LMFDB - Embedded newform 966.2.y.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	966.25
Dual form			966.2.y.b.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.494800 - 2.03959i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.60154 + 0.481642i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.494800 - 2.03959i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.60154 + 0.481642i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(2.06083 - 0.397192i) q^{10} +(-0.0302513 - 0.635052i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(2.58082 + 2.97842i) q^{13} +(-0.604883 + 2.57568i) q^{14} +(0.298684 - 2.07739i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-4.26700 - 5.99216i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(0.828230 - 1.16309i) q^{19} +(0.298684 + 2.07739i) q^{20} +(2.23618 + 1.41404i) q^{21} +0.635773 q^{22} +(4.06774 + 2.54038i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.529062 - 0.272750i) q^{25} +(-3.09785 + 2.43618i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-2.54398 - 0.726754i) q^{28} +(3.42151 - 7.49206i) q^{29} +(2.06083 + 0.397192i) q^{30} +(-2.27429 - 1.78852i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(0.207941 - 0.600806i) q^{33} +(6.18841 - 3.97705i) q^{34} +(-0.304889 - 5.54441i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(2.11559 + 2.01721i) q^{37} +(1.12236 + 0.882634i) q^{38} +(1.28898 + 3.72427i) q^{39} +(-2.08925 + 0.199499i) q^{40} +(7.09296 + 2.08268i) q^{41} +(-1.51884 + 2.16636i) q^{42} +(0.439493 + 3.05674i) q^{43} +(-0.0302513 + 0.635052i) q^{44} +(1.04938 - 1.81757i) q^{45} +(-2.73105 + 3.94225i) q^{46} +(5.96276 + 10.3278i) q^{47} +(0.841254 + 0.540641i) q^{48} +(6.53604 + 2.50602i) q^{49} +(0.247268 + 0.541440i) q^{50} +(-1.73428 - 7.14882i) q^{51} +(-2.28602 - 3.21026i) q^{52} +(-1.75975 - 5.08447i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(-1.28028 + 0.375924i) q^{55} +(0.846978 - 2.50652i) q^{56} +(1.20118 - 0.771950i) q^{57} +(7.32077 + 3.77412i) q^{58} +(4.88637 - 0.941771i) q^{59} +(-0.494800 + 2.03959i) q^{60} +(-7.41615 + 2.96898i) q^{61} +(1.89471 - 2.18662i) q^{62} +(1.55045 + 2.14385i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(4.79779 - 6.73755i) q^{65} +(0.590231 + 0.236293i) q^{66} +(5.32105 - 2.74319i) q^{67} +(3.67809 + 6.37064i) q^{68} +(2.83220 + 3.87023i) q^{69} +(5.55263 - 0.0407301i) q^{70} +(-0.235891 - 0.151598i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-3.12610 - 0.298507i) q^{73} +(-2.11559 + 2.01721i) q^{74} +(0.592535 - 0.0565802i) q^{75} +(-0.935038 + 1.07909i) q^{76} +(0.227168 - 1.66669i) q^{77} +(-3.78138 + 1.11031i) q^{78} +(-1.35418 + 3.91264i) q^{79} +(-0.0998628 - 2.09638i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-2.41782 + 6.98583i) q^{82} +(-13.5362 + 3.97459i) q^{83} +(-2.09164 - 1.62020i) q^{84} +(-10.1103 + 11.6679i) q^{85} +(-3.07419 + 0.293549i) q^{86} +(5.96094 - 5.68374i) q^{87} +(-0.632894 - 0.0604340i) q^{88} +(-4.79413 + 3.77015i) q^{89} +(1.76558 + 1.13467i) q^{90} +(5.27958 + 8.99153i) q^{91} +(-3.80784 - 2.91554i) q^{92} +(-1.44665 - 2.50568i) q^{93} +(-10.5998 + 5.46459i) q^{94} +(-2.78203 - 1.11376i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-8.33765 - 2.44815i) q^{97} +(-2.81418 + 6.40940i) q^{98} +(0.416342 - 0.480485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$3$	0.928368	+	0.371662i	0.535993	+	0.214579i
$3$	0.928368	+	0.371662i	0.535993	+	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	−0.494800	−	2.03959i	−0.221281	−	0.912134i	−0.968790	−	0.247882i	$-0.920265\pi$
$5$	−0.494800	−	2.03959i	−0.221281	−	0.912134i	0.747509	−	0.664252i	$-0.231250\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	2.60154	+	0.481642i	0.983290	+	0.182044i
$7$	2.60154	+	0.481642i	0.983290	+	0.182044i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	2.06083	−	0.397192i	0.651691	−	0.125603i
$11$	−0.0302513	−	0.635052i	−0.00912110	−	0.191476i	−0.998829	−	0.0483749i	$-0.984596\pi$
$11$	−0.0302513	−	0.635052i	−0.00912110	−	0.191476i	0.989708	−	0.143101i	$-0.0457073\pi$
$12$	−0.888835	−	0.458227i	−0.256585	−	0.132279i
$13$	2.58082	+	2.97842i	0.715791	+	0.826066i	0.990794	−	0.135377i	$-0.0432245\pi$
$13$	2.58082	+	2.97842i	0.715791	+	0.826066i	−0.275004	+	0.961443i	$0.588679\pi$
$14$	−0.604883	+	2.57568i	−0.161662	+	0.688379i
$15$	0.298684	−	2.07739i	0.0771198	−	0.536380i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	−4.26700	−	5.99216i	−1.03490	−	1.45331i	−0.885559	−	0.464528i	$-0.846224\pi$
$17$	−4.26700	−	5.99216i	−1.03490	−	1.45331i	−0.149341	−	0.988786i	$-0.547715\pi$
$18$	−0.723734	+	0.690079i	−0.170586	+	0.162653i
$19$	0.828230	−	1.16309i	0.190009	−	0.266830i	−0.708571	−	0.705639i	$-0.750660\pi$
$19$	0.828230	−	1.16309i	0.190009	−	0.266830i	0.898580	+	0.438809i	$0.144599\pi$
$20$	0.298684	+	2.07739i	0.0667877	+	0.464519i
$21$	2.23618	+	1.41404i	0.487974	+	0.308568i
$22$	0.635773			0.135547
$23$	4.06774	+	2.54038i	0.848182	+	0.529705i
$23$	4.06774	+	2.54038i	0.848182	+	0.529705i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	0.529062	−	0.272750i	0.105812	−	0.0545501i
$26$	−3.09785	+	2.43618i	−0.607539	+	0.477774i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	−2.54398	−	0.726754i	−0.480767	−	0.137344i
$29$	3.42151	−	7.49206i	0.635358	−	1.39124i	−0.268446	−	0.963295i	$-0.586510\pi$
$29$	3.42151	−	7.49206i	0.635358	−	1.39124i	0.903804	−	0.427946i	$-0.140763\pi$
$30$	2.06083	+	0.397192i	0.376254	+	0.0725170i
$31$	−2.27429	−	1.78852i	−0.408475	−	0.321228i	0.392691	−	0.919670i	$-0.371544\pi$
$31$	−2.27429	−	1.78852i	−0.408475	−	0.321228i	−0.801166	+	0.598442i	$0.795787\pi$
$32$	−0.235759	+	0.971812i	−0.0416767	+	0.171794i
$33$	0.207941	−	0.600806i	0.0361979	−	0.104587i
$34$	6.18841	−	3.97705i	1.06130	−	0.682058i
$35$	−0.304889	−	5.54441i	−0.0515356	−	0.937176i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	2.11559	+	2.01721i	0.347801	+	0.331628i	0.843762	−	0.536717i	$-0.180336\pi$
$37$	2.11559	+	2.01721i	0.347801	+	0.331628i	−0.495961	+	0.868345i	$0.665184\pi$
$38$	1.12236	+	0.882634i	0.182071	+	0.143182i
$39$	1.28898	+	3.72427i	0.206402	+	0.596360i
$40$	−2.08925	+	0.199499i	−0.330340	+	0.0315436i
$41$	7.09296	+	2.08268i	1.10773	+	0.325260i	0.783921	−	0.620861i	$-0.213217\pi$
$41$	7.09296	+	2.08268i	1.10773	+	0.325260i	0.323813	+	0.946121i	$0.395035\pi$
$42$	−1.51884	+	2.16636i	−0.234362	+	0.334277i
$43$	0.439493	+	3.05674i	0.0670220	+	0.466148i	0.995500	+	0.0947609i	$0.0302087\pi$
$43$	0.439493	+	3.05674i	0.0670220	+	0.466148i	−0.928478	+	0.371387i	$0.878882\pi$
$44$	−0.0302513	+	0.635052i	−0.00456055	+	0.0957378i
$45$	1.04938	−	1.81757i	0.156432	−	0.270948i
$46$	−2.73105	+	3.94225i	−0.402671	+	0.581254i
$47$	5.96276	+	10.3278i	0.869758	+	1.50646i	0.862244	+	0.506492i	$0.169058\pi$
$47$	5.96276	+	10.3278i	0.869758	+	1.50646i	0.00751311	+	0.999972i	$0.497608\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	6.53604	+	2.50602i	0.933720	+	0.358004i
$50$	0.247268	+	0.541440i	0.0349689	+	0.0765712i
$51$	−1.73428	−	7.14882i	−0.242848	−	1.00103i
$52$	−2.28602	−	3.21026i	−0.317013	−	0.445183i
$53$	−1.75975	−	5.08447i	−0.241720	−	0.698405i	−0.998974	−	0.0452845i	$-0.985581\pi$
$53$	−1.75975	−	5.08447i	−0.241720	−	0.698405i	0.757254	−	0.653121i	$-0.226541\pi$
$54$	−0.928368	+	0.371662i	−0.126335	+	0.0505769i
$55$	−1.28028	+	0.375924i	−0.172633	+	0.0506896i
$56$	0.846978	−	2.50652i	0.113182	−	0.334947i
$57$	1.20118	−	0.771950i	0.159100	−	0.102247i
$58$	7.32077	+	3.77412i	0.961264	+	0.495566i
$59$	4.88637	−	0.941771i	0.636152	−	0.122608i	0.139029	−	0.990288i	$-0.455602\pi$
$59$	4.88637	−	0.941771i	0.636152	−	0.122608i	0.497123	+	0.867680i	$0.334390\pi$
$60$	−0.494800	+	2.03959i	−0.0638784	+	0.263310i
$61$	−7.41615	+	2.96898i	−0.949540	+	0.380139i	−0.794155	−	0.607715i	$-0.792086\pi$
$61$	−7.41615	+	2.96898i	−0.949540	+	0.380139i	−0.155385	+	0.987854i	$0.549662\pi$
$62$	1.89471	−	2.18662i	0.240629	−	0.277700i
$63$	1.55045	+	2.14385i	0.195339	+	0.270100i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	4.79779	−	6.73755i	0.595092	−	0.835690i
$66$	0.590231	+	0.236293i	0.0726524	+	0.0290856i
$67$	5.32105	−	2.74319i	0.650070	−	0.335134i	−0.101454	−	0.994840i	$-0.532349\pi$
$67$	5.32105	−	2.74319i	0.650070	−	0.335134i	0.751524	+	0.659706i	$0.229319\pi$
$68$	3.67809	+	6.37064i	0.446034	+	0.772553i
$69$	2.83220	+	3.87023i	0.340956	+	0.465921i
$70$	5.55263	−	0.0407301i	0.663667	−	0.00486817i
$71$	−0.235891	−	0.151598i	−0.0279951	−	0.0179913i	0.526568	−	0.850133i	$-0.323478\pi$
$71$	−0.235891	−	0.151598i	−0.0279951	−	0.0179913i	−0.554564	+	0.832141i	$0.687115\pi$
$72$	0.786053	−	0.618159i	0.0926372	−	0.0728507i
$73$	−3.12610	−	0.298507i	−0.365883	−	0.0349375i	−0.0895041	−	0.995986i	$-0.528528\pi$
$73$	−3.12610	−	0.298507i	−0.365883	−	0.0349375i	−0.276378	+	0.961049i	$0.589134\pi$
$74$	−2.11559	+	2.01721i	−0.245932	+	0.234496i
$75$	0.592535	−	0.0565802i	0.0684200	−	0.00653332i
$76$	−0.935038	+	1.07909i	−0.107256	+	0.123780i
$77$	0.227168	−	1.66669i	0.0258882	−	0.189936i
$78$	−3.78138	+	1.11031i	−0.428157	+	0.125718i
$79$	−1.35418	+	3.91264i	−0.152357	+	0.440206i	−0.995189	−	0.0979696i	$-0.968765\pi$
$79$	−1.35418	+	3.91264i	−0.152357	+	0.440206i	0.842832	+	0.538176i	$0.180886\pi$
$80$	−0.0998628	−	2.09638i	−0.0111650	−	0.234382i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	−2.41782	+	6.98583i	−0.267003	+	0.771456i
$83$	−13.5362	+	3.97459i	−1.48579	+	0.436268i	−0.921196	−	0.389098i	$-0.872787\pi$
$83$	−13.5362	+	3.97459i	−1.48579	+	0.436268i	−0.564597	+	0.825367i	$0.690968\pi$
$84$	−2.09164	−	1.62020i	−0.228217	−	0.176778i
$85$	−10.1103	+	11.6679i	−1.09661	+	1.26556i
$86$	−3.07419	+	0.293549i	−0.331498	+	0.0316542i
$87$	5.96094	−	5.68374i	0.639079	−	0.609361i
$88$	−0.632894	−	0.0604340i	−0.0674667	−	0.00644229i
$89$	−4.79413	+	3.77015i	−0.508177	+	0.399635i	−0.839062	−	0.544037i	$-0.816895\pi$
$89$	−4.79413	+	3.77015i	−0.508177	+	0.399635i	0.330885	+	0.943671i	$0.392653\pi$
$90$	1.76558	+	1.13467i	0.186109	+	0.119605i
$91$	5.27958	+	8.99153i	0.553450	+	0.942568i
$92$	−3.80784	−	2.91554i	−0.396995	−	0.303966i
$93$	−1.44665	−	2.50568i	−0.150011	−	0.259827i
$94$	−10.5998	+	5.46459i	−1.09329	+	0.563629i
$95$	−2.78203	−	1.11376i	−0.285430	−	0.114269i
$96$	−0.580057	+	0.814576i	−0.0592018	+	0.0831373i
$97$	−8.33765	−	2.44815i	−0.846560	−	0.248572i	−0.170444	−	0.985367i	$-0.554520\pi$
$97$	−8.33765	−	2.44815i	−0.846560	−	0.248572i	−0.676116	+	0.736795i	$0.736338\pi$
$98$	−2.81418	+	6.40940i	−0.284275	+	0.647447i
$99$	0.416342	−	0.480485i	0.0418440	−	0.0482905i
$100$	−0.552593	+	0.221225i	−0.0552593	+	0.0221225i
$101$	0.0361604	−	0.149055i	0.00359810	−	0.0148316i	−0.969984	−	0.243168i	$-0.921813\pi$
$101$	0.0361604	−	0.149055i	0.00359810	−	0.0148316i	0.973582	+	0.228336i	$0.0733286\pi$
$102$	7.22324	−	1.39217i	0.715207	−	0.137845i
$103$	−7.25703	−	3.74126i	−0.715057	−	0.368637i	0.0619931	−	0.998077i	$-0.480254\pi$
$103$	−7.25703	−	3.74126i	−0.715057	−	0.368637i	−0.777050	+	0.629439i	$0.783285\pi$
$104$	3.31540	−	2.13068i	0.325101	−	0.208930i
$105$	1.77760	−	5.26056i	0.173476	−	0.513378i
$106$	5.16244	−	1.51583i	0.501421	−	0.147230i
$107$	6.74095	−	2.69867i	0.651672	−	0.260890i	−0.0221826	−	0.999754i	$-0.507062\pi$
$107$	6.74095	−	2.69867i	0.651672	−	0.260890i	0.673855	+	0.738864i	$0.264637\pi$
$108$	−0.327068	−	0.945001i	−0.0314721	−	0.0909327i
$109$	2.34861	+	3.29817i	0.224956	+	0.315907i	0.911593	−	0.411094i	$-0.134853\pi$
$109$	2.34861	+	3.29817i	0.224956	+	0.315907i	−0.686637	+	0.727001i	$0.740914\pi$
$110$	−0.314580	−	1.29672i	−0.0299941	−	0.123637i
$111$	1.21432	+	2.65900i	0.115259	+	0.252381i
$112$	2.46338	+	0.965283i	0.232767	+	0.0912107i
$113$	−15.9726	−	10.2650i	−1.50257	−	0.965646i	−0.994545	−	0.104306i	$-0.966738\pi$
$113$	−15.9726	−	10.2650i	−1.50257	−	0.965646i	−0.508029	−	0.861340i	$-0.669626\pi$
$114$	0.713921	+	1.23655i	0.0668649	+	0.115813i
$115$	3.16862	−	9.55351i	0.295475	−	0.890869i
$116$	−4.11818	+	7.13290i	−0.382364	+	0.662273i
$117$	−0.187521	+	3.93656i	−0.0173363	+	0.363935i
$118$	0.708201	+	4.92565i	0.0651952	+	0.453443i
$119$	−8.21470	−	17.6440i	−0.753041	−	1.61743i
$120$	−2.01374	−	0.591287i	−0.183828	−	0.0539769i
$121$	10.5478	−	1.00719i	0.958892	−	0.0915631i
$122$	−2.61274	−	7.54902i	−0.236546	−	0.683456i
$123$	5.81082	+	4.56968i	0.523944	+	0.412034i
$124$	2.09398	+	1.99661i	0.188045	+	0.179301i
$125$	−7.69004	−	8.87478i	−0.687818	−	0.793784i
$126$	−2.21520	+	1.44669i	−0.197345	+	0.128881i
$127$	−4.86579	+	3.12705i	−0.431769	+	0.277481i	−0.738420	−	0.674341i	$-0.764428\pi$
$127$	−4.86579	+	3.12705i	−0.431769	+	0.277481i	0.306651	+	0.951822i	$0.400792\pi$
$128$	0.327068	−	0.945001i	0.0289090	−	0.0835271i
$129$	−0.728064	+	3.00112i	−0.0641025	+	0.264234i
$130$	6.50163	+	5.11294i	0.570231	+	0.448434i
$131$	8.27206	+	1.59431i	0.722733	+	0.139295i	0.537336	−	0.843368i	$-0.319431\pi$
$131$	8.27206	+	1.59431i	0.722733	+	0.139295i	0.185397	+	0.982664i	$0.440643\pi$
$132$	−0.264109	+	0.578319i	−0.0229878	+	0.0503362i
$133$	2.71487	−	2.62691i	0.235409	−	0.227782i
$134$	2.48690	+	5.44555i	0.214835	+	0.470424i
$135$	1.64973	−	1.29736i	0.141986	−	0.111659i
$136$	−6.53843	+	3.37080i	−0.560666	+	0.289043i
$137$	−2.07884	+	3.60066i	−0.177607	+	0.307625i	−0.941060	−	0.338238i	$-0.890169\pi$
$137$	−2.07884	+	3.60066i	−0.177607	+	0.307625i	0.763453	+	0.645863i	$0.223502\pi$
$138$	−4.00061	+	2.64483i	−0.340554	+	0.225143i
$139$	−3.51350			−0.298011			−0.149006	−	0.988836i	$-0.547607\pi$
$139$	−3.51350			−0.298011			−0.149006	+	0.988836i	$0.547607\pi$
$140$	−0.223521	+	5.54828i	−0.0188910	+	0.468915i
$141$	1.69718	+	11.8041i	0.142928	+	0.994087i
$142$	0.162650	−	0.228410i	0.0136493	−	0.0191677i
$143$	1.81338	−	1.72906i	0.151643	−	0.144591i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	−16.9737	−	3.27142i	−1.40959	−	0.271676i
$146$	0.446914	−	3.10836i	0.0369869	−	0.257249i
$147$	5.13646	+	4.75571i	0.423648	+	0.392245i
$148$	−1.91426	−	2.20918i	−0.157351	−	0.181593i
$149$	−4.37778	−	2.25690i	−0.358642	−	0.184893i	0.269483	−	0.963005i	$-0.413147\pi$
$149$	−4.37778	−	2.25690i	−0.358642	−	0.184893i	−0.628125	+	0.778112i	$0.716177\pi$
$150$	0.0283222	+	0.594556i	0.00231250	+	0.0485453i
$151$	0.264701	−	0.0510169i	0.0215410	−	0.00415169i	−0.178469	−	0.983945i	$-0.557115\pi$
$151$	0.264701	−	0.0510169i	0.0215410	−	0.00415169i	0.200010	+	0.979794i	$0.435902\pi$
$152$	−1.03338	−	0.985324i	−0.0838181	−	0.0799203i
$153$	1.04689	−	7.28130i	0.0846363	−	0.588658i
$154$	1.65399	+	0.306215i	0.133282	+	0.0246755i
$155$	−2.52254	+	5.52360i	−0.202615	+	0.443666i
$156$	−0.929131	−	3.82993i	−0.0743900	−	0.306640i
$157$	5.50476	+	0.525641i	0.439328	+	0.0419507i	0.312377	−	0.949958i	$-0.398875\pi$
$157$	5.50476	+	0.525641i	0.439328	+	0.0419507i	0.126951	+	0.991909i	$0.459481\pi$
$158$	−3.84377	−	1.53881i	−0.305794	−	0.122422i
$159$	0.256009	−	5.37429i	0.0203028	−	0.426209i
$160$	2.09875			0.165921
$161$	9.35884	+	8.56809i	0.737580	+	0.675260i
$162$	−1.00000			−0.0785674
$163$	−0.863031	+	18.1173i	−0.0675978	+	1.41905i	0.669272	+	0.743018i	$0.266606\pi$
$163$	−0.863031	+	18.1173i	−0.0675978	+	1.41905i	−0.736870	+	0.676035i	$0.763697\pi$
$164$	−6.86287	−	2.74748i	−0.535900	−	0.214542i
$165$	−1.32829	−	0.126836i	−0.103407	−	0.00987418i
$166$	−3.32601	−	13.7100i	−0.258149	−	1.06410i
$167$	0.839545	−	1.83835i	0.0649660	−	0.142256i	−0.874364	−	0.485271i	$-0.838721\pi$
$167$	0.839545	−	1.83835i	0.0649660	−	0.142256i	0.939330	+	0.343015i	$0.111448\pi$
$168$	1.71789	−	2.01218i	0.132538	−	0.155243i
$169$	−0.360290	+	2.50587i	−0.0277146	+	0.192759i
$170$	−11.1736	−	10.6540i	−0.856975	−	0.817124i
$171$	1.40204	−	0.270221i	0.107217	−	0.0206643i
$172$	−0.146941	−	3.08467i	−0.0112042	−	0.235204i
$173$	−19.4059	−	10.0044i	−1.47540	−	0.760622i	−0.482093	−	0.876120i	$-0.660123\pi$
$173$	−19.4059	−	10.0044i	−1.47540	−	0.760622i	−0.993308	+	0.115498i	$0.963154\pi$
$174$	5.39367	+	6.22463i	0.408893	+	0.471888i
$175$	1.50774	−	0.454753i	0.113975	−	0.0343761i
$176$	0.0904799	−	0.629301i	0.00682018	−	0.0474354i
$177$	4.88637	+	0.941771i	0.367282	+	0.0707879i
$178$	−3.53776	−	4.96809i	−0.265166	−	0.372374i
$179$	2.91294	−	2.77748i	0.217723	−	0.207599i	−0.573366	−	0.819299i	$-0.694363\pi$
$179$	2.91294	−	2.77748i	0.217723	−	0.207599i	0.791089	+	0.611700i	$0.209514\pi$
$180$	−1.21740	+	1.70959i	−0.0907394	+	0.127426i
$181$	2.25223	+	15.6646i	0.167407	+	1.16434i	0.884219	+	0.467073i	$0.154691\pi$
$181$	2.25223	+	15.6646i	0.167407	+	1.16434i	−0.716812	+	0.697266i	$0.754400\pi$
$182$	−9.23256	+	4.84576i	−0.684363	+	0.359192i
$183$	−7.98837			−0.590517
$184$	3.09342	−	3.66480i	0.228050	−	0.270173i
$185$	3.06750	−	5.31306i	0.225527	−	0.390624i
$186$	2.57167	−	1.32579i	0.188564	−	0.0972116i
$187$	−3.67626	+	2.89104i	−0.268834	+	0.211414i
$188$	−4.95404	−	10.8478i	−0.361310	−	0.791159i
$189$	0.642602	+	2.56653i	0.0467425	+	0.186687i
$190$	1.24487	−	2.72589i	0.0903124	−	0.197757i
$191$	5.75953	+	1.11006i	0.416745	+	0.0803210i	0.393313	−	0.919404i	$-0.371329\pi$
$191$	5.75953	+	1.11006i	0.416745	+	0.0803210i	0.0234314	+	0.999725i	$0.492541\pi$
$192$	−0.786053	−	0.618159i	−0.0567285	−	0.0446118i
$193$	1.67298	−	6.89610i	0.120423	−	0.496392i	−0.879371	−	0.476136i	$-0.842037\pi$
$193$	1.67298	−	6.89610i	0.120423	−	0.496392i	0.999795	−	0.0202556i	$-0.00644798\pi$
$194$	2.84210	−	8.21172i	0.204051	−	0.589567i
$195$	6.95820	−	4.47177i	0.498287	−	0.320230i
$196$	−6.26823	−	3.11597i	−0.447731	−	0.222569i
$197$	13.4896	+	15.5678i	0.961092	+	1.10916i	0.993965	+	0.109700i	$0.0349890\pi$
$197$	13.4896	+	15.5678i	0.961092	+	1.10916i	−0.0328725	+	0.999460i	$0.510466\pi$
$198$	0.460130	+	0.438733i	0.0327000	+	0.0311794i
$199$	4.02461	+	3.16499i	0.285297	+	0.224360i	0.750543	−	0.660821i	$-0.229792\pi$
$199$	4.02461	+	3.16499i	0.285297	+	0.224360i	−0.465246	+	0.885181i	$0.654034\pi$
$200$	−0.194681	−	0.562493i	−0.0137660	−	0.0397743i
$201$	5.95943	−	0.569057i	0.420346	−	0.0401382i
$202$	0.147166	+	0.0432118i	0.0103546	+	0.00304037i
$203$	12.5097	−	17.8430i	0.878008	−	1.25233i
$204$	1.04689	+	7.28130i	0.0732972	+	0.509793i
$205$	0.738226	−	15.4973i	0.0515599	−	1.08238i
$206$	4.08233	−	7.07080i	0.284429	−	0.492646i
$207$	1.19090	+	4.64562i	0.0827733	+	0.322893i
$208$	1.97051	+	3.41302i	0.136630	+	0.236651i
$209$	−0.763676	−	0.490785i	−0.0528246	−	0.0339483i
$210$	5.17002	+	2.02589i	0.356766	+	0.139800i
$211$	−2.95385	−	6.46804i	−0.203352	−	0.445278i	0.780289	−	0.625419i	$-0.215072\pi$
$211$	−2.95385	−	6.46804i	−0.203352	−	0.445278i	−0.983641	+	0.180141i	$0.942345\pi$
$212$	1.26847	+	5.22872i	0.0871191	+	0.359110i
$213$	−0.162650	−	0.228410i	−0.0111446	−	0.0156504i
$214$	2.37487	+	6.86172i	0.162342	+	0.469058i
$215$	6.01704	−	2.40886i	0.410359	−	0.164283i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−5.05524	−	5.74832i	−0.343172	−	0.390221i
$218$	−3.40618	+	2.18902i	−0.230696	+	0.148259i
$219$	−2.79123	−	1.43898i	−0.188614	−	0.0972372i
$220$	1.31022	−	0.252524i	0.0883348	−	0.0170251i
$221$	6.83485	−	28.1736i	0.459762	−	1.89516i
$222$	−2.71377	+	1.08643i	−0.182136	+	0.0729163i
$223$	4.46741	−	5.15567i	0.299160	−	0.345249i	−0.586191	−	0.810173i	$-0.699373\pi$
$223$	4.46741	−	5.15567i	0.299160	−	0.345249i	0.885350	+	0.464924i	$0.153918\pi$
$224$	−1.08140	+	2.41466i	−0.0722542	+	0.161336i
$225$	0.571119	+	0.167696i	0.0380746	+	0.0111797i
$226$	11.0133	−	15.4661i	0.732596	−	1.02879i
$227$	−16.3476	−	6.54460i	−1.08503	−	0.434380i	−0.240917	−	0.970546i	$-0.577448\pi$
$227$	−16.3476	−	6.54460i	−1.08503	−	0.434380i	−0.844113	+	0.536166i	$0.819872\pi$
$228$	−1.26912	+	0.654275i	−0.0840493	+	0.0433304i
$229$	−3.01973	−	5.23033i	−0.199549	−	0.345630i	0.748833	−	0.662759i	$-0.230615\pi$
$229$	−3.01973	−	5.23033i	−0.199549	−	0.345630i	−0.948382	+	0.317129i	$0.897281\pi$
$230$	9.39192	+	3.61960i	0.619285	+	0.238670i
$231$	0.830340	−	1.46287i	0.0546324	−	0.0962496i
$232$	−6.92887	−	4.45291i	−0.454903	−	0.292348i
$233$	−15.5165	+	12.2023i	−1.01652	+	0.799402i	−0.979811	−	0.199924i	$-0.935930\pi$
$233$	−15.5165	+	12.2023i	−1.01652	+	0.799402i	−0.0367108	+	0.999326i	$0.511688\pi$
$234$	−3.92318	−	0.374618i	−0.256466	−	0.0244895i
$235$	18.1141	−	17.2718i	1.18164	−	1.12669i
$236$	−4.95377	+	0.473027i	−0.322463	+	0.0307915i
$237$	−2.71136	+	3.12907i	−0.176122	+	0.203255i
$238$	18.0149	−	7.36586i	1.16773	−	0.477458i
$239$	0.536820	−	0.157625i	0.0347240	−	0.0101959i	−0.264324	−	0.964434i	$-0.585149\pi$
$239$	0.536820	−	0.157625i	0.0347240	−	0.0101959i	0.299048	+	0.954238i	$0.403331\pi$
$240$	0.686435	−	1.98332i	0.0443092	−	0.128023i
$241$	1.26049	+	26.4609i	0.0811952	+	1.70450i	0.561566	+	0.827432i	$0.310199\pi$
$241$	1.26049	+	26.4609i	0.0811952	+	1.70450i	−0.480371	+	0.877065i	$0.659498\pi$
$242$	0.504168	+	10.5838i	0.0324092	+	0.680352i
$243$	−0.327068	+	0.945001i	−0.0209814	+	0.0606218i
$244$	7.66479	−	2.25058i	0.490688	−	0.144079i
$245$	1.87724	−	14.5709i	0.119932	−	0.930898i
$246$	−4.84100	+	5.58681i	−0.308651	+	0.356202i
$247$	5.60168	−	0.534895i	0.356426	−	0.0340346i
$248$	−2.09398	+	1.99661i	−0.132968	+	0.126785i
$249$	−14.0438	−	1.34102i	−0.889990	−	0.0849837i
$250$	9.23063	−	7.25905i	0.583796	−	0.459103i
$251$	−24.7445	−	15.9023i	−1.56186	−	1.00375i	−0.981967	−	0.189053i	$-0.939458\pi$
$251$	−24.7445	−	15.9023i	−1.56186	−	1.00375i	−0.579892	−	0.814693i	$-0.696905\pi$
$252$	−1.33965	−	2.28152i	−0.0843898	−	0.143722i
$253$	1.49022	−	2.66008i	0.0936892	−	0.167238i
$254$	−2.89199	−	5.00907i	−0.181460	−	0.314297i
$255$	−13.7226	+	7.07447i	−0.859340	+	0.443021i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−15.4743	+	21.7306i	−0.965261	+	1.35552i	−0.0307729	+	0.999526i	$0.509797\pi$
$257$	−15.4743	+	21.7306i	−0.965261	+	1.35552i	−0.934488	+	0.355994i	$0.884143\pi$
$258$	−2.96308	−	0.870038i	−0.184473	−	0.0541662i
$259$	4.53222	+	6.26682i	0.281619	+	0.389401i
$260$	−5.41651	+	6.25098i	−0.335917	+	0.387669i
$261$	7.64637	−	3.06115i	0.473299	−	0.189480i
$262$	−1.98610	+	8.18683i	−0.122702	+	0.505784i
$263$	−27.1744	+	5.23743i	−1.67564	+	0.322954i	−0.936519	−	0.350616i	$-0.885972\pi$
$263$	−27.1744	+	5.23743i	−1.67564	+	0.322954i	−0.739123	+	0.673570i	$0.764760\pi$
$264$	−0.565097	−	0.291328i	−0.0347793	−	0.0179300i
$265$	−9.49952	+	6.10497i	−0.583551	+	0.375026i
$266$	2.49475	+	2.83678i	0.152963	+	0.173934i
$267$	−5.85194	+	1.71828i	−0.358133	+	0.105157i
$268$	−5.55771	+	2.22497i	−0.339491	+	0.135912i
$269$	−2.59173	−	7.48831i	−0.158020	−	0.456570i	0.838003	−	0.545666i	$-0.183723\pi$
$269$	−2.59173	−	7.48831i	−0.158020	−	0.456570i	−0.996023	+	0.0890962i	$0.971602\pi$
$270$	1.21740	+	1.70959i	0.0740884	+	0.104043i
$271$	−5.45722	−	22.4950i	−0.331502	−	1.36647i	−0.856842	−	0.515579i	$-0.827577\pi$
$271$	−5.45722	−	22.4950i	−0.331502	−	1.36647i	0.525340	−	0.850892i	$-0.323938\pi$
$272$	−3.05587	−	6.69141i	−0.185289	−	0.405727i
$273$	1.55958	+	10.3097i	0.0943898	+	0.623969i
$274$	−3.49766	−	2.24781i	−0.211302	−	0.135795i
$275$	−0.189216	−	0.327731i	−0.0114101	−	0.0197629i
$276$	−2.45148	−	4.12192i	−0.147562	−	0.248111i
$277$	8.16315	−	14.1390i	0.490476	−	0.849529i	−0.509464	−	0.860492i	$-0.670156\pi$
$277$	8.16315	−	14.1390i	0.490476	−	0.849529i	0.999940	+	0.0109628i	$0.00348964\pi$
$278$	0.167179	−	3.50952i	0.0100267	−	0.210487i
$279$	−0.411761	−	2.86386i	−0.0246515	−	0.171455i
$280$	−5.53136	−	0.487266i	−0.330562	−	0.0291197i
$281$	−7.65201	−	2.24683i	−0.456481	−	0.134035i	0.0454051	−	0.998969i	$-0.485542\pi$
$281$	−7.65201	−	2.24683i	−0.456481	−	0.134035i	−0.501886	+	0.864934i	$0.667360\pi$
$282$	−11.8715	+	1.13359i	−0.706938	+	0.0675044i
$283$	−0.494604	−	1.42906i	−0.0294011	−	0.0849490i	0.929345	−	0.369212i	$-0.120372\pi$
$283$	−0.494604	−	1.42906i	−0.0294011	−	0.0849490i	−0.958746	+	0.284263i	$0.908251\pi$
$284$	0.220412	+	0.173334i	0.0130791	+	0.0102855i
$285$	−2.16881	−	2.06795i	−0.128469	−	0.122495i
$286$	1.64081	+	1.89360i	0.0970234	+	0.111971i
$287$	17.4495	+	8.83445i	1.03001	+	0.521481i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	−12.1386	+	35.0721i	−0.714034	+	2.06307i
$290$	4.07535	−	16.7988i	0.239313	−	0.986461i
$291$	−6.83052	−	5.37158i	−0.400412	−	0.314888i
$292$	3.08357	+	0.594310i	0.180452	+	0.0347793i
$293$	−11.6808	+	25.5774i	−0.682400	+	1.49425i	0.177680	+	0.984088i	$0.443141\pi$
$293$	−11.6808	+	25.5774i	−0.682400	+	1.49425i	−0.860080	+	0.510159i	$0.829586\pi$
$294$	−4.99473	+	4.90435i	−0.291299	+	0.286028i
$295$	−4.33861	−	9.50023i	−0.252604	−	0.553125i
$296$	2.29776	−	1.80698i	0.133555	−	0.105028i
$297$	0.565097	−	0.291328i	0.0327903	−	0.0169046i
$298$	2.46265	−	4.26543i	0.142657	−	0.247090i
$299$	2.93178	+	18.6717i	0.169549	+	1.07981i
$300$	−0.595230			−0.0343656
$301$	−0.328896	+	8.16391i	−0.0189572	+	0.470560i
$302$	0.0383641	+	0.266828i	0.00220761	+	0.0153542i
$303$	0.0889685	−	0.124939i	0.00511110	−	0.00717754i
$304$	1.03338	−	0.985324i	0.0592683	−	0.0565122i
$305$	9.72502	+	13.6569i	0.556853	+	0.781991i
$306$	7.22324	+	1.39217i	0.412925	+	0.0795848i
$307$	1.10716	−	7.70043i	0.0631887	−	0.439487i	−0.933527	−	0.358507i	$-0.883286\pi$
$307$	1.10716	−	7.70043i	0.0631887	−	0.439487i	0.996716	−	0.0809800i	$-0.0258050\pi$
$308$	−0.384568	+	1.63755i	−0.0219128	+	0.0933078i
$309$	−5.34671	−	6.17043i	−0.304164	−	0.351024i
$310$	−5.39731	−	2.78251i	−0.306547	−	0.158036i
$311$	−1.57908	−	33.1490i	−0.0895416	−	1.87971i	−0.383016	−	0.923742i	$-0.625115\pi$
$311$	−1.57908	−	33.1490i	−0.0895416	−	1.87971i	0.293474	−	0.955967i	$-0.405189\pi$
$312$	3.86980	−	0.745843i	0.219084	−	0.0422250i
$313$	−12.0358	−	11.4761i	−0.680301	−	0.648666i	0.268961	−	0.963151i	$-0.413320\pi$
$313$	−12.0358	−	11.4761i	−0.680301	−	0.648666i	−0.949262	+	0.314485i	$0.898168\pi$
$314$	−0.786973	+	5.47351i	−0.0444114	+	0.308888i
$315$	3.60542	−	4.22307i	0.203142	−	0.237943i
$316$	1.71997	−	3.76620i	0.0967557	−	0.211865i
$317$	4.98268	+	20.5389i	0.279855	+	1.15358i	0.922060	+	0.387046i	$0.126505\pi$
$317$	4.98268	+	20.5389i	0.279855	+	1.15358i	−0.642205	+	0.766533i	$0.721980\pi$
$318$	5.35602	+	0.511438i	0.300351	+	0.0286800i
$319$	−4.86135	−	1.94619i	−0.272184	−	0.108966i
$320$	−0.0998628	+	2.09638i	−0.00558250	+	0.117191i
$321$	7.26108			0.405274
$322$	−9.00369	+	8.94055i	−0.501756	+	0.498238i
$323$	−10.5035			−0.584428
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	2.17778	+	0.871851i	0.120801	+	0.0483616i
$326$	−18.0557	−	1.72411i	−1.00001	−	0.0954895i
$327$	0.954573	+	3.93480i	0.0527880	+	0.217595i
$328$	3.07092	−	6.72437i	0.169563	−	0.371291i
$329$	10.5381	+	29.7401i	0.580982	+	1.63963i
$330$	0.189895	−	1.32075i	0.0104534	−	0.0727048i
$331$	−10.6352	−	10.1407i	−0.584566	−	0.557382i	0.339018	−	0.940780i	$-0.389905\pi$
$331$	−10.6352	−	10.1407i	−0.584566	−	0.557382i	−0.923583	+	0.383398i	$0.874754\pi$
$332$	13.8527	−	2.66990i	0.760268	−	0.146530i
$333$	0.139090	+	2.91985i	0.00762206	+	0.160007i
$334$	1.79632	+	0.926066i	0.0982902	+	0.0506721i
$335$	−8.22785	−	9.49545i	−0.449536	−	0.518792i
$336$	1.92816	+	1.81168i	0.105190	+	0.0988354i
$337$	−4.69315	+	32.6416i	−0.255652	+	1.77810i	0.307302	+	0.951612i	$0.400574\pi$
$337$	−4.69315	+	32.6416i	−0.255652	+	1.77810i	−0.562954	+	0.826488i	$0.690335\pi$
$338$	−2.48589	−	0.479116i	−0.135215	−	0.0260605i
$339$	−11.0133	−	15.4661i	−0.598162	−	0.840001i
$340$	11.1736	−	10.6540i	0.605973	−	0.577794i
$341$	−1.06701	+	1.49840i	−0.0577816	+	0.0811429i
$342$	0.203203	+	1.41331i	0.0109880	+	0.0764230i
$343$	15.7968	+	9.66756i	0.852946	+	0.521999i
$344$	3.08817			0.166503
$345$	6.49232	−	7.69152i	0.349535	−	0.414097i
$346$	10.9165	−	18.9079i	0.586872	−	1.01649i
$347$	9.07125	−	4.67656i	0.486970	−	0.251051i	−0.197213	−	0.980361i	$-0.563189\pi$
$347$	9.07125	−	4.67656i	0.486970	−	0.251051i	0.684183	+	0.729310i	$0.260159\pi$
$348$	−6.47422	+	5.09138i	−0.347055	+	0.272927i
$349$	−13.0469	−	28.5688i	−0.698385	−	1.52925i	−0.841918	−	0.539605i	$-0.818573\pi$
$349$	−13.0469	−	28.5688i	−0.698385	−	1.52925i	0.143533	−	0.989646i	$-0.454154\pi$
$350$	0.382496	+	1.52767i	0.0204453	+	0.0816576i
$351$	−1.63716	+	3.58488i	−0.0873851	+	0.191347i
$352$	0.624283	+	0.120321i	0.0332744	+	0.00641312i
$353$	14.2323	+	11.1924i	0.757507	+	0.595710i	0.920420	−	0.390930i	$-0.127847\pi$
$353$	14.2323	+	11.1924i	0.757507	+	0.595710i	−0.162913	+	0.986640i	$0.552089\pi$
$354$	−1.17321	+	4.83603i	−0.0623553	+	0.257032i
$355$	−0.192479	+	0.556131i	−0.0102157	+	0.0295164i
$356$	5.13080	−	3.29736i	0.271932	−	0.174760i
$357$	−1.06864	−	19.4333i	−0.0565585	−	1.02852i
$358$	2.63573	+	3.04180i	0.139303	+	0.160764i
$359$	21.5060	+	20.5059i	1.13504	+	1.08226i	0.995758	+	0.0920087i	$0.0293287\pi$
$359$	21.5060	+	20.5059i	1.13504	+	1.08226i	0.139285	+	0.990252i	$0.455520\pi$
$360$	−1.64973	−	1.29736i	−0.0869485	−	0.0683771i
$361$	5.54749	+	16.0284i	0.291973	+	0.843601i
$362$	−15.7540	+	1.50432i	−0.828012	+	0.0790655i
$363$	10.1666	+	2.98518i	0.533608	+	0.156681i
$364$	−4.40097	−	9.45267i	−0.230674	−	0.495454i
$365$	0.937963	+	6.52368i	0.0490952	+	0.341465i
$366$	0.380102	−	7.97932i	0.0198683	−	0.417086i
$367$	5.49222	−	9.51281i	0.286692	−	0.496565i	−0.686326	−	0.727294i	$-0.740778\pi$
$367$	5.49222	−	9.51281i	0.286692	−	0.496565i	0.973018	+	0.230729i	$0.0741111\pi$
$368$	3.51346	+	3.26429i	0.183152	+	0.170163i
$369$	3.69620	+	6.40201i	0.192417	+	0.333275i
$370$	5.16109	+	3.31683i	0.268312	+	0.172434i
$371$	−2.12917	−	14.0750i	−0.110541	−	0.730739i
$372$	1.20192	+	2.63184i	0.0623168	+	0.136455i
$373$	−4.30063	−	17.7274i	−0.222678	−	0.917891i	−0.967953	−	0.251133i	$-0.919197\pi$
$373$	−4.30063	−	17.7274i	−0.222678	−	0.917891i	0.745275	−	0.666758i	$-0.232318\pi$
$374$	−2.71284	−	3.80965i	−0.140278	−	0.196993i
$375$	−3.84076	−	11.0972i	−0.198336	−	0.573055i
$376$	11.0713	−	4.43227i	0.570957	−	0.228577i
$377$	31.1448	−	9.14495i	1.60404	−	0.470989i
$378$	−2.59420	+	0.519754i	−0.133431	+	0.0267333i
$379$	−19.0478	+	12.2413i	−0.978419	+	0.628792i	−0.929037	−	0.369988i	$-0.879362\pi$
$379$	−19.0478	+	12.2413i	−0.978419	+	0.628792i	−0.0493828	+	0.998780i	$0.515725\pi$
$380$	2.66357	+	1.37316i	0.136638	+	0.0704418i
$381$	−5.67945	+	1.09463i	−0.290967	+	0.0560793i
$382$	−1.38285	+	5.70018i	−0.0707527	+	0.291647i
$383$	−4.45640	+	1.78407i	−0.227711	+	0.0911619i	−0.482712	−	0.875779i	$-0.660348\pi$
$383$	−4.45640	+	1.78407i	−0.227711	+	0.0911619i	0.255001	+	0.966941i	$0.417924\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−3.51176	+	0.361346i	−0.178976	+	0.0184159i
$386$	6.80868	+	1.99921i	0.346553	+	0.101757i
$387$	−1.79131	+	2.51555i	−0.0910577	+	0.127873i
$388$	8.06718	+	3.22961i	0.409549	+	0.163959i
$389$	−25.2352	+	13.0096i	−1.27948	+	0.659615i	−0.957855	−	0.287253i	$-0.907258\pi$
$389$	−25.2352	+	13.0096i	−1.27948	+	0.659615i	−0.321620	+	0.946869i	$0.604228\pi$
$390$	4.13562	+	7.16310i	0.209415	+	0.362718i
$391$	−2.13469	−	35.2143i	−0.107956	−	1.78087i
$392$	3.41069	−	6.11287i	0.172266	−	0.308747i
$393$	7.08697	+	4.55452i	0.357490	+	0.229745i
$394$	−16.1920	+	12.7335i	−0.815742	+	0.641507i
$395$	8.65024	+	0.825998i	0.435241	+	0.0415605i
$396$	−0.460130	+	0.438733i	−0.0231224	+	0.0220472i
$397$	−21.1112	+	2.01588i	−1.05954	+	0.101174i	−0.610248	−	0.792210i	$-0.708930\pi$
$397$	−21.1112	+	2.01588i	−1.05954	+	0.101174i	−0.449293	+	0.893384i	$0.648324\pi$
$398$	−3.35290	+	3.86945i	−0.168066	+	0.193958i
$399$	3.49672	−	1.42972i	0.175055	−	0.0715757i
$400$	0.571119	−	0.167696i	0.0285560	−	0.00838479i
$401$	−3.80826	+	11.0032i	−0.190175	+	0.549475i	−0.999270	−	0.0382029i	$-0.987837\pi$
$401$	−3.80826	+	11.0032i	−0.190175	+	0.549475i	0.809095	+	0.587678i	$0.199958\pi$
$402$	0.284851	+	5.97976i	0.0142071	+	0.298243i
$403$	−0.542557	−	11.3897i	−0.0270267	−	0.567360i
$404$	−0.0501653	+	0.144943i	−0.00249582	+	0.00721119i
$405$	2.01374	−	0.591287i	0.100064	−	0.0293813i
$406$	17.2275	+	13.3445i	0.854987	+	0.662278i
$407$	1.21704	−	1.40453i	0.0603262	−	0.0696202i
$408$	−7.32287	+	0.699249i	−0.362536	+	0.0346180i
$409$	−25.3301	+	24.1522i	−1.25249	+	1.19425i	−0.280338	+	0.959901i	$0.590446\pi$
$409$	−25.3301	+	24.1522i	−1.25249	+	1.19425i	−0.972153	+	0.234346i	$0.924705\pi$
$410$	15.4446	+	1.47478i	0.762754	+	0.0728342i
$411$	−3.26816	+	2.57011i	−0.161206	+	0.126774i
$412$	6.86854	+	4.41414i	0.338389	+	0.217469i
$413$	13.1657	−	0.0965740i	0.647842	−	0.00475209i
$414$	−4.69702	+	0.968504i	−0.230846	+	0.0475994i
$415$	14.8043	+	25.6418i	0.726713	+	1.25870i
$416$	−3.50292	+	1.80588i	−0.171745	+	0.0885406i
$417$	−3.26182	−	1.30584i	−0.159732	−	0.0639471i
$418$	0.526566	−	0.739458i	0.0257552	−	0.0361681i
$419$	16.7988	+	4.93257i	0.820674	+	0.240972i	0.665006	−	0.746838i	$-0.268429\pi$
$419$	16.7988	+	4.93257i	0.820674	+	0.240972i	0.155668	+	0.987809i	$0.450247\pi$
$420$	−2.26960	+	5.06777i	−0.110745	+	0.247282i
$421$	16.2220	−	18.7212i	0.790612	−	0.912415i	−0.207215	−	0.978295i	$-0.566440\pi$
$421$	16.2220	−	18.7212i	0.790612	−	0.912415i	0.997828	+	0.0658803i	$0.0209855\pi$
$422$	6.60126	−	2.64275i	0.321344	−	0.128647i
$423$	−2.81155	+	11.5894i	−0.136702	+	0.563494i
$424$	−5.28315	+	1.01824i	−0.256573	+	0.0494503i
$425$	−3.89187	−	2.00640i	−0.188783	−	0.0973247i
$426$	0.235891	−	0.151598i	0.0114289	−	0.00734493i
$427$	−20.7234	+	4.15199i	−1.00288	+	0.200929i
$428$	−6.96695	+	2.04568i	−0.336760	+	0.0988818i
$429$	2.32611	−	0.931235i	0.112306	−	0.0449604i
$430$	2.11983	+	6.12485i	0.102227	+	0.295366i
$431$	2.05744	+	2.88927i	0.0991035	+	0.139171i	0.861150	−	0.508351i	$-0.169745\pi$
$431$	2.05744	+	2.88927i	0.0991035	+	0.139171i	−0.762047	+	0.647522i	$0.775805\pi$
$432$	0.235759	+	0.971812i	0.0113430	+	0.0467563i
$433$	12.8761	+	28.1947i	0.618785	+	1.35495i	0.916400	+	0.400264i	$0.131081\pi$
$433$	12.8761	+	28.1947i	0.618785	+	1.35495i	−0.297615	+	0.954686i	$0.596191\pi$
$434$	5.98234	−	4.77600i	0.287162	−	0.229255i
$435$	−14.5420	−	9.34557i	−0.697235	−	0.448086i
$436$	−2.02447	−	3.50648i	−0.0969544	−	0.167930i
$437$	6.32370	−	2.62712i	0.302504	−	0.125672i
$438$	1.57016	−	2.71960i	0.0750252	−	0.129947i
$439$	0.969095	−	20.3438i	0.0462524	−	0.970957i	−0.849827	−	0.527062i	$-0.823293\pi$
$439$	0.969095	−	20.3438i	0.0462524	−	0.970957i	0.896079	−	0.443895i	$-0.146404\pi$
$440$	0.189895	+	1.32075i	0.00905289	+	0.0629642i
$441$	3.00100	+	6.32408i	0.142905	+	0.301147i
$442$	27.8165	+	8.16766i	1.32310	+	0.388496i
$443$	−1.35903	+	0.129772i	−0.0645695	+	0.00616564i	−0.127291	−	0.991865i	$-0.540628\pi$
$443$	−1.35903	+	0.129772i	−0.0645695	+	0.00616564i	0.0627213	+	0.998031i	$0.480022\pi$
$444$	−0.956072	−	2.76239i	−0.0453732	−	0.131097i
$445$	10.0617	+	7.91261i	0.476970	+	0.375094i
$446$	4.93726	+	4.70767i	0.233786	+	0.222914i
$447$	−3.22538	−	3.72229i	−0.152555	−	0.176058i
$448$	−2.36047	−	1.19507i	−0.111522	−	0.0564618i
$449$	−15.9050	+	10.2215i	−0.750605	+	0.482384i	−0.859161	−	0.511706i	$-0.829014\pi$
$449$	−15.9050	+	10.2215i	−0.750605	+	0.482384i	0.108556	+	0.994090i	$0.465377\pi$
$450$	−0.194681	+	0.562493i	−0.00917734	+	0.0265162i
$451$	1.10804	−	4.56741i	0.0521756	−	0.215071i
$452$	14.9245	+	11.7368i	0.701990	+	0.552051i
$453$	0.264701	+	0.0510169i	0.0124367	+	0.00239698i
$454$	7.31504	−	16.0177i	0.343312	−	0.751748i
$455$	15.7267	−	15.2172i	0.737280	−	0.713393i
$456$	−0.593147	−	1.29881i	−0.0277767	−	0.0608224i
$457$	26.1272	−	20.5466i	1.22218	−	0.961131i	0.222273	−	0.974984i	$-0.428652\pi$
$457$	26.1272	−	20.5466i	1.22218	−	0.961131i	0.999904	+	0.0138535i	$0.00440985\pi$
$458$	5.36809	−	2.76744i	0.250834	−	0.129314i
$459$	3.67809	−	6.37064i	0.171678	−	0.297356i
$460$	−4.06239	+	9.20906i	−0.189410	+	0.429374i
$461$	9.78295			0.455637			0.227819	−	0.973704i	$-0.426841\pi$
$461$	9.78295			0.455637			0.227819	+	0.973704i	$0.426841\pi$
$462$	1.42170	+	0.899006i	0.0661436	+	0.0418255i
$463$	4.67051	+	32.4841i	0.217057	+	1.50966i	0.748822	+	0.662772i	$0.230620\pi$
$463$	4.67051	+	32.4841i	0.217057	+	1.50966i	−0.531765	+	0.846892i	$0.678471\pi$
$464$	4.77756	−	6.70914i	0.221793	−	0.311464i
$465$	−4.39476	+	4.19039i	−0.203802	+	0.194325i
$466$	−11.4502	−	16.0796i	−0.530421	−	0.744872i
$467$	17.0584	+	3.28774i	0.789370	+	0.152139i	0.567975	−	0.823046i	$-0.307727\pi$
$467$	17.0584	+	3.28774i	0.789370	+	0.152139i	0.221395	+	0.975184i	$0.428939\pi$
$468$	0.560866	−	3.90091i	0.0259260	−	0.180319i
$469$	15.1642	−	4.57369i	0.700217	−	0.211193i
$470$	16.3903	+	18.9154i	0.756029	+	0.872505i
$471$	4.91508	+	2.53390i	0.226475	+	0.116756i
$472$	−0.236782	−	4.97066i	−0.0108988	−	0.228793i
$473$	1.92789	−	0.371571i	0.0886446	−	0.0170849i
$474$	−2.99652	−	2.85717i	−0.137635	−	0.131234i
$475$	0.120953	−	0.841244i	0.00554969	−	0.0385989i
$476$	6.50033	+	18.3450i	0.297942	+	0.840842i
$477$	2.23509	−	4.89417i	0.102338	−	0.224089i
$478$	0.131903	+	0.543713i	0.00603311	+	0.0248688i
$479$	42.3471	+	4.04365i	1.93489	+	0.184759i	0.989841	−	0.142179i	$-0.0454107\pi$
$479$	42.3471	+	4.04365i	1.93489	+	0.184759i	0.945046	+	0.326938i	$0.106017\pi$
$480$	1.94842	+	0.780028i	0.0889326	+	0.0356033i
$481$	−0.548155	+	11.5072i	−0.0249937	+	0.524683i
$482$	−26.4909			−1.20663
$483$	5.50401	+	11.4327i	0.250441	+	0.520204i
$484$	−10.5958			−0.481627
$485$	−0.867771	+	18.2168i	−0.0394035	+	0.827180i
$486$	−0.928368	−	0.371662i	−0.0421116	−	0.0168590i
$487$	−9.07540	−	0.866595i	−0.411245	−	0.0392692i	−0.112617	−	0.993639i	$-0.535923\pi$
$487$	−9.07540	−	0.866595i	−0.411245	−	0.0392692i	−0.298629	+	0.954369i	$0.596529\pi$
$488$	1.88333	+	7.76319i	0.0852543	+	0.351423i
$489$	−7.53471	+	16.4987i	−0.340731	+	0.746098i
$490$	14.4650	+	2.56842i	0.653463	+	0.116029i
$491$	−2.36593	+	16.4554i	−0.106773	+	0.742622i	0.864151	+	0.503233i	$0.167856\pi$
$491$	−2.36593	+	16.4554i	−0.106773	+	0.742622i	−0.970924	+	0.239389i	$0.923053\pi$
$492$	−5.35013	−	5.10134i	−0.241203	−	0.229986i
$493$	−59.4932	+	11.4664i	−2.67944	+	0.516420i
$494$	0.267751	+	5.62078i	0.0120467	+	0.252891i
$495$	−1.18600	−	0.611426i	−0.0533067	−	0.0274815i
$496$	−1.89471	−	2.18662i	−0.0850751	−	0.0981819i
$497$	−0.540663	−	0.508003i	−0.0242521	−	0.0227870i
$498$	2.00773	−	13.9641i	0.0899686	−	0.625746i
$499$	38.4763	+	7.41570i	1.72244	+	0.331972i	0.952128	−	0.305700i	$-0.0988903\pi$
$499$	38.4763	+	7.41570i	1.72244	+	0.331972i	0.770308	+	0.637672i	$0.220102\pi$
$500$	6.81162	+	9.56558i	0.304625	+	0.427786i
$501$	1.46265	−	1.39464i	0.0653465	−	0.0623077i
$502$	17.0617	−	23.9598i	0.761501	−	1.06938i
$503$	−1.02098	−	7.10105i	−0.0455231	−	0.316620i	−0.999841	−	0.0178272i	$-0.994325\pi$
$503$	−1.02098	−	7.10105i	−0.0455231	−	0.316620i	0.954318	−	0.298793i	$-0.0965840\pi$
$504$	2.34268	−	1.22957i	0.104351	−	0.0547694i
$505$	−0.321905			−0.0143246
$506$	2.58616	+	1.61510i	0.114969	+	0.0718000i
$507$	−1.26582	+	2.19247i	−0.0562171	+	0.0973708i
$508$	5.14101	−	2.65037i	0.228095	−	0.117591i
$509$	27.3968	−	21.5451i	1.21434	−	0.954969i	0.214579	−	0.976707i	$-0.431162\pi$
$509$	27.3968	−	21.5451i	1.21434	−	0.954969i	0.999764	+	0.0217372i	$0.00691971\pi$
$510$	−6.41351	−	14.0436i	−0.283995	−	0.621863i
$511$	−7.98891	−	2.28224i	−0.353409	−	0.100960i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	1.40204	+	0.270221i	0.0619016	+	0.0119305i
$514$	−20.9697	−	16.4908i	−0.924935	−	0.727377i
$515$	−4.03987	+	16.6526i	−0.178018	+	0.733800i
$516$	1.01004	−	2.91832i	0.0444646	−	0.128472i
$517$	6.37831	−	4.09909i	0.280518	−	0.180278i
$518$	−6.47537	+	4.22890i	−0.284512	+	0.185807i
$519$	−14.2975	−	16.5002i	−0.627592	−	0.724279i
$520$	−5.98617	−	5.70780i	−0.262511	−	0.250304i
$521$	−13.1591	−	10.3484i	−0.576509	−	0.453371i	0.286841	−	0.957978i	$-0.407395\pi$
$521$	−13.1591	−	10.3484i	−0.576509	−	0.453371i	−0.863349	+	0.504607i	$0.831637\pi$
$522$	2.69385	+	7.78337i	0.117907	+	0.340669i
$523$	31.4533	−	3.00343i	1.37536	−	0.131331i	0.618950	−	0.785431i	$-0.287558\pi$
$523$	31.4533	−	3.00343i	1.37536	−	0.131331i	0.756408	+	0.654100i	$0.226952\pi$
$524$	−8.08305	−	2.37340i	−0.353110	−	0.103682i
$525$	1.56876	+	0.138194i	0.0684661	+	0.00603128i
$526$	−3.93849	−	27.3928i	−0.171726	−	1.19438i
$527$	−1.01272	+	21.2596i	−0.0441147	+	0.926081i
$528$	0.317886	−	0.550595i	0.0138342	−	0.0239616i
$529$	10.0930	+	20.6672i	0.438825	+	0.898572i
$530$	−5.64605	−	9.77925i	−0.245249	−	0.424783i
$531$	4.18633	+	2.69039i	0.181671	+	0.116753i
$532$	−2.95228	+	2.35695i	−0.127997	+	0.102187i
$533$	12.1025	+	26.5009i	0.524219	+	1.14788i
$534$	−1.43789	−	5.92707i	−0.0622236	−	0.256489i
$535$	−8.83961	−	12.4135i	−0.382170	−	0.536682i
$536$	−1.95801	−	5.65729i	−0.0845730	−	0.244358i
$537$	3.73657	−	1.49590i	0.161245	−	0.0645527i
$538$	7.60314	−	2.23248i	0.327795	−	0.0962492i
$539$	1.39373	−	4.22654i	0.0600324	−	0.182050i
$540$	−1.76558	+	1.13467i	−0.0759787	+	0.0488285i
$541$	9.62661	+	4.96286i	0.413880	+	0.213370i	0.652574	−	0.757725i	$-0.273689\pi$
$541$	9.62661	+	4.96286i	0.413880	+	0.213370i	−0.238694	+	0.971095i	$0.576719\pi$
$542$	22.7291	−	4.38068i	0.976300	−	0.188166i
$543$	−3.73104	+	15.3796i	−0.160114	+	0.660000i
$544$	6.82924	−	2.73401i	0.292801	−	0.117220i
$545$	5.56482	−	6.42215i	0.238371	−	0.275095i
$546$	−10.3722	+	1.06726i	−0.443889	+	0.0456743i
$547$	37.0243	+	10.8713i	1.58304	+	0.464824i	0.950764	−	0.309916i	$-0.100301\pi$
$547$	37.0243	+	10.8713i	1.58304	+	0.464824i	0.632280	+	0.774740i	$0.282119\pi$
$548$	2.41169	−	3.38675i	0.103022	−	0.144675i
$549$	−7.41615	−	2.96898i	−0.316513	−	0.126713i
$550$	0.336363	−	0.173407i	0.0143426	−	0.00739411i
$551$	−5.88011	−	10.1847i	−0.250501	−	0.433881i
$552$	4.23390	−	2.25258i	0.180207	−	0.0958760i
$553$	−5.40744	+	9.52667i	−0.229948	+	0.405115i
$554$	13.7345	+	8.82666i	0.583525	+	0.375009i
$555$	4.82243	−	3.79240i	0.204701	−	0.160979i
$556$	3.49759	+	0.333979i	0.148331	+	0.0141639i
$557$	30.4315	−	29.0164i	1.28943	−	1.22946i	0.331164	−	0.943573i	$-0.392559\pi$
$557$	30.4315	−	29.0164i	1.28943	−	1.22946i	0.958262	−	0.285892i	$-0.0922898\pi$
$558$	2.88021	−	0.275026i	0.121929	−	0.0116428i
$559$	−7.97001	+	9.19788i	−0.337096	+	0.389029i
$560$	0.749907	−	5.50191i	0.0316893	−	0.232498i
$561$	−4.48741	+	1.31762i	−0.189459	+	0.0556301i
$562$	2.60839	−	7.53644i	0.110028	−	0.317905i
$563$	0.868500	+	18.2321i	0.0366029	+	0.768390i	0.940326	+	0.340274i	$0.110520\pi$
$563$	0.868500	+	18.2321i	0.0366029	+	0.768390i	−0.903724	+	0.428116i	$0.859177\pi$
$564$	−0.567439	−	11.9120i	−0.0238935	−	0.501586i
$565$	−13.0331	+	37.6567i	−0.548307	+	1.58423i
$566$	1.45098	−	0.426046i	0.0609892	−	0.0179080i
$567$	−0.357310	+	2.62151i	−0.0150056	+	0.110093i
$568$	−0.183625	+	0.211915i	−0.00770475	+	0.00889175i
$569$	25.6057	−	2.44505i	1.07345	−	0.102502i	0.456667	−	0.889638i	$-0.349043\pi$
$569$	25.6057	−	2.44505i	1.07345	−	0.102502i	0.616779	+	0.787136i	$0.288437\pi$
$570$	2.16881	−	2.06795i	0.0908413	−	0.0866170i
$571$	5.88295	+	0.561753i	0.246194	+	0.0235086i	0.217423	−	0.976077i	$-0.430235\pi$
$571$	5.88295	+	0.561753i	0.246194	+	0.0235086i	0.0287703	+	0.999586i	$0.490841\pi$
$572$	−1.96953	+	1.54885i	−0.0823501	+	0.0647609i
$573$	4.93439	+	3.17114i	0.206137	+	0.132476i
$574$	−9.65473	+	17.0094i	−0.402980	+	0.709959i
$575$	2.84497	+	0.234539i	0.118644	+	0.00978094i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−29.0735	+	14.9884i	−1.21034	+	0.623976i	−0.940784	−	0.339007i	$-0.889909\pi$
$577$	−29.0735	+	14.9884i	−1.21034	+	0.623976i	−0.269561	+	0.962983i	$0.586879\pi$
$578$	−34.4548	−	13.7936i	−1.43313	−	0.573739i
$579$	4.11616	−	5.78033i	0.171062	−	0.240222i
$580$	16.5859	+	4.87006i	0.688692	+	0.202218i
$581$	−37.1294	+	3.82046i	−1.54039	+	0.158499i
$582$	5.69050	−	6.56719i	0.235879	−	0.272219i
$583$	−3.17567	+	1.27135i	−0.131523	+	0.0526538i
$584$	−0.740359	+	3.05180i	−0.0306363	+	0.126284i
$585$	8.12176	−	1.56534i	0.335794	−	0.0647189i
$586$	−24.9926	−	12.8846i	−1.03244	−	0.532258i
$587$	−36.9657	+	23.7564i	−1.52574	+	0.980533i	−0.534986	+	0.844861i	$0.679683\pi$
$587$	−36.9657	+	23.7564i	−1.52574	+	0.980533i	−0.990754	+	0.135672i	$0.956681\pi$
$588$	−4.66114	−	5.22243i	−0.192222	−	0.215369i
$589$	−3.96385	+	1.16389i	−0.163327	+	0.0479572i
$590$	9.69591	−	3.88165i	0.399174	−	0.159805i
$591$	6.73732	+	19.4662i	0.277136	+	0.800733i
$592$	1.69560	+	2.38114i	0.0696887	+	0.0978641i
$593$	−3.95940	−	16.3209i	−0.162593	−	0.670218i	−0.993503	−	0.113810i	$-0.963694\pi$
$593$	−3.95940	−	16.3209i	−0.162593	−	0.670218i	0.830909	−	0.556408i	$-0.187821\pi$
$594$	0.264109	+	0.578319i	0.0108365	+	0.0237287i
$595$	−31.9220	+	25.4849i	−1.30868	+	1.04478i
$596$	4.14342	+	2.66282i	0.169721	+	0.109073i
$597$	2.56001	+	4.43407i	0.104774	+	0.181474i
$598$	−18.7901	+	2.04002i	−0.768382	+	0.0834228i
$599$	−10.0688	+	17.4396i	−0.411398	+	0.712563i	−0.995043	−	0.0994465i	$-0.968293\pi$
$599$	−10.0688	+	17.4396i	−0.411398	+	0.712563i	0.583645	+	0.812009i	$0.301626\pi$
$600$	0.0283222	−	0.594556i	0.00115625	−	0.0242726i
$601$	4.07097	+	28.3142i	0.166058	+	1.15496i	0.886934	+	0.461897i	$0.152831\pi$
$601$	4.07097	+	28.3142i	0.166058	+	1.15496i	−0.720875	+	0.693065i	$0.756260\pi$
$602$	−8.13901	−	0.716978i	−0.331721	−	0.0292218i
$603$	5.74405	+	1.68660i	0.233916	+	0.0686838i
$604$	−0.268352	+	0.0256245i	−0.0109191	+	0.00104264i
$605$	−7.27333	−	21.0149i	−0.295703	−	0.854377i
$606$	0.120564	+	0.0948125i	0.00489757	+	0.00385150i
$607$	−6.58463	−	6.27843i	−0.267262	−	0.254834i	0.544583	−	0.838707i	$-0.316688\pi$
$607$	−6.58463	−	6.27843i	−0.267262	−	0.254834i	−0.811845	+	0.583873i	$0.801536\pi$
$608$	0.935038	+	1.07909i	0.0379208	+	0.0437629i
$609$	18.2452	−	11.9155i	0.739331	−	0.482838i
$610$	−14.1041	+	9.06418i	−0.571060	+	0.366998i
$611$	−15.3718	+	44.4138i	−0.621875	+	1.79679i
$612$	−1.73428	+	7.14882i	−0.0701043	+	0.288974i
$613$	−20.3672	−	16.0169i	−0.822623	−	0.646918i	0.115466	−	0.993311i	$-0.463164\pi$
$613$	−20.3672	−	16.0169i	−0.822623	−	0.646918i	−0.938089	+	0.346393i	$0.887406\pi$
$614$	7.63903	+	1.47230i	0.308286	+	0.0594173i
$615$	6.44510	−	14.1128i	0.259891	−	0.569083i
$616$	−1.61739	−	0.462050i	−0.0651666	−	0.0186165i
$617$	2.06207	+	4.51530i	0.0830157	+	0.181779i	0.946588	−	0.322447i	$-0.104505\pi$
$617$	2.06207	+	4.51530i	0.0830157	+	0.181779i	−0.863572	+	0.504226i	$0.831778\pi$
$618$	6.41785	−	5.04705i	0.258164	−	0.203022i
$619$	−7.03889	+	3.62880i	−0.282917	+	0.145854i	−0.593845	−	0.804580i	$-0.702391\pi$
$619$	−7.03889	+	3.62880i	−0.282917	+	0.145854i	0.310928	+	0.950434i	$0.399360\pi$
$620$	3.03617	−	5.25880i	0.121936	−	0.211199i
$621$	−0.621007	+	4.75545i	−0.0249202	+	0.190830i
$622$	33.1866			1.33066
$623$	−14.2880	+	7.49914i	−0.572436	+	0.300447i
$624$	0.560866	+	3.90091i	0.0224526	+	0.156161i
$625$	−12.5696	+	17.6515i	−0.502783	+	0.706060i
$626$	12.0358	−	11.4761i	0.481045	−	0.458676i
$627$	−0.526566	−	0.739458i	−0.0210290	−	0.0295311i
$628$	−5.42987	−	1.04652i	−0.216675	−	0.0417608i
$629$	3.06024	−	21.2844i	0.122020	−	0.848665i
$630$	4.04674	+	3.80228i	0.161226	+	0.151486i
$631$	5.68047	+	6.55561i	0.226136	+	0.260975i	0.857467	−	0.514538i	$-0.172037\pi$
$631$	5.68047	+	6.55561i	0.226136	+	0.260975i	−0.631331	+	0.775513i	$0.717491\pi$
$632$	3.68010	+	1.89722i	0.146386	+	0.0754674i
$633$	−0.338337	−	7.10256i	−0.0134477	−	0.282301i
$634$	−20.7527	+	3.99976i	−0.824195	+	0.158851i
$635$	8.78552	+	8.37697i	0.348643	+	0.332430i
$636$	−0.765709	+	5.32562i	−0.0303623	+	0.211175i
$637$	9.40434	+	25.9347i	0.372613	+	1.02757i
$638$	2.17530	−	4.76325i	0.0861210	−	0.188579i
$639$	−0.0661077	−	0.272500i	−0.00261518	−	0.0107799i
$640$	−2.08925	−	0.199499i	−0.0825849	−	0.00788590i
$641$	29.3855	+	11.7642i	1.16066	+	0.464657i	0.870426	−	0.492299i	$-0.163844\pi$
$641$	29.3855	+	11.7642i	1.16066	+	0.464657i	0.290231	+	0.956957i	$0.406268\pi$
$642$	−0.345496	+	7.25285i	−0.0136356	+	0.286247i
$643$	18.8890			0.744908			0.372454	−	0.928051i	$-0.378516\pi$
$643$	18.8890			0.744908			0.372454	+	0.928051i	$0.378516\pi$
$644$	−8.50201	−	9.41891i	−0.335026	−	0.371157i
$645$	6.48131			0.255201
$646$	0.499775	−	10.4916i	0.0196634	−	0.412785i
$647$	18.0436	+	7.22358i	0.709368	+	0.283988i	0.698153	−	0.715949i	$-0.254006\pi$
$647$	18.0436	+	7.22358i	0.709368	+	0.283988i	0.0112155	+	0.999937i	$0.496430\pi$
$648$	0.995472	+	0.0950560i	0.0391058	+	0.00373415i
$649$	−0.745893	−	3.07461i	−0.0292789	−	0.120689i
$650$	−0.974487	+	2.13383i	−0.0382225	+	0.0836956i
$651$	−2.55669	−	7.21539i	−0.100205	−	0.282794i
$652$	2.58128	−	17.9532i	0.101091	−	0.703101i
$653$	12.6554	+	12.0669i	0.495244	+	0.472214i	0.896053	−	0.443948i	$-0.146422\pi$
$653$	12.6554	+	12.0669i	0.495244	+	0.472214i	−0.400809	+	0.916162i	$0.631271\pi$
$654$	−3.97577	+	0.766266i	−0.155465	+	0.0299634i
$655$	−0.841273	−	17.6605i	−0.0328713	−	0.690053i
$656$	6.57063	+	3.38740i	0.256540	+	0.132256i
$657$	−2.05647	−	2.37330i	−0.0802307	−	0.0925911i
$658$	−30.2079	+	9.11103i	−1.17762	+	0.355185i
$659$	1.01236	−	7.04109i	0.0394358	−	0.274282i	−0.960557	−	0.278083i	$-0.910301\pi$
$659$	1.01236	−	7.04109i	0.0394358	−	0.274282i	0.999993	+	0.00380129i	$0.00120999\pi$
$660$	1.31022	+	0.252524i	0.0510001	+	0.00982947i
$661$	−18.2535	−	25.6335i	−0.709980	−	0.997027i	−0.999209	−	0.0397673i	$-0.987338\pi$
$661$	−18.2535	−	25.6335i	−0.709980	−	0.997027i	0.289229	−	0.957260i	$-0.406601\pi$
$662$	10.6352	−	10.1407i	0.413350	−	0.394129i
$663$	16.8163	−	23.6152i	0.653092	−	0.917140i
$664$	2.00773	+	13.9641i	0.0779151	+	0.541912i
$665$	−6.70114	−	4.23743i	−0.259859	−	0.164321i
$666$	−2.92316			−0.113270
$667$	32.9504	−	21.7838i	1.27585	−	0.843473i
$668$	−1.01049	+	1.75022i	−0.0390970	+	0.0677180i
$669$	6.06357	−	3.12599i	0.234431	−	0.120858i
$670$	9.87619	−	7.76672i	0.381551	−	0.300055i
$671$	2.10980	+	4.61983i	0.0814481	+	0.178346i
$672$	−1.90138	+	1.83977i	−0.0733472	+	0.0709708i
$673$	−17.1769	+	37.6122i	−0.662122	+	1.44984i	0.218410	+	0.975857i	$0.429913\pi$
$673$	−17.1769	+	37.6122i	−0.662122	+	1.44984i	−0.880532	+	0.473987i	$0.842814\pi$
$674$	−32.3813	−	6.24098i	−1.24728	−	0.240394i
$675$	0.467883	+	0.367947i	0.0180088	+	0.0141623i
$676$	0.596857	−	2.46028i	0.0229560	−	0.0946261i
$677$	9.57887	−	27.6763i	0.368146	−	1.06369i	−0.597060	−	0.802197i	$-0.703665\pi$
$677$	9.57887	−	27.6763i	0.368146	−	1.06369i	0.965206	−	0.261491i	$-0.0842142\pi$
$678$	15.9726	−	10.2650i	0.613423	−	0.394223i
$679$	−20.5116	−	10.3847i	−0.787163	−	0.398530i
$680$	10.1103	+	11.6679i	0.387711	+	0.447442i
$681$	−12.7442	−	12.1516i	−0.488360	−	0.465650i
$682$	−1.44593	−	1.13709i	−0.0553676	−	0.0435416i
$683$	−10.7269	−	30.9935i	−0.410455	−	1.18593i	−0.941039	−	0.338299i	$-0.890148\pi$
$683$	−10.7269	−	30.9935i	−0.410455	−	1.18593i	0.530584	−	0.847633i	$-0.321973\pi$
$684$	−1.42138	+	0.135725i	−0.0543477	+	0.00518958i
$685$	8.37249	+	2.45838i	0.319896	+	0.0939300i
$686$	−10.4083	+	15.3189i	−0.397389	+	0.584878i
$687$	−0.859505	−	5.97799i	−0.0327922	−	0.228075i
$688$	−0.146941	+	3.08467i	−0.00560208	+	0.117602i
$689$	10.6021	−	18.3634i	0.403908	−	0.699589i
$690$	7.37389	+	6.85095i	0.280719	+	0.260811i
$691$	−16.2713	−	28.1828i	−0.618991	−	1.07212i	−0.989670	−	0.143362i	$-0.954209\pi$
$691$	−16.2713	−	28.1828i	−0.618991	−	1.07212i	0.370680	−	0.928761i	$-0.379125\pi$
$692$	18.3670	+	11.8038i	0.698209	+	0.448712i
$693$	1.31455	−	1.04947i	0.0499358	−	0.0398662i
$694$	4.23963	+	9.28350i	0.160934	+	0.352397i
$695$	1.73848	+	7.16611i	0.0659443	+	0.271826i
$696$	−4.77756	−	6.70914i	−0.181093	−	0.254309i
$697$	−17.7859	−	51.3890i	−0.673689	−	1.94650i
$698$	29.1572	−	11.6728i	1.10362	−	0.441821i
$699$	−18.9402	+	5.56135i	−0.716384	+	0.210349i
$700$	−1.54414	+	0.309373i	−0.0583632	+	0.0116932i
$701$	−20.1241	+	12.9330i	−0.760077	+	0.488472i	−0.862368	−	0.506283i	$-0.831019\pi$
$701$	−20.1241	+	12.9330i	−0.760077	+	0.488472i	0.102291	+	0.994755i	$0.467383\pi$
$702$	−3.50292	−	1.80588i	−0.132209	−	0.0681585i
$703$	4.09839	−	0.789899i	0.154574	−	0.0297916i
$704$	−0.149889	+	0.617851i	−0.00564916	+	0.0232861i
$705$	23.2359	−	9.30224i	0.875113	−	0.350343i
$706$	−11.8569	+	13.6836i	−0.446240	+	0.514989i
$707$	0.165864	−	0.370357i	0.00623797	−	0.0139287i
$708$	−4.77473	−	1.40199i	−0.179445	−	0.0526899i
$709$	8.32808	−	11.6952i	0.312768	−	0.439221i	−0.628030	−	0.778189i	$-0.716139\pi$
$709$	8.32808	−	11.6952i	0.312768	−	0.439221i	0.940798	+	0.338968i	$0.110078\pi$
$710$	−0.546343	−	0.218723i	−0.0205039	−	0.00820852i
$711$	−3.68010	+	1.89722i	−0.138014	+	0.0711513i
$712$	3.04950	+	5.28188i	0.114285	+	0.197947i
$713$	−4.70771	−	13.0528i	−0.176305	−	0.488831i
$714$	19.4621	−	0.142760i	0.728350	−	0.00534265i
$715$	−4.42384	−	2.84303i	−0.165442	−	0.106323i
$716$	−3.16377	+	2.48801i	−0.118236	+	0.0929814i
$717$	0.556950	+	0.0531823i	0.0207997	+	0.00198613i
$718$	−21.5060	+	20.5059i	−0.802596	+	0.765274i
$719$	−23.9307	+	2.28511i	−0.892465	+	0.0852201i	−0.531203	−	0.847244i	$-0.678260\pi$
$719$	−23.9307	+	2.28511i	−0.892465	+	0.0852201i	−0.361262	+	0.932464i	$0.617654\pi$
$720$	1.37439	−	1.58613i	0.0512206	−	0.0591117i
$721$	−17.0775	−	13.2283i	−0.636000	−	0.492649i
$722$	−16.2742	+	4.77854i	−0.605664	+	0.177839i
$723$	−8.66433	+	25.0339i	−0.322230	+	0.931022i
$724$	−0.753015	−	15.8077i	−0.0279856	−	0.587490i
$725$	−0.233272	−	4.89698i	−0.00866350	−	0.181869i
$726$	−3.46554	+	10.0130i	−0.128618	+	0.371619i
$727$	28.2706	−	8.30099i	1.04850	−	0.307867i	0.288287	−	0.957544i	$-0.406914\pi$
$727$	28.2706	−	8.30099i	1.04850	−	0.307867i	0.760210	+	0.649677i	$0.225096\pi$
$728$	9.65137	−	3.94621i	0.357704	−	0.146256i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−6.56092	+	0.626492i	−0.242831	+	0.0231875i
$731$	16.4412	−	15.6766i	0.608098	−	0.579821i
$732$	7.95220	+	0.759343i	0.293922	+	0.0280661i
$733$	16.8319	−	13.2368i	0.621701	−	0.488911i	−0.256919	−	0.966433i	$-0.582707\pi$
$733$	16.8319	−	13.2368i	0.621701	−	0.488911i	0.878620	+	0.477522i	$0.158465\pi$
$734$	9.24070	+	5.93864i	0.341081	+	0.219199i
$735$	7.15821	−	12.8294i	0.264034	−	0.473220i
$736$	−3.42777	+	3.35416i	−0.126349	+	0.123636i
$737$	−1.90304	−	3.29616i	−0.0700994	−	0.121416i
$738$	−6.57063	+	3.38740i	−0.241868	+	0.124692i
$739$	−15.6854	−	6.27950i	−0.576998	−	0.230995i	0.0647617	−	0.997901i	$-0.479371\pi$
$739$	−15.6854	−	6.27950i	−0.576998	−	0.230995i	−0.641760	+	0.766905i	$0.721796\pi$
$740$	−3.55865	+	4.99742i	−0.130818	+	0.183709i
$741$	5.39922	+	1.58535i	0.198345	+	0.0582394i
$742$	14.1604	−	1.45704i	0.519844	−	0.0534898i
$743$	−0.152161	+	0.175603i	−0.00558224	+	0.00644224i	−0.758534	−	0.651634i	$-0.774084\pi$
$743$	−0.152161	+	0.175603i	−0.00558224	+	0.00644224i	0.752952	+	0.658076i	$0.228629\pi$
$744$	−2.68605	+	1.07533i	−0.0984755	+	0.0394236i
$745$	−2.43704	+	10.0456i	−0.0892862	+	0.368043i
$746$	17.9120	−	3.45225i	0.655804	−	0.126396i
$747$	−12.5394	−	6.46451i	−0.458793	−	0.236524i
$748$	3.93442	−	2.52850i	0.143857	−	0.0924511i
$749$	18.8367	−	3.77398i	0.688277	−	0.137898i
$750$	11.2673	−	3.30839i	0.411425	−	0.120805i
$751$	32.4771	−	13.0019i	1.18511	−	0.474445i	0.306444	−	0.951889i	$-0.400861\pi$
$751$	32.4771	−	13.0019i	1.18511	−	0.474445i	0.878662	+	0.477444i	$0.158437\pi$
$752$	3.90045	+	11.2696i	0.142235	+	0.410961i
$753$	−17.0617	−	23.9598i	−0.621763	−	0.873144i
$754$	7.65266	+	31.5447i	0.278693	+	1.14879i
$755$	−0.235028	−	0.514639i	−0.00855353	−	0.0187296i
$756$	−0.395729	−	2.61599i	−0.0143925	−	0.0951426i
$757$	30.4129	+	19.5452i	1.10538	+	0.710382i	0.960281	−	0.279036i	$-0.0900150\pi$
$757$	30.4129	+	19.5452i	1.10538	+	0.710382i	0.145095	+	0.989418i	$0.453651\pi$
$758$	−11.3211	−	19.6087i	−0.411200	−	0.712219i
$759$	2.37212	−	1.91567i	0.0861025	−	0.0695345i
$760$	−1.49835	+	2.59521i	−0.0543507	+	0.0941382i
$761$	−1.11847	+	23.4796i	−0.0405445	+	0.851133i	0.883403	+	0.468614i	$0.155246\pi$
$761$	−1.11847	+	23.4796i	−0.0405445	+	0.851133i	−0.923947	+	0.382519i	$0.875057\pi$
$762$	−0.823146	−	5.72511i	−0.0298194	−	0.207399i
$763$	4.52148	+	9.71151i	0.163689	+	0.351580i
$764$	−5.62793	−	1.65251i	−0.203611	−	0.0597857i
$765$	−15.3689	+	1.46755i	−0.555664	+	0.0530595i
$766$	−1.57001	−	4.53624i	−0.0567267	−	0.163901i
$767$	15.4158	+	12.1232i	0.556634	+	0.437742i
$768$	0.723734	+	0.690079i	0.0261155	+	0.0249011i
$769$	−32.4200	−	37.4147i	−1.16909	−	1.34921i	−0.925234	−	0.379397i	$-0.876131\pi$
$769$	−32.4200	−	37.4147i	−1.16909	−	1.34921i	−0.243861	−	0.969810i	$-0.578414\pi$
$770$	−0.193840	−	3.52498i	−0.00698551	−	0.127031i
$771$	−22.4423	+	14.4228i	−0.808240	+	0.519425i
$772$	−2.32092	+	6.70584i	−0.0835316	+	0.241349i
$773$	−3.54088	+	14.5957i	−0.127356	+	0.524971i	0.872014	+	0.489482i	$0.162814\pi$
$773$	−3.54088	+	14.5957i	−0.127356	+	0.524971i	−0.999370	+	0.0354889i	$0.988701\pi$
$774$	−2.42747	−	1.90898i	−0.0872535	−	0.0686169i
$775$	−1.69106	−	0.325925i	−0.0607447	−	0.0117076i
$776$	−3.60981	+	7.90437i	−0.129584	+	0.283750i
$777$	1.87843	+	7.50237i	0.0673883	+	0.269146i
$778$	−11.7942	−	25.8256i	−0.422842	−	0.925894i
$779$	8.29694	−	6.52479i	0.297269	−	0.233775i
$780$	−7.35177	+	3.79010i	−0.263235	+	0.135707i
$781$	−0.0891365	+	0.154389i	−0.00318955	+	0.00552447i
$782$	35.2760	−	0.456711i	1.26147	−	0.0163319i
$783$	8.23636			0.294344
$784$	5.94366	+	3.69769i	0.212274	+	0.132060i
$785$	−1.65166	−	11.4876i	−0.0589503	−	0.410009i
$786$	−4.88657	+	6.86223i	−0.174298	+	0.244768i
$787$	23.3522	−	22.2662i	0.832415	−	0.793706i	−0.148343	−	0.988936i	$-0.547394\pi$
$787$	23.3522	−	22.2662i	0.832415	−	0.793706i	0.980757	+	0.195230i	$0.0625454\pi$
$788$	−11.9487	−	16.7796i	−0.425654	−	0.597747i
$789$	−27.1744	−	5.23743i	−0.967433	−	0.186457i
$790$	−1.23666	+	8.60114i	−0.0439983	+	0.306015i
$791$	−36.6093	−	34.3978i	−1.30168	−	1.22304i
$792$	−0.416342	−	0.480485i	−0.0147941	−	0.0170733i
$793$	−27.9826	−	14.4260i	−0.993692	−	0.512284i
$794$	−1.00908	−	21.1832i	−0.0358109	−	0.751764i
$795$	−11.0880	+	2.13704i	−0.393252	+	0.0757932i
$796$	−3.70553	−	3.53322i	−0.131339	−	0.125232i
$797$	−1.71150	+	11.9037i	−0.0606243	+	0.421652i	0.936796	+	0.349875i	$0.113776\pi$
$797$	−1.71150	+	11.9037i	−0.0606243	+	0.421652i	−0.997421	+	0.0717766i	$0.977133\pi$
$798$	1.26172	+	3.56079i	0.0446645	+	0.126050i
$799$	36.4428	−	79.7985i	1.28925	−	2.82307i
$800$	0.140331	+	0.578452i	0.00496144	+	0.0204514i
$801$	−6.07137	−	0.579746i	−0.214521	−	0.0204843i
$802$	−10.8096	−	4.32750i	−0.381699	−	0.152809i
$803$	−0.0949987	+	1.99427i	−0.00335243	+	0.0703762i
$804$	−5.98654			−0.211129
$805$	12.8447	−	23.3277i	0.452715	−	0.822194i
$806$	11.4026			0.401639
$807$	0.377045	−	7.91515i	0.0132726	−	0.278626i
$808$	−0.142392	−	0.0570052i	−0.00500933	−	0.00200543i
$809$	−47.9971	−	4.58317i	−1.68749	−	0.161136i	−0.793301	−	0.608829i	$-0.791639\pi$
$809$	−47.9971	−	4.58317i	−1.68749	−	0.161136i	−0.894187	+	0.447694i	$0.852245\pi$
$810$	0.494800	+	2.03959i	0.0173855	+	0.0716640i
$811$	−10.0074	+	21.9131i	−0.351406	+	0.769472i	0.648560	+	0.761164i	$0.275372\pi$
$811$	−10.0074	+	21.9131i	−0.351406	+	0.769472i	−0.999965	+	0.00830773i	$0.997356\pi$
$812$	−14.1491	+	16.5730i	−0.496537	+	0.581600i
$813$	3.29422	−	22.9118i	0.115533	−	0.803553i
$814$	1.34503	+	1.28249i	0.0471434	+	0.0449512i
$815$	37.3789	−	7.20418i	1.30932	−	0.252352i
$816$	−0.350021	−	7.34784i	−0.0122532	−	0.257226i
$817$	3.91925	+	2.02051i	0.137117	+	0.0706888i
$818$	−22.9196	−	26.4506i	−0.801363	−	0.924823i
$819$	−2.38386	+	10.1508i	−0.0832987	+	0.354698i
$820$	−2.20799	+	15.3569i	−0.0771064	+	0.536287i
$821$	2.88703	+	0.556429i	0.100758	+	0.0194195i	0.239381	−	0.970926i	$-0.423056\pi$
$821$	2.88703	+	0.556429i	0.100758	+	0.0194195i	−0.138623	+	0.990345i	$0.544268\pi$
$822$	−2.41169	−	3.38675i	−0.0841174	−	0.118126i
$823$	−27.1042	+	25.8438i	−0.944792	+	0.900857i	−0.995199	−	0.0978718i	$-0.968796\pi$
$823$	−27.1042	+	25.8438i	−0.944792	+	0.900857i	0.0504074	+	0.998729i	$0.483948\pi$
$824$	−4.73596	+	6.65073i	−0.164985	+	0.231689i
$825$	−0.0538564	−	0.374579i	−0.00187504	−	0.0130412i
$826$	−0.529985	+	13.1554i	−0.0184405	+	0.457734i
$827$	11.7044			0.407002			0.203501	−	0.979075i	$-0.434768\pi$
$827$	11.7044			0.407002			0.203501	+	0.979075i	$0.434768\pi$
$828$	−0.743914	−	4.73778i	−0.0258528	−	0.164649i
$829$	−5.16005	+	8.93746i	−0.179216	+	0.310411i	−0.941612	−	0.336699i	$-0.890689\pi$
$829$	−5.16005	+	8.93746i	−0.179216	+	0.310411i	0.762396	+	0.647110i	$0.224023\pi$
$830$	−26.3171	+	13.5674i	−0.913481	+	0.470932i
$831$	12.8333	−	10.0922i	0.445183	−	0.350096i
$832$	−1.63716	−	3.58488i	−0.0567583	−	0.124283i
$833$	−12.8728	−	49.8582i	−0.446016	−	1.72749i
$834$	1.45956	−	3.19599i	0.0505405	−	0.110668i
$835$	−4.16489	−	0.802717i	−0.144132	−	0.0277792i
$836$	0.713566	+	0.561154i	0.0246792	+	0.0194079i
$837$	0.682123	−	2.81175i	0.0235776	−	0.0971883i
$838$	−5.72630	+	16.5450i	−0.197812	+	0.571539i
$839$	−12.8219	+	8.24012i	−0.442660	+	0.284481i	−0.742924	−	0.669376i	$-0.766562\pi$
$839$	−12.8219	+	8.24012i	−0.442660	+	0.284481i	0.300264	+	0.953856i	$0.402925\pi$
$840$	−4.95404	−	2.50816i	−0.170931	−	0.0865398i
$841$	−25.4333	−	29.3515i	−0.877009	−	1.01212i
$842$	17.9281	+	17.0944i	0.617844	+	0.589113i
$843$	−6.26882	−	4.92986i	−0.215910	−	0.169793i
$844$	2.32565	+	6.71953i	0.0800523	+	0.231296i
$845$	5.28923	−	0.505061i	0.181955	−	0.0173746i
$846$	−11.4424	−	3.35981i	−0.393399	−	0.115512i
$847$	27.9257	+	2.46001i	0.959538	+	0.0845271i
$848$	−0.765709	−	5.32562i	−0.0262945	−	0.182883i
$849$	0.0719550	−	1.51052i	0.00246949	−	0.0518410i
$850$	2.18931	−	3.79200i	0.0750927	−	0.130064i
$851$	3.48119	+	13.5799i	0.119334	+	0.465512i
$852$	0.140202	+	0.242837i	0.00480324	+	0.00831945i
$853$	−35.2095	−	22.6278i	−1.20555	−	0.774760i	−0.225642	−	0.974210i	$-0.572448\pi$
$853$	−35.2095	−	22.6278i	−1.20555	−	0.774760i	−0.979908	+	0.199451i	$0.936084\pi$
$854$	−3.16123	−	20.8975i	−0.108175	−	0.715097i
$855$	−1.24487	−	2.72589i	−0.0425737	−	0.0932233i
$856$	−1.71186	−	7.05640i	−0.0585103	−	0.241183i
$857$	6.09434	+	8.55830i	0.208179	+	0.292346i	0.905443	−	0.424468i	$-0.139539\pi$
$857$	6.09434	+	8.55830i	0.208179	+	0.292346i	−0.697264	+	0.716814i	$0.745600\pi$
$858$	0.819499	+	2.36779i	0.0279772	+	0.0808349i
$859$	1.09304	−	0.437586i	0.0372939	−	0.0149302i	−0.352941	−	0.935646i	$-0.614818\pi$
$859$	1.09304	−	0.437586i	0.0372939	−	0.0149302i	0.390234	+	0.920716i	$0.372394\pi$
$860$	−6.21877	+	1.82600i	−0.212058	+	0.0622660i
$861$	12.9161	+	14.6870i	0.440181	+	0.500530i
$862$	−2.98390	+	1.91763i	−0.101632	+	0.0653149i
$863$	−20.5627	−	10.6008i	−0.699963	−	0.360856i	0.0712280	−	0.997460i	$-0.477308\pi$
$863$	−20.5627	−	10.6008i	−0.699963	−	0.360856i	−0.771191	+	0.636604i	$0.780339\pi$
$864$	−0.981929	+	0.189251i	−0.0334059	+	0.00643846i
$865$	−10.8029	+	44.5303i	−0.367311	+	1.51408i
$866$	−28.7754	+	11.5199i	−0.977828	+	0.391463i
$867$	−24.3041	+	28.0484i	−0.825409	+	0.952573i
$868$	4.48594	+	6.20282i	0.152263	+	0.210537i
$869$	2.52570	+	0.741612i	0.0856784	+	0.0251574i
$870$	10.0269	−	14.0808i	0.339944	−	0.477385i
$871$	21.9031	+	8.76866i	0.742157	+	0.297115i
$872$	3.59884	−	1.85533i	0.121872	−	0.0628294i
$873$	−4.34482	−	7.52545i	−0.147050	−	0.254698i
$874$	2.32325	+	6.44154i	0.0785850	+	0.217888i
$875$	−15.7315	−	26.7920i	−0.531821	−	0.905733i
$876$	2.64181	+	1.69779i	0.0892584	+	0.0573629i
$877$	35.6369	−	28.0251i	1.20337	−	0.946342i	0.203905	−	0.978991i	$-0.434637\pi$
$877$	35.6369	−	28.0251i	1.20337	−	0.946342i	0.999467	+	0.0326486i	$0.0103942\pi$
$878$	20.2747	+	1.93600i	0.684237	+	0.0653367i
$879$	−20.3502	+	19.4039i	−0.686397	+	0.654478i
$880$	−1.32829	+	0.126836i	−0.0447766	+	0.00427565i
$881$	−22.3848	+	25.8334i	−0.754163	+	0.870351i	−0.994965	−	0.100224i	$-0.968044\pi$
$881$	−22.3848	+	25.8334i	−0.754163	+	0.870351i	0.240802	+	0.970574i	$0.422590\pi$
$882$	−6.45971	+	2.69669i	−0.217510	+	0.0908023i
$883$	−10.8548	+	3.18725i	−0.365293	+	0.107260i	−0.459227	−	0.888319i	$-0.651874\pi$
$883$	−10.8548	+	3.18725i	−0.365293	+	0.107260i	0.0939348	+	0.995578i	$0.470055\pi$
$884$	−9.48198	+	27.3964i	−0.318913	+	0.921440i
$885$	−0.496947	−	10.4322i	−0.0167047	−	0.350675i
$886$	−0.0649595	−	1.36367i	−0.00218236	−	0.0458133i
$887$	0.481618	−	1.39154i	0.0161712	−	0.0467235i	−0.936626	−	0.350330i	$-0.886070\pi$
$887$	0.481618	−	1.39154i	0.0161712	−	0.0467235i	0.952798	+	0.303606i	$0.0981907\pi$
$888$	2.80475	−	0.823550i	0.0941213	−	0.0276365i
$889$	−14.1647	+	5.79159i	−0.475068	+	0.194244i
$890$	−8.38240	+	9.67381i	−0.280979	+	0.324267i
$891$	0.632894	−	0.0604340i	0.0212027	−	0.00202462i
$892$	−4.93726	+	4.70767i	−0.165312	+	0.157624i
$893$	16.9507	+	1.61859i	0.567232	+	0.0541641i
$894$	3.87155	−	3.04462i	0.129484	−	0.101827i
$895$	−7.10626	−	4.56692i	−0.237536	−	0.152655i
$896$	1.30603	−	2.30093i	0.0436315	−	0.0768687i
$897$	−4.21780	+	18.4238i	−0.140828	+	0.615154i
$898$	−9.45317	−	16.3734i	−0.315456	−	0.546386i
$899$	−21.1812	+	10.9197i	−0.706434	+	0.364192i
$900$	−0.552593	−	0.221225i	−0.0184198	−	0.00737416i
$901$	−22.9581	+	32.2401i	−0.764845	+	1.07408i
$902$	4.50951	+	1.32411i	0.150150	+	0.0440881i
$903$	−3.33955	+	7.45687i	−0.111133	+	0.248149i
$904$	−12.4336	+	14.3491i	−0.413536	+	0.477246i
$905$	30.8350	−	12.3445i	1.02499	−	0.410344i
$906$	−0.0635541	+	0.261973i	−0.00211144	+	0.00870348i
$907$	38.1814	−	7.35886i	1.26779	−	0.244347i	0.489363	−	0.872080i	$-0.337229\pi$
$907$	38.1814	−	7.35886i	1.26779	−	0.244347i	0.778428	+	0.627733i	$0.216017\pi$
$908$	15.6515	+	8.06890i	0.519413	+	0.267776i
$909$	0.129031	−	0.0829229i	0.00427967	−	0.00275038i
$910$	14.4517	+	16.4330i	0.479068	+	0.544748i
$911$	−22.1011	+	6.48946i	−0.732241	+	0.215005i	−0.626536	−	0.779392i	$-0.715528\pi$
$911$	−22.1011	+	6.48946i	−0.732241	+	0.215005i	−0.105705	+	0.994398i	$0.533710\pi$
$912$	1.32556	−	0.530676i	0.0438938	−	0.0175724i
$913$	2.93356	+	8.47597i	0.0970868	+	0.280514i
$914$	19.2802	+	27.0752i	0.637732	+	0.895569i
$915$	3.95265	+	16.2930i	0.130670	+	0.538631i
$916$	2.50888	+	5.49369i	0.0828959	+	0.181517i
$917$	20.7522	+	8.13183i	0.685299	+	0.268537i
$918$	6.18841	+	3.97705i	0.204248	+	0.131262i
$919$	−25.7807	−	44.6535i	−0.850427	−	1.47298i	−0.880824	−	0.473444i	$-0.843011\pi$
$919$	−25.7807	−	44.6535i	−0.850427	−	1.47298i	0.0303972	−	0.999538i	$-0.490323\pi$
$920$	−9.00533	−	4.49597i	−0.296897	−	0.148228i
$921$	3.88981	−	6.73735i	0.128174	−	0.222003i
$922$	−0.465491	+	9.77187i	−0.0153301	+	0.321819i
$923$	−0.157269	−	1.09383i	−0.00517656	−	0.0360038i
$924$	−0.965635	+	1.37732i	−0.0317671	+	0.0453103i
$925$	1.66947	+	0.490202i	0.0548919	+	0.0161177i
$926$	−32.6695	+	3.11956i	−1.07359	+	0.102515i
$927$	−2.67040	−	7.71560i	−0.0877073	−	0.253414i
$928$	6.47422	+	5.09138i	0.212527	+	0.167133i
$929$	12.8403	+	12.2432i	0.421276	+	0.401685i	0.870843	−	0.491561i	$-0.163573\pi$
$929$	12.8403	+	12.2432i	0.421276	+	0.401685i	−0.449568	+	0.893246i	$0.648422\pi$
$930$	−3.97654	−	4.58917i	−0.130396	−	0.150485i
$931$	8.32807	−	5.52642i	0.272941	−	0.181121i
$932$	16.6062	−	10.6721i	0.543954	−	0.349578i
$933$	10.8543	−	31.3614i	0.355353	−	1.02673i
$934$	−4.09569	+	16.8827i	−0.134015	+	0.552418i
$935$	7.71556	+	6.06758i	0.252326	+	0.198431i
$936$	3.86980	+	0.745843i	0.126488	+	0.0243786i
$937$	−6.81789	+	14.9291i	−0.222731	+	0.487712i	−0.987701	−	0.156353i	$-0.950026\pi$
$937$	−6.81789	+	14.9291i	−0.222731	+	0.487712i	0.764970	+	0.644065i	$0.222754\pi$
$938$	3.84697	+	15.3646i	0.125608	+	0.501673i
$939$	−6.90838	−	15.1272i	−0.225447	−	0.493659i
$940$	−19.6739	+	15.4717i	−0.641692	+	0.504632i
$941$	−5.60260	+	2.88834i	−0.182640	+	0.0941573i	−0.547121	−	0.837053i	$-0.684276\pi$
$941$	−5.60260	+	2.88834i	−0.182640	+	0.0941573i	0.364482	+	0.931210i	$0.381246\pi$
$942$	−2.76490	+	4.78895i	−0.0900853	+	0.156032i
$943$	23.5615	+	26.4906i	0.767268	+	0.862652i
$944$	4.97630			0.161965
$945$	4.91671	−	2.58057i	0.159941	−	0.0839458i
$946$	0.279417	+	1.94339i	0.00908464	+	0.0631851i
$947$	24.4700	−	34.3633i	0.795168	−	1.11666i	−0.195546	−	0.980694i	$-0.562648\pi$
$947$	24.4700	−	34.3633i	0.795168	−	1.11666i	0.990714	−	0.135962i	$-0.0434126\pi$
$948$	2.99652	−	2.85717i	0.0973223	−	0.0927967i
$949$	−7.17882	−	10.0812i	−0.233035	−	0.327251i
$950$	0.834536	+	0.160844i	0.0270759	+	0.00521846i
$951$	−3.00777	+	20.9195i	−0.0975337	+	0.678362i
$952$	−18.6335	+	5.62008i	−0.603916	+	0.182148i
$953$	10.5125	+	12.1320i	0.340532	+	0.392995i	0.900024	−	0.435841i	$-0.143549\pi$
$953$	10.5125	+	12.1320i	0.340532	+	0.392995i	−0.559491	+	0.828836i	$0.689003\pi$
$954$	4.78228	+	2.46543i	0.154832	+	0.0798214i
$955$	−0.585747	−	12.2964i	−0.0189543	−	0.397901i
$956$	−0.549373	+	0.105883i	−0.0177680	+	0.00342450i
$957$	−3.78980	−	3.61357i	−0.122507	−	0.116810i
$958$	−6.05403	+	42.1067i	−0.195597	+	1.36041i
$959$	−7.14242	+	8.36600i	−0.230641	+	0.270152i
$960$	−0.871854	+	1.90909i	−0.0281390	+	0.0616157i
$961$	−5.33494	−	21.9909i	−0.172095	−	0.709384i
$962$	−11.4681	−	1.09507i	−0.369745	−	0.0353064i
$963$	6.74095	+	2.69867i	0.217224	+	0.0869634i
$964$	1.26049	−	26.4609i	0.0405976	−	0.852249i
$965$	−14.8930			−0.479423
$966$	−11.6816	+	4.95379i	−0.375850	+	0.159385i
$967$	−42.9524			−1.38125			−0.690627	−	0.723211i	$-0.742666\pi$
$967$	−42.9524			−1.38125			−0.690627	+	0.723211i	$0.742666\pi$
$968$	0.504168	−	10.5838i	0.0162046	−	0.340176i
$969$	−9.75108	−	3.90374i	−0.313250	−	0.125406i
$970$	−18.1548	−	1.73358i	−0.582917	−	0.0556618i
$971$	−4.77781	−	19.6944i	−0.153327	−	0.632024i	−0.995660	−	0.0930658i	$-0.970333\pi$
$971$	−4.77781	−	19.6944i	−0.153327	−	0.632024i	0.842333	−	0.538958i	$-0.181182\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	−9.14052	−	1.69225i	−0.293032	−	0.0542510i
$974$	1.29744	−	9.02388i	0.0415726	−	0.289144i
$975$	1.69775	+	1.61880i	0.0543714	+	0.0518430i
$976$	−7.84401	+	1.51181i	−0.251081	+	0.0483918i
$977$	0.929683	+	19.5164i	0.0297432	+	0.624387i	0.963698	+	0.266995i	$0.0860308\pi$
$977$	0.929683	+	19.5164i	0.0297432	+	0.624387i	−0.933955	+	0.357391i	$0.883666\pi$
$978$	−16.1215	−	8.31122i	−0.515509	−	0.265763i
$979$	2.53927	+	2.93047i	0.0811554	+	0.0936583i
$980$	−3.25379	+	14.3264i	−0.103938	+	0.457641i
$981$	−0.576224	+	4.00772i	−0.0183974	+	0.127957i
$982$	−16.3242	−	3.14623i	−0.520926	−	0.100400i
$983$	28.4906	+	40.0094i	0.908709	+	1.27610i	0.960738	+	0.277458i	$0.0894918\pi$
$983$	28.4906	+	40.0094i	0.908709	+	1.27610i	−0.0520289	+	0.998646i	$0.516569\pi$
$984$	5.35013	−	5.10134i	0.170556	−	0.162625i
$985$	25.0773	−	35.2162i	0.799030	−	1.12208i
$986$	−8.62259	−	59.9714i	−0.274599	−	1.90988i
$987$	−1.27009	+	31.5264i	−0.0404273	+	1.00350i
$988$	−5.62716			−0.179024
$989$	−5.97752	+	13.5505i	−0.190074	+	0.430880i
$990$	0.667165	−	1.15556i	0.0212039	−	0.0367262i
$991$	37.2791	−	19.2187i	1.18421	−	0.610502i	0.250354	−	0.968154i	$-0.419453\pi$
$991$	37.2791	−	19.2187i	1.18421	−	0.610502i	0.933855	+	0.357653i	$0.116423\pi$
$992$	2.27429	−	1.78852i	0.0722089	−	0.0567857i
$993$	−6.10450	−	13.3670i	−0.193721	−	0.424189i
$994$	0.533153	−	0.515879i	0.0169106	−	0.0163627i
$995$	4.46391	−	9.77460i	0.141515	−	0.309876i
$996$	13.8527	+	2.66990i	0.438941	+	0.0845989i
$997$	41.0413	+	32.2753i	1.29979	+	1.02217i	0.997623	+	0.0689137i	$0.0219533\pi$
$997$	41.0413	+	32.2753i	1.29979	+	1.02217i	0.302170	+	0.953254i	$0.402289\pi$
$998$	−9.23808	+	38.0799i	−0.292426	+	1.20540i
$999$	−0.956072	+	2.76239i	−0.0302488	+	0.0873981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.25.2	✓	160
7.2	even	3	inner	966.2.y.b.163.2	yes	160
23.12	even	11	inner	966.2.y.b.403.2	yes	160
161.58	even	33	inner	966.2.y.b.541.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.25.2	✓	160	1.1	even	1	trivial
966.2.y.b.163.2	yes	160	7.2	even	3	inner
966.2.y.b.403.2	yes	160	23.12	even	11	inner
966.2.y.b.541.2	yes	160	161.58	even	33	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.494800 - 2.03959i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.60154 + 0.481642i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(-0.494800 - 2.03959i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(2.60154 + 0.481642i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(2.06083 - 0.397192i) q^{10} +(-0.0302513 - 0.635052i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(2.58082 + 2.97842i) q^{13} +(-0.604883 + 2.57568i) q^{14} +(0.298684 - 2.07739i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-4.26700 - 5.99216i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(0.828230 - 1.16309i) q^{19} +(0.298684 + 2.07739i) q^{20} +(2.23618 + 1.41404i) q^{21} +0.635773 q^{22} +(4.06774 + 2.54038i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.529062 - 0.272750i) q^{25} +(-3.09785 + 2.43618i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-2.54398 - 0.726754i) q^{28} +(3.42151 - 7.49206i) q^{29} +(2.06083 + 0.397192i) q^{30} +(-2.27429 - 1.78852i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(0.207941 - 0.600806i) q^{33} +(6.18841 - 3.97705i) q^{34} +(-0.304889 - 5.54441i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(2.11559 + 2.01721i) q^{37} +(1.12236 + 0.882634i) q^{38} +(1.28898 + 3.72427i) q^{39} +(-2.08925 + 0.199499i) q^{40} +(7.09296 + 2.08268i) q^{41} +(-1.51884 + 2.16636i) q^{42} +(0.439493 + 3.05674i) q^{43} +(-0.0302513 + 0.635052i) q^{44} +(1.04938 - 1.81757i) q^{45} +(-2.73105 + 3.94225i) q^{46} +(5.96276 + 10.3278i) q^{47} +(0.841254 + 0.540641i) q^{48} +(6.53604 + 2.50602i) q^{49} +(0.247268 + 0.541440i) q^{50} +(-1.73428 - 7.14882i) q^{51} +(-2.28602 - 3.21026i) q^{52} +(-1.75975 - 5.08447i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(-1.28028 + 0.375924i) q^{55} +(0.846978 - 2.50652i) q^{56} +(1.20118 - 0.771950i) q^{57} +(7.32077 + 3.77412i) q^{58} +(4.88637 - 0.941771i) q^{59} +(-0.494800 + 2.03959i) q^{60} +(-7.41615 + 2.96898i) q^{61} +(1.89471 - 2.18662i) q^{62} +(1.55045 + 2.14385i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(4.79779 - 6.73755i) q^{65} +(0.590231 + 0.236293i) q^{66} +(5.32105 - 2.74319i) q^{67} +(3.67809 + 6.37064i) q^{68} +(2.83220 + 3.87023i) q^{69} +(5.55263 - 0.0407301i) q^{70} +(-0.235891 - 0.151598i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-3.12610 - 0.298507i) q^{73} +(-2.11559 + 2.01721i) q^{74} +(0.592535 - 0.0565802i) q^{75} +(-0.935038 + 1.07909i) q^{76} +(0.227168 - 1.66669i) q^{77} +(-3.78138 + 1.11031i) q^{78} +(-1.35418 + 3.91264i) q^{79} +(-0.0998628 - 2.09638i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-2.41782 + 6.98583i) q^{82} +(-13.5362 + 3.97459i) q^{83} +(-2.09164 - 1.62020i) q^{84} +(-10.1103 + 11.6679i) q^{85} +(-3.07419 + 0.293549i) q^{86} +(5.96094 - 5.68374i) q^{87} +(-0.632894 - 0.0604340i) q^{88} +(-4.79413 + 3.77015i) q^{89} +(1.76558 + 1.13467i) q^{90} +(5.27958 + 8.99153i) q^{91} +(-3.80784 - 2.91554i) q^{92} +(-1.44665 - 2.50568i) q^{93} +(-10.5998 + 5.46459i) q^{94} +(-2.78203 - 1.11376i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-8.33765 - 2.44815i) q^{97} +(-2.81418 + 6.40940i) q^{98} +(0.416342 - 0.480485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

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Database

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