LMFDB - Embedded newform 62.2.g.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(7,62)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("62.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.1
Root			$0.669131 + 0.743145i$ of defining polynomial
Character	$\chi$	$=$	62.9
Dual form			62.2.g.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.604528 + 0.128496i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.139886 + 0.242290i) q^{5} +(0.309017 - 0.535233i) q^{6} +(-0.309017 + 0.137583i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-2.39169 - 1.06485i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.604528 + 0.128496i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.139886 + 0.242290i) q^{5} +(0.309017 - 0.535233i) q^{6} +(-0.309017 + 0.137583i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-2.39169 - 1.06485i) q^{9} +(0.273659 - 0.0581680i) q^{10} +(-0.521852 + 4.96509i) q^{11} +(-0.413545 - 0.459289i) q^{12} +(1.05849 - 1.17557i) q^{13} +(0.0353579 + 0.336408i) q^{14} +(0.0534318 + 0.164446i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.0201074 + 0.191309i) q^{17} +(-1.75181 + 1.94558i) q^{18} +(-0.644943 - 0.716282i) q^{19} +(0.0292442 - 0.278240i) q^{20} +(-0.204489 + 0.0434654i) q^{21} +(4.56082 + 2.03061i) q^{22} +(-3.17886 + 2.30958i) q^{23} +(-0.564602 + 0.251377i) q^{24} +(2.46086 - 4.26234i) q^{25} +(-0.790943 - 1.36995i) q^{26} +(-2.80902 - 2.04087i) q^{27} +(0.330869 + 0.0703285i) q^{28} +(2.23781 - 6.88728i) q^{29} +0.172909 q^{30} +(4.79912 - 2.82284i) q^{31} +1.00000 q^{32} +(-0.953472 + 2.93448i) q^{33} +(0.188160 + 0.0399946i) q^{34} +(-0.0765624 - 0.0556258i) q^{35} +(1.30902 + 2.26728i) q^{36} +(3.82991 - 6.63361i) q^{37} +(-0.880523 + 0.392034i) q^{38} +(0.790943 - 0.574654i) q^{39} +(-0.255585 - 0.113794i) q^{40} +(-8.03519 + 1.70793i) q^{41} +(-0.0218524 + 0.207912i) q^{42} +(2.29535 + 2.54924i) q^{43} +(3.34060 - 3.71011i) q^{44} +(-0.0765624 - 0.728442i) q^{45} +(1.21422 + 3.73697i) q^{46} +(3.04965 + 9.38587i) q^{47} +(0.0646021 + 0.614648i) q^{48} +(-4.60735 + 5.11698i) q^{49} +(-3.29328 - 3.65756i) q^{50} +(-0.0124271 + 0.118236i) q^{51} +(-1.54732 + 0.328893i) q^{52} +(8.58862 + 3.82390i) q^{53} +(-2.80902 + 2.04087i) q^{54} +(-1.27599 + 0.568109i) q^{55} +(0.169131 - 0.292943i) q^{56} +(-0.297847 - 0.515886i) q^{57} +(-5.85867 - 4.25657i) q^{58} +(-10.8349 - 2.30303i) q^{59} +(0.0534318 - 0.164446i) q^{60} -1.36685 q^{61} +(-1.20167 - 5.43654i) q^{62} +0.885579 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.432897 + 0.0920152i) q^{65} +(2.49622 + 1.81361i) q^{66} +(3.29173 + 5.70145i) q^{67} +(0.0961816 - 0.166591i) q^{68} +(-2.21848 + 0.987732i) q^{69} +(-0.0765624 + 0.0556258i) q^{70} +(-5.22394 - 2.32585i) q^{71} +(2.56082 - 0.544320i) q^{72} +(-1.61899 + 15.4037i) q^{73} +(-5.12543 - 5.69236i) q^{74} +(2.03536 - 2.26049i) q^{75} +(0.100750 + 0.958572i) q^{76} +(-0.521852 - 1.60610i) q^{77} +(-0.302113 - 0.929809i) q^{78} +(-1.42695 - 13.5765i) q^{79} +(-0.187205 + 0.207912i) q^{80} +(3.81953 + 4.24202i) q^{81} +(-0.858670 + 8.16970i) q^{82} +(14.2291 - 3.02449i) q^{83} +(0.190983 + 0.0850311i) q^{84} +(-0.0435397 + 0.0316334i) q^{85} +(3.13377 - 1.39525i) q^{86} +(2.23781 - 3.87601i) q^{87} +(-2.49622 - 4.32358i) q^{88} +(4.00973 + 2.91324i) q^{89} +(-0.716449 - 0.152286i) q^{90} +(-0.165352 + 0.508902i) q^{91} +3.92928 q^{92} +(3.26393 - 1.08981i) q^{93} +9.86889 q^{94} +(0.0833294 - 0.256462i) q^{95} +(0.604528 + 0.128496i) q^{96} +(-9.83810 - 7.14780i) q^{97} +(3.44279 + 5.96309i) q^{98} +(6.53519 - 11.3193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - 4 q^{10} - 13 q^{11} + 3 q^{12} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + q^{18} - 3 q^{19} - 4 q^{20} + q^{21} + 17 q^{22} + 3 q^{23} - 2 q^{24} + q^{25} - 10 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 14 q^{30} + 11 q^{31} + 8 q^{32} - 2 q^{33} + 18 q^{34} + 16 q^{35} + 6 q^{36} + 6 q^{37} + 12 q^{38} + 10 q^{39} - 4 q^{40} - 19 q^{41} - 9 q^{42} - 26 q^{43} + 7 q^{44} + 16 q^{45} - 17 q^{46} + q^{47} - 2 q^{48} - 23 q^{49} - 19 q^{50} - 16 q^{51} + 17 q^{53} - 18 q^{54} + 7 q^{55} - 3 q^{56} + 6 q^{57} - 19 q^{58} + 8 q^{59} - 6 q^{60} + 48 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} - 30 q^{65} + 3 q^{66} + 12 q^{67} - 17 q^{68} - 7 q^{69} + 16 q^{70} + 9 q^{71} + q^{72} - 33 q^{73} - 19 q^{74} + 18 q^{75} - 18 q^{76} - 13 q^{77} - 10 q^{78} - 19 q^{79} + 11 q^{80} - 16 q^{81} + 21 q^{82} + 40 q^{83} + 6 q^{84} + 29 q^{85} + 19 q^{86} + 11 q^{87} - 3 q^{88} + 8 q^{89} + 11 q^{90} + 20 q^{91} + 28 q^{92} + 44 q^{93} + 26 q^{94} + 36 q^{95} + 3 q^{96} - 23 q^{97} + 17 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - 4 * q^10 - 13 * q^11 + 3 * q^12 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + q^18 - 3 * q^19 - 4 * q^20 + q^21 + 17 * q^22 + 3 * q^23 - 2 * q^24 + q^25 - 10 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 14 * q^30 + 11 * q^31 + 8 * q^32 - 2 * q^33 + 18 * q^34 + 16 * q^35 + 6 * q^36 + 6 * q^37 + 12 * q^38 + 10 * q^39 - 4 * q^40 - 19 * q^41 - 9 * q^42 - 26 * q^43 + 7 * q^44 + 16 * q^45 - 17 * q^46 + q^47 - 2 * q^48 - 23 * q^49 - 19 * q^50 - 16 * q^51 + 17 * q^53 - 18 * q^54 + 7 * q^55 - 3 * q^56 + 6 * q^57 - 19 * q^58 + 8 * q^59 - 6 * q^60 + 48 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 - 30 * q^65 + 3 * q^66 + 12 * q^67 - 17 * q^68 - 7 * q^69 + 16 * q^70 + 9 * q^71 + q^72 - 33 * q^73 - 19 * q^74 + 18 * q^75 - 18 * q^76 - 13 * q^77 - 10 * q^78 - 19 * q^79 + 11 * q^80 - 16 * q^81 + 21 * q^82 + 40 * q^83 + 6 * q^84 + 29 * q^85 + 19 * q^86 + 11 * q^87 - 3 * q^88 + 8 * q^89 + 11 * q^90 + 20 * q^91 + 28 * q^92 + 44 * q^93 + 26 * q^94 + 36 * q^95 + 3 * q^96 - 23 * q^97 + 17 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.604528	+	0.128496i	0.349025	+	0.0741875i	0.379088	−	0.925361i	$-0.376238\pi$
$3$	0.604528	+	0.128496i	0.349025	+	0.0741875i	−0.0300636	+	0.999548i	$0.509571\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.139886	+	0.242290i	0.0625591	+	0.108356i	0.895609	−	0.444843i	$-0.146740\pi$
$5$	0.139886	+	0.242290i	0.0625591	+	0.108356i	−0.833050	+	0.553198i	$0.813407\pi$
$6$	0.309017	−	0.535233i	0.126156	−	0.218508i
$7$	−0.309017	+	0.137583i	−0.116797	+	0.0520016i	−0.464303	−	0.885676i	$-0.653695\pi$
$7$	−0.309017	+	0.137583i	−0.116797	+	0.0520016i	0.347506	+	0.937678i	$0.387029\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−2.39169	−	1.06485i	−0.797231	−	0.354950i
$10$	0.273659	−	0.0581680i	0.0865386	−	0.0183943i
$11$	−0.521852	+	4.96509i	−0.157344	+	1.49703i	0.576154	+	0.817341i	$0.304553\pi$
$11$	−0.521852	+	4.96509i	−0.157344	+	1.49703i	−0.733499	+	0.679691i	$0.762114\pi$
$12$	−0.413545	−	0.459289i	−0.119380	−	0.132585i
$13$	1.05849	−	1.17557i	0.293572	−	0.326045i	−0.578257	−	0.815854i	$-0.696267\pi$
$13$	1.05849	−	1.17557i	0.293572	−	0.326045i	0.871829	+	0.489810i	$0.162934\pi$
$14$	0.0353579	+	0.336408i	0.00944980	+	0.0899089i
$15$	0.0534318	+	0.164446i	0.0137960	+	0.0424599i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.0201074	+	0.191309i	0.00487677	+	0.0463993i	0.996690	−	0.0813003i	$-0.0259073\pi$
$17$	0.0201074	+	0.191309i	0.00487677	+	0.0463993i	−0.991813	+	0.127700i	$0.959241\pi$
$18$	−1.75181	+	1.94558i	−0.412905	+	0.458577i
$19$	−0.644943	−	0.716282i	−0.147960	−	0.164326i	0.664609	−	0.747192i	$-0.268598\pi$
$19$	−0.644943	−	0.716282i	−0.147960	−	0.164326i	−0.812569	+	0.582865i	$0.801932\pi$
$20$	0.0292442	−	0.278240i	0.00653921	−	0.0622164i
$21$	−0.204489	+	0.0434654i	−0.0446231	+	0.00948492i
$22$	4.56082	+	2.03061i	0.972371	+	0.432927i
$23$	−3.17886	+	2.30958i	−0.662838	+	0.481580i	−0.867620	−	0.497228i	$-0.834351\pi$
$23$	−3.17886	+	2.30958i	−0.662838	+	0.481580i	0.204782	+	0.978808i	$0.434351\pi$
$24$	−0.564602	+	0.251377i	−0.115249	+	0.0513121i
$25$	2.46086	−	4.26234i	0.492173	−	0.852468i
$26$	−0.790943	−	1.36995i	−0.155117	−	0.268670i
$27$	−2.80902	−	2.04087i	−0.540596	−	0.392766i
$28$	0.330869	+	0.0703285i	0.0625284	+	0.0132908i
$29$	2.23781	−	6.88728i	0.415551	−	1.27894i	−0.496205	−	0.868205i	$-0.665274\pi$
$29$	2.23781	−	6.88728i	0.415551	−	1.27894i	0.911757	−	0.410731i	$-0.134726\pi$
$30$	0.172909			0.0315687
$31$	4.79912	−	2.82284i	0.861948	−	0.506996i
$31$	4.79912	−	2.82284i	0.861948	−	0.506996i
$32$	1.00000			0.176777
$33$	−0.953472	+	2.93448i	−0.165978	+	0.510828i
$34$	0.188160	+	0.0399946i	0.0322691	+	0.00685901i
$35$	−0.0765624	−	0.0556258i	−0.0129414	−	0.00940248i
$36$	1.30902	+	2.26728i	0.218169	+	0.377881i
$37$	3.82991	−	6.63361i	0.629634	−	1.09056i	−0.357991	−	0.933725i	$-0.616538\pi$
$37$	3.82991	−	6.63361i	0.629634	−	1.09056i	0.987625	−	0.156833i	$-0.0501285\pi$
$38$	−0.880523	+	0.392034i	−0.142840	+	0.0635963i
$39$	0.790943	−	0.574654i	0.126652	−	0.0920182i
$40$	−0.255585	−	0.113794i	−0.0404116	−	0.0179924i
$41$	−8.03519	+	1.70793i	−1.25489	+	0.266734i	−0.786944	−	0.617025i	$-0.788338\pi$
$41$	−8.03519	+	1.70793i	−1.25489	+	0.266734i	−0.467942	+	0.883759i	$0.655005\pi$
$42$	−0.0218524	+	0.207912i	−0.00337190	+	0.0320815i
$43$	2.29535	+	2.54924i	0.350037	+	0.388756i	0.892292	−	0.451458i	$-0.149096\pi$
$43$	2.29535	+	2.54924i	0.350037	+	0.388756i	−0.542255	+	0.840214i	$0.682429\pi$
$44$	3.34060	−	3.71011i	0.503614	−	0.559320i
$45$	−0.0765624	−	0.728442i	−0.0114132	−	0.108590i
$46$	1.21422	+	3.73697i	0.179026	+	0.550986i
$47$	3.04965	+	9.38587i	0.444838	+	1.36907i	0.882662	+	0.470009i	$0.155749\pi$
$47$	3.04965	+	9.38587i	0.444838	+	1.36907i	−0.437824	+	0.899061i	$0.644251\pi$
$48$	0.0646021	+	0.614648i	0.00932452	+	0.0887168i
$49$	−4.60735	+	5.11698i	−0.658193	+	0.730998i
$50$	−3.29328	−	3.65756i	−0.465740	−	0.517257i
$51$	−0.0124271	+	0.118236i	−0.00174014	+	0.0165563i
$52$	−1.54732	+	0.328893i	−0.214574	+	0.0456092i
$53$	8.58862	+	3.82390i	1.17974	+	0.525253i	0.900452	−	0.434955i	$-0.143236\pi$
$53$	8.58862	+	3.82390i	1.17974	+	0.525253i	0.279286	+	0.960208i	$0.409902\pi$
$54$	−2.80902	+	2.04087i	−0.382259	+	0.277727i
$55$	−1.27599	+	0.568109i	−0.172055	+	0.0766038i
$56$	0.169131	−	0.292943i	0.0226010	−	0.0391461i
$57$	−0.297847	−	0.515886i	−0.0394508	−	0.0683307i
$58$	−5.85867	−	4.25657i	−0.769281	−	0.558915i
$59$	−10.8349	−	2.30303i	−1.41058	−	0.299829i	−0.561234	−	0.827657i	$-0.689673\pi$
$59$	−10.8349	−	2.30303i	−1.41058	−	0.299829i	−0.849351	+	0.527828i	$0.823006\pi$
$60$	0.0534318	−	0.164446i	0.00689802	−	0.0212299i
$61$	−1.36685			−0.175007			−0.0875037	−	0.996164i	$-0.527889\pi$
$61$	−1.36685			−0.175007			−0.0875037	+	0.996164i	$0.527889\pi$
$62$	−1.20167	−	5.43654i	−0.152612	−	0.690442i
$63$	0.885579			0.111573
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.432897	+	0.0920152i	0.0536943	+	0.0114131i
$66$	2.49622	+	1.81361i	0.307264	+	0.223240i
$67$	3.29173	+	5.70145i	0.402149	+	0.696543i	0.993985	−	0.109516i	$-0.0349300\pi$
$67$	3.29173	+	5.70145i	0.402149	+	0.696543i	−0.591836	+	0.806058i	$0.701597\pi$
$68$	0.0961816	−	0.166591i	0.0116637	−	0.0202022i
$69$	−2.21848	+	0.987732i	−0.267074	+	0.118909i
$70$	−0.0765624	+	0.0556258i	−0.00915095	+	0.00664856i
$71$	−5.22394	−	2.32585i	−0.619968	−	0.276028i	0.0726214	−	0.997360i	$-0.476864\pi$
$71$	−5.22394	−	2.32585i	−0.619968	−	0.276028i	−0.692589	+	0.721332i	$0.743530\pi$
$72$	2.56082	−	0.544320i	0.301796	−	0.0641487i
$73$	−1.61899	+	15.4037i	−0.189488	+	1.80286i	0.325371	+	0.945586i	$0.394511\pi$
$73$	−1.61899	+	15.4037i	−0.189488	+	1.80286i	−0.514859	+	0.857275i	$0.672156\pi$
$74$	−5.12543	−	5.69236i	−0.595819	−	0.661724i
$75$	2.03536	−	2.26049i	0.235023	−	0.261019i
$76$	0.100750	+	0.958572i	0.0115568	+	0.109956i
$77$	−0.521852	−	1.60610i	−0.0594706	−	0.183032i
$78$	−0.302113	−	0.929809i	−0.0342076	−	0.105280i
$79$	−1.42695	−	13.5765i	−0.160544	−	1.52748i	−0.717279	−	0.696786i	$-0.754613\pi$
$79$	−1.42695	−	13.5765i	−0.160544	−	1.52748i	0.556734	−	0.830691i	$-0.312054\pi$
$80$	−0.187205	+	0.207912i	−0.0209301	+	0.0232452i
$81$	3.81953	+	4.24202i	0.424393	+	0.471336i
$82$	−0.858670	+	8.16970i	−0.0948243	+	0.902193i
$83$	14.2291	−	3.02449i	1.56185	−	0.331981i	0.655726	−	0.754999i	$-0.272363\pi$
$83$	14.2291	−	3.02449i	1.56185	−	0.331981i	0.906121	+	0.423018i	$0.139029\pi$
$84$	0.190983	+	0.0850311i	0.0208380	+	0.00927765i
$85$	−0.0435397	+	0.0316334i	−0.00472254	+	0.00343113i
$86$	3.13377	−	1.39525i	0.337923	−	0.150453i
$87$	2.23781	−	3.87601i	0.239919	−	0.415551i
$88$	−2.49622	−	4.32358i	−0.266098	−	0.460895i
$89$	4.00973	+	2.91324i	0.425030	+	0.308803i	0.779659	−	0.626205i	$-0.215393\pi$
$89$	4.00973	+	2.91324i	0.425030	+	0.308803i	−0.354628	+	0.935007i	$0.615393\pi$
$90$	−0.716449	−	0.152286i	−0.0755203	−	0.0160523i
$91$	−0.165352	+	0.508902i	−0.0173336	+	0.0533474i
$92$	3.92928			0.409656
$93$	3.26393	−	1.08981i	0.338454	−	0.113008i
$94$	9.86889			1.01790
$95$	0.0833294	−	0.256462i	0.00854942	−	0.0263124i
$96$	0.604528	+	0.128496i	0.0616994	+	0.0131146i
$97$	−9.83810	−	7.14780i	−0.998907	−	0.725749i	−0.0370537	−	0.999313i	$-0.511797\pi$
$97$	−9.83810	−	7.14780i	−0.998907	−	0.725749i	−0.961854	+	0.273565i	$0.911797\pi$
$98$	3.44279	+	5.96309i	0.347774	+	0.602363i
$99$	6.53519	−	11.3193i	0.656812	−	1.13763i
$100$	−4.49622	+	2.00185i	−0.449622	+	0.200185i
$101$	3.93444	−	2.85854i	0.391492	−	0.284435i	−0.374575	−	0.927197i	$-0.622211\pi$
$101$	3.93444	−	2.85854i	0.391492	−	0.284435i	0.766066	+	0.642761i	$0.222211\pi$
$102$	0.108609	+	0.0483557i	0.0107539	+	0.00478793i
$103$	−7.30698	+	1.55315i	−0.719978	+	0.153036i	−0.553308	−	0.832977i	$-0.686635\pi$
$103$	−7.30698	+	1.55315i	−0.719978	+	0.153036i	−0.166670	+	0.986013i	$0.553302\pi$
$104$	−0.165352	+	1.57322i	−0.0162141	+	0.154267i
$105$	−0.0391364	−	0.0434654i	−0.00381932	−	0.00424179i
$106$	6.29078	−	6.98662i	0.611014	−	0.678600i
$107$	−0.290255	−	2.76159i	−0.0280600	−	0.266973i	−0.999553	−	0.0299041i	$-0.990480\pi$
$107$	−0.290255	−	2.76159i	−0.0280600	−	0.266973i	0.971493	−	0.237069i	$-0.0761868\pi$
$108$	1.07295	+	3.30220i	0.103245	+	0.317754i
$109$	1.17417	+	3.61371i	0.112465	+	0.346131i	0.991410	−	0.130792i	$-0.0417521\pi$
$109$	1.17417	+	3.61371i	0.112465	+	0.346131i	−0.878945	+	0.476923i	$0.841752\pi$
$110$	0.146000	+	1.38910i	0.0139206	+	0.132445i
$111$	3.16769	−	3.51807i	0.300664	−	0.333921i
$112$	−0.226341	−	0.251377i	−0.0213872	−	0.0237529i
$113$	−0.502398	+	4.78000i	−0.0472617	+	0.449665i	0.945144	+	0.326655i	$0.105921\pi$
$113$	−0.502398	+	4.78000i	−0.0472617	+	0.449665i	−0.992405	+	0.123010i	$0.960745\pi$
$114$	−0.582676	+	0.123852i	−0.0545726	+	0.0115998i
$115$	−1.00427	−	0.447128i	−0.0936484	−	0.0416949i
$116$	−5.85867	+	4.25657i	−0.543964	+	0.395213i
$117$	−3.78339	+	1.68447i	−0.349774	+	0.155729i
$118$	−5.53848	+	9.59293i	−0.509859	+	0.883101i
$119$	−0.0325345	−	0.0563514i	−0.00298243	−	0.00516573i
$120$	−0.139886	−	0.101633i	−0.0127698	−	0.00927782i
$121$	−13.6202	−	2.89506i	−1.23820	−	0.263188i
$122$	−0.422381	+	1.29995i	−0.0382405	+	0.117692i
$123$	−5.07697			−0.457775
$124$	−5.54179	−	0.537133i	−0.497668	−	0.0482359i
$125$	2.77583			0.248278
$126$	0.273659	−	0.842236i	0.0243795	−	0.0750323i
$127$	−1.81911	−	0.386664i	−0.161420	−	0.0343108i	0.126493	−	0.991968i	$-0.459628\pi$
$127$	−1.81911	−	0.386664i	−0.161420	−	0.0343108i	−0.287913	+	0.957657i	$0.592961\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	1.06003	+	1.83603i	0.0933308	+	0.161654i
$130$	0.221284	−	0.383276i	0.0194079	−	0.0336155i
$131$	−12.6463	+	5.63048i	−1.10491	+	0.491937i	−0.876390	−	0.481602i	$-0.840055\pi$
$131$	−12.6463	+	5.63048i	−1.10491	+	0.491937i	−0.228519	+	0.973539i	$0.573388\pi$
$132$	2.49622	−	1.81361i	0.217268	−	0.157855i
$133$	0.297847	+	0.132610i	0.0258266	+	0.0114987i
$134$	6.43960	−	1.36878i	0.556297	−	0.118245i
$135$	0.101540	−	0.966088i	0.00873916	−	0.0831476i
$136$	−0.128716	−	0.142954i	−0.0110373	−	0.0122582i
$137$	−4.78466	+	5.31391i	−0.408781	+	0.453998i	−0.912018	−	0.410151i	$-0.865476\pi$
$137$	−4.78466	+	5.31391i	−0.408781	+	0.453998i	0.503236	+	0.864149i	$0.332143\pi$
$138$	0.253840	+	2.41513i	0.0216083	+	0.205589i
$139$	−2.03363	−	6.25886i	−0.172490	−	0.530869i	0.827020	−	0.562172i	$-0.190034\pi$
$139$	−2.03363	−	6.25886i	−0.172490	−	0.530869i	−0.999510	+	0.0313031i	$0.990034\pi$
$140$	0.0292442	+	0.0900044i	0.00247159	+	0.00760676i
$141$	0.637551	+	6.06589i	0.0536915	+	0.510840i
$142$	−3.82630	+	4.24954i	−0.321096	+	0.356613i
$143$	5.28444	+	5.86897i	0.441907	+	0.490788i
$144$	0.273659	−	2.60369i	0.0228049	−	0.216974i
$145$	1.98176	−	0.421236i	0.164576	−	0.0349818i
$146$	14.1494	+	6.29974i	1.17102	+	0.521370i
$147$	−3.44279	+	2.50133i	−0.283957	+	0.206306i
$148$	−6.99760	+	3.11553i	−0.575199	+	0.256095i
$149$	9.44321	−	16.3561i	0.773618	−	1.33995i	−0.161949	−	0.986799i	$-0.551778\pi$
$149$	9.44321	−	16.3561i	0.773618	−	1.33995i	0.935568	−	0.353147i	$-0.114889\pi$
$150$	−1.52090	−	2.63427i	−0.124181	−	0.215087i
$151$	0.179813	+	0.130642i	0.0146330	+	0.0106315i	0.595078	−	0.803668i	$-0.297121\pi$
$151$	0.179813	+	0.130642i	0.0146330	+	0.0106315i	−0.580445	+	0.814300i	$0.697121\pi$
$152$	0.942790	+	0.200396i	0.0764703	+	0.0162543i
$153$	0.155625	−	0.478965i	0.0125815	−	0.0387220i
$154$	−1.68875			−0.136083
$155$	1.35528	+	0.767905i	0.108859	+	0.0616796i
$156$	−0.977659			−0.0782754
$157$	−6.80855	+	20.9546i	−0.543381	+	1.67236i	0.181426	+	0.983405i	$0.441929\pi$
$157$	−6.80855	+	20.9546i	−0.543381	+	1.67236i	−0.724807	+	0.688952i	$0.758071\pi$
$158$	−13.3530	−	2.83826i	−1.06231	−	0.225800i
$159$	4.70071	+	3.41527i	0.372791	+	0.270848i
$160$	0.139886	+	0.242290i	0.0110590	+	0.0191547i
$161$	0.664562	−	1.15106i	0.0523748	−	0.0907159i
$162$	5.21470	−	2.32174i	0.409706	−	0.182413i
$163$	15.7260	−	11.4256i	1.23176	−	0.894923i	0.234736	−	0.972059i	$-0.424578\pi$
$163$	15.7260	−	11.4256i	1.23176	−	0.894923i	0.997021	+	0.0771360i	$0.0245776\pi$
$164$	7.50451	+	3.34122i	0.586003	+	0.260906i
$165$	−0.844375	+	0.179477i	−0.0657345	+	0.0139723i
$166$	1.52057	−	14.4673i	0.118019	−	1.12288i
$167$	1.45945	+	1.62088i	0.112936	+	0.125428i	0.796962	−	0.604030i	$-0.206439\pi$
$167$	1.45945	+	1.62088i	0.112936	+	0.125428i	−0.684026	+	0.729458i	$0.739773\pi$
$168$	0.139886	−	0.155360i	0.0107925	−	0.0119863i
$169$	1.09730	+	10.4401i	0.0844078	+	0.803087i
$170$	0.0166307	+	0.0511839i	0.00127551	+	0.00392563i
$171$	0.779773	+	2.39989i	0.0596307	+	0.183524i
$172$	−0.358568	−	3.41155i	−0.0273406	−	0.260128i
$173$	9.47227	−	10.5200i	0.720164	−	0.799823i	−0.266285	−	0.963894i	$-0.585796\pi$
$173$	9.47227	−	10.5200i	0.720164	−	0.799823i	0.986448	+	0.164072i	$0.0524629\pi$
$174$	−2.99478	−	3.32604i	−0.227034	−	0.252146i
$175$	−0.174022	+	1.65571i	−0.0131548	+	0.125160i
$176$	−4.88335	+	1.03799i	−0.368096	+	0.0782412i
$177$	−6.25408	−	2.78450i	−0.470085	−	0.209295i
$178$	4.00973	−	2.91324i	0.300542	−	0.218356i
$179$	−0.518074	+	0.230661i	−0.0387227	+	0.0172404i	−0.426007	−	0.904720i	$-0.640080\pi$
$179$	−0.518074	+	0.230661i	−0.0387227	+	0.0172404i	0.387284	+	0.921960i	$0.373413\pi$
$180$	−0.366227	+	0.634324i	−0.0272970	+	0.0472797i
$181$	−5.99856	−	10.3898i	−0.445869	−	0.772268i	0.552243	−	0.833683i	$-0.313772\pi$
$181$	−5.99856	−	10.3898i	−0.445869	−	0.772268i	−0.998112	+	0.0614150i	$0.980439\pi$
$182$	0.432897	+	0.314518i	0.0320885	+	0.0233137i
$183$	−0.826301	−	0.175636i	−0.0610819	−	0.0129834i
$184$	1.21422	−	3.73697i	0.0895132	−	0.275493i
$185$	2.14301			0.157557
$186$	−0.0278640	−	3.44095i	−0.00204309	−	0.252303i
$187$	−0.960362			−0.0702286
$188$	3.04965	−	9.38587i	0.222419	−	0.684535i
$189$	1.14882	+	0.244190i	0.0835646	+	0.0177622i
$190$	−0.218159	−	0.158502i	−0.0158269	−	0.0114989i
$191$	3.81826	+	6.61341i	0.276279	+	0.478530i	0.970457	−	0.241274i	$-0.0775652\pi$
$191$	3.81826	+	6.61341i	0.276279	+	0.478530i	−0.694178	+	0.719804i	$0.744232\pi$
$192$	0.309017	−	0.535233i	0.0223014	−	0.0386271i
$193$	15.0673	−	6.70838i	1.08457	−	0.482880i	0.214958	−	0.976623i	$-0.431039\pi$
$193$	15.0673	−	6.70838i	1.08457	−	0.482880i	0.869607	+	0.493744i	$0.164372\pi$
$194$	−9.83810	+	7.14780i	−0.706334	+	0.513182i
$195$	0.249875	+	0.111252i	0.0178939	+	0.00796689i
$196$	6.73511	−	1.43159i	0.481079	−	0.102257i
$197$	0.906052	−	8.62050i	0.0645535	−	0.614186i	−0.913645	−	0.406513i	$-0.866745\pi$
$197$	0.906052	−	8.62050i	0.0645535	−	0.614186i	0.978198	−	0.207672i	$-0.0665888\pi$
$198$	−8.74580	−	9.71319i	−0.621537	−	0.690286i
$199$	−8.14923	+	9.05063i	−0.577683	+	0.641582i	−0.959183	−	0.282787i	$-0.908741\pi$
$199$	−8.14923	+	9.05063i	−0.577683	+	0.641582i	0.381499	+	0.924369i	$0.375408\pi$
$200$	0.514461	+	4.89477i	0.0363779	+	0.346112i
$201$	1.25733	+	3.86966i	0.0886852	+	0.272945i
$202$	−1.50282	−	4.62521i	−0.105738	−	0.325429i
$203$	0.256052	+	2.43617i	0.0179713	+	0.170986i
$204$	0.0795509	−	0.0883502i	0.00556968	−	0.00618575i
$205$	−1.53783	−	1.70793i	−0.107407	−	0.119287i
$206$	−0.780851	+	7.42930i	−0.0544045	+	0.517624i
$207$	10.0622	−	2.13879i	0.699372	−	0.148656i
$208$	1.44512	+	0.643411i	0.100201	+	0.0446125i
$209$	3.89297	−	2.82841i	0.269282	−	0.195645i
$210$	−0.0534318	+	0.0237894i	−0.00368715	+	0.00164162i
$211$	−0.495330	+	0.857936i	−0.0340999	+	0.0590627i	−0.882572	−	0.470178i	$-0.844190\pi$
$211$	−0.495330	+	0.857936i	−0.0340999	+	0.0590627i	0.848472	+	0.529241i	$0.177523\pi$
$212$	−4.70071	−	8.14187i	−0.322846	−	0.559186i
$213$	−2.85916	−	2.07730i	−0.195906	−	0.142334i
$214$	−2.71613	−	0.577330i	−0.185671	−	0.0394655i
$215$	−0.296569	+	0.912744i	−0.0202258	+	0.0622486i
$216$	3.47214			0.236249
$217$	−1.09464	+	1.53258i	−0.0743088	+	0.104039i
$218$	3.79968			0.257347
$219$	−2.95804	+	9.10391i	−0.199886	+	0.615185i
$220$	1.36623	+	0.290401i	0.0921110	+	0.0195788i
$221$	0.246181	+	0.178861i	0.0165599	+	0.0120315i
$222$	−2.36702	−	4.09979i	−0.158864	−	0.275160i
$223$	−6.82817	+	11.8267i	−0.457248	+	0.791977i	−0.998814	−	0.0486812i	$-0.984498\pi$
$223$	−6.82817	+	11.8267i	−0.457248	+	0.791977i	0.541566	+	0.840658i	$0.317832\pi$
$224$	−0.309017	+	0.137583i	−0.0206471	+	0.00919267i
$225$	−10.4244	+	7.57376i	−0.694959	+	0.504917i
$226$	4.39080	+	1.95491i	0.292072	+	0.130039i
$227$	−5.58192	+	1.18647i	−0.370485	+	0.0787490i	−0.389392	−	0.921072i	$-0.627315\pi$
$227$	−5.58192	+	1.18647i	−0.370485	+	0.0787490i	0.0189067	+	0.999821i	$0.493981\pi$
$228$	−0.0622669	+	0.592430i	−0.00412373	+	0.0392346i
$229$	16.6628	+	18.5059i	1.10111	+	1.22290i	0.972917	+	0.231155i	$0.0742504\pi$
$229$	16.6628	+	18.5059i	1.10111	+	1.22290i	0.128191	+	0.991749i	$0.459083\pi$
$230$	−0.735580	+	0.816944i	−0.0485027	+	0.0538677i
$231$	−0.109097	−	1.03799i	−0.00717805	−	0.0682945i
$232$	2.23781	+	6.88728i	0.146920	+	0.452172i
$233$	−4.09823	−	12.6130i	−0.268484	−	0.826308i	−0.990870	−	0.134819i	$-0.956955\pi$
$233$	−4.09823	−	12.6130i	−0.268484	−	0.826308i	0.722386	−	0.691490i	$-0.243045\pi$
$234$	0.432897	+	4.11874i	0.0282994	+	0.269251i
$235$	−1.84750	+	2.05186i	−0.120518	+	0.133848i
$236$	7.41194	+	8.23179i	0.482476	+	0.535844i
$237$	0.881903	−	8.39075i	0.0572858	−	0.545038i
$238$	−0.0636471	+	0.0135286i	−0.00412563	+	0.000876929i
$239$	−19.1367	−	8.52022i	−1.23785	−	0.551127i	−0.319762	−	0.947498i	$-0.603603\pi$
$239$	−19.1367	−	8.52022i	−1.23785	−	0.551127i	−0.918091	+	0.396371i	$0.870270\pi$
$240$	−0.139886	+	0.101633i	−0.00902963	+	0.00656041i
$241$	9.95304	−	4.43138i	0.641132	−	0.285450i	−0.0603070	−	0.998180i	$-0.519208\pi$
$241$	9.95304	−	4.43138i	0.641132	−	0.285450i	0.701439	+	0.712730i	$0.252541\pi$
$242$	−6.96224	+	12.0590i	−0.447550	+	0.775179i
$243$	6.97214	+	12.0761i	0.447263	+	0.774682i
$244$	1.10581	+	0.803416i	0.0707920	+	0.0514334i
$245$	−1.88430	−	0.400521i	−0.120384	−	0.0255883i
$246$	−1.56887	+	4.82848i	−0.100027	+	0.307853i
$247$	−1.52470			−0.0970146
$248$	−2.22335	+	5.10458i	−0.141183	+	0.324141i
$249$	8.99053			0.569752
$250$	0.857778	−	2.63997i	0.0542507	−	0.166966i
$251$	−11.8564	−	2.52016i	−0.748372	−	0.159071i	−0.182089	−	0.983282i	$-0.558286\pi$
$251$	−11.8564	−	2.52016i	−0.748372	−	0.159071i	−0.566283	+	0.824211i	$0.691619\pi$
$252$	−0.716449	−	0.520530i	−0.0451320	−	0.0327903i
$253$	−9.80836	−	16.9886i	−0.616647	−	1.06806i
$254$	−0.929874	+	1.61059i	−0.0583455	+	0.101057i
$255$	−0.0303857	+	0.0135286i	−0.00190283	+	0.000847194i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−24.7189	−	11.0055i	−1.54192	−	0.686507i	−0.552759	−	0.833341i	$-0.686425\pi$
$257$	−24.7189	−	11.0055i	−1.54192	−	0.686507i	−0.989161	+	0.146834i	$0.953092\pi$
$258$	2.07374	−	0.440787i	0.129105	−	0.0274422i
$259$	−0.270836	+	2.57683i	−0.0168289	+	0.160116i
$260$	−0.296136	−	0.328893i	−0.0183656	−	0.0203971i
$261$	−12.6861	+	14.0893i	−0.785249	+	0.872107i
$262$	1.44699	+	13.7672i	0.0893955	+	0.850542i
$263$	−1.06753	−	3.28551i	−0.0658266	−	0.202593i	0.912733	−	0.408556i	$-0.133967\pi$
$263$	−1.06753	−	3.28551i	−0.0658266	−	0.202593i	−0.978560	+	0.205963i	$0.933967\pi$
$264$	−0.953472	−	2.93448i	−0.0586821	−	0.180605i
$265$	0.274937	+	2.61585i	0.0168893	+	0.160691i
$266$	0.218159	−	0.242290i	0.0133762	−	0.0148558i
$267$	2.04965	+	2.27637i	0.125437	+	0.139312i
$268$	0.688160	−	6.54740i	0.0420360	−	0.399946i
$269$	−7.61028	+	1.61761i	−0.464007	+	0.0986277i	−0.433982	−	0.900921i	$-0.642892\pi$
$269$	−7.61028	+	1.61761i	−0.464007	+	0.0986277i	−0.0300246	+	0.999549i	$0.509559\pi$
$270$	−0.887426	−	0.395108i	−0.0540070	−	0.0240455i
$271$	22.4095	−	16.2815i	1.36128	−	0.989030i	0.362920	−	0.931820i	$-0.381780\pi$
$271$	22.4095	−	16.2815i	1.36128	−	0.989030i	0.998362	−	0.0572095i	$-0.0182203\pi$
$272$	−0.175733	+	0.0782412i	−0.0106553	+	0.00474407i
$273$	−0.165352	+	0.286398i	−0.0100076	+	0.0173336i
$274$	3.57528	+	6.19257i	0.215991	+	0.374107i
$275$	19.8787	+	14.4427i	1.19873	+	0.870929i
$276$	2.37536	+	0.504899i	0.142980	+	0.0303914i
$277$	−1.74238	+	5.36250i	−0.104690	+	0.322201i	−0.989657	−	0.143451i	$-0.954180\pi$
$277$	−1.74238	+	5.36250i	−0.104690	+	0.322201i	0.884968	+	0.465652i	$0.154180\pi$
$278$	−6.58095			−0.394699
$279$	−14.4839	+	1.64101i	−0.867130	+	0.0982445i
$280$	0.0946363			0.00565560
$281$	6.79857	−	20.9239i	0.405569	−	1.24821i	−0.514850	−	0.857280i	$-0.672153\pi$
$281$	6.79857	−	20.9239i	0.405569	−	1.24821i	0.920419	−	0.390933i	$-0.127847\pi$
$282$	5.96602	+	1.26812i	0.355271	+	0.0755153i
$283$	−17.3497	−	12.6053i	−1.03133	−	0.749307i	−0.0627572	−	0.998029i	$-0.519989\pi$
$283$	−17.3497	−	12.6053i	−1.03133	−	0.749307i	−0.968575	+	0.248722i	$0.919989\pi$
$284$	2.85916	+	4.95221i	0.169660	+	0.293859i
$285$	0.0833294	−	0.144331i	0.00493601	−	0.00854942i
$286$	7.21470	−	3.21219i	0.426614	−	0.189941i
$287$	2.24803	−	1.63329i	0.132697	−	0.0964099i
$288$	−2.39169	−	1.06485i	−0.140932	−	0.0627469i
$289$	16.5923	−	3.52681i	0.976018	−	0.207459i
$290$	0.211778	−	2.01494i	0.0124360	−	0.118321i
$291$	−5.02894	−	5.58521i	−0.294802	−	0.327411i
$292$	10.3638	−	11.5102i	0.606497	−	0.673583i
$293$	−0.973681	−	9.26396i	−0.0568831	−	0.541206i	−0.985441	−	0.170018i	$-0.945617\pi$
$293$	−0.973681	−	9.26396i	−0.0568831	−	0.541206i	0.928558	−	0.371188i	$-0.121049\pi$
$294$	1.31503	+	4.04724i	0.0766940	+	0.236040i
$295$	−0.957654	−	2.94736i	−0.0557568	−	0.171602i
$296$	0.800670	+	7.61787i	0.0465380	+	0.442780i
$297$	11.5990	−	12.8820i	0.673043	−	0.747489i
$298$	−12.6375	−	14.0354i	−0.732070	−	0.813046i
$299$	−0.649715	+	6.18163i	−0.0375740	+	0.357493i
$300$	−2.97532	+	0.632425i	−0.171780	+	0.0365131i
$301$	−1.06003	−	0.471957i	−0.0610993	−	0.0272032i
$302$	0.179813	−	0.130642i	0.0103471	−	0.00751758i
$303$	2.74580	−	1.22251i	0.157742	−	0.0702312i
$304$	0.481926	−	0.834720i	0.0276404	−	0.0478745i
$305$	−0.191204	−	0.331175i	−0.0109483	−	0.0189630i
$306$	−0.407432	−	0.296016i	−0.0232913	−	0.0169221i
$307$	25.2442	+	5.36582i	1.44076	+	0.306243i	0.861026	−	0.508561i	$-0.169822\pi$
$307$	25.2442	+	5.36582i	1.44076	+	0.306243i	0.579736	+	0.814804i	$0.303156\pi$
$308$	−0.521852	+	1.60610i	−0.0297353	+	0.0915158i
$309$	−4.61685			−0.262644
$310$	1.14913	−	1.05165i	0.0652659	−	0.0597297i
$311$	−29.2234			−1.65711			−0.828553	−	0.559911i	$-0.810835\pi$
$311$	−29.2234			−1.65711			−0.828553	+	0.559911i	$0.810835\pi$
$312$	−0.302113	+	0.929809i	−0.0171038	+	0.0526401i
$313$	15.9274	+	3.38546i	0.900267	+	0.191358i	0.634722	−	0.772741i	$-0.281115\pi$
$313$	15.9274	+	3.38546i	0.900267	+	0.191358i	0.265545	+	0.964098i	$0.414448\pi$
$314$	17.8250	+	12.9506i	1.00592	+	0.730846i
$315$	0.123880	+	0.214567i	0.00697988	+	0.0120895i
$316$	−6.82565	+	11.8224i	−0.383973	+	0.665060i
$317$	19.2030	−	8.54973i	1.07855	−	0.480201i	0.210965	−	0.977494i	$-0.432339\pi$
$317$	19.2030	−	8.54973i	1.07855	−	0.480201i	0.867583	+	0.497293i	$0.165673\pi$
$318$	4.70071	−	3.41527i	0.263603	−	0.191519i
$319$	33.0282	+	14.7051i	1.84922	+	0.823327i
$320$	0.273659	−	0.0581680i	0.0152980	−	0.00325169i
$321$	0.179388	−	1.70676i	0.0100124	−	0.0952620i
$322$	−0.889358	−	0.987732i	−0.0495620	−	0.0550441i
$323$	0.124063	−	0.137786i	0.00690307	−	0.00766663i
$324$	−0.596670	−	5.67693i	−0.0331483	−	0.315385i
$325$	−2.40589	−	7.40456i	−0.133455	−	0.410731i
$326$	−6.00680	−	18.4870i	−0.332686	−	1.02390i
$327$	0.245468	+	2.33547i	0.0135744	+	0.129152i
$328$	5.49671	−	6.10471i	0.303505	−	0.337076i
$329$	−2.23373	−	2.48081i	−0.123150	−	0.136772i
$330$	−0.0902330	+	0.858510i	−0.00496716	+	0.0472594i
$331$	−0.853877	+	0.181497i	−0.0469333	+	0.00997598i	−0.231318	−	0.972878i	$-0.574304\pi$
$331$	−0.853877	+	0.181497i	−0.0469333	+	0.00997598i	0.184385	+	0.982854i	$0.440971\pi$
$332$	−13.2893	−	5.91679i	−0.729347	−	0.324726i
$333$	−16.2238	+	11.7873i	−0.889058	+	0.645938i
$334$	1.99255	−	0.887138i	0.109027	−	0.0485420i
$335$	−0.920937	+	1.59511i	−0.0503162	+	0.0871502i
$336$	−0.104528	−	0.181049i	−0.00570250	−	0.00987701i
$337$	−4.21628	−	3.06331i	−0.229676	−	0.166869i	0.466996	−	0.884260i	$-0.345336\pi$
$337$	−4.21628	−	3.06331i	−0.229676	−	0.166869i	−0.696671	+	0.717391i	$0.745336\pi$
$338$	10.2682	+	2.18258i	0.558518	+	0.118717i
$339$	−0.917927	+	2.82509i	−0.0498550	+	0.153438i
$340$	0.0538180			0.00291869
$341$	11.5112	+	25.3012i	0.623367	+	1.37014i
$342$	2.52340			0.136450
$343$	1.45144	−	4.46707i	0.0783703	−	0.241199i
$344$	−3.35538	−	0.713208i	−0.180910	−	0.0384536i
$345$	−0.549653	−	0.399347i	−0.0295923	−	0.0215001i
$346$	−7.07804	−	12.2595i	−0.380518	−	0.659077i
$347$	−2.38286	+	4.12723i	−0.127919	+	0.221561i	−0.922870	−	0.385112i	$-0.874163\pi$
$347$	−2.38286	+	4.12723i	−0.127919	+	0.221561i	0.794951	+	0.606673i	$0.207496\pi$
$348$	−4.08869	+	1.82040i	−0.219177	+	0.0975837i
$349$	−10.8414	+	7.87670i	−0.580324	+	0.421630i	−0.838841	−	0.544377i	$-0.816766\pi$
$349$	−10.8414	+	7.87670i	−0.580324	+	0.421630i	0.258517	+	0.966007i	$0.416766\pi$
$350$	1.52090	+	0.677147i	0.0812954	+	0.0361950i
$351$	−5.37250	+	1.14196i	−0.286763	+	0.0609533i
$352$	−0.521852	+	4.96509i	−0.0278148	+	0.264640i
$353$	7.59887	+	8.43941i	0.404447	+	0.449184i	0.910618	−	0.413249i	$-0.135606\pi$
$353$	7.59887	+	8.43941i	0.404447	+	0.449184i	−0.506171	+	0.862433i	$0.668939\pi$
$354$	−4.58083	+	5.08753i	−0.243468	+	0.270399i
$355$	−0.167228	−	1.59107i	−0.00887553	−	0.0844450i
$356$	−1.53158	−	4.71372i	−0.0811735	−	0.249826i
$357$	−0.0124271	−	0.0382466i	−0.000657710	−	0.00202422i
$358$	0.0592784	+	0.563996i	0.00313296	+	0.0298081i
$359$	−13.4619	+	14.9509i	−0.710490	+	0.789079i	−0.985009	−	0.172503i	$-0.944815\pi$
$359$	−13.4619	+	14.9509i	−0.710490	+	0.789079i	0.274519	+	0.961582i	$0.411481\pi$
$360$	0.490108	+	0.544320i	0.0258309	+	0.0286882i
$361$	1.88893	−	17.9720i	0.0994175	−	0.945894i
$362$	−11.7349	+	2.49434i	−0.616775	+	0.131100i
$363$	−7.86180	−	3.50030i	−0.412637	−	0.183718i
$364$	0.432897	−	0.314518i	0.0226900	−	0.0164852i
$365$	−3.95863	+	1.76250i	−0.207204	+	0.0922532i
$366$	−0.422381	+	0.731585i	−0.0220782	+	0.0382405i
$367$	10.5270	+	18.2334i	0.549507	+	0.951775i	0.998308	+	0.0581428i	$0.0185179\pi$
$367$	10.5270	+	18.2334i	0.549507	+	0.951775i	−0.448801	+	0.893632i	$0.648149\pi$
$368$	−3.17886	−	2.30958i	−0.165709	−	0.120395i
$369$	21.0364	+	4.47143i	1.09511	+	0.232773i
$370$	0.662227	−	2.03813i	0.0344275	−	0.105957i
$371$	−3.18014			−0.165104
$372$	−3.28115	−	1.03681i	−0.170120	−	0.0537563i
$373$	−27.0380			−1.39997			−0.699987	−	0.714156i	$-0.746811\pi$
$373$	−27.0380			−1.39997			−0.699987	+	0.714156i	$0.746811\pi$
$374$	−0.296768	+	0.913359i	−0.0153455	+	0.0472287i
$375$	1.67807	+	0.356684i	0.0866550	+	0.0184191i
$376$	−7.98410	−	5.80079i	−0.411748	−	0.299153i
$377$	−5.72778	−	9.92081i	−0.294996	−	0.510948i
$378$	0.587244	−	1.01714i	0.0302046	−	0.0523159i
$379$	−22.6768	+	10.0964i	−1.16483	+	0.518616i	−0.895775	−	0.444508i	$-0.853378\pi$
$379$	−22.6768	+	10.0964i	−1.16483	+	0.518616i	−0.269056	+	0.963124i	$0.586712\pi$
$380$	−0.218159	+	0.158502i	−0.0111913	+	0.00813098i
$381$	−1.05002	−	0.467498i	−0.0537941	−	0.0239507i
$382$	7.46964	−	1.58772i	0.382180	−	0.0812348i
$383$	3.32903	−	31.6736i	0.170105	−	1.61844i	−0.493077	−	0.869986i	$-0.664128\pi$
$383$	3.32903	−	31.6736i	0.170105	−	1.61844i	0.663182	−	0.748458i	$-0.269206\pi$
$384$	−0.413545	−	0.459289i	−0.0211037	−	0.0234380i
$385$	0.316142	−	0.351111i	0.0161121	−	0.0178943i
$386$	−1.72401	−	16.4028i	−0.0877496	−	0.834881i
$387$	−2.77520	−	8.54120i	−0.141072	−	0.434174i
$388$	3.75782	+	11.5654i	0.190774	+	0.587143i
$389$	2.61980	+	24.9257i	0.132829	+	1.26378i	0.834390	+	0.551175i	$0.185820\pi$
$389$	2.61980	+	24.9257i	0.132829	+	1.26378i	−0.701561	+	0.712610i	$0.747513\pi$
$390$	0.183022	−	0.203267i	0.00926769	−	0.0102928i
$391$	−0.505762	−	0.561706i	−0.0255775	−	0.0284067i
$392$	0.719739	−	6.84786i	0.0363523	−	0.345869i
$393$	−8.36852	+	1.77878i	−0.422136	+	0.0897278i
$394$	−7.91860	−	3.52559i	−0.398933	−	0.177617i
$395$	3.08985	−	2.24491i	0.155467	−	0.112953i
$396$	−11.9404	+	5.31620i	−0.600027	+	0.267149i
$397$	−9.64130	+	16.6992i	−0.483883	+	0.838110i	−0.999829	−	0.0185113i	$-0.994107\pi$
$397$	−9.64130	+	16.6992i	−0.483883	+	0.838110i	0.515946	+	0.856621i	$0.327441\pi$
$398$	6.08941	+	10.5472i	0.305235	+	0.528682i
$399$	0.163017	+	0.118439i	0.00816105	+	0.00592935i
$400$	4.81418	+	1.02328i	0.240709	+	0.0511642i
$401$	−2.14757	+	6.60953i	−0.107244	+	0.330064i	−0.990251	−	0.139297i	$-0.955516\pi$
$401$	−2.14757	+	6.60953i	−0.107244	+	0.330064i	0.883006	+	0.469361i	$0.155516\pi$
$402$	4.06881			0.202934
$403$	1.76138	−	8.62965i	0.0877404	−	0.429873i
$404$	−4.86324			−0.241955
$405$	−0.493500	+	1.51884i	−0.0245222	+	0.0754716i
$406$	2.39606	+	0.509299i	0.118915	+	0.0252761i
$407$	30.9378	+	22.4776i	1.53353	+	1.11418i
$408$	−0.0594435	−	0.102959i	−0.00294289	−	0.00509724i
$409$	−13.4001	+	23.2096i	−0.662591	+	1.14764i	0.317341	+	0.948311i	$0.397210\pi$
$409$	−13.4001	+	23.2096i	−0.662591	+	1.14764i	−0.979932	+	0.199330i	$0.936123\pi$
$410$	−2.09956	+	0.934783i	−0.103690	+	0.0461656i
$411$	−3.57528	+	2.59760i	−0.176356	+	0.128130i
$412$	6.82439	+	3.03841i	0.336214	+	0.149692i
$413$	3.66503	−	0.779026i	0.180344	−	0.0383334i
$414$	1.07528	−	10.2306i	0.0528473	−	0.502809i
$415$	2.72326	+	3.02449i	0.133680	+	0.148466i
$416$	1.05849	−	1.17557i	0.0518967	−	0.0576371i
$417$	−0.425144	−	4.04497i	−0.0208194	−	0.198083i
$418$	−1.48698	−	4.57646i	−0.0727307	−	0.223842i
$419$	0.331596	+	1.02055i	0.0161995	+	0.0498570i	0.958830	−	0.283982i	$-0.0916557\pi$
$419$	0.331596	+	1.02055i	0.0161995	+	0.0498570i	−0.942630	+	0.333839i	$0.891656\pi$
$420$	0.00611371	+	0.0581680i	0.000298318	+	0.00283831i
$421$	−1.21623	+	1.35076i	−0.0592753	+	0.0658319i	−0.772053	−	0.635558i	$-0.780770\pi$
$421$	−1.21623	+	1.35076i	−0.0592753	+	0.0658319i	0.712778	+	0.701390i	$0.247437\pi$
$422$	0.662880	+	0.736203i	0.0322685	+	0.0358378i
$423$	2.70071	−	25.6955i	0.131313	−	1.24936i
$424$	−9.19598	+	1.95467i	−0.446596	+	0.0949269i
$425$	0.864907	+	0.385082i	0.0419542	+	0.0186792i
$426$	−2.85916	+	2.07730i	−0.138527	+	0.100646i
$427$	0.422381	−	0.188056i	0.0204404	−	0.00910066i
$428$	−1.38840	+	2.40478i	−0.0671110	+	0.116240i
$429$	2.44045	+	4.22699i	0.117826	+	0.204081i
$430$	0.776427	+	0.564107i	0.0374426	+	0.0272037i
$431$	17.7968	+	3.78282i	0.857240	+	0.182212i	0.615508	−	0.788131i	$-0.288951\pi$
$431$	17.7968	+	3.78282i	0.857240	+	0.182212i	0.241732	+	0.970343i	$0.422284\pi$
$432$	1.07295	−	3.30220i	0.0516223	−	0.158877i
$433$	11.0008			0.528665			0.264333	−	0.964432i	$-0.414848\pi$
$433$	11.0008			0.528665			0.264333	+	0.964432i	$0.414848\pi$
$434$	1.11931	+	1.51466i	0.0537287	+	0.0727058i
$435$	1.25216			0.0600364
$436$	1.17417	−	3.61371i	0.0562323	−	0.173065i
$437$	3.70449	+	0.787413i	0.177210	+	0.0376671i
$438$	7.74425	+	5.62653i	0.370035	+	0.268846i
$439$	−13.9055	−	24.0850i	−0.663671	−	1.14951i	−0.979644	−	0.200744i	$-0.935664\pi$
$439$	−13.9055	−	24.0850i	−0.663671	−	1.14951i	0.315972	−	0.948768i	$-0.397669\pi$
$440$	0.698375	−	1.20962i	0.0332937	−	0.0576664i
$441$	16.4682	−	7.33211i	0.784200	−	0.349148i
$442$	0.246181	−	0.178861i	0.0117096	−	0.00850755i
$443$	3.86379	+	1.72027i	0.183574	+	0.0817325i	0.496466	−	0.868056i	$-0.334631\pi$
$443$	3.86379	+	1.72027i	0.183574	+	0.0817325i	−0.312891	+	0.949789i	$0.601298\pi$
$444$	−4.63058	+	0.984261i	−0.219758	+	0.0467110i
$445$	−0.144943	+	1.37904i	−0.00687096	+	0.0653728i
$446$	9.13787	+	10.1486i	0.432691	+	0.480552i
$447$	7.81040	−	8.67432i	0.369419	−	0.410281i
$448$	0.0353579	+	0.336408i	0.00167050	+	0.0158938i
$449$	4.33922	+	13.3547i	0.204780	+	0.630249i	0.999722	+	0.0235635i	$0.00750120\pi$
$449$	4.33922	+	13.3547i	0.204780	+	0.630249i	−0.794942	+	0.606685i	$0.792499\pi$
$450$	3.98176	+	12.2546i	0.187702	+	0.577687i
$451$	−4.28686	−	40.7868i	−0.201860	−	1.92057i
$452$	3.21606	−	3.57180i	0.151271	−	0.168003i
$453$	0.0919149	+	0.102082i	0.00431854	+	0.00479622i
$454$	−0.596505	+	5.67536i	−0.0279954	+	0.266358i
$455$	−0.146432	+	0.0311252i	−0.00686486	+	0.00145917i
$456$	0.544193	+	0.242290i	0.0254842	+	0.0113463i
$457$	18.6396	−	13.5424i	0.871922	−	0.633488i	−0.0591803	−	0.998247i	$-0.518849\pi$
$457$	18.6396	−	13.5424i	0.871922	−	0.633488i	0.931102	+	0.364759i	$0.118849\pi$
$458$	22.7492	−	10.1286i	1.06300	−	0.473279i
$459$	0.333956	−	0.578428i	0.0155877	−	0.0269987i
$460$	0.549653	+	0.952028i	0.0256277	+	0.0443885i
$461$	0.674654	+	0.490165i	0.0314218	+	0.0228293i	0.603385	−	0.797450i	$-0.293818\pi$
$461$	0.674654	+	0.490165i	0.0314218	+	0.0228293i	−0.571964	+	0.820279i	$0.693818\pi$
$462$	−1.02090	−	0.216998i	−0.0474964	−	0.0100957i
$463$	−3.34577	+	10.2972i	−0.155491	+	0.478552i	−0.998210	−	0.0598010i	$-0.980953\pi$
$463$	−3.34577	+	10.2972i	−0.155491	+	0.478552i	0.842719	+	0.538353i	$0.180953\pi$
$464$	7.24171			0.336188
$465$	0.720631	+	0.638369i	0.0334185	+	0.0296037i
$466$	−13.2621			−0.614357
$467$	8.43260	−	25.9529i	0.390214	−	1.20096i	−0.542413	−	0.840112i	$-0.682489\pi$
$467$	8.43260	−	25.9529i	0.390214	−	1.20096i	0.932627	−	0.360843i	$-0.117511\pi$
$468$	4.05093	+	0.861052i	0.187254	+	0.0398021i
$469$	−1.80163	−	1.30896i	−0.0831913	−	0.0604420i
$470$	1.38052	+	2.39114i	0.0636788	+	0.110295i
$471$	−6.80855	+	11.7928i	−0.313721	+	0.543381i
$472$	10.1193	−	4.50541i	0.465779	−	0.207378i
$473$	−13.8550	+	10.0663i	−0.637056	+	0.462848i
$474$	−7.70755	−	3.43162i	−0.354020	−	0.157620i
$475$	−4.64015	+	0.986295i	−0.212905	+	0.0452543i
$476$	−0.00680156	+	0.0647125i	−0.000311749	+	0.00296609i
$477$	−16.4695	−	18.2912i	−0.754085	−	0.837497i
$478$	−14.0168	+	15.5672i	−0.641113	+	0.712028i
$479$	−4.00111	−	38.0680i	−0.182816	−	1.73937i	−0.573817	−	0.818983i	$-0.694538\pi$
$479$	−4.00111	−	38.0680i	−0.182816	−	1.73937i	0.391002	−	0.920390i	$-0.372129\pi$
$480$	0.0534318	+	0.164446i	0.00243882	+	0.00750591i
$481$	−3.74435	−	11.5239i	−0.170728	−	0.525446i
$482$	−1.13883	−	10.8353i	−0.0518725	−	0.493533i
$483$	0.549653	−	0.610452i	0.0250101	−	0.0277765i
$484$	9.31730	+	10.3479i	0.423514	+	0.470360i
$485$	0.355626	−	3.38355i	0.0161481	−	0.153639i
$486$	13.6396	−	2.89918i	0.618703	−	0.131509i
$487$	−27.4877	−	12.2383i	−1.24559	−	0.554571i	−0.325225	−	0.945637i	$-0.605440\pi$
$487$	−27.4877	−	12.2383i	−1.24559	−	0.554571i	−0.920363	+	0.391065i	$0.872107\pi$
$488$	1.10581	−	0.803416i	0.0500575	−	0.0363689i
$489$	10.9750	−	4.88637i	0.496305	−	0.220969i
$490$	−0.963199	+	1.66831i	−0.0435129	+	0.0753665i
$491$	10.2667	+	17.7824i	0.463329	+	0.802510i	0.999124	−	0.0418381i	$-0.0133214\pi$
$491$	10.2667	+	17.7824i	0.463329	+	0.802510i	−0.535795	+	0.844348i	$0.679988\pi$
$492$	4.10735	+	2.98417i	0.185174	+	0.134537i
$493$	1.36260	+	0.289629i	0.0613683	+	0.0130442i
$494$	−0.471160	+	1.45008i	−0.0211985	+	0.0652422i
$495$	3.65674			0.164358
$496$	4.16769	+	3.69193i	0.187135	+	0.165773i
$497$	1.93428			0.0867645
$498$	2.77823	−	8.55050i	0.124495	−	0.383157i
$499$	27.0074	+	5.74060i	1.20902	+	0.256984i	0.767962	−	0.640496i	$-0.221271\pi$
$499$	27.0074	+	5.74060i	1.20902	+	0.256984i	0.441055	+	0.897480i	$0.354604\pi$
$500$	−2.24569	−	1.63159i	−0.100430	−	0.0729670i
$501$	0.674001	+	1.16740i	0.0301121	+	0.0521557i
$502$	−6.06066	+	10.4974i	−0.270500	+	0.468520i
$503$	−14.9881	+	6.67312i	−0.668285	+	0.297540i	−0.712695	−	0.701474i	$-0.752526\pi$
$503$	−14.9881	+	6.67312i	−0.668285	+	0.297540i	0.0444102	+	0.999013i	$0.485859\pi$
$504$	−0.716449	+	0.520530i	−0.0319132	+	0.0231863i
$505$	1.24297	+	0.553407i	0.0553115	+	0.0246263i
$506$	−19.1881	+	4.07855i	−0.853013	+	0.181314i
$507$	−0.678170	+	6.45235i	−0.0301186	+	0.286559i
$508$	1.24441	+	1.38206i	0.0552120	+	0.0613191i
$509$	−7.94719	+	8.82625i	−0.352253	+	0.391216i	−0.893066	−	0.449927i	$-0.851450\pi$
$509$	−7.94719	+	8.82625i	−0.352253	+	0.391216i	0.540813	+	0.841143i	$0.318117\pi$
$510$	0.00347676	+	0.0330791i	0.000153953	+	0.00146477i
$511$	−1.61899	−	4.98274i	−0.0716199	−	0.220423i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	0.349818	+	3.32829i	0.0154448	+	0.146948i
$514$	−18.1054	+	20.1081i	−0.798597	+	0.886932i
$515$	−1.39846	−	1.55315i	−0.0616235	−	0.0684398i
$516$	0.221607	−	2.10845i	0.00975572	−	0.0928195i
$517$	−48.1932	+	10.2438i	−2.11953	+	0.450521i
$518$	2.36702	+	1.05386i	0.104001	+	0.0463041i
$519$	7.07804	−	5.14250i	0.310692	−	0.225731i
$520$	−0.404307	+	0.180009i	−0.0177300	+	0.00789391i
$521$	0.951727	−	1.64844i	0.0416959	−	0.0722194i	−0.844424	−	0.535675i	$-0.820057\pi$
$521$	0.951727	−	1.64844i	0.0416959	−	0.0722194i	0.886120	+	0.463455i	$0.153391\pi$
$522$	9.47953	+	16.4190i	0.414908	+	0.718641i
$523$	−13.6480	−	9.91586i	−0.596786	−	0.433590i	0.247951	−	0.968773i	$-0.420243\pi$
$523$	−13.6480	−	9.91586i	−0.596786	−	0.433590i	−0.844736	+	0.535182i	$0.820243\pi$
$524$	13.5406	+	2.87813i	0.591522	+	0.125732i
$525$	−0.317954	+	0.978562i	−0.0138767	+	0.0427080i
$526$	−3.45459			−0.150627
$527$	0.636533	+	0.861358i	0.0277278	+	0.0375213i
$528$	−3.08550			−0.134279
$529$	−2.33639	+	7.19068i	−0.101582	+	0.312638i
$530$	2.57278	+	0.546862i	0.111755	+	0.0237542i
$531$	23.4614	+	17.0457i	1.01814	+	0.739720i
$532$	−0.163017	−	0.282354i	−0.00706768	−	0.0122416i
$533$	−6.49736	+	11.2538i	−0.281432	+	0.487455i
$534$	2.79833	−	1.24590i	0.121096	−	0.0539153i
$535$	0.628505	−	0.456635i	0.0271726	−	0.0197421i
$536$	−6.01430	−	2.67774i	−0.259778	−	0.115661i
$537$	−0.342830	+	0.0728707i	−0.0147942	+	0.00314460i
$538$	−0.813262	+	7.73767i	−0.0350622	+	0.333595i
$539$	−23.0019	−	25.5462i	−0.990764	−	1.10035i
$540$	−0.650000	+	0.721898i	−0.0279715	+	0.0310655i
$541$	2.57025	+	24.4543i	0.110504	+	1.05137i	0.899484	+	0.436954i	$0.143943\pi$
$541$	2.57025	+	24.4543i	0.110504	+	1.05137i	−0.788980	+	0.614418i	$0.789391\pi$
$542$	−8.55968	−	26.3440i	−0.367670	−	1.13157i
$543$	−2.29124	−	7.05173i	−0.0983267	−	0.302619i
$544$	0.0201074	+	0.191309i	0.000862099	+	0.00820232i
$545$	−0.711317	+	0.789998i	−0.0304695	+	0.0338398i
$546$	0.221284	+	0.245761i	0.00947010	+	0.0105176i
$547$	−2.80413	+	26.6795i	−0.119896	+	1.14073i	0.754765	+	0.655996i	$0.227751\pi$
$547$	−2.80413	+	26.6795i	−0.119896	+	1.14073i	−0.874660	+	0.484736i	$0.838916\pi$
$548$	6.99431	−	1.48669i	0.298782	−	0.0635081i
$549$	3.26909	+	1.45549i	0.139521	+	0.0621189i
$550$	19.8787	−	14.4427i	0.847631	−	0.615840i
$551$	−6.37649	+	2.83900i	−0.271648	+	0.120945i
$552$	1.21422	−	2.10308i	0.0516804	−	0.0895132i
$553$	2.30885	+	3.99905i	0.0981824	+	0.170057i
$554$	4.56161	+	3.31421i	0.193804	+	0.140807i
$555$	1.29551	+	0.275369i	0.0549914	+	0.0116888i
$556$	−2.03363	+	6.25886i	−0.0862450	+	0.265435i
$557$	33.5441			1.42131			0.710655	−	0.703540i	$-0.248398\pi$
$557$	33.5441			1.42131			0.710655	+	0.703540i	$0.248398\pi$
$558$	−2.91509	+	14.2821i	−0.123406	+	0.604611i
$559$	5.42641			0.229513
$560$	0.0292442	−	0.0900044i	0.00123579	−	0.00380338i
$561$	−0.580566	−	0.123403i	−0.0245115	−	0.00521009i
$562$	−17.7989	−	12.9317i	−0.750801	−	0.545489i
$563$	4.32620	+	7.49320i	0.182328	+	0.315801i	0.942673	−	0.333719i	$-0.108304\pi$
$563$	4.32620	+	7.49320i	0.182328	+	0.315801i	−0.760345	+	0.649519i	$0.774970\pi$
$564$	3.04965	−	5.28215i	0.128414	−	0.222419i
$565$	−1.22843	+	0.546931i	−0.0516803	+	0.0230096i
$566$	−17.3497	+	12.6053i	−0.729262	+	0.529840i
$567$	−1.76393	−	0.785353i	−0.0740782	−	0.0329817i
$568$	5.59336	−	1.18890i	0.234692	−	0.0498853i
$569$	−1.04120	+	9.90640i	−0.0436496	+	0.415298i	0.950778	+	0.309874i	$0.100287\pi$
$569$	−1.04120	+	9.90640i	−0.0436496	+	0.415298i	−0.994427	+	0.105424i	$0.966380\pi$
$570$	−0.111517	−	0.123852i	−0.00467091	−	0.00518757i
$571$	20.7401	−	23.0343i	0.867948	−	0.963954i	−0.131679	−	0.991292i	$-0.542037\pi$
$571$	20.7401	−	23.0343i	0.867948	−	0.963954i	0.999626	+	0.0273390i	$0.00870334\pi$
$572$	−0.825511	−	7.85421i	−0.0345164	−	0.328401i
$573$	1.45844	+	4.48863i	0.0609274	+	0.187515i
$574$	−0.858670	−	2.64272i	−0.0358402	−	0.110305i
$575$	2.02146	+	19.2329i	0.0843008	+	0.802068i
$576$	−1.75181	+	1.94558i	−0.0729919	+	0.0810658i
$577$	−12.5362	−	13.9229i	−0.521890	−	0.579617i	0.423361	−	0.905961i	$-0.360850\pi$
$577$	−12.5362	−	13.9229i	−0.521890	−	0.579617i	−0.945251	+	0.326344i	$0.894183\pi$
$578$	1.77312	−	16.8701i	0.0737519	−	0.701702i
$579$	9.97059	−	2.11931i	0.414364	−	0.0880757i
$580$	−1.85087	−	0.824063i	−0.0768534	−	0.0342173i
$581$	−3.98092	+	2.89230i	−0.165156	+	0.119993i
$582$	−6.86588	+	3.05688i	−0.284600	+	0.126712i
$583$	−23.4680	+	40.6478i	−0.971946	+	1.68346i
$584$	−7.74425	−	13.4134i	−0.320459	−	0.555052i
$585$	−0.937376	−	0.681043i	−0.0387557	−	0.0281577i
$586$	−9.11143	−	1.93669i	−0.376390	−	0.0800041i
$587$	−4.42628	+	13.6227i	−0.182692	+	0.562269i	−0.999901	−	0.0140729i	$-0.995520\pi$
$587$	−4.42628	+	13.6227i	−0.182692	+	0.562269i	0.817209	+	0.576342i	$0.195520\pi$
$588$	4.25552			0.175495
$589$	−5.11711	−	1.61696i	−0.210847	−	0.0666256i
$590$	−3.09903			−0.127585
$591$	1.65544	−	5.09492i	0.0680956	−	0.209577i
$592$	7.49244	+	1.59257i	0.307938	+	0.0654541i
$593$	−4.22612	−	3.07046i	−0.173546	−	0.126089i	0.497622	−	0.867394i	$-0.334207\pi$
$593$	−4.22612	−	3.07046i	−0.173546	−	0.126089i	−0.671167	+	0.741306i	$0.734207\pi$
$594$	−8.66722	−	15.0121i	−0.355620	−	0.615953i
$595$	0.00910227	−	0.0157656i	0.000373157	−	0.000646326i
$596$	−17.2536	+	7.68180i	−0.706735	+	0.314659i
$597$	−6.08941	+	4.42422i	−0.249223	+	0.181071i
$598$	5.67831	+	2.52814i	0.232203	+	0.103384i
$599$	10.1686	−	2.16141i	0.415479	−	0.0883129i	0.00457113	−	0.999990i	$-0.498545\pi$
$599$	10.1686	−	2.16141i	0.415479	−	0.0883129i	0.410908	+	0.911677i	$0.365212\pi$
$600$	−0.317954	+	3.02513i	−0.0129804	+	0.123500i
$601$	14.6284	+	16.2464i	0.596703	+	0.662706i	0.963535	−	0.267581i	$-0.0862244\pi$
$601$	14.6284	+	16.2464i	0.596703	+	0.662706i	−0.366832	+	0.930287i	$0.619558\pi$
$602$	−0.776427	+	0.862309i	−0.0316448	+	0.0351451i
$603$	−1.80163	−	17.1413i	−0.0733678	−	0.698048i
$604$	−0.0686823	−	0.211383i	−0.00279464	−	0.00860103i
$605$	−1.20384	−	3.70502i	−0.0489429	−	0.150631i
$606$	−0.314176	−	2.98918i	−0.0127625	−	0.121427i
$607$	1.52315	−	1.69163i	0.0618227	−	0.0686610i	−0.711440	−	0.702747i	$-0.751957\pi$
$607$	1.52315	−	1.69163i	0.0618227	−	0.0686610i	0.773263	+	0.634086i	$0.218623\pi$
$608$	−0.644943	−	0.716282i	−0.0261559	−	0.0290491i
$609$	−0.158249	+	1.50564i	−0.00641257	+	0.0610115i
$610$	−0.374051	+	0.0795071i	−0.0151449	+	0.00321915i
$611$	14.2618	+	6.34975i	0.576970	+	0.256883i
$612$	−0.407432	+	0.296016i	−0.0164695	+	0.0119658i
$613$	25.8697	−	11.5179i	1.04487	−	0.465205i	0.188772	−	0.982021i	$-0.439549\pi$
$613$	25.8697	−	11.5179i	1.04487	−	0.465205i	0.856097	+	0.516816i	$0.172883\pi$
$614$	12.9041	−	22.3505i	0.520766	−	0.901994i
$615$	−0.710198	−	1.23010i	−0.0286380	−	0.0496024i
$616$	1.36623	+	0.992622i	0.0550469	+	0.0399939i
$617$	5.91651	+	1.25759i	0.238190	+	0.0506288i	0.325460	−	0.945556i	$-0.394481\pi$
$617$	5.91651	+	1.25759i	0.238190	+	0.0506288i	−0.0872699	+	0.996185i	$0.527814\pi$
$618$	−1.42669	+	4.39089i	−0.0573897	+	0.176627i
$619$	−31.1721			−1.25291			−0.626457	−	0.779456i	$-0.715495\pi$
$619$	−31.1721			−1.25291			−0.626457	+	0.779456i	$0.715495\pi$
$620$	−0.645080	−	1.41786i	−0.0259070	−	0.0569427i
$621$	13.6430			0.547475
$622$	−9.03052	+	27.7931i	−0.362091	+	1.11440i
$623$	−1.63989	−	0.348569i	−0.0657007	−	0.0139651i
$624$	0.790943	+	0.574654i	0.0316631	+	0.0230046i
$625$	−11.9160	−	20.6391i	−0.476641	−	0.825566i
$626$	8.14159	−	14.1016i	0.325403	−	0.563615i
$627$	2.71685	−	1.20962i	0.108501	−	0.0483076i
$628$	17.8250	−	12.9506i	0.711296	−	0.516786i
$629$	1.34608	+	0.599314i	0.0536718	+	0.0238962i
$630$	0.242347	−	0.0515124i	0.00965533	−	0.00205230i
$631$	1.94657	−	18.5204i	0.0774917	−	0.737284i	−0.884930	−	0.465724i	$-0.845794\pi$
$631$	1.94657	−	18.5204i	0.0774917	−	0.737284i	0.962422	−	0.271560i	$-0.0875394\pi$
$632$	9.13450	+	10.1449i	0.363351	+	0.403542i
$633$	−0.409683	+	0.454999i	−0.0162834	+	0.0180846i
$634$	−2.19722	−	20.9052i	−0.0872628	−	0.830250i
$635$	−0.160784	−	0.494841i	−0.00638051	−	0.0196372i
$636$	−1.79551	−	5.52602i	−0.0711967	−	0.219121i
$637$	1.13855	+	10.8325i	0.0451108	+	0.429201i
$638$	24.1916	−	26.8675i	0.957756	−	1.06370i
$639$	10.0174	+	11.1254i	0.396282	+	0.440115i
$640$	0.0292442	−	0.278240i	0.00115598	−	0.0109984i
$641$	−22.6529	+	4.81501i	−0.894734	+	0.190182i	−0.632259	−	0.774757i	$-0.717872\pi$
$641$	−22.6529	+	4.81501i	−0.894734	+	0.190182i	−0.262475	+	0.964939i	$0.584539\pi$
$642$	−1.56779	−	0.698025i	−0.0618758	−	0.0275489i
$643$	−28.3535	+	20.6001i	−1.11815	+	0.812387i	−0.983928	−	0.178564i	$-0.942855\pi$
$643$	−28.3535	+	20.6001i	−1.11815	+	0.812387i	−0.134226	+	0.990951i	$0.542855\pi$
$644$	−1.21422	+	0.540604i	−0.0478468	+	0.0213028i
$645$	−0.296569	+	0.513672i	−0.0116774	+	0.0202258i
$646$	−0.0927048	−	0.160569i	−0.00364742	−	0.00631752i
$647$	15.0612	+	10.9426i	0.592119	+	0.430199i	0.843073	−	0.537800i	$-0.180744\pi$
$647$	15.0612	+	10.9426i	0.592119	+	0.430199i	−0.250954	+	0.967999i	$0.580744\pi$
$648$	−5.58347	−	1.18680i	−0.219339	−	0.0466220i
$649$	17.0890	−	52.5945i	0.670801	−	2.06451i
$650$	−7.78561			−0.305377
$651$	−0.858670	+	0.785833i	−0.0336539	+	0.0307992i
$652$	−19.4384			−0.761267
$653$	−0.479918	+	1.47704i	−0.0187807	+	0.0578009i	−0.960008	−	0.279974i	$-0.909674\pi$
$653$	−0.479918	+	1.47704i	−0.0187807	+	0.0578009i	0.941227	+	0.337775i	$0.109674\pi$
$654$	2.29702	+	0.488246i	0.0898204	+	0.0190919i
$655$	−3.13325	−	2.27644i	−0.122426	−	0.0889478i
$656$	−4.10735	−	7.11414i	−0.160365	−	0.277761i
$657$	20.2747	−	35.1168i	0.790992	−	1.37004i
$658$	−3.04965	+	1.35779i	−0.118888	+	0.0529323i
$659$	17.4518	−	12.6795i	0.679824	−	0.493921i	−0.193475	−	0.981105i	$-0.561976\pi$
$659$	17.4518	−	12.6795i	0.679824	−	0.493921i	0.873299	+	0.487184i	$0.161976\pi$
$660$	0.788608	+	0.351111i	0.0306965	+	0.0136670i
$661$	27.9440	−	5.93968i	1.08690	−	0.231027i	0.370578	−	0.928801i	$-0.379160\pi$
$661$	27.9440	−	5.93968i	1.08690	−	0.231027i	0.716317	+	0.697775i	$0.245826\pi$
$662$	−0.0912484	+	0.868170i	−0.00354647	+	0.0337424i
$663$	0.125840	+	0.139760i	0.00488724	+	0.00542783i
$664$	−9.73383	+	10.8105i	−0.377746	+	0.419529i
$665$	0.00953460	+	0.0907157i	0.000369736	+	0.00351780i
$666$	6.19693	+	19.0722i	0.240126	+	0.739033i
$667$	8.79300	+	27.0621i	0.340466	+	1.04785i
$668$	−0.227988	−	2.16916i	−0.00882113	−	0.0839275i
$669$	−5.64752	+	6.27220i	−0.218346	+	0.242497i
$670$	1.23245	+	1.36878i	0.0476139	+	0.0528806i
$671$	0.713295	−	6.78655i	0.0275364	−	0.261992i
$672$	−0.204489	+	0.0434654i	−0.00788832	+	0.00167671i
$673$	26.4175	+	11.7618i	1.01832	+	0.453385i	0.846865	−	0.531807i	$-0.178487\pi$
$673$	26.4175	+	11.7618i	1.01832	+	0.453385i	0.171454	+	0.985192i	$0.445154\pi$
$674$	−4.21628	+	3.06331i	−0.162405	+	0.117994i
$675$	−15.6115	+	6.95068i	−0.600887	+	0.267532i
$676$	5.24882	−	9.09122i	0.201878	−	0.349662i
$677$	−12.4962	−	21.6440i	−0.480268	−	0.831848i	0.519476	−	0.854485i	$-0.326127\pi$
$677$	−12.4962	−	21.6440i	−0.480268	−	0.831848i	−0.999744	+	0.0226369i	$0.992794\pi$
$678$	2.40317	+	1.74600i	0.0922930	+	0.0670548i
$679$	4.02356	+	0.855233i	0.154410	+	0.0328208i
$680$	0.0166307	−	0.0511839i	0.000637757	−	0.00196281i
$681$	−3.52689			−0.135151
$682$	27.6200	−	3.12931i	1.05763	−	0.119827i
$683$	8.21442			0.314316			0.157158	−	0.987573i	$-0.449767\pi$
$683$	8.21442			0.314316			0.157158	+	0.987573i	$0.449767\pi$
$684$	0.779773	−	2.39989i	0.0298154	−	0.0917622i
$685$	−1.95682	−	0.415934i	−0.0747662	−	0.0158920i
$686$	−3.79991	−	2.76080i	−0.145081	−	0.105408i
$687$	7.69519	+	13.3285i	0.293590	+	0.508512i
$688$	−1.71517	+	2.97076i	−0.0653903	+	0.113259i
$689$	13.5862	−	6.04898i	0.517594	−	0.230448i
$690$	−0.549653	+	0.399347i	−0.0209249	+	0.0152029i
$691$	23.2422	+	10.3481i	0.884173	+	0.393659i	0.798026	−	0.602623i	$-0.205878\pi$
$691$	23.2422	+	10.3481i	0.884173	+	0.393659i	0.0861473	+	0.996282i	$0.472544\pi$
$692$	−13.8467	+	2.94322i	−0.526374	+	0.111884i
$693$	−0.462142	+	4.39698i	−0.0175553	+	0.167028i
$694$	3.18889	+	3.54162i	0.121048	+	0.134438i
$695$	1.23198	−	1.36826i	0.0467318	−	0.0519009i
$696$	0.467830	+	4.45111i	0.0177331	+	0.168719i
$697$	−0.488311	−	1.50287i	−0.0184961	−	0.0569251i
$698$	4.14103	+	12.7448i	0.156740	+	0.482397i
$699$	−0.856763	−	8.15156i	−0.0324058	−	0.308320i
$700$	1.11399	−	1.23721i	0.0421048	−	0.0467621i
$701$	−15.1069	−	16.7779i	−0.570581	−	0.633694i	0.386924	−	0.922112i	$-0.373538\pi$
$701$	−15.1069	−	16.7779i	−0.570581	−	0.633694i	−0.957505	+	0.288417i	$0.906871\pi$
$702$	−0.574125	+	5.46244i	−0.0216690	+	0.206166i
$703$	−7.22161	+	1.53500i	−0.272368	+	0.0578936i
$704$	4.56082	+	2.03061i	0.171893	+	0.0765315i
$705$	−1.38052	+	1.00301i	−0.0519935	+	0.0377755i
$706$	10.3745	−	4.61904i	0.390451	−	0.173840i
$707$	−0.822523	+	1.42465i	−0.0309341	+	0.0535795i
$708$	3.42297	+	5.92876i	0.128643	+	0.222816i
$709$	−15.2634	−	11.0895i	−0.573228	−	0.416475i	0.263048	−	0.964783i	$-0.415272\pi$
$709$	−15.2634	−	11.0895i	−0.573228	−	0.416475i	−0.836276	+	0.548308i	$0.815272\pi$
$710$	−1.56487	−	0.332623i	−0.0587285	−	0.0124831i
$711$	−11.0441	+	33.9903i	−0.414187	+	1.27474i
$712$	−4.95630			−0.185745
$713$	−8.73618	+	20.0573i	−0.327173	+	0.751153i
$714$	−0.0402149			−0.00150500
$715$	−0.682773	+	2.10136i	−0.0255343	+	0.0785863i
$716$	0.554710	+	0.117907i	0.0207305	+	0.00440640i
$717$	−10.4739	−	7.60972i	−0.391154	−	0.284190i
$718$	10.0592	+	17.4231i	0.375407	+	0.650223i
$719$	−13.3514	+	23.1254i	−0.497925	+	0.862431i	−0.999997	−	0.00239486i	$-0.999238\pi$
$719$	−13.3514	+	23.1254i	−0.497925	+	0.862431i	0.502073	+	0.864825i	$0.332571\pi$
$720$	0.669131	−	0.297916i	0.0249370	−	0.0111027i
$721$	2.04430	−	1.48527i	0.0761335	−	0.0553142i
$722$	−16.5087	−	7.35013i	−0.614389	−	0.273544i
$723$	6.58632	−	1.39996i	0.244948	−	0.0520652i
$724$	−1.25404	+	11.9314i	−0.0466060	+	0.443427i
$725$	−23.8490	−	26.4870i	−0.885729	−	0.983702i
$726$	−5.75841	+	6.39536i	−0.213715	+	0.237354i
$727$	3.03503	+	28.8764i	0.112563	+	1.07096i	0.894334	+	0.447400i	$0.147650\pi$
$727$	3.03503	+	28.8764i	0.112563	+	1.07096i	−0.781771	+	0.623565i	$0.785684\pi$
$728$	−0.165352	−	0.508902i	−0.00612836	−	0.0188611i
$729$	−2.62868	−	8.09024i	−0.0973584	−	0.299638i
$730$	0.452949	+	4.30952i	0.0167644	+	0.159503i
$731$	−0.441540	+	0.490380i	−0.0163310	+	0.0181374i
$732$	0.565255	+	0.627780i	0.0208924	+	0.0232034i
$733$	−1.96841	+	18.7282i	−0.0727050	+	0.691742i	0.896089	+	0.443875i	$0.146396\pi$
$733$	−1.96841	+	18.7282i	−0.0727050	+	0.691742i	−0.968794	+	0.247867i	$0.920270\pi$
$734$	20.5940	−	4.37739i	0.760139	−	0.161572i
$735$	−1.08765	−	0.484252i	−0.0401185	−	0.0178619i
$736$	−3.17886	+	2.30958i	−0.117174	+	0.0851321i
$737$	−30.0260	+	13.3684i	−1.10602	+	0.492433i
$738$	10.7532	−	18.6251i	0.395830	−	0.685598i
$739$	−24.5847	−	42.5819i	−0.904362	−	1.56640i	−0.821771	−	0.569818i	$-0.807014\pi$
$739$	−24.5847	−	42.5819i	−0.904362	−	1.56640i	−0.0825913	−	0.996584i	$-0.526320\pi$
$740$	−1.73373	−	1.25963i	−0.0637333	−	0.0463049i
$741$	−0.921727	−	0.195919i	−0.0338605	−	0.00719727i
$742$	−0.982716	+	3.02449i	−0.0360766	+	0.111032i
$743$	23.9942			0.880263			0.440131	−	0.897933i	$-0.354932\pi$
$743$	23.9942			0.880263			0.440131	+	0.897933i	$0.354932\pi$
$744$	−2.00000	+	2.80017i	−0.0733236	+	0.102659i
$745$	5.28391			0.193587
$746$	−8.35519	+	25.7146i	−0.305905	+	0.941480i
$747$	−37.2523	−	7.91821i	−1.36299	−	0.289712i
$748$	0.776949	+	0.564487i	0.0284081	+	0.0206397i
$749$	0.469643	+	0.813445i	0.0171604	+	0.0297226i
$750$	0.857778	−	1.48572i	0.0313216	−	0.0542507i
$751$	1.43246	−	0.637772i	0.0522712	−	0.0232726i	−0.380435	−	0.924808i	$-0.624226\pi$
$751$	1.43246	−	0.637772i	0.0522712	−	0.0232726i	0.432706	+	0.901535i	$0.357559\pi$
$752$	−7.98410	+	5.80079i	−0.291150	+	0.211533i
$753$	−6.84372	−	3.04702i	−0.249399	−	0.111040i
$754$	−11.2052	+	2.38175i	−0.408071	+	0.0867381i
$755$	−0.00649984	+	0.0618419i	−0.000236553	+	0.00225066i
$756$	−0.785886	−	0.872815i	−0.0285824	−	0.0317440i
$757$	9.79518	−	10.8787i	0.356012	−	0.395391i	−0.538360	−	0.842715i	$-0.680956\pi$
$757$	9.79518	−	10.8787i	0.356012	−	0.395391i	0.894372	+	0.447323i	$0.147623\pi$
$758$	2.59470	+	24.6869i	0.0942437	+	0.896669i
$759$	−3.74646	−	11.5304i	−0.135988	−	0.418528i
$760$	0.0833294	+	0.256462i	0.00302267	+	0.00930284i
$761$	3.03046	+	28.8329i	0.109854	+	1.04519i	0.901075	+	0.433663i	$0.142779\pi$
$761$	3.03046	+	28.8329i	0.109854	+	1.04519i	−0.791221	+	0.611530i	$0.790554\pi$
$762$	−0.769091	+	0.854162i	−0.0278612	+	0.0309430i
$763$	−0.860023	−	0.955153i	−0.0311349	−	0.0345788i
$764$	0.798233	−	7.59468i	0.0288791	−	0.274766i
$765$	0.137818	−	0.0292942i	0.00498283	−	0.00105913i
$766$	−29.0946	−	12.9538i	−1.05123	−	0.468039i
$767$	−14.1760	+	10.2995i	−0.511866	+	0.371892i
$768$	−0.564602	+	0.251377i	−0.0203733	+	0.00907079i
$769$	0.550545	−	0.953573i	0.0198532	−	0.0343867i	−0.855928	−	0.517095i	$-0.827013\pi$
$769$	0.550545	−	0.953573i	0.0198532	−	0.0343867i	0.875781	+	0.482708i	$0.160347\pi$
$770$	−0.236233	−	0.409168i	−0.00851325	−	0.0147454i
$771$	−13.5291	−	9.82945i	−0.487238	−	0.353999i
$772$	−16.1328	−	3.42912i	−0.580631	−	0.123417i
$773$	8.37882	−	25.7873i	0.301365	−	0.927506i	−0.679644	−	0.733543i	$-0.737866\pi$
$773$	8.37882	−	25.7873i	0.301365	−	0.927506i	0.981009	−	0.193964i	$-0.0621345\pi$
$774$	−8.98075			−0.322806
$775$	−0.221896	−	27.4021i	−0.00797074	−	0.984313i
$776$	12.1606			0.436539
$777$	−0.494841	+	1.52297i	−0.0177523	+	0.0546361i
$778$	24.5153	+	5.21090i	0.878918	+	0.186820i
$779$	6.40560	+	4.65394i	0.229505	+	0.166745i
$780$	−0.136761	−	0.236877i	−0.00489684	−	0.00848157i
$781$	14.2742	−	24.7236i	0.510771	−	0.884681i
$782$	−0.690503	+	0.307432i	−0.0246923	+	0.0109937i
$783$	−20.3421	+	14.7794i	−0.726967	+	0.528173i
$784$	−6.29029	−	2.80062i	−0.224653	−	0.100022i
$785$	−6.02951	+	1.28161i	−0.215202	+	0.0457427i
$786$	−0.894291	+	8.50861i	−0.0318983	+	0.303492i
$787$	21.3118	+	23.6692i	0.759685	+	0.843715i	0.991643	−	0.129010i	$-0.0411800\pi$
$787$	21.3118	+	23.6692i	0.759685	+	0.843715i	−0.231958	+	0.972726i	$0.574513\pi$
$788$	−5.80002	+	6.44157i	−0.206617	+	0.229471i
$789$	−0.223174	−	2.12336i	−0.00794521	−	0.0755936i
$790$	−1.18022	−	3.63233i	−0.0419902	−	0.129233i
$791$	−0.502398	−	1.54622i	−0.0178632	−	0.0549774i
$792$	1.36623	+	12.9988i	0.0485468	+	0.461892i
$793$	−1.44680	+	1.60683i	−0.0513773	+	0.0570602i
$794$	12.9026	+	14.3298i	0.457895	+	0.508544i
$795$	−0.169921	+	1.61669i	−0.00602646	+	0.0573379i
$796$	11.9127	−	2.53212i	0.422234	−	0.0897486i
$797$	29.3274	+	13.0574i	1.03883	+	0.462517i	0.854011	−	0.520255i	$-0.174163\pi$
$797$	29.3274	+	13.0574i	1.03883	+	0.462517i	0.184820	+	0.982772i	$0.440830\pi$
$798$	0.163017	−	0.118439i	0.00577074	−	0.00419268i
$799$	−1.73428	+	0.772153i	−0.0613546	+	0.0273168i
$800$	2.46086	−	4.26234i	0.0870047	−	0.150697i
$801$	−6.48787	−	11.2373i	−0.229238	−	0.397051i
$802$	5.62240	+	4.08491i	0.198534	+	0.144243i
$803$	−75.6357	−	16.0769i	−2.66913	−	0.567340i
$804$	1.25733	−	3.86966i	0.0443426	−	0.136473i
$805$	0.371853			0.0131061
$806$	−7.66299	−	4.34188i	−0.269917	−	0.152936i
$807$	−4.80849			−0.169267
$808$	−1.50282	+	4.62521i	−0.0528691	+	0.162714i
$809$	−32.9009	−	6.99330i	−1.15673	−	0.245871i	−0.410694	−	0.911773i	$-0.634714\pi$
$809$	−32.9009	−	6.99330i	−1.15673	−	0.245871i	−0.746039	+	0.665902i	$0.768047\pi$
$810$	1.29200	+	0.938693i	0.0453963	+	0.0329823i
$811$	26.2297	+	45.4313i	0.921051	+	1.59531i	0.797792	+	0.602933i	$0.206001\pi$
$811$	26.2297	+	45.4313i	0.921051	+	1.59531i	0.123259	+	0.992375i	$0.460665\pi$
$812$	1.22480	−	2.12141i	0.0429819	−	0.0744468i
$813$	15.6393	−	6.96307i	0.548495	−	0.244206i
$814$	30.9378	−	22.4776i	1.08437	−	0.787841i
$815$	4.96817	+	2.21197i	0.174027	+	0.0774820i
$816$	−0.116289	+	0.0247180i	−0.00407093	+	0.000865303i
$817$	0.345607	−	3.28823i	0.0120913	−	0.115041i
$818$	17.9328	+	19.9164i	0.627006	+	0.696361i
$819$	0.937376	−	1.04106i	0.0327546	−	0.0363776i
$820$	0.240233	+	2.28566i	0.00838929	+	0.0798187i
$821$	13.9376	+	42.8956i	0.486427	+	1.49707i	0.829904	+	0.557906i	$0.188395\pi$
$821$	13.9376	+	42.8956i	0.486427	+	1.49707i	−0.343477	+	0.939161i	$0.611605\pi$
$822$	1.36564	+	4.20300i	0.0476321	+	0.146596i
$823$	−5.08462	−	48.3769i	−0.177239	−	1.68631i	−0.616029	−	0.787724i	$-0.711260\pi$
$823$	−5.08462	−	48.3769i	−0.177239	−	1.68631i	0.438790	−	0.898589i	$-0.355407\pi$
$824$	4.99856	−	5.55146i	0.174133	−	0.193394i
$825$	10.1614	+	11.2854i	0.353775	+	0.392907i
$826$	0.391659	−	3.72638i	0.0136275	−	0.129657i
$827$	49.2590	−	10.4703i	1.71290	−	0.364089i	0.756017	−	0.654552i	$-0.227143\pi$
$827$	49.2590	−	10.4703i	1.71290	−	0.364089i	0.956886	+	0.290463i	$0.0938092\pi$
$828$	−9.39764	−	4.18410i	−0.326591	−	0.145408i
$829$	45.7613	−	33.2475i	1.58935	−	1.15473i	0.684500	−	0.729013i	$-0.260021\pi$
$829$	45.7613	−	33.2475i	1.58935	−	1.15473i	0.904855	−	0.425720i	$-0.139979\pi$
$830$	3.71799	−	1.65536i	0.129053	−	0.0574583i
$831$	−1.74238	+	3.01789i	−0.0604425	+	0.104690i
$832$	−0.790943	−	1.36995i	−0.0274210	−	0.0474946i
$833$	−1.07157	−	0.778540i	−0.0371277	−	0.0269748i
$834$	−3.97837	−	0.845629i	−0.137760	−	0.0292817i
$835$	−0.188567	+	0.580350i	−0.00652563	+	0.0200838i
$836$	−4.81198			−0.166426
$837$	−19.2419	−	1.86500i	−0.665096	−	0.0644638i
$838$	1.07307			0.0370685
$839$	9.71253	−	29.8921i	0.335314	−	1.03199i	−0.631253	−	0.775577i	$-0.717459\pi$
$839$	9.71253	−	29.8921i	0.335314	−	1.03199i	0.966567	−	0.256413i	$-0.0825408\pi$
$840$	0.0572103	+	0.0121604i	0.00197394	+	0.000419575i
$841$	−18.9653	−	13.7791i	−0.653977	−	0.475142i
$842$	0.908812	+	1.57411i	0.0313197	+	0.0542474i
$843$	6.79857	−	11.7755i	0.234155	−	0.405569i
$844$	0.905012	−	0.402937i	0.0311518	−	0.0138697i
$845$	−2.37604	+	1.72630i	−0.0817384	+	0.0593864i
$846$	−23.6033	−	10.5089i	−0.811500	−	0.361303i
$847$	4.60719	−	0.979288i	0.158305	−	0.0336487i
$848$	−0.982716	+	9.34992i	−0.0337466	+	0.321078i
$849$	−8.86865	−	9.84963i	−0.304371	−	0.338038i
$850$	0.633505	−	0.703579i	0.0217291	−	0.0241326i
$851$	3.14606	+	29.9328i	0.107846	+	1.02608i
$852$	1.09210	+	3.36114i	0.0374148	+	0.115151i
$853$	−8.49023	−	26.1302i	−0.290700	−	0.894683i	−0.984632	−	0.174642i	$-0.944123\pi$
$853$	−8.49023	−	26.1302i	−0.290700	−	0.894683i	0.693932	−	0.720041i	$-0.255877\pi$
$854$	−0.0483291	−	0.459820i	−0.00165379	−	0.0157347i
$855$	−0.472391	+	0.524644i	−0.0161554	+	0.0179424i
$856$	1.85805	+	2.06357i	0.0635067	+	0.0705313i
$857$	−1.04033	+	9.89808i	−0.0355370	+	0.338112i	0.962279	+	0.272063i	$0.0877060\pi$
$857$	−1.04033	+	9.89808i	−0.0355370	+	0.338112i	−0.997816	+	0.0660488i	$0.978961\pi$
$858$	4.77425	−	1.01480i	0.162990	−	0.0346446i
$859$	25.0254	+	11.1420i	0.853854	+	0.380160i	0.786516	−	0.617570i	$-0.211883\pi$
$859$	25.0254	+	11.1420i	0.853854	+	0.380160i	0.0673380	+	0.997730i	$0.478549\pi$
$860$	0.776427	−	0.564107i	0.0264759	−	0.0192359i
$861$	1.56887	−	0.698505i	0.0534669	−	0.0238050i
$862$	9.09718	−	15.7568i	0.309851	−	0.536678i
$863$	16.4610	+	28.5113i	0.560339	+	0.970536i	0.997467	+	0.0711363i	$0.0226625\pi$
$863$	16.4610	+	28.5113i	0.560339	+	0.970536i	−0.437127	+	0.899400i	$0.644004\pi$
$864$	−2.80902	−	2.04087i	−0.0955647	−	0.0694318i
$865$	3.87394	+	0.823432i	0.131718	+	0.0279975i
$866$	3.39944	−	10.4624i	0.115518	−	0.355526i
$867$	10.4837			0.356045
$868$	1.78641	−	0.596475i	0.0606347	−	0.0202457i
$869$	68.1533			2.31194
$870$	0.386938	−	1.19087i	0.0131184	−	0.0403744i
$871$	10.1867	+	2.16525i	0.345164	+	0.0733668i
$872$	−3.07401	−	2.23340i	−0.104099	−	0.0756323i
$873$	15.9184	+	27.5714i	0.538755	+	0.933152i
$874$	1.89362	−	3.27985i	0.0640528	−	0.110943i
$875$	−0.857778	+	0.381908i	−0.0289982	+	0.0129108i
$876$	7.74425	−	5.62653i	0.261654	−	0.190103i
$877$	−29.0559	−	12.9365i	−0.981149	−	0.436836i	−0.147459	−	0.989068i	$-0.547109\pi$
$877$	−29.0559	−	12.9365i	−0.981149	−	0.436836i	−0.833690	+	0.552232i	$0.813776\pi$
$878$	−27.2032	+	5.78221i	−0.918063	+	0.195140i
$879$	0.601768	−	5.72544i	0.0202971	−	0.193114i
$880$	−0.934608	−	1.03799i	−0.0315056	−	0.0349905i
$881$	2.38737	−	2.65145i	0.0804327	−	0.0893295i	−0.701585	−	0.712586i	$-0.747524\pi$
$881$	2.38737	−	2.65145i	0.0804327	−	0.0893295i	0.782018	+	0.623256i	$0.214191\pi$
$882$	−1.88430	−	17.9279i	−0.0634477	−	0.603665i
$883$	9.83703	+	30.2753i	0.331042	+	1.01884i	0.968639	+	0.248473i	$0.0799287\pi$
$883$	9.83703	+	30.2753i	0.331042	+	1.01884i	−0.637597	+	0.770370i	$0.720071\pi$
$884$	−0.0940328	−	0.289403i	−0.00316267	−	0.00973369i
$885$	−0.200204	−	1.90482i	−0.00672979	−	0.0640297i
$886$	2.83005	−	3.14309i	0.0950774	−	0.105594i
$887$	−9.02543	−	10.0238i	−0.303044	−	0.336565i	0.572318	−	0.820031i	$-0.306044\pi$
$887$	−9.02543	−	10.0238i	−0.303044	−	0.336565i	−0.875363	+	0.483467i	$0.839377\pi$
$888$	−0.494841	+	4.70810i	−0.0166058	+	0.157994i
$889$	0.615334	−	0.130793i	0.0206376	−	0.00438667i
$890$	1.26676	+	0.563996i	0.0424617	+	0.0189052i
$891$	−23.0553	+	16.7506i	−0.772381	+	0.561167i
$892$	12.4757	−	5.55453i	0.417717	−	0.185980i
$893$	4.75607	−	8.23776i	0.159156	−	0.275666i
$894$	−5.83623	−	10.1086i	−0.195193	−	0.338084i
$895$	−0.128359	−	0.0932579i	−0.00429055	−	0.00311727i
$896$	0.330869	+	0.0703285i	0.0110536	+	0.00234951i
$897$	−1.18709	+	3.65349i	−0.0396358	+	0.121986i
$898$	14.0420			0.468588
$899$	−8.70212	−	39.3699i	−0.290232	−	1.31306i
$900$	12.8852			0.429508
$901$	−0.558853	+	1.71997i	−0.0186181	+	0.0573006i
$902$	−40.1152	−	8.52676i	−1.33569	−	0.283910i
$903$	−0.580176	−	0.421522i	−0.0193070	−	0.0140274i
$904$	−2.40317	−	4.16240i	−0.0799281	−	0.138439i
$905$	1.67823	−	2.90678i	0.0557863	−	0.0966248i
$906$	0.125489	−	0.0558713i	0.00416909	−	0.00185620i
$907$	9.99143	−	7.25920i	0.331760	−	0.241038i	−0.409417	−	0.912347i	$-0.634268\pi$
$907$	9.99143	−	7.25920i	0.331760	−	0.241038i	0.741177	+	0.671310i	$0.234268\pi$
$908$	5.21326	+	2.32109i	0.173008	+	0.0770282i
$909$	−12.4539	+	2.64716i	−0.413070	+	0.0878007i
$910$	−0.0156483	+	0.148884i	−0.000518736	+	0.00493545i
$911$	−27.7041	−	30.7685i	−0.917876	−	1.01941i	−0.999741	−	0.0227616i	$-0.992754\pi$
$911$	−27.7041	−	30.7685i	−0.917876	−	1.01941i	0.0818644	−	0.996643i	$-0.473913\pi$
$912$	0.398597	−	0.442686i	0.0131989	−	0.0146588i
$913$	7.59138	+	72.2272i	0.251238	+	2.39037i
$914$	−7.11968	−	21.9121i	−0.235498	−	0.724788i
$915$	−0.0730334	−	0.224774i	−0.00241441	−	0.00743079i
$916$	−2.60298	−	24.7657i	−0.0860050	−	0.818283i
$917$	3.13325	−	3.47983i	0.103469	−	0.114914i
$918$	−0.446920	−	0.496355i	−0.0147506	−	0.0163821i
$919$	−4.26547	+	40.5833i	−0.140705	+	1.33872i	0.665196	+	0.746669i	$0.268348\pi$
$919$	−4.26547	+	40.5833i	−0.140705	+	1.33872i	−0.805901	+	0.592050i	$0.798319\pi$
$920$	1.07528	−	0.228559i	0.0354511	−	0.00753536i
$921$	14.5713	+	6.48758i	0.480142	+	0.213773i
$922$	0.674654	−	0.490165i	0.0222185	−	0.0161427i
$923$	−8.26368	+	3.67923i	−0.272002	+	0.121103i
$924$	−0.521852	+	0.903875i	−0.0171677	+	0.0297353i
$925$	−18.8498	−	32.6488i	−0.619777	−	1.07349i
$926$	8.75934	+	6.36403i	0.287850	+	0.209135i
$927$	19.1299	+	4.06619i	0.628309	+	0.133551i
$928$	2.23781	−	6.88728i	0.0734598	−	0.226086i
$929$	−40.0388			−1.31363			−0.656815	−	0.754052i	$-0.728097\pi$
$929$	−40.0388			−1.31363			−0.656815	+	0.754052i	$0.728097\pi$
$930$	0.829812	−	0.488094i	0.0272106	−	0.0160052i
$931$	6.63668			0.217508
$932$	−4.09823	+	12.6130i	−0.134242	+	0.413154i
$933$	−17.6664	−	3.75510i	−0.578371	−	0.122937i
$934$	−22.0768	−	16.0398i	−0.722376	−	0.524837i
$935$	−0.134342	−	0.232686i	−0.00439344	−	0.00760966i
$936$	2.07072	−	3.58659i	0.0676835	−	0.117231i
$937$	−24.3839	+	10.8564i	−0.796589	+	0.354664i	−0.764338	−	0.644816i	$-0.776934\pi$
$937$	−24.3839	+	10.8564i	−0.796589	+	0.354664i	−0.0322507	+	0.999480i	$0.510267\pi$
$938$	−1.80163	+	1.30896i	−0.0588251	+	0.0427390i
$939$	9.19352	+	4.09322i	0.300019	+	0.133577i
$940$	2.70071	−	0.574054i	0.0880874	−	0.0187236i
$941$	−1.27970	+	12.1755i	−0.0417169	+	0.396910i	0.953662	+	0.300881i	$0.0972807\pi$
$941$	−1.27970	+	12.1755i	−0.0417169	+	0.396910i	−0.995379	+	0.0960288i	$0.969386\pi$
$942$	9.11162	+	10.1195i	0.296873	+	0.329710i
$943$	21.5981	−	23.9872i	0.703332	−	0.781129i
$944$	−1.15786	−	11.0163i	−0.0376851	−	0.358550i
$945$	0.101540	+	0.312508i	0.00330309	+	0.0101659i
$946$	5.29216	+	16.2876i	0.172063	+	0.529555i
$947$	−0.317373	−	3.01960i	−0.0103132	−	0.0981238i	0.988154	−	0.153463i	$-0.0490426\pi$
$947$	−0.317373	−	3.01960i	−0.0103132	−	0.0981238i	−0.998468	+	0.0553393i	$0.982376\pi$
$948$	−5.64543	+	6.26989i	−0.183355	+	0.203636i
$949$	16.3944	+	18.2078i	0.532185	+	0.591051i
$950$	−0.495864	+	4.71783i	−0.0160880	+	0.153067i
$951$	12.7074	−	2.70104i	0.412065	−	0.0875871i
$952$	0.0594435	+	0.0264659i	0.00192657	+	0.000857766i
$953$	−48.1834	+	35.0073i	−1.56081	+	1.13400i	−0.625476	+	0.780244i	$0.715095\pi$
$953$	−48.1834	+	35.0073i	−1.56081	+	1.13400i	−0.935338	+	0.353754i	$0.884905\pi$
$954$	−22.4853	+	10.0111i	−0.727989	+	0.324122i
$955$	−1.06824	+	1.85025i	−0.0345676	+	0.0598728i
$956$	10.4739	+	18.1413i	0.338750	+	0.586731i
$957$	18.0769	+	13.1337i	0.584344	+	0.424551i
$958$	−37.4413	−	7.95839i	−1.20967	−	0.257124i
$959$	0.747438	−	2.30038i	0.0241360	−	0.0742831i
$960$	0.172909			0.00558062
$961$	15.0632	−	27.0943i	0.485910	−	0.874009i
$962$	−12.1170			−0.390667
$963$	−2.24648	+	6.91396i	−0.0723919	+	0.222799i
$964$	−10.6569	−	2.26519i	−0.343235	−	0.0729569i
$965$	3.73308	+	2.71224i	0.120172	+	0.0873101i
$966$	−0.410722	−	0.711391i	−0.0132148	−	0.0228886i
$967$	−1.47897	+	2.56165i	−0.0475605	+	0.0823773i	−0.888826	−	0.458246i	$-0.848478\pi$
$967$	−1.47897	+	2.56165i	−0.0475605	+	0.0823773i	0.841265	+	0.540623i	$0.181811\pi$
$968$	12.7207	−	5.66360i	0.408857	−	0.182035i
$969$	0.0927048	−	0.0673540i	0.00297811	−	0.00216372i
$970$	−3.10806	−	1.38380i	−0.0997937	−	0.0444310i
$971$	2.96371	−	0.629957i	0.0951101	−	0.0202163i	−0.160111	−	0.987099i	$-0.551185\pi$
$971$	2.96371	−	0.629957i	0.0951101	−	0.0202163i	0.255221	+	0.966883i	$0.417852\pi$
$972$	1.45757	−	13.8679i	0.0467517	−	0.444813i
$973$	1.48954	+	1.65430i	0.0477524	+	0.0530344i
$974$	−20.1335	+	22.3605i	−0.645119	+	0.716478i
$975$	−0.502967	−	4.78541i	−0.0161078	−	0.153256i
$976$	−0.422381	−	1.29995i	−0.0135201	−	0.0416105i
$977$	6.59963	+	20.3116i	0.211141	+	0.649825i	0.999405	+	0.0344881i	$0.0109801\pi$
$977$	6.59963	+	20.3116i	0.211141	+	0.649825i	−0.788264	+	0.615337i	$0.789020\pi$
$978$	−1.25576	−	11.9478i	−0.0401549	−	0.382048i
$979$	−16.5570	+	18.3884i	−0.529163	+	0.587696i
$980$	1.28901	+	1.43159i	0.0411760	+	0.0457305i
$981$	1.03982	−	9.89320i	0.0331988	−	0.315866i
$982$	20.0847	−	4.26913i	0.640928	−	0.136233i
$983$	0.299251	+	0.133235i	0.00954462	+	0.00424954i	0.411503	−	0.911408i	$-0.365004\pi$
$983$	0.299251	+	0.133235i	0.00954462	+	0.00424954i	−0.401959	+	0.915658i	$0.631670\pi$
$984$	4.10735	−	2.98417i	0.130938	−	0.0951317i
$985$	2.21541	−	0.986364i	0.0705888	−	0.0314282i
$986$	0.696520	−	1.20641i	0.0221817	−	0.0384198i
$987$	−1.03158	−	1.78675i	−0.0328355	−	0.0568728i
$988$	1.23351	+	0.896199i	0.0392432	+	0.0285119i
$989$	−13.1842	−	2.80240i	−0.419234	−	0.0891110i
$990$	1.12999	−	3.47776i	0.0359136	−	0.110531i
$991$	−38.8868			−1.23528			−0.617641	−	0.786461i	$-0.711911\pi$
$991$	−38.8868			−1.23528			−0.617641	+	0.786461i	$0.711911\pi$
$992$	4.79912	−	2.82284i	0.152372	−	0.0896251i
$993$	−0.539514			−0.0171210
$994$	0.597727	−	1.83961i	0.0189587	−	0.0583490i
$995$	−3.33285	−	0.708419i	−0.105658	−	0.0224584i
$996$	−7.27349	−	5.28450i	−0.230469	−	0.167446i
$997$	9.78047	+	16.9403i	0.309750	+	0.536503i	0.978308	−	0.207157i	$-0.0664212\pi$
$997$	9.78047	+	16.9403i	0.309750	+	0.536503i	−0.668557	+	0.743661i	$0.733088\pi$
$998$	13.8054	−	23.9116i	0.437002	−	0.756909i
$999$	−24.2966	+	10.8176i	−0.768711	+	0.342252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.g.a.9.1	yes	8
3.2	odd	2		558.2.ba.f.505.1		8
4.3	odd	2		496.2.bg.a.257.1		8
31.7	even	15	inner	62.2.g.a.7.1	✓	8
31.10	even	15		1922.2.a.q.1.2		4
31.21	odd	30		1922.2.a.o.1.4		4
93.38	odd	30		558.2.ba.f.379.1		8
124.7	odd	30		496.2.bg.a.193.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.g.a.7.1	✓	8	31.7	even	15	inner
62.2.g.a.9.1	yes	8	1.1	even	1	trivial
496.2.bg.a.193.1		8	124.7	odd	30
496.2.bg.a.257.1		8	4.3	odd	2
558.2.ba.f.379.1		8	93.38	odd	30
558.2.ba.f.505.1		8	3.2	odd	2
1922.2.a.o.1.4		4	31.21	odd	30
1922.2.a.q.1.2		4	31.10	even	15

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.604528 + 0.128496i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.139886 + 0.242290i) q^{5} +(0.309017 - 0.535233i) q^{6} +(-0.309017 + 0.137583i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-2.39169 - 1.06485i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.604528 + 0.128496i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.139886 + 0.242290i) q^{5} +(0.309017 - 0.535233i) q^{6} +(-0.309017 + 0.137583i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-2.39169 - 1.06485i) q^{9} +(0.273659 - 0.0581680i) q^{10} +(-0.521852 + 4.96509i) q^{11} +(-0.413545 - 0.459289i) q^{12} +(1.05849 - 1.17557i) q^{13} +(0.0353579 + 0.336408i) q^{14} +(0.0534318 + 0.164446i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.0201074 + 0.191309i) q^{17} +(-1.75181 + 1.94558i) q^{18} +(-0.644943 - 0.716282i) q^{19} +(0.0292442 - 0.278240i) q^{20} +(-0.204489 + 0.0434654i) q^{21} +(4.56082 + 2.03061i) q^{22} +(-3.17886 + 2.30958i) q^{23} +(-0.564602 + 0.251377i) q^{24} +(2.46086 - 4.26234i) q^{25} +(-0.790943 - 1.36995i) q^{26} +(-2.80902 - 2.04087i) q^{27} +(0.330869 + 0.0703285i) q^{28} +(2.23781 - 6.88728i) q^{29} +0.172909 q^{30} +(4.79912 - 2.82284i) q^{31} +1.00000 q^{32} +(-0.953472 + 2.93448i) q^{33} +(0.188160 + 0.0399946i) q^{34} +(-0.0765624 - 0.0556258i) q^{35} +(1.30902 + 2.26728i) q^{36} +(3.82991 - 6.63361i) q^{37} +(-0.880523 + 0.392034i) q^{38} +(0.790943 - 0.574654i) q^{39} +(-0.255585 - 0.113794i) q^{40} +(-8.03519 + 1.70793i) q^{41} +(-0.0218524 + 0.207912i) q^{42} +(2.29535 + 2.54924i) q^{43} +(3.34060 - 3.71011i) q^{44} +(-0.0765624 - 0.728442i) q^{45} +(1.21422 + 3.73697i) q^{46} +(3.04965 + 9.38587i) q^{47} +(0.0646021 + 0.614648i) q^{48} +(-4.60735 + 5.11698i) q^{49} +(-3.29328 - 3.65756i) q^{50} +(-0.0124271 + 0.118236i) q^{51} +(-1.54732 + 0.328893i) q^{52} +(8.58862 + 3.82390i) q^{53} +(-2.80902 + 2.04087i) q^{54} +(-1.27599 + 0.568109i) q^{55} +(0.169131 - 0.292943i) q^{56} +(-0.297847 - 0.515886i) q^{57} +(-5.85867 - 4.25657i) q^{58} +(-10.8349 - 2.30303i) q^{59} +(0.0534318 - 0.164446i) q^{60} -1.36685 q^{61} +(-1.20167 - 5.43654i) q^{62} +0.885579 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.432897 + 0.0920152i) q^{65} +(2.49622 + 1.81361i) q^{66} +(3.29173 + 5.70145i) q^{67} +(0.0961816 - 0.166591i) q^{68} +(-2.21848 + 0.987732i) q^{69} +(-0.0765624 + 0.0556258i) q^{70} +(-5.22394 - 2.32585i) q^{71} +(2.56082 - 0.544320i) q^{72} +(-1.61899 + 15.4037i) q^{73} +(-5.12543 - 5.69236i) q^{74} +(2.03536 - 2.26049i) q^{75} +(0.100750 + 0.958572i) q^{76} +(-0.521852 - 1.60610i) q^{77} +(-0.302113 - 0.929809i) q^{78} +(-1.42695 - 13.5765i) q^{79} +(-0.187205 + 0.207912i) q^{80} +(3.81953 + 4.24202i) q^{81} +(-0.858670 + 8.16970i) q^{82} +(14.2291 - 3.02449i) q^{83} +(0.190983 + 0.0850311i) q^{84} +(-0.0435397 + 0.0316334i) q^{85} +(3.13377 - 1.39525i) q^{86} +(2.23781 - 3.87601i) q^{87} +(-2.49622 - 4.32358i) q^{88} +(4.00973 + 2.91324i) q^{89} +(-0.716449 - 0.152286i) q^{90} +(-0.165352 + 0.508902i) q^{91} +3.92928 q^{92} +(3.26393 - 1.08981i) q^{93} +9.86889 q^{94} +(0.0833294 - 0.256462i) q^{95} +(0.604528 + 0.128496i) q^{96} +(-9.83810 - 7.14780i) q^{97} +(3.44279 + 5.96309i) q^{98} +(6.53519 - 11.3193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - 4 q^{10} - 13 q^{11} + 3 q^{12} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + q^{18} - 3 q^{19} - 4 q^{20} + q^{21} + 17 q^{22} + 3 q^{23} - 2 q^{24} + q^{25} - 10 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 14 q^{30} + 11 q^{31} + 8 q^{32} - 2 q^{33} + 18 q^{34} + 16 q^{35} + 6 q^{36} + 6 q^{37} + 12 q^{38} + 10 q^{39} - 4 q^{40} - 19 q^{41} - 9 q^{42} - 26 q^{43} + 7 q^{44} + 16 q^{45} - 17 q^{46} + q^{47} - 2 q^{48} - 23 q^{49} - 19 q^{50} - 16 q^{51} + 17 q^{53} - 18 q^{54} + 7 q^{55} - 3 q^{56} + 6 q^{57} - 19 q^{58} + 8 q^{59} - 6 q^{60} + 48 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} - 30 q^{65} + 3 q^{66} + 12 q^{67} - 17 q^{68} - 7 q^{69} + 16 q^{70} + 9 q^{71} + q^{72} - 33 q^{73} - 19 q^{74} + 18 q^{75} - 18 q^{76} - 13 q^{77} - 10 q^{78} - 19 q^{79} + 11 q^{80} - 16 q^{81} + 21 q^{82} + 40 q^{83} + 6 q^{84} + 29 q^{85} + 19 q^{86} + 11 q^{87} - 3 q^{88} + 8 q^{89} + 11 q^{90} + 20 q^{91} + 28 q^{92} + 44 q^{93} + 26 q^{94} + 36 q^{95} + 3 q^{96} - 23 q^{97} + 17 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - 4 * q^10 - 13 * q^11 + 3 * q^12 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + q^18 - 3 * q^19 - 4 * q^20 + q^21 + 17 * q^22 + 3 * q^23 - 2 * q^24 + q^25 - 10 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 14 * q^30 + 11 * q^31 + 8 * q^32 - 2 * q^33 + 18 * q^34 + 16 * q^35 + 6 * q^36 + 6 * q^37 + 12 * q^38 + 10 * q^39 - 4 * q^40 - 19 * q^41 - 9 * q^42 - 26 * q^43 + 7 * q^44 + 16 * q^45 - 17 * q^46 + q^47 - 2 * q^48 - 23 * q^49 - 19 * q^50 - 16 * q^51 + 17 * q^53 - 18 * q^54 + 7 * q^55 - 3 * q^56 + 6 * q^57 - 19 * q^58 + 8 * q^59 - 6 * q^60 + 48 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 - 30 * q^65 + 3 * q^66 + 12 * q^67 - 17 * q^68 - 7 * q^69 + 16 * q^70 + 9 * q^71 + q^72 - 33 * q^73 - 19 * q^74 + 18 * q^75 - 18 * q^76 - 13 * q^77 - 10 * q^78 - 19 * q^79 + 11 * q^80 - 16 * q^81 + 21 * q^82 + 40 * q^83 + 6 * q^84 + 29 * q^85 + 19 * q^86 + 11 * q^87 - 3 * q^88 + 8 * q^89 + 11 * q^90 + 20 * q^91 + 28 * q^92 + 44 * q^93 + 26 * q^94 + 36 * q^95 + 3 * q^96 - 23 * q^97 + 17 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more