LMFDB - Embedded newform 702.2.t.a.415.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(181,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.181"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.4
Character	$\chi$	$=$	702.415
Dual form			702.2.t.a.181.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.419378 + 0.242128i) q^{5} +(4.37722 - 2.52719i) q^{7} +1.00000i q^{8} -0.484256 q^{10} +(2.78126 - 1.60576i) q^{11} +(-0.722307 + 3.53246i) q^{13} +(-2.52719 + 4.37722i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.20245 q^{17} -3.21153i q^{19} +(0.419378 - 0.242128i) q^{20} +(-1.60576 + 2.78126i) q^{22} +(3.13608 - 5.43186i) q^{23} +(-2.38275 - 4.12704i) q^{25} +(-1.14069 - 3.42035i) q^{26} -5.05438i q^{28} +(2.29627 + 3.97725i) q^{29} +(-5.61504 - 3.24185i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.63943 - 2.10123i) q^{34} +2.44761 q^{35} +2.08429i q^{37} +(1.60576 + 2.78126i) q^{38} +(-0.242128 + 0.419378i) q^{40} +(9.57301 + 5.52698i) q^{41} +(4.73367 + 8.19896i) q^{43} -3.21153i q^{44} +6.27217i q^{46} +(4.57369 - 2.64062i) q^{47} +(9.27337 - 16.0619i) q^{49} +(4.12704 + 2.38275i) q^{50} +(2.69805 + 2.39177i) q^{52} -6.41990 q^{53} +1.55520 q^{55} +(2.52719 + 4.37722i) q^{56} +(-3.97725 - 2.29627i) q^{58} +(-3.13771 - 1.81156i) q^{59} +(0.500864 + 0.867521i) q^{61} +6.48369 q^{62} -1.00000 q^{64} +(-1.15823 + 1.30655i) q^{65} +(0.936987 + 0.540970i) q^{67} +(-2.10123 + 3.63943i) q^{68} +(-2.11969 + 1.22381i) q^{70} +4.63041i q^{71} +0.325525i q^{73} +(-1.04214 - 1.80504i) q^{74} +(-2.78126 - 1.60576i) q^{76} +(8.11614 - 14.0576i) q^{77} +(3.91818 + 6.78649i) q^{79} -0.484256i q^{80} -11.0540 q^{82} +(5.08022 - 2.93306i) q^{83} +(-1.76242 - 1.01753i) q^{85} +(-8.19896 - 4.73367i) q^{86} +(1.60576 + 2.78126i) q^{88} -8.42912i q^{89} +(5.76550 + 17.2878i) q^{91} +(-3.13608 - 5.43186i) q^{92} +(-2.64062 + 4.57369i) q^{94} +(0.777601 - 1.34684i) q^{95} +(11.3021 - 6.52525i) q^{97} +18.5467i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.419378	+	0.242128i	0.187552	+	0.108283i	0.590836	−	0.806792i	$-0.298798\pi$
$5$	0.419378	+	0.242128i	0.187552	+	0.108283i	−0.403284	+	0.915075i	$0.632131\pi$
$6$		0			0
$7$	4.37722	−	2.52719i	1.65443	−	0.955188i	0.679216	−	0.733938i	$-0.262320\pi$
$7$	4.37722	−	2.52719i	1.65443	−	0.955188i	0.975217	−	0.221249i	$-0.0710134\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.484256			−0.153135
$11$	2.78126	−	1.60576i	0.838583	−	0.484156i	−0.0181994	−	0.999834i	$-0.505793\pi$
$11$	2.78126	−	1.60576i	0.838583	−	0.484156i	0.856782	+	0.515678i	$0.172460\pi$
$12$		0			0
$13$	−0.722307	+	3.53246i	−0.200332	+	0.979728i
$13$	−0.722307	+	3.53246i	−0.200332	+	0.979728i
$14$	−2.52719	+	4.37722i	−0.675420	+	1.16986i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.20245			−1.01924			−0.509622	−	0.860398i	$-0.670215\pi$
$17$	−4.20245			−1.01924			−0.509622	+	0.860398i	$0.670215\pi$
$18$		0			0
$19$		−	3.21153i		−	0.736775i	−0.929672	−	0.368388i	$-0.879910\pi$
$19$		−	3.21153i		−	0.736775i	0.929672	−	0.368388i	$-0.120090\pi$
$20$	0.419378	−	0.242128i	0.0937758	−	0.0541415i
$21$		0			0
$22$	−1.60576	+	2.78126i	−0.342350	+	0.592968i
$23$	3.13608	−	5.43186i	0.653919	−	1.13262i	−0.328245	−	0.944593i	$-0.606457\pi$
$23$	3.13608	−	5.43186i	0.653919	−	1.13262i	0.982164	−	0.188028i	$-0.0602094\pi$
$24$		0			0
$25$	−2.38275	−	4.12704i	−0.476550	−	0.825408i
$26$	−1.14069	−	3.42035i	−0.223708	−	0.670787i
$27$		0			0
$28$		−	5.05438i		−	0.955188i
$29$	2.29627	+	3.97725i	0.426406	+	0.738557i	0.996551	−	0.0829873i	$-0.0264461\pi$
$29$	2.29627	+	3.97725i	0.426406	+	0.738557i	−0.570144	+	0.821544i	$0.693113\pi$
$30$		0			0
$31$	−5.61504	−	3.24185i	−1.00849	−	0.582253i	−0.0977420	−	0.995212i	$-0.531162\pi$
$31$	−5.61504	−	3.24185i	−1.00849	−	0.582253i	−0.910750	+	0.412959i	$0.864495\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	3.63943	−	2.10123i	0.624157	−	0.360357i
$35$	2.44761			0.413722
$36$		0			0
$37$			2.08429i			0.342654i	0.985214	+	0.171327i	$0.0548055\pi$
$37$			2.08429i			0.342654i	−0.985214	+	0.171327i	$0.945194\pi$
$38$	1.60576	+	2.78126i	0.260489	+	0.451181i
$39$		0			0
$40$	−0.242128	+	0.419378i	−0.0382838	+	0.0663095i
$41$	9.57301	+	5.52698i	1.49505	+	0.863169i	0.999984	−	0.00568392i	$-0.00180926\pi$
$41$	9.57301	+	5.52698i	1.49505	+	0.863169i	0.495070	+	0.868853i	$0.335143\pi$
$42$		0			0
$43$	4.73367	+	8.19896i	0.721879	+	1.25033i	0.960246	+	0.279155i	$0.0900544\pi$
$43$	4.73367	+	8.19896i	0.721879	+	1.25033i	−0.238367	+	0.971175i	$0.576612\pi$
$44$		−	3.21153i		−	0.484156i
$45$		0			0
$46$			6.27217i			0.924780i
$47$	4.57369	−	2.64062i	0.667141	−	0.385174i	−0.127851	−	0.991793i	$-0.540808\pi$
$47$	4.57369	−	2.64062i	0.667141	−	0.385174i	0.794992	+	0.606619i	$0.207475\pi$
$48$		0			0
$49$	9.27337	−	16.0619i	1.32477	−	2.29456i
$50$	4.12704	+	2.38275i	0.583652	+	0.336971i
$51$		0			0
$52$	2.69805	+	2.39177i	0.374152	+	0.331678i
$53$	−6.41990			−0.881841			−0.440921	−	0.897546i	$-0.645348\pi$
$53$	−6.41990			−0.881841			−0.440921	+	0.897546i	$0.645348\pi$
$54$		0			0
$55$	1.55520			0.209703
$56$	2.52719	+	4.37722i	0.337710	+	0.584931i
$57$		0			0
$58$	−3.97725	−	2.29627i	−0.522239	−	0.301515i
$59$	−3.13771	−	1.81156i	−0.408495	−	0.235844i	0.281648	−	0.959518i	$-0.409119\pi$
$59$	−3.13771	−	1.81156i	−0.408495	−	0.235844i	−0.690143	+	0.723673i	$0.742452\pi$
$60$		0			0
$61$	0.500864	+	0.867521i	0.0641290	+	0.111075i	0.896307	−	0.443433i	$-0.146240\pi$
$61$	0.500864	+	0.867521i	0.0641290	+	0.111075i	−0.832178	+	0.554508i	$0.812906\pi$
$62$	6.48369			0.823430
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.15823	+	1.30655i	−0.143660	+	0.162057i
$66$		0			0
$67$	0.936987	+	0.540970i	0.114471	+	0.0660900i	0.556142	−	0.831087i	$-0.312281\pi$
$67$	0.936987	+	0.540970i	0.114471	+	0.0660900i	−0.441671	+	0.897177i	$0.645614\pi$
$68$	−2.10123	+	3.63943i	−0.254811	+	0.441346i
$69$		0			0
$70$	−2.11969	+	1.22381i	−0.253352	+	0.146273i
$71$			4.63041i			0.549529i	0.961512	+	0.274764i	$0.0885999\pi$
$71$			4.63041i			0.549529i	−0.961512	+	0.274764i	$0.911400\pi$
$72$		0			0
$73$			0.325525i			0.0380998i	0.999819	+	0.0190499i	$0.00606414\pi$
$73$			0.325525i			0.0380998i	−0.999819	+	0.0190499i	$0.993936\pi$
$74$	−1.04214	−	1.80504i	−0.121147	−	0.209832i
$75$		0			0
$76$	−2.78126	−	1.60576i	−0.319033	−	0.184194i
$77$	8.11614	−	14.0576i	0.924920	−	1.60201i
$78$		0			0
$79$	3.91818	+	6.78649i	0.440830	+	0.763540i	0.997751	−	0.0670253i	$-0.0213508\pi$
$79$	3.91818	+	6.78649i	0.440830	+	0.763540i	−0.556921	+	0.830565i	$0.688017\pi$
$80$		−	0.484256i		−	0.0541415i
$81$		0			0
$82$	−11.0540			−1.22071
$83$	5.08022	−	2.93306i	0.557626	−	0.321946i	−0.194566	−	0.980889i	$-0.562330\pi$
$83$	5.08022	−	2.93306i	0.557626	−	0.321946i	0.752192	+	0.658944i	$0.228997\pi$
$84$		0			0
$85$	−1.76242	−	1.01753i	−0.191161	−	0.110367i
$86$	−8.19896	−	4.73367i	−0.884117	−	0.510445i
$87$		0			0
$88$	1.60576	+	2.78126i	0.171175	+	0.296484i
$89$		−	8.42912i		−	0.893485i	−0.894662	−	0.446743i	$-0.852584\pi$
$89$		−	8.42912i		−	0.893485i	0.894662	−	0.446743i	$-0.147416\pi$
$90$		0			0
$91$	5.76550	+	17.2878i	0.604388	+	1.81225i
$92$	−3.13608	−	5.43186i	−0.326959	−	0.566310i
$93$		0			0
$94$	−2.64062	+	4.57369i	−0.272359	+	0.471740i
$95$	0.777601	−	1.34684i	0.0797802	−	0.138183i
$96$		0			0
$97$	11.3021	−	6.52525i	1.14755	−	0.662539i	0.199262	−	0.979946i	$-0.436145\pi$
$97$	11.3021	−	6.52525i	1.14755	−	0.662539i	0.948289	+	0.317407i	$0.102812\pi$
$98$			18.5467i			1.87350i
$99$		0			0
$100$	−4.76550			−0.476550
$101$	−3.42351	−	5.92969i	−0.340652	−	0.590027i	0.643902	−	0.765108i	$-0.277314\pi$
$101$	−3.42351	−	5.92969i	−0.340652	−	0.590027i	−0.984554	+	0.175081i	$0.943981\pi$
$102$		0			0
$103$	−1.77760	+	3.07889i	−0.175152	+	0.303373i	−0.940214	−	0.340584i	$-0.889375\pi$
$103$	−1.77760	+	3.07889i	−0.175152	+	0.303373i	0.765062	+	0.643957i	$0.222708\pi$
$104$	−3.53246	−	0.722307i	−0.346386	−	0.0708280i
$105$		0			0
$106$	5.55980	−	3.20995i	0.540015	−	0.311778i
$107$	−1.41392			−0.136689			−0.0683445	−	0.997662i	$-0.521772\pi$
$107$	−1.41392			−0.136689			−0.0683445	+	0.997662i	$0.521772\pi$
$108$		0			0
$109$			4.97525i			0.476543i	0.971199	+	0.238271i	$0.0765808\pi$
$109$			4.97525i			0.476543i	−0.971199	+	0.238271i	$0.923419\pi$
$110$	−1.34684	+	0.777601i	−0.128417	+	0.0741413i
$111$		0			0
$112$	−4.37722	−	2.52719i	−0.413608	−	0.238797i
$113$	−6.54415	+	11.3348i	−0.615622	+	1.06629i	0.374653	+	0.927165i	$0.377762\pi$
$113$	−6.54415	+	11.3348i	−0.615622	+	1.06629i	−0.990275	+	0.139124i	$0.955571\pi$
$114$		0			0
$115$	2.63041	−	1.51867i	0.245287	−	0.141616i
$116$	4.59254			0.426406
$117$		0			0
$118$	3.62311			0.333534
$119$	−18.3951	+	10.6204i	−1.68627	+	0.973570i
$120$		0			0
$121$	−0.343044	+	0.594169i	−0.0311858	+	0.0540154i
$122$	−0.867521	−	0.500864i	−0.0785417	−	0.0453461i
$123$		0			0
$124$	−5.61504	+	3.24185i	−0.504246	+	0.291126i
$125$		−	4.72900i		−	0.422975i
$126$		0			0
$127$	−4.56300			−0.404901			−0.202450	−	0.979293i	$-0.564890\pi$
$127$	−4.56300			−0.404901			−0.202450	+	0.979293i	$0.564890\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	0.349781	−	1.71061i	0.0306779	−	0.150031i
$131$	1.23473	−	2.13862i	0.107879	−	0.186852i	−0.807032	−	0.590508i	$-0.798927\pi$
$131$	1.23473	−	2.13862i	0.107879	−	0.186852i	0.914911	+	0.403656i	$0.132261\pi$
$132$		0			0
$133$	−8.11614	−	14.0576i	−0.703758	−	1.21895i
$134$	−1.08194			−0.0934654
$135$		0			0
$136$		−	4.20245i		−	0.360357i
$137$	−16.9831	+	9.80519i	−1.45096	+	0.837714i	−0.998536	−	0.0540880i	$-0.982775\pi$
$137$	−16.9831	+	9.80519i	−1.45096	+	0.837714i	−0.452427	+	0.891802i	$0.649442\pi$
$138$		0			0
$139$	0.193698	−	0.335495i	0.0164293	−	0.0284563i	−0.857694	−	0.514161i	$-0.828104\pi$
$139$	0.193698	−	0.335495i	0.0164293	−	0.0284563i	0.874123	+	0.485704i	$0.161437\pi$
$140$	1.22381	−	2.11969i	0.103430	−	0.179147i
$141$		0			0
$142$	−2.31521	−	4.01005i	−0.194288	−	0.336516i
$143$	3.66337	+	10.9846i	0.306346	+	0.918575i
$144$		0			0
$145$			2.22396i			0.184690i
$146$	−0.162762	−	0.281913i	−0.0134703	−	0.0233313i
$147$		0			0
$148$	1.80504	+	1.04214i	0.148374	+	0.0856636i
$149$	−8.19151	−	4.72937i	−0.671075	−	0.387445i	0.125409	−	0.992105i	$-0.459976\pi$
$149$	−8.19151	−	4.72937i	−0.671075	−	0.387445i	−0.796484	+	0.604660i	$0.793309\pi$
$150$		0			0
$151$	1.15323	−	0.665819i	0.0938487	−	0.0541836i	−0.452341	−	0.891845i	$-0.649411\pi$
$151$	1.15323	−	0.665819i	0.0938487	−	0.0541836i	0.546190	+	0.837661i	$0.316078\pi$
$152$	3.21153			0.260489
$153$		0			0
$154$			16.2323i			1.30803i
$155$	−1.56988	−	2.71912i	−0.126096	−	0.218405i
$156$		0			0
$157$	2.92122	−	5.05970i	0.233139	−	0.403808i	−0.725592	−	0.688126i	$-0.758434\pi$
$157$	2.92122	−	5.05970i	0.233139	−	0.403808i	0.958730	+	0.284318i	$0.0917671\pi$
$158$	−6.78649	−	3.91818i	−0.539904	−	0.311714i
$159$		0			0
$160$	0.242128	+	0.419378i	0.0191419	+	0.0331547i
$161$		−	31.7019i		−	2.49846i
$162$		0			0
$163$			15.1340i			1.18538i	0.805430	+	0.592691i	$0.201935\pi$
$163$			15.1340i			1.18538i	−0.805430	+	0.592691i	$0.798065\pi$
$164$	9.57301	−	5.52698i	0.747527	−	0.431585i
$165$		0			0
$166$	−2.93306	+	5.08022i	−0.227650	+	0.394301i
$167$	−10.4155	−	6.01341i	−0.805978	−	0.465331i	0.0395794	−	0.999216i	$-0.487398\pi$
$167$	−10.4155	−	6.01341i	−0.805978	−	0.465331i	−0.845557	+	0.533885i	$0.820732\pi$
$168$		0			0
$169$	−11.9565	−	5.10304i	−0.919734	−	0.392542i
$170$	2.03506			0.156082
$171$		0			0
$172$	9.46735			0.721879
$173$	4.42932	+	7.67180i	0.336755	+	0.583276i	0.983820	−	0.179158i	$-0.0573374\pi$
$173$	4.42932	+	7.67180i	0.336755	+	0.583276i	−0.647066	+	0.762434i	$0.724004\pi$
$174$		0			0
$175$	−20.8596	−	12.0433i	−1.57684	−	0.910389i
$176$	−2.78126	−	1.60576i	−0.209646	−	0.121039i
$177$		0			0
$178$	4.21456	+	7.29984i	0.315895	+	0.547146i
$179$	−10.3704			−0.775121			−0.387561	−	0.921844i	$-0.626682\pi$
$179$	−10.3704			−0.775121			−0.387561	+	0.921844i	$0.626682\pi$
$180$		0			0
$181$	10.8407			0.805783			0.402892	−	0.915248i	$-0.368005\pi$
$181$	10.8407			0.805783			0.402892	+	0.915248i	$0.368005\pi$
$182$	−13.6369	−	12.0889i	−1.01084	−	0.896088i
$183$		0			0
$184$	5.43186	+	3.13608i	0.400442	+	0.231195i
$185$	−0.504664	+	0.874103i	−0.0371036	+	0.0642653i
$186$		0			0
$187$	−11.6881	+	6.74815i	−0.854721	+	0.493474i
$188$		−	5.28124i		−	0.385174i
$189$		0			0
$190$			1.55520i			0.112826i
$191$	5.62900	+	9.74971i	0.407300	+	0.705464i	0.994586	−	0.103915i	$-0.0331370\pi$
$191$	5.62900	+	9.74971i	0.407300	+	0.705464i	−0.587286	+	0.809379i	$0.699804\pi$
$192$		0			0
$193$	6.60401	+	3.81283i	0.475367	+	0.274453i	0.718484	−	0.695544i	$-0.244836\pi$
$193$	6.60401	+	3.81283i	0.475367	+	0.274453i	−0.243117	+	0.969997i	$0.578170\pi$
$194$	−6.52525	+	11.3021i	−0.468486	+	0.811441i
$195$		0			0
$196$	−9.27337	−	16.0619i	−0.662383	−	1.14728i
$197$			24.5170i			1.74677i	0.487035	+	0.873383i	$0.338079\pi$
$197$			24.5170i			1.74677i	−0.487035	+	0.873383i	$0.661921\pi$
$198$		0			0
$199$	−13.5310			−0.959187			−0.479593	−	0.877491i	$-0.659216\pi$
$199$	−13.5310			−0.959187			−0.479593	+	0.877491i	$0.659216\pi$
$200$	4.12704	−	2.38275i	0.291826	−	0.168486i
$201$		0			0
$202$	5.92969	+	3.42351i	0.417212	+	0.240877i
$203$	20.1025	+	11.6062i	1.41092	+	0.814596i
$204$		0			0
$205$	2.67647	+	4.63579i	0.186933	+	0.323777i
$206$		−	3.55520i		−	0.247703i
$207$		0			0
$208$	3.42035	−	1.14069i	0.237159	−	0.0790929i
$209$	−5.15696	−	8.93211i	−0.356714	−	0.617847i
$210$		0			0
$211$	−11.9346	+	20.6713i	−0.821610	+	1.42307i	0.0828724	+	0.996560i	$0.473591\pi$
$211$	−11.9346	+	20.6713i	−0.821610	+	1.42307i	−0.904483	+	0.426511i	$0.859743\pi$
$212$	−3.20995	+	5.55980i	−0.220460	+	0.381849i
$213$		0			0
$214$	1.22449	−	0.706961i	0.0837045	−	0.0483268i
$215$			4.58462i			0.312668i
$216$		0			0
$217$	−32.7710			−2.22464
$218$	−2.48763	−	4.30869i	−0.168483	−	0.291822i
$219$		0			0
$220$	0.777601	−	1.34684i	0.0524258	−	0.0908042i
$221$	3.03546	−	14.8450i	0.204187	−	0.998583i
$222$		0			0
$223$	−11.1456	+	6.43490i	−0.746363	+	0.430913i	−0.824378	−	0.566040i	$-0.808475\pi$
$223$	−11.1456	+	6.43490i	−0.746363	+	0.430913i	0.0780155	+	0.996952i	$0.475142\pi$
$224$	5.05438			0.337710
$225$		0			0
$226$		−	13.0883i		−	0.870621i
$227$	15.6362	−	9.02759i	1.03781	−	0.599182i	0.118600	−	0.992942i	$-0.462159\pi$
$227$	15.6362	−	9.02759i	1.03781	−	0.599182i	0.919213	+	0.393760i	$0.128826\pi$
$228$		0			0
$229$	−18.3370	−	10.5869i	−1.21174	−	0.699599i	−0.248603	−	0.968606i	$-0.579971\pi$
$229$	−18.3370	−	10.5869i	−1.21174	−	0.699599i	−0.963138	+	0.269006i	$0.913305\pi$
$230$	−1.51867	+	2.63041i	−0.100138	+	0.173444i
$231$		0			0
$232$	−3.97725	+	2.29627i	−0.261119	+	0.150757i
$233$	−29.0610			−1.90385			−0.951923	−	0.306337i	$-0.900897\pi$
$233$	−29.0610			−1.90385			−0.951923	+	0.306337i	$0.900897\pi$
$234$		0			0
$235$	2.55747			0.166831
$236$	−3.13771	+	1.81156i	−0.204247	+	0.117922i
$237$		0			0
$238$	10.6204	−	18.3951i	0.688418	−	1.19237i
$239$	−6.29516	−	3.63451i	−0.407200	−	0.235097i	0.282386	−	0.959301i	$-0.408874\pi$
$239$	−6.29516	−	3.63451i	−0.407200	−	0.235097i	−0.689586	+	0.724204i	$0.742207\pi$
$240$		0			0
$241$	15.5109	−	8.95521i	0.999144	−	0.576856i	0.0911491	−	0.995837i	$-0.470946\pi$
$241$	15.5109	−	8.95521i	0.999144	−	0.576856i	0.907995	+	0.418981i	$0.137613\pi$
$242$		−	0.686087i		−	0.0441034i
$243$		0			0
$244$	1.00173			0.0641290
$245$	7.77809	−	4.49068i	0.496924	−	0.286899i
$246$		0			0
$247$	11.3446	+	2.31971i	0.721839	+	0.147600i
$248$	3.24185	−	5.61504i	0.205857	−	0.356556i
$249$		0			0
$250$	2.36450	+	4.09543i	0.149544	+	0.259018i
$251$	3.84702			0.242822			0.121411	−	0.992602i	$-0.461258\pi$
$251$	3.84702			0.242822			0.121411	+	0.992602i	$0.461258\pi$
$252$		0			0
$253$		−	20.1432i		−	1.26639i
$254$	3.95167	−	2.28150i	0.247950	−	0.143154i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.38375	+	12.7890i	−0.460586	+	0.797758i	−0.998990	−	0.0449285i	$-0.985694\pi$
$257$	−7.38375	+	12.7890i	−0.460586	+	0.797758i	0.538404	+	0.842687i	$0.319027\pi$
$258$		0			0
$259$	5.26738	+	9.12337i	0.327299	+	0.566899i
$260$	0.552388	+	1.65633i	0.0342576	+	0.102721i
$261$		0			0
$262$			2.46946i			0.152564i
$263$	4.38124	+	7.58853i	0.270159	+	0.467929i	0.968902	−	0.247443i	$-0.0795904\pi$
$263$	4.38124	+	7.58853i	0.270159	+	0.467929i	−0.698743	+	0.715372i	$0.746257\pi$
$264$		0			0
$265$	−2.69237	−	1.55444i	−0.165391	−	0.0954884i
$266$	14.0576	+	8.11614i	0.861924	+	0.497632i
$267$		0			0
$268$	0.936987	−	0.540970i	0.0572356	−	0.0330450i
$269$	8.90736			0.543091			0.271546	−	0.962426i	$-0.412465\pi$
$269$	8.90736			0.543091			0.271546	+	0.962426i	$0.412465\pi$
$270$		0			0
$271$		−	3.58551i		−	0.217804i	−0.994052	−	0.108902i	$-0.965266\pi$
$271$		−	3.58551i		−	0.217804i	0.994052	−	0.108902i	$-0.0347335\pi$
$272$	2.10123	+	3.63943i	0.127406	+	0.220673i
$273$		0			0
$274$	9.80519	−	16.9831i	0.592353	−	1.02599i
$275$	−13.2541	−	7.65226i	−0.799253	−	0.461449i
$276$		0			0
$277$	7.43966	+	12.8859i	0.447006	+	0.774237i	0.998190	−	0.0601468i	$-0.0191569\pi$
$277$	7.43966	+	12.8859i	0.447006	+	0.774237i	−0.551183	+	0.834384i	$0.685824\pi$
$278$			0.387396i			0.0232345i
$279$		0			0
$280$			2.44761i			0.146273i
$281$	−14.2995	+	8.25582i	−0.853037	+	0.492501i	−0.861674	−	0.507462i	$-0.830584\pi$
$281$	−14.2995	+	8.25582i	−0.853037	+	0.492501i	0.00863764	+	0.999963i	$0.497251\pi$
$282$		0			0
$283$	0.267833	−	0.463900i	0.0159210	−	0.0275760i	−0.857955	−	0.513725i	$-0.828265\pi$
$283$	0.267833	−	0.463900i	0.0159210	−	0.0275760i	0.873876	+	0.486149i	$0.161599\pi$
$284$	4.01005	+	2.31521i	0.237953	+	0.137382i
$285$		0			0
$286$	−8.66485	−	7.68122i	−0.512363	−	0.454200i
$287$	55.8709			3.29795
$288$		0			0
$289$	0.660618			0.0388599
$290$	−1.11198	−	1.92601i	−0.0652978	−	0.113099i
$291$		0			0
$292$	0.281913	+	0.162762i	0.0164977	+	0.00952495i
$293$	16.9651	+	9.79482i	0.991113	+	0.572220i	0.905607	−	0.424118i	$-0.139416\pi$
$293$	16.9651	+	9.79482i	0.991113	+	0.572220i	0.0855065	+	0.996338i	$0.472749\pi$
$294$		0			0
$295$	−0.877257	−	1.51945i	−0.0510758	−	0.0884660i
$296$	−2.08429			−0.121147
$297$		0			0
$298$	9.45874			0.547930
$299$	16.9226	+	15.0016i	0.978659	+	0.867562i
$300$		0			0
$301$	41.4407	+	23.9258i	2.38860	+	1.37906i
$302$	−0.665819	+	1.15323i	−0.0383136	+	0.0663611i
$303$		0			0
$304$	−2.78126	+	1.60576i	−0.159516	+	0.0920969i
$305$			0.485092i			0.0277763i
$306$		0			0
$307$			1.26064i			0.0719485i	0.999353	+	0.0359743i	$0.0114534\pi$
$307$			1.26064i			0.0719485i	−0.999353	+	0.0359743i	$0.988547\pi$
$308$	−8.11614	−	14.0576i	−0.462460	−	0.801004i
$309$		0			0
$310$	2.71912	+	1.56988i	0.154436	+	0.0891634i
$311$	−8.79222	+	15.2286i	−0.498561	+	0.863533i	−0.999999	−	0.00166095i	$-0.999471\pi$
$311$	−8.79222	+	15.2286i	−0.498561	+	0.863533i	0.501438	+	0.865194i	$0.332805\pi$
$312$		0			0
$313$	−0.102706	−	0.177891i	−0.00580526	−	0.0100550i	0.863108	−	0.505019i	$-0.168515\pi$
$313$	−0.102706	−	0.177891i	−0.00580526	−	0.0100550i	−0.868913	+	0.494964i	$0.835181\pi$
$314$			5.84243i			0.329708i
$315$		0			0
$316$	7.83637			0.440830
$317$	15.6583	−	9.04030i	0.879455	−	0.507754i	0.00897641	−	0.999960i	$-0.497143\pi$
$317$	15.6583	−	9.04030i	0.879455	−	0.507754i	0.870479	+	0.492206i	$0.163809\pi$
$318$		0			0
$319$	12.7731	+	7.37453i	0.715154	+	0.412894i
$320$	−0.419378	−	0.242128i	−0.0234439	−	0.0135354i
$321$		0			0
$322$	15.8509	+	27.4546i	0.883339	+	1.52999i
$323$			13.4963i			0.750954i
$324$		0			0
$325$	16.2997	−	5.43597i	0.904144	−	0.301533i
$326$	−7.56698	−	13.1064i	−0.419096	−	0.725896i
$327$		0			0
$328$	−5.52698	+	9.57301i	−0.305176	+	0.528581i
$329$	13.3467	−	23.1171i	0.735827	−	1.27449i
$330$		0			0
$331$	3.63300	−	2.09751i	0.199688	−	0.115290i	−0.396822	−	0.917896i	$-0.629887\pi$
$331$	3.63300	−	2.09751i	0.199688	−	0.115290i	0.596510	+	0.802606i	$0.296554\pi$
$332$		−	5.86613i		−	0.321946i
$333$		0			0
$334$	12.0268			0.658078
$335$	0.261968	+	0.453742i	0.0143128	+	0.0247906i
$336$		0			0
$337$	−6.88041	+	11.9172i	−0.374800	+	0.649172i	−0.990297	−	0.138967i	$-0.955622\pi$
$337$	−6.88041	+	11.9172i	−0.374800	+	0.649172i	0.615497	+	0.788139i	$0.288955\pi$
$338$	12.9062	−	1.55891i	0.702004	−	0.0847935i
$339$		0			0
$340$	−1.76242	+	1.01753i	−0.0955805	+	0.0551834i
$341$	−20.8226			−1.12761
$342$		0			0
$343$		−	58.3615i		−	3.15123i
$344$	−8.19896	+	4.73367i	−0.442059	+	0.255223i
$345$		0			0
$346$	−7.67180	−	4.42932i	−0.412439	−	0.238122i
$347$	−11.9351	+	20.6722i	−0.640710	+	1.10974i	0.344565	+	0.938763i	$0.388026\pi$
$347$	−11.9351	+	20.6722i	−0.640710	+	1.10974i	−0.985275	+	0.170979i	$0.945307\pi$
$348$		0			0
$349$	−16.7557	+	9.67391i	−0.896913	+	0.517833i	−0.876197	−	0.481953i	$-0.839928\pi$
$349$	−16.7557	+	9.67391i	−0.896913	+	0.517833i	−0.0207153	+	0.999785i	$0.506594\pi$
$350$	24.0866			1.28748
$351$		0			0
$352$	3.21153			0.171175
$353$	24.0606	−	13.8914i	1.28062	−	0.739365i	0.303656	−	0.952782i	$-0.401793\pi$
$353$	24.0606	−	13.8914i	1.28062	−	0.739365i	0.976961	+	0.213417i	$0.0684593\pi$
$354$		0			0
$355$	−1.12115	+	1.94189i	−0.0595046	+	0.103065i
$356$	−7.29984	−	4.21456i	−0.386891	−	0.223371i
$357$		0			0
$358$	8.98104	−	5.18521i	0.474663	−	0.274047i
$359$		−	23.8304i		−	1.25772i	−0.777517	−	0.628861i	$-0.783521\pi$
$359$		−	23.8304i		−	1.25772i	0.777517	−	0.628861i	$-0.216479\pi$
$360$		0			0
$361$	8.68609			0.457162
$362$	−9.38833	+	5.42035i	−0.493440	+	0.284887i
$363$		0			0
$364$	17.8544	+	3.65081i	0.935824	+	0.191355i
$365$	−0.0788187	+	0.136518i	−0.00412556	+	0.00714568i
$366$		0			0
$367$	5.04643	+	8.74067i	0.263421	+	0.456259i	0.967149	−	0.254211i	$-0.0818157\pi$
$367$	5.04643	+	8.74067i	0.263421	+	0.456259i	−0.703728	+	0.710470i	$0.748482\pi$
$368$	−6.27217			−0.326959
$369$		0			0
$370$		−	1.00933i		−	0.0524724i
$371$	−28.1013	+	16.2243i	−1.45895	+	0.842324i
$372$		0			0
$373$	4.27370	−	7.40227i	0.221284	−	0.383275i	−0.733914	−	0.679242i	$-0.762309\pi$
$373$	4.27370	−	7.40227i	0.221284	−	0.383275i	0.955198	+	0.295967i	$0.0956419\pi$
$374$	6.74815	−	11.6881i	0.348938	−	0.604379i
$375$		0			0
$376$	2.64062	+	4.57369i	0.136180	+	0.235870i
$377$	−15.7081	+	5.23868i	−0.809008	+	0.269806i
$378$		0			0
$379$		−	30.7125i		−	1.57760i	−0.614653	−	0.788798i	$-0.710704\pi$
$379$		−	30.7125i		−	1.57760i	0.614653	−	0.788798i	$-0.289296\pi$
$380$	−0.777601	−	1.34684i	−0.0398901	−	0.0690916i
$381$		0			0
$382$	−9.74971	−	5.62900i	−0.498839	−	0.288005i
$383$	2.49892	+	1.44275i	0.127689	+	0.0737212i	0.562484	−	0.826808i	$-0.309846\pi$
$383$	2.49892	+	1.44275i	0.127689	+	0.0737212i	−0.434795	+	0.900529i	$0.643179\pi$
$384$		0			0
$385$	6.80746	−	3.93029i	0.346940	−	0.200306i
$386$	−7.62566			−0.388136
$387$		0			0
$388$		−	13.0505i		−	0.662539i
$389$	−5.94776	−	10.3018i	−0.301564	−	0.522323i	0.674927	−	0.737885i	$-0.264175\pi$
$389$	−5.94776	−	10.3018i	−0.301564	−	0.522323i	−0.976490	+	0.215561i	$0.930842\pi$
$390$		0			0
$391$	−13.1792	+	22.8271i	−0.666503	+	1.15442i
$392$	16.0619	+	9.27337i	0.811250	+	0.468376i
$393$		0			0
$394$	−12.2585	−	21.2324i	−0.617575	−	1.06967i
$395$			3.79481i			0.190937i
$396$		0			0
$397$			23.8021i			1.19459i	0.802020	+	0.597297i	$0.203759\pi$
$397$			23.8021i			1.19459i	−0.802020	+	0.597297i	$0.796241\pi$
$398$	11.7182	−	6.76550i	0.587379	−	0.339124i
$399$		0			0
$400$	−2.38275	+	4.12704i	−0.119137	+	0.206352i
$401$	7.79168	+	4.49853i	0.389098	+	0.224646i	0.681769	−	0.731567i	$-0.261211\pi$
$401$	7.79168	+	4.49853i	0.389098	+	0.224646i	−0.292671	+	0.956213i	$0.594544\pi$
$402$		0			0
$403$	15.5075	−	17.4933i	0.772483	−	0.871404i
$404$	−6.84702			−0.340652
$405$		0			0
$406$	−23.2124			−1.15201
$407$	3.34687	+	5.79695i	0.165898	+	0.287344i
$408$		0			0
$409$	−27.8344	−	16.0702i	−1.37632	−	0.794620i	−0.384608	−	0.923080i	$-0.625663\pi$
$409$	−27.8344	−	16.0702i	−1.37632	−	0.794620i	−0.991715	+	0.128460i	$0.958997\pi$
$410$	−4.63579	−	2.67647i	−0.228945	−	0.132182i
$411$		0			0
$412$	1.77760	+	3.07889i	0.0875761	+	0.151686i
$413$	−18.3126			−0.901103
$414$		0			0
$415$	2.84071			0.139445
$416$	−2.39177	+	2.69805i	−0.117266	+	0.132283i
$417$		0			0
$418$	8.93211	+	5.15696i	0.436884	+	0.252235i
$419$	1.68689	−	2.92177i	0.0824098	−	0.142738i	−0.821875	−	0.569668i	$-0.807072\pi$
$419$	1.68689	−	2.92177i	0.0824098	−	0.142738i	0.904285	+	0.426930i	$0.140405\pi$
$420$		0			0
$421$	−2.26626	+	1.30842i	−0.110451	+	0.0637687i	−0.554208	−	0.832378i	$-0.686979\pi$
$421$	−2.26626	+	1.30842i	−0.110451	+	0.0637687i	0.443757	+	0.896147i	$0.353645\pi$
$422$		−	23.8692i		−	1.16193i
$423$		0			0
$424$		−	6.41990i		−	0.311778i
$425$	10.0134	+	17.3437i	0.485721	+	0.841293i
$426$		0			0
$427$	4.38478	+	2.53155i	0.212194	+	0.122510i
$428$	−0.706961	+	1.22449i	−0.0341722	+	0.0591880i
$429$		0			0
$430$	−2.29231	−	3.97040i	−0.110545	−	0.191470i
$431$		−	1.25113i		−	0.0602647i	−0.999546	−	0.0301324i	$-0.990407\pi$
$431$		−	1.25113i		−	0.0602647i	0.999546	−	0.0301324i	$-0.00959288\pi$
$432$		0			0
$433$	−4.77117			−0.229288			−0.114644	−	0.993407i	$-0.536573\pi$
$433$	−4.77117			−0.229288			−0.114644	+	0.993407i	$0.536573\pi$
$434$	28.3806	−	16.3855i	1.36231	−	0.786530i
$435$		0			0
$436$	4.30869	+	2.48763i	0.206349	+	0.119136i
$437$	−17.4446	−	10.0716i	−0.834486	−	0.481791i
$438$		0			0
$439$	−16.8509	−	29.1867i	−0.804252	−	1.39300i	−0.916795	−	0.399358i	$-0.869233\pi$
$439$	−16.8509	−	29.1867i	−0.804252	−	1.39300i	0.112543	−	0.993647i	$-0.464100\pi$
$440$			1.55520i			0.0741413i
$441$		0			0
$442$	4.79371	+	14.3739i	0.228014	+	0.683696i
$443$	−2.68876	−	4.65706i	−0.127747	−	0.221264i	0.795057	−	0.606535i	$-0.207441\pi$
$443$	−2.68876	−	4.65706i	−0.127747	−	0.221264i	−0.922803	+	0.385272i	$0.874108\pi$
$444$		0			0
$445$	2.04093	−	3.53499i	0.0967492	−	0.167575i
$446$	6.43490	−	11.1456i	0.304701	−	0.527758i
$447$		0			0
$448$	−4.37722	+	2.52719i	−0.206804	+	0.119398i
$449$			16.7813i			0.791958i	0.918260	+	0.395979i	$0.129595\pi$
$449$			16.7813i			0.791958i	−0.918260	+	0.395979i	$0.870405\pi$
$450$		0			0
$451$	35.5001			1.67163
$452$	6.54415	+	11.3348i	0.307811	+	0.533145i
$453$		0			0
$454$	−9.02759	+	15.6362i	−0.423686	+	0.733845i
$455$	−1.76793	+	8.64609i	−0.0828817	+	0.405335i
$456$		0			0
$457$	−20.5067	+	11.8396i	−0.959263	+	0.553831i	−0.895946	−	0.444162i	$-0.853501\pi$
$457$	−20.5067	+	11.8396i	−0.959263	+	0.553831i	−0.0633172	+	0.997993i	$0.520168\pi$
$458$	21.1737			0.989383
$459$		0			0
$460$		−	3.03733i		−	0.141616i
$461$	29.8451	−	17.2311i	1.39003	−	0.802533i	0.396709	−	0.917944i	$-0.370152\pi$
$461$	29.8451	−	17.2311i	1.39003	−	0.802533i	0.993318	+	0.115412i	$0.0368188\pi$
$462$		0			0
$463$	19.4659	+	11.2386i	0.904657	+	0.522304i	0.878708	−	0.477359i	$-0.158406\pi$
$463$	19.4659	+	11.2386i	0.904657	+	0.522304i	0.0259487	+	0.999663i	$0.491739\pi$
$464$	2.29627	−	3.97725i	0.106602	−	0.184639i
$465$		0			0
$466$	25.1675	−	14.5305i	1.16586	−	0.673111i
$467$	4.43632			0.205288			0.102644	−	0.994718i	$-0.467270\pi$
$467$	4.43632			0.205288			0.102644	+	0.994718i	$0.467270\pi$
$468$		0			0
$469$	5.46853			0.252513
$470$	−2.21484	+	1.27874i	−0.102163	+	0.0589837i
$471$		0			0
$472$	1.81156	−	3.13771i	0.0833836	−	0.144425i
$473$	26.3312	+	15.2023i	1.21071	+	0.699004i
$474$		0			0
$475$	−13.2541	+	7.65226i	−0.608140	+	0.351110i
$476$			21.2408i			0.973570i
$477$		0			0
$478$	7.26902			0.332477
$479$	−10.2334	+	5.90827i	−0.467577	+	0.269956i	−0.715225	−	0.698894i	$-0.753676\pi$
$479$	−10.2334	+	5.90827i	−0.467577	+	0.269956i	0.247648	+	0.968850i	$0.420342\pi$
$480$		0			0
$481$	−7.36265	−	1.50549i	−0.335708	−	0.0686446i
$482$	−8.95521	+	15.5109i	−0.407899	+	0.706501i
$483$		0			0
$484$	0.343044	+	0.594169i	0.0155929	+	0.0270077i
$485$	6.31979			0.286967
$486$		0			0
$487$			25.8373i			1.17080i	0.810745	+	0.585400i	$0.199062\pi$
$487$			25.8373i			1.17080i	−0.810745	+	0.585400i	$0.800938\pi$
$488$	−0.867521	+	0.500864i	−0.0392708	+	0.0226730i
$489$		0			0
$490$	−4.49068	+	7.77809i	−0.202868	+	0.351378i
$491$	5.59995	−	9.69940i	0.252722	−	0.437728i	−0.711552	−	0.702633i	$-0.752007\pi$
$491$	5.59995	−	9.69940i	0.252722	−	0.437728i	0.964274	+	0.264906i	$0.0853408\pi$
$492$		0			0
$493$	−9.64996	−	16.7142i	−0.434612	−	0.752771i
$494$	−10.9846	+	3.66337i	−0.494219	+	0.164823i
$495$		0			0
$496$			6.48369i			0.291126i
$497$	11.7019	+	20.2683i	0.524903	+	0.909159i
$498$		0			0
$499$	−13.3884	−	7.72982i	−0.599349	−	0.346034i	0.169436	−	0.985541i	$-0.445805\pi$
$499$	−13.3884	−	7.72982i	−0.599349	−	0.346034i	−0.768786	+	0.639507i	$0.779139\pi$
$500$	−4.09543	−	2.36450i	−0.183153	−	0.105744i
$501$		0			0
$502$	−3.33162	+	1.92351i	−0.148697	+	0.0858505i
$503$	6.00330			0.267674			0.133837	−	0.991003i	$-0.457270\pi$
$503$	6.00330			0.267674			0.133837	+	0.991003i	$0.457270\pi$
$504$		0			0
$505$		−	3.31571i		−	0.147547i
$506$	10.0716	+	17.4446i	0.447738	+	0.775505i
$507$		0			0
$508$	−2.28150	+	3.95167i	−0.101225	+	0.175327i
$509$	−18.6801	−	10.7849i	−0.827979	−	0.478034i	0.0251810	−	0.999683i	$-0.491984\pi$
$509$	−18.6801	−	10.7849i	−0.827979	−	0.478034i	−0.853160	+	0.521649i	$0.825317\pi$
$510$		0			0
$511$	0.822663	+	1.42489i	0.0363925	+	0.0630336i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	14.7675i		−	0.651367i
$515$	−1.49097	+	0.860814i	−0.0657001	+	0.0379320i
$516$		0			0
$517$	8.48043	−	14.6885i	0.372969	−	0.646001i
$518$	−9.12337	−	5.26738i	−0.400858	−	0.231435i
$519$		0			0
$520$	−1.30655	−	1.15823i	−0.0572958	−	0.0507916i
$521$	−24.0543			−1.05384			−0.526918	−	0.849916i	$-0.676653\pi$
$521$	−24.0543			−1.05384			−0.526918	+	0.849916i	$0.676653\pi$
$522$		0			0
$523$	−10.8449			−0.474215			−0.237107	−	0.971483i	$-0.576199\pi$
$523$	−10.8449			−0.474215			−0.237107	+	0.971483i	$0.576199\pi$
$524$	−1.23473	−	2.13862i	−0.0539395	−	0.0934260i
$525$		0			0
$526$	−7.58853	−	4.38124i	−0.330876	−	0.191031i
$527$	23.5970	+	13.6237i	1.02790	+	0.593458i
$528$		0			0
$529$	−8.17003	−	14.1509i	−0.355219	−	0.615257i
$530$	3.10888			0.135041
$531$		0			0
$532$	−16.2323			−0.703758
$533$	−26.4385	+	29.8241i	−1.14518	+	1.29183i
$534$		0			0
$535$	−0.592967	−	0.342350i	−0.0256362	−	0.0148011i
$536$	−0.540970	+	0.936987i	−0.0233663	+	0.0404717i
$537$		0			0
$538$	−7.71400	+	4.45368i	−0.332574	+	0.192012i
$539$		−	59.5633i		−	2.56558i
$540$		0			0
$541$		−	12.2998i		−	0.528808i	−0.964412	−	0.264404i	$-0.914825\pi$
$541$		−	12.2998i		−	0.528808i	0.964412	−	0.264404i	$-0.0851753\pi$
$542$	1.79275	+	3.10514i	0.0770054	+	0.133377i
$543$		0			0
$544$	−3.63943	−	2.10123i	−0.156039	−	0.0900894i
$545$	−1.20465	+	2.08651i	−0.0516014	+	0.0893763i
$546$		0			0
$547$	10.3452	+	17.9183i	0.442327	+	0.766133i	0.997862	−	0.0653602i	$-0.0208196\pi$
$547$	10.3452	+	17.9183i	0.442327	+	0.766133i	−0.555534	+	0.831493i	$0.687486\pi$
$548$			19.6104i			0.837714i
$549$		0			0
$550$	15.3045			0.652587
$551$	12.7731	−	7.37453i	0.544151	−	0.314165i
$552$		0			0
$553$	34.3015	+	19.8040i	1.45865	+	0.842151i
$554$	−12.8859	−	7.43966i	−0.547468	−	0.316081i
$555$		0			0
$556$	−0.193698	−	0.335495i	−0.00821463	−	0.0142282i
$557$			14.2838i			0.605226i	0.953114	+	0.302613i	$0.0978589\pi$
$557$			14.2838i			0.605226i	−0.953114	+	0.302613i	$0.902141\pi$
$558$		0			0
$559$	−32.3817	+	10.7993i	−1.36960	+	0.456764i
$560$	−1.22381	−	2.11969i	−0.0517152	−	0.0895734i
$561$		0			0
$562$	8.25582	−	14.2995i	0.348251	−	0.603188i
$563$	−17.9673	+	31.1203i	−0.757231	+	1.31156i	0.187026	+	0.982355i	$0.440115\pi$
$563$	−17.9673	+	31.1203i	−0.757231	+	1.31156i	−0.944257	+	0.329208i	$0.893218\pi$
$564$		0			0
$565$	−5.48895	+	3.16905i	−0.230922	+	0.133323i
$566$			0.535666i			0.0225157i
$567$		0			0
$568$	−4.63041			−0.194288
$569$	−18.5315	−	32.0976i	−0.776882	−	1.34560i	−0.933730	−	0.357977i	$-0.883467\pi$
$569$	−18.5315	−	32.0976i	−0.776882	−	1.34560i	0.156848	−	0.987623i	$-0.449867\pi$
$570$		0			0
$571$	23.1732	−	40.1372i	0.969769	−	1.67969i	0.273551	−	0.961857i	$-0.411802\pi$
$571$	23.1732	−	40.1372i	0.969769	−	1.67969i	0.696217	−	0.717831i	$-0.254865\pi$
$572$	11.3446	+	2.31971i	0.474341	+	0.0969919i
$573$		0			0
$574$	−48.3856	+	27.9354i	−2.01958	+	1.16600i
$575$	−29.8900			−1.24650
$576$		0			0
$577$		−	31.4447i		−	1.30906i	−0.756036	−	0.654530i	$-0.772866\pi$
$577$		−	31.4447i		−	1.30906i	0.756036	−	0.654530i	$-0.227134\pi$
$578$	−0.572112	+	0.330309i	−0.0237967	+	0.0137390i
$579$		0			0
$580$	1.92601	+	1.11198i	0.0799731	+	0.0461725i
$581$	14.8248	−	25.6773i	0.615037	−	1.06527i
$582$		0			0
$583$	−17.8555	+	10.3088i	−0.739497	+	0.426949i
$584$	−0.325525			−0.0134703
$585$		0			0
$586$	−19.5896			−0.809241
$587$	−27.0638	+	15.6253i	−1.11704	+	0.644924i	−0.940644	−	0.339395i	$-0.889778\pi$
$587$	−27.0638	+	15.6253i	−1.11704	+	0.644924i	−0.176397	+	0.984319i	$0.556444\pi$
$588$		0			0
$589$	−10.4113	+	18.0329i	−0.428989	+	0.743031i
$590$	1.51945	+	0.877257i	0.0625549	+	0.0361161i
$591$		0			0
$592$	1.80504	−	1.04214i	0.0741868	−	0.0428318i
$593$		−	26.3978i		−	1.08403i	−0.840370	−	0.542013i	$-0.817662\pi$
$593$		−	26.3978i		−	1.08403i	0.840370	−	0.542013i	$-0.182338\pi$
$594$		0			0
$595$	−10.2860			−0.421684
$596$	−8.19151	+	4.72937i	−0.335537	+	0.193723i
$597$		0			0
$598$	−22.1562	−	4.53043i	−0.906033	−	0.185263i
$599$	−3.40524	+	5.89806i	−0.139135	+	0.240988i	−0.927169	−	0.374643i	$-0.877765\pi$
$599$	−3.40524	+	5.89806i	−0.139135	+	0.240988i	0.788035	+	0.615631i	$0.211099\pi$
$600$		0			0
$601$	−4.82516	−	8.35742i	−0.196822	−	0.340906i	0.750674	−	0.660673i	$-0.229729\pi$
$601$	−4.82516	−	8.35742i	−0.196822	−	0.340906i	−0.947496	+	0.319766i	$0.896396\pi$
$602$	−47.8516			−1.95028
$603$		0			0
$604$		−	1.33164i		−	0.0541836i
$605$	−0.287730	+	0.166121i	−0.0116979	+	0.00675377i
$606$		0			0
$607$	−13.7896	+	23.8842i	−0.559702	+	0.969432i	0.437819	+	0.899063i	$0.355751\pi$
$607$	−13.7896	+	23.8842i	−0.559702	+	0.969432i	−0.997521	+	0.0703688i	$0.977582\pi$
$608$	1.60576	−	2.78126i	0.0651223	−	0.112795i
$609$		0			0
$610$	−0.242546	−	0.420102i	−0.00982041	−	0.0170094i
$611$	6.02428	+	18.0637i	0.243716	+	0.730779i
$612$		0			0
$613$			16.0314i			0.647502i	0.946142	+	0.323751i	$0.104944\pi$
$613$			16.0314i			0.647502i	−0.946142	+	0.323751i	$0.895056\pi$
$614$	−0.630320	−	1.09175i	−0.0254377	−	0.0440593i
$615$		0			0
$616$	14.0576	+	8.11614i	0.566395	+	0.327009i
$617$	−11.4362	−	6.60269i	−0.460404	−	0.265814i	0.251810	−	0.967777i	$-0.418974\pi$
$617$	−11.4362	−	6.60269i	−0.460404	−	0.265814i	−0.712214	+	0.701962i	$0.752307\pi$
$618$		0			0
$619$	1.53649	−	0.887091i	0.0617566	−	0.0356552i	−0.468804	−	0.883302i	$-0.655315\pi$
$619$	1.53649	−	0.887091i	0.0617566	−	0.0356552i	0.530560	+	0.847647i	$0.321982\pi$
$620$	−3.13977			−0.126096
$621$		0			0
$622$		−	17.5844i		−	0.705072i
$623$	−21.3020	−	36.8961i	−0.853446	−	1.47821i
$624$		0			0
$625$	−10.7687	+	18.6520i	−0.430749	+	0.746079i
$626$	0.177891	+	0.102706i	0.00710997	+	0.00410494i
$627$		0			0
$628$	−2.92122	−	5.05970i	−0.116569	−	0.201904i
$629$		−	8.75911i		−	0.349249i
$630$		0			0
$631$			30.2211i			1.20308i	0.798841	+	0.601542i	$0.205447\pi$
$631$			30.2211i			1.20308i	−0.798841	+	0.601542i	$0.794553\pi$
$632$	−6.78649	+	3.91818i	−0.269952	+	0.155857i
$633$		0			0
$634$	−9.04030	+	15.6583i	−0.359036	+	0.621869i
$635$	−1.91362	−	1.10483i	−0.0759397	−	0.0438438i
$636$		0			0
$637$	50.0399	+	44.3594i	1.98265	+	1.75759i
$638$	−14.7491			−0.583921
$639$		0			0
$640$	0.484256			0.0191419
$641$	−0.301673	−	0.522512i	−0.0119154	−	0.0206380i	0.860006	−	0.510284i	$-0.170460\pi$
$641$	−0.301673	−	0.522512i	−0.0119154	−	0.0206380i	−0.871922	+	0.489646i	$0.837126\pi$
$642$		0			0
$643$	27.0250	+	15.6029i	1.06576	+	0.615317i	0.927020	−	0.375012i	$-0.122361\pi$
$643$	27.0250	+	15.6029i	1.06576	+	0.615317i	0.138740	+	0.990329i	$0.455695\pi$
$644$	−27.4546	−	15.8509i	−1.08186	−	0.624615i
$645$		0			0
$646$	−6.74815	−	11.6881i	−0.265502	−	0.459864i
$647$	48.8937			1.92221			0.961105	−	0.276182i	$-0.0890692\pi$
$647$	48.8937			1.92221			0.961105	+	0.276182i	$0.0890692\pi$
$648$		0			0
$649$	−11.6357			−0.456742
$650$	−11.3980	+	12.8575i	−0.447064	+	0.504314i
$651$		0			0
$652$	13.1064	+	7.56698i	0.513286	+	0.296346i
$653$	19.1944	−	33.2457i	0.751135	−	1.30100i	−0.196138	−	0.980576i	$-0.562840\pi$
$653$	19.1944	−	33.2457i	0.751135	−	1.30100i	0.947273	−	0.320427i	$-0.103827\pi$
$654$		0			0
$655$	1.03564	−	0.597926i	0.0404658	−	0.0233629i
$656$		−	11.0540i		−	0.431585i
$657$		0			0
$658$			26.6934i			1.04062i
$659$	−20.9568	−	36.2983i	−0.816362	−	1.41398i	−0.908346	−	0.418220i	$-0.862654\pi$
$659$	−20.9568	−	36.2983i	−0.816362	−	1.41398i	0.0919840	−	0.995760i	$-0.470679\pi$
$660$		0			0
$661$	10.5208	+	6.07418i	0.409211	+	0.236258i	0.690451	−	0.723379i	$-0.257412\pi$
$661$	10.5208	+	6.07418i	0.409211	+	0.236258i	−0.281240	+	0.959638i	$0.590746\pi$
$662$	−2.09751	+	3.63300i	−0.0815221	+	0.141200i
$663$		0			0
$664$	2.93306	+	5.08022i	0.113825	+	0.197151i
$665$		−	7.86058i		−	0.304820i
$666$		0			0
$667$	28.8051			1.11534
$668$	−10.4155	+	6.01341i	−0.402989	+	0.232666i
$669$		0			0
$670$	−0.453742	−	0.261968i	−0.0175296	−	0.0101207i
$671$	2.78607	+	1.60854i	0.107555	+	0.0620969i
$672$		0			0
$673$	−18.3252	−	31.7403i	−0.706386	−	1.22350i	−0.966189	−	0.257835i	$-0.916991\pi$
$673$	−18.3252	−	31.7403i	−0.706386	−	1.22350i	0.259803	−	0.965662i	$-0.416342\pi$
$674$		−	13.7608i		−	0.530047i
$675$		0			0
$676$	−10.3976	+	7.80315i	−0.399909	+	0.300121i
$677$	19.2964	+	33.4223i	0.741620	+	1.28452i	0.951757	+	0.306851i	$0.0992755\pi$
$677$	19.2964	+	33.4223i	0.741620	+	1.28452i	−0.210138	+	0.977672i	$0.567391\pi$
$678$		0			0
$679$	32.9811	−	57.1249i	1.26570	−	2.19225i
$680$	1.01753	−	1.76242i	0.0390206	−	0.0675856i
$681$		0			0
$682$	18.0329	−	10.4113i	0.690514	−	0.398669i
$683$			31.4038i			1.20163i	0.799387	+	0.600816i	$0.205158\pi$
$683$			31.4038i			1.20163i	−0.799387	+	0.600816i	$0.794842\pi$
$684$		0			0
$685$	−9.49644			−0.362840
$686$	29.1808	+	50.5426i	1.11413	+	1.92972i
$687$		0			0
$688$	4.73367	−	8.19896i	0.180470	−	0.312583i
$689$	4.63714	−	22.6780i	0.176661	−	0.863965i
$690$		0			0
$691$	−16.6786	+	9.62941i	−0.634485	+	0.366320i	−0.782487	−	0.622667i	$-0.786049\pi$
$691$	−16.6786	+	9.62941i	−0.634485	+	0.366320i	0.148002	+	0.988987i	$0.452716\pi$
$692$	8.85863			0.336755
$693$		0			0
$694$		−	23.8702i		−	0.906100i
$695$	0.162465	−	0.0937995i	0.00616266	−	0.00355802i
$696$		0			0
$697$	−40.2301	−	23.2269i	−1.52383	−	0.879781i
$698$	9.67391	−	16.7557i	0.366163	−	0.634213i
$699$		0			0
$700$	−20.8596	+	12.0433i	−0.788420	+	0.455194i
$701$	26.7781			1.01139			0.505697	−	0.862711i	$-0.331235\pi$
$701$	26.7781			1.01139			0.505697	+	0.862711i	$0.331235\pi$
$702$		0			0
$703$	6.69374			0.252459
$704$	−2.78126	+	1.60576i	−0.104823	+	0.0605195i
$705$		0			0
$706$	−13.8914	+	24.0606i	−0.522810	+	0.905533i
$707$	−29.9709	−	17.3037i	−1.12717	−	0.650773i
$708$		0			0
$709$	−40.2439	+	23.2348i	−1.51139	+	0.872602i	−0.511479	+	0.859296i	$0.670902\pi$
$709$	−40.2439	+	23.2348i	−1.51139	+	0.872602i	−0.999911	+	0.0133058i	$0.995764\pi$
$710$		−	2.24230i		−	0.0841522i
$711$		0			0
$712$	8.42912			0.315895
$713$	−35.2185	+	20.3334i	−1.31894	+	0.761492i
$714$		0			0
$715$	−1.12333	+	5.49369i	−0.0420103	+	0.205452i
$716$	−5.18521	+	8.98104i	−0.193780	+	0.335637i
$717$		0			0
$718$	11.9152	+	20.6378i	0.444672	+	0.770195i
$719$	4.81378			0.179524			0.0897619	−	0.995963i	$-0.471389\pi$
$719$	4.81378			0.179524			0.0897619	+	0.995963i	$0.471389\pi$
$720$		0			0
$721$			17.9693i			0.669213i
$722$	−7.52237	+	4.34304i	−0.279954	+	0.161631i
$723$		0			0
$724$	5.42035	−	9.38833i	0.201446	−	0.348914i
$725$	10.9429	−	18.9536i	0.406407	−	0.703918i
$726$		0			0
$727$	−6.35915	−	11.0144i	−0.235848	−	0.408501i	0.723671	−	0.690145i	$-0.242453\pi$
$727$	−6.35915	−	11.0144i	−0.235848	−	0.408501i	−0.959519	+	0.281645i	$0.909120\pi$
$728$	−17.2878	+	5.76550i	−0.640727	+	0.213684i
$729$		0			0
$730$		−	0.157637i		−	0.00583442i
$731$	−19.8930	−	34.4558i	−0.735771	−	1.27439i
$732$		0			0
$733$	3.68483	+	2.12744i	0.136102	+	0.0785787i	0.566505	−	0.824058i	$-0.308295\pi$
$733$	3.68483	+	2.12744i	0.136102	+	0.0785787i	−0.430403	+	0.902637i	$0.641628\pi$
$734$	−8.74067	−	5.04643i	−0.322624	−	0.186267i
$735$		0			0
$736$	5.43186	−	3.13608i	0.200221	−	0.115598i
$737$	3.47468			0.127991
$738$		0			0
$739$		−	9.71484i		−	0.357366i	−0.983907	−	0.178683i	$-0.942816\pi$
$739$		−	9.71484i		−	0.357366i	0.983907	−	0.178683i	$-0.0571837\pi$
$740$	0.504664	+	0.874103i	0.0185518	+	0.0321327i
$741$		0			0
$742$	16.2243	−	28.1013i	0.595613	−	1.03163i
$743$	10.6739	+	6.16261i	0.391589	+	0.226084i	0.682848	−	0.730560i	$-0.260741\pi$
$743$	10.6739	+	6.16261i	0.391589	+	0.226084i	−0.291259	+	0.956644i	$0.594074\pi$
$744$		0			0
$745$	−2.29023	−	3.96679i	−0.0839074	−	0.145332i
$746$			8.54741i			0.312943i
$747$		0			0
$748$			13.4963i			0.493474i
$749$	−6.18904	+	3.57325i	−0.226143	+	0.130564i
$750$		0			0
$751$	1.43490	−	2.48532i	0.0523603	−	0.0906908i	−0.838657	−	0.544660i	$-0.816659\pi$
$751$	1.43490	−	2.48532i	0.0523603	−	0.0906908i	0.891018	+	0.453969i	$0.149992\pi$
$752$	−4.57369	−	2.64062i	−0.166785	−	0.0962935i
$753$		0			0
$754$	10.9843	−	12.3909i	0.400024	−	0.451249i
$755$	0.644854			0.0234686
$756$		0			0
$757$	33.1438			1.20463			0.602316	−	0.798258i	$-0.294245\pi$
$757$	33.1438			1.20463			0.602316	+	0.798258i	$0.294245\pi$
$758$	15.3563	+	26.5978i	0.557764	+	0.966076i
$759$		0			0
$760$	1.34684	+	0.777601i	0.0488552	+	0.0282065i
$761$	−37.0264	−	21.3772i	−1.34221	−	0.774923i	−0.355075	−	0.934838i	$-0.615545\pi$
$761$	−37.0264	−	21.3772i	−1.34221	−	0.774923i	−0.987131	+	0.159915i	$0.948878\pi$
$762$		0			0
$763$	12.5734	+	21.7778i	0.455188	+	0.788408i
$764$	11.2580			0.407300
$765$		0			0
$766$	−2.88551			−0.104258
$767$	8.66563	−	9.77532i	0.312898	−	0.352966i
$768$		0			0
$769$	41.6797	+	24.0638i	1.50301	+	0.867762i	0.999994	+	0.00348401i	$0.00110900\pi$
$769$	41.6797	+	24.0638i	1.50301	+	0.867762i	0.503014	+	0.864278i	$0.332224\pi$
$770$	−3.93029	+	6.80746i	−0.141638	+	0.245324i
$771$		0			0
$772$	6.60401	−	3.81283i	0.237684	−	0.137227i
$773$			21.3661i			0.768484i	0.923232	+	0.384242i	$0.125537\pi$
$773$			21.3661i			0.768484i	−0.923232	+	0.384242i	$0.874463\pi$
$774$		0			0
$775$			30.8980i			1.10989i
$776$	6.52525	+	11.3021i	0.234243	+	0.405721i
$777$		0			0
$778$	10.3018	+	5.94776i	0.369338	+	0.213238i
$779$	17.7501	−	30.7440i	0.635962	−	1.10152i
$780$		0			0
$781$	7.43535	+	12.8784i	0.266058	+	0.460826i
$782$		−	26.3585i		−	0.942578i
$783$		0			0
$784$	−18.5467			−0.662383
$785$	2.45019	−	1.41462i	0.0874510	−	0.0504898i
$786$		0			0
$787$	−29.5928	−	17.0854i	−1.05487	−	0.609029i	−0.130860	−	0.991401i	$-0.541774\pi$
$787$	−29.5928	−	17.0854i	−1.05487	−	0.609029i	−0.924008	+	0.382372i	$0.875107\pi$
$788$	21.2324	+	12.2585i	0.756372	+	0.436691i
$789$		0			0
$790$	−1.89740	−	3.28640i	−0.0675066	−	0.116925i
$791$			66.1533i			2.35214i
$792$		0			0
$793$	−3.42626	+	1.14266i	−0.121670	+	0.0405772i
$794$	−11.9011	−	20.6132i	−0.422353	−	0.731537i
$795$		0			0
$796$	−6.76550	+	11.7182i	−0.239797	+	0.415340i
$797$	6.26917	−	10.8585i	0.222066	−	0.384629i	−0.733369	−	0.679830i	$-0.762053\pi$
$797$	6.26917	−	10.8585i	0.222066	−	0.384629i	0.955435	+	0.295201i	$0.0953868\pi$
$798$		0			0
$799$	−19.2207	+	11.0971i	−0.679980	+	0.392587i
$800$		−	4.76550i		−	0.168486i
$801$		0			0
$802$	−8.99705			−0.317697
$803$	0.522716	+	0.905371i	0.0184463	+	0.0319498i
$804$		0			0
$805$	7.67592	−	13.2951i	0.270540	−	0.468590i
$806$	−4.68322	+	22.9034i	−0.164959	+	0.806737i
$807$		0			0
$808$	5.92969	−	3.42351i	0.208606	−	0.120439i
$809$	23.7653			0.835543			0.417772	−	0.908552i	$-0.362811\pi$
$809$	23.7653			0.835543			0.417772	+	0.908552i	$0.362811\pi$
$810$		0			0
$811$		−	12.1844i		−	0.427853i	−0.976850	−	0.213926i	$-0.931375\pi$
$811$		−	12.1844i		−	0.427853i	0.976850	−	0.213926i	$-0.0686253\pi$
$812$	20.1025	−	11.6062i	0.705461	−	0.407298i
$813$		0			0
$814$	−5.79695	−	3.34687i	−0.203183	−	0.117308i
$815$	−3.66435	+	6.34685i	−0.128357	+	0.222320i
$816$		0			0
$817$	26.3312	−	15.2023i	0.921212	−	0.531862i
$818$	32.1404			1.12376
$819$		0			0
$820$	5.35295			0.186933
$821$	14.8532	−	8.57549i	0.518379	−	0.299287i	−0.217892	−	0.975973i	$-0.569918\pi$
$821$	14.8532	−	8.57549i	0.518379	−	0.299287i	0.736271	+	0.676686i	$0.236585\pi$
$822$		0			0
$823$	−19.0983	+	33.0792i	−0.665725	+	1.15307i	0.313363	+	0.949633i	$0.398544\pi$
$823$	−19.0983	+	33.0792i	−0.665725	+	1.15307i	−0.979088	+	0.203436i	$0.934789\pi$
$824$	−3.07889	−	1.77760i	−0.107258	−	0.0619257i
$825$		0			0
$826$	15.8592	−	9.15629i	0.551810	−	0.318588i
$827$			16.3182i			0.567441i	0.958907	+	0.283721i	$0.0915688\pi$
$827$			16.3182i			0.567441i	−0.958907	+	0.283721i	$0.908431\pi$
$828$		0			0
$829$	13.6052			0.472529			0.236265	−	0.971689i	$-0.424077\pi$
$829$	13.6052			0.472529			0.236265	+	0.971689i	$0.424077\pi$
$830$	−2.46012	+	1.42035i	−0.0853922	+	0.0493012i
$831$		0			0
$832$	0.722307	−	3.53246i	0.0250415	−	0.122466i
$833$	−38.9709	+	67.4996i	−1.35026	+	2.33872i
$834$		0			0
$835$	−2.91203	−	5.04378i	−0.100775	−	0.174547i
$836$	−10.3139			−0.356714
$837$		0			0
$838$			3.37377i			0.116545i
$839$	43.9792	−	25.3914i	1.51833	−	0.876609i	0.518563	−	0.855039i	$-0.326467\pi$
$839$	43.9792	−	25.3914i	1.51833	−	0.876609i	0.999767	−	0.0215696i	$-0.00686634\pi$
$840$		0			0
$841$	3.95431	−	6.84907i	0.136356	−	0.236175i
$842$	1.30842	−	2.26626i	0.0450913	−	0.0781004i
$843$		0			0
$844$	11.9346	+	20.6713i	0.410805	+	0.711535i
$845$	−3.77872	−	5.03512i	−0.129992	−	0.173213i
$846$		0			0
$847$			3.46774i			0.119153i
$848$	3.20995	+	5.55980i	0.110230	+	0.190924i
$849$		0			0
$850$	−17.3437	−	10.0134i	−0.594884	−	0.343456i
$851$	11.3215	+	6.53649i	0.388097	+	0.224068i
$852$		0			0
$853$	31.1360	−	17.9764i	1.06608	−	0.615499i	0.138969	−	0.990297i	$-0.455621\pi$
$853$	31.1360	−	17.9764i	1.06608	−	0.615499i	0.927106	+	0.374798i	$0.122288\pi$
$854$	−5.06311			−0.173256
$855$		0			0
$856$		−	1.41392i		−	0.0483268i
$857$	−2.28591	−	3.95932i	−0.0780853	−	0.135248i	0.824339	−	0.566097i	$-0.191547\pi$
$857$	−2.28591	−	3.95932i	−0.0780853	−	0.135248i	−0.902424	+	0.430849i	$0.858214\pi$
$858$		0			0
$859$	−5.82450	+	10.0883i	−0.198729	+	0.344209i	−0.948117	−	0.317923i	$-0.897015\pi$
$859$	−5.82450	+	10.0883i	−0.198729	+	0.344209i	0.749387	+	0.662132i	$0.230348\pi$
$860$	3.97040	+	2.29231i	0.135389	+	0.0781671i
$861$		0			0
$862$	0.625564	+	1.08351i	0.0213068	+	0.0369044i
$863$		−	26.2523i		−	0.893640i	−0.894624	−	0.446820i	$-0.852556\pi$
$863$		−	26.2523i		−	0.893640i	0.894624	−	0.446820i	$-0.147444\pi$
$864$		0			0
$865$			4.28985i			0.145859i
$866$	4.13195	−	2.38558i	0.140409	−	0.0810655i
$867$		0			0
$868$	−16.3855	+	28.3806i	−0.556161	+	0.963299i
$869$	21.7950	+	12.5834i	0.739345	+	0.426861i
$870$		0			0
$871$	−2.58775	+	2.91912i	−0.0876825	+	0.0989107i
$872$	−4.97525			−0.168483
$873$		0			0
$874$	20.1432			0.681355
$875$	−11.9511	−	20.6999i	−0.404020	−	0.699783i
$876$		0			0
$877$	−40.5146	−	23.3911i	−1.36808	−	0.789862i	−0.377398	−	0.926051i	$-0.623181\pi$
$877$	−40.5146	−	23.3911i	−1.36808	−	0.789862i	−0.990683	+	0.136189i	$0.956515\pi$
$878$	29.1867	+	16.8509i	0.985003	+	0.568692i
$879$		0			0
$880$	−0.777601	−	1.34684i	−0.0262129	−	0.0454021i
$881$	−52.3698			−1.76438			−0.882192	−	0.470889i	$-0.843933\pi$
$881$	−52.3698			−1.76438			−0.882192	+	0.470889i	$0.843933\pi$
$882$		0			0
$883$	−28.7233			−0.966617			−0.483309	−	0.875450i	$-0.660565\pi$
$883$	−28.7233			−0.966617			−0.483309	+	0.875450i	$0.660565\pi$
$884$	−11.3384	−	10.0513i	−0.381352	−	0.338061i
$885$		0			0
$886$	4.65706	+	2.68876i	0.156457	+	0.0903305i
$887$	6.01188	−	10.4129i	0.201859	−	0.349631i	−0.747268	−	0.664523i	$-0.768635\pi$
$887$	6.01188	−	10.4129i	0.201859	−	0.349631i	0.949128	+	0.314892i	$0.101968\pi$
$888$		0			0
$889$	−19.9732	+	11.5316i	−0.669881	+	0.386756i
$890$			4.08185i			0.136824i
$891$		0			0
$892$			12.8698i			0.430913i
$893$	−8.48043	−	14.6885i	−0.283787	−	0.491533i
$894$		0			0
$895$	−4.34912	−	2.51097i	−0.145375	−	0.0839324i
$896$	2.52719	−	4.37722i	0.0844274	−	0.146233i
$897$		0			0
$898$	−8.39064	−	14.5330i	−0.279999	−	0.484973i
$899$		−	29.7766i		−	0.993105i
$900$		0			0
$901$	26.9793			0.898812
$902$	−30.7440	+	17.7501i	−1.02366	+	0.591012i
$903$		0			0
$904$	−11.3348	−	6.54415i	−0.376990	−	0.217655i
$905$	4.54635	+	2.62484i	0.151126	+	0.0872526i
$906$		0			0
$907$	−13.8974	−	24.0710i	−0.461456	−	0.799265i	0.537578	−	0.843214i	$-0.319339\pi$
$907$	−13.8974	−	24.0710i	−0.461456	−	0.799265i	−0.999034	+	0.0439492i	$0.986006\pi$
$908$		−	18.0552i		−	0.599182i
$909$		0			0
$910$	−2.79198	−	8.37170i	−0.0925531	−	0.277519i
$911$	−10.3296	−	17.8914i	−0.342235	−	0.592769i	0.642612	−	0.766191i	$-0.277851\pi$
$911$	−10.3296	−	17.8914i	−0.342235	−	0.592769i	−0.984847	+	0.173423i	$0.944517\pi$
$912$		0			0
$913$	9.41962	−	16.3153i	0.311744	−	0.539956i
$914$	11.8396	−	20.5067i	0.391618	−	0.678302i
$915$		0			0
$916$	−18.3370	+	10.5869i	−0.605871	+	0.349800i
$917$		−	12.4816i		−	0.412179i
$918$		0			0
$919$	56.3658			1.85933			0.929667	−	0.368400i	$-0.120094\pi$
$919$	56.3658			1.85933			0.929667	+	0.368400i	$0.120094\pi$
$920$	1.51867	+	2.63041i	0.0500690	+	0.0867220i
$921$		0			0
$922$	−17.2311	+	29.8451i	−0.567476	+	0.982898i
$923$	−16.3567	−	3.34458i	−0.538389	−	0.110088i
$924$		0			0
$925$	8.60193	−	4.96633i	0.282830	−	0.163292i
$926$	−22.4773			−0.738649
$927$		0			0
$928$			4.59254i			0.150757i
$929$	1.75111	−	1.01100i	0.0574520	−	0.0331699i	−0.470999	−	0.882134i	$-0.656106\pi$
$929$	1.75111	−	1.01100i	0.0574520	−	0.0331699i	0.528451	+	0.848964i	$0.322773\pi$
$930$		0			0
$931$	−51.5834	−	29.7817i	−1.69058	−	0.976055i
$932$	−14.5305	+	25.1675i	−0.475962	+	0.824390i
$933$		0			0
$934$	−3.84196	+	2.21816i	−0.125713	+	0.0725804i
$935$	−6.53566			−0.213739
$936$		0			0
$937$	−15.3243			−0.500622			−0.250311	−	0.968166i	$-0.580533\pi$
$937$	−15.3243			−0.500622			−0.250311	+	0.968166i	$0.580533\pi$
$938$	−4.73589	+	2.73427i	−0.154632	+	0.0892770i
$939$		0			0
$940$	1.27874	−	2.21484i	0.0417078	−	0.0722400i
$941$	35.8714	+	20.7104i	1.16938	+	0.675139i	0.953533	−	0.301289i	$-0.0974170\pi$
$941$	35.8714	+	20.7104i	1.16938	+	0.675139i	0.215842	+	0.976428i	$0.430750\pi$
$942$		0			0
$943$	60.0435	−	34.6661i	1.95529	−	1.12888i
$944$			3.62311i			0.117922i
$945$		0			0
$946$	−30.4047			−0.988541
$947$	49.2660	−	28.4437i	1.60093	−	0.924297i	0.609628	−	0.792687i	$-0.291319\pi$
$947$	49.2660	−	28.4437i	1.60093	−	0.924297i	0.991302	−	0.131610i	$-0.0420146\pi$
$948$		0			0
$949$	−1.14990	−	0.235129i	−0.0373274	−	0.00763261i
$950$	7.65226	−	13.2541i	0.248272	−	0.430020i
$951$		0			0
$952$	−10.6204	−	18.3951i	−0.344209	−	0.596187i
$953$	40.5931			1.31494			0.657470	−	0.753481i	$-0.271627\pi$
$953$	40.5931			1.31494			0.657470	+	0.753481i	$0.271627\pi$
$954$		0			0
$955$			5.45175i			0.176415i
$956$	−6.29516	+	3.63451i	−0.203600	+	0.117548i
$957$		0			0
$958$	5.90827	−	10.2334i	0.190888	−	0.330627i
$959$	−49.5591	+	85.8389i	−1.60035	+	2.77188i
$960$		0			0
$961$	5.51914	+	9.55944i	0.178037	+	0.308369i
$962$	7.12899	−	2.37753i	0.229848	−	0.0766547i
$963$		0			0
$964$		−	17.9104i		−	0.576856i
$965$	1.84638	+	3.19803i	0.0594372	+	0.102948i
$966$		0			0
$967$	43.2958	+	24.9968i	1.39230	+	0.803844i	0.993569	−	0.113225i	$-0.0361182\pi$
$967$	43.2958	+	24.9968i	1.39230	+	0.803844i	0.398729	+	0.917069i	$0.369452\pi$
$968$	−0.594169	−	0.343044i	−0.0190973	−	0.0110258i
$969$		0			0
$970$	−5.47310	+	3.15989i	−0.175730	+	0.101458i
$971$	31.1467			0.999546			0.499773	−	0.866156i	$-0.333417\pi$
$971$	31.1467			0.999546			0.499773	+	0.866156i	$0.333417\pi$
$972$		0			0
$973$		−	1.95805i		−	0.0627721i
$974$	−12.9186	−	22.3758i	−0.413940	−	0.716965i
$975$		0			0
$976$	0.500864	−	0.867521i	0.0160323	−	0.0277687i
$977$	5.97565	+	3.45004i	0.191178	+	0.110377i	0.592534	−	0.805546i	$-0.298128\pi$
$977$	5.97565	+	3.45004i	0.191178	+	0.110377i	−0.401356	+	0.915922i	$0.631461\pi$
$978$		0			0
$979$	−13.5352	−	23.4436i	−0.432586	−	0.749262i
$980$		−	8.98136i		−	0.286899i
$981$		0			0
$982$			11.1999i			0.357403i
$983$	45.4067	−	26.2156i	1.44825	−	0.836147i	0.449872	−	0.893093i	$-0.351470\pi$
$983$	45.4067	−	26.2156i	1.44825	−	0.836147i	0.998377	+	0.0569461i	$0.0181363\pi$
$984$		0			0
$985$	−5.93626	+	10.2819i	−0.189145	+	0.327608i
$986$	16.7142	+	9.64996i	0.532289	+	0.307317i
$987$		0			0
$988$	7.68122	−	8.66485i	0.244372	−	0.275666i
$989$	59.3808			1.88820
$990$		0			0
$991$	−26.0277			−0.826799			−0.413399	−	0.910550i	$-0.635659\pi$
$991$	−26.0277			−0.826799			−0.413399	+	0.910550i	$0.635659\pi$
$992$	−3.24185	−	5.61504i	−0.102929	−	0.178278i
$993$		0			0
$994$	−20.2683	−	11.7019i	−0.642872	−	0.371163i
$995$	−5.67460	−	3.27623i	−0.179897	−	0.103864i
$996$		0			0
$997$	−13.6237	−	23.5970i	−0.431468	−	0.747324i	0.565532	−	0.824726i	$-0.308671\pi$
$997$	−13.6237	−	23.5970i	−0.431468	−	0.747324i	−0.997000	+	0.0774021i	$0.975337\pi$
$998$	15.4596			0.489367
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.t.a.415.4		28
3.2	odd	2		234.2.t.a.103.12	yes	28
9.2	odd	6		234.2.t.a.25.5	✓	28
9.4	even	3		2106.2.b.d.649.4		14
9.5	odd	6		2106.2.b.c.649.11		14
9.7	even	3	inner	702.2.t.a.181.11		28
13.12	even	2	inner	702.2.t.a.415.11		28
39.38	odd	2		234.2.t.a.103.5	yes	28
117.25	even	6	inner	702.2.t.a.181.4		28
117.38	odd	6		234.2.t.a.25.12	yes	28
117.77	odd	6		2106.2.b.c.649.4		14
117.103	even	6		2106.2.b.d.649.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.5	✓	28	9.2	odd	6
234.2.t.a.25.12	yes	28	117.38	odd	6
234.2.t.a.103.5	yes	28	39.38	odd	2
234.2.t.a.103.12	yes	28	3.2	odd	2
702.2.t.a.181.4		28	117.25	even	6	inner
702.2.t.a.181.11		28	9.7	even	3	inner
702.2.t.a.415.4		28	1.1	even	1	trivial
702.2.t.a.415.11		28	13.12	even	2	inner
2106.2.b.c.649.4		14	117.77	odd	6
2106.2.b.c.649.11		14	9.5	odd	6
2106.2.b.d.649.4		14	9.4	even	3
2106.2.b.d.649.11		14	117.103	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.419378 + 0.242128i) q^{5} +(4.37722 - 2.52719i) q^{7} +1.00000i q^{8} -0.484256 q^{10} +(2.78126 - 1.60576i) q^{11} +(-0.722307 + 3.53246i) q^{13} +(-2.52719 + 4.37722i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.20245 q^{17} -3.21153i q^{19} +(0.419378 - 0.242128i) q^{20} +(-1.60576 + 2.78126i) q^{22} +(3.13608 - 5.43186i) q^{23} +(-2.38275 - 4.12704i) q^{25} +(-1.14069 - 3.42035i) q^{26} -5.05438i q^{28} +(2.29627 + 3.97725i) q^{29} +(-5.61504 - 3.24185i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.63943 - 2.10123i) q^{34} +2.44761 q^{35} +2.08429i q^{37} +(1.60576 + 2.78126i) q^{38} +(-0.242128 + 0.419378i) q^{40} +(9.57301 + 5.52698i) q^{41} +(4.73367 + 8.19896i) q^{43} -3.21153i q^{44} +6.27217i q^{46} +(4.57369 - 2.64062i) q^{47} +(9.27337 - 16.0619i) q^{49} +(4.12704 + 2.38275i) q^{50} +(2.69805 + 2.39177i) q^{52} -6.41990 q^{53} +1.55520 q^{55} +(2.52719 + 4.37722i) q^{56} +(-3.97725 - 2.29627i) q^{58} +(-3.13771 - 1.81156i) q^{59} +(0.500864 + 0.867521i) q^{61} +6.48369 q^{62} -1.00000 q^{64} +(-1.15823 + 1.30655i) q^{65} +(0.936987 + 0.540970i) q^{67} +(-2.10123 + 3.63943i) q^{68} +(-2.11969 + 1.22381i) q^{70} +4.63041i q^{71} +0.325525i q^{73} +(-1.04214 - 1.80504i) q^{74} +(-2.78126 - 1.60576i) q^{76} +(8.11614 - 14.0576i) q^{77} +(3.91818 + 6.78649i) q^{79} -0.484256i q^{80} -11.0540 q^{82} +(5.08022 - 2.93306i) q^{83} +(-1.76242 - 1.01753i) q^{85} +(-8.19896 - 4.73367i) q^{86} +(1.60576 + 2.78126i) q^{88} -8.42912i q^{89} +(5.76550 + 17.2878i) q^{91} +(-3.13608 - 5.43186i) q^{92} +(-2.64062 + 4.57369i) q^{94} +(0.777601 - 1.34684i) q^{95} +(11.3021 - 6.52525i) q^{97} +18.5467i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{13} - 8 q^{14} - 14 q^{16} - 16 q^{17} + 8 q^{23} + 14 q^{25} - 8 q^{26} + 16 q^{29} + 68 q^{35} - 4 q^{43} + 10 q^{49} - 2 q^{52} + 120 q^{53} + 8 q^{56} + 28 q^{61} - 68 q^{62}+ \cdots - 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^13 - 8 * q^14 - 14 * q^16 - 16 * q^17 + 8 * q^23 + 14 * q^25 - 8 * q^26 + 16 * q^29 + 68 * q^35 - 4 * q^43 + 10 * q^49 - 2 * q^52 + 120 * q^53 + 8 * q^56 + 28 * q^61 - 68 * q^62 - 28 * q^64 + 8 * q^65 - 8 * q^68 - 16 * q^74 + 24 * q^77 + 28 * q^79 - 48 * q^82 - 8 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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