LMFDB - Embedded newform 668.2.e.a.9.11

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			9.11
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.200238 + 1.50264i) q^{3} +(-0.247141 - 0.109288i) q^{5} +(1.16135 - 2.49738i) q^{7} +(0.677472 - 0.183820i) q^{9} +O(q^{10})$	\(q+(0.200238 + 1.50264i) q^{3} +(-0.247141 - 0.109288i) q^{5} +(1.16135 - 2.49738i) q^{7} +(0.677472 - 0.183820i) q^{9} +(2.49761 - 3.20234i) q^{11} +(0.271031 - 0.529450i) q^{13} +(0.114733 - 0.393248i) q^{15} +(-4.18754 - 0.317608i) q^{17} +(1.83233 - 2.75637i) q^{19} +(3.98522 + 1.24503i) q^{21} +(3.58513 + 1.42574i) q^{23} +(-3.31523 - 3.64477i) q^{25} +(2.17209 + 5.17451i) q^{27} +(7.40935 - 2.94655i) q^{29} +(-7.51054 + 1.73561i) q^{31} +(5.31210 + 3.11179i) q^{33} +(-0.559950 + 0.490282i) q^{35} +(5.34597 + 1.45054i) q^{37} +(0.849845 + 0.301248i) q^{39} +(8.67736 - 4.23675i) q^{41} +(-0.643414 + 6.77922i) q^{43} +(-0.187520 - 0.0286098i) q^{45} +(0.215760 + 11.3993i) q^{47} +(-0.377389 - 0.447839i) q^{49} +(-0.361254 - 6.35597i) q^{51} +(-0.737486 - 4.28786i) q^{53} +(-0.967238 + 0.518471i) q^{55} +(4.50874 + 2.20141i) q^{57} +(1.52942 - 0.116001i) q^{59} +(-7.21740 + 7.35530i) q^{61} +(0.327714 - 1.90538i) q^{63} +(-0.124845 + 0.101228i) q^{65} +(-11.7033 + 5.17529i) q^{67} +(-1.42449 + 5.67267i) q^{69} +(-10.4610 + 1.19300i) q^{71} +(11.5486 - 8.66068i) q^{73} +(4.81296 - 5.71143i) q^{75} +(-5.09687 - 9.95653i) q^{77} +(3.00491 - 7.99342i) q^{79} +(-5.52342 + 3.23558i) q^{81} +(2.42434 - 3.36352i) q^{83} +(1.00020 + 0.536140i) q^{85} +(5.91125 + 10.5436i) q^{87} +(5.19207 + 17.7958i) q^{89} +(-1.00747 - 1.29175i) q^{91} +(-4.11190 - 10.9381i) q^{93} +(-0.754080 + 0.480960i) q^{95} +(1.75883 + 0.406447i) q^{97} +(1.10340 - 2.62861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.200238	+	1.50264i	0.115608	+	0.867552i	0.949090	+	0.315005i	$0.102006\pi$
$3$	0.200238	+	1.50264i	0.115608	+	0.867552i	−0.833482	+	0.552546i	$0.813656\pi$
$4$		0			0
$5$	−0.247141	−	0.109288i	−0.110525	−	0.0488749i	0.348429	−	0.937335i	$-0.386715\pi$
$5$	−0.247141	−	0.109288i	−0.110525	−	0.0488749i	−0.458953	+	0.888460i	$0.651776\pi$
$6$		0			0
$7$	1.16135	−	2.49738i	0.438950	−	0.943921i	−0.554768	−	0.832005i	$-0.687193\pi$
$7$	1.16135	−	2.49738i	0.438950	−	0.943921i	0.993718	−	0.111916i	$-0.0356987\pi$
$8$		0			0
$9$	0.677472	−	0.183820i	0.225824	−	0.0612734i
$10$		0			0
$11$	2.49761	−	3.20234i	0.753058	−	0.965543i	−0.246936	−	0.969032i	$-0.579424\pi$
$11$	2.49761	−	3.20234i	0.753058	−	0.965543i	0.999994	+	0.00348855i	$0.00111044\pi$
$12$		0			0
$13$	0.271031	−	0.529450i	0.0751706	−	0.146843i	−0.849527	−	0.527545i	$-0.823113\pi$
$13$	0.271031	−	0.529450i	0.0751706	−	0.146843i	0.924698	+	0.380702i	$0.124318\pi$
$14$		0			0
$15$	0.114733	−	0.393248i	0.0296240	−	0.101536i
$16$		0			0
$17$	−4.18754	−	0.317608i	−1.01563	−	0.0770312i	−0.442727	−	0.896656i	$-0.645989\pi$
$17$	−4.18754	−	0.317608i	−1.01563	−	0.0770312i	−0.572900	+	0.819625i	$0.694182\pi$
$18$		0			0
$19$	1.83233	−	2.75637i	0.420365	−	0.632355i	−0.560244	−	0.828328i	$-0.689293\pi$
$19$	1.83233	−	2.75637i	0.420365	−	0.632355i	0.980609	+	0.195973i	$0.0627866\pi$
$20$		0			0
$21$	3.98522	+	1.24503i	0.869646	+	0.271687i
$22$		0			0
$23$	3.58513	+	1.42574i	0.747552	+	0.297287i	0.712094	−	0.702084i	$-0.247747\pi$
$23$	3.58513	+	1.42574i	0.747552	+	0.297287i	0.0354583	+	0.999371i	$0.488711\pi$
$24$		0			0
$25$	−3.31523	−	3.64477i	−0.663046	−	0.728955i
$26$		0			0
$27$	2.17209	+	5.17451i	0.418019	+	0.995835i
$28$		0			0
$29$	7.40935	−	2.94655i	1.37588	−	0.547161i	0.439531	−	0.898227i	$-0.355145\pi$
$29$	7.40935	−	2.94655i	1.37588	−	0.547161i	0.936351	+	0.351066i	$0.114181\pi$
$30$		0			0
$31$	−7.51054	+	1.73561i	−1.34893	+	0.311724i	−0.836954	−	0.547274i	$-0.815666\pi$
$31$	−7.51054	+	1.73561i	−1.34893	+	0.311724i	−0.511979	+	0.858998i	$0.671087\pi$
$32$		0			0
$33$	5.31210	+	3.11179i	0.924718	+	0.541693i
$34$		0			0
$35$	−0.559950	+	0.490282i	−0.0946488	+	0.0828728i
$36$		0			0
$37$	5.34597	+	1.45054i	0.878873	+	0.238467i	0.672581	−	0.740024i	$-0.265186\pi$
$37$	5.34597	+	1.45054i	0.878873	+	0.238467i	0.206292	+	0.978491i	$0.433860\pi$
$38$		0			0
$39$	0.849845	+	0.301248i	0.136084	+	0.0482382i
$40$		0			0
$41$	8.67736	−	4.23675i	1.35518	−	0.661669i	0.389406	−	0.921066i	$-0.372680\pi$
$41$	8.67736	−	4.23675i	1.35518	−	0.661669i	0.965771	+	0.259397i	$0.0835238\pi$
$42$		0			0
$43$	−0.643414	+	6.77922i	−0.0981198	+	1.03382i	0.801749	+	0.597661i	$0.203903\pi$
$43$	−0.643414	+	6.77922i	−0.0981198	+	1.03382i	−0.899869	+	0.436161i	$0.856338\pi$
$44$		0			0
$45$	−0.187520	−	0.0286098i	−0.0279538	−	0.00426490i
$46$		0			0
$47$	0.215760	+	11.3993i	0.0314719	+	1.66276i	0.571119	+	0.820867i	$0.306509\pi$
$47$	0.215760	+	11.3993i	0.0314719	+	1.66276i	−0.539648	+	0.841891i	$0.681442\pi$
$48$		0			0
$49$	−0.377389	−	0.447839i	−0.0539127	−	0.0639770i
$50$		0			0
$51$	−0.361254	−	6.35597i	−0.0505856	−	0.890014i
$52$		0			0
$53$	−0.737486	−	4.28786i	−0.101301	−	0.588983i	−0.991152	−	0.132731i	$-0.957625\pi$
$53$	−0.737486	−	4.28786i	−0.101301	−	0.588983i	0.889851	−	0.456252i	$-0.150808\pi$
$54$		0			0
$55$	−0.967238	+	0.518471i	−0.130422	+	0.0699106i
$56$		0			0
$57$	4.50874	+	2.20141i	0.597198	+	0.291584i
$58$		0			0
$59$	1.52942	−	0.116001i	0.199114	−	0.0151020i	0.0243062	−	0.999705i	$-0.492262\pi$
$59$	1.52942	−	0.116001i	0.199114	−	0.0151020i	0.174808	+	0.984603i	$0.444070\pi$
$60$		0			0
$61$	−7.21740	+	7.35530i	−0.924093	+	0.941749i	−0.998460	−	0.0554817i	$-0.982331\pi$
$61$	−7.21740	+	7.35530i	−0.924093	+	0.941749i	0.0743668	+	0.997231i	$0.476306\pi$
$62$		0			0
$63$	0.327714	−	1.90538i	0.0412881	−	0.240056i
$64$		0			0
$65$	−0.124845	+	0.101228i	−0.0154851	+	0.0125558i
$66$		0			0
$67$	−11.7033	+	5.17529i	−1.42978	+	0.632262i	−0.967131	−	0.254278i	$-0.918162\pi$
$67$	−11.7033	+	5.17529i	−1.42978	+	0.632262i	−0.462651	+	0.886540i	$0.653102\pi$
$68$		0			0
$69$	−1.42449	+	5.67267i	−0.171489	+	0.682909i
$70$		0			0
$71$	−10.4610	+	1.19300i	−1.24150	+	0.141583i	−0.709221	−	0.704987i	$-0.750953\pi$
$71$	−10.4610	+	1.19300i	−1.24150	+	0.141583i	−0.532278	+	0.846570i	$0.678664\pi$
$72$		0			0
$73$	11.5486	−	8.66068i	1.35166	−	1.01366i	0.354763	−	0.934956i	$-0.384562\pi$
$73$	11.5486	−	8.66068i	1.35166	−	1.01366i	0.996898	−	0.0786999i	$-0.0250769\pi$
$74$		0			0
$75$	4.81296	−	5.71143i	0.555753	−	0.659499i
$76$		0			0
$77$	−5.09687	−	9.95653i	−0.580842	−	1.13465i
$78$		0			0
$79$	3.00491	−	7.99342i	0.338079	−	0.899330i	−0.651924	−	0.758284i	$-0.726038\pi$
$79$	3.00491	−	7.99342i	0.338079	−	0.899330i	0.990003	−	0.141046i	$-0.0450465\pi$
$80$		0			0
$81$	−5.52342	+	3.23558i	−0.613714	+	0.359509i
$82$		0			0
$83$	2.42434	−	3.36352i	0.266106	−	0.369194i	−0.656901	−	0.753977i	$-0.728133\pi$
$83$	2.42434	−	3.36352i	0.266106	−	0.369194i	0.923007	+	0.384782i	$0.125724\pi$
$84$		0			0
$85$	1.00020	+	0.536140i	0.108487	+	0.0581525i
$86$		0			0
$87$	5.91125	+	10.5436i	0.633753	+	1.13039i
$88$		0			0
$89$	5.19207	+	17.7958i	0.550358	+	1.88635i	0.454004	+	0.891000i	$0.349995\pi$
$89$	5.19207	+	17.7958i	0.550358	+	1.88635i	0.0963537	+	0.995347i	$0.469282\pi$
$90$		0			0
$91$	−1.00747	−	1.29175i	−0.105612	−	0.135412i
$92$		0			0
$93$	−4.11190	−	10.9381i	−0.426384	−	1.13423i
$94$		0			0
$95$	−0.754080	+	0.480960i	−0.0773670	+	0.0493454i
$96$		0			0
$97$	1.75883	+	0.406447i	0.178582	+	0.0412685i	0.313499	−	0.949588i	$-0.398499\pi$
$97$	1.75883	+	0.406447i	0.178582	+	0.0412685i	−0.134917	+	0.990857i	$0.543077\pi$
$98$		0			0
$99$	1.10340	−	2.62861i	0.110896	−	0.264185i
$100$		0			0
$101$	−1.70320	−	17.9454i	−0.169474	−	1.78564i	−0.525131	−	0.851021i	$-0.675984\pi$
$101$	−1.70320	−	17.9454i	−0.169474	−	1.78564i	0.355656	−	0.934617i	$-0.384257\pi$
$102$		0			0
$103$	−8.12832	+	5.62806i	−0.800907	+	0.554549i	−0.897624	−	0.440763i	$-0.854708\pi$
$103$	−8.12832	+	5.62806i	−0.800907	+	0.554549i	0.0967167	+	0.995312i	$0.469166\pi$
$104$		0			0
$105$	−0.848843	−	0.743232i	−0.0828386	−	0.0725320i
$106$		0			0
$107$	−7.64010	−	5.29002i	−0.738596	−	0.511405i	0.139304	−	0.990250i	$-0.455514\pi$
$107$	−7.64010	−	5.29002i	−0.738596	−	0.511405i	−0.877900	+	0.478844i	$0.841056\pi$
$108$		0			0
$109$	−14.8959	−	9.50073i	−1.42677	−	0.910005i	−0.999984	−	0.00565063i	$-0.998201\pi$
$109$	−14.8959	−	9.50073i	−1.42677	−	0.910005i	−0.426782	−	0.904354i	$-0.640353\pi$
$110$		0			0
$111$	−1.10917	+	8.32355i	−0.105278	+	0.790036i
$112$		0			0
$113$	5.21336	−	8.52552i	0.490431	−	0.802014i	−0.507799	−	0.861475i	$-0.669541\pi$
$113$	5.21336	−	8.52552i	0.490431	−	0.802014i	0.998231	+	0.0594618i	$0.0189384\pi$
$114$		0			0
$115$	−0.730216	−	0.744168i	−0.0680930	−	0.0693941i
$116$		0			0
$117$	0.0862925	−	0.408508i	0.00797775	−	0.0377666i
$118$		0			0
$119$	−5.65639	+	10.0890i	−0.518521	+	0.924859i
$120$		0			0
$121$	−1.33786	−	5.32766i	−0.121624	−	0.484333i
$122$		0			0
$123$	8.10387	+	12.1906i	0.730701	+	1.09919i
$124$		0			0
$125$	0.848237	+	2.54489i	0.0758686	+	0.227622i
$126$		0			0
$127$	−5.09852	−	0.581446i	−0.452421	−	0.0515950i	−0.115878	−	0.993263i	$-0.536968\pi$
$127$	−5.09852	−	0.581446i	−0.452421	−	0.0515950i	−0.336542	+	0.941668i	$0.609257\pi$
$128$		0			0
$129$	−10.3156	+	0.390637i	−0.908237	+	0.0343937i
$130$		0			0
$131$	−0.128148	+	2.25466i	−0.0111963	+	0.196991i	0.987920	+	0.154964i	$0.0495261\pi$
$131$	−0.128148	+	2.25466i	−0.0111963	+	0.196991i	−0.999116	+	0.0420269i	$0.986618\pi$
$132$		0			0
$133$	−4.75572	−	7.77714i	−0.412373	−	0.674364i
$134$		0			0
$135$	0.0286982	−	1.51621i	0.00246994	−	0.130495i
$136$		0			0
$137$	8.34193	−	2.95699i	0.712699	−	0.252633i	0.0470441	−	0.998893i	$-0.485020\pi$
$137$	8.34193	−	2.95699i	0.712699	−	0.252633i	0.665655	+	0.746260i	$0.268152\pi$
$138$		0			0
$139$	−6.83071	−	6.45349i	−0.579373	−	0.547378i	0.340172	−	0.940363i	$-0.389515\pi$
$139$	−6.83071	−	6.45349i	−0.579373	−	0.547378i	−0.919545	+	0.392985i	$0.871442\pi$
$140$		0			0
$141$	−17.0859	+	2.60679i	−1.43889	+	0.219531i
$142$		0			0
$143$	−1.01855	−	2.19030i	−0.0851754	−	0.183162i
$144$		0			0
$145$	−2.15317	−	0.0815376i	−0.178811	−	0.00677133i
$146$		0			0
$147$	0.597374	−	0.656756i	0.0492706	−	0.0541683i
$148$		0			0
$149$	−3.36740	−	2.73039i	−0.275868	−	0.223682i	0.481867	−	0.876245i	$-0.339959\pi$
$149$	−3.36740	−	2.73039i	−0.275868	−	0.223682i	−0.757735	+	0.652563i	$0.773694\pi$
$150$		0			0
$151$	5.36548	+	4.02376i	0.436637	+	0.327449i	0.795513	−	0.605937i	$-0.207201\pi$
$151$	5.36548	+	4.02376i	0.436637	+	0.327449i	−0.358876	+	0.933385i	$0.616840\pi$
$152$		0			0
$153$	−2.89532	+	0.554584i	−0.234073	+	0.0448354i
$154$		0			0
$155$	2.04584	+	0.391870i	0.164326	+	0.0314758i
$156$		0			0
$157$	3.37207	+	15.9634i	0.269121	+	1.27401i	0.877195	+	0.480134i	$0.159412\pi$
$157$	3.37207	+	15.9634i	0.269121	+	1.27401i	−0.608074	+	0.793880i	$0.708058\pi$
$158$		0			0
$159$	6.29546	−	1.96677i	0.499262	−	0.155975i
$160$		0			0
$161$	7.72421	−	7.29766i	0.608753	−	0.575136i
$162$		0			0
$163$	1.10580	−	3.31765i	0.0866132	−	0.259858i	−0.896444	−	0.443157i	$-0.853858\pi$
$163$	1.10580	−	3.31765i	0.0866132	−	0.259858i	0.983057	+	0.183299i	$0.0586777\pi$
$164$		0			0
$165$	−0.972755	−	1.34960i	−0.0757289	−	0.105066i
$166$		0			0
$167$	−8.23680	+	9.95767i	−0.637382	+	0.770548i
$167$	−8.23680	+	9.95767i	−0.637382	+	0.770548i
$168$		0			0
$169$	7.39449	+	10.2591i	0.568807	+	0.789159i
$170$		0			0
$171$	0.734675	−	2.20418i	0.0561820	−	0.168558i
$172$		0			0
$173$	−2.92107	+	2.75976i	−0.222085	+	0.209821i	−0.789733	−	0.613450i	$-0.789781\pi$
$173$	−2.92107	+	2.75976i	−0.222085	+	0.209821i	0.567648	+	0.823271i	$0.307853\pi$
$174$		0			0
$175$	−12.9525	+	4.04652i	−0.979119	+	0.305888i
$176$		0			0
$177$	0.480557	+	2.27495i	0.0361209	+	0.170996i
$178$		0			0
$179$	16.0825	+	3.08052i	1.20206	+	0.230249i	0.749817	−	0.661645i	$-0.230142\pi$
$179$	16.0825	+	3.08052i	1.20206	+	0.230249i	0.452244	+	0.891894i	$0.350624\pi$
$180$		0			0
$181$	−11.8450	+	2.26885i	−0.880432	+	0.168642i	−0.608385	−	0.793642i	$-0.708182\pi$
$181$	−11.8450	+	2.26885i	−0.880432	+	0.168642i	−0.272047	+	0.962284i	$0.587701\pi$
$182$		0			0
$183$	−12.4976	−	9.37236i	−0.923848	−	0.692825i
$184$		0			0
$185$	−1.16268	−	0.942735i	−0.0854820	−	0.0693113i
$186$		0			0
$187$	−11.4759	+	12.6167i	−0.839203	+	0.922623i
$188$		0			0
$189$	15.4453	+	0.584891i	1.12348	+	0.0425446i
$190$		0			0
$191$	9.45105	+	20.3236i	0.683854	+	1.47056i	0.872548	+	0.488528i	$0.162466\pi$
$191$	9.45105	+	20.3236i	0.683854	+	1.47056i	−0.188694	+	0.982036i	$0.560425\pi$
$192$		0			0
$193$	−16.0175	+	2.44378i	−1.15296	+	0.175907i	−0.699005	−	0.715117i	$-0.746374\pi$
$193$	−16.0175	+	2.44378i	−1.15296	+	0.175907i	−0.453957	+	0.891024i	$0.649988\pi$
$194$		0			0
$195$	−0.177108	−	0.167328i	−0.0126830	−	0.0119826i
$196$		0			0
$197$	−11.2829	+	3.99948i	−0.803871	+	0.284951i	−0.704138	−	0.710063i	$-0.748666\pi$
$197$	−11.2829	+	3.99948i	−0.803871	+	0.284951i	−0.0997328	+	0.995014i	$0.531799\pi$
$198$		0			0
$199$	−0.149578	+	7.90267i	−0.0106033	+	0.560205i	0.954482	+	0.298269i	$0.0964093\pi$
$199$	−0.149578	+	7.90267i	−0.0106033	+	0.560205i	−0.965085	+	0.261936i	$0.915639\pi$
$200$		0			0
$201$	−10.1201	−	16.5496i	−0.713814	−	1.16732i
$202$		0			0
$203$	1.24620	−	21.9260i	0.0874662	−	1.53890i
$204$		0			0
$205$	−2.60755	+	0.0987444i	−0.182119	+	0.00689661i
$206$		0			0
$207$	2.69091	+	0.306877i	0.187031	+	0.0213294i
$208$		0			0
$209$	−4.25040	−	12.7521i	−0.294006	−	0.882081i
$210$		0			0
$211$	−7.40703	−	11.1424i	−0.509921	−	0.767073i	0.484245	−	0.874932i	$-0.339094\pi$
$211$	−7.40703	−	11.1424i	−0.509921	−	0.767073i	−0.994166	+	0.107859i	$0.965600\pi$
$212$		0			0
$213$	−3.88736	−	15.4803i	−0.266357	−	1.06070i
$214$		0			0
$215$	0.899899	−	1.60510i	0.0613726	−	0.109467i
$216$		0			0
$217$	−4.38791	+	20.7723i	−0.297871	+	1.41012i
$218$		0			0
$219$	15.3264	+	15.6192i	1.03566	+	1.05545i
$220$		0			0
$221$	−1.30311	+	2.13101i	−0.0876568	+	0.143347i
$222$		0			0
$223$	−2.10069	+	15.7642i	−0.140673	+	1.05565i	0.768684	+	0.639629i	$0.220912\pi$
$223$	−2.10069	+	15.7642i	−0.140673	+	1.05565i	−0.909357	+	0.416017i	$0.863426\pi$
$224$		0			0
$225$	−2.91596	−	1.85982i	−0.194397	−	0.123988i
$226$		0			0
$227$	13.5606	+	9.38939i	0.900049	+	0.623196i	0.926434	−	0.376456i	$-0.122857\pi$
$227$	13.5606	+	9.38939i	0.900049	+	0.623196i	−0.0263850	+	0.999652i	$0.508400\pi$
$228$		0			0
$229$	−18.8871	−	16.5372i	−1.24809	−	1.09281i	−0.992011	−	0.126152i	$-0.959737\pi$
$229$	−18.8871	−	16.5372i	−1.24809	−	1.09281i	−0.256081	−	0.966655i	$-0.582431\pi$
$230$		0			0
$231$	13.9405	−	9.65245i	0.917220	−	0.635085i
$232$		0			0
$233$	0.401628	+	4.23169i	0.0263115	+	0.277227i	0.998985	+	0.0450487i	$0.0143443\pi$
$233$	0.401628	+	4.23169i	0.0263115	+	0.277227i	−0.972673	+	0.232178i	$0.925415\pi$
$234$		0			0
$235$	1.19248	−	2.84081i	0.0777887	−	0.185314i
$236$		0			0
$237$	12.6130	+	2.91473i	0.819300	+	0.189332i
$238$		0			0
$239$	−0.610311	+	0.389262i	−0.0394777	+	0.0251793i	−0.557334	−	0.830288i	$-0.688176\pi$
$239$	−0.610311	+	0.389262i	−0.0394777	+	0.0251793i	0.517857	+	0.855467i	$0.326730\pi$
$240$		0			0
$241$	5.53687	+	14.7287i	0.356661	+	0.948761i	0.985265	+	0.171035i	$0.0547111\pi$
$241$	5.53687	+	14.7287i	0.356661	+	0.948761i	−0.628604	+	0.777726i	$0.716373\pi$
$242$		0			0
$243$	4.38603	+	5.62360i	0.281364	+	0.360754i
$244$		0			0
$245$	0.0443249	+	0.151923i	0.00283181	+	0.00970601i
$246$		0			0
$247$	−0.962740	−	1.71719i	−0.0612577	−	0.109262i
$248$		0			0
$249$	5.53962	+	2.96942i	0.351059	+	0.188179i
$250$		0			0
$251$	13.2505	−	18.3837i	0.836366	−	1.16037i	−0.148817	−	0.988865i	$-0.547546\pi$
$251$	13.2505	−	18.3837i	0.836366	−	1.16037i	0.985183	−	0.171506i	$-0.0548632\pi$
$252$		0			0
$253$	13.5200	−	7.91990i	0.849993	−	0.497920i
$254$		0			0
$255$	−0.605349	+	1.61030i	−0.0379084	+	0.100841i
$256$		0			0
$257$	−5.99892	−	11.7187i	−0.374202	−	0.730990i	0.624547	−	0.780987i	$-0.285284\pi$
$257$	−5.99892	−	11.7187i	−0.374202	−	0.730990i	−0.998749	+	0.0499970i	$0.984079\pi$
$258$		0			0
$259$	9.83110	−	11.6663i	0.610875	−	0.724911i
$260$		0			0
$261$	4.47799	−	3.35819i	0.277181	−	0.207867i
$262$		0			0
$263$	3.41090	−	0.388987i	0.210325	−	0.0239859i	−0.00750857	−	0.999972i	$-0.502390\pi$
$263$	3.41090	−	0.388987i	0.210325	−	0.0239859i	0.217834	+	0.975986i	$0.430101\pi$
$264$		0			0
$265$	−0.286348	+	1.14030i	−0.0175902	+	0.0700482i
$266$		0			0
$267$	−25.7010	+	11.3652i	−1.57288	+	0.695540i
$268$		0			0
$269$	4.53647	−	3.67830i	0.276593	−	0.224270i	−0.481451	−	0.876473i	$-0.659890\pi$
$269$	4.53647	−	3.67830i	0.276593	−	0.224270i	0.758044	+	0.652203i	$0.226155\pi$
$270$		0			0
$271$	−3.61935	+	21.0435i	−0.219860	+	1.27830i	0.640241	+	0.768175i	$0.278835\pi$
$271$	−3.61935	+	21.0435i	−0.219860	+	1.27830i	−0.860100	+	0.510125i	$0.829599\pi$
$272$		0			0
$273$	1.73930	−	1.77253i	0.105267	−	0.107278i
$274$		0			0
$275$	−19.9520	+	1.51328i	−1.20315	+	0.0912540i
$276$		0			0
$277$	25.1050	+	12.2576i	1.50841	+	0.736487i	0.992738	−	0.120298i	$-0.0383850\pi$
$277$	25.1050	+	12.2576i	1.50841	+	0.736487i	0.515674	+	0.856785i	$0.327542\pi$
$278$		0			0
$279$	−4.76914	+	2.55641i	−0.285521	+	0.153049i
$280$		0			0
$281$	2.21858	+	12.8992i	0.132350	+	0.769502i	0.973498	+	0.228697i	$0.0734466\pi$
$281$	2.21858	+	12.8992i	0.132350	+	0.769502i	−0.841148	+	0.540805i	$0.818120\pi$
$282$		0			0
$283$	1.06882	+	18.8050i	0.0635346	+	1.11784i	0.859044	+	0.511901i	$0.171059\pi$
$283$	1.06882	+	18.8050i	0.0635346	+	1.11784i	−0.795510	+	0.605941i	$0.792797\pi$
$284$		0			0
$285$	−0.873706	−	1.03681i	−0.0517539	−	0.0614152i
$286$		0			0
$287$	−0.503302	−	26.5910i	−0.0297090	−	1.56962i
$288$		0			0
$289$	0.629072	+	0.0959772i	0.0370042	+	0.00564572i
$290$		0			0
$291$	−0.258561	+	2.72428i	−0.0151571	+	0.159700i
$292$		0			0
$293$	−3.30340	+	1.61290i	−0.192987	+	0.0942264i	−0.532706	−	0.846301i	$-0.678825\pi$
$293$	−3.30340	+	1.61290i	−0.192987	+	0.0942264i	0.339719	+	0.940527i	$0.389668\pi$
$294$		0			0
$295$	−0.390660	−	0.138479i	−0.0227451	−	0.00806254i
$296$		0			0
$297$	21.9956	+	5.96813i	1.27631	+	0.346306i
$298$		0			0
$299$	1.72654	−	1.51173i	0.0998484	−	0.0874255i
$300$		0			0
$301$	16.1831	+	9.47992i	0.932777	+	0.546413i
$302$		0			0
$303$	26.6246	−	6.15266i	1.52954	−	0.353461i
$304$		0			0
$305$	2.58755	−	1.02902i	0.148163	−	0.0589215i
$306$		0			0
$307$	1.67680	+	3.99460i	0.0957003	+	0.227984i	0.962835	−	0.270089i	$-0.0870532\pi$
$307$	1.67680	+	3.99460i	0.0957003	+	0.227984i	−0.867135	+	0.498073i	$0.834041\pi$
$308$		0			0
$309$	−10.0846	−	11.0870i	−0.573691	−	0.630718i
$310$		0			0
$311$	−15.2207	−	6.05299i	−0.863089	−	0.343234i	−0.104281	−	0.994548i	$-0.533254\pi$
$311$	−15.2207	−	6.05299i	−0.863089	−	0.343234i	−0.758808	+	0.651314i	$0.774218\pi$
$312$		0			0
$313$	9.43465	+	2.94749i	0.533278	+	0.166602i	0.552965	−	0.833204i	$-0.313496\pi$
$313$	9.43465	+	2.94749i	0.533278	+	0.166602i	−0.0196878	+	0.999806i	$0.506267\pi$
$314$		0			0
$315$	−0.289226	+	0.435082i	−0.0162961	+	0.0245141i
$316$		0			0
$317$	−2.44667	−	0.185570i	−0.137418	−	0.0104226i	0.00673976	−	0.999977i	$-0.497855\pi$
$317$	−2.44667	−	0.185570i	−0.137418	−	0.0104226i	−0.144158	+	0.989555i	$0.546047\pi$
$318$		0			0
$319$	9.06980	−	31.0866i	0.507811	−	1.74052i
$320$		0			0
$321$	6.41917	−	12.5396i	0.358283	−	0.699893i
$322$		0			0
$323$	−8.54840	+	10.9604i	−0.475646	+	0.609855i
$324$		0			0
$325$	−2.82826	+	0.767398i	−0.156883	+	0.0425676i
$326$		0			0
$327$	11.2935	−	24.2856i	0.624531	−	1.34300i
$328$		0			0
$329$	28.7189	+	12.6998i	1.58333	+	0.700161i
$330$		0			0
$331$	−2.70250	−	20.2803i	−0.148543	−	1.11471i	−0.893972	−	0.448122i	$-0.852093\pi$
$331$	−2.70250	−	20.2803i	−0.148543	−	1.11471i	0.745430	−	0.666584i	$-0.232244\pi$
$332$		0			0
$333$	3.88838			0.213082
$334$		0			0
$335$	3.45795			0.188928
$336$		0			0
$337$	−2.11788	−	15.8932i	−0.115368	−	0.865757i	−0.949406	−	0.314050i	$-0.898314\pi$
$337$	−2.11788	−	15.8932i	−0.115368	−	0.865757i	0.834038	−	0.551707i	$-0.186023\pi$
$338$		0			0
$339$	13.8547	+	6.12668i	0.752486	+	0.332756i
$340$		0			0
$341$	−13.2004	+	28.3862i	−0.714841	+	1.53720i
$342$		0			0
$343$	17.0500	−	4.62621i	0.920612	−	0.249792i
$344$		0			0
$345$	0.972003	−	1.24627i	0.0523309	−	0.0670967i
$346$		0			0
$347$	8.04335	−	15.7124i	0.431790	−	0.843485i	−0.568001	−	0.823028i	$-0.692283\pi$
$347$	8.04335	−	15.7124i	0.431790	−	0.843485i	0.999791	−	0.0204570i	$-0.00651212\pi$
$348$		0			0
$349$	3.91370	−	13.4142i	0.209495	−	0.718043i	−0.785566	−	0.618778i	$-0.787628\pi$
$349$	3.91370	−	13.4142i	0.209495	−	0.718043i	0.995061	−	0.0992650i	$-0.0316492\pi$
$350$		0			0
$351$	3.32835	+	0.252442i	0.177654	+	0.0134743i
$352$		0			0
$353$	2.54329	−	3.82587i	0.135366	−	0.203630i	−0.758851	−	0.651264i	$-0.774239\pi$
$353$	2.54329	−	3.82587i	0.135366	−	0.203630i	0.894217	+	0.447633i	$0.147733\pi$
$354$		0			0
$355$	2.71573	+	0.848425i	0.144136	+	0.0450297i
$356$		0			0
$357$	−16.2928	−	6.47934i	−0.862308	−	0.342923i
$358$		0			0
$359$	15.4888	+	17.0284i	0.817467	+	0.898726i	0.996369	−	0.0851406i	$-0.0271339\pi$
$359$	15.4888	+	17.0284i	0.817467	+	0.898726i	−0.178902	+	0.983867i	$0.557254\pi$
$360$		0			0
$361$	3.11382	+	7.41795i	0.163885	+	0.390419i
$362$		0			0
$363$	7.73769	−	3.07713i	0.406123	−	0.161507i
$364$		0			0
$365$	−3.80063	+	0.878287i	−0.198934	+	0.0459716i
$366$		0			0
$367$	−19.9202	−	11.6691i	−1.03983	−	0.609124i	−0.116522	−	0.993188i	$-0.537175\pi$
$367$	−19.9202	−	11.6691i	−1.03983	−	0.609124i	−0.923306	+	0.384065i	$0.874524\pi$
$368$		0			0
$369$	5.09987	−	4.46535i	0.265488	−	0.232457i
$370$		0			0
$371$	−11.5649	−	3.13794i	−0.600420	−	0.162914i
$372$		0			0
$373$	−17.6358	−	6.25144i	−0.913149	−	0.323687i	−0.164287	−	0.986413i	$-0.552532\pi$
$373$	−17.6358	−	6.25144i	−0.913149	−	0.323687i	−0.748863	+	0.662725i	$0.769400\pi$
$374$		0			0
$375$	−3.65421	+	1.78418i	−0.188703	+	0.0921347i
$376$		0			0
$377$	0.448115	−	4.72149i	0.0230791	−	0.243169i
$378$		0			0
$379$	−23.5684	−	3.59582i	−1.21063	−	0.184705i	−0.486070	−	0.873920i	$-0.661570\pi$
$379$	−23.5684	−	3.59582i	−1.21063	−	0.184705i	−0.724557	+	0.689215i	$0.757956\pi$
$380$		0			0
$381$	−0.147212	−	7.77769i	−0.00754191	−	0.398463i
$382$		0			0
$383$	8.32030	+	9.87351i	0.425148	+	0.504513i	0.934460	−	0.356069i	$-0.115883\pi$
$383$	8.32030	+	9.87351i	0.425148	+	0.504513i	−0.509312	+	0.860582i	$0.670100\pi$
$384$		0			0
$385$	0.171516	+	3.01769i	0.00874126	+	0.153796i
$386$		0			0
$387$	0.810263	+	4.71100i	0.0411880	+	0.239474i
$388$		0			0
$389$	19.6029	−	10.5078i	0.993908	−	0.532767i	0.106776	−	0.994283i	$-0.465947\pi$
$389$	19.6029	−	10.5078i	0.993908	−	0.532767i	0.887132	+	0.461516i	$0.152694\pi$
$390$		0			0
$391$	−14.5601	−	7.10900i	−0.736334	−	0.359517i
$392$		0			0
$393$	−3.41361	+	0.258909i	−0.172194	+	0.0130602i
$394$		0			0
$395$	−1.61622	+	1.64710i	−0.0813208	+	0.0828745i
$396$		0			0
$397$	−1.98213	+	11.5244i	−0.0994803	+	0.578395i	0.892403	+	0.451240i	$0.149018\pi$
$397$	−1.98213	+	11.5244i	−0.0994803	+	0.578395i	−0.991883	+	0.127155i	$0.959416\pi$
$398$		0			0
$399$	10.7340	−	8.70344i	0.537372	−	0.435717i
$400$		0			0
$401$	1.77807	−	0.786277i	0.0887925	−	0.0392648i	−0.359557	−	0.933123i	$-0.617072\pi$
$401$	1.77807	−	0.786277i	0.0887925	−	0.0392648i	0.448350	+	0.893858i	$0.352012\pi$
$402$		0			0
$403$	−1.11668	+	4.44686i	−0.0556255	+	0.221514i
$404$		0			0
$405$	1.71867	−	0.196001i	0.0854014	−	0.00973936i
$406$		0			0
$407$	17.9973	−	13.4968i	0.892092	−	0.669010i
$408$		0			0
$409$	−10.0717	+	11.9519i	−0.498015	+	0.590983i	−0.954300	−	0.298851i	$-0.903397\pi$
$409$	−10.0717	+	11.9519i	−0.498015	+	0.590983i	0.456285	+	0.889834i	$0.349180\pi$
$410$		0			0
$411$	6.11368	+	11.9428i	0.301565	+	0.589097i
$412$		0			0
$413$	1.48650	−	3.95427i	0.0731460	−	0.194577i
$414$		0			0
$415$	−0.966744	+	0.566311i	−0.0474556	+	0.0277991i
$416$		0			0
$417$	8.32953	−	11.5564i	0.407899	−	0.565917i
$418$		0			0
$419$	13.1663	+	7.05760i	0.643218	+	0.344786i	0.761472	−	0.648197i	$-0.224477\pi$
$419$	13.1663	+	7.05760i	0.643218	+	0.344786i	−0.118254	+	0.992983i	$0.537730\pi$
$420$		0			0
$421$	−6.75587	−	12.0501i	−0.329261	−	0.587286i	0.656722	−	0.754133i	$-0.271943\pi$
$421$	−6.75587	−	12.0501i	−0.329261	−	0.587286i	−0.985983	+	0.166847i	$0.946641\pi$
$422$		0			0
$423$	2.24159	+	7.68304i	0.108990	+	0.373562i
$424$		0			0
$425$	12.7250	+	16.3156i	0.617255	+	0.791421i
$426$		0			0
$427$	9.98703	+	26.5667i	0.483306	+	1.28565i
$428$		0			0
$429$	3.08728	−	1.96910i	0.149055	−	0.0950689i
$430$		0			0
$431$	−32.4457	−	7.49787i	−1.56286	−	0.361160i	−0.646943	−	0.762538i	$-0.723953\pi$
$431$	−32.4457	−	7.49787i	−1.56286	−	0.361160i	−0.915912	+	0.401379i	$0.868531\pi$
$432$		0			0
$433$	−6.88553	+	16.4032i	−0.330897	+	0.788287i	0.668124	+	0.744050i	$0.267098\pi$
$433$	−6.88553	+	16.4032i	−0.330897	+	0.788287i	−0.999021	+	0.0442368i	$0.985914\pi$
$434$		0			0
$435$	−0.308625	−	3.25178i	−0.0147975	−	0.155911i
$436$		0			0
$437$	10.4990	−	7.26953i	0.502236	−	0.347749i
$438$		0			0
$439$	−3.00689	−	2.63278i	−0.143511	−	0.125656i	0.583994	−	0.811758i	$-0.301489\pi$
$439$	−3.00689	−	2.63278i	−0.143511	−	0.125656i	−0.727505	+	0.686102i	$0.759320\pi$
$440$		0			0
$441$	−0.337992	−	0.234026i	−0.0160949	−	0.0111441i
$442$		0			0
$443$	15.9503	+	10.1733i	0.757823	+	0.483347i	0.859288	−	0.511492i	$-0.170907\pi$
$443$	15.9503	+	10.1733i	0.757823	+	0.483347i	−0.101465	+	0.994839i	$0.532353\pi$
$444$		0			0
$445$	0.661687	−	4.96548i	0.0313669	−	0.235386i
$446$		0			0
$447$	3.42852	−	5.60673i	0.162163	−	0.265189i
$448$		0			0
$449$	16.6433	+	16.9613i	0.785447	+	0.800454i	0.983723	−	0.179692i	$-0.0575102\pi$
$449$	16.6433	+	16.9613i	0.785447	+	0.800454i	−0.198276	+	0.980146i	$0.563534\pi$
$450$		0			0
$451$	8.10514	−	38.3697i	0.381656	−	1.80676i
$452$		0			0
$453$	−4.97190	+	8.86811i	−0.233600	+	0.416660i
$454$		0			0
$455$	0.107816	+	0.429347i	0.00505448	+	0.0201281i
$456$		0			0
$457$	20.4243	+	30.7242i	0.955409	+	1.43722i	0.898567	+	0.438836i	$0.144609\pi$
$457$	20.4243	+	30.7242i	0.955409	+	1.43722i	0.0568424	+	0.998383i	$0.481897\pi$
$458$		0			0
$459$	−7.45225	−	22.3583i	−0.347841	−	1.04360i
$460$		0			0
$461$	−6.26787	−	0.714801i	−0.291924	−	0.0332916i	−0.0338836	−	0.999426i	$-0.510788\pi$
$461$	−6.26787	−	0.714801i	−0.291924	−	0.0332916i	−0.258040	+	0.966134i	$0.583077\pi$
$462$		0			0
$463$	−0.912225	+	0.0345447i	−0.0423947	+	0.00160543i	−0.0590303	−	0.998256i	$-0.518801\pi$
$463$	−0.912225	+	0.0345447i	−0.0423947	+	0.00160543i	0.0166356	+	0.999862i	$0.494704\pi$
$464$		0			0
$465$	−0.179186	+	3.15263i	−0.00830954	+	0.146200i
$466$		0			0
$467$	13.2200	+	21.6190i	0.611749	+	1.00041i	0.996985	+	0.0775892i	$0.0247223\pi$
$467$	13.2200	+	21.6190i	0.611749	+	1.00041i	−0.385237	+	0.922818i	$0.625880\pi$
$468$		0			0
$469$	−0.666965	+	35.2379i	−0.0307976	+	1.62713i
$470$		0			0
$471$	−23.3120	+	8.26349i	−1.07416	+	0.380762i
$472$		0			0
$473$	20.1024	+	18.9923i	0.924310	+	0.873267i
$474$		0			0
$475$	−16.1209	+	2.45956i	−0.739679	+	0.112853i
$476$		0			0
$477$	−1.28782	−	2.76934i	−0.0589653	−	0.126799i
$478$		0			0
$479$	−12.6826	−	0.480274i	−0.579485	−	0.0219443i	−0.253527	−	0.967328i	$-0.581591\pi$
$479$	−12.6826	−	0.480274i	−0.579485	−	0.0219443i	−0.325958	+	0.945384i	$0.605687\pi$
$480$		0			0
$481$	2.21691	−	2.43728i	0.101083	−	0.111131i
$482$		0			0
$483$	12.5125	+	10.1455i	0.569337	+	0.461635i
$484$		0			0
$485$	−0.390258	−	0.292668i	−0.0177207	−	0.0132894i
$486$		0			0
$487$	−20.0413	+	3.83880i	−0.908157	+	0.173953i	−0.620890	−	0.783898i	$-0.713229\pi$
$487$	−20.0413	+	3.83880i	−0.908157	+	0.173953i	−0.287267	+	0.957851i	$0.592747\pi$
$488$		0			0
$489$	5.20666	+	0.997310i	0.235453	+	0.0450999i
$490$		0			0
$491$	−3.25925	−	15.4293i	−0.147088	−	0.696314i	−0.987913	−	0.155007i	$-0.950460\pi$
$491$	−3.25925	−	15.4293i	−0.147088	−	0.696314i	0.840825	−	0.541307i	$-0.182070\pi$
$492$		0			0
$493$	−31.9628	+	9.98554i	−1.43953	+	0.449726i
$494$		0			0
$495$	−0.559970	+	0.529047i	−0.0251688	+	0.0237789i
$496$		0			0
$497$	−9.16959	+	27.5107i	−0.411312	+	1.23402i
$498$		0			0
$499$	5.62572	+	7.80509i	0.251842	+	0.349404i	0.918122	−	0.396297i	$-0.129705\pi$
$499$	5.62572	+	7.80509i	0.251842	+	0.349404i	−0.666281	+	0.745701i	$0.732115\pi$
$500$		0			0
$501$	−16.6121	−	10.3831i	−0.742176	−	0.463881i
$502$		0			0
$503$	12.0017	+	16.6512i	0.535132	+	0.742439i	0.988884	−	0.148689i	$-0.0475053\pi$
$503$	12.0017	+	16.6512i	0.535132	+	0.742439i	−0.453752	+	0.891128i	$0.649915\pi$
$504$		0			0
$505$	−1.54029	+	4.62118i	−0.0685418	+	0.205640i
$506$		0			0
$507$	−13.9351	+	13.1655i	−0.618878	+	0.584702i
$508$		0			0
$509$	−7.54924	+	2.35847i	−0.334614	+	0.104537i	−0.460888	−	0.887458i	$-0.652469\pi$
$509$	−7.54924	+	2.35847i	−0.334614	+	0.104537i	0.126274	+	0.991995i	$0.459698\pi$
$510$		0			0
$511$	−8.21703	−	38.8993i	−0.363500	−	1.72081i
$512$		0			0
$513$	18.2428	+	3.49432i	0.805441	+	0.154278i
$514$		0			0
$515$	2.62391	−	0.502597i	0.115623	−	0.0221471i
$516$		0			0
$517$	37.0434	+	27.7801i	1.62917	+	1.22177i
$518$		0			0
$519$	−4.73184	−	3.83672i	−0.207705	−	0.168413i
$520$		0			0
$521$	22.5956	−	24.8417i	0.989933	−	1.08834i	−0.00615630	−	0.999981i	$-0.501960\pi$
$521$	22.5956	−	24.8417i	0.989933	−	1.08834i	0.996089	−	0.0883546i	$-0.0281609\pi$
$522$		0			0
$523$	−37.4028	−	1.41639i	−1.63551	−	0.0619345i	−0.796006	−	0.605289i	$-0.793058\pi$
$523$	−37.4028	−	1.41639i	−1.63551	−	0.0619345i	−0.839503	+	0.543354i	$0.817154\pi$
$524$		0			0
$525$	−8.67407	−	18.6528i	−0.378567	−	0.814074i
$526$		0			0
$527$	32.0019	−	4.88252i	1.39403	−	0.212686i
$528$		0			0
$529$	−5.89807	−	5.57236i	−0.256438	−	0.242277i
$530$		0			0
$531$	1.01482	−	0.359726i	0.0440394	−	0.0156108i
$532$		0			0
$533$	0.108692	−	5.74252i	0.00470796	−	0.248736i
$534$		0			0
$535$	1.31004	+	2.14235i	0.0566382	+	0.0926217i
$536$		0			0
$537$	−1.40859	+	24.7831i	−0.0607852	+	1.06947i
$538$		0			0
$539$	−2.37671	+	0.0900025i	−0.102372	+	0.00387668i
$540$		0			0
$541$	−29.9258	−	3.41280i	−1.28661	−	0.146728i	−0.556954	−	0.830543i	$-0.688030\pi$
$541$	−29.9258	−	3.41280i	−1.28661	−	0.146728i	−0.729655	+	0.683816i	$0.760319\pi$
$542$		0			0
$543$	−5.78109	−	17.3445i	−0.248090	−	0.744324i
$544$		0			0
$545$	2.64306	+	3.97595i	0.113216	+	0.170311i
$546$		0			0
$547$	−1.36330	−	5.42899i	−0.0582907	−	0.232127i	0.933773	−	0.357867i	$-0.116496\pi$
$547$	−1.36330	−	5.42899i	−0.0582907	−	0.232127i	−0.992063	+	0.125740i	$0.959869\pi$
$548$		0			0
$549$	−3.53753	+	6.30971i	−0.150978	+	0.269292i
$550$		0			0
$551$	5.45459	−	25.8220i	0.232373	−	1.10005i
$552$		0			0
$553$	−16.4728	−	16.7876i	−0.700497	−	0.713881i
$554$		0			0
$555$	1.18378	−	1.93587i	0.0502488	−	0.0821730i
$556$		0			0
$557$	−0.300539	+	2.25533i	−0.0127342	+	0.0955613i	−0.996453	−	0.0841554i	$-0.973181\pi$
$557$	−0.300539	+	2.25533i	−0.0127342	+	0.0955613i	0.983718	+	0.179717i	$0.0575181\pi$
$558$		0			0
$559$	3.41487	+	2.17804i	0.144434	+	0.0921212i
$560$		0			0
$561$	−21.2563	−	14.7179i	−0.897441	−	0.621390i
$562$		0			0
$563$	−27.1894	−	23.8066i	−1.14590	−	1.00333i	−0.999901	−	0.0140425i	$-0.995530\pi$
$563$	−27.1894	−	23.8066i	−1.14590	−	1.00333i	−0.145996	−	0.989285i	$-0.546639\pi$
$564$		0			0
$565$	−2.22017	+	1.53725i	−0.0934031	+	0.0646724i
$566$		0			0
$567$	1.66583	+	17.5517i	0.0699583	+	0.737104i
$568$		0			0
$569$	1.01975	−	2.42932i	0.0427502	−	0.101843i	−0.899276	−	0.437381i	$-0.855906\pi$
$569$	1.01975	−	2.42932i	0.0427502	−	0.101843i	0.942027	+	0.335538i	$0.108918\pi$
$570$		0			0
$571$	23.9245	+	5.52871i	1.00121	+	0.231369i	0.693769	−	0.720198i	$-0.255949\pi$
$571$	23.9245	+	5.52871i	1.00121	+	0.231369i	0.307441	+	0.951567i	$0.400527\pi$
$572$		0			0
$573$	−28.6467	+	18.2711i	−1.19673	+	0.763287i
$574$		0			0
$575$	−6.68905	−	17.7936i	−0.278952	−	0.742046i
$576$		0			0
$577$	−20.0853	−	25.7526i	−0.836162	−	1.07210i	−0.996380	−	0.0850142i	$-0.972906\pi$
$577$	−20.0853	−	25.7526i	−0.836162	−	1.07210i	0.160218	−	0.987082i	$-0.448780\pi$
$578$		0			0
$579$	−6.87944	−	23.5792i	−0.285900	−	0.979918i
$580$		0			0
$581$	−5.58447	−	9.96073i	−0.231683	−	0.413241i
$582$		0			0
$583$	−15.5732	−	8.34773i	−0.644975	−	0.345728i
$584$		0			0
$585$	−0.0659713	+	0.0915282i	−0.00272758	+	0.00378423i
$586$		0			0
$587$	−18.6090	+	10.9010i	−0.768076	+	0.449933i	−0.836667	−	0.547712i	$-0.815499\pi$
$587$	−18.6090	+	10.9010i	−0.768076	+	0.449933i	0.0685912	+	0.997645i	$0.478150\pi$
$588$		0			0
$589$	−8.97781	+	23.8820i	−0.369924	+	0.984042i
$590$		0			0
$591$	−8.26905	−	16.1533i	−0.340143	−	0.664457i
$592$		0			0
$593$	−19.4407	+	23.0699i	−0.798336	+	0.947366i	−0.999482	−	0.0321948i	$-0.989750\pi$
$593$	−19.4407	+	23.0699i	−0.798336	+	0.947366i	0.201146	+	0.979561i	$0.435533\pi$
$594$		0			0
$595$	2.50053	−	1.87523i	0.102512	−	0.0768770i
$596$		0			0
$597$	−11.9048	+	1.35765i	−0.487233	+	0.0555651i
$598$		0			0
$599$	−8.07912	+	32.1729i	−0.330104	+	1.31455i	0.548160	+	0.836373i	$0.315328\pi$
$599$	−8.07912	+	32.1729i	−0.330104	+	1.31455i	−0.878264	+	0.478176i	$0.841298\pi$
$600$		0			0
$601$	−10.0868	+	4.46049i	−0.411451	+	0.181947i	−0.599791	−	0.800157i	$-0.704750\pi$
$601$	−10.0868	+	4.46049i	−0.411451	+	0.181947i	0.188340	+	0.982104i	$0.439689\pi$
$602$		0			0
$603$	−6.97731	+	5.65741i	−0.284138	+	0.230387i
$604$		0			0
$605$	−0.251608	+	1.46289i	−0.0102293	+	0.0594750i
$606$		0			0
$607$	14.8500	−	15.1337i	0.602741	−	0.614257i	−0.342938	−	0.939358i	$-0.611422\pi$
$607$	14.8500	−	15.1337i	0.602741	−	0.614257i	0.945679	+	0.325100i	$0.105398\pi$
$608$		0			0
$609$	33.1964	−	2.51782i	1.34519	−	0.102027i
$610$		0			0
$611$	6.09383	+	2.97533i	0.246530	+	0.120369i
$612$		0			0
$613$	14.9785	−	8.02895i	0.604974	−	0.324286i	−0.141257	−	0.989973i	$-0.545114\pi$
$613$	14.9785	−	8.02895i	0.604974	−	0.324286i	0.746231	+	0.665687i	$0.231861\pi$
$614$		0			0
$615$	−0.670509	−	3.89845i	−0.0270375	−	0.157201i
$616$		0			0
$617$	0.681021	+	11.9820i	0.0274169	+	0.482378i	0.982526	+	0.186125i	$0.0595928\pi$
$617$	0.681021	+	11.9820i	0.0274169	+	0.482378i	−0.955109	+	0.296254i	$0.904263\pi$
$618$		0			0
$619$	7.85840	+	9.32538i	0.315856	+	0.374819i	0.899298	−	0.437336i	$-0.144078\pi$
$619$	7.85840	+	9.32538i	0.315856	+	0.374819i	−0.583443	+	0.812154i	$0.698295\pi$
$620$		0			0
$621$	0.409746	+	21.6481i	0.0164425	+	0.868710i
$622$		0			0
$623$	50.4726	+	7.70058i	2.02214	+	0.308517i
$624$		0			0
$625$	−2.25914	+	23.8030i	−0.0903656	+	0.952121i
$626$		0			0
$627$	18.3108	−	8.94029i	0.731261	−	0.357041i
$628$		0			0
$629$	−21.9258	−	7.77211i	−0.874238	−	0.309894i
$630$		0			0
$631$	−38.2555	−	10.3800i	−1.52293	−	0.413220i	−0.600575	−	0.799568i	$-0.705062\pi$
$631$	−38.2555	−	10.3800i	−1.52293	−	0.413220i	−0.922353	+	0.386348i	$0.873736\pi$
$632$		0			0
$633$	15.2599	−	13.3613i	0.606525	−	0.531062i
$634$		0			0
$635$	1.19651	+	0.700904i	0.0474819	+	0.0278145i
$636$		0			0
$637$	−0.339392	+	0.0784301i	−0.0134472	+	0.00310751i
$638$		0			0
$639$	−6.86777	+	2.73118i	−0.271685	+	0.108044i
$640$		0			0
$641$	−19.3269	−	46.0419i	−0.763366	−	1.81855i	−0.534703	−	0.845040i	$-0.679577\pi$
$641$	−19.3269	−	46.0419i	−0.763366	−	1.81855i	−0.228663	−	0.973506i	$-0.573435\pi$
$642$		0			0
$643$	26.0430	+	28.6318i	1.02704	+	1.12913i	0.991546	+	0.129756i	$0.0414194\pi$
$643$	26.0430	+	28.6318i	1.02704	+	1.12913i	0.0354892	+	0.999370i	$0.488701\pi$
$644$		0			0
$645$	2.59209	+	1.03082i	0.102064	+	0.0405887i
$646$		0			0
$647$	−15.6887	−	4.90132i	−0.616786	−	0.192691i	−0.0261881	−	0.999657i	$-0.508337\pi$
$647$	−15.6887	−	4.90132i	−0.616786	−	0.192691i	−0.590598	+	0.806966i	$0.701108\pi$
$648$		0			0
$649$	3.44843	−	5.18747i	0.135363	−	0.203626i
$650$		0			0
$651$	−32.0920	−	2.43405i	−1.25779	−	0.0953980i
$652$		0			0
$653$	9.38920	−	32.1814i	0.367428	−	1.25936i	−0.540897	−	0.841089i	$-0.681915\pi$
$653$	9.38920	−	32.1814i	0.367428	−	1.25936i	0.908324	−	0.418266i	$-0.137362\pi$
$654$		0			0
$655$	0.278077	−	0.543213i	0.0108654	−	0.0212251i
$656$		0			0
$657$	6.23184	−	7.99023i	0.243127	−	0.311729i
$658$		0			0
$659$	−21.3726	+	5.79910i	−0.832560	+	0.225901i	−0.652533	−	0.757761i	$-0.726293\pi$
$659$	−21.3726	+	5.79910i	−0.832560	+	0.225901i	−0.180028	+	0.983662i	$0.557619\pi$
$660$		0			0
$661$	10.4234	−	22.4145i	0.405423	−	0.871824i	−0.592386	−	0.805655i	$-0.701814\pi$
$661$	10.4234	−	22.4145i	0.405423	−	0.871824i	0.997808	−	0.0661695i	$-0.0210778\pi$
$662$		0			0
$663$	−3.46308	−	1.53140i	−0.134495	−	0.0594748i
$664$		0			0
$665$	0.325386	+	2.44179i	0.0126179	+	0.0946885i
$666$		0			0
$667$	30.7645			1.19121
$668$		0			0
$669$	−24.1085			−0.932090
$670$		0			0
$671$	5.52795	+	41.4833i	0.213404	+	1.60144i
$672$		0			0
$673$	4.30925	+	1.90559i	0.166109	+	0.0734549i	0.485814	−	0.874062i	$-0.338523\pi$
$673$	4.30925	+	1.90559i	0.166109	+	0.0734549i	−0.319704	+	0.947517i	$0.603584\pi$
$674$		0			0
$675$	11.6589	−	25.0715i	0.448753	−	0.965001i
$676$		0			0
$677$	−26.1094	+	7.08433i	−1.00347	+	0.272273i	−0.725428	−	0.688298i	$-0.758358\pi$
$677$	−26.1094	+	7.08433i	−1.00347	+	0.272273i	−0.278037	+	0.960570i	$0.589684\pi$
$678$		0			0
$679$	3.05767	−	3.92044i	0.117343	−	0.150453i
$680$		0			0
$681$	−11.3936	+	22.2569i	−0.436602	+	0.852886i
$682$		0			0
$683$	−6.88514	+	23.5987i	−0.263452	+	0.902981i	0.715452	+	0.698662i	$0.246221\pi$
$683$	−6.88514	+	23.5987i	−0.263452	+	0.902981i	−0.978904	+	0.204319i	$0.934502\pi$
$684$		0			0
$685$	−2.38479	−	0.180877i	−0.0911182	−	0.00691095i
$686$		0			0
$687$	21.0676	−	31.6919i	0.803778	−	1.20912i
$688$		0			0
$689$	−2.47009	−	0.771684i	−0.0941029	−	0.0293988i
$690$		0			0
$691$	−25.6193	−	10.1883i	−0.974603	−	0.387581i	−0.172661	−	0.984981i	$-0.555236\pi$
$691$	−25.6193	−	10.1883i	−0.974603	−	0.387581i	−0.801943	+	0.597401i	$0.796200\pi$
$692$		0			0
$693$	−5.28319	−	5.80836i	−0.200692	−	0.220641i
$694$		0			0
$695$	0.982857	+	2.34143i	0.0372819	+	0.0888156i
$696$		0			0
$697$	−37.6824	+	14.9856i	−1.42732	+	0.567619i
$698$		0			0
$699$	−6.27829	+	1.45085i	−0.237467	+	0.0548762i
$700$		0			0
$701$	−0.0197329	−	0.0115594i	−0.000745303	−	0.000436593i	0.505081	−	0.863072i	$-0.331463\pi$
$701$	−0.0197329	−	0.0115594i	−0.000745303	−	0.000436593i	−0.505826	+	0.862636i	$0.668812\pi$
$702$		0			0
$703$	13.7938	−	12.0776i	0.520243	−	0.455516i
$704$		0			0
$705$	4.50750	+	1.22303i	0.169762	+	0.0460621i
$706$		0			0
$707$	−46.7946	−	16.5875i	−1.75989	−	0.623835i
$708$		0			0
$709$	40.7020	−	19.8729i	1.52860	−	0.746342i	0.533551	−	0.845768i	$-0.320857\pi$
$709$	40.7020	−	19.8729i	1.52860	−	0.746342i	0.995045	+	0.0994255i	$0.0317005\pi$
$710$		0			0
$711$	0.566391	−	5.96768i	0.0212413	−	0.223805i
$712$		0			0
$713$	−29.4008	−	4.48567i	−1.10107	−	0.167990i
$714$		0			0
$715$	0.0123526	+	0.652626i	0.000461960	+	0.0244068i
$716$		0			0
$717$	−0.707130	−	0.839134i	−0.0264082	−	0.0313380i
$718$		0			0
$719$	0.866145	+	15.2391i	0.0323017	+	0.568324i	0.973246	+	0.229764i	$0.0737953\pi$
$719$	0.866145	+	15.2391i	0.0323017	+	0.568324i	−0.940945	+	0.338560i	$0.890060\pi$
$720$		0			0
$721$	4.61557	+	26.8357i	0.171893	+	0.999412i
$722$		0			0
$723$	−21.0233	+	11.2692i	−0.781866	+	0.419106i
$724$		0			0
$725$	−35.3032	−	17.2369i	−1.31113	−	0.640163i
$726$		0			0
$727$	1.61720	−	0.122658i	0.0599785	−	0.00454913i	−0.0456053	−	0.998960i	$-0.514522\pi$
$727$	1.61720	−	0.122658i	0.0599785	−	0.00454913i	0.105584	+	0.994410i	$0.466329\pi$
$728$		0			0
$729$	−21.0222	+	21.4239i	−0.778600	+	0.793477i
$730$		0			0
$731$	4.84746	−	28.1839i	0.179290	−	1.04242i
$732$		0			0
$733$	22.1891	−	17.9916i	0.819575	−	0.664535i	−0.125245	−	0.992126i	$-0.539972\pi$
$733$	22.1891	−	17.9916i	0.819575	−	0.664535i	0.944820	+	0.327591i	$0.106237\pi$
$734$		0			0
$735$	−0.219411	+	0.0970253i	−0.00809309	+	0.00357883i
$736$		0			0
$737$	−12.6572	+	50.4038i	−0.466233	+	1.85665i
$738$		0			0
$739$	28.2122	−	3.21738i	1.03780	−	0.118353i	0.422274	−	0.906468i	$-0.361232\pi$
$739$	28.2122	−	3.21738i	1.03780	−	0.118353i	0.615528	+	0.788115i	$0.288943\pi$
$740$		0			0
$741$	2.38755	−	1.79050i	0.0877087	−	0.0657757i
$742$		0			0
$743$	5.21684	−	6.19071i	0.191387	−	0.227115i	−0.660519	−	0.750810i	$-0.729664\pi$
$743$	5.21684	−	6.19071i	0.191387	−	0.227115i	0.851906	+	0.523695i	$0.175447\pi$
$744$		0			0
$745$	0.533824	+	1.04280i	0.0195578	+	0.0382054i
$746$		0			0
$747$	1.02414	−	2.72433i	0.0374713	−	0.0996781i
$748$		0			0
$749$	−22.0840	+	12.9367i	−0.806933	+	0.472695i
$750$		0			0
$751$	23.9981	−	33.2948i	0.875702	−	1.21494i	−0.0998123	−	0.995006i	$-0.531824\pi$
$751$	23.9981	−	33.2948i	0.875702	−	1.21494i	0.975514	−	0.219938i	$-0.0705854\pi$
$752$		0			0
$753$	30.2774	+	16.2297i	1.10337	+	0.591443i
$754$		0			0
$755$	−0.886281	−	1.58081i	−0.0322551	−	0.0575317i
$756$		0			0
$757$	4.05559	+	13.9005i	0.147403	+	0.505222i	0.999845	−	0.0175994i	$-0.00560235\pi$
$757$	4.05559	+	13.9005i	0.147403	+	0.505222i	−0.852442	+	0.522821i	$0.824879\pi$
$758$		0			0
$759$	14.6080	+	18.7298i	0.530237	+	0.679850i
$760$		0			0
$761$	−5.91798	−	15.7425i	−0.214527	−	0.570666i	0.784233	−	0.620467i	$-0.213057\pi$
$761$	−5.91798	−	15.7425i	−0.214527	−	0.570666i	−0.998759	+	0.0498011i	$0.984141\pi$
$762$		0			0
$763$	−41.0263	+	26.1670i	−1.48525	+	0.947308i
$764$		0			0
$765$	0.776160	+	0.179363i	0.0280621	+	0.00648487i
$766$		0			0
$767$	0.353106	−	0.841193i	0.0127499	−	0.0303737i
$768$		0			0
$769$	2.08849	+	22.0051i	0.0753130	+	0.793523i	0.950702	+	0.310104i	$0.100364\pi$
$769$	2.08849	+	22.0051i	0.0753130	+	0.793523i	−0.875389	+	0.483418i	$0.839395\pi$
$770$		0			0
$771$	16.4078	−	11.3608i	0.590911	−	0.409148i
$772$		0			0
$773$	−6.16645	−	5.39924i	−0.221792	−	0.194197i	0.540661	−	0.841240i	$-0.318174\pi$
$773$	−6.16645	−	5.39924i	−0.221792	−	0.194197i	−0.762453	+	0.647043i	$0.776005\pi$
$774$		0			0
$775$	31.2250	+	21.6203i	1.12164	+	0.776623i
$776$		0			0
$777$	19.4989	+	12.4366i	0.699520	+	0.446160i
$778$		0			0
$779$	4.22174	−	31.6811i	0.151260	−	1.13509i
$780$		0			0
$781$	−22.3072	+	36.4795i	−0.798216	+	1.30534i
$782$		0			0
$783$	31.3408	+	31.9396i	1.12003	+	1.14143i
$784$		0			0
$785$	0.911222	−	4.31372i	0.0325229	−	0.153963i
$786$		0			0
$787$	25.5986	−	45.6590i	0.912493	−	1.62757i	0.142236	−	0.989833i	$-0.454571\pi$
$787$	25.5986	−	45.6590i	0.912493	−	1.62757i	0.770257	−	0.637734i	$-0.220128\pi$
$788$		0			0
$789$	1.26750	+	5.04748i	0.0451242	+	0.179695i
$790$		0			0
$791$	−15.2369	−	22.9209i	−0.541763	−	0.814972i
$792$		0			0
$793$	1.93812	+	5.81476i	0.0688246	+	0.206488i
$794$		0			0
$795$	−1.77081	−	0.201946i	−0.0628040	−	0.00716230i
$796$		0			0
$797$	37.9499	−	1.43711i	1.34425	−	0.0509050i	0.644124	−	0.764921i	$-0.277222\pi$
$797$	37.9499	−	1.43711i	1.34425	−	0.0509050i	0.700129	+	0.714016i	$0.253126\pi$
$798$		0			0
$799$	2.71700	−	47.8035i	0.0961206	−	1.69117i
$800$		0			0
$801$	6.78870	+	11.1017i	0.239867	+	0.392260i
$802$		0			0
$803$	1.10941	−	58.6136i	0.0391502	−	2.06843i
$804$		0			0
$805$	−2.70651	+	0.959386i	−0.0953919	+	0.0338139i
$806$		0			0
$807$	6.43554	+	6.08016i	0.226542	+	0.214032i
$808$		0			0
$809$	8.04052	−	1.22674i	0.282690	−	0.0431298i	−0.00792982	−	0.999969i	$-0.502524\pi$
$809$	8.04052	−	1.22674i	0.282690	−	0.0431298i	0.290619	+	0.956839i	$0.406139\pi$
$810$		0			0
$811$	14.9246	+	32.0939i	0.524072	+	1.12697i	0.972447	+	0.233123i	$0.0748944\pi$
$811$	14.9246	+	32.0939i	0.524072	+	1.12697i	−0.448375	+	0.893845i	$0.647997\pi$
$812$		0			0
$813$	−32.3456	−	1.22488i	−1.13441	−	0.0429585i
$814$		0			0
$815$	−0.635866	+	0.699074i	−0.0222734	+	0.0244875i
$816$		0			0
$817$	17.5071	+	14.1953i	0.612496	+	0.496629i
$818$		0			0
$819$	−0.919984	−	0.689927i	−0.0321468	−	0.0241080i
$820$		0			0
$821$	18.2531	−	3.49629i	0.637038	−	0.122021i	0.140562	−	0.990072i	$-0.455109\pi$
$821$	18.2531	−	3.49629i	0.637038	−	0.122021i	0.496476	+	0.868050i	$0.334627\pi$
$822$		0			0
$823$	−42.5130	−	8.14315i	−1.48191	−	0.283852i	−0.617473	−	0.786592i	$-0.711843\pi$
$823$	−42.5130	−	8.14315i	−1.48191	−	0.283852i	−0.864438	+	0.502740i	$0.832325\pi$
$824$		0			0
$825$	−6.26906	−	29.6777i	−0.218261	−	1.03324i
$826$		0			0
$827$	−10.5846	+	3.30674i	−0.368061	+	0.114987i	−0.476634	−	0.879102i	$-0.658143\pi$
$827$	−10.5846	+	3.30674i	−0.368061	+	0.114987i	0.108572	+	0.994089i	$0.465372\pi$
$828$		0			0
$829$	−12.8512	+	12.1415i	−0.446339	+	0.421691i	−0.876753	−	0.480941i	$-0.840295\pi$
$829$	−12.8512	+	12.1415i	−0.446339	+	0.421691i	0.430414	+	0.902632i	$0.358368\pi$
$830$		0			0
$831$	−13.3918	+	40.1783i	−0.464557	+	1.39377i
$832$		0			0
$833$	1.43809	+	1.99520i	0.0498270	+	0.0691297i
$834$		0			0
$835$	3.12390	−	1.56076i	0.108107	−	0.0540124i
$836$		0			0
$837$	−25.2945	−	35.0935i	−0.874306	−	1.21301i
$838$		0			0
$839$	−17.1851	+	51.5590i	−0.593296	+	1.78001i	0.0318330	+	0.999493i	$0.489866\pi$
$839$	−17.1851	+	51.5590i	−0.593296	+	1.78001i	−0.625129	+	0.780521i	$0.714954\pi$
$840$		0			0
$841$	25.1364	−	23.7483i	0.866773	−	0.818907i
$842$		0			0
$843$	−18.9387	+	5.91666i	−0.652282	+	0.203780i
$844$		0			0
$845$	−0.706287	−	3.34356i	−0.0242970	−	0.115022i
$846$		0			0
$847$	−14.8589	−	2.84615i	−0.510559	−	0.0977949i
$848$		0			0
$849$	−28.0432	+	5.37153i	−0.962441	+	0.184351i
$850$		0			0
$851$	17.0979	+	12.8223i	0.586110	+	0.439544i
$852$		0			0
$853$	−0.490036	−	0.397336i	−0.0167785	−	0.0136045i	0.621385	−	0.783506i	$-0.286570\pi$
$853$	−0.490036	−	0.397336i	−0.0167785	−	0.0136045i	−0.638163	+	0.769901i	$0.720305\pi$
$854$		0			0
$855$	−0.422458	+	0.464452i	−0.0144478	+	0.0158839i
$856$		0			0
$857$	40.6614	+	1.53979i	1.38897	+	0.0525982i	0.721693	−	0.692214i	$-0.243364\pi$
$857$	40.6614	+	1.53979i	1.38897	+	0.0525982i	0.667274	+	0.744812i	$0.267461\pi$
$858$		0			0
$859$	5.51033	+	11.8494i	0.188010	+	0.404298i	0.977936	−	0.208904i	$-0.0669896\pi$
$859$	5.51033	+	11.8494i	0.188010	+	0.404298i	−0.789926	+	0.613202i	$0.789881\pi$
$860$		0			0
$861$	39.8561	−	6.08082i	1.35829	−	0.207234i
$862$		0			0
$863$	22.4793	+	21.2379i	0.765203	+	0.722946i	0.966523	−	0.256579i	$-0.0825955\pi$
$863$	22.4793	+	21.2379i	0.765203	+	0.722946i	−0.201320	+	0.979525i	$0.564523\pi$
$864$		0			0
$865$	1.02352	−	0.362812i	0.0348008	−	0.0123360i
$866$		0			0
$867$	−0.0182554	+	0.964489i	−0.000619985	+	0.0327558i
$868$		0			0
$869$	−18.0926	−	29.5872i	−0.613749	−	1.00368i
$870$		0			0
$871$	−0.431901	+	7.59896i	−0.0146344	+	0.257481i
$872$		0			0
$873$	1.26627	−	0.0479519i	0.0428568	−	0.00162293i
$874$		0			0
$875$	7.34066	+	0.837144i	0.248160	+	0.0283006i
$876$		0			0
$877$	13.2983	+	39.8976i	0.449051	+	1.34725i	0.892540	+	0.450968i	$0.148921\pi$
$877$	13.2983	+	39.8976i	0.449051	+	1.34725i	−0.443489	+	0.896280i	$0.646260\pi$
$878$		0			0
$879$	−3.08507	−	4.64087i	−0.104057	−	0.156533i
$880$		0			0
$881$	−9.95293	−	39.6348i	−0.335323	−	1.33533i	−0.871155	−	0.491008i	$-0.836629\pi$
$881$	−9.95293	−	39.6348i	−0.335323	−	1.33533i	0.535833	−	0.844324i	$-0.319998\pi$
$882$		0			0
$883$	2.04986	−	3.65623i	0.0689833	−	0.123042i	−0.835601	−	0.549337i	$-0.814880\pi$
$883$	2.04986	−	3.65623i	0.0689833	−	0.123042i	0.904584	+	0.426295i	$0.140182\pi$
$884$		0			0
$885$	0.129859	−	0.614752i	0.00436516	−	0.0206646i
$886$		0			0
$887$	18.8024	+	19.1616i	0.631323	+	0.643385i	0.952824	−	0.303524i	$-0.0981633\pi$
$887$	18.8024	+	19.1616i	0.631323	+	0.643385i	−0.321501	+	0.946909i	$0.604187\pi$
$888$		0			0
$889$	−7.37327	+	12.0577i	−0.247292	+	0.404402i
$890$		0			0
$891$	−3.43392	+	25.7691i	−0.115041	+	0.863298i
$892$		0			0
$893$	31.8160	+	20.2926i	1.06468	+	0.679065i
$894$		0			0
$895$	−3.63797	−	2.51894i	−0.121604	−	0.0841988i
$896$		0			0
$897$	2.61731	+	2.29167i	0.0873894	+	0.0765166i
$898$		0			0
$899$	−50.5342	+	34.9899i	−1.68541	+	1.16698i
$900$		0			0
$901$	1.72639	+	18.1898i	0.0575144	+	0.605991i
$902$		0			0
$903$	−11.0045	+	26.2156i	−0.366206	+	0.872401i
$904$		0			0
$905$	3.17534	+	0.733788i	0.105552	+	0.0243919i
$906$		0			0
$907$	38.9177	−	24.8221i	1.29224	−	0.824203i	0.300664	−	0.953730i	$-0.402792\pi$
$907$	38.9177	−	24.8221i	1.29224	−	0.824203i	0.991576	+	0.129527i	$0.0413460\pi$
$908$		0			0
$909$	−4.45260	−	11.8444i	−0.147684	−	0.392855i
$910$		0			0
$911$	9.47073	+	12.1430i	0.313779	+	0.402316i	0.919328	−	0.393492i	$-0.128733\pi$
$911$	9.47073	+	12.1430i	0.313779	+	0.402316i	−0.605549	+	0.795808i	$0.707046\pi$
$912$		0			0
$913$	−4.71608	−	16.1643i	−0.156080	−	0.534961i
$914$		0			0
$915$	2.06438	+	3.68212i	0.0682462	+	0.121727i
$916$		0			0
$917$	5.48192	+	2.93849i	0.181029	+	0.0970375i
$918$		0			0
$919$	25.4437	−	35.3005i	0.839312	−	1.16446i	−0.145246	−	0.989396i	$-0.546397\pi$
$919$	25.4437	−	35.3005i	0.839312	−	1.16446i	0.984558	−	0.175061i	$-0.0560124\pi$
$920$		0			0
$921$	−5.66670	+	3.31951i	−0.186724	+	0.109382i
$922$		0			0
$923$	−2.20364	+	5.86194i	−0.0725337	+	0.192948i
$924$		0			0
$925$	−12.4362	−	24.2937i	−0.408901	−	0.798773i
$926$		0			0
$927$	−4.47215	+	5.30700i	−0.146885	+	0.174305i
$928$		0			0
$929$	16.4317	−	12.3227i	0.539108	−	0.404295i	−0.295331	−	0.955395i	$-0.595430\pi$
$929$	16.4317	−	12.3227i	0.539108	−	0.404295i	0.834440	+	0.551099i	$0.185792\pi$
$930$		0			0
$931$	−1.92591	+	0.219635i	−0.0631192	+	0.00719824i
$932$		0			0
$933$	6.04772	−	24.0834i	0.197993	−	0.788455i
$934$		0			0
$935$	4.21501	−	1.86392i	0.137846	−	0.0609566i
$936$		0			0
$937$	22.2988	−	18.0805i	0.728469	−	0.590664i	−0.192039	−	0.981387i	$-0.561510\pi$
$937$	22.2988	−	18.0805i	0.728469	−	0.590664i	0.920508	+	0.390723i	$0.127775\pi$
$938$		0			0
$939$	−2.53985	+	14.7671i	−0.0828849	+	0.481906i
$940$		0			0
$941$	7.57090	−	7.71556i	0.246804	−	0.251520i	−0.579198	−	0.815187i	$-0.696634\pi$
$941$	7.57090	−	7.71556i	0.246804	−	0.251520i	0.826002	+	0.563667i	$0.190610\pi$
$942$		0			0
$943$	37.1500	−	2.81768i	1.20977	−	0.0917562i
$944$		0			0
$945$	−3.75323	−	1.83253i	−0.122093	−	0.0596122i
$946$		0			0
$947$	−10.3240	+	5.53400i	−0.335485	+	0.179831i	−0.631547	−	0.775338i	$-0.717580\pi$
$947$	−10.3240	+	5.53400i	−0.335485	+	0.179831i	0.296062	+	0.955169i	$0.404327\pi$
$948$		0			0
$949$	−1.45536	−	8.46172i	−0.0472431	−	0.274679i
$950$		0			0
$951$	−0.211071	−	3.71362i	−0.00684444	−	0.120423i
$952$		0			0
$953$	−19.5090	−	23.1509i	−0.631959	−	0.749931i	0.350469	−	0.936574i	$-0.386022\pi$
$953$	−19.5090	−	23.1509i	−0.631959	−	0.749931i	−0.982428	+	0.186643i	$0.940239\pi$
$954$		0			0
$955$	−0.114619	−	6.05567i	−0.00370898	−	0.195957i
$956$		0			0
$957$	48.5283	+	7.40394i	1.56870	+	0.239335i
$958$		0			0
$959$	2.30318	−	24.2671i	0.0743736	−	0.783625i
$960$		0			0
$961$	25.5390	−	12.4695i	0.823838	−	0.402241i
$962$		0			0
$963$	−6.14836	−	2.17943i	−0.198128	−	0.0702312i
$964$		0			0
$965$	4.22564	+	1.14655i	0.136028	+	0.0369089i
$966$		0			0
$967$	4.54221	−	3.97708i	0.146068	−	0.127894i	−0.582608	−	0.812753i	$-0.697968\pi$
$967$	4.54221	−	3.97708i	0.146068	−	0.127894i	0.728675	+	0.684859i	$0.240136\pi$
$968$		0			0
$969$	−18.1814	−	10.6505i	−0.584069	−	0.342143i
$970$		0			0
$971$	−10.0827	+	2.33001i	−0.323570	+	0.0747736i	−0.383815	−	0.923410i	$-0.625390\pi$
$971$	−10.0827	+	2.33001i	−0.323570	+	0.0747736i	0.0602454	+	0.998184i	$0.480812\pi$
$972$		0			0
$973$	−24.0497	+	9.56409i	−0.770997	+	0.306611i
$974$		0			0
$975$	−1.71945	−	4.09620i	−0.0550665	−	0.131183i
$976$		0			0
$977$	11.0656	+	12.1655i	0.354019	+	0.389210i	0.890712	−	0.454568i	$-0.150206\pi$
$977$	11.0656	+	12.1655i	0.354019	+	0.389210i	−0.536693	+	0.843777i	$0.680327\pi$
$978$		0			0
$979$	69.9559	+	27.8201i	2.23580	+	0.889134i
$980$		0			0
$981$	−11.8380	−	3.69831i	−0.377957	−	0.118078i
$982$		0			0
$983$	−13.4476	+	20.2292i	−0.428911	+	0.645210i	−0.982213	−	0.187771i	$-0.939874\pi$
$983$	−13.4476	+	20.2292i	−0.428911	+	0.645210i	0.553302	+	0.832981i	$0.313368\pi$
$984$		0			0
$985$	3.22555	+	0.244645i	0.102774	+	0.00779503i
$986$		0			0
$987$	−13.3326	+	45.6973i	−0.424381	+	1.45456i
$988$		0			0
$989$	−11.9721	+	23.3871i	−0.380691	+	0.743666i
$990$		0			0
$991$	11.7405	−	15.0532i	0.372949	−	0.478182i	−0.564932	−	0.825137i	$-0.691098\pi$
$991$	11.7405	−	15.0532i	0.372949	−	0.478182i	0.937882	+	0.346955i	$0.112784\pi$
$992$		0			0
$993$	29.9329	−	8.12178i	0.949893	−	0.257737i
$994$		0			0
$995$	0.900631	−	1.93672i	0.0285519	−	0.0613982i
$996$		0			0
$997$	12.2005	+	5.39515i	0.386393	+	0.170866i	0.588500	−	0.808497i	$-0.299719\pi$
$997$	12.2005	+	5.39515i	0.386393	+	0.170866i	−0.202107	+	0.979363i	$0.564779\pi$
$998$		0			0
$999$	4.10612	+	30.8135i	0.129912	+	0.974896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.11	✓	1148
167.130	even	83	inner	668.2.e.a.297.11	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.11	✓	1148	1.1	even	1	trivial
668.2.e.a.297.11	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)

\(f(q)\)	\(=\)	\(q+(0.200238 + 1.50264i) q^{3} +(-0.247141 - 0.109288i) q^{5} +(1.16135 - 2.49738i) q^{7} +(0.677472 - 0.183820i) q^{9} +O(q^{10})\)	\(q+(0.200238 + 1.50264i) q^{3} +(-0.247141 - 0.109288i) q^{5} +(1.16135 - 2.49738i) q^{7} +(0.677472 - 0.183820i) q^{9} +(2.49761 - 3.20234i) q^{11} +(0.271031 - 0.529450i) q^{13} +(0.114733 - 0.393248i) q^{15} +(-4.18754 - 0.317608i) q^{17} +(1.83233 - 2.75637i) q^{19} +(3.98522 + 1.24503i) q^{21} +(3.58513 + 1.42574i) q^{23} +(-3.31523 - 3.64477i) q^{25} +(2.17209 + 5.17451i) q^{27} +(7.40935 - 2.94655i) q^{29} +(-7.51054 + 1.73561i) q^{31} +(5.31210 + 3.11179i) q^{33} +(-0.559950 + 0.490282i) q^{35} +(5.34597 + 1.45054i) q^{37} +(0.849845 + 0.301248i) q^{39} +(8.67736 - 4.23675i) q^{41} +(-0.643414 + 6.77922i) q^{43} +(-0.187520 - 0.0286098i) q^{45} +(0.215760 + 11.3993i) q^{47} +(-0.377389 - 0.447839i) q^{49} +(-0.361254 - 6.35597i) q^{51} +(-0.737486 - 4.28786i) q^{53} +(-0.967238 + 0.518471i) q^{55} +(4.50874 + 2.20141i) q^{57} +(1.52942 - 0.116001i) q^{59} +(-7.21740 + 7.35530i) q^{61} +(0.327714 - 1.90538i) q^{63} +(-0.124845 + 0.101228i) q^{65} +(-11.7033 + 5.17529i) q^{67} +(-1.42449 + 5.67267i) q^{69} +(-10.4610 + 1.19300i) q^{71} +(11.5486 - 8.66068i) q^{73} +(4.81296 - 5.71143i) q^{75} +(-5.09687 - 9.95653i) q^{77} +(3.00491 - 7.99342i) q^{79} +(-5.52342 + 3.23558i) q^{81} +(2.42434 - 3.36352i) q^{83} +(1.00020 + 0.536140i) q^{85} +(5.91125 + 10.5436i) q^{87} +(5.19207 + 17.7958i) q^{89} +(-1.00747 - 1.29175i) q^{91} +(-4.11190 - 10.9381i) q^{93} +(-0.754080 + 0.480960i) q^{95} +(1.75883 + 0.406447i) q^{97} +(1.10340 - 2.62861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 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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