LMFDB - Embedded newform 1110.2.i.l.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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, 0, 4]))

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.i (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.l.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-2.43649 - 4.22013i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-2.43649 - 4.22013i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -5.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.500000 + 0.866025i) q^{13} -4.87298 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0635083 + 0.110000i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.87298 + 6.70820i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.43649 + 4.22013i) q^{21} +(-2.50000 + 4.33013i) q^{22} -6.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} +1.00000 q^{27} +(-2.43649 + 4.22013i) q^{28} +3.87298 q^{29} +(-0.500000 - 0.866025i) q^{30} +7.74597 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} +(0.0635083 + 0.110000i) q^{34} +(2.43649 - 4.22013i) q^{35} +1.00000 q^{36} +(-5.50000 - 2.59808i) q^{37} +7.74597 q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.436492 - 0.756026i) q^{41} +(2.43649 + 4.22013i) q^{42} -9.74597 q^{43} +(2.50000 + 4.33013i) q^{44} -1.00000 q^{45} +(-3.00000 + 5.19615i) q^{46} -10.7460 q^{47} +1.00000 q^{48} +(-8.37298 + 14.5024i) q^{49} +(0.500000 + 0.866025i) q^{50} +0.127017 q^{51} +(0.500000 - 0.866025i) q^{52} +(-0.436492 + 0.756026i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.50000 - 4.33013i) q^{55} +(2.43649 + 4.22013i) q^{56} +(3.87298 - 6.70820i) q^{57} +(1.93649 - 3.35410i) q^{58} +(-2.50000 + 4.33013i) q^{59} -1.00000 q^{60} +(4.43649 + 7.68423i) q^{61} +(3.87298 - 6.70820i) q^{62} +4.87298 q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +5.00000 q^{66} +(-3.06351 - 5.30615i) q^{67} +0.127017 q^{68} +(3.00000 + 5.19615i) q^{69} +(-2.43649 - 4.22013i) q^{70} +(-7.30948 - 12.6604i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-5.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(3.87298 - 6.70820i) q^{76} +(12.1825 + 21.1006i) q^{77} +(-0.500000 - 0.866025i) q^{78} +(-7.74597 - 13.4164i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -0.872983 q^{82} +(-1.43649 + 2.48808i) q^{83} +4.87298 q^{84} -0.127017 q^{85} +(-4.87298 + 8.44025i) q^{86} +(-1.93649 - 3.35410i) q^{87} +5.00000 q^{88} +(-5.87298 + 10.1723i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(2.43649 - 4.22013i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-3.87298 - 6.70820i) q^{93} +(-5.37298 + 9.30628i) q^{94} +(-3.87298 + 6.70820i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.0000 q^{97} +(8.37298 + 14.5024i) q^{98} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 4 q^{10} - 20 q^{11} - 2 q^{12} + 2 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{20} - 2 q^{21} - 10 q^{22} - 24 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 2 q^{28} - 2 q^{30} + 2 q^{32} + 10 q^{33} + 8 q^{34} + 2 q^{35} + 4 q^{36} - 22 q^{37} + 2 q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} - 8 q^{43} + 10 q^{44} - 4 q^{45} - 12 q^{46} - 12 q^{47} + 4 q^{48} - 18 q^{49} + 2 q^{50} + 16 q^{51} + 2 q^{52} + 6 q^{53} + 2 q^{54} - 10 q^{55} + 2 q^{56} - 10 q^{59} - 4 q^{60} + 10 q^{61} + 4 q^{63} + 4 q^{64} - 2 q^{65} + 20 q^{66} - 20 q^{67} + 16 q^{68} + 12 q^{69} - 2 q^{70} - 6 q^{71} + 2 q^{72} + 48 q^{73} - 20 q^{74} + 4 q^{75} + 10 q^{77} - 2 q^{78} - 4 q^{80} - 2 q^{81} + 12 q^{82} + 2 q^{83} + 4 q^{84} - 16 q^{85} - 4 q^{86} + 20 q^{88} - 8 q^{89} - 2 q^{90} + 2 q^{91} + 12 q^{92} - 6 q^{94} + 2 q^{96} - 40 q^{97} + 18 q^{98} + 10 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 + 4 * q^10 - 20 * q^11 - 2 * q^12 + 2 * q^13 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^20 - 2 * q^21 - 10 * q^22 - 24 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - 2 * q^28 - 2 * q^30 + 2 * q^32 + 10 * q^33 + 8 * q^34 + 2 * q^35 + 4 * q^36 - 22 * q^37 + 2 * q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 - 8 * q^43 + 10 * q^44 - 4 * q^45 - 12 * q^46 - 12 * q^47 + 4 * q^48 - 18 * q^49 + 2 * q^50 + 16 * q^51 + 2 * q^52 + 6 * q^53 + 2 * q^54 - 10 * q^55 + 2 * q^56 - 10 * q^59 - 4 * q^60 + 10 * q^61 + 4 * q^63 + 4 * q^64 - 2 * q^65 + 20 * q^66 - 20 * q^67 + 16 * q^68 + 12 * q^69 - 2 * q^70 - 6 * q^71 + 2 * q^72 + 48 * q^73 - 20 * q^74 + 4 * q^75 + 10 * q^77 - 2 * q^78 - 4 * q^80 - 2 * q^81 + 12 * q^82 + 2 * q^83 + 4 * q^84 - 16 * q^85 - 4 * q^86 + 20 * q^88 - 8 * q^89 - 2 * q^90 + 2 * q^91 + 12 * q^92 - 6 * q^94 + 2 * q^96 - 40 * q^97 + 18 * q^98 + 10 * q^99

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.00000			−0.408248
$7$	−2.43649	−	4.22013i	−0.920907	−	1.59506i	−0.798014	−	0.602638i	$-0.794116\pi$
$7$	−2.43649	−	4.22013i	−0.920907	−	1.59506i	−0.122893	−	0.992420i	$-0.539217\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$	−4.87298			−1.30236
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.0635083	+	0.110000i	−0.0154030	+	0.0266788i	−0.873624	−	0.486601i	$-0.838236\pi$
$17$	−0.0635083	+	0.110000i	−0.0154030	+	0.0266788i	0.858221	+	0.513280i	$0.171570\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.87298	+	6.70820i	0.888523	+	1.53897i	0.841621	+	0.540068i	$0.181602\pi$
$19$	3.87298	+	6.70820i	0.888523	+	1.53897i	0.0469020	+	0.998899i	$0.485065\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−2.43649	+	4.22013i	−0.531686	+	0.920907i
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.00000			0.196116
$27$	1.00000			0.192450
$28$	−2.43649	+	4.22013i	−0.460454	+	0.797529i
$29$	3.87298			0.719195			0.359597	−	0.933108i	$-0.382914\pi$
$29$	3.87298			0.719195			0.359597	+	0.933108i	$0.382914\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	7.74597			1.39122			0.695608	−	0.718421i	$-0.255135\pi$
$31$	7.74597			1.39122			0.695608	+	0.718421i	$0.255135\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.50000	+	4.33013i	0.435194	+	0.753778i
$34$	0.0635083	+	0.110000i	0.0108916	+	0.0188648i
$35$	2.43649	−	4.22013i	0.411842	−	0.713332i
$36$	1.00000			0.166667
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$38$	7.74597			1.25656
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−0.436492	−	0.756026i	−0.0681685	−	0.118071i	0.829927	−	0.557873i	$-0.188382\pi$
$41$	−0.436492	−	0.756026i	−0.0681685	−	0.118071i	−0.898095	+	0.439801i	$0.855049\pi$
$42$	2.43649	+	4.22013i	0.375959	+	0.651180i
$43$	−9.74597			−1.48625			−0.743123	−	0.669155i	$-0.766656\pi$
$43$	−9.74597			−1.48625			−0.743123	+	0.669155i	$0.766656\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$	−1.00000			−0.149071
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−10.7460			−1.56746			−0.783730	−	0.621101i	$-0.786685\pi$
$47$	−10.7460			−1.56746			−0.783730	+	0.621101i	$0.786685\pi$
$48$	1.00000			0.144338
$49$	−8.37298	+	14.5024i	−1.19614	+	2.07178i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	0.127017			0.0177859
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−0.436492	+	0.756026i	−0.0599567	+	0.103848i	−0.894446	−	0.447176i	$-0.852430\pi$
$53$	−0.436492	+	0.756026i	−0.0599567	+	0.103848i	0.834489	+	0.551025i	$0.185763\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−2.50000	−	4.33013i	−0.337100	−	0.583874i
$56$	2.43649	+	4.22013i	0.325590	+	0.563938i
$57$	3.87298	−	6.70820i	0.512989	−	0.888523i
$58$	1.93649	−	3.35410i	0.254274	−	0.440415i
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	−0.981608	−	0.190909i	$-0.938857\pi$
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	0.656136	+	0.754643i	$0.272190\pi$
$60$	−1.00000			−0.129099
$61$	4.43649	+	7.68423i	0.568035	+	0.983865i	0.996760	+	0.0804300i	$0.0256293\pi$
$61$	4.43649	+	7.68423i	0.568035	+	0.983865i	−0.428726	+	0.903435i	$0.641037\pi$
$62$	3.87298	−	6.70820i	0.491869	−	0.851943i
$63$	4.87298			0.613938
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	5.00000			0.615457
$67$	−3.06351	−	5.30615i	−0.374267	−	0.648250i	0.615950	−	0.787785i	$-0.288772\pi$
$67$	−3.06351	−	5.30615i	−0.374267	−	0.648250i	−0.990217	+	0.139536i	$0.955439\pi$
$68$	0.127017			0.0154030
$69$	3.00000	+	5.19615i	0.361158	+	0.625543i
$70$	−2.43649	−	4.22013i	−0.291216	−	0.504402i
$71$	−7.30948	−	12.6604i	−0.867475	−	1.50251i	−0.864568	−	0.502515i	$-0.832408\pi$
$71$	−7.30948	−	12.6604i	−0.867475	−	1.50251i	−0.00290669	−	0.999996i	$-0.500925\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	12.0000			1.40449			0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000			1.40449			0.702247	+	0.711934i	$0.252180\pi$
$74$	−5.00000	+	3.46410i	−0.581238	+	0.402694i
$75$	1.00000			0.115470
$76$	3.87298	−	6.70820i	0.444262	−	0.769484i
$77$	12.1825	+	21.1006i	1.38832	+	2.40464i
$78$	−0.500000	−	0.866025i	−0.0566139	−	0.0980581i
$79$	−7.74597	−	13.4164i	−0.871489	−	1.50946i	−0.860456	−	0.509525i	$-0.829821\pi$
$79$	−7.74597	−	13.4164i	−0.871489	−	1.50946i	−0.0110333	−	0.999939i	$-0.503512\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.872983			−0.0964049
$83$	−1.43649	+	2.48808i	−0.157675	+	0.273102i	−0.934030	−	0.357195i	$-0.883733\pi$
$83$	−1.43649	+	2.48808i	−0.157675	+	0.273102i	0.776355	+	0.630296i	$0.217067\pi$
$84$	4.87298			0.531686
$85$	−0.127017			−0.0137769
$86$	−4.87298	+	8.44025i	−0.525467	+	0.910136i
$87$	−1.93649	−	3.35410i	−0.207614	−	0.359597i
$88$	5.00000			0.533002
$89$	−5.87298	+	10.1723i	−0.622535	+	1.07826i	0.366477	+	0.930427i	$0.380564\pi$
$89$	−5.87298	+	10.1723i	−0.622535	+	1.07826i	−0.989012	+	0.147835i	$0.952769\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	2.43649	−	4.22013i	0.255414	−	0.442390i
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$	−3.87298	−	6.70820i	−0.401610	−	0.695608i
$94$	−5.37298	+	9.30628i	−0.554181	+	0.959870i
$95$	−3.87298	+	6.70820i	−0.397360	+	0.688247i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$	8.37298	+	14.5024i	0.845799	+	1.46497i
$99$	2.50000	−	4.33013i	0.251259	−	0.435194i
$100$	1.00000			0.100000
$101$	−11.6190			−1.15613			−0.578064	−	0.815991i	$-0.696192\pi$
$101$	−11.6190			−1.15613			−0.578064	+	0.815991i	$0.696192\pi$
$102$	0.0635083	−	0.110000i	0.00628826	−	0.0108916i
$103$	14.8730			1.46548			0.732739	−	0.680509i	$-0.238241\pi$
$103$	14.8730			1.46548			0.732739	+	0.680509i	$0.238241\pi$
$104$	−0.500000	−	0.866025i	−0.0490290	−	0.0849208i
$105$	−4.87298			−0.475554
$106$	0.436492	+	0.756026i	0.0423958	+	0.0734317i
$107$	2.56351	+	4.44013i	0.247824	+	0.429243i	0.962922	−	0.269781i	$-0.0869513\pi$
$107$	2.56351	+	4.44013i	0.247824	+	0.429243i	−0.715098	+	0.699024i	$0.753618\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	2.30948	−	4.00013i	0.221208	−	0.383143i	−0.733967	−	0.679185i	$-0.762333\pi$
$109$	2.30948	−	4.00013i	0.221208	−	0.383143i	0.955175	+	0.296042i	$0.0956668\pi$
$110$	−5.00000			−0.476731
$111$	0.500000	+	6.06218i	0.0474579	+	0.575396i
$112$	4.87298			0.460454
$113$	7.80948	−	13.5264i	0.734654	−	1.27246i	−0.220222	−	0.975450i	$-0.570678\pi$
$113$	7.80948	−	13.5264i	0.734654	−	1.27246i	0.954875	−	0.297007i	$-0.0959886\pi$
$114$	−3.87298	−	6.70820i	−0.362738	−	0.628281i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	−1.93649	−	3.35410i	−0.179799	−	0.311421i
$117$	−1.00000			−0.0924500
$118$	2.50000	+	4.33013i	0.230144	+	0.398621i
$119$	0.618950			0.0567391
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	14.0000			1.27273
$122$	8.87298			0.803322
$123$	−0.436492	+	0.756026i	−0.0393571	+	0.0681685i
$124$	−3.87298	−	6.70820i	−0.347804	−	0.602414i
$125$	−1.00000			−0.0894427
$126$	2.43649	−	4.22013i	0.217060	−	0.375959i
$127$	−0.436492	+	0.756026i	−0.0387324	+	0.0670864i	−0.884742	−	0.466082i	$-0.845665\pi$
$127$	−0.436492	+	0.756026i	−0.0387324	+	0.0670864i	0.846009	+	0.533168i	$0.178999\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.87298	+	8.44025i	0.429042	+	0.743123i
$130$	0.500000	+	0.866025i	0.0438529	+	0.0759555i
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$	2.50000	−	4.33013i	0.217597	−	0.376889i
$133$	18.8730	−	32.6890i	1.63650	−	2.83449i
$134$	−6.12702			−0.529294
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	0.0635083	−	0.110000i	0.00544579	−	0.00943239i
$137$	−17.8730			−1.52699			−0.763496	−	0.645813i	$-0.776519\pi$
$137$	−17.8730			−1.52699			−0.763496	+	0.645813i	$0.776519\pi$
$138$	6.00000			0.510754
$139$	−4.87298	+	8.44025i	−0.413321	+	0.715893i	−0.995251	−	0.0973462i	$-0.968965\pi$
$139$	−4.87298	+	8.44025i	−0.413321	+	0.715893i	0.581930	+	0.813239i	$0.302298\pi$
$140$	−4.87298			−0.411842
$141$	5.37298	+	9.30628i	0.452487	+	0.783730i
$142$	−14.6190			−1.22680
$143$	−2.50000	−	4.33013i	−0.209061	−	0.362103i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.93649	+	3.35410i	0.160817	+	0.278543i
$146$	6.00000	−	10.3923i	0.496564	−	0.860073i
$147$	16.7460			1.38118
$148$	0.500000	+	6.06218i	0.0410997	+	0.498308i
$149$	−6.12702			−0.501945			−0.250972	−	0.967994i	$-0.580750\pi$
$149$	−6.12702			−0.501945			−0.250972	+	0.967994i	$0.580750\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	0.511636	−	0.859202i	$-0.329040\pi$
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	−0.999909	+	0.0134886i	$0.995706\pi$
$152$	−3.87298	−	6.70820i	−0.314140	−	0.544107i
$153$	−0.0635083	−	0.110000i	−0.00513434	−	0.00889294i
$154$	24.3649			1.96338
$155$	3.87298	+	6.70820i	0.311086	+	0.538816i
$156$	−1.00000			−0.0800641
$157$	3.37298	−	5.84218i	0.269193	−	0.466257i	−0.699460	−	0.714671i	$-0.746576\pi$
$157$	3.37298	−	5.84218i	0.269193	−	0.466257i	0.968654	+	0.248415i	$0.0799096\pi$
$158$	−15.4919			−1.23247
$159$	0.872983			0.0692321
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	14.6190	+	25.3208i	1.15213	+	1.99556i
$162$	−1.00000			−0.0785674
$163$	5.06351	−	8.77025i	0.396605	−	0.686939i	−0.596700	−	0.802464i	$-0.703522\pi$
$163$	5.06351	−	8.77025i	0.396605	−	0.686939i	0.993305	+	0.115525i	$0.0368551\pi$
$164$	−0.436492	+	0.756026i	−0.0340843	+	0.0590357i
$165$	−2.50000	+	4.33013i	−0.194625	+	0.337100i
$166$	1.43649	+	2.48808i	0.111493	+	0.193112i
$167$	−3.37298	−	5.84218i	−0.261009	−	0.452081i	0.705501	−	0.708709i	$-0.250722\pi$
$167$	−3.37298	−	5.84218i	−0.261009	−	0.452081i	−0.966510	+	0.256627i	$0.917389\pi$
$168$	2.43649	−	4.22013i	0.187979	−	0.325590i
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−0.0635083	+	0.110000i	−0.00487087	+	0.00843659i
$171$	−7.74597			−0.592349
$172$	4.87298	+	8.44025i	0.371561	+	0.643563i
$173$	3.30948	−	5.73218i	0.251615	−	0.435809i	−0.712356	−	0.701818i	$-0.752372\pi$
$173$	3.30948	−	5.73218i	0.251615	−	0.435809i	0.963971	+	0.266009i	$0.0857051\pi$
$174$	−3.87298			−0.293610
$175$	4.87298			0.368363
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$	5.00000			0.375823
$178$	5.87298	+	10.1723i	0.440199	+	0.762447i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$	−2.43649	−	4.22013i	−0.180605	−	0.312817i
$183$	4.43649	−	7.68423i	0.327955	−	0.568035i
$184$	6.00000			0.442326
$185$	−0.500000	−	6.06218i	−0.0367607	−	0.445700i
$186$	−7.74597			−0.567962
$187$	0.317542	−	0.549998i	0.0232209	−	0.0402199i
$188$	5.37298	+	9.30628i	0.391865	+	0.678730i
$189$	−2.43649	−	4.22013i	−0.177229	−	0.306969i
$190$	3.87298	+	6.70820i	0.280976	+	0.486664i
$191$	4.61895			0.334215			0.167108	−	0.985939i	$-0.446557\pi$
$191$	4.61895			0.334215			0.167108	+	0.985939i	$0.446557\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−16.6190			−1.19626			−0.598129	−	0.801400i	$-0.704089\pi$
$193$	−16.6190			−1.19626			−0.598129	+	0.801400i	$0.704089\pi$
$194$	−5.00000	+	8.66025i	−0.358979	+	0.621770i
$195$	1.00000			0.0716115
$196$	16.7460			1.19614
$197$	−13.8730	+	24.0287i	−0.988409	+	1.71197i	−0.362730	+	0.931894i	$0.618155\pi$
$197$	−13.8730	+	24.0287i	−0.988409	+	1.71197i	−0.625679	+	0.780081i	$0.715178\pi$
$198$	−2.50000	−	4.33013i	−0.177667	−	0.307729i
$199$	−21.8730			−1.55053			−0.775267	−	0.631633i	$-0.782385\pi$
$199$	−21.8730			−1.55053			−0.775267	+	0.631633i	$0.782385\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−3.06351	+	5.30615i	−0.216083	+	0.374267i
$202$	−5.80948	+	10.0623i	−0.408753	+	0.707981i
$203$	−9.43649	−	16.3445i	−0.662312	−	1.14716i
$204$	−0.0635083	−	0.110000i	−0.00444647	−	0.00770152i
$205$	0.436492	−	0.756026i	0.0304859	−	0.0528031i
$206$	7.43649	−	12.8804i	0.518125	−	0.897419i
$207$	3.00000	−	5.19615i	0.208514	−	0.361158i
$208$	−1.00000			−0.0693375
$209$	−19.3649	−	33.5410i	−1.33950	−	2.32008i
$210$	−2.43649	+	4.22013i	−0.168134	+	0.291216i
$211$	2.25403			0.155174			0.0775870	−	0.996986i	$-0.475278\pi$
$211$	2.25403			0.155174			0.0775870	+	0.996986i	$0.475278\pi$
$212$	0.872983			0.0599567
$213$	−7.30948	+	12.6604i	−0.500837	+	0.867475i
$214$	5.12702			0.350476
$215$	−4.87298	−	8.44025i	−0.332335	−	0.575621i
$216$	−1.00000			−0.0680414
$217$	−18.8730	−	32.6890i	−1.28118	−	2.21907i
$218$	−2.30948	−	4.00013i	−0.156417	−	0.270923i
$219$	−6.00000	−	10.3923i	−0.405442	−	0.702247i
$220$	−2.50000	+	4.33013i	−0.168550	+	0.291937i
$221$	−0.127017			−0.00854406
$222$	5.50000	+	2.59808i	0.369136	+	0.174371i
$223$	7.49193			0.501697			0.250848	−	0.968026i	$-0.419290\pi$
$223$	7.49193			0.501697			0.250848	+	0.968026i	$0.419290\pi$
$224$	2.43649	−	4.22013i	0.162795	−	0.281969i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−7.80948	−	13.5264i	−0.519479	−	0.899763i
$227$	7.18246	+	12.4404i	0.476717	+	0.825697i	0.999644	−	0.0266799i	$-0.00849350\pi$
$227$	7.18246	+	12.4404i	0.476717	+	0.825697i	−0.522928	+	0.852377i	$0.675160\pi$
$228$	−7.74597			−0.512989
$229$	−1.30948	−	2.26808i	−0.0865325	−	0.149879i	0.819511	−	0.573064i	$-0.194245\pi$
$229$	−1.30948	−	2.26808i	−0.0865325	−	0.149879i	−0.906043	+	0.423185i	$0.860912\pi$
$230$	−6.00000			−0.395628
$231$	12.1825	−	21.1006i	0.801547	−	1.38832i
$232$	−3.87298			−0.254274
$233$	−2.00000			−0.131024			−0.0655122	−	0.997852i	$-0.520868\pi$
$233$	−2.00000			−0.131024			−0.0655122	+	0.997852i	$0.520868\pi$
$234$	−0.500000	+	0.866025i	−0.0326860	+	0.0566139i
$235$	−5.37298	−	9.30628i	−0.350495	−	0.607075i
$236$	5.00000			0.325472
$237$	−7.74597	+	13.4164i	−0.503155	+	0.871489i
$238$	0.309475	−	0.536026i	0.0200603	−	0.0347454i
$239$	6.87298	−	11.9044i	0.444576	−	0.770029i	−0.553446	−	0.832885i	$-0.686688\pi$
$239$	6.87298	−	11.9044i	0.444576	−	0.770029i	0.998023	+	0.0628561i	$0.0200209\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−13.1190	−	22.7227i	−0.845066	−	1.46370i	−0.885564	−	0.464517i	$-0.846228\pi$
$241$	−13.1190	−	22.7227i	−0.845066	−	1.46370i	0.0404981	−	0.999180i	$-0.487106\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	4.43649	−	7.68423i	0.284017	−	0.491932i
$245$	−16.7460			−1.06986
$246$	0.436492	+	0.756026i	0.0278297	+	0.0482024i
$247$	−3.87298	+	6.70820i	−0.246432	+	0.426833i
$248$	−7.74597			−0.491869
$249$	2.87298			0.182068
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	30.4919			1.92463			0.962317	−	0.271931i	$-0.0876621\pi$
$251$	30.4919			1.92463			0.962317	+	0.271931i	$0.0876621\pi$
$252$	−2.43649	−	4.22013i	−0.153485	−	0.265843i
$253$	30.0000			1.88608
$254$	0.436492	+	0.756026i	0.0273879	+	0.0474373i
$255$	0.0635083	+	0.110000i	0.00397705	+	0.00688845i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.8095	−	20.4546i	0.736655	−	1.27592i	−0.217339	−	0.976096i	$-0.569738\pi$
$257$	11.8095	−	20.4546i	0.736655	−	1.27592i	0.953993	−	0.299827i	$-0.0969291\pi$
$258$	9.74597			0.606757
$259$	2.43649	+	29.5409i	0.151396	+	1.83558i
$260$	1.00000			0.0620174
$261$	−1.93649	+	3.35410i	−0.119866	+	0.207614i
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$	3.87298	+	6.70820i	0.238818	+	0.413646i	0.960376	−	0.278709i	$-0.0899066\pi$
$263$	3.87298	+	6.70820i	0.238818	+	0.413646i	−0.721557	+	0.692355i	$0.756573\pi$
$264$	−2.50000	−	4.33013i	−0.153864	−	0.266501i
$265$	−0.872983			−0.0536269
$266$	−18.8730	−	32.6890i	−1.15718	−	2.00429i
$267$	11.7460			0.718841
$268$	−3.06351	+	5.30615i	−0.187134	+	0.324125i
$269$	−7.74597			−0.472280			−0.236140	−	0.971719i	$-0.575882\pi$
$269$	−7.74597			−0.472280			−0.236140	+	0.971719i	$0.575882\pi$
$270$	1.00000			0.0608581
$271$	−5.06351	+	8.77025i	−0.307586	+	0.532755i	−0.977834	−	0.209383i	$-0.932855\pi$
$271$	−5.06351	+	8.77025i	−0.307586	+	0.532755i	0.670248	+	0.742138i	$0.266188\pi$
$272$	−0.0635083	−	0.110000i	−0.00385076	−	0.00666971i
$273$	−4.87298			−0.294926
$274$	−8.93649	+	15.4785i	−0.539873	+	0.935088i
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−15.1190	−	26.1868i	−0.908410	−	1.57341i	−0.816274	−	0.577665i	$-0.803964\pi$
$277$	−15.1190	−	26.1868i	−0.908410	−	1.57341i	−0.0921359	−	0.995746i	$-0.529369\pi$
$278$	4.87298	+	8.44025i	0.292262	+	0.506213i
$279$	−3.87298	+	6.70820i	−0.231869	+	0.401610i
$280$	−2.43649	+	4.22013i	−0.145608	+	0.252201i
$281$	−5.87298	+	10.1723i	−0.350353	+	0.606829i	−0.986311	−	0.164894i	$-0.947272\pi$
$281$	−5.87298	+	10.1723i	−0.350353	+	0.606829i	0.635958	+	0.771723i	$0.280605\pi$
$282$	10.7460			0.639913
$283$	0.936492	+	1.62205i	0.0556687	+	0.0964209i	0.892517	−	0.451014i	$-0.148938\pi$
$283$	0.936492	+	1.62205i	0.0556687	+	0.0964209i	−0.836848	+	0.547435i	$0.815604\pi$
$284$	−7.30948	+	12.6604i	−0.433738	+	0.751255i
$285$	7.74597			0.458831
$286$	−5.00000			−0.295656
$287$	−2.12702	+	3.68410i	−0.125554	+	0.217466i
$288$	−1.00000			−0.0589256
$289$	8.49193	+	14.7085i	0.499525	+	0.865204i
$290$	3.87298			0.227429
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	1.87298	+	3.24410i	0.109421	+	0.189522i	0.915536	−	0.402237i	$-0.131767\pi$
$293$	1.87298	+	3.24410i	0.109421	+	0.189522i	−0.806115	+	0.591759i	$0.798434\pi$
$294$	8.37298	−	14.5024i	0.488322	−	0.845799i
$295$	−5.00000			−0.291111
$296$	5.50000	+	2.59808i	0.319681	+	0.151010i
$297$	−5.00000			−0.290129
$298$	−3.06351	+	5.30615i	−0.177464	+	0.307377i
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	23.7460	+	41.1292i	1.36869	+	2.37065i
$302$	−12.0000			−0.690522
$303$	5.80948	+	10.0623i	0.333746	+	0.578064i
$304$	−7.74597			−0.444262
$305$	−4.43649	+	7.68423i	−0.254033	+	0.439998i
$306$	−0.127017			−0.00726106
$307$	7.74597			0.442086			0.221043	−	0.975264i	$-0.429054\pi$
$307$	7.74597			0.442086			0.221043	+	0.975264i	$0.429054\pi$
$308$	12.1825	−	21.1006i	0.694160	−	1.20232i
$309$	−7.43649	−	12.8804i	−0.423047	−	0.732739i
$310$	7.74597			0.439941
$311$	9.30948	−	16.1245i	0.527892	−	0.914336i	−0.471579	−	0.881824i	$-0.656316\pi$
$311$	9.30948	−	16.1245i	0.527892	−	0.914336i	0.999471	−	0.0325120i	$-0.0103507\pi$
$312$	−0.500000	+	0.866025i	−0.0283069	+	0.0490290i
$313$	2.12702	−	3.68410i	0.120226	−	0.208238i	−0.799631	−	0.600492i	$-0.794971\pi$
$313$	2.12702	−	3.68410i	0.120226	−	0.208238i	0.919857	+	0.392254i	$0.128305\pi$
$314$	−3.37298	−	5.84218i	−0.190348	−	0.329693i
$315$	2.43649	+	4.22013i	0.137281	+	0.237777i
$316$	−7.74597	+	13.4164i	−0.435745	+	0.754732i
$317$	−5.30948	+	9.19628i	−0.298210	+	0.516515i	−0.975726	−	0.218993i	$-0.929723\pi$
$317$	−5.30948	+	9.19628i	−0.298210	+	0.516515i	0.677517	+	0.735507i	$0.263056\pi$
$318$	0.436492	−	0.756026i	0.0244772	−	0.0423958i
$319$	−19.3649			−1.08423
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	2.56351	−	4.44013i	0.143081	−	0.247824i
$322$	29.2379			1.62936
$323$	−0.983867			−0.0547438
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.00000			−0.0554700
$326$	−5.06351	−	8.77025i	−0.280442	−	0.485739i
$327$	−4.61895			−0.255429
$328$	0.436492	+	0.756026i	0.0241012	+	0.0417445i
$329$	26.1825	+	45.3493i	1.44349	+	2.50019i
$330$	2.50000	+	4.33013i	0.137620	+	0.238366i
$331$	−5.43649	+	9.41628i	−0.298817	+	0.517566i	−0.975865	−	0.218373i	$-0.929925\pi$
$331$	−5.43649	+	9.41628i	−0.298817	+	0.517566i	0.677049	+	0.735938i	$0.263259\pi$
$332$	2.87298			0.157675
$333$	5.00000	−	3.46410i	0.273998	−	0.189832i
$334$	−6.74597			−0.369123
$335$	3.06351	−	5.30615i	0.167377	−	0.289906i
$336$	−2.43649	−	4.22013i	−0.132922	−	0.230227i
$337$	1.69052	+	2.92808i	0.0920888	+	0.159502i	0.908390	−	0.418124i	$-0.137312\pi$
$337$	1.69052	+	2.92808i	0.0920888	+	0.159502i	−0.816301	+	0.577627i	$0.803979\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	−15.6190			−0.848305
$340$	0.0635083	+	0.110000i	0.00344422	+	0.00596557i
$341$	−38.7298			−2.09734
$342$	−3.87298	+	6.70820i	−0.209427	+	0.362738i
$343$	47.4919			2.56432
$344$	9.74597			0.525467
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$	−3.30948	−	5.73218i	−0.177918	−	0.308164i
$347$	9.49193			0.509554			0.254777	−	0.967000i	$-0.417998\pi$
$347$	9.49193			0.509554			0.254777	+	0.967000i	$0.417998\pi$
$348$	−1.93649	+	3.35410i	−0.103807	+	0.179799i
$349$	15.4919	−	26.8328i	0.829264	−	1.43633i	−0.0693521	−	0.997592i	$-0.522093\pi$
$349$	15.4919	−	26.8328i	0.829264	−	1.43633i	0.898616	−	0.438735i	$-0.144573\pi$
$350$	2.43649	−	4.22013i	0.130236	−	0.225575i
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	−5.00000	+	8.66025i	−0.266123	+	0.460939i	−0.967857	−	0.251500i	$-0.919076\pi$
$353$	−5.00000	+	8.66025i	−0.266123	+	0.460939i	0.701734	+	0.712439i	$0.252409\pi$
$354$	2.50000	−	4.33013i	0.132874	−	0.230144i
$355$	7.30948	−	12.6604i	0.387947	−	0.671943i
$356$	11.7460			0.622535
$357$	−0.309475	−	0.536026i	−0.0163792	−	0.0283695i
$358$	−5.00000	+	8.66025i	−0.264258	+	0.457709i
$359$	−4.25403			−0.224519			−0.112260	−	0.993679i	$-0.535809\pi$
$359$	−4.25403			−0.224519			−0.112260	+	0.993679i	$0.535809\pi$
$360$	1.00000			0.0527046
$361$	−20.5000	+	35.5070i	−1.07895	+	1.86879i
$362$	−2.00000			−0.105118
$363$	−7.00000	−	12.1244i	−0.367405	−	0.636364i
$364$	−4.87298			−0.255414
$365$	6.00000	+	10.3923i	0.314054	+	0.543958i
$366$	−4.43649	−	7.68423i	−0.231899	−	0.401661i
$367$	−1.12702	−	1.95205i	−0.0588298	−	0.101896i	0.835111	−	0.550082i	$-0.185404\pi$
$367$	−1.12702	−	1.95205i	−0.0588298	−	0.101896i	−0.893940	+	0.448186i	$0.852070\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$	0.872983			0.0454457
$370$	−5.50000	−	2.59808i	−0.285931	−	0.135068i
$371$	4.25403			0.220858
$372$	−3.87298	+	6.70820i	−0.200805	+	0.347804i
$373$	2.87298	+	4.97615i	0.148757	+	0.257655i	0.930768	−	0.365609i	$-0.119139\pi$
$373$	2.87298	+	4.97615i	0.148757	+	0.257655i	−0.782011	+	0.623265i	$0.785806\pi$
$374$	−0.317542	−	0.549998i	−0.0164197	−	0.0284397i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	10.7460			0.554181
$377$	1.93649	+	3.35410i	0.0997344	+	0.172745i
$378$	−4.87298			−0.250639
$379$	5.30948	−	9.19628i	0.272729	−	0.472381i	−0.696830	−	0.717236i	$-0.745407\pi$
$379$	5.30948	−	9.19628i	0.272729	−	0.472381i	0.969560	+	0.244855i	$0.0787403\pi$
$380$	7.74597			0.397360
$381$	0.872983			0.0447243
$382$	2.30948	−	4.00013i	0.118163	−	0.204664i
$383$	−2.37298	−	4.11013i	−0.121254	−	0.210018i	0.799009	−	0.601320i	$-0.205358\pi$
$383$	−2.37298	−	4.11013i	−0.121254	−	0.210018i	−0.920262	+	0.391302i	$0.872025\pi$
$384$	−1.00000			−0.0510310
$385$	−12.1825	+	21.1006i	−0.620876	+	1.07539i
$386$	−8.30948	+	14.3924i	−0.422941	+	0.732556i
$387$	4.87298	−	8.44025i	0.247708	−	0.429042i
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	−5.87298	−	10.1723i	−0.297772	−	0.515756i	0.677854	−	0.735197i	$-0.262910\pi$
$389$	−5.87298	−	10.1723i	−0.297772	−	0.515756i	−0.975626	+	0.219440i	$0.929577\pi$
$390$	0.500000	−	0.866025i	0.0253185	−	0.0438529i
$391$	0.381050	−	0.659998i	0.0192705	−	0.0333775i
$392$	8.37298	−	14.5024i	0.422900	−	0.732483i
$393$	1.00000			0.0504433
$394$	13.8730	+	24.0287i	0.698911	+	1.21055i
$395$	7.74597	−	13.4164i	0.389742	−	0.675053i
$396$	−5.00000			−0.251259
$397$	26.2379			1.31684			0.658421	−	0.752650i	$-0.271225\pi$
$397$	26.2379			1.31684			0.658421	+	0.752650i	$0.271225\pi$
$398$	−10.9365	+	18.9426i	−0.548197	+	0.949505i
$399$	−37.7460			−1.88966
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	2.61895			0.130784			0.0653921	−	0.997860i	$-0.479170\pi$
$401$	2.61895			0.130784			0.0653921	+	0.997860i	$0.479170\pi$
$402$	3.06351	+	5.30615i	0.152794	+	0.264647i
$403$	3.87298	+	6.70820i	0.192927	+	0.334159i
$404$	5.80948	+	10.0623i	0.289032	+	0.500618i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	−18.8730			−0.936650
$407$	27.5000	+	12.9904i	1.36312	+	0.643909i
$408$	−0.127017			−0.00628826
$409$	7.11895	−	12.3304i	0.352009	−	0.609698i	−0.634592	−	0.772847i	$-0.718832\pi$
$409$	7.11895	−	12.3304i	0.352009	−	0.609698i	0.986601	+	0.163149i	$0.0521652\pi$
$410$	−0.436492	−	0.756026i	−0.0215568	−	0.0373375i
$411$	8.93649	+	15.4785i	0.440805	+	0.763496i
$412$	−7.43649	−	12.8804i	−0.366370	−	0.634571i
$413$	24.3649			1.19892
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$	−2.87298			−0.141029
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	9.74597			0.477262
$418$	−38.7298			−1.89434
$419$	−7.00000	+	12.1244i	−0.341972	+	0.592314i	−0.984799	−	0.173698i	$-0.944428\pi$
$419$	−7.00000	+	12.1244i	−0.341972	+	0.592314i	0.642827	+	0.766012i	$0.277762\pi$
$420$	2.43649	+	4.22013i	0.118889	+	0.205921i
$421$	14.6190			0.712484			0.356242	−	0.934394i	$-0.384058\pi$
$421$	14.6190			0.712484			0.356242	+	0.934394i	$0.384058\pi$
$422$	1.12702	−	1.95205i	0.0548623	−	0.0950243i
$423$	5.37298	−	9.30628i	0.261243	−	0.452487i
$424$	0.436492	−	0.756026i	0.0211979	−	0.0367159i
$425$	−0.0635083	−	0.110000i	−0.00308061	−	0.00533577i
$426$	7.30948	+	12.6604i	0.354145	+	0.613398i
$427$	21.6190	−	37.4451i	1.04621	−	1.81210i
$428$	2.56351	−	4.44013i	0.123912	−	0.214622i
$429$	−2.50000	+	4.33013i	−0.120701	+	0.209061i
$430$	−9.74597			−0.469992
$431$	2.18246	+	3.78013i	0.105125	+	0.182082i	0.913789	−	0.406188i	$-0.133142\pi$
$431$	2.18246	+	3.78013i	0.105125	+	0.182082i	−0.808664	+	0.588271i	$0.799809\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−3.49193			−0.167812			−0.0839058	−	0.996474i	$-0.526739\pi$
$433$	−3.49193			−0.167812			−0.0839058	+	0.996474i	$0.526739\pi$
$434$	−37.7460			−1.81186
$435$	1.93649	−	3.35410i	0.0928477	−	0.160817i
$436$	−4.61895			−0.221208
$437$	−23.2379	−	40.2492i	−1.11162	−	1.92538i
$438$	−12.0000			−0.573382
$439$	15.6825	+	27.1628i	0.748483	+	1.29641i	0.948550	+	0.316628i	$0.102551\pi$
$439$	15.6825	+	27.1628i	0.748483	+	1.29641i	−0.200067	+	0.979782i	$0.564116\pi$
$440$	2.50000	+	4.33013i	0.119183	+	0.206431i
$441$	−8.37298	−	14.5024i	−0.398713	−	0.690592i
$442$	−0.0635083	+	0.110000i	−0.00302078	+	0.00523215i
$443$	−38.3649			−1.82277			−0.911386	−	0.411552i	$-0.864987\pi$
$443$	−38.3649			−1.82277			−0.911386	+	0.411552i	$0.864987\pi$
$444$	5.00000	−	3.46410i	0.237289	−	0.164399i
$445$	−11.7460			−0.556812
$446$	3.74597	−	6.48820i	0.177377	−	0.307225i
$447$	3.06351	+	5.30615i	0.144899	+	0.250972i
$448$	−2.43649	−	4.22013i	−0.115113	−	0.199382i
$449$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$449$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$450$	−1.00000			−0.0471405
$451$	2.18246	+	3.78013i	0.102768	+	0.177999i
$452$	−15.6190			−0.734654
$453$	−6.00000	+	10.3923i	−0.281905	+	0.488273i
$454$	14.3649			0.674179
$455$	4.87298			0.228449
$456$	−3.87298	+	6.70820i	−0.181369	+	0.314140i
$457$	3.12702	+	5.41615i	0.146276	+	0.253357i	0.929848	−	0.367943i	$-0.119938\pi$
$457$	3.12702	+	5.41615i	0.146276	+	0.253357i	−0.783572	+	0.621300i	$0.786605\pi$
$458$	−2.61895			−0.122375
$459$	−0.0635083	+	0.110000i	−0.00296431	+	0.00513434i
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$	10.8095	−	18.7226i	0.503447	−	0.871997i	−0.496545	−	0.868011i	$-0.665398\pi$
$461$	10.8095	−	18.7226i	0.503447	−	0.871997i	0.999992	−	0.00398535i	$-0.00126858\pi$
$462$	−12.1825	−	21.1006i	−0.566779	−	0.981690i
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	0.999916	+	0.0129968i	$0.00413714\pi$
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	−0.488702	+	0.872451i	$0.662530\pi$
$464$	−1.93649	+	3.35410i	−0.0898994	+	0.155710i
$465$	3.87298	−	6.70820i	0.179605	−	0.311086i
$466$	−1.00000	+	1.73205i	−0.0463241	+	0.0802357i
$467$	16.2540			0.752147			0.376073	−	0.926590i	$-0.377274\pi$
$467$	16.2540			0.752147			0.376073	+	0.926590i	$0.377274\pi$
$468$	0.500000	+	0.866025i	0.0231125	+	0.0400320i
$469$	−14.9284	+	25.8568i	−0.689331	+	1.19396i
$470$	−10.7460			−0.495674
$471$	−6.74597			−0.310838
$472$	2.50000	−	4.33013i	0.115072	−	0.199310i
$473$	48.7298			2.24060
$474$	7.74597	+	13.4164i	0.355784	+	0.616236i
$475$	−7.74597			−0.355409
$476$	−0.309475	−	0.536026i	−0.0141848	−	0.0245687i
$477$	−0.436492	−	0.756026i	−0.0199856	−	0.0346160i
$478$	−6.87298	−	11.9044i	−0.314363	−	0.544493i
$479$	−12.4919	+	21.6367i	−0.570771	+	0.988604i	0.425716	+	0.904857i	$0.360022\pi$
$479$	−12.4919	+	21.6367i	−0.570771	+	0.988604i	−0.996487	+	0.0837475i	$0.973311\pi$
$480$	1.00000			0.0456435
$481$	−0.500000	−	6.06218i	−0.0227980	−	0.276412i
$482$	−26.2379			−1.19510
$483$	14.6190	−	25.3208i	0.665185	−	1.15213i
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	15.7460			0.713518			0.356759	−	0.934196i	$-0.383882\pi$
$487$	15.7460			0.713518			0.356759	+	0.934196i	$0.383882\pi$
$488$	−4.43649	−	7.68423i	−0.200831	−	0.347849i
$489$	−10.1270			−0.457960
$490$	−8.37298	+	14.5024i	−0.378253	+	0.655153i
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$	0.872983			0.0393571
$493$	−0.245967	+	0.426027i	−0.0110778	+	0.0191873i
$494$	3.87298	+	6.70820i	0.174254	+	0.301816i
$495$	5.00000			0.224733
$496$	−3.87298	+	6.70820i	−0.173902	+	0.301207i
$497$	−35.6190	+	61.6938i	−1.59773	+	2.76735i
$498$	1.43649	−	2.48808i	0.0643707	−	0.111493i
$499$	−14.0554	−	24.3447i	−0.629208	−	1.08982i	−0.987711	−	0.156292i	$-0.950046\pi$
$499$	−14.0554	−	24.3447i	−0.629208	−	1.08982i	0.358503	−	0.933529i	$-0.383287\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−3.37298	+	5.84218i	−0.150694	+	0.261009i
$502$	15.2460	−	26.4068i	0.680461	−	1.17859i
$503$	−9.11895	+	15.7945i	−0.406594	+	0.704241i	−0.994506	−	0.104684i	$-0.966617\pi$
$503$	−9.11895	+	15.7945i	−0.406594	+	0.704241i	0.587912	+	0.808925i	$0.299950\pi$
$504$	−4.87298			−0.217060
$505$	−5.80948	−	10.0623i	−0.258518	−	0.447767i
$506$	15.0000	−	25.9808i	0.666831	−	1.15499i
$507$	−12.0000			−0.532939
$508$	0.872983			0.0387324
$509$	−21.4919	+	37.2251i	−0.952613	+	1.64997i	−0.212875	+	0.977079i	$0.568283\pi$
$509$	−21.4919	+	37.2251i	−0.952613	+	1.64997i	−0.739738	+	0.672895i	$0.765051\pi$
$510$	0.127017			0.00562439
$511$	−29.2379	−	50.6415i	−1.29341	−	2.24025i
$512$	−1.00000			−0.0441942
$513$	3.87298	+	6.70820i	0.170996	+	0.296174i
$514$	−11.8095	−	20.4546i	−0.520894	−	0.902214i
$515$	7.43649	+	12.8804i	0.327691	+	0.567577i
$516$	4.87298	−	8.44025i	0.214521	−	0.371561i
$517$	53.7298			2.36304
$518$	26.8014	+	12.6604i	1.17759	+	0.556265i
$519$	−6.61895			−0.290540
$520$	0.500000	−	0.866025i	0.0219265	−	0.0379777i
$521$	−11.1270	−	19.2726i	−0.487483	−	0.844346i	0.512413	−	0.858739i	$-0.328752\pi$
$521$	−11.1270	−	19.2726i	−0.487483	−	0.844346i	−0.999896	+	0.0143931i	$0.995418\pi$
$522$	1.93649	+	3.35410i	0.0847579	+	0.146805i
$523$	−20.6190	−	35.7131i	−0.901604	−	1.56162i	−0.825412	−	0.564530i	$-0.809057\pi$
$523$	−20.6190	−	35.7131i	−0.901604	−	1.56162i	−0.0761914	−	0.997093i	$-0.524276\pi$
$524$	1.00000			0.0436852
$525$	−2.43649	−	4.22013i	−0.106337	−	0.184181i
$526$	7.74597			0.337740
$527$	−0.491933	+	0.852054i	−0.0214290	+	0.0371160i
$528$	−5.00000			−0.217597
$529$	13.0000			0.565217
$530$	−0.436492	+	0.756026i	−0.0189600	+	0.0328397i
$531$	−2.50000	−	4.33013i	−0.108491	−	0.187912i
$532$	−37.7460			−1.63650
$533$	0.436492	−	0.756026i	0.0189066	−	0.0327471i
$534$	5.87298	−	10.1723i	0.254149	−	0.440199i
$535$	−2.56351	+	4.44013i	−0.110830	+	0.191963i
$536$	3.06351	+	5.30615i	0.132323	+	0.229191i
$537$	5.00000	+	8.66025i	0.215766	+	0.373718i
$538$	−3.87298	+	6.70820i	−0.166976	+	0.289211i
$539$	41.8649	−	72.5122i	1.80325	−	3.12332i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	34.6190			1.48838			0.744192	−	0.667965i	$-0.232835\pi$
$541$	34.6190			1.48838			0.744192	+	0.667965i	$0.232835\pi$
$542$	5.06351	+	8.77025i	0.217496	+	0.376715i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	−0.127017			−0.00544579
$545$	4.61895			0.197854
$546$	−2.43649	+	4.22013i	−0.104272	+	0.180605i
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	8.93649	+	15.4785i	0.381748	+	0.661207i
$549$	−8.87298			−0.378690
$550$	−2.50000	−	4.33013i	−0.106600	−	0.184637i
$551$	15.0000	+	25.9808i	0.639021	+	1.10682i
$552$	−3.00000	−	5.19615i	−0.127688	−	0.221163i
$553$	−37.7460	+	65.3779i	−1.60512	+	2.78015i
$554$	−30.2379			−1.28469
$555$	−5.00000	+	3.46410i	−0.212238	+	0.147043i
$556$	9.74597			0.413321
$557$	4.74597	−	8.22026i	0.201093	−	0.348303i	−0.747788	−	0.663938i	$-0.768884\pi$
$557$	4.74597	−	8.22026i	0.201093	−	0.348303i	0.948881	+	0.315634i	$0.102217\pi$
$558$	3.87298	+	6.70820i	0.163956	+	0.283981i
$559$	−4.87298	−	8.44025i	−0.206105	−	0.356985i
$560$	2.43649	+	4.22013i	0.102961	+	0.178333i
$561$	−0.635083			−0.0268132
$562$	5.87298	+	10.1723i	0.247737	+	0.429093i
$563$	−32.8730			−1.38543			−0.692716	−	0.721211i	$-0.743586\pi$
$563$	−32.8730			−1.38543			−0.692716	+	0.721211i	$0.743586\pi$
$564$	5.37298	−	9.30628i	0.226243	−	0.391865i
$565$	15.6190			0.657094
$566$	1.87298			0.0787274
$567$	−2.43649	+	4.22013i	−0.102323	+	0.177229i
$568$	7.30948	+	12.6604i	0.306699	+	0.531218i
$569$	−13.3810			−0.560963			−0.280481	−	0.959859i	$-0.590494\pi$
$569$	−13.3810			−0.560963			−0.280481	+	0.959859i	$0.590494\pi$
$570$	3.87298	−	6.70820i	0.162221	−	0.280976i
$571$	−5.25403	+	9.10025i	−0.219874	+	0.380834i	−0.954769	−	0.297347i	$-0.903898\pi$
$571$	−5.25403	+	9.10025i	−0.219874	+	0.380834i	0.734895	+	0.678181i	$0.237231\pi$
$572$	−2.50000	+	4.33013i	−0.104530	+	0.181052i
$573$	−2.30948	−	4.00013i	−0.0964797	−	0.167108i
$574$	2.12702	+	3.68410i	0.0887800	+	0.153771i
$575$	3.00000	−	5.19615i	0.125109	−	0.216695i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−19.9284	+	34.5170i	−0.829631	+	1.43696i	0.0686966	+	0.997638i	$0.478116\pi$
$577$	−19.9284	+	34.5170i	−0.829631	+	1.43696i	−0.898328	+	0.439326i	$0.855217\pi$
$578$	16.9839			0.706436
$579$	8.30948	+	14.3924i	0.345330	+	0.598129i
$580$	1.93649	−	3.35410i	0.0804084	−	0.139272i
$581$	14.0000			0.580818
$582$	10.0000			0.414513
$583$	2.18246	−	3.78013i	0.0903882	−	0.156557i
$584$	−12.0000			−0.496564
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$	3.74597			0.154744
$587$	8.56351	+	14.8324i	0.353454	+	0.612200i	0.986852	−	0.161626i	$-0.0516738\pi$
$587$	8.56351	+	14.8324i	0.353454	+	0.612200i	−0.633398	+	0.773826i	$0.718340\pi$
$588$	−8.37298	−	14.5024i	−0.345296	−	0.598070i
$589$	30.0000	+	51.9615i	1.23613	+	2.14104i
$590$	−2.50000	+	4.33013i	−0.102923	+	0.178269i
$591$	27.7460			1.14132
$592$	5.00000	−	3.46410i	0.205499	−	0.142374i
$593$	33.1109			1.35970			0.679851	−	0.733351i	$-0.262045\pi$
$593$	33.1109			1.35970			0.679851	+	0.733351i	$0.262045\pi$
$594$	−2.50000	+	4.33013i	−0.102576	+	0.177667i
$595$	0.309475	+	0.536026i	0.0126872	+	0.0219749i
$596$	3.06351	+	5.30615i	0.125486	+	0.217348i
$597$	10.9365	+	18.9426i	0.447601	+	0.775267i
$598$	−6.00000			−0.245358
$599$	−10.9284	−	18.9286i	−0.446523	−	0.773401i	0.551634	−	0.834087i	$-0.314005\pi$
$599$	−10.9284	−	18.9286i	−0.446523	−	0.773401i	−0.998157	+	0.0606854i	$0.980671\pi$
$600$	−1.00000			−0.0408248
$601$	−8.99193	+	15.5745i	−0.366789	+	0.635297i	−0.989061	−	0.147504i	$-0.952876\pi$
$601$	−8.99193	+	15.5745i	−0.366789	+	0.635297i	0.622273	+	0.782800i	$0.286209\pi$
$602$	47.4919			1.93563
$603$	6.12702			0.249511
$604$	−6.00000	+	10.3923i	−0.244137	+	0.422857i
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$	11.6190			0.471988
$607$	−21.0000	+	36.3731i	−0.852364	+	1.47634i	0.0267056	+	0.999643i	$0.491498\pi$
$607$	−21.0000	+	36.3731i	−0.852364	+	1.47634i	−0.879069	+	0.476694i	$0.841835\pi$
$608$	−3.87298	+	6.70820i	−0.157070	+	0.272054i
$609$	−9.43649	+	16.3445i	−0.382386	+	0.662312i
$610$	4.43649	+	7.68423i	0.179628	+	0.311125i
$611$	−5.37298	−	9.30628i	−0.217368	−	0.376492i
$612$	−0.0635083	+	0.110000i	−0.00256717	+	0.00444647i
$613$	−4.37298	+	7.57423i	−0.176623	+	0.305920i	−0.940722	−	0.339179i	$-0.889851\pi$
$613$	−4.37298	+	7.57423i	−0.176623	+	0.305920i	0.764099	+	0.645099i	$0.223184\pi$
$614$	3.87298	−	6.70820i	0.156301	−	0.270721i
$615$	−0.872983			−0.0352021
$616$	−12.1825	−	21.1006i	−0.490845	−	0.850169i
$617$	11.6825	−	20.2346i	0.470318	−	0.814615i	−0.529106	−	0.848556i	$-0.677473\pi$
$617$	11.6825	−	20.2346i	0.470318	−	0.814615i	0.999424	+	0.0339411i	$0.0108059\pi$
$618$	−14.8730			−0.598279
$619$	−7.12702			−0.286459			−0.143229	−	0.989690i	$-0.545749\pi$
$619$	−7.12702			−0.286459			−0.143229	+	0.989690i	$0.545749\pi$
$620$	3.87298	−	6.70820i	0.155543	−	0.269408i
$621$	−6.00000			−0.240772
$622$	−9.30948	−	16.1245i	−0.373276	−	0.646533i
$623$	57.2379			2.29319
$624$	0.500000	+	0.866025i	0.0200160	+	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.12702	−	3.68410i	−0.0850127	−	0.147246i
$627$	−19.3649	+	33.5410i	−0.773360	+	1.33950i
$628$	−6.74597			−0.269193
$629$	0.635083	−	0.439999i	0.0253224	−	0.0175439i
$630$	4.87298			0.194144
$631$	−19.6825	+	34.0910i	−0.783546	+	1.35714i	0.146317	+	0.989238i	$0.453258\pi$
$631$	−19.6825	+	34.0910i	−0.783546	+	1.35714i	−0.929864	+	0.367904i	$0.880075\pi$
$632$	7.74597	+	13.4164i	0.308118	+	0.533676i
$633$	−1.12702	−	1.95205i	−0.0447949	−	0.0775870i
$634$	5.30948	+	9.19628i	0.210866	+	0.365231i
$635$	−0.872983			−0.0346433
$636$	−0.436492	−	0.756026i	−0.0173080	−	0.0299784i
$637$	−16.7460			−0.663499
$638$	−9.68246	+	16.7705i	−0.383332	+	0.663951i
$639$	14.6190			0.578317
$640$	1.00000			0.0395285
$641$	−14.5635	+	25.2247i	−0.575224	+	0.996317i	0.420793	+	0.907157i	$0.361752\pi$
$641$	−14.5635	+	25.2247i	−0.575224	+	0.996317i	−0.996017	+	0.0891606i	$0.971582\pi$
$642$	−2.56351	−	4.44013i	−0.101174	−	0.175238i
$643$	1.61895			0.0638452			0.0319226	−	0.999490i	$-0.489837\pi$
$643$	1.61895			0.0638452			0.0319226	+	0.999490i	$0.489837\pi$
$644$	14.6190	−	25.3208i	0.576067	−	0.997778i
$645$	−4.87298	+	8.44025i	−0.191874	+	0.332335i
$646$	−0.491933	+	0.852054i	−0.0193549	+	0.0335236i
$647$	19.1190	+	33.1150i	0.751643	+	1.30188i	0.947026	+	0.321158i	$0.104072\pi$
$647$	19.1190	+	33.1150i	0.751643	+	1.30188i	−0.195382	+	0.980727i	$0.562595\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	12.5000	−	21.6506i	0.490668	−	0.849862i
$650$	−0.500000	+	0.866025i	−0.0196116	+	0.0339683i
$651$	−18.8730	+	32.6890i	−0.739691	+	1.28118i
$652$	−10.1270			−0.396605
$653$	−8.61895	−	14.9285i	−0.337286	−	0.584196i	0.646636	−	0.762799i	$-0.276175\pi$
$653$	−8.61895	−	14.9285i	−0.337286	−	0.584196i	−0.983921	+	0.178603i	$0.942842\pi$
$654$	−2.30948	+	4.00013i	−0.0903076	+	0.156417i
$655$	−1.00000			−0.0390732
$656$	0.872983			0.0340843
$657$	−6.00000	+	10.3923i	−0.234082	+	0.405442i
$658$	52.3649			2.04140
$659$	−1.75403	−	3.03807i	−0.0683274	−	0.118347i	0.829838	−	0.558005i	$-0.188433\pi$
$659$	−1.75403	−	3.03807i	−0.0683274	−	0.118347i	−0.898165	+	0.439658i	$0.855100\pi$
$660$	5.00000			0.194625
$661$	4.87298	+	8.44025i	0.189537	+	0.328288i	0.945096	−	0.326793i	$-0.105968\pi$
$661$	4.87298	+	8.44025i	0.189537	+	0.328288i	−0.755559	+	0.655081i	$0.772635\pi$
$662$	5.43649	+	9.41628i	0.211295	+	0.365974i
$663$	0.0635083	+	0.110000i	0.00246646	+	0.00427203i
$664$	1.43649	−	2.48808i	0.0557467	−	0.0965561i
$665$	37.7460			1.46373
$666$	−0.500000	−	6.06218i	−0.0193746	−	0.234905i
$667$	−23.2379			−0.899775
$668$	−3.37298	+	5.84218i	−0.130505	+	0.226041i
$669$	−3.74597	−	6.48820i	−0.144827	−	0.250848i
$670$	−3.06351	−	5.30615i	−0.118354	−	0.204995i
$671$	−22.1825	−	38.4211i	−0.856344	−	1.48323i
$672$	−4.87298			−0.187979
$673$	−4.56351	−	7.90423i	−0.175910	−	0.304686i	0.764566	−	0.644546i	$-0.222954\pi$
$673$	−4.56351	−	7.90423i	−0.175910	−	0.304686i	−0.940476	+	0.339860i	$0.889620\pi$
$674$	3.38105			0.130233
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−12.0000			−0.461538
$677$	6.87298			0.264150			0.132075	−	0.991240i	$-0.457836\pi$
$677$	6.87298			0.264150			0.132075	+	0.991240i	$0.457836\pi$
$678$	−7.80948	+	13.5264i	−0.299921	+	0.519479i
$679$	24.3649	+	42.2013i	0.935040	+	1.61954i
$680$	0.127017			0.00487087
$681$	7.18246	−	12.4404i	0.275232	−	0.476717i
$682$	−19.3649	+	33.5410i	−0.741521	+	1.28435i
$683$	−5.61895	+	9.73231i	−0.215003	+	0.372396i	−0.953274	−	0.302108i	$-0.902310\pi$
$683$	−5.61895	+	9.73231i	−0.215003	+	0.372396i	0.738270	+	0.674505i	$0.235643\pi$
$684$	3.87298	+	6.70820i	0.148087	+	0.256495i
$685$	−8.93649	−	15.4785i	−0.341446	−	0.591401i
$686$	23.7460	−	41.1292i	0.906625	−	1.57032i
$687$	−1.30948	+	2.26808i	−0.0499596	+	0.0865325i
$688$	4.87298	−	8.44025i	0.185781	−	0.321782i
$689$	−0.872983			−0.0332580
$690$	3.00000	+	5.19615i	0.114208	+	0.197814i
$691$	−6.12702	+	10.6123i	−0.233083	+	0.403711i	−0.958714	−	0.284373i	$-0.908215\pi$
$691$	−6.12702	+	10.6123i	−0.233083	+	0.403711i	0.725631	+	0.688084i	$0.241548\pi$
$692$	−6.61895			−0.251615
$693$	−24.3649			−0.925547
$694$	4.74597	−	8.22026i	0.180154	−	0.312037i
$695$	−9.74597			−0.369686
$696$	1.93649	+	3.35410i	0.0734025	+	0.127137i
$697$	0.110883			0.00420001
$698$	−15.4919	−	26.8328i	−0.586378	−	1.01564i
$699$	1.00000	+	1.73205i	0.0378235	+	0.0655122i
$700$	−2.43649	−	4.22013i	−0.0920907	−	0.159506i
$701$	12.6825	−	21.9667i	0.479010	−	0.829669i	−0.520700	−	0.853739i	$-0.674329\pi$
$701$	12.6825	−	21.9667i	0.479010	−	0.829669i	0.999710	+	0.0240701i	$0.00766248\pi$
$702$	1.00000			0.0377426
$703$	−3.87298	−	46.9574i	−0.146072	−	1.77103i
$704$	−5.00000			−0.188445
$705$	−5.37298	+	9.30628i	−0.202358	+	0.350495i
$706$	5.00000	+	8.66025i	0.188177	+	0.325933i
$707$	28.3095	+	49.0334i	1.06469	+	1.84409i
$708$	−2.50000	−	4.33013i	−0.0939558	−	0.162736i
$709$	28.8730			1.08435			0.542174	−	0.840266i	$-0.317601\pi$
$709$	28.8730			1.08435			0.542174	+	0.840266i	$0.317601\pi$
$710$	−7.30948	−	12.6604i	−0.274320	−	0.475136i
$711$	15.4919			0.580993
$712$	5.87298	−	10.1723i	0.220099	−	0.381223i
$713$	−46.4758			−1.74053
$714$	−0.618950			−0.0231636
$715$	2.50000	−	4.33013i	0.0934947	−	0.161938i
$716$	5.00000	+	8.66025i	0.186859	+	0.323649i
$717$	−13.7460			−0.513353
$718$	−2.12702	+	3.68410i	−0.0793796	+	0.137489i
$719$	22.9284	−	39.7132i	0.855086	−	1.48105i	−0.0214793	−	0.999769i	$-0.506838\pi$
$719$	22.9284	−	39.7132i	0.855086	−	1.48105i	0.876565	−	0.481283i	$-0.159829\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$	−36.2379	−	62.7659i	−1.34957	−	2.33752i
$722$	20.5000	+	35.5070i	0.762931	+	1.32144i
$723$	−13.1190	+	22.7227i	−0.487899	+	0.845066i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−1.93649	+	3.35410i	−0.0719195	+	0.124568i
$726$	−14.0000			−0.519589
$727$	2.61895	+	4.53615i	0.0971315	+	0.168237i	0.910496	−	0.413517i	$-0.135700\pi$
$727$	2.61895	+	4.53615i	0.0971315	+	0.168237i	−0.813365	+	0.581754i	$0.802367\pi$
$728$	−2.43649	+	4.22013i	−0.0903024	+	0.156408i
$729$	1.00000			0.0370370
$730$	12.0000			0.444140
$731$	0.618950	−	1.07205i	0.0228927	−	0.0396513i
$732$	−8.87298			−0.327955
$733$	−24.5000	−	42.4352i	−0.904928	−	1.56738i	−0.821014	−	0.570909i	$-0.806591\pi$
$733$	−24.5000	−	42.4352i	−0.904928	−	1.56738i	−0.0839145	−	0.996473i	$-0.526742\pi$
$734$	−2.25403			−0.0831979
$735$	8.37298	+	14.5024i	0.308842	+	0.534930i
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	15.3175	+	26.5308i	0.564229	+	0.977273i
$738$	0.436492	−	0.756026i	0.0160675	−	0.0278297i
$739$	3.74597			0.137798			0.0688988	−	0.997624i	$-0.478051\pi$
$739$	3.74597			0.137798			0.0688988	+	0.997624i	$0.478051\pi$
$740$	−5.00000	+	3.46410i	−0.183804	+	0.127343i
$741$	7.74597			0.284555
$742$	2.12702	−	3.68410i	0.0780852	−	0.135248i
$743$	2.88105	+	4.99012i	0.105695	+	0.183070i	0.914022	−	0.405664i	$-0.132960\pi$
$743$	2.88105	+	4.99012i	0.105695	+	0.183070i	−0.808327	+	0.588734i	$0.799626\pi$
$744$	3.87298	+	6.70820i	0.141990	+	0.245935i
$745$	−3.06351	−	5.30615i	−0.112238	−	0.194402i
$746$	5.74597			0.210375
$747$	−1.43649	−	2.48808i	−0.0525585	−	0.0910340i
$748$	−0.635083			−0.0232209
$749$	12.4919	−	21.6367i	0.456445	−	0.790586i
$750$	1.00000			0.0365148
$751$	10.3810			0.378810			0.189405	−	0.981899i	$-0.439344\pi$
$751$	10.3810			0.378810			0.189405	+	0.981899i	$0.439344\pi$
$752$	5.37298	−	9.30628i	0.195933	−	0.339365i
$753$	−15.2460	−	26.4068i	−0.555594	−	0.962317i
$754$	3.87298			0.141046
$755$	6.00000	−	10.3923i	0.218362	−	0.378215i
$756$	−2.43649	+	4.22013i	−0.0886143	+	0.153485i
$757$	−20.4919	+	35.4931i	−0.744792	+	1.29002i	0.205500	+	0.978657i	$0.434118\pi$
$757$	−20.4919	+	35.4931i	−0.744792	+	1.29002i	−0.950292	+	0.311360i	$0.899215\pi$
$758$	−5.30948	−	9.19628i	−0.192849	−	0.334024i
$759$	−15.0000	−	25.9808i	−0.544466	−	0.943042i
$760$	3.87298	−	6.70820i	0.140488	−	0.243332i
$761$	−9.43649	+	16.3445i	−0.342073	+	0.592487i	−0.984817	−	0.173593i	$-0.944462\pi$
$761$	−9.43649	+	16.3445i	−0.342073	+	0.592487i	0.642745	+	0.766080i	$0.277796\pi$
$762$	0.436492	−	0.756026i	0.0158124	−	0.0273879i
$763$	−22.5081			−0.814847
$764$	−2.30948	−	4.00013i	−0.0835539	−	0.144720i
$765$	0.0635083	−	0.110000i	0.00229615	−	0.00397705i
$766$	−4.74597			−0.171479
$767$	−5.00000			−0.180540
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−34.2379			−1.23465			−0.617325	−	0.786708i	$-0.711784\pi$
$769$	−34.2379			−1.23465			−0.617325	+	0.786708i	$0.711784\pi$
$770$	12.1825	+	21.1006i	0.439025	+	0.760414i
$771$	−23.6190			−0.850616
$772$	8.30948	+	14.3924i	0.299065	+	0.517995i
$773$	3.05544	+	5.29218i	0.109897	+	0.190346i	0.915728	−	0.401798i	$-0.131615\pi$
$773$	3.05544	+	5.29218i	0.109897	+	0.190346i	−0.805832	+	0.592145i	$0.798281\pi$
$774$	−4.87298	−	8.44025i	−0.175156	−	0.303379i
$775$	−3.87298	+	6.70820i	−0.139122	+	0.240966i
$776$	10.0000			0.358979
$777$	24.3649	−	16.8805i	0.874087	−	0.605585i
$778$	−11.7460			−0.421113
$779$	3.38105	−	5.85615i	0.121139	−	0.209818i
$780$	−0.500000	−	0.866025i	−0.0179029	−	0.0310087i
$781$	36.5474	+	63.3019i	1.30777	+	2.26512i
$782$	−0.381050	−	0.659998i	−0.0136263	−	0.0236015i
$783$	3.87298			0.138409
$784$	−8.37298	−	14.5024i	−0.299035	−	0.517944i
$785$	6.74597			0.240774
$786$	0.500000	−	0.866025i	0.0178344	−	0.0308901i
$787$	−27.8730			−0.993565			−0.496782	−	0.867875i	$-0.665485\pi$
$787$	−27.8730			−0.993565			−0.496782	+	0.867875i	$0.665485\pi$
$788$	27.7460			0.988409
$789$	3.87298	−	6.70820i	0.137882	−	0.238818i
$790$	−7.74597	−	13.4164i	−0.275589	−	0.477334i
$791$	−76.1109			−2.70619
$792$	−2.50000	+	4.33013i	−0.0888336	+	0.153864i
$793$	−4.43649	+	7.68423i	−0.157544	+	0.272875i
$794$	13.1190	−	22.7227i	0.465574	−	0.806398i
$795$	0.436492	+	0.756026i	0.0154808	+	0.0268135i
$796$	10.9365	+	18.9426i	0.387634	+	0.671401i
$797$	−9.74597	+	16.8805i	−0.345220	+	0.597938i	−0.985394	−	0.170292i	$-0.945529\pi$
$797$	−9.74597	+	16.8805i	−0.345220	+	0.597938i	0.640174	+	0.768230i	$0.278862\pi$
$798$	−18.8730	+	32.6890i	−0.668096	+	1.15718i
$799$	0.682458	−	1.18205i	0.0241436	−	0.0418180i
$800$	−1.00000			−0.0353553
$801$	−5.87298	−	10.1723i	−0.207512	−	0.359421i
$802$	1.30948	−	2.26808i	0.0462392	−	0.0800886i
$803$	−60.0000			−2.11735
$804$	6.12702			0.216083
$805$	−14.6190	+	25.3208i	−0.515250	+	0.892440i
$806$	7.74597			0.272840
$807$	3.87298	+	6.70820i	0.136335	+	0.236140i
$808$	11.6190			0.408753
$809$	−23.6190	−	40.9092i	−0.830398	−	1.43829i	−0.897723	−	0.440561i	$-0.854780\pi$
$809$	−23.6190	−	40.9092i	−0.830398	−	1.43829i	0.0673248	−	0.997731i	$-0.478554\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−3.69052	−	6.39218i	−0.129592	−	0.224460i	0.793927	−	0.608014i	$-0.208033\pi$
$811$	−3.69052	−	6.39218i	−0.129592	−	0.224460i	−0.923519	+	0.383554i	$0.874700\pi$
$812$	−9.43649	+	16.3445i	−0.331156	+	0.573579i
$813$	10.1270			0.355170
$814$	25.0000	−	17.3205i	0.876250	−	0.607083i
$815$	10.1270			0.354734
$816$	−0.0635083	+	0.110000i	−0.00222324	+	0.00385076i
$817$	−37.7460	−	65.3779i	−1.32056	−	2.28728i
$818$	−7.11895	−	12.3304i	−0.248908	−	0.431122i
$819$	2.43649	+	4.22013i	0.0851379	+	0.147463i
$820$	−0.872983			−0.0304859
$821$	−14.8095	−	25.6508i	−0.516854	−	0.895218i	−0.999808	−	0.0195722i	$-0.993770\pi$
$821$	−14.8095	−	25.6508i	−0.516854	−	0.895218i	0.482954	−	0.875646i	$-0.339564\pi$
$822$	17.8730			0.623392
$823$	−21.3095	+	36.9091i	−0.742802	+	1.28657i	0.208413	+	0.978041i	$0.433170\pi$
$823$	−21.3095	+	36.9091i	−0.742802	+	1.28657i	−0.951215	+	0.308529i	$0.900163\pi$
$824$	−14.8730			−0.518125
$825$	−5.00000			−0.174078
$826$	12.1825	−	21.1006i	0.423882	−	0.734185i
$827$	−10.7460	−	18.6126i	−0.373674	−	0.647222i	0.616454	−	0.787391i	$-0.288569\pi$
$827$	−10.7460	−	18.6126i	−0.373674	−	0.647222i	−0.990128	+	0.140169i	$0.955235\pi$
$828$	−6.00000			−0.208514
$829$	4.05544	−	7.02423i	0.140851	−	0.243962i	−0.786966	−	0.616996i	$-0.788349\pi$
$829$	4.05544	−	7.02423i	0.140851	−	0.243962i	0.927817	+	0.373035i	$0.121683\pi$
$830$	−1.43649	+	2.48808i	−0.0498614	+	0.0863624i
$831$	−15.1190	+	26.1868i	−0.524471	+	0.908410i
$832$	0.500000	+	0.866025i	0.0173344	+	0.0300240i
$833$	−1.06351	−	1.84205i	−0.0368484	−	0.0638233i
$834$	4.87298	−	8.44025i	0.168738	−	0.292262i
$835$	3.37298	−	5.84218i	0.116727	−	0.202177i
$836$	−19.3649	+	33.5410i	−0.669750	+	1.16004i
$837$	7.74597			0.267740
$838$	7.00000	+	12.1244i	0.241811	+	0.418829i
$839$	−15.0554	+	26.0768i	−0.519772	+	0.900271i	0.479964	+	0.877288i	$0.340650\pi$
$839$	−15.0554	+	26.0768i	−0.519772	+	0.900271i	−0.999736	+	0.0229827i	$0.992684\pi$
$840$	4.87298			0.168134
$841$	−14.0000			−0.482759
$842$	7.30948	−	12.6604i	0.251901	−	0.436306i
$843$	11.7460			0.404553
$844$	−1.12702	−	1.95205i	−0.0387935	−	0.0671923i
$845$	12.0000			0.412813
$846$	−5.37298	−	9.30628i	−0.184727	−	0.319957i
$847$	−34.1109	−	59.0818i	−1.17206	−	2.03007i
$848$	−0.436492	−	0.756026i	−0.0149892	−	0.0259620i
$849$	0.936492	−	1.62205i	0.0321403	−	0.0556687i
$850$	−0.127017			−0.00435664
$851$	33.0000	+	15.5885i	1.13123	+	0.534365i
$852$	14.6190			0.500837
$853$	14.5000	−	25.1147i	0.496471	−	0.859912i	−0.503521	−	0.863983i	$-0.667962\pi$
$853$	14.5000	−	25.1147i	0.496471	−	0.859912i	0.999992	+	0.00407068i	$0.00129574\pi$
$854$	−21.6190	−	37.4451i	−0.739785	−	1.28135i
$855$	−3.87298	−	6.70820i	−0.132453	−	0.229416i
$856$	−2.56351	−	4.44013i	−0.0876189	−	0.151760i
$857$	32.1270			1.09744			0.548719	−	0.836007i	$-0.315116\pi$
$857$	32.1270			1.09744			0.548719	+	0.836007i	$0.315116\pi$
$858$	2.50000	+	4.33013i	0.0853486	+	0.147828i
$859$	32.3649			1.10428			0.552138	−	0.833753i	$-0.313812\pi$
$859$	32.3649			1.10428			0.552138	+	0.833753i	$0.313812\pi$
$860$	−4.87298	+	8.44025i	−0.166167	+	0.287810i
$861$	4.25403			0.144977
$862$	4.36492			0.148670
$863$	5.37298	−	9.30628i	0.182898	−	0.316789i	−0.759968	−	0.649961i	$-0.774785\pi$
$863$	5.37298	−	9.30628i	0.182898	−	0.316789i	0.942866	+	0.333171i	$0.108119\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	6.61895			0.225051
$866$	−1.74597	+	3.02410i	−0.0593304	+	0.102763i
$867$	8.49193	−	14.7085i	0.288401	−	0.499525i
$868$	−18.8730	+	32.6890i	−0.640591	+	1.10954i
$869$	38.7298	+	67.0820i	1.31382	+	2.27560i
$870$	−1.93649	−	3.35410i	−0.0656532	−	0.113715i
$871$	3.06351	−	5.30615i	0.103803	−	0.179792i
$872$	−2.30948	+	4.00013i	−0.0782087	+	0.135461i
$873$	5.00000	−	8.66025i	0.169224	−	0.293105i
$874$	−46.4758			−1.57207
$875$	2.43649	+	4.22013i	0.0823685	+	0.142666i
$876$	−6.00000	+	10.3923i	−0.202721	+	0.351123i
$877$	24.7460			0.835612			0.417806	−	0.908536i	$-0.362799\pi$
$877$	24.7460			0.835612			0.417806	+	0.908536i	$0.362799\pi$
$878$	31.3649			1.05851
$879$	1.87298	−	3.24410i	0.0631742	−	0.109421i
$880$	5.00000			0.168550
$881$	11.4919	+	19.9046i	0.387173	+	0.670603i	0.992068	−	0.125702i	$-0.0401183\pi$
$881$	11.4919	+	19.9046i	0.387173	+	0.670603i	−0.604895	+	0.796305i	$0.706785\pi$
$882$	−16.7460			−0.563866
$883$	−11.8095	−	20.4546i	−0.397420	−	0.688352i	0.595986	−	0.802995i	$-0.296761\pi$
$883$	−11.8095	−	20.4546i	−0.397420	−	0.688352i	−0.993407	+	0.114642i	$0.963428\pi$
$884$	0.0635083	+	0.110000i	0.00213602	+	0.00369969i
$885$	2.50000	+	4.33013i	0.0840366	+	0.145556i
$886$	−19.1825	+	33.2250i	−0.644447	+	1.11622i
$887$	22.0000			0.738688			0.369344	−	0.929293i	$-0.379582\pi$
$887$	22.0000			0.738688			0.369344	+	0.929293i	$0.379582\pi$
$888$	−0.500000	−	6.06218i	−0.0167789	−	0.203433i
$889$	4.25403			0.142676
$890$	−5.87298	+	10.1723i	−0.196863	+	0.340976i
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	−3.74597	−	6.48820i	−0.125424	−	0.217241i
$893$	−41.6190	−	72.0861i	−1.39273	−	2.41227i
$894$	6.12702			0.204918
$895$	−5.00000	−	8.66025i	−0.167132	−	0.289480i
$896$	−4.87298			−0.162795
$897$	−3.00000	+	5.19615i	−0.100167	+	0.173494i
$898$		0			0
$899$	30.0000			1.00056
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−0.0554417	−	0.0960279i	−0.00184703	−	0.00319915i
$902$	4.36492			0.145336
$903$	23.7460	−	41.1292i	0.790216	−	1.36869i
$904$	−7.80948	+	13.5264i	−0.259739	+	0.449882i
$905$	1.00000	−	1.73205i	0.0332411	−	0.0575753i
$906$	6.00000	+	10.3923i	0.199337	+	0.345261i
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	0.830909	−	0.556408i	$-0.187821\pi$
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	−0.897318	+	0.441384i	$0.854488\pi$
$908$	7.18246	−	12.4404i	0.238358	−	0.412849i
$909$	5.80948	−	10.0623i	0.192688	−	0.333746i
$910$	2.43649	−	4.22013i	0.0807689	−	0.139896i
$911$	42.7298			1.41570			0.707851	−	0.706362i	$-0.249665\pi$
$911$	42.7298			1.41570			0.707851	+	0.706362i	$0.249665\pi$
$912$	3.87298	+	6.70820i	0.128247	+	0.222131i
$913$	7.18246	−	12.4404i	0.237705	−	0.411717i
$914$	6.25403			0.206865
$915$	8.87298			0.293332
$916$	−1.30948	+	2.26808i	−0.0432663	+	0.0749394i
$917$	4.87298			0.160920
$918$	0.0635083	+	0.110000i	0.00209609	+	0.00363053i
$919$	22.3810			0.738283			0.369141	−	0.929373i	$-0.379652\pi$
$919$	22.3810			0.738283			0.369141	+	0.929373i	$0.379652\pi$
$920$	3.00000	+	5.19615i	0.0989071	+	0.171312i
$921$	−3.87298	−	6.70820i	−0.127619	−	0.221043i
$922$	−10.8095	−	18.7226i	−0.355991	−	0.616595i
$923$	7.30948	−	12.6604i	0.240594	−	0.416722i
$924$	−24.3649			−0.801547
$925$	5.00000	−	3.46410i	0.164399	−	0.113899i
$926$	22.0000			0.722965
$927$	−7.43649	+	12.8804i	−0.244246	+	0.423047i
$928$	1.93649	+	3.35410i	0.0635685	+	0.110104i
$929$	−4.87298	−	8.44025i	−0.159877	−	0.276916i	0.774947	−	0.632026i	$-0.217777\pi$
$929$	−4.87298	−	8.44025i	−0.159877	−	0.276916i	−0.934824	+	0.355111i	$0.884443\pi$
$930$	−3.87298	−	6.70820i	−0.127000	−	0.219971i
$931$	−129.714			−4.25119
$932$	1.00000	+	1.73205i	0.0327561	+	0.0567352i
$933$	−18.6190			−0.609557
$934$	8.12702	−	14.0764i	0.265924	−	0.460594i
$935$	0.635083			0.0207694
$936$	1.00000			0.0326860
$937$	−8.30948	+	14.3924i	−0.271459	+	0.470180i	−0.969236	−	0.246135i	$-0.920839\pi$
$937$	−8.30948	+	14.3924i	−0.271459	+	0.470180i	0.697777	+	0.716315i	$0.254173\pi$
$938$	14.9284	+	25.8568i	0.487430	+	0.844254i
$939$	−4.25403			−0.138825
$940$	−5.37298	+	9.30628i	−0.175247	+	0.303537i
$941$	−17.7460	+	30.7369i	−0.578502	+	1.00199i	0.417149	+	0.908838i	$0.363029\pi$
$941$	−17.7460	+	30.7369i	−0.578502	+	1.00199i	−0.995651	+	0.0931569i	$0.970304\pi$
$942$	−3.37298	+	5.84218i	−0.109898	+	0.190348i
$943$	2.61895	+	4.53615i	0.0852847	+	0.147718i
$944$	−2.50000	−	4.33013i	−0.0813681	−	0.140934i
$945$	2.43649	−	4.22013i	0.0792591	−	0.137281i
$946$	24.3649	−	42.2013i	0.792172	−	1.37208i
$947$	4.49193	−	7.78026i	0.145968	−	0.252824i	−0.783766	−	0.621057i	$-0.786704\pi$
$947$	4.49193	−	7.78026i	0.145968	−	0.252824i	0.929734	+	0.368232i	$0.120037\pi$
$948$	15.4919			0.503155
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$	−3.87298	+	6.70820i	−0.125656	+	0.217643i
$951$	10.6190			0.344343
$952$	−0.618950			−0.0200603
$953$	2.19052	−	3.79410i	0.0709581	−	0.122903i	−0.828363	−	0.560191i	$-0.810728\pi$
$953$	2.19052	−	3.79410i	0.0709581	−	0.122903i	0.899321	+	0.437288i	$0.144061\pi$
$954$	−0.872983			−0.0282639
$955$	2.30948	+	4.00013i	0.0747329	+	0.129441i
$956$	−13.7460			−0.444576
$957$	9.68246	+	16.7705i	0.312989	+	0.542114i
$958$	12.4919	+	21.6367i	0.403596	+	0.699049i
$959$	43.5474	+	75.4263i	1.40622	+	2.43564i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	29.0000			0.935484
$962$	−5.50000	−	2.59808i	−0.177327	−	0.0837653i
$963$	−5.12702			−0.165216
$964$	−13.1190	+	22.7227i	−0.422533	+	0.731849i
$965$	−8.30948	−	14.3924i	−0.267491	−	0.463309i
$966$	−14.6190	−	25.3208i	−0.470357	−	0.814682i
$967$	−6.43649	−	11.1483i	−0.206984	−	0.358506i	0.743779	−	0.668425i	$-0.233031\pi$
$967$	−6.43649	−	11.1483i	−0.206984	−	0.358506i	−0.950763	+	0.309919i	$0.899698\pi$
$968$	−14.0000			−0.449977
$969$	0.491933	+	0.852054i	0.0158032	+	0.0273719i
$970$	−10.0000			−0.321081
$971$	2.38105	−	4.12410i	0.0764115	−	0.132349i	−0.825288	−	0.564713i	$-0.808987\pi$
$971$	2.38105	−	4.12410i	0.0764115	−	0.132349i	0.901699	+	0.432364i	$0.142320\pi$
$972$	1.00000			0.0320750
$973$	47.4919			1.52252
$974$	7.87298	−	13.6364i	0.252267	−	0.436939i
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$	−8.87298			−0.284017
$977$	−14.8095	+	25.6508i	−0.473797	+	0.820641i	−0.999550	−	0.0299967i	$-0.990450\pi$
$977$	−14.8095	+	25.6508i	−0.473797	+	0.820641i	0.525753	+	0.850637i	$0.323784\pi$
$978$	−5.06351	+	8.77025i	−0.161913	+	0.280442i
$979$	29.3649	−	50.8615i	0.938507	−	1.62554i
$980$	8.37298	+	14.5024i	0.267465	+	0.463263i
$981$	2.30948	+	4.00013i	0.0737359	+	0.127714i
$982$	15.0000	−	25.9808i	0.478669	−	0.829079i
$983$	11.0000	−	19.0526i	0.350846	−	0.607682i	−0.635552	−	0.772058i	$-0.719228\pi$
$983$	11.0000	−	19.0526i	0.350846	−	0.607682i	0.986398	+	0.164376i	$0.0525609\pi$
$984$	0.436492	−	0.756026i	0.0139148	−	0.0241012i
$985$	−27.7460			−0.884060
$986$	0.245967	+	0.426027i	0.00783318	+	0.0135675i
$987$	26.1825	−	45.3493i	0.833397	−	1.44349i
$988$	7.74597			0.246432
$989$	58.4758			1.85942
$990$	2.50000	−	4.33013i	0.0794552	−	0.137620i
$991$	−10.3810			−0.329765			−0.164882	−	0.986313i	$-0.552724\pi$
$991$	−10.3810			−0.329765			−0.164882	+	0.986313i	$0.552724\pi$
$992$	3.87298	+	6.70820i	0.122967	+	0.212986i
$993$	10.8730			0.345044
$994$	35.6190	+	61.6938i	1.12976	+	1.95681i
$995$	−10.9365	−	18.9426i	−0.346710	−	0.600519i
$996$	−1.43649	−	2.48808i	−0.0455170	−	0.0788377i
$997$	−9.24597	+	16.0145i	−0.292823	+	0.507184i	−0.974476	−	0.224491i	$-0.927928\pi$
$997$	−9.24597	+	16.0145i	−0.292823	+	0.507184i	0.681653	+	0.731675i	$0.261261\pi$
$998$	−28.1109			−0.889834
$999$	−5.50000	−	2.59808i	−0.174012	−	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.l.121.1	✓	4
37.26	even	3	inner	1110.2.i.l.211.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.l.121.1	✓	4	1.1	even	1	trivial
1110.2.i.l.211.1	yes	4	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-2.43649 - 4.22013i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-2.43649 - 4.22013i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} -5.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.500000 + 0.866025i) q^{13} -4.87298 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0635083 + 0.110000i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.87298 + 6.70820i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.43649 + 4.22013i) q^{21} +(-2.50000 + 4.33013i) q^{22} -6.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{26} +1.00000 q^{27} +(-2.43649 + 4.22013i) q^{28} +3.87298 q^{29} +(-0.500000 - 0.866025i) q^{30} +7.74597 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} +(0.0635083 + 0.110000i) q^{34} +(2.43649 - 4.22013i) q^{35} +1.00000 q^{36} +(-5.50000 - 2.59808i) q^{37} +7.74597 q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.436492 - 0.756026i) q^{41} +(2.43649 + 4.22013i) q^{42} -9.74597 q^{43} +(2.50000 + 4.33013i) q^{44} -1.00000 q^{45} +(-3.00000 + 5.19615i) q^{46} -10.7460 q^{47} +1.00000 q^{48} +(-8.37298 + 14.5024i) q^{49} +(0.500000 + 0.866025i) q^{50} +0.127017 q^{51} +(0.500000 - 0.866025i) q^{52} +(-0.436492 + 0.756026i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.50000 - 4.33013i) q^{55} +(2.43649 + 4.22013i) q^{56} +(3.87298 - 6.70820i) q^{57} +(1.93649 - 3.35410i) q^{58} +(-2.50000 + 4.33013i) q^{59} -1.00000 q^{60} +(4.43649 + 7.68423i) q^{61} +(3.87298 - 6.70820i) q^{62} +4.87298 q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +5.00000 q^{66} +(-3.06351 - 5.30615i) q^{67} +0.127017 q^{68} +(3.00000 + 5.19615i) q^{69} +(-2.43649 - 4.22013i) q^{70} +(-7.30948 - 12.6604i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-5.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(3.87298 - 6.70820i) q^{76} +(12.1825 + 21.1006i) q^{77} +(-0.500000 - 0.866025i) q^{78} +(-7.74597 - 13.4164i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} -0.872983 q^{82} +(-1.43649 + 2.48808i) q^{83} +4.87298 q^{84} -0.127017 q^{85} +(-4.87298 + 8.44025i) q^{86} +(-1.93649 - 3.35410i) q^{87} +5.00000 q^{88} +(-5.87298 + 10.1723i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(2.43649 - 4.22013i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-3.87298 - 6.70820i) q^{93} +(-5.37298 + 9.30628i) q^{94} +(-3.87298 + 6.70820i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.0000 q^{97} +(8.37298 + 14.5024i) q^{98} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 4 q^{10} - 20 q^{11} - 2 q^{12} + 2 q^{13} - 4 q^{14} + 2 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} + 2 q^{20} - 2 q^{21} - 10 q^{22} - 24 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 2 q^{28} - 2 q^{30} + 2 q^{32} + 10 q^{33} + 8 q^{34} + 2 q^{35} + 4 q^{36} - 22 q^{37} + 2 q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} - 8 q^{43} + 10 q^{44} - 4 q^{45} - 12 q^{46} - 12 q^{47} + 4 q^{48} - 18 q^{49} + 2 q^{50} + 16 q^{51} + 2 q^{52} + 6 q^{53} + 2 q^{54} - 10 q^{55} + 2 q^{56} - 10 q^{59} - 4 q^{60} + 10 q^{61} + 4 q^{63} + 4 q^{64} - 2 q^{65} + 20 q^{66} - 20 q^{67} + 16 q^{68} + 12 q^{69} - 2 q^{70} - 6 q^{71} + 2 q^{72} + 48 q^{73} - 20 q^{74} + 4 q^{75} + 10 q^{77} - 2 q^{78} - 4 q^{80} - 2 q^{81} + 12 q^{82} + 2 q^{83} + 4 q^{84} - 16 q^{85} - 4 q^{86} + 20 q^{88} - 8 q^{89} - 2 q^{90} + 2 q^{91} + 12 q^{92} - 6 q^{94} + 2 q^{96} - 40 q^{97} + 18 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 + 4 * q^10 - 20 * q^11 - 2 * q^12 + 2 * q^13 - 4 * q^14 + 2 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 + 2 * q^20 - 2 * q^21 - 10 * q^22 - 24 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - 2 * q^28 - 2 * q^30 + 2 * q^32 + 10 * q^33 + 8 * q^34 + 2 * q^35 + 4 * q^36 - 22 * q^37 + 2 * q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 - 8 * q^43 + 10 * q^44 - 4 * q^45 - 12 * q^46 - 12 * q^47 + 4 * q^48 - 18 * q^49 + 2 * q^50 + 16 * q^51 + 2 * q^52 + 6 * q^53 + 2 * q^54 - 10 * q^55 + 2 * q^56 - 10 * q^59 - 4 * q^60 + 10 * q^61 + 4 * q^63 + 4 * q^64 - 2 * q^65 + 20 * q^66 - 20 * q^67 + 16 * q^68 + 12 * q^69 - 2 * q^70 - 6 * q^71 + 2 * q^72 + 48 * q^73 - 20 * q^74 + 4 * q^75 + 10 * q^77 - 2 * q^78 - 4 * q^80 - 2 * q^81 + 12 * q^82 + 2 * q^83 + 4 * q^84 - 16 * q^85 - 4 * q^86 + 20 * q^88 - 8 * q^89 - 2 * q^90 + 2 * q^91 + 12 * q^92 - 6 * q^94 + 2 * q^96 - 40 * q^97 + 18 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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