LMFDB - Embedded newform 462.2.y.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	462.289
Dual form			462.2.y.b.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 - 0.994522i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-2.25946 + 1.00598i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-1.01628 + 2.44278i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.104528 - 0.994522i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-2.25946 + 1.00598i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-1.01628 + 2.44278i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(1.23664 + 2.14193i) q^{10} +(-2.26387 + 2.42382i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.35468 - 1.71077i) q^{13} +(2.53563 + 0.755368i) q^{14} +(-0.764287 + 2.35223i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.827071 + 7.86905i) q^{17} +(-0.978148 + 0.207912i) q^{18} +(0.188621 + 0.0400927i) q^{19} +(2.00093 - 1.45376i) q^{20} +(1.13532 + 2.38978i) q^{21} +(2.64718 + 1.99811i) q^{22} +(-1.18098 + 2.04552i) q^{23} +(0.913545 + 0.406737i) q^{24} +(0.747511 - 0.830195i) q^{25} +(-1.94753 - 2.16295i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.486184 - 2.60070i) q^{28} +(-0.615063 + 1.89297i) q^{29} +(2.41924 + 0.514225i) q^{30} +(0.577997 + 0.257341i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.286429 + 3.30423i) q^{33} +7.91240 q^{34} +(-0.161148 - 6.54171i) q^{35} +(0.309017 + 0.951057i) q^{36} +(1.33425 + 1.48184i) q^{37} +(0.0201568 - 0.191779i) q^{38} +(0.304234 - 2.89460i) q^{39} +(-1.65495 - 1.83801i) q^{40} +(-1.79509 - 5.52471i) q^{41} +(2.25802 - 1.37890i) q^{42} -6.01147 q^{43} +(1.71045 - 2.84154i) q^{44} +(1.23664 + 2.14193i) q^{45} +(2.15776 + 0.960695i) q^{46} +(10.1829 + 2.16443i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-4.93437 - 4.96508i) q^{49} +(-0.903783 - 0.656637i) q^{50} +(5.29443 + 5.88006i) q^{51} +(-1.94753 + 2.16295i) q^{52} +(-12.0686 - 5.37328i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.67680 - 7.75392i) q^{55} +(-2.63727 - 0.211674i) q^{56} +(0.156007 - 0.113346i) q^{57} +(1.94689 + 0.413825i) q^{58} +(-11.2389 + 2.38891i) q^{59} +(0.258529 - 2.45974i) q^{60} +(5.94472 - 2.64676i) q^{61} +(0.195514 - 0.601730i) q^{62} +(2.53563 + 0.755368i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.59930 + 6.23417i) q^{65} +(3.25619 - 0.630246i) q^{66} +(3.46463 + 6.00092i) q^{67} +(-0.827071 - 7.86905i) q^{68} +(0.729885 + 2.24636i) q^{69} +(-6.48903 + 0.844060i) q^{70} +(1.70329 + 1.23751i) q^{71} +(0.913545 - 0.406737i) q^{72} +(13.5426 - 2.87856i) q^{73} +(1.33425 - 1.48184i) q^{74} +(-0.116773 - 1.11102i) q^{75} -0.192835 q^{76} +(-3.62016 - 7.99340i) q^{77} -2.91054 q^{78} +(0.913652 + 8.69282i) q^{79} +(-1.65495 + 1.83801i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-5.30681 + 2.36274i) q^{82} +(-2.36465 - 1.71802i) q^{83} +(-1.60737 - 2.10151i) q^{84} +(-6.04734 - 18.6118i) q^{85} +(0.628370 + 5.97854i) q^{86} +(0.995193 + 1.72373i) q^{87} +(-3.00476 - 1.40406i) q^{88} +(-6.29774 + 10.9080i) q^{89} +(2.00093 - 1.45376i) q^{90} +(1.78605 + 7.49058i) q^{91} +(0.729885 - 2.24636i) q^{92} +(0.577997 - 0.257341i) q^{93} +(1.08818 - 10.3533i) q^{94} +(-0.466514 + 0.0991607i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-5.26739 + 3.82699i) q^{97} +(-4.42210 + 5.42633i) q^{98} +(2.64718 + 1.99811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{14} + 20 q^{15} + 3 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{22} + 24 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{27} - 2 q^{28} + 2 q^{29} - 10 q^{30} - 19 q^{31} - 12 q^{32} - 7 q^{33} + 24 q^{34} + 14 q^{35} - 6 q^{36} - q^{37} - 8 q^{38} - 5 q^{39} - 10 q^{40} + 16 q^{41} + 10 q^{42} - 68 q^{43} - 2 q^{44} + 10 q^{45} - 6 q^{46} + 25 q^{47} - 6 q^{48} - 21 q^{49} + 14 q^{50} - 2 q^{51} - 5 q^{53} - 12 q^{54} - 10 q^{55} - 10 q^{56} + 16 q^{57} - q^{58} - 36 q^{59} + 5 q^{60} - q^{61} - 52 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} + 8 q^{66} + 56 q^{67} + 8 q^{68} + 12 q^{69} - 17 q^{70} - 6 q^{71} + 3 q^{72} + 35 q^{73} - q^{74} - 7 q^{75} - 4 q^{76} + 38 q^{77} - 20 q^{78} - 3 q^{79} - 10 q^{80} + 3 q^{81} + 2 q^{82} - 28 q^{83} + 7 q^{84} - 80 q^{85} - 11 q^{86} + 4 q^{87} - 7 q^{88} - 6 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 19 q^{93} - 30 q^{94} - 44 q^{95} + 3 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 + 10 * q^10 - 2 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^14 + 20 * q^15 + 3 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^22 + 24 * q^23 + 3 * q^24 + 8 * q^25 - 6 * q^27 - 2 * q^28 + 2 * q^29 - 10 * q^30 - 19 * q^31 - 12 * q^32 - 7 * q^33 + 24 * q^34 + 14 * q^35 - 6 * q^36 - q^37 - 8 * q^38 - 5 * q^39 - 10 * q^40 + 16 * q^41 + 10 * q^42 - 68 * q^43 - 2 * q^44 + 10 * q^45 - 6 * q^46 + 25 * q^47 - 6 * q^48 - 21 * q^49 + 14 * q^50 - 2 * q^51 - 5 * q^53 - 12 * q^54 - 10 * q^55 - 10 * q^56 + 16 * q^57 - q^58 - 36 * q^59 + 5 * q^60 - q^61 - 52 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 + 8 * q^66 + 56 * q^67 + 8 * q^68 + 12 * q^69 - 17 * q^70 - 6 * q^71 + 3 * q^72 + 35 * q^73 - q^74 - 7 * q^75 - 4 * q^76 + 38 * q^77 - 20 * q^78 - 3 * q^79 - 10 * q^80 + 3 * q^81 + 2 * q^82 - 28 * q^83 + 7 * q^84 - 80 * q^85 - 11 * q^86 + 4 * q^87 - 7 * q^88 - 6 * q^89 - 10 * q^90 - 24 * q^91 + 12 * q^92 - 19 * q^93 - 30 * q^94 - 44 * q^95 + 3 * q^96 - 8 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	−2.25946	+	1.00598i	−1.01046	+	0.449886i	−0.844104	−	0.536180i	$-0.819867\pi$
$5$	−2.25946	+	1.00598i	−1.01046	+	0.449886i	−0.166357	+	0.986066i	$0.553200\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−1.01628	+	2.44278i	−0.384116	+	0.923285i
$7$	−1.01628	+	2.44278i	−0.384116	+	0.923285i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	1.23664	+	2.14193i	0.391061	+	0.677337i
$11$	−2.26387	+	2.42382i	−0.682581	+	0.730810i
$11$	−2.26387	+	2.42382i	−0.682581	+	0.730810i
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.35468	−	1.71077i	0.653070	−	0.474483i	−0.211246	−	0.977433i	$-0.567752\pi$
$13$	2.35468	−	1.71077i	0.653070	−	0.474483i	0.864315	+	0.502950i	$0.167752\pi$
$14$	2.53563	+	0.755368i	0.677676	+	0.201880i
$15$	−0.764287	+	2.35223i	−0.197338	+	0.607344i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−0.827071	+	7.86905i	−0.200594	+	1.90853i	0.179803	+	0.983703i	$0.442454\pi$
$17$	−0.827071	+	7.86905i	−0.200594	+	1.90853i	−0.380397	+	0.924823i	$0.624213\pi$
$18$	−0.978148	+	0.207912i	−0.230552	+	0.0490053i
$19$	0.188621	+	0.0400927i	0.0432727	+	0.00919790i	0.229497	−	0.973309i	$-0.426292\pi$
$19$	0.188621	+	0.0400927i	0.0432727	+	0.00919790i	−0.186224	+	0.982507i	$0.559625\pi$
$20$	2.00093	−	1.45376i	0.447421	−	0.325071i
$21$	1.13532	+	2.38978i	0.247747	+	0.521493i
$22$	2.64718	+	1.99811i	0.564381	+	0.425998i
$23$	−1.18098	+	2.04552i	−0.246251	+	0.426520i	−0.962483	−	0.271343i	$-0.912532\pi$
$23$	−1.18098	+	2.04552i	−0.246251	+	0.426520i	0.716231	+	0.697863i	$0.245866\pi$
$24$	0.913545	+	0.406737i	0.186477	+	0.0830248i
$25$	0.747511	−	0.830195i	0.149502	−	0.166039i
$26$	−1.94753	−	2.16295i	−0.381942	−	0.424190i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.486184	−	2.60070i	0.0918802	−	0.491486i
$29$	−0.615063	+	1.89297i	−0.114214	+	0.351516i	−0.991782	−	0.127937i	$-0.959165\pi$
$29$	−0.615063	+	1.89297i	−0.114214	+	0.351516i	0.877568	+	0.479452i	$0.159165\pi$
$30$	2.41924	+	0.514225i	0.441690	+	0.0938842i
$31$	0.577997	+	0.257341i	0.103811	+	0.0462198i	0.457985	−	0.888960i	$-0.348571\pi$
$31$	0.577997	+	0.257341i	0.103811	+	0.0462198i	−0.354174	+	0.935180i	$0.615238\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.286429	+	3.30423i	0.0498609	+	0.575193i
$34$	7.91240			1.35697
$35$	−0.161148	−	6.54171i	−0.0272390	−	1.10575i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	1.33425	+	1.48184i	0.219349	+	0.243612i	0.842769	−	0.538275i	$-0.180924\pi$
$37$	1.33425	+	1.48184i	0.219349	+	0.243612i	−0.623420	+	0.781887i	$0.714257\pi$
$38$	0.0201568	−	0.191779i	0.00326986	−	0.0311107i
$39$	0.304234	−	2.89460i	0.0487165	−	0.463506i
$40$	−1.65495	−	1.83801i	−0.261671	−	0.290615i
$41$	−1.79509	−	5.52471i	−0.280345	−	0.862815i	−0.987755	−	0.156011i	$-0.950136\pi$
$41$	−1.79509	−	5.52471i	−0.280345	−	0.862815i	0.707410	−	0.706804i	$-0.249864\pi$
$42$	2.25802	−	1.37890i	0.348419	−	0.212769i
$43$	−6.01147			−0.916741			−0.458370	−	0.888761i	$-0.651567\pi$
$43$	−6.01147			−0.916741			−0.458370	+	0.888761i	$0.651567\pi$
$44$	1.71045	−	2.84154i	0.257861	−	0.428378i
$45$	1.23664	+	2.14193i	0.184348	+	0.319300i
$46$	2.15776	+	0.960695i	0.318144	+	0.141647i
$47$	10.1829	+	2.16443i	1.48532	+	0.315715i	0.877970	−	0.478716i	$-0.158898\pi$
$47$	10.1829	+	2.16443i	1.48532	+	0.315715i	0.607354	+	0.794432i	$0.292231\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−4.93437	−	4.96508i	−0.704910	−	0.709297i
$50$	−0.903783	−	0.656637i	−0.127814	−	0.0928625i
$51$	5.29443	+	5.88006i	0.741368	+	0.823373i
$52$	−1.94753	+	2.16295i	−0.270074	+	0.299948i
$53$	−12.0686	−	5.37328i	−1.65775	−	0.738077i	−0.657862	−	0.753139i	$-0.728539\pi$
$53$	−12.0686	−	5.37328i	−1.65775	−	0.738077i	−0.999887	+	0.0150616i	$0.995206\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	2.67680	−	7.75392i	0.360940	−	1.04554i
$56$	−2.63727	−	0.211674i	−0.352420	−	0.0282861i
$57$	0.156007	−	0.113346i	0.0206636	−	0.0150130i
$58$	1.94689	+	0.413825i	0.255639	+	0.0543378i
$59$	−11.2389	+	2.38891i	−1.46318	+	0.311009i	−0.869598	−	0.493761i	$-0.835622\pi$
$59$	−11.2389	+	2.38891i	−1.46318	+	0.311009i	−0.593587	+	0.804770i	$0.702289\pi$
$60$	0.258529	−	2.45974i	0.0333759	−	0.317551i
$61$	5.94472	−	2.64676i	0.761143	−	0.338883i	0.0108092	−	0.999942i	$-0.496559\pi$
$61$	5.94472	−	2.64676i	0.761143	−	0.338883i	0.750334	+	0.661059i	$0.229893\pi$
$62$	0.195514	−	0.601730i	0.0248303	−	0.0764198i
$63$	2.53563	+	0.755368i	0.319459	+	0.0951674i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−3.59930	+	6.23417i	−0.446438	+	0.773253i
$66$	3.25619	−	0.630246i	0.400810	−	0.0775780i
$67$	3.46463	+	6.00092i	0.423272	+	0.733129i	0.996257	−	0.0864365i	$-0.0275480\pi$
$67$	3.46463	+	6.00092i	0.423272	+	0.733129i	−0.572985	+	0.819566i	$0.694215\pi$
$68$	−0.827071	−	7.86905i	−0.100297	−	0.954263i
$69$	0.729885	+	2.24636i	0.0878679	+	0.270430i
$70$	−6.48903	+	0.844060i	−0.775588	+	0.100885i
$71$	1.70329	+	1.23751i	0.202144	+	0.146866i	0.684252	−	0.729246i	$-0.260129\pi$
$71$	1.70329	+	1.23751i	0.202144	+	0.146866i	−0.482108	+	0.876112i	$0.660129\pi$
$72$	0.913545	−	0.406737i	0.107662	−	0.0479344i
$73$	13.5426	−	2.87856i	1.58504	−	0.336910i	0.670657	−	0.741767i	$-0.266012\pi$
$73$	13.5426	−	2.87856i	1.58504	−	0.336910i	0.914380	+	0.404857i	$0.132679\pi$
$74$	1.33425	−	1.48184i	0.155103	−	0.172260i
$75$	−0.116773	−	1.11102i	−0.0134837	−	0.128289i
$76$	−0.192835			−0.0221197
$77$	−3.62016	−	7.99340i	−0.412555	−	0.910933i
$78$	−2.91054			−0.329554
$79$	0.913652	+	8.69282i	0.102794	+	0.978019i	0.917390	+	0.397990i	$0.130292\pi$
$79$	0.913652	+	8.69282i	0.102794	+	0.978019i	−0.814596	+	0.580029i	$0.803041\pi$
$80$	−1.65495	+	1.83801i	−0.185029	+	0.205496i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−5.30681	+	2.36274i	−0.586039	+	0.260921i
$83$	−2.36465	−	1.71802i	−0.259554	−	0.188577i	0.450396	−	0.892829i	$-0.351283\pi$
$83$	−2.36465	−	1.71802i	−0.259554	−	0.188577i	−0.709951	+	0.704251i	$0.751283\pi$
$84$	−1.60737	−	2.10151i	−0.175379	−	0.229294i
$85$	−6.04734	−	18.6118i	−0.655927	−	2.01873i
$86$	0.628370	+	5.97854i	0.0677589	+	0.644683i
$87$	0.995193	+	1.72373i	0.106696	+	0.184803i
$88$	−3.00476	−	1.40406i	−0.320309	−	0.149673i
$89$	−6.29774	+	10.9080i	−0.667559	+	1.15625i	0.311025	+	0.950402i	$0.399328\pi$
$89$	−6.29774	+	10.9080i	−0.667559	+	1.15625i	−0.978585	+	0.205845i	$0.934006\pi$
$90$	2.00093	−	1.45376i	0.210916	−	0.153240i
$91$	1.78605	+	7.49058i	0.187228	+	0.785226i
$92$	0.729885	−	2.24636i	0.0760958	−	0.234199i
$93$	0.577997	−	0.257341i	0.0599355	−	0.0266850i
$94$	1.08818	−	10.3533i	0.112237	−	1.06786i
$95$	−0.466514	+	0.0991607i	−0.0478634	+	0.0101737i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	−5.26739	+	3.82699i	−0.534823	+	0.388572i	−0.822159	−	0.569258i	$-0.807230\pi$
$97$	−5.26739	+	3.82699i	−0.534823	+	0.388572i	0.287336	+	0.957830i	$0.407230\pi$
$98$	−4.42210	+	5.42633i	−0.446699	+	0.548142i
$99$	2.64718	+	1.99811i	0.266052	+	0.200817i
$100$	−0.558569	+	0.967469i	−0.0558569	+	0.0967469i
$101$	13.6038	+	6.05680i	1.35363	+	0.602674i	0.950000	−	0.312249i	$-0.101082\pi$
$101$	13.6038	+	6.05680i	1.35363	+	0.602674i	0.403628	+	0.914923i	$0.367749\pi$
$102$	5.29443	−	5.88006i	0.524227	−	0.582213i
$103$	1.20281	+	1.33586i	0.118517	+	0.131626i	0.799483	−	0.600688i	$-0.205107\pi$
$103$	1.20281	+	1.33586i	0.118517	+	0.131626i	−0.680966	+	0.732315i	$0.738440\pi$
$104$	2.35468	+	1.71077i	0.230895	+	0.167755i
$105$	−4.96927	−	4.25750i	−0.484951	−	0.415490i
$106$	−4.08234	+	12.5641i	−0.396512	+	1.22034i
$107$	−6.55409	−	1.39311i	−0.633608	−	0.134677i	−0.120099	−	0.992762i	$-0.538321\pi$
$107$	−6.55409	−	1.39311i	−0.633608	−	0.134677i	−0.513509	+	0.858084i	$0.671655\pi$
$108$	0.913545	+	0.406737i	0.0879060	+	0.0391383i
$109$	−2.92151	−	5.06020i	−0.279829	−	0.484679i	0.691513	−	0.722364i	$-0.256945\pi$
$109$	−2.92151	−	5.06020i	−0.279829	−	0.484679i	−0.971342	+	0.237685i	$0.923611\pi$
$110$	−7.99124	−	1.85163i	−0.761935	−	0.176546i
$111$	1.99401			0.189263
$112$	0.0651555	+	2.64495i	0.00615661	+	0.249924i
$113$	−1.90272	−	5.85596i	−0.178992	−	0.550882i	0.820801	−	0.571214i	$-0.193528\pi$
$113$	−1.90272	−	5.85596i	−0.178992	−	0.550882i	−0.999793	+	0.0203324i	$0.993528\pi$
$114$	−0.129032	−	0.143305i	−0.0120850	−	0.0134217i
$115$	0.610634	−	5.80980i	0.0569419	−	0.541766i
$116$	0.208052	−	1.97948i	0.0193171	−	0.183790i
$117$	−1.94753	−	2.16295i	−0.180049	−	0.199965i
$118$	3.55061	+	10.9277i	0.326860	+	1.00597i
$119$	−18.3819	−	10.0175i	−1.68506	−	0.918301i
$120$	−2.47328			−0.225779
$121$	−0.749826	−	10.9744i	−0.0681660	−	0.997674i
$122$	−3.25365	−	5.63549i	−0.294572	−	0.510213i
$123$	−5.30681	−	2.36274i	−0.478499	−	0.213041i
$124$	−0.618871	−	0.131545i	−0.0555762	−	0.0118131i
$125$	2.96762	−	9.13340i	0.265432	−	0.816916i
$126$	0.486184	−	2.60070i	0.0433127	−	0.231689i
$127$	−5.62525	−	4.08698i	−0.499160	−	0.362661i	0.309536	−	0.950888i	$-0.399826\pi$
$127$	−5.62525	−	4.08698i	−0.499160	−	0.362661i	−0.808696	+	0.588227i	$0.799826\pi$
$128$	0.669131	+	0.743145i	0.0591433	+	0.0656853i
$129$	−4.02246	+	4.46739i	−0.354158	+	0.393332i
$130$	6.57624	+	2.92793i	0.576775	+	0.256797i
$131$	6.81686	−	11.8071i	0.595592	−	1.03159i	−0.397871	−	0.917441i	$-0.630251\pi$
$131$	6.81686	−	11.8071i	0.595592	−	1.03159i	0.993463	−	0.114154i	$-0.0364157\pi$
$132$	−0.967159	−	3.17248i	−0.0841804	−	0.276129i
$133$	−0.289629	+	0.420016i	−0.0251140	+	0.0364200i
$134$	5.60590	−	4.07292i	0.484276	−	0.351847i
$135$	2.41924	+	0.514225i	0.208215	+	0.0442574i
$136$	−7.73949	+	1.64508i	−0.663656	+	0.141064i
$137$	−0.0396738	+	0.377471i	−0.00338956	+	0.0322496i	−0.996086	−	0.0883899i	$-0.971828\pi$
$137$	−0.0396738	+	0.377471i	−0.00338956	+	0.0322496i	0.992696	+	0.120640i	$0.0384945\pi$
$138$	2.15776	−	0.960695i	0.183680	−	0.0817798i
$139$	−2.01220	+	6.19292i	−0.170673	+	0.525276i	−0.999409	−	0.0343621i	$-0.989060\pi$
$139$	−2.01220	+	6.19292i	−0.170673	+	0.525276i	0.828737	+	0.559639i	$0.189060\pi$
$140$	1.51772	+	6.36526i	0.128271	+	0.537962i
$141$	8.42215	−	6.11905i	0.709273	−	0.515317i
$142$	1.05269	−	1.82332i	0.0883400	−	0.153009i
$143$	−1.18406	+	9.58028i	−0.0990163	+	0.801143i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.514572	−	4.89582i	−0.0427329	−	0.406576i
$146$	−4.27838	−	13.1675i	−0.354081	−	1.08975i
$147$	−6.99151	+	0.344666i	−0.576650	+	0.0284276i
$148$	−1.61318	−	1.17205i	−0.132603	−	0.0963417i
$149$	16.0427	−	7.14267i	1.31427	−	0.585150i	0.374584	−	0.927193i	$-0.377785\pi$
$149$	16.0427	−	7.14267i	1.31427	−	0.585150i	0.939684	+	0.342043i	$0.111119\pi$
$150$	−1.09273	+	0.232266i	−0.0892206	+	0.0189644i
$151$	−7.44642	+	8.27009i	−0.605981	+	0.673010i	−0.965583	−	0.260096i	$-0.916246\pi$
$151$	−7.44642	+	8.27009i	−0.605981	+	0.673010i	0.359602	+	0.933106i	$0.382913\pi$
$152$	0.0201568	+	0.191779i	0.00163493	+	0.0155553i
$153$	7.91240			0.639680
$154$	−7.57120	+	4.43587i	−0.610105	+	0.357452i
$155$	−1.56484			−0.125691
$156$	0.304234	+	2.89460i	0.0243582	+	0.231753i
$157$	10.3970	−	11.5470i	0.829768	−	0.921551i	−0.168169	−	0.985758i	$-0.553785\pi$
$157$	10.3970	−	11.5470i	0.829768	−	0.921551i	0.997937	+	0.0642075i	$0.0204520\pi$
$158$	8.54970	−	1.81729i	0.680177	−	0.144576i
$159$	−12.0686	+	5.37328i	−0.957101	+	0.426129i
$160$	2.00093	+	1.45376i	0.158187	+	0.114930i
$161$	−3.79655	−	4.96368i	−0.299210	−	0.391193i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	2.02468	+	19.2635i	0.158585	+	1.50884i	0.727310	+	0.686309i	$0.240770\pi$
$163$	2.02468	+	19.2635i	0.158585	+	1.50884i	−0.568724	+	0.822528i	$0.692563\pi$
$164$	2.90451	+	5.03076i	0.226804	+	0.392837i
$165$	−3.97115	−	7.17764i	−0.309154	−	0.558778i
$166$	−1.46144	+	2.53128i	−0.113429	+	0.196466i
$167$	6.85936	−	4.98362i	0.530793	−	0.385644i	−0.289861	−	0.957069i	$-0.593609\pi$
$167$	6.85936	−	4.98362i	0.530793	−	0.385644i	0.820654	+	0.571425i	$0.193609\pi$
$168$	−1.92198	+	1.81824i	−0.148284	+	0.140280i
$169$	−1.39946	+	4.30710i	−0.107651	+	0.331316i
$170$	−17.8777	+	7.95968i	−1.37116	+	0.610480i
$171$	0.0201568	−	0.191779i	0.00154143	−	0.0146657i
$172$	5.88011	−	1.24986i	0.448354	−	0.0953006i
$173$	10.8167	+	2.29915i	0.822375	+	0.174801i	0.599837	−	0.800123i	$-0.295232\pi$
$173$	10.8167	+	2.29915i	0.822375	+	0.174801i	0.222539	+	0.974924i	$0.428566\pi$
$174$	1.61026	−	1.16992i	0.122073	−	0.0886914i
$175$	1.26831	+	2.66971i	0.0958751	+	0.201811i
$176$	−1.08229	+	3.13507i	−0.0815804	+	0.236315i
$177$	−5.74501	+	9.95065i	−0.431821	+	0.747936i
$178$	11.5065	+	5.12305i	0.862452	+	0.383989i
$179$	−10.5030	+	11.6647i	−0.785029	+	0.871863i	−0.994368	−	0.105980i	$-0.966202\pi$
$179$	−10.5030	+	11.6647i	−0.785029	+	0.871863i	0.209339	+	0.977843i	$0.432869\pi$
$180$	−1.65495	−	1.83801i	−0.123353	−	0.136997i
$181$	17.6327	+	12.8109i	1.31063	+	0.952227i	0.999999	+	0.00169546i	$0.000539682\pi$
$181$	17.6327	+	12.8109i	1.31063	+	0.952227i	0.310629	+	0.950531i	$0.399460\pi$
$182$	7.26285	−	2.55924i	0.538358	−	0.189703i
$183$	2.01087	−	6.18882i	0.148648	−	0.457490i
$184$	−2.31034	−	0.491079i	−0.170321	−	0.0362028i
$185$	−4.50537	−	2.00592i	−0.331242	−	0.147478i
$186$	−0.316348	−	0.547931i	−0.0231958	−	0.0401763i
$187$	−17.2008	−	19.8192i	−1.25785	−	1.44932i
$188$	−10.4104			−0.759253
$189$	2.25802	−	1.37890i	0.164246	−	0.100300i
$190$	0.147382	+	0.453594i	0.0106922	+	0.0329071i
$191$	0.00203091	+	0.00225555i	0.000146951	+	0.000163206i	0.743218	−	0.669049i	$-0.233298\pi$
$191$	0.00203091	+	0.00225555i	0.000146951	+	0.000163206i	−0.743071	+	0.669212i	$0.766632\pi$
$192$	−0.104528	+	0.994522i	−0.00754369	+	0.0717734i
$193$	1.76055	−	16.7505i	0.126727	−	1.20573i	−0.727603	−	0.685999i	$-0.759365\pi$
$193$	1.76055	−	16.7505i	0.126727	−	1.20573i	0.854330	−	0.519731i	$-0.173968\pi$
$194$	4.35661	+	4.83851i	0.312787	+	0.347385i
$195$	2.22449	+	6.84627i	0.159299	+	0.490272i
$196$	5.85884	+	3.83067i	0.418489	+	0.273619i
$197$	24.3215			1.73284			0.866418	−	0.499320i	$-0.166417\pi$
$197$	24.3215			1.73284			0.866418	+	0.499320i	$0.166417\pi$
$198$	1.71045	−	2.84154i	0.121557	−	0.201939i
$199$	2.63006	+	4.55539i	0.186440	+	0.322923i	0.944061	−	0.329771i	$-0.106972\pi$
$199$	2.63006	+	4.55539i	0.186440	+	0.322923i	−0.757621	+	0.652695i	$0.773638\pi$
$200$	1.02056	+	0.454381i	0.0721642	+	0.0321296i
$201$	6.77785	+	1.44068i	0.478072	+	0.101617i
$202$	4.60164	−	14.1624i	0.323770	−	0.996462i
$203$	−3.99904	−	3.42624i	−0.280678	−	0.240475i
$204$	−6.40127	−	4.65079i	−0.448178	−	0.325621i
$205$	9.61365	+	10.6770i	0.671446	+	0.745717i
$206$	1.20281	−	1.33586i	0.0838041	−	0.0930739i
$207$	2.15776	+	0.960695i	0.149974	+	0.0667729i
$208$	1.45527	−	2.52060i	0.100905	−	0.174772i
$209$	−0.524191	+	0.366420i	−0.0362591	+	0.0253458i
$210$	−3.71475	+	5.38708i	−0.256342	+	0.371744i
$211$	−4.33558	+	3.14999i	−0.298474	+	0.216854i	−0.726935	−	0.686706i	$-0.759056\pi$
$211$	−4.33558	+	3.14999i	−0.298474	+	0.216854i	0.428461	+	0.903560i	$0.359056\pi$
$212$	12.9220	+	2.74666i	0.887489	+	0.188642i
$213$	2.05938	−	0.437734i	0.141106	−	0.0299930i
$214$	−0.700394	+	6.66380i	−0.0478779	+	0.455528i
$215$	13.5827	−	6.04739i	0.926330	−	0.412429i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	−1.21603	+	1.15039i	−0.0825496	+	0.0780937i
$218$	−4.72710	+	3.43444i	−0.320159	+	0.232609i
$219$	6.92256	−	11.9902i	0.467783	−	0.810224i
$220$	−1.00618	+	8.14101i	−0.0678366	+	0.548867i
$221$	11.5147	+	19.9440i	0.774561	+	1.34158i
$222$	−0.208430	−	1.98308i	−0.0139889	−	0.133096i
$223$	1.80216	+	5.54647i	0.120681	+	0.371419i	0.993090	−	0.117359i	$-0.0374427\pi$
$223$	1.80216	+	5.54647i	0.120681	+	0.371419i	−0.872408	+	0.488778i	$0.837443\pi$
$224$	2.62365	−	0.341271i	0.175300	−	0.0228021i
$225$	−0.903783	−	0.656637i	−0.0602522	−	0.0437758i
$226$	−5.62499	+	2.50441i	−0.374169	+	0.166591i
$227$	24.6273	−	5.23470i	1.63457	−	0.347439i	0.703056	−	0.711135i	$-0.251819\pi$
$227$	24.6273	−	5.23470i	1.63457	−	0.347439i	0.931518	+	0.363696i	$0.118485\pi$
$228$	−0.129032	+	0.143305i	−0.00854535	+	0.00949058i
$229$	−0.803430	−	7.64413i	−0.0530922	−	0.505138i	−0.988462	−	0.151468i	$-0.951600\pi$
$229$	−0.803430	−	7.64413i	−0.0530922	−	0.505138i	0.935370	−	0.353671i	$-0.115067\pi$
$230$	−5.84180			−0.385197
$231$	−8.36261	−	2.65833i	−0.550220	−	0.174905i
$232$	−1.99039			−0.130675
$233$	2.91288	+	27.7142i	0.190829	+	1.81562i	0.501561	+	0.865122i	$0.332759\pi$
$233$	2.91288	+	27.7142i	0.190829	+	1.81562i	−0.310732	+	0.950498i	$0.600574\pi$
$234$	−1.94753	+	2.16295i	−0.127314	+	0.141397i
$235$	−25.1851	+	5.35326i	−1.64290	+	0.349208i
$236$	10.4967	−	4.67341i	0.683274	−	0.304213i
$237$	7.07138	+	5.13766i	0.459335	+	0.333727i
$238$	−8.04117	+	19.3283i	−0.521232	+	1.25287i
$239$	1.37380	+	4.22812i	0.0888636	+	0.273494i	0.985606	−	0.169059i	$-0.0540728\pi$
$239$	1.37380	+	4.22812i	0.0888636	+	0.273494i	−0.896742	+	0.442553i	$0.854073\pi$
$240$	0.258529	+	2.45974i	0.0166880	+	0.158775i
$241$	6.51039	+	11.2763i	0.419371	+	0.726372i	0.995876	−	0.0907216i	$-0.0289173\pi$
$241$	6.51039	+	11.2763i	0.419371	+	0.726372i	−0.576505	+	0.817093i	$0.695584\pi$
$242$	−10.8359	+	1.89286i	−0.696559	+	0.121677i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.26452	+	3.82490i	−0.337026	+	0.244864i
$245$	16.1437	+	6.25453i	1.03139	+	0.399587i
$246$	−1.79509	+	5.52471i	−0.114451	+	0.352243i
$247$	0.512732	−	0.228283i	0.0326244	−	0.0145253i
$248$	−0.0661348	+	0.629231i	−0.00419956	+	0.0399562i
$249$	−2.85900	+	0.607699i	−0.181182	+	0.0385114i
$250$	−9.39357	−	1.99666i	−0.594101	−	0.126280i
$251$	−18.4235	+	13.3855i	−1.16288	+	0.844882i	−0.990140	−	0.140085i	$-0.955263\pi$
$251$	−18.4235	+	13.3855i	−1.16288	+	0.844882i	−0.172741	+	0.984967i	$0.555263\pi$
$252$	−2.63727	−	0.211674i	−0.166132	−	0.0133342i
$253$	−2.28439	−	7.49326i	−0.143618	−	0.471097i
$254$	−3.47659	+	6.02164i	−0.218141	+	0.377831i
$255$	−17.8777	−	7.95968i	−1.11955	−	0.498454i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−1.08092	−	1.20048i	−0.0674257	−	0.0748839i	0.708488	−	0.705723i	$-0.249378\pi$
$257$	−1.08092	−	1.20048i	−0.0674257	−	0.0748839i	−0.775914	+	0.630839i	$0.782711\pi$
$258$	4.86338	+	3.53345i	0.302781	+	0.219983i
$259$	−4.97577	+	1.75333i	−0.309179	+	0.108947i
$260$	2.22449	−	6.84627i	0.137957	−	0.424588i
$261$	1.94689	+	0.413825i	0.120510	+	0.0256151i
$262$	−12.4550	−	5.54533i	−0.769474	−	0.342592i
$263$	9.90748	+	17.1603i	0.610922	+	1.05815i	0.991085	+	0.133228i	$0.0425343\pi$
$263$	9.90748	+	17.1603i	0.610922	+	1.05815i	−0.380164	+	0.924919i	$0.624132\pi$
$264$	−3.05400	+	1.29347i	−0.187961	+	0.0796079i
$265$	32.6739			2.00714
$266$	0.447989	+	0.244139i	0.0274680	+	0.0149691i
$267$	3.89222	+	11.9790i	0.238200	+	0.733104i
$268$	−4.63659	−	5.14945i	−0.283225	−	0.314553i
$269$	2.24770	−	21.3854i	0.137044	−	1.30389i	−0.682504	−	0.730881i	$-0.739109\pi$
$269$	2.24770	−	21.3854i	0.137044	−	1.30389i	0.819549	−	0.573009i	$-0.194224\pi$
$270$	0.258529	−	2.45974i	0.0157336	−	0.149695i
$271$	16.3507	+	18.1593i	0.993235	+	1.10310i	0.994671	+	0.103101i	$0.0328764\pi$
$271$	16.3507	+	18.1593i	0.993235	+	1.10310i	−0.00143565	+	0.999999i	$0.500457\pi$
$272$	2.44507	+	7.52514i	0.148254	+	0.456279i
$273$	6.76168	+	3.68488i	0.409236	+	0.223019i
$274$	0.379551			0.0229295
$275$	0.319981	+	3.69128i	0.0192956	+	0.222593i
$276$	−1.18098	−	2.04552i	−0.0710866	−	0.123126i
$277$	−28.7754	−	12.8116i	−1.72895	−	0.769776i	−0.995986	−	0.0895045i	$-0.971472\pi$
$277$	−28.7754	−	12.8116i	−1.72895	−	0.769776i	−0.732960	−	0.680272i	$-0.761862\pi$
$278$	6.36932	+	1.35384i	0.382007	+	0.0811980i
$279$	0.195514	−	0.601730i	0.0117051	−	0.0360246i
$280$	6.17174	−	2.17476i	0.368832	−	0.129967i
$281$	12.3654	+	8.98400i	0.737659	+	0.535941i	0.891977	−	0.452081i	$-0.149318\pi$
$281$	12.3654	+	8.98400i	0.737659	+	0.535941i	−0.154318	+	0.988021i	$0.549318\pi$
$282$	−6.96589	−	7.73640i	−0.414812	−	0.460696i
$283$	14.4329	−	16.0294i	0.857946	−	0.952846i	−0.141365	−	0.989958i	$-0.545149\pi$
$283$	14.4329	−	16.0294i	0.857946	−	0.952846i	0.999311	+	0.0371116i	$0.0118157\pi$
$284$	−1.92336	−	0.856337i	−0.114131	−	0.0508142i
$285$	−0.238468	+	0.413039i	−0.0141256	+	0.0244663i
$286$	9.65156	+	0.176165i	0.570709	+	0.0104168i
$287$	15.3200	+	1.22962i	0.904309	+	0.0725821i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−44.6095	−	9.48203i	−2.62409	−	0.557767i
$290$	−4.81522	+	1.02351i	−0.282759	+	0.0601023i
$291$	−0.680570	+	6.47519i	−0.0398957	+	0.379582i
$292$	−12.6481	+	5.63131i	−0.740176	+	0.329548i
$293$	8.44970	−	26.0055i	0.493637	−	1.51926i	−0.325434	−	0.945565i	$-0.605510\pi$
$293$	8.44970	−	26.0055i	0.493637	−	1.51926i	0.819071	−	0.573693i	$-0.194490\pi$
$294$	1.07359	+	6.91718i	0.0626130	+	0.403418i
$295$	22.9907	−	16.7037i	1.33857	−	0.972529i
$296$	−0.997003	+	1.72686i	−0.0579496	+	0.100372i
$297$	3.25619	−	0.630246i	0.188943	−	0.0365706i
$298$	−8.78046	−	15.2082i	−0.508638	−	0.880987i
$299$	0.718589	+	6.83692i	0.0415571	+	0.395389i
$300$	0.345214	+	1.06246i	0.0199310	+	0.0613412i
$301$	6.10931	−	14.6847i	0.352135	−	0.846413i
$302$	9.00315	+	6.54117i	0.518073	+	0.376402i
$303$	13.6038	−	6.05680i	0.781518	−	0.347954i
$304$	0.188621	−	0.0400927i	0.0108182	−	0.00229948i
$305$	−10.7693	+	11.9605i	−0.616647	+	0.684855i
$306$	−0.827071	−	7.86905i	−0.0472805	−	0.449844i
$307$	−5.28204			−0.301462			−0.150731	−	0.988575i	$-0.548163\pi$
$307$	−5.28204			−0.301462			−0.150731	+	0.988575i	$0.548163\pi$
$308$	5.20297	+	7.06605i	0.296467	+	0.402626i
$309$	1.79758			0.102261
$310$	0.163570	+	1.55627i	0.00929016	+	0.0883900i
$311$	−0.320403	+	0.355844i	−0.0181684	+	0.0201781i	−0.752161	−	0.658980i	$-0.770988\pi$
$311$	−0.320403	+	0.355844i	−0.0181684	+	0.0201781i	0.733992	+	0.679158i	$0.237655\pi$
$312$	2.84694	−	0.605135i	0.161176	−	0.0342590i
$313$	4.94787	−	2.20293i	0.279670	−	0.124517i	−0.262108	−	0.965038i	$-0.584418\pi$
$313$	4.94787	−	2.20293i	0.279670	−	0.124517i	0.541779	+	0.840521i	$0.317751\pi$
$314$	−12.5705	−	9.13302i	−0.709396	−	0.515406i
$315$	−6.48903	+	0.844060i	−0.365615	+	0.0475574i
$316$	−2.70103	−	8.31290i	−0.151945	−	0.467637i
$317$	−1.36031	−	12.9425i	−0.0764024	−	0.726920i	−0.963928	−	0.266162i	$-0.914244\pi$
$317$	−1.36031	−	12.9425i	−0.0764024	−	0.726920i	0.887526	−	0.460758i	$-0.152422\pi$
$318$	6.60536	+	11.4408i	0.370410	+	0.641569i
$319$	−3.19580	−	5.77623i	−0.178931	−	0.323407i
$320$	1.23664	−	2.14193i	0.0691304	−	0.119737i
$321$	−5.42083	+	3.93846i	−0.302561	+	0.219823i
$322$	−4.53964	+	4.29460i	−0.252984	+	0.239329i
$323$	−0.471495	+	1.45111i	−0.0262347	+	0.0807421i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	0.339871	−	3.23366i	0.0188527	−	0.179371i
$326$	18.9464	−	4.02718i	1.04934	−	0.223045i
$327$	−5.71533	−	1.21483i	−0.316058	−	0.0671803i
$328$	4.69960	−	3.41446i	0.259492	−	0.188532i
$329$	−15.6358	+	22.6749i	−0.862031	+	1.25011i
$330$	−6.72322	+	4.69967i	−0.370101	+	0.258708i
$331$	−3.68723	+	6.38647i	−0.202668	+	0.351032i	−0.949387	−	0.314108i	$-0.898295\pi$
$331$	−3.68723	+	6.38647i	−0.202668	+	0.351032i	0.746719	+	0.665140i	$0.231628\pi$
$332$	2.67018	+	1.18884i	0.146545	+	0.0652460i
$333$	1.33425	−	1.48184i	0.0731165	−	0.0812041i
$334$	−5.67331	−	6.30085i	−0.310430	−	0.344767i
$335$	−13.8650	−	10.0735i	−0.757525	−	0.550374i
$336$	2.00918	+	1.72140i	0.109610	+	0.0939099i
$337$	3.55813	−	10.9508i	0.193823	−	0.596527i	−0.806165	−	0.591691i	$-0.798461\pi$
$337$	3.55813	−	10.9508i	0.193823	−	0.596527i	0.999988	−	0.00483630i	$-0.00153945\pi$
$338$	4.42979	+	0.941581i	0.240949	+	0.0512153i
$339$	−5.62499	−	2.50441i	−0.305508	−	0.136021i
$340$	9.78481	+	16.9478i	0.530656	+	0.919123i
$341$	−1.93226	+	0.818377i	−0.104638	+	0.0443176i
$342$	−0.192835			−0.0104273
$343$	17.1433	−	7.00771i	0.925650	−	0.378381i
$344$	−1.85765	−	5.71725i	−0.100158	−	0.308253i
$345$	−3.90893	−	4.34130i	−0.210449	−	0.233728i
$346$	1.15591	−	10.9977i	0.0621420	−	0.591242i
$347$	−0.524698	+	4.99217i	−0.0281673	+	0.267994i	0.971370	+	0.237572i	$0.0763516\pi$
$347$	−0.524698	+	4.99217i	−0.0281673	+	0.267994i	−0.999537	+	0.0304215i	$0.990315\pi$
$348$	−1.33183	−	1.47915i	−0.0713935	−	0.0792905i
$349$	0.537439	+	1.65407i	0.0287684	+	0.0885402i	0.964410	−	0.264412i	$-0.0851779\pi$
$349$	0.537439	+	1.65407i	0.0287684	+	0.0885402i	−0.935641	+	0.352952i	$0.885178\pi$
$350$	2.52251	−	1.54042i	0.134834	−	0.0823390i
$351$	−2.91054			−0.155353
$352$	3.23102	+	0.748654i	0.172214	+	0.0399034i
$353$	1.96088	+	3.39635i	0.104367	+	0.180769i	0.913480	−	0.406885i	$-0.133385\pi$
$353$	1.96088	+	3.39635i	0.104367	+	0.180769i	−0.809112	+	0.587654i	$0.800052\pi$
$354$	10.4967	+	4.67341i	0.557891	+	0.248389i
$355$	−5.09342	−	1.08264i	−0.270331	−	0.0574606i
$356$	3.89222	−	11.9790i	0.206287	−	0.634887i
$357$	−19.7443	+	6.95738i	−1.04498	+	0.368223i
$358$	12.6987	+	9.22614i	0.671147	+	0.487617i
$359$	2.77718	+	3.08437i	0.146574	+	0.162787i	0.811961	−	0.583712i	$-0.198400\pi$
$359$	2.77718	+	3.08437i	0.146574	+	0.162787i	−0.665387	+	0.746499i	$0.731733\pi$
$360$	−1.65495	+	1.83801i	−0.0872236	+	0.0968716i
$361$	−17.3234	−	7.71287i	−0.911758	−	0.405941i
$362$	10.8976	−	18.8752i	0.572765	−	0.992059i
$363$	−8.65731	−	6.78609i	−0.454391	−	0.356177i
$364$	−3.30439	−	6.95555i	−0.173197	−	0.364570i
$365$	−27.7031	+	20.1275i	−1.45005	+	1.05352i
$366$	−6.36511	−	1.35294i	−0.332709	−	0.0707196i
$367$	−29.2154	+	6.20992i	−1.52503	+	0.324155i	−0.892738	−	0.450575i	$-0.851219\pi$
$367$	−29.2154	+	6.20992i	−1.52503	+	0.324155i	−0.632292	+	0.774731i	$0.717886\pi$
$368$	−0.246892	+	2.34902i	−0.0128701	+	0.122451i
$369$	−5.30681	+	2.36274i	−0.276261	+	0.122999i
$370$	−1.52399	+	4.69037i	−0.0792286	+	0.243841i
$371$	25.3908	−	24.0202i	1.31822	−	1.24707i
$372$	−0.511862	+	0.371890i	−0.0265388	+	0.0192816i
$373$	−5.87191	+	10.1704i	−0.304036	+	0.526606i	−0.977046	−	0.213027i	$-0.931668\pi$
$373$	−5.87191	+	10.1704i	−0.304036	+	0.526606i	0.673010	+	0.739633i	$0.265001\pi$
$374$	−17.9126	+	19.1782i	−0.926239	+	0.991684i
$375$	−4.80171	−	8.31681i	−0.247959	−	0.429478i
$376$	1.08818	+	10.3533i	0.0561185	+	0.533932i
$377$	1.79017	+	5.50956i	0.0921982	+	0.283757i
$378$	−1.60737	−	2.10151i	−0.0826744	−	0.108090i
$379$	29.5549	+	21.4729i	1.51813	+	1.10299i	0.962403	+	0.271624i	$0.0875608\pi$
$379$	29.5549	+	21.4729i	1.51813	+	1.10299i	0.555729	+	0.831363i	$0.312439\pi$
$380$	0.435703	−	0.193988i	0.0223511	−	0.00995136i
$381$	−6.80124	+	1.44565i	−0.348438	+	0.0740629i
$382$	0.00203091	−	0.00225555i	0.000103910	−	0.000115404i
$383$	1.58698	+	15.0991i	0.0810907	+	0.771527i	0.957203	+	0.289419i	$0.0934620\pi$
$383$	1.58698	+	15.0991i	0.0810907	+	0.771527i	−0.876112	+	0.482108i	$0.839871\pi$
$384$	1.00000			0.0510310
$385$	16.2208	+	14.4190i	0.826687	+	0.734858i
$386$	−16.8428			−0.857276
$387$	0.628370	+	5.97854i	0.0319418	+	0.303906i
$388$	4.35661	−	4.83851i	0.221174	−	0.245638i
$389$	5.50361	−	1.16983i	0.279044	−	0.0593127i	−0.0662636	−	0.997802i	$-0.521108\pi$
$389$	5.50361	−	1.16983i	0.279044	−	0.0593127i	0.345308	+	0.938489i	$0.387774\pi$
$390$	6.57624	−	2.92793i	0.333001	−	0.148262i
$391$	−15.1195	−	10.9850i	−0.764627	−	0.555534i
$392$	3.19727	−	6.22716i	0.161486	−	0.314519i
$393$	−4.21305	−	12.9664i	−0.212520	−	0.654070i
$394$	−2.54229	−	24.1883i	−0.128079	−	1.21859i
$395$	−10.8091	−	18.7219i	−0.543866	−	0.942004i
$396$	−3.00476	−	1.40406i	−0.150995	−	0.0705568i
$397$	−0.789389	+	1.36726i	−0.0396183	+	0.0686209i	−0.885155	−	0.465297i	$-0.845948\pi$
$397$	−0.789389	+	1.36726i	−0.0396183	+	0.0686209i	0.845536	+	0.533918i	$0.179281\pi$
$398$	4.25552	−	3.09182i	0.213310	−	0.154979i
$399$	0.118333	+	0.496282i	0.00592406	+	0.0248452i
$400$	0.345214	−	1.06246i	0.0172607	−	0.0531230i
$401$	−26.3623	+	11.7373i	−1.31647	+	0.586130i	−0.940277	−	0.340411i	$-0.889434\pi$
$401$	−26.3623	+	11.7373i	−1.31647	+	0.586130i	−0.376193	+	0.926541i	$0.622767\pi$
$402$	0.724306	−	6.89131i	0.0361251	−	0.343707i
$403$	1.80125	−	0.382867i	0.0897265	−	0.0190720i
$404$	−14.5658	−	3.09606i	−0.724676	−	0.154035i
$405$	2.00093	−	1.45376i	0.0994270	−	0.0722379i
$406$	−2.98946	+	4.33527i	−0.148364	+	0.215156i
$407$	−6.61227	−	0.120690i	−0.327758	−	0.00598239i
$408$	−3.95620	+	6.85234i	−0.195861	+	0.339241i
$409$	−11.3137	−	5.03719i	−0.559427	−	0.249073i	0.107489	−	0.994206i	$-0.465719\pi$
$409$	−11.3137	−	5.03719i	−0.559427	−	0.249073i	−0.666915	+	0.745134i	$0.732386\pi$
$410$	9.61365	−	10.6770i	0.474784	−	0.527301i
$411$	0.253969	+	0.282061i	0.0125274	+	0.0139130i
$412$	−1.45427	−	1.05659i	−0.0716468	−	0.0520545i
$413$	5.58626	−	29.8821i	0.274882	−	1.47040i
$414$	0.729885	−	2.24636i	0.0358719	−	0.110402i
$415$	7.07112	+	1.50301i	0.347108	+	0.0737800i
$416$	−2.65891	−	1.18382i	−0.130364	−	0.0580417i
$417$	3.25581	+	5.63923i	0.159438	+	0.276154i
$418$	0.419206	+	0.483018i	0.0205040	+	0.0236252i
$419$	−34.4913			−1.68501			−0.842505	−	0.538689i	$-0.818920\pi$
$419$	−34.4913			−1.68501			−0.842505	+	0.538689i	$0.818920\pi$
$420$	5.74586	+	3.13130i	0.280369	+	0.152792i
$421$	3.53407	+	10.8767i	0.172240	+	0.530100i	0.999497	−	0.0317240i	$-0.0100998\pi$
$421$	3.53407	+	10.8767i	0.172240	+	0.530100i	−0.827257	+	0.561824i	$0.810100\pi$
$422$	3.58592	+	3.98257i	0.174560	+	0.193868i
$423$	1.08818	−	10.3533i	0.0529090	−	0.503396i
$424$	1.38090	−	13.1383i	0.0670622	−	0.638055i
$425$	5.91460	+	6.56883i	0.286900	+	0.318635i
$426$	−0.650599	−	2.00234i	−0.0315216	−	0.0970137i
$427$	0.423987	+	17.2115i	0.0205181	+	0.832922i
$428$	6.70051			0.323881
$429$	6.32724	+	7.29039i	0.305482	+	0.351983i
$430$	−7.43404	−	12.8761i	−0.358501	−	0.620942i
$431$	−20.2843	−	9.03117i	−0.977062	−	0.435016i	−0.144838	−	0.989455i	$-0.546266\pi$
$431$	−20.2843	−	9.03117i	−0.977062	−	0.435016i	−0.832224	+	0.554439i	$0.812933\pi$
$432$	−0.978148	−	0.207912i	−0.0470611	−	0.0100032i
$433$	−4.19256	+	12.9034i	−0.201482	+	0.620096i	0.798358	+	0.602183i	$0.205702\pi$
$433$	−4.19256	+	12.9034i	−0.201482	+	0.620096i	−0.999840	+	0.0179133i	$0.994298\pi$
$434$	1.27120	+	1.08912i	0.0610195	+	0.0522795i
$435$	−3.98262	−	2.89354i	−0.190952	−	0.138735i
$436$	3.90974	+	4.34220i	0.187242	+	0.207954i
$437$	−0.304768	+	0.338480i	−0.0145790	+	0.0161917i
$438$	−12.6481	−	5.63131i	−0.604352	−	0.269075i
$439$	−14.5100	+	25.1321i	−0.692525	+	1.19949i	0.278483	+	0.960441i	$0.410168\pi$
$439$	−14.5100	+	25.1321i	−0.692525	+	1.19949i	−0.971008	+	0.239047i	$0.923165\pi$
$440$	8.20159	+	0.149699i	0.390996	+	0.00713663i
$441$	−4.42210	+	5.42633i	−0.210576	+	0.258397i
$442$	18.6311	−	13.5363i	0.886193	−	0.643857i
$443$	11.7085	+	2.48873i	0.556290	+	0.118243i	0.477474	−	0.878646i	$-0.341553\pi$
$443$	11.7085	+	2.48873i	0.556290	+	0.118243i	0.0788162	+	0.996889i	$0.474886\pi$
$444$	−1.95043	+	0.414577i	−0.0925634	+	0.0196750i
$445$	3.25629	−	30.9816i	0.154363	−	1.46867i
$446$	5.32771	−	2.37205i	0.252275	−	0.112320i
$447$	5.42662	−	16.7014i	0.256670	−	0.789950i
$448$	−0.613647	−	2.57360i	−0.0289921	−	0.121591i
$449$	30.1549	−	21.9088i	1.42310	−	1.03394i	0.431846	−	0.901947i	$-0.357862\pi$
$449$	30.1549	−	21.9088i	1.42310	−	1.03394i	0.991251	−	0.131993i	$-0.0421376\pi$
$450$	−0.558569	+	0.967469i	−0.0263312	+	0.0456069i
$451$	17.4547	+	8.15623i	0.821912	+	0.384062i
$452$	3.07866	+	5.33239i	0.144808	+	0.250815i
$453$	1.16325	+	11.0675i	0.0546540	+	0.519998i
$454$	−7.78028	−	23.9452i	−0.365147	−	1.12381i
$455$	−11.5708	−	15.1279i	−0.542449	−	0.709208i
$456$	0.156007	+	0.113346i	0.00730570	+	0.00530790i
$457$	26.4605	−	11.7810i	1.23777	−	0.551091i	0.319703	−	0.947518i	$-0.396417\pi$
$457$	26.4605	−	11.7810i	1.23777	−	0.551091i	0.918066	+	0.396427i	$0.129750\pi$
$458$	−7.51827	+	1.59806i	−0.351306	+	0.0746723i
$459$	5.29443	−	5.88006i	0.247123	−	0.274458i
$460$	0.610634	+	5.80980i	0.0284710	+	0.270883i
$461$	−29.8197			−1.38884			−0.694420	−	0.719570i	$-0.744339\pi$
$461$	−29.8197			−1.38884			−0.694420	+	0.719570i	$0.744339\pi$
$462$	−1.76963	+	8.59467i	−0.0823308	+	0.399860i
$463$	−21.1262			−0.981818			−0.490909	−	0.871211i	$-0.663335\pi$
$463$	−21.1262			−0.981818			−0.490909	+	0.871211i	$0.663335\pi$
$464$	0.208052	+	1.97948i	0.00965857	+	0.0918952i
$465$	−1.04708	+	1.16290i	−0.0485572	+	0.0539283i
$466$	27.2579	−	5.79385i	1.26270	−	0.268395i
$467$	21.9549	−	9.77495i	1.01595	−	0.452331i	0.169916	−	0.985458i	$-0.445650\pi$
$467$	21.9549	−	9.77495i	1.01595	−	0.452331i	0.846035	+	0.533128i	$0.178984\pi$
$468$	2.35468	+	1.71077i	0.108845	+	0.0790805i
$469$	−18.1800	+	2.36476i	−0.839473	+	0.109194i
$470$	7.95650	+	24.4876i	0.367006	+	1.12953i
$471$	−1.62417	−	15.4529i	−0.0748376	−	0.712032i
$472$	−5.74501	−	9.95065i	−0.264435	−	0.458016i
$473$	13.6092	−	14.5707i	0.625750	−	0.669963i
$474$	4.37035	−	7.56967i	0.200737	−	0.347686i
$475$	0.174281	−	0.126623i	0.00799658	−	0.00580985i
$476$	20.0629	+	5.97677i	0.919582	+	0.273945i
$477$	−4.08234	+	12.5641i	−0.186917	+	0.575272i
$478$	4.06135	−	1.80823i	0.185762	−	0.0827066i
$479$	−2.30567	+	21.9370i	−0.105349	+	1.00233i	0.806342	+	0.591450i	$0.201444\pi$
$479$	−2.30567	+	21.9370i	−0.105349	+	1.00233i	−0.911691	+	0.410877i	$0.865222\pi$
$480$	2.41924	−	0.514225i	0.110423	−	0.0234710i
$481$	5.67681	+	1.20664i	0.258840	+	0.0550182i
$482$	10.5340	−	7.65342i	0.479812	−	0.348604i
$483$	−6.22912	−	0.499965i	−0.283435	−	0.0227492i
$484$	3.01515	+	10.5787i	0.137052	+	0.480850i
$485$	8.05160	−	13.9458i	0.365604	−	0.633245i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	25.9398	−	28.8090i	1.17544	−	1.30546i	0.232466	−	0.972604i	$-0.425320\pi$
$487$	25.9398	−	28.8090i	1.17544	−	1.30546i	0.942977	−	0.332858i	$-0.108013\pi$
$488$	4.35424	+	4.83587i	0.197107	+	0.218910i
$489$	15.6704	+	11.3852i	0.708639	+	0.514856i
$490$	4.53279	−	16.7091i	0.204770	−	0.754840i
$491$	5.45009	−	16.7737i	0.245959	−	0.756985i	−0.749518	−	0.661984i	$-0.769715\pi$
$491$	5.45009	−	16.7737i	0.245959	−	0.756985i	0.995477	−	0.0950007i	$-0.0302853\pi$
$492$	5.68208	+	1.20776i	0.256168	+	0.0544502i
$493$	−14.3872	−	6.40559i	−0.647966	−	0.288493i
$494$	−0.280627	−	0.486061i	−0.0126260	−	0.0218689i
$495$	−7.99124	−	1.85163i	−0.359180	−	0.0832248i
$496$	0.632697			0.0284089
$497$	−4.75399	+	2.90312i	−0.213246	+	0.130223i
$498$	0.903217	+	2.77982i	0.0404741	+	0.124567i
$499$	−16.7389	−	18.5904i	−0.749335	−	0.832221i	0.241056	−	0.970511i	$-0.422506\pi$
$499$	−16.7389	−	18.5904i	−0.749335	−	0.832221i	−0.990392	+	0.138290i	$0.955839\pi$
$500$	−1.00383	+	9.55082i	−0.0448927	+	0.427125i
$501$	0.886258	−	8.43219i	0.0395951	−	0.376722i
$502$	15.2379	+	16.9234i	0.680101	+	0.755329i
$503$	3.18625	+	9.80625i	0.142068	+	0.437239i	0.996622	−	0.0821223i	$-0.0261698\pi$
$503$	3.18625	+	9.80625i	0.142068	+	0.437239i	−0.854555	+	0.519362i	$0.826170\pi$
$504$	0.0651555	+	2.64495i	0.00290226	+	0.117815i
$505$	−36.8302			−1.63892
$506$	−7.21343	+	3.05513i	−0.320676	+	0.135817i
$507$	2.26438	+	3.92202i	0.100565	+	0.174183i
$508$	6.35205	+	2.82812i	0.281827	+	0.125477i
$509$	−19.0113	−	4.04098i	−0.842661	−	0.179113i	−0.233696	−	0.972310i	$-0.575082\pi$
$509$	−19.0113	−	4.04098i	−0.842661	−	0.179113i	−0.608966	+	0.793197i	$0.708415\pi$
$510$	−6.04734	+	18.6118i	−0.267781	+	0.824145i
$511$	−6.73127	+	36.0069i	−0.297774	+	1.59285i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.129032	−	0.143305i	−0.00569690	−	0.00632705i
$514$	−1.08092	+	1.20048i	−0.0476772	+	0.0529509i
$515$	−4.06155	−	1.80832i	−0.178973	−	0.0796841i
$516$	3.00574	−	5.20609i	0.132320	−	0.229185i
$517$	−28.2988	+	19.7815i	−1.24458	+	0.869988i
$518$	2.26383	+	4.76523i	0.0994672	+	0.209372i
$519$	8.94636	−	6.49991i	0.392702	−	0.285314i
$520$	−7.04129	−	1.49667i	−0.308781	−	0.0656334i
$521$	10.6675	−	2.26745i	0.467352	−	0.0993388i	0.0317845	−	0.999495i	$-0.489881\pi$
$521$	10.6675	−	2.26745i	0.467352	−	0.0993388i	0.435568	+	0.900156i	$0.356548\pi$
$522$	0.208052	−	1.97948i	0.00910619	−	0.0866396i
$523$	−19.1848	+	8.54161i	−0.838892	+	0.373499i	−0.780776	−	0.624811i	$-0.785176\pi$
$523$	−19.1848	+	8.54161i	−0.838892	+	0.373499i	−0.0581158	+	0.998310i	$0.518509\pi$
$524$	−4.21305	+	12.9664i	−0.184048	+	0.566441i
$525$	2.83265	+	0.843849i	0.123627	+	0.0368286i
$526$	16.0306	−	11.6469i	0.698969	−	0.507831i
$527$	−2.50307	+	4.33545i	−0.109036	+	0.188855i
$528$	1.60562	+	2.90207i	0.0698756	+	0.126296i
$529$	8.71057	+	15.0872i	0.378721	+	0.655963i
$530$	−3.41535	−	32.4949i	−0.148353	−	1.41149i
$531$	3.55061	+	10.9277i	0.154083	+	0.474220i
$532$	0.195974	−	0.471055i	0.00849654	−	0.0204228i
$533$	−13.6784	−	9.93792i	−0.592476	−	0.430459i
$534$	11.5065	−	5.12305i	0.497937	−	0.221696i
$535$	16.2101	−	3.44557i	0.700825	−	0.148965i
$536$	−4.63659	+	5.14945i	−0.200270	+	0.222422i
$537$	1.64073	+	15.6105i	0.0708025	+	0.673641i
$538$	−21.5032			−0.927069
$539$	23.2052	−	0.719765i	0.999519	−	0.0310025i
$540$	−2.47328			−0.106433
$541$	−1.79329	−	17.0620i	−0.0770994	−	0.733551i	−0.962968	−	0.269615i	$-0.913103\pi$
$541$	−1.79329	−	17.0620i	−0.0770994	−	0.733551i	0.885869	−	0.463936i	$-0.153563\pi$
$542$	16.3507	−	18.1593i	0.702323	−	0.780009i
$543$	21.3189	−	4.53148i	0.914883	−	0.194464i
$544$	7.22834	−	3.21826i	0.309912	−	0.137982i
$545$	11.6915	+	8.49434i	0.500807	+	0.363857i
$546$	2.95791	−	7.10982i	0.126587	−	0.304272i
$547$	−12.5345	−	38.5774i	−0.535938	−	1.64945i	−0.741613	−	0.670828i	$-0.765939\pi$
$547$	−12.5345	−	38.5774i	−0.535938	−	1.64945i	0.205674	−	0.978621i	$-0.434061\pi$
$548$	−0.0396738	−	0.377471i	−0.00169478	−	0.0161248i
$549$	−3.25365	−	5.63549i	−0.138863	−	0.240517i
$550$	3.63761	−	0.704072i	0.155108	−	0.0300217i
$551$	−0.191908	+	0.332395i	−0.00817557	+	0.0141605i
$552$	−1.91086	+	1.38832i	−0.0813318	+	0.0590910i
$553$	−22.1632	−	6.60244i	−0.942475	−	0.280764i
$554$	−9.73360	+	29.9569i	−0.413541	+	1.27275i
$555$	−4.50537	+	2.00592i	−0.191242	+	0.0851466i
$556$	0.680650	−	6.47595i	0.0288660	−	0.274641i
$557$	7.57344	−	1.60978i	0.320897	−	0.0682088i	−0.0446470	−	0.999003i	$-0.514216\pi$
$557$	7.57344	−	1.60978i	0.320897	−	0.0682088i	0.365544	+	0.930794i	$0.380883\pi$
$558$	−0.618871	−	0.131545i	−0.0261989	−	0.00556874i
$559$	−14.1551	+	10.2843i	−0.598696	+	0.434978i
$560$	−2.80797	−	5.91061i	−0.118658	−	0.249769i
$561$	−26.2381	−	0.478909i	−1.10777	−	0.0202196i
$562$	7.64225	−	13.2368i	0.322369	−	0.558359i
$563$	7.85961	+	3.49932i	0.331243	+	0.147479i	0.565618	−	0.824667i	$-0.308638\pi$
$563$	7.85961	+	3.49932i	0.331243	+	0.147479i	−0.234375	+	0.972146i	$0.575304\pi$
$564$	−6.96589	+	7.73640i	−0.293317	+	0.325761i
$565$	10.1901	+	11.3172i	0.428699	+	0.476118i
$566$	−17.4502	−	12.6783i	−0.733486	−	0.532909i
$567$	0.486184	−	2.60070i	0.0204178	−	0.109219i
$568$	−0.650599	+	2.00234i	−0.0272985	+	0.0840163i
$569$	−45.2049	−	9.60859i	−1.89509	−	0.402813i	−0.895943	−	0.444170i	$-0.853499\pi$
$569$	−45.2049	−	9.60859i	−1.89509	−	0.402813i	−0.999144	+	0.0413563i	$0.986832\pi$
$570$	0.435703	+	0.193988i	0.0182496	+	0.00812525i
$571$	12.2596	+	21.2343i	0.513049	+	0.888627i	0.999885	+	0.0151340i	$0.00481750\pi$
$571$	12.2596	+	21.2343i	0.513049	+	0.888627i	−0.486836	+	0.873493i	$0.661849\pi$
$572$	−0.833663	−	9.61710i	−0.0348572	−	0.402111i
$573$	0.00303514			0.000126795
$574$	−0.378490	−	15.3646i	−0.0157979	−	0.641305i
$575$	0.815382	+	2.50949i	0.0340038	+	0.104653i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	−3.08878	+	29.3878i	−0.128588	+	1.22343i	0.719849	+	0.694131i	$0.244211\pi$
$577$	−3.08878	+	29.3878i	−0.128588	+	1.22343i	−0.848436	+	0.529298i	$0.822455\pi$
$578$	−4.76713	+	45.3562i	−0.198287	+	1.88657i
$579$	−11.2700	−	12.5166i	−0.468367	−	0.520174i
$580$	1.52123	+	4.68185i	0.0631655	+	0.194403i
$581$	6.59989	−	4.03035i	0.273810	−	0.167207i
$582$	6.51086			0.269884
$583$	40.3455	−	17.0877i	1.67094	−	0.707701i
$584$	6.92256	+	11.9902i	0.286457	+	0.496159i
$585$	6.57624	+	2.92793i	0.271894	+	0.121055i
$586$	−26.7463	−	5.68510i	−1.10488	−	0.234849i
$587$	0.878443	−	2.70357i	0.0362572	−	0.111588i	−0.931290	−	0.364279i	$-0.881315\pi$
$587$	0.878443	−	2.70357i	0.0362572	−	0.111588i	0.967547	+	0.252691i	$0.0813155\pi$
$588$	6.76707	−	1.79075i	0.279069	−	0.0738493i
$589$	0.0987051	+	0.0717135i	0.00406707	+	0.00295490i
$590$	−19.0154	−	21.1188i	−0.782852	−	0.869445i
$591$	16.2743	−	18.0744i	0.669434	−	0.743481i
$592$	1.82161	+	0.811035i	0.0748679	+	0.0333333i
$593$	14.4306	−	24.9945i	0.592593	−	1.02640i	−0.401289	−	0.915951i	$-0.631438\pi$
$593$	14.4306	−	24.9945i	0.592593	−	1.02640i	0.993882	−	0.110449i	$-0.0352289\pi$
$594$	−0.967159	−	3.17248i	−0.0396830	−	0.130168i
$595$	51.6104	+	4.14238i	2.11582	+	0.169821i
$596$	−14.2071	+	10.3220i	−0.581945	+	0.422807i
$597$	5.14517	+	1.09364i	0.210578	+	0.0447597i
$598$	6.72435	−	1.42930i	0.274979	−	0.0584486i
$599$	−2.18132	+	20.7539i	−0.0891265	+	0.847982i	0.855051	+	0.518544i	$0.173526\pi$
$599$	−2.18132	+	20.7539i	−0.0891265	+	0.847982i	−0.944177	+	0.329438i	$0.893141\pi$
$600$	1.02056	−	0.454381i	0.0416640	−	0.0185500i
$601$	−10.4937	+	32.2964i	−0.428048	+	1.31740i	0.471998	+	0.881600i	$0.343533\pi$
$601$	−10.4937	+	32.2964i	−0.428048	+	1.31740i	−0.900045	+	0.435796i	$0.856467\pi$
$602$	−15.2429	−	4.54087i	−0.621253	−	0.185072i
$603$	5.60590	−	4.07292i	0.228290	−	0.165862i
$604$	5.56425	−	9.63757i	0.226406	−	0.392147i
$605$	12.7342	+	24.0419i	0.517719	+	0.977443i
$606$	−7.44561	−	12.8962i	−0.302457	−	0.523871i
$607$	2.22453	+	21.1650i	0.0902910	+	0.859062i	0.942128	+	0.335254i	$0.108822\pi$
$607$	2.22453	+	21.1650i	0.0902910	+	0.859062i	−0.851837	+	0.523807i	$0.824511\pi$
$608$	−0.0595894	−	0.183397i	−0.00241667	−	0.00743774i
$609$	−5.22208	+	0.679261i	−0.211609	+	0.0275250i
$610$	13.0207	+	9.46006i	0.527191	+	0.383027i
$611$	27.6802	−	12.3240i	1.11982	−	0.498576i
$612$	−7.73949	+	1.64508i	−0.312850	+	0.0664984i
$613$	−2.31257	+	2.56837i	−0.0934037	+	0.103735i	−0.788034	−	0.615631i	$-0.788901\pi$
$613$	−2.31257	+	2.56837i	−0.0934037	+	0.103735i	0.694631	+	0.719366i	$0.255568\pi$
$614$	0.552123	+	5.25310i	0.0222819	+	0.211998i
$615$	14.3674			0.579348
$616$	6.48348	−	5.91307i	0.261227	−	0.238244i
$617$	46.8258			1.88514			0.942569	−	0.334013i	$-0.108403\pi$
$617$	46.8258			1.88514			0.942569	+	0.334013i	$0.108403\pi$
$618$	−0.187898	−	1.78773i	−0.00755837	−	0.0719131i
$619$	−20.6387	+	22.9215i	−0.829537	+	0.921295i	−0.997922	−	0.0644267i	$-0.979478\pi$
$619$	−20.6387	+	22.9215i	−0.829537	+	0.921295i	0.168385	+	0.985721i	$0.446145\pi$
$620$	1.53064	−	0.325348i	0.0614721	−	0.0130663i
$621$	2.15776	−	0.960695i	0.0865878	−	0.0385514i
$622$	0.387386	+	0.281452i	0.0155328	+	0.0112852i
$623$	−20.2457	−	26.4696i	−0.811125	−	1.06048i
$624$	−0.899406	−	2.76809i	−0.0360051	−	0.110812i
$625$	3.06662	+	29.1770i	0.122665	+	1.16708i
$626$	−2.70806	−	4.69049i	−0.108236	−	0.187470i
$627$	−0.0784490	+	0.634733i	−0.00313295	+	0.0253488i
$628$	−7.76901	+	13.4563i	−0.310017	+	0.536966i
$629$	−12.7642	+	9.27370i	−0.508940	+	0.369767i
$630$	1.51772	+	6.36526i	0.0604676	+	0.253598i
$631$	−9.58218	+	29.4909i	−0.381461	+	1.17402i	0.557555	+	0.830140i	$0.311740\pi$
$631$	−9.58218	+	29.4909i	−0.381461	+	1.17402i	−0.939015	+	0.343875i	$0.888260\pi$
$632$	−7.98503	+	3.55516i	−0.317627	+	0.141417i
$633$	−0.560176	+	5.32972i	−0.0222650	+	0.211837i
$634$	−12.7294	+	2.70571i	−0.505547	+	0.107457i
$635$	16.8214	+	3.57550i	0.667537	+	0.141889i
$636$	10.6877	−	7.76506i	0.423795	−	0.307905i
$637$	−20.1130	−	3.24957i	−0.796905	−	0.128753i
$638$	−5.41054	+	3.78208i	−0.214205	+	0.149734i
$639$	1.05269	−	1.82332i	0.0416439	−	0.0721293i
$640$	−2.25946	−	1.00598i	−0.0893129	−	0.0397647i
$641$	−7.29764	+	8.10485i	−0.288239	+	0.320122i	−0.869823	−	0.493365i	$-0.835767\pi$
$641$	−7.29764	+	8.10485i	−0.288239	+	0.320122i	0.581583	+	0.813487i	$0.302433\pi$
$642$	4.48352	+	4.97945i	0.176950	+	0.196523i
$643$	8.65793	+	6.29036i	0.341435	+	0.248067i	0.745267	−	0.666766i	$-0.232322\pi$
$643$	8.65793	+	6.29036i	0.341435	+	0.248067i	−0.403832	+	0.914833i	$0.632322\pi$
$644$	4.74560	+	4.06587i	0.187003	+	0.160218i
$645$	4.59449	−	14.1404i	0.180908	−	0.556777i
$646$	1.49245	+	0.317230i	0.0587196	+	0.0124812i
$647$	−33.2212	−	14.7910i	−1.30606	−	0.581496i	−0.368601	−	0.929588i	$-0.620163\pi$
$647$	−33.2212	−	14.7910i	−1.30606	−	0.581496i	−0.937460	+	0.348092i	$0.886830\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	19.6531	−	32.6493i	0.771453	−	1.28160i
$650$	−3.25147			−0.127533
$651$	0.0412236	+	1.67345i	0.00161568	+	0.0655877i
$652$	−5.98555	−	18.4216i	−0.234412	−	0.721447i
$653$	6.80928	+	7.56247i	0.266468	+	0.295942i	0.861498	−	0.507761i	$-0.169527\pi$
$653$	6.80928	+	7.56247i	0.266468	+	0.295942i	−0.595030	+	0.803703i	$0.702860\pi$
$654$	−0.610761	+	5.81100i	−0.0238826	+	0.227228i
$655$	−3.52471	+	33.5353i	−0.137722	+	1.31033i
$656$	−3.88700	−	4.31695i	−0.151762	−	0.168548i
$657$	−4.27838	−	13.1675i	−0.166915	−	0.513713i
$658$	24.1850	+	13.1800i	0.942831	+	0.513810i
$659$	−11.0597			−0.430825			−0.215413	−	0.976523i	$-0.569110\pi$
$659$	−11.0597			−0.430825			−0.215413	+	0.976523i	$0.569110\pi$
$660$	5.37669	+	6.19514i	0.209287	+	0.241145i
$661$	−3.54050	−	6.13233i	−0.137710	−	0.238520i	0.788920	−	0.614496i	$-0.210641\pi$
$661$	−3.54050	−	6.13233i	−0.137710	−	0.238520i	−0.926629	+	0.375976i	$0.877307\pi$
$662$	6.73690	+	2.99946i	0.261837	+	0.116577i
$663$	22.5261	+	4.78807i	0.874842	+	0.185953i
$664$	0.903217	−	2.77982i	0.0350516	−	0.107878i
$665$	0.231879	−	1.24037i	0.00899188	−	0.0480994i
$666$	−1.61318	−	1.17205i	−0.0625096	−	0.0454159i
$667$	−3.14572	−	3.49368i	−0.121803	−	0.135276i
$668$	−5.67331	+	6.30085i	−0.219507	+	0.243787i
$669$	5.32771	+	2.37205i	0.205981	+	0.0917088i
$670$	−8.56903	+	14.8420i	−0.331050	+	0.573396i
$671$	−7.04277	+	20.4008i	−0.271883	+	0.787566i
$672$	1.50195	−	2.17811i	0.0579390	−	0.0840223i
$673$	−6.90522	+	5.01693i	−0.266177	+	0.193389i	−0.712866	−	0.701301i	$-0.752603\pi$
$673$	−6.90522	+	5.01693i	−0.266177	+	0.193389i	0.446689	+	0.894689i	$0.352603\pi$
$674$	−11.2627	−	2.39397i	−0.433824	−	0.0922121i
$675$	−1.09273	+	0.232266i	−0.0420590	+	0.00893992i
$676$	0.473384	−	4.50395i	0.0182071	−	0.173229i
$677$	−10.8571	+	4.83391i	−0.417274	+	0.185782i	−0.604624	−	0.796511i	$-0.706677\pi$
$677$	−10.8571	+	4.83391i	−0.417274	+	0.185782i	0.187350	+	0.982293i	$0.440010\pi$
$678$	−1.90272	+	5.85596i	−0.0730734	+	0.224897i
$679$	−3.99537	−	16.7564i	−0.153328	−	0.643050i
$680$	15.8322	−	11.5027i	0.607135	−	0.441110i
$681$	12.5888	−	21.8044i	0.482402	−	0.835545i
$682$	1.01587	+	1.83613i	0.0388997	+	0.0703090i
$683$	15.6873	+	27.1713i	0.600259	+	1.03968i	0.992782	+	0.119937i	$0.0382692\pi$
$683$	15.6873	+	27.1713i	0.600259	+	1.03968i	−0.392522	+	0.919742i	$0.628397\pi$
$684$	0.0201568	+	0.191779i	0.000770714	+	0.00733285i
$685$	−0.290086	−	0.892792i	−0.0110836	−	0.0341118i
$686$	−8.76128	−	16.3169i	−0.334507	−	0.622981i
$687$	−6.21829	−	4.51785i	−0.237243	−	0.172367i
$688$	−5.49175	+	2.44509i	−0.209371	+	0.0932180i
$689$	−37.6101	+	7.99427i	−1.43283	+	0.304557i
$690$	−3.90893	+	4.34130i	−0.148810	+	0.165271i
$691$	−0.270582	−	2.57441i	−0.0102934	−	0.0979353i	0.988169	−	0.153369i	$-0.0490124\pi$
$691$	−0.270582	−	2.57441i	−0.0102934	−	0.0979353i	−0.998462	+	0.0554340i	$0.982346\pi$
$692$	−11.0583			−0.420374
$693$	−7.57120	+	4.43587i	−0.287606	+	0.168505i
$694$	5.01967			0.190544
$695$	−1.68344	−	16.0169i	−0.0638565	−	0.607554i
$696$	−1.33183	+	1.47915i	−0.0504828	+	0.0560669i
$697$	44.9589	−	9.55631i	1.70294	−	0.361971i
$698$	1.58883	−	0.707392i	0.0601380	−	0.0267752i
$699$	22.5448	+	16.3797i	0.852722	+	0.619539i
$700$	−1.79566	−	2.34768i	−0.0678695	−	0.0887338i
$701$	9.05909	+	27.8810i	0.342157	+	1.05305i	0.963088	+	0.269186i	$0.0867546\pi$
$701$	9.05909	+	27.8810i	0.342157	+	1.05305i	−0.620931	+	0.783865i	$0.713245\pi$
$702$	0.304234	+	2.89460i	0.0114826	+	0.109249i
$703$	0.192257	+	0.333000i	0.00725112	+	0.0125593i
$704$	0.406819	−	3.29158i	0.0153326	−	0.124056i
$705$	−12.8739	+	22.2982i	−0.484859	+	0.839800i
$706$	3.17278	−	2.30516i	0.119409	−	0.0867557i
$707$	−28.6206	+	27.0757i	−1.07639	+	1.01829i
$708$	3.55061	−	10.9277i	0.133440	−	0.410686i
$709$	18.4030	−	8.19354i	0.691139	−	0.307715i	−0.0309444	−	0.999521i	$-0.509851\pi$
$709$	18.4030	−	8.19354i	0.691139	−	0.307715i	0.722083	+	0.691806i	$0.243185\pi$
$710$	−0.544302	+	5.17869i	−0.0204273	+	0.194353i
$711$	8.54970	−	1.81729i	0.320639	−	0.0681539i
$712$	−12.3202	−	2.61875i	−0.461721	−	0.0981418i
$713$	−1.20900	+	0.878388i	−0.0452773	+	0.0328959i
$714$	8.98311	+	18.9089i	0.336184	+	0.707647i
$715$	−6.96218	−	22.8374i	−0.260371	−	0.854069i
$716$	7.84822	−	13.5935i	0.293302	−	0.508014i
$717$	4.06135	+	1.80823i	0.151674	+	0.0675296i
$718$	2.77718	−	3.08437i	0.103644	−	0.115108i
$719$	−16.2353	−	18.0311i	−0.605473	−	0.672446i	0.359999	−	0.932953i	$-0.382777\pi$
$719$	−16.2353	−	18.0311i	−0.605473	−	0.672446i	−0.965472	+	0.260507i	$0.916110\pi$
$720$	2.00093	+	1.45376i	0.0745702	+	0.0541784i
$721$	−4.48561	+	1.58061i	−0.167053	+	0.0588651i
$722$	−5.85983	+	18.0347i	−0.218080	+	0.671182i
$723$	12.7362	+	2.70717i	0.473666	+	0.100681i
$724$	−19.9109	−	8.86491i	−0.739983	−	0.329462i
$725$	1.11177	+	1.92564i	0.0412900	+	0.0715164i
$726$	−5.84398	+	9.31922i	−0.216890	+	0.345869i
$727$	25.2945			0.938123			0.469061	−	0.883166i	$-0.344592\pi$
$727$	25.2945			0.938123			0.469061	+	0.883166i	$0.344592\pi$
$728$	−6.57204	+	4.01335i	−0.243576	+	0.148744i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	22.9130	+	25.4474i	0.848047	+	0.941852i
$731$	4.97191	−	47.3046i	0.183893	−	1.74962i
$732$	−0.680199	+	6.47166i	−0.0251409	+	0.239199i
$733$	12.3354	+	13.6998i	0.455618	+	0.506015i	0.926559	−	0.376150i	$-0.122752\pi$
$733$	12.3354	+	13.6998i	0.455618	+	0.506015i	−0.470941	+	0.882165i	$0.656086\pi$
$734$	9.22974	+	28.4062i	0.340676	+	1.04849i
$735$	15.4503	−	7.81205i	0.569893	−	0.288152i
$736$	2.36196			0.0870630
$737$	−22.3886	−	5.18762i	−0.824696	−	0.191089i
$738$	2.90451	+	5.03076i	0.106917	+	0.185185i
$739$	4.68815	+	2.08730i	0.172456	+	0.0767825i	0.491149	−	0.871076i	$-0.336577\pi$
$739$	4.68815	+	2.08730i	0.172456	+	0.0767825i	−0.318693	+	0.947858i	$0.603244\pi$
$740$	4.82397	+	1.02537i	0.177333	+	0.0376932i
$741$	0.173437	−	0.533785i	0.00637138	−	0.0196091i
$742$	−26.5427	−	22.7409i	−0.974412	−	0.834844i
$743$	−26.9687	−	19.5939i	−0.989386	−	0.718831i	−0.0295998	−	0.999562i	$-0.509423\pi$
$743$	−26.9687	−	19.5939i	−0.989386	−	0.718831i	−0.959787	+	0.280731i	$0.909423\pi$
$744$	0.423357	+	0.470185i	0.0155210	+	0.0172378i
$745$	−29.0624	+	32.2771i	−1.06477	+	1.18254i
$746$	10.7285	+	4.77664i	0.392799	+	0.174885i
$747$	−1.46144	+	2.53128i	−0.0534712	+	0.0926148i
$748$	20.9456	+	15.8098i	0.765846	+	0.578064i
$749$	10.0638	−	14.5944i	0.367724	−	0.533269i
$750$	−7.76933	+	5.64475i	−0.283696	+	0.206117i
$751$	11.7239	+	2.49200i	0.427812	+	0.0909342i	0.416785	−	0.909005i	$-0.363157\pi$
$751$	11.7239	+	2.49200i	0.427812	+	0.0909342i	0.0110266	+	0.999939i	$0.496490\pi$
$752$	10.1829	−	2.16443i	0.371331	−	0.0789288i
$753$	−2.38040	+	22.6479i	−0.0867464	+	0.825337i
$754$	5.29226	−	2.35627i	0.192733	−	0.0858101i
$755$	8.50537	−	26.1768i	0.309542	−	0.952673i
$756$	−1.92198	+	1.81824i	−0.0699018	+	0.0661286i
$757$	−14.9137	+	10.8355i	−0.542049	+	0.393821i	−0.824845	−	0.565359i	$-0.808738\pi$
$757$	−14.9137	+	10.8355i	−0.542049	+	0.393821i	0.282797	+	0.959180i	$0.408738\pi$
$758$	18.2659	−	31.6375i	0.663448	−	1.14913i
$759$	−7.09713	−	3.31634i	−0.257610	−	0.120375i
$760$	−0.238468	−	0.413039i	−0.00865016	−	0.0149825i
$761$	1.65516	+	15.7478i	0.0599995	+	0.570857i	0.982682	+	0.185298i	$0.0593249\pi$
$761$	1.65516	+	15.7478i	0.0599995	+	0.570857i	−0.922683	+	0.385560i	$0.874008\pi$
$762$	2.14865	+	6.61288i	0.0778375	+	0.239559i
$763$	15.3300	−	1.99405i	0.554984	−	0.0721895i
$764$	−0.00245548	−	0.00178401i	−8.88362e−5	−	6.45433e-5i
$765$	−17.8777	+	7.95968i	−0.646371	+	0.287783i
$766$	14.8505	−	3.15657i	0.536569	−	0.114051i
$767$	−22.3772	+	24.8524i	−0.807993	+	0.897367i
$768$	−0.104528	−	0.994522i	−0.00377185	−	0.0358867i
$769$	2.61248			0.0942086			0.0471043	−	0.998890i	$-0.485001\pi$
$769$	2.61248			0.0942086			0.0471043	+	0.998890i	$0.485001\pi$
$770$	12.6444	−	17.6391i	0.455674	−	0.635669i
$771$	−1.61540			−0.0581774
$772$	1.76055	+	16.7505i	0.0633637	+	0.602865i
$773$	−29.6443	+	32.9233i	−1.06623	+	1.18417i	−0.0840038	+	0.996465i	$0.526771\pi$
$773$	−29.6443	+	32.9233i	−1.06623	+	1.18417i	−0.982226	+	0.187703i	$0.939896\pi$
$774$	5.88011	−	1.24986i	0.211356	−	0.0449251i
$775$	0.645702	−	0.287485i	0.0231943	−	0.0103268i
$776$	−5.26739	−	3.82699i	−0.189088	−	0.137381i
$777$	−2.02646	+	4.87092i	−0.0726988	+	0.174743i
$778$	−1.73871	−	5.35118i	−0.0623356	−	0.191849i
$779$	−0.117091	−	1.11405i	−0.00419523	−	0.0399149i
$780$	−3.59930	−	6.23417i	−0.128876	−	0.223219i
$781$	−6.85554	+	1.32691i	−0.245310	+	0.0474806i
$782$	−9.34438	+	16.1849i	−0.334154	+	0.578772i
$783$	1.61026	−	1.16992i	0.0575459	−	0.0418095i
$784$	−6.52725	−	2.52884i	−0.233116	−	0.0903155i
$785$	−11.8755	+	36.5490i	−0.423855	+	1.30449i
$786$	−12.4550	+	5.54533i	−0.444256	+	0.197795i
$787$	−2.26988	+	21.5965i	−0.0809126	+	0.769832i	0.876557	+	0.481298i	$0.159834\pi$
$787$	−2.26988	+	21.5965i	−0.0809126	+	0.769832i	−0.957470	+	0.288534i	$0.906832\pi$
$788$	−23.7900	+	5.05672i	−0.847484	+	0.180138i
$789$	19.3820	+	4.11976i	0.690016	+	0.146667i
$790$	−17.4895	+	12.7069i	−0.622249	+	0.452091i
$791$	16.2385	+	1.30334i	0.577375	+	0.0463416i
$792$	−1.08229	+	3.13507i	−0.0384574	+	0.111400i
$793$	9.46989	−	16.4023i	0.336286	−	0.582464i
$794$	1.44229	+	0.642147i	0.0511848	+	0.0227890i
$795$	21.8631	−	24.2814i	0.775404	−	0.861173i
$796$	−3.51971	−	3.90903i	−0.124753	−	0.138552i
$797$	−0.0690097	−	0.0501385i	−0.00244445	−	0.00177600i	0.586562	−	0.809904i	$-0.300481\pi$
$797$	−0.0690097	−	0.0501385i	−0.00244445	−	0.00177600i	−0.589007	+	0.808128i	$0.700481\pi$
$798$	0.481194	−	0.169560i	0.0170341	−	0.00600237i
$799$	−25.4540	+	78.3394i	−0.900498	+	2.77145i
$800$	−1.09273	−	0.232266i	−0.0386337	−	0.00821184i
$801$	11.5065	+	5.12305i	0.406564	+	0.181014i
$802$	14.4286	+	24.9910i	0.509490	+	0.882463i
$803$	−23.6814	+	39.3414i	−0.835699	+	1.38833i
$804$	−6.92927			−0.244376
$805$	13.5715	+	7.39600i	0.478332	+	0.260675i
$806$	−0.569051	−	1.75136i	−0.0200440	−	0.0616890i
$807$	−14.3884	−	15.9800i	−0.506497	−	0.562522i
$808$	−1.55656	+	14.8096i	−0.0547594	+	0.521001i
$809$	1.50914	−	14.3585i	0.0530584	−	0.504817i	−0.935429	−	0.353514i	$-0.884987\pi$
$809$	1.50914	−	14.3585i	0.0530584	−	0.504817i	0.988487	−	0.151303i	$-0.0483468\pi$
$810$	−1.65495	−	1.83801i	−0.0581490	−	0.0645810i
$811$	−7.37082	−	22.6851i	−0.258824	−	0.796580i	−0.993052	−	0.117676i	$-0.962455\pi$
$811$	−7.37082	−	22.6851i	−0.258824	−	0.796580i	0.734228	−	0.678903i	$-0.237545\pi$
$812$	4.62401	+	2.51992i	0.162271	+	0.0884320i
$813$	24.4358			0.857000
$814$	0.571141	+	6.58866i	0.0200185	+	0.230932i
$815$	−23.9533	−	41.4884i	−0.839049	−	1.45328i
$816$	7.22834	+	3.21826i	0.253042	+	0.112662i
$817$	−1.13389	−	0.241016i	−0.0396699	−	0.00843209i
$818$	−3.82699	+	11.7783i	−0.133807	+	0.411817i
$819$	7.26285	−	2.55924i	0.253785	−	0.0894271i
$820$	−11.6234	−	8.44493i	−0.405908	−	0.294910i
$821$	−26.0047	−	28.8812i	−0.907571	−	1.00796i	−0.999925	−	0.0122336i	$-0.996106\pi$
$821$	−26.0047	−	28.8812i	−0.907571	−	1.00796i	0.0923540	−	0.995726i	$-0.470561\pi$
$822$	0.253969	−	0.282061i	0.00885818	−	0.00983801i
$823$	6.67633	+	2.97249i	0.232722	+	0.103615i	0.519785	−	0.854297i	$-0.326012\pi$
$823$	6.67633	+	2.97249i	0.232722	+	0.103615i	−0.287063	+	0.957912i	$0.592679\pi$
$824$	−0.898789	+	1.55675i	−0.0313108	+	0.0542319i
$825$	2.95727	+	2.23216i	0.102959	+	0.0777138i
$826$	−30.3023	−	2.43214i	−1.05435	−	0.0846249i
$827$	30.4171	−	22.0993i	1.05771	−	0.768468i	0.0840435	−	0.996462i	$-0.473217\pi$
$827$	30.4171	−	22.0993i	1.05771	−	0.768468i	0.973663	+	0.227994i	$0.0732165\pi$
$828$	−2.31034	−	0.491079i	−0.0802900	−	0.0170662i
$829$	36.6529	−	7.79081i	1.27301	−	0.270586i	0.478633	−	0.878015i	$-0.341133\pi$
$829$	36.6529	−	7.79081i	1.27301	−	0.270586i	0.794374	+	0.607429i	$0.207799\pi$
$830$	0.755646	−	7.18949i	0.0262289	−	0.249551i
$831$	−28.7754	+	12.8116i	−0.998208	+	0.444431i
$832$	−0.899406	+	2.76809i	−0.0311813	+	0.0959662i
$833$	43.1515	−	34.7223i	1.49511	−	1.20306i
$834$	5.26801	−	3.82743i	0.182416	−	0.132533i
$835$	−10.4850	+	18.1606i	−0.362850	+	0.628474i
$836$	0.436553	−	0.467399i	0.0150985	−	0.0161653i
$837$	−0.316348	−	0.547931i	−0.0109346	−	0.0189393i
$838$	3.60532	+	34.3023i	0.124544	+	1.18495i
$839$	−16.1150	−	49.5968i	−0.556351	−	1.71227i	−0.692349	−	0.721562i	$-0.743424\pi$
$839$	−16.1150	−	49.5968i	−0.556351	−	1.71227i	0.135999	−	0.990709i	$-0.456576\pi$
$840$	2.51354	−	6.04170i	0.0867253	−	0.208458i
$841$	20.2565	+	14.7172i	0.698499	+	0.507489i
$842$	10.4478	−	4.65164i	0.360053	−	0.160306i
$843$	14.9505	−	3.17783i	0.514922	−	0.109450i
$844$	3.58592	−	3.98257i	0.123433	−	0.137086i
$845$	−1.17081	−	11.1395i	−0.0402772	−	0.383212i
$846$	−10.4104			−0.357915
$847$	27.5701	+	9.32136i	0.947321	+	0.320286i
$848$	−13.2107			−0.453658
$849$	−2.25464	−	21.4515i	−0.0773790	−	0.736212i
$850$	5.91460	−	6.56883i	0.202869	−	0.225309i
$851$	−4.60684	+	0.979214i	−0.157920	+	0.0335670i
$852$	−1.92336	+	0.856337i	−0.0658934	+	0.0293376i
$853$	43.7747	+	31.8042i	1.49882	+	1.08895i	0.970850	+	0.239689i	$0.0770454\pi$
$853$	43.7747	+	31.8042i	1.49882	+	1.08895i	0.527967	+	0.849265i	$0.322955\pi$
$854$	17.0729	−	2.22075i	0.584222	−	0.0759927i
$855$	0.147382	+	0.453594i	0.00504034	+	0.0155126i
$856$	−0.700394	−	6.66380i	−0.0239390	−	0.227764i
$857$	8.33312	+	14.4334i	0.284654	+	0.493035i	0.972525	−	0.232798i	$-0.0747880\pi$
$857$	8.33312	+	14.4334i	0.284654	+	0.493035i	−0.687871	+	0.725833i	$0.741455\pi$
$858$	6.58907	−	7.05463i	0.224947	−	0.240841i
$859$	23.3801	−	40.4955i	0.797718	−	1.38169i	−0.123381	−	0.992359i	$-0.539374\pi$
$859$	23.3801	−	40.4955i	0.797718	−	1.38169i	0.921099	−	0.389328i	$-0.127293\pi$
$860$	−12.0285	+	8.73924i	−0.410170	+	0.298006i
$861$	11.1648	−	10.5622i	0.380497	−	0.359958i
$862$	−6.86140	+	21.1172i	−0.233700	+	0.719256i
$863$	12.6606	−	5.63685i	0.430971	−	0.191881i	−0.179774	−	0.983708i	$-0.557537\pi$
$863$	12.6606	−	5.63685i	0.430971	−	0.191881i	0.610745	+	0.791827i	$0.290870\pi$
$864$	−0.104528	+	0.994522i	−0.00355613	+	0.0338343i
$865$	−26.7527	+	5.68646i	−0.909618	+	0.193345i
$866$	13.2709	+	2.82082i	0.450964	+	0.0958555i
$867$	−36.8961	+	26.8066i	−1.25306	+	0.910399i
$868$	0.950279	−	1.37808i	0.0322546	−	0.0467751i
$869$	−23.1382	−	17.4648i	−0.784911	−	0.592454i
$870$	−2.46140	+	4.26326i	−0.0834491	+	0.144538i
$871$	18.4243	+	8.20303i	0.624284	+	0.277949i
$872$	3.90974	−	4.34220i	0.132400	−	0.147046i
$873$	4.35661	+	4.83851i	0.147449	+	0.163759i
$874$	0.368482	+	0.267718i	0.0124641	+	0.00905570i
$875$	19.2950	+	16.5313i	0.652290	+	0.558860i
$876$	−4.27838	+	13.1675i	−0.144553	+	0.444888i
$877$	0.113726	+	0.0241733i	0.00384026	+	0.000816273i	0.209831	−	0.977738i	$-0.432708\pi$
$877$	0.113726	+	0.0241733i	0.00384026	+	0.000816273i	−0.205991	+	0.978554i	$0.566042\pi$
$878$	26.5111	+	11.8035i	0.894706	+	0.398349i
$879$	−13.6719	−	23.6804i	−0.461142	−	0.798721i
$880$	−0.708421	−	8.17231i	−0.0238809	−	0.275489i
$881$	−27.3695			−0.922103			−0.461052	−	0.887373i	$-0.652528\pi$
$881$	−27.3695			−0.922103			−0.461052	+	0.887373i	$0.652528\pi$
$882$	5.85884	+	3.83067i	0.197277	+	0.128985i
$883$	−9.81731	−	30.2146i	−0.330379	−	1.01680i	−0.968954	−	0.247242i	$-0.920476\pi$
$883$	−9.81731	−	30.2146i	−0.330379	−	1.01680i	0.638575	−	0.769560i	$-0.279524\pi$
$884$	−15.4096	−	17.1141i	−0.518282	−	0.575611i
$885$	2.97050	−	28.2624i	0.0998522	−	0.950030i
$886$	1.25122	−	11.9045i	0.0420355	−	0.399941i
$887$	−2.21869	−	2.46410i	−0.0744962	−	0.0827364i	0.704744	−	0.709461i	$-0.251062\pi$
$887$	−2.21869	−	2.46410i	−0.0744962	−	0.0827364i	−0.779241	+	0.626725i	$0.784395\pi$
$888$	0.616182	+	1.89641i	0.0206777	+	0.0636394i
$889$	15.7004	−	9.58776i	0.526575	−	0.321563i
$890$	−31.1522			−1.04422
$891$	1.71045	−	2.84154i	0.0573024	−	0.0951952i
$892$	−2.91595	−	5.05058i	−0.0976334	−	0.169106i
$893$	1.83393	+	0.816517i	0.0613701	+	0.0273237i
$894$	−17.1772	−	3.65112i	−0.574490	−	0.122112i
$895$	11.9966	−	36.9217i	0.401002	−	1.23416i
$896$	−2.49536	+	0.879301i	−0.0833642	+	0.0293754i
$897$	5.56165	+	4.04077i	0.185698	+	0.134918i
$898$	−24.9408	−	27.6996i	−0.832286	−	0.924347i
$899$	−0.842643	+	0.935850i	−0.0281037	+	0.0312124i
$900$	1.02056	+	0.454381i	0.0340185	+	0.0151460i
$901$	52.2642	−	90.5243i	1.74117	−	3.01580i
$902$	6.28703	−	18.2117i	0.209335	−	0.606383i
$903$	−6.82495	−	14.3661i	−0.227120	−	0.478074i
$904$	4.98137	−	3.61918i	0.165678	−	0.120372i
$905$	−52.7278	−	11.2076i	−1.75273	−	0.372554i
$906$	10.8853	−	2.31375i	0.361641	−	0.0768691i
$907$	1.09521	−	10.4202i	0.0363659	−	0.345998i	−0.961177	−	0.275934i	$-0.911013\pi$
$907$	1.09521	−	10.4202i	0.0363659	−	0.345998i	0.997542	−	0.0700643i	$-0.0223205\pi$
$908$	−23.0008	+	10.2406i	−0.763309	+	0.339847i
$909$	4.60164	−	14.1624i	0.152627	−	0.469737i
$910$	−13.8356	+	13.0887i	−0.458645	+	0.433888i
$911$	38.9966	−	28.3327i	1.29201	−	0.938703i	0.292169	−	0.956367i	$-0.405623\pi$
$911$	38.9966	−	28.3327i	1.29201	−	0.938703i	0.999844	+	0.0176639i	$0.00562289\pi$
$912$	0.0964177	−	0.167000i	0.00319271	−	0.00552993i
$913$	9.51744	−	1.84213i	0.314981	−	0.0609656i
$914$	−14.4823	−	25.0841i	−0.479032	−	0.829708i
$915$	1.68232	+	16.0063i	0.0556159	+	0.529150i
$916$	2.37518	+	7.31004i	0.0784780	+	0.241531i
$917$	21.9145	+	28.6514i	0.723680	+	0.946153i
$918$	−6.40127	−	4.65079i	−0.211273	−	0.153499i
$919$	−27.8258	+	12.3888i	−0.917889	+	0.408670i	−0.810629	−	0.585561i	$-0.800874\pi$
$919$	−27.8258	+	12.3888i	−0.917889	+	0.408670i	−0.107260	+	0.994231i	$0.534208\pi$
$920$	5.71414	−	1.21458i	0.188390	−	0.0400434i
$921$	−3.53437	+	3.92532i	−0.116462	+	0.129344i
$922$	3.11700	+	29.6563i	0.102653	+	0.976679i
$923$	6.12781			0.201699
$924$	8.73257	+	0.861551i	0.287280	+	0.0283429i
$925$	2.22758			0.0732423
$926$	2.20829	+	21.0105i	0.0725689	+	0.690447i
$927$	1.20281	−	1.33586i	0.0395056	−	0.0438754i
$928$	1.94689	−	0.413825i	0.0639098	−	0.0135845i
$929$	15.9345	−	7.09450i	0.522794	−	0.232763i	−0.128334	−	0.991731i	$-0.540963\pi$
$929$	15.9345	−	7.09450i	0.522794	−	0.232763i	0.651128	+	0.758968i	$0.274296\pi$
$930$	1.26598	+	0.919789i	0.0415132	+	0.0301611i
$931$	−0.731664	−	1.13435i	−0.0239793	−	0.0371769i
$932$	−8.61134	−	26.5030i	−0.282074	−	0.868134i
$933$	0.0500519	+	0.476212i	0.00163863	+	0.0155905i
$934$	−12.0163	−	20.8129i	−0.393186	−	0.681018i
$935$	58.8021	+	27.4770i	1.92303	+	0.898592i
$936$	1.45527	−	2.52060i	0.0475670	−	0.0823884i
$937$	−12.0009	+	8.71920i	−0.392054	+	0.284844i	−0.766297	−	0.642487i	$-0.777903\pi$
$937$	−12.0009	+	8.71920i	−0.392054	+	0.284844i	0.374243	+	0.927331i	$0.377903\pi$
$938$	4.25213	+	17.8332i	0.138837	+	0.582274i
$939$	1.67367	−	5.15103i	0.0546182	−	0.168098i
$940$	23.5218	−	10.4726i	0.767195	−	0.341577i
$941$	−0.509896	+	4.85134i	−0.0166221	+	0.158149i	−0.999684	−	0.0251230i	$-0.992002\pi$
$941$	−0.509896	+	4.85134i	−0.0166221	+	0.158149i	0.983062	+	0.183272i	$0.0586689\pi$
$942$	−15.1985	+	3.23054i	−0.495193	+	0.105257i
$943$	13.4208	+	2.85269i	0.437043	+	0.0928963i
$944$	−9.29562	+	6.75366i	−0.302547	+	0.219813i
$945$	−3.71475	+	5.38708i	−0.120841	+	0.175242i
$946$	−15.9135	−	12.0116i	−0.517391	−	0.390529i
$947$	21.1955	−	36.7117i	0.688761	−	1.19297i	−0.283478	−	0.958979i	$-0.591488\pi$
$947$	21.1955	−	36.7117i	0.688761	−	1.19297i	0.972239	−	0.233990i	$-0.0751782\pi$
$948$	−7.98503	−	3.55516i	−0.259342	−	0.115466i
$949$	26.9638	−	29.9463i	0.875282	−	0.972099i
$950$	−0.144147	−	0.160091i	−0.00467673	−	0.00519403i
$951$	−10.5283	−	7.64928i	−0.341405	−	0.248045i
$952$	3.84688	−	20.5778i	0.124678	−	0.666929i
$953$	−7.96710	+	24.5202i	−0.258080	+	0.794288i	0.735128	+	0.677929i	$0.237122\pi$
$953$	−7.96710	+	24.5202i	−0.258080	+	0.794288i	−0.993207	+	0.116359i	$0.962878\pi$
$954$	12.9220	+	2.74666i	0.418366	+	0.0889265i
$955$	−0.00685777	−	0.00305328i	−0.000221912	−	9.88017e-5i
$956$	−2.22285	−	3.85009i	−0.0718922	−	0.124521i
$957$	−6.43099	−	1.49011i	−0.207884	−	0.0481684i
$958$	22.0578			0.712656
$959$	−0.881761	−	0.480529i	−0.0284735	−	0.0155171i
$960$	−0.764287	−	2.35223i	−0.0246673	−	0.0759180i
$961$	−20.4752	−	22.7400i	−0.660490	−	0.733549i
$962$	0.606645	−	5.77184i	0.0195590	−	0.186092i
$963$	−0.700394	+	6.66380i	−0.0225699	+	0.214738i
$964$	−8.71260	−	9.67632i	−0.280614	−	0.311653i
$965$	12.8727	+	39.6182i	0.414388	+	1.27536i
$966$	0.153895	+	6.24726i	0.00495148	+	0.201002i
$967$	−35.1707			−1.13101			−0.565507	−	0.824743i	$-0.691320\pi$
$967$	−35.1707			−1.13101			−0.565507	+	0.824743i	$0.691320\pi$
$968$	10.2056	−	4.10441i	0.328020	−	0.131921i
$969$	0.762895	+	1.32137i	0.0245077	+	0.0424486i
$970$	−14.7110	−	6.54976i	−0.472342	−	0.210300i
$971$	11.2321	+	2.38746i	0.360456	+	0.0766172i	0.384580	−	0.923092i	$-0.374346\pi$
$971$	11.2321	+	2.38746i	0.360456	+	0.0766172i	−0.0241241	+	0.999709i	$0.507680\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	−13.0830	−	11.2091i	−0.419422	−	0.359347i
$974$	−31.3627	−	22.7863i	−1.00492	−	0.730121i
$975$	−2.17566	−	2.41632i	−0.0696769	−	0.0773840i
$976$	4.35424	−	4.83587i	0.139376	−	0.154792i
$977$	−26.0045	−	11.5779i	−0.831957	−	0.370411i	−0.0538550	−	0.998549i	$-0.517151\pi$
$977$	−26.0045	−	11.5779i	−0.831957	−	0.370411i	−0.778102	+	0.628137i	$0.783818\pi$
$978$	9.68483	−	16.7746i	0.309687	−	0.536393i
$979$	−12.1818	−	39.9589i	−0.389333	−	1.27709i
$980$	−17.0914	−	2.76138i	−0.545963	−	0.0882090i
$981$	−4.72710	+	3.43444i	−0.150925	+	0.109653i
$982$	−17.2515	−	3.66691i	−0.550516	−	0.117016i
$983$	31.4592	−	6.68685i	1.00339	−	0.213277i	0.323215	−	0.946326i	$-0.395236\pi$
$983$	31.4592	−	6.68685i	1.00339	−	0.213277i	0.680177	+	0.733048i	$0.261903\pi$
$984$	0.607208	−	5.77720i	0.0193571	−	0.184170i
$985$	−54.9534	+	24.4668i	−1.75096	+	0.779578i
$986$	−4.86663	+	14.9779i	−0.154985	+	0.476995i
$987$	6.38829	+	26.7921i	0.203341	+	0.852803i
$988$	−0.454065	+	0.329897i	−0.0144457	+	0.0104954i
$989$	7.09943	−	12.2966i	0.225749	−	0.391008i
$990$	−1.00618	+	8.14101i	−0.0319785	+	0.258738i
$991$	−10.6461	−	18.4395i	−0.338183	−	0.585750i	0.645908	−	0.763415i	$-0.276479\pi$
$991$	−10.6461	−	18.4395i	−0.338183	−	0.585750i	−0.984091	+	0.177665i	$0.943146\pi$
$992$	−0.0661348	−	0.629231i	−0.00209978	−	0.0199781i
$993$	2.27883	+	7.01352i	0.0723165	+	0.222567i
$994$	3.38414	+	4.42449i	0.107338	+	0.140336i
$995$	−10.5251	−	7.64695i	−0.333669	−	0.242425i
$996$	2.67018	−	1.18884i	0.0846078	−	0.0376698i
$997$	32.3849	−	6.88363i	1.02564	−	0.218007i	0.335774	−	0.941943i	$-0.391002\pi$
$997$	32.3849	−	6.88363i	1.02564	−	0.218007i	0.689867	+	0.723936i	$0.257669\pi$
$998$	−16.7389	+	18.5904i	−0.529860	+	0.588469i
$999$	−0.208430	−	1.98308i	−0.00659444	−	0.0627419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.b.289.1	yes	24
7.4	even	3	inner	462.2.y.b.25.3	✓	24
11.4	even	5	inner	462.2.y.b.37.3	yes	24
77.4	even	15	inner	462.2.y.b.235.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.b.25.3	✓	24	7.4	even	3	inner
462.2.y.b.37.3	yes	24	11.4	even	5	inner
462.2.y.b.235.1	yes	24	77.4	even	15	inner
462.2.y.b.289.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 - 0.994522i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-2.25946 + 1.00598i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-1.01628 + 2.44278i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.104528 - 0.994522i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-2.25946 + 1.00598i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-1.01628 + 2.44278i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(1.23664 + 2.14193i) q^{10} +(-2.26387 + 2.42382i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.35468 - 1.71077i) q^{13} +(2.53563 + 0.755368i) q^{14} +(-0.764287 + 2.35223i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-0.827071 + 7.86905i) q^{17} +(-0.978148 + 0.207912i) q^{18} +(0.188621 + 0.0400927i) q^{19} +(2.00093 - 1.45376i) q^{20} +(1.13532 + 2.38978i) q^{21} +(2.64718 + 1.99811i) q^{22} +(-1.18098 + 2.04552i) q^{23} +(0.913545 + 0.406737i) q^{24} +(0.747511 - 0.830195i) q^{25} +(-1.94753 - 2.16295i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.486184 - 2.60070i) q^{28} +(-0.615063 + 1.89297i) q^{29} +(2.41924 + 0.514225i) q^{30} +(0.577997 + 0.257341i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.286429 + 3.30423i) q^{33} +7.91240 q^{34} +(-0.161148 - 6.54171i) q^{35} +(0.309017 + 0.951057i) q^{36} +(1.33425 + 1.48184i) q^{37} +(0.0201568 - 0.191779i) q^{38} +(0.304234 - 2.89460i) q^{39} +(-1.65495 - 1.83801i) q^{40} +(-1.79509 - 5.52471i) q^{41} +(2.25802 - 1.37890i) q^{42} -6.01147 q^{43} +(1.71045 - 2.84154i) q^{44} +(1.23664 + 2.14193i) q^{45} +(2.15776 + 0.960695i) q^{46} +(10.1829 + 2.16443i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-4.93437 - 4.96508i) q^{49} +(-0.903783 - 0.656637i) q^{50} +(5.29443 + 5.88006i) q^{51} +(-1.94753 + 2.16295i) q^{52} +(-12.0686 - 5.37328i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.67680 - 7.75392i) q^{55} +(-2.63727 - 0.211674i) q^{56} +(0.156007 - 0.113346i) q^{57} +(1.94689 + 0.413825i) q^{58} +(-11.2389 + 2.38891i) q^{59} +(0.258529 - 2.45974i) q^{60} +(5.94472 - 2.64676i) q^{61} +(0.195514 - 0.601730i) q^{62} +(2.53563 + 0.755368i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.59930 + 6.23417i) q^{65} +(3.25619 - 0.630246i) q^{66} +(3.46463 + 6.00092i) q^{67} +(-0.827071 - 7.86905i) q^{68} +(0.729885 + 2.24636i) q^{69} +(-6.48903 + 0.844060i) q^{70} +(1.70329 + 1.23751i) q^{71} +(0.913545 - 0.406737i) q^{72} +(13.5426 - 2.87856i) q^{73} +(1.33425 - 1.48184i) q^{74} +(-0.116773 - 1.11102i) q^{75} -0.192835 q^{76} +(-3.62016 - 7.99340i) q^{77} -2.91054 q^{78} +(0.913652 + 8.69282i) q^{79} +(-1.65495 + 1.83801i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-5.30681 + 2.36274i) q^{82} +(-2.36465 - 1.71802i) q^{83} +(-1.60737 - 2.10151i) q^{84} +(-6.04734 - 18.6118i) q^{85} +(0.628370 + 5.97854i) q^{86} +(0.995193 + 1.72373i) q^{87} +(-3.00476 - 1.40406i) q^{88} +(-6.29774 + 10.9080i) q^{89} +(2.00093 - 1.45376i) q^{90} +(1.78605 + 7.49058i) q^{91} +(0.729885 - 2.24636i) q^{92} +(0.577997 - 0.257341i) q^{93} +(1.08818 - 10.3533i) q^{94} +(-0.466514 + 0.0991607i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-5.26739 + 3.82699i) q^{97} +(-4.42210 + 5.42633i) q^{98} +(2.64718 + 1.99811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{14} + 20 q^{15} + 3 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{22} + 24 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{27} - 2 q^{28} + 2 q^{29} - 10 q^{30} - 19 q^{31} - 12 q^{32} - 7 q^{33} + 24 q^{34} + 14 q^{35} - 6 q^{36} - q^{37} - 8 q^{38} - 5 q^{39} - 10 q^{40} + 16 q^{41} + 10 q^{42} - 68 q^{43} - 2 q^{44} + 10 q^{45} - 6 q^{46} + 25 q^{47} - 6 q^{48} - 21 q^{49} + 14 q^{50} - 2 q^{51} - 5 q^{53} - 12 q^{54} - 10 q^{55} - 10 q^{56} + 16 q^{57} - q^{58} - 36 q^{59} + 5 q^{60} - q^{61} - 52 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} + 8 q^{66} + 56 q^{67} + 8 q^{68} + 12 q^{69} - 17 q^{70} - 6 q^{71} + 3 q^{72} + 35 q^{73} - q^{74} - 7 q^{75} - 4 q^{76} + 38 q^{77} - 20 q^{78} - 3 q^{79} - 10 q^{80} + 3 q^{81} + 2 q^{82} - 28 q^{83} + 7 q^{84} - 80 q^{85} - 11 q^{86} + 4 q^{87} - 7 q^{88} - 6 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 19 q^{93} - 30 q^{94} - 44 q^{95} + 3 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 + 10 * q^10 - 2 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^14 + 20 * q^15 + 3 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^22 + 24 * q^23 + 3 * q^24 + 8 * q^25 - 6 * q^27 - 2 * q^28 + 2 * q^29 - 10 * q^30 - 19 * q^31 - 12 * q^32 - 7 * q^33 + 24 * q^34 + 14 * q^35 - 6 * q^36 - q^37 - 8 * q^38 - 5 * q^39 - 10 * q^40 + 16 * q^41 + 10 * q^42 - 68 * q^43 - 2 * q^44 + 10 * q^45 - 6 * q^46 + 25 * q^47 - 6 * q^48 - 21 * q^49 + 14 * q^50 - 2 * q^51 - 5 * q^53 - 12 * q^54 - 10 * q^55 - 10 * q^56 + 16 * q^57 - q^58 - 36 * q^59 + 5 * q^60 - q^61 - 52 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 + 8 * q^66 + 56 * q^67 + 8 * q^68 + 12 * q^69 - 17 * q^70 - 6 * q^71 + 3 * q^72 + 35 * q^73 - q^74 - 7 * q^75 - 4 * q^76 + 38 * q^77 - 20 * q^78 - 3 * q^79 - 10 * q^80 + 3 * q^81 + 2 * q^82 - 28 * q^83 + 7 * q^84 - 80 * q^85 - 11 * q^86 + 4 * q^87 - 7 * q^88 - 6 * q^89 - 10 * q^90 - 24 * q^91 + 12 * q^92 - 19 * q^93 - 30 * q^94 - 44 * q^95 + 3 * q^96 - 8 * q^97 - 6 * q^99

Introduction

L-functions

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