LMFDB - Embedded newform 930.2.bg.c.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (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:	$7.42608738798$
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} + 40x^{14} + 654x^{12} + 5650x^{10} + 27831x^{8} + 78445x^{6} + 119819x^{4} + 87030x^{2} + 22801 $ x^16 + 40x^14 + 654x^12 + 5650x^10 + 27831x^8 + 78445x^6 + 119819x^4 + 87030*x^2 + 22801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.2
Root			$0.772036i$ of defining polynomial
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.c.661.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.84496 - 0.817271i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.84496 - 0.817271i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(2.81193 + 3.12296i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(-1.77083 + 0.788423i) q^{13} +(-2.63026 + 2.92119i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.32709 - 1.47388i) q^{17} +(0.913545 - 0.406737i) q^{18} +(7.60997 + 3.38818i) q^{19} +(-0.669131 - 0.743145i) q^{20} +(-0.410886 - 3.90932i) q^{21} +(-4.11053 - 0.873720i) q^{22} +(2.36419 + 7.27623i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.969206 - 1.67871i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.410886 - 3.90932i) q^{28} +(-5.80883 + 4.22036i) q^{29} +1.00000 q^{30} +(-2.17194 - 5.12666i) q^{31} +1.00000 q^{32} +(3.39978 - 2.47008i) q^{33} +(-0.207312 + 1.97244i) q^{34} +(1.21470 - 3.73846i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-4.54151 - 7.86612i) q^{37} +(-8.14812 + 1.73194i) q^{38} +(0.599002 + 1.84354i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-0.0138138 - 0.131430i) q^{41} +(2.63026 + 2.92119i) q^{42} +(4.37847 + 1.94942i) q^{43} +(3.83905 - 1.70925i) q^{44} +(-0.669131 + 0.743145i) q^{45} +(-6.18953 - 4.49696i) q^{46} +(-7.34439 - 5.33601i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(7.72094 - 3.43758i) q^{49} +(0.913545 + 0.406737i) q^{50} +(-1.32709 - 1.47388i) q^{51} +(0.202619 + 1.92779i) q^{52} +(9.49676 + 2.01860i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(4.11053 - 0.873720i) q^{55} +(1.96543 + 3.40422i) q^{56} +(4.16508 - 7.21412i) q^{57} +(2.21878 - 6.82869i) q^{58} +(0.135017 - 1.28460i) q^{59} +(-0.809017 + 0.587785i) q^{60} +0.737960 q^{61} +(4.77051 + 2.87092i) q^{62} -3.93085 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.202619 + 1.92779i) q^{65} +(-1.29860 + 3.99668i) q^{66} +(7.52167 - 13.0279i) q^{67} +(-0.991653 - 1.71759i) q^{68} +(7.48349 - 1.59067i) q^{69} +(1.21470 + 3.73846i) q^{70} +(-3.75177 - 0.797464i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(7.66042 + 8.50775i) q^{73} +(8.29775 + 3.69440i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(5.57396 - 6.19051i) q^{76} +(13.3640 + 9.70954i) q^{77} +(-1.56821 - 1.13937i) q^{78} +(-6.64837 + 7.38377i) q^{79} +(-0.913545 + 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(0.0884280 + 0.0982093i) q^{82} +(-0.579411 - 5.51273i) q^{83} +(-3.84496 - 0.817271i) q^{84} +(-0.612875 - 1.88624i) q^{85} +(-4.68809 + 0.996485i) q^{86} +(3.59006 + 6.21816i) q^{87} +(-2.10118 + 3.63935i) q^{88} +(-0.924482 + 2.84526i) q^{89} +(0.104528 - 0.994522i) q^{90} +(-6.16440 + 4.47870i) q^{91} +7.65068 q^{92} +(-5.32561 + 1.62416i) q^{93} +9.07816 q^{94} +(6.73923 - 4.89634i) q^{95} +(0.104528 - 0.994522i) q^{96} +(2.79014 - 8.58716i) q^{97} +(-4.22581 + 7.31932i) q^{98} +(-2.10118 - 3.63935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	3.84496	−	0.817271i	1.45326	−	0.308899i	0.587443	−	0.809266i	$-0.300135\pi$
$7$	3.84496	−	0.817271i	1.45326	−	0.308899i	0.865814	+	0.500366i	$0.166801\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	0.104528	+	0.994522i	0.0330548	+	0.314495i
$11$	2.81193	+	3.12296i	0.847828	+	0.941608i	0.998899	−	0.0469145i	$-0.0149388\pi$
$11$	2.81193	+	3.12296i	0.847828	+	0.941608i	−0.151071	+	0.988523i	$0.548272\pi$
$12$	−0.913545	−	0.406737i	−0.263718	−	0.117415i
$13$	−1.77083	+	0.788423i	−0.491139	+	0.218669i	−0.637336	−	0.770586i	$-0.719963\pi$
$13$	−1.77083	+	0.788423i	−0.491139	+	0.218669i	0.146197	+	0.989256i	$0.453297\pi$
$14$	−2.63026	+	2.92119i	−0.702965	+	0.780722i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.32709	−	1.47388i	0.321867	−	0.357469i	−0.560397	−	0.828224i	$-0.689352\pi$
$17$	1.32709	−	1.47388i	0.321867	−	0.357469i	0.882264	+	0.470755i	$0.156018\pi$
$18$	0.913545	−	0.406737i	0.215325	−	0.0958687i
$19$	7.60997	+	3.38818i	1.74585	+	0.777301i	0.992863	+	0.119263i	$0.0380531\pi$
$19$	7.60997	+	3.38818i	1.74585	+	0.777301i	0.752984	+	0.658039i	$0.228614\pi$
$20$	−0.669131	−	0.743145i	−0.149622	−	0.166172i
$21$	−0.410886	−	3.90932i	−0.0896627	−	0.853084i
$22$	−4.11053	−	0.873720i	−0.876367	−	0.186278i
$23$	2.36419	+	7.27623i	0.492968	+	1.51720i	0.820100	+	0.572220i	$0.193918\pi$
$23$	2.36419	+	7.27623i	0.492968	+	1.51720i	−0.327133	+	0.944978i	$0.606082\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.969206	−	1.67871i	0.190077	−	0.329223i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	0.410886	−	3.90932i	0.0776502	−	0.738792i
$29$	−5.80883	+	4.22036i	−1.07867	+	0.783702i	−0.977451	−	0.211162i	$-0.932275\pi$
$29$	−5.80883	+	4.22036i	−1.07867	+	0.783702i	−0.101222	+	0.994864i	$0.532275\pi$
$30$	1.00000			0.182574
$31$	−2.17194	−	5.12666i	−0.390092	−	0.920776i
$31$	−2.17194	−	5.12666i	−0.390092	−	0.920776i
$32$	1.00000			0.176777
$33$	3.39978	−	2.47008i	0.591826	−	0.429987i
$34$	−0.207312	+	1.97244i	−0.0355537	+	0.338271i
$35$	1.21470	−	3.73846i	0.205322	−	0.631916i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−4.54151	−	7.86612i	−0.746619	−	1.29318i	−0.949434	−	0.313966i	$-0.898342\pi$
$37$	−4.54151	−	7.86612i	−0.746619	−	1.29318i	0.202815	−	0.979217i	$-0.434991\pi$
$38$	−8.14812	+	1.73194i	−1.32180	+	0.280957i
$39$	0.599002	+	1.84354i	0.0959171	+	0.295202i
$40$	0.978148	+	0.207912i	0.154659	+	0.0328737i
$41$	−0.0138138	−	0.131430i	−0.00215736	−	0.0205259i	0.993390	−	0.114786i	$-0.0366182\pi$
$41$	−0.0138138	−	0.131430i	−0.00215736	−	0.0205259i	−0.995548	+	0.0942600i	$0.969952\pi$
$42$	2.63026	+	2.92119i	0.405857	+	0.450750i
$43$	4.37847	+	1.94942i	0.667710	+	0.297284i	0.712458	−	0.701715i	$-0.247582\pi$
$43$	4.37847	+	1.94942i	0.667710	+	0.297284i	−0.0447482	+	0.998998i	$0.514249\pi$
$44$	3.83905	−	1.70925i	0.578758	−	0.257680i
$45$	−0.669131	+	0.743145i	−0.0997481	+	0.110781i
$46$	−6.18953	−	4.49696i	−0.912596	−	0.663040i
$47$	−7.34439	−	5.33601i	−1.07129	−	0.778337i	−0.0951456	−	0.995463i	$-0.530332\pi$
$47$	−7.34439	−	5.33601i	−1.07129	−	0.778337i	−0.976144	+	0.217126i	$0.930332\pi$
$48$	−0.669131	+	0.743145i	−0.0965807	+	0.107264i
$49$	7.72094	−	3.43758i	1.10299	−	0.491083i
$50$	0.913545	+	0.406737i	0.129195	+	0.0575212i
$51$	−1.32709	−	1.47388i	−0.185830	−	0.206385i
$52$	0.202619	+	1.92779i	0.0280982	+	0.267337i
$53$	9.49676	+	2.01860i	1.30448	+	0.277276i	0.807181	−	0.590304i	$-0.200992\pi$
$53$	9.49676	+	2.01860i	1.30448	+	0.277276i	0.497299	+	0.867579i	$0.334325\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	4.11053	−	0.873720i	0.554263	−	0.117812i
$56$	1.96543	+	3.40422i	0.262641	+	0.454908i
$57$	4.16508	−	7.21412i	0.551678	−	0.955534i
$58$	2.21878	−	6.82869i	0.291340	−	0.896651i
$59$	0.135017	−	1.28460i	0.0175777	−	0.167241i	−0.982211	−	0.187779i	$-0.939871\pi$
$59$	0.135017	−	1.28460i	0.0175777	−	0.167241i	0.999789	+	0.0205379i	$0.00653788\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	0.737960			0.0944861			0.0472431	−	0.998883i	$-0.484956\pi$
$61$	0.737960			0.0944861			0.0472431	+	0.998883i	$0.484956\pi$
$62$	4.77051	+	2.87092i	0.605856	+	0.364607i
$63$	−3.93085			−0.495241
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.202619	+	1.92779i	−0.0251318	+	0.239113i
$66$	−1.29860	+	3.99668i	−0.159847	+	0.491957i
$67$	7.52167	−	13.0279i	0.918918	−	1.59161i	0.117857	−	0.993031i	$-0.462398\pi$
$67$	7.52167	−	13.0279i	0.918918	−	1.59161i	0.801061	−	0.598582i	$-0.204269\pi$
$68$	−0.991653	−	1.71759i	−0.120256	−	0.208289i
$69$	7.48349	−	1.59067i	0.900907	−	0.191494i
$70$	1.21470	+	3.73846i	0.145185	+	0.446832i
$71$	−3.75177	−	0.797464i	−0.445253	−	0.0946415i	−0.0201718	−	0.999797i	$-0.506421\pi$
$71$	−3.75177	−	0.797464i	−0.445253	−	0.0946415i	−0.425082	+	0.905155i	$0.639755\pi$
$72$	−0.104528	−	0.994522i	−0.0123188	−	0.117206i
$73$	7.66042	+	8.50775i	0.896584	+	0.995757i	0.999999	+	0.00111914i	$0.000356233\pi$
$73$	7.66042	+	8.50775i	0.896584	+	0.995757i	−0.103415	+	0.994638i	$0.532977\pi$
$74$	8.29775	+	3.69440i	0.964594	+	0.429465i
$75$	−0.913545	+	0.406737i	−0.105487	+	0.0469659i
$76$	5.57396	−	6.19051i	0.639377	−	0.710100i
$77$	13.3640	+	9.70954i	1.52297	+	1.10651i
$78$	−1.56821	−	1.13937i	−0.177565	−	0.129008i
$79$	−6.64837	+	7.38377i	−0.748001	+	0.830739i	−0.990225	−	0.139482i	$-0.955456\pi$
$79$	−6.64837	+	7.38377i	−0.748001	+	0.830739i	0.242224	+	0.970220i	$0.422123\pi$
$80$	−0.913545	+	0.406737i	−0.102137	+	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	0.0884280	+	0.0982093i	0.00976524	+	0.0108454i
$83$	−0.579411	−	5.51273i	−0.0635987	−	0.605101i	−0.979184	−	0.202976i	$-0.934939\pi$
$83$	−0.579411	−	5.51273i	−0.0635987	−	0.605101i	0.915585	−	0.402125i	$-0.131728\pi$
$84$	−3.84496	−	0.817271i	−0.419519	−	0.0891715i
$85$	−0.612875	−	1.88624i	−0.0664757	−	0.204591i
$86$	−4.68809	+	0.996485i	−0.505530	+	0.107454i
$87$	3.59006	+	6.21816i	0.384894	+	0.666657i
$88$	−2.10118	+	3.63935i	−0.223987	+	0.387956i
$89$	−0.924482	+	2.84526i	−0.0979949	+	0.301597i	−0.988023	−	0.154309i	$-0.950685\pi$
$89$	−0.924482	+	2.84526i	−0.0979949	+	0.301597i	0.890028	+	0.455906i	$0.150685\pi$
$90$	0.104528	−	0.994522i	0.0110183	−	0.104832i
$91$	−6.16440	+	4.47870i	−0.646204	+	0.469495i
$92$	7.65068			0.797638
$93$	−5.32561	+	1.62416i	−0.552240	+	0.168418i
$94$	9.07816			0.936341
$95$	6.73923	−	4.89634i	0.691431	−	0.502354i
$96$	0.104528	−	0.994522i	0.0106684	−	0.101503i
$97$	2.79014	−	8.58716i	0.283295	−	0.871894i	−0.703609	−	0.710587i	$-0.748429\pi$
$97$	2.79014	−	8.58716i	0.283295	−	0.871894i	0.986904	−	0.161306i	$-0.0515707\pi$
$98$	−4.22581	+	7.31932i	−0.426871	+	0.739363i
$99$	−2.10118	−	3.63935i	−0.211177	−	0.365768i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	4.48429	+	13.8012i	0.446204	+	1.37327i	0.881158	+	0.472822i	$0.156765\pi$
$101$	4.48429	+	13.8012i	0.446204	+	1.37327i	−0.434954	+	0.900453i	$0.643235\pi$
$102$	1.93997	+	0.412353i	0.192085	+	0.0408290i
$103$	−0.356014	−	3.38725i	−0.0350791	−	0.333755i	−0.997961	−	0.0638313i	$-0.979668\pi$
$103$	−0.356014	−	3.38725i	−0.0350791	−	0.333755i	0.962882	−	0.269924i	$-0.0869986\pi$
$104$	−1.29705	−	1.44052i	−0.127186	−	0.141255i
$105$	−3.59101	−	1.59882i	−0.350447	−	0.156029i
$106$	−8.86954	+	3.94897i	−0.861486	+	0.383558i
$107$	−1.88796	+	2.09680i	−0.182516	+	0.202705i	−0.827459	−	0.561526i	$-0.810214\pi$
$107$	−1.88796	+	2.09680i	−0.182516	+	0.202705i	0.644943	+	0.764231i	$0.276881\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	−13.2185	−	9.60377i	−1.26610	−	0.919874i	−0.267058	−	0.963680i	$-0.586052\pi$
$109$	−13.2185	−	9.60377i	−1.26610	−	0.919874i	−0.999040	+	0.0438064i	$0.986052\pi$
$110$	−2.81193	+	3.12296i	−0.268107	+	0.297763i
$111$	−8.29775	+	3.69440i	−0.787587	+	0.350657i
$112$	−3.59101	−	1.59882i	−0.339319	−	0.151075i
$113$	−13.2163	−	14.6782i	−1.24328	−	1.38080i	−0.896612	−	0.442817i	$-0.853979\pi$
$113$	−13.2163	−	14.6782i	−1.24328	−	1.38080i	−0.346670	−	0.937987i	$-0.612688\pi$
$114$	0.870738	+	8.28452i	0.0815521	+	0.775916i
$115$	7.48349	+	1.59067i	0.697839	+	0.148330i
$116$	2.21878	+	6.82869i	0.206008	+	0.634028i
$117$	1.89605	−	0.403018i	0.175290	−	0.0372591i
$118$	0.645839	+	1.11863i	0.0594543	+	0.102978i
$119$	3.89804	−	6.75161i	0.357333	−	0.618919i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	−0.696141	+	6.62334i	−0.0632856	+	0.602122i
$122$	−0.597022	+	0.433762i	−0.0540519	+	0.0392710i
$123$	−0.132154			−0.0119159
$124$	−5.54691	+	0.481414i	−0.498127	+	0.0432323i
$125$	−1.00000			−0.0894427
$126$	3.18013	−	2.31050i	0.283308	−	0.205836i
$127$	0.864465	−	8.22484i	0.0767089	−	0.729837i	−0.886799	−	0.462156i	$-0.847076\pi$
$127$	0.864465	−	8.22484i	0.0767089	−	0.729837i	0.963508	−	0.267681i	$-0.0862572\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	2.39641	−	4.15071i	0.210992	−	0.365450i
$130$	−0.969206	−	1.67871i	−0.0850050	−	0.147233i
$131$	−15.2181	+	3.23470i	−1.32961	+	0.282617i	−0.817315	−	0.576192i	$-0.804538\pi$
$131$	−15.2181	+	3.23470i	−1.32961	+	0.282617i	−0.512296	+	0.858809i	$0.671205\pi$
$132$	−1.29860	−	3.99668i	−0.113029	−	0.347866i
$133$	32.0291	+	6.80799i	2.77727	+	0.590327i
$134$	1.57246	+	14.9609i	0.135840	+	1.29243i
$135$	0.669131	+	0.743145i	0.0575896	+	0.0639597i
$136$	1.81184	+	0.806683i	0.155364	+	0.0691725i
$137$	8.81525	−	3.92480i	0.753138	−	0.335319i	0.00599494	−	0.999982i	$-0.498092\pi$
$137$	8.81525	−	3.92480i	0.753138	−	0.335319i	0.747143	+	0.664663i	$0.231425\pi$
$138$	−5.11930	+	5.68556i	−0.435784	+	0.483987i
$139$	7.04832	+	5.12090i	0.597831	+	0.434349i	0.845108	−	0.534595i	$-0.179536\pi$
$139$	7.04832	+	5.12090i	0.597831	+	0.434349i	−0.247278	+	0.968945i	$0.579536\pi$
$140$	−3.18013	−	2.31050i	−0.268770	−	0.195273i
$141$	−6.07448	+	6.74639i	−0.511563	+	0.568149i
$142$	3.50399	−	1.56007i	0.294048	−	0.130919i
$143$	−7.44165	−	3.31324i	−0.622302	−	0.277067i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	0.750526	+	7.14078i	0.0623278	+	0.593009i
$146$	−11.1981	−	2.38024i	−0.926765	−	0.196990i
$147$	−2.61169	−	8.03797i	−0.215409	−	0.662960i
$148$	−8.88453	+	1.88847i	−0.730304	+	0.155231i
$149$	4.19957	+	7.27387i	0.344042	+	0.595898i	0.985179	−	0.171528i	$-0.0548704\pi$
$149$	4.19957	+	7.27387i	0.344042	+	0.595898i	−0.641137	+	0.767426i	$0.721537\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−1.87380	+	5.76698i	−0.152488	+	0.469310i	−0.997898	−	0.0648084i	$-0.979356\pi$
$151$	−1.87380	+	5.76698i	−0.152488	+	0.469310i	0.845410	+	0.534118i	$0.179356\pi$
$152$	−0.870738	+	8.28452i	−0.0706262	+	0.671963i
$153$	−1.60453	+	1.16576i	−0.129718	+	0.0942460i
$154$	−16.5189			−1.33113
$155$	−5.52579	−	0.682374i	−0.443842	−	0.0548096i
$156$	1.93841			0.155197
$157$	3.69206	−	2.68244i	0.294658	−	0.214082i	−0.430627	−	0.902530i	$-0.641708\pi$
$157$	3.69206	−	2.68244i	0.294658	−	0.214082i	0.725286	+	0.688448i	$0.241708\pi$
$158$	1.03858	−	9.88141i	0.0826248	−	0.786123i
$159$	3.00022	−	9.23373i	0.237933	−	0.732283i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	15.0369	+	26.0446i	1.18507	+	2.05260i
$162$	−0.978148	+	0.207912i	−0.0768505	+	0.0163351i
$163$	−2.58345	−	7.95105i	−0.202352	−	0.622775i	−0.999812	−	0.0194028i	$-0.993824\pi$
$163$	−2.58345	−	7.95105i	−0.202352	−	0.622775i	0.797460	−	0.603372i	$-0.206176\pi$
$164$	−0.129266	−	0.0274763i	−0.0100940	−	0.00214554i
$165$	−0.439266	−	4.17934i	−0.0341968	−	0.325361i
$166$	3.70906	+	4.11932i	0.287879	+	0.319722i
$167$	3.73841	+	1.66445i	0.289287	+	0.128799i	0.546249	−	0.837623i	$-0.316055\pi$
$167$	3.73841	+	1.66445i	0.289287	+	0.128799i	−0.256963	+	0.966421i	$0.582722\pi$
$168$	3.59101	−	1.59882i	0.277053	−	0.123352i
$169$	−6.18448	+	6.86856i	−0.475729	+	0.528351i
$170$	1.60453	+	1.16576i	0.123062	+	0.0894096i
$171$	−6.73923	−	4.89634i	−0.515362	−	0.374432i
$172$	3.20703	−	3.56177i	0.244534	−	0.271582i
$173$	−5.97407	+	2.65983i	−0.454200	+	0.202223i	−0.621069	−	0.783756i	$-0.713301\pi$
$173$	−5.97407	+	2.65983i	−0.454200	+	0.202223i	0.166868	+	0.985979i	$0.446635\pi$
$174$	−6.55936	−	2.92041i	−0.497264	−	0.221396i
$175$	−2.63026	−	2.92119i	−0.198829	−	0.220822i
$176$	−0.439266	−	4.17934i	−0.0331109	−	0.315029i
$177$	−1.26345	−	0.268555i	−0.0949668	−	0.0201858i
$178$	−0.924482	−	2.84526i	−0.0692929	−	0.213262i
$179$	−2.40381	+	0.510945i	−0.179669	+	0.0381898i	−0.296868	−	0.954919i	$-0.595942\pi$
$179$	−2.40381	+	0.510945i	−0.179669	+	0.0381898i	0.117198	+	0.993109i	$0.462609\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	1.23442	−	2.13808i	0.0917536	−	0.158922i	−0.816495	−	0.577352i	$-0.804086\pi$
$181$	1.23442	−	2.13808i	0.0917536	−	0.158922i	0.908249	+	0.418430i	$0.137419\pi$
$182$	2.35459	−	7.24668i	0.174534	−	0.537160i
$183$	0.0771378	−	0.733918i	0.00570219	−	0.0542527i
$184$	−6.18953	+	4.49696i	−0.456298	+	0.331520i
$185$	−9.08302			−0.667797
$186$	3.35385	−	4.44429i	0.245916	−	0.325871i
$187$	8.33457			0.609484
$188$	−7.34439	+	5.33601i	−0.535645	+	0.389169i
$189$	−0.410886	+	3.90932i	−0.0298876	+	0.284361i
$190$	−2.57416	+	7.92244i	−0.186749	+	0.574754i
$191$	1.07875	−	1.86845i	0.0780558	−	0.135197i	−0.824355	−	0.566073i	$-0.808462\pi$
$191$	1.07875	−	1.86845i	0.0780558	−	0.135197i	0.902411	+	0.430876i	$0.141795\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−26.2709	+	5.58406i	−1.89102	+	0.401950i	−0.998770	−	0.0495836i	$-0.984211\pi$
$193$	−26.2709	+	5.58406i	−1.89102	+	0.401950i	−0.892254	+	0.451533i	$0.850877\pi$
$194$	2.79014	+	8.58716i	0.200320	+	0.616522i
$195$	1.89605	+	0.403018i	0.135779	+	0.0288607i
$196$	−0.883435	−	8.40532i	−0.0631025	−	0.600380i
$197$	−13.7626	−	15.2849i	−0.980541	−	1.08900i	−0.996021	−	0.0891214i	$-0.971594\pi$
$197$	−13.7626	−	15.2849i	−0.980541	−	1.08900i	0.0154793	−	0.999880i	$-0.495073\pi$
$198$	3.83905	+	1.70925i	0.272829	+	0.121471i
$199$	−9.31055	+	4.14532i	−0.660007	+	0.293854i	−0.709276	−	0.704931i	$-0.750978\pi$
$199$	−9.31055	+	4.14532i	−0.660007	+	0.293854i	0.0492681	+	0.998786i	$0.484311\pi$
$200$	0.669131	−	0.743145i	0.0473147	−	0.0525483i
$201$	−12.1703	−	8.84225i	−0.858428	−	0.623684i
$202$	−11.7400	−	8.52963i	−0.826026	−	0.600143i
$203$	−18.8855	+	20.9745i	−1.32550	+	1.47212i
$204$	−1.81184	+	0.806683i	−0.126854	+	0.0564791i
$205$	−0.120728	−	0.0537517i	−0.00843203	−	0.00375418i
$206$	2.27900	+	2.53108i	0.158785	+	0.176349i
$207$	−0.799714	−	7.60877i	−0.0555839	−	0.528846i
$208$	1.89605	+	0.403018i	0.131468	+	0.0279443i
$209$	10.8175	+	33.2930i	0.748265	+	2.30292i
$210$	3.84496	−	0.817271i	0.265327	−	0.0563970i
$211$	−9.59505	−	16.6191i	−0.660550	−	1.14411i	−0.980471	−	0.196663i	$-0.936990\pi$
$211$	−9.59505	−	16.6191i	−0.660550	−	1.14411i	0.319921	−	0.947444i	$-0.396344\pi$
$212$	4.85446	−	8.40817i	0.333406	−	0.577476i
$213$	−1.18526	+	3.64786i	−0.0812128	+	0.249947i
$214$	0.294929	−	2.80606i	0.0201609	−	0.191818i
$215$	3.87748	−	2.81715i	0.264442	−	0.192128i
$216$	−1.00000			−0.0680414
$217$	−12.5409	−	17.9367i	−0.851331	−	1.21762i
$218$	16.3389			1.10661
$219$	9.26188	−	6.72915i	0.625860	−	0.454714i
$220$	0.439266	−	4.17934i	0.0296153	−	0.281771i
$221$	−1.18800	+	3.65630i	−0.0799138	+	0.245950i
$222$	4.54151	−	7.86612i	0.304806	−	0.527940i
$223$	−1.70872	−	2.95958i	−0.114424	−	0.198188i	0.803125	−	0.595810i	$-0.203169\pi$
$223$	−1.70872	−	2.95958i	−0.114424	−	0.198188i	−0.917549	+	0.397622i	$0.869836\pi$
$224$	3.84496	−	0.817271i	0.256902	−	0.0546062i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	19.3198	+	4.10655i	1.28513	+	0.273163i
$227$	−0.115365	−	1.09762i	−0.00765703	−	0.0728518i	0.990026	−	0.140884i	$-0.0449945\pi$
$227$	−0.115365	−	1.09762i	−0.00765703	−	0.0728518i	−0.997683	+	0.0680324i	$0.978328\pi$
$228$	−5.57396	−	6.19051i	−0.369144	−	0.409976i
$229$	4.97598	+	2.21545i	0.328822	+	0.146401i	0.564506	−	0.825429i	$-0.309067\pi$
$229$	4.97598	+	2.21545i	0.328822	+	0.146401i	−0.235685	+	0.971830i	$0.575733\pi$
$230$	−6.98924	+	3.11181i	−0.460857	+	0.205187i
$231$	11.0533	−	12.2759i	0.727252	−	0.807695i
$232$	−5.80883	−	4.22036i	−0.381369	−	0.277080i
$233$	−7.41764	−	5.38923i	−0.485946	−	0.353060i	0.317677	−	0.948199i	$-0.397097\pi$
$233$	−7.41764	−	5.38923i	−0.485946	−	0.353060i	−0.803623	+	0.595138i	$0.797097\pi$
$234$	−1.29705	+	1.44052i	−0.0847908	+	0.0941698i
$235$	−8.29331	+	3.69242i	−0.540996	+	0.240867i
$236$	−1.18001	−	0.525372i	−0.0768118	−	0.0341988i
$237$	6.64837	+	7.38377i	0.431858	+	0.479627i
$238$	0.814913	+	7.75338i	0.0528230	+	0.502577i
$239$	−18.3595	−	3.90242i	−1.18757	−	0.252427i	−0.428568	−	0.903510i	$-0.640982\pi$
$239$	−18.3595	−	3.90242i	−1.18757	−	0.252427i	−0.759007	+	0.651083i	$0.774315\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	5.06178	−	1.07592i	0.326058	−	0.0693058i	−0.0419745	−	0.999119i	$-0.513365\pi$
$241$	5.06178	−	1.07592i	0.326058	−	0.0693058i	0.368033	+	0.929813i	$0.380031\pi$
$242$	−3.32991	−	5.76758i	−0.214055	−	0.370754i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.228042	−	0.701842i	0.0145989	−	0.0449308i
$245$	0.883435	−	8.40532i	0.0564406	−	0.536996i
$246$	0.106915	−	0.0776779i	0.00681662	−	0.00495256i
$247$	−16.1473			−1.02743
$248$	4.20458	−	3.64987i	0.266991	−	0.231767i
$249$	−5.54310			−0.351279
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	2.78967	−	26.5419i	0.176082	−	1.67531i	−0.448062	−	0.894002i	$-0.647886\pi$
$251$	2.78967	−	26.5419i	0.176082	−	1.67531i	0.624145	−	0.781309i	$-0.285448\pi$
$252$	−1.21470	+	3.73846i	−0.0765190	+	0.235501i
$253$	−16.0755	+	27.8435i	−1.01065	+	1.75051i
$254$	4.13507	+	7.16216i	0.259458	+	0.449394i
$255$	−1.93997	+	0.412353i	−0.121485	+	0.0258225i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	28.1807	+	5.99000i	1.75787	+	0.373646i	0.970171	−	0.242421i	$-0.0779414\pi$
$257$	28.1807	+	5.99000i	1.75787	+	0.373646i	0.787694	+	0.616066i	$0.211275\pi$
$258$	0.500987	+	4.76657i	0.0311901	+	0.296754i
$259$	−23.8907	−	26.5333i	−1.48449	−	1.64870i
$260$	1.77083	+	0.788423i	0.109822	+	0.0488959i
$261$	6.55936	−	2.92041i	0.406014	−	0.180769i
$262$	10.4104	−	11.5619i	0.643155	−	0.714296i
$263$	23.1234	+	16.8002i	1.42585	+	1.03594i	0.990770	+	0.135552i	$0.0432807\pi$
$263$	23.1234	+	16.8002i	1.42585	+	1.03594i	0.435082	+	0.900391i	$0.356719\pi$
$264$	3.39978	+	2.47008i	0.209242	+	0.152023i
$265$	6.49654	−	7.21514i	0.399079	−	0.443222i
$266$	−29.9137	+	13.3184i	−1.83413	+	0.816605i
$267$	2.73304	+	1.21683i	0.167259	+	0.0744687i
$268$	−10.0660	−	11.1794i	−0.614876	−	0.682889i
$269$	−1.79990	−	17.1249i	−0.109742	−	1.04412i	−0.901349	−	0.433093i	$-0.857422\pi$
$269$	−1.79990	−	17.1249i	−0.109742	−	1.04412i	0.791607	−	0.611030i	$-0.209245\pi$
$270$	−0.978148	−	0.207912i	−0.0595282	−	0.0126531i
$271$	1.76633	+	5.43622i	0.107297	+	0.330227i	0.990263	−	0.139211i	$-0.0444566\pi$
$271$	1.76633	+	5.43622i	0.107297	+	0.330227i	−0.882966	+	0.469438i	$0.844457\pi$
$272$	−1.93997	+	0.412353i	−0.117628	+	0.0250025i
$273$	3.80981	+	6.59878i	0.230580	+	0.399376i
$274$	−4.82475	+	8.35671i	−0.291474	+	0.504847i
$275$	1.29860	−	3.99668i	0.0783086	−	0.241009i
$276$	0.799714	−	7.60877i	0.0481371	−	0.457994i
$277$	−7.90579	+	5.74389i	−0.475013	+	0.345117i	−0.799392	−	0.600810i	$-0.794845\pi$
$277$	−7.90579	+	5.74389i	−0.475013	+	0.345117i	0.324379	+	0.945927i	$0.394845\pi$
$278$	−8.71220			−0.522523
$279$	1.05859	+	5.46620i	0.0633760	+	0.327253i
$280$	3.93085			0.234913
$281$	−24.7027	+	17.9476i	−1.47364	+	1.07066i	−0.494102	+	0.869404i	$0.664503\pi$
$281$	−24.7027	+	17.9476i	−1.47364	+	1.07066i	−0.979538	+	0.201259i	$0.935497\pi$
$282$	0.948926	−	9.02843i	0.0565077	−	0.537635i
$283$	−2.75059	+	8.46544i	−0.163505	+	0.503218i	−0.998923	−	0.0463977i	$-0.985226\pi$
$283$	−2.75059	+	8.46544i	−0.163505	+	0.503218i	0.835418	+	0.549616i	$0.185226\pi$
$284$	−1.91779	+	3.32172i	−0.113800	+	0.197108i
$285$	−4.16508	−	7.21412i	−0.246718	−	0.427328i
$286$	7.96789	−	1.69363i	0.471151	−	0.100146i
$287$	−0.160527	−	0.494052i	−0.00947561	−	0.0291629i
$288$	−0.978148	−	0.207912i	−0.0576379	−	0.0122513i
$289$	1.36582	+	12.9949i	0.0803424	+	0.764407i
$290$	−4.80443	−	5.33586i	−0.282126	−	0.313333i
$291$	−8.24847	−	3.67245i	−0.483534	−	0.215283i
$292$	10.4586	−	4.65645i	0.612041	−	0.272498i
$293$	−2.04233	+	2.26824i	−0.119314	+	0.132512i	−0.799842	−	0.600210i	$-0.795084\pi$
$293$	−2.04233	+	2.26824i	−0.119314	+	0.132512i	0.680528	+	0.732722i	$0.261750\pi$
$294$	6.83750	+	4.96774i	0.398771	+	0.289724i
$295$	−1.04499	−	0.759229i	−0.0608416	−	0.0442040i
$296$	6.07772	−	6.75000i	0.353261	−	0.392336i
$297$	−3.83905	+	1.70925i	−0.222764	+	0.0991810i
$298$	−7.67299	−	3.41624i	−0.444485	−	0.197897i
$299$	−9.92332	−	11.0210i	−0.573880	−	0.637359i
$300$	0.104528	+	0.994522i	0.00603495	+	0.0574187i
$301$	18.4282	+	3.91704i	1.06218	+	0.225774i
$302$	−1.87380	−	5.76698i	−0.107825	−	0.331852i
$303$	14.1944	−	3.01711i	0.815445	−	0.173328i
$304$	−4.16508	−	7.21412i	−0.238883	−	0.413758i
$305$	0.368980	−	0.639092i	0.0211277	−	0.0365943i
$306$	0.612875	−	1.88624i	0.0350358	−	0.107829i
$307$	−2.43648	+	23.1816i	−0.139057	+	1.32304i	0.673077	+	0.739572i	$0.264972\pi$
$307$	−2.43648	+	23.1816i	−0.139057	+	1.32304i	−0.812134	+	0.583470i	$0.801694\pi$
$308$	13.3640	−	9.70954i	0.761487	−	0.553253i
$309$	−3.40591			−0.193755
$310$	4.87155	−	2.69593i	0.276685	−	0.153118i
$311$	−28.0856			−1.59259			−0.796294	−	0.604909i	$-0.793209\pi$
$311$	−28.0856			−1.59259			−0.796294	+	0.604909i	$0.793209\pi$
$312$	−1.56821	+	1.13937i	−0.0887823	+	0.0645041i
$313$	1.04726	−	9.96402i	0.0591947	−	0.563200i	−0.924224	−	0.381851i	$-0.875287\pi$
$313$	1.04726	−	9.96402i	0.0591947	−	0.563200i	0.983419	−	0.181349i	$-0.0580464\pi$
$314$	−1.41024	+	4.34027i	−0.0795845	+	0.244936i
$315$	−1.96543	+	3.40422i	−0.110739	+	0.191806i
$316$	4.96792	+	8.60469i	0.279467	+	0.484052i
$317$	7.86827	−	1.67245i	0.441926	−	0.0939343i	0.0184258	−	0.999830i	$-0.494135\pi$
$317$	7.86827	−	1.67245i	0.441926	−	0.0939343i	0.423500	+	0.905896i	$0.360801\pi$
$318$	3.00022	+	9.23373i	0.168244	+	0.517802i
$319$	−29.5141	−	6.27341i	−1.65247	−	0.351243i
$320$	0.104528	+	0.994522i	0.00584332	+	0.0555955i
$321$	1.88796	+	2.09680i	0.105376	+	0.117032i
$322$	−27.4737	−	12.2321i	−1.53105	−	0.681667i
$323$	15.0929	−	6.71979i	0.839792	−	0.373899i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	1.56821	+	1.13937i	0.0869885	+	0.0632009i
$326$	6.76357	+	4.91402i	0.374600	+	0.272162i
$327$	−10.9329	+	12.1422i	−0.604589	+	0.671464i
$328$	0.120728	−	0.0537517i	0.00666611	−	0.00296794i
$329$	−32.5998	−	14.5144i	−1.79729	−	0.800203i
$330$	2.81193	+	3.12296i	0.154792	+	0.171913i
$331$	1.62317	+	15.4434i	0.0892172	+	0.848845i	0.944019	+	0.329891i	$0.107012\pi$
$331$	1.62317	+	15.4434i	0.0892172	+	0.848845i	−0.854802	+	0.518954i	$0.826321\pi$
$332$	−5.42197	−	1.15247i	−0.297569	−	0.0632503i
$333$	2.80681	+	8.63846i	0.153812	+	0.473385i
$334$	−4.00277	+	0.850815i	−0.219022	+	0.0465545i
$335$	−7.52167	−	13.0279i	−0.410953	−	0.711791i
$336$	−1.96543	+	3.40422i	−0.107223	+	0.185715i
$337$	−4.24589	+	13.0675i	−0.231289	+	0.711833i	0.766304	+	0.642479i	$0.222094\pi$
$337$	−4.24589	+	13.0675i	−0.231289	+	0.711833i	−0.997592	+	0.0693543i	$0.977906\pi$
$338$	0.966111	−	9.19193i	0.0525495	−	0.499975i
$339$	−15.9792	+	11.6096i	−0.867872	+	0.630546i
$340$	−1.98331			−0.107560
$341$	9.90303	−	21.1987i	0.536279	−	1.14797i
$342$	8.33015			0.450443
$343$	4.61633	−	3.35396i	0.249258	−	0.181097i
$344$	−0.500987	+	4.76657i	−0.0270114	+	0.256996i
$345$	2.36419	−	7.27623i	0.127284	−	0.391739i
$346$	3.26972	−	5.66332i	0.175781	−	0.304462i
$347$	5.57712	+	9.65986i	0.299396	+	0.518569i	0.975998	−	0.217780i	$-0.0698816\pi$
$347$	5.57712	+	9.65986i	0.299396	+	0.518569i	−0.676602	+	0.736349i	$0.736548\pi$
$348$	7.02321	−	1.49283i	0.376484	−	0.0800241i
$349$	8.36534	+	25.7459i	0.447787	+	1.37815i	0.879399	+	0.476086i	$0.157945\pi$
$349$	8.36534	+	25.7459i	0.447787	+	1.37815i	−0.431612	+	0.902059i	$0.642055\pi$
$350$	3.84496	+	0.817271i	0.205522	+	0.0436850i
$351$	−0.202619	−	1.92779i	−0.0108150	−	0.102898i
$352$	2.81193	+	3.12296i	0.149876	+	0.166454i
$353$	−21.6385	−	9.63407i	−1.15170	−	0.512770i	−0.260095	−	0.965583i	$-0.583754\pi$
$353$	−21.6385	−	9.63407i	−1.15170	−	0.512770i	−0.891605	+	0.452813i	$0.850420\pi$
$354$	1.18001	−	0.525372i	0.0627166	−	0.0279232i
$355$	−2.56651	+	2.85040i	−0.136216	+	0.151283i
$356$	2.42033	+	1.75847i	0.128277	+	0.0931987i
$357$	−6.30717	−	4.58243i	−0.333811	−	0.242528i
$358$	1.64440	−	1.82629i	0.0869090	−	0.0965223i
$359$	2.77366	−	1.23491i	0.146388	−	0.0651763i	−0.332235	−	0.943197i	$-0.607803\pi$
$359$	2.77366	−	1.23491i	0.146388	−	0.0651763i	0.478623	+	0.878020i	$0.341136\pi$
$360$	−0.913545	−	0.406737i	−0.0481481	−	0.0214369i
$361$	33.7184	+	37.4481i	1.77465	+	1.97095i
$362$	0.258064	+	2.45531i	0.0135635	+	0.129048i
$363$	6.51429	+	1.38466i	0.341912	+	0.0726756i
$364$	2.35459	+	7.24668i	0.123414	+	0.379829i
$365$	11.1981	−	2.38024i	0.586137	−	0.124587i
$366$	0.368980	+	0.639092i	0.0192869	+	0.0334059i
$367$	−18.2344	+	31.5829i	−0.951828	+	1.64862i	−0.210364	+	0.977623i	$0.567465\pi$
$367$	−18.2344	+	31.5829i	−0.951828	+	1.64862i	−0.741464	+	0.670992i	$0.765868\pi$
$368$	2.36419	−	7.27623i	0.123242	−	0.379300i
$369$	−0.0138138	+	0.131430i	−0.000719118	+	0.00684195i
$370$	7.34831	−	5.33886i	0.382021	−	0.277554i
$371$	38.1644			1.98139
$372$	−0.101033	+	5.56685i	−0.00523833	+	0.288628i
$373$	33.4178			1.73031			0.865153	−	0.501508i	$-0.167221\pi$
$373$	33.4178			1.73031			0.865153	+	0.501508i	$0.167221\pi$
$374$	−6.74281	+	4.89893i	−0.348662	+	0.253318i
$375$	−0.104528	+	0.994522i	−0.00539783	+	0.0513569i
$376$	2.80531	−	8.63385i	0.144673	−	0.445257i
$377$	6.95901	−	12.0534i	0.358407	−	0.620779i
$378$	−1.96543	−	3.40422i	−0.101091	−	0.175094i
$379$	32.7123	−	6.95322i	1.68032	−	0.357163i	0.733689	−	0.679485i	$-0.237797\pi$
$379$	32.7123	−	6.95322i	1.68032	−	0.357163i	0.946630	+	0.322323i	$0.104464\pi$
$380$	−2.57416	−	7.92244i	−0.132052	−	0.406413i
$381$	−8.08942	−	1.71946i	−0.414434	−	0.0880906i
$382$	0.225521	+	2.14569i	0.0115386	+	0.109783i
$383$	12.0042	+	13.3320i	0.613383	+	0.681231i	0.967180	−	0.254091i	$-0.0817762\pi$
$383$	12.0042	+	13.3320i	0.613383	+	0.681231i	−0.353797	+	0.935322i	$0.615110\pi$
$384$	−0.913545	−	0.406737i	−0.0466192	−	0.0207562i
$385$	15.0907	−	6.71883i	0.769095	−	0.342423i
$386$	17.9714	−	19.9593i	0.914721	−	1.01590i
$387$	−3.87748	−	2.81715i	−0.197103	−	0.143204i
$388$	−7.30467	−	5.30715i	−0.370838	−	0.269430i
$389$	0.0997209	−	0.110751i	0.00505605	−	0.00561531i	−0.740611	−	0.671933i	$-0.765464\pi$
$389$	0.0997209	−	0.110751i	0.00505605	−	0.00561531i	0.745668	+	0.666318i	$0.232131\pi$
$390$	−1.77083	+	0.788423i	−0.0896693	+	0.0399234i
$391$	13.8618	+	6.17167i	0.701022	+	0.312115i
$392$	5.65524	+	6.28078i	0.285633	+	0.317227i
$393$	1.62626	+	15.4728i	0.0820340	+	0.780501i
$394$	20.1184	+	4.27629i	1.01355	+	0.215436i
$395$	3.07034	+	9.44955i	0.154486	+	0.475458i
$396$	−4.11053	+	0.873720i	−0.206562	+	0.0439061i
$397$	4.61075	+	7.98605i	0.231407	+	0.400809i	0.958222	−	0.286024i	$-0.0923338\pi$
$397$	4.61075	+	7.98605i	0.231407	+	0.400809i	−0.726815	+	0.686833i	$0.759000\pi$
$398$	5.09583	−	8.82624i	0.255431	−	0.442420i
$399$	10.1186	−	31.1420i	0.506566	−	1.55905i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	21.2555	−	15.4430i	1.06145	−	0.771187i	0.0870919	−	0.996200i	$-0.472243\pi$
$401$	21.2555	−	15.4430i	1.06145	−	0.771187i	0.974356	+	0.225013i	$0.0722426\pi$
$402$	15.0433			0.750293
$403$	7.88811	+	7.36602i	0.392935	+	0.366928i
$404$	14.5115			0.721973
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	2.95021	−	28.0694i	0.146416	−	1.39306i
$407$	11.7952	−	36.3019i	0.584667	−	1.79942i
$408$	0.991653	−	1.71759i	0.0490941	−	0.0850336i
$409$	13.3652	+	23.1492i	0.660868	+	1.14466i	0.980388	+	0.197077i	$0.0631449\pi$
$409$	13.3652	+	23.1492i	0.660868	+	1.14466i	−0.319520	+	0.947579i	$0.603522\pi$
$410$	0.129266	−	0.0274763i	0.00638398	−	0.00135696i
$411$	−2.98186	−	9.17721i	−0.147084	−	0.452679i
$412$	−3.33148	−	0.708128i	−0.164130	−	0.0348869i
$413$	−0.530732	−	5.04958i	−0.0261156	−	0.248474i
$414$	5.11930	+	5.68556i	0.251600	+	0.279430i
$415$	−5.06387	−	2.25458i	−0.248576	−	0.110673i
$416$	−1.77083	+	0.788423i	−0.0868219	+	0.0386556i
$417$	5.82960	−	6.47443i	0.285477	−	0.317054i
$418$	−28.3207	−	20.5762i	−1.38521	−	1.00641i
$419$	−9.91473	−	7.20347i	−0.484366	−	0.351913i	0.318647	−	0.947873i	$-0.396771\pi$
$419$	−9.91473	−	7.20347i	−0.484366	−	0.351913i	−0.803014	+	0.595961i	$0.796771\pi$
$420$	−2.63026	+	2.92119i	−0.128343	+	0.142540i
$421$	7.92261	−	3.52737i	0.386124	−	0.171914i	−0.204488	−	0.978869i	$-0.565553\pi$
$421$	7.92261	−	3.52737i	0.386124	−	0.171914i	0.590612	+	0.806955i	$0.298886\pi$
$422$	17.5310	+	7.80532i	0.853397	+	0.379957i
$423$	6.07448	+	6.74639i	0.295351	+	0.328021i
$424$	1.01486	+	9.65574i	0.0492859	+	0.468924i
$425$	−1.93997	−	0.412353i	−0.0941022	−	0.0200020i
$426$	−1.18526	−	3.64786i	−0.0574261	−	0.176739i
$427$	2.83742	−	0.603113i	0.137313	−	0.0291867i
$428$	1.41076	+	2.44350i	0.0681916	+	0.118111i
$429$	−4.07295	+	7.05456i	−0.196644	+	0.340597i
$430$	−1.48107	+	4.55825i	−0.0714233	+	0.219818i
$431$	0.204474	−	1.94544i	0.00984918	−	0.0937087i	−0.988493	−	0.151267i	$-0.951665\pi$
$431$	0.204474	−	1.94544i	0.00984918	−	0.0937087i	0.998342	+	0.0575580i	$0.0183314\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	−29.0880			−1.39788			−0.698941	−	0.715179i	$-0.746345\pi$
$433$	−29.0880			−1.39788			−0.698941	+	0.715179i	$0.746345\pi$
$434$	20.6887	+	7.13976i	0.993091	+	0.342720i
$435$	7.18011			0.344260
$436$	−13.2185	+	9.60377i	−0.633049	+	0.459937i
$437$	−6.66173	+	63.3822i	−0.318674	+	3.03198i
$438$	−3.53772	+	10.8880i	−0.169039	+	0.520248i
$439$	−14.2168	+	24.6243i	−0.678533	+	1.17525i	0.296890	+	0.954912i	$0.404051\pi$
$439$	−14.2168	+	24.6243i	−0.678533	+	1.17525i	−0.975423	+	0.220342i	$0.929283\pi$
$440$	2.10118	+	3.63935i	0.100170	+	0.173499i
$441$	−8.26693	+	1.75719i	−0.393663	+	0.0836757i
$442$	−1.18800	−	3.65630i	−0.0565076	−	0.173913i
$443$	−7.70892	−	1.63858i	−0.366262	−	0.0778514i	0.0211043	−	0.999777i	$-0.493282\pi$
$443$	−7.70892	−	1.63858i	−0.366262	−	0.0778514i	−0.387366	+	0.921926i	$0.626615\pi$
$444$	0.949434	+	9.03326i	0.0450581	+	0.428699i
$445$	2.00183	+	2.22326i	0.0948958	+	0.105392i
$446$	3.12198	+	1.38999i	0.147830	+	0.0658181i
$447$	7.67299	−	3.41624i	0.362920	−	0.161582i
$448$	−2.63026	+	2.92119i	−0.124268	+	0.138013i
$449$	−16.9711	−	12.3302i	−0.800916	−	0.581899i	0.110267	−	0.993902i	$-0.464829\pi$
$449$	−16.9711	−	12.3302i	−0.800916	−	0.581899i	−0.911183	+	0.412003i	$0.864829\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	0.371606	−	0.412711i	0.0174983	−	0.0194338i
$452$	−18.0438	+	8.03362i	−0.848709	+	0.377870i
$453$	5.53952	+	2.46635i	0.260269	+	0.115879i
$454$	0.738499	+	0.820186i	0.0346595	+	0.0384932i
$455$	0.796467	+	7.57787i	0.0373389	+	0.355256i
$456$	8.14812	+	1.73194i	0.381571	+	0.0811053i
$457$	−3.28202	−	10.1010i	−0.153527	−	0.472506i	0.844482	−	0.535584i	$-0.179908\pi$
$457$	−3.28202	−	10.1010i	−0.153527	−	0.472506i	−0.998009	+	0.0630776i	$0.979908\pi$
$458$	−5.32786	+	1.13247i	−0.248954	+	0.0529169i
$459$	0.991653	+	1.71759i	0.0462864	+	0.0801704i
$460$	3.82534	−	6.62568i	0.178357	−	0.308924i
$461$	4.00377	−	12.3223i	0.186474	−	0.573909i	−0.813496	−	0.581570i	$-0.802439\pi$
$461$	4.00377	−	12.3223i	0.186474	−	0.573909i	0.999971	+	0.00766132i	$0.00243870\pi$
$462$	−1.72669	+	16.4284i	−0.0803330	+	0.764317i
$463$	−13.7296	+	9.97512i	−0.638068	+	0.463583i	−0.859186	−	0.511664i	$-0.829029\pi$
$463$	−13.7296	+	9.97512i	−0.638068	+	0.463583i	0.221118	+	0.975247i	$0.429029\pi$
$464$	7.18011			0.333328
$465$	−1.25624	+	5.42419i	−0.0582566	+	0.251541i
$466$	9.16871			0.424732
$467$	19.4416	−	14.1251i	0.899648	−	0.653633i	−0.0387275	−	0.999250i	$-0.512330\pi$
$467$	19.4416	−	14.1251i	0.899648	−	0.653633i	0.938376	+	0.345617i	$0.112330\pi$
$468$	0.202619	−	1.92779i	0.00936607	−	0.0891122i
$469$	18.2732	−	56.2390i	0.843776	−	2.59688i
$470$	4.53908	−	7.86192i	0.209372	−	0.362643i
$471$	−2.28182	−	3.95222i	−0.105141	−	0.182109i
$472$	1.26345	−	0.268555i	0.0581550	−	0.0123612i
$473$	6.22397	+	19.1554i	0.286178	+	0.880767i
$474$	−9.71872	−	2.06578i	−0.446395	−	0.0948843i
$475$	−0.870738	−	8.28452i	−0.0399522	−	0.380120i
$476$	−5.21660	−	5.79362i	−0.239103	−	0.265550i
$477$	−8.86954	−	3.94897i	−0.406108	−	0.180811i
$478$	17.1469	−	7.63429i	0.784281	−	0.349184i
$479$	12.2208	−	13.5726i	0.558383	−	0.620148i	−0.396174	−	0.918176i	$-0.629662\pi$
$479$	12.2208	−	13.5726i	0.558383	−	0.620148i	0.954557	+	0.298028i	$0.0963289\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	14.2441	+	10.3489i	0.649473	+	0.471870i
$482$	−3.46266	+	3.84568i	−0.157720	+	0.175166i
$483$	27.4737	−	12.2321i	1.25010	−	0.556579i
$484$	6.08405	+	2.70879i	0.276548	+	0.123127i
$485$	−6.04163	−	6.70991i	−0.274336	−	0.304681i
$486$	0.104528	+	0.994522i	0.00474151	+	0.0451124i
$487$	0.0786318	+	0.0167137i	0.00356315	+	0.000757371i	0.209693	−	0.977767i	$-0.432754\pi$
$487$	0.0786318	+	0.0167137i	0.00356315	+	0.000757371i	−0.206130	+	0.978525i	$0.566087\pi$
$488$	0.228042	+	0.701842i	0.0103230	+	0.0317709i
$489$	−8.17754	+	1.73819i	−0.369801	+	0.0786037i
$490$	4.22581	+	7.31932i	0.190903	+	0.330653i
$491$	−5.61513	+	9.72568i	−0.253407	+	0.438914i	−0.964462	−	0.264223i	$-0.914885\pi$
$491$	−5.61513	+	9.72568i	−0.253407	+	0.438914i	0.711055	+	0.703137i	$0.248218\pi$
$492$	−0.0408377	+	0.125686i	−0.00184111	+	0.00566634i
$493$	−1.48852	+	14.1624i	−0.0670397	+	0.637840i
$494$	13.0634	−	9.49112i	0.587750	−	0.427026i
$495$	−4.20236			−0.188882
$496$	−1.25624	+	5.42419i	−0.0564068	+	0.243553i
$497$	−15.0771			−0.676302
$498$	4.48446	−	3.25815i	0.200953	−	0.146001i
$499$	0.427617	−	4.06851i	0.0191428	−	0.182131i	−0.980772	−	0.195155i	$-0.937479\pi$
$499$	0.427617	−	4.06851i	0.0191428	−	0.182131i	0.999915	+	0.0130237i	$0.00414568\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	2.04610	−	3.54394i	0.0914129	−	0.158332i
$502$	13.3441	+	23.1126i	0.595575	+	1.03157i
$503$	−12.4816	+	2.65305i	−0.556529	+	0.118294i	−0.477585	−	0.878585i	$-0.658488\pi$
$503$	−12.4816	+	2.65305i	−0.556529	+	0.118294i	−0.0789432	+	0.996879i	$0.525155\pi$
$504$	−1.21470	−	3.73846i	−0.0541071	−	0.166524i
$505$	14.1944	+	3.01711i	0.631641	+	0.134259i
$506$	−3.36068	−	31.9748i	−0.149401	−	1.42145i
$507$	6.18448	+	6.86856i	0.274662	+	0.305044i
$508$	−7.55515	−	3.36377i	−0.335206	−	0.149243i
$509$	0.256508	−	0.114205i	0.0113695	−	0.00506204i	−0.401044	−	0.916059i	$-0.631353\pi$
$509$	0.256508	−	0.114205i	0.0113695	−	0.00506204i	0.412414	+	0.910997i	$0.364686\pi$
$510$	1.32709	−	1.47388i	0.0587646	−	0.0652647i
$511$	36.4071	+	26.4513i	1.61056	+	1.17014i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−5.57396	+	6.19051i	−0.246096	+	0.273318i
$514$	−26.3195	+	11.7182i	−1.16090	+	0.516868i
$515$	−3.11145	−	1.38531i	−0.137107	−	0.0610439i
$516$	−3.20703	−	3.56177i	−0.141182	−	0.156798i
$517$	−3.98773	−	37.9407i	−0.175380	−	1.66863i
$518$	34.9238	+	7.42328i	1.53446	+	0.326160i
$519$	2.02080	+	6.21937i	0.0887031	+	0.273000i
$520$	−1.89605	+	0.403018i	−0.0831474	+	0.0176735i
$521$	2.06952	+	3.58452i	0.0906674	+	0.157040i	0.907792	−	0.419420i	$-0.137767\pi$
$521$	2.06952	+	3.58452i	0.0906674	+	0.157040i	−0.817125	+	0.576461i	$0.804433\pi$
$522$	−3.59006	+	6.21816i	−0.157132	+	0.272161i
$523$	12.2106	−	37.5804i	0.533933	−	1.64328i	−0.212010	−	0.977268i	$-0.568001\pi$
$523$	12.2106	−	37.5804i	0.533933	−	1.64328i	0.745943	−	0.666010i	$-0.231999\pi$
$524$	−1.62626	+	15.4728i	−0.0710435	+	0.675934i
$525$	−3.18013	+	2.31050i	−0.138792	+	0.100838i
$526$	−28.5821			−1.24624
$527$	−10.4385	−	3.60236i	−0.454707	−	0.156921i
$528$	−4.20236			−0.182884
$529$	−28.7467	+	20.8857i	−1.24986	+	0.908074i
$530$	−1.01486	+	9.65574i	−0.0440826	+	0.419418i
$531$	−0.399150	+	1.22846i	−0.0173216	+	0.0533105i
$532$	16.3723	−	28.3577i	0.709829	−	1.22946i
$533$	0.128084	+	0.221848i	0.00554794	+	0.00960931i
$534$	−2.92631	+	0.622007i	−0.126634	+	0.0269169i
$535$	0.871897	+	2.68342i	0.0376954	+	0.116014i
$536$	14.7146	+	3.12769i	0.635574	+	0.135095i
$537$	0.256880	+	2.44405i	0.0110852	+	0.105468i
$538$	11.5219	+	12.7964i	0.496745	+	0.551691i
$539$	32.4462	+	14.4460i	1.39755	+	0.622231i
$540$	0.913545	−	0.406737i	0.0393127	−	0.0175032i
$541$	20.1758	−	22.4075i	0.867427	−	0.963375i	−0.132185	−	0.991225i	$-0.542199\pi$
$541$	20.1758	−	22.4075i	0.867427	−	0.963375i	0.999612	+	0.0278497i	$0.00886597\pi$
$542$	−4.62432	−	3.35977i	−0.198632	−	0.144314i
$543$	−1.99733	−	1.45115i	−0.0857137	−	0.0622747i
$544$	1.32709	−	1.47388i	0.0568986	−	0.0631922i
$545$	−14.9263	+	6.64563i	−0.639374	+	0.284668i
$546$	−6.96086	−	3.09918i	−0.297897	−	0.132632i
$547$	1.20027	+	1.33304i	0.0513200	+	0.0569967i	0.768258	−	0.640140i	$-0.221124\pi$
$547$	1.20027	+	1.33304i	0.0513200	+	0.0569967i	−0.716938	+	0.697137i	$0.754457\pi$
$548$	−1.00865	−	9.59663i	−0.0430873	−	0.409948i
$549$	−0.721834	−	0.153431i	−0.0308071	−	0.00654826i
$550$	1.29860	+	3.99668i	0.0553725	+	0.170419i
$551$	−58.5044	+	12.4355i	−2.49237	+	0.529770i
$552$	3.82534	+	6.62568i	0.162817	+	0.282008i
$553$	−19.5282	+	33.8238i	−0.830422	+	1.43833i
$554$	3.01974	−	9.29382i	0.128297	−	0.394856i
$555$	−0.949434	+	9.03326i	−0.0403012	+	0.383440i
$556$	7.04832	−	5.12090i	0.298915	−	0.217175i
$557$	−37.5212			−1.58982			−0.794911	−	0.606726i	$-0.792483\pi$
$557$	−37.5212			−1.58982			−0.794911	+	0.606726i	$0.792483\pi$
$558$	−4.06937	−	3.80003i	−0.172270	−	0.160868i
$559$	−9.29047			−0.392945
$560$	−3.18013	+	2.31050i	−0.134385	+	0.0976364i
$561$	0.871199	−	8.28891i	0.0367821	−	0.349958i
$562$	9.43560	−	29.0398i	0.398017	−	1.22497i
$563$	15.3912	−	26.6584i	0.648662	−	1.12352i	−0.334781	−	0.942296i	$-0.608662\pi$
$563$	15.3912	−	26.6584i	0.648662	−	1.12352i	0.983443	−	0.181220i	$-0.0580045\pi$
$564$	4.53908	+	7.86192i	0.191130	+	0.331047i
$565$	−19.3198	+	4.10655i	−0.812790	+	0.172764i
$566$	−2.75059	−	8.46544i	−0.115616	−	0.355829i
$567$	3.84496	+	0.817271i	0.161473	+	0.0343221i
$568$	−0.400928	−	3.81458i	−0.0168226	−	0.160056i
$569$	18.0512	+	20.0479i	0.756745	+	0.840450i	0.991296	−	0.131653i	$-0.0420286\pi$
$569$	18.0512	+	20.0479i	0.756745	+	0.840450i	−0.234551	+	0.972104i	$0.575362\pi$
$570$	7.60997	+	3.38818i	0.318747	+	0.141915i
$571$	−1.77080	+	0.788409i	−0.0741055	+	0.0329939i	−0.443455	−	0.896297i	$-0.646247\pi$
$571$	−1.77080	+	0.788409i	−0.0741055	+	0.0329939i	0.369349	+	0.929291i	$0.379581\pi$
$572$	−5.45067	+	6.05358i	−0.227904	+	0.253113i
$573$	−1.74546	−	1.26815i	−0.0729175	−	0.0529777i
$574$	0.420265	+	0.305341i	0.0175415	+	0.0127447i
$575$	5.11930	−	5.68556i	0.213490	−	0.237104i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	−22.4236	−	9.98363i	−0.933506	−	0.415624i	−0.117112	−	0.993119i	$-0.537364\pi$
$577$	−22.4236	−	9.98363i	−0.933506	−	0.415624i	−0.816394	+	0.577495i	$0.804030\pi$
$578$	−8.74319	−	9.71030i	−0.363669	−	0.403895i
$579$	2.80741	+	26.7107i	0.116672	+	1.11006i
$580$	7.02321	+	1.49283i	0.291623	+	0.0619864i
$581$	−6.73320	−	20.7227i	−0.279340	−	0.859721i
$582$	8.83176	−	1.87725i	0.366088	−	0.0778145i
$583$	20.4002	+	35.3342i	0.844890	+	1.46339i
$584$	−5.72416	+	9.91453i	−0.236867	+	0.410266i
$585$	0.599002	−	1.84354i	0.0247657	−	0.0762210i
$586$	0.319043	−	3.03549i	0.0131796	−	0.125395i
$587$	14.9022	−	10.8271i	0.615080	−	0.446882i	−0.236120	−	0.971724i	$-0.575876\pi$
$587$	14.9022	−	10.8271i	0.615080	−	0.446882i	0.851199	+	0.524842i	$0.175876\pi$
$588$	−8.45162			−0.348539
$589$	0.841621	−	46.3727i	0.0346784	−	1.91075i
$590$	1.29168			0.0531775
$591$	−16.6397	+	12.0895i	−0.684466	+	0.497294i
$592$	−0.949434	+	9.03326i	−0.0390215	+	0.371265i
$593$	3.69530	−	11.3730i	0.151748	−	0.467032i	−0.846069	−	0.533073i	$-0.821037\pi$
$593$	3.69530	−	11.3730i	0.151748	−	0.467032i	0.997817	+	0.0660414i	$0.0210369\pi$
$594$	2.10118	−	3.63935i	0.0862124	−	0.149324i
$595$	−3.89804	−	6.75161i	−0.159804	−	0.276789i
$596$	8.21560	−	1.74628i	0.336524	−	0.0715304i
$597$	3.14940	+	9.69285i	0.128896	+	0.396702i
$598$	14.5061	+	3.08336i	0.593198	+	0.126088i
$599$	−2.76075	−	26.2668i	−0.112801	−	1.07323i	−0.893728	−	0.448609i	$-0.851920\pi$
$599$	−2.76075	−	26.2668i	−0.112801	−	1.07323i	0.780927	−	0.624622i	$-0.214747\pi$
$600$	−0.669131	−	0.743145i	−0.0273171	−	0.0303388i
$601$	42.7377	+	19.0281i	1.74331	+	0.776171i	0.993410	+	0.114619i	$0.0365648\pi$
$601$	42.7377	+	19.0281i	1.74331	+	0.776171i	0.749899	+	0.661552i	$0.230102\pi$
$602$	−17.2111	+	7.66288i	−0.701473	+	0.312316i
$603$	−10.0660	+	11.1794i	−0.409917	+	0.455259i
$604$	4.90569	+	3.56419i	0.199609	+	0.145025i
$605$	5.38791	+	3.91455i	0.219050	+	0.159149i
$606$	−9.71007	+	10.7841i	−0.394445	+	0.438075i
$607$	19.0636	−	8.48767i	0.773768	−	0.344504i	0.0184225	−	0.999830i	$-0.494136\pi$
$607$	19.0636	−	8.48767i	0.773768	−	0.344504i	0.755346	+	0.655326i	$0.227469\pi$
$608$	7.60997	+	3.38818i	0.308625	+	0.137409i
$609$	18.8855	+	20.9745i	0.765280	+	0.849930i
$610$	0.0771378	+	0.733918i	0.00312322	+	0.0297155i
$611$	17.2127	+	3.65867i	0.696350	+	0.148014i
$612$	0.612875	+	1.88624i	0.0247740	+	0.0762466i
$613$	5.60968	−	1.19237i	0.226573	−	0.0481595i	−0.0932262	−	0.995645i	$-0.529718\pi$
$613$	5.60968	−	1.19237i	0.226573	−	0.0481595i	0.319799	+	0.947485i	$0.396385\pi$
$614$	−11.6546	−	20.1864i	−0.470343	−	0.814658i
$615$	−0.0660768	+	0.114448i	−0.00266447	+	0.00461500i
$616$	−5.10461	+	15.7104i	−0.205671	+	0.632989i
$617$	0.835382	−	7.94813i	0.0336312	−	0.319980i	−0.964753	−	0.263157i	$-0.915236\pi$
$617$	0.835382	−	7.94813i	0.0336312	−	0.319980i	0.998384	−	0.0568227i	$-0.0180970\pi$
$618$	2.75544	−	2.00194i	0.110840	−	0.0805299i
$619$	−3.10537			−0.124815			−0.0624076	−	0.998051i	$-0.519878\pi$
$619$	−3.10537			−0.124815			−0.0624076	+	0.998051i	$0.519878\pi$
$620$	−2.35654	+	5.04447i	−0.0946409	+	0.202591i
$621$	−7.65068			−0.307011
$622$	22.7217	−	16.5083i	0.911059	−	0.661923i
$623$	−1.22924	+	11.6955i	−0.0492486	+	0.468569i
$624$	0.599002	−	1.84354i	0.0239793	−	0.0738006i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.00945	+	8.67663i	0.200218	+	0.346788i
$627$	34.2413	−	7.27822i	1.36747	−	0.290664i
$628$	−1.41024	−	4.34027i	−0.0562747	−	0.173196i
$629$	−17.6207	−	3.74541i	−0.702585	−	0.149339i
$630$	−0.410886	−	3.90932i	−0.0163701	−	0.155751i
$631$	−1.62622	−	1.80610i	−0.0647386	−	0.0718995i	0.709905	−	0.704297i	$-0.248738\pi$
$631$	−1.62622	−	1.80610i	−0.0647386	−	0.0718995i	−0.774644	+	0.632397i	$0.782071\pi$
$632$	−9.07684	−	4.04127i	−0.361057	−	0.160753i
$633$	−17.5310	+	7.80532i	−0.696796	+	0.310233i
$634$	−5.38252	+	5.97790i	−0.213767	+	0.237413i
$635$	−6.69069	−	4.86107i	−0.265512	−	0.192906i
$636$	−7.85468	−	5.70676i	−0.311458	−	0.226288i
$637$	−10.9622	+	12.1747i	−0.434337	+	0.482380i
$638$	27.5648	−	12.2726i	1.09130	−	0.485878i
$639$	3.50399	+	1.56007i	0.138616	+	0.0617156i
$640$	−0.669131	−	0.743145i	−0.0264497	−	0.0293754i
$641$	3.26773	+	31.0904i	0.129068	+	1.22800i	0.846889	+	0.531770i	$0.178473\pi$
$641$	3.26773	+	31.0904i	0.129068	+	1.22800i	−0.717821	+	0.696227i	$0.754861\pi$
$642$	−2.75986	−	0.586626i	−0.108923	−	0.0231523i
$643$	1.52274	+	4.68651i	0.0600510	+	0.184818i	0.976582	−	0.215146i	$-0.0690227\pi$
$643$	1.52274	+	4.68651i	0.0600510	+	0.184818i	−0.916531	+	0.399964i	$0.869023\pi$
$644$	29.4165	−	6.25267i	1.15917	−	0.246390i
$645$	−2.39641	−	4.15071i	−0.0943587	−	0.163434i
$646$	−8.26062	+	14.3078i	−0.325010	+	0.562933i
$647$	2.52949	−	7.78497i	0.0994445	−	0.306059i	−0.888942	−	0.458020i	$-0.848559\pi$
$647$	2.52949	−	7.78497i	0.0994445	−	0.306059i	0.988386	+	0.151961i	$0.0485589\pi$
$648$	−0.104528	+	0.994522i	−0.00410627	+	0.0390685i
$649$	4.39142	−	3.19055i	0.172378	−	0.125240i
$650$	−1.93841			−0.0760308
$651$	−19.1493	+	10.5973i	−0.750522	+	0.415341i
$652$	−8.36023			−0.327412
$653$	2.40081	−	1.74429i	0.0939511	−	0.0682595i	−0.539818	−	0.841782i	$-0.681507\pi$
$653$	2.40081	−	1.74429i	0.0939511	−	0.0682595i	0.633769	+	0.773522i	$0.281507\pi$
$654$	1.70788	−	16.2494i	0.0667834	−	0.635402i
$655$	−4.80771	+	14.7966i	−0.187853	+	0.578151i
$656$	−0.0660768	+	0.114448i	−0.00257987	+	0.00446846i
$657$	−5.72416	−	9.91453i	−0.223321	−	0.386803i
$658$	34.9051	−	7.41932i	1.36074	−	0.289235i
$659$	1.18937	+	3.66051i	0.0463313	+	0.142593i	0.971546	−	0.236851i	$-0.0761153\pi$
$659$	1.18937	+	3.66051i	0.0463313	+	0.142593i	−0.925215	+	0.379444i	$0.876115\pi$
$660$	−4.11053	−	0.873720i	−0.160002	−	0.0340095i
$661$	1.63741	+	15.5789i	0.0636878	+	0.605949i	0.979093	+	0.203415i	$0.0652039\pi$
$661$	1.63741	+	15.5789i	0.0636878	+	0.605949i	−0.915405	+	0.402534i	$0.868129\pi$
$662$	−10.3906	−	11.5399i	−0.403841	−	0.448510i
$663$	3.51209	+	1.56368i	0.136398	+	0.0607285i
$664$	5.06387	−	2.25458i	0.196516	−	0.0874947i
$665$	21.9104	−	24.3340i	0.849650	−	0.943632i
$666$	−7.34831	−	5.33886i	−0.284741	−	0.206877i
$667$	−44.4415	−	32.2887i	−1.72078	−	1.25022i
$668$	2.73821	−	3.04109i	0.105945	−	0.117663i
$669$	−3.12198	+	1.38999i	−0.120703	+	0.0537403i
$670$	13.7428	+	6.11868i	0.530930	+	0.236385i
$671$	2.07509	+	2.30462i	0.0801080	+	0.0889689i
$672$	−0.410886	−	3.90932i	−0.0158503	−	0.150805i
$673$	15.1019	+	3.21001i	0.582136	+	0.123737i	0.489561	−	0.871969i	$-0.337157\pi$
$673$	15.1019	+	3.21001i	0.582136	+	0.123737i	0.0925746	+	0.995706i	$0.470490\pi$
$674$	−4.24589	−	13.0675i	−0.163546	−	0.503342i
$675$	0.978148	−	0.207912i	0.0376489	−	0.00800252i
$676$	4.62128	+	8.00429i	0.177742	+	0.307857i
$677$	−5.26272	+	9.11530i	−0.202263	+	0.350329i	−0.949257	−	0.314501i	$-0.898163\pi$
$677$	−5.26272	+	9.11530i	−0.202263	+	0.350329i	0.746994	+	0.664830i	$0.231496\pi$
$678$	6.10352	−	18.7847i	0.234404	−	0.721422i
$679$	3.70992	−	35.2975i	0.142374	−	1.35459i
$680$	1.60453	−	1.16576i	0.0615309	−	0.0447048i
$681$	−1.10367			−0.0422927
$682$	4.44856	+	22.9710i	0.170344	+	0.879603i
$683$	−14.5878			−0.558186			−0.279093	−	0.960264i	$-0.590034\pi$
$683$	−14.5878			−0.558186			−0.279093	+	0.960264i	$0.590034\pi$
$684$	−6.73923	+	4.89634i	−0.257681	+	0.187216i
$685$	1.00865	−	9.59663i	0.0385384	−	0.366669i
$686$	−1.76328	+	5.42682i	−0.0673224	+	0.207197i
$687$	2.72344	−	4.71714i	0.103906	−	0.179970i
$688$	−2.39641	−	4.15071i	−0.0913624	−	0.158244i
$689$	−18.4086	+	3.91287i	−0.701313	+	0.149069i
$690$	2.36419	+	7.27623i	0.0900032	+	0.277001i
$691$	−43.3869	−	9.22217i	−1.65052	−	0.350828i	−0.713646	−	0.700507i	$-0.752957\pi$
$691$	−43.3869	−	9.22217i	−1.65052	−	0.350828i	−0.936870	+	0.349679i	$0.886291\pi$
$692$	0.683557	+	6.50361i	0.0259849	+	0.247230i
$693$	−11.0533	−	12.2759i	−0.419879	−	0.466323i
$694$	−10.1899	−	4.53684i	−0.386804	−	0.172216i
$695$	7.95899	−	3.54357i	0.301902	−	0.134415i
$696$	−4.80443	+	5.33586i	−0.182112	+	0.202255i
$697$	−0.212044	−	0.154059i	−0.00803175	−	0.00583541i
$698$	−21.9008	−	15.9118i	−0.828956	−	0.602272i
$699$	−6.13507	+	6.81368i	−0.232050	+	0.257717i
$700$	−3.59101	+	1.59882i	−0.135728	+	0.0604298i
$701$	−13.6807	−	6.09106i	−0.516715	−	0.230056i	0.131775	−	0.991280i	$-0.457932\pi$
$701$	−13.6807	−	6.09106i	−0.516715	−	0.230056i	−0.648490	+	0.761223i	$0.724599\pi$
$702$	1.29705	+	1.44052i	0.0489540	+	0.0543689i
$703$	−7.90893	−	75.2484i	−0.298291	−	2.83805i
$704$	−4.11053	−	0.873720i	−0.154921	−	0.0329295i
$705$	2.80531	+	8.63385i	0.105654	+	0.325169i
$706$	23.1687	−	4.92465i	0.871964	−	0.185342i
$707$	28.5213	+	49.4003i	1.07265	+	1.85789i
$708$	−0.645839	+	1.11863i	−0.0242721	+	0.0420405i
$709$	7.99402	−	24.6031i	0.300222	−	0.923987i	−0.681196	−	0.732101i	$-0.738540\pi$
$709$	7.99402	−	24.6031i	0.300222	−	0.923987i	0.981417	−	0.191886i	$-0.0614603\pi$
$710$	0.400928	−	3.81458i	0.0150466	−	0.143159i
$711$	8.03826	−	5.84014i	0.301458	−	0.219022i
$712$	−2.99169			−0.112118
$713$	32.1679	−	27.9239i	1.20470	−	1.04576i
$714$	7.79609			0.291761
$715$	−6.59017	+	4.78804i	−0.246459	+	0.179063i
$716$	−0.256880	+	2.44405i	−0.00960005	+	0.0913384i
$717$	−5.80013	+	17.8510i	−0.216610	+	0.666657i
$718$	−1.51808	+	2.62938i	−0.0566541	+	0.0981277i
$719$	−1.37187	−	2.37614i	−0.0511620	−	0.0886151i	0.839310	−	0.543653i	$-0.182959\pi$
$719$	−1.37187	−	2.37614i	−0.0511620	−	0.0886151i	−0.890472	+	0.455038i	$0.849626\pi$
$720$	0.978148	−	0.207912i	0.0364534	−	0.00774841i
$721$	−4.13716	−	12.7329i	−0.154076	−	0.474196i
$722$	−49.2902	−	10.4770i	−1.83439	−	0.389912i
$723$	−0.540921	−	5.14652i	−0.0201171	−	0.191401i
$724$	−1.65198	−	1.83470i	−0.0613952	−	0.0681862i
$725$	6.55936	+	2.92041i	0.243608	+	0.108461i
$726$	−6.08405	+	2.70879i	−0.225800	+	0.100533i
$727$	−14.9646	+	16.6199i	−0.555006	+	0.616396i	−0.953726	−	0.300676i	$-0.902788\pi$
$727$	−14.9646	+	16.6199i	−0.555006	+	0.616396i	0.398720	+	0.917073i	$0.369454\pi$
$728$	−6.16440	−	4.47870i	−0.228468	−	0.165992i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−7.66042	+	8.50775i	−0.283525	+	0.314886i
$731$	8.68384	−	3.86629i	0.321183	−	0.143000i
$732$	−0.674160	−	0.300155i	−0.0249177	−	0.0110941i
$733$	23.5231	+	26.1251i	0.868846	+	0.964951i	0.999650	−	0.0264574i	$-0.00842264\pi$
$733$	23.5231	+	26.1251i	0.868846	+	0.964951i	−0.130804	+	0.991408i	$0.541756\pi$
$734$	−3.81203	−	36.2690i	−0.140705	−	1.33871i
$735$	−8.26693	−	1.75719i	−0.304930	−	0.0648149i
$736$	2.36419	+	7.27623i	0.0871452	+	0.268205i
$737$	61.8361	−	13.1437i	2.27776	−	0.484153i
$738$	−0.0660768	−	0.114448i	−0.00243232	−	0.00421290i
$739$	24.0420	−	41.6419i	0.884398	−	1.53182i	0.0379961	−	0.999278i	$-0.487903\pi$
$739$	24.0420	−	41.6419i	0.884398	−	1.53182i	0.846402	−	0.532545i	$-0.178764\pi$
$740$	−2.80681	+	8.63846i	−0.103180	+	0.317556i
$741$	−1.68785	+	16.0588i	−0.0620047	+	0.589935i
$742$	−30.8756	+	22.4324i	−1.13348	+	0.823521i
$743$	−44.5933			−1.63597			−0.817985	−	0.575240i	$-0.804909\pi$
$743$	−44.5933			−1.63597			−0.817985	+	0.575240i	$0.804909\pi$
$744$	−3.19037	−	4.56306i	−0.116965	−	0.167290i
$745$	8.39914			0.307721
$746$	−27.0355	+	19.6425i	−0.989841	+	0.719162i
$747$	−0.579411	+	5.51273i	−0.0211996	+	0.201700i
$748$	2.57552	−	7.92664i	0.0941704	−	0.289827i
$749$	−5.54549	+	9.60506i	−0.202628	+	0.350961i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−35.6135	+	7.56988i	−1.29956	+	0.276229i	−0.805186	−	0.593023i	$-0.797934\pi$
$751$	−35.6135	+	7.56988i	−1.29956	+	0.276229i	−0.494370	+	0.869252i	$0.664601\pi$
$752$	2.80531	+	8.63385i	0.102299	+	0.314844i
$753$	−26.1049	−	5.54877i	−0.951316	−	0.202209i
$754$	1.45483	+	13.8418i	0.0529817	+	0.504087i
$755$	4.05745	+	4.50625i	0.147666	+	0.163999i
$756$	3.59101	+	1.59882i	0.130604	+	0.0581486i
$757$	−26.3851	+	11.7474i	−0.958984	+	0.426967i	−0.825699	−	0.564111i	$-0.809219\pi$
$757$	−26.3851	+	11.7474i	−0.958984	+	0.426967i	−0.133285	+	0.991078i	$0.542553\pi$
$758$	−22.3778	+	24.8531i	−0.812799	+	0.902705i
$759$	26.0106	+	18.8978i	0.944126	+	0.685948i
$760$	6.73923	+	4.89634i	0.244458	+	0.177609i
$761$	11.4630	−	12.7309i	0.415532	−	0.461495i	−0.498647	−	0.866805i	$-0.666170\pi$
$761$	11.4630	−	12.7309i	0.415532	−	0.461495i	0.914179	+	0.405310i	$0.132836\pi$
$762$	7.55515	−	3.36377i	0.273694	−	0.121857i
$763$	−58.6732	−	26.1230i	−2.12411	−	0.945716i
$764$	−1.44365	−	1.60334i	−0.0522295	−	0.0580067i
$765$	0.207312	+	1.97244i	0.00749538	+	0.0713138i
$766$	−17.5479	−	3.72992i	−0.634031	−	0.134767i
$767$	0.773717	+	2.38126i	0.0279373	+	0.0859822i
$768$	0.978148	−	0.207912i	0.0352959	−	0.00750237i
$769$	18.1853	+	31.4979i	0.655780	+	1.13584i	0.981698	+	0.190446i	$0.0609933\pi$
$769$	18.1853	+	31.4979i	0.655780	+	1.13584i	−0.325918	+	0.945398i	$0.605673\pi$
$770$	−8.25943	+	14.3058i	−0.297649	+	0.515544i
$771$	8.90287	−	27.4002i	0.320629	−	0.986795i
$772$	−2.80741	+	26.7107i	−0.101041	+	0.961340i
$773$	−4.99294	+	3.62759i	−0.179584	+	0.130475i	−0.673946	−	0.738781i	$-0.735402\pi$
$773$	−4.99294	+	3.62759i	−0.179584	+	0.130475i	0.494362	+	0.869256i	$0.335402\pi$
$774$	4.79283			0.172275
$775$	−3.35385	+	4.44429i	−0.120474	+	0.159644i
$776$	9.02907			0.324125
$777$	−28.8852	+	20.9863i	−1.03625	+	0.752879i
$778$	−0.0155779	+	0.148214i	−0.000558496	+	0.00531373i
$779$	0.340184	−	1.04698i	0.0121884	−	0.0375119i
$780$	0.969206	−	1.67871i	0.0347031	−	0.0601076i
$781$	−8.05926	−	13.9591i	−0.288383	−	0.499494i
$782$	−14.8421	+	3.15478i	−0.530751	+	0.112815i
$783$	−2.21878	−	6.82869i	−0.0792926	−	0.244038i
$784$	−8.26693	−	1.75719i	−0.295247	−	0.0627568i
$785$	−0.477030	−	4.53863i	−0.0170259	−	0.161991i
$786$	−10.4104	−	11.5619i	−0.371326	−	0.412399i
$787$	−49.4187	−	22.0026i	−1.76159	−	0.784309i	−0.988726	−	0.149734i	$-0.952158\pi$
$787$	−49.4187	−	22.0026i	−1.76159	−	0.784309i	−0.772861	−	0.634575i	$-0.781175\pi$
$788$	−18.7896	+	8.36568i	−0.669353	+	0.298015i
$789$	19.1252	−	21.2407i	0.680875	−	0.756188i
$790$	−8.03826	−	5.84014i	−0.285989	−	0.207783i
$791$	−62.8120	−	45.6356i	−2.23334	−	1.62261i
$792$	2.81193	−	3.12296i	0.0999175	−	0.110970i
$793$	−1.30680	+	0.581825i	−0.0464058	+	0.0206612i
$794$	−8.42426	−	3.75072i	−0.298966	−	0.133108i
$795$	−6.49654	−	7.21514i	−0.230408	−	0.255894i
$796$	1.06532	+	10.1358i	0.0377592	+	0.359255i
$797$	29.4153	+	6.25241i	1.04194	+	0.221472i	0.696939	−	0.717130i	$-0.254545\pi$
$797$	29.4153	+	6.25241i	1.04194	+	0.221472i	0.345003	+	0.938602i	$0.387878\pi$
$798$	10.1186	+	31.1420i	0.358196	+	1.10241i
$799$	−17.6113	+	3.74340i	−0.623044	+	0.132432i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	1.49584	−	2.59088i	0.0528530	−	0.0915442i
$802$	−8.11887	+	24.9873i	−0.286687	+	0.882332i
$803$	−5.02886	+	47.8464i	−0.177465	+	1.68846i
$804$	−12.1703	+	8.84225i	−0.429214	+	0.311842i
$805$	30.0737			1.05996
$806$	−10.7113	−	1.32272i	−0.377288	−	0.0465909i
$807$	−17.2192			−0.606146
$808$	−11.7400	+	8.52963i	−0.413013	+	0.300071i
$809$	−0.986506	+	9.38598i	−0.0346837	+	0.329993i	0.963398	+	0.268077i	$0.0863880\pi$
$809$	−0.986506	+	9.38598i	−0.0346837	+	0.329993i	−0.998081	+	0.0619169i	$0.980279\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	−5.19153	+	8.99200i	−0.182299	+	0.315752i	−0.942663	−	0.333746i	$-0.891687\pi$
$811$	−5.19153	+	8.99200i	−0.182299	+	0.315752i	0.760364	+	0.649497i	$0.225021\pi$
$812$	14.1120	+	24.4427i	0.495234	+	0.857770i
$813$	5.59107	−	1.18842i	0.196087	−	0.0416797i
$814$	11.7952	+	36.3019i	0.413422	+	1.27238i
$815$	−8.17754	−	1.73819i	−0.286447	−	0.0608861i
$816$	0.207312	+	1.97244i	0.00725737	+	0.0690493i
$817$	26.7150	+	29.6700i	0.934640	+	1.03802i
$818$	−24.4195	−	10.8723i	−0.853807	−	0.380139i
$819$	6.96086	−	3.09918i	0.243232	−	0.108294i
$820$	−0.0884280	+	0.0982093i	−0.00308804	+	0.00342962i
$821$	−13.6833	−	9.94152i	−0.477551	−	0.346961i	0.322825	−	0.946459i	$-0.395367\pi$
$821$	−13.6833	−	9.94152i	−0.477551	−	0.346961i	−0.800377	+	0.599497i	$0.795367\pi$
$822$	7.80661	+	5.67183i	0.272287	+	0.197828i
$823$	−25.9997	+	28.8756i	−0.906294	+	1.00654i	0.0936465	+	0.995606i	$0.470148\pi$
$823$	−25.9997	+	28.8756i	−0.906294	+	1.00654i	−0.999940	+	0.0109356i	$0.996519\pi$
$824$	3.11145	−	1.38531i	0.108392	−	0.0482594i
$825$	−3.83905	−	1.70925i	−0.133658	−	0.0595086i
$826$	3.39744	+	3.77324i	0.118212	+	0.131288i
$827$	−0.951007	−	9.04823i	−0.0330698	−	0.314638i	−0.998535	−	0.0541065i	$-0.982769\pi$
$827$	−0.951007	−	9.04823i	−0.0330698	−	0.314638i	0.965465	−	0.260531i	$-0.0838977\pi$
$828$	−7.48349	−	1.59067i	−0.260069	−	0.0552794i
$829$	−5.18774	−	15.9662i	−0.180178	−	0.554529i	0.819654	−	0.572858i	$-0.194165\pi$
$829$	−5.18774	−	15.9662i	−0.180178	−	0.554529i	−0.999832	+	0.0183288i	$0.994165\pi$
$830$	5.42197	−	1.15247i	0.188199	−	0.0400030i
$831$	4.88605	+	8.46288i	0.169495	+	0.293574i
$832$	0.969206	−	1.67871i	0.0336012	−	0.0581989i
$833$	5.17979	−	15.9417i	0.179469	−	0.552349i
$834$	−0.910673	+	8.66447i	−0.0315340	+	0.300026i
$835$	3.31065	−	2.40533i	0.114570	−	0.0832399i
$836$	35.0063			1.21072
$837$	5.54691	−	0.481414i	0.191729	−	0.0166401i
$838$	12.2553			0.423351
$839$	23.5271	−	17.0934i	0.812244	−	0.590130i	−0.102236	−	0.994760i	$-0.532600\pi$
$839$	23.5271	−	17.0934i	0.812244	−	0.590130i	0.914480	+	0.404630i	$0.132600\pi$
$840$	0.410886	−	3.90932i	0.0141769	−	0.134884i
$841$	6.96958	−	21.4501i	0.240330	−	0.739660i
$842$	−4.33619	+	7.51049i	−0.149435	+	0.258829i
$843$	15.2671	+	26.4434i	0.525827	+	0.910760i
$844$	−18.7707	+	3.98985i	−0.646116	+	0.137336i
$845$	2.85611	+	8.79020i	0.0982531	+	0.302392i
$846$	−8.87978	−	1.88746i	−0.305293	−	0.0648921i
$847$	2.73643	+	26.0354i	0.0940249	+	0.894587i
$848$	−6.49654	−	7.21514i	−0.223092	−	0.247769i
$849$	8.13155	+	3.62040i	0.279074	+	0.124252i
$850$	1.81184	−	0.806683i	0.0621456	−	0.0276690i
$851$	46.4987	−	51.6421i	1.59396	−	1.77027i
$852$	3.10306	+	2.25450i	0.106309	+	0.0772380i
$853$	−9.57935	−	6.95981i	−0.327991	−	0.238299i	0.411587	−	0.911371i	$-0.364975\pi$
$853$	−9.57935	−	6.95981i	−0.327991	−	0.238299i	−0.739578	+	0.673071i	$0.764975\pi$
$854$	−1.94102	+	2.15573i	−0.0664205	+	0.0737674i
$855$	−7.60997	+	3.38818i	−0.260256	+	0.115873i
$856$	−2.57758	−	1.14761i	−0.0881000	−	0.0392246i
$857$	−18.9059	−	20.9971i	−0.645814	−	0.717249i	0.327979	−	0.944685i	$-0.393632\pi$
$857$	−18.9059	−	20.9971i	−0.645814	−	0.717249i	−0.973793	+	0.227436i	$0.926966\pi$
$858$	−0.851479	−	8.10128i	−0.0290690	−	0.276573i
$859$	25.1015	+	5.33549i	0.856453	+	0.182045i	0.615155	−	0.788406i	$-0.289093\pi$
$859$	25.1015	+	5.33549i	0.856453	+	0.182045i	0.241298	+	0.970451i	$0.422427\pi$
$860$	−1.48107	−	4.55825i	−0.0505039	−	0.155435i
$861$	−0.508125	+	0.108005i	−0.0173168	+	0.00368081i
$862$	0.978079	+	1.69408i	0.0333135	+	0.0577007i
$863$	21.3738	−	37.0205i	0.727573	−	1.26019i	−0.230333	−	0.973112i	$-0.573982\pi$
$863$	21.3738	−	37.0205i	0.727573	−	1.26019i	0.957906	−	0.287081i	$-0.0926850\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−0.683557	+	6.50361i	−0.0232416	+	0.221129i
$866$	23.5327	−	17.0975i	0.799674	−	0.580997i
$867$	13.0665			0.443761
$868$	−20.9342	+	6.38435i	−0.710553	+	0.216699i
$869$	−41.7540			−1.41641
$870$	−5.80883	+	4.22036i	−0.196938	+	0.143084i
$871$	−3.04807	+	29.0004i	−0.103280	+	0.982642i
$872$	5.04900	−	15.5392i	0.170981	−	0.526224i
$873$	−4.51453	+	7.81940i	−0.152794	+	0.264647i
$874$	−31.8656	−	55.1929i	−1.07787	−	1.86693i
$875$	−3.84496	+	0.817271i	−0.129983	+	0.0276288i
$876$	−3.53772	−	10.8880i	−0.119529	−	0.367871i
$877$	−42.6540	−	9.06638i	−1.44032	−	0.306150i	−0.579465	−	0.814997i	$-0.696739\pi$
$877$	−42.6540	−	9.06638i	−1.44032	−	0.306150i	−0.860857	+	0.508847i	$0.830072\pi$
$878$	−2.97213	−	28.2779i	−0.100305	−	0.954334i
$879$	2.04233	+	2.26824i	0.0688861	+	0.0765057i
$880$	−3.83905	−	1.70925i	−0.129414	−	0.0576189i
$881$	−10.2231	+	4.55163i	−0.344426	+	0.153348i	−0.571657	−	0.820492i	$-0.693699\pi$
$881$	−10.2231	+	4.55163i	−0.344426	+	0.153348i	0.227231	+	0.973841i	$0.427033\pi$
$882$	5.65524	−	6.28078i	0.190422	−	0.211485i
$883$	45.0570	+	32.7358i	1.51629	+	1.10165i	0.963289	+	0.268467i	$0.0865171\pi$
$883$	45.0570	+	32.7358i	1.51629	+	1.10165i	0.553000	+	0.833181i	$0.313483\pi$
$884$	3.11024	+	2.25972i	0.104609	+	0.0760026i
$885$	−0.864301	+	0.959903i	−0.0290532	+	0.0322668i
$886$	7.19979	−	3.20555i	0.241882	−	0.107693i
$887$	40.9413	+	18.2282i	1.37467	+	0.612044i	0.955265	−	0.295753i	$-0.0955704\pi$
$887$	40.9413	+	18.2282i	1.37467	+	0.612044i	0.419410	+	0.907797i	$0.362237\pi$
$888$	−6.07772	−	6.75000i	−0.203955	−	0.226515i
$889$	−3.39809	−	32.3306i	−0.113968	−	1.08434i
$890$	−2.92631	−	0.622007i	−0.0980902	−	0.0208497i
$891$	1.29860	+	3.99668i	0.0435048	+	0.133894i
$892$	−3.34275	+	0.710524i	−0.111924	+	0.0237901i
$893$	−37.8112	−	65.4910i	−1.26530	−	2.19157i
$894$	−4.19957	+	7.27387i	−0.140455	+	0.243275i
$895$	−0.759413	+	2.33723i	−0.0253844	+	0.0781251i
$896$	0.410886	−	3.90932i	0.0137267	−	0.130601i
$897$	−11.9979	+	8.71695i	−0.400597	+	0.291051i
$898$	20.9774			0.700026
$899$	34.2528	+	20.6135i	1.14240	+	0.687500i
$900$	1.00000			0.0333333
$901$	15.5782	−	11.3183i	0.518986	−	0.377066i
$902$	−0.0580506	+	0.552315i	−0.00193287	+	0.0183901i
$903$	5.82185	−	17.9178i	0.193739	−	0.596268i
$904$	9.87570	−	17.1052i	0.328461	−	0.568911i
$905$	−1.23442	−	2.13808i	−0.0410335	−	0.0710721i
$906$	−5.93125	+	1.26073i	−0.197053	+	0.0418848i
$907$	3.48046	+	10.7117i	0.115567	+	0.355678i	0.992065	−	0.125728i	$-0.0401265\pi$
$907$	3.48046	+	10.7117i	0.115567	+	0.355678i	−0.876498	+	0.481405i	$0.840127\pi$
$908$	−1.07955	−	0.229466i	−0.0358262	−	0.00761508i
$909$	−1.51686	−	14.4320i	−0.0503112	−	0.478679i
$910$	−5.09852	−	5.66248i	−0.169014	−	0.187709i
$911$	−52.0484	−	23.1734i	−1.72444	−	0.767770i	−0.996633	−	0.0819877i	$-0.973873\pi$
$911$	−52.0484	−	23.1734i	−1.72444	−	0.767770i	−0.727807	−	0.685782i	$-0.759460\pi$
$912$	−7.60997	+	3.38818i	−0.251991	+	0.112194i
$913$	15.5868	−	17.3109i	0.515847	−	0.572906i
$914$	8.59245	+	6.24278i	0.284213	+	0.206493i
$915$	−0.597022	−	0.433762i	−0.0197369	−	0.0143397i
$916$	3.64468	−	4.04782i	0.120424	−	0.133744i
$917$	−55.8692	+	24.8746i	−1.84496	+	0.821431i
$918$	−1.81184	−	0.806683i	−0.0597996	−	0.0266245i
$919$	8.22411	+	9.13380i	0.271288	+	0.301296i	0.863359	−	0.504589i	$-0.168356\pi$
$919$	8.22411	+	9.13380i	0.271288	+	0.301296i	−0.592071	+	0.805886i	$0.701689\pi$
$920$	0.799714	+	7.60877i	0.0263658	+	0.250854i
$921$	22.7999	+	4.84627i	0.751283	+	0.159690i
$922$	4.00377	+	12.3223i	0.131857	+	0.405815i
$923$	7.27248	−	1.54581i	0.239377	−	0.0508811i
$924$	−8.25943	−	14.3058i	−0.271715	−	0.470625i
$925$	−4.54151	+	7.86612i	−0.149324	+	0.258637i
$926$	5.24423	−	16.1401i	0.172336	−	0.530396i
$927$	−0.356014	+	3.38725i	−0.0116930	+	0.111252i
$928$	−5.80883	+	4.22036i	−0.190684	+	0.138540i
$929$	−9.31682			−0.305675			−0.152838	−	0.988251i	$-0.548841\pi$
$929$	−9.31682			−0.305675			−0.152838	+	0.988251i	$0.548841\pi$
$930$	−2.17194	−	5.12666i	−0.0712208	−	0.168110i
$931$	70.4032			2.30737
$932$	−7.41764	+	5.38923i	−0.242973	+	0.176530i
$933$	−2.93575	+	27.9318i	−0.0961120	+	0.914445i
$934$	−7.42601	+	22.8549i	−0.242987	+	0.747836i
$935$	4.16728	−	7.21795i	0.136285	−	0.236052i
$936$	0.969206	+	1.67871i	0.0316795	+	0.0548705i
$937$	15.8446	−	3.36787i	0.517620	−	0.110024i	0.0583084	−	0.998299i	$-0.481429\pi$
$937$	15.8446	−	3.36787i	0.517620	−	0.110024i	0.459312	+	0.888275i	$0.348096\pi$
$938$	18.2732	+	56.2390i	0.596640	+	1.83627i
$939$	−9.79997	−	2.08305i	−0.319810	−	0.0679777i
$940$	0.948926	+	9.02843i	0.0309506	+	0.294475i
$941$	27.2706	+	30.2870i	0.888995	+	0.987329i	0.999979	−	0.00649358i	$-0.00206698\pi$
$941$	27.2706	+	30.2870i	0.888995	+	0.987329i	−0.110984	+	0.993822i	$0.535400\pi$
$942$	4.16909	+	1.85620i	0.135836	+	0.0604782i
$943$	0.923654	−	0.411237i	0.0300783	−	0.0133917i
$944$	−0.864301	+	0.959903i	−0.0281306	+	0.0312422i
$945$	3.18013	+	2.31050i	0.103450	+	0.0751605i
$946$	−16.2946	−	11.8387i	−0.529782	−	0.384909i
$947$	10.2653	−	11.4008i	0.333579	−	0.370477i	−0.552899	−	0.833249i	$-0.686478\pi$
$947$	10.2653	−	11.4008i	0.333579	−	0.370477i	0.886478	+	0.462772i	$0.153145\pi$
$948$	9.07684	−	4.04127i	0.294802	−	0.131254i
$949$	−20.2730	−	9.02611i	−0.658089	−	0.293000i
$950$	5.57396	+	6.19051i	0.180843	+	0.200847i
$951$	−0.840833	−	7.99999i	−0.0272659	−	0.259417i
$952$	7.62573	+	1.62090i	0.247151	+	0.0525336i
$953$	5.67569	+	17.4680i	0.183854	+	0.565843i	0.999927	−	0.0121054i	$-0.00385337\pi$
$953$	5.67569	+	17.4680i	0.183854	+	0.565843i	−0.816073	+	0.577949i	$0.803853\pi$
$954$	9.49676	−	2.01860i	0.307469	−	0.0653545i
$955$	−1.07875	−	1.86845i	−0.0349076	−	0.0604617i
$956$	−9.38481	+	16.2550i	−0.303526	+	0.525723i
$957$	−9.32410	+	28.6966i	−0.301405	+	0.927630i
$958$	−1.90908	+	18.1637i	−0.0616795	+	0.586842i
$959$	30.6866	−	22.2951i	0.990923	−	0.719948i
$960$	1.00000			0.0322749
$961$	−21.5653	+	22.2696i	−0.695656	+	0.718375i
$962$	−17.6066			−0.567660
$963$	2.28265	−	1.65845i	0.0735575	−	0.0534427i
$964$	0.540921	−	5.14652i	0.0174219	−	0.165758i
$965$	−8.29953	+	25.5433i	−0.267171	+	0.822269i
$966$	−15.0369	+	26.0446i	−0.483803	+	0.837971i
$967$	−7.81680	−	13.5391i	−0.251371	−	0.435388i	0.712532	−	0.701639i	$-0.247548\pi$
$967$	−7.81680	−	13.5391i	−0.251371	−	0.435388i	−0.963904	+	0.266251i	$0.914215\pi$
$968$	−6.51429	+	1.38466i	−0.209377	+	0.0445045i
$969$	−5.10534	−	15.7126i	−0.164007	−	0.504762i
$970$	8.83176	+	1.87725i	0.283571	+	0.0602748i
$971$	2.70291	+	25.7165i	0.0867405	+	0.825281i	0.948247	+	0.317534i	$0.102855\pi$
$971$	2.70291	+	25.7165i	0.0867405	+	0.825281i	−0.861506	+	0.507747i	$0.830479\pi$
$972$	−0.669131	−	0.743145i	−0.0214624	−	0.0238364i
$973$	31.2856	+	13.9293i	1.00297	+	0.446552i
$974$	−0.0734386	+	0.0326970i	−0.00235312	+	0.00104768i
$975$	1.29705	−	1.44052i	0.0415389	−	0.0461336i
$976$	−0.597022	−	0.433762i	−0.0191102	−	0.0138844i
$977$	−13.0317	−	9.46806i	−0.416920	−	0.302910i	0.359477	−	0.933154i	$-0.382955\pi$
$977$	−13.0317	−	9.46806i	−0.416920	−	0.302910i	−0.776397	+	0.630244i	$0.782955\pi$
$978$	5.59409	−	6.21286i	0.178879	−	0.198665i
$979$	−11.4852	+	5.11355i	−0.367069	+	0.163430i
$980$	−7.72094	−	3.43758i	−0.246636	−	0.109810i
$981$	10.9329	+	12.1422i	0.349059	+	0.387670i
$982$	−1.17388	−	11.1687i	−0.0374600	−	0.356409i
$983$	−51.2540	−	10.8944i	−1.63475	−	0.347477i	−0.703171	−	0.711020i	$-0.748233\pi$
$983$	−51.2540	−	10.8944i	−1.63475	−	0.347477i	−0.931577	+	0.363544i	$0.881567\pi$
$984$	−0.0408377	−	0.125686i	−0.00130186	−	0.00400671i
$985$	−20.1184	+	4.27629i	−0.641024	+	0.136254i
$986$	−7.12018	−	12.3325i	−0.226753	−	0.392747i
$987$	−17.8425	+	30.9041i	−0.567932	+	0.983687i
$988$	−4.98978	+	15.3570i	−0.158746	+	0.488570i
$989$	−3.83289	+	36.4675i	−0.121879	+	1.15960i
$990$	3.39978	−	2.47008i	0.108052	−	0.0785045i
$991$	22.8777			0.726733			0.363367	−	0.931646i	$-0.381627\pi$
$991$	22.8777			0.726733			0.363367	+	0.931646i	$0.381627\pi$
$992$	−2.17194	−	5.12666i	−0.0689592	−	0.162772i
$993$	15.5285			0.492780
$994$	12.1977	−	8.86212i	0.386886	−	0.281089i
$995$	−1.06532	+	10.1358i	−0.0337729	+	0.321328i
$996$	−1.71291	+	5.27180i	−0.0542757	+	0.167043i
$997$	−9.10295	+	15.7668i	−0.288293	+	0.499338i	−0.973402	−	0.229102i	$-0.926421\pi$
$997$	−9.10295	+	15.7668i	−0.288293	+	0.499338i	0.685109	+	0.728440i	$0.259754\pi$
$998$	2.04546	+	3.54284i	0.0647478	+	0.112147i
$999$	8.88453	−	1.88847i	0.281094	−	0.0597484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.c.121.2	✓	16
31.10	even	15	inner	930.2.bg.c.661.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.c.121.2	✓	16	1.1	even	1	trivial
930.2.bg.c.661.2	yes	16	31.10	even	15	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.84496 - 0.817271i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.84496 - 0.817271i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(2.81193 + 3.12296i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(-1.77083 + 0.788423i) q^{13} +(-2.63026 + 2.92119i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.32709 - 1.47388i) q^{17} +(0.913545 - 0.406737i) q^{18} +(7.60997 + 3.38818i) q^{19} +(-0.669131 - 0.743145i) q^{20} +(-0.410886 - 3.90932i) q^{21} +(-4.11053 - 0.873720i) q^{22} +(2.36419 + 7.27623i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.969206 - 1.67871i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.410886 - 3.90932i) q^{28} +(-5.80883 + 4.22036i) q^{29} +1.00000 q^{30} +(-2.17194 - 5.12666i) q^{31} +1.00000 q^{32} +(3.39978 - 2.47008i) q^{33} +(-0.207312 + 1.97244i) q^{34} +(1.21470 - 3.73846i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-4.54151 - 7.86612i) q^{37} +(-8.14812 + 1.73194i) q^{38} +(0.599002 + 1.84354i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-0.0138138 - 0.131430i) q^{41} +(2.63026 + 2.92119i) q^{42} +(4.37847 + 1.94942i) q^{43} +(3.83905 - 1.70925i) q^{44} +(-0.669131 + 0.743145i) q^{45} +(-6.18953 - 4.49696i) q^{46} +(-7.34439 - 5.33601i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(7.72094 - 3.43758i) q^{49} +(0.913545 + 0.406737i) q^{50} +(-1.32709 - 1.47388i) q^{51} +(0.202619 + 1.92779i) q^{52} +(9.49676 + 2.01860i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(4.11053 - 0.873720i) q^{55} +(1.96543 + 3.40422i) q^{56} +(4.16508 - 7.21412i) q^{57} +(2.21878 - 6.82869i) q^{58} +(0.135017 - 1.28460i) q^{59} +(-0.809017 + 0.587785i) q^{60} +0.737960 q^{61} +(4.77051 + 2.87092i) q^{62} -3.93085 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.202619 + 1.92779i) q^{65} +(-1.29860 + 3.99668i) q^{66} +(7.52167 - 13.0279i) q^{67} +(-0.991653 - 1.71759i) q^{68} +(7.48349 - 1.59067i) q^{69} +(1.21470 + 3.73846i) q^{70} +(-3.75177 - 0.797464i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(7.66042 + 8.50775i) q^{73} +(8.29775 + 3.69440i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(5.57396 - 6.19051i) q^{76} +(13.3640 + 9.70954i) q^{77} +(-1.56821 - 1.13937i) q^{78} +(-6.64837 + 7.38377i) q^{79} +(-0.913545 + 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(0.0884280 + 0.0982093i) q^{82} +(-0.579411 - 5.51273i) q^{83} +(-3.84496 - 0.817271i) q^{84} +(-0.612875 - 1.88624i) q^{85} +(-4.68809 + 0.996485i) q^{86} +(3.59006 + 6.21816i) q^{87} +(-2.10118 + 3.63935i) q^{88} +(-0.924482 + 2.84526i) q^{89} +(0.104528 - 0.994522i) q^{90} +(-6.16440 + 4.47870i) q^{91} +7.65068 q^{92} +(-5.32561 + 1.62416i) q^{93} +9.07816 q^{94} +(6.73923 - 4.89634i) q^{95} +(0.104528 - 0.994522i) q^{96} +(2.79014 - 8.58716i) q^{97} +(-4.22581 + 7.31932i) q^{98} +(-2.10118 - 3.63935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

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Database

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