LMFDB - Embedded newform 115.2.l.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	115.7
Dual form			115.2.l.a.33.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05653 + 0.0755644i) q^{2} +(0.0308132 - 0.141646i) q^{3} +(-0.869101 + 0.124958i) q^{4} +(2.18100 - 0.493172i) q^{5} +(-0.0218516 + 0.151981i) q^{6} +(0.717546 - 1.31409i) q^{7} +(2.97883 - 0.648004i) q^{8} +(2.70978 + 1.23752i) q^{9} +O(q^{10})$	\(q+(-1.05653 + 0.0755644i) q^{2} +(0.0308132 - 0.141646i) q^{3} +(-0.869101 + 0.124958i) q^{4} +(2.18100 - 0.493172i) q^{5} +(-0.0218516 + 0.151981i) q^{6} +(0.717546 - 1.31409i) q^{7} +(2.97883 - 0.648004i) q^{8} +(2.70978 + 1.23752i) q^{9} +(-2.26703 + 0.685856i) q^{10} +(-0.998057 + 0.864822i) q^{11} +(-0.00908000 + 0.126955i) q^{12} +(3.34773 - 1.82800i) q^{13} +(-0.658809 + 1.44259i) q^{14} +(-0.00265209 - 0.324127i) q^{15} +(-1.41331 + 0.414985i) q^{16} +(-3.94697 - 5.27254i) q^{17} +(-2.95647 - 1.10271i) q^{18} +(0.898560 + 6.24963i) q^{19} +(-1.83389 + 0.701150i) q^{20} +(-0.164025 - 0.142129i) q^{21} +(0.989126 - 0.989126i) q^{22} +(-3.42622 + 3.35575i) q^{23} -0.441906i q^{24} +(4.51356 - 2.15122i) q^{25} +(-3.39884 + 2.18430i) q^{26} +(0.519398 - 0.693834i) q^{27} +(-0.459414 + 1.23174i) q^{28} +(-8.17984 - 1.17608i) q^{29} +(0.0272944 + 0.342249i) q^{30} +(-3.45032 - 2.21738i) q^{31} +(-4.25073 + 1.58544i) q^{32} +(0.0917452 + 0.168019i) q^{33} +(4.56851 + 5.27234i) q^{34} +(0.916900 - 3.21990i) q^{35} +(-2.50971 - 0.736918i) q^{36} +(0.655955 + 1.75868i) q^{37} +(-1.42160 - 6.53501i) q^{38} +(-0.155774 - 0.530519i) q^{39} +(6.17726 - 2.88238i) q^{40} +(2.66058 + 5.82585i) q^{41} +(0.184037 + 0.137768i) q^{42} +(0.463730 + 0.100878i) q^{43} +(0.759346 - 0.876332i) q^{44} +(6.52036 + 1.36264i) q^{45} +(3.36632 - 3.80434i) q^{46} +(-1.63886 - 1.63886i) q^{47} +(0.0152324 + 0.212976i) q^{48} +(2.57253 + 4.00294i) q^{49} +(-4.60615 + 2.61389i) q^{50} +(-0.868453 + 0.396609i) q^{51} +(-2.68109 + 2.00704i) q^{52} +(0.329990 + 0.180188i) q^{53} +(-0.496329 + 0.772303i) q^{54} +(-1.75026 + 2.37839i) q^{55} +(1.28591 - 4.37941i) q^{56} +(0.912922 + 0.0652934i) q^{57} +(8.73110 + 0.624461i) q^{58} +(3.45672 - 11.7725i) q^{59} +(0.0428071 + 0.281367i) q^{60} +(1.76790 - 2.75090i) q^{61} +(3.81291 + 2.08201i) q^{62} +(3.57060 - 2.67291i) q^{63} +(7.05094 - 3.22006i) q^{64} +(6.39990 - 5.63788i) q^{65} +(-0.109628 - 0.170584i) q^{66} +(0.776524 + 10.8572i) q^{67} +(4.08916 + 4.08916i) q^{68} +(0.369756 + 0.588711i) q^{69} +(-0.725421 + 3.47120i) q^{70} +(-4.26013 + 4.91645i) q^{71} +(8.87389 + 1.93040i) q^{72} +(-6.54201 - 4.89729i) q^{73} +(-0.825929 - 1.80853i) q^{74} +(-0.165634 - 0.705614i) q^{75} +(-1.56188 - 5.31927i) q^{76} +(0.420299 + 1.93208i) q^{77} +(0.204668 + 0.548737i) q^{78} +(-7.55266 - 2.21766i) q^{79} +(-2.87777 + 1.60209i) q^{80} +(5.77019 + 6.65915i) q^{81} +(-3.25120 - 5.95413i) q^{82} +(-13.6074 + 5.07529i) q^{83} +(0.160315 + 0.103028i) q^{84} +(-11.2086 - 9.55290i) q^{85} +(-0.497566 - 0.0715393i) q^{86} +(-0.418634 + 1.12240i) q^{87} +(-2.41263 + 3.22290i) q^{88} +(-8.93857 + 5.74447i) q^{89} +(-6.99191 - 0.946961i) q^{90} -5.71088i q^{91} +(2.55840 - 3.34462i) q^{92} +(-0.420399 + 0.420399i) q^{93} +(1.85534 + 1.60766i) q^{94} +(5.04190 + 13.1873i) q^{95} +(0.0935927 + 0.650952i) q^{96} +(-1.34281 - 0.500840i) q^{97} +(-3.02043 - 4.03483i) q^{98} +(-3.77475 + 1.10837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−1.05653	+	0.0755644i	−0.747078	+	0.0534321i	−0.439687	−	0.898151i	$-0.644911\pi$
$2$	−1.05653	+	0.0755644i	−0.747078	+	0.0534321i	−0.307391	+	0.951583i	$0.599456\pi$
$3$	0.0308132	−	0.141646i	0.0177900	−	0.0817793i	−0.967396	−	0.253269i	$-0.918494\pi$
$3$	0.0308132	−	0.141646i	0.0177900	−	0.0817793i	0.985186	+	0.171489i	$0.0548579\pi$
$4$	−0.869101	+	0.124958i	−0.434550	+	0.0624789i
$5$	2.18100	−	0.493172i	0.975375	−	0.220553i
$5$	2.18100	−	0.493172i	0.975375	−	0.220553i
$6$	−0.0218516	+	0.151981i	−0.00892089	+	0.0620461i
$7$	0.717546	−	1.31409i	0.271207	−	0.496678i	−0.706209	−	0.708003i	$-0.749596\pi$
$7$	0.717546	−	1.31409i	0.271207	−	0.496678i	0.977416	+	0.211325i	$0.0677779\pi$
$8$	2.97883	−	0.648004i	1.05317	−	0.229104i
$9$	2.70978	+	1.23752i	0.903261	+	0.412505i
$10$	−2.26703	+	0.685856i	−0.716897	+	0.216887i
$11$	−0.998057	+	0.864822i	−0.300926	+	0.260754i	−0.792214	−	0.610243i	$-0.791072\pi$
$11$	−0.998057	+	0.864822i	−0.300926	+	0.260754i	0.491288	+	0.870997i	$0.336526\pi$
$12$	−0.00908000	+	0.126955i	−0.00262117	+	0.0366487i
$13$	3.34773	−	1.82800i	0.928493	−	0.506996i	0.0575299	−	0.998344i	$-0.481678\pi$
$13$	3.34773	−	1.82800i	0.928493	−	0.506996i	0.870963	+	0.491348i	$0.163496\pi$
$14$	−0.658809	+	1.44259i	−0.176074	+	0.385549i
$15$	−0.00265209	−	0.324127i	−0.000684767	−	0.0836891i
$16$	−1.41331	+	0.414985i	−0.353327	+	0.103746i
$17$	−3.94697	−	5.27254i	−0.957282	−	1.27878i	−0.960354	−	0.278783i	$-0.910069\pi$
$17$	−3.94697	−	5.27254i	−0.957282	−	1.27878i	0.00307241	−	0.999995i	$-0.499022\pi$
$18$	−2.95647	−	1.10271i	−0.696847	−	0.259911i
$19$	0.898560	+	6.24963i	0.206144	+	1.43376i	0.785588	+	0.618750i	$0.212361\pi$
$19$	0.898560	+	6.24963i	0.206144	+	1.43376i	−0.579444	+	0.815012i	$0.696730\pi$
$20$	−1.83389	+	0.701150i	−0.410070	+	0.156782i
$21$	−0.164025	−	0.142129i	−0.0357932	−	0.0310150i
$22$	0.989126	−	0.989126i	0.210882	−	0.210882i
$23$	−3.42622	+	3.35575i	−0.714415	+	0.699722i
$23$	−3.42622	+	3.35575i	−0.714415	+	0.699722i
$24$		−	0.441906i		−	0.0902037i
$25$	4.51356	−	2.15122i	0.902713	−	0.430244i
$26$	−3.39884	+	2.18430i	−0.666567	+	0.428377i
$27$	0.519398	−	0.693834i	0.0999581	−	0.133528i
$28$	−0.459414	+	1.23174i	−0.0868211	+	0.232776i
$29$	−8.17984	−	1.17608i	−1.51896	−	0.218393i	−0.668212	−	0.743971i	$-0.732940\pi$
$29$	−8.17984	−	1.17608i	−1.51896	−	0.218393i	−0.850746	+	0.525578i	$0.823849\pi$
$30$	0.0272944	+	0.342249i	0.00498326	+	0.0624858i
$31$	−3.45032	−	2.21738i	−0.619695	−	0.398254i	0.192786	−	0.981241i	$-0.438248\pi$
$31$	−3.45032	−	2.21738i	−0.619695	−	0.398254i	−0.812482	+	0.582987i	$0.801884\pi$
$32$	−4.25073	+	1.58544i	−0.751430	+	0.280269i
$33$	0.0917452	+	0.168019i	0.0159708	+	0.0292483i
$34$	4.56851	+	5.27234i	0.783492	+	0.904198i
$35$	0.916900	−	3.21990i	0.154984	−	0.544263i
$36$	−2.50971	−	0.736918i	−0.418285	−	0.122820i
$37$	0.655955	+	1.75868i	0.107838	+	0.289126i	0.979649	−	0.200717i	$-0.0643271\pi$
$37$	0.655955	+	1.75868i	0.107838	+	0.289126i	−0.871811	+	0.489842i	$0.837054\pi$
$38$	−1.42160	−	6.53501i	−0.230615	−	1.06012i
$39$	−0.155774	−	0.530519i	−0.0249439	−	0.0849510i
$40$	6.17726	−	2.88238i	0.976711	−	0.455744i
$41$	2.66058	+	5.82585i	0.415512	+	0.909845i	0.995459	+	0.0951903i	$0.0303460\pi$
$41$	2.66058	+	5.82585i	0.415512	+	0.909845i	−0.579947	+	0.814654i	$0.696927\pi$
$42$	0.184037	+	0.137768i	0.0283976	+	0.0212581i
$43$	0.463730	+	0.100878i	0.0707181	+	0.0153838i	0.247785	−	0.968815i	$-0.420297\pi$
$43$	0.463730	+	0.100878i	0.0707181	+	0.0153838i	−0.177067	+	0.984199i	$0.556661\pi$
$44$	0.759346	−	0.876332i	0.114476	−	0.132112i
$45$	6.52036	+	1.36264i	0.971997	+	0.203130i
$46$	3.36632	−	3.80434i	0.496337	−	0.560920i
$47$	−1.63886	−	1.63886i	−0.239052	−	0.239052i	0.577406	−	0.816457i	$-0.304065\pi$
$47$	−1.63886	−	1.63886i	−0.239052	−	0.239052i	−0.816457	+	0.577406i	$0.804065\pi$
$48$	0.0152324	+	0.212976i	0.00219860	+	0.0307405i
$49$	2.57253	+	4.00294i	0.367505	+	0.571849i
$50$	−4.60615	+	2.61389i	−0.651408	+	0.369660i
$51$	−0.868453	+	0.396609i	−0.121608	+	0.0555364i
$52$	−2.68109	+	2.00704i	−0.371800	+	0.278326i
$53$	0.329990	+	0.180188i	0.0453276	+	0.0247507i	0.501753	−	0.865011i	$-0.332689\pi$
$53$	0.329990	+	0.180188i	0.0453276	+	0.0247507i	−0.456425	+	0.889762i	$0.650870\pi$
$54$	−0.496329	+	0.772303i	−0.0675419	+	0.105097i
$55$	−1.75026	+	2.37839i	−0.236005	+	0.320703i
$56$	1.28591	−	4.37941i	0.171837	−	0.585224i
$57$	0.912922	+	0.0652934i	0.120919	+	0.00864833i
$58$	8.73110	+	0.624461i	1.14645	+	0.0819957i
$59$	3.45672	−	11.7725i	0.450027	−	1.53265i	−0.352370	−	0.935861i	$-0.614624\pi$
$59$	3.45672	−	11.7725i	0.450027	−	1.53265i	0.802397	−	0.596790i	$-0.203558\pi$
$60$	0.0428071	+	0.281367i	0.00552637	+	0.0363244i
$61$	1.76790	−	2.75090i	0.226356	−	0.352217i	−0.709436	−	0.704770i	$-0.751050\pi$
$61$	1.76790	−	2.75090i	0.226356	−	0.352217i	0.935792	+	0.352553i	$0.114686\pi$
$62$	3.81291	+	2.08201i	0.484241	+	0.264415i
$63$	3.57060	−	2.67291i	0.449853	−	0.336756i
$64$	7.05094	−	3.22006i	0.881368	−	0.402507i
$65$	6.39990	−	5.63788i	0.793809	−	0.699293i
$66$	−0.109628	−	0.170584i	−0.0134942	−	0.0209974i
$67$	0.776524	+	10.8572i	0.0948675	+	1.32642i	0.792459	+	0.609925i	$0.208801\pi$
$67$	0.776524	+	10.8572i	0.0948675	+	1.32642i	−0.697592	+	0.716496i	$0.745745\pi$
$68$	4.08916	+	4.08916i	0.495884	+	0.495884i
$69$	0.369756	+	0.588711i	0.0445133	+	0.0708725i
$70$	−0.725421	+	3.47120i	−0.0867044	+	0.414888i
$71$	−4.26013	+	4.91645i	−0.505584	+	0.583475i	−0.949962	−	0.312364i	$-0.898879\pi$
$71$	−4.26013	+	4.91645i	−0.505584	+	0.583475i	0.444379	+	0.895839i	$0.353425\pi$
$72$	8.87389	+	1.93040i	1.04580	+	0.227499i
$73$	−6.54201	−	4.89729i	−0.765684	−	0.573184i	0.143464	−	0.989655i	$-0.454176\pi$
$73$	−6.54201	−	4.89729i	−0.765684	−	0.573184i	−0.909149	+	0.416471i	$0.863267\pi$
$74$	−0.825929	−	1.80853i	−0.0960122	−	0.210237i
$75$	−0.165634	−	0.705614i	−0.0191258	−	0.0814773i
$76$	−1.56188	−	5.31927i	−0.179160	−	0.610162i
$77$	0.420299	+	1.93208i	0.0478975	+	0.220181i
$78$	0.204668	+	0.548737i	0.0231741	+	0.0621322i
$79$	−7.55266	−	2.21766i	−0.849740	−	0.249506i	−0.172264	−	0.985051i	$-0.555108\pi$
$79$	−7.55266	−	2.21766i	−0.849740	−	0.249506i	−0.677476	+	0.735545i	$0.736926\pi$
$80$	−2.87777	+	1.60209i	−0.321745	+	0.179119i
$81$	5.77019	+	6.65915i	0.641132	+	0.739906i
$82$	−3.25120	−	5.95413i	−0.359035	−	0.657523i
$83$	−13.6074	+	5.07529i	−1.49360	+	0.557086i	−0.957845	−	0.287285i	$-0.907247\pi$
$83$	−13.6074	+	5.07529i	−1.49360	+	0.557086i	−0.535760	+	0.844371i	$0.679975\pi$
$84$	0.160315	+	0.103028i	0.0174917	+	0.0112413i
$85$	−11.2086	−	9.55290i	−1.21575	−	1.03616i
$86$	−0.497566	−	0.0715393i	−0.0536540	−	0.00771428i
$87$	−0.418634	+	1.12240i	−0.0448823	+	0.120334i
$88$	−2.41263	+	3.22290i	−0.257188	+	0.343562i
$89$	−8.93857	+	5.74447i	−0.947487	+	0.608913i	−0.920508	−	0.390723i	$-0.872225\pi$
$89$	−8.93857	+	5.74447i	−0.947487	+	0.608913i	−0.0269786	+	0.999636i	$0.508589\pi$
$90$	−6.99191	−	0.946961i	−0.737012	−	0.0998184i
$91$		−	5.71088i		−	0.598663i
$92$	2.55840	−	3.34462i	0.266732	−	0.348700i
$93$	−0.420399	+	0.420399i	−0.0435933	+	0.0435933i
$94$	1.85534	+	1.60766i	0.191363	+	0.165817i
$95$	5.04190	+	13.1873i	0.517288	+	1.35299i
$96$	0.0935927	+	0.650952i	0.00955227	+	0.0664375i
$97$	−1.34281	−	0.500840i	−0.136341	−	0.0508526i	0.280367	−	0.959893i	$-0.409544\pi$
$97$	−1.34281	−	0.500840i	−0.136341	−	0.0508526i	−0.416709	+	0.909040i	$0.636816\pi$
$98$	−3.02043	−	4.03483i	−0.305110	−	0.407579i
$99$	−3.77475	+	1.10837i	−0.379377	+	0.111395i
$100$	−3.65393	+	2.43363i	−0.365393	+	0.243363i
$101$	1.90443	−	4.17011i	0.189497	−	0.414941i	−0.790907	−	0.611936i	$-0.790391\pi$
$101$	1.90443	−	4.17011i	0.189497	−	0.414941i	0.980405	+	0.196995i	$0.0631182\pi$
$102$	0.887575	−	0.484653i	0.0878830	−	0.0479878i
$103$	−0.372107	+	5.20274i	−0.0366648	+	0.512641i	0.945623	+	0.325264i	$0.105453\pi$
$103$	−0.372107	+	5.20274i	−0.0366648	+	0.512641i	−0.982288	+	0.187377i	$0.940001\pi$
$104$	8.78776	−	7.61464i	0.861711	−	0.746677i
$105$	−0.427834	−	0.229091i	−0.0417523	−	0.0223570i
$106$	−0.362259	−	0.165438i	−0.0351857	−	0.0160688i
$107$	−5.99595	+	1.30434i	−0.579650	+	0.126095i	−0.492825	−	0.870128i	$-0.664036\pi$
$107$	−5.99595	+	1.30434i	−0.579650	+	0.126095i	−0.0868252	+	0.996224i	$0.527672\pi$
$108$	−0.364709	+	0.667914i	−0.0350941	+	0.0642701i
$109$	1.66415	−	11.5744i	0.159397	−	1.10863i	−0.740352	−	0.672219i	$-0.765341\pi$
$109$	1.66415	−	11.5744i	0.159397	−	1.10863i	0.899749	−	0.436408i	$-0.143750\pi$
$110$	1.66948	−	2.64510i	0.159179	−	0.252200i
$111$	0.269322	−	0.0387227i	0.0255629	−	0.00367540i
$112$	−0.468787	+	2.15498i	−0.0442962	+	0.203626i
$113$	−0.247324	+	0.0176889i	−0.0232663	+	0.00166404i	−0.0829675	−	0.996552i	$-0.526440\pi$
$113$	−0.247324	+	0.0176889i	−0.0232663	+	0.00166404i	0.0597012	+	0.998216i	$0.480985\pi$
$114$	−0.969461			−0.0907984
$115$	−5.81763	+	9.00862i	−0.542497	+	0.840058i
$116$	7.25606			0.673709
$117$	11.3338	−	0.810609i	1.04781	−	0.0749408i
$118$	−2.76254	+	12.6992i	−0.254313	+	1.16906i
$119$	−9.76071	+	1.40338i	−0.894763	+	0.128647i
$120$	−0.217936	−	0.963799i	−0.0198947	−	0.0879824i
$121$	−1.31726	+	9.16175i	−0.119751	+	0.832887i
$122$	−1.65996	+	3.04000i	−0.150286	+	0.275228i
$123$	0.907189	−	0.197347i	0.0817984	−	0.0177942i
$124$	3.27575	+	1.49599i	0.294171	+	0.134344i
$125$	8.78318	−	6.91778i	0.785592	−	0.618745i
$126$	−3.57046	+	3.09382i	−0.318082	+	0.275619i
$127$	0.743263	−	10.3922i	0.0659540	−	0.922157i	−0.851510	−	0.524338i	$-0.824313\pi$
$127$	0.743263	−	10.3922i	0.0659540	−	0.922157i	0.917464	−	0.397819i	$-0.130233\pi$
$128$	0.757468	−	0.413609i	0.0669513	−	0.0365582i
$129$	0.0285780	−	0.0625771i	0.00251615	−	0.00550960i
$130$	−6.33565	+	6.44018i	−0.555673	+	0.564841i
$131$	10.2130	−	2.99880i	0.892313	−	0.262007i	0.196735	−	0.980457i	$-0.436966\pi$
$131$	10.2130	−	2.99880i	0.892313	−	0.262007i	0.695579	+	0.718450i	$0.255148\pi$
$132$	−0.100731	−	0.134561i	−0.00876751	−	0.0117120i
$133$	8.85731	+	3.30361i	0.768026	+	0.286459i
$134$	−1.64084	−	11.4123i	−0.141747	−	0.985871i
$135$	0.790629	−	1.76941i	0.0680465	−	0.152286i
$136$	−15.1740	−	13.1483i	−1.30116	−	1.12746i
$137$	−2.54085	+	2.54085i	−0.217080	+	0.217080i	−0.807267	−	0.590187i	$-0.799054\pi$
$137$	−2.54085	+	2.54085i	−0.217080	+	0.217080i	0.590187	+	0.807267i	$0.299054\pi$
$138$	−0.435143	−	0.594049i	−0.0370418	−	0.0505688i
$139$		−	5.99216i		−	0.508248i	−0.967172	−	0.254124i	$-0.918213\pi$
$139$		−	5.99216i		−	0.508248i	0.967172	−	0.254124i	$-0.0817872\pi$
$140$	−0.394526	+	2.91299i	−0.0333436	+	0.246193i
$141$	−0.282636	+	0.181639i	−0.0238022	+	0.0152967i
$142$	4.12943	−	5.51628i	0.346534	−	0.462916i
$143$	−1.76033	+	4.71964i	−0.147206	+	0.394676i
$144$	−4.34331	−	0.624473i	−0.361942	−	0.0520394i
$145$	−18.4203	+	1.46902i	−1.52972	+	0.121996i
$146$	7.28188	+	4.67978i	0.602653	+	0.387301i
$147$	0.646268	−	0.241046i	0.0533033	−	0.0198811i
$148$	−0.789852	−	1.44651i	−0.0649254	−	0.118902i
$149$	8.28315	+	9.55927i	0.678582	+	0.783126i	0.985693	−	0.168548i	$-0.0539078\pi$
$149$	8.28315	+	9.55927i	0.678582	+	0.783126i	−0.307111	+	0.951674i	$0.599362\pi$
$150$	0.228317	+	0.732985i	0.0186420	+	0.0598480i
$151$	18.1786	+	5.33773i	1.47936	+	0.434378i	0.919128	−	0.393959i	$-0.128895\pi$
$151$	18.1786	+	5.33773i	1.47936	+	0.434378i	0.560229	+	0.828338i	$0.310713\pi$
$152$	6.72644	+	18.0343i	0.545586	+	1.46277i
$153$	−4.17059	−	19.1719i	−0.337172	−	1.54995i
$154$	−0.590055	−	2.00954i	−0.0475480	−	0.161933i
$155$	−8.61871	−	3.13453i	−0.692272	−	0.251771i
$156$	0.201676	+	0.441609i	0.0161470	+	0.0353570i
$157$	0.273445	+	0.204699i	0.0218233	+	0.0163367i	0.610134	−	0.792299i	$-0.291116\pi$
$157$	0.273445	+	0.204699i	0.0218233	+	0.0163367i	−0.588310	+	0.808635i	$0.700207\pi$
$158$	8.14717	+	1.77231i	0.648154	+	0.140997i
$159$	0.0356909	−	0.0411895i	0.00283047	−	0.00326654i
$160$	−8.48897	+	5.55420i	−0.671112	+	0.439098i
$161$	1.95128	+	6.91025i	0.153782	+	0.544604i
$162$	−6.59956	−	6.59956i	−0.518511	−	0.518511i
$163$	−0.650388	−	9.09361i	−0.0509423	−	0.712266i	−0.957179	−	0.289496i	$-0.906512\pi$
$163$	−0.650388	−	9.09361i	−0.0509423	−	0.712266i	0.906237	−	0.422770i	$-0.138942\pi$
$164$	−3.04029	−	4.73079i	−0.237407	−	0.369413i
$165$	0.282959	+	0.321203i	0.0220283	+	0.0250057i
$166$	13.9931	−	6.39043i	1.08607	−	0.495993i
$167$	14.2243	−	10.6481i	1.10071	−	0.823978i	0.115154	−	0.993348i	$-0.463264\pi$
$167$	14.2243	−	10.6481i	1.10071	−	0.823978i	0.985553	+	0.169369i	$0.0541731\pi$
$168$	−0.580703	−	0.317088i	−0.0448022	−	0.0244639i
$169$	0.837383	−	1.30299i	0.0644141	−	0.100230i
$170$	12.5641	+	9.24593i	0.963622	+	0.709131i
$171$	−5.29911	+	18.0471i	−0.405233	+	1.38010i
$172$	−0.415633	−	0.0297267i	−0.0316917	−	0.00226664i
$173$	7.81725	+	0.559101i	0.594335	+	0.0425077i	0.365267	−	0.930903i	$-0.380978\pi$
$173$	7.81725	+	0.559101i	0.594335	+	0.0425077i	0.229068	+	0.973410i	$0.426432\pi$
$174$	0.357485	−	1.21748i	0.0271009	−	0.0922972i
$175$	0.411797	−	7.47481i	0.0311289	−	0.565043i
$176$	1.05167	−	1.63644i	0.0792730	−	0.123351i
$177$	−1.56102	−	0.852380i	−0.117333	−	0.0640688i
$178$	9.00978	−	6.74464i	0.675311	−	0.505532i
$179$	0.0174190	−	0.00795498i	0.00130195	−	0.000594583i	−0.414764	−	0.909929i	$-0.636136\pi$
$179$	0.0174190	−	0.00795498i	0.00130195	−	0.000594583i	0.416066	+	0.909334i	$0.363409\pi$
$180$	−5.83712	−	0.369502i	−0.435073	−	0.0275410i
$181$	2.58317	+	4.01948i	0.192005	+	0.298766i	0.923887	−	0.382666i	$-0.124994\pi$
$181$	2.58317	+	4.01948i	0.192005	+	0.298766i	−0.731882	+	0.681432i	$0.761358\pi$
$182$	0.431539	+	6.03371i	0.0319878	+	0.447248i
$183$	−0.335180	−	0.335180i	−0.0247772	−	0.0247772i
$184$	−8.03157	+	12.2164i	−0.592095	+	0.900605i
$185$	2.29797	+	3.51220i	0.168950	+	0.258222i
$186$	0.412396	−	0.475930i	0.0302384	−	0.0348969i
$187$	8.49911	+	1.84887i	0.621517	+	0.135203i
$188$	1.62912	+	1.21954i	0.118816	+	0.0889443i
$189$	−0.539067	−	1.18039i	−0.0392113	−	0.0858608i
$190$	−6.32341	−	13.5518i	−0.458748	−	0.983150i
$191$	−2.21248	−	7.53500i	−0.160089	−	0.545214i	−0.999997	−	0.00248446i	$-0.999209\pi$
$191$	−2.21248	−	7.53500i	−0.160089	−	0.545214i	0.839908	−	0.542729i	$-0.182609\pi$
$192$	−0.238846	−	1.09796i	−0.0172372	−	0.0792383i
$193$	0.915286	+	2.45398i	0.0658837	+	0.176641i	0.965720	−	0.259588i	$-0.0835866\pi$
$193$	0.915286	+	2.45398i	0.0658837	+	0.176641i	−0.899836	+	0.436229i	$0.856314\pi$
$194$	1.45656	+	0.427684i	0.104575	+	0.0307059i
$195$	−0.601382	−	1.08024i	−0.0430658	−	0.0773576i
$196$	−2.73599	−	3.15750i	−0.195428	−	0.225536i
$197$	−2.45085	−	4.48840i	−0.174616	−	0.319785i	0.775684	−	0.631122i	$-0.217405\pi$
$197$	−2.45085	−	4.48840i	−0.174616	−	0.319785i	−0.950300	+	0.311337i	$0.899223\pi$
$198$	3.90438	−	1.45626i	0.277472	−	0.103492i
$199$	−5.30098	−	3.40673i	−0.375777	−	0.241497i	0.339096	−	0.940752i	$-0.389879\pi$
$199$	−5.30098	−	3.40673i	−0.375777	−	0.241497i	−0.714872	+	0.699255i	$0.753515\pi$
$200$	12.0511	−	9.33292i	0.852143	−	0.659937i
$201$	1.56181	+	0.224554i	0.110161	+	0.0158388i
$202$	−1.69697	+	4.54975i	−0.119398	+	0.320119i
$203$	−7.41488	+	9.90512i	−0.520423	+	0.695203i
$204$	0.705213	−	0.453213i	0.0493748	−	0.0317313i
$205$	8.67587	+	11.3941i	0.605949	+	0.795797i
$206$		−	5.52496i		−	0.384942i
$207$	−13.4371	+	4.85335i	−0.933942	+	0.337331i
$208$	−3.97278	+	3.97278i	−0.275463	+	0.275463i
$209$	−6.30163	−	5.46039i	−0.435893	−	0.377703i
$210$	0.469329	+	0.209712i	0.0323868	+	0.0144715i
$211$	−0.0354062	−	0.246255i	−0.00243746	−	0.0169529i	0.988566	−	0.150786i	$-0.0481805\pi$
$211$	−0.0354062	−	0.246255i	−0.00243746	−	0.0169529i	−0.991004	+	0.133833i	$0.957271\pi$
$212$	−0.309310	−	0.115367i	−0.0212435	−	0.00792342i
$213$	0.565127	+	0.754921i	0.0387218	+	0.0517263i
$214$	6.23633	−	1.83115i	0.426307	−	0.125175i
$215$	1.06115	−	0.00868259i	0.0723696	−	0.000592148i
$216$	1.09759	−	2.40338i	0.0746815	−	0.163530i
$217$	−5.38960	+	2.94294i	−0.365870	+	0.199780i
$218$	−0.883607	+	12.3544i	−0.0598454	+	0.836749i
$219$	−0.895261	+	0.775748i	−0.0604961	+	0.0524202i
$220$	1.22396	−	2.28577i	0.0825190	−	0.154107i
$221$	−22.8516	−	10.4360i	−1.53716	−	0.701999i
$222$	−0.281621	+	0.0612628i	−0.0189011	+	0.00411169i
$223$	−11.0239	+	20.1888i	−0.738216	+	1.35194i	0.190699	+	0.981649i	$0.438925\pi$
$223$	−11.0239	+	20.1888i	−0.738216	+	1.35194i	−0.928915	+	0.370293i	$0.879257\pi$
$224$	−0.966687	+	6.72346i	−0.0645895	+	0.449230i
$225$	14.8929	−	0.243732i	0.992863	−	0.0162488i
$226$	0.259968	−	0.0373778i	0.0172928	−	0.00248633i
$227$	4.79506	−	22.0425i	0.318259	−	1.46301i	−0.488724	−	0.872439i	$-0.662537\pi$
$227$	4.79506	−	22.0425i	0.318259	−	1.46301i	0.806983	−	0.590575i	$-0.201099\pi$
$228$	−0.801580	+	0.0573301i	−0.0530859	+	0.00379678i
$229$	29.3757			1.94120			0.970599	−	0.240701i	$-0.0773772\pi$
$229$	29.3757			1.94120			0.970599	+	0.240701i	$0.0773772\pi$
$230$	5.46576	−	9.95747i	0.360402	−	0.656576i
$231$	0.286623			0.0188584
$232$	−25.1284	+	1.79722i	−1.64976	+	0.117993i
$233$	2.18385	−	10.0390i	0.143068	−	0.657675i	−0.848619	−	0.529005i	$-0.822565\pi$
$233$	2.18385	−	10.0390i	0.143068	−	0.657675i	0.991687	−	0.128670i	$-0.0410709\pi$
$234$	−11.9132	+	1.71286i	−0.778792	+	0.111973i
$235$	−4.38259	−	2.76611i	−0.285889	−	0.180441i
$236$	−1.53317	+	10.6634i	−0.0998010	+	0.694131i
$237$	−0.546844	+	1.00147i	−0.0355213	+	0.0650525i
$238$	10.2064	−	2.22027i	0.661584	−	0.143919i
$239$	10.0458	+	4.58775i	0.649807	+	0.296757i	0.712916	−	0.701250i	$-0.247374\pi$
$239$	10.0458	+	4.58775i	0.649807	+	0.296757i	−0.0631088	+	0.998007i	$0.520102\pi$
$240$	0.138256	+	0.456990i	0.00892437	+	0.0294986i
$241$	7.71515	−	6.68521i	0.496976	−	0.430633i	−0.369963	−	0.929047i	$-0.620630\pi$
$241$	7.71515	−	6.68521i	0.496976	−	0.430633i	0.866939	+	0.498414i	$0.166084\pi$
$242$	0.699421	−	9.77919i	0.0449605	−	0.628630i
$243$	3.40311	−	1.85824i	0.218310	−	0.119206i
$244$	−1.19273	+	2.61172i	−0.0763570	+	0.167199i
$245$	7.58484	+	7.46173i	0.484578	+	0.476712i
$246$	−0.943558	+	0.277054i	−0.0601591	+	0.0176643i
$247$	14.4324	+	19.2795i	0.918314	+	1.22672i
$248$	−11.7148	−	4.36939i	−0.743889	−	0.277456i
$249$	0.299608	+	2.08382i	0.0189869	+	0.132057i
$250$	−8.75694	+	7.97253i	−0.553838	+	0.504227i
$251$	−4.47832	−	3.88049i	−0.282669	−	0.244934i	0.501973	−	0.864883i	$-0.332608\pi$
$251$	−4.47832	−	3.88049i	−0.282669	−	0.244934i	−0.784642	+	0.619949i	$0.787153\pi$
$252$	−2.76921	+	2.76921i	−0.174444	+	0.174444i
$253$	0.517435	−	6.31230i	0.0325309	−	0.396851i
$254$			11.0358i			0.692447i
$255$	−1.69850	+	1.29330i	−0.106364	+	0.0809897i
$256$	−13.8109	+	8.87570i	−0.863179	+	0.554731i
$257$	−2.07001	+	2.76522i	−0.129124	+	0.172489i	−0.860444	−	0.509545i	$-0.829814\pi$
$257$	−2.07001	+	2.76522i	−0.129124	+	0.172489i	0.731320	+	0.682035i	$0.238905\pi$
$258$	−0.0254649	+	0.0682739i	−0.00158537	+	0.00425055i
$259$	2.78174	+	0.399954i	0.172849	+	0.0248519i
$260$	−4.85766	+	5.69960i	−0.301259	+	0.353474i
$261$	−20.7102	−	13.3096i	−1.28193	−	0.823844i
$262$	−10.5637	+	3.94006i	−0.652628	+	0.243418i
$263$	−13.4420	−	24.6171i	−0.828868	−	1.51796i	−0.855196	−	0.518304i	$-0.826563\pi$
$263$	−13.4420	−	24.6171i	−0.828868	−	1.51796i	0.0263285	−	0.999653i	$-0.491618\pi$
$264$	0.382170	+	0.441048i	0.0235209	+	0.0271446i
$265$	0.808572	+	0.230249i	0.0496702	+	0.0141441i
$266$	−9.60763	−	2.82106i	−0.589082	−	0.172970i
$267$	0.538255	+	1.44312i	0.0329407	+	0.0883174i
$268$	−2.03157	−	9.33899i	−0.124098	−	0.570469i
$269$	5.79226	+	19.7266i	0.353160	+	1.20275i	0.924225	+	0.381848i	$0.124712\pi$
$269$	5.79226	+	19.7266i	0.353160	+	1.20275i	−0.571065	+	0.820905i	$0.693470\pi$
$270$	−0.701618	+	1.92917i	−0.0426991	+	0.117406i
$271$	−6.46744	−	14.1617i	−0.392869	−	0.860263i	−0.997944	−	0.0640944i	$-0.979584\pi$
$271$	−6.46744	−	14.1617i	−0.392869	−	0.860263i	0.605075	−	0.796169i	$-0.293143\pi$
$272$	7.76631	+	5.81379i	0.470902	+	0.352513i
$273$	−0.808923	−	0.175970i	−0.0489582	−	0.0106502i
$274$	2.49248	−	2.87648i	0.150576	−	0.173774i
$275$	−2.64437	+	6.05047i	−0.159462	+	0.364857i
$276$	−0.394919	−	0.465445i	−0.0237713	−	0.0280165i
$277$	−7.96648	−	7.96648i	−0.478659	−	0.478659i	0.426043	−	0.904703i	$-0.359907\pi$
$277$	−7.96648	−	7.96648i	−0.478659	−	0.478659i	−0.904703	+	0.426043i	$0.859907\pi$
$278$	0.452794	+	6.33088i	0.0271568	+	0.379701i
$279$	−6.60556	−	10.2785i	−0.395465	−	0.615355i
$280$	0.644776	−	10.1857i	0.0385327	−	0.608712i
$281$	−22.3200	+	10.1932i	−1.33150	+	0.608075i	−0.948823	−	0.315807i	$-0.897725\pi$
$281$	−22.3200	+	10.1932i	−1.33150	+	0.608075i	−0.382676	+	0.923883i	$0.624997\pi$
$282$	0.284887	−	0.213264i	0.0169648	−	0.0126997i
$283$	17.6084	+	9.61492i	1.04671	+	0.571547i	0.908080	−	0.418797i	$-0.137548\pi$
$283$	17.6084	+	9.61492i	1.04671	+	0.571547i	0.138631	+	0.990344i	$0.455730\pi$
$284$	3.08813	−	4.80522i	0.183247	−	0.285138i
$285$	2.02329	−	0.307822i	0.119849	−	0.0182338i
$286$	1.50321	−	5.11945i	0.0888864	−	0.302719i
$287$	9.56475	+	0.684085i	0.564590	+	0.0403802i
$288$	−13.4806	−	0.964149i	−0.794350	−	0.0568130i
$289$	−7.43162	+	25.3098i	−0.437154	+	1.48881i
$290$	19.3505	−	2.94398i	1.13630	−	0.172877i
$291$	−0.112318	+	0.174770i	−0.00658421	+	0.0102452i
$292$	6.29762	+	3.43876i	0.368540	+	0.201238i
$293$	−9.31405	+	6.97241i	−0.544133	+	0.407333i	−0.835674	−	0.549225i	$-0.814923\pi$
$293$	−9.31405	+	6.97241i	−0.544133	+	0.407333i	0.291541	+	0.956558i	$0.405832\pi$
$294$	−0.664586	+	0.303506i	−0.0387595	+	0.0177008i
$295$	1.73325	−	27.3807i	0.100914	−	1.59416i
$296$	3.09361	+	4.81375i	0.179812	+	0.279794i
$297$	0.0816540	+	1.14167i	0.00473805	+	0.0662466i
$298$	−9.47372	−	9.47372i	−0.548798	−	0.548798i
$299$	−5.33574	+	17.4973i	−0.308574	+	1.01189i
$300$	0.232125	+	0.592552i	0.0134017	+	0.0342110i
$301$	0.465310	−	0.536996i	0.0268200	−	0.0309520i
$302$	−19.6096	−	4.26581i	−1.12841	−	0.245470i
$303$	−0.531998	−	0.398249i	−0.0305625	−	0.0228788i
$304$	−3.86344	−	8.45976i	−0.221584	−	0.485200i
$305$	2.49913	−	6.87161i	0.143100	−	0.393467i
$306$	5.85505	+	19.9405i	0.334711	+	1.13992i
$307$	1.56947	+	7.21472i	0.0895741	+	0.411766i	0.999998	−	0.00191064i	$-0.000608177\pi$
$307$	1.56947	+	7.21472i	0.0895741	+	0.411766i	−0.910424	+	0.413676i	$0.864245\pi$
$308$	−0.606711	−	1.62666i	−0.0345706	−	0.0926873i
$309$	0.725481	+	0.213021i	0.0412712	+	0.0121183i
$310$	9.34277	+	2.66045i	0.530634	+	0.151103i
$311$	22.2937	+	25.7282i	1.26416	+	1.45892i	0.829687	+	0.558229i	$0.188519\pi$
$311$	22.2937	+	25.7282i	1.26416	+	1.45892i	0.434470	+	0.900686i	$0.356936\pi$
$312$	−0.807804	−	1.47938i	−0.0457329	−	0.0837535i
$313$	−11.9578	+	4.46004i	−0.675897	+	0.252096i	−0.663889	−	0.747831i	$-0.731095\pi$
$313$	−11.9578	+	4.46004i	−0.675897	+	0.252096i	−0.0120082	+	0.999928i	$0.503822\pi$
$314$	−0.304371	−	0.195607i	−0.0171766	−	0.0110388i
$315$	6.46928	−	7.59056i	0.364503	−	0.427679i
$316$	6.84113	+	0.983606i	0.384844	+	0.0553322i
$317$	4.45739	−	11.9507i	0.250352	−	0.671219i	−0.749605	−	0.661886i	$-0.769756\pi$
$317$	4.45739	−	11.9507i	0.250352	−	0.671219i	0.999956	−	0.00933332i	$-0.00297093\pi$
$318$	−0.0345960	+	0.0462149i	−0.00194005	+	0.00259160i
$319$	9.18105	−	5.90030i	0.514040	−	0.330353i
$320$	13.7901	−	10.5003i	0.770890	−	0.586984i
$321$			0.889493i			0.0496466i
$322$	−2.58375	−	7.15343i	−0.143987	−	0.398645i
$323$	29.4048	−	29.4048i	1.63613	−	1.63613i
$324$	−5.84699	−	5.06645i	−0.324833	−	0.281469i
$325$	11.1778	−	15.4525i	0.620031	−	0.857150i
$326$	1.37431	+	9.55851i	0.0761158	+	0.529397i
$327$	−1.58819	−	0.592365i	−0.0878272	−	0.0327578i
$328$	11.7006	+	15.6301i	0.646056	+	0.863030i
$329$	−3.32955	+	0.977645i	−0.183564	+	0.0538993i
$330$	−0.323225	−	0.317979i	−0.0177930	−	0.0175042i
$331$	9.70663	−	21.2546i	0.533525	−	1.16826i	−0.430536	−	0.902573i	$-0.641675\pi$
$331$	9.70663	−	21.2546i	0.533525	−	1.16826i	0.964061	−	0.265682i	$-0.0855972\pi$
$332$	11.1920	−	6.11129i	0.614240	−	0.335401i
$333$	−0.398904	+	5.57740i	−0.0218598	+	0.305640i
$334$	−14.2237	+	12.3249i	−0.778287	+	0.674389i
$335$	7.04808	+	23.2967i	0.385078	+	1.27283i
$336$	0.290799	+	0.132804i	0.0158644	+	0.00724503i
$337$	−33.3922	+	7.26404i	−1.81899	+	0.395697i	−0.987212	−	0.159410i	$-0.949041\pi$
$337$	−33.3922	+	7.26404i	−1.81899	+	0.395697i	−0.831779	+	0.555108i	$0.812677\pi$
$338$	−0.786259	+	1.43993i	−0.0427668	+	0.0783216i
$339$	−0.00511527	+	0.0355775i	−0.000277823	+	0.00193230i
$340$	10.9351	+	6.90182i	0.593041	+	0.374304i
$341$	5.36126	−	0.770833i	0.290328	−	0.0417429i
$342$	4.23494	−	19.4677i	0.228999	−	1.05269i
$343$	17.5600	−	1.25592i	0.948152	−	0.0678132i
$344$	1.44674			0.0780030
$345$	1.09677	+	1.10163i	0.0590483	+	0.0593097i
$346$	−8.30140			−0.446286
$347$	25.9067	−	1.85288i	1.39074	−	0.0994680i	0.644227	−	0.764834i	$-0.277179\pi$
$347$	25.9067	−	1.85288i	1.39074	−	0.0994680i	0.746517	+	0.665366i	$0.231724\pi$
$348$	0.223582	−	1.02779i	0.0119853	−	0.0550954i
$349$	28.9967	−	4.16910i	1.55216	−	0.223167i	0.687746	−	0.725951i	$-0.258600\pi$
$349$	28.9967	−	4.16910i	1.55216	−	0.223167i	0.864412	+	0.502784i	$0.167691\pi$
$350$	0.129754	+	7.92847i	0.00693567	+	0.423795i
$351$	0.470475	−	3.27223i	0.0251121	−	0.174659i
$352$	2.87135	−	5.25849i	0.153044	−	0.280278i
$353$	10.0958	−	2.19621i	0.537345	−	0.116892i	0.0643002	−	0.997931i	$-0.479518\pi$
$353$	10.0958	−	2.19621i	0.537345	−	0.116892i	0.473045	+	0.881038i	$0.343155\pi$
$354$	1.71367	+	0.782606i	0.0910804	+	0.0415950i
$355$	−6.86670	+	12.8238i	−0.364447	+	0.680615i
$356$	7.05070	−	6.10947i	0.373687	−	0.323801i
$357$	−0.101976	+	1.42581i	−0.00539713	+	0.0754617i
$358$	−0.0178025	+	0.00972091i	−0.000940892	+	0.000513766i
$359$	10.3812	−	22.7317i	0.547900	−	1.19973i	−0.409856	−	0.912150i	$-0.634421\pi$
$359$	10.3812	−	22.7317i	0.547900	−	1.19973i	0.957756	−	0.287583i	$-0.0928518\pi$
$360$	20.3060	−	0.166149i	1.07022	−	0.00875684i
$361$	−20.0200	+	5.87841i	−1.05369	+	0.309390i
$362$	−3.03292	−	4.05150i	−0.159407	−	0.212942i
$363$	1.25714	+	0.468888i	0.0659825	+	0.0246102i
$364$	0.713619	+	4.96333i	0.0374038	+	0.260149i
$365$	−16.6834	−	7.45467i	−0.873247	−	0.390195i
$366$	0.379454	+	0.328799i	0.0198344	+	0.0171866i
$367$	−15.7808	+	15.7808i	−0.823753	+	0.823753i	−0.986644	−	0.162891i	$-0.947918\pi$
$367$	−15.7808	+	15.7808i	−0.823753	+	0.823753i	0.162891	+	0.986644i	$0.447918\pi$
$368$	3.44971	−	6.16453i	0.179829	−	0.321349i
$369$			19.0793i			0.993228i
$370$	−2.69327	−	3.53709i	−0.140016	−	0.183885i
$371$	0.473565	−	0.304342i	0.0245863	−	0.0158006i
$372$	0.312837	−	0.417901i	0.0162198	−	0.0216672i
$373$	5.70464	−	15.2947i	0.295375	−	0.791932i	−0.701480	−	0.712689i	$-0.747477\pi$
$373$	5.70464	−	15.2947i	0.295375	−	0.791932i	0.996855	−	0.0792427i	$-0.0252502\pi$
$374$	−9.11926	−	1.31115i	−0.471546	−	0.0677981i
$375$	−0.709238	−	1.45726i	−0.0366249	−	0.0752526i
$376$	−5.94385	−	3.81988i	−0.306531	−	0.196995i
$377$	−29.5338	+	11.0155i	−1.52107	+	0.567328i
$378$	0.658735	+	1.20638i	0.0338817	+	0.0620496i
$379$	−13.8346	−	15.9660i	−0.710638	−	0.820120i	0.279510	−	0.960143i	$-0.409828\pi$
$379$	−13.8346	−	15.9660i	−0.710638	−	0.820120i	−0.990148	+	0.140023i	$0.955282\pi$
$380$	−6.02978	−	10.8311i	−0.309321	−	0.555623i
$381$	−1.44911	−	0.425496i	−0.0742400	−	0.0217988i
$382$	2.90692	+	7.79376i	0.148731	+	0.398763i
$383$	4.61124	+	21.1975i	0.235623	+	1.08314i	0.931148	+	0.364641i	$0.118808\pi$
$383$	4.61124	+	21.1975i	0.235623	+	1.08314i	−0.695525	+	0.718502i	$0.744828\pi$
$384$	−0.0352460	−	0.120037i	−0.00179864	−	0.00612560i
$385$	1.86952	+	4.00660i	0.0952797	+	0.204195i
$386$	−1.15246	−	2.52353i	−0.0586586	−	0.128444i
$387$	1.13177	+	0.847231i	0.0575310	+	0.0430672i
$388$	1.22962	+	0.267487i	0.0624243	+	0.0135796i
$389$	−1.19596	+	1.38021i	−0.0606377	+	0.0699796i	−0.785258	−	0.619169i	$-0.787470\pi$
$389$	−1.19596	+	1.38021i	−0.0606377	+	0.0699796i	0.724620	+	0.689148i	$0.242015\pi$
$390$	0.717004	+	1.09586i	0.0363069	+	0.0554911i
$391$	31.2165	+	4.81980i	1.57869	+	0.243748i
$392$	10.2571	+	10.2571i	0.518060	+	0.518060i
$393$	−0.110074	−	1.53903i	−0.00555248	−	0.0776339i
$394$	2.92855	+	4.55692i	0.147538	+	0.229574i
$395$	−17.5661	−	1.11197i	−0.883845	−	0.0559492i
$396$	3.14214	−	1.43497i	0.157898	−	0.0721098i
$397$	26.1198	−	19.5530i	1.31091	−	0.981337i	0.311395	−	0.950280i	$-0.399204\pi$
$397$	26.1198	−	19.5530i	1.31091	−	0.981337i	0.999518	−	0.0310568i	$-0.00988728\pi$
$398$	5.85806	+	3.19874i	0.293638	+	0.160339i
$399$	0.740864	−	1.15281i	0.0370896	−	0.0577126i
$400$	−5.48633	+	4.91340i	−0.274317	+	0.245670i
$401$	−4.19068	+	14.2722i	−0.209273	+	0.712718i	0.786226	+	0.617939i	$0.212032\pi$
$401$	−4.19068	+	14.2722i	−0.209273	+	0.712718i	−0.995498	+	0.0947781i	$0.969786\pi$
$402$	−1.66706	−	0.119231i	−0.0831456	−	0.00594669i
$403$	−15.6041	−	1.11603i	−0.777296	−	0.0555933i
$404$	−1.13405	+	3.86222i	−0.0564211	+	0.192153i
$405$	15.8689	+	11.6780i	0.788533	+	0.580282i
$406$	7.08556	−	11.0253i	0.351650	−	0.547179i
$407$	−2.17563	−	1.18798i	−0.107842	−	0.0588861i
$408$	−2.32997	+	1.74419i	−0.115351	+	0.0863503i
$409$	−11.2113	+	5.12001i	−0.554361	+	0.253168i	−0.672840	−	0.739788i	$-0.734926\pi$
$409$	−11.2113	+	5.12001i	−0.554361	+	0.253168i	0.118479	+	0.992957i	$0.462198\pi$
$410$	−10.0273	−	11.3826i	−0.495213	−	0.562146i
$411$	0.281610	+	0.438193i	0.0138908	+	0.0216145i
$412$	−0.326724	−	4.56820i	−0.0160966	−	0.225059i
$413$	−12.9898	−	12.9898i	−0.639184	−	0.639184i
$414$	13.8299	−	6.14307i	0.679704	−	0.301915i
$415$	−27.1748	+	17.7800i	−1.33396	+	0.872787i
$416$	−11.3321	+	13.0780i	−0.555603	+	0.641200i
$417$	−0.848765	−	0.184637i	−0.0415642	−	0.00904174i
$418$	7.07046	+	5.29288i	0.345827	+	0.258883i
$419$	2.37839	+	5.20794i	0.116192	+	0.254424i	0.958789	−	0.284120i	$-0.0917015\pi$
$419$	2.37839	+	5.20794i	0.116192	+	0.254424i	−0.842597	+	0.538545i	$0.818974\pi$
$420$	0.400457	+	0.145642i	0.0195403	+	0.00710659i
$421$	−10.6528	−	36.2802i	−0.519188	−	1.76819i	−0.632424	−	0.774623i	$-0.717940\pi$
$421$	−10.6528	−	36.2802i	−0.519188	−	1.76819i	0.113236	−	0.993568i	$-0.463878\pi$
$422$	0.0560158	+	0.257500i	0.00272680	+	0.0125349i
$423$	−2.41283	−	6.46905i	−0.117316	−	0.314536i
$424$	1.09974	+	0.322914i	0.0534083	+	0.0156821i
$425$	−29.1573	−	15.3071i	−1.41434	−	0.742505i
$426$	−0.654117	−	0.754892i	−0.0316921	−	0.0365746i
$427$	−2.34638	−	4.29707i	−0.113549	−	0.207950i
$428$	5.04810	−	1.88284i	0.244009	−	0.0910106i
$429$	0.614276	+	0.394771i	0.0296575	+	0.0190597i
$430$	−1.12048	+	0.0893583i	−0.0540341	+	0.00430924i
$431$	−19.5188	−	2.80638i	−0.940187	−	0.135178i	−0.344853	−	0.938657i	$-0.612071\pi$
$431$	−19.5188	−	2.80638i	−0.940187	−	0.135178i	−0.595334	+	0.803478i	$0.702980\pi$
$432$	−0.446138	+	1.19614i	−0.0214648	+	0.0575495i
$433$	−20.1710	+	26.9453i	−0.969357	+	1.29491i	−0.0138608	+	0.999904i	$0.504412\pi$
$433$	−20.1710	+	26.9453i	−0.969357	+	1.29491i	−0.955496	+	0.295005i	$0.904679\pi$
$434$	5.47188	−	3.51656i	0.262659	−	0.168800i
$435$	−0.359506	+	2.65442i	−0.0172370	+	0.127270i
$436$			10.2673i			0.491713i
$437$	−24.0508	−	18.3972i	−1.15051	−	0.880058i
$438$	0.887250	−	0.887250i	0.0423944	−	0.0423944i
$439$	−2.19870	−	1.90518i	−0.104938	−	0.0909293i	0.600812	−	0.799391i	$-0.294844\pi$
$439$	−2.19870	−	1.90518i	−0.104938	−	0.0909293i	−0.705750	+	0.708461i	$0.749390\pi$
$440$	−3.67252	+	8.21901i	−0.175081	+	0.391826i
$441$	2.01730	+	14.0306i	0.0960620	+	0.668126i
$442$	24.9319	+	9.29913i	1.18589	+	0.442315i
$443$	10.2466	+	13.6878i	0.486829	+	0.650327i	0.974944	−	0.222452i	$-0.0714062\pi$
$443$	10.2466	+	13.6878i	0.486829	+	0.650327i	−0.488115	+	0.872779i	$0.662315\pi$
$444$	−0.229230	+	0.0673079i	−0.0108788	+	0.00319429i
$445$	−16.6621	+	16.9370i	−0.789857	+	0.802890i
$446$	10.1215	−	22.1630i	0.479268	−	1.04945i
$447$	1.60926	−	0.878723i	0.0761155	−	0.0415622i
$448$	0.827939	−	11.5761i	0.0391164	−	0.546919i
$449$	−26.5635	+	23.0174i	−1.25361	+	1.08626i	−0.260946	+	0.965353i	$0.584035\pi$
$449$	−26.5635	+	23.0174i	−1.25361	+	1.08626i	−0.992664	+	0.120906i	$0.961420\pi$
$450$	−15.7164	+	1.38289i	−0.740878	+	0.0651899i
$451$	−7.69373	−	3.51361i	−0.362283	−	0.165449i
$452$	0.212739	−	0.0462785i	0.0100064	−	0.00217676i
$453$	1.31621	−	2.41046i	0.0618409	−	0.113253i
$454$	−3.40048	+	23.6509i	−0.159593	+	1.10999i
$455$	−2.81645	−	12.4555i	−0.132037	−	0.583921i
$456$	2.76175	−	0.397079i	0.129331	−	0.0185949i
$457$	−3.66884	+	16.8654i	−0.171621	+	0.788929i	0.808177	+	0.588939i	$0.200454\pi$
$457$	−3.66884	+	16.8654i	−0.171621	+	0.788929i	−0.979798	+	0.199989i	$0.935909\pi$
$458$	−31.0362	+	2.21975i	−1.45023	+	0.103722i
$459$	−5.70832			−0.266441
$460$	3.93041	−	8.55635i	0.183256	−	0.398942i
$461$	6.06698			0.282568			0.141284	−	0.989969i	$-0.454877\pi$
$461$	6.06698			0.282568			0.141284	+	0.989969i	$0.454877\pi$
$462$	−0.302825	+	0.0216585i	−0.0140887	+	0.00100764i
$463$	3.74158	−	17.1998i	0.173886	−	0.799341i	−0.804729	−	0.593642i	$-0.797690\pi$
$463$	3.74158	−	17.1998i	0.173886	−	0.799341i	0.978615	−	0.205699i	$-0.0659467\pi$
$464$	12.0487	−	1.73234i	0.559346	−	0.0804218i
$465$	−0.709563	+	1.12422i	−0.0329052	+	0.0521345i
$466$	−1.54871	+	10.7715i	−0.0717424	+	0.498979i
$467$	2.35082	−	4.30521i	0.108783	−	0.199222i	−0.817616	−	0.575763i	$-0.804705\pi$
$467$	2.35082	−	4.30521i	0.108783	−	0.199222i	0.926400	+	0.376542i	$0.122887\pi$
$468$	−9.74892	+	2.12075i	−0.450644	+	0.0980316i
$469$	14.8245	+	6.77013i	0.684533	+	0.312616i
$470$	4.83935	+	2.59131i	0.223222	+	0.119528i
$471$	0.0374205	−	0.0324250i	0.00172424	−	0.00149407i
$472$	2.66834	−	37.3083i	0.122820	−	1.71725i
$473$	−0.550071	+	0.300361i	−0.0252923	+	0.0138106i
$474$	0.502081	−	1.09940i	0.0230613	−	0.0504973i
$475$	17.5000	+	26.2751i	0.802956	+	1.20558i
$476$	8.30768	−	2.43935i	0.380782	−	0.111808i
$477$	0.671214	+	0.896637i	0.0307328	+	0.0410542i
$478$	−10.9603	−	4.08798i	−0.501313	−	0.186980i
$479$	−2.97940	−	20.7222i	−0.136132	−	0.946821i	−0.937335	−	0.348429i	$-0.886715\pi$
$479$	−2.97940	−	20.7222i	−0.136132	−	0.946821i	0.801203	−	0.598393i	$-0.204194\pi$
$480$	0.525157	+	1.37357i	0.0239700	+	0.0626947i
$481$	5.41083	+	4.68851i	0.246713	+	0.213778i
$482$	−7.64611	+	7.64611i	−0.348271	+	0.348271i
$483$	1.03893	−	0.0634641i	0.0472731	−	0.00288772i
$484$		−	8.12709i		−	0.369413i
$485$	−3.17567	−	0.430102i	−0.144200	−	0.0195299i
$486$	−3.45507	+	2.22044i	−0.156725	+	0.100721i
$487$	10.7750	−	14.3937i	0.488263	−	0.652243i	−0.486971	−	0.873418i	$-0.661898\pi$
$487$	10.7750	−	14.3937i	0.488263	−	0.652243i	0.975234	+	0.221175i	$0.0709892\pi$
$488$	3.48367	−	9.34007i	0.157698	−	0.422805i
$489$	−1.30811	−	0.188078i	−0.0591549	−	0.00850519i
$490$	−8.57744	−	7.31038i	−0.387489	−	0.330249i
$491$	19.1572	+	12.3116i	0.864553	+	0.555615i	0.896082	−	0.443888i	$-0.146401\pi$
$491$	19.1572	+	12.3116i	0.864553	+	0.555615i	−0.0315289	+	0.999503i	$0.510038\pi$
$492$	−0.763778	+	0.284875i	−0.0344338	+	0.0128431i
$493$	26.0847	+	47.7705i	1.17479	+	2.15147i
$494$	−16.7051	−	19.2787i	−0.751599	−	0.867392i
$495$	−7.68613	+	4.27895i	−0.345466	+	0.192325i
$496$	5.79654	+	1.70202i	0.260272	+	0.0764229i
$497$	3.40380	+	9.12595i	0.152681	+	0.409355i
$498$	−0.474006	−	2.17897i	−0.0212407	−	0.0976421i
$499$	−12.1883	−	41.5097i	−0.545625	−	1.85823i	−0.512341	−	0.858782i	$-0.671222\pi$
$499$	−12.1883	−	41.5097i	−0.545625	−	1.85823i	−0.0332836	−	0.999446i	$-0.510596\pi$
$500$	−6.76904	+	7.10978i	−0.302721	+	0.317959i
$501$	−1.06997	−	2.34291i	−0.0478028	−	0.104674i
$502$	5.02470	+	3.76144i	0.224263	+	0.167881i
$503$	6.70532	+	1.45865i	0.298976	+	0.0650382i	0.359551	−	0.933125i	$-0.382930\pi$
$503$	6.70532	+	1.45865i	0.298976	+	0.0650382i	−0.0605753	+	0.998164i	$0.519294\pi$
$504$	8.90413	−	10.2759i	0.396622	−	0.457726i
$505$	2.09698	−	10.0342i	0.0933144	−	0.446518i
$506$	−0.0696999	+	6.70822i	−0.00309854	+	0.298217i
$507$	−0.158761	−	0.158761i	−0.00705083	−	0.00705083i
$508$	0.652613	+	9.12473i	0.0289550	+	0.404844i
$509$	−6.76674	−	10.5292i	−0.299930	−	0.466701i	0.658277	−	0.752776i	$-0.271286\pi$
$509$	−6.76674	−	10.5292i	−0.299930	−	0.466701i	−0.958207	+	0.286075i	$0.907649\pi$
$510$	1.69679	−	1.49476i	0.0751351	−	0.0661890i
$511$	−11.1297	+	5.08274i	−0.492347	+	0.224847i
$512$	12.5391	−	9.38664i	0.554155	−	0.414835i
$513$	4.80291	+	2.62259i	0.212054	+	0.115790i
$514$	1.97808	−	3.07795i	0.0872493	−	0.135763i
$515$	1.75428	+	11.5307i	0.0773027	+	0.508104i
$516$	−0.0170177	+	0.0579568i	−0.000749160	+	0.00255141i
$517$	3.05299	+	0.218354i	0.134270	+	0.00960320i
$518$	−2.96921	−	0.212362i	−0.130460	−	0.00933065i
$519$	0.320069	−	1.09005i	0.0140495	−	0.0478481i
$520$	15.4108	−	20.9414i	0.675809	−	0.918343i
$521$	2.52487	−	3.92877i	0.110617	−	0.172123i	−0.781532	−	0.623866i	$-0.785561\pi$
$521$	2.52487	−	3.92877i	0.110617	−	0.172123i	0.892148	+	0.451743i	$0.149198\pi$
$522$	22.8866	+	12.4970i	1.00172	+	0.546980i
$523$	−8.06882	+	6.04024i	−0.352825	+	0.264121i	−0.760958	−	0.648801i	$-0.775271\pi$
$523$	−8.06882	+	6.04024i	−0.352825	+	0.264121i	0.408133	+	0.912922i	$0.366180\pi$
$524$	−8.50139	+	3.88246i	−0.371385	+	0.169606i
$525$	−1.04609	−	0.288652i	−0.0456550	−	0.0125978i
$526$	16.0620	+	24.9930i	0.700337	+	1.08975i
$527$	1.92707	+	26.9439i	0.0839443	+	1.17369i
$528$	−0.199389	−	0.199389i	−0.00867731	−	0.00867731i
$529$	0.477899	−	22.9950i	0.0207782	−	0.999784i
$530$	−0.871678	−	0.182165i	−0.0378633	−	0.00791276i
$531$	23.9356	−	27.6232i	1.03872	−	1.19874i
$532$	−8.11070	−	1.76438i	−0.351644	−	0.0764954i
$533$	19.5565	+	14.6398i	0.847087	+	0.634122i
$534$	−0.677730	−	1.48402i	−0.0293283	−	0.0642199i
$535$	−12.4339	+	5.80180i	−0.537566	+	0.250834i
$536$	9.34866	+	31.8386i	0.403801	+	1.37522i
$537$	−0.000590056	−	0.00271244i	−2.54628e−5	−	0.000117051i
$538$	−7.61031	−	20.4040i	−0.328104	−	0.879681i
$539$	−6.02937	−	1.77038i	−0.259703	−	0.0762557i
$540$	−0.466035	+	1.63659i	−0.0200550	+	0.0704276i
$541$	−1.21398	−	1.40100i	−0.0521929	−	0.0602338i	0.729053	−	0.684457i	$-0.239961\pi$
$541$	−1.21398	−	1.40100i	−0.0521929	−	0.0602338i	−0.781246	+	0.624224i	$0.785415\pi$
$542$	7.90315	+	14.4735i	0.339470	+	0.621692i
$543$	0.648939	−	0.242042i	0.0278486	−	0.0103870i
$544$	25.1368	+	16.1545i	1.07773	+	0.692617i
$545$	−2.07866	−	26.0646i	−0.0890399	−	1.11648i
$546$	0.867947	+	0.124792i	0.0371447	+	0.00534060i
$547$	−12.2592	+	32.8681i	−0.524165	+	1.40534i	0.357699	+	0.933837i	$0.383561\pi$
$547$	−12.2592	+	32.8681i	−0.524165	+	1.40534i	−0.881864	+	0.471504i	$0.843711\pi$
$548$	1.89076	−	2.52575i	0.0807691	−	0.107895i
$549$	8.19490	−	5.26654i	0.349750	−	0.224771i
$550$	2.33665	−	6.59231i	0.0996353	−	0.281097i
$551$		−	52.1777i		−	2.22284i
$552$	1.48293	+	1.51407i	0.0631175	+	0.0644429i
$553$	−8.33357	+	8.33357i	−0.354380	+	0.354380i
$554$	9.01879	+	7.81483i	0.383172	+	0.332020i
$555$	0.568296	−	0.217277i	0.0241228	−	0.00922288i
$556$	0.748767	+	5.20779i	0.0317548	+	0.220859i
$557$	−15.5762	−	5.80961i	−0.659983	−	0.246161i	−0.00291905	−	0.999996i	$-0.500929\pi$
$557$	−15.5762	−	5.80961i	−0.659983	−	0.246161i	−0.657064	+	0.753835i	$0.728202\pi$
$558$	7.75565	+	10.3603i	0.328323	+	0.438588i
$559$	1.73685	−	0.509984i	0.0734608	−	0.0215700i
$560$	0.0403485	+	4.93121i	0.00170504	+	0.208382i
$561$	0.523770	−	1.14690i	0.0221136	−	0.0484220i
$562$	22.8115	−	12.4560i	0.962244	−	0.525425i
$563$	1.89210	−	26.4550i	0.0797424	−	1.11494i	−0.787254	−	0.616629i	$-0.788498\pi$
$563$	1.89210	−	26.4550i	0.0797424	−	1.11494i	0.866996	−	0.498315i	$-0.166048\pi$
$564$	0.222942	−	0.193180i	0.00938753	−	0.00813434i
$565$	−0.530691	+	0.160553i	−0.0223263	+	0.00675451i
$566$	−19.3303	−	8.82786i	−0.812514	−	0.371063i
$567$	12.8911	−	2.80428i	0.541375	−	0.117769i
$568$	−9.50430	+	17.4058i	−0.398792	+	0.730332i
$569$	0.938446	−	6.52703i	0.0393417	−	0.273627i	−0.960650	−	0.277763i	$-0.910407\pi$
$569$	0.938446	−	6.52703i	0.0393417	−	0.273627i	0.999991	+	0.00413512i	$0.00131625\pi$
$570$	−2.11440	+	0.478111i	−0.0885625	+	0.0200259i
$571$	3.81515	−	0.548536i	0.159659	−	0.0229555i	−0.0620216	−	0.998075i	$-0.519755\pi$
$571$	3.81515	−	0.548536i	0.159659	−	0.0229555i	0.221681	+	0.975119i	$0.428846\pi$
$572$	0.940152	−	4.32181i	0.0393097	−	0.180704i
$573$	−1.13548	+	0.0812109i	−0.0474352	+	0.00339263i
$574$	−10.1571			−0.423950
$575$	−8.24548	+	22.5169i	−0.343860	+	0.939021i
$576$	23.0914			0.962142
$577$	15.1180	−	1.08126i	0.629369	−	0.0450134i	0.246989	−	0.969018i	$-0.420559\pi$
$577$	15.1180	−	1.08126i	0.629369	−	0.0450134i	0.382380	+	0.924005i	$0.375104\pi$
$578$	5.93920	−	27.3020i	0.247038	−	1.13562i
$579$	0.375799	−	0.0540317i	0.0156177	−	0.00224548i
$580$	15.8255	−	3.57849i	0.657118	−	0.148589i
$581$	−3.09455	+	21.5230i	−0.128383	+	0.892926i
$582$	0.105461	−	0.193137i	0.00437149	−	0.00800579i
$583$	−0.485179	+	0.105544i	−0.0200941	+	0.00437120i
$584$	−22.6610	−	10.3489i	−0.937718	−	0.428242i
$585$	24.3193	−	7.35745i	1.00548	−	0.304193i
$586$	9.31370	−	8.07036i	0.384745	−	0.333384i
$587$	−1.93520	+	27.0577i	−0.0798744	+	1.11679i	0.786565	+	0.617508i	$0.211858\pi$
$587$	−1.93520	+	27.0577i	−0.0798744	+	1.11679i	−0.866439	+	0.499283i	$0.833597\pi$
$588$	−0.531552	+	0.290249i	−0.0219208	+	0.0119697i
$589$	10.7575	−	23.5556i	0.443255	−	0.970594i
$590$	0.237772	+	29.0594i	0.00978892	+	1.19636i
$591$	−0.711282	+	0.208851i	−0.0292582	+	0.00859099i
$592$	−1.65689	−	2.21335i	−0.0680979	−	0.0909681i
$593$	−18.1009	−	6.75129i	−0.743316	−	0.277242i	−0.0508629	−	0.998706i	$-0.516197\pi$
$593$	−18.1009	−	6.75129i	−0.743316	−	0.277242i	−0.692453	+	0.721463i	$0.743470\pi$
$594$	−0.172540	−	1.20004i	−0.00707939	−	0.0492382i
$595$	−20.5960	+	7.87448i	−0.844356	+	0.322822i
$596$	−8.39340	−	7.27292i	−0.343807	−	0.297910i
$597$	−0.645890	+	0.645890i	−0.0264345	+	0.0264345i
$598$	4.31519	−	18.8895i	0.176461	−	0.772451i
$599$		−	9.54728i		−	0.390091i	−0.980794	−	0.195046i	$-0.937514\pi$
$599$		−	9.54728i		−	0.390091i	0.980794	−	0.195046i	$-0.0624855\pi$
$600$	−0.950637	−	1.99457i	−0.0388096	−	0.0814280i
$601$	12.1467	−	7.80622i	0.495475	−	0.318422i	−0.268929	−	0.963160i	$-0.586670\pi$
$601$	12.1467	−	7.80622i	0.495475	−	0.318422i	0.764404	+	0.644738i	$0.223033\pi$
$602$	−0.451036	+	0.602513i	−0.0183828	+	0.0245566i
$603$	−11.3318	+	30.3817i	−0.461466	+	1.23724i
$604$	−16.4661	−	2.36746i	−0.669995	−	0.0963307i
$605$	1.64537	+	20.6315i	0.0668937	+	0.838788i
$606$	0.592164	+	0.380561i	0.0240550	+	0.0154592i
$607$	−37.8948	+	14.1340i	−1.53810	+	0.573683i	−0.968670	−	0.248353i	$-0.920111\pi$
$607$	−37.8948	+	14.1340i	−1.53810	+	0.573683i	−0.569435	+	0.822037i	$0.692838\pi$
$608$	−13.7280	−	25.1409i	−0.556742	−	1.01960i
$609$	1.17454	+	1.35550i	0.0475949	+	0.0549275i
$610$	−2.12115	+	7.44889i	−0.0858828	+	0.301597i
$611$	−8.48227	−	2.49062i	−0.343156	−	0.100760i
$612$	6.02033	+	16.1411i	0.243358	+	0.652467i
$613$	−0.799794	−	3.67659i	−0.0323034	−	0.148496i	0.958170	−	0.286199i	$-0.0923918\pi$
$613$	−0.799794	−	3.67659i	−0.0323034	−	0.148496i	−0.990474	+	0.137703i	$0.956028\pi$
$614$	−2.20336	−	7.50396i	−0.0889204	−	0.302835i
$615$	1.88126	−	0.877814i	0.0758596	−	0.0353969i
$616$	2.50400	+	5.48299i	0.100889	+	0.220916i
$617$	28.3636	+	21.2327i	1.14187	+	0.854797i	0.991014	−	0.133758i	$-0.0427045\pi$
$617$	28.3636	+	21.2327i	1.14187	+	0.854797i	0.150861	+	0.988555i	$0.451795\pi$
$618$	−0.782589	−	0.170242i	−0.0314803	−	0.00684813i
$619$	16.2741	−	18.7813i	0.654110	−	0.754883i	−0.327693	−	0.944784i	$-0.606271\pi$
$619$	16.2741	−	18.7813i	0.654110	−	0.754883i	0.981803	+	0.189901i	$0.0608167\pi$
$620$	7.88221	+	1.64724i	0.316557	+	0.0661549i
$621$	0.548765	+	4.12019i	0.0220212	+	0.165338i
$622$	−25.4980	−	25.4980i	−1.02238	−	1.02238i
$623$	1.13490	+	15.8680i	0.0454688	+	0.635737i
$624$	0.440314	+	0.685142i	0.0176267	+	0.0274276i
$625$	15.7445	−	19.4193i	0.629780	−	0.776774i
$626$	12.2968	−	5.61575i	0.491478	−	0.224450i
$627$	−0.967615	+	0.724348i	−0.0386428	+	0.0289277i
$628$	−0.263230	−	0.143735i	−0.0105040	−	0.00573564i
$629$	6.68369	−	10.4000i	0.266496	−	0.414676i
$630$	−6.26140	+	8.50849i	−0.249460	+	0.338986i
$631$	4.83228	−	16.4572i	0.192370	−	0.655152i	−0.805658	−	0.592381i	$-0.798188\pi$
$631$	4.83228	−	16.4572i	0.192370	−	0.655152i	0.998028	−	0.0627708i	$-0.0199937\pi$
$632$	−23.9351	−	1.71187i	−0.952088	−	0.0680947i
$633$	−0.0359720	−	0.00257277i	−0.00142976	−	0.000102258i
$634$	−3.80631	+	12.9631i	−0.151168	+	0.514830i
$635$	−3.50407	−	23.0319i	−0.139055	−	0.913995i
$636$	−0.0258721	+	0.0402577i	−0.00102589	+	0.00159632i
$637$	15.9295	+	8.69817i	0.631150	+	0.344634i
$638$	−9.25419	+	6.92760i	−0.366377	+	0.274266i
$639$	−17.6282	+	8.05052i	−0.697360	+	0.318474i
$640$	1.44806	−	1.27564i	0.0572396	−	0.0504243i
$641$	−6.88145	−	10.7077i	−0.271801	−	0.422931i	0.678341	−	0.734747i	$-0.262699\pi$
$641$	−6.88145	−	10.7077i	−0.271801	−	0.422931i	−0.950142	+	0.311816i	$0.899063\pi$
$642$	−0.0672140	−	0.939774i	−0.00265272	−	0.0370899i
$643$	13.1734	+	13.1734i	0.519507	+	0.519507i	0.917422	−	0.397915i	$-0.130266\pi$
$643$	13.1734	+	13.1734i	0.519507	+	0.519507i	−0.397915	+	0.917422i	$0.630266\pi$
$644$	−2.55935	−	5.76187i	−0.100852	−	0.227050i
$645$	0.0314675	−	0.150575i	0.00123903	−	0.00592887i
$646$	−28.8450	+	33.2890i	−1.13489	+	1.30974i
$647$	35.2766	+	7.67396i	1.38687	+	0.301694i	0.843197	−	0.537605i	$-0.180671\pi$
$647$	35.2766	+	7.67396i	1.38687	+	0.301694i	0.543670	+	0.839299i	$0.317034\pi$
$648$	21.5036	+	16.0974i	0.844740	+	0.632364i
$649$	6.73112	+	14.7391i	0.264220	+	0.578560i
$650$	−10.6420	+	17.1706i	−0.417412	+	0.673488i
$651$	0.250785	+	0.854096i	0.00982905	+	0.0334747i
$652$	1.70157	+	7.82199i	0.0666386	+	0.306333i
$653$	−13.1874	−	35.3568i	−0.516063	−	1.38362i	−0.889913	−	0.456129i	$-0.849235\pi$
$653$	−13.1874	−	35.3568i	−0.516063	−	1.38362i	0.373850	−	0.927489i	$-0.378037\pi$
$654$	1.72273	+	0.505839i	0.0673641	+	0.0197799i
$655$	20.7957	−	11.5772i	0.812553	−	0.452357i
$656$	−6.17785	−	7.12962i	−0.241205	−	0.278365i
$657$	−11.6670	−	21.3664i	−0.455171	−	0.833584i
$658$	3.44389	−	1.28450i	0.134257	−	0.0500752i
$659$	36.2183	+	23.2761i	1.41086	+	0.906707i	0.999988	−	0.00498365i	$-0.00158635\pi$
$659$	36.2183	+	23.2761i	1.41086	+	0.906707i	0.410877	+	0.911691i	$0.365223\pi$
$660$	−0.286057	−	0.243800i	−0.0111347	−	0.00948991i
$661$	−2.43794	−	0.350523i	−0.0948249	−	0.0136338i	0.0947390	−	0.995502i	$-0.469798\pi$
$661$	−2.43794	−	0.350523i	−0.0948249	−	0.0136338i	−0.189564	+	0.981868i	$0.560707\pi$
$662$	−8.64924	+	23.1895i	−0.336162	+	0.901286i
$663$	−2.18234	+	2.91527i	−0.0847552	+	0.113220i
$664$	−37.2453	+	23.9361i	−1.44540	+	0.928900i
$665$	20.9471	+	2.83700i	0.812293	+	0.110014i
$666$		−	5.92282i		−	0.229505i
$667$	31.9725	−	23.4200i	1.23798	−	0.906825i
$668$	−11.0317	+	11.0317i	−0.426831	+	0.426831i
$669$	2.51998	+	2.18357i	0.0974280	+	0.0844218i
$670$	−9.20690	−	24.0810i	−0.355693	−	0.930331i
$671$	0.614577	+	4.27448i	0.0237255	+	0.165014i
$672$	0.922564	+	0.344099i	0.0355887	+	0.0132739i
$673$	−13.4401	−	17.9538i	−0.518076	−	0.692069i	0.462853	−	0.886435i	$-0.346826\pi$
$673$	−13.4401	−	17.9538i	−0.518076	−	0.692069i	−0.980929	+	0.194366i	$0.937735\pi$
$674$	34.7309	−	10.1979i	1.33779	−	0.392809i
$675$	0.851744	−	4.24900i	0.0327836	−	0.163544i
$676$	−0.564951	+	1.23707i	−0.0217289	+	0.0475796i
$677$	−9.21550	+	5.03204i	−0.354180	+	0.193397i	−0.646482	−	0.762929i	$-0.723761\pi$
$677$	−9.21550	+	5.03204i	−0.354180	+	0.193397i	0.292302	+	0.956326i	$0.405579\pi$
$678$	0.00271604	−	0.0379751i	0.000104309	−	0.00145843i
$679$	−1.62167	+	1.40519i	−0.0622341	+	0.0539261i
$680$	−39.5789	−	21.1932i	−1.51778	−	0.812722i
$681$	−2.97448	−	1.35840i	−0.113982	−	0.0520540i
$682$	−5.60607	+	1.21953i	−0.214668	+	0.0466981i
$683$	−9.62836	+	17.6330i	−0.368419	+	0.674709i	−0.994464	−	0.105078i	$-0.966491\pi$
$683$	−9.62836	+	17.6330i	−0.368419	+	0.674709i	0.626045	+	0.779787i	$0.284673\pi$
$684$	2.35033	−	16.3469i	0.0898672	−	0.625040i
$685$	−4.28853	+	6.79468i	−0.163856	+	0.259612i
$686$	−18.4578	+	2.65383i	−0.704721	+	0.101324i
$687$	0.905158	−	4.16094i	0.0345339	−	0.158750i
$688$	−0.697256	+	0.0498687i	−0.0265826	+	0.00190123i
$689$	1.43410			0.0546348
$690$	−1.24202	−	1.08102i	−0.0472828	−	0.0411539i
$691$	−5.75470			−0.218919			−0.109460	−	0.993991i	$-0.534912\pi$
$691$	−5.75470			−0.218919			−0.109460	+	0.993991i	$0.534912\pi$
$692$	−6.86384	+	0.490912i	−0.260924	+	0.0186617i
$693$	−1.25207	+	5.75565i	−0.0475620	+	0.218639i
$694$	−27.2312	+	3.91525i	−1.03368	+	0.148621i
$695$	−2.95516	−	13.0689i	−0.112096	−	0.495733i
$696$	−0.519718	+	3.61472i	−0.0196999	+	0.137016i
$697$	20.2158	−	37.0225i	0.765728	−	1.40233i
$698$	−30.3208	+	6.59589i	−1.14766	+	0.249658i
$699$	−1.35469	−	0.618666i	−0.0512390	−	0.0234001i
$700$	0.576143	+	6.54782i	0.0217762	+	0.247484i
$701$	−8.75175	+	7.58344i	−0.330549	+	0.286422i	−0.804284	−	0.594245i	$-0.797451\pi$
$701$	−8.75175	+	7.58344i	−0.330549	+	0.286422i	0.473735	+	0.880667i	$0.342905\pi$
$702$	−0.249807	+	3.49275i	−0.00942834	+	0.131825i
$703$	−10.4017	+	5.67975i	−0.392307	+	0.214216i
$704$	−4.25247	+	9.31161i	−0.160271	+	0.350945i
$705$	−0.526850	+	0.535543i	−0.0198423	+	0.0201697i
$706$	−10.5005	+	3.08324i	−0.395193	+	0.116039i
$707$	−4.11338	−	5.49483i	−0.154699	−	0.206654i
$708$	1.46319	+	0.545742i	0.0549901	+	0.0205103i
$709$	3.57007	+	24.8304i	0.134077	+	0.932526i	0.940162	+	0.340727i	$0.110673\pi$
$709$	3.57007	+	24.8304i	0.134077	+	0.932526i	−0.806085	+	0.591799i	$0.798418\pi$
$710$	6.28584	−	14.0676i	0.235903	−	0.527946i
$711$	−17.7217	−	15.3559i	−0.664614	−	0.575892i
$712$	−22.9040	+	22.9040i	−0.858365	+	0.858365i
$713$	19.2625	−	3.98116i	0.721387	−	0.149096i
$714$		−	1.51411i		−	0.0566642i
$715$	−1.51170	+	11.1617i	−0.0565345	+	0.417424i
$716$	−0.0141448	+	0.00909031i	−0.000528616	+	0.000339721i
$717$	0.959378	−	1.28158i	0.0358286	−	0.0478615i
$718$	−9.25035	+	24.8011i	−0.345220	+	0.925571i
$719$	21.1959	+	3.04751i	0.790475	+	0.113653i	0.525714	−	0.850661i	$-0.323798\pi$
$719$	21.1959	+	3.04751i	0.790475	+	0.113653i	0.264760	+	0.964314i	$0.414707\pi$
$720$	−9.78074	+	0.780018i	−0.364507	+	0.0290695i
$721$	6.56985	+	4.22219i	0.244674	+	0.157242i
$722$	20.7075	−	7.72351i	0.770655	−	0.287439i
$723$	−0.709205	−	1.29881i	−0.0263756	−	0.0483033i
$724$	−2.74730	−	3.17055i	−0.102102	−	0.117833i
$725$	−39.4502	+	12.2883i	−1.46514	+	0.456376i
$726$	−1.36363	−	0.400398i	−0.0506091	−	0.0148602i
$727$	−0.728664	−	1.95362i	−0.0270246	−	0.0724559i	0.922737	−	0.385431i	$-0.125947\pi$
$727$	−0.728664	−	1.95362i	−0.0270246	−	0.0724559i	−0.949761	+	0.312975i	$0.898674\pi$
$728$	−3.70068	−	17.0117i	−0.137156	−	0.630497i
$729$	7.28896	+	24.8239i	0.269961	+	0.919404i
$730$	18.1898	+	6.61540i	0.673233	+	0.244847i
$731$	−1.29844	−	2.84320i	−0.0480247	−	0.105159i
$732$	0.333188	+	0.249422i	0.0123150	+	0.00921889i
$733$	44.4357	+	9.66639i	1.64127	+	0.357036i	0.936026	−	0.351930i	$-0.114475\pi$
$733$	44.4357	+	9.66639i	1.64127	+	0.357036i	0.705242	+	0.708966i	$0.250838\pi$
$734$	15.4804	−	17.8654i	0.571393	−	0.659423i
$735$	1.29064	−	0.844443i	0.0476059	−	0.0311477i
$736$	9.24358	−	19.6965i	0.340723	−	0.726021i
$737$	−10.1646	−	10.1646i	−0.374417	−	0.374417i
$738$	−1.44171	−	20.1578i	−0.0530702	−	0.742019i
$739$	−9.48781	−	14.7633i	−0.349015	−	0.543078i	0.621717	−	0.783242i	$-0.286435\pi$
$739$	−9.48781	−	14.7633i	−0.349015	−	0.543078i	−0.970732	+	0.240164i	$0.922799\pi$
$740$	−2.43605	−	2.76530i	−0.0895509	−	0.101655i
$741$	3.17557	−	1.45023i	0.116658	−	0.0532757i
$742$	−0.477338	+	0.357331i	−0.0175236	+	0.0131180i
$743$	34.9943	+	19.1083i	1.28382	+	0.701017i	0.968747	−	0.248052i	$-0.0797904\pi$
$743$	34.9943	+	19.1083i	1.28382	+	0.701017i	0.315069	+	0.949069i	$0.397972\pi$
$744$	−0.979876	+	1.52472i	−0.0359240	+	0.0558988i
$745$	22.7800	+	16.7638i	0.834593	+	0.614178i
$746$	−4.87138	+	16.5904i	−0.178354	+	0.607418i
$747$	−43.1538	−	3.08642i	−1.57892	−	0.112926i
$748$	−7.61762	−	0.544823i	−0.278528	−	0.0199207i
$749$	−2.58835	+	8.81512i	−0.0945764	+	0.322098i
$750$	0.859447	+	1.48604i	0.0313826	+	0.0542627i
$751$	−7.04513	+	10.9624i	−0.257080	+	0.400025i	−0.945671	−	0.325126i	$-0.894593\pi$
$751$	−7.04513	+	10.9624i	−0.257080	+	0.400025i	0.688590	+	0.725150i	$0.258230\pi$
$752$	2.99631	+	1.63611i	0.109264	+	0.0596627i
$753$	−0.687647	+	0.514766i	−0.0250592	+	0.0187591i
$754$	30.3709	−	13.8699i	1.10604	−	0.505112i
$755$	42.2801	+	2.67642i	1.53873	+	0.0974049i
$756$	0.616002	+	0.958518i	0.0224038	+	0.0348610i
$757$	1.90353	+	26.6148i	0.0691850	+	0.967333i	0.906933	+	0.421275i	$0.138417\pi$
$757$	1.90353	+	26.6148i	0.0691850	+	0.967333i	−0.837748	+	0.546057i	$0.816128\pi$
$758$	15.8232	+	15.8232i	0.574723	+	0.574723i
$759$	−0.878167	−	0.267795i	−0.0318755	−	0.00972033i
$760$	23.5644	+	36.0156i	0.854771	+	1.30642i
$761$	18.7552	−	21.6447i	0.679876	−	0.784619i	−0.306012	−	0.952028i	$-0.598995\pi$
$761$	18.7552	−	21.6447i	0.679876	−	0.784619i	0.985887	+	0.167409i	$0.0535401\pi$
$762$	1.56318	+	0.340048i	0.0566279	+	0.0123186i
$763$	−14.0157	−	10.4920i	−0.507402	−	0.379836i
$764$	2.86442	+	6.27221i	0.103631	+	0.226921i
$765$	−18.5511	−	39.7571i	−0.670716	−	1.43742i
$766$	−6.47368	−	22.0473i	−0.233904	−	0.796602i
$767$	−9.94797	−	45.7301i	−0.359200	−	1.65122i
$768$	0.831650	+	2.22974i	0.0300096	+	0.0804589i
$769$	−8.83828	−	2.59515i	−0.318716	−	0.0935836i	0.118461	−	0.992959i	$-0.462204\pi$
$769$	−8.83828	−	2.59515i	−0.318716	−	0.0935836i	−0.437178	+	0.899375i	$0.644022\pi$
$770$	−2.27796	−	4.09182i	−0.0820920	−	0.147459i
$771$	0.327898	+	0.378414i	0.0118090	+	0.0136283i
$772$	−1.10212	−	2.01838i	−0.0396661	−	0.0726431i
$773$	1.84947	−	0.689816i	0.0665208	−	0.0248110i	−0.315984	−	0.948765i	$-0.602334\pi$
$773$	1.84947	−	0.689816i	0.0665208	−	0.0248110i	0.382504	+	0.923954i	$0.375062\pi$
$774$	−1.25977	−	0.809602i	−0.0452813	−	0.0291005i
$775$	−20.3433	−	2.58591i	−0.730753	−	0.0928887i
$776$	−4.32453	−	0.621774i	−0.155242	−	0.0223204i
$777$	0.142366	−	0.381698i	0.00510736	−	0.0136933i
$778$	1.15927	−	1.54861i	0.0415619	−	0.0555202i
$779$	−34.0187	+	21.8625i	−1.21885	+	0.783304i
$780$	0.657646	+	0.863690i	0.0235475	+	0.0309251i
$781$		−	8.59114i		−	0.307415i
$782$	−33.3453	−	2.73340i	−1.19243	−	0.0977462i
$783$	−5.06459	+	5.06459i	−0.180994	+	0.180994i
$784$	−5.29694	−	4.58982i	−0.189176	−	0.163922i
$785$	0.697337	+	0.311593i	0.0248890	+	0.0111212i
$786$	0.232592	+	1.61771i	0.00829628	+	0.0577019i
$787$	6.40776	+	2.38997i	0.228412	+	0.0851933i	0.461064	−	0.887367i	$-0.347468\pi$
$787$	6.40776	+	2.38997i	0.228412	+	0.0851933i	−0.232652	+	0.972560i	$0.574740\pi$
$788$	2.69090	+	3.59461i	0.0958592	+	0.128053i
$789$	−3.90111	+	1.14547i	−0.138883	+	0.0407798i
$790$	18.6431	−	0.152543i	0.663291	−	0.00542722i
$791$	−0.154221	+	0.337698i	−0.00548348	+	0.0120071i
$792$	−10.5261	+	5.74769i	−0.374029	+	0.204235i
$793$	0.889797	−	12.4410i	0.0315976	−	0.441793i
$794$	−26.1188	+	22.6320i	−0.926920	+	0.803181i
$795$	0.0575286	−	0.107436i	0.00204033	−	0.00381037i
$796$	5.03278	+	2.29840i	0.178382	+	0.0814645i
$797$	−31.7502	+	6.90683i	−1.12465	+	0.244653i	−0.736165	−	0.676802i	$-0.763365\pi$
$797$	−31.7502	+	6.90683i	−1.12465	+	0.244653i	−0.388485	+	0.921455i	$0.627001\pi$
$798$	−0.695633	+	1.27396i	−0.0246251	+	0.0450976i
$799$	−2.17241	+	15.1094i	−0.0768543	+	0.534534i
$800$	−15.7753	+	16.3003i	−0.557742	+	0.576301i
$801$	−31.3305	+	4.50464i	−1.10701	+	0.159164i
$802$	3.34911	−	15.3956i	0.118261	−	0.543638i
$803$	10.7646	−	0.769898i	0.379874	−	0.0271691i
$804$	−1.38543			−0.0488603
$805$	7.66369	+	14.1090i	0.270110	+	0.497276i
$806$	16.5705			0.583671
$807$	2.97267	−	0.212610i	0.104643	−	0.00748422i
$808$	2.97071	−	13.6561i	0.104509	−	0.480421i
$809$	−7.46348	+	1.07309i	−0.262402	+	0.0377277i	−0.272260	−	0.962224i	$-0.587771\pi$
$809$	−7.46348	+	1.07309i	−0.262402	+	0.0377277i	0.00985818	+	0.999951i	$0.496862\pi$
$810$	−17.6484	−	11.1390i	−0.620102	−	0.391383i
$811$	−3.09200	+	21.5054i	−0.108575	+	0.755156i	0.860689	+	0.509132i	$0.170033\pi$
$811$	−3.09200	+	21.5054i	−0.108575	+	0.755156i	−0.969264	+	0.246024i	$0.920876\pi$
$812$	5.20656	−	9.53510i	0.182714	−	0.334616i
$813$	−2.20523	+	0.479719i	−0.0773409	+	0.0168245i
$814$	2.38838	+	1.09074i	0.0837127	+	0.0382303i
$815$	−5.90321	−	19.5124i	−0.206780	−	0.683491i
$816$	1.06280	−	0.920925i	0.0372056	−	0.0322388i
$817$	−0.213762	+	2.98878i	−0.00747858	+	0.104564i
$818$	11.4581	−	6.25661i	0.400624	−	0.218757i
$819$	7.06731	−	15.4752i	0.246952	−	0.540749i
$820$	−8.96399	−	8.81848i	−0.313036	−	0.307955i
$821$	−26.5228	+	7.78778i	−0.925650	+	0.271795i	−0.709615	−	0.704590i	$-0.751131\pi$
$821$	−26.5228	+	7.78778i	−0.925650	+	0.271795i	−0.216036	+	0.976385i	$0.569313\pi$
$822$	−0.330640	−	0.441684i	−0.0115324	−	0.0154055i
$823$	−19.4902	−	7.26946i	−0.679385	−	0.253397i	−0.0140044	−	0.999902i	$-0.504458\pi$
$823$	−19.4902	−	7.26946i	−0.679385	−	0.253397i	−0.665380	+	0.746505i	$0.731731\pi$
$824$	2.26296	+	15.7392i	0.0788338	+	0.548301i
$825$	0.775543	+	0.560999i	0.0270009	+	0.0195315i
$826$	14.7056	+	12.7425i	0.511673	+	0.443368i
$827$	11.7611	−	11.7611i	0.408975	−	0.408975i	−0.472406	−	0.881381i	$-0.656614\pi$
$827$	11.7611	−	11.7611i	0.408975	−	0.408975i	0.881381	+	0.472406i	$0.156614\pi$
$828$	11.0717	−	5.89712i	0.384769	−	0.204939i
$829$			18.4347i			0.640264i	0.947373	+	0.320132i	$0.103727\pi$
$829$			18.4347i			0.640264i	−0.947373	+	0.320132i	$0.896273\pi$
$830$	27.3674	−	20.8385i	0.949936	−	0.723316i
$831$	−1.37389	+	0.882947i	−0.0476598	+	0.0306291i
$832$	17.7184	−	23.6690i	0.614275	−	0.820575i
$833$	10.9519	−	29.3633i	0.379462	−	1.01738i
$834$	0.910696	+	0.130938i	0.0315348	+	0.00453402i
$835$	25.7718	−	30.2387i	0.891870	−	1.04645i
$836$	6.15907	+	3.95819i	0.213016	+	0.136897i
$837$	−3.33058	+	1.24224i	−0.115122	+	0.0429382i
$838$	−2.90637	−	5.32261i	−0.100399	−	0.183867i
$839$	13.3655	+	15.4246i	0.461429	+	0.532517i	0.938008	−	0.346614i	$-0.112669\pi$
$839$	13.3655	+	15.4246i	0.461429	+	0.532517i	−0.476579	+	0.879132i	$0.658123\pi$
$840$	−1.42289	−	0.405184i	−0.0490945	−	0.0139802i
$841$	37.7013	+	11.0701i	1.30004	+	0.381727i
$842$	13.9965	+	37.5261i	0.482352	+	1.29324i
$843$	0.756075	+	3.47562i	0.0260406	+	0.119707i
$844$	0.0615431	+	0.209596i	0.00211840	+	0.00721461i
$845$	1.18374	−	3.25481i	0.0407218	−	0.111969i
$846$	3.03805	+	6.65241i	0.104450	+	0.228715i
$847$	11.0941	+	8.30497i	0.381199	+	0.285362i
$848$	−0.541152	−	0.117720i	−0.0185832	−	0.00404254i
$849$	1.90449	−	2.19789i	0.0653618	−	0.0754315i
$850$	31.9622	+	13.9692i	1.09629	+	0.479138i
$851$	−8.14914	−	3.82441i	−0.279349	−	0.131099i
$852$	−0.585485	−	0.585485i	−0.0200584	−	0.0200584i
$853$	−1.56973	−	21.9476i	−0.0537464	−	0.751473i	−0.950850	−	0.309652i	$-0.899787\pi$
$853$	−1.56973	−	21.9476i	−0.0537464	−	0.751473i	0.897103	−	0.441821i	$-0.145667\pi$
$854$	2.80372	+	4.36267i	0.0959413	+	0.149288i
$855$	−2.65705	+	41.9742i	−0.0908693	+	1.43549i
$856$	−17.0157	+	7.77080i	−0.581584	+	0.265601i
$857$	3.73064	−	2.79272i	0.127436	−	0.0953975i	−0.533658	−	0.845700i	$-0.679183\pi$
$857$	3.73064	−	2.79272i	0.127436	−	0.0953975i	0.661094	+	0.750303i	$0.270092\pi$
$858$	−0.678831	−	0.370670i	−0.0231749	−	0.0126544i
$859$	−11.2930	+	17.5723i	−0.385313	+	0.599559i	−0.978684	−	0.205370i	$-0.934160\pi$
$859$	−11.2930	+	17.5723i	−0.385313	+	0.599559i	0.593371	+	0.804929i	$0.297797\pi$
$860$	−0.921159	+	0.140145i	−0.0314113	+	0.00477889i
$861$	0.391618	−	1.33373i	0.0133463	−	0.0454534i
$862$	20.8342	+	1.49009i	0.709616	+	0.0507528i
$863$	40.4908	+	2.89596i	1.37832	+	0.0985795i	0.740734	−	0.671798i	$-0.234478\pi$
$863$	40.4908	+	2.89596i	1.37832	+	0.0985795i	0.637587	+	0.770378i	$0.279932\pi$
$864$	−1.10779	+	3.77278i	−0.0376877	+	0.128353i
$865$	17.3252	−	2.63585i	0.589074	−	0.0896215i
$866$	19.2751	−	29.9927i	0.654996	−	1.01919i
$867$	3.35603	+	1.83253i	0.113977	+	0.0622361i
$868$	4.31636	−	3.23119i	0.146507	−	0.109674i
$869$	9.45587	−	4.31835i	0.320768	−	0.146490i
$870$	0.179249	−	2.83164i	0.00607710	−	0.0960015i
$871$	22.4466	+	34.9276i	0.760573	+	1.18348i
$872$	−2.54306	−	35.5566i	−0.0861187	−	1.20410i
$873$	−3.01891	−	3.01891i	−0.102175	−	0.102175i
$874$	26.8006	+	17.6198i	0.906543	+	0.595998i
$875$	−2.78824	−	16.5057i	−0.0942596	−	0.557994i
$876$	0.681136	−	0.786073i	0.0230135	−	0.0265590i
$877$	−31.9318	−	6.94634i	−1.07826	−	0.234561i	−0.361847	−	0.932237i	$-0.617854\pi$
$877$	−31.9318	−	6.94634i	−1.07826	−	0.234561i	−0.716413	+	0.697676i	$0.754217\pi$
$878$	2.46695	+	1.84673i	0.0832555	+	0.0623243i
$879$	0.700618	+	1.53414i	0.0236313	+	0.0517453i
$880$	1.48666	−	4.08774i	0.0501154	−	0.137798i
$881$	14.5512	+	49.5567i	0.490241	+	1.66961i	0.718121	+	0.695918i	$0.245002\pi$
$881$	14.5512	+	49.5567i	0.490241	+	1.66961i	−0.227881	+	0.973689i	$0.573180\pi$
$882$	−3.19155	−	14.6713i	−0.107465	−	0.494010i
$883$	−13.8991	−	37.2650i	−0.467743	−	1.25407i	−0.930078	−	0.367362i	$-0.880261\pi$
$883$	−13.8991	−	37.2650i	−0.467743	−	1.25407i	0.462335	−	0.886705i	$-0.347012\pi$
$884$	21.1644	+	6.21443i	0.711836	+	0.209014i
$885$	−3.82495	−	1.08919i	−0.128574	−	0.0366129i
$886$	−11.8601	−	13.6873i	−0.398448	−	0.459833i
$887$	−8.16258	−	14.9486i	−0.274073	−	0.501926i	0.703998	−	0.710202i	$-0.251397\pi$
$887$	−8.16258	−	14.9486i	−0.274073	−	0.501926i	−0.978070	+	0.208276i	$0.933215\pi$
$888$	0.777172	−	0.289870i	0.0260802	−	0.00972741i
$889$	−13.1229	−	8.43358i	−0.440128	−	0.282853i
$890$	16.3241	−	19.1535i	0.547185	−	0.642025i
$891$	−11.5180	−	1.65603i	−0.385866	−	0.0554792i
$892$	7.05814	−	18.9236i	0.236324	−	0.633610i
$893$	8.76962	−	11.7148i	0.293464	−	0.392022i
$894$	−1.63383	+	1.05000i	−0.0546435	+	0.0351172i
$895$	0.0340677	−	0.0259404i	0.00113876	−	0.000867091i
$896$		−	1.29216i		−	0.0431681i
$897$	2.31400	+	1.29493i	0.0772624	+	0.0432365i
$898$	26.3258	−	26.3258i	0.878504	−	0.878504i
$899$	25.6152	+	22.1957i	0.854315	+	0.740268i
$900$	−12.9130	+	2.07282i	−0.430434	+	0.0690939i
$901$	−0.352412	−	2.45108i	−0.0117405	−	0.0816573i
$902$	8.39414	+	3.13085i	0.279494	+	0.104246i
$903$	−0.0617257	−	0.0824559i	−0.00205410	−	0.00274396i
$904$	−0.725273	+	0.212959i	−0.0241222	+	0.00708292i
$905$	7.61619	+	7.49257i	0.253171	+	0.249061i
$906$	−1.20847	+	2.64618i	−0.0401487	+	0.0879133i
$907$	−28.4219	+	15.5195i	−0.943734	+	0.515318i	−0.875960	−	0.482383i	$-0.839771\pi$
$907$	−28.4219	+	15.5195i	−0.943734	+	0.515318i	−0.0677737	+	0.997701i	$0.521590\pi$
$908$	−1.41300	+	19.7564i	−0.0468921	+	0.655638i
$909$	10.3212	−	8.94333i	0.342331	−	0.296632i
$910$	3.91684	+	12.9467i	0.129842	+	0.429180i
$911$	17.1903	+	7.85055i	0.569540	+	0.260100i	0.679303	−	0.733858i	$-0.262282\pi$
$911$	17.1903	+	7.85055i	0.569540	+	0.260100i	−0.109763	+	0.993958i	$0.535009\pi$
$912$	−1.31734	+	0.286569i	−0.0436213	+	0.00948924i
$913$	9.19173	−	16.8334i	0.304202	−	0.557104i
$914$	2.60181	−	18.0960i	0.0860602	−	0.598562i
$915$	−0.896330	−	0.565727i	−0.0296317	−	0.0187024i
$916$	−25.5304	+	3.67072i	−0.843549	+	0.121284i
$917$	3.38760	−	15.5725i	0.111868	−	0.514250i
$918$	6.03100	−	0.431345i	0.199053	−	0.0142365i
$919$	−32.5679			−1.07431			−0.537157	−	0.843482i	$-0.680502\pi$
$919$	−32.5679			−1.07431			−0.537157	+	0.843482i	$0.680502\pi$
$920$	−11.4921	+	30.6050i	−0.378883	+	1.00902i
$921$	1.07030			0.0352674
$922$	−6.40994	+	0.458448i	−0.211100	+	0.0150982i
$923$	−5.27449	+	24.2464i	−0.173612	+	0.798081i
$924$	−0.249104	+	0.0358157i	−0.00819492	+	0.00117825i
$925$	6.74401	+	6.52682i	0.221742	+	0.214601i
$926$	−2.65339	+	18.4548i	−0.0871959	+	0.606461i
$927$	−7.44681	+	13.6378i	−0.244585	+	0.447924i
$928$	36.6349	−	7.96944i	1.20260	−	0.261610i
$929$	10.7143	+	4.89304i	0.351523	+	0.160535i	0.583348	−	0.812222i	$-0.301742\pi$
$929$	10.7143	+	4.89304i	0.351523	+	0.160535i	−0.231825	+	0.972758i	$0.574470\pi$
$930$	0.664722	−	1.24139i	0.0217971	−	0.0407067i
$931$	−22.7053	+	19.6743i	−0.744136	+	0.644798i
$932$	−0.643533	+	8.99777i	−0.0210796	+	0.294732i
$933$	4.33124	−	2.36504i	0.141798	−	0.0774278i
$934$	−2.15839	+	4.72622i	−0.0706247	+	0.154647i
$935$	19.4484	−	0.159132i	0.636031	−	0.00520418i
$936$	33.2361	−	9.75901i	1.08636	−	0.318983i
$937$	−19.2839	−	25.7603i	−0.629978	−	0.841552i	0.366050	−	0.930595i	$-0.380710\pi$
$937$	−19.2839	−	25.7603i	−0.629978	−	0.841552i	−0.996028	+	0.0890435i	$0.971619\pi$
$938$	−16.1741	−	6.03263i	−0.528104	−	0.196972i
$939$	0.263288	+	1.83121i	0.00859207	+	0.0597592i
$940$	4.15456	+	1.85639i	0.135507	+	0.0605488i
$941$	−15.3121	−	13.2680i	−0.499160	−	0.432524i	0.368541	−	0.929612i	$-0.379857\pi$
$941$	−15.3121	−	13.2680i	−0.499160	−	0.432524i	−0.867701	+	0.497087i	$0.834403\pi$
$942$	−0.0370856	+	0.0370856i	−0.00120831	+	0.00120831i
$943$	−28.6658	−	11.0324i	−0.933486	−	0.359264i
$944$			18.0727i			0.588216i
$945$	−1.75784	−	2.30859i	−0.0571826	−	0.0750983i
$946$	0.558469	−	0.358906i	0.0181574	−	0.0116690i
$947$	19.4422	−	25.9717i	0.631787	−	0.843968i	−0.364398	−	0.931243i	$-0.618725\pi$
$947$	19.4422	−	25.9717i	0.631787	−	0.843968i	0.996184	+	0.0872753i	$0.0278160\pi$
$948$	0.350121	−	0.938711i	0.0113714	−	0.0304879i
$949$	−30.8531	−	4.43601i	−1.00153	−	0.143999i
$950$	−20.4747	−	26.4380i	−0.664288	−	0.857761i
$951$	−1.55542	−	0.999611i	−0.0504381	−	0.0324146i
$952$	−28.1661	+	10.5054i	−0.912868	+	0.340482i
$953$	17.8170	+	32.6293i	0.577148	+	1.05697i	0.989306	+	0.145855i	$0.0465932\pi$
$953$	17.8170	+	32.6293i	0.577148	+	1.05697i	−0.412158	+	0.911112i	$0.635225\pi$
$954$	−0.776911	−	0.896603i	−0.0251534	−	0.0290286i
$955$	−8.54147	−	15.3427i	−0.276396	−	0.496480i
$956$	−9.30406	−	2.73192i	−0.300915	−	0.0883566i
$957$	−0.552856	−	1.48227i	−0.0178713	−	0.0479148i
$958$	4.71368	+	21.6685i	0.152292	+	0.700076i
$959$	1.51572	+	5.16208i	0.0489452	+	0.166692i
$960$	−1.06241	−	2.27686i	−0.0342890	−	0.0734853i
$961$	−5.88997	−	12.8972i	−0.189999	−	0.416040i
$962$	−6.07098	−	4.54468i	−0.195736	−	0.146526i
$963$	−17.8619	−	3.88561i	−0.575590	−	0.125212i
$964$	−5.86987	+	6.77419i	−0.189056	+	0.218182i
$965$	3.20648	+	4.90074i	0.103220	+	0.157760i
$966$	−1.09287	+	0.145558i	−0.0351624	+	0.00468325i
$967$	−2.18782	−	2.18782i	−0.0703555	−	0.0703555i	0.671053	−	0.741409i	$-0.265842\pi$
$967$	−2.18782	−	2.18782i	−0.0703555	−	0.0703555i	−0.741409	+	0.671053i	$0.765842\pi$
$968$	2.01296	+	28.1449i	0.0646990	+	0.904611i
$969$	−3.25901	−	5.07113i	−0.104695	−	0.162908i
$970$	3.38768	+	0.214447i	0.108772	+	0.00688549i
$971$	16.0493	−	7.32947i	0.515047	−	0.235214i	−0.140896	−	0.990024i	$-0.544998\pi$
$971$	16.0493	−	7.32947i	0.515047	−	0.235214i	0.655943	+	0.754810i	$0.272271\pi$
$972$	−2.72544	+	2.04024i	−0.0874186	+	0.0654408i
$973$	−7.87422	−	4.29965i	−0.252436	−	0.137840i
$974$	−10.2965	+	16.0216i	−0.329920	+	0.513365i
$975$	−1.84436	−	2.05942i	−0.0590668	−	0.0659544i
$976$	−1.35700	+	4.62152i	−0.0434366	+	0.147931i
$977$	31.2111	+	2.23226i	0.998531	+	0.0714164i	0.561025	−	0.827799i	$-0.310407\pi$
$977$	31.2111	+	2.23226i	0.998531	+	0.0714164i	0.437506	+	0.899215i	$0.355862\pi$
$978$	1.39627	+	0.0998632i	0.0446478	+	0.00319327i
$979$	3.95327	−	13.4636i	0.126347	−	0.430298i
$980$	−7.52439	−	5.53721i	−0.240358	−	0.176880i
$981$	18.8330	−	29.3047i	0.601291	−	0.935628i
$982$	−21.1705	−	11.5599i	−0.675577	−	0.368893i
$983$	−27.9781	+	20.9442i	−0.892364	+	0.668015i	−0.943749	−	0.330664i	$-0.892727\pi$
$983$	−27.9781	+	20.9442i	−0.892364	+	0.668015i	0.0513847	+	0.998679i	$0.483637\pi$
$984$	2.57448	−	1.17572i	0.0820713	−	0.0374807i
$985$	−7.55886	−	8.58052i	−0.240845	−	0.273398i
$986$	−31.1689	−	48.4998i	−0.992621	−	1.54455i
$987$	0.0358853	+	0.501742i	0.00114224	+	0.0159706i
$988$	−14.9524	−	14.9524i	−0.475698	−	0.475698i
$989$	−1.92736	+	1.21053i	−0.0612865	+	0.0384926i
$990$	7.79728	−	5.10163i	0.247814	−	0.162141i
$991$	−28.8910	+	33.3420i	−0.917754	+	1.05914i	0.0802992	+	0.996771i	$0.474412\pi$
$991$	−28.8910	+	33.3420i	−0.917754	+	1.05914i	−0.998053	+	0.0623735i	$0.980133\pi$
$992$	18.1819	+	3.95523i	0.577276	+	0.125579i
$993$	−2.71153	−	2.02983i	−0.0860478	−	0.0644145i
$994$	−4.28581	−	9.38462i	−0.135938	−	0.297662i
$995$	−13.2416	−	4.81581i	−0.419786	−	0.152671i
$996$	−0.520779	−	1.77361i	−0.0165015	−	0.0561989i
$997$	9.07960	+	41.7382i	0.287554	+	1.32186i	0.863489	+	0.504368i	$0.168274\pi$
$997$	9.07960	+	41.7382i	0.287554	+	1.32186i	−0.575935	+	0.817495i	$0.695362\pi$
$998$	16.0140	+	42.9351i	0.506914	+	1.35909i
$999$	1.56094	+	0.458332i	0.0493858	+	0.0145010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.7.4	✓	200
5.2	odd	4		575.2.r.b.168.4		200
5.3	odd	4	inner	115.2.l.a.53.7	yes	200
5.4	even	2		575.2.r.b.7.7		200
23.10	odd	22	inner	115.2.l.a.102.7	yes	200
115.33	even	44	inner	115.2.l.a.33.4	yes	200
115.79	odd	22		575.2.r.b.332.4		200
115.102	even	44		575.2.r.b.493.7		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.4	✓	200	1.1	even	1	trivial
115.2.l.a.33.4	yes	200	115.33	even	44	inner
115.2.l.a.53.7	yes	200	5.3	odd	4	inner
115.2.l.a.102.7	yes	200	23.10	odd	22	inner
575.2.r.b.7.7		200	5.4	even	2
575.2.r.b.168.4		200	5.2	odd	4
575.2.r.b.332.4		200	115.79	odd	22
575.2.r.b.493.7		200	115.102	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05653 + 0.0755644i) q^{2} +(0.0308132 - 0.141646i) q^{3} +(-0.869101 + 0.124958i) q^{4} +(2.18100 - 0.493172i) q^{5} +(-0.0218516 + 0.151981i) q^{6} +(0.717546 - 1.31409i) q^{7} +(2.97883 - 0.648004i) q^{8} +(2.70978 + 1.23752i) q^{9} +O(q^{10})\)	\(q+(-1.05653 + 0.0755644i) q^{2} +(0.0308132 - 0.141646i) q^{3} +(-0.869101 + 0.124958i) q^{4} +(2.18100 - 0.493172i) q^{5} +(-0.0218516 + 0.151981i) q^{6} +(0.717546 - 1.31409i) q^{7} +(2.97883 - 0.648004i) q^{8} +(2.70978 + 1.23752i) q^{9} +(-2.26703 + 0.685856i) q^{10} +(-0.998057 + 0.864822i) q^{11} +(-0.00908000 + 0.126955i) q^{12} +(3.34773 - 1.82800i) q^{13} +(-0.658809 + 1.44259i) q^{14} +(-0.00265209 - 0.324127i) q^{15} +(-1.41331 + 0.414985i) q^{16} +(-3.94697 - 5.27254i) q^{17} +(-2.95647 - 1.10271i) q^{18} +(0.898560 + 6.24963i) q^{19} +(-1.83389 + 0.701150i) q^{20} +(-0.164025 - 0.142129i) q^{21} +(0.989126 - 0.989126i) q^{22} +(-3.42622 + 3.35575i) q^{23} -0.441906i q^{24} +(4.51356 - 2.15122i) q^{25} +(-3.39884 + 2.18430i) q^{26} +(0.519398 - 0.693834i) q^{27} +(-0.459414 + 1.23174i) q^{28} +(-8.17984 - 1.17608i) q^{29} +(0.0272944 + 0.342249i) q^{30} +(-3.45032 - 2.21738i) q^{31} +(-4.25073 + 1.58544i) q^{32} +(0.0917452 + 0.168019i) q^{33} +(4.56851 + 5.27234i) q^{34} +(0.916900 - 3.21990i) q^{35} +(-2.50971 - 0.736918i) q^{36} +(0.655955 + 1.75868i) q^{37} +(-1.42160 - 6.53501i) q^{38} +(-0.155774 - 0.530519i) q^{39} +(6.17726 - 2.88238i) q^{40} +(2.66058 + 5.82585i) q^{41} +(0.184037 + 0.137768i) q^{42} +(0.463730 + 0.100878i) q^{43} +(0.759346 - 0.876332i) q^{44} +(6.52036 + 1.36264i) q^{45} +(3.36632 - 3.80434i) q^{46} +(-1.63886 - 1.63886i) q^{47} +(0.0152324 + 0.212976i) q^{48} +(2.57253 + 4.00294i) q^{49} +(-4.60615 + 2.61389i) q^{50} +(-0.868453 + 0.396609i) q^{51} +(-2.68109 + 2.00704i) q^{52} +(0.329990 + 0.180188i) q^{53} +(-0.496329 + 0.772303i) q^{54} +(-1.75026 + 2.37839i) q^{55} +(1.28591 - 4.37941i) q^{56} +(0.912922 + 0.0652934i) q^{57} +(8.73110 + 0.624461i) q^{58} +(3.45672 - 11.7725i) q^{59} +(0.0428071 + 0.281367i) q^{60} +(1.76790 - 2.75090i) q^{61} +(3.81291 + 2.08201i) q^{62} +(3.57060 - 2.67291i) q^{63} +(7.05094 - 3.22006i) q^{64} +(6.39990 - 5.63788i) q^{65} +(-0.109628 - 0.170584i) q^{66} +(0.776524 + 10.8572i) q^{67} +(4.08916 + 4.08916i) q^{68} +(0.369756 + 0.588711i) q^{69} +(-0.725421 + 3.47120i) q^{70} +(-4.26013 + 4.91645i) q^{71} +(8.87389 + 1.93040i) q^{72} +(-6.54201 - 4.89729i) q^{73} +(-0.825929 - 1.80853i) q^{74} +(-0.165634 - 0.705614i) q^{75} +(-1.56188 - 5.31927i) q^{76} +(0.420299 + 1.93208i) q^{77} +(0.204668 + 0.548737i) q^{78} +(-7.55266 - 2.21766i) q^{79} +(-2.87777 + 1.60209i) q^{80} +(5.77019 + 6.65915i) q^{81} +(-3.25120 - 5.95413i) q^{82} +(-13.6074 + 5.07529i) q^{83} +(0.160315 + 0.103028i) q^{84} +(-11.2086 - 9.55290i) q^{85} +(-0.497566 - 0.0715393i) q^{86} +(-0.418634 + 1.12240i) q^{87} +(-2.41263 + 3.22290i) q^{88} +(-8.93857 + 5.74447i) q^{89} +(-6.99191 - 0.946961i) q^{90} -5.71088i q^{91} +(2.55840 - 3.34462i) q^{92} +(-0.420399 + 0.420399i) q^{93} +(1.85534 + 1.60766i) q^{94} +(5.04190 + 13.1873i) q^{95} +(0.0935927 + 0.650952i) q^{96} +(-1.34281 - 0.500840i) q^{97} +(-3.02043 - 4.03483i) q^{98} +(-3.77475 + 1.10837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more