LMFDB - Embedded newform 366.2.e.d.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [366,2,Mod(13,366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(366, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("366.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 366 = 2 \cdot 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	366.e (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:	$2.92252471398$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.65370672.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 10x^{4} - 13x^{3} + 92x^{2} - 99x + 121 $ x^6 - x^5 + 10x^4 - 13x^3 + 92x^2 - 99x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.2
Root			$1.40489 + 2.43335i$ of defining polynomial
Character	$\chi$	$=$	366.13
Dual form			366.2.e.d.169.2

$q$-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} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.947448 + 1.64103i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.904893 + 1.56732i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +(0.947448 + 1.64103i) q^{10} -1.80979 q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.80979 + 4.86669i) q^{13} +(0.904893 + 1.56732i) q^{14} +(0.947448 - 1.64103i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.25723 + 2.17759i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +1.89490 q^{20} +(0.904893 - 1.56732i) q^{21} +(-0.904893 + 1.56732i) q^{22} -2.70468 q^{23} +1.00000 q^{24} +(0.704683 + 1.22055i) q^{25} +(2.80979 + 4.86669i) q^{26} -1.00000 q^{27} +1.80979 q^{28} +(-1.30979 - 2.26862i) q^{29} +(-0.947448 - 1.64103i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +1.80979 q^{33} +2.51447 q^{34} +(-1.71468 - 2.96991i) q^{35} +(-0.500000 - 0.866025i) q^{36} +1.70468 q^{37} +2.00000 q^{38} +(2.80979 - 4.86669i) q^{39} +(0.947448 - 1.64103i) q^{40} +1.19021 q^{41} +(-0.904893 - 1.56732i) q^{42} +(2.45744 - 4.25642i) q^{43} +(0.904893 + 1.56732i) q^{44} +(-0.947448 + 1.64103i) q^{45} +(-1.35234 + 2.34232i) q^{46} +(-5.24724 - 9.08848i) q^{47} +(0.500000 - 0.866025i) q^{48} +(1.86234 + 3.22566i) q^{49} +1.40937 q^{50} +(-1.25723 - 2.17759i) q^{51} +5.61957 q^{52} -13.3043 q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.71468 - 2.96991i) q^{55} +(0.904893 - 1.56732i) q^{56} +(-1.00000 - 1.73205i) q^{57} -2.61957 q^{58} +(0.894897 - 1.55001i) q^{59} -1.89490 q^{60} +(-4.55702 + 6.34299i) q^{61} +2.00000 q^{62} +(-0.904893 + 1.56732i) q^{63} +1.00000 q^{64} +(-5.32425 - 9.22188i) q^{65} +(0.904893 - 1.56732i) q^{66} +(-2.35234 + 4.07437i) q^{67} +(1.25723 - 2.17759i) q^{68} +2.70468 q^{69} -3.42936 q^{70} +(-0.809786 - 1.40259i) q^{71} -1.00000 q^{72} +(2.50000 + 4.33013i) q^{73} +(0.852341 - 1.47630i) q^{74} +(-0.704683 - 1.22055i) q^{75} +(1.00000 - 1.73205i) q^{76} +(1.63766 - 2.83651i) q^{77} +(-2.80979 - 4.86669i) q^{78} +(5.51447 - 9.55134i) q^{79} +(-0.947448 - 1.64103i) q^{80} +1.00000 q^{81} +(0.595107 - 1.03076i) q^{82} +(-1.09511 + 1.89678i) q^{83} -1.80979 q^{84} -4.76466 q^{85} +(-2.45744 - 4.25642i) q^{86} +(1.30979 + 2.26862i) q^{87} +1.80979 q^{88} +15.1540 q^{89} +(0.947448 + 1.64103i) q^{90} +(-5.08511 - 8.80767i) q^{91} +(1.35234 + 2.34232i) q^{92} +(-1.00000 - 1.73205i) q^{93} -10.4945 q^{94} -3.78979 q^{95} +(-0.500000 - 0.866025i) q^{96} +(7.75723 + 13.4359i) q^{97} +3.72467 q^{98} -1.80979 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - q^{5} - 3 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} + q^{10} + 4 q^{11} + 3 q^{12} - 2 q^{13} - 2 q^{14} + q^{15} - 3 q^{16} - 12 q^{17} + 3 q^{18} + 6 q^{19} + 2 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - q^5 - 3 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 + q^10 + 4 * q^11 + 3 * q^12 - 2 * q^13 - 2 * q^14 + q^15 - 3 * q^16 - 12 * q^17 + 3 * q^18 + 6 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 + 8 * q^23 + 6 * q^24 - 20 * q^25 + 2 * q^26 - 6 * q^27 - 4 * q^28 + 7 * q^29 - q^30 + 6 * q^31 + 3 * q^32 - 4 * q^33 - 24 * q^34 + 12 * q^35 - 3 * q^36 - 14 * q^37 + 12 * q^38 + 2 * q^39 + q^40 + 22 * q^41 + 2 * q^42 + 12 * q^43 - 2 * q^44 - q^45 + 4 * q^46 - 10 * q^47 + 3 * q^48 + q^49 - 40 * q^50 + 12 * q^51 + 4 * q^52 - 22 * q^53 - 3 * q^54 - 12 * q^55 - 2 * q^56 - 6 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 9 * q^61 + 12 * q^62 + 2 * q^63 + 6 * q^64 + 22 * q^65 - 2 * q^66 - 2 * q^67 - 12 * q^68 - 8 * q^69 + 24 * q^70 + 10 * q^71 - 6 * q^72 + 15 * q^73 - 7 * q^74 + 20 * q^75 + 6 * q^76 + 20 * q^77 - 2 * q^78 - 6 * q^79 - q^80 + 6 * q^81 + 11 * q^82 - 14 * q^83 + 4 * q^84 - 16 * q^85 - 12 * q^86 - 7 * q^87 - 4 * q^88 + 26 * q^89 + q^90 - 36 * q^91 - 4 * q^92 - 6 * q^93 - 20 * q^94 - 4 * q^95 - 3 * q^96 + 27 * q^97 + 2 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/366\mathbb{Z}\right)^\times$.

$n$	$245$	$307$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.947448	+	1.64103i	−0.423712	+	0.733890i	−0.996299	−	0.0859533i	$-0.972606\pi$
$5$	−0.947448	+	1.64103i	−0.423712	+	0.733890i	0.572587	+	0.819844i	$0.305940\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.904893	+	1.56732i	−0.342017	+	0.592391i	−0.984807	−	0.173651i	$-0.944444\pi$
$7$	−0.904893	+	1.56732i	−0.342017	+	0.592391i	0.642790	+	0.766043i	$0.277777\pi$
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	0.947448	+	1.64103i	0.299610	+	0.518939i
$11$	−1.80979			−0.545671			−0.272835	−	0.962061i	$-0.587961\pi$
$11$	−1.80979			−0.545671			−0.272835	+	0.962061i	$0.587961\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−2.80979	+	4.86669i	−0.779294	+	1.34978i	0.153055	+	0.988218i	$0.451089\pi$
$13$	−2.80979	+	4.86669i	−0.779294	+	1.34978i	−0.932349	+	0.361560i	$0.882244\pi$
$14$	0.904893	+	1.56732i	0.241843	+	0.418884i
$15$	0.947448	−	1.64103i	0.244630	−	0.423712i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.25723	+	2.17759i	0.304924	+	0.528144i	0.977244	−	0.212116i	$-0.0680356\pi$
$17$	1.25723	+	2.17759i	0.304924	+	0.528144i	−0.672320	+	0.740260i	$0.734702\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	1.89490			0.423712
$21$	0.904893	−	1.56732i	0.197464	−	0.342017i
$22$	−0.904893	+	1.56732i	−0.192924	+	0.334154i
$23$	−2.70468			−0.563965			−0.281983	−	0.959419i	$-0.590992\pi$
$23$	−2.70468			−0.563965			−0.281983	+	0.959419i	$0.590992\pi$
$24$	1.00000			0.204124
$25$	0.704683	+	1.22055i	0.140937	+	0.244109i
$26$	2.80979	+	4.86669i	0.551044	+	0.954437i
$27$	−1.00000			−0.192450
$28$	1.80979			0.342017
$29$	−1.30979	−	2.26862i	−0.243221	−	0.421271i	0.718409	−	0.695621i	$-0.244871\pi$
$29$	−1.30979	−	2.26862i	−0.243221	−	0.421271i	−0.961630	+	0.274350i	$0.911537\pi$
$30$	−0.947448	−	1.64103i	−0.172980	−	0.299610i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.80979			0.315043
$34$	2.51447			0.431228
$35$	−1.71468	−	2.96991i	−0.289834	−	0.502007i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.70468			0.280248			0.140124	−	0.990134i	$-0.455250\pi$
$37$	1.70468			0.280248			0.140124	+	0.990134i	$0.455250\pi$
$38$	2.00000			0.324443
$39$	2.80979	−	4.86669i	0.449926	−	0.779294i
$40$	0.947448	−	1.64103i	0.149805	−	0.259469i
$41$	1.19021			0.185880			0.0929401	−	0.995672i	$-0.470373\pi$
$41$	1.19021			0.185880			0.0929401	+	0.995672i	$0.470373\pi$
$42$	−0.904893	−	1.56732i	−0.139628	−	0.241843i
$43$	2.45744	−	4.25642i	0.374757	−	0.649098i	−0.615534	−	0.788110i	$-0.711060\pi$
$43$	2.45744	−	4.25642i	0.374757	−	0.649098i	0.990291	+	0.139013i	$0.0443929\pi$
$44$	0.904893	+	1.56732i	0.136418	+	0.236282i
$45$	−0.947448	+	1.64103i	−0.141237	+	0.244630i
$46$	−1.35234	+	2.34232i	−0.199392	+	0.345357i
$47$	−5.24724	−	9.08848i	−0.765388	−	1.32569i	−0.940041	−	0.341061i	$-0.889214\pi$
$47$	−5.24724	−	9.08848i	−0.765388	−	1.32569i	0.174653	−	0.984630i	$-0.444120\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	1.86234	+	3.22566i	0.266048	+	0.460809i
$50$	1.40937			0.199314
$51$	−1.25723	−	2.17759i	−0.176048	−	0.304924i
$52$	5.61957			0.779294
$53$	−13.3043			−1.82748			−0.913741	−	0.406298i	$-0.866819\pi$
$53$	−13.3043			−1.82748			−0.913741	+	0.406298i	$0.866819\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	1.71468	−	2.96991i	0.231207	−	0.400463i
$56$	0.904893	−	1.56732i	0.120921	−	0.209442i
$57$	−1.00000	−	1.73205i	−0.132453	−	0.229416i
$58$	−2.61957			−0.343967
$59$	0.894897	−	1.55001i	0.116506	−	0.201794i	−0.801875	−	0.597492i	$-0.796164\pi$
$59$	0.894897	−	1.55001i	0.116506	−	0.201794i	0.918381	+	0.395698i	$0.129497\pi$
$60$	−1.89490			−0.244630
$61$	−4.55702	+	6.34299i	−0.583467	+	0.812137i
$61$	−4.55702	+	6.34299i	−0.583467	+	0.812137i
$62$	2.00000			0.254000
$63$	−0.904893	+	1.56732i	−0.114006	+	0.197464i
$64$	1.00000			0.125000
$65$	−5.32425	−	9.22188i	−0.660393	−	1.14383i
$66$	0.904893	−	1.56732i	0.111385	−	0.192924i
$67$	−2.35234	+	4.07437i	−0.287384	+	0.497764i	−0.973185	−	0.230026i	$-0.926119\pi$
$67$	−2.35234	+	4.07437i	−0.287384	+	0.497764i	0.685800	+	0.727790i	$0.259452\pi$
$68$	1.25723	−	2.17759i	0.152462	−	0.264072i
$69$	2.70468			0.325606
$70$	−3.42936			−0.409887
$71$	−0.809786	−	1.40259i	−0.0961039	−	0.166457i	0.813965	−	0.580914i	$-0.197305\pi$
$71$	−0.809786	−	1.40259i	−0.0961039	−	0.166457i	−0.910069	+	0.414457i	$0.863971\pi$
$72$	−1.00000			−0.117851
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	0.974424	−	0.224716i	$-0.0721453\pi$
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	−0.681822	+	0.731519i	$0.738812\pi$
$74$	0.852341	−	1.47630i	0.0990827	−	0.171616i
$75$	−0.704683	−	1.22055i	−0.0813698	−	0.140937i
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$	1.63766	−	2.83651i	0.186629	−	0.323251i
$78$	−2.80979	−	4.86669i	−0.318146	−	0.551044i
$79$	5.51447	−	9.55134i	0.620426	−	1.07461i	−0.368980	−	0.929437i	$-0.620293\pi$
$79$	5.51447	−	9.55134i	0.620426	−	1.07461i	0.989406	−	0.145172i	$-0.0463737\pi$
$80$	−0.947448	−	1.64103i	−0.105928	−	0.183473i
$81$	1.00000			0.111111
$82$	0.595107	−	1.03076i	0.0657186	−	0.113828i
$83$	−1.09511	+	1.89678i	−0.120204	+	0.208199i	−0.919848	−	0.392275i	$-0.871688\pi$
$83$	−1.09511	+	1.89678i	−0.120204	+	0.208199i	0.799644	+	0.600474i	$0.205021\pi$
$84$	−1.80979			−0.197464
$85$	−4.76466			−0.516800
$86$	−2.45744	−	4.25642i	−0.264993	−	0.458981i
$87$	1.30979	+	2.26862i	0.140424	+	0.243221i
$88$	1.80979			0.192924
$89$	15.1540			1.60632			0.803162	−	0.595761i	$-0.203149\pi$
$89$	15.1540			1.60632			0.803162	+	0.595761i	$0.203149\pi$
$90$	0.947448	+	1.64103i	0.0998698	+	0.172980i
$91$	−5.08511	−	8.80767i	−0.533064	−	0.923295i
$92$	1.35234	+	2.34232i	0.140991	+	0.244204i
$93$	−1.00000	−	1.73205i	−0.103695	−	0.179605i
$94$	−10.4945			−1.08242
$95$	−3.78979			−0.388825
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	7.75723	+	13.4359i	0.787628	+	1.36421i	0.927417	+	0.374030i	$0.122024\pi$
$97$	7.75723	+	13.4359i	0.787628	+	1.36421i	−0.139789	+	0.990181i	$0.544642\pi$
$98$	3.72467			0.376249
$99$	−1.80979			−0.181890
$100$	0.704683	−	1.22055i	0.0704683	−	0.122055i
$101$	3.05255	−	5.28717i	0.303740	−	0.526094i	−0.673240	−	0.739424i	$-0.735098\pi$
$101$	3.05255	−	5.28717i	0.303740	−	0.526094i	0.976980	+	0.213331i	$0.0684312\pi$
$102$	−2.51447			−0.248970
$103$	−0.105103	−	0.182044i	−0.0103561	−	0.0179373i	0.860801	−	0.508942i	$-0.169963\pi$
$103$	−0.105103	−	0.182044i	−0.0103561	−	0.0179373i	−0.871157	+	0.491005i	$0.836630\pi$
$104$	2.80979	−	4.86669i	0.275522	−	0.477218i
$105$	1.71468	+	2.96991i	0.167336	+	0.289834i
$106$	−6.65213	+	11.5218i	−0.646112	+	1.11910i
$107$	−4.78979	+	8.29617i	−0.463047	+	0.802021i	−0.999111	−	0.0421566i	$-0.986577\pi$
$107$	−4.78979	+	8.29617i	−0.463047	+	0.802021i	0.536064	+	0.844177i	$0.319911\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	1.59511	−	2.76281i	0.152784	−	0.264629i	−0.779466	−	0.626444i	$-0.784510\pi$
$109$	1.59511	−	2.76281i	0.152784	−	0.264629i	0.932250	+	0.361815i	$0.117843\pi$
$110$	−1.71468	−	2.96991i	−0.163488	−	0.283170i
$111$	−1.70468			−0.161801
$112$	−0.904893	−	1.56732i	−0.0855043	−	0.148098i
$113$	13.6196			1.28122			0.640611	−	0.767866i	$-0.278681\pi$
$113$	13.6196			1.28122			0.640611	+	0.767866i	$0.278681\pi$
$114$	−2.00000			−0.187317
$115$	2.56255	−	4.43846i	0.238959	−	0.413889i
$116$	−1.30979	+	2.26862i	−0.121611	+	0.210636i
$117$	−2.80979	+	4.86669i	−0.259765	+	0.449926i
$118$	−0.894897	−	1.55001i	−0.0823819	−	0.142690i
$119$	−4.55065			−0.417157
$120$	−0.947448	+	1.64103i	−0.0864898	+	0.149805i
$121$	−7.72467			−0.702243
$122$	3.21468	+	7.11799i	0.291043	+	0.644433i
$123$	−1.19021			−0.107318
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	−12.1451			−1.08629
$126$	0.904893	+	1.56732i	0.0806143	+	0.139628i
$127$	0.904893	−	1.56732i	0.0802963	−	0.139077i	−0.823081	−	0.567924i	$-0.807747\pi$
$127$	0.904893	−	1.56732i	0.0802963	−	0.139077i	0.903377	+	0.428847i	$0.141080\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.45744	+	4.25642i	−0.216366	+	0.374757i
$130$	−10.6485			−0.933936
$131$	16.8187			1.46946			0.734730	−	0.678360i	$-0.237309\pi$
$131$	16.8187			1.46946			0.734730	+	0.678360i	$0.237309\pi$
$132$	−0.904893	−	1.56732i	−0.0787608	−	0.136418i
$133$	−3.61957			−0.313857
$134$	2.35234	+	4.07437i	0.203211	+	0.351972i
$135$	0.947448	−	1.64103i	0.0815434	−	0.141237i
$136$	−1.25723	−	2.17759i	−0.107807	−	0.186727i
$137$	−0.147659	+	0.255752i	−0.0126153	+	0.0218504i	−0.872264	−	0.489035i	$-0.837349\pi$
$137$	−0.147659	+	0.255752i	−0.0126153	+	0.0218504i	0.859649	+	0.510885i	$0.170682\pi$
$138$	1.35234	−	2.34232i	0.115119	−	0.199392i
$139$	0.752762	+	1.30382i	0.0638484	+	0.110589i	0.896183	−	0.443685i	$-0.146329\pi$
$139$	0.752762	+	1.30382i	0.0638484	+	0.110589i	−0.832334	+	0.554274i	$0.812996\pi$
$140$	−1.71468	+	2.96991i	−0.144917	+	0.251003i
$141$	5.24724	+	9.08848i	0.441897	+	0.765388i
$142$	−1.61957			−0.135911
$143$	5.08511	−	8.80767i	0.425238	−	0.736534i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	4.96382			0.412223
$146$	5.00000			0.413803
$147$	−1.86234	−	3.22566i	−0.153603	−	0.266048i
$148$	−0.852341	−	1.47630i	−0.0700620	−	0.121351i
$149$	0.789794			0.0647024			0.0323512	−	0.999477i	$-0.489700\pi$
$149$	0.789794			0.0647024			0.0323512	+	0.999477i	$0.489700\pi$
$150$	−1.40937			−0.115074
$151$	−0.714679	−	1.23786i	−0.0581597	−	0.100736i	0.835480	−	0.549521i	$-0.185190\pi$
$151$	−0.714679	−	1.23786i	−0.0581597	−	0.100736i	−0.893639	+	0.448786i	$0.851857\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$	1.25723	+	2.17759i	0.101641	+	0.176048i
$154$	−1.63766	−	2.83651i	−0.131967	−	0.228573i
$155$	−3.78979			−0.304404
$156$	−5.61957			−0.449926
$157$	10.5996	+	18.3590i	0.845939	+	1.46521i	0.884804	+	0.465964i	$0.154292\pi$
$157$	10.5996	+	18.3590i	0.845939	+	1.46521i	−0.0388651	+	0.999244i	$0.512374\pi$
$158$	−5.51447	−	9.55134i	−0.438708	−	0.759864i
$159$	13.3043			1.05510
$160$	−1.89490			−0.149805
$161$	2.44745	−	4.23911i	0.192886	−	0.334088i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	10.2843			0.805526			0.402763	−	0.915304i	$-0.368050\pi$
$163$	10.2843			0.805526			0.402763	+	0.915304i	$0.368050\pi$
$164$	−0.595107	−	1.03076i	−0.0464701	−	0.0804885i
$165$	−1.71468	+	2.96991i	−0.133488	+	0.231207i
$166$	1.09511	+	1.89678i	0.0849968	+	0.147219i
$167$	−6.16213	+	10.6731i	−0.476840	+	0.825911i	−0.999648	−	0.0265398i	$-0.991551\pi$
$167$	−6.16213	+	10.6731i	−0.476840	+	0.825911i	0.522808	+	0.852450i	$0.324884\pi$
$168$	−0.904893	+	1.56732i	−0.0698140	+	0.120921i
$169$	−9.28979	−	16.0904i	−0.714600	−	1.23772i
$170$	−2.38233	+	4.12632i	−0.182716	+	0.316474i
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	−4.91489			−0.374757
$173$	1.41489	+	2.45066i	0.107572	+	0.186320i	0.914786	−	0.403939i	$-0.132359\pi$
$173$	1.41489	+	2.45066i	0.107572	+	0.186320i	−0.807214	+	0.590259i	$0.799026\pi$
$174$	2.61957			0.198589
$175$	−2.55065			−0.192811
$176$	0.904893	−	1.56732i	0.0682089	−	0.118141i
$177$	−0.894897	+	1.55001i	−0.0672646	+	0.116506i
$178$	7.57702	−	13.1238i	0.567921	−	0.983669i
$179$	5.69469	+	9.86349i	0.425641	+	0.737232i	0.996480	−	0.0838303i	$-0.0267154\pi$
$179$	5.69469	+	9.86349i	0.425641	+	0.737232i	−0.570839	+	0.821062i	$0.693382\pi$
$180$	1.89490			0.141237
$181$	−7.10958	+	12.3141i	−0.528451	+	0.915303i	0.470999	+	0.882134i	$0.343893\pi$
$181$	−7.10958	+	12.3141i	−0.528451	+	0.915303i	−0.999450	+	0.0331696i	$0.989440\pi$
$182$	−10.1702			−0.753867
$183$	4.55702	−	6.34299i	0.336865	−	0.468887i
$184$	2.70468			0.199392
$185$	−1.61510	+	2.79743i	−0.118744	+	0.205671i
$186$	−2.00000			−0.146647
$187$	−2.27533	−	3.94098i	−0.166388	−	0.288193i
$188$	−5.24724	+	9.08848i	−0.382694	+	0.662846i
$189$	0.904893	−	1.56732i	0.0658213	−	0.114006i
$190$	−1.89490	+	3.28206i	−0.137470	+	0.238105i
$191$	7.29532			0.527871			0.263935	−	0.964540i	$-0.414979\pi$
$191$	7.29532			0.527871			0.263935	+	0.964540i	$0.414979\pi$
$192$	−1.00000			−0.0721688
$193$	13.1866	+	22.8398i	0.949192	+	1.64405i	0.747133	+	0.664675i	$0.231430\pi$
$193$	13.1866	+	22.8398i	0.949192	+	1.64405i	0.202059	+	0.979373i	$0.435237\pi$
$194$	15.5145			1.11387
$195$	5.32425	+	9.22188i	0.381278	+	0.660393i
$196$	1.86234	−	3.22566i	0.133024	−	0.230405i
$197$	11.3568	+	19.6706i	0.809140	+	1.40147i	0.913461	+	0.406927i	$0.133400\pi$
$197$	11.3568	+	19.6706i	0.809140	+	1.40147i	−0.104321	+	0.994544i	$0.533267\pi$
$198$	−0.904893	+	1.56732i	−0.0643079	+	0.111385i
$199$	11.9238	−	20.6527i	0.845258	−	1.46403i	−0.0401386	−	0.999194i	$-0.512780\pi$
$199$	11.9238	−	20.6527i	0.845258	−	1.46403i	0.885397	−	0.464836i	$-0.153887\pi$
$200$	−0.704683	−	1.22055i	−0.0498286	−	0.0863057i
$201$	2.35234	−	4.07437i	0.165921	−	0.287384i
$202$	−3.05255	−	5.28717i	−0.214777	−	0.372004i
$203$	4.74086			0.332743
$204$	−1.25723	+	2.17759i	−0.0880240	+	0.152462i
$205$	−1.12767	+	1.95318i	−0.0787596	+	0.136416i
$206$	−0.210206			−0.0146458
$207$	−2.70468			−0.187988
$208$	−2.80979	−	4.86669i	−0.194824	−	0.337444i
$209$	−1.80979	−	3.13464i	−0.125186	−	0.216828i
$210$	3.42936			0.236648
$211$	−13.9038			−0.957180			−0.478590	−	0.878039i	$-0.658852\pi$
$211$	−13.9038			−0.957180			−0.478590	+	0.878039i	$0.658852\pi$
$212$	6.65213	+	11.5218i	0.456870	+	0.791322i
$213$	0.809786	+	1.40259i	0.0554856	+	0.0961039i
$214$	4.78979	+	8.29617i	0.327424	+	0.567114i
$215$	4.65660	+	8.06547i	0.317578	+	0.550061i
$216$	1.00000			0.0680414
$217$	−3.61957			−0.245713
$218$	−1.59511	−	2.76281i	−0.108034	−	0.187121i
$219$	−2.50000	−	4.33013i	−0.168934	−	0.292603i
$220$	−3.42936			−0.231207
$221$	−14.1302			−0.950503
$222$	−0.852341	+	1.47630i	−0.0572054	+	0.0990827i
$223$	6.58958	−	11.4135i	0.441271	−	0.764304i	−0.556513	−	0.830839i	$-0.687861\pi$
$223$	6.58958	−	11.4135i	0.441271	−	0.764304i	0.997784	+	0.0665349i	$0.0211944\pi$
$224$	−1.80979			−0.120921
$225$	0.704683	+	1.22055i	0.0469789	+	0.0813698i
$226$	6.80979	−	11.7949i	0.452980	−	0.784585i
$227$	−2.90489	−	5.03142i	−0.192805	−	0.333947i	0.753374	−	0.657592i	$-0.228425\pi$
$227$	−2.90489	−	5.03142i	−0.192805	−	0.333947i	−0.946179	+	0.323645i	$0.895092\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	14.8143	−	25.6590i	0.978954	−	1.69560i	0.312737	−	0.949840i	$-0.398754\pi$
$229$	14.8143	−	25.6590i	0.978954	−	1.69560i	0.666217	−	0.745758i	$-0.267912\pi$
$230$	−2.56255	−	4.43846i	−0.168969	−	0.292664i
$231$	−1.63766	+	2.83651i	−0.107750	+	0.186629i
$232$	1.30979	+	2.26862i	0.0859917	+	0.148942i
$233$	−15.1902			−0.995144			−0.497572	−	0.867423i	$-0.665775\pi$
$233$	−15.1902			−0.995144			−0.497572	+	0.867423i	$0.665775\pi$
$234$	2.80979	+	4.86669i	0.183681	+	0.318146i
$235$	19.8860			1.29722
$236$	−1.78979			−0.116506
$237$	−5.51447	+	9.55134i	−0.358203	+	0.620426i
$238$	−2.27533	+	3.94098i	−0.147487	+	0.255456i
$239$	−12.7817	+	22.1386i	−0.826779	+	1.43202i	0.0737724	+	0.997275i	$0.476496\pi$
$239$	−12.7817	+	22.1386i	−0.826779	+	1.43202i	−0.900552	+	0.434749i	$0.856837\pi$
$240$	0.947448	+	1.64103i	0.0611575	+	0.105928i
$241$	−16.2391			−1.04606			−0.523028	−	0.852316i	$-0.675198\pi$
$241$	−16.2391			−1.04606			−0.523028	+	0.852316i	$0.675198\pi$
$242$	−3.86234	+	6.68976i	−0.248280	+	0.430034i
$243$	−1.00000			−0.0641500
$244$	7.77170	+	0.775003i	0.497532	+	0.0496145i
$245$	−7.05788			−0.450911
$246$	−0.595107	+	1.03076i	−0.0379426	+	0.0657186i
$247$	−11.2391			−0.715130
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	1.09511	−	1.89678i	0.0693996	−	0.120204i
$250$	−6.07254	+	10.5180i	−0.384061	+	0.665214i
$251$	−4.73467	+	8.20069i	−0.298850	+	0.517623i	−0.975873	−	0.218339i	$-0.929936\pi$
$251$	−4.73467	+	8.20069i	−0.298850	+	0.517623i	0.677023	+	0.735962i	$0.263270\pi$
$252$	1.80979			0.114006
$253$	4.89490			0.307740
$254$	−0.904893	−	1.56732i	−0.0567780	−	0.0983424i
$255$	4.76466			0.298375
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.19469	+	3.80131i	−0.136901	+	0.237119i	−0.926322	−	0.376733i	$-0.877047\pi$
$257$	−2.19469	+	3.80131i	−0.136901	+	0.237119i	0.789421	+	0.613852i	$0.210381\pi$
$258$	2.45744	+	4.25642i	0.152994	+	0.264993i
$259$	−1.54256	+	2.67178i	−0.0958497	+	0.166017i
$260$	−5.32425	+	9.22188i	−0.330196	+	0.571917i
$261$	−1.30979	−	2.26862i	−0.0810737	−	0.140424i
$262$	8.40937	−	14.5654i	0.519532	−	0.899856i
$263$	3.33235	+	5.77180i	0.205481	+	0.355904i	0.950286	−	0.311378i	$-0.100791\pi$
$263$	3.33235	+	5.77180i	0.205481	+	0.355904i	−0.744805	+	0.667283i	$0.767457\pi$
$264$	−1.80979			−0.111385
$265$	12.6051	−	21.8327i	0.774325	−	1.34117i
$266$	−1.80979	+	3.13464i	−0.110965	+	0.192197i
$267$	−15.1540			−0.927412
$268$	4.70468			0.287384
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	0.932119	−	0.362151i	$-0.117958\pi$
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	−0.779692	+	0.626164i	$0.784624\pi$
$270$	−0.947448	−	1.64103i	−0.0576599	−	0.0998698i
$271$	−9.63956			−0.585562			−0.292781	−	0.956180i	$-0.594581\pi$
$271$	−9.63956			−0.585562			−0.292781	+	0.956180i	$0.594581\pi$
$272$	−2.51447			−0.152462
$273$	5.08511	+	8.80767i	0.307765	+	0.533064i
$274$	0.147659	+	0.255752i	0.00892038	+	0.0154506i
$275$	−1.27533	−	2.20893i	−0.0769050	−	0.133203i
$276$	−1.35234	−	2.34232i	−0.0814014	−	0.140991i
$277$	−13.7536			−0.826374			−0.413187	−	0.910646i	$-0.635585\pi$
$277$	−13.7536			−0.826374			−0.413187	+	0.910646i	$0.635585\pi$
$278$	1.50552			0.0902953
$279$	1.00000	+	1.73205i	0.0598684	+	0.103695i
$280$	1.71468	+	2.96991i	0.102472	+	0.177486i
$281$	−1.87490			−0.111847			−0.0559237	−	0.998435i	$-0.517810\pi$
$281$	−1.87490			−0.111847			−0.0559237	+	0.998435i	$0.517810\pi$
$282$	10.4945			0.624937
$283$	−13.5145	+	23.4077i	−0.803352	+	1.39145i	0.114046	+	0.993475i	$0.463619\pi$
$283$	−13.5145	+	23.4077i	−0.803352	+	1.39145i	−0.917398	+	0.397971i	$0.869715\pi$
$284$	−0.809786	+	1.40259i	−0.0480520	+	0.0832284i
$285$	3.78979			0.224488
$286$	−5.08511	−	8.80767i	−0.300689	−	0.520808i
$287$	−1.07702	+	1.86545i	−0.0635743	+	0.110114i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	5.33872	−	9.24694i	0.314043	−	0.543938i
$290$	2.48191	−	4.29879i	0.145743	−	0.252434i
$291$	−7.75723	−	13.4359i	−0.454737	−	0.787628i
$292$	2.50000	−	4.33013i	0.146301	−	0.253402i
$293$	−4.46744	−	7.73783i	−0.260991	−	0.452049i	0.705515	−	0.708695i	$-0.250716\pi$
$293$	−4.46744	−	7.73783i	−0.260991	−	0.452049i	−0.966505	+	0.256646i	$0.917383\pi$
$294$	−3.72467			−0.217227
$295$	1.69574	+	2.93710i	0.0987296	+	0.171005i
$296$	−1.70468			−0.0990827
$297$	1.80979			0.105014
$298$	0.394897	−	0.683982i	0.0228758	−	0.0396220i
$299$	7.59958	−	13.1629i	0.439495	−	0.761228i
$300$	−0.704683	+	1.22055i	−0.0406849	+	0.0704683i
$301$	4.44745	+	7.70321i	0.256347	+	0.444005i
$302$	−1.42936			−0.0822503
$303$	−3.05255	+	5.28717i	−0.175365	+	0.303740i
$304$	−2.00000			−0.114708
$305$	−6.09149	−	13.4879i	−0.348797	−	0.772313i
$306$	2.51447			0.143743
$307$	1.18212	−	2.04749i	0.0674671	−	0.116856i	−0.830319	−	0.557289i	$-0.811842\pi$
$307$	1.18212	−	2.04749i	0.0674671	−	0.116856i	0.897786	+	0.440433i	$0.145175\pi$
$308$	−3.27533			−0.186629
$309$	0.105103	+	0.182044i	0.00597911	+	0.0103561i
$310$	−1.89490	+	3.28206i	−0.107623	+	0.186408i
$311$	−9.08511	+	15.7359i	−0.515169	+	0.892300i	0.484676	+	0.874694i	$0.338938\pi$
$311$	−9.08511	+	15.7359i	−0.515169	+	0.892300i	−0.999845	+	0.0176056i	$0.994396\pi$
$312$	−2.80979	+	4.86669i	−0.159073	+	0.275522i
$313$	11.3732			0.642850			0.321425	−	0.946935i	$-0.395838\pi$
$313$	11.3732			0.642850			0.321425	+	0.946935i	$0.395838\pi$
$314$	21.1992			1.19634
$315$	−1.71468	−	2.96991i	−0.0966112	−	0.167336i
$316$	−11.0289			−0.620426
$317$	−3.85681	−	6.68020i	−0.216620	−	0.375197i	0.737152	−	0.675727i	$-0.236170\pi$
$317$	−3.85681	−	6.68020i	−0.216620	−	0.375197i	−0.953773	+	0.300529i	$0.902837\pi$
$318$	6.65213	−	11.5218i	0.373033	−	0.646112i
$319$	2.37043	+	4.10571i	0.132719	+	0.229876i
$320$	−0.947448	+	1.64103i	−0.0529640	+	0.0917363i
$321$	4.78979	−	8.29617i	0.267340	−	0.463047i
$322$	−2.44745	−	4.23911i	−0.136391	−	0.236236i
$323$	−2.51447	+	4.35519i	−0.139909	+	0.242329i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−7.92003			−0.439324
$326$	5.14214	−	8.90644i	0.284797	−	0.493282i
$327$	−1.59511	+	2.76281i	−0.0882096	+	0.152784i
$328$	−1.19021			−0.0657186
$329$	18.9928			1.04710
$330$	1.71468	+	2.96991i	0.0943900	+	0.163488i
$331$	−15.1911	−	26.3117i	−0.834976	−	1.44622i	−0.894050	−	0.447968i	$-0.852148\pi$
$331$	−15.1911	−	26.3117i	−0.834976	−	1.44622i	0.0590732	−	0.998254i	$-0.481185\pi$
$332$	2.19021			0.120204
$333$	1.70468			0.0934160
$334$	6.16213	+	10.6731i	0.337177	+	0.584007i
$335$	−4.45744	−	7.72052i	−0.243536	−	0.421817i
$336$	0.904893	+	1.56732i	0.0493660	+	0.0855043i
$337$	−14.5996	−	25.2872i	−0.795290	−	1.37748i	−0.922655	−	0.385626i	$-0.873985\pi$
$337$	−14.5996	−	25.2872i	−0.795290	−	1.37748i	0.127365	−	0.991856i	$-0.459348\pi$
$338$	−18.5796			−1.01060
$339$	−13.6196			−0.739714
$340$	2.38233	+	4.12632i	0.129200	+	0.223781i
$341$	−1.80979	−	3.13464i	−0.0980054	−	0.169750i
$342$	2.00000			0.108148
$343$	−19.4094			−1.04801
$344$	−2.45744	+	4.25642i	−0.132497	+	0.229491i
$345$	−2.56255	+	4.43846i	−0.137963	+	0.238959i
$346$	2.82978			0.152130
$347$	−0.210206	−	0.364088i	−0.0112845	−	0.0195453i	0.860328	−	0.509741i	$-0.170259\pi$
$347$	−0.210206	−	0.364088i	−0.0112845	−	0.0195453i	−0.871612	+	0.490196i	$0.836925\pi$
$348$	1.30979	−	2.26862i	0.0702119	−	0.121611i
$349$	−0.147659	−	0.255752i	−0.00790398	−	0.0136901i	0.862046	−	0.506829i	$-0.169183\pi$
$349$	−0.147659	−	0.255752i	−0.00790398	−	0.0136901i	−0.869950	+	0.493139i	$0.835849\pi$
$350$	−1.27533	+	2.20893i	−0.0681690	+	0.118072i
$351$	2.80979	−	4.86669i	0.149975	−	0.259765i
$352$	−0.904893	−	1.56732i	−0.0482310	−	0.0835385i
$353$	17.8387	−	30.8976i	0.949459	−	1.64451i	0.202893	−	0.979201i	$-0.434966\pi$
$353$	17.8387	−	30.8976i	0.949459	−	1.64451i	0.746566	−	0.665311i	$-0.231701\pi$
$354$	0.894897	+	1.55001i	0.0475632	+	0.0823819i
$355$	3.06892			0.162881
$356$	−7.57702	−	13.1238i	−0.401581	−	0.695559i
$357$	4.55065			0.240846
$358$	11.3894			0.601947
$359$	17.9719	−	31.1283i	0.948521	−	1.64289i	0.199979	−	0.979800i	$-0.435913\pi$
$359$	17.9719	−	31.1283i	0.948521	−	1.64289i	0.748542	−	0.663087i	$-0.230754\pi$
$360$	0.947448	−	1.64103i	0.0499349	−	0.0864898i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	7.10958	+	12.3141i	0.373671	+	0.647217i
$363$	7.72467			0.405440
$364$	−5.08511	+	8.80767i	−0.266532	+	0.461647i
$365$	−9.47448			−0.495917
$366$	−3.21468	−	7.11799i	−0.168034	−	0.372064i
$367$	−6.85872			−0.358022			−0.179011	−	0.983847i	$-0.557290\pi$
$367$	−6.85872			−0.358022			−0.179011	+	0.983847i	$0.557290\pi$
$368$	1.35234	−	2.34232i	0.0704957	−	0.122102i
$369$	1.19021			0.0619601
$370$	1.61510	+	2.79743i	0.0839650	+	0.145432i
$371$	12.0389	−	20.8520i	0.625030	−	1.08258i
$372$	−1.00000	+	1.73205i	−0.0518476	+	0.0898027i
$373$	15.5389	−	26.9142i	0.804575	−	1.39357i	−0.112002	−	0.993708i	$-0.535726\pi$
$373$	15.5389	−	26.9142i	0.804575	−	1.39357i	0.916577	−	0.399858i	$-0.130940\pi$
$374$	−4.55065			−0.235309
$375$	12.1451			0.627170
$376$	5.24724	+	9.08848i	0.270606	+	0.468703i
$377$	14.7209			0.758163
$378$	−0.904893	−	1.56732i	−0.0465427	−	0.0806143i
$379$	−5.56255	+	9.63462i	−0.285729	+	0.494897i	−0.972786	−	0.231707i	$-0.925569\pi$
$379$	−5.56255	+	9.63462i	−0.285729	+	0.494897i	0.687057	+	0.726604i	$0.258902\pi$
$380$	1.89490	+	3.28206i	0.0972062	+	0.168366i
$381$	−0.904893	+	1.56732i	−0.0463591	+	0.0802963i
$382$	3.64766	−	6.31793i	0.186630	−	0.323253i
$383$	9.53446	+	16.5142i	0.487188	+	0.843835i	0.999891	−	0.0147312i	$-0.00468924\pi$
$383$	9.53446	+	16.5142i	0.487188	+	0.843835i	−0.512703	+	0.858566i	$0.671356\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	3.10320	+	5.37490i	0.158154	+	0.273930i
$386$	26.3732			1.34236
$387$	2.45744	−	4.25642i	0.124919	−	0.216366i
$388$	7.75723	−	13.4359i	0.393814	−	0.682106i
$389$	−10.7136			−0.543203			−0.271601	−	0.962410i	$-0.587553\pi$
$389$	−10.7136			−0.543203			−0.271601	+	0.962410i	$0.587553\pi$
$390$	10.6485			0.539208
$391$	−3.40042	−	5.88970i	−0.171967	−	0.297855i
$392$	−1.86234	−	3.22566i	−0.0940622	−	0.162921i
$393$	−16.8187			−0.848393
$394$	22.7136			1.14430
$395$	10.4493	+	18.0988i	0.525764	+	0.910650i
$396$	0.904893	+	1.56732i	0.0454726	+	0.0787608i
$397$	2.68022	+	4.64227i	0.134516	+	0.232989i	0.925413	−	0.378961i	$-0.123719\pi$
$397$	2.68022	+	4.64227i	0.134516	+	0.232989i	−0.790896	+	0.611950i	$0.790385\pi$
$398$	−11.9238	−	20.6527i	−0.597688	−	1.03523i
$399$	3.61957			0.181205
$400$	−1.40937			−0.0704683
$401$	−2.64214	−	4.57631i	−0.131942	−	0.228530i	0.792483	−	0.609894i	$-0.208788\pi$
$401$	−2.64214	−	4.57631i	−0.131942	−	0.228530i	−0.924425	+	0.381364i	$0.875455\pi$
$402$	−2.35234	−	4.07437i	−0.117324	−	0.203211i
$403$	−11.2391			−0.559862
$404$	−6.10510			−0.303740
$405$	−0.947448	+	1.64103i	−0.0470791	+	0.0815434i
$406$	2.37043	−	4.10571i	0.117643	−	0.203763i
$407$	−3.08511			−0.152923
$408$	1.25723	+	2.17759i	0.0622424	+	0.107807i
$409$	15.3187	−	26.5328i	0.757463	−	1.31196i	−0.186678	−	0.982421i	$-0.559772\pi$
$409$	15.3187	−	26.5328i	0.757463	−	1.31196i	0.944141	−	0.329542i	$-0.106894\pi$
$410$	1.12767	+	1.95318i	0.0556915	+	0.0964605i
$411$	0.147659	−	0.255752i	0.00728346	−	0.0126153i
$412$	−0.105103	+	0.182044i	−0.00517806	+	0.00896866i
$413$	1.61957	+	2.80518i	0.0796939	+	0.138034i
$414$	−1.35234	+	2.34232i	−0.0664640	+	0.115119i
$415$	−2.07511	−	3.59420i	−0.101863	−	0.176433i
$416$	−5.61957			−0.275522
$417$	−0.752762	−	1.30382i	−0.0368629	−	0.0638484i
$418$	−3.61957			−0.177039
$419$	−33.4294			−1.63313			−0.816565	−	0.577253i	$-0.804125\pi$
$419$	−33.4294			−1.63313			−0.816565	+	0.577253i	$0.804125\pi$
$420$	1.71468	−	2.96991i	0.0836678	−	0.144917i
$421$	−14.5434	+	25.1899i	−0.708802	+	1.22768i	0.256499	+	0.966544i	$0.417431\pi$
$421$	−14.5434	+	25.1899i	−0.708802	+	1.22768i	−0.965302	+	0.261137i	$0.915903\pi$
$422$	−6.95192	+	12.0411i	−0.338414	+	0.586151i
$423$	−5.24724	−	9.08848i	−0.255129	−	0.441897i
$424$	13.3043			0.646112
$425$	−1.77190	+	3.06903i	−0.0859499	+	0.148870i
$426$	1.61957			0.0784685
$427$	−5.81788	−	12.8820i	−0.281547	−	0.623406i
$428$	9.57959			0.463047
$429$	−5.08511	+	8.80767i	−0.245511	+	0.425238i
$430$	9.31321			0.449123
$431$	19.5434	+	33.8502i	0.941373	+	1.63051i	0.762856	+	0.646569i	$0.223797\pi$
$431$	19.5434	+	33.8502i	0.941373	+	1.63051i	0.178517	+	0.983937i	$0.442870\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−9.67212	+	16.7526i	−0.464813	+	0.805079i	−0.999193	−	0.0401650i	$-0.987212\pi$
$433$	−9.67212	+	16.7526i	−0.464813	+	0.805079i	0.534380	+	0.845244i	$0.320545\pi$
$434$	−1.80979	+	3.13464i	−0.0868725	+	0.150468i
$435$	−4.96382			−0.237997
$436$	−3.19021			−0.152784
$437$	−2.70468	−	4.68465i	−0.129383	−	0.224097i
$438$	−5.00000			−0.238909
$439$	−4.33425	−	7.50714i	−0.206863	−	0.358296i	0.743862	−	0.668333i	$-0.232992\pi$
$439$	−4.33425	−	7.50714i	−0.206863	−	0.358296i	−0.950725	+	0.310037i	$0.899659\pi$
$440$	−1.71468	+	2.96991i	−0.0817441	+	0.141585i
$441$	1.86234	+	3.22566i	0.0886827	+	0.153603i
$442$	−7.06512	+	12.2371i	−0.336053	+	0.582062i
$443$	5.71468	−	9.89811i	0.271513	−	0.470274i	−0.697737	−	0.716354i	$-0.745809\pi$
$443$	5.71468	−	9.89811i	0.271513	−	0.470274i	0.969249	+	0.246081i	$0.0791428\pi$
$444$	0.852341	+	1.47630i	0.0404503	+	0.0700620i
$445$	−14.3577	+	24.8682i	−0.680619	+	1.17887i
$446$	−6.58958	−	11.4135i	−0.312026	−	0.540445i
$447$	−0.789794			−0.0373560
$448$	−0.904893	+	1.56732i	−0.0427522	+	0.0740489i
$449$	−6.57254	+	11.3840i	−0.310178	+	0.537243i	−0.978401	−	0.206718i	$-0.933722\pi$
$449$	−6.57254	+	11.3840i	−0.310178	+	0.537243i	0.668223	+	0.743961i	$0.267055\pi$
$450$	1.40937			0.0664381
$451$	−2.15403			−0.101429
$452$	−6.80979	−	11.7949i	−0.320305	−	0.554785i
$453$	0.714679	+	1.23786i	0.0335785	+	0.0581597i
$454$	−5.80979			−0.272667
$455$	19.2715			0.903463
$456$	1.00000	+	1.73205i	0.0468293	+	0.0811107i
$457$	2.88043	+	4.98905i	0.134741	+	0.233378i	0.925498	−	0.378752i	$-0.123647\pi$
$457$	2.88043	+	4.98905i	0.134741	+	0.233378i	−0.790758	+	0.612129i	$0.790313\pi$
$458$	−14.8143	−	25.6590i	−0.692225	−	1.19897i
$459$	−1.25723	−	2.17759i	−0.0586827	−	0.101641i
$460$	−5.12510			−0.238959
$461$	−9.07617			−0.422719			−0.211360	−	0.977408i	$-0.567789\pi$
$461$	−9.07617			−0.422719			−0.211360	+	0.977408i	$0.567789\pi$
$462$	1.63766	+	2.83651i	0.0761910	+	0.131967i
$463$	5.50447	+	9.53403i	0.255815	+	0.443084i	0.965116	−	0.261821i	$-0.0843230\pi$
$463$	5.50447	+	9.53403i	0.255815	+	0.443084i	−0.709302	+	0.704905i	$0.750990\pi$
$464$	2.61957			0.121611
$465$	3.78979			0.175747
$466$	−7.59511	+	13.1551i	−0.351837	+	0.609399i
$467$	−5.00000	+	8.66025i	−0.231372	+	0.400749i	−0.958212	−	0.286058i	$-0.907655\pi$
$467$	−5.00000	+	8.66025i	−0.231372	+	0.400749i	0.726840	+	0.686807i	$0.240988\pi$
$468$	5.61957			0.259765
$469$	−4.25723	−	7.37375i	−0.196581	−	0.340488i
$470$	9.94298	−	17.2217i	0.458635	−	0.794380i
$471$	−10.5996	−	18.3590i	−0.488403	−	0.845939i
$472$	−0.894897	+	1.55001i	−0.0411910	+	0.0713449i
$473$	−4.44745	+	7.70321i	−0.204494	+	0.354194i
$474$	5.51447	+	9.55134i	0.253288	+	0.438708i
$475$	−1.40937	+	2.44109i	−0.0646661	+	0.112005i
$476$	2.27533	+	3.94098i	0.104289	+	0.180634i
$477$	−13.3043			−0.609160
$478$	12.7817	+	22.1386i	0.584621	+	1.01259i
$479$	42.8587			1.95826			0.979132	−	0.203224i	$-0.0651418\pi$
$479$	42.8587			1.95826			0.979132	+	0.203224i	$0.0651418\pi$
$480$	1.89490			0.0864898
$481$	−4.78979	+	8.29617i	−0.218396	+	0.378273i
$482$	−8.11957	+	14.0635i	−0.369836	+	0.640575i
$483$	−2.44745	+	4.23911i	−0.111363	+	0.192886i
$484$	3.86234	+	6.68976i	0.175561	+	0.304080i
$485$	−29.3983			−1.33491
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−13.2391			−0.599923			−0.299961	−	0.953951i	$-0.596974\pi$
$487$	−13.2391			−0.599923			−0.299961	+	0.953951i	$0.596974\pi$
$488$	4.55702	−	6.34299i	0.206287	−	0.287134i
$489$	−10.2843			−0.465071
$490$	−3.52894	+	6.11230i	−0.159421	+	0.276126i
$491$	−4.15023			−0.187297			−0.0936486	−	0.995605i	$-0.529853\pi$
$491$	−4.15023			−0.187297			−0.0936486	+	0.995605i	$0.529853\pi$
$492$	0.595107	+	1.03076i	0.0268295	+	0.0464701i
$493$	3.29342	−	5.70436i	0.148328	−	0.256912i
$494$	−5.61957	+	9.73338i	−0.252836	+	0.437926i
$495$	1.71468	−	2.96991i	0.0770691	−	0.133488i
$496$	−2.00000			−0.0898027
$497$	2.93108			0.131477
$498$	−1.09511	−	1.89678i	−0.0490729	−	0.0849968i
$499$	39.1268			1.75156			0.875778	−	0.482714i	$-0.160349\pi$
$499$	39.1268			1.75156			0.875778	+	0.482714i	$0.160349\pi$
$500$	6.07254	+	10.5180i	0.271572	+	0.470377i
$501$	6.16213	−	10.6731i	0.275304	−	0.476840i
$502$	4.73467	+	8.20069i	0.211319	+	0.366015i
$503$	−19.4664	+	33.7168i	−0.867963	+	1.50336i	−0.00388915	+	0.999992i	$0.501238\pi$
$503$	−19.4664	+	33.7168i	−0.867963	+	1.50336i	−0.864074	+	0.503364i	$0.832095\pi$
$504$	0.904893	−	1.56732i	0.0403071	−	0.0698140i
$505$	5.78427	+	10.0187i	0.257397	+	0.445824i
$506$	2.44745	−	4.23911i	0.108802	−	0.188451i
$507$	9.28979	+	16.0904i	0.412574	+	0.714600i
$508$	−1.80979			−0.0802963
$509$	16.1196	−	27.9199i	0.714487	−	1.23753i	−0.248669	−	0.968588i	$-0.579993\pi$
$509$	16.1196	−	27.9199i	0.714487	−	1.23753i	0.963157	−	0.268940i	$-0.0866734\pi$
$510$	2.38233	−	4.12632i	0.105491	−	0.182716i
$511$	−9.04893			−0.400301
$512$	−1.00000			−0.0441942
$513$	−1.00000	−	1.73205i	−0.0441511	−	0.0764719i
$514$	2.19469	+	3.80131i	0.0968035	+	0.167669i
$515$	0.398319			0.0175520
$516$	4.91489			0.216366
$517$	9.49638	+	16.4482i	0.417650	+	0.723391i
$518$	1.54256	+	2.67178i	0.0677760	+	0.117391i
$519$	−1.41489	−	2.45066i	−0.0621067	−	0.107572i
$520$	5.32425	+	9.22188i	0.233484	+	0.404406i
$521$	21.5524			0.944226			0.472113	−	0.881538i	$-0.343491\pi$
$521$	21.5524			0.944226			0.472113	+	0.881538i	$0.343491\pi$
$522$	−2.61957			−0.114656
$523$	16.0089	+	27.7283i	0.700022	+	1.21247i	0.968458	+	0.249177i	$0.0801600\pi$
$523$	16.0089	+	27.7283i	0.700022	+	1.21247i	−0.268436	+	0.963298i	$0.586507\pi$
$524$	−8.40937	−	14.5654i	−0.367365	−	0.636295i
$525$	2.55065			0.111319
$526$	6.66470			0.290595
$527$	−2.51447	+	4.35519i	−0.109532	+	0.189715i
$528$	−0.904893	+	1.56732i	−0.0393804	+	0.0682089i
$529$	−15.6847			−0.681943
$530$	−12.6051	−	21.8327i	−0.547531	−	0.948351i
$531$	0.894897	−	1.55001i	0.0388352	−	0.0672646i
$532$	1.80979	+	3.13464i	0.0784642	+	0.135904i
$533$	−3.34425	+	5.79241i	−0.144855	+	0.250897i
$534$	−7.57702	+	13.1238i	−0.327890	+	0.567921i
$535$	−9.07617	−	15.7204i	−0.392397	−	0.679651i
$536$	2.35234	−	4.07437i	0.101606	−	0.175986i
$537$	−5.69469	−	9.86349i	−0.245744	−	0.425641i
$538$	5.00000			0.215565
$539$	−3.37043	−	5.83776i	−0.145175	−	0.251450i
$540$	−1.89490			−0.0815434
$541$	−11.0289			−0.474171			−0.237086	−	0.971489i	$-0.576192\pi$
$541$	−11.0289			−0.474171			−0.237086	+	0.971489i	$0.576192\pi$
$542$	−4.81978	+	8.34811i	−0.207027	+	0.358582i
$543$	7.10958	−	12.3141i	0.305101	−	0.528451i
$544$	−1.25723	+	2.17759i	−0.0539035	+	0.0933636i
$545$	3.02256	+	5.23523i	0.129472	+	0.224253i
$546$	10.1702			0.435245
$547$	−18.1340	+	31.4091i	−0.775356	+	1.34296i	0.159239	+	0.987240i	$0.449096\pi$
$547$	−18.1340	+	31.4091i	−0.775356	+	1.34296i	−0.934594	+	0.355715i	$0.884237\pi$
$548$	0.295317			0.0126153
$549$	−4.55702	+	6.34299i	−0.194489	+	0.270712i
$550$	−2.55065			−0.108760
$551$	2.61957	−	4.53723i	0.111598	−	0.193293i
$552$	−2.70468			−0.115119
$553$	9.98001	+	17.2859i	0.424393	+	0.735070i
$554$	−6.87681	+	11.9110i	−0.292167	+	0.506049i
$555$	1.61510	−	2.79743i	0.0685571	−	0.118744i
$556$	0.752762	−	1.30382i	0.0319242	−	0.0552943i
$557$	13.5145			0.572626			0.286313	−	0.958136i	$-0.407570\pi$
$557$	13.5145			0.572626			0.286313	+	0.958136i	$0.407570\pi$
$558$	2.00000			0.0846668
$559$	13.8098	+	23.9193i	0.584092	+	1.01168i
$560$	3.42936			0.144917
$561$	2.27533	+	3.94098i	0.0960643	+	0.166388i
$562$	−0.937452	+	1.62372i	−0.0395440	+	0.0684923i
$563$	9.68469	+	16.7744i	0.408161	+	0.706956i	0.994684	−	0.102977i	$-0.0328368\pi$
$563$	9.68469	+	16.7744i	0.408161	+	0.706956i	−0.586523	+	0.809933i	$0.699504\pi$
$564$	5.24724	−	9.08848i	0.220949	−	0.382694i
$565$	−12.9038	+	22.3501i	−0.542869	+	0.940276i
$566$	13.5145	+	23.4077i	0.568055	+	0.983901i
$567$	−0.904893	+	1.56732i	−0.0380019	+	0.0658213i
$568$	0.809786	+	1.40259i	0.0339779	+	0.0588514i
$569$	13.2391			0.555014			0.277507	−	0.960724i	$-0.410492\pi$
$569$	13.2391			0.555014			0.277507	+	0.960724i	$0.410492\pi$
$570$	1.89490	−	3.28206i	0.0793685	−	0.137470i
$571$	−18.5715	+	32.1668i	−0.777193	+	1.34614i	0.156361	+	0.987700i	$0.450024\pi$
$571$	−18.5715	+	32.1668i	−0.777193	+	1.34614i	−0.933554	+	0.358437i	$0.883310\pi$
$572$	−10.1702			−0.425238
$573$	−7.29532			−0.304766
$574$	1.07702	+	1.86545i	0.0449538	+	0.0778623i
$575$	−1.90594	−	3.30119i	−0.0794833	−	0.137669i
$576$	1.00000			0.0416667
$577$	−8.27533			−0.344506			−0.172253	−	0.985053i	$-0.555105\pi$
$577$	−8.27533			−0.344506			−0.172253	+	0.985053i	$0.555105\pi$
$578$	−5.33872	−	9.24694i	−0.222062	−	0.384622i
$579$	−13.1866	−	22.8398i	−0.548016	−	0.949192i
$580$	−2.48191	−	4.29879i	−0.103056	−	0.178498i
$581$	−1.98191	−	3.43277i	−0.0822235	−	0.142415i
$582$	−15.5145			−0.643095
$583$	24.0779			0.997203
$584$	−2.50000	−	4.33013i	−0.103451	−	0.179182i
$585$	−5.32425	−	9.22188i	−0.220131	−	0.381278i
$586$	−8.93488			−0.369097
$587$	−14.6085			−0.602958			−0.301479	−	0.953473i	$-0.597480\pi$
$587$	−14.6085			−0.602958			−0.301479	+	0.953473i	$0.597480\pi$
$588$	−1.86234	+	3.22566i	−0.0768015	+	0.133024i
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$	3.39147			0.139625
$591$	−11.3568	−	19.6706i	−0.467157	−	0.809140i
$592$	−0.852341	+	1.47630i	−0.0350310	+	0.0606755i
$593$	−3.91746	−	6.78524i	−0.160871	−	0.278636i	0.774310	−	0.632806i	$-0.218097\pi$
$593$	−3.91746	−	6.78524i	−0.160871	−	0.278636i	−0.935181	+	0.354170i	$0.884764\pi$
$594$	0.904893	−	1.56732i	0.0371282	−	0.0643079i
$595$	4.31151	−	7.46775i	0.176755	−	0.306148i
$596$	−0.394897	−	0.683982i	−0.0161756	−	0.0280170i
$597$	−11.9238	+	20.6527i	−0.488010	+	0.845258i
$598$	−7.59958	−	13.1629i	−0.310770	−	0.538269i
$599$	−16.5345			−0.675580			−0.337790	−	0.941222i	$-0.609679\pi$
$599$	−16.5345			−0.675580			−0.337790	+	0.941222i	$0.609679\pi$
$600$	0.704683	+	1.22055i	0.0287686	+	0.0498286i
$601$	33.4745			1.36545			0.682726	−	0.730674i	$-0.260794\pi$
$601$	33.4745			1.36545			0.682726	+	0.730674i	$0.260794\pi$
$602$	8.89490			0.362529
$603$	−2.35234	+	4.07437i	−0.0957947	+	0.165921i
$604$	−0.714679	+	1.23786i	−0.0290799	+	0.0503678i
$605$	7.31873	−	12.6764i	0.297549	−	0.515370i
$606$	3.05255	+	5.28717i	0.124001	+	0.214777i
$607$	30.0179			1.21839			0.609194	−	0.793021i	$-0.291493\pi$
$607$	30.0179			1.21839			0.609194	+	0.793021i	$0.291493\pi$
$608$	−1.00000	+	1.73205i	−0.0405554	+	0.0702439i
$609$	−4.74086			−0.192110
$610$	−14.7266	−	1.46855i	−0.596262	−	0.0594599i
$611$	58.9745			2.38585
$612$	1.25723	−	2.17759i	0.0508207	−	0.0880240i
$613$	−20.4655			−0.826595			−0.413298	−	0.910596i	$-0.635623\pi$
$613$	−20.4655			−0.826595			−0.413298	+	0.910596i	$0.635623\pi$
$614$	−1.18212	−	2.04749i	−0.0477065	−	0.0826300i
$615$	1.12767	−	1.95318i	0.0454719	−	0.0787596i
$616$	−1.63766	+	2.83651i	−0.0659833	+	0.114286i
$617$	15.0000	−	25.9808i	0.603877	−	1.04595i	−0.388351	−	0.921512i	$-0.626955\pi$
$617$	15.0000	−	25.9808i	0.603877	−	1.04595i	0.992228	−	0.124434i	$-0.0397116\pi$
$618$	0.210206			0.00845573
$619$	−28.3983			−1.14142			−0.570712	−	0.821150i	$-0.693333\pi$
$619$	−28.3983			−1.14142			−0.570712	+	0.821150i	$0.693333\pi$
$620$	1.89490	+	3.28206i	0.0761009	+	0.131811i
$621$	2.70468			0.108535
$622$	9.08511	+	15.7359i	0.364280	+	0.630951i
$623$	−13.7128	+	23.7512i	−0.549391	+	0.951573i
$624$	2.80979	+	4.86669i	0.112481	+	0.194824i
$625$	7.98343	−	13.8277i	0.319337	−	0.553108i
$626$	5.68659	−	9.84947i	0.227282	−	0.393664i
$627$	1.80979	+	3.13464i	0.0722759	+	0.125186i
$628$	10.5996	−	18.3590i	0.422969	−	0.732604i
$629$	2.14319	+	3.71211i	0.0854544	+	0.148011i
$630$	−3.42936			−0.136629
$631$	10.9900	−	19.0352i	0.437505	−	0.757781i	−0.559991	−	0.828499i	$-0.689196\pi$
$631$	10.9900	−	19.0352i	0.437505	−	0.757781i	0.997496	+	0.0707174i	$0.0225288\pi$
$632$	−5.51447	+	9.55134i	−0.219354	+	0.379932i
$633$	13.9038			0.552628
$634$	−7.71363			−0.306347
$635$	1.71468	+	2.96991i	0.0680450	+	0.117857i
$636$	−6.65213	−	11.5218i	−0.263774	−	0.456870i
$637$	−20.9311			−0.829320
$638$	4.74086			0.187693
$639$	−0.809786	−	1.40259i	−0.0320346	−	0.0554856i
$640$	0.947448	+	1.64103i	0.0374512	+	0.0648674i
$641$	−18.7092	−	32.4052i	−0.738967	−	1.27993i	−0.952961	−	0.303094i	$-0.901980\pi$
$641$	−18.7092	−	32.4052i	−0.738967	−	1.27993i	0.213994	−	0.976835i	$-0.431353\pi$
$642$	−4.78979	−	8.29617i	−0.189038	−	0.327424i
$643$	23.7336			0.935963			0.467981	−	0.883738i	$-0.344981\pi$
$643$	23.7336			0.935963			0.467981	+	0.883738i	$0.344981\pi$
$644$	−4.89490			−0.192886
$645$	−4.65660	−	8.06547i	−0.183354	−	0.317578i
$646$	2.51447	+	4.35519i	0.0989305	+	0.171353i
$647$	−26.6485			−1.04766			−0.523831	−	0.851823i	$-0.675497\pi$
$647$	−26.6485			−1.04766			−0.523831	+	0.851823i	$0.675497\pi$
$648$	−1.00000			−0.0392837
$649$	−1.61957	+	2.80518i	−0.0635738	+	0.110113i
$650$	−3.96002	+	6.85895i	−0.155325	+	0.269030i
$651$	3.61957			0.141862
$652$	−5.14214	−	8.90644i	−0.201382	−	0.348803i
$653$	1.98553	−	3.43904i	0.0776998	−	0.134580i	−0.824557	−	0.565778i	$-0.808576\pi$
$653$	1.98553	−	3.43904i	0.0776998	−	0.134580i	0.902257	+	0.431198i	$0.141909\pi$
$654$	1.59511	+	2.76281i	0.0623736	+	0.108034i
$655$	−15.9349	+	27.6000i	−0.622627	+	1.07842i
$656$	−0.595107	+	1.03076i	−0.0232350	+	0.0402442i
$657$	2.50000	+	4.33013i	0.0975343	+	0.168934i
$658$	9.49638	−	16.4482i	0.370207	−	0.641218i
$659$	−6.19021	−	10.7218i	−0.241137	−	0.417661i	0.719902	−	0.694076i	$-0.244187\pi$
$659$	−6.19021	−	10.7218i	−0.241137	−	0.417661i	−0.961038	+	0.276415i	$0.910853\pi$
$660$	3.42936			0.133488
$661$	18.9375	+	32.8006i	0.736582	+	1.27580i	0.954026	+	0.299724i	$0.0968946\pi$
$661$	18.9375	+	32.8006i	0.736582	+	1.27580i	−0.217444	+	0.976073i	$0.569772\pi$
$662$	−30.3821			−1.18084
$663$	14.1302			0.548773
$664$	1.09511	−	1.89678i	0.0424984	−	0.0736094i
$665$	3.42936	−	5.93982i	0.132985	−	0.230336i
$666$	0.852341	−	1.47630i	0.0330276	−	0.0572054i
$667$	3.54256	+	6.13589i	0.137168	+	0.237582i
$668$	12.3243			0.476840
$669$	−6.58958	+	11.4135i	−0.254768	+	0.441271i
$670$	−8.91489			−0.344412
$671$	8.24724	−	11.4795i	0.318381	−	0.443159i
$672$	1.80979			0.0698140
$673$	−2.56702	+	4.44621i	−0.0989514	+	0.171389i	−0.911251	−	0.411852i	$-0.864882\pi$
$673$	−2.56702	+	4.44621i	−0.0989514	+	0.171389i	0.812300	+	0.583241i	$0.198215\pi$
$674$	−29.1992			−1.12471
$675$	−0.704683	−	1.22055i	−0.0271233	−	0.0469789i
$676$	−9.28979	+	16.0904i	−0.357300	+	0.618861i
$677$	10.1196	−	17.5276i	0.388927	−	0.673641i	−0.603379	−	0.797455i	$-0.706179\pi$
$677$	10.1196	−	17.5276i	0.388927	−	0.673641i	0.992305	+	0.123814i	$0.0395126\pi$
$678$	−6.80979	+	11.7949i	−0.261528	+	0.452980i
$679$	−28.0779			−1.07753
$680$	4.76466			0.182716
$681$	2.90489	+	5.03142i	0.111316	+	0.192805i
$682$	−3.61957			−0.138601
$683$	−3.99000	−	6.91089i	−0.152673	−	0.264438i	0.779536	−	0.626357i	$-0.215455\pi$
$683$	−3.99000	−	6.91089i	−0.152673	−	0.264438i	−0.932209	+	0.361919i	$0.882122\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$	−0.279798	−	0.484624i	−0.0106905	−	0.0185165i
$686$	−9.70468	+	16.8090i	−0.370527	+	0.641771i
$687$	−14.8143	+	25.6590i	−0.565199	+	0.978954i
$688$	2.45744	+	4.25642i	0.0936892	+	0.162274i
$689$	37.3821	−	64.7477i	1.42415	−	2.46669i
$690$	2.56255	+	4.43846i	0.0975545	+	0.168969i
$691$	33.5234			1.27529			0.637645	−	0.770330i	$-0.279909\pi$
$691$	33.5234			1.27529			0.637645	+	0.770330i	$0.279909\pi$
$692$	1.41489	−	2.45066i	0.0537860	−	0.0931601i
$693$	1.63766	−	2.83651i	0.0622097	−	0.107750i
$694$	−0.420412			−0.0159586
$695$	−2.85281			−0.108213
$696$	−1.30979	−	2.26862i	−0.0496473	−	0.0859917i
$697$	1.49638	+	2.59180i	0.0566794	+	0.0981715i
$698$	−0.295317			−0.0111779
$699$	15.1902			0.574547
$700$	1.27533	+	2.20893i	0.0482028	+	0.0834896i
$701$	21.8713	+	37.8822i	0.826067	+	1.43079i	0.901101	+	0.433609i	$0.142760\pi$
$701$	21.8713	+	37.8822i	0.826067	+	1.43079i	−0.0750342	+	0.997181i	$0.523907\pi$
$702$	−2.80979	−	4.86669i	−0.106049	−	0.183681i
$703$	1.70468	+	2.95260i	0.0642933	+	0.111359i
$704$	−1.80979			−0.0682089
$705$	−19.8860			−0.748948
$706$	−17.8387	−	30.8976i	−0.671369	−	1.16285i
$707$	5.52446	+	9.56865i	0.207769	+	0.359866i
$708$	1.78979			0.0672646
$709$	−16.5055			−0.619878			−0.309939	−	0.950756i	$-0.600309\pi$
$709$	−16.5055			−0.619878			−0.309939	+	0.950756i	$0.600309\pi$
$710$	1.53446	−	2.65776i	0.0575873	−	0.0997441i
$711$	5.51447	−	9.55134i	0.206809	−	0.358203i
$712$	−15.1540			−0.567921
$713$	−2.70468	−	4.68465i	−0.101291	−	0.175441i
$714$	2.27533	−	3.94098i	0.0851519	−	0.147487i
$715$	9.63576	+	16.6896i	0.360357	+	0.624157i
$716$	5.69469	−	9.86349i	0.212820	−	0.368616i
$717$	12.7817	−	22.1386i	0.477341	−	0.826779i
$718$	−17.9719	−	31.1283i	−0.670706	−	1.16170i
$719$	−20.0208	+	34.6771i	−0.746651	+	1.29324i	0.202768	+	0.979227i	$0.435006\pi$
$719$	−20.0208	+	34.6771i	−0.746651	+	1.29324i	−0.949419	+	0.314011i	$0.898327\pi$
$720$	−0.947448	−	1.64103i	−0.0353093	−	0.0611575i
$721$	0.380428			0.0141679
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$	16.2391			0.603940
$724$	14.2192			0.528451
$725$	1.84597	−	3.19731i	0.0685575	−	0.118745i
$726$	3.86234	−	6.68976i	0.143345	−	0.248280i
$727$	12.4493	−	21.5629i	0.461721	−	0.799724i	−0.537326	−	0.843375i	$-0.680566\pi$
$727$	12.4493	−	21.5629i	0.461721	−	0.799724i	0.999047	+	0.0436507i	$0.0138989\pi$
$728$	5.08511	+	8.80767i	0.188467	+	0.326434i
$729$	1.00000			0.0370370
$730$	−4.73724	+	8.20514i	−0.175333	+	0.303686i
$731$	12.3583			0.457090
$732$	−7.77170	−	0.775003i	−0.287250	−	0.0286450i
$733$	12.9438			0.478091			0.239046	−	0.971008i	$-0.423165\pi$
$733$	12.9438			0.478091			0.239046	+	0.971008i	$0.423165\pi$
$734$	−3.42936	+	5.93982i	−0.126580	+	0.219243i
$735$	7.05788			0.260334
$736$	−1.35234	−	2.34232i	−0.0498480	−	0.0863392i
$737$	4.25723	−	7.37375i	0.156817	−	0.271615i
$738$	0.595107	−	1.03076i	0.0219062	−	0.0379426i
$739$	13.8298	−	23.9539i	0.508737	−	0.881158i	−0.491212	−	0.871040i	$-0.663446\pi$
$739$	13.8298	−	23.9539i	0.508737	−	0.881158i	0.999949	−	0.0101177i	$-0.00322062\pi$
$740$	3.23020			0.118744
$741$	11.2391			0.412880
$742$	−12.0389	−	20.8520i	−0.441963	−	0.765503i
$743$	23.3694			0.857339			0.428670	−	0.903461i	$-0.358982\pi$
$743$	23.3694			0.857339			0.428670	+	0.903461i	$0.358982\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$	−0.748289	+	1.29607i	−0.0274152	+	0.0474845i
$746$	−15.5389	−	26.9142i	−0.568921	−	0.985400i
$747$	−1.09511	+	1.89678i	−0.0400679	+	0.0693996i
$748$	−2.27533	+	3.94098i	−0.0831941	+	0.144096i
$749$	−8.66850	−	15.0143i	−0.316740	−	0.548610i
$750$	6.07254	−	10.5180i	0.221738	−	0.384061i
$751$	20.8787	+	36.1630i	0.761875	+	1.31961i	0.941883	+	0.335941i	$0.109054\pi$
$751$	20.8787	+	36.1630i	0.761875	+	1.31961i	−0.180008	+	0.983665i	$0.557612\pi$
$752$	10.4945			0.382694
$753$	4.73467	−	8.20069i	0.172541	−	0.298850i
$754$	7.36044	−	12.7486i	0.268051	−	0.464278i
$755$	2.70849			0.0985719
$756$	−1.80979			−0.0658213
$757$	−22.1185	−	38.3104i	−0.803911	−	1.39242i	−0.917024	−	0.398833i	$-0.869415\pi$
$757$	−22.1185	−	38.3104i	−0.803911	−	1.39242i	0.113112	−	0.993582i	$-0.463918\pi$
$758$	5.56255	+	9.63462i	0.202041	+	0.349945i
$759$	−4.89490			−0.177674
$760$	3.78979			0.137470
$761$	−0.789794	−	1.36796i	−0.0286300	−	0.0495886i	0.851355	−	0.524589i	$-0.175781\pi$
$761$	−0.789794	−	1.36796i	−0.0286300	−	0.0495886i	−0.879985	+	0.475001i	$0.842448\pi$
$762$	0.904893	+	1.56732i	0.0327808	+	0.0567780i
$763$	2.88680	+	5.00009i	0.104509	+	0.181015i
$764$	−3.64766	−	6.31793i	−0.131968	−	0.228575i
$765$	−4.76466			−0.172267
$766$	19.0689			0.688988
$767$	5.02894	+	8.71038i	0.181584	+	0.314513i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	19.0038			0.685295			0.342647	−	0.939464i	$-0.388676\pi$
$769$	19.0038			0.685295			0.342647	+	0.939464i	$0.388676\pi$
$770$	6.20640			0.223663
$771$	2.19469	−	3.80131i	0.0790397	−	0.136901i
$772$	13.1866	−	22.8398i	0.474596	−	0.822024i
$773$	2.27913			0.0819745			0.0409873	−	0.999160i	$-0.486950\pi$
$773$	2.27913			0.0819745			0.0409873	+	0.999160i	$0.486950\pi$
$774$	−2.45744	−	4.25642i	−0.0883310	−	0.152994i
$775$	−1.40937	+	2.44109i	−0.0506259	+	0.0876866i
$776$	−7.75723	−	13.4359i	−0.278468	−	0.482322i
$777$	1.54256	−	2.67178i	0.0553389	−	0.0958497i
$778$	−5.35681	+	9.27827i	−0.192051	+	0.332642i
$779$	1.19021	+	2.06151i	0.0426438	+	0.0738613i
$780$	5.32425	−	9.22188i	0.190639	−	0.330196i
$781$	1.46554	+	2.53839i	0.0524411	+	0.0908307i
$782$	−6.80084			−0.243198
$783$	1.30979	+	2.26862i	0.0468079	+	0.0810737i
$784$	−3.72467			−0.133024
$785$	−40.1702			−1.43374
$786$	−8.40937	+	14.5654i	−0.299952	+	0.519532i
$787$	10.0941	−	17.4834i	0.359814	−	0.623217i	−0.628115	−	0.778120i	$-0.716173\pi$
$787$	10.0941	−	17.4834i	0.359814	−	0.623217i	0.987930	+	0.154904i	$0.0495067\pi$
$788$	11.3568	−	19.6706i	0.404570	−	0.700735i
$789$	−3.33235	−	5.77180i	−0.118635	−	0.205481i
$790$	20.8987			0.743542
$791$	−12.3243	+	21.3462i	−0.438200	+	0.758985i
$792$	1.80979			0.0643079
$793$	−18.0651	−	40.0001i	−0.641511	−	1.42044i
$794$	5.36044			0.190235
$795$	−12.6051	+	21.8327i	−0.447057	+	0.774325i
$796$	−23.8477			−0.845258
$797$	1.90746	+	3.30383i	0.0675659	+	0.117027i	0.897829	−	0.440344i	$-0.145143\pi$
$797$	1.90746	+	3.30383i	0.0675659	+	0.117027i	−0.830263	+	0.557371i	$0.811810\pi$
$798$	1.80979	−	3.13464i	0.0640657	−	0.110965i
$799$	13.1940	−	22.8527i	0.466771	−	0.808471i
$800$	−0.704683	+	1.22055i	−0.0249143	+	0.0431528i
$801$	15.1540			0.535441
$802$	−5.28427			−0.186594
$803$	−4.52446	−	7.83660i	−0.159665	−	0.276548i
$804$	−4.70468			−0.165921
$805$	4.63766	+	8.03267i	0.163456	+	0.283114i
$806$	−5.61957	+	9.73338i	−0.197941	+	0.342844i
$807$	−2.50000	−	4.33013i	−0.0880042	−	0.152428i
$808$	−3.05255	+	5.28717i	−0.107388	+	0.186002i
$809$	−16.2817	+	28.2007i	−0.572434	+	0.991485i	0.423881	+	0.905718i	$0.360667\pi$
$809$	−16.2817	+	28.2007i	−0.572434	+	0.991485i	−0.996315	+	0.0857671i	$0.972666\pi$
$810$	0.947448	+	1.64103i	0.0332899	+	0.0576599i
$811$	−11.9519	+	20.7013i	−0.419689	+	0.726922i	−0.995908	−	0.0903730i	$-0.971194\pi$
$811$	−11.9519	+	20.7013i	−0.419689	+	0.726922i	0.576219	+	0.817295i	$0.304527\pi$
$812$	−2.37043	−	4.10571i	−0.0831859	−	0.144082i
$813$	9.63956			0.338074
$814$	−1.54256	+	2.67178i	−0.0540665	+	0.0936460i
$815$	−9.74382	+	16.8768i	−0.341311	+	0.591168i
$816$	2.51447			0.0880240
$817$	9.82978			0.343900
$818$	−15.3187	−	26.5328i	−0.535607	−	0.927698i
$819$	−5.08511	−	8.80767i	−0.177688	−	0.307765i
$820$	2.25533			0.0787596
$821$	34.2391			1.19495			0.597477	−	0.801886i	$-0.296170\pi$
$821$	34.2391			1.19495			0.597477	+	0.801886i	$0.296170\pi$
$822$	−0.147659	−	0.255752i	−0.00515018	−	0.00892038i
$823$	−7.98001	−	13.8218i	−0.278166	−	0.481797i	0.692763	−	0.721165i	$-0.256393\pi$
$823$	−7.98001	−	13.8218i	−0.278166	−	0.481797i	−0.970929	+	0.239368i	$0.923060\pi$
$824$	0.105103	+	0.182044i	0.00366144	+	0.00634180i
$825$	1.27533	+	2.20893i	0.0444011	+	0.0769050i
$826$	3.23914			0.112704
$827$	−8.26808			−0.287509			−0.143755	−	0.989613i	$-0.545918\pi$
$827$	−8.26808			−0.287509			−0.143755	+	0.989613i	$0.545918\pi$
$828$	1.35234	+	2.34232i	0.0469971	+	0.0814014i
$829$	−4.61957	−	8.00133i	−0.160444	−	0.277898i	0.774584	−	0.632471i	$-0.217959\pi$
$829$	−4.61957	−	8.00133i	−0.160444	−	0.277898i	−0.935028	+	0.354574i	$0.884626\pi$
$830$	−4.15023			−0.144057
$831$	13.7536			0.477108
$832$	−2.80979	+	4.86669i	−0.0974118	+	0.168722i
$833$	−4.68279	+	8.11083i	−0.162249	+	0.281024i
$834$	−1.50552			−0.0521320
$835$	−11.6766	−	20.2245i	−0.404085	−	0.699896i
$836$	−1.80979	+	3.13464i	−0.0625928	+	0.108414i
$837$	−1.00000	−	1.73205i	−0.0345651	−	0.0598684i
$838$	−16.7147	+	28.9507i	−0.577399	+	1.00008i
$839$	−21.4583	+	37.1669i	−0.740823	+	1.28314i	0.211299	+	0.977422i	$0.432231\pi$
$839$	−21.4583	+	37.1669i	−0.740823	+	1.28314i	−0.952121	+	0.305721i	$0.901103\pi$
$840$	−1.71468	−	2.96991i	−0.0591620	−	0.102472i
$841$	11.0689	−	19.1719i	0.381687	−	0.661101i
$842$	14.5434	+	25.1899i	0.501199	+	0.868102i
$843$	1.87490			0.0645752
$844$	6.95192	+	12.0411i	0.239295	+	0.414471i
$845$	35.2064			1.21114
$846$	−10.4945			−0.360808
$847$	6.99000	−	12.1070i	0.240179	−	0.416003i
$848$	6.65213	−	11.5218i	0.228435	−	0.395661i
$849$	13.5145	−	23.4077i	0.463815	−	0.803352i
$850$	1.77190	+	3.06903i	0.0607758	+	0.105267i
$851$	−4.61063			−0.158050
$852$	0.809786	−	1.40259i	0.0277428	−	0.0480520i
$853$	9.19916			0.314973			0.157487	−	0.987521i	$-0.449661\pi$
$853$	9.19916			0.314973			0.157487	+	0.987521i	$0.449661\pi$
$854$	−14.0651	−	1.40259i	−0.481298	−	0.0479957i
$855$	−3.78979			−0.129608
$856$	4.78979	−	8.29617i	0.163712	−	0.283557i
$857$	−23.3783			−0.798588			−0.399294	−	0.916823i	$-0.630745\pi$
$857$	−23.3783			−0.798588			−0.399294	+	0.916823i	$0.630745\pi$
$858$	5.08511	+	8.80767i	0.173603	+	0.300689i
$859$	21.6085	−	37.4271i	0.737273	−	1.27699i	−0.216445	−	0.976295i	$-0.569446\pi$
$859$	21.6085	−	37.4271i	0.737273	−	1.27699i	0.953719	−	0.300700i	$-0.0972204\pi$
$860$	4.65660	−	8.06547i	0.158789	−	0.275030i
$861$	1.07702	−	1.86545i	0.0367046	−	0.0635743i
$862$	39.0868			1.33130
$863$	−51.7174			−1.76048			−0.880241	−	0.474527i	$-0.842619\pi$
$863$	−51.7174			−1.76048			−0.880241	+	0.474527i	$0.842619\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−5.36214			−0.182318
$866$	9.67212	+	16.7526i	0.328672	+	0.569277i
$867$	−5.33872	+	9.24694i	−0.181313	+	0.314043i
$868$	1.80979	+	3.13464i	0.0614281	+	0.106397i
$869$	−9.98001	+	17.2859i	−0.338549	+	0.586383i
$870$	−2.48191	+	4.29879i	−0.0841446	+	0.145743i
$871$	−13.2192	−	22.8962i	−0.447914	−	0.775810i
$872$	−1.59511	+	2.76281i	−0.0540171	+	0.0935604i
$873$	7.75723	+	13.4359i	0.262543	+	0.454737i
$874$	−5.40937			−0.182975
$875$	10.9900	−	19.0352i	0.371530	−	0.643509i
$876$	−2.50000	+	4.33013i	−0.0844672	+	0.146301i
$877$	9.06512			0.306107			0.153054	−	0.988218i	$-0.451089\pi$
$877$	9.06512			0.306107			0.153054	+	0.988218i	$0.451089\pi$
$878$	−8.66850			−0.292548
$879$	4.46744	+	7.73783i	0.150683	+	0.260991i
$880$	1.71468	+	2.96991i	0.0578018	+	0.100116i
$881$	−28.0668			−0.945595			−0.472798	−	0.881171i	$-0.656756\pi$
$881$	−28.0668			−0.945595			−0.472798	+	0.881171i	$0.656756\pi$
$882$	3.72467			0.125416
$883$	−13.1340	−	22.7488i	−0.441996	−	0.765559i	0.555842	−	0.831288i	$-0.312396\pi$
$883$	−13.1340	−	22.7488i	−0.441996	−	0.765559i	−0.997838	+	0.0657291i	$0.979063\pi$
$884$	7.06512	+	12.2371i	0.237626	+	0.411580i
$885$	−1.69574	−	2.93710i	−0.0570016	−	0.0987296i
$886$	−5.71468	−	9.89811i	−0.191988	−	0.332534i
$887$	−50.2119			−1.68595			−0.842975	−	0.537952i	$-0.819198\pi$
$887$	−50.2119			−1.68595			−0.842975	+	0.537952i	$0.819198\pi$
$888$	1.70468			0.0572054
$889$	1.63766	+	2.83651i	0.0549254	+	0.0951337i
$890$	14.3577	+	24.8682i	0.481270	+	0.833584i
$891$	−1.80979			−0.0606301
$892$	−13.1792			−0.441271
$893$	10.4945	−	18.1770i	0.351184	−	0.608269i
$894$	−0.394897	+	0.683982i	−0.0132073	+	0.0228758i
$895$	−21.5817			−0.721396
$896$	0.904893	+	1.56732i	0.0302304	+	0.0523605i
$897$	−7.59958	+	13.1629i	−0.253743	+	0.439495i
$898$	6.57254	+	11.3840i	0.219329	+	0.379888i
$899$	2.61957	−	4.53723i	0.0873676	−	0.151325i
$900$	0.704683	−	1.22055i	0.0234894	−	0.0406849i
$901$	−16.7266	−	28.9713i	−0.557243	−	0.965173i
$902$	−1.07702	+	1.86545i	−0.0358607	+	0.0621126i
$903$	−4.44745	−	7.70321i	−0.148002	−	0.256347i
$904$	−13.6196			−0.452980
$905$	−13.4719	−	23.3340i	−0.447822	−	0.775650i
$906$	1.42936			0.0474872
$907$	−4.03998			−0.134145			−0.0670727	−	0.997748i	$-0.521366\pi$
$907$	−4.03998			−0.134145			−0.0670727	+	0.997748i	$0.521366\pi$
$908$	−2.90489	+	5.03142i	−0.0964023	+	0.166974i
$909$	3.05255	−	5.28717i	0.101247	−	0.175365i
$910$	9.63576	−	16.6896i	0.319422	−	0.553256i
$911$	3.42936	+	5.93982i	0.113620	+	0.196795i	0.917227	−	0.398365i	$-0.130422\pi$
$911$	3.42936	+	5.93982i	0.113620	+	0.196795i	−0.803607	+	0.595160i	$0.797089\pi$
$912$	2.00000			0.0662266
$913$	1.98191	−	3.43277i	0.0655916	−	0.113608i
$914$	5.76086			0.190552
$915$	6.09149	+	13.4879i	0.201378	+	0.445895i
$916$	−29.6285			−0.978954
$917$	−15.2192	+	26.3603i	−0.502581	+	0.870495i
$918$	−2.51447			−0.0829898
$919$	−15.3994	−	26.6725i	−0.507978	−	0.879844i	−0.999957	−	0.00923722i	$-0.997060\pi$
$919$	−15.3994	−	26.6725i	−0.507978	−	0.879844i	0.491979	−	0.870607i	$-0.336274\pi$
$920$	−2.56255	+	4.43846i	−0.0844847	+	0.146332i
$921$	−1.18212	+	2.04749i	−0.0389522	+	0.0674671i
$922$	−4.53808	+	7.86019i	−0.149454	+	0.258862i
$923$	9.10130			0.299573
$924$	3.27533			0.107750
$925$	1.20126	+	2.08064i	0.0394972	+	0.0684112i
$926$	11.0089			0.361776
$927$	−0.105103	−	0.182044i	−0.00345204	−	0.00597911i
$928$	1.30979	−	2.26862i	0.0429958	−	0.0744710i
$929$	−2.07149	−	3.58793i	−0.0679635	−	0.117716i	0.830041	−	0.557702i	$-0.188317\pi$
$929$	−2.07149	−	3.58793i	−0.0679635	−	0.117716i	−0.898005	+	0.439986i	$0.854983\pi$
$930$	1.89490	−	3.28206i	0.0621361	−	0.107623i
$931$	−3.72467	+	6.45133i	−0.122071	+	0.211434i
$932$	7.59511	+	13.1551i	0.248786	+	0.430910i
$933$	9.08511	−	15.7359i	0.297433	−	0.515169i
$934$	5.00000	+	8.66025i	0.163605	+	0.283372i
$935$	8.62301			0.282003
$936$	2.80979	−	4.86669i	0.0918407	−	0.159073i
$937$	3.35681	−	5.81417i	0.109662	−	0.189941i	−0.805971	−	0.591955i	$-0.798356\pi$
$937$	3.35681	−	5.81417i	0.109662	−	0.189941i	0.915633	+	0.402014i	$0.131690\pi$
$938$	−8.51447			−0.278007
$939$	−11.3732			−0.371150
$940$	−9.94298	−	17.2217i	−0.324304	−	0.561711i
$941$	−5.02361	−	8.70115i	−0.163765	−	0.283650i	0.772451	−	0.635074i	$-0.219031\pi$
$941$	−5.02361	−	8.70115i	−0.163765	−	0.283650i	−0.936216	+	0.351425i	$0.885697\pi$
$942$	−21.1992			−0.690706
$943$	−3.21915			−0.104830
$944$	0.894897	+	1.55001i	0.0291264	+	0.0504484i
$945$	1.71468	+	2.96991i	0.0557785	+	0.0966112i
$946$	4.44745	+	7.70321i	0.144599	+	0.250453i
$947$	18.6947	+	32.3801i	0.607496	+	1.05221i	0.991652	+	0.128945i	$0.0411591\pi$
$947$	18.6947	+	32.3801i	0.607496	+	1.05221i	−0.384156	+	0.923268i	$0.625508\pi$
$948$	11.0289			0.358203
$949$	−28.0979			−0.912095
$950$	1.40937	+	2.44109i	0.0457259	+	0.0791995i
$951$	3.85681	+	6.68020i	0.125066	+	0.216620i
$952$	4.55065			0.147487
$953$	28.0489			0.908594			0.454297	−	0.890850i	$-0.349891\pi$
$953$	28.0489			0.908594			0.454297	+	0.890850i	$0.349891\pi$
$954$	−6.65213	+	11.5218i	−0.215371	+	0.373033i
$955$	−6.91194	+	11.9718i	−0.223665	+	0.387399i
$956$	25.5634			0.826779
$957$	−2.37043	−	4.10571i	−0.0766252	−	0.132719i
$958$	21.4294	−	37.1167i	0.692351	−	1.19919i
$959$	−0.267230	−	0.462857i	−0.00862932	−	0.0149464i
$960$	0.947448	−	1.64103i	0.0305788	−	0.0529640i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	4.78979	+	8.29617i	0.154429	+	0.267479i
$963$	−4.78979	+	8.29617i	−0.154349	+	0.267340i
$964$	8.11957	+	14.0635i	0.261514	+	0.452955i
$965$	−49.9745			−1.60873
$966$	2.44745	+	4.23911i	0.0787454	+	0.136391i
$967$	25.8298			0.830630			0.415315	−	0.909678i	$-0.363671\pi$
$967$	25.8298			0.830630			0.415315	+	0.909678i	$0.363671\pi$
$968$	7.72467			0.248280
$969$	2.51447	−	4.35519i	0.0807764	−	0.139909i
$970$	−14.6992	+	25.4597i	−0.471962	+	0.817461i
$971$	12.8387	−	22.2373i	0.412014	−	0.713630i	−0.583096	−	0.812404i	$-0.698159\pi$
$971$	12.8387	−	22.2373i	0.412014	−	0.713630i	0.995110	+	0.0987739i	$0.0314921\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−2.72467			−0.0873491
$974$	−6.61957	+	11.4654i	−0.212105	+	0.367376i
$975$	7.92003			0.253644
$976$	−3.21468	−	7.11799i	−0.102899	−	0.227841i
$977$	−2.25533			−0.0721545			−0.0360772	−	0.999349i	$-0.511486\pi$
$977$	−2.25533			−0.0721545			−0.0360772	+	0.999349i	$0.511486\pi$
$978$	−5.14214	+	8.90644i	−0.164427	+	0.284797i
$979$	−27.4256			−0.876525
$980$	3.52894	+	6.11230i	0.112728	+	0.195250i
$981$	1.59511	−	2.76281i	0.0509278	−	0.0882096i
$982$	−2.07511	+	3.59420i	−0.0662196	+	0.114696i
$983$	−4.76980	+	8.26154i	−0.152133	+	0.263502i	−0.932011	−	0.362429i	$-0.881948\pi$
$983$	−4.76980	+	8.26154i	−0.152133	+	0.263502i	0.779878	+	0.625931i	$0.215281\pi$
$984$	1.19021			0.0379426
$985$	−43.0400			−1.37137
$986$	−3.29342	−	5.70436i	−0.104884	−	0.181664i
$987$	−18.9928			−0.604546
$988$	5.61957	+	9.73338i	0.178782	+	0.309660i
$989$	−6.64661	+	11.5123i	−0.211350	+	0.366069i
$990$	−1.71468	−	2.96991i	−0.0544961	−	0.0943900i
$991$	−27.4283	+	47.5072i	−0.871289	+	1.50912i	−0.0106247	+	0.999944i	$0.503382\pi$
$991$	−27.4283	+	47.5072i	−0.871289	+	1.50912i	−0.860664	+	0.509173i	$0.829951\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	15.1911	+	26.3117i	0.482074	+	0.834976i
$994$	1.46554	−	2.53839i	0.0464841	−	0.0805128i
$995$	22.5944	+	39.1347i	0.716292	+	1.24065i
$996$	−2.19021			−0.0693996
$997$	16.0689	−	27.8322i	0.508908	−	0.881454i	−0.491039	−	0.871138i	$-0.663383\pi$
$997$	16.0689	−	27.8322i	0.508908	−	0.881454i	0.999947	−	0.0103166i	$-0.00328394\pi$
$998$	19.5634	−	33.8848i	0.619269	−	1.07260i
$999$	−1.70468			−0.0539338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	366.2.e.d.13.2	✓	6
3.2	odd	2		1098.2.f.f.379.2		6
61.47	even	3	inner	366.2.e.d.169.2	yes	6
183.47	odd	6		1098.2.f.f.901.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
366.2.e.d.13.2	✓	6	1.1	even	1	trivial
366.2.e.d.169.2	yes	6	61.47	even	3	inner
1098.2.f.f.379.2		6	3.2	odd	2
1098.2.f.f.901.2		6	183.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 366 = 2 \cdot 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	366.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.947448 + 1.64103i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.904893 + 1.56732i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +(0.947448 + 1.64103i) q^{10} -1.80979 q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.80979 + 4.86669i) q^{13} +(0.904893 + 1.56732i) q^{14} +(0.947448 - 1.64103i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.25723 + 2.17759i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +1.89490 q^{20} +(0.904893 - 1.56732i) q^{21} +(-0.904893 + 1.56732i) q^{22} -2.70468 q^{23} +1.00000 q^{24} +(0.704683 + 1.22055i) q^{25} +(2.80979 + 4.86669i) q^{26} -1.00000 q^{27} +1.80979 q^{28} +(-1.30979 - 2.26862i) q^{29} +(-0.947448 - 1.64103i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +1.80979 q^{33} +2.51447 q^{34} +(-1.71468 - 2.96991i) q^{35} +(-0.500000 - 0.866025i) q^{36} +1.70468 q^{37} +2.00000 q^{38} +(2.80979 - 4.86669i) q^{39} +(0.947448 - 1.64103i) q^{40} +1.19021 q^{41} +(-0.904893 - 1.56732i) q^{42} +(2.45744 - 4.25642i) q^{43} +(0.904893 + 1.56732i) q^{44} +(-0.947448 + 1.64103i) q^{45} +(-1.35234 + 2.34232i) q^{46} +(-5.24724 - 9.08848i) q^{47} +(0.500000 - 0.866025i) q^{48} +(1.86234 + 3.22566i) q^{49} +1.40937 q^{50} +(-1.25723 - 2.17759i) q^{51} +5.61957 q^{52} -13.3043 q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.71468 - 2.96991i) q^{55} +(0.904893 - 1.56732i) q^{56} +(-1.00000 - 1.73205i) q^{57} -2.61957 q^{58} +(0.894897 - 1.55001i) q^{59} -1.89490 q^{60} +(-4.55702 + 6.34299i) q^{61} +2.00000 q^{62} +(-0.904893 + 1.56732i) q^{63} +1.00000 q^{64} +(-5.32425 - 9.22188i) q^{65} +(0.904893 - 1.56732i) q^{66} +(-2.35234 + 4.07437i) q^{67} +(1.25723 - 2.17759i) q^{68} +2.70468 q^{69} -3.42936 q^{70} +(-0.809786 - 1.40259i) q^{71} -1.00000 q^{72} +(2.50000 + 4.33013i) q^{73} +(0.852341 - 1.47630i) q^{74} +(-0.704683 - 1.22055i) q^{75} +(1.00000 - 1.73205i) q^{76} +(1.63766 - 2.83651i) q^{77} +(-2.80979 - 4.86669i) q^{78} +(5.51447 - 9.55134i) q^{79} +(-0.947448 - 1.64103i) q^{80} +1.00000 q^{81} +(0.595107 - 1.03076i) q^{82} +(-1.09511 + 1.89678i) q^{83} -1.80979 q^{84} -4.76466 q^{85} +(-2.45744 - 4.25642i) q^{86} +(1.30979 + 2.26862i) q^{87} +1.80979 q^{88} +15.1540 q^{89} +(0.947448 + 1.64103i) q^{90} +(-5.08511 - 8.80767i) q^{91} +(1.35234 + 2.34232i) q^{92} +(-1.00000 - 1.73205i) q^{93} -10.4945 q^{94} -3.78979 q^{95} +(-0.500000 - 0.866025i) q^{96} +(7.75723 + 13.4359i) q^{97} +3.72467 q^{98} -1.80979 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - q^{5} - 3 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} + q^{10} + 4 q^{11} + 3 q^{12} - 2 q^{13} - 2 q^{14} + q^{15} - 3 q^{16} - 12 q^{17} + 3 q^{18} + 6 q^{19} + 2 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - q^5 - 3 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 + q^10 + 4 * q^11 + 3 * q^12 - 2 * q^13 - 2 * q^14 + q^15 - 3 * q^16 - 12 * q^17 + 3 * q^18 + 6 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 + 8 * q^23 + 6 * q^24 - 20 * q^25 + 2 * q^26 - 6 * q^27 - 4 * q^28 + 7 * q^29 - q^30 + 6 * q^31 + 3 * q^32 - 4 * q^33 - 24 * q^34 + 12 * q^35 - 3 * q^36 - 14 * q^37 + 12 * q^38 + 2 * q^39 + q^40 + 22 * q^41 + 2 * q^42 + 12 * q^43 - 2 * q^44 - q^45 + 4 * q^46 - 10 * q^47 + 3 * q^48 + q^49 - 40 * q^50 + 12 * q^51 + 4 * q^52 - 22 * q^53 - 3 * q^54 - 12 * q^55 - 2 * q^56 - 6 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 9 * q^61 + 12 * q^62 + 2 * q^63 + 6 * q^64 + 22 * q^65 - 2 * q^66 - 2 * q^67 - 12 * q^68 - 8 * q^69 + 24 * q^70 + 10 * q^71 - 6 * q^72 + 15 * q^73 - 7 * q^74 + 20 * q^75 + 6 * q^76 + 20 * q^77 - 2 * q^78 - 6 * q^79 - q^80 + 6 * q^81 + 11 * q^82 - 14 * q^83 + 4 * q^84 - 16 * q^85 - 12 * q^86 - 7 * q^87 - 4 * q^88 + 26 * q^89 + q^90 - 36 * q^91 - 4 * q^92 - 6 * q^93 - 20 * q^94 - 4 * q^95 - 3 * q^96 + 27 * q^97 + 2 * q^98 + 4 * q^99

Introduction

L-functions

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