LMFDB - Embedded newform 961.2.g.s.448.1

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,-3] 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			448.1
Root			$2.52368i$ of defining polynomial
Character	$\chi$	$=$	961.448
Dual form			961.2.g.s.547.1

$q$-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} +(-1.93599 + 2.15013i) q^{3} +(1.51812 + 1.10298i) q^{4} +(-1.48661 + 2.57489i) q^{5} +(0.508398 + 0.880572i) q^{6} +(0.113113 - 1.07620i) q^{7} +(1.10215 - 0.800755i) q^{8} +(-0.561437 - 5.34171i) q^{9} +(0.699168 + 0.776504i) q^{10} +(-2.22117 + 0.988927i) q^{11} +(-5.31061 + 1.12880i) q^{12} +(-2.81086 - 0.597466i) q^{13} +(-0.347416 - 0.154680i) q^{14} +(-2.65829 - 8.18139i) q^{15} +(1.01179 + 3.11397i) q^{16} +(-1.66701 - 0.742199i) q^{17} +(-1.84634 - 0.392453i) q^{18} +(-2.07198 + 0.440414i) q^{19} +(-5.09690 + 2.26929i) q^{20} +(2.09499 + 2.32672i) q^{21} +(0.0893157 + 0.849782i) q^{22} +(0.357760 - 0.259928i) q^{23} +(-0.412010 + 3.92002i) q^{24} +(-1.92005 - 3.32562i) q^{25} +(-0.504947 + 0.874594i) q^{26} +(5.55018 + 4.03244i) q^{27} +(1.35874 - 1.50903i) q^{28} +(-0.976227 + 3.00452i) q^{29} -3.02317 q^{30} +3.87532 q^{32} +(2.17383 - 6.69036i) q^{33} +(-0.429101 + 0.476565i) q^{34} +(2.60294 + 1.89115i) q^{35} +(5.03946 - 8.72860i) q^{36} +(-1.57338 - 2.72517i) q^{37} +(-0.0778141 + 0.740352i) q^{38} +(6.72642 - 4.88703i) q^{39} +(0.423394 + 4.02832i) q^{40} +(-4.64794 - 5.16206i) q^{41} +(1.00518 - 0.447533i) q^{42} +(8.22855 - 1.74903i) q^{43} +(-4.46275 - 0.948588i) q^{44} +(14.5890 + 6.49543i) q^{45} +(-0.0480240 - 0.147803i) q^{46} +(-2.46041 - 7.57236i) q^{47} +(-8.65428 - 3.85313i) q^{48} +(5.70163 + 1.21192i) q^{49} +(-1.32004 + 0.280584i) q^{50} +(4.82313 - 2.14740i) q^{51} +(-3.60822 - 4.00733i) q^{52} +(0.520238 + 4.94973i) q^{53} +(1.95051 - 1.41713i) q^{54} +(0.755639 - 7.18942i) q^{55} +(-0.737104 - 1.27670i) q^{56} +(3.06439 - 5.30768i) q^{57} +(0.898189 + 0.652573i) q^{58} +(-8.03889 + 8.92809i) q^{59} +(4.98828 - 15.3523i) q^{60} -14.4351 q^{61} -5.81225 q^{63} +(-1.60273 + 4.93269i) q^{64} +(5.71707 - 6.34945i) q^{65} +(-2.00006 - 1.45313i) q^{66} +(3.21879 - 5.57511i) q^{67} +(-1.71208 - 2.96541i) q^{68} +(-0.133740 + 1.27245i) q^{69} +(0.914757 - 0.664610i) q^{70} +(-0.175386 - 1.66868i) q^{71} +(-4.89619 - 5.43777i) q^{72} +(13.1187 - 5.84081i) q^{73} +(-1.08170 + 0.229923i) q^{74} +(10.8677 + 2.31001i) q^{75} +(-3.63128 - 1.61675i) q^{76} +(0.813039 + 2.50228i) q^{77} +(-0.902923 - 2.77891i) q^{78} +(-3.14958 - 1.40228i) q^{79} +(-9.52229 - 2.02403i) q^{80} +(-3.65408 + 0.776698i) q^{81} +(-2.23009 + 0.992898i) q^{82} +(8.60075 + 9.55210i) q^{83} +(0.614118 + 5.84295i) q^{84} +(4.38928 - 3.18900i) q^{85} +(0.309026 - 2.94019i) q^{86} +(-4.57015 - 7.91573i) q^{87} +(-1.65616 + 2.86855i) q^{88} +(-1.82788 - 1.32803i) q^{89} +(3.75533 - 4.17071i) q^{90} +(-0.960936 + 2.95746i) q^{91} +0.829816 q^{92} -2.79812 q^{94} +(1.94622 - 5.98986i) q^{95} +(-7.50258 + 8.33246i) 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} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} - 2 q^{11} - 20 q^{12} - 27 q^{13} - 6 q^{14} + 4 q^{15} - 2 q^{16} - 16 q^{17} + 22 q^{18} - 4 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 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 - 2 * q^11 - 20 * q^12 - 27 * q^13 - 6 * q^14 + 4 * q^15 - 2 * q^16 - 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 + 29 * q^21 + 4 * q^22 + 21 * q^23 - 25 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 40 * 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 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 - 51 * q^42 + 8 * q^43 + 4 * q^44 + 25 * q^45 - 16 * q^46 + 4 * q^47 - 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 + 24 * q^52 + 66 * q^53 + 39 * q^54 - 52 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 - 51 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 18 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 + 27 * q^73 + 28 * q^74 - 32 * q^75 + 18 * q^76 - 42 * q^77 + 15 * q^78 + 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 + 4 * q^83 - 27 * q^84 - 63 * q^85 + 34 * q^86 + 15 * q^87 - 17 * q^88 + 26 * q^89 + 57 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 - 62 * q^96 - 37 * q^97 - 10 * q^98 + 6 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

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	−0.905291	−	0.424791i	$-0.860347\pi$
$2$	0.108599	−	0.334232i	0.0767908	−	0.236338i	0.982082	+	0.188453i	$0.0603475\pi$
$3$	−1.93599	+	2.15013i	−1.11774	+	1.24138i	−0.150207	+	0.988655i	$0.547994\pi$
$3$	−1.93599	+	2.15013i	−1.11774	+	1.24138i	−0.967538	+	0.252726i	$0.918673\pi$
$4$	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
$7$	0.113113	−	1.07620i	0.0427527	−	0.406765i	−0.952127	−	0.305702i	$-0.901109\pi$
$7$	0.113113	−	1.07620i	0.0427527	−	0.406765i	0.994880	−	0.101063i	$-0.0322243\pi$
$8$	1.10215	−	0.800755i	0.389667	−	0.283110i
$9$	−0.561437	−	5.34171i	−0.187146	−	1.78057i
$10$	0.699168	+	0.776504i	0.221096	+	0.245552i
$11$	−2.22117	+	0.988927i	−0.669707	+	0.298173i	−0.713282	−	0.700877i	$-0.752792\pi$
$11$	−2.22117	+	0.988927i	−0.669707	+	0.298173i	0.0435747	+	0.999050i	$0.486125\pi$
$12$	−5.31061	+	1.12880i	−1.53304	+	0.325858i
$13$	−2.81086	−	0.597466i	−0.779591	−	0.165707i	−0.199106	−	0.979978i	$-0.563804\pi$
$13$	−2.81086	−	0.597466i	−0.779591	−	0.165707i	−0.580485	+	0.814271i	$0.697137\pi$
$14$	−0.347416	−	0.154680i	−0.0928508	−	0.0413399i
$15$	−2.65829	−	8.18139i	−0.686369	−	2.11243i
$16$	1.01179	+	3.11397i	0.252948	+	0.778493i
$17$	−1.66701	−	0.742199i	−0.404308	−	0.180010i	0.194499	−	0.980903i	$-0.437692\pi$
$17$	−1.66701	−	0.742199i	−0.404308	−	0.180010i	−0.598807	+	0.800893i	$0.704359\pi$
$18$	−1.84634	−	0.392453i	−0.435187	−	0.0925020i
$19$	−2.07198	+	0.440414i	−0.475346	+	0.101038i	−0.439354	−	0.898314i	$-0.644792\pi$
$19$	−2.07198	+	0.440414i	−0.475346	+	0.101038i	−0.0359922	+	0.999352i	$0.511459\pi$
$20$	−5.09690	+	2.26929i	−1.13970	+	0.507428i
$21$	2.09499	+	2.32672i	0.457163	+	0.507731i
$22$	0.0893157	+	0.849782i	0.0190422	+	0.181174i
$23$	0.357760	−	0.259928i	0.0745981	−	0.0541987i	−0.549861	−	0.835256i	$-0.685319\pi$
$23$	0.357760	−	0.259928i	0.0745981	−	0.0541987i	0.624459	+	0.781057i	$0.285319\pi$
$24$	−0.412010	+	3.92002i	−0.0841012	+	0.800170i
$25$	−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
$28$	1.35874	−	1.50903i	0.256778	−	0.285180i
$29$	−0.976227	+	3.00452i	−0.181281	+	0.557925i	−0.999864	−	0.0164625i	$-0.994760\pi$
$29$	−0.976227	+	3.00452i	−0.181281	+	0.557925i	0.818584	+	0.574387i	$0.194760\pi$
$30$	−3.02317			−0.551953
$31$		0			0
$31$		0			0
$32$	3.87532			0.685067
$33$	2.17383	−	6.69036i	0.378415	−	1.16464i
$34$	−0.429101	+	0.476565i	−0.0735902	+	0.0817303i
$35$	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	0.707222	−	0.706991i	$-0.249948\pi$
$37$	−1.57338	−	2.72517i	−0.258661	−	0.448015i	−0.965884	+	0.258977i	$0.916615\pi$
$38$	−0.0778141	+	0.740352i	−0.0126231	+	0.120101i
$39$	6.72642	−	4.88703i	1.07709	−	0.782551i
$40$	0.423394	+	4.02832i	0.0669444	+	0.636933i
$41$	−4.64794	−	5.16206i	−0.725886	−	0.806178i	0.261383	−	0.965235i	$-0.415821\pi$
$41$	−4.64794	−	5.16206i	−0.725886	−	0.806178i	−0.987269	+	0.159057i	$0.949155\pi$
$42$	1.00518	−	0.447533i	0.155102	−	0.0690559i
$43$	8.22855	−	1.74903i	1.25484	−	0.266725i	0.467916	−	0.883773i	$-0.345005\pi$
$43$	8.22855	−	1.74903i	1.25484	−	0.266725i	0.786926	+	0.617048i	$0.211672\pi$
$44$	−4.46275	−	0.948588i	−0.672786	−	0.143005i
$45$	14.5890	+	6.49543i	2.17480	+	0.968282i
$46$	−0.0480240	−	0.147803i	−0.00708075	−	0.0217923i
$47$	−2.46041	−	7.57236i	−0.358888	−	1.10454i	−0.953721	−	0.300693i	$-0.902782\pi$
$47$	−2.46041	−	7.57236i	−0.358888	−	1.10454i	0.594833	−	0.803849i	$-0.297218\pi$
$48$	−8.65428	−	3.85313i	−1.24914	−	0.556152i
$49$	5.70163	+	1.21192i	0.814518	+	0.173131i
$50$	−1.32004	+	0.280584i	−0.186682	+	0.0396806i
$51$	4.82313	−	2.14740i	0.675374	−	0.300696i
$52$	−3.60822	−	4.00733i	−0.500370	−	0.555717i
$53$	0.520238	+	4.94973i	0.0714602	+	0.679898i	0.970347	+	0.241717i	$0.0777105\pi$
$53$	0.520238	+	4.94973i	0.0714602	+	0.679898i	−0.898887	+	0.438181i	$0.855623\pi$
$54$	1.95051	−	1.41713i	0.265431	−	0.192847i
$55$	0.755639	−	7.18942i	0.101890	−	0.969421i
$56$	−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
$59$	−8.03889	+	8.92809i	−1.04657	+	1.16234i	−0.0601391	+	0.998190i	$0.519154\pi$
$59$	−8.03889	+	8.92809i	−1.04657	+	1.16234i	−0.986436	+	0.164149i	$0.947512\pi$
$60$	4.98828	−	15.3523i	0.643984	−	1.98198i
$61$	−14.4351			−1.84823			−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351			−1.84823			−0.924115	+	0.382115i	$0.875196\pi$
$62$		0			0
$63$	−5.81225			−0.732274
$64$	−1.60273	+	4.93269i	−0.200341	+	0.616586i
$65$	5.71707	−	6.34945i	0.709115	−	0.787552i
$66$	−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
$69$	−0.133740	+	1.27245i	−0.0161004	+	0.153185i
$70$	0.914757	−	0.664610i	0.109334	−	0.0794361i
$71$	−0.175386	−	1.66868i	−0.0208144	−	0.198036i	0.979173	−	0.203027i	$-0.0650780\pi$
$71$	−0.175386	−	1.66868i	−0.0208144	−	0.198036i	−0.999988	+	0.00499096i	$0.998411\pi$
$72$	−4.89619	−	5.43777i	−0.577022	−	0.640848i
$73$	13.1187	−	5.84081i	1.53542	−	0.683615i	0.547252	−	0.836968i	$-0.315674\pi$
$73$	13.1187	−	5.84081i	1.53542	−	0.683615i	0.988171	+	0.153353i	$0.0490072\pi$
$74$	−1.08170	+	0.229923i	−0.125746	+	0.0267281i
$75$	10.8677	+	2.31001i	1.25490	+	0.266737i
$76$	−3.63128	−	1.61675i	−0.416536	−	0.185454i
$77$	0.813039	+	2.50228i	0.0926544	+	0.285161i
$78$	−0.902923	−	2.77891i	−0.102236	−	0.314650i
$79$	−3.14958	−	1.40228i	−0.354355	−	0.157769i	0.221836	−	0.975084i	$-0.428795\pi$
$79$	−3.14958	−	1.40228i	−0.354355	−	0.157769i	−0.576191	+	0.817315i	$0.695462\pi$
$80$	−9.52229	−	2.02403i	−1.06462	−	0.226293i
$81$	−3.65408	+	0.776698i	−0.406009	+	0.0862998i
$82$	−2.23009	+	0.992898i	−0.246272	+	0.109647i
$83$	8.60075	+	9.55210i	0.944055	+	1.04848i	0.998750	+	0.0499757i	$0.0159144\pi$
$83$	8.60075	+	9.55210i	0.944055	+	1.04848i	−0.0546959	+	0.998503i	$0.517419\pi$
$84$	0.614118	+	5.84295i	0.0670058	+	0.637518i
$85$	4.38928	−	3.18900i	0.476084	−	0.345895i
$86$	0.309026	−	2.94019i	0.0333232	−	0.317049i
$87$	−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	$-0.338208\pi$
$89$	−1.82788	−	1.32803i	−0.193755	−	0.140771i	−0.680433	+	0.732810i	$0.738208\pi$
$90$	3.75533	−	4.17071i	0.395846	−	0.439632i
$91$	−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
$96$	−7.50258	+	8.33246i	−0.765729	+	0.850429i
$97$	−2.76106	−	2.00603i	−0.280343	−	0.203681i	0.438724	−	0.898622i	$-0.355431\pi$
$97$	−2.76106	−	2.00603i	−0.280343	−	0.203681i	−0.719067	+	0.694941i	$0.755431\pi$
$98$	1.02425	−	1.77405i	0.103465	−	0.179207i
$99$	6.52961	+	11.3096i	0.656251	+	1.13666i
$100$	0.753224	−	7.16645i	0.0753224	−	0.716645i
$101$	−14.3336	+	10.4140i	−1.42625	+	1.03623i	−0.435546	+	0.900167i	$0.643445\pi$
$101$	−14.3336	+	10.4140i	−1.42625	+	1.03623i	−0.990700	+	0.136062i	$0.956555\pi$
$102$	−0.193944	−	1.84525i	−0.0192033	−	0.182707i
$103$	5.40246	+	6.00004i	0.532320	+	0.591201i	0.947984	−	0.318317i	$-0.103118\pi$
$103$	5.40246	+	6.00004i	0.532320	+	0.591201i	−0.415664	+	0.909518i	$0.636451\pi$
$104$	−3.57640	+	1.59231i	−0.350694	+	0.156139i
$105$	−9.10548	+	1.93543i	−0.888604	+	0.188879i
$106$	1.71086	+	0.363654i	0.166173	+	0.0353212i
$107$	−11.1007	−	4.94234i	−1.07314	−	0.477794i	−0.207386	−	0.978259i	$-0.566495\pi$
$107$	−11.1007	−	4.94234i	−1.07314	−	0.477794i	−0.865756	+	0.500466i	$0.833162\pi$
$108$	3.97813	+	12.2434i	0.382796	+	1.17812i
$109$	−0.195330	−	0.601165i	−0.0187093	−	0.0575812i	0.941266	−	0.337666i	$-0.109637\pi$
$109$	−0.195330	−	0.601165i	−0.0187093	−	0.0575812i	−0.959975	+	0.280085i	$0.909637\pi$
$110$	−2.32087	−	1.03332i	−0.221287	−	0.0985232i
$111$	8.90552	+	1.89293i	0.845274	+	0.179669i
$112$	3.46570	−	0.736657i	0.327478	−	0.0696075i
$113$	−10.3234	+	4.59626i	−0.971142	+	0.432380i	−0.830094	−	0.557623i	$-0.811714\pi$
$113$	−10.3234	+	4.59626i	−0.971142	+	0.432380i	−0.141047	+	0.990003i	$0.545047\pi$
$114$	−1.44121	−	1.60063i	−0.134982	−	0.149912i
$115$	0.137435	+	1.30761i	0.0128159	+	0.121935i
$116$	−4.79594	+	3.48445i	−0.445291	+	0.323523i
$117$	−1.61337	+	15.3502i	−0.149157	+	1.41913i
$118$	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
$121$	−3.40483	+	3.78145i	−0.309530	+	0.343768i
$122$	−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
$127$	0.0788277	−	0.0875470i	0.00699483	−	0.00776854i	−0.739637	−	0.673006i	$-0.765003\pi$
$127$	0.0788277	−	0.0875470i	0.00699483	−	0.00776854i	0.746632	+	0.665237i	$0.231670\pi$
$128$	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
$131$	−0.604588	+	5.75227i	−0.0528231	+	0.502578i	0.935840	+	0.352426i	$0.114643\pi$
$131$	−0.604588	+	5.75227i	−0.0528231	+	0.502578i	−0.988663	+	0.150152i	$0.952024\pi$
$132$	10.6794	−	7.75907i	0.929526	−	0.675340i
$133$	0.239604	+	2.27968i	0.0207763	+	0.197673i
$134$	−1.51383	−	1.68127i	−0.130775	−	0.145240i
$135$	−18.6341	+	8.29642i	−1.60377	+	0.714043i
$136$	−2.43160	+	0.516853i	−0.208508	+	0.0443198i
$137$	−11.5474	−	2.45449i	−0.986565	−	0.209701i	−0.313745	−	0.949507i	$-0.601584\pi$
$137$	−11.5474	−	2.45449i	−0.986565	−	0.209701i	−0.672820	+	0.739806i	$0.734917\pi$
$138$	0.410770	+	0.182886i	0.0349670	+	0.0155683i
$139$	−4.76566	−	14.6672i	−0.404218	−	1.24406i	−0.921546	−	0.388268i	$-0.873073\pi$
$139$	−4.76566	−	14.6672i	−0.404218	−	1.24406i	0.517328	−	0.855787i	$-0.326927\pi$
$140$	1.86568	+	5.74196i	0.157678	+	0.485284i
$141$	21.0449	+	9.36981i	1.77230	+	0.789080i
$142$	−0.576774	−	0.122597i	−0.0484018	−	0.0102881i
$143$	6.83423	−	1.45266i	0.571507	−	0.121478i
$144$	16.0659	−	7.15300i	1.33882	−	0.596083i
$145$	−6.28503	−	6.98024i	−0.521944	−	0.579677i
$146$	−0.527516	−	5.01898i	−0.0436576	−	0.415374i
$147$	−13.6441	+	9.91300i	−1.12534	+	0.817611i
$148$	0.617226	−	5.87252i	0.0507357	−	0.482718i
$149$	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	$-0.243728\pi$
$151$	3.49668	+	2.54048i	0.284556	+	0.206742i	−0.436346	+	0.899779i	$0.643728\pi$
$152$	−1.93096	+	2.14455i	−0.156622	+	0.173946i
$153$	−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	0.784506	+	0.620121i	$0.212917\pi$
$157$	−2.68982	+	8.27841i	−0.214671	+	0.660689i	−0.999177	+	0.0405678i	$0.987083\pi$
$158$	−0.810728	+	0.900405i	−0.0644981	+	0.0716324i
$159$	−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
$162$	−0.137230	+	1.30566i	−0.0107818	+	0.102582i
$163$	−2.53053	+	1.83853i	−0.198206	+	0.144005i	−0.682462	−	0.730922i	$-0.739091\pi$
$163$	−2.53053	+	1.83853i	−0.198206	+	0.144005i	0.484255	+	0.874927i	$0.339091\pi$
$164$	−1.36248	−	12.9632i	−0.106392	−	1.01225i
$165$	13.9953	+	15.5434i	1.08953	+	1.21005i
$166$	4.12665	−	1.83730i	0.320290	−	0.142602i
$167$	13.0631	−	2.77665i	1.01085	−	0.214863i	0.327422	−	0.944878i	$-0.393820\pi$
$167$	13.0631	−	2.77665i	1.01085	−	0.214863i	0.683431	+	0.730015i	$0.260487\pi$
$168$	4.17211	+	0.886809i	0.321885	+	0.0684188i
$169$	−4.33214	−	1.92880i	−0.333242	−	0.148369i
$170$	−0.589196	−	1.81336i	−0.0451893	−	0.139078i
$171$	3.51585	+	10.8207i	0.268864	+	0.827478i
$172$	14.4210	+	6.42066i	1.09959	+	0.489571i
$173$	−18.6286	−	3.95962i	−1.41630	−	0.301045i	−0.564728	−	0.825277i	$-0.691019\pi$
$173$	−18.6286	−	3.95962i	−1.41630	−	0.301045i	−0.851575	+	0.524232i	$0.824352\pi$
$174$	−3.14200	+	0.667854i	−0.238195	+	0.0506299i
$175$	−3.79621	+	1.69018i	−0.286966	+	0.127766i
$176$	−5.32685	−	5.91607i	−0.401526	−	0.445940i
$177$	−3.63339	−	34.5694i	−0.273102	−	2.59840i
$178$	−0.642377	+	0.466714i	−0.0481482	+	0.0349817i
$179$	0.00829224	−	0.0788954i	0.000619791	−	0.00589692i	−0.994208	−	0.107476i	$-0.965723\pi$
$179$	0.00829224	−	0.0788954i	0.000619791	−	0.00589692i	0.994827	+	0.101580i	$0.0323896\pi$
$180$	14.9835	+	25.9521i	1.11680	+	1.93436i
$181$	−1.08143	+	1.87308i	−0.0803817	+	0.139225i	−0.903414	−	0.428769i	$-0.858947\pi$
$181$	−1.08143	+	1.87308i	−0.0803817	+	0.139225i	0.823032	+	0.567995i	$0.192281\pi$
$182$	0.884121	+	0.642351i	0.0655354	+	0.0476142i
$183$	27.9463	−	31.0375i	2.06585	−	2.29436i
$184$	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
$189$	4.96750	−	5.51697i	0.361332	−	0.401300i
$190$	−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
$193$	0.223030	−	2.12199i	0.0160540	−	0.152744i	−0.983558	−	0.180592i	$-0.942199\pi$
$193$	0.223030	−	2.12199i	0.0160540	−	0.152744i	0.999612	+	0.0278478i	$0.00886537\pi$
$194$	−0.970327	+	0.704984i	−0.0696654	+	0.0506149i
$195$	2.58398	+	24.5849i	0.185043	+	1.76056i
$196$	7.31902	+	8.12859i	0.522787	+	0.580614i
$197$	−5.36775	+	2.38987i	−0.382436	+	0.170272i	−0.588945	−	0.808173i	$-0.700456\pi$
$197$	−5.36775	+	2.38987i	−0.382436	+	0.170272i	0.206509	+	0.978445i	$0.433790\pi$
$198$	4.48915	−	0.954197i	0.319030	−	0.0678119i
$199$	−6.77657	−	1.44040i	−0.480378	−	0.102108i	−0.0386432	−	0.999253i	$-0.512304\pi$
$199$	−6.77657	−	1.44040i	−0.480378	−	0.102108i	−0.441735	+	0.897146i	$0.645637\pi$
$200$	−4.77918	−	2.12783i	−0.337939	−	0.150460i
$201$	5.75569	+	17.7142i	0.405975	+	1.24946i
$202$	1.92407	+	5.92169i	0.135377	+	0.416649i
$203$	3.12303	+	1.39046i	0.219194	+	0.0975913i
$204$	9.69061	+	2.05980i	0.678478	+	0.144215i
$205$	20.2014	−	4.29395i	1.41093	−	0.299902i
$206$	2.59210	−	1.15408i	0.180601	−	0.0804085i
$207$	−1.58932	−	1.76512i	−0.110465	−	0.122684i
$208$	−0.983507	−	9.35744i	−0.0681939	−	0.648822i
$209$	4.16669	−	3.02727i	0.288216	−	0.209401i
$210$	−0.341960	+	3.25353i	−0.0235975	+	0.224515i
$211$	−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
$214$	−2.85740	+	3.17347i	−0.195328	+	0.216934i
$215$	−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
$220$	9.07691	−	10.0809i	0.611965	−	0.679656i
$221$	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	0.951605	−	0.307323i	$-0.0994333\pi$
$223$	3.13078	+	5.42267i	0.209653	+	0.363129i	−0.741952	+	0.670453i	$0.766100\pi$
$224$	0.438349	−	4.17061i	0.0292884	−	0.278661i
$225$	−16.6865	+	12.1235i	−1.11244	+	0.808232i
$226$	0.415115	+	3.94955i	0.0276130	+	0.262720i
$227$	−5.25101	−	5.83184i	−0.348522	−	0.387073i	0.543240	−	0.839577i	$-0.317197\pi$
$227$	−5.25101	−	5.83184i	−0.348522	−	0.387073i	−0.891762	+	0.452505i	$0.850531\pi$
$228$	10.5064	−	4.67773i	0.695800	−	0.309790i
$229$	−12.4939	+	2.65565i	−0.825618	+	0.175490i	−0.601298	−	0.799025i	$-0.705349\pi$
$229$	−12.4939	+	2.65565i	−0.825618	+	0.175490i	−0.224320	+	0.974516i	$0.572016\pi$
$230$	0.451969	+	0.0960690i	0.0298020	+	0.00633460i
$231$	−6.95427	−	3.09624i	−0.457557	−	0.203718i
$232$	1.32994	+	4.09313i	0.0873148	+	0.268727i
$233$	3.92992	+	12.0950i	0.257457	+	0.792372i	0.993336	+	0.115258i	$0.0367696\pi$
$233$	3.92992	+	12.0950i	0.257457	+	0.792372i	−0.735878	+	0.677114i	$0.763230\pi$
$234$	4.95533	+	2.20626i	0.323940	+	0.144227i
$235$	23.1557	+	4.92190i	1.51051	+	0.321069i
$236$	−22.0515	+	4.68718i	−1.43543	+	0.305109i
$237$	9.11265	−	4.05721i	0.591930	−	0.263544i
$238$	0.464342	+	0.515703i	0.0300988	+	0.0334281i
$239$	2.65760	+	25.2853i	0.171906	+	1.63557i	0.651903	+	0.758302i	$0.273971\pi$
$239$	2.65760	+	25.2853i	0.171906	+	1.63557i	−0.479997	+	0.877270i	$0.659362\pi$
$240$	22.7870	−	16.5557i	1.47089	−	1.06867i
$241$	−0.246790	+	2.34805i	−0.0158971	+	0.151251i	−0.999591	−	0.0286003i	$-0.990895\pi$
$241$	−0.246790	+	2.34805i	−0.0158971	+	0.151251i	0.983694	+	0.179851i	$0.0575617\pi$
$242$	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
$245$	−11.5967	+	12.8794i	−0.740885	+	0.822836i
$246$	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
$251$	1.57690	−	1.75132i	0.0995329	−	0.110542i	−0.691320	−	0.722549i	$-0.742971\pi$
$251$	1.57690	−	1.75132i	0.0995329	−	0.110542i	0.790853	+	0.612006i	$0.209637\pi$
$252$	−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
$255$	−1.64082	+	15.6114i	−0.102752	+	0.977624i
$256$	−5.67014	+	4.11960i	−0.354384	+	0.257475i
$257$	2.71920	+	25.8715i	0.169619	+	1.61382i	0.666162	+	0.745807i	$0.267936\pi$
$257$	2.71920	+	25.8715i	0.169619	+	1.61382i	−0.496542	+	0.868013i	$0.665397\pi$
$258$	5.72353	+	6.35662i	0.356331	+	0.395746i
$259$	−3.11079	+	1.38501i	−0.193295	+	0.0860604i
$260$	15.6825	−	3.33341i	0.972586	−	0.206729i
$261$	16.5974	+	3.52788i	1.02735	+	0.218370i
$262$	1.85694	+	0.826761i	0.114722	+	0.0510775i
$263$	7.08747	+	21.8130i	0.437032	+	1.34505i	0.890990	+	0.454024i	$0.150012\pi$
$263$	7.08747	+	21.8130i	0.437032	+	1.34505i	−0.453957	+	0.891023i	$0.649988\pi$
$264$	−2.96147	−	9.11446i	−0.182266	−	0.560956i
$265$	−13.5184	−	6.01879i	−0.830430	−	0.369731i
$266$	0.787964	+	0.167487i	0.0483131	+	0.0102693i
$267$	6.39421	−	1.35913i	0.391319	−	0.0831775i
$268$	11.0357	−	4.91342i	0.674114	−	0.300135i
$269$	−11.4069	−	12.6686i	−0.695490	−	0.772420i	0.287161	−	0.957882i	$-0.407288\pi$
$269$	−11.4069	−	12.6686i	−0.695490	−	0.772420i	−0.982651	+	0.185462i	$0.940622\pi$
$270$	0.749297	+	7.12909i	0.0456008	+	0.433862i
$271$	−5.86255	+	4.25939i	−0.356124	+	0.258739i	−0.751434	−	0.659809i	$-0.770637\pi$
$271$	−5.86255	+	4.25939i	−0.356124	+	0.258739i	0.395309	+	0.918548i	$0.370637\pi$
$272$	0.624525	−	5.94196i	0.0378674	−	0.360284i
$273$	−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
$276$	−1.60651	+	1.78422i	−0.0967008	+	0.107397i
$277$	4.66717	−	14.3641i	0.280423	−	0.863053i	−0.707310	−	0.706903i	$-0.750092\pi$
$277$	4.66717	−	14.3641i	0.280423	−	0.863053i	0.987733	−	0.156150i	$-0.0499083\pi$
$278$	−5.41979			−0.325058
$279$		0			0
$280$	4.38316			0.261944
$281$	−0.768550	+	2.36535i	−0.0458479	+	0.141105i	−0.971360	−	0.237613i	$-0.923635\pi$
$281$	−0.768550	+	2.36535i	−0.0458479	+	0.141105i	0.925512	+	0.378718i	$0.123635\pi$
$282$	5.41714	−	6.01634i	0.322586	−	0.358268i
$283$	3.82370	+	2.77808i	0.227296	+	0.165140i	0.695605	−	0.718425i	$-0.255137\pi$
$283$	3.82370	+	2.77808i	0.227296	+	0.165140i	−0.468309	+	0.883565i	$0.655137\pi$
$284$	1.57426	−	2.72670i	0.0934153	−	0.161800i
$285$	9.11114	+	15.7810i	0.539697	+	0.934783i
$286$	0.256662	−	2.44198i	0.0151767	−	0.144397i
$287$	−6.08114	+	4.41821i	−0.358958	+	0.260798i
$288$	−2.17575	−	20.7009i	−0.128207	−	1.21981i
$289$	−9.14717	−	10.1590i	−0.538069	−	0.597586i
$290$	−3.01557	+	1.34262i	−0.177080	+	0.0788411i
$291$	9.65862	−	2.05300i	0.566198	−	0.120349i
$292$	26.3579	+	5.60255i	1.54248	+	0.327864i
$293$	−9.63689	−	4.29062i	−0.562993	−	0.250661i	0.105449	−	0.994425i	$-0.466372\pi$
$293$	−9.63689	−	4.29062i	−0.562993	−	0.250661i	−0.668442	+	0.743764i	$0.733039\pi$
$294$	1.83152	+	5.63683i	0.106816	+	0.328746i
$295$	−11.0381	−	33.9719i	−0.642666	−	1.97792i
$296$	−3.91628	−	1.74364i	−0.227629	−	0.101347i
$297$	−16.3157	−	3.46800i	−0.946731	−	0.201234i
$298$	4.10792	−	0.873166i	0.237966	−	0.0505812i
$299$	−1.16091	+	0.516870i	−0.0671372	+	0.0298914i
$300$	13.9506	+	15.4937i	0.805438	+	0.894529i
$301$	−0.951549	−	9.05338i	−0.0548464	−	0.521828i
$302$	1.22885	−	0.892809i	0.0707121	−	0.0513754i
$303$	5.35827	−	50.9805i	0.307824	−	2.92875i
$304$	−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
$307$	1.77219	−	1.96822i	0.101144	−	0.112332i	−0.690447	−	0.723383i	$-0.742586\pi$
$307$	1.77219	−	1.96822i	0.101144	−	0.112332i	0.791592	+	0.611051i	$0.209253\pi$
$308$	−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
$313$	−17.8494	+	19.8237i	−1.00891	+	1.12050i	−0.0162089	+	0.999869i	$0.505160\pi$
$313$	−17.8494	+	19.8237i	−1.00891	+	1.12050i	−0.992697	+	0.120635i	$0.961507\pi$
$314$	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
$317$	−1.12266	+	10.6814i	−0.0630549	+	0.599927i	0.916679	+	0.399624i	$0.130859\pi$
$317$	−1.12266	+	10.6814i	−0.0630549	+	0.599927i	−0.979734	+	0.200303i	$0.935807\pi$
$318$	−4.09411	+	2.97454i	−0.229586	+	0.166804i
$319$	−0.802886	−	7.63895i	−0.0449530	−	0.427699i
$320$	−10.3185	−	11.4599i	−0.576822	−	0.640626i
$321$	32.1175	−	14.2996i	1.79262	−	0.798127i
$322$	−0.164497	+	0.0349649i	−0.00916706	+	0.00194852i
$323$	3.78088	+	0.803652i	0.210374	+	0.0447164i
$324$	−6.40400	−	2.85124i	−0.355778	−	0.158402i
$325$	3.41003	+	10.4950i	0.189155	+	0.582158i
$326$	0.339686	+	1.04545i	0.0188135	+	0.0579019i
$327$	1.67074	+	0.743863i	0.0923923	+	0.0411357i
$328$	−9.25625	−	1.96748i	−0.511091	−	0.108636i
$329$	−8.42766	+	1.79136i	−0.464632	+	0.0987606i
$330$	6.71497	−	2.98970i	0.369647	−	0.164577i
$331$	13.1468	+	14.6010i	0.722614	+	0.802545i	0.986803	−	0.161926i	$-0.0517707\pi$
$331$	13.1468	+	14.6010i	0.722614	+	0.802545i	−0.264188	+	0.964471i	$0.585104\pi$
$332$	2.52120	+	23.9876i	0.138369	+	1.31649i
$333$	−13.6737	+	9.93453i	−0.749315	+	0.544409i
$334$	0.490589	−	4.66765i	0.0268439	−	0.255402i
$335$	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	$-0.474950\pi$
$337$	−15.5159	−	11.2730i	−0.845206	−	0.614078i	−0.923820	+	0.382827i	$0.874950\pi$
$338$	−1.11513	+	1.23848i	−0.0606551	+	0.0673643i
$339$	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
$344$	7.66851	−	8.51674i	0.413458	−	0.459192i
$345$	−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	0.686754	−	0.726890i	$-0.259035\pi$
$347$	−5.32998	−	9.23180i	−0.286128	−	0.495589i	−0.972882	+	0.231301i	$0.925702\pi$
$348$	1.79284	−	17.0578i	0.0961065	−	0.914393i
$349$	15.1299	−	10.9925i	0.809884	−	0.588415i	−0.103913	−	0.994586i	$-0.533136\pi$
$349$	15.1299	−	10.9925i	0.809884	−	0.588415i	0.913797	+	0.406171i	$0.133136\pi$
$350$	0.152650	+	1.45237i	0.00815948	+	0.0776322i
$351$	−13.1915	−	14.6506i	−0.704110	−	0.781994i
$352$	−8.60774	+	3.83241i	−0.458794	+	0.204268i
$353$	12.3855	−	2.63263i	0.659216	−	0.140121i	0.133856	−	0.991001i	$-0.457264\pi$
$353$	12.3855	−	2.63263i	0.659216	−	0.140121i	0.525360	+	0.850880i	$0.323931\pi$
$354$	−11.9488	−	2.53979i	−0.635071	−	0.134988i
$355$	4.55741	+	2.02909i	0.241882	+	0.107693i
$356$	−1.31015	−	4.03222i	−0.0694377	−	0.213707i
$357$	−1.76547	−	5.43355i	−0.0934384	−	0.287574i
$358$	−0.0254688	−	0.0113395i	−0.00134607	−	0.000599309i
$359$	22.1826	+	4.71505i	1.17075	+	0.248851i	0.751945	−	0.659226i	$-0.229116\pi$
$359$	22.1826	+	4.71505i	1.17075	+	0.248851i	0.418805	+	0.908076i	$0.362449\pi$
$360$	21.2804	−	4.52329i	1.12158	−	0.238399i
$361$	−13.2582	+	5.90293i	−0.697800	+	0.310681i
$362$	0.508604	+	0.564862i	0.0267316	+	0.0296885i
$363$	−1.53890	−	14.6417i	−0.0807715	−	0.768489i
$364$	−4.72082	+	3.42987i	−0.247438	+	0.179774i
$365$	−4.46295	+	42.4622i	−0.233602	+	2.22257i
$366$	−7.33880	−	12.7112i	−0.383605	−	0.664424i
$367$	−4.35984	+	7.55147i	−0.227582	+	0.394183i	−0.957091	−	0.289788i	$-0.906415\pi$
$367$	−4.35984	+	7.55147i	−0.227582	+	0.394183i	0.729509	+	0.683971i	$0.239749\pi$
$368$	1.17139	+	0.851062i	0.0610628	+	0.0443647i
$369$	−24.9647	+	27.7261i	−1.29961	+	1.44337i
$370$	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
$375$	6.67658	−	7.41509i	0.344777	−	0.382914i
$376$	−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
$379$	−2.30986	+	21.9768i	−0.118649	+	1.12887i	0.759507	+	0.650499i	$0.225440\pi$
$379$	−2.30986	+	21.9768i	−0.118649	+	1.12887i	−0.878156	+	0.478374i	$0.841226\pi$
$380$	9.56127	−	6.94667i	0.490483	−	0.356357i
$381$	0.0356283	+	0.338980i	0.00182529	+	0.0173665i
$382$	−1.25612	−	1.39506i	−0.0642688	−	0.0713777i
$383$	−24.3393	+	10.8365i	−1.24368	+	0.553721i	−0.919804	−	0.392379i	$-0.871652\pi$
$383$	−24.3393	+	10.8365i	−1.24368	+	0.553721i	−0.323874	+	0.946100i	$0.604985\pi$
$384$	−27.0932	+	5.75885i	−1.38260	+	0.293880i
$385$	−7.65177	−	1.62643i	−0.389970	−	0.0828907i
$386$	−0.685016	−	0.304989i	−0.0348664	−	0.0155235i
$387$	−13.9626	−	42.9726i	−0.709761	−	2.18442i
$388$	−1.97901	−	6.09077i	−0.100469	−	0.309212i
$389$	−11.8350	−	5.26930i	−0.600060	−	0.267164i	0.0841452	−	0.996454i	$-0.473184\pi$
$389$	−11.8350	−	5.26930i	−0.600060	−	0.267164i	−0.684205	+	0.729290i	$0.739851\pi$
$390$	8.49770	+	1.80624i	0.430298	+	0.0914626i
$391$	−0.789306	+	0.167772i	−0.0399169	+	0.00848461i
$392$	7.25447	−	3.22990i	0.366406	−	0.163134i
$393$	−11.1977	−	12.4363i	−0.564848	−	0.627327i
$394$	0.215843	+	2.05361i	0.0108740	+	0.103459i
$395$	8.29294	−	6.02517i	0.417263	−	0.303159i
$396$	−2.56153	+	24.3713i	−0.128722	+	1.22471i
$397$	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
$400$	8.41320	−	9.34381i	0.420660	−	0.467190i
$401$	−3.79302	+	11.6737i	−0.189414	+	0.582957i	−0.999996	−	0.00266786i	$-0.999151\pi$
$401$	−3.79302	+	11.6737i	−0.189414	+	0.582957i	0.810582	+	0.585625i	$0.199151\pi$
$402$	6.54572			0.326471
$403$		0			0
$404$	−33.2464			−1.65407
$405$	3.43229	−	10.5635i	0.170552	−	0.524905i
$406$	0.803894	−	0.892815i	0.0398966	−	0.0443097i
$407$	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	0.996437	−	0.0843442i	$-0.0268795\pi$
$409$	8.59861	+	14.8932i	0.425174	+	0.736423i	−0.571263	+	0.820767i	$0.693546\pi$
$410$	0.758673	−	7.21829i	0.0374682	−	0.356486i
$411$	27.6332	−	20.0767i	1.36305	−	0.990311i
$412$	1.58366	+	15.0675i	0.0780214	+	0.742324i
$413$	8.69909	+	9.66132i	0.428054	+	0.475403i
$414$	−0.762557	+	0.339512i	−0.0374777	+	0.0166861i
$415$	−37.3816	+	7.94571i	−1.83499	+	0.390039i
$416$	−10.8930	−	2.31537i	−0.534072	−	0.113520i
$417$	40.7627	+	18.1487i	1.99616	+	0.888747i
$418$	−0.559316	−	1.72140i	−0.0273571	−	0.0841963i
$419$	7.15236	+	22.0127i	0.349416	+	1.07539i	0.959177	+	0.282806i	$0.0912652\pi$
$419$	7.15236	+	22.0127i	0.349416	+	1.07539i	−0.609762	+	0.792585i	$0.708735\pi$
$420$	−15.9579	−	7.10492i	−0.778667	−	0.346685i
$421$	−28.5445	−	6.06733i	−1.39118	−	0.295703i	−0.549413	−	0.835551i	$-0.685149\pi$
$421$	−28.5445	−	6.06733i	−1.39118	−	0.295703i	−0.841763	+	0.539848i	$0.818482\pi$
$422$	−5.74368	+	1.22086i	−0.279598	+	0.0594304i
$423$	−39.0680	+	17.3942i	−1.89955	+	0.845735i
$424$	4.53690	+	5.03874i	0.220332	+	0.244703i
$425$	0.732459	+	6.96889i	0.0355295	+	0.338041i
$426$	1.38023	−	1.00280i	0.0668723	−	0.0485856i
$427$	−1.63280	+	15.5351i	−0.0790168	+	0.751794i
$428$	−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
$431$	20.3096	−	22.5561i	0.978279	−	1.08649i	−0.0179599	−	0.999839i	$-0.505717\pi$
$431$	20.3096	−	22.5561i	0.978279	−	1.08649i	0.996239	−	0.0866501i	$-0.0276162\pi$
$432$	−6.94129	+	21.3631i	−0.333963	+	1.02783i
$433$	−13.8400			−0.665107			−0.332553	−	0.943084i	$-0.607910\pi$
$433$	−13.8400			−0.665107			−0.332553	+	0.943084i	$0.607910\pi$
$434$		0			0
$435$	27.1762			1.30300
$436$	0.366536	−	1.12808i	0.0175539	−	0.0540254i
$437$	−0.626797	+	0.696129i	−0.0299838	+	0.0333004i
$438$	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
$441$	3.27262	−	31.1369i	0.155839	−	1.48271i
$442$	1.49087	−	1.08318i	0.0709136	−	0.0515218i
$443$	−2.48341	−	23.6281i	−0.117991	−	1.12261i	−0.879978	−	0.475014i	$-0.842443\pi$
$443$	−2.48341	−	23.6281i	−0.117991	−	1.12261i	0.761988	−	0.647592i	$-0.224224\pi$
$444$	11.4318	+	12.6963i	0.542527	+	0.602538i
$445$	6.13690	−	2.73232i	0.290917	−	0.129525i
$446$	2.15243	−	0.457513i	0.101921	−	0.0216639i
$447$	−33.8199	−	7.18865i	−1.59963	−	0.340012i
$448$	5.12726	+	2.28280i	0.242240	+	0.107852i
$449$	−5.99891	−	18.4627i	−0.283106	−	0.871311i	−0.986960	−	0.160966i	$-0.948539\pi$
$449$	−5.99891	−	18.4627i	−0.283106	−	0.871311i	0.703854	−	0.710345i	$-0.251461\pi$
$450$	2.23992	+	6.89377i	0.105591	+	0.324975i
$451$	15.4288	+	6.86932i	0.726512	+	0.323464i
$452$	−20.7417	−	4.40878i	−0.975605	−	0.207371i
$453$	−12.2319	+	2.59997i	−0.574706	+	0.122157i
$454$	−2.51944	+	1.12173i	−0.118243	+	0.0526453i
$455$	−6.18659	−	6.87090i	−0.290032	−	0.322113i
$456$	−0.872750	−	8.30367i	−0.0408703	−	0.388855i
$457$	−19.6931	+	14.3078i	−0.921202	+	0.669293i	−0.943823	−	0.330452i	$-0.892799\pi$
$457$	−19.6931	+	14.3078i	−0.921202	+	0.669293i	0.0226207	+	0.999744i	$0.492799\pi$
$458$	−0.469212	+	4.46425i	−0.0219248	+	0.208601i
$459$	−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	0.987022	+	0.160587i	$0.0513388\pi$
$461$	31.0202	+	22.5375i	1.44476	+	1.04968i	0.457734	+	0.889089i	$0.348661\pi$
$462$	−1.79009	+	1.98809i	−0.0832823	+	0.0924944i
$463$	−2.03775	+	6.27154i	−0.0947022	+	0.291463i	−0.987176	−	0.159636i	$-0.948968\pi$
$463$	−2.03775	+	6.27154i	−0.0947022	+	0.291463i	0.892474	+	0.451099i	$0.148968\pi$
$464$	−10.3437			−0.480195
$465$		0			0
$466$	4.46933			0.207038
$467$	11.8667	−	36.5219i	0.549125	−	1.69003i	−0.161850	−	0.986815i	$-0.551746\pi$
$467$	11.8667	−	36.5219i	0.549125	−	1.69003i	0.710975	−	0.703217i	$-0.248254\pi$
$468$	−19.3802	+	21.5239i	−0.895851	+	0.994944i
$469$	−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
$472$	−1.71081	+	16.2772i	−0.0787463	+	0.749221i
$473$	−16.5473	+	12.0223i	−0.760846	+	0.552787i
$474$	−0.366430	−	3.48635i	−0.0168307	−	0.160133i
$475$	5.44296	+	6.04502i	0.249740	+	0.277364i
$476$	−3.38503	+	1.50711i	−0.155153	+	0.0690784i
$477$	26.1480	−	5.55793i	1.19723	−	0.254480i
$478$	8.73978	+	1.85770i	0.399748	+	0.0849691i
$479$	6.87457	+	3.06075i	0.314107	+	0.139849i	0.557734	−	0.830019i	$-0.311671\pi$
$479$	6.87457	+	3.06075i	0.314107	+	0.139849i	−0.243627	+	0.969869i	$0.578337\pi$
$480$	−10.3017	−	31.7055i	−0.470208	−	1.44715i
$481$	2.79434	+	8.60009i	0.127411	+	0.392130i
$482$	0.757992	+	0.337480i	0.0345256	+	0.0153718i
$483$	1.35428	+	0.287861i	0.0616219	+	0.0130981i
$484$	−9.33977	+	1.98523i	−0.424535	+	0.0902377i
$485$	9.26995	−	4.12725i	0.420927	−	0.187409i
$486$	2.29809	+	2.55228i	0.104243	+	0.115774i
$487$	−2.61658	−	24.8951i	−0.118569	−	1.12811i	−0.878380	−	0.477962i	$-0.841375\pi$
$487$	−2.61658	−	24.8951i	−0.118569	−	1.12811i	0.759812	−	0.650143i	$-0.225291\pi$
$488$	−15.9096	+	11.5590i	−0.720194	+	0.523252i
$489$	0.945976	−	9.00036i	0.0427785	−	0.407010i
$490$	3.04533	+	5.27467i	0.137574	+	0.238285i
$491$	19.8550	−	34.3899i	0.896044	−	1.55199i	0.0635377	−	0.997979i	$-0.479762\pi$
$491$	19.8550	−	34.3899i	0.896044	−	1.55199i	0.832507	−	0.554015i	$-0.186905\pi$
$492$	30.5103	+	22.1671i	1.37551	+	0.999368i
$493$	3.85732	−	4.28399i	0.173725	−	0.192941i
$494$	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
$499$	−15.8277	+	17.5784i	−0.708544	+	0.786918i	−0.984712	−	0.174192i	$-0.944269\pi$
$499$	−15.8277	+	17.5784i	−0.708544	+	0.786918i	0.276168	+	0.961109i	$0.410935\pi$
$500$	−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
$503$	2.11006	−	20.0758i	0.0940828	−	0.895138i	−0.841078	−	0.540914i	$-0.818078\pi$
$503$	2.11006	−	20.0758i	0.0940828	−	0.895138i	0.935161	−	0.354224i	$-0.115255\pi$
$504$	−6.40594	+	4.65419i	−0.285343	+	0.207314i
$505$	−5.50631	−	52.3890i	−0.245028	−	2.33128i
$506$	0.252835	+	0.280802i	0.0112399	+	0.0124832i
$507$	12.5342	−	5.58057i	0.556662	−	0.247842i
$508$	0.216232	−	0.0459615i	0.00959374	−	0.00203921i
$509$	−11.5803	−	2.46147i	−0.513288	−	0.109103i	−0.0560163	−	0.998430i	$-0.517840\pi$
$509$	−11.5803	−	2.46147i	−0.513288	−	0.109103i	−0.457271	+	0.889327i	$0.651173\pi$
$510$	5.03964	+	2.24379i	0.223159	+	0.0993568i
$511$	−4.80197	−	14.7789i	−0.212427	−	0.653782i
$512$	6.67779	+	20.5521i	0.295120	+	0.908285i
$513$	−13.2758	−	5.91078i	−0.586142	−	0.260967i
$514$	8.94239	+	1.90076i	0.394432	+	0.0838391i
$515$	−23.4808	+	4.99100i	−1.03469	+	0.219930i
$516$	−41.7243	+	18.5768i	−1.83681	+	0.817800i
$517$	12.9535	+	14.3863i	0.569694	+	0.632709i
$518$	0.125088	+	1.19014i	0.00549606	+	0.0522916i
$519$	44.5784	−	32.3881i	1.95678	−	1.42168i
$520$	1.21669	−	11.5760i	0.0533552	−	0.507641i
$521$	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	$-0.0768446\pi$
$523$	23.8682	+	17.3412i	1.04368	+	0.758279i	0.0726806	+	0.997355i	$0.476845\pi$
$524$	−7.26245	+	8.06577i	−0.317262	+	0.352355i
$525$	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
$530$	−3.47976	+	3.86466i	−0.151151	+	0.167870i
$531$	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
$534$	0.240137	−	2.28475i	0.0103917	−	0.0988708i
$535$	29.2284	−	21.2357i	1.26365	−	0.918098i
$536$	−0.916724	−	8.72205i	−0.0395965	−	0.376735i
$537$	0.153582	+	0.170570i	0.00662755	+	0.00736064i
$538$	−5.47304	+	2.43675i	−0.235959	+	0.105056i
$539$	−13.8628	+	2.94662i	−0.597112	+	0.126920i
$540$	−37.4395	−	7.95800i	−1.61114	−	0.342458i
$541$	12.1189	+	5.39570i	0.521034	+	0.231979i	0.650364	−	0.759622i	$-0.274616\pi$
$541$	12.1189	+	5.39570i	0.521034	+	0.231979i	−0.129331	+	0.991602i	$0.541283\pi$
$542$	0.786961	+	2.42202i	0.0338028	+	0.104034i
$543$	−1.93375	−	5.95148i	−0.0829853	−	0.255403i
$544$	−6.46018	−	2.87626i	−0.276978	−	0.123319i
$545$	1.83832	+	0.390746i	0.0787448	+	0.0167377i
$546$	−3.09279	+	0.657393i	−0.132359	+	0.0281338i
$547$	34.4990	−	15.3599i	1.47507	−	0.656744i	0.497521	−	0.867452i	$-0.334244\pi$
$547$	34.4990	−	15.3599i	1.47507	−	0.656744i	0.977549	+	0.210708i	$0.0675769\pi$
$548$	−14.8231	−	16.4628i	−0.633213	−	0.703254i
$549$	8.10442	+	77.1084i	0.345888	+	3.29090i
$550$	2.65456	−	1.92865i	0.113191	−	0.0822380i
$551$	0.699495	−	6.65525i	0.0297995	−	0.283523i
$552$	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
$555$	−18.1132	+	20.1167i	−0.768860	+	0.853906i
$556$	8.94274	−	27.5229i	0.379257	−	1.16723i
$557$	−11.3637			−0.481496			−0.240748	−	0.970588i	$-0.577393\pi$
$557$	−11.3637			−0.481496			−0.240748	+	0.970588i	$0.577393\pi$
$558$		0			0
$559$	−24.1743			−1.02246
$560$	−3.25535	+	10.0189i	−0.137563	+	0.423377i
$561$	−8.58937	+	9.53946i	−0.362643	+	0.402756i
$562$	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
$565$	3.51200	−	33.4145i	0.147751	−	1.40576i
$566$	1.34377	−	0.976309i	0.0564830	−	0.0410373i
$567$	0.422558	+	4.02037i	0.0177457	+	0.168840i
$568$	−1.52951	−	1.69869i	−0.0641767	−	0.0712754i
$569$	−28.3105	+	12.6046i	−1.18684	+	0.528414i	−0.902658	−	0.430358i	$-0.858387\pi$
$569$	−28.3105	+	12.6046i	−1.18684	+	0.528414i	−0.284178	+	0.958772i	$0.591721\pi$
$570$	6.26396	−	1.33145i	0.262368	−	0.0557681i
$571$	10.1724	+	2.16222i	0.425703	+	0.0904861i	0.415781	−	0.909465i	$-0.363508\pi$
$571$	10.1724	+	2.16222i	0.425703	+	0.0904861i	0.00992234	+	0.999951i	$0.496842\pi$
$572$	11.9774	+	5.33269i	0.500801	+	0.222971i
$573$	4.77588	+	14.6987i	0.199515	+	0.614045i
$574$	0.816303	+	2.51232i	0.0340718	+	0.104862i
$575$	−1.55134	−	0.690700i	−0.0646953	−	0.0288042i
$576$	27.2488	+	5.79192i	1.13537	+	0.241330i
$577$	−5.29555	+	1.12560i	−0.220457	+	0.0468595i	−0.316816	−	0.948487i	$-0.602614\pi$
$577$	−5.29555	+	1.12560i	−0.220457	+	0.0468595i	0.0963589	+	0.995347i	$0.469280\pi$
$578$	−4.38882	+	1.95403i	−0.182551	+	0.0812769i
$579$	4.13078	+	4.58769i	0.171669	+	0.190658i
$580$	−1.84238	−	17.5291i	−0.0765006	−	0.727854i
$581$	11.2528	−	8.17564i	0.466845	−	0.339183i
$582$	0.362733	−	3.45118i	0.0150358	−	0.143056i
$583$	−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
$586$	−2.48062	+	2.75500i	−0.102473	+	0.113808i
$587$	−3.88212	+	11.9479i	−0.160232	+	0.493145i	−0.998653	−	0.0518785i	$-0.983479\pi$
$587$	−3.88212	+	11.9479i	−0.160232	+	0.493145i	0.838421	+	0.545023i	$0.183479\pi$
$588$	−31.6471			−1.30510
$589$		0			0
$590$	−12.5532			−0.516809
$591$	5.25335	−	16.1682i	0.216094	−	0.665069i
$592$	6.89417	−	7.65675i	0.283348	−	0.314690i
$593$	−21.9001	−	15.9114i	−0.899330	−	0.653401i	0.0389638	−	0.999241i	$-0.487594\pi$
$593$	−21.9001	−	15.9114i	−0.899330	−	0.653401i	−0.938294	+	0.345839i	$0.887594\pi$
$594$	−2.93098	+	5.07660i	−0.120259	+	0.208295i
$595$	−2.93551	−	5.08445i	−0.120344	−	0.208442i
$596$	−2.34400	+	22.3017i	−0.0960141	+	0.913513i
$597$	16.2164	−	11.7819i	0.663695	−	0.482202i
$598$	0.0466815	+	0.444145i	0.00190895	+	0.0181624i
$599$	−9.60542	−	10.6679i	−0.392467	−	0.435879i	0.514236	−	0.857649i	$-0.328076\pi$
$599$	−9.60542	−	10.6679i	−0.392467	−	0.435879i	−0.906703	+	0.421770i	$0.861409\pi$
$600$	13.8276	−	6.15643i	0.564508	−	0.251335i
$601$	−0.626031	+	0.133067i	−0.0255363	+	0.00542791i	−0.220662	−	0.975350i	$-0.570822\pi$
$601$	−0.626031	+	0.133067i	−0.0255363	+	0.00542791i	0.195126	+	0.980778i	$0.437488\pi$
$602$	−3.12927	−	0.665147i	−0.127539	−	0.0271094i
$603$	−31.5878	−	14.0638i	−1.28636	−	0.572722i
$604$	2.50627	+	7.71350i	0.101979	+	0.313858i
$605$	−4.67515	−	14.3886i	−0.190072	−	0.584981i
$606$	−16.4574	−	7.32732i	−0.668537	−	0.297652i
$607$	6.37539	+	1.35513i	0.258769	+	0.0550031i	0.335469	−	0.942051i	$-0.391105\pi$
$607$	6.37539	+	1.35513i	0.258769	+	0.0550031i	−0.0767002	+	0.997054i	$0.524438\pi$
$608$	−8.02961	+	1.70675i	−0.325644	+	0.0692177i
$609$	−9.03584	+	4.02301i	−0.366151	+	0.163021i
$610$	−10.0926	−	11.2089i	−0.408636	−	0.453837i
$611$	2.39163	+	22.7548i	0.0967550	+	0.920562i
$612$	−14.8792	+	10.8103i	−0.601454	+	0.436982i
$613$	−1.09183	+	10.3881i	−0.0440987	+	0.419572i	0.950095	+	0.311962i	$0.100986\pi$
$613$	−1.09183	+	10.3881i	−0.0440987	+	0.419572i	−0.994193	+	0.107609i	$0.965680\pi$
$614$	−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
$617$	14.5224	−	16.1287i	0.584649	−	0.649318i	−0.376152	−	0.926558i	$-0.622753\pi$
$617$	14.5224	−	16.1287i	0.584649	−	0.649318i	0.960801	+	0.277240i	$0.0894196\pi$
$618$	−2.53686	+	7.80766i	−0.102048	+	0.314070i
$619$	28.5478			1.14743			0.573716	−	0.819054i	$-0.305501\pi$
$619$	28.5478			1.14743			0.573716	+	0.819054i	$0.305501\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$	0.598686	−	1.84257i	0.0240051	−	0.0738802i
$623$	−1.63598	+	1.81694i	−0.0655443	+	0.0727943i
$624$	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
$627$	−1.55761	+	14.8197i	−0.0622051	+	0.591842i
$628$	−13.2143	+	9.60079i	−0.527310	+	0.383113i
$629$	0.600211	+	5.71063i	0.0239320	+	0.227698i
$630$	−4.06374	−	4.51324i	−0.161903	−	0.179812i
$631$	24.8854	−	11.0797i	0.990674	−	0.441076i	0.153580	−	0.988136i	$-0.450920\pi$
$631$	24.8854	−	11.0797i	0.990674	−	0.441076i	0.837094	+	0.547060i	$0.184253\pi$
$632$	−4.59418	+	0.976523i	−0.182747	+	0.0388440i
$633$	47.2869	+	10.0511i	1.87948	+	0.399497i
$634$	3.44815	+	1.53521i	0.136943	+	0.0609711i
$635$	0.108238	+	0.333122i	0.00429529	+	0.0132195i
$636$	−8.35006	−	25.6988i	−0.331101	−	1.01903i
$637$	−15.3024	−	6.81305i	−0.606302	−	0.269943i
$638$	−2.64038	−	0.561229i	−0.104533	−	0.0222193i
$639$	−8.81516	+	1.87372i	−0.348722	+	0.0741232i
$640$	−26.0030	+	11.5773i	−1.02786	+	0.457632i
$641$	27.5736	+	30.6236i	1.08909	+	1.20956i	0.976409	+	0.215928i	$0.0692775\pi$
$641$	27.5736	+	30.6236i	1.08909	+	1.20956i	0.112682	+	0.993631i	$0.464056\pi$
$642$	−1.29148	−	12.2876i	−0.0509706	−	0.484953i
$643$	24.9278	−	18.1111i	0.983055	−	0.714232i	0.0246661	−	0.999696i	$-0.492148\pi$
$643$	24.9278	−	18.1111i	0.983055	−	0.714232i	0.958389	+	0.285464i	$0.0921478\pi$
$644$	0.0938629	−	0.893046i	0.00369872	−	0.0351909i
$645$	−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	$-0.356078\pi$
$647$	−7.21333	−	5.24079i	−0.283585	−	0.206037i	−0.720480	+	0.693476i	$0.756078\pi$
$648$	−3.40538	+	3.78206i	−0.133776	+	0.148573i
$649$	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	−0.372044	−	0.928215i	$-0.621343\pi$
$653$	12.1263	−	37.3208i	0.474537	−	1.46047i	0.846581	−	0.532260i	$-0.178657\pi$
$654$	0.430063	−	0.477634i	0.0168168	−	0.0186770i
$655$	−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
$658$	−0.316504	+	3.01133i	−0.0123386	+	0.117394i
$659$	−26.6600	+	19.3696i	−1.03853	+	0.754533i	−0.969997	−	0.243117i	$-0.921830\pi$
$659$	−26.6600	+	19.3696i	−1.03853	+	0.754533i	−0.0685280	+	0.997649i	$0.521830\pi$
$660$	4.10255	+	39.0332i	0.159692	+	1.51936i
$661$	−0.113535	−	0.126093i	−0.00441599	−	0.00490446i	0.740933	−	0.671579i	$-0.234384\pi$
$661$	−0.113535	−	0.126093i	−0.00441599	−	0.00490446i	−0.745349	+	0.666675i	$0.767717\pi$
$662$	6.30786	−	2.80844i	0.245162	−	0.109153i
$663$	−14.8401	+	3.15437i	−0.576343	+	0.122505i
$664$	17.1282	+	3.64070i	0.664702	+	0.141287i
$665$	−6.22613	−	2.77205i	−0.241439	−	0.107496i
$666$	1.83549	+	5.64907i	0.0711240	+	0.218897i
$667$	0.431703	+	1.32864i	0.0167156	+	0.0514453i
$668$	22.8939	+	10.1930i	0.885791	+	0.394379i
$669$	−17.7206	−	3.76664i	−0.685120	−	0.145627i
$670$	6.57957	−	1.39853i	0.254191	−	0.0540300i
$671$	32.0628	−	14.2753i	1.23777	−	0.551092i
$672$	8.11874	+	9.01678i	0.313187	+	0.347830i
$673$	1.52469	+	14.5064i	0.0587724	+	0.559182i	0.983798	+	0.179278i	$0.0573763\pi$
$673$	1.52469	+	14.5064i	0.0587724	+	0.559182i	−0.925026	+	0.379904i	$0.875957\pi$
$674$	−5.45280	+	3.96169i	−0.210034	+	0.152599i
$675$	2.75376	−	26.2003i	0.105992	−	1.00845i
$676$	−4.44929	−	7.70639i	−0.171126	−	0.296400i
$677$	−7.88341	+	13.6545i	−0.302984	+	0.524784i	−0.976810	−	0.214106i	$-0.931316\pi$
$677$	−7.88341	+	13.6545i	−0.302984	+	0.524784i	0.673826	+	0.738890i	$0.264650\pi$
$678$	−9.29573	−	6.75374i	−0.357000	−	0.259376i
$679$	−2.47120	+	2.74454i	−0.0948358	+	0.105326i
$680$	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
$685$	23.4866	−	26.0846i	0.897378	−	0.996640i
$686$	−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
$689$	1.49498	−	14.2238i	0.0569543	−	0.541884i
$690$	−1.08157	+	0.785806i	−0.0411746	+	0.0299151i
$691$	0.622123	+	5.91911i	0.0236667	+	0.225173i	0.999962	+	0.00873020i	$0.00277894\pi$
$691$	0.622123	+	5.91911i	0.0236667	+	0.225173i	−0.976295	+	0.216443i	$0.930554\pi$
$692$	−23.9130	−	26.5580i	−0.909034	−	1.00958i
$693$	12.9100	−	5.74789i	0.490409	−	0.218344i
$694$	−3.66439	+	0.778890i	−0.139098	+	0.0295663i
$695$	44.8512	+	9.53341i	1.70130	+	0.361623i
$696$	−11.3755	−	5.06471i	−0.431189	−	0.191978i
$697$	3.91687	+	12.0549i	0.148362	+	0.456611i
$698$	−2.03096	−	6.25066i	−0.0768731	−	0.236591i
$699$	−33.6142	−	14.9660i	−1.27141	−	0.566067i
$700$	−7.62731	−	1.62124i	−0.288285	−	0.0612770i
$701$	26.0485	−	5.53677i	0.983837	−	0.209121i	0.312212	−	0.950012i	$-0.398930\pi$
$701$	26.0485	−	5.53677i	0.983837	−	0.209121i	0.671625	+	0.740891i	$0.265597\pi$
$702$	−6.32930	+	2.81798i	−0.238884	+	0.106358i
$703$	4.46021	+	4.95357i	0.168220	+	0.186827i
$704$	−1.31814	−	12.5413i	−0.0496794	−	0.472668i
$705$	−55.4120	+	40.2591i	−2.08693	+	1.51625i
$706$	0.465144	−	4.42555i	0.0175059	−	0.166558i
$707$	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	$-0.284197\pi$
$709$	2.13805	+	1.55338i	0.0802962	+	0.0583386i	−0.546913	+	0.837189i	$0.684197\pi$
$710$	1.17312	−	1.30288i	0.0440262	−	0.0488961i
$711$	−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
$716$	0.0996083	−	0.110626i	0.00372254	−	0.00413430i
$717$	−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	0.813482	−	0.581590i	$-0.197569\pi$
$719$	−2.59912	−	4.50181i	−0.0969308	−	0.167889i	−0.910413	+	0.413701i	$0.864236\pi$
$720$	−5.46560	+	52.0017i	−0.203691	+	1.93799i
$721$	7.06832	−	5.13543i	0.263238	−	0.191253i
$722$	0.533128	+	5.07237i	0.0198410	+	0.188774i
$723$	−4.57084	−	5.07643i	−0.169991	−	0.188794i
$724$	−3.70770	+	1.65077i	−0.137796	+	0.0613505i
$725$	11.8663	−	2.52226i	0.440703	−	0.0936742i
$726$	−5.06085	−	1.07572i	−0.187826	−	0.0399236i
$727$	22.1137	+	9.84565i	0.820151	+	0.365155i	0.773531	−	0.633758i	$-0.218488\pi$
$727$	22.1137	+	9.84565i	0.820151	+	0.365155i	0.0466196	+	0.998913i	$0.485155\pi$
$728$	1.30911	+	4.02902i	0.0485188	+	0.149325i
$729$	−12.2007	−	37.5499i	−0.451878	−	1.39074i
$730$	13.7076	+	6.10300i	0.507339	+	0.225882i
$731$	−15.0152	−	3.19157i	−0.555356	−	0.118045i
$732$	76.6593	−	16.2944i	2.83341	−	0.602260i
$733$	36.8732	−	16.4170i	1.36194	−	0.606376i	0.409841	−	0.912157i	$-0.365584\pi$
$733$	36.8732	−	16.4170i	1.36194	−	0.606376i	0.952102	+	0.305781i	$0.0989174\pi$
$734$	2.05047	+	2.27728i	0.0756843	+	0.0840559i
$735$	−5.24143	−	49.8689i	−0.193333	−	1.83944i
$736$	1.38644	−	1.00730i	0.0511047	−	0.0371297i
$737$	−1.63610	+	15.5664i	−0.0602664	+	0.573396i
$738$	6.55583	+	11.3550i	0.241324	+	0.417985i
$739$	−3.04893	+	5.28089i	−0.112157	+	0.194261i	−0.916640	−	0.399715i	$-0.869109\pi$
$739$	−3.04893	+	5.28089i	−0.112157	+	0.194261i	0.804483	+	0.593976i	$0.202442\pi$
$740$	14.2035	+	10.3195i	0.522132	+	0.379351i
$741$	−11.7847	+	13.0883i	−0.432923	+	0.480809i
$742$	0.584884	−	1.80009i	0.0214718	−	0.0660833i
$743$	16.2263			0.595284			0.297642	−	0.954678i	$-0.403800\pi$
$743$	16.2263			0.595284			0.297642	+	0.954678i	$0.403800\pi$
$744$		0			0
$745$	−35.5308			−1.30175
$746$	2.75986	−	8.49397i	0.101046	−	0.310986i
$747$	46.1958	−	51.3056i	1.69022	−	1.87717i
$748$	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
$751$	−3.80948	+	36.2448i	−0.139010	+	1.32259i	0.673301	+	0.739368i	$0.264876\pi$
$751$	−3.80948	+	36.2448i	−0.139010	+	1.32259i	−0.812311	+	0.583224i	$0.801791\pi$
$752$	21.0907	−	15.3233i	0.769099	−	0.558783i
$753$	0.712721	+	6.78109i	0.0259730	+	0.247116i
$754$	−2.13479	−	2.37093i	−0.0777445	−	0.0863440i
$755$	−11.7397	+	5.22684i	−0.427251	+	0.190224i
$756$	13.6263	−	2.89637i	0.495585	−	0.105340i
$757$	−42.6103	−	9.05709i	−1.54870	−	0.329186i	−0.647319	−	0.762220i	$-0.724110\pi$
$757$	−42.6103	−	9.05709i	−1.54870	−	0.329186i	−0.901378	+	0.433034i	$0.857443\pi$
$758$	7.09451	+	3.15868i	0.257684	+	0.114728i
$759$	−0.961302	−	2.95858i	−0.0348931	−	0.107390i
$760$	−2.65139	−	8.16015i	−0.0961761	−	0.296000i
$761$	3.01404	+	1.34194i	0.109259	+	0.0486452i	0.460638	−	0.887588i	$-0.347621\pi$
$761$	3.01404	+	1.34194i	0.109259	+	0.0486452i	−0.351379	+	0.936233i	$0.614287\pi$
$762$	0.117167	+	0.0249047i	0.00424452	+	0.000902202i
$763$	−0.669067	+	0.142215i	−0.0242218	+	0.00514851i
$764$	9.15707	−	4.07699i	0.331291	−	0.147500i
$765$	−19.4990	−	21.6558i	−0.704988	−	0.782969i
$766$	0.978709	+	9.31179i	0.0353622	+	0.336449i
$767$	27.9304	−	20.2926i	1.00851	−	0.732724i
$768$	2.11965	−	20.1671i	0.0764861	−	0.727717i
$769$	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
$772$	2.67909	−	2.97543i	0.0964225	−	0.107088i
$773$	9.27071	−	28.5323i	0.333444	−	1.02624i	−0.634039	−	0.773301i	$-0.718604\pi$
$773$	9.27071	−	28.5323i	0.333444	−	1.02624i	0.967483	−	0.252935i	$-0.0813959\pi$
$774$	−15.8791			−0.570764
$775$		0			0
$776$	−4.64943			−0.166905
$777$	3.04449	−	9.36998i	0.109221	−	0.336146i
$778$	−3.04644	+	3.38341i	−0.109220	+	0.121301i
$779$	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
$782$	−0.0296427	+	0.282031i	−0.00106002	+	0.0100854i
$783$	−17.5338	+	12.7390i	−0.626605	+	0.455256i
$784$	1.99497	+	18.9809i	0.0712491	+	0.677890i
$785$	−17.3173	−	19.2328i	−0.618081	−	0.686448i
$786$	−5.37266	+	2.39206i	−0.191636	+	0.0853220i
$787$	42.2873	−	8.98843i	1.50738	−	0.320403i	0.621164	−	0.783680i	$-0.286660\pi$
$787$	42.2873	−	8.98843i	1.50738	−	0.320403i	0.886213	+	0.463277i	$0.153327\pi$
$788$	−10.7848	−	2.29239i	−0.384194	−	0.0816629i
$789$	−60.6222	−	26.9907i	−2.15821	−	0.960895i
$790$	−1.11320	−	3.42609i	−0.0396061	−	0.121895i
$791$	3.77878	+	11.6299i	0.134358	+	0.413511i
$792$	16.2528	+	7.23622i	0.577519	+	0.257128i
$793$	40.5751	+	8.62450i	1.44086	+	0.306265i
$794$	1.00625	−	0.213885i	0.0357106	−	0.00759051i
$795$	39.1128	−	17.4141i	1.38719	−	0.617615i
$796$	−8.69889	−	9.66110i	−0.308324	−	0.342429i
$797$	−2.38573	−	22.6987i	−0.0845069	−	0.804030i	−0.951901	−	0.306407i	$-0.900873\pi$
$797$	−2.38573	−	22.6987i	−0.0845069	−	0.804030i	0.867394	−	0.497623i	$-0.165794\pi$
$798$	−1.88561	+	1.36998i	−0.0667498	+	0.0484966i
$799$	−1.51868	+	14.4493i	−0.0537271	+	0.511179i
$800$	−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
$803$	−23.3626	+	25.9468i	−0.824449	+	0.915643i
$804$	−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
$809$	−14.2113	+	15.7832i	−0.499642	+	0.554908i	−0.939229	−	0.343291i	$-0.888458\pi$
$809$	−14.2113	+	15.7832i	−0.499642	+	0.554908i	0.439587	+	0.898200i	$0.355125\pi$
$810$	−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
$813$	2.19157	−	20.8514i	0.0768617	−	0.731291i
$814$	2.17527	−	1.58043i	0.0762431	−	0.0553939i
$815$	−0.972112	−	9.24903i	−0.0340516	−	0.323979i
$816$	11.5669	+	12.8464i	0.404924	+	0.449714i
$817$	−16.2791	+	7.24793i	−0.569535	+	0.253573i
$818$	5.91160	−	1.25655i	0.206694	−	0.0439342i
$819$	16.3374	+	3.47262i	0.570875	+	0.121343i
$820$	35.4043	+	15.7630i	1.23637	+	0.550468i
$821$	12.9144	+	39.7465i	0.450716	+	1.38716i	0.876092	+	0.482144i	$0.160142\pi$
$821$	12.9144	+	39.7465i	0.450716	+	1.38716i	−0.425376	+	0.905017i	$0.639858\pi$
$822$	−3.70935	−	11.4162i	−0.129379	−	0.398186i
$823$	14.8894	+	6.62920i	0.519013	+	0.231079i	0.649487	−	0.760372i	$-0.274984\pi$
$823$	14.8894	+	6.62920i	0.519013	+	0.231079i	−0.130475	+	0.991452i	$0.541650\pi$
$824$	10.7589	+	2.28687i	0.374802	+	0.0796667i
$825$	−26.4235	+	5.61648i	−0.919947	+	0.195541i
$826$	4.17383	−	1.85831i	0.145226	−	0.0646589i
$827$	−20.8029	−	23.1040i	−0.723389	−	0.803405i	0.263525	−	0.964653i	$-0.415115\pi$
$827$	−20.8029	−	23.1040i	−0.723389	−	0.803405i	−0.986914	+	0.161247i	$0.948448\pi$
$828$	−0.465889	−	4.43264i	−0.0161908	−	0.154045i
$829$	22.6920	−	16.4867i	0.788125	−	0.572606i	−0.119282	−	0.992860i	$-0.538059\pi$
$829$	22.6920	−	16.4867i	0.788125	−	0.572606i	0.907406	+	0.420254i	$0.138059\pi$
$830$	−1.40388	+	13.3570i	−0.0487294	+	0.463629i
$831$	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
$834$	10.4927	−	11.6533i	0.363331	−	0.403520i
$835$	−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	0.749359	+	0.662164i	$0.230362\pi$
$839$	−7.12828	+	21.9386i	−0.246096	+	0.757404i	−0.995454	+	0.0952401i	$0.969638\pi$
$840$	−8.48576	+	9.42439i	−0.292786	+	0.325172i
$841$	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
$844$	3.27737	−	31.1821i	0.112812	−	1.07333i
$845$	11.4067	−	8.28743i	0.392401	−	0.285096i
$846$	1.57097	+	14.9468i	0.0540111	+	0.513881i
$847$	3.68445	+	4.09200i	0.126599	+	0.140603i
$848$	−14.8870	+	6.62810i	−0.511220	+	0.227610i
$849$	−13.3759	+	2.84314i	−0.459060	+	0.0975762i
$850$	2.40877	+	0.512000i	0.0826201	+	0.0175614i
$851$	−1.27124	−	0.565991i	−0.0435775	−	0.0194019i
$852$	2.81502	+	8.66374i	0.0964410	+	0.296815i
$853$	9.27697	+	28.5516i	0.317637	+	0.977587i	0.974655	+	0.223712i	$0.0718176\pi$
$853$	9.27697	+	28.5516i	0.317637	+	0.977587i	−0.657018	+	0.753875i	$0.728182\pi$
$854$	5.01500	+	2.23282i	0.171610	+	0.0764055i
$855$	−33.0888	−	7.03325i	−1.13161	−	0.240532i
$856$	−16.1921	+	3.44175i	−0.553436	+	0.117637i
$857$	−49.8681	+	22.2027i	−1.70346	+	0.758429i	−0.704656	+	0.709550i	$0.748898\pi$
$857$	−49.8681	+	22.2027i	−1.70346	+	0.758429i	−0.998805	+	0.0488799i	$0.984435\pi$
$858$	4.75368	+	5.27950i	0.162288	+	0.180239i
$859$	−0.975920	−	9.28526i	−0.0332980	−	0.316809i	−0.998475	−	0.0552105i	$-0.982417\pi$
$859$	−0.975920	−	9.28526i	−0.0332980	−	0.316809i	0.965177	−	0.261599i	$-0.0842496\pi$
$860$	−37.9710	+	27.5876i	−1.29480	+	0.940728i
$861$	2.27329	−	21.6289i	0.0774734	−	0.737110i
$862$	−5.33338	−	9.23768i	−0.181656	−	0.314637i
$863$	−6.65836	+	11.5326i	−0.226653	+	0.392575i	−0.956814	−	0.290700i	$-0.906112\pi$
$863$	−6.65836	+	11.5326i	−0.226653	+	0.392575i	0.730161	+	0.683275i	$0.239445\pi$
$864$	21.5087	+	15.6270i	0.731741	+	0.531641i
$865$	37.8891	−	42.0801i	1.28827	−	1.43077i
$866$	−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
$871$	−12.3785	+	13.7477i	−0.419430	+	0.465824i
$872$	−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
$875$	−0.390088	+	3.71144i	−0.0131874	+	0.125470i
$876$	−63.0749	+	45.8266i	−2.13110	+	1.54834i
$877$	4.44936	+	42.3329i	0.150244	+	1.42948i	0.766657	+	0.642056i	$0.221919\pi$
$877$	4.44936	+	42.3329i	0.150244	+	1.42948i	−0.616413	+	0.787423i	$0.711415\pi$
$878$	3.03822	+	3.37429i	0.102535	+	0.113877i
$879$	27.8823	−	12.4140i	0.940448	−	0.418714i
$880$	23.1522	−	4.92115i	0.780461	−	0.165892i
$881$	5.64698	+	1.20030i	0.190251	+	0.0404392i	0.302052	−	0.953291i	$-0.402328\pi$
$881$	5.64698	+	1.20030i	0.190251	+	0.0404392i	−0.111800	+	0.993731i	$0.535662\pi$
$882$	−10.0515	−	4.47524i	−0.338453	−	0.150689i
$883$	8.40436	+	25.8660i	0.282829	+	0.870459i	0.987041	+	0.160469i	$0.0513006\pi$
$883$	8.40436	+	25.8660i	0.282829	+	0.870459i	−0.704212	+	0.709990i	$0.748699\pi$
$884$	3.04068	+	9.35826i	0.102269	+	0.314752i
$885$	94.4140	+	42.0358i	3.17369	+	1.41302i
$886$	−8.16697	−	1.73594i	−0.274375	−	0.0583201i
$887$	7.21060	−	1.53266i	0.242108	−	0.0514617i	−0.0852592	−	0.996359i	$-0.527172\pi$
$887$	7.21060	−	1.53266i	0.242108	−	0.0514617i	0.327367	+	0.944897i	$0.393839\pi$
$888$	11.3309	−	5.04486i	0.380241	−	0.169294i
$889$	−0.0853015	−	0.0947369i	−0.00286092	−	0.00317737i
$890$	−0.246772	−	2.34787i	−0.00827180	−	0.0787009i
$891$	7.34822	−	5.33880i	0.246175	−	0.178856i
$892$	−1.22819	+	11.6854i	−0.0411228	+	0.391257i
$893$	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
$896$	6.93191	−	7.69867i	0.231579	−	0.257194i
$897$	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
$902$	3.97149	−	4.41079i	0.132236	−	0.146863i
$903$	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
$906$	−0.459374	+	4.37065i	−0.0152617	+	0.145205i
$907$	−13.3350	+	9.68848i	−0.442783	+	0.321701i	−0.786740	−	0.617285i	$-0.788233\pi$
$907$	−13.3350	+	9.68848i	−0.442783	+	0.321701i	0.343957	+	0.938985i	$0.388233\pi$
$908$	−1.53927	−	14.6452i	−0.0510824	−	0.486016i
$909$	63.6758	+	70.7192i	2.11199	+	2.34561i
$910$	−2.96833	+	1.32159i	−0.0983993	+	0.0438102i
$911$	−43.8279	+	9.31591i	−1.45208	+	0.308650i	−0.865365	−	0.501142i	$-0.832913\pi$
$911$	−43.8279	+	9.31591i	−1.45208	+	0.308650i	−0.586718	+	0.809792i	$0.699580\pi$
$912$	19.6285	+	4.17217i	0.649965	+	0.138154i
$913$	−28.5500	−	12.7113i	−0.944868	−	0.420682i
$914$	2.64350	+	8.13586i	0.0874393	+	0.269110i
$915$	38.3728	+	118.099i	1.26857	+	3.90425i
$916$	−21.8963	−	9.74884i	−0.723473	−	0.322111i
$917$	6.12219	+	1.30131i	0.202173	+	0.0429731i
$918$	−4.30331	+	0.914696i	−0.142030	+	0.0301895i
$919$	−9.46142	+	4.21250i	−0.312104	+	0.138957i	−0.556810	−	0.830640i	$-0.687975\pi$
$919$	−9.46142	+	4.21250i	−0.312104	+	0.138957i	0.244707	+	0.969597i	$0.421308\pi$
$920$	1.19855	+	1.33112i	0.0395149	+	0.0438857i
$921$	0.800990	+	7.62091i	0.0263935	+	0.251118i
$922$	10.9015	−	7.92041i	0.359022	−	0.260845i
$923$	−0.503997	+	4.79522i	−0.0165893	+	0.157836i
$924$	−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
$927$	29.0174	−	32.2270i	0.953055	−	1.05847i
$928$	−3.78319	+	11.6435i	−0.124189	+	0.382216i
$929$	44.0624			1.44564			0.722820	−	0.691037i	$-0.242846\pi$
$929$	44.0624			1.44564			0.722820	+	0.691037i	$0.242846\pi$
$930$		0			0
$931$	−12.3474			−0.404671
$932$	−7.37447	+	22.6963i	−0.241559	+	0.743441i
$933$	−10.6728	+	11.8533i	−0.349411	+	0.388061i
$934$	−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
$937$	3.61323	−	34.3776i	0.118039	−	1.12307i	−0.761806	−	0.647805i	$-0.775687\pi$
$937$	3.61323	−	34.3776i	0.118039	−	1.12307i	0.879845	−	0.475261i	$-0.157646\pi$
$938$	−1.98062	+	1.43900i	−0.0646694	+	0.0469851i
$939$	−8.06750	−	76.7571i	−0.263273	−	2.50487i
$940$	29.7243	+	33.0122i	0.969500	+	1.07674i
$941$	−20.2342	+	9.00884i	−0.659616	+	0.293680i	−0.709113	−	0.705094i	$-0.750905\pi$
$941$	−20.2342	+	9.00884i	−0.659616	+	0.293680i	0.0494979	+	0.998774i	$0.484238\pi$
$942$	−8.65724	+	1.84015i	−0.282068	+	0.0599554i
$943$	−3.00461	−	0.638650i	−0.0978436	−	0.0207973i
$944$	−35.9355	−	15.9995i	−1.16960	−	0.520740i
$945$	6.82084	+	20.9924i	0.221882	+	0.682882i
$946$	2.22123	+	6.83625i	0.0722185	+	0.222266i
$947$	−25.6547	−	11.4222i	−0.833665	−	0.371172i	−0.0549038	−	0.998492i	$-0.517485\pi$
$947$	−25.6547	−	11.4222i	−0.833665	−	0.371172i	−0.778762	+	0.627320i	$0.784152\pi$
$948$	18.3091	+	3.89172i	0.594651	+	0.126397i
$949$	−40.3644	+	8.57971i	−1.31028	+	0.278509i
$950$	2.61154	−	1.16273i	0.0847294	−	0.0377240i
$951$	−20.7930	−	23.0930i	−0.674259	−	0.748840i
$952$	0.281190	+	2.67535i	0.00911343	+	0.0867085i
$953$	−6.20254	+	4.50641i	−0.200920	+	0.145977i	−0.683696	−	0.729767i	$-0.739629\pi$
$953$	−6.20254	+	4.50641i	−0.200920	+	0.145977i	0.482776	+	0.875744i	$0.339629\pi$
$954$	0.981997	−	9.34308i	0.0317933	−	0.302493i
$955$	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
$958$	1.76957	−	1.96531i	0.0571722	−	0.0634962i
$959$	−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
$964$	−2.96450	+	3.29241i	−0.0954800	+	0.106041i
$965$	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	0.880518	−	0.474013i	$-0.157195\pi$
$967$	0.925182	+	1.60246i	0.0297518	+	0.0515317i	−0.850766	+	0.525545i	$0.823862\pi$
$968$	−0.724603	+	6.89414i	−0.0232896	+	0.221586i
$969$	−9.04772	+	6.57355i	−0.290654	+	0.211173i
$970$	−0.372755	−	3.54653i	−0.0119684	−	0.113872i
$971$	33.0360	+	36.6901i	1.06017	+	1.17744i	0.983597	+	0.180379i	$0.0577325\pi$
$971$	33.0360	+	36.6901i	1.06017	+	1.17744i	0.0765771	+	0.997064i	$0.475601\pi$
$972$	−16.7529	+	7.45889i	−0.537351	+	0.239244i
$973$	−16.3239	+	3.46974i	−0.523319	+	0.111235i
$974$	−8.60491	−	1.82903i	−0.275719	−	0.0586059i
$975$	−29.1675	−	12.9862i	−0.934106	−	0.415891i
$976$	−14.6053	−	44.9506i	−0.467505	−	1.43883i
$977$	−11.0079	−	33.8790i	−0.352175	−	1.08388i	−0.957629	−	0.288004i	$-0.907008\pi$
$977$	−11.0079	−	33.8790i	−0.352175	−	1.08388i	0.605454	−	0.795880i	$-0.292992\pi$
$978$	−2.90548	−	1.29360i	−0.0929069	−	0.0413648i
$979$	5.37336	+	1.14214i	0.171733	+	0.0365030i
$980$	−31.8108	+	6.76160i	−1.01616	+	0.215991i
$981$	−3.10159	+	1.38092i	−0.0990260	+	0.0440892i
$982$	−9.33798	−	10.3709i	−0.297987	−	0.330948i
$983$	0.667267	+	6.34862i	0.0212825	+	0.202490i	0.999996	−	0.00274063i	$-0.000872371\pi$
$983$	0.667267	+	6.34862i	0.0212825	+	0.202490i	−0.978714	+	0.205230i	$0.934206\pi$
$984$	22.1504	−	16.0932i	0.706127	−	0.513032i
$985$	1.82610	−	17.3742i	0.0581844	−	0.553588i
$986$	−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
$989$	2.48922	−	2.76456i	0.0791527	−	0.0879080i
$990$	−4.21668	+	12.9776i	−0.134015	+	0.412455i
$991$	−44.2919			−1.40698			−0.703489	−	0.710706i	$-0.748376\pi$
$991$	−44.2919			−1.40698			−0.703489	+	0.710706i	$0.748376\pi$
$992$		0			0
$993$	−56.8463			−1.80396
$994$	−0.197179	+	0.606856i	−0.00625415	+	0.0192483i
$995$	13.7830	−	15.3076i	0.436952	−	0.485284i
$996$	−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
$999$	2.25656	−	21.4697i	0.0713943	−	0.679271i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	31.18	even	15
31.2.g.a.28.2	yes	16	31.8	even	5
279.2.y.c.10.1		16	93.80	odd	30
279.2.y.c.28.1		16	93.8	odd	10
496.2.bg.c.289.1		16	124.111	odd	30
496.2.bg.c.369.1		16	124.39	odd	10
775.2.bl.a.276.1		16	155.39	even	10
775.2.bl.a.351.1		16	155.49	even	30
775.2.ck.a.524.2		32	155.132	odd	20
775.2.ck.a.524.3		32	155.8	odd	20
775.2.ck.a.599.2		32	155.18	odd	60
775.2.ck.a.599.3		32	155.142	odd	60
961.2.a.i.1.4		8	31.19	even	15
961.2.a.j.1.4		8	31.12	odd	30
961.2.c.i.439.4		16	31.21	odd	30
961.2.c.i.521.4		16	31.29	odd	10
961.2.c.j.439.4		16	31.10	even	15
961.2.c.j.521.4		16	31.2	even	5
961.2.d.n.374.3		16	31.3	odd	30
961.2.d.n.388.3		16	31.17	odd	30
961.2.d.o.374.3		16	31.28	even	15
961.2.d.o.388.3		16	31.14	even	15
961.2.d.p.531.2		16	31.7	even	15
961.2.d.p.628.2		16	31.25	even	3
961.2.d.q.531.2		16	31.24	odd	30
961.2.d.q.628.2		16	31.6	odd	6
961.2.g.j.235.2		16	31.22	odd	30
961.2.g.j.732.2		16	31.15	odd	10
961.2.g.k.235.2		16	31.9	even	15
961.2.g.k.732.2		16	31.16	even	5
961.2.g.l.338.2		16	31.23	odd	10
961.2.g.l.816.2		16	31.13	odd	30
961.2.g.m.448.1		16	31.30	odd	2
961.2.g.m.547.1		16	31.11	odd	30
961.2.g.n.844.1		16	31.27	odd	10
961.2.g.n.846.1		16	31.26	odd	6
961.2.g.s.448.1		16	1.1	even	1	trivial
961.2.g.s.547.1		16	31.20	even	15	inner
961.2.g.t.844.1		16	31.4	even	5
961.2.g.t.846.1		16	31.5	even	3
8649.2.a.be.1.5		8	93.74	even	30
8649.2.a.bf.1.5		8	93.50	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.108599 - 0.334232i) q^{2} +(-1.93599 + 2.15013i) q^{3} +(1.51812 + 1.10298i) q^{4} +(-1.48661 + 2.57489i) q^{5} +(0.508398 + 0.880572i) q^{6} +(0.113113 - 1.07620i) q^{7} +(1.10215 - 0.800755i) q^{8} +(-0.561437 - 5.34171i) q^{9} +(0.699168 + 0.776504i) q^{10} +(-2.22117 + 0.988927i) q^{11} +(-5.31061 + 1.12880i) q^{12} +(-2.81086 - 0.597466i) q^{13} +(-0.347416 - 0.154680i) q^{14} +(-2.65829 - 8.18139i) q^{15} +(1.01179 + 3.11397i) q^{16} +(-1.66701 - 0.742199i) q^{17} +(-1.84634 - 0.392453i) q^{18} +(-2.07198 + 0.440414i) q^{19} +(-5.09690 + 2.26929i) q^{20} +(2.09499 + 2.32672i) q^{21} +(0.0893157 + 0.849782i) q^{22} +(0.357760 - 0.259928i) q^{23} +(-0.412010 + 3.92002i) q^{24} +(-1.92005 - 3.32562i) q^{25} +(-0.504947 + 0.874594i) q^{26} +(5.55018 + 4.03244i) q^{27} +(1.35874 - 1.50903i) q^{28} +(-0.976227 + 3.00452i) q^{29} -3.02317 q^{30} +3.87532 q^{32} +(2.17383 - 6.69036i) q^{33} +(-0.429101 + 0.476565i) q^{34} +(2.60294 + 1.89115i) q^{35} +(5.03946 - 8.72860i) q^{36} +(-1.57338 - 2.72517i) q^{37} +(-0.0778141 + 0.740352i) q^{38} +(6.72642 - 4.88703i) q^{39} +(0.423394 + 4.02832i) q^{40} +(-4.64794 - 5.16206i) q^{41} +(1.00518 - 0.447533i) q^{42} +(8.22855 - 1.74903i) q^{43} +(-4.46275 - 0.948588i) q^{44} +(14.5890 + 6.49543i) q^{45} +(-0.0480240 - 0.147803i) q^{46} +(-2.46041 - 7.57236i) q^{47} +(-8.65428 - 3.85313i) q^{48} +(5.70163 + 1.21192i) q^{49} +(-1.32004 + 0.280584i) q^{50} +(4.82313 - 2.14740i) q^{51} +(-3.60822 - 4.00733i) q^{52} +(0.520238 + 4.94973i) q^{53} +(1.95051 - 1.41713i) q^{54} +(0.755639 - 7.18942i) q^{55} +(-0.737104 - 1.27670i) q^{56} +(3.06439 - 5.30768i) q^{57} +(0.898189 + 0.652573i) q^{58} +(-8.03889 + 8.92809i) q^{59} +(4.98828 - 15.3523i) q^{60} -14.4351 q^{61} -5.81225 q^{63} +(-1.60273 + 4.93269i) q^{64} +(5.71707 - 6.34945i) q^{65} +(-2.00006 - 1.45313i) q^{66} +(3.21879 - 5.57511i) q^{67} +(-1.71208 - 2.96541i) q^{68} +(-0.133740 + 1.27245i) q^{69} +(0.914757 - 0.664610i) q^{70} +(-0.175386 - 1.66868i) q^{71} +(-4.89619 - 5.43777i) q^{72} +(13.1187 - 5.84081i) q^{73} +(-1.08170 + 0.229923i) q^{74} +(10.8677 + 2.31001i) q^{75} +(-3.63128 - 1.61675i) q^{76} +(0.813039 + 2.50228i) q^{77} +(-0.902923 - 2.77891i) q^{78} +(-3.14958 - 1.40228i) q^{79} +(-9.52229 - 2.02403i) q^{80} +(-3.65408 + 0.776698i) q^{81} +(-2.23009 + 0.992898i) q^{82} +(8.60075 + 9.55210i) q^{83} +(0.614118 + 5.84295i) q^{84} +(4.38928 - 3.18900i) q^{85} +(0.309026 - 2.94019i) q^{86} +(-4.57015 - 7.91573i) q^{87} +(-1.65616 + 2.86855i) q^{88} +(-1.82788 - 1.32803i) q^{89} +(3.75533 - 4.17071i) q^{90} +(-0.960936 + 2.95746i) q^{91} +0.829816 q^{92} -2.79812 q^{94} +(1.94622 - 5.98986i) q^{95} +(-7.50258 + 8.33246i) q^{96} +(-2.76106 - 2.00603i) q^{97} +(1.02425 - 1.77405i) q^{98} +(6.52961 + 11.3096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} + 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} - 2 q^{11} - 20 q^{12} - 27 q^{13} - 6 q^{14} + 4 q^{15} - 2 q^{16} - 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 + 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 - 2 * q^11 - 20 * q^12 - 27 * q^13 - 6 * q^14 + 4 * q^15 - 2 * q^16 - 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 + 29 * q^21 + 4 * q^22 + 21 * q^23 - 25 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 40 * 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 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 - 51 * q^42 + 8 * q^43 + 4 * q^44 + 25 * q^45 - 16 * q^46 + 4 * q^47 - 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 + 24 * q^52 + 66 * q^53 + 39 * q^54 - 52 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 - 51 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 18 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 + 27 * q^73 + 28 * q^74 - 32 * q^75 + 18 * q^76 - 42 * q^77 + 15 * q^78 + 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 + 4 * q^83 - 27 * q^84 - 63 * q^85 + 34 * q^86 + 15 * q^87 - 17 * q^88 + 26 * q^89 + 57 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 - 62 * q^96 - 37 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more