LMFDB - Embedded newform 668.2.e.a.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			9.4
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.198520 - 1.48975i) q^{3} +(-0.0282706 - 0.0125015i) q^{5} +(2.06702 - 4.44493i) q^{7} +(0.715369 - 0.194103i) q^{9} +O(q^{10})$	\(q+(-0.198520 - 1.48975i) q^{3} +(-0.0282706 - 0.0125015i) q^{5} +(2.06702 - 4.44493i) q^{7} +(0.715369 - 0.194103i) q^{9} +(1.41544 - 1.81482i) q^{11} +(-2.91156 + 5.68762i) q^{13} +(-0.0130118 + 0.0445980i) q^{15} +(6.97762 + 0.529224i) q^{17} +(0.209281 - 0.314820i) q^{19} +(-7.03218 - 2.19693i) q^{21} +(-8.13282 - 3.23426i) q^{23} +(-3.36372 - 3.69809i) q^{25} +(-2.17630 - 5.18453i) q^{27} +(-5.14171 + 2.04476i) q^{29} +(3.60376 - 0.832792i) q^{31} +(-2.98462 - 1.74837i) q^{33} +(-0.114004 + 0.0998202i) q^{35} +(5.79065 + 1.57119i) q^{37} +(9.05114 + 3.20839i) q^{39} +(7.28078 - 3.55486i) q^{41} +(-0.603945 + 6.36336i) q^{43} +(-0.0226505 - 0.00345578i) q^{45} +(-0.0246519 - 1.30244i) q^{47} +(-10.9741 - 13.0227i) q^{49} +(-0.596785 - 10.5000i) q^{51} +(-0.848005 - 4.93044i) q^{53} +(-0.0627033 + 0.0336110i) q^{55} +(-0.510550 - 0.249278i) q^{57} +(-1.08146 + 0.0820246i) q^{59} +(-6.52529 + 6.64997i) q^{61} +(0.615906 - 3.58098i) q^{63} +(0.153416 - 0.124394i) q^{65} +(7.57019 - 3.34760i) q^{67} +(-3.20372 + 12.7579i) q^{69} +(6.58962 - 0.751495i) q^{71} +(-4.31633 + 3.23696i) q^{73} +(-4.84146 + 5.74525i) q^{75} +(-5.14102 - 10.0428i) q^{77} +(-4.94963 + 13.1666i) q^{79} +(-5.37288 + 3.14739i) q^{81} +(-0.616826 + 0.855781i) q^{83} +(-0.190646 - 0.102192i) q^{85} +(4.06691 + 7.25394i) q^{87} +(-0.357183 - 1.22424i) q^{89} +(19.2628 + 24.6981i) q^{91} +(-1.95607 - 5.20338i) q^{93} +(-0.00985223 + 0.00628384i) q^{95} +(5.87162 + 1.35687i) q^{97} +(0.660298 - 1.57301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

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
$3$	−0.198520	−	1.48975i	−0.114616	−	0.860108i	−0.950396	−	0.311043i	$-0.899322\pi$
$3$	−0.198520	−	1.48975i	−0.114616	−	0.860108i	0.835780	−	0.549064i	$-0.185016\pi$
$4$		0			0
$5$	−0.0282706	−	0.0125015i	−0.0126430	−	0.00559085i	0.398099	−	0.917342i	$-0.369670\pi$
$5$	−0.0282706	−	0.0125015i	−0.0126430	−	0.00559085i	−0.410742	+	0.911752i	$0.634730\pi$
$6$		0			0
$7$	2.06702	−	4.44493i	0.781259	−	1.68003i	0.0491957	−	0.998789i	$-0.484334\pi$
$7$	2.06702	−	4.44493i	0.781259	−	1.68003i	0.732064	−	0.681236i	$-0.238557\pi$
$8$		0			0
$9$	0.715369	−	0.194103i	0.238456	−	0.0647010i
$10$		0			0
$11$	1.41544	−	1.81482i	0.426770	−	0.547189i	−0.526157	−	0.850387i	$-0.676368\pi$
$11$	1.41544	−	1.81482i	0.426770	−	0.547189i	0.952928	+	0.303198i	$0.0980544\pi$
$12$		0			0
$13$	−2.91156	+	5.68762i	−0.807521	+	1.57746i	0.00886860	+	0.999961i	$0.497177\pi$
$13$	−2.91156	+	5.68762i	−0.807521	+	1.57746i	−0.816390	+	0.577501i	$0.804028\pi$
$14$		0			0
$15$	−0.0130118	+	0.0445980i	−0.00335964	+	0.0115152i
$16$		0			0
$17$	6.97762	+	0.529224i	1.69232	+	0.128356i	0.886172	−	0.463357i	$-0.153355\pi$
$17$	6.97762	+	0.529224i	1.69232	+	0.128356i	0.806149	+	0.591713i	$0.201548\pi$
$18$		0			0
$19$	0.209281	−	0.314820i	0.0480123	−	0.0722247i	−0.807992	−	0.589193i	$-0.799446\pi$
$19$	0.209281	−	0.314820i	0.0480123	−	0.0722247i	0.856004	+	0.516969i	$0.172940\pi$
$20$		0			0
$21$	−7.03218	−	2.19693i	−1.53455	−	0.479410i
$22$		0			0
$23$	−8.13282	−	3.23426i	−1.69581	−	0.674390i	−0.696732	−	0.717331i	$-0.745364\pi$
$23$	−8.13282	−	3.23426i	−1.69581	−	0.674390i	−0.999078	+	0.0429406i	$0.986327\pi$
$24$		0			0
$25$	−3.36372	−	3.69809i	−0.672744	−	0.739617i
$26$		0			0
$27$	−2.17630	−	5.18453i	−0.418828	−	0.997762i
$28$		0			0
$29$	−5.14171	+	2.04476i	−0.954792	+	0.379702i	−0.794430	−	0.607356i	$-0.792230\pi$
$29$	−5.14171	+	2.04476i	−0.954792	+	0.379702i	−0.160362	+	0.987058i	$0.551266\pi$
$30$		0			0
$31$	3.60376	−	0.832792i	0.647255	−	0.149574i	0.111255	−	0.993792i	$-0.464513\pi$
$31$	3.60376	−	0.832792i	0.647255	−	0.149574i	0.536000	+	0.844218i	$0.319935\pi$
$32$		0			0
$33$	−2.98462	−	1.74837i	−0.519556	−	0.304352i
$34$		0			0
$35$	−0.114004	+	0.0998202i	−0.0192702	+	0.0168727i
$36$		0			0
$37$	5.79065	+	1.57119i	0.951978	+	0.258303i	0.703789	−	0.710409i	$-0.251490\pi$
$37$	5.79065	+	1.57119i	0.951978	+	0.258303i	0.248189	+	0.968712i	$0.420165\pi$
$38$		0			0
$39$	9.05114	+	3.20839i	1.44934	+	0.513753i
$40$		0			0
$41$	7.28078	−	3.55486i	1.13707	−	0.555177i	0.228761	−	0.973483i	$-0.426533\pi$
$41$	7.28078	−	3.55486i	1.13707	−	0.555177i	0.908306	+	0.418306i	$0.137376\pi$
$42$		0			0
$43$	−0.603945	+	6.36336i	−0.0921007	+	0.970403i	0.823232	+	0.567705i	$0.192169\pi$
$43$	−0.603945	+	6.36336i	−0.0921007	+	0.970403i	−0.915333	+	0.402698i	$0.868072\pi$
$44$		0			0
$45$	−0.0226505	−	0.00345578i	−0.00337654	−	0.000515157i
$46$		0			0
$47$	−0.0246519	−	1.30244i	−0.00359585	−	0.189980i	−0.997096	−	0.0761514i	$-0.975737\pi$
$47$	−0.0246519	−	1.30244i	−0.00359585	−	0.189980i	0.993500	−	0.113828i	$-0.0363114\pi$
$48$		0			0
$49$	−10.9741	−	13.0227i	−1.56772	−	1.86038i
$50$		0			0
$51$	−0.596785	−	10.5000i	−0.0835666	−	1.47029i
$52$		0			0
$53$	−0.848005	−	4.93044i	−0.116483	−	0.677248i	−0.983769	−	0.179439i	$-0.942572\pi$
$53$	−0.848005	−	4.93044i	−0.116483	−	0.677248i	0.867287	−	0.497809i	$-0.165862\pi$
$54$		0			0
$55$	−0.0627033	+	0.0336110i	−0.00845492	+	0.00453211i
$56$		0			0
$57$	−0.510550	−	0.249278i	−0.0676240	−	0.0330176i
$58$		0			0
$59$	−1.08146	+	0.0820246i	−0.140794	+	0.0106787i	−0.145837	−	0.989309i	$-0.546588\pi$
$59$	−1.08146	+	0.0820246i	−0.140794	+	0.0106787i	0.00504280	+	0.999987i	$0.498395\pi$
$60$		0			0
$61$	−6.52529	+	6.64997i	−0.835478	+	0.851441i	−0.990647	−	0.136447i	$-0.956432\pi$
$61$	−6.52529	+	6.64997i	−0.835478	+	0.851441i	0.155170	+	0.987888i	$0.450408\pi$
$62$		0			0
$63$	0.615906	−	3.58098i	0.0775969	−	0.451161i
$64$		0			0
$65$	0.153416	−	0.124394i	0.0190289	−	0.0154291i
$66$		0			0
$67$	7.57019	−	3.34760i	0.924845	−	0.408974i	0.113498	−	0.993538i	$-0.463795\pi$
$67$	7.57019	−	3.34760i	0.924845	−	0.408974i	0.811348	+	0.584564i	$0.198734\pi$
$68$		0			0
$69$	−3.20372	+	12.7579i	−0.385682	+	1.53587i
$70$		0			0
$71$	6.58962	−	0.751495i	0.782044	−	0.0891860i	0.286858	−	0.957973i	$-0.407389\pi$
$71$	6.58962	−	0.751495i	0.782044	−	0.0891860i	0.495186	+	0.868787i	$0.335100\pi$
$72$		0			0
$73$	−4.31633	+	3.23696i	−0.505189	+	0.378858i	−0.821871	−	0.569674i	$-0.807070\pi$
$73$	−4.31633	+	3.23696i	−0.505189	+	0.378858i	0.316682	+	0.948532i	$0.397431\pi$
$74$		0			0
$75$	−4.84146	+	5.74525i	−0.559043	+	0.663404i
$76$		0			0
$77$	−5.14102	−	10.0428i	−0.585873	−	1.14448i
$78$		0			0
$79$	−4.94963	+	13.1666i	−0.556877	+	1.48136i	0.293902	+	0.955835i	$0.405046\pi$
$79$	−4.94963	+	13.1666i	−0.556877	+	1.48136i	−0.850779	+	0.525523i	$0.823870\pi$
$80$		0			0
$81$	−5.37288	+	3.14739i	−0.596986	+	0.349710i
$82$		0			0
$83$	−0.616826	+	0.855781i	−0.0677054	+	0.0939342i	−0.843728	−	0.536771i	$-0.819644\pi$
$83$	−0.616826	+	0.855781i	−0.0677054	+	0.0939342i	0.776023	+	0.630705i	$0.217234\pi$
$84$		0			0
$85$	−0.190646	−	0.102192i	−0.0206784	−	0.0110843i
$86$		0			0
$87$	4.06691	+	7.25394i	0.436019	+	0.777704i
$88$		0			0
$89$	−0.357183	−	1.22424i	−0.0378613	−	0.129769i	0.938850	−	0.344326i	$-0.111892\pi$
$89$	−0.357183	−	1.22424i	−0.0378613	−	0.129769i	−0.976712	+	0.214556i	$0.931169\pi$
$90$		0			0
$91$	19.2628	+	24.6981i	2.01929	+	2.58906i
$92$		0			0
$93$	−1.95607	−	5.20338i	−0.202835	−	0.539565i
$94$		0			0
$95$	−0.00985223	+	0.00628384i	−0.00101082	+	0.000644709i
$96$		0			0
$97$	5.87162	+	1.35687i	0.596173	+	0.137769i	0.512446	−	0.858719i	$-0.328739\pi$
$97$	5.87162	+	1.35687i	0.596173	+	0.137769i	0.0837268	+	0.996489i	$0.473318\pi$
$98$		0			0
$99$	0.660298	−	1.57301i	0.0663624	−	0.158093i
$100$		0			0
$101$	−1.04374	−	10.9972i	−0.103856	−	1.09427i	−0.883624	−	0.468197i	$-0.844904\pi$
$101$	−1.04374	−	10.9972i	−0.103856	−	1.09427i	0.779768	−	0.626069i	$-0.215337\pi$
$102$		0			0
$103$	0.308695	−	0.213741i	0.0304166	−	0.0210605i	−0.553957	−	0.832546i	$-0.686883\pi$
$103$	0.308695	−	0.213741i	0.0304166	−	0.0210605i	0.584373	+	0.811485i	$0.301340\pi$
$104$		0			0
$105$	0.171339	+	0.150022i	0.0167210	+	0.0146406i
$106$		0			0
$107$	−2.57701	−	1.78433i	−0.249129	−	0.172497i	0.438126	−	0.898914i	$-0.355642\pi$
$107$	−2.57701	−	1.78433i	−0.249129	−	0.172497i	−0.687255	+	0.726416i	$0.741185\pi$
$108$		0			0
$109$	9.31293	+	5.93988i	0.892017	+	0.568937i	0.902347	−	0.431010i	$-0.141843\pi$
$109$	9.31293	+	5.93988i	0.892017	+	0.568937i	−0.0103304	+	0.999947i	$0.503288\pi$
$110$		0			0
$111$	1.19113	−	8.93854i	0.113057	−	0.848409i
$112$		0			0
$113$	−10.1344	+	16.5731i	−0.953368	+	1.55906i	−0.130033	+	0.991510i	$0.541508\pi$
$113$	−10.1344	+	16.5731i	−0.953368	+	1.55906i	−0.823335	+	0.567555i	$0.807889\pi$
$114$		0			0
$115$	0.189487	+	0.193107i	0.0176697	+	0.0180073i
$116$		0			0
$117$	−0.978855	+	4.63389i	−0.0904951	+	0.428403i
$118$		0			0
$119$	16.7752	−	29.9211i	1.53778	−	2.74286i
$120$		0			0
$121$	1.38898	+	5.53123i	0.126271	+	0.502839i
$122$		0			0
$123$	−6.74124	−	10.1408i	−0.607837	−	0.914368i
$124$		0			0
$125$	0.0977350	+	0.293226i	0.00874168	+	0.0262269i
$126$		0			0
$127$	−3.07736	−	0.350949i	−0.273072	−	0.0311417i	−0.0243031	−	0.999705i	$-0.507737\pi$
$127$	−3.07736	−	0.350949i	−0.273072	−	0.0311417i	−0.248769	+	0.968563i	$0.580026\pi$
$128$		0			0
$129$	9.59971	−	0.363528i	0.845207	−	0.0320068i
$130$		0			0
$131$	−0.636760	+	11.2033i	−0.0556340	+	0.978836i	0.842384	+	0.538878i	$0.181151\pi$
$131$	−0.636760	+	11.2033i	−0.0556340	+	0.978836i	−0.898018	+	0.439959i	$0.854993\pi$
$132$		0			0
$133$	−0.966767	−	1.58098i	−0.0838293	−	0.137088i
$134$		0			0
$135$	−0.00328916	+	0.173777i	−0.000283086	+	0.0149563i
$136$		0			0
$137$	17.0189	−	6.03274i	1.45402	−	0.515412i	0.514377	−	0.857564i	$-0.328023\pi$
$137$	17.0189	−	6.03274i	1.45402	−	0.515412i	0.939644	+	0.342152i	$0.111156\pi$
$138$		0			0
$139$	12.1293	+	11.4595i	1.02880	+	0.971982i	0.999619	−	0.0275918i	$-0.00878386\pi$
$139$	12.1293	+	11.4595i	1.02880	+	0.971982i	0.0291763	+	0.999574i	$0.490712\pi$
$140$		0			0
$141$	−1.93541	+	0.295285i	−0.162991	+	0.0248675i
$142$		0			0
$143$	6.20089	+	13.3344i	0.518544	+	1.11508i
$144$		0			0
$145$	0.170922	+	0.00647258i	0.0141943	+	0.000537518i
$146$		0			0
$147$	−17.2219	+	18.9339i	−1.42044	+	1.56164i
$148$		0			0
$149$	11.2464	+	9.11887i	0.921337	+	0.747047i	0.967760	−	0.251875i	$-0.0810472\pi$
$149$	11.2464	+	9.11887i	0.921337	+	0.747047i	−0.0464226	+	0.998922i	$0.514782\pi$
$150$		0			0
$151$	18.3831	+	13.7861i	1.49600	+	1.12190i	0.960825	+	0.277156i	$0.0893920\pi$
$151$	18.3831	+	13.7861i	1.49600	+	1.12190i	0.535173	+	0.844743i	$0.320247\pi$
$152$		0			0
$153$	5.09430	−	0.975786i	0.411849	−	0.0788876i
$154$		0			0
$155$	−0.112292	−	0.0215089i	−0.00901950	−	0.00172764i
$156$		0			0
$157$	1.59874	+	7.56842i	0.127593	+	0.604026i	0.994427	+	0.105428i	$0.0336214\pi$
$157$	1.59874	+	7.56842i	0.127593	+	0.604026i	−0.866834	+	0.498598i	$0.833849\pi$
$158$		0			0
$159$	−7.17678	+	2.24211i	−0.569156	+	0.177811i
$160$		0			0
$161$	−31.1868	+	29.4645i	−2.45786	+	2.32213i
$162$		0			0
$163$	4.56759	−	13.7037i	0.357761	−	1.07336i	−0.603416	−	0.797427i	$-0.706194\pi$
$163$	4.56759	−	13.7037i	0.357761	−	1.07336i	0.961177	−	0.275933i	$-0.0889866\pi$
$164$		0			0
$165$	0.0625199	+	0.0867398i	0.00486717	+	0.00675269i
$166$		0			0
$167$	−8.49817	−	9.73556i	−0.657608	−	0.753360i
$167$	−8.49817	−	9.73556i	−0.657608	−	0.753360i
$168$		0			0
$169$	−16.2705	−	22.5736i	−1.25158	−	1.73643i
$170$		0			0
$171$	0.0886053	−	0.265835i	0.00677581	−	0.0203289i
$172$		0			0
$173$	12.6495	−	11.9509i	0.961720	−	0.908611i	−0.0341487	−	0.999417i	$-0.510872\pi$
$173$	12.6495	−	11.9509i	0.961720	−	0.908611i	0.995869	+	0.0908058i	$0.0289443\pi$
$174$		0			0
$175$	−23.3906	+	7.30749i	−1.76816	+	0.552394i
$176$		0			0
$177$	0.336888	+	1.59483i	0.0253221	+	0.119874i
$178$		0			0
$179$	15.6538	+	2.99840i	1.17002	+	0.224111i	0.736120	−	0.676851i	$-0.236656\pi$
$179$	15.6538	+	2.99840i	1.17002	+	0.224111i	0.433898	+	0.900962i	$0.357138\pi$
$180$		0			0
$181$	24.1431	−	4.62449i	1.79454	−	0.343735i	0.820770	−	0.571259i	$-0.193545\pi$
$181$	24.1431	−	4.62449i	1.79454	−	0.343735i	0.973773	+	0.227524i	$0.0730629\pi$
$182$		0			0
$183$	11.2022	+	8.40090i	0.828089	+	0.621012i
$184$		0			0
$185$	−0.144063	−	0.116811i	−0.0105917	−	0.00858809i
$186$		0			0
$187$	10.8368	−	11.9140i	0.792467	−	0.871241i
$188$		0			0
$189$	−27.5433	−	1.04303i	−2.00348	−	0.0758690i
$190$		0			0
$191$	−6.49496	−	13.9668i	−0.469959	−	1.01060i	−0.987887	−	0.155178i	$-0.950405\pi$
$191$	−6.49496	−	13.9668i	−0.469959	−	1.01060i	0.517928	−	0.855424i	$-0.326704\pi$
$192$		0			0
$193$	2.70297	−	0.412392i	0.194564	−	0.0296846i	−0.0528100	−	0.998605i	$-0.516818\pi$
$193$	2.70297	−	0.412392i	0.194564	−	0.0296846i	0.247374	+	0.968920i	$0.420432\pi$
$194$		0			0
$195$	−0.215772	−	0.203856i	−0.0154517	−	0.0145984i
$196$		0			0
$197$	−15.2052	+	5.38982i	−1.08332	+	0.384009i	−0.815084	−	0.579343i	$-0.803309\pi$
$197$	−15.2052	+	5.38982i	−1.08332	+	0.384009i	−0.268239	+	0.963353i	$0.586442\pi$
$198$		0			0
$199$	−0.326444	+	17.2471i	−0.0231410	+	1.22261i	0.779598	+	0.626281i	$0.215424\pi$
$199$	−0.326444	+	17.2471i	−0.0231410	+	1.22261i	−0.802739	+	0.596331i	$0.796625\pi$
$200$		0			0
$201$	−6.48992	−	10.6131i	−0.457764	−	0.748592i
$202$		0			0
$203$	−1.53920	+	27.0811i	−0.108031	+	1.90072i
$204$		0			0
$205$	−0.250274	+	0.00947751i	−0.0174799	+	0.000661938i
$206$		0			0
$207$	−6.44575	−	0.735087i	−0.448010	−	0.0510921i
$208$		0			0
$209$	−0.275119	−	0.825415i	−0.0190304	−	0.0570951i
$210$		0			0
$211$	−0.228415	−	0.343604i	−0.0157247	−	0.0236546i	0.824835	−	0.565373i	$-0.191268\pi$
$211$	−0.228415	−	0.343604i	−0.0157247	−	0.0236546i	−0.840560	+	0.541719i	$0.817774\pi$
$212$		0			0
$213$	−2.42771	−	9.66770i	−0.166344	−	0.662420i
$214$		0			0
$215$	0.0966256	−	0.172346i	0.00658981	−	0.0117539i
$216$		0			0
$217$	3.74734	−	17.7399i	0.254386	−	1.20426i
$218$		0			0
$219$	5.67915	+	5.78766i	0.383761	+	0.391094i
$220$		0			0
$221$	−23.3258	+	38.1452i	−1.56906	+	2.56592i
$222$		0			0
$223$	2.01049	−	15.0873i	0.134632	−	1.01032i	−0.785542	−	0.618808i	$-0.787616\pi$
$223$	2.01049	−	15.0873i	0.134632	−	1.01032i	0.920174	−	0.391509i	$-0.128047\pi$
$224$		0			0
$225$	−3.12411	−	1.99259i	−0.208274	−	0.132839i
$226$		0			0
$227$	−2.61858	−	1.81311i	−0.173801	−	0.120340i	0.479173	−	0.877721i	$-0.340937\pi$
$227$	−2.61858	−	1.81311i	−0.173801	−	0.120340i	−0.652974	+	0.757380i	$0.726479\pi$
$228$		0			0
$229$	3.91192	+	3.42521i	0.258507	+	0.226344i	0.778212	−	0.628002i	$-0.216127\pi$
$229$	3.91192	+	3.42521i	0.258507	+	0.226344i	−0.519705	+	0.854346i	$0.673958\pi$
$230$		0			0
$231$	−13.9406	+	9.65253i	−0.917227	+	0.635090i
$232$		0			0
$233$	0.553791	+	5.83493i	0.0362801	+	0.382259i	0.995147	+	0.0984019i	$0.0313731\pi$
$233$	0.553791	+	5.83493i	0.0362801	+	0.382259i	−0.958867	+	0.283857i	$0.908386\pi$
$234$		0			0
$235$	−0.0155855	+	0.0371289i	−0.00101669	+	0.00242202i
$236$		0			0
$237$	20.5975	+	4.75988i	1.33795	+	0.309187i
$238$		0			0
$239$	−8.01696	+	5.11329i	−0.518574	+	0.330751i	−0.770969	−	0.636873i	$-0.780228\pi$
$239$	−8.01696	+	5.11329i	−0.518574	+	0.330751i	0.252395	+	0.967624i	$0.418782\pi$
$240$		0			0
$241$	1.60271	+	4.26339i	0.103239	+	0.274629i	0.977538	−	0.210760i	$-0.0675938\pi$
$241$	1.60271	+	4.26339i	0.103239	+	0.274629i	−0.874298	+	0.485389i	$0.838678\pi$
$242$		0			0
$243$	−4.61854	−	5.92172i	−0.296279	−	0.379879i
$244$		0			0
$245$	0.147441	+	0.505351i	0.00941963	+	0.0322857i
$246$		0			0
$247$	1.18125	+	2.10693i	0.0751608	+	0.134060i
$248$		0			0
$249$	1.39735	+	0.749027i	0.0885536	+	0.0474676i
$250$		0			0
$251$	−2.10514	+	2.92066i	−0.132875	+	0.184350i	−0.872420	−	0.488757i	$-0.837450\pi$
$251$	−2.10514	+	2.92066i	−0.132875	+	0.184350i	0.739545	+	0.673107i	$0.235041\pi$
$252$		0			0
$253$	−17.3811	+	10.1817i	−1.09274	+	0.640119i
$254$		0			0
$255$	−0.114394	+	0.304302i	−0.00716363	+	0.0190561i
$256$		0			0
$257$	−10.8116	−	21.1200i	−0.674407	−	1.31743i	−0.935915	−	0.352227i	$-0.885425\pi$
$257$	−10.8116	−	21.1200i	−0.674407	−	1.31743i	0.261508	−	0.965201i	$-0.415780\pi$
$258$		0			0
$259$	18.9532	−	22.4914i	1.17770	−	1.39755i
$260$		0			0
$261$	−3.28133	+	2.46078i	−0.203109	+	0.152318i
$262$		0			0
$263$	2.56867	−	0.292937i	0.158391	−	0.0180632i	−0.0337516	−	0.999430i	$-0.510746\pi$
$263$	2.56867	−	0.292937i	0.158391	−	0.0180632i	0.192143	+	0.981367i	$0.438456\pi$
$264$		0			0
$265$	−0.0376644	+	0.149988i	−0.00231370	+	0.00921370i
$266$		0			0
$267$	−1.75291	+	0.775150i	−0.107276	+	0.0474384i
$268$		0			0
$269$	−4.14893	+	3.36408i	−0.252965	+	0.205111i	−0.747887	−	0.663826i	$-0.768932\pi$
$269$	−4.14893	+	3.36408i	−0.252965	+	0.205111i	0.494922	+	0.868937i	$0.335197\pi$
$270$		0			0
$271$	−2.48639	+	14.4563i	−0.151037	+	0.878156i	0.806796	+	0.590830i	$0.201200\pi$
$271$	−2.48639	+	14.4563i	−0.151037	+	0.878156i	−0.957833	+	0.287325i	$0.907234\pi$
$272$		0			0
$273$	32.9699	−	33.5999i	1.99543	−	2.03356i
$274$		0			0
$275$	−11.4725	+	0.870143i	−0.691818	+	0.0524716i
$276$		0			0
$277$	−12.7916	−	6.24556i	−0.768575	−	0.375259i	0.0123179	−	0.999924i	$-0.496079\pi$
$277$	−12.7916	−	6.24556i	−0.768575	−	0.375259i	−0.780893	+	0.624665i	$0.785236\pi$
$278$		0			0
$279$	2.41637	−	1.29525i	0.144664	−	0.0775449i
$280$		0			0
$281$	−2.75347	−	16.0091i	−0.164258	−	0.955023i	−0.944249	−	0.329232i	$-0.893210\pi$
$281$	−2.75347	−	16.0091i	−0.164258	−	0.955023i	0.779991	−	0.625791i	$-0.215224\pi$
$282$		0			0
$283$	−0.143015	−	2.51624i	−0.00850135	−	0.149575i	−0.999834	−	0.0182015i	$-0.994206\pi$
$283$	−0.143015	−	2.51624i	−0.00850135	−	0.149575i	0.991333	−	0.131373i	$-0.0419386\pi$
$284$		0			0
$285$	0.0113172	+	0.0134299i	0.000670374	+	0.000795518i
$286$		0			0
$287$	−0.751622	−	39.7105i	−0.0443668	−	2.34404i
$288$		0			0
$289$	31.6015	+	4.82143i	1.85891	+	0.283614i
$290$		0			0
$291$	0.855765	−	9.01662i	0.0501658	−	0.528563i
$292$		0			0
$293$	18.6203	−	9.09141i	1.08781	−	0.531126i	0.194652	−	0.980872i	$-0.437642\pi$
$293$	18.6203	−	9.09141i	1.08781	−	0.531126i	0.893156	+	0.449746i	$0.148486\pi$
$294$		0			0
$295$	0.0315991	+	0.0112010i	0.00183977	+	0.000652150i
$296$		0			0
$297$	−12.4894	−	3.38878i	−0.724708	−	0.196637i
$298$		0			0
$299$	42.0744	−	36.8396i	2.43323	−	2.13049i
$300$		0			0
$301$	27.0363	+	15.8377i	1.55835	+	0.912868i
$302$		0			0
$303$	−16.1759	+	3.73809i	−0.929283	+	0.214748i
$304$		0			0
$305$	0.267609	−	0.106423i	0.0153232	−	0.00609375i
$306$		0			0
$307$	−2.16696	−	5.16228i	−0.123675	−	0.294627i	0.848377	−	0.529392i	$-0.177580\pi$
$307$	−2.16696	−	5.16228i	−0.123675	−	0.294627i	−0.972052	+	0.234765i	$0.924568\pi$
$308$		0			0
$309$	−0.379702	−	0.417446i	−0.0216005	−	0.0237477i
$310$		0			0
$311$	−9.81929	−	3.90494i	−0.556801	−	0.221429i	0.0741561	−	0.997247i	$-0.476374\pi$
$311$	−9.81929	−	3.90494i	−0.556801	−	0.221429i	−0.630957	+	0.775818i	$0.717338\pi$
$312$		0			0
$313$	−4.93567	−	1.54196i	−0.278981	−	0.0871567i	0.155506	−	0.987835i	$-0.450299\pi$
$313$	−4.93567	−	1.54196i	−0.278981	−	0.0871567i	−0.434487	+	0.900678i	$0.643070\pi$
$314$		0			0
$315$	−0.0621797	+	0.0935368i	−0.00350343	+	0.00527020i
$316$		0			0
$317$	−26.2675	−	1.99228i	−1.47533	−	0.111898i	−0.686779	−	0.726866i	$-0.740976\pi$
$317$	−26.2675	−	1.99228i	−1.47533	−	0.111898i	−0.788552	+	0.614969i	$0.789169\pi$
$318$		0			0
$319$	−3.56690	+	12.2255i	−0.199708	+	0.684497i
$320$		0			0
$321$	−2.14661	+	4.19333i	−0.119812	+	0.234049i
$322$		0			0
$323$	1.62689	−	2.08594i	0.0905226	−	0.116065i
$324$		0			0
$325$	30.8270	−	8.36437i	1.70997	−	0.463972i
$326$		0			0
$327$	7.00013	−	15.0531i	0.387108	−	0.832439i
$328$		0			0
$329$	−5.84019	−	2.58258i	−0.321980	−	0.142382i
$330$		0			0
$331$	−0.0221989	−	0.166587i	−0.00122016	−	0.00915644i	0.990617	−	0.136666i	$-0.0436389\pi$
$331$	−0.0221989	−	0.166587i	−0.00122016	−	0.00915644i	−0.991837	+	0.127510i	$0.959302\pi$
$332$		0			0
$333$	4.44743			0.243718
$334$		0			0
$335$	−0.255864			−0.0139793
$336$		0			0
$337$	−1.71530	−	12.8721i	−0.0934386	−	0.701189i	−0.973885	−	0.227043i	$-0.927094\pi$
$337$	−1.71530	−	12.8721i	−0.0934386	−	0.701189i	0.880446	−	0.474146i	$-0.157243\pi$
$338$		0			0
$339$	26.7016	+	11.8077i	1.45023	+	0.641306i
$340$		0			0
$341$	3.58953	−	7.71895i	0.194384	−	0.418004i
$342$		0			0
$343$	−47.4515	+	12.8752i	−2.56214	+	0.695193i
$344$		0			0
$345$	0.250065	−	0.320624i	0.0134630	−	0.0172618i
$346$		0			0
$347$	−8.76259	+	17.1174i	−0.470400	+	0.918909i	0.527205	+	0.849738i	$0.323240\pi$
$347$	−8.76259	+	17.1174i	−0.470400	+	0.918909i	−0.997605	+	0.0691707i	$0.977965\pi$
$348$		0			0
$349$	−6.84398	+	23.4577i	−0.366350	+	1.25566i	0.543037	+	0.839709i	$0.317274\pi$
$349$	−6.84398	+	23.4577i	−0.366350	+	1.25566i	−0.909387	+	0.415952i	$0.863448\pi$
$350$		0			0
$351$	35.8240	+	2.71711i	1.91215	+	0.145028i
$352$		0			0
$353$	7.53022	−	11.3277i	0.400793	−	0.602912i	−0.575909	−	0.817514i	$-0.695352\pi$
$353$	7.53022	−	11.3277i	0.400793	−	0.602912i	0.976702	+	0.214602i	$0.0688455\pi$
$354$		0			0
$355$	−0.195688	−	0.0611351i	−0.0103860	−	0.00324471i
$356$		0			0
$357$	−47.9052	−	19.0510i	−2.53541	−	1.00828i
$358$		0			0
$359$	13.4397	+	14.7757i	0.709322	+	0.779832i	0.983317	−	0.181900i	$-0.0582246\pi$
$359$	13.4397	+	14.7757i	0.709322	+	0.779832i	−0.273995	+	0.961731i	$0.588345\pi$
$360$		0			0
$361$	7.29864	+	17.3873i	0.384139	+	0.915123i
$362$		0			0
$363$	7.96441	−	3.16729i	0.418023	−	0.166240i
$364$		0			0
$365$	0.162492	−	0.0375503i	0.00850525	−	0.00196547i
$366$		0			0
$367$	−0.809045	−	0.473932i	−0.0422318	−	0.0247391i	0.484186	−	0.874965i	$-0.339116\pi$
$367$	−0.809045	−	0.473932i	−0.0422318	−	0.0247391i	−0.526418	+	0.850226i	$0.676465\pi$
$368$		0			0
$369$	4.51843	−	3.95626i	0.235220	−	0.205955i
$370$		0			0
$371$	−23.6683	−	6.42199i	−1.22880	−	0.333413i
$372$		0			0
$373$	6.90448	+	2.44745i	0.357500	+	0.126724i	0.506791	−	0.862069i	$-0.330832\pi$
$373$	6.90448	+	2.44745i	0.357500	+	0.126724i	−0.149291	+	0.988793i	$0.547699\pi$
$374$		0			0
$375$	0.417431	−	0.203812i	0.0215560	−	0.0105248i
$376$		0			0
$377$	3.34059	−	35.1975i	0.172049	−	1.81277i
$378$		0			0
$379$	−27.1672	−	4.14489i	−1.39548	−	0.212908i	−0.590899	−	0.806746i	$-0.701227\pi$
$379$	−27.1672	−	4.14489i	−1.39548	−	0.212908i	−0.804585	+	0.593837i	$0.797612\pi$
$380$		0			0
$381$	0.0880919	+	4.65417i	0.00451308	+	0.238440i
$382$		0			0
$383$	−6.61825	−	7.85373i	−0.338177	−	0.401307i	0.568808	−	0.822471i	$-0.307405\pi$
$383$	−6.61825	−	7.85373i	−0.338177	−	0.401307i	−0.906985	+	0.421164i	$0.861622\pi$
$384$		0			0
$385$	0.0197898	+	0.348187i	0.00100858	+	0.0177452i
$386$		0			0
$387$	0.803104	+	4.66938i	0.0408241	+	0.237358i
$388$		0			0
$389$	−30.7791	+	16.4986i	−1.56056	+	0.836512i	−0.560597	+	0.828089i	$0.689428\pi$
$389$	−30.7791	+	16.4986i	−1.56056	+	0.836512i	−0.999965	+	0.00842353i	$0.997319\pi$
$390$		0			0
$391$	−55.0361	−	26.8715i	−2.78329	−	1.35895i
$392$		0			0
$393$	16.8165	−	1.27546i	0.848281	−	0.0643387i
$394$		0			0
$395$	0.304532	−	0.310350i	0.0153227	−	0.0156154i
$396$		0			0
$397$	−4.73738	+	27.5439i	−0.237762	+	1.38239i	0.583628	+	0.812021i	$0.301633\pi$
$397$	−4.73738	+	27.5439i	−0.237762	+	1.38239i	−0.821390	+	0.570367i	$0.806801\pi$
$398$		0			0
$399$	−2.16334	+	1.75410i	−0.108302	+	0.0878147i
$400$		0			0
$401$	17.0728	−	7.54975i	0.852576	−	0.377016i	0.0684775	−	0.997653i	$-0.478186\pi$
$401$	17.0728	−	7.54975i	0.852576	−	0.377016i	0.784099	+	0.620636i	$0.213126\pi$
$402$		0			0
$403$	−5.75596	+	22.9216i	−0.286725	+	1.14180i
$404$		0			0
$405$	0.191242	−	0.0218096i	0.00950288	−	0.00108373i
$406$		0			0
$407$	11.0477	−	8.28508i	0.547616	−	0.410676i
$408$		0			0
$409$	3.49299	−	4.14506i	0.172717	−	0.204960i	−0.671434	−	0.741064i	$-0.734321\pi$
$409$	3.49299	−	4.14506i	0.172717	−	0.204960i	0.844152	+	0.536104i	$0.180105\pi$
$410$		0			0
$411$	−12.3659	−	24.1563i	−0.609963	−	1.19154i
$412$		0			0
$413$	−1.87081	+	4.97657i	−0.0920565	+	0.244881i
$414$		0			0
$415$	0.0281366	−	0.0164822i	0.00138117	−	0.000809080i
$416$		0			0
$417$	14.6639	−	20.3446i	0.718093	−	0.996279i
$418$		0			0
$419$	−10.9202	−	5.85361i	−0.533488	−	0.285967i	0.183539	−	0.983012i	$-0.441245\pi$
$419$	−10.9202	−	5.85361i	−0.533488	−	0.285967i	−0.717027	+	0.697045i	$0.754498\pi$
$420$		0			0
$421$	7.67685	+	13.6928i	0.374147	+	0.667346i	0.992994	−	0.118165i	$-0.0377012\pi$
$421$	7.67685	+	13.6928i	0.374147	+	0.667346i	−0.618847	+	0.785511i	$0.712400\pi$
$422$		0			0
$423$	−0.270442	−	0.926938i	−0.0131493	−	0.0450693i
$424$		0			0
$425$	−21.5136	−	27.5840i	−1.04356	−	1.33802i
$426$		0			0
$427$	16.0707	+	42.7500i	0.777718	+	2.06882i
$428$		0			0
$429$	18.6340	−	11.8849i	0.899656	−	0.573809i
$430$		0			0
$431$	4.41981	+	1.02137i	0.212895	+	0.0491978i	0.330256	−	0.943892i	$-0.392865\pi$
$431$	4.41981	+	1.02137i	0.212895	+	0.0491978i	−0.117361	+	0.993089i	$0.537443\pi$
$432$		0			0
$433$	−6.42673	+	15.3102i	−0.308849	+	0.735762i	0.691067	+	0.722791i	$0.257141\pi$
$433$	−6.42673	+	15.3102i	−0.308849	+	0.735762i	−0.999916	+	0.0129713i	$0.995871\pi$
$434$		0			0
$435$	−0.0242889	−	0.255916i	−0.00116456	−	0.0122702i
$436$		0			0
$437$	−2.72025	+	1.88351i	−0.130127	+	0.0901004i
$438$		0			0
$439$	−2.25687	−	1.97608i	−0.107715	−	0.0943130i	0.603205	−	0.797586i	$-0.293890\pi$
$439$	−2.25687	−	1.97608i	−0.107715	−	0.0943130i	−0.710920	+	0.703273i	$0.751721\pi$
$440$		0			0
$441$	−10.3782	−	7.18591i	−0.494202	−	0.342186i
$442$		0			0
$443$	25.3810	+	16.1883i	1.20589	+	0.769128i	0.978814	−	0.204750i	$-0.0656380\pi$
$443$	25.3810	+	16.1883i	1.20589	+	0.769128i	0.227075	+	0.973877i	$0.427084\pi$
$444$		0			0
$445$	−0.00520709	+	0.0390754i	−0.000246840	+	0.00185235i
$446$		0			0
$447$	11.3522	−	18.5645i	0.536941	−	0.878072i
$448$		0			0
$449$	26.7536	+	27.2647i	1.26258	+	1.28670i	0.940419	+	0.340018i	$0.110433\pi$
$449$	26.7536	+	27.2647i	1.26258	+	1.28670i	0.322160	+	0.946685i	$0.395591\pi$
$450$		0			0
$451$	3.85404	−	18.2450i	0.181480	−	0.859124i
$452$		0			0
$453$	16.8885	−	30.1231i	0.793489	−	1.41531i
$454$		0			0
$455$	−0.235809	−	0.939045i	−0.0110549	−	0.0440231i
$456$		0			0
$457$	10.7267	+	16.1362i	0.501775	+	0.754818i	0.993240	−	0.116079i	$-0.0370325\pi$
$457$	10.7267	+	16.1362i	0.501775	+	0.754818i	−0.491465	+	0.870897i	$0.663539\pi$
$458$		0			0
$459$	−12.4416	−	37.3274i	−0.580723	−	1.74229i
$460$		0			0
$461$	−9.66163	−	1.10183i	−0.449987	−	0.0513175i	−0.114629	−	0.993408i	$-0.536568\pi$
$461$	−9.66163	−	1.10183i	−0.449987	−	0.0513175i	−0.335358	+	0.942091i	$0.608857\pi$
$462$		0			0
$463$	29.7817	−	1.12779i	1.38407	−	0.0524130i	0.664739	−	0.747076i	$-0.268543\pi$
$463$	29.7817	−	1.12779i	1.38407	−	0.0524130i	0.719336	+	0.694663i	$0.244446\pi$
$464$		0			0
$465$	−0.00975074	+	0.171557i	−0.000452180	+	0.00795575i
$466$		0			0
$467$	−7.03357	−	11.5022i	−0.325475	−	0.532256i	0.647827	−	0.761788i	$-0.275678\pi$
$467$	−7.03357	−	11.5022i	−0.325475	−	0.532256i	−0.973301	+	0.229532i	$0.926281\pi$
$468$		0			0
$469$	0.767861	−	40.5685i	0.0354565	−	1.87328i
$470$		0			0
$471$	10.9577	−	3.88421i	0.504903	−	0.178975i
$472$		0			0
$473$	10.6935	+	10.1030i	0.491688	+	0.464536i
$474$		0			0
$475$	−1.86819	+	0.285029i	−0.0857186	+	0.0130780i
$476$		0			0
$477$	−1.56365	−	3.36248i	−0.0715946	−	0.153958i
$478$		0			0
$479$	−21.1175	−	0.799691i	−0.964884	−	0.0365388i	−0.449303	−	0.893379i	$-0.648328\pi$
$479$	−21.1175	−	0.799691i	−0.964884	−	0.0365388i	−0.515581	+	0.856841i	$0.672424\pi$
$480$		0			0
$481$	−25.7962	+	28.3604i	−1.17620	+	1.29312i
$482$		0			0
$483$	50.0860	+	40.6112i	2.27899	+	1.84787i
$484$		0			0
$485$	−0.149032	−	0.111764i	−0.00676718	−	0.00507493i
$486$		0			0
$487$	−17.5514	+	3.36189i	−0.795331	+	0.152342i	−0.569680	−	0.821866i	$-0.692933\pi$
$487$	−17.5514	+	3.36189i	−0.795331	+	0.152342i	−0.225651	+	0.974208i	$0.572451\pi$
$488$		0			0
$489$	−21.3219	−	4.08410i	−0.964209	−	0.184689i
$490$		0			0
$491$	−4.45486	−	21.0893i	−0.201045	−	0.951746i	−0.955408	−	0.295289i	$-0.904584\pi$
$491$	−4.45486	−	21.0893i	−0.201045	−	0.951746i	0.754363	−	0.656458i	$-0.227946\pi$
$492$		0			0
$493$	−36.9590	+	11.5464i	−1.66455	+	0.520025i
$494$		0			0
$495$	−0.0383320	+	0.0362152i	−0.00172290	+	0.00162775i
$496$		0			0
$497$	10.2805	−	30.8438i	0.461145	−	1.38353i
$498$		0			0
$499$	−0.631286	−	0.875843i	−0.0282602	−	0.0392081i	0.796869	−	0.604152i	$-0.206488\pi$
$499$	−0.631286	−	0.875843i	−0.0282602	−	0.0392081i	−0.825129	+	0.564944i	$0.808898\pi$
$500$		0			0
$501$	−12.8165	+	14.5929i	−0.572599	+	0.651960i
$502$		0			0
$503$	3.49432	+	4.84801i	0.155804	+	0.216162i	0.881906	−	0.471425i	$-0.156260\pi$
$503$	3.49432	+	4.84801i	0.155804	+	0.216162i	−0.726102	+	0.687587i	$0.758670\pi$
$504$		0			0
$505$	−0.107975	+	0.323947i	−0.00480482	+	0.0144155i
$506$		0			0
$507$	−30.3990	+	28.7203i	−1.35007	+	1.27551i
$508$		0			0
$509$	15.6984	−	4.90435i	0.695819	−	0.217382i	0.0702255	−	0.997531i	$-0.477628\pi$
$509$	15.6984	−	4.90435i	0.695819	−	0.217382i	0.625593	+	0.780149i	$0.284857\pi$
$510$		0			0
$511$	5.46614	+	25.8767i	0.241808	+	1.14472i
$512$		0			0
$513$	−2.08765	−	0.399879i	−0.0921720	−	0.0176551i
$514$		0			0
$515$	−0.0113991	+	0.00218344i	−0.000502304	+	9.62137e-5i
$516$		0			0
$517$	−2.39858	−	1.79878i	−0.105490	−	0.0791102i
$518$		0			0
$519$	−20.3150	−	16.4720i	−0.891731	−	0.723042i
$520$		0			0
$521$	−6.28114	+	6.90551i	−0.275182	+	0.302536i	−0.861718	−	0.507387i	$-0.830612\pi$
$521$	−6.28114	+	6.90551i	−0.275182	+	0.302536i	0.586537	+	0.809923i	$0.300491\pi$
$522$		0			0
$523$	−4.29876	−	0.162788i	−0.187972	−	0.00711822i	−0.0563121	−	0.998413i	$-0.517934\pi$
$523$	−4.29876	−	0.162788i	−0.187972	−	0.00711822i	−0.131660	+	0.991295i	$0.542031\pi$
$524$		0			0
$525$	15.5298	+	33.3955i	0.677777	+	1.45750i
$526$		0			0
$527$	25.5864	−	3.90371i	1.11456	−	0.170048i
$528$		0			0
$529$	38.9638	+	36.8121i	1.69408	+	1.60053i
$530$		0			0
$531$	−0.757724	+	0.268593i	−0.0328824	+	0.0116559i
$532$		0			0
$533$	−0.979698	+	51.7605i	−0.0424354	+	2.24200i
$534$		0			0
$535$	0.0505469	+	0.0826606i	0.00218534	+	0.00357373i
$536$		0			0
$537$	1.35928	−	23.9155i	0.0586572	−	1.03203i
$538$		0			0
$539$	−39.1669	+	1.48320i	−1.68704	+	0.0638857i
$540$		0			0
$541$	−18.7307	−	2.13609i	−0.805297	−	0.0918377i	−0.299062	−	0.954234i	$-0.596674\pi$
$541$	−18.7307	−	2.13609i	−0.805297	−	0.0918377i	−0.506234	+	0.862396i	$0.668963\pi$
$542$		0			0
$543$	−11.6822	−	35.0491i	−0.501332	−	1.50410i
$544$		0			0
$545$	−0.189025	−	0.284350i	−0.00809694	−	0.0121802i
$546$		0			0
$547$	−3.09273	−	12.3159i	−0.132235	−	0.526592i	−0.999583	−	0.0288883i	$-0.990803\pi$
$547$	−3.09273	−	12.3159i	−0.132235	−	0.526592i	0.867347	−	0.497703i	$-0.165823\pi$
$548$		0			0
$549$	−3.37721	+	6.02376i	−0.144136	+	0.257088i
$550$		0			0
$551$	−0.432329	+	2.04664i	−0.0184178	+	0.0871899i
$552$		0			0
$553$	48.2936	+	49.2164i	2.05365	+	2.09289i
$554$		0			0
$555$	−0.145419	+	0.237807i	−0.00617270	+	0.0100944i
$556$		0			0
$557$	−1.11352	+	8.35614i	−0.0471812	+	0.354061i	0.951711	+	0.306996i	$0.0993240\pi$
$557$	−1.11352	+	8.35614i	−0.0471812	+	0.354061i	−0.998892	+	0.0470645i	$0.985013\pi$
$558$		0			0
$559$	−34.4340	−	21.9623i	−1.45640	−	0.928907i
$560$		0			0
$561$	−19.9003	−	13.7790i	−0.840190	−	0.581749i
$562$		0			0
$563$	−14.0007	−	12.2587i	−0.590058	−	0.516644i	0.310962	−	0.950422i	$-0.399349\pi$
$563$	−14.0007	−	12.2587i	−0.590058	−	0.516644i	−0.901020	+	0.433778i	$0.857180\pi$
$564$		0			0
$565$	0.493696	−	0.341836i	0.0207699	−	0.0143811i
$566$		0			0
$567$	2.88410	+	30.3878i	0.121121	+	1.27617i
$568$		0			0
$569$	−6.90253	+	16.4437i	−0.289369	+	0.689355i	−0.999898	−	0.0143130i	$-0.995444\pi$
$569$	−6.90253	+	16.4437i	−0.289369	+	0.689355i	0.710529	+	0.703668i	$0.248456\pi$
$570$		0			0
$571$	−10.5611	−	2.44057i	−0.441970	−	0.102135i	−0.00169653	−	0.999999i	$-0.500540\pi$
$571$	−10.5611	−	2.44057i	−0.441970	−	0.102135i	−0.440273	+	0.897864i	$0.645118\pi$
$572$		0			0
$573$	−19.5177	+	12.4486i	−0.815362	+	0.520046i
$574$		0			0
$575$	15.3959	+	40.9550i	0.642055	+	1.70794i
$576$		0			0
$577$	−7.95813	−	10.2036i	−0.331301	−	0.424782i	0.593735	−	0.804660i	$-0.297653\pi$
$577$	−7.95813	−	10.2036i	−0.331301	−	0.424782i	−0.925037	+	0.379878i	$0.875966\pi$
$578$		0			0
$579$	−1.15096	−	3.94489i	−0.0478321	−	0.163944i
$580$		0			0
$581$	2.52890	+	4.51066i	0.104916	+	0.187134i
$582$		0			0
$583$	−10.1482	−	5.43975i	−0.420294	−	0.225292i
$584$		0			0
$585$	0.0856035	−	0.118766i	0.00353927	−	0.00491036i
$586$		0			0
$587$	26.0538	−	15.2621i	1.07536	−	0.629935i	0.142358	−	0.989815i	$-0.454532\pi$
$587$	26.0538	−	15.2621i	1.07536	−	0.629935i	0.932999	+	0.359880i	$0.117182\pi$
$588$		0			0
$589$	0.492017	−	1.30882i	0.0202732	−	0.0539292i
$590$		0			0
$591$	11.0480	+	21.5819i	0.454455	+	0.887760i
$592$		0			0
$593$	27.5631	−	32.7085i	1.13188	−	1.34318i	0.200261	−	0.979743i	$-0.435821\pi$
$593$	27.5631	−	32.7085i	1.13188	−	1.34318i	0.931620	−	0.363435i	$-0.118396\pi$
$594$		0			0
$595$	−0.848306	+	0.636173i	−0.0347771	+	0.0260806i
$596$		0			0
$597$	25.7586	−	2.93757i	1.05423	−	0.120227i
$598$		0			0
$599$	−2.28873	+	9.11424i	−0.0935149	+	0.372398i	−0.998604	−	0.0528245i	$-0.983178\pi$
$599$	−2.28873	+	9.11424i	−0.0935149	+	0.372398i	0.905089	+	0.425222i	$0.139804\pi$
$600$		0			0
$601$	−14.8167	+	6.55209i	−0.604388	+	0.267265i	−0.683908	−	0.729568i	$-0.739721\pi$
$601$	−14.8167	+	6.55209i	−0.604388	+	0.267265i	0.0795207	+	0.996833i	$0.474661\pi$
$602$		0			0
$603$	4.76570	−	3.86417i	0.194074	−	0.157361i
$604$		0			0
$605$	0.0298815	−	0.173736i	0.00121485	−	0.00706336i
$606$		0			0
$607$	−14.9247	+	15.2099i	−0.605776	+	0.617350i	−0.946457	−	0.322829i	$-0.895366\pi$
$607$	−14.9247	+	15.2099i	−0.605776	+	0.617350i	0.340682	+	0.940179i	$0.389342\pi$
$608$		0			0
$609$	40.6496	−	3.08311i	1.64721	−	0.124934i
$610$		0			0
$611$	7.47954	+	3.65191i	0.302590	+	0.147740i
$612$		0			0
$613$	−0.301107	+	0.161403i	−0.0121616	+	0.00651902i	−0.478509	−	0.878083i	$-0.658823\pi$
$613$	−0.301107	+	0.161403i	−0.0121616	+	0.00651902i	0.466348	+	0.884602i	$0.345570\pi$
$614$		0			0
$615$	0.0638034	+	0.370964i	0.00257280	+	0.0149587i
$616$		0			0
$617$	2.13791	+	37.6148i	0.0860689	+	1.51431i	0.693798	+	0.720170i	$0.255936\pi$
$617$	2.13791	+	37.6148i	0.0860689	+	1.51431i	−0.607729	+	0.794145i	$0.707919\pi$
$618$		0			0
$619$	−12.5913	−	14.9418i	−0.506086	−	0.600561i	0.450224	−	0.892916i	$-0.351344\pi$
$619$	−12.5913	−	14.9418i	−0.506086	−	0.600561i	−0.956310	+	0.292355i	$0.905561\pi$
$620$		0			0
$621$	0.931301	+	49.2035i	0.0373718	+	1.97447i
$622$		0			0
$623$	−6.17997	−	0.942876i	−0.247595	−	0.0377755i
$624$		0			0
$625$	−2.36077	+	24.8739i	−0.0944310	+	0.994956i
$626$		0			0
$627$	−1.17505	+	0.573720i	−0.0469268	+	0.0229122i
$628$		0			0
$629$	39.5735	+	14.0277i	1.57790	+	0.559323i
$630$		0			0
$631$	−36.0767	−	9.78878i	−1.43619	−	0.389685i	−0.543139	−	0.839643i	$-0.682764\pi$
$631$	−36.0767	−	9.78878i	−1.43619	−	0.389685i	−0.893050	+	0.449958i	$0.851439\pi$
$632$		0			0
$633$	−0.466539	+	0.408493i	−0.0185432	+	0.0162361i
$634$		0			0
$635$	0.0826116	+	0.0483932i	0.00327834	+	0.00192043i
$636$		0			0
$637$	106.020	−	24.5000i	4.20065	−	0.970726i
$638$		0			0
$639$	4.56815	−	1.81666i	0.180713	−	0.0718660i
$640$		0			0
$641$	2.36857	+	5.64257i	0.0935528	+	0.222868i	0.962077	−	0.272779i	$-0.0879429\pi$
$641$	2.36857	+	5.64257i	0.0935528	+	0.222868i	−0.868524	+	0.495647i	$0.834931\pi$
$642$		0			0
$643$	−16.6062	−	18.2569i	−0.654884	−	0.719982i	0.318815	−	0.947817i	$-0.396715\pi$
$643$	−16.6062	−	18.2569i	−0.654884	−	0.719982i	−0.973700	+	0.227835i	$0.926835\pi$
$644$		0			0
$645$	−0.275935	−	0.109734i	−0.0108649	−	0.00432076i
$646$		0			0
$647$	−3.48800	−	1.08969i	−0.137127	−	0.0428402i	0.228864	−	0.973458i	$-0.426499\pi$
$647$	−3.48800	−	1.08969i	−0.137127	−	0.0428402i	−0.365991	+	0.930618i	$0.619270\pi$
$648$		0			0
$649$	−1.38188	+	2.07876i	−0.0542436	+	0.0815986i
$650$		0			0
$651$	−27.1719	−	2.06088i	−1.06495	−	0.0807722i
$652$		0			0
$653$	6.04993	−	20.7361i	0.236752	−	0.811466i	−0.751644	−	0.659569i	$-0.770739\pi$
$653$	6.04993	−	20.7361i	0.236752	−	0.811466i	0.988396	−	0.151897i	$-0.0485383\pi$
$654$		0			0
$655$	0.158060	−	0.308764i	0.00617591	−	0.0120644i
$656$		0			0
$657$	−2.45947	+	3.15344i	−0.0959529	+	0.123027i
$658$		0			0
$659$	−33.5955	+	9.11555i	−1.30869	+	0.355091i	−0.846832	−	0.531861i	$-0.821493\pi$
$659$	−33.5955	+	9.11555i	−1.30869	+	0.355091i	−0.461861	+	0.886952i	$0.652818\pi$
$660$		0			0
$661$	4.82598	−	10.3778i	0.187709	−	0.403650i	−0.790151	−	0.612912i	$-0.789998\pi$
$661$	4.82598	−	10.3778i	0.187709	−	0.403650i	0.977860	+	0.209262i	$0.0671062\pi$
$662$		0			0
$663$	61.4574	+	27.1770i	2.38681	+	1.05547i
$664$		0			0
$665$	0.00756652	+	0.0567813i	0.000293417	+	0.00220188i
$666$		0			0
$667$	48.4299			1.87521
$668$		0			0
$669$	−22.8754			−0.884412
$670$		0			0
$671$	2.83236	+	21.2548i	0.109342	+	0.820534i
$672$		0			0
$673$	−16.0994	−	7.11930i	−0.620587	−	0.274429i	0.0701484	−	0.997537i	$-0.477653\pi$
$673$	−16.0994	−	7.11930i	−0.620587	−	0.274429i	−0.690735	+	0.723108i	$0.742713\pi$
$674$		0			0
$675$	−11.8524	+	25.4874i	−0.456198	+	0.981011i
$676$		0			0
$677$	2.03577	−	0.552370i	0.0782409	−	0.0212293i	−0.222529	−	0.974926i	$-0.571431\pi$
$677$	2.03577	−	0.552370i	0.0782409	−	0.0212293i	0.300770	+	0.953697i	$0.402756\pi$
$678$		0			0
$679$	18.1679	−	23.2943i	0.697222	−	0.893952i
$680$		0			0
$681$	−2.18124	+	4.26096i	−0.0835852	+	0.163280i
$682$		0			0
$683$	1.81222	−	6.21138i	0.0693428	−	0.237672i	−0.917921	−	0.396763i	$-0.870133\pi$
$683$	1.81222	−	6.21138i	0.0693428	−	0.237672i	0.987264	+	0.159091i	$0.0508564\pi$
$684$		0			0
$685$	−0.556553	−	0.0422123i	−0.0212648	−	0.00161285i
$686$		0			0
$687$	4.32611	−	6.50775i	0.165051	−	0.248286i
$688$		0			0
$689$	30.5115	+	9.53214i	1.16240	+	0.363146i
$690$		0			0
$691$	−13.0370	−	5.18457i	−0.495952	−	0.197231i	0.108154	−	0.994134i	$-0.465506\pi$
$691$	−13.0370	−	5.18457i	−0.495952	−	0.197231i	−0.604106	+	0.796904i	$0.706470\pi$
$692$		0			0
$693$	−5.62706	−	6.18641i	−0.213754	−	0.235002i
$694$		0			0
$695$	−0.199643	−	0.475602i	−0.00757287	−	0.0180406i
$696$		0			0
$697$	52.6838	−	20.9513i	1.99554	−	0.793588i
$698$		0			0
$699$	8.58264	−	1.98336i	0.324625	−	0.0750176i
$700$		0			0
$701$	−8.88196	−	5.20298i	−0.335467	−	0.196514i	0.328078	−	0.944651i	$-0.393599\pi$
$701$	−8.88196	−	5.20298i	−0.335467	−	0.196514i	−0.663545	+	0.748137i	$0.730949\pi$
$702$		0			0
$703$	1.70652	−	1.49419i	0.0643624	−	0.0563546i
$704$		0			0
$705$	0.0584068	+	0.0158477i	0.00219973	+	0.000596858i
$706$		0			0
$707$	−51.0394	−	18.0921i	−1.91953	−	0.680424i
$708$		0			0
$709$	2.45861	−	1.20042i	0.0923349	−	0.0450828i	−0.392002	−	0.919964i	$-0.628217\pi$
$709$	2.45861	−	1.20042i	0.0923349	−	0.0450828i	0.484337	+	0.874881i	$0.339061\pi$
$710$		0			0
$711$	−0.985136	+	10.3797i	−0.0369455	+	0.389270i
$712$		0			0
$713$	−32.0022	−	4.88256i	−1.19849	−	0.182853i
$714$		0			0
$715$	−0.00860243	−	0.454493i	−0.000321713	−	0.0169971i
$716$		0			0
$717$	9.20906	+	10.9282i	0.343919	+	0.408120i
$718$		0			0
$719$	−1.25873	−	22.1463i	−0.0469425	−	0.825917i	−0.932452	−	0.361295i	$-0.882335\pi$
$719$	−1.25873	−	22.1463i	−0.0469425	−	0.825917i	0.885509	−	0.464622i	$-0.153810\pi$
$720$		0			0
$721$	−0.311985	−	1.81393i	−0.0116189	−	0.0675544i
$722$		0			0
$723$	6.03321	−	3.23400i	0.224378	−	0.120274i
$724$		0			0
$725$	24.8570	+	12.1365i	0.923164	+	0.450738i
$726$		0			0
$727$	47.1428	−	3.57559i	1.74843	−	0.132611i	0.837838	−	0.545919i	$-0.183819\pi$
$727$	47.1428	−	3.57559i	1.74843	−	0.132611i	0.910591	+	0.413308i	$0.135627\pi$
$728$		0			0
$729$	−20.9886	+	21.3896i	−0.777356	+	0.792209i
$730$		0			0
$731$	−7.58174	+	44.0815i	−0.280421	+	1.63041i
$732$		0			0
$733$	−10.3277	+	8.37401i	−0.381463	+	0.309301i	−0.801260	−	0.598317i	$-0.795836\pi$
$733$	−10.3277	+	8.37401i	−0.381463	+	0.309301i	0.419797	+	0.907618i	$0.362101\pi$
$734$		0			0
$735$	0.723577	−	0.319972i	0.0266895	−	0.0118023i
$736$		0			0
$737$	4.63983	−	18.4769i	0.170910	−	0.680604i
$738$		0			0
$739$	−33.8770	+	3.86341i	−1.24619	+	0.142118i	−0.711350	−	0.702838i	$-0.751916\pi$
$739$	−33.8770	+	3.86341i	−1.24619	+	0.142118i	−0.534837	+	0.844956i	$0.679627\pi$
$740$		0			0
$741$	2.90429	−	2.17803i	0.106692	−	0.0800118i
$742$		0			0
$743$	−26.4738	+	31.4159i	−0.971231	+	1.15254i	0.0170441	+	0.999855i	$0.494574\pi$
$743$	−26.4738	+	31.4159i	−0.971231	+	1.15254i	−0.988275	+	0.152683i	$0.951209\pi$
$744$		0			0
$745$	−0.203942	−	0.398393i	−0.00747185	−	0.0145960i
$746$		0			0
$747$	−0.275148	+	0.731927i	−0.0100672	+	0.0267798i
$748$		0			0
$749$	−13.2579	+	7.76639i	−0.484434	+	0.283778i
$750$		0			0
$751$	19.5744	−	27.1574i	0.714279	−	0.990987i	−0.285192	−	0.958470i	$-0.592057\pi$
$751$	19.5744	−	27.1574i	0.714279	−	0.990987i	0.999471	−	0.0325169i	$-0.0103523\pi$
$752$		0			0
$753$	4.76896	+	2.55632i	0.173791	+	0.0931574i
$754$		0			0
$755$	−0.347355	−	0.619560i	−0.0126416	−	0.0225481i
$756$		0			0
$757$	7.50326	+	25.7173i	0.272711	+	0.934713i	0.974885	+	0.222708i	$0.0714897\pi$
$757$	7.50326	+	25.7173i	0.272711	+	0.934713i	−0.702175	+	0.712005i	$0.747787\pi$
$758$		0			0
$759$	18.6187	+	23.8722i	0.675816	+	0.866507i
$760$		0			0
$761$	−4.77730	−	12.7082i	−0.173177	−	0.460671i	0.820674	−	0.571397i	$-0.193598\pi$
$761$	−4.77730	−	12.7082i	−0.173177	−	0.460671i	−0.993851	+	0.110726i	$0.964683\pi$
$762$		0			0
$763$	45.6523	−	29.1175i	1.65272	−	1.05412i
$764$		0			0
$765$	−0.156218	−	0.0361003i	−0.00564807	−	0.00130521i
$766$		0			0
$767$	2.68222	−	6.38977i	0.0968493	−	0.230721i
$768$		0			0
$769$	−3.68697	−	38.8471i	−0.132956	−	1.40086i	−0.773916	−	0.633289i	$-0.781705\pi$
$769$	−3.68697	−	38.8471i	−0.132956	−	1.40086i	0.640960	−	0.767574i	$-0.278536\pi$
$770$		0			0
$771$	−29.3172	+	20.2993i	−1.05583	+	0.731060i
$772$		0			0
$773$	−8.75387	−	7.66473i	−0.314855	−	0.275681i	0.486743	−	0.873545i	$-0.338185\pi$
$773$	−8.75387	−	7.66473i	−0.314855	−	0.275681i	−0.801597	+	0.597864i	$0.796016\pi$
$774$		0			0
$775$	−15.2018	−	10.5257i	−0.546064	−	0.378096i
$776$		0			0
$777$	−37.2691	−	23.7706i	−1.33702	−	0.852765i
$778$		0			0
$779$	0.404582	−	3.03610i	0.0144957	−	0.108780i
$780$		0			0
$781$	7.96337	−	13.0227i	0.284952	−	0.465988i
$782$		0			0
$783$	21.7910	+	22.2073i	0.778746	+	0.793625i
$784$		0			0
$785$	0.0494194	−	0.233951i	0.00176385	−	0.00835007i
$786$		0			0
$787$	−20.8148	+	37.1263i	−0.741967	+	1.32341i	0.197341	+	0.980335i	$0.436769\pi$
$787$	−20.8148	+	37.1263i	−0.741967	+	1.32341i	−0.939309	+	0.343074i	$0.888532\pi$
$788$		0			0
$789$	−0.946335	−	3.76852i	−0.0336904	−	0.134163i
$790$		0			0
$791$	52.7181	+	79.3038i	1.87444	+	2.81972i
$792$		0			0
$793$	−18.8237	−	56.4751i	−0.668450	−	2.00549i
$794$		0			0
$795$	0.230922	+	0.0263348i	0.00818996	+	0.000934000i
$796$		0			0
$797$	−47.5010	+	1.79880i	−1.68257	+	0.0637167i	−0.861708	−	0.507405i	$-0.830605\pi$
$797$	−47.5010	+	1.79880i	−1.68257	+	0.0637167i	−0.820866	+	0.571121i	$0.806509\pi$
$798$		0			0
$799$	0.517269	−	9.10095i	0.0182997	−	0.321968i
$800$		0			0
$801$	−0.493147	−	0.806454i	−0.0174245	−	0.0284947i
$802$		0			0
$803$	−0.234987	+	12.4151i	−0.00829251	+	0.438119i
$804$		0			0
$805$	1.25002	−	0.443099i	0.0440575	−	0.0156172i
$806$		0			0
$807$	5.83528	+	5.51304i	0.205412	+	0.194068i
$808$		0			0
$809$	38.7101	−	5.90599i	1.36097	−	0.207643i	0.571084	−	0.820891i	$-0.306523\pi$
$809$	38.7101	−	5.90599i	1.36097	−	0.207643i	0.789890	+	0.613248i	$0.210137\pi$
$810$		0			0
$811$	−4.98820	−	10.7267i	−0.175159	−	0.376664i	0.799398	−	0.600802i	$-0.205152\pi$
$811$	−4.98820	−	10.7267i	−0.175159	−	0.376664i	−0.974557	+	0.224138i	$0.928043\pi$
$812$		0			0
$813$	22.0298	+	0.834239i	0.772620	+	0.0292580i
$814$		0			0
$815$	−0.300446	+	0.330312i	−0.0105242	+	0.0115703i
$816$		0			0
$817$	1.87692	+	1.52186i	0.0656651	+	0.0532432i
$818$		0			0
$819$	18.5740	+	13.9293i	0.649028	+	0.486728i
$820$		0			0
$821$	−43.5984	+	8.35105i	−1.52160	+	0.291454i	−0.879771	−	0.475398i	$-0.842304\pi$
$821$	−43.5984	+	8.35105i	−1.52160	+	0.291454i	−0.641824	+	0.766852i	$0.721822\pi$
$822$		0			0
$823$	13.5014	+	2.58613i	0.470631	+	0.0901469i	0.417961	−	0.908465i	$-0.362745\pi$
$823$	13.5014	+	2.58613i	0.470631	+	0.0901469i	0.0526699	+	0.998612i	$0.483227\pi$
$824$		0			0
$825$	3.57382	+	16.9184i	0.124424	+	0.589024i
$826$		0			0
$827$	5.05388	−	1.57889i	0.175741	−	0.0549034i	−0.209061	−	0.977903i	$-0.567041\pi$
$827$	5.05388	−	1.57889i	0.175741	−	0.0549034i	0.384802	+	0.922999i	$0.374270\pi$
$828$		0			0
$829$	7.16526	−	6.76957i	0.248860	−	0.235117i	−0.552185	−	0.833722i	$-0.686206\pi$
$829$	7.16526	−	6.76957i	0.248860	−	0.235117i	0.801045	+	0.598605i	$0.204278\pi$
$830$		0			0
$831$	−6.76493	+	20.2962i	−0.234673	+	0.704068i
$832$		0			0
$833$	−69.6809	−	96.6749i	−2.41430	−	3.34959i
$834$		0			0
$835$	0.118539	+	0.381471i	0.00410223	+	0.0132013i
$836$		0			0
$837$	−12.1605	−	16.8714i	−0.420328	−	0.583161i
$838$		0			0
$839$	1.43290	−	4.29901i	0.0494693	−	0.148418i	−0.921048	−	0.389448i	$-0.872666\pi$
$839$	1.43290	−	4.29901i	0.0494693	−	0.148418i	0.970518	+	0.241030i	$0.0774851\pi$
$840$		0			0
$841$	1.17628	−	1.11132i	0.0405612	−	0.0383213i
$842$		0			0
$843$	−23.3030	+	7.28011i	−0.802596	+	0.250740i
$844$		0			0
$845$	0.177773	+	0.841577i	0.00611558	+	0.0289511i
$846$		0			0
$847$	27.4570	+	5.25924i	0.943433	+	0.180710i
$848$		0			0
$849$	−3.72017	+	0.712579i	−0.127676	+	0.0244557i
$850$		0			0
$851$	−42.0127	−	31.5067i	−1.44018	−	1.08004i
$852$		0			0
$853$	1.47540	+	1.19630i	0.0505167	+	0.0409604i	0.654736	−	0.755858i	$-0.272780\pi$
$853$	1.47540	+	1.19630i	0.0505167	+	0.0409604i	−0.604219	+	0.796818i	$0.706515\pi$
$854$		0			0
$855$	−0.00582826	+	0.00640761i	−0.000199322	+	0.000219136i
$856$		0			0
$857$	26.7920	+	1.01458i	0.915198	+	0.0346573i	0.491240	−	0.871024i	$-0.336544\pi$
$857$	26.7920	+	1.01458i	0.915198	+	0.0346573i	0.423958	+	0.905682i	$0.360640\pi$
$858$		0			0
$859$	−22.0705	−	47.4605i	−0.753035	−	1.61933i	−0.784733	−	0.619834i	$-0.787200\pi$
$859$	−22.0705	−	47.4605i	−0.753035	−	1.61933i	0.0316981	−	0.999497i	$-0.489909\pi$
$860$		0			0
$861$	−59.0095	+	9.00306i	−2.01104	+	0.306824i
$862$		0			0
$863$	1.06661	+	1.00771i	0.0363077	+	0.0343027i	0.704691	−	0.709514i	$-0.251086\pi$
$863$	1.06661	+	1.00771i	0.0363077	+	0.0343027i	−0.668383	+	0.743817i	$0.733013\pi$
$864$		0			0
$865$	−0.507013	+	0.179723i	−0.0172389	+	0.00611075i
$866$		0			0
$867$	0.909194	−	48.0355i	0.0308778	−	1.63137i
$868$		0			0
$869$	16.8891	+	27.6192i	0.572925	+	0.936917i
$870$		0			0
$871$	−3.00116	+	52.8031i	−0.101690	+	1.78916i
$872$		0			0
$873$	4.46375	−	0.169036i	0.151075	−	0.00572100i
$874$		0			0
$875$	1.50539	+	0.171678i	0.0508914	+	0.00580376i
$876$		0			0
$877$	1.52662	+	4.58019i	0.0515503	+	0.154662i	0.971308	−	0.237824i	$-0.0764343\pi$
$877$	1.52662	+	4.58019i	0.0515503	+	0.154662i	−0.919758	+	0.392486i	$0.871615\pi$
$878$		0			0
$879$	−17.2404	−	25.9347i	−0.581505	−	0.874757i
$880$		0			0
$881$	1.98691	+	7.91234i	0.0669408	+	0.266574i	0.994156	−	0.107956i	$-0.0344306\pi$
$881$	1.98691	+	7.91234i	0.0669408	+	0.266574i	−0.927215	+	0.374530i	$0.877804\pi$
$882$		0			0
$883$	−21.9357	+	39.1256i	−0.738196	+	1.31668i	0.203119	+	0.979154i	$0.434892\pi$
$883$	−21.9357	+	39.1256i	−0.738196	+	1.31668i	−0.941315	+	0.337528i	$0.890409\pi$
$884$		0			0
$885$	0.0104137	−	0.0492984i	0.000350053	−	0.00165715i
$886$		0			0
$887$	11.4659	+	11.6850i	0.384989	+	0.392345i	0.878773	−	0.477240i	$-0.158363\pi$
$887$	11.4659	+	11.6850i	0.384989	+	0.392345i	−0.493784	+	0.869584i	$0.664387\pi$
$888$		0			0
$889$	−7.92090	+	12.9532i	−0.265659	+	0.434438i
$890$		0			0
$891$	−1.89302	+	14.2057i	−0.0634185	+	0.475910i
$892$		0			0
$893$	−0.415192	−	0.264814i	−0.0138939	−	0.00886165i
$894$		0			0
$895$	−0.405058	−	0.280463i	−0.0135396	−	0.00937483i
$896$		0			0
$897$	−63.2345	−	55.3670i	−2.11134	−	1.84865i
$898$		0			0
$899$	−16.8266	+	11.6508i	−0.561200	+	0.388576i
$900$		0			0
$901$	−3.30775	−	34.8515i	−0.110197	−	1.16107i
$902$		0			0
$903$	18.2269	−	43.4215i	0.606554	−	1.44498i
$904$		0			0
$905$	−0.740354	−	0.171088i	−0.0246102	−	0.00568716i
$906$		0			0
$907$	−29.6504	+	18.9113i	−0.984525	+	0.627940i	−0.928829	−	0.370508i	$-0.879184\pi$
$907$	−29.6504	+	18.9113i	−0.984525	+	0.627940i	−0.0556961	+	0.998448i	$0.517738\pi$
$908$		0			0
$909$	−2.88126	−	7.66449i	−0.0955653	−	0.254215i
$910$		0			0
$911$	17.7264	+	22.7282i	0.587303	+	0.753018i	0.986485	−	0.163854i	$-0.0523924\pi$
$911$	17.7264	+	22.7282i	0.587303	+	0.753018i	−0.399182	+	0.916872i	$0.630706\pi$
$912$		0			0
$913$	0.680012	+	2.33073i	0.0225051	+	0.0771360i
$914$		0			0
$915$	−0.211669	−	0.377543i	−0.00699756	−	0.0124812i
$916$		0			0
$917$	48.4817	+	25.9878i	1.60101	+	0.858192i
$918$		0			0
$919$	7.25159	−	10.0608i	0.239208	−	0.331876i	−0.674479	−	0.738294i	$-0.735632\pi$
$919$	7.25159	−	10.0608i	0.239208	−	0.331876i	0.913687	+	0.406418i	$0.133222\pi$
$920$		0			0
$921$	−7.26032	+	4.25304i	−0.239236	+	0.140142i
$922$		0			0
$923$	−14.9119	+	39.6673i	−0.490830	+	1.30566i
$924$		0			0
$925$	−13.6677	−	26.6994i	−0.449392	−	0.877871i
$926$		0			0
$927$	0.179343	−	0.212822i	0.00589039	−	0.00699000i
$928$		0			0
$929$	−7.71084	+	5.78262i	−0.252984	+	0.189721i	−0.718912	−	0.695102i	$-0.755359\pi$
$929$	−7.71084	+	5.78262i	−0.252984	+	0.189721i	0.465927	+	0.884823i	$0.345721\pi$
$930$		0			0
$931$	−6.39645	+	0.729465i	−0.209635	+	0.0239073i
$932$		0			0
$933$	−3.86806	+	15.4035i	−0.126635	+	0.504288i
$934$		0			0
$935$	−0.455308	+	0.201341i	−0.0148902	+	0.00658455i
$936$		0			0
$937$	32.0704	−	26.0036i	1.04769	−	0.849501i	0.0588224	−	0.998268i	$-0.481265\pi$
$937$	32.0704	−	26.0036i	1.04769	−	0.849501i	0.988872	+	0.148767i	$0.0475305\pi$
$938$		0			0
$939$	−1.31730	+	7.65903i	−0.0429886	+	0.249943i
$940$		0			0
$941$	−12.4841	+	12.7226i	−0.406970	+	0.414745i	−0.886463	−	0.462800i	$-0.846845\pi$
$941$	−12.4841	+	12.7226i	−0.406970	+	0.414745i	0.479493	+	0.877546i	$0.340821\pi$
$942$		0			0
$943$	−70.7106	+	5.36312i	−2.30266	+	0.174647i
$944$		0			0
$945$	0.765627	+	0.373820i	0.0249059	+	0.0121604i
$946$		0			0
$947$	12.6536	−	6.78273i	0.411186	−	0.220409i	−0.253813	−	0.967253i	$-0.581685\pi$
$947$	12.6536	−	6.78273i	0.411186	−	0.220409i	0.664999	+	0.746844i	$0.268432\pi$
$948$		0			0
$949$	−5.84336	−	33.9743i	−0.189684	−	1.10285i
$950$		0			0
$951$	2.24662	+	39.5275i	0.0728517	+	1.28177i
$952$		0			0
$953$	11.4123	+	13.5428i	0.369682	+	0.438693i	0.917398	−	0.397971i	$-0.130286\pi$
$953$	11.4123	+	13.5428i	0.369682	+	0.438693i	−0.547716	+	0.836665i	$0.684502\pi$
$954$		0			0
$955$	0.00901039	+	0.476047i	0.000291569	+	0.0154045i
$956$		0			0
$957$	18.9211	+	2.88678i	0.611631	+	0.0933163i
$958$		0			0
$959$	8.36321	−	88.1175i	0.270062	−	2.84546i
$960$		0			0
$961$	−15.5633	+	7.59885i	−0.502043	+	0.245124i
$962$		0			0
$963$	−2.18986	−	0.776246i	−0.0705671	−	0.0250142i
$964$		0			0
$965$	−0.0815703	−	0.0221327i	−0.00262584	−	0.000712477i
$966$		0			0
$967$	−5.48537	+	4.80289i	−0.176398	+	0.154451i	−0.742409	−	0.669947i	$-0.766317\pi$
$967$	−5.48537	+	4.80289i	−0.176398	+	0.154451i	0.566012	+	0.824397i	$0.308486\pi$
$968$		0			0
$969$	−3.43050	−	2.00956i	−0.110203	−	0.0645563i
$970$		0			0
$971$	25.4995	−	5.89267i	0.818318	−	0.189105i	0.204819	−	0.978800i	$-0.434340\pi$
$971$	25.4995	−	5.89267i	0.818318	−	0.189105i	0.613500	+	0.789695i	$0.289761\pi$
$972$		0			0
$973$	76.0082	−	30.2270i	2.43671	−	0.969032i
$974$		0			0
$975$	−18.5806	−	44.2640i	−0.595055	−	1.41758i
$976$		0			0
$977$	−1.59886	−	1.75779i	−0.0511521	−	0.0562368i	0.713648	−	0.700505i	$-0.247042\pi$
$977$	−1.59886	−	1.75779i	−0.0511521	−	0.0562368i	−0.764800	+	0.644268i	$0.777162\pi$
$978$		0			0
$979$	−2.72735	−	1.08461i	−0.0871665	−	0.0346644i
$980$		0			0
$981$	7.81513	+	2.44153i	0.249518	+	0.0779522i
$982$		0			0
$983$	29.1707	−	43.8814i	0.930400	−	1.39960i	0.0137509	−	0.999905i	$-0.495623\pi$
$983$	29.1707	−	43.8814i	0.930400	−	1.39960i	0.916649	−	0.399693i	$-0.130883\pi$
$984$		0			0
$985$	0.497240	+	0.0377137i	0.0158434	+	0.00120166i
$986$		0			0
$987$	−2.68801	+	9.21312i	−0.0855603	+	0.293257i
$988$		0			0
$989$	25.4926	−	49.7987i	0.810616	−	1.58351i
$990$		0			0
$991$	8.58181	−	11.0033i	0.272610	−	0.349531i	−0.632612	−	0.774469i	$-0.718017\pi$
$991$	8.58181	−	11.0033i	0.272610	−	0.349531i	0.905223	+	0.424938i	$0.139704\pi$
$992$		0			0
$993$	−0.243766	+	0.0661417i	−0.00773568	+	0.00209894i
$994$		0			0
$995$	0.224843	−	0.483504i	0.00712801	−	0.0153281i
$996$		0			0
$997$	9.06599	+	4.00906i	0.287123	+	0.126968i	0.542978	−	0.839747i	$-0.317297\pi$
$997$	9.06599	+	4.00906i	0.287123	+	0.126968i	−0.255855	+	0.966715i	$0.582357\pi$
$998$		0			0
$999$	−4.45628	−	33.4412i	−0.140990	−	1.05803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.4	✓	1148
167.130	even	83	inner	668.2.e.a.297.4	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.4	✓	1148	1.1	even	1	trivial
668.2.e.a.297.4	yes	1148	167.130	even	83	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.198520 - 1.48975i) q^{3} +(-0.0282706 - 0.0125015i) q^{5} +(2.06702 - 4.44493i) q^{7} +(0.715369 - 0.194103i) q^{9} +O(q^{10})\)	\(q+(-0.198520 - 1.48975i) q^{3} +(-0.0282706 - 0.0125015i) q^{5} +(2.06702 - 4.44493i) q^{7} +(0.715369 - 0.194103i) q^{9} +(1.41544 - 1.81482i) q^{11} +(-2.91156 + 5.68762i) q^{13} +(-0.0130118 + 0.0445980i) q^{15} +(6.97762 + 0.529224i) q^{17} +(0.209281 - 0.314820i) q^{19} +(-7.03218 - 2.19693i) q^{21} +(-8.13282 - 3.23426i) q^{23} +(-3.36372 - 3.69809i) q^{25} +(-2.17630 - 5.18453i) q^{27} +(-5.14171 + 2.04476i) q^{29} +(3.60376 - 0.832792i) q^{31} +(-2.98462 - 1.74837i) q^{33} +(-0.114004 + 0.0998202i) q^{35} +(5.79065 + 1.57119i) q^{37} +(9.05114 + 3.20839i) q^{39} +(7.28078 - 3.55486i) q^{41} +(-0.603945 + 6.36336i) q^{43} +(-0.0226505 - 0.00345578i) q^{45} +(-0.0246519 - 1.30244i) q^{47} +(-10.9741 - 13.0227i) q^{49} +(-0.596785 - 10.5000i) q^{51} +(-0.848005 - 4.93044i) q^{53} +(-0.0627033 + 0.0336110i) q^{55} +(-0.510550 - 0.249278i) q^{57} +(-1.08146 + 0.0820246i) q^{59} +(-6.52529 + 6.64997i) q^{61} +(0.615906 - 3.58098i) q^{63} +(0.153416 - 0.124394i) q^{65} +(7.57019 - 3.34760i) q^{67} +(-3.20372 + 12.7579i) q^{69} +(6.58962 - 0.751495i) q^{71} +(-4.31633 + 3.23696i) q^{73} +(-4.84146 + 5.74525i) q^{75} +(-5.14102 - 10.0428i) q^{77} +(-4.94963 + 13.1666i) q^{79} +(-5.37288 + 3.14739i) q^{81} +(-0.616826 + 0.855781i) q^{83} +(-0.190646 - 0.102192i) q^{85} +(4.06691 + 7.25394i) q^{87} +(-0.357183 - 1.22424i) q^{89} +(19.2628 + 24.6981i) q^{91} +(-1.95607 - 5.20338i) q^{93} +(-0.00985223 + 0.00628384i) q^{95} +(5.87162 + 1.35687i) q^{97} +(0.660298 - 1.57301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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