LMFDB - Embedded newform 231.2.y.a.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	231.16
Dual form			231.2.y.a.130.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72647 + 0.366972i) q^{2} +(0.104528 - 0.994522i) q^{3} +(1.01892 + 0.453654i) q^{4} +(0.597146 + 0.663197i) q^{5} +(0.545426 - 1.67865i) q^{6} +(2.29418 + 1.31786i) q^{7} +(-1.26323 - 0.917790i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(1.72647 + 0.366972i) q^{2} +(0.104528 - 0.994522i) q^{3} +(1.01892 + 0.453654i) q^{4} +(0.597146 + 0.663197i) q^{5} +(0.545426 - 1.67865i) q^{6} +(2.29418 + 1.31786i) q^{7} +(-1.26323 - 0.917790i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.787577 + 1.36412i) q^{10} +(2.64231 - 2.00454i) q^{11} +(0.557675 - 0.965922i) q^{12} +(0.294823 + 0.907373i) q^{13} +(3.47720 + 3.11714i) q^{14} +(0.721983 - 0.524551i) q^{15} +(-3.33675 - 3.70584i) q^{16} +(-2.03247 + 0.432014i) q^{17} +(-1.61244 - 0.717905i) q^{18} +(-7.53962 + 3.35686i) q^{19} +(0.307584 + 0.946645i) q^{20} +(1.55045 - 2.14385i) q^{21} +(5.29747 - 2.49112i) q^{22} +(-1.55359 + 2.69090i) q^{23} +(-1.04481 + 1.16037i) q^{24} +(0.439394 - 4.18056i) q^{25} +(0.176022 + 1.67474i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.73974 + 2.38356i) q^{28} +(1.61792 - 1.17549i) q^{29} +(1.43897 - 0.640673i) q^{30} +(-3.13536 + 3.48217i) q^{31} +(-2.83941 - 4.91800i) q^{32} +(-1.71736 - 2.83737i) q^{33} -3.66752 q^{34} +(0.495956 + 2.30845i) q^{35} +(-0.902338 - 0.655587i) q^{36} +(1.05034 + 9.99336i) q^{37} +(-14.2488 + 3.02867i) q^{38} +(0.933220 - 0.198362i) q^{39} +(-0.145656 - 1.38582i) q^{40} +(-4.45800 - 3.23893i) q^{41} +(3.46353 - 3.13232i) q^{42} -1.89038 q^{43} +(3.60168 - 0.843780i) q^{44} +(-0.446210 - 0.772859i) q^{45} +(-3.66971 + 4.07562i) q^{46} +(3.11516 - 1.38696i) q^{47} +(-4.03432 + 2.93111i) q^{48} +(3.52649 + 6.04681i) q^{49} +(2.29275 - 7.05634i) q^{50} +(0.217197 + 2.06649i) q^{51} +(-0.111231 + 1.05829i) q^{52} +(7.50257 - 8.33245i) q^{53} +(-0.882518 + 1.52857i) q^{54} +(2.90725 + 0.555371i) q^{55} +(-1.68855 - 3.77033i) q^{56} +(2.55036 + 7.84921i) q^{57} +(3.22465 - 1.43571i) q^{58} +(0.769105 + 0.342428i) q^{59} +(0.973611 - 0.206947i) q^{60} +(-0.783160 - 0.869787i) q^{61} +(-6.69094 + 4.86125i) q^{62} +(-1.97004 - 1.76605i) q^{63} +(-0.0154285 - 0.0474840i) q^{64} +(-0.425715 + 0.737360i) q^{65} +(-1.92374 - 5.52884i) q^{66} +(-6.19006 - 10.7215i) q^{67} +(-2.26691 - 0.481847i) q^{68} +(2.51377 + 1.82636i) q^{69} +(0.00911741 + 4.16745i) q^{70} +(3.62070 - 11.1434i) q^{71} +(1.04481 + 1.16037i) q^{72} +(8.71468 + 3.88002i) q^{73} +(-1.85390 + 17.6386i) q^{74} +(-4.11173 - 0.873975i) q^{75} -9.20515 q^{76} +(8.70363 - 1.11658i) q^{77} +1.68397 q^{78} +(6.08408 + 1.29321i) q^{79} +(0.465175 - 4.42585i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-6.50799 - 7.22785i) q^{82} +(4.51266 - 13.8885i) q^{83} +(2.55236 - 1.48106i) q^{84} +(-1.50019 - 1.08995i) q^{85} +(-3.26367 - 0.693715i) q^{86} +(-0.999929 - 1.73193i) q^{87} +(-5.17759 + 0.107109i) q^{88} +(4.42449 - 7.66344i) q^{89} +(-0.486749 - 1.49806i) q^{90} +(-0.519414 + 2.47021i) q^{91} +(-2.80373 + 2.03703i) q^{92} +(3.13536 + 3.48217i) q^{93} +(5.88719 - 1.25136i) q^{94} +(-6.72851 - 2.99573i) q^{95} +(-5.18786 + 2.30978i) q^{96} +(5.64383 + 17.3699i) q^{97} +(3.86936 + 11.7337i) q^{98} +(-3.00134 + 1.41137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.72647	+	0.366972i	1.22080	+	0.259488i	0.772859	−	0.634577i	$-0.218826\pi$
$2$	1.72647	+	0.366972i	1.22080	+	0.259488i	0.447936	+	0.894066i	$0.352159\pi$
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	1.01892	+	0.453654i	0.509462	+	0.226827i
$5$	0.597146	+	0.663197i	0.267052	+	0.296591i	0.861724	−	0.507377i	$-0.169385\pi$
$5$	0.597146	+	0.663197i	0.267052	+	0.296591i	−0.594672	+	0.803968i	$0.702718\pi$
$6$	0.545426	−	1.67865i	0.222669	−	0.685305i
$7$	2.29418	+	1.31786i	0.867117	+	0.498104i
$7$	2.29418	+	1.31786i	0.867117	+	0.498104i
$8$	−1.26323	−	0.917790i	−0.446619	−	0.324488i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	0.787577	+	1.36412i	0.249054	+	0.431374i
$11$	2.64231	−	2.00454i	0.796687	−	0.604392i
$11$	2.64231	−	2.00454i	0.796687	−	0.604392i
$12$	0.557675	−	0.965922i	0.160987	−	0.278838i
$13$	0.294823	+	0.907373i	0.0817693	+	0.251660i	0.983580	−	0.180470i	$-0.0577620\pi$
$13$	0.294823	+	0.907373i	0.0817693	+	0.251660i	−0.901811	+	0.432130i	$0.857762\pi$
$14$	3.47720	+	3.11714i	0.929321	+	0.833090i
$15$	0.721983	−	0.524551i	0.186415	−	0.135439i
$16$	−3.33675	−	3.70584i	−0.834187	−	0.926459i
$17$	−2.03247	+	0.432014i	−0.492946	+	0.104779i	−0.447676	−	0.894196i	$-0.647748\pi$
$17$	−2.03247	+	0.432014i	−0.492946	+	0.104779i	−0.0452698	+	0.998975i	$0.514415\pi$
$18$	−1.61244	−	0.717905i	−0.380056	−	0.169212i
$19$	−7.53962	+	3.35686i	−1.72971	+	0.770116i	−0.733838	+	0.679324i	$0.762273\pi$
$19$	−7.53962	+	3.35686i	−1.72971	+	0.770116i	−0.995870	+	0.0907912i	$0.971060\pi$
$20$	0.307584	+	0.946645i	0.0687778	+	0.211676i
$21$	1.55045	−	2.14385i	0.338335	−	0.467827i
$22$	5.29747	−	2.49112i	1.12942	−	0.531108i
$23$	−1.55359	+	2.69090i	−0.323947	+	0.561092i	−0.981299	−	0.192492i	$-0.938343\pi$
$23$	−1.55359	+	2.69090i	−0.323947	+	0.561092i	0.657352	+	0.753584i	$0.271676\pi$
$24$	−1.04481	+	1.16037i	−0.213270	+	0.236860i
$25$	0.439394	−	4.18056i	0.0878789	−	0.836112i
$26$	0.176022	+	1.67474i	0.0345208	+	0.328444i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.73974	+	2.38356i	0.328780	+	0.450451i
$29$	1.61792	−	1.17549i	0.300440	−	0.218283i	−0.427344	−	0.904089i	$-0.640551\pi$
$29$	1.61792	−	1.17549i	0.300440	−	0.218283i	0.727784	+	0.685807i	$0.240551\pi$
$30$	1.43897	−	0.640673i	0.262720	−	0.116970i
$31$	−3.13536	+	3.48217i	−0.563127	+	0.625416i	−0.955713	−	0.294299i	$-0.904914\pi$
$31$	−3.13536	+	3.48217i	−0.563127	+	0.625416i	0.392586	+	0.919715i	$0.371580\pi$
$32$	−2.83941	−	4.91800i	−0.501941	−	0.869388i
$33$	−1.71736	−	2.83737i	−0.298955	−	0.493922i
$34$	−3.66752			−0.628974
$35$	0.495956	+	2.30845i	0.0838319	+	0.390199i
$36$	−0.902338	−	0.655587i	−0.150390	−	0.109264i
$37$	1.05034	+	9.99336i	0.172676	+	1.64290i	0.646958	+	0.762526i	$0.276041\pi$
$37$	1.05034	+	9.99336i	0.172676	+	1.64290i	−0.474283	+	0.880373i	$0.657292\pi$
$38$	−14.2488	+	3.02867i	−2.31146	+	0.491315i
$39$	0.933220	−	0.198362i	0.149435	−	0.0317633i
$40$	−0.145656	−	1.38582i	−0.0230302	−	0.219118i
$41$	−4.45800	−	3.23893i	−0.696223	−	0.505835i	0.182477	−	0.983210i	$-0.441588\pi$
$41$	−4.45800	−	3.23893i	−0.696223	−	0.505835i	−0.878700	+	0.477375i	$0.841588\pi$
$42$	3.46353	−	3.13232i	0.534434	−	0.483328i
$43$	−1.89038			−0.288280			−0.144140	−	0.989557i	$-0.546042\pi$
$43$	−1.89038			−0.288280			−0.144140	+	0.989557i	$0.546042\pi$
$44$	3.60168	−	0.843780i	0.542974	−	0.127205i
$45$	−0.446210	−	0.772859i	−0.0665171	−	0.115211i
$46$	−3.66971	+	4.07562i	−0.541069	+	0.600918i
$47$	3.11516	−	1.38696i	0.454393	−	0.202309i	−0.166761	−	0.985997i	$-0.553331\pi$
$47$	3.11516	−	1.38696i	0.454393	−	0.202309i	0.621154	+	0.783689i	$0.286664\pi$
$48$	−4.03432	+	2.93111i	−0.582304	+	0.423069i
$49$	3.52649	+	6.04681i	0.503785	+	0.863829i
$50$	2.29275	−	7.05634i	0.324243	−	0.997918i
$51$	0.217197	+	2.06649i	0.0304136	+	0.289367i
$52$	−0.111231	+	1.05829i	−0.0154250	+	0.146759i
$53$	7.50257	−	8.33245i	1.03056	−	1.14455i	0.0411839	−	0.999152i	$-0.486887\pi$
$53$	7.50257	−	8.33245i	1.03056	−	1.14455i	0.989373	−	0.145398i	$-0.0464463\pi$
$54$	−0.882518	+	1.52857i	−0.120095	+	0.208011i
$55$	2.90725	+	0.555371i	0.392014	+	0.0748862i
$56$	−1.68855	−	3.77033i	−0.225642	−	0.503832i
$57$	2.55036	+	7.84921i	0.337804	+	1.03965i
$58$	3.22465	−	1.43571i	0.423418	−	0.188518i
$59$	0.769105	+	0.342428i	0.100129	+	0.0445803i	0.456190	−	0.889882i	$-0.349214\pi$
$59$	0.769105	+	0.342428i	0.100129	+	0.0445803i	−0.356061	+	0.934463i	$0.615880\pi$
$60$	0.973611	−	0.206947i	0.125693	−	0.0267168i
$61$	−0.783160	−	0.869787i	−0.100273	−	0.111365i	0.690919	−	0.722932i	$-0.257206\pi$
$61$	−0.783160	−	0.869787i	−0.100273	−	0.111365i	−0.791192	+	0.611567i	$0.790539\pi$
$62$	−6.69094	+	4.86125i	−0.849750	+	0.617380i
$63$	−1.97004	−	1.76605i	−0.248202	−	0.222501i
$64$	−0.0154285	−	0.0474840i	−0.00192856	−	0.00593551i
$65$	−0.425715	+	0.737360i	−0.0528035	+	0.0914583i
$66$	−1.92374	−	5.52884i	−0.236796	−	0.680553i
$67$	−6.19006	−	10.7215i	−0.756237	−	1.30984i	−0.944757	−	0.327771i	$-0.893703\pi$
$67$	−6.19006	−	10.7215i	−0.756237	−	1.30984i	0.188521	−	0.982069i	$-0.439631\pi$
$68$	−2.26691	−	0.481847i	−0.274904	−	0.0584326i
$69$	2.51377	+	1.82636i	0.302622	+	0.219868i
$70$	0.00911741	+	4.16745i	0.00108974	+	0.498106i
$71$	3.62070	−	11.1434i	0.429698	−	1.32247i	−0.468726	−	0.883344i	$-0.655287\pi$
$71$	3.62070	−	11.1434i	0.429698	−	1.32247i	0.898424	−	0.439130i	$-0.144713\pi$
$72$	1.04481	+	1.16037i	0.123132	+	0.136751i
$73$	8.71468	+	3.88002i	1.01998	+	0.454123i	0.847446	−	0.530882i	$-0.178139\pi$
$73$	8.71468	+	3.88002i	1.01998	+	0.454123i	0.172530	+	0.985004i	$0.444806\pi$
$74$	−1.85390	+	17.6386i	−0.215511	+	2.05045i
$75$	−4.11173	−	0.873975i	−0.474781	−	0.100918i
$76$	−9.20515			−1.05590
$77$	8.70363	−	1.11658i	0.991871	−	0.127246i
$78$	1.68397			0.190671
$79$	6.08408	+	1.29321i	0.684512	+	0.145498i	0.537025	−	0.843566i	$-0.319548\pi$
$79$	6.08408	+	1.29321i	0.684512	+	0.145498i	0.147487	+	0.989064i	$0.452881\pi$
$80$	0.465175	−	4.42585i	0.0520082	−	0.494825i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−6.50799	−	7.22785i	−0.718687	−	0.798183i
$83$	4.51266	−	13.8885i	0.495329	−	1.52447i	−0.321114	−	0.947040i	$-0.604057\pi$
$83$	4.51266	−	13.8885i	0.495329	−	1.52447i	0.816443	−	0.577426i	$-0.195943\pi$
$84$	2.55236	−	1.48106i	0.278485	−	0.161597i
$85$	−1.50019	−	1.08995i	−0.162718	−	0.118222i
$86$	−3.26367	−	0.693715i	−0.351931	−	0.0748052i
$87$	−0.999929	−	1.73193i	−0.107204	−	0.185682i
$88$	−5.17759	+	0.107109i	−0.551933	+	0.0114179i
$89$	4.42449	−	7.66344i	0.468995	−	0.812324i	−0.530377	−	0.847762i	$-0.677949\pi$
$89$	4.42449	−	7.66344i	0.468995	−	0.812324i	0.999372	+	0.0354386i	$0.0112828\pi$
$90$	−0.486749	−	1.49806i	−0.0513079	−	0.157909i
$91$	−0.519414	+	2.47021i	−0.0544493	+	0.258948i
$92$	−2.80373	+	2.03703i	−0.292309	+	0.212375i
$93$	3.13536	+	3.48217i	0.325121	+	0.361084i
$94$	5.88719	−	1.25136i	0.607218	−	0.129068i
$95$	−6.72851	−	2.99573i	−0.690331	−	0.307355i
$96$	−5.18786	+	2.30978i	−0.529484	+	0.235741i
$97$	5.64383	+	17.3699i	0.573044	+	1.76365i	0.642745	+	0.766080i	$0.277795\pi$
$97$	5.64383	+	17.3699i	0.573044	+	1.76365i	−0.0697014	+	0.997568i	$0.522205\pi$
$98$	3.86936	+	11.7337i	0.390864	+	1.18528i
$99$	−3.00134	+	1.41137i	−0.301646	+	0.141848i
$100$	2.34424	−	4.06034i	0.234424	−	0.406034i
$101$	−8.60980	+	9.56215i	−0.856707	+	0.951469i	−0.999266	−	0.0383171i	$-0.987800\pi$
$101$	−8.60980	+	9.56215i	−0.856707	+	0.951469i	0.142559	+	0.989786i	$0.454467\pi$
$102$	−0.383360	+	3.64743i	−0.0379583	+	0.361149i
$103$	−0.247087	−	2.35087i	−0.0243462	−	0.231639i	−0.999928	−	0.0120021i	$-0.996180\pi$
$103$	−0.247087	−	2.35087i	−0.0243462	−	0.231639i	0.975582	−	0.219637i	$-0.0704871\pi$
$104$	0.460348	−	1.41681i	0.0451409	−	0.138929i
$105$	2.34764	−	0.251941i	0.229106	−	0.0245869i
$106$	16.0107	−	11.6325i	1.55510	−	1.12984i
$107$	−10.7433	+	4.78324i	−1.03860	+	0.462413i	−0.853930	−	0.520388i	$-0.825787\pi$
$107$	−10.7433	+	4.78324i	−1.03860	+	0.462413i	−0.184667	+	0.982801i	$0.559121\pi$
$108$	−0.746315	+	0.828867i	−0.0718142	+	0.0797578i
$109$	3.89100	+	6.73942i	0.372691	+	0.645519i	0.989978	−	0.141218i	$-0.0451020\pi$
$109$	3.89100	+	6.73942i	0.372691	+	0.645519i	−0.617288	+	0.786737i	$0.711769\pi$
$110$	4.81546	+	2.02571i	0.459137	+	0.193144i
$111$	10.0484			0.953752
$112$	−2.77132	−	12.8992i	−0.261865	−	1.21886i
$113$	6.53243	+	4.74609i	0.614520	+	0.446475i	0.851003	−	0.525161i	$-0.175995\pi$
$113$	6.53243	+	4.74609i	0.614520	+	0.446475i	−0.236483	+	0.971636i	$0.575995\pi$
$114$	1.52268	+	14.4873i	0.142612	+	1.35686i
$115$	−2.71232	+	0.576522i	−0.252925	+	0.0537609i
$116$	2.18180	−	0.463756i	0.202575	−	0.0430587i
$117$	−0.0997273	−	0.948842i	−0.00921979	−	0.0877205i
$118$	1.20217	+	0.873429i	0.110669	+	0.0804057i
$119$	−5.23217	−	1.68739i	−0.479632	−	0.154683i
$120$	−1.39346			−0.127205
$121$	2.96362	−	10.5932i	0.269420	−	0.963023i
$122$	−1.03291	−	1.78905i	−0.0935154	−	0.161973i
$123$	−3.68717	+	4.09502i	−0.332461	+	0.369235i
$124$	−4.77439	+	2.12569i	−0.428753	+	0.190893i
$125$	6.64483	−	4.82775i	0.594332	−	0.431807i
$126$	−2.75312	−	3.77197i	−0.245268	−	0.336034i
$127$	−2.87279	+	8.84153i	−0.254919	+	0.784559i	0.738927	+	0.673785i	$0.235333\pi$
$127$	−2.87279	+	8.84153i	−0.254919	+	0.784559i	−0.993846	+	0.110773i	$0.964667\pi$
$128$	1.17798	+	11.2078i	0.104120	+	0.990637i
$129$	−0.197598	+	1.88002i	−0.0173976	+	0.165527i
$130$	−1.00557	+	1.11680i	−0.0881945	+	0.0979500i
$131$	−2.78673	+	4.82675i	−0.243477	+	0.421715i	−0.961702	−	0.274096i	$-0.911622\pi$
$131$	−2.78673	+	4.82675i	−0.243477	+	0.421715i	0.718225	+	0.695811i	$0.244955\pi$
$132$	−0.462679	−	3.67015i	−0.0402710	−	0.319446i
$133$	−21.7211	−	2.23494i	−1.88346	−	0.193794i
$134$	−6.75244	−	20.7819i	−0.583322	−	1.79528i
$135$	−0.815266	+	0.362980i	−0.0701670	+	0.0312403i
$136$	2.96397	+	1.31964i	0.254158	+	0.113159i
$137$	2.04026	−	0.433671i	0.174311	−	0.0370510i	−0.119929	−	0.992782i	$-0.538267\pi$
$137$	2.04026	−	0.433671i	0.174311	−	0.0370510i	0.294240	+	0.955731i	$0.404933\pi$
$138$	3.66971	+	4.07562i	0.312386	+	0.346940i
$139$	0.517331	−	0.375863i	0.0438794	−	0.0318803i	−0.565629	−	0.824660i	$-0.691367\pi$
$139$	0.517331	−	0.375863i	0.0438794	−	0.0318803i	0.609509	+	0.792779i	$0.291367\pi$
$140$	−0.541894	+	2.57712i	−0.0457984	+	0.217807i
$141$	−1.05374	−	3.24307i	−0.0887408	−	0.273116i
$142$	10.3403	−	17.9099i	0.867739	−	1.50297i
$143$	2.59788	+	1.80658i	0.217246	+	0.151074i
$144$	2.49335	+	4.31860i	0.207779	+	0.359884i
$145$	1.74571	+	0.371063i	0.144974	+	0.0308151i
$146$	13.6217	+	9.89677i	1.12734	+	0.819062i
$147$	6.38230	−	2.87511i	0.526403	−	0.237135i
$148$	−3.46331	+	10.6590i	−0.284682	+	0.876161i
$149$	8.33929	+	9.26172i	0.683181	+	0.758749i	0.980605	−	0.195996i	$-0.0627940\pi$
$149$	8.33929	+	9.26172i	0.683181	+	0.758749i	−0.297424	+	0.954746i	$0.596127\pi$
$150$	−6.77803	−	3.01777i	−0.553424	−	0.246400i
$151$	−0.0880424	+	0.837668i	−0.00716479	+	0.0681684i	−0.997520	−	0.0703828i	$-0.977578\pi$
$151$	−0.0880424	+	0.837668i	−0.00716479	+	0.0681684i	0.990355	+	0.138551i	$0.0442446\pi$
$152$	12.6052	+	2.67931i	1.02241	+	0.217321i
$153$	2.07787			0.167986
$154$	15.4363	+	1.26626i	1.24389	+	0.102038i
$155$	−4.18163			−0.335877
$156$	1.04087	+	0.221243i	0.0833361	+	0.0177136i
$157$	1.58398	−	15.0705i	0.126415	−	1.20276i	−0.728888	−	0.684633i	$-0.759963\pi$
$157$	1.58398	−	15.0705i	0.126415	−	1.20276i	0.855303	−	0.518128i	$-0.173371\pi$
$158$	10.0294	+	4.46537i	0.797894	+	0.355245i
$159$	−7.50257	−	8.33245i	−0.594992	−	0.660806i
$160$	1.56606	−	4.81985i	0.123808	−	0.381043i
$161$	−7.11045	+	4.12599i	−0.560382	+	0.325173i
$162$	1.42794	+	1.03746i	0.112190	+	0.0815107i
$163$	−14.7479	−	3.13476i	−1.15514	−	0.245534i	−0.409776	−	0.912186i	$-0.634393\pi$
$163$	−14.7479	−	3.13476i	−1.15514	−	0.245534i	−0.745369	+	0.666652i	$0.767727\pi$
$164$	−3.07301	−	5.32261i	−0.239962	−	0.415626i
$165$	0.856219	−	2.83327i	0.0666566	−	0.220570i
$166$	12.8877	−	22.3221i	1.00028	−	1.73253i
$167$	2.63040	+	8.09555i	0.203547	+	0.626452i	0.999770	+	0.0214493i	$0.00682805\pi$
$167$	2.63040	+	8.09555i	0.203547	+	0.626452i	−0.796223	+	0.605003i	$0.793172\pi$
$168$	−3.92618	+	1.28520i	−0.302911	+	0.0991550i
$169$	9.78082	−	7.10618i	0.752370	−	0.546629i
$170$	−2.19004	−	2.43229i	−0.167969	−	0.186548i
$171$	8.07279	−	1.71593i	0.617342	−	0.131220i
$172$	−1.92615	−	0.857578i	−0.146868	−	0.0653897i
$173$	12.6307	−	5.62355i	0.960294	−	0.427550i	0.134120	−	0.990965i	$-0.457179\pi$
$173$	12.6307	−	5.62355i	0.960294	−	0.427550i	0.826174	+	0.563415i	$0.190513\pi$
$174$	−1.09077	−	3.35706i	−0.0826914	−	0.254498i
$175$	6.51744	−	9.01188i	0.492672	−	0.681234i
$176$	−16.2452	−	3.10332i	−1.22453	−	0.233922i
$177$	0.420945	−	0.729099i	0.0316402	−	0.0548024i
$178$	10.4510	−	11.6070i	0.783335	−	0.869982i
$179$	−0.885950	+	8.42925i	−0.0662190	+	0.630032i	0.910203	+	0.414162i	$0.135925\pi$
$179$	−0.885950	+	8.42925i	−0.0662190	+	0.630032i	−0.976422	+	0.215870i	$0.930741\pi$
$180$	−0.104044	−	0.989909i	−0.00775495	−	0.0737835i
$181$	0.0725069	−	0.223153i	0.00538939	−	0.0165868i	−0.948326	−	0.317299i	$-0.897224\pi$
$181$	0.0725069	−	0.223153i	0.00538939	−	0.0165868i	0.953715	+	0.300712i	$0.0972242\pi$
$182$	−1.80325	+	4.07412i	−0.133666	+	0.301994i
$183$	−0.946885	+	0.687952i	−0.0699957	+	0.0508549i
$184$	4.43223	−	1.97335i	0.326748	−	0.145478i
$185$	−6.00036	+	6.66408i	−0.441155	+	0.489953i
$186$	4.13523	+	7.16243i	0.303210	+	0.525175i
$187$	−4.50442	+	5.21568i	−0.329396	+	0.381408i
$188$	3.80331			0.277385
$189$	−1.96230	+	1.77465i	−0.142736	+	0.129087i
$190$	−10.5172	−	7.64119i	−0.762998	−	0.554350i
$191$	−0.422764	−	4.02233i	−0.0305902	−	0.291046i	−0.999113	−	0.0421195i	$-0.986589\pi$
$191$	−0.422764	−	4.02233i	−0.0305902	−	0.291046i	0.968522	−	0.248926i	$-0.0800777\pi$
$192$	−0.0488366	+	0.0103805i	−0.00352448	+	0.000749152i
$193$	−5.52917	+	1.17526i	−0.397999	+	0.0845972i	−0.402563	−	0.915392i	$-0.631881\pi$
$193$	−5.52917	+	1.17526i	−0.397999	+	0.0845972i	0.00456414	+	0.999990i	$0.498547\pi$
$194$	3.36961	+	32.0597i	0.241924	+	2.30175i
$195$	0.688821	+	0.500458i	0.0493275	+	0.0358385i
$196$	0.850068	+	7.76104i	0.0607191	+	0.554360i
$197$	−10.5753			−0.753459			−0.376729	−	0.926323i	$-0.622951\pi$
$197$	−10.5753			−0.753459			−0.376729	+	0.926323i	$0.622951\pi$
$198$	−5.69964	+	1.33528i	−0.405056	+	0.0948939i
$199$	−1.81898	−	3.15056i	−0.128944	−	0.223338i	0.794324	−	0.607495i	$-0.207825\pi$
$199$	−1.81898	−	3.15056i	−0.128944	−	0.223338i	−0.923268	+	0.384157i	$0.874492\pi$
$200$	−4.39193	+	4.87773i	−0.310556	+	0.344908i
$201$	−11.3098	+	5.03545i	−0.797732	+	0.355173i
$202$	−18.3736	+	13.3492i	−1.29276	+	0.939244i
$203$	5.26092	−	0.564585i	0.369244	−	0.0396261i
$204$	−0.716165	+	2.20413i	−0.0501416	+	0.154320i
$205$	−0.514028	−	4.89065i	−0.0359012	−	0.341577i
$206$	0.436117	−	4.14938i	0.0303857	−	0.289101i
$207$	2.07911	−	2.30909i	0.144508	−	0.160493i
$208$	2.37882	−	4.12024i	0.164942	−	0.285688i
$209$	−13.1931	+	23.9833i	−0.912584	+	1.65896i
$210$	4.14558	+	0.426550i	0.286072	+	0.0294348i
$211$	−1.85315	−	5.70342i	−0.127576	−	0.392639i	0.866785	−	0.498681i	$-0.166182\pi$
$211$	−1.85315	−	5.70342i	−0.127576	−	0.392639i	−0.994362	+	0.106042i	$0.966182\pi$
$212$	11.4246	−	5.08656i	0.784644	−	0.349346i
$213$	−10.7038	−	4.76566i	−0.733416	−	0.326538i
$214$	−20.3033	+	4.31560i	−1.38791	+	0.295008i
$215$	−1.12883	−	1.25369i	−0.0769857	−	0.0855012i
$216$	1.26323	−	0.917790i	0.0859519	−	0.0624477i
$217$	−11.7821	+	3.85674i	−0.799819	+	0.261813i
$218$	4.24451	+	13.0633i	0.287474	+	0.884755i
$219$	4.76970	−	8.26137i	0.322307	−	0.558251i
$220$	2.71032	+	1.88477i	0.182730	+	0.127071i
$221$	−0.991217	−	1.71684i	−0.0666765	−	0.115487i
$222$	17.3482	+	3.68748i	1.16434	+	0.247487i
$223$	−21.2601	−	15.4463i	−1.42368	−	1.03436i	−0.991151	−	0.132742i	$-0.957622\pi$
$223$	−21.2601	−	15.4463i	−1.42368	−	1.03436i	−0.432528	−	0.901621i	$-0.642378\pi$
$224$	−0.0328705	−	15.0247i	−0.00219625	−	1.00388i
$225$	−1.29898	+	3.99785i	−0.0865986	+	0.266523i
$226$	9.53634	+	10.5912i	0.634348	+	0.704515i
$227$	−11.5024	−	5.12119i	−0.763439	−	0.339905i	−0.0121918	−	0.999926i	$-0.503881\pi$
$227$	−11.5024	−	5.12119i	−0.763439	−	0.339905i	−0.751247	+	0.660021i	$0.770548\pi$
$228$	−0.962200	+	9.15472i	−0.0637233	+	0.606286i
$229$	−3.90295	−	0.829598i	−0.257914	−	0.0548214i	0.0771397	−	0.997020i	$-0.475421\pi$
$229$	−3.90295	−	0.829598i	−0.257914	−	0.0548214i	−0.335054	+	0.942199i	$0.608755\pi$
$230$	−4.89429			−0.322720
$231$	−0.200682	−	8.77267i	−0.0132039	−	0.577199i
$232$	−3.12265			−0.205012
$233$	−10.4074	−	2.21216i	−0.681812	−	0.144924i	−0.146030	−	0.989280i	$-0.546650\pi$
$233$	−10.4074	−	2.21216i	−0.681812	−	0.144924i	−0.535782	+	0.844357i	$0.679983\pi$
$234$	0.176022	−	1.67474i	0.0115069	−	0.109481i
$235$	2.78003	+	1.23775i	0.181349	+	0.0807419i
$236$	0.628316	+	0.697815i	0.0408999	+	0.0454239i
$237$	1.92209	−	5.91557i	0.124853	−	0.384258i
$238$	−8.41394	−	4.83328i	−0.545395	−	0.313295i
$239$	2.20565	+	1.60250i	0.142672	+	0.103657i	0.656832	−	0.754037i	$-0.271896\pi$
$239$	2.20565	+	1.60250i	0.142672	+	0.103657i	−0.514160	+	0.857694i	$0.671896\pi$
$240$	−4.35298	−	0.925254i	−0.280984	−	0.0597249i
$241$	10.6071	+	18.3720i	0.683264	+	1.18345i	0.973979	+	0.226638i	$0.0727734\pi$
$241$	10.6071	+	18.3720i	0.683264	+	1.18345i	−0.290715	+	0.956810i	$0.593893\pi$
$242$	9.00402	−	17.2013i	0.578800	−	1.10574i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.403398	−	1.24153i	−0.0258249	−	0.0794808i
$245$	−1.90440	+	5.94958i	−0.121667	+	0.380105i
$246$	−7.86853	+	5.71682i	−0.501679	+	0.364491i
$247$	−5.26878	−	5.85157i	−0.335244	−	0.372327i
$248$	7.15657	−	1.52118i	0.454443	−	0.0965948i
$249$	−13.3408	−	5.93969i	−0.845436	−	0.376413i
$250$	13.2437	−	5.89649i	0.837607	−	0.372927i
$251$	−5.39219	−	16.5954i	−0.340352	−	1.04750i	−0.964025	−	0.265810i	$-0.914361\pi$
$251$	−5.39219	−	16.5954i	−0.340352	−	1.04750i	0.623674	−	0.781685i	$-0.285639\pi$
$252$	−1.20615	−	2.69319i	−0.0759803	−	0.169655i
$253$	1.28895	+	10.2244i	0.0810355	+	0.642805i
$254$	−8.20436	+	14.2104i	−0.514787	+	0.891637i
$255$	−1.24079	+	1.37804i	−0.0777015	+	0.0862962i
$256$	−2.08962	+	19.8814i	−0.130601	+	1.24259i
$257$	−2.45643	−	23.3714i	−0.153228	−	1.45787i	−0.753170	−	0.657825i	$-0.771476\pi$
$257$	−2.45643	−	23.3714i	−0.153228	−	1.45787i	0.599942	−	0.800043i	$-0.295190\pi$
$258$	−1.03106	+	3.17328i	−0.0641911	+	0.197560i
$259$	−10.7602	+	24.3107i	−0.668604	+	1.51060i
$260$	−0.768277	+	0.558186i	−0.0476465	+	0.0346172i
$261$	−1.82696	+	0.813416i	−0.113086	+	0.0503492i
$262$	−6.58247	+	7.31057i	−0.406666	+	0.451649i
$263$	7.81691	+	13.5393i	0.482011	+	0.834868i	0.999787	−	0.0206486i	$-0.00657313\pi$
$263$	7.81691	+	13.5393i	0.482011	+	0.834868i	−0.517776	+	0.855516i	$0.673240\pi$
$264$	−0.434684	+	5.16043i	−0.0267529	+	0.317602i
$265$	10.0062			0.614675
$266$	−36.6805	−	11.8296i	−2.24903	−	0.725318i
$267$	−7.15898	−	5.20130i	−0.438122	−	0.318315i
$268$	−1.44335	−	13.7325i	−0.0881665	−	0.838849i
$269$	−3.03421	+	0.644942i	−0.184999	+	0.0393228i	−0.299480	−	0.954103i	$-0.596813\pi$
$269$	−3.03421	+	0.644942i	−0.184999	+	0.0393228i	0.114480	+	0.993426i	$0.463480\pi$
$270$	−1.54073	+	0.327493i	−0.0937660	+	0.0199306i
$271$	0.0745187	+	0.708998i	0.00452669	+	0.0430686i	0.996552	−	0.0829697i	$-0.0264405\pi$
$271$	0.0745187	+	0.708998i	0.00452669	+	0.0430686i	−0.992025	+	0.126038i	$0.959774\pi$
$272$	8.38281	+	6.09046i	0.508282	+	0.369289i
$273$	2.40238	+	0.774775i	0.145399	+	0.0468915i
$274$	3.68158			0.222413
$275$	−7.21909	−	11.9271i	−0.435327	−	0.719233i
$276$	1.73280	+	3.00130i	0.104302	+	0.180657i
$277$	11.1544	−	12.3883i	0.670205	−	0.744338i	−0.308135	−	0.951343i	$-0.599705\pi$
$277$	11.1544	−	12.3883i	0.670205	−	0.744338i	0.978340	+	0.207005i	$0.0663716\pi$
$278$	1.03108	−	0.459068i	0.0618403	−	0.0275331i
$279$	3.79083	−	2.75420i	0.226951	−	0.164889i
$280$	1.49216	−	3.37128i	0.0891737	−	0.201473i
$281$	−8.92709	+	27.4748i	−0.532546	+	1.63901i	0.216347	+	0.976316i	$0.430586\pi$
$281$	−8.92709	+	27.4748i	−0.532546	+	1.63901i	−0.748893	+	0.662691i	$0.769414\pi$
$282$	−0.629127	−	5.98575i	−0.0374640	−	0.356446i
$283$	−1.39119	+	13.2363i	−0.0826978	+	0.786817i	0.872053	+	0.489411i	$0.162788\pi$
$283$	−1.39119	+	13.2363i	−0.0826978	+	0.786817i	−0.954751	+	0.297406i	$0.903878\pi$
$284$	8.74444	−	9.71169i	0.518887	−	0.576283i
$285$	−3.68264	+	6.37851i	−0.218141	+	0.377831i
$286$	3.82219	+	4.07234i	0.226011	+	0.240803i
$287$	−5.95899	−	13.3057i	−0.351748	−	0.785410i
$288$	1.75485	+	5.40088i	0.103406	+	0.318250i
$289$	−11.5860	+	5.15841i	−0.681529	+	0.303436i
$290$	2.87775	+	1.28125i	0.168987	+	0.0752379i
$291$	17.8647	−	3.79726i	1.04725	−	0.222599i
$292$	7.11940	+	7.90690i	0.416632	+	0.462716i
$293$	19.1870	−	13.9401i	1.12091	−	0.814392i	0.136567	−	0.990631i	$-0.456393\pi$
$293$	19.1870	−	13.9401i	1.12091	−	0.814392i	0.984347	+	0.176239i	$0.0563931\pi$
$294$	12.0739	−	2.62166i	0.704164	−	0.152898i
$295$	0.232171	+	0.714548i	0.0135175	+	0.0416026i
$296$	7.84498	−	13.5879i	0.455980	−	0.789781i
$297$	1.08991	+	3.13243i	0.0632432	+	0.181762i
$298$	10.9987	+	19.0503i	0.637138	+	1.10356i
$299$	−2.89969	−	0.616348i	−0.167693	−	0.0356443i
$300$	−3.79305	−	2.75582i	−0.218992	−	0.159107i
$301$	−4.33686	−	2.49125i	−0.249973	−	0.143593i
$302$	−0.459402	+	1.41390i	−0.0264356	+	0.0813605i
$303$	8.60980	+	9.56215i	0.494620	+	0.549331i
$304$	37.5978	+	16.7396i	2.15638	+	0.960083i
$305$	0.109180	−	1.03878i	0.00625163	−	0.0594803i
$306$	3.58738	+	0.762520i	0.205077	+	0.0435904i
$307$	−14.4775			−0.826273			−0.413136	−	0.910669i	$-0.635567\pi$
$307$	−14.4775			−0.826273			−0.413136	+	0.910669i	$0.635567\pi$
$308$	9.37488	+	2.81073i	0.534183	+	0.160156i
$309$	−2.36382			−0.134473
$310$	−7.21944	−	1.53454i	−0.410037	−	0.0871560i
$311$	2.62189	−	24.9456i	0.148674	−	1.41454i	−0.624838	−	0.780754i	$-0.714835\pi$
$311$	2.62189	−	24.9456i	0.148674	−	1.41454i	0.773512	−	0.633781i	$-0.218498\pi$
$312$	−1.36093	−	0.605923i	−0.0770472	−	0.0343036i
$313$	8.80699	+	9.78115i	0.497801	+	0.552863i	0.938719	−	0.344684i	$-0.112014\pi$
$313$	8.80699	+	9.78115i	0.497801	+	0.552863i	−0.440918	+	0.897547i	$0.645347\pi$
$314$	8.26515	−	25.4375i	0.466429	−	1.43552i
$315$	−0.00516557	−	2.36112i	−0.000291047	−	0.133034i
$316$	5.61254	+	4.07775i	0.315730	+	0.229391i
$317$	−24.5372	−	5.21554i	−1.37815	−	0.292934i	−0.541510	−	0.840694i	$-0.682147\pi$
$317$	−24.5372	−	5.21554i	−1.37815	−	0.292934i	−0.836635	+	0.547760i	$0.815481\pi$
$318$	−9.89515	−	17.1389i	−0.554893	−	0.961102i
$319$	1.91873	−	6.34919i	0.107429	−	0.355486i
$320$	0.0222782	−	0.0385870i	0.00124539	−	0.00215708i
$321$	3.63405	+	11.1845i	0.202833	+	0.624256i
$322$	−13.7901	+	4.51404i	−0.768490	+	0.251558i
$323$	13.8738	−	10.0799i	0.771960	−	0.560862i
$324$	0.746315	+	0.828867i	0.0414620	+	0.0460482i
$325$	3.92287	−	0.833832i	0.217602	−	0.0462527i
$326$	−24.3114	−	10.8241i	−1.34648	−	0.599493i
$327$	7.10922	−	3.16523i	0.393141	−	0.175037i
$328$	2.65882	+	8.18301i	0.146809	+	0.451831i
$329$	8.97455	+	0.923417i	0.494783	+	0.0509096i
$330$	2.51796	−	4.57734i	0.138609	−	0.251974i
$331$	−0.972470	+	1.68437i	−0.0534518	+	0.0925812i	−0.891513	−	0.452995i	$-0.850356\pi$
$331$	−0.972470	+	1.68437i	−0.0534518	+	0.0925812i	0.838061	+	0.545576i	$0.183689\pi$
$332$	10.8987	−	12.1042i	0.598141	−	0.664303i
$333$	1.05034	−	9.99336i	0.0575585	−	0.547633i
$334$	1.57046	+	14.9420i	0.0859319	+	0.817588i
$335$	3.41411	−	10.5075i	0.186532	−	0.574088i
$336$	−13.1182	+	1.40780i	−0.715658	+	0.0768020i
$337$	23.7354	−	17.2448i	1.29295	−	0.939384i	0.293090	−	0.956085i	$-0.405316\pi$
$337$	23.7354	−	17.2448i	1.29295	−	0.939384i	0.999861	+	0.0167013i	$0.00531642\pi$
$338$	19.4940	−	8.67929i	1.06033	−	0.472091i
$339$	5.40292	−	6.00055i	0.293446	−	0.325905i
$340$	−1.03412	−	1.79114i	−0.0560829	−	0.0971384i
$341$	−1.30444	+	15.4859i	−0.0706395	+	0.838610i
$342$	14.5671			0.787698
$343$	0.121553	+	18.5199i	0.00656324	+	0.999978i
$344$	2.38798	+	1.73497i	0.128751	+	0.0935433i
$345$	0.289849	+	2.75773i	0.0156049	+	0.148471i
$346$	23.8701	−	5.07375i	1.28327	−	0.272767i
$347$	5.90189	−	1.25448i	0.316830	−	0.0673443i	−0.0467520	−	0.998907i	$-0.514887\pi$
$347$	5.90189	−	1.25448i	0.316830	−	0.0673443i	0.363582	+	0.931562i	$0.381554\pi$
$348$	−0.233155	−	2.21832i	−0.0124984	−	0.118915i
$349$	−8.83687	−	6.42036i	−0.473027	−	0.343674i	0.325593	−	0.945510i	$-0.394436\pi$
$349$	−8.83687	−	6.42036i	−0.473027	−	0.343674i	−0.798620	+	0.601836i	$0.794436\pi$
$350$	14.5592	−	13.1670i	0.778224	−	0.703805i
$351$	−0.954069			−0.0509244
$352$	−17.3609	−	7.30318i	−0.925341	−	0.389261i
$353$	15.8637	+	27.4767i	0.844338	+	1.46244i	0.886195	+	0.463313i	$0.153339\pi$
$353$	15.8637	+	27.4767i	0.844338	+	1.46244i	−0.0418568	+	0.999124i	$0.513327\pi$
$354$	0.994306	−	1.10429i	0.0528468	−	0.0586923i
$355$	9.55233	−	4.25297i	0.506985	−	0.225724i
$356$	7.98477	−	5.80128i	0.423192	−	0.307467i
$357$	−2.22506	+	5.02713i	−0.117762	+	0.266064i
$358$	−4.62286	+	14.2277i	−0.244326	+	0.751957i
$359$	3.23228	+	30.7531i	0.170593	+	1.62309i	0.660162	+	0.751123i	$0.270487\pi$
$359$	3.23228	+	30.7531i	0.170593	+	1.62309i	−0.489569	+	0.871965i	$0.662846\pi$
$360$	−0.145656	+	1.38582i	−0.00767675	+	0.0730394i
$361$	32.8639	−	36.4991i	1.72968	−	1.92101i
$362$	0.207071	−	0.358658i	0.0108834	−	0.0188507i
$363$	−10.2254	−	4.05469i	−0.536696	−	0.212816i
$364$	−1.64986	+	2.28132i	−0.0864763	+	0.119574i
$365$	2.63071	+	8.09649i	0.137698	+	0.423790i
$366$	−1.88722	+	0.840245i	−0.0986467	+	0.0439203i
$367$	12.5088	+	5.56929i	0.652956	+	0.290715i	0.706354	−	0.707859i	$-0.250339\pi$
$367$	12.5088	+	5.56929i	0.652956	+	0.290715i	−0.0533985	+	0.998573i	$0.517005\pi$
$368$	15.1560	−	3.22151i	0.790061	−	0.167933i
$369$	3.68717	+	4.09502i	0.191946	+	0.213178i
$370$	−12.8049	+	9.30334i	−0.665697	+	0.483657i
$371$	28.1932	−	9.22877i	1.46372	−	0.479134i
$372$	1.61499	+	4.97043i	0.0837334	+	0.257705i
$373$	1.29832	−	2.24876i	0.0672245	−	0.116436i	−0.830454	−	0.557087i	$-0.811919\pi$
$373$	1.29832	−	2.24876i	0.0672245	−	0.116436i	0.897679	+	0.440651i	$0.145252\pi$
$374$	−9.69073	+	7.35170i	−0.501096	+	0.380147i
$375$	−4.10673	−	7.11307i	−0.212071	−	0.367317i
$376$	−5.20810	−	1.10702i	−0.268587	−	0.0570900i
$377$	1.54361	+	1.12150i	0.0794998	+	0.0577600i
$378$	−4.03909	+	2.34376i	−0.207748	+	0.120550i
$379$	−3.92265	+	12.0727i	−0.201493	+	0.620131i	0.798346	+	0.602199i	$0.205708\pi$
$379$	−3.92265	+	12.0727i	−0.201493	+	0.620131i	−0.999839	+	0.0179326i	$0.994292\pi$
$380$	−5.49682	−	6.10483i	−0.281981	−	0.313171i
$381$	8.49281	+	3.78124i	0.435100	+	0.193719i
$382$	0.746194	−	7.09956i	0.0381786	−	0.363245i
$383$	−28.7980	−	6.12121i	−1.47151	−	0.312779i	−0.598753	−	0.800933i	$-0.704337\pi$
$383$	−28.7980	−	6.12121i	−1.47151	−	0.312779i	−0.872757	+	0.488154i	$0.837670\pi$
$384$	11.2695			0.575095
$385$	5.93785	+	5.10547i	0.302621	+	0.260199i
$386$	−9.97722			−0.507827
$387$	1.84907	+	0.393032i	0.0939935	+	0.0199789i
$388$	−2.12930	+	20.2590i	−0.108099	+	1.02849i
$389$	−16.5120	−	7.35163i	−0.837193	−	0.372742i	−0.0570713	−	0.998370i	$-0.518176\pi$
$389$	−16.5120	−	7.35163i	−0.837193	−	0.372742i	−0.780122	+	0.625628i	$0.784843\pi$
$390$	1.00557	+	1.11680i	0.0509191	+	0.0565514i
$391$	1.99512	−	6.14034i	0.100897	−	0.310530i
$392$	1.09493	−	10.8751i	0.0553023	−	0.549275i
$393$	4.50902	+	3.27599i	0.227450	+	0.165252i
$394$	−18.2579	−	3.88083i	−0.919819	−	0.195514i
$395$	2.77543	+	4.80718i	0.139647	+	0.241875i
$396$	−3.69841	+	0.0765091i	−0.185852	+	0.00384473i
$397$	2.38915	−	4.13812i	0.119908	−	0.207686i	−0.799823	−	0.600236i	$-0.795073\pi$
$397$	2.38915	−	4.13812i	0.119908	−	0.207686i	0.919731	+	0.392549i	$0.128407\pi$
$398$	−1.98424	−	6.10685i	−0.0994608	−	0.306109i
$399$	−4.49317	+	21.3685i	−0.224940	+	1.06976i
$400$	−16.9586	+	12.3212i	−0.847931	+	0.616058i
$401$	7.32003	+	8.12972i	0.365545	+	0.405979i	0.897657	−	0.440695i	$-0.145268\pi$
$401$	7.32003	+	8.12972i	0.365545	+	0.405979i	−0.532112	+	0.846674i	$0.678601\pi$
$402$	−21.3739	+	4.54315i	−1.06603	+	0.226592i
$403$	−4.08400	−	1.81831i	−0.203439	−	0.0905767i
$404$	−13.1106	+	5.83723i	−0.652278	+	0.290413i
$405$	0.275773	+	0.848742i	0.0137033	+	0.0421743i
$406$	9.28998	+	0.955873i	0.461054	+	0.0474392i
$407$	22.8074	+	24.3001i	1.13052	+	1.20451i
$408$	1.62223	−	2.80979i	0.0803126	−	0.139105i
$409$	−5.51680	+	6.12703i	−0.272788	+	0.302962i	−0.863936	−	0.503601i	$-0.832008\pi$
$409$	−5.51680	+	6.12703i	−0.272788	+	0.302962i	0.591148	+	0.806563i	$0.298675\pi$
$410$	0.907277	−	8.63216i	0.0448072	−	0.426312i
$411$	−0.218030	−	2.07441i	−0.0107546	−	0.102323i
$412$	0.814721	−	2.50745i	0.0401384	−	0.123533i
$413$	1.31319	+	1.79916i	0.0646179	+	0.0885310i
$414$	4.43689	−	3.22359i	0.218061	−	0.158431i
$415$	11.9056	−	5.30070i	0.584421	−	0.260201i
$416$	3.62534	−	4.02635i	0.177747	−	0.197408i
$417$	−0.319728	−	0.553785i	−0.0156571	−	0.0271190i
$418$	−31.5786	+	36.5649i	−1.54456	+	1.78845i
$419$	5.64738			0.275892			0.137946	−	0.990440i	$-0.455950\pi$
$419$	5.64738			0.275892			0.137946	+	0.990440i	$0.455950\pi$
$420$	2.50636	+	0.808308i	0.122298	+	0.0394414i
$421$	5.19620	+	3.77526i	0.253247	+	0.183995i	0.707165	−	0.707049i	$-0.249974\pi$
$421$	5.19620	+	3.77526i	0.253247	+	0.183995i	−0.453918	+	0.891044i	$0.649974\pi$
$422$	−1.10641	−	10.5268i	−0.0538593	−	0.512437i
$423$	−3.33545	+	0.708972i	−0.162175	+	0.0344714i
$424$	−17.1249	+	3.64001i	−0.831659	+	0.176775i
$425$	0.913006	+	8.68667i	0.0442873	+	0.421365i
$426$	−16.7310	−	12.1558i	−0.810618	−	0.588948i
$427$	−0.650449	−	3.02754i	−0.0314774	−	0.146513i
$428$	−13.1166			−0.634013
$429$	2.06823	−	2.39481i	0.0998552	−	0.115623i
$430$	−1.48882	−	2.57871i	−0.0717972	−	0.124356i
$431$	−12.2009	+	13.5505i	−0.587696	+	0.652702i	−0.961500	−	0.274805i	$-0.911387\pi$
$431$	−12.2009	+	13.5505i	−0.587696	+	0.652702i	0.373804	+	0.927508i	$0.378053\pi$
$432$	4.55557	−	2.02827i	0.219180	−	0.0975852i
$433$	29.3416	−	21.3179i	1.41007	−	1.02447i	0.416754	−	0.909019i	$-0.363168\pi$
$433$	29.3416	−	21.3179i	1.41007	−	1.02447i	0.993313	−	0.115454i	$-0.0368324\pi$
$434$	−21.7567	+	2.33485i	−1.04435	+	0.112076i
$435$	0.551507	−	1.69736i	0.0264427	−	0.0813824i
$436$	0.907272	+	8.63212i	0.0434505	+	0.413403i
$437$	2.68053	−	25.5036i	0.128227	−	1.22000i
$438$	11.2664	−	12.5126i	0.538330	−	0.597876i
$439$	−10.6811	+	18.5002i	−0.509782	+	0.882968i	0.490154	+	0.871636i	$0.336940\pi$
$439$	−10.6811	+	18.5002i	−0.509782	+	0.882968i	−0.999936	+	0.0113320i	$0.996393\pi$
$440$	−3.16281	−	3.36981i	−0.150781	−	0.160649i
$441$	−2.19223	−	6.64787i	−0.104392	−	0.316565i
$442$	−1.08127	−	3.32781i	−0.0514308	−	0.158288i
$443$	31.2787	−	13.9262i	1.48609	−	0.661652i	0.506427	−	0.862283i	$-0.330966\pi$
$443$	31.2787	−	13.9262i	1.48609	−	0.661652i	0.979667	+	0.200631i	$0.0642993\pi$
$444$	10.2386	+	4.55850i	0.485900	+	0.216337i
$445$	7.72444	−	1.64188i	0.366174	−	0.0778326i
$446$	−31.0364	−	34.4694i	−1.46962	−	1.63217i
$447$	10.0827	−	7.32549i	0.476894	−	0.346484i
$448$	0.0271816	−	0.129269i	0.00128421	−	0.00610740i
$449$	11.4288	+	35.1743i	0.539360	+	1.65998i	0.734035	+	0.679112i	$0.237635\pi$
$449$	11.4288	+	35.1743i	0.539360	+	1.65998i	−0.194675	+	0.980868i	$0.562365\pi$
$450$	−3.70974	+	6.42546i	−0.174879	+	0.302899i
$451$	−18.2720	+	0.377993i	−0.860394	+	0.0177990i
$452$	4.50297	+	7.79937i	0.211802	+	0.366851i
$453$	0.823876	+	0.175120i	0.0387091	+	0.00822787i
$454$	−17.9791	−	13.0626i	−0.843802	−	0.613058i
$455$	−1.94840	+	1.13060i	−0.0913425	+	0.0530034i
$456$	3.98223	−	12.2560i	0.186485	−	0.573942i
$457$	−16.6390	−	18.4794i	−0.778338	−	0.864432i	0.215359	−	0.976535i	$-0.430908\pi$
$457$	−16.6390	−	18.4794i	−0.778338	−	0.864432i	−0.993697	+	0.112103i	$0.964241\pi$
$458$	−6.43387	−	2.86454i	−0.300635	−	0.133851i
$459$	0.217197	−	2.06649i	0.0101379	−	0.0964555i
$460$	−3.02519	−	0.643024i	−0.141050	−	0.0299811i
$461$	−38.4862			−1.79248			−0.896239	−	0.443571i	$-0.853711\pi$
$461$	−38.4862			−1.79248			−0.896239	+	0.443571i	$0.853711\pi$
$462$	2.87285	−	15.2194i	0.133657	−	0.708068i
$463$	−6.22486			−0.289294			−0.144647	−	0.989483i	$-0.546205\pi$
$463$	−6.22486			−0.289294			−0.144647	+	0.989483i	$0.546205\pi$
$464$	−9.75476	−	2.07344i	−0.452853	−	0.0962569i
$465$	−0.437099	+	4.15872i	−0.0202700	+	0.192856i
$466$	−17.1562	−	7.63844i	−0.794747	−	0.353844i
$467$	6.35134	+	7.05388i	0.293905	+	0.326414i	0.871954	−	0.489587i	$-0.162853\pi$
$467$	6.35134	+	7.05388i	0.293905	+	0.326414i	−0.578049	+	0.816002i	$0.696186\pi$
$468$	0.328832	−	1.01204i	0.0152002	−	0.0467815i
$469$	−0.0716595	−	32.7547i	−0.00330893	−	1.51247i
$470$	4.34541	+	3.15713i	0.200439	+	0.145627i
$471$	−14.8224	−	3.15060i	−0.682981	−	0.145172i
$472$	−0.657280	−	1.13844i	−0.0302538	−	0.0524010i
$473$	−4.99497	+	3.78934i	−0.229669	+	0.174234i
$474$	5.48926	−	9.50768i	0.252130	−	0.436702i
$475$	10.7207	+	32.9948i	0.491898	+	1.51391i
$476$	−4.56569	−	4.09292i	−0.209268	−	0.187599i
$477$	−9.07103	+	6.59049i	−0.415334	+	0.301758i
$478$	3.21991	+	3.57607i	0.147275	+	0.163566i
$479$	7.45632	−	1.58489i	0.340688	−	0.0724154i	−0.0343907	−	0.999408i	$-0.510949\pi$
$479$	7.45632	−	1.58489i	0.340688	−	0.0724154i	0.375079	+	0.926993i	$0.377616\pi$
$480$	−4.62975	−	2.06130i	−0.211318	−	0.0940849i
$481$	−8.75804	+	3.89933i	−0.399332	+	0.177794i
$482$	11.5708	+	35.6112i	0.527035	+	1.62205i
$483$	3.36014	+	7.50278i	0.152892	+	0.341388i
$484$	7.82538	−	9.44925i	0.355699	−	0.429511i
$485$	−8.14950	+	14.1153i	−0.370050	+	0.640945i
$486$	1.18104	−	1.31168i	0.0535730	−	0.0594989i
$487$	−0.541314	+	5.15025i	−0.0245293	+	0.233380i	0.975388	+	0.220497i	$0.0707678\pi$
$487$	−0.541314	+	5.15025i	−0.0245293	+	0.233380i	−0.999917	+	0.0128837i	$0.995899\pi$
$488$	0.191029	+	1.81752i	0.00864746	+	0.0822751i
$489$	−4.65917	+	14.3394i	−0.210695	+	0.648452i
$490$	−5.47120	+	9.57289i	−0.247164	+	0.432459i
$491$	−32.8844	+	23.8919i	−1.48405	+	1.07823i	−0.507827	+	0.861459i	$0.669551\pi$
$491$	−32.8844	+	23.8919i	−1.48405	+	1.07823i	−0.976223	+	0.216767i	$0.930449\pi$
$492$	−5.61467	+	2.49981i	−0.253129	+	0.112700i
$493$	−2.78054	+	3.08810i	−0.125229	+	0.139081i
$494$	−6.94900	−	12.0360i	−0.312650	−	0.541526i
$495$	−2.72825	−	1.14769i	−0.122626	−	0.0515847i
$496$	23.3662			1.04918
$497$	22.9919	−	20.7933i	1.03133	−	0.932705i
$498$	−20.8527	−	15.1503i	−0.934430	−	0.678903i
$499$	0.163013	+	1.55096i	0.00729745	+	0.0694306i	0.997565	−	0.0697495i	$-0.0222200\pi$
$499$	0.163013	+	1.55096i	0.00729745	+	0.0694306i	−0.990267	+	0.139180i	$0.955553\pi$
$500$	8.96071	−	1.90466i	0.400735	−	0.0851789i
$501$	8.32615	−	1.76978i	0.371985	−	0.0790678i
$502$	−3.21937	−	30.6302i	−0.143687	−	1.36709i
$503$	−26.4976	−	19.2517i	−1.18147	−	0.858390i	−0.189135	−	0.981951i	$-0.560568\pi$
$503$	−26.4976	−	19.2517i	−1.18147	−	0.858390i	−0.992337	+	0.123562i	$0.960568\pi$
$504$	0.867758	+	4.03901i	0.0386530	+	0.179912i
$505$	−11.4829			−0.510982
$506$	−1.52676	+	18.1252i	−0.0678726	+	0.805761i
$507$	−6.04488	−	10.4700i	−0.268462	−	0.464991i
$508$	−6.93815	+	7.70559i	−0.307830	+	0.341880i
$509$	−12.2485	+	5.45337i	−0.542904	+	0.241717i	−0.659818	−	0.751426i	$-0.729367\pi$
$509$	−12.2485	+	5.45337i	−0.542904	+	0.241717i	0.116914	+	0.993142i	$0.462700\pi$
$510$	−2.64789	+	1.92380i	−0.117250	+	0.0851874i
$511$	14.8797	+	20.3862i	0.658238	+	0.901832i
$512$	−3.93864	+	12.1219i	−0.174065	+	0.535717i
$513$	−0.862688	−	8.20793i	−0.0380886	−	0.362389i
$514$	4.33569	−	41.2514i	0.191239	−	1.81952i
$515$	1.41155	−	1.56768i	0.0622002	−	0.0690803i
$516$	−1.05422	+	1.82596i	−0.0464093	+	0.0803833i
$517$	5.45101	−	9.90925i	0.239735	−	0.435808i
$518$	−27.4984	+	38.0230i	−1.20821	+	1.67063i
$519$	−4.27247	−	13.1493i	−0.187541	−	0.577191i
$520$	1.21452	−	0.540738i	0.0532601	−	0.0237129i
$521$	5.42255	+	2.41428i	0.237566	+	0.105771i	0.522067	−	0.852905i	$-0.325161\pi$
$521$	5.42255	+	2.41428i	0.237566	+	0.105771i	−0.284501	+	0.958676i	$0.591828\pi$
$522$	−3.45269	+	0.733891i	−0.151120	+	0.0321215i
$523$	−15.6463	−	17.3770i	−0.684165	−	0.759842i	0.296607	−	0.955000i	$-0.404145\pi$
$523$	−15.6463	−	17.3770i	−0.684165	−	0.759842i	−0.980772	+	0.195158i	$0.937478\pi$
$524$	−5.02914	+	3.65388i	−0.219699	+	0.159621i
$525$	−8.28125	−	7.42373i	−0.361424	−	0.323998i
$526$	8.52709	+	26.2437i	0.371799	+	1.14428i
$527$	4.86816	−	8.43191i	0.212061	−	0.367300i
$528$	−4.78441	+	15.8319i	−0.208215	+	0.688993i
$529$	6.67270	+	11.5575i	0.290117	+	0.502498i
$530$	17.2753	+	3.67198i	0.750392	+	0.159501i
$531$	−0.681104	−	0.494851i	−0.0295574	−	0.0214747i
$532$	−21.1182	−	12.1311i	−0.915592	−	0.525950i
$533$	1.62459	−	4.99998i	0.0703689	−	0.216573i
$534$	−10.4510	−	11.6070i	−0.452259	−	0.502284i
$535$	−9.58757	−	4.26866i	−0.414507	−	0.184550i
$536$	−2.02062	+	19.2249i	−0.0872774	+	0.830389i
$537$	8.29046	+	1.76219i	0.357760	+	0.0760442i
$538$	−5.47514			−0.236050
$539$	21.4392	+	8.90855i	0.923450	+	0.383718i
$540$	−0.995362			−0.0428335
$541$	40.8334	+	8.67941i	1.75556	+	0.373157i	0.969520	−	0.245013i	$-0.0787921\pi$
$541$	40.8334	+	8.67941i	1.75556	+	0.373157i	0.786045	+	0.618170i	$0.212125\pi$
$542$	−0.131528	+	1.25141i	−0.00564962	+	0.0537525i
$543$	−0.214352	−	0.0954355i	−0.00919871	−	0.00409553i
$544$	7.89565	+	8.76901i	0.338523	+	0.375968i
$545$	−2.14607	+	6.60492i	−0.0919274	+	0.282924i
$546$	3.86331	+	2.21923i	0.165335	+	0.0949743i
$547$	−3.90108	−	2.83430i	−0.166798	−	0.121186i	0.501255	−	0.865300i	$-0.332872\pi$
$547$	−3.90108	−	2.83430i	−0.166798	−	0.121186i	−0.668053	+	0.744114i	$0.732872\pi$
$548$	2.27561	+	0.483695i	0.0972091	+	0.0206624i
$549$	0.585207	+	1.01361i	0.0249760	+	0.0432597i
$550$	−8.08659	−	23.2410i	−0.344813	−	0.990998i
$551$	−8.25256	+	14.2939i	−0.351571	+	0.608939i
$552$	−1.49925	−	4.61422i	−0.0638123	−	0.196394i
$553$	12.2537	+	10.9848i	0.521079	+	0.467122i
$554$	23.8039	−	17.2945i	1.01133	−	0.734774i
$555$	6.00036	+	6.66408i	0.254701	+	0.282874i
$556$	0.697632	−	0.148286i	0.0295862	−	0.00628874i
$557$	3.12717	+	1.39231i	0.132503	+	0.0589940i	0.471917	−	0.881643i	$-0.343562\pi$
$557$	3.12717	+	1.39231i	0.132503	+	0.0589940i	−0.339414	+	0.940637i	$0.610229\pi$
$558$	7.55544	−	3.36390i	0.319847	−	0.142405i
$559$	−0.557328	−	1.71528i	−0.0235725	−	0.0725486i
$560$	6.89984	−	9.54064i	0.291572	−	0.403166i
$561$	4.71627	+	5.02493i	0.199121	+	0.212153i
$562$	−25.4948	+	44.1582i	−1.07543	+	1.86270i
$563$	27.2806	−	30.2982i	1.14974	−	1.27692i	0.194559	−	0.980891i	$-0.437672\pi$
$563$	27.2806	−	30.2982i	1.14974	−	1.27692i	0.955180	−	0.296024i	$-0.0956610\pi$
$564$	0.397554	−	3.78248i	0.0167401	−	0.159271i
$565$	0.753219	+	7.16640i	0.0316882	+	0.301493i
$566$	−7.25920	+	22.3415i	−0.305127	+	0.939084i
$567$	1.55981	+	2.13705i	0.0655060	+	0.0897477i
$568$	−14.8010	+	10.7536i	−0.621038	+	0.451210i
$569$	−0.998195	+	0.444425i	−0.0418465	+	0.0186313i	−0.427553	−	0.903990i	$-0.640624\pi$
$569$	−0.998195	+	0.444425i	−0.0418465	+	0.0186313i	0.385707	+	0.922621i	$0.373958\pi$
$570$	−8.69868	+	9.66086i	−0.364347	+	0.404649i
$571$	15.6656	+	27.1335i	0.655583	+	1.13550i	0.981747	+	0.190190i	$0.0609103\pi$
$571$	15.6656	+	27.1335i	0.655583	+	1.13550i	−0.326164	+	0.945313i	$0.605756\pi$
$572$	1.82748	+	3.01930i	0.0764109	+	0.126243i
$573$	−4.04449			−0.168961
$574$	−5.40518	−	25.1586i	−0.225608	−	1.05010i
$575$	10.5668	+	7.67725i	0.440667	+	0.320164i
$576$	0.00521886	+	0.0496542i	0.000217453	+	0.00206892i
$577$	−23.0505	+	4.89953i	−0.959604	+	0.203970i	−0.660982	−	0.750402i	$-0.729860\pi$
$577$	−23.0505	+	4.89953i	−0.959604	+	0.203970i	−0.298621	+	0.954372i	$0.596527\pi$
$578$	−21.8958	+	4.65410i	−0.910745	+	0.193585i
$579$	0.590868	+	5.62173i	0.0245556	+	0.233631i
$580$	1.61041	+	1.17003i	0.0668688	+	0.0485831i
$581$	28.6560	−	25.9157i	1.18885	−	1.07517i
$582$	32.2363			1.33624
$583$	3.12139	−	37.0561i	0.129275	−	1.53471i
$584$	−7.44759	−	12.8996i	−0.308183	−	0.533789i
$585$	0.569718	−	0.632736i	0.0235549	−	0.0261604i
$586$	38.2413	−	17.0261i	1.57973	−	0.703342i
$587$	−20.2403	+	14.7054i	−0.835405	+	0.606957i	−0.921083	−	0.389366i	$-0.872694\pi$
$587$	−20.2403	+	14.7054i	−0.835405	+	0.606957i	0.0856783	+	0.996323i	$0.472694\pi$
$588$	7.80738	−	0.0341616i	0.321971	−	0.00140880i
$589$	11.9503	−	36.7792i	0.492403	−	1.51546i
$590$	0.138616	+	1.31884i	0.00570673	+	0.0542959i
$591$	−1.10542	+	10.5174i	−0.0454709	+	0.432626i
$592$	33.5290	−	37.2377i	1.37803	−	1.53046i
$593$	7.78274	−	13.4801i	0.319599	−	0.553561i	−0.660805	−	0.750557i	$-0.729785\pi$
$593$	7.78274	−	13.4801i	0.319599	−	0.553561i	0.980404	+	0.196996i	$0.0631185\pi$
$594$	0.732187	+	5.80799i	0.0300420	+	0.238305i
$595$	−2.00530	−	4.47758i	−0.0822091	−	0.183563i
$596$	4.29548	+	13.2201i	0.175950	+	0.541518i
$597$	−3.32344	+	1.47969i	−0.136019	+	0.0605597i
$598$	−4.78003	−	2.12821i	−0.195470	−	0.0870288i
$599$	24.6567	−	5.24094i	1.00745	−	0.214139i	0.325500	−	0.945542i	$-0.394467\pi$
$599$	24.6567	−	5.24094i	1.00745	−	0.214139i	0.681945	+	0.731403i	$0.261134\pi$
$600$	4.39193	+	4.87773i	0.179300	+	0.199133i
$601$	−30.6811	+	22.2912i	−1.25151	+	0.909275i	−0.998309	−	0.0581384i	$-0.981484\pi$
$601$	−30.6811	+	22.2912i	−1.25151	+	0.909275i	−0.253201	+	0.967414i	$0.581484\pi$
$602$	−6.57322	−	5.89257i	−0.267905	−	0.240163i
$603$	3.82567	+	11.7742i	0.155793	+	0.479483i
$604$	−0.469720	+	0.813579i	−0.0191126	+	0.0331040i
$605$	8.79513	−	4.36025i	0.357573	−	0.177269i
$606$	11.3555	+	19.6683i	0.461285	+	0.798969i
$607$	36.3067	+	7.71723i	1.47364	+	0.313233i	0.873565	−	0.486708i	$-0.161802\pi$
$607$	36.3067	+	7.71723i	1.47364	+	0.313233i	0.600079	+	0.799941i	$0.295136\pi$
$608$	37.9171	+	27.5484i	1.53774	+	1.11723i
$609$	−0.0115757	−	5.29112i	−0.000469072	−	0.214407i
$610$	0.569698	−	1.75335i	0.0230664	−	0.0709911i
$611$	2.17691	+	2.41771i	0.0880684	+	0.0978099i
$612$	2.11719	+	0.942635i	0.0855825	+	0.0381038i
$613$	2.76999	−	26.3547i	0.111879	−	1.06446i	−0.784184	−	0.620529i	$-0.786918\pi$
$613$	2.76999	−	26.3547i	0.111879	−	1.06446i	0.896062	−	0.443928i	$-0.146415\pi$
$614$	−24.9948	−	5.31282i	−1.00871	−	0.214408i
$615$	−4.91758			−0.198296
$616$	−12.0195	−	6.57762i	−0.484278	−	0.265020i
$617$	−2.98017			−0.119977			−0.0599886	−	0.998199i	$-0.519106\pi$
$617$	−2.98017			−0.119977			−0.0599886	+	0.998199i	$0.519106\pi$
$618$	−4.08106	−	0.867456i	−0.164164	−	0.0348942i
$619$	0.196869	−	1.87309i	0.00791285	−	0.0752858i	−0.989853	−	0.142096i	$-0.954616\pi$
$619$	0.196869	−	1.87309i	0.00791285	−	0.0752858i	0.997766	+	0.0668107i	$0.0212824\pi$
$620$	−4.26076	−	1.89701i	−0.171116	−	0.0761859i
$621$	−2.07911	−	2.30909i	−0.0834319	−	0.0926606i
$622$	13.6809	−	42.1056i	0.548555	−	1.68828i
$623$	20.2499	−	11.7504i	0.811296	−	0.470771i
$624$	−3.84902	−	2.79648i	−0.154084	−	0.111949i
$625$	−13.3889	−	2.84591i	−0.535558	−	0.113836i
$626$	11.6156	+	20.1187i	0.464251	+	0.804106i
$627$	22.4729	+	15.6277i	0.897482	+	0.624112i
$628$	8.45077	−	14.6372i	0.337222	−	0.584086i
$629$	−6.45206	−	19.8574i	−0.257261	−	0.791767i
$630$	0.857544	−	4.07828i	0.0341654	−	0.162483i
$631$	4.01811	−	2.91933i	0.159959	−	0.116217i	−0.504927	−	0.863162i	$-0.668480\pi$
$631$	4.01811	−	2.91933i	0.159959	−	0.116217i	0.664885	+	0.746946i	$0.268480\pi$
$632$	−6.49869	−	7.21753i	−0.258504	−	0.287098i
$633$	−5.86588	+	1.24683i	−0.233148	+	0.0495571i
$634$	−40.4487	−	18.0089i	−1.60642	−	0.715225i
$635$	−7.57915	+	3.37446i	−0.300769	+	0.133911i
$636$	−3.86450	−	11.8937i	−0.153237	−	0.471616i
$637$	−4.44702	+	4.98258i	−0.176197	+	0.197417i
$638$	5.64260	−	10.2575i	0.223393	−	0.406100i
$639$	−5.85841	+	10.1471i	−0.231755	+	0.401412i
$640$	−6.72954	+	7.47391i	−0.266008	+	0.295432i
$641$	−4.44877	+	42.3273i	−0.175716	+	1.67183i	0.450958	+	0.892545i	$0.351082\pi$
$641$	−4.44877	+	42.3273i	−0.175716	+	1.67183i	−0.626674	+	0.779281i	$0.715584\pi$
$642$	2.16969	+	20.6432i	0.0856307	+	0.814722i
$643$	14.6436	−	45.0684i	0.577488	−	1.77732i	−0.0500608	−	0.998746i	$-0.515942\pi$
$643$	14.6436	−	45.0684i	0.577488	−	1.77732i	0.627548	−	0.778578i	$-0.284058\pi$
$644$	−9.11677	+	0.978382i	−0.359251	+	0.0385536i
$645$	−1.36482	+	0.991601i	−0.0537398	+	0.0390442i
$646$	27.6517	−	12.3113i	1.08794	−	0.484383i
$647$	−20.9104	+	23.2233i	−0.822071	+	0.913002i	−0.997441	−	0.0715005i	$-0.977221\pi$
$647$	−20.9104	+	23.2233i	−0.822071	+	0.913002i	0.175370	+	0.984503i	$0.443888\pi$
$648$	−0.780719	−	1.35224i	−0.0306695	−	0.0531212i
$649$	2.71863	−	0.636903i	0.106715	−	0.0250006i
$650$	7.07869			0.277649
$651$	2.60406	+	12.1207i	0.102061	+	0.475046i
$652$	−13.6049	−	9.88453i	−0.532809	−	0.387108i
$653$	0.534375	+	5.08424i	0.0209117	+	0.198961i	0.999990	−	0.00452346i	$-0.00143987\pi$
$653$	0.534375	+	5.08424i	0.0209117	+	0.198961i	−0.979078	+	0.203485i	$0.934773\pi$
$654$	13.4354	−	2.85577i	0.525364	−	0.111670i
$655$	−4.86517	+	1.03412i	−0.190098	+	0.0404066i
$656$	2.87230	+	27.3281i	0.112144	+	1.06698i
$657$	−7.71754	−	5.60712i	−0.301090	−	0.218755i
$658$	15.1554	+	4.88765i	0.590818	+	0.190540i
$659$	−13.3637			−0.520574			−0.260287	−	0.965531i	$-0.583817\pi$
$659$	−13.3637			−0.520574			−0.260287	+	0.965531i	$0.583817\pi$
$660$	2.15775	−	2.49846i	0.0839902	−	0.0972525i
$661$	13.1340	+	22.7488i	0.510855	+	0.884827i	0.999921	+	0.0125800i	$0.00400444\pi$
$661$	13.1340	+	22.7488i	0.510855	+	0.884827i	−0.489066	+	0.872247i	$0.662662\pi$
$662$	−2.29705	+	2.55113i	−0.0892774	+	0.0991526i
$663$	−1.81104	+	0.806328i	−0.0703351	+	0.0313152i
$664$	−18.4473	+	13.4027i	−0.715894	+	0.520127i
$665$	−11.4884	−	15.7400i	−0.445503	−	0.610369i
$666$	5.48066	−	16.8677i	0.212371	−	0.653612i
$667$	0.649533	+	6.17989i	0.0251500	+	0.239286i
$668$	−0.992398	+	9.44204i	−0.0383970	+	0.365323i
$669$	−17.5840	+	19.5290i	−0.679837	+	0.755035i
$670$	9.75030	−	16.8880i	0.376687	−	0.652441i
$671$	−3.81288	−	0.728372i	−0.147194	−	0.0281185i
$672$	−14.9458	−	1.53782i	−0.576548	−	0.0593226i
$673$	−10.3145	−	31.7447i	−0.397594	−	1.22367i	−0.926923	−	0.375252i	$-0.877556\pi$
$673$	−10.3145	−	31.7447i	−0.397594	−	1.22367i	0.529329	−	0.848417i	$-0.322444\pi$
$674$	47.3067	−	21.0623i	1.82219	−	0.811290i
$675$	3.84017	+	1.70975i	0.147808	+	0.0658084i
$676$	13.1897	−	2.80355i	0.507294	−	0.107829i
$677$	−30.3036	−	33.6556i	−1.16466	−	1.29349i	−0.948372	−	0.317162i	$-0.897270\pi$
$677$	−30.3036	−	33.6556i	−1.16466	−	1.29349i	−0.216292	−	0.976329i	$-0.569396\pi$
$678$	11.5300	−	8.37702i	0.442806	−	0.321718i
$679$	−9.94318	+	47.2874i	−0.381584	+	1.81472i
$680$	0.894737	+	2.75372i	0.0343116	+	0.105600i
$681$	−6.29546	+	10.9041i	−0.241242	+	0.417844i
$682$	−7.93497	+	26.2572i	−0.303846	+	1.00544i
$683$	19.8359	+	34.3568i	0.758999	+	1.31462i	0.943361	+	0.331767i	$0.107645\pi$
$683$	19.8359	+	34.3568i	0.758999	+	1.31462i	−0.184362	+	0.982858i	$0.559022\pi$
$684$	9.00400	+	1.91386i	0.344276	+	0.0731782i
$685$	1.50594	+	1.09413i	0.0575391	+	0.0418046i
$686$	−6.58640	+	32.0185i	−0.251470	+	1.22247i
$687$	−1.23302	+	3.79486i	−0.0470428	+	0.144783i
$688$	6.30772	+	7.00543i	0.240480	+	0.267080i
$689$	9.77257	+	4.35103i	0.372305	+	0.165761i
$690$	−0.511593	+	4.86748i	−0.0194760	+	0.185302i
$691$	10.2346	+	2.17544i	0.389344	+	0.0827576i	0.398424	−	0.917201i	$-0.369557\pi$
$691$	10.2346	+	2.17544i	0.389344	+	0.0827576i	−0.00908046	+	0.999959i	$0.502890\pi$
$692$	15.4209			0.586213
$693$	−8.74559	−	0.717411i	−0.332217	−	0.0272522i
$694$	10.6498			0.404259
$695$	0.558193	+	0.118648i	0.0211735	+	0.00450056i
$696$	−0.326406	+	3.10555i	−0.0123724	+	0.117715i
$697$	10.4600	+	4.65709i	0.396201	+	0.176400i
$698$	−12.9005	−	14.3274i	−0.488289	−	0.542300i
$699$	−3.28791	+	10.1192i	−0.124360	+	0.382742i
$700$	10.7290	−	6.22575i	0.405520	−	0.235311i
$701$	−29.5509	−	21.4700i	−1.11612	−	0.810911i	−0.132506	−	0.991182i	$-0.542302\pi$
$701$	−29.5509	−	21.4700i	−1.11612	−	0.810911i	−0.983617	+	0.180271i	$0.942302\pi$
$702$	−1.64717	−	0.350116i	−0.0621683	−	0.0132143i
$703$	−41.4655	−	71.8203i	−1.56390	−	2.70875i
$704$	−0.135951	−	0.0945406i	−0.00512383	−	0.00356313i
$705$	1.52156	−	2.63542i	0.0573054	−	0.0992558i
$706$	17.3049	+	53.2591i	0.651279	+	2.00443i
$707$	−32.3540	+	10.5908i	−1.21680	+	0.398306i
$708$	0.759670	−	0.551932i	0.0285501	−	0.0207429i
$709$	−17.3077	−	19.2221i	−0.650004	−	0.721902i	0.324597	−	0.945852i	$-0.394771\pi$
$709$	−17.3077	−	19.2221i	−0.650004	−	0.721902i	−0.974601	+	0.223950i	$0.928105\pi$
$710$	18.0525	−	3.83717i	0.677498	−	0.144007i
$711$	−5.68225	−	2.52990i	−0.213101	−	0.0948787i
$712$	−12.6226	+	5.61994i	−0.473051	+	0.210616i
$713$	−4.49910	−	13.8468i	−0.168493	−	0.518567i
$714$	−5.68630	+	7.86263i	−0.212804	+	0.294252i
$715$	0.353197	+	2.80170i	0.0132088	+	0.104778i
$716$	−4.72668	+	8.18685i	−0.176644	+	0.305957i
$717$	1.82427	−	2.02606i	0.0681288	−	0.0756647i
$718$	−5.70509	+	54.2803i	−0.212912	+	2.02572i
$719$	−3.94928	−	37.5749i	−0.147283	−	1.40131i	−0.779445	−	0.626471i	$-0.784499\pi$
$719$	−3.94928	−	37.5749i	−0.147283	−	1.40131i	0.632161	−	0.774837i	$-0.282168\pi$
$720$	−1.37520	+	4.23242i	−0.0512505	+	0.157733i
$721$	2.53126	−	5.71895i	0.0942691	−	0.212985i
$722$	70.1326	−	50.9543i	2.61006	−	1.89632i
$723$	19.3801	−	8.62860i	0.720755	−	0.320901i
$724$	0.175113	−	0.194483i	0.00650804	−	0.00722791i
$725$	−4.20329	−	7.28031i	−0.156106	−	0.270384i
$726$	−16.1659	−	10.7527i	−0.599973	−	0.399071i
$727$	2.74114			0.101663			0.0508316	−	0.998707i	$-0.483813\pi$
$727$	2.74114			0.101663			0.0508316	+	0.998707i	$0.483813\pi$
$728$	2.92327	−	2.64373i	0.108344	−	0.0979831i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	1.57065	+	14.9437i	0.0581323	+	0.553092i
$731$	3.84213	−	0.816670i	0.142106	−	0.0302056i
$732$	−1.27690	+	0.271412i	−0.0471954	+	0.0100317i
$733$	0.973601	+	9.26320i	0.0359608	+	0.342144i	0.997678	+	0.0681016i	$0.0216942\pi$
$733$	0.973601	+	9.26320i	0.0359608	+	0.342144i	−0.961718	+	0.274042i	$0.911639\pi$
$734$	19.5523	+	14.2056i	0.721688	+	0.524337i
$735$	5.71793	+	2.51587i	0.210909	+	0.0927991i
$736$	17.6451			0.650409
$737$	−37.8478	−	15.9213i	−1.39414	−	0.586469i
$738$	4.86302	+	8.42299i	0.179010	+	0.310055i
$739$	−28.1972	+	31.3161i	−1.03725	+	1.15198i	−0.0490517	+	0.998796i	$0.515620\pi$
$739$	−28.1972	+	31.3161i	−1.03725	+	1.15198i	−0.988197	+	0.153186i	$0.951047\pi$
$740$	−9.13710	+	4.06810i	−0.335886	+	0.149546i
$741$	−6.37025	+	4.62826i	−0.234017	+	0.170023i
$742$	52.0613	−	5.58705i	1.91123	−	0.205107i
$743$	2.88811	−	8.88868i	0.105954	−	0.326094i	−0.883999	−	0.467489i	$-0.845159\pi$
$743$	2.88811	−	8.88868i	0.105954	−	0.326094i	0.989953	+	0.141395i	$0.0451587\pi$
$744$	−0.764778	−	7.27637i	−0.0280381	−	0.266765i
$745$	−1.16258	+	11.0612i	−0.0425936	+	0.405251i
$746$	3.06674	−	3.40596i	0.112281	−	0.124701i
$747$	−7.30164	+	12.6468i	−0.267153	+	0.462723i
$748$	−6.95577	+	3.27093i	−0.254328	+	0.119597i
$749$	−30.9507	−	3.18461i	−1.13092	−	0.116363i
$750$	−4.47984	−	13.7875i	−0.163581	−	0.503449i
$751$	29.0044	−	12.9136i	1.05838	−	0.471223i	0.197647	−	0.980273i	$-0.436670\pi$
$751$	29.0044	−	12.9136i	1.05838	−	0.471223i	0.860737	+	0.509050i	$0.170003\pi$
$752$	−15.5344	−	6.91634i	−0.566480	−	0.252213i
$753$	−17.0682	+	3.62795i	−0.621999	+	0.132210i
$754$	2.25343	+	2.50268i	0.0820649	+	0.0911423i
$755$	−0.608113	+	0.441820i	−0.0221315	+	0.0160795i
$756$	−2.80451	+	0.918029i	−0.101999	+	0.0333884i
$757$	−14.0725	−	43.3108i	−0.511475	−	1.57416i	−0.789606	−	0.613614i	$-0.789715\pi$
$757$	−14.0725	−	43.3108i	−0.511475	−	1.57416i	0.278132	−	0.960543i	$-0.410285\pi$
$758$	−11.2026	+	19.4035i	−0.406898	+	0.704768i
$759$	10.3032	−	0.213142i	0.373981	−	0.00773656i
$760$	5.75021	+	9.95965i	0.208582	+	0.361274i
$761$	7.45948	+	1.58556i	0.270406	+	0.0574766i	0.341119	−	0.940020i	$-0.389194\pi$
$761$	7.45948	+	1.58556i	0.270406	+	0.0574766i	−0.0707130	+	0.997497i	$0.522527\pi$
$762$	13.2749	+	9.64480i	0.480900	+	0.349394i
$763$	0.0450443	+	20.5892i	0.00163071	+	0.745379i
$764$	1.39398	−	4.29024i	0.0504325	−	0.155215i
$765$	1.24079	+	1.37804i	0.0448610	+	0.0498231i
$766$	−47.4725	−	21.1361i	−1.71525	−	0.763679i
$767$	−0.0839595	+	0.798821i	−0.00303160	+	0.0288438i
$768$	19.5541	+	4.15635i	0.705598	+	0.149979i
$769$	19.9352			0.718883			0.359441	−	0.933168i	$-0.382967\pi$
$769$	19.9352			0.718883			0.359441	+	0.933168i	$0.382967\pi$
$770$	8.37793	+	10.9934i	0.301920	+	0.396176i
$771$	−23.5001			−0.846337
$772$	−6.16697	−	1.31083i	−0.221954	−	0.0471778i
$773$	0.311539	−	2.96410i	0.0112053	−	0.106611i	−0.987490	−	0.157684i	$-0.949597\pi$
$773$	0.311539	−	2.96410i	0.0112053	−	0.106611i	0.998695	+	0.0510726i	$0.0162640\pi$
$774$	3.04812	+	1.35711i	0.109563	+	0.0487804i
$775$	13.1797	+	14.6376i	0.473430	+	0.525798i
$776$	8.81248	−	27.1220i	0.316350	−	0.973624i
$777$	23.0528	+	13.2424i	0.827015	+	0.475068i
$778$	−25.8096	−	18.7518i	−0.925319	−	0.672284i
$779$	44.4842	+	9.45542i	1.59381	+	0.338776i
$780$	0.474822	+	0.822415i	0.0170013	+	0.0294472i
$781$	−12.7703	−	36.7021i	−0.456958	−	1.31330i
$782$	5.69783	−	9.86894i	0.203754	−	0.352912i
$783$	0.617990	+	1.90198i	0.0220852	+	0.0679712i
$784$	10.6414	−	33.2453i	0.380052	−	1.18733i
$785$	10.9406	−	7.94882i	0.390487	−	0.283706i
$786$	6.58247	+	7.31057i	0.234789	+	0.260759i
$787$	−36.7676	+	7.81520i	−1.31062	+	0.278582i	−0.809666	−	0.586890i	$-0.800352\pi$
$787$	−36.7676	+	7.81520i	−1.31062	+	0.278582i	−0.500957	+	0.865472i	$0.667019\pi$
$788$	−10.7754	−	4.79753i	−0.383858	−	0.170905i
$789$	14.2822	−	6.35885i	0.508460	−	0.226381i
$790$	3.02758	+	9.31793i	0.107716	+	0.331517i
$791$	8.73187	+	19.4972i	0.310470	+	0.693241i
$792$	5.08672	+	0.971714i	0.180749	+	0.0345284i
$793$	0.558327	−	0.967052i	0.0198268	−	0.0343410i
$794$	5.64335	−	6.26757i	0.200275	−	0.222428i
$795$	1.04593	−	9.95137i	0.0370954	−	0.352939i
$796$	−0.424135	−	4.03537i	−0.0150330	−	0.143030i
$797$	−10.4858	+	32.2718i	−0.371425	+	1.14313i	0.574435	+	0.818550i	$0.305222\pi$
$797$	−10.4858	+	32.2718i	−0.371425	+	1.14313i	−0.945859	+	0.324577i	$0.894778\pi$
$798$	−15.5989	+	35.2431i	−0.552196	+	1.24759i
$799$	−5.73228	+	4.16474i	−0.202793	+	0.147338i
$800$	−21.8076	+	9.70937i	−0.771015	+	0.343278i
$801$	−5.92113	+	6.57608i	−0.209213	+	0.232354i
$802$	9.65440	+	16.7219i	0.340909	+	0.590471i
$803$	30.8046	−	7.21670i	1.08707	−	0.254672i
$804$	−13.8082			−0.486977
$805$	−6.98232	−	2.25182i	−0.246094	−	0.0793661i
$806$	−6.38362	−	4.63797i	−0.224853	−	0.163366i
$807$	0.324247	+	3.08501i	0.0114140	+	0.108597i
$808$	19.6522	−	4.17720i	0.691362	−	0.146953i
$809$	−15.3587	+	3.26460i	−0.539985	+	0.114777i	−0.469827	−	0.882759i	$-0.655684\pi$
$809$	−15.3587	+	3.26460i	−0.539985	+	0.114777i	−0.0701579	+	0.997536i	$0.522350\pi$
$810$	0.164648	+	1.56652i	0.00578515	+	0.0550421i
$811$	36.3249	+	26.3916i	1.27554	+	0.926733i	0.999409	−	0.0343867i	$-0.0109478\pi$
$811$	36.3249	+	26.3916i	1.27554	+	0.926733i	0.276131	+	0.961120i	$0.410948\pi$
$812$	5.61660	+	1.81137i	0.197104	+	0.0635666i
$813$	0.712903			0.0250026
$814$	30.4588	+	50.3230i	1.06758	+	1.76382i
$815$	−6.72768	−	11.6527i	−0.235660	−	0.408176i
$816$	6.93334	−	7.70026i	0.242716	−	0.269563i
$817$	14.2527	−	6.34573i	0.498640	−	0.222009i
$818$	−11.7730	+	8.55360i	−0.411634	+	0.299070i
$819$	1.02165	−	2.30824i	0.0356993	−	0.0806564i
$820$	1.69491	−	5.21638i	0.0591887	−	0.182164i
$821$	−2.64713	−	25.1858i	−0.0923856	−	0.878990i	−0.938335	−	0.345727i	$-0.887632\pi$
$821$	−2.64713	−	25.1858i	−0.0923856	−	0.878990i	0.845949	−	0.533263i	$-0.179034\pi$
$822$	0.384830	−	3.66142i	0.0134225	−	0.127707i
$823$	−2.50974	+	2.78735i	−0.0874842	+	0.0971610i	−0.785297	−	0.619119i	$-0.787490\pi$
$823$	−2.50974	+	2.78735i	−0.0874842	+	0.0971610i	0.697813	+	0.716280i	$0.254157\pi$
$824$	−1.84548	+	3.19647i	−0.0642904	+	0.111354i
$825$	−12.6164	+	5.93282i	−0.439246	+	0.206554i
$826$	1.60694	+	3.58810i	0.0559125	+	0.124846i
$827$	−9.77624	−	30.0882i	−0.339953	−	1.04627i	−0.964230	−	0.265065i	$-0.914607\pi$
$827$	−9.77624	−	30.0882i	−0.339953	−	1.04627i	0.624277	−	0.781203i	$-0.285393\pi$
$828$	3.16598	−	1.40959i	0.110026	−	0.0489865i
$829$	−30.2354	−	13.4617i	−1.05012	−	0.467544i	−0.192216	−	0.981353i	$-0.561567\pi$
$829$	−30.2354	−	13.4617i	−1.05012	−	0.467544i	−0.857905	+	0.513809i	$0.828234\pi$
$830$	22.4998	−	4.78247i	0.780978	−	0.166002i
$831$	−11.1544	−	12.3883i	−0.386943	−	0.429744i
$832$	0.0385371	−	0.0279988i	0.00133603	−	0.000970684i
$833$	−9.77978	−	10.7664i	−0.338849	−	0.373035i
$834$	−0.348776	−	1.07342i	−0.0120771	−	0.0371696i
$835$	−3.79821	+	6.57870i	−0.131443	+	0.227665i
$836$	−24.3229	+	18.4521i	−0.841224	+	0.638180i
$837$	−2.34286	−	4.05795i	−0.0809810	−	0.140263i
$838$	9.75000	+	2.07243i	0.336808	+	0.0715908i
$839$	−19.8621	−	14.4307i	−0.685716	−	0.498202i	0.189533	−	0.981874i	$-0.439303\pi$
$839$	−19.8621	−	14.4307i	−0.685716	−	0.498202i	−0.875249	+	0.483672i	$0.839303\pi$
$840$	−3.19684	−	1.83638i	−0.110301	−	0.0633612i
$841$	−7.72560	+	23.7770i	−0.266400	+	0.819895i
$842$	7.58564	+	8.42471i	0.261418	+	0.290335i
$843$	26.3911	+	11.7501i	0.908959	+	0.404694i
$844$	0.699157	−	6.65204i	0.0240660	−	0.228973i
$845$	10.5534	+	2.24319i	0.363047	+	0.0771680i
$846$	−6.01872			−0.206928
$847$	20.7595	−	20.3971i	0.713305	−	0.700854i
$848$	−55.9129			−1.92006
$849$	13.0184	+	2.76714i	0.446790	+	0.0949681i
$850$	−1.61149	+	15.3323i	−0.0552736	+	0.525893i
$851$	−28.5230	−	12.6992i	−0.977754	−	0.435324i
$852$	−8.74444	−	9.71169i	−0.299580	−	0.332717i
$853$	−2.04141	+	6.28281i	−0.0698965	+	0.215119i	−0.979903	−	0.199475i	$-0.936076\pi$
$853$	−2.04141	+	6.28281i	−0.0698965	+	0.215119i	0.910006	+	0.414594i	$0.136076\pi$
$854$	−0.0119575	−	5.46564i	−0.000409178	−	0.187030i
$855$	5.95863	+	4.32920i	0.203781	+	0.148055i
$856$	17.9613	+	3.81779i	0.613905	+	0.130489i
$857$	6.62995	+	11.4834i	0.226475	+	0.392266i	0.956761	−	0.290876i	$-0.0939466\pi$
$857$	6.62995	+	11.4834i	0.226475	+	0.392266i	−0.730286	+	0.683141i	$0.760613\pi$
$858$	4.44956	−	3.37558i	0.151905	−	0.115240i
$859$	−2.67238	+	4.62870i	−0.0911804	+	0.157929i	−0.908008	−	0.418953i	$-0.862397\pi$
$859$	−2.67238	+	4.62870i	−0.0911804	+	0.157929i	0.816828	+	0.576882i	$0.195731\pi$
$860$	−0.581450	−	1.78952i	−0.0198273	−	0.0610220i
$861$	−13.8557	+	4.53552i	−0.472200	+	0.154570i
$862$	−26.0370	+	18.9170i	−0.886825	+	0.644316i
$863$	16.2483	+	18.0456i	0.553099	+	0.614279i	0.953254	−	0.302169i	$-0.0977106\pi$
$863$	16.2483	+	18.0456i	0.553099	+	0.614279i	−0.400156	+	0.916447i	$0.631044\pi$
$864$	5.55472	−	1.18069i	0.188975	−	0.0401680i
$865$	11.2719	+	5.01857i	0.383256	+	0.170636i
$866$	58.4803	−	26.0371i	1.98724	−	0.884777i
$867$	3.91909	+	12.0617i	0.133099	+	0.409638i
$868$	−13.7547	−	1.41526i	−0.466863	−	0.0480369i
$869$	18.6683	−	8.77872i	0.633279	−	0.297798i
$870$	1.57504	−	2.72805i	0.0533989	−	0.0924897i
$871$	7.90343	−	8.77765i	0.267798	−	0.297419i
$872$	1.27014	−	12.0846i	0.0430123	−	0.409235i
$873$	−1.90909	−	18.1638i	−0.0646128	−	0.614750i
$874$	13.9869	−	43.0474i	0.473115	−	1.45610i
$875$	21.6067	−	2.31876i	0.730441	−	0.0783885i
$876$	8.60776	−	6.25391i	0.290829	−	0.211300i
$877$	−27.4039	+	12.2010i	−0.925364	+	0.411999i	−0.813394	−	0.581713i	$-0.802383\pi$
$877$	−27.4039	+	12.2010i	−0.925364	+	0.411999i	−0.111970	+	0.993712i	$0.535716\pi$
$878$	−25.2296	+	28.0203i	−0.851459	+	0.945641i
$879$	−11.8582	−	20.5390i	−0.399967	−	0.692763i
$880$	−7.64266	−	12.6269i	−0.257634	−	0.425654i
$881$	43.8487			1.47730			0.738649	−	0.674090i	$-0.235464\pi$
$881$	43.8487			1.47730			0.738649	+	0.674090i	$0.235464\pi$
$882$	−1.34523	−	12.2818i	−0.0452962	−	0.413550i
$883$	3.23267	+	2.34867i	0.108788	+	0.0790391i	0.640849	−	0.767667i	$-0.278582\pi$
$883$	3.23267	+	2.34867i	0.108788	+	0.0790391i	−0.532061	+	0.846706i	$0.678582\pi$
$884$	−0.231124	−	2.19900i	−0.00777353	−	0.0739602i
$885$	0.734902	−	0.156208i	0.0247035	−	0.00525088i
$886$	59.1120	−	12.5646i	1.98591	−	0.422118i
$887$	2.01687	+	19.1893i	0.0677200	+	0.644313i	0.974758	+	0.223264i	$0.0716712\pi$
$887$	2.01687	+	19.1893i	0.0677200	+	0.644313i	−0.907038	+	0.421049i	$0.861662\pi$
$888$	−12.6934	−	9.22233i	−0.425964	−	0.309481i
$889$	−18.2426	+	16.4981i	−0.611836	+	0.553328i
$890$	13.9385			0.467220
$891$	3.22919	−	0.756515i	0.108182	−	0.0253442i
$892$	−14.6551	−	25.3833i	−0.490688	−	0.849897i
$893$	−18.8313	+	20.9143i	−0.630166	+	0.699870i
$894$	20.0956	−	8.94715i	0.672099	−	0.299238i
$895$	−6.11930	+	4.44593i	−0.204546	+	0.148611i
$896$	−12.0678	+	27.2650i	−0.403156	+	0.910861i
$897$	−0.916071	+	2.81938i	−0.0305867	+	0.0941363i
$898$	6.82351	+	64.9213i	0.227703	+	2.16645i
$899$	−0.979512	+	9.31944i	−0.0326686	+	0.310821i
$900$	−3.13720	+	3.48421i	−0.104573	+	0.116140i
$901$	−11.6490	+	20.1766i	−0.388084	+	0.672181i
$902$	−31.6847	−	6.05271i	−1.05498	−	0.201533i
$903$	−2.93093	+	4.05270i	−0.0975353	+	0.134865i
$904$	−3.89605	−	11.9908i	−0.129581	−	0.398808i
$905$	0.191292	−	0.0851686i	0.00635876	−	0.00283110i
$906$	1.35813	+	0.604678i	0.0451208	+	0.0200891i
$907$	−46.1514	+	9.80979i	−1.53243	+	0.325729i	−0.895454	−	0.445153i	$-0.853149\pi$
$907$	−46.1514	+	9.80979i	−1.53243	+	0.325729i	−0.636978	+	0.770882i	$0.719816\pi$
$908$	−9.39679	−	10.4362i	−0.311844	−	0.346337i
$909$	10.4097	−	7.56311i	0.345269	−	0.250853i
$910$	−3.77875	+	1.23694i	−0.125264	+	0.0410040i
$911$	−4.20128	−	12.9302i	−0.139195	−	0.428397i	0.857024	−	0.515276i	$-0.172311\pi$
$911$	−4.20128	−	12.9302i	−0.139195	−	0.428397i	−0.996219	+	0.0868789i	$0.972311\pi$
$912$	20.5780	−	35.6421i	0.681404	−	1.18023i
$913$	−15.9163	−	45.7437i	−0.526753	−	1.51390i
$914$	−21.9452	−	38.0101i	−0.725882	−	1.25726i
$915$	−1.02168	−	0.217164i	−0.0337756	−	0.00717922i
$916$	−3.60046	−	2.61589i	−0.118963	−	0.0864313i
$917$	−12.7542	+	7.40091i	−0.421182	+	0.244399i
$918$	1.13333	−	3.48802i	0.0374053	−	0.115122i
$919$	19.8376	+	22.0319i	0.654383	+	0.726766i	0.975433	−	0.220296i	$-0.0707024\pi$
$919$	19.8376	+	22.0319i	0.654383	+	0.726766i	−0.321050	+	0.947062i	$0.604036\pi$
$920$	3.95541	+	1.76106i	0.130406	+	0.0580605i
$921$	−1.51331	+	14.3982i	−0.0498652	+	0.474435i
$922$	−66.4450	−	14.1233i	−2.18825	−	0.465127i
$923$	11.1787			0.367950
$924$	3.77528	−	9.02972i	0.124197	−	0.297056i
$925$	42.2393			1.38882
$926$	−10.7470	−	2.28435i	−0.353168	−	0.0750682i
$927$	−0.247087	+	2.35087i	−0.00811540	+	0.0772129i
$928$	−10.3750	−	4.61924i	−0.340576	−	0.151634i
$929$	6.53823	+	7.26144i	0.214512	+	0.238240i	0.840792	−	0.541358i	$-0.182090\pi$
$929$	6.53823	+	7.26144i	0.214512	+	0.238240i	−0.626280	+	0.779599i	$0.715423\pi$
$930$	−2.28077	+	7.01949i	−0.0747894	+	0.230178i
$931$	−46.8867	−	33.7527i	−1.53665	−	1.10620i
$932$	−9.60079	−	6.97538i	−0.314484	−	0.228486i
$933$	−24.5349	−	5.21505i	−0.803236	−	0.170733i
$934$	8.37679	+	14.5090i	0.274097	+	0.474750i
$935$	−6.14882	+	0.127201i	−0.201088	+	0.00415991i
$936$	−0.744859	+	1.29013i	−0.0243465	+	0.0421693i
$937$	5.33033	+	16.4051i	0.174134	+	0.535930i	0.999593	−	0.0285325i	$-0.00908342\pi$
$937$	5.33033	+	16.4051i	0.174134	+	0.535930i	−0.825459	+	0.564463i	$0.809083\pi$
$938$	11.8963	−	56.5761i	0.388428	−	1.84727i
$939$	10.6482	−	7.73634i	0.347489	−	0.252466i
$940$	2.27113	+	2.52235i	0.0740761	+	0.0822699i
$941$	−30.6962	+	6.52467i	−1.00067	+	0.212698i	−0.678987	−	0.734150i	$-0.737581\pi$
$941$	−30.6962	+	6.52467i	−1.00067	+	0.212698i	−0.321680	+	0.946849i	$0.604247\pi$
$942$	−24.4342	−	10.8788i	−0.796110	−	0.354451i
$943$	15.6416	−	6.96407i	0.509359	−	0.226781i
$944$	−1.29733	−	3.99277i	−0.0422245	−	0.129954i
$945$	−2.34872	−	0.241667i	−0.0764039	−	0.00786141i
$946$	−10.0142	+	4.70916i	−0.325591	+	0.153108i
$947$	16.1643	−	27.9975i	0.525271	−	0.909796i	−0.474296	−	0.880365i	$-0.657297\pi$
$947$	16.1643	−	27.9975i	0.525271	−	0.909796i	0.999567	−	0.0294303i	$-0.00936930\pi$
$948$	4.64208	−	5.15555i	0.150768	−	0.167445i
$949$	−0.951339	+	9.05139i	−0.0308818	+	0.293820i
$950$	6.40070	+	60.8986i	0.207666	+	1.97581i
$951$	−7.75180	+	23.8576i	−0.251369	+	0.773636i
$952$	5.06076	+	6.93359i	0.164020	+	0.224719i
$953$	−4.45231	+	3.23480i	−0.144225	+	0.104785i	−0.657558	−	0.753404i	$-0.728410\pi$
$953$	−4.45231	+	3.23480i	−0.144225	+	0.104785i	0.513333	+	0.858189i	$0.328410\pi$
$954$	−18.0793	+	8.04944i	−0.585340	+	0.260610i
$955$	2.41515	−	2.68230i	0.0781524	−	0.0867970i
$956$	1.52041	+	2.63343i	0.0491736	+	0.0851712i
$957$	−6.11385	−	2.57189i	−0.197633	−	0.0831375i
$958$	13.4547			0.434701
$959$	5.25223	+	1.69386i	0.169603	+	0.0546976i
$960$	−0.0360469	−	0.0261896i	−0.00116341	−	0.000845267i
$961$	0.945361	+	8.99451i	0.0304955	+	0.290145i
$962$	−16.5514	+	3.51811i	−0.533638	+	0.113428i
$963$	11.5031	−	2.44505i	0.370681	−	0.0787907i
$964$	2.47328	+	23.5317i	0.0796589	+	0.757904i
$965$	−4.08115	−	2.96513i	−0.131377	−	0.0954510i
$966$	3.04786	+	14.1864i	0.0980632	+	0.456439i
$967$	10.1320			0.325825			0.162912	−	0.986641i	$-0.447911\pi$
$967$	10.1320			0.325825			0.162912	+	0.986641i	$0.447911\pi$
$968$	−13.4661	+	10.6617i	−0.432817	+	0.342681i
$969$	−8.57449	−	14.8515i	−0.275452	−	0.477098i
$970$	−19.2498	+	21.3790i	−0.618072	+	0.686439i
$971$	−29.7452	+	13.2434i	−0.954568	+	0.425001i	−0.824095	−	0.566451i	$-0.808316\pi$
$971$	−29.7452	+	13.2434i	−0.954568	+	0.425001i	−0.130472	+	0.991452i	$0.541649\pi$
$972$	0.902338	−	0.655587i	0.0289425	−	0.0210280i
$973$	1.68218	−	0.180526i	0.0539283	−	0.00578740i
$974$	−2.82456	+	8.69309i	−0.0905046	+	0.278545i
$975$	−0.419212	−	3.98854i	−0.0134255	−	0.127735i
$976$	−0.610080	+	5.80452i	−0.0195282	+	0.185798i
$977$	11.0755	−	12.3006i	0.354338	−	0.393532i	−0.539453	−	0.842016i	$-0.681369\pi$
$977$	11.0755	−	12.3006i	0.354338	−	0.393532i	0.893791	+	0.448483i	$0.148036\pi$
$978$	−13.3061	+	23.0468i	−0.425481	+	0.736954i
$979$	−3.67081	−	29.1183i	−0.117320	−	0.930625i
$980$	−4.63949	+	5.19823i	−0.148203	+	0.166052i
$981$	−2.40477	−	7.40113i	−0.0767785	−	0.236300i
$982$	−65.5414	+	29.1809i	−2.09151	+	0.931200i
$983$	−7.05433	−	3.14079i	−0.224998	−	0.100176i	0.291142	−	0.956680i	$-0.405965\pi$
$983$	−7.05433	−	3.14079i	−0.224998	−	0.100176i	−0.516140	+	0.856504i	$0.672632\pi$
$984$	8.41611	−	1.78890i	0.268296	−	0.0570280i
$985$	−6.31499	−	7.01351i	−0.201212	−	0.223469i
$986$	−5.93375	+	4.31112i	−0.188969	+	0.137294i
$987$	1.85645	−	8.82886i	0.0590916	−	0.281026i
$988$	−2.71389	−	8.35251i	−0.0863405	−	0.265729i
$989$	2.93688	−	5.08682i	0.0933873	−	0.161752i
$990$	−4.28907	−	2.98263i	−0.136316	−	0.0947943i
$991$	24.9536	+	43.2209i	0.792678	+	1.37296i	0.924303	+	0.381659i	$0.124647\pi$
$991$	24.9536	+	43.2209i	0.792678	+	1.37296i	−0.131626	+	0.991300i	$0.542020\pi$
$992$	26.0279	+	5.53239i	0.826385	+	0.175654i
$993$	1.57349	+	1.14321i	0.0499332	+	0.0362786i
$994$	47.3253	−	27.4615i	1.50107	−	0.871025i
$995$	1.00325	−	3.08769i	0.0318052	−	0.0978863i
$996$	−10.8987	−	12.1042i	−0.345337	−	0.383536i
$997$	46.6455	+	20.7679i	1.47728	+	0.657726i	0.977979	−	0.208704i	$-0.0669244\pi$
$997$	46.6455	+	20.7679i	1.47728	+	0.657726i	0.499299	+	0.866430i	$0.333591\pi$
$998$	−0.287723	+	2.73750i	−0.00910771	+	0.0866541i
$999$	−9.82882	−	2.08918i	−0.310970	−	0.0660988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.a.16.6	✓	64
3.2	odd	2		693.2.by.d.478.3		64
7.4	even	3	inner	231.2.y.a.214.3	yes	64
11.9	even	5	inner	231.2.y.a.163.3	yes	64
21.11	odd	6		693.2.by.d.676.6		64
33.20	odd	10		693.2.by.d.163.6		64
77.53	even	15	inner	231.2.y.a.130.6	yes	64
231.53	odd	30		693.2.by.d.361.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.16.6	✓	64	1.1	even	1	trivial
231.2.y.a.130.6	yes	64	77.53	even	15	inner
231.2.y.a.163.3	yes	64	11.9	even	5	inner
231.2.y.a.214.3	yes	64	7.4	even	3	inner
693.2.by.d.163.6		64	33.20	odd	10
693.2.by.d.361.3		64	231.53	odd	30
693.2.by.d.478.3		64	3.2	odd	2
693.2.by.d.676.6		64	21.11	odd	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72647 + 0.366972i) q^{2} +(0.104528 - 0.994522i) q^{3} +(1.01892 + 0.453654i) q^{4} +(0.597146 + 0.663197i) q^{5} +(0.545426 - 1.67865i) q^{6} +(2.29418 + 1.31786i) q^{7} +(-1.26323 - 0.917790i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(1.72647 + 0.366972i) q^{2} +(0.104528 - 0.994522i) q^{3} +(1.01892 + 0.453654i) q^{4} +(0.597146 + 0.663197i) q^{5} +(0.545426 - 1.67865i) q^{6} +(2.29418 + 1.31786i) q^{7} +(-1.26323 - 0.917790i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.787577 + 1.36412i) q^{10} +(2.64231 - 2.00454i) q^{11} +(0.557675 - 0.965922i) q^{12} +(0.294823 + 0.907373i) q^{13} +(3.47720 + 3.11714i) q^{14} +(0.721983 - 0.524551i) q^{15} +(-3.33675 - 3.70584i) q^{16} +(-2.03247 + 0.432014i) q^{17} +(-1.61244 - 0.717905i) q^{18} +(-7.53962 + 3.35686i) q^{19} +(0.307584 + 0.946645i) q^{20} +(1.55045 - 2.14385i) q^{21} +(5.29747 - 2.49112i) q^{22} +(-1.55359 + 2.69090i) q^{23} +(-1.04481 + 1.16037i) q^{24} +(0.439394 - 4.18056i) q^{25} +(0.176022 + 1.67474i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.73974 + 2.38356i) q^{28} +(1.61792 - 1.17549i) q^{29} +(1.43897 - 0.640673i) q^{30} +(-3.13536 + 3.48217i) q^{31} +(-2.83941 - 4.91800i) q^{32} +(-1.71736 - 2.83737i) q^{33} -3.66752 q^{34} +(0.495956 + 2.30845i) q^{35} +(-0.902338 - 0.655587i) q^{36} +(1.05034 + 9.99336i) q^{37} +(-14.2488 + 3.02867i) q^{38} +(0.933220 - 0.198362i) q^{39} +(-0.145656 - 1.38582i) q^{40} +(-4.45800 - 3.23893i) q^{41} +(3.46353 - 3.13232i) q^{42} -1.89038 q^{43} +(3.60168 - 0.843780i) q^{44} +(-0.446210 - 0.772859i) q^{45} +(-3.66971 + 4.07562i) q^{46} +(3.11516 - 1.38696i) q^{47} +(-4.03432 + 2.93111i) q^{48} +(3.52649 + 6.04681i) q^{49} +(2.29275 - 7.05634i) q^{50} +(0.217197 + 2.06649i) q^{51} +(-0.111231 + 1.05829i) q^{52} +(7.50257 - 8.33245i) q^{53} +(-0.882518 + 1.52857i) q^{54} +(2.90725 + 0.555371i) q^{55} +(-1.68855 - 3.77033i) q^{56} +(2.55036 + 7.84921i) q^{57} +(3.22465 - 1.43571i) q^{58} +(0.769105 + 0.342428i) q^{59} +(0.973611 - 0.206947i) q^{60} +(-0.783160 - 0.869787i) q^{61} +(-6.69094 + 4.86125i) q^{62} +(-1.97004 - 1.76605i) q^{63} +(-0.0154285 - 0.0474840i) q^{64} +(-0.425715 + 0.737360i) q^{65} +(-1.92374 - 5.52884i) q^{66} +(-6.19006 - 10.7215i) q^{67} +(-2.26691 - 0.481847i) q^{68} +(2.51377 + 1.82636i) q^{69} +(0.00911741 + 4.16745i) q^{70} +(3.62070 - 11.1434i) q^{71} +(1.04481 + 1.16037i) q^{72} +(8.71468 + 3.88002i) q^{73} +(-1.85390 + 17.6386i) q^{74} +(-4.11173 - 0.873975i) q^{75} -9.20515 q^{76} +(8.70363 - 1.11658i) q^{77} +1.68397 q^{78} +(6.08408 + 1.29321i) q^{79} +(0.465175 - 4.42585i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-6.50799 - 7.22785i) q^{82} +(4.51266 - 13.8885i) q^{83} +(2.55236 - 1.48106i) q^{84} +(-1.50019 - 1.08995i) q^{85} +(-3.26367 - 0.693715i) q^{86} +(-0.999929 - 1.73193i) q^{87} +(-5.17759 + 0.107109i) q^{88} +(4.42449 - 7.66344i) q^{89} +(-0.486749 - 1.49806i) q^{90} +(-0.519414 + 2.47021i) q^{91} +(-2.80373 + 2.03703i) q^{92} +(3.13536 + 3.48217i) q^{93} +(5.88719 - 1.25136i) q^{94} +(-6.72851 - 2.99573i) q^{95} +(-5.18786 + 2.30978i) q^{96} +(5.64383 + 17.3699i) q^{97} +(3.86936 + 11.7337i) q^{98} +(-3.00134 + 1.41137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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