LMFDB - Embedded newform 966.2.y.d.151.3

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			151.3
Character	$\chi$	$=$	966.151
Dual form			966.2.y.d.499.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.688242 + 0.0657192i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.529942 + 2.59213i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.688242 + 0.0657192i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.529942 + 2.59213i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.162997 - 0.671884i) q^{10} +(-0.0272369 - 0.0786957i) q^{11} +(0.981929 + 0.189251i) q^{12} +(-1.15597 + 0.339424i) q^{13} +(-2.27624 - 1.34860i) q^{14} +(0.581620 - 0.373784i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-6.02025 - 2.41014i) q^{17} +(0.580057 + 0.814576i) q^{18} +(0.105416 - 0.0422021i) q^{19} +(0.581620 + 0.373784i) q^{20} +(-0.716754 - 2.54681i) q^{21} +0.0832758 q^{22} +(4.08272 - 2.51623i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.44028 + 0.855795i) q^{25} +(0.0573254 - 1.20341i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(2.01891 - 1.70997i) q^{28} +(1.01320 + 7.04695i) q^{29} +(0.162997 + 0.671884i) q^{30} +(-0.0791064 - 1.66065i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(0.0602696 + 0.0574669i) q^{33} +(4.24662 - 4.90086i) q^{34} +(0.194376 - 1.81884i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.03879 + 1.45878i) q^{37} +(0.00540291 + 0.113421i) q^{38} +(0.871935 - 0.831388i) q^{39} +(-0.543456 + 0.427378i) q^{40} +(4.40214 - 9.63933i) q^{41} +(2.64117 + 0.155649i) q^{42} +(-7.68417 - 4.93831i) q^{43} +(-0.0272369 + 0.0786957i) q^{44} +(-0.345687 + 0.598747i) q^{45} +(1.04251 + 4.68115i) q^{46} +(-3.83788 - 6.64740i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(-6.43832 - 2.74736i) q^{49} +(0.643548 - 4.47598i) q^{50} +(6.45540 - 0.616416i) q^{51} +(1.11847 + 0.447769i) q^{52} +(6.83325 - 6.51550i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(0.0239174 + 0.0523718i) q^{55} +(0.955598 + 2.46715i) q^{56} +(-0.0743592 + 0.0858151i) q^{57} +(-6.99076 - 1.34736i) q^{58} +(3.31088 - 13.6476i) q^{59} +(-0.688242 - 0.0657192i) q^{60} +(0.499662 + 0.257594i) q^{61} +(1.59519 + 0.468389i) q^{62} +(1.80409 + 1.93526i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.773282 - 0.309575i) q^{65} +(-0.0740185 + 0.0381592i) q^{66} +(7.92804 - 1.52800i) q^{67} +(3.24238 + 5.61597i) q^{68} +(-2.47586 + 4.10732i) q^{69} +(1.65524 + 0.778571i) q^{70} +(-4.17739 - 4.82096i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-4.55053 - 3.57857i) q^{73} +(-1.03879 - 1.45878i) q^{74} +(3.55453 - 2.79532i) q^{75} +(-0.108950 - 0.0319906i) q^{76} +(0.218424 - 0.0288974i) q^{77} +(0.500481 + 1.09590i) q^{78} +(2.62865 + 2.50641i) q^{79} +(-0.226126 - 0.653348i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(7.66938 + 7.31274i) q^{82} +(-4.35093 - 9.52721i) q^{83} +(-1.01093 + 2.44500i) q^{84} +(4.30178 + 1.26312i) q^{85} +(7.17996 - 5.64638i) q^{86} +(-4.12966 - 5.79930i) q^{87} +(-0.0654592 - 0.0514777i) q^{88} +(-0.813308 + 17.0734i) q^{89} +(-0.452753 - 0.522505i) q^{90} +(-0.267234 - 3.17631i) q^{91} +(-4.76466 - 0.545878i) q^{92} +(0.831266 + 1.43979i) q^{93} +(7.53704 - 1.45265i) q^{94} +(-0.0697782 + 0.0359731i) q^{95} +(0.928368 - 0.371662i) q^{96} +(-7.90282 + 17.3048i) q^{97} +(4.70203 - 5.18565i) q^{98} +(-0.0799026 - 0.0234615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−0.688242	+	0.0657192i	−0.307791	+	0.0293905i	−0.247809	−	0.968809i	$-0.579711\pi$
$5$	−0.688242	+	0.0657192i	−0.307791	+	0.0293905i	−0.0599824	+	0.998199i	$0.519104\pi$
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−0.529942	+	2.59213i	−0.200299	+	0.979735i
$7$	−0.529942	+	2.59213i	−0.200299	+	0.979735i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.580057	−	0.814576i	0.193352	−	0.271525i
$10$	0.162997	−	0.671884i	0.0515443	−	0.212468i
$11$	−0.0272369	−	0.0786957i	−0.00821222	−	0.0237277i	0.940820	−	0.338906i	$-0.110057\pi$
$11$	−0.0272369	−	0.0786957i	−0.00821222	−	0.0237277i	−0.949032	+	0.315178i	$0.897936\pi$
$12$	0.981929	+	0.189251i	0.283458	+	0.0546321i
$13$	−1.15597	+	0.339424i	−0.320609	+	0.0941392i	−0.438077	−	0.898937i	$-0.644340\pi$
$13$	−1.15597	+	0.339424i	−0.320609	+	0.0941392i	0.117468	+	0.993077i	$0.462522\pi$
$14$	−2.27624	−	1.34860i	−0.608351	−	0.360428i
$15$	0.581620	−	0.373784i	0.150174	−	0.0965107i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−6.02025	−	2.41014i	−1.46012	−	0.584546i	−0.500476	−	0.865750i	$-0.666842\pi$
$17$	−6.02025	−	2.41014i	−1.46012	−	0.584546i	−0.959648	+	0.281205i	$0.909266\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	0.105416	−	0.0422021i	0.0241841	−	0.00968183i	−0.359539	−	0.933130i	$-0.617066\pi$
$19$	0.105416	−	0.0422021i	0.0241841	−	0.00968183i	0.383723	+	0.923448i	$0.374642\pi$
$20$	0.581620	+	0.373784i	0.130054	+	0.0835808i
$21$	−0.716754	−	2.54681i	−0.156408	−	0.555760i
$22$	0.0832758			0.0177545
$23$	4.08272	−	2.51623i	0.851305	−	0.524670i
$23$	4.08272	−	2.51623i	0.851305	−	0.524670i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.44028	+	0.855795i	−0.888057	+	0.171159i
$26$	0.0573254	−	1.20341i	0.0112424	−	0.236008i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	2.01891	−	1.70997i	0.381539	−	0.323153i
$29$	1.01320	+	7.04695i	0.188146	+	1.30859i	0.836803	+	0.547504i	$0.184422\pi$
$29$	1.01320	+	7.04695i	0.188146	+	1.30859i	−0.648657	+	0.761081i	$0.724669\pi$
$30$	0.162997	+	0.671884i	0.0297591	+	0.122669i
$31$	−0.0791064	−	1.66065i	−0.0142079	−	0.298261i	−0.994776	−	0.102082i	$-0.967450\pi$
$31$	−0.0791064	−	1.66065i	−0.0142079	−	0.298261i	0.980568	−	0.196179i	$-0.0628534\pi$
$32$	−0.995472	−	0.0950560i	−0.175976	−	0.0168037i
$33$	0.0602696	+	0.0574669i	0.0104916	+	0.0100037i
$34$	4.24662	−	4.90086i	0.728289	−	0.840490i
$35$	0.194376	−	1.81884i	0.0328555	−	0.307441i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−1.03879	+	1.45878i	−0.170777	+	0.239822i	−0.891090	−	0.453826i	$-0.850059\pi$
$37$	−1.03879	+	1.45878i	−0.170777	+	0.239822i	0.720313	+	0.693649i	$0.243998\pi$
$38$	0.00540291	+	0.113421i	0.000876468	+	0.0183993i
$39$	0.871935	−	0.831388i	0.139621	−	0.133129i
$40$	−0.543456	+	0.427378i	−0.0859279	+	0.0675745i
$41$	4.40214	−	9.63933i	0.687498	−	1.50541i	−0.167000	−	0.985957i	$-0.553408\pi$
$41$	4.40214	−	9.63933i	0.687498	−	1.50541i	0.854498	−	0.519454i	$-0.173865\pi$
$42$	2.64117	+	0.155649i	0.407541	+	0.0240171i
$43$	−7.68417	−	4.93831i	−1.17182	−	0.753086i	−0.197959	−	0.980210i	$-0.563431\pi$
$43$	−7.68417	−	4.93831i	−1.17182	−	0.753086i	−0.973866	+	0.227124i	$0.927068\pi$
$44$	−0.0272369	+	0.0786957i	−0.00410611	+	0.0118638i
$45$	−0.345687	+	0.598747i	−0.0515319	+	0.0892559i
$46$	1.04251	+	4.68115i	0.153710	+	0.690198i
$47$	−3.83788	−	6.64740i	−0.559812	−	0.969623i	−0.997512	−	0.0705016i	$-0.977540\pi$
$47$	−3.83788	−	6.64740i	−0.559812	−	0.969623i	0.437700	−	0.899121i	$-0.355793\pi$
$48$	−0.654861	−	0.755750i	−0.0945210	−	0.109083i
$49$	−6.43832	−	2.74736i	−0.919760	−	0.392480i
$50$	0.643548	−	4.47598i	0.0910115	−	0.632999i
$51$	6.45540	−	0.616416i	0.903937	−	0.0863155i
$52$	1.11847	+	0.447769i	0.155104	+	0.0620944i
$53$	6.83325	−	6.51550i	0.938620	−	0.894972i	−0.0560141	−	0.998430i	$-0.517839\pi$
$53$	6.83325	−	6.51550i	0.938620	−	0.894972i	0.994634	+	0.103458i	$0.0329907\pi$
$54$	−0.888835	−	0.458227i	−0.120955	−	0.0623567i
$55$	0.0239174	+	0.0523718i	0.00322502	+	0.00706181i
$56$	0.955598	+	2.46715i	0.127697	+	0.329687i
$57$	−0.0743592	+	0.0858151i	−0.00984912	+	0.0113665i
$58$	−6.99076	−	1.34736i	−0.917931	−	0.176917i
$59$	3.31088	−	13.6476i	0.431039	−	1.77677i	−0.178423	−	0.983954i	$-0.557100\pi$
$59$	3.31088	−	13.6476i	0.431039	−	1.77677i	0.609463	−	0.792815i	$-0.291385\pi$
$60$	−0.688242	−	0.0657192i	−0.0888517	−	0.00848431i
$61$	0.499662	+	0.257594i	0.0639752	+	0.0329815i	0.489917	−	0.871769i	$-0.337027\pi$
$61$	0.499662	+	0.257594i	0.0639752	+	0.0329815i	−0.425942	+	0.904750i	$0.640057\pi$
$62$	1.59519	+	0.468389i	0.202589	+	0.0594855i
$63$	1.80409	+	1.93526i	0.227294	+	0.243820i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.773282	−	0.309575i	0.0959138	−	0.0383981i
$66$	−0.0740185	+	0.0381592i	−0.00911105	+	0.00469707i
$67$	7.92804	−	1.52800i	0.968564	−	0.186675i	0.319649	−	0.947536i	$-0.396435\pi$
$67$	7.92804	−	1.52800i	0.968564	−	0.186675i	0.648915	+	0.760861i	$0.275223\pi$
$68$	3.24238	+	5.61597i	0.393197	+	0.681036i
$69$	−2.47586	+	4.10732i	−0.298059	+	0.494464i
$70$	1.65524	+	0.778571i	0.197838	+	0.0930570i
$71$	−4.17739	−	4.82096i	−0.495765	−	0.572143i	0.451632	−	0.892204i	$-0.350842\pi$
$71$	−4.17739	−	4.82096i	−0.495765	−	0.572143i	−0.947397	+	0.320061i	$0.896296\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	−4.55053	−	3.57857i	−0.532599	−	0.418840i	0.315305	−	0.948990i	$-0.397893\pi$
$73$	−4.55053	−	3.57857i	−0.532599	−	0.418840i	−0.847904	+	0.530150i	$0.822136\pi$
$74$	−1.03879	−	1.45878i	−0.120757	−	0.169580i
$75$	3.55453	−	2.79532i	0.410442	−	0.322775i
$76$	−0.108950	−	0.0319906i	−0.0124974	−	0.00366958i
$77$	0.218424	−	0.0288974i	0.0248917	−	0.00329317i
$78$	0.500481	+	1.09590i	0.0566683	+	0.124086i
$79$	2.62865	+	2.50641i	0.295746	+	0.281993i	0.823394	−	0.567470i	$-0.192078\pi$
$79$	2.62865	+	2.50641i	0.295746	+	0.281993i	−0.527648	+	0.849463i	$0.676926\pi$
$80$	−0.226126	−	0.653348i	−0.0252817	−	0.0730465i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	7.66938	+	7.31274i	0.846941	+	0.807557i
$83$	−4.35093	−	9.52721i	−0.477577	−	1.04575i	−0.983123	−	0.182947i	$-0.941436\pi$
$83$	−4.35093	−	9.52721i	−0.477577	−	1.04575i	0.505546	−	0.862800i	$-0.331291\pi$
$84$	−1.01093	+	2.44500i	−0.110301	+	0.266771i
$85$	4.30178	+	1.26312i	0.466594	+	0.137004i
$86$	7.17996	−	5.64638i	0.774235	−	0.608865i
$87$	−4.12966	−	5.79930i	−0.442747	−	0.621751i
$88$	−0.0654592	−	0.0514777i	−0.00697798	−	0.00548754i
$89$	−0.813308	+	17.0734i	−0.0862104	+	1.80978i	0.379873	+	0.925039i	$0.375968\pi$
$89$	−0.813308	+	17.0734i	−0.0862104	+	1.80978i	−0.466083	+	0.884741i	$0.654335\pi$
$90$	−0.452753	−	0.522505i	−0.0477244	−	0.0550769i
$91$	−0.267234	−	3.17631i	−0.0280138	−	0.332968i
$92$	−4.76466	−	0.545878i	−0.496750	−	0.0569117i
$93$	0.831266	+	1.43979i	0.0861982	+	0.149300i
$94$	7.53704	−	1.45265i	0.777387	−	0.149829i
$95$	−0.0697782	+	0.0359731i	−0.00715909	+	0.00369077i
$96$	0.928368	−	0.371662i	0.0947512	−	0.0379326i
$97$	−7.90282	+	17.3048i	−0.802409	+	1.75703i	−0.165322	+	0.986240i	$0.552866\pi$
$97$	−7.90282	+	17.3048i	−0.802409	+	1.75703i	−0.637087	+	0.770792i	$0.719861\pi$
$98$	4.70203	−	5.18565i	0.474977	−	0.523829i
$99$	−0.0799026	−	0.0234615i	−0.00803051	−	0.00235797i
$100$	4.01932	+	2.07210i	0.401932	+	0.207210i
$101$	−1.86855	−	0.178425i	−0.185928	−	0.0177540i	0.00167675	−	0.999999i	$-0.499466\pi$
$101$	−1.86855	−	0.178425i	−0.185928	−	0.0177540i	−0.187605	+	0.982245i	$0.560072\pi$
$102$	−1.52884	+	6.30197i	−0.151378	+	0.623988i
$103$	−8.00700	−	1.54322i	−0.788953	−	0.152058i	−0.221169	−	0.975236i	$-0.570987\pi$
$103$	−8.00700	−	1.54322i	−0.788953	−	0.152058i	−0.567784	+	0.823177i	$0.692199\pi$
$104$	−0.788958	+	0.910507i	−0.0773637	+	0.0892825i
$105$	0.660675	+	1.70572i	0.0644753	+	0.166461i
$106$	3.92221	+	8.58844i	0.380959	+	0.834183i
$107$	−13.5871	−	7.00464i	−1.31351	−	0.677164i	−0.347996	−	0.937496i	$-0.613138\pi$
$107$	−13.5871	−	7.00464i	−1.31351	−	0.677164i	−0.965519	+	0.260332i	$0.916168\pi$
$108$	0.723734	−	0.690079i	0.0696413	−	0.0664029i
$109$	4.75080	+	1.90193i	0.455044	+	0.182172i	0.587850	−	0.808970i	$-0.299974\pi$
$109$	4.75080	+	1.90193i	0.455044	+	0.182172i	−0.132806	+	0.991142i	$0.542399\pi$
$110$	−0.0573140	+	0.00547282i	−0.00546467	+	0.000521813i
$111$	0.254864	−	1.77262i	0.0241906	−	0.168250i
$112$	−2.64400	+	0.0961152i	−0.249835	+	0.00908203i
$113$	5.21052	+	6.01326i	0.490164	+	0.565680i	0.945909	−	0.324431i	$-0.105173\pi$
$113$	5.21052	+	6.01326i	0.490164	+	0.565680i	−0.455745	+	0.890110i	$0.650627\pi$
$114$	−0.0567748	−	0.0983369i	−0.00531745	−	0.00921009i
$115$	−2.64454	+	2.00009i	−0.246604	+	0.186509i
$116$	3.55971	−	6.16559i	0.330510	−	0.572461i
$117$	−0.394043	+	1.13851i	−0.0364293	+	0.105255i
$118$	11.8141	+	7.59248i	1.08758	+	0.698944i
$119$	9.43780	−	14.3281i	0.865161	−	1.31345i
$120$	0.287207	−	0.628895i	0.0262183	−	0.0574100i
$121$	8.64113	−	6.79546i	0.785558	−	0.617769i
$122$	−0.406850	+	0.387931i	−0.0368345	+	0.0351216i
$123$	0.504224	+	10.5850i	0.0454643	+	0.954414i
$124$	−0.964363	+	1.35426i	−0.0866023	+	0.121616i
$125$	6.31659	−	1.85472i	0.564973	−	0.165891i
$126$	−2.41889	+	1.07191i	−0.215492	+	0.0954931i
$127$	−11.1906	+	12.9146i	−0.993002	+	1.14599i	−0.00371607	+	0.999993i	$0.501183\pi$
$127$	−11.1906	+	12.9146i	−0.993002	+	1.14599i	−0.989286	+	0.145992i	$0.953363\pi$
$128$	0.723734	+	0.690079i	0.0639697	+	0.0609949i
$129$	9.09283	+	0.868260i	0.800579	+	0.0764460i
$130$	0.0396332	+	0.832004i	0.00347606	+	0.0729716i
$131$	−0.652064	−	2.68784i	−0.0569711	−	0.234838i	0.936206	−	0.351451i	$-0.114312\pi$
$131$	−0.652064	−	2.68784i	−0.0569711	−	0.234838i	−0.993177	+	0.116613i	$0.962796\pi$
$132$	−0.0118514	−	0.0824282i	−0.00103153	−	0.00717445i
$133$	0.0535293	+	0.295617i	0.00464158	+	0.0256332i
$134$	−1.14904	+	7.99177i	−0.0992622	+	0.690383i
$135$	0.0328969	−	0.690590i	0.00283131	−	0.0594365i
$136$	−6.36758	+	1.22725i	−0.546015	+	0.105236i
$137$	5.39323	−	9.34134i	0.460774	−	0.798085i	−0.538225	−	0.842801i	$-0.680905\pi$
$137$	5.39323	−	9.34134i	0.460774	−	0.798085i	0.999000	+	0.0447162i	$0.0142384\pi$
$138$	−3.07165	−	3.68306i	−0.261476	−	0.313523i
$139$	−3.46452			−0.293857			−0.146928	−	0.989147i	$-0.546939\pi$
$139$	−3.46452			−0.293857			−0.146928	+	0.989147i	$0.546939\pi$
$140$	−1.27712	+	1.30955i	−0.107937	+	0.110677i
$141$	6.45726	+	4.14983i	0.543799	+	0.349478i
$142$	5.92210	−	2.37085i	0.496972	−	0.198958i
$143$	0.0581962	+	0.0817251i	0.00486661	+	0.00683420i
$144$	0.928368	+	0.371662i	0.0773640	+	0.0309719i
$145$	−1.16045	−	4.78342i	−0.0963698	−	0.397242i
$146$	4.87009	−	3.12981i	0.403051	−	0.259025i
$147$	6.98152	−	0.508258i	0.575826	−	0.0419204i
$148$	1.71831	−	0.504540i	0.141244	−	0.0414730i
$149$	−6.11963	−	1.17946i	−0.501339	−	0.0966252i	−0.0676890	−	0.997706i	$-0.521563\pi$
$149$	−6.11963	−	1.17946i	−0.501339	−	0.0966252i	−0.433650	+	0.901081i	$0.642775\pi$
$150$	1.47900	+	4.27330i	0.120760	+	0.348913i
$151$	−1.95884	+	8.07447i	−0.159408	+	0.657091i	0.834886	+	0.550423i	$0.185533\pi$
$151$	−1.95884	+	8.07447i	−0.159408	+	0.657091i	−0.994295	+	0.106668i	$0.965982\pi$
$152$	0.0658653	−	0.0924948i	0.00534238	−	0.00750232i
$153$	−5.45533	+	3.50593i	−0.441037	+	0.283437i
$154$	−0.0441314	+	0.215862i	−0.00355621	+	0.0173947i
$155$	0.163581	+	1.13773i	0.0131391	+	0.0913847i
$156$	−1.19932	+	0.114521i	−0.0960223	+	0.00916901i
$157$	−12.6028	−	9.91094i	−1.00581	−	0.790980i	−0.0278184	−	0.999613i	$-0.508856\pi$
$157$	−12.6028	−	9.91094i	−1.00581	−	0.790980i	−0.977994	+	0.208633i	$0.933098\pi$
$158$	−3.22831	+	1.66431i	−0.256830	+	0.132405i
$159$	−3.08807	+	8.92238i	−0.244900	+	0.707591i
$160$	0.691373			0.0546578
$161$	4.35880	+	11.9164i	0.343522	+	0.939145i
$162$	1.00000			0.0785674
$163$	−0.0934283	+	0.269943i	−0.00731787	+	0.0211436i	−0.948601	−	0.316476i	$-0.897500\pi$
$163$	−0.0934283	+	0.269943i	−0.00731787	+	0.0211436i	0.941283	+	0.337619i	$0.109622\pi$
$164$	−9.41895	+	4.85581i	−0.735497	+	0.379175i
$165$	−0.0452567	−	0.0355903i	−0.00352323	−	0.00277070i
$166$	10.4263	−	0.995588i	0.809235	−	0.0772726i
$167$	1.55857	+	10.8401i	0.120606	+	0.838832i	0.956872	+	0.290509i	$0.0938245\pi$
$167$	1.55857	+	10.8401i	0.120606	+	0.838832i	−0.836267	+	0.548323i	$0.815266\pi$
$168$	−1.97988	−	1.75501i	−0.152751	−	0.135402i
$169$	−9.71524	+	6.24360i	−0.747326	+	0.480277i
$170$	−2.60062	+	3.65206i	−0.199459	+	0.280100i
$171$	0.0267703	−	0.110349i	0.00204718	−	0.00843859i
$172$	2.98750	+	8.63182i	0.227795	+	0.658170i
$173$	−19.0579	−	3.67311i	−1.44894	−	0.279261i	−0.596725	−	0.802446i	$-0.703532\pi$
$173$	−19.0579	−	3.67311i	−1.44894	−	0.279261i	−0.852219	+	0.523185i	$0.824744\pi$
$174$	6.83103	−	2.00577i	0.517859	−	0.152057i
$175$	0.134758	−	11.9633i	0.0101868	−	0.904343i
$176$	0.0700561	−	0.0450223i	0.00528068	−	0.00339368i
$177$	3.31088	+	13.6476i	0.248861	+	1.02582i
$178$	−15.8684	−	6.35275i	−1.18939	−	0.476159i
$179$	−4.76041	−	6.68505i	−0.355809	−	0.499664i	0.597413	−	0.801934i	$-0.296195\pi$
$179$	−4.76041	−	6.68505i	−0.355809	−	0.499664i	−0.953223	+	0.302269i	$0.902256\pi$
$180$	0.641849	−	0.256957i	0.0478406	−	0.0191525i
$181$	11.4656	+	7.36850i	0.852233	+	0.547697i	0.892270	−	0.451502i	$-0.149111\pi$
$181$	11.4656	+	7.36850i	0.852233	+	0.547697i	−0.0400377	+	0.999198i	$0.512748\pi$
$182$	3.08902	+	0.786332i	0.228973	+	0.0582868i
$183$	−0.562154			−0.0415556
$184$	2.07422	−	4.32407i	0.152914	−	0.318775i
$185$	0.619072	−	1.07226i	0.0455151	−	0.0788344i
$186$	−1.63249	+	0.314636i	−0.119700	+	0.0230702i
$187$	−0.0256954	+	0.539412i	−0.00187903	+	0.0394457i
$188$	−1.09237	+	7.59763i	−0.0796696	+	0.554114i
$189$	−2.49033	−	0.893447i	−0.181145	−	0.0649887i
$190$	−0.0111724	−	0.0777061i	−0.000810535	−	0.00563739i
$191$	5.85792	+	24.1467i	0.423864	+	1.74719i	0.637664	+	0.770315i	$0.279901\pi$
$191$	5.85792	+	24.1467i	0.423864	+	1.74719i	−0.213799	+	0.976878i	$0.568584\pi$
$192$	0.0475819	+	0.998867i	0.00343393	+	0.0720870i
$193$	4.07267	+	0.388893i	0.293157	+	0.0279931i	0.240599	−	0.970625i	$-0.422656\pi$
$193$	4.07267	+	0.388893i	0.293157	+	0.0279931i	0.0525588	+	0.998618i	$0.483262\pi$
$194$	−13.7682	−	13.1280i	−0.988503	−	0.942535i
$195$	−0.545465	+	0.629500i	−0.0390615	+	0.0450794i
$196$	3.36256	+	6.13948i	0.240183	+	0.438534i
$197$	−4.89662	+	1.43778i	−0.348870	+	0.102437i	−0.451472	−	0.892285i	$-0.649101\pi$
$197$	−4.89662	+	1.43778i	−0.348870	+	0.102437i	0.102603	+	0.994722i	$0.467283\pi$
$198$	0.0483047	−	0.0678345i	0.00343287	−	0.00482079i
$199$	−0.536961	−	11.2722i	−0.0380642	−	0.799065i	−0.934515	−	0.355923i	$-0.884167\pi$
$199$	−0.536961	−	11.2722i	−0.0380642	−	0.799065i	0.896451	−	0.443142i	$-0.146136\pi$
$200$	−3.27273	+	3.12054i	−0.231417	+	0.220655i
$201$	−6.34655	+	4.99098i	−0.447651	+	0.352037i
$202$	0.779755	−	1.70743i	0.0548634	−	0.120134i
$203$	−18.8036	−	1.10813i	−1.31975	−	0.0777753i
$204$	−5.45533	−	3.50593i	−0.381950	−	0.245464i
$205$	−2.39625	+	6.92350i	−0.167361	+	0.483558i
$206$	4.07718	−	7.06188i	0.284071	−	0.492025i
$207$	0.318548	−	4.78524i	0.0221406	−	0.332597i
$208$	−0.602386	−	1.04336i	−0.0417680	−	0.0723443i
$209$	−0.00619232	−	0.00714632i	−0.000428332	−	0.000494321i
$210$	−1.82799	+	0.0664514i	−0.126144	+	0.00458558i
$211$	−3.25418	+	22.6333i	−0.224027	+	1.55814i	0.498556	+	0.866857i	$0.333864\pi$
$211$	−3.25418	+	22.6333i	−0.224027	+	1.55814i	−0.722583	+	0.691284i	$0.757045\pi$
$212$	−9.39891	+	0.897487i	−0.645520	+	0.0616397i
$213$	5.92210	+	2.37085i	0.405776	+	0.162448i
$214$	11.0633	−	10.5488i	0.756271	−	0.721103i
$215$	5.61311	+	2.89376i	0.382811	+	0.197353i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	4.34655	+	0.674993i	0.295063	+	0.0458215i
$218$	−3.35116	+	3.86745i	−0.226969	+	0.261937i
$219$	5.68447	+	1.09559i	0.384121	+	0.0740332i
$220$	0.0135737	−	0.0559517i	0.000915141	−	0.00377226i
$221$	7.77729	+	0.742641i	0.523157	+	0.0499555i
$222$	1.59177	+	0.820614i	0.106833	+	0.0550760i
$223$	−7.50497	−	2.20366i	−0.502570	−	0.147568i	0.0206140	−	0.999788i	$-0.493438\pi$
$223$	−7.50497	−	2.20366i	−0.502570	−	0.147568i	−0.523184	+	0.852220i	$0.675256\pi$
$224$	0.773940	−	2.53002i	0.0517111	−	0.169044i
$225$	−1.87851	+	4.11336i	−0.125234	+	0.274224i
$226$	−7.38672	+	2.95720i	−0.491358	+	0.196710i
$227$	−12.5303	+	6.45984i	−0.831668	+	0.428754i	−0.820820	−	0.571187i	$-0.806483\pi$
$227$	−12.5303	+	6.45984i	−0.831668	+	0.428754i	−0.0108475	+	0.999941i	$0.503453\pi$
$228$	0.111498	−	0.0214894i	0.00738411	−	0.00142317i
$229$	−9.82291	−	17.0138i	−0.649116	−	1.12430i	−0.983334	−	0.181807i	$-0.941806\pi$
$229$	−9.82291	−	17.0138i	−0.649116	−	1.12430i	0.334218	−	0.942496i	$-0.391528\pi$
$230$	−1.02514	−	3.15325i	−0.0675960	−	0.207919i
$231$	−0.180901	+	0.125773i	−0.0119024	+	0.00827523i
$232$	4.66222	+	5.38049i	0.306090	+	0.353247i
$233$	0.328096	−	6.88758i	0.0214943	−	0.451220i	−0.962308	−	0.271963i	$-0.912327\pi$
$233$	0.328096	−	6.88758i	0.0214943	−	0.451220i	0.983802	−	0.179258i	$-0.0573697\pi$
$234$	−0.947015	−	0.744741i	−0.0619083	−	0.0486853i
$235$	3.07825	+	4.32280i	0.200803	+	0.281988i
$236$	−11.0389	+	8.68110i	−0.718573	+	0.565092i
$237$	−3.48494	−	1.02327i	−0.226371	−	0.0664686i
$238$	10.4532	+	13.6050i	0.677582	+	0.881879i
$239$	−4.96440	−	10.8705i	−0.321120	−	0.703156i	0.678382	−	0.734710i	$-0.262682\pi$
$239$	−4.96440	−	10.8705i	−0.321120	−	0.703156i	−0.999502	+	0.0315540i	$0.989954\pi$
$240$	0.500370	+	0.477102i	0.0322988	+	0.0307968i
$241$	−0.0684273	−	0.197708i	−0.00440779	−	0.0127355i	0.942775	−	0.333428i	$-0.108206\pi$
$241$	−0.0684273	−	0.197708i	−0.00440779	−	0.0127355i	−0.947183	+	0.320693i	$0.896084\pi$
$242$	3.59548	+	10.3885i	0.231126	+	0.667795i
$243$	0.723734	+	0.690079i	0.0464276	+	0.0442686i
$244$	−0.233527	−	0.511353i	−0.0149500	−	0.0327360i
$245$	4.61168	+	1.46773i	0.294630	+	0.0937698i
$246$	−10.1677	−	2.98551i	−0.648269	−	0.190349i
$247$	−0.107533	+	0.0845651i	−0.00684218	+	0.00538075i
$248$	−0.964363	−	1.35426i	−0.0612371	−	0.0859955i
$249$	8.23288	+	6.47441i	0.521737	+	0.410299i
$250$	−0.313244	+	6.57580i	−0.0198113	+	0.415890i
$251$	−4.34233	−	5.01132i	−0.274085	−	0.316311i	0.601973	−	0.798516i	$-0.294381\pi$
$251$	−4.34233	−	5.01132i	−0.274085	−	0.316311i	−0.876058	+	0.482205i	$0.839836\pi$
$252$	−0.221813	−	2.63644i	−0.0139729	−	0.166080i
$253$	−0.309217	−	0.252758i	−0.0194403	−	0.0158908i
$254$	−8.54423	−	14.7990i	−0.536113	−	0.928574i
$255$	−4.40237	+	0.848487i	−0.275687	+	0.0531343i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−17.0041	+	6.80741i	−1.06069	+	0.424635i	−0.835391	−	0.549656i	$-0.814759\pi$
$257$	−17.0041	+	6.80741i	−1.06069	+	0.424635i	−0.225295	+	0.974291i	$0.572335\pi$
$258$	−3.79448	+	8.30875i	−0.236234	+	0.517280i
$259$	−3.23086	−	3.46576i	−0.200756	−	0.215352i
$260$	−0.799207	−	0.234668i	−0.0495647	−	0.0145535i
$261$	6.32799	+	3.26230i	0.391693	+	0.201932i
$262$	2.75328	+	0.262907i	0.170098	+	0.0162424i
$263$	6.22701	−	25.6681i	0.383974	−	1.58276i	−0.372047	−	0.928214i	$-0.621344\pi$
$263$	6.22701	−	25.6681i	0.383974	−	1.58276i	0.756020	−	0.654548i	$-0.227141\pi$
$264$	0.0817709	+	0.0157601i	0.00503265	+	0.000969964i
$265$	−4.27474	+	4.93332i	−0.262595	+	0.303051i
$266$	−0.296866	−	0.0461015i	−0.0182020	−	0.00282666i
$267$	−7.10060	−	15.5481i	−0.434550	−	0.951531i
$268$	−7.17641	−	3.69970i	−0.438369	−	0.225995i
$269$	−0.175760	+	0.167587i	−0.0107163	+	0.0102180i	−0.695418	−	0.718605i	$-0.744781\pi$
$269$	−0.175760	+	0.167587i	−0.0107163	+	0.0102180i	0.684702	+	0.728823i	$0.259932\pi$
$270$	0.641849	+	0.256957i	0.0390617	+	0.0156379i
$271$	27.9163	−	2.66569i	1.69580	−	0.161929i	0.798094	−	0.602533i	$-0.205842\pi$
$271$	27.9163	−	2.66569i	1.69580	−	0.161929i	0.897702	+	0.440604i	$0.145236\pi$
$272$	0.922878	−	6.41876i	0.0559577	−	0.389194i
$273$	1.69300	+	2.70076i	0.102465	+	0.163457i
$274$	7.06362	+	8.15186i	0.426729	+	0.492472i
$275$	0.188287	+	0.326122i	0.0113541	+	0.0196659i
$276$	4.48514	−	1.69810i	0.269974	−	0.102214i
$277$	−5.92731	+	10.2664i	−0.356138	+	0.616848i	−0.987312	−	0.158793i	$-0.949240\pi$
$277$	−5.92731	+	10.2664i	−0.356138	+	0.616848i	0.631174	+	0.775641i	$0.282573\pi$
$278$	1.13313	−	3.27397i	0.0679608	−	0.196360i
$279$	−1.39861	−	0.898832i	−0.0837326	−	0.0538117i
$280$	−0.819822	−	1.63520i	−0.0489938	−	0.0977217i
$281$	−8.14402	+	17.8329i	−0.485831	+	1.06382i	0.494987	+	0.868900i	$0.335173\pi$
$281$	−8.14402	+	17.8329i	−0.485831	+	1.06382i	−0.980819	+	0.194922i	$0.937555\pi$
$282$	−6.03355	+	4.74484i	−0.359293	+	0.282551i
$283$	−22.4397	+	21.3962i	−1.33390	+	1.27187i	−0.399010	+	0.916947i	$0.630646\pi$
$283$	−22.4397	+	21.3962i	−1.33390	+	1.27187i	−0.934894	+	0.354928i	$0.884505\pi$
$284$	0.303527	+	6.37182i	0.0180110	+	0.378098i
$285$	0.0455375	−	0.0639484i	0.00269741	−	0.00378798i
$286$	−0.0962645	+	0.0282658i	−0.00569224	+	0.00167139i
$287$	22.6536	+	16.5192i	1.33720	+	0.975099i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	18.1311	+	17.2880i	1.06654	+	1.01694i
$290$	4.89988	+	0.467882i	0.287731	+	0.0274750i
$291$	−0.905194	−	19.0024i	−0.0530634	−	1.11394i
$292$	1.36483	+	5.62590i	0.0798705	+	0.329231i
$293$	1.36637	+	9.50334i	0.0798244	+	0.555191i	0.990011	+	0.140992i	$0.0450291\pi$
$293$	1.36637	+	9.50334i	0.0798244	+	0.555191i	−0.910186	+	0.414199i	$0.864062\pi$
$294$	−1.80313	+	6.76378i	−0.105161	+	0.394472i
$295$	−1.38178	+	9.61046i	−0.0804501	+	0.559543i
$296$	−0.0852120	+	1.78882i	−0.00495285	+	0.103973i
$297$	0.0817709	−	0.0157601i	0.00474483	−	0.000914491i
$298$	3.11613	−	5.39729i	0.180512	−	0.312657i
$299$	−3.86544	+	4.29446i	−0.223544	+	0.248355i
$300$	−4.52200			−0.261078
$301$	16.8729	−	17.3014i	0.972540	−	0.997235i
$302$	−6.98970	−	4.49201i	−0.402212	−	0.258486i
$303$	1.74259	−	0.697629i	0.100109	−	0.0400778i
$304$	0.0658653	+	0.0924948i	0.00377763	+	0.00530494i
$305$	−0.360818	−	0.144450i	−0.0206604	−	0.00827116i
$306$	−1.52884	−	6.30197i	−0.0873980	−	0.360260i
$307$	10.0289	−	6.44520i	0.572381	−	0.367847i	−0.222204	−	0.975000i	$-0.571325\pi$
$307$	10.0289	−	6.44520i	0.572381	−	0.367847i	0.794585	+	0.607153i	$0.207689\pi$
$308$	−0.189556	−	0.112306i	−0.0108010	−	0.00639921i
$309$	7.82405	−	2.29735i	0.445095	−	0.130692i
$310$	−1.12866	−	0.217531i	−0.0641035	−	0.0123549i
$311$	−0.468644	−	1.35406i	−0.0265743	−	0.0767815i	0.930934	−	0.365189i	$-0.118996\pi$
$311$	−0.468644	−	1.35406i	−0.0265743	−	0.0767815i	−0.957508	+	0.288407i	$0.906874\pi$
$312$	0.284036	−	1.17081i	0.0160804	−	0.0662842i
$313$	−7.47809	+	10.5015i	−0.422687	+	0.593580i	−0.969927	−	0.243395i	$-0.921739\pi$
$313$	−7.47809	+	10.5015i	−0.422687	+	0.593580i	0.547241	+	0.836975i	$0.315678\pi$
$314$	13.4878	−	8.66810i	0.761162	−	0.489169i
$315$	−1.36884	−	1.21337i	−0.0771253	−	0.0683655i
$316$	−0.516897	−	3.59510i	−0.0290777	−	0.202240i
$317$	24.0302	−	2.29461i	1.34967	−	0.128878i	0.604956	−	0.796259i	$-0.293191\pi$
$317$	24.0302	−	2.29461i	1.34967	−	0.128878i	0.744716	+	0.667381i	$0.232585\pi$
$318$	−7.42165	−	5.83645i	−0.416185	−	0.327292i
$319$	0.526968	−	0.271671i	0.0295046	−	0.0152107i
$320$	−0.226126	+	0.653348i	−0.0126408	+	0.0365233i
$321$	15.2864			0.853204
$322$	−12.6866	+	0.221598i	−0.706999	+	0.0123492i
$323$	−0.736343			−0.0409712
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	4.84236	−	2.49641i	0.268606	−	0.138476i
$326$	−0.224539	−	0.176580i	−0.0124361	−	0.00977985i
$327$	−5.09420	+	0.486437i	−0.281710	+	0.0269000i
$328$	−1.50810	−	10.4891i	−0.0832712	−	0.579164i
$329$	19.2648	−	6.42556i	1.06210	−	0.354253i
$330$	0.0484349	−	0.0311272i	0.00266625	−	0.00171350i
$331$	17.1426	−	24.0734i	0.942242	−	1.32319i	−0.00408793	−	0.999992i	$-0.501301\pi$
$331$	17.1426	−	24.0734i	0.942242	−	1.32319i	0.946330	−	0.323202i	$-0.104759\pi$
$332$	−2.46927	+	10.1785i	−0.135519	+	0.558615i
$333$	0.585729	+	1.69235i	0.0320978	+	0.0927404i
$334$	−10.7537	−	2.07260i	−0.588414	−	0.113407i
$335$	−5.35599	+	1.57266i	−0.292629	+	0.0859237i
$336$	2.30604	−	1.29698i	0.125805	−	0.0707563i
$337$	−21.4781	+	13.8031i	−1.16999	+	0.751904i	−0.973519	−	0.228607i	$-0.926583\pi$
$337$	−21.4781	+	13.8031i	−1.16999	+	0.751904i	−0.196466	+	0.980511i	$0.562947\pi$
$338$	−2.72267	−	11.2230i	−0.148094	−	0.610450i
$339$	−7.38672	−	2.95720i	−0.401192	−	0.160613i
$340$	−2.60062	−	3.65206i	−0.141039	−	0.198061i
$341$	−0.128531	+	0.0514562i	−0.00696036	+	0.00278651i
$342$	0.0955240	+	0.0613896i	0.00516535	+	0.00331957i
$343$	10.5335	−	15.2331i	0.568754	−	0.822508i
$344$	−9.13419			−0.492482
$345$	1.43406	−	2.98955i	0.0772073	−	0.160952i
$346$	9.70431	−	16.8084i	0.521707	−	0.903623i
$347$	−0.904920	+	0.174409i	−0.0485786	+	0.00936276i	−0.213483	−	0.976947i	$-0.568481\pi$
$347$	−0.904920	+	0.174409i	−0.0485786	+	0.00936276i	0.164904	+	0.986310i	$0.447269\pi$
$348$	−0.338755	+	7.11135i	−0.0181592	+	0.381208i
$349$	3.52477	−	24.5153i	0.188677	−	1.31227i	−0.646763	−	0.762691i	$-0.723878\pi$
$349$	3.52477	−	24.5153i	0.188677	−	1.31227i	0.835439	−	0.549583i	$-0.185213\pi$
$350$	11.2613	+	4.04017i	0.601941	+	0.215956i
$351$	−0.171457	−	1.19251i	−0.00915170	−	0.0636515i
$352$	0.0196330	+	0.0809284i	0.00104644	+	0.00431350i
$353$	1.04569	+	21.9518i	0.0556567	+	1.16838i	0.838050	+	0.545594i	$0.183696\pi$
$353$	1.04569	+	21.9518i	0.0556567	+	1.16838i	−0.782393	+	0.622785i	$0.786001\pi$
$354$	−13.9799	−	1.33492i	−0.743023	−	0.0709501i
$355$	3.19189	+	3.04346i	0.169408	+	0.161530i
$356$	11.1934	−	12.9179i	0.593249	−	0.684646i
$357$	−1.82315	+	17.0599i	−0.0964916	+	0.902907i
$358$	7.87436	−	2.31212i	0.416173	−	0.122199i
$359$	−4.41140	+	6.19494i	−0.232825	+	0.326956i	−0.914415	−	0.404777i	$-0.867349\pi$
$359$	−4.41140	+	6.19494i	−0.232825	+	0.326956i	0.681591	+	0.731734i	$0.261288\pi$
$360$	0.0328969	+	0.690590i	0.00173382	+	0.0363973i
$361$	−13.7416	+	13.1026i	−0.723243	+	0.689611i
$362$	−10.7133	+	8.42502i	−0.563077	+	0.442809i
$363$	−4.56668	+	9.99964i	−0.239689	+	0.524845i
$364$	−1.75340	+	2.66194i	−0.0919033	+	0.139524i
$365$	3.36705	+	2.16387i	0.176239	+	0.113262i
$366$	0.183863	−	0.531236i	0.00961065	−	0.0277681i
$367$	2.34866	−	4.06800i	0.122599	−	0.212348i	−0.798193	−	0.602402i	$-0.794210\pi$
$367$	2.34866	−	4.06800i	0.122599	−	0.212348i	0.920792	+	0.390054i	$0.127544\pi$
$368$	3.40784	+	3.37441i	0.177646	+	0.175903i
$369$	−5.29848	−	9.17724i	−0.275828	−	0.477748i
$370$	0.810812	+	0.935727i	0.0421521	+	0.0486461i
$371$	13.2678	+	21.1656i	0.688830	+	1.09886i
$372$	0.236603	−	1.64561i	0.0122673	−	0.0853209i
$373$	27.5138	−	2.62725i	1.42461	−	0.136034i	0.645903	−	0.763420i	$-0.276481\pi$
$373$	27.5138	−	2.62725i	1.42461	−	0.136034i	0.778709	+	0.627386i	$0.215875\pi$
$374$	−0.501341	−	0.200707i	−0.0259237	−	0.0103783i
$375$	−4.76453	+	4.54297i	−0.246039	+	0.234598i
$376$	−6.82248	−	3.51723i	−0.351843	−	0.181388i
$377$	−3.56313	−	7.80216i	−0.183510	−	0.401832i
$378$	1.65882	−	2.06115i	0.0853203	−	0.106014i
$379$	8.76888	−	10.1198i	0.450427	−	0.519821i	−0.484437	−	0.874826i	$-0.660976\pi$
$379$	8.76888	−	10.1198i	0.450427	−	0.519821i	0.934864	+	0.355005i	$0.115521\pi$
$380$	0.0770865	+	0.0148572i	0.00395445	+	0.000762158i
$381$	4.02876	−	16.6068i	0.206399	−	0.850790i
$382$	−24.7346	−	2.36187i	−1.26553	−	0.120844i
$383$	−17.0206	−	8.77473i	−0.869712	−	0.448368i	−0.0352148	−	0.999380i	$-0.511212\pi$
$383$	−17.0206	−	8.77473i	−0.869712	−	0.448368i	−0.834497	+	0.551012i	$0.814242\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	−0.148429	+	0.0342431i	−0.00756467	+	0.00174519i
$386$	−1.69955	+	3.72148i	−0.0865046	+	0.189419i
$387$	−8.47989	+	3.39483i	−0.431057	+	0.172569i
$388$	16.9091	−	8.71726i	0.858431	−	0.442552i
$389$	−7.93506	+	1.52936i	−0.402324	+	0.0775415i	−0.386399	−	0.922332i	$-0.626281\pi$
$389$	−7.93506	+	1.52936i	−0.402324	+	0.0775415i	−0.0159245	+	0.999873i	$0.505069\pi$
$390$	−0.416474	−	0.721354i	−0.0210890	−	0.0365272i
$391$	−30.6434	+	5.30839i	−1.54971	+	0.268457i
$392$	−6.90160	+	1.16959i	−0.348583	+	0.0590733i
$393$	1.81122	+	2.09026i	0.0913639	+	0.105440i
$394$	0.242827	−	5.09756i	0.0122334	−	0.256811i
$395$	−1.97387	−	1.55227i	−0.0993161	−	0.0781030i
$396$	0.0483047	+	0.0678345i	0.00242740	+	0.00340881i
$397$	2.89795	−	2.27897i	0.145444	−	0.114378i	−0.542786	−	0.839871i	$-0.682631\pi$
$397$	2.89795	−	2.27897i	0.145444	−	0.114378i	0.688230	+	0.725493i	$0.258388\pi$
$398$	10.8279	+	3.17935i	0.542752	+	0.159366i
$399$	−0.183038	−	0.238226i	−0.00916337	−	0.0119262i
$400$	−1.87851	−	4.11336i	−0.0939254	−	0.205668i
$401$	10.1014	+	9.63162i	0.504438	+	0.480980i	0.899037	−	0.437873i	$-0.144268\pi$
$401$	10.1014	+	9.63162i	0.504438	+	0.480980i	−0.394599	+	0.918853i	$0.629117\pi$
$402$	−2.64073	−	7.62989i	−0.131708	−	0.380544i
$403$	0.655108	+	1.89281i	0.0326333	+	0.0942876i
$404$	1.35849	+	1.29531i	0.0675872	+	0.0644442i
$405$	0.287207	+	0.628895i	0.0142714	+	0.0312500i
$406$	7.19723	−	17.4070i	0.357192	−	0.863893i
$407$	0.143093	+	0.0420160i	0.00709288	+	0.00208266i
$408$	5.09737	−	4.00861i	0.252357	−	0.198456i
$409$	−14.2821	−	20.0564i	−0.706206	−	0.991727i	−0.999364	−	0.0356631i	$-0.988646\pi$
$409$	−14.2821	−	20.0564i	−0.706206	−	0.991727i	0.293158	−	0.956064i	$-0.405294\pi$
$410$	−5.75898	−	4.52891i	−0.284416	−	0.223667i
$411$	−0.513240	+	10.7742i	−0.0253163	+	0.531454i
$412$	5.33997	+	6.16265i	0.263081	+	0.303612i
$413$	33.6219	+	15.8147i	1.65443	+	0.778190i
$414$	4.41787	+	1.86613i	0.217126	+	0.0917151i
$415$	3.62061	+	6.27109i	0.177729	+	0.307836i
$416$	1.18300	−	0.228005i	0.0580014	−	0.0111789i
$417$	3.07939	−	1.58753i	0.150798	−	0.0777419i
$418$	0.00877859	−	0.00351442i	0.000429375	−	0.000171896i
$419$	14.9625	−	32.7632i	0.730964	−	1.60059i	−0.0669070	−	0.997759i	$-0.521313\pi$
$419$	14.9625	−	32.7632i	0.730964	−	1.60059i	0.797871	−	0.602828i	$-0.205960\pi$
$420$	0.535082	−	1.74919i	0.0261093	−	0.0853517i
$421$	1.78788	+	0.524969i	0.0871359	+	0.0255854i	0.325010	−	0.945711i	$-0.394632\pi$
$421$	1.78788	+	0.524969i	0.0871359	+	0.0255854i	−0.237874	+	0.971296i	$0.576451\pi$
$422$	−20.3242	−	10.4778i	−0.989365	−	0.510053i
$423$	−7.64100	−	0.729627i	−0.371518	−	0.0354757i
$424$	2.22596	−	9.17552i	0.108102	−	0.445603i
$425$	28.7942	+	5.54963i	1.39672	+	0.269196i
$426$	−4.17739	+	4.82096i	−0.202395	+	0.233576i
$427$	−0.932510	+	1.15868i	−0.0451273	+	0.0560726i
$428$	6.35020	+	13.9050i	0.306949	+	0.672124i
$429$	−0.0891755	−	0.0459732i	−0.00430543	−	0.00221961i
$430$	−4.57048	+	4.35794i	−0.220408	+	0.210159i
$431$	−12.0025	−	4.80509i	−0.578142	−	0.231453i	0.0641149	−	0.997943i	$-0.479578\pi$
$431$	−12.0025	−	4.80509i	−0.578142	−	0.231453i	−0.642257	+	0.766489i	$0.722002\pi$
$432$	−0.995472	+	0.0950560i	−0.0478947	+	0.00457339i
$433$	−1.26255	+	8.78120i	−0.0606741	+	0.421997i	0.936734	+	0.350043i	$0.113833\pi$
$433$	−1.26255	+	8.78120i	−0.0606741	+	0.421997i	−0.997408	+	0.0719549i	$0.977076\pi$
$434$	−2.05948	+	3.88672i	−0.0988584	+	0.186569i
$435$	3.22334	+	3.71993i	0.154547	+	0.178357i
$436$	−2.55868	−	4.43177i	−0.122539	−	0.212243i
$437$	0.324193	−	0.437550i	0.0155082	−	0.0209309i
$438$	−2.89454	+	5.01349i	−0.138307	+	0.239554i
$439$	−1.29744	+	3.74872i	−0.0619236	+	0.178916i	−0.971719	−	0.236141i	$-0.924117\pi$
$439$	−1.29744	+	3.74872i	−0.0619236	+	0.178916i	0.909795	+	0.415057i	$0.136239\pi$
$440$	0.0484349	+	0.0311272i	0.00230904	+	0.00148393i
$441$	−5.97253	+	3.65088i	−0.284406	+	0.173851i
$442$	−3.24550	+	7.10665i	−0.154373	+	0.338029i
$443$	27.9713	−	21.9969i	1.32896	−	1.04510i	0.334237	−	0.942489i	$-0.391522\pi$
$443$	27.9713	−	21.9969i	1.32896	−	1.04510i	0.994721	−	0.102615i	$-0.0327209\pi$
$444$	−1.29610	+	1.23583i	−0.0615101	+	0.0586497i
$445$	−0.562299	−	11.8041i	−0.0266555	−	0.559568i
$446$	4.53710	−	6.37146i	0.214838	−	0.301697i
$447$	5.97980	−	1.75583i	0.282835	−	0.0830478i
$448$	2.13774	+	1.55886i	0.100999	+	0.0736494i
$449$	0.314565	−	0.363027i	0.0148452	−	0.0171323i	−0.748278	−	0.663385i	$-0.769119\pi$
$449$	0.314565	−	0.363027i	0.0148452	−	0.0171323i	0.763124	+	0.646253i	$0.223665\pi$
$450$	−3.27273	−	3.12054i	−0.154278	−	0.147104i
$451$	−0.878475	−	0.0838842i	−0.0413658	−	0.00394995i
$452$	−0.378594	−	7.94767i	−0.0178076	−	0.373827i
$453$	−1.95884	−	8.07447i	−0.0920345	−	0.379372i
$454$	−2.00628	−	13.9540i	−0.0941594	−	0.654893i
$455$	0.392666	+	2.16851i	0.0184085	+	0.101661i
$456$	−0.0161598	+	0.112394i	−0.000756752	+	0.00526332i
$457$	−1.65850	+	34.8163i	−0.0775815	+	1.62864i	0.539674	+	0.841874i	$0.318548\pi$
$457$	−1.65850	+	34.8163i	−0.0775815	+	1.62864i	−0.617255	+	0.786763i	$0.711756\pi$
$458$	19.2908	−	3.71800i	0.901400	−	0.173731i
$459$	3.24238	−	5.61597i	0.151341	−	0.262131i
$460$	3.31512	+	0.0625665i	0.154568	+	0.00291718i
$461$	−27.3581			−1.27419			−0.637097	−	0.770784i	$-0.719865\pi$
$461$	−27.3581			−1.27419			−0.637097	+	0.770784i	$0.719865\pi$
$462$	−0.0596882	−	0.212088i	−0.00277695	−	0.00986723i
$463$	−30.2091	−	19.4142i	−1.40393	−	0.902254i	−0.404013	−	0.914753i	$-0.632385\pi$
$463$	−30.2091	−	19.4142i	−1.40393	−	0.902254i	−0.999922	+	0.0124995i	$0.996021\pi$
$464$	−6.60943	+	2.64602i	−0.306835	+	0.122838i
$465$	−0.666735	−	0.936298i	−0.0309191	−	0.0434198i
$466$	6.40146	+	2.56276i	0.296542	+	0.118717i
$467$	−5.82446	−	24.0088i	−0.269524	−	1.11099i	−0.932159	−	0.362050i	$-0.882077\pi$
$467$	−5.82446	−	24.0088i	−0.269524	−	1.11099i	0.662634	−	0.748943i	$-0.269438\pi$
$468$	1.01352	−	0.651349i	0.0468500	−	0.0301086i
$469$	−0.240608	+	21.3603i	−0.0111102	+	0.986327i
$470$	−5.09185	+	1.49510i	−0.234869	+	0.0689639i
$471$	15.7433	+	3.03427i	0.725411	+	0.139812i
$472$	−4.59317	−	13.2711i	−0.211418	−	0.610852i
$473$	−0.179332	+	0.739215i	−0.00824568	+	0.0339892i
$474$	2.10680	−	2.95859i	0.0967688	−	0.135893i
$475$	−0.431960	+	0.277604i	−0.0198197	+	0.0127373i
$476$	−16.2756	+	5.42855i	−0.745992	+	0.248817i
$477$	−1.34369	−	9.34556i	−0.0615233	−	0.427904i
$478$	11.8964	−	1.13596i	0.544126	−	0.0519578i
$479$	18.9648	+	14.9141i	0.866525	+	0.681443i	0.949043	−	0.315147i	$-0.102054\pi$
$479$	18.9648	+	14.9141i	0.866525	+	0.681443i	−0.0825180	+	0.996590i	$0.526296\pi$
$480$	−0.614517	+	0.316805i	−0.0280487	+	0.0144601i
$481$	0.705671	−	2.03890i	0.0321758	−	0.0929659i
$482$	0.209214			0.00952945
$483$	−9.33468	−	8.59441i	−0.424742	−	0.391059i
$484$	−10.9931			−0.499685
$485$	4.30180	−	12.4292i	0.195335	−	0.564382i
$486$	−0.888835	+	0.458227i	−0.0403184	+	0.0207856i
$487$	1.63795	+	1.28810i	0.0742228	+	0.0583694i	0.654581	−	0.755992i	$-0.272845\pi$
$487$	1.63795	+	1.28810i	0.0742228	+	0.0583694i	−0.580358	+	0.814361i	$0.697087\pi$
$488$	0.559608	−	0.0534361i	0.0253323	−	0.00241894i
$489$	−0.0406528	−	0.282747i	−0.00183838	−	0.0127862i
$490$	−2.89534	+	3.87800i	−0.130798	+	0.175190i
$491$	16.8743	−	10.8444i	0.761525	−	0.489402i	−0.101331	−	0.994853i	$-0.532310\pi$
$491$	16.8743	−	10.8444i	0.761525	−	0.489402i	0.862856	+	0.505451i	$0.168674\pi$
$492$	6.14684	−	8.63203i	0.277121	−	0.389162i
$493$	10.8845	−	44.8663i	0.490211	−	2.02068i
$494$	−0.0447434	−	0.129278i	−0.00201310	−	0.00581647i
$495$	0.0565342	+	0.0108961i	0.00254102	+	0.000489742i
$496$	1.59519	−	0.468389i	0.0716260	−	0.0210313i
$497$	14.7104	−	8.27352i	0.659850	−	0.371118i
$498$	−8.81103	+	5.66251i	−0.394832	+	0.253743i
$499$	6.31747	+	26.0410i	0.282809	+	1.16575i	0.919011	+	0.394231i	$0.128989\pi$
$499$	6.31747	+	26.0410i	0.282809	+	1.16575i	−0.636202	+	0.771522i	$0.719496\pi$
$500$	−6.11168	−	2.44675i	−0.273323	−	0.109422i
$501$	−6.35253	−	8.92088i	−0.283810	−	0.398556i
$502$	6.15594	−	2.46446i	0.274753	−	0.109994i
$503$	10.6633	+	6.85286i	0.475451	+	0.305554i	0.756331	−	0.654189i	$-0.226990\pi$
$503$	10.6633	+	6.85286i	0.475451	+	0.305554i	−0.280880	+	0.959743i	$0.590626\pi$
$504$	2.56398	+	0.652680i	0.114209	+	0.0290727i
$505$	1.29774			0.0577488
$506$	0.339992	−	0.209541i	0.0151145	−	0.00931524i
$507$	5.77426	−	10.0013i	0.256444	−	0.444174i
$508$	16.7797	−	3.23401i	0.744477	−	0.143486i
$509$	−1.00942	+	21.1904i	−0.0447419	+	0.939249i	0.859212	+	0.511619i	$0.170954\pi$
$509$	−1.00942	+	21.1904i	−0.0447419	+	0.939249i	−0.903954	+	0.427629i	$0.859349\pi$
$510$	0.638053	−	4.43776i	0.0282535	−	0.196507i
$511$	11.6877	−	9.89914i	0.517031	−	0.437912i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	0.0267703	+	0.110349i	0.00118194	+	0.00487202i
$514$	−0.871516	−	18.2954i	−0.0384409	−	0.806974i
$515$	5.61217	+	0.535898i	0.247302	+	0.0236145i
$516$	−6.61072	−	6.30331i	−0.291021	−	0.277488i
$517$	−0.418590	+	0.483079i	−0.0184096	+	0.0212458i
$518$	4.33186	−	1.91962i	0.190331	−	0.0843434i
$519$	18.6224	−	5.46804i	0.817434	−	0.240020i
$520$	0.483157	−	0.678499i	0.0211878	−	0.0297541i
$521$	1.68554	+	35.3838i	0.0738447	+	1.55019i	0.666972	+	0.745083i	$0.267590\pi$
$521$	1.68554	+	35.3838i	0.0738447	+	1.55019i	−0.593128	+	0.805108i	$0.702107\pi$
$522$	−5.15256	+	4.91296i	−0.225521	+	0.215034i
$523$	11.6834	−	9.18792i	0.510879	−	0.401760i	−0.329170	−	0.944271i	$-0.606769\pi$
$523$	11.6834	−	9.18792i	0.510879	−	0.401760i	0.840049	+	0.542511i	$0.182526\pi$
$524$	−1.14896	+	2.51587i	−0.0501924	+	0.109906i
$525$	5.36214	+	10.6952i	0.234023	+	0.466776i
$526$	22.2197	+	14.2797i	0.968825	+	0.622626i
$527$	−3.52616	+	10.1882i	−0.153602	+	0.443804i
$528$	−0.0416379	+	0.0721190i	−0.00181206	+	0.00313858i
$529$	10.3372	−	20.5461i	0.449442	−	0.893309i
$530$	−3.26386	−	5.65317i	−0.141773	−	0.245558i
$531$	−9.19653	−	10.6134i	−0.399095	−	0.460580i
$532$	0.140661	−	0.265460i	0.00609844	−	0.0115092i
$533$	−1.81692	+	12.6370i	−0.0786997	+	0.547368i
$534$	17.0154	−	1.62477i	0.736328	−	0.0703108i
$535$	9.81156	+	3.92796i	0.424191	+	0.169820i
$536$	5.84339	−	5.57166i	0.252396	−	0.240659i
$537$	7.29449	+	3.76057i	0.314780	+	0.162281i
$538$	−0.100884	−	0.220906i	−0.00434944	−	0.00952394i
$539$	−0.0408460	+	0.581498i	−0.00175936	+	0.0250469i
$540$	−0.452753	+	0.522505i	−0.0194834	+	0.0224850i
$541$	−24.4780	−	4.71774i	−1.05239	−	0.202831i	−0.366411	−	0.930453i	$-0.619413\pi$
$541$	−24.4780	−	4.71774i	−1.05239	−	0.202831i	−0.685979	+	0.727622i	$0.740626\pi$
$542$	−6.61146	+	27.2528i	−0.283986	+	1.17061i
$543$	−13.5675	−	1.29554i	−0.582237	−	0.0555969i
$544$	5.76389	+	2.97149i	0.247125	+	0.127402i
$545$	−3.39470	−	0.996773i	−0.145413	−	0.0426971i
$546$	−3.10595	+	0.716550i	−0.132922	+	0.0306655i
$547$	10.7894	−	23.6256i	0.461323	−	1.01016i	−0.525861	−	0.850570i	$-0.676257\pi$
$547$	10.7894	−	23.6256i	0.461323	−	1.01016i	0.987184	−	0.159586i	$-0.0510158\pi$
$548$	−10.0138	+	4.00892i	−0.427768	+	0.171253i
$549$	0.499662	−	0.257594i	0.0213251	−	0.0109938i
$550$	−0.369768	+	0.0712670i	−0.0157670	+	0.00303884i
$551$	0.404203	+	0.700101i	0.0172196	+	0.0298253i
$552$	0.137761	+	4.79385i	0.00586348	+	0.204040i
$553$	−7.88999	+	5.48556i	−0.335516	+	0.233270i
$554$	−7.76313	−	8.95913i	−0.329824	−	0.380637i
$555$	−0.0589133	+	1.23674i	−0.00250073	+	0.0524968i
$556$	2.72330	+	2.14162i	0.115493	+	0.0908251i
$557$	2.38493	+	3.34917i	0.101053	+	0.141909i	0.862006	−	0.506898i	$-0.169208\pi$
$557$	2.38493	+	3.34917i	0.101053	+	0.141909i	−0.760953	+	0.648807i	$0.775268\pi$
$558$	1.30684	−	1.02771i	0.0553229	−	0.0435064i
$559$	10.5589	+	3.10036i	0.446592	+	0.131131i
$560$	1.81340	−	0.239912i	0.0766301	−	0.0101381i
$561$	−0.224334	−	0.491223i	−0.00947139	−	0.0207395i
$562$	−14.1885	−	13.5287i	−0.598504	−	0.570673i
$563$	2.76505	+	7.98909i	0.116533	+	0.336700i	0.988151	−	0.153486i	$-0.0490500\pi$
$563$	2.76505	+	7.98909i	0.116533	+	0.336700i	−0.871618	+	0.490186i	$0.836929\pi$
$564$	−2.51049	−	7.25359i	−0.105711	−	0.305431i
$565$	−3.98128	−	3.79615i	−0.167494	−	0.159705i
$566$	−12.8801	−	28.2036i	−0.541393	−	1.18549i
$567$	2.62290	−	0.347009i	0.110151	−	0.0145730i
$568$	−6.12065	−	1.79719i	−0.256817	−	0.0754082i
$569$	7.05639	−	5.54921i	0.295819	−	0.232635i	−0.459207	−	0.888329i	$-0.651866\pi$
$569$	7.05639	−	5.54921i	0.295819	−	0.232635i	0.755026	+	0.655694i	$0.227624\pi$
$570$	0.0455375	+	0.0639484i	0.00190735	+	0.00267850i
$571$	−4.55255	−	3.58016i	−0.190518	−	0.149825i	0.518344	−	0.855172i	$-0.326549\pi$
$571$	−4.55255	−	3.58016i	−0.190518	−	0.149825i	−0.708862	+	0.705347i	$0.750791\pi$
$572$	0.00477382	−	0.100215i	0.000199603	−	0.00419019i
$573$	−16.2714	−	18.7782i	−0.679747	−	0.784469i
$574$	−23.0199	+	16.0047i	−0.960833	+	0.668025i
$575$	−15.9751	+	14.6667i	−0.666206	+	0.611646i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−1.72780	+	0.333006i	−0.0719292	+	0.0138632i	−0.225089	−	0.974338i	$-0.572267\pi$
$577$	−1.72780	+	0.333006i	−0.0719292	+	0.0138632i	0.153160	+	0.988201i	$0.451055\pi$
$578$	−22.2672	+	11.4796i	−0.926195	+	0.477487i
$579$	−3.79814	+	1.52054i	−0.157845	+	0.0631917i
$580$	−2.04474	+	4.47736i	−0.0849034	+	0.185912i
$581$	27.0015	−	6.22933i	1.12021	−	0.258436i
$582$	18.2533	+	5.35965i	0.756624	+	0.222165i
$583$	−0.698858	−	0.360286i	−0.0289437	−	0.0149215i
$584$	−5.76287	−	0.550287i	−0.238469	−	0.0227710i
$585$	0.196375	−	0.809468i	0.00811910	−	0.0334674i
$586$	−9.42756	−	1.81701i	−0.389449	−	0.0750601i
$587$	10.2119	−	11.7852i	0.421491	−	0.486426i	−0.504800	−	0.863236i	$-0.668434\pi$
$587$	10.2119	−	11.7852i	0.421491	−	0.486426i	0.926290	+	0.376810i	$0.122979\pi$
$588$	−5.80203	−	3.91617i	−0.239272	−	0.161500i
$589$	−0.0784220	−	0.171720i	−0.00323132	−	0.00707561i
$590$	−8.62996	−	4.44905i	−0.355290	−	0.183165i
$591$	3.69346	−	3.52171i	0.151929	−	0.144864i
$592$	−1.66257	−	0.665591i	−0.0683310	−	0.0273556i
$593$	−28.1365	+	2.68671i	−1.15543	+	0.110330i	−0.655125	−	0.755520i	$-0.727384\pi$
$593$	−28.1365	+	2.68671i	−1.15543	+	0.110330i	−0.500303	+	0.865850i	$0.666778\pi$
$594$	−0.0118514	+	0.0824282i	−0.000486268	+	0.00338207i
$595$	−5.55386	+	10.4814i	−0.227686	+	0.429696i
$596$	4.08126	+	4.71002i	0.167175	+	0.192930i
$597$	5.64249	+	9.77308i	0.230932	+	0.399986i
$598$	−2.79401	−	5.05742i	−0.114256	−	0.206813i
$599$	14.7815	−	25.6024i	0.603957	−	1.04608i	−0.388259	−	0.921550i	$-0.626923\pi$
$599$	14.7815	−	25.6024i	0.603957	−	1.04608i	0.992215	−	0.124533i	$-0.0397434\pi$
$600$	1.47900	−	4.27330i	0.0603800	−	0.174457i
$601$	−20.9233	−	13.4466i	−0.853478	−	0.548497i	0.0391799	−	0.999232i	$-0.487525\pi$
$601$	−20.9233	−	13.4466i	−0.853478	−	0.548497i	−0.892658	+	0.450735i	$0.851162\pi$
$602$	10.8312	+	21.6037i	0.441447	+	0.880500i
$603$	3.35404	−	7.34432i	0.136587	−	0.299084i
$604$	6.53106	−	5.13608i	0.265745	−	0.208984i
$605$	−5.50060	+	5.24481i	−0.223631	+	0.213232i
$606$	0.0893137	+	1.87492i	0.00362812	+	0.0761636i
$607$	20.0425	−	28.1457i	0.813498	−	1.14240i	−0.173996	−	0.984746i	$-0.555668\pi$
$607$	20.0425	−	28.1457i	0.813498	−	1.14240i	0.987495	−	0.157652i	$-0.0503925\pi$
$608$	−0.108950	+	0.0319906i	−0.00441851	+	0.00129739i
$609$	17.2211	−	7.63135i	0.697832	−	0.309238i
$610$	0.254517	−	0.293728i	0.0103051	−	0.0118927i
$611$	6.69276	+	6.38153i	0.270760	+	0.258169i
$612$	6.45540	+	0.616416i	0.260944	+	0.0249171i
$613$	−1.59807	−	33.5476i	−0.0645454	−	1.35498i	−0.766266	−	0.642523i	$-0.777888\pi$
$613$	−1.59807	−	33.5476i	−0.0645454	−	1.35498i	0.701721	−	0.712452i	$-0.252415\pi$
$614$	2.81058	+	11.5854i	0.113426	+	0.467547i
$615$	−1.04266	−	7.25188i	−0.0420442	−	0.292424i
$616$	0.168127	−	0.142399i	0.00677402	−	0.00573742i
$617$	−2.66750	+	18.5528i	−0.107389	+	0.746909i	0.862972	+	0.505251i	$0.168600\pi$
$617$	−2.66750	+	18.5528i	−0.107389	+	0.746909i	−0.970362	+	0.241658i	$0.922309\pi$
$618$	−0.388000	+	8.14512i	−0.0156076	+	0.327645i
$619$	6.24146	−	1.20294i	0.250865	−	0.0483504i	−0.0622681	−	0.998059i	$-0.519833\pi$
$619$	6.24146	−	1.20294i	0.250865	−	0.0483504i	0.313134	+	0.949709i	$0.398621\pi$
$620$	0.574715	−	0.995435i	0.0230811	−	0.0399776i
$621$	1.90959	+	4.39926i	0.0766291	+	0.176536i
$622$	1.43286			0.0574526
$623$	−43.8256	−	11.1561i	−1.75584	−	0.446961i
$624$	1.01352	+	0.651349i	0.0405732	+	0.0260748i
$625$	16.7650	−	6.71168i	0.670598	−	0.268467i
$626$	−7.47809	−	10.5015i	−0.298885	−	0.419725i
$627$	0.00877859	+	0.00351442i	0.000350583	+	0.000140352i
$628$	3.77992	+	15.5811i	0.150835	+	0.621752i
$629$	9.76967	−	6.27858i	0.389542	−	0.250344i
$630$	1.59434	−	0.896700i	0.0635199	−	0.0357254i
$631$	31.1349	−	9.14204i	1.23946	−	0.363939i	0.404649	−	0.914472i	$-0.367394\pi$
$631$	31.1349	−	9.14204i	1.23946	−	0.363939i	0.834813	+	0.550533i	$0.185576\pi$
$632$	3.56643	+	0.687373i	0.141865	+	0.0273422i
$633$	−7.47875	−	21.6084i	−0.297254	−	0.858858i
$634$	−5.69111	+	23.4591i	−0.226023	+	0.931679i
$635$	6.85308	−	9.62381i	0.271956	−	0.381909i
$636$	7.94283	−	5.10455i	0.314954	−	0.202409i
$637$	8.37504	+	0.990551i	0.331831	+	0.0392471i
$638$	0.0843749	+	0.586840i	0.00334043	+	0.0232332i
$639$	−6.35016	+	0.606367i	−0.251209	+	0.0239875i
$640$	−0.543456	−	0.427378i	−0.0214820	−	0.0168936i
$641$	−6.76525	+	3.48773i	−0.267211	+	0.137757i	−0.586626	−	0.809858i	$-0.699544\pi$
$641$	−6.76525	+	3.48773i	−0.267211	+	0.137757i	0.319415	+	0.947615i	$0.396514\pi$
$642$	−4.99969	+	14.4457i	−0.197322	+	0.570125i
$643$	10.5045			0.414257			0.207128	−	0.978314i	$-0.433588\pi$
$643$	10.5045			0.414257			0.207128	+	0.978314i	$0.433588\pi$
$644$	3.93998	−	12.0614i	0.155257	−	0.475284i
$645$	−6.31513			−0.248658
$646$	0.240834	−	0.695844i	0.00947549	−	0.0273776i
$647$	−40.5322	+	20.8958i	−1.59348	+	0.821498i	−0.593624	+	0.804743i	$0.702303\pi$
$647$	−40.5322	+	20.8958i	−1.59348	+	0.821498i	−0.999860	+	0.0167554i	$0.994666\pi$
$648$	−0.786053	−	0.618159i	−0.0308791	−	0.0242836i
$649$	−1.16419	+	0.111166i	−0.0456983	+	0.00436366i
$650$	0.775329	+	5.39253i	0.0304109	+	0.211513i
$651$	−4.17266	+	1.39175i	−0.163540	+	0.0545468i
$652$	0.240308	−	0.154436i	0.00941117	−	0.00604819i
$653$	6.85963	−	9.63301i	0.268438	−	0.376969i	−0.658250	−	0.752799i	$-0.728703\pi$
$653$	6.85963	−	9.63301i	0.268438	−	0.376969i	0.926688	+	0.375831i	$0.122643\pi$
$654$	1.20647	−	4.97312i	0.0471765	−	0.194464i
$655$	0.625421	+	1.80703i	0.0244372	+	0.0706067i
$656$	10.4055	+	2.00549i	0.406265	+	0.0783012i
$657$	−5.55458	+	1.63097i	−0.216705	+	0.0636303i
$658$	−0.228742	+	20.3069i	−0.00891728	+	0.791643i
$659$	−25.5567	+	16.4243i	−0.995548	+	0.639800i	−0.933614	−	0.358281i	$-0.883363\pi$
$659$	−25.5567	+	16.4243i	−0.995548	+	0.639800i	−0.0619336	+	0.998080i	$0.519727\pi$
$660$	0.0135737	+	0.0559517i	0.000528357	+	0.00217792i
$661$	−41.7186	−	16.7016i	−1.62267	−	0.649618i	−0.630689	−	0.776036i	$-0.717228\pi$
$661$	−41.7186	−	16.7016i	−1.62267	−	0.649618i	−0.991977	+	0.126418i	$0.959652\pi$
$662$	17.1426	+	24.0734i	0.666266	+	0.935639i
$663$	−7.25303	+	2.90367i	−0.281684	+	0.112769i
$664$	−8.81103	−	5.66251i	−0.341934	−	0.219748i
$665$	−0.0562689	−	0.199938i	−0.00218201	−	0.00775327i
$666$	−1.79085			−0.0693940
$667$	21.8683	+	26.2213i	0.846746	+	1.01529i
$668$	5.47578	−	9.48433i	0.211864	−	0.366960i
$669$	7.68046	−	1.48029i	0.296944	−	0.0572312i
$670$	0.265607	−	5.57579i	0.0102613	−	0.215411i
$671$	0.00666230	−	0.0463373i	0.000257195	−	0.00178883i
$672$	0.471418	+	2.60341i	0.0181853	+	0.100429i
$673$	−2.40186	−	16.7053i	−0.0925847	−	0.643941i	−0.982285	−	0.187395i	$-0.939996\pi$
$673$	−2.40186	−	16.7053i	−0.0925847	−	0.643941i	0.889700	−	0.456546i	$-0.150914\pi$
$674$	−6.01917	−	24.8114i	−0.231850	−	0.955698i
$675$	−0.215166	−	4.51688i	−0.00828173	−	0.173855i
$676$	11.4962	+	1.09776i	0.442163	+	0.0422214i
$677$	6.42411	+	6.12538i	0.246899	+	0.235417i	0.803415	−	0.595419i	$-0.203014\pi$
$677$	6.42411	+	6.12538i	0.246899	+	0.235417i	−0.556517	+	0.830837i	$0.687862\pi$
$678$	5.21052	−	6.01326i	0.200109	−	0.230938i
$679$	−40.6682	−	29.6557i	−1.56070	−	1.13808i
$680$	4.30178	−	1.26312i	0.164966	−	0.0484383i
$681$	8.17734	−	11.4835i	0.313356	−	0.440047i
$682$	−0.00658765	−	0.138292i	−0.000252254	−	0.00529547i
$683$	−14.0718	+	13.4175i	−0.538444	+	0.513405i	−0.909779	−	0.415094i	$-0.863749\pi$
$683$	−14.0718	+	13.4175i	−0.538444	+	0.513405i	0.371335	+	0.928499i	$0.378900\pi$
$684$	−0.0892560	+	0.0701917i	−0.00341279	+	0.00268385i
$685$	−3.09794	+	6.78355i	−0.118366	+	0.259186i
$686$	10.9501	+	14.9364i	0.418076	+	0.570274i
$687$	16.5271	+	10.6213i	0.630549	+	0.405229i
$688$	2.98750	−	8.63182i	0.113897	−	0.329085i
$689$	−5.68753	+	9.85109i	−0.216678	+	0.375297i
$690$	2.35609	+	2.33298i	0.0896947	+	0.0888148i
$691$	−19.1006	−	33.0832i	−0.726621	−	1.25854i	−0.958303	−	0.285753i	$-0.907756\pi$
$691$	−19.1006	−	33.0832i	−0.726621	−	1.25854i	0.231683	−	0.972791i	$-0.425577\pi$
$692$	12.7099	+	14.6681i	0.483160	+	0.557596i
$693$	0.103159	−	0.194685i	0.00391869	−	0.00739547i
$694$	0.131154	−	0.912193i	0.00497852	−	0.0346264i
$695$	2.38443	−	0.227685i	0.0904466	−	0.00863660i
$696$	−6.60943	−	2.64602i	−0.250530	−	0.100297i
$697$	−49.7341	+	47.4214i	−1.88381	+	1.79621i
$698$	22.0141	+	11.3491i	0.833248	+	0.429569i
$699$	2.86445	+	6.27227i	0.108343	+	0.237239i
$700$	−7.50117	+	9.32052i	−0.283518	+	0.352282i
$701$	−11.2489	+	12.9819i	−0.424864	+	0.490319i	−0.927312	−	0.374288i	$-0.877887\pi$
$701$	−11.2489	+	12.9819i	−0.424864	+	0.490319i	0.502449	+	0.864607i	$0.332433\pi$
$702$	1.18300	+	0.228005i	0.0446495	+	0.00860549i
$703$	−0.0479416	+	0.197618i	−0.00180815	+	0.00745331i
$704$	−0.0828987	−	0.00791587i	−0.00312436	−	0.000298341i
$705$	−4.71688	−	2.43172i	−0.177648	−	0.0915839i
$706$	−21.0865	−	6.19156i	−0.793602	−	0.233022i
$707$	1.45273	−	4.74898i	0.0546354	−	0.178604i
$708$	5.83387	−	12.7744i	0.219250	−	0.480091i
$709$	−37.0165	+	14.8192i	−1.39019	+	0.556546i	−0.941460	−	0.337124i	$-0.890546\pi$
$709$	−37.0165	+	14.8192i	−1.39019	+	0.556546i	−0.448725	+	0.893670i	$0.648122\pi$
$710$	−3.92003	+	2.02092i	−0.147116	+	0.0758437i
$711$	3.56643	−	0.687373i	0.133752	−	0.0257785i
$712$	8.54639	+	14.8028i	0.320290	+	0.554758i
$713$	−4.50154	−	6.58091i	−0.168584	−	0.246457i
$714$	−15.5254	−	7.30264i	−0.581022	−	0.273294i
$715$	−0.0454240	−	0.0524221i	−0.00169876	−	0.00196048i
$716$	−0.390495	+	8.19749i	−0.0145935	+	0.306355i
$717$	9.39370	+	7.38729i	0.350814	+	0.275883i
$718$	−4.41140	−	6.19494i	−0.164632	−	0.231193i
$719$	−1.32361	+	1.04090i	−0.0493624	+	0.0388191i	−0.642535	−	0.766256i	$-0.722117\pi$
$719$	−1.32361	+	1.04090i	−0.0493624	+	0.0388191i	0.593173	+	0.805075i	$0.297875\pi$
$720$	−0.663368	−	0.194782i	−0.0247222	−	0.00725911i
$721$	8.24348	−	19.9374i	0.307003	−	0.742507i
$722$	−7.88753	−	17.2713i	−0.293543	−	0.642770i
$723$	0.151416	+	0.144374i	0.00563120	+	0.00536934i
$724$	−4.45768	−	12.8796i	−0.165668	−	0.478667i
$725$	−10.5296	−	30.4234i	−0.391061	−	1.12990i
$726$	−7.95606	−	7.58608i	−0.295277	−	0.281546i
$727$	11.9442	+	26.1542i	0.442986	+	0.970004i	0.991041	+	0.133561i	$0.0426413\pi$
$727$	11.9442	+	26.1542i	0.442986	+	0.970004i	−0.548055	+	0.836442i	$0.684631\pi$
$728$	−1.94205	−	2.52760i	−0.0719773	−	0.0936792i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−3.14611	+	2.47413i	−0.116443	+	0.0915716i
$731$	34.3585	+	48.2498i	1.27080	+	1.78458i
$732$	0.441883	+	0.347500i	0.0163325	+	0.0128440i
$733$	−0.600813	+	12.6126i	−0.0221916	+	0.465858i	0.960233	+	0.279199i	$0.0900689\pi$
$733$	−0.600813	+	12.6126i	−0.0221916	+	0.465858i	−0.982425	+	0.186659i	$0.940234\pi$
$734$	3.07609	+	3.55000i	0.113541	+	0.131033i
$735$	−4.77158	+	0.808625i	−0.176002	+	0.0298266i
$736$	−4.30341	+	2.11675i	−0.158626	+	0.0780244i
$737$	−0.336182	−	0.582285i	−0.0123834	−	0.0214487i
$738$	10.4055	−	2.00549i	0.383030	−	0.0738230i
$739$	−6.41052	+	3.30485i	−0.235815	+	0.121571i	−0.572084	−	0.820195i	$-0.693865\pi$
$739$	−6.41052	+	3.30485i	−0.235815	+	0.121571i	0.336270	+	0.941766i	$0.390835\pi$
$740$	−1.14945	+	0.460172i	−0.0422547	+	0.0169162i
$741$	0.0568294	−	0.124439i	0.00208768	−	0.00457138i
$742$	−24.3409	+	5.61552i	−0.893584	+	0.206152i
$743$	−19.7201	−	5.79035i	−0.723462	−	0.212427i	−0.100787	−	0.994908i	$-0.532136\pi$
$743$	−19.7201	−	5.79035i	−0.723462	−	0.212427i	−0.622675	+	0.782481i	$0.713954\pi$
$744$	1.47772	+	0.761816i	0.0541757	+	0.0279295i
$745$	4.28930	+	0.409579i	0.157148	+	0.0150058i
$746$	−6.51613	+	26.8599i	−0.238573	+	0.983410i
$747$	−10.2844	−	1.98216i	−0.376287	−	0.0725234i
$748$	0.353641	−	0.408123i	0.0129304	−	0.0149225i
$749$	25.3573	−	31.5075i	0.926537	−	1.15126i
$750$	−2.73478	−	5.98834i	−0.0998602	−	0.218663i
$751$	−3.99553	−	2.05984i	−0.145799	−	0.0751646i	0.383783	−	0.923423i	$-0.374621\pi$
$751$	−3.99553	−	2.05984i	−0.145799	−	0.0751646i	−0.529582	+	0.848259i	$0.677651\pi$
$752$	5.55521	−	5.29688i	0.202577	−	0.193157i
$753$	6.15594	+	2.46446i	0.224335	+	0.0898101i
$754$	8.53844	−	0.815322i	0.310952	−	0.0296923i
$755$	0.817512	−	5.68592i	0.0297523	−	0.206932i
$756$	1.40524	+	2.24172i	0.0511081	+	0.0815305i
$757$	28.6358	+	33.0475i	1.04079	+	1.20113i	0.979172	+	0.203032i	$0.0650794\pi$
$757$	28.6358	+	33.0475i	1.04079	+	1.20113i	0.0616144	+	0.998100i	$0.480375\pi$
$758$	6.69523	+	11.5965i	0.243182	+	0.421203i
$759$	0.390664	+	0.0829690i	0.0141802	+	0.00301159i
$760$	−0.0392526	+	0.0679875i	−0.00142384	+	0.00246616i
$761$	−0.720852	+	2.08277i	−0.0261309	+	0.0755002i	−0.957312	−	0.289057i	$-0.906658\pi$
$761$	−0.720852	+	2.08277i	−0.0261309	+	0.0755002i	0.931181	+	0.364557i	$0.118780\pi$
$762$	14.3757	+	9.23872i	0.520778	+	0.334684i
$763$	−7.44772	+	11.3068i	−0.269625	+	0.409334i
$764$	10.3219	−	22.6017i	0.373431	−	0.817701i
$765$	3.52418	−	2.77145i	0.127417	−	0.100202i
$766$	13.8590	−	13.2145i	0.500747	−	0.477461i
$767$	0.805048	+	16.9000i	0.0290686	+	0.610225i
$768$	0.580057	−	0.814576i	0.0209310	−	0.0293935i
$769$	0.980954	−	0.288034i	0.0353741	−	0.0103868i	−0.263998	−	0.964523i	$-0.585041\pi$
$769$	0.980954	−	0.288034i	0.0353741	−	0.0103868i	0.299372	+	0.954137i	$0.403223\pi$
$770$	0.0161868	−	0.151466i	0.000583331	−	0.00545845i
$771$	11.9945	−	13.8424i	0.431972	−	0.498522i
$772$	−2.96094	−	2.82325i	−0.106567	−	0.101611i
$773$	28.7078	+	2.74127i	1.03255	+	0.0985965i	0.597548	−	0.801833i	$-0.296142\pi$
$773$	28.7078	+	2.74127i	1.03255	+	0.0985965i	0.435001	+	0.900430i	$0.356748\pi$
$774$	−0.434622	−	9.12384i	−0.0156222	−	0.327950i
$775$	1.77243	+	7.30605i	0.0636675	+	0.262441i
$776$	2.70738	+	18.8303i	0.0971894	+	0.675967i
$777$	4.45981	+	1.60003i	0.159995	+	0.0574007i
$778$	1.15006	−	7.99884i	0.0412317	−	0.286772i
$779$	0.0572544	−	1.20192i	0.00205135	−	0.0430632i
$780$	0.817895	−	0.157636i	0.0292853	−	0.00564429i
$781$	−0.265610	+	0.460050i	−0.00950428	+	0.0164619i
$782$	5.00605	−	30.6943i	0.179016	−	1.09763i
$783$	−7.11941			−0.254427
$784$	1.15203	−	6.90455i	0.0411438	−	0.246591i
$785$	9.32512	+	5.99289i	0.332828	+	0.213895i
$786$	−2.56769	+	1.02795i	−0.0915863	+	0.0366656i
$787$	18.9624	+	26.6289i	0.675935	+	0.949219i	0.999995	+	0.00318180i	$0.00101280\pi$
$787$	18.9624	+	26.6289i	0.675935	+	0.949219i	−0.324060	+	0.946037i	$0.605048\pi$
$788$	4.73778	+	1.89672i	0.168776	+	0.0675678i
$789$	6.22701	+	25.6681i	0.221687	+	0.913808i
$790$	2.11248	−	1.35761i	0.0751587	−	0.0483016i
$791$	−18.3484	+	10.3197i	−0.652395	+	0.366926i
$792$	−0.0799026	+	0.0234615i	−0.00283921	+	0.000833669i
$793$	−0.665029	−	0.128174i	−0.0236159	−	0.00455158i
$794$	1.20580	+	3.48394i	0.0427923	+	0.123640i
$795$	1.53897	−	6.34371i	0.0545815	−	0.224988i
$796$	−6.54593	+	9.19247i	−0.232014	+	0.325819i
$797$	−29.3309	+	18.8498i	−1.03895	+	0.667695i	−0.944728	−	0.327856i	$-0.893674\pi$
$797$	−29.3309	+	18.8498i	−1.03895	+	0.667695i	−0.0942256	+	0.995551i	$0.530037\pi$
$798$	0.284990	−	0.0950551i	0.0100885	−	0.00336492i
$799$	7.08379	+	49.2688i	0.250606	+	1.74301i
$800$	4.50153	−	0.429844i	0.159153	−	0.0151973i
$801$	13.4358	+	10.5661i	0.474732	+	0.373333i
$802$	−12.4057	+	6.39559i	−0.438061	+	0.225836i
$803$	−0.157676	+	0.455576i	−0.00556428	+	0.0160769i
$804$	8.07395			0.284746
$805$	−3.78305	−	7.91492i	−0.133335	−	0.278964i
$806$	−2.00297			−0.0705517
$807$	0.0794292	−	0.229495i	0.00279604	−	0.00807862i
$808$	−1.66839	+	0.860114i	−0.0586937	+	0.0302587i
$809$	−32.7048	−	25.7194i	−1.14984	−	0.904245i	−0.153369	−	0.988169i	$-0.549012\pi$
$809$	−32.7048	−	25.7194i	−1.14984	−	0.904245i	−0.996472	+	0.0839239i	$0.973255\pi$
$810$	−0.688242	+	0.0657192i	−0.0241824	+	0.00230914i
$811$	−1.19723	−	8.32691i	−0.0420404	−	0.292397i	−0.999985	−	0.00544481i	$-0.998267\pi$
$811$	−1.19723	−	8.32691i	−0.0420404	−	0.292397i	0.957945	−	0.286953i	$-0.0926422\pi$
$812$	14.0956	+	12.4946i	0.494659	+	0.438476i
$813$	−23.5915	+	15.1614i	−0.827391	+	0.531732i
$814$	−0.0865064	+	0.121481i	−0.00303205	+	0.00425792i
$815$	0.0465609	−	0.191927i	0.00163096	−	0.00672289i
$816$	2.12096	+	6.12811i	0.0742484	+	0.214527i
$817$	−1.01844	−	0.196288i	−0.0356307	−	0.00686726i
$818$	23.6246	−	6.93680i	0.826014	−	0.242540i
$819$	−2.74235	−	1.62476i	−0.0958256	−	0.0567736i
$820$	6.16340	−	3.96098i	0.215235	−	0.138323i
$821$	−8.57817	−	35.3597i	−0.299380	−	1.23406i	−0.900483	−	0.434891i	$-0.856787\pi$
$821$	−8.57817	−	35.3597i	−0.299380	−	1.23406i	0.601103	−	0.799172i	$-0.294728\pi$
$822$	−10.0138	−	4.00892i	−0.349271	−	0.139827i
$823$	−2.78744	−	3.91441i	−0.0971640	−	0.136448i	0.763132	−	0.646243i	$-0.223661\pi$
$823$	−2.78744	−	3.91441i	−0.0971640	−	0.136448i	−0.860296	+	0.509795i	$0.829721\pi$
$824$	−7.57024	+	3.03067i	−0.263722	+	0.105578i
$825$	−0.316794	−	0.203591i	−0.0110293	−	0.00708813i
$826$	−25.9415	+	26.6002i	−0.902621	+	0.925541i
$827$	−11.5998			−0.403363			−0.201681	−	0.979451i	$-0.564641\pi$
$827$	−11.5998			−0.403363			−0.201681	+	0.979451i	$0.564641\pi$
$828$	−3.20843	+	3.56454i	−0.111501	+	0.123876i
$829$	11.0920	−	19.2118i	0.385240	−	0.667255i	−0.606563	−	0.795036i	$-0.707452\pi$
$829$	11.0920	−	19.2118i	0.385240	−	0.667255i	0.991802	+	0.127781i	$0.0407854\pi$
$830$	−7.11037	+	1.37041i	−0.246805	+	0.0475677i
$831$	0.564066	−	11.8412i	0.0195672	−	0.410767i
$832$	−0.171457	+	1.19251i	−0.00594420	+	0.0413428i
$833$	32.1388	+	32.0571i	1.11354	+	1.11071i
$834$	0.493053	+	3.42926i	0.0170730	+	0.118745i
$835$	−1.78508	−	7.35818i	−0.0617751	−	0.254640i
$836$	0.000449932		0.00944523i	1.55612e−5		0.000326670i
$837$	1.65500	+	0.158034i	0.0572053	+	0.00546244i
$838$	26.0675	+	24.8553i	0.900488	+	0.858613i
$839$	−14.1884	+	16.3743i	−0.489839	+	0.565305i	−0.945823	−	0.324683i	$-0.894742\pi$
$839$	−14.1884	+	16.3743i	−0.489839	+	0.565305i	0.455983	+	0.889988i	$0.349288\pi$
$840$	1.47798	+	1.07776i	0.0509951	+	0.0371861i
$841$	−20.8076	+	6.10966i	−0.717504	+	0.210678i
$842$	−1.08085	+	1.51785i	−0.0372487	+	0.0523085i
$843$	−0.932821	−	19.5823i	−0.0321281	−	0.674451i
$844$	16.5489	−	15.7794i	0.569638	−	0.543149i
$845$	6.27611	−	4.93559i	0.215905	−	0.169789i
$846$	3.18862	−	6.98211i	0.109627	−	0.240050i
$847$	13.0355	+	26.0002i	0.447903	+	0.893377i
$848$	7.94283	+	5.10455i	0.272758	+	0.175291i
$849$	10.1409	−	29.3002i	0.348035	−	1.00558i
$850$	−14.6621	+	25.3954i	−0.502905	+	0.871056i
$851$	−0.570471	+	8.56964i	−0.0195555	+	0.293763i
$852$	−3.18952	−	5.52442i	−0.109271	−	0.189263i
$853$	−6.81317	−	7.86282i	−0.233279	−	0.269218i	0.627026	−	0.778998i	$-0.284272\pi$
$853$	−6.81317	−	7.86282i	−0.233279	−	0.269218i	−0.860304	+	0.509781i	$0.829727\pi$
$854$	−0.789961	−	1.26019i	−0.0270319	−	0.0431228i
$855$	−0.0111724	+	0.0777061i	−0.000382090	+	0.00265749i
$856$	−15.2172	+	1.45307i	−0.520113	+	0.0496648i
$857$	49.2454	+	19.7149i	1.68219	+	0.673448i	0.998417	−	0.0562451i	$-0.0179128\pi$
$857$	49.2454	+	19.7149i	1.68219	+	0.673448i	0.683775	+	0.729693i	$0.260337\pi$
$858$	0.0726111	−	0.0692346i	0.00247890	−	0.00236363i
$859$	13.6779	+	7.05145i	0.466684	+	0.240592i	0.675496	−	0.737363i	$-0.263929\pi$
$859$	13.6779	+	7.05145i	0.466684	+	0.240592i	−0.208812	+	0.977956i	$0.566960\pi$
$860$	−2.62340	−	5.74445i	−0.0894572	−	0.195884i
$861$	−27.7048	−	4.30240i	−0.944179	−	0.146625i
$862$	8.46647	−	9.77082i	0.288369	−	0.332796i
$863$	−46.7553	−	9.01134i	−1.59157	−	0.306749i	−0.684913	−	0.728625i	$-0.740160\pi$
$863$	−46.7553	−	9.01134i	−1.59157	−	0.306749i	−0.906654	+	0.421875i	$0.861372\pi$
$864$	0.235759	−	0.971812i	0.00802068	−	0.0330617i
$865$	13.3578	+	1.27552i	0.454180	+	0.0433690i
$866$	−7.88530	−	4.06516i	−0.267953	−	0.138140i
$867$	−24.0374	−	7.05801i	−0.816352	−	0.239703i
$868$	−2.99936	−	3.21744i	−0.101805	−	0.109207i
$869$	0.125648	−	0.275130i	0.00426231	−	0.00933316i
$870$	−4.56959	+	1.82939i	−0.154923	+	0.0620220i
$871$	−8.64594	+	4.45729i	−0.292957	+	0.151030i
$872$	5.02489	−	0.968468i	0.170164	−	0.0327965i
$873$	9.51195	+	16.4752i	0.321931	+	0.557601i
$874$	0.307452	+	0.449471i	0.0103997	+	0.0152036i
$875$	1.46025	+	17.3563i	0.0493655	+	0.586751i
$876$	−3.79104	−	4.37510i	−0.128087	−	0.147821i
$877$	−0.426206	+	8.94716i	−0.0143919	+	0.302124i	0.980182	+	0.198097i	$0.0634760\pi$
$877$	−0.426206	+	8.94716i	−0.0143919	+	0.302124i	−0.994574	+	0.104027i	$0.966827\pi$
$878$	−3.11819	−	2.45217i	−0.105234	−	0.0827567i
$879$	−5.56916	−	7.82079i	−0.187843	−	0.263789i
$880$	−0.0452567	+	0.0355903i	−0.00152560	+	0.00119975i
$881$	31.1922	+	9.15886i	1.05089	+	0.308570i	0.761178	−	0.648543i	$-0.224621\pi$
$881$	31.1922	+	9.15886i	1.05089	+	0.308570i	0.289715	+	0.957113i	$0.406440\pi$
$882$	−1.49666	−	6.83813i	−0.0503951	−	0.230252i
$883$	13.8802	+	30.3934i	0.467107	+	1.02282i	0.985810	+	0.167866i	$0.0536877\pi$
$883$	13.8802	+	30.3934i	0.467107	+	1.02282i	−0.518703	+	0.854954i	$0.673585\pi$
$884$	−5.65429	−	5.39136i	−0.190174	−	0.181331i
$885$	−3.17560	−	9.17528i	−0.106746	−	0.308424i
$886$	11.6386	+	33.6274i	0.391005	+	1.12973i
$887$	13.7045	+	13.0672i	0.460150	+	0.438753i	0.884356	−	0.466813i	$-0.154598\pi$
$887$	13.7045	+	13.0672i	0.460150	+	0.438753i	−0.424205	+	0.905566i	$0.639447\pi$
$888$	−0.743945	−	1.62901i	−0.0249652	−	0.0546661i
$889$	−27.5460	−	35.8514i	−0.923864	−	1.20242i
$890$	11.3388	+	3.32937i	0.380077	+	0.111601i
$891$	−0.0654592	+	0.0514777i	−0.00219297	+	0.00172457i
$892$	4.53710	+	6.37146i	0.151913	+	0.213332i
$893$	−0.685108	−	0.538775i	−0.0229262	−	0.0180294i
$894$	−0.296542	+	6.22519i	−0.00991786	+	0.208202i
$895$	3.71565	+	4.28809i	0.124200	+	0.143335i
$896$	−2.17231	+	1.51031i	−0.0725719	+	0.0504561i
$897$	1.46790	−	5.58831i	0.0490118	−	0.186588i
$898$	0.240177	+	0.415999i	0.00801481	+	0.0138821i
$899$	11.6224	−	2.24002i	0.387627	−	0.0747090i
$900$	4.01932	−	2.07210i	0.133977	−	0.0690701i
$901$	−56.8412	+	22.7558i	−1.89365	+	0.758104i
$902$	0.366592	−	0.802724i	0.0122062	−	0.0267278i
$903$	−7.06932	+	23.1097i	−0.235252	+	0.769043i
$904$	7.63438	+	2.24166i	0.253916	+	0.0745563i
$905$	−8.37538	−	4.31781i	−0.278407	−	0.143529i
$906$	8.27105	+	0.789790i	0.274787	+	0.0262390i
$907$	1.66079	−	6.84585i	0.0551455	−	0.227313i	−0.937570	−	0.347797i	$-0.886930\pi$
$907$	1.66079	−	6.84585i	0.0551455	−	0.227313i	0.992715	+	0.120485i	$0.0384449\pi$
$908$	13.8427	+	2.66796i	0.459387	+	0.0885395i
$909$	−1.22921	+	1.41858i	−0.0407702	+	0.0470513i
$910$	−2.17767	−	0.338179i	−0.0721890	−	0.0112105i
$911$	−9.63506	−	21.0978i	−0.319224	−	0.699002i	0.680197	−	0.733029i	$-0.261894\pi$
$911$	−9.63506	−	21.0978i	−0.319224	−	0.699002i	−0.999421	+	0.0340269i	$0.989167\pi$
$912$	−0.100927	−	0.0520315i	−0.00334202	−	0.00172293i
$913$	−0.631245	+	0.601891i	−0.0208912	+	0.0199197i
$914$	−32.3590	−	12.9546i	−1.07034	−	0.428499i
$915$	0.386898	−	0.0369443i	0.0127905	−	0.00122134i
$916$	−2.79589	+	19.4459i	−0.0923789	+	0.642509i
$917$	7.31281	−	0.265836i	0.241490	−	0.00877867i
$918$	4.24662	+	4.90086i	0.140159	+	0.161752i
$919$	−5.22148	−	9.04387i	−0.172241	−	0.298330i	0.766962	−	0.641692i	$-0.221767\pi$
$919$	−5.22148	−	9.04387i	−0.172241	−	0.298330i	−0.939203	+	0.343362i	$0.888434\pi$
$920$	−1.14339	+	3.11233i	−0.0376966	+	0.102610i
$921$	−5.96070	+	10.3242i	−0.196412	+	0.340195i
$922$	8.94795	−	25.8534i	0.294685	−	0.851437i
$923$	6.46529	+	4.15499i	0.212808	+	0.136763i
$924$	0.219946	+	0.0129618i	0.00723568	+	0.000426411i
$925$	3.36412	−	7.36640i	0.110612	−	0.242206i
$926$	28.2268	−	22.1978i	0.927592	−	0.729466i
$927$	−5.90159	+	5.62715i	−0.193834	+	0.184820i
$928$	−0.338755	−	7.11135i	−0.0111202	−	0.233441i
$929$	14.7509	−	20.7147i	0.483961	−	0.679628i	−0.498331	−	0.866987i	$-0.666054\pi$
$929$	14.7509	−	20.7147i	0.483961	−	0.679628i	0.982291	+	0.187359i	$0.0599929\pi$
$930$	1.10287	−	0.323832i	0.0361645	−	0.0106189i
$931$	−0.794646	−	0.0179045i	−0.0260435	−	0.000586795i
$932$	−4.51552	+	5.21119i	−0.147911	+	0.170698i
$933$	1.03701	+	0.988789i	0.0339502	+	0.0323715i
$934$	24.5933	+	2.34838i	0.804717	+	0.0768412i
$935$	−0.0177651	−	0.372935i	−0.000580981	−	0.0121963i
$936$	0.284036	+	1.17081i	0.00928401	+	0.0382692i
$937$	1.46678	+	10.2017i	0.0479176	+	0.333274i	0.999653	+	0.0263534i	$0.00838952\pi$
$937$	1.46678	+	10.2017i	0.0479176	+	0.333274i	−0.951735	+	0.306921i	$0.900701\pi$
$938$	−20.1068	−	7.21364i	−0.656511	−	0.235534i
$939$	1.83472	−	12.7608i	0.0598739	−	0.416432i
$940$	0.252508	−	5.30080i	0.00823591	−	0.172893i
$941$	−10.3582	+	1.99637i	−0.337667	+	0.0650799i	−0.355266	−	0.934765i	$-0.615610\pi$
$941$	−10.3582	+	1.99637i	−0.337667	+	0.0650799i	0.0175995	+	0.999845i	$0.494398\pi$
$942$	−8.01650	+	13.8850i	−0.261192	+	0.452397i
$943$	−6.28211	−	50.4315i	−0.204574	−	1.64227i
$944$	14.0435			0.457076
$945$	1.77267	+	0.451246i	0.0576649	+	0.0146790i
$946$	−0.639905	−	0.411242i	−0.0208051	−	0.0133706i
$947$	−51.1452	+	20.4754i	−1.66199	+	0.665362i	−0.996697	−	0.0812152i	$-0.974120\pi$
$947$	−51.1452	+	20.4754i	−1.66199	+	0.665362i	−0.665298	+	0.746578i	$0.731696\pi$
$948$	2.10680	+	2.95859i	0.0684258	+	0.0960906i
$949$	6.47493	+	2.59217i	0.210185	+	0.0841454i
$950$	−0.121056	−	0.498998i	−0.00392756	−	0.0161896i
$951$	−20.3075	+	13.0508i	−0.658515	+	0.423202i
$952$	0.193249	−	17.1560i	0.00626325	−	0.556029i
$953$	−0.393757	+	0.115617i	−0.0127550	+	0.00374522i	−0.288104	−	0.957599i	$-0.593025\pi$
$953$	−0.393757	+	0.115617i	−0.0127550	+	0.00374522i	0.275349	+	0.961344i	$0.411207\pi$
$954$	9.27104	+	1.78685i	0.300161	+	0.0578513i
$955$	−5.61857	−	16.2338i	−0.181813	−	0.525313i
$956$	−2.81743	+	11.6136i	−0.0911221	+	0.375611i
$957$	−0.343901	+	0.482942i	−0.0111167	+	0.0156113i
$958$	−20.2966	+	13.0438i	−0.655754	+	0.421428i
$959$	21.3559	+	18.9303i	0.689619	+	0.611293i
$960$	−0.0983926	−	0.684336i	−0.00317561	−	0.0220868i
$961$	28.1081	−	2.68400i	0.906714	−	0.0865807i
$962$	1.69596	+	1.33372i	0.0546800	+	0.0430008i
$963$	−13.5871	+	7.00464i	−0.437838	+	0.225721i
$964$	−0.0684273	+	0.197708i	−0.00220389	+	0.00636774i
$965$	−2.82854			−0.0910541
$966$	11.1748	−	6.01032i	0.359543	−	0.193379i
$967$	−44.3619			−1.42658			−0.713291	−	0.700868i	$-0.752796\pi$
$967$	−44.3619			−1.42658			−0.713291	+	0.700868i	$0.752796\pi$
$968$	3.59548	−	10.3885i	0.115563	−	0.333898i
$969$	0.654487	−	0.337412i	0.0210252	−	0.0108392i
$970$	10.3387	+	8.13041i	0.331954	+	0.261052i
$971$	21.0510	−	2.01013i	0.675558	−	0.0645080i	0.248363	−	0.968667i	$-0.420108\pi$
$971$	21.0510	−	2.01013i	0.675558	−	0.0645080i	0.427196	+	0.904159i	$0.359501\pi$
$972$	−0.142315	−	0.989821i	−0.00456475	−	0.0317485i
$973$	1.83599	−	8.98050i	0.0588593	−	0.287902i
$974$	−1.75298	+	1.12657i	−0.0561691	+	0.0360977i
$975$	−3.16014	+	4.43780i	−0.101206	+	0.142123i
$976$	−0.132533	+	0.546308i	−0.00424227	+	0.0174869i
$977$	11.3227	+	32.7147i	0.362245	+	1.04664i	0.967992	+	0.250980i	$0.0807529\pi$
$977$	11.3227	+	32.7147i	0.362245	+	1.04664i	−0.605748	+	0.795657i	$0.707126\pi$
$978$	0.280492	+	0.0540604i	0.00896915	+	0.00172866i
$979$	1.36576	−	0.401023i	0.0436498	−	0.0128167i
$980$	−2.71774	−	4.00447i	−0.0868149	−	0.127918i
$981$	4.30500	−	2.76666i	0.137448	−	0.0883326i
$982$	4.72896	+	19.4931i	0.150907	+	0.622048i
$983$	16.2573	+	6.50843i	0.518526	+	0.207587i	0.616138	−	0.787638i	$-0.288696\pi$
$983$	16.2573	+	6.50843i	0.518526	+	0.207587i	−0.0976120	+	0.995225i	$0.531120\pi$
$984$	6.14684	+	8.63203i	0.195954	+	0.275179i
$985$	3.27557	−	1.31134i	0.104368	−	0.0417828i
$986$	38.8387	+	24.9601i	1.23688	+	0.794893i
$987$	−14.1789	+	14.5389i	−0.451319	+	0.462779i
$988$	0.136802			0.00435224
$989$	−43.7982	−	0.826608i	−1.39270	−	0.0262846i
$990$	−0.0287873	+	0.0498611i	−0.000914921	+	0.00158469i
$991$	13.0033	−	2.50617i	0.413062	−	0.0796112i	0.0215134	−	0.999769i	$-0.493152\pi$
$991$	13.0033	−	2.50617i	0.413062	−	0.0796112i	0.391549	+	0.920157i	$0.371939\pi$
$992$	−0.0791064	+	1.66065i	−0.00251163	+	0.0527256i
$993$	−4.20587	+	29.2525i	−0.133469	+	0.928299i
$994$	3.00720	+	16.6073i	0.0953825	+	0.526752i
$995$	1.11036	+	7.72272i	0.0352008	+	0.244827i
$996$	−2.46927	−	10.1785i	−0.0782417	−	0.322517i
$997$	−0.249206	−	5.23148i	−0.00789243	−	0.165683i	−0.999372	−	0.0354233i	$-0.988722\pi$
$997$	−0.249206	−	5.23148i	−0.00789243	−	0.165683i	0.991480	−	0.130259i	$-0.0415810\pi$
$998$	−26.6750	−	2.54715i	−0.844381	−	0.0806287i
$999$	−1.29610	−	1.23583i	−0.0410067	−	0.0390998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.151.3	✓	160
7.2	even	3	inner	966.2.y.d.289.6	yes	160
23.16	even	11	inner	966.2.y.d.361.6	yes	160
161.16	even	33	inner	966.2.y.d.499.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.151.3	✓	160	1.1	even	1	trivial
966.2.y.d.289.6	yes	160	7.2	even	3	inner
966.2.y.d.361.6	yes	160	23.16	even	11	inner
966.2.y.d.499.3	yes	160	161.16	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)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.688242 + 0.0657192i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.529942 + 2.59213i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.688242 + 0.0657192i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.529942 + 2.59213i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.162997 - 0.671884i) q^{10} +(-0.0272369 - 0.0786957i) q^{11} +(0.981929 + 0.189251i) q^{12} +(-1.15597 + 0.339424i) q^{13} +(-2.27624 - 1.34860i) q^{14} +(0.581620 - 0.373784i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-6.02025 - 2.41014i) q^{17} +(0.580057 + 0.814576i) q^{18} +(0.105416 - 0.0422021i) q^{19} +(0.581620 + 0.373784i) q^{20} +(-0.716754 - 2.54681i) q^{21} +0.0832758 q^{22} +(4.08272 - 2.51623i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.44028 + 0.855795i) q^{25} +(0.0573254 - 1.20341i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(2.01891 - 1.70997i) q^{28} +(1.01320 + 7.04695i) q^{29} +(0.162997 + 0.671884i) q^{30} +(-0.0791064 - 1.66065i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(0.0602696 + 0.0574669i) q^{33} +(4.24662 - 4.90086i) q^{34} +(0.194376 - 1.81884i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.03879 + 1.45878i) q^{37} +(0.00540291 + 0.113421i) q^{38} +(0.871935 - 0.831388i) q^{39} +(-0.543456 + 0.427378i) q^{40} +(4.40214 - 9.63933i) q^{41} +(2.64117 + 0.155649i) q^{42} +(-7.68417 - 4.93831i) q^{43} +(-0.0272369 + 0.0786957i) q^{44} +(-0.345687 + 0.598747i) q^{45} +(1.04251 + 4.68115i) q^{46} +(-3.83788 - 6.64740i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(-6.43832 - 2.74736i) q^{49} +(0.643548 - 4.47598i) q^{50} +(6.45540 - 0.616416i) q^{51} +(1.11847 + 0.447769i) q^{52} +(6.83325 - 6.51550i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(0.0239174 + 0.0523718i) q^{55} +(0.955598 + 2.46715i) q^{56} +(-0.0743592 + 0.0858151i) q^{57} +(-6.99076 - 1.34736i) q^{58} +(3.31088 - 13.6476i) q^{59} +(-0.688242 - 0.0657192i) q^{60} +(0.499662 + 0.257594i) q^{61} +(1.59519 + 0.468389i) q^{62} +(1.80409 + 1.93526i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.773282 - 0.309575i) q^{65} +(-0.0740185 + 0.0381592i) q^{66} +(7.92804 - 1.52800i) q^{67} +(3.24238 + 5.61597i) q^{68} +(-2.47586 + 4.10732i) q^{69} +(1.65524 + 0.778571i) q^{70} +(-4.17739 - 4.82096i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-4.55053 - 3.57857i) q^{73} +(-1.03879 - 1.45878i) q^{74} +(3.55453 - 2.79532i) q^{75} +(-0.108950 - 0.0319906i) q^{76} +(0.218424 - 0.0288974i) q^{77} +(0.500481 + 1.09590i) q^{78} +(2.62865 + 2.50641i) q^{79} +(-0.226126 - 0.653348i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(7.66938 + 7.31274i) q^{82} +(-4.35093 - 9.52721i) q^{83} +(-1.01093 + 2.44500i) q^{84} +(4.30178 + 1.26312i) q^{85} +(7.17996 - 5.64638i) q^{86} +(-4.12966 - 5.79930i) q^{87} +(-0.0654592 - 0.0514777i) q^{88} +(-0.813308 + 17.0734i) q^{89} +(-0.452753 - 0.522505i) q^{90} +(-0.267234 - 3.17631i) q^{91} +(-4.76466 - 0.545878i) q^{92} +(0.831266 + 1.43979i) q^{93} +(7.53704 - 1.45265i) q^{94} +(-0.0697782 + 0.0359731i) q^{95} +(0.928368 - 0.371662i) q^{96} +(-7.90282 + 17.3048i) q^{97} +(4.70203 - 5.18565i) q^{98} +(-0.0799026 - 0.0234615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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