LMFDB - Embedded newform 930.2.r.b.719.31

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			719.31
Character	$\chi$	$=$	930.719
Dual form			930.2.r.b.119.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.67140 + 0.454332i) q^{3} +1.00000 q^{4} +(2.23397 + 0.0968727i) q^{5} +(1.67140 + 0.454332i) q^{6} +(-2.75588 + 1.59111i) q^{7} +1.00000 q^{8} +(2.58717 + 1.51874i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.67140 + 0.454332i) q^{3} +1.00000 q^{4} +(2.23397 + 0.0968727i) q^{5} +(1.67140 + 0.454332i) q^{6} +(-2.75588 + 1.59111i) q^{7} +1.00000 q^{8} +(2.58717 + 1.51874i) q^{9} +(2.23397 + 0.0968727i) 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} +(3.68985 + 1.17688i) q^{15} +1.00000 q^{16} +(-0.182184 + 0.105184i) q^{17} +(2.58717 + 1.51874i) q^{18} +(0.00830895 + 0.0143915i) q^{19} +(2.23397 + 0.0968727i) q^{20} +(-5.32908 + 1.40730i) q^{21} +(1.12854 - 1.95469i) q^{22} -0.800056i q^{23} +(1.67140 + 0.454332i) q^{24} +(4.98123 + 0.432821i) 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} +(2.58717 + 1.51874i) q^{36} +(-4.13062 - 7.15444i) q^{37} +(0.00830895 + 0.0143915i) q^{38} +(-3.48393 + 3.45884i) q^{39} +(2.23397 + 0.0968727i) 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} +(5.63252 + 3.64345i) q^{45} -0.800056i q^{46} -8.04444 q^{47} +(1.67140 + 0.454332i) q^{48} +(1.56326 - 2.70764i) q^{49} +(4.98123 + 0.432821i) 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} +(2.71048 - 4.25739i) q^{55} +(-2.75588 + 1.59111i) q^{56} +(0.00734906 + 0.0278290i) 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} +(-3.40376 + 5.34633i) 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} +(8.12899 + 2.98655i) q^{75} +(0.00830895 + 0.0143915i) q^{76} +7.18252i q^{77} +(-3.48393 + 3.45884i) q^{78} +(13.1233 - 7.57675i) q^{79} +(2.23397 + 0.0968727i) 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} +(5.63252 + 3.64345i) 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} + 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

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
$5$	2.23397	+	0.0968727i	0.999061	+	0.0433228i
$5$	2.23397	+	0.0968727i	0.999061	+	0.0433228i
$6$	1.67140	+	0.454332i	0.682347	+	0.185480i
$7$	−2.75588	+	1.59111i	−1.04163	+	0.601383i	−0.920293	−	0.391229i	$-0.872050\pi$
$7$	−2.75588	+	1.59111i	−1.04163	+	0.601383i	−0.121332	+	0.992612i	$0.538717\pi$
$8$	1.00000			0.353553
$9$	2.58717	+	1.51874i	0.862388	+	0.506247i
$10$	2.23397	+	0.0968727i	0.706443	+	0.0306338i
$11$	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	−0.992851	−	0.119357i	$-0.961917\pi$
$13$	−1.41720	+	2.45465i	−0.393059	+	0.680799i	0.599792	+	0.800156i	$0.295250\pi$
$14$	−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	−0.521930	−	0.852988i	$-0.674788\pi$
$17$	−0.182184	+	0.105184i	−0.0441861	+	0.0255108i	0.477744	+	0.878499i	$0.341455\pi$
$18$	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	$0.832727\pi$
$20$	2.23397	+	0.0968727i	0.499531	+	0.0216614i
$21$	−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	$-0.973418\pi$
$23$		−	0.800056i		−	0.166823i	0.996515	−	0.0834116i	$-0.0265816\pi$
$24$	1.67140	+	0.454332i	0.341173	+	0.0927401i
$25$	4.98123	+	0.432821i	0.996246	+	0.0865642i
$26$	−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	$0.513374\pi$
$30$	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
$36$	2.58717	+	1.51874i	0.431194	+	0.253124i
$37$	−4.13062	−	7.15444i	−0.679070	−	1.17618i	−0.975261	−	0.221055i	$-0.929050\pi$
$37$	−4.13062	−	7.15444i	−0.679070	−	1.17618i	0.296192	−	0.955128i	$-0.404283\pi$
$38$	0.00830895	+	0.0143915i	0.00134789	+	0.00233461i
$39$	−3.48393	+	3.45884i	−0.557875	+	0.553857i
$40$	2.23397	+	0.0968727i	0.353221	+	0.0153169i
$41$	−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	0.979493	−	0.201480i	$-0.0645751\pi$
$43$	2.06729	+	3.58066i	0.315259	+	0.546045i	−0.664233	+	0.747525i	$0.731242\pi$
$44$	1.12854	−	1.95469i	0.170134	−	0.294680i
$45$	5.63252	+	3.64345i	0.839647	+	0.543133i
$46$		−	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	$0.699574\pi$
$48$	1.67140	+	0.454332i	0.241246	+	0.0655772i
$49$	1.56326	−	2.70764i	0.223323	−	0.386806i
$50$	4.98123	+	0.432821i	0.704452	+	0.0612102i
$51$	−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	0.793549	−	0.608507i	$-0.208231\pi$
$53$	4.82919	+	2.78814i	0.663341	+	0.382980i	−0.130208	+	0.991487i	$0.541564\pi$
$54$	3.63418	+	3.71386i	0.494549	+	0.505392i
$55$	2.71048	−	4.25739i	0.365481	−	0.574066i
$56$	−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	$0.258617\pi$
$60$	3.68985	+	1.17688i	0.476357	+	0.151934i
$61$		−	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
$65$	−3.40376	+	5.34633i	−0.422184	+	0.663131i
$66$	2.77432	−	2.75434i	0.341495	−	0.339035i
$67$	−7.31490	−	4.22326i	−0.893657	−	0.515953i	−0.0185202	−	0.999828i	$-0.505896\pi$
$67$	−7.31490	−	4.22326i	−0.893657	−	0.515953i	−0.875137	+	0.483875i	$0.839229\pi$
$68$	−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	$0.341273\pi$
$73$	−4.45521	+	7.71666i	−0.521443	+	0.903166i	−0.999689	+	0.0249402i	$0.992060\pi$
$74$	−4.13062	−	7.15444i	−0.480175	−	0.831687i
$75$	8.12899	+	2.98655i	0.938655	+	0.344857i
$76$	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	$0.00844866\pi$
$80$	2.23397	+	0.0968727i	0.249765	+	0.0108307i
$81$	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	−0.303416	−	0.952858i	$-0.598127\pi$
$83$	−11.6643	−	6.73438i	−1.28032	−	0.739195i	−0.976907	+	0.213664i	$0.931460\pi$
$84$	−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	$0.348797\pi$
$90$	5.63252	+	3.64345i	0.593720	+	0.384053i
$91$		−	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	$-0.921495\pi$
$97$		−	4.80894i		−	0.488273i	0.969741	−	0.244137i	$-0.0785046\pi$
$98$	1.56326	−	2.70764i	0.157913	−	0.273513i
$99$	5.88838	−	3.34314i	0.591805	−	0.335998i
$100$	4.98123	+	0.432821i	0.498123	+	0.0432821i
$101$			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	$-0.994560\pi$
$103$	−15.3713	−	8.87463i	−1.51458	−	0.874444i	−0.514727	−	0.857354i	$-0.672107\pi$
$104$	−1.41720	+	2.45465i	−0.138967	+	0.240699i
$105$	−12.0413	+	2.62762i	−1.17511	+	0.256429i
$106$	4.82919	+	2.78814i	0.469053	+	0.270808i
$107$	9.24636	+	16.0152i	0.893880	+	1.54825i	0.835185	+	0.549969i	$0.185361\pi$
$107$	9.24636	+	16.0152i	0.893880	+	1.54825i	0.0586947	+	0.998276i	$0.481306\pi$
$108$	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	$0.507185\pi$
$110$	2.71048	−	4.25739i	0.258434	−	0.405926i
$111$	−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	−0.914308	−	0.405019i	$-0.867265\pi$
$113$	−1.13102	+	1.95898i	−0.106397	+	0.184286i	0.807911	+	0.589305i	$0.200598\pi$
$114$	0.00734906	+	0.0278290i	0.000688303	+	0.00260643i
$115$	0.0775036	−	1.78730i	0.00722725	−	0.166667i
$116$	−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
$120$	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	$-0.0984301\pi$
$127$	2.39738	+	4.15239i	0.212733	+	0.368465i	−0.739836	+	0.672788i	$0.765097\pi$
$128$	1.00000			0.0883883
$129$	1.82847	+	6.92396i	0.160988	+	0.609620i
$130$	−3.40376	+	5.34633i	−0.298529	+	0.468904i
$131$	−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
$135$	7.75887	+	8.64870i	0.667777	+	0.744361i
$136$	−0.182184	+	0.105184i	−0.0156221	+	0.00901944i
$137$	7.42153	+	4.28482i	0.634064	+	0.366077i	0.782324	−	0.622871i	$-0.214034\pi$
$137$	7.42153	+	4.28482i	0.634064	+	0.366077i	−0.148260	+	0.988948i	$0.547367\pi$
$138$	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
$145$	−1.01060	−	0.0438232i	−0.0839258	−	0.00363932i
$146$	−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	$0.276435\pi$
$150$	8.12899	+	2.98655i	0.663729	+	0.243851i
$151$		−	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
$155$	−0.292572	−	12.4465i	−0.0235000	−	0.999724i
$156$	−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
$160$	2.23397	+	0.0968727i	0.176611	+	0.00765846i
$161$	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	$-0.844322\pi$
$163$		−	11.9963i		−	0.939623i	0.882767	−	0.469812i	$-0.155678\pi$
$164$	−0.681306	−	0.393352i	−0.0532011	−	0.0307157i
$165$	6.46456	−	5.88435i	0.503266	−	0.458096i
$166$	−11.6643	−	6.73438i	−0.905325	−	0.522690i
$167$	−0.0740101	+	0.0427297i	−0.00572707	+	0.00330653i	−0.502861	−	0.864367i	$-0.667719\pi$
$167$	−0.0740101	+	0.0427297i	−0.00572707	+	0.00330653i	0.497134	+	0.867674i	$0.334386\pi$
$168$	−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	−0.500530	−	0.865719i	$-0.666862\pi$
$173$	6.56949	−	11.3787i	0.499469	−	0.865106i	1.00000		0.000612653i	$0.000195014\pi$
$174$	−0.756107	−	0.205530i	−0.0573203	−	0.0155812i
$175$	−14.4164	+	6.73288i	−1.08977	+	0.508958i
$176$	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	$0.784308\pi$
$180$	5.63252	+	3.64345i	0.419823	+	0.271567i
$181$	−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	−0.912183	−	0.409782i	$-0.865605\pi$
$193$	−14.0785	+	8.12823i	−1.01339	+	0.585083i	−0.101210	+	0.994865i	$0.532271\pi$
$194$		−	4.80894i		−	0.345261i
$195$	−8.11806	+	7.38943i	−0.581346	+	0.529168i
$196$	1.56326	−	2.70764i	0.111661	−	0.193403i
$197$	−4.90072	−	2.82943i	−0.349162	−	0.201589i	0.315154	−	0.949040i	$-0.397944\pi$
$197$	−4.90072	−	2.82943i	−0.349162	−	0.201589i	−0.664316	+	0.747452i	$0.731277\pi$
$198$	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	$0.571346\pi$
$200$	4.98123	+	0.432821i	0.352226	+	0.0306051i
$201$	−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
$205$	−1.48391	−	0.944737i	−0.103641	−	0.0659833i
$206$	−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
$210$	−12.0413	+	2.62762i	−0.830930	+	0.181323i
$211$	−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
$220$	2.71048	−	4.25739i	0.182740	−	0.287033i
$221$		−	0.596264i		−	0.0401091i
$222$	−3.65343	−	13.8346i	−0.245202	−	0.928519i
$223$	−5.80910	−	10.0617i	−0.389006	−	0.673778i	0.603310	−	0.797507i	$-0.293848\pi$
$223$	−5.80910	−	10.0617i	−0.389006	−	0.673778i	−0.992316	+	0.123729i	$0.960515\pi$
$224$	−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	−0.265436	−	0.964129i	$-0.585516\pi$
$227$	10.5803	−	18.3257i	0.702242	−	1.21632i	0.967678	−	0.252190i	$-0.0811509\pi$
$228$	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	$0.666593\pi$
$230$	0.0775036	−	1.78730i	0.00511044	−	0.117851i
$231$	−3.26325	+	12.0049i	−0.214706	+	0.789863i
$232$	−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	$0.535491\pi$
$234$	−7.39450	+	4.19824i	−0.483394	+	0.274448i
$235$	−17.9710	−	0.779287i	−1.17230	−	0.0508351i
$236$	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	$0.0534792\pi$
$240$	3.68985	+	1.17688i	0.238179	+	0.0759670i
$241$	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
$245$	3.75457	−	5.89735i	0.239870	−	0.376768i
$246$	−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
$255$	−0.796019	+	0.173704i	−0.0498486	+	0.0108778i
$256$	1.00000			0.0625000
$257$	−8.48270	+	14.6925i	−0.529136	+	0.916491i	0.470286	+	0.882514i	$0.344151\pi$
$257$	−8.48270	+	14.6925i	−0.529136	+	0.916491i	−0.999423	+	0.0339770i	$0.989183\pi$
$258$	1.82847	+	6.92396i	0.113836	+	0.431067i
$259$	22.7670	+	13.1445i	1.41467	+	0.816762i
$260$	−3.40376	+	5.34633i	−0.211092	+	0.331565i
$261$	−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	$0.399140\pi$
$263$			30.8199i			1.90044i	−0.311586	+	0.950218i	$0.600860\pi$
$264$	2.77432	−	2.75434i	0.170748	−	0.169518i
$265$	10.5182	+	6.69643i	0.646126	+	0.411358i
$266$	−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	$0.123877\pi$
$270$	7.75887	+	8.64870i	0.472190	+	0.526343i
$271$			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	$-0.261490\pi$
$277$	22.6724			1.36225			0.681127	+	0.732165i	$0.261490\pi$
$278$			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	$0.0172201\pi$
$283$			1.81927i			0.108145i	−0.998537	+	0.0540723i	$0.982780\pi$
$284$	−13.0393	−	7.52824i	−0.773740	−	0.446719i
$285$	0.0137217	+	0.0628811i	0.000812804	+	0.00372476i
$286$	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
$290$	−1.01060	−	0.0438232i	−0.0593445	−	0.00257339i
$291$	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	$0.0176157\pi$
$293$	9.36548	+	16.2215i	0.547137	+	0.947669i	−0.451332	+	0.892356i	$0.649051\pi$
$294$	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
$300$	8.12899	+	2.98655i	0.469328	+	0.172429i
$301$	−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
$305$	0.788874	−	18.1921i	0.0451708	−	1.04168i
$306$	−0.631087	−	0.00456213i	−0.0360768	−	0.000260799i
$307$	−0.206088	+	0.118985i	−0.0117621	+	0.00679084i	−0.505870	−	0.862610i	$-0.668828\pi$
$307$	−0.206088	+	0.118985i	−0.0117621	+	0.00679084i	0.494107	+	0.869401i	$0.335495\pi$
$308$			7.18252i			0.409262i
$309$	−21.6596	−	21.8168i	−1.23217	−	1.24111i
$310$	−0.292572	−	12.4465i	−0.0166170	−	0.706912i
$311$			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	$0.0487975\pi$
$313$	11.0818	+	19.1942i	0.626380	+	1.08492i	−0.361892	+	0.932220i	$0.617869\pi$
$314$		−	5.82296i		−	0.328609i
$315$	−21.3197	−	1.07895i	−1.20123	−	0.0607922i
$316$	13.1233	−	7.57675i	0.738244	−	0.426225i
$317$	−0.869811	−	1.50656i	−0.0488535	−	0.0846167i	0.840565	−	0.541711i	$-0.182223\pi$
$317$	−0.869811	−	1.50656i	−0.0488535	−	0.0846167i	−0.889418	+	0.457095i	$0.848890\pi$
$318$	6.80478	+	6.85415i	0.381593	+	0.384362i
$319$	−0.510527	+	0.884260i	−0.0285841	+	0.0495090i
$320$	2.23397	+	0.0968727i	0.124883	+	0.00541535i
$321$	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
$330$	6.46456	−	5.88435i	0.355862	−	0.323923i
$331$	−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
$335$	−15.9321	−	10.1432i	−0.870466	−	0.554185i
$336$	−5.32908	+	1.40730i	−0.290725	+	0.0767744i
$337$	−1.69991			−0.0926000			−0.0463000	−	0.998928i	$-0.514743\pi$
$337$	−1.69991			−0.0926000			−0.0463000	+	0.998928i	$0.514743\pi$
$338$	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	−0.933644	−	0.358203i	$-0.883389\pi$
$347$	−20.3091	+	11.7255i	−1.09025	+	0.629457i	−0.156609	+	0.987661i	$0.550056\pi$
$348$	−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	$0.654829\pi$
$350$	−14.4164	+	6.73288i	−0.770586	+	0.359888i
$351$	−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	0.413124	−	0.910675i	$-0.364437\pi$
$353$	26.4606	−	15.2770i	1.40835	−	0.813114i	0.995230	+	0.0975610i	$0.0311041\pi$
$354$	5.98340	−	1.58009i	0.318014	−	0.0839809i
$355$	−28.4001	−	18.0810i	−1.50732	−	0.959640i
$356$	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	$0.378762\pi$
$360$	5.63252	+	3.64345i	0.296860	+	0.192027i
$361$	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
$365$	−10.7003	+	16.8072i	−0.560081	+	0.879728i
$366$	3.69981	−	13.6109i	0.193392	−	0.711453i
$367$	14.4856	−	25.0897i	0.756140	−	1.30967i	−0.188666	−	0.982041i	$-0.560416\pi$
$367$	14.4856	−	25.0897i	0.756140	−	1.30967i	0.944806	−	0.327631i	$-0.106250\pi$
$368$		−	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	$0.0243570\pi$
$373$			2.95280i			0.152890i	−0.997074	+	0.0764451i	$0.975643\pi$
$374$			0.474817i			0.0245522i
$375$	17.8706	+	7.45934i	0.922834	+	0.385198i
$376$	−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	0.745696	−	0.666286i	$-0.232117\pi$
$383$	10.5978	+	6.11865i	0.541523	+	0.312649i	−0.204173	+	0.978935i	$0.565450\pi$
$384$	1.67140	+	0.454332i	0.0852933	+	0.0231850i
$385$	−0.695790	+	16.0455i	−0.0354607	+	0.817756i
$386$	−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	$0.555324\pi$
$390$	−8.11806	+	7.38943i	−0.411074	+	0.374178i
$391$	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	0.0122063	−	0.999926i	$-0.496115\pi$
$397$	17.6190	−	10.1723i	0.884270	−	0.510534i	0.872064	+	0.489392i	$0.162781\pi$
$398$	7.20797	+	4.16152i	0.361303	+	0.208598i
$399$	−0.0645322	−	0.0650004i	−0.00323065	−	0.00325409i
$400$	4.98123	+	0.432821i	0.249062	+	0.0216411i
$401$	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
$405$	9.03881	+	17.9805i	0.449142	+	0.893460i
$406$	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	$0.182302\pi$
$410$	−1.48391	−	0.944737i	−0.0732852	−	0.0466572i
$411$	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
$415$	−25.4053	−	16.1744i	−1.24710	−	0.793968i
$416$	−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	$0.953888\pi$
$420$	−12.0413	+	2.62762i	−0.587556	+	0.128215i
$421$	−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
$425$	−0.953026	+	0.445092i	−0.0462285	+	0.0215901i
$426$	−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	$-0.415565\pi$
$433$	10.9104			0.524320			0.262160	+	0.965024i	$0.415565\pi$
$434$	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	−0.858602	−	0.512644i	$-0.828666\pi$
$439$	0.307195	−	0.532078i	0.0146616	−	0.0253947i	0.873263	+	0.487249i	$0.162000\pi$
$440$	2.71048	−	4.25739i	0.129217	−	0.202963i
$441$	8.15662	−	4.63093i	0.388410	−	0.220521i
$442$		−	0.596264i		−	0.0283614i
$443$	−3.88123	+	6.72249i	−0.184403	+	0.319395i	−0.943375	−	0.331728i	$-0.892368\pi$
$443$	−3.88123	+	6.72249i	−0.184403	+	0.319395i	0.758972	+	0.651123i	$0.225702\pi$
$444$	−3.65343	−	13.8346i	−0.173384	−	0.656562i
$445$	19.2777	+	0.835949i	0.913851	+	0.0396278i
$446$	−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	$0.382834\pi$
$450$	12.2299	+	8.68498i	0.576524	+	0.409414i
$451$	−1.53776	+	0.887827i	−0.0724104	+	0.0418062i
$452$	−1.13102	+	1.95898i	−0.0531987	+	0.0921429i
$453$	1.78456	−	6.56506i	0.0838459	−	0.308453i
$454$	10.5803	−	18.3257i	0.496560	−	0.860067i
$455$	0.873758	−	20.1496i	0.0409624	−	0.944629i
$456$	0.00734906	+	0.0278290i	0.000344151	+	0.00130321i
$457$	9.40285			0.439847			0.219923	−	0.975517i	$-0.429419\pi$
$457$	9.40285			0.439847			0.219923	+	0.975517i	$0.429419\pi$
$458$	−22.6961	+	13.1036i	−1.06052	+	0.612290i
$459$	−1.05273	−	0.294348i	−0.0491371	−	0.0137390i
$460$	0.0775036	−	1.78730i	0.00361362	−	0.0833333i
$461$	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	$-0.434168\pi$
$463$	8.83708			0.410694			0.205347	+	0.978689i	$0.434168\pi$
$464$	−0.452379			−0.0210012
$465$	5.16582	−	20.9360i	0.239559	−	0.970882i
$466$	−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	$0.501466\pi$
$468$	−7.39450	+	4.19824i	−0.341811	+	0.194064i
$469$	26.8787			1.24114
$470$	−17.9710	−	0.779287i	−0.828942	−	0.0359458i
$471$	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
$475$	0.0351598	+	0.0752838i	0.00161324	+	0.00345426i
$476$	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	$0.596291\pi$
$480$	3.68985	+	1.17688i	0.168418	+	0.0537168i
$481$	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
$485$	0.465855	−	10.7430i	0.0211534	−	0.487815i
$486$	3.76183	+	15.1277i	0.170640	+	0.686208i
$487$	−4.86941	+	8.43407i	−0.220654	+	0.382184i	−0.955007	−	0.296584i	$-0.904153\pi$
$487$	−4.86941	+	8.43407i	−0.220654	+	0.382184i	0.734353	+	0.678768i	$0.237486\pi$
$488$		−	8.14341i		−	0.368635i
$489$	5.45030	−	20.0506i	0.246471	−	0.906721i
$490$	3.75457	−	5.89735i	0.169614	−	0.266415i
$491$	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
$495$	13.4783	−	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	−0.223879	−	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	$0.146455\pi$
$503$	18.6722	+	32.3413i	0.832554	+	1.44203i	−0.0634527	+	0.997985i	$0.520211\pi$
$504$	−9.54641	−	0.0690110i	−0.425231	−	0.00307399i
$505$	−1.05835	+	24.4065i	−0.0470961	+	1.08608i
$506$	−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	$0.955119\pi$
$510$	−0.796019	+	0.173704i	−0.0352483	+	0.00769176i
$511$		−	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
$515$	−33.4793	−	21.3147i	−1.47528	−	0.939238i
$516$	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
$520$	−3.40376	+	5.34633i	−0.149265	+	0.234452i
$521$	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	$-0.258495\pi$
$523$	31.4674			1.37597			0.687987	+	0.725723i	$0.258495\pi$
$524$	−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
$530$	10.5182	+	6.69643i	0.456880	+	0.290874i
$531$	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
$540$	7.75887	+	8.64870i	0.333889	+	0.372181i
$541$	−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
$545$	−1.05285	−	0.0456552i	−0.0450991	−	0.00195566i
$546$	4.09791	−	15.0755i	0.175375	−	0.645170i
$547$	27.5845	+	15.9259i	1.17943	+	0.680943i	0.955882	−	0.293751i	$-0.0949036\pi$
$547$	27.5845	+	15.9259i	1.17943	+	0.680943i	0.223545	+	0.974694i	$0.428237\pi$
$548$	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
$555$	−6.82145	−	31.2600i	−0.289555	−	1.32691i
$556$			15.8192i			0.670884i
$557$			26.5057i			1.12308i	0.827449	+	0.561541i	$0.189791\pi$
$557$			26.5057i			1.12308i	−0.827449	+	0.561541i	$0.810209\pi$
$558$	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	$-0.591217\pi$
$563$	16.3573	−	28.3317i	0.689379	−	1.19404i	0.972039	−	0.234819i	$-0.0754496\pi$
$564$	−13.4455	−	3.65485i	−0.566157	−	0.153897i
$565$	−2.71644	+	4.26674i	−0.114281	+	0.179503i
$566$			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	$0.325071\pi$
$570$	0.0137217	+	0.0628811i	0.000574739	+	0.00263380i
$571$	−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
$575$	0.346281	−	3.98526i	0.0144409	−	0.166197i
$576$	2.58717	+	1.51874i	0.107799	+	0.0632809i
$577$	12.6544	−	7.30604i	0.526811	−	0.304154i	−0.212906	−	0.977073i	$-0.568293\pi$
$577$	12.6544	−	7.30604i	0.526811	−	0.304154i	0.739717	+	0.672918i	$0.234959\pi$
$578$	−8.47787	+	14.6841i	−0.352633	+	0.610778i
$579$	−27.2237	+	7.18922i	−1.13138	+	0.298774i
$580$	−1.01060	−	0.0438232i	−0.0419629	−	0.00181966i
$581$	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
$585$	−16.9258	+	8.66242i	−0.699795	+	0.358147i
$586$	9.36548	+	16.2215i	0.386884	+	0.670103i
$587$			6.32226i			0.260948i	0.991452	+	0.130474i	$0.0416498\pi$
$587$			6.32226i			0.260948i	−0.991452	+	0.130474i	$0.958350\pi$
$588$	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	$0.601858\pi$
$594$	11.3607	−	2.91245i	0.466137	−	0.119499i
$595$	0.803912	−	1.26272i	0.0329572	−	0.0517663i
$596$	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	$-0.731816\pi$
$600$	8.12899	+	2.98655i	0.331865	+	0.121925i
$601$	−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	0.149449	−	0.988769i	$-0.452250\pi$
$607$	−15.5739	−	8.99161i	−0.632126	−	0.364958i	−0.781575	+	0.623811i	$0.785583\pi$
$608$	0.00830895	+	0.0143915i	0.000336972	+	0.000583653i
$609$	2.41076	−	0.636632i	0.0976890	−	0.0257976i
$610$	0.788874	−	18.1921i	0.0319406	−	0.736577i
$611$	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	$0.0866071\pi$
$613$	17.6863	+	30.6335i	0.714342	+	1.23728i	−0.248871	+	0.968537i	$0.580060\pi$
$614$	−0.206088	+	0.118985i	−0.00831704	+	0.00480185i
$615$	−2.05099	−	2.25322i	−0.0827038	−	0.0908587i
$616$			7.18252i			0.289392i
$617$	−12.0346	−	20.8445i	−0.484494	−	0.839168i	0.515348	−	0.856981i	$-0.327663\pi$
$617$	−12.0346	−	20.8445i	−0.484494	−	0.839168i	−0.999841	+	0.0178134i	$0.994330\pi$
$618$	−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	$0.791572\pi$
$620$	−0.292572	−	12.4465i	−0.0117500	−	0.499862i
$621$	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
$625$	24.6253	+	4.31196i	0.985013	+	0.172479i
$626$	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
$630$	−21.3197	−	1.07895i	−0.849397	−	0.0429866i
$631$	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
$640$	2.23397	+	0.0968727i	0.0883054	+	0.00382923i
$641$	−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	$-0.440147\pi$
$643$	9.47997			0.373854			0.186927	+	0.982374i	$0.440147\pi$
$644$	1.27298	+	2.20486i	0.0501623	+	0.0868837i
$645$	3.41400	+	15.6450i	0.134426	+	0.616022i
$646$	−0.00302751	−	0.00174794i	−0.000119116	−	6.87716e-5i
$647$		−	31.5526i		−	1.24046i	−0.784420	−	0.620230i	$-0.787039\pi$
$647$		−	31.5526i		−	1.24046i	0.784420	−	0.620230i	$-0.212961\pi$
$648$	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	$-0.627153\pi$
$653$	−19.8770			−0.777848			−0.388924	+	0.921270i	$0.627153\pi$
$654$	−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	$-0.0813121\pi$
$660$	6.46456	−	5.88435i	0.251633	−	0.229048i
$661$	−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
$665$	−0.0997476	−	0.0635046i	−0.00386805	−	0.00246260i
$666$	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
$670$	−15.9321	−	10.1432i	−0.615512	−	0.391868i
$671$	−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	$-0.602442\pi$
$673$	17.2103	−	29.8092i	0.663410	−	1.14906i	0.979714	−	0.200402i	$-0.0642247\pi$
$674$	−1.69991			−0.0654781
$675$	16.4952	+	20.0725i	0.634902	+	0.772592i
$676$	2.48312	+	4.30088i	0.0955044	+	0.165419i
$677$	−22.3852	−	12.9241i	−0.860334	−	0.496714i	0.00379030	−	0.999993i	$-0.498794\pi$
$677$	−22.3852	−	12.9241i	−0.860334	−	0.496714i	−0.864124	+	0.503279i	$0.832127\pi$
$678$	−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
$685$	16.1644	+	10.2911i	0.617610	+	0.393203i
$686$		−	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
$690$	0.941567	−	2.95208i	0.0358448	−	0.112384i
$691$	−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
$695$	−1.53245	+	35.3396i	−0.0581291	+	1.34051i
$696$	−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
$700$	−14.4164	+	6.73288i	−0.544887	+	0.254479i
$701$	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
$705$	−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
$708$	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	$0.932082\pi$
$710$	−28.4001	−	18.0810i	−1.06584	−	0.678568i
$711$	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	$0.874876\pi$
$720$	5.63252	+	3.64345i	0.209912	+	0.135783i
$721$	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
$725$	−2.25340	−	0.195799i	−0.0836893	−	0.00727180i
$726$	2.61168	+	9.88975i	0.0969284	+	0.367043i
$727$	−10.6708	+	6.16079i	−0.395758	+	0.228491i	−0.684652	−	0.728870i	$-0.740046\pi$
$727$	−10.6708	+	6.16079i	−0.395758	+	0.228491i	0.288894	+	0.957361i	$0.406713\pi$
$728$		−	9.01965i		−	0.334291i
$729$	−0.585493	+	26.9937i	−0.0216849	+	0.999765i
$730$	−10.7003	+	16.8072i	−0.396037	+	0.622062i
$731$	−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	0.0584948	−	0.998288i	$-0.481370\pi$
$733$	−21.0311	−	12.1423i	−0.776800	−	0.448486i	−0.835295	+	0.549802i	$0.814703\pi$
$734$	14.4856	−	25.0897i	0.534672	−	0.926079i
$735$	8.95474	−	8.15102i	0.330301	−	0.300655i
$736$		−	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	$0.327329\pi$
$743$			46.6897i			1.71288i	−0.516246	+	0.856440i	$0.672671\pi$
$744$	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
$750$	17.8706	+	7.45934i	0.652542	+	0.272376i
$751$	−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
$755$	0.380504	−	8.77475i	0.0138480	−	0.319346i
$756$	−15.9245	−	4.45258i	−0.579169	−	0.161939i
$757$	19.0466	−	32.9897i	0.692261	−	1.19903i	−0.278834	−	0.960339i	$-0.589948\pi$
$757$	19.0466	−	32.9897i	0.692261	−	1.19903i	0.971095	−	0.238693i	$-0.0767188\pi$
$758$	−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
$765$	−1.40939	−	0.0713267i	−0.0509565	−	0.00257882i
$766$	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	$0.894405\pi$
$770$	−0.695790	+	16.0455i	−0.0250745	+	0.578241i
$771$	−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	$-0.886435\pi$
$773$		−	19.4206i		−	0.698509i	0.937028	−	0.349255i	$-0.113565\pi$
$774$	−0.0896645	+	12.4034i	−0.00322292	+	0.445832i
$775$	0.552125	−	27.8333i	0.0198329	−	0.999803i
$776$		−	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
$780$	−8.11806	+	7.38943i	−0.290673	+	0.264584i
$781$	−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
$785$	0.564086	−	13.0083i	0.0201331	−	0.464287i
$786$	−8.81449	+	2.32772i	−0.314402	+	0.0830270i
$787$	4.30542	+	7.45721i	0.153472	+	0.265821i	0.932501	−	0.361166i	$-0.117621\pi$
$787$	4.30542	+	7.45721i	0.153472	+	0.265821i	−0.779030	+	0.626987i	$0.784288\pi$
$788$	−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
$795$	14.5377	+	15.9712i	0.515599	+	0.566439i
$796$	7.20797	+	4.16152i	0.255480	+	0.147501i
$797$	−0.466790	−	0.269502i	−0.0165346	−	0.00954623i	0.491710	−	0.870759i	$-0.336372\pi$
$797$	−0.466790	−	0.269502i	−0.0165346	−	0.00954623i	−0.508244	+	0.861213i	$0.669705\pi$
$798$	−0.0645322	−	0.0650004i	−0.00228441	−	0.00230099i
$799$	1.46557	−	0.846146i	0.0518480	−	0.0299345i
$800$	4.98123	+	0.432821i	0.176113	+	0.0153025i
$801$	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	$0.846359\pi$
$810$	9.03881	+	17.9805i	0.317591	+	0.631772i
$811$	−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
$815$	1.16211	−	26.7994i	0.0407071	−	0.938741i
$816$	−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
$820$	−1.48391	−	0.944737i	−0.0518204	−	0.0329916i
$821$	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	0.570047	−	0.821612i	$-0.306925\pi$
$823$	−12.2358	−	21.1931i	−0.426514	−	0.738744i	−0.996560	+	0.0828687i	$0.973592\pi$
$824$	−15.3713	−	8.87463i	−0.535485	−	0.309162i
$825$	15.0117	−	12.5192i	0.522639	−	0.435863i
$826$	−5.68494	+	9.84661i	−0.197805	+	0.342607i
$827$	8.89168	+	5.13362i	0.309194	+	0.178513i	0.646566	−	0.762858i	$-0.276205\pi$
$827$	8.89168	+	5.13362i	0.309194	+	0.178513i	−0.337372	+	0.941372i	$0.609538\pi$
$828$	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	$0.799672\pi$
$830$	−25.4053	−	16.1744i	−0.881831	−	0.561420i
$831$	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	$-0.208040\pi$
$840$	−12.0413	+	2.62762i	−0.415465	+	0.0906614i
$841$	−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
$850$	−0.953026	+	0.445092i	−0.0326885	+	0.0152665i
$851$	−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
$855$	−0.00563442	+	0.111334i	−0.000192693	+	0.00380754i
$856$	9.24636	+	16.0152i	0.316034	+	0.547387i
$857$	3.90938	−	6.77125i	0.133542	−	0.231302i	−0.791498	−	0.611172i	$-0.790698\pi$
$857$	3.90938	−	6.77125i	0.133542	−	0.231302i	0.925040	+	0.379871i	$0.124032\pi$
$858$	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	0.938415	−	0.345509i	$-0.112294\pi$
$863$	32.5614	+	18.7993i	1.10840	+	0.639937i	0.169988	+	0.985446i	$0.445627\pi$
$864$	3.63418	+	3.71386i	0.123637	+	0.126348i
$865$	15.7783	−	24.7832i	0.536479	−	0.842656i
$866$	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
$873$	7.30353	−	12.4415i	0.247187	−	0.421081i
$874$	0.0115140	−	0.00664763i	0.000389468	−	0.000224859i
$875$	−32.8579	+	13.6445i	−1.11080	+	0.461268i
$876$	−10.9524	+	10.8735i	−0.370046	+	0.367381i
$877$	−31.6253	−	18.2589i	−1.06791	−	0.616558i	−0.140301	−	0.990109i	$-0.544807\pi$
$877$	−31.6253	−	18.2589i	−1.06791	−	0.616558i	−0.927610	+	0.373551i	$0.878140\pi$
$878$	0.307195	−	0.532078i	0.0103673	−	0.0179567i
$879$	8.28354	+	31.3677i	0.279397	+	1.05800i
$880$	2.71048	−	4.25739i	0.0913702	−	0.143516i
$881$	−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	$-0.536335\pi$
$883$	−6.76930			−0.227805			−0.113902	+	0.993492i	$0.536335\pi$
$884$		−	0.596264i		−	0.0200545i
$885$	13.5198	−	2.95024i	0.454463	−	0.0991714i
$886$	−3.88123	+	6.72249i	−0.130392	+	0.225846i
$887$	7.67225	+	13.2887i	0.257609	+	0.446192i	0.965601	−	0.260029i	$-0.0837320\pi$
$887$	7.67225	+	13.2887i	0.257609	+	0.446192i	−0.707992	+	0.706221i	$0.750399\pi$
$888$	−3.65343	−	13.8346i	−0.122601	−	0.464259i
$889$	−13.2138	−	7.62900i	−0.443177	−	0.255869i
$890$	19.2777	+	0.835949i	0.646190	+	0.0280211i
$891$	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
$900$	12.2299	+	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
$905$	−37.9530	−	24.1629i	−1.26160	−	0.803202i
$906$	1.78456	−	6.56506i	0.0592880	−	0.218109i
$907$		−	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
$909$	−16.5925	+	28.2653i	−0.550340	+	0.937500i
$910$	0.873758	−	20.1496i	0.0289648	−	0.667953i
$911$	−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
$915$	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
$918$	−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	$0.317277\pi$
$920$	0.0775036	−	1.78730i	0.00255522	−	0.0589255i
$921$	−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
$925$	−17.4790	−	37.4257i	−0.574705	−	1.23055i
$926$	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	$0.718112\pi$
$930$	5.16582	−	20.9360i	0.169394	−	0.686517i
$931$	0.0519561			0.00170279
$932$	−3.39689			−0.111269
$933$	−4.03042	+	14.8272i	−0.131950	+	0.485419i
$934$	−0.199102			−0.00651481
$935$	−0.0459968	+	1.06073i	−0.00150426	+	0.0346894i
$936$	−7.39450	+	4.19824i	−0.241697	+	0.137224i
$937$	−25.5568	+	14.7552i	−0.834905	+	0.482032i	−0.855529	−	0.517755i	$-0.826768\pi$
$937$	−25.5568	+	14.7552i	−0.834905	+	0.482032i	0.0206244	+	0.999787i	$0.493435\pi$
$938$	26.8787			0.877620
$939$	9.80157	+	37.1161i	0.319862	+	1.21124i
$940$	−17.9710	−	0.779287i	−0.586150	−	0.0254175i
$941$	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
$945$	−35.1436	−	11.4896i	−1.14322	−	0.373756i
$946$	9.33209			0.303413
$947$	0.353723	−	0.204222i	0.0114945	−	0.00663633i	−0.494242	−	0.869324i	$-0.664554\pi$
$947$	0.353723	−	0.204222i	0.0114945	−	0.00663633i	0.505736	+	0.862688i	$0.331221\pi$
$948$	25.3767	−	6.70145i	0.824196	−	0.217653i
$949$	−12.6278	−	21.8720i	−0.409916	−	0.709996i
$950$	0.0351598	+	0.0752838i	0.00114074	+	0.00244253i
$951$	−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	$-0.891025\pi$
$953$		−	20.7269i		−	0.671411i	0.941967	−	0.335706i	$-0.108975\pi$
$954$	8.25946	+	14.5477i	0.267410	+	0.470998i
$955$	1.53424	+	0.976780i	0.0496469	+	0.0316079i
$956$	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
$966$	1.12592	+	4.26356i	0.0362258	+	0.137178i
$967$	−8.27261	−	14.3286i	−0.266029	−	0.460776i	0.701804	−	0.712370i	$-0.252378\pi$
$967$	−8.27261	−	14.3286i	−0.266029	−	0.460776i	−0.967833	+	0.251595i	$0.919045\pi$
$968$	2.95280	+	5.11439i	0.0949065	+	0.164383i
$969$	−0.00426605	−	0.00429700i	−0.000137045	−	0.000138039i
$970$	0.465855	−	10.7430i	0.0149577	−	0.344937i
$971$	−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
$975$	−18.8513	+	15.7213i	−0.603725	+	0.503486i
$976$		−	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	$0.564575\pi$
$978$	5.45030	−	20.0506i	0.174282	−	0.641149i
$979$	9.73857	−	16.8677i	0.311246	−	0.539094i
$980$	3.75457	−	5.89735i	0.119935	−	0.188384i
$981$	−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	−0.338434	−	0.940990i	$-0.609897\pi$
$983$	−41.4664	−	23.9406i	−1.32257	−	0.763588i	−0.984138	+	0.177402i	$0.943231\pi$
$984$	−0.960024	−	0.966989i	−0.0306044	−	0.0308265i
$985$	−10.6740	−	6.79561i	−0.340101	−	0.216526i
$986$	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
$990$	13.4783	−	6.89805i	0.428369	−	0.219234i
$991$			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
$995$	15.6992	+	9.99497i	0.497699	+	0.316862i
$996$	−16.4361	−	16.5553i	−0.520797	−	0.524575i
$997$	−27.9670	−	16.1468i	−0.885725	−	0.511374i	−0.0131834	−	0.999913i	$-0.504197\pi$
$997$	−27.9670	−	16.1468i	−0.885725	−	0.511374i	−0.872542	+	0.488539i	$0.837530\pi$
$998$	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.b.719.31	yes	64
3.2	odd	2		930.2.r.a.719.14	yes	64
5.4	even	2		930.2.r.a.719.2	yes	64
15.14	odd	2	inner	930.2.r.b.719.19	yes	64
31.26	odd	6	inner	930.2.r.b.119.19	yes	64
93.26	even	6		930.2.r.a.119.2	✓	64
155.119	odd	6		930.2.r.a.119.14	yes	64
465.119	even	6	inner	930.2.r.b.119.31	yes	64

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

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.67140 + 0.454332i) q^{3} +1.00000 q^{4} +(2.23397 + 0.0968727i) q^{5} +(1.67140 + 0.454332i) q^{6} +(-2.75588 + 1.59111i) q^{7} +1.00000 q^{8} +(2.58717 + 1.51874i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.67140 + 0.454332i) q^{3} +1.00000 q^{4} +(2.23397 + 0.0968727i) q^{5} +(1.67140 + 0.454332i) q^{6} +(-2.75588 + 1.59111i) q^{7} +1.00000 q^{8} +(2.58717 + 1.51874i) q^{9} +(2.23397 + 0.0968727i) 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} +(3.68985 + 1.17688i) q^{15} +1.00000 q^{16} +(-0.182184 + 0.105184i) q^{17} +(2.58717 + 1.51874i) q^{18} +(0.00830895 + 0.0143915i) q^{19} +(2.23397 + 0.0968727i) q^{20} +(-5.32908 + 1.40730i) q^{21} +(1.12854 - 1.95469i) q^{22} -0.800056i q^{23} +(1.67140 + 0.454332i) q^{24} +(4.98123 + 0.432821i) 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} +(2.58717 + 1.51874i) q^{36} +(-4.13062 - 7.15444i) q^{37} +(0.00830895 + 0.0143915i) q^{38} +(-3.48393 + 3.45884i) q^{39} +(2.23397 + 0.0968727i) 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} +(5.63252 + 3.64345i) q^{45} -0.800056i q^{46} -8.04444 q^{47} +(1.67140 + 0.454332i) q^{48} +(1.56326 - 2.70764i) q^{49} +(4.98123 + 0.432821i) 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} +(2.71048 - 4.25739i) q^{55} +(-2.75588 + 1.59111i) q^{56} +(0.00734906 + 0.0278290i) 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} +(-3.40376 + 5.34633i) 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} +(8.12899 + 2.98655i) q^{75} +(0.00830895 + 0.0143915i) q^{76} +7.18252i q^{77} +(-3.48393 + 3.45884i) q^{78} +(13.1233 - 7.57675i) q^{79} +(2.23397 + 0.0968727i) 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} +(5.63252 + 3.64345i) 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	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 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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