LMFDB - Embedded newform 1110.2.bb.e.1009.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (of order $6$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.7
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.e.1099.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.61819 - 1.54320i) q^{5} -1.00000 q^{6} +(1.82925 - 1.05612i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.61819 - 1.54320i) q^{5} -1.00000 q^{6} +(1.82925 - 1.05612i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.17299 + 0.527353i) q^{10} +1.56784 q^{11} +(0.866025 + 0.500000i) q^{12} +(0.735613 - 0.424706i) q^{13} -2.11224 q^{14} +(0.629796 - 2.14554i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.36455 + 3.09722i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-0.926239 - 1.60429i) q^{19} +(2.14554 + 0.629796i) q^{20} +(1.05612 - 1.82925i) q^{21} +(-1.35779 - 0.783922i) q^{22} +2.02604i q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.237084 - 4.99438i) q^{25} -0.849412 q^{26} -1.00000i q^{27} +(1.82925 + 1.05612i) q^{28} +2.74901 q^{29} +(-1.61819 + 1.54320i) q^{30} -5.35881 q^{31} +(0.866025 - 0.500000i) q^{32} +(1.35779 - 0.783922i) q^{33} +(-3.09722 - 5.36455i) q^{34} +(1.33028 - 4.53190i) q^{35} +1.00000 q^{36} +(-3.54207 + 4.94508i) q^{37} +1.85248i q^{38} +(0.424706 - 0.735613i) q^{39} +(-1.54320 - 1.61819i) q^{40} +(-1.71563 - 2.97156i) q^{41} +(-1.82925 + 1.05612i) q^{42} -2.80562i q^{43} +(0.783922 + 1.35779i) q^{44} +(-0.527353 - 2.17299i) q^{45} +(1.01302 - 1.75460i) q^{46} +8.42766i q^{47} +1.00000i q^{48} +(-1.26922 + 2.19835i) q^{49} +(-2.70251 + 4.20671i) q^{50} +6.19445 q^{51} +(0.735613 + 0.424706i) q^{52} +(7.19076 + 4.15159i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.53707 - 2.41949i) q^{55} +(-1.05612 - 1.82925i) q^{56} +(-1.60429 - 0.926239i) q^{57} +(-2.38071 - 1.37451i) q^{58} +(0.267356 - 0.463075i) q^{59} +(2.17299 - 0.527353i) q^{60} +(-5.39914 - 9.35159i) q^{61} +(4.64086 + 2.67940i) q^{62} -2.11224i q^{63} -1.00000 q^{64} +(0.534956 - 1.82245i) q^{65} -1.56784 q^{66} +(-0.0321948 + 0.0185877i) q^{67} +6.19445i q^{68} +(1.01302 + 1.75460i) q^{69} +(-3.41801 + 3.25960i) q^{70} +(-5.11238 - 8.85491i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.96121i q^{73} +(5.54006 - 2.51153i) q^{74} +(-2.29187 - 4.44380i) q^{75} +(0.926239 - 1.60429i) q^{76} +(2.86799 - 1.65583i) q^{77} +(-0.735613 + 0.424706i) q^{78} +(4.21801 + 7.30581i) q^{79} +(0.527353 + 2.17299i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.43126i q^{82} +(0.938843 + 0.542041i) q^{83} +2.11224 q^{84} +(13.4605 - 3.26666i) q^{85} +(-1.40281 + 2.42974i) q^{86} +(2.38071 - 1.37451i) q^{87} -1.56784i q^{88} +(-4.64567 + 8.04654i) q^{89} +(-0.629796 + 2.14554i) q^{90} +(0.897081 - 1.55379i) q^{91} +(-1.75460 + 1.01302i) q^{92} +(-4.64086 + 2.67940i) q^{93} +(4.21383 - 7.29857i) q^{94} +(-3.97457 - 1.16668i) q^{95} +(0.500000 - 0.866025i) q^{96} -11.7183i q^{97} +(2.19835 - 1.26922i) q^{98} +(0.783922 - 1.35779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.61819	−	1.54320i	0.723677	−	0.690139i
$5$	1.61819	−	1.54320i	0.723677	−	0.690139i
$6$	−1.00000			−0.408248
$7$	1.82925	−	1.05612i	0.691393	−	0.399176i	−0.112741	−	0.993624i	$-0.535963\pi$
$7$	1.82925	−	1.05612i	0.691393	−	0.399176i	0.804134	+	0.594449i	$0.202630\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.17299	+	0.527353i	−0.687161	+	0.166764i
$11$	1.56784			0.472723			0.236361	−	0.971665i	$-0.424045\pi$
$11$	1.56784			0.472723			0.236361	+	0.971665i	$0.424045\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	0.735613	−	0.424706i	0.204022	−	0.117792i	−0.394508	−	0.918893i	$-0.629085\pi$
$13$	0.735613	−	0.424706i	0.204022	−	0.117792i	0.598530	+	0.801100i	$0.295752\pi$
$14$	−2.11224			−0.564520
$15$	0.629796	−	2.14554i	0.162613	−	0.553977i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.36455	+	3.09722i	1.30109	+	0.751187i	0.980592	−	0.196061i	$-0.0628150\pi$
$17$	5.36455	+	3.09722i	1.30109	+	0.751187i	0.320502	+	0.947248i	$0.396148\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−0.926239	−	1.60429i	−0.212494	−	0.368050i	0.740001	−	0.672606i	$-0.234825\pi$
$19$	−0.926239	−	1.60429i	−0.212494	−	0.368050i	−0.952494	+	0.304556i	$0.901492\pi$
$20$	2.14554	+	0.629796i	0.479758	+	0.140827i
$21$	1.05612	−	1.82925i	0.230464	−	0.399176i
$22$	−1.35779	−	0.783922i	−0.289483	−	0.167133i
$23$			2.02604i			0.422458i	0.977437	+	0.211229i	$0.0677466\pi$
$23$			2.02604i			0.422458i	−0.977437	+	0.211229i	$0.932253\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	0.237084	−	4.99438i	0.0474167	−	0.998875i
$26$	−0.849412			−0.166583
$27$		−	1.00000i		−	0.192450i
$28$	1.82925	+	1.05612i	0.345696	+	0.199588i
$29$	2.74901			0.510479			0.255239	−	0.966878i	$-0.417846\pi$
$29$	2.74901			0.510479			0.255239	+	0.966878i	$0.417846\pi$
$30$	−1.61819	+	1.54320i	−0.295440	+	0.281748i
$31$	−5.35881			−0.962470			−0.481235	−	0.876592i	$-0.659812\pi$
$31$	−5.35881			−0.962470			−0.481235	+	0.876592i	$0.659812\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.35779	−	0.783922i	0.236361	−	0.136463i
$34$	−3.09722	−	5.36455i	−0.531169	−	0.920012i
$35$	1.33028	−	4.53190i	0.224858	−	0.766032i
$36$	1.00000			0.166667
$37$	−3.54207	+	4.94508i	−0.582312	+	0.812965i
$37$	−3.54207	+	4.94508i	−0.582312	+	0.812965i
$38$			1.85248i			0.300512i
$39$	0.424706	−	0.735613i	0.0680074	−	0.117792i
$40$	−1.54320	−	1.61819i	−0.244001	−	0.255858i
$41$	−1.71563	−	2.97156i	−0.267937	−	0.464080i	0.700392	−	0.713758i	$-0.253008\pi$
$41$	−1.71563	−	2.97156i	−0.267937	−	0.464080i	−0.968329	+	0.249678i	$0.919675\pi$
$42$	−1.82925	+	1.05612i	−0.282260	+	0.162963i
$43$		−	2.80562i		−	0.427852i	−0.976850	−	0.213926i	$-0.931375\pi$
$43$		−	2.80562i		−	0.427852i	0.976850	−	0.213926i	$-0.0686252\pi$
$44$	0.783922	+	1.35779i	0.118181	+	0.204695i
$45$	−0.527353	−	2.17299i	−0.0786131	−	0.323931i
$46$	1.01302	−	1.75460i	0.149362	−	0.258702i
$47$			8.42766i			1.22930i	0.788800	+	0.614650i	$0.210703\pi$
$47$			8.42766i			1.22930i	−0.788800	+	0.614650i	$0.789297\pi$
$48$			1.00000i			0.144338i
$49$	−1.26922	+	2.19835i	−0.181317	+	0.314051i
$50$	−2.70251	+	4.20671i	−0.382192	+	0.594919i
$51$	6.19445			0.867396
$52$	0.735613	+	0.424706i	0.102011	+	0.0588961i
$53$	7.19076	+	4.15159i	0.987727	+	0.570264i	0.904594	−	0.426274i	$-0.140174\pi$
$53$	7.19076	+	4.15159i	0.987727	+	0.570264i	0.0831328	+	0.996538i	$0.473507\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	2.53707	−	2.41949i	0.342099	−	0.326244i
$56$	−1.05612	−	1.82925i	−0.141130	−	0.244444i
$57$	−1.60429	−	0.926239i	−0.212494	−	0.122683i
$58$	−2.38071	−	1.37451i	−0.312603	−	0.180481i
$59$	0.267356	−	0.463075i	0.0348068	−	0.0602872i	−0.848097	−	0.529841i	$-0.822252\pi$
$59$	0.267356	−	0.463075i	0.0348068	−	0.0602872i	0.882904	+	0.469553i	$0.155585\pi$
$60$	2.17299	−	0.527353i	0.280532	−	0.0680809i
$61$	−5.39914	−	9.35159i	−0.691290	−	1.19735i	−0.971416	−	0.237385i	$-0.923710\pi$
$61$	−5.39914	−	9.35159i	−0.691290	−	1.19735i	0.280126	−	0.959963i	$-0.409624\pi$
$62$	4.64086	+	2.67940i	0.589390	+	0.340285i
$63$		−	2.11224i		−	0.266117i
$64$	−1.00000			−0.125000
$65$	0.534956	−	1.82245i	0.0663532	−	0.226047i
$66$	−1.56784			−0.192988
$67$	−0.0321948	+	0.0185877i	−0.00393322	+	0.00227085i	−0.501965	−	0.864888i	$-0.667390\pi$
$67$	−0.0321948	+	0.0185877i	−0.00393322	+	0.00227085i	0.498032	+	0.867159i	$0.334056\pi$
$68$			6.19445i			0.751187i
$69$	1.01302	+	1.75460i	0.121953	+	0.211229i
$70$	−3.41801	+	3.25960i	−0.408530	+	0.389597i
$71$	−5.11238	−	8.85491i	−0.606728	−	1.05088i	−0.991776	−	0.127987i	$-0.959148\pi$
$71$	−5.11238	−	8.85491i	−0.606728	−	1.05088i	0.385048	−	0.922897i	$-0.374185\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	2.96121i		−	0.346583i	−0.984871	−	0.173292i	$-0.944560\pi$
$73$		−	2.96121i		−	0.346583i	0.984871	−	0.173292i	$-0.0554403\pi$
$74$	5.54006	−	2.51153i	0.644019	−	0.291959i
$75$	−2.29187	−	4.44380i	−0.264642	−	0.513126i
$76$	0.926239	−	1.60429i	0.106247	−	0.184025i
$77$	2.86799	−	1.65583i	0.326837	−	0.188700i
$78$	−0.735613	+	0.424706i	−0.0832917	+	0.0480885i
$79$	4.21801	+	7.30581i	0.474563	+	0.821967i	0.999576	−	0.0291271i	$-0.00927274\pi$
$79$	4.21801	+	7.30581i	0.474563	+	0.821967i	−0.525013	+	0.851094i	$0.675939\pi$
$80$	0.527353	+	2.17299i	0.0589598	+	0.242948i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			3.43126i			0.378920i
$83$	0.938843	+	0.542041i	0.103051	+	0.0594967i	0.550640	−	0.834743i	$-0.314384\pi$
$83$	0.938843	+	0.542041i	0.103051	+	0.0594967i	−0.447589	+	0.894240i	$0.647717\pi$
$84$	2.11224			0.230464
$85$	13.4605	−	3.26666i	1.45999	−	0.354319i
$86$	−1.40281	+	2.42974i	−0.151269	+	0.262005i
$87$	2.38071	−	1.37451i	0.255239	−	0.147362i
$88$		−	1.56784i		−	0.167133i
$89$	−4.64567	+	8.04654i	−0.492441	+	0.852932i	−0.999962	−	0.00870703i	$-0.997228\pi$
$89$	−4.64567	+	8.04654i	−0.492441	+	0.852932i	0.507522	+	0.861639i	$0.330562\pi$
$90$	−0.629796	+	2.14554i	−0.0663863	+	0.226160i
$91$	0.897081	−	1.55379i	0.0940397	−	0.162882i
$92$	−1.75460	+	1.01302i	−0.182930	+	0.105615i
$93$	−4.64086	+	2.67940i	−0.481235	+	0.277841i
$94$	4.21383	−	7.29857i	0.434623	−	0.752790i
$95$	−3.97457	−	1.16668i	−0.407783	−	0.119699i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	11.7183i		−	1.18981i	−0.803796	−	0.594906i	$-0.797189\pi$
$97$		−	11.7183i		−	1.18981i	0.803796	−	0.594906i	$-0.202811\pi$
$98$	2.19835	−	1.26922i	0.222067	−	0.128211i
$99$	0.783922	−	1.35779i	0.0787872	−	0.136463i
$100$	4.44380	−	2.29187i	0.444380	−	0.229187i
$101$	−8.27019			−0.822914			−0.411457	−	0.911429i	$-0.634980\pi$
$101$	−8.27019			−0.822914			−0.411457	+	0.911429i	$0.634980\pi$
$102$	−5.36455	−	3.09722i	−0.531169	−	0.306671i
$103$		−	15.8947i		−	1.56615i	−0.621928	−	0.783074i	$-0.713650\pi$
$103$		−	15.8947i		−	1.56615i	0.621928	−	0.783074i	$-0.286350\pi$
$104$	−0.424706	−	0.735613i	−0.0416459	−	0.0721328i
$105$	−1.11390	−	4.58988i	−0.108705	−	0.447927i
$106$	−4.15159	−	7.19076i	−0.403238	−	0.698428i
$107$	2.19348	−	1.26640i	0.212051	−	0.122428i	−0.390213	−	0.920725i	$-0.627599\pi$
$107$	2.19348	−	1.26640i	0.212051	−	0.122428i	0.602264	+	0.798297i	$0.294265\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−2.21207	+	3.83141i	−0.211878	+	0.366983i	−0.952302	−	0.305157i	$-0.901291\pi$
$109$	−2.21207	+	3.83141i	−0.211878	+	0.366983i	0.740424	+	0.672140i	$0.234625\pi$
$110$	−3.40692	+	0.826807i	−0.324837	+	0.0788330i
$111$	−0.594981	+	6.05359i	−0.0564731	+	0.574582i
$112$			2.11224i			0.199588i
$113$	6.85069	+	3.95525i	0.644459	+	0.372078i	0.786330	−	0.617807i	$-0.211979\pi$
$113$	6.85069	+	3.95525i	0.644459	+	0.372078i	−0.141871	+	0.989885i	$0.545312\pi$
$114$	0.926239	+	1.60429i	0.0867503	+	0.150256i
$115$	3.12658	+	3.27852i	0.291555	+	0.305723i
$116$	1.37451	+	2.38071i	0.127620	+	0.221044i
$117$		−	0.849412i		−	0.0785282i
$118$	−0.463075	+	0.267356i	−0.0426295	+	0.0246122i
$119$	13.0842			1.19942
$120$	−2.14554	−	0.629796i	−0.195860	−	0.0574922i
$121$	−8.54186			−0.776533
$122$			10.7983i			0.977631i
$123$	−2.97156	−	1.71563i	−0.267937	−	0.154693i
$124$	−2.67940	−	4.64086i	−0.240618	−	0.416762i
$125$	−7.32366	−	8.44772i	−0.655048	−	0.755587i
$126$	−1.05612	+	1.82925i	−0.0940867	+	0.162963i
$127$	−1.66148	−	0.959256i	−0.147433	−	0.0851202i	0.424469	−	0.905442i	$-0.360461\pi$
$127$	−1.66148	−	0.959256i	−0.147433	−	0.0851202i	−0.571902	+	0.820322i	$0.693794\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.40281	−	2.42974i	−0.123510	−	0.213926i
$130$	−1.37451	+	1.31081i	−0.120553	+	0.114966i
$131$	2.41159	−	4.17700i	0.210702	−	0.364947i	−0.741232	−	0.671248i	$-0.765758\pi$
$131$	2.41159	−	4.17700i	0.210702	−	0.364947i	0.951934	+	0.306302i	$0.0990917\pi$
$132$	1.35779	+	0.783922i	0.118181	+	0.0682317i
$133$	−3.38865	−	1.95644i	−0.293834	−	0.169645i
$134$	0.0371754			0.00321146
$135$	−1.54320	−	1.61819i	−0.132817	−	0.139272i
$136$	3.09722	−	5.36455i	0.265585	−	0.460006i
$137$		−	5.12029i		−	0.437456i	−0.975786	−	0.218728i	$-0.929809\pi$
$137$		−	5.12029i		−	0.437456i	0.975786	−	0.218728i	$-0.0701907\pi$
$138$		−	2.02604i		−	0.172468i
$139$	−4.50630	+	7.80515i	−0.382220	+	0.662024i	−0.991379	−	0.131024i	$-0.958174\pi$
$139$	−4.50630	+	7.80515i	−0.382220	+	0.662024i	0.609160	+	0.793048i	$0.291507\pi$
$140$	4.58988	−	1.11390i	0.387916	−	0.0941414i
$141$	4.21383	+	7.29857i	0.354869	+	0.614650i
$142$			10.2248i			0.858043i
$143$	1.15333	−	0.665873i	0.0964460	−	0.0556831i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	4.44843	−	4.24227i	0.369422	−	0.352301i
$146$	−1.48060	+	2.56448i	−0.122536	+	0.212238i
$147$			2.53844i			0.209367i
$148$	−6.05359	−	0.594981i	−0.497602	−	0.0489072i
$149$	7.65736			0.627316			0.313658	−	0.949536i	$-0.398446\pi$
$149$	7.65736			0.627316			0.313658	+	0.949536i	$0.398446\pi$
$150$	−0.237084	+	4.99438i	−0.0193578	+	0.407789i
$151$	−6.31425	−	10.9366i	−0.513847	−	0.890008i	−0.999871	−	0.0160631i	$-0.994887\pi$
$151$	−6.31425	−	10.9366i	−0.513847	−	0.890008i	0.486024	−	0.873945i	$-0.338447\pi$
$152$	−1.60429	+	0.926239i	−0.130125	+	0.0751279i
$153$	5.36455	−	3.09722i	0.433698	−	0.250396i
$154$	−3.31166			−0.266862
$155$	−8.67157	+	8.26970i	−0.696518	+	0.664238i
$156$	0.849412			0.0680074
$157$	21.1965	+	12.2378i	1.69166	+	0.976681i	0.953178	+	0.302410i	$0.0977912\pi$
$157$	21.1965	+	12.2378i	1.69166	+	0.976681i	0.738484	+	0.674271i	$0.235542\pi$
$158$		−	8.43602i		−	0.671134i
$159$	8.30317			0.658485
$160$	0.629796	−	2.14554i	0.0497897	−	0.169620i
$161$	2.13974	+	3.70614i	0.168635	+	0.292085i
$162$			1.00000i			0.0785674i
$163$	−20.9716	−	12.1079i	−1.64262	−	0.948367i	−0.979897	−	0.199503i	$-0.936067\pi$
$163$	−20.9716	−	12.1079i	−1.64262	−	0.948367i	−0.662723	−	0.748864i	$-0.730599\pi$
$164$	1.71563	−	2.97156i	0.133968	−	0.232040i
$165$	0.987422	−	3.36388i	0.0768707	−	0.261878i
$166$	−0.542041	−	0.938843i	−0.0420705	−	0.0728683i
$167$	−16.8294	+	9.71649i	−1.30230	+	0.751884i	−0.980798	−	0.195024i	$-0.937521\pi$
$167$	−16.8294	+	9.71649i	−1.30230	+	0.751884i	−0.321503	+	0.946908i	$0.604188\pi$
$168$	−1.82925	−	1.05612i	−0.141130	−	0.0814814i
$169$	−6.13925	+	10.6335i	−0.472250	+	0.817961i
$170$	−13.2905	−	3.90124i	−1.01933	−	0.299211i
$171$	−1.85248			−0.141663
$172$	2.42974	−	1.40281i	0.185266	−	0.106963i
$173$	8.62589	+	4.98016i	0.655814	+	0.378635i	0.790680	−	0.612229i	$-0.209727\pi$
$173$	8.62589	+	4.98016i	0.655814	+	0.378635i	−0.134866	+	0.990864i	$0.543060\pi$
$174$	−2.74901			−0.208402
$175$	−4.84097	−	9.38637i	−0.365943	−	0.709543i
$176$	−0.783922	+	1.35779i	−0.0590904	+	0.102348i
$177$		−	0.534713i		−	0.0401915i
$178$	8.04654	−	4.64567i	0.603114	−	0.348208i
$179$	−16.4502			−1.22954			−0.614772	−	0.788705i	$-0.710752\pi$
$179$	−16.4502			−1.22954			−0.614772	+	0.788705i	$0.710752\pi$
$180$	1.61819	−	1.54320i	0.120613	−	0.115023i
$181$	−2.37638	−	4.11602i	−0.176635	−	0.305941i	0.764091	−	0.645109i	$-0.223188\pi$
$181$	−2.37638	−	4.11602i	−0.176635	−	0.305941i	−0.940726	+	0.339168i	$0.889855\pi$
$182$	−1.55379	+	0.897081i	−0.115175	+	0.0664961i
$183$	−9.35159	−	5.39914i	−0.691290	−	0.399116i
$184$	2.02604			0.149362
$185$	1.89949	+	13.4682i	0.139653	+	0.990200i
$186$	5.35881			0.392927
$187$	8.41078	+	4.85596i	0.615057	+	0.355103i
$188$	−7.29857	+	4.21383i	−0.532303	+	0.307325i
$189$	−1.05612	−	1.82925i	−0.0768214	−	0.133059i
$190$	2.85874	+	2.99766i	0.207395	+	0.217473i
$191$	18.5239			1.34034			0.670172	−	0.742206i	$-0.266220\pi$
$191$	18.5239			1.34034			0.670172	+	0.742206i	$0.266220\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$		−	8.28698i		−	0.596510i	−0.954486	−	0.298255i	$-0.903595\pi$
$193$		−	8.28698i		−	0.596510i	0.954486	−	0.298255i	$-0.0964046\pi$
$194$	−5.85914	+	10.1483i	−0.420662	+	0.728608i
$195$	−0.447940	−	1.84577i	−0.0320776	−	0.132178i
$196$	−2.53844			−0.181317
$197$	20.1144	+	11.6130i	1.43309	+	0.827394i	0.997355	−	0.0726815i	$-0.0231557\pi$
$197$	20.1144	+	11.6130i	1.43309	+	0.827394i	0.435734	+	0.900076i	$0.356489\pi$
$198$	−1.35779	+	0.783922i	−0.0964942	+	0.0557109i
$199$	10.3048			0.730489			0.365245	−	0.930912i	$-0.380985\pi$
$199$	10.3048			0.730489			0.365245	+	0.930912i	$0.380985\pi$
$200$	−4.99438	−	0.237084i	−0.353156	−	0.0167643i
$201$	−0.0185877	+	0.0321948i	−0.00131107	+	0.00227085i
$202$	7.16219	+	4.13509i	0.503930	+	0.290944i
$203$	5.02864	−	2.90329i	0.352941	−	0.203771i
$204$	3.09722	+	5.36455i	0.216849	+	0.375593i
$205$	−7.36193	−	2.16100i	−0.514179	−	0.150930i
$206$	−7.94734	+	13.7652i	−0.553717	+	0.959066i
$207$	1.75460	+	1.01302i	0.121953	+	0.0704097i
$208$			0.849412i			0.0588961i
$209$	−1.45220	−	2.51528i	−0.100451	−	0.173986i
$210$	−1.33028	+	4.53190i	−0.0917980	+	0.312731i
$211$	2.35940			0.162428			0.0812139	−	0.996697i	$-0.474120\pi$
$211$	2.35940			0.162428			0.0812139	+	0.996697i	$0.474120\pi$
$212$			8.30317i			0.570264i
$213$	−8.85491	−	5.11238i	−0.606728	−	0.350295i
$214$	−2.53281			−0.173139
$215$	−4.32962	−	4.54002i	−0.295278	−	0.309627i
$216$	−1.00000			−0.0680414
$217$	−9.80262	+	5.65955i	−0.665445	+	0.384195i
$218$	3.83141	−	2.21207i	0.259496	−	0.149820i
$219$	−1.48060	−	2.56448i	−0.100050	−	0.173292i
$220$	3.36388	+	0.987422i	0.226793	+	0.0665720i
$221$	5.26164			0.353936
$222$	3.54207	−	4.94508i	0.237728	−	0.331892i
$223$			14.6121i			0.978501i	0.872143	+	0.489251i	$0.162730\pi$
$223$			14.6121i			0.978501i	−0.872143	+	0.489251i	$0.837270\pi$
$224$	1.05612	−	1.82925i	0.0705650	−	0.122222i
$225$	−4.20671	−	2.70251i	−0.280448	−	0.180167i
$226$	−3.95525	−	6.85069i	−0.263099	−	0.455701i
$227$	−4.91807	+	2.83945i	−0.326424	+	0.188461i	−0.654252	−	0.756276i	$-0.727016\pi$
$227$	−4.91807	+	2.83945i	−0.326424	+	0.188461i	0.327829	+	0.944737i	$0.393683\pi$
$228$		−	1.85248i		−	0.122683i
$229$	6.00398	+	10.3992i	0.396754	+	0.687199i	0.993323	−	0.115363i	$-0.0368031\pi$
$229$	6.00398	+	10.3992i	0.396754	+	0.687199i	−0.596569	+	0.802562i	$0.703470\pi$
$230$	−1.06844	−	4.40257i	−0.0704506	−	0.290297i
$231$	1.65583	−	2.86799i	0.108946	−	0.188700i
$232$		−	2.74901i		−	0.180481i
$233$			9.13538i			0.598479i	0.954178	+	0.299239i	$0.0967329\pi$
$233$			9.13538i			0.598479i	−0.954178	+	0.299239i	$0.903267\pi$
$234$	−0.424706	+	0.735613i	−0.0277639	+	0.0480885i
$235$	13.0055	+	13.6376i	0.848388	+	0.889617i
$236$	0.534713			0.0348068
$237$	7.30581	+	4.21801i	0.474563	+	0.273989i
$238$	−11.3312	−	6.54208i	−0.734493	−	0.424060i
$239$	−11.3800	+	19.7107i	−0.736111	+	1.27498i	0.218124	+	0.975921i	$0.430006\pi$
$239$	−11.3800	+	19.7107i	−0.736111	+	1.27498i	−0.954234	+	0.299060i	$0.903327\pi$
$240$	1.54320	+	1.61819i	0.0996130	+	0.104454i
$241$	7.99602	+	13.8495i	0.515069	+	0.892126i	0.999847	+	0.0174887i	$0.00556711\pi$
$241$	7.99602	+	13.8495i	0.515069	+	0.892126i	−0.484778	+	0.874637i	$0.661100\pi$
$242$	7.39747	+	4.27093i	0.475527	+	0.274546i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.39914	−	9.35159i	0.345645	−	0.598674i
$245$	1.33865	+	5.51601i	0.0855234	+	0.352405i
$246$	1.71563	+	2.97156i	0.109385	+	0.189460i
$247$	−1.36271	−	0.786759i	−0.0867070	−	0.0500603i
$248$			5.35881i			0.340285i
$249$	1.08408			0.0687009
$250$	2.11862	+	10.9778i	0.133993	+	0.694295i
$251$	−11.4135			−0.720413			−0.360207	−	0.932873i	$-0.617294\pi$
$251$	−11.4135			−0.720413			−0.360207	+	0.932873i	$0.617294\pi$
$252$	1.82925	−	1.05612i	0.115232	−	0.0665293i
$253$			3.17651i			0.199706i
$254$	0.959256	+	1.66148i	0.0601891	+	0.104251i
$255$	10.0238	−	9.55925i	0.627714	−	0.598624i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.86841	+	3.38813i	0.366061	+	0.211345i	0.671736	−	0.740790i	$-0.265549\pi$
$257$	5.86841	+	3.38813i	0.366061	+	0.211345i	−0.305675	+	0.952136i	$0.598882\pi$
$258$			2.80562i			0.174670i
$259$	−1.25674	+	12.7866i	−0.0780902	+	0.794523i
$260$	1.84577	−	0.447940i	0.114470	−	0.0277801i
$261$	1.37451	−	2.38071i	0.0850798	−	0.147362i
$262$	−4.17700	+	2.41159i	−0.258056	+	0.148989i
$263$	0.509375	−	0.294088i	0.0314094	−	0.0181342i	−0.484213	−	0.874950i	$-0.660894\pi$
$263$	0.509375	−	0.294088i	0.0314094	−	0.0181342i	0.515622	+	0.856816i	$0.327561\pi$
$264$	−0.783922	−	1.35779i	−0.0482471	−	0.0835664i
$265$	18.0427	−	4.37870i	1.10836	−	0.268981i
$266$	1.95644	+	3.38865i	0.119957	+	0.207772i
$267$			9.29135i			0.568621i
$268$	−0.0321948	−	0.0185877i	−0.00196661	−	0.00113542i
$269$	−0.844610			−0.0514968			−0.0257484	−	0.999668i	$-0.508197\pi$
$269$	−0.844610			−0.0514968			−0.0257484	+	0.999668i	$0.508197\pi$
$270$	0.527353	+	2.17299i	0.0320937	+	0.132244i
$271$	−13.4818	+	23.3512i	−0.818963	+	1.41849i	0.0874843	+	0.996166i	$0.472117\pi$
$271$	−13.4818	+	23.3512i	−0.818963	+	1.41849i	−0.906447	+	0.422319i	$0.861216\pi$
$272$	−5.36455	+	3.09722i	−0.325273	+	0.187797i
$273$		−	1.79416i		−	0.108588i
$274$	−2.56015	+	4.43430i	−0.154664	+	0.267886i
$275$	0.371710	−	7.83041i	0.0224150	−	0.472191i
$276$	−1.01302	+	1.75460i	−0.0609766	+	0.105615i
$277$	11.8611	−	6.84804i	0.712667	−	0.411459i	−0.0993806	−	0.995049i	$-0.531686\pi$
$277$	11.8611	−	6.84804i	0.712667	−	0.411459i	0.812048	+	0.583591i	$0.198353\pi$
$278$	7.80515	−	4.50630i	0.468122	−	0.270270i
$279$	−2.67940	+	4.64086i	−0.160412	+	0.277841i
$280$	−4.53190	−	1.33028i	−0.270833	−	0.0794994i
$281$	−7.97306	+	13.8097i	−0.475633	+	0.823820i	−0.999610	−	0.0279121i	$-0.991114\pi$
$281$	−7.97306	+	13.8097i	−0.475633	+	0.823820i	0.523978	+	0.851732i	$0.324447\pi$
$282$		−	8.42766i		−	0.501860i
$283$	−15.7018	+	9.06543i	−0.933374	+	0.538884i	−0.887877	−	0.460081i	$-0.847820\pi$
$283$	−15.7018	+	9.06543i	−0.933374	+	0.538884i	−0.0454970	+	0.998964i	$0.514487\pi$
$284$	5.11238	−	8.85491i	0.303364	−	0.525442i
$285$	−4.02542	+	0.976910i	−0.238446	+	0.0578671i
$286$	−1.33175			−0.0787478
$287$	−6.27665	−	3.62383i	−0.370499	−	0.213908i
$288$		−	1.00000i		−	0.0589256i
$289$	10.6856	+	18.5080i	0.628563	+	1.08870i
$290$	−5.97358	+	1.44970i	−0.350781	+	0.0851292i
$291$	−5.85914	−	10.1483i	−0.343469	−	0.594906i
$292$	2.56448	−	1.48060i	0.150075	−	0.0866458i
$293$	4.15189	−	2.39710i	0.242556	−	0.140040i	−0.373795	−	0.927511i	$-0.621944\pi$
$293$	4.15189	−	2.39710i	0.242556	−	0.140040i	0.616351	+	0.787472i	$0.288610\pi$
$294$	1.26922	−	2.19835i	0.0740224	−	0.128211i
$295$	−0.281982	−	1.16193i	−0.0164176	−	0.0676500i
$296$	4.94508	+	3.54207i	0.287427	+	0.205878i
$297$		−	1.56784i		−	0.0909756i
$298$	−6.63147	−	3.82868i	−0.384151	−	0.221790i
$299$	0.860471	+	1.49038i	0.0497623	+	0.0861909i
$300$	2.70251	−	4.20671i	0.156029	−	0.242875i
$301$	−2.96307	−	5.13218i	−0.170788	−	0.295814i
$302$			12.6285i			0.726689i
$303$	−7.16219	+	4.13509i	−0.411457	+	0.237555i
$304$	1.85248			0.106247
$305$	−23.1682	−	6.80072i	−1.32661	−	0.389408i
$306$	−6.19445			−0.354113
$307$			27.6637i			1.57885i	0.613848	+	0.789424i	$0.289621\pi$
$307$			27.6637i			1.57885i	−0.613848	+	0.789424i	$0.710379\pi$
$308$	2.86799	+	1.65583i	0.163419	+	0.0943498i
$309$	−7.94734	−	13.7652i	−0.452108	−	0.783074i
$310$	11.6447	−	2.82598i	0.661372	−	0.160505i
$311$	6.75280	−	11.6962i	0.382916	−	0.663230i	−0.608562	−	0.793506i	$-0.708253\pi$
$311$	6.75280	−	11.6962i	0.382916	−	0.663230i	0.991478	+	0.130277i	$0.0415866\pi$
$312$	−0.735613	−	0.424706i	−0.0416459	−	0.0240443i
$313$	−14.2993	−	8.25573i	−0.808247	−	0.466641i	0.0381001	−	0.999274i	$-0.487869\pi$
$313$	−14.2993	−	8.25573i	−0.808247	−	0.466641i	−0.846347	+	0.532633i	$0.821203\pi$
$314$	−12.2378	−	21.1965i	−0.690618	−	1.19619i
$315$	−3.25960	−	3.41801i	−0.183658	−	0.192583i
$316$	−4.21801	+	7.30581i	−0.237282	+	0.410984i
$317$	19.8264	+	11.4468i	1.11356	+	0.642915i	0.939749	−	0.341864i	$-0.111058\pi$
$317$	19.8264	+	11.4468i	1.11356	+	0.642915i	0.173812	+	0.984779i	$0.444392\pi$
$318$	−7.19076	−	4.15159i	−0.403238	−	0.232809i
$319$	4.31002			0.241315
$320$	−1.61819	+	1.54320i	−0.0904596	+	0.0862674i
$321$	1.26640	−	2.19348i	0.0706838	−	0.122428i
$322$		−	4.27948i		−	0.238486i
$323$		−	11.4751i		−	0.638490i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−1.94674	−	3.77462i	−0.107986	−	0.209378i
$326$	12.1079	+	20.9716i	0.670597	+	1.16151i
$327$			4.42414i			0.244655i
$328$	−2.97156	+	1.71563i	−0.164077	+	0.0947299i
$329$	8.90062	+	15.4163i	0.490707	+	0.849930i
$330$	−2.53707	+	2.41949i	−0.139661	+	0.133189i
$331$	−4.68552	+	8.11557i	−0.257540	+	0.446072i	−0.965582	−	0.260098i	$-0.916245\pi$
$331$	−4.68552	+	8.11557i	−0.257540	+	0.446072i	0.708043	+	0.706170i	$0.249578\pi$
$332$			1.08408i			0.0594967i
$333$	2.51153	+	5.54006i	0.137631	+	0.303593i
$334$	19.4330			1.06332
$335$	−0.0234129	+	0.0797613i	−0.00127918	+	0.00435783i
$336$	1.05612	+	1.82925i	0.0576161	+	0.0997940i
$337$	−19.0182	+	10.9801i	−1.03599	+	0.598126i	−0.918694	−	0.394971i	$-0.870755\pi$
$337$	−19.0182	+	10.9801i	−1.03599	+	0.598126i	−0.117292	+	0.993097i	$0.537421\pi$
$338$	10.6335	−	6.13925i	0.578386	−	0.333931i
$339$	7.91049			0.429639
$340$	9.55925	+	10.0238i	0.518423	+	0.543617i
$341$	−8.40178			−0.454982
$342$	1.60429	+	0.926239i	0.0867503	+	0.0500853i
$343$			20.1475i			1.08786i
$344$	−2.80562			−0.151269
$345$	4.34695	+	1.27599i	0.234032	+	0.0686970i
$346$	−4.98016	−	8.62589i	−0.267735	−	0.463731i
$347$			10.9899i			0.589968i	0.955502	+	0.294984i	$0.0953144\pi$
$347$			10.9899i			0.589968i	−0.955502	+	0.294984i	$0.904686\pi$
$348$	2.38071	+	1.37451i	0.127620	+	0.0736812i
$349$	0.0486829	−	0.0843213i	0.00260594	−	0.00451361i	−0.864719	−	0.502255i	$-0.832504\pi$
$349$	0.0486829	−	0.0843213i	0.00260594	−	0.00451361i	0.867325	+	0.497741i	$0.165837\pi$
$350$	−0.500778	+	10.5493i	−0.0267677	+	0.563885i
$351$	−0.424706	−	0.735613i	−0.0226691	−	0.0392641i
$352$	1.35779	−	0.783922i	0.0723706	−	0.0417832i
$353$	14.5752	+	8.41502i	0.775762	+	0.447886i	0.834926	−	0.550362i	$-0.185510\pi$
$353$	14.5752	+	8.41502i	0.775762	+	0.447886i	−0.0591643	+	0.998248i	$0.518844\pi$
$354$	−0.267356	+	0.463075i	−0.0142098	+	0.0246122i
$355$	−21.9377	−	6.43951i	−1.16433	−	0.341774i
$356$	−9.29135			−0.492441
$357$	11.3312	−	6.54208i	0.599711	−	0.346244i
$358$	14.2463	+	8.22509i	0.752939	+	0.434709i
$359$	−13.2580			−0.699730			−0.349865	−	0.936800i	$-0.613772\pi$
$359$	−13.2580			−0.699730			−0.349865	+	0.936800i	$0.613772\pi$
$360$	−2.17299	+	0.527353i	−0.114527	+	0.0277939i
$361$	7.78416	−	13.4826i	0.409693	−	0.709609i
$362$			4.75277i			0.249800i
$363$	−7.39747	+	4.27093i	−0.388267	+	0.224166i
$364$	1.79416			0.0940397
$365$	−4.56973	−	4.79180i	−0.239191	−	0.250814i
$366$	5.39914	+	9.35159i	0.282218	+	0.488816i
$367$	13.4634	−	7.77308i	0.702782	−	0.405752i	−0.105601	−	0.994409i	$-0.533677\pi$
$367$	13.4634	−	7.77308i	0.702782	−	0.405752i	0.808383	+	0.588657i	$0.200343\pi$
$368$	−1.75460	−	1.01302i	−0.0914649	−	0.0528073i
$369$	−3.43126			−0.178624
$370$	5.08909	−	12.6135i	0.264569	−	0.655746i
$371$	17.5383			0.910543
$372$	−4.64086	−	2.67940i	−0.240618	−	0.138921i
$373$	2.53801	−	1.46532i	0.131413	−	0.0758715i	−0.432852	−	0.901465i	$-0.642493\pi$
$373$	2.53801	−	1.46532i	0.131413	−	0.0758715i	0.564265	+	0.825593i	$0.309159\pi$
$374$	−4.85596	−	8.41078i	−0.251096	−	0.434911i
$375$	−10.5663	−	3.65411i	−0.545643	−	0.188697i
$376$	8.42766			0.434623
$377$	2.02221	−	1.16752i	0.104149	−	0.0601304i
$378$			2.11224i			0.108642i
$379$	−7.13585	+	12.3597i	−0.366544	+	0.634873i	−0.989023	−	0.147764i	$-0.952792\pi$
$379$	−7.13585	+	12.3597i	−0.366544	+	0.634873i	0.622479	+	0.782637i	$0.286126\pi$
$380$	−0.976910	−	4.02542i	−0.0501144	−	0.206500i
$381$	−1.91851			−0.0982884
$382$	−16.0422	−	9.26196i	−0.820789	−	0.473883i
$383$	−16.7141	+	9.64989i	−0.854051	+	0.493087i	−0.862016	−	0.506882i	$-0.830798\pi$
$383$	−16.7141	+	9.64989i	−0.854051	+	0.493087i	0.00796467	+	0.999968i	$0.497465\pi$
$384$	1.00000			0.0510310
$385$	2.08567	−	7.10532i	0.106296	−	0.362121i
$386$	−4.14349	+	7.17673i	−0.210898	+	0.365286i
$387$	−2.42974	−	1.40281i	−0.123510	−	0.0713087i
$388$	10.1483	−	5.85914i	0.515203	−	0.297453i
$389$	−12.0126	−	20.8064i	−0.609062	−	1.05493i	−0.991395	−	0.130901i	$-0.958213\pi$
$389$	−12.0126	−	20.8064i	−0.609062	−	1.05493i	0.382334	−	0.924024i	$-0.375120\pi$
$390$	−0.534956	+	1.82245i	−0.0270886	+	0.0922834i
$391$	−6.27509	+	10.8688i	−0.317345	+	0.549658i
$392$	2.19835	+	1.26922i	0.111034	+	0.0641053i
$393$		−	4.82319i		−	0.243298i
$394$	−11.6130	−	20.1144i	−0.585056	−	1.01335i
$395$	18.0998	+	5.31297i	0.910702	+	0.267324i
$396$	1.56784			0.0787872
$397$			33.6932i			1.69101i	0.533967	+	0.845506i	$0.320701\pi$
$397$			33.6932i			1.69101i	−0.533967	+	0.845506i	$0.679299\pi$
$398$	−8.92423	−	5.15241i	−0.447331	−	0.258267i
$399$	−3.91288			−0.195889
$400$	4.20671	+	2.70251i	0.210336	+	0.135125i
$401$	7.15825			0.357466			0.178733	−	0.983898i	$-0.442800\pi$
$401$	7.15825			0.357466			0.178733	+	0.983898i	$0.442800\pi$
$402$	0.0321948	−	0.0185877i	0.00160573	−	0.000927069i
$403$	−3.94201	+	2.27592i	−0.196365	+	0.113372i
$404$	−4.13509	−	7.16219i	−0.205729	−	0.356332i
$405$	−2.14554	−	0.629796i	−0.106613	−	0.0312948i
$406$	−5.80657			−0.288175
$407$	−5.55341	+	7.75311i	−0.275272	+	0.384307i
$408$		−	6.19445i		−	0.306671i
$409$	−1.10773	+	1.91864i	−0.0547737	+	0.0948708i	−0.892112	−	0.451814i	$-0.850777\pi$
$409$	−1.10773	+	1.91864i	−0.0547737	+	0.0948708i	0.837338	+	0.546685i	$0.184110\pi$
$410$	5.29512	+	5.55244i	0.261507	+	0.274216i
$411$	−2.56015	−	4.43430i	−0.126283	−	0.218728i
$412$	13.7652	−	7.94734i	0.678162	−	0.391537i
$413$		−	1.12944i		−	0.0555762i
$414$	−1.01302	−	1.75460i	−0.0497872	−	0.0862339i
$415$	2.35570	−	0.571694i	0.115637	−	0.0280633i
$416$	0.424706	−	0.735613i	0.0208229	−	0.0360664i
$417$			9.01261i			0.441349i
$418$			2.90440i			0.142059i
$419$	12.3445	−	21.3813i	0.603067	−	1.04454i	−0.389287	−	0.921117i	$-0.627278\pi$
$419$	12.3445	−	21.3813i	0.603067	−	1.04454i	0.992354	−	0.123426i	$-0.0393882\pi$
$420$	3.41801	−	3.25960i	0.166782	−	0.159052i
$421$	2.46103			0.119943			0.0599717	−	0.998200i	$-0.480899\pi$
$421$	2.46103			0.119943			0.0599717	+	0.998200i	$0.480899\pi$
$422$	−2.04330	−	1.17970i	−0.0994663	−	0.0574269i
$423$	7.29857	+	4.21383i	0.354869	+	0.204883i
$424$	4.15159	−	7.19076i	0.201619	−	0.349214i
$425$	16.7405	−	26.0583i	0.812036	−	1.26401i
$426$	5.11238	+	8.85491i	0.247696	+	0.429022i
$427$	−19.7528	−	11.4043i	−0.955905	−	0.551892i
$428$	2.19348	+	1.26640i	0.106026	+	0.0612139i
$429$	0.665873	−	1.15333i	0.0321487	−	0.0556831i
$430$	1.47955	+	6.09659i	0.0713502	+	0.294003i
$431$	−7.23664	−	12.5342i	−0.348577	−	0.603753i	0.637420	−	0.770516i	$-0.280002\pi$
$431$	−7.23664	−	12.5342i	−0.348577	−	0.603753i	−0.985997	+	0.166764i	$0.946668\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$		−	16.3708i		−	0.786729i	−0.919383	−	0.393364i	$-0.871311\pi$
$433$		−	16.3708i		−	0.786729i	0.919383	−	0.393364i	$-0.128689\pi$
$434$	11.3191			0.543334
$435$	1.73132	−	5.89812i	0.0830102	−	0.282793i
$436$	−4.42414			−0.211878
$437$	3.25036	−	1.87660i	0.155486	−	0.0897698i
$438$			2.96121i			0.141492i
$439$	−3.33341	−	5.77363i	−0.159095	−	0.275560i	0.775448	−	0.631412i	$-0.217524\pi$
$439$	−3.33341	−	5.77363i	−0.159095	−	0.275560i	−0.934543	+	0.355852i	$0.884191\pi$
$440$	−2.41949	−	2.53707i	−0.115345	−	0.120950i
$441$	1.26922	+	2.19835i	0.0604391	+	0.104684i
$442$	−4.55671	−	2.63082i	−0.216741	−	0.125135i
$443$		−	10.6641i		−	0.506665i	−0.967379	−	0.253333i	$-0.918473\pi$
$443$		−	10.6641i		−	0.506665i	0.967379	−	0.253333i	$-0.0815267\pi$
$444$	−5.54006	+	2.51153i	−0.262919	+	0.119192i
$445$	4.89982	+	20.1900i	0.232274	+	0.957100i
$446$	7.30607	−	12.6545i	0.345952	−	0.599207i
$447$	6.63147	−	3.82868i	0.313658	−	0.181090i
$448$	−1.82925	+	1.05612i	−0.0864241	+	0.0498970i
$449$	−12.5287	−	21.7003i	−0.591265	−	1.02410i	−0.994062	−	0.108812i	$-0.965296\pi$
$449$	−12.5287	−	21.7003i	−0.591265	−	1.02410i	0.402798	−	0.915289i	$-0.368038\pi$
$450$	2.29187	+	4.44380i	0.108040	+	0.209483i
$451$	−2.68984	−	4.65895i	−0.126660	−	0.219381i
$452$			7.91049i			0.372078i
$453$	−10.9366	−	6.31425i	−0.513847	−	0.296669i
$454$	5.67890			0.266524
$455$	−0.946157	−	3.89870i	−0.0443565	−	0.182774i
$456$	−0.926239	+	1.60429i	−0.0433751	+	0.0751279i
$457$	25.5118	−	14.7293i	1.19339	−	0.689006i	0.234319	−	0.972160i	$-0.424714\pi$
$457$	25.5118	−	14.7293i	1.19339	−	0.689006i	0.959075	+	0.283154i	$0.0913806\pi$
$458$		−	12.0080i		−	0.561096i
$459$	3.09722	−	5.36455i	0.144566	−	0.250396i
$460$	−1.27599	+	4.34695i	−0.0594934	+	0.202678i
$461$	−7.17644	+	12.4300i	−0.334240	+	0.578921i	−0.983339	−	0.181783i	$-0.941813\pi$
$461$	−7.17644	+	12.4300i	−0.334240	+	0.578921i	0.649098	+	0.760705i	$0.275146\pi$
$462$	−2.86799	+	1.65583i	−0.133431	+	0.0770363i
$463$	−27.3310	+	15.7795i	−1.27018	+	0.733337i	−0.975021	−	0.222112i	$-0.928705\pi$
$463$	−27.3310	+	15.7795i	−1.27018	+	0.733337i	−0.295156	+	0.955449i	$0.595372\pi$
$464$	−1.37451	+	2.38071i	−0.0638098	+	0.110522i
$465$	−3.37495	+	11.4976i	−0.156510	+	0.533186i
$466$	4.56769	−	7.91147i	0.211594	−	0.366492i
$467$		−	36.6899i		−	1.69781i	−0.528549	−	0.848903i	$-0.677264\pi$
$467$		−	36.6899i		−	1.69781i	0.528549	−	0.848903i	$-0.322736\pi$
$468$	0.735613	−	0.424706i	0.0340037	−	0.0196320i
$469$	−0.0392616	+	0.0680032i	−0.00181293	+	0.00314009i
$470$	−4.44435	−	18.3132i	−0.205003	−	0.844727i
$471$	24.4756			1.12777
$472$	−0.463075	−	0.267356i	−0.0213147	−	0.0123061i
$473$		−	4.39877i		−	0.202256i
$474$	−4.21801	−	7.30581i	−0.193740	−	0.335567i
$475$	−8.23204	+	4.24564i	−0.377712	+	0.194803i
$476$	6.54208	+	11.3312i	0.299856	+	0.519365i
$477$	7.19076	−	4.15159i	0.329242	−	0.190088i
$478$	19.7107	−	11.3800i	0.901548	−	0.520509i
$479$	2.68638	−	4.65295i	0.122744	−	0.212599i	−0.798105	−	0.602519i	$-0.794164\pi$
$479$	2.68638	−	4.65295i	0.122744	−	0.212599i	0.920849	+	0.389920i	$0.127497\pi$
$480$	−0.527353	−	2.17299i	−0.0240702	−	0.0991831i
$481$	−0.505385	+	5.14200i	−0.0230435	+	0.234455i
$482$		−	15.9920i		−	0.728418i
$483$	3.70614	+	2.13974i	0.168635	+	0.0973616i
$484$	−4.27093	−	7.39747i	−0.194133	−	0.336249i
$485$	−18.0836	−	18.9624i	−0.821135	−	0.861039i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$			5.64669i			0.255876i	0.991782	+	0.127938i	$0.0408359\pi$
$487$			5.64669i			0.255876i	−0.991782	+	0.127938i	$0.959164\pi$
$488$	−9.35159	+	5.39914i	−0.423327	+	0.244408i
$489$	−24.2159			−1.09508
$490$	1.59870	−	5.44634i	0.0722219	−	0.246040i
$491$	44.0007			1.98572			0.992862	−	0.119268i	$-0.0380547\pi$
$491$	44.0007			1.98572			0.992862	+	0.119268i	$0.0380547\pi$
$492$		−	3.43126i		−	0.154693i
$493$	14.7472	+	8.51430i	0.664181	+	0.383465i
$494$	0.786759	+	1.36271i	0.0353980	+	0.0613111i
$495$	−0.826807	−	3.40692i	−0.0371622	−	0.153129i
$496$	2.67940	−	4.64086i	0.120309	−	0.208381i
$497$	−18.7037	−	10.7986i	−0.838975	−	0.484382i
$498$	−0.938843	−	0.542041i	−0.0420705	−	0.0242894i
$499$	−8.61516	−	14.9219i	−0.385668	−	0.667996i	0.606194	−	0.795317i	$-0.292696\pi$
$499$	−8.61516	−	14.9219i	−0.385668	−	0.667996i	−0.991862	+	0.127321i	$0.959362\pi$
$500$	3.65411	−	10.5663i	0.163417	−	0.472541i
$501$	−9.71649	+	16.8294i	−0.434101	+	0.751884i
$502$	9.88437	+	5.70674i	0.441161	+	0.254704i
$503$	−14.7755	−	8.53063i	−0.658807	−	0.380362i	0.133016	−	0.991114i	$-0.457534\pi$
$503$	−14.7755	−	8.53063i	−0.658807	−	0.380362i	−0.791822	+	0.610752i	$0.790867\pi$
$504$	−2.11224			−0.0940867
$505$	−13.3827	+	12.7625i	−0.595524	+	0.567925i
$506$	1.58826	−	2.75094i	0.0706066	−	0.122294i
$507$			12.2785i			0.545307i
$508$		−	1.91851i		−	0.0851202i
$509$	1.68925	−	2.92587i	0.0748747	−	0.129687i	−0.826157	−	0.563440i	$-0.809478\pi$
$509$	1.68925	−	2.92587i	0.0748747	−	0.129687i	0.901032	+	0.433753i	$0.142811\pi$
$510$	−13.4605	+	3.26666i	−0.596040	+	0.144650i
$511$	−3.12739	−	5.41680i	−0.138348	−	0.239625i
$512$			1.00000i			0.0441942i
$513$	−1.60429	+	0.926239i	−0.0708313	+	0.0408945i
$514$	−3.38813	−	5.86841i	−0.149444	−	0.258844i
$515$	−24.5286	−	25.7206i	−1.08086	−	1.13339i
$516$	1.40281	−	2.42974i	0.0617552	−	0.106963i
$517$			13.2133i			0.581119i
$518$	7.48169	−	10.4452i	0.328727	−	0.458935i
$519$	9.96032			0.437210
$520$	−1.82245	−	0.534956i	−0.0799198	−	0.0234594i
$521$	1.94270	+	3.36486i	0.0851113	+	0.147417i	0.905439	−	0.424477i	$-0.139542\pi$
$521$	1.94270	+	3.36486i	0.0851113	+	0.147417i	−0.820327	+	0.571894i	$0.806209\pi$
$522$	−2.38071	+	1.37451i	−0.104201	+	0.0601605i
$523$	−1.62240	+	0.936694i	−0.0709426	+	0.0409587i	−0.535052	−	0.844819i	$-0.679708\pi$
$523$	−1.62240	+	0.936694i	−0.0709426	+	0.0409587i	0.464109	+	0.885778i	$0.346375\pi$
$524$	4.82319			0.210702
$525$	−8.88559	−	5.70835i	−0.387799	−	0.249133i
$526$	−0.588175			−0.0256457
$527$	−28.7476	−	16.5974i	−1.25226	−	0.722995i
$528$			1.56784i			0.0682317i
$529$	18.8952			0.821529
$530$	−17.8148	−	5.22930i	−0.773826	−	0.227146i
$531$	−0.267356	−	0.463075i	−0.0116023	−	0.0200957i
$532$		−	3.91288i		−	0.169645i
$533$	−2.52408	−	1.45728i	−0.109330	−	0.0631218i
$534$	4.64567	−	8.04654i	0.201038	−	0.348208i
$535$	1.59515	−	5.43425i	0.0689644	−	0.234943i
$536$	0.0185877	+	0.0321948i	0.000802865	+	0.00139060i
$537$	−14.2463	+	8.22509i	−0.614772	+	0.354939i
$538$	0.731454	+	0.422305i	0.0315352	+	0.0182069i
$539$	−1.98994	+	3.44668i	−0.0857128	+	0.148459i
$540$	0.629796	−	2.14554i	0.0271021	−	0.0923295i
$541$	−13.5792			−0.583816			−0.291908	−	0.956446i	$-0.594290\pi$
$541$	−13.5792			−0.583816			−0.291908	+	0.956446i	$0.594290\pi$
$542$	23.3512	−	13.4818i	1.00302	−	0.579094i
$543$	−4.11602	−	2.37638i	−0.176635	−	0.101980i
$544$	6.19445			0.265585
$545$	2.33308	+	9.61362i	0.0999382	+	0.411802i
$546$	−0.897081	+	1.55379i	−0.0383915	+	0.0664961i
$547$		−	5.63584i		−	0.240971i	−0.992715	−	0.120486i	$-0.961555\pi$
$547$		−	5.63584i		−	0.240971i	0.992715	−	0.120486i	$-0.0384452\pi$
$548$	4.43430	−	2.56015i	0.189424	−	0.109364i
$549$	−10.7983			−0.460860
$550$	−4.23711	+	6.59548i	−0.180671	+	0.281232i
$551$	−2.54624	−	4.41022i	−0.108474	−	0.187882i
$552$	1.75460	−	1.01302i	0.0746808	−	0.0431170i
$553$	15.4316	+	8.90945i	0.656219	+	0.378868i
$554$	−13.6961			−0.581890
$555$	8.37910	+	10.7140i	0.355673	+	0.454786i
$556$	−9.01261			−0.382220
$557$	−6.56034	−	3.78762i	−0.277971	−	0.160486i	0.354534	−	0.935043i	$-0.384640\pi$
$557$	−6.56034	−	3.78762i	−0.277971	−	0.160486i	−0.632504	+	0.774557i	$0.717973\pi$
$558$	4.64086	−	2.67940i	0.196463	−	0.113428i
$559$	−1.19156	−	2.06385i	−0.0503977	−	0.0872914i
$560$	3.25960	+	3.41801i	0.137743	+	0.144437i
$561$	9.71193			0.410038
$562$	13.8097	−	7.97306i	0.582529	−	0.336323i
$563$		−	4.50969i		−	0.190061i	−0.995474	−	0.0950305i	$-0.969705\pi$
$563$		−	4.50969i		−	0.190061i	0.995474	−	0.0950305i	$-0.0302949\pi$
$564$	−4.21383	+	7.29857i	−0.177434	+	0.307325i
$565$	17.1894	−	4.17162i	0.723165	−	0.175501i
$566$	18.1309			0.762097
$567$	−1.82925	−	1.05612i	−0.0768214	−	0.0443529i
$568$	−8.85491	+	5.11238i	−0.371544	+	0.214511i
$569$	31.0022			1.29968			0.649841	−	0.760070i	$-0.274836\pi$
$569$	31.0022			1.29968			0.649841	+	0.760070i	$0.274836\pi$
$570$	3.97457	+	1.16668i	0.166477	+	0.0488670i
$571$	9.25090	−	16.0230i	0.387138	−	0.670543i	−0.604925	−	0.796282i	$-0.706797\pi$
$571$	9.25090	−	16.0230i	0.387138	−	0.670543i	0.992063	+	0.125739i	$0.0401303\pi$
$572$	1.15333	+	0.665873i	0.0482230	+	0.0278416i
$573$	16.0422	−	9.26196i	0.670172	−	0.386924i
$574$	3.62383	+	6.27665i	0.151256	+	0.261982i
$575$	10.1188	+	0.480341i	0.421983	+	0.0200316i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	18.6143	+	10.7470i	0.774922	+	0.447401i	0.834628	−	0.550815i	$-0.185683\pi$
$577$	18.6143	+	10.7470i	0.774922	+	0.447401i	−0.0597056	+	0.998216i	$0.519016\pi$
$578$		−	21.3712i		−	0.888923i
$579$	−4.14349	−	7.17673i	−0.172198	−	0.298255i
$580$	5.89812	+	1.73132i	0.244906	+	0.0718890i
$581$	2.28984			0.0949986
$582$			11.7183i			0.485738i
$583$	11.2740	+	6.50904i	0.466921	+	0.269577i
$584$	−2.96121			−0.122536
$585$	−1.31081	−	1.37451i	−0.0541954	−	0.0568290i
$586$	−4.79419			−0.198046
$587$	2.86006	−	1.65126i	0.118047	−	0.0681546i	−0.439814	−	0.898089i	$-0.644956\pi$
$587$	2.86006	−	1.65126i	0.118047	−	0.0681546i	0.557861	+	0.829934i	$0.311622\pi$
$588$	−2.19835	+	1.26922i	−0.0906586	+	0.0523418i
$589$	4.96354	+	8.59710i	0.204519	+	0.354237i
$590$	−0.336760	+	1.14725i	−0.0138642	+	0.0472315i
$591$	23.2261			0.955392
$592$	−2.51153	−	5.54006i	−0.103223	−	0.227695i
$593$		−	9.31881i		−	0.382678i	−0.981524	−	0.191339i	$-0.938717\pi$
$593$		−	9.31881i		−	0.382678i	0.981524	−	0.191339i	$-0.0612829\pi$
$594$	−0.783922	+	1.35779i	−0.0321647	+	0.0557109i
$595$	21.1727	−	20.1914i	0.867995	−	0.827768i
$596$	3.82868	+	6.63147i	0.156829	+	0.271636i
$597$	8.92423	−	5.15241i	0.365245	−	0.210874i
$598$		−	1.72094i		−	0.0703746i
$599$	12.3963	+	21.4711i	0.506501	+	0.877285i	0.999972	+	0.00752263i	$0.00239455\pi$
$599$	12.3963	+	21.4711i	0.506501	+	0.877285i	−0.493471	+	0.869762i	$0.664272\pi$
$600$	−4.44380	+	2.29187i	−0.181417	+	0.0935651i
$601$	−3.67364	+	6.36293i	−0.149851	+	0.259549i	−0.931172	−	0.364580i	$-0.881213\pi$
$601$	−3.67364	+	6.36293i	−0.149851	+	0.259549i	0.781321	+	0.624129i	$0.214546\pi$
$602$			5.92614i			0.241531i
$603$			0.0371754i			0.00151390i
$604$	6.31425	−	10.9366i	0.256923	−	0.445004i
$605$	−13.8224	+	13.1818i	−0.561959	+	0.535916i
$606$	8.27019			0.335953
$607$	−40.2949	−	23.2643i	−1.63552	−	0.944267i	−0.982350	−	0.187054i	$-0.940106\pi$
$607$	−40.2949	−	23.2643i	−1.63552	−	0.944267i	−0.653169	−	0.757213i	$-0.726561\pi$
$608$	−1.60429	−	0.926239i	−0.0650627	−	0.0375640i
$609$	2.90329	−	5.02864i	0.117647	−	0.203771i
$610$	16.6639	+	17.4737i	0.674701	+	0.707489i
$611$	3.57928	+	6.19949i	0.144802	+	0.250805i
$612$	5.36455	+	3.09722i	0.216849	+	0.125198i
$613$	23.2523	+	13.4247i	0.939152	+	0.542219i	0.889694	−	0.456557i	$-0.150917\pi$
$613$	23.2523	+	13.4247i	0.939152	+	0.542219i	0.0494573	+	0.998776i	$0.484251\pi$
$614$	13.8318	−	23.9574i	0.558207	−	0.966843i
$615$	−7.45611	+	1.80949i	−0.300660	+	0.0729655i
$616$	−1.65583	−	2.86799i	−0.0667154	−	0.115554i
$617$	−4.98207	−	2.87640i	−0.200570	−	0.115799i	0.396351	−	0.918099i	$-0.370276\pi$
$617$	−4.98207	−	2.87640i	−0.200570	−	0.115799i	−0.596922	+	0.802300i	$0.703610\pi$
$618$			15.8947i			0.639378i
$619$	9.77292			0.392807			0.196403	−	0.980523i	$-0.437074\pi$
$619$	9.77292			0.392807			0.196403	+	0.980523i	$0.437074\pi$
$620$	−11.4976	−	3.37495i	−0.461753	−	0.135541i
$621$	2.02604			0.0813021
$622$	−11.6962	+	6.75280i	−0.468974	+	0.270762i
$623$			19.6256i			0.786282i
$624$	0.424706	+	0.735613i	0.0170019	+	0.0294481i
$625$	−24.8876	−	2.36817i	−0.995503	−	0.0947268i
$626$	8.25573	+	14.2993i	0.329965	+	0.571517i
$627$	−2.51528	−	1.45220i	−0.100451	−	0.0579953i
$628$			24.4756i			0.976681i
$629$	−34.3176	+	15.5575i	−1.36833	+	0.620319i
$630$	1.11390	+	4.58988i	0.0443787	+	0.182865i
$631$	5.12631	−	8.87903i	0.204075	−	0.353469i	−0.745762	−	0.666212i	$-0.767915\pi$
$631$	5.12631	−	8.87903i	0.204075	−	0.353469i	0.949838	+	0.312743i	$0.101248\pi$
$632$	7.30581	−	4.21801i	0.290609	−	0.167783i
$633$	2.04330	−	1.17970i	0.0812139	−	0.0468889i
$634$	−11.4468	−	19.8264i	−0.454609	−	0.787407i
$635$	−4.16891	+	1.01173i	−0.165438	+	0.0401494i
$636$	4.15159	+	7.19076i	0.164621	+	0.285132i
$637$			2.15618i			0.0854311i
$638$	−3.73259	−	2.15501i	−0.147775	−	0.0853177i
$639$	−10.2248			−0.404485
$640$	2.17299	−	0.527353i	0.0858951	−	0.0208454i
$641$	12.8424	−	22.2437i	0.507244	−	0.878572i	−0.492721	−	0.870187i	$-0.663998\pi$
$641$	12.8424	−	22.2437i	0.507244	−	0.878572i	0.999965	−	0.00838481i	$-0.00266900\pi$
$642$	−2.19348	+	1.26640i	−0.0865696	+	0.0499810i
$643$		−	14.2486i		−	0.561909i	−0.959721	−	0.280955i	$-0.909349\pi$
$643$		−	14.2486i		−	0.561909i	0.959721	−	0.280955i	$-0.0906510\pi$
$644$	−2.13974	+	3.70614i	−0.0843176	+	0.146042i
$645$	−6.01957	−	1.76697i	−0.237020	−	0.0695742i
$646$	−5.73754	+	9.93771i	−0.225740	+	0.390994i
$647$	−6.03428	+	3.48389i	−0.237232	+	0.136966i	−0.613904	−	0.789381i	$-0.710402\pi$
$647$	−6.03428	+	3.48389i	−0.237232	+	0.136966i	0.376672	+	0.926347i	$0.377068\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	0.419173	−	0.726029i	0.0164540	−	0.0284992i
$650$	−0.201382	+	4.24228i	−0.00789884	+	0.166396i
$651$	−5.65955	+	9.80262i	−0.221815	+	0.384195i
$652$		−	24.2159i		−	0.948367i
$653$	34.1138	−	19.6956i	1.33498	−	0.770748i	0.348918	−	0.937153i	$-0.386549\pi$
$653$	34.1138	−	19.6956i	1.33498	−	0.770748i	0.986058	+	0.166405i	$0.0532159\pi$
$654$	2.21207	−	3.83141i	0.0864987	−	0.149820i
$655$	−2.54352	−	10.4808i	−0.0993836	−	0.409517i
$656$	3.43126			0.133968
$657$	−2.56448	−	1.48060i	−0.100050	−	0.0577639i
$658$		−	17.8012i		−	0.693965i
$659$	−3.47562	−	6.01996i	−0.135391	−	0.234504i	0.790356	−	0.612648i	$-0.209896\pi$
$659$	−3.47562	−	6.01996i	−0.135391	−	0.234504i	−0.925747	+	0.378144i	$0.876562\pi$
$660$	3.40692	−	0.826807i	0.132614	−	0.0321834i
$661$	−17.2104	−	29.8093i	−0.669407	−	1.15945i	−0.978070	−	0.208276i	$-0.933215\pi$
$661$	−17.2104	−	29.8093i	−0.669407	−	1.15945i	0.308663	−	0.951172i	$-0.400119\pi$
$662$	8.11557	−	4.68552i	0.315420	−	0.182108i
$663$	4.55671	−	2.63082i	0.176968	−	0.102173i
$664$	0.542041	−	0.938843i	0.0210353	−	0.0364342i
$665$	−8.50266	+	2.06347i	−0.329719	+	0.0800178i
$666$	0.594981	−	6.05359i	0.0230551	−	0.234572i
$667$			5.56960i			0.215656i
$668$	−16.8294	−	9.71649i	−0.651151	−	0.375942i
$669$	7.30607	+	12.6545i	0.282469	+	0.489251i
$670$	0.0601568	−	0.0573689i	0.00232406	−	0.00221635i
$671$	−8.46502	−	14.6618i	−0.326788	−	0.566014i
$672$		−	2.11224i		−	0.0814814i
$673$	17.3682	−	10.0275i	0.669494	−	0.386533i	−0.126391	−	0.991981i	$-0.540339\pi$
$673$	17.3682	−	10.0275i	0.669494	−	0.386533i	0.795885	+	0.605448i	$0.207006\pi$
$674$	21.9603			0.845879
$675$	−4.99438	−	0.237084i	−0.192234	−	0.00912536i
$676$	−12.2785			−0.472250
$677$			0.967209i			0.0371728i	0.999827	+	0.0185864i	$0.00591658\pi$
$677$			0.967209i			0.0371728i	−0.999827	+	0.0185864i	$0.994083\pi$
$678$	−6.85069	−	3.95525i	−0.263099	−	0.151900i
$679$	−12.3759	−	21.4357i	−0.474944	−	0.822627i
$680$	−3.26666	−	13.4605i	−0.125271	−	0.516186i
$681$	−2.83945	+	4.91807i	−0.108808	+	0.188461i
$682$	7.27615	+	4.20089i	0.278618	+	0.160860i
$683$	−3.50941	−	2.02616i	−0.134284	−	0.0775289i	0.431353	−	0.902183i	$-0.358036\pi$
$683$	−3.50941	−	2.02616i	−0.134284	−	0.0775289i	−0.565637	+	0.824654i	$0.691370\pi$
$684$	−0.926239	−	1.60429i	−0.0354156	−	0.0613417i
$685$	−7.90162	−	8.28561i	−0.301905	−	0.316577i
$686$	10.0737	−	17.4482i	0.384617	−	0.666176i
$687$	10.3992	+	6.00398i	0.396754	+	0.229066i
$688$	2.42974	+	1.40281i	0.0926328	+	0.0534816i
$689$	7.05282			0.268691
$690$	−3.12658	−	3.27852i	−0.119027	−	0.124811i
$691$	8.21968	−	14.2369i	0.312691	−	0.541597i	−0.666253	−	0.745726i	$-0.732103\pi$
$691$	8.21968	−	14.2369i	0.312691	−	0.541597i	0.978944	+	0.204129i	$0.0654361\pi$
$692$			9.96032i			0.378635i
$693$		−	3.31166i		−	0.125800i
$694$	5.49495	−	9.51753i	0.208585	−	0.361280i
$695$	4.75282	+	19.5843i	0.180285	+	0.742876i
$696$	−1.37451	−	2.38071i	−0.0521005	−	0.0902407i
$697$		−	21.2548i		−	0.805082i
$698$	−0.0843213	+	0.0486829i	−0.00319161	+	0.00184268i
$699$	4.56769	+	7.91147i	0.172766	+	0.299239i
$700$	5.70835	−	8.88559i	0.215755	−	0.335844i
$701$	0.374107	−	0.647972i	0.0141298	−	0.0244736i	−0.858874	−	0.512187i	$-0.828836\pi$
$701$	0.374107	−	0.647972i	0.0141298	−	0.0244736i	0.873004	+	0.487713i	$0.162169\pi$
$702$			0.849412i			0.0320590i
$703$	11.2142	+	1.10219i	0.422950	+	0.0415699i
$704$	−1.56784			−0.0590904
$705$	18.0819	+	5.30770i	0.681004	+	0.199900i
$706$	−8.41502	−	14.5752i	−0.316703	−	0.548547i
$707$	−15.1283	+	8.73431i	−0.568957	+	0.328488i
$708$	0.463075	−	0.267356i	0.0174034	−	0.0100479i
$709$	47.4282			1.78120			0.890601	−	0.454786i	$-0.150284\pi$
$709$	47.4282			1.78120			0.890601	+	0.454786i	$0.150284\pi$
$710$	15.7788	+	16.5456i	0.592169	+	0.620946i
$711$	8.43602			0.316375
$712$	8.04654	+	4.64567i	0.301557	+	0.174104i
$713$		−	10.8572i		−	0.406604i
$714$	−13.0842			−0.489662
$715$	0.838728	−	2.85732i	0.0313667	−	0.106858i
$716$	−8.22509	−	14.2463i	−0.307386	−	0.532408i
$717$			22.7600i			0.849987i
$718$	11.4818	+	6.62899i	0.428495	+	0.247392i
$719$	−13.3284	+	23.0855i	−0.497066	+	0.860944i	−0.999994	−	0.00338428i	$-0.998923\pi$
$719$	−13.3284	+	23.0855i	−0.497066	+	0.860944i	0.502928	+	0.864328i	$0.332256\pi$
$720$	2.14554	+	0.629796i	0.0799597	+	0.0234711i
$721$	−16.7867	−	29.0754i	−0.625169	−	1.08282i
$722$	−13.4826	+	7.78416i	−0.501769	+	0.289696i
$723$	13.8495	+	7.99602i	0.515069	+	0.297375i
$724$	2.37638	−	4.11602i	0.0883176	−	0.152971i
$725$	0.651746	−	13.7296i	0.0242052	−	0.509904i
$726$	8.54186			0.317018
$727$	11.6312	−	6.71526i	0.431376	−	0.249055i	−0.268557	−	0.963264i	$-0.586547\pi$
$727$	11.6312	−	6.71526i	0.431376	−	0.249055i	0.699933	+	0.714209i	$0.253213\pi$
$728$	−1.55379	−	0.897081i	−0.0575873	−	0.0332481i
$729$	−1.00000			−0.0370370
$730$	1.56160	+	6.43468i	0.0577974	+	0.238158i
$731$	8.68962	−	15.0509i	0.321397	−	0.556676i
$732$		−	10.7983i		−	0.399116i
$733$	−10.7195	+	6.18891i	−0.395934	+	0.228592i	−0.684728	−	0.728799i	$-0.740079\pi$
$733$	−10.7195	+	6.18891i	−0.395934	+	0.228592i	0.288794	+	0.957391i	$0.406746\pi$
$734$	−15.5462			−0.573819
$735$	3.91732	+	4.10768i	0.144492	+	0.151514i
$736$	1.01302	+	1.75460i	0.0373404	+	0.0646755i
$737$	−0.0504765	+	0.0291426i	−0.00185932	+	0.00107348i
$738$	2.97156	+	1.71563i	0.109385	+	0.0631533i
$739$	−30.0450			−1.10522			−0.552612	−	0.833439i	$-0.686369\pi$
$739$	−30.0450			−1.10522			−0.552612	+	0.833439i	$0.686369\pi$
$740$	−10.7140	+	8.37910i	−0.393856	+	0.308022i
$741$	−1.57352			−0.0578046
$742$	−15.1886	−	8.76915i	−0.557592	−	0.321926i
$743$	18.5475	−	10.7084i	0.680443	−	0.392854i	−0.119579	−	0.992825i	$-0.538154\pi$
$743$	18.5475	−	10.7084i	0.680443	−	0.392854i	0.800022	+	0.599971i	$0.204821\pi$
$744$	2.67940	+	4.64086i	0.0982317	+	0.170142i
$745$	12.3911	−	11.8168i	0.453974	−	0.432935i
$746$	−2.93065			−0.107299
$747$	0.938843	−	0.542041i	0.0343505	−	0.0198322i
$748$			9.71193i			0.355103i
$749$	2.67495	−	4.63315i	0.0977405	−	0.169292i
$750$	7.32366	+	8.44772i	0.267422	+	0.308467i
$751$	−28.8218			−1.05172			−0.525861	−	0.850571i	$-0.676257\pi$
$751$	−28.8218			−1.05172			−0.525861	+	0.850571i	$0.676257\pi$
$752$	−7.29857	−	4.21383i	−0.266151	−	0.153663i
$753$	−9.88437	+	5.70674i	−0.360207	+	0.207965i
$754$	−2.33504			−0.0850373
$755$	−27.0950	−	7.95338i	−0.986088	−	0.289453i
$756$	1.05612	−	1.82925i	0.0384107	−	0.0665293i
$757$	44.8996	+	25.9228i	1.63190	+	0.942180i	0.983505	+	0.180878i	$0.0578940\pi$
$757$	44.8996	+	25.9228i	1.63190	+	0.942180i	0.648398	+	0.761302i	$0.275439\pi$
$758$	12.3597	−	7.13585i	0.448923	−	0.259186i
$759$	1.58826	+	2.75094i	0.0576501	+	0.0998529i
$760$	−1.16668	+	3.97457i	−0.0423200	+	0.144173i
$761$	−23.9758	+	41.5273i	−0.869122	+	1.50536i	−0.00622649	+	0.999981i	$0.501982\pi$
$761$	−23.9758	+	41.5273i	−0.869122	+	1.50536i	−0.862895	+	0.505383i	$0.831351\pi$
$762$	1.66148	+	0.959256i	0.0601891	+	0.0347502i
$763$			9.34484i			0.338306i
$764$	9.26196	+	16.0422i	0.335086	+	0.580386i
$765$	3.90124	−	13.2905i	0.141049	−	0.480517i
$766$	19.2998			0.697330
$767$		−	0.454192i		−	0.0163999i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	5.36100			0.193323			0.0966614	−	0.995317i	$-0.469184\pi$
$769$	5.36100			0.193323			0.0966614	+	0.995317i	$0.469184\pi$
$770$	−5.35891	+	5.11055i	−0.193122	+	0.184172i
$771$	6.77625			0.244041
$772$	7.17673	−	4.14349i	0.258296	−	0.149127i
$773$	−22.3825	+	12.9226i	−0.805044	+	0.464792i	−0.845232	−	0.534400i	$-0.820538\pi$
$773$	−22.3825	+	12.9226i	−0.805044	+	0.464792i	0.0401878	+	0.999192i	$0.487204\pi$
$774$	1.40281	+	2.42974i	0.0504229	+	0.0873350i
$775$	−1.27049	+	26.7639i	−0.0456372	+	0.961388i
$776$	−11.7183			−0.420662
$777$	5.30495	+	11.7019i	0.190314	+	0.419804i
$778$			24.0251i			0.861343i
$779$	−3.17817	+	5.50476i	−0.113870	+	0.197228i
$780$	1.37451	−	1.31081i	0.0492154	−	0.0469346i
$781$	−8.01542	−	13.8831i	−0.286814	−	0.496777i
$782$	10.8688	−	6.27509i	0.388667	−	0.224397i
$783$		−	2.74901i		−	0.0982416i
$784$	−1.26922	−	2.19835i	−0.0453293	−	0.0785127i
$785$	53.1852	−	12.9073i	1.89826	−	0.460680i
$786$	−2.41159	+	4.17700i	−0.0860187	+	0.148989i
$787$			48.1214i			1.71534i	0.514198	+	0.857671i	$0.328090\pi$
$787$			48.1214i			1.71534i	−0.514198	+	0.857671i	$0.671910\pi$
$788$			23.2261i			0.827394i
$789$	0.294088	−	0.509375i	0.0104698	−	0.0181342i
$790$	−13.0184	−	13.6511i	−0.463175	−	0.485684i
$791$	16.7089			0.594099
$792$	−1.35779	−	0.783922i	−0.0482471	−	0.0278555i
$793$	−7.94336	−	4.58610i	−0.282077	−	0.162857i
$794$	16.8466	−	29.1791i	0.597863	−	1.03553i
$795$	13.4361	−	12.8134i	0.476530	−	0.454446i
$796$	5.15241	+	8.92423i	0.182622	+	0.316311i
$797$	−29.6895	−	17.1412i	−1.05166	−	0.607174i	−0.128543	−	0.991704i	$-0.541030\pi$
$797$	−29.6895	−	17.1412i	−1.05166	−	0.607174i	−0.923112	+	0.384530i	$0.874364\pi$
$798$	3.38865	+	1.95644i	0.119957	+	0.0692572i
$799$	−26.1023	+	45.2106i	−0.923434	+	1.59944i
$800$	−2.29187	−	4.44380i	−0.0810298	−	0.157112i
$801$	4.64567	+	8.04654i	0.164147	+	0.284311i
$802$	−6.19922	−	3.57912i	−0.218902	−	0.126383i
$803$		−	4.64271i		−	0.163838i
$804$	−0.0371754			−0.00131107
$805$	9.18181	+	2.69520i	0.323616	+	0.0949933i
$806$	4.55184			0.160332
$807$	−0.731454	+	0.422305i	−0.0257484	+	0.0148658i
$808$			8.27019i			0.290944i
$809$	−0.956968	−	1.65752i	−0.0336452	−	0.0582752i	0.848712	−	0.528855i	$-0.177378\pi$
$809$	−0.956968	−	1.65752i	−0.0336452	−	0.0582752i	−0.882358	+	0.470579i	$0.844045\pi$
$810$	1.54320	+	1.61819i	0.0542224	+	0.0568574i
$811$	−14.4460	−	25.0212i	−0.507268	−	0.878614i	−0.999965	−	0.00841264i	$-0.997322\pi$
$811$	−14.4460	−	25.0212i	−0.507268	−	0.878614i	0.492697	−	0.870201i	$-0.336011\pi$
$812$	5.02864	+	2.90329i	0.176471	+	0.101885i
$813$			26.9637i			0.945657i
$814$	8.68595	−	3.93769i	0.304442	−	0.138016i
$815$	−52.6210	+	12.7703i	−1.84323	+	0.447325i
$816$	−3.09722	+	5.36455i	−0.108424	+	0.187797i
$817$	−4.50103	+	2.59867i	−0.157471	+	0.0909160i
$818$	1.91864	−	1.10773i	0.0670838	−	0.0387308i
$819$	−0.897081	−	1.55379i	−0.0313466	−	0.0542938i
$820$	−1.80949	−	7.45611i	−0.0631900	−	0.260379i
$821$	18.7099	+	32.4065i	0.652980	+	1.13099i	0.982396	+	0.186809i	$0.0598147\pi$
$821$	18.7099	+	32.4065i	0.652980	+	1.13099i	−0.329416	+	0.944185i	$0.606852\pi$
$822$			5.12029i			0.178591i
$823$	−35.1125	−	20.2722i	−1.22395	−	0.706645i	−0.258189	−	0.966095i	$-0.583126\pi$
$823$	−35.1125	−	20.2722i	−1.22395	−	0.706645i	−0.965757	+	0.259449i	$0.916459\pi$
$824$	−15.8947			−0.553717
$825$	−3.59329	−	6.96719i	−0.125102	−	0.242566i
$826$	−0.564721	+	0.978125i	−0.0196492	+	0.0340333i
$827$	−22.9483	+	13.2492i	−0.797991	+	0.460720i	−0.842768	−	0.538277i	$-0.819076\pi$
$827$	−22.9483	+	13.2492i	−0.797991	+	0.460720i	0.0447773	+	0.998997i	$0.485742\pi$
$828$			2.02604i			0.0704097i
$829$	−1.85148	+	3.20686i	−0.0643047	+	0.111379i	−0.896385	−	0.443276i	$-0.853816\pi$
$829$	−1.85148	+	3.20686i	−0.0643047	+	0.111379i	0.832081	+	0.554655i	$0.187150\pi$
$830$	−2.32595	−	0.682750i	−0.0807347	−	0.0236986i
$831$	6.84804	−	11.8611i	0.237556	−	0.411459i
$832$	−0.735613	+	0.424706i	−0.0255028	+	0.0147240i
$833$	−13.6176	+	7.86212i	−0.471821	+	0.272406i
$834$	4.50630	−	7.80515i	0.156041	−	0.270270i
$835$	−12.2388	+	41.6943i	−0.423541	+	1.44289i
$836$	1.45220	−	2.51528i	0.0502254	−	0.0869929i
$837$			5.35881i			0.185228i
$838$	−21.3813	+	12.3445i	−0.738603	+	0.426433i
$839$	−7.21458	+	12.4960i	−0.249075	+	0.431411i	−0.963269	−	0.268537i	$-0.913460\pi$
$839$	−7.21458	+	12.4960i	−0.249075	+	0.431411i	0.714194	+	0.699947i	$0.246793\pi$
$840$	−4.58988	+	1.11390i	−0.158366	+	0.0384330i
$841$	−21.4429			−0.739412
$842$	−2.13132	−	1.23052i	−0.0734501	−	0.0424064i
$843$			15.9461i			0.549213i
$844$	1.17970	+	2.04330i	0.0406069	+	0.0703333i
$845$	6.47510	+	26.6811i	0.222750	+	0.917858i
$846$	−4.21383	−	7.29857i	−0.144874	−	0.250930i
$847$	−15.6252	+	9.02123i	−0.536889	+	0.309973i
$848$	−7.19076	+	4.15159i	−0.246932	+	0.142566i
$849$	−9.06543	+	15.7018i	−0.311125	+	0.538884i
$850$	−27.5269	+	14.1968i	−0.944164	+	0.486948i
$851$	−10.0189	−	7.17636i	−0.343444	−	0.246003i
$852$		−	10.2248i		−	0.350295i
$853$	33.2029	+	19.1697i	1.13685	+	0.656359i	0.945648	−	0.325192i	$-0.105429\pi$
$853$	33.2029	+	19.1697i	1.13685	+	0.656359i	0.191199	+	0.981551i	$0.438762\pi$
$854$	11.4043	+	19.7528i	0.390247	+	0.675927i
$855$	−2.99766	+	2.85874i	−0.102518	+	0.0977669i
$856$	−1.26640	−	2.19348i	−0.0432848	−	0.0749715i
$857$		−	26.1064i		−	0.891778i	−0.895088	−	0.445889i	$-0.852888\pi$
$857$		−	26.1064i		−	0.891778i	0.895088	−	0.445889i	$-0.147112\pi$
$858$	−1.15333	+	0.665873i	−0.0393739	+	0.0227325i
$859$	1.87037			0.0638163			0.0319082	−	0.999491i	$-0.489842\pi$
$859$	1.87037			0.0638163			0.0319082	+	0.999491i	$0.489842\pi$
$860$	1.76697	−	6.01957i	0.0602530	−	0.205266i
$861$	−7.24765			−0.246999
$862$			14.4733i			0.492962i
$863$	11.2721	+	6.50794i	0.383706	+	0.221533i	0.679430	−	0.733741i	$-0.262227\pi$
$863$	11.2721	+	6.50794i	0.383706	+	0.221533i	−0.295723	+	0.955274i	$0.595561\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	21.6437	−	5.25260i	0.735908	−	0.178594i
$866$	−8.18538	+	14.1775i	−0.278151	+	0.481771i
$867$	18.5080	+	10.6856i	0.628563	+	0.362901i
$868$	−9.80262	−	5.65955i	−0.332723	−	0.192097i
$869$	6.61318	+	11.4544i	0.224337	+	0.388563i
$870$	−4.44843	+	4.24227i	−0.150816	+	0.143826i
$871$	−0.0157886	+	0.0273467i	−0.000534976	+	0.000926606i
$872$	3.83141	+	2.21207i	0.129748	+	0.0749101i
$873$	−10.1483	−	5.85914i	−0.343469	−	0.198302i
$874$	−3.75319			−0.126954
$875$	−22.3186	−	7.71836i	−0.754508	−	0.260928i
$876$	1.48060	−	2.56448i	0.0500250	−	0.0866458i
$877$		−	18.1748i		−	0.613720i	−0.951755	−	0.306860i	$-0.900722\pi$
$877$		−	18.1748i		−	0.613720i	0.951755	−	0.306860i	$-0.0992783\pi$
$878$			6.66681i			0.224994i
$879$	2.39710	−	4.15189i	0.0808520	−	0.140040i
$880$	0.826807	+	3.40692i	0.0278717	+	0.114847i
$881$	−10.4233	−	18.0536i	−0.351169	−	0.608242i	0.635286	−	0.772277i	$-0.280882\pi$
$881$	−10.4233	−	18.0536i	−0.351169	−	0.608242i	−0.986454	+	0.164035i	$0.947549\pi$
$882$		−	2.53844i		−	0.0854737i
$883$	21.8125	−	12.5935i	0.734050	−	0.423804i	−0.0858518	−	0.996308i	$-0.527361\pi$
$883$	21.8125	−	12.5935i	0.734050	−	0.423804i	0.819902	+	0.572504i	$0.194028\pi$
$884$	2.63082	+	4.55671i	0.0884840	+	0.153259i
$885$	−0.825167	−	0.865267i	−0.0277377	−	0.0290856i
$886$	−5.33203	+	9.23535i	−0.179133	+	0.310268i
$887$		−	36.8352i		−	1.23681i	−0.785861	−	0.618403i	$-0.787780\pi$
$887$		−	36.8352i		−	1.23681i	0.785861	−	0.618403i	$-0.212220\pi$
$888$	6.05359	+	0.594981i	0.203145	+	0.0199663i
$889$	−4.05236			−0.135912
$890$	5.85165	−	19.9350i	0.196148	−	0.668223i
$891$	−0.783922	−	1.35779i	−0.0262624	−	0.0454878i
$892$	−12.6545	+	7.30607i	−0.423703	+	0.244625i
$893$	13.5204	−	7.80603i	0.452444	−	0.261219i
$894$	−7.65736			−0.256100
$895$	−26.6195	+	25.3859i	−0.889793	+	0.848556i
$896$	2.11224			0.0705650
$897$	1.49038	+	0.860471i	0.0497623	+	0.0287303i
$898$			25.0574i			0.836175i
$899$	−14.7314			−0.491321
$900$	0.237084	−	4.99438i	0.00790279	−	0.166479i
$901$	25.7168	+	44.5428i	0.856750	+	1.48393i
$902$			5.37969i			0.179124i
$903$	−5.13218	−	2.96307i	−0.170788	−	0.0986047i
$904$	3.95525	−	6.85069i	0.131550	−	0.227850i
$905$	−10.1973	−	2.99327i	−0.338969	−	0.0994997i
$906$	6.31425	+	10.9366i	0.209777	+	0.363344i
$907$	−14.9872	+	8.65284i	−0.497641	+	0.287313i	−0.727739	−	0.685854i	$-0.759429\pi$
$907$	−14.9872	+	8.65284i	−0.497641	+	0.287313i	0.230098	+	0.973167i	$0.426095\pi$
$908$	−4.91807	−	2.83945i	−0.163212	−	0.0942304i
$909$	−4.13509	+	7.16219i	−0.137152	+	0.237555i
$910$	−1.12996	+	3.84945i	−0.0374577	+	0.127608i
$911$	44.9518			1.48932			0.744660	−	0.667444i	$-0.232612\pi$
$911$	44.9518			1.48932			0.744660	+	0.667444i	$0.232612\pi$
$912$	1.60429	−	0.926239i	0.0531235	−	0.0306708i
$913$	1.47196	+	0.849836i	0.0487147	+	0.0281255i
$914$	−29.4585			−0.974402
$915$	−23.4646	+	5.69451i	−0.775716	+	0.188255i
$916$	−6.00398	+	10.3992i	−0.198377	+	0.343599i
$917$		−	10.1877i		−	0.336429i
$918$	−5.36455	+	3.09722i	−0.177056	+	0.102224i
$919$	−10.3578			−0.341672			−0.170836	−	0.985299i	$-0.554647\pi$
$919$	−10.3578			−0.341672			−0.170836	+	0.985299i	$0.554647\pi$
$920$	3.27852	−	3.12658i	0.108090	−	0.103080i
$921$	13.8318	+	23.9574i	0.455774	+	0.789424i
$922$	12.4300	−	7.17644i	0.409359	−	0.236344i
$923$	−7.52147	−	4.34252i	−0.247572	−	0.142936i
$924$	3.31166			0.108946
$925$	23.8578	+	18.8628i	0.784440	+	0.620205i
$926$	31.5591			1.03710
$927$	−13.7652	−	7.94734i	−0.452108	−	0.261025i
$928$	2.38071	−	1.37451i	0.0781508	−	0.0451204i
$929$	6.52364	+	11.2993i	0.214034	+	0.370717i	0.952973	−	0.303055i	$-0.0980065\pi$
$929$	6.52364	+	11.2993i	0.214034	+	0.370717i	−0.738940	+	0.673772i	$0.764673\pi$
$930$	8.67157	−	8.26970i	0.284352	−	0.271174i
$931$	4.70241			0.154115
$932$	−7.91147	+	4.56769i	−0.259149	+	0.149620i
$933$		−	13.5056i		−	0.442153i
$934$	−18.3449	+	31.7744i	−0.600265	+	1.03969i
$935$	21.1040	−	5.12161i	0.690173	−	0.167495i
$936$	−0.849412			−0.0277639
$937$	−27.4435	−	15.8445i	−0.896541	−	0.517618i	−0.0204646	−	0.999791i	$-0.506515\pi$
$937$	−27.4435	−	15.8445i	−0.896541	−	0.517618i	−0.876076	+	0.482172i	$0.839848\pi$
$938$	0.0680032	−	0.0392616i	0.00222038	−	0.00128194i
$939$	−16.5115			−0.538831
$940$	−5.30770	+	18.0819i	−0.173118	+	0.589767i
$941$	−18.4484	+	31.9536i	−0.601401	+	1.04166i	0.391208	+	0.920302i	$0.372057\pi$
$941$	−18.4484	+	31.9536i	−0.601401	+	1.04166i	−0.992609	+	0.121355i	$0.961276\pi$
$942$	−21.1965	−	12.2378i	−0.690618	−	0.398728i
$943$	6.02050	−	3.47594i	0.196054	−	0.113192i
$944$	0.267356	+	0.463075i	0.00870171	+	0.0150718i
$945$	−4.53190	−	1.33028i	−0.147423	−	0.0432740i
$946$	−2.19939	+	3.80945i	−0.0715082	+	0.123856i
$947$	−4.31668	−	2.49224i	−0.140273	−	0.0809869i	0.428221	−	0.903674i	$-0.359141\pi$
$947$	−4.31668	−	2.49224i	−0.140273	−	0.0809869i	−0.568494	+	0.822687i	$0.692474\pi$
$948$			8.43602i			0.273989i
$949$	−1.25764	−	2.17830i	−0.0408248	−	0.0707107i
$950$	9.25197	+	0.439192i	0.300174	+	0.0142493i
$951$	22.8935			0.742374
$952$		−	13.0842i		−	0.424060i
$953$	−19.9319	−	11.5077i	−0.645658	−	0.372771i	0.141133	−	0.989991i	$-0.454926\pi$
$953$	−19.9319	−	11.5077i	−0.645658	−	0.372771i	−0.786791	+	0.617220i	$0.788259\pi$
$954$	−8.30317			−0.268825
$955$	29.9752	−	28.5861i	0.969976	−	0.925023i
$956$	−22.7600			−0.736111
$957$	3.73259	−	2.15501i	0.120657	−	0.0696616i
$958$	−4.65295	+	2.68638i	−0.150330	+	0.0867931i
$959$	−5.40764	−	9.36631i	−0.174622	−	0.302454i
$960$	−0.629796	+	2.14554i	−0.0203266	+	0.0692471i
$961$	−2.28318			−0.0736508
$962$	3.00867	−	4.20041i	0.0970036	−	0.135427i
$963$		−	2.53281i		−	0.0816186i
$964$	−7.99602	+	13.8495i	−0.257535	+	0.446063i
$965$	−12.7884	−	13.4099i	−0.411675	−	0.431680i
$966$	−2.13974	−	3.70614i	−0.0688450	−	0.119243i
$967$	−1.43100	+	0.826185i	−0.0460177	+	0.0265683i	−0.522832	−	0.852436i	$-0.675125\pi$
$967$	−1.43100	+	0.826185i	−0.0460177	+	0.0265683i	0.476815	+	0.879004i	$0.341791\pi$
$968$			8.54186i			0.274546i
$969$	−5.73754	−	9.93771i	−0.184316	−	0.319245i
$970$	6.17967	+	25.4637i	0.198417	+	0.817592i
$971$	20.7646	−	35.9654i	0.666369	−	1.15418i	−0.312543	−	0.949904i	$-0.601181\pi$
$971$	20.7646	−	35.9654i	0.666369	−	1.15418i	0.978912	−	0.204281i	$-0.0654857\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			19.0368i			0.610292i
$974$	2.82335	−	4.89018i	0.0904658	−	0.156691i
$975$	−3.57324	−	2.29554i	−0.114435	−	0.0735162i
$976$	10.7983			0.345645
$977$	−49.7738	−	28.7369i	−1.59240	−	0.919375i	−0.992893	−	0.119009i	$-0.962028\pi$
$977$	−49.7738	−	28.7369i	−1.59240	−	0.919375i	−0.599511	−	0.800366i	$-0.704638\pi$
$978$	20.9716	+	12.1079i	0.670597	+	0.387169i
$979$	−7.28370	+	12.6157i	−0.232788	+	0.403201i
$980$	−4.10768	+	3.91732i	−0.131215	+	0.125134i
$981$	2.21207	+	3.83141i	0.0706259	+	0.122328i
$982$	−38.1057	−	22.0004i	−1.21600	−	0.702060i
$983$	53.8428	+	31.0862i	1.71732	+	0.991495i	0.923733	+	0.383037i	$0.125122\pi$
$983$	53.8428	+	31.0862i	1.71732	+	0.991495i	0.793586	+	0.608458i	$0.208212\pi$
$984$	−1.71563	+	2.97156i	−0.0546924	+	0.0947299i
$985$	50.4701	−	12.2483i	1.60811	−	0.390264i
$986$	−8.51430	−	14.7472i	−0.271151	−	0.469647i
$987$	15.4163	+	8.90062i	0.490707	+	0.283310i
$988$		−	1.57352i		−	0.0500603i
$989$	5.68429			0.180750
$990$	−0.987422	+	3.36388i	−0.0313823	+	0.106911i
$991$	−52.4317			−1.66555			−0.832773	−	0.553614i	$-0.813248\pi$
$991$	−52.4317			−1.66555			−0.832773	+	0.553614i	$0.813248\pi$
$992$	−4.64086	+	2.67940i	−0.147348	+	0.0850712i
$993$			9.37105i			0.297381i
$994$	10.7986	+	18.7037i	0.342510	+	0.593245i
$995$	16.6752	−	15.9024i	0.528638	−	0.504139i
$996$	0.542041	+	0.938843i	0.0171752	+	0.0297484i
$997$	51.0074	+	29.4492i	1.61542	+	0.932664i	0.988084	+	0.153917i	$0.0491887\pi$
$997$	51.0074	+	29.4492i	1.61542	+	0.932664i	0.627338	+	0.778747i	$0.284145\pi$
$998$			17.2303i			0.545416i
$999$	4.94508	+	3.54207i	0.156455	+	0.112066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.e.1009.7	✓	40
5.4	even	2	inner	1110.2.bb.e.1009.14	yes	40
37.26	even	3	inner	1110.2.bb.e.1099.14	yes	40
185.174	even	6	inner	1110.2.bb.e.1099.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.e.1009.7	✓	40	1.1	even	1	trivial
1110.2.bb.e.1009.14	yes	40	5.4	even	2	inner
1110.2.bb.e.1099.7	yes	40	185.174	even	6	inner
1110.2.bb.e.1099.14	yes	40	37.26	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.61819 - 1.54320i) q^{5} -1.00000 q^{6} +(1.82925 - 1.05612i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.61819 - 1.54320i) q^{5} -1.00000 q^{6} +(1.82925 - 1.05612i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.17299 + 0.527353i) q^{10} +1.56784 q^{11} +(0.866025 + 0.500000i) q^{12} +(0.735613 - 0.424706i) q^{13} -2.11224 q^{14} +(0.629796 - 2.14554i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.36455 + 3.09722i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-0.926239 - 1.60429i) q^{19} +(2.14554 + 0.629796i) q^{20} +(1.05612 - 1.82925i) q^{21} +(-1.35779 - 0.783922i) q^{22} +2.02604i q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.237084 - 4.99438i) q^{25} -0.849412 q^{26} -1.00000i q^{27} +(1.82925 + 1.05612i) q^{28} +2.74901 q^{29} +(-1.61819 + 1.54320i) q^{30} -5.35881 q^{31} +(0.866025 - 0.500000i) q^{32} +(1.35779 - 0.783922i) q^{33} +(-3.09722 - 5.36455i) q^{34} +(1.33028 - 4.53190i) q^{35} +1.00000 q^{36} +(-3.54207 + 4.94508i) q^{37} +1.85248i q^{38} +(0.424706 - 0.735613i) q^{39} +(-1.54320 - 1.61819i) q^{40} +(-1.71563 - 2.97156i) q^{41} +(-1.82925 + 1.05612i) q^{42} -2.80562i q^{43} +(0.783922 + 1.35779i) q^{44} +(-0.527353 - 2.17299i) q^{45} +(1.01302 - 1.75460i) q^{46} +8.42766i q^{47} +1.00000i q^{48} +(-1.26922 + 2.19835i) q^{49} +(-2.70251 + 4.20671i) q^{50} +6.19445 q^{51} +(0.735613 + 0.424706i) q^{52} +(7.19076 + 4.15159i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.53707 - 2.41949i) q^{55} +(-1.05612 - 1.82925i) q^{56} +(-1.60429 - 0.926239i) q^{57} +(-2.38071 - 1.37451i) q^{58} +(0.267356 - 0.463075i) q^{59} +(2.17299 - 0.527353i) q^{60} +(-5.39914 - 9.35159i) q^{61} +(4.64086 + 2.67940i) q^{62} -2.11224i q^{63} -1.00000 q^{64} +(0.534956 - 1.82245i) q^{65} -1.56784 q^{66} +(-0.0321948 + 0.0185877i) q^{67} +6.19445i q^{68} +(1.01302 + 1.75460i) q^{69} +(-3.41801 + 3.25960i) q^{70} +(-5.11238 - 8.85491i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.96121i q^{73} +(5.54006 - 2.51153i) q^{74} +(-2.29187 - 4.44380i) q^{75} +(0.926239 - 1.60429i) q^{76} +(2.86799 - 1.65583i) q^{77} +(-0.735613 + 0.424706i) q^{78} +(4.21801 + 7.30581i) q^{79} +(0.527353 + 2.17299i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.43126i q^{82} +(0.938843 + 0.542041i) q^{83} +2.11224 q^{84} +(13.4605 - 3.26666i) q^{85} +(-1.40281 + 2.42974i) q^{86} +(2.38071 - 1.37451i) q^{87} -1.56784i q^{88} +(-4.64567 + 8.04654i) q^{89} +(-0.629796 + 2.14554i) q^{90} +(0.897081 - 1.55379i) q^{91} +(-1.75460 + 1.01302i) q^{92} +(-4.64086 + 2.67940i) q^{93} +(4.21383 - 7.29857i) q^{94} +(-3.97457 - 1.16668i) q^{95} +(0.500000 - 0.866025i) q^{96} -11.7183i q^{97} +(2.19835 - 1.26922i) q^{98} +(0.783922 - 1.35779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more