LMFDB - Embedded newform 116.2.g.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(25,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("116.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	116.g (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} + 12 x^{10} - 16 x^{9} + 22 x^{8} + 28 x^{7} + 71 x^{6} + 154 x^{5} + 442 x^{4} + \cdots + 841 $ x^12 - 5x^11 + 12x^10 - 16x^9 + 22x^8 + 28x^7 + 71x^6 + 154x^5 + 442x^4 + 555x^3 + 1573x^2 + 1363*x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.1
Root			$2.94643 - 1.41893i$ of defining polynomial
Character	$\chi$	$=$	116.25
Dual form			116.2.g.b.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.04546 + 0.985042i) q^{3} +(-0.299629 + 1.31276i) q^{5} +(-3.84740 + 1.85281i) q^{7} +(1.34313 - 1.68423i) q^{9} +(1.30367 + 1.63475i) q^{11} +(0.703677 + 0.882383i) q^{13} +(-0.680245 - 2.98035i) q^{15} -1.88433 q^{17} +(4.62603 + 2.22778i) q^{19} +(6.04461 - 7.57970i) q^{21} +(-1.77825 - 7.79102i) q^{23} +(2.87128 + 1.38274i) q^{25} +(0.427279 - 1.87203i) q^{27} +(5.38428 + 0.0974899i) q^{29} +(-2.33321 + 10.2224i) q^{31} +(-4.27690 - 2.05965i) q^{33} +(-1.27950 - 5.60587i) q^{35} +(-3.28770 + 4.12265i) q^{37} +(-2.30853 - 1.11173i) q^{39} -8.84415 q^{41} +(1.02523 + 4.49182i) q^{43} +(1.80856 + 2.26786i) q^{45} +(4.31634 + 5.41252i) q^{47} +(7.00514 - 8.78417i) q^{49} +(3.85432 - 1.85614i) q^{51} +(-0.592990 + 2.59806i) q^{53} +(-2.53665 + 1.22159i) q^{55} -11.6568 q^{57} +5.29544 q^{59} +(-4.27483 + 2.05865i) q^{61} +(-2.04700 + 8.96849i) q^{63} +(-1.36920 + 0.659372i) q^{65} +(1.32608 - 1.66285i) q^{67} +(11.3118 + 14.1846i) q^{69} +(-10.2916 - 12.9052i) q^{71} +(1.28570 + 5.63301i) q^{73} -7.23514 q^{75} +(-8.04461 - 3.87408i) q^{77} +(7.06600 - 8.86048i) q^{79} +(2.40812 + 10.5507i) q^{81} +(11.6640 + 5.61710i) q^{83} +(0.564599 - 2.47367i) q^{85} +(-11.1094 + 5.10433i) q^{87} +(1.21866 - 5.33931i) q^{89} +(-4.34221 - 2.09110i) q^{91} +(-5.29706 - 23.2079i) q^{93} +(-4.31063 + 5.40536i) q^{95} +(2.98370 + 1.43688i) q^{97} +4.50430 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9} + 3 q^{11} - 21 q^{13} + 29 q^{15} - 10 q^{17} + 17 q^{19} + 3 q^{21} - 19 q^{23} - 3 q^{25} + 9 q^{27} - 5 q^{29} - 27 q^{31} - 47 q^{33} + 27 q^{35} - 3 q^{37}+ \cdots - 16 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9 + 3 * q^11 - 21 * q^13 + 29 * q^15 - 10 * q^17 + 17 * q^19 + 3 * q^21 - 19 * q^23 - 3 * q^25 + 9 * q^27 - 5 * q^29 - 27 * q^31 - 47 * q^33 + 27 * q^35 - 3 * q^37 - 37 * q^39 - 2 * q^41 - 9 * q^43 + 22 * q^45 + 19 * q^47 + 17 * q^49 + 2 * q^51 + 22 * q^53 + 49 * q^55 + 30 * q^57 + 36 * q^59 - 33 * q^61 + 9 * q^63 + 38 * q^65 - 3 * q^67 + 47 * q^69 - 35 * q^71 + 34 * q^73 - 44 * q^75 - 27 * q^77 - 19 * q^79 - 39 * q^81 - q^83 - 34 * q^85 - 25 * q^87 - 11 * q^89 - 23 * q^91 + 7 * q^93 - 105 * q^95 + 38 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$1$	$e\left(\frac{4}{7}\right)$

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			0
$2$		0			0
$3$	−2.04546	+	0.985042i	−1.18095	+	0.568714i	−0.918187	−	0.396147i	$-0.870347\pi$
$3$	−2.04546	+	0.985042i	−1.18095	+	0.568714i	−0.262760	+	0.964861i	$0.584633\pi$
$4$		0			0
$5$	−0.299629	+	1.31276i	−0.133998	+	0.587085i	0.862688	+	0.505737i	$0.168780\pi$
$5$	−0.299629	+	1.31276i	−0.133998	+	0.587085i	−0.996686	+	0.0813475i	$0.974078\pi$
$6$		0			0
$7$	−3.84740	+	1.85281i	−1.45418	+	0.700296i	−0.983315	−	0.181909i	$-0.941772\pi$
$7$	−3.84740	+	1.85281i	−1.45418	+	0.700296i	−0.470865	+	0.882205i	$0.656058\pi$
$8$		0			0
$9$	1.34313	−	1.68423i	0.447711	−	0.561411i
$10$		0			0
$11$	1.30367	+	1.63475i	0.393071	+	0.492895i	0.938508	−	0.345256i	$-0.112208\pi$
$11$	1.30367	+	1.63475i	0.393071	+	0.492895i	−0.545438	+	0.838151i	$0.683637\pi$
$12$		0			0
$13$	0.703677	+	0.882383i	0.195165	+	0.244729i	0.869779	−	0.493442i	$-0.164261\pi$
$13$	0.703677	+	0.882383i	0.195165	+	0.244729i	−0.674614	+	0.738171i	$0.735690\pi$
$14$		0			0
$15$	−0.680245	−	2.98035i	−0.175639	−	0.769523i
$16$		0			0
$17$	−1.88433			−0.457016			−0.228508	−	0.973542i	$-0.573385\pi$
$17$	−1.88433			−0.457016			−0.228508	+	0.973542i	$0.573385\pi$
$18$		0			0
$19$	4.62603	+	2.22778i	1.06128	+	0.511087i	0.881288	−	0.472580i	$-0.156677\pi$
$19$	4.62603	+	2.22778i	1.06128	+	0.511087i	0.179996	+	0.983667i	$0.442392\pi$
$20$		0			0
$21$	6.04461	−	7.57970i	1.31904	−	1.65403i
$22$		0			0
$23$	−1.77825	−	7.79102i	−0.370791	−	1.62454i	−0.724563	−	0.689208i	$-0.757959\pi$
$23$	−1.77825	−	7.79102i	−0.370791	−	1.62454i	0.353773	−	0.935331i	$-0.384899\pi$
$24$		0			0
$25$	2.87128	+	1.38274i	0.574256	+	0.276547i
$26$		0			0
$27$	0.427279	−	1.87203i	0.0822298	−	0.360272i
$28$		0			0
$29$	5.38428	+	0.0974899i	0.999836	+	0.0181034i
$29$	5.38428	+	0.0974899i	0.999836	+	0.0181034i
$30$		0			0
$31$	−2.33321	+	10.2224i	−0.419056	+	1.83601i	0.118732	+	0.992926i	$0.462117\pi$
$31$	−2.33321	+	10.2224i	−0.419056	+	1.83601i	−0.537789	+	0.843080i	$0.680740\pi$
$32$		0			0
$33$	−4.27690	−	2.05965i	−0.744512	−	0.358538i
$34$		0			0
$35$	−1.27950	−	5.60587i	−0.216276	−	0.947565i
$36$		0			0
$37$	−3.28770	+	4.12265i	−0.540495	+	0.677759i	−0.974819	−	0.222997i	$-0.928416\pi$
$37$	−3.28770	+	4.12265i	−0.540495	+	0.677759i	0.434324	+	0.900757i	$0.356987\pi$
$38$		0			0
$39$	−2.30853	−	1.11173i	−0.369660	−	0.178019i
$40$		0			0
$41$	−8.84415			−1.38122			−0.690612	−	0.723225i	$-0.742659\pi$
$41$	−8.84415			−1.38122			−0.690612	+	0.723225i	$0.742659\pi$
$42$		0			0
$43$	1.02523	+	4.49182i	0.156346	+	0.684996i	0.990960	+	0.134161i	$0.0428338\pi$
$43$	1.02523	+	4.49182i	0.156346	+	0.684996i	−0.834614	+	0.550836i	$0.814309\pi$
$44$		0			0
$45$	1.80856	+	2.26786i	0.269604	+	0.338072i
$46$		0			0
$47$	4.31634	+	5.41252i	0.629603	+	0.789497i	0.989660	−	0.143433i	$-0.0458143\pi$
$47$	4.31634	+	5.41252i	0.629603	+	0.789497i	−0.360057	+	0.932930i	$0.617243\pi$
$48$		0			0
$49$	7.00514	−	8.78417i	1.00073	−	1.25488i
$50$		0			0
$51$	3.85432	−	1.85614i	0.539712	−	0.259912i
$52$		0			0
$53$	−0.592990	+	2.59806i	−0.0814535	+	0.356871i	−0.999187	−	0.0403267i	$-0.987160\pi$
$53$	−0.592990	+	2.59806i	−0.0814535	+	0.356871i	0.917733	+	0.397198i	$0.130017\pi$
$54$		0			0
$55$	−2.53665	+	1.22159i	−0.342042	+	0.164719i
$56$		0			0
$57$	−11.6568			−1.54398
$58$		0			0
$59$	5.29544			0.689408			0.344704	−	0.938711i	$-0.387979\pi$
$59$	5.29544			0.689408			0.344704	+	0.938711i	$0.387979\pi$
$60$		0			0
$61$	−4.27483	+	2.05865i	−0.547336	+	0.263583i	−0.687052	−	0.726609i	$-0.741095\pi$
$61$	−4.27483	+	2.05865i	−0.547336	+	0.263583i	0.139716	+	0.990192i	$0.455381\pi$
$62$		0			0
$63$	−2.04700	+	8.96849i	−0.257898	+	1.12992i
$64$		0			0
$65$	−1.36920	+	0.659372i	−0.169828	+	0.0817850i
$66$		0			0
$67$	1.32608	−	1.66285i	0.162006	−	0.203150i	−0.694202	−	0.719780i	$-0.744243\pi$
$67$	1.32608	−	1.66285i	0.162006	−	0.203150i	0.856208	+	0.516631i	$0.172814\pi$
$68$		0			0
$69$	11.3118	+	14.1846i	1.36178	+	1.70762i
$70$		0			0
$71$	−10.2916	−	12.9052i	−1.22139	−	1.53157i	−0.768280	−	0.640114i	$-0.778887\pi$
$71$	−10.2916	−	12.9052i	−1.22139	−	1.53157i	−0.453107	−	0.891456i	$-0.649684\pi$
$72$		0			0
$73$	1.28570	+	5.63301i	0.150479	+	0.659294i	0.992746	+	0.120232i	$0.0383639\pi$
$73$	1.28570	+	5.63301i	0.150479	+	0.659294i	−0.842266	+	0.539062i	$0.818779\pi$
$74$		0			0
$75$	−7.23514			−0.835442
$76$		0			0
$77$	−8.04461	−	3.87408i	−0.916768	−	0.441492i
$78$		0			0
$79$	7.06600	−	8.86048i	0.794987	−	0.996882i	−0.204850	−	0.978793i	$-0.565671\pi$
$79$	7.06600	−	8.86048i	0.794987	−	0.996882i	0.999836	−	0.0180884i	$-0.00575803\pi$
$80$		0			0
$81$	2.40812	+	10.5507i	0.267569	+	1.17230i
$82$		0			0
$83$	11.6640	+	5.61710i	1.28029	+	0.616557i	0.945465	−	0.325723i	$-0.105608\pi$
$83$	11.6640	+	5.61710i	1.28029	+	0.616557i	0.334828	+	0.942279i	$0.391322\pi$
$84$		0			0
$85$	0.564599	−	2.47367i	0.0612394	−	0.268307i
$86$		0			0
$87$	−11.1094	+	5.10433i	−1.19105	+	0.547242i
$88$		0			0
$89$	1.21866	−	5.33931i	0.129178	−	0.565966i	−0.868366	−	0.495924i	$-0.834830\pi$
$89$	1.21866	−	5.33931i	0.129178	−	0.565966i	0.997544	−	0.0700419i	$-0.0223133\pi$
$90$		0			0
$91$	−4.34221	−	2.09110i	−0.455187	−	0.219207i
$92$		0			0
$93$	−5.29706	−	23.2079i	−0.549279	−	2.40655i
$94$		0			0
$95$	−4.31063	+	5.40536i	−0.442262	+	0.554578i
$96$		0			0
$97$	2.98370	+	1.43688i	0.302949	+	0.145893i	0.579182	−	0.815198i	$-0.303372\pi$
$97$	2.98370	+	1.43688i	0.302949	+	0.145893i	−0.276233	+	0.961091i	$0.589086\pi$
$98$		0			0
$99$	4.50430			0.452699
$100$		0			0
$101$	0.895051	+	3.92148i	0.0890609	+	0.390201i	0.999737	−	0.0229190i	$-0.00729600\pi$
$101$	0.895051	+	3.92148i	0.0890609	+	0.390201i	−0.910676	+	0.413120i	$0.864439\pi$
$102$		0			0
$103$	−2.88002	−	3.61143i	−0.283776	−	0.355844i	0.619429	−	0.785053i	$-0.287364\pi$
$103$	−2.88002	−	3.61143i	−0.283776	−	0.355844i	−0.903206	+	0.429208i	$0.858793\pi$
$104$		0			0
$105$	8.13919	+	10.2062i	0.794304	+	0.996026i
$106$		0			0
$107$	9.24831	−	11.5970i	0.894068	−	1.12113i	−0.0979707	−	0.995189i	$-0.531235\pi$
$107$	9.24831	−	11.5970i	0.894068	−	1.12113i	0.992038	−	0.125936i	$-0.0401934\pi$
$108$		0			0
$109$	−3.22737	+	1.55422i	−0.309126	+	0.148867i	−0.582014	−	0.813179i	$-0.697735\pi$
$109$	−3.22737	+	1.55422i	−0.309126	+	0.148867i	0.272889	+	0.962046i	$0.412021\pi$
$110$		0			0
$111$	2.66388	−	11.6712i	0.252845	−	1.10779i
$112$		0			0
$113$	13.7393	−	6.61649i	1.29248	−	0.622427i	0.343915	−	0.939001i	$-0.388247\pi$
$113$	13.7393	−	6.61649i	1.29248	−	0.622427i	0.948568	+	0.316574i	$0.102532\pi$
$114$		0			0
$115$	10.7606			1.00343
$116$		0			0
$117$	2.43127			0.224771
$118$		0			0
$119$	7.24975	−	3.49130i	0.664584	−	0.320047i
$120$		0			0
$121$	1.47488	−	6.46187i	0.134080	−	0.587443i
$122$		0			0
$123$	18.0904	−	8.71186i	1.63115	−	0.785522i
$124$		0			0
$125$	−6.87323	+	8.61876i	−0.614761	+	0.770886i
$126$		0			0
$127$	6.43919	+	8.07449i	0.571386	+	0.716495i	0.980617	−	0.195936i	$-0.0627744\pi$
$127$	6.43919	+	8.07449i	0.571386	+	0.716495i	−0.409231	+	0.912431i	$0.634203\pi$
$128$		0			0
$129$	−6.52170	−	8.17795i	−0.574203	−	0.720028i
$130$		0			0
$131$	−0.750417	−	3.28779i	−0.0655642	−	0.287256i	0.931508	−	0.363721i	$-0.118494\pi$
$131$	−0.750417	−	3.28779i	−0.0655642	−	0.287256i	−0.997072	+	0.0764652i	$0.975637\pi$
$132$		0			0
$133$	−21.9258			−1.90121
$134$		0			0
$135$	2.32950	+	1.12183i	0.200492	+	0.0965518i
$136$		0			0
$137$	−5.98677	+	7.50717i	−0.511484	+	0.641381i	−0.968777	−	0.247935i	$-0.920248\pi$
$137$	−5.98677	+	7.50717i	−0.511484	+	0.641381i	0.457292	+	0.889316i	$0.348819\pi$
$138$		0			0
$139$	−0.373458	−	1.63623i	−0.0316763	−	0.138783i	0.956617	−	0.291348i	$-0.0941038\pi$
$139$	−0.373458	−	1.63623i	−0.0316763	−	0.138783i	−0.988293	+	0.152565i	$0.951247\pi$
$140$		0			0
$141$	−14.1605	−	6.81932i	−1.19253	−	0.574290i
$142$		0			0
$143$	−0.525112	+	2.30067i	−0.0439121	+	0.192392i
$144$		0			0
$145$	−1.74127	+	7.03907i	−0.144605	+	0.584563i
$146$		0			0
$147$	−5.67597	+	24.8680i	−0.468146	+	2.05108i
$148$		0			0
$149$	−12.7632	−	6.14645i	−1.04561	−	0.503537i	−0.169437	−	0.985541i	$-0.554195\pi$
$149$	−12.7632	−	6.14645i	−1.04561	−	0.503537i	−0.876169	+	0.482004i	$0.839909\pi$
$150$		0			0
$151$	2.54164	+	11.1357i	0.206836	+	0.906208i	0.966657	+	0.256075i	$0.0824295\pi$
$151$	2.54164	+	11.1357i	0.206836	+	0.906208i	−0.759821	+	0.650133i	$0.774713\pi$
$152$		0			0
$153$	−2.53090	+	3.17365i	−0.204611	+	0.256574i
$154$		0			0
$155$	−12.7205	−	6.12589i	−1.02174	−	0.492043i
$156$		0			0
$157$	−9.87360			−0.787999			−0.394000	−	0.919111i	$-0.628909\pi$
$157$	−9.87360			−0.787999			−0.394000	+	0.919111i	$0.628909\pi$
$158$		0			0
$159$	−1.34626	−	5.89835i	−0.106765	−	0.467770i
$160$		0			0
$161$	21.2769	+	26.6804i	1.67686	+	2.10271i
$162$		0			0
$163$	0.864907	+	1.08456i	0.0677447	+	0.0849492i	0.814549	−	0.580094i	$-0.196984\pi$
$163$	0.864907	+	1.08456i	0.0677447	+	0.0849492i	−0.746805	+	0.665044i	$0.768413\pi$
$164$		0			0
$165$	3.98531	−	4.99742i	0.310256	−	0.389048i
$166$		0			0
$167$	−7.17500	+	3.45530i	−0.555218	+	0.267379i	−0.690383	−	0.723444i	$-0.742558\pi$
$167$	−7.17500	+	3.45530i	−0.555218	+	0.267379i	0.135165	+	0.990823i	$0.456844\pi$
$168$		0			0
$169$	2.60933	−	11.4322i	0.200718	−	0.879403i
$170$		0			0
$171$	9.96546	−	4.79911i	0.762078	−	0.366997i
$172$		0			0
$173$	12.6447			0.961362			0.480681	−	0.876896i	$-0.340390\pi$
$173$	12.6447			0.961362			0.480681	+	0.876896i	$0.340390\pi$
$174$		0			0
$175$	−13.6089			−1.02874
$176$		0			0
$177$	−10.8316	+	5.21623i	−0.814154	+	0.392076i
$178$		0			0
$179$	−4.98404	+	21.8365i	−0.372525	+	1.63214i	0.347139	+	0.937814i	$0.387153\pi$
$179$	−4.98404	+	21.8365i	−0.372525	+	1.63214i	−0.719663	+	0.694323i	$0.755704\pi$
$180$		0			0
$181$	6.77160	−	3.26103i	0.503329	−	0.242390i	−0.164949	−	0.986302i	$-0.552746\pi$
$181$	6.77160	−	3.26103i	0.503329	−	0.242390i	0.668278	+	0.743912i	$0.267032\pi$
$182$		0			0
$183$	6.71614	−	8.42177i	0.496471	−	0.622555i
$184$		0			0
$185$	−4.42696	−	5.55124i	−0.325477	−	0.408135i
$186$		0			0
$187$	−2.45654	−	3.08040i	−0.179640	−	0.225261i
$188$		0			0
$189$	1.82460	+	7.99411i	0.132720	+	0.581486i
$190$		0			0
$191$	6.81136			0.492853			0.246426	−	0.969162i	$-0.420744\pi$
$191$	6.81136			0.492853			0.246426	+	0.969162i	$0.420744\pi$
$192$		0			0
$193$	14.0750	+	6.77814i	1.01314	+	0.487901i	0.865377	−	0.501122i	$-0.167079\pi$
$193$	14.0750	+	6.77814i	1.01314	+	0.487901i	0.147761	+	0.989023i	$0.452794\pi$
$194$		0			0
$195$	2.15114	−	2.69744i	0.154046	−	0.193168i
$196$		0			0
$197$	−0.478661	−	2.09715i	−0.0341032	−	0.149416i	0.955010	−	0.296575i	$-0.0958443\pi$
$197$	−0.478661	−	2.09715i	−0.0341032	−	0.149416i	−0.989113	+	0.147159i	$0.952987\pi$
$198$		0			0
$199$	−4.68025	−	2.25389i	−0.331774	−	0.159774i	0.260579	−	0.965453i	$-0.416087\pi$
$199$	−4.68025	−	2.25389i	−0.331774	−	0.159774i	−0.592353	+	0.805679i	$0.701801\pi$
$200$		0			0
$201$	−1.07447	+	4.70754i	−0.0757870	+	0.332044i
$202$		0			0
$203$	−20.8961	+	9.60097i	−1.46662	+	0.673856i
$204$		0			0
$205$	2.64997	−	11.6103i	0.185082	−	0.810896i
$206$		0			0
$207$	−15.5103	−	7.46938i	−1.07804	−	0.519158i
$208$		0			0
$209$	2.38895	+	10.4667i	0.165247	+	0.723995i
$210$		0			0
$211$	−0.333112	+	0.417709i	−0.0229324	+	0.0287563i	−0.793165	−	0.609006i	$-0.791568\pi$
$211$	−0.333112	+	0.417709i	−0.0229324	+	0.0287563i	0.770233	+	0.637762i	$0.220140\pi$
$212$		0			0
$213$	33.7632	+	16.2595i	2.31342	+	1.11408i
$214$		0			0
$215$	−6.20388			−0.423101
$216$		0			0
$217$	−9.96347	−	43.6528i	−0.676365	−	2.96335i
$218$		0			0
$219$	−8.17859	−	10.2556i	−0.552658	−	0.693011i
$220$		0			0
$221$	−1.32596	−	1.66270i	−0.0891935	−	0.111845i
$222$		0			0
$223$	−7.58919	+	9.51654i	−0.508210	+	0.637275i	−0.968059	−	0.250722i	$-0.919332\pi$
$223$	−7.58919	+	9.51654i	−0.508210	+	0.637275i	0.459849	+	0.887997i	$0.347903\pi$
$224$		0			0
$225$	6.18536	−	2.97871i	0.412357	−	0.198581i
$226$		0			0
$227$	−0.673635	+	2.95139i	−0.0447107	+	0.195891i	−0.992351	−	0.123450i	$-0.960604\pi$
$227$	−0.673635	+	2.95139i	−0.0447107	+	0.195891i	0.947640	+	0.319340i	$0.103461\pi$
$228$		0			0
$229$	13.5870	−	6.54317i	0.897856	−	0.432385i	0.0727422	−	0.997351i	$-0.476825\pi$
$229$	13.5870	−	6.54317i	0.897856	−	0.432385i	0.825114	+	0.564966i	$0.191111\pi$
$230$		0			0
$231$	20.2711			1.33374
$232$		0			0
$233$	11.5349			0.755679			0.377840	−	0.925871i	$-0.376667\pi$
$233$	11.5349			0.755679			0.377840	+	0.925871i	$0.376667\pi$
$234$		0			0
$235$	−8.39865	+	4.04458i	−0.547867	+	0.263839i
$236$		0			0
$237$	−5.72527	+	25.0841i	−0.371897	+	1.62939i
$238$		0			0
$239$	−10.1962	+	4.91024i	−0.659538	+	0.317617i	−0.733545	−	0.679641i	$-0.762136\pi$
$239$	−10.1962	+	4.91024i	−0.659538	+	0.317617i	0.0740067	+	0.997258i	$0.476421\pi$
$240$		0			0
$241$	15.7153	−	19.7064i	1.01231	−	1.26940i	0.0496322	−	0.998768i	$-0.484195\pi$
$241$	15.7153	−	19.7064i	1.01231	−	1.26940i	0.962682	−	0.270634i	$-0.0872335\pi$
$242$		0			0
$243$	−11.7269	−	14.7051i	−0.752284	−	0.943334i
$244$		0			0
$245$	9.43258	+	11.8281i	0.602625	+	0.755668i
$246$		0			0
$247$	1.28948	+	5.64956i	0.0820473	+	0.359473i
$248$		0			0
$249$	−29.3914			−1.86260
$250$		0			0
$251$	10.9496	+	5.27306i	0.691134	+	0.332833i	0.746267	−	0.665646i	$-0.231844\pi$
$251$	10.9496	+	5.27306i	0.691134	+	0.332833i	−0.0551331	+	0.998479i	$0.517558\pi$
$252$		0			0
$253$	10.4181	−	13.0639i	0.654981	−	0.821320i
$254$		0			0
$255$	1.28180	+	5.61595i	0.0802697	+	0.351685i
$256$		0			0
$257$	−12.7696	−	6.14950i	−0.796544	−	0.383595i	−0.00908185	−	0.999959i	$-0.502891\pi$
$257$	−12.7696	−	6.14950i	−0.796544	−	0.383595i	−0.787462	+	0.616364i	$0.788605\pi$
$258$		0			0
$259$	5.01062	−	21.9530i	0.311345	−	1.36409i
$260$		0			0
$261$	7.39600	−	8.93745i	0.457801	−	0.553214i
$262$		0			0
$263$	4.49743	−	19.7045i	0.277324	−	1.21503i	−0.623839	−	0.781553i	$-0.714428\pi$
$263$	4.49743	−	19.7045i	0.277324	−	1.21503i	0.901163	−	0.433481i	$-0.142715\pi$
$264$		0			0
$265$	−3.23296	−	1.55691i	−0.198599	−	0.0956402i
$266$		0			0
$267$	2.76672	+	12.1218i	0.169320	+	0.741841i
$268$		0			0
$269$	1.20007	−	1.50483i	0.0731693	−	0.0917514i	−0.743900	−	0.668291i	$-0.767026\pi$
$269$	1.20007	−	1.50483i	0.0731693	−	0.0917514i	0.817069	+	0.576540i	$0.195597\pi$
$270$		0			0
$271$	−6.11513	−	2.94489i	−0.371467	−	0.178889i	0.238830	−	0.971061i	$-0.423236\pi$
$271$	−6.11513	−	2.94489i	−0.371467	−	0.178889i	−0.610298	+	0.792172i	$0.708950\pi$
$272$		0			0
$273$	10.9416			0.662218
$274$		0			0
$275$	1.48277	+	6.49645i	0.0894145	+	0.391750i
$276$		0			0
$277$	3.29697	+	4.13427i	0.198096	+	0.248404i	0.870951	−	0.491370i	$-0.163504\pi$
$277$	3.29697	+	4.13427i	0.198096	+	0.248404i	−0.672855	+	0.739774i	$0.734932\pi$
$278$		0			0
$279$	14.0832	+	17.6598i	0.843139	+	1.05726i
$280$		0			0
$281$	4.44808	−	5.57771i	0.265350	−	0.332738i	−0.631250	−	0.775579i	$-0.717458\pi$
$281$	4.44808	−	5.57771i	0.265350	−	0.332738i	0.896600	+	0.442841i	$0.146029\pi$
$282$		0			0
$283$	−23.2663	+	11.2045i	−1.38304	+	0.666037i	−0.969646	−	0.244515i	$-0.921371\pi$
$283$	−23.2663	+	11.2045i	−1.38304	+	0.666037i	−0.413395	+	0.910552i	$0.635657\pi$
$284$		0			0
$285$	3.49272	−	15.3026i	0.206891	−	0.906448i
$286$		0			0
$287$	34.0270	−	16.3865i	2.00855	−	0.967266i
$288$		0			0
$289$	−13.4493			−0.791136
$290$		0			0
$291$	−7.51843			−0.440738
$292$		0			0
$293$	12.4805	−	6.01029i	0.729119	−	0.351125i	−0.0322188	−	0.999481i	$-0.510257\pi$
$293$	12.4805	−	6.01029i	0.729119	−	0.351125i	0.761337	+	0.648356i	$0.224543\pi$
$294$		0			0
$295$	−1.58667	+	6.95165i	−0.0923795	+	0.404741i
$296$		0			0
$297$	3.61733	−	1.74201i	0.209899	−	0.101082i
$298$		0			0
$299$	5.62335	−	7.05145i	0.325207	−	0.407796i
$300$		0			0
$301$	−12.2670	−	15.3823i	−0.707055	−	0.886619i
$302$		0			0
$303$	−5.69361	−	7.13956i	−0.327089	−	0.410157i
$304$		0			0
$305$	−1.42165	−	6.22866i	−0.0814035	−	0.356652i
$306$		0			0
$307$	24.8359			1.41746			0.708729	−	0.705481i	$-0.249269\pi$
$307$	24.8359			1.41746			0.708729	+	0.705481i	$0.249269\pi$
$308$		0			0
$309$	9.44837	+	4.55009i	0.537499	+	0.258846i
$310$		0			0
$311$	−6.66824	+	8.36171i	−0.378121	+	0.474149i	−0.934082	−	0.357060i	$-0.883779\pi$
$311$	−6.66824	+	8.36171i	−0.378121	+	0.474149i	0.555960	+	0.831209i	$0.312351\pi$
$312$		0			0
$313$	5.43835	+	23.8270i	0.307394	+	1.34678i	0.858700	+	0.512478i	$0.171272\pi$
$313$	5.43835	+	23.8270i	0.307394	+	1.34678i	−0.551306	+	0.834303i	$0.685870\pi$
$314$		0			0
$315$	−11.1601	−	5.37444i	−0.628803	−	0.302816i
$316$		0			0
$317$	−5.44713	+	23.8654i	−0.305941	+	1.34042i	0.555059	+	0.831811i	$0.312696\pi$
$317$	−5.44713	+	23.8654i	−0.305941	+	1.34042i	−0.861000	+	0.508605i	$0.830161\pi$
$318$		0			0
$319$	6.85995	+	8.92904i	0.384083	+	0.499930i
$320$		0			0
$321$	−7.49351	+	32.8312i	−0.418247	+	1.83246i
$322$		0			0
$323$	−8.71694	−	4.19786i	−0.485024	−	0.233575i
$324$		0			0
$325$	0.800351	+	3.50657i	0.0443955	+	0.194509i
$326$		0			0
$327$	5.07048	−	6.35818i	0.280398	−	0.351608i
$328$		0			0
$329$	−26.6350	−	12.8268i	−1.46844	−	0.707162i
$330$		0			0
$331$	−33.2717			−1.82878			−0.914389	−	0.404836i	$-0.867328\pi$
$331$	−33.2717			−1.82878			−0.914389	+	0.404836i	$0.867328\pi$
$332$		0			0
$333$	2.52769	+	11.0745i	0.138516	+	0.606880i
$334$		0			0
$335$	1.78560	+	2.23907i	0.0975575	+	0.122333i
$336$		0			0
$337$	−6.57784	−	8.24835i	−0.358318	−	0.449316i	0.569700	−	0.821853i	$-0.307060\pi$
$337$	−6.57784	−	8.24835i	−0.358318	−	0.449316i	−0.928018	+	0.372537i	$0.878488\pi$
$338$		0			0
$339$	−21.5856	+	27.0675i	−1.17237	+	1.47011i
$340$		0			0
$341$	−19.7529	+	9.51247i	−1.06968	+	0.515129i
$342$		0			0
$343$	−4.02458	+	17.6328i	−0.217307	+	0.952083i
$344$		0			0
$345$	−22.0103	+	10.5996i	−1.18500	+	0.570664i
$346$		0			0
$347$	6.91676			0.371311			0.185655	−	0.982615i	$-0.440559\pi$
$347$	6.91676			0.371311			0.185655	+	0.982615i	$0.440559\pi$
$348$		0			0
$349$	−1.63878			−0.0877218			−0.0438609	−	0.999038i	$-0.513966\pi$
$349$	−1.63878			−0.0877218			−0.0438609	+	0.999038i	$0.513966\pi$
$350$		0			0
$351$	1.95251	−	0.940281i	0.104217	−	0.0501885i
$352$		0			0
$353$	7.61510	−	33.3639i	0.405311	−	1.77578i	−0.200001	−	0.979796i	$-0.564095\pi$
$353$	7.61510	−	33.3639i	0.405311	−	1.77578i	0.605312	−	0.795988i	$-0.293048\pi$
$354$		0			0
$355$	20.0252	−	9.64361i	1.06283	−	0.511830i
$356$		0			0
$357$	−11.3900	+	14.2826i	−0.602823	+	0.755917i
$358$		0			0
$359$	10.6106	+	13.3053i	0.560005	+	0.702224i	0.978559	−	0.205968i	$-0.0660342\pi$
$359$	10.6106	+	13.3053i	0.560005	+	0.702224i	−0.418554	+	0.908192i	$0.637463\pi$
$360$		0			0
$361$	4.59082	+	5.75670i	0.241622	+	0.302984i
$362$		0			0
$363$	3.34840	+	14.6703i	0.175746	+	0.769992i
$364$		0			0
$365$	−7.78003			−0.407225
$366$		0			0
$367$	−9.16301	−	4.41267i	−0.478305	−	0.230340i	0.179167	−	0.983819i	$-0.442660\pi$
$367$	−9.16301	−	4.41267i	−0.478305	−	0.230340i	−0.657472	+	0.753479i	$0.728374\pi$
$368$		0			0
$369$	−11.8789	+	14.8956i	−0.618389	+	0.775436i
$370$		0			0
$371$	−2.53224	−	11.0945i	−0.131467	−	0.575996i
$372$		0			0
$373$	5.95244	+	2.86655i	0.308206	+	0.148424i	0.581593	−	0.813480i	$-0.302430\pi$
$373$	5.95244	+	2.86655i	0.308206	+	0.148424i	−0.273387	+	0.961904i	$0.588144\pi$
$374$		0			0
$375$	5.56909	−	24.3998i	0.287586	−	1.26000i
$376$		0			0
$377$	3.70277	+	4.81960i	0.190702	+	0.248222i
$378$		0			0
$379$	3.08165	−	13.5016i	0.158294	−	0.693529i	−0.832028	−	0.554734i	$-0.812820\pi$
$379$	3.08165	−	13.5016i	0.158294	−	0.693529i	0.990321	−	0.138795i	$-0.0443229\pi$
$380$		0			0
$381$	−21.1248	−	10.1732i	−1.08226	−	0.521188i
$382$		0			0
$383$	−3.31791	−	14.5367i	−0.169537	−	0.742792i	−0.986184	−	0.165654i	$-0.947027\pi$
$383$	−3.31791	−	14.5367i	−0.169537	−	0.742792i	0.816647	−	0.577138i	$-0.195831\pi$
$384$		0			0
$385$	7.49614	−	9.39986i	0.382039	−	0.479061i
$386$		0			0
$387$	8.94230	+	4.30638i	0.454562	+	0.218906i
$388$		0			0
$389$	36.3063			1.84080			0.920401	−	0.390976i	$-0.127862\pi$
$389$	36.3063			1.84080			0.920401	+	0.390976i	$0.127862\pi$
$390$		0			0
$391$	3.35080	+	14.6808i	0.169457	+	0.742441i
$392$		0			0
$393$	4.77356	+	5.98585i	0.240794	+	0.301946i
$394$		0			0
$395$	9.51452	+	11.9308i	0.478727	+	0.600305i
$396$		0			0
$397$	9.15347	−	11.4781i	0.459400	−	0.576069i	−0.497140	−	0.867670i	$-0.665617\pi$
$397$	9.15347	−	11.4781i	0.459400	−	0.576069i	0.956540	+	0.291601i	$0.0941880\pi$
$398$		0			0
$399$	44.8484	−	21.5978i	2.24523	−	1.08124i
$400$		0			0
$401$	−4.00830	+	17.5615i	−0.200165	+	0.876980i	0.770670	+	0.637234i	$0.219921\pi$
$401$	−4.00830	+	17.5615i	−0.200165	+	0.876980i	−0.970836	+	0.239746i	$0.922936\pi$
$402$		0			0
$403$	−10.6619	+	5.13452i	−0.531109	+	0.255769i
$404$		0			0
$405$	−14.5721			−0.724091
$406$		0			0
$407$	−11.0256			−0.546517
$408$		0			0
$409$	10.1958	−	4.91006i	0.504152	−	0.242787i	−0.164480	−	0.986380i	$-0.552594\pi$
$409$	10.1958	−	4.91006i	0.504152	−	0.242787i	0.668632	+	0.743594i	$0.266880\pi$
$410$		0			0
$411$	4.85082	−	21.2528i	0.239273	−	1.04833i
$412$		0			0
$413$	−20.3737	+	9.81144i	−1.00252	+	0.482790i
$414$		0			0
$415$	−10.8688	+	13.6290i	−0.533528	+	0.669023i
$416$		0			0
$417$	2.37565	+	2.97896i	0.116336	+	0.145881i
$418$		0			0
$419$	−16.3076	−	20.4491i	−0.796680	−	0.999005i	−0.999803	−	0.0198517i	$-0.993681\pi$
$419$	−16.3076	−	20.4491i	−0.796680	−	0.999005i	0.203123	−	0.979153i	$-0.434891\pi$
$420$		0			0
$421$	2.79100	+	12.2282i	0.136025	+	0.595964i	0.996286	+	0.0861098i	$0.0274436\pi$
$421$	2.79100	+	12.2282i	0.136025	+	0.595964i	−0.860261	+	0.509854i	$0.829699\pi$
$422$		0			0
$423$	14.9134			0.725112
$424$		0			0
$425$	−5.41043	−	2.60552i	−0.262444	−	0.126386i
$426$		0			0
$427$	12.6327	−	15.8409i	0.611338	−	0.766594i
$428$		0			0
$429$	−1.19216	−	5.22318i	−0.0575579	−	0.252178i
$430$		0			0
$431$	19.8055	+	9.53782i	0.953997	+	0.459421i	0.845086	−	0.534631i	$-0.179549\pi$
$431$	19.8055	+	9.53782i	0.953997	+	0.459421i	0.108911	+	0.994052i	$0.465264\pi$
$432$		0			0
$433$	−2.61653	+	11.4638i	−0.125743	+	0.550914i	0.872333	+	0.488911i	$0.162606\pi$
$433$	−2.61653	+	11.4638i	−0.125743	+	0.550914i	−0.998076	+	0.0620026i	$0.980251\pi$
$434$		0			0
$435$	−3.37208	−	16.1134i	−0.161679	−	0.772577i
$436$		0			0
$437$	9.13042	−	40.0030i	0.436767	−	1.91360i
$438$		0			0
$439$	26.7736	+	12.8935i	1.27784	+	0.615374i	0.944833	−	0.327552i	$-0.106224\pi$
$439$	26.7736	+	12.8935i	1.27784	+	0.615374i	0.333003	+	0.942926i	$0.391938\pi$
$440$		0			0
$441$	−5.38577	−	23.5966i	−0.256465	−	1.12365i
$442$		0			0
$443$	−10.7485	+	13.4782i	−0.510677	+	0.640368i	−0.968600	−	0.248623i	$-0.920022\pi$
$443$	−10.7485	+	13.4782i	−0.510677	+	0.640368i	0.457923	+	0.888992i	$0.348593\pi$
$444$		0			0
$445$	6.64409	+	3.19963i	0.314960	+	0.151677i
$446$		0			0
$447$	32.1612			1.52117
$448$		0			0
$449$	−0.854732	−	3.74483i	−0.0403373	−	0.176729i	0.950746	−	0.309970i	$-0.100319\pi$
$449$	−0.854732	−	3.74483i	−0.0403373	−	0.176729i	−0.991084	+	0.133240i	$0.957462\pi$
$450$		0			0
$451$	−11.5298	−	14.4580i	−0.542919	−	0.680799i
$452$		0			0
$453$	−16.1679	−	20.2739i	−0.759636	−	0.952553i
$454$		0			0
$455$	4.04617	−	5.07373i	0.189687	−	0.237860i
$456$		0			0
$457$	9.85882	−	4.74776i	0.461176	−	0.222091i	−0.188845	−	0.982007i	$-0.560474\pi$
$457$	9.85882	−	4.74776i	0.461176	−	0.222091i	0.650021	+	0.759916i	$0.274760\pi$
$458$		0			0
$459$	−0.805133	+	3.52752i	−0.0375804	+	0.164650i
$460$		0			0
$461$	−29.3573	+	14.1377i	−1.36730	+	0.658459i	−0.966252	−	0.257597i	$-0.917069\pi$
$461$	−29.3573	+	14.1377i	−1.36730	+	0.658459i	−0.401051	+	0.916056i	$0.631355\pi$
$462$		0			0
$463$	−13.0581			−0.606861			−0.303431	−	0.952854i	$-0.598132\pi$
$463$	−13.0581			−0.606861			−0.303431	+	0.952854i	$0.598132\pi$
$464$		0			0
$465$	32.0536			1.48645
$466$		0			0
$467$	−19.1059	+	9.20091i	−0.884115	+	0.425767i	−0.820126	−	0.572183i	$-0.806097\pi$
$467$	−19.1059	+	9.20091i	−0.884115	+	0.425767i	−0.0639891	+	0.997951i	$0.520382\pi$
$468$		0			0
$469$	−2.02101	+	8.85463i	−0.0933216	+	0.408869i
$470$		0			0
$471$	20.1961	−	9.72591i	0.930586	−	0.448146i
$472$		0			0
$473$	−6.00644	+	7.53183i	−0.276176	+	0.346314i
$474$		0			0
$475$	10.2022	+	12.7931i	0.468108	+	0.586989i
$476$		0			0
$477$	3.57928	+	4.48827i	0.163884	+	0.205504i
$478$		0			0
$479$	−0.407929	−	1.78725i	−0.0186388	−	0.0816617i	0.964753	−	0.263157i	$-0.0847636\pi$
$479$	−0.407929	−	1.78725i	−0.0186388	−	0.0816617i	−0.983392	+	0.181495i	$0.941906\pi$
$480$		0			0
$481$	−5.95123			−0.271353
$482$		0			0
$483$	−69.8024	−	33.6151i	−3.17612	−	1.52954i
$484$		0			0
$485$	−2.78028	+	3.48636i	−0.126246	+	0.158308i
$486$		0			0
$487$	−2.63744	−	11.5554i	−0.119514	−	0.523624i	−0.998873	−	0.0474649i	$-0.984886\pi$
$487$	−2.63744	−	11.5554i	−0.119514	−	0.523624i	0.879359	−	0.476159i	$-0.157971\pi$
$488$		0			0
$489$	−2.83747	−	1.36645i	−0.128315	−	0.0617931i
$490$		0			0
$491$	−1.56913	+	6.87480i	−0.0708137	+	0.310255i	−0.997914	−	0.0645584i	$-0.979436\pi$
$491$	−1.56913	+	6.87480i	−0.0708137	+	0.310255i	0.927100	+	0.374814i	$0.122293\pi$
$492$		0			0
$493$	−10.1457	−	0.183703i	−0.456941	−	0.00827356i
$494$		0			0
$495$	−1.34962	+	5.91307i	−0.0606609	+	0.265773i
$496$		0			0
$497$	63.5068	+	30.5833i	2.84867	+	1.37185i
$498$		0			0
$499$	3.87463	+	16.9758i	0.173452	+	0.759943i	0.984560	+	0.175047i	$0.0560077\pi$
$499$	3.87463	+	16.9758i	0.173452	+	0.759943i	−0.811108	+	0.584896i	$0.801135\pi$
$500$		0			0
$501$	11.2726	−	14.1354i	0.503621	−	0.631521i
$502$		0			0
$503$	−23.5324	−	11.3326i	−1.04926	−	0.505296i	−0.171891	−	0.985116i	$-0.554988\pi$
$503$	−23.5324	−	11.3326i	−1.04926	−	0.505296i	−0.877367	+	0.479820i	$0.840702\pi$
$504$		0			0
$505$	−5.41615			−0.241015
$506$		0			0
$507$	5.92394	+	25.9545i	0.263092	+	1.15268i
$508$		0			0
$509$	−2.36441	−	2.96488i	−0.104801	−	0.131416i	0.726665	−	0.686992i	$-0.241069\pi$
$509$	−2.36441	−	2.96488i	−0.104801	−	0.131416i	−0.831466	+	0.555576i	$0.812498\pi$
$510$		0			0
$511$	−15.3835	−	19.2903i	−0.680525	−	0.853351i
$512$		0			0
$513$	6.14707	−	7.70818i	0.271400	−	0.340324i
$514$		0			0
$515$	5.60388	−	2.69869i	0.246936	−	0.118918i
$516$		0			0
$517$	−3.22103	+	14.1123i	−0.141661	+	0.620656i
$518$		0			0
$519$	−25.8643	+	12.4556i	−1.13532	+	0.546740i
$520$		0			0
$521$	0.974452			0.0426915			0.0213458	−	0.999772i	$-0.493205\pi$
$521$	0.974452			0.0426915			0.0213458	+	0.999772i	$0.493205\pi$
$522$		0			0
$523$	41.7600			1.82604			0.913019	−	0.407917i	$-0.133745\pi$
$523$	41.7600			1.82604			0.913019	+	0.407917i	$0.133745\pi$
$524$		0			0
$525$	27.8365	−	13.4053i	1.21488	−	0.585057i
$526$		0			0
$527$	4.39652	−	19.2624i	0.191516	−	0.839085i
$528$		0			0
$529$	−36.8155	+	17.7294i	−1.60067	+	0.770844i
$530$		0			0
$531$	7.11248	−	8.91877i	0.308655	−	0.387041i
$532$		0			0
$533$	−6.22343	−	7.80393i	−0.269566	−	0.338026i
$534$		0			0
$535$	12.4530	+	15.6156i	0.538392	+	0.675122i
$536$		0			0
$537$	−11.3152	−	49.5752i	−0.488288	−	2.13933i
$538$		0			0
$539$	23.4923			1.01188
$540$		0			0
$541$	27.2407	+	13.1184i	1.17117	+	0.564006i	0.915327	−	0.402712i	$-0.131932\pi$
$541$	27.2407	+	13.1184i	1.17117	+	0.564006i	0.255844	+	0.966718i	$0.417647\pi$
$542$		0			0
$543$	−10.6388	+	13.3406i	−0.456554	+	0.572501i
$544$		0			0
$545$	−1.07330	−	4.70245i	−0.0459753	−	0.201431i
$546$		0			0
$547$	29.9389	+	14.4178i	1.28010	+	0.616461i	0.945415	−	0.325870i	$-0.105657\pi$
$547$	29.9389	+	14.4178i	1.28010	+	0.616461i	0.334681	+	0.942332i	$0.391372\pi$
$548$		0			0
$549$	−2.27441	+	9.96485i	−0.0970695	+	0.425289i
$550$		0			0
$551$	24.6906	+	12.4460i	1.05186	+	0.530216i
$552$		0			0
$553$	−10.7689	+	47.1817i	−0.457941	+	2.00637i
$554$		0			0
$555$	14.5234	+	6.99409i	0.616483	+	0.296883i
$556$		0			0
$557$	−5.66389	−	24.8151i	−0.239987	−	1.05145i	−0.941028	−	0.338329i	$-0.890138\pi$
$557$	−5.66389	−	24.8151i	−0.239987	−	1.05145i	0.701041	−	0.713121i	$-0.252719\pi$
$558$		0			0
$559$	−3.24207	+	4.06543i	−0.137125	+	0.171950i
$560$		0			0
$561$	8.05907	+	3.88104i	0.340254	+	0.163858i
$562$		0			0
$563$	−8.50862			−0.358596			−0.179298	−	0.983795i	$-0.557383\pi$
$563$	−8.50862			−0.358596			−0.179298	+	0.983795i	$0.557383\pi$
$564$		0			0
$565$	4.56918	+	20.0189i	0.192227	+	0.842201i
$566$		0			0
$567$	−28.8134	−	36.1308i	−1.21005	−	1.51735i
$568$		0			0
$569$	−6.24080	−	7.82571i	−0.261628	−	0.328071i	0.633616	−	0.773648i	$-0.281570\pi$
$569$	−6.24080	−	7.82571i	−0.261628	−	0.328071i	−0.895244	+	0.445577i	$0.852999\pi$
$570$		0			0
$571$	−10.5332	+	13.2083i	−0.440802	+	0.552748i	−0.951754	−	0.306861i	$-0.900721\pi$
$571$	−10.5332	+	13.2083i	−0.440802	+	0.552748i	0.510952	+	0.859609i	$0.329293\pi$
$572$		0			0
$573$	−13.9324	+	6.70947i	−0.582033	+	0.280292i
$574$		0			0
$575$	5.66707	−	24.8290i	0.236333	−	1.03544i
$576$		0			0
$577$	−23.0001	+	11.0763i	−0.957509	+	0.461112i	−0.846313	−	0.532687i	$-0.821182\pi$
$577$	−23.0001	+	11.0763i	−0.957509	+	0.461112i	−0.111196	+	0.993798i	$0.535468\pi$
$578$		0			0
$579$	−35.4665			−1.47394
$580$		0			0
$581$	−55.2836			−2.29355
$582$		0			0
$583$	−5.02024	+	2.41762i	−0.207917	+	0.100128i
$584$		0			0
$585$	−0.728480	+	3.19168i	−0.0301189	+	0.131960i
$586$		0			0
$587$	−29.3312	+	14.1252i	−1.21063	+	0.583008i	−0.926687	−	0.375834i	$-0.877356\pi$
$587$	−29.3312	+	14.1252i	−1.21063	+	0.583008i	−0.283941	+	0.958842i	$0.591642\pi$
$588$		0			0
$589$	−33.5668	+	42.0914i	−1.38310	+	1.73435i
$590$		0			0
$591$	3.04487	+	3.81814i	0.125249	+	0.157057i
$592$		0			0
$593$	−10.8310	−	13.5817i	−0.444777	−	0.557732i	0.508019	−	0.861346i	$-0.330378\pi$
$593$	−10.8310	−	13.5817i	−0.444777	−	0.557732i	−0.952795	+	0.303614i	$0.901807\pi$
$594$		0			0
$595$	2.41100	+	10.5633i	0.0988415	+	0.433053i
$596$		0			0
$597$	11.7934			0.482673
$598$		0			0
$599$	16.9591	+	8.16707i	0.692930	+	0.333698i	0.746985	−	0.664840i	$-0.231500\pi$
$599$	16.9591	+	8.16707i	0.692930	+	0.333698i	−0.0540553	+	0.998538i	$0.517215\pi$
$600$		0			0
$601$	−13.7735	+	17.2714i	−0.561833	+	0.704516i	−0.978896	−	0.204361i	$-0.934488\pi$
$601$	−13.7735	+	17.2714i	−0.561833	+	0.704516i	0.417062	+	0.908878i	$0.363060\pi$
$602$		0			0
$603$	−1.01953	−	4.46686i	−0.0415185	−	0.181905i
$604$		0			0
$605$	8.04098	+	3.87233i	0.326912	+	0.157433i
$606$		0			0
$607$	−1.78643	+	7.82687i	−0.0725091	+	0.317683i	−0.998156	−	0.0607062i	$-0.980665\pi$
$607$	−1.78643	+	7.82687i	−0.0725091	+	0.317683i	0.925647	+	0.378389i	$0.123522\pi$
$608$		0			0
$609$	33.2848	−	40.2219i	1.34877	−	1.62988i
$610$		0			0
$611$	−1.73860	+	7.61732i	−0.0703364	+	0.308164i
$612$		0			0
$613$	16.8069	+	8.09380i	0.678826	+	0.326905i	0.741331	−	0.671139i	$-0.234195\pi$
$613$	16.8069	+	8.09380i	0.678826	+	0.326905i	−0.0625053	+	0.998045i	$0.519909\pi$
$614$		0			0
$615$	6.01620	+	26.3587i	0.242596	+	1.06288i
$616$		0			0
$617$	−10.5367	+	13.2126i	−0.424193	+	0.531921i	−0.947301	−	0.320346i	$-0.896201\pi$
$617$	−10.5367	+	13.2126i	−0.424193	+	0.531921i	0.523108	+	0.852266i	$0.324772\pi$
$618$		0			0
$619$	−5.28505	−	2.54515i	−0.212424	−	0.102298i	0.324646	−	0.945836i	$-0.394755\pi$
$619$	−5.28505	−	2.54515i	−0.212424	−	0.102298i	−0.537070	+	0.843537i	$0.680469\pi$
$620$		0			0
$621$	−15.3448			−0.615767
$622$		0			0
$623$	5.20404	+	22.8004i	0.208496	+	0.913479i
$624$		0			0
$625$	0.679974	+	0.852661i	0.0271990	+	0.0341064i
$626$		0			0
$627$	−15.1966	−	19.0559i	−0.606894	−	0.761021i
$628$		0			0
$629$	6.19510	−	7.76842i	0.247015	−	0.309747i
$630$		0			0
$631$	17.4904	−	8.42292i	0.696281	−	0.335311i	−0.0520430	−	0.998645i	$-0.516573\pi$
$631$	17.4904	−	8.42292i	0.696281	−	0.335311i	0.748324	+	0.663334i	$0.230859\pi$
$632$		0			0
$633$	0.269906	−	1.18254i	0.0107278	−	0.0470016i
$634$		0			0
$635$	−12.5293	+	6.03377i	−0.497208	+	0.239443i
$636$		0			0
$637$	12.6804			0.502414
$638$		0			0
$639$	−35.5584			−1.40667
$640$		0			0
$641$	3.52772	−	1.69886i	0.139337	−	0.0671009i	−0.362916	−	0.931822i	$-0.618219\pi$
$641$	3.52772	−	1.69886i	0.139337	−	0.0671009i	0.502253	+	0.864721i	$0.332505\pi$
$642$		0			0
$643$	7.86740	−	34.4693i	0.310260	−	1.35934i	−0.543823	−	0.839200i	$-0.683024\pi$
$643$	7.86740	−	34.4693i	0.310260	−	1.35934i	0.854083	−	0.520137i	$-0.174119\pi$
$644$		0			0
$645$	12.6898	−	6.11108i	0.499660	−	0.240624i
$646$		0			0
$647$	11.5009	−	14.4216i	0.452146	−	0.566973i	−0.502553	−	0.864546i	$-0.667606\pi$
$647$	11.5009	−	14.4216i	0.452146	−	0.566973i	0.954699	+	0.297573i	$0.0961772\pi$
$648$		0			0
$649$	6.90350	+	8.65671i	0.270986	+	0.339806i
$650$		0			0
$651$	63.3797	+	79.4757i	2.48405	+	3.11490i
$652$		0			0
$653$	−5.26947	−	23.0871i	−0.206210	−	0.903466i	−0.967062	−	0.254541i	$-0.918076\pi$
$653$	−5.26947	−	23.0871i	−0.206210	−	0.903466i	0.760852	−	0.648926i	$-0.224781\pi$
$654$		0			0
$655$	4.54093			0.177429
$656$		0			0
$657$	11.2142	+	5.40046i	0.437506	+	0.210692i
$658$		0			0
$659$	8.91783	−	11.1826i	0.347389	−	0.435612i	−0.577185	−	0.816613i	$-0.695849\pi$
$659$	8.91783	−	11.1826i	0.347389	−	0.435612i	0.924575	+	0.381001i	$0.124420\pi$
$660$		0			0
$661$	−10.8875	−	47.7013i	−0.423475	−	1.85537i	−0.511551	−	0.859253i	$-0.670929\pi$
$661$	−10.8875	−	47.7013i	−0.423475	−	1.85537i	0.0880751	−	0.996114i	$-0.471928\pi$
$662$		0			0
$663$	4.35002	+	2.09486i	0.168941	+	0.0813576i
$664$		0			0
$665$	6.56961	−	28.7834i	0.254759	−	1.11617i
$666$		0			0
$667$	−8.81505	−	42.1224i	−0.341320	−	1.63099i
$668$		0			0
$669$	6.14920	−	26.9414i	0.237742	−	1.04161i
$670$		0			0
$671$	−8.93833	−	4.30447i	−0.345060	−	0.166172i
$672$		0			0
$673$	3.20650	+	14.0486i	0.123602	+	0.541534i	0.998374	+	0.0570001i	$0.0181535\pi$
$673$	3.20650	+	14.0486i	0.123602	+	0.541534i	−0.874773	+	0.484534i	$0.838989\pi$
$674$		0			0
$675$	3.81536	−	4.78431i	0.146853	−	0.184148i
$676$		0			0
$677$	42.4357	+	20.4360i	1.63094	+	0.785418i	0.999954	+	0.00962221i	$0.00306289\pi$
$677$	42.4357	+	20.4360i	1.63094	+	0.785418i	0.630984	+	0.775796i	$0.282651\pi$
$678$		0			0
$679$	−14.1418			−0.542711
$680$		0			0
$681$	−1.52935	−	6.70051i	−0.0586047	−	0.256764i
$682$		0			0
$683$	−0.292000	−	0.366156i	−0.0111731	−	0.0140106i	0.776214	−	0.630470i	$-0.217138\pi$
$683$	−0.292000	−	0.366156i	−0.0111731	−	0.0140106i	−0.787387	+	0.616459i	$0.788566\pi$
$684$		0			0
$685$	−8.06132	−	10.1086i	−0.308007	−	0.386229i
$686$		0			0
$687$	−21.3464	+	26.7676i	−0.814418	+	1.02125i
$688$		0			0
$689$	−2.70976	+	1.30495i	−0.103234	+	0.0497146i
$690$		0			0
$691$	3.13009	−	13.7138i	0.119074	−	0.521698i	−0.879847	−	0.475257i	$-0.842355\pi$
$691$	3.13009	−	13.7138i	0.119074	−	0.521698i	0.998921	−	0.0464410i	$-0.0147879\pi$
$692$		0			0
$693$	−17.3298	+	8.34560i	−0.658306	+	0.317023i
$694$		0			0
$695$	2.25987			0.0857219
$696$		0			0
$697$	16.6653			0.631242
$698$		0			0
$699$	−23.5943	+	11.3624i	−0.892417	+	0.429765i
$700$		0			0
$701$	8.42479	−	36.9114i	0.318200	−	1.39413i	−0.522507	−	0.852635i	$-0.675003\pi$
$701$	8.42479	−	36.9114i	0.318200	−	1.39413i	0.840707	−	0.541490i	$-0.182140\pi$
$702$		0			0
$703$	−24.3933	+	11.7472i	−0.920012	+	0.443054i
$704$		0			0
$705$	13.1950	−	16.5460i	0.496953	−	0.623160i
$706$		0			0
$707$	−10.7094	−	13.4291i	−0.402767	−	0.505054i
$708$		0			0
$709$	14.6087	+	18.3187i	0.548641	+	0.687974i	0.976413	−	0.215913i	$-0.0692726\pi$
$709$	14.6087	+	18.3187i	0.548641	+	0.687974i	−0.427772	+	0.903887i	$0.640701\pi$
$710$		0			0
$711$	−5.43256	−	23.8016i	−0.203737	−	0.892629i
$712$		0			0
$713$	83.7923			3.13805
$714$		0			0
$715$	−2.86289	−	1.37870i	−0.107066	−	0.0515603i
$716$		0			0
$717$	16.0192	−	20.0874i	0.598247	−	0.750178i
$718$		0			0
$719$	−1.14696	−	5.02516i	−0.0427744	−	0.187407i	0.949027	−	0.315194i	$-0.102070\pi$
$719$	−1.14696	−	5.02516i	−0.0427744	−	0.187407i	−0.991802	+	0.127787i	$0.959213\pi$
$720$		0			0
$721$	17.7719	+	8.55847i	0.661858	+	0.318734i
$722$		0			0
$723$	−12.7335	+	55.7890i	−0.473563	+	2.07481i
$724$		0			0
$725$	15.3250	+	7.72496i	0.569155	+	0.286898i
$726$		0			0
$727$	9.63820	−	42.2277i	0.357461	−	1.56614i	−0.402033	−	0.915625i	$-0.631696\pi$
$727$	9.63820	−	42.2277i	0.357461	−	1.56614i	0.759494	−	0.650514i	$-0.225447\pi$
$728$		0			0
$729$	9.22131	+	4.44075i	0.341530	+	0.164472i
$730$		0			0
$731$	−1.93187	−	8.46406i	−0.0714526	−	0.313054i
$732$		0			0
$733$	27.2882	−	34.2183i	1.00791	−	1.26388i	0.0436173	−	0.999048i	$-0.486112\pi$
$733$	27.2882	−	34.2183i	1.00791	−	1.26388i	0.964294	−	0.264833i	$-0.0853168\pi$
$734$		0			0
$735$	−30.9451	−	14.9024i	−1.14143	−	0.549683i
$736$		0			0
$737$	4.44711			0.163811
$738$		0			0
$739$	−6.44093	−	28.2196i	−0.236934	−	1.03807i	−0.943746	−	0.330672i	$-0.892725\pi$
$739$	−6.44093	−	28.2196i	−0.236934	−	1.03807i	0.706812	−	0.707401i	$-0.250133\pi$
$740$		0			0
$741$	−8.20262	−	10.2858i	−0.301331	−	0.377857i
$742$		0			0
$743$	5.37897	+	6.74501i	0.197335	+	0.247451i	0.870647	−	0.491908i	$-0.163700\pi$
$743$	5.37897	+	6.74501i	0.197335	+	0.247451i	−0.673312	+	0.739358i	$0.735129\pi$
$744$		0			0
$745$	11.8931	−	14.9134i	0.435728	−	0.546386i
$746$		0			0
$747$	25.1268	−	12.1004i	0.919343	−	0.442732i
$748$		0			0
$749$	−14.0949	+	61.7537i	−0.515015	+	2.25643i
$750$		0			0
$751$	17.2619	−	8.31291i	0.629897	−	0.303342i	−0.0915621	−	0.995799i	$-0.529186\pi$
$751$	17.2619	−	8.31291i	0.629897	−	0.303342i	0.721459	+	0.692457i	$0.243472\pi$
$752$		0			0
$753$	−27.5912			−1.00548
$754$		0			0
$755$	−15.3800			−0.559737
$756$		0			0
$757$	−14.0242	+	6.75368i	−0.509717	+	0.245467i	−0.671021	−	0.741438i	$-0.734144\pi$
$757$	−14.0242	+	6.75368i	−0.509717	+	0.245467i	0.161305	+	0.986905i	$0.448430\pi$
$758$		0			0
$759$	−8.44134	+	36.9839i	−0.306401	+	1.34243i
$760$		0			0
$761$	−29.8165	+	14.3589i	−1.08085	+	0.520509i	−0.887588	−	0.460638i	$-0.847621\pi$
$761$	−29.8165	+	14.3589i	−1.08085	+	0.520509i	−0.193261	+	0.981147i	$0.561906\pi$
$762$		0			0
$763$	9.53729	−	11.9594i	0.345273	−	0.432959i
$764$		0			0
$765$	−3.40791	−	4.27339i	−0.123213	−	0.154505i
$766$		0			0
$767$	3.72628	+	4.67261i	0.134548	+	0.168718i
$768$		0			0
$769$	−4.60266	−	20.1656i	−0.165976	−	0.727190i	−0.987578	−	0.157128i	$-0.949776\pi$
$769$	−4.60266	−	20.1656i	−0.165976	−	0.727190i	0.821602	−	0.570062i	$-0.193081\pi$
$770$		0			0
$771$	32.1772			1.15883
$772$		0			0
$773$	−14.3719	−	6.92113i	−0.516920	−	0.248936i	0.157187	−	0.987569i	$-0.449757\pi$
$773$	−14.3719	−	6.92113i	−0.516920	−	0.248936i	−0.674108	+	0.738633i	$0.735472\pi$
$774$		0			0
$775$	−20.8342	+	26.1253i	−0.748388	+	0.938448i
$776$		0			0
$777$	11.3756	+	49.8396i	0.408096	+	1.78798i
$778$		0			0
$779$	−40.9133	−	19.7028i	−1.46587	−	0.705926i
$780$		0			0
$781$	7.68001	−	33.6483i	0.274812	−	1.20403i
$782$		0			0
$783$	2.48309	−	10.0379i	0.0887385	−	0.358725i
$784$		0			0
$785$	2.95842	−	12.9617i	0.105591	−	0.462622i
$786$		0			0
$787$	35.1795	+	16.9416i	1.25401	+	0.603902i	0.938585	−	0.345047i	$-0.112137\pi$
$787$	35.1795	+	16.9416i	1.25401	+	0.603902i	0.315429	+	0.948949i	$0.397851\pi$
$788$		0			0
$789$	10.2105	+	44.7350i	0.363503	+	1.59261i
$790$		0			0
$791$	−40.6014	+	50.9125i	−1.44362	+	1.81024i
$792$		0			0
$793$	−4.82461	−	2.32341i	−0.171327	−	0.0825067i
$794$		0			0
$795$	8.14651			0.288927
$796$		0			0
$797$	−8.91131	−	39.0430i	−0.315655	−	1.38297i	−0.845090	−	0.534624i	$-0.820453\pi$
$797$	−8.91131	−	39.0430i	−0.315655	−	1.38297i	0.529436	−	0.848350i	$-0.322404\pi$
$798$		0			0
$799$	−8.13339	−	10.1990i	−0.287739	−	0.360813i
$800$		0			0
$801$	−7.35582	−	9.22391i	−0.259905	−	0.325911i
$802$		0			0
$803$	−7.53243	+	9.44536i	−0.265814	+	0.333320i
$804$		0			0
$805$	−41.4002	+	19.9373i	−1.45916	+	0.702697i
$806$		0			0
$807$	−0.972361	+	4.26019i	−0.0342287	+	0.149966i
$808$		0			0
$809$	−15.0565	+	7.25082i	−0.529358	+	0.254925i	−0.679418	−	0.733751i	$-0.737768\pi$
$809$	−15.0565	+	7.25082i	−0.529358	+	0.254925i	0.150060	+	0.988677i	$0.452053\pi$
$810$		0			0
$811$	0.618522			0.0217192			0.0108596	−	0.999941i	$-0.496543\pi$
$811$	0.618522			0.0217192			0.0108596	+	0.999941i	$0.496543\pi$
$812$		0			0
$813$	15.4091			0.540420
$814$		0			0
$815$	−1.68292	+	0.810451i	−0.0589501	+	0.0283889i
$816$		0			0
$817$	−5.26404	+	23.0633i	−0.184165	+	0.806881i
$818$		0			0
$819$	−9.35406	+	4.50468i	−0.326857	+	0.157406i
$820$		0			0
$821$	−4.73264	+	5.93454i	−0.165170	+	0.207117i	−0.857528	−	0.514438i	$-0.828001\pi$
$821$	−4.73264	+	5.93454i	−0.165170	+	0.207117i	0.692358	+	0.721555i	$0.256572\pi$
$822$		0			0
$823$	−15.1241	−	18.9650i	−0.527193	−	0.661079i	0.444926	−	0.895567i	$-0.353230\pi$
$823$	−15.1241	−	18.9650i	−0.527193	−	0.661079i	−0.972119	+	0.234489i	$0.924658\pi$
$824$		0			0
$825$	−9.43222	−	11.8276i	−0.328388	−	0.411785i
$826$		0			0
$827$	3.18469	+	13.9531i	0.110743	+	0.485195i	0.999633	+	0.0270759i	$0.00861958\pi$
$827$	3.18469	+	13.9531i	0.110743	+	0.485195i	−0.888891	+	0.458119i	$0.848523\pi$
$828$		0			0
$829$	−29.5741			−1.02715			−0.513576	−	0.858044i	$-0.671679\pi$
$829$	−29.5741			−1.02715			−0.513576	+	0.858044i	$0.671679\pi$
$830$		0			0
$831$	−10.8163	−	5.20883i	−0.375212	−	0.180692i
$832$		0			0
$833$	−13.2000	+	16.5522i	−0.457352	+	0.573501i
$834$		0			0
$835$	−2.38614	−	10.4544i	−0.0825759	−	0.361789i
$836$		0			0
$837$	18.1398	+	8.73567i	0.627003	+	0.301949i
$838$		0			0
$839$	5.01169	−	21.9576i	0.173023	−	0.758062i	−0.811720	−	0.584047i	$-0.801469\pi$
$839$	5.01169	−	21.9576i	0.173023	−	0.758062i	0.984743	−	0.174016i	$-0.0556743\pi$
$840$		0			0
$841$	28.9810	+	1.04983i	0.999345	+	0.0362009i
$842$		0			0
$843$	−3.60409	+	15.7905i	−0.124131	+	0.543855i
$844$		0			0
$845$	14.2260	+	6.85087i	0.489388	+	0.235677i
$846$		0			0
$847$	6.29816	+	27.5941i	0.216407	+	0.948143i
$848$		0			0
$849$	36.5535	−	45.8366i	1.25451	−	1.57311i
$850$		0			0
$851$	37.9660	+	18.2835i	1.30146	+	0.626749i
$852$		0			0
$853$	19.8193			0.678600			0.339300	−	0.940678i	$-0.389810\pi$
$853$	19.8193			0.678600			0.339300	+	0.940678i	$0.389810\pi$
$854$		0			0
$855$	3.31415	+	14.5202i	0.113341	+	0.496581i
$856$		0			0
$857$	−12.0411	−	15.0990i	−0.411315	−	0.515772i	0.532418	−	0.846482i	$-0.321283\pi$
$857$	−12.0411	−	15.0990i	−0.411315	−	0.515772i	−0.943733	+	0.330709i	$0.892712\pi$
$858$		0			0
$859$	−12.1131	−	15.1893i	−0.413293	−	0.518253i	0.530994	−	0.847375i	$-0.321818\pi$
$859$	−12.1131	−	15.1893i	−0.413293	−	0.518253i	−0.944287	+	0.329123i	$0.893247\pi$
$860$		0			0
$861$	−53.4594	+	67.0360i	−1.82189	+	2.28458i
$862$		0			0
$863$	33.3600	−	16.0653i	1.13559	−	0.546870i	0.230913	−	0.972974i	$-0.425829\pi$
$863$	33.3600	−	16.0653i	1.13559	−	0.546870i	0.904674	+	0.426104i	$0.140114\pi$
$864$		0			0
$865$	−3.78873	+	16.5995i	−0.128821	+	0.564401i
$866$		0			0
$867$	27.5100	−	13.2481i	0.934290	−	0.449930i
$868$		0			0
$869$	23.6964			0.803844
$870$		0			0
$871$	2.40040			0.0813346
$872$		0			0
$873$	6.42755	−	3.09534i	0.217539	−	0.104761i
$874$		0			0
$875$	10.4751	−	45.8946i	0.354124	−	1.55152i
$876$		0			0
$877$	36.7338	−	17.6901i	1.24041	−	0.597351i	0.305487	−	0.952196i	$-0.401181\pi$
$877$	36.7338	−	17.6901i	1.24041	−	0.597351i	0.934925	+	0.354846i	$0.115467\pi$
$878$		0			0
$879$	−19.6080	+	24.5876i	−0.661361	+	0.829320i
$880$		0			0
$881$	−18.6816	−	23.4260i	−0.629400	−	0.789243i	0.360233	−	0.932862i	$-0.382697\pi$
$881$	−18.6816	−	23.4260i	−0.629400	−	0.789243i	−0.989633	+	0.143620i	$0.954126\pi$
$882$		0			0
$883$	−15.8437	−	19.8674i	−0.533184	−	0.668591i	0.440166	−	0.897916i	$-0.354919\pi$
$883$	−15.8437	−	19.8674i	−0.533184	−	0.668591i	−0.973350	+	0.229325i	$0.926348\pi$
$884$		0			0
$885$	−3.60220	−	15.7823i	−0.121087	−	0.530515i
$886$		0			0
$887$	−14.8245			−0.497759			−0.248879	−	0.968534i	$-0.580062\pi$
$887$	−14.8245			−0.497759			−0.248879	+	0.968534i	$0.580062\pi$
$888$		0			0
$889$	−39.7346	−	19.1352i	−1.33266	−	0.641774i
$890$		0			0
$891$	−14.1083	+	17.6912i	−0.472646	+	0.592679i
$892$		0			0
$893$	7.90961	+	34.6543i	0.264685	+	1.15966i
$894$		0			0
$895$	−27.1728	−	13.0857i	−0.908285	−	0.437407i
$896$		0			0
$897$	−4.55636	+	19.9627i	−0.152132	+	0.666535i
$898$		0			0
$899$	−13.5592	+	54.8131i	−0.452226	+	1.82812i
$900$		0			0
$901$	1.11739	−	4.89559i	0.0372256	−	0.163096i
$902$		0			0
$903$	40.2437	+	19.3804i	1.33923	+	0.644938i
$904$		0			0
$905$	2.25199	+	9.86659i	0.0748585	+	0.327977i
$906$		0			0
$907$	10.2633	−	12.8697i	0.340786	−	0.427332i	−0.581676	−	0.813421i	$-0.697603\pi$
$907$	10.2633	−	12.8697i	0.340786	−	0.427332i	0.922462	+	0.386089i	$0.126174\pi$
$908$		0			0
$909$	7.80686	+	3.75958i	0.258937	+	0.124698i
$910$		0			0
$911$	10.4862			0.347422			0.173711	−	0.984797i	$-0.444424\pi$
$911$	10.4862			0.347422			0.173711	+	0.984797i	$0.444424\pi$
$912$		0			0
$913$	6.02348	+	26.3906i	0.199348	+	0.873401i
$914$		0			0
$915$	9.04342	+	11.3401i	0.298966	+	0.374892i
$916$		0			0
$917$	8.97880	+	11.2591i	0.296506	+	0.371807i
$918$		0			0
$919$	−12.8073	+	16.0599i	−0.422474	+	0.529766i	−0.946830	−	0.321733i	$-0.895735\pi$
$919$	−12.8073	+	16.0599i	−0.422474	+	0.529766i	0.524356	+	0.851499i	$0.324306\pi$
$920$		0			0
$921$	−50.8008	+	24.4644i	−1.67394	+	0.806129i
$922$		0			0
$923$	4.14541	−	18.1622i	0.136448	−	0.597817i
$924$		0			0
$925$	−15.1404	+	7.29125i	−0.497815	+	0.239735i
$926$		0			0
$927$	−9.95073			−0.326825
$928$		0			0
$929$	−39.5714			−1.29830			−0.649148	−	0.760662i	$-0.724874\pi$
$929$	−39.5714			−1.29830			−0.649148	+	0.760662i	$0.724874\pi$
$930$		0			0
$931$	51.9751	−	25.0299i	1.70342	−	0.820322i
$932$		0			0
$933$	5.40299	−	23.6720i	0.176886	−	0.774988i
$934$		0			0
$935$	4.77988	−	2.30187i	0.156319	−	0.0752792i
$936$		0			0
$937$	−0.724114	+	0.908010i	−0.0236558	+	0.0296634i	−0.793519	−	0.608546i	$-0.791753\pi$
$937$	−0.724114	+	0.908010i	−0.0236558	+	0.0296634i	0.769863	+	0.638209i	$0.220325\pi$
$938$		0			0
$939$	−34.5945	−	43.3802i	−1.12895	−	1.41566i
$940$		0			0
$941$	19.1225	+	23.9789i	0.623377	+	0.781690i	0.988815	−	0.149146i	$-0.0476524\pi$
$941$	19.1225	+	23.9789i	0.623377	+	0.781690i	−0.365438	+	0.930836i	$0.619081\pi$
$942$		0			0
$943$	15.7271	+	68.9050i	0.512145	+	2.24385i
$944$		0			0
$945$	−11.0411			−0.359166
$946$		0			0
$947$	46.6013	+	22.4420i	1.51434	+	0.729267i	0.992324	−	0.123668i	$-0.0394659\pi$
$947$	46.6013	+	22.4420i	1.51434	+	0.729267i	0.522016	+	0.852936i	$0.325180\pi$
$948$		0			0
$949$	−4.06575	+	5.09829i	−0.131980	+	0.165498i
$950$		0			0
$951$	−12.3666	−	54.1814i	−0.401013	−	1.75695i
$952$		0			0
$953$	−43.0360	−	20.7250i	−1.39407	−	0.671349i	−0.422122	−	0.906539i	$-0.638715\pi$
$953$	−43.0360	−	20.7250i	−1.39407	−	0.671349i	−0.971950	+	0.235190i	$0.924429\pi$
$954$		0			0
$955$	−2.04088	+	8.94169i	−0.0660414	+	0.289346i
$956$		0			0
$957$	−22.8272	−	11.5067i	−0.737899	−	0.371958i
$958$		0			0
$959$	9.12413	−	39.9754i	0.294634	−	1.29087i
$960$		0			0
$961$	−71.1246	−	34.2518i	−2.29434	−	1.10490i
$962$		0			0
$963$	−7.11039	−	31.1526i	−0.229129	−	1.00388i
$964$		0			0
$965$	−13.1153	+	16.4461i	−0.422198	+	0.529420i
$966$		0			0
$967$	−32.7038	−	15.7493i	−1.05168	−	0.506464i	−0.173523	−	0.984830i	$-0.555515\pi$
$967$	−32.7038	−	15.7493i	−1.05168	−	0.506464i	−0.878161	+	0.478366i	$0.841229\pi$
$968$		0			0
$969$	21.9652			0.705625
$970$		0			0
$971$	11.1459	+	48.8332i	0.357687	+	1.56713i	0.758938	+	0.651163i	$0.225718\pi$
$971$	11.1459	+	48.8332i	0.357687	+	1.56713i	−0.401251	+	0.915968i	$0.631424\pi$
$972$		0			0
$973$	4.46846	+	5.60327i	0.143252	+	0.179633i
$974$		0			0
$975$	−5.09120	−	6.38416i	−0.163049	−	0.204457i
$976$		0			0
$977$	−11.4414	+	14.3471i	−0.366043	+	0.459004i	−0.930410	−	0.366521i	$-0.880549\pi$
$977$	−11.4414	+	14.3471i	−0.366043	+	0.459004i	0.564367	+	0.825524i	$0.309120\pi$
$978$		0			0
$979$	10.3172	−	4.96848i	0.329738	−	0.158793i
$980$		0			0
$981$	−1.71711	+	7.52316i	−0.0548232	+	0.240196i
$982$		0			0
$983$	−18.6006	+	8.95757i	−0.593267	+	0.285702i	−0.706327	−	0.707886i	$-0.749649\pi$
$983$	−18.6006	+	8.95757i	−0.593267	+	0.285702i	0.113060	+	0.993588i	$0.463935\pi$
$984$		0			0
$985$	2.89648			0.0922896
$986$		0			0
$987$	67.1158			2.13632
$988$		0			0
$989$	33.1727	−	15.9752i	1.05483	−	0.507980i
$990$		0			0
$991$	5.78698	−	25.3544i	0.183829	−	0.805409i	−0.795955	−	0.605355i	$-0.793031\pi$
$991$	5.78698	−	25.3544i	0.183829	−	0.805409i	0.979785	−	0.200054i	$-0.0641118\pi$
$992$		0			0
$993$	68.0560	−	32.7740i	2.15969	−	1.04005i
$994$		0			0
$995$	4.36116	−	5.46872i	0.138258	−	0.173370i
$996$		0			0
$997$	−1.14766	−	1.43911i	−0.0363466	−	0.0455772i	0.763326	−	0.646014i	$-0.223565\pi$
$997$	−1.14766	−	1.43911i	−0.0363466	−	0.0455772i	−0.799673	+	0.600436i	$0.794994\pi$
$998$		0			0
$999$	6.31296	+	7.91620i	0.199733	+	0.250457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.g.b.25.1	✓	12
3.2	odd	2		1044.2.u.c.721.1		12
4.3	odd	2		464.2.u.g.257.2		12
29.6	even	14		3364.2.a.p.1.1		6
29.7	even	7	inner	116.2.g.b.65.1	yes	12
29.14	odd	28		3364.2.c.j.1681.4		12
29.15	odd	28		3364.2.c.j.1681.9		12
29.23	even	7		3364.2.a.m.1.6		6
87.65	odd	14		1044.2.u.c.181.1		12
116.7	odd	14		464.2.u.g.65.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.g.b.25.1	✓	12	1.1	even	1	trivial
116.2.g.b.65.1	yes	12	29.7	even	7	inner
464.2.u.g.65.2		12	116.7	odd	14
464.2.u.g.257.2		12	4.3	odd	2
1044.2.u.c.181.1		12	87.65	odd	14
1044.2.u.c.721.1		12	3.2	odd	2
3364.2.a.m.1.6		6	29.23	even	7
3364.2.a.p.1.1		6	29.6	even	14
3364.2.c.j.1681.4		12	29.14	odd	28
3364.2.c.j.1681.9		12	29.15	odd	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.04546 + 0.985042i) q^{3} +(-0.299629 + 1.31276i) q^{5} +(-3.84740 + 1.85281i) q^{7} +(1.34313 - 1.68423i) q^{9} +(1.30367 + 1.63475i) q^{11} +(0.703677 + 0.882383i) q^{13} +(-0.680245 - 2.98035i) q^{15} -1.88433 q^{17} +(4.62603 + 2.22778i) q^{19} +(6.04461 - 7.57970i) q^{21} +(-1.77825 - 7.79102i) q^{23} +(2.87128 + 1.38274i) q^{25} +(0.427279 - 1.87203i) q^{27} +(5.38428 + 0.0974899i) q^{29} +(-2.33321 + 10.2224i) q^{31} +(-4.27690 - 2.05965i) q^{33} +(-1.27950 - 5.60587i) q^{35} +(-3.28770 + 4.12265i) q^{37} +(-2.30853 - 1.11173i) q^{39} -8.84415 q^{41} +(1.02523 + 4.49182i) q^{43} +(1.80856 + 2.26786i) q^{45} +(4.31634 + 5.41252i) q^{47} +(7.00514 - 8.78417i) q^{49} +(3.85432 - 1.85614i) q^{51} +(-0.592990 + 2.59806i) q^{53} +(-2.53665 + 1.22159i) q^{55} -11.6568 q^{57} +5.29544 q^{59} +(-4.27483 + 2.05865i) q^{61} +(-2.04700 + 8.96849i) q^{63} +(-1.36920 + 0.659372i) q^{65} +(1.32608 - 1.66285i) q^{67} +(11.3118 + 14.1846i) q^{69} +(-10.2916 - 12.9052i) q^{71} +(1.28570 + 5.63301i) q^{73} -7.23514 q^{75} +(-8.04461 - 3.87408i) q^{77} +(7.06600 - 8.86048i) q^{79} +(2.40812 + 10.5507i) q^{81} +(11.6640 + 5.61710i) q^{83} +(0.564599 - 2.47367i) q^{85} +(-11.1094 + 5.10433i) q^{87} +(1.21866 - 5.33931i) q^{89} +(-4.34221 - 2.09110i) q^{91} +(-5.29706 - 23.2079i) q^{93} +(-4.31063 + 5.40536i) q^{95} +(2.98370 + 1.43688i) q^{97} +4.50430 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9} + 3 q^{11} - 21 q^{13} + 29 q^{15} - 10 q^{17} + 17 q^{19} + 3 q^{21} - 19 q^{23} - 3 q^{25} + 9 q^{27} - 5 q^{29} - 27 q^{31} - 47 q^{33} + 27 q^{35} - 3 q^{37}+ \cdots - 16 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9 + 3 * q^11 - 21 * q^13 + 29 * q^15 - 10 * q^17 + 17 * q^19 + 3 * q^21 - 19 * q^23 - 3 * q^25 + 9 * q^27 - 5 * q^29 - 27 * q^31 - 47 * q^33 + 27 * q^35 - 3 * q^37 - 37 * q^39 - 2 * q^41 - 9 * q^43 + 22 * q^45 + 19 * q^47 + 17 * q^49 + 2 * q^51 + 22 * q^53 + 49 * q^55 + 30 * q^57 + 36 * q^59 - 33 * q^61 + 9 * q^63 + 38 * q^65 - 3 * q^67 + 47 * q^69 - 35 * q^71 + 34 * q^73 - 44 * q^75 - 27 * q^77 - 19 * q^79 - 39 * q^81 - q^83 - 34 * q^85 - 25 * q^87 - 11 * q^89 - 23 * q^91 + 7 * q^93 - 105 * q^95 + 38 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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