LMFDB - Embedded newform 231.2.be.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (of order $30$, 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:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.1
Character	$\chi$	$=$	231.2
Dual form			231.2.be.a.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69754 - 1.88531i) q^{2} +(-1.50120 - 0.863943i) q^{3} +(-0.463691 + 4.41173i) q^{4} +(0.0606689 - 0.285425i) q^{5} +(0.919548 + 4.29680i) q^{6} +(0.885230 + 2.49326i) q^{7} +(4.99976 - 3.63254i) q^{8} +(1.50720 + 2.59390i) q^{9} +O(q^{10})$	\(q+(-1.69754 - 1.88531i) q^{2} +(-1.50120 - 0.863943i) q^{3} +(-0.463691 + 4.41173i) q^{4} +(0.0606689 - 0.285425i) q^{5} +(0.919548 + 4.29680i) q^{6} +(0.885230 + 2.49326i) q^{7} +(4.99976 - 3.63254i) q^{8} +(1.50720 + 2.59390i) q^{9} +(-0.641101 + 0.370140i) q^{10} +(3.31186 + 0.177766i) q^{11} +(4.50758 - 6.22228i) q^{12} +(-1.48788 - 0.483440i) q^{13} +(3.19786 - 5.90135i) q^{14} +(-0.337667 + 0.376065i) q^{15} +(-6.65756 - 1.41511i) q^{16} +(-2.99446 + 3.32569i) q^{17} +(2.33177 - 7.24480i) q^{18} +(3.49594 - 0.367438i) q^{19} +(1.23108 + 0.400004i) q^{20} +(0.825130 - 4.50768i) q^{21} +(-5.28686 - 6.54564i) q^{22} +(-2.99246 - 1.72770i) q^{23} +(-10.6439 + 1.13366i) q^{24} +(4.48994 + 1.99905i) q^{25} +(1.61429 + 3.62577i) q^{26} +(-0.0216317 - 5.19611i) q^{27} +(-11.4101 + 2.74929i) q^{28} +(2.63799 + 1.91661i) q^{29} +(1.28220 - 0.00177928i) q^{30} +(2.78689 - 0.592371i) q^{31} +(2.45351 + 4.24961i) q^{32} +(-4.81818 - 3.12812i) q^{33} +11.3532 q^{34} +(0.765345 - 0.101403i) q^{35} +(-12.1425 + 5.44661i) q^{36} +(8.60817 - 3.83260i) q^{37} +(-6.62723 - 5.96718i) q^{38} +(1.81594 + 2.01118i) q^{39} +(-0.733486 - 1.64744i) q^{40} +(-4.18873 + 3.04329i) q^{41} +(-9.89906 + 6.09634i) q^{42} +3.10620i q^{43} +(-2.31994 + 14.5286i) q^{44} +(0.831804 - 0.272824i) q^{45} +(1.82258 + 8.57455i) q^{46} +(10.5251 - 1.10624i) q^{47} +(8.77176 + 7.87611i) q^{48} +(-5.43273 + 4.41423i) q^{49} +(-3.85302 - 11.8584i) q^{50} +(7.36849 - 2.40548i) q^{51} +(2.82272 - 6.33994i) q^{52} +(2.86772 + 13.4916i) q^{53} +(-9.75955 + 8.86138i) q^{54} +(0.251666 - 0.934501i) q^{55} +(13.4828 + 9.25009i) q^{56} +(-5.56555 - 2.46869i) q^{57} +(-0.864688 - 8.22695i) q^{58} +(12.0095 + 1.26225i) q^{59} +(-1.50252 - 1.66407i) q^{60} +(-1.06859 + 5.02734i) q^{61} +(-5.84766 - 4.24857i) q^{62} +(-5.13306 + 6.05406i) q^{63} +(-0.359629 + 1.10682i) q^{64} +(-0.228254 + 0.395347i) q^{65} +(2.28158 + 14.3939i) q^{66} +(-1.96822 - 3.40906i) q^{67} +(-13.2835 - 14.7528i) q^{68} +(2.99965 + 5.17894i) q^{69} +(-1.49038 - 1.27078i) q^{70} +(-1.52829 + 0.496572i) q^{71} +(16.9581 + 7.49391i) q^{72} +(-10.7577 - 1.13068i) q^{73} +(-21.8383 - 9.72306i) q^{74} +(-5.01323 - 6.88003i) q^{75} +15.5935i q^{76} +(2.48854 + 8.41470i) q^{77} +(0.709075 - 6.83766i) q^{78} +(8.34383 - 7.51282i) q^{79} +(-0.807814 + 1.81438i) q^{80} +(-4.45667 + 7.81909i) q^{81} +(12.8481 + 2.73094i) q^{82} +(-3.92861 - 12.0910i) q^{83} +(19.5040 + 5.73042i) q^{84} +(0.767562 + 1.05646i) q^{85} +(5.85614 - 5.27290i) q^{86} +(-2.30431 - 5.15629i) q^{87} +(17.2042 - 11.1417i) q^{88} +(-8.20014 - 4.73436i) q^{89} +(-1.92638 - 1.10508i) q^{90} +(-0.111769 - 4.13763i) q^{91} +(9.00971 - 12.4008i) q^{92} +(-4.69545 - 1.51844i) q^{93} +(-19.9524 - 17.9652i) q^{94} +(0.107219 - 1.02012i) q^{95} +(-0.0117942 - 8.49922i) q^{96} +(2.09639 - 6.45201i) q^{97} +(17.5445 + 2.74906i) q^{98} +(4.53054 + 8.85857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.69754	−	1.88531i	−1.20034	−	1.33311i	−0.928752	−	0.370701i	$-0.879117\pi$
$2$	−1.69754	−	1.88531i	−1.20034	−	1.33311i	−0.271590	−	0.962413i	$-0.587549\pi$
$3$	−1.50120	−	0.863943i	−0.866718	−	0.498798i
$3$	−1.50120	−	0.863943i	−0.866718	−	0.498798i
$4$	−0.463691	+	4.41173i	−0.231846	+	2.20586i
$5$	0.0606689	−	0.285425i	0.0271319	−	0.127646i	−0.962497	−	0.271292i	$-0.912549\pi$
$5$	0.0606689	−	0.285425i	0.0271319	−	0.127646i	0.989629	+	0.143646i	$0.0458826\pi$
$6$	0.919548	+	4.29680i	0.375404	+	1.75416i
$7$	0.885230	+	2.49326i	0.334586	+	0.942365i
$7$	0.885230	+	2.49326i	0.334586	+	0.942365i
$8$	4.99976	−	3.63254i	1.76768	−	1.28430i
$9$	1.50720	+	2.59390i	0.502402	+	0.864634i
$10$	−0.641101	+	0.370140i	−0.202734	+	0.117049i
$11$	3.31186	+	0.177766i	0.998563	+	0.0535986i
$11$	3.31186	+	0.177766i	0.998563	+	0.0535986i
$12$	4.50758	−	6.22228i	1.30122	−	1.79622i
$13$	−1.48788	−	0.483440i	−0.412663	−	0.134082i	0.0953258	−	0.995446i	$-0.469611\pi$
$13$	−1.48788	−	0.483440i	−0.412663	−	0.134082i	−0.507988	+	0.861364i	$0.669611\pi$
$14$	3.19786	−	5.90135i	0.854664	−	1.57720i
$15$	−0.337667	+	0.376065i	−0.0871852	+	0.0970996i
$16$	−6.65756	−	1.41511i	−1.66439	−	0.353777i
$17$	−2.99446	+	3.32569i	−0.726264	+	0.806597i	−0.987323	−	0.158725i	$-0.949262\pi$
$17$	−2.99446	+	3.32569i	−0.726264	+	0.806597i	0.261059	+	0.965323i	$0.415928\pi$
$18$	2.33177	−	7.24480i	0.549603	−	1.70762i
$19$	3.49594	−	0.367438i	0.802023	−	0.0842960i	0.305357	−	0.952238i	$-0.401224\pi$
$19$	3.49594	−	0.367438i	0.802023	−	0.0842960i	0.496666	+	0.867942i	$0.334557\pi$
$20$	1.23108	+	0.400004i	0.275279	+	0.0894435i
$21$	0.825130	−	4.50768i	0.180058	−	0.983656i
$22$	−5.28686	−	6.54564i	−1.12716	−	1.39553i
$23$	−2.99246	−	1.72770i	−0.623971	−	0.360250i	0.154442	−	0.988002i	$-0.450642\pi$
$23$	−2.99246	−	1.72770i	−0.623971	−	0.360250i	−0.778414	+	0.627752i	$0.783975\pi$
$24$	−10.6439	+	1.13366i	−2.17269	+	0.231407i
$25$	4.48994	+	1.99905i	0.897988	+	0.399810i
$26$	1.61429	+	3.62577i	0.316589	+	0.711071i
$27$	−0.0216317	−	5.19611i	−0.00416302	−	0.999991i
$28$	−11.4101	+	2.74929i	−2.15630	+	0.519567i
$29$	2.63799	+	1.91661i	0.489863	+	0.355906i	0.805131	−	0.593096i	$-0.202095\pi$
$29$	2.63799	+	1.91661i	0.489863	+	0.355906i	−0.315269	+	0.949002i	$0.602095\pi$
$30$	1.28220	−	0.00177928i	0.234097	−	0.000324851i
$31$	2.78689	−	0.592371i	0.500540	−	0.106393i	0.0492789	−	0.998785i	$-0.484308\pi$
$31$	2.78689	−	0.592371i	0.500540	−	0.106393i	0.451261	+	0.892392i	$0.350974\pi$
$32$	2.45351	+	4.24961i	0.433724	+	0.751232i
$33$	−4.81818	−	3.12812i	−0.838738	−	0.544536i
$34$	11.3532			1.94705
$35$	0.765345	−	0.101403i	0.129367	−	0.0171402i
$36$	−12.1425	+	5.44661i	−2.02375	+	0.907768i
$37$	8.60817	−	3.83260i	1.41517	−	0.630076i	0.450321	−	0.892867i	$-0.351309\pi$
$37$	8.60817	−	3.83260i	1.41517	−	0.630076i	0.964853	+	0.262791i	$0.0846428\pi$
$38$	−6.62723	−	5.96718i	−1.07508	−	0.968005i
$39$	1.81594	+	2.01118i	0.290782	+	0.322047i
$40$	−0.733486	−	1.64744i	−0.115974	−	0.260483i
$41$	−4.18873	+	3.04329i	−0.654169	+	0.475282i	−0.864689	−	0.502308i	$-0.832484\pi$
$41$	−4.18873	+	3.04329i	−0.654169	+	0.475282i	0.210520	+	0.977590i	$0.432484\pi$
$42$	−9.89906	+	6.09634i	−1.52746	+	0.940685i
$43$			3.10620i			0.473691i	0.971547	+	0.236845i	$0.0761135\pi$
$43$			3.10620i			0.473691i	−0.971547	+	0.236845i	$0.923886\pi$
$44$	−2.31994	+	14.5286i	−0.349744	+	2.19027i
$45$	0.831804	−	0.272824i	0.123998	−	0.0406702i
$46$	1.82258	+	8.57455i	0.268724	+	1.26425i
$47$	10.5251	−	1.10624i	1.53525	−	0.161361i	0.701165	−	0.712999i	$-0.252664\pi$
$47$	10.5251	−	1.10624i	1.53525	−	0.161361i	0.834084	+	0.551638i	$0.185997\pi$
$48$	8.77176	+	7.87611i	1.26609	+	1.13682i
$49$	−5.43273	+	4.41423i	−0.776105	+	0.630604i
$50$	−3.85302	−	11.8584i	−0.544900	−	1.67703i
$51$	7.36849	−	2.40548i	1.03180	−	0.336834i
$52$	2.82272	−	6.33994i	0.391441	−	0.879191i
$53$	2.86772	+	13.4916i	0.393912	+	1.85321i	0.510288	+	0.860003i	$0.329539\pi$
$53$	2.86772	+	13.4916i	0.393912	+	1.85321i	−0.116377	+	0.993205i	$0.537128\pi$
$54$	−9.75955	+	8.86138i	−1.32811	+	1.20588i
$55$	0.251666	−	0.934501i	0.0339346	−	0.126008i
$56$	13.4828	+	9.25009i	1.80172	+	1.23610i
$57$	−5.56555	−	2.46869i	−0.737175	−	0.326987i
$58$	−0.864688	−	8.22695i	−0.113539	−	1.08025i
$59$	12.0095	+	1.26225i	1.56351	+	0.164331i	0.846368	−	0.532598i	$-0.178784\pi$
$59$	12.0095	+	1.26225i	1.56351	+	0.164331i	0.717140	+	0.696930i	$0.245451\pi$
$60$	−1.50252	−	1.66407i	−0.193975	−	0.214831i
$61$	−1.06859	+	5.02734i	−0.136819	+	0.643685i	0.855273	+	0.518177i	$0.173389\pi$
$61$	−1.06859	+	5.02734i	−0.136819	+	0.643685i	−0.992093	+	0.125507i	$0.959944\pi$
$62$	−5.84766	−	4.24857i	−0.742653	−	0.539569i
$63$	−5.13306	+	6.05406i	−0.646705	+	0.762740i
$64$	−0.359629	+	1.10682i	−0.0449537	+	0.138353i
$65$	−0.228254	+	0.395347i	−0.0283114	+	0.0490367i
$66$	2.28158	+	14.3939i	0.280843	+	1.77176i
$67$	−1.96822	−	3.40906i	−0.240457	−	0.416483i	0.720388	−	0.693572i	$-0.243964\pi$
$67$	−1.96822	−	3.40906i	−0.240457	−	0.416483i	−0.960844	+	0.277088i	$0.910631\pi$
$68$	−13.2835	−	14.7528i	−1.61086	−	1.78904i
$69$	2.99965	+	5.17894i	0.361116	+	0.623471i
$70$	−1.49038	−	1.27078i	−0.178134	−	0.151887i
$71$	−1.52829	+	0.496572i	−0.181375	+	0.0589322i	−0.398296	−	0.917257i	$-0.630398\pi$
$71$	−1.52829	+	0.496572i	−0.181375	+	0.0589322i	0.216922	+	0.976189i	$0.430398\pi$
$72$	16.9581	+	7.49391i	1.99853	+	0.883166i
$73$	−10.7577	−	1.13068i	−1.25910	−	0.132337i	−0.548630	−	0.836065i	$-0.684850\pi$
$73$	−10.7577	−	1.13068i	−1.25910	−	0.132337i	−0.710469	+	0.703729i	$0.751517\pi$
$74$	−21.8383	−	9.72306i	−2.53866	−	1.13028i
$75$	−5.01323	−	6.88003i	−0.578878	−	0.794437i
$76$			15.5935i			1.78870i
$77$	2.48854	+	8.41470i	0.283595	+	0.958944i
$78$	0.709075	−	6.83766i	0.0802869	−	0.774212i
$79$	8.34383	−	7.51282i	0.938755	−	0.845258i	−0.0493908	−	0.998780i	$-0.515728\pi$
$79$	8.34383	−	7.51282i	0.938755	−	0.845258i	0.988145	+	0.153521i	$0.0490613\pi$
$80$	−0.807814	+	1.81438i	−0.0903163	+	0.202854i
$81$	−4.45667	+	7.81909i	−0.495185	+	0.868787i
$82$	12.8481	+	2.73094i	1.41883	+	0.301582i
$83$	−3.92861	−	12.0910i	−0.431221	−	1.32716i	−0.896910	−	0.442214i	$-0.854193\pi$
$83$	−3.92861	−	12.0910i	−0.431221	−	1.32716i	0.465689	−	0.884949i	$-0.345807\pi$
$84$	19.5040	+	5.73042i	2.12807	+	0.625240i
$85$	0.767562	+	1.05646i	0.0832538	+	0.114589i
$86$	5.85614	−	5.27290i	0.631484	−	0.568591i
$87$	−2.30431	−	5.15629i	−0.247048	−	0.552813i
$88$	17.2042	−	11.1417i	1.83398	−	1.18770i
$89$	−8.20014	−	4.73436i	−0.869214	−	0.501841i	−0.00212674	−	0.999998i	$-0.500677\pi$
$89$	−8.20014	−	4.73436i	−0.869214	−	0.501841i	−0.867087	+	0.498157i	$0.834010\pi$
$90$	−1.92638	−	1.10508i	−0.203058	−	0.116485i
$91$	−0.111769	−	4.13763i	−0.0117165	−	0.433741i
$92$	9.00971	−	12.4008i	0.939327	−	1.29287i
$93$	−4.69545	−	1.51844i	−0.486896	−	0.157455i
$94$	−19.9524	−	17.9652i	−2.05794	−	1.85297i
$95$	0.107219	−	1.02012i	0.0110004	−	0.104662i
$96$	−0.0117942	−	8.49922i	−0.00120374	−	0.867448i
$97$	2.09639	−	6.45201i	0.212856	−	0.655103i	−0.786443	−	0.617663i	$-0.788080\pi$
$97$	2.09639	−	6.45201i	0.212856	−	0.655103i	0.999299	−	0.0374401i	$-0.0119203\pi$
$98$	17.5445	+	2.74906i	1.77226	+	0.277697i
$99$	4.53054	+	8.85857i	0.455336	+	0.890320i
$100$	−10.9012	+	18.8815i	−1.09012	+	1.88815i
$101$	−9.05931	+	1.92562i	−0.901435	+	0.191606i	−0.635241	−	0.772314i	$-0.719099\pi$
$101$	−9.05931	+	1.92562i	−0.901435	+	0.191606i	−0.266194	+	0.963920i	$0.585766\pi$
$102$	−17.0434	−	9.80849i	−1.68755	−	0.971185i
$103$	−11.9506	+	5.32076i	−1.17753	+	0.524270i	−0.899763	−	0.436378i	$-0.856261\pi$
$103$	−11.9506	+	5.32076i	−1.17753	+	0.524270i	−0.277767	+	0.960648i	$0.589594\pi$
$104$	−9.19514	+	2.98768i	−0.901657	+	0.292966i
$105$	−1.23654	−	0.508988i	−0.120674	−	0.0496722i
$106$	20.5677	−	28.3090i	1.99771	−	2.74961i
$107$	1.04846	+	9.97540i	0.101358	+	0.964358i	0.920494	+	0.390758i	$0.127787\pi$
$107$	1.04846	+	9.97540i	0.101358	+	0.964358i	−0.819135	+	0.573600i	$0.805546\pi$
$108$	22.9338	+	2.31396i	2.20681	+	0.222661i
$109$	−5.97981	+	3.45245i	−0.572762	+	0.330684i	−0.758252	−	0.651962i	$-0.773946\pi$
$109$	−5.97981	+	3.45245i	−0.572762	+	0.330684i	0.185490	+	0.982646i	$0.440613\pi$
$110$	−2.18903	+	1.11188i	−0.208716	+	0.106014i
$111$	−16.2337	−	1.68346i	−1.54084	−	0.159787i
$112$	−2.36524	−	17.8518i	−0.223494	−	1.68683i
$113$	0.563121	+	0.775069i	0.0529740	+	0.0729124i	0.834682	−	0.550732i	$-0.185651\pi$
$113$	0.563121	+	0.775069i	0.0529740	+	0.0729124i	−0.781708	+	0.623644i	$0.785651\pi$
$114$	4.79349	+	14.6835i	0.448952	+	1.37523i
$115$	−0.674677	+	0.749305i	−0.0629139	+	0.0698730i
$116$	−9.67879	+	10.7494i	−0.898653	+	0.998055i
$117$	−0.988537	−	4.58805i	−0.0913903	−	0.424165i
$118$	−18.0069	−	24.7844i	−1.65767	−	2.28159i
$119$	−10.9426	−	4.52199i	−1.00311	−	0.414530i
$120$	−0.322182	+	3.10682i	−0.0294111	+	0.283613i
$121$	10.9368	+	1.17747i	0.994254	+	0.107043i
$122$	11.2921	−	6.51948i	1.02234	−	0.590246i
$123$	8.91735	−	0.949764i	0.804050	−	0.0856373i
$124$	1.32113	+	12.5697i	0.118641	+	1.12879i
$125$	1.70056	−	2.34062i	0.152103	−	0.209351i
$126$	20.1274	−	0.599601i	1.79309	−	0.0534167i
$127$	8.26212	−	2.68453i	0.733145	−	0.238213i	0.0814319	−	0.996679i	$-0.474051\pi$
$127$	8.26212	−	2.68453i	0.733145	−	0.238213i	0.651713	+	0.758466i	$0.274051\pi$
$128$	11.6628	−	5.19260i	1.03085	−	0.458966i
$129$	2.68358	−	4.66303i	0.236276	−	0.410557i
$130$	1.13282	−	0.240788i	0.0993549	−	0.0211185i
$131$	1.32364	−	2.29261i	0.115647	−	0.200306i	−0.802391	−	0.596798i	$-0.796439\pi$
$131$	1.32364	−	2.29261i	0.115647	−	0.200306i	0.918038	+	0.396492i	$0.129773\pi$
$132$	16.0346	−	19.8060i	1.39563	−	1.72389i
$133$	4.01083	+	8.39103i	0.347783	+	0.727595i
$134$	−3.08600	+	9.49773i	−0.266590	+	0.820479i
$135$	−1.48441	−	0.309068i	−0.127758	−	0.0266003i
$136$	−2.89091	+	27.5051i	−0.247893	+	2.35855i
$137$	13.2016	+	11.8868i	1.12789	+	1.01556i	0.999717	+	0.0238051i	$0.00757810\pi$
$137$	13.2016	+	11.8868i	1.12789	+	1.01556i	0.128173	+	0.991752i	$0.459089\pi$
$138$	4.67187	−	14.4467i	0.397696	−	1.22979i
$139$	−2.80004	+	3.85392i	−0.237496	+	0.326885i	−0.911083	−	0.412223i	$-0.864753\pi$
$139$	−2.80004	+	3.85392i	−0.237496	+	0.326885i	0.673587	+	0.739108i	$0.264753\pi$
$140$	0.0924786	+	3.42351i	0.00781587	+	0.289340i
$141$	−16.7561	−	7.43244i	−1.41111	−	0.625924i
$142$	3.53052	+	2.03835i	0.296275	+	0.171054i
$143$	−4.84169	−	1.86558i	−0.404883	−	0.156008i
$144$	−6.36365	−	19.4019i	−0.530304	−	1.61683i
$145$	0.707092	−	0.636669i	0.0587208	−	0.0528725i
$146$	16.1300	+	22.2010i	1.33493	+	1.83737i
$147$	11.9693	−	1.93307i	0.987208	−	0.159437i
$148$	12.9169	+	39.7540i	1.06176	+	3.26776i
$149$	−6.23127	−	1.32450i	−0.510486	−	0.108507i	−0.0545346	−	0.998512i	$-0.517368\pi$
$149$	−6.23127	−	1.32450i	−0.510486	−	0.108507i	−0.455951	+	0.890005i	$0.650701\pi$
$150$	−4.46081	+	21.1306i	−0.364224	+	1.72531i
$151$	−1.94889	+	4.37728i	−0.158598	+	0.356218i	−0.975314	−	0.220823i	$-0.929126\pi$
$151$	−1.94889	+	4.37728i	−0.158598	+	0.356218i	0.816716	+	0.577040i	$0.195792\pi$
$152$	16.1441	−	14.5362i	1.30946	−	1.17904i
$153$	−13.1398	−	2.75485i	−1.06229	−	0.222717i
$154$	11.6399	−	18.9759i	0.937971	−	1.52913i
$155$		−	0.831385i		−	0.0667785i
$156$	−9.71482	+	7.07885i	−0.777808	+	0.566761i
$157$	8.50833	+	3.78815i	0.679038	+	0.302327i	0.717122	−	0.696947i	$-0.245459\pi$
$157$	8.50833	+	3.78815i	0.679038	+	0.302327i	−0.0380841	+	0.999275i	$0.512125\pi$
$158$	−28.3280	−	2.97739i	−2.25365	−	0.236868i
$159$	7.35092	−	22.7311i	0.582966	−	1.80269i
$160$	1.36180	−	0.442474i	0.107659	−	0.0349807i
$161$	1.65859	−	8.99041i	0.130715	−	0.708543i
$162$	22.3068	−	4.87101i	1.75258	−	0.382703i
$163$	−4.06117	−	4.51038i	−0.318095	−	0.353280i	0.562799	−	0.826594i	$-0.309724\pi$
$163$	−4.06117	−	4.51038i	−0.318095	−	0.353280i	−0.880894	+	0.473313i	$0.843058\pi$
$164$	−11.4839	−	19.8907i	−0.896741	−	1.55320i
$165$	−1.18516	+	1.18545i	−0.0922643	+	0.0922870i
$166$	−16.1263	+	27.9316i	−1.25165	+	2.16792i
$167$	−2.51744	+	7.74788i	−0.194805	+	0.599549i	0.805173	+	0.593039i	$0.202072\pi$
$167$	−2.51744	+	7.74788i	−0.194805	+	0.599549i	−0.999979	+	0.00650979i	$0.997928\pi$
$168$	−12.2489	−	25.5346i	−0.945020	−	1.97004i
$169$	−8.53716	−	6.20261i	−0.656705	−	0.477124i
$170$	0.688784	−	3.24047i	0.0528273	−	0.248533i
$171$	6.22219	+	8.51432i	0.475823	+	0.651106i
$172$	−13.7037	−	1.44032i	−1.04490	−	0.109823i
$173$	1.57754	+	15.0093i	0.119938	+	1.14113i	0.874541	+	0.484952i	$0.161163\pi$
$173$	1.57754	+	15.0093i	0.119938	+	1.14113i	−0.754603	+	0.656182i	$0.772170\pi$
$174$	−5.80955	+	13.0973i	−0.440421	+	0.992907i
$175$	−1.00953	+	12.9642i	−0.0763133	+	0.980004i
$176$	−21.7973	−	5.87013i	−1.64304	−	0.442478i
$177$	−16.9382	−	12.2704i	−1.27315	−	0.922303i
$178$	4.99435	+	23.4966i	0.374342	+	1.76114i
$179$	7.83898	−	17.6066i	0.585913	−	1.31598i	−0.340773	−	0.940146i	$-0.610689\pi$
$179$	7.83898	−	17.6066i	0.585913	−	1.31598i	0.926686	−	0.375837i	$-0.122645\pi$
$180$	0.817926	+	3.79620i	0.0609646	+	0.282952i
$181$	−1.27301	−	3.91792i	−0.0946220	−	0.291216i	0.892533	−	0.450982i	$-0.148926\pi$
$181$	−1.27301	−	3.91792i	−0.0946220	−	0.291216i	−0.987155	+	0.159766i	$0.948926\pi$
$182$	−7.61097	+	7.23450i	−0.564163	+	0.536257i
$183$	5.94751	−	6.62384i	0.439652	−	0.489648i
$184$	−21.2375	+	2.23215i	−1.56565	+	0.164556i
$185$	−0.571672	−	2.68950i	−0.0420301	−	0.197736i
$186$	5.10798	+	11.4300i	0.374535	+	0.838088i
$187$	−10.5084	+	10.4819i	−0.768452	+	0.766511i
$188$			46.9470i			3.42396i
$189$	12.9361	−	4.65369i	0.940964	−	0.338506i
$190$	−2.10525	+	1.52955i	−0.152731	+	0.110965i
$191$	−3.42922	−	7.70215i	−0.248129	−	0.557308i	0.745945	−	0.666007i	$-0.231998\pi$
$191$	−3.42922	−	7.70215i	−0.248129	−	0.557308i	−0.994075	+	0.108699i	$0.965331\pi$
$192$	1.49611	−	1.35087i	0.107972	−	0.0974904i
$193$	−3.06647	−	2.76106i	−0.220729	−	0.198745i	0.551346	−	0.834277i	$-0.314114\pi$
$193$	−3.06647	−	2.76106i	−0.220729	−	0.198745i	−0.772075	+	0.635531i	$0.780781\pi$
$194$	−15.7227	+	7.00021i	−1.12883	+	0.502586i
$195$	0.684211	−	0.396297i	0.0489974	−	0.0283794i
$196$	−16.9553	−	26.0146i	−1.21109	−	1.85818i
$197$	−3.94078			−0.280769			−0.140384	−	0.990097i	$-0.544834\pi$
$197$	−3.94078			−0.280769			−0.140384	+	0.990097i	$0.544834\pi$
$198$	9.01037	−	23.5792i	0.640339	−	1.67570i
$199$	−9.16059	−	15.8666i	−0.649377	−	1.12475i	−0.983272	−	0.182144i	$-0.941696\pi$
$199$	−9.16059	−	15.8666i	−0.649377	−	1.12475i	0.333895	−	0.942610i	$-0.391637\pi$
$200$	29.7102	−	6.31511i	2.10083	−	0.446546i
$201$	0.00946135	+	6.81812i	0.000667352	+	0.480913i
$202$	19.0089	+	13.8108i	1.33746	+	0.971723i
$203$	−2.44339	+	8.27385i	−0.171493	+	0.580711i
$204$	7.19561	+	33.6232i	0.503793	+	2.35409i
$205$	0.614504	+	1.38020i	0.0429188	+	0.0963973i
$206$	30.3179	+	13.4984i	2.11235	+	0.940479i
$207$	−0.0287698	−	10.3661i	−0.00199964	−	0.720497i
$208$	9.22151	+	5.32404i	0.639396	+	0.369156i
$209$	11.6434	−	0.595442i	0.805389	−	0.0411876i
$210$	1.13948	+	3.19529i	0.0786316	+	0.220496i
$211$	−7.27308	−	2.36317i	−0.500700	−	0.162687i	0.0477689	−	0.998858i	$-0.484789\pi$
$211$	−7.27308	−	2.36317i	−0.500700	−	0.162687i	−0.548468	+	0.836171i	$0.684789\pi$
$212$	−60.8508	+	6.39568i	−4.17925	+	0.439257i
$213$	2.72328	+	0.574902i	0.186596	+	0.0393917i
$214$	17.0269	−	18.9103i	1.16394	−	1.29268i
$215$	0.886586	+	0.188450i	0.0604646	+	0.0128522i
$216$	−18.9832	−	25.9007i	−1.29164	−	1.76232i
$217$	3.94398	+	6.42406i	0.267735	+	0.436094i
$218$	16.6599	+	5.41313i	1.12835	+	0.366623i
$219$	15.1727	+	10.9915i	1.02527	+	0.742734i
$220$	4.00607	+	1.54360i	0.270089	+	0.104069i
$221$	6.06316	−	3.50057i	0.407852	−	0.235474i
$222$	24.3836	+	33.4633i	1.63652	+	2.24591i
$223$	3.92133	−	2.84902i	0.262592	−	0.190784i	−0.448697	−	0.893684i	$-0.648112\pi$
$223$	3.92133	−	2.84902i	0.262592	−	0.190784i	0.711289	+	0.702900i	$0.248112\pi$
$224$	−8.42348	+	9.87915i	−0.562818	+	0.660078i
$225$	1.58192	+	14.6595i	0.105461	+	0.977297i
$226$	0.505325	−	2.37737i	0.0336137	−	0.158140i
$227$	0.00403431	−	0.0383839i	0.000267767	−	0.00254763i	−0.994387	−	0.105802i	$-0.966259\pi$
$227$	0.00403431	−	0.0383839i	0.000267767	−	0.00254763i	0.994655	+	0.103255i	$0.0329256\pi$
$228$	13.4719	−	23.4090i	0.892199	−	1.55030i
$229$	9.09923	+	10.1057i	0.601294	+	0.667805i	0.964555	−	0.263883i	$-0.0850033\pi$
$229$	9.09923	+	10.1057i	0.601294	+	0.667805i	−0.363261	+	0.931688i	$0.618337\pi$
$230$	2.55796			0.168667
$231$	3.53403	−	14.7821i	0.232522	−	0.972591i
$232$	20.1515			1.32301
$233$	−0.942543	−	1.04680i	−0.0617481	−	0.0685782i	0.711479	−	0.702707i	$-0.248026\pi$
$233$	−0.942543	−	1.04680i	−0.0617481	−	0.0685782i	−0.773227	+	0.634129i	$0.781359\pi$
$234$	−6.97181	+	9.65209i	−0.455762	+	0.630977i
$235$	0.322801	−	3.07125i	0.0210572	−	0.200346i
$236$	−11.1374	+	52.3975i	−0.724985	+	3.41079i
$237$	−19.0164	+	4.06965i	−1.23525	+	0.264352i
$238$	10.0502	+	28.3064i	0.651455	+	1.83483i
$239$	−13.6684	+	9.93064i	−0.884132	+	0.642360i	−0.934342	−	0.356379i	$-0.884011\pi$
$239$	−13.6684	+	9.93064i	−0.884132	+	0.642360i	0.0502091	+	0.998739i	$0.484011\pi$
$240$	2.78021	−	2.02584i	0.179462	−	0.130767i
$241$	18.6577	−	10.7720i	1.20185	−	0.693889i	0.240884	−	0.970554i	$-0.422563\pi$
$241$	18.6577	−	10.7720i	1.20185	−	0.693889i	0.960966	+	0.276665i	$0.0892293\pi$
$242$	−16.3457	−	22.6180i	−1.05074	−	1.45394i
$243$	13.4456	−	7.88771i	0.862535	−	0.505997i
$244$	−21.6837	−	7.04548i	−1.38816	−	0.451040i
$245$	0.930331	+	1.81844i	0.0594367	+	0.116176i
$246$	−16.9281	−	15.1997i	−1.07930	−	0.969097i
$247$	−5.37916	−	1.14338i	−0.342268	−	0.0727512i
$248$	11.7820	−	13.0852i	0.748155	−	0.830910i
$249$	−4.54832	+	21.5451i	−0.288238	+	1.36537i
$250$	−7.29956	+	0.767215i	−0.461665	+	0.0485229i
$251$	7.35882	+	2.39103i	0.464485	+	0.150920i	0.531904	−	0.846804i	$-0.321477\pi$
$251$	7.35882	+	2.39103i	0.464485	+	0.150920i	−0.0674195	+	0.997725i	$0.521477\pi$
$252$	−24.3287	−	25.4529i	−1.53257	−	1.60338i
$253$	−9.60348	−	6.25385i	−0.603765	−	0.393176i
$254$	−19.0864	−	11.0196i	−1.19759	−	0.691429i
$255$	−0.239544	−	2.24909i	−0.0150009	−	0.140843i
$256$	−27.4614	−	12.2266i	−1.71633	−	0.764161i
$257$	−9.78304	−	21.9731i	−0.610249	−	1.37064i	−0.909195	−	0.416372i	$-0.863302\pi$
$257$	−9.78304	−	21.9731i	−0.610249	−	1.37064i	0.298946	−	0.954270i	$-0.403365\pi$
$258$	−13.3467	+	2.85630i	−0.830931	+	0.177825i
$259$	17.1759	+	18.0697i	1.06726	+	1.12280i
$260$	−1.63832	−	1.19031i	−0.101604	−	0.0738200i
$261$	−0.995515	+	9.73142i	−0.0616208	+	0.602360i
$262$	−6.56921	+	1.39633i	−0.405847	+	0.0862655i
$263$	2.59219	+	4.48981i	0.159842	+	0.276854i	0.934811	−	0.355144i	$-0.115568\pi$
$263$	2.59219	+	4.48981i	0.159842	+	0.276854i	−0.774970	+	0.631998i	$0.782235\pi$
$264$	−35.4528	+	1.86238i	−2.18197	+	0.114622i
$265$	4.02481			0.247242
$266$	9.01114	−	21.8058i	0.552509	−	1.33700i
$267$	8.21985	+	14.1917i	0.503046	+	0.868516i
$268$	15.9525	−	7.10252i	0.974455	−	0.433855i
$269$	−19.2818	−	17.3614i	−1.17563	−	1.05854i	−0.997214	−	0.0745899i	$-0.976235\pi$
$269$	−19.2818	−	17.3614i	−1.17563	−	1.05854i	−0.178419	−	0.983955i	$-0.557098\pi$
$270$	1.93716	+	3.32322i	0.117892	+	0.202245i
$271$	−1.47548	−	3.31399i	−0.0896291	−	0.201310i	0.863169	−	0.504915i	$-0.168476\pi$
$271$	−1.47548	−	3.31399i	−0.0896291	−	0.201310i	−0.952798	+	0.303605i	$0.901810\pi$
$272$	24.6420	−	17.9035i	1.49414	−	1.08556i
$273$	−3.40689	+	6.30797i	−0.206194	+	0.381775i
$274$		−	45.0674i		−	2.72262i
$275$	14.5147	+	7.41873i	0.875268	+	0.447366i
$276$	−24.2390	+	10.8322i	−1.45901	+	0.652023i
$277$	−2.89474	−	13.6187i	−0.173928	−	0.818267i	−0.975436	−	0.220283i	$-0.929302\pi$
$277$	−2.89474	−	13.6187i	−0.173928	−	0.818267i	0.801508	−	0.597984i	$-0.204031\pi$
$278$	12.0190	−	1.26325i	0.720852	−	0.0757646i
$279$	5.73697	+	6.33609i	0.343463	+	0.379332i
$280$	3.45819	−	3.28714i	0.206666	−	0.196444i
$281$	−8.65894	−	26.6495i	−0.516549	−	1.58977i	−0.780446	−	0.625223i	$-0.785008\pi$
$281$	−8.65894	−	26.6495i	−0.516549	−	1.58977i	0.263897	−	0.964551i	$-0.414992\pi$
$282$	14.4316	+	44.2072i	0.859392	+	2.63250i
$283$	8.21529	−	18.4518i	0.488348	−	1.09685i	−0.486439	−	0.873714i	$-0.661705\pi$
$283$	8.21529	−	18.4518i	0.488348	−	1.09685i	0.974788	−	0.223134i	$-0.0716288\pi$
$284$	−1.48208	−	6.97266i	−0.0879455	−	0.413751i
$285$	−1.04228	+	1.43877i	−0.0617394	+	0.0852255i
$286$	4.70177	+	12.2950i	0.278022	+	0.727018i
$287$	−11.2957	−	7.74959i	−0.666765	−	0.457444i
$288$	−7.32513	+	12.7692i	−0.431638	+	0.752433i
$289$	−0.316407	−	3.01041i	−0.0186122	−	0.177083i
$290$	−2.40063	−	0.252317i	−0.140970	−	0.0148166i
$291$	−8.72127	+	7.87461i	−0.511250	+	0.461618i
$292$	9.97654	−	46.9359i	0.583833	−	2.74672i
$293$	9.17832	+	6.66844i	0.536203	+	0.389574i	0.822673	−	0.568515i	$-0.192482\pi$
$293$	9.17832	+	6.66844i	0.536203	+	0.389574i	−0.286470	+	0.958089i	$0.592482\pi$
$294$	−23.9627	−	19.2843i	−1.39753	−	1.12468i
$295$	1.08888	−	3.35124i	0.0633972	−	0.195117i
$296$	29.1167	−	50.4316i	1.69237	−	2.93128i
$297$	0.852052	−	17.2126i	0.0494411	−	0.998777i
$298$	8.08075	+	13.9963i	0.468105	+	0.810782i
$299$	3.61717	+	4.01728i	0.209187	+	0.232325i
$300$	32.6774	−	18.9268i	1.88663	−	1.09274i
$301$	−7.74458	+	2.74970i	−0.446390	+	0.158490i
$302$	11.5608	−	3.75634i	0.665251	−	0.216153i
$303$	15.2635	+	4.93599i	0.876863	+	0.283565i
$304$	−23.7944	−	2.50089i	−1.36470	−	0.143436i
$305$	1.37010	+	0.610006i	0.0784515	+	0.0349288i
$306$	17.1115	+	29.4490i	0.978202	+	1.68349i
$307$		−	5.65766i		−	0.322900i	−0.986881	−	0.161450i	$-0.948383\pi$
$307$		−	5.65766i		−	0.322900i	0.986881	−	0.161450i	$-0.0516170\pi$
$308$	−38.2773	+	7.07693i	−2.18105	+	0.403245i
$309$	22.5371	+	2.33713i	1.28209	+	0.132955i
$310$	−1.56742	+	1.41131i	−0.0890233	+	0.0801570i
$311$	−9.79937	+	22.0098i	−0.555671	+	1.24806i	0.389362	+	0.921085i	$0.372696\pi$
$311$	−9.79937	+	22.0098i	−0.555671	+	1.24806i	−0.945033	+	0.326974i	$0.893971\pi$
$312$	16.3849	+	3.45897i	0.927614	+	0.195825i
$313$	−24.7663	−	5.26425i	−1.39988	−	0.297553i	−0.554705	−	0.832047i	$-0.687169\pi$
$313$	−24.7663	−	5.26425i	−1.39988	−	0.297553i	−0.845172	+	0.534494i	$0.820502\pi$
$314$	−7.30139	−	22.4714i	−0.412041	−	1.26813i
$315$	1.41656	+	1.83240i	0.0798142	+	0.103244i
$316$	29.2756	+	40.2944i	1.64688	+	2.26673i
$317$	7.07347	−	6.36898i	0.397286	−	0.357718i	−0.446140	−	0.894963i	$-0.647202\pi$
$317$	7.07347	−	6.36898i	0.397286	−	0.357718i	0.843426	+	0.537245i	$0.180535\pi$
$318$	−55.3336	+	24.7282i	−3.10295	+	1.38669i
$319$	8.39594	+	6.81649i	0.470082	+	0.381650i
$320$	0.294097	+	0.169797i	0.0164405	+	0.00949193i
$321$	7.04423	−	15.8809i	0.393171	−	0.886384i
$322$	−19.7652	+	12.1346i	−1.10147	+	0.676236i
$323$	−9.24647	+	12.7267i	−0.514487	+	0.708131i
$324$	−32.4292	−	23.2872i	−1.80162	−	1.29374i
$325$	−5.71405	−	5.14496i	−0.316959	−	0.285391i
$326$	−1.60947	+	15.3131i	−0.0891404	+	0.848114i
$327$	11.9596	−	0.0165961i	0.661368	−	0.000917765i
$328$	−9.88777	+	30.4314i	−0.545961	+	1.68029i
$329$	12.0753	+	25.2627i	0.665733	+	1.39278i
$330$	4.24678	+	0.222040i	0.233778	+	0.0122229i
$331$	4.26415	−	7.38572i	0.234379	−	0.405956i	−0.724713	−	0.689051i	$-0.758028\pi$
$331$	4.26415	−	7.38572i	0.234379	−	0.405956i	0.959092	+	0.283095i	$0.0913611\pi$
$332$	55.1640	−	11.7255i	3.02752	−	0.643518i
$333$	22.9157	+	16.5522i	1.25577	+	0.907057i
$334$	18.8806	−	8.40619i	1.03310	−	0.459966i
$335$	−1.09244	+	0.354956i	−0.0596864	+	0.0193933i
$336$	−11.8722	+	28.8425i	−0.647682	+	1.57349i
$337$	1.18208	−	1.62700i	0.0643922	−	0.0886282i	−0.775606	−	0.631217i	$-0.782556\pi$
$337$	1.18208	−	1.62700i	0.0643922	−	0.0886282i	0.839999	+	0.542589i	$0.182556\pi$
$338$	2.79833	+	26.6244i	0.152209	+	1.44817i
$339$	−0.175741	−	1.65004i	−0.00954496	−	0.0896178i
$340$	−5.01672	+	2.89641i	−0.272070	+	0.157080i
$341$	9.33508	−	1.46643i	0.505523	−	0.0794119i
$342$	5.48970	−	26.1842i	0.296849	−	1.41588i
$343$	−15.8151	−	9.63764i	−0.853933	−	0.520383i
$344$	11.2834	+	15.5302i	0.608359	+	0.837335i
$345$	1.66018	−	0.541974i	0.0893812	−	0.0291789i
$346$	25.6192	−	28.4530i	1.37730	−	1.52964i
$347$	6.60860	−	7.33959i	0.354768	−	0.394010i	−0.539172	−	0.842195i	$-0.681263\pi$
$347$	6.60860	−	7.33959i	0.354768	−	0.394010i	0.893941	+	0.448185i	$0.147930\pi$
$348$	23.8167	−	7.77505i	1.27671	−	0.416787i
$349$	12.2311	+	16.8347i	0.654718	+	0.901141i	0.999292	−	0.0376175i	$-0.0119768\pi$
$349$	12.2311	+	16.8347i	0.654718	+	0.901141i	−0.344575	+	0.938759i	$0.611977\pi$
$350$	26.1553	−	20.1040i	1.39806	−	1.07460i
$351$	−2.47982	+	7.74162i	−0.132363	+	0.413217i
$352$	7.37025	+	14.5103i	0.392836	+	0.773400i
$353$	20.0371	−	11.5684i	1.06647	−	0.615725i	0.139252	−	0.990257i	$-0.455530\pi$
$353$	20.0371	−	11.5684i	1.06647	−	0.615725i	0.927214	+	0.374532i	$0.122197\pi$
$354$	5.61968	+	52.7633i	0.298683	+	2.80434i
$355$	0.0490141	+	0.466338i	0.00260140	+	0.0247507i
$356$	24.6890	−	33.9815i	1.30852	−	1.80102i
$357$	12.5203	+	16.2422i	0.662645	+	0.859628i
$358$	−46.5009	+	15.1091i	−2.45765	+	0.798539i
$359$	7.40251	−	3.29581i	0.390689	−	0.173946i	−0.201984	−	0.979389i	$-0.564739\pi$
$359$	7.40251	−	3.29581i	0.390689	−	0.173946i	0.592674	+	0.805443i	$0.298072\pi$
$360$	3.16778	−	4.38562i	0.166957	−	0.231142i
$361$	−6.49823	+	1.38124i	−0.342012	+	0.0726969i
$362$	−5.22550	+	9.05083i	−0.274646	+	0.475701i
$363$	−15.4011	−	11.2164i	−0.808346	−	0.588708i
$364$	18.3059	+	1.42549i	0.959490	+	0.0747158i
$365$	−0.975385	+	3.00193i	−0.0510540	+	0.157128i
$366$	−22.5841	+	0.0313395i	−1.18049	+	0.00163814i
$367$	−2.52361	+	24.0106i	−0.131732	+	1.25334i	0.706376	+	0.707837i	$0.250329\pi$
$367$	−2.52361	+	24.0106i	−0.131732	+	1.25334i	−0.838108	+	0.545505i	$0.816338\pi$
$368$	17.4776	+	15.7369i	0.911084	+	0.820343i
$369$	−14.2073	−	6.27829i	−0.739601	−	0.326835i
$370$	−4.10011	+	5.64331i	−0.213154	+	0.293382i
$371$	−31.0994	+	19.0931i	−1.61460	+	0.991266i
$372$	8.87621	−	20.0110i	0.460210	−	1.03752i
$373$	−24.9792	−	14.4217i	−1.29337	−	0.746728i	−0.314121	−	0.949383i	$-0.601710\pi$
$373$	−24.9792	−	14.4217i	−1.29337	−	0.746728i	−0.979250	+	0.202654i	$0.935043\pi$
$374$	37.6001	+	2.01821i	1.94425	+	0.104359i
$375$	−4.57504	+	2.04455i	−0.236254	+	0.105580i
$376$	48.6047	−	43.7639i	2.50660	−	2.25695i
$377$	−2.99844	−	4.12699i	−0.154427	−	0.212551i
$378$	−30.7332	−	16.4888i	−1.58075	−	0.848091i
$379$	1.15294	+	3.54839i	0.0592226	+	0.182268i	0.976291	−	0.216461i	$-0.0694513\pi$
$379$	1.15294	+	3.54839i	0.0592226	+	0.182268i	−0.917069	+	0.398729i	$0.869451\pi$
$380$	4.45077	+	0.946041i	0.228320	+	0.0485309i
$381$	−14.7224	−	3.10799i	−0.754250	−	0.159227i
$382$	−8.69969	+	19.5398i	−0.445115	+	0.999745i
$383$	−9.08586	+	8.18095i	−0.464266	+	0.418027i	−0.867782	−	0.496946i	$-0.834455\pi$
$383$	−9.08586	+	8.18095i	−0.464266	+	0.418027i	0.403516	+	0.914973i	$0.367788\pi$
$384$	−21.9943	−	2.28084i	−1.12239	−	0.116394i
$385$	2.55274	−	0.199780i	0.130100	−	0.0101817i
$386$			10.4682i			0.532820i
$387$	−8.05718	+	4.68168i	−0.409569	+	0.237983i
$388$	27.4925	+	12.2404i	1.39572	+	0.621414i
$389$	8.47277	+	0.890524i	0.429586	+	0.0451513i	0.316855	−	0.948474i	$-0.397373\pi$
$389$	8.47277	+	0.890524i	0.429586	+	0.0451513i	0.112732	+	0.993625i	$0.464040\pi$
$390$	−1.90862	−	0.617221i	−0.0966466	−	0.0312542i
$391$	14.7066	−	4.77846i	0.743744	−	0.241657i
$392$	−11.1275	+	41.8047i	−0.562025	+	2.11146i
$393$	−3.96773	+	2.29812i	−0.200146	+	0.115925i
$394$	6.68962	+	7.42958i	0.337018	+	0.374297i
$395$	−1.63813	−	2.83733i	−0.0824234	−	0.142762i
$396$	−41.1824	+	15.8799i	−2.06949	+	0.797993i
$397$	6.24746	−	10.8209i	0.313551	−	0.543087i	−0.665577	−	0.746329i	$-0.731815\pi$
$397$	6.24746	−	10.8209i	0.313551	−	0.543087i	0.979128	+	0.203242i	$0.0651479\pi$
$398$	−14.3630	+	44.2047i	−0.719952	+	2.21578i
$399$	1.22831	−	16.0617i	0.0614926	−	0.804093i
$400$	−27.0632	−	19.6626i	−1.35316	−	0.983128i
$401$	5.14453	−	24.2031i	0.256906	−	1.20865i	−0.640681	−	0.767807i	$-0.721348\pi$
$401$	5.14453	−	24.2031i	0.256906	−	1.20865i	0.897586	−	0.440839i	$-0.145319\pi$
$402$	12.8382	−	11.5919i	0.640311	−	0.578150i
$403$	−4.43292	−	0.465919i	−0.220820	−	0.0232091i
$404$	−4.29457	−	40.8601i	−0.213663	−	2.03287i
$405$	1.96138	+	1.74642i	0.0974617	+	0.0867802i
$406$	19.7465	−	9.43864i	0.980003	−	0.468432i
$407$	29.1903	−	11.1628i	1.44691	−	0.553319i
$408$	28.1027	−	38.7931i	1.39129	−	1.92055i
$409$	1.24492	+	5.85689i	0.0615574	+	0.289605i	0.998149	−	0.0608185i	$-0.0193711\pi$
$409$	1.24492	+	5.85689i	0.0615574	+	0.289605i	−0.936591	+	0.350423i	$0.886038\pi$
$410$	1.55896	−	3.50147i	0.0769913	−	0.172925i
$411$	−9.54876	−	29.2499i	−0.471006	−	1.44279i
$412$	−17.9324	−	55.1901i	−0.883464	−	2.71902i
$413$	7.48407	+	31.0603i	0.368267	+	1.52838i
$414$	−19.4946	+	17.6512i	−0.958105	+	0.867509i
$415$	−3.68942	+	0.387774i	−0.181107	+	0.0190351i
$416$	−1.59609	−	7.50903i	−0.0782549	−	0.368160i
$417$	7.53299	−	3.36643i	0.368892	−	0.164855i
$418$	−20.8877	−	20.9406i	−1.02165	−	1.02424i
$419$		−	15.9545i		−	0.779429i	−0.920936	−	0.389714i	$-0.872574\pi$
$419$		−	15.9545i		−	0.779429i	0.920936	−	0.389714i	$-0.127426\pi$
$420$	2.81889	−	5.21928i	0.137548	−	0.254675i
$421$	−20.8863	+	15.1748i	−1.01794	+	0.739573i	−0.965859	−	0.259070i	$-0.916584\pi$
$421$	−20.8863	+	15.1748i	−1.01794	+	0.739573i	−0.0520765	+	0.998643i	$0.516584\pi$
$422$	7.89104	+	17.7236i	0.384130	+	0.862770i
$423$	18.7330	+	25.6339i	0.910830	+	1.24636i
$424$	63.3465	+	57.0375i	3.07638	+	2.76998i
$425$	−20.0932	+	8.94606i	−0.974662	+	0.433947i
$426$	−3.53901	−	6.11014i	−0.171465	−	0.296037i
$427$	−13.4804	+	1.78607i	−0.652364	+	0.0864338i
$428$	−44.4949			−2.15074
$429$	5.65660	+	6.98356i	0.273103	+	0.337169i
$430$	−1.14973	−	1.99139i	−0.0554448	−	0.0960333i
$431$	−12.8053	+	2.72186i	−0.616811	+	0.131107i	−0.505712	−	0.862702i	$-0.668770\pi$
$431$	−12.8053	+	2.72186i	−0.616811	+	0.131107i	−0.111098	+	0.993809i	$0.535437\pi$
$432$	−7.20904	+	34.6240i	−0.346845	+	1.66585i
$433$	−17.0994	−	12.4234i	−0.821743	−	0.597031i	0.0954682	−	0.995432i	$-0.469565\pi$
$433$	−17.0994	−	12.4234i	−0.821743	−	0.597031i	−0.917211	+	0.398401i	$0.869565\pi$
$434$	5.41629	−	18.3407i	0.259990	−	0.880383i
$435$	−1.61153	+	0.344880i	−0.0772671	+	0.0165357i
$436$	−12.4585	−	27.9822i	−0.596652	−	1.34010i
$437$	−11.0963	−	4.94038i	−0.530807	−	0.236331i
$438$	−5.03393	−	47.2636i	−0.240530	−	2.25834i
$439$	12.2812	+	7.09053i	0.586148	+	0.338413i	0.763573	−	0.645722i	$-0.223443\pi$
$439$	12.2812	+	7.09053i	0.586148	+	0.338413i	−0.177425	+	0.984134i	$0.556777\pi$
$440$	−2.13634	−	5.58646i	−0.101846	−	0.266324i
$441$	−19.6383	−	7.43884i	−0.935158	−	0.354231i
$442$	−16.8921	−	5.48858i	−0.803475	−	0.261065i
$443$	−16.4266	+	1.72650i	−0.780449	+	0.0820285i	−0.486371	−	0.873753i	$-0.661679\pi$
$443$	−16.4266	+	1.72650i	−0.780449	+	0.0820285i	−0.294079	+	0.955781i	$0.595013\pi$
$444$	14.9544	−	70.8382i	0.709705	−	3.36183i
$445$	−1.84880	+	2.05330i	−0.0876413	+	0.0973355i
$446$	−12.0279	−	2.55661i	−0.569537	−	0.121059i
$447$	8.21010	+	7.37180i	0.388324	+	0.348674i
$448$	−3.07796	+	0.0831443i	−0.145420	+	0.00392820i
$449$	11.2352	+	3.65053i	0.530221	+	0.172279i	0.561879	−	0.827220i	$-0.310079\pi$
$449$	11.2352	+	3.65053i	0.530221	+	0.172279i	−0.0316579	+	0.999499i	$0.510079\pi$
$450$	24.9522	−	27.8674i	1.17626	−	1.31368i
$451$	−14.4135	+	9.33432i	−0.678703	+	0.439536i
$452$	−3.68051	+	2.12494i	−0.173117	+	0.0999489i
$453$	6.70739	−	4.88744i	0.315141	−	0.229632i
$454$	−0.0792139	+	0.0575523i	−0.00371769	+	0.00270106i
$455$	−1.18776	−	0.219124i	−0.0556831	−	0.0102727i
$456$	−36.7940	+	7.87419i	−1.72304	+	0.368743i
$457$	−4.44811	+	20.9267i	−0.208074	+	0.978911i	0.742843	+	0.669465i	$0.233477\pi$
$457$	−4.44811	+	20.9267i	−0.208074	+	0.978911i	−0.950917	+	0.309445i	$0.899857\pi$
$458$	3.60610	−	34.3097i	0.168502	−	1.60319i
$459$	17.3454	+	15.4876i	0.809614	+	0.722899i
$460$	−2.99289	−	3.32394i	−0.139544	−	0.154979i
$461$	−7.06593			−0.329093			−0.164546	−	0.986369i	$-0.552616\pi$
$461$	−7.06593			−0.329093			−0.164546	+	0.986369i	$0.552616\pi$
$462$	−33.8680	+	18.4305i	−1.57568	+	0.857463i
$463$	−18.8176			−0.874527			−0.437264	−	0.899333i	$-0.644052\pi$
$463$	−18.8176			−0.874527			−0.437264	+	0.899333i	$0.644052\pi$
$464$	−14.8504	−	16.4930i	−0.689411	−	0.765669i
$465$	−0.718269	+	1.24808i	−0.0333089	+	0.0578781i
$466$	−0.373537	+	3.55397i	−0.0173038	+	0.164634i
$467$	0.972221	−	4.57394i	0.0449890	−	0.211657i	−0.949911	−	0.312520i	$-0.898827\pi$
$467$	0.972221	−	4.57394i	0.0449890	−	0.211657i	0.994900	+	0.100863i	$0.0321604\pi$
$468$	20.6996	−	2.23372i	0.956840	−	0.103254i
$469$	6.75737	−	7.92511i	0.312026	−	0.365948i
$470$	−6.33822	+	4.60498i	−0.292360	+	0.212412i
$471$	−9.49995	−	13.0375i	−0.437735	−	0.600735i
$472$	64.6299	−	37.3141i	2.97483	−	1.71752i
$473$	−0.552178	+	10.2873i	−0.0253892	+	0.473010i
$474$	39.9537	+	28.9434i	1.83513	+	1.32942i
$475$	16.4311	+	5.33878i	0.753910	+	0.244960i
$476$	25.0238	−	46.1790i	1.14696	−	2.11661i
$477$	−30.6736	+	27.7731i	−1.40445	+	1.27164i
$478$	41.9249	+	8.91141i	1.91760	+	0.407598i
$479$	−11.3726	+	12.6305i	−0.519626	+	0.577103i	−0.944650	−	0.328079i	$-0.893599\pi$
$479$	−11.3726	+	12.6305i	−0.519626	+	0.577103i	0.425024	+	0.905182i	$0.360266\pi$
$480$	−2.42660	−	0.512272i	−0.110759	−	0.0233819i
$481$	−14.6607	+	1.54090i	−0.668471	+	0.0702592i
$482$	−51.9809	−	16.8896i	−2.36766	−	0.769301i
$483$	−10.2571	+	12.0635i	−0.466713	+	0.548907i
$484$	−10.2660	+	47.7042i	−0.466636	+	2.16837i
$485$	−1.71438	−	0.989797i	−0.0778459	−	0.0449444i
$486$	−37.6952	−	11.9594i	−1.70989	−	0.542489i
$487$	−20.8618	−	9.28828i	−0.945339	−	0.420892i	−0.124607	−	0.992206i	$-0.539767\pi$
$487$	−20.8618	−	9.28828i	−0.945339	−	0.420892i	−0.820731	+	0.571314i	$0.806434\pi$
$488$	12.9193	+	29.0172i	0.584828	+	1.31355i
$489$	2.19991	+	10.2796i	0.0994834	+	0.464860i
$490$	1.84905	−	4.84084i	0.0835316	−	0.218687i
$491$	−16.2862	−	11.8326i	−0.734987	−	0.533999i	0.156150	−	0.987733i	$-0.450092\pi$
$491$	−16.2862	−	11.8326i	−0.734987	−	0.533999i	−0.891137	+	0.453734i	$0.850092\pi$
$492$	0.0552036	+	39.7813i	0.00248877	+	1.79348i
$493$	−14.2734	+	3.03391i	−0.642842	+	0.136640i
$494$	6.97572	+	12.0823i	0.313852	+	0.543608i
$495$	2.80332	−	0.755688i	0.126000	−	0.0339656i
$496$	−19.3921			−0.870733
$497$	−2.59097	−	3.37085i	−0.116221	−	0.151203i
$498$	48.3402	−	27.9987i	2.16618	−	1.25465i
$499$	7.44912	−	3.31656i	0.333468	−	0.148470i	−0.233171	−	0.972436i	$-0.574910\pi$
$499$	7.44912	−	3.31656i	0.333468	−	0.148470i	0.566639	+	0.823966i	$0.308243\pi$
$500$	9.53764	+	8.58773i	0.426536	+	0.384055i
$501$	10.4729	−	9.45620i	0.467895	−	0.422472i
$502$	−7.98407	−	17.9325i	−0.356347	−	0.800367i
$503$	31.6279	−	22.9790i	1.41022	−	1.02458i	0.416929	−	0.908939i	$-0.363106\pi$
$503$	31.6279	−	22.9790i	1.41022	−	1.02458i	0.993291	−	0.115646i	$-0.0368937\pi$
$504$	−3.67247	+	48.9149i	−0.163585	+	2.17884i
$505$			2.70257i			0.120263i
$506$	4.51185	+	28.7217i	0.200576	+	1.27683i
$507$	7.45729	+	16.6870i	0.331190	+	0.741095i
$508$	8.01233	+	37.6950i	0.355489	+	1.67245i
$509$	34.0713	−	3.58103i	1.51018	−	0.158727i	0.687064	−	0.726597i	$-0.258899\pi$
$509$	34.0713	−	3.58103i	1.51018	−	0.158727i	0.823118	+	0.567870i	$0.192232\pi$
$510$	−3.83359	+	4.26953i	−0.169754	+	0.189058i
$511$	−6.70398	−	27.8228i	−0.296567	−	1.23081i
$512$	15.6757	+	48.2449i	0.692775	+	2.13214i
$513$	−1.98487	−	18.1573i	−0.0876342	−	0.801665i
$514$	−24.8189	+	55.7442i	−1.09472	+	2.45877i
$515$	0.793646	+	3.73381i	0.0349722	+	0.164531i
$516$	19.3277	+	14.0014i	0.850853	+	0.616378i
$517$	35.0544	−	1.79268i	1.54169	−	0.0788420i
$518$	4.91019	−	63.0559i	0.215741	−	2.77052i
$519$	10.5990	−	23.8948i	0.465243	−	1.04887i
$520$	0.294899	+	2.80578i	0.0129322	+	0.123042i
$521$	13.2309	+	1.39062i	0.579654	+	0.0609241i	0.389818	−	0.920892i	$-0.372538\pi$
$521$	13.2309	+	1.39062i	0.579654	+	0.0609241i	0.189836	+	0.981816i	$0.439204\pi$
$522$	20.0367	−	14.6426i	0.876981	−	0.640890i
$523$	0.848534	−	3.99204i	0.0371038	−	0.174560i	−0.955694	−	0.294362i	$-0.904893\pi$
$523$	0.848534	−	3.99204i	0.0371038	−	0.174560i	0.992798	+	0.119803i	$0.0382261\pi$
$524$	9.50062	+	6.90260i	0.415036	+	0.301542i
$525$	12.7159	−	18.5897i	0.554966	−	0.811322i
$526$	4.06433	−	12.5087i	0.177213	−	0.545406i
$527$	−6.37519	+	11.0422i	−0.277708	+	0.481004i
$528$	27.6507	+	27.6439i	1.20334	+	1.20305i
$529$	−5.53012	−	9.57844i	−0.240440	−	0.416454i
$530$	−6.83227	−	7.58800i	−0.296775	−	0.329602i
$531$	14.8267	+	33.0540i	0.643422	+	1.43442i
$532$	−38.8787	+	13.8038i	−1.68561	+	0.598473i
$533$	7.70356	−	2.50304i	0.333678	−	0.108419i
$534$	12.8022	−	39.5879i	0.554004	−	1.71313i
$535$	2.91083	+	0.305941i	0.125846	+	0.0132270i
$536$	−22.2242	−	9.89485i	−0.959939	−	0.427392i
$537$	−26.9790	+	19.6587i	−1.16423	+	0.848334i
$538$			65.8239i			2.83787i
$539$	−18.7771	+	13.6535i	−0.808789	+	0.588099i
$540$	2.05183	−	6.40550i	0.0882967	−	0.275649i
$541$	9.26560	−	8.34278i	0.398359	−	0.358684i	−0.445469	−	0.895297i	$-0.646963\pi$
$541$	9.26560	−	8.34278i	0.398359	−	0.358684i	0.843828	+	0.536613i	$0.180296\pi$
$542$	−3.74320	+	8.40736i	−0.160784	+	0.361127i
$543$	−1.47382	+	6.98139i	−0.0632475	+	0.299600i
$544$	−21.4798	−	4.56568i	−0.920940	−	0.195752i
$545$	0.622625	+	1.91624i	0.0266703	+	0.0820828i
$546$	17.6758	−	4.28499i	0.756454	−	0.183381i
$547$	0.743696	+	1.02361i	0.0317982	+	0.0437664i	0.824620	−	0.565687i	$-0.191389\pi$
$547$	0.743696	+	1.02361i	0.0317982	+	0.0437664i	−0.792822	+	0.609453i	$0.791389\pi$
$548$	−58.5627	+	52.7301i	−2.50168	+	2.25252i
$549$	−14.6510	+	4.80540i	−0.625290	+	0.205089i
$550$	−10.6526	−	39.9582i	−0.454230	−	1.70382i
$551$	9.92649	+	5.73106i	0.422883	+	0.244151i
$552$	33.8102	+	14.9971i	1.43906	+	0.638319i
$553$	26.1177	+	14.1528i	1.11064	+	0.601839i
$554$	−20.7615	+	28.5757i	−0.882071	+	1.21407i
$555$	−1.46538	+	4.53137i	−0.0622021	+	0.192346i
$556$	−15.7041	−	14.1400i	−0.666002	−	0.599671i
$557$	−0.763572	+	7.26491i	−0.0323536	+	0.307824i	0.966363	+	0.257181i	$0.0827937\pi$
$557$	−0.763572	+	7.26491i	−0.0323536	+	0.307824i	−0.998717	+	0.0506429i	$0.983873\pi$
$558$	2.20677	−	21.5717i	0.0934199	−	0.913204i
$559$	1.50166	−	4.62164i	0.0635135	−	0.195475i
$560$	−5.23883	−	0.407949i	−0.221381	−	0.0172390i
$561$	24.8310	−	6.65673i	1.04837	−	0.281047i
$562$	−35.5436	+	61.5633i	−1.49932	+	2.59689i
$563$	−29.6633	+	6.30512i	−1.25016	+	0.265729i	−0.784998	−	0.619498i	$-0.787336\pi$
$563$	−29.6633	+	6.30512i	−1.25016	+	0.265729i	−0.465159	+	0.885227i	$0.654003\pi$
$564$	40.5595	−	70.4768i	1.70786	−	2.96761i
$565$	0.255388	−	0.113706i	0.0107442	−	0.00478365i
$566$	−48.7332	+	15.8344i	−2.04841	+	0.665569i
$567$	−23.4402	−	4.18996i	−0.984397	−	0.175962i
$568$	−5.83727	+	8.03431i	−0.244926	+	0.337112i
$569$	−2.33497	−	22.2157i	−0.0978869	−	0.931332i	−0.927709	−	0.373304i	$-0.878225\pi$
$569$	−2.33497	−	22.2157i	−0.0978869	−	0.931332i	0.829822	−	0.558028i	$-0.188442\pi$
$570$	4.48184	−	0.477350i	0.187724	−	0.0199940i
$571$	18.9666	−	10.9504i	0.793728	−	0.458259i	−0.0475454	−	0.998869i	$-0.515140\pi$
$571$	18.9666	−	10.9504i	0.793728	−	0.458259i	0.841273	+	0.540610i	$0.181807\pi$
$572$	10.4755	−	20.4952i	0.438002	−	0.856947i
$573$	−1.50628	+	14.5251i	−0.0629255	+	0.606795i
$574$	4.56454	+	34.4511i	0.190520	+	1.43796i
$575$	−9.98222	−	13.7393i	−0.416287	−	0.572970i
$576$	−3.41303	+	0.735368i	−0.142210	+	0.0306404i
$577$	−26.0163	+	28.8941i	−1.08307	+	1.20288i	−0.105032	+	0.994469i	$0.533494\pi$
$577$	−26.0163	+	28.8941i	−1.08307	+	1.20288i	−0.978042	+	0.208407i	$0.933172\pi$
$578$	−5.13844	+	5.70681i	−0.213731	+	0.237372i
$579$	2.21798	+	6.79416i	0.0921763	+	0.282356i
$580$	2.48094	+	3.41472i	0.103015	+	0.141788i
$581$	26.6684	−	20.4984i	1.10639	−	0.850417i
$582$	29.6508	+	3.07483i	1.22906	+	0.127456i
$583$	7.09913	+	45.1919i	0.294016	+	1.87166i
$584$	−57.8934	+	33.4248i	−2.39564	+	1.38313i
$585$	−1.36952	+	0.00380090i	−0.0566225	+	0.000157148i
$586$	−3.00849	−	28.6239i	−0.124280	−	1.18244i
$587$	17.3336	−	23.8577i	0.715435	−	0.984712i	−0.284228	−	0.958757i	$-0.591737\pi$
$587$	17.3336	−	23.8577i	0.715435	−	0.984712i	0.999663	−	0.0259554i	$-0.00826279\pi$
$588$	2.97811	+	53.7015i	0.122815	+	2.21461i
$589$	9.52513	−	3.09490i	0.392476	−	0.127523i
$590$	−8.16654	+	3.63598i	−0.336211	+	0.149691i
$591$	5.91589	+	3.40461i	0.243347	+	0.140047i
$592$	−62.7329	+	13.3343i	−2.57831	+	0.548036i
$593$	10.4065	−	18.0246i	0.427344	−	0.740182i	−0.569292	−	0.822135i	$-0.692783\pi$
$593$	10.4065	−	18.0246i	0.427344	−	0.740182i	0.996636	+	0.0819538i	$0.0261160\pi$
$594$	−33.8975	+	27.6127i	−1.39083	+	1.13296i
$595$	−1.95456	+	2.84895i	−0.0801292	+	0.116795i
$596$	8.73271	−	26.8765i	0.357706	−	1.10091i
$597$	0.0440354	+	31.7332i	0.00180225	+	1.29875i
$598$	1.43351	−	13.6390i	0.0586207	−	0.557739i
$599$	−15.4265	−	13.8901i	−0.630309	−	0.567533i	0.290826	−	0.956776i	$-0.406070\pi$
$599$	−15.4265	−	13.8901i	−0.630309	−	0.567533i	−0.921135	+	0.389243i	$0.872737\pi$
$600$	−50.0569	−	16.1877i	−2.04357	−	0.660861i
$601$	7.22305	−	9.94168i	0.294635	−	0.405530i	−0.635878	−	0.771790i	$-0.719362\pi$
$601$	7.22305	−	9.94168i	0.294635	−	0.405530i	0.930513	+	0.366260i	$0.119362\pi$
$602$	18.3308	+	9.93319i	0.747106	+	0.404847i
$603$	5.87626	−	10.2435i	0.239300	−	0.417149i
$604$	−18.4077	−	10.6277i	−0.748997	−	0.432434i
$605$	0.999603	−	3.05020i	0.0406397	−	0.124008i
$606$	−16.6045	−	37.1554i	−0.674510	−	1.50933i
$607$	1.85979	−	1.67456i	0.0754864	−	0.0679682i	−0.630524	−	0.776170i	$-0.717160\pi$
$607$	1.85979	−	1.67456i	0.0754864	−	0.0679682i	0.706010	+	0.708202i	$0.250493\pi$
$608$	10.1388	+	13.9549i	0.411183	+	0.565945i
$609$	10.8162	−	10.3098i	0.438293	−	0.417772i
$610$	−1.17574	−	3.61856i	−0.0476044	−	0.146511i
$611$	−16.1949	−	3.44233i	−0.655175	−	0.139262i
$612$	18.2465	−	56.6917i	0.737569	−	2.29163i
$613$	16.8705	−	37.8917i	0.681393	−	1.53043i	−0.158311	−	0.987389i	$-0.550605\pi$
$613$	16.8705	−	37.8917i	0.681393	−	1.53043i	0.839704	−	0.543044i	$-0.182728\pi$
$614$	−10.6664	+	9.60411i	−0.430463	+	0.387590i
$615$	0.269919	−	2.60285i	0.0108842	−	0.104957i
$616$	43.0088	+	33.0318i	1.73287	+	1.33089i
$617$			34.0869i			1.37229i	0.727466	+	0.686144i	$0.240698\pi$
$617$			34.0869i			1.37229i	−0.727466	+	0.686144i	$0.759302\pi$
$618$	−33.8514	−	46.4568i	−1.36170	−	1.86877i
$619$	−1.76096	−	0.784029i	−0.0707788	−	0.0315128i	0.371042	−	0.928616i	$-0.379001\pi$
$619$	−1.76096	−	0.784029i	−0.0707788	−	0.0315128i	−0.441821	+	0.897103i	$0.645667\pi$
$620$	3.66785	+	0.385506i	0.147304	+	0.0154823i
$621$	−8.91257	+	15.5865i	−0.357649	+	0.625466i
$622$	58.1300	−	18.8876i	2.33080	−	0.757323i
$623$	4.54498	−	24.6361i	0.182091	−	0.987025i
$624$	−9.24366	−	15.9593i	−0.370043	−	0.638884i
$625$	15.8785	+	17.6348i	0.635140	+	0.705394i
$626$	32.1171	+	55.6285i	1.28366	+	2.22336i
$627$	−17.9935	−	9.16533i	−0.718589	−	0.366028i
$628$	−20.6575	+	35.7799i	−0.824325	+	1.42777i
$629$	−13.0308	+	40.1046i	−0.519572	+	1.59908i
$630$	1.04996	−	5.78122i	0.0418315	−	0.230329i
$631$	17.5324	+	12.7380i	0.697953	+	0.507092i	0.879265	−	0.476333i	$-0.158034\pi$
$631$	17.5324	+	12.7380i	0.697953	+	0.507092i	−0.181312	+	0.983426i	$0.558034\pi$
$632$	14.4266	−	67.8716i	0.573857	−	2.69979i
$633$	8.87671	+	9.83112i	0.352818	+	0.390752i
$634$	−24.0150	−	2.52408i	−0.953757	−	0.100244i
$635$	−0.264976	−	2.52108i	−0.0105153	−	0.100046i
$636$	96.8748	+	42.9705i	3.84134	+	1.70389i
$637$	10.2173	−	3.94142i	0.404822	−	0.156165i
$638$	−1.40125	−	27.4002i	−0.0554759	−	1.08478i
$639$	−3.59151	−	3.21580i	−0.142078	−	0.127215i
$640$	−0.774529	−	3.64387i	−0.0306160	−	0.144037i
$641$	11.5795	−	26.0080i	0.457363	−	1.02725i	−0.526800	−	0.849989i	$-0.676609\pi$
$641$	11.5795	−	26.0080i	0.457363	−	1.02725i	0.984163	−	0.177265i	$-0.0567248\pi$
$642$	−41.8982	+	13.6779i	−1.65359	+	0.539822i
$643$	7.14365	+	21.9859i	0.281718	+	0.867038i	0.987363	+	0.158473i	$0.0506572\pi$
$643$	7.14365	+	21.9859i	0.281718	+	0.867038i	−0.705645	+	0.708565i	$0.749343\pi$
$644$	38.8942	+	11.4860i	1.53264	+	0.452613i
$645$	−1.16813	−	1.04886i	−0.0459952	−	0.0412988i
$646$	39.6900	−	4.17158i	1.56158	−	0.164129i
$647$	6.82788	+	32.1227i	0.268432	+	1.26287i	0.881251	+	0.472649i	$0.156702\pi$
$647$	6.82788	+	32.1227i	0.268432	+	1.26287i	−0.612819	+	0.790223i	$0.709964\pi$
$648$	6.12086	+	55.2826i	0.240450	+	2.17170i
$649$	39.5495	+	6.31529i	1.55245	+	0.247897i
$650$			19.5065i			0.765109i
$651$	−0.370673	−	13.0512i	−0.0145278	−	0.511516i
$652$	21.7817	−	15.8253i	0.853037	−	0.619768i
$653$	3.27919	+	7.36517i	0.128324	+	0.288221i	0.966269	−	0.257533i	$-0.0829097\pi$
$653$	3.27919	+	7.36517i	0.128324	+	0.288221i	−0.837945	+	0.545755i	$0.816243\pi$
$654$	−20.3332	−	22.5194i	−0.795091	−	0.880578i
$655$	−0.574064	−	0.516890i	−0.0224305	−	0.0201965i
$656$	32.1933	−	14.3334i	1.25694	−	0.559624i
$657$	−13.2812	−	29.6087i	−0.518150	−	1.15515i
$658$	27.1296	−	65.6501i	1.05762	−	2.55931i
$659$	20.7231			0.807257			0.403628	−	0.914923i	$-0.367749\pi$
$659$	20.7231			0.807257			0.403628	+	0.914923i	$0.367749\pi$
$660$	−4.68033	−	5.77827i	−0.182182	−	0.224919i
$661$	4.87997	+	8.45236i	0.189809	+	0.328759i	0.945186	−	0.326531i	$-0.105880\pi$
$661$	4.87997	+	8.45236i	0.189809	+	0.328759i	−0.755377	+	0.655290i	$0.772546\pi$
$662$	−21.1629	+	4.49832i	−0.822520	+	0.174832i
$663$	−12.1263	+	0.0168274i	−0.470947	+	0.000653522i
$664$	−63.5632	−	46.1814i	−2.46673	−	1.79218i
$665$	2.63834	−	0.635715i	0.102310	−	0.0246520i
$666$	−7.69419	−	71.3012i	−0.298144	−	2.76287i
$667$	−4.58276	−	10.2930i	−0.177445	−	0.398548i
$668$	−33.0142	−	14.6989i	−1.27736	−	0.568717i
$669$	−8.34809	+	0.889134i	−0.322756	+	0.0343759i
$670$	2.52366	+	1.45704i	0.0974976	+	0.0562902i
$671$	−4.43272	+	16.4599i	−0.171123	+	0.635426i
$672$	21.1804	−	7.55317i	0.817050	−	0.291370i
$673$	32.4492	+	10.5434i	1.25082	+	0.406418i	0.858216	−	0.513288i	$-0.171573\pi$
$673$	32.4492	+	10.5434i	1.25082	+	0.406418i	0.392608	+	0.919706i	$0.371573\pi$
$674$	−5.07403	+	0.533302i	−0.195444	+	0.0205420i
$675$	10.2902	−	23.3735i	0.396068	−	0.899645i
$676$	31.3228	−	34.7875i	1.20472	−	1.33798i
$677$	42.3321	+	8.99797i	1.62696	+	0.345820i	0.928931	−	0.370254i	$-0.120729\pi$
$677$	42.3321	+	8.99797i	1.62696	+	0.345820i	0.698025	+	0.716074i	$0.254063\pi$
$678$	−2.81250	+	3.13233i	−0.108014	+	0.120297i
$679$	17.9424	−	0.484673i	0.688565	−	0.0186000i
$680$	7.67525	+	2.49384i	0.294333	+	0.0956344i
$681$	−0.0392178	+	0.0541365i	−0.00150283	+	0.00207452i
$682$	−18.6113	−	15.1102i	−0.712665	−	0.578599i
$683$	15.6245	−	9.02078i	0.597853	−	0.345171i	−0.170343	−	0.985385i	$-0.554488\pi$
$683$	15.6245	−	9.02078i	0.597853	−	0.345171i	0.768197	+	0.640214i	$0.221154\pi$
$684$	−40.4480	+	23.5026i	−1.54657	+	0.898645i
$685$	4.19371	−	3.04691i	0.160233	−	0.116416i
$686$	8.67676	+	46.1765i	0.331280	+	1.76303i
$687$	−4.92900	−	23.0319i	−0.188053	−	0.878723i
$688$	4.39561	−	20.6797i	0.167581	−	0.788407i
$689$	2.25555	−	21.4601i	0.0859297	−	0.817566i
$690$	−3.84001	−	2.20993i	−0.146187	−	0.0841307i
$691$	−11.9490	−	13.2707i	−0.454562	−	0.504842i	0.471681	−	0.881769i	$-0.343647\pi$
$691$	−11.9490	−	13.2707i	−0.454562	−	0.504842i	−0.926243	+	0.376927i	$0.876981\pi$
$692$	−66.9483			−2.54499
$693$	−18.0762	+	19.1377i	−0.686657	+	0.726981i
$694$	−25.0558			−0.951104
$695$	0.930129	+	1.03301i	0.0352818	+	0.0391844i
$696$	−30.2514	−	17.4097i	−1.14668	−	0.659914i
$697$	2.42196	−	23.0434i	0.0917383	−	0.872831i
$698$	10.9758	−	51.6370i	0.415440	−	1.95449i
$699$	0.510570	+	2.38576i	0.0193115	+	0.0902378i
$700$	−56.7265	−	10.4652i	−2.14406	−	0.395546i
$701$	−5.14699	+	3.73951i	−0.194399	+	0.141239i	−0.680727	−	0.732537i	$-0.738336\pi$
$701$	−5.14699	+	3.73951i	−0.194399	+	0.141239i	0.486328	+	0.873776i	$0.338336\pi$
$702$	18.8049	−	8.46648i	0.709747	−	0.319547i
$703$	28.6854	−	16.5615i	1.08189	−	0.624629i
$704$	−1.38780	+	3.60172i	−0.0523046	+	0.135745i
$705$	−3.13797	+	4.33168i	−0.118183	+	0.163140i
$706$	−55.8238	−	18.1382i	−2.10096	−	0.682642i
$707$	−12.8206	−	20.8826i	−0.482170	−	0.785372i
$708$	61.9880	−	69.0370i	2.32965	−	2.59457i
$709$	−20.2893	−	4.31262i	−0.761981	−	0.161964i	−0.189498	−	0.981881i	$-0.560686\pi$
$709$	−20.2893	−	4.31262i	−0.761981	−	0.161964i	−0.572482	+	0.819917i	$0.694020\pi$
$710$	0.795988	−	0.884034i	0.0298729	−	0.0331772i
$711$	32.0634	+	10.3197i	1.20247	+	0.387020i
$712$	−58.1965	+	6.11670i	−2.18100	+	0.229233i
$713$	−9.36309	−	3.04225i	−0.350651	−	0.113933i
$714$	9.36784	−	51.1764i	0.350583	−	1.91523i
$715$	−0.826223	+	1.26876i	−0.0308990	+	0.0474488i
$716$	74.0409	+	42.7475i	2.76704	+	1.59755i
$717$	29.0984	−	3.09920i	1.08670	−	0.115742i
$718$	−18.7797	−	8.36124i	−0.700851	−	0.312039i
$719$	10.0050	+	22.4716i	0.373123	+	0.838048i	0.998340	+	0.0575968i	$0.0183438\pi$
$719$	10.0050	+	22.4716i	0.373123	+	0.838048i	−0.625217	+	0.780451i	$0.714990\pi$
$720$	−5.92386	+	0.639251i	−0.220769	+	0.0238235i
$721$	−23.8451	−	25.0860i	−0.888039	−	0.934251i
$722$	13.6351	+	9.90645i	0.507445	+	0.368680i
$723$	−37.3154	+	0.0517818i	−1.38778	+	0.00192579i
$724$	17.8751	−	3.79946i	0.664322	−	0.141206i
$725$	8.01302	+	13.8790i	0.297596	+	0.515451i
$726$	4.99753	+	48.0760i	0.185476	+	1.78427i
$727$	6.34055			0.235158			0.117579	−	0.993064i	$-0.462487\pi$
$727$	6.34055			0.235158			0.117579	+	0.993064i	$0.462487\pi$
$728$	−15.5889	−	20.2811i	−0.577763	−	0.751668i
$729$	−26.9991	+	0.224801i	−0.999965	+	0.00832596i
$730$	7.31531	−	3.25699i	0.270752	−	0.120547i
$731$	−10.3302	−	9.30139i	−0.382078	−	0.344024i
$732$	26.4648	+	29.3102i	0.978166	+	1.08334i
$733$	12.2976	+	27.6208i	0.454221	+	1.02020i	0.984979	+	0.172673i	$0.0552404\pi$
$733$	12.2976	+	27.6208i	0.454221	+	1.02020i	−0.530759	+	0.847523i	$0.678093\pi$
$734$	49.5513	−	36.0011i	1.82897	−	1.32882i
$735$	0.174417	−	3.53360i	0.00643348	−	0.130339i
$736$		−	16.9557i		−	0.624997i
$737$	−5.91246	−	11.6402i	−0.217788	−	0.428773i
$738$	12.2809	+	37.4427i	0.452065	+	1.37829i
$739$	−7.67312	−	36.0992i	−0.282260	−	1.32793i	−0.859408	−	0.511290i	$-0.829168\pi$
$739$	−7.67312	−	36.0992i	−0.282260	−	1.32793i	0.577148	−	0.816639i	$-0.304166\pi$
$740$	12.1304	−	1.27496i	0.445924	−	0.0468685i
$741$	7.08738	+	6.36372i	0.260362	+	0.233777i
$742$	88.7890	+	26.2207i	3.25954	+	0.962592i
$743$	−4.12179	−	12.6856i	−0.151214	−	0.465388i	0.846544	−	0.532319i	$-0.178679\pi$
$743$	−4.12179	−	12.6856i	−0.151214	−	0.465388i	−0.997758	+	0.0669310i	$0.978679\pi$
$744$	−28.9919	+	9.46455i	−1.06290	+	0.346987i
$745$	−0.756089	+	1.69820i	−0.0277009	+	0.0622174i
$746$	15.2137	+	71.5749i	0.557013	+	2.62054i
$747$	25.4417	−	28.4141i	0.930864	−	1.03962i
$748$	−41.3706	−	51.2207i	−1.51266	−	1.87281i
$749$	−23.9432	+	11.4446i	−0.874865	+	0.418177i
$750$	11.6209	+	5.15466i	0.424336	+	0.188222i
$751$	−1.81597	−	17.2778i	−0.0662655	−	0.630474i	−0.976372	−	0.216099i	$-0.930667\pi$
$751$	−1.81597	−	17.2778i	−0.0662655	−	0.630474i	0.910106	−	0.414376i	$-0.136000\pi$
$752$	−71.6372	−	7.52937i	−2.61234	−	0.274568i
$753$	−8.98136	−	9.94702i	−0.327299	−	0.362489i
$754$	−2.69069	+	12.6587i	−0.0979892	+	0.461003i
$755$	1.13115	+	0.821825i	0.0411666	+	0.0299093i
$756$	14.5324	+	59.2285i	0.528539	+	2.15412i
$757$	−9.40801	+	28.9549i	−0.341940	+	1.05238i	0.621262	+	0.783603i	$0.286620\pi$
$757$	−9.40801	+	28.9549i	−0.341940	+	1.05238i	−0.963202	+	0.268779i	$0.913380\pi$
$758$	4.73264	−	8.19718i	0.171897	−	0.297735i
$759$	9.01377	+	17.6851i	0.327179	+	0.641930i
$760$	−3.16955	−	5.48983i	−0.114972	−	0.199137i
$761$	−13.0415	−	14.4840i	−0.472754	−	0.525046i	0.458854	−	0.888512i	$-0.348260\pi$
$761$	−13.0415	−	14.4840i	−0.472754	−	0.525046i	−0.931608	+	0.363465i	$0.881593\pi$
$762$	19.1323	+	33.0322i	0.693090	+	1.19663i
$763$	−13.9014	−	11.8530i	−0.503263	−	0.429109i
$764$	35.5699	−	11.5574i	1.28687	−	0.418130i
$765$	−1.58348	+	3.58328i	−0.0572508	+	0.129554i
$766$	30.8472	+	3.24217i	1.11456	+	0.117144i
$767$	−17.2585	−	7.68397i	−0.623167	−	0.277452i
$768$	30.6619	+	42.0796i	1.10642	+	1.51842i
$769$			30.8014i			1.11073i	0.831608	+	0.555363i	$0.187421\pi$
$769$			30.8014i			1.11073i	−0.831608	+	0.555363i	$0.812579\pi$
$770$	−4.71002	−	4.47357i	−0.169737	−	0.161216i
$771$	−4.29717	+	41.4379i	−0.154759	+	1.49235i
$772$	13.6029	−	12.2481i	0.489581	−	0.440820i
$773$	2.68480	−	6.03015i	0.0965655	−	0.216890i	−0.858803	−	0.512306i	$-0.828792\pi$
$773$	2.68480	−	6.03015i	0.0965655	−	0.216890i	0.955369	+	0.295416i	$0.0954582\pi$
$774$	22.5038	+	7.24294i	0.808882	+	0.260342i
$775$	13.6971	+	2.91142i	0.492016	+	0.104581i
$776$	−12.9558	−	39.8737i	−0.465085	−	1.43138i
$777$	−10.1733	−	41.9652i	−0.364964	−	1.50549i
$778$	−12.7039	−	17.4855i	−0.455459	−	0.626885i
$779$	−13.5253	+	12.1782i	−0.484595	+	0.436331i
$780$	1.43109	+	3.20231i	0.0512412	+	0.114661i
$781$	−5.14975	+	1.37290i	−0.184273	+	0.0491261i
$782$	−33.9739	−	19.6148i	−1.21490	−	0.701425i
$783$	9.90186	−	13.7487i	0.353864	−	0.491340i
$784$	42.4154	−	21.7001i	1.51483	−	0.775003i
$785$	1.59742	−	2.19866i	0.0570144	−	0.0784736i
$786$	11.0680	+	3.57925i	0.394784	+	0.127668i
$787$	22.2544	+	20.0380i	0.793284	+	0.714277i	0.962494	−	0.271304i	$-0.0874547\pi$
$787$	22.2544	+	20.0380i	0.793284	+	0.714277i	−0.169209	+	0.985580i	$0.554121\pi$
$788$	1.82730	−	17.3856i	0.0650950	−	0.619337i
$789$	−0.0124608	−	8.97962i	−0.000443617	−	0.319683i
$790$	−2.56845	+	7.90487i	−0.0913812	+	0.281243i
$791$	−1.43396	+	2.09012i	−0.0509858	+	0.0743163i
$792$	54.8307	+	27.8334i	1.94832	+	0.989015i
$793$	4.02035	−	6.96346i	0.142767	−	0.247280i
$794$	−31.0061	+	6.59055i	−1.10037	+	0.233890i
$795$	−6.04204	−	3.47720i	−0.214289	−	0.123324i
$796$	74.2469	−	33.0568i	2.63161	−	1.17167i
$797$	−17.6702	+	5.74139i	−0.625910	+	0.203371i	−0.604763	−	0.796406i	$-0.706732\pi$
$797$	−17.6702	+	5.74139i	−0.625910	+	0.203371i	−0.0211475	+	0.999776i	$0.506732\pi$
$798$	−32.3665	+	24.9497i	−1.14576	+	0.883210i
$799$	−27.8381	+	38.3159i	−0.984842	+	1.35552i
$800$	2.52095	+	23.9852i	0.0891289	+	0.848005i
$801$	−0.0788369	−	28.4060i	−0.00278557	−	1.00368i
$802$	−54.3634	+	31.3867i	−1.91964	+	1.10830i
$803$	−35.4271	−	5.65703i	−1.25020	−	0.199632i
$804$	−30.0841	−	3.11976i	−1.06098	−	0.110026i
$805$	−2.46546	−	1.01884i	−0.0868960	−	0.0359094i
$806$	6.64666	+	9.14834i	0.234119	+	0.322237i
$807$	13.9466	+	42.7214i	0.490943	+	1.50386i
$808$	−38.2995	+	42.5359i	−1.34737	+	1.49641i
$809$	−13.6423	+	15.1514i	−0.479639	+	0.532694i	−0.933595	−	0.358331i	$-0.883346\pi$
$809$	−13.6423	+	15.1514i	−0.479639	+	0.532694i	0.453955	+	0.891025i	$0.350013\pi$
$810$	−0.0369815	−	6.66242i	−0.00129940	−	0.234094i
$811$	21.0970	+	29.0375i	0.740815	+	1.01964i	0.998571	+	0.0534344i	$0.0170168\pi$
$811$	21.0970	+	29.0375i	0.740815	+	1.01964i	−0.257756	+	0.966210i	$0.582983\pi$
$812$	−35.3690	−	14.6161i	−1.24121	−	0.512924i
$813$	−0.648102	+	6.24969i	−0.0227299	+	0.219186i
$814$	−70.5970	−	36.0835i	−2.47443	−	1.26473i
$815$	−1.53376	+	0.885517i	−0.0537253	+	0.0310183i
$816$	−52.4602	+	5.58740i	−1.83647	+	0.195598i
$817$	1.14134	+	10.8591i	0.0399303	+	0.379911i
$818$	8.92875	−	12.2894i	0.312186	−	0.429688i
$819$	10.5641	−	6.52617i	0.369141	−	0.228043i
$820$	−6.37400	+	2.07104i	−0.222590	+	0.0723238i
$821$	42.7453	−	19.0314i	1.49182	−	0.664201i	0.511083	−	0.859532i	$-0.329245\pi$
$821$	42.7453	−	19.0314i	1.49182	−	0.664201i	0.980737	+	0.195330i	$0.0625779\pi$
$822$	−38.9357	+	67.6552i	−1.35804	+	2.35975i
$823$	−18.3137	+	3.89270i	−0.638376	+	0.135691i	−0.515719	−	0.856758i	$-0.672475\pi$
$823$	−18.3137	+	3.89270i	−0.638376	+	0.135691i	−0.122658	+	0.992449i	$0.539142\pi$
$824$	−40.4224	+	70.0136i	−1.40818	+	2.43904i
$825$	−15.3801	−	23.6769i	−0.535466	−	0.824322i
$826$	45.8538	−	66.8359i	1.59546	−	2.32552i
$827$	1.28583	−	3.95737i	0.0447126	−	0.137611i	−0.926208	−	0.377013i	$-0.876951\pi$
$827$	1.28583	−	3.95737i	0.0447126	−	0.137611i	0.970921	+	0.239402i	$0.0769513\pi$
$828$	45.7460	+	4.67977i	1.58978	+	0.162633i
$829$	0.455376	−	4.33262i	0.0158159	−	0.150478i	−0.983764	−	0.179468i	$-0.942562\pi$
$829$	0.455376	−	4.33262i	0.0158159	−	0.150478i	0.999580	+	0.0289899i	$0.00922906\pi$
$830$	6.99401	+	6.29744i	0.242766	+	0.218587i
$831$	−7.42018	+	22.9453i	−0.257403	+	0.795962i
$832$	1.07017	−	1.47296i	0.0371014	−	0.0510657i
$833$	1.58778	−	31.2858i	0.0550134	−	1.08399i
$834$	−19.1343	−	8.48735i	−0.662567	−	0.293893i
$835$	2.05871	+	1.18859i	0.0712445	+	0.0411330i
$836$	−2.77200	+	51.6435i	−0.0958717	+	1.78613i
$837$	−3.13831	−	14.4682i	−0.108476	−	0.500093i
$838$	−30.0792	+	27.0834i	−1.03907	+	0.935581i
$839$	−19.4284	−	26.7409i	−0.670742	−	0.923197i	0.329035	−	0.944318i	$-0.393277\pi$
$839$	−19.4284	−	26.7409i	−0.670742	−	0.923197i	−0.999777	+	0.0211206i	$0.993277\pi$
$840$	−8.03133	+	1.94697i	−0.277107	+	0.0671768i
$841$	−5.67590	−	17.4686i	−0.195721	−	0.602366i
$842$	64.0644	+	13.6173i	2.20781	+	0.469284i
$843$	−10.0248	+	47.4870i	−0.345273	+	1.63554i
$844$	13.7981	−	30.9911i	0.474951	−	1.06676i
$845$	−2.28832	+	2.06041i	−0.0787205	+	0.0708803i
$846$	16.5277	−	78.8320i	0.568235	−	2.71030i
$847$	6.74583	+	28.3107i	0.231790	+	0.972766i
$848$		−	93.8790i		−	3.22382i
$849$	−28.2741	+	20.6024i	−0.970366	+	0.707072i
$850$	50.9750	+	22.6955i	1.74843	+	0.778451i
$851$	−32.3812	−	3.40340i	−1.11001	−	0.116667i
$852$	−3.79907	+	11.7478i	−0.130154	+	0.402473i
$853$	−16.0950	+	5.22957i	−0.551081	+	0.179057i	−0.571304	−	0.820738i	$-0.693562\pi$
$853$	−16.0950	+	5.22957i	−0.551081	+	0.179057i	0.0202231	+	0.999795i	$0.493562\pi$
$854$	26.2509	+	22.3829i	0.898286	+	0.765926i
$855$	2.80769	−	1.25941i	0.0960210	−	0.0430710i
$856$	41.4780	+	46.0660i	1.41769	+	1.57450i
$857$	−27.4093	−	47.4743i	−0.936284	−	1.62169i	−0.772327	−	0.635225i	$-0.780907\pi$
$857$	−27.4093	−	47.4743i	−0.936284	−	1.62169i	−0.163957	−	0.986467i	$-0.552426\pi$
$858$	3.56386	−	22.5193i	0.121668	−	0.768796i
$859$	−0.617374	+	1.06932i	−0.0210645	+	0.0364849i	−0.876366	−	0.481647i	$-0.840039\pi$
$859$	−0.617374	+	1.06932i	−0.0210645	+	0.0364849i	0.855301	+	0.518131i	$0.173372\pi$
$860$	−1.24249	+	3.82399i	−0.0423686	+	0.130397i
$861$	10.2619	+	21.3925i	0.349725	+	0.729056i
$862$	26.8691	+	19.5215i	0.915164	+	0.664906i
$863$	−10.2563	+	48.2522i	−0.349130	+	1.64253i	0.356754	+	0.934198i	$0.383883\pi$
$863$	−10.2563	+	48.2522i	−0.349130	+	1.64253i	−0.705884	+	0.708327i	$0.749450\pi$
$864$	22.0284	−	12.8407i	0.749420	−	0.436848i
$865$	4.37972	+	0.460328i	0.148915	+	0.0156516i
$866$	5.60488	+	53.3268i	0.190461	+	1.81212i
$867$	−2.12583	+	4.79258i	−0.0721970	+	0.162765i
$868$	−30.1700	+	14.4210i	−1.02404	+	0.489480i
$869$	28.9691	−	23.3981i	0.982710	−	0.793728i
$870$	3.38585	+	2.45279i	0.114791	+	0.0831574i
$871$	1.28039	+	6.02378i	0.0433845	+	0.204108i
$872$	−17.3565	+	38.9833i	−0.587764	+	1.32014i
$873$	19.8956	−	4.28668i	0.673364	−	0.145082i
$874$	9.52223	+	29.3064i	0.322094	+	0.991304i
$875$	7.34117	+	2.16796i	0.248177	+	0.0732904i
$876$	−55.5268	+	61.8411i	−1.87608	+	2.08942i
$877$	−27.9277	+	2.93532i	−0.943052	+	0.0991188i	−0.563559	−	0.826076i	$-0.690568\pi$
$877$	−27.9277	+	2.93532i	−0.943052	+	0.0991188i	−0.379493	+	0.925194i	$0.623902\pi$
$878$	−7.47991	−	35.1902i	−0.252435	−	1.18761i
$879$	−8.01734	−	17.9402i	−0.270418	−	0.605108i
$880$	−2.99790	+	5.86536i	−0.101059	+	0.197721i
$881$		−	39.6038i		−	1.33429i	−0.744929	−	0.667144i	$-0.767517\pi$
$881$		−	39.6038i		−	1.33429i	0.744929	−	0.667144i	$-0.232483\pi$
$882$	19.3123	+	49.6520i	0.650279	+	1.67187i
$883$	45.1904	−	32.8328i	1.52078	−	1.10491i	0.559678	−	0.828710i	$-0.310925\pi$
$883$	45.1904	−	32.8328i	1.52078	−	1.10491i	0.961100	−	0.276200i	$-0.0890752\pi$
$884$	12.6321	+	28.3722i	0.424864	+	0.954260i
$885$	−4.52991	+	4.09014i	−0.152271	+	0.137489i
$886$	31.1397	+	28.0383i	1.04616	+	0.941966i
$887$	−30.4825	+	13.5717i	−1.02350	+	0.455693i	−0.848680	−	0.528907i	$-0.822602\pi$
$887$	−30.4825	+	13.5717i	−1.02350	+	0.455693i	−0.174823	+	0.984600i	$0.555935\pi$
$888$	−87.2800	+	50.5528i	−2.92893	+	1.69644i
$889$	14.0071	+	18.2232i	0.469784	+	0.611188i
$890$	7.00950			0.234959
$891$	−16.1498	+	25.1035i	−0.541039	+	0.840997i
$892$	10.7508	+	18.6209i	0.359963	+	0.623475i
$893$	36.3888	−	7.73467i	1.21770	−	0.258831i
$894$	−0.0388446	−	27.9925i	−0.00129916	−	0.936209i
$895$	−4.54979	−	3.30561i	−0.152083	−	0.110495i
$896$	23.2708	+	24.4817i	0.777422	+	0.817878i
$897$	−1.95940	−	9.15577i	−0.0654225	−	0.305702i
$898$	−12.1898	−	27.3787i	−0.406778	−	0.913639i
$899$	8.48713	+	3.77871i	0.283062	+	0.126027i
$900$	−65.4070	+	0.181528i	−2.18023	+	0.00605093i
$901$	−53.4560	−	30.8628i	−1.78088	−	1.02819i
$902$	42.0655	+	11.3284i	1.40063	+	0.377196i
$903$	14.0017	+	2.56302i	0.465949	+	0.0852919i
$904$	5.63094	+	1.82960i	0.187282	+	0.0608517i
$905$	−1.19550	+	0.125652i	−0.0397398	+	0.00417683i
$906$	−20.6004	−	4.34888i	−0.684402	−	0.144482i
$907$	−7.32446	+	8.13464i	−0.243205	+	0.270106i	−0.852372	−	0.522935i	$-0.824837\pi$
$907$	−7.32446	+	8.13464i	−0.243205	+	0.270106i	0.609168	+	0.793041i	$0.291504\pi$
$908$	0.167469	+	0.0355966i	0.00555764	+	0.00118131i
$909$	−18.6491	−	20.5967i	−0.618551	−	0.683148i
$910$	1.60316	+	2.61127i	0.0531441	+	0.0865627i
$911$	−16.6616	−	5.41367i	−0.552023	−	0.179363i	0.0197060	−	0.999806i	$-0.493727\pi$
$911$	−16.6616	−	5.41367i	−0.552023	−	0.179363i	−0.571729	+	0.820443i	$0.693727\pi$
$912$	33.5595	+	24.3113i	1.11127	+	0.805029i
$913$	−10.8616	−	40.7421i	−0.359467	−	1.34837i
$914$	47.0042	−	27.1379i	1.55476	−	0.897641i
$915$	−1.52978	−	2.09943i	−0.0505729	−	0.0694049i
$916$	−48.8029	+	35.4574i	−1.61249	+	1.17155i
$917$	6.88781	+	1.27069i	0.227456	+	0.0419620i
$918$	−0.245588	−	58.9922i	−0.00810561	−	1.94703i
$919$	7.09810	−	33.3939i	0.234145	−	1.10156i	−0.691267	−	0.722600i	$-0.742947\pi$
$919$	7.09810	−	33.3939i	0.234145	−	1.10156i	0.925411	−	0.378964i	$-0.123720\pi$
$920$	−0.651345	+	6.19713i	−0.0214742	+	0.204313i
$921$	−4.88790	+	8.49329i	−0.161062	+	0.279863i
$922$	11.9947	+	13.3215i	0.395024	+	0.438719i
$923$	2.51397			0.0827483
$924$	63.5759	+	22.4455i	2.09149	+	0.738403i
$925$	46.3117			1.52272
$926$	31.9436	+	35.4769i	1.04973	+	1.16584i
$927$	−31.8136	−	22.9793i	−1.04490	−	0.754739i
$928$	−1.67251	+	15.9129i	−0.0549029	+	0.522366i
$929$	−3.40026	+	15.9970i	−0.111559	+	0.524844i	0.886509	+	0.462712i	$0.153123\pi$
$929$	−3.40026	+	15.9970i	−0.111559	+	0.524844i	−0.998068	+	0.0621324i	$0.980210\pi$
$930$	3.57230	−	0.764498i	0.117140	−	0.0250689i
$931$	−17.3706	+	17.4281i	−0.569297	+	0.571182i
$932$	5.05525	−	3.67285i	0.165590	−	0.120308i
$933$	33.7260	−	24.5749i	1.10414	−	0.804548i
$934$	−10.2737	+	5.93151i	−0.336165	+	0.194085i
$935$	2.35425	+	3.63529i	0.0769923	+	0.118887i
$936$	−21.6087	−	19.3483i	−0.706303	−	0.632417i
$937$	47.1064	+	15.3058i	1.53890	+	0.500019i	0.951072	−	0.308968i	$-0.0999837\pi$
$937$	47.1064	+	15.3058i	1.53890	+	0.500019i	0.587827	+	0.808987i	$0.299984\pi$
$938$	−26.4122	+	0.713466i	−0.862388	+	0.0232955i
$939$	32.6312	+	29.2994i	1.06488	+	0.956150i
$940$	13.3998	+	2.84822i	0.437054	+	0.0928987i
$941$	5.54789	−	6.16156i	0.180856	−	0.200861i	−0.645899	−	0.763423i	$-0.723517\pi$
$941$	5.54789	−	6.16156i	0.180856	−	0.200861i	0.826755	+	0.562562i	$0.190184\pi$
$942$	−8.45313	+	40.0420i	−0.275418	+	1.30464i
$943$	17.7925	−	1.87007i	0.579403	−	0.0608977i
$944$	−78.1680	−	25.3983i	−2.54415	−	0.826644i
$945$	−0.543457	−	3.97462i	−0.0176786	−	0.129294i
$946$	20.3321	−	16.4221i	0.661052	−	0.533927i
$947$	−29.7286	−	17.1638i	−0.966050	−	0.557749i	−0.0680205	−	0.997684i	$-0.521668\pi$
$947$	−29.7286	−	17.1638i	−0.966050	−	0.557749i	−0.898030	+	0.439934i	$0.855002\pi$
$948$	−9.13646	−	85.7823i	−0.296738	−	2.78608i
$949$	15.4596	+	6.88304i	0.501839	+	0.223433i
$950$	−17.8272	−	40.0405i	−0.578389	−	1.29908i
$951$	−16.1211	+	3.45004i	−0.522764	+	0.111875i
$952$	−71.1367	+	17.1406i	−2.30555	+	0.555529i
$953$	−29.8218	−	21.6668i	−0.966024	−	0.701858i	−0.0114822	−	0.999934i	$-0.503655\pi$
$953$	−29.8218	−	21.6668i	−0.966024	−	0.701858i	−0.954542	+	0.298076i	$0.903655\pi$
$954$	104.431	+	10.6831i	3.38106	+	0.345879i
$955$	−2.40643	+	0.511502i	−0.0778702	+	0.0165518i
$956$	−37.4734	−	64.9058i	−1.21198	−	2.09920i
$957$	−6.71493	−	17.4865i	−0.217063	−	0.565259i
$958$	43.1178			1.39307
$959$	−17.9504	+	43.4377i	−0.579650	+	1.40268i
$960$	−0.294803	−	0.508982i	−0.00951474	−	0.0164273i
$961$	−20.9041	+	9.30709i	−0.674325	+	0.300229i
$962$	27.7922	+	25.0242i	0.896058	+	0.806814i
$963$	−24.2950	+	17.7546i	−0.782895	+	0.572133i
$964$	38.8719	+	87.3078i	1.25198	+	2.81199i
$965$	−0.974114	+	0.707735i	−0.0313578	+	0.0227828i
$966$	40.1552	−	1.14047i	1.29197	−	0.0366939i
$967$		−	37.4281i		−	1.20361i	−0.798645	−	0.601803i	$-0.794449\pi$
$967$		−	37.4281i		−	1.20361i	0.798645	−	0.601803i	$-0.205551\pi$
$968$	58.9586	−	33.8412i	1.89500	−	1.08770i
$969$	24.8759	−	11.1169i	0.799130	−	0.357125i
$970$	1.04415	+	4.91235i	0.0335257	+	0.157726i
$971$	−1.97346	+	0.207419i	−0.0633314	+	0.00665640i	−0.136141	−	0.990689i	$-0.543470\pi$
$971$	−1.97346	+	0.207419i	−0.0633314	+	0.00665640i	0.0728098	+	0.997346i	$0.476803\pi$
$972$	28.5638	+	62.9758i	0.916185	+	2.01995i
$973$	−12.0875	−	3.56963i	−0.387508	−	0.114437i
$974$	17.9025	+	55.0982i	0.573632	+	1.76546i
$975$	4.13299	+	12.6602i	0.132362	+	0.405452i
$976$	14.2285	−	31.9576i	0.455442	−	1.02294i
$977$	5.76544	+	27.1243i	0.184453	+	0.867782i	0.968874	+	0.247554i	$0.0796267\pi$
$977$	5.76544	+	27.1243i	0.184453	+	0.867782i	−0.784421	+	0.620228i	$0.787040\pi$
$978$	15.6458	−	21.5975i	0.500297	−	0.690613i
$979$	−26.3161	−	17.1372i	−0.841066	−	0.547708i
$980$	−8.45386	+	3.26117i	−0.270049	+	0.104174i
$981$	−17.9681	−	10.3075i	−0.573678	−	0.329093i
$982$	5.33834	+	50.7909i	0.170353	+	1.62080i
$983$	27.7535	+	2.91701i	0.885200	+	0.0930382i	0.536206	−	0.844087i	$-0.319857\pi$
$983$	27.7535	+	2.91701i	0.885200	+	0.0930382i	0.348993	+	0.937125i	$0.386524\pi$
$984$	41.1345	−	37.1412i	1.31132	−	1.18402i
$985$	−0.239082	+	1.12479i	−0.00761780	+	0.0358389i
$986$	29.9495	+	21.7596i	0.953788	+	0.692967i
$987$	3.69805	−	48.3567i	0.117710	−	1.53921i
$988$	7.53853	−	23.2012i	0.239833	−	0.738129i
$989$	5.36657	−	9.29518i	0.170647	−	0.295570i
$990$	−6.18345	−	4.00231i	−0.196523	−	0.127202i
$991$	0.606659	+	1.05076i	0.0192712	+	0.0333786i	0.875500	−	0.483218i	$-0.160532\pi$
$991$	0.606659	+	1.05076i	0.0192712	+	0.0333786i	−0.856229	+	0.516596i	$0.827199\pi$
$992$	9.35502	+	10.3898i	0.297022	+	0.329877i
$993$	−12.7822	+	7.40347i	−0.405630	+	0.234942i
$994$	−1.95682	+	10.6069i	−0.0620664	+	0.336432i
$995$	−5.08449	+	1.65205i	−0.161189	+	0.0523735i
$996$	−92.9423	−	30.0563i	−2.94499	−	0.952369i
$997$	36.5353	+	3.84002i	1.15709	+	0.121615i	0.663564	−	0.748119i	$-0.269043\pi$
$997$	36.5353	+	3.84002i	1.15709	+	0.121615i	0.493521	+	0.869734i	$0.335710\pi$
$998$	−18.8979	−	8.41389i	−0.598203	−	0.266337i
$999$	−20.1008	−	44.6461i	−0.635962	−	1.41254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.2.1	✓	224
3.2	odd	2	inner	231.2.be.a.2.28	yes	224
7.4	even	3	inner	231.2.be.a.200.28	yes	224
11.6	odd	10	inner	231.2.be.a.149.1	yes	224
21.11	odd	6	inner	231.2.be.a.200.1	yes	224
33.17	even	10	inner	231.2.be.a.149.28	yes	224
77.39	odd	30	inner	231.2.be.a.116.28	yes	224
231.116	even	30	inner	231.2.be.a.116.1	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.1	✓	224	1.1	even	1	trivial
231.2.be.a.2.28	yes	224	3.2	odd	2	inner
231.2.be.a.116.1	yes	224	231.116	even	30	inner
231.2.be.a.116.28	yes	224	77.39	odd	30	inner
231.2.be.a.149.1	yes	224	11.6	odd	10	inner
231.2.be.a.149.28	yes	224	33.17	even	10	inner
231.2.be.a.200.1	yes	224	21.11	odd	6	inner
231.2.be.a.200.28	yes	224	7.4	even	3	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.be (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69754 - 1.88531i) q^{2} +(-1.50120 - 0.863943i) q^{3} +(-0.463691 + 4.41173i) q^{4} +(0.0606689 - 0.285425i) q^{5} +(0.919548 + 4.29680i) q^{6} +(0.885230 + 2.49326i) q^{7} +(4.99976 - 3.63254i) q^{8} +(1.50720 + 2.59390i) q^{9} +O(q^{10})\)	\(q+(-1.69754 - 1.88531i) q^{2} +(-1.50120 - 0.863943i) q^{3} +(-0.463691 + 4.41173i) q^{4} +(0.0606689 - 0.285425i) q^{5} +(0.919548 + 4.29680i) q^{6} +(0.885230 + 2.49326i) q^{7} +(4.99976 - 3.63254i) q^{8} +(1.50720 + 2.59390i) q^{9} +(-0.641101 + 0.370140i) q^{10} +(3.31186 + 0.177766i) q^{11} +(4.50758 - 6.22228i) q^{12} +(-1.48788 - 0.483440i) q^{13} +(3.19786 - 5.90135i) q^{14} +(-0.337667 + 0.376065i) q^{15} +(-6.65756 - 1.41511i) q^{16} +(-2.99446 + 3.32569i) q^{17} +(2.33177 - 7.24480i) q^{18} +(3.49594 - 0.367438i) q^{19} +(1.23108 + 0.400004i) q^{20} +(0.825130 - 4.50768i) q^{21} +(-5.28686 - 6.54564i) q^{22} +(-2.99246 - 1.72770i) q^{23} +(-10.6439 + 1.13366i) q^{24} +(4.48994 + 1.99905i) q^{25} +(1.61429 + 3.62577i) q^{26} +(-0.0216317 - 5.19611i) q^{27} +(-11.4101 + 2.74929i) q^{28} +(2.63799 + 1.91661i) q^{29} +(1.28220 - 0.00177928i) q^{30} +(2.78689 - 0.592371i) q^{31} +(2.45351 + 4.24961i) q^{32} +(-4.81818 - 3.12812i) q^{33} +11.3532 q^{34} +(0.765345 - 0.101403i) q^{35} +(-12.1425 + 5.44661i) q^{36} +(8.60817 - 3.83260i) q^{37} +(-6.62723 - 5.96718i) q^{38} +(1.81594 + 2.01118i) q^{39} +(-0.733486 - 1.64744i) q^{40} +(-4.18873 + 3.04329i) q^{41} +(-9.89906 + 6.09634i) q^{42} +3.10620i q^{43} +(-2.31994 + 14.5286i) q^{44} +(0.831804 - 0.272824i) q^{45} +(1.82258 + 8.57455i) q^{46} +(10.5251 - 1.10624i) q^{47} +(8.77176 + 7.87611i) q^{48} +(-5.43273 + 4.41423i) q^{49} +(-3.85302 - 11.8584i) q^{50} +(7.36849 - 2.40548i) q^{51} +(2.82272 - 6.33994i) q^{52} +(2.86772 + 13.4916i) q^{53} +(-9.75955 + 8.86138i) q^{54} +(0.251666 - 0.934501i) q^{55} +(13.4828 + 9.25009i) q^{56} +(-5.56555 - 2.46869i) q^{57} +(-0.864688 - 8.22695i) q^{58} +(12.0095 + 1.26225i) q^{59} +(-1.50252 - 1.66407i) q^{60} +(-1.06859 + 5.02734i) q^{61} +(-5.84766 - 4.24857i) q^{62} +(-5.13306 + 6.05406i) q^{63} +(-0.359629 + 1.10682i) q^{64} +(-0.228254 + 0.395347i) q^{65} +(2.28158 + 14.3939i) q^{66} +(-1.96822 - 3.40906i) q^{67} +(-13.2835 - 14.7528i) q^{68} +(2.99965 + 5.17894i) q^{69} +(-1.49038 - 1.27078i) q^{70} +(-1.52829 + 0.496572i) q^{71} +(16.9581 + 7.49391i) q^{72} +(-10.7577 - 1.13068i) q^{73} +(-21.8383 - 9.72306i) q^{74} +(-5.01323 - 6.88003i) q^{75} +15.5935i q^{76} +(2.48854 + 8.41470i) q^{77} +(0.709075 - 6.83766i) q^{78} +(8.34383 - 7.51282i) q^{79} +(-0.807814 + 1.81438i) q^{80} +(-4.45667 + 7.81909i) q^{81} +(12.8481 + 2.73094i) q^{82} +(-3.92861 - 12.0910i) q^{83} +(19.5040 + 5.73042i) q^{84} +(0.767562 + 1.05646i) q^{85} +(5.85614 - 5.27290i) q^{86} +(-2.30431 - 5.15629i) q^{87} +(17.2042 - 11.1417i) q^{88} +(-8.20014 - 4.73436i) q^{89} +(-1.92638 - 1.10508i) q^{90} +(-0.111769 - 4.13763i) q^{91} +(9.00971 - 12.4008i) q^{92} +(-4.69545 - 1.51844i) q^{93} +(-19.9524 - 17.9652i) q^{94} +(0.107219 - 1.02012i) q^{95} +(-0.0117942 - 8.49922i) q^{96} +(2.09639 - 6.45201i) q^{97} +(17.5445 + 2.74906i) q^{98} +(4.53054 + 8.85857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more