LMFDB - Embedded newform 930.2.bs.a.107.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(107,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 15, 44]))

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

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

chi := DirichletCharacter("930.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bs (of order $60$, degree $16$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			107.15
Character	$\chi$	$=$	930.107
Dual form			930.2.bs.a.113.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(-0.205138 - 1.71986i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.37425 - 1.76393i) q^{5} +(-1.43928 + 0.963580i) q^{6} +(1.73979 - 1.40885i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.91584 + 0.705618i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.205138 - 1.71986i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.37425 - 1.76393i) q^{5} +(-1.43928 + 0.963580i) q^{6} +(1.73979 - 1.40885i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.91584 + 0.705618i) q^{9} +(-2.19557 - 0.423656i) q^{10} +(-0.838623 - 1.88358i) q^{11} +(1.51197 + 0.844948i) q^{12} +(-5.35574 + 3.47806i) q^{13} +(-2.04515 - 0.910558i) q^{14} +(-3.31562 - 2.00166i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(4.15906 - 1.59651i) q^{17} +(1.95247 + 2.27769i) q^{18} +(-0.280971 - 1.32187i) q^{19} +(0.619287 + 2.14860i) q^{20} +(-2.77993 - 2.70319i) q^{21} +(-1.29755 + 1.60234i) q^{22} +(-6.98644 - 1.10654i) q^{23} +(0.0664328 - 1.73078i) q^{24} +(-1.22289 - 4.84815i) q^{25} +(5.53043 + 3.19300i) q^{26} +(1.81171 + 4.87008i) q^{27} +(0.117164 + 2.23562i) q^{28} +(2.19453 - 6.75406i) q^{29} +(-0.278234 + 3.86298i) q^{30} +(-5.32205 - 1.63579i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.06746 + 1.82871i) q^{33} +(-3.31068 - 2.98095i) q^{34} +(-0.0942185 - 5.00498i) q^{35} +(1.14303 - 2.77371i) q^{36} +(-2.64932 + 9.88741i) q^{37} +(-1.05023 + 0.850462i) q^{38} +(7.08044 + 8.49765i) q^{39} +(1.63327 - 1.52723i) q^{40} +(6.78355 - 6.10794i) q^{41} +(-1.14649 + 3.70416i) q^{42} +(5.30391 - 8.16730i) q^{43} +(2.01678 + 0.428679i) q^{44} +(-2.76242 + 6.11302i) q^{45} +(2.18584 + 6.72732i) q^{46} +(0.717792 + 0.365733i) q^{47} +(-1.57229 + 0.726564i) q^{48} +(-0.413383 + 1.94481i) q^{49} +(-3.76455 + 3.29062i) q^{50} +(-3.59896 - 6.82550i) q^{51} +(0.334217 - 6.37724i) q^{52} +(-2.77148 + 3.42249i) q^{53} +(3.51677 - 3.82522i) q^{54} +(-4.47497 - 1.10923i) q^{55} +(1.93876 - 1.11935i) q^{56} +(-2.21579 + 0.754397i) q^{57} +(-7.01421 + 1.11094i) q^{58} +(3.94822 - 4.38494i) q^{59} +(3.56825 - 1.50585i) q^{60} -4.01193 q^{61} +(0.958655 + 5.48461i) q^{62} +(-4.07883 + 5.33562i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-1.22506 + 14.2269i) q^{65} +(3.02199 + 1.90291i) q^{66} +(-4.21925 + 1.13054i) q^{67} +(-1.15303 + 4.30316i) q^{68} +(-0.469914 + 12.2427i) q^{69} +(-4.41669 + 2.35616i) q^{70} +(-6.25571 + 0.657501i) q^{71} +(-2.99032 + 0.240793i) q^{72} +(-1.72574 + 4.49571i) q^{73} +(10.0125 - 2.12823i) q^{74} +(-8.08727 + 3.09774i) q^{75} +(1.23456 + 0.549663i) q^{76} +(-4.11271 - 2.09553i) q^{77} +(4.35700 - 10.1666i) q^{78} +(1.09736 - 2.46470i) q^{79} +(-2.10226 - 0.761902i) q^{80} +(8.00421 - 4.11493i) q^{81} +(-8.52188 - 3.27124i) q^{82} +(-0.166887 + 3.18440i) q^{83} +(3.82092 - 0.660117i) q^{84} +(2.89944 - 9.53030i) q^{85} +(-9.68504 - 1.01794i) q^{86} +(-12.0662 - 2.38876i) q^{87} +(-0.533641 - 1.99158i) q^{88} +(6.76702 + 4.91653i) q^{89} +(6.70085 - 0.313921i) q^{90} +(-4.41779 + 13.5966i) q^{91} +(5.00174 - 5.00174i) q^{92} +(-1.72158 + 9.48874i) q^{93} -0.805597i q^{94} +(-2.71780 - 1.32096i) q^{95} +(1.36118 + 1.07107i) q^{96} +(0.310135 + 1.95812i) q^{97} +(1.92051 - 0.514600i) q^{98} +(3.77437 + 4.90046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) $ 1024 * q - 8 * q^3 + 24 * q^7	$ 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) $ 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	−0.205138	−	1.71986i	−0.118437	−	0.992962i
$3$	−0.205138	−	1.71986i	−0.118437	−	0.992962i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	1.37425	−	1.76393i	0.614582	−	0.788853i
$5$	1.37425	−	1.76393i	0.614582	−	0.788853i
$6$	−1.43928	+	0.963580i	−0.587582	+	0.393380i
$7$	1.73979	−	1.40885i	0.657579	−	0.532497i	−0.241435	−	0.970417i	$-0.577618\pi$
$7$	1.73979	−	1.40885i	0.657579	−	0.532497i	0.899014	+	0.437920i	$0.144285\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	−2.91584	+	0.705618i	−0.971946	+	0.235206i
$10$	−2.19557	−	0.423656i	−0.694299	−	0.133972i
$11$	−0.838623	−	1.88358i	−0.252854	−	0.567920i	0.741865	−	0.670549i	$-0.233941\pi$
$11$	−0.838623	−	1.88358i	−0.252854	−	0.567920i	−0.994720	+	0.102629i	$0.967275\pi$
$12$	1.51197	+	0.844948i	0.436469	+	0.243915i
$13$	−5.35574	+	3.47806i	−1.48542	+	0.964640i	−0.489728	+	0.871875i	$0.662904\pi$
$13$	−5.35574	+	3.47806i	−1.48542	+	0.964640i	−0.995688	+	0.0927652i	$0.970429\pi$
$14$	−2.04515	−	0.910558i	−0.546588	−	0.243357i
$15$	−3.31562	−	2.00166i	−0.856090	−	0.516827i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	4.15906	−	1.59651i	1.00872	−	0.387212i	0.202790	−	0.979222i	$-0.434999\pi$
$17$	4.15906	−	1.59651i	1.00872	−	0.387212i	0.805930	+	0.592011i	$0.201666\pi$
$18$	1.95247	+	2.27769i	0.460202	+	0.536856i
$19$	−0.280971	−	1.32187i	−0.0644593	−	0.303257i	0.934094	−	0.357027i	$-0.116210\pi$
$19$	−0.280971	−	1.32187i	−0.0644593	−	0.303257i	−0.998553	+	0.0537699i	$0.982876\pi$
$20$	0.619287	+	2.14860i	0.138477	+	0.480442i
$21$	−2.77993	−	2.70319i	−0.606630	−	0.589883i
$22$	−1.29755	+	1.60234i	−0.276639	+	0.341621i
$23$	−6.98644	−	1.10654i	−1.45677	−	0.230730i	−0.622733	−	0.782434i	$-0.713978\pi$
$23$	−6.98644	−	1.10654i	−1.45677	−	0.230730i	−0.834040	+	0.551704i	$0.813978\pi$
$24$	0.0664328	−	1.73078i	0.0135605	−	0.353293i
$25$	−1.22289	−	4.84815i	−0.244579	−	0.969629i
$26$	5.53043	+	3.19300i	1.08461	+	0.626198i
$27$	1.81171	+	4.87008i	0.348664	+	0.937248i
$28$	0.117164	+	2.23562i	0.0221419	+	0.422493i
$29$	2.19453	−	6.75406i	0.407514	−	1.25420i	−0.511265	−	0.859423i	$-0.670823\pi$
$29$	2.19453	−	6.75406i	0.407514	−	1.25420i	0.918778	−	0.394774i	$-0.129177\pi$
$30$	−0.278234	+	3.86298i	−0.0507983	+	0.705280i
$31$	−5.32205	−	1.63579i	−0.955868	−	0.293797i
$31$	−5.32205	−	1.63579i	−0.955868	−	0.293797i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−3.06746	+	1.82871i	−0.533976	+	0.318337i
$34$	−3.31068	−	2.98095i	−0.567777	−	0.511229i
$35$	−0.0942185	−	5.00498i	−0.0159258	−	0.845996i
$36$	1.14303	−	2.77371i	0.190505	−	0.462286i
$37$	−2.64932	+	9.88741i	−0.435546	+	1.62548i	0.304210	+	0.952605i	$0.401608\pi$
$37$	−2.64932	+	9.88741i	−0.435546	+	1.62548i	−0.739756	+	0.672875i	$0.765059\pi$
$38$	−1.05023	+	0.850462i	−0.170370	+	0.137963i
$39$	7.08044	+	8.49765i	1.13378	+	1.36071i
$40$	1.63327	−	1.52723i	0.258242	−	0.241477i
$41$	6.78355	−	6.10794i	1.05941	−	0.953900i	0.0603934	−	0.998175i	$-0.480764\pi$
$41$	6.78355	−	6.10794i	1.05941	−	0.953900i	0.999019	+	0.0442751i	$0.0140978\pi$
$42$	−1.14649	+	3.70416i	−0.176908	+	0.571564i
$43$	5.30391	−	8.16730i	0.808838	−	1.24550i	−0.157319	−	0.987548i	$-0.550285\pi$
$43$	5.30391	−	8.16730i	0.808838	−	1.24550i	0.966157	−	0.257954i	$-0.0830483\pi$
$44$	2.01678	+	0.428679i	0.304040	+	0.0646258i
$45$	−2.76242	+	6.11302i	−0.411797	+	0.911276i
$46$	2.18584	+	6.72732i	0.322284	+	0.991889i
$47$	0.717792	+	0.365733i	0.104701	+	0.0533477i	0.505557	−	0.862793i	$-0.331287\pi$
$47$	0.717792	+	0.365733i	0.104701	+	0.0533477i	−0.400856	+	0.916141i	$0.631287\pi$
$48$	−1.57229	+	0.726564i	−0.226941	+	0.104870i
$49$	−0.413383	+	1.94481i	−0.0590547	+	0.277830i
$50$	−3.76455	+	3.29062i	−0.532388	+	0.465364i
$51$	−3.59896	−	6.82550i	−0.503956	−	0.955761i
$52$	0.334217	−	6.37724i	0.0463476	−	0.884364i
$53$	−2.77148	+	3.42249i	−0.380692	+	0.470115i	−0.931091	−	0.364786i	$-0.881142\pi$
$53$	−2.77148	+	3.42249i	−0.380692	+	0.470115i	0.550400	+	0.834901i	$0.314475\pi$
$54$	3.51677	−	3.82522i	0.478572	−	0.520546i
$55$	−4.47497	−	1.10923i	−0.603405	−	0.149568i
$56$	1.93876	−	1.11935i	0.259078	−	0.149579i
$57$	−2.21579	+	0.754397i	−0.293488	+	0.0999223i
$58$	−7.01421	+	1.11094i	−0.921011	+	0.145874i
$59$	3.94822	−	4.38494i	0.514014	−	0.570870i	−0.429135	−	0.903240i	$-0.641182\pi$
$59$	3.94822	−	4.38494i	0.514014	−	0.570870i	0.943149	+	0.332370i	$0.107848\pi$
$60$	3.56825	−	1.50585i	0.460659	−	0.194404i
$61$	−4.01193			−0.513675			−0.256837	−	0.966455i	$-0.582680\pi$
$61$	−4.01193			−0.513675			−0.256837	+	0.966455i	$0.582680\pi$
$62$	0.958655	+	5.48461i	0.121749	+	0.696547i
$63$	−4.07883	+	5.33562i	−0.513884	+	0.672224i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−1.22506	+	14.2269i	−0.151950	+	1.76463i
$66$	3.02199	+	1.90291i	0.371981	+	0.234232i
$67$	−4.21925	+	1.13054i	−0.515463	+	0.138118i	−0.507167	−	0.861848i	$-0.669307\pi$
$67$	−4.21925	+	1.13054i	−0.515463	+	0.138118i	−0.00829589	+	0.999966i	$0.502641\pi$
$68$	−1.15303	+	4.30316i	−0.139825	+	0.521835i
$69$	−0.469914	+	12.2427i	−0.0565710	+	1.47385i
$70$	−4.41669	+	2.35616i	−0.527896	+	0.281615i
$71$	−6.25571	+	0.657501i	−0.742416	+	0.0780310i	−0.468182	−	0.883632i	$-0.655091\pi$
$71$	−6.25571	+	0.657501i	−0.742416	+	0.0780310i	−0.274234	+	0.961663i	$0.588424\pi$
$72$	−2.99032	+	0.240793i	−0.352413	+	0.0283778i
$73$	−1.72574	+	4.49571i	−0.201983	+	0.526183i	−0.996734	−	0.0807517i	$-0.974268\pi$
$73$	−1.72574	+	4.49571i	−0.201983	+	0.526183i	0.794751	+	0.606935i	$0.207601\pi$
$74$	10.0125	−	2.12823i	1.16393	−	0.247401i
$75$	−8.08727	+	3.09774i	−0.933838	+	0.357697i
$76$	1.23456	+	0.549663i	0.141614	+	0.0630507i
$77$	−4.11271	−	2.09553i	−0.468687	−	0.238808i
$78$	4.35700	−	10.1666i	0.493333	−	1.15114i
$79$	1.09736	−	2.46470i	0.123462	−	0.277301i	−0.841231	−	0.540675i	$-0.818169\pi$
$79$	1.09736	−	2.46470i	0.123462	−	0.277301i	0.964694	+	0.263375i	$0.0848355\pi$
$80$	−2.10226	−	0.761902i	−0.235040	−	0.0851832i
$81$	8.00421	−	4.11493i	0.889356	−	0.457215i
$82$	−8.52188	−	3.27124i	−0.941084	−	0.361248i
$83$	−0.166887	+	3.18440i	−0.0183183	+	0.349534i	0.974059	+	0.226295i	$0.0726614\pi$
$83$	−0.166887	+	3.18440i	−0.0183183	+	0.349534i	−0.992377	+	0.123239i	$0.960672\pi$
$84$	3.82092	−	0.660117i	0.416897	−	0.0720247i
$85$	2.89944	−	9.53030i	0.314488	−	1.03371i
$86$	−9.68504	−	1.01794i	−1.04437	−	0.109767i
$87$	−12.0662	−	2.38876i	−1.29363	−	0.256102i
$88$	−0.533641	−	1.99158i	−0.0568864	−	0.212303i
$89$	6.76702	+	4.91653i	0.717303	+	0.521151i	0.885521	−	0.464599i	$-0.153801\pi$
$89$	6.76702	+	4.91653i	0.717303	+	0.521151i	−0.168218	+	0.985750i	$0.553801\pi$
$90$	6.70085	−	0.313921i	0.706332	−	0.0330902i
$91$	−4.41779	+	13.5966i	−0.463110	+	1.42531i
$92$	5.00174	−	5.00174i	0.521467	−	0.521467i
$93$	−1.72158	+	9.48874i	−0.178520	+	0.983936i
$94$		−	0.805597i		−	0.0830910i
$95$	−2.71780	−	1.32096i	−0.278841	−	0.135527i
$96$	1.36118	+	1.07107i	0.138925	+	0.109316i
$97$	0.310135	+	1.95812i	0.0314895	+	0.198817i	0.998418	−	0.0562318i	$-0.0179086\pi$
$97$	0.310135	+	1.95812i	0.0314895	+	0.198817i	−0.966928	+	0.255048i	$0.917909\pi$
$98$	1.92051	−	0.514600i	0.194001	−	0.0519824i
$99$	3.77437	+	4.90046i	0.379339	+	0.492514i
$100$	4.64103	+	1.86033i	0.464103	+	0.186033i
$101$	1.75057	+	2.40945i	0.174188	+	0.239749i	0.887181	−	0.461422i	$-0.152661\pi$
$101$	1.75057	+	2.40945i	0.174188	+	0.239749i	−0.712993	+	0.701172i	$0.752661\pi$
$102$	−4.44767	+	6.30541i	−0.440385	+	0.624329i
$103$	8.20414	+	0.429961i	0.808378	+	0.0423653i	0.452047	−	0.891994i	$-0.350694\pi$
$103$	8.20414	+	0.429961i	0.808378	+	0.0423653i	0.356331	+	0.934360i	$0.384027\pi$
$104$	−5.83389	+	2.59742i	−0.572060	+	0.254698i
$105$	−8.58854	+	1.18876i	−0.838155	+	0.116011i
$106$	4.30769	+	0.915627i	0.418399	+	0.0889335i
$107$	12.8939	−	4.94949i	1.24650	−	0.478485i	0.356433	−	0.934321i	$-0.383993\pi$
$107$	12.8939	−	4.94949i	1.24650	−	0.478485i	0.890064	+	0.455836i	$0.150660\pi$
$108$	−5.00488	−	1.39686i	−0.481595	−	0.134412i
$109$	−1.16957	+	0.380018i	−0.112025	+	0.0363991i	−0.364493	−	0.931206i	$-0.618758\pi$
$109$	−1.16957	+	0.380018i	−0.112025	+	0.0363991i	0.252468	+	0.967605i	$0.418758\pi$
$110$	1.04326	+	4.49081i	0.0994714	+	0.428182i
$111$	17.5484	+	2.52818i	1.66562	+	0.239964i
$112$	−1.87752	−	1.21928i	−0.177409	−	0.115211i
$113$	−11.3859	−	4.37064i	−1.07110	−	0.411155i	−0.242008	−	0.970274i	$-0.577806\pi$
$113$	−11.3859	−	4.37064i	−1.07110	−	0.411155i	−0.829087	+	0.559119i	$0.811139\pi$
$114$	1.67812	+	1.63179i	0.157170	+	0.152831i
$115$	−11.5530	+	10.8029i	−1.07732	+	1.00738i
$116$	4.17424	+	5.74535i	0.387568	+	0.533442i
$117$	13.1623	−	13.9206i	1.21685	−	1.28696i
$118$	−5.69946	−	1.52717i	−0.524678	−	0.140587i
$119$	4.98664	−	8.63711i	0.457124	−	0.791763i
$120$	−2.96167	−	2.49570i	−0.270362	−	0.227825i
$121$	4.51586	−	5.01537i	0.410533	−	0.455943i
$122$	1.82138	+	3.57465i	0.164900	+	0.323634i
$123$	−11.8964	−	10.4138i	−1.07266	−	0.938980i
$124$	4.45161	−	3.34413i	0.399766	−	0.300312i
$125$	−10.2323	−	4.50545i	−0.915209	−	0.402980i
$126$	6.60582	+	1.21195i	0.588493	+	0.107969i
$127$	13.9800	−	0.732659i	1.24052	−	0.0650130i	0.579244	−	0.815154i	$-0.303348\pi$
$127$	13.9800	−	0.732659i	1.24052	−	0.0650130i	0.661277	+	0.750141i	$0.270015\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	−15.1347	−	7.44655i	−1.33253	−	0.655633i
$130$	13.2324	−	5.36733i	1.16056	−	0.470746i
$131$	12.5357	+	1.31755i	1.09525	+	0.115115i	0.634878	−	0.772612i	$-0.281050\pi$
$131$	12.5357	+	1.31755i	1.09525	+	0.115115i	0.460369	+	0.887727i	$0.347717\pi$
$132$	0.323550	−	3.55651i	0.0281614	−	0.309555i
$133$	−2.35115	−	1.90392i	−0.203870	−	0.165091i
$134$	2.92282	+	3.24612i	0.252493	+	0.280422i
$135$	11.0802	+	3.49696i	0.953634	+	0.300970i
$136$	4.35761	−	0.926238i	0.373662	−	0.0794242i
$137$	−15.5104	+	10.0726i	−1.32515	+	0.860560i	−0.996475	−	0.0838853i	$-0.973267\pi$
$137$	−15.5104	+	10.0726i	−1.32515	+	0.860560i	−0.328670	+	0.944445i	$0.606600\pi$
$138$	11.1217	−	5.13937i	0.946738	−	0.437492i
$139$	15.7235	−	5.10888i	1.33365	−	0.433329i	0.446489	−	0.894789i	$-0.352674\pi$
$139$	15.7235	−	5.10888i	1.33365	−	0.433329i	0.887161	+	0.461460i	$0.152674\pi$
$140$	4.10449	+	2.86563i	0.346893	+	0.242190i
$141$	0.481763	−	1.30953i	0.0405718	−	0.110282i
$142$	3.42587	+	5.27538i	0.287493	+	0.442700i
$143$	11.0426	+	7.17118i	0.923432	+	0.599684i
$144$	1.57213	+	2.55508i	0.131010	+	0.212923i
$145$	−8.89786	−	13.1527i	−0.738927	−	1.09228i
$146$	4.78918	−	0.503363i	0.396355	−	0.0416586i
$147$	3.42961	+	0.312005i	0.282869	+	0.0257337i
$148$	−6.44185	−	7.95502i	−0.529517	−	0.653899i
$149$	0.289510	+	0.501446i	0.0237176	+	0.0410800i	0.877641	−	0.479319i	$-0.159116\pi$
$149$	0.289510	+	0.501446i	0.0237176	+	0.0410800i	−0.853923	+	0.520399i	$0.825783\pi$
$150$	6.43166	+	5.79947i	0.525142	+	0.473524i
$151$	−15.4083	−	11.1948i	−1.25391	−	0.911017i	−0.255465	−	0.966818i	$-0.582229\pi$
$151$	−15.4083	−	11.1948i	−1.25391	−	0.911017i	−0.998442	+	0.0558016i	$0.982229\pi$
$152$	−0.0707267	−	1.34955i	−0.00573669	−	0.109463i
$153$	−11.0006	+	7.58988i	−0.889347	+	0.613606i
$154$			4.61581i			0.371952i
$155$	−10.1992	+	7.13973i	−0.819222	+	0.573477i
$156$	−11.0365	+	0.733409i	−0.883629	+	0.0587197i
$157$	4.08639	−	2.08212i	0.326129	−	0.166171i	−0.283258	−	0.959044i	$-0.591415\pi$
$157$	4.08639	−	2.08212i	0.326129	−	0.166171i	0.609388	+	0.792872i	$0.291415\pi$
$158$	−2.69425	+	0.141200i	−0.214343	+	0.0112333i
$159$	6.45474	+	4.06447i	0.511894	+	0.322333i
$160$	0.275547	+	2.21903i	0.0217839	+	0.175429i
$161$	−13.7139	+	7.91772i	−1.08081	+	0.624004i
$162$	−7.30027	−	5.26366i	−0.573563	−	0.413552i
$163$	2.84079	−	17.9361i	0.222508	−	1.40486i	−0.583094	−	0.812405i	$-0.698158\pi$
$163$	2.84079	−	17.9361i	0.222508	−	1.40486i	0.805602	−	0.592457i	$-0.201842\pi$
$164$	0.954153	+	9.07816i	0.0745069	+	0.708886i
$165$	−0.989731	+	7.92387i	−0.0770504	+	0.616872i
$166$	2.91309	−	1.29699i	0.226100	−	0.100666i
$167$	−0.613338	+	0.944457i	−0.0474615	+	0.0730843i	−0.861605	−	0.507580i	$-0.830540\pi$
$167$	−0.613338	+	0.944457i	−0.0474615	+	0.0730843i	0.814143	+	0.580664i	$0.197207\pi$
$168$	−2.32283	−	3.10478i	−0.179210	−	0.239539i
$169$	11.2995	−	25.3791i	0.869193	−	1.95224i
$170$	−9.80787	+	1.74324i	−0.752230	+	0.133701i
$171$	1.75200	+	3.65609i	0.133979	+	0.279588i
$172$	3.48993	+	9.09157i	0.266104	+	0.693226i
$173$	−12.0599	−	18.5706i	−0.916899	−	1.41190i	−0.911222	−	0.411916i	$-0.864860\pi$
$173$	−12.0599	−	18.5706i	−0.916899	−	1.41190i	−0.00567690	−	0.999984i	$-0.501807\pi$
$174$	3.34955	+	11.8356i	0.253928	+	0.897251i
$175$	−8.95791	−	6.71188i	−0.677154	−	0.507371i
$176$	−1.53224	+	1.37964i	−0.115497	+	0.103994i
$177$	−8.35141	−	5.89086i	−0.627731	−	0.442784i
$178$	1.30850	−	8.26152i	0.0980759	−	0.619227i
$179$	0.815643	−	7.76033i	0.0609641	−	0.580034i	−0.920814	−	0.390002i	$-0.872474\pi$
$179$	0.815643	−	7.76033i	0.0609641	−	0.580034i	0.981778	−	0.190032i	$-0.0608591\pi$
$180$	−3.32183	−	5.82799i	−0.247595	−	0.434393i
$181$	−2.75741	+	4.77597i	−0.204956	+	0.354995i	−0.950119	−	0.311888i	$-0.899039\pi$
$181$	−2.75741	+	4.77597i	−0.204956	+	0.354995i	0.745162	+	0.666883i	$0.232372\pi$
$182$	14.1203	−	2.23643i	1.04666	−	0.165775i
$183$	0.822999	+	6.89995i	0.0608379	+	0.510059i
$184$	−6.72732	−	2.18584i	−0.495945	−	0.161142i
$185$	13.7999	+	18.2610i	1.01459	+	1.34257i
$186$	9.23611	−	2.77386i	0.677224	−	0.203389i
$187$	−6.49504	−	6.49504i	−0.474965	−	0.474965i
$188$	−0.717792	+	0.365733i	−0.0523504	+	0.0266738i
$189$	10.0132	+	5.92048i	0.728356	+	0.430651i
$190$	0.0568755	+	3.02128i	0.00412618	+	0.219187i
$191$	17.9449	+	10.3605i	1.29845	+	0.749658i	0.980136	−	0.198328i	$-0.0635511\pi$
$191$	17.9449	+	10.3605i	1.29845	+	0.749658i	0.318311	+	0.947986i	$0.396884\pi$
$192$	0.336368	−	1.69908i	0.0242753	−	0.122620i
$193$	1.40210	+	1.73144i	0.100925	+	0.124632i	0.825106	−	0.564978i	$-0.191115\pi$
$193$	1.40210	+	1.73144i	0.100925	+	0.124632i	−0.724181	+	0.689610i	$0.757782\pi$
$194$	1.60390	−	1.16530i	0.115153	−	0.0836636i
$195$	24.7195	−	0.811542i	1.77020	−	0.0581157i
$196$	−1.33041	−	1.47757i	−0.0950290	−	0.105540i
$197$	9.13800	−	23.8053i	0.651056	−	1.69606i	−0.0648811	−	0.997893i	$-0.520667\pi$
$197$	9.13800	−	23.8053i	0.651056	−	1.69606i	0.715937	−	0.698165i	$-0.246000\pi$
$198$	2.65281	−	5.58775i	0.188527	−	0.397104i
$199$	2.30625	−	10.8501i	0.163486	−	0.769140i	−0.817634	−	0.575739i	$-0.804715\pi$
$199$	2.30625	−	10.8501i	0.163486	−	0.769140i	0.981120	−	0.193402i	$-0.0619521\pi$
$200$	−0.449419	−	4.97976i	−0.0317787	−	0.352122i
$201$	2.80991	+	7.02460i	0.198195	+	0.495477i
$202$	1.35209	−	2.65363i	0.0951330	−	0.186709i
$203$	−5.69747	−	14.8424i	−0.399884	−	1.04173i
$204$	7.63736	+	1.10030i	0.534722	+	0.0770367i
$205$	−1.45170	−	20.3595i	−0.101391	−	1.42197i
$206$	−3.34150	−	7.50514i	−0.232814	−	0.522908i
$207$	21.1521	−	1.70326i	1.47017	−	0.118385i
$208$	4.96285	+	4.01884i	0.344112	+	0.278656i
$209$	−2.25421	+	1.63778i	−0.155927	+	0.113288i
$210$	4.95830	+	7.11276i	0.342155	+	0.490827i
$211$	−3.74427	−	6.48526i	−0.257766	−	0.446464i	0.707877	−	0.706336i	$-0.249653\pi$
$211$	−3.74427	−	6.48526i	−0.257766	−	0.446464i	−0.965643	+	0.259872i	$0.916320\pi$
$212$	−1.13982	−	4.25386i	−0.0782831	−	0.292156i
$213$	2.41409	+	10.6241i	0.165411	+	0.727949i
$214$	−10.2637	−	9.24149i	−0.701613	−	0.631736i
$215$	−7.11767	−	20.5796i	−0.485421	−	1.40352i
$216$	1.02756	+	5.09354i	0.0699166	+	0.346571i
$217$	−11.5638	+	4.65205i	−0.785004	+	0.315802i
$218$	0.869573	+	0.869573i	0.0588949	+	0.0588949i
$219$	8.08601	+	2.04579i	0.546402	+	0.138242i
$220$	3.52771	−	2.96834i	0.237838	−	0.200125i
$221$	−16.7221	+	23.0160i	−1.12485	+	1.54822i
$222$	−5.71420	−	16.7835i	−0.383512	−	1.12644i
$223$	25.6548	+	6.87417i	1.71797	+	0.460329i	0.977356	−	0.211602i	$-0.0678679\pi$
$223$	25.6548	+	6.87417i	1.71797	+	0.460329i	0.740614	+	0.671930i	$0.234535\pi$
$224$	−0.234007	+	2.22643i	−0.0156352	+	0.148759i
$225$	6.98669	+	13.2735i	0.465780	+	0.884901i
$226$	1.27482	+	12.1291i	0.0848000	+	0.806818i
$227$	−3.44050	−	0.180309i	−0.228354	−	0.0119675i	−0.0621841	−	0.998065i	$-0.519807\pi$
$227$	−3.44050	−	0.180309i	−0.228354	−	0.0119675i	−0.166170	+	0.986097i	$0.553140\pi$
$228$	0.692087	−	2.23603i	0.0458346	−	0.148085i
$229$	−3.09711	−	14.5708i	−0.204663	−	0.962864i	−0.953798	−	0.300447i	$-0.902864\pi$
$229$	−3.09711	−	14.5708i	−0.204663	−	0.962864i	0.749135	−	0.662417i	$-0.230469\pi$
$230$	14.8704	+	5.38933i	0.980525	+	0.355362i
$231$	−2.76035	+	7.50316i	−0.181618	+	0.493672i
$232$	3.22408	−	6.32761i	0.211671	−	0.415428i
$233$	6.80720	−	13.3599i	0.445954	−	0.875234i	−0.553157	−	0.833077i	$-0.686577\pi$
$233$	6.80720	−	13.3599i	0.445954	−	0.875234i	0.999111	−	0.0421573i	$-0.0134231\pi$
$234$	−18.3789	−	5.40788i	−1.20146	−	0.353524i
$235$	1.63155	−	0.763526i	0.106431	−	0.0498070i
$236$	1.22679	+	5.77158i	0.0798570	+	0.375698i
$237$	−4.46405	−	1.38169i	−0.289971	−	0.0897507i
$238$	−9.95961	−	0.521961i	−0.645586	−	0.0338337i
$239$	−0.528911	−	5.03225i	−0.0342124	−	0.325509i	−0.998220	−	0.0596353i	$-0.981006\pi$
$239$	−0.528911	−	5.03225i	−0.0342124	−	0.325509i	0.964008	−	0.265874i	$-0.0856604\pi$
$240$	−0.879111	+	3.77189i	−0.0567464	+	0.243475i
$241$	−1.12167	+	10.6720i	−0.0722532	+	0.687443i	0.897109	+	0.441809i	$0.145663\pi$
$241$	−1.12167	+	10.6720i	−0.0722532	+	0.687443i	−0.969363	+	0.245634i	$0.921004\pi$
$242$	−6.51889	−	1.74673i	−0.419050	−	0.112284i
$243$	−8.71908	−	12.9220i	−0.559329	−	0.828946i
$244$	2.35815	−	3.24572i	0.150965	−	0.207786i
$245$	2.86242	+	3.40183i	0.182873	+	0.217335i
$246$	−3.87792	+	15.3275i	−0.247247	+	0.977246i
$247$	6.10234	+	6.10234i	0.388283	+	0.388283i
$248$	−5.00063	−	2.44821i	−0.317540	−	0.155461i
$249$	5.51096	−	0.366219i	0.349243	−	0.0232082i
$250$	0.630998	+	11.1625i	0.0399078	+	0.705980i
$251$	−9.24173	−	8.32130i	−0.583333	−	0.525235i	0.323774	−	0.946134i	$-0.395048\pi$
$251$	−9.24173	−	8.32130i	−0.583333	−	0.525235i	−0.907108	+	0.420899i	$0.861715\pi$
$252$	−1.91913	−	6.43604i	−0.120894	−	0.405432i
$253$	3.77473	+	14.0875i	0.237315	+	0.885671i
$254$	−6.99957	−	12.1236i	−0.439192	−	0.760704i
$255$	−16.9856	−	3.03160i	−1.06368	−	0.189846i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	9.93097	+	8.04194i	0.619477	+	0.501642i	0.886915	−	0.461933i	$-0.152844\pi$
$257$	9.93097	+	8.04194i	0.619477	+	0.501642i	−0.267438	+	0.963575i	$0.586177\pi$
$258$	0.236060	+	16.8657i	0.0146964	+	1.05001i
$259$	9.32065	+	20.9345i	0.579157	+	1.30081i
$260$	−10.7897	−	9.35344i	−0.669149	−	0.580075i
$261$	−1.63310	+	21.2422i	−0.101086	+	1.31486i
$262$	−4.51713	−	11.7675i	−0.279069	−	0.727000i
$263$	−8.75882	+	17.1902i	−0.540092	+	1.05999i	0.446192	+	0.894937i	$0.352780\pi$
$263$	−8.75882	+	17.1902i	−0.540092	+	1.05999i	−0.986285	+	0.165053i	$0.947220\pi$
$264$	−3.31576	+	1.32634i	−0.204071	+	0.0816304i
$265$	2.22834	+	9.59204i	0.136886	+	0.589234i
$266$	−0.629008	+	2.95925i	−0.0385670	+	0.181443i
$267$	7.06757	−	12.6469i	0.432528	−	0.773978i
$268$	1.56538	−	4.07796i	0.0956209	−	0.249101i
$269$	−18.2606	−	20.2804i	−1.11337	−	1.23652i	−0.969017	−	0.246993i	$-0.920557\pi$
$269$	−18.2606	−	20.2804i	−1.11337	−	1.23652i	−0.144351	−	0.989527i	$-0.546109\pi$
$270$	−1.91450	−	11.4601i	−0.116513	−	0.697442i
$271$	12.3927	−	9.00385i	0.752805	−	0.546945i	−0.143890	−	0.989594i	$-0.545961\pi$
$271$	12.3927	−	9.00385i	0.752805	−	0.546945i	0.896695	+	0.442649i	$0.145961\pi$
$272$	−2.80360	−	3.46215i	−0.169993	−	0.209924i
$273$	24.2904	+	4.80881i	1.47012	+	0.291042i
$274$	16.0163	+	9.24703i	0.967582	+	0.558634i
$275$	−8.10632	+	6.36918i	−0.488829	+	0.384076i
$276$	−9.62833	−	7.57624i	−0.579558	−	0.456036i
$277$	−3.42852	+	1.74692i	−0.206000	+	0.104962i	−0.553947	−	0.832552i	$-0.686879\pi$
$277$	−3.42852	+	1.74692i	−0.206000	+	0.104962i	0.347947	+	0.937514i	$0.386879\pi$
$278$	−11.6904	−	11.6904i	−0.701142	−	0.701142i
$279$	16.6725	+	1.01438i	0.998154	+	0.0607293i
$280$	0.689893	−	4.95810i	0.0412290	−	0.296303i
$281$	19.8815	+	6.45989i	1.18603	+	0.385365i	0.834604	−	0.550850i	$-0.185697\pi$
$281$	19.8815	+	6.45989i	1.18603	+	0.385365i	0.351427	+	0.936215i	$0.385697\pi$
$282$	−1.38551	+	0.165259i	−0.0825061	+	0.00984101i
$283$	−15.1465	+	2.39896i	−0.900364	+	0.142604i	−0.589422	−	0.807825i	$-0.700644\pi$
$283$	−15.1465	+	2.39896i	−0.900364	+	0.142604i	−0.310942	+	0.950429i	$0.600644\pi$
$284$	3.14508	−	5.44744i	0.186626	−	0.323246i
$285$	−1.71434	+	4.94522i	−0.101548	+	0.292930i
$286$	1.37631	−	13.0947i	0.0813829	−	0.774307i
$287$	3.19676	−	20.1836i	0.188699	−	1.19140i
$288$	1.56286	−	2.56076i	0.0920924	−	0.150894i
$289$	2.11548	−	1.90478i	0.124440	−	0.112046i
$290$	−7.67963	+	13.8993i	−0.450963	+	0.816193i
$291$	3.30407	−	0.935073i	0.193688	−	0.0548150i
$292$	−2.62274	−	4.03867i	−0.153484	−	0.236345i
$293$	−2.44215	−	6.36201i	−0.142672	−	0.371672i	0.843562	−	0.537032i	$-0.180455\pi$
$293$	−2.44215	−	6.36201i	−0.142672	−	0.371672i	−0.986233	+	0.165360i	$0.947121\pi$
$294$	−1.27901	−	3.19745i	−0.0745934	−	0.186479i
$295$	−2.30890	−	12.9904i	−0.134429	−	0.756328i
$296$	−4.16344	+	9.35124i	−0.241995	+	0.543530i
$297$	7.65383	−	7.49666i	0.444120	−	0.435001i
$298$	0.315357	−	0.485607i	0.0182681	−	0.0281304i
$299$	41.2662	−	18.3729i	2.38649	−	1.06253i
$300$	2.24745	−	8.36355i	0.129757	−	0.482870i
$301$	−2.27885	−	21.6818i	−0.131351	−	1.24972i
$302$	−2.97940	+	18.8112i	−0.171445	+	1.08246i
$303$	3.78481	−	3.50500i	0.217431	−	0.201357i
$304$	−1.17034	+	0.675699i	−0.0671239	+	0.0387540i
$305$	−5.51338	+	7.07676i	−0.315695	+	0.405214i
$306$	11.7568	+	6.35589i	0.672092	+	0.363342i
$307$	−4.23222	+	0.221801i	−0.241545	+	0.0126589i	−0.172724	−	0.984970i	$-0.555257\pi$
$307$	−4.23222	+	0.221801i	−0.241545	+	0.0126589i	−0.0688208	+	0.997629i	$0.521924\pi$
$308$	4.11271	−	2.09553i	0.234344	−	0.119404i
$309$	−0.943510	−	14.1982i	−0.0536744	−	0.807706i
$310$	10.9919	+	5.84621i	0.624298	+	0.332043i
$311$		−	28.8109i		−	1.63372i	−0.576838	−	0.816859i	$-0.695714\pi$
$311$		−	28.8109i		−	1.63372i	0.576838	−	0.816859i	$-0.304286\pi$
$312$	5.66395	+	9.50065i	0.320658	+	0.537868i
$313$	1.22719	+	23.4162i	0.0693651	+	1.32356i	0.782550	+	0.622588i	$0.213919\pi$
$313$	1.22719	+	23.4162i	0.0693651	+	1.32356i	−0.713185	+	0.700976i	$0.752748\pi$
$314$	−3.71036	−	2.69574i	−0.209388	−	0.152129i
$315$	3.80633	+	14.5272i	0.214462	+	0.818516i
$316$	1.34898	+	2.33650i	0.0758858	+	0.131438i
$317$	−0.285477	−	0.352534i	−0.0160340	−	0.0198003i	0.769066	−	0.639169i	$-0.220722\pi$
$317$	−0.285477	−	0.352534i	−0.0160340	−	0.0198003i	−0.785100	+	0.619369i	$0.787388\pi$
$318$	0.691079	−	7.59645i	0.0387538	−	0.425988i
$319$	−14.5622	+	1.53055i	−0.815325	+	0.0856942i
$320$	1.85207	−	1.25293i	0.103534	−	0.0700410i
$321$	−11.1575	−	21.1603i	−0.622748	−	1.18105i
$322$	13.2807	+	8.62460i	0.740105	+	0.480630i
$323$	−3.27896	−	5.04915i	−0.182446	−	0.280942i
$324$	−1.37570	+	8.89424i	−0.0764280	+	0.494124i
$325$	23.4116	+	21.7121i	1.29864	+	1.20437i
$326$	−17.2708	+	5.61164i	−0.956544	+	0.310800i
$327$	0.893501	+	1.93355i	0.0494107	+	0.106925i
$328$	7.65553	−	4.97156i	0.422706	−	0.274508i
$329$	1.76407	−	0.374965i	0.0972564	−	0.0206725i
$330$	7.50955	−	2.71551i	0.413387	−	0.149484i
$331$	6.89447	+	7.65709i	0.378954	+	0.420872i	0.902205	−	0.431307i	$-0.141948\pi$
$331$	6.89447	+	7.65709i	0.378954	+	0.420872i	−0.523251	+	0.852179i	$0.675281\pi$
$332$	−2.47814	−	2.00676i	−0.136006	−	0.110135i
$333$	0.748261	−	30.6995i	0.0410045	−	1.68232i
$334$	1.11997	+	0.117713i	0.0612819	+	0.00644098i
$335$	−3.80409	+	8.99610i	−0.207839	+	0.491509i
$336$	−1.71184	+	3.47920i	−0.0933883	+	0.189806i
$337$	4.60686	+	29.0866i	0.250952	+	1.58445i	0.715315	+	0.698802i	$0.246283\pi$
$337$	4.60686	+	29.0866i	0.250952	+	1.58445i	−0.464363	+	0.885645i	$0.653717\pi$
$338$	−27.7428	+	1.45394i	−1.50901	+	0.0790839i
$339$	−5.18120	+	20.4787i	−0.281404	+	1.11225i
$340$	6.00592	+	7.94746i	0.325717	+	0.431012i
$341$	1.38204	+	11.3963i	0.0748418	+	0.617144i
$342$	2.46221	−	3.22087i	0.133141	−	0.174165i
$343$	9.13517	+	17.9288i	0.493253	+	0.968063i
$344$	6.51626	−	7.23704i	0.351333	−	0.390195i
$345$	20.9495	+	17.6534i	1.12788	+	0.950425i
$346$	−11.0715	+	19.1764i	−0.595206	+	1.03093i
$347$	−2.23567	−	0.599045i	−0.120017	−	0.0321584i	0.198311	−	0.980139i	$-0.436455\pi$
$347$	−2.23567	−	0.599045i	−0.120017	−	0.0321584i	−0.318328	+	0.947981i	$0.603121\pi$
$348$	9.02490	−	8.35770i	0.483785	−	0.448020i
$349$	5.30316	+	7.29917i	0.283871	+	0.390715i	0.927011	−	0.375033i	$-0.122369\pi$
$349$	5.30316	+	7.29917i	0.283871	+	0.390715i	−0.643140	+	0.765749i	$0.722369\pi$
$350$	−1.91352	+	11.0287i	−0.102282	+	0.589508i
$351$	−26.6415	−	19.7817i	−1.42202	−	1.05587i
$352$	1.92489	+	0.738895i	0.102597	+	0.0393832i
$353$	13.6064	+	8.83608i	0.724194	+	0.470297i	0.853358	−	0.521326i	$-0.174562\pi$
$353$	13.6064	+	8.83608i	0.724194	+	0.470297i	−0.129163	+	0.991623i	$0.541229\pi$
$354$	−1.45733	+	10.1156i	−0.0774565	+	0.537636i
$355$	−7.43710	+	11.9382i	−0.394720	+	0.633613i
$356$	−7.95511	+	2.58477i	−0.421620	+	0.136993i
$357$	−15.8776	−	6.80452i	−0.840330	−	0.360133i
$358$	−7.28480	+	2.79637i	−0.385014	+	0.147793i
$359$	19.2956	+	4.10141i	1.01838	+	0.216464i	0.686711	−	0.726930i	$-0.259054\pi$
$359$	19.2956	+	4.10141i	1.01838	+	0.216464i	0.331673	+	0.943395i	$0.392387\pi$
$360$	−3.68470	+	5.60562i	−0.194201	+	0.295442i
$361$	15.6890	−	6.98518i	0.825736	−	0.367641i
$362$	5.50726	+	0.288623i	0.289455	+	0.0151697i
$363$	−9.55211	−	6.73780i	−0.501356	−	0.353643i
$364$	−8.40313	−	11.5659i	−0.440444	−	0.606219i
$365$	5.55852	+	9.22231i	0.290946	+	0.482718i
$366$	5.77427	−	3.86581i	0.301826	−	0.202069i
$367$	−3.03602	+	0.813499i	−0.158479	+	0.0424643i	−0.337186	−	0.941438i	$-0.609475\pi$
$367$	−3.03602	+	0.813499i	−0.158479	+	0.0424643i	0.178707	+	0.983902i	$0.442808\pi$
$368$	1.10654	+	6.98644i	0.0576825	+	0.364193i
$369$	−15.4699	+	22.5963i	−0.805329	+	1.17632i
$370$	10.0056	−	20.5861i	0.520168	−	1.07022i
$371$			9.85902i			0.511855i
$372$	−6.66463	−	6.97013i	−0.345545	−	0.361384i
$373$	−26.7614	+	26.7614i	−1.38565	+	1.38565i	−0.551429	+	0.834222i	$0.685917\pi$
$373$	−26.7614	+	26.7614i	−1.38565	+	1.38565i	−0.834222	+	0.551429i	$0.814083\pi$
$374$	−2.83844	+	8.73581i	−0.146772	+	0.451718i
$375$	−5.64971	+	18.5224i	−0.291750	+	0.956495i
$376$	0.651741	+	0.473518i	0.0336110	+	0.0244198i
$377$	11.7377	+	43.8057i	0.604523	+	2.25611i
$378$	0.729272	−	11.6097i	0.0375097	−	0.597138i
$379$	−26.9459	−	2.83213i	−1.38412	−	0.145477i	−0.616989	−	0.786971i	$-0.711648\pi$
$379$	−26.9459	−	2.83213i	−1.38412	−	0.145477i	−0.767127	+	0.641495i	$0.778315\pi$
$380$	2.66616	−	1.42231i	0.136771	−	0.0729630i
$381$	−4.12790	−	23.8933i	−0.211478	−	1.22409i
$382$	1.08445	−	20.6926i	0.0554854	−	1.05872i
$383$	5.32816	+	2.04529i	0.272256	+	0.104509i	0.490666	−	0.871348i	$-0.336754\pi$
$383$	5.32816	+	2.04529i	0.272256	+	0.104509i	−0.218410	+	0.975857i	$0.570087\pi$
$384$	−1.66659	+	0.471658i	−0.0850481	+	0.0240692i
$385$	−9.34825	+	4.37476i	−0.476431	+	0.222958i
$386$	0.906189	−	2.03533i	0.0461238	−	0.103596i
$387$	−9.70234	+	27.5571i	−0.493197	+	1.40080i
$388$	−1.76644	−	0.900047i	−0.0896775	−	0.0456930i
$389$	−27.3027	−	12.1560i	−1.38430	−	0.616331i	−0.426692	−	0.904397i	$-0.640321\pi$
$389$	−27.3027	−	12.1560i	−1.38430	−	0.616331i	−0.957611	+	0.288066i	$0.906988\pi$
$390$	−11.9455	−	21.6568i	−0.604885	−	1.09664i
$391$	−30.8236	+	6.55177i	−1.55882	+	0.331337i
$392$	−0.712529	+	1.85620i	−0.0359882	+	0.0937523i
$393$	−0.305540	−	21.8299i	−0.0154125	−	1.10117i
$394$	−25.3593	+	2.66536i	−1.27758	+	0.134279i
$395$	−2.83952	−	5.32277i	−0.142872	−	0.267817i
$396$	−6.18307	+	0.173115i	−0.310711	+	0.00869938i
$397$	−0.584285	+	2.18058i	−0.0293244	+	0.109440i	−0.979037	−	0.203683i	$-0.934709\pi$
$397$	−0.584285	+	2.18058i	−0.0293244	+	0.109440i	0.949712	+	0.313123i	$0.101375\pi$
$398$	−10.7145	+	2.87094i	−0.537069	+	0.143907i
$399$	−2.79217	+	4.43421i	−0.139783	+	0.221988i
$400$	−4.23297	+	2.66120i	−0.211648	+	0.133060i
$401$	36.7973	+	11.9562i	1.83757	+	0.597063i	0.998600	+	0.0528879i	$0.0168426\pi$
$401$	36.7973	+	11.9562i	1.83757	+	0.597063i	0.838971	+	0.544175i	$0.183157\pi$
$402$	4.98329	−	5.69275i	0.248544	−	0.283928i
$403$	34.1929	−	9.74950i	1.70327	−	0.485657i
$404$	−2.97824			−0.148173
$405$	3.74130	−	19.7738i	0.185907	−	0.982567i
$406$	−10.6381	+	11.8148i	−0.527960	+	0.586359i
$407$	20.8455	−	3.30160i	1.03327	−	0.163654i
$408$	−2.48691	−	7.30447i	−0.123120	−	0.361625i
$409$	−27.7170	+	16.0024i	−1.37052	+	0.791269i	−0.990993	−	0.133913i	$-0.957246\pi$
$409$	−27.7170	+	16.0024i	−1.37052	+	0.791269i	−0.379524	+	0.925182i	$0.623912\pi$
$410$	−17.4814	+	10.5365i	−0.863345	+	0.520361i
$411$	20.5052	+	24.6095i	1.01145	+	1.21390i
$412$	−5.17012	+	6.38456i	−0.254713	+	0.314545i
$413$	0.691329	−	13.1913i	0.0340181	−	0.649103i
$414$	−11.1205	−	18.0734i	−0.546541	−	0.888259i
$415$	5.38772	+	4.67053i	0.264473	+	0.229267i
$416$	1.32772	−	6.24644i	0.0650969	−	0.306257i
$417$	−12.0120	−	25.9942i	−0.588232	−	1.27294i
$418$	2.48266	+	1.26498i	0.121431	+	0.0618721i
$419$	−4.44585	−	13.6829i	−0.217194	−	0.668455i	−0.998991	−	0.0449210i	$-0.985696\pi$
$419$	−4.44585	−	13.6829i	−0.217194	−	0.668455i	0.781796	−	0.623534i	$-0.214304\pi$
$420$	4.08649	−	7.64700i	0.199400	−	0.373136i
$421$	8.43619	+	1.79317i	0.411155	+	0.0873937i	0.408845	−	0.912604i	$-0.365932\pi$
$421$	8.43619	+	1.79317i	0.411155	+	0.0873937i	0.00230950	+	0.999997i	$0.499265\pi$
$422$	−4.07855	+	6.28042i	−0.198541	+	0.305726i
$423$	−2.35103	−	0.559932i	−0.114311	−	0.0272248i
$424$	−3.27275	+	2.94680i	−0.158939	+	0.143109i
$425$	−12.8262	−	18.2114i	−0.622163	−	0.883382i
$426$	8.37013	−	6.97420i	0.405534	−	0.337901i
$427$	−6.97991	+	5.65222i	−0.337782	+	0.273530i
$428$	−3.57460	+	13.3406i	−0.172785	+	0.644842i
$429$	10.0682	−	20.4629i	0.486095	−	0.987957i
$430$	−15.1052	+	15.6848i	−0.728438	+	0.756390i
$431$	20.0332	+	18.0380i	0.964965	+	0.868858i	0.991410	−	0.130792i	$-0.0417520\pi$
$431$	20.0332	+	18.0380i	0.964965	+	0.868858i	−0.0264449	+	0.999650i	$0.508419\pi$
$432$	4.07187	−	3.22798i	0.195908	−	0.155306i
$433$	−10.5714	+	10.5714i	−0.508030	+	0.508030i	−0.913921	−	0.405891i	$-0.866961\pi$
$433$	−10.5714	+	10.5714i	−0.508030	+	0.508030i	0.405891	+	0.913921i	$0.366961\pi$
$434$	9.39488	+	8.19147i	0.450969	+	0.393203i
$435$	−20.7956	+	18.0012i	−0.997072	+	0.863092i
$436$	0.380018	−	1.16957i	0.0181995	−	0.0560124i
$437$	0.500287	+	9.54604i	0.0239320	+	0.456649i
$438$	−1.84816	−	8.13346i	−0.0883084	−	0.388632i
$439$	3.51057	+	2.02683i	0.167550	+	0.0967352i	0.581430	−	0.813596i	$-0.302493\pi$
$439$	3.51057	+	2.02683i	0.167550	+	0.0967352i	−0.413880	+	0.910331i	$0.635827\pi$
$440$	−4.24636	−	1.79561i	−0.202437	−	0.0856024i
$441$	−0.166938	−	5.96245i	−0.00794944	−	0.283926i
$442$	28.0991	+	4.45046i	1.33654	+	0.211687i
$443$	17.0903	−	21.1048i	0.811985	−	1.00272i	−0.187805	−	0.982206i	$-0.560137\pi$
$443$	17.0903	−	21.1048i	0.811985	−	1.00272i	0.999790	−	0.0205112i	$-0.00652937\pi$
$444$	−12.3601	+	12.7110i	−0.586582	+	0.603236i
$445$	17.9720	−	5.18002i	0.851953	−	0.245557i
$446$	−5.52209	−	25.9794i	−0.261478	−	1.23016i
$447$	0.803027	−	0.600782i	0.0379819	−	0.0284160i
$448$	2.09000	−	0.802275i	0.0987431	−	0.0379039i
$449$	−6.32253	−	19.4587i	−0.298379	−	0.918315i	−0.982066	−	0.188539i	$-0.939625\pi$
$449$	−6.32253	−	19.4587i	−0.298379	−	0.918315i	0.683687	−	0.729775i	$-0.260375\pi$
$450$	8.65489	−	12.2512i	0.407996	−	0.577529i
$451$	−17.1936	−	7.65509i	−0.809616	−	0.360464i
$452$	10.2284	−	6.64239i	0.481103	−	0.312432i
$453$	−16.0926	+	28.7965i	−0.756096	+	1.35298i
$454$	1.40130	+	3.14736i	0.0657661	+	0.147713i
$455$	17.9122	+	26.4777i	0.839738	+	1.24129i
$456$	−2.30652	+	0.398483i	−0.108013	+	0.0186607i
$457$	14.1613	+	2.24293i	0.662437	+	0.104920i	0.478594	−	0.878036i	$-0.341146\pi$
$457$	14.1613	+	2.24293i	0.662437	+	0.104920i	0.183842	+	0.982956i	$0.441146\pi$
$458$	−11.5766	+	9.37454i	−0.540939	+	0.438044i
$459$	15.3102	+	17.3625i	0.714618	+	0.810414i
$460$	−1.94909	−	15.6963i	−0.0908768	−	0.731845i
$461$	−3.09010	+	4.25315i	−0.143920	+	0.198089i	−0.874891	−	0.484319i	$-0.839067\pi$
$461$	−3.09010	+	4.25315i	−0.143920	+	0.198089i	0.730971	+	0.682408i	$0.239067\pi$
$462$	7.93854	−	0.946878i	0.369334	−	0.0440528i
$463$	−11.5997	−	22.7657i	−0.539084	−	1.05801i	−0.986511	−	0.163692i	$-0.947660\pi$
$463$	−11.5997	−	22.7657i	−0.539084	−	1.05801i	0.447427	−	0.894320i	$-0.352340\pi$
$464$	−7.10164			−0.329685
$465$	14.3716	+	16.0766i	0.666466	+	0.745535i
$466$	−14.9941			−0.694590
$467$	−7.46260	−	14.6462i	−0.345328	−	0.677744i	0.651386	−	0.758746i	$-0.274188\pi$
$467$	−7.46260	−	14.6462i	−0.345328	−	0.677744i	−0.996714	+	0.0810025i	$0.974188\pi$
$468$	3.52537	+	18.8308i	0.162960	+	0.870455i
$469$	−5.74783	+	7.91121i	−0.265410	+	0.365306i
$470$	−1.42102	−	1.10709i	−0.0655466	−	0.0510662i
$471$	−4.41923	−	6.60089i	−0.203627	−	0.304153i
$472$	4.58556	−	3.71332i	0.211068	−	0.170919i
$473$	−19.8317	−	3.14104i	−0.911864	−	0.144425i
$474$	0.795539	+	4.60478i	0.0365403	+	0.211504i
$475$	−6.06501	+	2.97869i	−0.278282	+	0.136672i
$476$	4.05650	+	9.11104i	0.185929	+	0.417604i
$477$	5.66621	−	11.9350i	0.259438	−	0.546467i
$478$	−4.24365	+	2.75586i	−0.194100	+	0.126050i
$479$	8.05289	+	3.58538i	0.367946	+	0.163820i	0.582377	−	0.812919i	$-0.302123\pi$
$479$	8.05289	+	3.58538i	0.367946	+	0.163820i	−0.214431	+	0.976739i	$0.568790\pi$
$480$	3.75989	−	0.929109i	0.171615	−	0.0424079i
$481$	−20.1999	−	62.1690i	−0.921037	−	2.83466i
$482$	10.0180	−	3.84556i	0.456309	−	0.175161i
$483$	16.4306	+	21.9617i	0.747619	+	0.999294i
$484$	1.40316	+	6.60137i	0.0637802	+	0.300062i
$485$	3.88018	+	2.14388i	0.176190	+	0.0973485i
$486$	−7.55519	+	13.6352i	−0.342711	+	0.618506i
$487$	16.5207	−	20.4014i	0.748626	−	0.924476i	−0.250420	−	0.968137i	$-0.580569\pi$
$487$	16.5207	−	20.4014i	0.748626	−	0.924476i	0.999046	+	0.0436609i	$0.0139021\pi$
$488$	−3.96253	−	0.627604i	−0.179375	−	0.0284103i
$489$	−31.4303	−	1.20640i	−1.42133	−	0.0545551i
$490$	1.73154	−	4.09484i	0.0782230	−	0.184986i
$491$	−5.15118	−	2.97403i	−0.232469	−	0.134216i	0.379241	−	0.925298i	$-0.376185\pi$
$491$	−5.15118	−	2.97403i	−0.232469	−	0.134216i	−0.611711	+	0.791082i	$0.709518\pi$
$492$	15.4174	−	3.50329i	0.695072	−	0.157940i
$493$	−1.65578	−	31.5942i	−0.0745726	−	1.42293i
$494$	2.66682	−	8.20763i	0.119986	−	0.369279i
$495$	13.8310	+	0.0767098i	0.621656	+	0.00344785i
$496$	0.0888696	+	5.56706i	0.00399036	+	0.249968i
$497$	−9.95729	+	9.95729i	−0.446646	+	0.446646i
$498$	−2.82823	−	4.74404i	−0.126736	−	0.212586i
$499$	10.3230	+	9.29491i	0.462123	+	0.416097i	0.867027	−	0.498262i	$-0.166028\pi$
$499$	10.3230	+	9.29491i	0.462123	+	0.416097i	−0.404903	+	0.914359i	$0.632695\pi$
$500$	9.65941	−	5.62990i	0.431982	−	0.251777i
$501$	1.75015	+	0.861111i	0.0781911	+	0.0384716i
$502$	−3.21867	+	12.0122i	−0.143656	+	0.536132i
$503$	−16.7991	+	13.6037i	−0.749035	+	0.606557i	−0.925940	−	0.377671i	$-0.876725\pi$
$503$	−16.7991	+	13.6037i	−0.749035	+	0.606557i	0.176904	+	0.984228i	$0.443392\pi$
$504$	−4.86329	+	4.63186i	−0.216628	+	0.206319i
$505$	6.65581	+	0.223301i	0.296180	+	0.00993674i
$506$	10.8383	−	9.75888i	0.481823	−	0.433835i
$507$	−45.9665	−	14.2273i	−2.04144	−	0.631859i
$508$	−7.62448	+	11.7407i	−0.338282	+	0.520908i
$509$	−12.0194	−	2.55480i	−0.532751	−	0.113240i	−0.0663217	−	0.997798i	$-0.521126\pi$
$509$	−12.0194	−	2.55480i	−0.532751	−	0.113240i	−0.466429	+	0.884559i	$0.654460\pi$
$510$	5.01011	+	16.5106i	0.221851	+	0.731100i
$511$	3.33137	+	10.2529i	0.147371	+	0.453562i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	5.92856	−	3.76320i	0.261752	−	0.166149i
$514$	2.65686	−	12.4995i	0.117189	−	0.551330i
$515$	12.0329	−	13.8807i	0.530234	−	0.611655i
$516$	14.9203	−	7.86722i	0.656830	−	0.346335i
$517$	0.0869303	−	1.65873i	0.00382319	−	0.0729508i
$518$	14.4213	−	17.8088i	0.633636	−	0.782476i
$519$	−29.4650	+	24.5509i	−1.29337	+	1.07767i
$520$	−3.43555	+	13.8601i	−0.150659	+	0.607804i
$521$	23.9642	−	13.8358i	1.04989	−	0.606156i	0.127273	−	0.991868i	$-0.459378\pi$
$521$	23.9642	−	13.8358i	1.04989	−	0.606156i	0.922619	+	0.385712i	$0.126044\pi$
$522$	19.6684	−	8.18867i	0.860862	−	0.358409i
$523$	−20.7761	+	3.29061i	−0.908475	+	0.143888i	−0.593147	−	0.805094i	$-0.702115\pi$
$523$	−20.7761	+	3.29061i	−0.908475	+	0.143888i	−0.315328	+	0.948983i	$0.602115\pi$
$524$	−8.43421	+	9.36714i	−0.368450	+	0.409205i
$525$	−9.70589	+	16.7832i	−0.423600	+	0.732479i
$526$	19.2930			0.841213
$527$	−24.7463	+	1.69335i	−1.07797	+	0.0737636i
$528$	2.68710	+	2.35222i	0.116941	+	0.102367i
$529$	25.7116	+	8.35419i	1.11789	+	0.363226i
$530$	7.53492	−	6.34015i	0.327296	−	0.275399i
$531$	−8.41826	+	15.5717i	−0.365322	+	0.675754i
$532$	2.92228	−	0.783022i	0.126697	−	0.0339483i
$533$	−15.0872	+	56.3062i	−0.653499	+	2.43889i
$534$	−14.4771	−	0.555677i	−0.626484	−	0.0240465i
$535$	8.98880	−	29.5457i	0.388620	−	1.27737i
$536$	−4.34416	+	0.456589i	−0.187639	+	0.0197217i
$537$	−13.5140	+	0.189147i	−0.583172	+	0.00816231i
$538$	−9.77987	+	25.4774i	−0.421640	+	1.09841i
$539$	4.00988	−	0.852326i	0.172718	−	0.0367123i
$540$	−9.34189	+	6.90863i	−0.402011	+	0.297300i
$541$	17.0323	+	7.58328i	0.732277	+	0.326031i	0.738779	−	0.673948i	$-0.235403\pi$
$541$	17.0323	+	7.58328i	0.732277	+	0.326031i	−0.00650177	+	0.999979i	$0.502070\pi$
$542$	−13.6487	−	6.95435i	−0.586261	−	0.298715i
$543$	8.77965	+	3.76262i	0.376771	+	0.161469i
$544$	−1.81199	+	4.06981i	−0.0776886	+	0.174492i
$545$	−0.936959	+	2.58528i	−0.0401349	+	0.110741i
$546$	−6.74295	−	23.8261i	−0.288572	−	1.01966i
$547$	16.0523	+	6.16192i	0.686349	+	0.263465i	0.676452	−	0.736487i	$-0.263517\pi$
$547$	16.0523	+	6.16192i	0.686349	+	0.263465i	0.00989630	+	0.999951i	$0.496850\pi$
$548$	0.967905	−	18.4687i	0.0413468	−	0.788945i
$549$	11.6981	−	2.83089i	0.499264	−	0.120819i
$550$	9.35517	+	4.33123i	0.398906	+	0.184684i
$551$	−9.54457	−	1.00317i	−0.406612	−	0.0427367i
$552$	−2.37931	+	12.0184i	−0.101270	+	0.511539i
$553$	−1.56324	−	5.83408i	−0.0664756	−	0.248090i
$554$	3.11303	+	2.26175i	0.132260	+	0.0960926i
$555$	28.5754	−	27.4799i	1.21296	−	1.16646i
$556$	−5.10888	+	15.7235i	−0.216665	+	0.666825i
$557$	−21.4040	+	21.4040i	−0.906916	+	0.906916i	−0.996022	−	0.0891058i	$-0.971599\pi$
$557$	−21.4040	+	21.4040i	−0.906916	+	0.906916i	0.0891058	+	0.996022i	$0.471599\pi$
$558$	−6.66532	−	15.3158i	−0.282166	−	0.648369i
$559$			62.1893i			2.63033i
$560$	−4.73090	+	1.63623i	−0.199917	+	0.0691434i
$561$	−9.83818	+	12.5029i	−0.415368	+	0.527875i
$562$	−3.27021	−	20.6473i	−0.137945	−	0.870953i
$563$	−29.4489	+	7.89081i	−1.24112	+	0.332558i	−0.818901	−	0.573935i	$-0.805416\pi$
$563$	−29.4489	+	7.89081i	−1.24112	+	0.332558i	−0.422222	+	0.906492i	$0.638750\pi$
$564$	0.776257	+	1.15948i	0.0326863	+	0.0488227i
$565$	−23.3565	+	14.0776i	−0.982616	+	0.592248i
$566$	9.01385	+	12.4065i	0.378880	+	0.521484i
$567$	8.12830	−	18.4359i	0.341356	−	0.774234i
$568$	−6.28154	−	0.329202i	−0.263568	−	0.0138130i
$569$	17.7143	−	7.88692i	0.742622	−	0.330637i	−0.000312918	−	1.00000i	$-0.500100\pi$
$569$	17.7143	−	7.88692i	0.742622	−	0.330637i	0.742935	+	0.669363i	$0.233433\pi$
$570$	5.18452	−	0.717598i	0.217155	−	0.0300569i
$571$	−12.0101	−	2.55282i	−0.502607	−	0.106832i	−0.0503706	−	0.998731i	$-0.516040\pi$
$571$	−12.0101	−	2.55282i	−0.502607	−	0.106832i	−0.452236	+	0.891898i	$0.649374\pi$
$572$	−12.2923	+	4.71857i	−0.513967	+	0.197294i
$573$	14.1374	−	32.9880i	0.590599	−	1.37809i
$574$	−19.4350	+	6.31481i	−0.811201	+	0.263575i
$575$	3.17898	+	35.2245i	0.132573	+	1.46896i
$576$	−2.99117	−	0.229961i	−0.124632	−	0.00958169i
$577$	−11.2677	−	7.31730i	−0.469079	−	0.304623i	0.288369	−	0.957519i	$-0.406887\pi$
$577$	−11.2677	−	7.31730i	−0.469079	−	0.304623i	−0.757447	+	0.652896i	$0.773554\pi$
$578$	−2.65758	−	1.02015i	−0.110541	−	0.0424326i
$579$	2.69022	−	2.76659i	0.111802	−	0.114976i
$580$	15.8708	+	0.532462i	0.659000	+	0.0221093i
$581$	4.19601	+	5.77531i	0.174080	+	0.239600i
$582$	−2.33317	−	2.51943i	−0.0967130	−	0.104434i
$583$	8.77075	+	2.35011i	0.363247	+	0.0973318i
$584$	−2.40778	+	4.17040i	−0.0996347	+	0.172572i
$585$	−6.46666	−	42.3476i	−0.267363	−	1.75086i
$586$	−4.55988	+	5.06426i	−0.188367	+	0.209203i
$587$	−15.6700	−	30.7541i	−0.646769	−	1.26936i	−0.948746	−	0.316041i	$-0.897646\pi$
$587$	−15.6700	−	30.7541i	−0.646769	−	1.26936i	0.301976	−	0.953315i	$-0.402354\pi$
$588$	−2.26829	+	2.59122i	−0.0935427	+	0.106860i
$589$	−0.666959	+	7.49465i	−0.0274816	+	0.308812i
$590$	−10.5263	+	7.95474i	−0.433360	+	0.327492i
$591$	−42.8164	−	10.8327i	−1.76123	−	0.445598i
$592$	10.2222	−	0.535721i	0.420129	−	0.0220180i
$593$	−3.86304	−	24.3903i	−0.158636	−	1.00159i	−0.930631	−	0.365960i	$-0.880741\pi$
$593$	−3.86304	−	24.3903i	−0.158636	−	1.00159i	0.771995	−	0.635629i	$-0.219259\pi$
$594$	−10.1543	−	3.41620i	−0.416638	−	0.140168i
$595$	−8.38238	−	20.6656i	−0.343644	−	0.847207i
$596$	−0.575848	−	0.0605240i	−0.0235876	−	0.00247916i
$597$	−19.1337	−	1.74067i	−0.783090	−	0.0712408i
$598$	−35.1048	−	28.4273i	−1.43554	−	1.16248i
$599$	13.1821	+	14.6402i	0.538607	+	0.598183i	0.949604	−	0.313454i	$-0.101486\pi$
$599$	13.1821	+	14.6402i	0.538607	+	0.598183i	−0.410997	+	0.911637i	$0.634819\pi$
$600$	−8.47230	+	1.79448i	−0.345880	+	0.0732592i
$601$	4.32751	−	0.919841i	0.176523	−	0.0375211i	−0.118802	−	0.992918i	$-0.537905\pi$
$601$	4.32751	−	0.919841i	0.176523	−	0.0375211i	0.295325	+	0.955397i	$0.404572\pi$
$602$	−18.2841	+	11.8738i	−0.745203	+	0.483941i
$603$	11.5049	−	6.27366i	0.468516	−	0.255483i
$604$	18.1135	−	5.88543i	0.737028	−	0.239475i
$605$	−2.64085	−	14.8580i	−0.107366	−	0.604064i
$606$	−4.84124	−	1.78105i	−0.196662	−	0.0723502i
$607$	0.236488	+	0.364160i	0.00959877	+	0.0147808i	0.843437	−	0.537227i	$-0.180528\pi$
$607$	0.236488	+	0.364160i	0.00959877	+	0.0147808i	−0.833839	+	0.552008i	$0.813862\pi$
$608$	1.13338	+	0.736024i	0.0459645	+	0.0298497i
$609$	−24.3581	+	12.8436i	−0.987041	+	0.520449i
$610$	8.80846	+	1.69968i	0.356644	+	0.0688178i
$611$	−5.11635	+	0.537750i	−0.206985	+	0.0217550i
$612$	0.325655	−	13.3609i	0.0131638	−	0.540083i
$613$	22.7481	+	28.0916i	0.918788	+	1.13461i	0.990545	+	0.137186i	$0.0438059\pi$
$613$	22.7481	+	28.0916i	0.918788	+	1.13461i	−0.0717576	+	0.997422i	$0.522861\pi$
$614$	2.11901	+	3.67024i	0.0855163	+	0.148119i
$615$	−34.7177	+	6.67323i	−1.39995	+	0.269091i
$616$	−3.73427	−	2.71310i	−0.150458	−	0.109314i
$617$	0.376455	+	7.18318i	0.0151555	+	0.289184i	0.995684	+	0.0928075i	$0.0295841\pi$
$617$	0.376455	+	7.18318i	0.0151555	+	0.289184i	−0.980529	+	0.196376i	$0.937083\pi$
$618$	−12.2223	+	7.28651i	−0.491654	+	0.293106i
$619$			45.1255i			1.81375i	0.421402	+	0.906874i	$0.361538\pi$
$619$			45.1255i			1.81375i	−0.421402	+	0.906874i	$0.638462\pi$
$620$	0.218796	−	12.4480i	0.00878705	−	0.499923i
$621$	−7.26847	−	36.0293i	−0.291674	−	1.44580i
$622$	−25.6707	+	13.0799i	−1.02930	+	0.524456i
$623$	18.6999	−	0.980019i	0.749195	−	0.0392636i
$624$	5.89376	−	9.35982i	0.235939	−	0.374693i
$625$	−22.0091	+	11.8575i	−0.880363	+	0.474301i
$626$	20.3069	−	11.7242i	0.811627	−	0.468593i
$627$	3.27917	+	3.54095i	0.130958	+	0.141412i
$628$	−0.717449	+	4.52980i	−0.0286293	+	0.180759i
$629$	4.76669	+	45.3520i	0.190060	+	1.80830i
$630$	11.2158	−	9.98668i	0.446849	−	0.397879i
$631$	16.1697	−	7.19923i	0.643707	−	0.286597i	−0.0588040	−	0.998270i	$-0.518729\pi$
$631$	16.1697	−	7.19923i	0.643707	−	0.286597i	0.702511	+	0.711673i	$0.252062\pi$
$632$	1.46941	−	2.26269i	0.0584500	−	0.0900051i
$633$	−10.3857	+	7.76999i	−0.412793	+	0.308830i
$634$	−0.184507	+	0.414409i	−0.00732770	+	0.0164583i
$635$	17.9196	−	25.6665i	0.711116	−	1.01854i
$636$	−7.08223	+	2.83296i	−0.280829	+	0.112334i
$637$	−4.55021	−	11.8537i	−0.180286	−	0.469660i
$638$	7.97482	+	12.2801i	0.315726	+	0.486176i
$639$	17.7767	−	6.33130i	0.703234	−	0.250463i
$640$	−1.95719	−	1.08139i	−0.0773648	−	0.0427456i
$641$	−20.6195	+	18.5659i	−0.814421	+	0.733308i	−0.966943	−	0.254992i	$-0.917927\pi$
$641$	−20.6195	+	18.5659i	−0.814421	+	0.733308i	0.152522	+	0.988300i	$0.451260\pi$
$642$	−13.7886	+	19.5479i	−0.544192	+	0.771496i
$643$	4.19127	−	26.4626i	0.165288	−	1.04358i	−0.755963	−	0.654615i	$-0.772831\pi$
$643$	4.19127	−	26.4626i	0.165288	−	1.04358i	0.921250	−	0.388970i	$-0.127169\pi$
$644$	1.65525	−	15.7487i	0.0652261	−	0.620585i
$645$	−33.9339	+	16.4631i	−1.33615	+	0.648232i
$646$	−3.01021	+	5.21384i	−0.118435	+	0.205136i
$647$	29.5166	−	4.67496i	1.16042	−	0.183792i	0.453610	−	0.891200i	$-0.350136\pi$
$647$	29.5166	−	4.67496i	1.16042	−	0.183792i	0.706805	+	0.707408i	$0.250136\pi$
$648$	8.54938	−	2.81214i	0.335851	−	0.110471i
$649$	−11.5704	−	3.75946i	−0.454179	−	0.147572i
$650$	8.71699	−	30.7170i	0.341909	−	1.20482i
$651$	10.3731	+	18.9339i	0.406552	+	0.742077i
$652$	12.8408	+	12.8408i	0.502885	+	0.502885i
$653$	−2.43262	+	1.23948i	−0.0951958	+	0.0485047i	−0.500940	−	0.865482i	$-0.667012\pi$
$653$	−2.43262	+	1.23948i	−0.0951958	+	0.0485047i	0.405744	+	0.913987i	$0.367012\pi$
$654$	1.31716	−	1.67393i	0.0515051	−	0.0654557i
$655$	19.5512	−	20.3014i	0.763928	−	0.793242i
$656$	−7.90523	−	4.56408i	−0.308647	−	0.178198i
$657$	1.85973	−	14.3265i	0.0725549	−	0.558929i
$658$	−1.13497	−	1.40157i	−0.0442457	−	0.0546389i
$659$	−9.67097	+	7.02637i	−0.376727	+	0.273708i	−0.759995	−	0.649929i	$-0.774799\pi$
$659$	−9.67097	+	7.02637i	−0.376727	+	0.273708i	0.383268	+	0.923637i	$0.374799\pi$
$660$	−5.82880	−	5.45824i	−0.226886	−	0.212462i
$661$	−4.88455	−	5.42484i	−0.189987	−	0.211002i	0.640624	−	0.767854i	$-0.278676\pi$
$661$	−4.88455	−	5.42484i	−0.189987	−	0.211002i	−0.830611	+	0.556852i	$0.812009\pi$
$662$	3.69249	−	9.61926i	0.143513	−	0.373863i
$663$	43.0146	+	24.0382i	1.67055	+	0.933567i
$664$	−0.662983	+	3.11909i	−0.0257287	+	0.121044i
$665$	−6.58944	+	1.53080i	−0.255528	+	0.0593619i
$666$	−27.6932	+	13.2706i	−1.07309	+	0.514224i
$667$	−22.8056	+	44.7585i	−0.883036	+	1.73306i
$668$	−0.403571	−	1.05134i	−0.0156146	−	0.0406775i
$669$	6.55984	−	45.5328i	0.253618	−	1.76040i
$670$	9.74260	−	0.694678i	0.376390	−	0.0268377i
$671$	3.36449	+	7.55678i	0.129885	+	0.291726i
$672$	3.87715	−	0.0542661i	0.149564	−	0.00209336i
$673$	16.0227	+	12.9749i	0.617628	+	0.500145i	0.886315	−	0.463082i	$-0.153257\pi$
$673$	16.0227	+	12.9749i	0.617628	+	0.500145i	−0.268687	+	0.963227i	$0.586590\pi$
$674$	23.8249	−	17.3098i	0.917699	−	0.666748i
$675$	21.3953	−	14.7390i	0.823507	−	0.567306i
$676$	13.8904	+	24.0590i	0.534248	+	0.925345i
$677$	10.9131	+	40.7281i	0.419423	+	1.56531i	0.775808	+	0.630968i	$0.217342\pi$
$677$	10.9131	+	40.7281i	0.419423	+	1.56531i	−0.356386	+	0.934339i	$0.615991\pi$
$678$	20.5989	−	4.68067i	0.791096	−	0.179760i
$679$	3.29827	+	2.96978i	0.126576	+	0.113970i
$680$	4.35461	−	8.95939i	0.166992	−	0.343577i
$681$	0.395671	+	5.95416i	0.0151622	+	0.228164i
$682$	9.52674	−	6.40522i	0.364798	−	0.245269i
$683$	10.3539	+	10.3539i	0.396180	+	0.396180i	0.876883	−	0.480704i	$-0.159619\pi$
$683$	10.3539	+	10.3539i	0.396180	+	0.396180i	−0.480704	+	0.876883i	$0.659619\pi$
$684$	−3.98764	−	0.731598i	−0.152471	−	0.0279733i
$685$	−3.54782	+	41.2015i	−0.135555	+	1.57423i
$686$	11.8274	−	16.2790i	0.451572	−	0.621535i
$687$	−24.4244	+	8.31563i	−0.931848	+	0.317261i
$688$	−9.40656	−	2.52048i	−0.358622	−	0.0960924i
$689$	2.93970	−	27.9693i	0.111994	−	1.06555i
$690$	6.21841	−	26.6806i	0.236731	−	1.01571i
$691$	0.997188	+	9.48761i	0.0379348	+	0.360926i	0.996979	+	0.0776697i	$0.0247480\pi$
$691$	0.997188	+	9.48761i	0.0379348	+	0.360926i	−0.959044	+	0.283256i	$0.908585\pi$
$692$	22.1126	+	1.15887i	0.840595	+	0.0440537i
$693$	13.4706	+	3.20822i	0.511707	+	0.121870i
$694$	0.481218	+	2.26395i	0.0182668	+	0.0859386i
$695$	12.5963	−	34.7560i	0.477804	−	1.31837i
$696$	−11.5440	−	4.24693i	−0.437573	−	0.160979i
$697$	18.4618	−	36.2333i	0.699291	−	1.37244i
$698$	4.09602	−	8.03890i	0.155037	−	0.304277i
$699$	−24.3735	−	8.96680i	−0.921892	−	0.339156i
$700$	10.6954	−	3.30196i	0.404246	−	0.124802i
$701$	−8.73736	−	41.1061i	−0.330006	−	1.55255i	−0.760122	−	0.649781i	$-0.774861\pi$
$701$	−8.73736	−	41.1061i	−0.330006	−	1.55255i	0.430116	−	0.902774i	$-0.358473\pi$
$702$	−5.53059	+	32.7184i	−0.208739	+	1.23488i
$703$	13.8142	+	0.723973i	0.521013	+	0.0273052i
$704$	−0.215520	−	2.05054i	−0.00812272	−	0.0772825i
$705$	−1.64785	−	2.64941i	−0.0620617	−	0.0997826i
$706$	1.69584	−	16.1349i	0.0638239	−	0.607244i
$707$	6.44018	+	1.72564i	0.242208	+	0.0648994i
$708$	9.67464	−	3.29387i	0.363595	−	0.123791i
$709$	2.43415	−	3.35032i	0.0914163	−	0.125824i	−0.760859	−	0.648917i	$-0.775222\pi$
$709$	2.43415	−	3.35032i	0.0914163	−	0.125824i	0.852275	+	0.523093i	$0.175222\pi$
$710$	14.0134	+	1.20668i	0.525913	+	0.0452858i
$711$	−1.46057	+	7.96098i	−0.0547758	+	0.298560i
$712$	5.91460	+	5.91460i	0.221659	+	0.221659i
$713$	35.3721	+	17.3174i	1.32469	+	0.648544i
$714$	1.14540	+	17.2362i	0.0428654	+	0.645049i
$715$	27.8248	−	9.62348i	1.04059	−	0.359898i
$716$	5.79882	+	5.22128i	0.216712	+	0.195128i
$717$	−8.54626	+	1.94196i	−0.319166	+	0.0725238i
$718$	−5.10564	−	19.0545i	−0.190541	−	0.711109i
$719$	−8.10959	−	14.0462i	−0.302437	−	0.523836i	0.674251	−	0.738503i	$-0.264467\pi$
$719$	−8.10959	−	14.0462i	−0.302437	−	0.523836i	−0.976687	+	0.214667i	$0.931133\pi$
$720$	6.66746	+	0.738188i	0.248482	+	0.0275107i
$721$	14.8792	−	10.8104i	0.554132	−	0.402600i
$722$	−13.3465	−	10.8078i	−0.496705	−	0.402224i
$723$	18.5844	−	0.260115i	0.691162	−	0.00967378i
$724$	−2.24308	−	5.03803i	−0.0833633	−	0.187237i
$725$	−35.4284	−	2.37990i	−1.31578	−	0.0883873i
$726$	−1.66686	+	11.5699i	−0.0618629	+	0.429399i
$727$	10.6900	+	27.8484i	0.396471	+	1.03284i	0.975977	+	0.217874i	$0.0699122\pi$
$727$	10.6900	+	27.8484i	0.396471	+	1.03284i	−0.579506	+	0.814968i	$0.696755\pi$
$728$	−6.49037	+	12.7381i	−0.240549	+	0.472104i
$729$	−20.4354	+	17.6464i	−0.756866	+	0.653570i
$730$	5.69362	−	9.13952i	0.210730	−	0.338269i
$731$	9.02007	−	42.4361i	0.333619	−	1.56956i
$732$	−6.06593	−	3.38987i	−0.224203	−	0.125293i
$733$	11.3995	−	29.6968i	0.421051	−	1.09688i	−0.544979	−	0.838449i	$-0.683463\pi$
$733$	11.3995	−	29.6968i	0.421051	−	1.09688i	0.966031	−	0.258427i	$-0.0832041\pi$
$734$	2.10316	+	2.33579i	0.0776289	+	0.0862156i
$735$	5.26348	−	5.62081i	0.194146	−	0.207327i
$736$	5.72260	−	4.15771i	0.210938	−	0.153255i
$737$	5.66782	+	6.99918i	0.208777	+	0.257818i
$738$	27.1567	+	3.52522i	0.999650	+	0.129765i
$739$	12.2870	+	7.09388i	0.451983	+	0.260953i	0.708667	−	0.705543i	$-0.249297\pi$
$739$	12.2870	+	7.09388i	0.451983	+	0.260953i	−0.256684	+	0.966495i	$0.582630\pi$
$740$	−22.8848	+	0.430805i	−0.841262	+	0.0158367i
$741$	9.24335	−	11.7470i	0.339563	−	0.431537i
$742$	8.78445	−	4.47590i	0.322487	−	0.164316i
$743$	5.95941	+	5.95941i	0.218630	+	0.218630i	0.807921	−	0.589291i	$-0.200593\pi$
$743$	5.95941	+	5.95941i	0.218630	+	0.218630i	−0.589291	+	0.807921i	$0.700593\pi$
$744$	−3.18475	+	9.10260i	−0.116759	+	0.333718i
$745$	1.28237	+	0.178435i	0.0469825	+	0.00653736i
$746$	35.9940	+	11.6951i	1.31783	+	0.428190i
$747$	−1.76035	−	9.40296i	−0.0644080	−	0.344036i
$748$	9.07229	−	1.43691i	0.331716	−	0.0525386i
$749$	15.4595	−	26.7766i	0.564878	−	0.978397i
$750$	19.0685	−	3.37509i	0.696284	−	0.123241i
$751$	−2.25283	+	21.4342i	−0.0822069	+	0.782146i	0.873301	+	0.487181i	$0.161975\pi$
$751$	−2.25283	+	21.4342i	−0.0822069	+	0.782146i	−0.955508	+	0.294965i	$0.904692\pi$
$752$	0.126023	−	0.795678i	0.00459559	−	0.0290154i
$753$	−12.4156	+	17.6015i	−0.452451	+	0.641434i
$754$	33.7024	−	30.3458i	1.22737	−	1.10513i
$755$	−40.9215	+	11.7947i	−1.48929	+	0.429254i
$756$	−10.6754	+	4.62091i	−0.388261	+	0.168061i
$757$	25.6796	+	39.5432i	0.933343	+	1.43722i	0.899068	+	0.437809i	$0.144245\pi$
$757$	25.6796	+	39.5432i	0.933343	+	1.43722i	0.0342747	+	0.999412i	$0.489088\pi$
$758$	9.70973	+	25.2947i	0.352673	+	0.918745i
$759$	23.4541	−	9.38188i	0.851331	−	0.340541i
$760$	−2.47770	−	1.72985i	−0.0898756	−	0.0627483i
$761$	−2.41604	+	5.42652i	−0.0875814	+	0.196711i	−0.952026	−	0.306017i	$-0.901004\pi$
$761$	−2.41604	+	5.42652i	−0.0875814	+	0.196711i	0.864445	+	0.502728i	$0.167670\pi$
$762$	−19.4150	+	14.5253i	−0.703333	+	0.526196i
$763$	−1.49942	+	2.30891i	−0.0542828	+	0.0835881i
$764$	−18.9296	+	8.42798i	−0.684847	+	0.304914i
$765$	−1.72954	+	29.8347i	−0.0625317	+	1.07868i
$766$	−0.596568	−	5.67596i	−0.0215549	−	0.205081i
$767$	−5.89455	+	37.2167i	−0.212840	+	1.34382i
$768$	1.17687	+	1.27082i	0.0424666	+	0.0458567i
$769$	6.78078	−	3.91488i	0.244521	−	0.141174i	−0.372732	−	0.927939i	$-0.621579\pi$
$769$	6.78078	−	3.91488i	0.244521	−	0.141174i	0.617253	+	0.786765i	$0.288246\pi$
$770$	8.14195	+	6.34326i	0.293416	+	0.228595i
$771$	11.7938	−	18.7296i	0.424743	−	0.674530i
$772$	−2.22490	+	0.116602i	−0.0800758	+	0.00419660i
$773$	8.05943	−	4.10649i	0.289878	−	0.147700i	−0.303005	−	0.952989i	$-0.597990\pi$
$773$	8.05943	−	4.10649i	0.289878	−	0.147700i	0.592882	+	0.805289i	$0.297990\pi$
$774$	28.9583	−	3.86580i	1.04088	−	0.138953i
$775$	−1.42228	+	27.8025i	−0.0510899	+	0.998694i
$776$			1.98252i			0.0711685i
$777$	34.0924	−	20.3247i	1.22306	−	0.729144i
$778$	1.56414	+	29.8456i	0.0560772	+	1.07002i
$779$	−9.97986	−	7.25079i	−0.357566	−	0.259787i
$780$	−13.8732	+	20.4755i	−0.496741	+	0.733141i
$781$	6.48463	+	11.2317i	0.232038	+	0.401902i
$782$	19.8313	+	24.4896i	0.709166	+	0.875747i
$783$	36.8687	−	1.54890i	1.31758	−	0.0553530i
$784$	1.97737	−	0.207830i	0.0706203	−	0.00742250i
$785$	1.94300	−	10.0694i	0.0693485	−	0.359394i
$786$	−19.3119	+	10.1828i	−0.688832	+	0.363209i
$787$	−13.8916	−	9.02130i	−0.495182	−	0.321575i	0.272774	−	0.962078i	$-0.412059\pi$
$787$	−13.8916	−	9.02130i	−0.495182	−	0.321575i	−0.767955	+	0.640504i	$0.778726\pi$
$788$	13.8877	+	21.3852i	0.494729	+	0.761817i
$789$	31.3614	+	11.5376i	1.11650	+	0.410749i
$790$	−3.45350	+	4.94652i	−0.122870	+	0.175989i
$791$	−25.9667	+	8.43708i	−0.923268	+	0.299988i
$792$	2.96130	+	5.43057i	0.105225	+	0.192967i
$793$	21.4869	−	13.9537i	0.763021	−	0.495511i
$794$	2.20817	−	0.469361i	0.0783651	−	0.0166570i
$795$	16.0398	−	5.80012i	0.568875	−	0.205709i
$796$	7.42230	+	8.24330i	0.263077	+	0.292176i
$797$	−8.62993	−	6.98838i	−0.305688	−	0.247541i	0.464185	−	0.885738i	$-0.346347\pi$
$797$	−8.62993	−	6.98838i	−0.305688	−	0.247541i	−0.769873	+	0.638197i	$0.779681\pi$
$798$	5.21853	+	0.474751i	0.184734	+	0.0168060i
$799$	3.56924	+	0.375142i	0.126271	+	0.0132716i
$800$	4.29287	+	2.56344i	0.151776	+	0.0906314i
$801$	−23.2007	−	9.56087i	−0.819757	−	0.337817i
$802$	−6.05261	−	38.2147i	−0.213725	−	1.34941i
$803$	9.91527	−	0.519637i	0.349902	−	0.0183376i
$804$	−7.33464	−	1.85569i	−0.258673	−	0.0654452i
$805$	−4.87997	+	35.0712i	−0.171996	+	1.23610i
$806$	−24.2101	−	26.0399i	−0.852765	−	0.917217i
$807$	−31.1336	+	35.5659i	−1.09595	+	1.25198i
$808$	1.35209	+	2.65363i	0.0475665	+	0.0933545i
$809$	15.0674	−	16.7341i	0.529743	−	0.588339i	−0.417572	−	0.908644i	$-0.637119\pi$
$809$	15.0674	−	16.7341i	0.529743	−	0.588339i	0.947314	+	0.320305i	$0.103785\pi$
$810$	−19.3171	+	5.64359i	−0.678733	+	0.198295i
$811$	24.9417	−	43.2003i	0.875822	−	1.51697i	0.0199366	−	0.999801i	$-0.493654\pi$
$811$	24.9417	−	43.2003i	0.875822	−	1.51697i	0.855885	−	0.517166i	$-0.173013\pi$
$812$	15.3567	+	4.11480i	0.538913	+	0.144401i
$813$	−18.0276	−	19.4667i	−0.632255	−	0.682729i
$814$	−12.4054	−	17.0746i	−0.434809	−	0.598463i
$815$	−27.7340	−	29.6595i	−0.971480	−	1.03893i
$816$	−5.37929	+	5.53201i	−0.188313	+	0.193659i
$817$	−12.2863	−	4.71628i	−0.429844	−	0.165002i
$818$	26.8415	+	17.4311i	0.938492	+	0.609464i
$819$	3.28758	−	42.7626i	0.114877	−	1.49425i
$820$	17.3245	+	10.7926i	0.604997	+	0.376893i
$821$	−8.41054	+	2.73275i	−0.293530	+	0.0953737i	−0.452080	−	0.891977i	$-0.649318\pi$
$821$	−8.41054	+	2.73275i	−0.293530	+	0.0953737i	0.158550	+	0.987351i	$0.449318\pi$
$822$	12.6180	−	29.4428i	0.440105	−	1.02693i
$823$	−0.979394	+	0.375954i	−0.0341395	+	0.0131049i	−0.375378	−	0.926872i	$-0.622487\pi$
$823$	−0.979394	+	0.375954i	−0.0341395	+	0.0131049i	0.341238	+	0.939977i	$0.389154\pi$
$824$	8.03587	+	1.70808i	0.279943	+	0.0595037i
$825$	12.6170	+	12.6352i	0.439268	+	0.439900i
$826$	−12.0674	+	5.37276i	−0.419879	+	0.186942i
$827$	38.8480	+	2.03594i	1.35088	+	0.0707965i	0.713987	−	0.700159i	$-0.246887\pi$
$827$	38.8480	+	2.03594i	1.35088	+	0.0707965i	0.636890	+	0.770955i	$0.280221\pi$
$828$	−11.0549	+	18.1136i	−0.384185	+	0.629490i
$829$	−17.4909	−	24.0742i	−0.607485	−	0.836131i	0.388883	−	0.921287i	$-0.372861\pi$
$829$	−17.4909	−	24.0742i	−0.607485	−	0.836131i	−0.996368	+	0.0851561i	$0.972861\pi$
$830$	1.71550	−	6.92087i	0.0595460	−	0.240227i
$831$	3.70778	+	5.53822i	0.128621	+	0.192119i
$832$	−6.16839	+	1.65282i	−0.213851	+	0.0573011i
$833$	1.38564	+	8.74857i	0.0480095	+	0.303120i
$834$	−17.7077	+	22.5039i	−0.613166	+	0.779247i
$835$	0.823078	+	2.37980i	0.0284838	+	0.0823564i
$836$		−	2.78636i		−	0.0963681i
$837$	−1.67557	−	28.8824i	−0.0579162	−	0.998321i
$838$	−10.1732	+	10.1732i	−0.351427	+	0.351427i
$839$	−3.62313	+	11.1508i	−0.125084	+	0.384970i	−0.993916	−	0.110137i	$-0.964871\pi$
$839$	−3.62313	+	11.1508i	−0.125084	+	0.384970i	0.868832	+	0.495107i	$0.164871\pi$
$840$	−8.66876	−	0.169424i	−0.299101	−	0.00584567i
$841$	−17.3399	−	12.5982i	−0.597928	−	0.434420i
$842$	−2.23223	−	8.33078i	−0.0769276	−	0.287098i
$843$	7.03165	−	35.5186i	0.242183	−	1.22332i
$844$	7.44752	+	0.782765i	0.256354	+	0.0269439i
$845$	−29.2386	−	54.8087i	−1.00584	−	1.88548i
$846$	0.568443	+	2.34899i	0.0195435	+	0.0807599i
$847$	0.790722	−	15.0879i	0.0271695	−	0.518426i
$848$	4.11141	+	1.57822i	0.141187	+	0.0541964i
$849$	7.23300	+	25.5577i	0.248236	+	0.877137i
$850$	−10.4035	+	19.6960i	−0.356836	+	0.675569i
$851$	29.4502	−	66.1462i	1.00954	−	2.26746i
$852$	−10.0140	−	4.29162i	−0.343074	−	0.147029i
$853$	−21.0223	−	10.7114i	−0.719789	−	0.366751i	0.0554135	−	0.998463i	$-0.482352\pi$
$853$	−21.0223	−	10.7114i	−0.719789	−	0.366751i	−0.775203	+	0.631713i	$0.782352\pi$
$854$	8.20498	+	3.65309i	0.280769	+	0.125006i
$855$	8.85676	+	1.93396i	0.302895	+	0.0661402i
$856$	13.5094	−	2.87151i	0.461741	−	0.0981462i
$857$	5.17254	−	13.4749i	0.176691	−	0.460295i	−0.816422	−	0.577455i	$-0.804046\pi$
$857$	5.17254	−	13.4749i	0.176691	−	0.460295i	0.993113	+	0.117160i	$0.0373791\pi$
$858$	−22.8034	+	0.319166i	−0.778496	+	0.0108961i
$859$	30.9504	−	3.25302i	1.05602	−	0.110992i	0.439428	−	0.898278i	$-0.355181\pi$
$859$	30.9504	−	3.25302i	1.05602	−	0.110992i	0.616588	+	0.787286i	$0.288515\pi$
$860$	20.8329	+	6.33808i	0.710396	+	0.216127i
$861$	−35.3687	−	1.35756i	−1.20536	−	0.0462657i
$862$	6.97707	−	26.0388i	0.237640	−	0.886884i
$863$	−32.2141	+	8.63176i	−1.09658	+	0.293828i	−0.761372	−	0.648315i	$-0.775474\pi$
$863$	−32.2141	+	8.63176i	−1.09658	+	0.293828i	−0.335210	+	0.942143i	$0.608807\pi$
$864$	−4.72474	−	2.16259i	−0.160739	−	0.0735729i
$865$	−49.3306	−	4.24780i	−1.67729	−	0.144430i
$866$	14.2185	+	4.61988i	0.483165	+	0.156990i
$867$	−3.70993	−	3.24758i	−0.125996	−	0.110294i
$868$	3.03347	−	12.0897i	0.102963	−	0.410353i
$869$	−5.56272			−0.188703
$870$	25.4802	+	10.3566i	0.863859	+	0.351122i
$871$	18.6651	−	20.7297i	0.632443	−	0.702399i
$872$	−1.21462	+	0.192377i	−0.0411323	+	0.00651472i
$873$	−2.28599	−	5.49071i	−0.0773689	−	0.185832i
$874$	8.27846	−	4.77957i	0.280023	−	0.161671i
$875$	−24.1497	+	6.57734i	−0.816407	+	0.222355i
$876$	−6.40792	+	5.33923i	−0.216504	+	0.180396i
$877$	8.27776	−	10.2222i	0.279520	−	0.345179i	−0.617979	−	0.786194i	$-0.712048\pi$
$877$	8.27776	−	10.2222i	0.279520	−	0.345179i	0.897499	+	0.441016i	$0.145382\pi$
$878$	0.212152	−	4.04810i	0.00715978	−	0.136617i
$879$	−10.4408	+	5.50524i	−0.352159	+	0.185687i
$880$	0.327903	+	4.59872i	0.0110536	+	0.155023i
$881$	7.21964	−	33.9657i	0.243236	−	1.14433i	−0.671728	−	0.740798i	$-0.734447\pi$
$881$	7.21964	−	33.9657i	0.243236	−	1.14433i	0.914964	−	0.403537i	$-0.132219\pi$
$882$	−5.23679	+	2.85564i	−0.176332	+	0.0961543i
$883$	46.7417	+	23.8161i	1.57298	+	0.801476i	0.999838	−	0.0179777i	$-0.00572280\pi$
$883$	46.7417	+	23.8161i	1.57298	+	0.801476i	0.573146	+	0.819453i	$0.305723\pi$
$884$	−8.79133	−	27.0569i	−0.295684	−	0.910023i
$885$	−21.8680	+	6.63580i	−0.735083	+	0.223060i
$886$	−26.5633	−	5.64621i	−0.892412	−	0.189688i
$887$	−18.0333	+	27.7688i	−0.605499	+	0.932386i	0.394411	+	0.918934i	$0.370949\pi$
$887$	−18.0333	+	27.7688i	−0.605499	+	0.932386i	−0.999910	+	0.0134521i	$0.995718\pi$
$888$	16.9369	+	5.24224i	0.568365	+	0.175918i
$889$	23.2900	−	20.9704i	0.781121	−	0.703325i
$890$	−12.7745	−	13.6615i	−0.428204	−	0.457933i
$891$	−14.4633	−	11.6257i	−0.484539	−	0.389474i
$892$	−20.6408	+	16.7146i	−0.691106	+	0.559646i
$893$	0.281772	−	1.05159i	0.00942913	−	0.0351900i
$894$	−0.899867	−	0.442753i	−0.0300961	−	0.0148079i
$895$	−12.5678	−	12.1033i	−0.420094	−	0.404570i
$896$	−1.66367	−	1.49798i	−0.0555794	−	0.0500439i
$897$	−40.0641	−	67.2031i	−1.33770	−	2.24385i
$898$	−14.4675	+	14.4675i	−0.482787	+	0.482787i
$899$	−22.7276	+	32.3556i	−0.758009	+	1.07912i
$900$	−14.8452	−	2.14962i	−0.494839	−	0.0716540i
$901$	−6.06269	+	18.6591i	−0.201978	+	0.621623i
$902$	0.985002	+	18.7950i	0.0327970	+	0.625804i
$903$	−36.8222	+	8.36708i	−1.22537	+	0.278439i
$904$	−10.5620	−	6.09797i	−0.351287	−	0.202816i
$905$	4.63511	+	11.4272i	0.154076	+	0.379854i
$906$	32.9638	+	1.26526i	1.09515	+	0.0420353i
$907$	−13.7604	−	2.17943i	−0.456907	−	0.0723669i	−0.0762610	−	0.997088i	$-0.524298\pi$
$907$	−13.7604	−	2.17943i	−0.456907	−	0.0723669i	−0.380646	+	0.924721i	$0.624298\pi$
$908$	2.16815	−	2.67744i	0.0719524	−	0.0888538i
$909$	−6.80452	−	5.79033i	−0.225692	−	0.192053i
$910$	15.4598	−	27.9805i	0.512488	−	0.927546i
$911$	0.115134	+	0.541664i	0.00381457	+	0.0179461i	0.980014	−	0.198930i	$-0.0637466\pi$
$911$	0.115134	+	0.541664i	0.00381457	+	0.0179461i	−0.976199	+	0.216876i	$0.930413\pi$
$912$	1.40219	+	1.87422i	0.0464312	+	0.0620616i
$913$	6.13802	−	2.35617i	0.203139	−	0.0779777i
$914$	−4.43062	−	13.6361i	−0.146552	−	0.451041i
$915$	13.3020	+	8.03052i	0.439752	+	0.265481i
$916$	13.6084	+	6.05887i	0.449636	+	0.200191i
$917$	23.6657	−	15.3687i	0.781510	−	0.507519i
$918$	8.51946	−	21.5239i	0.281184	−	0.710395i
$919$	−13.1936	−	29.6332i	−0.435216	−	0.977510i	−0.989413	−	0.145125i	$-0.953641\pi$
$919$	−13.1936	−	29.6332i	−0.435216	−	0.977510i	0.554198	−	0.832385i	$-0.313025\pi$
$920$	−13.1007	+	8.86264i	−0.431916	+	0.292192i
$921$	1.24966	+	7.23332i	0.0411776	+	0.238346i
$922$	5.19246	+	0.822405i	0.171005	+	0.0270845i
$923$	31.2171	−	25.2791i	1.02752	−	0.832073i
$924$	−4.44770	−	6.64342i	−0.146318	−	0.218552i
$925$	51.1755	+	0.753071i	1.68264	+	0.0247608i
$926$	−15.0182	+	20.6708i	−0.493530	+	0.679286i
$927$	−24.2253	+	4.53529i	−0.795664	+	0.148959i
$928$	3.22408	+	6.32761i	0.105836	+	0.207714i
$929$	54.1467			1.77650			0.888248	−	0.459363i	$-0.151922\pi$
$929$	54.1467			1.77650			0.888248	+	0.459363i	$0.151922\pi$
$930$	7.79981	−	20.1038i	0.255766	−	0.659230i
$931$	2.68693			0.0880606
$932$	6.80720	+	13.3599i	0.222977	+	0.437617i
$933$	−49.5507	+	5.91022i	−1.62222	+	0.193492i
$934$	−9.66188	+	13.2984i	−0.316147	+	0.435138i
$935$	−20.3826	+	2.53100i	−0.666582	+	0.0827727i
$936$	15.1779	−	11.6901i	0.496105	−	0.382104i
$937$	−11.8140	+	9.56677i	−0.385946	+	0.312533i	−0.802583	−	0.596540i	$-0.796542\pi$
$937$	−11.8140	+	9.56677i	−0.385946	+	0.312533i	0.416637	+	0.909073i	$0.363208\pi$
$938$	9.65840	+	1.52974i	0.315358	+	0.0499478i
$939$	40.0209	−	6.91417i	1.30603	−	0.225635i
$940$	−0.341296	+	1.76874i	−0.0111318	+	0.0576900i
$941$	13.3510	+	29.9868i	0.435230	+	0.977543i	0.989410	+	0.145146i	$0.0463652\pi$
$941$	13.3510	+	29.9868i	0.435230	+	0.977543i	−0.554180	+	0.832397i	$0.686968\pi$
$942$	−3.87515	+	6.93430i	−0.126259	+	0.225932i
$943$	−54.1516	+	35.1664i	−1.76342	+	1.14518i
$944$	−5.39039	−	2.39996i	−0.175442	−	0.0781119i
$945$	24.2040	−	9.52644i	0.787355	−	0.309895i
$946$	6.20473	+	19.0962i	0.201733	+	0.620871i
$947$	−17.2029	+	6.60359i	−0.559020	+	0.214588i	−0.621439	−	0.783462i	$-0.713452\pi$
$947$	−17.2029	+	6.60359i	−0.559020	+	0.214588i	0.0624192	+	0.998050i	$0.480118\pi$
$948$	3.74172	−	2.79935i	0.121525	−	0.0909188i
$949$	−6.39373	−	30.0801i	−0.207549	−	0.976442i
$950$	5.40749	+	4.05166i	0.175442	+	0.131453i
$951$	−0.547747	+	0.563298i	−0.0177619	+	0.0182662i
$952$	6.27639	−	7.75069i	0.203419	−	0.251201i
$953$	7.20304	+	1.14085i	0.233329	+	0.0369557i	0.272004	−	0.962296i	$-0.412314\pi$
$953$	7.20304	+	1.14085i	0.233329	+	0.0369557i	−0.0386747	+	0.999252i	$0.512314\pi$
$954$	−13.2066	+	0.369762i	−0.427579	+	0.0119715i
$955$	42.9359	−	17.4157i	1.38937	−	0.563557i
$956$	4.38206	+	2.52998i	0.141726	+	0.0818255i
$957$	5.61958	+	24.7309i	0.181655	+	0.799438i
$958$	−0.461341	−	8.80291i	−0.0149052	−	0.284409i
$959$	−12.7941	+	39.3761i	−0.413142	+	1.27152i
$960$	−2.53480	−	2.92828i	−0.0818102	−	0.0945098i
$961$	25.6484	+	17.4115i	0.827366	+	0.561663i
$962$	−46.2224	+	46.2224i	−1.49027	+	1.49027i
$963$	−34.1039	+	23.5300i	−1.09898	+	0.758245i
$964$	−7.97451	−	7.18029i	−0.256842	−	0.231261i
$965$	4.98097	−	0.0937665i	0.160343	−	0.00301845i
$966$	12.1087	−	24.6102i	0.389592	−	0.791820i
$967$	−9.31551	+	34.7659i	−0.299566	+	1.11800i	0.637956	+	0.770073i	$0.279780\pi$
$967$	−9.31551	+	34.7659i	−0.299566	+	1.11800i	−0.937523	+	0.347925i	$0.886887\pi$
$968$	5.24484	−	4.24719i	0.168576	−	0.136510i
$969$	−8.01119	+	6.67512i	−0.257357	+	0.214436i
$970$	0.148644	−	4.43057i	0.00477268	−	0.142257i
$971$	−4.51944	+	4.06932i	−0.145036	+	0.130591i	−0.738455	−	0.674303i	$-0.764444\pi$
$971$	−4.51944	+	4.06932i	−0.145036	+	0.130591i	0.593419	+	0.804894i	$0.297778\pi$
$972$	15.5791	+	0.541470i	0.499698	+	0.0173677i
$973$	20.1579	−	31.0405i	0.646234	−	0.995113i
$974$	−25.6781	−	5.45804i	−0.822778	−	0.174887i
$975$	32.5392	−	44.7187i	1.04209	−	1.43215i
$976$	1.23975	+	3.81557i	0.0396835	+	0.122133i
$977$	38.4209	+	19.5764i	1.22919	+	0.626305i	0.943295	−	0.331955i	$-0.107708\pi$
$977$	38.4209	+	19.5764i	1.22919	+	0.626305i	0.285898	+	0.958260i	$0.407708\pi$
$978$	13.1941	+	28.5523i	0.421902	+	0.913001i
$979$	3.58569	−	16.8693i	0.114599	−	0.539146i
$980$	−4.43463	+	0.316203i	−0.141659	+	0.0101007i
$981$	3.14214	−	1.93334i	0.100321	−	0.0617268i
$982$	−0.311298	+	5.93991i	−0.00993391	+	0.189550i
$983$	−16.4365	+	20.2974i	−0.524244	+	0.647387i	−0.968647	−	0.248439i	$-0.920082\pi$
$983$	−16.4365	+	20.2974i	−0.524244	+	0.647387i	0.444404	+	0.895827i	$0.353416\pi$
$984$	−10.1208	−	12.1466i	−0.322640	−	0.387219i
$985$	−29.4330	−	48.8332i	−0.937814	−	1.55595i
$986$	−27.3989	+	15.8188i	−0.872558	+	0.503772i
$987$	−1.00677	−	2.95704i	−0.0320457	−	0.0941235i
$988$	−8.52377	+	1.35003i	−0.271177	+	0.0429502i
$989$	−46.0929	+	51.1913i	−1.46567	+	1.62779i
$990$	−6.21078	−	12.3583i	−0.197392	−	0.392773i
$991$	−29.5077			−0.937344			−0.468672	−	0.883372i	$-0.655267\pi$
$991$	−29.5077			−0.937344			−0.468672	+	0.883372i	$0.655267\pi$
$992$	4.91994	−	2.60657i	0.156208	−	0.0827588i
$993$	11.7548	−	13.4283i	0.373027	−	0.426134i
$994$	13.3925	+	4.35150i	0.424785	+	0.138021i
$995$	−15.9694	−	18.9787i	−0.506263	−	0.601666i
$996$	−2.94298	+	4.67372i	−0.0932520	+	0.148092i
$997$	26.1939	−	7.01863i	0.829569	−	0.222282i	0.181043	−	0.983475i	$-0.442053\pi$
$997$	26.1939	−	7.01863i	0.829569	−	0.222282i	0.648526	+	0.761193i	$0.275386\pi$
$998$	3.59526	−	13.4177i	0.113806	−	0.424730i
$999$	−52.9523	+	5.01073i	−1.67534	+	0.158533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bs.a.107.15	✓	1024
3.2	odd	2	inner	930.2.bs.a.107.48	yes	1024
5.3	odd	4	inner	930.2.bs.a.293.31	yes	1024
15.8	even	4	inner	930.2.bs.a.293.64	yes	1024
31.20	even	15	inner	930.2.bs.a.857.64	yes	1024
93.20	odd	30	inner	930.2.bs.a.857.31	yes	1024
155.113	odd	60	inner	930.2.bs.a.113.48	yes	1024
465.113	even	60	inner	930.2.bs.a.113.15	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bs.a.107.15	✓	1024	1.1	even	1	trivial
930.2.bs.a.107.48	yes	1024	3.2	odd	2	inner
930.2.bs.a.113.15	yes	1024	465.113	even	60	inner
930.2.bs.a.113.48	yes	1024	155.113	odd	60	inner
930.2.bs.a.293.31	yes	1024	5.3	odd	4	inner
930.2.bs.a.293.64	yes	1024	15.8	even	4	inner
930.2.bs.a.857.31	yes	1024	93.20	odd	30	inner
930.2.bs.a.857.64	yes	1024	31.20	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.205138 - 1.71986i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.37425 - 1.76393i) q^{5} +(-1.43928 + 0.963580i) q^{6} +(1.73979 - 1.40885i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.91584 + 0.705618i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.205138 - 1.71986i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.37425 - 1.76393i) q^{5} +(-1.43928 + 0.963580i) q^{6} +(1.73979 - 1.40885i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.91584 + 0.705618i) q^{9} +(-2.19557 - 0.423656i) q^{10} +(-0.838623 - 1.88358i) q^{11} +(1.51197 + 0.844948i) q^{12} +(-5.35574 + 3.47806i) q^{13} +(-2.04515 - 0.910558i) q^{14} +(-3.31562 - 2.00166i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(4.15906 - 1.59651i) q^{17} +(1.95247 + 2.27769i) q^{18} +(-0.280971 - 1.32187i) q^{19} +(0.619287 + 2.14860i) q^{20} +(-2.77993 - 2.70319i) q^{21} +(-1.29755 + 1.60234i) q^{22} +(-6.98644 - 1.10654i) q^{23} +(0.0664328 - 1.73078i) q^{24} +(-1.22289 - 4.84815i) q^{25} +(5.53043 + 3.19300i) q^{26} +(1.81171 + 4.87008i) q^{27} +(0.117164 + 2.23562i) q^{28} +(2.19453 - 6.75406i) q^{29} +(-0.278234 + 3.86298i) q^{30} +(-5.32205 - 1.63579i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-3.06746 + 1.82871i) q^{33} +(-3.31068 - 2.98095i) q^{34} +(-0.0942185 - 5.00498i) q^{35} +(1.14303 - 2.77371i) q^{36} +(-2.64932 + 9.88741i) q^{37} +(-1.05023 + 0.850462i) q^{38} +(7.08044 + 8.49765i) q^{39} +(1.63327 - 1.52723i) q^{40} +(6.78355 - 6.10794i) q^{41} +(-1.14649 + 3.70416i) q^{42} +(5.30391 - 8.16730i) q^{43} +(2.01678 + 0.428679i) q^{44} +(-2.76242 + 6.11302i) q^{45} +(2.18584 + 6.72732i) q^{46} +(0.717792 + 0.365733i) q^{47} +(-1.57229 + 0.726564i) q^{48} +(-0.413383 + 1.94481i) q^{49} +(-3.76455 + 3.29062i) q^{50} +(-3.59896 - 6.82550i) q^{51} +(0.334217 - 6.37724i) q^{52} +(-2.77148 + 3.42249i) q^{53} +(3.51677 - 3.82522i) q^{54} +(-4.47497 - 1.10923i) q^{55} +(1.93876 - 1.11935i) q^{56} +(-2.21579 + 0.754397i) q^{57} +(-7.01421 + 1.11094i) q^{58} +(3.94822 - 4.38494i) q^{59} +(3.56825 - 1.50585i) q^{60} -4.01193 q^{61} +(0.958655 + 5.48461i) q^{62} +(-4.07883 + 5.33562i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-1.22506 + 14.2269i) q^{65} +(3.02199 + 1.90291i) q^{66} +(-4.21925 + 1.13054i) q^{67} +(-1.15303 + 4.30316i) q^{68} +(-0.469914 + 12.2427i) q^{69} +(-4.41669 + 2.35616i) q^{70} +(-6.25571 + 0.657501i) q^{71} +(-2.99032 + 0.240793i) q^{72} +(-1.72574 + 4.49571i) q^{73} +(10.0125 - 2.12823i) q^{74} +(-8.08727 + 3.09774i) q^{75} +(1.23456 + 0.549663i) q^{76} +(-4.11271 - 2.09553i) q^{77} +(4.35700 - 10.1666i) q^{78} +(1.09736 - 2.46470i) q^{79} +(-2.10226 - 0.761902i) q^{80} +(8.00421 - 4.11493i) q^{81} +(-8.52188 - 3.27124i) q^{82} +(-0.166887 + 3.18440i) q^{83} +(3.82092 - 0.660117i) q^{84} +(2.89944 - 9.53030i) q^{85} +(-9.68504 - 1.01794i) q^{86} +(-12.0662 - 2.38876i) q^{87} +(-0.533641 - 1.99158i) q^{88} +(6.76702 + 4.91653i) q^{89} +(6.70085 - 0.313921i) q^{90} +(-4.41779 + 13.5966i) q^{91} +(5.00174 - 5.00174i) q^{92} +(-1.72158 + 9.48874i) q^{93} -0.805597i q^{94} +(-2.71780 - 1.32096i) q^{95} +(1.36118 + 1.07107i) q^{96} +(0.310135 + 1.95812i) q^{97} +(1.92051 - 0.514600i) q^{98} +(3.77437 + 4.90046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) 1024 * q - 8 * q^3 + 24 * q^7	\( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more