LMFDB - Embedded newform 930.2.r.b.119.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.19
Character	$\chi$	$=$	930.119
Dual form			930.2.r.b.719.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.442238 + 1.67464i) q^{3} +1.00000 q^{4} +(-1.20088 + 1.88624i) q^{5} +(0.442238 + 1.67464i) q^{6} +(2.75588 + 1.59111i) q^{7} +1.00000 q^{8} +(-2.60885 + 1.48118i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.442238 + 1.67464i) q^{3} +1.00000 q^{4} +(-1.20088 + 1.88624i) q^{5} +(0.442238 + 1.67464i) q^{6} +(2.75588 + 1.59111i) q^{7} +1.00000 q^{8} +(-2.60885 + 1.48118i) q^{9} +(-1.20088 + 1.88624i) q^{10} +(-1.12854 - 1.95469i) q^{11} +(0.442238 + 1.67464i) q^{12} +(1.41720 + 2.45465i) q^{13} +(2.75588 + 1.59111i) q^{14} +(-3.68985 - 1.17688i) q^{15} +1.00000 q^{16} +(-0.182184 - 0.105184i) q^{17} +(-2.60885 + 1.48118i) q^{18} +(0.00830895 - 0.0143915i) q^{19} +(-1.20088 + 1.88624i) q^{20} +(-1.44578 + 5.31876i) q^{21} +(-1.12854 - 1.95469i) q^{22} +0.800056i q^{23} +(0.442238 + 1.67464i) q^{24} +(-2.11578 - 4.53028i) q^{25} +(1.41720 + 2.45465i) q^{26} +(-3.63418 - 3.71386i) q^{27} +(2.75588 + 1.59111i) q^{28} +0.452379 q^{29} +(-3.68985 - 1.17688i) q^{30} +(-0.371864 + 5.55533i) q^{31} +1.00000 q^{32} +(2.77432 - 2.75434i) q^{33} +(-0.182184 - 0.105184i) q^{34} +(-6.31069 + 3.28752i) q^{35} +(-2.60885 + 1.48118i) q^{36} +(4.13062 - 7.15444i) q^{37} +(0.00830895 - 0.0143915i) q^{38} +(-3.48393 + 3.45884i) q^{39} +(-1.20088 + 1.88624i) q^{40} +(0.681306 - 0.393352i) q^{41} +(-1.44578 + 5.31876i) q^{42} +(-2.06729 + 3.58066i) q^{43} +(-1.12854 - 1.95469i) q^{44} +(0.339057 - 6.69963i) q^{45} +0.800056i q^{46} -8.04444 q^{47} +(0.442238 + 1.67464i) q^{48} +(1.56326 + 2.70764i) q^{49} +(-2.11578 - 4.53028i) q^{50} +(0.0955768 - 0.351609i) q^{51} +(1.41720 + 2.45465i) q^{52} +(4.82919 - 2.78814i) q^{53} +(-3.63418 - 3.71386i) q^{54} +(5.04224 + 0.218649i) q^{55} +(2.75588 + 1.59111i) q^{56} +(0.0277752 + 0.00755004i) q^{57} +0.452379 q^{58} +(-3.09426 - 1.78647i) q^{59} +(-3.68985 - 1.17688i) q^{60} +8.14341i q^{61} +(-0.371864 + 5.55533i) q^{62} +(-9.54641 - 0.0690110i) q^{63} +1.00000 q^{64} +(-6.33194 - 0.274575i) q^{65} +(2.77432 - 2.75434i) q^{66} +(7.31490 - 4.22326i) q^{67} +(-0.182184 - 0.105184i) q^{68} +(-1.33981 + 0.353815i) q^{69} +(-6.31069 + 3.28752i) q^{70} +(13.0393 - 7.52824i) q^{71} +(-2.60885 + 1.48118i) q^{72} +(4.45521 + 7.71666i) q^{73} +(4.13062 - 7.15444i) q^{74} +(6.65092 - 5.54664i) q^{75} +(0.00830895 - 0.0143915i) q^{76} -7.18252i q^{77} +(-3.48393 + 3.45884i) q^{78} +(13.1233 + 7.57675i) q^{79} +(-1.20088 + 1.88624i) q^{80} +(4.61221 - 7.72836i) q^{81} +(0.681306 - 0.393352i) q^{82} +(-11.6643 + 6.73438i) q^{83} +(-1.44578 + 5.31876i) q^{84} +(0.417182 - 0.217329i) q^{85} +(-2.06729 + 3.58066i) q^{86} +(0.200059 + 0.757573i) q^{87} +(-1.12854 - 1.95469i) q^{88} -8.62936 q^{89} +(0.339057 - 6.69963i) q^{90} +9.01965i q^{91} +0.800056i q^{92} +(-9.46764 + 1.83404i) q^{93} -8.04444 q^{94} +(0.0171678 + 0.0329551i) q^{95} +(0.442238 + 1.67464i) q^{96} -4.80894i q^{97} +(1.56326 + 2.70764i) q^{98} +(5.83944 + 3.42792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.442238	+	1.67464i	0.255326	+	0.966855i
$3$	0.442238	+	1.67464i	0.255326	+	0.966855i
$4$	1.00000			0.500000
$5$	−1.20088	+	1.88624i	−0.537049	+	0.843551i
$5$	−1.20088	+	1.88624i	−0.537049	+	0.843551i
$6$	0.442238	+	1.67464i	0.180543	+	0.683670i
$7$	2.75588	+	1.59111i	1.04163	+	0.601383i	0.920293	−	0.391229i	$-0.127950\pi$
$7$	2.75588	+	1.59111i	1.04163	+	0.601383i	0.121332	+	0.992612i	$0.461283\pi$
$8$	1.00000			0.353553
$9$	−2.60885	+	1.48118i	−0.869617	+	0.493727i
$10$	−1.20088	+	1.88624i	−0.379751	+	0.596481i
$11$	−1.12854	−	1.95469i	−0.340267	−	0.589361i	0.644215	−	0.764845i	$-0.277184\pi$
$11$	−1.12854	−	1.95469i	−0.340267	−	0.589361i	−0.984482	+	0.175484i	$0.943851\pi$
$12$	0.442238	+	1.67464i	0.127663	+	0.483428i
$13$	1.41720	+	2.45465i	0.393059	+	0.680799i	0.992851	−	0.119357i	$-0.0380834\pi$
$13$	1.41720	+	2.45465i	0.393059	+	0.680799i	−0.599792	+	0.800156i	$0.704750\pi$
$14$	2.75588	+	1.59111i	0.736541	+	0.425242i
$15$	−3.68985	−	1.17688i	−0.952714	−	0.303868i
$16$	1.00000			0.250000
$17$	−0.182184	−	0.105184i	−0.0441861	−	0.0255108i	0.477744	−	0.878499i	$-0.341455\pi$
$17$	−0.182184	−	0.105184i	−0.0441861	−	0.0255108i	−0.521930	+	0.852988i	$0.674788\pi$
$18$	−2.60885	+	1.48118i	−0.614912	+	0.349117i
$19$	0.00830895	−	0.0143915i	0.00190620	−	0.00330164i	−0.865071	−	0.501650i	$-0.832727\pi$
$19$	0.00830895	−	0.0143915i	0.00190620	−	0.00330164i	0.866977	+	0.498348i	$0.166060\pi$
$20$	−1.20088	+	1.88624i	−0.268525	+	0.421775i
$21$	−1.44578	+	5.31876i	−0.315496	+	1.16065i
$22$	−1.12854	−	1.95469i	−0.240605	−	0.416741i
$23$			0.800056i			0.166823i	0.996515	+	0.0834116i	$0.0265816\pi$
$23$			0.800056i			0.166823i	−0.996515	+	0.0834116i	$0.973418\pi$
$24$	0.442238	+	1.67464i	0.0902714	+	0.341835i
$25$	−2.11578	−	4.53028i	−0.423156	−	0.906057i
$26$	1.41720	+	2.45465i	0.277935	+	0.481397i
$27$	−3.63418	−	3.71386i	−0.699398	−	0.714732i
$28$	2.75588	+	1.59111i	0.520813	+	0.300691i
$29$	0.452379			0.0840047			0.0420023	−	0.999118i	$-0.486626\pi$
$29$	0.452379			0.0840047			0.0420023	+	0.999118i	$0.486626\pi$
$30$	−3.68985	−	1.17688i	−0.673671	−	0.214867i
$31$	−0.371864	+	5.55533i	−0.0667887	+	0.997767i
$31$	−0.371864	+	5.55533i	−0.0667887	+	0.997767i
$32$	1.00000			0.176777
$33$	2.77432	−	2.75434i	0.482947	−	0.479468i
$34$	−0.182184	−	0.105184i	−0.0312443	−	0.0180389i
$35$	−6.31069	+	3.28752i	−1.06670	+	0.555692i
$36$	−2.60885	+	1.48118i	−0.434809	+	0.246863i
$37$	4.13062	−	7.15444i	0.679070	−	1.17618i	−0.296192	−	0.955128i	$-0.595717\pi$
$37$	4.13062	−	7.15444i	0.679070	−	1.17618i	0.975261	−	0.221055i	$-0.0709499\pi$
$38$	0.00830895	−	0.0143915i	0.00134789	−	0.00233461i
$39$	−3.48393	+	3.45884i	−0.557875	+	0.553857i
$40$	−1.20088	+	1.88624i	−0.189876	+	0.298240i
$41$	0.681306	−	0.393352i	0.106402	−	0.0614313i	−0.445855	−	0.895105i	$-0.647100\pi$
$41$	0.681306	−	0.393352i	0.106402	−	0.0614313i	0.552257	+	0.833674i	$0.313767\pi$
$42$	−1.44578	+	5.31876i	−0.223089	+	0.820703i
$43$	−2.06729	+	3.58066i	−0.315259	+	0.546045i	−0.979493	−	0.201480i	$-0.935425\pi$
$43$	−2.06729	+	3.58066i	−0.315259	+	0.546045i	0.664233	+	0.747525i	$0.268758\pi$
$44$	−1.12854	−	1.95469i	−0.170134	−	0.294680i
$45$	0.339057	−	6.69963i	0.0505437	−	0.998722i
$46$			0.800056i			0.117962i
$47$	−8.04444			−1.17340			−0.586701	−	0.809803i	$-0.699574\pi$
$47$	−8.04444			−1.17340			−0.586701	+	0.809803i	$0.699574\pi$
$48$	0.442238	+	1.67464i	0.0638315	+	0.241714i
$49$	1.56326	+	2.70764i	0.223323	+	0.386806i
$50$	−2.11578	−	4.53028i	−0.299217	−	0.640679i
$51$	0.0955768	−	0.351609i	0.0133834	−	0.0492351i
$52$	1.41720	+	2.45465i	0.196530	+	0.340399i
$53$	4.82919	−	2.78814i	0.663341	−	0.382980i	−0.130208	−	0.991487i	$-0.541564\pi$
$53$	4.82919	−	2.78814i	0.663341	−	0.382980i	0.793549	+	0.608507i	$0.208231\pi$
$54$	−3.63418	−	3.71386i	−0.494549	−	0.505392i
$55$	5.04224	+	0.218649i	0.679896	+	0.0294827i
$56$	2.75588	+	1.59111i	0.368270	+	0.212621i
$57$	0.0277752	+	0.00755004i	0.00367891	+	0.00100003i
$58$	0.452379			0.0594003
$59$	−3.09426	−	1.78647i	−0.402838	−	0.232579i	0.284870	−	0.958566i	$-0.408050\pi$
$59$	−3.09426	−	1.78647i	−0.402838	−	0.232579i	−0.687708	+	0.725987i	$0.741383\pi$
$60$	−3.68985	−	1.17688i	−0.476357	−	0.151934i
$61$			8.14341i			1.04266i	0.853356	+	0.521328i	$0.174563\pi$
$61$			8.14341i			1.04266i	−0.853356	+	0.521328i	$0.825437\pi$
$62$	−0.371864	+	5.55533i	−0.0472268	+	0.705528i
$63$	−9.54641	−	0.0690110i	−1.20273	−	0.00869457i
$64$	1.00000			0.125000
$65$	−6.33194	−	0.274575i	−0.785380	−	0.0340568i
$66$	2.77432	−	2.75434i	0.341495	−	0.339035i
$67$	7.31490	−	4.22326i	0.893657	−	0.515953i	0.0185202	−	0.999828i	$-0.494104\pi$
$67$	7.31490	−	4.22326i	0.893657	−	0.515953i	0.875137	+	0.483875i	$0.160771\pi$
$68$	−0.182184	−	0.105184i	−0.0220930	−	0.0127554i
$69$	−1.33981	+	0.353815i	−0.161294	+	0.0425943i
$70$	−6.31069	+	3.28752i	−0.754272	+	0.392934i
$71$	13.0393	−	7.52824i	1.54748	−	0.893438i	0.549147	−	0.835726i	$-0.314953\pi$
$71$	13.0393	−	7.52824i	1.54748	−	0.893438i	0.998333	−	0.0577118i	$-0.0183804\pi$
$72$	−2.60885	+	1.48118i	−0.307456	+	0.174559i
$73$	4.45521	+	7.71666i	0.521443	+	0.903166i	0.999689	+	0.0249402i	$0.00793955\pi$
$73$	4.45521	+	7.71666i	0.521443	+	0.903166i	−0.478246	+	0.878226i	$0.658727\pi$
$74$	4.13062	−	7.15444i	0.480175	−	0.831687i
$75$	6.65092	−	5.54664i	0.767983	−	0.640471i
$76$	0.00830895	−	0.0143915i	0.000953102	−	0.00165082i
$77$		−	7.18252i		−	0.818524i
$78$	−3.48393	+	3.45884i	−0.394477	+	0.391636i
$79$	13.1233	+	7.57675i	1.47649	+	0.852451i	0.999648	−	0.0265391i	$-0.00844866\pi$
$79$	13.1233	+	7.57675i	1.47649	+	0.852451i	0.476840	+	0.878990i	$0.341782\pi$
$80$	−1.20088	+	1.88624i	−0.134262	+	0.210888i
$81$	4.61221	−	7.72836i	0.512468	−	0.858706i
$82$	0.681306	−	0.393352i	0.0752377	−	0.0434385i
$83$	−11.6643	+	6.73438i	−1.28032	+	0.739195i	−0.976907	−	0.213664i	$-0.931460\pi$
$83$	−11.6643	+	6.73438i	−1.28032	+	0.739195i	−0.303416	+	0.952858i	$0.598127\pi$
$84$	−1.44578	+	5.31876i	−0.157748	+	0.580325i
$85$	0.417182	−	0.217329i	0.0452498	−	0.0235726i
$86$	−2.06729	+	3.58066i	−0.222922	+	0.386112i
$87$	0.200059	+	0.757573i	0.0214486	+	0.0812203i
$88$	−1.12854	−	1.95469i	−0.120303	−	0.208370i
$89$	−8.62936			−0.914710			−0.457355	−	0.889284i	$-0.651203\pi$
$89$	−8.62936			−0.914710			−0.457355	+	0.889284i	$0.651203\pi$
$90$	0.339057	−	6.69963i	0.0357398	−	0.706203i
$91$			9.01965i			0.945516i
$92$			0.800056i			0.0834116i
$93$	−9.46764	+	1.83404i	−0.981749	+	0.190181i
$94$	−8.04444			−0.829721
$95$	0.0171678	+	0.0329551i	0.00176138	+	0.00338112i
$96$	0.442238	+	1.67464i	0.0451357	+	0.170917i
$97$		−	4.80894i		−	0.488273i	−0.969741	−	0.244137i	$-0.921495\pi$
$97$		−	4.80894i		−	0.488273i	0.969741	−	0.244137i	$-0.0785046\pi$
$98$	1.56326	+	2.70764i	0.157913	+	0.273513i
$99$	5.83944	+	3.42792i	0.586885	+	0.344519i
$100$	−2.11578	−	4.53028i	−0.211578	−	0.453028i
$101$			10.9252i			1.08710i	0.839378	+	0.543548i	$0.182920\pi$
$101$			10.9252i			1.08710i	−0.839378	+	0.543548i	$0.817080\pi$
$102$	0.0955768	−	0.351609i	0.00946351	−	0.0348145i
$103$	15.3713	−	8.87463i	1.51458	−	0.874444i	0.514727	−	0.857354i	$-0.327893\pi$
$103$	15.3713	−	8.87463i	1.51458	−	0.874444i	0.999854	−	0.0170892i	$-0.00543992\pi$
$104$	1.41720	+	2.45465i	0.138967	+	0.240699i
$105$	−8.29624	−	9.11428i	−0.809630	−	0.889463i
$106$	4.82919	−	2.78814i	0.469053	−	0.270808i
$107$	9.24636	−	16.0152i	0.893880	−	1.54825i	0.0586947	−	0.998276i	$-0.481306\pi$
$107$	9.24636	−	16.0152i	0.893880	−	1.54825i	0.835185	−	0.549969i	$-0.185361\pi$
$108$	−3.63418	−	3.71386i	−0.349699	−	0.357366i
$109$	−0.471291			−0.0451415			−0.0225707	−	0.999745i	$-0.507185\pi$
$109$	−0.471291			−0.0451415			−0.0225707	+	0.999745i	$0.507185\pi$
$110$	5.04224	+	0.218649i	0.480759	+	0.0208474i
$111$	13.8078	+	3.75334i	1.31058	+	0.356252i
$112$	2.75588	+	1.59111i	0.260406	+	0.150346i
$113$	−1.13102	−	1.95898i	−0.106397	−	0.184286i	0.807911	−	0.589305i	$-0.200598\pi$
$113$	−1.13102	−	1.95898i	−0.106397	−	0.184286i	−0.914308	+	0.405019i	$0.867265\pi$
$114$	0.0277752	+	0.00755004i	0.00260138	+	0.000707126i
$115$	−1.50910	−	0.960770i	−0.140724	−	0.0895923i
$116$	0.452379			0.0420023
$117$	−7.33304	−	4.30471i	−0.677939	−	0.397970i
$118$	−3.09426	−	1.78647i	−0.284850	−	0.164458i
$119$	−0.334718	−	0.579749i	−0.0306836	−	0.0531455i
$120$	−3.68985	−	1.17688i	−0.336835	−	0.107434i
$121$	2.95280	−	5.11439i	0.268436	−	0.464945i
$122$			8.14341i			0.737269i
$123$	0.960024	+	0.966989i	0.0865624	+	0.0871904i
$124$	−0.371864	+	5.55533i	−0.0333944	+	0.498884i
$125$	11.0860	+	1.44945i	0.991561	+	0.129643i
$126$	−9.54641	−	0.0690110i	−0.850462	−	0.00614799i
$127$	−2.39738	+	4.15239i	−0.212733	+	0.368465i	−0.952569	−	0.304323i	$-0.901570\pi$
$127$	−2.39738	+	4.15239i	−0.212733	+	0.368465i	0.739836	+	0.672788i	$0.234903\pi$
$128$	1.00000			0.0883883
$129$	−6.91056	−	1.87848i	−0.608441	−	0.165391i
$130$	−6.33194	−	0.274575i	−0.555348	−	0.0240818i
$131$	4.55833	+	2.63175i	0.398263	+	0.229937i	0.685734	−	0.727852i	$-0.259481\pi$
$131$	4.55833	+	2.63175i	0.398263	+	0.229937i	−0.287471	+	0.957789i	$0.592815\pi$
$132$	2.77432	−	2.75434i	0.241474	−	0.239734i
$133$	0.0457970	−	0.0264409i	0.00397110	−	0.00229272i
$134$	7.31490	−	4.22326i	0.631911	−	0.364834i
$135$	11.3694	−	2.39503i	0.978524	−	0.206131i
$136$	−0.182184	−	0.105184i	−0.0156221	−	0.00901944i
$137$	7.42153	−	4.28482i	0.634064	−	0.366077i	−0.148260	−	0.988948i	$-0.547367\pi$
$137$	7.42153	−	4.28482i	0.634064	−	0.366077i	0.782324	+	0.622871i	$0.214034\pi$
$138$	−1.33981	+	0.353815i	−0.114052	+	0.0301187i
$139$		−	15.8192i		−	1.34177i	−0.741563	−	0.670884i	$-0.765915\pi$
$139$		−	15.8192i		−	1.34177i	0.741563	−	0.670884i	$-0.234085\pi$
$140$	−6.31069	+	3.28752i	−0.533351	+	0.277846i
$141$	−3.55756	−	13.4716i	−0.299600	−	1.13451i
$142$	13.0393	−	7.52824i	1.09423	−	0.631756i
$143$	3.19872	−	5.54035i	0.267491	−	0.463307i
$144$	−2.60885	+	1.48118i	−0.217404	+	0.123432i
$145$	−0.543252	+	0.853294i	−0.0451146	+	0.0708622i
$146$	4.45521	+	7.71666i	0.368716	+	0.638635i
$147$	−3.84300	+	3.81532i	−0.316965	+	0.314682i
$148$	4.13062	−	7.15444i	0.339535	−	0.588091i
$149$	−3.75915	−	2.17035i	−0.307962	−	0.177802i	0.338052	−	0.941127i	$-0.390232\pi$
$149$	−3.75915	−	2.17035i	−0.307962	−	0.177802i	−0.646014	+	0.763325i	$0.723565\pi$
$150$	6.65092	−	5.54664i	0.543046	−	0.452881i
$151$			3.92788i			0.319646i	0.987146	+	0.159823i	$0.0510924\pi$
$151$			3.92788i			0.319646i	−0.987146	+	0.159823i	$0.948908\pi$
$152$	0.00830895	−	0.0143915i	0.000673945	−	0.00116731i
$153$	0.631087	+	0.00456213i	0.0510203	+	0.000368826i
$154$		−	7.18252i		−	0.578784i
$155$	−10.0321	−	7.37270i	−0.805799	−	0.592190i
$156$	−3.48393	+	3.45884i	−0.278938	+	0.276928i
$157$		−	5.82296i		−	0.464723i	−0.972630	−	0.232361i	$-0.925355\pi$
$157$		−	5.82296i		−	0.464723i	0.972630	−	0.232361i	$-0.0746452\pi$
$158$	13.1233	+	7.57675i	1.04403	+	0.602774i
$159$	6.80478	+	6.85415i	0.539654	+	0.543570i
$160$	−1.20088	+	1.88624i	−0.0949378	+	0.149120i
$161$	−1.27298	+	2.20486i	−0.100325	+	0.173767i
$162$	4.61221	−	7.72836i	0.362370	−	0.607197i
$163$		−	11.9963i		−	0.939623i	−0.882767	−	0.469812i	$-0.844322\pi$
$163$		−	11.9963i		−	0.939623i	0.882767	−	0.469812i	$-0.155678\pi$
$164$	0.681306	−	0.393352i	0.0532011	−	0.0307157i
$165$	1.86371	+	8.54065i	0.145090	+	0.664889i
$166$	−11.6643	+	6.73438i	−0.905325	+	0.522690i
$167$	−0.0740101	−	0.0427297i	−0.00572707	−	0.00330653i	0.497134	−	0.867674i	$-0.334386\pi$
$167$	−0.0740101	−	0.0427297i	−0.00572707	−	0.00330653i	−0.502861	+	0.864367i	$0.667719\pi$
$168$	−1.44578	+	5.31876i	−0.111545	+	0.410352i
$169$	2.48312	−	4.30088i	0.191009	−	0.330837i
$170$	0.417182	−	0.217329i	0.0319964	−	0.0166684i
$171$	−0.000360383		0.0498524i	−2.75592e−5		0.00381231i
$172$	−2.06729	+	3.58066i	−0.157630	+	0.273023i
$173$	6.56949	+	11.3787i	0.499469	+	0.865106i	1.00000		0.000612653i	$-0.000195014\pi$
$173$	6.56949	+	11.3787i	0.499469	+	0.865106i	−0.500530	+	0.865719i	$0.666862\pi$
$174$	0.200059	+	0.757573i	0.0151664	+	0.0574314i
$175$	1.37733	−	15.8514i	0.104116	−	1.19825i
$176$	−1.12854	−	1.95469i	−0.0850669	−	0.147340i
$177$	1.62330	−	5.97182i	0.122015	−	0.448870i
$178$	−8.62936			−0.646798
$179$	−2.05250	+	3.55503i	−0.153411	+	0.265715i	−0.932479	−	0.361224i	$-0.882359\pi$
$179$	−2.05250	+	3.55503i	−0.153411	+	0.265715i	0.779068	+	0.626939i	$0.215692\pi$
$180$	0.339057	−	6.69963i	0.0252718	−	0.499361i
$181$	−17.4253	+	10.0605i	−1.29521	+	0.747792i	−0.979573	−	0.201087i	$-0.935552\pi$
$181$	−17.4253	+	10.0605i	−1.29521	+	0.747792i	−0.315640	+	0.948879i	$0.602219\pi$
$182$			9.01965i			0.668581i
$183$	−13.6373	+	3.60132i	−1.00810	+	0.266217i
$184$			0.800056i			0.0589809i
$185$	8.53460	+	16.3829i	0.627476	+	1.20450i
$186$	−9.46764	+	1.83404i	−0.694201	+	0.134478i
$187$			0.474817i			0.0347220i
$188$	−8.04444			−0.586701
$189$	−4.10621	−	16.0173i	−0.298683	−	1.16509i
$190$	0.0171678	+	0.0329551i	0.00124548	+	0.00239082i
$191$	−0.704415	+	0.406694i	−0.0509697	+	0.0294273i	−0.525268	−	0.850937i	$-0.676035\pi$
$191$	−0.704415	+	0.406694i	−0.0509697	+	0.0294273i	0.474299	+	0.880364i	$0.342702\pi$
$192$	0.442238	+	1.67464i	0.0319158	+	0.120857i
$193$	14.0785	+	8.12823i	1.01339	+	0.585083i	0.912183	−	0.409782i	$-0.134395\pi$
$193$	14.0785	+	8.12823i	1.01339	+	0.585083i	0.101210	+	0.994865i	$0.467729\pi$
$194$		−	4.80894i		−	0.345261i
$195$	−2.34041	−	10.7252i	−0.167600	−	0.768045i
$196$	1.56326	+	2.70764i	0.111661	+	0.193403i
$197$	−4.90072	+	2.82943i	−0.349162	+	0.201589i	−0.664316	−	0.747452i	$-0.731277\pi$
$197$	−4.90072	+	2.82943i	−0.349162	+	0.201589i	0.315154	+	0.949040i	$0.397944\pi$
$198$	5.83944	+	3.42792i	0.414991	+	0.243612i
$199$	7.20797	−	4.16152i	0.510959	−	0.295003i	−0.222269	−	0.974985i	$-0.571346\pi$
$199$	7.20797	−	4.16152i	0.510959	−	0.295003i	0.733228	+	0.679983i	$0.238013\pi$
$200$	−2.11578	−	4.53028i	−0.149608	−	0.320339i
$201$	10.3074	+	10.3822i	0.727026	+	0.732301i
$202$			10.9252i			0.768694i
$203$	1.24670	+	0.719784i	0.0875014	+	0.0505190i
$204$	0.0955768	−	0.351609i	0.00669171	−	0.0246176i
$205$	−0.0762102	+	1.75747i	−0.00532275	+	0.122747i
$206$	15.3713	−	8.87463i	1.07097	−	0.618325i
$207$	−1.18503	−	2.08723i	−0.0823651	−	0.145072i
$208$	1.41720	+	2.45465i	0.0982648	+	0.170200i
$209$	−0.0375079			−0.00259448
$210$	−8.29624	−	9.11428i	−0.572495	−	0.628945i
$211$	−11.0068	+	19.0643i	−0.757739	+	1.31244i	0.186262	+	0.982500i	$0.440363\pi$
$211$	−11.0068	+	19.0643i	−0.757739	+	1.31244i	−0.944001	+	0.329942i	$0.892971\pi$
$212$	4.82919	−	2.78814i	0.331670	−	0.191490i
$213$	18.3736	+	18.5069i	1.25894	+	1.26807i
$214$	9.24636	−	16.0152i	0.632068	−	1.09477i
$215$	−4.27140	−	8.19934i	−0.291307	−	0.559191i
$216$	−3.63418	−	3.71386i	−0.247275	−	0.252696i
$217$	−9.86395	+	14.7182i	−0.669609	+	0.999134i
$218$	−0.471291			−0.0319198
$219$	−10.9524	+	10.8735i	−0.740093	+	0.734762i
$220$	5.04224	+	0.218649i	0.339948	+	0.0147413i
$221$		−	0.596264i		−	0.0401091i
$222$	13.8078	+	3.75334i	0.926722	+	0.251908i
$223$	5.80910	−	10.0617i	0.389006	−	0.673778i	−0.603310	−	0.797507i	$-0.706152\pi$
$223$	5.80910	−	10.0617i	0.389006	−	0.673778i	0.992316	+	0.123729i	$0.0394852\pi$
$224$	2.75588	+	1.59111i	0.184135	+	0.106310i
$225$	12.2299	+	8.68498i	0.815328	+	0.578999i
$226$	−1.13102	−	1.95898i	−0.0752343	−	0.130310i
$227$	10.5803	+	18.3257i	0.702242	+	1.21632i	0.967678	+	0.252190i	$0.0811509\pi$
$227$	10.5803	+	18.3257i	0.702242	+	1.21632i	−0.265436	+	0.964129i	$0.585516\pi$
$228$	0.0277752	+	0.00755004i	0.00183946	+	0.000500014i
$229$	−22.6961	−	13.1036i	−1.49980	−	0.865910i	−0.499799	−	0.866141i	$-0.666593\pi$
$229$	−22.6961	−	13.1036i	−1.49980	−	0.865910i	−1.00000		0.000231725i	$0.999926\pi$
$230$	−1.50910	−	0.960770i	−0.0995068	−	0.0633513i
$231$	12.0281	−	3.17638i	0.791394	−	0.208991i
$232$	0.452379			0.0297001
$233$	−3.39689			−0.222537			−0.111269	−	0.993790i	$-0.535491\pi$
$233$	−3.39689			−0.222537			−0.111269	+	0.993790i	$0.535491\pi$
$234$	−7.33304	−	4.30471i	−0.479376	−	0.281408i
$235$	9.66040	−	15.1737i	0.630175	−	0.989825i
$236$	−3.09426	−	1.78647i	−0.201419	−	0.116289i
$237$	−6.88472	+	25.3276i	−0.447210	+	1.64520i
$238$	−0.334718	−	0.579749i	−0.0216966	−	0.0375795i
$239$	−5.38215	−	9.32216i	−0.348142	−	0.603000i	0.637777	−	0.770221i	$-0.279854\pi$
$239$	−5.38215	−	9.32216i	−0.348142	−	0.603000i	−0.985919	+	0.167221i	$0.946521\pi$
$240$	−3.68985	−	1.17688i	−0.238179	−	0.0759670i
$241$	7.07114	+	4.08252i	0.455492	+	0.262979i	0.710147	−	0.704054i	$-0.248629\pi$
$241$	7.07114	+	4.08252i	0.455492	+	0.262979i	−0.254655	+	0.967032i	$0.581962\pi$
$242$	2.95280	−	5.11439i	0.189813	−	0.328766i
$243$	14.9819	+	4.30603i	0.961091	+	0.276232i
$244$			8.14341i			0.521328i
$245$	−6.98454	−	0.302874i	−0.446226	−	0.0193499i
$246$	0.960024	+	0.966989i	0.0612089	+	0.0616530i
$247$	0.0471016			0.00299700
$248$	−0.371864	+	5.55533i	−0.0236134	+	0.352764i
$249$	−16.4361	−	16.5553i	−1.04159	−	1.04915i
$250$	11.0860	+	1.44945i	0.701139	+	0.0916715i
$251$	9.18284	−	15.9051i	0.579615	−	1.00392i	−0.415908	−	0.909407i	$-0.636536\pi$
$251$	9.18284	−	15.9051i	0.579615	−	1.00392i	0.995523	−	0.0945166i	$-0.0301306\pi$
$252$	−9.54641	−	0.0690110i	−0.601367	−	0.00434728i
$253$	1.56386	−	0.902895i	0.0983190	−	0.0567645i
$254$	−2.39738	+	4.15239i	−0.150425	+	0.260544i
$255$	0.548442	+	0.602520i	0.0343448	+	0.0377313i
$256$	1.00000			0.0625000
$257$	−8.48270	−	14.6925i	−0.529136	−	0.916491i	−0.999423	−	0.0339770i	$-0.989183\pi$
$257$	−8.48270	−	14.6925i	−0.529136	−	0.916491i	0.470286	−	0.882514i	$-0.344151\pi$
$258$	−6.91056	−	1.87848i	−0.430232	−	0.116949i
$259$	22.7670	−	13.1445i	1.41467	−	0.816762i
$260$	−6.33194	−	0.274575i	−0.392690	−	0.0170284i
$261$	−1.18019	+	0.670054i	−0.0730519	+	0.0414753i
$262$	4.55833	+	2.63175i	0.281615	+	0.162590i
$263$		−	30.8199i		−	1.90044i	−0.311586	−	0.950218i	$-0.600860\pi$
$263$		−	30.8199i		−	1.90044i	0.311586	−	0.950218i	$-0.399140\pi$
$264$	2.77432	−	2.75434i	0.170748	−	0.169518i
$265$	−0.540189	+	12.4572i	−0.0331835	+	0.765241i
$266$	0.0457970	−	0.0264409i	0.00280799	−	0.00162120i
$267$	−3.81623	−	14.4511i	−0.233549	−	0.884392i
$268$	7.31490	−	4.22326i	0.446829	−	0.257977i
$269$	−2.19816	−	3.80733i	−0.134024	−	0.232137i	0.791200	−	0.611558i	$-0.209457\pi$
$269$	−2.19816	−	3.80733i	−0.134024	−	0.232137i	−0.925224	+	0.379421i	$0.876123\pi$
$270$	11.3694	−	2.39503i	0.691921	−	0.145757i
$271$		−	15.1797i		−	0.922100i	−0.887374	−	0.461050i	$-0.847473\pi$
$271$		−	15.1797i		−	0.922100i	0.887374	−	0.461050i	$-0.152527\pi$
$272$	−0.182184	−	0.105184i	−0.0110465	−	0.00637771i
$273$	−15.1047	+	3.98883i	−0.914177	+	0.241415i
$274$	7.42153	−	4.28482i	0.448351	−	0.258856i
$275$	−6.46755	+	9.24830i	−0.390008	+	0.557693i
$276$	−1.33981	+	0.353815i	−0.0806469	+	0.0212972i
$277$	−22.6724			−1.36225			−0.681127	−	0.732165i	$-0.738510\pi$
$277$	−22.6724			−1.36225			−0.681127	+	0.732165i	$0.738510\pi$
$278$		−	15.8192i		−	0.948773i
$279$	−7.25831	−	15.0438i	−0.434544	−	0.900651i
$280$	−6.31069	+	3.28752i	−0.377136	+	0.196467i
$281$			24.6672i			1.47152i	0.677241	+	0.735761i	$0.263176\pi$
$281$			24.6672i			1.47152i	−0.677241	+	0.735761i	$0.736824\pi$
$282$	−3.55756	−	13.4716i	−0.211849	−	0.802220i
$283$			1.81927i			0.108145i	0.998537	+	0.0540723i	$0.0172201\pi$
$283$			1.81927i			0.108145i	−0.998537	+	0.0540723i	$0.982780\pi$
$284$	13.0393	−	7.52824i	0.773740	−	0.446719i
$285$	−0.0475958	+	0.0433239i	−0.00281933	+	0.00256629i
$286$	3.19872	−	5.54035i	0.189144	−	0.327608i
$287$	2.50347			0.147775
$288$	−2.60885	+	1.48118i	−0.153728	+	0.0872794i
$289$	−8.47787	−	14.6841i	−0.498698	−	0.863771i
$290$	−0.543252	+	0.853294i	−0.0319009	+	0.0501071i
$291$	8.05324	−	2.12669i	0.472090	−	0.124669i
$292$	4.45521	+	7.71666i	0.260722	+	0.451583i
$293$	9.36548	−	16.2215i	0.547137	−	0.947669i	−0.451332	−	0.892356i	$-0.649051\pi$
$293$	9.36548	−	16.2215i	0.547137	−	0.947669i	0.998469	−	0.0553132i	$-0.0176157\pi$
$294$	−3.84300	+	3.81532i	−0.224128	+	0.222514i
$295$	7.08554	−	3.69117i	0.412536	−	0.214908i
$296$	4.13062	−	7.15444i	0.240087	−	0.415843i
$297$	−3.15812	+	11.2949i	−0.183253	+	0.655398i
$298$	−3.75915	−	2.17035i	−0.217762	−	0.125725i
$299$	−1.96386	+	1.13384i	−0.113573	+	0.0655714i
$300$	6.65092	−	5.54664i	0.383991	−	0.320235i
$301$	−11.3944	+	6.57858i	−0.656765	+	0.379183i
$302$			3.92788i			0.226024i
$303$	−18.2958	+	4.83153i	−1.05107	+	0.277564i
$304$	0.00830895	−	0.0143915i	0.000476551	−	0.000825411i
$305$	−15.3604	−	9.77924i	−0.879534	−	0.559958i
$306$	0.631087	+	0.00456213i	0.0360768	+	0.000260799i
$307$	0.206088	+	0.118985i	0.0117621	+	0.00679084i	0.505870	−	0.862610i	$-0.331172\pi$
$307$	0.206088	+	0.118985i	0.0117621	+	0.00679084i	−0.494107	+	0.869401i	$0.664505\pi$
$308$		−	7.18252i		−	0.409262i
$309$	21.6596	+	21.8168i	1.23217	+	1.24111i
$310$	−10.0321	−	7.37270i	−0.569786	−	0.418741i
$311$			8.87109i			0.503034i	0.967853	+	0.251517i	$0.0809294\pi$
$311$			8.87109i			0.503034i	−0.967853	+	0.251517i	$0.919071\pi$
$312$	−3.48393	+	3.45884i	−0.197239	+	0.195818i
$313$	−11.0818	+	19.1942i	−0.626380	+	1.08492i	0.361892	+	0.932220i	$0.382131\pi$
$313$	−11.0818	+	19.1942i	−0.626380	+	1.08492i	−0.988272	+	0.152702i	$0.951203\pi$
$314$		−	5.82296i		−	0.328609i
$315$	11.5942	−	17.9239i	0.653262	−	1.00990i
$316$	13.1233	+	7.57675i	0.738244	+	0.426225i
$317$	−0.869811	+	1.50656i	−0.0488535	+	0.0846167i	−0.889418	−	0.457095i	$-0.848890\pi$
$317$	−0.869811	+	1.50656i	−0.0488535	+	0.0846167i	0.840565	+	0.541711i	$0.182223\pi$
$318$	6.80478	+	6.85415i	0.381593	+	0.384362i
$319$	−0.510527	−	0.884260i	−0.0285841	−	0.0495090i
$320$	−1.20088	+	1.88624i	−0.0671312	+	0.105444i
$321$	30.9088	+	8.40184i	1.72516	+	0.468945i
$322$	−1.27298	+	2.20486i	−0.0709402	+	0.122872i
$323$	−0.00302751	+	0.00174794i	−0.000168455	+	9.72577e-5i
$324$	4.61221	−	7.72836i	0.256234	−	0.429353i
$325$	8.12180	−	11.6138i	0.450517	−	0.644218i
$326$		−	11.9963i		−	0.664414i
$327$	−0.208423	−	0.789244i	−0.0115258	−	0.0436453i
$328$	0.681306	−	0.393352i	0.0376188	−	0.0217192i
$329$	−22.1695	−	12.7996i	−1.22225	−	0.705664i
$330$	1.86371	+	8.54065i	0.102594	+	0.470147i
$331$	−13.4962	+	7.79202i	−0.741817	+	0.428288i	−0.822730	−	0.568433i	$-0.807550\pi$
$331$	−13.4962	+	7.79202i	−0.741817	+	0.428288i	0.0809126	+	0.996721i	$0.474217\pi$
$332$	−11.6643	+	6.73438i	−0.640161	+	0.369597i
$333$	−0.179157	+	24.7831i	−0.00981773	+	1.35810i
$334$	−0.0740101	−	0.0427297i	−0.00404965	−	0.00233807i
$335$	−0.818237	+	18.8693i	−0.0447051	+	1.03094i
$336$	−1.44578	+	5.31876i	−0.0788740	+	0.290162i
$337$	1.69991			0.0926000			0.0463000	−	0.998928i	$-0.485257\pi$
$337$	1.69991			0.0926000			0.0463000	+	0.998928i	$0.485257\pi$
$338$	2.48312	−	4.30088i	0.135064	−	0.233937i
$339$	2.78042	−	2.76039i	0.151012	−	0.149924i
$340$	0.417182	−	0.217329i	0.0226249	−	0.0117863i
$341$	11.2786	−	5.54253i	0.610771	−	0.300145i
$342$	−0.000360383		0.0498524i	−1.94873e−5		0.00269571i
$343$		−	12.3263i		−	0.665556i
$344$	−2.06729	+	3.58066i	−0.111461	+	0.193056i
$345$	0.941567	−	2.95208i	0.0506923	−	0.158935i
$346$	6.56949	+	11.3787i	0.353178	+	0.611723i
$347$	−20.3091	−	11.7255i	−1.09025	−	0.629457i	−0.156609	−	0.987661i	$-0.550056\pi$
$347$	−20.3091	−	11.7255i	−1.09025	−	0.629457i	−0.933644	+	0.358203i	$0.883389\pi$
$348$	0.200059	+	0.757573i	0.0107243	+	0.0406102i
$349$	−17.4656			−0.934912			−0.467456	−	0.884016i	$-0.654829\pi$
$349$	−17.4656			−0.934912			−0.467456	+	0.884016i	$0.654829\pi$
$350$	1.37733	−	15.8514i	0.0736215	−	0.847291i
$351$	3.96590	−	14.1839i	0.211684	−	0.757081i
$352$	−1.12854	−	1.95469i	−0.0601514	−	0.104185i
$353$	26.4606	+	15.2770i	1.40835	+	0.813114i	0.995230	−	0.0975610i	$-0.0311041\pi$
$353$	26.4606	+	15.2770i	1.40835	+	0.813114i	0.413124	+	0.910675i	$0.364437\pi$
$354$	1.62330	−	5.97182i	0.0862775	−	0.317399i
$355$	−1.45856	+	33.6357i	−0.0774124	+	1.78520i
$356$	−8.62936			−0.457355
$357$	0.822847	−	0.816920i	0.0435497	−	0.0432360i
$358$	−2.05250	+	3.55503i	−0.108478	+	0.187889i
$359$	−25.7981	+	14.8945i	−1.36157	+	0.786104i	−0.989833	−	0.142234i	$-0.954572\pi$
$359$	−25.7981	+	14.8945i	−1.36157	+	0.786104i	−0.371739	+	0.928337i	$0.621238\pi$
$360$	0.339057	−	6.69963i	0.0178699	−	0.353101i
$361$	9.49986	+	16.4542i	0.499993	+	0.866013i
$362$	−17.4253	+	10.0605i	−0.915854	+	0.528769i
$363$	9.87062	+	2.68310i	0.518073	+	0.140826i
$364$			9.01965i			0.472758i
$365$	−19.9056	−	0.863177i	−1.04191	−	0.0451808i
$366$	−13.6373	+	3.60132i	−0.712833	+	0.188244i
$367$	−14.4856	−	25.0897i	−0.756140	−	1.30967i	−0.944806	−	0.327631i	$-0.893750\pi$
$367$	−14.4856	−	25.0897i	−0.756140	−	1.30967i	0.188666	−	0.982041i	$-0.439584\pi$
$368$			0.800056i			0.0417058i
$369$	−1.19480	+	2.03533i	−0.0621989	+	0.105955i
$370$	8.53460	+	16.3829i	0.443693	+	0.851709i
$371$	17.7449			0.921270
$372$	−9.46764	+	1.83404i	−0.490875	+	0.0950905i
$373$			2.95280i			0.152890i	0.997074	+	0.0764451i	$0.0243570\pi$
$373$			2.95280i			0.152890i	−0.997074	+	0.0764451i	$0.975643\pi$
$374$			0.474817i			0.0245522i
$375$	2.47532	+	19.2061i	0.127825	+	0.991797i
$376$	−8.04444			−0.414860
$377$	0.641109	+	1.11043i	0.0330188	+	0.0571902i
$378$	−4.10621	−	16.0173i	−0.211201	−	0.823843i
$379$	−3.80420	+	6.58906i	−0.195408	+	0.338457i	−0.947034	−	0.321132i	$-0.895937\pi$
$379$	−3.80420	+	6.58906i	−0.195408	+	0.338457i	0.751626	+	0.659590i	$0.229270\pi$
$380$	0.0171678	+	0.0329551i	0.000880689	+	0.00169056i
$381$	−8.01398	−	2.17842i	−0.410569	−	0.111604i
$382$	−0.704415	+	0.406694i	−0.0360410	+	0.0208083i
$383$	10.5978	−	6.11865i	0.541523	−	0.312649i	−0.204173	−	0.978935i	$-0.565450\pi$
$383$	10.5978	−	6.11865i	0.541523	−	0.312649i	0.745696	+	0.666286i	$0.232117\pi$
$384$	0.442238	+	1.67464i	0.0225679	+	0.0854587i
$385$	13.5479	+	8.62533i	0.690467	+	0.439588i
$386$	14.0785	+	8.12823i	0.716577	+	0.413716i
$387$	0.0896645	−	12.4034i	0.00455790	−	0.630502i
$388$		−	4.80894i		−	0.244137i
$389$	−15.1180	+	26.1851i	−0.766511	+	1.32764i	0.172933	+	0.984934i	$0.444676\pi$
$389$	−15.1180	+	26.1851i	−0.766511	+	1.32764i	−0.939444	+	0.342703i	$0.888658\pi$
$390$	−2.34041	−	10.7252i	−0.118511	−	0.543090i
$391$	0.0841530	−	0.145757i	0.00425580	−	0.00737126i
$392$	1.56326	+	2.70764i	0.0789565	+	0.136757i
$393$	−2.39138	+	8.79743i	−0.120629	+	0.443772i
$394$	−4.90072	+	2.82943i	−0.246895	+	0.142545i
$395$	−30.0510	+	15.6549i	−1.51203	+	0.787685i
$396$	5.83944	+	3.42792i	0.293443	+	0.172259i
$397$	−17.6190	−	10.1723i	−0.884270	−	0.510534i	−0.0122063	−	0.999926i	$-0.503885\pi$
$397$	−17.6190	−	10.1723i	−0.884270	−	0.510534i	−0.872064	+	0.489392i	$0.837219\pi$
$398$	7.20797	−	4.16152i	0.361303	−	0.208598i
$399$	0.0645322	+	0.0650004i	0.00323065	+	0.00325409i
$400$	−2.11578	−	4.53028i	−0.105789	−	0.226514i
$401$	−32.1710			−1.60654			−0.803271	−	0.595614i	$-0.796909\pi$
$401$	−32.1710			−1.60654			−0.803271	+	0.595614i	$0.796909\pi$
$402$	10.3074	+	10.3822i	0.514085	+	0.517815i
$403$	−14.1634	+	6.96019i	−0.705530	+	0.346712i
$404$			10.9252i			0.543548i
$405$	9.03881	+	17.9805i	0.449142	+	0.893460i
$406$	1.24670	+	0.719784i	0.0618728	+	0.0357223i
$407$	−18.6463			−0.924261
$408$	0.0955768	−	0.351609i	0.00473176	−	0.0174072i
$409$	16.0037	+	9.23975i	0.791333	+	0.456876i	0.840432	−	0.541918i	$-0.182302\pi$
$409$	16.0037	+	9.23975i	0.791333	+	0.456876i	−0.0490987	+	0.998794i	$0.515635\pi$
$410$	−0.0762102	+	1.75747i	−0.00376375	+	0.0867954i
$411$	10.4576	+	10.5335i	0.515837	+	0.519579i
$412$	15.3713	−	8.87463i	0.757290	−	0.437222i
$413$	−5.68494	−	9.84661i	−0.279738	−	0.484520i
$414$	−1.18503	−	2.08723i	−0.0582409	−	0.102582i
$415$	1.30476	−	30.0888i	0.0640480	−	1.47700i
$416$	1.41720	+	2.45465i	0.0694837	+	0.120349i
$417$	26.4915	−	6.99585i	1.29729	−	0.342588i
$418$	−0.0375079			−0.00183457
$419$			5.90988i			0.288716i	0.989526	+	0.144358i	$0.0461117\pi$
$419$			5.90988i			0.288716i	−0.989526	+	0.144358i	$0.953888\pi$
$420$	−8.29624	−	9.11428i	−0.404815	−	0.444731i
$421$	−5.40623	−	9.36386i	−0.263483	−	0.456367i	0.703682	−	0.710515i	$-0.251538\pi$
$421$	−5.40623	−	9.36386i	−0.263483	−	0.456367i	−0.967165	+	0.254149i	$0.918205\pi$
$422$	−11.0068	+	19.0643i	−0.535802	+	0.928037i
$423$	20.9868	−	11.9153i	1.02041	−	0.579340i
$424$	4.82919	−	2.78814i	0.234526	−	0.135404i
$425$	−0.0910516	+	1.04789i	−0.00441665	+	0.0508302i
$426$	18.3736	+	18.5069i	0.890203	+	0.896661i
$427$	−12.9571	+	22.4423i	−0.627036	+	1.08606i
$428$	9.24636	−	16.0152i	0.446940	−	0.774123i
$429$	10.6927	+	2.90656i	0.516248	+	0.140330i
$430$	−4.27140	−	8.19934i	−0.205985	−	0.395407i
$431$	33.7037	+	19.4588i	1.62345	+	0.937299i	0.985988	+	0.166817i	$0.0533489\pi$
$431$	33.7037	+	19.4588i	1.62345	+	0.937299i	0.637462	+	0.770482i	$0.279984\pi$
$432$	−3.63418	−	3.71386i	−0.174849	−	0.178683i
$433$	−10.9104			−0.524320			−0.262160	−	0.965024i	$-0.584435\pi$
$433$	−10.9104			−0.524320			−0.262160	+	0.965024i	$0.584435\pi$
$434$	−9.86395	+	14.7182i	−0.473485	+	0.706495i
$435$	−1.66921	−	0.532394i	−0.0800324	−	0.0255263i
$436$	−0.471291			−0.0225707
$437$	0.0115140	+	0.00664763i	0.000550791	+	0.000317999i
$438$	−10.9524	+	10.8735i	−0.523325	+	0.519555i
$439$	0.307195	+	0.532078i	0.0146616	+	0.0253947i	0.873263	−	0.487249i	$-0.162000\pi$
$439$	0.307195	+	0.532078i	0.0146616	+	0.0253947i	−0.858602	+	0.512644i	$0.828666\pi$
$440$	5.04224	+	0.218649i	0.240380	+	0.0104237i
$441$	−8.08881	−	4.74837i	−0.385182	−	0.226113i
$442$		−	0.596264i		−	0.0283614i
$443$	−3.88123	−	6.72249i	−0.184403	−	0.319395i	0.758972	−	0.651123i	$-0.225702\pi$
$443$	−3.88123	−	6.72249i	−0.184403	−	0.319395i	−0.943375	+	0.331728i	$0.892368\pi$
$444$	13.8078	+	3.75334i	0.655291	+	0.178126i
$445$	10.3628	−	16.2770i	0.491244	−	0.771605i
$446$	5.80910	−	10.0617i	0.275069	−	0.476433i
$447$	1.97212	−	7.25505i	0.0932780	−	0.343152i
$448$	2.75588	+	1.59111i	0.130203	+	0.0751729i
$449$	−15.2495			−0.719666			−0.359833	−	0.933017i	$-0.617166\pi$
$449$	−15.2495			−0.719666			−0.359833	+	0.933017i	$0.617166\pi$
$450$	12.2299	+	8.68498i	0.576524	+	0.409414i
$451$	−1.53776	−	0.887827i	−0.0724104	−	0.0418062i
$452$	−1.13102	−	1.95898i	−0.0531987	−	0.0921429i
$453$	−6.57779	+	1.73706i	−0.309051	+	0.0816140i
$454$	10.5803	+	18.3257i	0.496560	+	0.860067i
$455$	−17.0132	−	10.8315i	−0.797591	−	0.507789i
$456$	0.0277752	+	0.00755004i	0.00130069	+	0.000353563i
$457$	−9.40285			−0.439847			−0.219923	−	0.975517i	$-0.570581\pi$
$457$	−9.40285			−0.439847			−0.219923	+	0.975517i	$0.570581\pi$
$458$	−22.6961	−	13.1036i	−1.06052	−	0.612290i
$459$	0.271450	+	1.05886i	0.0126702	+	0.0494234i
$460$	−1.50910	−	0.960770i	−0.0703619	−	0.0447961i
$461$	−26.2525			−1.22270			−0.611351	−	0.791360i	$-0.709373\pi$
$461$	−26.2525			−1.22270			−0.611351	+	0.791360i	$0.709373\pi$
$462$	12.0281	−	3.17638i	0.559600	−	0.147779i
$463$	−8.83708			−0.410694			−0.205347	−	0.978689i	$-0.565832\pi$
$463$	−8.83708			−0.410694			−0.205347	+	0.978689i	$0.565832\pi$
$464$	0.452379			0.0210012
$465$	7.91006	−	20.0607i	0.366820	−	0.930292i
$466$	−3.39689			−0.157358
$467$	−0.199102			−0.00921334			−0.00460667	−	0.999989i	$-0.501466\pi$
$467$	−0.199102			−0.00921334			−0.00460667	+	0.999989i	$0.501466\pi$
$468$	−7.33304	−	4.30471i	−0.338970	−	0.198985i
$469$	26.8787			1.24114
$470$	9.66040	−	15.1737i	0.445601	−	0.699912i
$471$	9.75137	−	2.57513i	0.449320	−	0.118656i
$472$	−3.09426	−	1.78647i	−0.142425	−	0.0822290i
$473$	9.33209			0.429090
$474$	−6.88472	+	25.3276i	−0.316226	+	1.16333i
$475$	−0.0827776	−	0.00719258i	−0.00379810	−	0.000330018i
$476$	−0.334718	−	0.579749i	−0.0153418	−	0.0265727i
$477$	−8.46892	+	14.4267i	−0.387765	+	0.660555i
$478$	−5.38215	−	9.32216i	−0.246174	−	0.426386i
$479$	27.8735	+	16.0928i	1.27357	+	0.735298i	0.975659	−	0.219295i	$-0.0703757\pi$
$479$	27.8735	+	16.0928i	1.27357	+	0.735298i	0.297914	+	0.954593i	$0.403709\pi$
$480$	−3.68985	−	1.17688i	−0.168418	−	0.0537168i
$481$	23.4156			1.06766
$482$	7.07114	+	4.08252i	0.322082	+	0.185954i
$483$	−4.25531	−	1.15671i	−0.193623	−	0.0526320i
$484$	2.95280	−	5.11439i	0.134218	−	0.232472i
$485$	9.07079	+	5.77495i	0.411883	+	0.262227i
$486$	14.9819	+	4.30603i	0.679594	+	0.195326i
$487$	4.86941	+	8.43407i	0.220654	+	0.382184i	0.955007	−	0.296584i	$-0.0958475\pi$
$487$	4.86941	+	8.43407i	0.220654	+	0.382184i	−0.734353	+	0.678768i	$0.762514\pi$
$488$			8.14341i			0.368635i
$489$	20.0895	−	5.30522i	0.908479	−	0.239910i
$490$	−6.98454	−	0.302874i	−0.315529	−	0.0136825i
$491$	−1.53335	−	2.65584i	−0.0691991	−	0.119856i	0.829350	−	0.558730i	$-0.188711\pi$
$491$	−1.53335	−	2.65584i	−0.0691991	−	0.119856i	−0.898549	+	0.438873i	$0.855378\pi$
$492$	0.960024	+	0.966989i	0.0432812	+	0.0435952i
$493$	−0.0824161	−	0.0475830i	−0.00371184	−	0.00214303i
$494$	0.0471016			0.00211920
$495$	−13.4783	+	6.89805i	−0.605806	+	0.310044i
$496$	−0.371864	+	5.55533i	−0.0166972	+	0.249442i
$497$	47.9130			2.14919
$498$	−16.4361	−	16.5553i	−0.736518	−	0.741862i
$499$	11.3529	+	6.55458i	0.508224	+	0.293423i	0.732103	−	0.681194i	$-0.238539\pi$
$499$	11.3529	+	6.55458i	0.508224	+	0.293423i	−0.223879	+	0.974617i	$0.571872\pi$
$500$	11.0860	+	1.44945i	0.495780	+	0.0648216i
$501$	0.0388270	−	0.142837i	0.00173466	−	0.00638149i
$502$	9.18284	−	15.9051i	0.409850	−	0.709881i
$503$	18.6722	−	32.3413i	0.832554	−	1.44203i	−0.0634527	−	0.997985i	$-0.520211\pi$
$503$	18.6722	−	32.3413i	0.832554	−	1.44203i	0.896007	−	0.444041i	$-0.146455\pi$
$504$	−9.54641	−	0.0690110i	−0.425231	−	0.00307399i
$505$	−20.6075	−	13.1198i	−0.917022	−	0.583825i
$506$	1.56386	−	0.902895i	0.0695220	−	0.0401386i
$507$	8.30056	+	2.25632i	0.368641	+	0.100207i
$508$	−2.39738	+	4.15239i	−0.106367	+	0.184233i
$509$	13.9143	+	24.1003i	0.616742	+	1.06823i	0.990076	+	0.140532i	$0.0448813\pi$
$509$	13.9143	+	24.1003i	0.616742	+	1.06823i	−0.373334	+	0.927697i	$0.621785\pi$
$510$	0.548442	+	0.602520i	0.0242854	+	0.0266800i
$511$			28.3549i			1.25435i
$512$	1.00000			0.0441942
$513$	−0.0836443	+	0.0214431i	−0.00369299	+	0.000946736i
$514$	−8.48270	−	14.6925i	−0.374156	−	0.648057i
$515$	−1.71942	+	39.6513i	−0.0757667	+	1.74725i
$516$	−6.91056	−	1.87848i	−0.304220	−	0.0826953i
$517$	9.07847	+	15.7244i	0.399271	+	0.691557i
$518$	22.7670	−	13.1445i	1.00032	−	0.577538i
$519$	−16.1500	+	16.0336i	−0.708905	+	0.703799i
$520$	−6.33194	−	0.274575i	−0.277674	−	0.0120409i
$521$	−11.8145	−	6.82108i	−0.517601	−	0.298837i	0.218352	−	0.975870i	$-0.429932\pi$
$521$	−11.8145	−	6.82108i	−0.517601	−	0.298837i	−0.735952	+	0.677033i	$0.763265\pi$
$522$	−1.18019	+	0.670054i	−0.0516555	+	0.0293275i
$523$	−31.4674			−1.37597			−0.687987	−	0.725723i	$-0.741505\pi$
$523$	−31.4674			−1.37597			−0.687987	+	0.725723i	$0.741505\pi$
$524$	4.55833	+	2.63175i	0.199132	+	0.114969i
$525$	27.1545	−	4.70354i	1.18512	−	0.205279i
$526$		−	30.8199i		−	1.34381i
$527$	0.652079	−	0.972978i	0.0284050	−	0.0423836i
$528$	2.77432	−	2.75434i	0.120737	−	0.119867i
$529$	22.3599			0.972170
$530$	−0.540189	+	12.4572i	−0.0234643	+	0.541107i
$531$	10.7186	+	0.0774844i	0.465145	+	0.00336254i
$532$	0.0457970	−	0.0264409i	0.00198555	−	0.00114636i
$533$	1.93109	+	1.11491i	0.0836447	+	0.0482923i
$534$	−3.81623	−	14.4511i	−0.165144	−	0.625360i
$535$	19.1047	+	36.6731i	0.825966	+	1.58552i
$536$	7.31490	−	4.22326i	0.315956	−	0.182417i
$537$	−6.86109	−	1.86503i	−0.296078	−	0.0804819i
$538$	−2.19816	−	3.80733i	−0.0947695	−	0.164146i
$539$	3.52840	−	6.11136i	0.151979	−	0.263235i
$540$	11.3694	−	2.39503i	0.489262	−	0.103066i
$541$	−8.47766	+	14.6837i	−0.364483	+	0.631303i	−0.988693	−	0.149954i	$-0.952088\pi$
$541$	−8.47766	+	14.6837i	−0.364483	+	0.631303i	0.624210	+	0.781257i	$0.285421\pi$
$542$		−	15.1797i		−	0.652023i
$543$	−24.5539	−	24.7320i	−1.05371	−	1.06135i
$544$	−0.182184	−	0.105184i	−0.00781107	−	0.00450972i
$545$	0.565963	−	0.888966i	0.0242432	−	0.0380791i
$546$	−15.1047	+	3.98883i	−0.646421	+	0.170706i
$547$	−27.5845	+	15.9259i	−1.17943	+	0.680943i	−0.955882	−	0.293751i	$-0.905096\pi$
$547$	−27.5845	+	15.9259i	−1.17943	+	0.680943i	−0.223545	+	0.974694i	$0.571763\pi$
$548$	7.42153	−	4.28482i	0.317032	−	0.183039i
$549$	−12.0618	−	21.2449i	−0.514787	−	0.906712i
$550$	−6.46755	+	9.24830i	−0.275777	+	0.394349i
$551$	0.00375879	−	0.00651042i	0.000160130	−	0.000277353i
$552$	−1.33981	+	0.353815i	−0.0570260	+	0.0150594i
$553$	24.1109	+	41.7613i	1.02530	+	1.77587i
$554$	−22.6724			−0.963259
$555$	−23.6612	+	21.5376i	−1.00436	+	0.914218i
$556$		−	15.8192i		−	0.670884i
$557$		−	26.5057i		−	1.12308i	−0.827449	−	0.561541i	$-0.810209\pi$
$557$		−	26.5057i		−	1.12308i	0.827449	−	0.561541i	$-0.189791\pi$
$558$	−7.25831	−	15.0438i	−0.307269	−	0.636856i
$559$	−11.7190			−0.495662
$560$	−6.31069	+	3.28752i	−0.266675	+	0.138923i
$561$	−0.795148	+	0.209982i	−0.0335712	+	0.00886544i
$562$			24.6672i			1.04052i
$563$	16.3573	+	28.3317i	0.689379	+	1.19404i	0.972039	+	0.234819i	$0.0754496\pi$
$563$	16.3573	+	28.3317i	0.689379	+	1.19404i	−0.282661	+	0.959220i	$0.591217\pi$
$564$	−3.55756	−	13.4716i	−0.149800	−	0.567255i
$565$	5.05333	+	0.219130i	0.212595	+	0.00921887i
$566$			1.81927i			0.0764698i
$567$	25.0074	−	13.9599i	1.05021	−	0.586261i
$568$	13.0393	−	7.52824i	0.547117	−	0.315878i
$569$	11.3867	+	19.7223i	0.477354	+	0.826801i	0.999663	−	0.0259548i	$-0.00826260\pi$
$569$	11.3867	+	19.7223i	0.477354	+	0.826801i	−0.522309	+	0.852756i	$0.674929\pi$
$570$	−0.0475958	+	0.0433239i	−0.00199357	+	0.00181464i
$571$	−14.0140	+	8.09098i	−0.586467	+	0.338597i	−0.763699	−	0.645572i	$-0.776619\pi$
$571$	−14.0140	+	8.09098i	−0.586467	+	0.338597i	0.177232	+	0.984169i	$0.443286\pi$
$572$	3.19872	−	5.54035i	0.133745	−	0.231654i
$573$	−0.992586	−	0.999787i	−0.0414659	−	0.0417667i
$574$	2.50347			0.104493
$575$	3.62448	−	1.69274i	0.151151	−	0.0705923i
$576$	−2.60885	+	1.48118i	−0.108702	+	0.0617158i
$577$	−12.6544	−	7.30604i	−0.526811	−	0.304154i	0.212906	−	0.977073i	$-0.431707\pi$
$577$	−12.6544	−	7.30604i	−0.526811	−	0.304154i	−0.739717	+	0.672918i	$0.765041\pi$
$578$	−8.47787	−	14.6841i	−0.352633	−	0.610778i
$579$	−7.38583	+	27.1711i	−0.306944	+	1.12919i
$580$	−0.543252	+	0.853294i	−0.0225573	+	0.0354311i
$581$	−42.8606			−1.77816
$582$	8.05324	−	2.12669i	0.333818	−	0.0881542i
$583$	−10.8999	−	6.29305i	−0.451427	−	0.260631i
$584$	4.45521	+	7.71666i	0.184358	+	0.319318i
$585$	16.9258	−	8.66242i	0.699795	−	0.358147i
$586$	9.36548	−	16.2215i	0.386884	−	0.670103i
$587$		−	6.32226i		−	0.260948i	−0.991452	−	0.130474i	$-0.958350\pi$
$587$		−	6.32226i		−	0.260948i	0.991452	−	0.130474i	$-0.0416498\pi$
$588$	−3.84300	+	3.81532i	−0.158483	+	0.157341i
$589$	0.0768599	+	0.0515107i	0.00316696	+	0.00212246i
$590$	7.08554	−	3.69117i	0.291707	−	0.151963i
$591$	−6.90557	−	6.95567i	−0.284057	−	0.286118i
$592$	4.13062	−	7.15444i	0.169767	−	0.294046i
$593$	−15.3203			−0.629128			−0.314564	−	0.949236i	$-0.601858\pi$
$593$	−15.3203			−0.629128			−0.314564	+	0.949236i	$0.601858\pi$
$594$	−3.15812	+	11.2949i	−0.129579	+	0.463436i
$595$	1.49550	+	0.0648501i	0.0613095	+	0.00265860i
$596$	−3.75915	−	2.17035i	−0.153981	−	0.0889010i
$597$	10.1567	+	10.2304i	0.415686	+	0.418702i
$598$	−1.96386	+	1.13384i	−0.0803082	+	0.0463660i
$599$	40.2534	−	23.2403i	1.64471	−	0.949572i	0.665580	−	0.746327i	$-0.268184\pi$
$599$	40.2534	−	23.2403i	1.64471	−	0.949572i	0.979128	−	0.203246i	$-0.0651490\pi$
$600$	6.65092	−	5.54664i	0.271523	−	0.226441i
$601$	−16.3913	−	9.46350i	−0.668614	−	0.386024i	0.126938	−	0.991911i	$-0.459485\pi$
$601$	−16.3913	−	9.46350i	−0.668614	−	0.386024i	−0.795551	+	0.605886i	$0.792819\pi$
$602$	−11.3944	+	6.57858i	−0.464403	+	0.268123i
$603$	−12.8281	+	21.8525i	−0.522400	+	0.889904i
$604$			3.92788i			0.159823i
$605$	6.10101	+	11.7114i	0.248041	+	0.476138i
$606$	−18.2958	+	4.83153i	−0.743215	+	0.196268i
$607$	15.5739	−	8.99161i	0.632126	−	0.364958i	−0.149449	−	0.988769i	$-0.547750\pi$
$607$	15.5739	−	8.99161i	0.632126	−	0.364958i	0.781575	+	0.623811i	$0.214417\pi$
$608$	0.00830895	−	0.0143915i	0.000336972	−	0.000583653i
$609$	−0.654042	+	2.40610i	−0.0265031	+	0.0975000i
$610$	−15.3604	−	9.77924i	−0.621924	−	0.395950i
$611$	−11.4005	−	19.7463i	−0.461217	−	0.798851i
$612$	0.631087	+	0.00456213i	0.0255102	+	0.000184413i
$613$	−17.6863	+	30.6335i	−0.714342	+	1.23728i	0.248871	+	0.968537i	$0.419940\pi$
$613$	−17.6863	+	30.6335i	−0.714342	+	1.23728i	−0.963213	+	0.268740i	$0.913393\pi$
$614$	0.206088	+	0.118985i	0.00831704	+	0.00480185i
$615$	−2.97684	+	0.649596i	−0.120038	+	0.0261943i
$616$		−	7.18252i		−	0.289392i
$617$	−12.0346	+	20.8445i	−0.484494	+	0.839168i	−0.999841	−	0.0178134i	$-0.994330\pi$
$617$	−12.0346	+	20.8445i	−0.484494	+	0.839168i	0.515348	+	0.856981i	$0.327663\pi$
$618$	21.6596	+	21.8168i	0.871277	+	0.877598i
$619$		−	30.3033i		−	1.21799i	−0.793173	−	0.608996i	$-0.791572\pi$
$619$		−	30.3033i		−	1.21799i	0.793173	−	0.608996i	$-0.208428\pi$
$620$	−10.0321	−	7.37270i	−0.402899	−	0.296095i
$621$	2.97130	−	2.90755i	0.119234	−	0.116676i
$622$			8.87109i			0.355698i
$623$	−23.7815	−	13.7303i	−0.952786	−	0.550091i
$624$	−3.48393	+	3.45884i	−0.139469	+	0.138464i
$625$	−16.0469	+	19.1702i	−0.641877	+	0.766807i
$626$	−11.0818	+	19.1942i	−0.442918	+	0.767156i
$627$	−0.0165874	−	0.0628123i	−0.000662438	−	0.00250848i
$628$		−	5.82296i		−	0.232361i
$629$	−1.50506	+	0.868949i	−0.0600108	+	0.0346473i
$630$	11.5942	−	17.9239i	0.461926	−	0.714106i
$631$	28.9841	−	16.7340i	1.15384	−	0.666169i	0.204019	−	0.978967i	$-0.434600\pi$
$631$	28.9841	−	16.7340i	1.15384	−	0.666169i	0.949820	+	0.312798i	$0.101266\pi$
$632$	13.1233	+	7.57675i	0.522017	+	0.301387i
$633$	−36.7935	−	10.0015i	−1.46241	−	0.397523i
$634$	−0.869811	+	1.50656i	−0.0345446	+	0.0598330i
$635$	−4.95343	−	9.50855i	−0.196571	−	0.377335i
$636$	6.80478	+	6.85415i	0.269827	+	0.271785i
$637$	−4.43088	+	7.67452i	−0.175558	+	0.304075i
$638$	−0.510527	−	0.884260i	−0.0202120	−	0.0350082i
$639$	−22.8669	+	38.9536i	−0.904601	+	1.54098i
$640$	−1.20088	+	1.88624i	−0.0474689	+	0.0745601i
$641$	6.96794	+	12.0688i	0.275217	+	0.476690i	0.970190	−	0.242346i	$-0.0779169\pi$
$641$	6.96794	+	12.0688i	0.275217	+	0.476690i	−0.694973	+	0.719036i	$0.744584\pi$
$642$	30.9088	+	8.40184i	1.21987	+	0.331594i
$643$	−9.47997			−0.373854			−0.186927	−	0.982374i	$-0.559853\pi$
$643$	−9.47997			−0.373854			−0.186927	+	0.982374i	$0.559853\pi$
$644$	−1.27298	+	2.20486i	−0.0501623	+	0.0868837i
$645$	11.8420	−	10.7791i	0.466278	−	0.424428i
$646$	−0.00302751	+	0.00174794i	−0.000119116	+	6.87716e-5i
$647$			31.5526i			1.24046i	0.784420	+	0.620230i	$0.212961\pi$
$647$			31.5526i			1.24046i	−0.784420	+	0.620230i	$0.787039\pi$
$648$	4.61221	−	7.72836i	0.181185	−	0.303599i
$649$			8.06442i			0.316556i
$650$	8.12180	−	11.6138i	0.318563	−	0.455531i
$651$	−29.0099	−	10.0097i	−1.13699	−	0.392310i
$652$		−	11.9963i		−	0.469812i
$653$	−19.8770			−0.777848			−0.388924	−	0.921270i	$-0.627153\pi$
$653$	−19.8770			−0.777848			−0.388924	+	0.921270i	$0.627153\pi$
$654$	−0.208423	−	0.789244i	−0.00814997	−	0.0308619i
$655$	−10.4381	+	5.43767i	−0.407851	+	0.212468i
$656$	0.681306	−	0.393352i	0.0266005	−	0.0153578i
$657$	−23.0527	−	13.5326i	−0.899373	−	0.527959i
$658$	−22.1695	−	12.7996i	−0.864258	−	0.498980i
$659$		−	12.9731i		−	0.505361i	−0.967550	−	0.252680i	$-0.918688\pi$
$659$		−	12.9731i		−	0.505361i	0.967550	−	0.252680i	$-0.0813121\pi$
$660$	1.86371	+	8.54065i	0.0725449	+	0.332444i
$661$	−23.7171	−	41.0792i	−0.922488	−	1.59780i	−0.795552	−	0.605885i	$-0.792819\pi$
$661$	−23.7171	−	41.0792i	−0.922488	−	1.59780i	−0.126936	−	0.991911i	$-0.540514\pi$
$662$	−13.4962	+	7.79202i	−0.524544	+	0.302846i
$663$	0.998529	−	0.263691i	0.0387797	−	0.0102409i
$664$	−11.6643	+	6.73438i	−0.452662	+	0.261345i
$665$	−0.00512280	+	0.118136i	−0.000198654	+	0.00458113i
$666$	−0.179157	+	24.7831i	−0.00694219	+	0.960324i
$667$			0.361928i			0.0140139i
$668$	−0.0740101	−	0.0427297i	−0.00286353	−	0.00165326i
$669$	19.4187	+	5.27852i	0.750769	+	0.204079i
$670$	−0.818237	+	18.8693i	−0.0316113	+	0.728983i
$671$	15.9178	−	9.19016i	0.614501	−	0.354782i
$672$	−1.44578	+	5.31876i	−0.0557723	+	0.205176i
$673$	−17.2103	−	29.8092i	−0.663410	−	1.14906i	−0.979714	−	0.200402i	$-0.935775\pi$
$673$	−17.2103	−	29.8092i	−0.663410	−	1.14906i	0.316304	−	0.948658i	$-0.397558\pi$
$674$	1.69991			0.0654781
$675$	−9.13570	+	24.3216i	−0.351633	+	0.936138i
$676$	2.48312	−	4.30088i	0.0955044	−	0.165419i
$677$	−22.3852	+	12.9241i	−0.860334	+	0.496714i	−0.864124	−	0.503279i	$-0.832127\pi$
$677$	−22.3852	+	12.9241i	−0.860334	+	0.496714i	0.00379030	+	0.999993i	$0.498794\pi$
$678$	2.78042	−	2.76039i	0.106781	−	0.106012i
$679$	7.65154	−	13.2529i	0.293639	−	0.508598i
$680$	0.417182	−	0.217329i	0.0159982	−	0.00833418i
$681$	−26.0099	+	25.8226i	−0.996703	+	0.989524i
$682$	11.2786	−	5.54253i	0.431880	−	0.212235i
$683$	45.2214			1.73035			0.865174	−	0.501472i	$-0.167208\pi$
$683$	45.2214			1.73035			0.865174	+	0.501472i	$0.167208\pi$
$684$	−0.000360383		0.0498524i	−1.37796e−5		0.00190615i
$685$	−0.830165	+	19.1443i	−0.0317190	+	0.731467i
$686$		−	12.3263i		−	0.470619i
$687$	11.9068	−	43.8027i	0.454271	−	1.67118i
$688$	−2.06729	+	3.58066i	−0.0788148	+	0.136511i
$689$	13.6878	+	7.90267i	0.521465	+	0.301068i
$690$	0.941567	−	2.95208i	0.0358448	−	0.112384i
$691$	−12.1864	−	21.1075i	−0.463593	−	0.802967i	0.535543	−	0.844508i	$-0.320107\pi$
$691$	−12.1864	−	21.1075i	−0.463593	−	0.802967i	−0.999137	+	0.0415404i	$0.986773\pi$
$692$	6.56949	+	11.3787i	0.249735	+	0.432553i
$693$	10.6386	+	18.7381i	0.404127	+	0.711803i
$694$	−20.3091	−	11.7255i	−0.770925	−	0.445094i
$695$	29.8388	+	18.9969i	1.13185	+	0.720595i
$696$	0.200059	+	0.757573i	0.00758322	+	0.0287157i
$697$	−0.165497			−0.00626866
$698$	−17.4656			−0.661083
$699$	−1.50223	−	5.68857i	−0.0568196	−	0.215161i
$700$	1.37733	−	15.8514i	0.0520582	−	0.599125i
$701$	−29.9318	−	17.2812i	−1.13051	−	0.652700i	−0.186447	−	0.982465i	$-0.559697\pi$
$701$	−29.9318	−	17.2812i	−1.13051	−	0.652700i	−0.944063	+	0.329765i	$0.893031\pi$
$702$	3.96590	−	14.1839i	0.149683	−	0.535337i
$703$	−0.0686422	−	0.118892i	−0.00258889	−	0.00448409i
$704$	−1.12854	−	1.95469i	−0.0425334	−	0.0736701i
$705$	29.6828	+	9.46731i	1.11792	+	0.356560i
$706$	26.4606	+	15.2770i	0.995857	+	0.574958i
$707$	−17.3832	+	30.1085i	−0.653761	+	1.13235i
$708$	1.62330	−	5.97182i	0.0610074	−	0.224435i
$709$		−	11.2769i		−	0.423512i	−0.977323	−	0.211756i	$-0.932082\pi$
$709$		−	11.2769i		−	0.423512i	0.977323	−	0.211756i	$-0.0679183\pi$
$710$	−1.45856	+	33.6357i	−0.0547389	+	1.26233i
$711$	−45.4593	−	0.328625i	−1.70486	−	0.0123244i
$712$	−8.62936			−0.323399
$713$	−4.44458	−	0.297512i	−0.166451	−	0.0111419i
$714$	0.822847	−	0.816920i	0.0307943	−	0.0305725i
$715$	6.60914	+	12.6868i	0.247168	+	0.474461i
$716$	−2.05250	+	3.55503i	−0.0767054	+	0.132858i
$717$	13.2311	−	13.1358i	0.494124	−	0.490565i
$718$	−25.7981	+	14.8945i	−0.962777	+	0.555859i
$719$	3.48956	−	6.04409i	0.130138	−	0.225406i	−0.793591	−	0.608451i	$-0.791791\pi$
$719$	3.48956	−	6.04409i	0.130138	−	0.225406i	0.923730	+	0.383045i	$0.125124\pi$
$720$	0.339057	−	6.69963i	0.0126359	−	0.249680i
$721$	56.4820			2.10350
$722$	9.49986	+	16.4542i	0.353548	+	0.612364i
$723$	−3.70964	+	13.6471i	−0.137963	+	0.507540i
$724$	−17.4253	+	10.0605i	−0.647607	+	0.373896i
$725$	−0.957135	−	2.04940i	−0.0355471	−	0.0761130i
$726$	9.87062	+	2.68310i	0.366333	+	0.0995792i
$727$	10.6708	+	6.16079i	0.395758	+	0.228491i	0.684652	−	0.728870i	$-0.259954\pi$
$727$	10.6708	+	6.16079i	0.395758	+	0.228491i	−0.288894	+	0.957361i	$0.593287\pi$
$728$			9.01965i			0.334291i
$729$	−0.585493	+	26.9937i	−0.0216849	+	0.999765i
$730$	−19.9056	−	0.863177i	−0.736740	−	0.0319476i
$731$	0.753255	−	0.434892i	0.0278601	−	0.0160851i
$732$	−13.6373	+	3.60132i	−0.504049	+	0.133109i
$733$	21.0311	−	12.1423i	0.776800	−	0.448486i	−0.0584948	−	0.998288i	$-0.518630\pi$
$733$	21.0311	−	12.1423i	0.776800	−	0.448486i	0.835295	+	0.549802i	$0.185297\pi$
$734$	−14.4856	−	25.0897i	−0.534672	−	0.926079i
$735$	−2.58162	−	11.8305i	−0.0952245	−	0.436376i
$736$			0.800056i			0.0294905i
$737$	−16.5103	−	9.53223i	−0.608165	−	0.351124i
$738$	−1.19480	+	2.03533i	−0.0439812	+	0.0749217i
$739$	−19.8079	+	11.4361i	−0.728647	+	0.420685i	−0.817927	−	0.575322i	$-0.804877\pi$
$739$	−19.8079	+	11.4361i	−0.728647	+	0.420685i	0.0892800	+	0.996007i	$0.471543\pi$
$740$	8.53460	+	16.3829i	0.313738	+	0.602249i
$741$	0.0208301	+	0.0788784i	0.000765213	+	0.00289767i
$742$	17.7449			0.651437
$743$		−	46.6897i		−	1.71288i	−0.516246	−	0.856440i	$-0.672671\pi$
$743$		−	46.6897i		−	1.71288i	0.516246	−	0.856440i	$-0.327329\pi$
$744$	−9.46764	+	1.83404i	−0.347101	+	0.0672391i
$745$	8.60808	−	4.48433i	0.315376	−	0.164293i
$746$			2.95280i			0.108110i
$747$	20.4556	−	34.8459i	0.748431	−	1.27495i
$748$			0.474817i			0.0173610i
$749$	50.9638	−	29.4240i	1.86218	−	1.07513i
$750$	2.47532	+	19.2061i	0.0903861	+	0.701306i
$751$	−20.0245	+	34.6835i	−0.730705	+	1.26562i	0.225877	+	0.974156i	$0.427475\pi$
$751$	−20.0245	+	34.6835i	−0.730705	+	1.26562i	−0.956582	+	0.291463i	$0.905858\pi$
$752$	−8.04444			−0.293351
$753$	30.6964	+	8.34411i	1.11864	+	0.304076i
$754$	0.641109	+	1.11043i	0.0233478	+	0.0404396i
$755$	−7.40891	−	4.71690i	−0.269638	−	0.171666i
$756$	−4.10621	−	16.0173i	−0.149342	−	0.582545i
$757$	−19.0466	−	32.9897i	−0.692261	−	1.19903i	−0.971095	−	0.238693i	$-0.923281\pi$
$757$	−19.0466	−	32.9897i	−0.692261	−	1.19903i	0.278834	−	0.960339i	$-0.410052\pi$
$758$	−3.80420	+	6.58906i	−0.138175	+	0.239325i
$759$	2.20362	+	2.21961i	0.0799865	+	0.0805668i
$760$	0.0171678	+	0.0329551i	0.000622741	+	0.00119541i
$761$	9.56061	−	16.5595i	0.346572	−	0.600280i	−0.639066	−	0.769152i	$-0.720679\pi$
$761$	9.56061	−	16.5595i	0.346572	−	0.600280i	0.985638	+	0.168872i	$0.0540123\pi$
$762$	−8.01398	−	2.17842i	−0.290316	−	0.0789157i
$763$	−1.29882	−	0.749875i	−0.0470205	−	0.0271473i
$764$	−0.704415	+	0.406694i	−0.0254848	+	0.0147137i
$765$	−0.766464	+	1.18490i	−0.0277116	+	0.0428402i
$766$	10.5978	−	6.11865i	0.382915	−	0.221076i
$767$		−	10.1271i		−	0.365669i
$768$	0.442238	+	1.67464i	0.0159579	+	0.0604284i
$769$	−5.28795	+	9.15900i	−0.190688	+	0.330282i	−0.945479	−	0.325684i	$-0.894405\pi$
$769$	−5.28795	+	9.15900i	−0.190688	+	0.330282i	0.754790	+	0.655966i	$0.227739\pi$
$770$	13.5479	+	8.62533i	0.488234	+	0.310835i
$771$	20.8533	−	20.7030i	0.751011	−	0.745602i
$772$	14.0785	+	8.12823i	0.506697	+	0.292541i
$773$			19.4206i			0.698509i	0.937028	+	0.349255i	$0.113565\pi$
$773$			19.4206i			0.698509i	−0.937028	+	0.349255i	$0.886435\pi$
$774$	0.0896645	−	12.4034i	0.00322292	−	0.445832i
$775$	25.9540	−	10.0692i	0.932296	−	0.361697i
$776$		−	4.80894i		−	0.172631i
$777$	32.0808	+	32.3136i	1.15089	+	1.15924i
$778$	−15.1180	+	26.1851i	−0.542005	+	0.938781i
$779$		−	0.0130734i		−	0.000468402i
$780$	−2.34041	−	10.7252i	−0.0838000	−	0.384022i
$781$	−29.4307	−	16.9918i	−1.05311	−	0.608016i
$782$	0.0841530	−	0.145757i	0.00300931	−	0.00521227i
$783$	−1.64403	−	1.68007i	−0.0587527	−	0.0600409i
$784$	1.56326	+	2.70764i	0.0558307	+	0.0967015i
$785$	10.9835	+	6.99267i	0.392017	+	0.249579i
$786$	−2.39138	+	8.79743i	−0.0852976	+	0.313794i
$787$	−4.30542	+	7.45721i	−0.153472	+	0.265821i	−0.932501	−	0.361166i	$-0.882379\pi$
$787$	−4.30542	+	7.45721i	−0.153472	+	0.265821i	0.779030	+	0.626987i	$0.215712\pi$
$788$	−4.90072	+	2.82943i	−0.174581	+	0.100794i
$789$	51.6123	−	13.6297i	1.83745	−	0.485231i
$790$	−30.0510	+	15.6549i	−1.06917	+	0.556977i
$791$		−	7.19831i		−	0.255942i
$792$	5.83944	+	3.42792i	0.207495	+	0.121806i
$793$	−19.9892	+	11.5408i	−0.709839	+	0.409826i
$794$	−17.6190	−	10.1723i	−0.625274	−	0.361002i
$795$	−21.1003	+	4.60443i	−0.748350	+	0.163302i
$796$	7.20797	−	4.16152i	0.255480	−	0.147501i
$797$	−0.466790	+	0.269502i	−0.0165346	+	0.00954623i	−0.508244	−	0.861213i	$-0.669705\pi$
$797$	−0.466790	+	0.269502i	−0.0165346	+	0.00954623i	0.491710	+	0.870759i	$0.336372\pi$
$798$	0.0645322	+	0.0650004i	0.00228441	+	0.00230099i
$799$	1.46557	+	0.846146i	0.0518480	+	0.0299345i
$800$	−2.11578	−	4.53028i	−0.0748042	−	0.160170i
$801$	22.5127	−	12.7816i	0.795448	−	0.451617i
$802$	−32.1710			−1.13600
$803$	10.0558	−	17.4171i	0.354860	−	0.614636i
$804$	10.3074	+	10.3822i	0.363513	+	0.366150i
$805$	−2.63020	−	5.04891i	−0.0927023	−	0.177951i
$806$	−14.1634	+	6.96019i	−0.498885	+	0.245162i
$807$	5.40380	−	5.36488i	0.190223	−	0.188853i
$808$			10.9252i			0.384347i
$809$	1.16363	−	2.01547i	0.0409111	−	0.0708601i	−0.844845	−	0.535011i	$-0.820307\pi$
$809$	1.16363	−	2.01547i	0.0409111	−	0.0708601i	0.885756	+	0.464151i	$0.153641\pi$
$810$	9.03881	+	17.9805i	0.317591	+	0.631772i
$811$	−22.8583	−	39.5917i	−0.802664	−	1.39025i	−0.917857	−	0.396911i	$-0.870082\pi$
$811$	−22.8583	−	39.5917i	−0.802664	−	1.39025i	0.115193	−	0.993343i	$-0.463251\pi$
$812$	1.24670	+	0.719784i	0.0437507	+	0.0252595i
$813$	25.4205	−	6.71303i	0.891537	−	0.235436i
$814$	−18.6463			−0.653551
$815$	22.6279	+	14.4061i	0.792620	+	0.504624i
$816$	0.0955768	−	0.351609i	0.00334586	−	0.0123088i
$817$	0.0343541	+	0.0595030i	0.00120190	+	0.00208175i
$818$	16.0037	+	9.23975i	0.559557	+	0.323060i
$819$	−13.3597	−	23.5309i	−0.466827	−	0.822237i
$820$	−0.0762102	+	1.75747i	−0.00266138	+	0.0613736i
$821$	−20.2881			−0.708058			−0.354029	−	0.935234i	$-0.615189\pi$
$821$	−20.2881			−0.708058			−0.354029	+	0.935234i	$0.615189\pi$
$822$	10.4576	+	10.5335i	0.364752	+	0.367398i
$823$	12.2358	−	21.1931i	0.426514	−	0.738744i	−0.570047	−	0.821612i	$-0.693075\pi$
$823$	12.2358	−	21.1931i	0.426514	−	0.738744i	0.996560	+	0.0828687i	$0.0264082\pi$
$824$	15.3713	−	8.87463i	0.535485	−	0.309162i
$825$	−18.3478	−	6.74088i	−0.638788	−	0.234687i
$826$	−5.68494	−	9.84661i	−0.197805	−	0.342607i
$827$	8.89168	−	5.13362i	0.309194	−	0.178513i	−0.337372	−	0.941372i	$-0.609538\pi$
$827$	8.89168	−	5.13362i	0.309194	−	0.178513i	0.646566	+	0.762858i	$0.276205\pi$
$828$	−1.18503	−	2.08723i	−0.0411825	−	0.0725362i
$829$		−	33.8954i		−	1.17724i	−0.808411	−	0.588618i	$-0.799672\pi$
$829$		−	33.8954i		−	1.17724i	0.808411	−	0.588618i	$-0.200328\pi$
$830$	1.30476	−	30.0888i	0.0452887	−	1.04440i
$831$	−10.0266	−	37.9682i	−0.347819	−	1.31710i
$832$	1.41720	+	2.45465i	0.0491324	+	0.0850998i
$833$		−	0.657718i		−	0.0227886i
$834$	26.4915	−	6.99585i	0.917325	−	0.242246i
$835$	0.169475	−	0.0882873i	0.00586494	−	0.00305531i
$836$	−0.0375079			−0.00129724
$837$	21.9831	−	18.8080i	0.759848	−	0.650100i
$838$			5.90988i			0.204153i
$839$		−	35.2238i		−	1.21606i	−0.793914	−	0.608030i	$-0.791960\pi$
$839$		−	35.2238i		−	1.21606i	0.793914	−	0.608030i	$-0.208040\pi$
$840$	−8.29624	−	9.11428i	−0.286248	−	0.314473i
$841$	−28.7954			−0.992943
$842$	−5.40623	−	9.36386i	−0.186311	−	0.322700i
$843$	−41.3088	+	10.9088i	−1.42275	+	0.375718i
$844$	−11.0068	+	19.0643i	−0.378869	+	0.656221i
$845$	5.13056	+	9.84858i	0.176497	+	0.338801i
$846$	20.9868	−	11.9153i	0.721539	−	0.409655i
$847$	16.2751	−	9.39645i	0.559220	−	0.322866i
$848$	4.82919	−	2.78814i	0.165835	−	0.0957450i
$849$	−3.04663	+	0.804552i	−0.104560	+	0.0276121i
$850$	−0.0910516	+	1.04789i	−0.00312305	+	0.0359424i
$851$	5.72395	+	3.30473i	0.196215	+	0.113285i
$852$	18.3736	+	18.5069i	0.629468	+	0.634035i
$853$		−	42.2445i		−	1.44643i	−0.690625	−	0.723213i	$-0.742665\pi$
$853$		−	42.2445i		−	1.44643i	0.690625	−	0.723213i	$-0.257335\pi$
$854$	−12.9571	+	22.4423i	−0.443381	+	0.767959i
$855$	−0.0936007	−	0.0605464i	−0.00320108	−	0.00207064i
$856$	9.24636	−	16.0152i	0.316034	−	0.547387i
$857$	3.90938	+	6.77125i	0.133542	+	0.231302i	0.925040	−	0.379871i	$-0.124032\pi$
$857$	3.90938	+	6.77125i	0.133542	+	0.231302i	−0.791498	+	0.611172i	$0.790698\pi$
$858$	10.6927	+	2.90656i	0.365043	+	0.0992284i
$859$	−25.4656	+	14.7026i	−0.868874	+	0.501645i	−0.866974	−	0.498353i	$-0.833938\pi$
$859$	−25.4656	+	14.7026i	−0.868874	+	0.501645i	−0.00190018	+	0.999998i	$0.500605\pi$
$860$	−4.27140	−	8.19934i	−0.145654	−	0.279595i
$861$	1.10713	+	4.19241i	0.0377308	+	0.142877i
$862$	33.7037	+	19.4588i	1.14795	+	0.662770i
$863$	32.5614	−	18.7993i	1.10840	−	0.639937i	0.169988	−	0.985446i	$-0.445627\pi$
$863$	32.5614	−	18.7993i	1.10840	−	0.639937i	0.938415	+	0.345509i	$0.112294\pi$
$864$	−3.63418	−	3.71386i	−0.123637	−	0.126348i
$865$	−29.3521	−	1.27281i	−0.998001	−	0.0432768i
$866$	−10.9104			−0.370751
$867$	20.8414	−	20.6913i	0.707811	−	0.702712i
$868$	−9.86395	+	14.7182i	−0.334804	+	0.499567i
$869$		−	34.2026i		−	1.16025i
$870$	−1.66921	−	0.532394i	−0.0565915	−	0.0180498i
$871$	20.7333	+	11.9704i	0.702520	+	0.405600i
$872$	−0.471291			−0.0159599
$873$	7.12290	+	12.5458i	0.241074	+	0.424611i
$874$	0.0115140	+	0.00664763i	0.000389468	+	0.000224859i
$875$	28.2454	+	21.6335i	0.954870	+	0.731347i
$876$	−10.9524	+	10.8735i	−0.370046	+	0.367381i
$877$	31.6253	−	18.2589i	1.06791	−	0.616558i	0.140301	−	0.990109i	$-0.455193\pi$
$877$	31.6253	−	18.2589i	1.06791	−	0.616558i	0.927610	+	0.373551i	$0.121860\pi$
$878$	0.307195	+	0.532078i	0.0103673	+	0.0179567i
$879$	31.3070	+	8.51007i	1.05596	+	0.287038i
$880$	5.04224	+	0.218649i	0.169974	+	0.00737067i
$881$	22.7281	+	39.3662i	0.765729	+	1.32628i	0.939860	+	0.341559i	$0.110955\pi$
$881$	22.7281	+	39.3662i	0.765729	+	1.32628i	−0.174132	+	0.984722i	$0.555712\pi$
$882$	−8.08881	−	4.74837i	−0.272365	−	0.159886i
$883$	6.76930			0.227805			0.113902	−	0.993492i	$-0.463665\pi$
$883$	6.76930			0.227805			0.113902	+	0.993492i	$0.463665\pi$
$884$		−	0.596264i		−	0.0200545i
$885$	9.31489	+	10.2334i	0.313116	+	0.343991i
$886$	−3.88123	−	6.72249i	−0.130392	−	0.225846i
$887$	7.67225	−	13.2887i	0.257609	−	0.446192i	−0.707992	−	0.706221i	$-0.750399\pi$
$887$	7.67225	−	13.2887i	0.257609	−	0.446192i	0.965601	+	0.260029i	$0.0837320\pi$
$888$	13.8078	+	3.75334i	0.463361	+	0.125954i
$889$	−13.2138	+	7.62900i	−0.443177	+	0.255869i
$890$	10.3628	−	16.2770i	0.347362	−	0.545607i
$891$	−20.3116	−	0.293680i	−0.680464	−	0.00983866i
$892$	5.80910	−	10.0617i	0.194503	−	0.336889i
$893$	−0.0668409	+	0.115772i	−0.00223674	+	0.00387416i
$894$	1.97212	−	7.25505i	0.0659575	−	0.242645i
$895$	−4.24083	−	8.14065i	−0.141755	−	0.272112i
$896$	2.75588	+	1.59111i	0.0920676	+	0.0531552i
$897$	−2.76726	−	2.78734i	−0.0923962	−	0.0930665i
$898$	−15.2495			−0.508881
$899$	−0.168223	+	2.51312i	−0.00561056	+	0.0838171i
$900$	12.2299	+	8.68498i	0.407664	+	0.289499i
$901$	−1.17307			−0.0390806
$902$	−1.53776	−	0.887827i	−0.0512019	−	0.0295614i
$903$	−16.0558	−	16.1723i	−0.534304	−	0.538181i
$904$	−1.13102	−	1.95898i	−0.0376172	−	0.0651549i
$905$	1.94918	−	44.9497i	0.0647928	−	1.49418i
$906$	−6.57779	+	1.73706i	−0.218532	+	0.0577098i
$907$		−	28.7022i		−	0.953040i	−0.879164	−	0.476520i	$-0.841898\pi$
$907$		−	28.7022i		−	0.953040i	0.879164	−	0.476520i	$-0.158102\pi$
$908$	10.5803	+	18.3257i	0.351121	+	0.608159i
$909$	−16.1822	−	28.5022i	−0.536729	−	0.945358i
$910$	−17.0132	−	10.8315i	−0.563982	−	0.359061i
$911$	5.26971	−	9.12741i	0.174593	−	0.302405i	−0.765427	−	0.643523i	$-0.777472\pi$
$911$	5.26971	−	9.12741i	0.174593	−	0.302405i	0.940020	+	0.341118i	$0.110806\pi$
$912$	0.0277752	+	0.00755004i	0.000919728	+	0.000250007i
$913$	26.3272	+	15.2000i	0.871304	+	0.503048i
$914$	−9.40285			−0.311019
$915$	9.58378	−	30.0479i	0.316830	−	0.993353i
$916$	−22.6961	−	13.1036i	−0.749900	−	0.432955i
$917$	8.37481	+	14.5056i	0.276561	+	0.479017i
$918$	0.271450	+	1.05886i	0.00895920	+	0.0349477i
$919$	−13.8145	−	23.9274i	−0.455698	−	0.789291i	0.543030	−	0.839713i	$-0.317277\pi$
$919$	−13.8145	−	23.9274i	−0.455698	−	0.789291i	−0.998728	+	0.0504216i	$0.983944\pi$
$920$	−1.50910	−	0.960770i	−0.0497534	−	0.0316757i
$921$	−0.108117	+	0.397744i	−0.00356259	+	0.0131061i
$922$	−26.2525			−0.864580
$923$	36.9585	+	21.3380i	1.21650	+	0.702348i
$924$	12.0281	−	3.17638i	0.395697	−	0.104495i
$925$	−41.1511	−	3.57564i	−1.35304	−	0.117566i
$926$	−8.83708			−0.290405
$927$	−26.9566	+	45.9203i	−0.885369	+	1.50822i
$928$	0.452379			0.0148501
$929$	38.5774			1.26568			0.632842	−	0.774281i	$-0.281888\pi$
$929$	38.5774			1.26568			0.632842	+	0.774281i	$0.281888\pi$
$930$	7.91006	−	20.0607i	0.259381	−	0.657816i
$931$	0.0519561			0.00170279
$932$	−3.39689			−0.111269
$933$	−14.8559	+	3.92313i	−0.486361	+	0.128438i
$934$	−0.199102			−0.00651481
$935$	−0.895617	−	0.570197i	−0.0292898	−	0.0186474i
$936$	−7.33304	−	4.30471i	−0.239688	−	0.140704i
$937$	25.5568	+	14.7552i	0.834905	+	0.482032i	0.855529	−	0.517755i	$-0.173232\pi$
$937$	25.5568	+	14.7552i	0.834905	+	0.482032i	−0.0206244	+	0.999787i	$0.506565\pi$
$938$	26.8787			0.877620
$939$	−37.0442	−	10.0696i	−1.20889	−	0.328610i
$940$	9.66040	−	15.1737i	0.315087	−	0.494912i
$941$	−2.51403	−	4.35444i	−0.0819552	−	0.141951i	0.822135	−	0.569293i	$-0.192783\pi$
$941$	−2.51403	−	4.35444i	−0.0819552	−	0.141951i	−0.904090	+	0.427343i	$0.859450\pi$
$942$	9.75137	−	2.57513i	0.317717	−	0.0839024i
$943$	0.314704	+	0.545083i	0.0102482	+	0.0177503i
$944$	−3.09426	−	1.78647i	−0.100710	−	0.0581447i
$945$	35.1436	+	11.4896i	1.14322	+	0.373756i
$946$	9.33209			0.303413
$947$	0.353723	+	0.204222i	0.0114945	+	0.00663633i	0.505736	−	0.862688i	$-0.331221\pi$
$947$	0.353723	+	0.204222i	0.0114945	+	0.00663633i	−0.494242	+	0.869324i	$0.664554\pi$
$948$	−6.88472	+	25.3276i	−0.223605	+	0.822601i
$949$	−12.6278	+	21.8720i	−0.409916	+	0.709996i
$950$	−0.0827776	−	0.00719258i	−0.00268566	−	0.000233358i
$951$	−2.90761	−	0.790366i	−0.0942856	−	0.0256294i
$952$	−0.334718	−	0.579749i	−0.0108483	−	0.0187898i
$953$			20.7269i			0.671411i	0.941967	+	0.335706i	$0.108975\pi$
$953$			20.7269i			0.671411i	−0.941967	+	0.335706i	$0.891025\pi$
$954$	−8.46892	+	14.4267i	−0.274191	+	0.467083i
$955$	0.0787951	−	1.81708i	0.00254975	−	0.0587994i
$956$	−5.38215	−	9.32216i	−0.174071	−	0.301500i
$957$	1.25504	−	1.24600i	0.0405698	−	0.0402776i
$958$	27.8735	+	16.0928i	0.900552	+	0.519934i
$959$	27.2705			0.880610
$960$	−3.68985	−	1.17688i	−0.119089	−	0.0379835i
$961$	−30.7234	−	4.13166i	−0.991079	−	0.133279i
$962$	23.4156			0.754948
$963$	−0.401041	+	55.4767i	−0.0129234	+	1.78771i
$964$	7.07114	+	4.08252i	0.227746	+	0.131489i
$965$	−32.2383	+	16.7944i	−1.03779	+	0.540630i
$966$	−4.25531	−	1.15671i	−0.136912	−	0.0372165i
$967$	8.27261	−	14.3286i	0.266029	−	0.460776i	−0.701804	−	0.712370i	$-0.747622\pi$
$967$	8.27261	−	14.3286i	0.266029	−	0.460776i	0.967833	+	0.251595i	$0.0809549\pi$
$968$	2.95280	−	5.11439i	0.0949065	−	0.164383i
$969$	−0.00426605	−	0.00429700i	−0.000137045	−	0.000138039i
$970$	9.07079	+	5.77495i	0.291246	+	0.185422i
$971$	29.6416	−	17.1136i	0.951245	−	0.549202i	0.0577777	−	0.998329i	$-0.481599\pi$
$971$	29.6416	−	17.1136i	0.951245	−	0.549202i	0.893468	+	0.449128i	$0.148265\pi$
$972$	14.9819	+	4.30603i	0.480545	+	0.138116i
$973$	25.1701	−	43.5959i	0.806916	−	1.39762i
$974$	4.86941	+	8.43407i	0.156026	+	0.270245i
$975$	23.0407	+	8.46505i	0.737894	+	0.271099i
$976$			8.14341i			0.260664i
$977$	−12.5953			−0.402958			−0.201479	−	0.979493i	$-0.564575\pi$
$977$	−12.5953			−0.402958			−0.201479	+	0.979493i	$0.564575\pi$
$978$	20.0895	−	5.30522i	0.642392	−	0.169642i
$979$	9.73857	+	16.8677i	0.311246	+	0.539094i
$980$	−6.98454	−	0.302874i	−0.223113	−	0.00967496i
$981$	1.22953	−	0.698067i	0.0392558	−	0.0222876i
$982$	−1.53335	−	2.65584i	−0.0489312	−	0.0847513i
$983$	−41.4664	+	23.9406i	−1.32257	+	0.763588i	−0.984138	−	0.177402i	$-0.943231\pi$
$983$	−41.4664	+	23.9406i	−1.32257	+	0.763588i	−0.338434	+	0.940990i	$0.609897\pi$
$984$	0.960024	+	0.966989i	0.0306044	+	0.0308265i
$985$	0.548189	−	12.6417i	0.0174668	−	0.402799i
$986$	−0.0824161	−	0.0475830i	−0.00262466	−	0.00151535i
$987$	11.6305	−	42.7865i	0.370204	−	1.36191i
$988$	0.0471016			0.00149850
$989$	−2.86473	−	1.65395i	−0.0910930	−	0.0525926i
$990$	−13.4783	+	6.89805i	−0.428369	+	0.219234i
$991$		−	30.8609i		−	0.980330i	−0.871630	−	0.490165i	$-0.836937\pi$
$991$		−	30.8609i		−	0.980330i	0.871630	−	0.490165i	$-0.163063\pi$
$992$	−0.371864	+	5.55533i	−0.0118067	+	0.176382i
$993$	−19.0174	−	19.1553i	−0.603498	−	0.607876i
$994$	47.9130			1.51971
$995$	−0.806276	+	18.5934i	−0.0255607	+	0.589451i
$996$	−16.4361	−	16.5553i	−0.520797	−	0.524575i
$997$	27.9670	−	16.1468i	0.885725	−	0.511374i	0.0131834	−	0.999913i	$-0.495803\pi$
$997$	27.9670	−	16.1468i	0.885725	−	0.511374i	0.872542	+	0.488539i	$0.162470\pi$
$998$	11.3529	+	6.55458i	0.359368	+	0.207481i
$999$	−41.5820	+	10.6600i	−1.31560	+	0.337267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.b.119.19	yes	64
3.2	odd	2		930.2.r.a.119.2	✓	64
5.4	even	2		930.2.r.a.119.14	yes	64
15.14	odd	2	inner	930.2.r.b.119.31	yes	64
31.6	odd	6	inner	930.2.r.b.719.31	yes	64
93.68	even	6		930.2.r.a.719.14	yes	64
155.99	odd	6		930.2.r.a.719.2	yes	64
465.254	even	6	inner	930.2.r.b.719.19	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.2	✓	64	3.2	odd	2
930.2.r.a.119.14	yes	64	5.4	even	2
930.2.r.a.719.2	yes	64	155.99	odd	6
930.2.r.a.719.14	yes	64	93.68	even	6
930.2.r.b.119.19	yes	64	1.1	even	1	trivial
930.2.r.b.119.31	yes	64	15.14	odd	2	inner
930.2.r.b.719.19	yes	64	465.254	even	6	inner
930.2.r.b.719.31	yes	64	31.6	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.442238 + 1.67464i) q^{3} +1.00000 q^{4} +(-1.20088 + 1.88624i) q^{5} +(0.442238 + 1.67464i) q^{6} +(2.75588 + 1.59111i) q^{7} +1.00000 q^{8} +(-2.60885 + 1.48118i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.442238 + 1.67464i) q^{3} +1.00000 q^{4} +(-1.20088 + 1.88624i) q^{5} +(0.442238 + 1.67464i) q^{6} +(2.75588 + 1.59111i) q^{7} +1.00000 q^{8} +(-2.60885 + 1.48118i) q^{9} +(-1.20088 + 1.88624i) q^{10} +(-1.12854 - 1.95469i) q^{11} +(0.442238 + 1.67464i) q^{12} +(1.41720 + 2.45465i) q^{13} +(2.75588 + 1.59111i) q^{14} +(-3.68985 - 1.17688i) q^{15} +1.00000 q^{16} +(-0.182184 - 0.105184i) q^{17} +(-2.60885 + 1.48118i) q^{18} +(0.00830895 - 0.0143915i) q^{19} +(-1.20088 + 1.88624i) q^{20} +(-1.44578 + 5.31876i) q^{21} +(-1.12854 - 1.95469i) q^{22} +0.800056i q^{23} +(0.442238 + 1.67464i) q^{24} +(-2.11578 - 4.53028i) q^{25} +(1.41720 + 2.45465i) q^{26} +(-3.63418 - 3.71386i) q^{27} +(2.75588 + 1.59111i) q^{28} +0.452379 q^{29} +(-3.68985 - 1.17688i) q^{30} +(-0.371864 + 5.55533i) q^{31} +1.00000 q^{32} +(2.77432 - 2.75434i) q^{33} +(-0.182184 - 0.105184i) q^{34} +(-6.31069 + 3.28752i) q^{35} +(-2.60885 + 1.48118i) q^{36} +(4.13062 - 7.15444i) q^{37} +(0.00830895 - 0.0143915i) q^{38} +(-3.48393 + 3.45884i) q^{39} +(-1.20088 + 1.88624i) q^{40} +(0.681306 - 0.393352i) q^{41} +(-1.44578 + 5.31876i) q^{42} +(-2.06729 + 3.58066i) q^{43} +(-1.12854 - 1.95469i) q^{44} +(0.339057 - 6.69963i) q^{45} +0.800056i q^{46} -8.04444 q^{47} +(0.442238 + 1.67464i) q^{48} +(1.56326 + 2.70764i) q^{49} +(-2.11578 - 4.53028i) q^{50} +(0.0955768 - 0.351609i) q^{51} +(1.41720 + 2.45465i) q^{52} +(4.82919 - 2.78814i) q^{53} +(-3.63418 - 3.71386i) q^{54} +(5.04224 + 0.218649i) q^{55} +(2.75588 + 1.59111i) q^{56} +(0.0277752 + 0.00755004i) q^{57} +0.452379 q^{58} +(-3.09426 - 1.78647i) q^{59} +(-3.68985 - 1.17688i) q^{60} +8.14341i q^{61} +(-0.371864 + 5.55533i) q^{62} +(-9.54641 - 0.0690110i) q^{63} +1.00000 q^{64} +(-6.33194 - 0.274575i) q^{65} +(2.77432 - 2.75434i) q^{66} +(7.31490 - 4.22326i) q^{67} +(-0.182184 - 0.105184i) q^{68} +(-1.33981 + 0.353815i) q^{69} +(-6.31069 + 3.28752i) q^{70} +(13.0393 - 7.52824i) q^{71} +(-2.60885 + 1.48118i) q^{72} +(4.45521 + 7.71666i) q^{73} +(4.13062 - 7.15444i) q^{74} +(6.65092 - 5.54664i) q^{75} +(0.00830895 - 0.0143915i) q^{76} -7.18252i q^{77} +(-3.48393 + 3.45884i) q^{78} +(13.1233 + 7.57675i) q^{79} +(-1.20088 + 1.88624i) q^{80} +(4.61221 - 7.72836i) q^{81} +(0.681306 - 0.393352i) q^{82} +(-11.6643 + 6.73438i) q^{83} +(-1.44578 + 5.31876i) q^{84} +(0.417182 - 0.217329i) q^{85} +(-2.06729 + 3.58066i) q^{86} +(0.200059 + 0.757573i) q^{87} +(-1.12854 - 1.95469i) q^{88} -8.62936 q^{89} +(0.339057 - 6.69963i) q^{90} +9.01965i q^{91} +0.800056i q^{92} +(-9.46764 + 1.83404i) q^{93} -8.04444 q^{94} +(0.0171678 + 0.0329551i) q^{95} +(0.442238 + 1.67464i) q^{96} -4.80894i q^{97} +(1.56326 + 2.70764i) q^{98} +(5.83944 + 3.42792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

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