LMFDB - Embedded newform 740.2.cc.a.17.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(17,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.cc (of order $36$, degree $12$, 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	740.17
Dual form			740.2.cc.a.653.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.37198 + 1.66088i) q^{3} +(2.22911 - 0.176315i) q^{5} +(0.449992 + 5.14343i) q^{7} +(1.84172 - 5.06008i) q^{9} +(3.78226 - 2.18369i) q^{11} +(6.33254 - 2.30486i) q^{13} +(-4.99456 + 4.12049i) q^{15} +(-0.665988 + 1.82979i) q^{17} +(-0.587167 - 0.838562i) q^{19} +(-9.61000 - 11.4527i) q^{21} +(-0.711249 + 1.23192i) q^{23} +(4.93783 - 0.786050i) q^{25} +(1.78731 + 6.67032i) q^{27} +(-0.983941 + 3.67212i) q^{29} +(2.70555 - 2.70555i) q^{31} +(-5.34460 + 11.4615i) q^{33} +(1.90994 + 11.3859i) q^{35} +(4.62565 - 3.95010i) q^{37} +(-11.1926 + 15.9847i) q^{39} +(1.10822 + 3.04481i) q^{41} +1.12664 q^{43} +(3.21322 - 11.6042i) q^{45} +(-6.86330 + 1.83901i) q^{47} +(-19.3588 + 3.41347i) q^{49} +(-1.45934 - 5.44635i) q^{51} +(-0.734425 + 8.39451i) q^{53} +(8.04603 - 5.53454i) q^{55} +(2.78550 + 1.01384i) q^{57} +(-0.537340 + 6.14183i) q^{59} +(-1.34663 + 2.88786i) q^{61} +(26.8549 + 7.19576i) q^{63} +(13.7095 - 6.25430i) q^{65} +(-5.21520 + 0.456271i) q^{67} +(-0.359000 - 4.10339i) q^{69} +(1.89150 - 10.7272i) q^{71} +(-8.08390 - 8.08390i) q^{73} +(-10.4069 + 10.0656i) q^{75} +(12.9336 + 18.4711i) q^{77} +(8.71830 - 0.762752i) q^{79} +(-2.94303 - 2.46950i) q^{81} +(-7.42217 + 3.46102i) q^{83} +(-1.16194 + 4.19621i) q^{85} +(-3.76506 - 10.3444i) q^{87} +(-10.5253 - 0.920846i) q^{89} +(14.7045 + 31.5338i) q^{91} +(-1.92392 + 10.9111i) q^{93} +(-1.45671 - 1.76572i) q^{95} +(-5.56990 - 3.21578i) q^{97} +(-4.08378 - 23.1602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) $ 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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			0
$2$		0			0
$3$	−2.37198	+	1.66088i	−1.36946	+	0.958910i	−0.369910	+	0.929068i	$0.620612\pi$
$3$	−2.37198	+	1.66088i	−1.36946	+	0.958910i	−0.999555	+	0.0298420i	$0.990500\pi$
$4$		0			0
$5$	2.22911	−	0.176315i	0.996886	−	0.0788505i
$5$	2.22911	−	0.176315i	0.996886	−	0.0788505i
$6$		0			0
$7$	0.449992	+	5.14343i	0.170081	+	1.94403i	0.303183	+	0.952932i	$0.401951\pi$
$7$	0.449992	+	5.14343i	0.170081	+	1.94403i	−0.133102	+	0.991102i	$0.542494\pi$
$8$		0			0
$9$	1.84172	−	5.06008i	0.613906	−	1.68669i
$10$		0			0
$11$	3.78226	−	2.18369i	1.14039	−	0.658406i	0.193865	−	0.981028i	$-0.437898\pi$
$11$	3.78226	−	2.18369i	1.14039	−	0.658406i	0.946528	+	0.322622i	$0.104564\pi$
$12$		0			0
$13$	6.33254	−	2.30486i	1.75633	−	0.639253i	0.756442	−	0.654061i	$-0.226936\pi$
$13$	6.33254	−	2.30486i	1.75633	−	0.639253i	0.999890	+	0.0148087i	$0.00471394\pi$
$14$		0			0
$15$	−4.99456	+	4.12049i	−1.28959	+	1.06391i
$16$		0			0
$17$	−0.665988	+	1.82979i	−0.161526	+	0.443788i	−0.993881	−	0.110454i	$-0.964770\pi$
$17$	−0.665988	+	1.82979i	−0.161526	+	0.443788i	0.832356	+	0.554242i	$0.186992\pi$
$18$		0			0
$19$	−0.587167	−	0.838562i	−0.134705	−	0.192379i	0.746132	−	0.665798i	$-0.231909\pi$
$19$	−0.587167	−	0.838562i	−0.134705	−	0.192379i	−0.880838	+	0.473419i	$0.843020\pi$
$20$		0			0
$21$	−9.61000	−	11.4527i	−2.09707	−	2.49919i
$22$		0			0
$23$	−0.711249	+	1.23192i	−0.148306	+	0.256873i	−0.930601	−	0.366034i	$-0.880715\pi$
$23$	−0.711249	+	1.23192i	−0.148306	+	0.256873i	0.782296	+	0.622907i	$0.214049\pi$
$24$		0			0
$25$	4.93783	−	0.786050i	0.987565	−	0.157210i
$26$		0			0
$27$	1.78731	+	6.67032i	0.343968	+	1.28370i
$28$		0			0
$29$	−0.983941	+	3.67212i	−0.182713	+	0.681895i	0.812395	+	0.583107i	$0.198163\pi$
$29$	−0.983941	+	3.67212i	−0.182713	+	0.681895i	−0.995109	+	0.0987879i	$0.968503\pi$
$30$		0			0
$31$	2.70555	−	2.70555i	0.485931	−	0.485931i	−0.421089	−	0.907020i	$-0.638352\pi$
$31$	2.70555	−	2.70555i	0.485931	−	0.485931i	0.907020	+	0.421089i	$0.138352\pi$
$32$		0			0
$33$	−5.34460	+	11.4615i	−0.930376	+	1.99520i
$34$		0			0
$35$	1.90994	+	11.3859i	0.322840	+	1.92457i
$36$		0			0
$37$	4.62565	−	3.95010i	0.760453	−	0.649393i
$37$	4.62565	−	3.95010i	0.760453	−	0.649393i
$38$		0			0
$39$	−11.1926	+	15.9847i	−1.79225	+	2.55960i
$40$		0			0
$41$	1.10822	+	3.04481i	0.173075	+	0.475520i	0.995654	−	0.0931313i	$-0.0296876\pi$
$41$	1.10822	+	3.04481i	0.173075	+	0.475520i	−0.822579	+	0.568651i	$0.807465\pi$
$42$		0			0
$43$	1.12664			0.171811			0.0859054	−	0.996303i	$-0.472622\pi$
$43$	1.12664			0.171811			0.0859054	+	0.996303i	$0.472622\pi$
$44$		0			0
$45$	3.21322	−	11.6042i	0.478998	−	1.72985i
$46$		0			0
$47$	−6.86330	+	1.83901i	−1.00111	+	0.268248i	−0.721912	−	0.691984i	$-0.756737\pi$
$47$	−6.86330	+	1.83901i	−1.00111	+	0.268248i	−0.279202	+	0.960232i	$0.590070\pi$
$48$		0			0
$49$	−19.3588	+	3.41347i	−2.76554	+	0.487639i
$50$		0			0
$51$	−1.45934	−	5.44635i	−0.204349	−	0.762641i
$52$		0			0
$53$	−0.734425	+	8.39451i	−0.100881	+	1.15308i	0.761968	+	0.647614i	$0.224233\pi$
$53$	−0.734425	+	8.39451i	−0.100881	+	1.15308i	−0.862849	+	0.505461i	$0.831322\pi$
$54$		0			0
$55$	8.04603	−	5.53454i	1.08493	−	0.746277i
$56$		0			0
$57$	2.78550	+	1.01384i	0.368949	+	0.134286i
$58$		0			0
$59$	−0.537340	+	6.14183i	−0.0699557	+	0.799598i	0.877472	+	0.479628i	$0.159228\pi$
$59$	−0.537340	+	6.14183i	−0.0699557	+	0.799598i	−0.947428	+	0.319970i	$0.896327\pi$
$60$		0			0
$61$	−1.34663	+	2.88786i	−0.172418	+	0.369752i	−0.973460	−	0.228856i	$-0.926501\pi$
$61$	−1.34663	+	2.88786i	−0.172418	+	0.369752i	0.801042	+	0.598608i	$0.204279\pi$
$62$		0			0
$63$	26.8549	+	7.19576i	3.38340	+	0.906580i
$64$		0			0
$65$	13.7095	−	6.25430i	1.70046	−	0.775750i
$66$		0			0
$67$	−5.21520	+	0.456271i	−0.637138	+	0.0557424i	−0.401148	−	0.916013i	$-0.631389\pi$
$67$	−5.21520	+	0.456271i	−0.637138	+	0.0557424i	−0.235990	+	0.971755i	$0.575833\pi$
$68$		0			0
$69$	−0.359000	−	4.10339i	−0.0432185	−	0.493990i
$70$		0			0
$71$	1.89150	−	10.7272i	0.224480	−	1.27309i	−0.639198	−	0.769042i	$-0.720733\pi$
$71$	1.89150	−	10.7272i	0.224480	−	1.27309i	0.863677	−	0.504045i	$-0.168155\pi$
$72$		0			0
$73$	−8.08390	−	8.08390i	−0.946149	−	0.946149i	0.0524735	−	0.998622i	$-0.483289\pi$
$73$	−8.08390	−	8.08390i	−0.946149	−	0.946149i	−0.998622	+	0.0524735i	$0.983289\pi$
$74$		0			0
$75$	−10.4069	+	10.0656i	−1.20169	+	1.16228i
$76$		0			0
$77$	12.9336	+	18.4711i	1.47392	+	2.10498i
$78$		0			0
$79$	8.71830	−	0.762752i	0.980885	−	0.0858163i	0.414581	−	0.910013i	$-0.363928\pi$
$79$	8.71830	−	0.762752i	0.980885	−	0.0858163i	0.566304	+	0.824196i	$0.308373\pi$
$80$		0			0
$81$	−2.94303	−	2.46950i	−0.327003	−	0.274388i
$82$		0			0
$83$	−7.42217	+	3.46102i	−0.814690	+	0.379896i	−0.784871	−	0.619659i	$-0.787271\pi$
$83$	−7.42217	+	3.46102i	−0.814690	+	0.379896i	−0.0298187	+	0.999555i	$0.509493\pi$
$84$		0			0
$85$	−1.16194	+	4.19621i	−0.126030	+	0.455143i
$86$		0			0
$87$	−3.76506	−	10.3444i	−0.403656	−	1.10904i
$88$		0			0
$89$	−10.5253	−	0.920846i	−1.11568	−	0.0976095i	−0.485631	−	0.874164i	$-0.661410\pi$
$89$	−10.5253	−	0.920846i	−1.11568	−	0.0976095i	−0.630050	+	0.776554i	$0.716966\pi$
$90$		0			0
$91$	14.7045	+	31.5338i	1.54145	+	3.30565i
$92$		0			0
$93$	−1.92392	+	10.9111i	−0.199502	+	1.13143i
$94$		0			0
$95$	−1.45671	−	1.76572i	−0.149455	−	0.181159i
$96$		0			0
$97$	−5.56990	−	3.21578i	−0.565538	−	0.326513i	0.189827	−	0.981817i	$-0.439207\pi$
$97$	−5.56990	−	3.21578i	−0.565538	−	0.326513i	−0.755365	+	0.655304i	$0.772541\pi$
$98$		0			0
$99$	−4.08378	−	23.1602i	−0.410435	−	2.32769i
$100$		0			0
$101$	−10.0063	−	5.77712i	−0.995660	−	0.574845i	−0.0886990	−	0.996058i	$-0.528271\pi$
$101$	−10.0063	−	5.77712i	−0.995660	−	0.574845i	−0.906961	+	0.421214i	$0.861604\pi$
$102$		0			0
$103$	12.6734	−	7.31699i	1.24875	−	0.720964i	0.277887	−	0.960614i	$-0.410366\pi$
$103$	12.6734	−	7.31699i	1.24875	−	0.720964i	0.970859	+	0.239650i	$0.0770326\pi$
$104$		0			0
$105$	−23.4410	−	23.8350i	−2.28761	−	2.32606i
$106$		0			0
$107$	−12.6329	−	5.89083i	−1.22127	−	0.569488i	−0.298342	−	0.954459i	$-0.596434\pi$
$107$	−12.6329	−	5.89083i	−1.22127	−	0.569488i	−0.922929	+	0.384971i	$0.874211\pi$
$108$		0			0
$109$	0.348060	+	0.243714i	0.0333381	+	0.0233436i	0.590127	−	0.807311i	$-0.299078\pi$
$109$	0.348060	+	0.243714i	0.0333381	+	0.0233436i	−0.556789	+	0.830654i	$0.687967\pi$
$110$		0			0
$111$	−4.41132	+	17.0522i	−0.418704	+	1.61853i
$112$		0			0
$113$	5.54393	−	0.977544i	0.521529	−	0.0919596i	0.0933144	−	0.995637i	$-0.470254\pi$
$113$	5.54393	−	0.977544i	0.521529	−	0.0919596i	0.428215	+	0.903677i	$0.359143\pi$
$114$		0			0
$115$	−1.36824	+	2.87148i	−0.127589	+	0.267767i
$116$		0			0
$117$		−	36.2881i		−	3.35483i
$118$		0			0
$119$	−9.71107	−	2.60207i	−0.890212	−	0.238532i
$120$		0			0
$121$	4.03697	−	6.99224i	0.366998	−	0.635658i
$122$		0			0
$123$	−7.68575	−	5.38162i	−0.693001	−	0.485244i
$124$		0			0
$125$	10.8683	−	2.62280i	0.972094	−	0.234591i
$126$		0			0
$127$	13.1653	+	1.15182i	1.16823	+	0.102207i	0.654718	−	0.755873i	$-0.272787\pi$
$127$	13.1653	+	1.15182i	1.16823	+	0.102207i	0.513516	+	0.858080i	$0.328343\pi$
$128$		0			0
$129$	−2.67237	+	1.87121i	−0.235289	+	0.164751i
$130$		0			0
$131$	18.3745	−	8.56818i	1.60539	−	0.748606i	0.606471	−	0.795105i	$-0.292584\pi$
$131$	18.3745	−	8.56818i	1.60539	−	0.748606i	0.998918	+	0.0464998i	$0.0148067\pi$
$132$		0			0
$133$	4.04887	−	3.39740i	0.351081	−	0.294592i
$134$		0			0
$135$	5.16018	+	14.5537i	0.444117	+	1.25259i
$136$		0			0
$137$	0.219604	−	0.819574i	0.0187620	−	0.0700209i	−0.955910	−	0.293659i	$-0.905127\pi$
$137$	0.219604	−	0.819574i	0.0187620	−	0.0700209i	0.974672	+	0.223639i	$0.0717935\pi$
$138$		0			0
$139$	−9.76785	−	3.55521i	−0.828498	−	0.301549i	−0.107256	−	0.994231i	$-0.534206\pi$
$139$	−9.76785	−	3.55521i	−0.828498	−	0.301549i	−0.721242	+	0.692683i	$0.756429\pi$
$140$		0			0
$141$	13.2252	−	15.7612i	1.11377	−	1.32733i
$142$		0			0
$143$	18.9182	−	22.5459i	1.58202	−	1.88538i
$144$		0			0
$145$	−1.54586	+	8.35902i	−0.128377	+	0.694179i
$146$		0			0
$147$	40.2493	−	40.2493i	3.31970	−	3.31970i
$148$		0			0
$149$			9.13261i			0.748173i	0.927394	+	0.374086i	$0.122044\pi$
$149$			9.13261i			0.748173i	−0.927394	+	0.374086i	$0.877956\pi$
$150$		0			0
$151$	−8.97699	−	1.58289i	−0.730537	−	0.128813i	−0.204006	−	0.978970i	$-0.565396\pi$
$151$	−8.97699	−	1.58289i	−0.730537	−	0.128813i	−0.526531	+	0.850156i	$0.676507\pi$
$152$		0			0
$153$	8.03230	+	6.73990i	0.649373	+	0.544889i
$154$		0			0
$155$	5.55393	−	6.50799i	0.446102	−	0.522734i
$156$		0			0
$157$	2.09367	+	4.48988i	0.167093	+	0.358332i	0.971968	−	0.235112i	$-0.0755457\pi$
$157$	2.09367	+	4.48988i	0.167093	+	0.358332i	−0.804875	+	0.593444i	$0.797768\pi$
$158$		0			0
$159$	−12.2002	−	21.1314i	−0.967542	−	1.67583i
$160$		0			0
$161$	−6.65635	−	3.10391i	−0.524594	−	0.244622i
$162$		0			0
$163$	−3.31328	−	3.94862i	−0.259516	−	0.309279i	0.620516	−	0.784194i	$-0.286923\pi$
$163$	−3.31328	−	3.94862i	−0.259516	−	0.309279i	−0.880032	+	0.474915i	$0.842479\pi$
$164$		0			0
$165$	−9.89284	+	26.4913i	−0.770157	+	2.06235i
$166$		0			0
$167$	−12.3021	−	2.16919i	−0.951965	−	0.167857i	−0.323964	−	0.946069i	$-0.605016\pi$
$167$	−12.3021	−	2.16919i	−0.951965	−	0.167857i	−0.628001	+	0.778212i	$0.716127\pi$
$168$		0			0
$169$	24.8302	−	20.8350i	1.91001	−	1.60269i
$170$		0			0
$171$	−5.32459	+	1.42672i	−0.407181	+	0.109104i
$172$		0			0
$173$	−6.31682	+	9.02135i	−0.480259	+	0.685880i	−0.984039	−	0.177951i	$-0.943053\pi$
$173$	−6.31682	+	9.02135i	−0.480259	+	0.685880i	0.503781	+	0.863832i	$0.331942\pi$
$174$		0			0
$175$	6.26498	+	25.0437i	0.473588	+	1.89312i
$176$		0			0
$177$	−8.92627	−	15.4608i	−0.670940	−	1.16210i
$178$		0			0
$179$	1.47777	+	1.47777i	0.110454	+	0.110454i	0.760174	−	0.649720i	$-0.225114\pi$
$179$	1.47777	+	1.47777i	0.110454	+	0.110454i	−0.649720	+	0.760174i	$0.725114\pi$
$180$		0			0
$181$	14.6490	−	5.33180i	1.08885	−	0.396309i	0.265656	−	0.964068i	$-0.414412\pi$
$181$	14.6490	−	5.33180i	1.08885	−	0.396309i	0.823195	+	0.567759i	$0.192189\pi$
$182$		0			0
$183$	−1.60220	−	9.08653i	−0.118438	−	0.671696i
$184$		0			0
$185$	9.61461	−	9.62077i	0.706880	−	0.707333i
$186$		0			0
$187$	1.47674	+	8.37503i	0.107990	+	0.612443i
$188$		0			0
$189$	−33.5041	+	12.1945i	−2.43706	+	0.887019i
$190$		0			0
$191$	−14.8395	−	14.8395i	−1.07375	−	1.07375i	−0.997055	−	0.0766940i	$-0.975564\pi$
$191$	−14.8395	−	14.8395i	−1.07375	−	1.07375i	−0.0766940	−	0.997055i	$-0.524436\pi$
$192$		0			0
$193$	6.60672	+	11.4432i	0.475562	+	0.823698i	0.999608	−	0.0279922i	$-0.00891137\pi$
$193$	6.60672	+	11.4432i	0.475562	+	0.823698i	−0.524046	+	0.851690i	$0.675578\pi$
$194$		0			0
$195$	−22.1311	+	37.6050i	−1.58484	+	2.69295i
$196$		0			0
$197$	1.76551	−	2.52141i	0.125787	−	0.179643i	−0.751319	−	0.659939i	$-0.770582\pi$
$197$	1.76551	−	2.52141i	0.125787	−	0.179643i	0.877106	+	0.480296i	$0.159471\pi$
$198$		0			0
$199$	1.20297	−	0.322336i	0.0852766	−	0.0228498i	−0.215928	−	0.976409i	$-0.569278\pi$
$199$	1.20297	−	0.322336i	0.0852766	−	0.0228498i	0.301205	+	0.953559i	$0.402611\pi$
$200$		0			0
$201$	11.6126	−	9.74409i	0.819086	−	0.687295i
$202$		0			0
$203$	−19.3301	−	3.40841i	−1.35670	−	0.239223i
$204$		0			0
$205$	3.00719	+	6.59182i	0.210031	+	0.460392i
$206$		0			0
$207$	4.92369	+	5.86782i	0.342220	+	0.407842i
$208$		0			0
$209$	−4.05197	−	1.88947i	−0.280281	−	0.130697i
$210$		0			0
$211$	−3.08530	−	5.34390i	−0.212401	−	0.367889i	0.740064	−	0.672536i	$-0.234795\pi$
$211$	−3.08530	−	5.34390i	−0.212401	−	0.367889i	−0.952465	+	0.304647i	$0.901462\pi$
$212$		0			0
$213$	13.3300	+	28.5863i	0.913359	+	1.95870i
$214$		0			0
$215$	2.51140	−	0.198643i	0.171276	−	0.0135474i
$216$		0			0
$217$	15.1333	+	12.6983i	1.02731	+	0.862019i
$218$		0			0
$219$	32.6013	+	5.74848i	2.20299	+	0.388446i
$220$		0			0
$221$			13.1222i			0.882695i
$222$		0			0
$223$	−12.9231	+	12.9231i	−0.865395	+	0.865395i	−0.991958	−	0.126564i	$-0.959605\pi$
$223$	−12.9231	+	12.9231i	−0.865395	+	0.865395i	0.126564	+	0.991958i	$0.459605\pi$
$224$		0			0
$225$	5.11661	−	26.4335i	0.341107	−	1.76223i
$226$		0			0
$227$	−14.6394	+	17.4466i	−0.971652	+	1.15797i	0.0157715	+	0.999876i	$0.494980\pi$
$227$	−14.6394	+	17.4466i	−0.971652	+	1.15797i	−0.987424	+	0.158095i	$0.949465\pi$
$228$		0			0
$229$	3.36919	−	4.01525i	0.222643	−	0.265335i	−0.643148	−	0.765742i	$-0.722372\pi$
$229$	3.36919	−	4.01525i	0.222643	−	0.265335i	0.865790	+	0.500407i	$0.166816\pi$
$230$		0			0
$231$	−61.3567	−	22.3320i	−4.03697	−	1.46934i
$232$		0			0
$233$	4.68733	−	17.4933i	0.307077	−	1.14603i	−0.624066	−	0.781372i	$-0.714520\pi$
$233$	4.68733	−	17.4933i	0.307077	−	1.14603i	0.931143	−	0.364655i	$-0.118813\pi$
$234$		0			0
$235$	−14.9748	+	5.30946i	−0.976846	+	0.346351i
$236$		0			0
$237$	−19.4128	+	16.2893i	−1.26100	+	1.05810i
$238$		0			0
$239$	1.50544	−	0.702000i	0.0973791	−	0.0454086i	−0.373318	−	0.927703i	$-0.621780\pi$
$239$	1.50544	−	0.702000i	0.0973791	−	0.0454086i	0.470698	+	0.882295i	$0.344002\pi$
$240$		0			0
$241$	−10.6809	+	7.47886i	−0.688019	+	0.481756i	−0.864555	−	0.502538i	$-0.832400\pi$
$241$	−10.6809	+	7.47886i	−0.688019	+	0.481756i	0.176536	+	0.984294i	$0.443511\pi$
$242$		0			0
$243$	−9.55570	−	0.836015i	−0.612998	−	0.0536304i
$244$		0			0
$245$	−42.5509	+	11.0222i	−2.71847	+	0.704184i
$246$		0			0
$247$	−5.65103	−	3.95689i	−0.359566	−	0.251771i
$248$		0			0
$249$	11.8569	−	20.5368i	0.751403	−	1.30147i
$250$		0			0
$251$	15.1264	+	4.05312i	0.954773	+	0.255831i	0.702386	−	0.711796i	$-0.252118\pi$
$251$	15.1264	+	4.05312i	0.954773	+	0.255831i	0.252386	+	0.967627i	$0.418785\pi$
$252$		0			0
$253$			6.21258i			0.390581i
$254$		0			0
$255$	−4.21330	−	11.8832i	−0.263847	−	0.744153i
$256$		0			0
$257$	5.86476	−	1.03412i	0.365834	−	0.0645064i	0.0122903	−	0.999924i	$-0.496088\pi$
$257$	5.86476	−	1.03412i	0.365834	−	0.0645064i	0.353543	+	0.935418i	$0.384977\pi$
$258$		0			0
$259$	22.3986	+	22.0142i	1.39178	+	1.36790i
$260$		0			0
$261$	16.7691	+	11.7418i	1.03798	+	0.726801i
$262$		0			0
$263$	5.15491	+	2.40377i	0.317865	+	0.148223i	0.575002	−	0.818152i	$-0.305001\pi$
$263$	5.15491	+	2.40377i	0.317865	+	0.148223i	−0.257137	+	0.966375i	$0.582779\pi$
$264$		0			0
$265$	−0.157031	+	18.8417i	−0.00964634	+	1.15744i
$266$		0			0
$267$	26.4953	−	15.2971i	1.62149	−	0.936165i
$268$		0			0
$269$	9.33416	+	5.38908i	0.569114	+	0.328578i	0.756795	−	0.653652i	$-0.226764\pi$
$269$	9.33416	+	5.38908i	0.569114	+	0.328578i	−0.187682	+	0.982230i	$0.560097\pi$
$270$		0			0
$271$	0.0676794	+	0.383829i	0.00411123	+	0.0233159i	0.986794	−	0.161978i	$-0.0517874\pi$
$271$	0.0676794	+	0.383829i	0.00411123	+	0.0233159i	−0.982683	+	0.185294i	$0.940676\pi$
$272$		0			0
$273$	−87.2527	−	50.3754i	−5.28077	−	3.04886i
$274$		0			0
$275$	16.9596	−	13.7557i	1.02270	−	0.829500i
$276$		0			0
$277$	−1.66995	+	9.47076i	−0.100338	+	0.569043i	0.892643	+	0.450765i	$0.148849\pi$
$277$	−1.66995	+	9.47076i	−0.100338	+	0.569043i	−0.992980	+	0.118278i	$0.962263\pi$
$278$		0			0
$279$	−8.70743	−	18.6732i	−0.521300	−	1.11793i
$280$		0			0
$281$	−22.5264	−	1.97080i	−1.34381	−	0.117568i	−0.607558	−	0.794275i	$-0.707851\pi$
$281$	−22.5264	−	1.97080i	−1.34381	−	0.117568i	−0.736252	+	0.676707i	$0.763406\pi$
$282$		0			0
$283$	7.16490	+	19.6854i	0.425909	+	1.17018i	0.948274	+	0.317453i	$0.102828\pi$
$283$	7.16490	+	19.6854i	0.425909	+	1.17018i	−0.522365	+	0.852722i	$0.674950\pi$
$284$		0			0
$285$	6.38793	+	1.76883i	0.378389	+	0.104776i
$286$		0			0
$287$	−15.1621	+	7.07020i	−0.894991	+	0.417341i
$288$		0			0
$289$	10.1182	+	8.49016i	0.595187	+	0.499421i
$290$		0			0
$291$	18.5527	−	1.62315i	1.08758	−	0.0951510i
$292$		0			0
$293$	14.9832	+	21.3982i	0.875327	+	1.25010i	0.967121	+	0.254318i	$0.0818511\pi$
$293$	14.9832	+	21.3982i	0.875327	+	1.25010i	−0.0917935	+	0.995778i	$0.529260\pi$
$294$		0			0
$295$	−0.114891	+	13.7855i	−0.00668923	+	0.802624i
$296$		0			0
$297$	21.3260	+	21.3260i	1.23746	+	1.23746i
$298$		0			0
$299$	−1.66462	+	9.44051i	−0.0962672	+	0.545959i
$300$		0			0
$301$	0.506978	+	5.79479i	0.0292218	+	0.334006i
$302$		0			0
$303$	33.3298	−	2.91598i	1.91475	−	0.167519i
$304$		0			0
$305$	−2.49261	+	6.67477i	−0.142726	+	0.382196i
$306$		0			0
$307$	12.7502	+	3.41641i	0.727692	+	0.194985i	0.603601	−	0.797286i	$-0.293732\pi$
$307$	12.7502	+	3.41641i	0.727692	+	0.194985i	0.124091	+	0.992271i	$0.460399\pi$
$308$		0			0
$309$	−17.9084	+	38.4047i	−1.01877	+	2.18477i
$310$		0			0
$311$	−0.276186	+	3.15682i	−0.0156611	+	0.179007i	0.984335	+	0.176307i	$0.0564150\pi$
$311$	−0.276186	+	3.15682i	−0.0156611	+	0.179007i	−0.999996	+	0.00270013i	$0.999141\pi$
$312$		0			0
$313$	−3.23747	−	1.17834i	−0.182993	−	0.0666038i	0.248899	−	0.968530i	$-0.419931\pi$
$313$	−3.23747	−	1.17834i	−0.182993	−	0.0666038i	−0.431891	+	0.901926i	$0.642154\pi$
$314$		0			0
$315$	61.1312	+	11.3052i	3.44435	+	0.636974i
$316$		0			0
$317$	1.99919	−	22.8508i	0.112286	−	1.28343i	−0.705832	−	0.708379i	$-0.749427\pi$
$317$	1.99919	−	22.8508i	0.112286	−	1.28343i	0.818118	−	0.575051i	$-0.195018\pi$
$318$		0			0
$319$	4.29724	+	16.0375i	0.240599	+	0.897928i
$320$		0			0
$321$	39.7490	−	7.00883i	2.21857	−	0.391195i
$322$		0			0
$323$	1.92544	−	0.515919i	0.107134	−	0.0287065i
$324$		0			0
$325$	29.4573	−	16.3587i	1.63400	−	0.907417i
$326$		0			0
$327$	−1.23037			−0.0680397
$328$		0			0
$329$	−12.5473	−	34.4734i	−0.691754	−	1.90058i
$330$		0			0
$331$	11.1462	−	15.9185i	0.612653	−	0.874959i	−0.386221	−	0.922406i	$-0.626220\pi$
$331$	11.1462	−	15.9185i	0.612653	−	0.874959i	0.998874	+	0.0474477i	$0.0151087\pi$
$332$		0			0
$333$	−11.4687	−	30.6812i	−0.628480	−	1.68132i
$334$		0			0
$335$	−11.5448	+	1.93660i	−0.630759	+	0.105807i
$336$		0			0
$337$	−2.48273	+	5.32423i	−0.135243	+	0.290029i	−0.962252	−	0.272159i	$-0.912262\pi$
$337$	−2.48273	+	5.32423i	−0.135243	+	0.290029i	0.827009	+	0.562188i	$0.190040\pi$
$338$		0			0
$339$	−11.5265	+	11.5265i	−0.626035	+	0.626035i
$340$		0			0
$341$	4.32501	−	16.1412i	0.234212	−	0.874092i
$342$		0			0
$343$	−16.9141	−	63.1243i	−0.913276	−	3.40839i
$344$		0			0
$345$	−1.52374	−	9.08359i	−0.0820353	−	0.489044i
$346$		0			0
$347$	−10.2526	+	17.7579i	−0.550386	+	0.953296i	0.447861	+	0.894103i	$0.352186\pi$
$347$	−10.2526	+	17.7579i	−0.550386	+	0.953296i	−0.998247	+	0.0591929i	$0.981147\pi$
$348$		0			0
$349$	−9.25517	−	11.0299i	−0.495418	−	0.590416i	0.459169	−	0.888349i	$-0.348147\pi$
$349$	−9.25517	−	11.0299i	−0.495418	−	0.590416i	−0.954587	+	0.297933i	$0.903703\pi$
$350$		0			0
$351$	26.6924	+	38.1206i	1.42473	+	2.03473i
$352$		0			0
$353$	−1.12365	+	3.08721i	−0.0598059	+	0.164315i	−0.965997	−	0.258553i	$-0.916754\pi$
$353$	−1.12365	+	3.08721i	−0.0598059	+	0.164315i	0.906191	+	0.422868i	$0.138977\pi$
$354$		0			0
$355$	2.32498	−	24.2456i	0.123397	−	1.28682i
$356$		0			0
$357$	27.3562	−	9.95685i	1.44784	−	0.526972i
$358$		0			0
$359$	7.39719	−	4.27077i	0.390409	−	0.225403i	−0.291928	−	0.956440i	$-0.594297\pi$
$359$	7.39719	−	4.27077i	0.390409	−	0.225403i	0.682337	+	0.731038i	$0.260964\pi$
$360$		0			0
$361$	6.13996	−	16.8694i	0.323156	−	0.887864i
$362$		0			0
$363$	2.03765	+	23.2904i	0.106949	+	1.22243i
$364$		0			0
$365$	−19.4452	−	16.5946i	−1.01781	−	0.868599i
$366$		0			0
$367$	−10.1160	+	7.08326i	−0.528048	+	0.369743i	−0.806990	−	0.590564i	$-0.798905\pi$
$367$	−10.1160	+	7.08326i	−0.528048	+	0.369743i	0.278942	+	0.960308i	$0.410016\pi$
$368$		0			0
$369$	17.4480			0.908308
$370$		0			0
$371$	−43.5071			−2.25878
$372$		0			0
$373$	15.5941	−	10.9191i	0.807430	−	0.565368i	−0.0953638	−	0.995442i	$-0.530401\pi$
$373$	15.5941	−	10.9191i	0.807430	−	0.565368i	0.902794	+	0.430074i	$0.141513\pi$
$374$		0			0
$375$	−21.4234	+	24.2723i	−1.10630	+	1.25341i
$376$		0			0
$377$	2.23286	+	25.5217i	0.114998	+	1.31443i
$378$		0			0
$379$	1.84761	−	5.07628i	0.0949056	−	0.260751i	−0.883152	−	0.469088i	$-0.844583\pi$
$379$	1.84761	−	5.07628i	0.0949056	−	0.260751i	0.978057	+	0.208337i	$0.0668050\pi$
$380$		0			0
$381$	−33.1410	+	19.1339i	−1.69786	+	0.980262i
$382$		0			0
$383$	6.95404	−	2.53106i	0.355335	−	0.129331i	−0.158184	−	0.987410i	$-0.550564\pi$
$383$	6.95404	−	2.53106i	0.355335	−	0.129331i	0.513519	+	0.858078i	$0.328342\pi$
$384$		0			0
$385$	32.0872	+	38.8937i	1.63531	+	1.98221i
$386$		0			0
$387$	2.07495	−	5.70088i	0.105476	−	0.289792i
$388$		0			0
$389$	−13.8608	−	19.7953i	−0.702771	−	1.00366i	−0.998824	−	0.0484894i	$-0.984559\pi$
$389$	−13.8608	−	19.7953i	−0.702771	−	1.00366i	0.296053	−	0.955172i	$-0.404330\pi$
$390$		0			0
$391$	−1.78046	−	2.12188i	−0.0900420	−	0.107308i
$392$		0			0
$393$	−29.3533	+	50.8415i	−1.48068	+	2.56461i
$394$		0			0
$395$	19.2995	−	3.23742i	0.971064	−	0.162892i
$396$		0			0
$397$	−10.0062	−	37.3437i	−0.502197	−	1.87423i	−0.485261	−	0.874369i	$-0.661275\pi$
$397$	−10.0062	−	37.3437i	−0.502197	−	1.87423i	−0.0169365	−	0.999857i	$-0.505391\pi$
$398$		0			0
$399$	−3.96116	+	14.7833i	−0.198306	+	0.740089i
$400$		0			0
$401$	7.71890	−	7.71890i	0.385464	−	0.385464i	−0.487602	−	0.873066i	$-0.662128\pi$
$401$	7.71890	−	7.71890i	0.385464	−	0.385464i	0.873066	+	0.487602i	$0.162128\pi$
$402$		0			0
$403$	10.8971	−	23.3689i	0.542824	−	1.16409i
$404$		0			0
$405$	−6.99573	−	4.98587i	−0.347621	−	0.247750i
$406$		0			0
$407$	8.86962	−	25.0413i	0.439651	−	1.24125i
$408$		0			0
$409$	−0.429560	+	0.613476i	−0.0212404	+	0.0303344i	−0.829632	−	0.558311i	$-0.811450\pi$
$409$	−0.429560	+	0.613476i	−0.0212404	+	0.0303344i	0.808391	+	0.588645i	$0.200339\pi$
$410$		0			0
$411$	0.840316	+	2.30875i	0.0414498	+	0.113882i
$412$		0			0
$413$	−31.8319			−1.56634
$414$		0			0
$415$	−15.9346	+	9.02361i	−0.782198	+	0.442952i
$416$		0			0
$417$	29.0739	−	7.79034i	1.42376	−	0.381495i
$418$		0			0
$419$	6.42635	−	1.13314i	0.313948	−	0.0553574i	−0.0144543	−	0.999896i	$-0.504601\pi$
$419$	6.42635	−	1.13314i	0.313948	−	0.0553574i	0.328402	+	0.944538i	$0.393490\pi$
$420$		0			0
$421$	3.11390	+	11.6212i	0.151762	+	0.566384i	0.999361	+	0.0357462i	$0.0113808\pi$
$421$	3.11390	+	11.6212i	0.151762	+	0.566384i	−0.847599	+	0.530638i	$0.821953\pi$
$422$		0			0
$423$	−3.33470	+	38.1158i	−0.162139	+	1.85325i
$424$		0			0
$425$	−1.85023	+	9.55866i	−0.0897492	+	0.463663i
$426$		0			0
$427$	−15.4595	−	5.62678i	−0.748136	−	0.272299i
$428$		0			0
$429$	−7.42772	+	84.8993i	−0.358614	+	4.09897i
$430$		0			0
$431$	−2.30774	+	4.94896i	−0.111160	+	0.238383i	−0.954016	−	0.299756i	$-0.903095\pi$
$431$	−2.30774	+	4.94896i	−0.111160	+	0.238383i	0.842856	+	0.538139i	$0.180872\pi$
$432$		0			0
$433$	−4.52974	−	1.21374i	−0.217685	−	0.0583286i	0.148328	−	0.988938i	$-0.452611\pi$
$433$	−4.52974	−	1.21374i	−0.217685	−	0.0583286i	−0.366013	+	0.930610i	$0.619278\pi$
$434$		0			0
$435$	−10.2166	−	22.3949i	−0.489848	−	1.07376i
$436$		0			0
$437$	1.45066	−	0.126917i	0.0693946	−	0.00607124i
$438$		0			0
$439$	−0.0665522	−	0.760695i	−0.00317636	−	0.0363060i	0.994441	−	0.105294i	$-0.0335784\pi$
$439$	−0.0665522	−	0.760695i	−0.00317636	−	0.0363060i	−0.997617	+	0.0689883i	$0.978023\pi$
$440$		0			0
$441$	−18.3809	+	104.243i	−0.875283	+	4.96397i
$442$		0			0
$443$	−20.9545	−	20.9545i	−0.995579	−	0.995579i	0.00441176	−	0.999990i	$-0.498596\pi$
$443$	−20.9545	−	20.9545i	−0.995579	−	0.995579i	−0.999990	+	0.00441176i	$0.998596\pi$
$444$		0			0
$445$	−23.6244	−	0.196891i	−1.11990	−	0.00933351i
$446$		0			0
$447$	−15.1682	−	21.6624i	−0.717430	−	1.02460i
$448$		0			0
$449$	−2.74368	+	0.240041i	−0.129482	+	0.0113282i	−0.151713	−	0.988425i	$-0.548479\pi$
$449$	−2.74368	+	0.240041i	−0.129482	+	0.0113282i	0.0222303	+	0.999753i	$0.492923\pi$
$450$		0			0
$451$	10.8405	+	9.09625i	0.510459	+	0.428326i
$452$		0			0
$453$	23.9222	−	11.1551i	1.12397	−	0.524114i
$454$		0			0
$455$	38.3377	+	67.6997i	1.79730	+	3.17381i
$456$		0			0
$457$	−10.7344	−	29.4925i	−0.502133	−	1.37960i	−0.889187	−	0.457543i	$-0.848729\pi$
$457$	−10.7344	−	29.4925i	−0.502133	−	1.37960i	0.387054	−	0.922057i	$-0.373493\pi$
$458$		0			0
$459$	−13.3956	−	1.17196i	−0.625253	−	0.0547025i
$460$		0			0
$461$	14.0487	+	30.1274i	0.654311	+	1.40317i	0.900888	+	0.434051i	$0.142916\pi$
$461$	14.0487	+	30.1274i	0.654311	+	1.40317i	−0.246577	+	0.969123i	$0.579306\pi$
$462$		0			0
$463$	1.29847	−	7.36397i	0.0603448	−	0.342233i	−0.939655	−	0.342123i	$-0.888854\pi$
$463$	1.29847	−	7.36397i	0.0603448	−	0.342233i	1.00000		0.000109481i	$-3.48489e-5\pi$
$464$		0			0
$465$	−2.36483	+	24.6612i	−0.109667	+	1.14364i
$466$		0			0
$467$	−30.2415	−	17.4600i	−1.39941	−	0.807950i	−0.405080	−	0.914281i	$-0.632756\pi$
$467$	−30.2415	−	17.4600i	−1.39941	−	0.807950i	−0.994331	+	0.106331i	$0.966090\pi$
$468$		0			0
$469$	−4.69360	−	26.6187i	−0.216730	−	1.22914i
$470$		0			0
$471$	−12.4233	−	7.17259i	−0.572435	−	0.330496i
$472$		0			0
$473$	4.26124	−	2.46023i	0.195932	−	0.113121i
$474$		0			0
$475$	−3.55848	−	3.67913i	−0.163274	−	0.168810i
$476$		0			0
$477$	41.1243	+	19.1766i	1.88295	+	0.878035i
$478$		0			0
$479$	−12.8203	−	8.97685i	−0.585773	−	0.410163i	0.242773	−	0.970083i	$-0.421943\pi$
$479$	−12.8203	−	8.97685i	−0.585773	−	0.410163i	−0.828547	+	0.559920i	$0.810832\pi$
$480$		0			0
$481$	20.1877	−	35.6757i	0.920481	−	1.62667i
$482$		0			0
$483$	20.9440	−	3.69298i	0.952983	−	0.168037i
$484$		0			0
$485$	−12.9829	−	6.18627i	−0.589523	−	0.280904i
$486$		0			0
$487$			14.5972i			0.661462i	0.943725	+	0.330731i	$0.107295\pi$
$487$			14.5972i			0.661462i	−0.943725	+	0.330731i	$0.892705\pi$
$488$		0			0
$489$	14.4172	+	3.86308i	0.651969	+	0.174695i
$490$		0			0
$491$	3.65464	−	6.33003i	0.164932	−	0.285670i	−0.771699	−	0.635988i	$-0.780593\pi$
$491$	3.65464	−	6.33003i	0.164932	−	0.285670i	0.936631	+	0.350317i	$0.113926\pi$
$492$		0			0
$493$	−6.06389	−	4.24598i	−0.273104	−	0.191230i
$494$		0			0
$495$	−13.1867	−	50.9066i	−0.592697	−	2.28808i
$496$		0			0
$497$	56.0259	+	4.90163i	2.51311	+	0.219868i
$498$		0			0
$499$	22.5900	−	15.8177i	1.01127	−	0.708098i	0.0543698	−	0.998521i	$-0.482685\pi$
$499$	22.5900	−	15.8177i	1.01127	−	0.708098i	0.956898	+	0.290423i	$0.0937961\pi$
$500$		0			0
$501$	32.7831	−	15.2870i	1.46464	−	0.682974i
$502$		0			0
$503$	1.71384	−	1.43809i	0.0764165	−	0.0641211i	−0.603779	−	0.797152i	$-0.706339\pi$
$503$	1.71384	−	1.43809i	0.0764165	−	0.0641211i	0.680196	+	0.733030i	$0.261895\pi$
$504$		0			0
$505$	−23.3236	−	11.1136i	−1.03789	−	0.494547i
$506$		0			0
$507$	−24.2923	+	90.6602i	−1.07886	+	4.02636i
$508$		0			0
$509$	10.0246	+	3.64864i	0.444331	+	0.161723i	0.554489	−	0.832191i	$-0.312914\pi$
$509$	10.0246	+	3.64864i	0.444331	+	0.161723i	−0.110159	+	0.993914i	$0.535136\pi$
$510$		0			0
$511$	37.9413	−	45.2167i	1.67842	−	2.00027i
$512$		0			0
$513$	4.54403	−	5.41537i	0.200624	−	0.239094i
$514$		0			0
$515$	26.9602	−	18.5448i	1.18801	−	0.817184i
$516$		0			0
$517$	−21.9429	+	21.9429i	−0.965048	+	0.965048i
$518$		0			0
$519$		−	31.8900i		−	1.39981i
$520$		0			0
$521$	−24.2375	−	4.27372i	−1.06186	−	0.187235i	−0.384680	−	0.923050i	$-0.625688\pi$
$521$	−24.2375	−	4.27372i	−1.06186	−	0.187235i	−0.677183	+	0.735815i	$0.736799\pi$
$522$		0			0
$523$	26.5353	+	22.2658i	1.16031	+	0.973615i	0.999910	−	0.0134366i	$-0.00427713\pi$
$523$	26.5353	+	22.2658i	1.16031	+	0.973615i	0.160400	+	0.987052i	$0.448722\pi$
$524$		0			0
$525$	−56.4549	−	48.9977i	−2.46390	−	2.13844i
$526$		0			0
$527$	3.14871	+	6.75244i	0.137160	+	0.294141i
$528$		0			0
$529$	10.4883	+	18.1662i	0.456011	+	0.789834i
$530$		0			0
$531$	30.0885	+	14.0305i	1.30573	+	0.608872i
$532$		0			0
$533$	14.0357	+	16.7271i	0.607955	+	0.724532i
$534$		0			0
$535$	−29.1988	−	10.9039i	−1.26237	−	0.471417i
$536$		0			0
$537$	−5.95966	−	1.05085i	−0.257178	−	0.0453475i
$538$		0			0
$539$	−65.7658	+	55.1841i	−2.83273	+	2.37695i
$540$		0			0
$541$	22.1577	−	5.93713i	0.952633	−	0.255257i	0.251154	−	0.967947i	$-0.419190\pi$
$541$	22.1577	−	5.93713i	0.952633	−	0.255257i	0.701479	+	0.712690i	$0.252523\pi$
$542$		0			0
$543$	−25.8917	+	36.9771i	−1.11112	+	1.58684i
$544$		0			0
$545$	0.818833	+	0.481897i	0.0350750	+	0.0206422i
$546$		0			0
$547$	0.861438	+	1.49205i	0.0368324	+	0.0637956i	0.883854	−	0.467763i	$-0.154940\pi$
$547$	0.861438	+	1.49205i	0.0368324	+	0.0637956i	−0.847022	+	0.531559i	$0.821607\pi$
$548$		0			0
$549$	12.1327	+	12.1327i	0.517810	+	0.517810i
$550$		0			0
$551$	3.65704	−	1.33105i	0.155795	−	0.0567047i
$552$		0			0
$553$	7.84633	+	44.4987i	0.333660	+	1.89228i
$554$		0			0
$555$	−6.82674	+	38.7890i	−0.289779	+	1.64650i
$556$		0			0
$557$	−8.10783	−	45.9818i	−0.343540	−	1.94831i	−0.316227	−	0.948683i	$-0.602416\pi$
$557$	−8.10783	−	45.9818i	−0.343540	−	1.94831i	−0.0273122	−	0.999627i	$-0.508695\pi$
$558$		0			0
$559$	7.13449	−	2.59674i	0.301757	−	0.109830i
$560$		0			0
$561$	−17.4127	−	17.4127i	−0.735166	−	0.735166i
$562$		0			0
$563$	2.67024	+	4.62499i	0.112537	+	0.194920i	0.916793	−	0.399364i	$-0.130769\pi$
$563$	2.67024	+	4.62499i	0.112537	+	0.194920i	−0.804255	+	0.594284i	$0.797436\pi$
$564$		0			0
$565$	12.1857	−	3.15653i	0.512654	−	0.132796i
$566$		0			0
$567$	11.3773	−	16.2485i	0.477803	−	0.682374i
$568$		0			0
$569$	18.3105	−	4.90627i	0.767614	−	0.205682i	0.146297	−	0.989241i	$-0.453264\pi$
$569$	18.3105	−	4.90627i	0.767614	−	0.205682i	0.621317	+	0.783559i	$0.286598\pi$
$570$		0			0
$571$	−7.89137	+	6.62164i	−0.330243	+	0.277107i	−0.792799	−	0.609483i	$-0.791377\pi$
$571$	−7.89137	+	6.62164i	−0.330243	+	0.277107i	0.462556	+	0.886590i	$0.346933\pi$
$572$		0			0
$573$	59.8457	+	10.5524i	2.50009	+	0.440833i
$574$		0			0
$575$	−2.54367	+	6.64208i	−0.106078	+	0.276994i
$576$		0			0
$577$	−3.84967	−	4.58785i	−0.160264	−	0.190995i	0.679937	−	0.733271i	$-0.262007\pi$
$577$	−3.84967	−	4.58785i	−0.160264	−	0.190995i	−0.840200	+	0.542276i	$0.817563\pi$
$578$		0			0
$579$	−34.6768	−	16.1700i	−1.44112	−	0.672004i
$580$		0			0
$581$	−21.1414	−	36.6180i	−0.877094	−	1.51917i
$582$		0			0
$583$	15.5532	+	33.3539i	0.644148	+	1.38138i
$584$		0			0
$585$	−6.39814	−	80.8900i	−0.264530	−	3.34439i
$586$		0			0
$587$	−7.92000	−	6.64567i	−0.326893	−	0.274296i	0.464539	−	0.885553i	$-0.346220\pi$
$587$	−7.92000	−	6.64567i	−0.326893	−	0.274296i	−0.791433	+	0.611256i	$0.790664\pi$
$588$		0			0
$589$	−3.85738	−	0.680160i	−0.158941	−	0.0280255i
$590$		0			0
$591$			8.91303i			0.366633i
$592$		0			0
$593$	−17.0508	+	17.0508i	−0.700194	+	0.700194i	−0.964452	−	0.264258i	$-0.914873\pi$
$593$	−17.0508	+	17.0508i	−0.700194	+	0.700194i	0.264258	+	0.964452i	$0.414873\pi$
$594$		0			0
$595$	−22.1058	−	4.08809i	−0.906249	−	0.167595i
$596$		0			0
$597$	−2.31807	+	2.76257i	−0.0948724	+	0.113064i
$598$		0			0
$599$	8.77283	−	10.4551i	0.358448	−	0.427182i	−0.556441	−	0.830887i	$-0.687833\pi$
$599$	8.77283	−	10.4551i	0.358448	−	0.427182i	0.914889	+	0.403705i	$0.132278\pi$
$600$		0			0
$601$	−26.8804	−	9.78367i	−1.09648	−	0.399084i	−0.270459	−	0.962731i	$-0.587176\pi$
$601$	−26.8804	−	9.78367i	−1.09648	−	0.399084i	−0.826016	+	0.563647i	$0.809398\pi$
$602$		0			0
$603$	−7.29616	+	27.2297i	−0.297123	+	1.10888i
$604$		0			0
$605$	7.76600	−	16.2982i	0.315733	−	0.662617i
$606$		0			0
$607$	−21.0154	+	17.6340i	−0.852987	+	0.715741i	−0.960445	−	0.278468i	$-0.910173\pi$
$607$	−21.0154	+	17.6340i	−0.852987	+	0.715741i	0.107458	+	0.994210i	$0.465729\pi$
$608$		0			0
$609$	51.5115	−	24.0202i	2.08735	−	0.973348i
$610$		0			0
$611$	−39.2235	+	27.4646i	−1.58681	+	1.11110i
$612$		0			0
$613$	24.6836	+	2.15954i	0.996962	+	0.0872228i	0.573940	−	0.818897i	$-0.305414\pi$
$613$	24.6836	+	2.15954i	0.996962	+	0.0872228i	0.423021	+	0.906120i	$0.360970\pi$
$614$		0			0
$615$	−18.0812	−	10.6411i	−0.729105	−	0.429090i
$616$		0			0
$617$	7.69288	+	5.38661i	0.309704	+	0.216857i	0.718086	−	0.695954i	$-0.245018\pi$
$617$	7.69288	+	5.38661i	0.309704	+	0.216857i	−0.408383	+	0.912811i	$0.633907\pi$
$618$		0			0
$619$	12.8199	−	22.2047i	0.515276	−	0.892484i	−0.484567	−	0.874754i	$-0.661023\pi$
$619$	12.8199	−	22.2047i	0.515276	−	0.892484i	0.999843	−	0.0177298i	$-0.00564387\pi$
$620$		0			0
$621$	−9.48852	−	2.54244i	−0.380761	−	0.102025i
$622$		0			0
$623$		−	54.5506i		−	2.18553i
$624$		0			0
$625$	23.7643	−	7.76276i	0.950570	−	0.310510i
$626$		0			0
$627$	12.7494	−	2.24806i	0.509162	−	0.0897789i
$628$		0			0
$629$	4.14722	+	11.0947i	0.165360	+	0.442374i
$630$		0			0
$631$	−39.7965	−	27.8658i	−1.58427	−	1.10932i	−0.938226	−	0.346023i	$-0.887532\pi$
$631$	−39.7965	−	27.8658i	−1.58427	−	1.10932i	−0.646048	−	0.763297i	$-0.723579\pi$
$632$		0			0
$633$	16.1939	+	7.55132i	0.643648	+	0.300138i
$634$		0			0
$635$	29.5500	+	0.246276i	1.17266	+	0.00977315i
$636$		0			0
$637$	−114.723	+	66.2351i	−4.54547	+	2.62433i
$638$		0			0
$639$	−50.7970	−	29.3277i	−2.00950	−	1.16018i
$640$		0			0
$641$	−0.0599138	−	0.339788i	−0.00236645	−	0.0134208i	0.983602	−	0.180355i	$-0.0577245\pi$
$641$	−0.0599138	−	0.339788i	−0.00236645	−	0.0134208i	−0.985968	+	0.166934i	$0.946613\pi$
$642$		0			0
$643$	−23.0821	−	13.3265i	−0.910271	−	0.525545i	−0.0297524	−	0.999557i	$-0.509472\pi$
$643$	−23.0821	−	13.3265i	−0.910271	−	0.525545i	−0.880518	+	0.474012i	$0.842805\pi$
$644$		0			0
$645$	−5.62707	+	4.64231i	−0.221566	+	0.182791i
$646$		0			0
$647$	4.46400	−	25.3166i	0.175498	−	0.995299i	−0.762069	−	0.647495i	$-0.775816\pi$
$647$	4.46400	−	25.3166i	0.175498	−	0.995299i	0.937567	−	0.347804i	$-0.113072\pi$
$648$		0			0
$649$	11.3795	+	24.4033i	0.446683	+	0.957915i
$650$		0			0
$651$	−56.9863	−	4.98566i	−2.23347	−	0.195403i
$652$		0			0
$653$	−13.1004	−	35.9929i	−0.512656	−	1.40851i	−0.878458	−	0.477819i	$-0.841427\pi$
$653$	−13.1004	−	35.9929i	−0.512656	−	1.40851i	0.365802	−	0.930693i	$-0.380795\pi$
$654$		0			0
$655$	39.4481	−	22.3391i	1.54136	−	0.872860i
$656$		0			0
$657$	−55.7934	+	26.0169i	−2.17671	+	1.01502i
$658$		0			0
$659$	−6.78289	−	5.69152i	−0.264224	−	0.221710i	0.501045	−	0.865421i	$-0.332949\pi$
$659$	−6.78289	−	5.69152i	−0.264224	−	0.221710i	−0.765268	+	0.643711i	$0.777394\pi$
$660$		0			0
$661$	35.4091	−	3.09790i	1.37726	−	0.120494i	0.625649	−	0.780105i	$-0.284834\pi$
$661$	35.4091	−	3.09790i	1.37726	−	0.120494i	0.751607	+	0.659611i	$0.229279\pi$
$662$		0			0
$663$	−21.7944	−	31.1256i	−0.846425	−	1.20882i
$664$		0			0
$665$	8.42634	−	8.28705i	0.326759	−	0.321358i
$666$		0			0
$667$	−3.82392	−	3.82392i	−0.148063	−	0.148063i
$668$		0			0
$669$	9.18965	−	52.1171i	0.355292	−	2.01496i
$670$		0			0
$671$	1.21287	+	13.8632i	0.0468225	+	0.535184i
$672$		0			0
$673$	−1.52740	+	0.133630i	−0.0588771	+	0.00515108i	−0.116556	−	0.993184i	$-0.537186\pi$
$673$	−1.52740	+	0.133630i	−0.0588771	+	0.00515108i	0.0576791	+	0.998335i	$0.481630\pi$
$674$		0			0
$675$	14.0686	+	31.5320i	0.541502	+	1.21367i
$676$		0			0
$677$	−8.42503	−	2.25748i	−0.323800	−	0.0867620i	0.0932576	−	0.995642i	$-0.470272\pi$
$677$	−8.42503	−	2.25748i	−0.323800	−	0.0867620i	−0.417058	+	0.908880i	$0.636939\pi$
$678$		0			0
$679$	14.0338	−	30.0955i	0.538566	−	1.15496i
$680$		0			0
$681$	5.74777	−	65.6973i	0.220255	−	2.51753i
$682$		0			0
$683$	48.6219	+	17.6969i	1.86046	+	0.677153i	0.978643	+	0.205569i	$0.0659046\pi$
$683$	48.6219	+	17.6969i	1.86046	+	0.677153i	0.881821	+	0.471584i	$0.156318\pi$
$684$		0			0
$685$	0.345018	−	1.86564i	0.0131824	−	0.0712823i
$686$		0			0
$687$	−1.32282	+	15.1199i	−0.0504688	+	0.576861i
$688$		0			0
$689$	14.6974	+	54.8514i	0.559926	+	2.08967i
$690$		0			0
$691$	−12.8230	+	2.26104i	−0.487810	+	0.0860140i	−0.412143	−	0.911119i	$-0.635220\pi$
$691$	−12.8230	+	2.26104i	−0.487810	+	0.0860140i	−0.0756666	+	0.997133i	$0.524108\pi$
$692$		0			0
$693$	117.285	−	31.4266i	4.45531	−	1.19380i
$694$		0			0
$695$	−22.4004	−	6.20271i	−0.849696	−	0.235282i
$696$		0			0
$697$	−6.30942			−0.238986
$698$		0			0
$699$	17.9361	+	49.2790i	0.678405	+	1.86390i
$700$		0			0
$701$	−25.6541	+	36.6378i	−0.968941	+	1.38379i	−0.0459607	+	0.998943i	$0.514635\pi$
$701$	−25.6541	+	36.6378i	−0.968941	+	1.38379i	−0.922980	+	0.384848i	$0.874254\pi$
$702$		0			0
$703$	−6.02844	−	1.55953i	−0.227367	−	0.0588186i
$704$		0			0
$705$	26.7015	−	37.4652i	1.00564	−	1.41102i
$706$		0			0
$707$	25.2115	−	54.0662i	0.948175	−	2.03337i
$708$		0			0
$709$	−27.5998	+	27.5998i	−1.03653	+	1.03653i	−0.0372247	+	0.999307i	$0.511852\pi$
$709$	−27.5998	+	27.5998i	−1.03653	+	1.03653i	−0.999307	+	0.0372247i	$0.988148\pi$
$710$		0			0
$711$	12.1971	−	45.5200i	0.457425	−	1.70714i
$712$		0			0
$713$	1.40870	+	5.25734i	0.0527562	+	0.196889i
$714$		0			0
$715$	38.1955	−	53.5927i	1.42843	−	2.00425i
$716$		0			0
$717$	−2.40495	+	4.16550i	−0.0898145	+	0.155563i
$718$		0			0
$719$	−0.297999	−	0.355141i	−0.0111135	−	0.0132445i	0.760459	−	0.649386i	$-0.224974\pi$
$719$	−0.297999	−	0.355141i	−0.0111135	−	0.0132445i	−0.771573	+	0.636141i	$0.780530\pi$
$720$		0			0
$721$	43.3374	+	61.8922i	1.61397	+	2.30498i
$722$		0			0
$723$	12.9135	−	35.4795i	0.480257	−	1.31950i
$724$		0			0
$725$	−1.97206	+	18.9057i	−0.0732405	+	0.702140i
$726$		0			0
$727$	−8.81459	+	3.20825i	−0.326915	+	0.118987i	−0.500264	−	0.865873i	$-0.666764\pi$
$727$	−8.81459	+	3.20825i	−0.326915	+	0.118987i	0.173348	+	0.984861i	$0.444541\pi$
$728$		0			0
$729$	34.0359	−	19.6506i	1.26059	−	0.727801i
$730$		0			0
$731$	−0.750327	+	2.06151i	−0.0277519	+	0.0762476i
$732$		0			0
$733$	−2.96696	−	33.9125i	−0.109587	−	1.25259i	−0.829494	−	0.558515i	$-0.811371\pi$
$733$	−2.96696	−	33.9125i	−0.109587	−	1.25259i	0.719907	−	0.694070i	$-0.244184\pi$
$734$		0			0
$735$	82.6233	−	96.8164i	3.04761	−	3.57113i
$736$		0			0
$737$	−18.7289	+	13.1141i	−0.689887	+	0.483064i
$738$		0			0
$739$	−12.5174			−0.460460			−0.230230	−	0.973136i	$-0.573948\pi$
$739$	−12.5174			−0.460460			−0.230230	+	0.973136i	$0.573948\pi$
$740$		0			0
$741$	19.9761			0.733839
$742$		0			0
$743$	24.3964	−	17.0825i	0.895017	−	0.626698i	−0.0329105	−	0.999458i	$-0.510478\pi$
$743$	24.3964	−	17.0825i	0.895017	−	0.626698i	0.927928	+	0.372761i	$0.121589\pi$
$744$		0			0
$745$	1.61022	+	20.3576i	0.0589938	+	0.745843i
$746$		0			0
$747$	3.84347	+	43.9310i	0.140625	+	1.60735i
$748$		0			0
$749$	24.6144	−	67.6274i	0.899389	−	2.47105i
$750$		0			0
$751$	19.1433	−	11.0524i	0.698549	−	0.403308i	−0.108257	−	0.994123i	$-0.534527\pi$
$751$	19.1433	−	11.0524i	0.698549	−	0.403308i	0.806807	+	0.590815i	$0.201194\pi$
$752$		0			0
$753$	−42.6114	+	15.5093i	−1.55285	+	0.565190i
$754$		0			0
$755$	−20.2897	−	1.94564i	−0.738420	−	0.0708091i
$756$		0			0
$757$	7.18179	−	19.7318i	0.261027	−	0.717165i	−0.738072	−	0.674722i	$-0.764264\pi$
$757$	7.18179	−	19.7318i	0.261027	−	0.717165i	0.999099	−	0.0424432i	$-0.0135141\pi$
$758$		0			0
$759$	−10.3183	−	14.7361i	−0.374532	−	0.534887i
$760$		0			0
$761$	25.6949	+	30.6220i	0.931439	+	1.11005i	0.993710	+	0.111987i	$0.0357213\pi$
$761$	25.6949	+	30.6220i	0.931439	+	1.11005i	−0.0622707	+	0.998059i	$0.519834\pi$
$762$		0			0
$763$	−1.09690	+	1.89989i	−0.0397106	+	0.0687807i
$764$		0			0
$765$	19.0932	+	13.6077i	0.690316	+	0.491989i
$766$		0			0
$767$	10.7533	+	40.1319i	0.388279	+	1.44908i
$768$		0			0
$769$	−6.20014	+	23.1392i	−0.223583	+	0.834422i	0.759385	+	0.650642i	$0.225500\pi$
$769$	−6.20014	+	23.1392i	−0.223583	+	0.834422i	−0.982967	+	0.183780i	$0.941167\pi$
$770$		0			0
$771$	−12.1936	+	12.1936i	−0.439141	+	0.439141i
$772$		0			0
$773$	−23.3342	+	50.0404i	−0.839274	+	1.79983i	−0.312180	+	0.950023i	$0.601059\pi$
$773$	−23.3342	+	50.0404i	−0.839274	+	1.79983i	−0.527095	+	0.849807i	$0.676719\pi$
$774$		0			0
$775$	11.2328	−	15.4862i	0.403495	−	0.556282i
$776$		0			0
$777$	−89.6921	−	15.0160i	−3.21769	−	0.538695i
$778$		0			0
$779$	1.90255	−	2.71713i	0.0681660	−	0.0973512i
$780$		0			0
$781$	−16.2708	−	44.7036i	−0.582214	−	1.59962i
$782$		0			0
$783$	−26.2528			−0.938199
$784$		0			0
$785$	5.45864	+	9.63928i	0.194827	+	0.344041i
$786$		0			0
$787$	37.8525	−	10.1426i	1.34930	−	0.361543i	0.489422	−	0.872047i	$-0.337208\pi$
$787$	37.8525	−	10.1426i	1.34930	−	0.361543i	0.859875	+	0.510504i	$0.170541\pi$
$788$		0			0
$789$	−16.2197	+	2.85997i	−0.577437	+	0.101818i
$790$		0			0
$791$	7.52266	+	28.0749i	0.267475	+	0.998230i
$792$		0			0
$793$	−1.87149	+	21.3913i	−0.0664587	+	0.759626i
$794$		0			0
$795$	−30.9214	−	44.9531i	−1.09667	−	1.59432i
$796$		0			0
$797$	−6.22261	−	2.26485i	−0.220416	−	0.0802249i	0.229452	−	0.973320i	$-0.426307\pi$
$797$	−6.22261	−	2.26485i	−0.220416	−	0.0802249i	−0.449868	+	0.893095i	$0.648529\pi$
$798$		0			0
$799$	1.20587	−	13.7831i	0.0426605	−	0.487612i
$800$		0			0
$801$	−24.0442	+	51.5630i	−0.849561	+	1.82189i
$802$		0			0
$803$	−48.2281	−	12.9227i	−1.70193	−	0.456031i
$804$		0			0
$805$	−15.3850	−	5.74532i	−0.542249	−	0.202496i
$806$		0			0
$807$	−31.0911	+	2.72012i	−1.09446	+	0.0957527i
$808$		0			0
$809$	0.109239	+	1.24861i	0.00384063	+	0.0438987i	0.997873	−	0.0651853i	$-0.0207638\pi$
$809$	0.109239	+	1.24861i	0.00384063	+	0.0438987i	−0.994033	+	0.109084i	$0.965208\pi$
$810$		0			0
$811$	−1.65611	+	9.39227i	−0.0581539	+	0.329807i	−0.999980	−	0.00629291i	$-0.997997\pi$
$811$	−1.65611	+	9.39227i	−0.0581539	+	0.329807i	0.941826	+	0.336100i	$0.109108\pi$
$812$		0			0
$813$	−0.798028	−	0.798028i	−0.0279881	−	0.0279881i
$814$		0			0
$815$	−8.08186	−	8.21770i	−0.283095	−	0.287853i
$816$		0			0
$817$	−0.661526	−	0.944756i	−0.0231439	−	0.0330528i
$818$		0			0
$819$	186.645	−	16.3293i	6.52191	−	0.570593i
$820$		0			0
$821$	18.7612	+	15.7425i	0.654770	+	0.549417i	0.908514	−	0.417854i	$-0.137218\pi$
$821$	18.7612	+	15.7425i	0.654770	+	0.549417i	−0.253744	+	0.967271i	$0.581662\pi$
$822$		0			0
$823$	−26.9006	+	12.5440i	−0.937697	+	0.437255i	−0.830523	−	0.556985i	$-0.811958\pi$
$823$	−26.9006	+	12.5440i	−0.937697	+	0.437255i	−0.107174	+	0.994240i	$0.534180\pi$
$824$		0			0
$825$	−17.3814	+	60.7962i	−0.605142	+	2.11665i
$826$		0			0
$827$	8.84460	+	24.3003i	0.307557	+	0.845005i	0.993132	+	0.117003i	$0.0373287\pi$
$827$	8.84460	+	24.3003i	0.307557	+	0.845005i	−0.685575	+	0.728002i	$0.740449\pi$
$828$		0			0
$829$	30.3917	+	2.65893i	1.05555	+	0.0923485i	0.601693	−	0.798727i	$-0.294493\pi$
$829$	30.3917	+	2.65893i	1.05555	+	0.0923485i	0.453855	+	0.891076i	$0.350048\pi$
$830$		0			0
$831$	−11.7687	−	25.2381i	−0.408252	−	0.875499i
$832$		0			0
$833$	6.64677	−	37.6957i	0.230297	−	1.30608i
$834$		0			0
$835$	−27.8051	−	2.66631i	−0.962237	−	0.0922716i
$836$		0			0
$837$	22.8825	+	13.2112i	0.790936	+	0.456647i
$838$		0			0
$839$	−7.98295	−	45.2735i	−0.275602	−	1.56302i	−0.737043	−	0.675845i	$-0.763779\pi$
$839$	−7.98295	−	45.2735i	−0.275602	−	1.56302i	0.461441	−	0.887171i	$-0.347332\pi$
$840$		0			0
$841$	12.5984	+	7.27371i	0.434429	+	0.250818i
$842$		0			0
$843$	56.7054	−	32.7389i	1.95304	−	1.12759i
$844$		0			0
$845$	51.6756	−	50.8213i	1.77769	−	1.74831i
$846$		0			0
$847$	37.7807	+	17.6174i	1.29816	+	0.605342i
$848$		0			0
$849$	−49.6901	−	34.7934i	−1.70536	−	1.19411i
$850$		0			0
$851$	1.57622	+	8.50794i	0.0540320	+	0.291648i
$852$		0			0
$853$	−35.0978	+	6.18869i	−1.20173	+	0.211897i	−0.738444	−	0.674315i	$-0.764439\pi$
$853$	−35.0978	+	6.18869i	−1.20173	+	0.211897i	−0.463281	+	0.886211i	$0.653328\pi$
$854$		0			0
$855$	−11.6175	+	4.11911i	−0.397311	+	0.140871i
$856$		0			0
$857$		−	37.1902i		−	1.27039i	−0.772350	−	0.635197i	$-0.780919\pi$
$857$		−	37.1902i		−	1.27039i	0.772350	−	0.635197i	$-0.219081\pi$
$858$		0			0
$859$	44.4090	+	11.8993i	1.51521	+	0.406000i	0.918163	−	0.396203i	$-0.129672\pi$
$859$	44.4090	+	11.8993i	1.51521	+	0.406000i	0.597051	+	0.802203i	$0.296339\pi$
$860$		0			0
$861$	24.2215	−	41.9528i	0.825466	−	1.42975i
$862$		0			0
$863$	−43.5642	−	30.5040i	−1.48294	−	1.03837i	−0.985271	−	0.171003i	$-0.945299\pi$
$863$	−43.5642	−	30.5040i	−1.48294	−	1.03837i	−0.497672	−	0.867365i	$-0.665812\pi$
$864$		0			0
$865$	−12.4903	+	21.2233i	−0.424681	+	0.721613i
$866$		0			0
$867$	−38.1013	−	3.33343i	−1.29399	−	0.113209i
$868$		0			0
$869$	31.3092	−	21.9230i	1.06209	−	0.743685i
$870$		0			0
$871$	−31.9739	+	14.9097i	−1.08339	+	0.505194i
$872$		0			0
$873$	−26.5303	+	22.2616i	−0.897915	+	0.753440i
$874$		0			0
$875$	18.3809	+	54.7204i	0.621387	+	1.84989i
$876$		0			0
$877$	−7.35570	+	27.4518i	−0.248384	+	0.926983i	0.723268	+	0.690568i	$0.242639\pi$
$877$	−7.35570	+	27.4518i	−0.248384	+	0.926983i	−0.971652	+	0.236415i	$0.924027\pi$
$878$		0			0
$879$	−71.0797	−	25.8709i	−2.39746	−	0.872604i
$880$		0			0
$881$	−7.61409	+	9.07412i	−0.256525	+	0.305715i	−0.878901	−	0.477003i	$-0.841723\pi$
$881$	−7.61409	+	9.07412i	−0.256525	+	0.305715i	0.622376	+	0.782718i	$0.286167\pi$
$882$		0			0
$883$	−28.4702	+	33.9295i	−0.958099	+	1.14182i	0.0317211	+	0.999497i	$0.489901\pi$
$883$	−28.4702	+	33.9295i	−0.958099	+	1.14182i	−0.989820	+	0.142322i	$0.954543\pi$
$884$		0			0
$885$	−22.6236	−	32.8898i	−0.760483	−	1.10558i
$886$		0			0
$887$	7.55475	−	7.55475i	0.253664	−	0.253664i	−0.568807	−	0.822471i	$-0.692595\pi$
$887$	7.55475	−	7.55475i	0.253664	−	0.253664i	0.822471	+	0.568807i	$0.192595\pi$
$888$		0			0
$889$			68.2333i			2.28847i
$890$		0			0
$891$	−16.5239	−	2.91361i	−0.553571	−	0.0976096i
$892$		0			0
$893$	5.57203	+	4.67549i	0.186461	+	0.156459i
$894$		0			0
$895$	3.55467	+	3.03356i	0.118820	+	0.101401i
$896$		0			0
$897$	−11.7311	−	25.1574i	−0.391690	−	0.839983i
$898$		0			0
$899$	7.27299	+	12.5972i	0.242568	+	0.420140i
$900$		0			0
$901$	−14.8710	−	6.93448i	−0.495426	−	0.231021i
$902$		0			0
$903$	−10.8270	−	12.9031i	−0.360300	−	0.429389i
$904$		0			0
$905$	31.7141	−	14.4680i	1.05421	−	0.480932i
$906$		0			0
$907$	40.6151	+	7.16154i	1.34860	+	0.237795i	0.800860	−	0.598852i	$-0.204376\pi$
$907$	40.6151	+	7.16154i	1.34860	+	0.237795i	0.547742	+	0.836647i	$0.315487\pi$
$908$		0			0
$909$	−47.6614	+	39.9927i	−1.58083	+	1.32647i
$910$		0			0
$911$	3.06802	−	0.822074i	0.101648	−	0.0272365i	−0.207637	−	0.978206i	$-0.566577\pi$
$911$	3.06802	−	0.822074i	0.101648	−	0.0272365i	0.309285	+	0.950970i	$0.399910\pi$
$912$		0			0
$913$	−20.5148	+	29.2982i	−0.678940	+	0.969627i
$914$		0			0
$915$	−5.17357	−	19.9723i	−0.171033	−	0.660266i
$916$		0			0
$917$	52.3383	+	90.6525i	1.72836	+	2.99361i
$918$		0			0
$919$	34.8838	+	34.8838i	1.15071	+	1.15071i	0.986411	+	0.164299i	$0.0525361\pi$
$919$	34.8838	+	34.8838i	1.15071	+	1.15071i	0.164299	+	0.986411i	$0.447464\pi$
$920$		0			0
$921$	−35.9175	+	13.0729i	−1.18352	+	0.430767i
$922$		0			0
$923$	−12.7467	−	72.2903i	−0.419564	−	2.37946i
$924$		0			0
$925$	19.7357	−	23.1409i	0.648906	−	0.760869i
$926$		0			0
$927$	−13.6837	−	77.6042i	−0.449432	−	2.54886i
$928$		0			0
$929$	4.78619	−	1.74203i	0.157030	−	0.0571541i	−0.262309	−	0.964984i	$-0.584484\pi$
$929$	4.78619	−	1.74203i	0.157030	−	0.0571541i	0.419339	+	0.907830i	$0.362262\pi$
$930$		0			0
$931$	14.2292	+	14.2292i	0.466344	+	0.466344i
$932$		0			0
$933$	−4.58799	−	7.94663i	−0.150204	−	0.260161i
$934$		0			0
$935$	4.76846	+	18.4084i	0.155945	+	0.602021i
$936$		0			0
$937$	−14.1193	+	20.1644i	−0.461257	+	0.658743i	−0.980645	−	0.195795i	$-0.937271\pi$
$937$	−14.1193	+	20.1644i	−0.461257	+	0.658743i	0.519388	+	0.854539i	$0.326160\pi$
$938$		0			0
$939$	9.63630	−	2.58204i	0.314469	−	0.0842617i
$940$		0			0
$941$	−30.2787	+	25.4069i	−0.987058	+	0.828240i	−0.985139	−	0.171758i	$-0.945055\pi$
$941$	−30.2787	+	25.4069i	−0.987058	+	0.828240i	−0.00191913	+	0.999998i	$0.500611\pi$
$942$		0			0
$943$	−4.53918	−	0.800381i	−0.147816	−	0.0260640i
$944$		0			0
$945$	−72.5341	+	33.0901i	−2.35953	+	1.07642i
$946$		0			0
$947$	2.60506	+	3.10459i	0.0846531	+	0.100886i	0.806708	−	0.590950i	$-0.201247\pi$
$947$	2.60506	+	3.10459i	0.0846531	+	0.100886i	−0.722055	+	0.691835i	$0.756802\pi$
$948$		0			0
$949$	−69.8239	−	32.5594i	−2.26658	−	1.05692i
$950$		0			0
$951$	33.2104	+	57.5222i	1.07692	+	1.86528i
$952$		0			0
$953$	−21.6701	−	46.4718i	−0.701965	−	1.50537i	−0.855820	−	0.517274i	$-0.826947\pi$
$953$	−21.6701	−	46.4718i	−0.701965	−	1.50537i	0.153855	−	0.988093i	$-0.450831\pi$
$954$		0			0
$955$	−35.6953	−	30.4624i	−1.15507	−	0.985740i
$956$		0			0
$957$	−36.8293	−	30.9035i	−1.19052	−	0.998968i
$958$		0			0
$959$	4.31424	+	0.760717i	0.139314	+	0.0245648i
$960$		0			0
$961$			16.3600i			0.527742i
$962$		0			0
$963$	−53.0743	+	53.0743i	−1.71030	+	1.71030i
$964$		0			0
$965$	16.7447	+	24.3432i	0.539030	+	0.783635i
$966$		0			0
$967$	4.32001	−	5.14839i	0.138922	−	0.165561i	−0.692098	−	0.721804i	$-0.743313\pi$
$967$	4.32001	−	5.14839i	0.138922	−	0.165561i	0.831020	+	0.556243i	$0.187758\pi$
$968$		0			0
$969$	−3.71022	+	4.42167i	−0.119189	+	0.142044i
$970$		0			0
$971$	27.1382	+	9.87748i	0.870905	+	0.316984i	0.738534	−	0.674217i	$-0.235519\pi$
$971$	27.1382	+	9.87748i	0.870905	+	0.316984i	0.132372	+	0.991200i	$0.457741\pi$
$972$		0			0
$973$	13.8905	−	51.8401i	0.445309	−	1.66192i
$974$		0			0
$975$	−42.7023	+	87.7275i	−1.36757	+	2.80953i
$976$		0			0
$977$	−2.27478	+	1.90877i	−0.0727766	+	0.0610669i	−0.678450	−	0.734646i	$-0.737348\pi$
$977$	−2.27478	+	1.90877i	−0.0727766	+	0.0610669i	0.605674	+	0.795713i	$0.292904\pi$
$978$		0			0
$979$	−41.8203	+	19.5011i	−1.33658	+	0.623259i
$980$		0			0
$981$	1.87424	−	1.31236i	0.0598399	−	0.0419004i
$982$		0			0
$983$	10.4389	+	0.913283i	0.332948	+	0.0291292i	0.252404	−	0.967622i	$-0.418779\pi$
$983$	10.4389	+	0.913283i	0.332948	+	0.0291292i	0.0805440	+	0.996751i	$0.474334\pi$
$984$		0			0
$985$	3.49094	−	5.93177i	0.111231	−	0.189002i
$986$		0			0
$987$	87.0180	+	60.9307i	2.76981	+	1.93945i
$988$		0			0
$989$	−0.801320	+	1.38793i	−0.0254805	+	0.0441335i
$990$		0			0
$991$	−43.4130	−	11.6325i	−1.37906	−	0.369518i	−0.508280	−	0.861192i	$-0.669718\pi$
$991$	−43.4130	−	11.6325i	−1.37906	−	0.369518i	−0.870779	+	0.491674i	$0.836385\pi$
$992$		0			0
$993$			56.2709i			1.78570i
$994$		0			0
$995$	2.62472	−	0.930623i	0.0832093	−	0.0295027i
$996$		0			0
$997$	−52.5902	+	9.27307i	−1.66555	+	0.293681i	−0.925465	−	0.378834i	$-0.876325\pi$
$997$	−52.5902	+	9.27307i	−1.66555	+	0.293681i	−0.740083	+	0.672515i	$0.765214\pi$
$998$		0			0
$999$	34.6159	+	23.7946i	1.09520	+	0.752827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.cc.a.17.3	✓	228
5.3	odd	4		740.2.ch.a.313.3	yes	228
37.24	odd	36		740.2.ch.a.357.3	yes	228
185.98	even	36	inner	740.2.cc.a.653.3	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.cc.a.17.3	✓	228	1.1	even	1	trivial
740.2.cc.a.653.3	yes	228	185.98	even	36	inner
740.2.ch.a.313.3	yes	228	5.3	odd	4
740.2.ch.a.357.3	yes	228	37.24	odd	36

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.cc (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37198 + 1.66088i) q^{3} +(2.22911 - 0.176315i) q^{5} +(0.449992 + 5.14343i) q^{7} +(1.84172 - 5.06008i) q^{9} +(3.78226 - 2.18369i) q^{11} +(6.33254 - 2.30486i) q^{13} +(-4.99456 + 4.12049i) q^{15} +(-0.665988 + 1.82979i) q^{17} +(-0.587167 - 0.838562i) q^{19} +(-9.61000 - 11.4527i) q^{21} +(-0.711249 + 1.23192i) q^{23} +(4.93783 - 0.786050i) q^{25} +(1.78731 + 6.67032i) q^{27} +(-0.983941 + 3.67212i) q^{29} +(2.70555 - 2.70555i) q^{31} +(-5.34460 + 11.4615i) q^{33} +(1.90994 + 11.3859i) q^{35} +(4.62565 - 3.95010i) q^{37} +(-11.1926 + 15.9847i) q^{39} +(1.10822 + 3.04481i) q^{41} +1.12664 q^{43} +(3.21322 - 11.6042i) q^{45} +(-6.86330 + 1.83901i) q^{47} +(-19.3588 + 3.41347i) q^{49} +(-1.45934 - 5.44635i) q^{51} +(-0.734425 + 8.39451i) q^{53} +(8.04603 - 5.53454i) q^{55} +(2.78550 + 1.01384i) q^{57} +(-0.537340 + 6.14183i) q^{59} +(-1.34663 + 2.88786i) q^{61} +(26.8549 + 7.19576i) q^{63} +(13.7095 - 6.25430i) q^{65} +(-5.21520 + 0.456271i) q^{67} +(-0.359000 - 4.10339i) q^{69} +(1.89150 - 10.7272i) q^{71} +(-8.08390 - 8.08390i) q^{73} +(-10.4069 + 10.0656i) q^{75} +(12.9336 + 18.4711i) q^{77} +(8.71830 - 0.762752i) q^{79} +(-2.94303 - 2.46950i) q^{81} +(-7.42217 + 3.46102i) q^{83} +(-1.16194 + 4.19621i) q^{85} +(-3.76506 - 10.3444i) q^{87} +(-10.5253 - 0.920846i) q^{89} +(14.7045 + 31.5338i) q^{91} +(-1.92392 + 10.9111i) q^{93} +(-1.45671 - 1.76572i) q^{95} +(-5.56990 - 3.21578i) q^{97} +(-4.08378 - 23.1602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) \) 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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