LMFDB - Embedded newform 930.2.r.a.719.2

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			719.2
Character	$\chi$	$=$	930.719
Dual form			930.2.r.a.119.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.67140 - 0.454332i) q^{3} +1.00000 q^{4} +(1.20088 + 1.88624i) q^{5} +(1.67140 + 0.454332i) q^{6} +(2.75588 - 1.59111i) q^{7} -1.00000 q^{8} +(2.58717 + 1.51874i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.67140 - 0.454332i) q^{3} +1.00000 q^{4} +(1.20088 + 1.88624i) q^{5} +(1.67140 + 0.454332i) q^{6} +(2.75588 - 1.59111i) q^{7} -1.00000 q^{8} +(2.58717 + 1.51874i) q^{9} +(-1.20088 - 1.88624i) q^{10} +(1.12854 - 1.95469i) q^{11} +(-1.67140 - 0.454332i) q^{12} +(1.41720 - 2.45465i) q^{13} +(-2.75588 + 1.59111i) q^{14} +(-1.15017 - 3.69826i) q^{15} +1.00000 q^{16} +(0.182184 - 0.105184i) q^{17} +(-2.58717 - 1.51874i) q^{18} +(0.00830895 + 0.0143915i) q^{19} +(1.20088 + 1.88624i) q^{20} +(-5.32908 + 1.40730i) q^{21} +(-1.12854 + 1.95469i) q^{22} +0.800056i q^{23} +(1.67140 + 0.454332i) 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} +(1.15017 + 3.69826i) 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} +(2.58717 + 1.51874i) 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} +(5.32908 - 1.40730i) q^{42} +(-2.06729 - 3.58066i) q^{43} +(1.12854 - 1.95469i) q^{44} +(0.242164 + 6.70383i) q^{45} -0.800056i q^{46} +8.04444 q^{47} +(-1.67140 - 0.454332i) q^{48} +(1.56326 - 2.70764i) q^{49} +(2.11578 - 4.53028i) q^{50} +(-0.352291 + 0.0930326i) 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} +(-0.00734906 - 0.0278290i) q^{57} +0.452379 q^{58} +(3.09426 - 1.78647i) q^{59} +(-1.15017 - 3.69826i) 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} +(0.363491 - 1.33721i) q^{69} +(-6.31069 - 3.28752i) q^{70} +(-13.0393 - 7.52824i) q^{71} +(-2.58717 - 1.51874i) q^{72} +(4.45521 - 7.71666i) q^{73} +(-4.13062 - 7.15444i) q^{74} +(5.59457 - 6.61066i) 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} +(4.38685 + 7.85847i) q^{81} +(0.681306 + 0.393352i) q^{82} +(11.6643 + 6.73438i) q^{83} +(-5.32908 + 1.40730i) q^{84} +(0.417182 + 0.217329i) q^{85} +(2.06729 + 3.58066i) q^{86} +(0.756107 + 0.205530i) q^{87} +(-1.12854 + 1.95469i) q^{88} +8.62936 q^{89} +(-0.242164 - 6.70383i) q^{90} -9.01965i q^{91} +0.800056i q^{92} +(-1.90243 + 9.45414i) q^{93} -8.04444 q^{94} +(-0.0171678 + 0.0329551i) q^{95} +(1.67140 + 0.454332i) q^{96} +4.80894i q^{97} +(-1.56326 + 2.70764i) q^{98} +(5.88838 - 3.34314i) 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} + 5 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} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 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 + 5 * 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 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.67140	−	0.454332i	−0.964984	−	0.262309i
$3$	−1.67140	−	0.454332i	−0.964984	−	0.262309i
$4$	1.00000			0.500000
$5$	1.20088	+	1.88624i	0.537049	+	0.843551i
$5$	1.20088	+	1.88624i	0.537049	+	0.843551i
$6$	1.67140	+	0.454332i	0.682347	+	0.185480i
$7$	2.75588	−	1.59111i	1.04163	−	0.601383i	0.121332	−	0.992612i	$-0.461283\pi$
$7$	2.75588	−	1.59111i	1.04163	−	0.601383i	0.920293	+	0.391229i	$0.127950\pi$
$8$	−1.00000			−0.353553
$9$	2.58717	+	1.51874i	0.862388	+	0.506247i
$10$	−1.20088	−	1.88624i	−0.379751	−	0.596481i
$11$	1.12854	−	1.95469i	0.340267	−	0.589361i	−0.644215	−	0.764845i	$-0.722816\pi$
$11$	1.12854	−	1.95469i	0.340267	−	0.589361i	0.984482	+	0.175484i	$0.0561490\pi$
$12$	−1.67140	−	0.454332i	−0.482492	−	0.131154i
$13$	1.41720	−	2.45465i	0.393059	−	0.680799i	−0.599792	−	0.800156i	$-0.704750\pi$
$13$	1.41720	−	2.45465i	0.393059	−	0.680799i	0.992851	+	0.119357i	$0.0380834\pi$
$14$	−2.75588	+	1.59111i	−0.736541	+	0.425242i
$15$	−1.15017	−	3.69826i	−0.296973	−	0.954886i
$16$	1.00000			0.250000
$17$	0.182184	−	0.105184i	0.0441861	−	0.0255108i	−0.477744	−	0.878499i	$-0.658545\pi$
$17$	0.182184	−	0.105184i	0.0441861	−	0.0255108i	0.521930	+	0.852988i	$0.325212\pi$
$18$	−2.58717	−	1.51874i	−0.609801	−	0.357971i
$19$	0.00830895	+	0.0143915i	0.00190620	+	0.00330164i	0.866977	−	0.498348i	$-0.166060\pi$
$19$	0.00830895	+	0.0143915i	0.00190620	+	0.00330164i	−0.865071	+	0.501650i	$0.832727\pi$
$20$	1.20088	+	1.88624i	0.268525	+	0.421775i
$21$	−5.32908	+	1.40730i	−1.16290	+	0.307097i
$22$	−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	$0.973418\pi$
$24$	1.67140	+	0.454332i	0.341173	+	0.0927401i
$25$	−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	$-0.513374\pi$
$29$	−0.452379			−0.0840047			−0.0420023	+	0.999118i	$0.513374\pi$
$30$	1.15017	+	3.69826i	0.209992	+	0.675206i
$31$	−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
$36$	2.58717	+	1.51874i	0.431194	+	0.253124i
$37$	4.13062	+	7.15444i	0.679070	+	1.17618i	0.975261	+	0.221055i	$0.0709499\pi$
$37$	4.13062	+	7.15444i	0.679070	+	1.17618i	−0.296192	+	0.955128i	$0.595717\pi$
$38$	−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	$-0.352900\pi$
$41$	−0.681306	−	0.393352i	−0.106402	−	0.0614313i	−0.552257	+	0.833674i	$0.686233\pi$
$42$	5.32908	−	1.40730i	0.822294	−	0.217151i
$43$	−2.06729	−	3.58066i	−0.315259	−	0.546045i	0.664233	−	0.747525i	$-0.268758\pi$
$43$	−2.06729	−	3.58066i	−0.315259	−	0.546045i	−0.979493	+	0.201480i	$0.935425\pi$
$44$	1.12854	−	1.95469i	0.170134	−	0.294680i
$45$	0.242164	+	6.70383i	0.0360996	+	0.999348i
$46$		−	0.800056i		−	0.117962i
$47$	8.04444			1.17340			0.586701	−	0.809803i	$-0.300426\pi$
$47$	8.04444			1.17340			0.586701	+	0.809803i	$0.300426\pi$
$48$	−1.67140	−	0.454332i	−0.241246	−	0.0655772i
$49$	1.56326	−	2.70764i	0.223323	−	0.386806i
$50$	2.11578	−	4.53028i	0.299217	−	0.640679i
$51$	−0.352291	+	0.0930326i	−0.0493306	+	0.0130272i
$52$	1.41720	−	2.45465i	0.196530	−	0.340399i
$53$	−4.82919	−	2.78814i	−0.663341	−	0.382980i	0.130208	−	0.991487i	$-0.458436\pi$
$53$	−4.82919	−	2.78814i	−0.663341	−	0.382980i	−0.793549	+	0.608507i	$0.791769\pi$
$54$	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
$57$	−0.00734906	−	0.0278290i	−0.000973407	−	0.00368605i
$58$	0.452379			0.0594003
$59$	3.09426	−	1.78647i	0.402838	−	0.232579i	−0.284870	−	0.958566i	$-0.591950\pi$
$59$	3.09426	−	1.78647i	0.402838	−	0.232579i	0.687708	+	0.725987i	$0.258617\pi$
$60$	−1.15017	−	3.69826i	−0.148487	−	0.477443i
$61$		−	8.14341i		−	1.04266i	−0.853356	−	0.521328i	$-0.825437\pi$
$61$		−	8.14341i		−	1.04266i	0.853356	−	0.521328i	$-0.174563\pi$
$62$	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	0.875137	−	0.483875i	$-0.160771\pi$
$67$	7.31490	+	4.22326i	0.893657	+	0.515953i	0.0185202	+	0.999828i	$0.494104\pi$
$68$	0.182184	−	0.105184i	0.0220930	−	0.0127554i
$69$	0.363491	−	1.33721i	0.0437592	−	0.160982i
$70$	−6.31069	−	3.28752i	−0.754272	−	0.392934i
$71$	−13.0393	−	7.52824i	−1.54748	−	0.893438i	−0.998333	−	0.0577118i	$-0.981620\pi$
$71$	−13.0393	−	7.52824i	−1.54748	−	0.893438i	−0.549147	−	0.835726i	$-0.685047\pi$
$72$	−2.58717	−	1.51874i	−0.304900	−	0.178985i
$73$	4.45521	−	7.71666i	0.521443	−	0.903166i	−0.478246	−	0.878226i	$-0.658727\pi$
$73$	4.45521	−	7.71666i	0.521443	−	0.903166i	0.999689	−	0.0249402i	$-0.00793955\pi$
$74$	−4.13062	−	7.15444i	−0.480175	−	0.831687i
$75$	5.59457	−	6.61066i	0.646006	−	0.763333i
$76$	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	0.476840	−	0.878990i	$-0.341782\pi$
$79$	13.1233	−	7.57675i	1.47649	−	0.852451i	0.999648	+	0.0265391i	$0.00844866\pi$
$80$	1.20088	+	1.88624i	0.134262	+	0.210888i
$81$	4.38685	+	7.85847i	0.487427	+	0.873164i
$82$	0.681306	+	0.393352i	0.0752377	+	0.0434385i
$83$	11.6643	+	6.73438i	1.28032	+	0.739195i	0.976907	−	0.213664i	$-0.0685396\pi$
$83$	11.6643	+	6.73438i	1.28032	+	0.739195i	0.303416	+	0.952858i	$0.401873\pi$
$84$	−5.32908	+	1.40730i	−0.581450	+	0.153549i
$85$	0.417182	+	0.217329i	0.0452498	+	0.0235726i
$86$	2.06729	+	3.58066i	0.222922	+	0.386112i
$87$	0.756107	+	0.205530i	0.0810631	+	0.0220351i
$88$	−1.12854	+	1.95469i	−0.120303	+	0.208370i
$89$	8.62936			0.914710			0.457355	−	0.889284i	$-0.348797\pi$
$89$	8.62936			0.914710			0.457355	+	0.889284i	$0.348797\pi$
$90$	−0.242164	−	6.70383i	−0.0255263	−	0.706646i
$91$		−	9.01965i		−	0.945516i
$92$			0.800056i			0.0834116i
$93$	−1.90243	+	9.45414i	−0.197273	+	0.980349i
$94$	−8.04444			−0.829721
$95$	−0.0171678	+	0.0329551i	−0.00176138	+	0.00338112i
$96$	1.67140	+	0.454332i	0.170587	+	0.0463701i
$97$			4.80894i			0.488273i	0.969741	+	0.244137i	$0.0785046\pi$
$97$			4.80894i			0.488273i	−0.969741	+	0.244137i	$0.921495\pi$
$98$	−1.56326	+	2.70764i	−0.157913	+	0.273513i
$99$	5.88838	−	3.34314i	0.591805	−	0.335998i
$100$	−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	$0.817080\pi$
$102$	0.352291	−	0.0930326i	0.0348820	−	0.00921160i
$103$	15.3713	+	8.87463i	1.51458	+	0.874444i	0.999854	+	0.0170892i	$0.00543992\pi$
$103$	15.3713	+	8.87463i	1.51458	+	0.874444i	0.514727	+	0.857354i	$0.327893\pi$
$104$	−1.41720	+	2.45465i	−0.138967	+	0.240699i
$105$	−9.05407	−	8.36191i	−0.883587	−	0.816039i
$106$	4.82919	+	2.78814i	0.469053	+	0.270808i
$107$	−9.24636	−	16.0152i	−0.893880	−	1.54825i	−0.835185	−	0.549969i	$-0.814639\pi$
$107$	−9.24636	−	16.0152i	−0.893880	−	1.54825i	−0.0586947	−	0.998276i	$-0.518694\pi$
$108$	−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
$111$	−3.65343	−	13.8346i	−0.346768	−	1.31312i
$112$	2.75588	−	1.59111i	0.260406	−	0.150346i
$113$	1.13102	−	1.95898i	0.106397	−	0.184286i	−0.807911	−	0.589305i	$-0.799402\pi$
$113$	1.13102	−	1.95898i	0.106397	−	0.184286i	0.914308	+	0.405019i	$0.132735\pi$
$114$	0.00734906	+	0.0278290i	0.000688303	+	0.00260643i
$115$	−1.50910	+	0.960770i	−0.140724	+	0.0895923i
$116$	−0.452379			−0.0420023
$117$	7.39450	−	4.19824i	0.683622	−	0.388128i
$118$	−3.09426	+	1.78647i	−0.284850	+	0.164458i
$119$	0.334718	−	0.579749i	0.0306836	−	0.0531455i
$120$	1.15017	+	3.69826i	0.104996	+	0.337603i
$121$	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	0.739836	−	0.672788i	$-0.234903\pi$
$127$	−2.39738	−	4.15239i	−0.212733	−	0.368465i	−0.952569	+	0.304323i	$0.901570\pi$
$128$	−1.00000			−0.0883883
$129$	1.82847	+	6.92396i	0.160988	+	0.609620i
$130$	−6.33194	+	0.274575i	−0.555348	+	0.0240818i
$131$	−4.55833	+	2.63175i	−0.398263	+	0.229937i	−0.685734	−	0.727852i	$-0.740519\pi$
$131$	−4.55833	+	2.63175i	−0.398263	+	0.229937i	0.287471	+	0.957789i	$0.407185\pi$
$132$	−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
$135$	2.64101	−	11.3148i	0.227302	−	0.973824i
$136$	−0.182184	+	0.105184i	−0.0156221	+	0.00901944i
$137$	−7.42153	−	4.28482i	−0.634064	−	0.366077i	0.148260	−	0.988948i	$-0.452633\pi$
$137$	−7.42153	−	4.28482i	−0.634064	−	0.366077i	−0.782324	+	0.622871i	$0.785966\pi$
$138$	−0.363491	+	1.33721i	−0.0309424	+	0.113831i
$139$			15.8192i			1.34177i	0.741563	+	0.670884i	$0.234085\pi$
$139$			15.8192i			1.34177i	−0.741563	+	0.670884i	$0.765915\pi$
$140$	6.31069	+	3.28752i	0.533351	+	0.277846i
$141$	−13.4455	−	3.65485i	−1.13231	−	0.307794i
$142$	13.0393	+	7.52824i	1.09423	+	0.631756i
$143$	−3.19872	−	5.54035i	−0.267491	−	0.463307i
$144$	2.58717	+	1.51874i	0.215597	+	0.126562i
$145$	−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	$-0.609768\pi$
$149$	3.75915	−	2.17035i	0.307962	−	0.177802i	0.646014	+	0.763325i	$0.276435\pi$
$150$	−5.59457	+	6.61066i	−0.456795	+	0.539758i
$151$		−	3.92788i		−	0.319646i	−0.987146	−	0.159823i	$-0.948908\pi$
$151$		−	3.92788i		−	0.319646i	0.987146	−	0.159823i	$-0.0510924\pi$
$152$	−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	$0.0746452\pi$
$157$			5.82296i			0.464723i	−0.972630	+	0.232361i	$0.925355\pi$
$158$	−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
$162$	−4.38685	−	7.85847i	−0.344663	−	0.617420i
$163$			11.9963i			0.939623i	0.882767	+	0.469812i	$0.155678\pi$
$163$			11.9963i			0.939623i	−0.882767	+	0.469812i	$0.844322\pi$
$164$	−0.681306	−	0.393352i	−0.0532011	−	0.0307157i
$165$	−8.52695	−	1.92540i	−0.663822	−	0.149892i
$166$	−11.6643	−	6.73438i	−0.905325	−	0.522690i
$167$	0.0740101	−	0.0427297i	0.00572707	−	0.00330653i	−0.497134	−	0.867674i	$-0.665614\pi$
$167$	0.0740101	−	0.0427297i	0.00572707	−	0.00330653i	0.502861	+	0.864367i	$0.332281\pi$
$168$	5.32908	−	1.40730i	0.411147	−	0.108575i
$169$	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	$-0.999805\pi$
$173$	−6.56949	+	11.3787i	−0.499469	+	0.865106i	0.500530	+	0.865719i	$0.333138\pi$
$174$	−0.756107	−	0.205530i	−0.0573203	−	0.0155812i
$175$	1.37733	+	15.8514i	0.104116	+	1.19825i
$176$	1.12854	−	1.95469i	0.0850669	−	0.147340i
$177$	−5.98340	+	1.58009i	−0.449740	+	0.118767i
$178$	−8.62936			−0.646798
$179$	2.05250	+	3.55503i	0.153411	+	0.265715i	0.932479	−	0.361224i	$-0.117641\pi$
$179$	2.05250	+	3.55503i	0.153411	+	0.265715i	−0.779068	+	0.626939i	$0.784308\pi$
$180$	0.242164	+	6.70383i	0.0180498	+	0.499674i
$181$	−17.4253	−	10.0605i	−1.29521	−	0.747792i	−0.315640	−	0.948879i	$-0.602219\pi$
$181$	−17.4253	−	10.0605i	−1.29521	−	0.747792i	−0.979573	+	0.201087i	$0.935552\pi$
$182$			9.01965i			0.668581i
$183$	−3.69981	+	13.6109i	−0.273498	+	1.00615i
$184$		−	0.800056i		−	0.0589809i
$185$	−8.53460	+	16.3829i	−0.627476	+	1.20450i
$186$	1.90243	−	9.45414i	0.139493	−	0.693211i
$187$		−	0.474817i		−	0.0347220i
$188$	8.04444			0.586701
$189$	−15.9245	−	4.45258i	−1.15834	−	0.323878i
$190$	0.0171678	−	0.0329551i	0.00124548	−	0.00239082i
$191$	0.704415	+	0.406694i	0.0509697	+	0.0294273i	0.525268	−	0.850937i	$-0.323965\pi$
$191$	0.704415	+	0.406694i	0.0509697	+	0.0294273i	−0.474299	+	0.880364i	$0.657298\pi$
$192$	−1.67140	−	0.454332i	−0.120623	−	0.0327886i
$193$	14.0785	−	8.12823i	1.01339	−	0.585083i	0.101210	−	0.994865i	$-0.467729\pi$
$193$	14.0785	−	8.12823i	1.01339	−	0.585083i	0.912183	+	0.409782i	$0.134395\pi$
$194$		−	4.80894i		−	0.345261i
$195$	−10.7080	−	2.41788i	−0.766813	−	0.173148i
$196$	1.56326	−	2.70764i	0.111661	−	0.193403i
$197$	4.90072	+	2.82943i	0.349162	+	0.201589i	0.664316	−	0.747452i	$-0.268723\pi$
$197$	4.90072	+	2.82943i	0.349162	+	0.201589i	−0.315154	+	0.949040i	$0.602056\pi$
$198$	−5.88838	+	3.34314i	−0.418469	+	0.237587i
$199$	7.20797	+	4.16152i	0.510959	+	0.295003i	0.733228	−	0.679983i	$-0.238013\pi$
$199$	7.20797	+	4.16152i	0.510959	+	0.295003i	−0.222269	+	0.974985i	$0.571346\pi$
$200$	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
$204$	−0.352291	+	0.0930326i	−0.0246653	+	0.00651358i
$205$	−0.0762102	−	1.75747i	−0.00532275	−	0.122747i
$206$	−15.3713	−	8.87463i	−1.07097	−	0.618325i
$207$	−1.21508	+	2.06988i	−0.0844538	+	0.143866i
$208$	1.41720	−	2.45465i	0.0982648	−	0.170200i
$209$	0.0375079			0.00259448
$210$	9.05407	+	8.36191i	0.624790	+	0.577027i
$211$	−11.0068	−	19.0643i	−0.757739	−	1.31244i	−0.944001	−	0.329942i	$-0.892971\pi$
$211$	−11.0068	−	19.0643i	−0.757739	−	1.31244i	0.186262	−	0.982500i	$-0.440363\pi$
$212$	−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
$222$	3.65343	+	13.8346i	0.245202	+	0.928519i
$223$	5.80910	+	10.0617i	0.389006	+	0.673778i	0.992316	−	0.123729i	$-0.0394852\pi$
$223$	5.80910	+	10.0617i	0.389006	+	0.673778i	−0.603310	+	0.797507i	$0.706152\pi$
$224$	−2.75588	+	1.59111i	−0.184135	+	0.106310i
$225$	−12.3542	+	8.50727i	−0.823614	+	0.567151i
$226$	−1.13102	+	1.95898i	−0.0752343	+	0.130310i
$227$	−10.5803	+	18.3257i	−0.702242	+	1.21632i	0.265436	+	0.964129i	$0.414484\pi$
$227$	−10.5803	+	18.3257i	−0.702242	+	1.21632i	−0.967678	+	0.252190i	$0.918849\pi$
$228$	−0.00734906	−	0.0278290i	−0.000486704	−	0.00184302i
$229$	−22.6961	+	13.1036i	−1.49980	+	0.865910i	−1.00000		0.000231725i	$-0.999926\pi$
$229$	−22.6961	+	13.1036i	−1.49980	+	0.865910i	−0.499799	+	0.866141i	$0.666593\pi$
$230$	1.50910	−	0.960770i	0.0995068	−	0.0633513i
$231$	−3.26325	+	12.0049i	−0.214706	+	0.789863i
$232$	0.452379			0.0297001
$233$	3.39689			0.222537			0.111269	−	0.993790i	$-0.464509\pi$
$233$	3.39689			0.222537			0.111269	+	0.993790i	$0.464509\pi$
$234$	−7.39450	+	4.19824i	−0.483394	+	0.274448i
$235$	9.66040	+	15.1737i	0.630175	+	0.989825i
$236$	3.09426	−	1.78647i	0.201419	−	0.116289i
$237$	−25.3767	+	6.70145i	−1.64839	+	0.435306i
$238$	−0.334718	+	0.579749i	−0.0216966	+	0.0375795i
$239$	5.38215	−	9.32216i	0.348142	−	0.603000i	−0.637777	−	0.770221i	$-0.720146\pi$
$239$	5.38215	−	9.32216i	0.348142	−	0.603000i	0.985919	+	0.167221i	$0.0534792\pi$
$240$	−1.15017	−	3.69826i	−0.0742433	−	0.238721i
$241$	7.07114	−	4.08252i	0.455492	−	0.262979i	−0.254655	−	0.967032i	$-0.581962\pi$
$241$	7.07114	−	4.08252i	0.455492	−	0.262979i	0.710147	+	0.704054i	$0.248629\pi$
$242$	−2.95280	−	5.11439i	−0.189813	−	0.328766i
$243$	−3.76183	−	15.1277i	−0.241321	−	0.970445i
$244$		−	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	−0.995523	−	0.0945166i	$-0.969869\pi$
$251$	−9.18284	−	15.9051i	−0.579615	−	1.00392i	0.415908	−	0.909407i	$-0.363464\pi$
$252$	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
$255$	−0.598540	−	0.552783i	−0.0374820	−	0.0346166i
$256$	1.00000			0.0625000
$257$	8.48270	−	14.6925i	0.529136	−	0.916491i	−0.470286	−	0.882514i	$-0.655849\pi$
$257$	8.48270	−	14.6925i	0.529136	−	0.916491i	0.999423	−	0.0339770i	$-0.0108173\pi$
$258$	−1.82847	−	6.92396i	−0.113836	−	0.431067i
$259$	22.7670	+	13.1445i	1.41467	+	0.816762i
$260$	6.33194	−	0.274575i	0.392690	−	0.0170284i
$261$	−1.17038	−	0.687047i	−0.0724446	−	0.0425271i
$262$	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
$267$	−14.4231	−	3.92059i	−0.882681	−	0.239936i
$268$	7.31490	+	4.22326i	0.446829	+	0.257977i
$269$	2.19816	−	3.80733i	0.134024	−	0.232137i	−0.791200	−	0.611558i	$-0.790543\pi$
$269$	2.19816	−	3.80733i	0.134024	−	0.232137i	0.925224	+	0.379421i	$0.123877\pi$
$270$	−2.64101	+	11.3148i	−0.160727	+	0.688598i
$271$			15.1797i			0.922100i	0.887374	+	0.461050i	$0.152527\pi$
$271$			15.1797i			0.922100i	−0.887374	+	0.461050i	$0.847473\pi$
$272$	0.182184	−	0.105184i	0.0110465	−	0.00637771i
$273$	−4.09791	+	15.0755i	−0.248017	+	0.912408i
$274$	7.42153	+	4.28482i	0.448351	+	0.258856i
$275$	6.46755	+	9.24830i	0.390008	+	0.557693i
$276$	0.363491	−	1.33721i	0.0218796	−	0.0804909i
$277$	−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
$279$	7.47504	−	14.9373i	0.447519	−	0.894274i
$280$	−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	$0.736824\pi$
$282$	13.4455	+	3.65485i	0.800667	+	0.217643i
$283$		−	1.81927i		−	0.108145i	−0.998537	−	0.0540723i	$-0.982780\pi$
$283$		−	1.81927i		−	0.108145i	0.998537	−	0.0540723i	$-0.0172201\pi$
$284$	−13.0393	−	7.52824i	−0.773740	−	0.446719i
$285$	0.0436668	−	0.0472814i	0.00258660	−	0.00280071i
$286$	3.19872	+	5.54035i	0.189144	+	0.327608i
$287$	−2.50347			−0.147775
$288$	−2.58717	−	1.51874i	−0.152450	−	0.0894927i
$289$	−8.47787	+	14.6841i	−0.498698	+	0.863771i
$290$	0.543252	+	0.853294i	0.0319009	+	0.0501071i
$291$	2.18485	−	8.03766i	0.128078	−	0.471176i
$292$	4.45521	−	7.71666i	0.260722	−	0.451583i
$293$	−9.36548	−	16.2215i	−0.547137	−	0.947669i	−0.998469	−	0.0553132i	$-0.982384\pi$
$293$	−9.36548	−	16.2215i	−0.547137	−	0.947669i	0.451332	−	0.892356i	$-0.350949\pi$
$294$	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
$297$	−11.3607	+	2.91245i	−0.659218	+	0.168997i
$298$	−3.75915	+	2.17035i	−0.217762	+	0.125725i
$299$	1.96386	+	1.13384i	0.113573	+	0.0655714i
$300$	5.59457	−	6.61066i	0.323003	−	0.381666i
$301$	−11.3944	−	6.57858i	−0.656765	−	0.379183i
$302$			3.92788i			0.226024i
$303$	4.96366	−	18.2604i	0.285155	−	1.04903i
$304$	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	−0.494107	−	0.869401i	$-0.664505\pi$
$307$	0.206088	−	0.118985i	0.0117621	−	0.00679084i	0.505870	+	0.862610i	$0.331172\pi$
$308$		−	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	−0.988272	−	0.152702i	$-0.951203\pi$
$313$	−11.0818	−	19.1942i	−0.626380	−	1.08492i	0.361892	−	0.932220i	$-0.382131\pi$
$314$		−	5.82296i		−	0.328609i
$315$	11.3339	+	18.0897i	0.638593	+	1.01924i
$316$	13.1233	−	7.57675i	0.738244	−	0.426225i
$317$	0.869811	+	1.50656i	0.0488535	+	0.0846167i	0.889418	−	0.457095i	$-0.151110\pi$
$317$	0.869811	+	1.50656i	0.0488535	+	0.0846167i	−0.840565	+	0.541711i	$0.817777\pi$
$318$	−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
$321$	8.17818	+	30.9687i	0.456462	+	1.72850i
$322$	−1.27298	−	2.20486i	−0.0709402	−	0.122872i
$323$	0.00302751	+	0.00174794i	0.000168455	+	9.72577e-5i
$324$	4.38685	+	7.85847i	0.243714	+	0.436582i
$325$	8.12180	+	11.6138i	0.450517	+	0.644218i
$326$		−	11.9963i		−	0.664414i
$327$	0.787716	+	0.214122i	0.0435608	+	0.0118410i
$328$	0.681306	+	0.393352i	0.0376188	+	0.0217192i
$329$	22.1695	−	12.7996i	1.22225	−	0.705664i
$330$	8.52695	+	1.92540i	0.469393	+	0.105990i
$331$	−13.4962	−	7.79202i	−0.741817	−	0.428288i	0.0809126	−	0.996721i	$-0.474217\pi$
$331$	−13.4962	−	7.79202i	−0.741817	−	0.428288i	−0.822730	+	0.568433i	$0.807550\pi$
$332$	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
$336$	−5.32908	+	1.40730i	−0.290725	+	0.0767744i
$337$	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
$345$	2.95881	−	0.920202i	0.159297	−	0.0495420i
$346$	6.56949	−	11.3787i	0.353178	−	0.611723i
$347$	20.3091	−	11.7255i	1.09025	−	0.629457i	0.156609	−	0.987661i	$-0.449944\pi$
$347$	20.3091	−	11.7255i	1.09025	−	0.629457i	0.933644	+	0.358203i	$0.116611\pi$
$348$	0.756107	+	0.205530i	0.0405316	+	0.0110176i
$349$	−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
$351$	−14.2666	+	3.65739i	−0.761494	+	0.195217i
$352$	−1.12854	+	1.95469i	−0.0601514	+	0.104185i
$353$	−26.4606	+	15.2770i	−1.40835	+	0.813114i	−0.995230	−	0.0975610i	$-0.968896\pi$
$353$	−26.4606	+	15.2770i	−1.40835	+	0.813114i	−0.413124	+	0.910675i	$0.635563\pi$
$354$	5.98340	−	1.58009i	0.318014	−	0.0839809i
$355$	−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	$-0.0454284\pi$
$359$	25.7981	+	14.8945i	1.36157	+	0.786104i	0.371739	+	0.928337i	$0.378762\pi$
$360$	−0.242164	−	6.70383i	−0.0127631	−	0.353323i
$361$	9.49986	−	16.4542i	0.499993	−	0.866013i
$362$	17.4253	+	10.0605i	0.915854	+	0.528769i
$363$	−2.61168	−	9.88975i	−0.137077	−	0.519078i
$364$		−	9.01965i		−	0.472758i
$365$	19.9056	−	0.863177i	1.04191	−	0.0451808i
$366$	3.69981	−	13.6109i	0.193392	−	0.711453i
$367$	−14.4856	+	25.0897i	−0.756140	+	1.30967i	0.188666	+	0.982041i	$0.439584\pi$
$367$	−14.4856	+	25.0897i	−0.756140	+	1.30967i	−0.944806	+	0.327631i	$0.893750\pi$
$368$			0.800056i			0.0417058i
$369$	−1.16525	−	2.05240i	−0.0606605	−	0.106843i
$370$	8.53460	−	16.3829i	0.443693	−	0.851709i
$371$	−17.7449			−0.921270
$372$	−1.90243	+	9.45414i	−0.0986364	+	0.490174i
$373$		−	2.95280i		−	0.152890i	−0.997074	−	0.0764451i	$-0.975643\pi$
$373$		−	2.95280i		−	0.152890i	0.997074	−	0.0764451i	$-0.0243570\pi$
$374$			0.474817i			0.0245522i
$375$	19.1877	+	2.61410i	0.990847	+	0.134991i
$376$	−8.04444			−0.414860
$377$	−0.641109	+	1.11043i	−0.0330188	+	0.0571902i
$378$	15.9245	+	4.45258i	0.819069	+	0.229016i
$379$	−3.80420	−	6.58906i	−0.195408	−	0.338457i	0.751626	−	0.659590i	$-0.229270\pi$
$379$	−3.80420	−	6.58906i	−0.195408	−	0.338457i	−0.947034	+	0.321132i	$0.895937\pi$
$380$	−0.0171678	+	0.0329551i	−0.000880689	+	0.00169056i
$381$	2.12043	+	8.02952i	0.108633	+	0.411365i
$382$	−0.704415	−	0.406694i	−0.0360410	−	0.0208083i
$383$	−10.5978	−	6.11865i	−0.541523	−	0.312649i	0.204173	−	0.978935i	$-0.434550\pi$
$383$	−10.5978	−	6.11865i	−0.541523	−	0.312649i	−0.745696	+	0.666286i	$0.767883\pi$
$384$	1.67140	+	0.454332i	0.0852933	+	0.0231850i
$385$	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	0.939444	+	0.342703i	$0.111342\pi$
$389$	15.1180	+	26.1851i	0.766511	+	1.32764i	−0.172933	+	0.984934i	$0.555324\pi$
$390$	10.7080	+	2.41788i	0.542219	+	0.122434i
$391$	0.0841530	+	0.145757i	0.00425580	+	0.00737126i
$392$	−1.56326	+	2.70764i	−0.0789565	+	0.136757i
$393$	8.81449	−	2.32772i	0.444632	−	0.117418i
$394$	−4.90072	−	2.82943i	−0.246895	−	0.142545i
$395$	30.0510	+	15.6549i	1.51203	+	0.787685i
$396$	5.88838	−	3.34314i	0.295902	−	0.167999i
$397$	−17.6190	+	10.1723i	−0.884270	+	0.510534i	−0.872064	−	0.489392i	$-0.837219\pi$
$397$	−17.6190	+	10.1723i	−0.884270	+	0.510534i	−0.0122063	+	0.999926i	$0.503885\pi$
$398$	−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	$-0.203091\pi$
$401$	32.1710			1.60654			0.803271	+	0.595614i	$0.203091\pi$
$402$	10.3074	+	10.3822i	0.514085	+	0.517815i
$403$	−14.1634	−	6.96019i	−0.705530	−	0.346712i
$404$			10.9252i			0.543548i
$405$	−9.55487	+	17.7117i	−0.474785	+	0.880102i
$406$	1.24670	−	0.719784i	0.0618728	−	0.0357223i
$407$	18.6463			0.924261
$408$	0.352291	−	0.0930326i	0.0174410	−	0.00460580i
$409$	16.0037	−	9.23975i	0.791333	−	0.456876i	−0.0490987	−	0.998794i	$-0.515635\pi$
$409$	16.0037	−	9.23975i	0.791333	−	0.456876i	0.840432	+	0.541918i	$0.182302\pi$
$410$	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
$414$	1.21508	−	2.06988i	0.0597179	−	0.101729i
$415$	1.30476	+	30.0888i	0.0640480	+	1.47700i
$416$	−1.41720	+	2.45465i	−0.0694837	+	0.120349i
$417$	7.18717	−	26.4402i	0.351957	−	1.29478i
$418$	−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	$0.953888\pi$
$420$	−9.05407	−	8.36191i	−0.441793	−	0.408019i
$421$	−5.40623	+	9.36386i	−0.263483	+	0.456367i	−0.967165	−	0.254149i	$-0.918205\pi$
$421$	−5.40623	+	9.36386i	−0.263483	+	0.456367i	0.703682	+	0.710515i	$0.251538\pi$
$422$	11.0068	+	19.0643i	0.535802	+	0.928037i
$423$	20.8123	+	12.2174i	1.01193	+	0.594032i
$424$	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
$429$	2.82919	+	10.7134i	0.136595	+	0.517249i
$430$	−4.27140	+	8.19934i	−0.205985	+	0.395407i
$431$	−33.7037	+	19.4588i	−1.62345	+	0.937299i	−0.637462	+	0.770482i	$0.720016\pi$
$431$	−33.7037	+	19.4588i	−1.62345	+	0.937299i	−0.985988	+	0.166817i	$0.946651\pi$
$432$	−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
$435$	0.520314	+	1.67301i	0.0249471	+	0.0802149i
$436$	−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	−0.858602	−	0.512644i	$-0.828666\pi$
$439$	0.307195	−	0.532078i	0.0146616	−	0.0253947i	0.873263	+	0.487249i	$0.162000\pi$
$440$	−5.04224	+	0.218649i	−0.240380	+	0.0104237i
$441$	8.15662	−	4.63093i	0.388410	−	0.220521i
$442$			0.596264i			0.0283614i
$443$	3.88123	−	6.72249i	0.184403	−	0.319395i	−0.758972	−	0.651123i	$-0.774298\pi$
$443$	3.88123	−	6.72249i	0.184403	−	0.319395i	0.943375	+	0.331728i	$0.107632\pi$
$444$	−3.65343	−	13.8346i	−0.173384	−	0.656562i
$445$	10.3628	+	16.2770i	0.491244	+	0.771605i
$446$	−5.80910	−	10.0617i	−0.275069	−	0.476433i
$447$	−7.26911	+	1.91962i	−0.343817	+	0.0907949i
$448$	2.75588	−	1.59111i	0.130203	−	0.0751729i
$449$	15.2495			0.719666			0.359833	−	0.933017i	$-0.382834\pi$
$449$	15.2495			0.719666			0.359833	+	0.933017i	$0.382834\pi$
$450$	12.3542	−	8.50727i	0.582383	−	0.401036i
$451$	−1.53776	+	0.887827i	−0.0724104	+	0.0418062i
$452$	1.13102	−	1.95898i	0.0531987	−	0.0921429i
$453$	−1.78456	+	6.56506i	−0.0838459	+	0.308453i
$454$	10.5803	−	18.3257i	0.496560	−	0.860067i
$455$	17.0132	−	10.8315i	0.797591	−	0.507789i
$456$	0.00734906	+	0.0278290i	0.000344151	+	0.00130321i
$457$	−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
$459$	−1.05273	−	0.294348i	−0.0491371	−	0.0137390i
$460$	−1.50910	+	0.960770i	−0.0703619	+	0.0447961i
$461$	26.2525			1.22270			0.611351	−	0.791360i	$-0.290627\pi$
$461$	26.2525			1.22270			0.611351	+	0.791360i	$0.290627\pi$
$462$	3.26325	−	12.0049i	0.151820	−	0.558517i
$463$	−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
$465$	−20.1173	+	7.76484i	−0.932919	+	0.360086i
$466$	−3.39689			−0.157358
$467$	0.199102			0.00921334			0.00460667	−	0.999989i	$-0.498534\pi$
$467$	0.199102			0.00921334			0.00460667	+	0.999989i	$0.498534\pi$
$468$	7.39450	−	4.19824i	0.341811	−	0.194064i
$469$	26.8787			1.24114
$470$	−9.66040	−	15.1737i	−0.445601	−	0.699912i
$471$	2.64556	−	9.73250i	0.121901	−	0.448450i
$472$	−3.09426	+	1.78647i	−0.142425	+	0.0822290i
$473$	−9.33209			−0.429090
$474$	25.3767	−	6.70145i	1.16559	−	0.307808i
$475$	−0.0827776	+	0.00719258i	−0.00379810	+	0.000330018i
$476$	0.334718	−	0.579749i	0.0153418	−	0.0265727i
$477$	−8.25946	−	14.5477i	−0.378175	−	0.666092i
$478$	−5.38215	+	9.32216i	−0.246174	+	0.426386i
$479$	−27.8735	+	16.0928i	−1.27357	+	0.735298i	−0.975659	−	0.219295i	$-0.929624\pi$
$479$	−27.8735	+	16.0928i	−1.27357	+	0.735298i	−0.297914	+	0.954593i	$0.596291\pi$
$480$	1.15017	+	3.69826i	0.0524979	+	0.168802i
$481$	23.4156			1.06766
$482$	−7.07114	+	4.08252i	−0.322082	+	0.185954i
$483$	−1.12592	−	4.26356i	−0.0512310	−	0.193999i
$484$	2.95280	+	5.11439i	0.134218	+	0.232472i
$485$	−9.07079	+	5.77495i	−0.411883	+	0.262227i
$486$	3.76183	+	15.1277i	0.170640	+	0.686208i
$487$	4.86941	−	8.43407i	0.220654	−	0.382184i	−0.734353	−	0.678768i	$-0.762514\pi$
$487$	4.86941	−	8.43407i	0.220654	−	0.382184i	0.955007	+	0.296584i	$0.0958475\pi$
$488$			8.14341i			0.368635i
$489$	5.45030	−	20.0506i	0.246471	−	0.906721i
$490$	−6.98454	+	0.302874i	−0.315529	+	0.0136825i
$491$	1.53335	−	2.65584i	0.0691991	−	0.119856i	−0.829350	−	0.558730i	$-0.811289\pi$
$491$	1.53335	−	2.65584i	0.0691991	−	0.119856i	0.898549	+	0.438873i	$0.144622\pi$
$492$	0.960024	+	0.966989i	0.0432812	+	0.0435952i
$493$	−0.0824161	+	0.0475830i	−0.00371184	+	0.00214303i
$494$	−0.0471016			−0.00211920
$495$	13.3772	+	7.09218i	0.601260	+	0.318770i
$496$	−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	−0.223879	−	0.974617i	$-0.571872\pi$
$499$	11.3529	−	6.55458i	0.508224	−	0.293423i	0.732103	+	0.681194i	$0.238539\pi$
$500$	−11.0860	+	1.44945i	−0.495780	+	0.0648216i
$501$	−0.143114	+	0.0377934i	−0.00639386	+	0.00168848i
$502$	9.18284	+	15.9051i	0.409850	+	0.709881i
$503$	−18.6722	−	32.3413i	−0.832554	−	1.44203i	−0.896007	−	0.444041i	$-0.853545\pi$
$503$	−18.6722	−	32.3413i	−0.832554	−	1.44203i	0.0634527	−	0.997985i	$-0.479789\pi$
$504$	−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
$507$	−2.19625	−	8.31666i	−0.0975391	−	0.369356i
$508$	−2.39738	−	4.15239i	−0.106367	−	0.184233i
$509$	−13.9143	+	24.1003i	−0.616742	+	1.06823i	0.373334	+	0.927697i	$0.378215\pi$
$509$	−13.9143	+	24.1003i	−0.616742	+	1.06823i	−0.990076	+	0.140532i	$0.955119\pi$
$510$	0.598540	+	0.552783i	0.0265038	+	0.0244776i
$511$		−	28.3549i		−	1.25435i
$512$	−1.00000			−0.0441942
$513$	0.0232519	−	0.0831596i	0.00102660	−	0.00367159i
$514$	−8.48270	+	14.6925i	−0.374156	+	0.648057i
$515$	1.71942	+	39.6513i	0.0757667	+	1.74725i
$516$	1.82847	+	6.92396i	0.0804939	+	0.304810i
$517$	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	$-0.570068\pi$
$521$	11.8145	−	6.82108i	0.517601	−	0.298837i	0.735952	+	0.677033i	$0.236735\pi$
$522$	1.17038	+	0.687047i	0.0512261	+	0.0300712i
$523$	−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
$525$	4.89971	−	27.1198i	0.213841	−	1.18360i
$526$			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
$534$	14.4231	+	3.92059i	0.624149	+	0.169661i
$535$	19.1047	−	36.6731i	0.825966	−	1.58552i
$536$	−7.31490	−	4.22326i	−0.315956	−	0.182417i
$537$	−1.81538	−	6.87439i	−0.0783395	−	0.296652i
$538$	−2.19816	+	3.80733i	−0.0947695	+	0.164146i
$539$	−3.52840	−	6.11136i	−0.151979	−	0.263235i
$540$	2.64101	−	11.3148i	0.113651	−	0.486912i
$541$	−8.47766	−	14.6837i	−0.364483	−	0.631303i	0.624210	−	0.781257i	$-0.285421\pi$
$541$	−8.47766	−	14.6837i	−0.364483	−	0.631303i	−0.988693	+	0.149954i	$0.952088\pi$
$542$		−	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
$546$	4.09791	−	15.0755i	0.175375	−	0.645170i
$547$	−27.5845	−	15.9259i	−1.17943	−	0.680943i	−0.223545	−	0.974694i	$-0.571763\pi$
$547$	−27.5845	−	15.9259i	−1.17943	−	0.680943i	−0.955882	+	0.293751i	$0.905096\pi$
$548$	−7.42153	−	4.28482i	−0.317032	−	0.183039i
$549$	12.3677	−	21.0683i	0.527842	−	0.899175i
$550$	−6.46755	−	9.24830i	−0.275777	−	0.394349i
$551$	−0.00375879	−	0.00651042i	−0.000160130	−	0.000277353i
$552$	−0.363491	+	1.33721i	−0.0154712	+	0.0569156i
$553$	24.1109	−	41.7613i	1.02530	−	1.77587i
$554$	22.6724			0.963259
$555$	21.7080	−	23.5049i	0.921455	−	0.997729i
$556$			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	$-0.189791\pi$
$558$	−7.47504	+	14.9373i	−0.316444	+	0.632347i
$559$	−11.7190			−0.495662
$560$	6.31069	+	3.28752i	0.266675	+	0.138923i
$561$	−0.215724	+	0.793609i	−0.00910789	+	0.0335062i
$562$		−	24.6672i		−	1.04052i
$563$	−16.3573	+	28.3317i	−0.689379	+	1.19404i	0.282661	+	0.959220i	$0.408783\pi$
$563$	−16.3573	+	28.3317i	−0.689379	+	1.19404i	−0.972039	+	0.234819i	$0.924550\pi$
$564$	−13.4455	−	3.65485i	−0.566157	−	0.153897i
$565$	5.05333	−	0.219130i	0.212595	−	0.00921887i
$566$			1.81927i			0.0764698i
$567$	24.5933	+	14.6771i	1.03282	+	0.616379i
$568$	13.0393	+	7.52824i	0.547117	+	0.315878i
$569$	−11.3867	+	19.7223i	−0.477354	+	0.826801i	−0.999663	−	0.0259548i	$-0.991737\pi$
$569$	−11.3867	+	19.7223i	−0.477354	+	0.826801i	0.522309	+	0.852756i	$0.325071\pi$
$570$	−0.0436668	+	0.0472814i	−0.00182900	+	0.00198040i
$571$	−14.0140	−	8.09098i	−0.586467	−	0.338597i	0.177232	−	0.984169i	$-0.443286\pi$
$571$	−14.0140	−	8.09098i	−0.586467	−	0.338597i	−0.763699	+	0.645572i	$0.776619\pi$
$572$	−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
$576$	2.58717	+	1.51874i	0.107799	+	0.0632809i
$577$	−12.6544	+	7.30604i	−0.526811	+	0.304154i	−0.739717	−	0.672918i	$-0.765041\pi$
$577$	−12.6544	+	7.30604i	−0.526811	+	0.304154i	0.212906	+	0.977073i	$0.431707\pi$
$578$	8.47787	−	14.6841i	0.352633	−	0.610778i
$579$	−27.2237	+	7.18922i	−1.13138	+	0.298774i
$580$	−0.543252	−	0.853294i	−0.0225573	−	0.0354311i
$581$	42.8606			1.77816
$582$	−2.18485	+	8.03766i	−0.0905651	+	0.333172i
$583$	−10.8999	+	6.29305i	−0.451427	+	0.260631i
$584$	−4.45521	+	7.71666i	−0.184358	+	0.319318i
$585$	16.7988	+	8.90621i	0.694544	+	0.368226i
$586$	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	$-0.398142\pi$
$593$	15.3203			0.629128			0.314564	+	0.949236i	$0.398142\pi$
$594$	11.3607	−	2.91245i	0.466137	−	0.119499i
$595$	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	−0.979128	−	0.203246i	$-0.934851\pi$
$599$	−40.2534	−	23.2403i	−1.64471	−	0.949572i	−0.665580	−	0.746327i	$-0.731816\pi$
$600$	−5.59457	+	6.61066i	−0.228397	+	0.269879i
$601$	−16.3913	+	9.46350i	−0.668614	+	0.386024i	−0.795551	−	0.605886i	$-0.792819\pi$
$601$	−16.3913	+	9.46350i	−0.668614	+	0.386024i	0.126938	+	0.991911i	$0.459485\pi$
$602$	11.3944	+	6.57858i	0.464403	+	0.268123i
$603$	12.5108	+	22.0357i	0.509480	+	0.897364i
$604$		−	3.92788i		−	0.159823i
$605$	−6.10101	+	11.7114i	−0.248041	+	0.476138i
$606$	−4.96366	+	18.2604i	−0.201635	+	0.741777i
$607$	15.5739	+	8.99161i	0.632126	+	0.364958i	0.781575	−	0.623811i	$-0.214417\pi$
$607$	15.5739	+	8.99161i	0.632126	+	0.364958i	−0.149449	+	0.988769i	$0.547750\pi$
$608$	−0.00830895	−	0.0143915i	−0.000336972	−	0.000583653i
$609$	2.41076	−	0.636632i	0.0976890	−	0.0257976i
$610$	−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	−0.963213	−	0.268740i	$-0.913393\pi$
$613$	−17.6863	−	30.6335i	−0.714342	−	1.23728i	0.248871	−	0.968537i	$-0.419940\pi$
$614$	−0.206088	+	0.118985i	−0.00831704	+	0.00480185i
$615$	−0.671098	+	2.97207i	−0.0270613	+	0.119845i
$616$			7.18252i			0.289392i
$617$	12.0346	+	20.8445i	0.484494	+	0.839168i	0.999841	−	0.0178134i	$-0.00567048\pi$
$617$	12.0346	+	20.8445i	0.484494	+	0.839168i	−0.515348	+	0.856981i	$0.672337\pi$
$618$	21.6596	+	21.8168i	0.871277	+	0.877598i
$619$			30.3033i			1.21799i	0.793173	+	0.608996i	$0.208428\pi$
$619$			30.3033i			1.21799i	−0.793173	+	0.608996i	$0.791572\pi$
$620$	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
$627$	−0.0626908	−	0.0170410i	−0.00250363	−	0.000680554i
$628$			5.82296i			0.232361i
$629$	1.50506	+	0.868949i	0.0600108	+	0.0346473i
$630$	−11.3339	−	18.0897i	−0.451554	−	0.720709i
$631$	28.9841	+	16.7340i	1.15384	+	0.666169i	0.949820	−	0.312798i	$-0.101266\pi$
$631$	28.9841	+	16.7340i	1.15384	+	0.666169i	0.204019	+	0.978967i	$0.434600\pi$
$632$	−13.1233	+	7.57675i	−0.522017	+	0.301387i
$633$	9.73524	+	36.8649i	0.386941	+	1.46525i
$634$	−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
$639$	−22.3014	−	39.2801i	−0.882228	−	1.55390i
$640$	−1.20088	−	1.88624i	−0.0474689	−	0.0745601i
$641$	−6.96794	+	12.0688i	−0.275217	+	0.476690i	−0.970190	−	0.242346i	$-0.922083\pi$
$641$	−6.96794	+	12.0688i	−0.275217	+	0.476690i	0.694973	+	0.719036i	$0.255416\pi$
$642$	−8.17818	−	30.9687i	−0.322767	−	1.22224i
$643$	−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
$645$	−10.8645	+	11.7638i	−0.427787	+	0.463198i
$646$	−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	$0.787039\pi$
$648$	−4.38685	−	7.85847i	−0.172332	−	0.308710i
$649$		−	8.06442i		−	0.316556i
$650$	−8.12180	−	11.6138i	−0.318563	−	0.455531i
$651$	9.79970	+	29.0815i	0.384080	+	1.13979i
$652$			11.9963i			0.469812i
$653$	19.8770			0.777848			0.388924	−	0.921270i	$-0.372847\pi$
$653$	19.8770			0.777848			0.388924	+	0.921270i	$0.372847\pi$
$654$	−0.787716	−	0.214122i	−0.0308021	−	0.00837285i
$655$	−10.4381	−	5.43767i	−0.407851	−	0.212468i
$656$	−0.681306	−	0.393352i	−0.0266005	−	0.0153578i
$657$	23.2460	−	13.1979i	0.906912	−	0.514901i
$658$	−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	$-0.0813121\pi$
$660$	−8.52695	−	1.92540i	−0.331911	−	0.0749461i
$661$	−23.7171	+	41.0792i	−0.922488	+	1.59780i	−0.126936	+	0.991911i	$0.540514\pi$
$661$	−23.7171	+	41.0792i	−0.922488	+	1.59780i	−0.795552	+	0.605885i	$0.792819\pi$
$662$	13.4962	+	7.79202i	0.524544	+	0.302846i
$663$	−0.270902	+	0.996597i	−0.0105210	+	0.0387046i
$664$	−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
$669$	−5.13800	−	19.4563i	−0.198647	−	0.752225i
$670$	−0.818237	−	18.8693i	−0.0316113	−	0.728983i
$671$	−15.9178	−	9.19016i	−0.614501	−	0.354782i
$672$	5.32908	−	1.40730i	0.205574	−	0.0542877i
$673$	−17.2103	+	29.8092i	−0.663410	+	1.14906i	0.316304	+	0.948658i	$0.397558\pi$
$673$	−17.2103	+	29.8092i	−0.663410	+	1.14906i	−0.979714	+	0.200402i	$0.935775\pi$
$674$	−1.69991			−0.0654781
$675$	24.5140	−	8.60615i	0.943543	−	0.331251i
$676$	2.48312	+	4.30088i	0.0955044	+	0.165419i
$677$	22.3852	+	12.9241i	0.860334	+	0.496714i	0.864124	−	0.503279i	$-0.167873\pi$
$677$	22.3852	+	12.9241i	0.860334	+	0.496714i	−0.00379030	+	0.999993i	$0.501206\pi$
$678$	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	$-0.832792\pi$
$683$	−45.2214			−1.73035			−0.865174	+	0.501472i	$0.832792\pi$
$684$	−0.000360383		0.0498524i	−1.37796e−5		0.00190615i
$685$	−0.830165	−	19.1443i	−0.0317190	−	0.731467i
$686$		−	12.3263i		−	0.470619i
$687$	43.8876	−	11.5898i	1.67442	−	0.442179i
$688$	−2.06729	−	3.58066i	−0.0788148	−	0.136511i
$689$	−13.6878	+	7.90267i	−0.521465	+	0.301068i
$690$	−2.95881	+	0.920202i	−0.112640	+	0.0350315i
$691$	−12.1864	+	21.1075i	−0.463593	+	0.802967i	−0.999137	−	0.0415404i	$-0.986773\pi$
$691$	−12.1864	+	21.1075i	−0.463593	+	0.802967i	0.535543	+	0.844508i	$0.320107\pi$
$692$	−6.56949	+	11.3787i	−0.249735	+	0.432553i
$693$	10.9084	−	18.5824i	0.414376	−	0.705886i
$694$	−20.3091	+	11.7255i	−0.770925	+	0.445094i
$695$	−29.8388	+	18.9969i	−1.13185	+	0.720595i
$696$	−0.756107	−	0.205530i	−0.0286602	−	0.00779060i
$697$	−0.165497			−0.00626866
$698$	17.4656			0.661083
$699$	−5.67756	−	1.54331i	−0.214745	−	0.0583735i
$700$	1.37733	+	15.8514i	0.0520582	+	0.599125i
$701$	29.9318	−	17.2812i	1.13051	−	0.652700i	0.186447	−	0.982465i	$-0.440303\pi$
$701$	29.9318	−	17.2812i	1.13051	−	0.652700i	0.944063	+	0.329765i	$0.106969\pi$
$702$	14.2666	−	3.65739i	0.538457	−	0.138039i
$703$	−0.0686422	+	0.118892i	−0.00258889	+	0.00448409i
$704$	1.12854	−	1.95469i	0.0425334	−	0.0736701i
$705$	−9.25249	−	29.7504i	−0.348469	−	1.12047i
$706$	26.4606	−	15.2770i	0.995857	−	0.574958i
$707$	17.3832	+	30.1085i	0.653761	+	1.13235i
$708$	−5.98340	+	1.58009i	−0.224870	+	0.0593834i
$709$			11.2769i			0.423512i	0.977323	+	0.211756i	$0.0679183\pi$
$709$			11.2769i			0.423512i	−0.977323	+	0.211756i	$0.932082\pi$
$710$	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	$-0.208209\pi$
$719$	−3.48956	−	6.04409i	−0.130138	−	0.225406i	−0.923730	+	0.383045i	$0.874876\pi$
$720$	0.242164	+	6.70383i	0.00902491	+	0.249837i
$721$	56.4820			2.10350
$722$	−9.49986	+	16.4542i	−0.353548	+	0.612364i
$723$	−13.6735	+	3.61089i	−0.508524	+	0.134291i
$724$	−17.4253	−	10.0605i	−0.647607	−	0.373896i
$725$	0.957135	−	2.04940i	0.0355471	−	0.0761130i
$726$	2.61168	+	9.88975i	0.0969284	+	0.367043i
$727$	10.6708	−	6.16079i	0.395758	−	0.228491i	−0.288894	−	0.957361i	$-0.593287\pi$
$727$	10.6708	−	6.16079i	0.395758	−	0.228491i	0.684652	+	0.728870i	$0.259954\pi$
$728$			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
$732$	−3.69981	+	13.6109i	−0.136749	+	0.503073i
$733$	21.0311	+	12.1423i	0.776800	+	0.448486i	0.835295	−	0.549802i	$-0.185297\pi$
$733$	21.0311	+	12.1423i	0.776800	+	0.448486i	−0.0584948	+	0.998288i	$0.518630\pi$
$734$	14.4856	−	25.0897i	0.534672	−	0.926079i
$735$	−11.8116	−	2.66707i	−0.435676	−	0.0983765i
$736$		−	0.800056i		−	0.0294905i
$737$	16.5103	−	9.53223i	0.608165	−	0.351124i
$738$	1.16525	+	2.05240i	0.0428935	+	0.0755497i
$739$	−19.8079	−	11.4361i	−0.728647	−	0.420685i	0.0892800	−	0.996007i	$-0.471543\pi$
$739$	−19.8079	−	11.4361i	−0.728647	−	0.420685i	−0.817927	+	0.575322i	$0.804877\pi$
$740$	−8.53460	+	16.3829i	−0.313738	+	0.602249i
$741$	−0.0787257	−	0.0213998i	−0.00289206	−	0.000786140i
$742$	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	$-0.327329\pi$
$744$	1.90243	−	9.45414i	0.0697465	−	0.346606i
$745$	8.60808	+	4.48433i	0.315376	+	0.164293i
$746$			2.95280i			0.108110i
$747$	19.9497	+	35.1380i	0.729920	+	1.28563i
$748$		−	0.474817i		−	0.0173610i
$749$	−50.9638	−	29.4240i	−1.86218	−	1.07513i
$750$	−19.1877	−	2.61410i	−0.700634	−	0.0954533i
$751$	−20.0245	−	34.6835i	−0.730705	−	1.26562i	−0.956582	−	0.291463i	$-0.905858\pi$
$751$	−20.0245	−	34.6835i	−0.730705	−	1.26562i	0.225877	−	0.974156i	$-0.427475\pi$
$752$	8.04444			0.293351
$753$	8.12199	+	30.7559i	0.295982	+	1.12081i
$754$	0.641109	−	1.11043i	0.0233478	−	0.0404396i
$755$	7.40891	−	4.71690i	0.269638	−	0.171666i
$756$	−15.9245	−	4.45258i	−0.579169	−	0.161939i
$757$	−19.0466	+	32.9897i	−0.692261	+	1.19903i	0.278834	+	0.960339i	$0.410052\pi$
$757$	−19.0466	+	32.9897i	−0.692261	+	1.19903i	−0.971095	+	0.238693i	$0.923281\pi$
$758$	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	$-0.279321\pi$
$761$	−9.56061	−	16.5595i	−0.346572	−	0.600280i	−0.985638	+	0.168872i	$0.945988\pi$
$762$	−2.12043	−	8.02952i	−0.0768150	−	0.290879i
$763$	−1.29882	+	0.749875i	−0.0470205	+	0.0271473i
$764$	0.704415	+	0.406694i	0.0254848	+	0.0147137i
$765$	0.749253	+	1.19586i	0.0270893	+	0.0432363i
$766$	10.5978	+	6.11865i	0.382915	+	0.221076i
$767$		−	10.1271i		−	0.365669i
$768$	−1.67140	−	0.454332i	−0.0603115	−	0.0163943i
$769$	−5.28795	−	9.15900i	−0.190688	−	0.330282i	0.754790	−	0.655966i	$-0.227739\pi$
$769$	−5.28795	−	9.15900i	−0.190688	−	0.330282i	−0.945479	+	0.325684i	$0.894405\pi$
$770$	−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
$780$	−10.7080	−	2.41788i	−0.383406	−	0.0865739i
$781$	−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
$786$	−8.81449	+	2.32772i	−0.314402	+	0.0830270i
$787$	−4.30542	−	7.45721i	−0.153472	−	0.265821i	0.779030	−	0.626987i	$-0.215712\pi$
$787$	−4.30542	−	7.45721i	−0.153472	−	0.265821i	−0.932501	+	0.361166i	$0.882379\pi$
$788$	4.90072	+	2.82943i	0.174581	+	0.100794i
$789$	−14.0025	+	51.5124i	−0.498501	+	1.83389i
$790$	−30.0510	−	15.6549i	−1.06917	−	0.556977i
$791$		−	7.19831i		−	0.255942i
$792$	−5.88838	+	3.34314i	−0.209235	+	0.118793i
$793$	−19.9892	−	11.5408i	−0.709839	−	0.409826i
$794$	17.6190	−	10.1723i	0.625274	−	0.361002i
$795$	−4.75684	+	21.0664i	−0.168708	+	0.747150i
$796$	7.20797	+	4.16152i	0.255480	+	0.147501i
$797$	0.466790	+	0.269502i	0.0165346	+	0.00954623i	0.508244	−	0.861213i	$-0.330295\pi$
$797$	0.466790	+	0.269502i	0.0165346	+	0.00954623i	−0.491710	+	0.870759i	$0.663628\pi$
$798$	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
$801$	22.3256	+	13.1058i	0.788835	+	0.463070i
$802$	−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	$-0.179693\pi$
$809$	−1.16363	−	2.01547i	−0.0409111	−	0.0708601i	−0.885756	+	0.464151i	$0.846359\pi$
$810$	9.55487	−	17.7117i	0.335724	−	0.622326i
$811$	−22.8583	+	39.5917i	−0.802664	+	1.39025i	0.115193	+	0.993343i	$0.463251\pi$
$811$	−22.8583	+	39.5917i	−0.802664	+	1.39025i	−0.917857	+	0.396911i	$0.870082\pi$
$812$	−1.24670	+	0.719784i	−0.0437507	+	0.0252595i
$813$	6.89661	−	25.3713i	0.241875	−	0.889812i
$814$	−18.6463			−0.653551
$815$	−22.6279	+	14.4061i	−0.792620	+	0.504624i
$816$	−0.352291	+	0.0930326i	−0.0123326	+	0.00325679i
$817$	0.0343541	−	0.0595030i	0.00120190	−	0.00208175i
$818$	−16.0037	+	9.23975i	−0.559557	+	0.323060i
$819$	13.6985	−	23.3353i	0.478665	−	0.815402i
$820$	−0.0762102	−	1.75747i	−0.00266138	−	0.0613736i
$821$	20.2881			0.708058			0.354029	−	0.935234i	$-0.384811\pi$
$821$	20.2881			0.708058			0.354029	+	0.935234i	$0.384811\pi$
$822$	−10.4576	−	10.5335i	−0.364752	−	0.367398i
$823$	12.2358	+	21.1931i	0.426514	+	0.738744i	0.996560	−	0.0828687i	$-0.0264082\pi$
$823$	12.2358	+	21.1931i	0.426514	+	0.738744i	−0.570047	+	0.821612i	$0.693075\pi$
$824$	−15.3713	−	8.87463i	−0.535485	−	0.309162i
$825$	−6.60807	−	18.3960i	−0.230064	−	0.640468i
$826$	−5.68494	+	9.84661i	−0.197805	+	0.342607i
$827$	−8.89168	−	5.13362i	−0.309194	−	0.178513i	0.337372	−	0.941372i	$-0.390462\pi$
$827$	−8.89168	−	5.13362i	−0.309194	−	0.178513i	−0.646566	+	0.762858i	$0.723795\pi$
$828$	−1.21508	+	2.06988i	−0.0422269	+	0.0719332i
$829$			33.8954i			1.17724i	0.808411	+	0.588618i	$0.200328\pi$
$829$			33.8954i			1.17724i	−0.808411	+	0.588618i	$0.799672\pi$
$830$	−1.30476	−	30.0888i	−0.0452887	−	1.04440i
$831$	37.8947	+	10.3008i	1.31455	+	0.357331i
$832$	1.41720	−	2.45465i	0.0491324	−	0.0850998i
$833$		−	0.657718i		−	0.0227886i
$834$	−7.18717	+	26.4402i	−0.248871	+	0.915550i
$835$	0.169475	+	0.0882873i	0.00586494	+	0.00305531i
$836$	0.0375079			0.00129724
$837$	−19.2803	+	21.5701i	−0.666425	+	0.745572i
$838$		−	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	$-0.208040\pi$
$840$	9.05407	+	8.36191i	0.312395	+	0.288513i
$841$	−28.7954			−0.992943
$842$	5.40623	−	9.36386i	0.186311	−	0.322700i
$843$	11.2071	−	41.2288i	0.385993	−	1.42000i
$844$	−11.0068	−	19.0643i	−0.378869	−	0.656221i
$845$	−5.13056	+	9.84858i	−0.176497	+	0.338801i
$846$	−20.8123	−	12.2174i	−0.715542	−	0.420044i
$847$	16.2751	+	9.39645i	0.559220	+	0.322866i
$848$	−4.82919	−	2.78814i	−0.165835	−	0.0957450i
$849$	−0.826554	+	3.04074i	−0.0283673	+	0.104358i
$850$	−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	$0.257335\pi$
$853$			42.2445i			1.44643i	−0.690625	+	0.723213i	$0.742665\pi$
$854$	12.9571	+	22.4423i	0.443381	+	0.767959i
$855$	−0.0944662	+	0.0591869i	−0.00323068	+	0.00202415i
$856$	9.24636	+	16.0152i	0.316034	+	0.547387i
$857$	−3.90938	+	6.77125i	−0.133542	+	0.231302i	−0.925040	−	0.379871i	$-0.875968\pi$
$857$	−3.90938	+	6.77125i	−0.133542	+	0.231302i	0.791498	+	0.611172i	$0.209302\pi$
$858$	−2.82919	−	10.7134i	−0.0965870	−	0.365750i
$859$	−25.4656	−	14.7026i	−0.868874	−	0.501645i	−0.00190018	−	0.999998i	$-0.500605\pi$
$859$	−25.4656	−	14.7026i	−0.868874	−	0.501645i	−0.866974	+	0.498353i	$0.833938\pi$
$860$	4.27140	−	8.19934i	0.145654	−	0.279595i
$861$	4.18430	+	1.13740i	0.142600	+	0.0387626i
$862$	33.7037	−	19.4588i	1.14795	−	0.662770i
$863$	−32.5614	−	18.7993i	−1.10840	−	0.639937i	−0.169988	−	0.985446i	$-0.554373\pi$
$863$	−32.5614	−	18.7993i	−1.10840	−	0.639937i	−0.938415	+	0.345509i	$0.887706\pi$
$864$	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
$870$	−0.520314	−	1.67301i	−0.0176403	−	0.0567205i
$871$	20.7333	−	11.9704i	0.702520	−	0.405600i
$872$	0.471291			0.0159599
$873$	−7.30353	+	12.4415i	−0.247187	+	0.421081i
$874$	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	0.927610	−	0.373551i	$-0.121860\pi$
$877$	31.6253	+	18.2589i	1.06791	+	0.616558i	0.140301	+	0.990109i	$0.455193\pi$
$878$	−0.307195	+	0.532078i	−0.0103673	+	0.0179567i
$879$	8.28354	+	31.3677i	0.279397	+	1.05800i
$880$	5.04224	−	0.218649i	0.169974	−	0.00737067i
$881$	−22.7281	+	39.3662i	−0.765729	+	1.32628i	0.174132	+	0.984722i	$0.444288\pi$
$881$	−22.7281	+	39.3662i	−0.765729	+	1.32628i	−0.939860	+	0.341559i	$0.889045\pi$
$882$	−8.15662	+	4.63093i	−0.274648	+	0.155932i
$883$	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
$885$	−10.1658	−	9.38862i	−0.341718	−	0.315595i
$886$	−3.88123	+	6.72249i	−0.130392	+	0.225846i
$887$	−7.67225	−	13.2887i	−0.257609	−	0.446192i	0.707992	−	0.706221i	$-0.249601\pi$
$887$	−7.67225	−	13.2887i	−0.257609	−	0.446192i	−0.965601	+	0.260029i	$0.916268\pi$
$888$	3.65343	+	13.8346i	0.122601	+	0.464259i
$889$	−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
$894$	7.26911	−	1.91962i	0.243116	−	0.0642017i
$895$	−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
$900$	−12.3542	+	8.50727i	−0.411807	+	0.283576i
$901$	−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
$906$	1.78456	−	6.56506i	0.0592880	−	0.218109i
$907$			28.7022i			0.953040i	0.879164	+	0.476520i	$0.158102\pi$
$907$			28.7022i			0.953040i	−0.879164	+	0.476520i	$0.841898\pi$
$908$	−10.5803	+	18.3257i	−0.351121	+	0.608159i
$909$	−16.5925	+	28.2653i	−0.550340	+	0.937500i
$910$	−17.0132	+	10.8315i	−0.563982	+	0.359061i
$911$	−5.26971	−	9.12741i	−0.174593	−	0.302405i	0.765427	−	0.643523i	$-0.222528\pi$
$911$	−5.26971	−	9.12741i	−0.174593	−	0.302405i	−0.940020	+	0.341118i	$0.889194\pi$
$912$	−0.00734906	−	0.0278290i	−0.000243352	−	0.000921511i
$913$	26.3272	−	15.2000i	0.871304	−	0.503048i
$914$	9.40285			0.311019
$915$	−30.1164	+	9.36632i	−0.995618	+	0.309641i
$916$	−22.6961	+	13.1036i	−0.749900	+	0.432955i
$917$	−8.37481	+	14.5056i	−0.276561	+	0.479017i
$918$	1.05273	+	0.294348i	0.0347452	+	0.00971493i
$919$	−13.8145	+	23.9274i	−0.455698	+	0.789291i	−0.998728	−	0.0504216i	$-0.983944\pi$
$919$	−13.8145	+	23.9274i	−0.455698	+	0.789291i	0.543030	+	0.839713i	$0.317277\pi$
$920$	1.50910	−	0.960770i	0.0497534	−	0.0316757i
$921$	−0.398515	+	0.105239i	−0.0131315	+	0.00346776i
$922$	−26.2525			−0.864580
$923$	−36.9585	+	21.3380i	−1.21650	+	0.702348i
$924$	−3.26325	+	12.0049i	−0.107353	+	0.394931i
$925$	−41.1511	+	3.57564i	−1.35304	+	0.117566i
$926$	8.83708			0.290405
$927$	26.2899	+	46.3052i	0.863472	+	1.52086i
$928$	0.452379			0.0148501
$929$	−38.5774			−1.26568			−0.632842	−	0.774281i	$-0.718112\pi$
$929$	−38.5774			−1.26568			−0.632842	+	0.774281i	$0.718112\pi$
$930$	20.1173	−	7.76484i	0.659674	−	0.254619i
$931$	0.0519561			0.00170279
$932$	3.39689			0.111269
$933$	4.03042	−	14.8272i	0.131950	−	0.485419i
$934$	−0.199102			−0.00651481
$935$	0.895617	−	0.570197i	0.0292898	−	0.0186474i
$936$	−7.39450	+	4.19824i	−0.241697	+	0.137224i
$937$	25.5568	−	14.7552i	0.834905	−	0.482032i	−0.0206244	−	0.999787i	$-0.506565\pi$
$937$	25.5568	−	14.7552i	0.834905	−	0.482032i	0.855529	+	0.517755i	$0.173232\pi$
$938$	−26.8787			−0.877620
$939$	9.80157	+	37.1161i	0.319862	+	1.21124i
$940$	9.66040	+	15.1737i	0.315087	+	0.494912i
$941$	2.51403	−	4.35444i	0.0819552	−	0.141951i	−0.822135	−	0.569293i	$-0.807217\pi$
$941$	2.51403	−	4.35444i	0.0819552	−	0.141951i	0.904090	+	0.427343i	$0.140550\pi$
$942$	−2.64556	+	9.73250i	−0.0861969	+	0.317102i
$943$	0.314704	−	0.545083i	0.0102482	−	0.0177503i
$944$	3.09426	−	1.78647i	0.100710	−	0.0581447i
$945$	−10.7248	−	35.3844i	−0.348878	−	1.15106i
$946$	9.33209			0.303413
$947$	−0.353723	+	0.204222i	−0.0114945	+	0.00663633i	−0.505736	−	0.862688i	$-0.668779\pi$
$947$	−0.353723	+	0.204222i	−0.0114945	+	0.00663633i	0.494242	+	0.869324i	$0.335446\pi$
$948$	−25.3767	+	6.70145i	−0.824196	+	0.217653i
$949$	−12.6278	−	21.8720i	−0.409916	−	0.709996i
$950$	0.0827776	−	0.00719258i	0.00268566	−	0.000233358i
$951$	−0.769327	−	2.91324i	−0.0249471	−	0.0944684i
$952$	−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	$0.891025\pi$
$954$	8.25946	+	14.5477i	0.267410	+	0.470998i
$955$	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
$960$	−1.15017	−	3.69826i	−0.0371217	−	0.119361i
$961$	−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
$966$	1.12592	+	4.26356i	0.0362258	+	0.137178i
$967$	8.27261	+	14.3286i	0.266029	+	0.460776i	0.967833	−	0.251595i	$-0.0809549\pi$
$967$	8.27261	+	14.3286i	0.266029	+	0.460776i	−0.701804	+	0.712370i	$0.747622\pi$
$968$	−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	$-0.518401\pi$
$971$	−29.6416	−	17.1136i	−0.951245	−	0.549202i	−0.893468	+	0.449128i	$0.851735\pi$
$972$	−3.76183	−	15.1277i	−0.120661	−	0.485223i
$973$	25.1701	+	43.5959i	0.806916	+	1.39762i
$974$	−4.86941	+	8.43407i	−0.156026	+	0.270245i
$975$	−8.29827	−	23.1013i	−0.265757	−	0.739835i
$976$		−	8.14341i		−	0.260664i
$977$	12.5953			0.402958			0.201479	−	0.979493i	$-0.435425\pi$
$977$	12.5953			0.402958			0.201479	+	0.979493i	$0.435425\pi$
$978$	−5.45030	+	20.0506i	−0.174282	+	0.641149i
$979$	9.73857	−	16.8677i	0.311246	−	0.539094i
$980$	6.98454	−	0.302874i	0.223113	−	0.00967496i
$981$	−1.21931	−	0.715769i	−0.0389295	−	0.0228528i
$982$	−1.53335	+	2.65584i	−0.0489312	+	0.0847513i
$983$	41.4664	+	23.9406i	1.32257	+	0.763588i	0.984138	−	0.177402i	$-0.0567694\pi$
$983$	41.4664	+	23.9406i	1.32257	+	0.763588i	0.338434	+	0.940990i	$0.390103\pi$
$984$	−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
$987$	−42.8695	+	11.3209i	−1.36455	+	0.360349i
$988$	0.0471016			0.00149850
$989$	2.86473	−	1.65395i	0.0910930	−	0.0525926i
$990$	−13.3772	−	7.09218i	−0.425155	−	0.225404i
$991$			30.8609i			0.980330i	0.871630	+	0.490165i	$0.163063\pi$
$991$			30.8609i			0.980330i	−0.871630	+	0.490165i	$0.836937\pi$
$992$	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	0.872542	−	0.488539i	$-0.162470\pi$
$997$	27.9670	+	16.1468i	0.885725	+	0.511374i	0.0131834	+	0.999913i	$0.495803\pi$
$998$	−11.3529	+	6.55458i	−0.359368	+	0.207481i
$999$	11.5592	−	41.3411i	0.365716	−	1.30797i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.2	✓	64	465.119	even	6	inner
930.2.r.a.119.14	yes	64	31.26	odd	6	inner
930.2.r.a.719.2	yes	64	1.1	even	1	trivial
930.2.r.a.719.14	yes	64	15.14	odd	2	inner
930.2.r.b.119.19	yes	64	155.119	odd	6
930.2.r.b.119.31	yes	64	93.26	even	6
930.2.r.b.719.19	yes	64	3.2	odd	2
930.2.r.b.719.31	yes	64	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.67140 - 0.454332i) q^{3} +1.00000 q^{4} +(1.20088 + 1.88624i) q^{5} +(1.67140 + 0.454332i) q^{6} +(2.75588 - 1.59111i) q^{7} -1.00000 q^{8} +(2.58717 + 1.51874i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.67140 - 0.454332i) q^{3} +1.00000 q^{4} +(1.20088 + 1.88624i) q^{5} +(1.67140 + 0.454332i) q^{6} +(2.75588 - 1.59111i) q^{7} -1.00000 q^{8} +(2.58717 + 1.51874i) q^{9} +(-1.20088 - 1.88624i) q^{10} +(1.12854 - 1.95469i) q^{11} +(-1.67140 - 0.454332i) q^{12} +(1.41720 - 2.45465i) q^{13} +(-2.75588 + 1.59111i) q^{14} +(-1.15017 - 3.69826i) q^{15} +1.00000 q^{16} +(0.182184 - 0.105184i) q^{17} +(-2.58717 - 1.51874i) q^{18} +(0.00830895 + 0.0143915i) q^{19} +(1.20088 + 1.88624i) q^{20} +(-5.32908 + 1.40730i) q^{21} +(-1.12854 + 1.95469i) q^{22} +0.800056i q^{23} +(1.67140 + 0.454332i) 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} +(1.15017 + 3.69826i) 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} +(2.58717 + 1.51874i) 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} +(5.32908 - 1.40730i) q^{42} +(-2.06729 - 3.58066i) q^{43} +(1.12854 - 1.95469i) q^{44} +(0.242164 + 6.70383i) q^{45} -0.800056i q^{46} +8.04444 q^{47} +(-1.67140 - 0.454332i) q^{48} +(1.56326 - 2.70764i) q^{49} +(2.11578 - 4.53028i) q^{50} +(-0.352291 + 0.0930326i) 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} +(-0.00734906 - 0.0278290i) q^{57} +0.452379 q^{58} +(3.09426 - 1.78647i) q^{59} +(-1.15017 - 3.69826i) 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} +(0.363491 - 1.33721i) q^{69} +(-6.31069 - 3.28752i) q^{70} +(-13.0393 - 7.52824i) q^{71} +(-2.58717 - 1.51874i) q^{72} +(4.45521 - 7.71666i) q^{73} +(-4.13062 - 7.15444i) q^{74} +(5.59457 - 6.61066i) 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} +(4.38685 + 7.85847i) q^{81} +(0.681306 + 0.393352i) q^{82} +(11.6643 + 6.73438i) q^{83} +(-5.32908 + 1.40730i) q^{84} +(0.417182 + 0.217329i) q^{85} +(2.06729 + 3.58066i) q^{86} +(0.756107 + 0.205530i) q^{87} +(-1.12854 + 1.95469i) q^{88} +8.62936 q^{89} +(-0.242164 - 6.70383i) q^{90} -9.01965i q^{91} +0.800056i q^{92} +(-1.90243 + 9.45414i) q^{93} -8.04444 q^{94} +(-0.0171678 + 0.0329551i) q^{95} +(1.67140 + 0.454332i) q^{96} +4.80894i q^{97} +(-1.56326 + 2.70764i) q^{98} +(5.88838 - 3.34314i) 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	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) \) 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 + 5 * 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 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more