190$	−1.79065	+	1.30098i	−0.129907	+	0.0943831i
$191$	2.67085	−	4.62604i	0.193256	−	0.334729i	−0.753072	−	0.657939i	$-0.771429\pi$
$191$	2.67085	−	4.62604i	0.193256	−	0.334729i	0.946327	+	0.323210i	$0.104762\pi$
$192$	7.50308	+	12.9957i	0.541488	+	0.937885i
$193$	−1.94921	−	0.867844i	−0.140307	−	0.0624688i	0.335382	−	0.942082i	$-0.391135\pi$
$193$	−1.94921	−	0.867844i	−0.140307	−	0.0624688i	−0.475689	+	0.879613i	$0.657801\pi$
$194$	−0.970327	−	0.704984i	−0.0696654	−	0.0506149i
$195$	−22.5832	+	10.0547i	−1.61722	+	0.720031i
$196$	−10.6991	−	2.27416i	−0.764220	−	0.162440i
$197$	−0.614181	−	5.84354i	−0.0437586	−	0.416335i	−0.994371	−	0.105955i	$-0.966210\pi$
$197$	−0.614181	−	5.84354i	−0.0437586	−	0.416335i	0.950612	−	0.310381i	$-0.100456\pi$
$198$	3.07093	−	3.41062i	0.218242	−	0.242382i
$199$	−4.63571	−	5.14848i	−0.328617	−	0.364966i	0.556083	−	0.831127i	$-0.312304\pi$
$199$	−4.63571	−	5.14848i	−0.328617	−	0.364966i	−0.884700	+	0.466161i	$0.845637\pi$
$200$	0.546837	−	5.20280i	0.0386672	−	0.367894i
$201$	−5.75569	+	17.7142i	−0.405975	+	1.24946i
$202$	1.92407	−	5.92169i	0.135377	−	0.416649i
$203$	0.357339	−	3.39985i	0.0250803	−	0.238623i
$204$	−6.62915	−	7.36241i	−0.464133	−	0.515472i
$205$	−13.8194	+	15.3480i	−0.965188	+	1.07195i
$206$	−0.296590	−	2.82187i	−0.0206644	−	0.196609i
$207$	−2.32330	−	0.493832i	−0.161480	−	0.0343237i
$208$	−8.59553	+	3.82698i	−0.595993	+	0.265353i
$209$	−4.16669	−	3.02727i	−0.288216	−	0.209401i
$210$	−2.98862	−	1.33062i	−0.206234	−	0.0918214i
$211$	−8.35437	−	14.4702i	−0.575139	−	0.996170i	−0.996027	−	0.0890568i	$-0.971615\pi$
$211$	−8.35437	−	14.4702i	−0.575139	−	0.996170i	0.420888	−	0.907113i	$-0.361719\pi$
$212$	4.66966	−	8.08808i	0.320713	−	0.555492i
$213$	−3.92744	+	2.85345i	−0.269104	+	0.195515i
$214$	4.17701	−	0.887850i	0.285534	−	0.0606922i
$215$	7.72911	+	23.7878i	0.527121	+	1.62231i
$216$	−9.34610			−0.635921
$217$		0			0
$218$	−0.222141			−0.0150453
$219$	−12.8391	−	39.5146i	−0.867585	−	2.67015i
$220$	13.2688	−	2.82037i	0.894582	−	0.190149i
$221$	4.24227	−	3.08219i	0.285366	−	0.207331i
$222$	1.59980	−	2.77094i	0.107372	−	0.185973i
$223$	−3.13078	−	5.42267i	−0.209653	−	0.363129i	0.741952	−	0.670453i	$-0.233900\pi$
$223$	−3.13078	−	5.42267i	−0.209653	−	0.363129i	−0.951605	+	0.307323i	$0.900567\pi$
$224$	−3.83103	−	1.70568i	−0.255972	−	0.113966i
$225$	−16.6865	−	12.1235i	−1.11244	−	0.808232i
$226$	−3.62797	+	1.61528i	−0.241329	+	0.107447i
$227$	7.67603	+	1.63159i	0.509476	+	0.108292i	0.455475	−	0.890248i	$-0.349469\pi$
$227$	7.67603	+	1.63159i	0.509476	+	0.108292i	0.0540006	+	0.998541i	$0.482803\pi$
$228$	1.20214	+	11.4376i	0.0796139	+	0.757476i
$229$	−8.54679	+	9.49218i	−0.564788	+	0.627261i	−0.956115	−	0.292991i	$-0.905349\pi$
$229$	−8.54679	+	9.49218i	−0.564788	+	0.627261i	0.391327	+	0.920252i	$0.372016\pi$
$230$	0.309183	+	0.343382i	0.0203869	+	0.0226420i
$231$	0.795712	−	7.57069i	0.0523540	−	0.498115i
$232$	−1.32994	+	4.09313i	−0.0873148	+	0.268727i
$233$	3.92992	−	12.0950i	0.257457	−	0.792372i	−0.735878	−	0.677114i	$-0.763230\pi$
$233$	3.92992	−	12.0950i	0.257457	−	0.792372i	0.993336	−	0.115258i	$-0.0367696\pi$
$234$	0.566992	−	5.39457i	0.0370654	−	0.352654i
$235$	−15.8403	−	17.5925i	−1.03331	−	1.14761i
$236$	15.0849	−	16.7535i	0.981946	−	1.09056i
$237$	−1.04268	−	9.92040i	−0.0677291	−	0.644399i
$238$	0.678783	+	0.144280i	0.0439990	+	0.00935227i
$239$	23.2265	−	10.3411i	1.50240	−	0.668912i	0.519739	−	0.854325i	$-0.326029\pi$
$239$	23.2265	−	10.3411i	1.50240	−	0.668912i	0.982661	+	0.185413i	$0.0593624\pi$
$240$	−22.7870	−	16.5557i	−1.47089	−	1.06867i
$241$	−2.15686	−	0.960297i	−0.138936	−	0.0618582i	0.336091	−	0.941829i	$-0.390895\pi$
$241$	−2.15686	−	0.960297i	−0.138936	−	0.0618582i	−0.475027	+	0.879971i	$0.657562\pi$
$242$	0.894121	+	1.54866i	0.0574763	+	0.0995519i
$243$	4.88634	−	8.46339i	0.313459	−	0.542927i
$244$	21.9142	−	15.9216i	1.40291	−	1.01928i
$245$	16.9522	−	3.60331i	1.08304	−	0.230207i
$246$	−2.18256	−	6.71723i	−0.139155	−	0.428275i
$247$	−6.08718			−0.387318
$248$		0			0
$249$	−37.1893			−2.35677
$250$	−0.374520	−	1.15265i	−0.0236867	−	0.0729002i
$251$	2.30514	−	0.489972i	0.145499	−	0.0309268i	−0.134586	−	0.990902i	$-0.542971\pi$
$251$	2.30514	−	0.489972i	0.145499	−	0.0309268i	0.280085	+	0.959975i	$0.409637\pi$
$252$	−8.82367	+	6.41077i	−0.555839	+	0.403841i
$253$	−0.537595	+	0.931142i	−0.0337983	+	0.0585404i
$254$	0.0207005	+	0.0358542i	0.00129886	+	0.00224970i
$255$	14.3403	+	6.38471i	0.898024	+	0.399826i
$256$	−5.67014	−	4.11960i	−0.354384	−	0.257475i
$257$	−23.7650	+	10.5809i	−1.48242	+	0.660015i	−0.978969	−	0.204009i	$-0.934603\pi$
$257$	−23.7650	+	10.5809i	−1.48242	+	0.660015i	−0.503450	+	0.864024i	$0.667936\pi$
$258$	−8.36676	−	1.77841i	−0.520892	−	0.110719i
$259$	−0.355938	−	3.38653i	−0.0221169	−	0.210429i
$260$	10.7281	−	11.9147i	0.665326	−	0.738919i
$261$	11.3539	+	12.6098i	0.702789	+	0.780527i
$262$	−0.212472	+	2.02153i	−0.0131265	+	0.124891i
$263$	−7.08747	+	21.8130i	−0.437032	+	1.34505i	0.453957	+	0.891023i	$0.350012\pi$
$263$	−7.08747	+	21.8130i	−0.437032	+	1.34505i	−0.890990	+	0.454024i	$0.849988\pi$
$264$	−2.96147	+	9.11446i	−0.182266	+	0.560956i
$265$	−1.54679	+	14.7167i	−0.0950184	+	0.904039i
$266$	−0.539030	−	0.598653i	−0.0330500	−	0.0367058i
$267$	−4.37415	+	4.85798i	−0.267693	+	0.297304i
$268$	−1.26271	−	12.0139i	−0.0771325	−	0.733867i
$269$	−16.6748	−	3.54434i	−1.01668	−	0.216102i	−0.330711	−	0.943732i	$-0.607288\pi$
$269$	−16.6748	−	3.54434i	−1.01668	−	0.216102i	−0.685970	+	0.727630i	$0.740622\pi$
$270$	6.54862	−	2.91563i	0.398536	−	0.177440i
$271$	5.86255	+	4.25939i	0.356124	+	0.258739i	0.751434	−	0.659809i	$-0.229363\pi$
$271$	5.86255	+	4.25939i	0.356124	+	0.258739i	−0.395309	+	0.918548i	$0.629363\pi$
$272$	5.45815	+	2.43013i	0.330949	+	0.147348i
$273$	−4.49857	−	7.79175i	−0.272266	−	0.471578i
$274$	2.07440	−	3.59297i	0.125319	−	0.217059i
$275$	−7.55354	+	5.48797i	−0.455496	+	0.330937i
$276$	2.34843	−	0.499175i	0.141359	−	0.0300468i
$277$	−4.66717	−	14.3641i	−0.280423	−	0.863053i	−0.987733	−	0.156150i	$-0.950092\pi$
$277$	−4.66717	−	14.3641i	−0.280423	−	0.863053i	0.707310	−	0.706903i	$-0.249908\pi$
$278$	5.41979			0.325058
$279$		0			0
$280$	4.38316			0.261944
$281$	−0.768550	−	2.36535i	−0.0458479	−	0.141105i	0.925512	−	0.378718i	$-0.123635\pi$
$281$	−0.768550	−	2.36535i	−0.0458479	−	0.141105i	−0.971360	+	0.237613i	$0.923635\pi$
$282$	7.91888	−	1.68321i	0.471562	−	0.100234i
$283$	3.82370	−	2.77808i	0.227296	−	0.165140i	−0.468309	−	0.883565i	$-0.655137\pi$
$283$	3.82370	−	2.77808i	0.227296	−	0.165140i	0.695605	+	0.718425i	$0.255137\pi$
$284$	1.57426	−	2.72670i	0.0934153	−	0.161800i
$285$	−9.11114	−	15.7810i	−0.539697	−	0.934783i
$286$	−2.24315	−	0.998713i	−0.132640	−	0.0590551i
$287$	−6.08114	−	4.41821i	−0.358958	−	0.260798i
$288$	19.0153	−	8.46618i	1.12049	−	0.498874i
$289$	13.3715	+	2.84220i	0.786559	+	0.167188i
$290$	−0.345043	−	3.28286i	−0.0202616	−	0.192776i
$291$	6.60726	−	7.33811i	0.387325	−	0.430168i
$292$	18.0309	+	20.0254i	1.05518	+	1.17190i
$293$	1.10266	−	10.4911i	0.0644180	−	0.612897i	−0.913922	−	0.405891i	$-0.866961\pi$
$293$	1.10266	−	10.4911i	0.0644180	−	0.612897i	0.978340	−	0.207006i	$-0.0663720\pi$
$294$	−1.83152	+	5.63683i	−0.106816	+	0.328746i
$295$	−11.0381	+	33.9719i	−0.642666	+	1.97792i
$296$	−0.448103	+	4.26342i	−0.0260455	+	0.247806i
$297$	11.1612	+	12.3958i	0.647639	+	0.719276i
$298$	−2.81015	+	3.12098i	−0.162787	+	0.180794i
$299$	0.132832	+	1.26381i	0.00768188	+	0.0730882i
$300$	20.3932	+	4.33472i	1.17740	+	0.250265i
$301$	−8.31624	+	3.70263i	−0.479340	+	0.213416i
$302$	−1.22885	−	0.892809i	−0.0707121	−	0.0513754i
$303$	46.8295	+	20.8499i	2.69029	+	1.19779i
$304$	−3.46785	−	6.00650i	−0.198895	−	0.344496i
$305$	−21.4595	+	37.1689i	−1.22877	+	2.12829i
$306$	−2.78659	+	2.02458i	−0.159299	+	0.115737i
$307$	−2.59063	+	0.550655i	−0.147855	+	0.0314275i	−0.281244	−	0.959636i	$-0.590747\pi$
$307$	−2.59063	+	0.550655i	−0.147855	+	0.0314275i	0.133390	+	0.991064i	$0.457414\pi$
$308$	1.52566	+	4.69551i	0.0869327	+	0.267551i
$309$	23.3600			1.32890
$310$		0			0
$311$	5.51283			0.312604			0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283			0.312604			0.156302	+	0.987709i	$0.450043\pi$
$312$	3.50018	+	10.7724i	0.198158	+	0.609869i
$313$	−26.0925	+	5.54614i	−1.47484	+	0.313486i	−0.874016	−	0.485897i	$-0.838493\pi$
$313$	−26.0925	+	5.54614i	−1.47484	+	0.313486i	−0.600821	+	0.799383i	$0.705160\pi$
$314$	2.47480	−	1.79805i	0.139661	−	0.101470i
$315$	8.64057	−	14.9659i	0.486841	−	0.843234i
$316$	3.23474	+	5.60274i	0.181969	+	0.315179i
$317$	9.81169	+	4.36845i	0.551080	+	0.245356i	0.663335	−	0.748323i	$-0.269141\pi$
$317$	9.81169	+	4.36845i	0.551080	+	0.245356i	−0.112255	+	0.993679i	$0.535807\pi$
$318$	−4.09411	−	2.97454i	−0.229586	−	0.166804i
$319$	7.01697	−	3.12416i	0.392875	−	0.174919i
$320$	15.0838	+	3.20616i	0.843209	+	0.179230i
$321$	3.67490	+	34.9644i	0.205113	+	1.95152i
$322$	−0.112529	+	0.124976i	−0.00627100	+	0.00696465i
$323$	2.58643	+	2.87252i	0.143913	+	0.159831i
$324$	0.732749	−	6.97165i	0.0407083	−	0.387314i
$325$	−3.41003	+	10.4950i	−0.189155	+	0.582158i
$326$	0.339686	−	1.04545i	0.0188135	−	0.0579019i
$327$	0.191168	−	1.81884i	0.0105716	−	0.100582i
$328$	6.33201	+	7.03241i	0.349627	+	0.388300i
$329$	5.76519	−	6.40289i	0.317845	−	0.353003i
$330$	−0.768331	−	7.31018i	−0.0422952	−	0.402412i
$331$	19.2183	+	4.08497i	1.05633	+	0.224530i	0.703162	−	0.711029i	$-0.251771\pi$
$331$	19.2183	+	4.08497i	1.05633	+	0.224530i	0.353169	+	0.935560i	$0.385104\pi$
$332$	22.0345	−	9.81038i	1.20930	−	0.538415i
$333$	13.6737	+	9.93453i	0.749315	+	0.544409i
$334$	4.28759	+	1.90896i	0.234607	+	0.104454i
$335$	9.57021	+	16.5761i	0.522876	+	0.905649i
$336$	5.12565	−	8.87788i	0.279627	−	0.484328i
$337$	15.5159	−	11.2730i	0.845206	−	0.614078i	−0.0786142	−	0.996905i	$-0.525050\pi$
$337$	15.5159	−	11.2730i	0.845206	−	0.614078i	0.923820	+	0.382827i	$0.125050\pi$
$338$	1.63012	−	0.346492i	0.0886667	−	0.0188467i
$339$	−10.1034	−	31.0950i	−0.548740	−	1.68885i
$340$	−10.1808			−0.552133
$341$		0			0
$342$	3.99844			0.216211
$343$	4.28996	+	13.2031i	0.231636	+	0.712902i
$344$	11.2100	−	2.38275i	0.604401	−	0.128469i
$345$	−3.07760	+	2.23601i	−0.165693	+	0.120383i
$346$	−3.34647	+	5.79626i	−0.179907	+	0.311609i
$347$	5.32998	+	9.23180i	0.286128	+	0.495589i	0.972882	−	0.231301i	$-0.0742983\pi$
$347$	5.32998	+	9.23180i	0.286128	+	0.495589i	−0.686754	+	0.726890i	$0.740965\pi$
$348$	−15.6689	−	6.97624i	−0.839941	−	0.373966i
$349$	15.1299	+	10.9925i	0.809884	+	0.588415i	0.913797	−	0.406171i	$-0.133136\pi$
$349$	15.1299	+	10.9925i	0.809884	+	0.588415i	−0.103913	+	0.994586i	$0.533136\pi$
$350$	−1.33411	+	0.593984i	−0.0713112	+	0.0317498i
$351$	19.2836	+	4.09885i	1.02928	+	0.218781i
$352$	−0.984903	−	9.37073i	−0.0524955	−	0.499461i
$353$	8.47269	−	9.40988i	0.450956	−	0.500837i	−0.474204	−	0.880415i	$-0.657264\pi$
$353$	8.47269	−	9.40988i	0.450956	−	0.500837i	0.925160	+	0.379578i	$0.123931\pi$
$354$	−8.17392	−	9.07806i	−0.434439	−	0.482493i
$355$	−0.521462	+	4.96138i	−0.0276763	+	0.263323i
$356$	1.31015	−	4.03222i	0.0694377	−	0.213707i
$357$	−1.76547	+	5.43355i	−0.0934384	+	0.287574i
$358$	−0.00291416	+	0.0277264i	−0.000154018	+	0.00146539i
$359$	−15.1746	−	16.8531i	−0.800886	−	0.889474i	0.194933	−	0.980816i	$-0.437551\pi$
$359$	−15.1746	−	16.8531i	−0.800886	−	0.889474i	−0.995820	+	0.0913423i	$0.970884\pi$
$360$	−14.5575	+	16.1677i	−0.767248	+	0.852115i
$361$	1.51701	+	14.4334i	0.0798428	+	0.759653i
$362$	0.743486	+	0.158033i	0.0390768	+	0.00830602i
$363$	−13.4495	+	5.98811i	−0.705917	+	0.314294i
$364$	4.72082	+	3.42987i	0.247438	+	0.179774i
$365$	−39.0048	−	17.3661i	−2.04160	−	0.908981i
$366$	−7.33880	−	12.7112i	−0.383605	−	0.664424i
$367$	4.35984	−	7.55147i	0.227582	−	0.394183i	−0.729509	−	0.683971i	$-0.760251\pi$
$367$	4.35984	−	7.55147i	0.227582	−	0.394183i	0.957091	+	0.289788i	$0.0935847\pi$
$368$	−1.17139	+	0.851062i	−0.0610628	+	0.0443647i
$369$	36.4939	−	7.75702i	1.89980	−	0.403814i
$370$	−1.01605	−	3.12708i	−0.0528219	−	0.162569i
$371$	−5.38574			−0.279614
$372$		0			0
$373$	25.4134			1.31586			0.657928	−	0.753081i	$-0.271433\pi$
$373$	25.4134			1.31586			0.657928	+	0.753081i	$0.271433\pi$
$374$	0.481817	+	1.48288i	0.0249142	+	0.0766779i
$375$	9.75994	−	2.07454i	0.504001	−	0.107129i
$376$	−8.77534	+	6.37566i	−0.452553	+	0.328799i
$377$	4.53913	−	7.86200i	0.233777	−	0.404914i
$378$	1.30448	+	2.25943i	0.0670954	+	0.116213i
$379$	20.1874	+	8.98802i	1.03696	+	0.461683i	0.853362	−	0.521318i	$-0.174560\pi$
$379$	20.1874	+	8.98802i	1.03696	+	0.461683i	0.183596	+	0.983002i	$0.441226\pi$
$380$	9.56127	+	6.94667i	0.490483	+	0.356357i
$381$	−0.311380	+	0.138635i	−0.0159525	+	0.00710250i
$382$	1.83622	+	0.390301i	0.0939493	+	0.0199695i
$383$	−2.78491	−	26.4967i	−0.142302	−	1.35392i	−0.799712	−	0.600384i	$-0.795015\pi$
$383$	−2.78491	−	26.4967i	−0.142302	−	1.35392i	0.657410	−	0.753533i	$-0.271652\pi$
$384$	−18.5339	+	20.5840i	−0.945806	+	1.05042i
$385$	−5.23442	−	5.81341i	−0.266771	−	0.296279i
$386$	0.0783799	−	0.745735i	0.00398943	−	0.0379569i
$387$	13.9626	−	42.9726i	0.709761	−	2.18442i
$388$	−1.97901	+	6.09077i	−0.100469	+	0.309212i
$389$	−1.35417	+	12.8841i	−0.0686592	+	0.653249i	0.905027	+	0.425355i	$0.139851\pi$
$389$	−1.35417	+	12.8841i	−0.0686592	+	0.653249i	−0.973686	+	0.227894i	$0.926816\pi$
$390$	−5.81310	−	6.45610i	−0.294358	−	0.326917i
$391$	0.539948	−	0.599673i	0.0273063	−	0.0303268i
$392$	−0.830061	−	7.89750i	−0.0419244	−	0.398884i
$393$	−16.3690	−	3.47933i	−0.825705	−	0.175509i
$394$	1.88640	−	0.839879i	0.0950355	−	0.0423125i
$395$	−8.29294	−	6.02517i	−0.417263	−	0.303159i
$396$	−22.3870	−	9.96732i	−1.12499	−	0.500876i
$397$	1.46363	+	2.53508i	0.0734574	+	0.127232i	0.900414	−	0.435033i	$-0.143263\pi$
$397$	1.46363	+	2.53508i	0.0734574	+	0.127232i	−0.826957	+	0.562265i	$0.809930\pi$
$398$	1.21736	−	2.10852i	0.0610205	−	0.105691i
$399$	5.36549	−	3.89826i	0.268611	−	0.195157i
$400$	−12.2986	+	2.61414i	−0.614929	+	0.130707i
$401$	3.79302	+	11.6737i	0.189414	+	0.582957i	0.999996	−	0.00266786i	$-0.000849206\pi$
$401$	3.79302	+	11.6737i	0.189414	+	0.582957i	−0.810582	+	0.585625i	$0.800849\pi$
$402$	−6.54572			−0.326471
$403$		0			0
$404$	−33.2464			−1.65407
$405$	3.43229	+	10.5635i	0.170552	+	0.524905i
$406$	1.17515	−	0.249785i	0.0583216	−	0.0123966i
$407$	6.18972	−	4.49710i	0.306813	−	0.222913i
$408$	3.59625	−	6.22889i	0.178041	−	0.308376i
$409$	−8.59861	−	14.8932i	−0.425174	−	0.736423i	0.571263	−	0.820767i	$-0.306454\pi$
$409$	−8.59861	−	14.8932i	−0.425174	−	0.736423i	−0.996437	+	0.0843442i	$0.973120\pi$
$410$	−6.63056	−	2.95211i	−0.327460	−	0.145795i
$411$	27.6332	+	20.0767i	1.36305	+	0.990311i
$412$	−13.8407	+	6.16228i	−0.681882	+	0.303594i
$413$	−12.7165	−	2.70297i	−0.625738	−	0.133005i
$414$	−0.0872523	−	0.830150i	−0.00428822	−	0.0407997i
$415$	−25.5720	+	28.4006i	−1.25528	+	1.39413i
$416$	−7.45166	−	8.27590i	−0.365348	−	0.405760i
$417$	−4.66410	+	44.3759i	−0.228402	+	2.17310i
$418$	0.559316	−	1.72140i	0.0273571	−	0.0841963i
$419$	7.15236	−	22.0127i	0.349416	−	1.07539i	−0.609762	−	0.792585i	$-0.708735\pi$
$419$	7.15236	−	22.0127i	0.349416	−	1.07539i	0.959177	−	0.282806i	$-0.0912652\pi$
$420$	−1.82591	+	17.3724i	−0.0890955	+	0.847687i
$421$	19.5267	+	21.6866i	0.951674	+	1.05694i	0.998315	+	0.0580298i	$0.0184818\pi$
$421$	19.5267	+	21.6866i	0.951674	+	1.05694i	−0.0466404	+	0.998912i	$0.514851\pi$
$422$	3.92913	−	4.36374i	0.191267	−	0.212424i
$423$	4.47019	+	42.5310i	0.217348	+	2.06793i
$424$	6.63213	+	1.40970i	0.322085	+	0.0684612i
$425$	6.40146	−	2.85011i	0.310516	−	0.138251i
$426$	−1.38023	−	1.00280i	−0.0668723	−	0.0485856i
$427$	−14.2702	−	6.35348i	−0.690581	−	0.307467i
$428$	−11.4008	−	19.7468i	−0.551080	−	0.954498i
$429$	10.1076	−	17.5069i	0.487999	−	0.845239i
$430$	−7.11126	+	5.16664i	−0.342936	+	0.249157i
$431$	−29.6890	+	6.31058i	−1.43007	+	0.303970i	−0.856906	−	0.515473i	$-0.827616\pi$
$431$	−29.6890	+	6.31058i	−1.43007	+	0.303970i	−0.573161	+	0.819443i	$0.694283\pi$
$432$	6.94129	+	21.3631i	0.333963	+	1.02783i
$433$	13.8400			0.665107			0.332553	−	0.943084i	$-0.392090\pi$
$433$	13.8400			0.665107			0.332553	+	0.943084i	$0.392090\pi$
$434$		0			0
$435$	27.1762			1.30300
$436$	0.366536	+	1.12808i	0.0175539	+	0.0540254i
$437$	−0.916264	+	0.194758i	−0.0438309	+	0.00931654i
$438$	11.8128	−	8.58247i	0.564435	−	0.410086i
$439$	−6.46006	+	11.1892i	−0.308322	+	0.534029i	−0.977995	−	0.208626i	$-0.933101\pi$
$439$	−6.46006	+	11.1892i	−0.308322	+	0.534029i	0.669674	+	0.742656i	$0.266434\pi$
$440$	4.92414	+	8.52887i	0.234749	+	0.406598i
$441$	−28.6016	−	12.7343i	−1.36198	−	0.606394i
$442$	1.49087	+	1.08318i	0.0709136	+	0.0515218i
$443$	21.7043	−	9.66336i	1.03120	−	0.459120i	0.179837	−	0.983696i	$-0.442443\pi$
$443$	21.7043	−	9.66336i	1.03120	−	0.459120i	0.851363	+	0.524577i	$0.175776\pi$
$444$	−16.7112	−	3.55207i	−0.793076	−	0.168574i
$445$	0.702188	+	6.68087i	0.0332869	+	0.316704i
$446$	1.47243	−	1.63530i	0.0697217	−	0.0774338i
$447$	−23.1355	−	25.6946i	−1.09427	−	1.21531i
$448$	−0.586664	+	5.58174i	−0.0277173	+	0.263712i
$449$	5.99891	−	18.4627i	0.283106	−	0.871311i	−0.703854	−	0.710345i	$-0.748539\pi$
$449$	5.99891	−	18.4627i	0.283106	−	0.871311i	0.986960	−	0.160966i	$-0.0514610\pi$
$450$	2.23992	−	6.89377i	0.105591	−	0.324975i
$451$	1.76537	−	16.7964i	0.0831279	−	0.790909i
$452$	14.1889	+	15.7584i	0.667392	+	0.741213i
$453$	8.36760	−	9.29316i	0.393144	−	0.436631i
$454$	0.288276	+	2.74276i	0.0135295	+	0.128724i
$455$	−9.04367	−	1.92229i	−0.423974	−	0.0901184i
$456$	−7.62756	+	3.39601i	−0.357193	+	0.159033i
$457$	19.6931	+	14.3078i	0.921202	+	0.669293i	0.943823	−	0.330452i	$-0.107201\pi$
$457$	19.6931	+	14.3078i	0.921202	+	0.669293i	−0.0226207	+	0.999744i	$0.507201\pi$
$458$	−4.10076	−	1.82578i	−0.191616	−	0.0853129i
$459$	−6.25931	−	10.8414i	−0.292159	−	0.506035i
$460$	1.23362	−	2.13669i	0.0575177	−	0.0996235i
$461$	−31.0202	+	22.5375i	−1.44476	+	1.04968i	−0.457734	+	0.889089i	$0.651339\pi$
$461$	−31.0202	+	22.5375i	−1.44476	+	1.04968i	−0.987022	+	0.160587i	$0.948661\pi$
$462$	2.61678	−	0.556214i	0.121744	−	0.0258774i
$463$	2.03775	+	6.27154i	0.0947022	+	0.291463i	0.987176	−	0.159636i	$-0.0510320\pi$
$463$	2.03775	+	6.27154i	0.0947022	+	0.291463i	−0.892474	+	0.451099i	$0.851032\pi$
$464$	10.3437			0.480195
$465$		0			0
$466$	4.46933			0.207038
$467$	11.8667	+	36.5219i	0.549125	+	1.69003i	0.710975	+	0.703217i	$0.248254\pi$
$467$	11.8667	+	36.5219i	0.549125	+	1.69003i	−0.161850	+	0.986815i	$0.551746\pi$
$468$	−28.3304	+	6.02181i	−1.30957	+	0.278358i
$469$	−5.63584	+	4.09468i	−0.260239	+	0.189075i
$470$	4.15973	−	7.20487i	0.191874	−	0.332336i
$471$	12.5922	+	21.8104i	0.580220	+	1.00497i
$472$	14.9519	+	6.65702i	0.688217	+	0.306414i
$473$	−16.5473	−	12.0223i	−0.760846	−	0.552787i
$474$	3.20248	−	1.42584i	0.147095	−	0.0654909i
$475$	−7.95662	−	1.69123i	−0.365075	−	0.0775990i
$476$	−0.387317	−	3.68508i	−0.0177527	−	0.168905i
$477$	17.8873	−	19.8659i	0.819003	−	0.909595i
$478$	5.97871	+	6.64002i	0.273460	+	0.303708i
$479$	−0.786592	+	7.48393i	−0.0359403	+	0.341949i	0.961745	+	0.273947i	$0.0883292\pi$
$479$	−0.786592	+	7.48393i	−0.0359403	+	0.341949i	−0.997685	+	0.0680025i	$0.978337\pi$
$480$	10.3017	−	31.7055i	0.470208	−	1.44715i
$481$	2.79434	−	8.60009i	0.127411	−	0.392130i
$482$	0.0867299	−	0.825180i	0.00395044	−	0.0375859i
$483$	−0.926435	−	1.02891i	−0.0421543	−	0.0468171i
$484$	6.38915	−	7.09587i	0.290416	−	0.322539i
$485$	−1.06067	−	10.0916i	−0.0481627	−	0.458237i
$486$	3.35939	+	0.714060i	0.152385	+	0.0323904i
$487$	−22.8681	+	10.1815i	−1.03625	+	0.461369i	−0.853118	−	0.521718i	$-0.825291\pi$
$487$	−22.8681	+	10.1815i	−1.03625	+	0.461369i	−0.183135	+	0.983088i	$0.558625\pi$
$488$	15.9096	+	11.5590i	0.720194	+	0.523252i
$489$	8.26753	+	3.68094i	0.373870	+	0.166458i
$490$	3.04533	+	5.27467i	0.137574	+	0.238285i
$491$	−19.8550	+	34.3899i	−0.896044	+	1.55199i	−0.0635377	+	0.997979i	$0.520238\pi$
$491$	−19.8550	+	34.3899i	−0.896044	+	1.55199i	−0.832507	+	0.554015i	$0.813095\pi$
$492$	−30.5103	+	22.1671i	−1.37551	+	0.999368i
$493$	−5.63871	+	1.19854i	−0.253955	+	0.0539797i
$494$	−0.661059	−	2.03453i	−0.0297425	−	0.0915379i
$495$	38.8281			1.74519
$496$		0			0
$497$	−1.81567			−0.0814440
$498$	−4.03870	−	12.4298i	−0.180979	−	0.556995i
$499$	−23.1372	+	4.91796i	−1.03576	+	0.220158i	−0.694261	−	0.719723i	$-0.744269\pi$
$499$	−23.1372	+	4.91796i	−1.03576	+	0.220158i	−0.341501	+	0.939881i	$0.610935\pi$
$500$	−5.23547	+	3.80379i	−0.234137	+	0.170111i
$501$	−19.3199	+	33.4630i	−0.863148	+	1.49502i
$502$	0.414099	+	0.717241i	0.0184822	+	0.0320120i
$503$	−18.4412	−	8.21056i	−0.822253	−	0.366091i	−0.0479063	−	0.998852i	$-0.515255\pi$
$503$	−18.4412	−	8.21056i	−0.822253	−	0.366091i	−0.774347	+	0.632761i	$0.781922\pi$
$504$	−6.40594	−	4.65419i	−0.285343	−	0.207314i
$505$	48.1234	−	21.4259i	2.14146	−	0.953440i
$506$	−0.369600	−	0.0785608i	−0.0164307	−	0.00349245i
$507$	1.43417	+	13.6452i	0.0636936	+	0.606004i
$508$	0.147920	−	0.164282i	0.00656288	−	0.00728882i
$509$	−7.92184	−	8.79810i	−0.351130	−	0.389969i	0.541544	−	0.840672i	$-0.317840\pi$
$509$	−7.92184	−	8.79810i	−0.351130	−	0.389969i	−0.892674	+	0.450703i	$0.851173\pi$
$510$	−0.576639	+	5.48636i	−0.0255340	+	0.242940i
$511$	4.80197	−	14.7789i	0.212427	−	0.653782i
$512$	6.67779	−	20.5521i	0.295120	−	0.908285i
$513$	−1.51903	+	14.4526i	−0.0670667	+	0.638097i
$514$	−6.11730	−	6.79395i	−0.269823	−	0.299669i
$515$	16.0627	−	17.8395i	0.707809	−	0.786102i
$516$	4.77412	+	45.4227i	0.210169	+	1.99962i
$517$	18.9357	+	4.02490i	0.832790	+	0.177015i
$518$	1.09323	−	0.486738i	0.0480338	−	0.0213860i
$519$	−44.5784	−	32.3881i	−1.95678	−	1.42168i
$520$	10.6334	+	4.73431i	0.466307	+	0.207613i
$521$	16.3742	+	28.3610i	0.717368	+	1.24252i	0.962039	+	0.272911i	$0.0879865\pi$
$521$	16.3742	+	28.3610i	0.717368	+	1.24252i	−0.244672	+	0.969606i	$0.578680\pi$
$522$	−2.98158	+	5.16425i	−0.130500	+	0.226033i
$523$	−23.8682	+	17.3412i	−1.04368	+	0.758279i	−0.971001	−	0.239076i	$-0.923155\pi$
$523$	−23.8682	+	17.3412i	−1.04368	+	0.758279i	−0.0726806	+	0.997355i	$0.523155\pi$
$524$	10.6164	−	2.25658i	0.463779	−	0.0985792i
$525$	−3.71530	−	11.4345i	−0.162149	−	0.499044i
$526$	−8.06030			−0.351446
$527$		0			0
$528$	23.0331			1.00239
$529$	−7.04696	−	21.6883i	−0.306390	−	0.942970i
$530$	−5.08677	+	1.08123i	−0.220955	+	0.0469655i
$531$	52.2047	−	37.9289i	2.26549	−	1.64597i
$532$	−2.15069	+	3.72510i	−0.0932441	+	0.161504i
$533$	−9.98053	−	17.2868i	−0.432305	−	0.748774i
$534$	−2.09872	−	0.934410i	−0.0908205	−	0.0404359i
$535$	29.2284	+	21.2357i	1.26365	+	0.918098i
$536$	8.01188	−	3.56712i	0.346060	−	0.154076i
$537$	−0.224509	−	0.0477209i	−0.00968828	−	0.00205931i
$538$	−0.626228	−	5.95817i	−0.0269986	−	0.256875i
$539$	−9.48323	+	10.5322i	−0.408472	+	0.453654i
$540$	−25.6116	−	28.4445i	−1.10215	−	1.22406i
$541$	−1.38666	+	13.1932i	−0.0596170	+	0.567218i	0.923417	+	0.383797i	$0.125384\pi$
$541$	−1.38666	+	13.1932i	−0.0596170	+	0.567218i	−0.983034	+	0.183421i	$0.941283\pi$
$542$	−0.786961	+	2.42202i	−0.0338028	+	0.104034i
$543$	−1.93375	+	5.95148i	−0.0829853	+	0.255403i
$544$	−0.739178	+	7.03281i	−0.0316920	+	0.301529i
$545$	−1.25755	−	1.39666i	−0.0538677	−	0.0598261i
$546$	2.11571	−	2.34974i	0.0905442	−	0.100560i
$547$	−3.94740	−	37.5570i	−0.168779	−	1.60582i	−0.671253	−	0.741228i	$-0.734244\pi$
$547$	−3.94740	−	37.5570i	−0.168779	−	1.60582i	0.502474	−	0.864592i	$-0.332423\pi$
$548$	−21.6687	−	4.60583i	−0.925642	−	0.196751i
$549$	70.8300	−	31.5356i	3.02295	−	1.34590i
$550$	−2.65456	−	1.92865i	−0.113191	−	0.0822380i
$551$	6.11337	+	2.72185i	0.260438	+	0.115955i
$552$	0.871520	+	1.50952i	0.0370944	+	0.0642493i
$553$	1.86539	−	3.23095i	0.0793245	−	0.137394i
$554$	4.29408	−	3.11983i	0.182438	−	0.132549i
$555$	26.4781	−	5.62810i	1.12393	−	0.238900i
$556$	−8.94274	−	27.5229i	−0.379257	−	1.16723i
$557$	11.3637			0.481496			0.240748	−	0.970588i	$-0.422607\pi$
$557$	11.3637			0.481496			0.240748	+	0.970588i	$0.422607\pi$
$558$		0			0
$559$	−24.1743			−1.02246
$560$	−3.25535	−	10.0189i	−0.137563	−	0.423377i
$561$	−12.5561	+	2.66888i	−0.530119	+	0.112680i
$562$	0.707114	−	0.513748i	0.0298278	−	0.0216712i
$563$	10.0933	−	17.4821i	0.425381	−	0.736781i	−0.571075	−	0.820898i	$-0.693474\pi$
$563$	10.0933	−	17.4821i	0.425381	−	0.736781i	0.996456	+	0.0841167i	$0.0268068\pi$
$564$	−21.6140	−	37.4365i	−0.910113	−	1.57636i
$565$	−30.6938	−	13.6657i	−1.29130	−	0.574922i
$566$	1.34377	+	0.976309i	0.0564830	+	0.0410373i
$567$	−3.69302	+	1.64424i	−0.155092	+	0.0690515i
$568$	2.23586	+	0.475247i	0.0938147	+	0.0199409i
$569$	−3.23930	−	30.8199i	−0.135799	−	1.29204i	−0.824030	−	0.566546i	$-0.808279\pi$
$569$	−3.23930	−	30.8199i	−0.135799	−	1.29204i	0.688232	−	0.725491i	$-0.258387\pi$
$570$	4.28505	−	4.75903i	0.179481	−	0.199334i
$571$	6.95876	+	7.72848i	0.291215	+	0.323427i	0.870944	−	0.491382i	$-0.163508\pi$
$571$	6.95876	+	7.72848i	0.291215	+	0.323427i	−0.579729	+	0.814809i	$0.696842\pi$
$572$	−1.37046	+	13.0391i	−0.0573019	+	0.545192i
$573$	−4.77588	+	14.6987i	−0.199515	+	0.614045i
$574$	0.816303	−	2.51232i	0.0340718	−	0.104862i
$575$	−0.177505	+	1.68885i	−0.00740247	+	0.0704298i
$576$	−18.6404	−	20.7022i	−0.776682	−	0.862593i
$577$	3.62258	−	4.02328i	0.150810	−	0.167491i	−0.663006	−	0.748614i	$-0.730720\pi$
$577$	3.62258	−	4.02328i	0.150810	−	0.167491i	0.813816	+	0.581123i	$0.197386\pi$
$578$	0.502172	+	4.77785i	0.0208876	+	0.198732i
$579$	6.03845	+	1.28351i	0.250949	+	0.0533409i
$580$	−16.1018	+	7.16898i	−0.668591	+	0.297676i
$581$	−11.2528	−	8.17564i	−0.466845	−	0.339183i
$582$	3.17017	+	1.41145i	0.131408	+	0.0585065i
$583$	−6.05046	−	10.4797i	−0.250585	−	0.434025i
$584$	−9.78162	+	16.9423i	−0.404766	+	0.701076i
$585$	37.1267	−	26.9741i	1.53500	−	1.11524i
$586$	3.62621	−	0.770775i	0.149797	−	0.0318404i
$587$	3.88212	+	11.9479i	0.160232	+	0.493145i	0.998653	−	0.0518785i	$-0.0165209\pi$
$587$	3.88212	+	11.9479i	0.160232	+	0.493145i	−0.838421	+	0.545023i	$0.816521\pi$
$588$	31.6471			1.30510
$589$		0			0
$590$	−12.5532			−0.516809
$591$	5.25335	+	16.1682i	0.216094	+	0.665069i
$592$	10.0780	−	2.14215i	0.414204	−	0.0880418i
$593$	−21.9001	+	15.9114i	−0.899330	+	0.653401i	−0.938294	−	0.345839i	$-0.887594\pi$
$593$	−21.9001	+	15.9114i	−0.899330	+	0.653401i	0.0389638	+	0.999241i	$0.487594\pi$
$594$	−2.93098	+	5.07660i	−0.120259	+	0.208295i
$595$	2.93551	+	5.08445i	0.120344	+	0.208442i
$596$	20.4858	+	9.12088i	0.839133	+	0.373606i
$597$	16.2164	+	11.7819i	0.663695	+	0.482202i
$598$	−0.407981	+	0.181645i	−0.0166836	+	0.00742802i
$599$	14.0414	+	2.98459i	0.573716	+	0.121947i	0.485628	−	0.874166i	$-0.338591\pi$
$599$	14.0414	+	2.98459i	0.573716	+	0.121947i	0.0880878	+	0.996113i	$0.471924\pi$
$600$	1.58216	+	15.0532i	0.0645914	+	0.614546i
$601$	−0.428255	+	0.475625i	−0.0174689	+	0.0194012i	−0.751816	−	0.659373i	$-0.770822\pi$
$601$	−0.428255	+	0.475625i	−0.0174689	+	0.0194012i	0.734347	+	0.678774i	$0.237488\pi$
$602$	−2.14067	−	2.37745i	−0.0872471	−	0.0968978i
$603$	3.61430	−	34.3877i	0.147186	−	1.40038i
$604$	−2.50627	+	7.71350i	−0.101979	+	0.313858i
$605$	−4.67515	+	14.3886i	−0.190072	+	0.584981i
$606$	−1.88307	+	17.9162i	−0.0764944	+	0.727796i
$607$	−4.36127	−	4.84368i	−0.177019	−	0.196599i	0.648106	−	0.761551i	$-0.275562\pi$
$607$	−4.36127	−	4.84368i	−0.177019	−	0.196599i	−0.825124	+	0.564951i	$0.808895\pi$
$608$	5.49289	−	6.10047i	0.222766	−	0.247407i
$609$	1.03389	+	9.83677i	0.0418952	+	0.398606i
$610$	−14.7535	−	3.13596i	−0.597352	−	0.126971i
$611$	20.9021	−	9.30620i	0.845607	−	0.376489i
$612$	14.8792	+	10.8103i	0.601454	+	0.436982i
$613$	−9.54228	−	4.24850i	−0.385409	−	0.171595i	0.204880	−	0.978787i	$-0.434320\pi$
$613$	−9.54228	−	4.24850i	−0.385409	−	0.171595i	−0.590289	+	0.807192i	$0.700986\pi$
$614$	−0.465385	−	0.806070i	−0.0187814	−	0.0325303i
$615$	29.8772	−	51.7489i	1.20477	−	2.08672i
$616$	−2.89980	+	2.10683i	−0.116836	+	0.0848864i
$617$	−21.2291	+	4.51238i	−0.854651	+	0.181662i	−0.614347	−	0.789036i	$-0.710580\pi$
$617$	−21.2291	+	4.51238i	−0.854651	+	0.181662i	−0.240304	+	0.970698i	$0.577247\pi$
$618$	2.53686	+	7.80766i	0.102048	+	0.314070i
$619$	−28.5478			−1.14743			−0.573716	−	0.819054i	$-0.694499\pi$
$619$	−28.5478			−1.14743			−0.573716	+	0.819054i	$0.694499\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$	0.598686	+	1.84257i	0.0240051	+	0.0738802i
$623$	−2.39151	+	0.508331i	−0.0958139	+	0.0203659i
$624$	22.0238	−	16.0012i	0.881658	−	0.640562i
$625$	14.7271	−	25.5080i	0.589083	−	1.02032i
$626$	−4.68731	−	8.11866i	−0.187343	−	0.324487i
$627$	13.6131	+	6.06092i	0.543653	+	0.242050i
$628$	−13.2143	−	9.60079i	−0.527310	−	0.383113i
$629$	−5.24565	+	2.33551i	−0.209158	+	0.0931231i
$630$	5.94044	+	1.26268i	0.236673	+	0.0503064i
$631$	2.84741	+	27.0913i	0.113354	+	1.07849i	0.892314	+	0.451414i	$0.149080\pi$
$631$	2.84741	+	27.0913i	0.113354	+	1.07849i	−0.778961	+	0.627072i	$0.784253\pi$
$632$	−3.14278	+	3.49041i	−0.125013	+	0.138841i
$633$	32.3480	+	35.9261i	1.28572	+	1.42793i
$634$	−0.394539	+	3.75379i	−0.0156692	+	0.149082i
$635$	−0.108238	+	0.333122i	−0.00429529	+	0.0132195i
$636$	−8.35006	+	25.6988i	−0.331101	+	1.01903i
$637$	−1.75091	+	16.6588i	−0.0693735	+	0.660044i
$638$	1.80623	+	2.00602i	0.0715092	+	0.0794190i
$639$	6.03027	−	6.69729i	0.238554	−	0.264941i
$640$	2.97528	+	28.3079i	0.117608	+	1.11897i
$641$	40.3076	+	8.56764i	1.59205	+	0.338402i	0.916851	−	0.399230i	$-0.130722\pi$
$641$	40.3076	+	8.56764i	1.59205	+	0.338402i	0.675204	+	0.737632i	$0.264056\pi$
$642$	−11.2871	+	5.02535i	−0.445467	+	0.198335i
$643$	−24.9278	−	18.1111i	−0.983055	−	0.714232i	−0.0246661	−	0.999696i	$-0.507852\pi$
$643$	−24.9278	−	18.1111i	−0.983055	−	0.714232i	−0.958389	+	0.285464i	$0.907852\pi$
$644$	0.820332	+	0.365235i	0.0323256	+	0.0143923i
$645$	−36.1834	−	62.6715i	−1.42472	−	2.46769i
$646$	−0.679205	+	1.17642i	−0.0267230	+	0.0462855i
$647$	7.21333	−	5.24079i	0.283585	−	0.206037i	−0.436894	−	0.899513i	$-0.643922\pi$
$647$	7.21333	−	5.24079i	0.283585	−	0.206037i	0.720480	+	0.693476i	$0.243922\pi$
$648$	4.97805	−	1.05812i	0.195556	−	0.0415667i
$649$	−9.02649	−	27.7807i	−0.354321	−	1.09049i
$650$	−3.87809			−0.152111
$651$		0			0
$652$	−5.86949			−0.229867
$653$	12.1263	+	37.3208i	0.474537	+	1.46047i	0.846581	+	0.532260i	$0.178657\pi$
$653$	12.1263	+	37.3208i	0.474537	+	1.46047i	−0.372044	+	0.928215i	$0.621343\pi$
$654$	0.628675	−	0.133629i	0.0245831	−	0.00522530i
$655$	−13.9127	+	10.1082i	−0.543613	+	0.394958i
$656$	11.3718	−	19.6965i	0.443993	−	0.769018i
$657$	38.5652	+	66.7969i	1.50457	+	2.60600i
$658$	2.76614	+	1.23157i	0.107836	+	0.0480115i
$659$	−26.6600	−	19.3696i	−1.03853	−	0.754533i	−0.0685280	−	0.997649i	$-0.521830\pi$
$659$	−26.6600	−	19.3696i	−1.03853	−	0.754533i	−0.969997	+	0.243117i	$0.921830\pi$
$660$	−35.8550	+	15.9637i	−1.39565	+	0.621385i
$661$	0.165967	+	0.0352774i	0.00645538	+	0.00137213i	0.211138	−	0.977456i	$-0.432283\pi$
$661$	0.165967	+	0.0352774i	0.00645538	+	0.00137213i	−0.204683	+	0.978828i	$0.565616\pi$
$662$	0.721749	+	6.86698i	0.0280516	+	0.266893i
$663$	−10.1518	+	11.2747i	−0.394264	+	0.437875i
$664$	11.7170	+	13.0131i	0.454709	+	0.505005i
$665$	0.712398	−	6.77802i	0.0276256	−	0.262840i
$666$	−1.83549	+	5.64907i	−0.0711240	+	0.218897i
$667$	0.431703	−	1.32864i	0.0167156	−	0.0514453i
$668$	2.61953	−	24.9232i	0.101353	−	0.964307i
$669$	12.1223	+	13.4632i	0.468676	+	0.520518i
$670$	−4.50095	+	4.99881i	−0.173887	+	0.193121i
$671$	−3.66865	−	34.9049i	−0.141627	−	1.34749i
$672$	11.8681	+	2.52265i	0.457823	+	0.0973133i
$673$	13.3253	−	5.93280i	0.513652	−	0.228693i	−0.133507	−	0.991048i	$-0.542624\pi$
$673$	13.3253	−	5.93280i	0.513652	−	0.228693i	0.647159	+	0.762355i	$0.275957\pi$
$674$	5.45280	+	3.96169i	0.210034	+	0.152599i
$675$	24.0670	+	10.7153i	0.926338	+	0.412432i
$676$	−4.44929	−	7.70639i	−0.171126	−	0.296400i
$677$	7.88341	−	13.6545i	0.302984	−	0.524784i	−0.673826	−	0.738890i	$-0.735350\pi$
$677$	7.88341	−	13.6545i	0.302984	−	0.524784i	0.976810	+	0.214106i	$0.0686837\pi$
$678$	9.29573	−	6.75374i	0.357000	−	0.259376i
$679$	3.61244	−	0.767848i	0.138633	−	0.0294673i
$680$	−2.28401	−	7.02948i	−0.0875880	−	0.269568i
$681$	−22.7051			−0.870063
$682$		0			0
$683$	20.5935			0.787988			0.393994	−	0.919113i	$-0.371093\pi$
$683$	20.5935			0.787988			0.393994	+	0.919113i	$0.371093\pi$
$684$	−6.59748	−	20.3050i	−0.252261	−	0.776380i
$685$	34.3332	−	7.29775i	1.31180	−	0.278833i
$686$	−3.94703	+	2.86768i	−0.150698	+	0.109489i
$687$	18.4780	−	32.0048i	0.704979	−	1.22106i
$688$	−13.7720	−	23.8538i	−0.525053	−	0.909418i
$689$	−13.0657	−	5.81721i	−0.497763	−	0.221618i
$690$	−1.08157	−	0.785806i	−0.0411746	−	0.0299151i
$691$	−5.43716	+	2.42078i	−0.206839	+	0.0920908i	−0.507542	−	0.861627i	$-0.669446\pi$
$691$	−5.43716	+	2.42078i	−0.206839	+	0.0920908i	0.300702	+	0.953718i	$0.402779\pi$
$692$	34.9564	+	7.43021i	1.32884	+	0.282454i
$693$	1.47717	+	14.0543i	0.0561130	+	0.533879i
$694$	−2.50673	+	2.78401i	−0.0951543	+	0.105680i
$695$	30.6817	+	34.0755i	1.16383	+	1.29256i
$696$	1.30160	−	12.3839i	0.0493369	−	0.469409i
$697$	−3.91687	+	12.0549i	−0.148362	+	0.456611i
$698$	−2.03096	+	6.25066i	−0.0768731	+	0.236591i
$699$	−3.84616	+	36.5938i	−0.145475	+	1.38410i
$700$	5.21769	+	5.79483i	0.197210	+	0.219024i
$701$	−17.8192	+	19.7903i	−0.673023	+	0.747468i	−0.978841	−	0.204622i	$-0.934403\pi$
$701$	−17.8192	+	19.7903i	−0.673023	+	0.747468i	0.305818	+	0.952090i	$0.401070\pi$
$702$	0.724202	+	6.89032i	0.0273333	+	0.260059i
$703$	6.52002	+	1.38587i	0.245907	+	0.0522692i
$704$	−11.5202	+	5.12911i	−0.434182	+	0.193311i
$705$	55.4120	+	40.2591i	2.08693	+	1.51625i
$706$	4.06521	+	1.80995i	0.152996	+	0.0681183i
$707$	9.58617	+	16.6037i	0.360525	+	0.624448i
$708$	−32.6133	+	56.4879i	−1.22568	+	2.12295i
$709$	−2.13805	+	1.55338i	−0.0802962	+	0.0583386i	−0.627209	−	0.778851i	$-0.715803\pi$
$709$	−2.13805	+	1.55338i	−0.0802962	+	0.0583386i	0.546913	+	0.837189i	$0.315803\pi$
$710$	−1.71488	+	0.364509i	−0.0643584	+	0.0136798i
$711$	5.72231	+	17.6114i	0.214603	+	0.660481i
$712$	3.07802			0.115354
$713$		0			0
$714$	−2.00779			−0.0751398
$715$	−6.41943	−	19.7570i	−0.240073	−	0.738868i
$716$	0.145609	−	0.0309502i	0.00544168	−	0.00115666i
$717$	−59.5120	+	43.2380i	−2.22251	+	1.61475i
$718$	3.98491	−	6.90207i	0.148716	−	0.257583i
$719$	2.59912	+	4.50181i	0.0969308	+	0.167889i	0.910413	−	0.413701i	$-0.135764\pi$
$719$	2.59912	+	4.50181i	0.0969308	+	0.167889i	−0.813482	+	0.581590i	$0.802431\pi$
$720$	47.7676	+	21.2675i	1.78019	+	0.792593i
$721$	7.06832	+	5.13543i	0.263238	+	0.191253i
$722$	−4.65937	+	2.07448i	−0.173404	+	0.0772043i
$723$	6.68173	+	1.42025i	0.248496	+	0.0528195i
$724$	−0.424237	−	4.03635i	−0.0157667	−	0.150010i
$725$	8.11748	−	9.01537i	0.301476	−	0.334823i
$726$	−3.46202	−	3.84496i	−0.128488	−	0.142700i
$727$	−2.53026	+	24.0738i	−0.0938422	+	0.892849i	0.841774	+	0.539830i	$0.181512\pi$
$727$	−2.53026	+	24.0738i	−0.0938422	+	0.892849i	−0.935616	+	0.353019i	$0.885155\pi$
$728$	−1.30911	+	4.02902i	−0.0485188	+	0.149325i
$729$	−12.2007	+	37.5499i	−0.451878	+	1.39074i
$730$	1.56843	−	14.9226i	0.0580501	−	0.552310i
$731$	10.2716	+	11.4077i	0.379908	+	0.421930i
$732$	−52.4411	+	58.2417i	−1.93828	+	2.15267i
$733$	−4.21906	−	40.1416i	−0.155834	−	1.48267i	−0.740865	−	0.671654i	$-0.765584\pi$
$733$	−4.21906	−	40.1416i	−0.155834	−	1.48267i	0.585030	−	0.811011i	$-0.301083\pi$
$734$	2.99742	+	0.637120i	0.110637	+	0.0235165i
$735$	−45.8084	+	20.3952i	−1.68967	+	0.752289i
$736$	−1.38644	−	1.00730i	−0.0511047	−	0.0371297i
$737$	−14.2990	−	6.36631i	−0.526709	−	0.234506i
$738$	6.55583	+	11.3550i	0.241324	+	0.417985i
$739$	3.04893	−	5.28089i	0.112157	−	0.194261i	−0.804483	−	0.593976i	$-0.797558\pi$
$739$	3.04893	−	5.28089i	0.112157	−	0.194261i	0.916640	+	0.399715i	$0.130891\pi$
$740$	−14.2035	+	10.3195i	−0.522132	+	0.379351i
$741$	17.2271	−	3.66174i	0.632854	−	0.134517i
$742$	−0.584884	−	1.80009i	−0.0214718	−	0.0660833i
$743$	−16.2263			−0.595284			−0.297642	−	0.954678i	$-0.596200\pi$
$743$	−16.2263			−0.595284			−0.297642	+	0.954678i	$0.596200\pi$
$744$		0			0
$745$	−35.5308			−1.30175
$746$	2.75986	+	8.49397i	0.101046	+	0.310986i
$747$	67.5299	−	14.3539i	2.47079	−	0.525182i
$748$	6.73540	−	4.89355i	0.246270	−	0.178926i
$749$	−6.57456	+	11.3875i	−0.240229	+	0.416089i
$750$	1.75329	+	3.03680i	0.0640213	+	0.110888i
$751$	33.2937	+	14.8233i	1.21490	+	0.540910i	0.911242	−	0.411870i	$-0.135124\pi$
$751$	33.2937	+	14.8233i	1.21490	+	0.540910i	0.303661	+	0.952780i	$0.401791\pi$
$752$	21.0907	+	15.3233i	0.769099	+	0.558783i
$753$	−6.22895	+	2.77331i	−0.226996	+	0.101065i
$754$	3.12068	+	0.663320i	0.113648	+	0.0241567i
$755$	−1.34326	−	12.7803i	−0.0488863	−	0.465122i
$756$	9.32149	−	10.3526i	0.339019	−	0.376519i
$757$	−29.1488	−	32.3730i	−1.05943	−	1.17662i	−0.983761	−	0.179484i	$-0.942557\pi$
$757$	−29.1488	−	32.3730i	−1.05943	−	1.17662i	−0.0756702	−	0.997133i	$-0.524110\pi$
$758$	−0.811759	+	7.72337i	−0.0294844	+	0.280525i
$759$	0.961302	−	2.95858i	0.0348931	−	0.107390i
$760$	−2.65139	+	8.16015i	−0.0961761	+	0.296000i
$761$	0.344869	−	3.28120i	0.0125015	−	0.118944i	−0.986491	−	0.163813i	$-0.947621\pi$
$761$	0.344869	−	3.28120i	0.0125015	−	0.118944i	0.998993	+	0.0448696i	$0.0142872\pi$
$762$	−0.0801518	−	0.0890175i	−0.00290359	−	0.00322477i
$763$	0.457695	−	0.508322i	0.0165697	−	0.0184025i
$764$	−1.04776	−	9.96875i	−0.0379066	−	0.360657i
$765$	−28.5040	−	6.05872i	−1.03057	−	0.219053i
$766$	8.55360	−	3.80831i	0.309054	−	0.137600i
$767$	−27.9304	−	20.2926i	−1.00851	−	0.732724i
$768$	18.5250	+	8.24787i	0.668464	+	0.297619i
$769$	22.8568	+	39.5891i	0.824237	+	1.42762i	0.902501	+	0.430688i	$0.141729\pi$
$769$	22.8568	+	39.5891i	0.824237	+	1.42762i	−0.0782634	+	0.996933i	$0.524938\pi$
$770$	1.37458	−	2.38084i	0.0495363	−	0.0857995i
$771$	60.8916	−	44.2403i	2.19296	−	1.59328i
$772$	−3.91634	+	0.832444i	−0.140952	+	0.0299603i
$773$	−9.27071	−	28.5323i	−0.333444	−	1.02624i	−0.967483	−	0.252935i	$-0.918604\pi$
$773$	−9.27071	−	28.5323i	−0.333444	−	1.02624i	0.634039	−	0.773301i	$-0.281396\pi$
$774$	15.8791			0.570764
$775$		0			0
$776$	−4.64943			−0.166905
$777$	3.04449	+	9.36998i	0.109221	+	0.336146i
$778$	−4.45334	+	0.946586i	−0.159660	+	0.0339368i
$779$	11.9039	−	8.64869i	0.426501	−	0.309871i
$780$	−23.1938	+	40.1729i	−0.830472	+	1.43842i
$781$	−2.03977	−	3.53298i	−0.0729886	−	0.126420i
$782$	0.259068	+	0.115344i	0.00926424	+	0.00412471i
$783$	−17.5338	−	12.7390i	−0.626605	−	0.455256i
$784$	−17.4354	+	7.76276i	−0.622694	+	0.277241i
$785$	25.3147	+	5.38081i	0.903522	+	0.192050i
$786$	−0.614743	−	5.84889i	−0.0219271	−	0.208623i
$787$	28.9278	−	32.1276i	1.03117	−	1.14523i	0.0418969	−	0.999122i	$-0.486660\pi$
$787$	28.9278	−	32.1276i	1.03117	−	1.14523i	0.989269	−	0.146104i	$-0.0466734\pi$
$788$	−7.37769	−	8.19375i	−0.262819	−	0.291890i
$789$	6.93643	−	65.9957i	0.246943	−	2.34951i
$790$	1.11320	−	3.42609i	0.0396061	−	0.121895i
$791$	3.77878	−	11.6299i	0.134358	−	0.413511i
$792$	1.85966	−	17.6935i	0.0660801	−	0.628710i
$793$	−27.7566	−	30.8268i	−0.985665	−	1.09469i
$794$	−0.688356	+	0.764497i	−0.0244289	+	0.0271310i
$795$	−4.47531	−	42.5797i	−0.158723	−	1.51015i
$796$	−12.7162	−	2.70291i	−0.450714	−	0.0958022i
$797$	−20.8505	+	9.28325i	−0.738564	+	0.328830i	−0.741307	−	0.671167i	$-0.765794\pi$
$797$	−20.8505	+	9.28325i	−0.738564	+	0.328830i	0.00274302	+	0.999996i	$0.499127\pi$
$798$	1.88561	+	1.36998i	0.0667498	+	0.0484966i
$799$	−13.2728	−	5.90943i	−0.469557	−	0.209060i
$800$	−7.44080	−	12.8878i	−0.263072	−	0.455654i
$801$	6.06773	−	10.5096i	0.214393	−	0.371339i
$802$	−3.48981	+	2.53550i	−0.123230	+	0.0895315i
$803$	34.1519	−	7.25921i	1.20519	−	0.256172i
$804$	10.8005	+	33.2406i	0.380905	+	1.17231i
$805$	−1.42279			−0.0501467
$806$		0			0
$807$	49.3229			1.73625
$808$	−7.45866	−	22.9554i	−0.262395	−	0.807568i
$809$	−20.7743	+	4.41572i	−0.730386	+	0.155248i	−0.558070	−	0.829794i	$-0.688458\pi$
$809$	−20.7743	+	4.41572i	−0.730386	+	0.155248i	−0.172315	+	0.985042i	$0.555125\pi$
$810$	−3.15792	+	2.29437i	−0.110958	+	0.0806158i
$811$	−1.06157	+	1.83869i	−0.0372767	+	0.0645652i	−0.884062	−	0.467370i	$-0.845202\pi$
$811$	−1.06157	+	1.83869i	−0.0372767	+	0.0645652i	0.846785	+	0.531935i	$0.178535\pi$
$812$	−3.20748	−	5.55551i	−0.112560	−	0.194960i
$813$	−19.1536	−	8.52775i	−0.671747	−	0.299081i
$814$	2.17527	+	1.58043i	0.0762431	+	0.0553939i
$815$	8.49595	−	3.78264i	0.297600	−	0.132500i
$816$	−16.9088	−	3.59407i	−0.591925	−	0.125818i
$817$	−1.86267	−	17.7221i	−0.0651665	−	0.620018i
$818$	4.04400	−	4.49132i	0.141395	−	0.157035i
$819$	11.1761	+	12.4123i	0.390524	+	0.433720i
$820$	−4.05098	+	38.5425i	−0.141466	+	1.34596i
$821$	−12.9144	+	39.7465i	−0.450716	+	1.38716i	0.425376	+	0.905017i	$0.360142\pi$
$821$	−12.9144	+	39.7465i	−0.450716	+	1.38716i	−0.876092	+	0.482144i	$0.839858\pi$
$822$	−3.70935	+	11.4162i	−0.129379	+	0.398186i
$823$	1.70366	−	16.2092i	0.0593858	−	0.565018i	−0.923860	−	0.382731i	$-0.874984\pi$
$823$	1.70366	−	16.2092i	0.0593858	−	0.565018i	0.983245	−	0.182286i	$-0.0583498\pi$
$824$	−7.35991	−	8.17401i	−0.256395	−	0.284755i
$825$	18.0757	−	20.0752i	0.629317	−	0.698927i
$826$	−0.477573	−	4.54380i	−0.0166169	−	0.158099i
$827$	−30.4101	−	6.46387i	−1.05746	−	0.224771i	−0.353813	−	0.935316i	$-0.615115\pi$
$827$	−30.4101	−	6.46387i	−1.05746	−	0.224771i	−0.703651	+	0.710545i	$0.748448\pi$
$828$	−4.07172	+	1.81285i	−0.141502	+	0.0630008i
$829$	−22.6920	−	16.4867i	−0.788125	−	0.572606i	0.119282	−	0.992860i	$-0.461941\pi$
$829$	−22.6920	−	16.4867i	−0.788125	−	0.572606i	−0.907406	+	0.420254i	$0.861941\pi$
$830$	−12.2695	−	5.46272i	−0.425879	−	0.189614i
$831$	21.8491	+	37.8437i	0.757936	+	1.31278i
$832$	−7.45215	+	12.9075i	−0.258357	+	0.447487i
$833$	8.60516	−	6.25201i	0.298151	−	0.216619i
$834$	−15.3384	+	3.26027i	−0.531124	+	0.112894i
$835$	12.2702	+	37.7639i	0.424629	+	1.30687i
$836$	−9.66453			−0.334255
$837$		0			0
$838$	8.13409			0.280987
$839$	−7.12828	−	21.9386i	−0.246096	−	0.757404i	−0.995454	−	0.0952401i	$-0.969638\pi$
$839$	−7.12828	−	21.9386i	−0.246096	−	0.757404i	0.749359	−	0.662164i	$-0.230362\pi$
$840$	−12.4046	+	2.63669i	−0.428001	+	0.0909743i
$841$	15.3874	−	11.1796i	0.530600	−	0.385503i
$842$	−5.12779	+	8.88160i	−0.176715	+	0.306080i
$843$	3.59793	+	6.23179i	0.123919	+	0.214634i
$844$	−28.6432	−	12.7528i	−0.985939	−	0.438969i
$845$	11.4067	+	8.28743i	0.392401	+	0.285096i
$846$	−13.7298	+	6.11289i	−0.472039	+	0.210165i
$847$	−5.38600	−	1.14483i	−0.185065	−	0.0393368i
$848$	−1.70338	−	16.2065i	−0.0584942	−	0.556535i
$849$	−9.15018	+	10.1623i	−0.314033	+	0.348770i
$850$	1.64779	+	1.83006i	0.0565187	+	0.0627704i
$851$	0.145456	−	1.38392i	0.00498616	−	0.0474402i
$852$	−2.81502	+	8.66374i	−0.0964410	+	0.296815i
$853$	9.27697	−	28.5516i	0.317637	−	0.977587i	−0.657018	−	0.753875i	$-0.728182\pi$
$853$	9.27697	−	28.5516i	0.317637	−	0.977587i	0.974655	−	0.223712i	$-0.0718176\pi$
$854$	0.573819	−	5.45952i	0.0196357	−	0.186821i
$855$	22.6354	+	25.1391i	0.774114	+	0.859740i
$856$	11.0767	−	12.3019i	0.378594	−	0.420472i
$857$	5.70594	+	54.2883i	0.194911	+	1.85445i	0.457071	+	0.889430i	$0.348898\pi$
$857$	5.70594	+	54.2883i	0.194911	+	1.85445i	−0.262160	+	0.965024i	$0.584435\pi$
$858$	6.94902	+	1.47706i	0.237236	+	0.0504260i
$859$	−8.52923	+	3.79746i	−0.291014	+	0.129568i	−0.547051	−	0.837099i	$-0.684250\pi$
$859$	−8.52923	+	3.79746i	−0.291014	+	0.129568i	0.256037	+	0.966667i	$0.417583\pi$
$860$	37.9710	+	27.5876i	1.29480	+	0.940728i
$861$	19.8678	+	8.84571i	0.677093	+	0.301461i
$862$	−5.33338	−	9.23768i	−0.181656	−	0.314637i
$863$	6.65836	−	11.5326i	0.226653	−	0.392575i	−0.730161	−	0.683275i	$-0.760555\pi$
$863$	6.65836	−	11.5326i	0.226653	−	0.392575i	0.956814	+	0.290700i	$0.0938882\pi$
$864$	−21.5087	+	15.6270i	−0.731741	+	0.531641i
$865$	−55.3870	+	11.7729i	−1.88321	+	0.400290i
$866$	1.50300	+	4.62577i	0.0510741	+	0.157190i
$867$	−39.5520			−1.34326
$868$		0			0
$869$	8.38250			0.284357
$870$	2.95130	+	9.08317i	0.100058	+	0.307948i
$871$	−18.0951	+	3.84624i	−0.613130	+	0.130325i
$872$	−0.696668	+	0.506159i	−0.0235922	+	0.0171407i
$873$	−9.16547	+	15.8751i	−0.310204	+	0.537290i
$874$	−0.164599	−	0.285094i	−0.00556766	−	0.00964346i
$875$	3.40925	+	1.51790i	0.115254	+	0.0513142i
$876$	−63.0749	−	45.8266i	−2.13110	−	1.54834i
$877$	−38.8860	+	17.3132i	−1.31309	+	0.584624i	−0.939366	−	0.342916i	$-0.888585\pi$
$877$	−38.8860	+	17.3132i	−1.31309	+	0.584624i	−0.373722	+	0.927541i	$0.621919\pi$
$878$	−4.44133	−	0.944034i	−0.149888	−	0.0318596i
$879$	3.19032	+	30.3538i	0.107607	+	1.02381i
$880$	15.8379	−	17.5898i	0.533897	−	0.592953i
$881$	3.86298	+	4.29027i	0.130147	+	0.144543i	0.804696	−	0.593687i	$-0.202328\pi$
$881$	3.86298	+	4.29027i	0.130147	+	0.144543i	−0.674549	+	0.738230i	$0.735662\pi$
$882$	1.15010	−	10.9425i	0.0387260	−	0.368453i
$883$	−8.40436	+	25.8660i	−0.282829	+	0.870459i	0.704212	+	0.709990i	$0.251301\pi$
$883$	−8.40436	+	25.8660i	−0.282829	+	0.870459i	−0.987041	+	0.160469i	$0.948699\pi$
$884$	3.04068	−	9.35826i	0.102269	−	0.314752i
$885$	10.8029	−	102.783i	0.363136	−	3.45501i
$886$	5.58686	+	6.20483i	0.187694	+	0.208455i
$887$	−4.93262	+	5.47823i	−0.165621	+	0.183941i	−0.820242	−	0.572016i	$-0.806161\pi$
$887$	−4.93262	+	5.47823i	−0.165621	+	0.183941i	0.654621	+	0.755957i	$0.272828\pi$
$888$	−1.29649	−	12.3353i	−0.0435075	−	0.413946i
$889$	−0.124695	−	0.0265048i	−0.00418215	−	0.000888943i
$890$	−2.15671	+	0.960227i	−0.0722929	+	0.0321869i
$891$	−7.34822	−	5.33880i	−0.246175	−	0.178856i
$892$	−10.7340	−	4.77907i	−0.359400	−	0.160015i
$893$	8.43290	+	14.6062i	0.282196	+	0.488778i
$894$	6.07548	−	10.5230i	0.203194	−	0.351943i
$895$	−0.190820	+	0.138639i	−0.00637840	+	0.00463418i
$896$	−10.1332	+	2.15388i	−0.338526	+	0.0719560i
$897$	−1.13617	−	3.49677i	−0.0379356	−	0.116754i
$898$	6.82232			0.227664
$899$		0			0
$900$	−38.7040			−1.29013
$901$	2.80645	+	8.63736i	0.0934963	+	0.287752i
$902$	5.80560	−	1.23402i	0.193305	−	0.0410883i
$903$	21.3082	−	15.4813i	0.709092	−	0.515186i
$904$	−7.69738	+	13.3322i	−0.256011	+	0.443424i
$905$	3.21533	+	5.56911i	0.106881	+	0.185123i
$906$	4.01478	+	1.78750i	0.133382	+	0.0593856i
$907$	−13.3350	−	9.68848i	−0.442783	−	0.321701i	0.343957	−	0.938985i	$-0.388233\pi$
$907$	−13.3350	−	9.68848i	−0.442783	−	0.321701i	−0.786740	+	0.617285i	$0.788233\pi$
$908$	13.4527	−	5.98953i	0.446444	−	0.198770i
$909$	−93.0825	−	19.7853i	−3.08735	−	0.656237i
$910$	−0.339639	−	3.23144i	−0.0112589	−	0.107121i
$911$	−29.9818	+	33.2981i	−0.993340	+	1.10322i	0.00131908	+	0.999999i	$0.499580\pi$
$911$	−29.9818	+	33.2981i	−0.993340	+	1.10322i	−0.994659	+	0.103217i	$0.967087\pi$
$912$	13.4275	+	14.9127i	0.444627	+	0.493809i
$913$	3.26671	−	31.0807i	0.108112	−	1.02862i
$914$	−2.64350	+	8.13586i	−0.0874393	+	0.269110i
$915$	38.3728	−	118.099i	1.26857	−	3.90425i
$916$	−2.50538	+	23.8371i	−0.0827802	+	0.787601i
$917$	−4.18806	−	4.65132i	−0.138302	−	0.153600i
$918$	2.94380	−	3.26943i	0.0971600	−	0.107907i
$919$	1.08258	+	10.3001i	0.0357111	+	0.339768i	0.997760	+	0.0668920i	$0.0213083\pi$
$919$	1.08258	+	10.3001i	0.0357111	+	0.339768i	−0.962049	+	0.272876i	$0.912025\pi$
$920$	1.75206	+	0.372411i	0.0577636	+	0.0122780i
$921$	7.00040	−	3.11678i	0.230671	−	0.102701i
$922$	−10.9015	−	7.92041i	−0.359022	−	0.260845i
$923$	−4.40478	−	1.96113i	−0.144985	−	0.0645515i
$924$	−7.14231	−	12.3708i	−0.234965	−	0.406971i
$925$	6.04191	−	10.4649i	0.198657	−	0.344084i
$926$	−1.87486	+	1.36216i	−0.0616116	+	0.0447634i
$927$	−42.4181	+	9.01625i	−1.39319	+	0.296132i
$928$	3.78319	+	11.6435i	0.124189	+	0.382216i
$929$	−44.0624			−1.44564			−0.722820	−	0.691037i	$-0.757154\pi$
$929$	−44.0624			−1.44564			−0.722820	+	0.691037i	$0.757154\pi$
$930$		0			0
$931$	−12.3474			−0.404671
$932$	−7.37447	−	22.6963i	−0.241559	−	0.743441i
$933$	−15.6017	+	3.31624i	−0.510776	+	0.108569i
$934$	−10.9181	+	7.93246i	−0.357251	+	0.259558i
$935$	−6.59563	+	11.4240i	−0.215700	+	0.373604i
$936$	−10.5136	−	18.2101i	−0.343648	−	0.595216i
$937$	−31.5785	−	14.0596i	−1.03162	−	0.459308i	−0.180113	−	0.983646i	$-0.557646\pi$
$937$	−31.5785	−	14.0596i	−1.03162	−	0.459308i	−0.851511	+	0.524337i	$0.824313\pi$
$938$	−1.98062	−	1.43900i	−0.0646694	−	0.0469851i
$939$	70.5073	−	31.3919i	2.30092	−	1.02444i
$940$	−43.4516	−	9.23591i	−1.41723	−	0.301242i
$941$	−2.31521	−	22.0277i	−0.0754736	−	0.718084i	−0.965186	−	0.261563i	$-0.915762\pi$
$941$	−2.31521	−	22.0277i	−0.0754736	−	0.718084i	0.889713	−	0.456521i	$-0.150905\pi$
$942$	−5.92224	+	6.57731i	−0.192957	+	0.214300i
$943$	−2.05539	−	2.28274i	−0.0669328	−	0.0743364i
$944$	4.11177	−	39.1208i	0.133827	−	1.27327i
$945$	−6.82084	+	20.9924i	−0.221882	+	0.682882i
$946$	2.22123	−	6.83625i	0.0722185	−	0.222266i
$947$	−2.93543	+	27.9287i	−0.0953885	+	0.907561i	0.837267	+	0.546794i	$0.184152\pi$
$947$	−2.93543	+	27.9287i	−0.0953885	+	0.907561i	−0.932656	+	0.360767i	$0.882515\pi$
$948$	−12.5249	−	13.9103i	−0.406789	−	0.451785i
$949$	27.6124	−	30.6667i	0.896337	−	0.995483i
$950$	−0.298814	−	2.84302i	−0.00969480	−	0.0922398i
$951$	−30.3956	−	6.46078i	−0.985644	−	0.209505i
$952$	2.45751	−	1.09416i	0.0796485	−	0.0354618i
$953$	6.20254	+	4.50641i	0.200920	+	0.145977i	0.683696	−	0.729767i	$-0.260371\pi$
$953$	6.20254	+	4.50641i	0.200920	+	0.145977i	−0.482776	+	0.875744i	$0.660371\pi$
$954$	8.58234	+	3.82111i	0.277864	+	0.123713i
$955$	7.94104	+	13.7543i	0.256966	+	0.445078i
$956$	23.8546	−	41.3173i	0.771512	−	1.33630i
$957$	−17.9792	+	13.0626i	−0.581184	+	0.422255i
$958$	−2.58679	+	0.549840i	−0.0835754	+	0.0177645i
$959$	3.94768	+	12.1497i	0.127477	+	0.392334i
$960$	−44.6168			−1.44000
$961$		0			0
$962$	3.17789			0.102459
$963$	−20.1682	−	62.0714i	−0.649912	−	2.00022i
$964$	−4.33356	+	0.921126i	−0.139574	+	0.0296675i
$965$	5.13233	−	3.72886i	0.165216	−	0.120036i
$966$	0.243285	−	0.421383i	0.00782758	−	0.0135578i
$967$	−0.925182	−	1.60246i	−0.0297518	−	0.0515317i	0.850766	−	0.525545i	$-0.176138\pi$
$967$	−0.925182	−	1.60246i	−0.0297518	−	0.0515317i	−0.880518	+	0.474013i	$0.842805\pi$
$968$	6.33280	+	2.81954i	0.203544	+	0.0906236i
$969$	−9.04772	−	6.57355i	−0.290654	−	0.211173i
$970$	3.25776	−	1.45045i	0.104600	−	0.0465711i
$971$	−48.2926	−	10.2649i	−1.54978	−	0.329416i	−0.648011	−	0.761631i	$-0.724399\pi$
$971$	−48.2926	−	10.2649i	−1.54978	−	0.329416i	−0.901771	+	0.432214i	$0.857732\pi$
$972$	−1.91688	−	18.2379i	−0.0614841	−	0.584982i
$973$	−11.1668	+	12.4020i	−0.357992	+	0.397590i
$974$	−5.88644	−	6.53755i	−0.188614	−	0.209477i
$975$	3.33736	−	31.7529i	0.106881	−	1.01691i
$976$	14.6053	−	44.9506i	0.467505	−	1.43883i
$977$	−11.0079	+	33.8790i	−0.352175	+	1.08388i	0.605454	+	0.795880i	$0.292992\pi$
$977$	−11.0079	+	33.8790i	−0.352175	+	1.08388i	−0.957629	+	0.288004i	$0.907008\pi$
$978$	−0.332447	+	3.16302i	−0.0106305	+	0.101142i
$979$	−3.67580	−	4.08239i	−0.117479	−	0.130474i
$980$	21.7611	−	24.1682i	0.695133	−	0.772024i
$981$	0.354885	+	3.37651i	0.0113306	+	0.107804i
$982$	−13.6504	−	2.90149i	−0.435603	−	0.0925903i
$983$	5.83170	−	2.59644i	0.186002	−	0.0828136i	−0.311622	−	0.950206i	$-0.600872\pi$
$983$	5.83170	−	2.59644i	0.186002	−	0.0828136i	0.497625	+	0.867392i	$0.334206\pi$
$984$	−22.1504	−	16.0932i	−0.706127	−	0.513032i
$985$	15.9595	+	7.10565i	0.508513	+	0.226405i
$986$	−1.01295	−	1.75448i	−0.0322588	−	0.0558739i
$987$	−12.4642	+	21.5887i	−0.396740	+	0.687175i
$988$	−9.24105	+	6.71402i	−0.293997	+	0.213601i
$989$	−3.63879	+	0.773449i	−0.115707	+	0.0245943i
$990$	4.21668	+	12.9776i	0.134015	+	0.412455i
$991$	44.2919			1.40698			0.703489	−	0.710706i	$-0.251624\pi$
$991$	44.2919			1.40698			0.703489	+	0.710706i	$0.251624\pi$
$992$		0			0
$993$	−56.8463			−1.80396
$994$	−0.197179	−	0.606856i	−0.00625415	−	0.0192483i
$995$	20.1483	−	4.28265i	0.638744	−	0.135769i
$996$	−56.4576	+	41.0189i	−1.78893	+	1.29973i
$997$	−2.66158	+	4.60999i	−0.0842931	+	0.146000i	−0.905090	−	0.425221i	$-0.860197\pi$
$997$	−2.66158	+	4.60999i	−0.0842931	+	0.146000i	0.820797	+	0.571220i	$0.193530\pi$
$998$	−4.15641	−	7.19911i	−0.131569	−	0.227884i
$999$	−19.7216	−	8.78061i	−0.623963	−	0.277806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.n.844.1		16
31.2	even	5		961.2.g.l.338.2		16
31.3	odd	30		961.2.a.i.1.4		8
31.4	even	5		961.2.g.j.732.2		16
31.5	even	3		961.2.g.m.547.1		16
31.6	odd	6		961.2.d.p.531.2		16
31.7	even	15		961.2.d.n.374.3		16
31.8	even	5		961.2.g.m.448.1		16
31.9	even	15	inner	961.2.g.n.846.1		16
31.10	even	15		961.2.g.j.235.2		16
31.11	odd	30		31.2.g.a.10.2	✓	16
31.12	odd	30		961.2.d.o.388.3		16
31.13	odd	30		961.2.c.j.439.4		16
31.14	even	15		961.2.d.q.628.2		16
31.15	odd	10		961.2.c.j.521.4		16
31.16	even	5		961.2.c.i.521.4		16
31.17	odd	30		961.2.d.p.628.2		16
31.18	even	15		961.2.c.i.439.4		16
31.19	even	15		961.2.d.n.388.3		16
31.20	even	15		961.2.g.l.816.2		16
31.21	odd	30		961.2.g.k.235.2		16
31.22	odd	30		961.2.g.t.846.1		16
31.23	odd	10		961.2.g.s.448.1		16
31.24	odd	30		961.2.d.o.374.3		16
31.25	even	3		961.2.d.q.531.2		16
31.26	odd	6		961.2.g.s.547.1		16
31.27	odd	10		961.2.g.k.732.2		16
31.28	even	15		961.2.a.j.1.4		8
31.29	odd	10		31.2.g.a.28.2	yes	16
31.30	odd	2		961.2.g.t.844.1		16
93.11	even	30		279.2.y.c.10.1		16
93.29	even	10		279.2.y.c.28.1		16
93.59	odd	30		8649.2.a.be.1.5		8
93.65	even	30		8649.2.a.bf.1.5		8
124.11	even	30		496.2.bg.c.289.1		16
124.91	even	10		496.2.bg.c.369.1		16
155.29	odd	10		775.2.bl.a.276.1		16
155.42	even	60		775.2.ck.a.599.3		32
155.73	even	60		775.2.ck.a.599.2		32
155.104	odd	30		775.2.bl.a.351.1		16
155.122	even	20		775.2.ck.a.524.2		32
155.153	even	20		775.2.ck.a.524.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	31.11	odd	30
31.2.g.a.28.2	yes	16	31.29	odd	10
279.2.y.c.10.1		16	93.11	even	30
279.2.y.c.28.1		16	93.29	even	10
496.2.bg.c.289.1		16	124.11	even	30
496.2.bg.c.369.1		16	124.91	even	10
775.2.bl.a.276.1		16	155.29	odd	10
775.2.bl.a.351.1		16	155.104	odd	30
775.2.ck.a.524.2		32	155.122	even	20
775.2.ck.a.524.3		32	155.153	even	20
775.2.ck.a.599.2		32	155.73	even	60
775.2.ck.a.599.3		32	155.42	even	60
961.2.a.i.1.4		8	31.3	odd	30
961.2.a.j.1.4		8	31.28	even	15
961.2.c.i.439.4		16	31.18	even	15
961.2.c.i.521.4		16	31.16	even	5
961.2.c.j.439.4		16	31.13	odd	30
961.2.c.j.521.4		16	31.15	odd	10
961.2.d.n.374.3		16	31.7	even	15
961.2.d.n.388.3		16	31.19	even	15
961.2.d.o.374.3		16	31.24	odd	30
961.2.d.o.388.3		16	31.12	odd	30
961.2.d.p.531.2		16	31.6	odd	6
961.2.d.p.628.2		16	31.17	odd	30
961.2.d.q.531.2		16	31.25	even	3
961.2.d.q.628.2		16	31.14	even	15
961.2.g.j.235.2		16	31.10	even	15
961.2.g.j.732.2		16	31.4	even	5
961.2.g.k.235.2		16	31.21	odd	30
961.2.g.k.732.2		16	31.27	odd	10
961.2.g.l.338.2		16	31.2	even	5
961.2.g.l.816.2		16	31.20	even	15
961.2.g.m.448.1		16	31.8	even	5
961.2.g.m.547.1		16	31.5	even	3
961.2.g.n.844.1		16	1.1	even	1	trivial
961.2.g.n.846.1		16	31.9	even	15	inner
961.2.g.s.448.1		16	31.23	odd	10
961.2.g.s.547.1		16	31.26	odd	6
961.2.g.t.844.1		16	31.30	odd	2
961.2.g.t.846.1		16	31.22	odd	30
8649.2.a.be.1.5		8	93.59	odd	30
8649.2.a.bf.1.5		8	93.65	even	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+(0.108599 + 0.334232i) q^{2} +(-2.83007 + 0.601549i) q^{3} +(1.51812 - 1.10298i) q^{4} +(-1.48661 + 2.57489i) q^{5} +(-0.508398 - 0.880572i) q^{6} +(-0.988571 - 0.440140i) q^{7} +(1.10215 + 0.800755i) q^{8} +(4.90678 - 2.18464i) q^{9} +(-1.02206 - 0.217245i) q^{10} +(-0.254147 - 2.41805i) q^{11} +(-3.63288 + 4.03472i) q^{12} +(-1.92285 - 2.13554i) q^{13} +(0.0397516 - 0.378211i) q^{14} +(2.65829 - 8.18139i) q^{15} +(1.01179 - 3.11397i) q^{16} +(-0.190740 + 1.81477i) q^{17} +(1.26305 + 1.40275i) q^{18} +(1.41740 - 1.57418i) q^{19} +(0.583191 + 5.54869i) q^{20} +(3.06249 + 0.650952i) q^{21} +(0.780590 - 0.347541i) q^{22} +(-0.357760 - 0.259928i) q^{23} +(-3.60084 - 1.60320i) q^{24} +(-1.92005 - 3.32562i) q^{25} +(0.504947 - 0.874594i) q^{26} +(-5.55018 + 4.03244i) q^{27} +(-1.98623 + 0.422186i) q^{28} +(0.976227 + 3.00452i) q^{29} +3.02317 q^{30} +3.87532 q^{32} +(2.17383 + 6.69036i) q^{33} +(-0.627268 + 0.133330i) q^{34} +(2.60294 - 1.89115i) q^{35} +(5.03946 - 8.72860i) q^{36} +(1.57338 + 2.72517i) q^{37} +(0.680071 + 0.302787i) q^{38} +(6.72642 + 4.88703i) q^{39} +(-3.70032 + 1.64749i) q^{40} +(6.79444 + 1.44420i) q^{41} +(0.115013 + 1.09427i) q^{42} +(5.62898 - 6.25162i) q^{43} +(-3.05288 - 3.39056i) q^{44} +(-1.66928 + 15.8821i) q^{45} +(0.0480240 - 0.147803i) q^{46} +(-2.46041 + 7.57236i) q^{47} +(-0.990228 + 9.42139i) q^{48} +(-3.90036 - 4.33179i) q^{49} +(0.903015 - 1.00290i) q^{50} +(-0.551866 - 5.25066i) q^{51} +(-5.27456 - 1.12114i) q^{52} +(4.54671 - 2.02433i) q^{53} +(-1.95051 - 1.41713i) q^{54} +(6.60404 + 2.94031i) q^{55} +(-0.737104 - 1.27670i) q^{56} +(-3.06439 + 5.30768i) q^{57} +(-0.898189 + 0.652573i) q^{58} +(11.7514 - 2.49784i) q^{59} +(-4.98828 - 15.3523i) q^{60} +14.4351 q^{61} -5.81225 q^{63} +(-1.60273 - 4.93269i) q^{64} +(8.35732 - 1.77640i) q^{65} +(-2.00006 + 1.45313i) q^{66} +(3.21879 - 5.57511i) q^{67} +(1.71208 + 2.96541i) q^{68} +(1.16884 + 0.520403i) q^{69} +(0.914757 + 0.664610i) q^{70} +(1.53281 - 0.682453i) q^{71} +(7.15734 + 1.52134i) q^{72} +(1.50105 + 14.2815i) q^{73} +(-0.739972 + 0.821822i) q^{74} +(7.43439 + 8.25672i) q^{75} +(0.415493 - 3.95316i) q^{76} +(-0.813039 + 2.50228i) q^{77} +(-0.902923 + 2.77891i) q^{78} +(-0.360377 + 3.42876i) q^{79} +(6.51400 + 7.23453i) q^{80} +(2.49968 - 2.77618i) q^{81} +(0.255168 + 2.42776i) q^{82} +(12.5727 + 2.67242i) q^{83} +(5.36720 - 2.38963i) q^{84} +(-4.38928 - 3.18900i) q^{85} +(2.70079 + 1.20247i) q^{86} +(-4.57015 - 7.91573i) q^{87} +(1.65616 - 2.86855i) q^{88} +(1.82788 - 1.32803i) q^{89} +(-5.48961 + 1.16685i) q^{90} +(0.960936 + 2.95746i) q^{91} -0.829816 q^{92} -2.79812 q^{94} +(1.94622 + 5.98986i) q^{95} +(-10.9674 + 2.33120i) q^{96} +(-2.76106 + 2.00603i) q^{97} +(1.02425 - 1.77405i) q^{98} +(-6.52961 - 11.3096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} + 2 q^{11} - 25 q^{12} - 18 q^{13} + 24 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 + 12 * q^7 - 8 * q^8 + 5 * q^9 - 12 * q^10 + 2 * q^11 - 25 * q^12 - 18 * q^13 + 24 * q^14 - 4 * q^15 - 2 * q^16 + q^17 - 8 * q^18 + 11 * q^19 - 18 * q^20 + 31 * q^21 - 4 * q^22 - 21 * q^23 - 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 + 3 * q^38 + 2 * q^39 + 29 * q^40 - 3 * q^41 - 39 * q^42 - 8 * q^43 + 41 * q^44 - 20 * q^45 + 16 * q^46 + 4 * q^47 - 49 * q^48 + 12 * q^49 + 48 * q^50 - 2 * q^51 + 6 * q^52 + 69 * q^53 - 39 * q^54 - 23 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 54 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 + 27 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 27 * q^69 + 27 * q^70 + 6 * q^71 + 2 * q^72 + 18 * q^73 + 92 * q^74 - 13 * q^75 - 27 * q^76 + 42 * q^77 + 15 * q^78 + 22 * q^79 + 21 * q^80 - 22 * q^81 - 61 * q^82 + 71 * q^83 + 12 * q^84 + 63 * q^85 + 11 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 - 33 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 58 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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