LMFDB - Embedded newform 930.2.bg.b.661.1

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} + 22x^{14} + 195x^{12} + 892x^{10} + 2229x^{8} + 2923x^{6} + 1685x^{4} + 213x^{2} + 1 $ x^16 + 22x^14 + 195x^12 + 892x^10 + 2229x^8 + 2923x^6 + 1685x^4 + 213*x^2 + 1
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			661.1
Root			$-0.0698697i$ of defining polynomial
Character	$\chi$	$=$	930.661
Dual form			930.2.bg.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.272042 + 0.0578243i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(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} +(0.272042 + 0.0578243i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-0.538031 + 0.597544i) q^{11} +(-0.913545 + 0.406737i) q^{12} +(-3.82639 - 1.70362i) q^{13} +(-0.186098 - 0.206683i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.46937 + 4.96374i) q^{17} +(0.913545 + 0.406737i) q^{18} +(-5.23919 + 2.33264i) q^{19} +(0.669131 - 0.743145i) q^{20} +(-0.0290714 + 0.276596i) q^{21} +(0.786504 - 0.167177i) q^{22} +(0.320264 - 0.985672i) q^{23} +(0.978148 + 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.09425 + 3.62735i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.0290714 + 0.276596i) q^{28} +(1.22412 + 0.889375i) q^{29} -1.00000 q^{30} +(-5.44888 + 1.14444i) q^{31} +1.00000 q^{32} +(-0.650511 - 0.472624i) q^{33} +(-0.698184 - 6.64278i) q^{34} +(-0.0859436 - 0.264507i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.82296 + 8.35361i) q^{37} +(5.60969 + 1.19238i) q^{38} +(1.29432 - 3.98350i) q^{39} +(-0.978148 + 0.207912i) q^{40} +(-0.311774 + 2.96633i) q^{41} +(0.186098 - 0.206683i) q^{42} +(1.48593 - 0.661581i) q^{43} +(-0.734559 - 0.327047i) q^{44} +(0.669131 + 0.743145i) q^{45} +(-0.838463 + 0.609179i) q^{46} +(9.06508 - 6.58617i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(-6.32416 - 2.81570i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-4.46937 + 4.96374i) q^{51} +(0.437818 - 4.16556i) q^{52} +(-11.0594 + 2.35074i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(0.786504 + 0.167177i) q^{55} +(0.139060 - 0.240858i) q^{56} +(-2.86751 - 4.96667i) q^{57} +(-0.467572 - 1.43904i) q^{58} +(0.504480 + 4.79981i) q^{59} +(0.809017 + 0.587785i) q^{60} -12.4236 q^{61} +(5.08092 + 2.27690i) q^{62} -0.278119 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.437818 + 4.16556i) q^{65} +(0.248473 + 0.764721i) q^{66} +(5.33122 + 9.23395i) q^{67} +(-3.33968 + 5.78450i) q^{68} +(1.01375 + 0.215479i) q^{69} +(-0.0859436 + 0.264507i) q^{70} +(-10.9322 + 2.32371i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(-2.05734 + 2.28491i) q^{73} +(8.81198 - 3.92335i) q^{74} +(-0.913545 - 0.406737i) q^{75} +(-3.83747 - 4.26195i) q^{76} +(-0.180920 + 0.131446i) q^{77} +(-3.38857 + 2.46194i) q^{78} +(-0.656411 - 0.729019i) q^{79} +(0.913545 + 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(1.99580 - 2.21656i) q^{82} +(-0.402279 + 3.82743i) q^{83} +(-0.272042 + 0.0578243i) q^{84} +(2.06404 - 6.35246i) q^{85} +(-1.59101 - 0.338180i) q^{86} +(-0.756548 + 1.31038i) q^{87} +(0.402038 + 0.696350i) q^{88} +(-2.74243 - 8.44034i) q^{89} +(-0.104528 - 0.994522i) q^{90} +(-0.942427 - 0.684713i) q^{91} +1.03640 q^{92} +(-1.70773 - 5.29940i) q^{93} -11.2051 q^{94} +(4.63972 + 3.37096i) q^{95} +(0.104528 + 0.994522i) q^{96} +(3.70497 + 11.4027i) q^{97} +(3.46132 + 5.99519i) q^{98} +(0.402038 - 0.696350i) 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} + 3 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 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{15}\right)$

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
$7$	0.272042	+	0.0578243i	0.102822	+	0.0218555i	0.259035	−	0.965868i	$-0.416595\pi$
$7$	0.272042	+	0.0578243i	0.102822	+	0.0218555i	−0.156213	+	0.987723i	$0.549929\pi$
$8$	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
$11$	−0.538031	+	0.597544i	−0.162223	+	0.180166i	−0.818776	−	0.574113i	$-0.805347\pi$
$11$	−0.538031	+	0.597544i	−0.162223	+	0.180166i	0.656553	+	0.754280i	$0.272014\pi$
$12$	−0.913545	+	0.406737i	−0.263718	+	0.117415i
$13$	−3.82639	−	1.70362i	−1.06125	−	0.472499i	−0.199534	−	0.979891i	$-0.563943\pi$
$13$	−3.82639	−	1.70362i	−1.06125	−	0.472499i	−0.861715	+	0.507392i	$0.830609\pi$
$14$	−0.186098	−	0.206683i	−0.0497368	−	0.0552384i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.46937	+	4.96374i	1.08398	+	1.20388i	0.977801	+	0.209536i	$0.0671955\pi$
$17$	4.46937	+	4.96374i	1.08398	+	1.20388i	0.106180	+	0.994347i	$0.466138\pi$
$18$	0.913545	+	0.406737i	0.215325	+	0.0958687i
$19$	−5.23919	+	2.33264i	−1.20195	+	0.535144i	−0.907310	−	0.420463i	$-0.861868\pi$
$19$	−5.23919	+	2.33264i	−1.20195	+	0.535144i	−0.294644	+	0.955607i	$0.595201\pi$
$20$	0.669131	−	0.743145i	0.149622	−	0.166172i
$21$	−0.0290714	+	0.276596i	−0.00634390	+	0.0603582i
$22$	0.786504	−	0.167177i	0.167683	−	0.0356422i
$23$	0.320264	−	0.985672i	0.0667797	−	0.205527i	−0.912098	−	0.409971i	$-0.865539\pi$
$23$	0.320264	−	0.985672i	0.0667797	−	0.205527i	0.978878	+	0.204444i	$0.0655387\pi$
$24$	0.978148	+	0.207912i	0.199664	+	0.0424398i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.09425	+	3.62735i	0.410717	+	0.711382i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.0290714	+	0.276596i	0.00549398	+	0.0522717i
$29$	1.22412	+	0.889375i	0.227313	+	0.165153i	0.695613	−	0.718417i	$-0.255133\pi$
$29$	1.22412	+	0.889375i	0.227313	+	0.165153i	−0.468299	+	0.883570i	$0.655133\pi$
$30$	−1.00000			−0.182574
$31$	−5.44888	+	1.14444i	−0.978647	+	0.205547i
$31$	−5.44888	+	1.14444i	−0.978647	+	0.205547i
$32$	1.00000			0.176777
$33$	−0.650511	−	0.472624i	−0.113239	−	0.0822732i
$34$	−0.698184	−	6.64278i	−0.119738	−	1.13923i
$35$	−0.0859436	−	0.264507i	−0.0145271	−	0.0447099i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−4.82296	+	8.35361i	−0.792889	+	1.37332i	0.131281	+	0.991345i	$0.458091\pi$
$37$	−4.82296	+	8.35361i	−0.792889	+	1.37332i	−0.924171	+	0.381980i	$0.875242\pi$
$38$	5.60969	+	1.19238i	0.910012	+	0.193429i
$39$	1.29432	−	3.98350i	0.207257	−	0.637871i
$40$	−0.978148	+	0.207912i	−0.154659	+	0.0328737i
$41$	−0.311774	+	2.96633i	−0.0486910	+	0.463264i	0.942826	+	0.333286i	$0.108157\pi$
$41$	−0.311774	+	2.96633i	−0.0486910	+	0.463264i	−0.991517	+	0.129978i	$0.958509\pi$
$42$	0.186098	−	0.206683i	0.0287156	−	0.0318919i
$43$	1.48593	−	0.661581i	0.226603	−	0.100890i	−0.290295	−	0.956937i	$-0.593753\pi$
$43$	1.48593	−	0.661581i	0.226603	−	0.100890i	0.516898	+	0.856047i	$0.327087\pi$
$44$	−0.734559	−	0.327047i	−0.110739	−	0.0493042i
$45$	0.669131	+	0.743145i	0.0997481	+	0.110781i
$46$	−0.838463	+	0.609179i	−0.123625	+	0.0898185i
$47$	9.06508	−	6.58617i	1.32228	−	0.960691i	0.322377	−	0.946611i	$-0.395518\pi$
$47$	9.06508	−	6.58617i	1.32228	−	0.960691i	0.999901	−	0.0140795i	$-0.00448180\pi$
$48$	−0.669131	−	0.743145i	−0.0965807	−	0.107264i
$49$	−6.32416	−	2.81570i	−0.903451	−	0.402242i
$50$	0.913545	−	0.406737i	0.129195	−	0.0575212i
$51$	−4.46937	+	4.96374i	−0.625837	+	0.695062i
$52$	0.437818	−	4.16556i	0.0607144	−	0.577659i
$53$	−11.0594	+	2.35074i	−1.51912	+	0.322899i	−0.890562	−	0.454862i	$-0.849689\pi$
$53$	−11.0594	+	2.35074i	−1.51912	+	0.322899i	−0.628560	+	0.777761i	$0.716355\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	0.786504	+	0.167177i	0.106052	+	0.0225421i
$56$	0.139060	−	0.240858i	0.0185826	−	0.0321861i
$57$	−2.86751	−	4.96667i	−0.379811	−	0.657851i
$58$	−0.467572	−	1.43904i	−0.0613952	−	0.188955i
$59$	0.504480	+	4.79981i	0.0656777	+	0.624882i	0.977008	+	0.213205i	$0.0683901\pi$
$59$	0.504480	+	4.79981i	0.0656777	+	0.624882i	−0.911330	+	0.411677i	$0.864943\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−12.4236			−1.59068			−0.795340	−	0.606164i	$-0.792707\pi$
$61$	−12.4236			−1.59068			−0.795340	+	0.606164i	$0.792707\pi$
$62$	5.08092	+	2.27690i	0.645277	+	0.289167i
$63$	−0.278119			−0.0350398
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.437818	+	4.16556i	0.0543046	+	0.516674i
$66$	0.248473	+	0.764721i	0.0305849	+	0.0941307i
$67$	5.33122	+	9.23395i	0.651313	+	1.12811i	0.982805	+	0.184648i	$0.0591146\pi$
$67$	5.33122	+	9.23395i	0.651313	+	1.12811i	−0.331492	+	0.943458i	$0.607552\pi$
$68$	−3.33968	+	5.78450i	−0.404996	+	0.701474i
$69$	1.01375	+	0.215479i	0.122041	+	0.0259406i
$70$	−0.0859436	+	0.264507i	−0.0102722	+	0.0316147i
$71$	−10.9322	+	2.32371i	−1.29742	+	0.275774i	−0.804317	−	0.594200i	$-0.797469\pi$
$71$	−10.9322	+	2.32371i	−1.29742	+	0.275774i	−0.493098	+	0.869974i	$0.664135\pi$
$72$	−0.104528	+	0.994522i	−0.0123188	+	0.117206i
$73$	−2.05734	+	2.28491i	−0.240794	+	0.267429i	−0.851413	−	0.524496i	$-0.824254\pi$
$73$	−2.05734	+	2.28491i	−0.240794	+	0.267429i	0.610619	+	0.791924i	$0.290921\pi$
$74$	8.81198	−	3.92335i	1.02437	−	0.456080i
$75$	−0.913545	−	0.406737i	−0.105487	−	0.0469659i
$76$	−3.83747	−	4.26195i	−0.440188	−	0.488879i
$77$	−0.180920	+	0.131446i	−0.0206177	+	0.0149796i
$78$	−3.38857	+	2.46194i	−0.383680	+	0.278760i
$79$	−0.656411	−	0.729019i	−0.0738521	−	0.0820210i	0.705086	−	0.709121i	$-0.250908\pi$
$79$	−0.656411	−	0.729019i	−0.0738521	−	0.0820210i	−0.778938	+	0.627100i	$0.784242\pi$
$80$	0.913545	+	0.406737i	0.102137	+	0.0454745i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	1.99580	−	2.21656i	0.220399	−	0.244778i
$83$	−0.402279	+	3.82743i	−0.0441559	+	0.420115i	0.950007	+	0.312228i	$0.101075\pi$
$83$	−0.402279	+	3.82743i	−0.0441559	+	0.420115i	−0.994163	+	0.107887i	$0.965591\pi$
$84$	−0.272042	+	0.0578243i	−0.0296822	+	0.00630915i
$85$	2.06404	−	6.35246i	0.223876	−	0.689021i
$86$	−1.59101	−	0.338180i	−0.171563	−	0.0364669i
$87$	−0.756548	+	1.31038i	−0.0811104	+	0.140487i
$88$	0.402038	+	0.696350i	0.0428574	+	0.0742311i
$89$	−2.74243	−	8.44034i	−0.290697	−	0.894674i	−0.984633	−	0.174637i	$-0.944125\pi$
$89$	−2.74243	−	8.44034i	−0.290697	−	0.894674i	0.693936	−	0.720037i	$-0.255875\pi$
$90$	−0.104528	−	0.994522i	−0.0110183	−	0.104832i
$91$	−0.942427	−	0.684713i	−0.0987932	−	0.0717775i
$92$	1.03640			0.108052
$93$	−1.70773	−	5.29940i	−0.177083	−	0.549522i
$94$	−11.2051			−1.15571
$95$	4.63972	+	3.37096i	0.476026	+	0.345853i
$96$	0.104528	+	0.994522i	0.0106684	+	0.101503i
$97$	3.70497	+	11.4027i	0.376182	+	1.15777i	0.942678	+	0.333705i	$0.108299\pi$
$97$	3.70497	+	11.4027i	0.376182	+	1.15777i	−0.566495	+	0.824065i	$0.691701\pi$
$98$	3.46132	+	5.99519i	0.349647	+	0.605606i
$99$	0.402038	−	0.696350i	0.0404063	−	0.0699858i
$100$	−0.978148	−	0.207912i	−0.0978148	−	0.0207912i
$101$	−3.32907	+	10.2458i	−0.331255	+	1.01950i	0.637283	+	0.770630i	$0.280058\pi$
$101$	−3.32907	+	10.2458i	−0.331255	+	1.01950i	−0.968538	+	0.248867i	$0.919942\pi$
$102$	6.53341	−	1.38872i	0.646904	−	0.137504i
$103$	0.361100	−	3.43563i	0.0355802	−	0.338523i	−0.962222	−	0.272265i	$-0.912227\pi$
$103$	0.361100	−	3.43563i	0.0355802	−	0.338523i	0.997803	−	0.0662581i	$-0.0211061\pi$
$104$	−2.80266	+	3.11266i	−0.274823	+	0.305222i
$105$	0.254075	−	0.113121i	0.0247952	−	0.0110395i
$106$	10.3290	+	4.59875i	1.00324	+	0.446670i
$107$	−7.31439	−	8.12345i	−0.707109	−	0.785324i	0.277382	−	0.960760i	$-0.410533\pi$
$107$	−7.31439	−	8.12345i	−0.707109	−	0.785324i	−0.984491	+	0.175436i	$0.943867\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	4.32711	−	3.14383i	0.414462	−	0.301124i	−0.360944	−	0.932588i	$-0.617545\pi$
$109$	4.32711	−	3.14383i	0.414462	−	0.301124i	0.775406	+	0.631463i	$0.217545\pi$
$110$	−0.538031	−	0.597544i	−0.0512993	−	0.0569736i
$111$	−8.81198	−	3.92335i	−0.836396	−	0.372388i
$112$	−0.254075	+	0.113121i	−0.0240078	+	0.0106890i
$113$	4.00910	−	4.45255i	0.377144	−	0.418861i	−0.524452	−	0.851440i	$-0.675730\pi$
$113$	4.00910	−	4.45255i	0.377144	−	0.418861i	0.901596	+	0.432579i	$0.142396\pi$
$114$	−0.599472	+	5.70360i	−0.0561457	+	0.534191i
$115$	−1.01375	+	0.215479i	−0.0945326	+	0.0200935i
$116$	−0.467572	+	1.43904i	−0.0434130	+	0.133611i
$117$	4.09697	+	0.870839i	0.378765	+	0.0805091i
$118$	2.41312	−	4.17965i	0.222146	−	0.384768i
$119$	0.928831	+	1.60878i	0.0851458	+	0.147477i
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	1.08223	+	10.2967i	0.0983847	+	0.936068i
$122$	10.0509	+	7.30241i	0.909966	+	0.661129i
$123$	−2.98267			−0.268939
$124$	−2.77222	−	4.82854i	−0.248953	−	0.433616i
$125$	1.00000			0.0894427
$126$	0.225003	+	0.163474i	0.0200449	+	0.0145635i
$127$	−1.91570	−	18.2267i	−0.169991	−	1.61736i	−0.663885	−	0.747835i	$-0.731093\pi$
$127$	−1.91570	−	18.2267i	−0.169991	−	1.61736i	0.493893	−	0.869522i	$-0.335573\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	0.813279	+	1.40864i	0.0716052	+	0.124024i
$130$	2.09425	−	3.62735i	0.183678	−	0.318140i
$131$	12.2622	+	2.60640i	1.07135	+	0.227722i	0.709637	−	0.704567i	$-0.248859\pi$
$131$	12.2622	+	2.60640i	1.07135	+	0.227722i	0.361713	+	0.932290i	$0.382192\pi$
$132$	0.248473	−	0.764721i	0.0216268	−	0.0665604i
$133$	−1.56016	+	0.331623i	−0.135283	+	0.0287554i
$134$	1.11453	−	10.6040i	0.0962806	−	0.916049i
$135$	−0.669131	+	0.743145i	−0.0575896	+	0.0639597i
$136$	6.10191	−	2.71674i	0.523234	−	0.232959i
$137$	10.3317	+	4.59997i	0.882697	+	0.393002i	0.797469	−	0.603359i	$-0.206172\pi$
$137$	10.3317	+	4.59997i	0.882697	+	0.393002i	0.0852277	+	0.996361i	$0.472838\pi$
$138$	−0.693485	−	0.770193i	−0.0590334	−	0.0655632i
$139$	−0.676332	+	0.491384i	−0.0573657	+	0.0416786i	−0.616099	−	0.787669i	$-0.711288\pi$
$139$	−0.676332	+	0.491384i	−0.0573657	+	0.0416786i	0.558733	+	0.829348i	$0.311288\pi$
$140$	0.225003	−	0.163474i	0.0190163	−	0.0138161i
$141$	7.49764	+	8.32698i	0.631416	+	0.701258i
$142$	10.2102	+	4.54587i	0.856820	+	0.381481i
$143$	3.07670	−	1.36984i	0.257287	−	0.114552i
$144$	0.669131	−	0.743145i	0.0557609	−	0.0619287i
$145$	0.158162	−	1.50481i	0.0131346	−	0.124967i
$146$	3.00746	−	0.639256i	0.248899	−	0.0529052i
$147$	2.13922	−	6.58383i	0.176440	−	0.543025i
$148$	−9.43513	−	2.00550i	−0.775563	−	0.164851i
$149$	−11.0323	+	19.1086i	−0.903804	+	1.56543i	−0.0812895	+	0.996691i	$0.525904\pi$
$149$	−11.0323	+	19.1086i	−0.903804	+	1.56543i	−0.822515	+	0.568744i	$0.807429\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−2.20642	−	6.79066i	−0.179556	−	0.552616i	0.820256	−	0.571996i	$-0.193831\pi$
$151$	−2.20642	−	6.79066i	−0.179556	−	0.552616i	−0.999812	+	0.0193799i	$0.993831\pi$
$152$	0.599472	+	5.70360i	0.0486236	+	0.462623i
$153$	−5.40372	−	3.92603i	−0.436865	−	0.317401i
$154$	0.223629			0.0180205
$155$	3.71555	+	4.14665i	0.298440	+	0.333067i
$156$	4.18850			0.335349
$157$	13.3947	+	9.73179i	1.06901	+	0.776681i	0.975734	−	0.218959i	$-0.0702661\pi$
$157$	13.3947	+	9.73179i	1.06901	+	0.776681i	0.0932759	+	0.995640i	$0.470266\pi$
$158$	0.102542	+	0.975618i	0.00815777	+	0.0776160i
$159$	−3.49388	−	10.7531i	−0.277083	−	0.852774i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	0.144121	−	0.249625i	0.0113583	−	0.0196732i
$162$	−0.978148	−	0.207912i	−0.0768505	−	0.0163351i
$163$	−4.48143	+	13.7924i	−0.351012	+	1.08031i	0.607273	+	0.794493i	$0.292263\pi$
$163$	−4.48143	+	13.7924i	−0.351012	+	1.08031i	−0.958286	+	0.285812i	$0.907737\pi$
$164$	−2.91749	+	0.620133i	−0.227818	+	0.0484242i
$165$	−0.0840488	+	0.799671i	−0.00654319	+	0.0622543i
$166$	2.57516	−	2.86000i	0.199871	−	0.221979i
$167$	9.99525	−	4.45017i	0.773455	−	0.344365i	0.0182335	−	0.999834i	$-0.494196\pi$
$167$	9.99525	−	4.45017i	0.773455	−	0.344365i	0.755222	+	0.655469i	$0.227529\pi$
$168$	0.254075	+	0.113121i	0.0196023	+	0.00872750i
$169$	3.04023	+	3.37652i	0.233864	+	0.259733i
$170$	−5.40372	+	3.92603i	−0.414447	+	0.301113i
$171$	4.63972	−	3.37096i	0.354808	−	0.257783i
$172$	1.08838	+	1.20877i	0.0829882	+	0.0921677i
$173$	20.2805	+	9.02944i	1.54190	+	0.686496i	0.989157	−	0.146859i	$-0.0469165\pi$
$173$	20.2805	+	9.02944i	1.54190	+	0.686496i	0.552738	+	0.833355i	$0.313583\pi$
$174$	1.38228	−	0.615431i	0.104790	−	0.0466557i
$175$	−0.186098	+	0.206683i	−0.0140677	+	0.0156238i
$176$	0.0840488	−	0.799671i	0.00633541	−	0.0602774i
$177$	−4.72078	+	1.00343i	−0.354836	+	0.0754226i
$178$	−2.74243	+	8.44034i	−0.205554	+	0.632630i
$179$	3.71349	+	0.789326i	0.277559	+	0.0589970i	0.344588	−	0.938754i	$-0.388019\pi$
$179$	3.71349	+	0.789326i	0.277559	+	0.0589970i	−0.0670289	+	0.997751i	$0.521352\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−9.25765	−	16.0347i	−0.688116	−	1.19185i	−0.972447	−	0.233125i	$-0.925105\pi$
$181$	−9.25765	−	16.0347i	−0.688116	−	1.19185i	0.284331	−	0.958726i	$-0.408229\pi$
$182$	0.359975	+	1.10789i	0.0266831	+	0.0821222i
$183$	−1.29862	−	12.3555i	−0.0959967	−	0.913348i
$184$	−0.838463	−	0.609179i	−0.0618123	−	0.0449093i
$185$	9.64592			0.709182
$186$	−1.73333	+	5.29108i	−0.127094	+	0.387961i
$187$	−5.37072			−0.392746
$188$	9.06508	+	6.58617i	0.661139	+	0.480345i
$189$	−0.0290714	−	0.276596i	−0.00211463	−	0.0201194i
$190$	−1.77222	−	5.45432i	−0.128570	−	0.395698i
$191$	−12.8937	−	22.3326i	−0.932959	−	1.61593i	−0.778234	−	0.627974i	$-0.783884\pi$
$191$	−12.8937	−	22.3326i	−0.932959	−	1.61593i	−0.154724	−	0.987958i	$-0.549449\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−7.95718	−	1.69135i	−0.572771	−	0.121746i	−0.0875845	−	0.996157i	$-0.527915\pi$
$193$	−7.95718	−	1.69135i	−0.572771	−	0.121746i	−0.485186	+	0.874411i	$0.661248\pi$
$194$	3.70497	−	11.4027i	0.266001	−	0.818667i
$195$	−4.09697	+	0.870839i	−0.293390	+	0.0623621i
$196$	0.723614	−	6.88473i	0.0516867	−	0.491766i
$197$	4.84323	−	5.37895i	0.345066	−	0.383234i	−0.545483	−	0.838122i	$-0.683654\pi$
$197$	4.84323	−	5.37895i	0.345066	−	0.383234i	0.890549	+	0.454887i	$0.150320\pi$
$198$	−0.734559	+	0.327047i	−0.0522029	+	0.0232422i
$199$	−3.04744	−	1.35681i	−0.216027	−	0.0961815i	0.295870	−	0.955228i	$-0.404390\pi$
$199$	−3.04744	−	1.35681i	−0.216027	−	0.0961815i	−0.511897	+	0.859047i	$0.671057\pi$
$200$	0.669131	+	0.743145i	0.0473147	+	0.0525483i
$201$	−8.62610	+	6.26723i	−0.608438	+	0.442056i
$202$	8.71561	−	6.33226i	0.613228	−	0.445536i
$203$	0.281584	+	0.312731i	0.0197633	+	0.0219494i
$204$	−6.10191	−	2.71674i	−0.427219	−	0.190210i
$205$	2.72481	−	1.21316i	0.190309	−	0.0847310i
$206$	−2.31155	+	2.56724i	−0.161053	+	0.178868i
$207$	−0.108333	+	1.03072i	−0.00752966	+	0.0716400i
$208$	4.09697	−	0.870839i	0.284074	−	0.0603818i
$209$	1.42500	−	4.38569i	0.0985690	−	0.303364i
$210$	−0.272042	−	0.0578243i	−0.0187727	−	0.00399025i
$211$	8.92848	−	15.4646i	0.614662	−	1.06463i	−0.375782	−	0.926708i	$-0.622626\pi$
$211$	8.92848	−	15.4646i	0.614662	−	1.06463i	0.990444	−	0.137918i	$-0.0440410\pi$
$212$	−5.65322	−	9.79167i	−0.388265	−	0.672495i
$213$	−3.45371	−	10.6294i	−0.236644	−	0.728317i
$214$	1.14262	+	10.8713i	0.0781079	+	0.743147i
$215$	−1.31591	−	0.956067i	−0.0897445	−	0.0652032i
$216$	−1.00000			−0.0680414
$217$	−1.54850	−	0.00374305i	−0.105119	−	0.000254095i
$218$	−5.34860			−0.362253
$219$	−2.48744	−	1.80723i	−0.168086	−	0.122122i
$220$	0.0840488	+	0.799671i	0.00566657	+	0.0539138i
$221$	−8.64523	−	26.6073i	−0.581541	−	1.78980i
$222$	4.82296	+	8.35361i	0.323696	+	0.560657i
$223$	10.2807	−	17.8066i	0.688444	−	1.19242i	−0.283897	−	0.958855i	$-0.591627\pi$
$223$	10.2807	−	17.8066i	0.688444	−	1.19242i	0.972341	−	0.233566i	$-0.0750394\pi$
$224$	0.272042	+	0.0578243i	0.0181766	+	0.00386355i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−5.86057	+	1.24570i	−0.389839	+	0.0828629i
$227$	1.88669	−	17.9506i	0.125224	−	1.19142i	−0.733755	−	0.679414i	$-0.762234\pi$
$227$	1.88669	−	17.9506i	0.125224	−	1.19142i	0.858979	−	0.512011i	$-0.171099\pi$
$228$	3.83747	−	4.26195i	0.254143	−	0.282254i
$229$	3.86085	−	1.71896i	0.255132	−	0.113592i	−0.275186	−	0.961391i	$-0.588739\pi$
$229$	3.86085	−	1.71896i	0.255132	−	0.113592i	0.530318	+	0.847799i	$0.322073\pi$
$230$	0.946796	+	0.421541i	0.0624299	+	0.0277956i
$231$	−0.149637	−	0.166189i	−0.00984539	−	0.0109344i
$232$	1.22412	−	0.889375i	0.0803674	−	0.0583903i
$233$	12.5468	−	9.11579i	0.821969	−	0.597195i	−0.0953070	−	0.995448i	$-0.530383\pi$
$233$	12.5468	−	9.11579i	0.821969	−	0.597195i	0.917276	+	0.398253i	$0.130383\pi$
$234$	−2.80266	−	3.11266i	−0.183215	−	0.203481i
$235$	−10.2363	−	4.55751i	−0.667744	−	0.297299i
$236$	−4.40900	+	1.96301i	−0.287001	+	0.127781i
$237$	0.656411	−	0.729019i	0.0426385	−	0.0473549i
$238$	0.194179	−	1.84749i	0.0125867	−	0.119755i
$239$	−7.12487	+	1.51444i	−0.460870	+	0.0979609i	−0.432495	−	0.901636i	$-0.642367\pi$
$239$	−7.12487	+	1.51444i	−0.460870	+	0.0979609i	−0.0283751	+	0.999597i	$0.509033\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	28.8485	+	6.13193i	1.85829	+	0.394992i	0.994127	−	0.108217i	$-0.0345140\pi$
$241$	28.8485	+	6.13193i	1.85829	+	0.394992i	0.864165	+	0.503209i	$0.167847\pi$
$242$	5.17673	−	8.96636i	0.332773	−	0.576380i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−3.83910	−	11.8155i	−0.245773	−	0.756413i
$245$	0.723614	+	6.88473i	0.0462300	+	0.439849i
$246$	2.41303	+	1.75317i	0.153849	+	0.111778i
$247$	24.0211			1.52843
$248$	−0.595373	+	5.53584i	−0.0378062	+	0.351526i
$249$	−3.84852			−0.243890
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	2.05093	+	19.5133i	0.129453	+	1.23167i	0.845638	+	0.533756i	$0.179220\pi$
$251$	2.05093	+	19.5133i	0.129453	+	1.23167i	−0.716185	+	0.697910i	$0.754113\pi$
$252$	−0.0859436	−	0.264507i	−0.00541394	−	0.0166624i
$253$	0.416671	+	0.721695i	0.0261959	+	0.0453726i
$254$	−9.16355	+	15.8717i	−0.574972	+	0.995881i
$255$	6.53341	+	1.38872i	0.409138	+	0.0869649i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	22.2801	−	4.73578i	1.38979	−	0.295410i	0.548573	−	0.836102i	$-0.315171\pi$
$257$	22.2801	−	4.73578i	1.38979	−	0.295410i	0.841220	+	0.540693i	$0.181838\pi$
$258$	0.170022	−	1.61765i	0.0105851	−	0.100710i
$259$	−1.79509	+	1.99365i	−0.111541	+	0.123879i
$260$	−3.82639	+	1.70362i	−0.237303	+	0.105654i
$261$	−1.38228	−	0.615431i	−0.0855611	−	0.0380942i
$262$	−8.38829	−	9.31614i	−0.518230	−	0.575553i
$263$	−12.9364	+	9.39888i	−0.797695	+	0.579560i	−0.910237	−	0.414087i	$-0.864101\pi$
$263$	−12.9364	+	9.39888i	−0.797695	+	0.579560i	0.112542	+	0.993647i	$0.464101\pi$
$264$	−0.650511	+	0.472624i	−0.0400362	+	0.0290880i
$265$	7.56549	+	8.40233i	0.464744	+	0.516151i
$266$	1.45712	+	0.648752i	0.0893419	+	0.0397776i
$267$	8.10744	−	3.60967i	0.496167	−	0.220908i
$268$	−7.13457	+	7.92374i	−0.435813	+	0.484020i
$269$	1.48770	−	14.1545i	0.0907064	−	0.863014i	−0.850680	−	0.525684i	$-0.823810\pi$
$269$	1.48770	−	14.1545i	0.0907064	−	0.863014i	0.941386	−	0.337330i	$-0.109524\pi$
$270$	0.978148	−	0.207912i	0.0595282	−	0.0126531i
$271$	−4.37097	+	13.4525i	−0.265518	+	0.817180i	0.726056	+	0.687636i	$0.241351\pi$
$271$	−4.37097	+	13.4525i	−0.265518	+	0.817180i	−0.991574	+	0.129544i	$0.958649\pi$
$272$	−6.53341	−	1.38872i	−0.396146	−	0.0842034i
$273$	0.582452	−	1.00884i	0.0352516	−	0.0610576i
$274$	−5.65473	−	9.79428i	−0.341615	−	0.591694i
$275$	−0.248473	−	0.764721i	−0.0149835	−	0.0461144i
$276$	0.108333	+	1.03072i	0.00652088	+	0.0620420i
$277$	5.16198	+	3.75040i	0.310154	+	0.225340i	0.731962	−	0.681345i	$-0.238605\pi$
$277$	5.16198	+	3.75040i	0.310154	+	0.225340i	−0.421809	+	0.906685i	$0.638605\pi$
$278$	0.835992			0.0501395
$279$	5.09187	−	2.25231i	0.304842	−	0.134842i
$280$	−0.278119			−0.0166208
$281$	−14.1920	−	10.3111i	−0.846625	−	0.615109i	0.0775882	−	0.996985i	$-0.475278\pi$
$281$	−14.1920	−	10.3111i	−0.846625	−	0.615109i	−0.924213	+	0.381876i	$0.875278\pi$
$282$	−1.17125	−	11.1437i	−0.0697467	−	0.663596i
$283$	−9.80848	−	30.1874i	−0.583054	−	1.79446i	−0.606949	−	0.794741i	$-0.707607\pi$
$283$	−9.80848	−	30.1874i	−0.583054	−	1.79446i	0.0238949	−	0.999714i	$-0.492393\pi$
$284$	−5.58822	−	9.67909i	−0.331600	−	0.574348i
$285$	−2.86751	+	4.96667i	−0.169856	+	0.294200i
$286$	−3.29428	−	0.700220i	−0.194795	−	0.0414049i
$287$	−0.256342	+	0.788939i	−0.0151314	+	0.0465696i
$288$	−0.978148	+	0.207912i	−0.0576379	+	0.0122513i
$289$	−2.88644	+	27.4627i	−0.169791	+	1.61545i
$290$	−1.01246	+	1.12445i	−0.0594536	+	0.0660299i
$291$	−10.9530	+	4.87658i	−0.642075	+	0.285870i
$292$	−2.80883	−	1.25057i	−0.164374	−	0.0731842i
$293$	−2.62954	−	2.92039i	−0.153619	−	0.170611i	0.661423	−	0.750013i	$-0.269953\pi$
$293$	−2.62954	−	2.92039i	−0.153619	−	0.170611i	−0.815042	+	0.579402i	$0.803286\pi$
$294$	−5.60054	+	4.06903i	−0.326630	+	0.237311i
$295$	3.90452	−	2.83680i	0.227330	−	0.165165i
$296$	6.45438	+	7.16831i	0.375153	+	0.416650i
$297$	0.734559	+	0.327047i	0.0426235	+	0.0189772i
$298$	20.1571	−	8.97451i	1.16767	−	0.519879i
$299$	−2.90466	+	3.22596i	−0.167981	+	0.186562i
$300$	0.104528	−	0.994522i	0.00603495	−	0.0574187i
$301$	0.442492	−	0.0940545i	0.0255048	−	0.00542121i
$302$	−2.20642	+	6.79066i	−0.126965	+	0.390759i
$303$	−10.5377	−	2.23985i	−0.605373	−	0.128676i
$304$	2.86751	−	4.96667i	0.164463	−	0.284858i
$305$	6.21180	+	10.7592i	0.355687	+	0.616067i
$306$	2.06404	+	6.35246i	0.117993	+	0.363146i
$307$	0.0737474	+	0.701659i	0.00420898	+	0.0400458i	0.996425	−	0.0844844i	$-0.0269243\pi$
$307$	0.0737474	+	0.701659i	0.00420898	+	0.0400458i	−0.992216	+	0.124530i	$0.960258\pi$
$308$	−0.180920	−	0.131446i	−0.0103089	−	0.00748982i
$309$	3.45456			0.196523
$310$	−0.568603	−	5.53865i	−0.0322945	−	0.314574i
$311$	10.5584			0.598713			0.299356	−	0.954141i	$-0.403228\pi$
$311$	10.5584			0.598713			0.299356	+	0.954141i	$0.403228\pi$
$312$	−3.38857	−	2.46194i	−0.191840	−	0.139380i
$313$	1.41622	+	13.4744i	0.0800493	+	0.761618i	0.958751	+	0.284247i	$0.0917436\pi$
$313$	1.41622	+	13.4744i	0.0800493	+	0.761618i	−0.878702	+	0.477371i	$0.841590\pi$
$314$	−5.11630	−	15.7464i	−0.288730	−	0.888619i
$315$	0.139060	+	0.240858i	0.00783513	+	0.0135708i
$316$	0.490496	−	0.849564i	0.0275925	−	0.0477917i
$317$	9.15248	+	1.94542i	0.514054	+	0.109266i	0.457633	−	0.889141i	$-0.348698\pi$
$317$	9.15248	+	1.94542i	0.514054	+	0.109266i	0.0564218	+	0.998407i	$0.482031\pi$
$318$	−3.49388	+	10.7531i	−0.195927	+	0.603002i
$319$	−1.19006	+	0.252954i	−0.0666304	+	0.0141627i
$320$	−0.104528	+	0.994522i	−0.00584332	+	0.0555955i
$321$	7.31439	−	8.12345i	0.408249	−	0.453407i
$322$	−0.263322	+	0.117239i	−0.0146744	+	0.00653345i
$323$	−34.9945	−	15.5806i	−1.94715	−	0.866926i
$324$	0.669131	+	0.743145i	0.0371739	+	0.0412858i
$325$	3.38857	−	2.46194i	0.187964	−	0.136564i
$326$	11.7325	−	8.52418i	0.649805	−	0.472111i
$327$	3.57891	+	3.97479i	0.197914	+	0.219806i
$328$	2.72481	+	1.21316i	0.150452	+	0.0669857i
$329$	2.84692	−	1.26753i	0.156956	−	0.0698812i
$330$	0.538031	−	0.597544i	0.0296177	−	0.0328937i
$331$	1.19447	−	11.3646i	0.0656541	−	0.624657i	−0.911379	−	0.411569i	$-0.864981\pi$
$331$	1.19447	−	11.3646i	0.0656541	−	0.624657i	0.977033	−	0.213089i	$-0.0683523\pi$
$332$	−3.76442	+	0.800151i	−0.206599	+	0.0439140i
$333$	2.98075	−	9.17381i	0.163344	−	0.502722i
$334$	−10.7021	−	2.27480i	−0.585591	−	0.124471i
$335$	5.33122	−	9.23395i	0.291276	−	0.504505i
$336$	−0.139060	−	0.240858i	−0.00758633	−	0.0131399i
$337$	0.677764	+	2.08594i	0.0369202	+	0.113629i	0.967818	−	0.251651i	$-0.0809734\pi$
$337$	0.677764	+	2.08594i	0.0369202	+	0.113629i	−0.930898	+	0.365279i	$0.880973\pi$
$338$	−0.474931	−	4.51867i	−0.0258329	−	0.245783i
$339$	4.84722	+	3.52171i	0.263265	+	0.191273i
$340$	6.67937			0.362240
$341$	2.24782	−	3.87169i	0.121726	−	0.209664i
$342$	−5.73501			−0.310114
$343$	−3.13264	−	2.27600i	−0.169147	−	0.122892i
$344$	−0.170022	−	1.61765i	−0.00916695	−	0.0872177i
$345$	−0.320264	−	0.985672i	−0.0172425	−	0.0530668i
$346$	−11.0999	−	19.2255i	−0.596732	−	1.03357i
$347$	−9.96009	+	17.2514i	−0.534686	+	0.926103i	0.464493	+	0.885577i	$0.346237\pi$
$347$	−9.96009	+	17.2514i	−0.534686	+	0.926103i	−0.999178	+	0.0405260i	$0.987097\pi$
$348$	−1.48003	−	0.314590i	−0.0793380	−	0.0168638i
$349$	−9.90451	+	30.4829i	−0.530176	+	1.63171i	0.223671	+	0.974665i	$0.428196\pi$
$349$	−9.90451	+	30.4829i	−0.530176	+	1.63171i	−0.753847	+	0.657050i	$0.771804\pi$
$350$	0.272042	−	0.0578243i	0.0145412	−	0.00309084i
$351$	−0.437818	+	4.16556i	−0.0233690	+	0.222341i
$352$	−0.538031	+	0.597544i	−0.0286772	+	0.0318492i
$353$	−12.0418	+	5.36134i	−0.640918	+	0.285355i	−0.701350	−	0.712817i	$-0.747419\pi$
$353$	−12.0418	+	5.36134i	−0.640918	+	0.285355i	0.0604318	+	0.998172i	$0.480752\pi$
$354$	4.40900	+	1.96301i	0.234335	+	0.104333i
$355$	7.47850	+	8.30572i	0.396918	+	0.440822i
$356$	7.17978	−	5.21642i	0.380528	−	0.276470i
$357$	−1.50288	+	1.09191i	−0.0795408	+	0.0577898i
$358$	−2.54032	−	2.82131i	−0.134260	−	0.149111i
$359$	21.0101	+	9.35429i	1.10887	+	0.493700i	0.877699	−	0.479213i	$-0.159078\pi$
$359$	21.0101	+	9.35429i	1.10887	+	0.493700i	0.231170	+	0.972913i	$0.425744\pi$
$360$	0.913545	−	0.406737i	0.0481481	−	0.0214369i
$361$	9.29447	−	10.3226i	0.489183	−	0.543293i
$362$	−1.93538	+	18.4139i	−0.101721	+	0.967812i
$363$	−10.1272	+	2.15261i	−0.531541	+	0.112983i
$364$	0.359975	−	1.10789i	0.0188678	−	0.0580692i
$365$	3.00746	+	0.639256i	0.157418	+	0.0334602i
$366$	−6.21180	+	10.7592i	−0.324696	+	0.562390i
$367$	10.0421	+	17.3934i	0.524192	+	0.907926i	0.999603	+	0.0281630i	$0.00896574\pi$
$367$	10.0421	+	17.3934i	0.524192	+	0.907926i	−0.475412	+	0.879763i	$0.657701\pi$
$368$	0.320264	+	0.985672i	0.0166949	+	0.0513817i
$369$	−0.311774	−	2.96633i	−0.0162303	−	0.154421i
$370$	−7.80371	−	5.66973i	−0.405696	−	0.294755i
$371$	−3.14454			−0.163257
$372$	4.51231	−	3.26175i	0.233953	−	0.169114i
$373$	−11.8891			−0.615596			−0.307798	−	0.951452i	$-0.599592\pi$
$373$	−11.8891			−0.615596			−0.307798	+	0.951452i	$0.599592\pi$
$374$	4.34500	+	3.15683i	0.224675	+	0.163236i
$375$	0.104528	+	0.994522i	0.00539783	+	0.0513569i
$376$	−3.46255	−	10.6566i	−0.178567	−	0.549574i
$377$	−3.16880	−	5.48853i	−0.163202	−	0.282674i
$378$	−0.139060	+	0.240858i	−0.00715246	+	0.0123884i
$379$	13.6072	+	2.89230i	0.698954	+	0.148567i	0.543666	−	0.839302i	$-0.317036\pi$
$379$	13.6072	+	2.89230i	0.698954	+	0.148567i	0.155289	+	0.987869i	$0.450369\pi$
$380$	−1.77222	+	5.45432i	−0.0909128	+	0.279801i
$381$	17.9266	−	3.81042i	0.918408	−	0.195214i
$382$	−2.69553	+	25.6462i	−0.137915	+	1.31217i
$383$	−1.70476	+	1.89332i	−0.0871089	+	0.0967443i	−0.785123	−	0.619339i	$-0.787400\pi$
$383$	−1.70476	+	1.89332i	−0.0871089	+	0.0967443i	0.698014	+	0.716084i	$0.254067\pi$
$384$	−0.913545	+	0.406737i	−0.0466192	+	0.0207562i
$385$	0.204295	+	0.0909581i	0.0104118	+	0.00463565i
$386$	5.44334	+	6.04545i	0.277059	+	0.307705i
$387$	−1.31591	+	0.956067i	−0.0668916	+	0.0485996i
$388$	−9.69973	+	7.04726i	−0.492429	+	0.357771i
$389$	−9.06504	−	10.0677i	−0.459616	−	0.510455i	0.468134	−	0.883657i	$-0.344926\pi$
$389$	−9.06504	−	10.0677i	−0.459616	−	0.510455i	−0.927750	+	0.373202i	$0.878260\pi$
$390$	3.82639	+	1.70362i	0.193757	+	0.0862660i
$391$	6.32400	−	2.81563i	0.319818	−	0.142392i
$392$	−4.63216	+	5.14453i	−0.233959	+	0.259838i
$393$	−1.31038	+	12.4674i	−0.0660999	+	0.628899i
$394$	−7.07992	+	1.50488i	−0.356681	+	0.0758150i
$395$	−0.303143	+	0.932978i	−0.0152528	+	0.0469432i
$396$	0.786504	+	0.167177i	0.0395233	+	0.00840094i
$397$	−16.0317	+	27.7678i	−0.804610	+	1.39363i	0.111944	+	0.993715i	$0.464292\pi$
$397$	−16.0317	+	27.7678i	−0.804610	+	1.39363i	−0.916554	+	0.399911i	$0.869041\pi$
$398$	1.66792	+	2.88892i	0.0836052	+	0.144808i
$399$	−0.492888	−	1.51695i	−0.0246753	−	0.0759426i
$400$	−0.104528	−	0.994522i	−0.00522642	−	0.0497261i
$401$	5.32271	+	3.86718i	0.265803	+	0.193118i	0.712702	−	0.701467i	$-0.247471\pi$
$401$	5.32271	+	3.86718i	0.265803	+	0.193118i	−0.446898	+	0.894585i	$0.647471\pi$
$402$	10.6624			0.531794
$403$	22.7992	+	4.90375i	1.13571	+	0.244273i
$404$	−10.7731			−0.535981
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	−0.0439878	−	0.418516i	−0.00218308	−	0.0207706i
$407$	−2.39675	−	7.37644i	−0.118802	−	0.365636i
$408$	3.33968	+	5.78450i	0.165339	+	0.286376i
$409$	−10.4776	+	18.1477i	−0.518083	+	0.897346i	0.481696	+	0.876338i	$0.340021\pi$
$409$	−10.4776	+	18.1477i	−0.518083	+	0.897346i	−0.999779	+	0.0210079i	$0.993312\pi$
$410$	−2.91749	−	0.620133i	−0.144085	−	0.0306262i
$411$	−3.49482	+	10.7559i	−0.172387	+	0.530551i
$412$	3.37907	−	0.718243i	0.166475	−	0.0353853i
$413$	−0.140306	+	1.33492i	−0.00690399	+	0.0656871i
$414$	0.693485	−	0.770193i	0.0340829	−	0.0378529i
$415$	3.51579	−	1.56533i	0.172584	−	0.0768391i
$416$	−3.82639	−	1.70362i	−0.187604	−	0.0835267i
$417$	−0.559388	−	0.621263i	−0.0273933	−	0.0304234i
$418$	−3.73069	+	2.71050i	−0.182474	+	0.132575i
$419$	−10.9167	+	7.93142i	−0.533314	+	0.387475i	−0.821596	−	0.570070i	$-0.806916\pi$
$419$	−10.9167	+	7.93142i	−0.533314	+	0.387475i	0.288282	+	0.957546i	$0.406916\pi$
$420$	0.186098	+	0.206683i	0.00908066	+	0.0100851i
$421$	18.7023	+	8.32681i	0.911496	+	0.405824i	0.808255	−	0.588832i	$-0.200412\pi$
$421$	18.7023	+	8.32681i	0.911496	+	0.405824i	0.103241	+	0.994656i	$0.467079\pi$
$422$	−16.3132	+	7.26308i	−0.794112	+	0.353561i
$423$	−7.49764	+	8.32698i	−0.364548	+	0.404872i
$424$	−1.18185	+	11.2445i	−0.0573955	+	0.546082i
$425$	−6.53341	+	1.38872i	−0.316917	+	0.0673627i
$426$	−3.45371	+	10.6294i	−0.167333	+	0.514998i
$427$	−3.37974	−	0.718386i	−0.163557	−	0.0347651i
$428$	5.46559	−	9.46668i	0.264189	−	0.457589i
$429$	1.68394	+	2.91666i	0.0813012	+	0.140818i
$430$	0.502634	+	1.54695i	0.0242392	+	0.0746005i
$431$	1.87454	+	17.8350i	0.0902933	+	0.859084i	0.942124	+	0.335266i	$0.108826\pi$
$431$	1.87454	+	17.8350i	0.0902933	+	0.859084i	−0.851830	+	0.523818i	$0.824507\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−8.96148			−0.430661			−0.215331	−	0.976541i	$-0.569083\pi$
$433$	−8.96148			−0.430661			−0.215331	+	0.976541i	$0.569083\pi$
$434$	1.25056	+	0.913213i	0.0600289	+	0.0438356i
$435$	1.51310			0.0725474
$436$	4.32711	+	3.14383i	0.207231	+	0.150562i
$437$	0.621291	+	5.91119i	0.0297204	+	0.282771i
$438$	0.950119	+	2.92417i	0.0453984	+	0.139722i
$439$	1.97896	+	3.42765i	0.0944504	+	0.163593i	0.909379	−	0.415968i	$-0.136557\pi$
$439$	1.97896	+	3.42765i	0.0944504	+	0.163593i	−0.814929	+	0.579561i	$0.803224\pi$
$440$	0.402038	−	0.696350i	0.0191664	−	0.0331972i
$441$	6.77137	+	1.43930i	0.322446	+	0.0685381i
$442$	−8.64523	+	26.6073i	−0.411212	+	1.26558i
$443$	18.2943	−	3.88857i	0.869188	−	0.184752i	0.248331	−	0.968675i	$-0.420118\pi$
$443$	18.2943	−	3.88857i	0.869188	−	0.184752i	0.620857	+	0.783924i	$0.286785\pi$
$444$	1.00827	−	9.59307i	0.0478505	−	0.455267i
$445$	−5.93833	+	6.59519i	−0.281504	+	0.312642i
$446$	−18.7837	+	8.36305i	−0.889435	+	0.396002i
$447$	−20.1571	−	8.97451i	−0.953397	−	0.424480i
$448$	−0.186098	−	0.206683i	−0.00879231	−	0.00976485i
$449$	−12.6343	+	9.17934i	−0.596249	+	0.433200i	−0.844545	−	0.535484i	$-0.820129\pi$
$449$	−12.6343	+	9.17934i	−0.596249	+	0.433200i	0.248297	+	0.968684i	$0.420129\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	−1.60477	−	1.78228i	−0.0755658	−	0.0839243i
$452$	5.47351	+	2.43696i	0.257452	+	0.114625i
$453$	6.52283	−	2.90415i	0.306469	−	0.136449i
$454$	−12.0775	+	13.4134i	−0.566824	+	0.629522i
$455$	−0.121766	+	1.15852i	−0.00570846	+	0.0543124i
$456$	−5.60969	+	1.19238i	−0.262698	+	0.0558381i
$457$	−4.57669	+	14.0856i	−0.214088	+	0.658896i	0.785129	+	0.619333i	$0.212597\pi$
$457$	−4.57669	+	14.0856i	−0.214088	+	0.658896i	−0.999217	+	0.0395635i	$0.987403\pi$
$458$	−4.13387	−	0.878681i	−0.193163	−	0.0410581i
$459$	3.33968	−	5.78450i	0.155883	−	0.269997i
$460$	−0.518199	−	0.897546i	−0.0241611	−	0.0418483i
$461$	−0.777096	−	2.39166i	−0.0361930	−	0.111391i	0.931328	−	0.364182i	$-0.118651\pi$
$461$	−0.777096	−	2.39166i	−0.0361930	−	0.111391i	−0.967521	+	0.252791i	$0.918651\pi$
$462$	0.0233756	+	0.222404i	0.00108753	+	0.0103472i
$463$	19.1398	+	13.9059i	0.889503	+	0.646262i	0.935748	−	0.352668i	$-0.114726\pi$
$463$	19.1398	+	13.9059i	0.889503	+	0.646262i	−0.0462451	+	0.998930i	$0.514726\pi$
$464$	−1.51310			−0.0702437
$465$	−3.73555	+	4.12864i	−0.173232	+	0.191461i
$466$	−15.5087			−0.718427
$467$	−18.7495	−	13.6223i	−0.867624	−	0.630365i	0.0623247	−	0.998056i	$-0.480149\pi$
$467$	−18.7495	−	13.6223i	−0.867624	−	0.630365i	−0.929948	+	0.367691i	$0.880149\pi$
$468$	0.437818	+	4.16556i	0.0202381	+	0.192553i
$469$	0.916369	+	2.82029i	0.0423140	+	0.130229i
$470$	5.60253	+	9.70386i	0.258425	+	0.447606i
$471$	−8.27835	+	14.3385i	−0.381446	+	0.660684i
$472$	4.72078	+	1.00343i	0.217292	+	0.0461868i
$473$	−0.404156	+	1.24386i	−0.0185831	+	0.0571929i
$474$	−0.959555	+	0.203960i	−0.0440738	+	0.00936818i
$475$	0.599472	−	5.70360i	0.0275057	−	0.261699i
$476$	−1.24302	+	1.38051i	−0.0569737	+	0.0632757i
$477$	10.3290	−	4.59875i	0.472930	−	0.210562i
$478$	6.65431	+	2.96269i	0.304361	+	0.135510i
$479$	−9.83062	−	10.9180i	−0.449173	−	0.498857i	0.475449	−	0.879743i	$-0.342286\pi$
$479$	−9.83062	−	10.9180i	−0.449173	−	0.498857i	−0.924622	+	0.380886i	$0.875619\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	32.6859	−	23.7477i	1.49035	−	1.08280i
$482$	−19.7346	−	21.9175i	−0.898888	−	0.998316i
$483$	0.263322	+	0.117239i	0.0119816	+	0.00533454i
$484$	−9.45836	+	4.21113i	−0.429925	+	0.191415i
$485$	8.02256	−	8.90995i	0.364285	−	0.404580i
$486$	0.104528	−	0.994522i	0.00474151	−	0.0451124i
$487$	6.52224	−	1.38635i	0.295551	−	0.0628213i	−0.0577497	−	0.998331i	$-0.518393\pi$
$487$	6.52224	−	1.38635i	0.295551	−	0.0628213i	0.353301	+	0.935510i	$0.385059\pi$
$488$	−3.83910	+	11.8155i	−0.173788	+	0.534865i
$489$	−14.1853	−	3.01518i	−0.641481	−	0.136351i
$490$	3.46132	−	5.99519i	0.156367	−	0.270835i
$491$	7.34740	+	12.7261i	0.331583	+	0.574319i	0.982823	−	0.184553i	$-0.0590838\pi$
$491$	7.34740	+	12.7261i	0.331583	+	0.574319i	−0.651239	+	0.758873i	$0.725751\pi$
$492$	−0.921697	−	2.83669i	−0.0415533	−	0.127888i
$493$	1.05642	+	10.0512i	0.0475787	+	0.452681i
$494$	−19.4335	−	14.1193i	−0.874354	−	0.635256i
$495$	−0.804075			−0.0361405
$496$	3.73555	−	4.12864i	0.167731	−	0.185381i
$497$	−3.10839			−0.139430
$498$	3.11351	+	2.26210i	0.139520	+	0.101367i
$499$	−2.12920	−	20.2580i	−0.0953161	−	0.906872i	−0.932796	−	0.360404i	$-0.882639\pi$
$499$	−2.12920	−	20.2580i	−0.0953161	−	0.906872i	0.837480	−	0.546468i	$-0.184028\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	5.47058	+	9.47532i	0.244407	+	0.423326i
$502$	9.81038	−	16.9921i	0.437859	−	0.758393i
$503$	−22.7795	−	4.84193i	−1.01569	−	0.215891i	−0.330150	−	0.943929i	$-0.607099\pi$
$503$	−22.7795	−	4.84193i	−1.01569	−	0.215891i	−0.685537	+	0.728038i	$0.740433\pi$
$504$	−0.0859436	+	0.264507i	−0.00382823	+	0.0117821i
$505$	10.5377	−	2.23985i	0.468920	−	0.0996720i
$506$	0.0871079	−	0.828776i	0.00387242	−	0.0368436i
$507$	−3.04023	+	3.37652i	−0.135022	+	0.149957i
$508$	16.7426	−	7.45430i	0.742834	−	0.330731i
$509$	25.5199	+	11.3622i	1.13115	+	0.503620i	0.884990	−	0.465609i	$-0.154165\pi$
$509$	25.5199	+	11.3622i	1.13115	+	0.503620i	0.246159	+	0.969229i	$0.420831\pi$
$510$	−4.46937	−	4.96374i	−0.197907	−	0.219798i
$511$	−0.691807	+	0.502627i	−0.0306037	+	0.0222349i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	3.83747	+	4.26195i	0.169429	+	0.188169i
$514$	−20.8086	−	9.26458i	−0.917827	−	0.408643i
$515$	−3.15590	+	1.40510i	−0.139065	+	0.0619159i
$516$	−1.08838	+	1.20877i	−0.0479132	+	0.0532130i
$517$	−0.941771	+	8.96035i	−0.0414190	+	0.394076i
$518$	2.62409	−	0.557768i	0.115296	−	0.0245069i
$519$	−6.86009	+	21.1132i	−0.301125	+	0.926767i
$520$	4.09697	+	0.870839i	0.179664	+	0.0381888i
$521$	−3.76461	+	6.52050i	−0.164931	+	0.285668i	−0.936631	−	0.350318i	$-0.886073\pi$
$521$	−3.76461	+	6.52050i	−0.164931	+	0.285668i	0.771700	+	0.635987i	$0.219407\pi$
$522$	0.756548	+	1.31038i	0.0331132	+	0.0573537i
$523$	−5.93066	−	18.2527i	−0.259330	−	0.798135i	−0.992946	−	0.118571i	$-0.962169\pi$
$523$	−5.93066	−	18.2527i	−0.259330	−	0.798135i	0.733616	−	0.679565i	$-0.237831\pi$
$524$	1.31038	+	12.4674i	0.0572442	+	0.544642i
$525$	−0.225003	−	0.163474i	−0.00981995	−	0.00713461i
$526$	15.9903			0.697211
$527$	−30.0337	−	21.9319i	−1.30829	−	0.955368i
$528$	0.804075			0.0349929
$529$	17.7384	+	12.8877i	0.771235	+	0.560335i
$530$	−1.18185	−	11.2445i	−0.0513361	−	0.488430i
$531$	−1.49139	−	4.59003i	−0.0647209	−	0.199190i
$532$	−0.797509	−	1.38133i	−0.0345764	−	0.0598881i
$533$	6.24647	−	10.8192i	0.270565	−	0.468632i
$534$	−8.68077	−	1.84515i	−0.375654	−	0.0798476i
$535$	−3.37792	+	10.3962i	−0.146040	+	0.449466i
$536$	10.4294	−	2.21685i	0.450483	−	0.0957532i
$537$	−0.396837	+	3.77565i	−0.0171248	+	0.162931i
$538$	−9.52336	+	10.5768i	−0.410581	+	0.455997i
$539$	5.08510	−	2.26403i	0.219031	−	0.0975187i
$540$	−0.913545	−	0.406737i	−0.0393127	−	0.0175032i
$541$	−22.4442	−	24.9268i	−0.964949	−	1.07168i	−0.997389	−	0.0722112i	$-0.976994\pi$
$541$	−22.4442	−	24.9268i	−0.964949	−	1.07168i	0.0324399	−	0.999474i	$-0.489672\pi$
$542$	11.4434	−	8.31409i	0.491534	−	0.357121i
$543$	14.9792	−	10.8830i	0.642819	−	0.467035i
$544$	4.46937	+	4.96374i	0.191623	+	0.212818i
$545$	−4.88619	−	2.17547i	−0.209301	−	0.0931870i
$546$	−1.06419	+	0.473809i	−0.0455432	+	0.0202772i
$547$	−28.3151	+	31.4471i	−1.21067	+	1.34458i	−0.288649	+	0.957435i	$0.593206\pi$
$547$	−28.3151	+	31.4471i	−1.21067	+	1.34458i	−0.922018	+	0.387147i	$0.873461\pi$
$548$	−1.18216	+	11.2475i	−0.0504994	+	0.480470i
$549$	12.1521	−	2.58301i	0.518640	−	0.110240i
$550$	−0.248473	+	0.764721i	−0.0105949	+	0.0326078i
$551$	−8.48799	−	1.80418i	−0.361601	−	0.0768606i
$552$	0.518199	−	0.897546i	0.0220560	−	0.0382021i
$553$	−0.136416	−	0.236280i	−0.00580102	−	0.0100477i
$554$	−1.97170	−	6.06828i	−0.0837696	−	0.257816i
$555$	1.00827	+	9.59307i	0.0427988	+	0.407203i
$556$	−0.676332	−	0.491384i	−0.0286829	−	0.0208393i
$557$	14.6099			0.619041			0.309520	−	0.950893i	$-0.399832\pi$
$557$	14.6099			0.619041			0.309520	+	0.950893i	$0.399832\pi$
$558$	−5.44328	−	1.17076i	−0.230432	−	0.0495624i
$559$	−6.81284			−0.288152
$560$	0.225003	+	0.163474i	0.00950813	+	0.00690806i
$561$	−0.561393	−	5.34129i	−0.0237020	−	0.225510i
$562$	5.42087	+	16.6837i	0.228666	+	0.703761i
$563$	0.544872	+	0.943747i	0.0229636	+	0.0397742i	0.877279	−	0.479981i	$-0.159356\pi$
$563$	0.544872	+	0.943747i	0.0229636	+	0.0397742i	−0.854315	+	0.519755i	$0.826023\pi$
$564$	−5.60253	+	9.70386i	−0.235909	+	0.408606i
$565$	−5.86057	−	1.24570i	−0.246556	−	0.0524071i
$566$	−9.80848	+	30.1874i	−0.412281	+	1.26887i
$567$	0.272042	−	0.0578243i	0.0114247	−	0.00242839i
$568$	−1.16826	+	11.1152i	−0.0490190	+	0.466384i
$569$	−11.5858	+	12.8674i	−0.485704	+	0.539429i	−0.935325	−	0.353791i	$-0.884892\pi$
$569$	−11.5858	+	12.8674i	−0.485704	+	0.539429i	0.449621	+	0.893220i	$0.351559\pi$
$570$	5.23919	−	2.33264i	0.219446	−	0.0977035i
$571$	−32.3935	−	14.4225i	−1.35563	−	0.603564i	−0.405119	−	0.914264i	$-0.632770\pi$
$571$	−32.3935	−	14.4225i	−1.35563	−	0.603564i	−0.950508	+	0.310700i	$0.899436\pi$
$572$	2.25355	+	2.50282i	0.0942255	+	0.104648i
$573$	20.8625	−	15.1575i	0.871544	−	0.633214i
$574$	0.671111	−	0.487591i	0.0280117	−	0.0203517i
$575$	0.693485	+	0.770193i	0.0289203	+	0.0321193i
$576$	0.913545	+	0.406737i	0.0380644	+	0.0169474i
$577$	−10.3773	+	4.62027i	−0.432012	+	0.192344i	−0.611209	−	0.791469i	$-0.709317\pi$
$577$	−10.3773	+	4.62027i	−0.432012	+	0.192344i	0.179197	+	0.983813i	$0.442650\pi$
$578$	18.4773	−	20.5212i	0.768556	−	0.853568i
$579$	0.850334	−	8.09039i	0.0353387	−	0.336225i
$580$	1.48003	−	0.314590i	0.0614549	−	0.0130626i
$581$	−0.330755	+	1.01796i	−0.0137220	+	0.0422321i
$582$	11.7275	+	2.49276i	0.486121	+	0.103328i
$583$	4.54562	−	7.87324i	0.188260	−	0.326076i
$584$	1.53733	+	2.66273i	0.0636150	+	0.110184i
$585$	−1.29432	−	3.98350i	−0.0535135	−	0.164698i
$586$	0.410774	+	3.90825i	0.0169689	+	0.161448i
$587$	−6.72740	−	4.88775i	−0.277670	−	0.201739i	0.440231	−	0.897885i	$-0.354897\pi$
$587$	−6.72740	−	4.88775i	−0.277670	−	0.201739i	−0.717900	+	0.696146i	$0.754897\pi$
$588$	6.92265			0.285485
$589$	25.8782	−	18.7062i	1.06629	−	0.770775i
$590$	−4.82625			−0.198693
$591$	5.85574	+	4.25444i	0.240873	+	0.175004i
$592$	−1.00827	−	9.59307i	−0.0414398	−	0.394273i
$593$	7.19815	+	22.1536i	0.295592	+	0.909740i	0.983022	+	0.183489i	$0.0587391\pi$
$593$	7.19815	+	22.1536i	0.295592	+	0.909740i	−0.687429	+	0.726251i	$0.741261\pi$
$594$	−0.402038	−	0.696350i	−0.0164958	−	0.0285716i
$595$	0.928831	−	1.60878i	0.0380784	−	0.0659536i
$596$	−21.5825	−	4.58750i	−0.884054	−	0.187911i
$597$	1.03083	−	3.17257i	0.0421891	−	0.129845i
$598$	4.24609	−	0.902535i	0.173636	−	0.0369074i
$599$	0.609741	−	5.80130i	0.0249133	−	0.237035i	−0.974978	−	0.222301i	$-0.928643\pi$
$599$	0.609741	−	5.80130i	0.0249133	−	0.237035i	0.999891	−	0.0147338i	$-0.00469007\pi$
$600$	−0.669131	+	0.743145i	−0.0273171	+	0.0303388i
$601$	−21.3825	+	9.52011i	−0.872211	+	0.388333i	−0.793504	−	0.608565i	$-0.791746\pi$
$601$	−21.3825	+	9.52011i	−0.872211	+	0.388333i	−0.0787064	+	0.996898i	$0.525079\pi$
$602$	−0.413267	−	0.183998i	−0.0168435	−	0.00749921i
$603$	−7.13457	−	7.92374i	−0.290542	−	0.322680i
$604$	5.77648	−	4.19686i	0.235042	−	0.170768i
$605$	8.37613	−	6.08561i	0.340538	−	0.247415i
$606$	7.20860	+	8.00596i	0.292829	+	0.325220i
$607$	26.6525	+	11.8664i	1.08179	+	0.481644i	0.868675	−	0.495383i	$-0.164972\pi$
$607$	26.6525	+	11.8664i	1.08179	+	0.481644i	0.213115	+	0.977027i	$0.431639\pi$
$608$	−5.23919	+	2.33264i	−0.212477	+	0.0946010i
$609$	−0.281584	+	0.312731i	−0.0114104	+	0.0126725i
$610$	1.29862	−	12.3555i	0.0525796	−	0.500261i
$611$	−45.9068	+	9.75780i	−1.85719	+	0.394758i
$612$	2.06404	−	6.35246i	0.0834338	−	0.256783i
$613$	−41.2262	−	8.76290i	−1.66511	−	0.353930i	−0.723420	−	0.690408i	$-0.757431\pi$
$613$	−41.2262	−	8.76290i	−1.66511	−	0.353930i	−0.941691	+	0.336478i	$0.890764\pi$
$614$	0.352762	−	0.611002i	0.0142363	−	0.0246580i
$615$	1.49134	+	2.58307i	0.0601365	+	0.104159i
$616$	0.0691052	+	0.212684i	0.00278433	+	0.00856927i
$617$	−1.29144	−	12.2872i	−0.0519915	−	0.494666i	−0.989272	−	0.146089i	$-0.953332\pi$
$617$	−1.29144	−	12.2872i	−0.0519915	−	0.494666i	0.937280	−	0.348577i	$-0.113335\pi$
$618$	−2.79480	−	2.03054i	−0.112423	−	0.0816802i
$619$	32.8755			1.32138			0.660690	−	0.750659i	$-0.270264\pi$
$619$	32.8755			1.32138			0.660690	+	0.750659i	$0.270264\pi$
$620$	−2.79553	+	4.81508i	−0.112271	+	0.193378i
$621$	−1.03640			−0.0415892
$622$	−8.54194	−	6.20608i	−0.342500	−	0.248841i
$623$	−0.258000	−	2.45471i	−0.0103365	−	0.0983457i
$624$	1.29432	+	3.98350i	0.0518142	+	0.159468i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.77431	−	11.7335i	0.270756	−	0.468963i
$627$	4.51061	+	0.958760i	0.180137	+	0.0382892i
$628$	−5.11630	+	15.7464i	−0.204163	+	0.628348i
$629$	−63.0207	+	13.3955i	−2.51280	+	0.534112i
$630$	0.0290714	−	0.276596i	0.00115823	−	0.0110198i
$631$	8.44378	−	9.37777i	0.336142	−	0.373323i	−0.551249	−	0.834340i	$-0.685849\pi$
$631$	8.44378	−	9.37777i	0.336142	−	0.373323i	0.887391	+	0.461017i	$0.152515\pi$
$632$	−0.896180	+	0.399005i	−0.0356481	+	0.0158716i
$633$	16.3132	+	7.26308i	0.648390	+	0.288682i
$634$	−6.26102	−	6.95357i	−0.248657	−	0.276161i
$635$	−14.8269	+	10.7724i	−0.588389	+	0.427489i
$636$	9.14711	−	6.64576i	0.362706	−	0.263522i
$637$	19.4018	+	21.5479i	0.768727	+	0.853758i
$638$	1.11146	+	0.494853i	0.0440031	+	0.0195914i
$639$	10.2102	−	4.54587i	0.403909	−	0.179832i
$640$	0.669131	−	0.743145i	0.0264497	−	0.0293754i
$641$	2.59777	−	24.7161i	0.102606	−	0.976229i	−0.815195	−	0.579187i	$-0.803370\pi$
$641$	2.59777	−	24.7161i	0.102606	−	0.976229i	0.917801	−	0.397042i	$-0.129963\pi$
$642$	−10.6923	+	2.27272i	−0.421992	+	0.0896972i
$643$	−8.68857	+	26.7407i	−0.342644	+	1.05455i	0.620189	+	0.784452i	$0.287056\pi$
$643$	−8.68857	+	26.7407i	−0.342644	+	1.05455i	−0.962833	+	0.270097i	$0.912944\pi$
$644$	0.281943	+	0.0599289i	0.0111101	+	0.00236153i
$645$	0.813279	−	1.40864i	0.0320228	−	0.0554652i
$646$	19.1531	+	33.1742i	0.753570	+	1.30522i
$647$	−14.6225	−	45.0033i	−0.574868	−	1.76926i	−0.636627	−	0.771172i	$-0.719671\pi$
$647$	−14.6225	−	45.0033i	−0.574868	−	1.76926i	0.0617591	−	0.998091i	$-0.480329\pi$
$648$	−0.104528	−	0.994522i	−0.00410627	−	0.0390685i
$649$	−3.13952	−	2.28100i	−0.123237	−	0.0895370i
$650$	−4.18850			−0.164287
$651$	−0.158140	−	1.54041i	−0.00619798	−	0.0603733i
$652$	−14.5022			−0.567950
$653$	29.2554	+	21.2553i	1.14485	+	0.831785i	0.987788	−	0.155803i	$-0.0497965\pi$
$653$	29.2554	+	21.2553i	1.14485	+	0.831785i	0.157066	+	0.987588i	$0.449797\pi$
$654$	−0.559081	−	5.31930i	−0.0218618	−	0.208001i
$655$	−3.87387	−	11.9225i	−0.151365	−	0.465852i
$656$	−1.49134	−	2.58307i	−0.0582269	−	0.100852i
$657$	1.53733	−	2.66273i	0.0599768	−	0.103883i
$658$	−3.04824	−	0.647924i	−0.118833	−	0.0252587i
$659$	12.2827	−	37.8021i	0.478464	−	1.47256i	−0.362764	−	0.931881i	$-0.618167\pi$
$659$	12.2827	−	37.8021i	0.478464	−	1.47256i	0.841228	−	0.540680i	$-0.181833\pi$
$660$	−0.786504	+	0.167177i	−0.0306146	+	0.00650734i
$661$	1.10840	−	10.5457i	0.0431118	−	0.410182i	−0.951589	−	0.307372i	$-0.900550\pi$
$661$	1.10840	−	10.5457i	0.0431118	−	0.410182i	0.994701	−	0.102809i	$-0.0327831\pi$
$662$	−7.64632	+	8.49210i	−0.297183	+	0.330055i
$663$	25.5579	−	11.3791i	0.992585	−	0.441927i
$664$	3.51579	+	1.56533i	0.136439	+	0.0607467i
$665$	1.06728	+	1.18533i	0.0413872	+	0.0459651i
$666$	−7.80371	+	5.66973i	−0.302388	+	0.219697i
$667$	1.26867	−	0.921746i	0.0491233	−	0.0356901i
$668$	7.32106	+	8.13087i	0.283261	+	0.314593i
$669$	18.7837	+	8.36305i	0.726220	+	0.323334i
$670$	−9.74063	+	4.33681i	−0.376313	+	0.167545i
$671$	6.68429	−	7.42365i	0.258044	−	0.286587i
$672$	−0.0290714	+	0.276596i	−0.00112145	+	0.0106699i
$673$	−22.2829	+	4.73638i	−0.858944	+	0.182574i	−0.616271	−	0.787534i	$-0.711357\pi$
$673$	−22.2829	+	4.73638i	−0.858944	+	0.182574i	−0.242673	+	0.970108i	$0.578024\pi$
$674$	0.677764	−	2.08594i	0.0261065	−	0.0803475i
$675$	0.978148	+	0.207912i	0.0376489	+	0.00800252i
$676$	−2.27178	+	3.93484i	−0.0873761	+	0.151340i
$677$	−9.03618	−	15.6511i	−0.347289	−	0.601522i	0.638478	−	0.769640i	$-0.279564\pi$
$677$	−9.03618	−	15.6511i	−0.347289	−	0.601522i	−0.985767	+	0.168118i	$0.946231\pi$
$678$	−1.85147	−	5.69825i	−0.0711055	−	0.218840i
$679$	0.348552	+	3.31625i	0.0133762	+	0.127266i
$680$	−5.40372	−	3.92603i	−0.207223	−	0.150557i
$681$	18.0495			0.691658
$682$	−4.09424	+	1.81103i	−0.156777	+	0.0693479i
$683$	−22.1728			−0.848419			−0.424209	−	0.905564i	$-0.639448\pi$
$683$	−22.1728			−0.848419			−0.424209	+	0.905564i	$0.639448\pi$
$684$	4.63972	+	3.37096i	0.177404	+	0.128892i
$685$	−1.18216	−	11.2475i	−0.0451680	−	0.429745i
$686$	1.19656	+	3.68264i	0.0456850	+	0.140604i
$687$	2.11311	+	3.66002i	0.0806203	+	0.139638i
$688$	−0.813279	+	1.40864i	−0.0310060	+	0.0537039i
$689$	46.3222	+	9.84609i	1.76474	+	0.375106i
$690$	−0.320264	+	0.985672i	−0.0121923	+	0.0375239i
$691$	33.9123	−	7.20828i	1.29008	−	0.274216i	0.488746	−	0.872426i	$-0.337455\pi$
$691$	33.9123	−	7.20828i	1.29008	−	0.274216i	0.801339	+	0.598210i	$0.204121\pi$
$692$	−2.32050	+	22.0781i	−0.0882123	+	0.839284i
$693$	0.149637	−	0.166189i	0.00568424	−	0.00631299i
$694$	18.1980	−	8.10227i	0.690786	−	0.307558i
$695$	0.763717	+	0.340029i	0.0289694	+	0.0128980i
$696$	1.01246	+	1.12445i	0.0383771	+	0.0426221i
$697$	−16.1175	+	11.7101i	−0.610495	+	0.443551i
$698$	25.9303	−	18.8395i	0.981478	−	0.713086i
$699$	10.3774	+	11.5252i	0.392507	+	0.435924i
$700$	−0.254075	−	0.113121i	−0.00960312	−	0.00427559i
$701$	38.7712	−	17.2620i	1.46437	−	0.651978i	0.488943	−	0.872316i	$-0.337383\pi$
$701$	38.7712	−	17.2620i	1.46437	−	0.651978i	0.975424	+	0.220338i	$0.0707160\pi$
$702$	2.80266	−	3.11266i	0.105779	−	0.117480i
$703$	5.78246	−	55.0164i	0.218090	−	2.07498i
$704$	0.786504	−	0.167177i	0.0296425	−	0.00630071i
$705$	3.46255	−	10.6566i	0.130407	−	0.401352i
$706$	12.8933	+	2.74056i	0.485246	+	0.103142i
$707$	−1.49810	+	2.59479i	−0.0563419	+	0.0975871i
$708$	−2.41312	−	4.17965i	−0.0906907	−	0.157081i
$709$	−3.58548	−	11.0350i	−0.134655	−	0.414427i	0.860881	−	0.508807i	$-0.169913\pi$
$709$	−3.58548	−	11.0350i	−0.134655	−	0.414427i	−0.995536	+	0.0943799i	$0.969913\pi$
$710$	−1.16826	−	11.1152i	−0.0438439	−	0.417147i
$711$	0.793639	+	0.576612i	0.0297638	+	0.0216247i
$712$	−8.87470			−0.332593
$713$	−0.617043	+	5.73733i	−0.0231084	+	0.214865i
$714$	1.85766			0.0695212
$715$	−2.72467	−	1.97959i	−0.101897	−	0.0740323i
$716$	0.396837	+	3.77565i	0.0148305	+	0.141103i
$717$	−2.25089	−	6.92754i	−0.0840612	−	0.258714i
$718$	−11.4992	−	19.9172i	−0.429146	−	0.743303i
$719$	−9.37764	+	16.2425i	−0.349727	+	0.605745i	−0.986201	−	0.165553i	$-0.947059\pi$
$719$	−9.37764	+	16.2425i	−0.349727	+	0.605745i	0.636474	+	0.771298i	$0.280392\pi$
$720$	−0.978148	−	0.207912i	−0.0364534	−	0.00774841i
$721$	0.296897	−	0.913756i	0.0110570	−	0.0340301i
$722$	−13.5868	+	2.88797i	−0.505650	+	0.107479i
$723$	−3.08285	+	29.3314i	−0.114653	+	1.09085i
$724$	12.3892	−	13.7596i	0.460439	−	0.511370i
$725$	−1.38228	+	0.615431i	−0.0513366	+	0.0228565i
$726$	9.45836	+	4.21113i	0.351033	+	0.156290i
$727$	−22.4738	−	24.9597i	−0.833507	−	0.925703i	0.164652	−	0.986352i	$-0.447350\pi$
$727$	−22.4738	−	24.9597i	−0.833507	−	0.925703i	−0.998159	+	0.0606486i	$0.980683\pi$
$728$	−0.942427	+	0.684713i	−0.0349287	+	0.0253772i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−2.05734	−	2.28491i	−0.0761457	−	0.0845683i
$731$	9.92510	+	4.41894i	0.367093	+	0.163440i
$732$	11.3495	−	5.05313i	0.419490	−	0.186769i
$733$	−8.94750	+	9.93720i	−0.330483	+	0.367039i	−0.885370	−	0.464887i	$-0.846095\pi$
$733$	−8.94750	+	9.93720i	−0.330483	+	0.367039i	0.554887	+	0.831926i	$0.312762\pi$
$734$	2.09936	−	19.9741i	0.0774889	−	0.737258i
$735$	−6.77137	+	1.43930i	−0.249766	+	0.0530894i
$736$	0.320264	−	0.985672i	0.0118051	−	0.0363324i
$737$	−8.38606	−	1.78251i	−0.308905	−	0.0656597i
$738$	−1.49134	+	2.58307i	−0.0548969	+	0.0950842i
$739$	9.66761	+	16.7448i	0.355629	+	0.615967i	0.987225	−	0.159330i	$-0.0509335\pi$
$739$	9.66761	+	16.7448i	0.355629	+	0.615967i	−0.631597	+	0.775297i	$0.717600\pi$
$740$	2.98075	+	9.17381i	0.109575	+	0.337236i
$741$	2.51089	+	23.8895i	0.0922399	+	0.877604i
$742$	2.54399	+	1.84832i	0.0933928	+	0.0678538i
$743$	−26.5333			−0.973412			−0.486706	−	0.873566i	$-0.661802\pi$
$743$	−26.5333			−0.973412			−0.486706	+	0.873566i	$0.661802\pi$
$744$	−5.56775	−	0.0134584i	−0.204124	−	0.000493410i
$745$	22.0647			0.808387
$746$	9.61852	+	6.98826i	0.352159	+	0.255858i
$747$	−0.402279	−	3.82743i	−0.0147186	−	0.140038i
$748$	−1.65964	−	5.10785i	−0.0606825	−	0.186762i
$749$	−1.52009	−	2.63287i	−0.0555428	−	0.0962029i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−24.3842	−	5.18303i	−0.889794	−	0.189132i	−0.259736	−	0.965680i	$-0.583636\pi$
$751$	−24.3842	−	5.18303i	−0.889794	−	0.189132i	−0.630058	+	0.776548i	$0.716969\pi$
$752$	−3.46255	+	10.6566i	−0.126266	+	0.388608i
$753$	−19.1920	+	4.07938i	−0.699395	+	0.148661i
$754$	−0.662460	+	6.30289i	−0.0241254	+	0.229538i
$755$	−4.77768	+	5.30615i	−0.173877	+	0.193110i
$756$	0.254075	−	0.113121i	0.00924061	−	0.00411418i
$757$	−32.8472	−	14.6245i	−1.19385	−	0.531536i	−0.289026	−	0.957321i	$-0.593331\pi$
$757$	−32.8472	−	14.6245i	−1.19385	−	0.531536i	−0.904824	+	0.425785i	$0.859998\pi$
$758$	−9.30840	−	10.3380i	−0.338096	−	0.375494i
$759$	−0.674187	+	0.489826i	−0.0244714	+	0.0177795i
$760$	4.63972	−	3.37096i	0.168300	−	0.122277i
$761$	−8.05781	−	8.94911i	−0.292096	−	0.324405i	0.579179	−	0.815200i	$-0.303373\pi$
$761$	−8.05781	−	8.94911i	−0.292096	−	0.324405i	−0.871275	+	0.490795i	$0.836706\pi$
$762$	−16.7426	−	7.45430i	−0.606522	−	0.270041i
$763$	1.35894	−	0.605041i	0.0491971	−	0.0219040i
$764$	17.2552	−	19.1638i	0.624271	−	0.693323i
$765$	−0.698184	+	6.64278i	−0.0252429	+	0.240170i
$766$	2.49204	−	0.529700i	0.0900412	−	0.0191388i
$767$	6.24670	−	19.2254i	0.225555	−	0.694188i
$768$	0.978148	+	0.207912i	0.0352959	+	0.00750237i
$769$	−0.729643	+	1.26378i	−0.0263116	+	0.0455730i	−0.878881	−	0.477040i	$-0.841710\pi$
$769$	−0.729643	+	1.26378i	−0.0263116	+	0.0455730i	0.852570	+	0.522613i	$0.175043\pi$
$770$	−0.111814	−	0.193668i	−0.00402951	−	0.00697932i
$771$	7.03874	+	21.6630i	0.253494	+	0.780174i
$772$	−0.850334	−	8.09039i	−0.0306042	−	0.291179i
$773$	−21.5879	−	15.6845i	−0.776462	−	0.564133i	0.127453	−	0.991845i	$-0.459320\pi$
$773$	−21.5879	−	15.6845i	−0.776462	−	0.564133i	−0.903915	+	0.427712i	$0.859320\pi$
$774$	1.62656			0.0584654
$775$	1.73333	−	5.29108i	0.0622630	−	0.190061i
$776$	11.9895			0.430399
$777$	−2.17036	−	1.57686i	−0.0778614	−	0.0565696i
$778$	1.41610	+	13.4733i	0.0507696	+	0.483040i
$779$	−5.28594	−	16.2685i	−0.189389	−	0.582878i
$780$	−2.09425	−	3.62735i	−0.0749862	−	0.129880i
$781$	4.49335	−	7.78272i	0.160785	−	0.278487i
$782$	−6.77120	−	1.43926i	−0.242138	−	0.0514680i
$783$	0.467572	−	1.43904i	0.0167097	−	0.0514271i
$784$	6.77137	−	1.43930i	0.241835	−	0.0514036i
$785$	1.73065	−	16.4660i	0.0617694	−	0.587697i
$786$	8.38829	−	9.31614i	0.299200	−	0.332296i
$787$	−3.77187	+	1.67935i	−0.134453	+	0.0598622i	−0.472860	−	0.881137i	$-0.656778\pi$
$787$	−3.77187	+	1.67935i	−0.134453	+	0.0598622i	0.338407	+	0.941000i	$0.390112\pi$
$788$	6.61233	+	2.94400i	0.235554	+	0.104876i
$789$	−10.6996	−	11.8831i	−0.380916	−	0.423051i
$790$	0.793639	−	0.576612i	0.0282364	−	0.0205149i
$791$	1.34811	−	0.979457i	0.0479332	−	0.0348255i
$792$	−0.538031	−	0.597544i	−0.0191181	−	0.0212328i
$793$	47.5375	+	21.1651i	1.68811	+	0.751594i
$794$	29.2915	−	13.0414i	1.03951	−	0.462822i
$795$	−7.56549	+	8.40233i	−0.268320	+	0.298000i
$796$	0.348690	−	3.31756i	0.0123590	−	0.117588i
$797$	−0.284652	+	0.0605047i	−0.0100829	+	0.00214319i	−0.212950	−	0.977063i	$-0.568307\pi$
$797$	−0.284652	+	0.0605047i	−0.0100829	+	0.00214319i	0.202867	+	0.979206i	$0.434974\pi$
$798$	−0.492888	+	1.51695i	−0.0174480	+	0.0536995i
$799$	73.2072	+	15.5607i	2.58988	+	0.550497i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	4.43735	+	7.68572i	0.156786	+	0.271561i
$802$	−2.03309	−	6.25722i	−0.0717911	−	0.220950i
$803$	−0.258421	−	2.45871i	−0.00911946	−	0.0867659i
$804$	−8.62610	−	6.26723i	−0.304219	−	0.221028i
$805$	−0.288242			−0.0101592
$806$	−15.5626	−	17.3683i	−0.548169	−	0.611771i
$807$	14.2324			0.501006
$808$	8.71561	+	6.33226i	0.306614	+	0.222768i
$809$	0.487543	+	4.63866i	0.0171411	+	0.163087i	0.999744	−	0.0226331i	$-0.00720496\pi$
$809$	0.487543	+	4.63866i	0.0171411	+	0.163087i	−0.982603	+	0.185720i	$0.940538\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	20.1001	+	34.8144i	0.705810	+	1.22250i	0.966398	+	0.257049i	$0.0827501\pi$
$811$	20.1001	+	34.8144i	0.705810	+	1.22250i	−0.260589	+	0.965450i	$0.583917\pi$
$812$	−0.210411	+	0.364442i	−0.00738396	+	0.0127894i
$813$	−13.8357	−	2.94086i	−0.485238	−	0.103141i
$814$	−2.39675	+	7.37644i	−0.0840060	+	0.258544i
$815$	14.1853	−	3.01518i	0.496889	−	0.105617i
$816$	0.698184	−	6.64278i	0.0244413	−	0.232544i
$817$	−6.24187	+	6.93230i	−0.218375	+	0.242530i
$818$	19.1435	−	8.52323i	0.669337	−	0.298008i
$819$	1.06419	+	0.473809i	0.0371859	+	0.0165562i
$820$	1.99580	+	2.21656i	0.0696963	+	0.0774056i
$821$	−26.2775	+	19.0917i	−0.917092	+	0.666306i	−0.942798	−	0.333363i	$-0.891816\pi$
$821$	−26.2775	+	19.0917i	−0.917092	+	0.666306i	0.0257068	+	0.999670i	$0.491816\pi$
$822$	9.14954	−	6.64753i	0.319127	−	0.231859i
$823$	−8.87064	−	9.85184i	−0.309211	−	0.343414i	0.568430	−	0.822731i	$-0.307551\pi$
$823$	−8.87064	−	9.85184i	−0.309211	−	0.343414i	−0.877641	+	0.479318i	$0.840884\pi$
$824$	−3.15590	−	1.40510i	−0.109941	−	0.0489488i
$825$	0.734559	−	0.327047i	0.0255741	−	0.0113863i
$826$	0.898156	−	0.997503i	0.0312508	−	0.0347076i
$827$	−2.49595	+	23.7474i	−0.0867928	+	0.825778i	0.861367	+	0.507984i	$0.169609\pi$
$827$	−2.49595	+	23.7474i	−0.0867928	+	0.825778i	−0.948160	+	0.317795i	$0.897058\pi$
$828$	−1.01375	+	0.215479i	−0.0352302	+	0.00748842i
$829$	−2.02757	+	6.24021i	−0.0704204	+	0.216732i	−0.980073	−	0.198639i	$-0.936348\pi$
$829$	−2.02757	+	6.24021i	−0.0704204	+	0.216732i	0.909652	+	0.415370i	$0.136348\pi$
$830$	−3.76442	−	0.800151i	−0.130665	−	0.0277737i
$831$	−3.19028	+	5.52573i	−0.110670	+	0.191685i
$832$	2.09425	+	3.62735i	0.0726051	+	0.125756i
$833$	−14.2886	−	43.9758i	−0.495071	−	1.52367i
$834$	0.0873850	+	0.831412i	0.00302589	+	0.0287895i
$835$	−8.85158	−	6.43105i	−0.306322	−	0.222556i
$836$	4.61138			0.159488
$837$	2.77222	+	4.82854i	0.0958219	+	0.166899i
$838$	13.4937			0.466134
$839$	11.1396	+	8.09339i	0.384582	+	0.279415i	0.763232	−	0.646125i	$-0.223612\pi$
$839$	11.1396	+	8.09339i	0.384582	+	0.279415i	−0.378650	+	0.925540i	$0.623612\pi$
$840$	−0.0290714	−	0.276596i	−0.00100306	−	0.00954346i
$841$	−8.25401	−	25.4032i	−0.284621	−	0.875974i
$842$	−10.2361	−	17.7295i	−0.352760	−	0.610998i
$843$	8.77115	−	15.1921i	0.302095	−	0.523243i
$844$	17.4667	+	3.71267i	0.601230	+	0.127795i
$845$	1.40404	−	4.32118i	0.0483003	−	0.148653i
$846$	10.9602	−	2.32966i	0.376819	−	0.0800954i
$847$	−0.300990	+	2.86372i	−0.0103421	+	0.0983988i
$848$	7.56549	−	8.40233i	0.259800	−	0.288537i
$849$	28.9968	−	12.9102i	0.995167	−	0.443077i
$850$	6.10191	+	2.71674i	0.209294	+	0.0931835i
$851$	6.68930	+	7.42922i	0.229306	+	0.254670i
$852$	9.04193	−	6.56935i	0.309772	−	0.225062i
$853$	25.0103	−	18.1711i	0.856337	−	0.622165i	−0.0705488	−	0.997508i	$-0.522475\pi$
$853$	25.0103	−	18.1711i	0.856337	−	0.622165i	0.926886	+	0.375343i	$0.122475\pi$
$854$	2.31201	+	2.56775i	0.0791154	+	0.0878665i
$855$	−5.23919	−	2.33264i	−0.179177	−	0.0797746i
$856$	−9.98613	+	4.44611i	−0.341319	+	0.151965i
$857$	6.34520	−	7.04706i	0.216748	−	0.240723i	−0.624959	−	0.780658i	$-0.714884\pi$
$857$	6.34520	−	7.04706i	0.216748	−	0.240723i	0.841707	+	0.539935i	$0.181551\pi$
$858$	0.352039	−	3.34942i	0.0120184	−	0.114347i
$859$	−54.0545	+	11.4896i	−1.84432	+	0.392022i	−0.991491	−	0.130175i	$-0.958446\pi$
$859$	−54.0545	+	11.4896i	−1.84432	+	0.392022i	−0.852825	+	0.522197i	$0.825113\pi$
$860$	0.502634	−	1.54695i	0.0171397	−	0.0527505i
$861$	−0.811412	−	0.172471i	−0.0276528	−	0.00587779i
$862$	8.96664	−	15.5307i	0.305405	−	0.528977i
$863$	21.1285	+	36.5956i	0.719222	+	1.24573i	0.961308	+	0.275474i	$0.0888349\pi$
$863$	21.1285	+	36.5956i	0.719222	+	1.24573i	−0.242086	+	0.970255i	$0.577832\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−2.32050	−	22.0781i	−0.0788995	−	0.750679i
$866$	7.24999	+	5.26742i	0.246365	+	0.178994i
$867$	−27.6140			−0.937819
$868$	−0.474953	−	1.47387i	−0.0161209	−	0.0500263i
$869$	0.788791			0.0267579
$870$	−1.22412	−	0.889375i	−0.0415015	−	0.0301526i
$871$	−4.66821	−	44.4150i	−0.158176	−	1.50495i
$872$	−1.65281	−	5.08682i	−0.0559712	−	0.172262i
$873$	−5.99476	−	10.3832i	−0.202892	−	0.351419i
$874$	2.97188	−	5.14744i	0.100525	−	0.174115i
$875$	0.272042	+	0.0578243i	0.00919669	+	0.00195482i
$876$	0.950119	−	2.92417i	0.0321015	−	0.0987984i
$877$	−56.0004	+	11.9032i	−1.89100	+	0.401944i	−0.998767	−	0.0496362i	$-0.984194\pi$
$877$	−56.0004	+	11.9032i	−1.89100	+	0.401944i	−0.892231	+	0.451580i	$0.850860\pi$
$878$	0.413714	−	3.93623i	0.0139622	−	0.132841i
$879$	2.62954	−	2.92039i	0.0886920	−	0.0985025i
$880$	−0.734559	+	0.327047i	−0.0247620	+	0.0110247i
$881$	7.90379	+	3.51899i	0.266285	+	0.118558i	0.535536	−	0.844512i	$-0.320109\pi$
$881$	7.90379	+	3.51899i	0.266285	+	0.118558i	−0.269251	+	0.963070i	$0.586776\pi$
$882$	−4.63216	−	5.14453i	−0.155973	−	0.173225i
$883$	−28.8007	+	20.9249i	−0.969221	+	0.704180i	−0.955274	−	0.295723i	$-0.904440\pi$
$883$	−28.8007	+	20.9249i	−0.969221	+	0.704180i	−0.0139468	+	0.999903i	$0.504440\pi$
$884$	22.6335	−	16.4442i	0.761247	−	0.553078i
$885$	3.22939	+	3.58660i	0.108555	+	0.120562i
$886$	−17.0860	−	7.60719i	−0.574017	−	0.255569i
$887$	36.9222	−	16.4388i	1.23973	−	0.551962i	0.321084	−	0.947051i	$-0.395953\pi$
$887$	36.9222	−	16.4388i	1.23973	−	0.551962i	0.918643	+	0.395088i	$0.129286\pi$
$888$	−6.45438	+	7.16831i	−0.216595	+	0.240553i
$889$	0.532794	−	5.06920i	0.0178693	−	0.170015i
$890$	8.68077	−	1.84515i	0.290980	−	0.0618497i
$891$	−0.248473	+	0.764721i	−0.00832416	+	0.0256191i
$892$	20.1120	+	4.27494i	0.673400	+	0.143136i
$893$	−32.1306	+	55.6518i	−1.07521	+	1.86232i
$894$	11.0323	+	19.1086i	0.368976	+	0.639086i
$895$	−1.17317	−	3.61064i	−0.0392146	−	0.120690i
$896$	0.0290714	+	0.276596i	0.000971207	+	0.00924042i
$897$	−3.51190	−	2.55155i	−0.117259	−	0.0851937i
$898$	15.6168			0.521141
$899$	−7.68791	−	3.44517i	−0.256406	−	0.114903i
$900$	1.00000			0.0333333
$901$	−61.0969	−	44.3895i	−2.03543	−	1.47883i
$902$	0.250690	+	2.38516i	0.00834706	+	0.0794170i
$903$	0.139792	+	0.430236i	0.00465199	+	0.0143174i
$904$	−2.99575	−	5.18879i	−0.0996371	−	0.172577i
$905$	−9.25765	+	16.0347i	−0.307735	+	0.533012i
$906$	−6.98410	−	1.48452i	−0.232031	−	0.0493197i
$907$	3.71108	−	11.4215i	0.123225	−	0.379246i	−0.870349	−	0.492436i	$-0.836107\pi$
$907$	3.71108	−	11.4215i	0.123225	−	0.379246i	0.993573	+	0.113189i	$0.0361067\pi$
$908$	17.6551	−	3.75270i	0.585904	−	0.124538i
$909$	1.12609	−	10.7141i	0.0373502	−	0.355363i
$910$	0.779473	−	0.865692i	0.0258393	−	0.0286974i
$911$	16.0460	−	7.14414i	0.531628	−	0.236696i	−0.123324	−	0.992366i	$-0.539355\pi$
$911$	16.0460	−	7.14414i	0.531628	−	0.236696i	0.654952	+	0.755670i	$0.272689\pi$
$912$	5.23919	+	2.33264i	0.173487	+	0.0772414i
$913$	−2.07062	−	2.29966i	−0.0685276	−	0.0761076i
$914$	11.9819	−	8.70537i	0.396327	−	0.287948i
$915$	−10.0509	+	7.30241i	−0.332273	+	0.241410i
$916$	2.82790	+	3.14070i	0.0934363	+	0.103772i
$917$	3.18511	+	1.41810i	0.105182	+	0.0468298i
$918$	−6.10191	+	2.71674i	−0.201393	+	0.0896659i
$919$	−5.88941	+	6.54085i	−0.194274	+	0.215763i	−0.832410	−	0.554161i	$-0.813039\pi$
$919$	−5.88941	+	6.54085i	−0.194274	+	0.215763i	0.638136	+	0.769924i	$0.279706\pi$
$920$	−0.108333	+	1.03072i	−0.00357163	+	0.0339818i
$921$	−0.690107	+	0.146687i	−0.0227398	+	0.00483349i
$922$	−0.777096	+	2.39166i	−0.0255923	+	0.0787650i
$923$	45.7896	+	9.73288i	1.50718	+	0.320362i
$924$	0.111814	−	0.193668i	0.00367843	−	0.00637122i
$925$	−4.82296	−	8.35361i	−0.158578	−	0.274665i
$926$	−7.31077	−	22.5002i	−0.240247	−	0.739403i
$927$	0.361100	+	3.43563i	0.0118601	+	0.112841i
$928$	1.22412	+	0.889375i	0.0401837	+	0.0291952i
$929$	19.4637			0.638585			0.319292	−	0.947656i	$-0.396555\pi$
$929$	19.4637			0.638585			0.319292	+	0.947656i	$0.396555\pi$
$930$	5.44888	−	1.14444i	0.178676	−	0.0375275i
$931$	39.7015			1.30116
$932$	12.5468	+	9.11579i	0.410984	+	0.298598i
$933$	1.10365	+	10.5006i	0.0361320	+	0.343773i
$934$	7.16167	+	22.0414i	0.234337	+	0.721215i
$935$	2.68536	+	4.65118i	0.0878206	+	0.152110i
$936$	2.09425	−	3.62735i	0.0684528	−	0.118564i
$937$	−32.0411	−	6.81055i	−1.04674	−	0.222491i	−0.347722	−	0.937598i	$-0.613045\pi$
$937$	−32.0411	−	6.81055i	−1.04674	−	0.222491i	−0.699015	+	0.715107i	$0.746378\pi$
$938$	0.916369	−	2.82029i	0.0299205	−	0.0920859i
$939$	−13.2526	+	2.81692i	−0.432481	+	0.0919266i
$940$	1.17125	−	11.1437i	0.0382019	−	0.363466i
$941$	−34.8916	+	38.7511i	−1.13743	+	1.26325i	−0.177162	+	0.984182i	$0.556692\pi$
$941$	−34.8916	+	38.7511i	−1.13743	+	1.26325i	−0.960272	+	0.279067i	$0.909975\pi$
$942$	15.1253	−	6.73422i	0.492809	−	0.219413i
$943$	2.82398	+	1.25732i	0.0919615	+	0.0409439i
$944$	−3.22939	−	3.58660i	−0.105108	−	0.116734i
$945$	−0.225003	+	0.163474i	−0.00731936	+	0.00531783i
$946$	1.05809	−	0.768750i	0.0344016	−	0.0249942i
$947$	17.6406	+	19.5919i	0.573242	+	0.636650i	0.958137	−	0.286311i	$-0.0924290\pi$
$947$	17.6406	+	19.5919i	0.573242	+	0.636650i	−0.384895	+	0.922960i	$0.625762\pi$
$948$	0.896180	+	0.399005i	0.0291066	+	0.0129591i
$949$	11.7648	−	5.23803i	0.381902	−	0.170034i
$950$	−3.83747	+	4.26195i	−0.124504	+	0.138276i
$951$	−0.978067	+	9.30569i	−0.0317160	+	0.301758i
$952$	1.81707	−	0.386230i	0.0588915	−	0.0125178i
$953$	−1.63289	+	5.02552i	−0.0528945	+	0.162793i	−0.974014	−	0.226487i	$-0.927276\pi$
$953$	−1.63289	+	5.02552i	−0.0528945	+	0.162793i	0.921120	+	0.389279i	$0.127276\pi$
$954$	−11.0594	−	2.35074i	−0.358060	−	0.0761081i
$955$	−12.8937	+	22.3326i	−0.417232	+	0.722667i
$956$	−3.64202	−	6.30817i	−0.117791	−	0.204021i
$957$	−0.375963	−	1.15710i	−0.0121532	−	0.0374036i
$958$	1.53569	+	14.6112i	0.0496160	+	0.472065i
$959$	2.54467	+	1.84881i	0.0821716	+	0.0597011i
$960$	−1.00000			−0.0322749
$961$	28.3805	−	12.4718i	0.915501	−	0.402315i
$962$	−40.4020			−1.30261
$963$	8.84351	+	6.42519i	0.284978	+	0.207049i
$964$	3.08285	+	29.3314i	0.0992920	+	0.944700i
$965$	2.51384	+	7.73680i	0.0809233	+	0.249056i
$966$	−0.144121	−	0.249625i	−0.00463702	−	0.00803155i
$967$	−12.2800	+	21.2695i	−0.394897	+	0.683982i	−0.993088	−	0.117372i	$-0.962553\pi$
$967$	−12.2800	+	21.2695i	−0.394897	+	0.683982i	0.598191	+	0.801354i	$0.295886\pi$
$968$	10.1272	+	2.15261i	0.325501	+	0.0691874i
$969$	11.8373	−	36.4314i	0.380268	−	1.17035i
$970$	−11.7275	+	2.49276i	−0.376548	+	0.0800377i
$971$	−0.537180	+	5.11092i	−0.0172389	+	0.164017i	−0.999754	−	0.0221638i	$-0.992944\pi$
$971$	−0.537180	+	5.11092i	−0.0172389	+	0.164017i	0.982515	+	0.186181i	$0.0596111\pi$
$972$	−0.669131	+	0.743145i	−0.0214624	+	0.0238364i
$973$	−0.212404	+	0.0945685i	−0.00680937	+	0.00303173i
$974$	−6.09148	−	2.71210i	−0.195184	−	0.0869013i
$975$	2.80266	+	3.11266i	0.0897568	+	0.0996850i
$976$	10.0509	−	7.30241i	0.321722	−	0.233744i
$977$	36.4003	−	26.4463i	1.16455	−	0.846093i	0.174202	−	0.984710i	$-0.444266\pi$
$977$	36.4003	−	26.4463i	1.16455	−	0.846093i	0.990346	+	0.138617i	$0.0442656\pi$
$978$	9.70387	+	10.7772i	0.310295	+	0.344618i
$979$	6.51899	+	2.90244i	0.208348	+	0.0927625i
$980$	−6.32416	+	2.81570i	−0.202018	+	0.0899441i
$981$	−3.57891	+	3.97479i	−0.114266	+	0.126905i
$982$	1.53602	−	14.6143i	0.0490165	−	0.466361i
$983$	24.4471	−	5.19640i	0.779742	−	0.165739i	0.199189	−	0.979961i	$-0.436169\pi$
$983$	24.4471	−	5.19640i	0.779742	−	0.165739i	0.580554	+	0.814222i	$0.302836\pi$
$984$	−0.921697	+	2.83669i	−0.0293826	+	0.0904304i
$985$	−7.07992	−	1.50488i	−0.225585	−	0.0479496i
$986$	5.05326	−	8.75250i	0.160929	−	0.278736i
$987$	1.55817	+	2.69883i	0.0495971	+	0.0859048i
$988$	7.42293	+	22.8454i	0.236155	+	0.726810i
$989$	−0.176210	−	1.67652i	−0.00560315	−	0.0533104i
$990$	0.650511	+	0.472624i	0.0206746	+	0.0150210i
$991$	7.14311			0.226908			0.113454	−	0.993543i	$-0.463808\pi$
$991$	7.14311			0.226908			0.113454	+	0.993543i	$0.463808\pi$
$992$	−5.44888	+	1.14444i	−0.173002	+	0.0363359i
$993$	11.4272			0.362633
$994$	2.51474	+	1.82706i	0.0797626	+	0.0579509i
$995$	0.348690	+	3.31756i	0.0110542	+	0.105174i
$996$	−1.18926	−	3.66016i	−0.0376830	−	0.115976i
$997$	28.0866	+	48.6475i	0.889513	+	1.54068i	0.840452	+	0.541885i	$0.182289\pi$
$997$	28.0866	+	48.6475i	0.889513	+	1.54068i	0.0490604	+	0.998796i	$0.484377\pi$
$998$	−10.1848	+	17.6406i	−0.322394	+	0.558402i
$999$	9.43513	+	2.00550i	0.298514	+	0.0634512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.b.661.1	yes	16
31.28	even	15	inner	930.2.bg.b.121.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.b.121.1	✓	16	31.28	even	15	inner
930.2.bg.b.661.1	yes	16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.272042 + 0.0578243i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(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} +(0.272042 + 0.0578243i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-0.538031 + 0.597544i) q^{11} +(-0.913545 + 0.406737i) q^{12} +(-3.82639 - 1.70362i) q^{13} +(-0.186098 - 0.206683i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.46937 + 4.96374i) q^{17} +(0.913545 + 0.406737i) q^{18} +(-5.23919 + 2.33264i) q^{19} +(0.669131 - 0.743145i) q^{20} +(-0.0290714 + 0.276596i) q^{21} +(0.786504 - 0.167177i) q^{22} +(0.320264 - 0.985672i) q^{23} +(0.978148 + 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.09425 + 3.62735i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.0290714 + 0.276596i) q^{28} +(1.22412 + 0.889375i) q^{29} -1.00000 q^{30} +(-5.44888 + 1.14444i) q^{31} +1.00000 q^{32} +(-0.650511 - 0.472624i) q^{33} +(-0.698184 - 6.64278i) q^{34} +(-0.0859436 - 0.264507i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.82296 + 8.35361i) q^{37} +(5.60969 + 1.19238i) q^{38} +(1.29432 - 3.98350i) q^{39} +(-0.978148 + 0.207912i) q^{40} +(-0.311774 + 2.96633i) q^{41} +(0.186098 - 0.206683i) q^{42} +(1.48593 - 0.661581i) q^{43} +(-0.734559 - 0.327047i) q^{44} +(0.669131 + 0.743145i) q^{45} +(-0.838463 + 0.609179i) q^{46} +(9.06508 - 6.58617i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(-6.32416 - 2.81570i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-4.46937 + 4.96374i) q^{51} +(0.437818 - 4.16556i) q^{52} +(-11.0594 + 2.35074i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(0.786504 + 0.167177i) q^{55} +(0.139060 - 0.240858i) q^{56} +(-2.86751 - 4.96667i) q^{57} +(-0.467572 - 1.43904i) q^{58} +(0.504480 + 4.79981i) q^{59} +(0.809017 + 0.587785i) q^{60} -12.4236 q^{61} +(5.08092 + 2.27690i) q^{62} -0.278119 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.437818 + 4.16556i) q^{65} +(0.248473 + 0.764721i) q^{66} +(5.33122 + 9.23395i) q^{67} +(-3.33968 + 5.78450i) q^{68} +(1.01375 + 0.215479i) q^{69} +(-0.0859436 + 0.264507i) q^{70} +(-10.9322 + 2.32371i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(-2.05734 + 2.28491i) q^{73} +(8.81198 - 3.92335i) q^{74} +(-0.913545 - 0.406737i) q^{75} +(-3.83747 - 4.26195i) q^{76} +(-0.180920 + 0.131446i) q^{77} +(-3.38857 + 2.46194i) q^{78} +(-0.656411 - 0.729019i) q^{79} +(0.913545 + 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(1.99580 - 2.21656i) q^{82} +(-0.402279 + 3.82743i) q^{83} +(-0.272042 + 0.0578243i) q^{84} +(2.06404 - 6.35246i) q^{85} +(-1.59101 - 0.338180i) q^{86} +(-0.756548 + 1.31038i) q^{87} +(0.402038 + 0.696350i) q^{88} +(-2.74243 - 8.44034i) q^{89} +(-0.104528 - 0.994522i) q^{90} +(-0.942427 - 0.684713i) q^{91} +1.03640 q^{92} +(-1.70773 - 5.29940i) q^{93} -11.2051 q^{94} +(4.63972 + 3.37096i) q^{95} +(0.104528 + 0.994522i) q^{96} +(3.70497 + 11.4027i) q^{97} +(3.46132 + 5.99519i) q^{98} +(0.402038 - 0.696350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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